LMFDB - Embedded newform 525.2.bs.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(2,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 3, 20]))

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

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

chi := DirichletCharacter("525.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$1216$
Relative dimension:	$76$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	525.2
Dual form			525.2.bs.a.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14544 - 1.73734i) q^{2} +(1.64793 + 0.533222i) q^{3} +(1.16873 + 5.49845i) q^{4} +(2.07100 + 0.843193i) q^{5} +(-2.60915 - 4.00702i) q^{6} +(0.291962 + 2.62959i) q^{7} +(4.53862 - 8.90754i) q^{8} +(2.43135 + 1.75743i) q^{9} +O(q^{10})$	\(q+(-2.14544 - 1.73734i) q^{2} +(1.64793 + 0.533222i) q^{3} +(1.16873 + 5.49845i) q^{4} +(2.07100 + 0.843193i) q^{5} +(-2.60915 - 4.00702i) q^{6} +(0.291962 + 2.62959i) q^{7} +(4.53862 - 8.90754i) q^{8} +(2.43135 + 1.75743i) q^{9} +(-2.97829 - 5.40705i) q^{10} +(-0.225117 + 0.505622i) q^{11} +(-1.00591 + 9.68425i) q^{12} +(-0.714343 + 0.113141i) q^{13} +(3.94212 - 6.14888i) q^{14} +(2.96325 + 2.49382i) q^{15} +(-14.9422 + 6.65269i) q^{16} +(-0.261049 - 4.98111i) q^{17} +(-2.16306 - 7.99454i) q^{18} +(0.236131 - 1.11091i) q^{19} +(-2.21581 + 12.3727i) q^{20} +(-0.921026 + 4.48907i) q^{21} +(1.36142 - 0.693676i) q^{22} +(0.770349 - 0.951302i) q^{23} +(12.2290 - 12.2589i) q^{24} +(3.57805 + 3.49250i) q^{25} +(1.72915 + 0.998323i) q^{26} +(3.06959 + 4.19257i) q^{27} +(-14.1174 + 4.67862i) q^{28} +(-3.01332 + 9.27405i) q^{29} +(-2.02484 - 10.4985i) q^{30} +(-3.11083 + 3.45493i) q^{31} +(24.3026 + 6.51186i) q^{32} +(-0.640587 + 0.713192i) q^{33} +(-8.09384 + 11.1402i) q^{34} +(-1.61260 + 5.69206i) q^{35} +(-6.82152 + 15.4226i) q^{36} +(7.45524 + 2.86180i) q^{37} +(-2.43664 + 1.97315i) q^{38} +(-1.23752 - 0.194456i) q^{39} +(16.9102 - 14.6205i) q^{40} +(1.01159 - 1.39234i) q^{41} +(9.77506 - 8.03089i) q^{42} +(6.79642 - 6.79642i) q^{43} +(-3.04324 - 0.646860i) q^{44} +(3.55346 + 5.68972i) q^{45} +(-3.30548 + 0.702601i) q^{46} +(-9.16853 - 0.480502i) q^{47} +(-28.1711 + 2.99566i) q^{48} +(-6.82952 + 1.53548i) q^{49} +(-1.60883 - 13.7093i) q^{50} +(2.22585 - 8.34772i) q^{51} +(-1.45697 - 3.79555i) q^{52} +(-0.443324 - 0.287898i) q^{53} +(0.698301 - 14.3278i) q^{54} +(-0.892554 + 0.857324i) q^{55} +(24.7483 + 9.33405i) q^{56} +(0.981490 - 1.70479i) q^{57} +(22.5771 - 14.6618i) q^{58} +(0.653828 - 6.22076i) q^{59} +(-10.2489 + 19.2079i) q^{60} +(-0.167190 - 1.59071i) q^{61} +(12.6765 - 2.00776i) q^{62} +(-3.91146 + 6.90656i) q^{63} +(-21.5985 - 29.7278i) q^{64} +(-1.57480 - 0.368015i) q^{65} +(2.61340 - 0.417192i) q^{66} +(-6.38137 + 0.334434i) q^{67} +(27.0833 - 7.25694i) q^{68} +(1.77674 - 1.15691i) q^{69} +(13.3488 - 9.41033i) q^{70} +(-4.99523 - 1.62305i) q^{71} +(26.6893 - 13.6810i) q^{72} +(10.0480 - 3.85708i) q^{73} +(-11.0229 - 19.0922i) q^{74} +(4.03410 + 7.66329i) q^{75} +6.38425 q^{76} +(-1.39530 - 0.444345i) q^{77} +(2.31718 + 2.56719i) q^{78} +(3.28376 - 2.95671i) q^{79} +(-36.5547 + 1.17856i) q^{80} +(2.82290 + 8.54583i) q^{81} +(-4.58928 + 1.22969i) q^{82} +(-0.937343 + 1.83964i) q^{83} +(-25.7593 + 0.182299i) q^{84} +(3.65940 - 10.5360i) q^{85} +(-26.3890 + 2.77360i) q^{86} +(-9.91087 + 13.6762i) q^{87} +(3.48212 + 4.30006i) q^{88} +(0.159434 + 1.51691i) q^{89} +(2.26125 - 18.3805i) q^{90} +(-0.506075 - 1.84540i) q^{91} +(6.13101 + 3.12391i) q^{92} +(-6.96868 + 4.03472i) q^{93} +(18.8357 + 16.9598i) q^{94} +(1.42574 - 2.10159i) q^{95} +(36.5767 + 23.6898i) q^{96} +(2.79913 - 1.42623i) q^{97} +(17.3200 + 8.57094i) q^{98} +(-1.43593 + 0.833715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.14544	−	1.73734i	−1.51706	−	1.22849i	−0.895453	−	0.445155i	$-0.853148\pi$
$2$	−2.14544	−	1.73734i	−1.51706	−	1.22849i	−0.621603	−	0.783333i	$-0.713518\pi$
$3$	1.64793	+	0.533222i	0.951433	+	0.307856i
$3$	1.64793	+	0.533222i	0.951433	+	0.307856i
$4$	1.16873	+	5.49845i	0.584365	+	2.74922i
$5$	2.07100	+	0.843193i	0.926178	+	0.377087i
$5$	2.07100	+	0.843193i	0.926178	+	0.377087i
$6$	−2.60915	−	4.00702i	−1.06518	−	1.63586i
$7$	0.291962	+	2.62959i	0.110351	+	0.993893i
$7$	0.291962	+	2.62959i	0.110351	+	0.993893i
$8$	4.53862	−	8.90754i	1.60464	−	3.14929i
$9$	2.43135	+	1.75743i	0.810449	+	0.585809i
$10$	−2.97829	−	5.40705i	−0.941817	−	1.70986i
$11$	−0.225117	+	0.505622i	−0.0678754	+	0.152451i	−0.944298	−	0.329093i	$-0.893257\pi$
$11$	−0.225117	+	0.505622i	−0.0678754	+	0.152451i	0.876422	+	0.481544i	$0.159924\pi$
$12$	−1.00591	+	9.68425i	−0.290381	+	2.79560i
$13$	−0.714343	+	0.113141i	−0.198123	+	0.0313796i	−0.254707	−	0.967018i	$-0.581979\pi$
$13$	−0.714343	+	0.113141i	−0.198123	+	0.0313796i	0.0565841	+	0.998398i	$0.481979\pi$
$14$	3.94212	−	6.14888i	1.05358	−	1.64336i
$15$	2.96325	+	2.49382i	0.765107	+	0.643903i
$16$	−14.9422	+	6.65269i	−3.73555	+	1.66317i
$17$	−0.261049	−	4.98111i	−0.0633137	−	1.20810i	−0.826884	−	0.562372i	$-0.809889\pi$
$17$	−0.261049	−	4.98111i	−0.0633137	−	1.20810i	0.763570	−	0.645724i	$-0.223445\pi$
$18$	−2.16306	−	7.99454i	−0.509838	−	1.88433i
$19$	0.236131	−	1.11091i	0.0541722	−	0.254860i	−0.942725	−	0.333570i	$-0.891747\pi$
$19$	0.236131	−	1.11091i	0.0541722	−	0.254860i	0.996898	+	0.0787097i	$0.0250800\pi$
$20$	−2.21581	+	12.3727i	−0.495471	+	2.76663i
$21$	−0.921026	+	4.48907i	−0.200984	+	0.979594i
$22$	1.36142	−	0.693676i	0.290255	−	0.147892i
$23$	0.770349	−	0.951302i	0.160629	−	0.198360i	−0.690477	−	0.723355i	$-0.742599\pi$
$23$	0.770349	−	0.951302i	0.160629	−	0.198360i	0.851106	+	0.524994i	$0.175933\pi$
$24$	12.2290	−	12.2589i	2.49624	−	2.50234i
$25$	3.57805	+	3.49250i	0.715610	+	0.698500i
$26$	1.72915	+	0.998323i	0.339113	+	0.195787i
$27$	3.06959	+	4.19257i	0.590743	+	0.806860i
$28$	−14.1174	+	4.67862i	−2.66795	+	0.884176i
$29$	−3.01332	+	9.27405i	−0.559560	+	1.72215i	0.124028	+	0.992279i	$0.460419\pi$
$29$	−3.01332	+	9.27405i	−0.559560	+	1.72215i	−0.683587	+	0.729869i	$0.739581\pi$
$30$	−2.02484	−	10.4985i	−0.369684	−	1.91676i
$31$	−3.11083	+	3.45493i	−0.558722	+	0.620524i	−0.954640	−	0.297762i	$-0.903760\pi$
$31$	−3.11083	+	3.45493i	−0.558722	+	0.620524i	0.395918	+	0.918286i	$0.370426\pi$
$32$	24.3026	+	6.51186i	4.29613	+	1.15114i
$33$	−0.640587	+	0.713192i	−0.111512	+	0.124151i
$34$	−8.09384	+	11.1402i	−1.38808	+	1.91053i
$35$	−1.61260	+	5.69206i	−0.272580	+	0.962133i
$36$	−6.82152	+	15.4226i	−1.13692	+	2.57043i
$37$	7.45524	+	2.86180i	1.22563	+	0.470477i	0.883170	−	0.469054i	$-0.155405\pi$
$37$	7.45524	+	2.86180i	1.22563	+	0.470477i	0.342465	+	0.939531i	$0.388738\pi$
$38$	−2.43664	+	1.97315i	−0.395275	+	0.320087i
$39$	−1.23752	−	0.194456i	−0.198161	−	0.0311378i
$40$	16.9102	−	14.6205i	2.67374	−	2.31171i
$41$	1.01159	−	1.39234i	0.157984	−	0.217446i	−0.722686	−	0.691176i	$-0.757093\pi$
$41$	1.01159	−	1.39234i	0.157984	−	0.217446i	0.880670	+	0.473730i	$0.157093\pi$
$42$	9.77506	−	8.03089i	1.50832	−	1.23919i
$43$	6.79642	−	6.79642i	1.03644	−	1.03644i	0.0371339	−	0.999310i	$-0.488177\pi$
$43$	6.79642	−	6.79642i	1.03644	−	1.03644i	0.999310	−	0.0371339i	$-0.0118228\pi$
$44$	−3.04324	−	0.646860i	−0.458785	−	0.0975178i
$45$	3.55346	+	5.68972i	0.529719	+	0.848173i
$46$	−3.30548	+	0.702601i	−0.487366	+	0.103593i
$47$	−9.16853	−	0.480502i	−1.33737	−	0.0700885i	−0.629813	−	0.776747i	$-0.716868\pi$
$47$	−9.16853	−	0.480502i	−1.33737	−	0.0700885i	−0.707555	+	0.706658i	$0.750202\pi$
$48$	−28.1711	+	2.99566i	−4.06614	+	0.432386i
$49$	−6.82952	+	1.53548i	−0.975645	+	0.219354i
$50$	−1.60883	−	13.7093i	−0.227523	−	1.93878i
$51$	2.22585	−	8.34772i	0.311681	−	1.16891i
$52$	−1.45697	−	3.79555i	−0.202046	−	0.526348i
$53$	−0.443324	−	0.287898i	−0.0608952	−	0.0395458i	0.513832	−	0.857891i	$-0.328225\pi$
$53$	−0.443324	−	0.287898i	−0.0608952	−	0.0395458i	−0.574728	+	0.818345i	$0.694892\pi$
$54$	0.698301	−	14.3278i	0.0950267	−	1.94977i
$55$	−0.892554	+	0.857324i	−0.120352	+	0.115601i
$56$	24.7483	+	9.33405i	3.30713	+	1.24732i
$57$	0.981490	−	1.70479i	0.130002	−	0.225805i
$58$	22.5771	−	14.6618i	2.96452	−	1.92518i
$59$	0.653828	−	6.22076i	0.0851211	−	0.809873i	−0.865790	−	0.500408i	$-0.833183\pi$
$59$	0.653828	−	6.22076i	0.0851211	−	0.809873i	0.950911	−	0.309465i	$-0.100150\pi$
$60$	−10.2489	+	19.2079i	−1.32313	+	2.47972i
$61$	−0.167190	−	1.59071i	−0.0214065	−	0.203669i	0.978591	−	0.205814i	$-0.0659840\pi$
$61$	−0.167190	−	1.59071i	−0.0214065	−	0.203669i	−0.999998	+	0.00214456i	$0.999317\pi$
$62$	12.6765	−	2.00776i	1.60992	−	0.254986i
$63$	−3.91146	+	6.90656i	−0.492797	+	0.870144i
$64$	−21.5985	−	29.7278i	−2.69981	−	3.71597i
$65$	−1.57480	−	0.368015i	−0.195330	−	0.0456466i
$66$	2.61340	−	0.417192i	0.321687	−	0.0513528i
$67$	−6.38137	+	0.334434i	−0.779609	+	0.0408576i	−0.437989	−	0.898980i	$-0.644309\pi$
$67$	−6.38137	+	0.334434i	−0.779609	+	0.0408576i	−0.341620	+	0.939838i	$0.610976\pi$
$68$	27.0833	−	7.25694i	3.28433	−	0.880033i
$69$	1.77674	−	1.15691i	0.213894	−	0.139276i
$70$	13.3488	−	9.41033i	1.59549	−	1.12475i
$71$	−4.99523	−	1.62305i	−0.592824	−	0.192620i	−0.00278688	−	0.999996i	$-0.500887\pi$
$71$	−4.99523	−	1.62305i	−0.592824	−	0.192620i	−0.590038	+	0.807376i	$0.700887\pi$
$72$	26.6893	−	13.6810i	3.14536	−	1.61232i
$73$	10.0480	−	3.85708i	1.17603	−	0.451437i	0.309666	−	0.950845i	$-0.399783\pi$
$73$	10.0480	−	3.85708i	1.17603	−	0.451437i	0.866366	+	0.499409i	$0.166449\pi$
$74$	−11.0229	−	19.0922i	−1.28138	−	2.21942i
$75$	4.03410	+	7.66329i	0.465818	+	0.884881i
$76$	6.38425			0.732324
$77$	−1.39530	−	0.444345i	−0.159010	−	0.0506378i
$78$	2.31718	+	2.56719i	0.262369	+	0.290677i
$79$	3.28376	−	2.95671i	0.369451	−	0.332656i	−0.463403	−	0.886148i	$-0.653372\pi$
$79$	3.28376	−	2.95671i	0.369451	−	0.332656i	0.832854	+	0.553492i	$0.186705\pi$
$80$	−36.5547	+	1.17856i	−4.08694	+	0.131766i
$81$	2.82290	+	8.54583i	0.313656	+	0.949537i
$82$	−4.58928	+	1.22969i	−0.506801	+	0.135797i
$83$	−0.937343	+	1.83964i	−0.102887	+	0.201927i	−0.936711	−	0.350103i	$-0.886147\pi$
$83$	−0.937343	+	1.83964i	−0.102887	+	0.201927i	0.833824	+	0.552030i	$0.186147\pi$
$84$	−25.7593	+	0.182299i	−2.81057	+	0.0198905i
$85$	3.65940	−	10.5360i	0.396918	−	1.14279i
$86$	−26.3890	+	2.77360i	−2.84560	+	0.299085i
$87$	−9.91087	+	13.6762i	−1.06256	+	1.46624i
$88$	3.48212	+	4.30006i	0.371196	+	0.458388i
$89$	0.159434	+	1.51691i	0.0168999	+	0.160792i	0.999717	−	0.0237903i	$-0.00757341\pi$
$89$	0.159434	+	1.51691i	0.0168999	+	0.160792i	−0.982817	+	0.184582i	$0.940907\pi$
$90$	2.26125	−	18.3805i	0.238357	−	1.93748i
$91$	−0.506075	−	1.84540i	−0.0530511	−	0.193450i
$92$	6.13101	+	3.12391i	0.639202	+	0.325690i
$93$	−6.96868	+	4.03472i	−0.722619	+	0.418381i
$94$	18.8357	+	16.9598i	1.94276	+	1.74927i
$95$	1.42574	−	2.10159i	0.146278	−	0.215618i
$96$	36.5767	+	23.6898i	3.73309	+	2.41783i
$97$	2.79913	−	1.42623i	0.284208	−	0.144811i	−0.306075	−	0.952007i	$-0.599016\pi$
$97$	2.79913	−	1.42623i	0.284208	−	0.144811i	0.590284	+	0.807196i	$0.299016\pi$
$98$	17.3200	+	8.57094i	1.74958	+	0.865796i
$99$	−1.43593	+	0.833715i	−0.144317	+	0.0837915i
$100$	−15.0215	+	23.7555i	−1.50215	+	2.37555i
$101$	9.70927	−	5.60565i	0.966108	−	0.557783i	0.0680607	−	0.997681i	$-0.478319\pi$
$101$	9.70927	−	5.60565i	0.966108	−	0.557783i	0.898048	+	0.439898i	$0.144986\pi$
$102$	−19.2783	+	14.0425i	−1.90884	+	1.39041i
$103$	4.44018	+	0.232700i	0.437504	+	0.0229286i	0.269817	−	0.962912i	$-0.413037\pi$
$103$	4.44018	+	0.232700i	0.437504	+	0.0229286i	0.167687	+	0.985840i	$0.446370\pi$
$104$	−2.23432	+	6.87654i	−0.219093	+	0.674300i
$105$	−5.69259	+	8.52024i	−0.555540	+	0.831490i
$106$	0.450948	+	1.38787i	0.0437999	+	0.134802i
$107$	−0.543974	−	2.03014i	−0.0525879	−	0.196261i	0.934634	−	0.355610i	$-0.115727\pi$
$107$	−0.543974	−	2.03014i	−0.0525879	−	0.196261i	−0.987222	+	0.159350i	$0.949060\pi$
$108$	−19.4651	+	21.7780i	−1.87303	+	2.09559i
$109$	−6.86197	−	0.721222i	−0.657258	−	0.0690806i	−0.229972	−	0.973197i	$-0.573863\pi$
$109$	−6.86197	−	0.721222i	−0.657258	−	0.0690806i	−0.427286	+	0.904117i	$0.640530\pi$
$110$	3.40439	−	0.288664i	0.324596	−	0.0275231i
$111$	10.7597	+	8.69135i	1.02127	+	0.824946i
$112$	−21.8564	−	37.3496i	−2.06524	−	3.52920i
$113$	−2.48290	−	15.6764i	−0.233572	−	1.47471i	−0.773926	−	0.633276i	$-0.781710\pi$
$113$	−2.48290	−	15.6764i	−0.233572	−	1.47471i	0.540354	−	0.841438i	$-0.318290\pi$
$114$	−5.06754	+	1.95234i	−0.474619	+	0.182854i
$115$	2.39752	−	1.32059i	0.223570	−	0.123146i
$116$	−54.5146	−	5.72972i	−5.06155	−	0.531991i
$117$	−1.93565	−	0.980321i	−0.178951	−	0.0906307i
$118$	−12.2103	+	12.2103i	−1.12405	+	1.12405i
$119$	13.0221	−	2.14075i	1.19373	−	0.196242i
$120$	35.6629	−	15.0767i	3.25556	−	1.37631i
$121$	7.15546	+	7.94694i	0.650496	+	0.722450i
$122$	−2.40491	+	3.70323i	−0.217730	+	0.335275i
$123$	2.40946	−	1.75507i	0.217253	−	0.158249i
$124$	−22.6325	−	13.0669i	−2.03246	−	1.17344i
$125$	4.46528	+	10.2499i	0.399387	+	0.916782i
$126$	20.3909	−	8.02206i	1.81656	−	0.714662i
$127$	−10.5617	−	1.67280i	−0.937197	−	0.148437i	−0.330891	−	0.943669i	$-0.607349\pi$
$127$	−10.5617	−	1.67280i	−0.937197	−	0.148437i	−0.606306	+	0.795231i	$0.707349\pi$
$128$	−2.67554	+	51.0524i	−0.236487	+	4.51244i
$129$	14.8240	−	7.57602i	1.30518	−	0.667031i
$130$	2.73928	+	3.52553i	0.240250	+	0.309209i
$131$	−1.80487	+	8.49126i	−0.157693	+	0.741885i	0.826236	+	0.563324i	$0.190478\pi$
$131$	−1.80487	+	8.49126i	−0.157693	+	0.741885i	−0.983929	+	0.178561i	$0.942856\pi$
$132$	−4.67012	−	2.68870i	−0.406482	−	0.234021i
$133$	2.99018	+	0.296586i	0.259282	+	0.0257173i
$134$	14.2719	+	10.3691i	1.23290	+	0.895757i
$135$	2.82197	+	11.2710i	0.242877	+	0.970057i
$136$	−45.5542	−	20.2820i	−3.90624	−	1.73917i
$137$	2.30305	+	2.84402i	0.196762	+	0.242981i	0.865972	−	0.500092i	$-0.166701\pi$
$137$	2.30305	+	2.84402i	0.196762	+	0.242981i	−0.669210	+	0.743074i	$0.733367\pi$
$138$	−5.82184	−	0.604717i	−0.495588	−	0.0514770i
$139$	−3.00813	−	4.14033i	−0.255146	−	0.351178i	0.662159	−	0.749363i	$-0.269640\pi$
$139$	−3.00813	−	4.14033i	−0.255146	−	0.351178i	−0.917305	+	0.398185i	$0.869640\pi$
$140$	−33.1822	−	2.21432i	−2.80440	−	0.187144i
$141$	−14.8529	−	5.68070i	−1.25084	−	0.478401i
$142$	7.89718	+	12.1606i	0.662716	+	1.02049i
$143$	0.103605	−	0.386657i	0.00866385	−	0.0323339i
$144$	−48.0213	−	10.0848i	−4.00177	−	0.840400i
$145$	−14.0604	+	16.6657i	−1.16765	+	1.38401i
$146$	−28.2585	−	9.18175i	−2.33869	−	0.759887i
$147$	−12.0733	−	1.11129i	−0.995791	−	0.0916575i
$148$	−7.02228	+	44.3369i	−0.577228	+	3.64447i
$149$	7.77792	−	13.4717i	0.637192	−	1.10365i	−0.348854	−	0.937177i	$-0.613429\pi$
$149$	7.77792	−	13.4717i	0.637192	−	1.10365i	0.986046	−	0.166472i	$-0.0532374\pi$
$150$	4.65885	−	23.4498i	0.380393	−	1.91467i
$151$	−4.94845	−	8.57097i	−0.402699	−	0.697496i	0.591351	−	0.806414i	$-0.298595\pi$
$151$	−4.94845	−	8.57097i	−0.402699	−	0.697496i	−0.994051	+	0.108918i	$0.965261\pi$
$152$	−8.82376	−	7.14534i	−0.715702	−	0.579564i
$153$	8.11924	−	12.5696i	0.656401	−	1.01619i
$154$	2.22157	+	3.37744i	0.179019	+	0.272162i
$155$	−9.35569	+	4.53212i	−0.751467	+	0.364028i
$156$	−0.377120	−	7.03169i	−0.0301938	−	0.562985i
$157$	−3.04035	+	11.3468i	−0.242647	+	0.905570i	0.731905	+	0.681407i	$0.238631\pi$
$157$	−3.04035	+	11.3468i	−0.242647	+	0.905570i	−0.974552	+	0.224163i	$0.928035\pi$
$158$	−12.1819	+	0.638428i	−0.969142	+	0.0507906i
$159$	−0.577053	−	0.710826i	−0.0457633	−	0.0563722i
$160$	44.8398	+	33.9778i	3.54490	+	2.68618i
$161$	2.72645	+	1.74796i	0.214874	+	0.137759i
$162$	8.79068	−	23.2389i	0.690661	−	1.82582i
$163$	3.44216	−	8.96715i	0.269611	−	0.702361i	−0.730206	−	0.683227i	$-0.760576\pi$
$163$	3.44216	−	8.96715i	0.269611	−	0.702361i	0.999817	−	0.0191338i	$-0.00609083\pi$
$164$	8.83796	+	3.93492i	0.690129	+	0.307265i
$165$	−1.92801	+	0.936880i	−0.150095	+	0.0729360i
$166$	5.20710	−	2.31835i	0.404149	−	0.179939i
$167$	−10.4884	−	5.34410i	−0.811616	−	0.413539i	−0.00163756	−	0.999999i	$-0.500521\pi$
$167$	−10.4884	−	5.34410i	−0.811616	−	0.413539i	−0.809978	+	0.586460i	$0.800521\pi$
$168$	35.8063	+	28.5782i	2.76252	+	2.20486i
$169$	−11.8662	+	3.85558i	−0.912788	+	0.296583i
$170$	−26.1557	+	16.2467i	−2.00605	+	1.24606i
$171$	2.52646	−	2.28603i	0.193203	−	0.174817i
$172$	45.3129	+	29.4266i	3.45508	+	2.24375i
$173$	12.8001	−	15.8068i	0.973174	−	1.20177i	−0.00625547	−	0.999980i	$-0.501991\pi$
$173$	12.8001	−	15.8068i	0.973174	−	1.20177i	0.979429	−	0.201789i	$-0.0646755\pi$
$174$	45.0235	−	12.1229i	3.41322	−	0.919036i
$175$	−8.13919	+	10.4285i	−0.615265	+	0.788320i
$176$		−	9.05273i		−	0.682375i
$177$	4.39451	−	9.90273i	0.330312	−	0.744335i
$178$	2.29334	−	3.53143i	0.171893	−	0.264692i
$179$	3.74975	−	0.797033i	0.280269	−	0.0595731i	−0.0656323	−	0.997844i	$-0.520906\pi$
$179$	3.74975	−	0.797033i	0.280269	−	0.0595731i	0.345902	+	0.938271i	$0.387573\pi$
$180$	−27.1316	+	26.1883i	−2.02227	+	1.95196i
$181$	1.22106	+	3.75805i	0.0907610	+	0.279334i	0.986126	−	0.166000i	$-0.0530851\pi$
$181$	1.22106	+	3.75805i	0.0907610	+	0.279334i	−0.895365	+	0.445333i	$0.853085\pi$
$182$	−2.12034	+	4.83842i	−0.157170	+	0.358648i
$183$	0.572683	−	2.71052i	0.0423339	−	0.200367i
$184$	−4.97743	−	11.1795i	−0.366941	−	0.824164i
$185$	13.0267	+	12.2130i	0.957745	+	0.897917i
$186$	21.9606	+	3.45075i	1.61023	+	0.253021i
$187$	2.57732	+	0.989342i	0.188473	+	0.0723479i
$188$	−8.07353	−	50.9742i	−0.588822	−	3.71768i
$189$	−10.1285	+	9.29584i	−0.736743	+	0.676173i
$190$	−6.71002	+	2.03183i	−0.486796	+	0.147405i
$191$	10.9968	+	24.6993i	0.795702	+	1.78718i	0.587762	+	0.809034i	$0.300009\pi$
$191$	10.9968	+	24.6993i	0.795702	+	1.78718i	0.207940	+	0.978142i	$0.433324\pi$
$192$	−19.7413	−	60.5061i	−1.42470	−	4.36665i
$193$	1.83066	+	0.490524i	0.131774	+	0.0353087i	0.324103	−	0.946022i	$-0.394937\pi$
$193$	1.83066	+	0.490524i	0.131774	+	0.0353087i	−0.192329	+	0.981330i	$0.561604\pi$
$194$	−8.48321	−	1.80316i	−0.609059	−	0.129460i
$195$	−2.39893	−	1.44618i	−0.171791	−	0.103563i
$196$	−16.4246	−	35.7572i	−1.17319	−	2.55408i
$197$	−5.93519	−	11.6485i	−0.422865	−	0.829919i	−0.999913	−	0.0132088i	$-0.995795\pi$
$197$	−5.93519	−	11.6485i	−0.422865	−	0.829919i	0.577048	−	0.816710i	$-0.304205\pi$
$198$	4.52916	+	0.706021i	0.321873	+	0.0501747i
$199$	20.2562	−	11.6949i	1.43593	−	0.829032i	0.438362	−	0.898798i	$-0.355559\pi$
$199$	20.2562	−	11.6949i	1.43593	−	0.829032i	0.997563	+	0.0697664i	$0.0222254\pi$
$200$	47.3490	−	16.0205i	3.34808	−	1.13282i
$201$	−10.6944	−	2.85157i	−0.754324	−	0.201134i
$202$	−30.5696	−	4.84175i	−2.15087	−	0.340664i
$203$	−25.2667	−	5.21614i	−1.77338	−	0.366101i
$204$	48.5009	+	2.48248i	3.39574	+	0.173808i
$205$	3.26901	−	2.03056i	0.228318	−	0.141820i
$206$	−9.12186	−	8.21336i	−0.635550	−	0.572252i
$207$	3.54483	−	0.959113i	0.246383	−	0.0666630i
$208$	9.92116	−	6.44288i	0.687909	−	0.446733i
$209$	0.508543	+	0.369478i	0.0351767	+	0.0255573i
$210$	27.0157	−	8.38968i	1.86426	−	0.578943i
$211$	9.41299	−	6.83894i	0.648017	−	0.470812i	−0.214578	−	0.976707i	$-0.568838\pi$
$211$	9.41299	−	6.83894i	0.648017	−	0.470812i	0.862595	+	0.505895i	$0.168838\pi$
$212$	1.06486	−	2.77407i	0.0731352	−	0.190524i
$213$	−7.36634	−	5.33824i	−0.504733	−	0.365770i
$214$	−2.35998	+	5.30061i	−0.161325	+	0.362342i
$215$	19.8061	−	8.34467i	1.35076	−	0.569102i
$216$	51.2771	−	8.31405i	3.48897	−	0.565699i
$217$	−9.99330	−	7.17152i	−0.678390	−	0.486834i
$218$	13.4689	+	13.4689i	0.912232	+	0.912232i
$219$	18.6151	−	0.998358i	1.25789	−	0.0674628i
$220$	−5.75710	−	3.90568i	−0.388144	−	0.263321i
$221$	0.750046	+	3.52869i	0.0504535	+	0.237365i
$222$	−7.98454	−	37.3402i	−0.535887	−	2.50611i
$223$	3.51695	−	22.2051i	0.235512	−	1.48697i	−0.532444	−	0.846465i	$-0.678726\pi$
$223$	3.51695	−	22.2051i	0.235512	−	1.48697i	0.767957	−	0.640502i	$-0.221274\pi$
$224$	−10.0281	+	65.8071i	−0.670032	+	4.39692i
$225$	2.56168	+	14.7796i	0.170779	+	0.985309i
$226$	−21.9084	+	37.9465i	−1.45733	+	2.52416i
$227$	−14.1295	+	5.42380i	−0.937806	+	0.359990i	−0.778789	−	0.627286i	$-0.784166\pi$
$227$	−14.1295	+	5.42380i	−0.937806	+	0.359990i	−0.159017	+	0.987276i	$0.550832\pi$
$228$	10.5208	+	3.40423i	0.696757	+	0.225450i
$229$	−1.76678	+	1.59082i	−0.116752	+	0.105124i	−0.725439	−	0.688286i	$-0.758363\pi$
$229$	−1.76678	+	1.59082i	−0.116752	+	0.105124i	0.608687	+	0.793411i	$0.291697\pi$
$230$	−7.43806	−	1.33207i	−0.490451	−	0.0878341i
$231$	−2.06243	−	1.47626i	−0.135698	−	0.0971306i
$232$	68.9326	+	68.9326i	4.52565	+	4.52565i
$233$	−6.03595	−	9.29455i	−0.395428	−	0.608906i	0.583744	−	0.811938i	$-0.301587\pi$
$233$	−6.03595	−	9.29455i	−0.395428	−	0.608906i	−0.979172	+	0.203032i	$0.934921\pi$
$234$	2.44968	+	5.46612i	0.160140	+	0.357331i
$235$	−18.5828	−	8.72596i	−1.21221	−	0.569219i
$236$	34.9686	−	3.67535i	2.27626	−	0.239245i
$237$	6.98798	−	3.12147i	0.453918	−	0.202762i
$238$	−31.6573	−	18.0310i	−2.05204	−	1.16878i
$239$	−6.29590	+	4.57424i	−0.407248	+	0.295883i	−0.772487	−	0.635031i	$-0.780987\pi$
$239$	−6.29590	+	4.57424i	−0.407248	+	0.295883i	0.365239	+	0.930914i	$0.380987\pi$
$240$	−60.8681	−	17.5496i	−3.92902	−	1.13282i
$241$	2.25714	−	21.4752i	0.145395	−	1.38334i	−0.641912	−	0.766778i	$-0.721859\pi$
$241$	2.25714	−	21.4752i	0.145395	−	1.38334i	0.787307	−	0.616561i	$-0.211475\pi$
$242$	−1.54504	−	29.4812i	−0.0993192	−	1.89512i
$243$	0.0951166	+	15.5882i	0.00610173	+	0.999981i
$244$	8.55101	−	2.77839i	0.547422	−	0.177868i
$245$	−15.4386	−	2.57862i	−0.986337	−	0.164742i
$246$	−8.21851	−	0.420657i	−0.523993	−	0.0268201i
$247$	−0.0429894	+	0.820287i	−0.00273535	+	0.0521936i
$248$	16.6560	+	43.3904i	1.05766	+	2.75530i
$249$	−2.52561	+	2.53178i	−0.160054	+	0.160445i
$250$	8.22767	−	29.7484i	0.520363	−	1.88145i
$251$		−	19.1189i		−	1.20677i	−0.797449	−	0.603387i	$-0.793818\pi$
$251$		−	19.1189i		−	1.20677i	0.797449	−	0.603387i	$-0.206182\pi$
$252$	−42.5468	−	13.4350i	−2.68019	−	0.846327i
$253$	0.307580	+	0.603660i	0.0193374	+	0.0379518i
$254$	19.7532	+	21.9382i	1.23943	+	1.37652i
$255$	11.6485	−	15.4113i	0.729455	−	0.965092i
$256$	45.2607	−	50.2671i	2.82879	−	3.14169i
$257$	−3.64755	−	13.6128i	−0.227528	−	0.849145i	−0.981376	−	0.192097i	$-0.938471\pi$
$257$	−3.64755	−	13.6128i	−0.227528	−	0.849145i	0.753848	−	0.657049i	$-0.228195\pi$
$258$	−44.9662	−	9.50053i	−2.79948	−	0.591477i
$259$	−5.34872	+	20.4398i	−0.332354	+	1.27007i
$260$	0.182990	−	9.08907i	0.0113485	−	0.563680i
$261$	−23.6249	+	17.2527i	−1.46234	+	1.06792i
$262$	18.6245	−	15.0818i	1.15063	−	0.931758i
$263$	−16.3209	+	13.2164i	−1.00639	+	0.814957i	−0.982783	−	0.184765i	$-0.940848\pi$
$263$	−16.3209	+	13.2164i	−1.00639	+	0.814957i	−0.0236049	+	0.999721i	$0.507514\pi$
$264$	3.44540	+	8.94295i	0.212050	+	0.550401i
$265$	−0.675369	−	0.970043i	−0.0414876	−	0.0595893i
$266$	−5.89999	−	5.83128i	−0.361752	−	0.357539i
$267$	−0.546115	+	2.58477i	−0.0334217	+	0.158186i
$268$	−9.29697	−	34.6968i	−0.567903	−	2.11944i
$269$	−10.8193	+	12.0160i	−0.659664	+	0.732631i	−0.976421	−	0.215876i	$-0.930739\pi$
$269$	−10.8193	+	12.0160i	−0.659664	+	0.732631i	0.316757	+	0.948507i	$0.397406\pi$
$270$	13.5273	−	29.0841i	0.823246	−	1.77000i
$271$	−15.6305	−	17.3594i	−0.949485	−	1.05451i	−0.998447	−	0.0557088i	$-0.982258\pi$
$271$	−15.6305	−	17.3594i	−0.949485	−	1.05451i	0.0489625	−	0.998801i	$-0.484409\pi$
$272$	37.0384	+	72.6920i	2.24579	+	4.40760i
$273$	0.150032	−	3.31094i	0.00908033	−	0.200387i
$274$		−	10.1029i		−	0.610337i
$275$	−2.57136	+	1.02292i	−0.155059	+	0.0616844i
$276$	8.43774	+	8.41717i	0.507892	+	0.506654i
$277$	−3.08442	−	8.03519i	−0.185325	−	0.482788i	0.809170	−	0.587575i	$-0.199917\pi$
$277$	−3.08442	−	8.03519i	−0.185325	−	0.482788i	−0.994495	+	0.104787i	$0.966584\pi$
$278$	−0.739421	+	14.1090i	−0.0443475	+	0.846201i
$279$	−13.6353	+	2.93307i	−0.816324	+	0.175599i
$280$	43.3832	+	40.1984i	2.59264	+	2.40231i
$281$	9.32499	−	3.02987i	0.556282	−	0.180747i	−0.0173655	−	0.999849i	$-0.505528\pi$
$281$	9.32499	−	3.02987i	0.556282	−	0.180747i	0.573648	+	0.819102i	$0.305528\pi$
$282$	21.9967	+	37.9922i	1.30988	+	2.26240i
$283$	1.34728	+	25.7077i	0.0800876	+	1.52816i	0.683038	+	0.730383i	$0.260658\pi$
$283$	1.34728	+	25.7077i	0.0800876	+	1.52816i	−0.602950	+	0.797779i	$0.706008\pi$
$284$	3.08616	−	29.3629i	0.183130	−	1.74237i
$285$	3.47013	−	2.70303i	0.205553	−	0.160114i
$286$	−0.894035	+	0.649554i	−0.0528654	+	0.0384089i
$287$	3.95662	+	2.25357i	0.233552	+	0.133024i
$288$	47.6439	+	58.5426i	2.80744	+	3.44966i
$289$	−7.83644	+	0.823644i	−0.460967	+	0.0484496i
$290$	59.1198	−	11.3276i	3.47163	−	0.665178i
$291$	5.37326	−	0.857764i	0.314986	−	0.0502830i
$292$	32.9514	+	50.7406i	1.92833	+	2.96937i
$293$	5.04769	+	5.04769i	0.294889	+	0.294889i	0.839008	−	0.544119i	$-0.183136\pi$
$293$	5.04769	+	5.04769i	0.294889	+	0.294889i	−0.544119	+	0.839008i	$0.683136\pi$
$294$	23.9719	+	23.3597i	1.39807	+	1.36237i
$295$	6.59937	−	12.3319i	0.384230	−	0.717989i
$296$	59.3281	−	53.4192i	3.44837	−	3.10493i
$297$	−2.81087	+	0.608233i	−0.163103	+	0.0352933i
$298$	−40.0921	+	15.3899i	−2.32247	+	0.891515i
$299$	−0.442662	+	0.766714i	−0.0255998	+	0.0443402i
$300$	−37.4214	+	31.1376i	−2.16053	+	1.79773i
$301$	19.8561	+	15.8875i	1.14449	+	0.915742i
$302$	−4.27411	+	26.9857i	−0.245948	+	1.55285i
$303$	18.9893	−	4.06052i	1.09090	−	0.233271i
$304$	3.86223	+	18.1703i	0.221514	+	1.04214i
$305$	0.995022	−	3.43532i	0.0569748	−	0.196706i
$306$	−39.2570	+	12.8614i	−2.24418	+	0.735237i
$307$	−20.8405	−	20.8405i	−1.18943	−	1.18943i	−0.977225	−	0.212205i	$-0.931935\pi$
$307$	−20.8405	−	20.8405i	−1.18943	−	1.18943i	−0.212205	−	0.977225i	$-0.568065\pi$
$308$	0.812470	−	8.19133i	0.0462948	−	0.466744i
$309$	7.19302	+	2.75107i	0.409197	+	0.156503i
$310$	27.9459	+	6.53067i	1.58722	+	0.370917i
$311$	−8.56708	+	19.2420i	−0.485795	+	1.09111i	0.489860	+	0.871801i	$0.337048\pi$
$311$	−8.56708	+	19.2420i	−0.485795	+	1.09111i	−0.975655	+	0.219312i	$0.929619\pi$
$312$	−7.34873	+	10.1407i	−0.416040	+	0.574102i
$313$	−2.11354	+	5.50597i	−0.119465	+	0.311216i	−0.980253	−	0.197747i	$-0.936638\pi$
$313$	−2.11354	+	5.50597i	−0.119465	+	0.311216i	0.860789	+	0.508963i	$0.169971\pi$
$314$	26.2361	−	19.0617i	1.48059	−	1.07571i
$315$	−13.9242	+	11.0053i	−0.784538	+	0.620081i
$316$	20.0951	+	14.6000i	1.13044	+	0.821312i
$317$	−11.3144	+	7.34763i	−0.635477	+	0.412684i	−0.821777	−	0.569809i	$-0.807017\pi$
$317$	−11.3144	+	7.34763i	−0.635477	+	0.412684i	0.186300	+	0.982493i	$0.440350\pi$
$318$	0.00308454	+	2.52758i	0.000172972	+	0.141739i
$319$	−4.01081	−	3.61135i	−0.224562	−	0.202197i
$320$	−19.6642	−	79.7778i	−1.09926	−	4.45971i
$321$	0.186084	−	3.63558i	0.0103862	−	0.202919i
$322$	−2.81263	−	8.48693i	−0.156742	−	0.472958i
$323$	−5.59521	−	0.886194i	−0.311326	−	0.0493091i
$324$	−43.6896	+	25.5093i	−2.42720	+	1.41719i
$325$	−2.95110	−	2.09002i	−0.163698	−	0.115933i
$326$	−22.9640	+	13.2583i	−1.27186	+	0.734307i
$327$	−10.9235	−	4.84748i	−0.604070	−	0.268066i
$328$	−7.81106	−	15.3301i	−0.431294	−	0.846461i
$329$	−1.41333	−	24.2498i	−0.0779196	−	1.33693i
$330$	5.76412	+	1.33960i	0.317304	+	0.0737424i
$331$	12.1411	+	2.58068i	0.667337	+	0.141847i	0.529109	−	0.848554i	$-0.322526\pi$
$331$	12.1411	+	2.58068i	0.667337	+	0.141847i	0.138227	+	0.990401i	$0.455860\pi$
$332$	−11.2107	−	3.00389i	−0.615264	−	0.164860i
$333$	13.0969	+	20.0601i	0.717705	+	1.09929i
$334$	13.2177	+	29.6874i	0.723239	+	1.62442i
$335$	−13.4978	−	4.68812i	−0.737463	−	0.256139i
$336$	−16.1022	−	73.2038i	−0.878449	−	3.99359i
$337$	−1.74894	−	11.0424i	−0.0952709	−	0.601517i	−0.988418	−	0.151753i	$-0.951508\pi$
$337$	−1.74894	−	11.0424i	−0.0952709	−	0.601517i	0.893148	−	0.449764i	$-0.148492\pi$
$338$	32.1568	+	12.3438i	1.74910	+	0.671417i
$339$	4.26737	−	27.1576i	0.231772	−	1.47500i
$340$	62.2084	+	7.80732i	3.37372	+	0.423411i
$341$	−1.04659	−	2.35067i	−0.0566758	−	0.127296i
$342$	−9.39199	+	0.515202i	−0.507860	+	0.0278589i
$343$	−6.03164	−	17.5105i	−0.325678	−	0.945481i
$344$	−29.6930	−	91.3857i	−1.60094	−	4.92719i
$345$	4.65511	−	0.897828i	0.250623	−	0.0483374i
$346$	−54.9237	+	11.6744i	−2.95272	+	0.627620i
$347$	−4.68198	+	7.20962i	−0.251342	+	0.387032i	−0.941710	−	0.336426i	$-0.890782\pi$
$347$	−4.68198	+	7.20962i	−0.251342	+	0.387032i	0.690368	+	0.723458i	$0.257449\pi$
$348$	−86.7811	−	38.5106i	−4.65195	−	2.06438i
$349$			9.64169i			0.516108i	0.966131	+	0.258054i	$0.0830812\pi$
$349$			9.64169i			0.516108i	−0.966131	+	0.258054i	$0.916919\pi$
$350$	35.5801	−	8.23314i	1.90183	−	0.440080i
$351$	−2.66709	−	2.64763i	−0.142359	−	0.141320i
$352$	−8.76347	+	10.8220i	−0.467095	+	0.576814i
$353$	0.101935	+	0.0661971i	0.00542543	+	0.00352331i	0.547349	−	0.836905i	$-0.315637\pi$
$353$	0.101935	+	0.0661971i	0.00542543	+	0.00352331i	−0.541923	+	0.840428i	$0.682304\pi$
$354$	−26.6326	+	13.6110i	−1.41551	+	0.723415i
$355$	−8.97656	−	7.57327i	−0.476426	−	0.401947i
$356$	−8.15431	+	2.64950i	−0.432177	+	0.140423i
$357$	22.6010	+	3.41586i	1.19617	+	0.180787i
$358$	−9.42958	−	4.80461i	−0.498369	−	0.253932i
$359$	−4.76893	+	2.12326i	−0.251694	+	0.112062i	−0.528706	−	0.848805i	$-0.677323\pi$
$359$	−4.76893	+	2.12326i	−0.251694	+	0.112062i	0.277012	+	0.960867i	$0.410656\pi$
$360$	66.8092	−	5.82914i	3.52115	−	0.307223i
$361$	16.1790	+	7.20336i	0.851526	+	0.379124i
$362$	3.90930	−	10.1841i	0.205468	−	0.535264i
$363$	7.55421	+	16.9115i	0.396493	+	0.887622i
$364$	9.55536	−	4.93940i	0.500837	−	0.258895i
$365$	24.0617	+	0.484432i	1.25945	+	0.0253563i
$366$	−5.93777	+	4.82032i	−0.310372	+	0.251962i
$367$	2.82168	−	0.147878i	0.147290	−	0.00771917i	0.0214518	−	0.999770i	$-0.493171\pi$
$367$	2.82168	−	0.147878i	0.147290	−	0.00771917i	0.125839	+	0.992051i	$0.459838\pi$
$368$	−5.18198	+	19.3394i	−0.270130	+	1.00814i
$369$	4.90646	−	1.60746i	0.255420	−	0.0836808i
$370$	−6.72994	−	48.8342i	−0.349873	−	2.53877i
$371$	0.627621	−	1.24982i	0.0325845	−	0.0648873i
$372$	−30.3292	−	33.6014i	−1.57249	−	1.74215i
$373$	−4.43933	−	3.59490i	−0.229860	−	0.186137i	0.507471	−	0.861669i	$-0.330581\pi$
$373$	−4.43933	−	3.59490i	−0.229860	−	0.186137i	−0.737331	+	0.675532i	$0.763914\pi$
$374$	−3.81067	−	6.60028i	−0.197045	−	0.341292i
$375$	1.89298	+	19.2722i	0.0977530	+	0.995211i
$376$	−45.8925	+	79.4882i	−2.36673	+	4.09929i
$377$	1.10327	−	6.96578i	0.0568214	−	0.358756i
$378$	37.8803	−	2.34693i	1.94835	−	0.120713i
$379$	−10.8933	−	3.53945i	−0.559551	−	0.181809i	0.0155680	−	0.999879i	$-0.495044\pi$
$379$	−10.8933	−	3.53945i	−0.559551	−	0.181809i	−0.575119	+	0.818070i	$0.695044\pi$
$380$	13.2218	+	5.38315i	0.678262	+	0.276150i
$381$	−16.5129	−	8.38839i	−0.845983	−	0.429750i
$382$	19.3181	−	72.0961i	0.988399	−	3.68876i
$383$	−7.41635	−	11.4202i	−0.378958	−	0.583544i	0.596802	−	0.802389i	$-0.296438\pi$
$383$	−7.41635	−	11.4202i	−0.378958	−	0.583544i	−0.975760	+	0.218845i	$0.929771\pi$
$384$	−31.6314	+	82.7041i	−1.61418	+	4.22048i
$385$	−2.51500	−	2.09675i	−0.128176	−	0.106860i
$386$	−3.07537	−	4.23288i	−0.156532	−	0.215448i
$387$	28.4687	−	4.58025i	1.44714	−	0.232827i
$388$	11.1135	+	13.7240i	0.564200	+	0.696729i
$389$	18.8841	+	8.40776i	0.957464	+	0.426290i	0.825147	−	0.564917i	$-0.191092\pi$
$389$	18.8841	+	8.40776i	0.957464	+	0.426290i	0.132316	+	0.991208i	$0.457759\pi$
$390$	2.63425	+	7.27047i	0.133390	+	0.368154i
$391$	−4.93964	−	3.58886i	−0.249808	−	0.181496i
$392$	−17.3192	+	67.8031i	−0.874752	+	3.42457i
$393$	−7.50204	+	13.0306i	−0.378428	+	0.657307i
$394$	−7.50380	+	35.3026i	−0.378036	+	1.77852i
$395$	9.29372	−	3.35449i	0.467618	−	0.168783i
$396$	−6.26235	−	6.92100i	−0.314695	−	0.347794i
$397$	0.772135	−	14.7332i	0.0387524	−	0.739439i	−0.908292	−	0.418337i	$-0.862613\pi$
$397$	0.772135	−	14.7332i	0.0387524	−	0.739439i	0.947044	−	0.321103i	$-0.104053\pi$
$398$	−63.7767	−	10.1012i	−3.19684	−	0.506329i
$399$	4.76947	+	2.08319i	0.238772	+	0.104290i
$400$	−76.6985	−	28.3819i	−3.83492	−	1.41909i
$401$	−17.6852	−	10.2106i	−0.883159	−	0.509892i	−0.0114603	−	0.999934i	$-0.503648\pi$
$401$	−17.6852	−	10.2106i	−0.883159	−	0.509892i	−0.871699	+	0.490042i	$0.836981\pi$
$402$	17.9900	+	24.6977i	0.897261	+	1.23181i
$403$	1.83131	−	2.81997i	0.0912240	−	0.140473i
$404$	42.1699	+	46.8344i	2.09803	+	2.33010i
$405$	−1.35956	+	20.0786i	−0.0675572	+	0.997715i
$406$	45.1461	+	55.0880i	2.24056	+	2.73397i
$407$	−3.12529	+	3.12529i	−0.154915	+	0.154915i
$408$	−64.2553	−	57.7139i	−3.18111	−	2.85727i
$409$	2.39108	+	0.251312i	0.118231	+	0.0124266i	0.163459	−	0.986550i	$-0.447735\pi$
$409$	2.39108	+	0.251312i	0.118231	+	0.0124266i	−0.0452280	+	0.998977i	$0.514401\pi$
$410$	−10.5412	−	1.32296i	−0.520595	−	0.0653361i
$411$	2.27876	+	5.91479i	0.112403	+	0.291755i
$412$	3.90988	+	24.6860i	0.192626	+	1.21619i
$413$	16.5489	−	0.0969209i	0.814320	−	0.00476917i
$414$	−9.27153	−	4.10087i	−0.455671	−	0.201547i
$415$	−3.49240	+	3.01952i	−0.171435	+	0.148223i
$416$	−18.0971	−	1.90209i	−0.887286	−	0.0932575i
$417$	−2.74947	−	8.42698i	−0.134642	−	0.412671i
$418$	−0.449139	−	1.67621i	−0.0219681	−	0.0819860i
$419$	2.13501	+	6.57088i	0.104302	+	0.321009i	0.989566	−	0.144080i	$-0.0460223\pi$
$419$	2.13501	+	6.57088i	0.104302	+	0.321009i	−0.885264	+	0.465089i	$0.846022\pi$
$420$	−53.5012	−	21.3425i	−2.61059	−	1.04141i
$421$	4.44762	−	13.6884i	0.216764	−	0.667130i	−0.782260	−	0.622952i	$-0.785933\pi$
$421$	4.44762	−	13.6884i	0.216764	−	0.667130i	0.999024	−	0.0441779i	$-0.0140668\pi$
$422$	−32.0766	−	1.68106i	−1.56146	−	0.0818329i
$423$	−21.4474	−	17.2813i	−1.04281	−	0.840245i
$424$	−4.57654	+	2.64227i	−0.222256	+	0.128320i
$425$	16.4625	−	18.7344i	0.798547	−	0.908751i
$426$	6.52970	+	24.2507i	0.316365	+	1.17495i
$427$	4.13409	−	0.904066i	0.200063	−	0.0437508i
$428$	10.5268	−	5.36370i	0.508834	−	0.259264i
$429$	0.376908	−	0.581940i	0.0181973	−	0.0280963i
$430$	−56.9903	−	16.5069i	−2.74832	−	0.796035i
$431$	21.8596	+	19.6824i	1.05294	+	0.948070i	0.998726	−	0.0504598i	$-0.0160687\pi$
$431$	21.8596	+	19.6824i	1.05294	+	0.948070i	0.0542120	+	0.998529i	$0.482735\pi$
$432$	−73.7583	−	42.2251i	−3.54870	−	2.03155i
$433$	20.9155	+	10.6570i	1.00513	+	0.512142i	0.877448	−	0.479673i	$-0.159245\pi$
$433$	20.9155	+	10.6570i	1.00513	+	0.512142i	0.127687	+	0.991814i	$0.459245\pi$
$434$	8.98065	+	32.7479i	0.431085	+	1.57195i
$435$	−32.0571	+	19.9666i	−1.53702	+	0.957326i
$436$	−4.05420	−	38.5731i	−0.194161	−	1.84732i
$437$	−0.874907	−	1.08042i	−0.0418525	−	0.0516835i
$438$	−41.6722	−	30.1990i	−1.99117	−	1.44296i
$439$	1.62087	−	0.170360i	0.0773598	−	0.00813084i	−0.0657695	−	0.997835i	$-0.520950\pi$
$439$	1.62087	−	0.170360i	0.0773598	−	0.00813084i	0.143129	+	0.989704i	$0.454284\pi$
$440$	3.58568	+	11.8415i	0.170941	+	0.564522i
$441$	−19.3034	−	8.26909i	−0.919211	−	0.393766i
$442$	4.52137	−	8.87368i	0.215059	−	0.422078i
$443$	−13.9481	+	3.73739i	−0.662696	+	0.177569i	−0.574463	−	0.818531i	$-0.694789\pi$
$443$	−13.9481	+	3.73739i	−0.662696	+	0.177569i	−0.0882337	+	0.996100i	$0.528122\pi$
$444$	−35.2137	+	69.3197i	−1.67117	+	3.28977i
$445$	−0.948861	+	3.27595i	−0.0449803	+	0.155295i
$446$	−46.1234	+	41.5297i	−2.18401	+	1.96649i
$447$	20.0009	−	18.0531i	0.946010	−	0.853884i
$448$	71.8660	−	65.4746i	3.39535	−	3.09338i
$449$	2.95735			0.139566			0.0697831	−	0.997562i	$-0.477769\pi$
$449$	2.95735			0.139566			0.0697831	+	0.997562i	$0.477769\pi$
$450$	20.1814	−	36.1594i	0.951360	−	1.70457i
$451$	0.476269	+	0.824922i	0.0224266	+	0.0388441i
$452$	83.2941	−	31.9736i	3.91782	−	1.50391i
$453$	−3.58447	−	16.7630i	−0.168413	−	0.787594i
$454$	39.7370	+	12.9113i	1.86495	+	0.605958i
$455$	0.507947	−	4.24853i	0.0238129	−	0.199174i
$456$	−10.7309	−	16.4801i	−0.502520	−	0.771749i
$457$	3.20322	−	0.858300i	0.149840	−	0.0401496i	−0.183119	−	0.983091i	$-0.558619\pi$
$457$	3.20322	−	0.858300i	0.149840	−	0.0401496i	0.332959	+	0.942941i	$0.391953\pi$
$458$	6.55433	−	0.343498i	0.306264	−	0.0160506i
$459$	20.0823	−	16.3844i	0.937362	−	0.764760i
$460$	10.0632	+	11.6392i	0.469201	+	0.542681i
$461$	8.19474	+	11.2791i	0.381667	+	0.525320i	0.956025	−	0.293284i	$-0.0947482\pi$
$461$	8.19474	+	11.2791i	0.381667	+	0.525320i	−0.574358	+	0.818604i	$0.694748\pi$
$462$	1.86006	+	6.75037i	0.0865377	+	0.314056i
$463$	−4.37251	+	0.692537i	−0.203208	+	0.0321849i	−0.257208	−	0.966356i	$-0.582803\pi$
$463$	−4.37251	+	0.692537i	−0.203208	+	0.0321849i	0.0540007	+	0.998541i	$0.482803\pi$
$464$	−16.6718	−	158.621i	−0.773968	−	7.36381i
$465$	−17.8342	+	2.47994i	−0.827039	+	0.115005i
$466$	−3.19805	+	30.4274i	−0.148147	+	1.40952i
$467$	12.5416	−	8.14461i	0.580356	−	0.376888i	−0.220822	−	0.975314i	$-0.570874\pi$
$467$	12.5416	−	8.14461i	0.580356	−	0.376888i	0.801178	+	0.598427i	$0.204207\pi$
$468$	3.12799	−	11.7888i	0.144591	−	0.544938i
$469$	−2.74254	−	16.6828i	−0.126639	−	0.770339i
$470$	24.7084	+	51.0058i	1.13971	+	2.35272i
$471$	−11.0606	+	17.0775i	−0.509647	+	0.786888i
$472$	−52.4441	−	34.0576i	−2.41394	−	1.56763i
$473$	1.90643	+	4.96641i	0.0876576	+	0.228356i
$474$	−20.4154	−	5.44359i	−0.937710	−	0.250032i
$475$	4.72474	−	3.15021i	0.216786	−	0.144541i
$476$	26.9901	+	69.0992i	1.23709	+	3.16716i
$477$	−0.571915	−	1.47909i	−0.0261862	−	0.0677229i
$478$	21.4545	+	1.12438i	0.981306	+	0.0514281i
$479$	−32.6566	+	6.94137i	−1.49212	+	0.317159i	−0.880519	−	0.474010i	$-0.842806\pi$
$479$	−32.6566	+	6.94137i	−1.49212	+	0.317159i	−0.611597	+	0.791169i	$0.709473\pi$
$480$	55.7752	+	79.9026i	2.54578	+	3.64704i
$481$	−5.64939	−	1.20081i	−0.257590	−	0.0547524i
$482$	−42.1524	+	42.1524i	−1.91999	+	1.91999i
$483$	3.56094	+	4.33432i	0.162029	+	0.197218i
$484$	−35.3330	+	48.6318i	−1.60605	+	2.21053i
$485$	6.99957	−	0.593507i	0.317834	−	0.0269497i
$486$	26.8779	−	33.6088i	1.21921	−	1.52452i
$487$	−28.9052	+	23.4070i	−1.30982	+	1.06067i	−0.316107	+	0.948723i	$0.602376\pi$
$487$	−28.9052	+	23.4070i	−1.30982	+	1.06067i	−0.993714	+	0.111949i	$0.964291\pi$
$488$	−14.9281	−	5.73035i	−0.675762	−	0.259401i
$489$	10.4539	−	12.9418i	0.472743	−	0.585248i
$490$	28.6427	+	32.3545i	1.29394	+	1.46163i
$491$	−14.0428	+	19.3282i	−0.633742	+	0.872271i	−0.998262	−	0.0589242i	$-0.981233\pi$
$491$	−14.0428	+	19.3282i	−0.633742	+	0.872271i	0.364520	+	0.931195i	$0.381233\pi$
$492$	12.4662	+	11.1971i	0.562018	+	0.504803i
$493$	46.9817	+	12.5887i	2.11595	+	0.566967i
$494$	1.51735	−	1.68519i	0.0682689	−	0.0758203i
$495$	−3.67679	+	0.515854i	−0.165260	+	0.0231859i
$496$	23.4981	−	72.3196i	1.05509	−	3.24725i
$497$	2.80954	−	13.6093i	0.126025	−	0.610460i
$498$	9.81713	−	1.04394i	0.439916	−	0.0467799i
$499$	20.6254	+	11.9081i	0.923319	+	0.533078i	0.884692	−	0.466175i	$-0.154368\pi$
$499$	20.6254	+	11.9081i	0.923319	+	0.533078i	0.0386263	+	0.999254i	$0.487702\pi$
$500$	−51.1400	+	36.5315i	−2.28705	+	1.63374i
$501$	−14.4345	−	14.3994i	−0.644888	−	0.643316i
$502$	−33.2161	+	41.0185i	−1.48251	+	1.83074i
$503$	20.6856	−	10.5398i	0.922325	−	0.469948i	0.0727107	−	0.997353i	$-0.476835\pi$
$503$	20.6856	−	10.5398i	0.922325	−	0.469948i	0.849614	+	0.527405i	$0.176835\pi$
$504$	43.7678	+	66.1876i	1.94957	+	2.94823i
$505$	24.8345	−	3.42249i	1.10512	−	0.152299i
$506$	0.388870	−	1.82949i	0.0172874	−	0.0813307i
$507$	−21.6106	+	0.0263726i	−0.959762	+	0.00117125i
$508$	−3.14593	−	60.0279i	−0.139578	−	2.66331i
$509$	25.1100	−	11.1797i	1.11298	−	0.495532i	0.233929	−	0.972254i	$-0.424842\pi$
$509$	25.1100	−	11.1797i	1.11298	−	0.495532i	0.879054	+	0.476722i	$0.158175\pi$
$510$	−51.7658	+	12.8266i	−2.29223	+	0.567972i
$511$	13.0762	+	25.2961i	0.578456	+	1.11903i
$512$	−83.4492	+	13.2171i	−3.68797	+	0.584117i
$513$	5.38239	−	2.42004i	0.237638	−	0.106848i
$514$	−15.8246	+	35.5426i	−0.697992	+	1.56772i
$515$	8.99938	+	4.22584i	0.396560	+	0.186213i
$516$	58.9816	+	72.6548i	2.59652	+	3.19845i
$517$	2.30695	−	4.52764i	0.101459	−	0.199125i
$518$	46.9863	−	34.5598i	2.06446	−	1.51847i
$519$	29.5222	−	19.2232i	1.29588	−	0.843805i
$520$	−10.4255	+	12.3573i	−0.457189	+	0.541905i
$521$	−6.09055	−	28.6538i	−0.266832	−	1.25535i	−0.883616	−	0.468213i	$-0.844898\pi$
$521$	−6.09055	−	28.6538i	−0.266832	−	1.25535i	0.616784	−	0.787132i	$-0.288435\pi$
$522$	80.6598	+	4.02982i	3.53038	+	0.176380i
$523$	15.5804	+	12.6168i	0.681284	+	0.551693i	0.906286	−	0.422665i	$-0.138905\pi$
$523$	15.5804	+	12.6168i	0.681284	+	0.551693i	−0.225002	+	0.974358i	$0.572239\pi$
$524$	−48.7982			−2.13176
$525$	−18.9735	+	12.8454i	−0.828073	+	0.560621i
$526$	57.9769			2.52791
$527$	18.0215	+	14.5935i	0.785027	+	0.635703i
$528$	4.82712	−	14.9183i	0.210073	−	0.649235i
$529$	4.47043	+	21.0317i	0.194367	+	0.914423i
$530$	−0.236334	+	3.25452i	−0.0102657	+	0.141367i
$531$	12.5222	−	13.9758i	0.543417	−	0.606497i
$532$	1.86396	+	16.7880i	0.0808128	+	0.727851i
$533$	−0.565094	+	1.10906i	−0.0244769	+	0.0480387i
$534$	5.66230	−	4.59669i	0.245032	−	0.198918i
$535$	0.585230	−	4.66308i	0.0253017	−	0.201603i
$536$	−25.9836	+	58.3602i	−1.12232	+	2.52078i
$537$	6.60432	+	0.685994i	0.284997	+	0.0296028i
$538$	44.0882	−	6.98288i	1.90078	−	0.301053i
$539$	0.761070	−	3.79882i	0.0327816	−	0.163627i
$540$	−58.6751	+	28.6893i	−2.52497	+	1.23459i
$541$	25.7452	−	11.4625i	1.10687	−	0.492812i	0.229834	−	0.973230i	$-0.426182\pi$
$541$	25.7452	−	11.4625i	1.10687	−	0.492812i	0.877040	+	0.480418i	$0.159515\pi$
$542$	3.37502	+	64.3991i	0.144969	+	2.76618i
$543$	0.00835223	+	6.84410i	0.000358429	+	0.293709i
$544$	26.0921	−	122.754i	1.11869	−	5.26302i
$545$	−13.6030	−	7.27961i	−0.582688	−	0.311824i
$546$	−6.07413	+	6.84277i	−0.259949	+	0.292844i
$547$	−27.4784	+	14.0010i	−1.17489	+	0.598637i	−0.928790	−	0.370606i	$-0.879150\pi$
$547$	−27.4784	+	14.0010i	−1.17489	+	0.598637i	−0.246102	+	0.969244i	$0.579150\pi$
$548$	−12.9461	+	15.9871i	−0.553029	+	0.682934i
$549$	2.38905	−	4.16138i	0.101962	−	0.177603i
$550$	7.29388	+	2.27273i	0.311012	+	0.0969096i
$551$	9.59109	+	5.53742i	0.408594	+	0.235902i
$552$	−2.24130	−	21.0771i	−0.0953962	−	0.897102i
$553$	8.73367	+	7.77170i	0.371393	+	0.330486i
$554$	−7.34245	+	22.5977i	−0.311951	+	0.960086i
$555$	14.9549	+	27.0723i	0.634801	+	1.14915i
$556$	19.2497	−	21.3790i	0.816369	−	0.906670i
$557$	−5.18010	−	1.38800i	−0.219488	−	0.0588115i	0.147399	−	0.989077i	$-0.452910\pi$
$557$	−5.18010	−	1.38800i	−0.219488	−	0.0588115i	−0.366887	+	0.930266i	$0.619576\pi$
$558$	34.3495	+	17.3965i	1.45413	+	0.736451i
$559$	−4.08602	+	5.62393i	−0.172820	+	0.237867i
$560$	−13.7717	−	95.7800i	−0.581960	−	4.04744i
$561$	3.71971	+	3.00465i	0.157046	+	0.126857i
$562$	−25.2701	−	9.70030i	−1.06596	−	0.409182i
$563$	8.32634	−	6.74253i	0.350913	−	0.284164i	−0.437615	−	0.899162i	$-0.644177\pi$
$563$	8.32634	−	6.74253i	0.350913	−	0.284164i	0.788528	+	0.614999i	$0.210843\pi$
$564$	13.8760	−	88.3070i	0.584285	−	3.71839i
$565$	8.07616	−	34.5594i	0.339767	−	1.45392i
$566$	41.7725	−	57.4950i	1.75583	−	2.41669i
$567$	−21.6479	+	9.91814i	−0.909125	+	0.416523i
$568$	−37.1288	+	37.1288i	−1.55789	+	1.55789i
$569$	11.8276	+	2.51402i	0.495837	+	0.105393i	0.449041	−	0.893511i	$-0.351766\pi$
$569$	11.8276	+	2.51402i	0.495837	+	0.105393i	0.0467957	+	0.998904i	$0.485099\pi$
$570$	−12.1411	−	0.229613i	−0.508533	−	0.00961743i
$571$	−36.9092	+	7.84529i	−1.54460	+	0.328315i	−0.899892	−	0.436112i	$-0.856355\pi$
$571$	−36.9092	+	7.84529i	−1.54460	+	0.328315i	−0.644710	+	0.764427i	$0.723022\pi$
$572$	2.24710	+	0.117766i	0.0939560	+	0.00492403i
$573$	4.95179	+	46.5664i	0.206864	+	1.94534i
$574$	−4.57349	−	11.7089i	−0.190894	−	0.488720i
$575$	6.07877	−	0.713365i	0.253502	−	0.0297494i
$576$	−0.269055	−	110.236i	−0.0112106	−	4.59318i
$577$	−9.10649	−	23.7232i	−0.379108	−	0.987611i	−0.981847	−	0.189673i	$-0.939257\pi$
$577$	−9.10649	−	23.7232i	−0.379108	−	0.987611i	0.602739	−	0.797938i	$-0.294076\pi$
$578$	18.2436	+	11.8475i	0.758833	+	0.492792i
$579$	2.75524	+	1.78450i	0.114504	+	0.0741613i
$580$	−108.068	−	57.8325i	−4.48729	−	2.40137i
$581$	−5.11117	−	1.92773i	−0.212047	−	0.0799755i
$582$	−13.0183	−	7.49493i	−0.539624	−	0.310675i
$583$	0.245367	−	0.159343i	0.0101621	−	0.00659933i
$584$	11.2471	−	107.009i	0.465408	−	4.42806i
$585$	−3.18213	−	3.66237i	−0.131565	−	0.151420i
$586$	−2.05995	−	19.5991i	−0.0850957	−	0.809631i
$587$	−10.0906	+	1.59820i	−0.416485	+	0.0659647i	−0.361160	−	0.932504i	$-0.617619\pi$
$587$	−10.0906	+	1.59820i	−0.416485	+	0.0659647i	−0.0553244	+	0.998468i	$0.517619\pi$
$588$	−8.00010	−	67.6833i	−0.329919	−	2.79121i
$589$	3.10355	+	4.27167i	0.127880	+	0.176011i
$590$	−35.5832	+	14.9919i	−1.46494	+	0.617207i
$591$	−3.56956	−	22.3606i	−0.146832	−	0.919794i
$592$	−130.436	+	6.83588i	−5.36090	+	0.280953i
$593$	−39.1513	+	10.4906i	−1.60775	+	0.430796i	−0.947372	−	0.320135i	$-0.896272\pi$
$593$	−39.1513	+	10.4906i	−1.60775	+	0.430796i	−0.660381	+	0.750931i	$0.729605\pi$
$594$	7.08727	+	3.57852i	0.290794	+	0.146829i
$595$	28.7737	+	6.54664i	1.17961	+	0.268386i
$596$	83.1640	+	27.0216i	3.40653	+	1.10685i
$597$	39.6168	−	8.47136i	1.62141	−	0.346710i
$598$	2.28175	−	0.875883i	0.0933078	−	0.0358175i
$599$	9.26830	+	16.0532i	0.378693	+	0.655915i	0.990872	−	0.134804i	$-0.0430404\pi$
$599$	9.26830	+	16.0532i	0.378693	+	0.655915i	−0.612180	+	0.790719i	$0.709707\pi$
$600$	86.5703	−	1.15317i	3.53422	−	0.0470779i
$601$	−12.3390			−0.503319			−0.251660	−	0.967816i	$-0.580976\pi$
$601$	−12.3390			−0.503319			−0.251660	+	0.967816i	$0.580976\pi$
$602$	−14.9980	−	68.5826i	−0.611274	−	2.79522i
$603$	−16.1031	−	10.4017i	−0.655768	−	0.423589i
$604$	41.3436	−	37.2260i	1.68225	−	1.51470i
$605$	8.11813	+	22.4915i	0.330049	+	0.914411i
$606$	−47.7948	−	24.2793i	−1.94153	−	0.986278i
$607$	−15.5408	+	4.16415i	−0.630783	+	0.169018i	−0.560025	−	0.828476i	$-0.689208\pi$
$607$	−15.5408	+	4.16415i	−0.630783	+	0.169018i	−0.0707579	+	0.997494i	$0.522542\pi$
$608$	12.9727	−	25.4603i	0.526112	−	1.03255i
$609$	−38.8565	−	22.0686i	−1.57454	−	0.894266i
$610$	−8.10309	+	5.64158i	−0.328085	+	0.228421i
$611$	6.60384	−	0.694092i	0.267163	−	0.0280800i
$612$	78.6024	+	29.9527i	3.17731	+	1.21077i
$613$	12.1119	+	14.9570i	0.489196	+	0.604107i	0.960642	−	0.277788i	$-0.0896012\pi$
$613$	12.1119	+	14.9570i	0.489196	+	0.604107i	−0.471446	+	0.881895i	$0.656268\pi$
$614$	8.50495	+	80.9192i	0.343232	+	3.26563i
$615$	6.46984	−	1.60311i	0.260889	−	0.0646435i
$616$	−10.2908	+	10.4120i	−0.414627	+	0.419512i
$617$	12.5235	+	6.38105i	0.504178	+	0.256892i	0.687530	−	0.726156i	$-0.258695\pi$
$617$	12.5235	+	6.38105i	0.504178	+	0.256892i	−0.183352	+	0.983047i	$0.558695\pi$
$618$	−10.6526	−	18.3990i	−0.428512	−	0.740117i
$619$	−29.9187	−	26.9389i	−1.20253	−	1.08277i	−0.994510	−	0.104643i	$-0.966630\pi$
$619$	−29.9187	−	26.9389i	−1.20253	−	1.08277i	−0.208024	−	0.978124i	$-0.566703\pi$
$620$	−35.8539	−	46.1450i	−1.43993	−	1.85323i
$621$	6.35305	+	0.309631i	0.254939	+	0.0124251i
$622$	51.8101	−	26.3986i	2.07740	−	1.05849i
$623$	−3.94231	+	0.862125i	−0.157945	+	0.0345403i
$624$	19.7849	−	5.32723i	0.792029	−	0.213260i
$625$	0.604914	+	24.9927i	0.0241966	+	0.999707i
$626$	14.1002	−	8.14078i	0.563559	−	0.325371i
$627$	0.641029	+	0.880041i	0.0256002	+	0.0351454i
$628$	−65.9429	−	3.45592i	−2.63141	−	0.137906i
$629$	12.3088	−	37.8825i	0.490782	−	1.51047i
$630$	48.9936	+	0.579765i	1.95195	+	0.0230984i
$631$	13.1972	+	40.6167i	0.525372	+	1.61693i	0.763580	+	0.645713i	$0.223440\pi$
$631$	13.1972	+	40.6167i	0.525372	+	1.61693i	−0.238209	+	0.971214i	$0.576560\pi$
$632$	−11.4333	−	42.6695i	−0.454791	−	1.69730i
$633$	19.1586	−	6.25087i	0.761487	−	0.248450i
$634$	37.0396	+	3.89302i	1.47103	+	0.154612i
$635$	−20.4627	−	12.3699i	−0.812037	−	0.490885i
$636$	3.23402	−	4.00366i	0.128237	−	0.158755i
$637$	4.70489	−	1.86956i	0.186415	−	0.0740746i
$638$	2.33080	+	14.7161i	0.0922773	+	0.582616i
$639$	−9.29275	−	12.7249i	−0.367615	−	0.503391i
$640$	−48.5880	+	103.473i	−1.92061	+	4.09014i
$641$	2.60440	+	0.273733i	0.102867	+	0.0108118i	0.155822	−	0.987785i	$-0.450197\pi$
$641$	2.60440	+	0.273733i	0.102867	+	0.0108118i	−0.0529548	+	0.998597i	$0.516864\pi$
$642$	−6.71550	+	7.47664i	−0.265039	+	0.295080i
$643$	12.4142	−	12.4142i	0.489567	−	0.489567i	−0.418602	−	0.908170i	$-0.637480\pi$
$643$	12.4142	−	12.4142i	0.489567	−	0.489567i	0.908170	+	0.418602i	$0.137480\pi$
$644$	−6.42458	+	17.0341i	−0.253164	+	0.671238i
$645$	37.0886	−	3.19040i	1.46036	−	0.125622i
$646$	10.4646	+	11.6221i	0.411723	+	0.457265i
$647$	−17.9613	+	27.6580i	−0.706133	+	1.08735i	0.285515	+	0.958374i	$0.407835\pi$
$647$	−17.9613	+	27.6580i	−0.706133	+	1.08735i	−0.991648	+	0.128975i	$0.958831\pi$
$648$	88.9344	+	13.6411i	3.49367	+	0.535875i
$649$	2.99816	+	1.73099i	0.117688	+	0.0679473i
$650$	2.70033	+	9.61109i	0.105916	+	0.376978i
$651$	−12.6442	−	17.1468i	−0.495567	−	0.672037i
$652$	53.3283	+	8.44638i	2.08850	+	0.330786i
$653$	−0.789782	+	15.0699i	−0.0309066	+	0.589732i	0.938651	+	0.344869i	$0.112077\pi$
$653$	−0.789782	+	15.0699i	−0.0309066	+	0.589732i	−0.969558	+	0.244864i	$0.921257\pi$
$654$	15.0139	+	29.3778i	0.587091	+	1.14876i
$655$	−10.8977	+	16.0635i	−0.425807	+	0.627654i
$656$	−5.85261	+	27.5344i	−0.228506	+	1.07504i
$657$	31.2088	+	8.28078i	1.21757	+	0.323064i
$658$	−39.0980	+	54.4820i	−1.52420	+	2.12393i
$659$	−31.4142	−	22.8238i	−1.22372	−	0.889088i	−0.227320	−	0.973820i	$-0.572996\pi$
$659$	−31.4142	−	22.8238i	−1.22372	−	0.889088i	−0.996404	+	0.0847324i	$0.972996\pi$
$660$	−7.40471	−	9.50610i	−0.288228	−	0.370024i
$661$	22.9734	+	10.2284i	0.893562	+	0.397840i	0.801557	−	0.597919i	$-0.204006\pi$
$661$	22.9734	+	10.2284i	0.893562	+	0.397840i	0.0920057	+	0.995758i	$0.470672\pi$
$662$	−21.5646	−	26.6300i	−0.838130	−	1.03500i
$663$	−0.645553	+	6.21497i	−0.0250712	+	0.241370i
$664$	12.1324	+	16.6988i	0.470829	+	0.648040i
$665$	5.94258	+	3.13553i	0.230443	+	0.121591i
$666$	6.75266	−	65.7915i	0.261660	−	2.54937i
$667$	6.50111	+	10.0108i	0.251724	+	0.387621i
$668$	17.1261	−	63.9157i	0.662631	−	2.47297i
$669$	17.6360	−	34.7172i	0.681846	−	1.34225i
$670$	20.8139	+	33.5084i	0.804109	+	1.29454i
$671$	0.841933	+	0.273561i	0.0325024	+	0.0105607i
$672$	−51.6155	+	103.098i	−1.99111	+	3.97710i
$673$	−3.86651	+	24.4122i	−0.149043	+	0.941019i	0.793896	+	0.608054i	$0.208049\pi$
$673$	−3.86651	+	24.4122i	−0.149043	+	0.941019i	−0.942939	+	0.332966i	$0.891951\pi$
$674$	−15.4322	+	26.7293i	−0.594425	+	1.02957i
$675$	−3.65937	+	25.7218i	−0.140849	+	0.990031i
$676$	−35.0681	−	60.7398i	−1.34877	−	2.33615i
$677$	33.2200	+	26.9010i	1.27675	+	1.03389i	0.997278	+	0.0737362i	$0.0234923\pi$
$677$	33.2200	+	26.9010i	1.27675	+	1.03389i	0.279471	+	0.960154i	$0.409841\pi$
$678$	−56.3375	+	50.8511i	−2.16363	+	1.95293i
$679$	4.56763	+	6.94416i	0.175290	+	0.266493i
$680$	−77.2410	−	80.4150i	−2.96206	−	3.08378i
$681$	−26.1765	+	1.40389i	−1.00308	+	0.0537970i
$682$	−1.83853	+	6.86150i	−0.0704011	+	0.262740i
$683$	−37.1497	+	1.94694i	−1.42150	+	0.0744974i	−0.747512	−	0.664249i	$-0.768752\pi$
$683$	−37.1497	+	1.94694i	−1.42150	+	0.0744974i	−0.673984	+	0.738746i	$0.735418\pi$
$684$	15.5223	+	11.2199i	0.593511	+	0.429002i
$685$	2.37154	+	7.83187i	0.0906118	+	0.299241i
$686$	−17.4813	+	48.0469i	−0.667439	+	1.83444i
$687$	−3.75980	+	1.67947i	−0.143445	+	0.0640758i
$688$	−56.3389	+	146.768i	−2.14790	+	5.59547i
$689$	0.349259	+	0.155500i	0.0133057	+	0.00592407i
$690$	−11.5471	−	6.16130i	−0.439591	−	0.234557i
$691$	18.8860	−	8.40857i	0.718456	−	0.319877i	−0.0147433	−	0.999891i	$-0.504693\pi$
$691$	18.8860	−	8.40857i	0.718456	−	0.319877i	0.733199	+	0.680014i	$0.238026\pi$
$692$	101.873	+	51.9068i	3.87262	+	1.97320i
$693$	−2.61157	−	3.53250i	−0.0992053	−	0.134189i
$694$	22.5705	−	7.33360i	0.856764	−	0.278380i
$695$	−2.73872	−	11.1110i	−0.103886	−	0.421466i
$696$	76.8397	+	150.353i	2.91260	+	5.69910i
$697$	−7.19946	−	4.67538i	−0.272699	−	0.177093i
$698$	16.7509	−	20.6857i	0.634032	−	0.782965i
$699$	−4.99076	−	18.5353i	−0.188768	−	0.701068i
$700$	−66.8530	−	32.5648i	−2.52681	−	1.23083i
$701$			6.09166i			0.230079i	0.993361	+	0.115039i	$0.0366994\pi$
$701$			6.09166i			0.230079i	−0.993361	+	0.115039i	$0.963301\pi$
$702$	1.12224	+	10.3140i	0.0423561	+	0.389277i
$703$	4.93962	−	7.60635i	0.186301	−	0.286879i
$704$	19.8932	−	4.22843i	0.749753	−	0.159365i
$705$	−25.9703	−	24.2886i	−0.978100	−	0.914760i
$706$	−0.103687	−	0.319117i	−0.00390233	−	0.0120101i
$707$	17.5753	+	23.8948i	0.660987	+	0.898656i
$708$	59.5856	+	12.5893i	2.23937	+	0.473136i
$709$	−16.0770	−	36.1095i	−0.603784	−	1.35612i	−0.914101	−	0.405487i	$-0.867102\pi$
$709$	−16.0770	−	36.1095i	−0.603784	−	1.35612i	0.310317	−	0.950633i	$-0.399565\pi$
$710$	6.10131	+	31.8434i	0.228978	+	1.19506i
$711$	13.1801	−	1.41782i	0.494294	−	0.0531725i
$712$	14.2355	+	5.46451i	0.533499	+	0.204791i
$713$	0.890254	+	5.62084i	0.0333403	+	0.210502i
$714$	−42.5545	−	46.5942i	−1.59256	−	1.74374i
$715$	0.540591	−	0.713408i	0.0202170	−	0.0266799i
$716$	8.76489	+	19.6863i	0.327559	+	0.735710i
$717$	−12.8143	+	4.18091i	−0.478558	+	0.156139i
$718$	13.9203	+	3.72993i	0.519501	+	0.139200i
$719$	−7.00541	−	1.48905i	−0.261258	−	0.0555321i	0.0754204	−	0.997152i	$-0.475970\pi$
$719$	−7.00541	−	1.48905i	−0.261258	−	0.0555321i	−0.336678	+	0.941620i	$0.609303\pi$
$720$	−90.9485	−	61.3768i	−3.38945	−	2.28738i
$721$	0.684455	+	11.7438i	0.0254904	+	0.437362i
$722$	−22.1964	−	43.5629i	−0.826064	−	1.62124i
$723$	15.1707	−	34.1861i	0.564203	−	1.27139i
$724$	−19.2363	+	11.1061i	−0.714913	+	0.412755i
$725$	−43.1714	+	22.6590i	−1.60335	+	0.841535i
$726$	13.1739	−	49.4068i	0.488930	−	1.83366i
$727$	12.0297	+	1.90532i	0.446158	+	0.0706645i	0.375471	−	0.926834i	$-0.377481\pi$
$727$	12.0297	+	1.90532i	0.446158	+	0.0706645i	0.0706869	+	0.997499i	$0.477481\pi$
$728$	−18.7348	−	3.86768i	−0.694359	−	0.143346i
$729$	−8.15522	+	25.7389i	−0.302045	+	0.953294i
$730$	−50.7813	−	42.8427i	−1.87950	−	1.58568i
$731$	−35.6279	−	32.0795i	−1.31775	−	1.18650i
$732$	15.5730	−	0.0190045i	0.575593	−	0.000702428i
$733$	15.6934	−	10.1914i	0.579649	−	0.376428i	−0.221260	−	0.975215i	$-0.571017\pi$
$733$	15.6934	−	10.1914i	0.579649	−	0.376428i	0.800909	+	0.598786i	$0.204350\pi$
$734$	−6.31066	−	4.58496i	−0.232931	−	0.169234i
$735$	−24.0668	−	12.4816i	−0.887716	−	0.460391i
$736$	24.9162	−	18.1027i	0.918424	−	0.667274i
$737$	1.26746	−	3.30185i	0.0466875	−	0.121625i
$738$	−13.3192	−	5.07551i	−0.490288	−	0.186832i
$739$	5.00932	−	11.2511i	0.184271	−	0.413879i	−0.797663	−	0.603103i	$-0.793931\pi$
$739$	5.00932	−	11.2511i	0.184271	−	0.413879i	0.981934	+	0.189224i	$0.0605973\pi$
$740$	−51.9277	+	85.9005i	−1.90890	+	3.15776i
$741$	−0.508239	+	1.32885i	−0.0186706	+	0.0488166i
$742$	−3.51789	+	1.59102i	−0.129146	+	0.0584080i
$743$	4.78043	+	4.78043i	0.175377	+	0.175377i	0.789337	−	0.613960i	$-0.210424\pi$
$743$	4.78043	+	4.78043i	0.175377	+	0.175377i	−0.613960	+	0.789337i	$0.710424\pi$
$744$	4.31122	+	80.3858i	0.158057	+	2.94709i
$745$	27.4673	−	21.3417i	1.00632	−	0.781898i
$746$	3.27875	+	15.4253i	0.120044	+	0.564760i
$747$	−5.51204	+	2.82549i	−0.201675	+	0.103379i
$748$	−2.42765	+	15.3276i	−0.0887635	+	0.560431i
$749$	5.17962	−	2.02315i	0.189259	−	0.0739244i
$750$	29.4211	−	44.6361i	1.07431	−	1.62988i
$751$	15.8850	−	27.5137i	0.579653	−	1.00399i	−0.415865	−	0.909426i	$-0.636521\pi$
$751$	15.8850	−	27.5137i	0.579653	−	1.00399i	0.995519	−	0.0945631i	$-0.0301454\pi$
$752$	140.195	−	53.8157i	5.11237	−	1.96246i
$753$	10.1946	−	31.5066i	0.371513	−	1.14816i
$754$	−14.4690	+	13.0279i	−0.526929	+	0.474449i
$755$	−3.02125	−	21.9230i	−0.109954	−	0.797858i
$756$	−62.9502	−	44.8269i	−2.28948	−	1.63034i
$757$	−15.7937	−	15.7937i	−0.574032	−	0.574032i	0.359221	−	0.933253i	$-0.383042\pi$
$757$	−15.7937	−	15.7937i	−0.574032	−	0.574032i	−0.933253	+	0.359221i	$0.883042\pi$
$758$	17.2217	+	26.5191i	0.625520	+	0.963217i
$759$	0.184985	+	1.15880i	0.00671454	+	0.0420617i
$760$	−12.2491	−	22.2381i	−0.444321	−	0.806661i
$761$	36.0986	−	3.79411i	1.30857	−	0.137537i	0.575564	−	0.817756i	$-0.304782\pi$
$761$	36.0986	−	3.79411i	1.30857	−	0.137537i	0.733008	+	0.680220i	$0.238116\pi$
$762$	20.8540	+	46.6854i	0.755461	+	1.69123i
$763$	−0.106911	−	18.2548i	−0.00387045	−	0.660867i
$764$	−122.955	+	89.3322i	−4.44836	+	3.23193i
$765$	27.4135	−	19.1855i	0.991137	−	0.693653i
$766$	−3.92943	+	37.3861i	−0.141976	+	1.35081i
$767$	0.236764	+	4.51773i	0.00854906	+	0.163126i
$768$	101.390	−	58.7026i	3.65859	−	2.11825i
$769$	−18.0408	+	5.86180i	−0.650566	+	0.211382i	−0.615664	−	0.788009i	$-0.711112\pi$
$769$	−18.0408	+	5.86180i	−0.650566	+	0.211382i	−0.0349024	+	0.999391i	$0.511112\pi$
$770$	1.75302	+	8.86788i	0.0631745	+	0.319576i
$771$	1.24777	−	24.3780i	0.0449372	−	0.877951i
$772$	−0.557571	+	10.6391i	−0.0200674	+	0.382909i
$773$	12.1304	+	31.6007i	0.436299	+	1.13660i	0.958831	+	0.283978i	$0.0916544\pi$
$773$	12.1304	+	31.6007i	0.436299	+	1.13660i	−0.522531	+	0.852620i	$0.675012\pi$
$774$	−69.0353	−	39.6332i	−2.48142	−	1.42459i
$775$	−23.1971	+	1.49734i	−0.833263	+	0.0537861i
$776$		−	31.4064i		−	1.12743i
$777$	−19.7133	+	30.8313i	−0.707210	+	1.10607i
$778$	−25.9076	−	50.8466i	−0.928834	−	1.82294i
$779$	−1.30789	−	1.45256i	−0.0468601	−	0.0520434i
$780$	5.14805	−	14.8806i	0.184330	−	0.532810i
$781$	1.94516	−	2.16032i	0.0696033	−	0.0773023i
$782$	4.36262	+	16.2815i	0.156007	+	0.582226i
$783$	−48.1317	+	15.8340i	−1.72009	+	0.565861i
$784$	91.8329	−	68.3781i	3.27975	−	2.44208i
$785$	−15.8641	+	20.9355i	−0.566213	+	0.747219i
$786$	38.7338	−	14.9228i	1.38159	−	0.532278i
$787$	−12.8310	+	10.3903i	−0.457375	+	0.370375i	−0.830144	−	0.557549i	$-0.811742\pi$
$787$	−12.8310	+	10.3903i	−0.457375	+	0.370375i	0.372769	+	0.927924i	$0.378408\pi$
$788$	57.1118	−	46.2483i	2.03452	−	1.64753i
$789$	−33.9429	+	13.0770i	−1.20840	+	0.465554i
$790$	−25.7670	−	8.94953i	−0.916750	−	0.318410i
$791$	40.4977	−	11.1059i	1.43993	−	0.394881i
$792$	0.909204	+	16.5745i	0.0323072	+	0.588950i
$793$	0.299405	+	1.11739i	0.0106322	+	0.0396798i
$794$	−27.2532	+	30.2678i	−0.967182	+	1.07416i
$795$	−0.595712	−	1.95869i	−0.0211277	−	0.0694674i
$796$	87.9780	+	97.7095i	3.11830	+	3.46322i
$797$	−0.940750	−	1.84633i	−0.0333231	−	0.0654002i	0.873745	−	0.486385i	$-0.161685\pi$
$797$	−0.940750	−	1.84633i	−0.0333231	−	0.0654002i	−0.907068	+	0.420985i	$0.861685\pi$
$798$	−6.61340	−	12.7556i	−0.234112	−	0.451542i
$799$			45.7949i			1.62011i
$800$	64.2133	+	108.176i	2.27028	+	3.82462i
$801$	−2.27822	+	3.96833i	−0.0804969	+	0.140214i
$802$	20.2034	+	52.6316i	0.713406	+	1.85848i
$803$	−0.311763	+	5.94880i	−0.0110019	+	0.209928i
$804$	3.18034	−	62.1352i	0.112162	−	2.19134i
$805$	4.17260	+	5.91894i	0.147065	+	0.208615i
$806$	−8.82822	+	2.86846i	−0.310961	+	0.101037i
$807$	−24.2367	+	14.0325i	−0.853171	+	0.493968i
$808$	−5.86587	−	111.928i	−0.206361	−	3.93760i
$809$	−4.62575	+	44.0111i	−0.162633	+	1.54735i	0.543586	+	0.839354i	$0.317066\pi$
$809$	−4.62575	+	44.0111i	−0.162633	+	1.54735i	−0.706219	+	0.707994i	$0.749600\pi$
$810$	37.8004	−	40.7155i	1.32817	−	1.43060i
$811$	12.9997	−	9.44480i	0.456480	−	0.331652i	−0.335669	−	0.941980i	$-0.608962\pi$
$811$	12.9997	−	9.44480i	0.456480	−	0.331652i	0.792149	+	0.610328i	$0.208962\pi$
$812$	−0.849351	−	145.024i	−0.0298064	−	5.08935i
$813$	−16.5015	−	36.9416i	−0.578734	−	1.29560i
$814$	12.1348	−	1.27542i	0.425326	−	0.0447036i
$815$	14.6897	−	15.6685i	0.514559	−	0.548844i
$816$	22.2757	+	139.541i	0.779807	+	4.88492i
$817$	−5.94536	−	9.15506i	−0.208002	−	0.320295i
$818$	−4.69330	−	4.69330i	−0.164097	−	0.164097i
$819$	2.01271	−	5.37620i	0.0703298	−	0.187860i
$820$	14.9855	+	15.6013i	0.523316	+	0.544821i
$821$	−24.1555	+	21.7497i	−0.843033	+	0.759070i	−0.972596	−	0.232501i	$-0.925309\pi$
$821$	−24.1555	+	21.7497i	−0.843033	+	0.759070i	0.129563	+	0.991571i	$0.458642\pi$
$822$	5.38708	−	16.6488i	0.187896	−	0.580694i
$823$	−22.1911	+	8.51836i	−0.773532	+	0.296931i	−0.712934	−	0.701231i	$-0.752634\pi$
$823$	−22.1911	+	8.51836i	−0.773532	+	0.296931i	−0.0605982	+	0.998162i	$0.519301\pi$
$824$	22.2250	−	38.4949i	0.774246	−	1.34103i
$825$	−4.78287	+	0.314590i	−0.166518	+	0.0109526i
$826$	−35.6732	−	28.5433i	−1.24123	−	0.993148i
$827$	1.39021	−	8.77747i	0.0483425	−	0.305222i	−0.951656	−	0.307167i	$-0.900619\pi$
$827$	1.39021	−	8.77747i	0.0483425	−	0.305222i	0.999998	+	0.00194459i	$0.000618982\pi$
$828$	9.41658	+	18.3701i	0.327249	+	0.638405i
$829$	−6.16491	−	29.0036i	−0.214116	−	1.00734i	−0.945563	−	0.325439i	$-0.894488\pi$
$829$	−6.16491	−	29.0036i	−0.214116	−	1.00734i	0.731447	−	0.681898i	$-0.238845\pi$
$830$	12.7387	−	0.410706i	0.442167	−	0.0142558i
$831$	−0.798366	−	14.8861i	−0.0276950	−	0.516394i
$832$	18.7922	+	18.7922i	0.651501	+	0.651501i
$833$	9.43123	+	33.6177i	0.326773	+	1.16479i
$834$	−8.74175	+	22.8564i	−0.302702	+	0.791451i
$835$	−17.2153	−	19.9113i	−0.595760	−	0.689061i
$836$	−1.43721	+	3.22802i	−0.0497068	+	0.111643i
$837$	−24.0340	−	2.43715i	−0.830737	−	0.0842401i
$838$	6.83535	−	17.8067i	0.236123	−	0.615122i
$839$	16.3301	−	11.8645i	0.563777	−	0.409608i	−0.269062	−	0.963123i	$-0.586714\pi$
$839$	16.3301	−	11.8645i	0.563777	−	0.409608i	0.832839	+	0.553515i	$0.186714\pi$
$840$	50.0578	+	89.3770i	1.72716	+	3.08380i
$841$	−53.4664	−	38.8456i	−1.84367	−	1.33950i
$842$	−33.3235	+	21.6405i	−1.14840	+	0.745782i
$843$	16.9825	−	0.0207247i	0.584909	−	0.000713797i
$844$	48.6048	+	43.7639i	1.67305	+	1.50642i
$845$	−27.8260	−	2.02065i	−0.957242	−	0.0695123i
$846$	15.9907	+	74.3376i	0.549771	+	2.55578i
$847$	−18.8081	+	21.1362i	−0.646254	+	0.726247i
$848$	8.53953	+	1.35253i	0.293249	+	0.0464460i
$849$	−11.4877	+	43.0828i	−0.394256	+	1.47860i
$850$	−67.8673	+	11.5925i	−2.32783	+	0.397621i
$851$	8.46557	−	4.88760i	0.290196	−	0.167545i
$852$	20.7427	−	46.7424i	0.710635	−	1.60137i
$853$	−18.7257	−	36.7512i	−0.641154	−	1.25834i	−0.951481	−	0.307706i	$-0.900439\pi$
$853$	−18.7257	−	36.7512i	−0.641154	−	1.25834i	0.310327	−	0.950630i	$-0.399561\pi$
$854$	−10.4401	−	5.24272i	−0.357254	−	0.179402i
$855$	7.15985	−	2.60406i	0.244862	−	0.0890569i
$856$	−20.5524	−	4.36855i	−0.702467	−	0.149314i
$857$	−9.74795	−	2.61196i	−0.332984	−	0.0892227i	0.0884534	−	0.996080i	$-0.471808\pi$
$857$	−9.74795	−	2.61196i	−0.332984	−	0.0892227i	−0.421437	+	0.906858i	$0.638474\pi$
$858$	−1.81966	+	0.593701i	−0.0621223	+	0.0202686i
$859$	8.60770	+	19.3332i	0.293691	+	0.659641i	0.998775	−	0.0494830i	$-0.0157574\pi$
$859$	8.60770	+	19.3332i	0.293691	+	0.659641i	−0.705084	+	0.709124i	$0.749091\pi$
$860$	69.0306	+	99.1498i	2.35393	+	3.38098i
$861$	5.31859	+	5.82348i	0.181257	+	0.198464i
$862$	−12.7032	−	80.2051i	−0.432674	−	2.73180i
$863$	−25.5083	−	9.79172i	−0.868313	−	0.333314i	−0.116898	−	0.993144i	$-0.537295\pi$
$863$	−25.5083	−	9.79172i	−0.868313	−	0.333314i	−0.751415	+	0.659830i	$0.770628\pi$
$864$	47.2976	+	121.879i	1.60910	+	4.14641i
$865$	39.8371	−	21.9429i	1.35450	−	0.746081i
$866$	−26.3581	−	59.2014i	−0.895686	−	2.01174i
$867$	−13.3531	−	2.82126i	−0.453495	−	0.0958151i
$868$	27.7527	−	63.3292i	0.941988	−	2.14953i
$869$	0.755745	+	2.32594i	0.0256369	+	0.0789023i
$870$	103.465	+	12.8570i	3.50781	+	0.435892i
$871$	4.52065	−	0.960895i	0.153177	−	0.0325587i
$872$	−37.5682	+	57.8499i	−1.27222	+	1.95904i
$873$	9.31214	+	1.45161i	0.315168	+	0.0491295i
$874$			3.83799i			0.129822i
$875$	−25.6495	+	14.7345i	−0.867110	+	0.498116i
$876$	27.2455	+	101.187i	0.920540	+	3.41881i
$877$	−27.4298	+	33.8730i	−0.926238	+	1.14381i	0.0630763	+	0.998009i	$0.479909\pi$
$877$	−27.4298	+	33.8730i	−0.926238	+	1.14381i	−0.989314	+	0.145800i	$0.953424\pi$
$878$	−3.77345	−	2.45051i	−0.127348	−	0.0827006i
$879$	5.62670	+	11.0098i	0.189784	+	0.371351i
$880$	7.63320	−	18.7482i	0.257315	−	0.632001i
$881$	36.7676	−	11.9465i	1.23873	−	0.402489i	0.384862	−	0.922974i	$-0.374249\pi$
$881$	36.7676	−	11.9465i	1.23873	−	0.402489i	0.853870	+	0.520486i	$0.174249\pi$
$882$	27.0481	+	51.2775i	0.910757	+	1.72660i
$883$	−20.4920	−	10.4412i	−0.689611	−	0.351375i	0.0738127	−	0.997272i	$-0.476483\pi$
$883$	−20.4920	−	10.4412i	−0.689611	−	0.351375i	−0.763424	+	0.645898i	$0.776483\pi$
$884$	−18.5257	+	8.24817i	−0.623087	+	0.277416i
$885$	17.4509	−	16.8031i	0.586606	−	0.564830i
$886$	36.4181	+	16.2144i	1.22349	+	0.544732i
$887$	−6.50244	+	16.9394i	−0.218330	+	0.568770i	−0.998377	−	0.0569512i	$-0.981862\pi$
$887$	−6.50244	+	16.9394i	−0.218330	+	0.568770i	0.780046	+	0.625722i	$0.215195\pi$
$888$	126.253	−	56.3961i	4.23677	−	1.89253i
$889$	1.31519	−	28.2613i	0.0441101	−	0.947854i
$890$	7.72717	−	5.37986i	0.259015	−	0.180333i
$891$	−4.95644	−	0.496494i	−0.166047	−	0.0166332i
$892$	126.204	−	6.61408i	4.22563	−	0.221456i
$893$	−2.69877	+	10.0720i	−0.0903109	+	0.337045i
$894$	−74.2753	+	3.98350i	−2.48414	+	0.133228i
$895$	8.43776	+	1.51111i	0.282043	+	0.0505107i
$896$	−135.028	+	7.86975i	−4.51097	+	0.262910i
$897$	−1.13831	+	1.02745i	−0.0380069	+	0.0343057i
$898$	−6.34483	−	5.13794i	−0.211730	−	0.171455i
$899$	−22.6672	−	39.2608i	−0.755995	−	1.30942i
$900$	−78.2711	+	31.3587i	−2.60904	+	1.04529i
$901$	−1.31832	+	2.28340i	−0.0439197	+	0.0760711i
$902$	0.411366	−	2.59726i	0.0136970	−	0.0864794i
$903$	24.2499	+	36.7692i	0.806986	+	1.22360i
$904$	−150.907	−	49.0327i	−5.01910	−	1.63080i
$905$	−0.639940	+	8.81250i	−0.0212723	+	0.292937i
$906$	−21.4328	+	42.1915i	−0.712058	+	1.40172i
$907$	−2.87508	+	10.7299i	−0.0954654	+	0.356282i	−0.997090	−	0.0762385i	$-0.975709\pi$
$907$	−2.87508	+	10.7299i	−0.0954654	+	0.356282i	0.901624	+	0.432520i	$0.142376\pi$
$908$	−46.3360	−	71.3512i	−1.53771	−	2.36787i
$909$	33.4581	+	3.43405i	1.10974	+	0.113900i
$910$	−8.47094	+	8.23250i	−0.280809	+	0.272905i
$911$	−14.3782	−	19.7898i	−0.476370	−	0.655667i	0.501433	−	0.865197i	$-0.332807\pi$
$911$	−14.3782	−	19.7898i	−0.476370	−	0.655667i	−0.977802	+	0.209530i	$0.932807\pi$
$912$	−3.32416	+	32.0029i	−0.110074	+	1.05972i
$913$	−0.719149	−	0.888075i	−0.0238004	−	0.0293910i
$914$	−8.36348	−	3.72366i	−0.276639	−	0.123168i
$915$	3.47152	−	5.13060i	0.114765	−	0.169612i
$916$	−10.8119	−	7.85532i	−0.357236	−	0.259547i
$917$	−22.8555	−	2.26696i	−0.754756	−	0.0748616i
$918$	−71.5509	+	0.261953i	−2.36153	+	0.00864575i
$919$	−5.85510	+	27.5461i	−0.193142	+	0.908661i	0.769660	+	0.638454i	$0.220426\pi$
$919$	−5.85510	+	27.5461i	−0.193142	+	0.908661i	−0.962802	+	0.270207i	$0.912908\pi$
$920$	−0.881775	−	27.3496i	−0.0290713	−	0.901691i
$921$	−23.2311	−	45.4563i	−0.765490	−	1.49784i
$922$	2.01433	−	38.4357i	0.0663385	−	1.26581i
$923$	3.75194	+	0.594249i	0.123497	+	0.0195599i
$924$	5.70669	−	13.0655i	0.187736	−	0.429824i
$925$	16.6804	+	36.2771i	0.548449	+	1.19278i
$926$	10.5841	+	6.11075i	0.347816	+	0.200812i
$927$	10.3867	+	8.36906i	0.341143	+	0.274876i
$928$	−133.623	+	205.761i	−4.38638	+	6.75444i
$929$	−19.2491	−	21.3783i	−0.631541	−	0.701398i	0.339420	−	0.940635i	$-0.389769\pi$
$929$	−19.2491	−	21.3783i	−0.631541	−	0.701398i	−0.970961	+	0.239237i	$0.923103\pi$
$930$	42.5707	+	25.6635i	1.39595	+	0.841539i
$931$	0.0931182	+	7.94955i	0.00305183	+	0.260536i
$932$	44.0512	−	44.0512i	1.44294	−	1.44294i
$933$	−24.3782	+	27.1413i	−0.798107	+	0.888565i
$934$	−41.0573	−	4.31529i	−1.34343	−	0.141201i
$935$	4.50342	+	4.22211i	0.147278	+	0.138078i
$936$	−17.5174	+	12.7926i	−0.572575	+	0.418139i
$937$	−1.71559	−	10.8318i	−0.0560459	−	0.353860i	−0.999735	−	0.0230258i	$-0.992670\pi$
$937$	−1.71559	−	10.8318i	−0.0560459	−	0.353860i	0.943689	−	0.330834i	$-0.107330\pi$
$938$	−23.0998	+	40.5567i	−0.754234	+	1.32422i
$939$	−6.41888	+	7.94646i	−0.209472	+	0.259323i
$940$	26.2609	−	112.375i	0.856535	−	3.66527i
$941$	16.2356	+	1.70643i	0.529265	+	0.0556280i	0.365393	−	0.930853i	$-0.380935\pi$
$941$	16.2356	+	1.70643i	0.529265	+	0.0556280i	0.163873	+	0.986481i	$0.447601\pi$
$942$	53.3994	−	17.4226i	1.73985	−	0.567659i
$943$	−0.545253	−	2.03491i	−0.0177559	−	0.0662659i
$944$	31.6152	+	97.3014i	1.02899	+	3.16689i
$945$	−28.8144	+	10.7114i	−0.937331	+	0.348440i
$946$	4.53824	−	13.9673i	0.147551	−	0.454115i
$947$	50.2858	+	2.63537i	1.63407	+	0.0856380i	0.847128	−	0.531389i	$-0.178330\pi$
$947$	50.2858	+	2.63537i	1.63407	+	0.0856380i	0.786942	+	0.617027i	$0.211663\pi$
$948$	25.3303	+	34.7749i	0.822691	+	1.12944i
$949$	−6.74135	+	3.89212i	−0.218833	+	0.126344i
$950$	−15.6096	−	1.44992i	−0.506444	−	0.0470416i
$951$	−22.5632	+	6.07531i	−0.731661	+	0.197005i
$952$	40.0334	−	125.711i	1.29749	−	4.07430i
$953$	25.9800	−	13.2375i	0.841574	−	0.428804i	0.0206131	−	0.999788i	$-0.493438\pi$
$953$	25.9800	−	13.2375i	0.841574	−	0.428804i	0.820961	+	0.570984i	$0.193438\pi$
$954$	−1.34268	+	4.16691i	−0.0434708	+	0.134909i
$955$	1.94814	+	60.4245i	0.0630402	+	1.95529i
$956$	−32.5094	−	29.2716i	−1.05143	−	0.946711i
$957$	−4.68388	−	8.08991i	−0.151408	−	0.261510i
$958$	82.1223	+	41.8434i	2.65325	+	1.35190i
$959$	−6.80622	+	6.88642i	−0.219784	+	0.222374i
$960$	10.1342	−	141.954i	0.327079	−	4.58153i
$961$	0.981123	+	9.33476i	0.0316491	+	0.301121i
$962$	10.0342	+	12.3912i	0.323516	+	0.399509i
$963$	2.24523	−	5.89197i	0.0723515	−	0.189866i
$964$	120.718	−	12.6880i	3.88807	−	0.408653i
$965$	3.37769	+	2.55948i	0.108732	+	0.0823924i
$966$	−0.109592	−	15.4856i	−0.00352607	−	0.498242i
$967$	2.95818	−	5.80576i	0.0951287	−	0.186701i	−0.838539	−	0.544842i	$-0.816590\pi$
$967$	2.95818	−	5.80576i	0.0951287	−	0.186701i	0.933667	+	0.358142i	$0.116590\pi$
$968$	103.264	−	27.6694i	3.31902	−	0.889328i
$969$	−8.74797	−	4.44388i	−0.281025	−	0.142758i
$970$	−16.0483	−	10.8873i	−0.515279	−	0.349571i
$971$	12.4015	−	11.1663i	0.397982	−	0.358344i	−0.445705	−	0.895180i	$-0.647047\pi$
$971$	12.4015	−	11.1663i	0.397982	−	0.358344i	0.843687	+	0.536835i	$0.180380\pi$
$972$	−85.5995	+	18.7414i	−2.74561	+	0.601129i
$973$	10.0091	−	9.11897i	0.320878	−	0.292341i
$974$	102.681			3.29010
$975$	−3.74876	−	5.01780i	−0.120057	−	0.160698i
$976$	13.0807	+	22.6564i	0.418702	+	0.725213i
$977$	43.7411	−	16.7906i	1.39940	−	0.537180i	0.462452	−	0.886644i	$-0.346970\pi$
$977$	43.7411	−	16.7906i	1.39940	−	0.537180i	0.936950	+	0.349464i	$0.113636\pi$
$978$	−44.9126	+	9.60378i	−1.43615	+	0.307095i
$979$	−0.802874	−	0.260869i	−0.0256600	−	0.00833742i
$980$	−3.86515	−	87.9021i	−0.123468	−	2.80793i
$981$	−15.4163	−	13.8130i	−0.492206	−	0.441014i
$982$	63.7078	−	17.0705i	2.03300	−	0.544740i
$983$	49.1533	−	2.57601i	1.56775	−	0.0821621i	0.751447	−	0.659793i	$-0.229356\pi$
$983$	49.1533	−	2.57601i	1.56775	−	0.0821621i	0.816298	+	0.577631i	$0.196023\pi$
$984$	−4.69774	−	29.4279i	−0.149759	−	0.938128i
$985$	−2.46986	−	29.1284i	−0.0786962	−	0.928110i
$986$	−78.9255	−	108.632i	−2.51350	−	3.45954i
$987$	10.6015	−	40.7156i	0.337448	−	1.29599i
$988$	−4.56055	+	0.722320i	−0.145090	+	0.0229801i
$989$	−1.22983	−	11.7011i	−0.0391063	−	0.372072i
$990$	8.78456	+	5.28112i	0.279192	+	0.167845i
$991$	5.74954	−	54.7032i	0.182640	−	1.73771i	−0.392590	−	0.919714i	$-0.628421\pi$
$991$	5.74954	−	54.7032i	0.182640	−	1.73771i	0.575230	−	0.817992i	$-0.304913\pi$
$992$	−98.0993	+	63.7064i	−3.11466	+	2.02268i
$993$	18.6317	+	10.7267i	0.591258	+	0.340401i
$994$	−29.6717	+	24.3168i	−0.941130	+	0.771281i
$995$	51.8116	−	7.14027i	1.64254	−	0.226362i
$996$	−16.8726	−	10.9280i	−0.534630	−	0.346266i
$997$	29.0056	+	18.8364i	0.918616	+	0.596556i	0.915007	−	0.403438i	$-0.132185\pi$
$997$	29.0056	+	18.8364i	0.918616	+	0.596556i	0.00360839	+	0.999993i	$0.498851\pi$
$998$	−23.5621	−	61.3814i	−0.745846	−	1.94300i
$999$	10.8863	+	40.0412i	0.344426	+	1.26685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bs.a.2.1	✓	1216
3.2	odd	2	inner	525.2.bs.a.2.76	yes	1216
7.4	even	3	inner	525.2.bs.a.452.76	yes	1216
21.11	odd	6	inner	525.2.bs.a.452.1	yes	1216
25.13	odd	20	inner	525.2.bs.a.338.1	yes	1216
75.38	even	20	inner	525.2.bs.a.338.76	yes	1216
175.88	odd	60	inner	525.2.bs.a.263.76	yes	1216
525.263	even	60	inner	525.2.bs.a.263.1	yes	1216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bs.a.2.1	✓	1216	1.1	even	1	trivial
525.2.bs.a.2.76	yes	1216	3.2	odd	2	inner
525.2.bs.a.263.1	yes	1216	525.263	even	60	inner
525.2.bs.a.263.76	yes	1216	175.88	odd	60	inner
525.2.bs.a.338.1	yes	1216	25.13	odd	20	inner
525.2.bs.a.338.76	yes	1216	75.38	even	20	inner
525.2.bs.a.452.1	yes	1216	21.11	odd	6	inner
525.2.bs.a.452.76	yes	1216	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14544 - 1.73734i) q^{2} +(1.64793 + 0.533222i) q^{3} +(1.16873 + 5.49845i) q^{4} +(2.07100 + 0.843193i) q^{5} +(-2.60915 - 4.00702i) q^{6} +(0.291962 + 2.62959i) q^{7} +(4.53862 - 8.90754i) q^{8} +(2.43135 + 1.75743i) q^{9} +O(q^{10})\)	\(q+(-2.14544 - 1.73734i) q^{2} +(1.64793 + 0.533222i) q^{3} +(1.16873 + 5.49845i) q^{4} +(2.07100 + 0.843193i) q^{5} +(-2.60915 - 4.00702i) q^{6} +(0.291962 + 2.62959i) q^{7} +(4.53862 - 8.90754i) q^{8} +(2.43135 + 1.75743i) q^{9} +(-2.97829 - 5.40705i) q^{10} +(-0.225117 + 0.505622i) q^{11} +(-1.00591 + 9.68425i) q^{12} +(-0.714343 + 0.113141i) q^{13} +(3.94212 - 6.14888i) q^{14} +(2.96325 + 2.49382i) q^{15} +(-14.9422 + 6.65269i) q^{16} +(-0.261049 - 4.98111i) q^{17} +(-2.16306 - 7.99454i) q^{18} +(0.236131 - 1.11091i) q^{19} +(-2.21581 + 12.3727i) q^{20} +(-0.921026 + 4.48907i) q^{21} +(1.36142 - 0.693676i) q^{22} +(0.770349 - 0.951302i) q^{23} +(12.2290 - 12.2589i) q^{24} +(3.57805 + 3.49250i) q^{25} +(1.72915 + 0.998323i) q^{26} +(3.06959 + 4.19257i) q^{27} +(-14.1174 + 4.67862i) q^{28} +(-3.01332 + 9.27405i) q^{29} +(-2.02484 - 10.4985i) q^{30} +(-3.11083 + 3.45493i) q^{31} +(24.3026 + 6.51186i) q^{32} +(-0.640587 + 0.713192i) q^{33} +(-8.09384 + 11.1402i) q^{34} +(-1.61260 + 5.69206i) q^{35} +(-6.82152 + 15.4226i) q^{36} +(7.45524 + 2.86180i) q^{37} +(-2.43664 + 1.97315i) q^{38} +(-1.23752 - 0.194456i) q^{39} +(16.9102 - 14.6205i) q^{40} +(1.01159 - 1.39234i) q^{41} +(9.77506 - 8.03089i) q^{42} +(6.79642 - 6.79642i) q^{43} +(-3.04324 - 0.646860i) q^{44} +(3.55346 + 5.68972i) q^{45} +(-3.30548 + 0.702601i) q^{46} +(-9.16853 - 0.480502i) q^{47} +(-28.1711 + 2.99566i) q^{48} +(-6.82952 + 1.53548i) q^{49} +(-1.60883 - 13.7093i) q^{50} +(2.22585 - 8.34772i) q^{51} +(-1.45697 - 3.79555i) q^{52} +(-0.443324 - 0.287898i) q^{53} +(0.698301 - 14.3278i) q^{54} +(-0.892554 + 0.857324i) q^{55} +(24.7483 + 9.33405i) q^{56} +(0.981490 - 1.70479i) q^{57} +(22.5771 - 14.6618i) q^{58} +(0.653828 - 6.22076i) q^{59} +(-10.2489 + 19.2079i) q^{60} +(-0.167190 - 1.59071i) q^{61} +(12.6765 - 2.00776i) q^{62} +(-3.91146 + 6.90656i) q^{63} +(-21.5985 - 29.7278i) q^{64} +(-1.57480 - 0.368015i) q^{65} +(2.61340 - 0.417192i) q^{66} +(-6.38137 + 0.334434i) q^{67} +(27.0833 - 7.25694i) q^{68} +(1.77674 - 1.15691i) q^{69} +(13.3488 - 9.41033i) q^{70} +(-4.99523 - 1.62305i) q^{71} +(26.6893 - 13.6810i) q^{72} +(10.0480 - 3.85708i) q^{73} +(-11.0229 - 19.0922i) q^{74} +(4.03410 + 7.66329i) q^{75} +6.38425 q^{76} +(-1.39530 - 0.444345i) q^{77} +(2.31718 + 2.56719i) q^{78} +(3.28376 - 2.95671i) q^{79} +(-36.5547 + 1.17856i) q^{80} +(2.82290 + 8.54583i) q^{81} +(-4.58928 + 1.22969i) q^{82} +(-0.937343 + 1.83964i) q^{83} +(-25.7593 + 0.182299i) q^{84} +(3.65940 - 10.5360i) q^{85} +(-26.3890 + 2.77360i) q^{86} +(-9.91087 + 13.6762i) q^{87} +(3.48212 + 4.30006i) q^{88} +(0.159434 + 1.51691i) q^{89} +(2.26125 - 18.3805i) q^{90} +(-0.506075 - 1.84540i) q^{91} +(6.13101 + 3.12391i) q^{92} +(-6.96868 + 4.03472i) q^{93} +(18.8357 + 16.9598i) q^{94} +(1.42574 - 2.10159i) q^{95} +(36.5767 + 23.6898i) q^{96} +(2.79913 - 1.42623i) q^{97} +(17.3200 + 8.57094i) q^{98} +(-1.43593 + 0.833715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more