LMFDB - Embedded newform 20.8.e.b.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,8,Mod(3,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("20.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	20.e (of order $4$, degree $2$, 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:	$6.24770050968$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	20.3
Dual form			20.8.e.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.35451 + 6.36342i) q^{2} +(56.5129 - 56.5129i) q^{3} +(47.0138 - 119.053i) q^{4} +(-240.823 + 141.877i) q^{5} +(-169.035 + 888.266i) q^{6} +(-764.897 - 764.897i) q^{7} +(317.795 + 1412.85i) q^{8} -4200.41i q^{9} +O(q^{10})$	\(q+(-9.35451 + 6.36342i) q^{2} +(56.5129 - 56.5129i) q^{3} +(47.0138 - 119.053i) q^{4} +(-240.823 + 141.877i) q^{5} +(-169.035 + 888.266i) q^{6} +(-764.897 - 764.897i) q^{7} +(317.795 + 1412.85i) q^{8} -4200.41i q^{9} +(1349.96 - 2859.65i) q^{10} -1507.09i q^{11} +(-4071.16 - 9384.94i) q^{12} +(-5391.78 - 5391.78i) q^{13} +(12022.6 + 2287.88i) q^{14} +(-5591.75 + 21627.5i) q^{15} +(-11963.4 - 11194.3i) q^{16} +(2875.49 - 2875.49i) q^{17} +(26729.0 + 39292.8i) q^{18} +1541.88 q^{19} +(5568.91 + 35341.0i) q^{20} -86453.0 q^{21} +(9590.22 + 14098.1i) q^{22} +(49300.6 - 49300.6i) q^{23} +(97804.0 + 61885.0i) q^{24} +(37866.8 - 68334.6i) q^{25} +(84747.6 + 16127.3i) q^{26} +(-113784. - 113784. i) q^{27} +(-127024. + 55102.8i) q^{28} +84003.4i q^{29} +(-85316.8 - 237897. i) q^{30} +303876. i q^{31} +(183146. + 28589.1i) q^{32} +(-85169.8 - 85169.8i) q^{33} +(-8600.86 + 45196.8i) q^{34} +(292726. + 75683.7i) q^{35} +(-500073. - 197477. i) q^{36} +(174112. - 174112. i) q^{37} +(-14423.5 + 9811.63i) q^{38} -609410. q^{39} +(-276984. - 295161. i) q^{40} +114783. q^{41} +(808726. - 550137. i) q^{42} +(585971. - 585971. i) q^{43} +(-179424. - 70853.9i) q^{44} +(595942. + 1.01156e6i) q^{45} +(-147463. + 774903. i) q^{46} +(-161312. - 161312. i) q^{47} +(-1.30871e6 + 43464.3i) q^{48} +346591. i q^{49} +(80616.2 + 880199. i) q^{50} -325005. i q^{51} +(-895397. + 388421. i) q^{52} +(222455. + 222455. i) q^{53} +(1.78845e6 + 340338. i) q^{54} +(213821. + 362942. i) q^{55} +(837607. - 1.32377e6i) q^{56} +(87136.1 - 87136.1i) q^{57} +(-534549. - 785811. i) q^{58} +2.00202e6 q^{59} +(2.31194e6 + 1.68251e6i) q^{60} -2.52056e6 q^{61} +(-1.93369e6 - 2.84261e6i) q^{62} +(-3.21288e6 + 3.21288e6i) q^{63} +(-1.89516e6 + 897997. i) q^{64} +(2.06344e6 + 533497. i) q^{65} +(1.33869e6 + 254751. i) q^{66} +(291345. + 291345. i) q^{67} +(-207149. - 477525. i) q^{68} -5.57223e6i q^{69} +(-3.21992e6 + 1.15476e6i) q^{70} -1.18847e6i q^{71} +(5.93457e6 - 1.33487e6i) q^{72} +(-3.12091e6 - 3.12091e6i) q^{73} +(-520787. + 2.73669e6i) q^{74} +(-1.72182e6 - 6.00175e6i) q^{75} +(72489.6 - 183566. i) q^{76} +(-1.15277e6 + 1.15277e6i) q^{77} +(5.70073e6 - 3.87793e6i) q^{78} -82028.3 q^{79} +(4.46928e6 + 998517. i) q^{80} -3.67420e6 q^{81} +(-1.07374e6 + 730415. i) q^{82} +(466272. - 466272. i) q^{83} +(-4.06449e6 + 1.02925e7i) q^{84} +(-284519. + 1.10045e6i) q^{85} +(-1.75269e6 + 9.21025e6i) q^{86} +(4.74728e6 + 4.74728e6i) q^{87} +(2.12929e6 - 478945. i) q^{88} -2.67579e6i q^{89} +(-1.20117e7 - 5.67040e6i) q^{90} +8.24830e6i q^{91} +(-3.55159e6 - 8.18720e6i) q^{92} +(1.71729e7 + 1.71729e7i) q^{93} +(2.53549e6 + 482500. i) q^{94} +(-371321. + 218757. i) q^{95} +(1.19658e7 - 8.73445e6i) q^{96} +(-6.84970e6 + 6.84970e6i) q^{97} +(-2.20550e6 - 3.24219e6i) q^{98} -6.33039e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8}+O(q^{10}) $ 36 * q + 14 * q^2 - 560 * q^5 + 104 * q^6 - 3052 * q^8	$ 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8} + 390 q^{10} + 10960 q^{12} - 28564 q^{13} - 12104 q^{16} - 27012 q^{17} + 95298 q^{18} + 97180 q^{20} - 2352 q^{21} - 191320 q^{22} - 112580 q^{25} + 604628 q^{26} - 142800 q^{28} - 252760 q^{30} - 73976 q^{32} - 248080 q^{33} - 328580 q^{36} - 108732 q^{37} - 406560 q^{38} - 680660 q^{40} + 2019472 q^{41} + 1616840 q^{42} - 827660 q^{45} - 2690616 q^{46} + 549280 q^{48} + 1343690 q^{50} - 6025332 q^{52} + 5672196 q^{53} + 4064064 q^{56} - 1796160 q^{57} + 3463736 q^{58} + 3280240 q^{60} - 5624928 q^{61} + 2750760 q^{62} + 75940 q^{65} - 2175120 q^{66} - 5673084 q^{68} - 11417280 q^{70} + 4328964 q^{72} - 22930604 q^{73} - 4045600 q^{76} + 10982160 q^{77} + 27127080 q^{78} + 34488560 q^{80} + 21593004 q^{81} - 13289192 q^{82} - 28299060 q^{85} - 2245656 q^{86} - 38612320 q^{88} - 38642970 q^{90} - 22809360 q^{92} + 31343120 q^{93} + 49033664 q^{96} - 11169292 q^{97} + 45095638 q^{98}+O(q^{100}) $ 36 * q + 14 * q^2 - 560 * q^5 + 104 * q^6 - 3052 * q^8 + 390 * q^10 + 10960 * q^12 - 28564 * q^13 - 12104 * q^16 - 27012 * q^17 + 95298 * q^18 + 97180 * q^20 - 2352 * q^21 - 191320 * q^22 - 112580 * q^25 + 604628 * q^26 - 142800 * q^28 - 252760 * q^30 - 73976 * q^32 - 248080 * q^33 - 328580 * q^36 - 108732 * q^37 - 406560 * q^38 - 680660 * q^40 + 2019472 * q^41 + 1616840 * q^42 - 827660 * q^45 - 2690616 * q^46 + 549280 * q^48 + 1343690 * q^50 - 6025332 * q^52 + 5672196 * q^53 + 4064064 * q^56 - 1796160 * q^57 + 3463736 * q^58 + 3280240 * q^60 - 5624928 * q^61 + 2750760 * q^62 + 75940 * q^65 - 2175120 * q^66 - 5673084 * q^68 - 11417280 * q^70 + 4328964 * q^72 - 22930604 * q^73 - 4045600 * q^76 + 10982160 * q^77 + 27127080 * q^78 + 34488560 * q^80 + 21593004 * q^81 - 13289192 * q^82 - 28299060 * q^85 - 2245656 * q^86 - 38612320 * q^88 - 38642970 * q^90 - 22809360 * q^92 + 31343120 * q^93 + 49033664 * q^96 - 11169292 * q^97 + 45095638 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−9.35451	+	6.36342i	−0.826830	+	0.562452i
$2$	−9.35451	+	6.36342i	−0.826830	+	0.562452i
$3$	56.5129	−	56.5129i	1.20843	−	1.20843i	0.236901	−	0.971534i	$-0.423868\pi$
$3$	56.5129	−	56.5129i	1.20843	−	1.20843i	0.971534	−	0.236901i	$-0.0761316\pi$
$4$	47.0138	−	119.053i	0.367295	−	0.930104i
$5$	−240.823	+	141.877i	−0.861596	+	0.507595i
$5$	−240.823	+	141.877i	−0.861596	+	0.507595i
$6$	−169.035	+	888.266i	−0.319483	+	1.67886i
$7$	−764.897	−	764.897i	−0.842868	−	0.842868i	0.146363	−	0.989231i	$-0.453243\pi$
$7$	−764.897	−	764.897i	−0.842868	−	0.842868i	−0.989231	+	0.146363i	$0.953243\pi$
$8$	317.795	+	1412.85i	0.219448	+	0.975624i
$9$		−	4200.41i		−	1.92063i
$10$	1349.96	−	2859.65i	0.426896	−	0.904301i
$11$		−	1507.09i		−	0.341400i	−0.985323	−	0.170700i	$-0.945397\pi$
$11$		−	1507.09i		−	0.341400i	0.985323	−	0.170700i	$-0.0546029\pi$
$12$	−4071.16	−	9384.94i	−0.680118	−	1.56782i
$13$	−5391.78	−	5391.78i	−0.680660	−	0.680660i	0.279489	−	0.960149i	$-0.409835\pi$
$13$	−5391.78	−	5391.78i	−0.680660	−	0.680660i	−0.960149	+	0.279489i	$0.909835\pi$
$14$	12022.6	+	2287.88i	1.17098	+	0.222836i
$15$	−5591.75	+	21627.5i	−0.427787	+	1.65458i
$16$	−11963.4	−	11194.3i	−0.730188	−	0.683246i
$17$	2875.49	−	2875.49i	0.141952	−	0.141952i	−0.632560	−	0.774512i	$-0.717996\pi$
$17$	2875.49	−	2875.49i	0.141952	−	0.141952i	0.774512	+	0.632560i	$0.217996\pi$
$18$	26729.0	+	39292.8i	1.08026	+	1.58803i
$19$	1541.88			0.0515719			0.0257859	−	0.999667i	$-0.491791\pi$
$19$	1541.88			0.0515719			0.0257859	+	0.999667i	$0.491791\pi$
$20$	5568.91	+	35341.0i	0.155656	+	0.987811i
$21$	−86453.0			−2.03710
$22$	9590.22	+	14098.1i	0.192021	+	0.282280i
$23$	49300.6	−	49300.6i	0.844898	−	0.844898i	−0.144593	−	0.989491i	$-0.546187\pi$
$23$	49300.6	−	49300.6i	0.844898	−	0.844898i	0.989491	+	0.144593i	$0.0461873\pi$
$24$	97804.0	+	61885.0i	1.44417	+	0.913789i
$25$	37866.8	−	68334.6i	0.484695	−	0.874683i
$26$	84747.6	+	16127.3i	0.945628	+	0.179951i
$27$	−113784.	−	113784.i	−1.11252	−	1.11252i
$28$	−127024.	+	55102.8i	−1.09354	+	0.474374i
$29$			84003.4i			0.639594i	0.947486	+	0.319797i	$0.103615\pi$
$29$			84003.4i			0.639594i	−0.947486	+	0.319797i	$0.896385\pi$
$30$	−85316.8	−	237897.i	−0.576913	−	1.60866i
$31$			303876.i			1.83202i	0.401155	+	0.916010i	$0.368609\pi$
$31$			303876.i			1.83202i	−0.401155	+	0.916010i	$0.631391\pi$
$32$	183146.	+	28589.1i	0.988035	+	0.154232i
$33$	−85169.8	−	85169.8i	−0.412560	−	0.412560i
$34$	−8600.86	+	45196.8i	−0.0375289	+	0.197211i
$35$	292726.	+	75683.7i	1.15405	+	0.298376i
$36$	−500073.	−	197477.i	−1.78638	−	0.705438i
$37$	174112.	−	174112.i	0.565098	−	0.565098i	−0.365653	−	0.930751i	$-0.619154\pi$
$37$	174112.	−	174112.i	0.565098	−	0.565098i	0.930751	+	0.365653i	$0.119154\pi$
$38$	−14423.5	+	9811.63i	−0.0426412	+	0.0290067i
$39$	−609410.			−1.64507
$40$	−276984.	−	295161.i	−0.684297	−	0.729203i
$41$	114783.			0.260097			0.130049	−	0.991508i	$-0.458487\pi$
$41$	114783.			0.260097			0.130049	+	0.991508i	$0.458487\pi$
$42$	808726.	−	550137.i	1.68434	−	1.14577i
$43$	585971.	−	585971.i	1.12392	−	1.12392i	0.132776	−	0.991146i	$-0.457611\pi$
$43$	585971.	−	585971.i	1.12392	−	1.12392i	0.991146	−	0.132776i	$-0.0423891\pi$
$44$	−179424.	−	70853.9i	−0.317538	−	0.125395i
$45$	595942.	+	1.01156e6i	0.974901	+	1.65481i
$46$	−147463.	+	774903.i	−0.223372	+	1.17380i
$47$	−161312.	−	161312.i	−0.226634	−	0.226634i	0.584651	−	0.811285i	$-0.301231\pi$
$47$	−161312.	−	161312.i	−0.226634	−	0.226634i	−0.811285	+	0.584651i	$0.801231\pi$
$48$	−1.30871e6	+	43464.3i	−1.70804	+	0.0567269i
$49$			346591.i			0.420853i
$50$	80616.2	+	880199.i	0.0912068	+	0.995832i
$51$		−	325005.i		−	0.343079i
$52$	−895397.	+	388421.i	−0.883088	+	0.383082i
$53$	222455.	+	222455.i	0.205247	+	0.205247i	0.802244	−	0.596997i	$-0.203640\pi$
$53$	222455.	+	222455.i	0.205247	+	0.205247i	−0.596997	+	0.802244i	$0.703640\pi$
$54$	1.78845e6	+	340338.i	1.54560	+	0.294125i
$55$	213821.	+	362942.i	0.173293	+	0.294149i
$56$	837607.	−	1.32377e6i	0.637356	−	1.00729i
$57$	87136.1	−	87136.1i	0.0623213	−	0.0623213i
$58$	−534549.	−	785811.i	−0.359741	−	0.528835i
$59$	2.00202e6			1.26907			0.634537	−	0.772892i	$-0.281191\pi$
$59$	2.00202e6			1.26907			0.634537	+	0.772892i	$0.281191\pi$
$60$	2.31194e6	+	1.68251e6i	1.38181	+	1.00561i
$61$	−2.52056e6			−1.42182			−0.710908	−	0.703285i	$-0.751716\pi$
$61$	−2.52056e6			−1.42182			−0.710908	+	0.703285i	$0.751716\pi$
$62$	−1.93369e6	−	2.84261e6i	−1.03042	−	1.51477i
$63$	−3.21288e6	+	3.21288e6i	−1.61884	+	1.61884i
$64$	−1.89516e6	+	897997.i	−0.903685	+	0.428198i
$65$	2.06344e6	+	533497.i	0.931953	+	0.240954i
$66$	1.33869e6	+	254751.i	0.573162	+	0.109072i
$67$	291345.	+	291345.i	0.118344	+	0.118344i	0.763799	−	0.645455i	$-0.223332\pi$
$67$	291345.	+	291345.i	0.118344	+	0.118344i	−0.645455	+	0.763799i	$0.723332\pi$
$68$	−207149.	−	477525.i	−0.0798917	−	0.184168i
$69$		−	5.57223e6i		−	2.04201i
$70$	−3.21992e6	+	1.15476e6i	−1.12202	+	0.402390i
$71$		−	1.18847e6i		−	0.394078i	−0.980396	−	0.197039i	$-0.936867\pi$
$71$		−	1.18847e6i		−	0.394078i	0.980396	−	0.197039i	$-0.0631326\pi$
$72$	5.93457e6	−	1.33487e6i	1.87381	−	0.421479i
$73$	−3.12091e6	−	3.12091e6i	−0.938970	−	0.938970i	0.0592721	−	0.998242i	$-0.481122\pi$
$73$	−3.12091e6	−	3.12091e6i	−0.938970	−	0.938970i	−0.998242	+	0.0592721i	$0.981122\pi$
$74$	−520787.	+	2.73669e6i	−0.149399	+	0.785081i
$75$	−1.72182e6	−	6.00175e6i	−0.471275	−	1.64272i
$76$	72489.6	−	183566.i	0.0189421	−	0.0479672i
$77$	−1.15277e6	+	1.15277e6i	−0.287755	+	0.287755i
$78$	5.70073e6	−	3.87793e6i	1.36019	−	0.925271i
$79$	−82028.3			−0.0187184			−0.00935920	−	0.999956i	$-0.502979\pi$
$79$	−82028.3			−0.0187184			−0.00935920	+	0.999956i	$0.502979\pi$
$80$	4.46928e6	+	998517.i	0.975939	+	0.218042i
$81$	−3.67420e6			−0.768185
$82$	−1.07374e6	+	730415.i	−0.215056	+	0.146292i
$83$	466272.	−	466272.i	0.0895088	−	0.0895088i	−0.660935	−	0.750443i	$-0.729840\pi$
$83$	466272.	−	466272.i	0.0895088	−	0.0895088i	0.750443	+	0.660935i	$0.229840\pi$
$84$	−4.06449e6	+	1.02925e7i	−0.748218	+	1.89472i
$85$	−284519.	+	1.10045e6i	−0.0502511	+	0.194359i
$86$	−1.75269e6	+	9.21025e6i	−0.297140	+	1.56144i
$87$	4.74728e6	+	4.74728e6i	0.772907	+	0.772907i
$88$	2.12929e6	−	478945.i	0.333078	−	0.0749197i
$89$		−	2.67579e6i		−	0.402334i	−0.979557	−	0.201167i	$-0.935527\pi$
$89$		−	2.67579e6i		−	0.402334i	0.979557	−	0.201167i	$-0.0644735\pi$
$90$	−1.20117e7	−	5.67040e6i	−1.73683	−	0.819908i
$91$			8.24830e6i			1.14741i
$92$	−3.55159e6	−	8.18720e6i	−0.475516	−	1.09617i
$93$	1.71729e7	+	1.71729e7i	2.21388	+	2.21388i
$94$	2.53549e6	+	482500.i	0.314858	+	0.0599169i
$95$	−371321.	+	218757.i	−0.0444341	+	0.0261776i
$96$	1.19658e7	−	8.73445e6i	1.38035	−	1.00760i
$97$	−6.84970e6	+	6.84970e6i	−0.762027	+	0.762027i	−0.976689	−	0.214661i	$-0.931135\pi$
$97$	−6.84970e6	+	6.84970e6i	−0.762027	+	0.762027i	0.214661	+	0.976689i	$0.431135\pi$
$98$	−2.20550e6	−	3.24219e6i	−0.236710	−	0.347974i
$99$	−6.33039e6			−0.655703
$100$	−6.35520e6	−	7.72084e6i	−0.635520	−	0.772084i
$101$	−4.35613e6			−0.420703			−0.210352	−	0.977626i	$-0.567461\pi$
$101$	−4.35613e6			−0.420703			−0.210352	+	0.977626i	$0.567461\pi$
$102$	2.06814e6	+	3.04026e6i	0.192965	+	0.283668i
$103$	9.95053e6	−	9.95053e6i	0.897255	−	0.897255i	−0.0979373	−	0.995193i	$-0.531224\pi$
$103$	9.95053e6	−	9.95053e6i	0.897255	−	0.897255i	0.995193	+	0.0979373i	$0.0312245\pi$
$104$	5.90431e6	−	9.33128e6i	0.514698	−	0.813438i
$105$	2.08199e7	−	1.22657e7i	1.75516	−	1.03402i
$106$	−3.49653e6	−	665383.i	−0.285146	−	0.0542627i
$107$	−1.98257e6	−	1.98257e6i	−0.156453	−	0.156453i	0.624540	−	0.780993i	$-0.285287\pi$
$107$	−1.98257e6	−	1.98257e6i	−0.156453	−	0.156453i	−0.780993	+	0.624540i	$0.785287\pi$
$108$	−1.88958e7	+	8.19694e6i	−1.44338	+	0.626136i
$109$		−	7.41131e6i		−	0.548154i	−0.961708	−	0.274077i	$-0.911628\pi$
$109$		−	7.41131e6i		−	0.548154i	0.961708	−	0.274077i	$-0.0883723\pi$
$110$	−4.30974e6	−	2.03451e6i	−0.308729	−	0.145742i
$111$		−	1.96792e7i		−	1.36577i
$112$	588286.	+	1.77133e7i	0.0395663	+	1.19134i
$113$	−3.41692e6	−	3.41692e6i	−0.222772	−	0.222772i	0.586893	−	0.809665i	$-0.300351\pi$
$113$	−3.41692e6	−	3.41692e6i	−0.222772	−	0.222772i	−0.809665	+	0.586893i	$0.800351\pi$
$114$	−260632.	+	1.36960e6i	−0.0164764	+	0.0865818i
$115$	−4.87811e6	+	1.88673e7i	−0.299095	+	1.15683i
$116$	1.00009e7	+	3.94932e6i	0.594889	+	0.234920i
$117$	−2.26477e7	+	2.26477e7i	−1.30729	+	1.30729i
$118$	−1.87280e7	+	1.27397e7i	−1.04931	+	0.713794i
$119$	−4.39891e6			−0.239293
$120$	−3.23336e7	−	1.02720e6i	−1.70812	−	0.0542653i
$121$	1.72159e7			0.883446
$122$	2.35786e7	−	1.60394e7i	1.17560	−	0.799703i
$123$	6.48675e6	−	6.48675e6i	0.314311	−	0.314311i
$124$	3.61774e7	+	1.42864e7i	1.70397	+	0.672893i
$125$	575895.	+	2.18290e7i	0.0263729	+	0.999652i
$126$	9.61003e6	−	5.04999e7i	0.427984	−	2.24902i
$127$	−1.38012e7	−	1.38012e7i	−0.597865	−	0.597865i	0.341879	−	0.939744i	$-0.388937\pi$
$127$	−1.38012e7	−	1.38012e7i	−0.597865	−	0.597865i	−0.939744	+	0.341879i	$0.888937\pi$
$128$	1.20140e7	−	2.04600e7i	0.506352	−	0.862327i
$129$		−	6.62298e7i		−	2.71637i
$130$	−2.26973e7	+	8.13990e6i	−0.906092	+	0.324951i
$131$			3.53461e7i			1.37370i	0.726799	+	0.686850i	$0.241007\pi$
$131$			3.53461e7i			1.37370i	−0.726799	+	0.686850i	$0.758993\pi$
$132$	−1.41439e7	+	6.13560e6i	−0.535255	+	0.232192i
$133$	−1.17938e6	−	1.17938e6i	−0.0434683	−	0.0434683i
$134$	−4.57934e6	−	871440.i	−0.164413	−	0.0312875i
$135$	4.35451e7	+	1.12585e7i	1.52325	+	0.393833i
$136$	4.97647e6	+	3.14883e6i	0.169643	+	0.107340i
$137$	−1.56876e7	+	1.56876e7i	−0.521235	+	0.521235i	−0.917944	−	0.396709i	$-0.870152\pi$
$137$	−1.56876e7	+	1.56876e7i	−0.521235	+	0.521235i	0.396709	+	0.917944i	$0.370152\pi$
$138$	3.54585e7	+	5.21255e7i	1.14853	+	1.68839i
$139$	−3.36917e7			−1.06407			−0.532036	−	0.846721i	$-0.678573\pi$
$139$	−3.36917e7			−1.06407			−0.532036	+	0.846721i	$0.678573\pi$
$140$	2.27726e7	−	3.12919e7i	0.701397	−	0.963792i
$141$	−1.82324e7			−0.547744
$142$	7.56271e6	+	1.11175e7i	0.221650	+	0.325836i
$143$	−8.12587e6	+	8.12587e6i	−0.232377	+	0.232377i
$144$	−4.70207e7	+	5.02513e7i	−1.31226	+	1.40242i
$145$	−1.19182e7	−	2.02300e7i	−0.324654	−	0.551071i
$146$	4.90543e7	+	9.33494e6i	1.30449	+	0.248243i
$147$	1.95868e7	+	1.95868e7i	0.508573	+	0.508573i
$148$	−1.25430e7	−	2.89144e7i	−0.318042	−	0.733158i
$149$			5.18105e7i			1.28311i	0.767075	+	0.641557i	$0.221711\pi$
$149$			5.18105e7i			1.28311i	−0.767075	+	0.641557i	$0.778289\pi$
$150$	5.42985e7	+	4.51868e7i	1.31362	+	1.09318i
$151$		−	1.87500e7i		−	0.443182i	−0.975140	−	0.221591i	$-0.928875\pi$
$151$		−	1.87500e7i		−	0.443182i	0.975140	−	0.221591i	$-0.0711249\pi$
$152$	490002.	+	2.17845e6i	0.0113174	+	0.0503148i
$153$	−1.20783e7	−	1.20783e7i	−0.272637	−	0.272637i
$154$	3.44803e6	−	1.81191e7i	0.0760761	−	0.399773i
$155$	−4.31130e7	−	7.31804e7i	−0.929924	−	1.57846i
$156$	−2.86507e7	+	7.25523e7i	−0.604225	+	1.53008i
$157$	3.22414e7	−	3.22414e7i	0.664913	−	0.664913i	−0.291621	−	0.956534i	$-0.594195\pi$
$157$	3.22414e7	−	3.22414e7i	0.664913	−	0.664913i	0.956534	+	0.291621i	$0.0941947\pi$
$158$	767335.	−	521980.i	0.0154769	−	0.0105282i
$159$	2.51431e7			0.496055
$160$	−4.81619e7	+	1.90993e7i	−0.929574	+	0.368635i
$161$	−7.54197e7			−1.42428
$162$	3.43704e7	−	2.33805e7i	0.635158	−	0.432067i
$163$	1.50508e7	−	1.50508e7i	0.272210	−	0.272210i	−0.557779	−	0.829989i	$-0.688346\pi$
$163$	1.50508e7	−	1.50508e7i	0.272210	−	0.272210i	0.829989	+	0.557779i	$0.188346\pi$
$164$	5.39641e6	−	1.36654e7i	0.0955325	−	0.241918i
$165$	3.25945e7	+	8.42724e6i	0.564873	+	0.146047i
$166$	−1.39466e6	+	7.32883e6i	−0.0236641	+	0.124353i
$167$	2.67334e7	+	2.67334e7i	0.444168	+	0.444168i	0.893410	−	0.449242i	$-0.148306\pi$
$167$	2.67334e7	+	2.67334e7i	0.444168	+	0.444168i	−0.449242	+	0.893410i	$0.648306\pi$
$168$	−2.74744e7	−	1.22146e8i	−0.447039	−	1.98745i
$169$		−	4.60601e6i		−	0.0734043i
$170$	−4.34109e6	−	1.21047e7i	−0.0677685	−	0.188966i
$171$		−	6.47654e6i		−	0.0990504i
$172$	−4.22131e7	−	9.73105e7i	−0.632554	−	1.45818i
$173$	1.26039e7	+	1.26039e7i	0.185074	+	0.185074i	0.793562	−	0.608489i	$-0.208224\pi$
$173$	1.26039e7	+	1.26039e7i	0.185074	+	0.185074i	−0.608489	+	0.793562i	$0.708224\pi$
$174$	−7.46174e7	−	1.41995e7i	−1.07379	−	0.204339i
$175$	−8.12331e7	+	2.33047e7i	−1.14578	+	0.328708i
$176$	−1.68708e7	+	1.80299e7i	−0.233260	+	0.249286i
$177$	1.13140e8	−	1.13140e8i	1.53359	−	1.53359i
$178$	1.70272e7	+	2.50307e7i	0.226294	+	0.332662i
$179$	8.53190e7			1.11189			0.555943	−	0.831221i	$-0.312357\pi$
$179$	8.53190e7			1.11189			0.555943	+	0.831221i	$0.312357\pi$
$180$	1.48447e8	−	2.33917e7i	1.89722	−	0.298957i
$181$	7.92693e7			0.993642			0.496821	−	0.867853i	$-0.334501\pi$
$181$	7.92693e7			0.993642			0.496821	+	0.867853i	$0.334501\pi$
$182$	−5.24874e7	−	7.71588e7i	−0.645365	−	0.948715i
$183$	−1.42444e8	+	1.42444e8i	−1.71817	+	1.71817i
$184$	8.53220e7	+	5.39870e7i	1.00971	+	0.638891i
$185$	−1.72278e7	+	6.66329e7i	−0.200045	+	0.773727i
$186$	−2.69923e8	−	5.13658e7i	−3.07570	−	0.585300i
$187$	−4.33361e6	−	4.33361e6i	−0.0484624	−	0.0484624i
$188$	−2.67886e7	+	1.16209e7i	−0.294035	+	0.127552i
$189$			1.74066e8i			1.87541i
$190$	2.08148e6	−	4.40924e6i	0.0220158	−	0.0466365i
$191$		−	3.05453e7i		−	0.317196i	−0.987343	−	0.158598i	$-0.949303\pi$
$191$		−	3.05453e7i		−	0.317196i	0.987343	−	0.158598i	$-0.0506973\pi$
$192$	−5.63528e7	+	1.57850e8i	−0.574594	+	1.60949i
$193$	1.25949e7	+	1.25949e7i	0.126108	+	0.126108i	0.767344	−	0.641236i	$-0.221578\pi$
$193$	1.25949e7	+	1.25949e7i	0.126108	+	0.126108i	−0.641236	+	0.767344i	$0.721578\pi$
$194$	2.04881e7	−	1.07663e8i	0.201463	−	1.05867i
$195$	1.46760e8	−	8.64612e7i	1.41738	−	0.835027i
$196$	4.12628e7	+	1.62945e7i	0.391437	+	0.154577i
$197$	−1.12175e8	+	1.12175e8i	−1.04536	+	1.04536i	−0.0464358	+	0.998921i	$0.514786\pi$
$197$	−1.12175e8	+	1.12175e8i	−1.04536	+	1.04536i	−0.998921	+	0.0464358i	$0.985214\pi$
$198$	5.92177e7	−	4.02829e7i	0.542155	−	0.368801i
$199$	1.93208e8			1.73795			0.868977	−	0.494853i	$-0.164778\pi$
$199$	1.93208e8			1.73795			0.868977	+	0.494853i	$0.164778\pi$
$200$	1.08581e8	+	3.17839e7i	0.959728	+	0.280933i
$201$	3.29295e7			0.286022
$202$	4.07495e7	−	2.77199e7i	0.347850	−	0.236626i
$203$	6.42539e7	−	6.42539e7i	0.539093	−	0.539093i
$204$	−3.86929e7	−	1.52797e7i	−0.319099	−	0.126011i
$205$	−2.76426e7	+	1.62851e7i	−0.224099	+	0.132024i
$206$	−2.97630e7	+	1.56402e8i	−0.237214	+	1.24654i
$207$	−2.07083e8	−	2.07083e8i	−1.62274	−	1.62274i
$208$	4.14684e6	+	1.24861e8i	0.0319518	+	0.962068i
$209$		−	2.32375e6i		−	0.0176067i
$210$	−1.16708e8	+	2.47225e8i	−0.869630	+	1.84215i
$211$			7.77568e6i			0.0569836i	0.999594	+	0.0284918i	$0.00907045\pi$
$211$			7.77568e6i			0.0569836i	−0.999594	+	0.0284918i	$0.990930\pi$
$212$	3.69425e7	−	1.60256e7i	0.266287	−	0.115515i
$213$	−6.71637e7	−	6.71637e7i	−0.476218	−	0.476218i
$214$	3.11619e7	+	5.93005e6i	0.217358	+	0.0413628i
$215$	−5.79797e7	+	2.24251e8i	−0.397870	+	1.53886i
$216$	1.24600e8	−	1.96920e8i	0.841260	−	1.32954i
$217$	2.32434e8	−	2.32434e8i	1.54415	−	1.54415i
$218$	4.71613e7	+	6.93292e7i	0.308310	+	0.453230i
$219$	−3.52744e8			−2.26937
$220$	5.32620e7	−	8.39284e6i	0.337239	−	0.0531410i
$221$	−3.10080e7			−0.193242
$222$	1.25227e8	+	1.84089e8i	0.768179	+	1.12926i
$223$	1.20703e8	−	1.20703e8i	0.728873	−	0.728873i	−0.241523	−	0.970395i	$-0.577647\pi$
$223$	1.20703e8	−	1.20703e8i	0.728873	−	0.728873i	0.970395	+	0.241523i	$0.0776468\pi$
$224$	−1.18220e8	−	1.61955e8i	−0.702785	−	0.962780i
$225$	−2.87034e8	−	1.59056e8i	−1.67994	−	0.930920i
$226$	5.37069e7	+	1.02203e7i	0.309493	+	0.0588959i
$227$	2.18045e8	+	2.18045e8i	1.23724	+	1.23724i	0.961124	+	0.276119i	$0.0890482\pi$
$227$	2.18045e8	+	2.18045e8i	1.23724	+	1.23724i	0.276119	+	0.961124i	$0.410952\pi$
$228$	−6.27725e6	−	1.44704e7i	−0.0350750	−	0.0808556i
$229$			1.16504e8i			0.641085i	0.947234	+	0.320542i	$0.103865\pi$
$229$			1.16504e8i			0.641085i	−0.947234	+	0.320542i	$0.896135\pi$
$230$	−7.44285e7	−	2.07536e8i	−0.403359	−	1.12473i
$231$			1.30292e8i			0.695467i
$232$	−1.18685e8	+	2.66959e7i	−0.624003	+	0.140358i
$233$	−2.20176e8	−	2.20176e8i	−1.14032	−	1.14032i	−0.988392	−	0.151923i	$-0.951453\pi$
$233$	−2.20176e8	−	2.20176e8i	−1.14032	−	1.14032i	−0.151923	−	0.988392i	$-0.548547\pi$
$234$	6.77414e7	−	3.55975e8i	0.345620	−	1.81620i
$235$	6.17342e7	+	1.59613e7i	0.310305	+	0.0802286i
$236$	9.41227e7	−	2.38348e8i	0.466125	−	1.18037i
$237$	−4.63566e6	+	4.63566e6i	−0.0226200	+	0.0226200i
$238$	4.11496e7	−	2.79921e7i	0.197855	−	0.134591i
$239$	−1.41086e8			−0.668484			−0.334242	−	0.942487i	$-0.608480\pi$
$239$	−1.41086e8			−0.668484			−0.334242	+	0.942487i	$0.608480\pi$
$240$	3.09001e8	−	1.96143e8i	1.44285	−	0.915869i
$241$	2.71359e8			1.24877			0.624387	−	0.781115i	$-0.285349\pi$
$241$	2.71359e8			1.24877			0.624387	+	0.781115i	$0.285349\pi$
$242$	−1.61046e8	+	1.09552e8i	−0.730459	+	0.496896i
$243$	4.12054e7	−	4.12054e7i	0.184218	−	0.184218i
$244$	−1.18501e8	+	3.00081e8i	−0.522226	+	1.32244i
$245$	−4.91732e7	−	8.34671e7i	−0.213623	−	0.362605i
$246$	−1.94025e7	+	1.01958e8i	−0.0830968	+	0.436666i
$247$	−8.31347e6	−	8.31347e6i	−0.0351029	−	0.0351029i
$248$	−4.29332e8	+	9.65703e7i	−1.78736	+	0.402034i
$249$		−	5.27007e7i		−	0.216331i
$250$	−1.44294e8	−	2.00535e8i	−0.584062	−	0.811709i
$251$		−	4.74607e7i		−	0.189442i	−0.995504	−	0.0947209i	$-0.969804\pi$
$251$		−	4.74607e7i		−	0.189442i	0.995504	−	0.0947209i	$-0.0301959\pi$
$252$	2.31455e8	+	5.33554e8i	0.911096	+	2.10028i
$253$	−7.43002e7	−	7.43002e7i	−0.288448	−	0.288448i
$254$	2.16926e8	+	4.12806e7i	0.830603	+	0.158062i
$255$	4.61107e7	+	7.82687e7i	0.174145	+	0.295595i
$256$	1.78107e7	+	2.67844e8i	0.0663500	+	0.997796i
$257$	−3.80565e8	+	3.80565e8i	−1.39850	+	1.39850i	−0.594137	+	0.804364i	$0.702506\pi$
$257$	−3.80565e8	+	3.80565e8i	−1.39850	+	1.39850i	−0.804364	+	0.594137i	$0.797494\pi$
$258$	4.21448e8	+	6.19547e8i	1.52783	+	2.24598i
$259$	−2.66356e8			−0.952606
$260$	1.60524e8	−	2.20577e8i	0.566415	−	0.778312i
$261$	3.52849e8			1.22842
$262$	−2.24922e8	−	3.30646e8i	−0.772641	−	1.13582i
$263$	1.39430e8	−	1.39430e8i	0.472618	−	0.472618i	−0.430143	−	0.902761i	$-0.641537\pi$
$263$	1.39430e8	−	1.39430e8i	0.472618	−	0.472618i	0.902761	+	0.430143i	$0.141537\pi$
$264$	9.32660e7	−	1.47399e8i	0.311968	−	0.493039i
$265$	−8.51336e7	−	2.20111e7i	−0.281022	−	0.0726576i
$266$	1.85374e7	+	3.52763e6i	0.0603897	+	0.0114921i
$267$	−1.51217e8	−	1.51217e8i	−0.486195	−	0.486195i
$268$	4.83828e7	−	2.09884e7i	0.153539	−	0.0666050i
$269$			1.64791e8i			0.516179i	0.966121	+	0.258089i	$0.0830929\pi$
$269$			1.64791e8i			0.516179i	−0.966121	+	0.258089i	$0.916907\pi$
$270$	−4.78986e8	+	1.71778e8i	−1.48098	+	0.531123i
$271$		−	5.02355e8i		−	1.53327i	−0.642084	−	0.766635i	$-0.721930\pi$
$271$		−	5.02355e8i		−	1.53327i	0.642084	−	0.766635i	$-0.278070\pi$
$272$	−6.65898e7	+	2.21155e6i	−0.200639	+	0.00666356i
$273$	4.66135e8	+	4.66135e8i	1.38657	+	1.38657i
$274$	4.69230e7	−	2.46576e8i	0.137803	−	0.724143i
$275$	−1.02986e8	−	5.70686e7i	−0.298617	−	0.165475i
$276$	−6.63393e8	−	2.61972e8i	−1.89928	−	0.750020i
$277$	2.39762e8	−	2.39762e8i	0.677798	−	0.677798i	−0.281703	−	0.959502i	$-0.590899\pi$
$277$	2.39762e8	−	2.39762e8i	0.677798	−	0.677798i	0.959502	+	0.281703i	$0.0908994\pi$
$278$	3.15170e8	−	2.14395e8i	0.879807	−	0.598490i
$279$	1.27640e9			3.51863
$280$	−1.39031e7	+	4.37632e8i	−0.0378494	+	1.19139i
$281$	6.89202e7			0.185300			0.0926498	−	0.995699i	$-0.470466\pi$
$281$	6.89202e7			0.185300			0.0926498	+	0.995699i	$0.470466\pi$
$282$	1.70555e8	−	1.16021e8i	0.452891	−	0.308080i
$283$	−2.69464e8	+	2.69464e8i	−0.706722	+	0.706722i	−0.965844	−	0.259123i	$-0.916567\pi$
$283$	−2.69464e8	+	2.69464e8i	−0.706722	+	0.706722i	0.259123	+	0.965844i	$0.416567\pi$
$284$	−1.41491e8	−	5.58743e7i	−0.366534	−	0.144743i
$285$	−8.62180e6	+	3.33470e7i	−0.0220618	+	0.0853297i
$286$	2.43052e7	−	1.27722e8i	0.0614354	−	0.322838i
$287$	−8.77975e7	−	8.77975e7i	−0.219228	−	0.219228i
$288$	1.20086e8	−	7.69288e8i	0.296223	−	1.89765i
$289$			3.93802e8i			0.959699i
$290$	2.40220e8	+	1.13401e8i	0.578385	+	0.273040i
$291$			7.74193e8i			1.84172i
$292$	−5.18281e8	+	2.24829e8i	−1.21822	+	0.528461i
$293$	3.99109e8	+	3.99109e8i	0.926946	+	0.926946i	0.997507	−	0.0705615i	$-0.0224791\pi$
$293$	3.99109e8	+	3.99109e8i	0.926946	+	0.926946i	−0.0705615	+	0.997507i	$0.522479\pi$
$294$	−3.07865e8	−	5.85860e7i	−0.706552	−	0.134455i
$295$	−4.82134e8	+	2.84041e8i	−1.09343	+	0.644176i
$296$	3.01328e8	+	1.90664e8i	0.675333	+	0.427313i
$297$	−1.71482e8	+	1.71482e8i	−0.379814	+	0.379814i
$298$	−3.29692e8	−	4.84662e8i	−0.721691	−	1.06092i
$299$	−5.31635e8			−1.15018
$300$	−7.95478e8	−	7.71762e7i	−1.70100	−	0.165029i
$301$	−8.96414e8			−1.89464
$302$	1.19314e8	+	1.75397e8i	0.249268	+	0.366436i
$303$	−2.46178e8	+	2.46178e8i	−0.508393	+	0.508393i
$304$	−1.84461e7	−	1.72603e7i	−0.0376572	−	0.0352363i
$305$	6.07011e8	−	3.57610e8i	1.22503	−	0.721706i
$306$	1.89845e8	+	3.61272e7i	0.378769	+	0.0720790i
$307$	5.80469e8	+	5.80469e8i	1.14497	+	1.14497i	0.987528	+	0.157444i	$0.0503252\pi$
$307$	5.80469e8	+	5.80469e8i	1.14497	+	1.14497i	0.157444	+	0.987528i	$0.449675\pi$
$308$	8.30447e7	+	1.91436e8i	0.161951	+	0.373334i
$309$		−	1.12467e9i		−	2.16855i
$310$	8.68979e8	+	4.10221e8i	1.65670	+	0.782082i
$311$		−	7.09861e8i		−	1.33817i	−0.743185	−	0.669086i	$-0.766686\pi$
$311$		−	7.09861e8i		−	1.33817i	0.743185	−	0.669086i	$-0.233314\pi$
$312$	−1.93668e8	−	8.61007e8i	−0.361007	−	1.60497i
$313$	−5.67648e7	−	5.67648e7i	−0.104634	−	0.104634i	0.652852	−	0.757486i	$-0.273573\pi$
$313$	−5.67648e7	−	5.67648e7i	−0.104634	−	0.104634i	−0.757486	+	0.652852i	$0.773573\pi$
$314$	−9.64369e7	+	5.06767e8i	−0.175788	+	0.923751i
$315$	3.17903e8	−	1.22957e9i	0.573070	−	2.21650i
$316$	−3.85646e6	+	9.76575e6i	−0.00687518	+	0.0174101i
$317$	5.43385e8	−	5.43385e8i	0.958077	−	0.958077i	−0.0410788	−	0.999156i	$-0.513079\pi$
$317$	5.43385e8	−	5.43385e8i	0.958077	−	0.958077i	0.999156	+	0.0410788i	$0.0130795\pi$
$318$	−2.35202e8	+	1.59996e8i	−0.410153	+	0.279007i
$319$	1.26600e8			0.218357
$320$	3.28995e8	−	4.85139e8i	0.561260	−	0.827640i
$321$	−2.24081e8			−0.378127
$322$	7.05514e8	−	4.79927e8i	1.17763	−	0.801087i
$323$	4.43366e6	−	4.43366e6i	0.00732072	−	0.00732072i
$324$	−1.72738e8	+	4.37426e8i	−0.282151	+	0.714492i
$325$	−5.72614e8	+	1.64276e8i	−0.925274	+	0.265449i
$326$	−4.50185e7	+	2.36568e8i	−0.0719663	+	0.378176i
$327$	−4.18835e8	−	4.18835e8i	−0.662408	−	0.662408i
$328$	3.64777e7	+	1.62172e8i	0.0570780	+	0.253757i
$329$			2.46774e8i			0.382045i
$330$	−3.58532e8	+	1.28580e8i	−0.549198	+	0.196958i
$331$		−	1.62728e8i		−	0.246640i	−0.992367	−	0.123320i	$-0.960646\pi$
$331$		−	1.62728e8i		−	0.246640i	0.992367	−	0.123320i	$-0.0393541\pi$
$332$	−3.35900e7	−	7.74324e7i	−0.0503764	−	0.116129i
$333$	−7.31345e8	−	7.31345e8i	−1.08534	−	1.08534i
$334$	−4.20194e8	−	7.99621e7i	−0.617074	−	0.117428i
$335$	−1.11498e8	−	2.88275e7i	−0.162035	−	0.0418939i
$336$	1.03427e9	+	9.67781e8i	1.48747	+	1.39184i
$337$	−7.42208e8	+	7.42208e8i	−1.05638	+	1.05638i	−0.0580692	+	0.998313i	$0.518494\pi$
$337$	−7.42208e8	+	7.42208e8i	−1.05638	+	1.05638i	−0.998313	+	0.0580692i	$0.981506\pi$
$338$	2.93100e7	+	4.30870e7i	0.0412864	+	0.0606929i
$339$	−3.86200e8			−0.538410
$340$	1.17636e8	+	8.56094e7i	0.162317	+	0.118126i
$341$	4.57967e8			0.625452
$342$	4.12129e7	+	6.05848e7i	0.0557111	+	0.0818979i
$343$	−3.64819e8	+	3.64819e8i	−0.488144	+	0.488144i
$344$	1.01411e9	+	6.41673e8i	1.34317	+	0.849883i
$345$	7.90572e8	+	1.34192e9i	1.03651	+	1.75939i
$346$	−1.98108e8	−	3.76995e7i	−0.257119	−	0.0489294i
$347$	9.42859e8	+	9.42859e8i	1.21142	+	1.21142i	0.970561	+	0.240855i	$0.0774279\pi$
$347$	9.42859e8	+	9.42859e8i	1.21142	+	1.21142i	0.240855	+	0.970561i	$0.422572\pi$
$348$	7.88367e8	−	3.41992e8i	1.00277	−	0.434999i
$349$		−	7.87978e8i		−	0.992259i	−0.868248	−	0.496130i	$-0.834754\pi$
$349$		−	7.87978e8i		−	0.992259i	0.868248	−	0.496130i	$-0.165246\pi$
$350$	6.11599e8	−	7.34925e8i	0.762480	−	0.916230i
$351$			1.22699e9i			1.51449i
$352$	4.30862e7	−	2.76017e8i	0.0526549	−	0.337315i
$353$	−8.69154e8	−	8.69154e8i	−1.05168	−	1.05168i	−0.998590	−	0.0530942i	$-0.983092\pi$
$353$	−8.69154e8	−	8.69154e8i	−1.05168	−	1.05168i	−0.0530942	−	0.998590i	$-0.516908\pi$
$354$	−3.38413e8	+	1.77833e9i	−0.405448	+	2.13059i
$355$	1.68616e8	+	2.86210e8i	0.200032	+	0.339536i
$356$	−3.18562e8	−	1.25799e8i	−0.374213	−	0.147776i
$357$	−2.48595e8	+	2.48595e8i	−0.289170	+	0.289170i
$358$	−7.98117e8	+	5.42920e8i	−0.919340	+	0.625382i
$359$	−5.52377e8			−0.630094			−0.315047	−	0.949076i	$-0.602020\pi$
$359$	−5.52377e8			−0.630094			−0.315047	+	0.949076i	$0.602020\pi$
$360$	−1.23980e9	+	1.16345e9i	−1.40053	+	1.31428i
$361$	−8.91494e8			−0.997340
$362$	−7.41526e8	+	5.04424e8i	−0.821573	+	0.558876i
$363$	9.72918e8	−	9.72918e8i	1.06759	−	1.06759i
$364$	9.81988e8	+	3.87784e8i	1.06721	+	0.421439i
$365$	1.19437e9	+	3.08803e8i	1.28563	+	0.332397i
$366$	4.26064e8	−	2.23893e9i	0.454246	−	2.38702i
$367$	−2.67409e8	−	2.67409e8i	−0.282387	−	0.282387i	0.551673	−	0.834060i	$-0.313990\pi$
$367$	−2.67409e8	−	2.67409e8i	−0.282387	−	0.282387i	−0.834060	+	0.551673i	$0.813990\pi$
$368$	−1.14169e9	+	3.79173e7i	−1.19421	+	0.0396616i
$369$		−	4.82138e8i		−	0.499550i
$370$	−2.62856e8	−	7.32946e8i	−0.269781	−	0.752257i
$371$		−	3.40310e8i		−	0.345992i
$372$	2.85186e9	−	1.23713e9i	2.87228	−	1.24599i
$373$	8.17059e8	+	8.17059e8i	0.815216	+	0.815216i	0.985411	−	0.170194i	$-0.0544396\pi$
$373$	8.17059e8	+	8.17059e8i	0.815216	+	0.815216i	−0.170194	+	0.985411i	$0.554440\pi$
$374$	6.81154e7	+	1.29622e7i	0.0673279	+	0.0128124i
$375$	1.26617e9	+	1.20107e9i	1.23988	+	1.17614i
$376$	1.76646e8	−	2.79175e8i	0.171375	−	0.270844i
$377$	4.52928e8	−	4.52928e8i	0.435346	−	0.435346i
$378$	−1.10765e9	−	1.62830e9i	−1.05483	−	1.55065i
$379$	−2.56945e8			−0.242439			−0.121219	−	0.992626i	$-0.538680\pi$
$379$	−2.56945e8			−0.242439			−0.121219	+	0.992626i	$0.538680\pi$
$380$	8.58660e6	+	5.44916e7i	0.00802747	+	0.0509433i
$381$	−1.55989e9			−1.44496
$382$	1.94372e8	+	2.85736e8i	0.178407	+	0.262267i
$383$	−4.30631e8	+	4.30631e8i	−0.391660	+	0.391660i	−0.875279	−	0.483619i	$-0.839322\pi$
$383$	−4.30631e8	+	4.30631e8i	−0.391660	+	0.391660i	0.483619	+	0.875279i	$0.339322\pi$
$384$	−4.77310e8	−	1.83520e9i	−0.430171	−	1.65396i
$385$	1.14062e8	−	4.41164e8i	0.101866	−	0.393992i
$386$	−1.97965e8	−	3.76724e7i	−0.175200	−	0.0333401i
$387$	−2.46132e9	−	2.46132e9i	−2.15864	−	2.15864i
$388$	4.93450e8	+	1.13751e9i	0.428876	+	0.988654i
$389$		−	5.65314e8i		−	0.486929i	−0.969910	−	0.243465i	$-0.921716\pi$
$389$		−	5.65314e8i		−	0.486929i	0.969910	−	0.243465i	$-0.0782840\pi$
$390$	−8.22680e8	+	1.74270e9i	−0.702271	+	1.48763i
$391$		−	2.83527e8i		−	0.239870i
$392$	−4.89682e8	+	1.10145e8i	−0.410594	+	0.0923555i
$393$	1.99751e9	+	1.99751e9i	1.66003	+	1.66003i
$394$	3.35526e8	−	1.76316e9i	0.276369	−	1.45230i
$395$	1.97543e7	−	1.16379e7i	0.0161277	−	0.00950136i
$396$	−2.97616e8	+	7.53654e8i	−0.240837	+	0.609872i
$397$	3.36139e8	−	3.36139e8i	0.269620	−	0.269620i	−0.559327	−	0.828947i	$-0.688940\pi$
$397$	3.36139e8	−	3.36139e8i	0.269620	−	0.269620i	0.828947	+	0.559327i	$0.188940\pi$
$398$	−1.80736e9	+	1.22946e9i	−1.43699	+	0.977516i
$399$	−1.33300e8			−0.105057
$400$	−1.21797e9	+	3.93622e8i	−0.951542	+	0.307517i
$401$	1.06888e9			0.827795			0.413898	−	0.910323i	$-0.364167\pi$
$401$	1.06888e9			0.827795			0.413898	+	0.910323i	$0.364167\pi$
$402$	−3.08039e8	+	2.09544e8i	−0.236491	+	0.160873i
$403$	1.63843e9	−	1.63843e9i	1.24698	−	1.24698i
$404$	−2.04798e8	+	5.18612e8i	−0.154522	+	0.391298i
$405$	8.84834e8	−	5.21285e8i	0.661865	−	0.389927i
$406$	−1.92190e8	+	1.00994e9i	−0.142524	+	0.748952i
$407$	−2.62403e8	−	2.62403e8i	−0.192925	−	0.192925i
$408$	4.59184e8	−	1.03285e8i	0.334716	−	0.0752881i
$409$			6.73733e8i			0.486918i	0.969911	+	0.243459i	$0.0782822\pi$
$409$			6.73733e8i			0.486918i	−0.969911	+	0.243459i	$0.921718\pi$
$410$	1.54953e8	−	3.28241e8i	0.111034	−	0.235206i
$411$			1.77310e9i			1.25976i
$412$	−7.16832e8	−	1.65246e9i	−0.504983	−	1.16410i
$413$	−1.53134e9	−	1.53134e9i	−1.06966	−	1.06966i
$414$	3.25491e9	+	6.19404e8i	2.25444	+	0.429015i
$415$	−4.61359e7	+	1.78442e8i	−0.0316862	+	0.122555i
$416$	−8.33336e8	−	1.14163e9i	−0.567536	−	0.777495i
$417$	−1.90402e9	+	1.90402e9i	−1.28586	+	1.28586i
$418$	1.47870e7	+	2.17375e7i	0.00990290	+	0.0145577i
$419$	1.73896e9			1.15489			0.577444	−	0.816430i	$-0.304050\pi$
$419$	1.73896e9			1.15489			0.577444	+	0.816430i	$0.304050\pi$
$420$	−4.81450e8	−	3.05534e9i	−0.317087	−	2.01227i
$421$	1.01837e8			0.0665149			0.0332574	−	0.999447i	$-0.489412\pi$
$421$	1.01837e8			0.0665149			0.0332574	+	0.999447i	$0.489412\pi$
$422$	−4.94799e7	−	7.27377e7i	−0.0320506	−	0.0471158i
$423$	−6.77578e8	+	6.77578e8i	−0.435279	+	0.435279i
$424$	−2.43601e8	+	3.84992e8i	−0.155203	+	0.245285i
$425$	−8.76099e7	−	3.05381e8i	−0.0553594	−	0.192966i
$426$	1.05567e9	+	2.00893e8i	0.661601	+	0.125901i
$427$	1.92797e9	+	1.92797e9i	1.19840	+	1.19840i
$428$	−3.29239e8	+	1.42823e8i	−0.202983	+	0.0880534i
$429$			9.18433e8i			0.561626i
$430$	−8.84633e8	−	2.46671e9i	−0.536566	−	1.49616i
$431$		−	1.05149e9i		−	0.632608i	−0.948658	−	0.316304i	$-0.897558\pi$
$431$		−	1.05149e9i		−	0.632608i	0.948658	−	0.316304i	$-0.102442\pi$
$432$	8.75117e7	+	2.63497e9i	0.0522244	+	1.57247i
$433$	1.57285e9	+	1.57285e9i	0.931066	+	0.931066i	0.997773	−	0.0667064i	$-0.0212491\pi$
$433$	1.57285e9	+	1.57285e9i	0.931066	+	0.931066i	−0.0667064	+	0.997773i	$0.521249\pi$
$434$	−6.95231e8	+	3.65338e9i	−0.408239	+	2.14526i
$435$	−1.81678e9	−	4.69726e8i	−1.05826	−	0.273610i
$436$	−8.82342e8	−	3.48434e8i	−0.509840	−	0.201334i
$437$	7.60156e7	−	7.60156e7i	0.0435730	−	0.0435730i
$438$	3.29974e9	−	2.24466e9i	1.87638	−	1.27641i
$439$	−1.94914e9			−1.09956			−0.549779	−	0.835310i	$-0.685288\pi$
$439$	−1.94914e9			−1.09956			−0.549779	+	0.835310i	$0.685288\pi$
$440$	−4.44833e8	+	4.17439e8i	−0.248950	+	0.233619i
$441$	1.45582e9			0.808302
$442$	2.90065e8	−	1.97317e8i	0.159778	−	0.108689i
$443$	−9.13886e8	+	9.13886e8i	−0.499435	+	0.499435i	−0.911262	−	0.411827i	$-0.864891\pi$
$443$	−9.13886e8	+	9.13886e8i	−0.499435	+	0.499435i	0.411827	+	0.911262i	$0.364891\pi$
$444$	−2.34288e9	−	9.25194e8i	−1.27031	−	0.501640i
$445$	3.79633e8	+	6.44393e8i	0.204223	+	0.346650i
$446$	−3.61034e8	+	1.89720e9i	−0.192698	+	1.01261i
$447$	2.92796e9	+	2.92796e9i	1.55056	+	1.55056i
$448$	2.13648e9	+	7.62730e8i	1.12260	+	0.400772i
$449$		−	6.50526e8i		−	0.339158i	−0.985517	−	0.169579i	$-0.945759\pi$
$449$		−	6.50526e8i		−	0.339158i	0.985517	−	0.169579i	$-0.0542408\pi$
$450$	3.69720e9	−	3.38621e8i	1.91262	−	0.175174i
$451$		−	1.72989e8i		−	0.0887973i
$452$	−5.67438e8	+	2.46153e8i	−0.289024	+	0.125378i
$453$	−1.05962e9	−	1.05962e9i	−0.535556	−	0.535556i
$454$	−3.42721e9	−	6.52192e8i	−1.71888	−	0.327099i
$455$	−1.17024e9	−	1.98638e9i	−0.582421	−	0.988606i
$456$	1.50802e8	+	9.54192e7i	0.0744784	+	0.0471258i
$457$	6.75864e8	−	6.75864e8i	0.331248	−	0.331248i	−0.521813	−	0.853060i	$-0.674744\pi$
$457$	6.75864e8	−	6.75864e8i	0.331248	−	0.331248i	0.853060	+	0.521813i	$0.174744\pi$
$458$	−7.41362e8	−	1.08983e9i	−0.360579	−	0.530068i
$459$	−6.54369e8			−0.315848
$460$	2.01688e9	+	1.46778e9i	0.966113	+	0.703087i
$461$	−2.31119e7			−0.0109871			−0.00549354	−	0.999985i	$-0.501749\pi$
$461$	−2.31119e7			−0.0109871			−0.00549354	+	0.999985i	$0.501749\pi$
$462$	−8.29104e8	−	1.21882e9i	−0.391167	−	0.575033i
$463$	1.79107e9	−	1.79107e9i	0.838646	−	0.838646i	−0.150035	−	0.988681i	$-0.547939\pi$
$463$	1.79107e9	−	1.79107e9i	0.838646	−	0.838646i	0.988681	+	0.150035i	$0.0479386\pi$
$464$	9.40360e8	−	1.00497e9i	0.437000	−	0.467024i
$465$	−6.57208e9	−	1.69920e9i	−3.03122	−	0.783715i
$466$	3.46072e9	+	6.58568e8i	1.58422	+	0.301474i
$467$	−2.93612e8	−	2.93612e8i	−0.133403	−	0.133403i	0.637253	−	0.770655i	$-0.280071\pi$
$467$	−2.93612e8	−	2.93612e8i	−0.133403	−	0.133403i	−0.770655	+	0.637253i	$0.780071\pi$
$468$	1.63153e9	+	3.76104e9i	0.735757	+	1.69608i
$469$		−	4.45697e8i		−	0.199496i
$470$	−6.79062e8	+	2.43531e8i	−0.301694	+	0.108196i
$471$		−	3.64411e9i		−	1.60701i
$472$	6.36234e8	+	2.82857e9i	0.278496	+	1.23814i
$473$	−8.83108e8	−	8.83108e8i	−0.383707	−	0.383707i
$474$	1.38657e7	−	7.28629e7i	0.00598022	−	0.0314255i
$475$	5.83861e7	−	1.05364e8i	0.0249967	−	0.0451091i
$476$	−2.06809e8	+	5.23705e8i	−0.0878913	+	0.222568i
$477$	9.34403e8	−	9.34403e8i	0.394203	−	0.394203i
$478$	1.31979e9	−	8.97788e8i	0.552722	−	0.375990i
$479$	2.59661e9			1.07952			0.539762	−	0.841818i	$-0.318514\pi$
$479$	2.59661e9			1.07952			0.539762	+	0.841818i	$0.318514\pi$
$480$	−1.64242e9	+	3.80113e9i	−0.677858	+	1.56880i
$481$	−1.87755e9			−0.769279
$482$	−2.53843e9	+	1.72677e9i	−1.03252	+	0.702376i
$483$	−4.26218e9	+	4.26218e9i	−1.72114	+	1.72114i
$484$	8.09383e8	−	2.04961e9i	0.324486	−	0.821697i
$485$	6.77753e8	−	2.62138e9i	0.269759	−	1.04336i
$486$	−1.23249e8	+	6.47663e8i	−0.0487031	+	0.255931i
$487$	−2.18041e9	−	2.18041e9i	−0.855434	−	0.855434i	0.135362	−	0.990796i	$-0.456780\pi$
$487$	−2.18041e9	−	2.18041e9i	−0.855434	−	0.855434i	−0.990796	+	0.135362i	$0.956780\pi$
$488$	−8.01023e8	−	3.56119e9i	−0.312015	−	1.38716i
$489$		−	1.70113e9i		−	0.657896i
$490$	9.91128e8	+	4.67884e8i	0.380578	+	0.179660i
$491$			1.10490e9i			0.421249i	0.977567	+	0.210625i	$0.0675498\pi$
$491$			1.10490e9i			0.421249i	−0.977567	+	0.210625i	$0.932450\pi$
$492$	−4.67302e8	−	1.07724e9i	−0.176897	−	0.407787i
$493$	2.41551e8	+	2.41551e8i	0.0907914	+	0.0907914i
$494$	1.30671e8	+	2.48664e7i	0.0487678	+	0.00928043i
$495$	1.52451e9	−	8.98137e8i	0.564951	−	0.332831i
$496$	3.40168e9	−	3.63539e9i	1.25172	−	1.33772i
$497$	−9.09054e8	+	9.09054e8i	−0.332156	+	0.332156i
$498$	3.35357e8	+	4.92990e8i	0.121676	+	0.178869i
$499$	1.43676e9			0.517645			0.258823	−	0.965925i	$-0.416665\pi$
$499$	1.43676e9			0.517645			0.258823	+	0.965925i	$0.416665\pi$
$500$	2.62589e9	+	9.57702e8i	0.939468	+	0.342638i
$501$	3.02157e9			1.07349
$502$	3.02012e8	+	4.43972e8i	0.106552	+	0.156636i
$503$	−9.06558e8	+	9.06558e8i	−0.317620	+	0.317620i	−0.847852	−	0.530232i	$-0.822105\pi$
$503$	−9.06558e8	+	9.06558e8i	−0.317620	+	0.317620i	0.530232	+	0.847852i	$0.322105\pi$
$504$	−5.56037e9	−	3.51830e9i	−1.93463	−	1.22412i
$505$	1.04906e9	−	6.18035e8i	0.362476	−	0.213547i
$506$	1.16785e9	+	2.22239e8i	0.400736	+	0.0762594i
$507$	−2.60299e8	−	2.60299e8i	−0.0887043	−	0.0887043i
$508$	−2.29192e9	+	9.94231e8i	−0.775670	+	0.336484i
$509$			4.48280e9i			1.50673i	0.657600	+	0.753367i	$0.271572\pi$
$509$			4.48280e9i			1.50673i	−0.657600	+	0.753367i	$0.728428\pi$
$510$	−9.29400e8	−	4.38744e8i	−0.310246	−	0.146459i
$511$			4.77435e9i			1.58286i
$512$	−1.87101e9	−	2.39221e9i	−0.616073	−	0.787689i
$513$	−1.75441e8	−	1.75441e8i	−0.0573747	−	0.0573747i
$514$	1.13830e9	−	5.98169e9i	0.369733	−	1.94291i
$515$	−9.84569e8	+	3.80807e9i	−0.317630	+	1.22851i
$516$	−7.88488e9	−	3.11371e9i	−2.52651	−	0.997711i
$517$	−2.43111e8	+	2.43111e8i	−0.0773728	+	0.0773728i
$518$	2.49163e9	−	1.69494e9i	0.787643	−	0.535795i
$519$	1.42457e9			0.447299
$520$	−9.80033e7	+	3.08488e9i	−0.0305653	+	0.962113i
$521$	6.17104e9			1.91173			0.955864	−	0.293808i	$-0.0949228\pi$
$521$	6.17104e9			1.91173			0.955864	+	0.293808i	$0.0949228\pi$
$522$	−3.30073e9	+	2.24533e9i	−1.01570	+	0.690928i
$523$	−1.76096e8	+	1.76096e8i	−0.0538261	+	0.0538261i	−0.733507	−	0.679681i	$-0.762118\pi$
$523$	−1.76096e8	+	1.76096e8i	−0.0538261	+	0.0538261i	0.679681	+	0.733507i	$0.262118\pi$
$524$	4.20807e9	+	1.66175e9i	1.27769	+	0.504554i
$525$	−3.27370e9	+	5.90773e9i	−0.987374	+	1.78182i
$526$	−4.17048e8	+	2.19155e9i	−0.124950	+	0.656600i
$527$	8.73792e8	+	8.73792e8i	0.260059	+	0.260059i
$528$	6.55045e7	+	1.97234e9i	0.0193666	+	0.583126i
$529$		−	1.45626e9i		−	0.427706i
$530$	9.36449e8	−	3.35837e8i	0.273224	−	0.0979859i
$531$		−	8.40933e9i		−	2.43742i
$532$	−1.95856e8	+	8.49619e7i	−0.0563958	+	0.0244644i
$533$	−6.18887e8	−	6.18887e8i	−0.177038	−	0.177038i
$534$	2.37681e9	+	4.52303e8i	0.675462	+	0.128539i
$535$	7.58730e8	+	1.96168e8i	0.214214	+	0.0553847i
$536$	−3.19040e8	+	5.04216e8i	−0.0894887	+	0.141429i
$537$	4.82162e9	−	4.82162e9i	1.34364	−	1.34364i
$538$	−1.04863e9	−	1.54154e9i	−0.290326	−	0.426792i
$539$	5.22342e8			0.143679
$540$	3.38758e9	−	4.65489e9i	0.925789	−	1.27213i
$541$	−1.39504e9			−0.378788			−0.189394	−	0.981901i	$-0.560652\pi$
$541$	−1.39504e9			−0.378788			−0.189394	+	0.981901i	$0.560652\pi$
$542$	3.19670e9	+	4.69929e9i	0.862390	+	1.26775i
$543$	4.47974e9	−	4.47974e9i	1.20075	−	1.20075i
$544$	6.08842e8	−	4.44427e8i	0.162147	−	0.118360i
$545$	1.05150e9	+	1.78482e9i	0.278240	+	0.472287i
$546$	−7.32668e9	−	1.39425e9i	−1.92634	−	0.366579i
$547$	−3.54493e9	−	3.54493e9i	−0.926087	−	0.926087i	0.0713638	−	0.997450i	$-0.477265\pi$
$547$	−3.54493e9	−	3.54493e9i	−0.926087	−	0.926087i	−0.997450	+	0.0713638i	$0.977265\pi$
$548$	1.13013e9	+	2.60519e9i	0.293356	+	0.676251i
$549$			1.05874e10i			2.73078i
$550$	1.32654e9	−	1.21496e8i	0.339977	−	0.0311380i
$551$			1.29523e8i			0.0329850i
$552$	7.87276e9	−	1.77083e9i	1.99223	−	0.448116i
$553$	6.27432e7	+	6.27432e7i	0.0157771	+	0.0157771i
$554$	−7.17149e8	+	3.76856e9i	−0.179195	+	0.941653i
$555$	2.79203e9	+	4.73921e9i	0.693257	+	1.17674i
$556$	−1.58398e9	+	4.01111e9i	−0.390829	+	0.989699i
$557$	−1.96493e9	+	1.96493e9i	−0.481785	+	0.481785i	−0.905701	−	0.423916i	$-0.860655\pi$
$557$	−1.96493e9	+	1.96493e9i	−0.481785	+	0.481785i	0.423916	+	0.905701i	$0.360655\pi$
$558$	−1.19401e10	+	8.12230e9i	−2.90931	+	1.97906i
$559$	−6.31884e9			−1.53002
$560$	−2.65478e9	−	4.18230e9i	−0.638807	−	1.00637i
$561$	−4.89810e8			−0.117127
$562$	−6.44715e8	+	4.38568e8i	−0.153211	+	0.104222i
$563$	2.45202e9	−	2.45202e9i	0.579087	−	0.579087i	−0.355564	−	0.934652i	$-0.615711\pi$
$563$	2.45202e9	−	2.45202e9i	0.579087	−	0.579087i	0.934652	+	0.355564i	$0.115711\pi$
$564$	−8.57176e8	+	2.17063e9i	−0.201184	+	0.509459i
$565$	1.30766e9	+	3.38092e8i	0.305017	+	0.0788615i
$566$	8.05993e8	−	4.23542e9i	0.186842	−	0.981836i
$567$	2.81039e9	+	2.81039e9i	0.647478	+	0.647478i
$568$	1.67913e9	−	3.77689e8i	0.384472	−	0.0864799i
$569$			3.14995e9i			0.716821i	0.933564	+	0.358410i	$0.116681\pi$
$569$			3.14995e9i			0.716821i	−0.933564	+	0.358410i	$0.883319\pi$
$570$	−1.31548e8	−	3.66809e8i	−0.0297525	−	0.0829618i
$571$			3.35692e9i			0.754597i	0.926092	+	0.377299i	$0.123147\pi$
$571$			3.35692e9i			0.754597i	−0.926092	+	0.377299i	$0.876853\pi$
$572$	5.85384e8	+	1.34944e9i	0.130784	+	0.301486i
$573$	−1.72620e9	−	1.72620e9i	−0.383310	−	0.383310i
$574$	1.38000e9	+	2.62611e8i	0.304569	+	0.0579589i
$575$	−1.50208e9	−	5.23579e9i	−0.329500	−	1.14854i
$576$	3.77196e9	+	7.96047e9i	0.822410	+	1.73564i
$577$	1.65031e9	−	1.65031e9i	0.357644	−	0.357644i	−0.505300	−	0.862944i	$-0.668618\pi$
$577$	1.65031e9	−	1.65031e9i	0.357644	−	0.357644i	0.862944	+	0.505300i	$0.168618\pi$
$578$	−2.50593e9	−	3.68382e9i	−0.539785	−	0.793508i
$579$	1.42354e9			0.304786
$580$	−2.96877e9	+	4.67808e8i	−0.631798	+	0.0995565i
$581$	−7.13300e8			−0.150888
$582$	−4.92651e9	−	7.24220e9i	−1.03588	−	1.52279i
$583$	3.35259e8	−	3.35259e8i	0.0700713	−	0.0700713i
$584$	3.41758e9	−	5.40121e9i	0.710026	−	1.12214i
$585$	2.24091e9	−	8.66728e9i	0.462784	−	1.78994i
$586$	−6.27316e9	−	1.19377e9i	−1.28779	−	0.245064i
$587$	−3.42760e9	−	3.42760e9i	−0.699450	−	0.699450i	0.264842	−	0.964292i	$-0.414680\pi$
$587$	−3.42760e9	−	3.42760e9i	−0.699450	−	0.699450i	−0.964292	+	0.264842i	$0.914680\pi$
$588$	3.25273e9	−	1.41103e9i	0.659823	−	0.286230i
$589$			4.68540e8i			0.0944808i
$590$	2.70266e9	−	5.72509e9i	0.541762	−	1.14763i
$591$			1.26787e10i			2.52649i
$592$	−4.03205e9	+	1.33911e8i	−0.798729	+	0.0265271i
$593$	−5.63976e9	−	5.63976e9i	−1.11063	−	1.11063i	−0.993065	−	0.117564i	$-0.962492\pi$
$593$	−5.63976e9	−	5.63976e9i	−1.11063	−	1.11063i	−0.117564	−	0.993065i	$-0.537508\pi$
$594$	5.12919e8	−	2.69534e9i	0.100414	−	0.527669i
$595$	1.05936e9	−	6.24104e8i	0.206174	−	0.121464i
$596$	6.16821e9	+	2.43581e9i	1.19343	+	0.471282i
$597$	1.09187e10	−	1.09187e10i	2.10020	−	2.10020i
$598$	4.97319e9	−	3.38302e9i	0.951000	−	0.646919i
$599$	−8.53947e9			−1.62344			−0.811721	−	0.584045i	$-0.801469\pi$
$599$	−8.53947e9			−1.62344			−0.811721	+	0.584045i	$0.801469\pi$
$600$	7.93241e9	−	4.34001e9i	1.49926	−	0.820279i
$601$	−5.26368e9			−0.989073			−0.494537	−	0.869157i	$-0.664662\pi$
$601$	−5.26368e9			−0.989073			−0.494537	+	0.869157i	$0.664662\pi$
$602$	8.38551e9	−	5.70426e9i	1.56654	−	1.06564i
$603$	1.22377e9	−	1.22377e9i	0.227295	−	0.227295i
$604$	−2.23225e9	−	8.81508e8i	−0.412205	−	0.162779i
$605$	−4.14598e9	+	2.44254e9i	−0.761173	+	0.448432i
$606$	7.36340e8	−	3.86940e9i	0.134408	−	0.706301i
$607$	−1.60860e9	−	1.60860e9i	−0.291937	−	0.291937i	0.545908	−	0.837845i	$-0.316185\pi$
$607$	−1.60860e9	−	1.60860e9i	−0.291937	−	0.291937i	−0.837845	+	0.545908i	$0.816185\pi$
$608$	2.82389e8	+	4.40809e7i	0.0509548	+	0.00795404i
$609$		−	7.26235e9i		−	1.30292i
$610$	−3.40267e9	+	7.20793e9i	−0.606967	+	1.28575i
$611$			1.73952e9i			0.308521i
$612$	−2.00580e9	+	8.70112e8i	−0.353719	+	0.153442i
$613$	5.44978e9	+	5.44978e9i	0.955581	+	0.955581i	0.999055	−	0.0434733i	$-0.0138423\pi$
$613$	5.44978e9	+	5.44978e9i	0.955581	+	0.955581i	−0.0434733	+	0.999055i	$0.513842\pi$
$614$	−9.12377e9	−	1.73624e9i	−1.59069	−	0.302705i
$615$	−6.41840e8	+	2.48248e9i	−0.111266	+	0.430351i
$616$	−1.99503e9	−	1.26235e9i	−0.343888	−	0.217594i
$617$	−7.72051e9	+	7.72051e9i	−1.32327	+	1.32327i	−0.412153	+	0.911115i	$0.635223\pi$
$617$	−7.72051e9	+	7.72051e9i	−1.32327	+	1.32327i	−0.911115	+	0.412153i	$0.864777\pi$
$618$	7.15673e9	+	1.05207e10i	1.21970	+	1.79302i
$619$	1.05166e10			1.78220			0.891101	−	0.453806i	$-0.149934\pi$
$619$	1.05166e10			1.78220			0.891101	+	0.453806i	$0.149934\pi$
$620$	−1.07393e10	+	1.69226e9i	−1.80969	+	0.285165i
$621$	−1.12192e10			−1.87993
$622$	4.51714e9	+	6.64040e9i	0.752657	+	1.10644i
$623$	−2.04670e9	+	2.04670e9i	−0.339115	+	0.339115i
$624$	7.29062e9	+	6.82192e9i	1.20121	+	1.12398i
$625$	−3.23572e9	−	5.17523e9i	−0.530141	−	0.847910i
$626$	8.92225e8	+	1.69789e8i	0.145367	+	0.0276630i
$627$	−1.31322e8	−	1.31322e8i	−0.0212765	−	0.0212765i
$628$	−2.32265e9	−	5.35423e9i	−0.374219	−	0.862657i
$629$		−	1.00132e9i		−	0.160433i
$630$	4.85045e9	+	1.35250e10i	0.772841	+	2.15499i
$631$		−	1.59768e9i		−	0.253155i	−0.991957	−	0.126578i	$-0.959601\pi$
$631$		−	1.59768e9i		−	0.253155i	0.991957	−	0.126578i	$-0.0403993\pi$
$632$	−2.60682e7	−	1.15894e8i	−0.00410773	−	0.0182621i
$633$	4.39426e8	+	4.39426e8i	0.0688610	+	0.0688610i
$634$	−1.62532e9	+	8.54089e9i	−0.253294	+	1.33104i
$635$	5.28172e9	+	1.36558e9i	0.818591	+	0.211645i
$636$	1.18207e9	−	2.99338e9i	0.182199	−	0.461383i
$637$	1.86874e9	−	1.86874e9i	0.286458	−	0.286458i
$638$	−1.18429e9	+	8.05612e8i	−0.180544	+	0.122816i
$639$	−4.99205e9			−0.756878
$640$	9.55723e6	+	6.63177e9i	0.00144113	+	0.999999i
$641$	4.99905e9			0.749695			0.374847	−	0.927087i	$-0.377695\pi$
$641$	4.99905e9			0.749695			0.374847	+	0.927087i	$0.377695\pi$
$642$	2.09617e9	−	1.42592e9i	0.312647	−	0.212678i
$643$	−5.71343e9	+	5.71343e9i	−0.847537	+	0.847537i	−0.989825	−	0.142289i	$-0.954554\pi$
$643$	−5.71343e9	+	5.71343e9i	−0.847537	+	0.847537i	0.142289	+	0.989825i	$0.454554\pi$
$644$	−3.54576e9	+	8.97896e9i	−0.523130	+	1.32472i
$645$	9.39648e9	+	1.59497e10i	1.37882	+	2.34042i
$646$	−1.32615e7	+	6.96880e7i	−0.00193544	+	0.0101705i
$647$	1.63330e9	+	1.63330e9i	0.237083	+	0.237083i	0.815641	−	0.578558i	$-0.196384\pi$
$647$	1.63330e9	+	1.63330e9i	0.237083	+	0.237083i	−0.578558	+	0.815641i	$0.696384\pi$
$648$	−1.16764e9	−	5.19112e9i	−0.168577	−	0.749460i
$649$		−	3.01722e9i		−	0.433262i
$650$	4.31117e9	−	5.18050e9i	0.615742	−	0.739904i
$651$		−	2.62710e10i		−	3.73201i
$652$	−1.08426e9	−	2.49945e9i	−0.153202	−	0.353165i
$653$	−2.85888e9	−	2.85888e9i	−0.401791	−	0.401791i	0.477073	−	0.878864i	$-0.341698\pi$
$653$	−2.85888e9	−	2.85888e9i	−0.401791	−	0.401791i	−0.878864	+	0.477073i	$0.841698\pi$
$654$	6.58322e9	+	1.25277e9i	0.920272	+	0.175126i
$655$	−5.01480e9	−	8.51217e9i	−0.697283	−	1.18358i
$656$	−1.37320e9	−	1.28492e9i	−0.189920	−	0.177710i
$657$	−1.31091e10	+	1.31091e10i	−1.80341	+	1.80341i
$658$	−1.57033e9	−	2.30845e9i	−0.214882	−	0.315886i
$659$	1.42786e10			1.94351			0.971755	−	0.235991i	$-0.0758336\pi$
$659$	1.42786e10			1.94351			0.971755	+	0.235991i	$0.0758336\pi$
$660$	2.53568e9	−	3.48429e9i	0.343314	−	0.471749i
$661$	−9.21164e8			−0.124060			−0.0620300	−	0.998074i	$-0.519757\pi$
$661$	−9.21164e8			−0.124060			−0.0620300	+	0.998074i	$0.519757\pi$
$662$	1.03550e9	+	1.52224e9i	0.138723	+	0.203929i
$663$	−1.75235e9	+	1.75235e9i	−0.233520	+	0.233520i
$664$	8.06953e8	+	5.10595e8i	0.106970	+	0.0676844i
$665$	4.51349e8	+	1.16695e8i	0.0595164	+	0.0153878i
$666$	1.14952e10	+	2.18752e9i	1.50785	+	0.286941i
$667$	4.14142e9	+	4.14142e9i	0.540391	+	0.540391i
$668$	4.43954e9	−	1.92586e9i	0.576263	−	0.249982i
$669$		−	1.36426e10i		−	1.76159i
$670$	1.22645e9	−	4.39840e8i	0.157539	−	0.0564980i
$671$			3.79871e9i			0.485408i
$672$	−1.58335e10	−	2.47161e9i	−2.01273	−	0.314187i
$673$	2.04546e9	+	2.04546e9i	0.258665	+	0.258665i	0.824511	−	0.565846i	$-0.191450\pi$
$673$	2.04546e9	+	2.04546e9i	0.258665	+	0.258665i	−0.565846	+	0.824511i	$0.691450\pi$
$674$	2.22001e9	−	1.16660e10i	0.279284	−	1.46761i
$675$	−1.20840e10	+	3.46674e9i	−1.51233	+	0.433869i
$676$	−5.48361e8	−	2.16546e8i	−0.0682737	−	0.0269611i
$677$	−2.18593e9	+	2.18593e9i	−0.270755	+	0.270755i	−0.829404	−	0.558649i	$-0.811320\pi$
$677$	−2.18593e9	+	2.18593e9i	−0.270755	+	0.270755i	0.558649	+	0.829404i	$0.311320\pi$
$678$	3.61271e9	−	2.45755e9i	0.445174	−	0.302830i
$679$	1.04786e10			1.28458
$680$	−1.64520e9	−	5.22662e7i	−0.200649	−	0.00637441i
$681$	2.46447e10			2.99025
$682$	−4.28406e9	+	2.91424e9i	−0.517143	+	0.351787i
$683$	−8.29443e9	+	8.29443e9i	−0.996125	+	0.996125i	−0.999993	−	0.00386747i	$-0.998769\pi$
$683$	−8.29443e9	+	8.29443e9i	−0.996125	+	0.996125i	0.00386747	+	0.999993i	$0.498769\pi$
$684$	−7.71053e8	−	3.04487e8i	−0.0921272	−	0.0363808i
$685$	1.55223e9	−	6.00364e9i	0.184518	−	0.713671i
$686$	1.09121e9	−	5.73420e9i	0.129055	−	0.678170i
$687$	6.58396e9	+	6.58396e9i	0.774709	+	0.774709i
$688$	−1.35697e10	+	4.50673e8i	−1.58859	+	0.0527596i
$689$		−	2.39885e9i		−	0.279407i
$690$	−1.59346e10	−	7.52231e9i	−1.84659	−	0.871725i
$691$			9.34640e9i			1.07763i	0.842423	+	0.538817i	$0.181129\pi$
$691$			9.34640e9i			1.07763i	−0.842423	+	0.538817i	$0.818871\pi$
$692$	2.09310e9	−	9.07981e8i	0.240114	−	0.104161i
$693$	4.84209e9	+	4.84209e9i	0.552671	+	0.552671i
$694$	−1.48198e10	−	2.82018e9i	−1.68300	−	0.320272i
$695$	8.11375e9	−	4.78008e9i	0.916801	−	0.540118i
$696$	−5.19855e9	+	8.21587e9i	−0.584453	+	0.923680i
$697$	3.30059e8	−	3.30059e8i	0.0369213	−	0.0369213i
$698$	5.01424e9	+	7.37115e9i	0.558098	+	0.820430i
$699$	−2.48856e10			−2.75599
$700$	−1.04457e9	+	1.07667e10i	−0.115105	+	1.18642i
$701$	−8.52234e9			−0.934428			−0.467214	−	0.884144i	$-0.654742\pi$
$701$	−8.52234e9			−0.934428			−0.467214	+	0.884144i	$0.654742\pi$
$702$	−7.80788e9	−	1.14779e10i	−0.851830	−	1.25223i
$703$	2.68461e8	−	2.68461e8i	0.0291432	−	0.0291432i
$704$	1.35336e9	+	2.85618e9i	0.146187	+	0.308518i
$705$	4.39080e9	−	2.58676e9i	0.471934	−	0.278032i
$706$	1.36613e10	+	2.59972e9i	1.46109	+	0.278042i
$707$	3.33199e9	+	3.33199e9i	0.354597	+	0.354597i
$708$	−8.15057e9	−	1.87889e10i	−0.863121	−	1.98968i
$709$			2.61467e9i			0.275521i	0.990466	+	0.137760i	$0.0439904\pi$
$709$			2.61467e9i			0.275521i	−0.990466	+	0.137760i	$0.956010\pi$
$710$	−3.39860e9	−	1.60438e9i	−0.356365	−	0.168230i
$711$			3.44553e8i			0.0359511i
$712$	3.78050e9	−	8.50354e8i	0.392527	−	0.0882917i
$713$	1.49813e10	+	1.49813e10i	1.54787	+	1.54787i
$714$	7.43570e8	−	3.90740e9i	0.0764502	−	0.401739i
$715$	8.04026e8	−	3.10978e9i	0.0822619	−	0.318169i
$716$	4.01117e9	−	1.01575e10i	0.408390	−	1.03417i
$717$	−7.97317e9	+	7.97317e9i	−0.807819	+	0.807819i
$718$	5.16722e9	−	3.51501e9i	0.520980	−	0.354397i
$719$	1.02803e9			0.103147			0.0515734	−	0.998669i	$-0.483576\pi$
$719$	1.02803e9			0.103147			0.0515734	+	0.998669i	$0.483576\pi$
$720$	4.19419e9	−	1.87728e10i	0.418778	−	1.87442i
$721$	−1.52223e10			−1.51254
$722$	8.33949e9	−	5.67295e9i	0.824631	−	0.560956i
$723$	1.53353e10	−	1.53353e10i	1.50906	−	1.50906i
$724$	3.72675e9	−	9.43728e9i	0.364960	−	0.924191i
$725$	5.74034e9	+	3.18094e9i	0.559442	+	0.310008i
$726$	−2.91009e9	+	1.52923e10i	−0.282246	+	1.48318i
$727$	1.76636e9	+	1.76636e9i	0.170494	+	0.170494i	0.787196	−	0.616702i	$-0.211532\pi$
$727$	1.76636e9	+	1.76636e9i	0.170494	+	0.170494i	−0.616702	+	0.787196i	$0.711532\pi$
$728$	−1.16537e10	+	2.62127e9i	−1.11944	+	0.251798i
$729$		−	1.26928e10i		−	1.21342i
$730$	−1.31378e10	+	4.71160e9i	−1.24995	+	0.448269i
$731$		−	3.36991e9i		−	0.319085i
$732$	1.02616e10	+	2.36553e10i	0.967002	+	2.22915i
$733$	1.38263e9	+	1.38263e9i	0.129670	+	0.129670i	0.768963	−	0.639293i	$-0.220773\pi$
$733$	1.38263e9	+	1.38263e9i	0.129670	+	0.129670i	−0.639293	+	0.768963i	$0.720773\pi$
$734$	4.20312e9	+	7.99846e8i	0.392315	+	0.0746569i
$735$	−7.49589e9	−	1.93805e9i	−0.696334	−	0.180036i
$736$	1.04386e10	−	7.61974e9i	0.965099	−	0.704478i
$737$	4.39082e8	−	4.39082e8i	0.0404026	−	0.0404026i
$738$	3.06805e9	+	4.51017e9i	0.280973	+	0.413043i
$739$	−4.87822e9			−0.444637			−0.222318	−	0.974974i	$-0.571362\pi$
$739$	−4.87822e9			−0.444637			−0.222318	+	0.974974i	$0.571362\pi$
$740$	7.12293e9	+	5.18369e9i	0.646171	+	0.470250i
$741$	−9.39637e8			−0.0848392
$742$	2.16553e9	+	3.18343e9i	0.194604	+	0.286076i
$743$	8.99294e9	−	8.99294e9i	0.804342	−	0.804342i	−0.179429	−	0.983771i	$-0.557425\pi$
$743$	8.99294e9	−	8.99294e9i	0.804342	−	0.804342i	0.983771	+	0.179429i	$0.0574249\pi$
$744$	−1.88054e10	+	2.97203e10i	−1.67408	+	2.64574i
$745$	−7.35071e9	−	1.24772e10i	−0.651302	−	1.10553i
$746$	−1.28425e10	−	2.44390e9i	−1.13257	−	0.215525i
$747$	−1.95854e9	−	1.95854e9i	−0.171913	−	0.171913i
$748$	−7.19671e8	+	3.12192e8i	−0.0628750	+	0.0272751i
$749$			3.03292e9i			0.263739i
$750$	−1.94873e10	−	3.17833e9i	−1.68670	−	0.275096i
$751$		−	1.49774e10i		−	1.29032i	−0.764048	−	0.645159i	$-0.776791\pi$
$751$		−	1.49774e10i		−	1.29032i	0.764048	−	0.645159i	$-0.223209\pi$
$752$	1.24066e8	+	3.73562e9i	0.0106387	+	0.320332i
$753$	−2.68214e9	−	2.68214e9i	−0.228928	−	0.228928i
$754$	−1.35475e9	+	7.11909e9i	−0.115096	+	0.604818i
$755$	2.66019e9	+	4.51544e9i	0.224957	+	0.381844i
$756$	2.07231e10	+	8.18349e9i	1.74433	+	0.688831i
$757$	1.00411e10	−	1.00411e10i	0.841292	−	0.841292i	−0.147735	−	0.989027i	$-0.547198\pi$
$757$	1.00411e10	−	1.00411e10i	0.841292	−	0.841292i	0.989027	+	0.147735i	$0.0471984\pi$
$758$	2.40359e9	−	1.63505e9i	0.200456	−	0.136360i
$759$	−8.39784e9			−0.697142
$760$	−4.27076e8	−	4.55102e8i	−0.0352905	−	0.0376064i
$761$	1.23892e9			0.101906			0.0509529	−	0.998701i	$-0.483774\pi$
$761$	1.23892e9			0.101906			0.0509529	+	0.998701i	$0.483774\pi$
$762$	1.45920e10	−	9.92623e9i	1.19474	−	0.812722i
$763$	−5.66889e9	+	5.66889e9i	−0.462021	+	0.462021i
$764$	−3.63652e9	−	1.43605e9i	−0.295025	−	0.116505i
$765$	4.62235e9	+	1.19510e9i	0.373291	+	0.0965137i
$766$	1.28806e9	−	6.76863e9i	0.103546	−	0.544127i
$767$	−1.07945e10	−	1.07945e10i	−0.863808	−	0.863808i
$768$	1.61432e10	+	1.41301e10i	1.28595	+	1.12559i
$769$			1.26329e10i			1.00176i	0.865518	+	0.500878i	$0.166989\pi$
$769$			1.26329e10i			1.00176i	−0.865518	+	0.500878i	$0.833011\pi$
$770$	1.74032e9	+	4.85270e9i	0.137376	+	0.383059i
$771$			4.30136e10i			3.37999i
$772$	2.09159e9	−	9.07328e8i	0.163612	−	0.0709747i
$773$	−1.27546e10	−	1.27546e10i	−0.993202	−	0.993202i	0.00677525	−	0.999977i	$-0.497843\pi$
$773$	−1.27546e10	−	1.27546e10i	−0.993202	−	0.993202i	−0.999977	+	0.00677525i	$0.997843\pi$
$774$	3.86868e10	+	7.36203e9i	2.99895	+	0.570696i
$775$	2.07652e10	+	1.15068e10i	1.60244	+	0.887972i
$776$	−1.18544e10	−	7.50083e9i	−0.910678	−	0.576227i
$777$	−1.50526e10	+	1.50526e10i	−1.15116	+	1.15116i
$778$	3.59733e9	+	5.28824e9i	0.273875	+	0.402608i
$779$	1.76982e8			0.0134137
$780$	−3.39375e9	−	2.15372e10i	−0.256064	−	1.62501i
$781$	−1.79112e9			−0.134538
$782$	1.80420e9	+	2.65225e9i	0.134915	+	0.198331i
$783$	9.55824e9	−	9.55824e9i	0.711560	−	0.711560i
$784$	3.87984e9	−	4.14640e9i	0.287546	−	0.307302i
$785$	−3.19017e9	+	1.23388e10i	−0.235380	+	0.910392i
$786$	−3.13967e10	−	5.97474e9i	−2.30625	−	0.438874i
$787$	−1.13125e10	−	1.13125e10i	−0.827271	−	0.827271i	0.159867	−	0.987139i	$-0.448893\pi$
$787$	−1.13125e10	−	1.13125e10i	−0.827271	−	0.827271i	−0.987139	+	0.159867i	$0.948893\pi$
$788$	8.08105e9	+	1.86286e10i	0.588336	+	1.35625i
$789$		−	1.57592e10i		−	1.14226i
$790$	−1.10735e8	+	2.34572e8i	−0.00799081	+	0.0169271i
$791$			5.22718e9i			0.375534i
$792$	−2.01177e9	−	8.94392e9i	−0.143893	−	0.639720i
$793$	1.35903e10	+	1.35903e10i	0.967773	+	0.967773i
$794$	−1.00542e9	+	5.28341e9i	−0.0712816	+	0.374578i
$795$	−6.05506e9	+	3.56723e9i	−0.427399	+	0.251795i
$796$	9.08342e9	−	2.30020e10i	0.638342	−	1.61648i
$797$	−6.81864e9	+	6.81864e9i	−0.477083	+	0.477083i	−0.904197	−	0.427115i	$-0.859530\pi$
$797$	−6.81864e9	+	6.81864e9i	−0.477083	+	0.477083i	0.427115	+	0.904197i	$0.359530\pi$
$798$	1.24696e9	−	8.48245e8i	0.0868644	−	0.0590896i
$799$	−9.27703e8			−0.0643421
$800$	8.88877e9	−	1.14326e10i	0.613800	−	0.789462i
$801$	−1.12394e10			−0.772735
$802$	−9.99884e9	+	6.80172e9i	−0.684446	+	0.465595i
$803$	−4.70349e9	+	4.70349e9i	−0.320564	+	0.320564i
$804$	1.54814e9	−	3.92037e9i	0.105054	−	0.266030i
$805$	1.81628e10	−	1.07003e10i	1.22715	−	0.722955i
$806$	−4.90070e9	+	2.57527e10i	−0.329675	+	1.73241i
$807$	9.31281e9	+	9.31281e9i	0.623768	+	0.623768i
$808$	−1.38436e9	−	6.15458e9i	−0.0923227	−	0.410448i
$809$		−	2.33008e10i		−	1.54722i	−0.633664	−	0.773608i	$-0.718450\pi$
$809$		−	2.33008e10i		−	1.54722i	0.633664	−	0.773608i	$-0.281550\pi$
$810$	−4.96004e9	+	1.05069e10i	−0.327935	+	0.694670i
$811$		−	3.99344e8i		−	0.0262890i	−0.999914	−	0.0131445i	$-0.995816\pi$
$811$		−	3.99344e8i		−	0.0262890i	0.999914	−	0.0131445i	$-0.00418414\pi$
$812$	−4.62883e9	−	1.06705e10i	−0.303406	−	0.699419i
$813$	−2.83895e10	−	2.83895e10i	−1.85286	−	1.85286i
$814$	4.12443e9	+	7.84871e8i	0.268027	+	0.0510050i
$815$	−1.48923e9	+	5.75996e9i	−0.0963627	+	0.372707i
$816$	−3.63820e9	+	3.88816e9i	−0.234407	+	0.250512i
$817$	9.03496e8	−	9.03496e8i	0.0579628	−	0.0579628i
$818$	−4.28724e9	−	6.30244e9i	−0.273868	−	0.402599i
$819$	3.46463e10			2.20375
$820$	6.39219e8	+	4.05656e9i	0.0404857	+	0.256927i
$821$	−4.48830e9			−0.283062			−0.141531	−	0.989934i	$-0.545202\pi$
$821$	−4.48830e9			−0.283062			−0.141531	+	0.989934i	$0.545202\pi$
$822$	−1.12830e10	−	1.65865e10i	−0.708553	−	1.04161i
$823$	−9.14288e9	+	9.14288e9i	−0.571720	+	0.571720i	−0.932609	−	0.360889i	$-0.882473\pi$
$823$	−9.14288e9	+	9.14288e9i	−0.571720	+	0.571720i	0.360889	+	0.932609i	$0.382473\pi$
$824$	1.72209e10	+	1.08964e10i	1.07229	+	0.678483i
$825$	−9.04516e9	+	2.59494e9i	−0.560825	+	0.160893i
$826$	2.40695e10	+	4.58038e9i	1.48606	+	0.282795i
$827$	−1.02978e10	−	1.02978e10i	−0.633107	−	0.633107i	0.315739	−	0.948846i	$-0.397748\pi$
$827$	−1.02978e10	−	1.02978e10i	−0.633107	−	0.633107i	−0.948846	+	0.315739i	$0.897748\pi$
$828$	−3.43896e10	+	1.49182e10i	−2.10534	+	0.913290i
$829$			2.68948e10i			1.63956i	0.572680	+	0.819779i	$0.305904\pi$
$829$			2.68948e10i			1.63956i	−0.572680	+	0.819779i	$0.694096\pi$
$830$	−7.03925e8	−	1.96282e9i	−0.0427320	−	0.119154i
$831$		−	2.70992e10i		−	1.63815i
$832$	1.50601e10	+	5.37650e9i	0.906559	+	0.323644i
$833$	9.96618e8	+	9.96618e8i	0.0597408	+	0.0597408i
$834$	5.69509e9	−	2.99272e10i	0.339953	−	1.78643i
$835$	−1.02309e10	−	2.64517e9i	−0.608150	−	0.157236i
$836$	−2.76650e8	−	1.09248e8i	−0.0163760	−	0.00646684i
$837$	3.45762e10	−	3.45762e10i	2.03816	−	2.03816i
$838$	−1.62671e10	+	1.10657e10i	−0.954896	+	0.649569i
$839$	−2.30059e10			−1.34484			−0.672421	−	0.740169i	$-0.734746\pi$
$839$	−2.30059e10			−1.34484			−0.672421	+	0.740169i	$0.734746\pi$
$840$	2.39461e10	+	2.55175e10i	1.39398	+	1.48546i
$841$	1.01933e10			0.590920
$842$	−9.52637e8	+	6.48032e8i	−0.0549965	+	0.0374114i
$843$	3.89488e9	−	3.89488e9i	0.223922	−	0.223922i
$844$	9.25721e8	+	3.65564e8i	0.0530007	+	0.0209298i
$845$	6.53487e8	+	1.10924e9i	0.0372596	+	0.0632449i
$846$	2.02670e9	−	1.06501e10i	0.115078	−	0.604725i
$847$	−1.31684e10	−	1.31684e10i	−0.744628	−	0.744628i
$848$	−1.71091e8	−	5.15154e9i	−0.00963479	−	0.290103i
$849$			3.04564e10i			1.70805i
$850$	2.76282e9	+	2.29919e9i	0.154307	+	0.128413i
$851$		−	1.71677e10i		−	0.954901i
$852$	−1.11537e10	+	4.83844e9i	−0.617845	+	0.268020i
$853$	−8.51772e9	−	8.51772e9i	−0.469896	−	0.469896i	0.431985	−	0.901881i	$-0.357813\pi$
$853$	−8.51772e9	−	8.51772e9i	−0.469896	−	0.469896i	−0.901881	+	0.431985i	$0.857813\pi$
$854$	−3.03037e10	−	5.76674e9i	−1.66492	−	0.316831i
$855$	9.18872e8	+	1.55970e9i	0.0502775	+	0.0853415i
$856$	2.17103e9	−	3.43113e9i	0.118306	−	0.186973i
$857$	5.94649e9	−	5.94649e9i	0.322722	−	0.322722i	−0.527089	−	0.849810i	$-0.676716\pi$
$857$	5.94649e9	−	5.94649e9i	0.322722	−	0.322722i	0.849810	+	0.527089i	$0.176716\pi$
$858$	−5.84438e9	−	8.59149e9i	−0.315888	−	0.464369i
$859$	−1.99099e10			−1.07175			−0.535874	−	0.844298i	$-0.680018\pi$
$859$	−1.99099e10			−1.07175			−0.535874	+	0.844298i	$0.680018\pi$
$860$	2.39720e10	+	1.74456e10i	1.28517	+	0.935278i
$861$	−9.92338e9			−0.529845
$862$	6.69107e9	+	9.83617e9i	0.355812	+	0.523059i
$863$	−9.58522e9	+	9.58522e9i	−0.507650	+	0.507650i	−0.913804	−	0.406154i	$-0.866870\pi$
$863$	−9.58522e9	+	9.58522e9i	−0.507650	+	0.507650i	0.406154	+	0.913804i	$0.366870\pi$
$864$	−1.75861e10	−	2.40920e10i	−0.927621	−	1.27079i
$865$	−4.82353e9	−	1.24711e9i	−0.253401	−	0.0655163i
$866$	−2.47220e10	−	4.70455e9i	−1.29351	−	0.246153i
$867$	2.22549e10	+	2.22549e10i	1.15973	+	1.15973i
$868$	−1.67444e10	−	3.85996e10i	−0.869063	−	2.00338i
$869$			1.23624e8i			0.00639047i
$870$	1.99842e10	−	7.16691e9i	1.02889	−	0.368990i
$871$		−	3.14173e9i		−	0.161104i
$872$	1.04711e10	−	2.35528e9i	0.534792	−	0.120292i
$873$	2.87716e10	+	2.87716e10i	1.46357	+	1.46357i
$874$	−2.27370e8	+	1.19481e9i	−0.0115197	+	0.0605352i
$875$	1.62564e10	−	1.71374e10i	0.820346	−	0.864804i
$876$	−1.65838e10	+	4.19953e10i	−0.833528	+	2.11075i
$877$	2.07047e10	−	2.07047e10i	1.03650	−	1.03650i	0.0371946	−	0.999308i	$-0.488158\pi$
$877$	2.07047e10	−	2.07047e10i	1.03650	−	1.03650i	0.999308	−	0.0371946i	$-0.0118421\pi$
$878$	1.82333e10	−	1.24032e10i	0.909147	−	0.618448i
$879$	4.51096e10			2.24031
$880$	1.50485e9	−	6.73559e9i	0.0744397	−	0.333186i
$881$	1.86740e10			0.920070			0.460035	−	0.887901i	$-0.347837\pi$
$881$	1.86740e10			0.920070			0.460035	+	0.887901i	$0.347837\pi$
$882$	−1.36185e10	+	9.26402e9i	−0.668328	+	0.454631i
$883$	2.68178e10	−	2.68178e10i	1.31087	−	1.31087i	0.390102	−	0.920772i	$-0.372440\pi$
$883$	2.68178e10	−	2.68178e10i	1.31087	−	1.31087i	0.920772	−	0.390102i	$-0.127560\pi$
$884$	−1.45780e9	+	3.69161e9i	−0.0709768	+	0.179735i
$885$	−1.11948e10	+	4.32988e10i	−0.542894	+	2.09978i
$886$	2.73352e9	−	1.43644e10i	0.132040	−	0.693856i
$887$	2.20063e10	+	2.20063e10i	1.05880	+	1.05880i	0.998160	+	0.0606411i	$0.0193145\pi$
$887$	2.20063e10	+	2.20063e10i	1.05880	+	1.05880i	0.0606411	+	0.998160i	$0.480685\pi$
$888$	2.78039e10	−	6.25396e9i	1.33248	−	0.299716i
$889$			2.11129e10i			1.00784i
$890$	−7.65183e9	−	3.61222e9i	−0.363831	−	0.171755i
$891$			5.53734e9i			0.262258i
$892$	−8.69540e9	−	2.00448e10i	−0.410216	−	0.945639i
$893$	−2.48724e8	−	2.48724e8i	−0.0116879	−	0.0116879i
$894$	−4.60215e10	−	8.75780e9i	−2.15417	−	0.409934i
$895$	−2.05468e10	+	1.21048e10i	−0.957996	+	0.564387i
$896$	−2.48393e10	+	6.46035e9i	−1.15362	+	0.300039i
$897$	−3.00442e10	+	3.00442e10i	−1.38991	+	1.38991i
$898$	4.13957e9	+	6.08535e9i	0.190760	+	0.280426i
$899$	−2.55266e10			−1.17175
$900$	−3.24307e10	+	2.66945e10i	−1.48289	+	1.22060i
$901$	1.27933e9			0.0582703
$902$	1.10080e9	+	1.61822e9i	0.0499442	+	0.0734203i
$903$	−5.06589e10	+	5.06589e10i	−2.28954	+	2.28954i
$904$	3.74173e9	−	5.91349e9i	0.168455	−	0.266228i
$905$	−1.90899e10	+	1.12465e10i	−0.856118	+	0.504367i
$906$	1.66550e10	+	3.16941e9i	0.744038	+	0.141589i
$907$	1.48296e10	+	1.48296e10i	0.659938	+	0.659938i	0.955365	−	0.295427i	$-0.0954620\pi$
$907$	1.48296e10	+	1.48296e10i	0.659938	+	0.659938i	−0.295427	+	0.955365i	$0.595462\pi$
$908$	3.62100e10	−	1.57078e10i	1.60520	−	0.696331i
$909$			1.82976e10i			0.808015i
$910$	2.35873e10	+	1.11349e10i	1.03761	+	0.489826i
$911$			4.24472e10i			1.86009i	0.367441	+	0.930047i	$0.380234\pi$
$911$			4.24472e10i			1.86009i	−0.367441	+	0.930047i	$0.619766\pi$
$912$	−2.01787e9	+	6.70168e7i	−0.0880870	+	0.00292551i
$913$	−7.02712e8	−	7.02712e8i	−0.0305583	−	0.0305583i
$914$	−2.02157e9	+	1.06232e10i	−0.0875745	+	0.460196i
$915$	1.40943e10	−	5.45135e10i	0.608235	−	2.35250i
$916$	1.38702e10	+	5.47728e9i	0.596276	+	0.235467i
$917$	2.70361e10	−	2.70361e10i	1.15785	−	1.15785i
$918$	6.12130e9	−	4.16402e9i	0.261153	−	0.177649i
$919$	3.09651e10			1.31604			0.658018	−	0.753002i	$-0.271395\pi$
$919$	3.09651e10			1.31604			0.658018	+	0.753002i	$0.271395\pi$
$920$	−2.82071e10	−	8.96109e8i	−1.19426	−	0.0379405i
$921$	6.56080e10			2.76725
$922$	2.16201e8	−	1.47071e8i	0.00908445	−	0.00617971i
$923$	−6.40794e9	+	6.40794e9i	−0.268233	+	0.268233i
$924$	1.55117e10	+	6.12553e9i	0.646857	+	0.255442i
$925$	−5.30482e9	−	1.84910e10i	−0.220381	−	0.768182i
$926$	−5.35725e9	+	2.81519e10i	−0.221719	+	1.16512i
$927$	−4.17964e10	−	4.17964e10i	−1.72329	−	1.72329i
$928$	−2.40158e9	+	1.53849e10i	−0.0986459	+	0.631941i
$929$		−	2.57183e10i		−	1.05242i	−0.850356	−	0.526208i	$-0.823613\pi$
$929$		−	2.57183e10i		−	1.05242i	0.850356	−	0.526208i	$-0.176387\pi$
$930$	7.22913e10	−	2.59257e10i	2.94711	−	1.05692i
$931$			5.34401e8i			0.0217042i
$932$	−3.65641e10	+	1.58614e10i	−1.47944	+	0.641780i
$933$	−4.01163e10	−	4.01163e10i	−1.61709	−	1.61709i
$934$	4.61497e9	+	8.78220e8i	0.185334	+	0.0352687i
$935$	1.65848e9	+	4.28795e8i	0.0663542	+	0.0171557i
$936$	−3.91952e10	−	2.48006e10i	−1.56231	−	0.988544i
$937$	−1.83197e10	+	1.83197e10i	−0.727496	+	0.727496i	−0.970120	−	0.242625i	$-0.921992\pi$
$937$	−1.83197e10	+	1.83197e10i	−0.727496	+	0.727496i	0.242625	+	0.970120i	$0.421992\pi$
$938$	2.83616e9	+	4.16928e9i	0.112207	+	0.164950i
$939$	−6.41589e9			−0.252887
$940$	4.80260e9	−	6.59927e9i	0.188594	−	0.259148i
$941$	1.85550e10			0.725935			0.362967	−	0.931802i	$-0.381764\pi$
$941$	1.85550e10			0.725935			0.362967	+	0.931802i	$0.381764\pi$
$942$	2.31890e10	+	3.40888e10i	0.903864	+	1.32872i
$943$	5.65889e9	−	5.65889e9i	0.219756	−	0.219756i
$944$	−2.39510e10	−	2.24113e10i	−0.926664	−	0.867090i
$945$	−2.46959e10	−	4.19191e10i	−0.951950	−	1.61585i
$946$	1.38806e10	+	2.64146e9i	0.533078	+	0.101444i
$947$	8.30686e8	+	8.30686e8i	0.0317842	+	0.0317842i	0.722820	−	0.691036i	$-0.242845\pi$
$947$	8.30686e8	+	8.30686e8i	0.0317842	+	0.0317842i	−0.691036	+	0.722820i	$0.742845\pi$
$948$	3.33951e8	+	7.69830e8i	0.0127307	+	0.0293471i
$949$			3.36545e10i			1.27824i
$950$	1.24300e8	+	1.35716e9i	0.00470371	+	0.0513569i
$951$		−	6.14165e10i		−	2.31555i
$952$	−1.39795e9	−	6.21501e9i	−0.0525125	−	0.233460i
$953$	−8.99693e9	−	8.99693e9i	−0.336720	−	0.336720i	0.518411	−	0.855131i	$-0.326524\pi$
$953$	−8.99693e9	−	8.99693e9i	−0.336720	−	0.336720i	−0.855131	+	0.518411i	$0.826524\pi$
$954$	−2.79489e9	+	1.46869e10i	−0.104218	+	0.547659i
$955$	4.33367e9	+	7.35602e9i	0.161007	+	0.273295i
$956$	−6.63298e9	+	1.67967e10i	−0.245531	+	0.621760i
$957$	7.15456e9	−	7.15456e9i	0.263871	−	0.263871i
$958$	−2.42900e10	+	1.65233e10i	−0.892583	+	0.607181i
$959$	2.39987e10			0.878665
$960$	−8.82416e9	−	4.60091e10i	−0.321902	−	1.67839i
$961$	−6.48280e10			−2.35630
$962$	1.75636e10	−	1.19476e10i	0.636063	−	0.432683i
$963$	−8.32761e9	+	8.32761e9i	−0.300489	+	0.300489i
$964$	1.27576e10	−	3.23061e10i	0.458669	−	1.16149i
$965$	−4.82006e9	−	1.24622e9i	−0.172666	−	0.0446424i
$966$	1.27486e10	−	6.69927e10i	0.455032	−	2.39115i
$967$	−1.74125e9	−	1.74125e9i	−0.0619252	−	0.0619252i	0.675466	−	0.737391i	$-0.263943\pi$
$967$	−1.74125e9	−	1.74125e9i	−0.0619252	−	0.0619252i	−0.737391	+	0.675466i	$0.763943\pi$
$968$	5.47112e9	+	2.43235e10i	0.193871	+	0.861911i
$969$		−	5.01118e8i		−	0.0176932i
$970$	1.03409e10	+	2.88346e10i	0.363796	+	1.01441i
$971$		−	3.72931e10i		−	1.30726i	−0.756815	−	0.653629i	$-0.773246\pi$
$971$		−	3.72931e10i		−	1.30726i	0.756815	−	0.653629i	$-0.226754\pi$
$972$	−2.96842e9	−	6.84286e9i	−0.103680	−	0.239004i
$973$	2.57707e10	+	2.57707e10i	0.896873	+	0.896873i
$974$	3.42715e10	+	6.52181e9i	1.18844	+	0.226158i
$975$	−2.30764e10	+	4.16438e10i	−0.797356	+	1.43891i
$976$	3.01545e10	+	2.82159e10i	1.03819	+	0.971449i
$977$	2.32526e10	−	2.32526e10i	0.797701	−	0.797701i	−0.185032	−	0.982733i	$-0.559239\pi$
$977$	2.32526e10	−	2.32526e10i	0.797701	−	0.797701i	0.982733	+	0.185032i	$0.0592388\pi$
$978$	1.08250e10	+	1.59133e10i	0.370035	+	0.543968i
$979$	−4.03265e9			−0.137357
$980$	−1.22489e10	+	1.93013e9i	−0.415723	+	0.0655082i
$981$	−3.11306e10			−1.05280
$982$	−7.03097e9	−	1.03358e10i	−0.236933	−	0.348302i
$983$	2.68650e10	−	2.68650e10i	0.902089	−	0.902089i	−0.0935275	−	0.995617i	$-0.529814\pi$
$983$	2.68650e10	−	2.68650e10i	0.902089	−	0.902089i	0.995617	+	0.0935275i	$0.0298143\pi$
$984$	1.12263e10	+	7.10337e9i	0.375624	+	0.237674i
$985$	1.10993e10	−	4.29295e10i	0.370058	−	1.43129i
$986$	−3.79668e9	−	7.22502e8i	−0.126135	−	0.0240032i
$987$	1.39459e10	+	1.39459e10i	0.461676	+	0.461676i
$988$	−1.38059e9	+	5.98899e8i	−0.0455425	+	0.0197562i
$989$		−	5.77774e10i		−	1.89920i
$990$	−8.54579e9	+	1.81027e10i	−0.279917	+	0.592953i
$991$			4.76758e10i			1.55611i	0.628196	+	0.778055i	$0.283793\pi$
$991$			4.76758e10i			1.55611i	−0.628196	+	0.778055i	$0.716207\pi$
$992$	−8.68753e9	+	5.56536e10i	−0.282557	+	1.81010i
$993$	−9.19620e9	−	9.19620e9i	−0.298048	−	0.298048i
$994$	2.71906e9	−	1.42884e10i	0.0878147	−	0.461458i
$995$	−4.65289e10	+	2.74117e10i	−1.49741	+	0.882176i
$996$	−6.27420e9	−	2.47766e9i	−0.201211	−	0.0794574i
$997$	−2.25636e10	+	2.25636e10i	−0.721066	+	0.721066i	−0.968822	−	0.247756i	$-0.920307\pi$
$997$	−2.25636e10	+	2.25636e10i	−0.721066	+	0.721066i	0.247756	+	0.968822i	$0.420307\pi$
$998$	−1.34402e10	+	9.14271e9i	−0.428005	+	0.291151i
$999$	−3.96224e10			−1.25737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.8.e.b.3.4	✓	36
4.3	odd	2	inner	20.8.e.b.3.6	yes	36
5.2	odd	4	inner	20.8.e.b.7.6	yes	36
5.3	odd	4		100.8.e.e.7.13		36
5.4	even	2		100.8.e.e.43.15		36
20.3	even	4		100.8.e.e.7.15		36
20.7	even	4	inner	20.8.e.b.7.4	yes	36
20.19	odd	2		100.8.e.e.43.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.8.e.b.3.4	✓	36	1.1	even	1	trivial
20.8.e.b.3.6	yes	36	4.3	odd	2	inner
20.8.e.b.7.4	yes	36	20.7	even	4	inner
20.8.e.b.7.6	yes	36	5.2	odd	4	inner
100.8.e.e.7.13		36	5.3	odd	4
100.8.e.e.7.15		36	20.3	even	4
100.8.e.e.43.13		36	20.19	odd	2
100.8.e.e.43.15		36	5.4	even	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.35451 + 6.36342i) q^{2} +(56.5129 - 56.5129i) q^{3} +(47.0138 - 119.053i) q^{4} +(-240.823 + 141.877i) q^{5} +(-169.035 + 888.266i) q^{6} +(-764.897 - 764.897i) q^{7} +(317.795 + 1412.85i) q^{8} -4200.41i q^{9} +O(q^{10})\)	\(q+(-9.35451 + 6.36342i) q^{2} +(56.5129 - 56.5129i) q^{3} +(47.0138 - 119.053i) q^{4} +(-240.823 + 141.877i) q^{5} +(-169.035 + 888.266i) q^{6} +(-764.897 - 764.897i) q^{7} +(317.795 + 1412.85i) q^{8} -4200.41i q^{9} +(1349.96 - 2859.65i) q^{10} -1507.09i q^{11} +(-4071.16 - 9384.94i) q^{12} +(-5391.78 - 5391.78i) q^{13} +(12022.6 + 2287.88i) q^{14} +(-5591.75 + 21627.5i) q^{15} +(-11963.4 - 11194.3i) q^{16} +(2875.49 - 2875.49i) q^{17} +(26729.0 + 39292.8i) q^{18} +1541.88 q^{19} +(5568.91 + 35341.0i) q^{20} -86453.0 q^{21} +(9590.22 + 14098.1i) q^{22} +(49300.6 - 49300.6i) q^{23} +(97804.0 + 61885.0i) q^{24} +(37866.8 - 68334.6i) q^{25} +(84747.6 + 16127.3i) q^{26} +(-113784. - 113784. i) q^{27} +(-127024. + 55102.8i) q^{28} +84003.4i q^{29} +(-85316.8 - 237897. i) q^{30} +303876. i q^{31} +(183146. + 28589.1i) q^{32} +(-85169.8 - 85169.8i) q^{33} +(-8600.86 + 45196.8i) q^{34} +(292726. + 75683.7i) q^{35} +(-500073. - 197477. i) q^{36} +(174112. - 174112. i) q^{37} +(-14423.5 + 9811.63i) q^{38} -609410. q^{39} +(-276984. - 295161. i) q^{40} +114783. q^{41} +(808726. - 550137. i) q^{42} +(585971. - 585971. i) q^{43} +(-179424. - 70853.9i) q^{44} +(595942. + 1.01156e6i) q^{45} +(-147463. + 774903. i) q^{46} +(-161312. - 161312. i) q^{47} +(-1.30871e6 + 43464.3i) q^{48} +346591. i q^{49} +(80616.2 + 880199. i) q^{50} -325005. i q^{51} +(-895397. + 388421. i) q^{52} +(222455. + 222455. i) q^{53} +(1.78845e6 + 340338. i) q^{54} +(213821. + 362942. i) q^{55} +(837607. - 1.32377e6i) q^{56} +(87136.1 - 87136.1i) q^{57} +(-534549. - 785811. i) q^{58} +2.00202e6 q^{59} +(2.31194e6 + 1.68251e6i) q^{60} -2.52056e6 q^{61} +(-1.93369e6 - 2.84261e6i) q^{62} +(-3.21288e6 + 3.21288e6i) q^{63} +(-1.89516e6 + 897997. i) q^{64} +(2.06344e6 + 533497. i) q^{65} +(1.33869e6 + 254751. i) q^{66} +(291345. + 291345. i) q^{67} +(-207149. - 477525. i) q^{68} -5.57223e6i q^{69} +(-3.21992e6 + 1.15476e6i) q^{70} -1.18847e6i q^{71} +(5.93457e6 - 1.33487e6i) q^{72} +(-3.12091e6 - 3.12091e6i) q^{73} +(-520787. + 2.73669e6i) q^{74} +(-1.72182e6 - 6.00175e6i) q^{75} +(72489.6 - 183566. i) q^{76} +(-1.15277e6 + 1.15277e6i) q^{77} +(5.70073e6 - 3.87793e6i) q^{78} -82028.3 q^{79} +(4.46928e6 + 998517. i) q^{80} -3.67420e6 q^{81} +(-1.07374e6 + 730415. i) q^{82} +(466272. - 466272. i) q^{83} +(-4.06449e6 + 1.02925e7i) q^{84} +(-284519. + 1.10045e6i) q^{85} +(-1.75269e6 + 9.21025e6i) q^{86} +(4.74728e6 + 4.74728e6i) q^{87} +(2.12929e6 - 478945. i) q^{88} -2.67579e6i q^{89} +(-1.20117e7 - 5.67040e6i) q^{90} +8.24830e6i q^{91} +(-3.55159e6 - 8.18720e6i) q^{92} +(1.71729e7 + 1.71729e7i) q^{93} +(2.53549e6 + 482500. i) q^{94} +(-371321. + 218757. i) q^{95} +(1.19658e7 - 8.73445e6i) q^{96} +(-6.84970e6 + 6.84970e6i) q^{97} +(-2.20550e6 - 3.24219e6i) q^{98} -6.33039e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8}+O(q^{10}) \) 36 * q + 14 * q^2 - 560 * q^5 + 104 * q^6 - 3052 * q^8	\( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8} + 390 q^{10} + 10960 q^{12} - 28564 q^{13} - 12104 q^{16} - 27012 q^{17} + 95298 q^{18} + 97180 q^{20} - 2352 q^{21} - 191320 q^{22} - 112580 q^{25} + 604628 q^{26} - 142800 q^{28} - 252760 q^{30} - 73976 q^{32} - 248080 q^{33} - 328580 q^{36} - 108732 q^{37} - 406560 q^{38} - 680660 q^{40} + 2019472 q^{41} + 1616840 q^{42} - 827660 q^{45} - 2690616 q^{46} + 549280 q^{48} + 1343690 q^{50} - 6025332 q^{52} + 5672196 q^{53} + 4064064 q^{56} - 1796160 q^{57} + 3463736 q^{58} + 3280240 q^{60} - 5624928 q^{61} + 2750760 q^{62} + 75940 q^{65} - 2175120 q^{66} - 5673084 q^{68} - 11417280 q^{70} + 4328964 q^{72} - 22930604 q^{73} - 4045600 q^{76} + 10982160 q^{77} + 27127080 q^{78} + 34488560 q^{80} + 21593004 q^{81} - 13289192 q^{82} - 28299060 q^{85} - 2245656 q^{86} - 38612320 q^{88} - 38642970 q^{90} - 22809360 q^{92} + 31343120 q^{93} + 49033664 q^{96} - 11169292 q^{97} + 45095638 q^{98}+O(q^{100}) \) 36 * q + 14 * q^2 - 560 * q^5 + 104 * q^6 - 3052 * q^8 + 390 * q^10 + 10960 * q^12 - 28564 * q^13 - 12104 * q^16 - 27012 * q^17 + 95298 * q^18 + 97180 * q^20 - 2352 * q^21 - 191320 * q^22 - 112580 * q^25 + 604628 * q^26 - 142800 * q^28 - 252760 * q^30 - 73976 * q^32 - 248080 * q^33 - 328580 * q^36 - 108732 * q^37 - 406560 * q^38 - 680660 * q^40 + 2019472 * q^41 + 1616840 * q^42 - 827660 * q^45 - 2690616 * q^46 + 549280 * q^48 + 1343690 * q^50 - 6025332 * q^52 + 5672196 * q^53 + 4064064 * q^56 - 1796160 * q^57 + 3463736 * q^58 + 3280240 * q^60 - 5624928 * q^61 + 2750760 * q^62 + 75940 * q^65 - 2175120 * q^66 - 5673084 * q^68 - 11417280 * q^70 + 4328964 * q^72 - 22930604 * q^73 - 4045600 * q^76 + 10982160 * q^77 + 27127080 * q^78 + 34488560 * q^80 + 21593004 * q^81 - 13289192 * q^82 - 28299060 * q^85 - 2245656 * q^86 - 38612320 * q^88 - 38642970 * q^90 - 22809360 * q^92 + 31343120 * q^93 + 49033664 * q^96 - 11169292 * q^97 + 45095638 * q^98

Introduction

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