LMFDB - Embedded newform 380.2.be.a.51.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.12
Character	$\chi$	$=$	380.51
Dual form			380.2.be.a.231.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.234248 - 1.39468i) q^{2} +(-2.22536 - 0.809964i) q^{3} +(-1.89026 - 0.653401i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-1.65093 + 2.91393i) q^{6} +(1.02771 + 0.593350i) q^{7} +(-1.35407 + 2.48324i) q^{8} +(1.99805 + 1.67656i) q^{9} +O(q^{10})$	\(q+(0.234248 - 1.39468i) q^{2} +(-2.22536 - 0.809964i) q^{3} +(-1.89026 - 0.653401i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-1.65093 + 2.91393i) q^{6} +(1.02771 + 0.593350i) q^{7} +(-1.35407 + 2.48324i) q^{8} +(1.99805 + 1.67656i) q^{9} +(1.41417 - 0.0114942i) q^{10} +(-4.46697 + 2.57901i) q^{11} +(3.67727 + 2.98509i) q^{12} +(1.70385 + 4.68129i) q^{13} +(1.06827 - 1.29434i) q^{14} +(0.411230 - 2.33220i) q^{15} +(3.14613 + 2.47019i) q^{16} +(2.50933 - 2.10558i) q^{17} +(2.80630 - 2.39390i) q^{18} +(0.726798 - 4.29788i) q^{19} +(0.315235 - 1.97500i) q^{20} +(-1.80643 - 2.15283i) q^{21} +(2.55051 + 6.83412i) q^{22} +(2.78343 + 0.490793i) q^{23} +(5.02463 - 4.42935i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(6.92801 - 1.27974i) q^{26} +(0.463852 + 0.803415i) q^{27} +(-1.55494 - 1.79309i) q^{28} +(-2.64295 + 3.14975i) q^{29} +(-3.15634 - 1.11985i) q^{30} +(-3.17320 + 5.49614i) q^{31} +(4.18210 - 3.80921i) q^{32} +(12.0295 - 2.12113i) q^{33} +(-2.34880 - 3.99293i) q^{34} +(-0.405875 + 1.11513i) q^{35} +(-2.68135 - 4.47465i) q^{36} +11.7312i q^{37} +(-5.82391 - 2.02042i) q^{38} -11.7976i q^{39} +(-2.68065 - 0.902291i) q^{40} +(0.230499 - 0.633292i) q^{41} +(-3.42565 + 2.01510i) q^{42} +(6.23161 - 1.09880i) q^{43} +(10.1288 - 1.95626i) q^{44} +(-1.30413 + 2.25882i) q^{45} +(1.33651 - 3.76702i) q^{46} +(-5.14511 + 6.13171i) q^{47} +(-5.00051 - 8.04531i) q^{48} +(-2.79587 - 4.84259i) q^{49} +(0.256887 + 1.39069i) q^{50} +(-7.28959 + 2.65320i) q^{51} +(-0.161953 - 9.96213i) q^{52} +(-7.21998 - 1.27308i) q^{53} +(1.22916 - 0.458726i) q^{54} +(-3.31551 - 3.95127i) q^{55} +(-2.86503 + 1.74862i) q^{56} +(-5.09851 + 8.97564i) q^{57} +(3.77378 + 4.42389i) q^{58} +(-9.18314 + 7.70557i) q^{59} +(-2.30119 + 4.13976i) q^{60} +(-0.330596 + 1.87491i) q^{61} +(6.92203 + 5.71305i) q^{62} +(1.05863 + 2.90856i) q^{63} +(-4.33297 - 6.72498i) q^{64} +(-4.31430 + 2.49086i) q^{65} +(-0.140403 - 17.2742i) q^{66} +(-1.88012 - 1.57761i) q^{67} +(-6.11906 + 2.34048i) q^{68} +(-5.79659 - 3.34667i) q^{69} +(1.46018 + 0.827283i) q^{70} +(1.39818 + 7.92947i) q^{71} +(-6.86880 + 2.69145i) q^{72} +(2.87603 + 1.04679i) q^{73} +(16.3613 + 2.74801i) q^{74} +2.36818 q^{75} +(-4.18207 + 7.64920i) q^{76} -6.12101 q^{77} +(-16.4539 - 2.76356i) q^{78} +(4.30760 + 1.56784i) q^{79} +(-1.88634 + 3.52728i) q^{80} +(-1.74026 - 9.86950i) q^{81} +(-0.829245 - 0.469820i) q^{82} +(6.93456 + 4.00367i) q^{83} +(2.00797 + 5.24972i) q^{84} +(2.50933 + 2.10558i) q^{85} +(-0.0727324 - 8.94848i) q^{86} +(8.43270 - 4.86862i) q^{87} +(-0.355693 - 14.5847i) q^{88} +(-3.02233 - 8.30379i) q^{89} +(2.84484 + 2.34797i) q^{90} +(-1.02657 + 5.82199i) q^{91} +(-4.94070 - 2.74642i) q^{92} +(11.5132 - 9.66070i) q^{93} +(7.34653 + 8.61212i) q^{94} +(4.35879 - 0.0305629i) q^{95} +(-12.3920 + 5.08951i) q^{96} +(-5.22736 - 6.22973i) q^{97} +(-7.40879 + 2.76498i) q^{98} +(-13.2491 - 2.33617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 36 * q^8 + 6 * q^9	$ 120 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} + 18 q^{14} - 15 q^{16} - 48 q^{17} - 12 q^{21} + 18 q^{24} - 69 q^{28} - 12 q^{30} - 33 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} + 18 q^{38} - 36 q^{41} - 27 q^{42} - 27 q^{44} - 60 q^{45} - 117 q^{46} + 45 q^{48} + 60 q^{49} - 15 q^{52} + 48 q^{53} + 69 q^{54} + 48 q^{57} + 6 q^{60} + 18 q^{62} - 24 q^{64} - 18 q^{65} + 168 q^{66} + 12 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 24 q^{76} - 60 q^{77} - 54 q^{78} + 21 q^{80} - 66 q^{81} - 63 q^{82} + 252 q^{84} - 48 q^{85} - 45 q^{86} + 135 q^{88} - 3 q^{90} - 42 q^{92} + 96 q^{93} + 78 q^{96} - 54 q^{97} - 33 q^{98}+O(q^{100}) $ 120 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 + 18 * q^14 - 15 * q^16 - 48 * q^17 - 12 * q^21 + 18 * q^24 - 69 * q^28 - 12 * q^30 - 33 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 + 18 * q^38 - 36 * q^41 - 27 * q^42 - 27 * q^44 - 60 * q^45 - 117 * q^46 + 45 * q^48 + 60 * q^49 - 15 * q^52 + 48 * q^53 + 69 * q^54 + 48 * q^57 + 6 * q^60 + 18 * q^62 - 24 * q^64 - 18 * q^65 + 168 * q^66 + 12 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 24 * q^76 - 60 * q^77 - 54 * q^78 + 21 * q^80 - 66 * q^81 - 63 * q^82 + 252 * q^84 - 48 * q^85 - 45 * q^86 + 135 * q^88 - 3 * q^90 - 42 * q^92 + 96 * q^93 + 78 * q^96 - 54 * q^97 - 33 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	0.234248	−	1.39468i	0.165638	−	0.986187i
$2$	0.234248	−	1.39468i	0.165638	−	0.986187i
$3$	−2.22536	−	0.809964i	−1.28481	−	0.467633i	−0.392791	−	0.919628i	$-0.628490\pi$
$3$	−2.22536	−	0.809964i	−1.28481	−	0.467633i	−0.892021	+	0.451995i	$0.850713\pi$
$4$	−1.89026	−	0.653401i	−0.945128	−	0.326700i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$	−1.65093	+	2.91393i	−0.673987	+	1.18961i
$7$	1.02771	+	0.593350i	0.388438	+	0.224265i	0.681483	−	0.731834i	$-0.261335\pi$
$7$	1.02771	+	0.593350i	0.388438	+	0.224265i	−0.293045	+	0.956099i	$0.594669\pi$
$8$	−1.35407	+	2.48324i	−0.478737	+	0.877958i
$9$	1.99805	+	1.67656i	0.666015	+	0.558853i
$10$	1.41417	−	0.0114942i	0.447199	−	0.00363479i
$11$	−4.46697	+	2.57901i	−1.34684	+	0.777600i	−0.987801	−	0.155722i	$-0.950230\pi$
$11$	−4.46697	+	2.57901i	−1.34684	+	0.777600i	−0.359042	+	0.933322i	$0.616896\pi$
$12$	3.67727	+	2.98509i	1.06154	+	0.861722i
$13$	1.70385	+	4.68129i	0.472563	+	1.29836i	0.915686	+	0.401895i	$0.131648\pi$
$13$	1.70385	+	4.68129i	0.472563	+	1.29836i	−0.443123	+	0.896461i	$0.646130\pi$
$14$	1.06827	−	1.29434i	0.285507	−	0.345926i
$15$	0.411230	−	2.33220i	0.106179	−	0.602171i
$16$	3.14613	+	2.47019i	0.786534	+	0.617548i
$17$	2.50933	−	2.10558i	0.608601	−	0.510677i	−0.285596	−	0.958350i	$-0.592192\pi$
$17$	2.50933	−	2.10558i	0.608601	−	0.510677i	0.894197	+	0.447673i	$0.147747\pi$
$18$	2.80630	−	2.39390i	0.661451	−	0.564248i
$19$	0.726798	−	4.29788i	0.166739	−	0.986001i
$19$	0.726798	−	4.29788i	0.166739	−	0.986001i
$20$	0.315235	−	1.97500i	0.0704887	−	0.441624i
$21$	−1.80643	−	2.15283i	−0.394196	−	0.469785i
$22$	2.55051	+	6.83412i	0.543770	+	1.45704i
$23$	2.78343	+	0.490793i	0.580384	+	0.102337i	0.456130	−	0.889913i	$-0.349235\pi$
$23$	2.78343	+	0.490793i	0.580384	+	0.102337i	0.124254	+	0.992250i	$0.460346\pi$
$24$	5.02463	−	4.42935i	1.02565	−	0.904138i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	6.92801	−	1.27974i	1.35870	−	0.250978i
$27$	0.463852	+	0.803415i	0.0892683	+	0.154617i
$28$	−1.55494	−	1.79309i	−0.293857	−	0.338862i
$29$	−2.64295	+	3.14975i	−0.490784	+	0.584893i	−0.953417	−	0.301657i	$-0.902460\pi$
$29$	−2.64295	+	3.14975i	−0.490784	+	0.584893i	0.462633	+	0.886550i	$0.346905\pi$
$30$	−3.15634	−	1.11985i	−0.576266	−	0.204455i
$31$	−3.17320	+	5.49614i	−0.569923	+	0.987136i	0.426650	+	0.904417i	$0.359694\pi$
$31$	−3.17320	+	5.49614i	−0.569923	+	0.987136i	−0.996573	+	0.0827188i	$0.973640\pi$
$32$	4.18210	−	3.80921i	0.739297	−	0.673379i
$33$	12.0295	−	2.12113i	2.09407	−	0.369241i
$34$	−2.34880	−	3.99293i	−0.402815	−	0.684782i
$35$	−0.405875	+	1.11513i	−0.0686054	+	0.188492i
$36$	−2.68135	−	4.47465i	−0.446892	−	0.745775i
$37$			11.7312i			1.92860i	0.264814	+	0.964300i	$0.414690\pi$
$37$			11.7312i			1.92860i	−0.264814	+	0.964300i	$0.585310\pi$
$38$	−5.82391	−	2.02042i	−0.944763	−	0.327755i
$39$		−	11.7976i		−	1.88913i
$40$	−2.68065	−	0.902291i	−0.423848	−	0.142665i
$41$	0.230499	−	0.633292i	0.0359980	−	0.0989036i	−0.920392	−	0.390998i	$-0.872130\pi$
$41$	0.230499	−	0.633292i	0.0359980	−	0.0989036i	0.956389	+	0.292094i	$0.0943522\pi$
$42$	−3.42565	+	2.01510i	−0.528590	+	0.310937i
$43$	6.23161	−	1.09880i	0.950312	−	0.167566i	0.323057	−	0.946380i	$-0.395290\pi$
$43$	6.23161	−	1.09880i	0.950312	−	0.167566i	0.627255	+	0.778814i	$0.284178\pi$
$44$	10.1288	−	1.95626i	1.52698	−	0.294917i
$45$	−1.30413	+	2.25882i	−0.194408	+	0.336725i
$46$	1.33651	−	3.76702i	0.197058	−	0.555416i
$47$	−5.14511	+	6.13171i	−0.750492	+	0.894402i	−0.997207	−	0.0746865i	$-0.976204\pi$
$47$	−5.14511	+	6.13171i	−0.750492	+	0.894402i	0.246715	+	0.969088i	$0.420649\pi$
$48$	−5.00051	−	8.04531i	−0.721762	−	1.16124i
$49$	−2.79587	−	4.84259i	−0.399410	−	0.691799i
$50$	0.256887	+	1.39069i	0.0363293	+	0.196673i
$51$	−7.28959	+	2.65320i	−1.02075	+	0.371522i
$52$	−0.161953	−	9.96213i	−0.0224589	−	1.38150i
$53$	−7.21998	−	1.27308i	−0.991740	−	0.174871i	−0.345841	−	0.938293i	$-0.612406\pi$
$53$	−7.21998	−	1.27308i	−0.991740	−	0.174871i	−0.645899	+	0.763423i	$0.723517\pi$
$54$	1.22916	−	0.458726i	0.167268	−	0.0624247i
$55$	−3.31551	−	3.95127i	−0.447063	−	0.532789i
$56$	−2.86503	+	1.74862i	−0.382855	+	0.233669i
$57$	−5.09851	+	8.97564i	−0.675315	+	1.18885i
$58$	3.77378	+	4.42389i	0.495521	+	0.580885i
$59$	−9.18314	+	7.70557i	−1.19554	+	1.00318i	−0.195797	+	0.980644i	$0.562729\pi$
$59$	−9.18314	+	7.70557i	−1.19554	+	1.00318i	−0.999746	+	0.0225351i	$0.992826\pi$
$60$	−2.30119	+	4.13976i	−0.297082	+	0.534440i
$61$	−0.330596	+	1.87491i	−0.0423285	+	0.240057i	−0.998630	−	0.0523251i	$-0.983337\pi$
$61$	−0.330596	+	1.87491i	−0.0423285	+	0.240057i	0.956302	+	0.292382i	$0.0944479\pi$
$62$	6.92203	+	5.71305i	0.879099	+	0.725558i
$63$	1.05863	+	2.90856i	0.133375	+	0.366444i
$64$	−4.33297	−	6.72498i	−0.541622	−	0.840622i
$65$	−4.31430	+	2.49086i	−0.535123	+	0.308953i
$66$	−0.140403	−	17.2742i	−0.0172824	−	2.12630i
$67$	−1.88012	−	1.57761i	−0.229693	−	0.192736i	0.520676	−	0.853754i	$-0.325680\pi$
$67$	−1.88012	−	1.57761i	−0.229693	−	0.192736i	−0.750369	+	0.661019i	$0.770124\pi$
$68$	−6.11906	+	2.34048i	−0.742044	+	0.283825i
$69$	−5.79659	−	3.34667i	−0.697828	−	0.402891i
$70$	1.46018	+	0.827283i	0.174524	+	0.0988792i
$71$	1.39818	+	7.92947i	0.165933	+	0.941055i	0.948097	+	0.317982i	$0.103005\pi$
$71$	1.39818	+	7.92947i	0.165933	+	0.941055i	−0.782163	+	0.623073i	$0.785884\pi$
$72$	−6.86880	+	2.69145i	−0.809496	+	0.317190i
$73$	2.87603	+	1.04679i	0.336613	+	0.122517i	0.504796	−	0.863239i	$-0.331568\pi$
$73$	2.87603	+	1.04679i	0.336613	+	0.122517i	−0.168183	+	0.985756i	$0.553790\pi$
$74$	16.3613	+	2.74801i	1.90196	+	0.319450i
$75$	2.36818			0.273454
$76$	−4.18207	+	7.64920i	−0.479717	+	0.877424i
$77$	−6.12101			−0.697554
$78$	−16.4539	−	2.76356i	−1.86303	−	0.312912i
$79$	4.30760	+	1.56784i	0.484643	+	0.176396i	0.572774	−	0.819713i	$-0.305867\pi$
$79$	4.30760	+	1.56784i	0.484643	+	0.176396i	−0.0881309	+	0.996109i	$0.528089\pi$
$80$	−1.88634	+	3.52728i	−0.210899	+	0.394362i
$81$	−1.74026	−	9.86950i	−0.193362	−	1.09661i
$82$	−0.829245	−	0.469820i	−0.0915748	−	0.0518829i
$83$	6.93456	+	4.00367i	0.761167	+	0.439460i	0.829715	−	0.558188i	$-0.188503\pi$
$83$	6.93456	+	4.00367i	0.761167	+	0.439460i	−0.0685477	+	0.997648i	$0.521837\pi$
$84$	2.00797	+	5.24972i	0.219087	+	0.572791i
$85$	2.50933	+	2.10558i	0.272175	+	0.228382i
$86$	−0.0727324	−	8.94848i	−0.00784294	−	0.964940i
$87$	8.43270	−	4.86862i	0.904080	−	0.521971i
$88$	−0.355693	−	14.5847i	−0.0379170	−	1.55474i
$89$	−3.02233	−	8.30379i	−0.320367	−	0.880200i	−0.990445	−	0.137909i	$-0.955962\pi$
$89$	−3.02233	−	8.30379i	−0.320367	−	0.880200i	0.670078	−	0.742290i	$-0.266260\pi$
$90$	2.84484	+	2.34797i	0.299872	+	0.247498i
$91$	−1.02657	+	5.82199i	−0.107614	+	0.610311i
$92$	−4.94070	−	2.74642i	−0.515104	−	0.286334i
$93$	11.5132	−	9.66070i	1.19386	−	1.00177i
$94$	7.34653	+	8.61212i	0.757737	+	0.888272i
$95$	4.35879	−	0.0305629i	0.447203	−	0.00313569i
$96$	−12.3920	+	5.08951i	−1.26475	+	0.519446i
$97$	−5.22736	−	6.22973i	−0.530758	−	0.632533i	0.432331	−	0.901715i	$-0.357691\pi$
$97$	−5.22736	−	6.22973i	−0.530758	−	0.632533i	−0.963089	+	0.269182i	$0.913247\pi$
$98$	−7.40879	+	2.76498i	−0.748401	+	0.279305i
$99$	−13.2491	−	2.33617i	−1.33158	−	0.234794i
$100$	1.99974	−	0.0325095i	0.199974	−	0.00325095i
$101$	−10.4267	+	3.79502i	−1.03750	+	0.377619i	−0.803931	−	0.594722i	$-0.797262\pi$
$101$	−10.4267	+	3.79502i	−1.03750	+	0.377619i	−0.233567	+	0.972341i	$0.575040\pi$
$102$	1.99278	+	10.7881i	0.197315	+	1.06819i
$103$	5.46664	+	9.46849i	0.538644	+	0.932958i	0.998977	+	0.0452124i	$0.0143964\pi$
$103$	5.46664	+	9.46849i	0.538644	+	0.932958i	−0.460334	+	0.887746i	$0.652270\pi$
$104$	−13.9319	−	2.10774i	−1.36614	−	0.206680i
$105$	1.80643	−	2.15283i	0.176290	−	0.210094i
$106$	−3.46680	+	9.77133i	−0.336725	+	0.949076i
$107$	4.78124	−	8.28135i	0.462220	−	0.800588i	−0.536851	−	0.843677i	$-0.680386\pi$
$107$	4.78124	−	8.28135i	0.462220	−	0.800588i	0.999071	+	0.0430885i	$0.0137198\pi$
$108$	−0.351846	−	1.82174i	−0.0338564	−	0.175297i
$109$	13.7467	−	2.42391i	1.31669	−	0.232169i	0.529203	−	0.848495i	$-0.322491\pi$
$109$	13.7467	−	2.42391i	1.31669	−	0.232169i	0.787491	+	0.616327i	$0.211380\pi$
$110$	−6.28740	+	3.69849i	−0.599480	+	0.352637i
$111$	9.50186	−	26.1062i	0.901877	−	2.47789i
$112$	1.76763	+	4.40540i	0.167026	+	0.416271i
$113$			11.3759i			1.07016i	0.844802	+	0.535079i	$0.179718\pi$
$113$			11.3759i			1.07016i	−0.844802	+	0.535079i	$0.820282\pi$
$114$	11.3238	+	9.21331i	1.06057	+	0.862906i
$115$			2.82636i			0.263560i
$116$	7.05390	−	4.22692i	0.654938	−	0.392460i
$117$	−4.44409	+	12.2100i	−0.410856	+	1.12882i
$118$	8.59566	+	14.6125i	0.791295	+	1.34519i
$119$	3.82821	−	0.675016i	0.350931	−	0.0618786i
$120$	5.23458	+	4.17915i	0.477849	+	0.381502i
$121$	7.80256	−	13.5144i	0.709323	−	1.22858i
$122$	2.53745	+	0.900268i	0.229730	+	0.0815065i
$123$	−1.02589	+	1.22261i	−0.0925012	+	0.110239i
$124$	9.58934	−	8.31574i	0.861148	−	0.746775i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	4.30448	−	0.795123i	0.383474	−	0.0708352i
$127$	−5.48244	+	1.99544i	−0.486487	+	0.177067i	−0.573607	−	0.819131i	$-0.694456\pi$
$127$	−5.48244	+	1.99544i	−0.486487	+	0.177067i	0.0871191	+	0.996198i	$0.472234\pi$
$128$	−10.3942	+	4.46779i	−0.918724	+	0.394901i
$129$	−14.7576	−	2.60216i	−1.29933	−	0.229107i
$130$	2.46334	+	6.60054i	0.216049	+	0.578905i
$131$	4.37599	+	5.21510i	0.382332	+	0.455645i	0.922549	−	0.385880i	$-0.126102\pi$
$131$	4.37599	+	5.21510i	0.382332	+	0.455645i	−0.540217	+	0.841526i	$0.681658\pi$
$132$	−24.1248	−	3.85062i	−2.09980	−	0.335154i
$133$	3.29708	−	3.98574i	0.285893	−	0.345607i
$134$	−2.64067	+	2.25261i	−0.228119	+	0.194596i
$135$	−0.710662	+	0.596316i	−0.0611641	+	0.0513227i
$136$	1.83084	+	9.08237i	0.156993	+	0.778807i
$137$	2.61520	−	14.8315i	0.223432	−	1.26714i	−0.642229	−	0.766513i	$-0.721990\pi$
$137$	2.61520	−	14.8315i	0.223432	−	1.26714i	0.865661	−	0.500631i	$-0.166899\pi$
$138$	−6.02536	+	7.30044i	−0.512913	+	0.621454i
$139$	−0.175218	−	0.481406i	−0.0148618	−	0.0408323i	0.932040	−	0.362356i	$-0.118027\pi$
$139$	−0.175218	−	0.481406i	−0.0148618	−	0.0408323i	−0.946902	+	0.321523i	$0.895805\pi$
$140$	1.49584	−	1.84269i	0.126421	−	0.155735i
$141$	16.4162	−	9.47789i	1.38249	−	0.798182i
$142$	11.3866	−	0.0925491i	0.955541	−	0.00776655i
$143$	−19.6841	−	16.5169i	−1.64607	−	1.38122i
$144$	2.14470	+	10.2102i	0.178725	+	0.850853i
$145$	−3.56084	−	2.05585i	−0.295712	−	0.170729i
$146$	2.13364	−	3.76592i	0.176581	−	0.311670i
$147$	2.29949	+	13.0411i	0.189659	+	1.07561i
$148$	7.66519	−	22.1750i	0.630074	−	1.82277i
$149$	−9.20973	−	3.35207i	−0.754490	−	0.274612i	−0.0639962	−	0.997950i	$-0.520385\pi$
$149$	−9.20973	−	3.35207i	−0.754490	−	0.274612i	−0.690494	+	0.723338i	$0.742607\pi$
$150$	0.554741	−	3.30285i	0.0452944	−	0.269676i
$151$	0.750167			0.0610477			0.0305239	−	0.999534i	$-0.490282\pi$
$151$	0.750167			0.0610477			0.0305239	+	0.999534i	$0.490282\pi$
$152$	9.68853	+	7.62445i	0.785844	+	0.618425i
$153$	8.54387			0.690731
$154$	−1.43383	+	8.53684i	−0.115542	+	0.687918i
$155$	−5.96366	−	2.17059i	−0.479013	−	0.174346i
$156$	−7.70856	+	22.3005i	−0.617179	+	1.78547i
$157$	1.85838	+	10.5394i	0.148315	+	0.841137i	0.964645	+	0.263551i	$0.0848939\pi$
$157$	1.85838	+	10.5394i	0.148315	+	0.841137i	−0.816330	+	0.577585i	$0.803995\pi$
$158$	3.19568	−	5.64046i	0.254235	−	0.448731i
$159$	15.0359	+	8.68098i	1.19242	+	0.688446i
$160$	4.47755	+	3.45710i	0.353982	+	0.273308i
$161$	2.56935	+	2.15594i	0.202493	+	0.169912i
$162$	−14.1724	+	0.115192i	−1.11349	+	0.00905035i
$163$	5.06908	−	2.92663i	0.397041	−	0.229232i	−0.288166	−	0.957581i	$-0.593045\pi$
$163$	5.06908	−	2.92663i	0.397041	−	0.229232i	0.685206	+	0.728349i	$0.259712\pi$
$164$	−0.849496	+	1.04648i	−0.0663345	+	0.0817160i
$165$	4.17781	+	11.4784i	0.325242	+	0.893595i
$166$	7.20824	−	8.73363i	0.559468	−	0.677861i
$167$	3.61079	−	20.4778i	0.279412	−	1.58462i	−0.445178	−	0.895442i	$-0.646860\pi$
$167$	3.61079	−	20.4778i	0.279412	−	1.58462i	0.724590	−	0.689180i	$-0.242029\pi$
$168$	7.79203	−	1.57073i	0.601168	−	0.121185i
$169$	−9.05277	+	7.59618i	−0.696367	+	0.584322i
$170$	3.52441	−	3.00648i	0.270310	−	0.230586i
$171$	8.65782	−	7.36884i	0.662080	−	0.563509i
$172$	−12.4973	−	1.99473i	−0.952910	−	0.152096i
$173$	−9.41303	−	11.2180i	−0.715659	−	0.852889i	0.278542	−	0.960424i	$-0.410149\pi$
$173$	−9.41303	−	11.2180i	−0.715659	−	0.852889i	−0.994201	+	0.107535i	$0.965704\pi$
$174$	−4.81482	−	12.9014i	−0.365010	−	0.978050i
$175$	−1.16867	−	0.206068i	−0.0883432	−	0.0155773i
$176$	−20.4243	−	2.92037i	−1.53954	−	0.220131i
$177$	26.6770	−	9.70964i	2.00517	−	0.729821i
$178$	−12.2891	+	2.27004i	−0.921106	+	0.170146i
$179$	−10.4630	−	18.1224i	−0.782038	−	1.35453i	−0.930753	−	0.365650i	$-0.880847\pi$
$179$	−10.4630	−	18.1224i	−0.782038	−	1.35453i	0.148715	−	0.988880i	$-0.452486\pi$
$180$	3.94106	−	3.41763i	0.293749	−	0.254735i
$181$	−6.98134	+	8.32004i	−0.518919	+	0.618424i	−0.960325	−	0.278884i	$-0.910036\pi$
$181$	−6.98134	+	8.32004i	−0.518919	+	0.618424i	0.441406	+	0.897308i	$0.354480\pi$
$182$	7.87933	+	2.79553i	0.584055	+	0.207219i
$183$	2.25430	−	3.90457i	0.166643	−	0.288634i
$184$	−4.98772	+	6.24735i	−0.367699	+	0.460561i
$185$	−11.5530	+	2.03710i	−0.849393	+	0.149771i
$186$	−10.7766	−	18.3202i	−0.790181	−	1.34330i
$187$	−5.77880	+	15.8771i	−0.422588	+	1.16105i
$188$	13.7320	−	8.22867i	1.00151	−	0.600138i
$189$			1.10091i			0.0800791i
$190$	0.978412	−	6.08627i	0.0709815	−	0.441545i
$191$			10.2314i			0.740315i	0.928969	+	0.370158i	$0.120696\pi$
$191$			10.2314i			0.740315i	−0.928969	+	0.370158i	$0.879304\pi$
$192$	4.19543	+	18.4750i	0.302779	+	1.33332i
$193$	5.77016	−	15.8534i	0.415345	−	1.14115i	−0.538964	−	0.842329i	$-0.681184\pi$
$193$	5.77016	−	15.8534i	0.415345	−	1.14115i	0.954309	−	0.298822i	$-0.0965938\pi$
$194$	−9.91296	+	5.83119i	−0.711709	+	0.418655i
$195$	11.6184	−	2.04863i	0.832009	−	0.146706i
$196$	2.12076	+	10.9806i	0.151483	+	0.784326i
$197$	10.4458	−	18.0927i	0.744236	−	1.28905i	−0.206315	−	0.978486i	$-0.566147\pi$
$197$	10.4458	−	18.0927i	0.744236	−	1.28905i	0.950551	−	0.310568i	$-0.100519\pi$
$198$	−6.36177	+	17.9309i	−0.452111	+	1.27430i
$199$	4.61894	−	5.50464i	0.327428	−	0.390213i	−0.577068	−	0.816696i	$-0.695803\pi$
$199$	4.61894	−	5.50464i	0.327428	−	0.390213i	0.904496	+	0.426483i	$0.140248\pi$
$200$	0.423094	−	2.79660i	0.0299172	−	0.197750i
$201$	2.90614	+	5.03357i	0.204983	+	0.355041i
$202$	2.85039	+	15.4309i	0.200553	+	1.08572i
$203$	−4.58509	+	1.66884i	−0.321810	+	0.117129i
$204$	15.5128	−	0.252190i	1.08611	−	0.0176568i
$205$	0.663697	+	0.117028i	0.0463546	+	0.00817356i
$206$	14.4861	−	5.40623i	1.00929	−	0.376670i
$207$	4.73857	+	5.64720i	0.329353	+	0.392508i
$208$	−6.20313	+	18.9368i	−0.430110	+	1.31303i
$209$	7.83768	+	21.0729i	0.542143	+	1.45764i
$210$	−2.57935	−	3.02369i	−0.177992	−	0.208654i
$211$	11.4165	−	9.57958i	0.785945	−	0.659486i	−0.158794	−	0.987312i	$-0.550760\pi$
$211$	11.4165	−	9.57958i	0.785945	−	0.659486i	0.944738	+	0.327826i	$0.106316\pi$
$212$	12.8158	+	7.12398i	0.880191	+	0.489277i
$213$	3.31114	−	18.7784i	0.226875	−	1.28667i
$214$	−10.4298	−	8.60818i	−0.712968	−	0.588443i
$215$	2.16422	+	5.94613i	0.147598	+	0.405523i
$216$	−2.62316	+	0.0639737i	−0.178484	+	0.00435286i
$217$	−6.52226	+	3.76563i	−0.442760	+	0.255628i
$218$	−0.160445	−	19.7400i	−0.0108667	−	1.33696i
$219$	−5.55233	−	4.65896i	−0.375192	−	0.314823i
$220$	3.68540	+	9.63526i	0.248469	+	0.649609i
$221$	14.1323	+	8.15930i	0.950643	+	0.548854i
$222$	−34.1839	−	19.3674i	−2.29427	−	1.29985i
$223$	2.06943	+	11.7363i	0.138579	+	0.785923i	0.972300	+	0.233736i	$0.0750953\pi$
$223$	2.06943	+	11.7363i	0.138579	+	0.785923i	−0.833721	+	0.552186i	$0.813794\pi$
$224$	6.55818	−	1.43332i	0.438187	−	0.0957679i
$225$	−2.45097	−	0.892078i	−0.163398	−	0.0594719i
$226$	15.8658	+	2.66479i	1.05538	+	0.177259i
$227$	−11.8747			−0.788151			−0.394076	−	0.919078i	$-0.628935\pi$
$227$	−11.8747			−0.788151			−0.394076	+	0.919078i	$0.628935\pi$
$228$	15.5022	−	13.6349i	1.02666	−	0.902992i
$229$	1.27129			0.0840094			0.0420047	−	0.999117i	$-0.486626\pi$
$229$	1.27129			0.0840094			0.0420047	+	0.999117i	$0.486626\pi$
$230$	3.94187	+	0.662070i	0.259919	+	0.0436556i
$231$	13.6214	+	4.95780i	0.896225	+	0.326199i
$232$	−4.24283	−	10.8281i	−0.278556	−	0.710898i
$233$	1.13968	+	6.46344i	0.0746628	+	0.423434i	0.999112	+	0.0421291i	$0.0134141\pi$
$233$	1.13968	+	6.46344i	0.0746628	+	0.423434i	−0.924449	+	0.381305i	$0.875475\pi$
$234$	15.9880	+	9.05825i	1.04517	+	0.592156i
$235$	−6.93199	−	4.00219i	−0.452193	−	0.261074i
$236$	22.3933	−	8.56522i	1.45768	−	0.557549i
$237$	−8.31607	−	6.97801i	−0.540187	−	0.453271i
$238$	−0.0446810	−	5.49724i	−0.00289624	−	0.356333i
$239$	15.9785	−	9.22520i	1.03356	−	0.596729i	0.115561	−	0.993300i	$-0.463134\pi$
$239$	15.9785	−	9.22520i	1.03356	−	0.596729i	0.918004	+	0.396572i	$0.129800\pi$
$240$	7.05476	−	6.32160i	0.455383	−	0.408057i
$241$	10.0827	+	27.7021i	0.649485	+	1.78445i	0.619633	+	0.784892i	$0.287282\pi$
$241$	10.0827	+	27.7021i	0.649485	+	1.78445i	0.0298527	+	0.999554i	$0.490496\pi$
$242$	−17.0205	−	14.0478i	−1.09412	−	0.903026i
$243$	−3.63796	+	20.6319i	−0.233375	+	1.32354i
$244$	1.84998	−	3.32804i	0.118433	−	0.213056i
$245$	4.28353	−	3.59430i	0.273664	−	0.229632i
$246$	1.46483	+	1.71718i	0.0933941	+	0.109483i
$247$	21.3580	−	3.92059i	1.35897	−	0.249461i
$248$	−9.35150	−	15.3220i	−0.593821	−	0.972947i
$249$	−12.1891	−	14.5263i	−0.772450	−	0.920570i
$250$	−1.32495	+	0.494475i	−0.0837973	+	0.0312733i
$251$	−19.8700	−	3.50361i	−1.25418	−	0.221146i	−0.493198	−	0.869917i	$-0.664172\pi$
$251$	−19.8700	−	3.50361i	−1.25418	−	0.221146i	−0.760984	+	0.648771i	$0.775283\pi$
$252$	−0.100624	−	6.18963i	−0.00633872	−	0.389910i
$253$	−13.6992	+	4.98612i	−0.861264	+	0.313474i
$254$	1.49875	+	8.11366i	0.0940401	+	0.509096i
$255$	−3.87871	−	6.71813i	−0.242894	−	0.420705i
$256$	3.79632	+	15.5431i	0.237270	+	0.971444i
$257$	−11.4178	+	13.6072i	−0.712221	+	0.848793i	−0.993850	−	0.110731i	$-0.964681\pi$
$257$	−11.4178	+	13.6072i	−0.712221	+	0.848793i	0.281629	+	0.959523i	$0.409125\pi$
$258$	−7.08610	+	19.9725i	−0.441161	+	1.24343i
$259$	−6.96071	+	12.0563i	−0.432517	+	0.749142i
$260$	9.78266	−	1.88940i	0.606695	−	0.117176i
$261$	−10.5615	+	1.86227i	−0.653739	+	0.115272i
$262$	8.29845	−	4.88147i	0.512680	−	0.301578i
$263$	−8.68249	+	23.8549i	−0.535385	+	1.47096i	0.317194	+	0.948361i	$0.397259\pi$
$263$	−8.68249	+	23.8549i	−0.535385	+	1.47096i	−0.852579	+	0.522598i	$0.824963\pi$
$264$	−11.0216	+	32.7444i	−0.678331	+	2.01528i
$265$		−	7.33136i		−	0.450362i
$266$	−4.78648	−	5.53202i	−0.293478	−	0.339190i
$267$			20.9269i			1.28070i
$268$	2.52310	+	4.21056i	0.154123	+	0.257201i
$269$	−8.39652	+	23.0692i	−0.511945	+	1.40656i	0.367263	+	0.930117i	$0.380295\pi$
$269$	−8.39652	+	23.0692i	−0.511945	+	1.40656i	−0.879207	+	0.476439i	$0.841927\pi$
$270$	0.665198	+	1.13083i	0.0404827	+	0.0688202i
$271$	23.1199	−	4.07667i	1.40444	−	0.247640i	0.580471	−	0.814281i	$-0.302868\pi$
$271$	23.1199	−	4.07667i	1.40444	−	0.247640i	0.823965	+	0.566641i	$0.191757\pi$
$272$	13.0959	−	0.425908i	0.794053	−	0.0258245i
$273$	7.00010	−	12.1245i	0.423665	−	0.733810i
$274$	−20.0726	−	7.12162i	−1.21263	−	0.430233i
$275$	3.31551	−	3.95127i	0.199933	−	0.238270i
$276$	8.77033	+	10.1136i	0.527912	+	0.608764i
$277$	−6.76540	−	11.7180i	−0.406493	−	0.704067i	0.588001	−	0.808860i	$-0.299915\pi$
$277$	−6.76540	−	11.7180i	−0.406493	−	0.704067i	−0.994494	+	0.104793i	$0.966582\pi$
$278$	−0.712451	+	0.131604i	−0.0427300	+	0.00789307i
$279$	−15.5548	+	5.66148i	−0.931241	+	0.338944i
$280$	−2.21956	−	2.51786i	−0.132644	−	0.150471i
$281$	14.2216	+	2.50765i	0.848388	+	0.149594i	0.580908	−	0.813970i	$-0.302698\pi$
$281$	14.2216	+	2.50765i	0.848388	+	0.149594i	0.267481	+	0.963563i	$0.413809\pi$
$282$	−9.37315	−	25.1155i	−0.558163	−	1.49561i
$283$	10.4374	+	12.4388i	0.620437	+	0.739409i	0.981146	−	0.193270i	$-0.0619094\pi$
$283$	10.4374	+	12.4388i	0.620437	+	0.739409i	−0.360708	+	0.932679i	$0.617465\pi$
$284$	2.53821	−	15.9023i	0.150615	−	0.943628i
$285$	−9.72463	−	3.46245i	−0.576037	−	0.205098i
$286$	−27.6468	+	23.5840i	−1.63479	+	1.39455i
$287$	0.612650	−	0.514075i	0.0361636	−	0.0303449i
$288$	14.7424	−	0.599440i	0.868703	−	0.0353224i
$289$	−1.08874	+	6.17458i	−0.0640438	+	0.363210i
$290$	−3.70137	+	4.48465i	−0.217352	+	0.263347i
$291$	6.58690	+	18.0973i	0.386131	+	1.06089i
$292$	−4.75245	−	3.85790i	−0.278116	−	0.225766i
$293$	−2.43249	+	1.40440i	−0.142108	+	0.0820460i	−0.569368	−	0.822083i	$-0.692812\pi$
$293$	−2.43249	+	1.40440i	−0.142108	+	0.0820460i	0.427260	+	0.904129i	$0.359479\pi$
$294$	18.7267	−	0.152209i	1.09217	−	0.00887702i
$295$	−9.18314	−	7.70557i	−0.534663	−	0.448636i
$296$	−29.1314	−	15.8849i	−1.69323	−	0.923292i
$297$	−4.14403	−	2.39255i	−0.240461	−	0.138830i
$298$	−6.83241	+	12.0594i	−0.395791	+	0.698582i
$299$	2.44499	+	13.8663i	0.141398	+	0.801906i
$300$	−4.47646	−	1.54737i	−0.258449	−	0.0893374i
$301$	7.05627	+	2.56827i	0.406717	+	0.148033i
$302$	0.175725	−	1.04624i	0.0101118	−	0.0602044i
$303$	26.2771			1.50958
$304$	12.9032	−	11.7264i	0.740048	−	0.672554i
$305$	−1.90383			−0.109013
$306$	2.00138	−	11.9160i	0.114411	−	0.681190i
$307$	−7.98026	−	2.90458i	−0.455458	−	0.165773i	0.104096	−	0.994567i	$-0.466805\pi$
$307$	−7.98026	−	2.90458i	−0.455458	−	0.165773i	−0.559553	+	0.828794i	$0.689027\pi$
$308$	11.5703	+	3.99947i	0.659278	+	0.227891i
$309$	−4.49609	−	25.4986i	−0.255773	−	1.45056i
$310$	−4.42426	+	7.80893i	−0.251281	+	0.443517i
$311$	−10.8097	−	6.24099i	−0.612963	−	0.353894i	0.161161	−	0.986928i	$-0.448476\pi$
$311$	−10.8097	−	6.24099i	−0.612963	−	0.353894i	−0.774124	+	0.633034i	$0.781809\pi$
$312$	29.2963	+	15.9748i	1.65858	+	0.904395i
$313$	3.11362	+	2.61264i	0.175992	+	0.147675i	0.726529	−	0.687136i	$-0.241132\pi$
$313$	3.11362	+	2.61264i	0.175992	+	0.147675i	−0.550537	+	0.834811i	$0.685577\pi$
$314$	15.1344	−	0.123011i	0.854085	−	0.00694192i
$315$	−2.68054	+	1.54761i	−0.151031	+	0.0871980i
$316$	−7.11805	−	5.77821i	−0.400421	−	0.325050i
$317$	9.03786	+	24.8313i	0.507617	+	1.39466i	0.883689	+	0.468075i	$0.155052\pi$
$317$	9.03786	+	24.8313i	0.507617	+	1.39466i	−0.376072	+	0.926590i	$0.622726\pi$
$318$	15.6293	−	18.9367i	0.876448	−	1.06192i
$319$	3.68277	−	20.8860i	0.206195	−	1.16939i
$320$	5.87040	−	5.43493i	0.328165	−	0.303822i
$321$	−17.3476	+	14.5563i	−0.968247	+	0.812456i
$322$	3.60870	−	3.07839i	0.201105	−	0.171552i
$323$	−7.22574	−	12.3151i	−0.402051	−	0.685231i
$324$	−3.15921	+	19.7930i	−0.175511	+	1.09961i
$325$	−3.20219	−	3.81622i	−0.177626	−	0.211686i
$326$	−2.89429	−	7.75529i	−0.160300	−	0.429526i
$327$	−32.5546	−	5.74025i	−1.80027	−	0.317437i
$328$	1.26050	+	1.42991i	0.0695997	+	0.0789535i
$329$	−8.92594	+	3.24878i	−0.492103	+	0.179111i
$330$	16.9874	−	3.13790i	0.935124	−	0.172736i
$331$	−3.05296	−	5.28789i	−0.167806	−	0.290649i	0.769842	−	0.638234i	$-0.220335\pi$
$331$	−3.05296	−	5.28789i	−0.167806	−	0.290649i	−0.937648	+	0.347586i	$0.887002\pi$
$332$	−10.4921	−	12.0990i	−0.575828	−	0.664019i
$333$	−19.6681	+	23.4395i	−1.07780	+	1.28448i
$334$	−27.7142	−	9.83278i	−1.51645	−	0.538026i
$335$	1.22716	−	2.12551i	0.0670470	−	0.116129i
$336$	−0.365399	−	11.2353i	−0.0199342	−	0.612937i
$337$	19.4506	−	3.42967i	1.05954	−	0.186826i	0.383390	−	0.923587i	$-0.374757\pi$
$337$	19.4506	−	3.42967i	1.05954	−	0.186826i	0.676154	+	0.736760i	$0.263645\pi$
$338$	8.47363	+	14.4051i	0.460905	+	0.783534i
$339$	9.21410	−	25.3155i	0.500441	−	1.37495i
$340$	−3.36749	−	5.61967i	−0.182628	−	0.304770i
$341$		−	32.7348i		−	1.77269i
$342$	−8.24908	−	13.8010i	−0.446059	−	0.746273i
$343$		−	14.9426i		−	0.806825i
$344$	−5.70947	+	16.9624i	−0.307834	+	0.914554i
$345$	2.28925	−	6.28967i	0.123249	−	0.338625i
$346$	−17.8505	+	10.5003i	−0.959649	+	0.564502i
$347$	10.3885	−	1.83177i	0.557683	−	0.0983345i	0.112299	−	0.993674i	$-0.464178\pi$
$347$	10.3885	−	1.83177i	0.557683	−	0.0983345i	0.445383	+	0.895340i	$0.353067\pi$
$348$	−19.1211	+	3.69300i	−1.02500	+	0.197966i
$349$	5.60402	−	9.70645i	0.299976	−	0.519574i	−0.676154	−	0.736760i	$-0.736355\pi$
$349$	5.60402	−	9.70645i	0.299976	−	0.519574i	0.976130	+	0.217186i	$0.0696879\pi$
$350$	−0.561157	+	1.58165i	−0.0299951	+	0.0845427i
$351$	−2.97068	+	3.54032i	−0.158563	+	0.188968i
$352$	−8.85733	+	27.8013i	−0.472097	+	1.48181i
$353$	8.45591	+	14.6461i	0.450063	+	0.779531i	0.998389	−	0.0567329i	$-0.0180684\pi$
$353$	8.45591	+	14.6461i	0.450063	+	0.779531i	−0.548327	+	0.836264i	$0.684735\pi$
$354$	−7.29279	−	39.4803i	−0.387607	−	2.09836i
$355$	−7.56621	+	2.75388i	−0.401573	+	0.146161i
$356$	0.287277	+	17.6711i	0.0152256	+	0.936565i
$357$	−9.06587	−	1.59856i	−0.479817	−	0.0846047i
$358$	−27.7258	+	10.3473i	−1.46535	+	0.546873i
$359$	−16.1236	−	19.2154i	−0.850971	−	1.01415i	−0.999681	−	0.0252669i	$-0.991956\pi$
$359$	−16.1236	−	19.2154i	−0.850971	−	1.01415i	0.148710	−	0.988881i	$-0.452488\pi$
$360$	−3.84331	−	6.29708i	−0.202560	−	0.331885i
$361$	−17.9435	−	6.24738i	−0.944396	−	0.328809i
$362$	9.96842	+	11.6857i	0.523928	+	0.614186i
$363$	−28.3097	+	23.7546i	−1.48587	+	1.24680i
$364$	5.74458	−	10.3343i	0.301098	−	0.541664i
$365$	−0.531468	+	3.01411i	−0.0278183	+	0.157766i
$366$	−4.91755	−	4.05866i	−0.257044	−	0.212150i
$367$	−2.43273	−	6.68388i	−0.126988	−	0.348896i	0.859864	−	0.510523i	$-0.170548\pi$
$367$	−2.43273	−	6.68388i	−0.126988	−	0.348896i	−0.986852	+	0.161627i	$0.948326\pi$
$368$	7.54468	+	8.41969i	0.393294	+	0.438907i
$369$	1.52230	−	0.878900i	0.0792477	−	0.0457537i
$370$	0.134841	+	16.5899i	0.00701005	+	0.862467i
$371$	−6.66468	−	5.59233i	−0.346013	−	0.290339i
$372$	−28.0752	+	10.7385i	−1.45563	+	0.556764i
$373$	4.33304	+	2.50168i	0.224356	+	0.129532i	0.607966	−	0.793963i	$-0.291986\pi$
$373$	4.33304	+	2.50168i	0.224356	+	0.129532i	−0.383610	+	0.923495i	$0.625319\pi$
$374$	20.7898	+	11.7787i	1.07502	+	0.609065i
$375$	0.411230	+	2.33220i	0.0212358	+	0.120434i
$376$	−8.25965	−	21.0793i	−0.425959	−	1.08708i
$377$	−19.2481	−	7.00572i	−0.991326	−	0.360813i
$378$	1.53541	+	0.257885i	0.0789729	+	0.0132642i
$379$	−4.52281			−0.232321			−0.116161	−	0.993230i	$-0.537059\pi$
$379$	−4.52281			−0.232321			−0.116161	+	0.993230i	$0.537059\pi$
$380$	−8.25920	−	2.79027i	−0.423688	−	0.143138i
$381$	13.8166			0.707847
$382$	14.2695	+	2.39667i	0.730089	+	0.122625i
$383$	10.7915	+	3.92777i	0.551418	+	0.200700i	0.602676	−	0.797986i	$-0.294101\pi$
$383$	10.7915	+	3.92777i	0.551418	+	0.200700i	−0.0512585	+	0.998685i	$0.516323\pi$
$384$	26.7495	−	1.52353i	1.36506	−	0.0777475i
$385$	−1.06290	−	6.02802i	−0.0541705	−	0.307216i
$386$	−20.7587	−	11.7611i	−1.05659	−	0.598626i
$387$	14.2932	+	8.25221i	0.726566	+	0.419483i
$388$	5.81054	+	15.1913i	0.294985	+	0.771223i
$389$	20.9469	+	17.5766i	1.06205	+	0.891167i	0.994309	−	0.106536i	$-0.0339758\pi$
$389$	20.9469	+	17.5766i	1.06205	+	0.891167i	0.0677428	+	0.997703i	$0.478420\pi$
$390$	−0.135604	−	16.6838i	−0.00686658	−	0.844816i
$391$	8.01793	−	4.62915i	0.405484	−	0.234106i
$392$	15.8111	−	0.385602i	0.798583	−	0.0194759i
$393$	−5.51410	−	15.1499i	−0.278149	−	0.764209i
$394$	−22.7866	−	18.8068i	−1.14797	−	0.947472i
$395$	−0.796013	+	4.51442i	−0.0400518	+	0.227145i
$396$	23.5177	+	13.0729i	1.18181	+	0.656938i
$397$	21.1726	−	17.7659i	1.06262	−	0.891645i	0.0682570	−	0.997668i	$-0.478256\pi$
$397$	21.1726	−	17.7659i	1.06262	−	0.891645i	0.994364	+	0.106023i	$0.0338118\pi$
$398$	−6.59522	−	7.73138i	−0.330589	−	0.387539i
$399$	−10.5655	+	6.19917i	−0.528936	+	0.310347i
$400$	−3.80125	−	1.24518i	−0.190063	−	0.0622589i
$401$	19.4258	+	23.1507i	0.970076	+	1.15609i	0.987718	+	0.156248i	$0.0499398\pi$
$401$	19.4258	+	23.1507i	0.970076	+	1.15609i	−0.0176414	+	0.999844i	$0.505616\pi$
$402$	7.70097	−	2.87402i	0.384090	−	0.143343i
$403$	−31.1357	−	5.49006i	−1.55098	−	0.273479i
$404$	22.1889	−	0.360722i	1.10394	−	0.0179466i
$405$	9.41737	−	3.42764i	0.467953	−	0.170321i
$406$	1.25344	+	6.78565i	0.0622073	+	0.336766i
$407$	−30.2549	−	52.4030i	−1.49968	−	2.59752i
$408$	3.28212	−	21.6944i	0.162489	−	1.07403i
$409$	−22.1851	+	26.4392i	−1.09698	+	1.30733i	−0.149063	+	0.988828i	$0.547626\pi$
$409$	−22.1851	+	26.4392i	−1.09698	+	1.30733i	−0.947921	+	0.318507i	$0.896819\pi$
$410$	0.318685	−	0.898230i	0.0157388	−	0.0443604i
$411$	−17.8328	+	30.8873i	−0.879626	+	1.52356i
$412$	−4.14662	−	21.4698i	−0.204289	−	1.05774i
$413$	−14.0097	+	2.47029i	−0.689373	+	0.121555i
$414$	8.98603	−	5.28593i	0.441639	−	0.259789i
$415$	−2.73867	+	7.52444i	−0.134436	+	0.369360i
$416$	24.9577	+	13.0873i	1.22365	+	0.641657i
$417$			1.21322i			0.0594117i
$418$	31.2259	−	5.99475i	1.52731	−	0.293213i
$419$		−	14.4160i		−	0.704267i	−0.935950	−	0.352134i	$-0.885456\pi$
$419$		−	14.4160i		−	0.704267i	0.935950	−	0.352134i	$-0.114544\pi$
$420$	−4.82128	+	2.88906i	−0.235254	+	0.140972i
$421$	7.74843	−	21.2886i	0.377635	−	1.03754i	−0.594698	−	0.803949i	$-0.702729\pi$
$421$	7.74843	−	21.2886i	0.377635	−	1.03754i	0.972334	−	0.233596i	$-0.0750493\pi$
$422$	−10.6861	−	18.1663i	−0.520194	−	0.884324i
$423$	−20.5603	+	3.62534i	−0.999678	+	0.176270i
$424$	12.9377	−	16.2051i	0.628312	−	0.786990i
$425$	−1.63785	+	2.83683i	−0.0794472	+	0.137607i
$426$	−25.4142	−	9.01677i	−1.23132	−	0.436864i
$427$	−1.45223	+	1.73070i	−0.0702784	+	0.0837546i
$428$	−14.4488	+	12.5298i	−0.698409	+	0.605651i
$429$	30.4261	+	52.6995i	1.46899	+	2.54436i
$430$	8.79991	−	1.62552i	0.424369	−	0.0783893i
$431$	−1.93042	+	0.702615i	−0.0929851	+	0.0338438i	−0.388094	−	0.921620i	$-0.626866\pi$
$431$	−1.93042	+	0.702615i	−0.0929851	+	0.0338438i	0.295109	+	0.955464i	$0.404644\pi$
$432$	−0.525247	+	3.67345i	−0.0252710	+	0.176739i
$433$	29.6603	+	5.22991i	1.42538	+	0.251334i	0.832532	−	0.553978i	$-0.186891\pi$
$433$	29.6603	+	5.22991i	1.42538	+	0.251334i	0.592852	+	0.805311i	$0.298002\pi$
$434$	3.72402	+	9.97855i	0.178759	+	0.478986i
$435$	6.25898	+	7.45916i	0.300095	+	0.357639i
$436$	−27.5685	−	4.40028i	−1.32029	−	0.210735i
$437$	4.13236	−	11.6061i	0.197677	−	0.555196i
$438$	−7.79837	+	6.65236i	−0.372621	+	0.317862i
$439$	−10.8392	+	9.09516i	−0.517326	+	0.434088i	−0.863699	−	0.504009i	$-0.831858\pi$
$439$	−10.8392	+	9.09516i	−0.517326	+	0.434088i	0.346372	+	0.938097i	$0.387413\pi$
$440$	14.3014	−	2.88290i	0.681792	−	0.137437i
$441$	2.53261	−	14.3632i	0.120601	−	0.683960i
$442$	14.6901	−	17.7987i	0.698735	−	0.846600i
$443$	4.20935	+	11.5651i	0.199992	+	0.549474i	0.998629	−	0.0523388i	$-0.0166676\pi$
$443$	4.20935	+	11.5651i	0.199992	+	0.549474i	−0.798637	+	0.601813i	$0.794445\pi$
$444$	−35.0187	+	43.1388i	−1.66192	+	2.04728i
$445$	7.65281	−	4.41835i	0.362778	−	0.209450i
$446$	16.8532	−	0.136981i	0.798021	−	0.00648624i
$447$	17.7799	+	14.9191i	0.840960	+	0.705649i
$448$	−0.462785	−	9.48231i	−0.0218645	−	0.447997i
$449$	−21.7030	−	12.5303i	−1.02423	−	0.591340i	−0.108904	−	0.994052i	$-0.534734\pi$
$449$	−21.7030	−	12.5303i	−1.02423	−	0.591340i	−0.915326	+	0.402713i	$0.868067\pi$
$450$	−1.81830	+	3.20934i	−0.0857153	+	0.151290i
$451$	0.603630	+	3.42336i	0.0284238	+	0.161200i
$452$	7.43305	−	21.5034i	0.349621	−	1.01144i
$453$	−1.66939	−	0.607608i	−0.0784348	−	0.0285479i
$454$	−2.78162	+	16.5614i	−0.130548	+	0.777264i
$455$	−5.91181			−0.277150
$456$	−15.3849	−	24.8145i	−0.720465	−	1.16205i
$457$	34.9036			1.63272			0.816360	−	0.577544i	$-0.195989\pi$
$457$	34.9036			1.63272			0.816360	+	0.577544i	$0.195989\pi$
$458$	0.297798	−	1.77304i	0.0139152	−	0.0828489i
$459$	2.85561	+	1.03936i	0.133288	+	0.0485130i
$460$	1.84675	−	5.34255i	0.0861051	−	0.249098i
$461$	−1.50637	−	8.54302i	−0.0701584	−	0.397888i	−0.999583	−	0.0288760i	$-0.990807\pi$
$461$	−1.50637	−	8.54302i	−0.0701584	−	0.397888i	0.929425	−	0.369012i	$-0.120304\pi$
$462$	10.1053	−	17.8362i	0.470143	−	0.829814i
$463$	11.9003	+	6.87065i	0.553055	+	0.319306i	0.750353	−	0.661037i	$-0.229883\pi$
$463$	11.9003	+	6.87065i	0.553055	+	0.319306i	−0.197298	+	0.980343i	$0.563217\pi$
$464$	−16.0956	+	3.38093i	−0.747217	+	0.156956i
$465$	11.5132	+	9.66070i	0.533911	+	0.448004i
$466$	9.28139	−	0.0754382i	0.429952	−	0.00349461i
$467$	3.42235	−	1.97589i	0.158367	−	0.0914334i	−0.418722	−	0.908114i	$-0.637522\pi$
$467$	3.42235	−	1.97589i	0.158367	−	0.0914334i	0.577089	+	0.816681i	$0.304188\pi$
$468$	16.3785	−	20.1763i	0.757097	−	0.932650i
$469$	−0.996148	−	2.73690i	−0.0459979	−	0.126378i
$470$	−7.20557	+	8.73040i	−0.332368	+	0.402703i
$471$	4.40098	−	24.9592i	0.202786	−	1.15006i
$472$	−6.70015	−	33.2379i	−0.308399	−	1.52990i
$473$	−25.0026	+	20.9797i	−1.14962	+	0.964647i
$474$	−11.6801	+	9.96366i	−0.536485	+	0.457646i
$475$	0.786995	+	4.28726i	0.0361098	+	0.196713i
$476$	−7.67735	−	1.22540i	−0.351891	−	0.0561662i
$477$	−12.2915	−	14.6484i	−0.562787	−	0.670703i
$478$	−9.12325	−	24.4459i	−0.417288	−	1.11813i
$479$	17.7651	+	3.13247i	0.811709	+	0.143126i	0.564071	−	0.825726i	$-0.309234\pi$
$479$	17.7651	+	3.13247i	0.811709	+	0.143126i	0.247638	+	0.968853i	$0.420346\pi$
$480$	−7.16403	−	11.3199i	−0.326992	−	0.516682i
$481$	−54.9172	+	19.9882i	−2.50401	+	0.911384i
$482$	40.9973	−	7.57301i	1.86738	−	0.344941i
$483$	−3.97149	−	6.87881i	−0.180709	−	0.312997i
$484$	−23.5792	+	20.4475i	−1.07178	+	0.929433i
$485$	5.22736	−	6.22973i	0.237362	−	0.282877i
$486$	27.9227	+	9.90676i	1.26660	+	0.449380i
$487$	2.13381	−	3.69586i	0.0966920	−	0.167475i	−0.813622	−	0.581395i	$-0.802507\pi$
$487$	2.13381	−	3.69586i	0.0966920	−	0.167475i	0.910314	+	0.413919i	$0.135840\pi$
$488$	−4.20819	−	3.35971i	−0.190496	−	0.152087i
$489$	−13.6510	+	2.40704i	−0.617319	+	0.108850i
$490$	−4.00949	−	6.81610i	−0.181130	−	0.307920i
$491$	5.13605	−	14.1112i	0.231787	−	0.636828i	−0.768208	−	0.640201i	$-0.778851\pi$
$491$	5.13605	−	14.1112i	0.231787	−	0.636828i	0.999994	+	0.00337223i	$0.00107341\pi$
$492$	2.73804	−	1.64072i	0.123440	−	0.0739694i
$493$			13.4687i			0.606599i
$494$	−0.464904	−	30.7059i	−0.0209170	−	1.38152i
$495$		−	13.4535i		−	0.604688i
$496$	−23.5598	+	9.45319i	−1.05787	+	0.424461i
$497$	−3.26802	+	8.97882i	−0.146591	+	0.402755i
$498$	−23.1148	+	13.5970i	−1.03580	+	0.609298i
$499$	8.78798	−	1.54956i	0.393404	−	0.0693677i	0.0265529	−	0.999647i	$-0.491547\pi$
$499$	8.78798	−	1.54956i	0.393404	−	0.0693677i	0.366851	+	0.930280i	$0.380436\pi$
$500$	0.379266	+	1.96371i	0.0169613	+	0.0878198i
$501$	−24.6216	+	42.6459i	−1.10001	+	1.90528i
$502$	−9.54091	+	26.8915i	−0.425832	+	1.20023i
$503$	10.9770	−	13.0818i	0.489439	−	0.583290i	−0.463636	−	0.886026i	$-0.653455\pi$
$503$	10.9770	−	13.0818i	0.489439	−	0.583290i	0.953075	+	0.302736i	$0.0978999\pi$
$504$	−8.65611	−	1.30957i	−0.385574	−	0.0583328i
$505$	−5.54795	−	9.60933i	−0.246880	−	0.427610i
$506$	3.74501	+	20.2740i	0.166486	+	0.901290i
$507$	26.2983	−	9.57180i	1.16795	−	0.425099i
$508$	11.6670	−	0.189670i	0.517641	−	0.00841523i
$509$	7.69415	+	1.35669i	0.341037	+	0.0601341i	0.341544	−	0.939866i	$-0.389050\pi$
$509$	7.69415	+	1.35669i	0.341037	+	0.0601341i	−0.000506669		1.00000i	$0.500161\pi$
$510$	−10.2782	+	3.83585i	−0.455127	+	0.169854i
$511$	2.33461	+	2.78229i	0.103277	+	0.123081i
$512$	22.5669	−	1.65371i	0.997326	−	0.0730843i
$513$	3.79011	−	1.40966i	0.167337	−	0.0622380i
$514$	16.3030	+	19.1116i	0.719097	+	0.842976i
$515$	−8.37537	+	7.02777i	−0.369063	+	0.309681i
$516$	26.1953	+	14.5613i	1.15318	+	0.641027i
$517$	7.16936	−	40.6595i	0.315308	−	1.78820i
$518$	15.1841	+	12.5321i	0.667152	+	0.550629i
$519$	11.8612	+	32.5883i	0.520648	+	1.43047i
$520$	−0.343536	−	14.0863i	−0.0150650	−	0.617723i
$521$	29.2824	−	16.9062i	1.28289	−	0.740675i	0.305512	−	0.952188i	$-0.401172\pi$
$521$	29.2824	−	16.9062i	1.28289	−	0.740675i	0.977375	+	0.211513i	$0.0678391\pi$
$522$	0.123269	+	15.1661i	0.00539532	+	0.663802i
$523$	−22.4660	−	18.8512i	−0.982370	−	0.824306i	0.00207539	−	0.999998i	$-0.499339\pi$
$523$	−22.4660	−	18.8512i	−0.982370	−	0.824306i	−0.984445	+	0.175692i	$0.943784\pi$
$524$	−4.86419	−	12.7171i	−0.212493	−	0.555551i
$525$	2.43380	+	1.40516i	0.106220	+	0.0613261i
$526$	31.2361	+	17.6972i	1.36196	+	0.771636i
$527$	3.60995	+	20.4730i	0.157252	+	0.891819i
$528$	43.0861	+	23.0418i	1.87508	+	1.00277i
$529$	−14.1064	−	5.13429i	−0.613320	−	0.223230i
$530$	−10.2249	−	1.71736i	−0.444141	−	0.0745971i
$531$	−31.2672			−1.35688
$532$	−8.83661	+	5.37974i	−0.383116	+	0.233241i
$533$	3.35736			0.145423
$534$	29.1863	+	4.90208i	1.26301	+	0.212134i
$535$	8.98579	+	3.27056i	0.388490	+	0.141399i
$536$	6.46340	−	2.53260i	0.279176	−	0.109391i
$537$	8.60536	+	48.8034i	0.371348	+	2.10602i
$538$	30.2073	+	17.1144i	1.30233	+	0.737853i
$539$	24.9782	+	14.4212i	1.07589	+	0.621163i
$540$	1.73297	−	0.662843i	0.0745750	−	0.0285242i
$541$	−16.2908	−	13.6696i	−0.700396	−	0.587702i	0.221491	−	0.975163i	$-0.428908\pi$
$541$	−16.2908	−	13.6696i	−0.700396	−	0.587702i	−0.921886	+	0.387461i	$0.873352\pi$
$542$	−0.269845	−	33.1998i	−0.0115908	−	1.42605i
$543$	22.2749	−	12.8604i	0.955909	−	0.551894i
$544$	2.47367	−	18.3643i	0.106058	−	0.787362i
$545$	4.77417	+	13.1169i	0.204503	+	0.561868i
$546$	−15.2701	−	12.6030i	−0.653498	−	0.539360i
$547$	−4.67526	+	26.5147i	−0.199900	+	1.13369i	0.705366	+	0.708843i	$0.250783\pi$
$547$	−4.67526	+	26.5147i	−0.199900	+	1.13369i	−0.905266	+	0.424845i	$0.860328\pi$
$548$	−14.6343	+	26.3266i	−0.625148	+	1.12462i
$549$	−3.80394	+	3.19188i	−0.162348	+	0.136226i
$550$	−4.73410	−	5.54964i	−0.201863	−	0.236638i
$551$	11.6163	+	13.6483i	0.494873	+	0.581438i
$552$	16.1596	−	9.86271i	0.687798	−	0.419785i
$553$	3.49670	+	4.16720i	0.148695	+	0.177207i
$554$	−17.9276	+	6.69063i	−0.761672	+	0.284258i
$555$	27.3595	+	4.82422i	1.16135	+	0.204777i
$556$	0.0166547	+	1.02447i	0.000706315	+	0.0434471i
$557$	31.4898	−	11.4613i	1.33426	−	0.485633i	0.426263	−	0.904599i	$-0.359830\pi$
$557$	31.4898	−	11.4613i	1.33426	−	0.485633i	0.908002	+	0.418967i	$0.137608\pi$
$558$	4.25227	+	23.0201i	0.180013	+	0.974519i
$559$	15.7615	+	27.2998i	0.666642	+	1.15466i
$560$	−4.03153	+	2.50577i	−0.170363	+	0.105888i
$561$	25.7198	−	30.6517i	1.08589	−	1.29411i
$562$	6.82874	−	19.2471i	0.288053	−	0.811891i
$563$	3.11341	−	5.39259i	0.131215	−	0.227271i	−0.792930	−	0.609312i	$-0.791446\pi$
$563$	3.11341	−	5.39259i	0.131215	−	0.227271i	0.924145	+	0.382042i	$0.124779\pi$
$564$	−37.2237	+	7.18928i	−1.56740	+	0.302723i
$565$	−11.2031	+	1.97541i	−0.471318	+	0.0831061i
$566$	19.7930	−	11.6430i	0.831963	−	0.489393i
$567$	4.06758	−	11.1756i	0.170822	−	0.469330i
$568$	−21.5840	−	7.26506i	−0.905646	−	0.304835i
$569$		−	0.566886i		−	0.0237651i	−0.999929	−	0.0118826i	$-0.996218\pi$
$569$		−	0.566886i		−	0.0237651i	0.999929	−	0.0118826i	$-0.00378242\pi$
$570$	−7.10698	+	12.7517i	−0.297679	+	0.534108i
$571$		−	0.673107i		−	0.0281686i	−0.999901	−	0.0140843i	$-0.995517\pi$
$571$		−	0.673107i		−	0.0281686i	0.999901	−	0.0140843i	$-0.00448333\pi$
$572$	26.4158	+	44.0829i	1.10450	+	1.84320i
$573$	8.28703	−	22.7684i	0.346196	−	0.951165i
$574$	−0.573457	−	0.974871i	−0.0239356	−	0.0406903i
$575$	−2.78343	+	0.490793i	−0.116077	+	0.0204675i
$576$	2.61735	−	20.7013i	0.109056	−	0.862554i
$577$	−19.8751	+	34.4247i	−0.827411	+	1.43312i	0.0726516	+	0.997357i	$0.476854\pi$
$577$	−19.8751	+	34.4247i	−0.827411	+	1.43312i	−0.900063	+	0.435761i	$0.856479\pi$
$578$	8.35651	+	2.96483i	0.347585	+	0.123321i
$579$	−25.6813	+	30.6058i	−1.06728	+	1.27194i
$580$	5.38760	+	6.21274i	0.223708	+	0.257970i
$581$	4.75115	+	8.22924i	0.197111	+	0.341406i
$582$	26.7829	−	4.94734i	1.11019	−	0.205074i
$583$	35.5347	−	12.9336i	1.47170	−	0.535654i
$584$	−6.49378	+	5.72444i	−0.268714	+	0.236879i
$585$	−12.7962	−	2.25632i	−0.529059	−	0.0932874i
$586$	1.38888	+	3.72152i	0.0573741	+	0.153735i
$587$	12.0297	+	14.3365i	0.496520	+	0.591730i	0.954863	−	0.297045i	$-0.0960013\pi$
$587$	12.0297	+	14.3365i	0.496520	+	0.591730i	−0.458343	+	0.888775i	$0.651557\pi$
$588$	4.17442	−	26.1534i	0.172150	−	1.07855i
$589$	21.3155	+	17.6326i	0.878289	+	0.726539i
$590$	−12.8979	+	11.0025i	−0.530999	+	0.452966i
$591$	−37.9002	+	31.8021i	−1.55901	+	1.30816i
$592$	−28.9783	+	36.9080i	−1.19100	+	1.51691i
$593$	−3.70332	+	21.0025i	−0.152077	+	0.862471i	0.809333	+	0.587350i	$0.199829\pi$
$593$	−3.70332	+	21.0025i	−0.152077	+	0.862471i	−0.961410	+	0.275121i	$0.911282\pi$
$594$	−4.30757	+	5.21913i	−0.176742	+	0.214144i
$595$	1.32952	+	3.65283i	0.0545051	+	0.149752i
$596$	15.2185	+	12.3539i	0.623374	+	0.506036i
$597$	−14.7374	+	8.50862i	−0.603160	+	0.348234i
$598$	19.9117	−	0.161840i	0.814250	−	0.00661815i
$599$	19.8220	+	16.6326i	0.809904	+	0.679590i	0.950585	−	0.310465i	$-0.100485\pi$
$599$	19.8220	+	16.6326i	0.809904	+	0.679590i	−0.140681	+	0.990055i	$0.544929\pi$
$600$	−3.20668	+	5.88075i	−0.130912	+	0.240081i
$601$	−26.1382	−	15.0909i	−1.06620	−	0.615571i	−0.139060	−	0.990284i	$-0.544408\pi$
$601$	−26.1382	−	15.0909i	−1.06620	−	0.615571i	−0.927141	+	0.374713i	$0.877741\pi$
$602$	5.23483	−	9.23962i	0.213356	−	0.376579i
$603$	−1.11161	−	6.30427i	−0.0452683	−	0.256730i
$604$	−1.41801	−	0.490160i	−0.0576979	−	0.0199443i
$605$	14.6640	+	5.33726i	0.596177	+	0.216991i
$606$	6.15534	−	36.6480i	0.250044	−	1.48872i
$607$	0.606408			0.0246134			0.0123067	−	0.999924i	$-0.496083\pi$
$607$	0.606408			0.0246134			0.0123067	+	0.999924i	$0.496083\pi$
$608$	−13.3320	−	20.7427i	−0.540683	−	0.841226i
$609$	11.5552			0.468239
$610$	−0.445968	+	2.65523i	−0.0180567	+	0.107507i
$611$	−37.4708	−	13.6383i	−1.51591	−	0.551745i
$612$	−16.1501	−	5.58257i	−0.652829	−	0.225662i
$613$	2.05830	+	11.6732i	0.0831341	+	0.471477i	0.997744	+	0.0671386i	$0.0213870\pi$
$613$	2.05830	+	11.6732i	0.0831341	+	0.471477i	−0.914610	+	0.404338i	$0.867502\pi$
$614$	−5.92031	+	10.4495i	−0.238924	+	0.421708i
$615$	−1.38217	−	0.797999i	−0.0557347	−	0.0321784i
$616$	8.28829	−	15.1999i	0.333945	−	0.612423i
$617$	−25.7631	−	21.6178i	−1.03718	−	0.870300i	−0.0454950	−	0.998965i	$-0.514487\pi$
$617$	−25.7631	−	21.6178i	−1.03718	−	0.870300i	−0.991688	+	0.128665i	$0.958931\pi$
$618$	−36.6155	+	0.297607i	−1.47289	+	0.0119715i
$619$	−22.4273	+	12.9484i	−0.901428	+	0.520440i	−0.877663	−	0.479278i	$-0.840899\pi$
$619$	−22.4273	+	12.9484i	−0.901428	+	0.520440i	−0.0237649	+	0.999718i	$0.507565\pi$
$620$	9.85457	+	7.99964i	0.395769	+	0.321273i
$621$	0.896787	+	2.46390i	0.0359868	+	0.0988729i
$622$	−11.2363	+	13.6141i	−0.450536	+	0.545877i
$623$	1.82096	−	10.3272i	0.0729554	−	0.413750i
$624$	29.1423	−	37.1168i	1.16663	−	1.48586i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	4.37314	−	3.73049i	0.174786	−	0.149100i
$627$	−0.373329	−	53.2430i	−0.0149093	−	2.12632i
$628$	3.37364	−	21.1365i	0.134623	−	0.843437i
$629$	24.7010	+	29.4374i	0.984891	+	1.17375i
$630$	1.53051	+	4.10102i	0.0609769	+	0.163388i
$631$	−15.7789	−	2.78224i	−0.628148	−	0.110759i	−0.149493	−	0.988763i	$-0.547764\pi$
$631$	−15.7789	−	2.78224i	−0.628148	−	0.110759i	−0.478654	+	0.878003i	$0.658875\pi$
$632$	−9.72614	+	8.57385i	−0.386885	+	0.341050i
$633$	−33.1649	+	12.0710i	−1.31819	+	0.479781i
$634$	36.7488	−	6.78822i	1.45948	−	0.269595i
$635$	−2.91714	−	5.05264i	−0.115763	−	0.200508i
$636$	−22.7495	−	26.2337i	−0.902077	−	1.04024i
$637$	17.9058	−	21.3393i	0.709455	−	0.845495i
$638$	−28.2666	−	10.0288i	−1.11909	−	0.397043i
$639$	−10.5006	+	18.1876i	−0.415397	+	0.719489i
$640$	−6.20485	−	9.46044i	−0.245268	−	0.373957i
$641$	−26.9648	+	4.75462i	−1.06505	+	0.187796i	−0.678594	−	0.734513i	$-0.737411\pi$
$641$	−26.9648	+	4.75462i	−1.06505	+	0.187796i	−0.386452	+	0.922310i	$0.626299\pi$
$642$	16.2378	+	27.6041i	0.640854	+	1.08945i
$643$	12.3385	−	33.8998i	0.486584	−	1.33688i	−0.417171	−	0.908828i	$-0.636978\pi$
$643$	12.3385	−	33.8998i	0.486584	−	1.33688i	0.903755	−	0.428050i	$-0.140799\pi$
$644$	−3.44803	−	5.75409i	−0.135871	−	0.226743i
$645$		−	14.9852i		−	0.590042i
$646$	−18.8682	+	7.19279i	−0.742361	+	0.282996i
$647$			22.7723i			0.895273i	0.894216	+	0.447637i	$0.147734\pi$
$647$			22.7723i			0.895273i	−0.894216	+	0.447637i	$0.852266\pi$
$648$	26.8648	+	9.04254i	1.05535	+	0.355224i
$649$	21.1481	−	58.1039i	0.830136	−	2.28078i
$650$	−6.07251	+	3.57208i	−0.238183	+	0.140109i
$651$	17.5644	−	3.09708i	0.688403	−	0.121384i
$652$	−11.4941	+	2.21995i	−0.450144	+	0.0869398i
$653$	−6.32472	+	10.9547i	−0.247505	+	0.428692i	−0.962833	−	0.270097i	$-0.912944\pi$
$653$	−6.32472	+	10.9547i	−0.247505	+	0.428692i	0.715328	+	0.698789i	$0.246277\pi$
$654$	−15.6316	+	44.0585i	−0.611246	+	1.72282i
$655$	−4.37599	+	5.21510i	−0.170984	+	0.203771i
$656$	2.28953	−	1.42304i	0.0893913	−	0.0555605i
$657$	3.99143	+	6.91336i	0.155720	+	0.269716i
$658$	2.44012	+	13.2098i	0.0951256	+	0.514973i
$659$	38.7404	−	14.1003i	1.50911	−	0.549271i	0.550709	−	0.834697i	$-0.314357\pi$
$659$	38.7404	−	14.1003i	1.50911	−	0.549271i	0.958401	+	0.285426i	$0.0921351\pi$
$660$	−0.397106	−	24.4270i	−0.0154573	−	0.950818i
$661$	−18.1536	−	3.20096i	−0.706091	−	0.124503i	−0.190939	−	0.981602i	$-0.561153\pi$
$661$	−18.1536	−	3.20096i	−0.706091	−	0.124503i	−0.515152	+	0.857099i	$0.672265\pi$
$662$	−8.09005	+	3.01923i	−0.314429	+	0.117346i
$663$	−24.8407	−	29.6040i	−0.964734	−	1.14973i
$664$	−19.3320	+	11.7989i	−0.750226	+	0.457887i
$665$	4.49772	+	2.55488i	0.174414	+	0.0990739i
$666$	28.0833	+	32.9213i	1.08821	+	1.27567i
$667$	−8.90233	+	7.46994i	−0.344700	+	0.289237i
$668$	−20.2056	+	36.3490i	−0.781776	+	1.40639i
$669$	4.90078	−	27.7937i	0.189475	−	1.07457i
$670$	−2.67694	−	2.20939i	−0.103419	−	0.0853562i
$671$	−3.35863	−	9.22776i	−0.129658	−	0.356234i
$672$	−15.7552	−	2.12223i	−0.607772	−	0.0818670i
$673$	35.7356	−	20.6319i	1.37751	−	0.795303i	0.385647	−	0.922647i	$-0.373978\pi$
$673$	35.7356	−	20.6319i	1.37751	−	0.795303i	0.991859	+	0.127344i	$0.0406451\pi$
$674$	−0.227019	−	27.9308i	−0.00874444	−	1.07585i
$675$	−0.710662	−	0.596316i	−0.0273534	−	0.0229522i
$676$	22.0754	−	8.44363i	0.849054	−	0.324755i
$677$	−39.6398	−	22.8861i	−1.52348	−	0.879582i	−0.999614	−	0.0277825i	$-0.991155\pi$
$677$	−39.6398	−	22.8861i	−1.52348	−	0.879582i	−0.523867	−	0.851800i	$-0.675511\pi$
$678$	−33.1486	−	18.7808i	−1.27307	−	0.721273i
$679$	−1.67581	−	9.50401i	−0.0643118	−	0.364731i
$680$	−8.62646	+	3.38016i	−0.330810	+	0.129623i
$681$	26.4255	+	9.61808i	1.01263	+	0.368566i
$682$	−45.6545	−	7.66806i	−1.74820	−	0.293625i
$683$	30.0676			1.15051			0.575253	−	0.817976i	$-0.304904\pi$
$683$	30.0676			1.15051			0.575253	+	0.817976i	$0.304904\pi$
$684$	−21.1803	+	8.27196i	−0.809849	+	0.316286i
$685$	15.0603			0.575426
$686$	−20.8401	−	3.50028i	−0.795680	−	0.133641i
$687$	−2.82908	−	1.02970i	−0.107936	−	0.0392856i
$688$	22.3197	+	11.9363i	0.850932	+	0.455067i
$689$	−6.34212	−	35.9679i	−0.241615	−	1.37027i
$690$	−8.23582	−	4.66612i	−0.313532	−	0.177636i
$691$	−4.54278	−	2.62278i	−0.172816	−	0.0997751i	0.411097	−	0.911592i	$-0.365146\pi$
$691$	−4.54278	−	2.62278i	−0.172816	−	0.0997751i	−0.583913	+	0.811816i	$0.698479\pi$
$692$	10.4632	+	27.3554i	0.397750	+	1.03990i
$693$	−12.2301	−	10.2622i	−0.464581	−	0.389830i
$694$	−0.121249	−	14.9177i	−0.00460257	−	0.566267i
$695$	0.443666	−	0.256151i	0.0168292	−	0.00971636i
$696$	0.671472	+	27.5329i	0.0254521	+	1.04363i
$697$	−0.755046	−	2.07447i	−0.0285994	−	0.0785762i
$698$	−12.2246	−	10.0895i	−0.462709	−	0.381894i
$699$	2.69896	−	15.3066i	0.102084	−	0.578948i
$700$	2.07444	+	1.15313i	0.0784065	+	0.0435843i
$701$	12.5671	−	10.5450i	0.474652	−	0.398280i	−0.373836	−	0.927495i	$-0.621958\pi$
$701$	12.5671	−	10.5450i	0.474652	−	0.398280i	0.848488	+	0.529215i	$0.177513\pi$
$702$	4.24173	+	4.97246i	0.160094	+	0.187673i
$703$	50.4193	+	8.52622i	1.90160	+	0.321572i
$704$	36.6990	+	18.8655i	1.38315	+	0.711021i
$705$	12.1845	+	14.5210i	0.458896	+	0.546891i
$706$	22.4073	−	8.36246i	0.843311	−	0.314725i
$707$	−12.9674	−	2.28651i	−0.487691	−	0.0859931i
$708$	−56.7707	+	0.922914i	−2.13357	+	0.0346852i
$709$	34.1447	−	12.4277i	1.28233	−	0.466731i	0.391129	−	0.920336i	$-0.372085\pi$
$709$	34.1447	−	12.4277i	1.28233	−	0.466731i	0.891203	+	0.453605i	$0.149862\pi$
$710$	2.06840	+	11.1975i	0.0776258	+	0.420236i
$711$	5.97821	+	10.3546i	0.224200	+	0.388327i
$712$	24.7128	+	3.73875i	0.926150	+	0.140116i
$713$	−11.5298	+	13.7407i	−0.431795	+	0.514594i
$714$	−4.35314	+	12.2695i	−0.162912	+	0.459175i
$715$	12.8479	−	22.2532i	0.480484	−	0.832223i
$716$	7.93649	+	41.0924i	0.296601	+	1.53570i
$717$	−43.0300	+	7.58735i	−1.60699	+	0.283355i
$718$	−30.5762	+	17.9861i	−1.14109	+	0.671235i
$719$	−8.60356	+	23.6381i	−0.320859	+	0.881552i	0.669473	+	0.742836i	$0.266520\pi$
$719$	−8.60356	+	23.6381i	−0.320859	+	0.881552i	−0.990332	+	0.138716i	$0.955702\pi$
$720$	−9.68269	+	3.88510i	−0.360853	+	0.144789i
$721$			12.9745i			0.483196i
$722$	−12.9163	+	23.5620i	−0.480696	+	0.876888i
$723$		−	69.8137i		−	2.59640i
$724$	18.6329	−	11.1654i	0.692484	−	0.414958i
$725$	1.40628	−	3.86374i	0.0522281	−	0.143496i
$726$	26.4986	+	45.0474i	0.983456	+	1.67187i
$727$	−45.1486	+	7.96091i	−1.67447	+	0.295254i	−0.928667	−	0.370915i	$-0.879044\pi$
$727$	−45.1486	+	7.96091i	−1.67447	+	0.295254i	−0.745801	+	0.666169i	$0.767933\pi$
$728$	−13.0674	−	10.4326i	−0.484308	−	0.386659i
$729$	9.77423	−	16.9295i	0.362009	−	0.627017i
$730$	4.07921	+	1.44728i	0.150978	+	0.0535661i
$731$	13.3235	−	15.8784i	0.492789	−	0.587283i
$732$	−6.81245	+	5.90766i	−0.251796	+	0.218354i
$733$	−9.21443	−	15.9599i	−0.340343	−	0.589491i	0.644154	−	0.764896i	$-0.277210\pi$
$733$	−9.21443	−	15.9599i	−0.340343	−	0.589491i	−0.984496	+	0.175405i	$0.943876\pi$
$734$	−9.89172	+	1.82720i	−0.365110	+	0.0674430i
$735$	−12.4436	+	4.52911i	−0.458990	+	0.167059i
$736$	13.5101	−	8.55011i	0.497988	−	0.315161i
$737$	12.4671	+	2.19829i	0.459232	+	0.0809750i
$738$	−0.869187	−	2.32900i	−0.0319952	−	0.0857316i
$739$	−23.8790	−	28.4578i	−0.878402	−	1.04684i	−0.998537	−	0.0540807i	$-0.982777\pi$
$739$	−23.8790	−	28.4578i	−0.878402	−	1.04684i	0.120135	−	0.992758i	$-0.461667\pi$
$740$	23.1691	+	3.69809i	0.851715	+	0.135944i
$741$	−50.7047	−	8.57447i	−1.86268	−	0.314991i
$742$	−9.36068	+	7.98509i	−0.343642	+	0.293142i
$743$	−0.356512	+	0.299149i	−0.0130792	+	0.0109747i	−0.649304	−	0.760529i	$-0.724940\pi$
$743$	−0.356512	+	0.299149i	−0.0130792	+	0.0109747i	0.636225	+	0.771504i	$0.280495\pi$
$744$	8.40018	+	41.6713i	0.307965	+	1.52774i
$745$	1.70189	−	9.65189i	0.0623524	−	0.353618i
$746$	4.50405	−	5.45718i	0.164905	−	0.199802i
$747$	7.14318	+	19.6257i	0.261355	+	0.718067i
$748$	21.2975	−	26.2359i	0.778715	−	0.959281i
$749$	9.82747	−	5.67389i	0.359088	−	0.207320i
$750$	3.34900	−	0.0272203i	0.122288	−	0.000993946i
$751$	−5.65211	−	4.74268i	−0.206248	−	0.173063i	0.533812	−	0.845603i	$-0.320759\pi$
$751$	−5.65211	−	4.74268i	−0.206248	−	0.173063i	−0.740061	+	0.672540i	$0.765203\pi$
$752$	−31.3337	+	6.58177i	−1.14262	+	0.240012i
$753$	41.3800	+	23.8908i	1.50797	+	0.870628i
$754$	−14.2795	+	25.2038i	−0.520030	+	0.917867i
$755$	0.130265	+	0.738770i	0.00474083	+	0.0268866i
$756$	0.719332	−	2.08099i	0.0261619	−	0.0756850i
$757$	5.71241	+	2.07915i	0.207621	+	0.0755680i	0.443737	−	0.896157i	$-0.353652\pi$
$757$	5.71241	+	2.07915i	0.207621	+	0.0755680i	−0.236116	+	0.971725i	$0.575875\pi$
$758$	−1.05946	+	6.30787i	−0.0384813	+	0.229112i
$759$	34.5243			1.25315
$760$	−5.82623	+	10.8653i	−0.211339	+	0.394126i
$761$	36.2041			1.31240			0.656199	−	0.754588i	$-0.272163\pi$
$761$	36.2041			1.31240			0.656199	+	0.754588i	$0.272163\pi$
$762$	3.23651	−	19.2697i	0.117247	−	0.698069i
$763$	15.5659	+	5.66551i	0.563522	+	0.205105i
$764$	6.68518	−	19.3399i	0.241861	−	0.699692i
$765$	1.48363	+	8.41407i	0.0536407	+	0.304211i
$766$	8.00585	−	14.1305i	0.289263	−	0.510557i
$767$	−51.7187	−	29.8598i	−1.86745	−	1.07817i
$768$	4.14118	−	37.6639i	0.149432	−	1.35908i
$769$	19.2700	+	16.1694i	0.694892	+	0.583084i	0.920315	−	0.391177i	$-0.127932\pi$
$769$	19.2700	+	16.1694i	0.694892	+	0.583084i	−0.225423	+	0.974261i	$0.572376\pi$
$770$	−8.65613	+	0.0703562i	−0.311945	+	0.00253546i
$771$	36.4300	−	21.0329i	1.31199	−	0.757480i
$772$	−21.2657	+	26.1967i	−0.765369	+	0.942841i
$773$	−8.30567	−	22.8196i	−0.298734	−	0.820765i	−0.994712	−	0.102702i	$-0.967251\pi$
$773$	−8.30567	−	22.8196i	−0.298734	−	0.820765i	0.695978	−	0.718063i	$-0.254971\pi$
$774$	14.8573	−	18.0014i	0.534036	−	0.647047i
$775$	1.10204	−	6.24998i	0.0395864	−	0.224506i
$776$	22.5481	−	4.54530i	0.809431	−	0.163167i
$777$	25.2552	−	21.1917i	0.906027	−	0.760247i
$778$	29.4204	−	25.0970i	1.05477	−	0.899770i
$779$	−2.55429	−	1.45093i	−0.0915168	−	0.0519851i
$780$	−23.3003	−	3.71902i	−0.834283	−	0.133162i
$781$	−26.6958	−	31.8148i	−0.955251	−	1.13842i
$782$	−4.57800	−	12.2668i	−0.163709	−	0.438660i
$783$	−3.75649	−	0.662371i	−0.134246	−	0.0236712i
$784$	3.16594	−	22.1418i	0.113069	−	0.790778i
$785$	−10.0566	+	3.66030i	−0.358935	+	0.130642i
$786$	−22.4209	+	4.14157i	−0.799725	+	0.147725i
$787$	16.0711	+	27.8360i	0.572873	+	0.992245i	0.996269	+	0.0863001i	$0.0275044\pi$
$787$	16.0711	+	27.8360i	0.572873	+	0.992245i	−0.423396	+	0.905944i	$0.639162\pi$
$788$	−31.5671	+	27.3746i	−1.12453	+	0.975179i
$789$	38.6433	−	46.0533i	1.37574	−	1.63954i
$790$	6.10969	+	2.16767i	0.217373	+	0.0771224i
$791$	−6.74991	+	11.6912i	−0.239999	+	0.415691i
$792$	23.7415	−	29.7373i	0.843616	−	1.05667i
$793$	−9.34026	+	1.64694i	−0.331682	+	0.0584845i
$794$	−19.8181	−	33.6905i	−0.703317	−	1.19563i
$795$	−5.93814	+	16.3149i	−0.210604	+	0.578630i
$796$	−12.3277	+	7.38715i	−0.436944	+	0.261831i
$797$			40.4263i			1.43197i	0.698115	+	0.715986i	$0.254022\pi$
$797$			40.4263i			1.43197i	−0.698115	+	0.715986i	$0.745978\pi$
$798$	6.17090	+	16.1876i	0.218448	+	0.573035i
$799$			26.2199i			0.927593i
$800$	−2.62706	+	5.00985i	−0.0928806	+	0.177125i
$801$	7.88303	−	21.6585i	0.278533	−	0.765264i
$802$	36.8383	−	21.6697i	1.30080	−	0.765183i
$803$	−15.5468	+	2.74132i	−0.548635	+	0.0967391i
$804$	−2.20440	−	11.4136i	−0.0777431	−	0.402527i
$805$	−1.67702	+	2.90469i	−0.0591073	+	0.102377i
$806$	−14.9503	+	42.1382i	−0.526603	+	1.48425i
$807$	37.3705	−	44.5365i	1.31550	−	1.56776i
$808$	4.69460	−	31.0308i	0.165156	−	1.09166i
$809$	−7.95524	−	13.7789i	−0.279691	−	0.484440i	0.691617	−	0.722265i	$-0.256899\pi$
$809$	−7.95524	−	13.7789i	−0.279691	−	0.484440i	−0.971308	+	0.237825i	$0.923565\pi$
$810$	−2.57446	−	13.9371i	−0.0904573	−	0.489700i
$811$	48.5062	−	17.6548i	1.70328	−	0.619944i	0.707090	−	0.707124i	$-0.250008\pi$
$811$	48.5062	−	17.6548i	1.70328	−	0.619944i	0.996193	+	0.0871798i	$0.0277855\pi$
$812$	9.75742	−	0.158625i	0.342418	−	0.00556665i
$813$	−54.7521	−	9.65427i	−1.92024	−	0.338590i
$814$	−80.1725	+	29.9205i	−2.81004	+	1.04871i
$815$	3.76241	+	4.48386i	0.131791	+	0.157063i
$816$	−29.4879	−	9.65937i	−1.03228	−	0.338146i
$817$	−0.193394	−	27.5813i	−0.00676601	−	0.964948i
$818$	31.6774	+	37.1344i	1.10757	+	1.29838i
$819$	−11.8121	+	9.91149i	−0.412747	+	0.346335i
$820$	−1.17809	−	0.654872i	−0.0411407	−	0.0228691i
$821$	−7.52215	+	42.6602i	−0.262525	+	1.48885i	0.513467	+	0.858109i	$0.328361\pi$
$821$	−7.52215	+	42.6602i	−0.262525	+	1.48885i	−0.775992	+	0.630743i	$0.782750\pi$
$822$	38.9005	+	32.1063i	1.35681	+	1.11983i
$823$	8.22709	+	22.6037i	0.286778	+	0.787917i	0.996512	+	0.0834471i	$0.0265930\pi$
$823$	8.22709	+	22.6037i	0.286778	+	0.787917i	−0.709734	+	0.704470i	$0.751185\pi$
$824$	−30.9148	+	0.753950i	−1.07697	+	0.0262651i
$825$	−10.5786	+	6.10755i	−0.368299	+	0.212637i
$826$	0.163515	+	20.1177i	0.00568941	+	0.699985i
$827$	41.8334	+	35.1024i	1.45469	+	1.22063i	0.929066	+	0.369913i	$0.120613\pi$
$827$	41.8334	+	35.1024i	1.45469	+	1.22063i	0.525624	+	0.850717i	$0.323832\pi$
$828$	−5.26721	−	13.7708i	−0.183048	−	0.478570i
$829$	−6.65244	−	3.84079i	−0.231049	−	0.133396i	0.380007	−	0.924984i	$-0.375922\pi$
$829$	−6.65244	−	3.84079i	−0.231049	−	0.133396i	−0.611056	+	0.791588i	$0.709255\pi$
$830$	9.85264	+	5.58215i	0.341990	+	0.193759i
$831$	5.56426	+	31.5565i	0.193022	+	1.09468i
$832$	24.0988	−	31.7422i	0.835476	−	1.10046i
$833$	−17.2122	−	6.26473i	−0.596368	−	0.217060i
$834$	1.69205	+	0.284195i	0.0585910	+	0.00984085i
$835$	20.7937			0.719597
$836$	−1.04615	−	44.9544i	−0.0361818	−	1.55478i
$837$	−5.88757			−0.203504
$838$	−20.1057	−	3.37692i	−0.694539	−	0.116654i
$839$	1.84390	+	0.671126i	0.0636587	+	0.0231699i	0.373653	−	0.927568i	$-0.378105\pi$
$839$	1.84390	+	0.671126i	0.0636587	+	0.0231699i	−0.309995	+	0.950738i	$0.600327\pi$
$840$	2.89994	+	7.40090i	0.100057	+	0.255355i
$841$	2.10008	+	11.9102i	0.0724167	+	0.410696i
$842$	−27.8758	−	15.7934i	−0.960662	−	0.544276i
$843$	−29.6170	−	17.0994i	−1.02006	−	0.588934i
$844$	−27.8394	+	10.6483i	−0.958272	+	0.366530i
$845$	−9.05277	−	7.59618i	−0.311425	−	0.261317i
$846$	0.239971	+	29.5243i	0.00825036	+	1.01507i
$847$	16.0376	−	9.25929i	0.551057	−	0.318153i
$848$	−19.5703	−	21.8400i	−0.672046	−	0.749988i
$849$	−13.1519	−	36.1346i	−0.451373	−	1.24014i
$850$	3.57281	+	2.94879i	0.122546	+	0.101143i
$851$	−5.75760	+	32.6530i	−0.197368	+	1.11933i
$852$	−18.5287	+	33.3325i	−0.634783	+	1.14195i
$853$	−5.18508	+	4.35080i	−0.177534	+	0.148968i	−0.727224	−	0.686400i	$-0.759190\pi$
$853$	−5.18508	+	4.35080i	−0.177534	+	0.148968i	0.549691	+	0.835368i	$0.314746\pi$
$854$	2.07359	+	2.43081i	0.0709568	+	0.0831806i
$855$	8.76030	+	7.24670i	0.299596	+	0.247832i
$856$	14.0904	+	23.0865i	0.481601	+	0.789081i
$857$	−9.81574	−	11.6979i	−0.335299	−	0.399594i	0.571881	−	0.820337i	$-0.306214\pi$
$857$	−9.81574	−	11.6979i	−0.335299	−	0.399594i	−0.907180	+	0.420743i	$0.861770\pi$
$858$	80.6262	−	30.0899i	2.75253	−	1.02725i
$859$	−51.5058	−	9.08186i	−1.75735	−	0.309869i	−0.800262	−	0.599651i	$-0.795306\pi$
$859$	−51.5058	−	9.08186i	−1.75735	−	0.309869i	−0.957093	+	0.289782i	$0.906417\pi$
$860$	−0.205712	−	12.6538i	−0.00701471	−	0.431491i
$861$	−1.77975	+	0.647776i	−0.0606537	+	0.0220761i
$862$	0.527726	+	2.85690i	0.0179744	+	0.0973065i
$863$	−4.64519	−	8.04570i	−0.158124	−	0.273879i	0.776068	−	0.630649i	$-0.217211\pi$
$863$	−4.64519	−	8.04570i	−0.158124	−	0.273879i	−0.934192	+	0.356770i	$0.883878\pi$
$864$	5.00025	+	1.59305i	0.170112	+	0.0541967i
$865$	9.41303	−	11.2180i	0.320052	−	0.381424i
$866$	14.2419	−	40.1415i	0.483960	−	1.36406i
$867$	7.42403	−	12.8588i	0.252133	−	0.436708i
$868$	14.7892	−	2.85635i	0.501979	−	0.0969509i
$869$	−23.2854	+	4.10585i	−0.789904	+	0.139281i
$870$	11.8693	−	6.98197i	0.402406	−	0.236711i
$871$	4.18180	−	11.4894i	0.141695	−	0.389303i
$872$	−12.5949	+	37.4185i	−0.426516	+	1.26715i
$873$		−	21.2113i		−	0.717892i
$874$	−15.2188	−	8.48202i	−0.514784	−	0.286909i
$875$		−	1.18670i		−	0.0401178i
$876$	7.45116	+	12.4345i	0.251751	+	0.420124i
$877$	−11.1851	+	30.7308i	−0.377694	+	1.03770i	0.594616	+	0.804010i	$0.297304\pi$
$877$	−11.1851	+	30.7308i	−0.377694	+	1.03770i	−0.972310	+	0.233695i	$0.924918\pi$
$878$	10.1458	+	17.2477i	0.342403	+	0.582082i
$879$	6.55068	−	1.15506i	0.220949	−	0.0389593i
$880$	−0.670649	−	20.6212i	−0.0226076	−	0.695139i
$881$	11.6637	−	20.2021i	0.392960	−	0.680626i	−0.599879	−	0.800091i	$-0.704785\pi$
$881$	11.6637	−	20.2021i	0.392960	−	0.680626i	0.992838	+	0.119465i	$0.0381179\pi$
$882$	−19.4387	−	6.89672i	−0.654536	−	0.232225i
$883$	−31.4711	+	37.5058i	−1.05909	+	1.26217i	−0.0953131	+	0.995447i	$0.530385\pi$
$883$	−31.4711	+	37.5058i	−1.05909	+	1.26217i	−0.963773	+	0.266723i	$0.914059\pi$
$884$	−21.3824	−	24.6572i	−0.719168	−	0.829313i
$885$	14.1945	+	24.5857i	0.477144	+	0.826438i
$886$	17.1156	−	3.16159i	0.575010	−	0.106216i
$887$	−46.8921	+	17.0673i	−1.57448	+	0.573065i	−0.973995	−	0.226570i	$-0.927249\pi$
$887$	−46.8921	+	17.0673i	−1.57448	+	0.573065i	−0.600487	+	0.799634i	$0.705027\pi$
$888$	51.9617	+	58.9450i	1.74372	+	1.97807i
$889$	−6.81836	−	1.20226i	−0.228680	−	0.0403225i
$890$	−4.36953	−	11.7082i	−0.146467	−	0.392460i
$891$	33.2272	+	39.5986i	1.11315	+	1.32660i
$892$	3.75677	−	23.5368i	0.125786	−	0.788072i
$893$	22.6139	+	26.5696i	0.756745	+	0.889117i
$894$	24.9722	−	21.3025i	0.835197	−	0.712461i
$895$	16.0302	−	13.4509i	0.535830	−	0.449615i
$896$	−13.3332	−	1.57577i	−0.445430	−	0.0526429i
$897$	5.79018	−	32.8377i	0.193328	−	1.09642i
$898$	−22.5596	+	27.3336i	−0.752823	+	0.912134i
$899$	−8.92484	−	24.5208i	−0.297660	−	0.817814i
$900$	4.05007	+	3.28772i	0.135002	+	0.109591i
$901$	−20.7978	+	12.0076i	−0.692877	+	0.400033i
$902$	4.91588	−	0.0399558i	0.163681	−	0.00133038i
$903$	−13.6225	−	11.4307i	−0.453329	−	0.380388i
$904$	−28.2492	−	15.4038i	−0.939554	−	0.512324i
$905$	−9.40594	−	5.43052i	−0.312664	−	0.180517i
$906$	−1.23847	+	2.18593i	−0.0411454	+	0.0726227i
$907$	1.91168	+	10.8417i	0.0634763	+	0.359992i	0.999957	+	0.00927282i	$0.00295167\pi$
$907$	1.91168	+	10.8417i	0.0634763	+	0.359992i	−0.936481	+	0.350719i	$0.885937\pi$
$908$	22.4462	+	7.75894i	0.744904	+	0.257489i
$909$	−27.1957	−	9.89841i	−0.902023	−	0.328310i
$910$	−1.38483	+	8.24507i	−0.0459066	+	0.273321i
$911$	−3.77288			−0.125001			−0.0625006	−	0.998045i	$-0.519908\pi$
$911$	−3.77288			−0.125001			−0.0625006	+	0.998045i	$0.519908\pi$
$912$	−38.2122	+	15.6443i	−1.26533	+	0.518034i
$913$	−41.3020			−1.36690
$914$	8.17608	−	48.6792i	0.270441	−	1.61017i
$915$	4.23670	+	1.54203i	0.140061	+	0.0509781i
$916$	−2.40307	−	0.830664i	−0.0793996	−	0.0274459i
$917$	1.40288	+	7.95611i	0.0463271	+	0.262734i
$918$	2.11849	−	3.73919i	0.0699205	−	0.123412i
$919$	12.0398	+	6.95119i	0.397157	+	0.229299i	0.685256	−	0.728302i	$-0.259690\pi$
$919$	12.0398	+	6.95119i	0.397157	+	0.229299i	−0.288100	+	0.957600i	$0.593023\pi$
$920$	−7.01854	−	3.82710i	−0.231395	−	0.126176i
$921$	15.4063	+	12.9275i	0.507656	+	0.425974i
$922$	−12.2676	+	0.0997101i	−0.404013	+	0.00328378i
$923$	−34.7379	+	20.0559i	−1.14341	+	0.660148i
$924$	−22.5086	−	18.2718i	−0.740478	−	0.601097i
$925$	−4.01231	−	11.0237i	−0.131924	−	0.362458i
$926$	12.3700	−	14.9877i	0.406503	−	0.492526i
$927$	−4.95190	+	28.0836i	−0.162642	+	0.922387i
$928$	0.944966	+	23.2401i	0.0310200	+	0.762894i
$929$	−16.3475	+	13.7171i	−0.536343	+	0.450045i	−0.870285	−	0.492549i	$-0.836065\pi$
$929$	−16.3475	+	13.7171i	−0.536343	+	0.450045i	0.333942	+	0.942594i	$0.391621\pi$
$930$	16.1705	−	13.7942i	0.530252	−	0.452329i
$931$	−22.8449	+	8.49674i	−0.748712	+	0.278469i
$932$	2.06893	−	12.9622i	0.0677702	−	0.424592i
$933$	19.0005	+	22.6439i	0.622049	+	0.741329i
$934$	−1.95406	−	5.23592i	−0.0639387	−	0.171325i
$935$	−16.6394	−	2.93397i	−0.544166	−	0.0959512i
$936$	−24.3028	−	27.5690i	−0.794363	−	0.901121i
$937$	−39.6039	+	14.4146i	−1.29380	+	0.470905i	−0.894973	−	0.446120i	$-0.852805\pi$
$937$	−39.6039	+	14.4146i	−1.29380	+	0.470905i	−0.398829	+	0.917025i	$0.630583\pi$
$938$	−4.05043	+	0.748195i	−0.132251	+	0.0244294i
$939$	−4.81277	−	8.33597i	−0.157059	−	0.272034i
$940$	10.4882	+	12.0945i	0.342088	+	0.394480i
$941$	13.5946	−	16.2015i	0.443172	−	0.528152i	−0.497502	−	0.867463i	$-0.665749\pi$
$941$	13.5946	−	16.2015i	0.443172	−	0.528152i	0.940674	+	0.339311i	$0.110194\pi$
$942$	−33.7791	−	11.9846i	−1.10058	−	0.390479i
$943$	0.952393	−	1.64959i	0.0310142	−	0.0537182i
$944$	−47.9256	+	1.55865i	−1.55985	+	0.0507299i
$945$	−1.08418	+	0.191170i	−0.0352684	+	0.00621877i
$946$	23.4031	+	39.7850i	0.760900	+	1.29352i
$947$	0.941714	−	2.58734i	0.0306016	−	0.0840772i	−0.923451	−	0.383716i	$-0.874644\pi$
$947$	0.941714	−	2.58734i	0.0306016	−	0.0840772i	0.954053	+	0.299639i	$0.0968663\pi$
$948$	11.1601	+	18.6240i	0.362462	+	0.604878i
$949$			15.2471i			0.494941i
$950$	6.16371	−	0.0933219i	0.199977	−	0.00302776i
$951$		−	62.5789i		−	2.02926i
$952$	−3.50744	+	10.4204i	−0.113677	+	0.337727i
$953$	−3.29515	+	9.05336i	−0.106740	+	0.293267i	−0.981552	−	0.191197i	$-0.938763\pi$
$953$	−3.29515	+	9.05336i	−0.106740	+	0.293267i	0.874811	+	0.484464i	$0.160985\pi$
$954$	−23.3090	+	13.7113i	−0.754658	+	0.443919i
$955$	−10.0759	+	1.77666i	−0.326049	+	0.0574913i
$956$	−36.2312	+	6.99761i	−1.17180	+	0.226319i
$957$	−25.1124	+	43.4960i	−0.811769	+	1.40602i
$958$	8.53023	−	24.0429i	0.275599	−	0.776789i
$959$	11.4880	−	13.6908i	0.370965	−	0.442099i
$960$	−17.4658	+	7.33985i	−0.563707	+	0.236893i
$961$	−4.63836	−	8.03387i	−0.149624	−	0.259157i
$962$	15.0129	+	81.2740i	0.484035	+	2.62038i
$963$	23.4373	−	8.53048i	0.755256	−	0.274891i
$964$	−0.958377	−	58.9520i	−0.0308672	−	1.89872i
$965$	16.6145	+	2.92959i	0.534840	+	0.0943067i
$966$	−10.5240	+	3.92760i	−0.338606	+	0.126368i
$967$	−31.6390	−	37.7059i	−1.01744	−	1.21254i	−0.976974	−	0.213358i	$-0.931560\pi$
$967$	−31.6390	−	37.7059i	−1.01744	−	1.21254i	−0.0404673	−	0.999181i	$-0.512885\pi$
$968$	22.9943	+	37.6751i	0.739066	+	1.21092i
$969$	6.10505	+	33.2581i	0.196123	+	1.06840i
$970$	−7.46397	−	8.74979i	−0.239654	−	0.280939i
$971$	41.3606	−	34.7056i	1.32732	−	1.11376i	0.342628	−	0.939471i	$-0.388683\pi$
$971$	41.3606	−	34.7056i	1.32732	−	1.11376i	0.984695	−	0.174286i	$-0.0557616\pi$
$972$	20.3576	−	36.6225i	0.652970	−	1.17467i
$973$	0.105569	−	0.598712i	0.00338439	−	0.0191938i
$974$	−4.65470	−	3.84172i	−0.149146	−	0.123097i
$975$	4.03502	+	11.0861i	0.129224	+	0.355040i
$976$	−5.67147	+	5.08207i	−0.181539	+	0.162673i
$977$	−4.61402	+	2.66391i	−0.147616	+	0.0852259i	−0.571989	−	0.820262i	$-0.693828\pi$
$977$	−4.61402	+	2.66391i	−0.147616	+	0.0852259i	0.424373	+	0.905487i	$0.360495\pi$
$978$	0.159328	+	19.6026i	0.00509475	+	0.626821i
$979$	34.9162	+	29.2982i	1.11593	+	0.936374i
$980$	−10.4455	+	3.99530i	−0.333669	+	0.127625i
$981$	31.5303	+	18.2040i	1.00669	+	0.581210i
$982$	−18.4774	−	10.4686i	−0.589639	−	0.334068i
$983$	−0.145788	−	0.826806i	−0.00464992	−	0.0263710i	0.982395	−	0.186818i	$-0.0598175\pi$
$983$	−0.145788	−	0.826806i	−0.00464992	−	0.0263710i	−0.987044	+	0.160447i	$0.948706\pi$
$984$	−1.64690	−	4.20302i	−0.0525012	−	0.133987i
$985$	19.6318	+	7.14538i	0.625520	+	0.227671i
$986$	18.7845	+	3.15501i	0.598220	+	0.100476i
$987$	22.4948			0.716018
$988$	−42.9337	−	6.54440i	−1.36590	−	0.208205i
$989$	17.8845			0.568694
$990$	−18.7632	−	3.15144i	−0.596335	−	0.100159i
$991$	−40.3621	−	14.6906i	−1.28215	−	0.466663i	−0.391004	−	0.920389i	$-0.627872\pi$
$991$	−40.3621	−	14.6906i	−1.28215	−	0.466663i	−0.891141	+	0.453726i	$0.850094\pi$
$992$	7.66532	+	35.0728i	0.243374	+	1.11356i
$993$	2.51094	+	14.2402i	0.0796822	+	0.451900i
$994$	11.7570	+	6.66111i	0.372911	+	0.211278i
$995$	6.22308	+	3.59290i	0.197285	+	0.113902i
$996$	13.5489	+	35.4229i	0.429313	+	1.12242i
$997$	15.9835	+	13.4117i	0.506202	+	0.424754i	0.859790	−	0.510647i	$-0.170594\pi$
$997$	15.9835	+	13.4117i	0.506202	+	0.424754i	−0.353588	+	0.935401i	$0.615039\pi$
$998$	−0.102569	−	12.6194i	−0.00324677	−	0.399460i
$999$	−9.42503	+	5.44154i	−0.298195	+	0.172163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.a.51.12	yes	120
4.3	odd	2	inner	380.2.be.a.51.1	✓	120
19.3	odd	18	inner	380.2.be.a.231.1	yes	120
76.3	even	18	inner	380.2.be.a.231.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.a.51.1	✓	120	4.3	odd	2	inner
380.2.be.a.51.12	yes	120	1.1	even	1	trivial
380.2.be.a.231.1	yes	120	19.3	odd	18	inner
380.2.be.a.231.12	yes	120	76.3	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.234248 - 1.39468i) q^{2} +(-2.22536 - 0.809964i) q^{3} +(-1.89026 - 0.653401i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-1.65093 + 2.91393i) q^{6} +(1.02771 + 0.593350i) q^{7} +(-1.35407 + 2.48324i) q^{8} +(1.99805 + 1.67656i) q^{9} +O(q^{10})\)	\(q+(0.234248 - 1.39468i) q^{2} +(-2.22536 - 0.809964i) q^{3} +(-1.89026 - 0.653401i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-1.65093 + 2.91393i) q^{6} +(1.02771 + 0.593350i) q^{7} +(-1.35407 + 2.48324i) q^{8} +(1.99805 + 1.67656i) q^{9} +(1.41417 - 0.0114942i) q^{10} +(-4.46697 + 2.57901i) q^{11} +(3.67727 + 2.98509i) q^{12} +(1.70385 + 4.68129i) q^{13} +(1.06827 - 1.29434i) q^{14} +(0.411230 - 2.33220i) q^{15} +(3.14613 + 2.47019i) q^{16} +(2.50933 - 2.10558i) q^{17} +(2.80630 - 2.39390i) q^{18} +(0.726798 - 4.29788i) q^{19} +(0.315235 - 1.97500i) q^{20} +(-1.80643 - 2.15283i) q^{21} +(2.55051 + 6.83412i) q^{22} +(2.78343 + 0.490793i) q^{23} +(5.02463 - 4.42935i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(6.92801 - 1.27974i) q^{26} +(0.463852 + 0.803415i) q^{27} +(-1.55494 - 1.79309i) q^{28} +(-2.64295 + 3.14975i) q^{29} +(-3.15634 - 1.11985i) q^{30} +(-3.17320 + 5.49614i) q^{31} +(4.18210 - 3.80921i) q^{32} +(12.0295 - 2.12113i) q^{33} +(-2.34880 - 3.99293i) q^{34} +(-0.405875 + 1.11513i) q^{35} +(-2.68135 - 4.47465i) q^{36} +11.7312i q^{37} +(-5.82391 - 2.02042i) q^{38} -11.7976i q^{39} +(-2.68065 - 0.902291i) q^{40} +(0.230499 - 0.633292i) q^{41} +(-3.42565 + 2.01510i) q^{42} +(6.23161 - 1.09880i) q^{43} +(10.1288 - 1.95626i) q^{44} +(-1.30413 + 2.25882i) q^{45} +(1.33651 - 3.76702i) q^{46} +(-5.14511 + 6.13171i) q^{47} +(-5.00051 - 8.04531i) q^{48} +(-2.79587 - 4.84259i) q^{49} +(0.256887 + 1.39069i) q^{50} +(-7.28959 + 2.65320i) q^{51} +(-0.161953 - 9.96213i) q^{52} +(-7.21998 - 1.27308i) q^{53} +(1.22916 - 0.458726i) q^{54} +(-3.31551 - 3.95127i) q^{55} +(-2.86503 + 1.74862i) q^{56} +(-5.09851 + 8.97564i) q^{57} +(3.77378 + 4.42389i) q^{58} +(-9.18314 + 7.70557i) q^{59} +(-2.30119 + 4.13976i) q^{60} +(-0.330596 + 1.87491i) q^{61} +(6.92203 + 5.71305i) q^{62} +(1.05863 + 2.90856i) q^{63} +(-4.33297 - 6.72498i) q^{64} +(-4.31430 + 2.49086i) q^{65} +(-0.140403 - 17.2742i) q^{66} +(-1.88012 - 1.57761i) q^{67} +(-6.11906 + 2.34048i) q^{68} +(-5.79659 - 3.34667i) q^{69} +(1.46018 + 0.827283i) q^{70} +(1.39818 + 7.92947i) q^{71} +(-6.86880 + 2.69145i) q^{72} +(2.87603 + 1.04679i) q^{73} +(16.3613 + 2.74801i) q^{74} +2.36818 q^{75} +(-4.18207 + 7.64920i) q^{76} -6.12101 q^{77} +(-16.4539 - 2.76356i) q^{78} +(4.30760 + 1.56784i) q^{79} +(-1.88634 + 3.52728i) q^{80} +(-1.74026 - 9.86950i) q^{81} +(-0.829245 - 0.469820i) q^{82} +(6.93456 + 4.00367i) q^{83} +(2.00797 + 5.24972i) q^{84} +(2.50933 + 2.10558i) q^{85} +(-0.0727324 - 8.94848i) q^{86} +(8.43270 - 4.86862i) q^{87} +(-0.355693 - 14.5847i) q^{88} +(-3.02233 - 8.30379i) q^{89} +(2.84484 + 2.34797i) q^{90} +(-1.02657 + 5.82199i) q^{91} +(-4.94070 - 2.74642i) q^{92} +(11.5132 - 9.66070i) q^{93} +(7.34653 + 8.61212i) q^{94} +(4.35879 - 0.0305629i) q^{95} +(-12.3920 + 5.08951i) q^{96} +(-5.22736 - 6.22973i) q^{97} +(-7.40879 + 2.76498i) q^{98} +(-13.2491 - 2.33617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 36 * q^8 + 6 * q^9	\( 120 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} + 18 q^{14} - 15 q^{16} - 48 q^{17} - 12 q^{21} + 18 q^{24} - 69 q^{28} - 12 q^{30} - 33 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} + 18 q^{38} - 36 q^{41} - 27 q^{42} - 27 q^{44} - 60 q^{45} - 117 q^{46} + 45 q^{48} + 60 q^{49} - 15 q^{52} + 48 q^{53} + 69 q^{54} + 48 q^{57} + 6 q^{60} + 18 q^{62} - 24 q^{64} - 18 q^{65} + 168 q^{66} + 12 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 24 q^{76} - 60 q^{77} - 54 q^{78} + 21 q^{80} - 66 q^{81} - 63 q^{82} + 252 q^{84} - 48 q^{85} - 45 q^{86} + 135 q^{88} - 3 q^{90} - 42 q^{92} + 96 q^{93} + 78 q^{96} - 54 q^{97} - 33 q^{98}+O(q^{100}) \) 120 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 + 18 * q^14 - 15 * q^16 - 48 * q^17 - 12 * q^21 + 18 * q^24 - 69 * q^28 - 12 * q^30 - 33 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 + 18 * q^38 - 36 * q^41 - 27 * q^42 - 27 * q^44 - 60 * q^45 - 117 * q^46 + 45 * q^48 + 60 * q^49 - 15 * q^52 + 48 * q^53 + 69 * q^54 + 48 * q^57 + 6 * q^60 + 18 * q^62 - 24 * q^64 - 18 * q^65 + 168 * q^66 + 12 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 24 * q^76 - 60 * q^77 - 54 * q^78 + 21 * q^80 - 66 * q^81 - 63 * q^82 + 252 * q^84 - 48 * q^85 - 45 * q^86 + 135 * q^88 - 3 * q^90 - 42 * q^92 + 96 * q^93 + 78 * q^96 - 54 * q^97 - 33 * q^98

Introduction

L-functions

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