LMFDB - Embedded newform 37.7.g.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(8,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("37.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.g (of order $12$, degree $4$, 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:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	37.14
Dual form			37.7.g.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.9349 + 3.73385i) q^{2} +(-44.2547 + 25.5505i) q^{3} +(124.814 - 72.0615i) q^{4} +(-58.7930 - 15.7535i) q^{5} +(521.284 - 521.284i) q^{6} +(-230.098 - 398.542i) q^{7} +(-817.340 + 817.340i) q^{8} +(941.155 - 1630.13i) q^{9} +O(q^{10})$	\(q+(-13.9349 + 3.73385i) q^{2} +(-44.2547 + 25.5505i) q^{3} +(124.814 - 72.0615i) q^{4} +(-58.7930 - 15.7535i) q^{5} +(521.284 - 521.284i) q^{6} +(-230.098 - 398.542i) q^{7} +(-817.340 + 817.340i) q^{8} +(941.155 - 1630.13i) q^{9} +878.096 q^{10} +1288.11i q^{11} +(-3682.42 + 6378.13i) q^{12} +(-2864.57 - 767.560i) q^{13} +(4694.49 + 4694.49i) q^{14} +(3004.38 - 805.021i) q^{15} +(3725.79 - 6453.27i) q^{16} +(-1056.04 - 3941.18i) q^{17} +(-7028.26 + 26229.8i) q^{18} +(-4452.75 - 1193.11i) q^{19} +(-8473.43 + 2270.45i) q^{20} +(20365.9 + 11758.2i) q^{21} +(-4809.59 - 17949.6i) q^{22} +(-835.843 + 835.843i) q^{23} +(15287.7 - 57054.6i) q^{24} +(-10323.2 - 5960.11i) q^{25} +42783.5 q^{26} +58935.3i q^{27} +(-57439.0 - 33162.4i) q^{28} +(3854.99 + 3854.99i) q^{29} +(-38859.9 + 22435.8i) q^{30} +(5018.05 + 5018.05i) q^{31} +(-8676.38 + 32380.7i) q^{32} +(-32911.8 - 57004.8i) q^{33} +(29431.5 + 50976.9i) q^{34} +(7249.71 + 27056.3i) q^{35} -271284. i q^{36} +(46170.9 + 20832.1i) q^{37} +66503.6 q^{38} +(146382. - 39223.1i) q^{39} +(60929.9 - 35177.9i) q^{40} +(-48954.8 + 28264.1i) q^{41} +(-327700. - 87806.9i) q^{42} +(-46504.6 + 46504.6i) q^{43} +(92823.0 + 160774. i) q^{44} +(-81013.6 + 81013.6i) q^{45} +(8526.48 - 14768.3i) q^{46} +90605.9 q^{47} +380784. i q^{48} +(-47065.8 + 81520.3i) q^{49} +(166107. + 44508.2i) q^{50} +(147434. + 147434. i) q^{51} +(-412851. + 110623. i) q^{52} +(-115311. + 199724. i) q^{53} +(-220055. - 821257. i) q^{54} +(20292.2 - 75731.6i) q^{55} +(513812. + 137676. i) q^{56} +(227540. - 60969.2i) q^{57} +(-68112.8 - 39325.0i) q^{58} +(10299.4 + 38437.9i) q^{59} +(316978. - 316978. i) q^{60} +(78118.3 - 291541. i) q^{61} +(-88662.7 - 51189.4i) q^{62} -866232. q^{63} -6716.17i q^{64} +(156325. + 90254.3i) q^{65} +(671469. + 671469. i) q^{66} +(248275. - 143342. i) q^{67} +(-415816. - 415816. i) q^{68} +(15633.8 - 58346.2i) q^{69} +(-202048. - 349958. i) q^{70} +(32924.0 + 57026.0i) q^{71} +(563126. + 2.10161e6i) q^{72} -349930. i q^{73} +(-721171. - 117898. i) q^{74} +609135. q^{75} +(-641745. + 171955. i) q^{76} +(513364. - 296391. i) q^{77} +(-1.89337e6 + 1.09314e6i) q^{78} +(45120.4 + 12090.0i) q^{79} +(-320712. + 320712. i) q^{80} +(-819723. - 1.41980e6i) q^{81} +(576647. - 576647. i) q^{82} +(-94084.2 + 162959. i) q^{83} +3.38927e6 q^{84} +248350. i q^{85} +(474396. - 821678. i) q^{86} +(-269098. - 72104.7i) q^{87} +(-1.05282e6 - 1.05282e6i) q^{88} +(-940089. + 251896. i) q^{89} +(826424. - 1.43141e6i) q^{90} +(353228. + 1.31827e6i) q^{91} +(-44093.0 + 164557. i) q^{92} +(-350286. - 93858.9i) q^{93} +(-1.26258e6 + 338309. i) q^{94} +(242995. + 140293. i) q^{95} +(-443371. - 1.65468e6i) q^{96} +(-131815. + 131815. i) q^{97} +(351473. - 1.31171e6i) q^{98} +(2.09978e6 + 1.21231e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) $ 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−13.9349	+	3.73385i	−1.74186	+	0.466731i	−0.982860	−	0.184356i	$-0.940980\pi$
$2$	−13.9349	+	3.73385i	−1.74186	+	0.466731i	−0.759003	+	0.651087i	$0.774313\pi$
$3$	−44.2547	+	25.5505i	−1.63906	+	0.946314i	−0.657909	+	0.753098i	$0.728559\pi$
$3$	−44.2547	+	25.5505i	−1.63906	+	0.946314i	−0.981156	+	0.193217i	$0.938108\pi$
$4$	124.814	−	72.0615i	1.95022	−	1.12596i
$5$	−58.7930	−	15.7535i	−0.470344	−	0.126028i	0.0158590	−	0.999874i	$-0.494952\pi$
$5$	−58.7930	−	15.7535i	−0.470344	−	0.126028i	−0.486203	+	0.873846i	$0.661618\pi$
$6$	521.284	−	521.284i	2.41335	−	2.41335i
$7$	−230.098	−	398.542i	−0.670840	−	1.16193i	−0.977666	−	0.210163i	$-0.932600\pi$
$7$	−230.098	−	398.542i	−0.670840	−	1.16193i	0.306826	−	0.951765i	$-0.400733\pi$
$8$	−817.340	+	817.340i	−1.59637	+	1.59637i
$9$	941.155	−	1630.13i	1.29102	−	2.23612i
$10$	878.096			0.878096
$11$			1288.11i			0.967774i	0.875131	+	0.483887i	$0.160775\pi$
$11$			1288.11i			0.967774i	−0.875131	+	0.483887i	$0.839225\pi$
$12$	−3682.42	+	6378.13i	−2.13103	+	3.69105i
$13$	−2864.57	−	767.560i	−1.30386	−	0.349367i	−0.460949	−	0.887426i	$-0.652491\pi$
$13$	−2864.57	−	767.560i	−1.30386	−	0.349367i	−0.842907	+	0.538059i	$0.819158\pi$
$14$	4694.49	+	4694.49i	1.71082	+	1.71082i
$15$	3004.38	−	805.021i	0.890186	−	0.238525i
$16$	3725.79	−	6453.27i	0.909618	−	1.57550i
$17$	−1056.04	−	3941.18i	−0.214947	−	0.802195i	−0.986185	−	0.165647i	$-0.947029\pi$
$17$	−1056.04	−	3941.18i	−0.214947	−	0.802195i	0.771238	−	0.636547i	$-0.219638\pi$
$18$	−7028.26	+	26229.8i	−1.20512	+	4.49757i
$19$	−4452.75	−	1193.11i	−0.649184	−	0.173948i	−0.0808242	−	0.996728i	$-0.525755\pi$
$19$	−4452.75	−	1193.11i	−0.649184	−	0.173948i	−0.568360	+	0.822780i	$0.692422\pi$
$20$	−8473.43	+	2270.45i	−1.05918	+	0.283806i
$21$	20365.9	+	11758.2i	2.19910	+	1.26965i
$22$	−4809.59	−	17949.6i	−0.451690	−	1.68573i
$23$	−835.843	+	835.843i	−0.0686975	+	0.0686975i	−0.740621	−	0.671923i	$-0.765468\pi$
$23$	−835.843	+	835.843i	−0.0686975	+	0.0686975i	0.671923	+	0.740621i	$0.265468\pi$
$24$	15287.7	−	57054.6i	1.10588	−	4.12722i
$25$	−10323.2	−	5960.11i	−0.660685	−	0.381447i
$26$	42783.5			2.43420
$27$			58935.3i			2.99422i
$28$	−57439.0	−	33162.4i	−2.61657	−	1.51068i
$29$	3854.99	+	3854.99i	0.158063	+	0.158063i	0.781708	−	0.623645i	$-0.214349\pi$
$29$	3854.99	+	3854.99i	0.158063	+	0.158063i	−0.623645	+	0.781708i	$0.714349\pi$
$30$	−38859.9	+	22435.8i	−1.43926	+	0.830955i
$31$	5018.05	+	5018.05i	0.168442	+	0.168442i	0.786294	−	0.617852i	$-0.211997\pi$
$31$	5018.05	+	5018.05i	0.168442	+	0.168442i	−0.617852	+	0.786294i	$0.711997\pi$
$32$	−8676.38	+	32380.7i	−0.264782	+	0.988180i
$33$	−32911.8	−	57004.8i	−0.915818	−	1.58624i
$34$	29431.5	+	50976.9i	0.748818	+	1.29699i
$35$	7249.71	+	27056.3i	0.169090	+	0.631051i
$36$		−	271284.i		−	5.81457i
$37$	46170.9	+	20832.1i	0.911514	+	0.411270i
$37$	46170.9	+	20832.1i	0.911514	+	0.411270i
$38$	66503.6			1.21198
$39$	146382.	−	39223.1i	2.46772	−	0.661223i
$40$	60929.9	−	35177.9i	0.952029	−	0.549654i
$41$	−48954.8	+	28264.1i	−0.710303	+	0.410094i	−0.811173	−	0.584806i	$-0.801171\pi$
$41$	−48954.8	+	28264.1i	−0.710303	+	0.410094i	0.100870	+	0.994900i	$0.467837\pi$
$42$	−327700.	−	87806.9i	−4.42312	−	1.18517i
$43$	−46504.6	+	46504.6i	−0.584912	+	0.584912i	−0.936249	−	0.351337i	$-0.885727\pi$
$43$	−46504.6	+	46504.6i	−0.584912	+	0.584912i	0.351337	+	0.936249i	$0.385727\pi$
$44$	92823.0	+	160774.i	1.08968	+	1.88737i
$45$	−81013.6	+	81013.6i	−0.889038	+	0.889038i
$46$	8526.48	−	14768.3i	0.0875984	−	0.151725i
$47$	90605.9			0.872696			0.436348	−	0.899778i	$-0.356272\pi$
$47$	90605.9			0.872696			0.436348	+	0.899778i	$0.356272\pi$
$48$			380784.i			3.44314i
$49$	−47065.8	+	81520.3i	−0.400052	+	0.692911i
$50$	166107.	+	44508.2i	1.32886	+	0.356066i
$51$	147434.	+	147434.i	1.11144	+	1.11144i
$52$	−412851.	+	110623.i	−2.93618	+	0.786748i
$53$	−115311.	+	199724.i	−0.774536	+	1.34154i	0.160518	+	0.987033i	$0.448683\pi$
$53$	−115311.	+	199724.i	−0.774536	+	1.34154i	−0.935055	+	0.354503i	$0.884650\pi$
$54$	−220055.	−	821257.i	−1.39750	−	5.21553i
$55$	20292.2	−	75731.6i	0.121967	−	0.455186i
$56$	513812.	+	137676.i	2.92577	+	0.783958i
$57$	227540.	−	60969.2i	1.22866	−	0.329220i
$58$	−68112.8	−	39325.0i	−0.349096	−	0.201551i
$59$	10299.4	+	38437.9i	0.0501483	+	0.187156i	0.986456	−	0.164024i	$-0.0524473\pi$
$59$	10299.4	+	38437.9i	0.0501483	+	0.187156i	−0.936308	+	0.351180i	$0.885781\pi$
$60$	316978.	−	316978.i	1.46749	−	1.46749i
$61$	78118.3	−	291541.i	0.344162	−	1.28443i	−0.549426	−	0.835542i	$-0.685154\pi$
$61$	78118.3	−	291541.i	0.344162	−	1.28443i	0.893588	−	0.448888i	$-0.148180\pi$
$62$	−88662.7	−	51189.4i	−0.372020	−	0.214786i
$63$	−866232.			−3.46428
$64$		−	6716.17i		−	0.0256201i
$65$	156325.	+	90254.3i	0.569231	+	0.328645i
$66$	671469.	+	671469.i	2.33558	+	2.33558i
$67$	248275.	−	143342.i	0.825483	−	0.476593i	−0.0268204	−	0.999640i	$-0.508538\pi$
$67$	248275.	−	143342.i	0.825483	−	0.476593i	0.852304	+	0.523047i	$0.175205\pi$
$68$	−415816.	−	415816.i	−1.32244	−	1.32244i
$69$	15633.8	−	58346.2i	0.0475902	−	0.177609i
$70$	−202048.	−	349958.i	−0.589062	−	1.02028i
$71$	32924.0	+	57026.0i	0.0919893	+	0.159330i	0.908348	−	0.418215i	$-0.137344\pi$
$71$	32924.0	+	57026.0i	0.0919893	+	0.159330i	−0.816359	+	0.577545i	$0.804011\pi$
$72$	563126.	+	2.10161e6i	1.50872	+	5.63061i
$73$		−	349930.i		−	0.899524i	−0.893148	−	0.449762i	$-0.851509\pi$
$73$		−	349930.i		−	0.899524i	0.893148	−	0.449762i	$-0.148491\pi$
$74$	−721171.	−	117898.i	−1.77968	−	0.290944i
$75$	609135.			1.44387
$76$	−641745.	+	171955.i	−1.46191	+	0.391718i
$77$	513364.	−	296391.i	1.12448	−	0.649221i
$78$	−1.89337e6	+	1.09314e6i	−3.98981	+	2.30352i
$79$	45120.4	+	12090.0i	0.0915148	+	0.0245213i	0.304286	−	0.952581i	$-0.401582\pi$
$79$	45120.4	+	12090.0i	0.0915148	+	0.0245213i	−0.212771	+	0.977102i	$0.568249\pi$
$80$	−320712.	+	320712.i	−0.626391	+	0.626391i
$81$	−819723.	−	1.41980e6i	−1.54245	−	2.67161i
$82$	576647.	−	576647.i	1.04585	−	1.04585i
$83$	−94084.2	+	162959.i	−0.164544	+	0.284999i	−0.936493	−	0.350685i	$-0.885949\pi$
$83$	−94084.2	+	162959.i	−0.164544	+	0.284999i	0.771949	+	0.635684i	$0.219282\pi$
$84$	3.38927e6			5.71831
$85$			248350.i			0.404397i
$86$	474396.	−	821678.i	0.745840	−	1.29183i
$87$	−269098.	−	72104.7i	−0.408652	−	0.109498i
$88$	−1.05282e6	−	1.05282e6i	−1.54492	−	1.54492i
$89$	−940089.	+	251896.i	−1.33352	+	0.357315i	−0.854026	−	0.520231i	$-0.825846\pi$
$89$	−940089.	+	251896.i	−1.33352	+	0.357315i	−0.479493	+	0.877546i	$0.659179\pi$
$90$	826424.	−	1.43141e6i	1.13364	−	1.96352i
$91$	353228.	+	1.31827e6i	0.468739	+	1.74936i
$92$	−44093.0	+	164557.i	−0.0566247	+	0.211326i
$93$	−350286.	−	93858.9i	−0.435486	−	0.116688i
$94$	−1.26258e6	+	338309.i	−1.52012	+	0.407314i
$95$	242995.	+	140293.i	0.283417	+	0.163631i
$96$	−443371.	−	1.65468e6i	−0.501134	−	1.87026i
$97$	−131815.	+	131815.i	−0.144428	+	0.144428i	−0.775623	−	0.631196i	$-0.782564\pi$
$97$	−131815.	+	131815.i	−0.144428	+	0.144428i	0.631196	+	0.775623i	$0.282564\pi$
$98$	351473.	−	1.31171e6i	0.373433	−	1.39367i
$99$	2.09978e6	+	1.21231e6i	2.16405	+	1.24942i
$100$	−1.71798e6			−1.71798
$101$		−	707452.i		−	0.686646i	−0.939217	−	0.343323i	$-0.888447\pi$
$101$		−	707452.i		−	0.686646i	0.939217	−	0.343323i	$-0.111553\pi$
$102$	−2.60497e6	−	1.50398e6i	−2.45472	−	1.41723i
$103$	1.18027e6	+	1.18027e6i	1.08012	+	1.08012i	0.996498	+	0.0836204i	$0.0266483\pi$
$103$	1.18027e6	+	1.18027e6i	1.08012	+	1.08012i	0.0836204	+	0.996498i	$0.473352\pi$
$104$	2.96869e6	−	1.71397e6i	2.63915	−	1.52372i
$105$	−1.01214e6	−	1.01214e6i	−0.874321	−	0.874321i
$106$	861104.	−	3.21368e6i	0.723000	−	2.69827i
$107$	950473.	+	1.64627e6i	0.775869	+	1.34385i	0.934305	+	0.356476i	$0.116022\pi$
$107$	950473.	+	1.64627e6i	0.775869	+	1.34385i	−0.158435	+	0.987369i	$0.550645\pi$
$108$	4.24697e6	+	7.35596e6i	3.37138	+	5.83940i
$109$	−276126.	−	1.03052e6i	−0.213220	−	0.795748i	−0.986786	−	0.162032i	$-0.948195\pi$
$109$	−276126.	−	1.03052e6i	−0.213220	−	0.795748i	0.773565	−	0.633716i	$-0.218471\pi$
$110$			1.13108e6i			0.849798i
$111$	−2.57555e6	+	257772.i	−1.88322	+	0.188481i
$112$	−3.42919e6			−2.44083
$113$	2.31122e6	−	619290.i	1.60179	−	0.429199i	0.656209	−	0.754579i	$-0.272159\pi$
$113$	2.31122e6	−	619290.i	1.60179	−	0.429199i	0.945583	+	0.325380i	$0.105492\pi$
$114$	−2.94310e6	+	1.69920e6i	−1.98651	+	1.14691i
$115$	62309.2	−	35974.2i	0.0409693	−	0.0236536i
$116$	758954.	+	203361.i	0.486230	+	0.130285i
$117$	−3.94723e6	+	3.94723e6i	−2.46453	+	2.46453i
$118$	−287043.	−	497173.i	−0.174703	−	0.302595i
$119$	−1.32773e6	+	1.32773e6i	−0.787898	+	0.787898i
$120$	−1.79762e6	+	3.11358e6i	−1.04029	+	1.80184i
$121$	112342.			0.0634143
$122$			4.35428e6i			2.39793i
$123$	1.44432e6	−	2.50164e6i	0.776155	−	1.34434i
$124$	987933.	+	264716.i	0.518158	+	0.138840i
$125$	1.18553e6	+	1.18553e6i	0.606992	+	0.606992i
$126$	1.20709e7	−	3.23438e6i	6.03429	−	1.61688i
$127$	552305.	−	956620.i	0.269630	−	0.467012i	−0.699136	−	0.714988i	$-0.746432\pi$
$127$	552305.	−	956620.i	0.269630	−	0.467012i	0.968766	+	0.247976i	$0.0797653\pi$
$128$	−530211.	−	1.97877e6i	−0.252824	−	0.943553i
$129$	869834.	−	3.24626e6i	0.405198	−	1.51222i
$130$	−2.51537e6	−	673991.i	−1.14491	−	0.306778i
$131$	−1.06019e6	+	284076.i	−0.471594	+	0.126363i	−0.486786	−	0.873521i	$-0.661831\pi$
$131$	−1.06019e6	+	284076.i	−0.471594	+	0.126363i	0.0151916	+	0.999885i	$0.495164\pi$
$132$	−8.21571e6	−	4.74334e6i	−3.57210	−	2.06235i
$133$	549066.	+	2.04914e6i	0.233383	+	0.870997i
$134$	−2.92447e6	+	2.92447e6i	−1.21544	+	1.21544i
$135$	928439.	−	3.46498e6i	0.377357	−	1.40831i
$136$	4.08443e6	+	2.35815e6i	1.62373	+	0.937463i
$137$	313284.			0.121836			0.0609181	−	0.998143i	$-0.480597\pi$
$137$	313284.			0.121836			0.0609181	+	0.998143i	$0.480597\pi$
$138$			871423.i			0.331583i
$139$	3.00617e6	+	1.73561e6i	1.11936	+	0.646261i	0.941237	−	0.337747i	$-0.109665\pi$
$139$	3.00617e6	+	1.73561e6i	1.11936	+	0.646261i	0.178120	+	0.984009i	$0.442998\pi$
$140$	2.85459e6	+	2.85459e6i	1.04030	+	1.04030i
$141$	−4.00974e6	+	2.31503e6i	−1.43041	+	0.825845i
$142$	−671719.	−	671719.i	−0.234597	−	0.234597i
$143$	988699.	−	3.68988e6i	0.338108	−	1.26184i
$144$	−7.01310e6	−	1.21470e7i	−2.34867	−	4.06802i
$145$	−165917.	−	287376.i	−0.0544234	−	0.0942641i
$146$	1.30658e6	+	4.87624e6i	0.419835	+	1.56685i
$147$		−	4.81021e6i		−	1.51430i
$148$	7.26398e6	−	727010.i	2.24073	−	0.224262i
$149$	1.58508e6			0.479173			0.239587	−	0.970875i	$-0.422988\pi$
$149$	1.58508e6			0.479173			0.239587	+	0.970875i	$0.422988\pi$
$150$	−8.48823e6	+	2.27441e6i	−2.51503	+	0.673901i
$151$	−1.53056e6	+	883672.i	−0.444550	+	0.256661i	−0.705526	−	0.708684i	$-0.749289\pi$
$151$	−1.53056e6	+	883672.i	−0.444550	+	0.256661i	0.260976	+	0.965345i	$0.415956\pi$
$152$	4.61459e6	−	2.66424e6i	1.31402	−	0.758651i
$153$	−7.41853e6	−	1.98779e6i	−2.07130	−	0.555004i
$154$	−6.04700e6	+	6.04700e6i	−1.65569	+	1.65569i
$155$	−215974.	−	374078.i	−0.0579972	−	0.100454i
$156$	1.54441e7	−	1.54441e7i	4.06809	−	4.06809i
$157$	913178.	−	1.58167e6i	0.235970	−	0.408712i	−0.723584	−	0.690236i	$-0.757507\pi$
$157$	913178.	−	1.58167e6i	0.235970	−	0.408712i	0.959554	+	0.281524i	$0.0908400\pi$
$158$	−673890.			−0.170851
$159$		−	1.17850e7i		−	2.93182i
$160$	1.02022e6	−	1.76707e6i	0.249077	−	0.431414i
$161$	525444.	+	140792.i	0.125907	+	0.0337366i
$162$	1.67241e7	+	1.67241e7i	3.93367	+	3.93367i
$163$	−2.08109e6	+	557627.i	−0.480539	+	0.128760i	−0.490954	−	0.871186i	$-0.663352\pi$
$163$	−2.08109e6	+	557627.i	−0.480539	+	0.128760i	0.0104146	+	0.999946i	$0.496685\pi$
$164$	−4.07350e6	+	7.05552e6i	−0.923499	+	1.59955i
$165$	1.03695e6	+	3.86996e6i	0.230838	+	0.861499i
$166$	702592.	−	2.62211e6i	0.153596	−	0.573227i
$167$	−466658.	−	125041.i	−0.100196	−	0.0268474i	0.208373	−	0.978049i	$-0.433183\pi$
$167$	−466658.	−	125041.i	−0.100196	−	0.0268474i	−0.308569	+	0.951202i	$0.599850\pi$
$168$	−2.62563e7	+	7.03536e6i	−5.53740	+	1.48374i
$169$	3.43649e6	+	1.98406e6i	0.711959	+	0.411050i
$170$	−927301.	−	3.46074e6i	−0.188744	−	0.704404i
$171$	−6.13566e6	+	6.13566e6i	−1.22708	+	1.22708i
$172$	−2.45324e6	+	9.15563e6i	−0.482120	+	1.79930i
$173$	−3.93178e6	−	2.27001e6i	−0.759365	−	0.438419i	0.0697029	−	0.997568i	$-0.477795\pi$
$173$	−3.93178e6	−	2.27001e6i	−0.759365	−	0.438419i	−0.829068	+	0.559148i	$0.811128\pi$
$174$	4.01909e6			0.762921
$175$			5.48564e6i			1.02356i
$176$	8.31249e6	+	4.79922e6i	1.52473	+	0.880304i
$177$	−1.43791e6	−	1.43791e6i	−0.259305	−	0.259305i
$178$	1.21595e7	−	7.02030e6i	2.15604	−	1.24479i
$179$	−6.56113e6	−	6.56113e6i	−1.14398	−	1.14398i	−0.987715	−	0.156268i	$-0.950054\pi$
$179$	−6.56113e6	−	6.56113e6i	−1.14398	−	1.14398i	−0.156268	−	0.987715i	$-0.549946\pi$
$180$	−4.27369e6	+	1.59496e7i	−0.732799	+	2.73484i
$181$	−1.17328e6	−	2.03218e6i	−0.197864	−	0.342710i	0.749972	−	0.661470i	$-0.230067\pi$
$181$	−1.17328e6	−	2.03218e6i	−0.197864	−	0.342710i	−0.947836	+	0.318760i	$0.896734\pi$
$182$	−9.84440e6	−	1.70510e7i	−1.63296	−	2.82837i
$183$	3.99192e6	+	1.48980e7i	0.651371	+	2.43095i
$184$		−	1.36634e6i		−	0.219333i
$185$	−2.38635e6	−	1.95213e6i	−0.376893	−	0.308315i
$186$	5.23166e6			0.813019
$187$	5.07666e6	−	1.36029e6i	0.776343	−	0.208020i
$188$	1.13089e7	−	6.52920e6i	1.70195	−	0.982622i
$189$	2.34882e7	−	1.35609e7i	3.47907	−	2.00864i
$190$	−3.90994e6	−	1.04767e6i	−0.570046	−	0.152743i
$191$	4.67342e6	−	4.67342e6i	0.670709	−	0.670709i	−0.287170	−	0.957880i	$-0.592715\pi$
$191$	4.67342e6	−	4.67342e6i	0.670709	−	0.670709i	0.957880	+	0.287170i	$0.0927146\pi$
$192$	171601.	+	297222.i	0.0242447	+	0.0419931i
$193$	3.49206e6	−	3.49206e6i	0.485746	−	0.485746i	−0.421215	−	0.906961i	$-0.638396\pi$
$193$	3.49206e6	−	3.49206e6i	0.485746	−	0.485746i	0.906961	+	0.421215i	$0.138396\pi$
$194$	1.34465e6	−	2.32901e6i	0.184164	−	0.318982i
$195$	−9.22416e6			−1.24401
$196$			1.35665e7i			1.80177i
$197$	−4.76638e6	+	8.25561e6i	−0.623433	+	1.07982i	0.365409	+	0.930847i	$0.380929\pi$
$197$	−4.76638e6	+	8.25561e6i	−0.623433	+	1.07982i	−0.988842	+	0.148970i	$0.952404\pi$
$198$	−3.37868e7	−	9.05314e6i	−4.35263	−	1.16628i
$199$	−2.44769e6	−	2.44769e6i	−0.310596	−	0.310596i	0.534544	−	0.845141i	$-0.320483\pi$
$199$	−2.44769e6	−	2.44769e6i	−0.310596	−	0.310596i	−0.845141	+	0.534544i	$0.820483\pi$
$200$	1.33090e7	−	3.56614e6i	1.66363	−	0.445767i
$201$	−7.32489e6	+	1.26871e7i	−0.902014	+	1.56233i
$202$	2.64152e6	+	9.85827e6i	0.320479	+	1.19604i
$203$	649348.	−	2.42340e6i	0.0776228	−	0.289692i
$204$	2.90262e7	+	7.77753e6i	3.41900	+	0.916118i
$205$	3.32346e6	−	890518.i	0.385770	−	0.103367i
$206$	−2.08540e7	−	1.20400e7i	−2.38554	−	1.37729i
$207$	575873.	+	2.14919e6i	0.0649256	+	0.242306i
$208$	−1.56261e7	+	1.56261e7i	−1.73644	+	1.73644i
$209$	1.53686e6	−	5.73562e6i	0.168343	−	0.628263i
$210$	1.78832e7	+	1.03249e7i	1.93102	+	1.11487i
$211$	1.07355e7			1.14282			0.571409	−	0.820666i	$-0.306397\pi$
$211$	1.07355e7			1.14282			0.571409	+	0.820666i	$0.306397\pi$
$212$			3.32379e7i			3.48839i
$213$	−2.91409e6	−	1.68245e6i	−0.301553	−	0.174102i
$214$	−1.93917e7	−	1.93917e7i	−1.97867	−	1.97867i
$215$	3.46675e6	−	2.00153e6i	0.348825	−	0.201394i
$216$	−4.81702e7	−	4.81702e7i	−4.77988	−	4.77988i
$217$	845258.	−	3.15455e6i	0.0827199	−	0.308715i
$218$	7.69558e6	+	1.33291e7i	0.742800	+	1.28657i
$219$	8.94089e6	+	1.54861e7i	0.851232	+	1.47438i
$220$	−2.92458e6	−	1.09147e7i	−0.274660	−	1.02504i
$221$			1.21004e7i			1.12104i
$222$	3.49276e7	−	1.32087e7i	3.19234	−	1.20726i
$223$	1.95222e7			1.76041			0.880206	−	0.474593i	$-0.157405\pi$
$223$	1.95222e7			1.76041			0.880206	+	0.474593i	$0.157405\pi$
$224$	1.49015e7	−	3.99284e6i	1.32582	−	0.355253i
$225$	−1.94315e7	+	1.12188e7i	−1.70592	+	0.984913i
$226$	−2.98943e7	+	1.72595e7i	−2.58978	+	1.49521i
$227$	−9.36262e6	−	2.50871e6i	−0.800423	−	0.214473i	−0.164654	−	0.986351i	$-0.552651\pi$
$227$	−9.36262e6	−	2.50871e6i	−0.800423	−	0.214473i	−0.635770	+	0.771879i	$0.719317\pi$
$228$	2.40067e7	−	2.40067e7i	2.02548	−	2.02548i
$229$	4.82249e6	+	8.35280e6i	0.401573	+	0.695546i	0.993916	−	0.110141i	$-0.0351301\pi$
$229$	4.82249e6	+	8.35280e6i	0.401573	+	0.695546i	−0.592343	+	0.805686i	$0.701797\pi$
$230$	−733950.	+	733950.i	−0.0603230	+	0.0603230i
$231$	−1.51459e7	+	2.62334e7i	−1.22873	+	2.12823i
$232$	−6.30168e6			−0.504652
$233$			2.30416e7i			1.82157i	0.412883	+	0.910784i	$0.364522\pi$
$233$			2.30416e7i			1.82157i	−0.412883	+	0.910784i	$0.635478\pi$
$234$	4.02659e7	−	6.97426e7i	3.14261	−	5.44315i
$235$	−5.32699e6	−	1.42736e6i	−0.410467	−	0.109984i
$236$	4.05541e6	+	4.05541e6i	0.308531	+	0.308531i
$237$	−2.30569e6	+	617809.i	−0.173204	+	0.0464098i
$238$	1.35443e7	−	2.34594e7i	1.00467	−	1.74015i
$239$	1.70821e6	+	6.37511e6i	0.125126	+	0.466975i	0.999844	−	0.0176560i	$-0.00562038\pi$
$239$	1.70821e6	+	6.37511e6i	0.125126	+	0.466975i	−0.874718	+	0.484631i	$0.838954\pi$
$240$	5.99868e6	−	2.23874e7i	0.433933	−	1.61946i
$241$	−1.97821e7	−	5.30060e6i	−1.41326	−	0.378681i	−0.530171	−	0.847891i	$-0.677872\pi$
$241$	−1.97821e7	−	5.30060e6i	−1.41326	−	0.378681i	−0.883087	+	0.469209i	$0.844539\pi$
$242$	−1.56548e6	+	419469.i	−0.110459	+	0.0295974i
$243$	3.53455e7	+	2.04068e7i	2.46329	+	1.42218i
$244$	−1.12586e7	−	4.20178e7i	−0.775027	−	2.89244i
$245$	4.05137e6	−	4.05137e6i	0.275488	−	0.275488i
$246$	−1.07857e7	+	4.02530e7i	−0.724511	+	2.70391i
$247$	1.18395e7	+	6.83551e6i	0.785671	+	0.453607i
$248$	−8.20291e6			−0.537790
$249$		−	9.61559e6i		−	0.622842i
$250$	−2.09468e7	−	1.20937e7i	−1.34060	−	0.773995i
$251$	−6.44603e6	−	6.44603e6i	−0.407635	−	0.407635i	0.473278	−	0.880913i	$-0.343071\pi$
$251$	−6.44603e6	−	6.44603e6i	−0.407635	−	0.407635i	−0.880913	+	0.473278i	$0.843071\pi$
$252$	−1.08118e8	+	6.24220e7i	−6.75611	+	3.90064i
$253$	−1.07665e6	−	1.07665e6i	−0.0664837	−	0.0664837i
$254$	−4.12444e6	+	1.53926e7i	−0.251689	+	0.939316i
$255$	−6.34547e6	−	1.09907e7i	−0.382687	−	0.662833i
$256$	1.49918e7	+	2.59665e7i	0.893581	+	1.54773i
$257$	−5.31506e6	−	1.98361e7i	−0.313119	−	1.16858i	−0.925728	−	0.378189i	$-0.876547\pi$
$257$	−5.31506e6	−	1.98361e7i	−0.313119	−	1.16858i	0.612609	−	0.790386i	$-0.290120\pi$
$258$			4.84842e7i			2.82320i
$259$	−2.32140e6	−	2.31944e7i	−0.133613	−	1.33501i
$260$	2.60154e7			1.48017
$261$	9.91227e6	−	2.65598e6i	0.557509	−	0.149384i
$262$	1.37129e7	−	7.91715e6i	0.762475	−	0.440215i
$263$	−2860.62	+	1651.58i	−0.000157251	+	9.07889e-5i	−0.500079	−	0.865980i	$-0.666696\pi$
$263$	−2860.62	+	1651.58i	−0.000157251	+	9.07889e-5i	0.499921	+	0.866071i	$0.333362\pi$
$264$	7.34924e7	+	1.96922e7i	3.99421	+	1.07025i
$265$	9.92581e6	−	9.92581e6i	0.533370	−	0.533370i
$266$	−1.53023e7	−	2.65044e7i	−0.813042	−	1.40823i
$267$	3.51673e7	−	3.51673e7i	1.84759	−	1.84759i
$268$	2.06588e7	−	3.57821e7i	1.07325	−	1.85893i
$269$	2.31079e7			1.18714			0.593571	−	0.804782i	$-0.297718\pi$
$269$	2.31079e7			1.18714			0.593571	+	0.804782i	$0.297718\pi$
$270$			5.17508e7i			2.62921i
$271$	−1.69947e7	+	2.94356e7i	−0.853895	+	1.47899i	0.0237717	+	0.999717i	$0.492433\pi$
$271$	−1.69947e7	+	2.94356e7i	−0.853895	+	1.47899i	−0.877667	+	0.479272i	$0.840901\pi$
$272$	−2.93681e7	−	7.86915e6i	−1.45938	−	0.391040i
$273$	−4.93143e7	−	4.93143e7i	−2.42374	−	2.42374i
$274$	−4.36558e6	+	1.16975e6i	−0.212222	+	0.0568647i
$275$	7.67725e6	−	1.32974e7i	0.369154	−	0.639394i
$276$	−2.25319e6	−	8.40904e6i	−0.107170	−	0.399962i
$277$	−4.58755e6	+	1.71210e7i	−0.215845	+	0.805544i	0.770022	+	0.638017i	$0.220245\pi$
$277$	−4.58755e6	+	1.71210e7i	−0.215845	+	0.805544i	−0.985867	+	0.167528i	$0.946422\pi$
$278$	−4.83711e7	−	1.29610e7i	−2.25140	−	0.603260i
$279$	1.29028e7	−	3.45730e6i	0.594118	−	0.159193i
$280$	−2.80397e7	−	1.61887e7i	−1.27732	−	0.737460i
$281$	7.86771e6	+	2.93627e7i	0.354592	+	1.32336i	0.880997	+	0.473122i	$0.156873\pi$
$281$	7.86771e6	+	2.93627e7i	0.354592	+	1.32336i	−0.526405	+	0.850234i	$0.676460\pi$
$282$	4.72314e7	−	4.72314e7i	2.10612	−	2.10612i
$283$	4.88489e6	−	1.82306e7i	0.215524	−	0.804346i	−0.770458	−	0.637491i	$-0.779972\pi$
$283$	4.88489e6	−	1.82306e7i	0.215524	−	0.804346i	0.985982	−	0.166855i	$-0.0533610\pi$
$284$	8.21877e6	+	4.74511e6i	0.358799	+	0.207153i
$285$	−1.43382e7			−0.619386
$286$			5.51097e7i			2.35575i
$287$	2.25288e7	+	1.30070e7i	0.952999	+	0.550214i
$288$	4.46189e7	+	4.46189e7i	1.86785	+	1.86785i
$289$	6.48604e6	−	3.74472e6i	0.268711	−	0.155141i
$290$	3.38505e6	+	3.38505e6i	0.138794	+	0.138794i
$291$	2.46550e6	−	9.20139e6i	0.100052	−	0.373400i
$292$	−2.52165e7	−	4.36763e7i	−1.01283	−	1.75427i
$293$	−1.28007e7	−	2.21715e7i	−0.508899	−	0.881440i	−0.999947	−	0.0103068i	$-0.996719\pi$
$293$	−1.28007e7	−	2.21715e7i	−0.508899	−	0.881440i	0.491047	−	0.871133i	$-0.336614\pi$
$294$	1.79606e7	+	6.70298e7i	0.706771	+	2.63770i
$295$		−	2.42213e6i		−	0.0943478i
$296$	−5.47642e7	+	2.07105e7i	−2.11165	+	0.798573i
$297$	−7.59149e7			−2.89773
$298$	−2.20880e7	+	5.91845e6i	−0.834654	+	0.223645i
$299$	3.03589e6	−	1.75277e6i	0.113572	−	0.0655710i
$300$	7.60287e7	−	4.38952e7i	2.81588	−	1.62575i
$301$	2.92346e7	+	7.83339e6i	1.07201	+	0.287244i
$302$	1.80288e7	−	1.80288e7i	0.654554	−	0.654554i
$303$	1.80757e7	+	3.13081e7i	0.649783	+	1.12546i
$304$	−2.42895e7	+	2.42895e7i	−0.864566	+	0.864566i
$305$	−9.18561e6	+	1.59099e7i	−0.323749	+	0.560750i
$306$	1.10799e8			3.86696
$307$			2.84027e7i			0.981622i	0.871266	+	0.490811i	$0.163299\pi$
$307$			2.84027e7i			0.981622i	−0.871266	+	0.490811i	$0.836701\pi$
$308$	4.27168e7	−	7.39876e7i	1.46200	−	2.53225i
$309$	−8.23893e7	−	2.20762e7i	−2.79251	−	0.748252i
$310$	4.40633e6	+	4.40633e6i	0.147908	+	0.147908i
$311$	−3.18582e7	+	8.53638e6i	−1.05911	+	0.283787i	−0.746010	−	0.665934i	$-0.768033\pi$
$311$	−3.18582e7	+	8.53638e6i	−1.05911	+	0.283787i	−0.313097	+	0.949721i	$0.601366\pi$
$312$	−8.75857e7	+	1.51703e8i	−2.88383	+	4.99494i
$313$	−4.75403e6	−	1.77423e7i	−0.155035	−	0.578598i	−0.999102	−	0.0423609i	$-0.986512\pi$
$313$	−4.75403e6	−	1.77423e7i	−0.155035	−	0.578598i	0.844068	−	0.536237i	$-0.180155\pi$
$314$	−6.81933e6	+	2.54501e7i	−0.220269	+	0.822054i
$315$	5.09284e7	+	1.36462e7i	1.62940	+	0.436597i
$316$	6.50289e6	−	1.74244e6i	0.206084	−	0.0552201i
$317$	3.36012e7	+	1.93997e7i	1.05482	+	0.608999i	0.923994	−	0.382407i	$-0.124905\pi$
$317$	3.36012e7	+	1.93997e7i	1.05482	+	0.608999i	0.130823	+	0.991406i	$0.458238\pi$
$318$	4.40033e7	+	1.64222e8i	1.36837	+	5.10683i
$319$	−4.96564e6	+	4.96564e6i	−0.152969	+	0.152969i
$320$	−105803.	+	394863.i	−0.00322886	+	0.0120503i
$321$	−8.41259e7	−	4.85701e7i	−2.54340	−	1.46843i
$322$	−7.84771e6			−0.235058
$323$			1.88091e7i			0.558162i
$324$	−2.04626e8	−	1.18141e8i	−6.01626	−	3.47349i
$325$	2.49968e7	+	2.49968e7i	0.728174	+	0.728174i
$326$	2.69177e7	−	1.55410e7i	0.776937	−	0.448565i
$327$	3.85501e7	+	3.85501e7i	1.10251	+	1.10251i
$328$	1.69114e7	−	6.31141e7i	0.479245	−	1.78856i
$329$	−2.08483e7	−	3.61102e7i	−0.585439	−	1.01401i
$330$	−2.88997e7	−	5.00557e7i	−0.804176	−	1.39287i
$331$	4.88172e6	+	1.82188e7i	0.134614	+	0.502385i	0.999999	+	0.00127830i	$0.000406894\pi$
$331$	4.88172e6	+	1.82188e7i	0.134614	+	0.502385i	−0.865386	+	0.501107i	$0.832926\pi$
$332$			2.71194e7i			0.741082i
$333$	7.74129e7	−	5.56583e7i	2.09643	−	1.50729i
$334$	6.96971e6			0.187058
$335$	−1.68550e7	+	4.51627e6i	−0.448325	+	0.120128i
$336$	1.51758e8	−	8.76176e7i	4.00068	−	2.30979i
$337$	4.80690e7	−	2.77527e7i	1.25596	−	0.725129i	0.283673	−	0.958921i	$-0.408447\pi$
$337$	4.80690e7	−	2.77527e7i	1.25596	−	0.725129i	0.972287	+	0.233792i	$0.0751136\pi$
$338$	−5.52953e7	−	1.48163e7i	−1.43198	−	0.383699i
$339$	−8.64594e7	+	8.64594e7i	−2.21928	+	2.21928i
$340$	1.78965e7	+	3.09976e7i	0.455335	+	0.788664i
$341$	−6.46379e6	+	6.46379e6i	−0.163014	+	0.163014i
$342$	6.25902e7	−	1.08409e8i	1.56469	−	2.71012i
$343$	−1.08227e7			−0.268196
$344$		−	7.60201e7i		−	1.86747i
$345$	−1.83832e6	+	3.18406e6i	−0.0447675	+	0.0775397i
$346$	6.32648e7	+	1.69517e7i	1.52733	+	0.409248i
$347$	−5.08667e7	−	5.08667e7i	−1.21743	−	1.21743i	−0.968528	−	0.248905i	$-0.919929\pi$
$347$	−5.08667e7	−	5.08667e7i	−1.21743	−	1.21743i	−0.248905	−	0.968528i	$-0.580071\pi$
$348$	−3.87833e7	+	1.03920e7i	−0.920253	+	0.246581i
$349$	1.54494e7	−	2.67592e7i	0.363443	−	0.629502i	−0.625082	−	0.780559i	$-0.714934\pi$
$349$	1.54494e7	−	2.67592e7i	0.363443	−	0.629502i	0.988525	+	0.151057i	$0.0482678\pi$
$350$	−2.04825e7	−	7.64418e7i	−0.477726	−	1.78290i
$351$	4.52364e7	−	1.68824e8i	1.04608	−	3.90404i
$352$	−4.17098e7	−	1.11761e7i	−0.956334	−	0.256249i
$353$	1.25527e7	−	3.36348e6i	0.285373	−	0.0764654i	−0.113293	−	0.993562i	$-0.536140\pi$
$353$	1.25527e7	−	3.36348e6i	0.285373	−	0.0764654i	0.398666	+	0.917096i	$0.369473\pi$
$354$	2.54060e7	+	1.46682e7i	0.572699	+	0.330648i
$355$	−1.03734e6	−	3.87140e6i	−0.0231865	−	0.0865332i
$356$	−9.91845e7	+	9.91845e7i	−2.19834	+	2.19834i
$357$	2.48343e7	−	9.26827e7i	0.545817	−	2.03701i
$358$	1.15927e8	+	6.69304e7i	2.52659	+	1.45873i
$359$	−3.90353e6			−0.0843672			−0.0421836	−	0.999110i	$-0.513431\pi$
$359$	−3.90353e6			−0.0843672			−0.0421836	+	0.999110i	$0.513431\pi$
$360$		−	1.32431e8i		−	2.83846i
$361$	−2.23394e7	−	1.28977e7i	−0.474843	−	0.274151i
$362$	2.39374e7	+	2.39374e7i	0.504605	+	0.504605i
$363$	−4.97168e6	+	2.87040e6i	−0.103940	+	0.0600099i
$364$	1.39084e8	+	1.39084e8i	2.88386	+	2.88386i
$365$	−5.51263e6	+	2.05734e7i	−0.113365	+	0.423085i
$366$	−1.11254e8	−	1.92698e8i	−2.26920	−	3.93037i
$367$	2.80594e7	+	4.86003e7i	0.567649	+	0.983197i	0.996798	+	0.0799629i	$0.0254802\pi$
$367$	2.80594e7	+	4.86003e7i	0.567649	+	0.983197i	−0.429149	+	0.903234i	$0.641186\pi$
$368$	2.27974e6	+	8.50809e6i	0.0457448	+	0.170722i
$369$			1.06403e8i			2.11776i
$370$	4.05425e7	+	1.82925e7i	0.800396	+	0.361134i
$371$	1.06131e8			2.07836
$372$	−5.04844e7	+	1.35272e7i	−0.980681	+	0.262773i
$373$	−3.11200e6	+	1.79672e6i	−0.0599671	+	0.0346220i	−0.529684	−	0.848195i	$-0.677689\pi$
$373$	−3.11200e6	+	1.79672e6i	−0.0599671	+	0.0346220i	0.469717	+	0.882817i	$0.344356\pi$
$374$	−6.56637e7	+	3.79110e7i	−1.25519	+	0.724686i
$375$	−8.27562e7	−	2.21745e7i	−1.56930	−	0.420494i
$376$	−7.40559e7	+	7.40559e7i	−1.39314	+	1.39314i
$377$	−8.08396e6	−	1.40018e7i	−0.150869	−	0.261313i
$378$	−2.76671e8	+	2.76671e8i	−5.12257	+	5.12257i
$379$	−3.25006e7	+	5.62927e7i	−0.596999	+	1.03403i	0.396262	+	0.918137i	$0.370307\pi$
$379$	−3.25006e7	+	5.62927e7i	−0.596999	+	1.03403i	−0.993261	+	0.115895i	$0.963026\pi$
$380$	4.04390e7			0.736969
$381$			5.64467e7i			1.02062i
$382$	−4.76738e7	+	8.25734e7i	−0.855243	+	1.48132i
$383$	−7.20213e6	−	1.92981e6i	−0.128193	−	0.0343492i	0.194152	−	0.980971i	$-0.437804\pi$
$383$	−7.20213e6	−	1.92981e6i	−0.128193	−	0.0343492i	−0.322345	+	0.946622i	$0.604471\pi$
$384$	7.40230e7	+	7.40230e7i	1.30729	+	1.30729i
$385$	−3.48514e7	+	9.33840e6i	−0.610714	+	0.163640i
$386$	−3.56227e7	+	6.17003e7i	−0.619390	+	1.07282i
$387$	3.20404e7	+	1.19576e8i	0.552797	+	2.06306i
$388$	−6.95361e6	+	2.59512e7i	−0.119046	+	0.444286i
$389$	−1.95611e7	−	5.24138e6i	−0.332310	−	0.0890423i	0.0888059	−	0.996049i	$-0.471695\pi$
$389$	−1.95611e7	−	5.24138e6i	−0.332310	−	0.0890423i	−0.421116	+	0.907007i	$0.638362\pi$
$390$	1.28538e8	−	3.44416e7i	2.16689	−	0.580617i
$391$	4.17689e6	+	2.41153e6i	0.0698752	+	0.0403424i
$392$	−2.81611e7	−	1.05099e8i	−0.467510	−	1.74477i
$393$	3.96600e7	−	3.96600e7i	0.653394	−	0.653394i
$394$	3.55938e7	−	1.32838e8i	0.581951	−	2.17187i
$395$	−2.46230e6	−	1.42161e6i	−0.0399530	−	0.0230669i
$396$	3.49443e8			5.62718
$397$		−	6.06420e7i		−	0.969174i	−0.874743	−	0.484587i	$-0.838970\pi$
$397$		−	6.06420e7i		−	0.969174i	0.874743	−	0.484587i	$-0.161030\pi$
$398$	4.32476e7	+	2.49690e7i	0.685981	+	0.396052i
$399$	−7.66553e7	−	7.66553e7i	−1.20677	−	1.20677i
$400$	−7.69243e7	+	4.44123e7i	−1.20194	+	0.693942i
$401$	4.25191e7	+	4.25191e7i	0.659403	+	0.659403i	0.955239	−	0.295836i	$-0.0955982\pi$
$401$	4.25191e7	+	4.25191e7i	0.659403	+	0.659403i	−0.295836	+	0.955239i	$0.595598\pi$
$402$	5.47000e7	−	2.04143e8i	0.841995	−	3.14237i
$403$	−1.05229e7	−	1.82262e7i	−0.160776	−	0.278472i
$404$	−5.09801e7	−	8.83001e7i	−0.773137	−	1.33911i
$405$	2.58271e7	+	9.63880e7i	0.388786	+	1.45097i
$406$			3.61944e7i			0.540833i
$407$	−2.68339e7	+	5.94730e7i	−0.398016	+	0.882139i
$408$	−2.41007e8			−3.54854
$409$	1.14637e8	−	3.07170e7i	1.67555	−	0.448962i	0.708950	−	0.705259i	$-0.249169\pi$
$409$	1.14637e8	−	3.07170e7i	1.67555	−	0.448962i	0.966598	+	0.256298i	$0.0825027\pi$
$410$	−4.29870e7	+	2.48185e7i	−0.623714	+	0.360101i
$411$	−1.38643e7	+	8.00456e6i	−0.199698	+	0.115295i
$412$	2.32367e8	+	6.22627e7i	3.32264	+	0.890299i
$413$	1.29492e7	−	1.29492e7i	0.183821	−	0.183821i
$414$	−1.60495e7	−	2.77985e7i	−0.226183	−	0.391760i
$415$	8.09867e6	−	8.09867e6i	0.113310	−	0.113310i
$416$	4.97082e7	−	8.60972e7i	0.690475	−	1.19594i
$417$	−1.77383e8			−2.44627
$418$			8.56637e7i			1.17292i
$419$	5.63087e7	−	9.75295e7i	0.765479	−	1.32585i	−0.174514	−	0.984655i	$-0.555835\pi$
$419$	5.63087e7	−	9.75295e7i	0.765479	−	1.32585i	0.939993	−	0.341194i	$-0.110831\pi$
$420$	−1.99265e8	−	5.33929e7i	−2.68957	−	0.720669i
$421$	7.17093e7	+	7.17093e7i	0.961013	+	0.961013i	0.999268	−	0.0382552i	$-0.0121800\pi$
$421$	7.17093e7	+	7.17093e7i	0.961013	+	0.961013i	−0.0382552	+	0.999268i	$0.512180\pi$
$422$	−1.49599e8	+	4.00849e7i	−1.99063	+	0.533388i
$423$	8.52742e7	−	1.47699e8i	1.12667	−	1.95145i
$424$	−6.89943e7	−	2.57490e8i	−0.905140	−	3.37803i
$425$	−1.25882e7	+	4.69797e7i	−0.163982	+	0.611989i
$426$	4.68895e7	+	1.25640e7i	0.606522	+	0.162517i
$427$	−1.34166e8	+	3.59497e7i	−1.72329	+	0.461755i
$428$	2.37265e8	+	1.36985e8i	3.02624	+	1.74720i
$429$	5.05235e7	+	1.88556e8i	0.639914	+	2.38819i
$430$	−4.08355e7	+	4.08355e7i	−0.513609	+	0.513609i
$431$	1.33368e7	−	4.97738e7i	0.166579	−	0.621683i	−0.831254	−	0.555893i	$-0.812377\pi$
$431$	1.33368e7	−	4.97738e7i	0.166579	−	0.621683i	0.997833	−	0.0657902i	$-0.0209568\pi$
$432$	3.80325e8	+	2.19581e8i	4.71741	+	2.72360i
$433$	−9.84027e7			−1.21211			−0.606057	−	0.795421i	$-0.707250\pi$
$433$	−9.84027e7			−1.21211			−0.606057	+	0.795421i	$0.707250\pi$
$434$			4.71144e7i			0.576347i
$435$	1.46852e7	+	8.47850e6i	0.178407	+	0.103003i
$436$	−1.08725e8	−	1.08725e8i	−1.31181	−	1.31181i
$437$	4.71906e6	−	2.72455e6i	0.0565472	−	0.0326475i
$438$	−1.82413e8	−	1.82413e8i	−2.17087	−	2.17087i
$439$	1.90040e7	−	7.09239e7i	0.224622	−	0.838299i	−0.757934	−	0.652331i	$-0.773791\pi$
$439$	1.90040e7	−	7.09239e7i	0.224622	−	0.838299i	0.982556	−	0.185968i	$-0.0595421\pi$
$440$	4.53128e7	+	7.84842e7i	0.531941	+	0.921348i
$441$	8.85924e7	+	1.53446e8i	1.03295	+	1.78913i
$442$	−4.51809e7	−	1.68618e8i	−0.523225	−	1.95270i
$443$		−	2.26792e7i		−	0.260866i	−0.991457	−	0.130433i	$-0.958363\pi$
$443$		−	2.26792e7i		−	0.260866i	0.991457	−	0.130433i	$-0.0416367\pi$
$444$	−3.02890e8	+	2.17772e8i	−3.46048	+	2.48801i
$445$	5.92389e7			0.672244
$446$	−2.72040e8	+	7.28929e7i	−3.06639	+	0.821638i
$447$	−7.01474e7	+	4.04996e7i	−0.785396	+	0.453449i
$448$	−2.67667e6	+	1.54538e6i	−0.0297688	+	0.0171870i
$449$	2.31988e7	+	6.21609e6i	0.256287	+	0.0686718i	0.384675	−	0.923052i	$-0.374314\pi$
$449$	2.31988e7	+	6.21609e6i	0.256287	+	0.0686718i	−0.128388	+	0.991724i	$0.540980\pi$
$450$	2.28887e8	−	2.28887e8i	2.51179	−	2.51179i
$451$	−3.64071e7	−	6.30590e7i	−0.396878	−	0.687412i
$452$	2.43846e8	−	2.43846e8i	2.64059	−	2.64059i
$453$	4.51565e7	−	7.82134e7i	0.485764	−	0.841369i
$454$	1.39834e8			1.49433
$455$		−	8.30693e7i		−	0.881874i
$456$	−1.36145e8	+	2.35810e8i	−1.43584	+	2.48696i
$457$	2.18053e7	+	5.84271e6i	0.228462	+	0.0612161i	0.371234	−	0.928539i	$-0.378935\pi$
$457$	2.18053e7	+	5.84271e6i	0.228462	+	0.0612161i	−0.142772	+	0.989756i	$0.545602\pi$
$458$	−9.83890e7	−	9.83890e7i	−1.02412	−	1.02412i
$459$	2.32275e8	−	6.22378e7i	2.40195	−	0.643601i
$460$	5.18471e6	−	8.98019e6i	0.0532662	−	0.0922597i
$461$	2.75603e7	+	1.02857e8i	0.281308	+	1.04985i	0.951495	+	0.307663i	$0.0995469\pi$
$461$	2.75603e7	+	1.02857e8i	0.281308	+	1.04985i	−0.670188	+	0.742192i	$0.733786\pi$
$462$	1.13105e8	−	4.22112e8i	1.14698	−	4.28057i
$463$	−1.84493e8	−	4.94347e7i	−1.85882	−	0.498068i	−0.858914	−	0.512119i	$-0.828861\pi$
$463$	−1.84493e8	−	4.94347e7i	−1.85882	−	0.498068i	−0.999901	+	0.0140511i	$0.995527\pi$
$464$	3.92402e7	−	1.05144e7i	0.392805	−	0.105252i
$465$	1.91158e7	+	1.10365e7i	0.190122	+	0.109767i
$466$	−8.60339e7	−	3.21083e8i	−0.850182	−	3.17292i
$467$	6.07446e7	−	6.07446e7i	0.596426	−	0.596426i	−0.342933	−	0.939360i	$-0.611421\pi$
$467$	6.07446e7	−	6.07446e7i	0.596426	−	0.596426i	0.939360	+	0.342933i	$0.111421\pi$
$468$	−2.08227e8	+	7.77114e8i	−2.03142	+	7.58136i
$469$	−1.14255e8	−	6.59652e7i	−1.10753	−	0.639435i
$470$	7.95607e7			0.766311
$471$			9.33286e7i			0.893207i
$472$	−3.98350e7	−	2.29987e7i	−0.378825	−	0.218715i
$473$	−5.99029e7	−	5.99029e7i	−0.566062	−	0.566062i
$474$	2.98228e7	−	1.72182e7i	0.280036	−	0.161679i
$475$	3.88556e7	+	3.88556e7i	0.362554	+	0.362554i
$476$	−7.00415e7	+	2.61399e8i	−0.649434	+	2.42372i
$477$	2.17050e8	+	3.75942e8i	1.99989	+	3.46391i
$478$	−4.76074e7	−	8.24584e7i	−0.435904	−	0.755007i
$479$	−1.40488e7	−	5.24309e7i	−0.127830	−	0.477068i	0.872095	−	0.489337i	$-0.162761\pi$
$479$	−1.40488e7	−	5.24309e7i	−0.127830	−	0.477068i	−0.999925	+	0.0122688i	$0.996095\pi$
$480$			1.04268e8i			0.942821i
$481$	−1.16270e8	−	9.51139e7i	−1.04480	−	0.854690i
$482$	2.95453e8			2.63844
$483$	−2.68507e7	+	7.19462e6i	−0.238295	+	0.0638509i
$484$	1.40219e7	−	8.09556e6i	0.123672	−	0.0714021i
$485$	9.82636e6	−	5.67325e6i	0.0861326	−	0.0497287i
$486$	−5.68732e8	−	1.52391e8i	−4.95449	−	1.32755i
$487$	−1.20614e8	+	1.20614e8i	−1.04427	+	1.04427i	−0.0452916	+	0.998974i	$0.514422\pi$
$487$	−1.20614e8	+	1.20614e8i	−1.04427	+	1.04427i	−0.998974	+	0.0452916i	$0.985578\pi$
$488$	1.74439e8	+	3.02138e8i	1.50101	+	2.59983i
$489$	7.78506e7	−	7.78506e7i	0.665787	−	0.665787i
$490$	−4.13282e7	+	7.15826e7i	−0.351284	+	0.608442i
$491$	−2.84042e7			−0.239959			−0.119980	−	0.992776i	$-0.538283\pi$
$491$	−2.84042e7			−0.239959			−0.119980	+	0.992776i	$0.538283\pi$
$492$		−	4.16320e8i		−	3.49568i
$493$	1.11222e7	−	1.92642e7i	0.0928219	−	0.160772i
$494$	−1.90504e8	−	5.10455e7i	−1.58024	−	0.423425i
$495$	−1.04354e8	−	1.04354e8i	−0.860387	−	0.860387i
$496$	5.10791e7	−	1.36866e7i	0.418599	−	0.112163i
$497$	1.51515e7	−	2.62432e7i	0.123420	−	0.213770i
$498$	3.59031e7	+	1.33992e8i	0.290700	+	1.08491i
$499$	−3.17055e7	+	1.18326e8i	−0.255172	+	0.952314i	0.712823	+	0.701344i	$0.247416\pi$
$499$	−3.17055e7	+	1.18326e8i	−0.255172	+	0.952314i	−0.967995	+	0.250970i	$0.919250\pi$
$500$	2.33402e8	+	6.25400e7i	1.86722	+	0.500320i
$501$	2.38467e7	−	6.38970e6i	0.189633	−	0.0508121i
$502$	1.13893e8	+	6.57563e7i	0.900300	+	0.519788i
$503$	3.82737e7	+	1.42839e8i	0.300744	+	1.12239i	0.936548	+	0.350540i	$0.114002\pi$
$503$	3.82737e7	+	1.42839e8i	0.300744	+	1.12239i	−0.635804	+	0.771850i	$0.719331\pi$
$504$	7.08006e8	−	7.08006e8i	5.53026	−	5.53026i
$505$	−1.11449e7	+	4.15932e7i	−0.0865367	+	0.322960i
$506$	1.90231e7	+	1.09830e7i	0.146835	+	0.0847754i
$507$	−2.02775e8			−1.55593
$508$		−	1.59200e8i		−	1.21437i
$509$	−1.81671e7	−	1.04888e7i	−0.137763	−	0.0795374i	0.429535	−	0.903050i	$-0.358678\pi$
$509$	−1.81671e7	−	1.04888e7i	−0.137763	−	0.0795374i	−0.567297	+	0.823513i	$0.692011\pi$
$510$	1.29461e8	+	1.29461e8i	0.975952	+	0.975952i
$511$	−1.39462e8	+	8.05182e7i	−1.04518	+	0.603437i
$512$	−2.13156e8	−	2.13156e8i	−1.58814	−	1.58814i
$513$	7.03164e7	−	2.62424e8i	0.520840	−	1.94380i
$514$	1.48130e8	+	2.56568e8i	1.09082	+	1.88936i
$515$	−5.07983e7	−	8.79853e7i	−0.371901	−	0.644152i
$516$	−1.25363e8	−	4.67862e8i	−0.912475	−	3.40540i
$517$			1.16710e8i			0.844572i
$518$	1.18953e8	+	3.14544e8i	0.855827	+	2.26304i
$519$	2.32000e8			1.65953
$520$	−2.01539e8	+	5.40022e7i	−1.43334	+	0.384062i
$521$	9.51650e7	−	5.49435e7i	0.672921	−	0.388511i	−0.124261	−	0.992250i	$-0.539656\pi$
$521$	9.51650e7	−	5.49435e7i	0.672921	−	0.388511i	0.797183	+	0.603738i	$0.206323\pi$
$522$	−1.28209e8	+	7.40218e7i	−0.901381	+	0.520413i
$523$	−2.36652e6	−	634106.i	−0.0165426	−	0.00443258i	0.250538	−	0.968107i	$-0.419392\pi$
$523$	−2.36652e6	−	634106.i	−0.0165426	−	0.00443258i	−0.267081	+	0.963674i	$0.586059\pi$
$524$	−1.11855e8	+	1.11855e8i	−0.777434	+	0.777434i
$525$	−1.40161e8	−	2.42765e8i	−0.968609	−	1.67768i
$526$	33695.8	−	33695.8i	0.000231536	−	0.000231536i
$527$	1.44778e7	−	2.50763e7i	0.0989171	−	0.171329i
$528$	−4.90490e8			−3.33218
$529$			1.46639e8i			0.990561i
$530$	−1.01254e8	+	1.75377e8i	−0.680117	+	1.17800i
$531$	7.23521e7	+	1.93867e7i	0.483245	+	0.129485i
$532$	2.16195e8	+	2.16195e8i	1.43586	+	1.43586i
$533$	1.61929e8	−	4.33887e7i	1.06941	−	0.286547i
$534$	−3.58744e8	+	6.21363e8i	−2.35592	+	4.08058i
$535$	−2.99466e7	−	1.11762e8i	−0.195563	−	0.729851i
$536$	−8.57662e7	+	3.20084e8i	−0.556957	+	2.07859i
$537$	4.58001e8	+	1.22721e8i	2.95763	+	0.792494i
$538$	−3.22006e8	+	8.62811e7i	−2.06784	+	0.554076i
$539$	−1.05007e8	−	6.06257e7i	−0.670581	−	0.387160i
$540$	−1.33809e8	−	4.99384e8i	−0.849778	−	3.17142i
$541$	6.49494e7	−	6.49494e7i	0.410189	−	0.410189i	−0.471616	−	0.881804i	$-0.656329\pi$
$541$	6.49494e7	−	6.49494e7i	0.410189	−	0.410189i	0.881804	+	0.471616i	$0.156329\pi$
$542$	1.26911e8	−	4.73638e8i	0.797078	−	2.97474i
$543$	1.03847e8	+	5.99558e7i	0.648623	+	0.374483i
$544$	1.36781e8			0.849627
$545$			6.49371e7i			0.401147i
$546$	8.71323e8	+	5.03058e8i	5.35305	+	3.09058i
$547$	−9.24519e7	−	9.24519e7i	−0.564877	−	0.564877i	0.365812	−	0.930689i	$-0.380791\pi$
$547$	−9.24519e7	−	9.24519e7i	−0.564877	−	0.564877i	−0.930689	+	0.365812i	$0.880791\pi$
$548$	3.91023e7	−	2.25757e7i	0.237608	−	0.137183i
$549$	−4.01728e8	−	4.01728e8i	−2.42781	−	2.42781i
$550$	−5.73314e7	+	2.13964e8i	−0.344591	+	1.28603i
$551$	−1.25659e7	−	2.17648e7i	−0.0751170	−	0.130106i
$552$	3.49106e7	+	6.04669e7i	0.207558	+	0.359501i
$553$	−5.56376e6	−	2.07642e7i	−0.0328998	−	0.122784i
$554$		−	2.55708e8i		−	1.50389i
$555$	1.55485e8	+	2.54188e7i	0.909515	+	0.148688i
$556$	5.00283e8			2.91066
$557$	5.83779e6	−	1.56423e6i	0.0337818	−	0.00905181i	−0.241889	−	0.970304i	$-0.577767\pi$
$557$	5.83779e6	−	1.56423e6i	0.0337818	−	0.00905181i	0.275670	+	0.961252i	$0.411100\pi$
$558$	−1.66891e8	+	9.63544e7i	−0.960571	+	0.554586i
$559$	1.68911e8	−	9.75207e7i	0.966990	−	0.558292i
$560$	2.01612e8	+	5.40219e7i	1.14803	+	0.307614i
$561$	−1.89910e8	+	1.89910e8i	−1.07562	+	1.07562i
$562$	−2.19271e8	−	3.79789e8i	−1.23530	−	2.13961i
$563$	−1.99021e7	+	1.99021e7i	−0.111525	+	0.111525i	−0.760667	−	0.649142i	$-0.775128\pi$
$563$	−1.99021e7	+	1.99021e7i	−0.111525	+	0.111525i	0.649142	+	0.760667i	$0.275128\pi$
$564$	−3.33649e8	+	5.77897e8i	−1.85974	+	3.22116i
$565$	−1.45640e8			−0.807484
$566$			2.72282e8i			1.50165i
$567$	−3.77234e8	+	6.53388e8i	−2.06948	+	3.58444i
$568$	−7.35198e7	−	1.96996e7i	−0.401198	−	0.107501i
$569$	2.71608e7	+	2.71608e7i	0.147437	+	0.147437i	0.776972	−	0.629535i	$-0.216755\pi$
$569$	2.71608e7	+	2.71608e7i	0.147437	+	0.147437i	−0.629535	+	0.776972i	$0.716755\pi$
$570$	1.99802e8	−	5.35368e7i	1.07889	−	0.289086i
$571$	1.47626e8	−	2.55696e8i	0.792966	−	1.37346i	−0.131157	−	0.991362i	$-0.541869\pi$
$571$	1.47626e8	−	2.55696e8i	0.792966	−	1.37346i	0.924123	−	0.382095i	$-0.124797\pi$
$572$	−1.42494e8	−	5.31796e8i	−0.761394	−	2.84156i
$573$	−8.74128e7	+	3.26229e8i	−0.464634	+	1.73404i
$574$	−3.62503e8	−	9.71324e7i	−1.91680	−	0.513604i
$575$	1.36103e7	−	3.64687e6i	0.0715919	−	0.0191830i
$576$	−1.09482e7	−	6.32096e6i	−0.0572896	−	0.0330762i
$577$	−2.58603e7	−	9.65119e7i	−0.134619	−	0.502404i	−0.999999	−	0.00128876i	$-0.999590\pi$
$577$	−2.58603e7	−	9.65119e7i	−0.134619	−	0.502404i	0.865380	−	0.501116i	$-0.167077\pi$
$578$	−7.64001e7	+	7.64001e7i	−0.395649	+	0.395649i
$579$	−6.53163e7	+	2.43764e8i	−0.336501	+	1.25584i
$580$	−4.14175e7	−	2.39124e7i	−0.212276	−	0.122557i
$581$	8.65944e7			0.441531
$582$			1.37426e8i			0.697109i
$583$	−2.57266e8	−	1.48532e8i	−1.29830	−	0.749576i
$584$	2.86012e8	+	2.86012e8i	1.43597	+	1.43597i
$585$	2.94252e8	−	1.69887e8i	1.46978	−	0.848577i
$586$	2.61162e8	+	2.61162e8i	1.29783	+	1.29783i
$587$	−1.97734e7	+	7.37953e7i	−0.0977612	+	0.364850i	−0.997424	−	0.0717364i	$-0.977146\pi$
$587$	−1.97734e7	+	7.37953e7i	−0.0977612	+	0.364850i	0.899662	+	0.436586i	$0.143813\pi$
$588$	−3.46631e8	−	6.00383e8i	−1.70505	−	2.95322i
$589$	−1.63571e7	−	2.83313e7i	−0.0800496	−	0.138650i
$590$	9.04387e6	+	3.37522e7i	0.0440350	+	0.164341i
$591$		−	4.87133e8i		−	2.35985i
$592$	3.06458e8	−	2.20337e8i	1.47709	−	1.06200i
$593$	1.08451e8			0.520079			0.260039	−	0.965598i	$-0.416264\pi$
$593$	1.08451e8			0.520079			0.260039	+	0.965598i	$0.416264\pi$
$594$	1.05787e9	−	2.83455e8i	5.04745	−	1.35246i
$595$	9.89779e7	−	5.71449e7i	0.469880	−	0.271286i
$596$	1.97841e8	−	1.14223e8i	0.934495	−	0.539531i
$597$	1.70861e8	+	4.57822e7i	0.803010	+	0.215166i
$598$	−3.57603e7	+	3.57603e7i	−0.167223	+	0.167223i
$599$	1.69021e8	+	2.92752e8i	0.786429	+	1.36213i	0.928142	+	0.372227i	$0.121406\pi$
$599$	1.69021e8	+	2.92752e8i	0.786429	+	1.36213i	−0.141713	+	0.989908i	$0.545261\pi$
$600$	−4.97870e8	+	4.97870e8i	−2.30495	+	2.30495i
$601$	2.32118e7	−	4.02040e7i	0.106926	−	0.185202i	−0.807597	−	0.589734i	$-0.799232\pi$
$601$	2.32118e7	−	4.02040e7i	0.106926	−	0.185202i	0.914524	+	0.404532i	$0.132566\pi$
$602$	−4.36630e8			−2.00136
$603$		−	5.39627e8i		−	2.46117i
$604$	−1.27358e8	+	2.20590e8i	−0.577981	+	1.00109i
$605$	−6.60494e6	−	1.76979e6i	−0.0298265	−	0.00799199i
$606$	−3.68783e8	−	3.68783e8i	−1.65712	−	1.65712i
$607$	−2.92931e8	+	7.84906e7i	−1.30978	+	0.350955i	−0.845141	−	0.534543i	$-0.820484\pi$
$607$	−2.92931e8	+	7.84906e7i	−1.30978	+	0.350955i	−0.464642	+	0.885499i	$0.653817\pi$
$608$	7.72675e7	−	1.33831e8i	0.343785	−	0.595452i
$609$	3.31823e7	+	1.23838e8i	0.146911	+	0.548280i
$610$	6.85953e7	−	2.56001e8i	0.302207	−	1.12785i
$611$	−2.59547e8	−	6.95455e7i	−1.13787	−	0.304892i
$612$	−1.06918e9	+	2.86486e8i	−4.66441	+	1.24983i
$613$	−5.38259e7	−	3.10764e7i	−0.233674	−	0.134911i	0.378592	−	0.925564i	$-0.376408\pi$
$613$	−5.38259e7	−	3.10764e7i	−0.233674	−	0.134911i	−0.612266	+	0.790652i	$0.709742\pi$
$614$	−1.06051e8	−	3.95789e8i	−0.458153	−	1.70985i
$615$	−1.24326e8	+	1.24326e8i	−0.534485	+	0.534485i
$616$	−1.77341e8	+	6.61845e8i	−0.758694	+	2.83149i
$617$	2.74289e8	+	1.58361e8i	1.16776	+	0.674207i	0.953151	−	0.302494i	$-0.0978191\pi$
$617$	2.74289e8	+	1.58361e8i	1.16776	+	0.674207i	0.214609	+	0.976700i	$0.431152\pi$
$618$	1.23052e9			5.21341
$619$			3.77169e7i			0.159024i	0.996834	+	0.0795122i	$0.0253363\pi$
$619$			3.77169e7i			0.159024i	−0.996834	+	0.0795122i	$0.974664\pi$
$620$	−5.39133e7	−	3.11269e7i	−0.226215	−	0.130605i
$621$	−4.92606e7	−	4.92606e7i	−0.205696	−	0.205696i
$622$	4.12067e8	−	2.37907e8i	1.71237	−	0.988636i
$623$	3.16704e8	+	3.16704e8i	1.30975	+	1.30975i
$624$	2.92274e8	−	1.09078e9i	1.20292	−	4.48936i
$625$	4.21021e7	+	7.29229e7i	0.172450	+	0.298692i
$626$	1.32494e8	+	2.29486e8i	0.540099	+	0.935478i
$627$	7.85348e7	+	2.93096e8i	0.318610	+	1.18907i
$628$		−	2.63220e8i		−	1.06277i
$629$	3.33448e7	−	2.03967e8i	0.133991	−	0.819613i
$630$	−7.60634e8			−3.04197
$631$	−7.06459e7	+	1.89295e7i	−0.281189	+	0.0753444i	−0.396657	−	0.917967i	$-0.629830\pi$
$631$	−7.06459e7	+	1.89295e7i	−0.281189	+	0.0753444i	0.115468	+	0.993311i	$0.463163\pi$
$632$	−4.67603e7	+	2.69971e7i	−0.185236	+	0.106946i
$633$	−4.75099e8	+	2.74299e8i	−1.87315	+	1.08146i
$634$	−5.40665e8	−	1.44871e8i	−2.12158	−	0.568477i
$635$	−4.75418e7	+	4.75418e7i	−0.185675	+	0.185675i
$636$	−8.49243e8	−	1.47093e9i	−3.30112	−	5.71770i
$637$	1.97395e8	−	1.97395e8i	0.763691	−	0.763691i
$638$	5.06547e7	−	8.77366e7i	0.195055	−	0.337846i
$639$	1.23946e8			0.475041
$640$			1.24691e8i			0.475657i
$641$	3.58857e7	−	6.21558e7i	0.136253	−	0.235998i	−0.789822	−	0.613336i	$-0.789827\pi$
$641$	3.58857e7	−	6.21558e7i	0.136253	−	0.235998i	0.926076	+	0.377338i	$0.123161\pi$
$642$	1.35364e9	+	3.62707e8i	5.11562	+	1.37073i
$643$	4.46789e7	+	4.46789e7i	0.168062	+	0.168062i	0.786127	−	0.618065i	$-0.212083\pi$
$643$	4.46789e7	+	4.46789e7i	0.168062	+	0.168062i	−0.618065	+	0.786127i	$0.712083\pi$
$644$	7.57286e7	−	2.02914e7i	0.283532	−	0.0759722i
$645$	−1.02280e8	+	1.77155e8i	−0.381165	+	0.660196i
$646$	−7.02302e7	−	2.62103e8i	−0.260511	−	0.972241i
$647$	−1.19033e8	+	4.44237e8i	−0.439496	+	1.64022i	0.290577	+	0.956852i	$0.406153\pi$
$647$	−1.19033e8	+	4.44237e8i	−0.439496	+	1.64022i	−0.730073	+	0.683369i	$0.760514\pi$
$648$	1.83045e9	+	4.90469e8i	6.72719	+	1.80255i
$649$	−4.95122e7	+	1.32667e7i	−0.181125	+	0.0485322i
$650$	−4.41663e8	−	2.54994e8i	−1.60824	−	0.928518i
$651$	4.31935e7	+	1.61200e8i	0.156558	+	0.584283i
$652$	−2.19567e8	+	2.19567e8i	−0.792179	+	0.792179i
$653$	1.92787e7	−	7.19490e7i	0.0692369	−	0.258396i	−0.922628	−	0.385691i	$-0.873963\pi$
$653$	1.92787e7	−	7.19490e7i	0.0692369	−	0.258396i	0.991865	+	0.127296i	$0.0406297\pi$
$654$	−6.81132e8	−	3.93252e8i	−2.43500	−	1.40585i
$655$	6.68067e7			0.237737
$656$			4.21224e8i			1.49211i
$657$	−5.70431e8	−	3.29338e8i	−2.01144	−	1.16131i
$658$	4.25348e8	+	4.25348e8i	1.49303	+	1.49303i
$659$	3.98618e8	−	2.30142e8i	1.39284	−	0.804155i	0.399209	−	0.916860i	$-0.369285\pi$
$659$	3.98618e8	−	2.30142e8i	1.39284	−	0.804155i	0.993628	+	0.112705i	$0.0359515\pi$
$660$	4.08302e8	+	4.08302e8i	1.42020	+	1.42020i
$661$	−1.23996e8	+	4.62759e8i	−0.429342	+	1.60232i	0.324914	+	0.945744i	$0.394665\pi$
$661$	−1.23996e8	+	4.62759e8i	−0.429342	+	1.60232i	−0.754255	+	0.656581i	$0.772002\pi$
$662$	−1.36053e8	−	2.35650e8i	−0.468957	−	0.812257i
$663$	−3.09171e8	−	5.35499e8i	−1.06086	−	1.83746i
$664$	−5.62939e7	−	2.10092e8i	−0.192290	−	0.717636i
$665$		−	1.29125e8i		−	0.439081i
$666$	−8.70922e8	+	1.06464e9i	−2.94820	+	3.60396i
$667$	−6.44433e6			−0.0217170
$668$	−6.72562e7	+	1.80212e7i	−0.225633	+	0.0604582i
$669$	−8.63950e8	+	4.98802e8i	−2.88543	+	1.66590i
$670$	2.18009e8	−	1.25868e8i	0.724853	−	0.418494i
$671$	3.75536e8	+	1.00625e8i	1.24304	+	0.333071i
$672$	−5.57442e8	+	5.57442e8i	−1.83693	+	1.83693i
$673$	1.33769e8	+	2.31694e8i	0.438843	+	0.760098i	0.997601	−	0.0692328i	$-0.0220551\pi$
$673$	1.33769e8	+	2.31694e8i	0.438843	+	0.760098i	−0.558758	+	0.829331i	$0.688722\pi$
$674$	−5.66213e8	+	5.66213e8i	−1.84927	+	1.84927i
$675$	3.51261e8	−	6.08401e8i	1.14214	−	1.97824i
$676$	5.71897e8			1.85130
$677$		−	2.53481e8i		−	0.816920i	−0.912776	−	0.408460i	$-0.866066\pi$
$677$		−	2.53481e8i		−	0.816920i	0.912776	−	0.408460i	$-0.133934\pi$
$678$	8.81977e8	−	1.52763e9i	2.82988	−	4.90150i
$679$	8.28642e7	+	2.22034e7i	0.264702	+	0.0709268i
$680$	−2.02987e8	−	2.02987e8i	−0.645566	−	0.645566i
$681$	4.78439e8	−	1.28197e8i	1.51490	−	0.405917i
$682$	6.59375e7	−	1.14207e8i	0.207864	−	0.360031i
$683$	5.79945e7	+	2.16438e8i	0.182022	+	0.679316i	0.995248	+	0.0973684i	$0.0310425\pi$
$683$	5.79945e7	+	2.16438e8i	0.182022	+	0.679316i	−0.813226	+	0.581948i	$0.802291\pi$
$684$	−3.23673e8	+	1.20796e9i	−1.01143	+	3.77472i
$685$	−1.84189e7	−	4.93533e6i	−0.0573049	−	0.0153548i
$686$	1.50813e8	−	4.04101e7i	0.467160	−	0.125175i
$687$	−4.26836e8	−	2.46434e8i	−1.31641	−	0.760029i
$688$	1.26840e8	+	4.73373e8i	0.389485	+	1.45358i
$689$	4.83616e8	−	4.83616e8i	1.47857	−	1.47857i
$690$	1.37280e7	−	5.12335e7i	0.0417888	−	0.155958i
$691$	6.36364e7	+	3.67405e7i	0.192873	+	0.111355i	0.593327	−	0.804962i	$-0.297814\pi$
$691$	6.36364e7	+	3.67405e7i	0.192873	+	0.111355i	−0.400454	+	0.916317i	$0.631148\pi$
$692$	−6.54322e8			−1.97457
$693$		−	1.11580e9i		−	3.35264i
$694$	8.98751e8	+	5.18894e8i	2.68881	+	1.55239i
$695$	−1.49399e8	−	1.49399e8i	−0.445036	−	0.445036i
$696$	2.78879e8	−	1.61011e8i	0.827157	−	0.477560i
$697$	1.63092e8	+	1.63092e8i	0.481653	+	0.481653i
$698$	−1.15372e8	+	4.30573e8i	−0.339260	+	1.26614i
$699$	−5.88725e8	−	1.01970e9i	−1.72378	−	2.98567i
$700$	3.95303e8	+	6.84686e8i	1.15249	+	1.99617i
$701$	1.08250e8	+	4.03996e8i	0.314250	+	1.17280i	0.924685	+	0.380732i	$0.124328\pi$
$701$	1.08250e8	+	4.03996e8i	0.314250	+	1.17280i	−0.610435	+	0.792066i	$0.709005\pi$
$702$			2.52146e9i			7.28854i
$703$	−1.80733e8	−	1.47847e8i	−0.520200	−	0.425546i
$704$	8.65114e6			0.0247945
$705$	2.72215e8	−	7.29397e7i	0.776862	−	0.208160i
$706$	−1.62362e8	+	9.37396e7i	−0.461391	+	0.266384i
$707$	−2.81949e8	+	1.62783e8i	−0.797833	+	0.460629i
$708$	−2.83089e8	−	7.58535e7i	−0.797670	−	0.213735i
$709$	−2.70120e7	+	2.70120e7i	−0.0757910	+	0.0757910i	−0.743986	−	0.668195i	$-0.767067\pi$
$709$	−2.70120e7	+	2.70120e7i	−0.0757910	+	0.0757910i	0.668195	+	0.743986i	$0.267067\pi$
$710$	2.89104e7	+	5.00743e7i	0.0807754	+	0.139907i
$711$	6.21735e7	−	6.21735e7i	0.172980	−	0.172980i
$712$	5.62488e8	−	9.74258e8i	1.55838	−	2.69919i
$713$	−8.38861e6			−0.0231431
$714$			1.38425e9i			3.80295i
$715$	−1.16257e8	+	2.01363e8i	−0.318054	+	0.550886i
$716$	−1.29173e9	−	3.46117e8i	−3.51910	−	0.942940i
$717$	−2.38483e8	−	2.38483e8i	−0.646995	−	0.646995i
$718$	5.43953e7	−	1.45752e7i	0.146956	−	0.0393768i
$719$	−2.15395e8	+	3.73075e8i	−0.579493	+	1.00371i	0.416044	+	0.909344i	$0.363416\pi$
$719$	−2.15395e8	+	3.73075e8i	−0.579493	+	1.00371i	−0.995537	+	0.0943674i	$0.969917\pi$
$720$	2.20962e8	+	8.24642e8i	0.591998	+	2.20937i
$721$	1.98809e8	−	7.41967e8i	0.530434	−	1.97961i
$722$	3.59456e8	+	9.63158e7i	0.955067	+	0.255909i
$723$	1.01089e9	−	2.70866e8i	2.67477	−	0.716703i
$724$	−2.92885e8	−	1.69097e8i	−0.771757	−	0.445574i
$725$	−1.68197e7	−	6.27720e7i	−0.0441372	−	0.164722i
$726$	5.85622e7	−	5.85622e7i	0.153041	−	0.153041i
$727$	−9.80472e6	+	3.65917e7i	−0.0255171	+	0.0952312i	−0.977510	−	0.210889i	$-0.932364\pi$
$727$	−9.80472e6	+	3.65917e7i	−0.0255171	+	0.0952312i	0.951993	+	0.306120i	$0.0990309\pi$
$728$	−1.36618e9	−	7.88764e8i	−3.54090	−	2.04434i
$729$	−8.90454e8			−2.29842
$730$		−	3.07272e8i		−	0.789868i
$731$	2.32394e8	+	1.34173e8i	0.594939	+	0.343488i
$732$	1.57182e9	+	1.57182e9i	4.00748	+	4.00748i
$733$	−2.14834e8	+	1.24035e8i	−0.545496	+	0.314942i	−0.747304	−	0.664483i	$-0.768652\pi$
$733$	−2.14834e8	+	1.24035e8i	−0.545496	+	0.314942i	0.201807	+	0.979425i	$0.435319\pi$
$734$	−5.72470e8	−	5.72470e8i	−1.44765	−	1.44765i
$735$	−7.57778e7	+	2.82807e8i	−0.190845	+	0.712242i
$736$	−1.98131e7	−	3.43172e7i	−0.0496956	−	0.0860754i
$737$	1.84639e8	+	3.19804e8i	0.461234	+	0.798881i
$738$	−3.97294e8	−	1.48272e9i	−0.988424	−	3.68885i
$739$			5.29388e8i			1.31172i	0.754884	+	0.655859i	$0.227693\pi$
$739$			5.29388e8i			1.31172i	−0.754884	+	0.655859i	$0.772307\pi$
$740$	−4.38524e8	−	7.16902e7i	−1.08218	−	0.176915i
$741$	−6.98603e8			−1.71702
$742$	−1.47893e9	+	3.96277e8i	−3.62022	+	0.970034i
$743$	−2.90822e6	+	1.67906e6i	−0.00709024	+	0.00409355i	−0.503541	−	0.863971i	$-0.667970\pi$
$743$	−2.90822e6	+	1.67906e6i	−0.00709024	+	0.00409355i	0.496451	+	0.868065i	$0.334636\pi$
$744$	3.63018e8	−	2.09588e8i	0.881473	−	0.508919i
$745$	−9.31916e7	−	2.49706e7i	−0.225376	−	0.0603894i
$746$	3.66568e7	−	3.66568e7i	0.0882954	−	0.0882954i
$747$	1.77096e8	+	3.06739e8i	0.424860	+	0.735880i
$748$	5.35616e8	−	5.35616e8i	1.27982	−	1.27982i
$749$	4.37404e8	−	7.57606e8i	1.04097	−	1.80301i
$750$	1.23600e9			2.92977
$751$			1.77941e8i			0.420104i	0.977690	+	0.210052i	$0.0673633\pi$
$751$			1.77941e8i			0.420104i	−0.977690	+	0.210052i	$0.932637\pi$
$752$	3.37579e8	−	5.84704e8i	0.793820	−	1.37494i
$753$	4.49967e8	+	1.20568e8i	1.05389	+	0.282389i
$754$	1.64930e8	+	1.64930e8i	0.384756	+	0.384756i
$755$	1.03907e8	−	2.78419e7i	0.241438	−	0.0646931i
$756$	1.95444e9	−	3.38519e9i	4.52331	−	7.83461i
$757$	−7.89282e7	−	2.94564e8i	−0.181947	−	0.679035i	−0.995264	−	0.0972134i	$-0.969007\pi$
$757$	−7.89282e7	−	2.94564e8i	−0.181947	−	0.679035i	0.813317	−	0.581821i	$-0.197660\pi$
$758$	2.42704e8	−	9.05785e8i	0.557276	−	2.07978i
$759$	7.51561e7	+	2.01380e7i	0.171885	+	0.0460566i
$760$	−3.13277e8	+	8.39423e7i	−0.713654	+	0.191223i
$761$	−1.61673e8	−	9.33422e7i	−0.366847	−	0.211799i	0.305233	−	0.952278i	$-0.401266\pi$
$761$	−1.61673e8	−	9.33422e7i	−0.366847	−	0.211799i	−0.672080	+	0.740478i	$0.734599\pi$
$762$	−2.10763e8	−	7.86579e8i	−0.476354	−	1.77778i
$763$	−3.47168e8	+	3.47168e8i	−0.781566	+	0.781566i
$764$	2.46535e8	−	9.20082e8i	0.552840	−	2.06323i
$765$	4.04843e8	+	2.33736e8i	0.904278	+	0.522085i
$766$	1.07567e8			0.239327
$767$		−	1.18014e8i		−	0.261545i
$768$	−1.32692e9	−	7.66095e8i	−2.92927	−	1.69122i
$769$	5.98817e8	+	5.98817e8i	1.31678	+	1.31678i	0.916306	+	0.400479i	$0.131156\pi$
$769$	5.98817e8	+	5.98817e8i	1.31678	+	1.31678i	0.400479	+	0.916306i	$0.368844\pi$
$770$	4.50783e8	−	2.60260e8i	0.987404	−	0.570078i
$771$	7.42039e8	+	7.42039e8i	1.61906	+	1.61906i
$772$	1.84215e8	−	6.87501e8i	0.400382	−	1.49424i
$773$	3.94102e8	+	6.82605e8i	0.853239	+	1.47785i	0.878270	+	0.478166i	$0.158698\pi$
$773$	3.94102e8	+	6.82605e8i	0.853239	+	1.47785i	−0.0250310	+	0.999687i	$0.507968\pi$
$774$	−8.92960e8	−	1.54665e9i	−1.92579	−	3.33557i
$775$	−2.18943e7	−	8.17105e7i	−0.0470355	−	0.175539i
$776$		−	2.15476e8i		−	0.461119i
$777$	6.95362e8	+	9.67151e8i	1.48234	+	2.06173i
$778$	2.92152e8			0.620398
$779$	2.51706e8	−	6.74444e7i	0.532453	−	0.142670i
$780$	−1.15131e9	+	6.64707e8i	−2.42609	+	1.40071i
$781$	−7.34556e7	+	4.24096e7i	−0.154196	+	0.0890248i
$782$	−6.72088e7	−	1.80086e7i	−0.140542	−	0.0376581i
$783$	−2.27195e8	+	2.27195e8i	−0.473275	+	0.473275i
$784$	3.50715e8	+	6.07456e8i	0.727789	+	1.26057i
$785$	−7.86054e7	+	7.86054e7i	−0.162496	+	0.162496i
$786$	−4.04574e8	+	7.00743e8i	−0.833164	+	1.44308i
$787$	−2.08114e8			−0.426951			−0.213475	−	0.976948i	$-0.568478\pi$
$787$	−2.08114e8			−0.426951			−0.213475	+	0.976948i	$0.568478\pi$
$788$			1.37389e9i			2.80785i
$789$	84397.5	−	146181.i	0.000171830	−	0.000297618i
$790$	3.96200e7	+	1.06161e7i	0.0803587	+	0.0215321i
$791$	−7.78621e8	−	7.78621e8i	−1.57325	−	1.57325i
$792$	−2.70710e9	+	7.25366e8i	−5.44915	+	1.46010i
$793$	−4.47551e8	+	7.75181e8i	−0.897476	+	1.55447i
$794$	2.26428e8	+	8.45040e8i	0.452343	+	1.68817i
$795$	−1.85655e8	+	6.92874e8i	−0.369492	+	1.37896i
$796$	−4.81890e8	−	1.29122e8i	−0.955452	−	0.256013i
$797$	−7.03152e8	+	1.88409e8i	−1.38891	+	0.372157i	−0.874349	−	0.485297i	$-0.838712\pi$
$797$	−7.03152e8	+	1.88409e8i	−1.38891	+	0.372157i	−0.514560	+	0.857454i	$0.672045\pi$
$798$	1.35440e9	+	7.81965e8i	2.66526	+	1.53879i
$799$	−9.56832e7	−	3.57095e8i	−0.187584	−	0.700072i
$800$	2.82560e8	−	2.82560e8i	0.551876	−	0.551876i
$801$	−4.74147e8	+	1.76954e9i	−0.922604	+	3.44320i
$802$	−7.51259e8	−	4.33739e8i	−1.45635	−	0.840825i
$803$	4.50747e8			0.870535
$804$			2.11137e9i			4.06253i
$805$	−2.86744e7	−	1.65552e7i	−0.0549677	−	0.0317356i
$806$	2.14690e8	+	2.14690e8i	0.410021	+	0.410021i
$807$	−1.02263e9	+	5.90417e8i	−1.94580	+	1.12341i
$808$	5.78229e8	+	5.78229e8i	1.09614	+	1.09614i
$809$	2.38010e8	−	8.88264e8i	0.449520	−	1.67763i	−0.254199	−	0.967152i	$-0.581812\pi$
$809$	2.38010e8	−	8.88264e8i	0.449520	−	1.67763i	0.703719	−	0.710479i	$-0.251522\pi$
$810$	−7.19795e8	−	1.24672e9i	−1.35442	−	2.34593i
$811$	1.23089e7	+	2.13197e7i	0.0230758	+	0.0399685i	0.877333	−	0.479883i	$-0.159321\pi$
$811$	1.23089e7	+	2.13197e7i	0.0230758	+	0.0399685i	−0.854257	+	0.519851i	$0.825987\pi$
$812$	−9.35860e7	−	3.49268e8i	−0.174801	−	0.652365i
$813$		−	1.73689e9i		−	3.23221i
$814$	1.51865e8	−	9.28945e8i	0.281568	−	1.72233i
$815$	1.31138e8			0.242246
$816$	1.50074e9	−	4.02121e8i	2.76207	−	0.740094i
$817$	2.62559e8	−	1.51588e8i	0.481460	−	0.277971i
$818$	−1.48277e9	+	8.56077e8i	−2.70903	+	1.56406i
$819$	2.48138e9	+	6.64885e8i	4.51692	+	1.21030i
$820$	3.50643e8	−	3.50643e8i	0.635950	−	0.635950i
$821$	5.22193e8	+	9.04465e8i	0.943630	+	1.63441i	0.758472	+	0.651706i	$0.225946\pi$
$821$	5.22193e8	+	9.04465e8i	0.943630	+	1.63441i	0.185158	+	0.982709i	$0.440720\pi$
$822$	1.63310e8	−	1.63310e8i	0.294034	−	0.294034i
$823$	5.25610e8	−	9.10383e8i	0.942897	−	1.63315i	0.182988	−	0.983115i	$-0.441423\pi$
$823$	5.25610e8	−	9.10383e8i	0.942897	−	1.63315i	0.759909	−	0.650030i	$-0.225244\pi$
$824$	−1.92937e9			−3.44853
$825$			7.84630e8i			1.39734i
$826$	−1.32096e8	+	2.28797e8i	−0.234396	+	0.405985i
$827$	−2.12739e8	−	5.70033e7i	−0.376124	−	0.100782i	0.0658043	−	0.997833i	$-0.479039\pi$
$827$	−2.12739e8	−	5.70033e7i	−0.376124	−	0.100782i	−0.441928	+	0.897050i	$0.645705\pi$
$828$	2.26751e8	+	2.26751e8i	0.399446	+	0.399446i
$829$	4.76182e8	−	1.27593e8i	0.835814	−	0.223956i	0.184566	−	0.982820i	$-0.440912\pi$
$829$	4.76182e8	−	1.27593e8i	0.835814	−	0.223956i	0.651249	+	0.758864i	$0.274245\pi$
$830$	−8.26150e7	+	1.43093e8i	−0.144486	+	0.250256i
$831$	−2.34429e8	−	8.74899e8i	−0.408514	−	1.52460i
$832$	−5.15506e6	+	1.92390e7i	−0.00895084	+	0.0334050i
$833$	3.70990e8	+	9.94063e7i	0.641840	+	0.171980i
$834$	2.47181e9	−	6.62320e8i	4.26106	−	1.14175i
$835$	2.54664e7	+	1.47030e7i	0.0437429	+	0.0252550i
$836$	−2.21496e8	−	8.26636e8i	−0.379095	−	1.41480i
$837$	−2.95740e8	+	2.95740e8i	−0.504353	+	0.504353i
$838$	−4.20496e8	+	1.56931e9i	−0.714545	+	2.66672i
$839$	−5.66229e8	−	3.26913e8i	−0.958753	−	0.553536i	−0.0629638	−	0.998016i	$-0.520055\pi$
$839$	−5.66229e8	−	3.26913e8i	−0.958753	−	0.553536i	−0.895789	+	0.444480i	$0.853389\pi$
$840$	1.65452e9			2.79148
$841$		−	5.65101e8i		−	0.950032i
$842$	−1.26701e9	−	7.31511e8i	−2.12249	−	1.22542i
$843$	−1.09841e9	−	1.09841e9i	−1.83351	−	1.83351i
$844$	1.33995e9	−	7.73620e8i	2.22875	−	1.28677i
$845$	−1.70786e8	−	1.70786e8i	−0.283062	−	0.283062i
$846$	−6.36802e8	+	2.37658e9i	−1.05170	+	3.92501i
$847$	−2.58497e7	−	4.47731e7i	−0.0425408	−	0.0736829i
$848$	8.59247e8	+	1.48826e9i	1.40906	+	2.44057i
$849$	2.49622e8	+	9.31604e8i	0.407907	+	1.52233i
$850$		−	7.01660e8i		−	1.14254i
$851$	−5.60039e7	+	2.11793e7i	−0.0908720	+	0.0343655i
$852$	−4.84959e8			−0.784127
$853$	9.61178e8	−	2.57547e8i	1.54866	−	0.414963i	0.619609	−	0.784910i	$-0.287291\pi$
$853$	9.61178e8	−	2.57547e8i	1.54866	−	0.414963i	0.929053	+	0.369948i	$0.120624\pi$
$854$	1.73536e9	−	1.00191e9i	2.78623	−	1.60863i
$855$	4.57392e8	−	2.64075e8i	0.731796	−	0.422503i
$856$	−2.12242e9	−	5.68701e8i	−3.38384	−	0.906698i
$857$	5.59065e8	−	5.59065e8i	0.888219	−	0.888219i	−0.106133	−	0.994352i	$-0.533847\pi$
$857$	5.59065e8	−	5.59065e8i	0.888219	−	0.888219i	0.994352	+	0.106133i	$0.0338468\pi$
$858$	−1.40808e9	−	2.43887e9i	−2.22928	−	3.86123i
$859$	−5.84643e8	+	5.84643e8i	−0.922383	+	0.922383i	−0.997197	−	0.0748143i	$-0.976164\pi$
$859$	−5.84643e8	+	5.84643e8i	−0.922383	+	0.922383i	0.0748143	+	0.997197i	$0.476164\pi$
$860$	2.88467e8	−	4.99639e8i	0.453524	−	0.785527i
$861$	−1.32934e9			−2.08270
$862$			7.43391e8i			1.16063i
$863$	−1.81324e8	+	3.14062e8i	−0.282113	+	0.488633i	−0.971905	−	0.235374i	$-0.924369\pi$
$863$	−1.81324e8	+	3.14062e8i	−0.282113	+	0.488633i	0.689792	+	0.724007i	$0.257702\pi$
$864$	−1.90836e9	−	5.11345e8i	−2.95883	−	0.792816i
$865$	1.95400e8	+	1.95400e8i	0.301909	+	0.301909i
$866$	1.37123e9	−	3.67421e8i	2.11134	−	0.565731i
$867$	−1.91359e8	+	3.31443e8i	−0.293623	+	0.508571i
$868$	−1.21821e8	−	4.54643e8i	−0.186279	−	0.695203i
$869$	−1.55732e7	+	5.81198e7i	−0.0237311	+	0.0885656i
$870$	−2.36294e8	−	6.33148e7i	−0.358835	−	0.0961496i
$871$	−8.21225e8	+	2.20046e8i	−1.24282	+	0.333012i
$872$	1.06797e9	+	6.16594e8i	1.61068	+	0.929929i
$873$	9.08171e7	+	3.38934e8i	0.136498	+	0.509416i
$874$	−5.55865e7	+	5.55865e7i	−0.0832598	+	0.0832598i
$875$	1.99695e8	−	7.45272e8i	0.298087	−	1.11248i
$876$	2.23190e9	+	1.28859e9i	3.32019	+	1.91691i
$877$	−9.08416e8			−1.34675			−0.673373	−	0.739303i	$-0.735155\pi$
$877$	−9.08416e8			−1.34675			−0.673373	+	0.739303i	$0.735155\pi$
$878$			1.05928e9i			1.56504i
$879$	1.13299e9	+	6.54130e8i	1.66824	+	0.963158i
$880$	−4.13112e8	−	4.13112e8i	−0.606205	−	0.606205i
$881$	−4.62180e8	+	2.66840e8i	−0.675901	+	0.390232i	−0.798309	−	0.602248i	$-0.794272\pi$
$881$	−4.62180e8	+	2.66840e8i	−0.675901	+	0.390232i	0.122408	+	0.992480i	$0.460938\pi$
$882$	−1.80747e9	−	1.80747e9i	−2.63430	−	2.63430i
$883$	−9.16870e6	+	3.42180e7i	−0.0133176	+	0.0497019i	−0.972265	−	0.233882i	$-0.924857\pi$
$883$	−9.16870e6	+	3.42180e7i	−0.0133176	+	0.0497019i	0.958947	+	0.283584i	$0.0915236\pi$
$884$	8.71972e8	+	1.51030e9i	1.26225	+	2.18628i
$885$	6.18867e7	+	1.07191e8i	0.0892827	+	0.154642i
$886$	8.46808e7	+	3.16033e8i	0.121754	+	0.454392i
$887$		−	8.36923e7i		−	0.119926i	−0.998201	−	0.0599632i	$-0.980902\pi$
$887$		−	8.36923e7i		−	0.119926i	0.998201	−	0.0599632i	$-0.0190983\pi$
$888$	1.89441e9	−	2.31579e9i	2.70543	−	3.30720i
$889$	−5.08337e8			−0.723514
$890$	−8.25488e8	+	2.21189e8i	−1.17096	+	0.313757i
$891$	1.82886e9	−	1.05589e9i	2.58551	−	1.49275i
$892$	2.43665e9	−	1.40680e9i	3.43319	−	1.98216i
$893$	−4.03446e8	−	1.08103e8i	−0.566541	−	0.151804i
$894$	8.26277e8	−	8.26277e8i	1.15641	−	1.15641i
$895$	2.82387e8	+	4.89109e8i	0.393891	+	0.682239i
$896$	−6.66623e8	+	6.66623e8i	−0.926737	+	0.926737i
$897$	−8.95684e7	+	1.55137e8i	−0.124102	+	0.214950i
$898$	−3.46482e8			−0.478467
$899$			3.86891e7i			0.0532487i
$900$	−1.61688e9	+	2.80052e9i	−2.21795	+	3.84160i
$901$	9.08921e8	+	2.43545e8i	1.24266	+	0.332969i
$902$	7.42782e8	+	7.42782e8i	1.01214	+	1.01214i
$903$	−1.49392e9	+	4.00294e8i	−2.02891	+	0.543646i
$904$	−1.38288e9	+	2.39523e9i	−1.87189	+	3.24221i
$905$	3.69666e7	+	1.37961e8i	0.0498729	+	0.186128i
$906$	−3.37215e8	+	1.25850e9i	−0.453442	+	1.69227i
$907$	−5.83576e8	−	1.56369e8i	−0.782123	−	0.209569i	−0.154403	−	0.988008i	$-0.549345\pi$
$907$	−5.83576e8	−	1.56369e8i	−0.782123	−	0.209569i	−0.627721	+	0.778439i	$0.716012\pi$
$908$	−1.34937e9	+	3.61563e8i	−1.80249	+	0.482976i
$909$	−1.15324e9	−	6.65822e8i	−1.53542	−	0.886475i
$910$	3.10168e8	+	1.15756e9i	0.411598	+	1.53610i
$911$	−3.84956e8	+	3.84956e8i	−0.509162	+	0.509162i	−0.914269	−	0.405107i	$-0.867234\pi$
$911$	−3.84956e8	+	3.84956e8i	−0.509162	+	0.509162i	0.405107	+	0.914269i	$0.367234\pi$
$912$	4.54317e8	−	1.69554e9i	0.598928	−	2.23523i
$913$	−2.09908e8	−	1.21191e8i	−0.275814	−	0.159242i
$914$	−3.25670e8			−0.426520
$915$		−	9.38787e8i		−	1.22547i
$916$	1.20383e9	+	6.95032e8i	1.56632	+	0.904313i
$917$	3.57163e8	+	3.57163e8i	0.463189	+	0.463189i
$918$	−3.00434e9	+	1.73456e9i	−3.88348	+	2.24213i
$919$	−7.09804e8	−	7.09804e8i	−0.914517	−	0.914517i	0.0821064	−	0.996624i	$-0.473835\pi$
$919$	−7.09804e8	−	7.09804e8i	−0.914517	−	0.914517i	−0.996624	+	0.0821064i	$0.973835\pi$
$920$	−2.15246e7	+	8.03310e7i	−0.0276422	+	0.103162i
$921$	−7.25702e8	−	1.25695e9i	−0.928923	−	1.60894i
$922$	−7.68101e8	−	1.33039e9i	−0.979999	−	1.69741i
$923$	−5.05423e7	−	1.88626e8i	−0.0642761	−	0.239882i
$924$			4.36574e9i			5.53403i
$925$	−3.52471e8	−	4.90237e8i	−0.445346	−	0.619414i
$926$	2.75547e9			3.47027
$927$	3.03482e9	−	8.13177e8i	3.80973	−	1.02081i
$928$	−1.58275e8	+	9.13798e7i	−0.198046	+	0.114342i
$929$	−1.96241e8	+	1.13300e8i	−0.244761	+	0.141313i	−0.617363	−	0.786678i	$-0.711799\pi$
$929$	−1.96241e8	+	1.13300e8i	−0.244761	+	0.141313i	0.372602	+	0.927991i	$0.378466\pi$
$930$	−3.07585e8	−	8.24171e7i	−0.382398	−	0.102463i
$931$	3.06835e8	−	3.06835e8i	0.380238	−	0.380238i
$932$	1.66042e9	+	2.87592e9i	2.05102	+	3.55246i
$933$	1.19177e9	−	1.19177e9i	1.46739	−	1.46739i
$934$	−6.19659e8	+	1.07328e9i	−0.760522	+	1.31726i
$935$	−3.19902e8			−0.391365
$936$		−	6.45246e9i		−	7.86860i
$937$	7.15752e8	−	1.23972e9i	0.870049	−	1.50697i	0.00810341	−	0.999967i	$-0.497421\pi$
$937$	7.15752e8	−	1.23972e9i	0.870049	−	1.50697i	0.861945	−	0.507001i	$-0.169246\pi$
$938$	1.83844e9	+	4.92608e8i	2.22762	+	0.596888i
$939$	6.63713e8	+	6.63713e8i	0.801647	+	0.801647i
$940$	−7.67743e8	+	2.05716e8i	−0.924341	+	0.247676i
$941$	−4.64148e8	+	8.03929e8i	−0.557042	+	0.964825i	0.440699	+	0.897655i	$0.354730\pi$
$941$	−4.64148e8	+	8.03929e8i	−0.557042	+	0.964825i	−0.997742	+	0.0671704i	$0.978603\pi$
$942$	−3.48475e8	−	1.30053e9i	−0.416887	−	1.55584i
$943$	1.72942e7	−	6.45428e7i	0.0206236	−	0.0769685i
$944$	2.86424e8	+	7.67470e7i	0.340481	+	0.0912316i
$945$	−1.59457e9	+	4.27264e8i	−1.88951	+	0.506292i
$946$	1.05841e9	+	6.11073e8i	1.25020	+	0.721804i
$947$	1.74985e8	+	6.53053e8i	0.206040	+	0.768951i	0.989130	+	0.147043i	$0.0469756\pi$
$947$	1.74985e8	+	6.53053e8i	0.206040	+	0.768951i	−0.783090	+	0.621908i	$0.786358\pi$
$948$	−2.43263e8	+	2.43263e8i	−0.285530	+	0.285530i
$949$	−2.68592e8	+	1.00240e9i	−0.314264	+	1.17285i
$950$	−6.86530e8	−	3.96368e8i	−0.800735	−	0.462305i
$951$	−1.98268e9			−2.30522
$952$		−	2.17042e9i		−	2.51555i
$953$	−9.52609e8	−	5.49989e8i	−1.10062	−	0.635441i	−0.164233	−	0.986422i	$-0.552515\pi$
$953$	−9.52609e8	−	5.49989e8i	−1.10062	−	0.635441i	−0.936383	+	0.350980i	$0.885848\pi$
$954$	−4.42829e9	−	4.42829e9i	−5.10024	−	5.10024i
$955$	−3.48387e8	+	2.01141e8i	−0.399992	+	0.230936i
$956$	6.72609e8	+	6.72609e8i	0.769819	+	0.769819i
$957$	9.28786e7	−	3.46627e8i	0.105969	−	0.395482i
$958$	3.91538e8	+	6.78163e8i	0.445325	+	0.771326i
$959$	−7.20861e7	−	1.24857e8i	−0.0817326	−	0.141565i
$960$	−5.40666e6	−	2.01779e7i	−0.00611104	−	0.0228067i
$961$		−	8.37142e8i		−	0.943255i
$962$	1.97535e9	+	8.91268e8i	2.21881	+	1.00111i
$963$	3.57817e9			4.00666
$964$	−2.85106e9	+	7.63939e8i	−3.18255	+	0.852761i
$965$	−2.60321e8	+	1.50296e8i	−0.289685	+	0.167250i
$966$	3.47298e8	−	2.00513e8i	0.385275	−	0.222439i
$967$	8.43607e8	+	2.26044e8i	0.932955	+	0.249984i	0.693114	−	0.720828i	$-0.256238\pi$
$967$	8.43607e8	+	2.26044e8i	0.932955	+	0.249984i	0.239841	+	0.970812i	$0.422905\pi$
$968$	−9.18219e7	+	9.18219e7i	−0.101233	+	0.101233i
$969$	−4.80581e8	−	8.32392e8i	−0.528197	−	0.914864i
$970$	−1.15746e8	+	1.15746e8i	−0.126821	+	0.126821i
$971$	1.08310e6	−	1.87598e6i	0.00118307	−	0.00204913i	−0.865433	−	0.501024i	$-0.832957\pi$
$971$	1.08310e6	−	1.87598e6i	0.00118307	−	0.00204913i	0.866616	+	0.498975i	$0.166290\pi$
$972$	5.88217e9			6.40529
$973$		−	1.59744e9i		−	1.73415i
$974$	1.23039e9	−	2.13110e9i	1.33158	−	2.30636i
$975$	−1.74491e9	−	4.67547e8i	−1.88261	−	0.504443i
$976$	−1.59034e9	−	1.59034e9i	−1.71057	−	1.71057i
$977$	6.31221e8	−	1.69135e8i	0.676858	−	0.181364i	0.0960160	−	0.995380i	$-0.469390\pi$
$977$	6.31221e8	−	1.69135e8i	0.676858	−	0.181364i	0.580842	+	0.814016i	$0.302723\pi$
$978$	−7.94158e8	+	1.37552e9i	−0.848966	+	1.47045i
$979$	−3.24469e8	−	1.21094e9i	−0.345800	−	1.29054i
$980$	2.13721e8	−	7.97616e8i	0.227074	−	0.847453i
$981$	−1.93975e9	−	5.19755e8i	−2.05466	−	0.550544i
$982$	3.95809e8	−	1.06057e8i	0.417976	−	0.111996i
$983$	−2.66180e8	−	1.53679e8i	−0.280231	−	0.161791i	0.353297	−	0.935511i	$-0.385060\pi$
$983$	−2.66180e8	−	1.53679e8i	−0.280231	−	0.161791i	−0.633528	+	0.773720i	$0.718394\pi$
$984$	8.64187e8	+	3.22519e9i	0.907032	+	3.38509i
$985$	4.10284e8	−	4.10284e8i	0.429315	−	0.429315i
$986$	−8.30572e7	+	3.09974e8i	−0.0866456	+	0.323366i
$987$	1.84527e9	+	1.06537e9i	1.91915	+	1.10802i
$988$	1.97031e9			2.04298
$989$		−	7.77411e7i		−	0.0803640i
$990$	1.84381e9	+	1.06452e9i	1.90025	+	1.09711i
$991$	1.01859e9	+	1.01859e9i	1.04659	+	1.04659i	0.998860	+	0.0477305i	$0.0151989\pi$
$991$	1.01859e9	+	1.01859e9i	1.04659	+	1.04659i	0.0477305	+	0.998860i	$0.484801\pi$
$992$	−2.06026e8	+	1.18949e8i	−0.211051	+	0.121851i
$993$	−6.81540e8	−	6.81540e8i	−0.696055	−	0.696055i
$994$	−1.13147e8	+	4.22269e8i	−0.115208	+	0.429962i
$995$	1.05347e8	+	1.82466e8i	0.106943	+	0.185231i
$996$	−6.92915e8	−	1.20016e9i	−0.701297	−	1.21468i
$997$	2.62403e7	+	9.79302e7i	0.0264779	+	0.0988169i	0.977900	−	0.209072i	$-0.0670442\pi$
$997$	2.62403e7	+	9.79302e7i	0.0264779	+	0.0988169i	−0.951422	+	0.307889i	$0.900378\pi$
$998$		−	1.76725e9i		−	1.77790i
$999$	−1.22774e9	+	2.72110e9i	−1.23143	+	2.72927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.14.2	yes	72
37.8	odd	12	inner	37.7.g.a.8.2	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.2	✓	72	37.8	odd	12	inner
37.7.g.a.14.2	yes	72	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.9349 + 3.73385i) q^{2} +(-44.2547 + 25.5505i) q^{3} +(124.814 - 72.0615i) q^{4} +(-58.7930 - 15.7535i) q^{5} +(521.284 - 521.284i) q^{6} +(-230.098 - 398.542i) q^{7} +(-817.340 + 817.340i) q^{8} +(941.155 - 1630.13i) q^{9} +O(q^{10})\)	\(q+(-13.9349 + 3.73385i) q^{2} +(-44.2547 + 25.5505i) q^{3} +(124.814 - 72.0615i) q^{4} +(-58.7930 - 15.7535i) q^{5} +(521.284 - 521.284i) q^{6} +(-230.098 - 398.542i) q^{7} +(-817.340 + 817.340i) q^{8} +(941.155 - 1630.13i) q^{9} +878.096 q^{10} +1288.11i q^{11} +(-3682.42 + 6378.13i) q^{12} +(-2864.57 - 767.560i) q^{13} +(4694.49 + 4694.49i) q^{14} +(3004.38 - 805.021i) q^{15} +(3725.79 - 6453.27i) q^{16} +(-1056.04 - 3941.18i) q^{17} +(-7028.26 + 26229.8i) q^{18} +(-4452.75 - 1193.11i) q^{19} +(-8473.43 + 2270.45i) q^{20} +(20365.9 + 11758.2i) q^{21} +(-4809.59 - 17949.6i) q^{22} +(-835.843 + 835.843i) q^{23} +(15287.7 - 57054.6i) q^{24} +(-10323.2 - 5960.11i) q^{25} +42783.5 q^{26} +58935.3i q^{27} +(-57439.0 - 33162.4i) q^{28} +(3854.99 + 3854.99i) q^{29} +(-38859.9 + 22435.8i) q^{30} +(5018.05 + 5018.05i) q^{31} +(-8676.38 + 32380.7i) q^{32} +(-32911.8 - 57004.8i) q^{33} +(29431.5 + 50976.9i) q^{34} +(7249.71 + 27056.3i) q^{35} -271284. i q^{36} +(46170.9 + 20832.1i) q^{37} +66503.6 q^{38} +(146382. - 39223.1i) q^{39} +(60929.9 - 35177.9i) q^{40} +(-48954.8 + 28264.1i) q^{41} +(-327700. - 87806.9i) q^{42} +(-46504.6 + 46504.6i) q^{43} +(92823.0 + 160774. i) q^{44} +(-81013.6 + 81013.6i) q^{45} +(8526.48 - 14768.3i) q^{46} +90605.9 q^{47} +380784. i q^{48} +(-47065.8 + 81520.3i) q^{49} +(166107. + 44508.2i) q^{50} +(147434. + 147434. i) q^{51} +(-412851. + 110623. i) q^{52} +(-115311. + 199724. i) q^{53} +(-220055. - 821257. i) q^{54} +(20292.2 - 75731.6i) q^{55} +(513812. + 137676. i) q^{56} +(227540. - 60969.2i) q^{57} +(-68112.8 - 39325.0i) q^{58} +(10299.4 + 38437.9i) q^{59} +(316978. - 316978. i) q^{60} +(78118.3 - 291541. i) q^{61} +(-88662.7 - 51189.4i) q^{62} -866232. q^{63} -6716.17i q^{64} +(156325. + 90254.3i) q^{65} +(671469. + 671469. i) q^{66} +(248275. - 143342. i) q^{67} +(-415816. - 415816. i) q^{68} +(15633.8 - 58346.2i) q^{69} +(-202048. - 349958. i) q^{70} +(32924.0 + 57026.0i) q^{71} +(563126. + 2.10161e6i) q^{72} -349930. i q^{73} +(-721171. - 117898. i) q^{74} +609135. q^{75} +(-641745. + 171955. i) q^{76} +(513364. - 296391. i) q^{77} +(-1.89337e6 + 1.09314e6i) q^{78} +(45120.4 + 12090.0i) q^{79} +(-320712. + 320712. i) q^{80} +(-819723. - 1.41980e6i) q^{81} +(576647. - 576647. i) q^{82} +(-94084.2 + 162959. i) q^{83} +3.38927e6 q^{84} +248350. i q^{85} +(474396. - 821678. i) q^{86} +(-269098. - 72104.7i) q^{87} +(-1.05282e6 - 1.05282e6i) q^{88} +(-940089. + 251896. i) q^{89} +(826424. - 1.43141e6i) q^{90} +(353228. + 1.31827e6i) q^{91} +(-44093.0 + 164557. i) q^{92} +(-350286. - 93858.9i) q^{93} +(-1.26258e6 + 338309. i) q^{94} +(242995. + 140293. i) q^{95} +(-443371. - 1.65468e6i) q^{96} +(-131815. + 131815. i) q^{97} +(351473. - 1.31171e6i) q^{98} +(2.09978e6 + 1.21231e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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