LMFDB - Embedded newform 531.2.m.a.121.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(4,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(174))

chi = DirichletCharacter(H, H._module([58, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("531.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.m (of order $87$, degree $56$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$3248$
Relative dimension:	$58$ over $\Q(\zeta_{87})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{87}]$

Embedding invariants

Embedding label			121.50
Character	$\chi$	$=$	531.121
Dual form			531.2.m.a.79.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73703 + 1.22409i) q^{2} +(-1.54872 - 0.775539i) q^{3} +(0.846165 + 2.36909i) q^{4} +(-0.601180 + 0.332767i) q^{5} +(-1.74085 - 3.24291i) q^{6} +(-4.63408 + 2.35065i) q^{7} +(-0.293154 + 1.05585i) q^{8} +(1.79708 + 2.40219i) q^{9} +O(q^{10})$	\(q+(1.73703 + 1.22409i) q^{2} +(-1.54872 - 0.775539i) q^{3} +(0.846165 + 2.36909i) q^{4} +(-0.601180 + 0.332767i) q^{5} +(-1.74085 - 3.24291i) q^{6} +(-4.63408 + 2.35065i) q^{7} +(-0.293154 + 1.05585i) q^{8} +(1.79708 + 2.40219i) q^{9} +(-1.45160 - 0.157871i) q^{10} +(-3.37594 + 1.27496i) q^{11} +(0.526843 - 4.32529i) q^{12} +(-0.676452 - 5.32375i) q^{13} +(-10.9269 - 1.58937i) q^{14} +(1.18913 - 0.0491248i) q^{15} +(2.09120 - 1.71226i) q^{16} +(0.0344366 + 0.635146i) q^{17} +(0.181093 + 6.37245i) q^{18} +(-4.50136 + 4.26391i) q^{19} +(-1.29705 - 1.14267i) q^{20} +(8.99993 - 0.0465993i) q^{21} +(-7.42477 - 1.91779i) q^{22} +(-0.574195 + 1.81160i) q^{23} +(1.27286 - 1.40786i) q^{24} +(-2.40401 + 3.83694i) q^{25} +(5.34171 - 10.0755i) q^{26} +(-0.920188 - 5.11403i) q^{27} +(-9.49010 - 8.98950i) q^{28} +(-0.262656 - 2.90158i) q^{29} +(2.12569 + 1.37027i) q^{30} +(-3.77175 + 1.12095i) q^{31} +(7.91429 - 0.572570i) q^{32} +(6.21717 + 0.643605i) q^{33} +(-0.717657 + 1.14542i) q^{34} +(2.00370 - 2.95524i) q^{35} +(-4.17036 + 6.29008i) q^{36} +(2.09520 + 7.54623i) q^{37} +(-13.0384 + 1.89649i) q^{38} +(-3.08113 + 8.76962i) q^{39} +(-0.175112 - 0.732306i) q^{40} +(-6.77309 + 7.41389i) q^{41} +(15.6902 + 10.9358i) q^{42} +(4.48710 - 3.67400i) q^{43} +(-5.87709 - 6.91905i) q^{44} +(-1.87974 - 0.846139i) q^{45} +(-3.21495 + 2.44394i) q^{46} +(4.24044 + 2.34718i) q^{47} +(-4.56661 + 1.03001i) q^{48} +(11.8142 - 16.1380i) q^{49} +(-8.87260 + 3.72216i) q^{50} +(0.439247 - 1.01037i) q^{51} +(12.0400 - 6.10734i) q^{52} +(4.58045 - 0.498154i) q^{53} +(4.66162 - 10.0096i) q^{54} +(1.60528 - 1.88988i) q^{55} +(-1.12343 - 5.58199i) q^{56} +(10.2782 - 3.11264i) q^{57} +(3.09554 - 5.36164i) q^{58} +(-1.69950 - 7.49077i) q^{59} +(1.12258 + 2.77559i) q^{60} +(8.82040 + 6.21575i) q^{61} +(-7.92378 - 2.66983i) q^{62} +(-13.9745 - 6.90762i) q^{63} +(9.81647 + 5.90637i) q^{64} +(2.17823 + 2.97543i) q^{65} +(10.0116 + 8.72832i) q^{66} +(6.24061 + 6.35432i) q^{67} +(-1.47558 + 0.619021i) q^{68} +(2.29424 - 2.36036i) q^{69} +(7.09795 - 2.68063i) q^{70} +(-4.07630 + 2.45263i) q^{71} +(-3.06316 + 1.19323i) q^{72} +(-3.28802 - 8.25231i) q^{73} +(-5.59782 + 15.6727i) q^{74} +(6.69885 - 4.07795i) q^{75} +(-13.9105 - 7.05613i) q^{76} +(12.6474 - 13.8439i) q^{77} +(-16.0868 + 11.4615i) q^{78} +(0.395655 + 0.348563i) q^{79} +(-0.687405 + 1.72526i) q^{80} +(-2.54101 + 8.63384i) q^{81} +(-20.8403 + 4.58730i) q^{82} +(-3.35282 - 0.242564i) q^{83} +(7.72582 + 21.2822i) q^{84} +(-0.232058 - 0.370378i) q^{85} +(12.2915 - 0.889247i) q^{86} +(-1.84350 + 4.69743i) q^{87} +(-0.356495 - 3.93823i) q^{88} +(-14.9053 - 6.89594i) q^{89} +(-2.22941 - 3.77073i) q^{90} +(15.6490 + 23.0806i) q^{91} +(-4.77771 + 0.172599i) q^{92} +(6.71073 + 1.18910i) q^{93} +(4.49261 + 9.26778i) q^{94} +(1.28724 - 4.06128i) q^{95} +(-12.7011 - 5.25109i) q^{96} +(11.6632 - 1.69646i) q^{97} +(40.2761 - 13.5706i) q^{98} +(-9.12953 - 5.81842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9}+O(q^{10}) $ 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18} - 120 q^{19} - 31 q^{20} - 60 q^{21} - 29 q^{22} - 29 q^{23} - 16 q^{24} + 29 q^{25} - 92 q^{26} - 55 q^{27} - 132 q^{28} - 27 q^{29} - 64 q^{30} - 21 q^{31} - 49 q^{32} - 32 q^{33} - 17 q^{34} - 136 q^{35} - 70 q^{36} - 120 q^{37} - 33 q^{38} - 80 q^{39} - 17 q^{40} - 17 q^{41} - 68 q^{42} - 21 q^{43} - 104 q^{44} - 58 q^{45} - 116 q^{46} - 17 q^{47} + 106 q^{48} + 19 q^{49} - 5 q^{50} - 250 q^{51} - 21 q^{52} - 108 q^{53} + 175 q^{54} - 116 q^{55} - q^{56} + 63 q^{57} - 58 q^{58} - 17 q^{59} - 816 q^{60} - 27 q^{61} - 128 q^{62} + 95 q^{63} - 256 q^{64} - 59 q^{65} + 67 q^{66} - 15 q^{67} - 43 q^{68} - 302 q^{69} - 41 q^{70} - 134 q^{71} + 210 q^{72} - 144 q^{73} - 51 q^{74} - 47 q^{75} - 9 q^{76} - 85 q^{77} + 36 q^{78} - 39 q^{79} - 128 q^{80} - 22 q^{81} - 164 q^{82} - 35 q^{83} - 190 q^{84} - 17 q^{85} + 31 q^{86} - 75 q^{87} - 29 q^{88} - 36 q^{89} - 86 q^{90} - 136 q^{91} - 31 q^{92} - 41 q^{94} - 13 q^{95} - 30 q^{96} - 3 q^{97} - 156 q^{98} - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{29}\right)$

Coefficient data

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

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

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

$2$	1.73703	+	1.22409i	1.22827	+	0.865561i	0.994293	−	0.106683i	$-0.0340229\pi$
$2$	1.73703	+	1.22409i	1.22827	+	0.865561i	0.233972	+	0.972243i	$0.424827\pi$
$3$	−1.54872	−	0.775539i	−0.894155	−	0.447757i
$3$	−1.54872	−	0.775539i	−0.894155	−	0.447757i
$4$	0.846165	+	2.36909i	0.423082	+	1.18454i
$5$	−0.601180	+	0.332767i	−0.268856	+	0.148818i	−0.612961	−	0.790113i	$-0.710022\pi$
$5$	−0.601180	+	0.332767i	−0.268856	+	0.148818i	0.344105	+	0.938931i	$0.388182\pi$
$6$	−1.74085	−	3.24291i	−0.710699	−	1.32391i
$7$	−4.63408	+	2.35065i	−1.75152	+	0.888464i	−0.790281	+	0.612745i	$0.790065\pi$
$7$	−4.63408	+	2.35065i	−1.75152	+	0.888464i	−0.961238	+	0.275719i	$0.911084\pi$
$8$	−0.293154	+	1.05585i	−0.103646	+	0.373298i
$9$	1.79708	+	2.40219i	0.599027	+	0.800729i
$10$	−1.45160	−	0.157871i	−0.459037	−	0.0499233i
$11$	−3.37594	+	1.27496i	−1.01788	+	0.384416i	−0.805389	−	0.592747i	$-0.798044\pi$
$11$	−3.37594	+	1.27496i	−1.01788	+	0.384416i	−0.212494	+	0.977162i	$0.568159\pi$
$12$	0.526843	−	4.32529i	0.152086	−	1.24860i
$13$	−0.676452	−	5.32375i	−0.187614	−	1.47654i	−0.756429	−	0.654076i	$-0.773058\pi$
$13$	−0.676452	−	5.32375i	−0.187614	−	1.47654i	0.568815	−	0.822466i	$-0.307402\pi$
$14$	−10.9269	−	1.58937i	−2.92035	−	0.424777i
$15$	1.18913	−	0.0491248i	0.307033	−	0.0126840i
$16$	2.09120	−	1.71226i	0.522800	−	0.428064i
$17$	0.0344366	+	0.635146i	0.00835210	+	0.154045i	0.999734	+	0.0230451i	$0.00733614\pi$
$17$	0.0344366	+	0.635146i	0.00835210	+	0.154045i	−0.991382	+	0.131000i	$0.958181\pi$
$18$	0.181093	+	6.37245i	0.0426841	+	1.50200i
$19$	−4.50136	+	4.26391i	−1.03268	+	0.978209i	−0.999774	−	0.0212495i	$-0.993236\pi$
$19$	−4.50136	+	4.26391i	−1.03268	+	0.978209i	−0.0329083	+	0.999458i	$0.510477\pi$
$20$	−1.29705	−	1.14267i	−0.290029	−	0.255509i
$21$	8.99993	−	0.0465993i	1.96395	−	0.0101688i
$22$	−7.42477	−	1.91779i	−1.58297	−	0.408875i
$23$	−0.574195	+	1.81160i	−0.119728	+	0.377745i	−0.994229	−	0.107278i	$-0.965787\pi$
$23$	−0.574195	+	1.81160i	−0.119728	+	0.377745i	0.874501	+	0.485023i	$0.161189\pi$
$24$	1.27286	−	1.40786i	0.259822	−	0.287378i
$25$	−2.40401	+	3.83694i	−0.480803	+	0.767389i
$26$	5.34171	−	10.0755i	1.04760	−	1.97598i
$27$	−0.920188	−	5.11403i	−0.177090	−	0.984195i
$28$	−9.49010	−	8.98950i	−1.79346	−	1.69886i
$29$	−0.262656	−	2.90158i	−0.0487739	−	0.538809i	−0.983185	−	0.182613i	$-0.941545\pi$
$29$	−0.262656	−	2.90158i	−0.0487739	−	0.538809i	0.934411	−	0.356197i	$-0.115927\pi$
$30$	2.12569	+	1.37027i	0.388097	+	0.250176i
$31$	−3.77175	+	1.12095i	−0.677426	+	0.201328i	−0.605216	−	0.796061i	$-0.706913\pi$
$31$	−3.77175	+	1.12095i	−0.677426	+	0.201328i	−0.0722103	+	0.997389i	$0.523005\pi$
$32$	7.91429	−	0.572570i	1.39906	−	0.101217i
$33$	6.21717	+	0.643605i	1.08227	+	0.112037i
$34$	−0.717657	+	1.14542i	−0.123077	+	0.196438i
$35$	2.00370	−	2.95524i	0.338687	−	0.499526i
$36$	−4.17036	+	6.29008i	−0.695060	+	1.04835i
$37$	2.09520	+	7.54623i	0.344449	+	1.24059i	0.909558	+	0.415577i	$0.136420\pi$
$37$	2.09520	+	7.54623i	0.344449	+	1.24059i	−0.565109	+	0.825016i	$0.691166\pi$
$38$	−13.0384	+	1.89649i	−2.11511	+	0.307651i
$39$	−3.08113	+	8.76962i	−0.493376	+	1.40426i
$40$	−0.175112	−	0.732306i	−0.0276877	−	0.115788i
$41$	−6.77309	+	7.41389i	−1.05778	+	1.15786i	−0.0707201	+	0.997496i	$0.522530\pi$
$41$	−6.77309	+	7.41389i	−1.05778	+	1.15786i	−0.987059	+	0.160360i	$0.948735\pi$
$42$	15.6902	+	10.9358i	2.42105	+	1.68742i
$43$	4.48710	−	3.67400i	0.684277	−	0.560280i	−0.226078	−	0.974109i	$-0.572590\pi$
$43$	4.48710	−	3.67400i	0.684277	−	0.560280i	0.910355	+	0.413829i	$0.135809\pi$
$44$	−5.87709	−	6.91905i	−0.886005	−	1.04309i
$45$	−1.87974	−	0.846139i	−0.280215	−	0.126135i
$46$	−3.21495	+	2.44394i	−0.474019	+	0.360340i
$47$	4.24044	+	2.34718i	0.618531	+	0.342371i	0.762284	−	0.647243i	$-0.224078\pi$
$47$	4.24044	+	2.34718i	0.618531	+	0.342371i	−0.143753	+	0.989614i	$0.545917\pi$
$48$	−4.56661	+	1.03001i	−0.659133	+	0.148668i
$49$	11.8142	−	16.1380i	1.68775	−	2.30543i
$50$	−8.87260	+	3.72216i	−1.25478	+	0.526393i
$51$	0.439247	−	1.01037i	0.0615069	−	0.141480i
$52$	12.0400	−	6.10734i	1.66965	−	0.846936i
$53$	4.58045	−	0.498154i	0.629173	−	0.0684267i	0.212024	−	0.977265i	$-0.431995\pi$
$53$	4.58045	−	0.498154i	0.629173	−	0.0684267i	0.417150	+	0.908838i	$0.363029\pi$
$54$	4.66162	−	10.0096i	0.634366	−	1.36213i
$55$	1.60528	−	1.88988i	0.216456	−	0.254832i
$56$	−1.12343	−	5.58199i	−0.150125	−	0.745925i
$57$	10.2782	−	3.11264i	1.36138	−	0.412279i
$58$	3.09554	−	5.36164i	0.406465	−	0.704018i
$59$	−1.69950	−	7.49077i	−0.221257	−	0.975216i
$59$	−1.69950	−	7.49077i	−0.221257	−	0.975216i
$60$	1.12258	+	2.77559i	0.144925	+	0.358327i
$61$	8.82040	+	6.21575i	1.12934	+	0.795845i	0.981176	−	0.193118i	$-0.0618601\pi$
$61$	8.82040	+	6.21575i	1.12934	+	0.795845i	0.148161	+	0.988963i	$0.452665\pi$
$62$	−7.92378	−	2.66983i	−1.00632	−	0.339069i
$63$	−13.9745	−	6.90762i	−1.76063	−	0.870279i
$64$	9.81647	+	5.90637i	1.22706	+	0.738297i
$65$	2.17823	+	2.97543i	0.270177	+	0.369057i
$66$	10.0116	+	8.72832i	1.23234	+	1.07438i
$67$	6.24061	+	6.35432i	0.762412	+	0.776303i	0.979842	−	0.199773i	$-0.0640204\pi$
$67$	6.24061	+	6.35432i	0.762412	+	0.776303i	−0.217430	+	0.976076i	$0.569767\pi$
$68$	−1.47558	+	0.619021i	−0.178940	+	0.0750674i
$69$	2.29424	−	2.36036i	0.276194	−	0.284154i
$70$	7.09795	−	2.68063i	0.848368	−	0.320396i
$71$	−4.07630	+	2.45263i	−0.483768	+	0.291073i	−0.736469	−	0.676471i	$-0.763508\pi$
$71$	−4.07630	+	2.45263i	−0.483768	+	0.291073i	0.252702	+	0.967544i	$0.418681\pi$
$72$	−3.06316	+	1.19323i	−0.360997	+	0.140623i
$73$	−3.28802	−	8.25231i	−0.384834	−	0.965860i	−0.986001	−	0.166737i	$-0.946677\pi$
$73$	−3.28802	−	8.25231i	−0.384834	−	0.965860i	0.601168	−	0.799123i	$-0.294702\pi$
$74$	−5.59782	+	15.6727i	−0.650734	+	1.82192i
$75$	6.69885	−	4.07795i	0.773516	−	0.470881i
$76$	−13.9105	−	7.05613i	−1.59564	−	0.809394i
$77$	12.6474	−	13.8439i	1.44130	−	1.57766i
$78$	−16.0868	+	11.4615i	−1.82147	+	1.29776i
$79$	0.395655	+	0.348563i	0.0445146	+	0.0392163i	0.683007	−	0.730411i	$-0.260672\pi$
$79$	0.395655	+	0.348563i	0.0445146	+	0.0392163i	−0.638493	+	0.769628i	$0.720442\pi$
$80$	−0.687405	+	1.72526i	−0.0768542	+	0.192890i
$81$	−2.54101	+	8.63384i	−0.282334	+	0.959316i
$82$	−20.8403	+	4.58730i	−2.30143	+	0.506583i
$83$	−3.35282	−	0.242564i	−0.368019	−	0.0266249i	−0.113091	−	0.993585i	$-0.536075\pi$
$83$	−3.35282	−	0.242564i	−0.368019	−	0.0266249i	−0.254929	+	0.966960i	$0.582052\pi$
$84$	7.72582	+	21.2822i	0.842956	+	2.32208i
$85$	−0.232058	−	0.370378i	−0.0251702	−	0.0401731i
$86$	12.2915	−	0.889247i	1.32543	−	0.0958900i
$87$	−1.84350	+	4.69743i	−0.197644	+	0.503618i
$88$	−0.356495	−	3.93823i	−0.0380025	−	0.419817i
$89$	−14.9053	−	6.89594i	−1.57996	−	0.730968i	−0.583272	−	0.812277i	$-0.698228\pi$
$89$	−14.9053	−	6.89594i	−1.57996	−	0.730968i	−0.996689	+	0.0813092i	$0.974090\pi$
$90$	−2.22941	−	3.77073i	−0.235000	−	0.397470i
$91$	15.6490	+	23.0806i	1.64046	+	2.41950i
$92$	−4.77771	+	0.172599i	−0.498110	+	0.0179947i
$93$	6.71073	+	1.18910i	0.695871	+	0.123304i
$94$	4.49261	+	9.26778i	0.463378	+	0.955899i
$95$	1.28724	−	4.06128i	0.132068	−	0.416679i
$96$	−12.7011	−	5.25109i	−1.29630	−	0.535937i
$97$	11.6632	−	1.69646i	1.18422	−	0.172250i	0.476781	−	0.879022i	$-0.341804\pi$
$97$	11.6632	−	1.69646i	1.18422	−	0.172250i	0.707441	+	0.706773i	$0.249850\pi$
$98$	40.2761	−	13.5706i	4.06850	−	1.37084i
$99$	−9.12953	−	5.81842i	−0.917552	−	0.584773i
$100$	−11.1242	−	2.44863i	−1.11242	−	0.244863i
$101$	−6.80971	+	4.43978i	−0.677591	+	0.441774i	−0.838287	−	0.545230i	$-0.816442\pi$
$101$	−6.80971	+	4.43978i	−0.677591	+	0.441774i	0.160696	+	0.987004i	$0.448626\pi$
$102$	1.99977	−	1.21737i	0.198007	−	0.120537i
$103$	−4.70640	+	0.859102i	−0.463735	+	0.0846498i	−0.406380	−	0.913704i	$-0.633209\pi$
$103$	−4.70640	+	0.859102i	−0.463735	+	0.0846498i	−0.0573549	+	0.998354i	$0.518267\pi$
$104$	5.81937	+	0.846450i	0.570636	+	0.0830013i
$105$	−5.39507	+	3.02289i	−0.526505	+	0.295004i
$106$	8.56616	+	4.74157i	0.832019	+	0.460542i
$107$	−2.01880	+	12.3141i	−0.195165	+	1.19045i	0.689521	+	0.724265i	$0.257821\pi$
$107$	−2.01880	+	12.3141i	−0.195165	+	1.19045i	−0.884686	+	0.466187i	$0.845627\pi$
$108$	11.3369	−	6.50731i	1.09090	−	0.626166i
$109$	−1.62796	−	1.23754i	−0.155930	−	0.118535i	0.524300	−	0.851534i	$-0.324327\pi$
$109$	−1.62796	−	1.23754i	−0.155930	−	0.118535i	−0.680230	+	0.732999i	$0.738120\pi$
$110$	5.10180	−	1.31778i	0.486437	−	0.125645i
$111$	2.60751	−	13.3119i	0.247494	−	1.26351i
$112$	−5.66587	+	12.8504i	−0.535374	+	1.21425i
$113$	−13.5132	+	7.47988i	−1.27122	+	0.703648i	−0.968400	−	0.249400i	$-0.919766\pi$
$113$	−13.5132	+	7.47988i	−1.27122	+	0.703648i	−0.302818	+	0.953048i	$0.597927\pi$
$114$	21.6637	+	7.17465i	2.02899	+	0.671967i
$115$	−0.257647	−	1.28017i	−0.0240257	−	0.119377i
$116$	6.65183	−	3.07747i	0.617607	−	0.285735i
$117$	11.5730	−	11.1922i	1.06992	−	1.03472i
$118$	6.21727	−	15.0920i	0.572346	−	1.38933i
$119$	−1.65259	−	2.86237i	−0.151493	−	0.262393i
$120$	−0.296732	+	1.26994i	−0.0270878	+	0.115930i
$121$	1.51756	−	1.33693i	0.137960	−	0.121540i
$122$	7.71267	+	21.5939i	0.698273	+	1.95502i
$123$	16.2394	−	6.22927i	1.46426	−	0.561674i
$124$	−5.84715	−	7.98709i	−0.525089	−	0.717262i
$125$	0.354442	−	6.53729i	0.0317022	−	0.584713i
$126$	−15.8186	−	29.1048i	−1.40924	−	2.59286i
$127$	−5.77280	−	4.38837i	−0.512253	−	0.389405i	0.316871	−	0.948469i	$-0.397368\pi$
$127$	−5.77280	−	4.38837i	−0.512253	−	0.389405i	−0.829125	+	0.559064i	$0.811161\pi$
$128$	3.41908	+	7.75463i	0.302207	+	0.685419i
$129$	−9.79860	+	2.21009i	−0.862719	+	0.194588i
$130$	0.141473	+	7.83476i	0.0124080	+	0.687154i
$131$	−0.549842	−	4.32731i	−0.0480399	−	0.378079i	−0.997866	−	0.0652994i	$-0.979200\pi$
$131$	−0.549842	−	4.32731i	−0.0480399	−	0.378079i	0.949826	−	0.312779i	$-0.101260\pi$
$132$	3.73599	+	15.2736i	0.325177	+	1.32940i
$133$	10.8367	−	30.3405i	0.939660	−	2.63085i
$134$	3.06189	+	18.6767i	0.264507	+	1.61342i
$135$	2.25498	+	2.76824i	0.194077	+	0.238252i
$136$	−0.680712	−	0.149836i	−0.0583706	−	0.0128483i
$137$	−7.31878	−	2.17511i	−0.625286	−	0.185832i	−0.0433408	−	0.999060i	$-0.513800\pi$
$137$	−7.31878	−	2.17511i	−0.625286	−	0.185832i	−0.581945	+	0.813228i	$0.697708\pi$
$138$	6.87444	−	1.29167i	0.585192	−	0.109954i
$139$	−0.409710	−	0.519232i	−0.0347511	−	0.0440407i	0.767353	−	0.641225i	$-0.221573\pi$
$139$	−0.409710	−	0.519232i	−0.0347511	−	0.0440407i	−0.802104	+	0.597184i	$0.796286\pi$
$140$	8.69666	+	2.24632i	0.735002	+	0.189849i
$141$	−4.74693	−	6.92375i	−0.399764	−	0.583085i
$142$	−10.0829	−	0.729460i	−0.846137	−	0.0612149i
$143$	9.07124	+	17.1102i	0.758575	+	1.43082i
$144$	7.87122	+	1.94639i	0.655935	+	0.162199i
$145$	1.12345	+	1.65697i	0.0932976	+	0.137604i
$146$	4.39016	−	18.3593i	0.363332	−	1.51943i
$147$	−30.8126	+	15.8309i	−2.54138	+	1.30571i
$148$	−16.1048	+	11.3491i	−1.32381	+	0.932888i
$149$	−16.9413	+	5.03490i	−1.38789	+	0.412475i	−0.890473	−	0.455037i	$-0.849626\pi$
$149$	−16.9413	+	5.03490i	−1.38789	+	0.412475i	−0.497417	+	0.867512i	$0.665718\pi$
$150$	16.6279	+	1.11645i	1.35766	+	0.0911580i
$151$	−1.38253	+	0.0499453i	−0.112509	+	0.00406449i	−0.0922996	−	0.995731i	$-0.529422\pi$
$151$	−1.38253	+	0.0499453i	−0.112509	+	0.00406449i	−0.0202093	+	0.999796i	$0.506433\pi$
$152$	−3.18245	−	6.00273i	−0.258131	−	0.486886i
$153$	−1.46385	+	1.22413i	−0.118346	+	0.0989651i
$154$	38.9151	−	8.56585i	3.13586	−	0.690256i
$155$	1.89449	−	1.92900i	0.152169	−	0.154941i
$156$	−23.3831	+	0.121072i	−1.87215	+	0.00969348i
$157$	−0.520945	+	2.58842i	−0.0415760	+	0.206579i	−0.995674	−	0.0929158i	$-0.970381\pi$
$157$	−0.520945	+	2.58842i	−0.0415760	+	0.206579i	0.954098	+	0.299495i	$0.0968180\pi$
$158$	0.260593	+	1.08978i	0.0207316	+	0.0866982i
$159$	−7.48018	−	2.78081i	−0.593217	−	0.220533i
$160$	−4.56738	+	2.97783i	−0.361083	+	0.235418i
$161$	−1.59759	−	9.74486i	−0.125908	−	0.768002i
$162$	−14.9824	+	11.8868i	−1.17713	+	0.933918i
$163$	3.35654	+	8.42427i	0.262904	+	0.659840i	0.999871	−	0.0160895i	$-0.00512166\pi$
$163$	3.35654	+	8.42427i	0.262904	+	0.659840i	−0.736966	+	0.675930i	$0.763742\pi$
$164$	−23.2953	−	9.77265i	−1.81906	−	0.763116i
$165$	−3.95181	+	1.68194i	−0.307648	+	0.130939i
$166$	−5.52702	−	4.52548i	−0.428980	−	0.351245i
$167$	−4.02493	+	5.49798i	−0.311458	+	0.425447i	−0.934073	−	0.357082i	$-0.883772\pi$
$167$	−4.02493	+	5.49798i	−0.311458	+	0.425447i	0.622615	+	0.782529i	$0.286070\pi$
$168$	−2.58917	+	9.51621i	−0.199759	+	0.734192i
$169$	−15.2978	+	3.95136i	−1.17675	+	0.303951i
$170$	0.0502830	−	0.927416i	0.00385653	−	0.0711296i
$171$	−18.3320	−	3.15051i	−1.40188	−	0.240926i
$172$	12.5009	+	7.52151i	0.953181	+	0.573510i
$173$	−6.94948	−	1.26855i	−0.528359	−	0.0964462i	−0.0912037	−	0.995832i	$-0.529071\pi$
$173$	−6.94948	−	1.26855i	−0.528359	−	0.0964462i	−0.437155	+	0.899386i	$0.644014\pi$
$174$	−8.95229	+	5.90297i	−0.678672	+	0.447503i
$175$	2.12108	−	23.4317i	0.160339	−	1.77127i
$176$	−4.87669	+	8.44667i	−0.367594	+	0.636692i
$177$	−3.17732	+	12.9192i	−0.238822	+	0.971063i
$178$	−17.4498	−	30.2239i	−1.30791	−	2.26537i
$179$	−10.8340	+	5.01236i	−0.809774	+	0.374641i	−0.780676	−	0.624935i	$-0.785125\pi$
$179$	−10.8340	+	5.01236i	−0.809774	+	0.374641i	−0.0290972	+	0.999577i	$0.509263\pi$
$180$	0.414008	−	5.16923i	0.0308583	−	0.385292i
$181$	7.34595	−	8.64832i	0.546020	−	0.642825i	−0.418065	−	0.908417i	$-0.637292\pi$
$181$	7.34595	−	8.64832i	0.546020	−	0.642825i	0.964085	+	0.265592i	$0.0855675\pi$
$182$	−1.06984	+	59.2474i	−0.0793015	+	4.39171i
$183$	−8.83979	−	16.4670i	−0.653456	−	1.21728i
$184$	−1.74445	−	1.13734i	−0.128602	−	0.0838459i
$185$	−3.77073	−	3.83943i	−0.277229	−	0.282281i
$186$	10.2012	+	10.2800i	0.747987	+	0.753768i
$187$	−0.926043	−	2.10031i	−0.0677190	−	0.153590i
$188$	−1.97255	+	12.0321i	−0.143863	+	0.877528i
$189$	16.2855	+	21.5358i	1.18460	+	1.56650i
$190$	7.20734	−	5.47887i	0.522875	−	0.397479i
$191$	−0.800451	+	1.01443i	−0.0579186	+	0.0734012i	−0.813138	−	0.582070i	$-0.802243\pi$
$191$	−0.800451	+	1.01443i	−0.0579186	+	0.0734012i	0.755220	+	0.655472i	$0.227530\pi$
$192$	−10.6224	−	16.7604i	−0.766603	−	1.20958i
$193$	9.27804	+	3.50397i	0.667848	+	0.252221i	0.663956	−	0.747771i	$-0.268876\pi$
$193$	9.27804	+	3.50397i	0.667848	+	0.252221i	0.00389181	+	0.999992i	$0.498761\pi$
$194$	22.3360	+	11.3300i	1.60363	+	0.813447i
$195$	−1.06592	−	6.29742i	−0.0763321	−	0.450967i
$196$	48.2292	+	14.3335i	3.44494	+	1.02382i
$197$	13.3913	−	4.51205i	0.954089	−	0.321470i	0.201150	−	0.979560i	$-0.435532\pi$
$197$	13.3913	−	4.51205i	0.954089	−	0.321470i	0.752939	+	0.658091i	$0.228636\pi$
$198$	−8.73600	−	21.2821i	−0.620841	−	1.51245i
$199$	3.94171	+	14.1967i	0.279420	+	1.00638i	0.961433	+	0.275040i	$0.0886911\pi$
$199$	3.94171	+	14.1967i	0.279420	+	1.00638i	−0.682013	+	0.731340i	$0.738895\pi$
$200$	−3.34648	−	3.66309i	−0.236632	−	0.259019i
$201$	−4.73695	−	14.6809i	−0.334119	−	1.03551i
$202$	−17.2633	−	0.623655i	−1.21464	−	0.0438802i
$203$	8.03777	+	12.8287i	0.564141	+	0.900401i
$204$	2.76533	+	0.185674i	0.193612	+	0.0129998i
$205$	1.60475	−	6.71094i	0.112081	−	0.468713i
$206$	−9.22677	−	4.26876i	−0.642860	−	0.297419i
$207$	−5.38368	+	1.87627i	−0.374192	+	0.130410i
$208$	−10.5302	−	9.97475i	−0.730139	−	0.691625i
$209$	9.75996	−	20.1338i	0.675111	−	1.39268i
$210$	−13.0717	−	1.35319i	−0.902032	−	0.0933788i
$211$	−9.47879	−	0.342430i	−0.652547	−	0.0235739i	−0.292149	−	0.956373i	$-0.594370\pi$
$211$	−9.47879	−	0.342430i	−0.652547	−	0.0235739i	−0.360397	+	0.932799i	$0.617359\pi$
$212$	5.05599	+	10.4300i	0.347247	+	0.716333i
$213$	8.21516	−	0.637112i	0.562894	−	0.0436542i
$214$	−18.5803	+	18.9188i	−1.27012	+	1.29327i
$215$	−1.47497	+	3.70190i	−0.100592	+	0.252467i
$216$	5.66939	+	0.527621i	0.385753	+	0.0359001i
$217$	14.8436	−	14.0607i	1.00765	−	0.954499i
$218$	−1.31295	−	4.14241i	−0.0889243	−	0.280559i
$219$	−1.30775	+	15.3305i	−0.0883698	+	1.03594i
$220$	5.83562	+	2.20389i	0.393437	+	0.148586i
$221$	3.35806	−	0.612977i	0.225888	−	0.0412333i
$222$	20.8243	−	19.9314i	1.39763	−	1.33771i
$223$	15.7891	+	6.62372i	1.05732	+	0.443557i	0.845624	−	0.533779i	$-0.179229\pi$
$223$	15.7891	+	6.62372i	1.05732	+	0.443557i	0.211694	+	0.977336i	$0.432102\pi$
$224$	−35.3296	+	21.2571i	−2.36056	+	1.42030i
$225$	−13.5373	+	1.12040i	−0.902484	+	0.0746933i
$226$	−32.6289	−	3.54861i	−2.17044	−	0.236050i
$227$	3.37989	−	26.6001i	0.224331	−	1.76551i	−0.340446	−	0.940264i	$-0.610578\pi$
$227$	3.37989	−	26.6001i	0.224331	−	1.76551i	0.564777	−	0.825244i	$-0.308962\pi$
$228$	16.0711	+	21.7161i	1.06434	+	1.43818i
$229$	−7.69751	−	5.01860i	−0.508666	−	0.331639i	0.266039	−	0.963962i	$-0.414285\pi$
$229$	−7.69751	−	5.01860i	−0.508666	−	0.331639i	−0.774704	+	0.632324i	$0.782101\pi$
$230$	1.11950	−	2.53908i	0.0738178	−	0.167422i
$231$	−30.3238	+	11.6319i	−1.99516	+	0.765323i
$232$	3.14062	+	0.573286i	0.206192	+	0.0376381i
$233$	−6.59126	−	2.22086i	−0.431808	−	0.145493i	0.0950002	−	0.995477i	$-0.469715\pi$
$233$	−6.59126	−	2.22086i	−0.431808	−	0.145493i	−0.526808	+	0.849984i	$0.676611\pi$
$234$	33.8028	−	5.27475i	2.20976	−	0.344822i
$235$	−3.33033			−0.217247
$236$	16.3082	−	10.3647i	1.06157	−	0.674684i
$237$	−0.342435	−	0.846672i	−0.0222436	−	0.0549972i
$238$	0.633194	−	6.99494i	0.0410438	−	0.453414i
$239$	1.68559	−	1.48497i	0.109032	−	0.0960546i	−0.604778	−	0.796394i	$-0.706738\pi$
$239$	1.68559	−	1.48497i	0.109032	−	0.0960546i	0.713810	+	0.700340i	$0.246968\pi$
$240$	2.40260	−	2.13883i	0.155087	−	0.138061i
$241$	−0.0176644	+	0.978255i	−0.00113787	+	0.0630149i	0.998772	+	0.0495526i	$0.0157796\pi$
$241$	−0.0176644	+	0.978255i	−0.00113787	+	0.0630149i	−0.999909	+	0.0134623i	$0.995715\pi$
$242$	4.27257	−	0.464670i	0.274651	−	0.0298701i
$243$	10.6312	−	11.4008i	0.681991	−	0.731360i
$244$	−7.26213	+	26.1558i	−0.464910	+	1.67446i
$245$	−1.73228	+	13.6333i	−0.110672	+	0.870996i
$246$	35.8335	+	9.05801i	2.28466	+	0.577518i
$247$	25.7449	+	21.0798i	1.63811	+	1.34127i
$248$	−0.0778442	−	4.31100i	−0.00494311	−	0.273749i
$249$	5.00446	+	2.97590i	0.317145	+	0.188590i
$250$	8.61790	−	10.9216i	0.545044	−	0.690743i
$251$	5.55432	+	6.53905i	0.350586	+	0.412741i	0.908984	−	0.416832i	$-0.136860\pi$
$251$	5.55432	+	6.53905i	0.350586	+	0.412741i	−0.558398	+	0.829573i	$0.688584\pi$
$252$	4.54000	−	38.9518i	0.285993	−	2.45374i
$253$	−0.371284	−	6.84793i	−0.0233424	−	0.430526i
$254$	−4.65578	−	14.6891i	−0.292130	−	0.921679i
$255$	0.0721512	+	0.753582i	0.00451828	+	0.0471911i
$256$	0.967464	−	4.80705i	0.0604665	−	0.300440i
$257$	18.4296	+	23.3561i	1.14960	+	1.45691i	0.867437	+	0.497548i	$0.165766\pi$
$257$	18.4296	+	23.3561i	1.14960	+	1.45691i	0.282167	+	0.959365i	$0.408947\pi$
$258$	−19.7258	−	8.15536i	−1.22808	−	0.507730i
$259$	−27.4479	−	30.0448i	−1.70553	−	1.86689i
$260$	−5.20590	+	7.67813i	−0.322856	+	0.476177i
$261$	6.49812	−	5.84531i	0.402223	−	0.361816i
$262$	4.34191	−	8.18972i	0.268244	−	0.505962i
$263$	12.4435	−	25.6696i	0.767297	−	1.58285i	−0.0445669	−	0.999006i	$-0.514191\pi$
$263$	12.4435	−	25.6696i	0.767297	−	1.58285i	0.811864	−	0.583846i	$-0.198453\pi$
$264$	−2.50214	+	6.37570i	−0.153996	+	0.392397i
$265$	−2.58791	+	1.82370i	−0.158974	+	0.112029i
$266$	55.9630	−	39.4372i	3.43131	−	2.41805i
$267$	17.7361	+	22.2395i	1.08543	+	1.36104i
$268$	−9.77333	+	20.1613i	−0.597001	+	1.23155i
$269$	−3.30928	+	6.24196i	−0.201770	+	0.380579i	−0.963662	−	0.267126i	$-0.913926\pi$
$269$	−3.30928	+	6.24196i	−0.201770	+	0.380579i	0.761892	+	0.647705i	$0.224271\pi$
$270$	0.528390	+	7.56881i	0.0321568	+	0.460623i
$271$	−3.13749	+	4.62746i	−0.190589	+	0.281098i	−0.910963	−	0.412488i	$-0.864660\pi$
$271$	−3.13749	+	4.62746i	−0.190589	+	0.281098i	0.720374	+	0.693586i	$0.243970\pi$
$272$	1.15955	+	1.26925i	0.0703079	+	0.0769597i
$273$	−6.33610	−	47.8818i	−0.383478	−	2.89794i
$274$	−10.0504	−	12.7371i	−0.607168	−	0.769474i
$275$	3.22384	−	16.0183i	0.194405	−	0.965940i
$276$	7.53320	+	3.43799i	0.453445	+	0.206943i
$277$	0.999218	+	3.15257i	0.0600372	+	0.189419i	0.978566	−	0.205936i	$-0.0660238\pi$
$277$	0.999218	+	3.15257i	0.0600372	+	0.189419i	−0.918528	+	0.395355i	$0.870622\pi$
$278$	−0.0760925	−	1.40344i	−0.00456372	−	0.0841729i
$279$	−9.47087	−	7.04602i	−0.567006	−	0.421834i
$280$	2.53288	+	2.98194i	0.151369	+	0.178205i
$281$	−0.988702	+	1.25300i	−0.0589810	+	0.0747476i	−0.813638	−	0.581372i	$-0.802516\pi$
$281$	−0.988702	+	1.25300i	−0.0589810	+	0.0747476i	0.754657	+	0.656120i	$0.227803\pi$
$282$	0.229713	−	17.8374i	0.0136792	−	1.06220i
$283$	−0.387401	−	21.4542i	−0.0230286	−	1.27532i	−0.781620	−	0.623755i	$-0.785606\pi$
$283$	−0.387401	−	21.4542i	−0.0230286	−	1.27532i	0.758591	−	0.651567i	$-0.225888\pi$
$284$	−9.25971	−	7.58177i	−0.549462	−	0.449896i
$285$	−5.14326	+	5.29149i	−0.304660	+	0.313441i
$286$	−5.18734	+	40.8249i	−0.306734	+	2.41402i
$287$	13.9596	−	50.2778i	0.824007	−	2.96780i
$288$	15.5980	+	17.9827i	0.919123	+	1.05964i
$289$	16.4981	−	1.79428i	0.970478	−	0.105546i
$290$	−0.0768041	+	4.25340i	−0.00451009	+	0.249768i
$291$	−19.3788	−	6.41793i	−1.13600	−	0.376226i
$292$	16.7682	−	14.7724i	0.981286	−	0.864490i
$293$	−2.23868	+	24.7308i	−0.130785	+	1.44479i	0.620185	+	0.784455i	$0.287057\pi$
$293$	−2.23868	+	24.7308i	−0.130785	+	1.44479i	−0.750970	+	0.660336i	$0.770414\pi$
$294$	−72.9009	−	10.2186i	−4.25167	−	0.595959i
$295$	3.51439	+	3.93776i	0.204616	+	0.229266i
$296$	−8.58189			−0.498812
$297$	9.62669	+	16.0914i	0.558597	+	0.933718i
$298$	−35.5908	−	11.9919i	−2.06172	−	0.694674i
$299$	10.0329	+	1.83140i	0.580219	+	0.105913i
$300$	15.3293	+	12.4195i	0.885040	+	0.717041i
$301$	−12.1573	+	27.5733i	−0.700735	+	1.58930i
$302$	−2.46264	−	1.60558i	−0.141709	−	0.0923910i
$303$	13.9896	−	1.59479i	0.803679	−	0.0916182i
$304$	−2.11232	+	16.6242i	−0.121150	+	0.953462i
$305$	−7.37104	−	0.801649i	−0.422065	−	0.0459023i
$306$	−4.04120	+	0.334466i	−0.231020	+	0.0191202i
$307$	2.58955	−	1.55808i	0.147793	−	0.0889243i	−0.439736	−	0.898127i	$-0.644928\pi$
$307$	2.58955	−	1.55808i	0.147793	−	0.0889243i	0.587530	+	0.809203i	$0.300101\pi$
$308$	43.4992	+	18.2484i	2.47860	+	1.03980i
$309$	7.95517	+	2.31948i	0.452554	+	0.131951i
$310$	5.65205	−	1.03172i	0.321015	−	0.0585978i
$311$	−26.6843	−	10.0777i	−1.51313	−	0.571452i	−0.548753	−	0.835985i	$-0.684897\pi$
$311$	−26.6843	−	10.0777i	−1.51313	−	0.571452i	−0.964377	+	0.264533i	$0.914782\pi$
$312$	−8.35613	−	5.82406i	−0.473072	−	0.329722i
$313$	−4.28786	−	13.5283i	−0.242364	−	0.764667i	−0.994413	−	0.105560i	$-0.966337\pi$
$313$	−4.28786	−	13.5283i	−0.242364	−	0.764667i	0.752049	−	0.659107i	$-0.229066\pi$
$314$	−4.07336	+	3.85849i	−0.229873	+	0.217747i
$315$	10.6998	−	0.497533i	0.602867	−	0.0280328i
$316$	−0.490986	+	1.23228i	−0.0276201	+	0.0693212i
$317$	−8.83900	+	9.00005i	−0.496448	+	0.505493i	−0.915417	−	0.402508i	$-0.868139\pi$
$317$	−8.83900	+	9.00005i	−0.496448	+	0.505493i	0.418969	+	0.908001i	$0.362392\pi$
$318$	−9.58934	−	13.9868i	−0.537744	−	0.784338i
$319$	4.58611	+	9.46066i	0.256773	+	0.529695i
$320$	−7.86691	−	0.284200i	−0.439774	−	0.0158872i
$321$	12.6767	−	17.5055i	0.707542	−	0.977063i
$322$	9.15350	−	18.8827i	0.510105	−	1.05229i
$323$	−2.86322	−	2.71218i	−0.159314	−	0.150910i
$324$	−22.6044	+	1.28579i	−1.25580	+	0.0714328i
$325$	22.0531	+	10.2029i	1.22329	+	0.565953i
$326$	−4.48164	+	18.7419i	−0.248215	+	1.03802i
$327$	1.56149	+	3.17915i	0.0863507	+	0.175807i
$328$	−5.84238	−	9.32476i	−0.322591	−	0.514874i
$329$	−25.1679	−	0.909216i	−1.38755	−	0.0501267i
$330$	−8.92325	−	1.91577i	−0.491209	−	0.105460i
$331$	1.82521	+	1.99789i	0.100322	+	0.109814i	0.786410	−	0.617705i	$-0.211938\pi$
$331$	1.82521	+	1.99789i	0.100322	+	0.109814i	−0.686087	+	0.727519i	$0.740673\pi$
$332$	−2.26238	−	8.14836i	−0.124164	−	0.447199i
$333$	−14.3622	+	18.5942i	−0.787045	+	1.01896i
$334$	−13.7214	+	4.62329i	−0.750804	+	0.252975i
$335$	−5.86623	−	1.74342i	−0.320507	−	0.0952532i
$336$	18.7409	−	15.5076i	1.02240	−	0.846012i
$337$	−3.51340	−	1.78218i	−0.191387	−	0.0970817i	0.354076	−	0.935217i	$-0.384796\pi$
$337$	−3.51340	−	1.78218i	−0.191387	−	0.0970817i	−0.545463	+	0.838135i	$0.683646\pi$
$338$	−31.4095	−	11.8622i	−1.70845	−	0.645218i
$339$	26.7292	−	1.10422i	1.45173	−	0.0599730i
$340$	0.681097	−	0.863166i	0.0369377	−	0.0468117i
$341$	11.3040	−	8.59309i	0.612147	−	0.465342i
$342$	−27.9868	−	27.9125i	−1.51335	−	1.50934i
$343$	−10.9287	+	66.6621i	−0.590094	+	3.59941i
$344$	2.56377	+	5.81474i	0.138229	+	0.313510i
$345$	−0.593800	+	2.18245i	−0.0319691	+	0.117499i
$346$	−10.5186	−	10.7103i	−0.565485	−	0.575788i
$347$	2.07781	+	1.35468i	0.111543	+	0.0727233i	0.600712	−	0.799466i	$-0.294884\pi$
$347$	2.07781	+	1.35468i	0.111543	+	0.0727233i	−0.489169	+	0.872189i	$0.662700\pi$
$348$	−12.6885	−	0.392614i	−0.680177	−	0.0210463i
$349$	−0.129836	+	7.19029i	−0.00694994	+	0.384887i	0.977667	+	0.210160i	$0.0673985\pi$
$349$	−0.129836	+	7.19029i	−0.00694994	+	0.384887i	−0.984617	+	0.174727i	$0.944096\pi$
$350$	32.3669	−	38.1052i	1.73008	−	2.03681i
$351$	−26.6033	+	8.35824i	−1.41998	+	0.446130i
$352$	−25.9881	+	12.0234i	−1.38517	+	0.640849i
$353$	3.81500	+	6.60777i	0.203052	+	0.351696i	0.949510	−	0.313736i	$-0.101581\pi$
$353$	3.81500	+	6.60777i	0.203052	+	0.351696i	−0.746458	+	0.665432i	$0.768247\pi$
$354$	−21.3333	+	18.5516i	−1.13385	+	0.986008i
$355$	1.63444	−	2.83093i	0.0867469	−	0.150250i
$356$	3.72470	−	41.1471i	0.197409	−	2.18079i
$357$	0.339524	+	5.71466i	0.0179695	+	0.302452i
$358$	−24.9546	−	4.55519i	−1.31889	−	0.240749i
$359$	8.43371	+	5.07440i	0.445114	+	0.267816i	0.720417	−	0.693541i	$-0.243950\pi$
$359$	8.43371	+	5.07440i	0.445114	+	0.267816i	−0.275303	+	0.961358i	$0.588778\pi$
$360$	1.44445	−	1.73666i	0.0761290	−	0.0915303i
$361$	1.05263	−	19.4147i	0.0554017	−	1.02183i
$362$	23.3464	−	6.03031i	1.22706	−	0.316946i
$363$	−3.38712	+	0.893615i	−0.177778	+	0.0469026i
$364$	−41.4382	+	56.6038i	−2.17195	+	2.96685i
$365$	4.72279	+	3.86698i	0.247202	+	0.202407i
$366$	4.80210	−	39.4244i	0.251010	−	2.06075i
$367$	24.7125	+	10.3672i	1.28998	+	0.541162i	0.921465	−	0.388460i	$-0.126993\pi$
$367$	24.7125	+	10.3672i	1.28998	+	0.541162i	0.368514	+	0.929622i	$0.379867\pi$
$368$	1.90118	+	4.77159i	0.0991057	+	0.248736i
$369$	−29.9813	−	2.94687i	−1.56077	−	0.153408i
$370$	−1.85007	−	11.2849i	−0.0961804	−	0.586674i
$371$	−20.0552	+	13.0755i	−1.04121	+	0.678849i
$372$	2.86130	+	16.9045i	0.148352	+	0.876456i
$373$	3.28305	+	13.7295i	0.169990	+	0.710885i	0.990298	+	0.138963i	$0.0443769\pi$
$373$	3.28305	+	13.7295i	0.169990	+	0.710885i	−0.820308	+	0.571922i	$0.806198\pi$
$374$	0.962394	−	4.78185i	0.0497642	−	0.247264i
$375$	−5.61885	+	9.84957i	−0.290156	+	0.508629i
$376$	−3.72136	+	3.78917i	−0.191915	+	0.195411i
$377$	−15.2696	+	3.36109i	−0.786423	+	0.173105i
$378$	1.92678	+	57.3432i	0.0991028	+	2.94942i
$379$	14.3452	+	27.0580i	0.736865	+	1.38987i	0.914011	+	0.405690i	$0.132969\pi$
$379$	14.3452	+	27.0580i	0.736865	+	1.38987i	−0.177146	+	0.984185i	$0.556686\pi$
$380$	10.7107	−	0.386936i	0.549449	−	0.0198494i
$381$	5.53712	+	11.2734i	0.283675	+	0.577554i
$382$	−2.63215	+	0.782265i	−0.134673	+	0.0400241i
$383$	−13.2415	+	9.33130i	−0.676609	+	0.476807i	−0.862694	−	0.505726i	$-0.831225\pi$
$383$	−13.2415	+	9.33130i	−0.676609	+	0.476807i	0.186085	+	0.982534i	$0.440420\pi$
$384$	0.718803	−	14.6614i	0.0366813	−	0.748186i
$385$	−2.99654	+	12.5313i	−0.152718	+	0.638655i
$386$	11.8271	+	17.4436i	0.601982	+	0.887857i
$387$	16.8893	+	4.17638i	0.858533	+	0.212297i
$388$	13.8881	+	26.1957i	0.705061	+	1.32989i
$389$	24.1843	+	1.74965i	1.22620	+	0.0887107i	0.670013	−	0.742350i	$-0.266289\pi$
$389$	24.1843	+	1.74965i	1.22620	+	0.0887107i	0.556182	+	0.831060i	$0.312266\pi$
$390$	5.85706	−	12.2436i	0.296584	−	0.619978i
$391$	−1.17041	−	0.302312i	−0.0591900	−	0.0152886i
$392$	13.5759	+	17.2050i	0.685687	+	0.868982i
$393$	−2.50444	+	7.12822i	−0.126332	+	0.359571i
$394$	28.7842	+	8.55454i	1.45013	+	0.430971i
$395$	−0.353850	−	0.0778882i	−0.0178041	−	0.00391898i
$396$	6.05925	−	26.5520i	0.304489	−	1.33429i
$397$	2.95312	+	18.0132i	0.148213	+	0.904059i	0.951316	+	0.308218i	$0.0997328\pi$
$397$	2.95312	+	18.0132i	0.148213	+	0.904059i	−0.803103	+	0.595841i	$0.796819\pi$
$398$	−10.5312	+	29.4852i	−0.527881	+	1.47796i
$399$	−40.3132	+	38.5847i	−2.01819	+	1.93165i
$400$	1.54256	+	12.1401i	0.0771280	+	0.607005i
$401$	−0.614904	−	34.0533i	−0.0307069	−	1.70054i	−0.541389	−	0.840773i	$-0.682101\pi$
$401$	−0.614904	−	34.0533i	−0.0307069	−	1.70054i	0.510682	−	0.859770i	$-0.329393\pi$
$402$	9.74248	−	31.2996i	0.485911	−	1.56108i
$403$	8.51905	+	19.3216i	0.424364	+	0.962476i
$404$	−16.2803	−	12.3760i	−0.809977	−	0.615729i
$405$	−1.34545	−	6.03606i	−0.0668561	−	0.299934i
$406$	−1.74165	+	32.1228i	−0.0864366	+	1.59423i
$407$	−16.6944	−	22.8043i	−0.827512	−	1.13037i
$408$	0.938030	+	0.759973i	0.0464394	+	0.0376243i
$409$	−5.71845	−	16.0105i	−0.282759	−	0.791667i	−0.995885	−	0.0906305i	$-0.971112\pi$
$409$	−5.71845	−	16.0105i	−0.282759	−	0.791667i	0.713125	−	0.701037i	$-0.247279\pi$
$410$	11.0023	−	9.69276i	0.543364	−	0.478691i
$411$	9.64788	+	9.04464i	0.475895	+	0.446139i
$412$	−6.01768	−	10.4229i	−0.296470	−	0.513500i
$413$	25.4839	+	30.7179i	1.25398	+	1.51153i
$414$	−11.6483	−	3.33096i	−0.572485	−	0.163708i
$415$	2.09636	−	0.969881i	0.102906	−	0.0476096i
$416$	−8.40186	−	41.7464i	−0.411935	−	2.04678i
$417$	0.231842	+	1.12189i	0.0113534	+	0.0549393i
$418$	41.5988	−	23.0259i	2.03467	−	1.12623i
$419$	−1.25309	+	2.84206i	−0.0612174	+	0.138844i	−0.942980	−	0.332850i	$-0.891990\pi$
$419$	−1.25309	+	2.84206i	−0.0612174	+	0.138844i	0.881762	+	0.471694i	$0.156357\pi$
$420$	−11.7266	−	10.2235i	−0.572200	−	0.498857i
$421$	−17.6443	+	4.55745i	−0.859929	+	0.222117i	−0.654041	−	0.756459i	$-0.726928\pi$
$421$	−17.6443	+	4.55745i	−0.859929	+	0.222117i	−0.205888	+	0.978576i	$0.566008\pi$
$422$	−16.0458	−	12.1977i	−0.781096	−	0.593774i
$423$	1.98204	+	14.4044i	0.0963702	+	0.700365i
$424$	−0.816805	+	4.98229i	−0.0396676	+	0.241961i
$425$	−2.51980	−	1.39477i	−0.122228	−	0.0676562i
$426$	15.0499	+	8.94940i	0.729168	+	0.433600i
$427$	−55.4855	−	8.07060i	−2.68513	−	0.390563i
$428$	−30.8815	+	5.63708i	−1.49271	+	0.272479i
$429$	−0.779229	−	33.5340i	−0.0376215	−	1.61904i
$430$	−7.09351	+	4.62481i	−0.342079	+	0.223028i
$431$	−18.1393	−	3.99277i	−0.873741	−	0.192325i	−0.244607	−	0.969622i	$-0.578659\pi$
$431$	−18.1393	−	3.99277i	−0.873741	−	0.192325i	−0.629133	+	0.777297i	$0.716590\pi$
$432$	−10.6808	−	9.11885i	−0.513881	−	0.438731i
$433$	−8.85942	+	2.98509i	−0.425757	+	0.143454i	−0.524019	−	0.851706i	$-0.675568\pi$
$433$	−8.85942	+	2.98509i	−0.425757	+	0.143454i	0.0982626	+	0.995161i	$0.468671\pi$
$434$	42.9953	−	6.25384i	2.06384	−	0.300194i
$435$	−0.454872	−	3.43746i	−0.0218095	−	0.164814i
$436$	1.55432	−	4.90393i	0.0744384	−	0.234856i
$437$	−5.13987	−	10.6030i	−0.245873	−	0.507210i
$438$	−21.0375	+	25.0288i	−1.00521	+	1.19592i
$439$	−7.38171	+	0.266671i	−0.352310	+	0.0127275i	−0.211692	−	0.977336i	$-0.567897\pi$
$439$	−7.38171	+	0.266671i	−0.352310	+	0.0127275i	−0.140618	+	0.990064i	$0.544909\pi$
$440$	1.52483	+	2.24896i	0.0726934	+	0.107215i
$441$	59.9977	−	0.621321i	2.85703	−	0.0295867i
$442$	6.58339	+	3.04580i	0.313140	+	0.144874i
$443$	−3.37755	−	37.3120i	−0.160472	−	1.77275i	−0.534343	−	0.845268i	$-0.679441\pi$
$443$	−3.37755	−	37.3120i	−0.160472	−	1.77275i	0.373870	−	0.927481i	$-0.378030\pi$
$444$	33.7435	−	5.08667i	1.60139	−	0.241403i
$445$	11.2555	−	0.814296i	0.533563	−	0.0386013i
$446$	19.3182	+	30.8329i	0.914741	+	1.45998i
$447$	30.1422	+	5.34101i	1.42568	+	0.252621i
$448$	−59.3742	−	4.29551i	−2.80517	−	0.202944i
$449$	15.9888	−	3.51940i	0.754558	−	0.166091i	0.178997	−	0.983850i	$-0.442715\pi$
$449$	15.9888	−	3.51940i	0.754558	−	0.166091i	0.575561	+	0.817759i	$0.304784\pi$
$450$	−24.8861	−	14.6246i	−1.17314	−	0.689412i
$451$	13.4131	−	33.6643i	0.631597	−	1.58519i
$452$	−29.1549	−	25.6848i	−1.37133	−	1.20811i
$453$	2.17989	+	0.994856i	0.102420	+	0.0467424i
$454$	38.4318	−	42.0678i	1.80369	−	1.97434i
$455$	−17.0883	−	8.66811i	−0.801113	−	0.406367i
$456$	0.273376	+	11.7647i	0.0128020	+	0.550931i
$457$	−7.25373	+	20.3089i	−0.339315	+	0.950012i	0.643504	+	0.765443i	$0.277480\pi$
$457$	−7.25373	+	20.3089i	−0.339315	+	0.950012i	−0.982819	+	0.184570i	$0.940911\pi$
$458$	−7.22759	−	18.1399i	−0.337723	−	0.847621i
$459$	3.21646	−	0.760563i	0.150132	−	0.0355001i
$460$	2.81483	−	1.69362i	0.131242	−	0.0789657i
$461$	11.5422	−	4.35906i	0.537575	−	0.203022i	−0.0696217	−	0.997573i	$-0.522179\pi$
$461$	11.5422	−	4.35906i	0.537575	−	0.203022i	0.607196	+	0.794552i	$0.292294\pi$
$462$	−66.9118	−	16.9140i	−3.11302	−	0.786911i
$463$	−22.3283	+	9.36700i	−1.03769	+	0.435321i	−0.838650	−	0.544671i	$-0.816655\pi$
$463$	−22.3283	+	9.36700i	−1.03769	+	0.435321i	−0.199036	+	0.979992i	$0.563781\pi$
$464$	−5.51751	−	5.61804i	−0.256144	−	0.260811i
$465$	−4.43005	+	1.51824i	−0.205439	+	0.0704069i
$466$	−8.73070	−	11.9260i	−0.404442	−	0.552460i
$467$	−6.65149	−	4.00207i	−0.307794	−	0.185194i	0.353273	−	0.935520i	$-0.385069\pi$
$467$	−6.65149	−	4.00207i	−0.307794	−	0.185194i	−0.661067	+	0.750327i	$0.729896\pi$
$468$	36.3078	+	17.9470i	1.67833	+	0.829601i
$469$	−43.8563	−	14.7769i	−2.02510	−	0.682334i
$470$	−5.78488	−	4.07661i	−0.266837	−	0.188040i
$471$	2.81422	−	3.60474i	0.129673	−	0.166098i
$472$	8.40733	+	0.401538i	0.386979	+	0.0184823i
$473$	−10.4639	+	18.1241i	−0.481133	+	0.833346i
$474$	0.441580	−	1.88986i	0.0202825	−	0.0868044i
$475$	−5.53906	−	27.5220i	−0.254150	−	1.26279i
$476$	5.38284	−	6.33716i	0.246722	−	0.290463i
$477$	9.42810	+	10.1079i	0.431683	+	0.462808i
$478$	4.74565	−	0.516121i	0.217061	−	0.0236068i
$479$	−19.4035	+	9.84251i	−0.886570	+	0.449716i	−0.835825	−	0.548996i	$-0.815010\pi$
$479$	−19.4035	+	9.84251i	−0.886570	+	0.449716i	−0.0507453	+	0.998712i	$0.516160\pi$
$480$	9.38303	−	1.06965i	0.428275	−	0.0488227i
$481$	38.7569	−	16.2590i	1.76716	−	0.741346i
$482$	−1.22815	+	1.67763i	−0.0559408	+	0.0764142i
$483$	−5.08329	+	16.3311i	−0.231298	+	0.743089i
$484$	4.45142	+	2.46396i	0.202337	+	0.111998i
$485$	−6.44717	+	4.90101i	−0.292751	+	0.222544i
$486$	32.4223	−	6.78997i	1.47070	−	0.307999i
$487$	2.85541	+	3.36165i	0.129391	+	0.152331i	0.823042	−	0.567980i	$-0.192275\pi$
$487$	2.85541	+	3.36165i	0.129391	+	0.152331i	−0.693651	+	0.720311i	$0.743999\pi$
$488$	−9.14862	+	7.49082i	−0.414139	+	0.339093i
$489$	1.33501	−	15.6500i	0.0603710	−	0.707717i
$490$	−19.6973	+	21.5609i	−0.889834	+	0.974022i
$491$	3.07121	+	12.8436i	0.138602	+	0.579622i	0.997698	+	0.0678089i	$0.0216008\pi$
$491$	3.07121	+	12.8436i	0.138602	+	0.579622i	−0.859097	+	0.511813i	$0.828974\pi$
$492$	28.4989	+	33.2015i	1.28483	+	1.49684i
$493$	1.83388	−	0.266745i	0.0825938	−	0.0120136i
$494$	18.9163	+	68.1302i	0.851083	+	3.06532i
$495$	7.42466	+	0.459915i	0.333714	+	0.0206716i
$496$	−5.96813	+	8.80234i	−0.267977	+	0.395237i
$497$	13.1246	−	20.9477i	0.588720	−	0.939631i
$498$	5.05013	+	11.2951i	0.226302	+	0.506147i
$499$	16.3398	−	1.18213i	0.731470	−	0.0529192i	0.298604	−	0.954377i	$-0.403479\pi$
$499$	16.3398	−	1.18213i	0.731470	−	0.0529192i	0.432867	+	0.901458i	$0.357502\pi$
$500$	15.7873	−	4.69192i	0.706030	−	0.209829i
$501$	10.4974	−	5.39336i	0.468989	−	0.240957i
$502$	1.64365	+	18.1575i	0.0733596	+	0.810409i
$503$	27.4150	+	25.9689i	1.22237	+	1.15789i	0.982335	+	0.187132i	$0.0599192\pi$
$503$	27.4150	+	25.9689i	1.22237	+	1.15789i	0.240040	+	0.970763i	$0.422839\pi$
$504$	11.3901	−	12.7300i	0.507355	−	0.567038i
$505$	2.61645	−	4.93515i	0.116430	−	0.219611i
$506$	7.73754	−	12.3495i	0.343976	−	0.549004i
$507$	26.7564	+	5.74446i	1.18830	+	0.255120i
$508$	5.51168	−	17.3895i	0.244541	−	0.771536i
$509$	31.1633	+	8.04937i	1.38129	+	0.356782i	0.865918	−	0.500185i	$-0.166735\pi$
$509$	31.1633	+	8.04937i	1.38129	+	0.356782i	0.515370	+	0.856968i	$0.327654\pi$
$510$	−0.797121	+	1.39731i	−0.0352971	+	0.0618741i
$511$	34.6353	+	30.5129i	1.53217	+	1.34981i
$512$	19.8703	−	18.8221i	0.878151	−	0.831829i
$513$	25.9479	+	19.0965i	1.14563	+	0.843129i
$514$	3.42279	+	63.1296i	0.150973	+	2.78453i
$515$	2.54351	−	2.08261i	0.112081	−	0.0917707i
$516$	−13.5271	−	21.3436i	−0.595498	−	0.939601i
$517$	−17.3080	−	2.51752i	−0.761205	−	0.110720i
$518$	−10.9004	−	85.7873i	−0.478937	−	3.76928i
$519$	9.77900	+	7.35422i	0.429250	+	0.322814i
$520$	−3.78016	+	1.42762i	−0.165771	+	0.0626054i
$521$	−26.3401	−	2.86466i	−1.15398	−	0.125503i	−0.488946	−	0.872314i	$-0.662618\pi$
$521$	−26.3401	−	2.86466i	−1.15398	−	0.125503i	−0.665036	+	0.746811i	$0.731584\pi$
$522$	18.4426	−	2.19922i	0.807211	−	0.0962571i
$523$	7.67769	−	27.6526i	0.335722	−	1.20916i	−0.582413	−	0.812893i	$-0.697891\pi$
$523$	7.67769	−	27.6526i	0.335722	−	1.20916i	0.918135	−	0.396268i	$-0.129695\pi$
$524$	9.78651	−	4.96424i	0.427526	−	0.216864i
$525$	−21.4572	+	34.6442i	−0.936468	+	1.51200i
$526$	53.0365	−	29.3569i	2.31250	−	1.28002i
$527$	−0.841852	−	2.35701i	−0.0366716	−	0.102673i
$528$	14.1034	−	9.29949i	0.613770	−	0.404708i
$529$	15.8485	+	11.1685i	0.689065	+	0.485586i
$530$	−6.72764			−0.292230
$531$	14.9401	−	17.5440i	0.648345	−	0.761347i
$532$	81.0488			3.51391
$533$	44.0514	+	31.0431i	1.90808	+	1.34462i
$534$	3.58505	+	60.3413i	0.155140	+	2.61122i
$535$	−2.88407	−	8.07480i	−0.124689	−	0.349104i
$536$	−8.53865	+	4.72633i	−0.368813	+	0.204147i
$537$	20.6662	+	0.639462i	0.891812	+	0.0275948i
$538$	−13.3890	+	6.79162i	−0.577241	+	0.292808i
$539$	−19.3087	+	69.5437i	−0.831685	+	2.99546i
$540$	−4.65012	+	7.68462i	−0.200109	+	0.330693i
$541$	1.32215	+	0.143792i	0.0568437	+	0.00618212i	0.136497	−	0.990641i	$-0.456416\pi$
$541$	1.32215	+	0.143792i	0.0568437	+	0.00618212i	−0.0796530	+	0.996823i	$0.525381\pi$
$542$	−11.1143	+	4.19746i	−0.477402	+	0.180297i
$543$	−18.0839	+	7.69678i	−0.776057	+	0.330300i
$544$	0.636207	+	5.00701i	0.0272771	+	0.214674i
$545$	1.39051	+	0.202255i	0.0595628	+	0.00866365i
$546$	47.6055	−	90.9281i	2.03733	−	3.89136i
$547$	−6.53009	+	5.34679i	−0.279206	+	0.228612i	−0.762726	−	0.646721i	$-0.776140\pi$
$547$	−6.53009	+	5.34679i	−0.279206	+	0.228612i	0.483520	+	0.875333i	$0.339358\pi$
$548$	−1.03987	−	19.1793i	−0.0444212	−	0.819300i
$549$	0.919567	+	32.3584i	0.0392462	+	1.38102i
$550$	25.2077	−	23.8780i	1.07486	−	1.01816i
$551$	13.5544	+	11.9411i	0.577436	+	0.508708i
$552$	1.81961	+	3.11431i	0.0774479	+	0.132554i
$553$	−2.65285	−	0.685221i	−0.112811	−	0.0291386i
$554$	−2.12335	+	6.69923i	−0.0902124	+	0.284623i
$555$	2.86218	+	8.87056i	0.121493	+	0.376534i
$556$	0.883424	−	1.40999i	0.0374655	−	0.0597971i
$557$	−19.1053	+	36.0365i	−0.809519	+	1.52691i	0.0399056	+	0.999203i	$0.487294\pi$
$557$	−19.1053	+	36.0365i	−0.809519	+	1.52691i	−0.849424	+	0.527711i	$0.823051\pi$
$558$	−7.82623	−	23.8323i	−0.331311	−	1.00890i
$559$	−22.5948	−	21.4029i	−0.955657	−	0.905246i
$560$	−0.869989	−	9.61084i	−0.0367638	−	0.406132i
$561$	−0.194685	+	3.97097i	−0.00821959	+	0.167655i
$562$	−3.25118	+	0.966238i	−0.137143	+	0.0407583i
$563$	−4.09479	+	0.296243i	−0.172575	+	0.0124852i	−0.158175	−	0.987411i	$-0.550561\pi$
$563$	−4.09479	+	0.296243i	−0.172575	+	0.0124852i	−0.0144003	+	0.999896i	$0.504584\pi$
$564$	12.3863	−	17.1045i	0.521556	−	0.720230i
$565$	5.63483	−	8.99351i	0.237059	−	0.378360i
$566$	25.5890	−	37.7409i	1.07558	−	1.58637i
$567$	−8.51994	−	45.9830i	−0.357804	−	1.93110i
$568$	−1.39461	−	5.02295i	−0.0585167	−	0.210758i
$569$	−22.0011	+	3.20015i	−0.922333	+	0.134157i	−0.588521	−	0.808482i	$-0.700289\pi$
$569$	−22.0011	+	3.20015i	−0.922333	+	0.134157i	−0.333813	+	0.942639i	$0.608335\pi$
$570$	−15.4112	+	2.89569i	−0.645506	+	0.121287i
$571$	3.54137	+	14.8097i	0.148202	+	0.619769i	0.995992	+	0.0894377i	$0.0285070\pi$
$571$	3.54137	+	14.8097i	0.148202	+	0.619769i	−0.847791	+	0.530331i	$0.822068\pi$
$572$	−32.8597	+	35.9686i	−1.37393	+	1.50392i
$573$	2.02640	−	0.950282i	0.0846542	−	0.0396986i
$574$	85.7926	−	70.2463i	3.58091	−	2.93202i
$575$	−5.57065	−	6.55827i	−0.232312	−	0.273499i
$576$	3.45276	+	34.1952i	0.143865	+	1.42480i
$577$	−12.5261	+	9.52210i	−0.521469	+	0.396410i	−0.832530	−	0.553980i	$-0.813109\pi$
$577$	−12.5261	+	9.52210i	−0.521469	+	0.396410i	0.311062	+	0.950390i	$0.399315\pi$
$578$	30.8541	+	17.0784i	1.28336	+	0.710369i
$579$	−11.6516	−	12.6221i	−0.484226	−	0.524558i
$580$	−2.97487	+	4.06362i	−0.123525	+	0.168733i
$581$	16.1074	−	6.75725i	0.668248	−	0.280338i
$582$	−25.8054	−	34.8695i	−1.06967	−	1.44539i
$583$	−14.8282	+	7.52164i	−0.614120	+	0.311515i
$584$	9.67707	−	1.05245i	0.400440	−	0.0435505i
$585$	−3.23308	+	10.5796i	−0.133671	+	0.437413i
$586$	−34.1614	+	40.2179i	−1.41119	+	1.66139i
$587$	1.76774	+	8.78341i	0.0729626	+	0.362530i	0.999920	−	0.0126364i	$-0.00402238\pi$
$587$	1.76774	+	8.78341i	0.0729626	+	0.362530i	−0.926958	+	0.375166i	$0.877586\pi$
$588$	−63.5774	−	59.6022i	−2.62189	−	2.45795i
$589$	12.1984	−	21.1282i	0.502625	−	0.870573i
$590$	1.28443	+	11.1419i	0.0528790	+	0.458706i
$591$	−24.2386	−	3.39755i	−0.997044	−	0.139756i
$592$	17.3026	+	12.1932i	0.711132	+	0.501136i
$593$	10.5110	+	3.54156i	0.431634	+	0.145435i	0.526728	−	0.850034i	$-0.323419\pi$
$593$	10.5110	+	3.54156i	0.431634	+	0.145435i	−0.0950938	+	0.995468i	$0.530315\pi$
$594$	−2.97545	+	39.7352i	−0.122084	+	1.63035i
$595$	1.94601	+	1.17087i	0.0797785	+	0.0480011i
$596$	−26.2633	−	35.8751i	−1.07579	−	1.46950i
$597$	4.90551	−	25.0438i	0.200769	−	1.02497i
$598$	15.1857	+	15.4624i	0.620990	+	0.632304i
$599$	19.5861	−	8.21662i	0.800268	−	0.335722i	0.0516010	−	0.998668i	$-0.483568\pi$
$599$	19.5861	−	8.21662i	0.800268	−	0.335722i	0.748667	+	0.662946i	$0.230694\pi$
$600$	2.34190	+	8.26843i	0.0956075	+	0.337557i
$601$	−7.79417	+	2.94356i	−0.317931	+	0.120070i	−0.507133	−	0.861868i	$-0.669295\pi$
$601$	−7.79417	+	2.94356i	−0.317931	+	0.120070i	0.189202	+	0.981938i	$0.439410\pi$
$602$	−54.8697	+	33.0140i	−2.23632	+	1.34555i
$603$	−4.04938	+	26.4103i	−0.164904	+	1.07551i
$604$	−1.28818	−	3.23308i	−0.0524151	−	0.131552i
$605$	−0.467439	+	1.30873i	−0.0190041	+	0.0532075i
$606$	26.2524	+	14.3543i	1.06643	+	0.583102i
$607$	−1.02322	−	0.519034i	−0.0415314	−	0.0210669i	0.431493	−	0.902116i	$-0.357987\pi$
$607$	−1.02322	−	0.519034i	−0.0415314	−	0.0210669i	−0.473024	+	0.881049i	$0.656838\pi$
$608$	−33.1837	+	36.3232i	−1.34578	+	1.47310i
$609$	−2.49909	−	26.1017i	−0.101268	−	1.05770i
$610$	−11.8224	−	10.4153i	−0.478676	−	0.421703i
$611$	9.62732	−	24.1628i	0.389480	−	0.977520i
$612$	−4.13873	−	2.43218i	−0.167298	−	0.0983150i
$613$	29.7626	−	6.55124i	1.20210	−	0.264602i	0.431614	−	0.902059i	$-0.357944\pi$
$613$	29.7626	−	6.55124i	1.20210	−	0.264602i	0.770486	+	0.637456i	$0.220013\pi$
$614$	6.40535	+	0.463404i	0.258499	+	0.0187014i
$615$	−7.68991	+	9.14884i	−0.310087	+	0.368917i
$616$	10.9095	+	17.4121i	0.439554	+	0.701554i
$617$	28.6229	−	2.07076i	1.15231	−	0.0833657i	0.517256	−	0.855831i	$-0.326953\pi$
$617$	28.6229	−	2.07076i	1.15231	−	0.0833657i	0.635057	+	0.772465i	$0.280976\pi$
$618$	10.9791	+	13.7668i	0.441645	+	0.553783i
$619$	−2.34414	−	25.8959i	−0.0942189	−	1.04084i	−0.896246	−	0.443557i	$-0.853717\pi$
$619$	−2.34414	−	25.8959i	−0.0942189	−	1.04084i	0.802027	−	0.597287i	$-0.203755\pi$
$620$	6.17303	+	2.85595i	0.247915	+	0.114698i
$621$	9.79295	+	1.26943i	0.392978	+	0.0509404i
$622$	−34.0155	−	50.1691i	−1.36390	−	2.01160i
$623$	85.2825	−	3.08091i	3.41677	−	0.123434i
$624$	8.57258	+	23.6147i	0.343178	+	0.945345i
$625$	−7.91307	−	16.3238i	−0.316523	−	0.652953i
$626$	9.11174	−	28.7479i	0.364178	−	1.14900i
$627$	−30.7300	+	23.6124i	−1.22724	+	0.942987i
$628$	−6.57301	+	0.956070i	−0.262291	+	0.0381513i
$629$	−4.72081	+	1.59062i	−0.188231	+	0.0634224i
$630$	19.1950	+	12.2333i	0.764745	+	0.487387i
$631$	13.9743	+	3.07598i	0.556310	+	0.122453i	0.484222	−	0.874945i	$-0.339103\pi$
$631$	13.9743	+	3.07598i	0.556310	+	0.122453i	0.0720878	+	0.997398i	$0.477034\pi$
$632$	−0.484017	+	0.315568i	−0.0192531	+	0.0125526i
$633$	14.4144	+	7.88149i	0.572922	+	0.313261i
$634$	−26.3704	+	4.81364i	−1.04730	+	0.191174i
$635$	4.93080	+	0.717204i	0.195673	+	0.0284614i
$636$	0.258519	−	20.0742i	0.0102509	−	0.795995i
$637$	−93.9066	−	51.9794i	−3.72071	−	2.05950i
$638$	−3.61446	+	22.0472i	−0.143098	+	0.872859i
$639$	−13.2171	−	5.38447i	−0.522861	−	0.213006i
$640$	−4.63597	−	3.52417i	−0.183253	−	0.139305i
$641$	28.4445	−	7.34713i	1.12349	−	0.290194i	0.358052	−	0.933702i	$-0.383441\pi$
$641$	28.4445	−	7.34713i	1.12349	−	0.290194i	0.765440	+	0.643508i	$0.222522\pi$
$642$	43.4480	−	14.8903i	1.71476	−	0.587672i
$643$	−9.56578	+	21.6956i	−0.377237	+	0.855591i	0.620227	+	0.784422i	$0.287041\pi$
$643$	−9.56578	+	21.6956i	−0.377237	+	0.855591i	−0.997464	+	0.0711682i	$0.977327\pi$
$644$	21.7346	−	12.0306i	0.856462	−	0.474071i
$645$	5.15528	−	4.58931i	0.202989	−	0.180704i
$646$	−1.65354	−	8.21597i	−0.0650578	−	0.323253i
$647$	−21.9449	+	10.1528i	−0.862743	+	0.399148i	−0.800800	−	0.598932i	$-0.795592\pi$
$647$	−21.9449	+	10.1528i	−0.862743	+	0.399148i	−0.0619435	+	0.998080i	$0.519730\pi$
$648$	−8.37111	−	5.21397i	−0.328848	−	0.204824i
$649$	15.2879	+	23.1216i	0.600102	+	0.907601i
$650$	25.8177	+	44.7176i	1.01265	+	1.75397i
$651$	−33.8933	+	10.2642i	−1.32838	+	0.402286i
$652$	−17.1176	+	15.0802i	−0.670379	+	0.590588i
$653$	−4.77953	−	13.3817i	−0.187037	−	0.523666i	0.811084	−	0.584929i	$-0.198878\pi$
$653$	−4.77953	−	13.3817i	−0.187037	−	0.523666i	−0.998122	+	0.0612636i	$0.980487\pi$
$654$	−1.17920	+	7.43368i	−0.0461103	+	0.290680i
$655$	1.77054	+	2.41852i	0.0691806	+	0.0944995i
$656$	−1.46938	+	27.1012i	−0.0573698	+	1.05812i
$657$	13.9148	−	22.7285i	0.542866	−	0.886723i
$658$	−42.6045	−	32.3871i	−1.66090	−	1.26258i
$659$	5.81185	+	13.1815i	0.226398	+	0.513479i	0.991450	−	0.130489i	$-0.0416547\pi$
$659$	5.81185	+	13.1815i	0.226398	+	0.513479i	−0.765052	+	0.643968i	$0.777287\pi$
$660$	−7.32855	−	7.93897i	−0.285263	−	0.309024i
$661$	0.803072	+	44.4741i	0.0312359	+	1.72984i	0.517202	+	0.855863i	$0.326974\pi$
$661$	0.803072	+	44.4741i	0.0312359	+	1.72984i	−0.485966	+	0.873978i	$0.661532\pi$
$662$	0.724845	+	5.70461i	0.0281719	+	0.221716i
$663$	−5.67609	−	1.65497i	−0.220441	−	0.0642738i
$664$	1.23900	−	3.46895i	0.0480827	−	0.134621i
$665$	3.58150	+	21.8462i	0.138885	+	0.847158i
$666$	−47.7086	+	14.7181i	−1.84867	+	0.570317i
$667$	5.40732	+	1.19024i	0.209372	+	0.0460863i
$668$	−16.4309	−	4.88321i	−0.635732	−	0.188937i
$669$	−19.3160	−	22.5034i	−0.746800	−	0.870031i
$670$	−8.05573	−	10.2092i	−0.311220	−	0.394414i
$671$	−37.7019	−	9.73828i	−1.45547	−	0.375942i
$672$	71.2014	−	5.52189i	2.74665	−	0.213012i
$673$	−27.4415	−	1.98530i	−1.05779	−	0.0765275i	−0.467720	−	0.883877i	$-0.654924\pi$
$673$	−27.4415	−	1.98530i	−1.05779	−	0.0765275i	−0.590074	+	0.807349i	$0.700901\pi$
$674$	−3.92133	−	7.39641i	−0.151044	−	0.284899i
$675$	21.8344	+	8.76348i	0.840405	+	0.337307i
$676$	−22.3056	−	32.8982i	−0.857906	−	1.26532i
$677$	3.55287	−	14.8578i	0.136548	−	0.571034i	−0.861453	−	0.507837i	$-0.830445\pi$
$677$	3.55287	−	14.8578i	0.136548	−	0.571034i	0.998001	−	0.0631965i	$-0.0201295\pi$
$678$	47.7810	+	30.8008i	1.83502	+	1.18290i
$679$	−50.0606	+	35.2778i	−1.92115	+	1.35384i
$680$	0.459091	−	0.136440i	0.0176053	−	0.00523223i
$681$	−25.8639	+	38.5749i	−0.991106	+	1.47819i
$682$	30.1541	−	1.08935i	1.15466	−	0.0417132i
$683$	−11.4173	−	21.5354i	−0.436872	−	0.824027i	0.563126	−	0.826371i	$-0.309599\pi$
$683$	−11.4173	−	21.5354i	−0.436872	−	0.824027i	−0.999997	+	0.00234399i	$0.999254\pi$
$684$	−8.04807	−	46.0960i	−0.307726	−	1.76252i
$685$	5.12371	−	1.12781i	0.195767	−	0.0430916i
$686$	−100.584	+	102.416i	−3.84030	+	3.91028i
$687$	8.02918	+	13.7421i	0.306332	+	0.524295i
$688$	3.09258	−	15.3661i	0.117904	−	0.585829i
$689$	−5.75050	−	24.0482i	−0.219077	−	0.916163i
$690$	−3.70295	+	3.06411i	−0.140969	+	0.116649i
$691$	31.0782	−	20.2623i	1.18227	−	0.770815i	0.204169	−	0.978936i	$-0.434551\pi$
$691$	31.0782	−	20.2623i	1.18227	−	0.770815i	0.978103	+	0.208121i	$0.0667347\pi$
$692$	−2.87510	−	17.5373i	−0.109295	−	0.666668i
$693$	55.9841	+	5.50268i	2.12666	+	0.209030i
$694$	1.95096	+	4.89655i	0.0740575	+	0.185870i
$695$	0.419093	+	0.175814i	0.0158971	+	0.00666902i
$696$	−4.41934	−	3.32353i	−0.167515	−	0.125978i
$697$	−4.94215	−	4.04659i	−0.187197	−	0.153276i
$698$	−9.02707	+	12.3308i	−0.341680	+	0.466728i
$699$	8.48568	+	8.55127i	0.320958	+	0.323439i
$700$	57.3065	−	14.8021i	2.16598	−	0.559466i
$701$	−0.529053	+	9.75780i	−0.0199820	+	0.368547i	0.971392	+	0.237483i	$0.0763223\pi$
$701$	−0.529053	+	9.75780i	−0.0199820	+	0.368547i	−0.991374	+	0.131065i	$0.958160\pi$
$702$	−56.4420	−	18.0463i	−2.13026	−	0.681112i
$703$	−41.6077	−	25.0345i	−1.56927	−	0.944196i
$704$	−40.6702	−	7.42390i	−1.53282	−	0.279799i
$705$	5.15775	+	2.58280i	0.194252	+	0.0972738i
$706$	−1.46173	+	16.1478i	−0.0550128	+	0.607730i
$707$	21.1204	−	36.5816i	0.794313	−	1.37579i
$708$	−33.2951	+	3.40438i	−1.25131	+	0.127945i
$709$	9.79076	+	16.9581i	0.367700	+	0.636875i	0.989206	−	0.146535i	$-0.0468121\pi$
$709$	9.79076	+	16.9581i	0.367700	+	0.636875i	−0.621506	+	0.783410i	$0.713479\pi$
$710$	6.30437	−	2.91671i	0.236599	−	0.109462i
$711$	−0.126290	+	1.57683i	−0.00473624	+	0.0591358i
$712$	11.6506	−	13.7162i	0.436625	−	0.514035i
$713$	0.135005	−	7.47656i	0.00505597	−	0.279999i
$714$	−6.40549	+	10.3421i	−0.239719	+	0.387045i
$715$	−11.1471	−	7.26769i	−0.416879	−	0.271796i
$716$	−21.0421	−	21.4255i	−0.786380	−	0.800707i
$717$	−3.76216	+	0.992561i	−0.140501	+	0.0370679i
$718$	8.43810	+	19.1380i	0.314907	+	0.714223i
$719$	−0.622899	+	3.79952i	−0.0232302	+	0.141698i	−0.995895	−	0.0905155i	$-0.971149\pi$
$719$	−0.622899	+	3.79952i	−0.0232302	+	0.141698i	0.972665	+	0.232214i	$0.0745968\pi$
$720$	−5.37971	+	1.44915i	−0.200490	+	0.0540066i
$721$	19.7904	−	15.0443i	0.737033	−	0.560278i
$722$	25.5937	−	32.4354i	0.952500	−	1.20712i
$723$	0.786031	−	1.50135i	0.0292328	−	0.0558356i
$724$	26.7045	+	10.0853i	0.992465	+	0.374817i
$725$	11.7646	+	5.96764i	0.436927	+	0.221632i
$726$	−6.97739	−	2.59390i	−0.258955	−	0.0962686i
$727$	22.0561	+	6.55499i	0.818016	+	0.243111i	0.666654	−	0.745367i	$-0.267726\pi$
$727$	22.0561	+	6.55499i	0.818016	+	0.243111i	0.151362	+	0.988478i	$0.451634\pi$
$728$	−28.9571	+	9.75680i	−1.07322	+	0.361611i
$729$	−25.3065	+	9.41173i	−0.937278	+	0.348583i
$730$	3.47010	+	12.4982i	0.128434	+	0.462578i
$731$	2.48805	+	2.72344i	0.0920238	+	0.100730i
$732$	31.5319	−	34.8760i	1.16545	−	1.28906i
$733$	27.2947	+	0.986047i	1.00815	+	0.0364205i	0.535249	−	0.844694i	$-0.320218\pi$
$733$	27.2947	+	0.986047i	1.00815	+	0.0364205i	0.472903	+	0.881115i	$0.343206\pi$
$734$	30.2360	+	48.2583i	1.11603	+	1.78125i
$735$	13.2559	−	19.7707i	0.488953	−	0.729252i
$736$	−3.50707	+	14.6663i	−0.129272	+	0.540608i
$737$	−29.1694	−	13.4952i	−1.07447	−	0.497102i
$738$	−48.4713	−	41.8186i	−1.78425	−	1.53936i
$739$	−1.31001	−	1.24091i	−0.0481894	−	0.0456474i	0.663226	−	0.748419i	$-0.269187\pi$
$739$	−1.31001	−	1.24091i	−0.0481894	−	0.0456474i	−0.711415	+	0.702772i	$0.751945\pi$
$740$	5.90528	−	12.1820i	0.217083	−	0.447818i
$741$	−23.5236	−	52.6129i	−0.864161	−	1.93278i
$742$	−50.8421	−	1.83672i	−1.86647	−	0.0674281i
$743$	−0.160274	−	0.330627i	−0.00587987	−	0.0121295i	0.896886	−	0.442261i	$-0.145824\pi$
$743$	−0.160274	−	0.330627i	−0.00587987	−	0.0121295i	−0.902766	+	0.430131i	$0.858467\pi$
$744$	−3.22279	+	6.73692i	−0.118153	+	0.246987i
$745$	8.50935	−	8.66439i	0.311759	−	0.317439i
$746$	−11.1033	+	27.8672i	−0.406522	+	1.02029i
$747$	−5.44259	−	8.49000i	−0.199134	−	0.310633i
$748$	4.19222	−	3.97108i	0.153283	−	0.145197i
$749$	−19.5910	−	61.8103i	−0.715839	−	2.25850i
$750$	−21.8169	+	10.2310i	−0.796639	+	0.373584i
$751$	−36.0492	−	13.6144i	−1.31545	−	0.496797i	−0.406484	−	0.913658i	$-0.633245\pi$
$751$	−36.0492	−	13.6144i	−1.31545	−	0.496797i	−0.908970	+	0.416861i	$0.863130\pi$
$752$	12.8866	−	2.35230i	0.469925	−	0.0857797i
$753$	−3.53081	−	14.4348i	−0.128670	−	0.526032i
$754$	−30.6380	−	12.8530i	−1.11577	−	0.468078i
$755$	0.814531	−	0.490087i	0.0296438	−	0.0178361i
$756$	−37.2399	+	56.8046i	−1.35440	+	2.06596i
$757$	−9.25532	−	1.00658i	−0.336390	−	0.0365847i	−0.0616349	−	0.998099i	$-0.519631\pi$
$757$	−9.25532	−	1.00658i	−0.336390	−	0.0365847i	−0.274756	+	0.961514i	$0.588597\pi$
$758$	−8.20324	+	64.5603i	−0.297955	+	2.34494i
$759$	−4.73582	+	10.8935i	−0.171899	+	0.395409i
$760$	3.91073	+	2.54971i	0.141857	+	0.0924877i
$761$	−18.9804	+	43.0483i	−0.688037	+	1.56050i	0.133947	+	0.990988i	$0.457235\pi$
$761$	−18.9804	+	43.0483i	−0.688037	+	1.56050i	−0.821985	+	0.569510i	$0.807133\pi$
$762$	−4.18149	+	26.3601i	−0.151479	+	0.954927i
$763$	10.4531	+	1.90810i	0.378428	+	0.0690780i
$764$	−3.08057	−	1.03797i	−0.111451	−	0.0375523i
$765$	0.472690	−	1.22304i	0.0170901	−	0.0442193i
$766$	−34.4232			−1.24376
$767$	−38.7293	+	14.1149i	−1.39844	+	0.509659i
$768$	−5.22638	+	6.69447i	−0.188591	+	0.241566i
$769$	1.41368	−	15.6170i	0.0509785	−	0.563164i	−0.929803	−	0.368057i	$-0.880023\pi$
$769$	1.41368	−	15.6170i	0.0509785	−	0.563164i	0.980782	−	0.195107i	$-0.0625055\pi$
$770$	−20.5445	+	18.0993i	−0.740373	+	0.652252i
$771$	−10.4287	−	50.4649i	−0.375581	−	1.81745i
$772$	−0.450441	+	24.9454i	−0.0162117	+	0.897805i
$773$	26.3307	−	2.86364i	0.947049	−	0.102998i	0.378458	−	0.925618i	$-0.376454\pi$
$773$	26.3307	−	2.86364i	0.947049	−	0.102998i	0.568591	+	0.822620i	$0.307489\pi$
$774$	24.2250	+	27.9285i	0.870750	+	1.00387i
$775$	4.76633	−	17.1668i	0.171212	−	0.616649i
$776$	−1.62792	+	12.8119i	−0.0584390	+	0.459921i
$777$	19.2083	+	67.8179i	0.689094	+	2.43296i
$778$	39.8672	+	32.6430i	1.42931	+	1.17031i
$779$	−1.12410	−	62.2525i	−0.0402750	−	2.23043i
$780$	14.0172	−	7.85391i	0.501895	−	0.281215i
$781$	10.6343	−	13.4770i	0.380526	−	0.482247i
$782$	−1.66297	−	1.95780i	−0.0594678	−	0.0700109i
$783$	−14.5970	+	4.01322i	−0.521656	+	0.143421i
$784$	−2.92654	−	53.9769i	−0.104519	−	1.92775i
$785$	−0.548160	−	1.72946i	−0.0195647	−	0.0617272i
$786$	−13.0759	+	9.31628i	−0.466400	+	0.332301i
$787$	−5.12655	+	25.4723i	−0.182742	+	0.907990i	0.777514	+	0.628866i	$0.216481\pi$
$787$	−5.12655	+	25.4723i	−0.182742	+	0.907990i	−0.960255	+	0.279123i	$0.909956\pi$
$788$	22.0206	+	27.9071i	0.784453	+	0.994151i
$789$	−39.1792	+	30.1046i	−1.39482	+	1.07175i
$790$	−0.519305	−	0.568437i	−0.0184761	−	0.0202241i
$791$	45.0389	−	66.4273i	1.60140	−	2.36188i
$792$	8.81972	−	7.93369i	0.313395	−	0.281911i
$793$	27.1245	−	51.1622i	0.963219	−	1.81682i
$794$	−16.9201	+	34.9044i	−0.600473	+	1.23871i
$795$	5.42230	−	0.817386i	0.192309	−	0.0289897i
$796$	−30.2980	+	21.3510i	−1.07388	+	0.756767i
$797$	−9.01638	+	6.35386i	−0.319376	+	0.225065i	−0.724628	−	0.689140i	$-0.757988\pi$
$797$	−9.01638	+	6.35386i	−0.319376	+	0.225065i	0.405252	+	0.914205i	$0.367184\pi$
$798$	−117.256	+	17.6758i	−4.15083	+	0.625718i
$799$	−1.34477	+	2.77412i	−0.0475747	+	0.0981414i
$800$	−16.8292	+	31.7432i	−0.595001	+	1.12229i
$801$	−10.2207	−	48.1979i	−0.361131	−	1.70299i
$802$	40.6162	−	59.9044i	1.43421	−	2.11530i
$803$	21.6215	+	23.6672i	0.763007	+	0.835196i
$804$	30.7721	−	23.6447i	1.08525	−	0.833885i
$805$	4.20320	+	5.32679i	0.148143	+	0.187745i
$806$	−8.85345	+	43.9902i	−0.311850	+	1.54949i
$807$	9.96603	−	7.10059i	0.350821	−	0.249952i
$808$	−2.69143	−	8.49155i	−0.0946841	−	0.298732i
$809$	−0.720261	−	13.2844i	−0.0253230	−	0.467056i	−0.983503	−	0.180890i	$-0.942102\pi$
$809$	−0.720261	−	13.2844i	−0.0253230	−	0.467056i	0.958180	−	0.286165i	$-0.0923807\pi$
$810$	5.05157	−	12.1318i	0.177494	−	0.426267i
$811$	13.0379	+	15.3493i	0.457821	+	0.538988i	0.941837	−	0.336071i	$-0.109098\pi$
$811$	13.0379	+	15.3493i	0.457821	+	0.538988i	−0.484016	+	0.875059i	$0.660822\pi$
$812$	−23.5911	+	29.8974i	−0.827885	+	1.04919i
$813$	8.44788	−	4.73340i	0.296280	−	0.166008i
$814$	−1.08428	−	60.0472i	−0.0380039	−	2.10465i
$815$	−4.82120	−	3.94756i	−0.168879	−	0.138277i
$816$	−0.811462	−	2.86499i	−0.0284068	−	0.100295i
$817$	−4.53242	+	35.6706i	−0.158569	+	1.24796i
$818$	9.66510	−	34.8106i	0.337932	−	1.21712i
$819$	−27.3213	+	79.0695i	−0.954685	+	2.76291i
$820$	17.2567	−	1.87678i	0.602629	−	0.0655399i
$821$	−0.220696	+	12.2221i	−0.00770236	+	0.426556i	0.972974	+	0.230917i	$0.0741724\pi$
$821$	−0.220696	+	12.2221i	−0.00770236	+	0.426556i	−0.980676	+	0.195639i	$0.937322\pi$
$822$	5.68722	+	27.5207i	0.198365	+	0.959893i
$823$	19.2623	−	16.9697i	0.671442	−	0.591525i	−0.255464	−	0.966819i	$-0.582228\pi$
$823$	19.2623	−	16.9697i	0.671442	−	0.591525i	0.926906	+	0.375293i	$0.122458\pi$
$824$	0.472622	−	5.22109i	0.0164646	−	0.181885i
$825$	−17.4156	+	22.3077i	−0.606335	+	0.776654i
$826$	6.66479	+	84.5524i	0.231898	+	2.94196i
$827$	−3.67268			−0.127712			−0.0638558	−	0.997959i	$-0.520340\pi$
$827$	−3.67268			−0.127712			−0.0638558	+	0.997959i	$0.520340\pi$
$828$	−9.00054	−	11.1668i	−0.312790	−	0.388072i
$829$	−17.7133	−	5.96832i	−0.615209	−	0.207288i	−0.00559254	−	0.999984i	$-0.501780\pi$
$829$	−17.7133	−	5.96832i	−0.615209	−	0.207288i	−0.609617	+	0.792696i	$0.708677\pi$
$830$	4.82866	+	0.881420i	0.167605	+	0.0305945i
$831$	0.897426	−	5.65738i	0.0311314	−	0.196252i
$832$	24.8037	−	56.2558i	0.859912	−	1.95032i
$833$	10.6568	+	6.94803i	0.369238	+	0.240735i
$834$	−0.970578	+	2.23256i	−0.0336084	+	0.0773071i
$835$	0.590163	−	4.64464i	0.0204234	−	0.160734i
$836$	55.9571	+	6.08571i	1.93532	+	0.210479i
$837$	9.20328	+	18.2573i	0.318112	+	0.631066i
$838$	−5.65558	+	3.40285i	−0.195369	+	0.117550i
$839$	5.65762	+	2.37344i	0.195323	+	0.0819401i	0.482335	−	0.875987i	$-0.339789\pi$
$839$	5.65762	+	2.37344i	0.195323	+	0.0819401i	−0.287013	+	0.957927i	$0.592662\pi$
$840$	−1.61012	−	6.58255i	−0.0555545	−	0.227119i
$841$	20.1784	−	3.68336i	0.695808	−	0.127012i
$842$	−36.2273	−	13.6817i	−1.24848	−	0.471502i
$843$	2.50297	−	1.17377i	0.0862070	−	0.0404268i
$844$	−7.20937	−	22.7458i	−0.248157	−	0.782943i
$845$	7.88184	−	7.46607i	0.271144	−	0.256841i
$846$	−14.1894	+	27.4470i	−0.487840	+	0.943649i
$847$	−3.88983	+	9.76273i	−0.133656	+	0.335451i
$848$	8.72567	−	8.88465i	0.299641	−	0.305100i
$849$	−16.0386	+	33.5271i	−0.550444	+	1.15065i
$850$	−2.66966	−	5.50722i	−0.0915684	−	0.188896i
$851$	−14.8738	−	0.537332i	−0.509868	−	0.0184195i
$852$	8.46075	+	18.9233i	0.289861	+	0.648302i
$853$	−8.11063	+	16.7314i	−0.277703	+	0.572871i	−0.991892	−	0.127081i	$-0.959439\pi$
$853$	−8.11063	+	16.7314i	−0.277703	+	0.572871i	0.714190	+	0.699952i	$0.246795\pi$
$854$	−86.5009	−	81.9380i	−2.96000	−	2.80386i
$855$	12.0692	−	4.20626i	0.412759	−	0.143851i
$856$	−12.4100	−	5.74149i	−0.424166	−	0.196240i
$857$	3.05951	−	12.7946i	0.104511	−	0.437057i	−0.895456	−	0.445149i	$-0.853151\pi$
$857$	3.05951	−	12.7946i	0.104511	−	0.437057i	0.999967	+	0.00809254i	$0.00257597\pi$
$858$	39.6950	−	59.2034i	1.35516	−	2.02117i
$859$	−10.0593	−	16.0551i	−0.343217	−	0.547794i	0.630316	−	0.776339i	$-0.282925\pi$
$859$	−10.0593	−	16.0551i	−0.343217	−	0.547794i	−0.973534	+	0.228544i	$0.926603\pi$
$860$	−10.0182	−	0.361916i	−0.341617	−	0.0123412i
$861$	−60.6119	+	67.0402i	−2.06565	+	2.28472i
$862$	−26.6211	−	29.1397i	−0.906717	−	0.992502i
$863$	11.9795	+	43.1463i	0.407787	+	1.46872i	0.827710	+	0.561156i	$0.189643\pi$
$863$	11.9795	+	43.1463i	0.407787	+	1.46872i	−0.419923	+	0.907560i	$0.637943\pi$
$864$	−10.2108	−	39.9470i	−0.347378	−	1.35903i
$865$	4.60002	−	1.54993i	0.156405	−	0.0526991i
$866$	−19.0431	−	5.65953i	−0.647111	−	0.192319i
$867$	−26.9425	−	10.0161i	−0.915016	−	0.340164i
$868$	45.8711	+	23.2682i	1.55697	+	0.789776i
$869$	−1.78011	−	0.672280i	−0.0603860	−	0.0228055i
$870$	3.41763	−	6.52777i	0.115868	−	0.221312i
$871$	29.6073	−	37.5218i	1.00320	−	1.27138i
$872$	1.78390	−	1.35608i	0.0604104	−	0.0459228i
$873$	25.0350	+	24.9686i	0.847306	+	0.845058i
$874$	4.05089	−	24.7094i	0.137024	−	0.835807i
$875$	13.7244	+	31.1275i	0.463970	+	1.05230i
$876$	−37.4259	+	9.87396i	−1.26450	+	0.333610i
$877$	22.4853	+	22.8950i	0.759275	+	0.773109i	0.979306	−	0.202383i	$-0.0648687\pi$
$877$	22.4853	+	22.8950i	0.759275	+	0.773109i	−0.220031	+	0.975493i	$0.570616\pi$
$878$	−13.1487	−	8.57264i	−0.443746	−	0.289313i
$879$	22.6468	−	36.5650i	0.763858	−	1.23331i
$880$	0.120996	−	6.70077i	0.00407879	−	0.225883i
$881$	−36.2904	+	42.7244i	−1.22266	+	1.43942i	−0.360515	+	0.932753i	$0.617399\pi$
$881$	−36.2904	+	42.7244i	−1.22266	+	1.43942i	−0.862141	+	0.506668i	$0.830877\pi$
$882$	104.978	+	72.3632i	3.53481	+	2.43660i
$883$	−23.9319	+	11.0721i	−0.805371	+	0.372604i	−0.778981	−	0.627047i	$-0.784263\pi$
$883$	−23.9319	+	11.0721i	−0.805371	+	0.372604i	−0.0263900	+	0.999652i	$0.508401\pi$
$884$	4.29367	+	7.43685i	0.144412	+	0.250128i
$885$	−2.38892	−	8.82405i	−0.0803027	−	0.296617i
$886$	39.8063	−	68.9466i	1.33732	−	2.31630i
$887$	3.74662	−	41.3892i	0.125799	−	1.38971i	−0.650575	−	0.759442i	$-0.725472\pi$
$887$	3.74662	−	41.3892i	0.125799	−	1.38971i	0.776374	−	0.630273i	$-0.217057\pi$
$888$	13.2910	+	6.65558i	0.446015	+	0.223347i
$889$	37.0672	+	6.76621i	1.24319	+	0.226932i
$890$	20.5479	+	12.3633i	0.688769	+	0.414418i
$891$	−2.42956	−	32.3870i	−0.0813932	−	1.08501i
$892$	−2.33196	+	43.0105i	−0.0780799	+	1.44010i
$893$	−29.0959	+	7.51537i	−0.973657	+	0.251492i
$894$	45.8200	+	46.1742i	1.53245	+	1.54430i
$895$	4.84526	−	6.61854i	0.161959	−	0.221233i
$896$	−34.0728	−	27.8985i	−1.13829	−	0.932024i
$897$	−14.1179	−	10.6173i	−0.471383	−	0.354500i
$898$	32.0811	+	13.4584i	1.07056	+	0.449112i
$899$	4.24319	+	10.6496i	0.141518	+	0.355184i
$900$	−14.1091	−	31.1229i	−0.470303	−	1.03743i
$901$	0.474136	+	2.89210i	0.0157957	+	0.0963498i
$902$	64.5069	−	42.0571i	2.14785	−	1.40035i
$903$	40.2124	−	33.2749i	1.33818	−	1.10732i
$904$	−3.93614	−	16.4607i	−0.130914	−	0.547474i
$905$	−1.53837	+	7.64369i	−0.0511370	+	0.254085i
$906$	2.56875	+	4.39648i	0.0853410	+	0.146063i
$907$	36.4634	−	37.1278i	1.21075	−	1.23281i	0.246105	−	0.969243i	$-0.420849\pi$
$907$	36.4634	−	37.1278i	1.21075	−	1.23281i	0.964642	−	0.263563i	$-0.0848978\pi$
$908$	65.8777	−	14.5008i	2.18623	−	0.481226i
$909$	−22.9028	−	8.37956i	−0.759636	−	0.277932i
$910$	−19.0724	−	35.9744i	−0.632244	−	1.19254i
$911$	−25.6729	+	0.927457i	−0.850580	+	0.0307280i	−0.457960	−	0.888973i	$-0.651420\pi$
$911$	−25.6729	+	0.927457i	−0.850580	+	0.0307280i	−0.392620	+	0.919701i	$0.628431\pi$
$912$	16.1641	−	24.1080i	0.535247	−	0.798297i
$913$	11.6281	−	3.45584i	0.384836	−	0.114371i
$914$	−37.4599	+	26.3980i	−1.23906	+	0.873170i
$915$	10.7940	+	6.95806i	0.356838	+	0.230026i
$916$	5.37614	−	22.4826i	0.177633	−	0.742847i
$917$	12.7200	+	18.7606i	0.420052	+	0.619530i
$918$	6.51809	+	2.61611i	0.215129	+	0.0863446i
$919$	−7.48694	−	14.1219i	−0.246971	−	0.465837i	0.728772	−	0.684757i	$-0.240092\pi$
$919$	−7.48694	−	14.1219i	−0.246971	−	0.465837i	−0.975743	+	0.218920i	$0.929747\pi$
$920$	1.42720	+	0.103252i	0.0470533	+	0.00340413i
$921$	−5.21884	+	0.404738i	−0.171967	+	0.0133366i
$922$	25.3850	+	6.55687i	0.836012	+	0.215939i
$923$	15.8146	+	20.0421i	0.520544	+	0.659694i
$924$	−53.2159	−	61.9971i	−1.75067	−	2.03956i
$925$	−33.9914	−	10.1021i	−1.11763	−	0.332155i
$926$	−50.2510	−	11.0611i	−1.65135	−	0.363490i
$927$	−10.5215	−	9.76178i	−0.345571	−	0.320619i
$928$	−3.74009	−	22.8135i	−0.122774	−	0.748891i
$929$	4.78347	−	13.3927i	0.156941	−	0.439401i	−0.837278	−	0.546778i	$-0.815854\pi$
$929$	4.78347	−	13.3927i	0.156941	−	0.439401i	0.994218	+	0.107377i	$0.0342450\pi$
$930$	−9.55360	−	2.78554i	−0.313275	−	0.0913413i
$931$	15.6311	+	123.018i	0.512287	+	4.03175i
$932$	−0.315899	−	17.4945i	−0.0103476	−	0.573051i
$933$	33.5110	+	36.3022i	1.09710	+	1.18848i
$934$	−6.65495	−	15.0937i	−0.217757	−	0.493882i
$935$	1.25563	+	0.954505i	0.0410635	+	0.0312157i
$936$	8.42453	+	15.5003i	0.275365	+	0.506645i
$937$	0.659216	−	12.1585i	0.0215356	−	0.397202i	−0.967816	−	0.251658i	$-0.919024\pi$
$937$	0.659216	−	12.1585i	0.0215356	−	0.397202i	0.989352	−	0.145544i	$-0.0464931\pi$
$938$	−58.0915	−	79.3519i	−1.89675	−	2.59093i
$939$	−3.85105	+	24.2770i	−0.125674	+	0.792252i
$940$	−2.81801	−	7.88983i	−0.0919132	−	0.257338i
$941$	−42.9765	+	37.8613i	−1.40099	+	1.23424i	−0.463564	+	0.886063i	$0.653430\pi$
$941$	−42.9765	+	37.8613i	−1.40099	+	1.23424i	−0.937428	+	0.348179i	$0.886800\pi$
$942$	9.30090	−	2.81668i	0.303040	−	0.0917724i
$943$	−9.54197	−	16.5272i	−0.310729	−	0.538199i
$944$	−16.3801	−	12.7547i	−0.533128	−	0.415131i
$945$	−16.9569	−	7.52760i	−0.551609	−	0.244873i
$946$	−40.3617	+	18.6733i	−1.31227	+	0.607121i
$947$	−3.61516	−	17.9627i	−0.117477	−	0.583708i	−0.994630	−	0.103497i	$-0.966997\pi$
$947$	−3.61516	−	17.9627i	−0.117477	−	0.583708i	0.877153	−	0.480211i	$-0.159440\pi$
$948$	1.71608	−	1.52768i	0.0557357	−	0.0496168i
$949$	−41.7090	+	23.0869i	−1.35393	+	0.749432i
$950$	24.0678	−	54.5868i	0.780862	−	1.77103i
$951$	20.6690	−	7.08358i	0.670239	−	0.229701i
$952$	3.50669	−	0.905766i	0.113652	−	0.0293560i
$953$	−11.5436	−	8.77522i	−0.373934	−	0.284257i	0.401281	−	0.915955i	$-0.368565\pi$
$953$	−11.5436	−	8.77522i	−0.373934	−	0.284257i	−0.775215	+	0.631698i	$0.782358\pi$
$954$	4.00395	+	29.0985i	0.129633	+	0.942099i
$955$	0.143648	−	0.876216i	0.00464835	−	0.0283537i
$956$	4.94430	+	2.73678i	0.159910	+	0.0885139i
$957$	0.234494	−	18.2086i	0.00758010	−	0.588602i
$958$	−45.7526	−	6.65490i	−1.47820	−	0.215010i
$959$	39.0288	−	7.12428i	1.26031	−	0.230055i
$960$	11.9633	+	6.54124i	0.386112	+	0.211118i
$961$	−12.9987	+	8.47485i	−0.419312	+	0.273382i
$962$	87.2243	+	19.1995i	2.81223	+	0.619018i
$963$	−33.2088	+	17.2800i	−1.07014	+	0.556839i
$964$	−2.33252	+	0.785916i	−0.0751253	+	0.0253127i
$965$	−6.74378	+	0.980909i	−0.217090	+	0.0315766i
$966$	−28.8205	+	22.1452i	−0.927284	+	0.712509i
$967$	4.97837	−	15.7069i	0.160093	−	0.505100i	−0.839154	−	0.543894i	$-0.816949\pi$
$967$	4.97837	−	15.7069i	0.160093	−	0.505100i	0.999247	+	0.0387938i	$0.0123516\pi$
$968$	0.966719	+	1.99424i	0.0310715	+	0.0640973i
$969$	2.33093	+	6.42096i	0.0748801	+	0.206271i
$970$	−17.1982	+	0.621302i	−0.552201	+	0.0199488i
$971$	−2.44607	−	3.60768i	−0.0784980	−	0.115776i	0.786413	−	0.617701i	$-0.211936\pi$
$971$	−2.44607	−	3.60768i	−0.0784980	−	0.115776i	−0.864911	+	0.501925i	$0.832625\pi$
$972$	36.0052	+	15.5393i	1.15487	+	0.498422i
$973$	3.11917	+	1.44308i	0.0999959	+	0.0462630i
$974$	0.844981	+	9.33457i	0.0270749	+	0.299099i
$975$	−26.2414	−	32.9044i	−0.840398	−	1.05378i
$976$	29.0882	−	2.10442i	0.931090	−	0.0673610i
$977$	−10.4425	−	16.6669i	−0.334086	−	0.533220i	0.637334	−	0.770588i	$-0.280037\pi$
$977$	−10.4425	−	16.6669i	−0.334086	−	0.533220i	−0.971420	+	0.237368i	$0.923715\pi$
$978$	21.4759	−	25.5503i	0.686723	−	0.817009i
$979$	59.1115	+	4.27650i	1.88921	+	0.136677i
$980$	−33.7641	+	7.43205i	−1.07856	+	0.237408i
$981$	0.0472360	−	6.13462i	0.00150813	−	0.195863i
$982$	−10.3869	+	26.0691i	−0.331459	+	0.831898i
$983$	−31.2543	−	27.5343i	−0.996856	−	0.878207i	−0.00429927	−	0.999991i	$-0.501369\pi$
$983$	−31.2543	−	27.5343i	−0.996856	−	0.878207i	−0.992557	+	0.121784i	$0.961139\pi$
$984$	1.81650	+	18.9725i	0.0579080	+	0.604820i
$985$	−6.54911	+	7.16872i	−0.208672	+	0.228414i
$986$	3.51202	+	1.78148i	0.111846	+	0.0567340i
$987$	38.2730	+	20.9268i	1.21824	+	0.666108i
$988$	−28.1553	+	78.8289i	−0.895739	+	2.50788i
$989$	4.07937	+	10.2384i	0.129716	+	0.325563i
$990$	12.3339	+	9.88733i	0.391997	+	0.314240i
$991$	21.4664	−	12.9159i	0.681902	−	0.410287i	−0.132031	−	0.991246i	$-0.542150\pi$
$991$	21.4664	−	12.9159i	0.681902	−	0.410287i	0.813933	+	0.580959i	$0.197322\pi$
$992$	−29.2089	+	11.0311i	−0.927384	+	0.350238i
$993$	−1.27730	−	4.50969i	−0.0405338	−	0.143111i
$994$	48.4396	−	20.3210i	1.53641	−	0.644543i
$995$	−7.09388	−	7.22313i	−0.224891	−	0.228989i
$996$	−2.81557	+	14.3741i	−0.0892146	+	0.455461i
$997$	−17.5484	−	23.9708i	−0.555764	−	0.759163i	0.434149	−	0.900841i	$-0.357049\pi$
$997$	−17.5484	−	23.9708i	−0.555764	−	0.759163i	−0.989913	+	0.141678i	$0.954750\pi$
$998$	29.8298	+	17.9480i	0.944244	+	0.568133i
$999$	36.6636	−	17.6589i	1.15999	−	0.558702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.m.a.121.50	yes	3248
9.7	even	3	inner	531.2.m.a.475.50	yes	3248
59.20	even	29	inner	531.2.m.a.256.50	yes	3248
531.79	even	87	inner	531.2.m.a.79.50	✓	3248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.m.a.79.50	✓	3248	531.79	even	87	inner
531.2.m.a.121.50	yes	3248	1.1	even	1	trivial
531.2.m.a.256.50	yes	3248	59.20	even	29	inner
531.2.m.a.475.50	yes	3248	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.m (of order \(87\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73703 + 1.22409i) q^{2} +(-1.54872 - 0.775539i) q^{3} +(0.846165 + 2.36909i) q^{4} +(-0.601180 + 0.332767i) q^{5} +(-1.74085 - 3.24291i) q^{6} +(-4.63408 + 2.35065i) q^{7} +(-0.293154 + 1.05585i) q^{8} +(1.79708 + 2.40219i) q^{9} +O(q^{10})\)	\(q+(1.73703 + 1.22409i) q^{2} +(-1.54872 - 0.775539i) q^{3} +(0.846165 + 2.36909i) q^{4} +(-0.601180 + 0.332767i) q^{5} +(-1.74085 - 3.24291i) q^{6} +(-4.63408 + 2.35065i) q^{7} +(-0.293154 + 1.05585i) q^{8} +(1.79708 + 2.40219i) q^{9} +(-1.45160 - 0.157871i) q^{10} +(-3.37594 + 1.27496i) q^{11} +(0.526843 - 4.32529i) q^{12} +(-0.676452 - 5.32375i) q^{13} +(-10.9269 - 1.58937i) q^{14} +(1.18913 - 0.0491248i) q^{15} +(2.09120 - 1.71226i) q^{16} +(0.0344366 + 0.635146i) q^{17} +(0.181093 + 6.37245i) q^{18} +(-4.50136 + 4.26391i) q^{19} +(-1.29705 - 1.14267i) q^{20} +(8.99993 - 0.0465993i) q^{21} +(-7.42477 - 1.91779i) q^{22} +(-0.574195 + 1.81160i) q^{23} +(1.27286 - 1.40786i) q^{24} +(-2.40401 + 3.83694i) q^{25} +(5.34171 - 10.0755i) q^{26} +(-0.920188 - 5.11403i) q^{27} +(-9.49010 - 8.98950i) q^{28} +(-0.262656 - 2.90158i) q^{29} +(2.12569 + 1.37027i) q^{30} +(-3.77175 + 1.12095i) q^{31} +(7.91429 - 0.572570i) q^{32} +(6.21717 + 0.643605i) q^{33} +(-0.717657 + 1.14542i) q^{34} +(2.00370 - 2.95524i) q^{35} +(-4.17036 + 6.29008i) q^{36} +(2.09520 + 7.54623i) q^{37} +(-13.0384 + 1.89649i) q^{38} +(-3.08113 + 8.76962i) q^{39} +(-0.175112 - 0.732306i) q^{40} +(-6.77309 + 7.41389i) q^{41} +(15.6902 + 10.9358i) q^{42} +(4.48710 - 3.67400i) q^{43} +(-5.87709 - 6.91905i) q^{44} +(-1.87974 - 0.846139i) q^{45} +(-3.21495 + 2.44394i) q^{46} +(4.24044 + 2.34718i) q^{47} +(-4.56661 + 1.03001i) q^{48} +(11.8142 - 16.1380i) q^{49} +(-8.87260 + 3.72216i) q^{50} +(0.439247 - 1.01037i) q^{51} +(12.0400 - 6.10734i) q^{52} +(4.58045 - 0.498154i) q^{53} +(4.66162 - 10.0096i) q^{54} +(1.60528 - 1.88988i) q^{55} +(-1.12343 - 5.58199i) q^{56} +(10.2782 - 3.11264i) q^{57} +(3.09554 - 5.36164i) q^{58} +(-1.69950 - 7.49077i) q^{59} +(1.12258 + 2.77559i) q^{60} +(8.82040 + 6.21575i) q^{61} +(-7.92378 - 2.66983i) q^{62} +(-13.9745 - 6.90762i) q^{63} +(9.81647 + 5.90637i) q^{64} +(2.17823 + 2.97543i) q^{65} +(10.0116 + 8.72832i) q^{66} +(6.24061 + 6.35432i) q^{67} +(-1.47558 + 0.619021i) q^{68} +(2.29424 - 2.36036i) q^{69} +(7.09795 - 2.68063i) q^{70} +(-4.07630 + 2.45263i) q^{71} +(-3.06316 + 1.19323i) q^{72} +(-3.28802 - 8.25231i) q^{73} +(-5.59782 + 15.6727i) q^{74} +(6.69885 - 4.07795i) q^{75} +(-13.9105 - 7.05613i) q^{76} +(12.6474 - 13.8439i) q^{77} +(-16.0868 + 11.4615i) q^{78} +(0.395655 + 0.348563i) q^{79} +(-0.687405 + 1.72526i) q^{80} +(-2.54101 + 8.63384i) q^{81} +(-20.8403 + 4.58730i) q^{82} +(-3.35282 - 0.242564i) q^{83} +(7.72582 + 21.2822i) q^{84} +(-0.232058 - 0.370378i) q^{85} +(12.2915 - 0.889247i) q^{86} +(-1.84350 + 4.69743i) q^{87} +(-0.356495 - 3.93823i) q^{88} +(-14.9053 - 6.89594i) q^{89} +(-2.22941 - 3.77073i) q^{90} +(15.6490 + 23.0806i) q^{91} +(-4.77771 + 0.172599i) q^{92} +(6.71073 + 1.18910i) q^{93} +(4.49261 + 9.26778i) q^{94} +(1.28724 - 4.06128i) q^{95} +(-12.7011 - 5.25109i) q^{96} +(11.6632 - 1.69646i) q^{97} +(40.2761 - 13.5706i) q^{98} +(-9.12953 - 5.81842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9}+O(q^{10}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18} - 120 q^{19} - 31 q^{20} - 60 q^{21} - 29 q^{22} - 29 q^{23} - 16 q^{24} + 29 q^{25} - 92 q^{26} - 55 q^{27} - 132 q^{28} - 27 q^{29} - 64 q^{30} - 21 q^{31} - 49 q^{32} - 32 q^{33} - 17 q^{34} - 136 q^{35} - 70 q^{36} - 120 q^{37} - 33 q^{38} - 80 q^{39} - 17 q^{40} - 17 q^{41} - 68 q^{42} - 21 q^{43} - 104 q^{44} - 58 q^{45} - 116 q^{46} - 17 q^{47} + 106 q^{48} + 19 q^{49} - 5 q^{50} - 250 q^{51} - 21 q^{52} - 108 q^{53} + 175 q^{54} - 116 q^{55} - q^{56} + 63 q^{57} - 58 q^{58} - 17 q^{59} - 816 q^{60} - 27 q^{61} - 128 q^{62} + 95 q^{63} - 256 q^{64} - 59 q^{65} + 67 q^{66} - 15 q^{67} - 43 q^{68} - 302 q^{69} - 41 q^{70} - 134 q^{71} + 210 q^{72} - 144 q^{73} - 51 q^{74} - 47 q^{75} - 9 q^{76} - 85 q^{77} + 36 q^{78} - 39 q^{79} - 128 q^{80} - 22 q^{81} - 164 q^{82} - 35 q^{83} - 190 q^{84} - 17 q^{85} + 31 q^{86} - 75 q^{87} - 29 q^{88} - 36 q^{89} - 86 q^{90} - 136 q^{91} - 31 q^{92} - 41 q^{94} - 13 q^{95} - 30 q^{96} - 3 q^{97} - 156 q^{98} - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

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Database

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