LMFDB - Embedded newform 360.2.br.e.77.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.12
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13577 - 0.842635i) q^{2} +(-1.19421 + 1.25454i) q^{3} +(0.579931 + 1.91407i) q^{4} +(1.72814 - 1.41899i) q^{5} +(2.41346 - 0.418586i) q^{6} +(0.183802 - 0.685960i) q^{7} +(0.954200 - 2.66261i) q^{8} +(-0.147746 - 2.99636i) q^{9} +O(q^{10})$	\(q+(-1.13577 - 0.842635i) q^{2} +(-1.19421 + 1.25454i) q^{3} +(0.579931 + 1.91407i) q^{4} +(1.72814 - 1.41899i) q^{5} +(2.41346 - 0.418586i) q^{6} +(0.183802 - 0.685960i) q^{7} +(0.954200 - 2.66261i) q^{8} +(-0.147746 - 2.99636i) q^{9} +(-3.15845 + 0.155449i) q^{10} +(1.61895 + 2.80410i) q^{11} +(-3.09384 - 1.55825i) q^{12} +(-5.46259 + 1.46370i) q^{13} +(-0.786771 + 0.624212i) q^{14} +(-0.283575 + 3.86259i) q^{15} +(-3.32736 + 2.22006i) q^{16} +(4.20231 - 4.20231i) q^{17} +(-2.35703 + 3.52766i) q^{18} +6.70132 q^{19} +(3.71825 + 2.48487i) q^{20} +(0.641067 + 1.04977i) q^{21} +(0.524086 - 4.54898i) q^{22} +(4.71097 - 1.26230i) q^{23} +(2.20085 + 4.37679i) q^{24} +(0.972938 - 4.90443i) q^{25} +(7.43759 + 2.94056i) q^{26} +(3.93549 + 3.39292i) q^{27} +(1.41957 - 0.0459983i) q^{28} +(2.38341 - 1.37606i) q^{29} +(3.57683 - 4.14805i) q^{30} +(0.182842 - 0.316692i) q^{31} +(5.64981 + 0.282276i) q^{32} +(-5.45121 - 1.31763i) q^{33} +(-8.31386 + 1.23183i) q^{34} +(-0.655734 - 1.44625i) q^{35} +(5.64957 - 2.02048i) q^{36} +(1.47174 - 1.47174i) q^{37} +(-7.61114 - 5.64677i) q^{38} +(4.68719 - 8.60100i) q^{39} +(-2.12923 - 5.95537i) q^{40} +(4.07637 + 2.35349i) q^{41} +(0.156467 - 1.73247i) q^{42} +(-2.35248 + 8.77956i) q^{43} +(-4.42837 + 4.72496i) q^{44} +(-4.50713 - 4.96848i) q^{45} +(-6.41422 - 2.53595i) q^{46} +(-1.55761 - 0.417360i) q^{47} +(1.18839 - 6.82552i) q^{48} +(5.62542 + 3.24784i) q^{49} +(-5.23767 + 4.75045i) q^{50} +(0.253547 + 10.2904i) q^{51} +(-5.96956 - 9.60696i) q^{52} +(1.69723 - 1.69723i) q^{53} +(-1.61081 - 7.16975i) q^{54} +(6.77675 + 2.54860i) q^{55} +(-1.65106 - 1.14394i) q^{56} +(-8.00276 + 8.40708i) q^{57} +(-3.86651 - 0.445459i) q^{58} +(-0.118636 - 0.0684948i) q^{59} +(-7.55773 + 1.69725i) q^{60} +(6.18766 - 3.57245i) q^{61} +(-0.474522 + 0.205619i) q^{62} +(-2.08254 - 0.449391i) q^{63} +(-6.17901 - 5.08133i) q^{64} +(-7.36316 + 10.2808i) q^{65} +(5.08101 + 6.08990i) q^{66} +(-2.44205 - 9.11386i) q^{67} +(10.4806 + 5.60649i) q^{68} +(-4.04226 + 7.41755i) q^{69} +(-0.473900 + 2.19515i) q^{70} -6.15502i q^{71} +(-8.11912 - 2.46574i) q^{72} +(3.00576 - 3.00576i) q^{73} +(-2.91169 + 0.431413i) q^{74} +(4.99091 + 7.07748i) q^{75} +(3.88631 + 12.8268i) q^{76} +(2.22106 - 0.595132i) q^{77} +(-12.5711 + 5.81914i) q^{78} +(-15.2990 + 8.83288i) q^{79} +(-2.59990 + 8.55807i) q^{80} +(-8.95634 + 0.885398i) q^{81} +(-2.64667 - 6.10791i) q^{82} +(-7.73393 - 2.07230i) q^{83} +(-1.63755 + 1.83584i) q^{84} +(1.29915 - 13.2252i) q^{85} +(10.0698 - 7.98925i) q^{86} +(-1.11995 + 4.63338i) q^{87} +(9.01101 - 1.63496i) q^{88} +1.57991 q^{89} +(0.932428 + 9.44090i) q^{90} +4.01615i q^{91} +(5.14818 + 8.28510i) q^{92} +(0.178952 + 0.607579i) q^{93} +(1.41740 + 1.78652i) q^{94} +(11.5808 - 9.50911i) q^{95} +(-7.10116 + 6.75082i) q^{96} +(-4.13888 + 15.4465i) q^{97} +(-3.65242 - 8.42896i) q^{98} +(8.16289 - 5.26523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.13577	−	0.842635i	−0.803108	−	0.595833i
$2$	−1.13577	−	0.842635i	−0.803108	−	0.595833i
$3$	−1.19421	+	1.25454i	−0.689475	+	0.724310i
$3$	−1.19421	+	1.25454i	−0.689475	+	0.724310i
$4$	0.579931	+	1.91407i	0.289966	+	0.957037i
$5$	1.72814	−	1.41899i	0.772848	−	0.634591i
$5$	1.72814	−	1.41899i	0.772848	−	0.634591i
$6$	2.41346	−	0.418586i	0.985291	−	0.170887i
$7$	0.183802	−	0.685960i	0.0694708	−	0.259269i	−0.922452	−	0.386112i	$-0.873818\pi$
$7$	0.183802	−	0.685960i	0.0694708	−	0.259269i	0.991923	+	0.126843i	$0.0404845\pi$
$8$	0.954200	−	2.66261i	0.337360	−	0.941376i
$9$	−0.147746	−	2.99636i	−0.0492485	−	0.998787i
$10$	−3.15845	+	0.155449i	−0.998791	+	0.0491572i
$11$	1.61895	+	2.80410i	0.488130	+	0.845467i	0.999907	−	0.0136521i	$-0.00434573\pi$
$11$	1.61895	+	2.80410i	0.488130	+	0.845467i	−0.511776	+	0.859119i	$0.671012\pi$
$12$	−3.09384	−	1.55825i	−0.893115	−	0.449828i
$13$	−5.46259	+	1.46370i	−1.51505	+	0.405957i	−0.918109	−	0.396328i	$-0.870284\pi$
$13$	−5.46259	+	1.46370i	−1.51505	+	0.405957i	−0.596942	+	0.802285i	$0.703618\pi$
$14$	−0.786771	+	0.624212i	−0.210273	+	0.166828i
$15$	−0.283575	+	3.86259i	−0.0732187	+	0.997316i
$16$	−3.32736	+	2.22006i	−0.831840	+	0.555016i
$17$	4.20231	−	4.20231i	1.01921	−	1.01921i	0.0193989	−	0.999812i	$-0.493825\pi$
$17$	4.20231	−	4.20231i	1.01921	−	1.01921i	0.999812	−	0.0193989i	$-0.00617524\pi$
$18$	−2.35703	+	3.52766i	−0.555558	+	0.831478i
$19$	6.70132			1.53739			0.768694	−	0.639616i	$-0.220907\pi$
$19$	6.70132			1.53739			0.768694	+	0.639616i	$0.220907\pi$
$20$	3.71825	+	2.48487i	0.831427	+	0.555634i
$21$	0.641067	+	1.04977i	0.139892	+	0.229078i
$22$	0.524086	−	4.54898i	0.111735	−	0.969845i
$23$	4.71097	−	1.26230i	0.982305	−	0.263208i	0.268290	−	0.963338i	$-0.413541\pi$
$23$	4.71097	−	1.26230i	0.982305	−	0.263208i	0.714015	+	0.700130i	$0.246875\pi$
$24$	2.20085	+	4.37679i	0.449246	+	0.893408i
$25$	0.972938	−	4.90443i	0.194588	−	0.980885i
$26$	7.43759	+	2.94056i	1.45863	+	0.576690i
$27$	3.93549	+	3.39292i	0.757386	+	0.652967i
$28$	1.41957	−	0.0459983i	0.268274	−	0.00869287i
$29$	2.38341	−	1.37606i	0.442587	−	0.255528i	−0.262107	−	0.965039i	$-0.584417\pi$
$29$	2.38341	−	1.37606i	0.442587	−	0.255528i	0.704695	+	0.709511i	$0.251084\pi$
$30$	3.57683	−	4.14805i	0.653036	−	0.757327i
$31$	0.182842	−	0.316692i	0.0328395	−	0.0568796i	−0.849139	−	0.528170i	$-0.822878\pi$
$31$	0.182842	−	0.316692i	0.0328395	−	0.0568796i	0.881978	+	0.471291i	$0.156212\pi$
$32$	5.64981	+	0.282276i	0.998754	+	0.0498998i
$33$	−5.45121	−	1.31763i	−0.948933	−	0.229371i
$34$	−8.31386	+	1.23183i	−1.42582	+	0.211257i
$35$	−0.655734	−	1.44625i	−0.110839	−	0.244461i
$36$	5.64957	−	2.02048i	0.941595	−	0.336747i
$37$	1.47174	−	1.47174i	0.241952	−	0.241952i	−0.575705	−	0.817657i	$-0.695272\pi$
$37$	1.47174	−	1.47174i	0.241952	−	0.241952i	0.817657	+	0.575705i	$0.195272\pi$
$38$	−7.61114	−	5.64677i	−1.23469	−	0.916027i
$39$	4.68719	−	8.60100i	0.750551	−	1.37726i
$40$	−2.12923	−	5.95537i	−0.336660	−	0.941626i
$41$	4.07637	+	2.35349i	0.636621	+	0.367553i	0.783312	−	0.621629i	$-0.213529\pi$
$41$	4.07637	+	2.35349i	0.636621	+	0.367553i	−0.146691	+	0.989182i	$0.546862\pi$
$42$	0.156467	−	1.73247i	0.0241433	−	0.267326i
$43$	−2.35248	+	8.77956i	−0.358749	+	1.33887i	0.516951	+	0.856015i	$0.327067\pi$
$43$	−2.35248	+	8.77956i	−0.358749	+	1.33887i	−0.875700	+	0.482855i	$0.839600\pi$
$44$	−4.42837	+	4.72496i	−0.667602	+	0.712315i
$45$	−4.50713	−	4.96848i	−0.671883	−	0.740657i
$46$	−6.41422	−	2.53595i	−0.945725	−	0.373905i
$47$	−1.55761	−	0.417360i	−0.227200	−	0.0608782i	0.143423	−	0.989662i	$-0.454189\pi$
$47$	−1.55761	−	0.417360i	−0.227200	−	0.0608782i	−0.370623	+	0.928783i	$0.620856\pi$
$48$	1.18839	−	6.82552i	0.171529	−	0.985179i
$49$	5.62542	+	3.24784i	0.803631	+	0.463977i
$50$	−5.23767	+	4.75045i	−0.740719	+	0.671815i
$51$	0.253547	+	10.2904i	0.0355037	+	1.44094i
$52$	−5.96956	−	9.60696i	−0.827828	−	1.33225i
$53$	1.69723	−	1.69723i	0.233133	−	0.233133i	−0.580866	−	0.813999i	$-0.697286\pi$
$53$	1.69723	−	1.69723i	0.233133	−	0.233133i	0.813999	+	0.580866i	$0.197286\pi$
$54$	−1.61081	−	7.16975i	−0.219204	−	0.975679i
$55$	6.77675	+	2.54860i	0.913776	+	0.343654i
$56$	−1.65106	−	1.14394i	−0.220632	−	0.152865i
$57$	−8.00276	+	8.40708i	−1.05999	+	1.11355i
$58$	−3.86651	−	0.445459i	−0.507698	−	0.0584916i
$59$	−0.118636	−	0.0684948i	−0.0154451	−	0.00891726i	0.492258	−	0.870450i	$-0.336172\pi$
$59$	−0.118636	−	0.0684948i	−0.0154451	−	0.00891726i	−0.507703	+	0.861532i	$0.669505\pi$
$60$	−7.55773	+	1.69725i	−0.975699	+	0.219114i
$61$	6.18766	−	3.57245i	0.792249	−	0.457405i	−0.0485048	−	0.998823i	$-0.515446\pi$
$61$	6.18766	−	3.57245i	0.792249	−	0.457405i	0.840754	+	0.541418i	$0.182112\pi$
$62$	−0.474522	+	0.205619i	−0.0602644	+	0.0261136i
$63$	−2.08254	−	0.449391i	−0.262375	−	0.0566179i
$64$	−6.17901	−	5.08133i	−0.772376	−	0.635166i
$65$	−7.36316	+	10.2808i	−0.913287	+	1.27518i
$66$	5.08101	+	6.08990i	0.625429	+	0.749615i
$67$	−2.44205	−	9.11386i	−0.298344	−	1.11344i	−0.938525	−	0.345211i	$-0.887807\pi$
$67$	−2.44205	−	9.11386i	−0.298344	−	1.11344i	0.640181	−	0.768224i	$-0.278859\pi$
$68$	10.4806	+	5.60649i	1.27096	+	0.679886i
$69$	−4.04226	+	7.41755i	−0.486631	+	0.892968i
$70$	−0.473900	+	2.19515i	−0.0566419	+	0.262370i
$71$		−	6.15502i		−	0.730467i	−0.930916	−	0.365233i	$-0.880989\pi$
$71$		−	6.15502i		−	0.730467i	0.930916	−	0.365233i	$-0.119011\pi$
$72$	−8.11912	−	2.46574i	−0.956848	−	0.290590i
$73$	3.00576	−	3.00576i	0.351798	−	0.351798i	−0.508980	−	0.860778i	$-0.669977\pi$
$73$	3.00576	−	3.00576i	0.351798	−	0.351798i	0.860778	+	0.508980i	$0.169977\pi$
$74$	−2.91169	+	0.431413i	−0.338477	+	0.0501507i
$75$	4.99091	+	7.07748i	0.576301	+	0.817237i
$76$	3.88631	+	12.8268i	0.445790	+	1.47134i
$77$	2.22106	−	0.595132i	0.253114	−	0.0678216i
$78$	−12.5711	+	5.81914i	−1.42339	+	0.658888i
$79$	−15.2990	+	8.83288i	−1.72127	+	0.993776i	−0.804939	+	0.593357i	$0.797802\pi$
$79$	−15.2990	+	8.83288i	−1.72127	+	0.993776i	−0.916332	+	0.400419i	$0.868864\pi$
$80$	−2.59990	+	8.55807i	−0.290677	+	0.956821i
$81$	−8.95634	+	0.885398i	−0.995149	+	0.0983775i
$82$	−2.64667	−	6.10791i	−0.292275	−	0.674505i
$83$	−7.73393	−	2.07230i	−0.848909	−	0.227465i	−0.191963	−	0.981402i	$-0.561485\pi$
$83$	−7.73393	−	2.07230i	−0.848909	−	0.227465i	−0.656946	+	0.753937i	$0.728152\pi$
$84$	−1.63755	+	1.83584i	−0.178672	+	0.200307i
$85$	1.29915	−	13.2252i	0.140912	−	1.43448i
$86$	10.0698	−	7.98925i	1.08586	−	0.861503i
$87$	−1.11995	+	4.63338i	−0.120072	+	0.496750i
$88$	9.01101	−	1.63496i	0.960577	−	0.174287i
$89$	1.57991			0.167471			0.0837353	−	0.996488i	$-0.473315\pi$
$89$	1.57991			0.167471			0.0837353	+	0.996488i	$0.473315\pi$
$90$	0.932428	+	9.44090i	0.0982866	+	0.995158i
$91$			4.01615i			0.421007i
$92$	5.14818	+	8.28510i	0.536734	+	0.863781i
$93$	0.178952	+	0.607579i	0.0185565	+	0.0630030i
$94$	1.41740	+	1.78652i	0.146193	+	0.184265i
$95$	11.5808	−	9.50911i	1.18817	−	0.975614i
$96$	−7.10116	+	6.75082i	−0.724759	+	0.689003i
$97$	−4.13888	+	15.4465i	−0.420240	+	1.56836i	0.353864	+	0.935297i	$0.384868\pi$
$97$	−4.13888	+	15.4465i	−0.420240	+	1.56836i	−0.774103	+	0.633059i	$0.781799\pi$
$98$	−3.65242	−	8.42896i	−0.368950	−	0.851454i
$99$	8.16289	−	5.26523i	0.820401	−	0.529176i
$100$	9.95167	−	0.981956i	0.995167	−	0.0981956i
$101$	−5.53970	−	9.59504i	−0.551221	−	0.954743i	−0.998187	−	0.0601917i	$-0.980829\pi$
$101$	−5.53970	−	9.59504i	−0.551221	−	0.954743i	0.446966	−	0.894551i	$-0.352505\pi$
$102$	8.38308	−	11.9011i	0.830049	−	1.17839i
$103$	1.65335	+	6.17039i	0.162909	+	0.607986i	0.998298	+	0.0583259i	$0.0185763\pi$
$103$	1.65335	+	6.17039i	0.162909	+	0.607986i	−0.835388	+	0.549661i	$0.814757\pi$
$104$	−1.31515	+	15.9414i	−0.128961	+	1.56319i
$105$	2.59746	+	0.904474i	0.253486	+	0.0882676i
$106$	−3.35781	+	0.497512i	−0.326139	+	0.0483226i
$107$	−4.61439	−	4.61439i	−0.446090	−	0.446090i	0.447963	−	0.894052i	$-0.352150\pi$
$107$	−4.61439	−	4.61439i	−0.446090	−	0.446090i	−0.894052	+	0.447963i	$0.852150\pi$
$108$	−4.21198	+	9.50049i	−0.405298	+	0.914185i
$109$	−9.24894			−0.885888			−0.442944	−	0.896549i	$-0.646066\pi$
$109$	−9.24894			−0.885888			−0.442944	+	0.896549i	$0.646066\pi$
$110$	−5.54926	−	8.60494i	−0.529101	−	0.820449i
$111$	0.0887976	+	3.60392i	0.00842830	+	0.342069i
$112$	0.911298	+	2.69049i	0.0861096	+	0.254227i
$113$	−10.7495	+	2.88031i	−1.01122	+	0.270957i	−0.726141	−	0.687546i	$-0.758688\pi$
$113$	−10.7495	+	2.88031i	−1.01122	+	0.270957i	−0.285084	+	0.958503i	$0.592021\pi$
$114$	16.1734	−	2.80508i	1.51477	−	0.262720i
$115$	6.35002	−	8.86625i	0.592143	−	0.826782i
$116$	4.01609	+	3.76400i	0.372885	+	0.349478i
$117$	5.19284	+	16.1516i	0.480078	+	1.49322i
$118$	0.0770272	+	0.177761i	0.00709092	+	0.0163643i
$119$	−2.11022	−	3.65501i	−0.193444	−	0.335055i
$120$	10.0140	+	4.44073i	0.914148	+	0.405381i
$121$	0.258033	−	0.446926i	0.0234575	−	0.0406297i
$122$	−10.0380	−	1.15647i	−0.908799	−	0.104702i
$123$	−7.82057	+	2.30342i	−0.705157	+	0.207692i
$124$	0.712208	+	0.166314i	0.0639582	+	0.0149354i
$125$	−5.27796	−	9.85612i	−0.472075	−	0.881559i
$126$	1.98661	+	2.26522i	0.176981	+	0.201802i
$127$	7.62683	+	7.62683i	0.676772	+	0.676772i	0.959268	−	0.282496i	$-0.0911625\pi$
$127$	7.62683	+	7.62683i	0.676772	+	0.676772i	−0.282496	+	0.959268i	$0.591163\pi$
$128$	2.73620	+	10.9778i	0.241849	+	0.970314i
$129$	−8.20498	−	13.4359i	−0.722408	−	1.18296i
$130$	17.0258	−	5.47218i	1.49326	−	0.479942i
$131$	−3.55704	+	6.16098i	−0.310780	+	0.538288i	−0.978532	−	0.206097i	$-0.933924\pi$
$131$	−3.55704	+	6.16098i	−0.310780	+	0.538288i	0.667751	+	0.744385i	$0.267257\pi$
$132$	−0.639277	−	11.1981i	−0.0556420	−	0.974674i
$133$	1.23172	−	4.59684i	0.106804	−	0.398597i
$134$	−4.90606	+	12.4090i	−0.423819	+	1.07197i
$135$	11.6156	+	0.279011i	0.999712	+	0.0240135i
$136$	−7.17928	−	15.1990i	−0.615619	−	1.30330i
$137$	11.8912	+	3.18624i	1.01593	+	0.272219i	0.728107	−	0.685464i	$-0.240400\pi$
$137$	11.8912	+	3.18624i	1.01593	+	0.272219i	0.287827	+	0.957682i	$0.407067\pi$
$138$	10.8414	−	5.01845i	0.922877	−	0.427199i
$139$	−4.06579	+	7.04216i	−0.344856	+	0.597308i	−0.985328	−	0.170674i	$-0.945406\pi$
$139$	−4.06579	+	7.04216i	−0.344856	+	0.597308i	0.640471	+	0.767982i	$0.278739\pi$
$140$	2.38795	−	2.09385i	0.201818	−	0.176962i
$141$	2.38370	−	1.45567i	0.200744	−	0.122589i
$142$	−5.18644	+	6.99067i	−0.435236	+	0.586644i
$143$	−12.9480	−	12.9480i	−1.08277	−	1.08277i
$144$	7.14371	+	9.64196i	0.595309	+	0.803497i
$145$	2.16625	−	5.76005i	0.179897	−	0.478346i
$146$	−5.94661	+	0.881083i	−0.492145	+	0.0729190i
$147$	−10.7925	+	3.17873i	−0.890147	+	0.262177i
$148$	3.67053	+	1.96351i	0.301715	+	0.161399i
$149$	−18.0468	−	10.4193i	−1.47845	−	0.853584i	−0.478748	−	0.877952i	$-0.658909\pi$
$149$	−18.0468	−	10.4193i	−1.47845	−	0.853584i	−0.999703	+	0.0243680i	$0.992243\pi$
$150$	0.295223	−	12.2439i	0.0241049	−	0.999709i
$151$	−9.01006	−	15.6059i	−0.733228	−	1.26999i	−0.955496	−	0.295003i	$-0.904680\pi$
$151$	−9.01006	−	15.6059i	−0.733228	−	1.26999i	0.222269	−	0.974985i	$-0.428654\pi$
$152$	6.39440	−	17.8430i	0.518654	−	1.44726i
$153$	−13.2125	−	11.9708i	−1.06817	−	0.967779i
$154$	−3.02409	−	1.19562i	−0.243688	−	0.0963454i
$155$	−0.133406	−	0.806740i	−0.0107154	−	0.0647989i
$156$	19.1812	+	3.98364i	1.53573	+	0.318946i
$157$	1.52540	+	5.69287i	0.121740	+	0.454341i	0.999703	−	0.0243891i	$-0.00776407\pi$
$157$	1.52540	+	5.69287i	0.121740	+	0.454341i	−0.877962	+	0.478730i	$0.841097\pi$
$158$	24.8190	+	2.85938i	1.97449	+	0.227480i
$159$	0.102403	+	4.15609i	0.00812107	+	0.329599i
$160$	10.1642	−	7.52920i	0.803551	−	0.595236i
$161$		−	3.46355i		−	0.272966i
$162$	10.9184	+	6.54133i	0.857829	+	0.513935i
$163$	2.60000	+	2.60000i	0.203648	+	0.203648i	0.801561	−	0.597913i	$-0.204003\pi$
$163$	2.60000	+	2.60000i	0.203648	+	0.203648i	−0.597913	+	0.801561i	$0.704003\pi$
$164$	−2.14074	+	9.16733i	−0.167164	+	0.715848i
$165$	−11.2902	+	5.45815i	−0.878937	+	0.424916i
$166$	7.03775	+	8.87054i	0.546235	+	0.688487i
$167$	−3.05550	−	11.4033i	−0.236442	−	0.882413i	−0.977494	−	0.210965i	$-0.932339\pi$
$167$	−3.05550	−	11.4033i	−0.236442	−	0.882413i	0.741052	−	0.671448i	$-0.234327\pi$
$168$	3.40682	−	0.705227i	0.262842	−	0.0544095i
$169$	16.4392	−	9.49117i	1.26455	−	0.730090i
$170$	−12.6196	+	13.9261i	−0.967877	+	1.06808i
$171$	−0.990091	−	20.0796i	−0.0757141	−	1.53552i
$172$	−18.1690	+	0.588730i	−1.38537	+	0.0448902i
$173$	4.90631	+	1.31464i	0.373020	+	0.0999504i	0.440458	−	0.897773i	$-0.354816\pi$
$173$	4.90631	+	1.31464i	0.373020	+	0.0999504i	−0.0674383	+	0.997723i	$0.521483\pi$
$174$	5.17626	−	4.31873i	0.392411	−	0.327402i
$175$	−3.18541	−	1.56884i	−0.240794	−	0.118593i
$176$	−11.6121	−	5.73607i	−0.875294	−	0.432373i
$177$	0.227606	−	0.0670374i	0.0171079	−	0.00503884i
$178$	−1.79441	−	1.33129i	−0.134497	−	0.0997846i
$179$		−	7.00655i		−	0.523694i	−0.965109	−	0.261847i	$-0.915668\pi$
$179$		−	7.00655i		−	0.523694i	0.965109	−	0.261847i	$-0.0843316\pi$
$180$	6.89621	−	11.5084i	0.514013	−	0.857782i
$181$		−	5.75675i		−	0.427896i	−0.976845	−	0.213948i	$-0.931368\pi$
$181$		−	5.75675i		−	0.427896i	0.976845	−	0.213948i	$-0.0686323\pi$
$182$	3.38415	−	4.56141i	0.250850	−	0.338114i
$183$	−2.90756	+	12.0289i	−0.214933	+	0.889203i
$184$	1.13419	−	13.7480i	0.0836135	−	1.01351i
$185$	0.454989	−	4.63175i	0.0334515	−	0.340533i
$186$	0.308720	−	0.840859i	0.0226364	−	0.0616548i
$187$	18.5870	+	4.98037i	1.35922	+	0.364201i
$188$	−0.104448	−	3.22342i	−0.00761768	−	0.235092i
$189$	3.05076	−	2.07597i	0.221910	−	0.151004i
$190$	−21.1658	+	1.04171i	−1.53553	+	0.0755738i
$191$	−0.203738	+	0.117628i	−0.0147420	+	0.00851128i	−0.507353	−	0.861738i	$-0.669376\pi$
$191$	−0.203738	+	0.117628i	−0.0147420	+	0.00851128i	0.492611	+	0.870250i	$0.336043\pi$
$192$	13.7537	−	1.68367i	0.992590	−	0.121508i
$193$	1.96928	+	7.34946i	0.141752	+	0.529026i	0.999879	+	0.0155876i	$0.00496188\pi$
$193$	1.96928	+	7.34946i	0.141752	+	0.529026i	−0.858126	+	0.513438i	$0.828371\pi$
$194$	17.7166	−	14.0561i	1.27198	−	1.00917i
$195$	−4.10461	−	21.5148i	−0.293937	−	1.54071i
$196$	−2.95424	+	12.6510i	−0.211017	+	0.903642i
$197$	13.8506	+	13.8506i	0.986814	+	0.986814i	0.999914	−	0.0131005i	$-0.00417014\pi$
$197$	13.8506	+	13.8506i	0.986814	+	0.986814i	−0.0131005	+	0.999914i	$0.504170\pi$
$198$	−13.7078	−	0.898258i	−0.974171	−	0.0638364i
$199$			26.4045i			1.87177i	0.352309	+	0.935884i	$0.385397\pi$
$199$			26.4045i			1.87177i	−0.352309	+	0.935884i	$0.614603\pi$
$200$	−12.1302	−	7.27036i	−0.857735	−	0.514092i
$201$	14.3500	+	7.82017i	1.01217	+	0.551592i
$202$	−1.79332	+	15.5657i	−0.126177	+	1.09520i
$203$	−0.505846	−	1.88784i	−0.0355035	−	0.132501i
$204$	−19.5495	+	6.45304i	−1.36874	+	0.451803i
$205$	10.3841	−	1.71716i	0.725258	−	0.119931i
$206$	3.32157	−	8.40129i	0.231425	−	0.585346i
$207$	−4.47833	−	13.9293i	−0.311265	−	0.968150i
$208$	14.9265	−	16.9976i	1.03497	−	1.17857i
$209$	10.8491	+	18.7911i	0.750446	+	1.29981i
$210$	−2.18797	−	3.21598i	−0.150984	−	0.221924i
$211$	10.2506	+	5.91820i	0.705682	+	0.407425i	0.809460	−	0.587175i	$-0.199760\pi$
$211$	10.2506	+	5.91820i	0.705682	+	0.407425i	−0.103778	+	0.994600i	$0.533093\pi$
$212$	4.23290	+	2.26435i	0.290717	+	0.155516i
$213$	7.72172	+	7.35036i	0.529084	+	0.503638i
$214$	1.35262	+	9.12911i	0.0924633	+	0.624053i
$215$	8.39270	+	18.5105i	0.572377	+	1.26240i
$216$	12.7893	−	7.24117i	0.870199	−	0.492700i
$217$	−0.183631	−	0.183631i	−0.0124657	−	0.0124657i
$218$	10.5046	+	7.79349i	0.711464	+	0.527842i
$219$	0.181353	+	7.36035i	0.0122547	+	0.497367i
$220$	−0.948168	+	14.4492i	−0.0639255	+	0.974166i
$221$	−16.8046	+	29.1064i	−1.13040	+	1.95791i
$222$	2.93593	−	4.16803i	0.197047	−	0.279740i
$223$	3.11667	+	0.835108i	0.208707	+	0.0559230i	0.361658	−	0.932311i	$-0.382211\pi$
$223$	3.11667	+	0.835108i	0.208707	+	0.0559230i	−0.152951	+	0.988234i	$0.548878\pi$
$224$	1.23208	−	3.82366i	0.0823217	−	0.255479i
$225$	−14.8392	−	2.19066i	−0.989278	−	0.146044i
$226$	14.6359	+	5.78652i	0.973568	+	0.384914i
$227$	−3.31114	+	12.3573i	−0.219768	+	0.820185i	0.764665	+	0.644427i	$0.222904\pi$
$227$	−3.31114	+	12.3573i	−0.219768	+	0.820185i	−0.984433	+	0.175758i	$0.943762\pi$
$228$	−20.7328	−	10.4423i	−1.37307	−	0.691561i
$229$	5.57911	−	9.66330i	0.368678	−	0.638569i	−0.620681	−	0.784063i	$-0.713144\pi$
$229$	5.57911	−	9.66330i	0.368678	−	0.638569i	0.989359	+	0.145494i	$0.0464772\pi$
$230$	−14.6832	+	4.71923i	−0.968179	+	0.311177i
$231$	−1.90579	+	3.49712i	−0.125392	+	0.230094i
$232$	−1.38967	−	7.65912i	−0.0912363	−	0.502846i
$233$	−0.231498	−	0.231498i	−0.0151659	−	0.0151659i	0.699483	−	0.714649i	$-0.253414\pi$
$233$	−0.231498	−	0.231498i	−0.0151659	−	0.0151659i	−0.714649	+	0.699483i	$0.753414\pi$
$234$	7.71209	−	22.7202i	0.504155	−	1.48526i
$235$	−3.28399	+	1.48897i	−0.214224	+	0.0971298i
$236$	0.0623031	−	0.266801i	0.00405558	−	0.0173673i
$237$	7.18894	−	29.7415i	0.466972	−	1.93192i
$238$	−0.683123	+	5.92939i	−0.0442803	+	0.384345i
$239$	−1.41311	+	2.44757i	−0.0914063	+	0.158320i	−0.908103	−	0.418747i	$-0.862470\pi$
$239$	−1.41311	+	2.44757i	−0.0914063	+	0.158320i	0.816697	+	0.577067i	$0.195803\pi$
$240$	−7.63164	−	13.4818i	−0.492620	−	0.870245i
$241$	−9.13819	−	15.8278i	−0.588643	−	1.01956i	−0.994411	−	0.105583i	$-0.966329\pi$
$241$	−9.13819	−	15.8278i	−0.588643	−	1.01956i	0.405768	−	0.913976i	$-0.367004\pi$
$242$	−0.669661	+	0.290176i	−0.0430474	+	0.0186532i
$243$	9.58495	−	12.2934i	0.614875	−	0.788625i
$244$	10.4264	+	9.77187i	0.667479	+	0.625580i
$245$	14.3302	−	2.36969i	0.915521	−	0.151394i
$246$	10.8233	+	3.97375i	0.690067	+	0.253357i
$247$	−36.6066	+	9.80871i	−2.32922	+	0.624113i
$248$	−0.668761	−	0.789026i	−0.0424663	−	0.0501032i
$249$	11.8357	−	7.22778i	0.750057	−	0.458042i
$250$	−2.31059	+	15.6416i	−0.146135	+	0.989265i
$251$	−13.3749			−0.844214			−0.422107	−	0.906546i	$-0.638709\pi$
$251$	−13.3749			−0.844214			−0.422107	+	0.906546i	$0.638709\pi$
$252$	−0.347563	−	4.24675i	−0.0218944	−	0.267520i
$253$	11.1664	+	11.1664i	0.702026	+	0.702026i
$254$	−2.23566	−	15.0889i	−0.140278	−	0.946764i
$255$	15.0401	+	17.4235i	0.941850	+	1.09110i
$256$	6.14264	−	14.7739i	0.383915	−	0.923369i
$257$	2.59370	+	9.67983i	0.161791	+	0.603811i	0.998428	+	0.0560536i	$0.0178518\pi$
$257$	2.59370	+	9.67983i	0.161791	+	0.603811i	−0.836637	+	0.547758i	$0.815482\pi$
$258$	−2.00261	+	22.1738i	−0.124677	+	1.38048i
$259$	−0.739045	−	1.28006i	−0.0459220	−	0.0795393i
$260$	−23.9484	−	8.13145i	−1.48522	−	0.504291i
$261$	−4.47531	−	6.93824i	−0.277015	−	0.429466i
$262$	9.23143	−	4.00015i	0.570320	−	0.247130i
$263$	3.70749	−	13.8366i	0.228614	−	0.853199i	−0.752310	−	0.658809i	$-0.771061\pi$
$263$	3.70749	−	13.8366i	0.228614	−	0.853199i	0.980924	−	0.194390i	$-0.0622727\pi$
$264$	−8.70989	+	13.2572i	−0.536056	+	0.815922i
$265$	0.524701	−	5.34141i	0.0322321	−	0.328120i
$266$	−5.27241	+	4.18305i	−0.323272	+	0.256479i
$267$	−1.88674	+	1.98207i	−0.115467	+	0.121301i
$268$	16.0284	−	9.95968i	0.979089	−	0.608384i
$269$			8.40097i			0.512216i	0.966648	+	0.256108i	$0.0824403\pi$
$269$			8.40097i			0.512216i	−0.966648	+	0.256108i	$0.917560\pi$
$270$	−12.9575	−	10.1046i	−0.788569	−	0.614947i
$271$	−3.30692			−0.200881			−0.100441	−	0.994943i	$-0.532025\pi$
$271$	−3.30692			−0.200881			−0.100441	+	0.994943i	$0.532025\pi$
$272$	−4.65320	+	23.3120i	−0.282142	+	1.41350i
$273$	−5.03843	−	4.79611i	−0.304939	−	0.290274i
$274$	−10.8208	−	13.6388i	−0.653708	−	0.823948i
$275$	15.3276	−	5.21179i	0.924290	−	0.314283i
$276$	−16.5420	−	3.43551i	−0.995710	−	0.206793i
$277$	−14.1053	−	3.77951i	−0.847507	−	0.227089i	−0.191170	−	0.981557i	$-0.561228\pi$
$277$	−14.1053	−	3.77951i	−0.847507	−	0.227089i	−0.656337	+	0.754468i	$0.727895\pi$
$278$	10.5518	−	4.57227i	0.632853	−	0.274227i
$279$	−0.975938	−	0.501072i	−0.0584279	−	0.0299984i
$280$	−4.47650	+	0.365954i	−0.267522	+	0.0218700i
$281$	−16.0342	+	9.25733i	−0.956518	+	0.552246i	−0.895100	−	0.445866i	$-0.852896\pi$
$281$	−16.0342	+	9.25733i	−0.956518	+	0.552246i	−0.0614184	+	0.998112i	$0.519562\pi$
$282$	−3.93392	−	0.355288i	−0.234262	−	0.0211571i
$283$	−15.6008	+	4.18021i	−0.927370	+	0.248488i	−0.690733	−	0.723110i	$-0.742712\pi$
$283$	−15.6008	+	4.18021i	−0.927370	+	0.248488i	−0.236637	+	0.971598i	$0.576045\pi$
$284$	11.7812	−	3.56949i	0.699084	−	0.211810i
$285$	−1.90033	+	25.8844i	−0.112566	+	1.53326i
$286$	3.79546	+	25.6163i	0.224430	+	1.51472i
$287$	2.36365	−	2.36365i	0.139522	−	0.139522i
$288$	0.0110665	−	16.9706i	0.000652099	−	1.00000i
$289$		−	18.3189i		−	1.07758i
$290$	−7.31397	+	4.71672i	−0.429491	+	0.276975i
$291$	−14.4356	−	23.6387i	−0.846231	−	1.38573i
$292$	7.49639	+	4.01012i	0.438693	+	0.234674i
$293$	5.99806	+	22.3850i	0.350410	+	1.30775i	0.886163	+	0.463374i	$0.153361\pi$
$293$	5.99806	+	22.3850i	0.350410	+	1.30775i	−0.535753	+	0.844375i	$0.679972\pi$
$294$	14.9362	+	5.48380i	0.871098	+	0.319822i
$295$	−0.302214	+	0.0499753i	−0.0175956	+	0.00290967i
$296$	−2.51434	−	5.32300i	−0.146143	−	0.309393i
$297$	−3.14271	+	16.5284i	−0.182359	+	0.959078i
$298$	11.7173	+	27.0408i	0.678763	+	1.56643i
$299$	−23.8865	+	13.7909i	−1.38139	+	0.797546i
$300$	−10.6524	+	13.6574i	−0.615019	+	0.788512i
$301$	5.59004	+	3.22741i	0.322204	+	0.186025i
$302$	−2.91674	+	25.3168i	−0.167840	+	1.45682i
$303$	18.6529	+	4.50867i	1.07158	+	0.259017i
$304$	−22.2977	+	14.8774i	−1.27886	+	0.853275i
$305$	5.62388	−	14.9539i	0.322022	−	0.856259i
$306$	4.91934	+	24.7293i	0.281220	+	1.41368i
$307$	5.09058	−	5.09058i	0.290535	−	0.290535i	−0.546757	−	0.837292i	$-0.684138\pi$
$307$	5.09058	−	5.09058i	0.290535	−	0.290535i	0.837292	+	0.546757i	$0.184138\pi$
$308$	2.42719	+	3.90614i	0.138302	+	0.222573i
$309$	−9.71545	−	5.29452i	−0.552692	−	0.301195i
$310$	−0.528270	+	1.02868i	−0.0300037	+	0.0584251i
$311$	−6.62551	−	3.82524i	−0.375698	−	0.216909i	0.300247	−	0.953862i	$-0.402931\pi$
$311$	−6.62551	−	3.82524i	−0.375698	−	0.216909i	−0.675945	+	0.736952i	$0.736264\pi$
$312$	−18.4286	−	20.6872i	−1.04331	−	1.17118i
$313$	25.5772	+	6.85339i	1.44571	+	0.387377i	0.894529	−	0.447010i	$-0.147511\pi$
$313$	25.5772	+	6.85339i	1.44571	+	0.387377i	0.551180	+	0.834386i	$0.314178\pi$
$314$	3.06452	−	7.75113i	0.172941	−	0.437421i
$315$	−4.23660	+	2.17849i	−0.238705	+	0.122744i
$316$	−25.7792	−	24.1609i	−1.45019	−	1.35916i
$317$	1.49854	−	5.59264i	0.0841665	−	0.314114i	−0.910989	−	0.412432i	$-0.864680\pi$
$317$	1.49854	−	5.59264i	0.0841665	−	0.314114i	0.995155	+	0.0983179i	$0.0313462\pi$
$318$	3.38576	−	4.80664i	0.189864	−	0.269543i
$319$	7.71721	+	4.45553i	0.432081	+	0.249462i
$320$	−17.8885	−	0.0133002i	−1.00000	−	0.000743505i
$321$	11.2995	−	0.278410i	0.630675	−	0.0155393i
$322$	−2.91851	+	3.93378i	−0.162642	+	0.219221i
$323$	28.1611	−	28.1611i	1.56692	−	1.56692i
$324$	−6.88878	−	16.6296i	−0.382710	−	0.923868i
$325$	1.86383	+	28.2150i	0.103387	+	1.56508i
$326$	−0.762141	−	5.14384i	−0.0422111	−	0.284891i
$327$	11.0451	−	11.6032i	0.610798	−	0.641657i
$328$	10.1561	−	8.60808i	0.560777	−	0.475302i
$329$	−0.572584	+	0.991745i	−0.0315676	+	0.0546766i
$330$	17.4222	+	3.31430i	0.959061	+	0.182446i
$331$	−4.82604	+	2.78632i	−0.265263	+	0.153150i	−0.626733	−	0.779234i	$-0.715608\pi$
$331$	−4.82604	+	2.78632i	−0.265263	+	0.153150i	0.361470	+	0.932384i	$0.382275\pi$
$332$	−0.518614	−	16.0051i	−0.0284626	−	0.878395i
$333$	−4.62730	−	4.19242i	−0.253575	−	0.229743i
$334$	−6.13848	+	15.5261i	−0.335882	+	0.849553i
$335$	−17.1527	−	12.2848i	−0.937151	−	0.671189i
$336$	−4.46361	−	2.06974i	−0.243510	−	0.112913i
$337$	−20.0697	+	5.37765i	−1.09326	+	0.292939i	−0.760019	−	0.649901i	$-0.774810\pi$
$337$	−20.0697	+	5.37765i	−1.09326	+	0.292939i	−0.333245	+	0.942840i	$0.608144\pi$
$338$	−26.6687	−	3.07249i	−1.45058	−	0.167121i
$339$	9.22361	−	16.9253i	0.500958	−	0.919258i
$340$	26.0675	−	5.18306i	1.41371	−	0.281091i
$341$	1.18405			0.0641197
$342$	−15.7952	+	23.6400i	−0.854109	+	1.27830i
$343$	6.77696	−	6.77696i	0.365921	−	0.365921i
$344$	21.1318	+	14.6412i	1.13935	+	0.789400i
$345$	3.53983	+	18.5545i	0.190578	+	0.998940i
$346$	−4.46466	−	5.62736i	−0.240022	−	0.302529i
$347$	10.0906	−	2.70377i	0.541692	−	0.145146i	0.0224100	−	0.999749i	$-0.492866\pi$
$347$	10.0906	−	2.70377i	0.541692	−	0.145146i	0.519282	+	0.854603i	$0.326199\pi$
$348$	−9.51813	+	0.543369i	−0.510225	+	0.0291276i
$349$	7.28709	+	12.6216i	0.390069	+	0.675619i	0.992458	−	0.122583i	$-0.0391178\pi$
$349$	7.28709	+	12.6216i	0.390069	+	0.675619i	−0.602389	+	0.798202i	$0.705784\pi$
$350$	2.29592	+	4.46598i	0.122722	+	0.238717i
$351$	−26.4642	−	12.7738i	−1.41255	−	0.681812i
$352$	8.35520	+	16.2996i	0.445334	+	0.868771i
$353$	2.28506	−	8.52796i	0.121621	−	0.453897i	−0.878075	−	0.478522i	$-0.841173\pi$
$353$	2.28506	−	8.52796i	0.121621	−	0.453897i	0.999697	+	0.0246251i	$0.00783919\pi$
$354$	−0.314995	−	0.115650i	−0.0167418	−	0.00614672i
$355$	−8.73391	−	10.6367i	−0.463548	−	0.564539i
$356$	0.916242	+	3.02407i	0.0485607	+	0.160276i
$357$	7.10541	+	1.71748i	0.376058	+	0.0908985i
$358$	−5.90396	+	7.95780i	−0.312034	+	0.420583i
$359$	−27.3980			−1.44601			−0.723006	−	0.690842i	$-0.757240\pi$
$359$	−27.3980			−1.44601			−0.723006	+	0.690842i	$0.757240\pi$
$360$	−17.5298	+	7.25981i	−0.923903	+	0.382626i
$361$	25.9077			1.36356
$362$	−4.85084	+	6.53833i	−0.254955	+	0.343647i
$363$	0.252543	+	0.857435i	0.0132551	+	0.0450037i
$364$	−7.68721	+	2.32909i	−0.402919	+	0.122078i
$365$	0.929234	−	9.45953i	0.0486383	−	0.495134i
$366$	13.4383	−	11.2120i	0.702431	−	0.586062i
$367$	2.50867	−	9.36249i	0.130952	−	0.488718i	−0.869030	−	0.494759i	$-0.835256\pi$
$367$	2.50867	−	9.36249i	0.130952	−	0.488718i	0.999982	+	0.00604110i	$0.00192295\pi$
$368$	−12.8727	+	14.6588i	−0.671036	+	0.764142i
$369$	6.44964	−	12.5620i	0.335755	−	0.653950i
$370$	−4.41964	+	4.87720i	−0.229766	+	0.253554i
$371$	−0.852278	−	1.47619i	−0.0442481	−	0.0766399i
$372$	−1.05917	+	0.694881i	−0.0549155	+	0.0360279i
$373$	−32.3776	+	8.67554i	−1.67645	+	0.449202i	−0.966837	−	0.255393i	$-0.917795\pi$
$373$	−32.3776	+	8.67554i	−1.67645	+	0.449202i	−0.709609	+	0.704596i	$0.751128\pi$
$374$	−16.9139	−	21.3186i	−0.874595	−	1.10236i
$375$	18.6679	+	5.14883i	0.964005	+	0.265884i
$376$	−2.59753	+	3.74906i	−0.133958	+	0.193343i
$377$	−11.0054	+	11.0054i	−0.566809	+	0.566809i
$378$	−5.21423	−	0.212865i	−0.268191	−	0.0109486i
$379$	−23.7114			−1.21797			−0.608987	−	0.793180i	$-0.708424\pi$
$379$	−23.7114			−1.21797			−0.608987	+	0.793180i	$0.708424\pi$
$380$	24.9172	+	16.6519i	1.27823	+	0.854226i
$381$	−18.6762	+	0.460166i	−0.956810	+	0.0235750i
$382$	0.330517	+	0.0380787i	0.0169107	+	0.00194828i
$383$	−2.09279	+	0.560761i	−0.106937	+	0.0286536i	−0.311890	−	0.950118i	$-0.600962\pi$
$383$	−2.09279	+	0.560761i	−0.106937	+	0.0286536i	0.204954	+	0.978772i	$0.434296\pi$
$384$	−17.0398	−	9.67713i	−0.869556	−	0.493834i
$385$	2.99382	−	4.18014i	0.152579	−	0.213040i
$386$	3.95627	−	10.0067i	0.201369	−	0.509326i
$387$	26.6543	+	5.75172i	1.35491	+	0.292377i
$388$	−31.9660	+	1.03580i	−1.62283	+	0.0525845i
$389$	25.2904	−	14.6014i	1.28228	−	0.740323i	0.305012	−	0.952348i	$-0.401339\pi$
$389$	25.2904	−	14.6014i	1.28228	−	0.740323i	0.977264	+	0.212026i	$0.0680061\pi$
$390$	−13.4673	+	27.8945i	−0.681942	+	1.41249i
$391$	14.4924	−	25.1015i	0.732911	−	1.26944i
$392$	14.0155	−	11.8792i	0.707890	−	0.599992i
$393$	−3.48136	−	11.8199i	−0.175611	−	0.596237i
$394$	−4.06004	−	27.4020i	−0.204542	−	1.38049i
$395$	−13.9050	+	36.9736i	−0.699639	+	1.86034i
$396$	14.8120	+	12.5709i	0.744329	+	0.631711i
$397$	−17.7896	+	17.7896i	−0.892833	+	0.892833i	−0.994789	−	0.101956i	$-0.967490\pi$
$397$	−17.7896	+	17.7896i	−0.892833	+	0.892833i	0.101956	+	0.994789i	$0.467490\pi$
$398$	22.2494	−	29.9894i	1.11526	−	1.50323i
$399$	4.29600	+	7.03481i	0.215069	+	0.352181i
$400$	7.65082	+	18.4788i	0.382541	+	0.923938i
$401$	30.9735	+	17.8825i	1.54674	+	0.893011i	0.998388	+	0.0567640i	$0.0180783\pi$
$401$	30.9735	+	17.8825i	1.54674	+	0.893011i	0.548353	+	0.836247i	$0.315255\pi$
$402$	−9.70872	−	20.9737i	−0.484227	−	1.04607i
$403$	−0.535252	+	1.99759i	−0.0266628	+	0.0995069i
$404$	15.1530	−	16.1679i	0.753889	−	0.804381i
$405$	−14.2214	+	14.2390i	−0.706669	+	0.707544i
$406$	−1.01624	+	2.57040i	−0.0504352	+	0.127567i
$407$	6.50956	+	1.74423i	0.322667	+	0.0864584i
$408$	27.6413	+	9.14400i	1.36845	+	0.452695i
$409$	−4.97124	−	2.87015i	−0.245812	−	0.141920i	0.372033	−	0.928219i	$-0.378661\pi$
$409$	−4.97124	−	2.87015i	−0.245812	−	0.141920i	−0.617845	+	0.786300i	$0.711994\pi$
$410$	−13.2409	−	6.79973i	−0.653920	−	0.335815i
$411$	−18.1978	+	11.1130i	−0.897632	+	0.548163i
$412$	−10.8518	+	6.74304i	−0.534627	+	0.332206i
$413$	−0.0687903	+	0.0687903i	−0.00338495	+	0.00338495i
$414$	−6.65095	+	19.5940i	−0.326876	+	0.962992i
$415$	−16.3059	+	7.39314i	−0.800425	+	0.362915i
$416$	−31.2758	+	6.72765i	−1.53342	+	0.329850i
$417$	−3.97929	−	13.5105i	−0.194866	−	0.661612i
$418$	3.51207	−	30.4842i	0.171781	−	1.49103i
$419$	8.79607	+	5.07841i	0.429716	+	0.248097i	0.699226	−	0.714901i	$-0.253528\pi$
$419$	8.79607	+	5.07841i	0.429716	+	0.248097i	−0.269510	+	0.962998i	$0.586862\pi$
$420$	−0.224882	+	5.49626i	−0.0109731	+	0.268190i
$421$	9.97514	−	5.75915i	0.486159	−	0.280684i	−0.236821	−	0.971553i	$-0.576105\pi$
$421$	9.97514	−	5.75915i	0.486159	−	0.280684i	0.722979	+	0.690870i	$0.242772\pi$
$422$	−6.65543	−	15.3592i	−0.323981	−	0.747675i
$423$	−1.02043	+	4.72881i	−0.0496150	+	0.229923i
$424$	−2.89957	−	6.13857i	−0.140816	−	0.298115i
$425$	−16.5213	−	24.6985i	−0.801403	−	1.19805i
$426$	−2.57640	−	14.8549i	−0.124827	−	0.719722i
$427$	−1.31325	−	4.90111i	−0.0635526	−	0.237181i
$428$	6.15625	−	11.5083i	0.297574	−	0.556275i
$429$	31.7063	−	0.781219i	1.53080	−	0.0377176i
$430$	6.06542	−	28.0955i	0.292500	−	1.35489i
$431$			18.8207i			0.906563i	0.891367	+	0.453282i	$0.149747\pi$
$431$			18.8207i			0.906563i	−0.891367	+	0.453282i	$0.850253\pi$
$432$	−20.6273	−	2.55240i	−0.992431	−	0.122803i
$433$	−9.88257	+	9.88257i	−0.474926	+	0.474926i	−0.903505	−	0.428579i	$-0.859015\pi$
$433$	−9.88257	+	9.88257i	−0.474926	+	0.474926i	0.428579	+	0.903505i	$0.359015\pi$
$434$	0.0538281	+	0.363297i	0.00258383	+	0.0174388i
$435$	4.63928	+	9.59633i	0.222436	+	0.460109i
$436$	−5.36375	−	17.7032i	−0.256877	−	0.847828i
$437$	31.5697	−	8.45908i	1.51018	−	0.404653i
$438$	5.99612	−	8.51246i	0.286506	−	0.406741i
$439$	−0.727784	+	0.420186i	−0.0347352	+	0.0200544i	−0.517267	−	0.855824i	$-0.673051\pi$
$439$	−0.727784	+	0.420186i	−0.0347352	+	0.0200544i	0.482532	+	0.875878i	$0.339717\pi$
$440$	13.2523	−	15.6120i	0.631779	−	0.744271i
$441$	8.90056	−	17.3356i	0.423836	−	0.825506i
$442$	43.6122	−	18.8980i	2.07442	−	0.898885i
$443$	−10.3226	−	2.76592i	−0.490440	−	0.131413i	0.00511985	−	0.999987i	$-0.498370\pi$
$443$	−10.3226	−	2.76592i	−0.490440	−	0.131413i	−0.495560	+	0.868574i	$0.665037\pi$
$444$	−6.84667	+	2.25999i	−0.324928	+	0.107254i
$445$	2.73031	−	2.24188i	0.129429	−	0.106275i
$446$	−2.83611	−	3.57470i	−0.134294	−	0.169267i
$447$	34.6231	−	10.1976i	1.63761	−	0.482331i
$448$	−4.62130	+	3.30459i	−0.218336	+	0.156127i
$449$	22.0229			1.03933			0.519663	−	0.854371i	$-0.326057\pi$
$449$	22.0229			1.03933			0.519663	+	0.854371i	$0.326057\pi$
$450$	15.0079	+	14.9921i	0.707479	+	0.706734i
$451$			15.2407i			0.717656i
$452$	−11.7471	−	18.9049i	−0.552536	−	0.889211i
$453$	30.3381	+	7.33314i	1.42541	+	0.344541i
$454$	14.1734	−	11.2450i	0.665191	−	0.527752i
$455$	5.69888	+	6.94047i	0.267167	+	0.325374i
$456$	14.7486	+	29.3303i	0.690665	+	1.37352i
$457$	6.87819	−	25.6697i	0.321748	−	1.20078i	−0.595793	−	0.803138i	$-0.703162\pi$
$457$	6.87819	−	25.6697i	0.321748	−	1.20078i	0.917541	−	0.397642i	$-0.130171\pi$
$458$	−14.4792	+	6.27410i	−0.676569	+	0.293169i
$459$	30.7963	−	2.28008i	1.43745	−	0.106425i
$460$	20.6532	+	7.01260i	0.962962	+	0.326964i
$461$	−2.13475	−	3.69749i	−0.0994251	−	0.172209i	0.812022	−	0.583627i	$-0.198367\pi$
$461$	−2.13475	−	3.69749i	−0.0994251	−	0.172209i	−0.911447	+	0.411418i	$0.865034\pi$
$462$	5.11133	−	2.36603i	0.237801	−	0.110078i
$463$	2.67823	+	9.99529i	0.124468	+	0.464520i	0.999820	−	0.0189653i	$-0.00603721\pi$
$463$	2.67823	+	9.99529i	0.124468	+	0.464520i	−0.875352	+	0.483486i	$0.839371\pi$
$464$	−4.87551	+	9.86996i	−0.226340	+	0.458201i
$465$	1.17140	+	0.796051i	0.0543225	+	0.0369160i
$466$	0.0678592	+	0.457995i	0.00314352	+	0.0212162i
$467$	−21.7368	−	21.7368i	−1.00586	−	1.00586i	−0.999983	−	0.00587456i	$-0.998130\pi$
$467$	−21.7368	−	21.7368i	−1.00586	−	1.00586i	−0.00587456	−	0.999983i	$-0.501870\pi$
$468$	−27.9039	+	19.3063i	−1.28986	+	0.892435i
$469$	−6.70060			−0.309405
$470$	4.98451	+	1.07608i	0.229918	+	0.0496360i
$471$	−8.96358	−	4.88478i	−0.413020	−	0.225079i
$472$	−0.295578	+	0.250525i	−0.0136051	+	0.0115314i
$473$	−28.4273	+	7.61706i	−1.30709	+	0.350233i
$474$	−33.2262	+	27.7217i	−1.52613	+	1.27330i
$475$	6.51997	−	32.8661i	0.299157	−	1.50800i
$476$	5.77218	−	6.15878i	0.264568	−	0.282287i
$477$	−5.33627	−	4.83476i	−0.244331	−	0.221368i
$478$	3.66737	−	1.58914i	0.167742	−	0.0726855i
$479$	18.2784	+	31.6592i	0.835163	+	1.44654i	0.893898	+	0.448271i	$0.147960\pi$
$479$	18.2784	+	31.6592i	0.835163	+	1.44654i	−0.0587347	+	0.998274i	$0.518707\pi$
$480$	−2.69246	+	21.7428i	−0.122893	+	0.992420i
$481$	−5.88533	+	10.1937i	−0.268348	+	0.464792i
$482$	−2.95822	+	25.6769i	−0.134743	+	1.16955i
$483$	4.34517	+	4.13619i	0.197712	+	0.188203i
$484$	1.00509	+	0.234708i	0.0456860	+	0.0106685i
$485$	14.7659	+	32.5668i	0.670484	+	1.47878i
$486$	−21.2452	+	5.88587i	−0.963700	+	0.266988i
$487$	−12.4417	−	12.4417i	−0.563787	−	0.563787i	0.366594	−	0.930381i	$-0.380524\pi$
$487$	−12.4417	−	12.4417i	−0.563787	−	0.563787i	−0.930381	+	0.366594i	$0.880524\pi$
$488$	−3.60778	−	19.8842i	−0.163317	−	0.900114i
$489$	−6.36674	+	0.156871i	−0.287914	+	0.00709397i
$490$	−18.2725	−	9.38368i	−0.825468	−	0.423912i
$491$	13.3371	−	23.1006i	0.601897	−	1.04252i	−0.390637	−	0.920545i	$-0.627745\pi$
$491$	13.3371	−	23.1006i	0.601897	−	1.04252i	0.992534	−	0.121971i	$-0.0389215\pi$
$492$	−8.94430	−	13.6333i	−0.403240	−	0.614638i
$493$	4.23318	−	15.7985i	0.190653	−	0.711527i
$494$	49.8417	+	19.7056i	2.24249	+	0.886597i
$495$	6.63530	−	20.6821i	0.298235	−	0.929592i
$496$	0.0946948	+	1.45967i	0.00425192	+	0.0655411i
$497$	−4.22210	−	1.13131i	−0.189387	−	0.0507461i
$498$	−19.5330	−	1.76410i	−0.875293	−	0.0790512i
$499$	9.32229	−	16.1467i	0.417323	−	0.722825i	−0.578346	−	0.815791i	$-0.696302\pi$
$499$	9.32229	−	16.1467i	0.417323	−	0.722825i	0.995669	+	0.0929669i	$0.0296351\pi$
$500$	15.8045	−	15.8183i	0.706799	−	0.707415i
$501$	17.9548	+	9.78462i	0.802161	+	0.437144i
$502$	15.1907	+	11.2701i	0.677995	+	0.503011i
$503$	9.53986	+	9.53986i	0.425361	+	0.425361i	0.887045	−	0.461684i	$-0.152754\pi$
$503$	9.53986	+	9.53986i	0.425361	+	0.425361i	−0.461684	+	0.887045i	$0.652754\pi$
$504$	−3.18371	+	5.11619i	−0.141814	+	0.227893i
$505$	−23.1886	−	8.72081i	−1.03188	−	0.388071i
$506$	−3.27322	−	22.0916i	−0.145513	−	0.982094i
$507$	−7.72471	+	31.9580i	−0.343066	+	1.41931i
$508$	−10.1753	+	19.0214i	−0.451455	+	0.843937i
$509$	−18.4626	−	10.6594i	−0.818340	−	0.472469i	0.0315038	−	0.999504i	$-0.489970\pi$
$509$	−18.4626	−	10.6594i	−0.818340	−	0.472469i	−0.849844	+	0.527035i	$0.823304\pi$
$510$	−2.40045	−	32.4623i	−0.106294	−	1.43746i
$511$	−1.50937	−	2.61430i	−0.0667705	−	0.115650i
$512$	−19.4256	+	11.6037i	−0.858499	+	0.512816i
$513$	26.3730	+	22.7370i	1.16440	+	1.00386i
$514$	5.21073	−	13.1796i	0.229835	−	0.581326i
$515$	11.6129	+	8.31721i	0.511727	+	0.366500i
$516$	20.9589	−	23.4968i	0.922666	−	1.03439i
$517$	−1.35136	−	5.04336i	−0.0594329	−	0.221807i
$518$	−0.239244	+	2.07660i	−0.0105118	+	0.0912405i
$519$	−7.50842	+	4.58522i	−0.329583	+	0.201269i
$520$	20.3480	+	29.4152i	0.892317	+	1.28994i
$521$			38.1663i			1.67210i	0.548657	+	0.836048i	$0.315139\pi$
$521$			38.1663i			1.67210i	−0.548657	+	0.836048i	$0.684861\pi$
$522$	−0.763496	+	11.6513i	−0.0334173	+	0.509962i
$523$	15.8178	+	15.8178i	0.691666	+	0.691666i	0.962598	−	0.270932i	$-0.0873320\pi$
$523$	15.8178	+	15.8178i	0.691666	+	0.691666i	−0.270932	+	0.962598i	$0.587332\pi$
$524$	−13.8554	−	3.23550i	−0.605277	−	0.141343i
$525$	5.77221	−	2.12271i	0.251920	−	0.0926426i
$526$	−15.8700	+	12.5910i	−0.691966	+	0.548995i
$527$	−0.562479	−	2.09920i	−0.0245020	−	0.0914426i
$528$	21.0633	−	7.71778i	0.916665	−	0.335873i
$529$	0.681239	−	0.393314i	0.0296191	−	0.0171006i
$530$	−5.09680	+	5.62446i	−0.221391	+	0.244311i
$531$	−0.187707	+	0.365597i	−0.00814579	+	0.0158656i
$532$	9.51300	−	0.308250i	0.412441	−	0.0133643i
$533$	−25.7123	−	6.88960i	−1.11372	−	0.298422i
$534$	3.81306	−	0.661330i	0.165007	−	0.0286185i
$535$	−14.5221	−	1.42654i	−0.627844	−	0.0616748i
$536$	−26.5969	−	2.19421i	−1.14881	−	0.0947753i
$537$	8.79000	+	8.36726i	0.379316	+	0.361074i
$538$	7.07896	−	9.54155i	0.305196	−	0.411365i
$539$			21.0323i			0.905925i
$540$	6.20220	+	22.3949i	0.266900	+	0.963724i
$541$		−	14.1506i		−	0.608380i	−0.952611	−	0.304190i	$-0.901614\pi$
$541$		−	14.1506i		−	0.608380i	0.952611	−	0.304190i	$-0.0983858\pi$
$542$	3.75589	+	2.78653i	0.161329	+	0.119692i
$543$	7.22208	+	6.87475i	0.309929	+	0.295024i
$544$	24.9285	−	22.5560i	1.06880	−	0.967083i
$545$	−15.9835	+	13.1242i	−0.684657	+	0.562177i
$546$	1.68110	+	9.69282i	0.0719446	+	0.414814i
$547$	−29.3873	−	7.87432i	−1.25651	−	0.336681i	−0.431663	−	0.902035i	$-0.642073\pi$
$547$	−29.3873	−	7.87432i	−1.25651	−	0.336681i	−0.824849	+	0.565353i	$0.808740\pi$
$548$	0.797387	+	24.6084i	0.0340627	+	1.05122i
$549$	−11.6185	−	18.0126i	−0.495867	−	0.768761i
$550$	−21.8002	−	6.99621i	−0.929565	−	0.298320i
$551$	15.9720	−	9.22143i	0.680429	−	0.392846i
$552$	15.8929	+	17.8408i	0.676448	+	0.759354i
$553$	3.24701	+	12.1180i	0.138077	+	0.515310i
$554$	12.8356	+	16.1783i	0.545333	+	0.687350i
$555$	5.26737	+	6.10207i	0.223588	+	0.259018i
$556$	−15.8371	−	3.69826i	−0.671643	−	0.156841i
$557$	31.2229	+	31.2229i	1.32295	+	1.32295i	0.911373	+	0.411582i	$0.135024\pi$
$557$	31.2229	+	31.2229i	1.32295	+	1.32295i	0.411582	+	0.911373i	$0.364976\pi$
$558$	0.686217	+	1.39146i	0.0290499	+	0.0589052i
$559$		−	51.4025i		−	2.17409i
$560$	5.39263	+	3.35642i	0.227880	+	0.141835i
$561$	−28.4448	+	17.3706i	−1.20094	+	0.733386i
$562$	26.0116	+	2.99679i	1.09723	+	0.126412i
$563$	−2.97679	−	11.1095i	−0.125457	−	0.468210i	0.874399	−	0.485208i	$-0.161256\pi$
$563$	−2.97679	−	11.1095i	−0.125457	−	0.468210i	−0.999856	+	0.0169973i	$0.994589\pi$
$564$	4.16864	+	3.71839i	0.175531	+	0.156572i
$565$	−14.4895	+	20.2310i	−0.609576	+	0.851123i
$566$	21.2412	+	8.39801i	0.892836	+	0.352995i
$567$	−1.03885	+	6.30643i	−0.0436276	+	0.264845i
$568$	−16.3884	−	5.87312i	−0.687643	−	0.246431i
$569$	−13.9720	−	24.2002i	−0.585738	−	1.01453i	−0.994783	−	0.102013i	$-0.967472\pi$
$569$	−13.9720	−	24.2002i	−0.585738	−	1.01453i	0.409045	−	0.912514i	$-0.365862\pi$
$570$	23.9695	−	27.7974i	1.00397	−	1.16431i
$571$	−0.0679250	−	0.0392165i	−0.00284257	−	0.00164116i	0.498578	−	0.866845i	$-0.333856\pi$
$571$	−0.0679250	−	0.0392165i	−0.00284257	−	0.00164116i	−0.501421	+	0.865204i	$0.667189\pi$
$572$	17.2745	−	32.2923i	0.722281	−	1.35021i
$573$	0.0957358	−	0.396070i	0.00399942	−	0.0165461i
$574$	−4.67624	+	0.692859i	−0.195183	+	0.0289194i
$575$	−1.60738	−	24.3327i	−0.0670323	−	1.01475i
$576$	−14.3126	+	19.2653i	−0.596357	+	0.802720i
$577$	32.6853	+	32.6853i	1.36071	+	1.36071i	0.873018	+	0.487689i	$0.162160\pi$
$577$	32.6853	+	32.6853i	1.36071	+	1.36071i	0.487689	+	0.873018i	$0.337840\pi$
$578$	−15.4361	+	20.8060i	−0.642058	+	0.865414i
$579$	−11.5719	−	6.30623i	−0.480913	−	0.262078i
$580$	12.2814	+	0.805918i	0.509959	+	0.0334639i
$581$	−2.84303	+	4.92428i	−0.117949	+	0.204293i
$582$	−3.52333	+	39.0120i	−0.146047	+	1.61710i
$583$	7.50692	+	2.01147i	0.310905	+	0.0833067i
$584$	−5.13508	−	10.8713i	−0.212491	−	0.449857i
$585$	31.8930	+	20.5437i	1.31861	+	0.849378i
$586$	12.0500	−	30.4784i	0.497783	−	1.25905i
$587$	−4.70185	+	17.5475i	−0.194066	+	0.724265i	0.798440	+	0.602074i	$0.205659\pi$
$587$	−4.70185	+	17.5475i	−0.194066	+	0.724265i	−0.992507	+	0.122191i	$0.961008\pi$
$588$	−12.3432	−	18.8141i	−0.509026	−	0.775881i
$589$	1.22529	−	2.12226i	0.0504870	−	0.0874461i
$590$	0.385355	+	0.197896i	0.0158648	+	0.00814724i
$591$	−33.9166	+	0.835678i	−1.39514	+	0.0343752i
$592$	−1.62965	+	8.16436i	−0.0669782	+	0.335553i
$593$	−1.89148	−	1.89148i	−0.0776740	−	0.0776740i	0.667202	−	0.744876i	$-0.267492\pi$
$593$	−1.89148	−	1.89148i	−0.0776740	−	0.0776740i	−0.744876	+	0.667202i	$0.767492\pi$
$594$	17.4968	−	16.1243i	0.717904	−	0.661588i
$595$	−8.83319	−	3.32199i	−0.362125	−	0.136188i
$596$	9.47745	−	40.5854i	0.388212	−	1.66244i
$597$	−33.1256	−	31.5324i	−1.35574	−	1.29054i
$598$	38.7501	+	4.46439i	1.58461	+	0.182562i
$599$	−1.50645	+	2.60925i	−0.0615520	+	0.106611i	−0.895159	−	0.445746i	$-0.852938\pi$
$599$	−1.50645	+	2.60925i	−0.0615520	+	0.106611i	0.833607	+	0.552358i	$0.186272\pi$
$600$	23.6069	−	6.53554i	0.963749	−	0.266812i
$601$	−18.3902	−	31.8527i	−0.750150	−	1.29930i	−0.947750	−	0.319015i	$-0.896648\pi$
$601$	−18.3902	−	31.8527i	−0.750150	−	1.29930i	0.197600	−	0.980283i	$-0.436685\pi$
$602$	−3.62945	−	8.37595i	−0.147925	−	0.341378i
$603$	−26.9476	+	8.66380i	−1.09739	+	0.352817i
$604$	24.6456	−	26.2963i	1.00281	−	1.06998i
$605$	−0.188266	−	1.13850i	−0.00765412	−	0.0462865i
$606$	−17.3862	−	20.8384i	−0.706266	−	0.846503i
$607$	26.5299	−	7.10867i	1.07682	−	0.288532i	0.323526	−	0.946219i	$-0.395132\pi$
$607$	26.5299	−	7.10867i	1.07682	−	0.288532i	0.753291	+	0.657687i	$0.228465\pi$
$608$	37.8612	+	1.89162i	1.53547	+	0.0767154i
$609$	2.97246	+	1.61987i	0.120450	+	0.0656404i
$610$	−18.9881	+	12.2453i	−0.768806	+	0.495797i
$611$	9.11946			0.368934
$612$	15.2506	−	32.2320i	0.616468	−	1.30290i
$613$	−29.6174	−	29.6174i	−1.19624	−	1.19624i	−0.975285	−	0.220951i	$-0.929084\pi$
$613$	−29.6174	−	29.6174i	−1.19624	−	1.19624i	−0.220951	−	0.975285i	$-0.570916\pi$
$614$	−10.0712	+	1.49221i	−0.406441	+	0.0602206i
$615$	−10.2465	+	15.0779i	−0.413180	+	0.608001i
$616$	0.534732	−	6.48170i	0.0215450	−	0.261155i
$617$	−2.79486	−	10.4306i	−0.112517	−	0.419919i	0.886572	−	0.462590i	$-0.153080\pi$
$617$	−2.79486	−	10.4306i	−0.112517	−	0.419919i	−0.999089	+	0.0426714i	$0.986413\pi$
$618$	6.57313	+	14.1999i	0.264410	+	0.571204i
$619$	21.6361	+	37.4748i	0.869627	+	1.50624i	0.862379	+	0.506264i	$0.168974\pi$
$619$	21.6361	+	37.4748i	0.869627	+	1.50624i	0.00724830	+	0.999974i	$0.497693\pi$
$620$	1.46679	−	0.723202i	0.0589079	−	0.0290445i
$621$	22.8229	+	11.0161i	0.915850	+	0.442063i
$622$	4.30175	+	9.92746i	0.172484	+	0.398055i
$623$	0.290392	−	1.08376i	0.0116343	−	0.0434199i
$624$	3.49880	+	39.0245i	0.140064	+	1.56223i
$625$	−23.1068	−	9.54340i	−0.924271	−	0.381736i
$626$	−23.2748	−	29.3361i	−0.930249	−	1.17251i
$627$	−36.5303	−	8.82989i	−1.45888	−	0.352632i
$628$	−10.0119	+	6.22120i	−0.399520	+	0.248253i
$629$		−	12.3694i		−	0.493201i
$630$	6.64746	+	1.09565i	0.264841	+	0.0436518i
$631$	6.46054			0.257190			0.128595	−	0.991697i	$-0.458953\pi$
$631$	6.46054			0.257190			0.128595	+	0.991697i	$0.458953\pi$
$632$	8.92024	+	49.1636i	0.354828	+	1.95562i
$633$	−19.6660	+	5.79227i	−0.781652	+	0.230222i
$634$	−6.41455	+	5.08921i	−0.254754	+	0.202118i
$635$	24.0026	+	2.35784i	0.952516	+	0.0935681i
$636$	−7.89568	+	2.60625i	−0.313084	+	0.103345i
$637$	−35.4832	−	9.50770i	−1.40590	−	0.376709i
$638$	−5.01056	−	11.5632i	−0.198370	−	0.457793i
$639$	−18.4427	+	0.909377i	−0.729580	+	0.0359744i
$640$	20.3060	+	15.0886i	0.802665	+	0.596430i
$641$	26.1341	−	15.0886i	1.03224	−	0.595962i	0.114612	−	0.993410i	$-0.463438\pi$
$641$	26.1341	−	15.0886i	1.03224	−	0.595962i	0.917625	+	0.397448i	$0.130104\pi$
$642$	−13.0682	−	9.20512i	−0.515759	−	0.363297i
$643$	14.7347	−	3.94815i	0.581080	−	0.155700i	0.0437066	−	0.999044i	$-0.486083\pi$
$643$	14.7347	−	3.94815i	0.581080	−	0.155700i	0.537373	+	0.843345i	$0.319417\pi$
$644$	6.62949	−	2.00862i	0.261239	−	0.0791508i
$645$	−33.2447	−	11.5763i	−1.30901	−	0.455817i
$646$	−55.7139	+	8.25489i	−2.19203	+	0.324784i
$647$	−25.0025	+	25.0025i	−0.982949	+	0.982949i	−0.999857	−	0.0169078i	$-0.994618\pi$
$647$	−25.0025	+	25.0025i	−0.982949	+	0.982949i	0.0169078	+	0.999857i	$0.494618\pi$
$648$	−6.18867	+	24.6921i	−0.243114	+	0.969998i
$649$		−	0.443557i		−	0.0174111i
$650$	21.6581	−	33.6162i	0.849499	−	1.31853i
$651$	0.449667	−	0.0110794i	0.0176238	−	0.000434237i
$652$	−3.46877	+	6.48441i	−0.135847	+	0.253949i
$653$	−9.62450	−	35.9191i	−0.376636	−	1.40562i	−0.850940	−	0.525263i	$-0.823967\pi$
$653$	−9.62450	−	35.9191i	−0.376636	−	1.40562i	0.474304	−	0.880361i	$-0.342700\pi$
$654$	−22.3219	+	3.87148i	−0.872857	+	0.151387i
$655$	2.59530	+	15.6945i	0.101407	+	0.613233i
$656$	−18.7884	+	1.21888i	−0.733565	+	0.0475894i
$657$	−9.45044	−	8.56226i	−0.368697	−	0.334046i
$658$	1.48600	−	0.643911i	0.0579303	−	0.0251023i
$659$	15.9750	−	9.22317i	0.622298	−	0.359284i	−0.155465	−	0.987841i	$-0.549688\pi$
$659$	15.9750	−	9.22317i	0.622298	−	0.359284i	0.777763	+	0.628558i	$0.216354\pi$
$660$	−16.9948	−	18.4448i	−0.661522	−	0.717965i
$661$	20.4052	+	11.7809i	0.793669	+	0.458225i	0.841253	−	0.540642i	$-0.181819\pi$
$661$	20.4052	+	11.7809i	0.793669	+	0.458225i	−0.0475835	+	0.998867i	$0.515152\pi$
$662$	7.82911	+	0.901989i	0.304287	+	0.0350568i
$663$	−16.4471	−	55.8412i	−0.638751	−	2.16869i
$664$	−12.8975	+	18.6151i	−0.500518	+	0.722405i
$665$	−4.39428	−	9.69178i	−0.170403	−	0.375831i
$666$	1.72286	+	8.66073i	0.0667594	+	0.335597i
$667$	9.49115	−	9.49115i	0.367499	−	0.367499i
$668$	20.0548	−	12.4616i	0.775942	−	0.482153i
$669$	−4.76962	+	2.91269i	−0.184404	+	0.112611i
$670$	9.12985	+	28.4061i	0.352717	+	1.09742i
$671$	20.0350	+	11.5672i	0.773441	+	0.446547i
$672$	3.32558	+	6.11193i	0.128287	+	0.235773i
$673$	−19.6668	−	5.26970i	−0.758099	−	0.203132i	−0.140991	−	0.990011i	$-0.545029\pi$
$673$	−19.6668	−	5.26970i	−0.758099	−	0.203132i	−0.617108	+	0.786879i	$0.711696\pi$
$674$	27.3259	+	10.8037i	1.05255	+	0.416141i
$675$	20.4693	−	16.0002i	0.787864	−	0.615850i
$676$	27.7004	+	25.9616i	1.06540	+	0.998523i
$677$	2.22332	−	8.29754i	0.0854491	−	0.318900i	−0.909950	−	0.414719i	$-0.863880\pi$
$677$	2.22332	−	8.29754i	0.0854491	−	0.318900i	0.995399	+	0.0958181i	$0.0305467\pi$
$678$	−24.7377	+	11.4511i	−0.950047	+	0.439776i
$679$	9.83496	+	5.67821i	0.377431	+	0.217910i
$680$	−33.9740	−	16.0786i	−1.30284	−	0.616587i
$681$	−11.5486	−	18.9112i	−0.442543	−	0.724677i
$682$	−1.34480	−	0.997720i	−0.0514951	−	0.0382047i
$683$	20.5151	−	20.5151i	0.784989	−	0.784989i	−0.195679	−	0.980668i	$-0.562691\pi$
$683$	20.5151	−	20.5151i	0.784989	−	0.784989i	0.980668	+	0.195679i	$0.0626911\pi$
$684$	37.8596	−	13.5399i	1.44760	−	0.517710i
$685$	25.0709	−	11.3672i	0.957910	−	0.434319i
$686$	−13.4075	+	1.98654i	−0.511902	+	0.0758464i
$687$	5.46040	+	18.5392i	0.208327	+	0.707314i
$688$	−11.6637	−	34.4354i	−0.444673	−	1.31284i
$689$	−6.78705	+	11.7555i	−0.258566	+	0.447850i
$690$	11.6142	−	24.0564i	0.442147	−	0.915810i
$691$	2.18052	−	1.25892i	0.0829509	−	0.0478917i	−0.457951	−	0.888978i	$-0.651416\pi$
$691$	2.18052	−	1.25892i	0.0829509	−	0.0478917i	0.540902	+	0.841086i	$0.318083\pi$
$692$	0.329002	+	10.1534i	0.0125068	+	0.385976i
$693$	−2.11138	−	6.56718i	−0.0802048	−	0.249466i
$694$	−13.7389	−	5.43185i	−0.521520	−	0.206190i
$695$	2.96649	+	17.9392i	0.112525	+	0.680471i
$696$	11.2682	+	7.40317i	0.427121	+	0.280616i
$697$	27.0203	−	7.24006i	1.02347	−	0.274237i
$698$	2.35898	−	20.4756i	0.0892888	−	0.775012i
$699$	0.566879	−	0.0139674i	0.0214413	−	0.000528297i
$700$	1.15556	−	7.00693i	0.0436760	−	0.264837i
$701$	−29.2412			−1.10442			−0.552212	−	0.833704i	$-0.686216\pi$
$701$	−29.2412			−1.10442			−0.552212	+	0.833704i	$0.686216\pi$
$702$	19.2935	+	36.8077i	0.728188	+	1.38922i
$703$	9.86260	−	9.86260i	0.371975	−	0.371975i
$704$	4.24505	−	25.5529i	0.159991	−	0.963062i
$705$	2.05379	−	5.89804i	0.0773501	−	0.222133i
$706$	−9.78125	+	7.76030i	−0.368122	+	0.292063i
$707$	−7.60003	+	2.03642i	−0.285828	+	0.0765875i
$708$	0.260310	+	0.396777i	0.00978306	+	0.0149118i
$709$	−0.478241	−	0.828337i	−0.0179607	−	0.0311089i	0.856905	−	0.515474i	$-0.172384\pi$
$709$	−0.478241	−	0.828337i	−0.0179607	−	0.0311089i	−0.874866	+	0.484365i	$0.839051\pi$
$710$	0.956791	+	19.4404i	0.0359077	+	0.729583i
$711$	28.7268	+	44.5363i	1.07734	+	1.67024i
$712$	1.50755	−	4.20670i	0.0564980	−	0.157653i
$713$	0.461604	−	1.72273i	0.0172872	−	0.0645167i
$714$	−6.62288	−	7.93792i	−0.247855	−	0.297069i
$715$	−40.7490	−	4.00288i	−1.52393	−	0.149699i
$716$	13.4111	−	4.06332i	0.501194	−	0.151853i
$717$	−1.38304	−	4.69571i	−0.0516506	−	0.175364i
$718$	31.1177	+	23.0865i	1.16130	+	0.861582i
$719$	−4.66555			−0.173996			−0.0869978	−	0.996209i	$-0.527727\pi$
$719$	−4.66555			−0.173996			−0.0869978	+	0.996209i	$0.527727\pi$
$720$	26.0272	+	6.52581i	0.969976	+	0.243202i
$721$	4.53653			0.168949
$722$	−29.4251	−	21.8308i	−1.09509	−	0.812457i
$723$	30.7695	+	7.43743i	1.14433	+	0.276601i
$724$	11.0189	−	3.33852i	0.409512	−	0.124075i
$725$	−4.42988	−	13.0281i	−0.164522	−	0.483850i
$726$	0.435675	−	1.18665i	0.0161694	−	0.0440406i
$727$	7.89542	−	29.4661i	0.292825	−	1.09284i	−0.650104	−	0.759845i	$-0.725275\pi$
$727$	7.89542	−	29.4661i	0.292825	−	1.09284i	0.942929	−	0.332993i	$-0.108059\pi$
$728$	10.6935	+	3.83221i	0.396326	+	0.142031i
$729$	3.97623	+	26.7056i	0.147268	+	0.989097i
$730$	−9.02633	+	9.96081i	−0.334079	+	0.368666i
$731$	27.0086	+	46.7803i	0.998950	+	1.73023i
$732$	−24.7104	+	1.41066i	−0.913323	+	0.0521396i
$733$	−4.87916	+	1.30737i	−0.180216	+	0.0482887i	−0.347798	−	0.937569i	$-0.613071\pi$
$733$	−4.87916	+	1.30737i	−0.180216	+	0.0482887i	0.167582	+	0.985858i	$0.446404\pi$
$734$	−10.7384	+	8.51971i	−0.396363	+	0.314468i
$735$	−14.1403	+	20.8077i	−0.521572	+	0.767503i
$736$	26.9724	−	5.80196i	0.994215	−	0.213863i
$737$	21.6026	−	21.6026i	0.795741	−	0.795741i
$738$	−17.9104	+	8.83278i	−0.659293	+	0.325139i
$739$	−50.4338			−1.85524			−0.927618	−	0.373531i	$-0.878147\pi$
$739$	−50.4338			−1.85524			−0.927618	+	0.373531i	$0.878147\pi$
$740$	9.12938	−	1.81522i	0.335603	−	0.0667287i
$741$	31.4104	−	57.6381i	1.15389	−	2.11739i
$742$	−0.275900	+	2.39476i	−0.0101286	+	0.0879146i
$743$	−47.3484	+	12.6870i	−1.73704	+	0.465440i	−0.981786	−	0.189988i	$-0.939155\pi$
$743$	−47.3484	+	12.6870i	−1.73704	+	0.465440i	−0.755258	+	0.655428i	$0.772488\pi$
$744$	1.78850	+	0.103272i	0.0655697	+	0.00378613i
$745$	−45.9723	+	7.60216i	−1.68430	+	0.278522i
$746$	44.0837	+	17.4291i	1.61402	+	0.638124i
$747$	−5.06671	+	23.4798i	−0.185381	+	0.859082i
$748$	1.24639	+	38.4652i	0.0455724	+	1.40643i
$749$	−4.01342	+	2.31715i	−0.146647	+	0.0846668i
$750$	−16.8638	−	21.5781i	−0.615778	−	0.787920i
$751$	−1.17670	+	2.03811i	−0.0429384	+	0.0743715i	−0.886696	−	0.462353i	$-0.847005\pi$
$751$	−1.17670	+	2.03811i	−0.0429384	+	0.0743715i	0.843757	+	0.536725i	$0.180339\pi$
$752$	6.10928	−	2.06928i	0.222783	−	0.0754590i
$753$	15.9723	−	16.7793i	0.582064	−	0.611472i
$754$	21.7732	−	3.22604i	0.792933	−	0.117485i
$755$	−37.7152	−	14.1840i	−1.37260	−	0.516207i
$756$	5.74278	+	4.63546i	0.208863	+	0.168590i
$757$	6.06795	−	6.06795i	0.220544	−	0.220544i	−0.588184	−	0.808727i	$-0.700157\pi$
$757$	6.06795	−	6.06795i	0.220544	−	0.220544i	0.808727	+	0.588184i	$0.200157\pi$
$758$	26.9306	+	19.9801i	0.978165	+	0.725709i
$759$	−27.3437	+	0.673727i	−0.992514	+	0.0244548i
$760$	−14.2686	−	39.9088i	−0.517578	−	1.44765i
$761$	2.84603	+	1.64316i	0.103169	+	0.0595645i	0.550697	−	0.834706i	$-0.314362\pi$
$761$	2.84603	+	1.64316i	0.103169	+	0.0595645i	−0.447528	+	0.894270i	$0.647695\pi$
$762$	21.5995	+	15.2146i	0.782469	+	0.551166i
$763$	−1.69998	+	6.34441i	−0.0615433	+	0.229683i
$764$	−0.343303	−	0.321753i	−0.0124203	−	0.0116406i
$765$	−39.8195	−	1.93875i	−1.43968	−	0.0700956i
$766$	2.84944	+	1.12656i	0.102954	+	0.0407044i
$767$	0.748318	+	0.200511i	0.0270202	+	0.00724004i
$768$	11.1989	+	25.3493i	0.404105	+	0.914713i
$769$	−13.8582	−	8.00105i	−0.499741	−	0.288525i	0.228866	−	0.973458i	$-0.426498\pi$
$769$	−13.8582	−	8.00105i	−0.499741	−	0.288525i	−0.728606	+	0.684933i	$0.759832\pi$
$770$	−6.92262	+	2.22496i	−0.249474	+	0.0801820i
$771$	−15.2412	−	8.30580i	−0.548897	−	0.299126i
$772$	−12.9254	+	8.03154i	−0.465194	+	0.289061i
$773$	−5.16954	+	5.16954i	−0.185935	+	0.185935i	−0.793936	−	0.608001i	$-0.791972\pi$
$773$	−5.16954	+	5.16954i	−0.185935	+	0.185935i	0.608001	+	0.793936i	$0.291972\pi$
$774$	−25.4264	−	28.9925i	−0.913935	−	1.04211i
$775$	−1.37530	−	1.20486i	−0.0494022	−	0.0432798i
$776$	37.1788	+	25.7593i	1.33464	+	0.924705i
$777$	2.48846	+	0.601497i	0.0892731	+	0.0215786i
$778$	−41.0277	−	4.72679i	−1.47092	−	0.169464i
$779$	27.3170	+	15.7715i	0.978735	+	0.565073i
$780$	38.8006	−	20.3336i	1.38928	−	0.728061i
$781$	17.2593	−	9.96464i	0.617585	−	0.356563i
$782$	−37.6114	+	16.2977i	−1.34498	+	0.582805i
$783$	14.0487	+	2.67122i	0.502061	+	0.0954617i
$784$	−25.9282	+	1.68207i	−0.926007	+	0.0600739i
$785$	10.7142	+	7.67355i	0.382407	+	0.273881i
$786$	−6.00588	+	16.3582i	−0.214223	+	0.583478i
$787$	3.14997	+	11.7558i	0.112284	+	0.419050i	0.999069	−	0.0431316i	$-0.0137335\pi$
$787$	3.14997	+	11.7558i	0.112284	+	0.419050i	−0.886785	+	0.462182i	$0.847067\pi$
$788$	−18.4787	+	34.5434i	−0.658275	+	1.23056i
$789$	12.9310	+	21.1749i	0.460356	+	0.753846i
$790$	46.9481	−	30.2765i	1.67034	−	1.07719i
$791$			7.90311i			0.281002i
$792$	−6.23026	−	26.7587i	−0.221382	−	0.950828i
$793$	−28.5717	+	28.5717i	−1.01461	+	1.01461i
$794$	35.1949	−	5.21468i	1.24902	−	0.185062i
$795$	6.07441	+	7.03700i	0.215437	+	0.249577i
$796$	−50.5402	+	15.3128i	−1.79135	+	0.542748i
$797$	−38.2087	+	10.2380i	−1.35342	+	0.362648i	−0.861397	−	0.507933i	$-0.830410\pi$
$797$	−38.2087	+	10.2380i	−1.35342	+	0.362648i	−0.492025	+	0.870581i	$0.663743\pi$
$798$	1.04853	−	11.6099i	0.0371177	−	0.410985i
$799$	−8.29943	+	4.79168i	−0.293613	+	0.169517i
$800$	6.88131	−	27.4344i	0.243291	−	0.969953i
$801$	−0.233425	−	4.73399i	−0.00824768	−	0.167267i
$802$	−20.1102	−	46.4097i	−0.710115	−	1.63878i
$803$	13.2946	+	3.56228i	0.469157	+	0.125710i
$804$	−6.64636	+	32.0022i	−0.234399	+	1.12863i
$805$	−4.91474	−	5.98550i	−0.173222	−	0.210961i
$806$	2.29116	−	1.81777i	0.0807026	−	0.0640282i
$807$	−10.5394	−	10.0325i	−0.371003	−	0.353160i
$808$	−30.8339	+	5.59449i	−1.08473	+	0.196813i
$809$	−55.4438			−1.94930			−0.974650	−	0.223737i	$-0.928174\pi$
$809$	−55.4438			−1.94930			−0.974650	+	0.223737i	$0.928174\pi$
$810$	28.1506	−	4.18874i	0.989110	−	0.147177i
$811$			35.9514i			1.26242i	0.775610	+	0.631212i	$0.217442\pi$
$811$			35.9514i			1.26242i	−0.775610	+	0.631212i	$0.782558\pi$
$812$	3.32012	−	2.06305i	0.116513	−	0.0723988i
$813$	3.94915	−	4.14867i	0.138503	−	0.145500i
$814$	−5.92359	−	7.46623i	−0.207622	−	0.261691i
$815$	8.18253	+	0.803792i	0.286622	+	0.0281556i
$816$	−23.6890	−	33.6770i	−0.829280	−	1.17893i
$817$	−15.7647	+	58.8347i	−0.551537	+	2.05836i
$818$	3.22768	+	7.44876i	0.112853	+	0.260440i
$819$	12.0338	−	0.593369i	0.420496	−	0.0207340i
$820$	9.30884	+	18.8801i	0.325079	+	0.659322i
$821$	4.92272	+	8.52640i	0.171804	+	0.297573i	0.939051	−	0.343779i	$-0.111707\pi$
$821$	4.92272	+	8.52640i	0.171804	+	0.297573i	−0.767247	+	0.641352i	$0.778374\pi$
$822$	30.0326	+	2.71237i	1.04751	+	0.0946047i
$823$	8.46560	+	31.5940i	0.295092	+	1.10130i	0.941144	+	0.338006i	$0.109752\pi$
$823$	8.46560	+	31.5940i	0.295092	+	1.10130i	−0.646052	+	0.763293i	$0.723581\pi$
$824$	18.0070	+	1.48555i	0.627303	+	0.0517516i
$825$	−11.7659	+	25.4531i	−0.409637	+	0.886162i
$826$	0.136095	−	0.0201646i	0.00473535	−	0.000701616i
$827$	−19.8960	−	19.8960i	−0.691853	−	0.691853i	0.270786	−	0.962640i	$-0.412716\pi$
$827$	−19.8960	−	19.8960i	−0.691853	−	0.691853i	−0.962640	+	0.270786i	$0.912716\pi$
$828$	24.0645	−	16.6499i	0.836299	−	0.578623i
$829$	31.5996			1.09750			0.548749	−	0.835987i	$-0.315104\pi$
$829$	31.5996			1.09750			0.548749	+	0.835987i	$0.315104\pi$
$830$	24.7494	+	5.34304i	0.859065	+	0.185460i
$831$	21.5862	−	13.1822i	0.748817	−	0.457285i
$832$	41.1909	+	18.7130i	1.42804	+	0.648757i
$833$	37.2882	−	9.99135i	1.29196	−	0.346180i
$834$	−6.86488	+	18.6979i	−0.237711	+	0.647454i
$835$	−21.4615	−	15.3708i	−0.742705	−	0.531927i
$836$	−29.6759	+	31.6635i	−1.02636	+	1.09511i
$837$	1.79409	−	0.625972i	0.0620127	−	0.0216367i
$838$	−5.71103	−	13.1798i	−0.197284	−	0.455288i
$839$	14.0346	+	24.3086i	0.484528	+	0.839226i	0.999842	−	0.0177748i	$-0.00565819\pi$
$839$	14.0346	+	24.3086i	0.484528	+	0.839226i	−0.515314	+	0.857001i	$0.672325\pi$
$840$	4.88676	−	6.05298i	0.168609	−	0.208848i
$841$	−10.7129	+	18.5553i	−0.369411	+	0.639838i
$842$	−16.1823	−	1.86436i	−0.557679	−	0.0642499i
$843$	7.53439	−	31.1707i	0.259498	−	1.07357i
$844$	−5.38321	+	23.0526i	−0.185298	+	0.793503i
$845$	14.9414	−	39.7291i	0.513998	−	1.36672i
$846$	5.14364	−	4.51098i	0.176842	−	0.155091i
$847$	−0.259146	−	0.259146i	−0.00890438	−	0.00890438i
$848$	−1.87934	+	9.41526i	−0.0645367	+	0.323321i
$849$	13.3863	−	24.5638i	0.459416	−	0.843029i
$850$	−2.04746	+	41.9732i	−0.0702272	+	1.43967i
$851$	5.07554	−	8.79109i	0.173987	−	0.301355i
$852$	−9.59106	+	19.0427i	−0.328584	+	0.652391i
$853$	−2.43828	+	9.09979i	−0.0834852	+	0.311571i	−0.995023	−	0.0996453i	$-0.968229\pi$
$853$	−2.43828	+	9.09979i	−0.0834852	+	0.311571i	0.911538	+	0.411216i	$0.134896\pi$
$854$	−2.63831	+	6.67311i	−0.0902810	+	0.228349i
$855$	−30.2037	−	33.2954i	−1.03295	−	1.13868i
$856$	−16.6894	+	7.88328i	−0.570431	+	0.269445i
$857$	−32.0531	−	8.58861i	−1.09491	−	0.293381i	−0.334222	−	0.942494i	$-0.608474\pi$
$857$	−32.0531	−	8.58861i	−1.09491	−	0.293381i	−0.760692	+	0.649113i	$0.775140\pi$
$858$	−36.6693	−	25.8296i	−1.25187	−	0.881808i
$859$	−1.93721	+	3.35534i	−0.0660967	+	0.114483i	−0.897180	−	0.441665i	$-0.854388\pi$
$859$	−1.93721	+	3.35534i	−0.0660967	+	0.114483i	0.831083	+	0.556148i	$0.187721\pi$
$860$	−30.5632	+	26.7990i	−1.04220	+	0.913840i
$861$	0.142611	+	5.78797i	0.00486017	+	0.197254i
$862$	15.8590	−	21.3760i	0.540160	−	0.728068i
$863$	25.0195	+	25.0195i	0.851674	+	0.851674i	0.990339	−	0.138665i	$-0.0442813\pi$
$863$	25.0195	+	25.0195i	0.851674	+	0.851674i	−0.138665	+	0.990339i	$0.544281\pi$
$864$	21.2770	+	20.2802i	0.723860	+	0.689947i
$865$	10.3443	−	4.69012i	0.351715	−	0.159469i
$866$	19.5517	−	2.89689i	0.664394	−	0.0984404i
$867$	22.9818	+	21.8765i	0.780502	+	0.742965i
$868$	0.244990	−	0.457978i	0.00831552	−	0.0155448i
$869$	−49.5365	−	28.5999i	−1.68041	−	0.970185i
$870$	2.81707	−	14.8084i	0.0955076	−	0.502052i
$871$	26.6799	+	46.2109i	0.904013	+	1.56580i
$872$	−8.82534	+	24.6263i	−0.298864	+	0.833953i
$873$	46.8948	+	10.1194i	1.58715	+	0.342491i
$874$	−42.9838	−	16.9942i	−1.45395	−	0.574838i
$875$	−7.73101	+	1.80889i	−0.261356	+	0.0611515i
$876$	−13.9831	+	4.61562i	−0.472445	+	0.155947i
$877$	−0.594165	−	2.21746i	−0.0200635	−	0.0748782i	0.955168	−	0.296064i	$-0.0956740\pi$
$877$	−0.594165	−	2.21746i	−0.0200635	−	0.0748782i	−0.975232	+	0.221185i	$0.929007\pi$
$878$	1.18066	+	0.136023i	0.0398452	+	0.00459055i
$879$	−35.2459	−	19.2075i	−1.18881	−	0.647854i
$880$	−28.2067	+	6.56469i	−0.950849	+	0.221296i
$881$		−	4.21903i		−	0.142143i	−0.997471	−	0.0710713i	$-0.977358\pi$
$881$		−	4.21903i		−	0.142143i	0.997471	−	0.0710713i	$-0.0226418\pi$
$882$	−24.7166	+	12.1893i	−0.832250	+	0.410435i
$883$	8.90100	+	8.90100i	0.299542	+	0.299542i	0.840835	−	0.541292i	$-0.182065\pi$
$883$	8.90100	+	8.90100i	0.299542	+	0.299542i	−0.541292	+	0.840835i	$0.682065\pi$
$884$	−65.4574	−	15.2855i	−2.20157	−	0.514108i
$885$	0.298209	−	0.438820i	0.0100242	−	0.0147508i
$886$	9.39336	+	11.8396i	0.315576	+	0.397759i
$887$	−4.98835	−	18.6168i	−0.167492	−	0.625090i	−0.997709	−	0.0676493i	$-0.978450\pi$
$887$	−4.98835	−	18.6168i	−0.167492	−	0.625090i	0.830217	−	0.557441i	$-0.188217\pi$
$888$	9.68056	+	3.20242i	0.324858	+	0.107466i
$889$	6.63353	−	3.82987i	0.222482	−	0.128450i
$890$	−4.99009	+	0.245596i	−0.167268	+	0.00823239i
$891$	−16.9826	−	23.6810i	−0.568937	−	0.793344i
$892$	0.208994	+	6.44983i	0.00699763	+	0.215956i
$893$	−10.4380	−	2.79686i	−0.349295	−	0.0935934i
$894$	−47.9166	−	17.5925i	−1.60257	−	0.588381i
$895$	−9.94222	−	12.1083i	−0.332332	−	0.404736i
$896$	8.03329	+	0.140829i	0.268373	+	0.00470477i
$897$	11.2242	−	46.4357i	0.374764	−	1.55044i
$898$	−25.0129	−	18.5573i	−0.834692	−	0.619265i
$899$		−	1.00641i		−	0.0335656i
$900$	−4.41261	−	29.6737i	−0.147087	−	0.989124i
$901$		−	14.2646i		−	0.475223i
$902$	12.8423	−	17.3099i	0.427603	−	0.576355i
$903$	−10.7246	+	3.15874i	−0.356891	+	0.105116i
$904$	−2.58799	+	31.3701i	−0.0860751	+	1.04335i
$905$	−8.16877	−	9.94848i	−0.271539	−	0.330699i
$906$	−28.2778	−	33.8927i	−0.939467	−	1.12601i
$907$	−0.254209	−	0.0681151i	−0.00844087	−	0.00226173i	0.254596	−	0.967047i	$-0.418057\pi$
$907$	−0.254209	−	0.0681151i	−0.00844087	−	0.00226173i	−0.263037	+	0.964786i	$0.584724\pi$
$908$	−25.5731	+	0.828645i	−0.848673	+	0.0274995i
$909$	−27.9317	+	18.0166i	−0.926437	+	0.597572i
$910$	−0.624306	−	12.6848i	−0.0206955	−	0.420498i
$911$	−23.2196	+	13.4058i	−0.769300	+	0.444156i	−0.832625	−	0.553837i	$-0.813163\pi$
$911$	−23.2196	+	13.4058i	−0.769300	+	0.444156i	0.0633248	+	0.997993i	$0.479830\pi$
$912$	7.96379	−	45.7400i	0.263707	−	1.51460i
$913$	−6.70988	−	25.0416i	−0.222065	−	0.828757i
$914$	−29.4423	+	23.3590i	−0.973863	+	0.772648i
$915$	12.0442	+	24.9134i	0.398170	+	0.823613i
$916$	21.7318	+	5.07477i	0.718038	+	0.167675i
$917$	3.57239	+	3.57239i	0.117971	+	0.117971i
$918$	−36.8987	−	23.3604i	−1.21784	−	0.771008i
$919$			13.8469i			0.456767i	0.973571	+	0.228384i	$0.0733440\pi$
$919$			13.8469i			0.456767i	−0.973571	+	0.228384i	$0.926656\pi$
$920$	−17.5482	−	25.3678i	−0.578547	−	0.836352i
$921$	0.307141	+	12.4655i	0.0101206	+	0.410754i
$922$	−0.691062	+	5.99830i	−0.0227589	+	0.197544i
$923$	9.00909	+	33.6224i	0.296538	+	1.10669i
$924$	−7.79898	−	1.61973i	−0.256568	−	0.0532851i
$925$	−5.78612	−	8.64995i	−0.190247	−	0.284408i
$926$	5.38054	−	13.6091i	0.176815	−	0.447222i
$927$	18.2444	−	5.86568i	0.599226	−	0.192654i
$928$	13.8542	−	7.10170i	0.454787	−	0.233125i
$929$	−9.74594	−	16.8805i	−0.319754	−	0.553830i	0.660683	−	0.750665i	$-0.270267\pi$
$929$	−9.74594	−	16.8805i	−0.319754	−	0.553830i	−0.980437	+	0.196835i	$0.936934\pi$
$930$	−0.659659	−	1.89119i	−0.0216311	−	0.0620146i
$931$	37.6978	+	21.7648i	1.23549	+	0.713313i
$932$	0.308851	−	0.577356i	0.0101167	−	0.0189119i
$933$	12.7111	−	3.74385i	0.416144	−	0.122568i
$934$	6.37172	+	43.0040i	0.208489	+	1.40714i
$935$	39.1880	−	17.7680i	1.28159	−	0.581075i
$936$	47.9606	+	1.58537i	1.56764	+	0.0518196i
$937$	−23.8125	−	23.8125i	−0.777921	−	0.777921i	0.201556	−	0.979477i	$-0.435400\pi$
$937$	−23.8125	−	23.8125i	−0.777921	−	0.777921i	−0.979477	+	0.201556i	$0.935400\pi$
$938$	7.61032	+	5.64616i	0.248486	+	0.184354i
$939$	−39.1423	+	23.9033i	−1.27736	+	0.780054i
$940$	−4.75449	−	5.42230i	−0.155075	−	0.176856i
$941$	3.80417	−	6.58902i	0.124012	−	0.214796i	−0.797334	−	0.603538i	$-0.793757\pi$
$941$	3.80417	−	6.58902i	0.124012	−	0.214796i	0.921346	+	0.388742i	$0.127090\pi$
$942$	6.06445	+	13.1010i	0.197590	+	0.426854i
$943$	22.1744	+	5.94162i	0.722099	+	0.193486i
$944$	0.546809	−	0.0354737i	0.0177971	−	0.00115457i
$945$	2.32637	−	7.91655i	0.0756767	−	0.257526i
$946$	38.7051	+	15.3026i	1.25841	+	0.497531i
$947$	10.2321	−	38.1866i	0.332497	−	1.24090i	−0.574060	−	0.818813i	$-0.694632\pi$
$947$	10.2321	−	38.1866i	0.332497	−	1.24090i	0.906557	−	0.422083i	$-0.138701\pi$
$948$	61.0965	−	3.48786i	1.98432	−	0.113281i
$949$	−12.0197	+	20.8188i	−0.390177	+	0.675807i
$950$	−35.0993	+	31.8343i	−1.13877	+	1.03284i
$951$	5.22662	+	8.55874i	0.169485	+	0.277536i
$952$	−11.7455	+	2.13109i	−0.380673	+	0.0690691i
$953$	18.2334	+	18.2334i	0.590639	+	0.590639i	0.937804	−	0.347165i	$-0.112856\pi$
$953$	18.2334	+	18.2334i	0.590639	+	0.590639i	−0.347165	+	0.937804i	$0.612856\pi$
$954$	1.98682	+	9.98769i	0.0643258	+	0.323363i
$955$	−0.185175	+	0.492380i	−0.00599212	+	0.0159331i
$956$	−5.50434	−	1.28537i	−0.178023	−	0.0415717i
$957$	−14.8056	+	4.36073i	−0.478597	+	0.140962i
$958$	5.91710	−	51.3595i	0.191173	−	1.65935i
$959$	4.37126	−	7.57125i	0.141155	−	0.244488i
$960$	21.3793	−	22.4260i	0.690013	−	0.723797i
$961$	15.4331	+	26.7310i	0.497843	+	0.862290i
$962$	15.2739	−	6.61847i	0.492451	−	0.213388i
$963$	−13.1446	+	14.5081i	−0.423579	+	0.467518i
$964$	24.9961	−	26.6702i	0.805069	−	0.858990i
$965$	13.8320	+	9.90651i	0.445268	+	0.318902i
$966$	−1.44979	−	8.35914i	−0.0466463	−	0.268951i
$967$	19.2917	−	5.16921i	0.620381	−	0.166230i	0.0650798	−	0.997880i	$-0.479270\pi$
$967$	19.2917	−	5.16921i	0.620381	−	0.166230i	0.555301	+	0.831650i	$0.312603\pi$
$968$	−0.943776	−	1.11350i	−0.0303341	−	0.0357892i
$969$	1.69910	+	68.9593i	0.0545830	+	2.21529i
$970$	10.6713	−	49.4305i	0.342636	−	1.58712i
$971$	−0.126718			−0.00406656			−0.00203328	−	0.999998i	$-0.500647\pi$
$971$	−0.126718			−0.00406656			−0.00203328	+	0.999998i	$0.500647\pi$
$972$	29.0892	+	11.2169i	0.933036	+	0.359784i
$973$	4.08334	+	4.08334i	0.130906	+	0.130906i
$974$	3.64705	+	24.6147i	0.116859	+	0.788705i
$975$	−37.6226	−	31.3562i	−1.20489	−	1.00420i
$976$	−12.6575	+	25.6238i	−0.405157	+	0.820198i
$977$	−14.9916	−	55.9494i	−0.479624	−	1.78998i	−0.603137	−	0.797638i	$-0.706083\pi$
$977$	−14.9916	−	55.9494i	−0.479624	−	1.78998i	0.123513	−	0.992343i	$-0.460584\pi$
$978$	7.36331	+	5.18667i	0.235453	+	0.165851i
$979$	2.55780	+	4.43023i	0.0817475	+	0.141591i
$980$	12.8463	+	26.0547i	0.410359	+	0.832288i
$981$	1.36649	+	27.7132i	0.0436287	+	0.884813i
$982$	−34.6133	+	14.9986i	−1.10455	+	0.478623i
$983$	8.35070	−	31.1652i	0.266346	−	0.994017i	−0.695075	−	0.718937i	$-0.744629\pi$
$983$	8.35070	−	31.1652i	0.266346	−	0.994017i	0.961421	−	0.275080i	$-0.0887043\pi$
$984$	−1.32928	+	23.0211i	−0.0423760	+	0.733885i
$985$	43.5896	+	4.28192i	1.38888	+	0.136433i
$986$	−18.1202	+	14.3763i	−0.577066	+	0.457836i
$987$	−0.560401	−	1.90268i	−0.0178378	−	0.0605629i
$988$	−40.0039	−	64.3794i	−1.27269	−	2.04818i
$989$			44.3298i			1.40960i
$990$	−24.9636	+	17.8989i	−0.793396	+	0.568865i
$991$	−7.05829			−0.224214			−0.112107	−	0.993696i	$-0.535760\pi$
$991$	−7.05829			−0.224214			−0.112107	+	0.993696i	$0.535760\pi$
$992$	1.12242	−	1.73764i	0.0356368	−	0.0551701i
$993$	2.26774	−	9.38191i	0.0719646	−	0.297726i
$994$	3.84204	+	4.84259i	0.121862	+	0.153598i
$995$	37.4677	+	45.6307i	1.18781	+	1.44659i
$996$	20.6984	+	18.4628i	0.655854	+	0.585015i
$997$	29.4551	+	7.89246i	0.932851	+	0.249957i	0.693070	−	0.720870i	$-0.256258\pi$
$997$	29.4551	+	7.89246i	0.932851	+	0.249957i	0.239781	+	0.970827i	$0.422924\pi$
$998$	−24.1937	+	10.4836i	−0.765838	+	0.331852i
$999$	10.7855	−	0.798532i	0.341238	−	0.0252644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.77.12	yes	256
5.3	odd	4	inner	360.2.br.e.293.19	yes	256
8.5	even	2	inner	360.2.br.e.77.2	✓	256
9.2	odd	6	inner	360.2.br.e.317.35	yes	256
40.13	odd	4	inner	360.2.br.e.293.35	yes	256
45.38	even	12	inner	360.2.br.e.173.2	yes	256
72.29	odd	6	inner	360.2.br.e.317.19	yes	256
360.173	even	12	inner	360.2.br.e.173.12	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.2	✓	256	8.5	even	2	inner
360.2.br.e.77.12	yes	256	1.1	even	1	trivial
360.2.br.e.173.2	yes	256	45.38	even	12	inner
360.2.br.e.173.12	yes	256	360.173	even	12	inner
360.2.br.e.293.19	yes	256	5.3	odd	4	inner
360.2.br.e.293.35	yes	256	40.13	odd	4	inner
360.2.br.e.317.19	yes	256	72.29	odd	6	inner
360.2.br.e.317.35	yes	256	9.2	odd	6	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13577 - 0.842635i) q^{2} +(-1.19421 + 1.25454i) q^{3} +(0.579931 + 1.91407i) q^{4} +(1.72814 - 1.41899i) q^{5} +(2.41346 - 0.418586i) q^{6} +(0.183802 - 0.685960i) q^{7} +(0.954200 - 2.66261i) q^{8} +(-0.147746 - 2.99636i) q^{9} +O(q^{10})\)	\(q+(-1.13577 - 0.842635i) q^{2} +(-1.19421 + 1.25454i) q^{3} +(0.579931 + 1.91407i) q^{4} +(1.72814 - 1.41899i) q^{5} +(2.41346 - 0.418586i) q^{6} +(0.183802 - 0.685960i) q^{7} +(0.954200 - 2.66261i) q^{8} +(-0.147746 - 2.99636i) q^{9} +(-3.15845 + 0.155449i) q^{10} +(1.61895 + 2.80410i) q^{11} +(-3.09384 - 1.55825i) q^{12} +(-5.46259 + 1.46370i) q^{13} +(-0.786771 + 0.624212i) q^{14} +(-0.283575 + 3.86259i) q^{15} +(-3.32736 + 2.22006i) q^{16} +(4.20231 - 4.20231i) q^{17} +(-2.35703 + 3.52766i) q^{18} +6.70132 q^{19} +(3.71825 + 2.48487i) q^{20} +(0.641067 + 1.04977i) q^{21} +(0.524086 - 4.54898i) q^{22} +(4.71097 - 1.26230i) q^{23} +(2.20085 + 4.37679i) q^{24} +(0.972938 - 4.90443i) q^{25} +(7.43759 + 2.94056i) q^{26} +(3.93549 + 3.39292i) q^{27} +(1.41957 - 0.0459983i) q^{28} +(2.38341 - 1.37606i) q^{29} +(3.57683 - 4.14805i) q^{30} +(0.182842 - 0.316692i) q^{31} +(5.64981 + 0.282276i) q^{32} +(-5.45121 - 1.31763i) q^{33} +(-8.31386 + 1.23183i) q^{34} +(-0.655734 - 1.44625i) q^{35} +(5.64957 - 2.02048i) q^{36} +(1.47174 - 1.47174i) q^{37} +(-7.61114 - 5.64677i) q^{38} +(4.68719 - 8.60100i) q^{39} +(-2.12923 - 5.95537i) q^{40} +(4.07637 + 2.35349i) q^{41} +(0.156467 - 1.73247i) q^{42} +(-2.35248 + 8.77956i) q^{43} +(-4.42837 + 4.72496i) q^{44} +(-4.50713 - 4.96848i) q^{45} +(-6.41422 - 2.53595i) q^{46} +(-1.55761 - 0.417360i) q^{47} +(1.18839 - 6.82552i) q^{48} +(5.62542 + 3.24784i) q^{49} +(-5.23767 + 4.75045i) q^{50} +(0.253547 + 10.2904i) q^{51} +(-5.96956 - 9.60696i) q^{52} +(1.69723 - 1.69723i) q^{53} +(-1.61081 - 7.16975i) q^{54} +(6.77675 + 2.54860i) q^{55} +(-1.65106 - 1.14394i) q^{56} +(-8.00276 + 8.40708i) q^{57} +(-3.86651 - 0.445459i) q^{58} +(-0.118636 - 0.0684948i) q^{59} +(-7.55773 + 1.69725i) q^{60} +(6.18766 - 3.57245i) q^{61} +(-0.474522 + 0.205619i) q^{62} +(-2.08254 - 0.449391i) q^{63} +(-6.17901 - 5.08133i) q^{64} +(-7.36316 + 10.2808i) q^{65} +(5.08101 + 6.08990i) q^{66} +(-2.44205 - 9.11386i) q^{67} +(10.4806 + 5.60649i) q^{68} +(-4.04226 + 7.41755i) q^{69} +(-0.473900 + 2.19515i) q^{70} -6.15502i q^{71} +(-8.11912 - 2.46574i) q^{72} +(3.00576 - 3.00576i) q^{73} +(-2.91169 + 0.431413i) q^{74} +(4.99091 + 7.07748i) q^{75} +(3.88631 + 12.8268i) q^{76} +(2.22106 - 0.595132i) q^{77} +(-12.5711 + 5.81914i) q^{78} +(-15.2990 + 8.83288i) q^{79} +(-2.59990 + 8.55807i) q^{80} +(-8.95634 + 0.885398i) q^{81} +(-2.64667 - 6.10791i) q^{82} +(-7.73393 - 2.07230i) q^{83} +(-1.63755 + 1.83584i) q^{84} +(1.29915 - 13.2252i) q^{85} +(10.0698 - 7.98925i) q^{86} +(-1.11995 + 4.63338i) q^{87} +(9.01101 - 1.63496i) q^{88} +1.57991 q^{89} +(0.932428 + 9.44090i) q^{90} +4.01615i q^{91} +(5.14818 + 8.28510i) q^{92} +(0.178952 + 0.607579i) q^{93} +(1.41740 + 1.78652i) q^{94} +(11.5808 - 9.50911i) q^{95} +(-7.10116 + 6.75082i) q^{96} +(-4.13888 + 15.4465i) q^{97} +(-3.65242 - 8.42896i) q^{98} +(8.16289 - 5.26523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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