LMFDB - Embedded newform 38.8.e.b.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	38.17
Dual form			38.8.e.b.9.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 + 7.87846i) q^{2} +(-12.0854 - 10.1408i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-307.410 + 111.888i) q^{5} +(96.6830 - 81.1267i) q^{6} +(444.097 + 769.199i) q^{7} +(256.000 - 443.405i) q^{8} +(-336.549 - 1908.66i) q^{9} +O(q^{10})$	\(q+(-1.38919 + 7.87846i) q^{2} +(-12.0854 - 10.1408i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-307.410 + 111.888i) q^{5} +(96.6830 - 81.1267i) q^{6} +(444.097 + 769.199i) q^{7} +(256.000 - 443.405i) q^{8} +(-336.549 - 1908.66i) q^{9} +(-454.457 - 2577.35i) q^{10} +(1665.01 - 2883.88i) q^{11} +(504.843 + 874.413i) q^{12} +(2839.61 - 2382.72i) q^{13} +(-6677.03 + 2430.24i) q^{14} +(4849.80 + 1765.18i) q^{15} +(3137.72 + 2632.86i) q^{16} +(3206.13 - 18182.8i) q^{17} +15504.9 q^{18} +(26846.2 - 13158.8i) q^{19} +20936.9 q^{20} +(2433.24 - 13799.6i) q^{21} +(20407.6 + 17124.0i) q^{22} +(39510.6 + 14380.7i) q^{23} +(-7590.35 + 2762.66i) q^{24} +(22134.7 - 18573.2i) q^{25} +(14827.4 + 25681.8i) q^{26} +(-32539.5 + 56360.1i) q^{27} +(-9870.93 - 55980.8i) q^{28} +(-31376.8 - 177946. i) q^{29} +(-20644.2 + 35756.8i) q^{30} +(-8989.89 - 15571.0i) q^{31} +(-25101.7 + 21062.9i) q^{32} +(-49367.3 + 17968.2i) q^{33} +(138799. + 50518.7i) q^{34} +(-222584. - 186770. i) q^{35} +(-21539.1 + 122154. i) q^{36} -21044.8 q^{37} +(66377.1 + 229787. i) q^{38} -58480.5 q^{39} +(-29085.2 + 164950. i) q^{40} +(-360569. - 302553. i) q^{41} +(105339. + 38340.3i) q^{42} +(-653299. + 237782. i) q^{43} +(-163260. + 136992. i) q^{44} +(317015. + 549086. i) q^{45} +(-168185. + 291305. i) q^{46} +(-95540.2 - 541835. i) q^{47} +(-11221.1 - 63638.1i) q^{48} +(17327.2 - 30011.7i) q^{49} +(115579. + 200189. i) q^{50} +(-223136. + 187234. i) q^{51} +(-222931. + 81140.4i) q^{52} +(1.86218e6 + 677778. i) q^{53} +(-398828. - 334656. i) q^{54} +(-189169. + 1.07283e6i) q^{55} +454755. q^{56} +(-457887. - 113213. i) q^{57} +1.44553e6 q^{58} +(359536. - 2.03903e6i) q^{59} +(-253030. - 212317. i) q^{60} +(-2.21750e6 - 807103. i) q^{61} +(135164. - 49195.6i) q^{62} +(1.31868e6 - 1.10650e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-606328. + 1.05019e6i) q^{65} +(-72981.6 - 413899. i) q^{66} +(-366437. - 2.07817e6i) q^{67} +(-590827. + 1.02334e6i) q^{68} +(-331668. - 574466. i) q^{69} +(1.78067e6 - 1.49416e6i) q^{70} +(3.72738e6 - 1.35666e6i) q^{71} +(-932467. - 339390. i) q^{72} +(2.93824e6 + 2.46548e6i) q^{73} +(29235.1 - 165801. i) q^{74} -455854. q^{75} +(-1.90257e6 + 203734. i) q^{76} +2.95771e6 q^{77} +(81240.3 - 460737. i) q^{78} +(1.08430e6 + 909835. i) q^{79} +(-1.25915e6 - 458294. i) q^{80} +(-3.01823e6 + 1.09855e6i) q^{81} +(2.88455e6 - 2.42043e6i) q^{82} +(480460. + 832180. i) q^{83} +(-448398. + 776648. i) q^{84} +(1.04885e6 + 5.94831e6i) q^{85} +(-965799. - 5.47732e6i) q^{86} +(-1.42532e6 + 2.46873e6i) q^{87} +(-852486. - 1.47655e6i) q^{88} +(-1.97640e6 + 1.65840e6i) q^{89} +(-4.76635e6 + 1.73481e6i) q^{90} +(3.09385e6 + 1.12607e6i) q^{91} +(-2.06140e6 - 1.72972e6i) q^{92} +(-49256.2 + 279346. i) q^{93} +4.40155e6 q^{94} +(-6.78046e6 + 7.04892e6i) q^{95} +516959. q^{96} +(-1.24295e6 + 7.04913e6i) q^{97} +(212375. + 178204. i) q^{98} +(-6.06472e6 - 2.20738e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) $ 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$3$	−12.0854	−	10.1408i	−0.258426	−	0.216845i	0.504365	−	0.863491i	$-0.331727\pi$
$3$	−12.0854	−	10.1408i	−0.258426	−	0.216845i	−0.762790	+	0.646646i	$0.776171\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−307.410	+	111.888i	−1.09982	+	0.400303i	−0.827251	−	0.561832i	$-0.810097\pi$
$5$	−307.410	+	111.888i	−1.09982	+	0.400303i	−0.272572	+	0.962135i	$0.587874\pi$
$6$	96.6830	−	81.1267i	0.182735	−	0.153332i
$7$	444.097	+	769.199i	0.489367	+	0.847609i	0.999925	−	0.0122347i	$-0.00389453\pi$
$7$	444.097	+	769.199i	0.489367	+	0.847609i	−0.510558	+	0.859843i	$0.670561\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	−336.549	−	1908.66i	−0.153886	−	0.872731i
$10$	−454.457	−	2577.35i	−0.143712	−	0.815030i
$11$	1665.01	−	2883.88i	0.377175	−	0.653286i	−0.613475	−	0.789714i	$-0.710229\pi$
$11$	1665.01	−	2883.88i	0.377175	−	0.653286i	0.990650	+	0.136428i	$0.0435623\pi$
$12$	504.843	+	874.413i	0.0843377	+	0.146077i
$13$	2839.61	−	2382.72i	0.358474	−	0.300795i	−0.445708	−	0.895178i	$-0.647048\pi$
$13$	2839.61	−	2382.72i	0.358474	−	0.300795i	0.804182	+	0.594383i	$0.202604\pi$
$14$	−6677.03	+	2430.24i	−0.650333	+	0.236702i
$15$	4849.80	+	1765.18i	0.371026	+	0.135043i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	3206.13	−	18182.8i	0.158274	−	0.897616i	−0.797457	−	0.603375i	$-0.793822\pi$
$17$	3206.13	−	18182.8i	0.158274	−	0.897616i	0.955731	−	0.294241i	$-0.0950667\pi$
$18$	15504.9			0.626634
$19$	26846.2	−	13158.8i	0.897935	−	0.440129i
$19$	26846.2	−	13158.8i	0.897935	−	0.440129i
$20$	20936.9			0.585204
$21$	2433.24	−	13799.6i	0.0573346	−	0.325161i
$22$	20407.6	+	17124.0i	0.408613	+	0.342867i
$23$	39510.6	+	14380.7i	0.677120	+	0.246452i	0.657610	−	0.753358i	$-0.271567\pi$
$23$	39510.6	+	14380.7i	0.677120	+	0.246452i	0.0195096	+	0.999810i	$0.493790\pi$
$24$	−7590.35	+	2762.66i	−0.112079	+	0.0407933i
$25$	22134.7	−	18573.2i	0.283324	−	0.237737i
$26$	14827.4	+	25681.8i	0.165447	+	0.286562i
$27$	−32539.5	+	56360.1i	−0.318155	+	0.551060i
$28$	−9870.93	−	55980.8i	−0.0849777	−	0.481932i
$29$	−31376.8	−	177946.i	−0.238899	−	1.35487i	−0.834244	−	0.551395i	$-0.814096\pi$
$29$	−31376.8	−	177946.i	−0.238899	−	1.35487i	0.595345	−	0.803470i	$-0.297015\pi$
$30$	−20644.2	+	35756.8i	−0.139596	+	0.241788i
$31$	−8989.89	−	15571.0i	−0.0541987	−	0.0938749i	0.837653	−	0.546203i	$-0.183927\pi$
$31$	−8989.89	−	15571.0i	−0.0541987	−	0.0938749i	−0.891852	+	0.452328i	$0.850594\pi$
$32$	−25101.7	+	21062.9i	−0.135419	+	0.113630i
$33$	−49367.3	+	17968.2i	−0.239133	+	0.0870374i
$34$	138799.	+	50518.7i	0.605633	+	0.220433i
$35$	−222584.	−	186770.i	−0.877517	−	0.736325i
$36$	−21539.1	+	122154.i	−0.0769430	+	0.436366i
$37$	−21044.8			−0.0683028			−0.0341514	−	0.999417i	$-0.510873\pi$
$37$	−21044.8			−0.0683028			−0.0341514	+	0.999417i	$0.510873\pi$
$38$	66377.1	+	229787.i	0.196235	+	0.679332i
$39$	−58480.5			−0.157865
$40$	−29085.2	+	164950.i	−0.0718559	+	0.407515i
$41$	−360569.	−	302553.i	−0.817043	−	0.685581i	0.135235	−	0.990814i	$-0.456821\pi$
$41$	−360569.	−	302553.i	−0.817043	−	0.685581i	−0.952278	+	0.305233i	$0.901266\pi$
$42$	105339.	+	38340.3i	0.219390	+	0.0798515i
$43$	−653299.	+	237782.i	−1.25306	+	0.456077i	−0.881435	−	0.472305i	$-0.843422\pi$
$43$	−653299.	+	237782.i	−1.25306	+	0.456077i	−0.371627	+	0.928382i	$0.621200\pi$
$44$	−163260.	+	136992.i	−0.288933	+	0.242443i
$45$	317015.	+	549086.i	0.518604	+	0.898249i
$46$	−168185.	+	291305.i	−0.254762	+	0.441261i
$47$	−95540.2	−	541835.i	−0.134228	−	0.761246i	−0.975394	−	0.220469i	$-0.929241\pi$
$47$	−95540.2	−	541835.i	−0.134228	−	0.761246i	0.841166	−	0.540777i	$-0.181870\pi$
$48$	−11221.1	−	63638.1i	−0.0146451	−	0.0830564i
$49$	17327.2	−	30011.7i	0.0210399	−	0.0364421i
$50$	115579.	+	200189.i	0.130763	+	0.226488i
$51$	−223136.	+	187234.i	−0.235545	+	0.197646i
$52$	−222931.	+	81140.4i	−0.219867	+	0.0800249i
$53$	1.86218e6	+	677778.i	1.71813	+	0.625348i	0.997675	−	0.0681535i	$-0.0217108\pi$
$53$	1.86218e6	+	677778.i	1.71813	+	0.625348i	0.720455	+	0.693502i	$0.243933\pi$
$54$	−398828.	−	334656.i	−0.344673	−	0.289215i
$55$	−189169.	+	1.07283e6i	−0.153313	+	0.869483i
$56$	454755.			0.346035
$57$	−457887.	−	113213.i	−0.327489	−	0.0809719i
$58$	1.44553e6			0.972814
$59$	359536.	−	2.03903e6i	0.227908	−	1.29253i	−0.629138	−	0.777293i	$-0.716592\pi$
$59$	359536.	−	2.03903e6i	0.227908	−	1.29253i	0.857047	−	0.515239i	$-0.172297\pi$
$60$	−253030.	−	212317.i	−0.151232	−	0.126898i
$61$	−2.21750e6	−	807103.i	−1.25086	−	0.455276i	−0.370168	−	0.928965i	$-0.620700\pi$
$61$	−2.21750e6	−	807103.i	−1.25086	−	0.455276i	−0.880692	+	0.473689i	$0.842922\pi$
$62$	135164.	−	49195.6i	0.0720260	−	0.0262153i
$63$	1.31868e6	−	1.10650e6i	0.664428	−	0.557521i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−606328.	+	1.05019e6i	−0.273849	+	0.474320i
$66$	−72981.6	−	413899.i	−0.0312471	−	0.177211i
$67$	−366437.	−	2.07817e6i	−0.148846	−	0.844147i	−0.964198	−	0.265182i	$-0.914568\pi$
$67$	−366437.	−	2.07817e6i	−0.148846	−	0.844147i	0.815352	−	0.578965i	$-0.196543\pi$
$68$	−590827.	+	1.02334e6i	−0.227866	+	0.394675i
$69$	−331668.	−	574466.i	−0.121543	−	0.210519i
$70$	1.78067e6	−	1.49416e6i	0.620499	−	0.520660i
$71$	3.72738e6	−	1.35666e6i	1.23595	−	0.449848i	0.360317	−	0.932830i	$-0.382669\pi$
$71$	3.72738e6	−	1.35666e6i	1.23595	−	0.449848i	0.875630	+	0.482982i	$0.160446\pi$
$72$	−932467.	−	339390.i	−0.294422	−	0.107161i
$73$	2.93824e6	+	2.46548e6i	0.884010	+	0.741772i	0.967000	−	0.254778i	$-0.0820024\pi$
$73$	2.93824e6	+	2.46548e6i	0.884010	+	0.741772i	−0.0829896	+	0.996550i	$0.526447\pi$
$74$	29235.1	−	165801.i	0.00838675	−	0.0475636i
$75$	−455854.			−0.124770
$76$	−1.90257e6	+	203734.i	−0.497158	+	0.0532372i
$77$	2.95771e6			0.738308
$78$	81240.3	−	460737.i	0.0193839	−	0.109931i
$79$	1.08430e6	+	909835.i	0.247431	+	0.207619i	0.758065	−	0.652179i	$-0.226145\pi$
$79$	1.08430e6	+	909835.i	0.247431	+	0.207619i	−0.510634	+	0.859798i	$0.670589\pi$
$80$	−1.25915e6	−	458294.i	−0.274956	−	0.100076i
$81$	−3.01823e6	+	1.09855e6i	−0.631037	+	0.229679i
$82$	2.88455e6	−	2.42043e6i	0.577737	−	0.484779i
$83$	480460.	+	832180.i	0.0922324	+	0.159751i	0.908450	−	0.417993i	$-0.137266\pi$
$83$	480460.	+	832180.i	0.0922324	+	0.159751i	−0.816218	+	0.577744i	$0.803933\pi$
$84$	−448398.	+	776648.i	−0.0825442	+	0.142971i
$85$	1.04885e6	+	5.94831e6i	0.185245	+	1.05058i
$86$	−965799.	−	5.47732e6i	−0.163735	−	0.928589i
$87$	−1.42532e6	+	2.46873e6i	−0.232058	+	0.401936i
$88$	−852486.	−	1.47655e6i	−0.133351	−	0.230971i
$89$	−1.97640e6	+	1.65840e6i	−0.297174	+	0.249358i	−0.779167	−	0.626817i	$-0.784357\pi$
$89$	−1.97640e6	+	1.65840e6i	−0.297174	+	0.249358i	0.481993	+	0.876175i	$0.339913\pi$
$90$	−4.76635e6	+	1.73481e6i	−0.689187	+	0.250843i
$91$	3.09385e6	+	1.12607e6i	0.430382	+	0.156646i
$92$	−2.06140e6	−	1.72972e6i	−0.275997	−	0.231589i
$93$	−49256.2	+	279346.i	−0.00634995	+	0.0360124i
$94$	4.40155e6			0.546586
$95$	−6.78046e6	+	7.04892e6i	−0.811384	+	0.843510i
$96$	516959.			0.0596357
$97$	−1.24295e6	+	7.04913e6i	−0.138278	+	0.784213i	0.834243	+	0.551397i	$0.185905\pi$
$97$	−1.24295e6	+	7.04913e6i	−0.138278	+	0.784213i	−0.972521	+	0.232816i	$0.925206\pi$
$98$	212375.	+	178204.i	0.0227936	+	0.0191261i
$99$	−6.06472e6	−	2.20738e6i	−0.628185	−	0.228641i
$100$	−1.73774e6	+	632487.i	−0.173774	+	0.0632487i
$101$	9.25691e6	−	7.76747e6i	0.894008	−	0.750161i	−0.0750023	−	0.997183i	$-0.523896\pi$
$101$	9.25691e6	−	7.76747e6i	0.894008	−	0.750161i	0.969010	+	0.247022i	$0.0794520\pi$
$102$	−1.16514e6	−	2.01807e6i	−0.108712	−	0.188294i
$103$	166034.	−	287580.i	0.0149716	−	0.0259315i	−0.858443	−	0.512910i	$-0.828568\pi$
$103$	166034.	−	287580.i	0.0149716	−	0.0259315i	0.873414	+	0.486978i	$0.161901\pi$
$104$	−329568.	−	1.86908e6i	−0.0287295	−	0.162933i
$105$	796006.	+	4.51437e6i	0.0671048	+	0.380570i
$106$	−7.92676e6	+	1.37296e7i	−0.646435	+	1.11966i
$107$	−4.55053e6	−	7.88175e6i	−0.359103	−	0.621984i	0.628708	−	0.777641i	$-0.283584\pi$
$107$	−4.55053e6	−	7.88175e6i	−0.359103	−	0.621984i	−0.987811	+	0.155657i	$0.950251\pi$
$108$	3.19062e6	−	2.67725e6i	0.243721	−	0.204506i
$109$	1.63087e6	−	593590.i	0.120622	−	0.0439029i	−0.281004	−	0.959707i	$-0.590667\pi$
$109$	1.63087e6	−	593590.i	0.120622	−	0.0439029i	0.401626	+	0.915804i	$0.368445\pi$
$110$	−8.18946e6	−	2.98072e6i	−0.586652	−	0.213524i
$111$	254334.	+	213412.i	0.0176512	+	0.0148111i
$112$	−631739.	+	3.58277e6i	−0.0424888	+	0.240966i
$113$	−2.46229e7			−1.60533			−0.802664	−	0.596431i	$-0.796585\pi$
$113$	−2.46229e7			−1.60533			−0.802664	+	0.596431i	$0.796585\pi$
$114$	1.52803e6	−	3.45018e6i	0.0965976	−	0.218109i
$115$	−1.37550e7			−0.843368
$116$	−2.00811e6	+	1.13886e7i	−0.119450	+	0.677433i
$117$	−5.50348e6	−	4.61797e6i	−0.317678	−	0.266563i
$118$	1.55650e7	+	5.66518e6i	0.872089	+	0.317414i
$119$	1.54100e7	−	5.60880e6i	0.838281	−	0.305109i
$120$	2.02424e6	−	1.69854e6i	0.106937	−	0.0897307i
$121$	4.19906e6	+	7.27299e6i	0.215478	+	0.373219i
$122$	9.43924e6	−	1.63493e7i	0.470628	−	0.815152i
$123$	1.28947e6	+	7.31294e6i	0.0624803	+	0.354343i
$124$	199818.	+	1.13322e6i	0.00941150	+	0.0533753i
$125$	8.05255e6	−	1.39474e7i	0.368764	−	0.638718i
$126$	6.88566e6	+	1.19263e7i	0.306654	+	0.531140i
$127$	8.23959e6	−	6.91384e6i	0.356938	−	0.299507i	−0.446631	−	0.894718i	$-0.647376\pi$
$127$	8.23959e6	−	6.91384e6i	0.356938	−	0.299507i	0.803569	+	0.595212i	$0.202932\pi$
$128$	1.97068e6	−	717268.i	0.0830579	−	0.0302306i
$129$	1.03067e7	+	3.75132e6i	0.422722	+	0.153858i
$130$	−7.43158e6	−	6.23584e6i	−0.296674	−	0.248939i
$131$	6.70109e6	−	3.80038e7i	0.260433	−	1.47699i	−0.521299	−	0.853374i	$-0.674552\pi$
$131$	6.70109e6	−	3.80038e7i	0.260433	−	1.47699i	0.781732	−	0.623614i	$-0.214336\pi$
$132$	3.36227e6			0.127240
$133$	2.20441e7	+	1.48062e7i	0.812477	+	0.545712i
$134$	1.68818e7			0.606110
$135$	3.69695e6	−	2.09665e7i	0.129323	−	0.733427i
$136$	−7.24159e6	−	6.07642e6i	−0.246858	−	0.207139i
$137$	−1.85136e6	−	673840.i	−0.0615133	−	0.0223890i	0.311080	−	0.950384i	$-0.399309\pi$
$137$	−1.85136e6	−	673840.i	−0.0615133	−	0.0223890i	−0.372594	+	0.927995i	$0.621531\pi$
$138$	4.98665e6	−	1.81499e6i	0.161522	−	0.0587893i
$139$	2.20746e7	−	1.85228e7i	0.697174	−	0.584998i	−0.223794	−	0.974636i	$-0.571844\pi$
$139$	2.20746e7	−	1.85228e7i	0.697174	−	0.584998i	0.920968	+	0.389638i	$0.127400\pi$
$140$	9.29801e6	+	1.61046e7i	0.286379	+	0.496024i
$141$	−4.34002e6	+	7.51714e6i	−0.130384	+	0.225832i
$142$	5.51034e6	+	3.12507e7i	0.161499	+	0.915905i
$143$	−2.14350e6	−	1.21564e7i	−0.0612980	−	0.347638i
$144$	3.96924e6	−	6.87493e6i	0.110774	−	0.191867i
$145$	2.95556e7	+	5.11918e7i	0.805104	+	1.39448i
$146$	−2.35059e7	+	1.97238e7i	−0.625089	+	0.524512i
$147$	−513749.	+	186989.i	−0.0133395	+	0.00485519i
$148$	1.26564e6	+	460656.i	0.0320918	+	0.0116805i
$149$	−4.04195e7	−	3.39160e7i	−1.00101	−	0.839949i	−0.0138880	−	0.999904i	$-0.504421\pi$
$149$	−4.04195e7	−	3.39160e7i	−1.00101	−	0.839949i	−0.987124	+	0.159954i	$0.948865\pi$
$150$	633266.	−	3.59143e6i	0.0153203	−	0.0868857i
$151$	−3.72349e7			−0.880098			−0.440049	−	0.897974i	$-0.645039\pi$
$151$	−3.72349e7			−0.880098			−0.440049	+	0.897974i	$0.645039\pi$
$152$	1.03792e6	−	1.52724e7i	0.0239724	−	0.352740i
$153$	−3.57839e7			−0.807733
$154$	−4.10880e6	+	2.33022e7i	−0.0906552	+	0.514131i
$155$	4.50579e6	+	3.78080e6i	0.0971873	+	0.0815499i
$156$	3.51704e6	+	1.28010e6i	0.0741722	+	0.0269965i
$157$	5.22193e6	−	1.90063e6i	0.107692	−	0.0391966i	−0.287612	−	0.957747i	$-0.592861\pi$
$157$	5.22193e6	−	1.90063e6i	0.107692	−	0.0391966i	0.395304	+	0.918550i	$0.370639\pi$
$158$	−8.67439e6	+	7.27868e6i	−0.174960	+	0.146809i
$159$	−1.56319e7	−	2.70752e7i	−0.308405	−	0.534174i
$160$	5.35984e6	−	9.28352e6i	0.103450	−	0.179181i
$161$	6.48493e6	+	3.67779e7i	0.122466	+	0.694538i
$162$	−4.46197e6	−	2.53051e7i	−0.0824563	−	0.467633i
$163$	4.93186e7	−	8.54223e7i	0.891978	−	1.54495i	0.0544764	−	0.998515i	$-0.482651\pi$
$163$	4.93186e7	−	8.54223e7i	0.891978	−	1.54495i	0.837501	−	0.546435i	$-0.184016\pi$
$164$	1.50621e7	+	2.60883e7i	0.266643	+	0.461840i
$165$	1.31656e7	−	1.10472e7i	0.228163	−	0.191452i
$166$	−7.22375e6	+	2.62923e6i	−0.122570	+	0.0446118i
$167$	−5.06527e7	−	1.84361e7i	−0.841579	−	0.306310i	−0.114977	−	0.993368i	$-0.536679\pi$
$167$	−5.06527e7	−	1.84361e7i	−0.841579	−	0.306310i	−0.726602	+	0.687058i	$0.758902\pi$
$168$	−5.49589e6	−	4.61160e6i	−0.0894243	−	0.0750359i
$169$	−8.51011e6	+	4.82632e7i	−0.135622	+	0.769153i
$170$	−4.83206e7			−0.754330
$171$	−3.41508e7	−	4.68117e7i	−0.522294	−	0.715926i
$172$	4.44945e7			0.666741
$173$	−1.37922e7	+	7.82192e7i	−0.202521	+	1.14856i	0.698772	+	0.715345i	$0.253730\pi$
$173$	−1.37922e7	+	7.82192e7i	−0.202521	+	1.14856i	−0.901293	+	0.433210i	$0.857381\pi$
$174$	−1.74698e7	−	1.46589e7i	−0.251400	−	0.210950i
$175$	2.41165e7	+	8.77768e6i	0.340158	+	0.123807i
$176$	1.28172e7	−	4.66508e6i	0.177214	−	0.0645007i
$177$	−2.50226e7	+	2.09964e7i	−0.339176	+	0.284603i
$178$	−1.03200e7	−	1.78748e7i	−0.137155	−	0.237559i
$179$	−7.18428e7	+	1.24435e8i	−0.936263	+	1.62165i	−0.163896	+	0.986478i	$0.552406\pi$
$179$	−7.18428e7	+	1.24435e8i	−0.936263	+	1.62165i	−0.772367	+	0.635177i	$0.780927\pi$
$180$	−7.04628e6	−	3.99615e7i	−0.0900547	−	0.510726i
$181$	1.24723e7	+	7.07339e7i	0.156341	+	0.886651i	0.957550	+	0.288267i	$0.0930791\pi$
$181$	1.24723e7	+	7.07339e7i	0.156341	+	0.886651i	−0.801210	+	0.598384i	$0.795810\pi$
$182$	−1.31696e7	+	2.28104e7i	−0.161928	+	0.280468i
$183$	1.86146e7	+	3.22414e7i	0.224530	+	0.388897i
$184$	1.64912e7	−	1.38377e7i	0.195159	−	0.163758i
$185$	6.46938e6	−	2.35466e6i	0.0751210	−	0.0273418i
$186$	−2.13239e6	−	776126.i	−0.0242980	−	0.00884376i
$187$	−4.70990e7	−	3.95207e7i	−0.526703	−	0.441956i
$188$	−6.11457e6	+	3.46775e7i	−0.0671141	+	0.380623i
$189$	−5.78028e7			−0.622777
$190$	−4.61154e7	−	6.32119e7i	−0.487762	−	0.668592i
$191$	2.67113e7			0.277382			0.138691	−	0.990336i	$-0.455711\pi$
$191$	2.67113e7			0.277382			0.138691	+	0.990336i	$0.455711\pi$
$192$	−718152.	+	4.07284e6i	−0.00732254	+	0.0415282i
$193$	1.20802e8	+	1.01365e8i	1.20955	+	1.01493i	0.999305	+	0.0372819i	$0.0118699\pi$
$193$	1.20802e8	+	1.01365e8i	1.20955	+	1.01493i	0.210243	+	0.977649i	$0.432575\pi$
$194$	−5.38096e7	−	1.95851e7i	−0.529119	−	0.192584i
$195$	1.79775e7	−	6.54328e6i	0.173623	−	0.0631937i
$196$	−1.69900e6	+	1.42563e6i	−0.0161175	+	0.0135242i
$197$	2.80157e6	+	4.85247e6i	0.0261078	+	0.0452200i	0.878784	−	0.477220i	$-0.158355\pi$
$197$	2.80157e6	+	4.85247e6i	0.0261078	+	0.0452200i	−0.852676	+	0.522440i	$0.825022\pi$
$198$	2.58158e7	−	4.47142e7i	0.236351	−	0.409371i
$199$	1.05964e6	+	6.00951e6i	0.00953174	+	0.0540572i	0.989203	−	0.146554i	$-0.0468183\pi$
$199$	1.05964e6	+	6.00951e6i	0.00953174	+	0.0540572i	−0.979671	+	0.200611i	$0.935707\pi$
$200$	−2.56898e6	−	1.45694e7i	−0.0227068	−	0.128777i
$201$	−1.66458e7	+	2.88314e7i	−0.144583	+	0.250426i
$202$	4.83362e7	+	8.37207e7i	0.412612	+	0.714666i
$203$	1.22942e8	−	1.03160e8i	1.03149	−	0.865520i
$204$	1.75179e7	−	6.37600e6i	0.144470	−	0.0525826i
$205$	1.44695e8	+	5.26645e7i	1.17304	+	0.426953i
$206$	2.03504e6	+	1.70760e6i	0.0162195	+	0.0136098i
$207$	1.41506e7	−	8.02521e7i	0.110887	−	0.628869i
$208$	1.51833e7			0.116989
$209$	6.75059e6	−	9.93308e7i	0.0511482	−	0.752614i
$210$	−3.66721e7			−0.273255
$211$	−2.65553e7	+	1.50603e8i	−0.194609	+	1.10368i	0.718365	+	0.695666i	$0.244891\pi$
$211$	−2.65553e7	+	1.50603e8i	−0.194609	+	1.10368i	−0.912974	+	0.408017i	$0.866220\pi$
$212$	−9.71560e7	−	8.15236e7i	−0.700316	−	0.587635i
$213$	−5.88044e7	−	2.14031e7i	−0.416948	−	0.151757i
$214$	6.84176e7	−	2.49020e7i	0.477221	−	0.173694i
$215$	1.74226e8	−	1.46193e8i	1.19558	−	1.00321i
$216$	1.66602e7	+	2.88564e7i	0.112485	+	0.194829i
$217$	7.98477e6	−	1.38300e7i	0.0530461	−	0.0918785i
$218$	2.41099e6	+	1.36734e7i	0.0157615	+	0.0893878i
$219$	−1.05077e7	−	5.95924e7i	−0.0676013	−	0.383386i
$220$	3.48601e7	−	6.03795e7i	0.220724	−	0.382305i
$221$	−3.42204e7	−	5.92715e7i	−0.213262	−	0.369380i
$222$	−2.03467e6	+	1.70729e6i	−0.0124813	+	0.0104730i
$223$	−1.27679e8	+	4.64713e7i	−0.770995	+	0.280619i	−0.697413	−	0.716670i	$-0.745665\pi$
$223$	−1.27679e8	+	4.64713e7i	−0.770995	+	0.280619i	−0.0735826	+	0.997289i	$0.523443\pi$
$224$	−2.73491e7	−	9.95427e6i	−0.162583	−	0.0591754i
$225$	−4.28995e7	−	3.59969e7i	−0.251081	−	0.210682i
$226$	3.42057e7	−	1.93990e8i	0.197115	−	1.11789i
$227$	−1.59449e8			−0.904754			−0.452377	−	0.891827i	$-0.649424\pi$
$227$	−1.59449e8			−0.904754			−0.452377	+	0.891827i	$0.649424\pi$
$228$	2.50594e7	+	1.68315e7i	0.140023	+	0.0940483i
$229$	1.76520e8			0.971338			0.485669	−	0.874143i	$-0.338576\pi$
$229$	1.76520e8			0.971338			0.485669	+	0.874143i	$0.338576\pi$
$230$	1.91082e7	−	1.08368e8i	0.103555	−	0.587291i
$231$	−3.57450e7	−	2.99936e7i	−0.190798	−	0.160098i
$232$	−8.69348e7	−	3.16417e7i	−0.457073	−	0.166361i
$233$	9.59854e7	−	3.49358e7i	0.497118	−	0.180936i	−0.0812792	−	0.996691i	$-0.525901\pi$
$233$	9.59854e7	−	3.49358e7i	0.497118	−	0.180936i	0.578397	+	0.815755i	$0.303678\pi$
$234$	4.40278e7	−	3.69437e7i	0.224632	−	0.188489i
$235$	8.99949e7	+	1.55876e8i	0.452356	+	0.783504i
$236$	−6.62555e7	+	1.14758e8i	−0.328118	+	0.568317i
$237$	−3.87768e6	−	2.19914e7i	−0.0189214	−	0.107308i
$238$	2.27813e7	+	1.29199e8i	0.109537	+	0.621213i
$239$	−1.06954e8	+	1.85249e8i	−0.506760	+	0.877735i	0.493209	+	0.869911i	$0.335824\pi$
$239$	−1.06954e8	+	1.85249e8i	−0.506760	+	0.877735i	−0.999969	+	0.00782387i	$0.997510\pi$
$240$	1.05698e7	+	1.83075e7i	0.0493547	+	0.0854849i
$241$	2.08157e7	−	1.74664e7i	0.0957923	−	0.0803792i	−0.593634	−	0.804735i	$-0.702307\pi$
$241$	2.08157e7	−	1.74664e7i	0.0957923	−	0.0803792i	0.689426	+	0.724356i	$0.257863\pi$
$242$	−6.31333e7	+	2.29786e7i	−0.286355	+	0.104225i
$243$	1.81361e8	+	6.60100e7i	0.810816	+	0.295113i
$244$	1.15694e8	+	9.70789e7i	0.509855	+	0.427819i
$245$	−1.96862e6	+	1.11646e7i	−0.00855225	+	0.0485022i
$246$	−5.94060e7			−0.254424
$247$	4.48789e7	−	1.01333e8i	0.189497	−	0.427869i
$248$	−9.20565e6			−0.0383242
$249$	2.63247e6	−	1.49295e7i	0.0108060	−	0.0612839i
$250$	9.86978e7	+	8.28173e7i	0.399501	+	0.335221i
$251$	−2.19219e8	−	7.97893e7i	−0.875026	−	0.318483i	−0.134825	−	0.990869i	$-0.543047\pi$
$251$	−2.19219e8	−	7.97893e7i	−0.875026	−	0.318483i	−0.740201	+	0.672386i	$0.765269\pi$
$252$	−1.03526e8	+	3.76806e7i	−0.407521	+	0.148325i
$253$	1.07258e8	−	8.99999e7i	0.416396	−	0.349398i
$254$	4.30241e7	+	7.45199e7i	0.164738	+	0.285335i
$255$	4.76451e7	−	8.25238e7i	0.179940	−	0.311665i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−3.26979e7	−	1.85439e8i	−0.120158	−	0.681452i	−0.984066	−	0.177802i	$-0.943101\pi$
$257$	−3.26979e7	−	1.85439e8i	−0.120158	−	0.681452i	0.863908	−	0.503650i	$-0.168010\pi$
$258$	−4.38725e7	+	7.59894e7i	−0.159046	+	0.275476i
$259$	−9.34593e6	−	1.61876e7i	−0.0334252	−	0.0578941i
$260$	5.94527e7	−	4.98867e7i	0.209780	−	0.176027i
$261$	−3.29080e8	+	1.19775e8i	−1.14567	+	0.416990i
$262$	2.90102e8	+	1.05589e8i	0.996544	+	0.362712i
$263$	2.51770e8	+	2.11260e8i	0.853413	+	0.716098i	0.960538	−	0.278147i	$-0.0897204\pi$
$263$	2.51770e8	+	2.11260e8i	0.853413	+	0.716098i	−0.107126	+	0.994245i	$0.534165\pi$
$264$	−4.67082e6	+	2.64895e7i	−0.0156235	+	0.0886055i
$265$	−6.48288e8			−2.13997
$266$	−1.47274e8	+	1.53105e8i	−0.479777	+	0.498773i
$267$	4.07031e7			0.130869
$268$	−2.34519e7	+	1.33003e8i	−0.0744230	+	0.422074i
$269$	652013.	+	547104.i	0.00204232	+	0.00171371i	0.643808	−	0.765187i	$-0.277353\pi$
$269$	652013.	+	547104.i	0.00204232	+	0.00171371i	−0.641766	+	0.766901i	$0.721798\pi$
$270$	1.60048e8	+	5.82526e7i	0.494853	+	0.180112i
$271$	−3.44663e8	+	1.25447e8i	−1.05197	+	0.382884i	−0.809404	−	0.587252i	$-0.800210\pi$
$271$	−3.44663e8	+	1.25447e8i	−1.05197	+	0.382884i	−0.242561	+	0.970136i	$0.577988\pi$
$272$	5.79328e7	−	4.86114e7i	0.174555	−	0.146469i
$273$	−2.59710e7	−	4.49831e7i	−0.0772538	−	0.133808i
$274$	7.88071e6	−	1.36498e7i	0.0231440	−	0.0400866i
$275$	−1.67085e7	−	9.47586e7i	−0.0484477	−	0.274761i
$276$	7.37197e6	+	4.18085e7i	0.0211058	+	0.119697i
$277$	−2.11762e8	+	3.66782e8i	−0.598643	+	1.03688i	0.394379	+	0.918948i	$0.370960\pi$
$277$	−2.11762e8	+	3.66782e8i	−0.598643	+	1.03688i	−0.993022	+	0.117932i	$0.962373\pi$
$278$	1.15265e8	+	1.99646e8i	0.321767	+	0.557318i
$279$	−2.66942e7	+	2.23991e7i	−0.0735871	+	0.0617469i
$280$	−1.39796e8	+	5.08817e7i	−0.380577	+	0.138519i
$281$	−1.86366e8	−	6.78318e7i	−0.501066	−	0.182373i	0.0791072	−	0.996866i	$-0.474793\pi$
$281$	−1.86366e8	−	6.78318e7i	−0.501066	−	0.182373i	−0.580174	+	0.814493i	$0.697015\pi$
$282$	−5.31944e7	−	4.46354e7i	−0.141252	−	0.118524i
$283$	9.64686e7	−	5.47101e8i	0.253008	−	1.43488i	−0.548128	−	0.836395i	$-0.684659\pi$
$283$	9.64686e7	−	5.47101e8i	0.253008	−	1.43488i	0.801136	−	0.598483i	$-0.204230\pi$
$284$	−2.53862e8			−0.657634
$285$	1.53426e8	−	1.64294e7i	0.392593	−	0.0420401i
$286$	9.87512e7			0.249610
$287$	7.25960e7	−	4.11712e8i	0.181270	−	1.02803i
$288$	4.86499e7	+	4.08221e7i	0.120007	+	0.100698i
$289$	6.52558e7	+	2.37512e7i	0.159029	+	0.0578818i
$290$	−4.44371e8	+	1.61738e8i	−1.06992	+	0.389420i
$291$	8.65055e7	−	7.25868e7i	0.205787	−	0.172676i
$292$	−1.22739e8	−	2.12590e8i	−0.288498	−	0.499694i
$293$	1.06099e8	−	1.83769e8i	0.246419	−	0.426810i	−0.716111	−	0.697987i	$-0.754079\pi$
$293$	1.06099e8	−	1.83769e8i	0.246419	−	0.426810i	0.962530	+	0.271177i	$0.0874128\pi$
$294$	−759496.	−	4.30732e6i	−0.00174305	−	0.00988533i
$295$	1.17618e8	+	6.67046e8i	0.266746	+	1.51279i
$296$	−5.38747e6	+	9.33137e6i	−0.0120743	+	0.0209134i
$297$	1.08357e8	+	1.87680e8i	0.240000	+	0.415692i
$298$	3.23356e8	−	2.71328e8i	0.707823	−	0.593934i
$299$	1.46460e8	−	5.33070e7i	0.316861	−	0.115328i
$300$	2.74152e7	+	9.97833e6i	0.0586229	+	0.0213370i
$301$	−4.73030e8	−	3.96919e8i	−0.999783	−	0.838917i
$302$	5.17262e7	−	2.93354e8i	0.108065	−	0.612869i
$303$	−1.90642e8			−0.393703
$304$	1.18881e8	+	2.93934e7i	0.242692	+	0.0600057i
$305$	7.71986e8			1.55797
$306$	4.97105e7	−	2.81922e8i	0.0991798	−	0.562477i
$307$	−3.95993e7	−	3.32278e7i	−0.0781094	−	0.0655416i	0.602897	−	0.797819i	$-0.294013\pi$
$307$	−3.95993e7	−	3.32278e7i	−0.0781094	−	0.0655416i	−0.681006	+	0.732277i	$0.738457\pi$
$308$	−1.77877e8	−	6.47421e7i	−0.346891	−	0.126258i
$309$	−4.92289e6	+	1.79178e6i	−0.00949216	+	0.00345487i
$310$	−3.60463e7	+	3.02464e7i	−0.0687218	+	0.0576645i
$311$	5.12212e8	+	8.87178e8i	0.965581	+	1.67244i	0.708045	+	0.706167i	$0.249577\pi$
$311$	5.12212e8	+	8.87178e8i	0.965581	+	1.67244i	0.257536	+	0.966269i	$0.417090\pi$
$312$	−1.49710e7	+	2.59306e7i	−0.0279068	+	0.0483360i
$313$	−9.63895e7	−	5.46652e8i	−0.177674	−	1.00764i	−0.935012	−	0.354617i	$-0.884611\pi$
$313$	−9.63895e7	−	5.46652e8i	−0.177674	−	1.00764i	0.757337	−	0.653024i	$-0.226500\pi$
$314$	7.71979e6	+	4.37811e7i	0.0140719	+	0.0798055i
$315$	−2.81571e8	+	4.87695e8i	−0.507576	+	0.879147i
$316$	−4.52945e7	−	7.84523e7i	−0.0807496	−	0.139862i
$317$	5.83636e8	−	4.89729e8i	1.02905	−	0.863472i	0.0383086	−	0.999266i	$-0.487803\pi$
$317$	5.83636e8	−	4.89729e8i	1.02905	−	0.863472i	0.990737	+	0.135794i	$0.0433586\pi$
$318$	2.35027e8	−	8.55428e7i	0.409848	−	0.149172i
$319$	−5.65419e8	−	2.05796e8i	−0.975222	−	0.354952i
$320$	6.56940e7	+	5.51239e7i	0.112073	+	0.0940404i
$321$	−2.49326e7	+	1.41400e8i	−0.0420727	+	0.238606i
$322$	−2.98762e8			−0.498689
$323$	−1.53193e8	−	5.30328e8i	−0.252947	−	0.875661i
$324$	2.05564e8			0.335768
$325$	1.85993e7	−	1.05482e8i	0.0300541	−	0.170445i
$326$	6.04484e8	+	5.07222e8i	0.966324	+	0.810842i
$327$	−2.57292e7	−	9.36467e6i	−0.0406920	−	0.0148107i
$328$	−2.26459e8	+	8.24245e7i	−0.354349	+	0.128973i
$329$	3.74350e8	−	3.14117e8i	0.579551	−	0.486301i
$330$	6.87457e7	+	1.19071e8i	0.105304	+	0.182393i
$331$	−3.96007e8	+	6.85904e8i	−0.600212	+	1.03960i	0.392576	+	0.919719i	$0.371584\pi$
$331$	−3.96007e8	+	6.85904e8i	−0.600212	+	1.03960i	−0.992789	+	0.119878i	$0.961750\pi$
$332$	−1.06792e7	−	6.05645e7i	−0.0160160	−	0.0908312i
$333$	7.08260e6	+	4.01674e7i	0.0105109	+	0.0596100i
$334$	2.15614e8	−	3.73454e8i	0.316639	−	0.548434i
$335$	3.45168e8	+	5.97849e8i	0.501619	+	0.868829i
$336$	4.39671e7	−	3.68928e7i	0.0632325	−	0.0530584i
$337$	1.16718e9	−	4.24819e8i	1.66124	−	0.604643i	0.670687	−	0.741741i	$-0.266000\pi$
$337$	1.16718e9	−	4.24819e8i	1.66124	−	0.604643i	0.990558	+	0.137097i	$0.0437774\pi$
$338$	−3.68418e8	−	1.34093e8i	−0.518958	−	0.188885i
$339$	2.97576e8	+	2.49696e8i	0.414858	+	0.348107i
$340$	6.71263e7	−	3.80692e8i	0.0926225	−	0.525288i
$341$	−5.98731e7			−0.0817695
$342$	4.16246e8	−	2.04026e8i	0.562676	−	0.275800i
$343$	7.62246e8			1.01992
$344$	−6.18111e7	+	3.50548e8i	−0.0818676	+	0.464294i
$345$	1.66234e8	+	1.39487e8i	0.217948	+	0.182880i
$346$	−5.97087e8	−	2.17322e8i	−0.774946	−	0.282057i
$347$	8.66442e8	−	3.15359e8i	1.11323	−	0.405184i	0.281055	−	0.959692i	$-0.409316\pi$
$347$	8.66442e8	−	3.15359e8i	1.11323	−	0.405184i	0.832179	+	0.554507i	$0.187093\pi$
$348$	1.39758e8	−	1.17271e8i	0.177767	−	0.149164i
$349$	−3.63870e8	−	6.30241e8i	−0.458202	−	0.793629i	0.540664	−	0.841239i	$-0.318173\pi$
$349$	−3.63870e8	−	6.30241e8i	−0.458202	−	0.793629i	−0.998866	+	0.0476094i	$0.984840\pi$
$350$	−1.02657e8	+	1.77807e8i	−0.127982	+	0.221672i
$351$	4.18906e7	+	2.37574e8i	0.0517061	+	0.293240i
$352$	1.89482e7	+	1.07460e8i	0.0231562	+	0.131326i
$353$	−6.27059e8	+	1.08610e9i	−0.758746	+	1.31419i	0.184744	+	0.982787i	$0.440855\pi$
$353$	−6.27059e8	+	1.08610e9i	−0.758746	+	1.31419i	−0.943490	+	0.331401i	$0.892479\pi$
$354$	−1.30659e8	−	2.26307e8i	−0.156540	−	0.271136i
$355$	−9.94041e8	+	8.34100e8i	−1.17925	+	0.989507i
$356$	1.55163e8	−	5.64746e7i	0.182269	−	0.0663404i
$357$	−2.43114e8	−	8.84863e7i	−0.282795	−	0.102929i
$358$	−8.80557e8	−	7.38875e8i	−1.01430	−	0.851099i
$359$	1.97983e8	−	1.12282e9i	0.225838	−	1.28079i	−0.635238	−	0.772317i	$-0.719098\pi$
$359$	1.97983e8	−	1.12282e9i	0.225838	−	1.28079i	0.861076	−	0.508476i	$-0.169791\pi$
$360$	3.24623e8			0.366709
$361$	5.47562e8	−	7.06529e8i	0.612573	−	0.790414i
$362$	−5.74601e8			−0.636629
$363$	2.30069e7	−	1.30479e8i	0.0252456	−	0.143175i
$364$	−1.61416e8	−	1.35444e8i	−0.175425	−	0.147199i
$365$	−1.17910e9	−	4.29158e8i	−1.26919	−	0.461947i
$366$	−2.79872e8	+	1.01865e8i	−0.298384	+	0.108603i
$367$	−9.48312e8	+	7.95728e8i	−1.00143	+	0.840298i	−0.987182	−	0.159600i	$-0.948979\pi$
$367$	−9.48312e8	+	7.95728e8i	−1.00143	+	0.840298i	−0.0142467	+	0.999899i	$0.504535\pi$
$368$	8.61107e7	+	1.49148e8i	0.0900720	+	0.156009i
$369$	−4.56123e8	+	7.90029e8i	−0.472596	+	0.818560i
$370$	9.56395e6	+	5.42398e7i	0.00981592	+	0.0556689i
$371$	3.05643e8	+	1.73338e9i	0.310746	+	1.76233i
$372$	9.07696e6	−	1.57218e7i	0.00914198	−	0.0158344i
$373$	5.77844e8	+	1.00085e9i	0.576540	+	0.998597i	0.995872	+	0.0907639i	$0.0289309\pi$
$373$	5.77844e8	+	1.00085e9i	0.576540	+	0.998597i	−0.419332	+	0.907833i	$0.637736\pi$
$374$	3.76792e8	−	3.16166e8i	0.372435	−	0.312510i
$375$	−2.38757e8	+	8.69003e7i	−0.233801	+	0.0850965i
$376$	−2.64711e8	−	9.63468e7i	−0.256811	−	0.0934717i
$377$	−5.13094e8	−	4.30537e8i	−0.493176	−	0.413824i
$378$	8.02989e7	−	4.55397e8i	0.0764695	−	0.433680i
$379$	−9.02835e8			−0.851866			−0.425933	−	0.904755i	$-0.640054\pi$
$379$	−9.02835e8			−0.851866			−0.425933	+	0.904755i	$0.640054\pi$
$380$	5.62075e8	−	2.75505e8i	0.525475	−	0.257565i
$381$	−1.69691e8			−0.157188
$382$	−3.71070e7	+	2.10444e8i	−0.0340591	+	0.193159i
$383$	5.82622e8	+	4.88878e8i	0.529897	+	0.444636i	0.868066	−	0.496449i	$-0.165363\pi$
$383$	5.82622e8	+	4.88878e8i	0.529897	+	0.444636i	−0.338169	+	0.941085i	$0.609807\pi$
$384$	−3.10901e7	−	1.13159e7i	−0.0280196	−	0.0101983i
$385$	−9.09228e8	+	3.30932e8i	−0.812008	+	0.295547i
$386$	−9.66415e8	+	8.10918e8i	−0.855279	+	0.717665i
$387$	6.73712e8	+	1.16690e9i	0.590862	+	1.02340i
$388$	2.29052e8	−	3.96730e8i	0.199078	−	0.344813i
$389$	−3.90003e8	−	2.21182e9i	−0.335927	−	1.90513i	−0.417887	−	0.908499i	$-0.637229\pi$
$389$	−3.90003e8	−	2.21182e9i	−0.335927	−	1.90513i	0.0819603	−	0.996636i	$-0.473882\pi$
$390$	2.65769e7	+	1.50725e8i	0.0226870	+	0.128665i
$391$	3.88157e8	−	6.72308e8i	0.328389	−	0.568787i
$392$	−8.87154e6	−	1.53660e7i	−0.00743872	−	0.0128842i
$393$	−4.66375e8	+	3.91335e8i	−0.387580	+	0.325218i
$394$	−4.21219e7	+	1.53311e7i	−0.0346953	+	0.0126281i
$395$	−4.35124e8	−	1.58372e8i	−0.355241	−	0.129297i
$396$	3.16416e8	+	2.65505e8i	0.256051	+	0.214852i
$397$	3.41940e8	−	1.93924e9i	0.274273	−	1.55548i	−0.466988	−	0.884264i	$-0.654661\pi$
$397$	3.41940e8	−	1.93924e9i	0.274273	−	1.55548i	0.741261	−	0.671217i	$-0.234228\pi$
$398$	−4.88177e7			−0.0388139
$399$	−1.16263e8	−	4.02484e8i	−0.0916299	−	0.317207i
$400$	1.18353e8			0.0924635
$401$	−3.34793e8	+	1.89871e9i	−0.259281	+	1.47046i	0.525557	+	0.850758i	$0.323857\pi$
$401$	−3.34793e8	+	1.89871e9i	−0.259281	+	1.47046i	−0.784839	+	0.619700i	$0.787254\pi$
$402$	−2.04023e8	−	1.71195e8i	−0.156635	−	0.131432i
$403$	−6.26290e7	−	2.27951e7i	−0.0476659	−	0.0173490i
$404$	−7.26738e8	+	2.64511e8i	−0.548331	+	0.199576i
$405$	8.04919e8	−	6.75408e8i	0.602088	−	0.505212i
$406$	6.41956e8	+	1.11190e9i	0.476063	+	0.824565i
$407$	−3.50398e7	+	6.06907e7i	−0.0257621	+	0.0446213i
$408$	2.58974e7	+	1.46872e8i	0.0188776	+	0.107060i
$409$	2.05704e8	+	1.16660e9i	0.148666	+	0.843124i	0.964351	+	0.264628i	$0.0852491\pi$
$409$	2.05704e8	+	1.16660e9i	0.148666	+	0.843124i	−0.815685	+	0.578496i	$0.803640\pi$
$410$	−6.15923e8	+	1.06681e9i	−0.441350	+	0.764441i
$411$	1.55411e7	+	2.69179e7i	0.0110417	+	0.0191247i
$412$	−1.62803e7	+	1.36608e7i	−0.0114689	+	0.00962355i
$413$	1.72809e9	−	6.28972e8i	1.20709	−	0.439346i
$414$	6.12606e8	+	2.22970e8i	0.424307	+	0.154435i
$415$	−2.40809e8	−	2.02063e8i	−0.165388	−	0.138777i
$416$	−2.10924e7	+	1.19621e8i	−0.0143648	+	0.0814667i
$417$	−4.54616e8			−0.307022
$418$	7.73196e8	+	1.91173e8i	0.517813	+	0.128030i
$419$	7.78037e8			0.516715			0.258358	−	0.966049i	$-0.416819\pi$
$419$	7.78037e8			0.516715			0.258358	+	0.966049i	$0.416819\pi$
$420$	5.09444e7	−	2.88920e8i	0.0335524	−	0.190285i
$421$	1.47337e9	+	1.23630e9i	0.962331	+	0.807492i	0.981331	−	0.192328i	$-0.0616037\pi$
$421$	1.47337e9	+	1.23630e9i	0.962331	+	0.807492i	−0.0189996	+	0.999819i	$0.506048\pi$
$422$	−1.14963e9	−	4.18430e8i	−0.744670	−	0.271038i
$423$	−1.00203e9	+	3.64708e8i	−0.643707	+	0.234290i
$424$	7.77248e8	−	6.52189e8i	0.495198	−	0.415521i
$425$	−2.66748e8	−	4.62020e8i	−0.168554	−	0.291944i
$426$	2.50314e8	−	4.33556e8i	0.156874	−	0.271714i
$427$	−3.63961e8	−	2.06413e9i	−0.226234	−	1.28304i
$428$	1.01145e8	+	5.73619e8i	0.0623576	+	0.353647i
$429$	−9.73707e7	+	1.68651e8i	−0.0595426	+	0.103131i
$430$	9.09743e8	+	1.57572e9i	0.551797	+	0.955740i
$431$	7.57270e8	−	6.35425e8i	0.455596	−	0.382291i	−0.385911	−	0.922536i	$-0.626113\pi$
$431$	7.57270e8	−	6.35425e8i	0.455596	−	0.382291i	0.841508	+	0.540245i	$0.181669\pi$
$432$	−2.50488e8	+	9.11702e7i	−0.149484	+	0.0544076i
$433$	−3.12245e9	−	1.13648e9i	−1.84837	−	0.672750i	−0.986067	−	0.166350i	$-0.946802\pi$
$433$	−3.12245e9	−	1.13648e9i	−1.84837	−	0.672750i	−0.862299	−	0.506400i	$-0.830976\pi$
$434$	9.78670e7	+	8.21202e7i	0.0574675	+	0.0482210i
$435$	1.61937e8	−	9.18391e8i	0.0943265	−	0.534952i
$436$	−1.11075e8			−0.0641818
$437$	1.24994e9	−	1.33847e8i	0.716480	−	0.0767229i
$438$	4.84094e8			0.275277
$439$	3.67581e8	−	2.08465e9i	0.207361	−	1.17600i	−0.686320	−	0.727300i	$-0.740775\pi$
$439$	3.67581e8	−	2.08465e9i	0.207361	−	1.17600i	0.893681	−	0.448703i	$-0.148114\pi$
$440$	4.27271e8	+	3.58523e8i	0.239122	+	0.200647i
$441$	−6.31136e7	−	2.29715e7i	−0.0350419	−	0.0127542i
$442$	5.14507e8	−	1.87265e8i	0.283409	−	0.103152i
$443$	1.78535e9	−	1.49809e9i	0.975686	−	0.818698i	−0.00774711	−	0.999970i	$-0.502466\pi$
$443$	1.78535e9	−	1.49809e9i	0.975686	−	0.818698i	0.983433	+	0.181272i	$0.0580216\pi$
$444$	−1.06243e7	−	1.84018e7i	−0.00576050	−	0.00997748i
$445$	4.22011e8	−	7.30944e8i	0.227020	−	0.393210i
$446$	−1.88753e8	−	1.07047e9i	−0.100744	−	0.571350i
$447$	1.44549e8	+	8.19776e8i	0.0765486	+	0.434129i
$448$	1.16417e8	−	2.01641e8i	0.0611709	−	0.105951i
$449$	9.95481e8	+	1.72422e9i	0.519004	+	0.898941i	0.999756	+	0.0220846i	$0.00703033\pi$
$449$	9.95481e8	+	1.72422e9i	0.519004	+	0.898941i	−0.480752	+	0.876856i	$0.659636\pi$
$450$	3.43196e8	−	2.87975e8i	0.177541	−	0.148974i
$451$	−1.47288e9	+	5.36085e8i	−0.756048	+	0.275179i
$452$	1.48083e9	+	5.38977e8i	0.754258	+	0.274527i
$453$	4.49998e8	+	3.77593e8i	0.227440	+	0.190845i
$454$	2.21504e8	−	1.25621e9i	0.111093	−	0.630039i
$455$	−1.07707e9			−0.536050
$456$	−1.67418e8	+	1.74047e8i	−0.0826849	+	0.0859587i
$457$	5.54610e8			0.271820			0.135910	−	0.990721i	$-0.456604\pi$
$457$	5.54610e8			0.271820			0.135910	+	0.990721i	$0.456604\pi$
$458$	−2.45219e8	+	1.39071e9i	−0.119268	+	0.676405i
$459$	9.20461e8	+	7.72359e8i	0.444284	+	0.372799i
$460$	8.27228e8	+	3.01086e8i	0.396253	+	0.144224i
$461$	−1.29744e9	+	4.72230e8i	−0.616785	+	0.224492i	−0.631470	−	0.775401i	$-0.717548\pi$
$461$	−1.29744e9	+	4.72230e8i	−0.616785	+	0.224492i	0.0146842	+	0.999892i	$0.495326\pi$
$462$	2.85960e8	−	2.39949e8i	0.134914	−	0.113207i
$463$	−6.87130e8	−	1.19014e9i	−0.321740	−	0.557271i	0.659107	−	0.752049i	$-0.270934\pi$
$463$	−6.87130e8	−	1.19014e9i	−0.321740	−	0.557271i	−0.980847	+	0.194779i	$0.937601\pi$
$464$	3.70056e8	−	6.40956e8i	0.171971	−	0.297862i
$465$	−1.61136e7	−	9.13849e7i	−0.00743203	−	0.0421492i
$466$	1.41899e8	+	8.04750e8i	0.0649575	+	0.368392i
$467$	−3.97045e8	+	6.87702e8i	−0.180397	+	0.312458i	−0.942016	−	0.335568i	$-0.891072\pi$
$467$	−3.97045e8	+	6.87702e8i	−0.180397	+	0.312458i	0.761618	+	0.648026i	$0.224405\pi$
$468$	2.29897e8	+	3.98193e8i	0.103675	+	0.179570i
$469$	1.43579e9	−	1.20477e9i	0.642666	−	0.539261i
$470$	−1.35308e9	+	4.92481e8i	−0.601148	+	0.218800i
$471$	−8.23829e7	−	2.99849e7i	−0.0363299	−	0.0132230i
$472$	−8.12075e8	−	6.81411e8i	−0.355467	−	0.298272i
$473$	−4.02016e8	+	2.27995e9i	−0.174675	+	0.990629i
$474$	1.78645e8			0.0770490
$475$	3.49830e8	−	7.89888e8i	0.149772	−	0.338172i
$476$	−1.04954e9			−0.446040
$477$	6.66935e8	−	3.78238e9i	0.281365	−	1.59570i
$478$	−1.31090e9	−	1.09997e9i	−0.548999	−	0.460665i
$479$	−3.18824e9	−	1.16042e9i	−1.32549	−	0.482438i	−0.420276	−	0.907396i	$-0.638067\pi$
$479$	−3.18824e9	−	1.16042e9i	−1.32549	−	0.482438i	−0.905213	+	0.424958i	$0.860289\pi$
$480$	−1.58918e8	+	5.78415e7i	−0.0655888	+	0.0238724i
$481$	−5.97591e7	+	5.01438e7i	−0.0244848	+	0.0205452i
$482$	1.08692e8	+	1.88259e8i	0.0442111	+	0.0765759i
$483$	2.94585e8	−	5.10237e8i	0.118959	−	0.206043i
$484$	−9.33324e7	−	5.29314e8i	−0.0374174	−	0.212205i
$485$	−4.06618e8	−	2.30604e9i	−0.161842	−	0.917849i
$486$	−7.72002e8	+	1.33715e9i	−0.305064	+	0.528387i
$487$	−5.56677e8	−	9.64193e8i	−0.218400	−	0.378279i	0.735919	−	0.677069i	$-0.236750\pi$
$487$	−5.56677e8	−	9.64193e8i	−0.218400	−	0.378279i	−0.954319	+	0.298790i	$0.903417\pi$
$488$	−9.25553e8	+	7.76631e8i	−0.360522	+	0.302514i
$489$	−1.46229e9	+	5.32229e8i	−0.565525	+	0.205834i
$490$	−8.52250e7	−	3.10194e7i	−0.0327251	−	0.0119110i
$491$	3.15550e9	+	2.64778e9i	1.20305	+	1.00948i	0.999538	+	0.0304061i	$0.00968006\pi$
$491$	3.15550e9	+	2.64778e9i	1.20305	+	1.00948i	0.203512	+	0.979072i	$0.434764\pi$
$492$	8.25260e7	−	4.68028e8i	0.0312401	−	0.177172i
$493$	−3.33617e9			−1.25396
$494$	7.36002e8	+	4.94347e8i	0.274685	+	0.184496i
$495$	2.11133e9			0.782418
$496$	1.27884e7	−	7.25264e7i	0.00470575	−	0.0266876i
$497$	2.69886e9	+	2.26461e9i	0.986127	+	0.827459i
$498$	1.13964e8	+	4.14796e7i	0.0413491	+	0.0150498i
$499$	−1.32941e8	+	4.83865e7i	−0.0478968	+	0.0174330i	−0.365857	−	0.930671i	$-0.619224\pi$
$499$	−1.32941e8	+	4.83865e7i	−0.0478968	+	0.0174330i	0.317961	+	0.948104i	$0.397002\pi$
$500$	−7.89582e8	+	6.62538e8i	−0.282490	+	0.237037i
$501$	4.25200e8	+	7.36467e8i	0.151064	+	0.261650i
$502$	9.33153e8	−	1.61627e9i	0.329223	−	0.570231i
$503$	−1.13592e7	−	6.44214e7i	−0.00397980	−	0.0225706i	0.982753	−	0.184922i	$-0.0592033\pi$
$503$	−1.13592e7	−	6.44214e7i	−0.00397980	−	0.0225706i	−0.986733	+	0.162351i	$0.948092\pi$
$504$	−1.53047e8	−	8.67975e8i	−0.0532499	−	0.301995i
$505$	−1.97658e9	+	3.42354e9i	−0.682959	+	1.18292i
$506$	5.60060e8	+	9.70052e8i	0.192180	+	0.332865i
$507$	5.92277e8	−	4.96979e8i	0.201835	−	0.169360i
$508$	−6.46871e8	+	2.35442e8i	−0.218925	+	0.0796821i
$509$	1.75797e9	+	6.39847e8i	0.590878	+	0.215062i	0.620116	−	0.784510i	$-0.287086\pi$
$509$	1.75797e9	+	6.39847e8i	0.590878	+	0.215062i	−0.0292374	+	0.999572i	$0.509308\pi$
$510$	5.83973e8	+	4.90011e8i	0.194938	+	0.163573i
$511$	−5.91577e8	+	3.35500e9i	−0.196127	+	1.11229i
$512$	−1.34218e8			−0.0441942
$513$	−1.31928e8	+	1.94124e9i	−0.0431445	+	0.634845i
$514$	1.50640e9			0.489293
$515$	−1.88639e7	+	1.06982e8i	−0.00608562	+	0.0345133i
$516$	−5.37733e8	−	4.51211e8i	−0.172303	−	0.144579i
$517$	−1.72167e9	−	6.26635e8i	−0.547939	−	0.199433i
$518$	1.40517e8	−	5.11439e7i	0.0444196	−	0.0161674i
$519$	9.59891e8	−	8.05444e8i	0.301395	−	0.252900i
$520$	3.10440e8	+	5.37698e8i	0.0968201	+	0.167697i
$521$	−1.37215e9	+	2.37663e9i	−0.425079	+	0.736258i	−0.996428	−	0.0844493i	$-0.973087\pi$
$521$	−1.37215e9	+	2.37663e9i	−0.425079	+	0.736258i	0.571349	+	0.820707i	$0.306420\pi$
$522$	−4.86492e8	−	2.75903e9i	−0.149702	−	0.849005i
$523$	6.88014e8	+	3.90192e9i	0.210301	+	1.19268i	0.888877	+	0.458146i	$0.151486\pi$
$523$	6.88014e8	+	3.90192e9i	0.210301	+	1.19268i	−0.678576	+	0.734530i	$0.737403\pi$
$524$	−1.23488e9	+	2.13888e9i	−0.374943	+	0.649421i
$525$	−2.02444e8	−	3.50643e8i	−0.0610586	−	0.105757i
$526$	−2.01416e9	+	1.69008e9i	−0.603454	+	0.506358i
$527$	−3.11947e8	+	1.13539e8i	−0.0928418	+	0.0337916i
$528$	−2.02208e8	−	7.35978e7i	−0.0597833	−	0.0217594i
$529$	−1.25397e9	−	1.05220e9i	−0.368291	−	0.309033i
$530$	9.00592e8	−	5.10751e9i	0.262762	−	1.49020i
$531$	−4.01282e9			−1.16311
$532$	−1.00164e9	−	1.37298e9i	−0.288417	−	0.395343i
$533$	−1.74478e9			−0.499108
$534$	−5.65441e7	+	3.20678e8i	−0.0160692	+	0.0911328i
$535$	2.28075e9	+	1.91378e9i	0.643932	+	0.540323i
$536$	−1.01528e9	−	3.69530e8i	−0.284779	−	0.103651i
$537$	2.13013e9	−	7.75302e8i	0.593602	−	0.216053i
$538$	−5.21610e6	+	4.37683e6i	−0.00144414	+	0.00121177i
$539$	−5.77001e7	−	9.99395e7i	−0.0158714	−	0.0274901i
$540$	−6.81277e8	+	1.18001e9i	−0.186185	+	0.322482i
$541$	6.20405e8	+	3.51849e9i	0.168455	+	0.955358i	0.945430	+	0.325826i	$0.105642\pi$
$541$	6.20405e8	+	3.51849e9i	0.168455	+	0.955358i	−0.776975	+	0.629532i	$0.783247\pi$
$542$	−5.09529e8	−	2.88968e9i	−0.137458	−	0.779565i
$543$	5.66568e8	−	9.81325e8i	0.151863	−	0.263035i
$544$	3.02503e8	+	5.23951e8i	0.0805627	+	0.139539i
$545$	−4.34931e8	+	3.64951e8i	−0.115089	+	0.0965710i
$546$	3.90477e8	−	1.42122e8i	0.102665	−	0.0373669i
$547$	3.11900e8	+	1.13522e8i	0.0814817	+	0.0296569i	0.382439	−	0.923981i	$-0.375084\pi$
$547$	3.11900e8	+	1.13522e8i	0.0814817	+	0.0296569i	−0.300958	+	0.953637i	$0.597306\pi$
$548$	9.65915e7	+	8.10499e7i	0.0250730	+	0.0210388i
$549$	−7.94192e8	+	4.50408e9i	−0.204843	+	1.16172i
$550$	7.69763e8			0.197282
$551$	−3.18391e9	−	4.36430e9i	−0.810832	−	1.11143i
$552$	−3.39628e8			−0.0859442
$553$	−2.18310e8	+	1.23810e9i	−0.0548953	+	0.311327i
$554$	−2.59550e9	−	2.17788e9i	−0.648540	−	0.544190i
$555$	−1.02063e8	−	3.71479e7i	−0.0253421	−	0.00922378i
$556$	−1.73302e9	+	6.30769e8i	−0.427605	+	0.155636i
$557$	3.14856e9	−	2.64196e9i	0.772004	−	0.647788i	−0.169217	−	0.985579i	$-0.554124\pi$
$557$	3.14856e9	−	2.64196e9i	0.772004	−	0.647788i	0.941221	+	0.337791i	$0.109680\pi$
$558$	−1.39387e8	−	2.41425e8i	−0.0339627	−	0.0588252i
$559$	−1.28855e9	+	2.23184e9i	−0.312004	+	0.540407i
$560$	−2.06667e8	−	1.17206e9i	−0.0497293	−	0.282029i
$561$	1.68436e8	+	9.55245e8i	0.0402776	+	0.228426i
$562$	7.93307e8	−	1.37405e9i	0.188523	−	0.326531i
$563$	−3.80902e9	−	6.59741e9i	−0.899567	−	1.55810i	−0.828049	−	0.560656i	$-0.810549\pi$
$563$	−3.80902e9	−	6.59741e9i	−0.899567	−	1.55810i	−0.0715181	−	0.997439i	$-0.522784\pi$
$564$	4.25555e8	−	3.57083e8i	0.0998801	−	0.0838094i
$565$	7.56931e9	−	2.75500e9i	1.76558	−	0.642618i
$566$	4.17630e9	+	1.52005e9i	0.968131	+	0.352371i
$567$	−2.18539e9	−	1.83376e9i	−0.503486	−	0.422475i
$568$	3.52662e8	−	2.00004e9i	0.0807494	−	0.457953i
$569$	2.11391e9			0.481054			0.240527	−	0.970643i	$-0.422680\pi$
$569$	2.11391e9			0.481054			0.240527	+	0.970643i	$0.422680\pi$
$570$	−8.36995e7	+	1.23159e9i	−0.0189305	+	0.278550i
$571$	5.38409e9			1.21028			0.605140	−	0.796119i	$-0.293117\pi$
$571$	5.38409e9			1.21028			0.605140	+	0.796119i	$0.293117\pi$
$572$	−1.37184e8	+	7.78008e8i	−0.0306490	+	0.173819i
$573$	−3.22816e8	−	2.70875e8i	−0.0716827	−	0.0601489i
$574$	3.14281e9	+	1.14389e9i	0.693628	+	0.252460i
$575$	1.14165e9	−	4.15527e8i	0.250435	−	0.0911511i
$576$	−3.89199e8	+	3.26577e8i	−0.0848580	+	0.0712044i
$577$	6.94022e8	+	1.20208e9i	0.150403	+	0.260506i	0.931376	−	0.364059i	$-0.118609\pi$
$577$	6.94022e8	+	1.20208e9i	0.150403	+	0.260506i	−0.780972	+	0.624566i	$0.785276\pi$
$578$	−2.77775e8	+	4.81120e8i	−0.0598337	+	0.103635i
$579$	−4.32012e8	−	2.45006e9i	−0.0924956	−	0.524568i
$580$	−6.56932e8	−	3.72564e9i	−0.139805	−	0.792872i
$581$	−4.26741e8	+	7.39138e8i	−0.0902710	+	0.156354i
$582$	4.51700e8	+	7.82367e8i	0.0949772	+	0.164505i
$583$	5.05518e9	−	4.24180e9i	1.05657	−	0.886565i
$584$	1.84539e9	−	6.71668e8i	0.383393	−	0.139544i
$585$	2.20852e9	+	8.03835e8i	0.456095	+	0.166005i
$586$	1.30042e9	+	1.09118e9i	0.266958	+	0.224004i
$587$	1.17983e9	−	6.69113e9i	0.240760	−	1.36542i	−0.589376	−	0.807859i	$-0.700626\pi$
$587$	1.17983e9	−	6.69113e9i	0.240760	−	1.36542i	0.830136	−	0.557561i	$-0.188263\pi$
$588$	3.49901e7			0.00709782
$589$	−4.46240e8	−	2.99724e8i	−0.0899839	−	0.0604391i
$590$	−5.41869e9			−1.08621
$591$	1.53500e7	−	8.70542e7i	0.00305881	−	0.0173474i
$592$	−6.60326e7	−	5.54080e7i	−0.0130808	−	0.0109761i
$593$	−3.22237e9	−	1.17285e9i	−0.634577	−	0.230967i	0.00464534	−	0.999989i	$-0.498521\pi$
$593$	−3.22237e9	−	1.17285e9i	−0.634577	−	0.230967i	−0.639222	+	0.769022i	$0.720744\pi$
$594$	−1.62916e9	+	5.92966e8i	−0.318942	+	0.116085i
$595$	−4.10964e9	+	3.44840e9i	−0.799825	+	0.671133i
$596$	1.68845e9	+	2.92448e9i	0.326682	+	0.565830i
$597$	4.81353e7	−	8.33728e7i	0.00925877	−	0.0160367i
$598$	2.16517e8	+	1.22793e9i	0.0414037	+	0.234812i
$599$	−2.95820e8	−	1.67768e9i	−0.0562385	−	0.318944i	0.943691	−	0.330829i	$-0.107328\pi$
$599$	−2.95820e8	−	1.67768e9i	−0.0562385	−	0.318944i	−0.999929	+	0.0118841i	$0.996217\pi$
$600$	−1.16699e8	+	2.02128e8i	−0.0220565	+	0.0382030i
$601$	4.72816e9	+	8.18941e9i	0.888447	+	1.53883i	0.841712	+	0.539928i	$0.181548\pi$
$601$	4.72816e9	+	8.18941e9i	0.888447	+	1.53883i	0.0467352	+	0.998907i	$0.485118\pi$
$602$	3.78424e9	−	3.17535e9i	0.706953	−	0.593204i
$603$	−3.84319e9	+	1.39881e9i	−0.713808	+	0.259805i
$604$	2.23932e9	+	8.15045e8i	0.413511	+	0.150506i
$605$	−2.10459e9	−	1.76596e9i	−0.386389	−	0.324219i
$606$	2.64837e8	−	1.50196e9i	0.0483420	−	0.274161i
$607$	2.60268e9			0.472346			0.236173	−	0.971711i	$-0.424107\pi$
$607$	2.60268e9			0.472346			0.236173	+	0.971711i	$0.424107\pi$
$608$	−3.96723e8	+	8.95767e8i	−0.0715854	+	0.161634i
$609$	−2.53193e9			−0.454246
$610$	−1.07243e9	+	6.08206e9i	−0.191300	+	1.08492i
$611$	−1.56234e9	−	1.31096e9i	−0.277096	−	0.232511i
$612$	2.15206e9	+	7.83285e8i	0.379511	+	0.138131i
$613$	3.93227e9	−	1.43123e9i	0.689496	−	0.250956i	0.0265765	−	0.999647i	$-0.491539\pi$
$613$	3.93227e9	−	1.43123e9i	0.689496	−	0.250956i	0.662919	+	0.748691i	$0.269317\pi$
$614$	3.16795e8	−	2.65822e8i	0.0552317	−	0.0463449i
$615$	−1.21463e9	−	2.10379e9i	−0.210562	−	0.364704i
$616$	7.57173e8	−	1.31146e9i	0.130516	−	0.226060i
$617$	1.34624e9	+	7.63490e9i	0.230741	+	1.30860i	0.851401	+	0.524516i	$0.175754\pi$
$617$	1.34624e9	+	7.63490e9i	0.230741	+	1.30860i	−0.620660	+	0.784080i	$0.713135\pi$
$618$	−7.27770e6	−	4.12739e7i	−0.00124032	−	0.00703422i
$619$	4.81628e9	−	8.34205e9i	0.816197	−	1.41369i	−0.0922688	−	0.995734i	$-0.529412\pi$
$619$	4.81628e9	−	8.34205e9i	0.816197	−	1.41369i	0.908465	−	0.417960i	$-0.137255\pi$
$620$	−1.88220e8	−	3.26007e8i	−0.0317173	−	0.0549359i
$621$	−2.09615e9	+	1.75888e9i	−0.351238	+	0.294724i
$622$	−7.70116e9	+	2.80299e9i	−1.28319	+	0.467041i
$623$	−2.15335e9	−	7.83756e8i	−0.356785	−	0.129859i
$624$	−1.83495e8	−	1.53971e8i	−0.0302329	−	0.0253684i
$625$	−1.30688e9	+	7.41168e9i	−0.214119	+	1.21433i
$626$	4.44068e9			0.723501
$627$	−1.08888e9	+	1.13199e9i	−0.176418	+	0.183403i
$628$	−3.55652e8			−0.0573016
$629$	−6.74723e7	+	3.82654e8i	−0.0108106	+	0.0613097i
$630$	−3.45113e9	−	2.89584e9i	−0.549882	−	0.461406i
$631$	9.30611e9	+	3.38715e9i	1.47457	+	0.536700i	0.949337	−	0.314259i	$-0.101756\pi$
$631$	9.30611e9	+	3.38715e9i	1.47457	+	0.536700i	0.525233	+	0.850959i	$0.323978\pi$
$632$	6.81006e8	−	2.47866e8i	0.107310	−	0.0390577i
$633$	1.84817e9	−	1.55080e9i	0.289620	−	0.243020i
$634$	3.04753e9	+	5.27848e9i	0.474937	+	0.822614i
$635$	−1.75936e9	+	3.04730e9i	−0.272675	+	0.472288i
$636$	3.47450e8	+	1.97049e9i	0.0535540	+	0.303720i
$637$	−2.23067e7	−	1.26507e8i	−0.00341938	−	0.0193922i
$638$	2.40683e9	−	4.16875e9i	0.366921	−	0.635526i
$639$	−3.84385e9	−	6.65774e9i	−0.582791	−	1.00942i
$640$	−5.25552e8	+	4.40991e8i	−0.0792476	+	0.0664966i
$641$	2.87055e9	−	1.04479e9i	0.430489	−	0.156685i	−0.117682	−	0.993051i	$-0.537546\pi$
$641$	2.87055e9	−	1.04479e9i	0.430489	−	0.156685i	0.548171	+	0.836366i	$0.315324\pi$
$642$	−1.07938e9	−	3.92862e8i	−0.160991	−	0.0585959i
$643$	−3.47114e9	−	2.91263e9i	−0.514913	−	0.432063i	0.347941	−	0.937516i	$-0.386881\pi$
$643$	−3.47114e9	−	2.91263e9i	−0.514913	−	0.432063i	−0.862854	+	0.505453i	$0.831325\pi$
$644$	4.15036e8	−	2.35378e9i	0.0612329	−	0.347269i
$645$	−3.58810e9			−0.526509
$646$	4.39099e9	−	4.70200e8i	0.640838	−	0.0686229i
$647$	5.51628e9			0.800721			0.400360	−	0.916358i	$-0.368885\pi$
$647$	5.51628e9			0.800721			0.400360	+	0.916358i	$0.368885\pi$
$648$	−2.85566e8	+	1.61953e9i	−0.0412282	+	0.233817i
$649$	−5.28169e9	−	4.43187e9i	−0.758432	−	0.636400i
$650$	8.05195e8	+	2.93067e8i	0.115002	+	0.0418572i
$651$	−2.36747e8	+	8.61688e7i	−0.0336319	+	0.0122410i
$652$	−4.83587e9	+	4.05778e9i	−0.683294	+	0.573352i
$653$	−3.59405e9	−	6.22507e9i	−0.505112	−	0.874880i	−0.999983	−	0.00591283i	$-0.998118\pi$
$653$	−3.59405e9	−	6.22507e9i	−0.505112	−	0.874880i	0.494871	−	0.868967i	$-0.335215\pi$
$654$	1.09522e8	−	1.89697e8i	0.0153101	−	0.0265179i
$655$	2.19219e9	+	1.24325e10i	0.304813	+	1.72868i
$656$	−3.34784e8	−	1.89865e9i	−0.0463022	−	0.262593i
$657$	3.71690e9	−	6.43786e9i	0.511331	−	0.885652i
$658$	1.95472e9	+	3.38567e9i	0.267481	+	0.463291i
$659$	−4.11729e9	+	3.45481e9i	−0.560418	+	0.470247i	−0.878451	−	0.477833i	$-0.841422\pi$
$659$	−4.11729e9	+	3.45481e9i	−0.560418	+	0.470247i	0.318032	+	0.948080i	$0.396978\pi$
$660$	−1.03360e9	+	3.76198e8i	−0.139942	+	0.0509346i
$661$	−1.22342e10	−	4.45288e9i	−1.64767	−	0.599703i	−0.659315	−	0.751867i	$-0.729154\pi$
$661$	−1.22342e10	−	4.45288e9i	−1.64767	−	0.599703i	−0.988355	+	0.152164i	$0.951376\pi$
$662$	−4.85374e9	−	4.07277e9i	−0.650240	−	0.545616i
$663$	−1.87496e8	+	1.06334e9i	−0.0249859	+	0.141702i
$664$	4.91991e8			0.0652182
$665$	−8.43321e9	−	2.08511e9i	−1.11203	−	0.274950i
$666$	−3.26297e8			−0.0428009
$667$	1.31927e9	−	7.48198e9i	0.172145	−	0.976284i
$668$	2.64272e9	+	2.21750e9i	0.343031	+	0.287837i
$669$	2.01430e9	+	7.33146e8i	0.260096	+	0.0946671i
$670$	−5.18963e9	+	1.88887e9i	−0.666614	+	0.242628i
$671$	−6.01975e9	+	5.05117e9i	−0.769218	+	0.645451i
$672$	2.29580e8	+	3.97644e8i	0.0291838	+	0.0505478i
$673$	−2.79931e9	+	4.84855e9i	−0.353996	+	0.613139i	−0.986946	−	0.161054i	$-0.948511\pi$
$673$	−2.79931e9	+	4.84855e9i	−0.353996	+	0.613139i	0.632950	+	0.774193i	$0.281844\pi$
$674$	1.72549e9	+	9.78574e9i	0.217072	+	1.23107i
$675$	3.26536e8	+	1.85188e9i	0.0408666	+	0.231766i
$676$	1.56825e9	−	2.71629e9i	0.195255	−	0.338191i
$677$	−3.75300e9	−	6.50039e9i	−0.464856	−	0.805155i	0.534339	−	0.845270i	$-0.320561\pi$
$677$	−3.75300e9	−	6.50039e9i	−0.464856	−	0.805155i	−0.999195	+	0.0401157i	$0.987227\pi$
$678$	−2.38061e9	+	1.99757e9i	−0.293349	+	0.246149i
$679$	−5.97417e9	+	2.17442e9i	−0.732375	+	0.266563i
$680$	2.90602e9	+	1.05770e9i	0.354419	+	0.128998i
$681$	1.92700e9	+	1.61694e9i	0.233812	+	0.196191i
$682$	8.31748e7	−	4.71708e8i	0.0100403	−	0.0569414i
$683$	−3.94621e7			−0.00473923			−0.00236962	−	0.999997i	$-0.500754\pi$
$683$	−3.94621e7			−0.00473923			−0.00236962	+	0.999997i	$0.500754\pi$
$684$	1.02917e9	+	3.56281e9i	0.122967	+	0.425693i
$685$	6.44521e8			0.0766161
$686$	−1.05890e9	+	6.00532e9i	−0.125234	+	0.710235i
$687$	−2.13331e9	−	1.79006e9i	−0.251019	−	0.210630i
$688$	−2.67591e9	−	9.73953e8i	−0.313266	−	0.114019i
$689$	6.90282e9	−	2.51242e9i	0.804007	−	0.292634i
$690$	−1.32987e9	+	1.11589e9i	−0.154112	+	0.129316i
$691$	−3.24409e9	−	5.61892e9i	−0.374041	−	0.647858i	0.616142	−	0.787635i	$-0.288695\pi$
$691$	−3.24409e9	−	5.61892e9i	−0.374041	−	0.647858i	−0.990183	+	0.139777i	$0.955361\pi$
$692$	2.54163e9	−	4.40223e9i	0.291568	−	0.505011i
$693$	−9.95412e8	−	5.64526e9i	−0.113615	−	0.644344i
$694$	1.28090e9	+	7.26433e9i	0.145464	+	0.824968i
$695$	−4.71347e9	+	8.16398e9i	−0.532592	+	0.922476i
$696$	7.29766e8	+	1.26399e9i	0.0820449	+	0.142106i
$697$	−6.65731e9	+	5.58615e9i	−0.744705	+	0.624881i
$698$	5.47081e9	−	1.99121e9i	0.608917	−	0.221628i
$699$	−1.51430e9	−	5.51159e8i	−0.167703	−	0.0610390i
$700$	−1.25824e9	−	1.05578e9i	−0.138650	−	0.116341i
$701$	−1.63630e9	+	9.27991e9i	−0.179411	+	1.01749i	0.753517	+	0.657429i	$0.228356\pi$
$701$	−1.63630e9	+	9.27991e9i	−0.179411	+	1.01749i	−0.932928	+	0.360063i	$0.882755\pi$
$702$	−1.92991e9			−0.210551
$703$	−5.64972e8	+	2.76925e8i	−0.0613315	+	0.0300621i
$704$	−8.72945e8			−0.0942937
$705$	4.93088e8	−	2.79644e9i	0.0529983	−	0.300569i
$706$	−7.68568e9	−	6.44905e9i	−0.821988	−	0.689730i
$707$	1.00857e10	+	3.67089e9i	1.07334	+	0.390664i
$708$	1.96446e9	−	7.15006e8i	0.208031	−	0.0757170i
$709$	1.35018e10	−	1.13294e10i	1.42276	−	1.19383i	0.472913	−	0.881109i	$-0.343202\pi$
$709$	1.35018e10	−	1.13294e10i	1.42276	−	1.19383i	0.949844	−	0.312726i	$-0.101242\pi$
$710$	−5.19051e9	−	8.99023e9i	−0.544260	−	0.942685i
$711$	1.37165e9	−	2.37577e9i	0.143120	−	0.247891i
$712$	2.29383e8	+	1.30090e9i	0.0238167	+	0.135071i
$713$	−1.31275e8	−	7.44498e8i	−0.0135634	−	0.0769219i
$714$	1.03487e9	−	1.79244e9i	0.106400	−	0.184290i
$715$	2.01908e9	+	3.49716e9i	0.206578	+	0.357803i
$716$	7.04445e9	−	5.91100e9i	0.717219	−	0.601818i
$717$	3.17115e9	−	1.15421e9i	0.321292	−	0.116941i
$718$	8.57105e9	+	3.11961e9i	0.864168	+	0.314532i
$719$	8.45482e9	+	7.09443e9i	0.848307	+	0.711814i	0.959416	−	0.281994i	$-0.0909958\pi$
$719$	8.45482e9	+	7.09443e9i	0.848307	+	0.711814i	−0.111109	+	0.993808i	$0.535440\pi$
$720$	−4.50962e8	+	2.55753e9i	−0.0450274	+	0.255363i
$721$	2.94942e8			0.0293064
$722$	4.80570e9	+	5.29544e9i	0.475200	+	0.523627i
$723$	−4.28689e8			−0.0421850
$724$	7.98227e8	−	4.52697e9i	0.0781703	−	0.443326i
$725$	−3.99956e9	−	3.35603e9i	−0.389788	−	0.327071i
$726$	9.96011e8	+	3.62518e8i	0.0966020	+	0.0351602i
$727$	1.44433e10	−	5.25692e9i	1.39410	−	0.507412i	0.467681	−	0.883897i	$-0.345089\pi$
$727$	1.44433e10	−	5.25692e9i	1.39410	−	0.507412i	0.926423	+	0.376485i	$0.122867\pi$
$728$	1.29133e9	−	1.08355e9i	0.124044	−	0.104086i
$729$	1.98983e9	+	3.44648e9i	0.190226	+	0.329481i
$730$	5.01909e9	−	8.69333e9i	0.477524	−	0.827096i
$731$	2.22898e9	+	1.26412e10i	0.211055	+	1.19695i
$732$	−4.13746e8	−	2.34647e9i	−0.0389892	−	0.221119i
$733$	7.49580e9	−	1.29831e10i	0.702998	−	1.21763i	−0.264411	−	0.964410i	$-0.585178\pi$
$733$	7.49580e9	−	1.29831e10i	0.702998	−	1.21763i	0.967409	−	0.253218i	$-0.0814891\pi$
$734$	−4.95173e9	−	8.57665e9i	−0.462190	−	0.800537i
$735$	1.37010e8	−	1.14965e8i	0.0127276	−	0.0106797i
$736$	−1.29468e9	+	4.71226e8i	−0.119699	+	0.0435669i
$737$	−6.60331e9	−	2.40341e9i	−0.607611	−	0.221152i
$738$	−5.59057e9	−	4.69105e9i	−0.511987	−	0.429608i
$739$	−3.11976e9	+	1.76930e10i	−0.284358	+	1.61268i	0.423211	+	0.906031i	$0.360903\pi$
$739$	−3.11976e9	+	1.76930e10i	−0.284358	+	1.61268i	−0.707569	+	0.706644i	$0.750208\pi$
$740$	−4.40613e8			−0.0399711
$741$	−1.56998e9	+	7.69536e8i	−0.141752	+	0.0694809i
$742$	−1.40810e10			−1.26538
$743$	−2.99101e9	+	1.69629e10i	−0.267521	+	1.51718i	0.494240	+	0.869326i	$0.335446\pi$
$743$	−2.99101e9	+	1.69629e10i	−0.267521	+	1.51718i	−0.761760	+	0.647859i	$0.775665\pi$
$744$	1.11254e8	+	9.33530e7i	0.00990397	+	0.00831042i
$745$	1.62202e10	+	5.90366e9i	1.43717	+	0.523087i
$746$	−8.68793e9	+	3.16215e9i	−0.766179	+	0.278866i
$747$	1.42665e9	−	1.19710e9i	0.125227	−	0.105078i
$748$	1.96747e9	+	3.40775e9i	0.171890	+	0.297723i
$749$	4.04175e9	−	7.00052e9i	0.351466	−	0.608757i
$750$	−3.52963e8	−	2.00176e9i	−0.0305503	−	0.173259i
$751$	−2.51182e9	−	1.42453e10i	−0.216396	−	1.22724i	−0.878467	−	0.477802i	$-0.841434\pi$
$751$	−2.51182e9	−	1.42453e10i	−0.216396	−	1.22724i	0.662071	−	0.749441i	$-0.269678\pi$
$752$	1.12680e9	−	1.95167e9i	0.0966236	−	0.167357i
$753$	1.84022e9	+	3.18735e9i	0.157068	+	0.272049i
$754$	4.10475e9	−	3.44430e9i	0.348728	−	0.292618i
$755$	1.14464e10	−	4.16614e9i	0.967952	−	0.352306i
$756$	3.47628e9	+	1.26526e9i	0.292610	+	0.106501i
$757$	1.14935e10	+	9.64415e9i	0.962975	+	0.808032i	0.981435	−	0.191798i	$-0.0614317\pi$
$757$	1.14935e10	+	9.64415e9i	0.962975	+	0.808032i	−0.0184594	+	0.999830i	$0.505876\pi$
$758$	1.25421e9	−	7.11295e9i	0.104599	−	0.593209i
$759$	−2.20892e9			−0.183373
$760$	1.38973e9	+	4.81102e9i	0.114837	+	0.397548i
$761$	−9.24120e9			−0.760119			−0.380060	−	0.924962i	$-0.624097\pi$
$761$	−9.24120e9			−0.760119			−0.380060	+	0.924962i	$0.624097\pi$
$762$	2.35732e8	−	1.33690e9i	0.0193008	−	0.109460i
$763$	1.18085e9	+	9.90855e8i	0.0962411	+	0.0807559i
$764$	−1.60643e9	−	5.84692e8i	−0.130327	−	0.0474351i
$765$	1.10003e10	−	4.00380e9i	0.888364	−	0.323338i
$766$	−4.66098e9	+	3.91103e9i	−0.374694	+	0.314405i
$767$	−3.83749e9	−	6.64673e9i	−0.307088	−	0.531893i
$768$	1.32341e8	−	2.29222e8i	0.0105422	−	0.0182596i
$769$	−2.38669e9	−	1.35356e10i	−0.189258	−	1.07334i	−0.920361	−	0.391069i	$-0.872105\pi$
$769$	−2.38669e9	−	1.35356e10i	−0.189258	−	1.07334i	0.731103	−	0.682267i	$-0.239006\pi$
$770$	−1.34415e9	−	7.62305e9i	−0.106104	−	0.601743i
$771$	−1.48534e9	+	2.57269e9i	−0.116717	+	0.202161i
$772$	−5.04626e9	−	8.74038e9i	−0.394738	−	0.683706i
$773$	−1.09497e10	+	9.18785e9i	−0.852652	+	0.715460i	−0.960372	−	0.278721i	$-0.910090\pi$
$773$	−1.09497e10	+	9.18785e9i	−0.852652	+	0.715460i	0.107720	+	0.994181i	$0.465645\pi$
$774$	−1.01293e10	+	3.68677e9i	−0.785212	+	0.285794i
$775$	−4.88192e8	−	1.77687e8i	−0.0376734	−	0.0137120i
$776$	2.80742e9	+	2.35571e9i	0.215671	+	0.180969i
$777$	−5.12069e7	+	2.90409e8i	−0.00391611	+	0.0222094i
$778$	1.79675e10			1.36792
$779$	−1.36611e10	−	3.37773e9i	−1.03540	−	0.256002i
$780$	−1.22440e9			−0.0923831
$781$	2.29369e9	−	1.30082e10i	0.172289	−	0.977098i
$782$	4.75753e9	+	3.99204e9i	0.355761	+	0.298519i
$783$	1.10501e10	+	4.02190e9i	0.822619	+	0.299409i
$784$	1.33384e8	−	4.85480e7i	0.00988550	−	0.00359803i
$785$	−1.39262e9	+	1.16854e9i	−0.102751	+	0.0862186i
$786$	−2.43524e9	−	4.21795e9i	−0.178880	−	0.309830i
$787$	−8.32321e9	+	1.44162e10i	−0.608666	+	1.05424i	0.382794	+	0.923834i	$0.374962\pi$
$787$	−8.32321e9	+	1.44162e10i	−0.608666	+	1.05424i	−0.991460	+	0.130408i	$0.958371\pi$
$788$	−6.22705e7	−	3.53153e8i	−0.00453357	−	0.0257112i
$789$	−9.00381e8	−	5.10632e9i	−0.0652615	−	0.370116i
$790$	1.85220e9	−	3.20810e9i	0.133657	−	0.231501i
$791$	−1.09349e10	−	1.89399e10i	−0.785595	−	1.36069i
$792$	−2.53133e9	+	2.12404e9i	−0.181055	+	0.151923i
$793$	−8.21993e9	+	2.99181e9i	−0.585345	+	0.213048i
$794$	1.48032e10	+	5.38792e9i	1.04950	+	0.381988i
$795$	7.83480e9	+	6.57418e9i	0.553023	+	0.464041i
$796$	6.78169e7	−	3.84609e8i	0.00476587	−	0.0270286i
$797$	1.90172e10			1.33059			0.665294	−	0.746582i	$-0.268306\pi$
$797$	1.90172e10			1.33059			0.665294	+	0.746582i	$0.268306\pi$
$798$	3.33247e9	−	3.56851e8i	0.232143	−	0.0248586i
$799$	−1.01584e10			−0.704551
$800$	−1.64415e8	+	9.32441e8i	−0.0113534	+	0.0643883i
$801$	3.83048e9	+	3.21415e9i	0.263354	+	0.220980i
$802$	−1.44938e10	−	5.27531e9i	−0.992138	−	0.361109i
$803$	1.20023e10	−	4.36850e9i	0.818016	−	0.297733i
$804$	1.63218e9	−	1.36956e9i	0.110757	−	0.0929364i
$805$	−6.10854e9	−	1.05803e10i	−0.412716	−	0.714846i
$806$	2.66594e8	−	4.61754e8i	0.0179340	−	0.0310626i
$807$	−2.33173e6	−	1.32239e7i	−0.000156178	−	0.000885732i
$808$	−1.07437e9	−	6.09303e9i	−0.0716494	−	0.406344i
$809$	−7.25805e9	+	1.25713e10i	−0.481948	+	0.834759i	−0.999785	−	0.0207206i	$-0.993404\pi$
$809$	−7.25805e9	+	1.25713e10i	−0.481948	+	0.834759i	0.517837	+	0.855479i	$0.326737\pi$
$810$	4.20299e9	+	7.27979e9i	0.277882	+	0.481306i
$811$	2.88309e9	−	2.41920e9i	0.189795	−	0.159257i	−0.542939	−	0.839772i	$-0.682688\pi$
$811$	2.88309e9	−	2.41920e9i	0.189795	−	0.159257i	0.732734	+	0.680515i	$0.238244\pi$
$812$	−9.65187e9	+	3.51299e9i	−0.632653	+	0.230267i
$813$	5.43751e9	+	1.97909e9i	0.354881	+	0.129166i
$814$	−4.29473e8	−	3.60371e8i	−0.0279094	−	0.0234188i
$815$	−5.60329e9	+	3.17778e10i	−0.362570	+	2.05623i
$816$	−1.19310e9			−0.0768707
$817$	−1.44097e10	+	1.49802e10i	−0.924435	+	0.961037i
$818$	−9.47680e9			−0.605376
$819$	1.10805e9	−	6.28409e9i	0.0704803	−	0.399713i
$820$	−7.54919e9	−	6.33453e9i	−0.478137	−	0.401204i
$821$	−1.28877e10	−	4.69075e9i	−0.812784	−	0.295829i	−0.0980108	−	0.995185i	$-0.531248\pi$
$821$	−1.28877e10	−	4.69075e9i	−0.812784	−	0.295829i	−0.714773	+	0.699356i	$0.753470\pi$
$822$	−2.33661e8	+	8.50458e7i	−0.0146736	+	0.00534074i
$823$	−9.93824e9	+	8.33917e9i	−0.621456	+	0.521463i	−0.898261	−	0.439463i	$-0.855169\pi$
$823$	−9.93824e9	+	8.33917e9i	−0.621456	+	0.521463i	0.276805	+	0.960926i	$0.410724\pi$
$824$	−8.50096e7	−	1.47241e8i	−0.00529325	−	0.00916819i
$825$	−7.59003e8	+	1.31463e9i	−0.0470603	+	0.0815108i
$826$	2.55470e9	+	1.44884e10i	0.157728	+	0.894522i
$827$	−4.91050e8	−	2.78488e9i	−0.0301895	−	0.171213i	0.965985	−	0.258598i	$-0.0832603\pi$
$827$	−4.91050e8	−	2.78488e9i	−0.0301895	−	0.171213i	−0.996175	+	0.0873842i	$0.972149\pi$
$828$	−2.60768e9	+	4.51664e9i	−0.159643	+	0.276509i
$829$	−7.91695e9	−	1.37126e10i	−0.482633	−	0.835945i	0.517168	−	0.855884i	$-0.326986\pi$
$829$	−7.91695e9	−	1.37126e10i	−0.482633	−	0.835945i	−0.999801	+	0.0199389i	$0.993653\pi$
$830$	1.92647e9	−	1.61650e9i	0.116947	−	0.0981303i
$831$	6.27869e9	−	2.28526e9i	0.379547	−	0.138144i
$832$	−9.13127e8	−	3.32351e8i	−0.0549667	−	0.0200062i
$833$	−4.90144e8	−	4.11279e8i	−0.0293810	−	0.0246536i
$834$	6.31546e8	−	3.58168e9i	0.0376985	−	0.213799i
$835$	1.76339e10			1.04821
$836$	−2.58026e9	+	5.82602e9i	−0.152736	+	0.344866i
$837$	1.17011e9			0.0689742
$838$	−1.08084e9	+	6.12974e9i	−0.0634463	+	0.359822i
$839$	1.44567e9	+	1.21306e9i	0.0845086	+	0.0709111i	0.684063	−	0.729423i	$-0.260211\pi$
$839$	1.44567e9	+	1.21306e9i	0.0845086	+	0.0709111i	−0.599555	+	0.800334i	$0.704656\pi$
$840$	2.20547e9	+	8.02727e8i	0.128388	+	0.0467294i
$841$	−1.44708e10	+	5.26696e9i	−0.838895	+	0.305333i
$842$	−1.17870e10	+	9.89043e9i	−0.680471	+	0.570983i
$843$	1.56444e9	+	2.70968e9i	0.0899417	+	0.155784i
$844$	4.89363e9	−	8.47602e9i	0.280177	−	0.485281i
$845$	−2.78399e9	−	1.57888e10i	−0.158734	−	0.900223i
$846$	−1.48134e9	−	8.40108e9i	−0.0841119	−	0.477022i
$847$	−3.72958e9	+	6.45983e9i	−0.210896	+	0.365282i
$848$	4.05850e9	+	7.02953e9i	0.228549	+	0.395859i
$849$	−6.71392e9	+	5.63364e9i	−0.376530	+	0.315946i
$850$	4.01057e9	−	1.45973e9i	0.223996	−	0.0815278i
$851$	−8.31492e8	−	3.02638e8i	−0.0462492	−	0.0168333i
$852$	3.06802e9	+	2.57437e9i	0.169949	+	0.142604i
$853$	−2.17520e9	+	1.23362e10i	−0.119999	+	0.680549i	0.864154	+	0.503228i	$0.167854\pi$
$853$	−2.17520e9	+	1.23362e10i	−0.119999	+	0.680549i	−0.984153	+	0.177321i	$0.943257\pi$
$854$	1.67678e10			0.921239
$855$	1.57360e10	+	1.05693e10i	0.861018	+	0.578316i
$856$	−4.65974e9			−0.253924
$857$	−3.25799e9	+	1.84770e10i	−0.176814	+	1.00276i	0.759215	+	0.650840i	$0.225583\pi$
$857$	−3.25799e9	+	1.84770e10i	−0.176814	+	1.00276i	−0.936029	+	0.351923i	$0.885528\pi$
$858$	−1.19345e9	−	1.00142e9i	−0.0645055	−	0.0541266i
$859$	−2.23640e10	−	8.13984e9i	−1.20385	−	0.438167i	−0.339286	−	0.940683i	$-0.610186\pi$
$859$	−2.23640e10	−	8.13984e9i	−1.20385	−	0.438167i	−0.864568	+	0.502516i	$0.832408\pi$
$860$	−1.36781e10	+	4.97841e9i	−0.733297	+	0.266898i
$861$	−5.05245e9	+	4.23951e9i	−0.269769	+	0.226363i
$862$	3.95418e9	+	6.84884e9i	0.210272	+	0.364202i
$863$	1.90004e9	−	3.29097e9i	0.100629	−	0.174295i	−0.811315	−	0.584610i	$-0.801248\pi$
$863$	1.90004e9	−	3.29097e9i	0.100629	−	0.174295i	0.911944	+	0.410314i	$0.134581\pi$
$864$	−3.70307e8	−	2.10011e9i	−0.0195327	−	0.110776i
$865$	−4.51195e9	−	2.55885e10i	−0.237032	−	1.34428i
$866$	1.32914e10	−	2.30213e10i	0.695436	−	1.20453i
$867$	−5.47784e8	−	9.48789e8i	−0.0285458	−	0.0494428i
$868$	−7.82936e8	+	6.56961e8i	−0.0406357	+	0.0340974i
$869$	4.42923e9	−	1.61211e9i	0.228960	−	0.0833345i
$870$	7.01054e9	+	2.55163e9i	0.360939	+	0.131371i
$871$	−5.99222e9	−	5.02807e9i	−0.307273	−	0.257833i
$872$	1.54303e8	−	8.75097e8i	0.00788074	−	0.0446939i
$873$	1.38727e10			0.705687
$874$	−6.81887e8	+	1.00335e10i	−0.0345479	+	0.508352i
$875$	1.43045e10			0.721844
$876$	−6.72496e8	+	3.81391e9i	−0.0338007	+	0.191693i
$877$	1.00813e10	+	8.45924e9i	0.504683	+	0.423480i	0.859254	−	0.511550i	$-0.170928\pi$
$877$	1.00813e10	+	8.45924e9i	0.504683	+	0.423480i	−0.354570	+	0.935029i	$0.615373\pi$
$878$	1.59132e10	+	5.79194e9i	0.793465	+	0.288797i
$879$	−3.14581e9	+	1.14498e9i	−0.156232	+	0.0568640i
$880$	−3.41817e9	+	2.86818e9i	−0.169084	+	0.141879i
$881$	7.32058e8	+	1.26796e9i	0.0360686	+	0.0624727i	0.883496	−	0.468438i	$-0.155183\pi$
$881$	7.32058e8	+	1.26796e9i	0.0360686	+	0.0624727i	−0.847428	+	0.530911i	$0.821850\pi$
$882$	2.68656e8	−	4.65326e8i	0.0131843	−	0.0228359i
$883$	−4.53478e8	−	2.57180e9i	−0.0221663	−	0.125711i	0.971717	−	0.236150i	$-0.0758856\pi$
$883$	−4.53478e8	−	2.57180e9i	−0.0221663	−	0.125711i	−0.993883	+	0.110438i	$0.964774\pi$
$884$	7.60617e8	+	4.31367e9i	0.0370325	+	0.210022i
$885$	5.34294e9	−	9.25424e9i	0.259107	−	0.448786i
$886$	9.32243e9	+	1.61469e10i	0.450309	+	0.779959i
$887$	−1.61824e10	+	1.35786e10i	−0.778590	+	0.653315i	−0.942893	−	0.333095i	$-0.891907\pi$
$887$	−1.61824e10	+	1.35786e10i	−0.778590	+	0.653315i	0.164303	+	0.986410i	$0.447463\pi$
$888$	1.59737e8	−	5.81397e7i	0.00765528	−	0.00278629i
$889$	8.97730e9	+	3.26747e9i	0.428538	+	0.155975i
$890$	5.17246e9	+	4.34021e9i	0.245942	+	0.206370i
$891$	−1.85731e9	+	1.05333e10i	−0.0879654	+	0.498876i
$892$	8.69587e9			0.410238
$893$	−9.69481e9	−	1.32890e10i	−0.455574	−	0.624471i
$894$	−6.65938e9			−0.311711
$895$	8.16236e9	−	4.62910e10i	0.380570	−	2.15832i
$896$	1.42689e9	+	1.19731e9i	0.0662695	+	0.0556067i
$897$	−2.31060e9	−	8.40989e8i	−0.106893	−	0.0389060i
$898$	−1.49671e10	+	5.44759e9i	−0.689718	+	0.251037i
$899$	−2.48872e9	+	2.08829e9i	−0.114240	+	0.0958586i
$900$	1.79204e9	+	3.10391e9i	0.0819406	+	0.141925i
$901$	1.82943e10	−	3.16867e10i	0.833257	−	1.44324i
$902$	−2.17742e9	−	1.23488e10i	−0.0987913	−	0.560274i
$903$	1.69165e9	+	9.59383e9i	0.0764546	+	0.433595i
$904$	−6.30345e9	+	1.09179e10i	−0.283785	+	0.491529i
$905$	−1.17484e10	−	2.03488e10i	−0.526876	−	0.912576i
$906$	−3.59998e9	+	3.02074e9i	−0.160824	+	0.134948i
$907$	−1.38465e10	+	5.03973e9i	−0.616192	+	0.224276i	−0.631210	−	0.775612i	$-0.717442\pi$
$907$	−1.38465e10	+	5.03973e9i	−0.616192	+	0.224276i	0.0150184	+	0.999887i	$0.495219\pi$
$908$	9.58930e9	+	3.49022e9i	0.425096	+	0.154722i
$909$	−1.79409e10	−	1.50542e10i	−0.792265	−	0.664789i
$910$	1.49625e9	−	8.48568e9i	0.0658204	−	0.373286i
$911$	1.58109e10			0.692857			0.346428	−	0.938076i	$-0.387394\pi$
$911$	1.58109e10			0.692857			0.346428	+	0.938076i	$0.387394\pi$
$912$	−1.13865e9	−	1.56078e9i	−0.0497059	−	0.0681335i
$913$	3.19988e9			0.139151
$914$	−7.70456e8	+	4.36948e9i	−0.0333762	+	0.189286i
$915$	−9.32974e9	−	7.82858e9i	−0.402620	−	0.337838i
$916$	−1.06160e10	−	3.86390e9i	−0.456380	−	0.166109i
$917$	3.22084e10	−	1.17229e10i	1.37936	−	0.502044i
$918$	−7.36369e9	+	6.17887e9i	−0.314157	+	0.263609i
$919$	−1.15061e10	−	1.99292e10i	−0.489017	−	0.847002i	0.510903	−	0.859638i	$-0.329311\pi$
$919$	−1.15061e10	−	1.99292e10i	−0.489017	−	0.847002i	−0.999920	+	0.0126359i	$0.995978\pi$
$920$	−3.52127e9	+	6.09902e9i	−0.149088	+	0.258228i
$921$	1.41615e8	+	8.03140e8i	0.00597312	+	0.0338753i
$922$	−1.91806e9	−	1.08778e10i	−0.0805941	−	0.457072i
$923$	7.35180e9	−	1.27337e10i	0.307743	−	0.533026i
$924$	1.49318e9	+	2.58626e9i	0.0622672	+	0.107850i
$925$	−4.65821e8	+	3.90870e8i	−0.0193519	+	0.0162381i
$926$	1.03311e10	−	3.76020e9i	0.427569	−	0.155622i
$927$	−6.04772e8	−	2.20119e8i	−0.0249352	−	0.00907567i
$928$	4.53567e9	+	3.80588e9i	0.186305	+	0.156328i
$929$	−5.69349e9	+	3.22894e10i	−0.232983	+	1.32131i	0.613838	+	0.789432i	$0.289625\pi$
$929$	−5.69349e9	+	3.22894e10i	−0.232983	+	1.32131i	−0.846820	+	0.531879i	$0.821486\pi$
$930$	7.42357e8			0.0302637
$931$	7.02513e7	−	1.03370e9i	0.00285319	−	0.0419829i
$932$	−6.53732e9			−0.264511
$933$	2.80644e9	−	1.59161e10i	0.113128	−	0.641582i
$934$	−4.86646e9	−	4.08345e9i	−0.195434	−	0.163988i
$935$	1.89006e10	+	6.87925e9i	0.756197	+	0.275233i
$936$	−3.45652e9	+	1.25807e9i	−0.137776	+	0.0501463i
$937$	9.76325e9	−	8.19234e9i	0.387709	−	0.325326i	−0.428011	−	0.903774i	$-0.640786\pi$
$937$	9.76325e9	−	8.19234e9i	0.387709	−	0.325326i	0.815720	+	0.578447i	$0.196341\pi$
$938$	7.49715e9	+	1.29855e10i	0.296610	+	0.513744i
$939$	−4.37860e9	+	7.58396e9i	−0.172586	+	0.298928i
$940$	−2.00031e9	−	1.13443e10i	−0.0785508	−	0.445484i
$941$	5.45450e9	+	3.09340e10i	0.213398	+	1.21024i	0.883664	+	0.468121i	$0.155069\pi$
$941$	5.45450e9	+	3.09340e10i	0.213398	+	1.21024i	−0.670266	+	0.742121i	$0.733820\pi$
$942$	3.50680e8	−	6.07396e8i	0.0136689	−	0.0236752i
$943$	−9.89536e9	−	1.71393e10i	−0.384274	−	0.665582i
$944$	6.49660e9	−	5.45129e9i	0.251353	−	0.210910i
$945$	1.77692e10	−	6.46745e9i	0.684945	−	0.249300i
$946$	−1.74040e10	−	6.33454e9i	−0.668391	−	0.243274i
$947$	1.44998e10	+	1.21668e10i	0.554801	+	0.465533i	0.876563	−	0.481287i	$-0.159831\pi$
$947$	1.44998e10	+	1.21668e10i	0.554801	+	0.465533i	−0.321762	+	0.946821i	$0.604275\pi$
$948$	−2.48171e8	+	1.40745e9i	−0.00946068	+	0.0536542i
$949$	1.42180e10			0.540016
$950$	5.73712e9	+	3.85342e9i	0.217101	+	0.145819i
$951$	−1.20197e10			−0.453171
$952$	1.45800e9	−	8.26874e9i	0.0547683	−	0.310606i
$953$	1.24740e10	+	1.04669e10i	0.466854	+	0.391737i	0.845645	−	0.533745i	$-0.179216\pi$
$953$	1.24740e10	+	1.04669e10i	0.466854	+	0.391737i	−0.378792	+	0.925482i	$0.623660\pi$
$954$	2.88728e10	+	1.05089e10i	1.07664	+	0.391864i
$955$	−8.21132e9	+	2.98868e9i	−0.305071	+	0.111037i
$956$	1.04872e10	−	8.79980e9i	0.388201	−	0.325739i
$957$	4.74636e9	+	8.22094e9i	0.175053	+	0.303200i
$958$	1.35714e10	−	2.35063e10i	0.498707	−	0.863785i
$959$	−3.03867e8	−	1.72331e9i	−0.0111255	−	0.0630956i
$960$	−2.34935e8	−	1.33238e9i	−0.00857036	−	0.0486049i
$961$	1.35947e10	−	2.35467e10i	0.494125	−	0.855850i
$962$	−3.12040e8	−	5.40469e8i	−0.0113005	−	0.0195730i
$963$	−1.35121e10	+	1.13380e10i	−0.487564	+	0.409115i
$964$	−1.63419e9	+	5.94796e8i	−0.0587533	+	0.0213845i
$965$	−4.84772e10	−	1.76443e10i	−1.73657	−	0.632059i
$966$	3.61065e9	+	3.02969e9i	0.128874	+	0.108138i
$967$	−4.26183e9	+	2.41700e10i	−0.151567	+	0.859577i	0.810291	+	0.586027i	$0.199309\pi$
$967$	−4.26183e9	+	2.41700e10i	−0.151567	+	0.859577i	−0.961858	+	0.273549i	$0.911802\pi$
$968$	4.29984e9			0.152366
$969$	−3.52658e9	+	7.96272e9i	−0.124515	+	0.281144i
$970$	1.87329e10			0.659030
$971$	3.85985e9	−	2.18903e10i	0.135302	−	0.767335i	−0.839347	−	0.543596i	$-0.817063\pi$
$971$	3.85985e9	−	2.18903e10i	0.135302	−	0.767335i	0.974649	−	0.223739i	$-0.0718264\pi$
$972$	−9.46220e9	−	7.93973e9i	−0.330491	−	0.277315i
$973$	2.40510e10	+	8.75384e9i	0.837023	+	0.304652i
$974$	8.36968e9	−	3.04632e9i	0.290237	−	0.105638i
$975$	−1.29445e9	+	1.08617e9i	−0.0447270	+	0.0375304i
$976$	−4.83289e9	−	8.37082e9i	−0.166392	−	0.288200i
$977$	−1.43356e10	+	2.48299e10i	−0.491795	+	0.851814i	−0.999955	−	0.00944851i	$-0.996992\pi$
$977$	−1.43356e10	+	2.48299e10i	−0.491795	+	0.851814i	0.508160	+	0.861262i	$0.330326\pi$
$978$	−2.16176e9	−	1.22599e10i	−0.0738960	−	0.419085i
$979$	1.49190e9	+	8.46097e9i	0.0508159	+	0.288191i
$980$	3.62778e8	−	6.28351e8i	0.0123126	−	0.0213261i
$981$	−1.68183e9	−	2.91302e9i	−0.0568776	−	0.0985148i
$982$	−2.52440e10	+	2.11823e10i	−0.850685	+	0.713809i
$983$	2.81499e10	−	1.02457e10i	0.945233	−	0.344037i	0.177003	−	0.984210i	$-0.443360\pi$
$983$	2.81499e10	−	1.02457e10i	0.945233	−	0.344037i	0.768230	+	0.640174i	$0.221138\pi$
$984$	3.57270e9	+	1.30036e9i	0.119540	+	0.0435090i
$985$	−1.40416e9	−	1.17823e9i	−0.0468157	−	0.0392830i
$986$	4.63456e9	−	2.62839e10i	0.153971	−	0.873213i
$987$	−7.70956e9			−0.255223
$988$	−4.91714e9	+	5.11183e9i	−0.162205	+	0.168627i
$989$	−2.92317e10			−0.960875
$990$	−2.93304e9	+	1.66341e10i	−0.0960714	+	0.544848i
$991$	1.54163e10	+	1.29358e10i	0.503179	+	0.422217i	0.858721	−	0.512443i	$-0.171259\pi$
$991$	1.54163e10	+	1.29358e10i	0.503179	+	0.422217i	−0.355542	+	0.934660i	$0.615704\pi$
$992$	5.53631e8	+	2.01505e8i	0.0180065	+	0.00655383i
$993$	1.17415e10	−	4.27357e9i	0.380542	−	0.138506i
$994$	−2.15909e10	+	1.81169e10i	−0.697297	+	0.585102i
$995$	−9.98136e8	−	1.72882e9i	−0.0321225	−	0.0556377i
$996$	−4.85113e8	+	8.40240e8i	−0.0155573	+	0.0269461i
$997$	5.58550e9	+	3.16769e10i	0.178496	+	1.01230i	0.934031	+	0.357193i	$0.116266\pi$
$997$	5.58550e9	+	3.16769e10i	0.178496	+	1.01230i	−0.755534	+	0.655109i	$0.772623\pi$
$998$	−1.96532e8	−	1.11459e9i	−0.00625858	−	0.0354942i
$999$	6.84788e8	−	1.18609e9i	0.0217309	−	0.0376389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.b.17.3	yes	36
19.9	even	9	inner	38.8.e.b.9.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.b.9.3	✓	36	19.9	even	9	inner
38.8.e.b.17.3	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-12.0854 - 10.1408i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-307.410 + 111.888i) q^{5} +(96.6830 - 81.1267i) q^{6} +(444.097 + 769.199i) q^{7} +(256.000 - 443.405i) q^{8} +(-336.549 - 1908.66i) q^{9} +O(q^{10})\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-12.0854 - 10.1408i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-307.410 + 111.888i) q^{5} +(96.6830 - 81.1267i) q^{6} +(444.097 + 769.199i) q^{7} +(256.000 - 443.405i) q^{8} +(-336.549 - 1908.66i) q^{9} +(-454.457 - 2577.35i) q^{10} +(1665.01 - 2883.88i) q^{11} +(504.843 + 874.413i) q^{12} +(2839.61 - 2382.72i) q^{13} +(-6677.03 + 2430.24i) q^{14} +(4849.80 + 1765.18i) q^{15} +(3137.72 + 2632.86i) q^{16} +(3206.13 - 18182.8i) q^{17} +15504.9 q^{18} +(26846.2 - 13158.8i) q^{19} +20936.9 q^{20} +(2433.24 - 13799.6i) q^{21} +(20407.6 + 17124.0i) q^{22} +(39510.6 + 14380.7i) q^{23} +(-7590.35 + 2762.66i) q^{24} +(22134.7 - 18573.2i) q^{25} +(14827.4 + 25681.8i) q^{26} +(-32539.5 + 56360.1i) q^{27} +(-9870.93 - 55980.8i) q^{28} +(-31376.8 - 177946. i) q^{29} +(-20644.2 + 35756.8i) q^{30} +(-8989.89 - 15571.0i) q^{31} +(-25101.7 + 21062.9i) q^{32} +(-49367.3 + 17968.2i) q^{33} +(138799. + 50518.7i) q^{34} +(-222584. - 186770. i) q^{35} +(-21539.1 + 122154. i) q^{36} -21044.8 q^{37} +(66377.1 + 229787. i) q^{38} -58480.5 q^{39} +(-29085.2 + 164950. i) q^{40} +(-360569. - 302553. i) q^{41} +(105339. + 38340.3i) q^{42} +(-653299. + 237782. i) q^{43} +(-163260. + 136992. i) q^{44} +(317015. + 549086. i) q^{45} +(-168185. + 291305. i) q^{46} +(-95540.2 - 541835. i) q^{47} +(-11221.1 - 63638.1i) q^{48} +(17327.2 - 30011.7i) q^{49} +(115579. + 200189. i) q^{50} +(-223136. + 187234. i) q^{51} +(-222931. + 81140.4i) q^{52} +(1.86218e6 + 677778. i) q^{53} +(-398828. - 334656. i) q^{54} +(-189169. + 1.07283e6i) q^{55} +454755. q^{56} +(-457887. - 113213. i) q^{57} +1.44553e6 q^{58} +(359536. - 2.03903e6i) q^{59} +(-253030. - 212317. i) q^{60} +(-2.21750e6 - 807103. i) q^{61} +(135164. - 49195.6i) q^{62} +(1.31868e6 - 1.10650e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-606328. + 1.05019e6i) q^{65} +(-72981.6 - 413899. i) q^{66} +(-366437. - 2.07817e6i) q^{67} +(-590827. + 1.02334e6i) q^{68} +(-331668. - 574466. i) q^{69} +(1.78067e6 - 1.49416e6i) q^{70} +(3.72738e6 - 1.35666e6i) q^{71} +(-932467. - 339390. i) q^{72} +(2.93824e6 + 2.46548e6i) q^{73} +(29235.1 - 165801. i) q^{74} -455854. q^{75} +(-1.90257e6 + 203734. i) q^{76} +2.95771e6 q^{77} +(81240.3 - 460737. i) q^{78} +(1.08430e6 + 909835. i) q^{79} +(-1.25915e6 - 458294. i) q^{80} +(-3.01823e6 + 1.09855e6i) q^{81} +(2.88455e6 - 2.42043e6i) q^{82} +(480460. + 832180. i) q^{83} +(-448398. + 776648. i) q^{84} +(1.04885e6 + 5.94831e6i) q^{85} +(-965799. - 5.47732e6i) q^{86} +(-1.42532e6 + 2.46873e6i) q^{87} +(-852486. - 1.47655e6i) q^{88} +(-1.97640e6 + 1.65840e6i) q^{89} +(-4.76635e6 + 1.73481e6i) q^{90} +(3.09385e6 + 1.12607e6i) q^{91} +(-2.06140e6 - 1.72972e6i) q^{92} +(-49256.2 + 279346. i) q^{93} +4.40155e6 q^{94} +(-6.78046e6 + 7.04892e6i) q^{95} +516959. q^{96} +(-1.24295e6 + 7.04913e6i) q^{97} +(212375. + 178204. i) q^{98} +(-6.06472e6 - 2.20738e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * q^99

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