LMFDB - Embedded newform 99.2.p.a.83.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,2,Mod(2,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			83.5
Character	$\chi$	$=$	99.83
Dual form			99.2.p.a.68.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.784831 - 0.166821i) q^{2} +(0.527446 + 1.64979i) q^{3} +(-1.23896 - 0.551620i) q^{4} +(0.600562 + 2.82542i) q^{5} +(-0.138737 - 1.38279i) q^{6} +(-1.32545 + 0.139311i) q^{7} +(2.17861 + 1.58285i) q^{8} +(-2.44360 + 1.74035i) q^{9} -2.31767i q^{10} +(3.24258 + 0.696897i) q^{11} +(0.256572 - 2.33497i) q^{12} +(-0.435761 - 0.392361i) q^{13} +(1.06350 + 0.111778i) q^{14} +(-4.34458 + 2.48106i) q^{15} +(0.369177 + 0.410013i) q^{16} +(0.407327 - 1.25362i) q^{17} +(2.20814 - 0.958237i) q^{18} +(4.21041 - 5.79513i) q^{19} +(0.814488 - 3.83187i) q^{20} +(-0.928938 - 2.11323i) q^{21} +(-2.42862 - 1.08788i) q^{22} +(-2.62500 + 1.51554i) q^{23} +(-1.46227 + 4.42911i) q^{24} +(-3.05460 + 1.36000i) q^{25} +(0.276545 + 0.380632i) q^{26} +(-4.16008 - 3.11348i) q^{27} +(1.71903 + 0.558546i) q^{28} +(-0.136407 - 1.29783i) q^{29} +(3.82366 - 1.22244i) q^{30} +(5.05291 - 5.61183i) q^{31} +(-2.91425 - 5.04763i) q^{32} +(0.560556 + 5.71715i) q^{33} +(-0.528814 + 0.915932i) q^{34} +(-1.18963 - 3.66129i) q^{35} +(3.98754 - 0.808283i) q^{36} +(-3.23755 + 2.35222i) q^{37} +(-4.27121 + 3.84582i) q^{38} +(0.417472 - 0.925863i) q^{39} +(-3.16383 + 7.10608i) q^{40} +(-0.235357 + 2.23927i) q^{41} +(0.376527 + 1.81350i) q^{42} +(11.2365 + 6.48742i) q^{43} +(-3.63301 - 2.65210i) q^{44} +(-6.38475 - 5.85901i) q^{45} +(2.31301 - 0.751541i) q^{46} +(4.70724 + 10.5726i) q^{47} +(-0.481713 + 0.825325i) q^{48} +(-5.10962 + 1.08608i) q^{49} +(2.62423 - 0.557796i) q^{50} +(2.28306 + 0.0107839i) q^{51} +(0.323456 + 0.726494i) q^{52} +(3.40948 - 1.10781i) q^{53} +(2.74556 + 3.13755i) q^{54} +(-0.0216557 + 9.58019i) q^{55} +(-3.10815 - 1.79449i) q^{56} +(11.7815 + 3.88966i) q^{57} +(-0.109449 + 1.04133i) q^{58} +(2.43702 - 5.47364i) q^{59} +(6.75136 - 0.677371i) q^{60} +(-5.87674 + 5.29144i) q^{61} +(-4.90186 + 3.56141i) q^{62} +(2.99642 - 2.64717i) q^{63} +(1.10416 + 3.39825i) q^{64} +(0.846884 - 1.46685i) q^{65} +(0.513798 - 4.58051i) q^{66} +(-4.35166 - 7.53730i) q^{67} +(-1.19619 + 1.32850i) q^{68} +(-3.88487 - 3.53132i) q^{69} +(0.322875 + 3.07195i) q^{70} +(-4.54327 - 1.47620i) q^{71} +(-8.07836 - 0.0763170i) q^{72} +(-5.16130 - 7.10392i) q^{73} +(2.93333 - 1.30600i) q^{74} +(-3.85485 - 4.32212i) q^{75} +(-8.41325 + 4.85739i) q^{76} +(-4.39497 - 0.471977i) q^{77} +(-0.482099 + 0.657003i) q^{78} +(2.86894 - 13.4973i) q^{79} +(-0.936746 + 1.28932i) q^{80} +(2.94237 - 8.50544i) q^{81} +(0.558273 - 1.71819i) q^{82} +(-7.20241 - 7.99909i) q^{83} +(-0.0147874 + 3.13063i) q^{84} +(3.78664 + 0.397992i) q^{85} +(-7.73655 - 6.96602i) q^{86} +(2.06920 - 0.909579i) q^{87} +(5.96123 + 6.65078i) q^{88} +8.87289i q^{89} +(4.03355 + 5.66345i) q^{90} +(0.632240 + 0.459350i) q^{91} +(4.08827 - 0.429695i) q^{92} +(11.9235 + 5.37630i) q^{93} +(-1.93065 - 9.08301i) q^{94} +(18.9023 + 8.41585i) q^{95} +(6.79040 - 7.47025i) q^{96} +(0.802287 + 0.170531i) q^{97} +4.19137 q^{98} +(-9.13642 + 3.94029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.784831	−	0.166821i	−0.554960	−	0.117960i	−0.0781093	−	0.996945i	$-0.524888\pi$
$2$	−0.784831	−	0.166821i	−0.554960	−	0.117960i	−0.476850	+	0.878984i	$0.658222\pi$
$3$	0.527446	+	1.64979i	0.304521	+	0.952506i
$3$	0.527446	+	1.64979i	0.304521	+	0.952506i
$4$	−1.23896	−	0.551620i	−0.619480	−	0.275810i
$5$	0.600562	+	2.82542i	0.268579	+	1.26357i	0.881031	+	0.473059i	$0.156850\pi$
$5$	0.600562	+	2.82542i	0.268579	+	1.26357i	−0.612451	+	0.790508i	$0.709817\pi$
$6$	−0.138737	−	1.38279i	−0.0566392	−	0.564524i
$7$	−1.32545	+	0.139311i	−0.500974	+	0.0526544i	−0.351645	−	0.936133i	$-0.614378\pi$
$7$	−1.32545	+	0.139311i	−0.500974	+	0.0526544i	−0.149328	+	0.988788i	$0.547711\pi$
$8$	2.17861	+	1.58285i	0.770254	+	0.559622i
$9$	−2.44360	+	1.74035i	−0.814534	+	0.580117i
$10$		−	2.31767i		−	0.732910i
$11$	3.24258	+	0.696897i	0.977675	+	0.210122i
$11$	3.24258	+	0.696897i	0.977675	+	0.210122i
$12$	0.256572	−	2.33497i	0.0740659	−	0.674048i
$13$	−0.435761	−	0.392361i	−0.120858	−	0.108821i	0.606486	−	0.795095i	$-0.292579\pi$
$13$	−0.435761	−	0.392361i	−0.120858	−	0.108821i	−0.727344	+	0.686273i	$0.759245\pi$
$14$	1.06350	+	0.111778i	0.284231	+	0.0298739i
$15$	−4.34458	+	2.48106i	−1.12177	+	0.640606i
$16$	0.369177	+	0.410013i	0.0922944	+	0.102503i
$17$	0.407327	−	1.25362i	0.0987913	−	0.304048i	−0.889432	−	0.457068i	$-0.848900\pi$
$17$	0.407327	−	1.25362i	0.0987913	−	0.304048i	0.988223	+	0.153019i	$0.0488997\pi$
$18$	2.20814	−	0.958237i	0.520464	−	0.225859i
$19$	4.21041	−	5.79513i	0.965935	−	1.32949i	0.0218608	−	0.999761i	$-0.493041\pi$
$19$	4.21041	−	5.79513i	0.965935	−	1.32949i	0.944074	−	0.329734i	$-0.106959\pi$
$20$	0.814488	−	3.83187i	0.182125	−	0.856831i
$21$	−0.928938	−	2.11323i	−0.202711	−	0.461146i
$22$	−2.42862	−	1.08788i	−0.517784	−	0.231936i
$23$	−2.62500	+	1.51554i	−0.547350	+	0.316013i	−0.748053	−	0.663639i	$-0.769011\pi$
$23$	−2.62500	+	1.51554i	−0.547350	+	0.316013i	0.200702	+	0.979652i	$0.435678\pi$
$24$	−1.46227	+	4.42911i	−0.298484	+	0.904088i
$25$	−3.05460	+	1.36000i	−0.610921	+	0.272000i
$26$	0.276545	+	0.380632i	0.0542349	+	0.0746480i
$27$	−4.16008	−	3.11348i	−0.800607	−	0.599190i
$28$	1.71903	+	0.558546i	0.324866	+	0.105555i
$29$	−0.136407	−	1.29783i	−0.0253302	−	0.241001i	−0.999860	−	0.0167422i	$-0.994671\pi$
$29$	−0.136407	−	1.29783i	−0.0253302	−	0.241001i	0.974530	−	0.224259i	$-0.0719961\pi$
$30$	3.82366	−	1.22244i	0.698101	−	0.223187i
$31$	5.05291	−	5.61183i	0.907530	−	1.00791i	−0.0923955	−	0.995722i	$-0.529452\pi$
$31$	5.05291	−	5.61183i	0.907530	−	1.00791i	0.999926	−	0.0121919i	$-0.00388091\pi$
$32$	−2.91425	−	5.04763i	−0.515171	−	0.892303i
$33$	0.560556	+	5.71715i	0.0975804	+	0.995228i
$34$	−0.528814	+	0.915932i	−0.0906908	+	0.157081i
$35$	−1.18963	−	3.66129i	−0.201084	−	0.618872i
$36$	3.98754	−	0.808283i	0.664589	−	0.134714i
$37$	−3.23755	+	2.35222i	−0.532250	+	0.386702i	−0.821199	−	0.570642i	$-0.806694\pi$
$37$	−3.23755	+	2.35222i	−0.532250	+	0.386702i	0.288949	+	0.957345i	$0.406694\pi$
$38$	−4.27121	+	3.84582i	−0.692882	+	0.623874i
$39$	0.417472	−	0.925863i	0.0668490	−	0.148257i
$40$	−3.16383	+	7.10608i	−0.500246	+	1.12357i
$41$	−0.235357	+	2.23927i	−0.0367566	+	0.349716i	0.960651	+	0.277758i	$0.0895913\pi$
$41$	−0.235357	+	2.23927i	−0.0367566	+	0.349716i	−0.997408	+	0.0719576i	$0.977075\pi$
$42$	0.376527	+	1.81350i	0.0580994	+	0.279829i
$43$	11.2365	+	6.48742i	1.71356	+	0.989322i	0.929652	+	0.368440i	$0.120108\pi$
$43$	11.2365	+	6.48742i	1.71356	+	0.989322i	0.783904	+	0.620882i	$0.213225\pi$
$44$	−3.63301	−	2.65210i	−0.547696	−	0.399819i
$45$	−6.38475	−	5.85901i	−0.951783	−	0.873410i
$46$	2.31301	−	0.751541i	0.341034	−	0.110809i
$47$	4.70724	+	10.5726i	0.686622	+	1.54218i	0.833196	+	0.552978i	$0.186509\pi$
$47$	4.70724	+	10.5726i	0.686622	+	1.54218i	−0.146574	+	0.989200i	$0.546825\pi$
$48$	−0.481713	+	0.825325i	−0.0695293	+	0.119125i
$49$	−5.10962	+	1.08608i	−0.729946	+	0.155155i
$50$	2.62423	−	0.557796i	0.371122	−	0.0788843i
$51$	2.28306	+	0.0107839i	0.319692	+	0.00151004i
$52$	0.323456	+	0.726494i	0.0448553	+	0.100747i
$53$	3.40948	−	1.10781i	0.468328	−	0.152169i	−0.0653400	−	0.997863i	$-0.520813\pi$
$53$	3.40948	−	1.10781i	0.468328	−	0.152169i	0.533668	+	0.845694i	$0.320813\pi$
$54$	2.74556	+	3.13755i	0.373624	+	0.426966i
$55$	−0.0216557	+	9.58019i	−0.00292006	+	1.29179i
$56$	−3.10815	−	1.79449i	−0.415343	−	0.239799i
$57$	11.7815	+	3.88966i	1.56050	+	0.515198i
$58$	−0.109449	+	1.04133i	−0.0143713	+	0.136734i
$59$	2.43702	−	5.47364i	0.317273	−	0.712608i	−0.682561	−	0.730829i	$-0.739134\pi$
$59$	2.43702	−	5.47364i	0.317273	−	0.712608i	0.999834	+	0.0182214i	$0.00580036\pi$
$60$	6.75136	−	0.677371i	0.871597	−	0.0874482i
$61$	−5.87674	+	5.29144i	−0.752439	+	0.677499i	−0.953268	−	0.302127i	$-0.902303\pi$
$61$	−5.87674	+	5.29144i	−0.752439	+	0.677499i	0.200829	+	0.979626i	$0.435637\pi$
$62$	−4.90186	+	3.56141i	−0.622536	+	0.452299i
$63$	2.99642	−	2.64717i	0.377514	−	0.333512i
$64$	1.10416	+	3.39825i	0.138020	+	0.424781i
$65$	0.846884	−	1.46685i	0.105043	−	0.181940i
$66$	0.513798	−	4.58051i	0.0632442	−	0.563822i
$67$	−4.35166	−	7.53730i	−0.531640	−	0.920828i	−0.999318	−	0.0369287i	$-0.988243\pi$
$67$	−4.35166	−	7.53730i	−0.531640	−	0.920828i	0.467678	−	0.883899i	$-0.345091\pi$
$68$	−1.19619	+	1.32850i	−0.145059	+	0.161104i
$69$	−3.88487	−	3.53132i	−0.467684	−	0.425121i
$70$	0.322875	+	3.07195i	0.0385910	+	0.367169i
$71$	−4.54327	−	1.47620i	−0.539187	−	0.175192i	0.0267483	−	0.999642i	$-0.491485\pi$
$71$	−4.54327	−	1.47620i	−0.539187	−	0.175192i	−0.565935	+	0.824450i	$0.691485\pi$
$72$	−8.07836	−	0.0763170i	−0.952044	−	0.00899404i
$73$	−5.16130	−	7.10392i	−0.604084	−	0.831451i	0.391990	−	0.919969i	$-0.371787\pi$
$73$	−5.16130	−	7.10392i	−0.604084	−	0.831451i	−0.996075	+	0.0885185i	$0.971787\pi$
$74$	2.93333	−	1.30600i	0.340993	−	0.151820i
$75$	−3.85485	−	4.32212i	−0.445119	−	0.499076i
$76$	−8.41325	+	4.85739i	−0.965065	+	0.557181i
$77$	−4.39497	−	0.471977i	−0.500853	−	0.0537867i
$78$	−0.482099	+	0.657003i	−0.0545869	+	0.0743910i
$79$	2.86894	−	13.4973i	0.322781	−	1.51857i	−0.455263	−	0.890357i	$-0.650455\pi$
$79$	2.86894	−	13.4973i	0.322781	−	1.51857i	0.778045	−	0.628209i	$-0.216212\pi$
$80$	−0.936746	+	1.28932i	−0.104731	+	0.144150i
$81$	2.94237	−	8.50544i	0.326930	−	0.945049i
$82$	0.558273	−	1.71819i	0.0616510	−	0.189742i
$83$	−7.20241	−	7.99909i	−0.790567	−	0.878014i	0.204331	−	0.978902i	$-0.434498\pi$
$83$	−7.20241	−	7.99909i	−0.790567	−	0.878014i	−0.994898	+	0.100888i	$0.967832\pi$
$84$	−0.0147874	+	3.13063i	−0.00161343	+	0.341580i
$85$	3.78664	+	0.397992i	0.410719	+	0.0431683i
$86$	−7.73655	−	6.96602i	−0.834254	−	0.751165i
$87$	2.06920	−	0.909579i	0.221841	−	0.0975171i
$88$	5.96123	+	6.65078i	0.635469	+	0.708976i
$89$			8.87289i			0.940524i	0.882527	+	0.470262i	$0.155841\pi$
$89$			8.87289i			0.940524i	−0.882527	+	0.470262i	$0.844159\pi$
$90$	4.03355	+	5.66345i	0.425173	+	0.596980i
$91$	0.632240	+	0.459350i	0.0662768	+	0.0481529i
$92$	4.08827	−	0.429695i	0.426232	−	0.0447988i
$93$	11.9235	+	5.37630i	1.23641	+	0.557496i
$94$	−1.93065	−	9.08301i	−0.199132	−	0.936841i
$95$	18.9023	+	8.41585i	1.93934	+	0.863448i
$96$	6.79040	−	7.47025i	0.693043	−	0.762429i
$97$	0.802287	+	0.170531i	0.0814599	+	0.0173148i	0.248461	−	0.968642i	$-0.420075\pi$
$97$	0.802287	+	0.170531i	0.0814599	+	0.0173148i	−0.167001	+	0.985957i	$0.553408\pi$
$98$	4.19137			0.423392
$99$	−9.13642	+	3.94029i	−0.918245	+	0.396014i
$100$	4.53473			0.453473
$101$	−16.7720	−	3.56501i	−1.66888	−	0.354732i	−0.725957	−	0.687740i	$-0.758603\pi$
$101$	−16.7720	−	3.56501i	−1.66888	−	0.354732i	−0.942924	+	0.333008i	$0.891936\pi$
$102$	−1.79002	−	0.389325i	−0.177238	−	0.0385490i
$103$	8.91310	+	3.96837i	0.878234	+	0.391015i	0.795784	−	0.605580i	$-0.207059\pi$
$103$	8.91310	+	3.96837i	0.878234	+	0.391015i	0.0824495	+	0.996595i	$0.473726\pi$
$104$	−0.328303	−	1.54455i	−0.0321928	−	0.151455i
$105$	5.41289	−	3.89377i	0.528244	−	0.379993i
$106$	−2.86067	+	0.300669i	−0.277853	+	0.0292035i
$107$	−2.38113	−	1.72999i	−0.230193	−	0.167245i	0.466710	−	0.884410i	$-0.345439\pi$
$107$	−2.38113	−	1.72999i	−0.230193	−	0.167245i	−0.696903	+	0.717165i	$0.745439\pi$
$108$	3.43671	+	6.15226i	0.330697	+	0.592002i
$109$		−	1.43952i		−	0.137881i	−0.997621	−	0.0689404i	$-0.978038\pi$
$109$		−	1.43952i		−	0.137881i	0.997621	−	0.0689404i	$-0.0219618\pi$
$110$	1.61517	−	7.51522i	0.154001	−	0.716548i
$111$	−5.58830	−	4.10060i	−0.530418	−	0.389212i
$112$	−0.546446	−	0.492022i	−0.0516343	−	0.0464917i
$113$	1.88118	+	0.197720i	0.176966	+	0.0185999i	0.192597	−	0.981278i	$-0.438309\pi$
$113$	1.88118	+	0.197720i	0.176966	+	0.0185999i	−0.0156308	+	0.999878i	$0.504976\pi$
$114$	−8.59762	−	5.01813i	−0.805241	−	0.469991i
$115$	−5.85853	−	6.50655i	−0.546310	−	0.606739i
$116$	−0.546906	+	1.68320i	−0.0507790	+	0.156282i
$117$	1.74767	+	0.200397i	0.161572	+	0.0185267i
$118$	−2.82577	+	3.88934i	−0.260133	+	0.358043i
$119$	−0.365249	+	1.71836i	−0.0334823	+	0.157522i
$120$	−13.3923	−	1.47157i	−1.22254	−	0.134336i
$121$	10.0287	+	4.51949i	0.911697	+	0.410863i
$122$	5.49497	−	3.17252i	0.497491	−	0.287227i
$123$	−3.81846	+	0.792807i	−0.344299	+	0.0714850i
$124$	−9.35596	+	4.16554i	−0.840190	+	0.374077i
$125$	2.81217	+	3.87062i	0.251528	+	0.346199i
$126$	−2.79329	+	1.57771i	−0.248846	+	0.140554i
$127$	−4.49091	−	1.45919i	−0.398504	−	0.129482i	0.102907	−	0.994691i	$-0.467186\pi$
$127$	−4.49091	−	1.45919i	−0.398504	−	0.129482i	−0.501411	+	0.865209i	$0.667186\pi$
$128$	0.918810	+	8.74189i	0.0812121	+	0.772681i
$129$	−4.77619	+	21.9597i	−0.420520	+	1.93344i
$130$	−0.909362	+	1.00995i	−0.0797563	+	0.0885784i
$131$	−3.94244	−	6.82851i	−0.344453	−	0.596609i	0.640802	−	0.767707i	$-0.278602\pi$
$131$	−3.94244	−	6.82851i	−0.344453	−	0.596609i	−0.985254	+	0.171097i	$0.945269\pi$
$132$	2.45919	−	7.39253i	0.214045	−	0.643437i
$133$	−4.77337	+	8.26772i	−0.413904	+	0.716903i
$134$	2.15794	+	6.64146i	0.186418	+	0.573735i
$135$	6.29851	−	13.6238i	0.542090	−	1.17255i
$136$	2.87170	−	2.08641i	0.246247	−	0.178909i
$137$	5.00586	−	4.50730i	0.427679	−	0.385084i	−0.426990	−	0.904256i	$-0.640426\pi$
$137$	5.00586	−	4.50730i	0.427679	−	0.385084i	0.854670	+	0.519172i	$0.173760\pi$
$138$	2.45987	+	3.41957i	0.209398	+	0.291093i
$139$	3.01617	−	6.77443i	0.255828	−	0.574600i	−0.739279	−	0.673399i	$-0.764834\pi$
$139$	3.01617	−	6.77443i	0.255828	−	0.574600i	0.995107	+	0.0987995i	$0.0315002\pi$
$140$	−0.545745	+	5.19242i	−0.0461239	+	0.438839i
$141$	−14.9598	+	13.3425i	−1.25984	+	1.12364i
$142$	3.31944	+	1.91648i	0.278561	+	0.160827i
$143$	−1.13956	−	1.57594i	−0.0952945	−	0.131787i
$144$	−1.61569	−	0.359410i	−0.134641	−	0.0299509i
$145$	3.58500	−	1.16484i	0.297718	−	0.0967344i
$146$	2.86567	+	6.43639i	0.237164	+	0.532680i
$147$	−4.48686	−	7.85694i	−0.370070	−	0.648029i
$148$	5.30873	−	1.12840i	0.436375	−	0.0927543i
$149$	6.02820	−	1.28133i	0.493850	−	0.104971i	0.0457470	−	0.998953i	$-0.485433\pi$
$149$	6.02820	−	1.28133i	0.493850	−	0.104971i	0.448103	+	0.893982i	$0.352100\pi$
$150$	2.30438	+	4.03521i	0.188152	+	0.329473i
$151$	−8.01969	−	18.0125i	−0.652633	−	1.46584i	−0.871656	−	0.490118i	$-0.836954\pi$
$151$	−8.01969	−	18.0125i	−0.652633	−	1.46584i	0.219023	−	0.975720i	$-0.429713\pi$
$152$	18.3457	−	5.96087i	1.48803	−	0.483490i
$153$	1.18640	+	3.77225i	0.0959146	+	0.304968i
$154$	3.37057	+	1.10360i	0.271609	+	0.0889303i
$155$	18.8904	+	10.9064i	1.51731	+	0.876020i
$156$	−1.02796	+	0.916821i	−0.0823023	+	0.0734044i
$157$	−0.509551	+	4.84805i	−0.0406666	+	0.386917i	0.955191	+	0.295990i	$0.0956495\pi$
$157$	−0.509551	+	4.84805i	−0.0406666	+	0.386917i	−0.995858	+	0.0909266i	$0.971017\pi$
$158$	−4.50327	+	10.1145i	−0.358261	+	0.804667i
$159$	3.62596	+	5.04061i	0.287558	+	0.399746i
$160$	12.5115	−	11.2654i	0.989120	−	0.890608i
$161$	3.26818	−	2.37447i	0.257569	−	0.187134i
$162$	−3.72815	+	6.18449i	−0.292911	+	0.485899i
$163$	3.43006	+	10.5566i	0.268663	+	0.826859i	0.990827	+	0.135137i	$0.0431476\pi$
$163$	3.43006	+	10.5566i	0.268663	+	0.826859i	−0.722164	+	0.691722i	$0.756852\pi$
$164$	1.52683	−	2.64454i	0.119225	−	0.206504i
$165$	−15.8167	+	5.01731i	−1.23133	+	0.390597i
$166$	4.31826	+	7.47945i	0.335162	+	0.580518i
$167$	−14.2119	+	15.7839i	−1.09975	+	1.22140i	−0.126425	+	0.991976i	$0.540350\pi$
$167$	−14.2119	+	15.7839i	−1.09975	+	1.22140i	−0.973327	+	0.229422i	$0.926316\pi$
$168$	1.32115	−	6.07428i	0.101929	−	0.468641i
$169$	−1.32293	−	12.5868i	−0.101764	−	0.968218i
$170$	−2.90548	−	0.944048i	−0.222840	−	0.0724052i
$171$	−0.203005	+	21.4886i	−0.0155241	+	1.64327i
$172$	−10.3430	−	14.2360i	−0.788648	−	1.08548i
$173$	−11.3216	+	5.04070i	−0.860764	+	0.383237i	−0.789154	−	0.614196i	$-0.789481\pi$
$173$	−11.3216	+	5.04070i	−0.860764	+	0.383237i	−0.0716106	+	0.997433i	$0.522814\pi$
$174$	−1.77571	+	0.368681i	−0.134616	+	0.0279496i
$175$	3.85927	−	2.22815i	0.291733	−	0.168432i
$176$	0.911351	+	1.58678i	0.0686957	+	0.119608i
$177$	10.3157	+	1.13352i	0.775379	+	0.0852004i
$178$	1.48019	−	6.96372i	0.110945	−	0.521953i
$179$	6.56098	−	9.03041i	0.490390	−	0.674964i	−0.490070	−	0.871683i	$-0.663029\pi$
$179$	6.56098	−	9.03041i	0.490390	−	0.674964i	0.980460	+	0.196719i	$0.0630286\pi$
$180$	4.67850	+	10.7810i	0.348715	+	0.803572i
$181$	−0.00588405	+	0.0181092i	−0.000437358	+	0.00134605i	−0.951275	−	0.308344i	$-0.900225\pi$
$181$	−0.00588405	+	0.0181092i	−0.000437358	+	0.00134605i	0.950838	+	0.309690i	$0.100225\pi$
$182$	−0.419573	−	0.465983i	−0.0311008	−	0.0345410i
$183$	−11.8294	−	6.90442i	−0.874455	−	0.510389i
$184$	−8.11772	−	0.853207i	−0.598446	−	0.0628992i
$185$	−8.59036	−	7.73479i	−0.631576	−	0.568673i
$186$	−8.46103	−	6.20857i	−0.620393	−	0.455235i
$187$	2.19444	−	3.78111i	0.160473	−	0.276502i
$188$		−	15.6957i		−	1.14473i
$189$	5.94772	+	3.54723i	0.432633	+	0.258023i
$190$	−13.4312	−	9.75833i	−0.974401	−	0.707943i
$191$	2.60097	−	0.273373i	0.188199	−	0.0197806i	−0.00995981	−	0.999950i	$-0.503170\pi$
$191$	2.60097	−	0.273373i	0.188199	−	0.0197806i	0.198159	+	0.980170i	$0.436504\pi$
$192$	−5.02400	+	3.61402i	−0.362576	+	0.260819i
$193$	2.67062	+	12.5643i	0.192236	+	0.904397i	0.963464	+	0.267839i	$0.0863094\pi$
$193$	2.67062	+	12.5643i	0.192236	+	0.904397i	−0.771228	+	0.636559i	$0.780357\pi$
$194$	−0.601212	−	0.267677i	−0.0431645	−	0.0192181i
$195$	2.86667	+	0.623496i	0.205287	+	0.0446495i
$196$	6.92972	+	1.47296i	0.494980	+	0.105211i
$197$	6.88153			0.490288			0.245144	−	0.969487i	$-0.421165\pi$
$197$	6.88153			0.490288			0.245144	+	0.969487i	$0.421165\pi$
$198$	7.82787	−	1.56832i	0.556303	−	0.111455i
$199$	0.0675681			0.00478977			0.00239489	−	0.999997i	$-0.499238\pi$
$199$	0.0675681			0.00478977			0.00239489	+	0.999997i	$0.499238\pi$
$200$	−8.80745	−	1.87208i	−0.622781	−	0.132376i
$201$	10.1397	−	11.1548i	0.715198	−	0.786802i
$202$	12.5685	+	5.59586i	0.884317	+	0.393723i
$203$	0.361603	+	1.70121i	0.0253796	+	0.119401i
$204$	−2.82267	−	1.27274i	−0.197626	−	0.0891097i
$205$	−6.46823	+	0.679839i	−0.451761	+	0.0474820i
$206$	−6.33327	−	4.60139i	−0.441260	−	0.320594i
$207$	3.77687	−	8.27180i	0.262511	−	0.574930i
$208$		−	0.323519i		−	0.0224320i
$209$	17.6912	−	15.8570i	1.22373	−	1.09685i
$210$	−4.89777	+	2.15297i	−0.337978	+	0.148569i
$211$	0.904851	+	0.814732i	0.0622925	+	0.0560884i	0.699689	−	0.714448i	$-0.253322\pi$
$211$	0.904851	+	0.814732i	0.0622925	+	0.0560884i	−0.637396	+	0.770536i	$0.719989\pi$
$212$	−4.83530	−	0.508210i	−0.332090	−	0.0349040i
$213$	0.0390820	−	8.27404i	0.00267785	−	0.566928i
$214$	1.58019	+	1.75498i	0.108019	+	0.119968i
$215$	−11.5815	+	35.6440i	−0.789848	+	2.43090i
$216$	−4.13499	−	13.3678i	−0.281351	−	0.909566i
$217$	−5.91561	+	8.14213i	−0.401577	+	0.552724i
$218$	−0.240142	+	1.12978i	−0.0162645	+	0.0765183i
$219$	8.99765	−	12.2620i	0.608005	−	0.828588i
$220$	5.31146	−	11.8575i	0.358098	−	0.799434i
$221$	−0.669370	+	0.386461i	−0.0450267	+	0.0259962i
$222$	3.70180	+	4.15053i	0.248449	+	0.278565i
$223$	−11.9233	+	5.30858i	−0.798441	+	0.355489i	−0.765064	−	0.643954i	$-0.777293\pi$
$223$	−11.9233	+	5.30858i	−0.798441	+	0.355489i	−0.0333766	+	0.999443i	$0.510626\pi$
$224$	4.56588	+	6.28440i	0.305071	+	0.419894i
$225$	5.09736	−	8.63937i	0.339824	−	0.575958i
$226$	−1.44342	−	0.468997i	−0.0960151	−	0.0311972i
$227$	0.0826876	+	0.786720i	0.00548817	+	0.0522164i	0.996923	−	0.0783842i	$-0.0249761\pi$
$227$	0.0826876	+	0.786720i	0.00548817	+	0.0522164i	−0.991435	+	0.130601i	$0.958309\pi$
$228$	−12.4512	−	11.3181i	−0.824601	−	0.749557i
$229$	−6.53565	+	7.25857i	−0.431888	+	0.479660i	−0.919326	−	0.393498i	$-0.871265\pi$
$229$	−6.53565	+	7.25857i	−0.431888	+	0.479660i	0.487438	+	0.873158i	$0.337932\pi$
$230$	3.51252	+	6.08387i	0.231609	+	0.401159i
$231$	−1.53945	−	7.49971i	−0.101288	−	0.493445i
$232$	1.75709	−	3.04337i	0.115359	−	0.199807i
$233$	−5.12103	−	15.7609i	−0.335490	−	1.03253i	−0.966480	−	0.256741i	$-0.917351\pi$
$233$	−5.12103	−	15.7609i	−0.335490	−	1.03253i	0.630991	−	0.775790i	$-0.282649\pi$
$234$	−1.33820	−	0.448826i	−0.0874807	−	0.0293407i
$235$	−27.0452	+	19.6495i	−1.76423	+	1.28179i
$236$	−6.03875	+	5.43731i	−0.393089	+	0.353939i
$237$	23.7809	−	2.38596i	1.54474	−	0.154985i
$238$	0.573318	−	1.28769i	0.0371627	−	0.0834688i
$239$	−0.127156	+	1.20981i	−0.00822505	+	0.0782562i	−0.997864	−	0.0653194i	$-0.979193\pi$
$239$	−0.127156	+	1.20981i	−0.00822505	+	0.0782562i	0.989639	+	0.143576i	$0.0458600\pi$
$240$	−2.62119	−	0.865385i	−0.169197	−	0.0558604i
$241$	0.657074	+	0.379362i	0.0423258	+	0.0244368i	0.521014	−	0.853548i	$-0.325554\pi$
$241$	0.657074	+	0.379362i	0.0423258	+	0.0244368i	−0.478688	+	0.877985i	$0.658887\pi$
$242$	−7.11687	−	5.22003i	−0.457490	−	0.335556i
$243$	15.5841	+	0.368119i	0.999721	+	0.0236148i
$244$	10.1999	−	3.31415i	0.652982	−	0.212167i
$245$	−6.13728	−	13.7846i	−0.392097	−	0.880664i
$246$	3.12911	+	0.0147801i	0.199505	+	0.000942348i
$247$	−4.10852	+	0.873293i	−0.261419	+	0.0555663i
$248$	19.8910	−	4.22796i	1.26308	−	0.268476i
$249$	9.39791	−	16.1015i	0.595568	−	1.02039i
$250$	−1.56138	−	3.50691i	−0.0987502	−	0.221797i
$251$	−9.34419	+	3.03611i	−0.589800	+	0.191638i	−0.588686	−	0.808362i	$-0.700355\pi$
$251$	−9.34419	+	3.03611i	−0.589800	+	0.191638i	−0.00111390	+	0.999999i	$0.500355\pi$
$252$	−5.17268	+	1.62685i	−0.325848	+	0.102482i
$253$	−9.56795	+	3.08492i	−0.601532	+	0.193947i
$254$	3.28119	+	1.89439i	0.205880	+	0.118865i
$255$	1.34065	+	6.45707i	0.0839546	+	0.404357i
$256$	1.48421	−	14.1213i	0.0927630	−	0.882581i
$257$	9.06399	−	20.3581i	0.565396	−	1.26990i	−0.374115	−	0.927382i	$-0.622053\pi$
$257$	9.06399	−	20.3581i	0.565396	−	1.26990i	0.939511	−	0.342518i	$-0.111280\pi$
$258$	7.41184	−	16.4379i	0.461441	−	1.02338i
$259$	3.96353	−	3.56878i	0.246282	−	0.221753i
$260$	−1.85840	+	1.35020i	−0.115253	+	0.0837361i
$261$	2.59200	+	2.93398i	0.160441	+	0.181609i
$262$	1.95501	+	6.01691i	0.120781	+	0.371726i
$263$	−7.68495	+	13.3107i	−0.473874	+	0.820774i	−0.999553	−	0.0299090i	$-0.990478\pi$
$263$	−7.68495	+	13.3107i	−0.473874	+	0.820774i	0.525678	+	0.850683i	$0.323812\pi$
$264$	−7.82816	+	13.3427i	−0.481790	+	0.821186i
$265$	5.17763	+	8.96791i	0.318059	+	0.550894i
$266$	5.12552	−	5.69247i	0.314266	−	0.349028i
$267$	−14.6384	+	4.67997i	−0.895855	+	0.286410i
$268$	1.23381	+	11.7389i	0.0753667	+	0.717066i
$269$	−0.906419	−	0.294513i	−0.0552653	−	0.0179568i	0.281254	−	0.959633i	$-0.409250\pi$
$269$	−0.906419	−	0.294513i	−0.0552653	−	0.0179568i	−0.336519	+	0.941677i	$0.609250\pi$
$270$	−7.21601	+	9.64167i	−0.439152	+	0.586773i
$271$	13.1444	+	18.0917i	0.798465	+	1.09899i	0.993002	+	0.118098i	$0.0376796\pi$
$271$	13.1444	+	18.0917i	0.798465	+	1.09899i	−0.194537	+	0.980895i	$0.562320\pi$
$272$	0.664378	−	0.295800i	0.0402838	−	0.0179355i
$273$	−0.424356	+	1.28534i	−0.0256832	+	0.0777926i
$274$	−4.68067	+	2.70238i	−0.282769	+	0.163257i
$275$	−10.8526	+	2.28116i	−0.654435	+	0.137559i
$276$	2.86525	+	6.51814i	0.172468	+	0.392346i
$277$	2.15548	−	10.1407i	0.129510	−	0.609298i	−0.864740	−	0.502219i	$-0.832517\pi$
$277$	2.15548	−	10.1407i	0.129510	−	0.609298i	0.994251	−	0.107079i	$-0.0341497\pi$
$278$	−3.49730	+	4.81362i	−0.209754	+	0.288702i
$279$	−2.58076	+	22.5069i	−0.154506	+	1.34745i
$280$	3.20355	−	9.85952i	0.191449	−	0.589219i
$281$	−6.35805	−	7.06133i	−0.379290	−	0.421244i	0.523028	−	0.852315i	$-0.324802\pi$
$281$	−6.35805	−	7.06133i	−0.379290	−	0.421244i	−0.902318	+	0.431072i	$0.858136\pi$
$282$	13.9667	−	7.97597i	0.831706	−	0.474962i
$283$	12.3436	+	1.29736i	0.733748	+	0.0771200i	0.464030	−	0.885819i	$-0.346403\pi$
$283$	12.3436	+	1.29736i	0.733748	+	0.0771200i	0.269718	+	0.962939i	$0.413070\pi$
$284$	4.81463	+	4.33511i	0.285696	+	0.257241i
$285$	−3.91441	+	35.6237i	−0.231870	+	2.11017i
$286$	0.631459	+	1.42695i	0.0373389	+	0.0843774i
$287$		−	3.00083i		−	0.177134i
$288$	15.9059	+	7.26257i	0.937264	+	0.427951i
$289$	12.3476	+	8.97108i	0.726331	+	0.527711i
$290$	−3.00794	+	0.316147i	−0.176632	+	0.0185648i
$291$	0.141823	+	1.41355i	0.00831380	+	0.0828637i
$292$	2.47598	+	11.6485i	0.144896	+	0.681680i
$293$	−23.7843	−	10.5894i	−1.38949	−	0.618642i	−0.430634	−	0.902527i	$-0.641710\pi$
$293$	−23.7843	−	10.5894i	−1.38949	−	0.618642i	−0.958858	+	0.283885i	$0.908377\pi$
$294$	2.21072	+	6.91487i	0.128932	+	0.403284i
$295$	16.9289	+	3.59836i	0.985640	+	0.209504i
$296$	−10.7766			−0.626375
$297$	−11.3196	−	12.9949i	−0.656830	−	0.754038i
$298$	−4.94488			−0.286449
$299$	1.73851	+	0.369532i	0.100541	+	0.0213706i
$300$	2.39183	+	7.48135i	0.138092	+	0.431936i
$301$	−15.7972	−	7.03339i	−0.910538	−	0.405398i
$302$	3.28924	+	15.4746i	0.189274	+	0.890466i
$303$	−2.96485	−	29.5507i	−0.170326	−	1.69764i
$304$	3.93047	−	0.413109i	0.225428	−	0.0236934i
$305$	−18.4799	−	13.4264i	−1.05815	−	0.768795i
$306$	−0.301833	−	3.15849i	−0.0172546	−	0.180559i
$307$			18.0274i			1.02888i	0.857527	+	0.514440i	$0.172000\pi$
$307$			18.0274i			1.02888i	−0.857527	+	0.514440i	$0.828000\pi$
$308$	5.18484	+	3.00912i	0.295434	+	0.171460i
$309$	−1.84578	+	16.7978i	−0.105003	+	0.955595i
$310$	−13.0063	−	11.7110i	−0.738711	−	0.665138i
$311$	12.5054	+	1.31437i	0.709117	+	0.0745312i	0.452218	−	0.891907i	$-0.350633\pi$
$311$	12.5054	+	1.31437i	0.709117	+	0.0745312i	0.256899	+	0.966438i	$0.417299\pi$
$312$	2.37501	−	1.35630i	0.134458	−	0.0767851i
$313$	7.82590	+	8.69154i	0.442346	+	0.491275i	0.922548	−	0.385883i	$-0.126103\pi$
$313$	7.82590	+	8.69154i	0.442346	+	0.491275i	−0.480202	+	0.877158i	$0.659437\pi$
$314$	1.20867	−	3.71990i	0.0682091	−	0.209926i
$315$	9.27890	+	6.87637i	0.522807	+	0.387440i
$316$	−10.9999	+	15.1401i	−0.618792	+	0.851695i
$317$	−3.42028	+	16.0912i	−0.192102	+	0.903769i	0.771459	+	0.636279i	$0.219527\pi$
$317$	−3.42028	+	16.0912i	−0.192102	+	0.903769i	−0.963561	+	0.267490i	$0.913806\pi$
$318$	−2.00489	−	4.56092i	−0.112429	−	0.255763i
$319$	0.462141	−	4.30338i	0.0258749	−	0.240943i
$320$	−8.93837	+	5.16057i	−0.499670	+	0.288485i
$321$	1.59820	−	4.84084i	0.0892030	−	0.270190i
$322$	−2.96108	+	1.31836i	−0.165015	+	0.0734692i
$323$	−5.54990	−	7.63878i	−0.308805	−	0.425033i
$324$	−8.33725	+	8.91483i	−0.463180	+	0.495268i
$325$	1.86469	+	0.605874i	0.103434	+	0.0336078i
$326$	−0.930948	−	8.85738i	−0.0515605	−	0.490565i
$327$	2.37490	−	0.759269i	0.131332	−	0.0419876i
$328$	−4.05718	+	4.50596i	−0.224020	+	0.248800i
$329$	−7.71210	−	13.3578i	−0.425182	−	0.736437i
$330$	13.2504	−	1.29918i	0.729413	−	0.0715177i
$331$	−9.81281	+	16.9963i	−0.539361	+	0.934201i	0.459577	+	0.888138i	$0.348001\pi$
$331$	−9.81281	+	16.9963i	−0.539361	+	0.934201i	−0.998939	+	0.0460631i	$0.985332\pi$
$332$	4.51104	+	13.8835i	0.247575	+	0.761958i
$333$	3.81760	−	11.3824i	0.209203	−	0.623749i
$334$	13.7871	−	10.0169i	0.754395	−	0.548100i
$335$	18.6826	−	16.8219i	1.02074	−	0.919078i
$336$	0.523511	−	1.16104i	0.0285599	−	0.0633397i
$337$	−4.33597	+	9.73874i	−0.236195	+	0.530503i	−0.992287	−	0.123963i	$-0.960440\pi$
$337$	−4.33597	+	9.73874i	−0.236195	+	0.530503i	0.756092	+	0.654466i	$0.227106\pi$
$338$	−1.06147	+	10.0992i	−0.0577365	+	0.549326i
$339$	0.666025	+	3.20783i	0.0361735	+	0.174226i
$340$	−4.47195	−	2.58188i	−0.242526	−	0.140022i
$341$	20.2954	−	14.6755i	1.09905	−	0.794721i
$342$	3.74407	−	16.8310i	0.202456	−	0.910119i
$343$	15.4939	−	5.03428i	0.836592	−	0.271825i
$344$	14.2114	+	31.9193i	0.766226	+	1.72097i
$345$	7.64437	−	13.0972i	0.411559	−	0.705129i
$346$	9.72643	−	2.06742i	0.522896	−	0.111145i
$347$	2.41627	−	0.513594i	0.129712	−	0.0275711i	−0.142598	−	0.989781i	$-0.545546\pi$
$347$	2.41627	−	0.513594i	0.129712	−	0.0275711i	0.272310	+	0.962210i	$0.412212\pi$
$348$	−3.06539	−	0.0144792i	−0.164322	−	0.000776167i
$349$	5.23329	+	11.7542i	0.280132	+	0.629186i	0.997735	−	0.0672661i	$-0.0214276\pi$
$349$	5.23329	+	11.7542i	0.280132	+	0.629186i	−0.717604	+	0.696452i	$0.754761\pi$
$350$	−3.40058	+	1.10491i	−0.181768	+	0.0590602i
$351$	0.591191	+	2.98899i	0.0315554	+	0.159540i
$352$	−5.93202	−	18.3983i	−0.316178	−	0.980631i
$353$	−2.97223	−	1.71602i	−0.158196	−	0.0913345i	0.418812	−	0.908073i	$-0.362447\pi$
$353$	−2.97223	−	1.71602i	−0.158196	−	0.0913345i	−0.577008	+	0.816738i	$0.695780\pi$
$354$	−7.90703	−	2.61050i	−0.420254	−	0.138747i
$355$	1.44237	−	13.7232i	0.0765528	−	0.728352i
$356$	4.89447	−	10.9932i	0.259406	−	0.582636i
$357$	−3.02758	+	0.303760i	−0.160237	+	0.0160767i
$358$	−6.65572	+	5.99284i	−0.351766	+	0.316731i
$359$	−4.07205	+	2.95852i	−0.214915	+	0.156145i	−0.690035	−	0.723776i	$-0.742405\pi$
$359$	−4.07205	+	2.95852i	−0.214915	+	0.156145i	0.475120	+	0.879921i	$0.342405\pi$
$360$	−4.63593	−	22.8706i	−0.244335	−	1.20539i
$361$	−9.98469	−	30.7297i	−0.525510	−	1.61735i
$362$	0.00763899	−	0.0132311i	0.000401496	−	0.000695412i
$363$	−2.16661	+	18.9290i	−0.113718	+	0.993513i
$364$	−0.529934	−	0.917872i	−0.0277761	−	0.0481096i
$365$	16.9719	−	18.8492i	0.888349	−	0.986612i
$366$	8.13229	+	7.39220i	0.425082	+	0.386396i
$367$	0.323937	+	3.08205i	0.0169093	+	0.160882i	0.999718	−	0.0237451i	$-0.00755902\pi$
$367$	0.323937	+	3.08205i	0.0169093	+	0.160882i	−0.982809	+	0.184627i	$0.940892\pi$
$368$	−1.59048	−	0.516779i	−0.0829097	−	0.0269390i
$369$	−3.32200	−	5.88149i	−0.172936	−	0.306178i
$370$	5.45166	+	7.50356i	0.283418	+	0.390092i
$371$	−4.36477	+	1.94332i	−0.226608	+	0.100892i
$372$	−11.8070	−	13.2382i	−0.612166	−	0.686371i
$373$	7.33934	−	4.23737i	0.380016	−	0.219403i	−0.297809	−	0.954625i	$-0.596256\pi$
$373$	7.33934	−	4.23737i	0.380016	−	0.219403i	0.677825	+	0.735223i	$0.262923\pi$
$374$	−2.35303	+	2.60146i	−0.121672	+	0.134518i
$375$	−4.90243	+	6.68103i	−0.253161	+	0.345007i
$376$	−6.47968	+	30.4845i	−0.334164	+	1.57212i
$377$	−0.449777	+	0.619065i	−0.0231647	+	0.0318835i
$378$	−4.07621	−	3.77618i	−0.209657	−	0.194226i
$379$	6.66353	−	20.5082i	0.342283	−	1.05344i	−0.620740	−	0.784016i	$-0.713168\pi$
$379$	6.66353	−	20.5082i	0.342283	−	1.05344i	0.963023	−	0.269421i	$-0.0868322\pi$
$380$	−18.7768	−	20.8538i	−0.963232	−	1.06978i
$381$	0.0386316	−	8.17870i	0.00197916	−	0.419007i
$382$	−2.08693	−	0.219345i	−0.106776	−	0.0112227i
$383$	−23.8855	−	21.5066i	−1.22049	−	1.09894i	−0.992111	−	0.125365i	$-0.959990\pi$
$383$	−23.8855	−	21.5066i	−1.22049	−	1.09894i	−0.228382	−	0.973572i	$-0.573344\pi$
$384$	−13.9376	+	6.12672i	−0.711252	+	0.312653i
$385$	−1.30592	−	12.7011i	−0.0665557	−	0.647308i
$386$		−	10.3064i		−	0.524580i
$387$	−38.7480	+	3.70284i	−1.96967	+	0.188226i
$388$	−0.899932	−	0.653839i	−0.0456871	−	0.0331937i
$389$	0.0138264	−	0.00145321i	0.000701024	−	7.36806e-5i	−0.104178	−	0.994559i	$-0.533221\pi$
$389$	0.0138264	−	0.00145321i	0.000701024	−	7.36806e-5i	0.104879	+	0.994485i	$0.466554\pi$
$390$	−2.14584	−	0.967561i	−0.108659	−	0.0489943i
$391$	0.830689	+	3.90808i	0.0420097	+	0.197640i
$392$	−12.8510	−	5.72161i	−0.649071	−	0.288985i
$393$	9.18616	−	10.1059i	0.463381	−	0.509773i
$394$	−5.40084	−	1.14798i	−0.272090	−	0.0578346i
$395$	39.8586			2.00550
$396$	13.4932	+	0.157976i	0.678059	+	0.00793858i
$397$	−13.9971			−0.702496			−0.351248	−	0.936283i	$-0.614243\pi$
$397$	−13.9971			−0.702496			−0.351248	+	0.936283i	$0.614243\pi$
$398$	−0.0530295	−	0.0112718i	−0.00265813	−	0.000565003i
$399$	−16.1577	−	3.51427i	−0.808896	−	0.175934i
$400$	−1.68531	−	0.750347i	−0.0842654	−	0.0375174i
$401$	7.39293	+	34.7810i	0.369185	+	1.73688i	0.634687	+	0.772769i	$0.281129\pi$
$401$	7.39293	+	34.7810i	0.369185	+	1.73688i	−0.265502	+	0.964110i	$0.585538\pi$
$402$	−9.81880	+	7.06316i	−0.489717	+	0.352278i
$403$	−4.40373	+	0.462850i	−0.219365	+	0.0230562i
$404$	18.8134	+	13.6687i	0.936000	+	0.680044i
$405$	25.7985	+	3.20539i	1.28194	+	0.159277i
$406$		−	1.39548i		−	0.0692567i
$407$	−12.1373	+	5.37102i	−0.601622	+	0.266232i
$408$	4.95681	+	3.63723i	0.245399	+	0.180070i
$409$	−10.4431	−	9.40301i	−0.516378	−	0.464949i	0.369259	−	0.929326i	$-0.379611\pi$
$409$	−10.4431	−	9.40301i	−0.516378	−	0.464949i	−0.885637	+	0.464377i	$0.846278\pi$
$410$	5.18988	+	0.545479i	0.256310	+	0.0269393i
$411$	10.0764	+	5.88125i	0.497032	+	0.290101i
$412$	−8.85394	−	9.83329i	−0.436202	−	0.484452i
$413$	−2.46762	+	7.59455i	−0.121424	+	0.373703i
$414$	−4.34412	+	5.86191i	−0.213502	+	0.288097i
$415$	18.2753	−	25.1538i	0.897099	−	1.23475i
$416$	−0.710576	+	3.34300i	−0.0348389	+	0.163904i
$417$	12.7672	+	1.40289i	0.625214	+	0.0687000i
$418$	−16.5299	+	9.49379i	−0.808504	+	0.464356i
$419$	−2.56407	+	1.48037i	−0.125263	+	0.0723206i	−0.561322	−	0.827597i	$-0.689707\pi$
$419$	−2.56407	+	1.48037i	−0.125263	+	0.0723206i	0.436059	+	0.899918i	$0.356374\pi$
$420$	−8.85424	+	1.83836i	−0.432043	+	0.0897027i
$421$	19.2476	−	8.56959i	0.938071	−	0.417656i	0.120001	−	0.992774i	$-0.461710\pi$
$421$	19.2476	−	8.56959i	0.938071	−	0.417656i	0.818071	+	0.575118i	$0.195044\pi$
$422$	−0.574241	−	0.790375i	−0.0279536	−	0.0384749i
$423$	−29.9027	−	17.6431i	−1.45392	−	0.857835i
$424$	9.18141	+	2.98322i	0.445889	+	0.144878i
$425$	0.460702	+	4.38329i	0.0223473	+	0.212621i
$426$	−1.41096	+	6.48721i	−0.0683611	+	0.314306i
$427$	7.05217	−	7.83223i	0.341279	−	0.379028i
$428$	1.99583	+	3.45688i	0.0964720	+	0.167094i
$429$	1.99892	−	2.71125i	0.0965087	−	0.130900i
$430$	15.0357	−	26.0425i	0.725084	−	1.25588i
$431$	11.7908	+	36.2884i	0.567944	+	1.74795i	0.659039	+	0.752109i	$0.270963\pi$
$431$	11.7908	+	36.2884i	0.567944	+	1.74795i	−0.0910950	+	0.995842i	$0.529037\pi$
$432$	−0.259238	−	2.85511i	−0.0124726	−	0.137367i
$433$	17.1848	−	12.4855i	0.825848	−	0.600014i	−0.0925338	−	0.995710i	$-0.529497\pi$
$433$	17.1848	−	12.4855i	0.825848	−	0.600014i	0.918382	+	0.395696i	$0.129497\pi$
$434$	6.00103	−	5.40335i	0.288059	−	0.259369i
$435$	3.81263	+	5.30010i	0.182801	+	0.254120i
$436$	−0.794067	+	1.78350i	−0.0380289	+	0.0854144i
$437$	−2.26955	+	21.5933i	−0.108567	+	1.03295i
$438$	−9.10720	+	8.12260i	−0.435159	+	0.388113i
$439$	−23.8477	−	13.7685i	−1.13819	−	0.657134i	−0.192208	−	0.981354i	$-0.561565\pi$
$439$	−23.8477	−	13.7685i	−1.13819	−	0.657134i	−0.945982	+	0.324220i	$0.894898\pi$
$440$	−15.2112	+	20.8372i	−0.725165	+	0.993374i
$441$	10.5957	−	11.5465i	0.504557	−	0.549832i
$442$	0.589813	−	0.191642i	0.0280545	−	0.00911547i
$443$	−10.8822	−	24.4419i	−0.517030	−	1.16127i	−0.963802	−	0.266620i	$-0.914093\pi$
$443$	−10.8822	−	24.4419i	−0.517030	−	1.16127i	0.446772	−	0.894648i	$-0.352574\pi$
$444$	4.66170	+	8.16310i	0.221234	+	0.387404i
$445$	−25.0697	+	5.32872i	−1.18842	+	0.252606i
$446$	10.2433	−	2.17729i	0.485036	−	0.103098i
$447$	5.29349	+	9.26942i	0.250373	+	0.438429i
$448$	−1.93692	−	4.35039i	−0.0915108	−	0.205537i
$449$	28.1364	−	9.14206i	1.32784	−	0.431441i	0.442658	−	0.896690i	$-0.354036\pi$
$449$	28.1364	−	9.14206i	1.32784	−	0.431441i	0.885179	+	0.465250i	$0.154036\pi$
$450$	−5.44180	+	5.93010i	−0.256529	+	0.279548i
$451$	−2.32371	+	7.09700i	−0.109419	+	0.334185i
$452$	−2.22164	−	1.28266i	−0.104497	−	0.0603314i
$453$	25.4869	−	22.7314i	1.19748	−	1.06802i
$454$	0.0663457	−	0.631237i	0.00311376	−	0.0296254i
$455$	−0.918156	+	2.06221i	−0.0430438	+	0.0966780i
$456$	19.5105	+	27.1224i	0.913664	+	1.27012i
$457$	0.244013	−	0.219710i	0.0114144	−	0.0102776i	−0.663404	−	0.748262i	$-0.730889\pi$
$457$	0.244013	−	0.219710i	0.0114144	−	0.0102776i	0.674818	+	0.737984i	$0.264222\pi$
$458$	6.34026	−	4.60647i	0.296261	−	0.215246i
$459$	−5.59764	+	3.94696i	−0.261276	+	0.184228i
$460$	3.66933	+	11.2930i	0.171083	+	0.526541i
$461$	−1.59304	+	2.75923i	−0.0741955	+	0.128510i	−0.900736	−	0.434367i	$-0.856972\pi$
$461$	−1.59304	+	2.75923i	−0.0741955	+	0.128510i	0.826541	+	0.562877i	$0.190306\pi$
$462$	−0.0429014	+	6.14282i	−0.00199595	+	0.285790i
$463$	−13.6457	−	23.6350i	−0.634169	−	1.09841i	−0.986691	−	0.162609i	$-0.948009\pi$
$463$	−13.6457	−	23.6350i	−0.634169	−	1.09841i	0.352521	−	0.935804i	$-0.385324\pi$
$464$	0.481769	−	0.535059i	0.0223656	−	0.0248395i
$465$	−8.02952	+	36.9176i	−0.372360	+	1.71201i
$466$	1.38989	+	13.2239i	0.0643855	+	0.612588i
$467$	−17.3622	−	5.64132i	−0.803427	−	0.261049i	−0.121615	−	0.992577i	$-0.538807\pi$
$467$	−17.3622	−	5.64132i	−0.803427	−	0.261049i	−0.681811	+	0.731528i	$0.738807\pi$
$468$	−2.05475	−	1.21234i	−0.0949809	−	0.0560402i
$469$	6.81794	+	9.38409i	0.314823	+	0.433317i
$470$	24.5038	−	10.9098i	1.13028	−	0.503232i
$471$	−8.26702	+	1.71644i	−0.380924	+	0.0790892i
$472$	13.9733	−	8.06747i	0.643172	−	0.371336i
$473$	31.9143	+	28.8667i	1.46742	+	1.32729i
$474$	−19.0620	−	2.09458i	−0.875548	−	0.0962072i
$475$	−4.97977	+	23.4280i	−0.228488	+	1.07495i
$476$	1.40041	−	1.92750i	0.0641878	−	0.0883469i
$477$	−6.40344	+	8.64072i	−0.293193	+	0.395632i
$478$	0.301618	−	0.928285i	0.0137957	−	0.0424588i
$479$	8.47331	+	9.41057i	0.387156	+	0.429980i	0.904945	−	0.425528i	$-0.139912\pi$
$479$	8.47331	+	9.41057i	0.387156	+	0.429980i	−0.517790	+	0.855508i	$0.673245\pi$
$480$	25.1847	+	14.6994i	1.14952	+	0.670933i
$481$	2.33372	+	0.245284i	0.106408	+	0.0111840i
$482$	−0.452407	−	0.407349i	−0.0206066	−	0.0185542i
$483$	5.64116	+	4.13939i	0.256682	+	0.188349i
$484$	−9.93208	−	11.1315i	−0.451458	−	0.505977i
$485$			2.36921i			0.107580i
$486$	−12.1695	−	2.88867i	−0.552019	−	0.131033i
$487$	12.3473	+	8.97085i	0.559510	+	0.406508i	0.831280	−	0.555854i	$-0.187609\pi$
$487$	12.3473	+	8.97085i	0.559510	+	0.406508i	−0.271769	+	0.962362i	$0.587609\pi$
$488$	−21.1786	+	2.22597i	−0.958712	+	0.100765i
$489$	−15.6070	+	11.2269i	−0.705774	+	0.507699i
$490$	2.51718	+	11.8424i	0.113714	+	0.534985i
$491$	25.9499	+	11.5536i	1.17110	+	0.521409i	0.897750	−	0.440505i	$-0.145201\pi$
$491$	25.9499	+	11.5536i	1.17110	+	0.521409i	0.273353	+	0.961914i	$0.411867\pi$
$492$	5.16825	+	1.12409i	0.233003	+	0.0506777i
$493$	−1.68255	−	0.357638i	−0.0757784	−	0.0161072i
$494$	3.37018			0.151632
$495$	−16.6200	−	23.4478i	−0.747012	−	1.05390i
$496$	4.16635			0.187074
$497$	6.22753	+	1.32370i	0.279343	+	0.0593762i
$498$	−10.0619	+	11.0692i	−0.450882	+	0.496024i
$499$	−19.9729	−	8.89250i	−0.894109	−	0.398083i	−0.0923473	−	0.995727i	$-0.529437\pi$
$499$	−19.9729	−	8.89250i	−0.894109	−	0.398083i	−0.801762	+	0.597644i	$0.796104\pi$
$500$	−1.34905	−	6.34679i	−0.0603315	−	0.283837i
$501$	−33.5362	−	15.1215i	−1.49829	−	0.675578i
$502$	7.84010	−	0.824028i	0.349921	−	0.0367782i
$503$	−16.0796	−	11.6825i	−0.716954	−	0.520898i	0.168455	−	0.985709i	$-0.446122\pi$
$503$	−16.0796	−	11.6825i	−0.716954	−	0.520898i	−0.885410	+	0.464812i	$0.846122\pi$
$504$	10.7181	−	1.02425i	0.477422	−	0.0456235i
$505$		−	49.5291i		−	2.20402i
$506$	8.02386	−	0.825008i	0.356704	−	0.0366761i
$507$	20.0678	−	8.82143i	0.891244	−	0.391774i
$508$	4.75915	+	4.28515i	0.211153	+	0.190123i
$509$	−30.6415	−	3.22056i	−1.35816	−	0.142749i	−0.602714	−	0.797957i	$-0.705914\pi$
$509$	−30.6415	−	3.22056i	−1.35816	−	0.142749i	−0.755448	+	0.655208i	$0.772581\pi$
$510$	0.0249934	−	5.29136i	0.00110673	−	0.234305i
$511$	7.83070	+	8.69688i	0.346410	+	0.384727i
$512$	1.91196	−	5.88441i	0.0844976	−	0.260057i
$513$	−35.5587	+	10.9992i	−1.56995	+	0.485625i
$514$	−10.5099	+	14.4656i	−0.463570	+	0.638049i
$515$	−5.85944	+	27.5665i	−0.258198	+	1.21473i
$516$	18.0309	−	24.5725i	0.793767	−	1.08174i
$517$	7.89558	+	37.5631i	0.347247	+	1.65202i
$518$	−3.70605	+	2.13969i	−0.162834	+	0.0940125i
$519$	−14.2876	−	16.0195i	−0.627156	−	0.703179i
$520$	4.16682	−	1.85519i	0.182727	−	0.0813555i
$521$	16.6718	+	22.9468i	0.730405	+	1.00532i	0.999114	+	0.0420947i	$0.0134031\pi$
$521$	16.6718	+	22.9468i	0.730405	+	1.00532i	−0.268709	+	0.963221i	$0.586597\pi$
$522$	−1.54484	−	2.73508i	−0.0676156	−	0.119711i
$523$	−12.9420	−	4.20510i	−0.565913	−	0.183876i	0.0120671	−	0.999927i	$-0.496159\pi$
$523$	−12.9420	−	4.20510i	−0.565913	−	0.183876i	−0.577980	+	0.816051i	$0.696159\pi$
$524$	1.11778	+	10.6350i	0.0488305	+	0.464591i
$525$	5.71153	+	5.19174i	0.249272	+	0.226586i
$526$	8.25190	−	9.16466i	0.359800	−	0.399598i
$527$	−4.97693	−	8.62030i	−0.216799	−	0.375506i
$528$	−2.13716	+	2.34048i	−0.0930080	+	0.101856i
$529$	−6.90625	+	11.9620i	−0.300272	+	0.520086i
$530$	−2.56753	−	7.90204i	−0.111526	−	0.343242i
$531$	3.57094	+	17.6167i	0.154966	+	0.764498i
$532$	10.4747	−	7.61029i	0.454134	−	0.329948i
$533$	0.981163	−	0.883443i	0.0424989	−	0.0382662i
$534$	12.2694	−	1.23100i	0.530948	−	0.0532706i
$535$	3.45795	−	7.76667i	0.149500	−	0.335783i
$536$	2.44986	−	23.3088i	0.105818	−	1.00679i
$537$	18.3588	+	6.06116i	0.792242	+	0.261558i
$538$	0.662255	+	0.382353i	0.0285518	+	0.0164844i
$539$	−17.3252	−	0.0391632i	−0.746251	−	0.00168688i
$540$	−15.3188	+	13.4050i	−0.659215	+	0.576858i
$541$	−17.0525	+	5.54068i	−0.733142	+	0.238212i	−0.651712	−	0.758467i	$-0.725949\pi$
$541$	−17.0525	+	5.54068i	−0.733142	+	0.238212i	−0.0814304	+	0.996679i	$0.525949\pi$
$542$	−7.29806	−	16.3917i	−0.313478	−	0.704084i
$543$	−0.0329799		0.000155779i	−0.00141530		6.68510e-6i
$544$	−7.51488	+	1.59734i	−0.322198	+	0.0684852i
$545$	4.06724	−	0.864519i	0.174222	−	0.0370319i
$546$	0.547471	−	0.937987i	0.0234296	−	0.0401422i
$547$	8.53304	+	19.1655i	0.364846	+	0.819458i	0.998932	+	0.0461958i	$0.0147098\pi$
$547$	8.53304	+	19.1655i	0.364846	+	0.819458i	−0.634086	+	0.773262i	$0.718624\pi$
$548$	−8.68837	+	2.82302i	−0.371149	+	0.120594i
$549$	5.15145	−	23.1577i	0.219858	−	0.988348i
$550$	8.89799	+	0.0201137i	0.379412	+	0.000857649i
$551$	−8.09543	−	4.67390i	−0.344877	−	0.199115i
$552$	−2.87405	−	13.8425i	−0.122328	−	0.589178i
$553$	−1.92233	+	18.2897i	−0.0817456	+	0.777757i
$554$	−3.38338	+	7.59919i	−0.143746	+	0.322859i
$555$	8.22982	−	18.2520i	0.349336	−	0.774753i
$556$	−7.47383	+	6.72946i	−0.316961	+	0.285393i
$557$	−6.91677	+	5.02533i	−0.293073	+	0.212930i	−0.724599	−	0.689170i	$-0.757975\pi$
$557$	−6.91677	+	5.02533i	−0.293073	+	0.212930i	0.431526	+	0.902100i	$0.357975\pi$
$558$	5.78009	−	17.2336i	0.244691	−	0.729557i
$559$	−2.35104	−	7.23574i	−0.0994382	−	0.306039i
$560$	1.06200	−	1.83943i	0.0448775	−	0.0777301i
$561$	7.39548	+	1.62602i	0.312237	+	0.0686507i
$562$	3.81202	+	6.60262i	0.160800	+	0.278515i
$563$	22.4251	−	24.9056i	0.945104	−	1.04964i	−0.0535905	−	0.998563i	$-0.517067\pi$
$563$	22.4251	−	24.9056i	0.945104	−	1.04964i	0.998694	−	0.0510813i	$-0.0162668\pi$
$564$	25.8946	−	8.27863i	1.09036	−	0.348593i
$565$	0.571122	+	5.43386i	0.0240273	+	0.228604i
$566$	−9.47118	−	3.07737i	−0.398103	−	0.129352i
$567$	−2.71507	+	11.6834i	−0.114022	+	0.490659i
$568$	−7.56140	−	10.4074i	−0.317269	−	0.436683i
$569$	36.2726	−	16.1496i	1.52063	−	0.677027i	0.534829	−	0.844960i	$-0.320376\pi$
$569$	36.2726	−	16.1496i	1.52063	−	0.677027i	0.985798	+	0.167934i	$0.0537094\pi$
$570$	9.01494	−	27.3056i	0.377594	−	1.14371i
$571$	11.7014	−	6.75580i	0.489688	−	0.282721i	−0.234757	−	0.972054i	$-0.575430\pi$
$571$	11.7014	−	6.75580i	0.489688	−	0.282721i	0.724445	+	0.689333i	$0.242096\pi$
$572$	0.542541	+	2.58113i	0.0226848	+	0.107923i
$573$	1.82288	+	4.14686i	0.0761518	+	0.173237i
$574$	−0.500602	+	2.35515i	−0.0208947	+	0.0983020i
$575$	5.95720	−	8.19938i	0.248432	−	0.341938i
$576$	−8.61226	−	6.38234i	−0.358844	−	0.265931i
$577$	−10.9864	+	33.8127i	−0.457370	+	1.40764i	0.410960	+	0.911654i	$0.365194\pi$
$577$	−10.9864	+	33.8127i	−0.457370	+	1.40764i	−0.868330	+	0.495987i	$0.834806\pi$
$578$	−8.19425	−	9.10063i	−0.340836	−	0.378536i
$579$	−19.3198	+	11.0329i	−0.802904	+	0.458514i
$580$	−5.08421	−	0.534372i	−0.211110	−	0.0221886i
$581$	10.6608	+	9.59903i	0.442285	+	0.398235i
$582$	0.124503	−	1.13306i	0.00516081	−	0.0469667i
$583$	11.8275	−	1.21610i	0.489847	−	0.0503657i
$584$		−	23.6462i		−	0.978487i
$585$	0.483379	+	5.05826i	0.0199853	+	0.209133i
$586$	16.9001	+	12.2786i	0.698137	+	0.507226i
$587$	−25.3030	+	2.65945i	−1.04437	+	0.109767i	−0.611144	−	0.791520i	$-0.709290\pi$
$587$	−25.3030	+	2.65945i	−1.04437	+	0.109767i	−0.433222	+	0.901287i	$0.642624\pi$
$588$	1.22499	+	12.2095i	0.0505177	+	0.503510i
$589$	−11.2465	−	52.9104i	−0.463402	−	2.18014i
$590$	−12.6861	−	5.64820i	−0.522277	−	0.232533i
$591$	3.62964	+	11.3531i	0.149303	+	0.467002i
$592$	−2.15967	−	0.459052i	−0.0887620	−	0.0188669i
$593$	−26.4048			−1.08431			−0.542157	−	0.840277i	$-0.682392\pi$
$593$	−26.4048			−1.08431			−0.542157	+	0.840277i	$0.682392\pi$
$594$	6.71617	+	12.0871i	0.275568	+	0.495941i
$595$	−5.07445			−0.208032
$596$	−8.17551	−	1.73776i	−0.334882	−	0.0711814i
$597$	0.0356385	+	0.111473i	0.00145859	+	0.00456228i
$598$	−1.30279	−	0.580041i	−0.0532752	−	0.0237197i
$599$	−2.38661	−	11.2281i	−0.0975143	−	0.458769i	−0.999628	−	0.0272704i	$-0.991318\pi$
$599$	−2.38661	−	11.2281i	−0.0975143	−	0.458769i	0.902114	−	0.431498i	$-0.142015\pi$
$600$	−1.55692	−	15.5179i	−0.0635611	−	0.633514i
$601$	29.8805	−	3.14057i	1.21885	−	0.128107i	0.526823	−	0.849975i	$-0.323383\pi$
$601$	29.8805	−	3.14057i	1.21885	−	0.128107i	0.692030	+	0.721869i	$0.256717\pi$
$602$	11.2249	+	8.15534i	0.457491	+	0.332387i
$603$	23.7513	+	10.8447i	0.967226	+	0.441632i
$604$			26.7406i			1.08806i
$605$	−6.74662	+	31.0495i	−0.274289	+	1.26234i
$606$	−2.60277	+	23.6869i	−0.105730	+	0.962214i
$607$	28.7307	+	25.8692i	1.16614	+	1.05000i	0.997934	+	0.0642479i	$0.0204648\pi$
$607$	28.7307	+	25.8692i	1.16614	+	1.05000i	0.168208	+	0.985751i	$0.446202\pi$
$608$	−41.5219	−	4.36412i	−1.68393	−	0.176989i
$609$	−2.61591	+	1.49386i	−0.106002	+	0.0605344i
$610$	12.2638	+	13.6203i	0.496546	+	0.551470i
$611$	2.09706	−	6.45408i	0.0848379	−	0.261104i
$612$	0.610948	−	5.32810i	0.0246961	−	0.215376i
$613$	17.6204	−	24.2524i	0.711681	−	0.979545i	−0.288078	−	0.957607i	$-0.593016\pi$
$613$	17.6204	−	24.2524i	0.711681	−	0.979545i	0.999759	−	0.0219380i	$-0.00698363\pi$
$614$	3.00735	−	14.1485i	0.121367	−	0.570986i
$615$	−4.53324	−	10.3126i	−0.182798	−	0.415846i
$616$	−8.82784	−	7.98483i	−0.355684	−	0.321718i
$617$	−3.50285	+	2.02237i	−0.141019	+	0.0814176i	−0.568850	−	0.822441i	$-0.692611\pi$
$617$	−3.50285	+	2.02237i	−0.141019	+	0.0814176i	0.427830	+	0.903859i	$0.359278\pi$
$618$	4.25086	−	12.8755i	0.170995	−	0.517930i
$619$	−23.9589	+	10.6672i	−0.962988	+	0.428750i	−0.827150	−	0.561981i	$-0.810039\pi$
$619$	−23.9589	+	10.6672i	−0.962988	+	0.428750i	−0.135838	+	0.990731i	$0.543373\pi$
$620$	−17.3882	−	23.9329i	−0.698328	−	0.961167i
$621$	15.6388	+	1.86811i	0.627564	+	0.0749646i
$622$	−9.59538	−	3.11773i	−0.384740	−	0.125009i
$623$	−1.23609	−	11.7606i	−0.0495228	−	0.471178i
$624$	0.533737	−	0.170639i	0.0213666	−	0.00683102i
$625$	−20.4340	+	22.6943i	−0.817362	+	0.907772i
$626$	−4.69208	−	8.12692i	−0.187533	−	0.324817i
$627$	35.4918	+	20.8230i	1.41741	+	0.831592i
$628$	3.30560	−	5.72546i	0.131908	−	0.228471i
$629$	1.63005	+	5.01679i	0.0649945	+	0.200033i
$630$	−6.13525	−	6.94471i	−0.244434	−	0.276684i
$631$	12.4984	−	9.08065i	0.497555	−	0.361495i	−0.310527	−	0.950564i	$-0.600506\pi$
$631$	12.4984	−	9.08065i	0.497555	−	0.361495i	0.808082	+	0.589070i	$0.200506\pi$
$632$	27.6145	−	24.8642i	1.09845	−	0.989046i
$633$	−0.866874	+	1.92254i	−0.0344551	+	0.0764141i
$634$	5.36869	−	12.0583i	0.213218	−	0.478895i
$635$	1.42575	−	13.5651i	0.0565790	−	0.538313i
$636$	−1.71192	−	8.24527i	−0.0678821	−	0.326946i
$637$	2.65271	+	1.53154i	0.105104	+	0.0606819i
$638$	−1.08060	+	3.30034i	−0.0427813	+	0.130662i
$639$	13.6710	−	4.29964i	0.540818	−	0.170091i
$640$	−24.1477	+	7.84607i	−0.954522	+	0.310143i
$641$	5.08517	+	11.4215i	0.200852	+	0.451121i	0.985687	−	0.168583i	$-0.0539192\pi$
$641$	5.08517	+	11.4215i	0.200852	+	0.451121i	−0.784835	+	0.619704i	$0.787253\pi$
$642$	−2.06188	+	3.53263i	−0.0813757	+	0.139422i
$643$	5.06277	−	1.07612i	0.199656	−	0.0424382i	−0.106998	−	0.994259i	$-0.534124\pi$
$643$	5.06277	−	1.07612i	0.199656	−	0.0424382i	0.306654	+	0.951821i	$0.400791\pi$
$644$	−5.35895	+	1.13908i	−0.211172	+	0.0448860i
$645$	−64.9137	−	0.306616i	−2.55597	−	0.0120730i
$646$	3.08143	+	6.92100i	0.121237	+	0.272303i
$647$	−5.07677	+	1.64954i	−0.199588	+	0.0648502i	−0.407105	−	0.913381i	$-0.633462\pi$
$647$	−5.07677	+	1.64954i	−0.199588	+	0.0648502i	0.207517	+	0.978231i	$0.433462\pi$
$648$	19.8731	−	13.8727i	0.780689	−	0.544970i
$649$	11.7168	−	16.0504i	0.459925	−	0.630033i
$650$	−1.36239	−	0.786578i	−0.0534375	−	0.0308521i
$651$	−16.5530	−	5.46496i	−0.648761	−	0.214188i
$652$	1.57355	−	14.9713i	0.0616250	−	0.586323i
$653$	−1.93129	+	4.33775i	−0.0755773	+	0.169749i	−0.947383	−	0.320103i	$-0.896283\pi$
$653$	−1.93129	+	4.33775i	−0.0755773	+	0.169749i	0.871806	+	0.489852i	$0.162949\pi$
$654$	−1.99056	+	0.199715i	−0.0778370	+	0.00780946i
$655$	16.9257	−	15.2400i	0.661343	−	0.595476i
$656$	−1.00502	+	0.730189i	−0.0392394	+	0.0285091i
$657$	24.9755	+	8.37668i	0.974385	+	0.326805i
$658$	3.82435	+	11.7701i	0.149089	+	0.458847i
$659$	−19.9356	+	34.5295i	−0.776581	+	1.34508i	0.157321	+	0.987547i	$0.449714\pi$
$659$	−19.9356	+	34.5295i	−0.776581	+	1.34508i	−0.933902	+	0.357529i	$0.883619\pi$
$660$	22.3639	+	2.50857i	0.870514	+	0.0976460i
$661$	−10.4257	−	18.0579i	−0.405515	−	0.702372i	0.588867	−	0.808230i	$-0.299574\pi$
$661$	−10.4257	−	18.0579i	−0.405515	−	0.702372i	−0.994381	+	0.105858i	$0.966241\pi$
$662$	10.5367	−	11.7022i	0.409522	−	0.454821i
$663$	−0.990636	−	0.900482i	−0.0384731	−	0.0349718i
$664$	−3.02986	−	28.8272i	−0.117581	−	1.11871i
$665$	−26.2265	−	8.52151i	−1.01702	−	0.330450i
$666$	−4.89499	+	8.29637i	−0.189677	+	0.321478i
$667$	2.32499	+	3.20007i	0.0900239	+	0.123907i
$668$	26.3148	−	11.7161i	1.01815	−	0.453309i
$669$	−15.0469	−	16.8709i	−0.581747	−	0.652265i
$670$	−17.4689	+	10.0857i	−0.674884	+	0.389645i
$671$	−22.7434	+	13.0624i	−0.877998	+	0.504270i
$672$	−7.95967	+	10.8474i	−0.307051	+	0.418448i
$673$	−4.25772	+	20.0310i	−0.164123	+	0.772137i	0.816673	+	0.577101i	$0.195816\pi$
$673$	−4.25772	+	20.0310i	−0.164123	+	0.772137i	−0.980796	+	0.195037i	$0.937517\pi$
$674$	5.02763	−	6.91994i	0.193657	−	0.266546i
$675$	16.9417	+	3.85276i	0.652087	+	0.148293i
$676$	−5.30410	+	16.3243i	−0.204004	+	0.627859i
$677$	−4.58020	−	5.08682i	−0.176031	−	0.195502i	0.648672	−	0.761068i	$-0.275325\pi$
$677$	−4.58020	−	5.08682i	−0.176031	−	0.195502i	−0.824703	+	0.565565i	$0.808658\pi$
$678$	0.0124166	−	2.62871i	0.000476856	−	0.100955i
$679$	−1.08715	−	0.114264i	−0.0417209	−	0.00438505i
$680$	7.61964	+	6.86075i	0.292200	+	0.263098i
$681$	−1.25431	+	0.551370i	−0.0480652	+	0.0211285i
$682$	−18.3766	+	8.13207i	−0.703677	+	0.311393i
$683$		−	4.76117i		−	0.182181i	−0.995843	−	0.0910905i	$-0.970965\pi$
$683$		−	4.76117i		−	0.182181i	0.995843	−	0.0910905i	$-0.0290353\pi$
$684$	12.1051	−	26.5115i	0.462848	−	1.01369i
$685$	15.7413	+	11.4368i	0.601446	+	0.436976i
$686$	−12.9999	+	1.36635i	−0.496340	+	0.0521674i
$687$	−15.4223	−	6.95393i	−0.588398	−	0.265309i
$688$	1.48835	+	7.00214i	0.0567428	+	0.266954i
$689$	−1.92038	−	0.855008i	−0.0731606	−	0.0325732i
$690$	−8.18443	+	9.00384i	−0.311576	+	0.342770i
$691$	−48.4865	−	10.3061i	−1.84451	−	0.392063i	−0.852983	−	0.521939i	$-0.825209\pi$
$691$	−48.4865	−	10.3061i	−1.84451	−	0.392063i	−0.991530	+	0.129876i	$0.958542\pi$
$692$	16.8075			0.638927
$693$	11.5610	−	6.49546i	0.439164	−	0.246742i
$694$	−1.98204			−0.0752372
$695$	20.9520	+	4.45349i	0.794755	+	0.168930i
$696$	5.94769	+	1.29361i	0.225447	+	0.0490343i
$697$	2.71134	+	1.20716i	0.102699	+	0.0457246i
$698$	−2.14641	−	10.0981i	−0.0812428	−	0.382217i
$699$	23.3011	−	16.7616i	0.881328	−	0.633984i
$700$	−6.01057	+	0.631736i	−0.227178	+	0.0238774i
$701$	−18.5663	−	13.4892i	−0.701240	−	0.509480i	0.179096	−	0.983832i	$-0.442683\pi$
$701$	−18.5663	−	13.4892i	−0.701240	−	0.509480i	−0.880336	+	0.474351i	$0.842683\pi$
$702$	0.0346410	−	2.44447i	0.00130744	−	0.0922607i
$703$			28.6659i			1.08115i
$704$	1.21209	+	11.7886i	0.0456825	+	0.444299i
$705$	−46.6823	−	34.2548i	−1.75816	−	1.29011i
$706$	2.04643	+	1.84262i	0.0770186	+	0.0693478i
$707$	22.7272	+	2.38872i	0.854743	+	0.0898372i
$708$	−12.1555	−	7.09476i	−0.456833	−	0.266637i
$709$	18.4538	+	20.4951i	0.693049	+	0.769709i	0.982253	−	0.187559i	$-0.0600575\pi$
$709$	18.4538	+	20.4951i	0.693049	+	0.769709i	−0.289205	+	0.957267i	$0.593391\pi$
$710$	−3.42133	+	10.5298i	−0.128400	+	0.395176i
$711$	16.4795	+	37.9750i	0.618029	+	1.42417i
$712$	−14.0445	+	19.3305i	−0.526338	+	0.724443i
$713$	−4.75892	+	22.3890i	−0.178223	+	0.838473i
$714$	2.42682	+	0.266664i	0.0908213	+	0.00997964i
$715$	3.76833	−	4.16618i	0.140928	−	0.155806i
$716$	−13.1101	+	7.56915i	−0.489949	+	0.282872i
$717$	−2.06300	+	0.428330i	−0.0770441	+	0.0159963i
$718$	3.68942	−	1.64263i	0.137688	−	0.0613025i
$719$	21.5090	+	29.6046i	0.802151	+	1.10407i	0.992487	+	0.122347i	$0.0390421\pi$
$719$	21.5090	+	29.6046i	0.802151	+	1.10407i	−0.190337	+	0.981719i	$0.560958\pi$
$720$	0.0451651	−	4.78085i	0.00168320	−	0.178172i
$721$	−12.3667	−	4.01819i	−0.460561	−	0.149645i
$722$	2.70994	+	25.7833i	0.100853	+	0.959556i
$723$	−0.279295	+	1.28413i	−0.0103871	+	0.0477571i
$724$	0.0172795	−	0.0191909i	0.000642188	−	0.000713223i
$725$	2.18172	+	3.77884i	0.0810269	+	0.140343i
$726$	4.85817	−	14.4946i	0.180304	−	0.537946i
$727$	20.4497	−	35.4200i	0.758438	−	1.31365i	−0.185208	−	0.982699i	$-0.559296\pi$
$727$	20.4497	−	35.4200i	0.758438	−	1.31365i	0.943647	−	0.330955i	$-0.107371\pi$
$728$	0.650321	+	2.00148i	0.0241025	+	0.0741799i
$729$	7.61247	+	25.9046i	0.281943	+	0.959431i
$730$	−16.4645	+	11.9622i	−0.609379	+	0.442740i
$731$	12.7097	−	11.4439i	0.470086	−	0.423267i
$732$	10.8475	+	15.0796i	0.400937	+	0.557360i
$733$	3.79338	−	8.52008i	0.140112	−	0.314696i	−0.829837	−	0.558006i	$-0.811567\pi$
$733$	3.79338	−	8.52008i	0.140112	−	0.314696i	0.969949	+	0.243310i	$0.0782332\pi$
$734$	0.259915	−	2.47293i	0.00959365	−	0.0912775i
$735$	19.5045	−	17.3958i	0.719435	−	0.641655i
$736$	15.2998	+	8.83335i	0.563958	+	0.325601i
$737$	−8.85790	−	27.4730i	−0.326285	−	1.01198i
$738$	1.62605	+	5.17016i	0.0598558	+	0.190316i
$739$	−25.6359	+	8.32960i	−0.943031	+	0.306409i	−0.739881	−	0.672738i	$-0.765118\pi$
$739$	−25.6359	+	8.32960i	−0.943031	+	0.306409i	−0.203150	+	0.979148i	$0.565118\pi$
$740$	6.37644	+	14.3217i	0.234403	+	0.526477i
$741$	−3.60777	−	6.31757i	−0.132535	−	0.232082i
$742$	3.74980	−	0.797044i	0.137659	−	0.0292604i
$743$	20.8264	−	4.42678i	0.764045	−	0.162403i	0.190623	−	0.981663i	$-0.438949\pi$
$743$	20.8264	−	4.42678i	0.764045	−	0.162403i	0.573421	+	0.819261i	$0.305616\pi$
$744$	17.4667	+	30.5859i	0.640359	+	1.12133i
$745$	7.24062	+	16.2627i	0.265276	+	0.595819i
$746$	−6.46702	+	2.10126i	−0.236775	+	0.0769327i
$747$	31.5210	+	7.01186i	1.15329	+	0.256551i
$748$	−4.80456	+	3.47415i	−0.175672	+	0.127027i
$749$	3.39708	+	1.96131i	0.124127	+	0.0716646i
$750$	4.96212	−	4.42565i	0.181191	−	0.161602i
$751$	−2.46206	+	23.4250i	−0.0898419	+	0.854789i	0.853081	+	0.521778i	$0.174731\pi$
$751$	−2.46206	+	23.4250i	−0.0898419	+	0.854789i	−0.942923	+	0.333011i	$0.891935\pi$
$752$	−2.59711	+	5.83321i	−0.0947070	+	0.212715i
$753$	−9.93750	−	13.8145i	−0.362143	−	0.503430i
$754$	0.456272	−	0.410829i	0.0166165	−	0.0149615i
$755$	46.0766	−	33.4766i	1.67690	−	1.21834i
$756$	−5.41226	−	7.67575i	−0.196842	−	0.279164i
$757$	−10.5548	−	32.4845i	−0.383622	−	1.18067i	−0.937475	−	0.348053i	$-0.886843\pi$
$757$	−10.5548	−	32.4845i	−0.383622	−	1.18067i	0.553853	−	0.832615i	$-0.313157\pi$
$758$	−8.65095	+	14.9839i	−0.314217	+	0.544239i
$759$	−10.1360	−	14.1580i	−0.367915	−	0.513901i
$760$	27.8597	+	48.2544i	1.01058	+	1.75037i
$761$	−24.3545	+	27.0484i	−0.882850	+	0.980504i	−0.999920	−	0.0126197i	$-0.995983\pi$
$761$	−24.3545	+	27.0484i	−0.882850	+	0.980504i	0.117071	+	0.993124i	$0.462650\pi$
$762$	−1.39470	+	6.41246i	−0.0505246	+	0.232299i
$763$	0.200540	+	1.90801i	0.00726004	+	0.0690746i
$764$	−3.37329	−	1.09605i	−0.122041	−	0.0396537i
$765$	−9.94568	+	5.61754i	−0.359587	+	0.203103i
$766$	15.1583	+	20.8637i	0.547693	+	0.753835i
$767$	−3.20960	+	1.42901i	−0.115892	+	0.0515985i
$768$	24.0800	−	4.99960i	0.868912	−	0.180407i
$769$	−13.6195	+	7.86320i	−0.491130	+	0.283554i	−0.725043	−	0.688703i	$-0.758180\pi$
$769$	−13.6195	+	7.86320i	−0.491130	+	0.283554i	0.233913	+	0.972258i	$0.424847\pi$
$770$	−1.09388	+	10.1861i	−0.0394209	+	0.367081i
$771$	38.3672	+	4.21588i	1.38176	+	0.151831i
$772$	3.62193	−	17.0398i	0.130356	−	0.613277i
$773$	−5.16073	+	7.10313i	−0.185619	+	0.255482i	−0.891678	−	0.452671i	$-0.850471\pi$
$773$	−5.16073	+	7.10313i	−0.185619	+	0.255482i	0.706059	+	0.708153i	$0.250471\pi$
$774$	31.0283	+	3.55787i	1.11529	+	0.127885i
$775$	−7.80258	+	24.0139i	−0.280277	+	0.862604i
$776$	1.47794	+	1.64142i	0.0530550	+	0.0589236i
$777$	7.97827	+	4.65664i	0.286219	+	0.167056i
$778$	−0.0110938	−	0.00116600i	−0.000397732	−	4.18033e-5i
$779$	11.9859	+	10.7922i	0.429441	+	0.386670i
$780$	−3.20776	−	2.35380i	−0.114856	−	0.0842796i
$781$	−13.7032	−	7.95288i	−0.490338	−	0.284576i
$782$		−	3.20576i		−	0.114638i
$783$	−3.47331	+	5.82378i	−0.124126	+	0.208125i
$784$	−2.33166	−	1.69405i	−0.0832737	−	0.0605019i
$785$	−14.0038	+	1.47186i	−0.499817	+	0.0525329i
$786$	−8.89546	+	6.39895i	−0.317291	+	0.228243i
$787$	−1.68918	−	7.94696i	−0.0602127	−	0.283279i	0.937732	−	0.347360i	$-0.112922\pi$
$787$	−1.68918	−	7.94696i	−0.0602127	−	0.283279i	−0.997945	+	0.0640811i	$0.979588\pi$
$788$	−8.52593	−	3.79599i	−0.303724	−	0.135227i
$789$	−26.0133	−	5.65784i	−0.926097	−	0.201425i
$790$	−31.2823	−	6.64925i	−1.11297	−	0.236570i
$791$	−2.52095			−0.0896348
$792$	−26.1415	−	5.87724i	−0.928899	−	0.208839i
$793$	4.63701			0.164665
$794$	10.9854	+	2.33502i	0.389857	+	0.0828666i
$795$	−12.0642	+	13.2721i	−0.427874	+	0.470712i
$796$	−0.0837141	−	0.0372719i	−0.00296717	−	0.00132107i
$797$	0.268588	+	1.26361i	0.00951387	+	0.0447592i	0.982648	−	0.185478i	$-0.0593832\pi$
$797$	0.268588	+	1.26361i	0.00951387	+	0.0447592i	−0.973135	+	0.230237i	$0.926050\pi$
$798$	12.0948	+	5.45355i	0.428152	+	0.193054i
$799$	15.1715	−	1.59459i	0.536729	−	0.0564125i
$800$	15.7666	+	11.4551i	0.557435	+	0.405000i
$801$	−15.4419	−	21.6818i	−0.545614	−	0.766089i
$802$		−	28.5305i		−	1.00745i
$803$	−11.7852	−	26.6319i	−0.415892	−	0.939820i
$804$	−18.7159	+	8.22715i	−0.660059	+	0.290149i
$805$	8.67162	+	7.80796i	0.305635	+	0.275195i
$806$	3.53340	+	0.371375i	0.124459	+	0.0130811i
$807$	0.00779717	−	1.65074i	0.000274473	−	0.0581088i
$808$	−30.8968	−	34.3144i	−1.08695	−	1.20718i
$809$	−12.8311	+	39.4900i	−0.451117	+	1.38840i	0.424517	+	0.905420i	$0.360444\pi$
$809$	−12.8311	+	39.4900i	−0.451117	+	1.38840i	−0.875634	+	0.482975i	$0.839556\pi$
$810$	−19.7128	−	6.81942i	−0.692636	−	0.239610i
$811$	8.32868	−	11.4634i	0.292459	−	0.402536i	−0.637352	−	0.770573i	$-0.719970\pi$
$811$	8.32868	−	11.4634i	0.292459	−	0.402536i	0.929811	+	0.368037i	$0.119970\pi$
$812$	0.490410	−	2.30720i	0.0172100	−	0.0809667i
$813$	−22.9145	+	31.2279i	−0.803647	+	1.09521i
$814$	10.4217	−	2.19059i	0.365281	−	0.0767803i
$815$	−27.7670	+	16.0313i	−0.972635	+	0.561551i
$816$	0.838431	+	0.940064i	0.0293510	+	0.0329088i
$817$	84.9059	−	37.8025i	2.97048	−	1.32254i
$818$	6.62746	+	9.12191i	0.231724	+	0.318940i
$819$	−2.34437	−	0.0221475i	−0.0819190	−	0.000773896i
$820$	8.38889	+	2.72572i	0.292953	+	0.0951862i
$821$	−5.67485	−	53.9926i	−0.198054	−	1.88436i	−0.417421	−	0.908713i	$-0.637066\pi$
$821$	−5.67485	−	53.9926i	−0.198054	−	1.88436i	0.219367	−	0.975642i	$-0.429601\pi$
$822$	−6.92716	−	6.29675i	−0.241613	−	0.219624i
$823$	17.3905	−	19.3141i	0.606195	−	0.673248i	−0.359434	−	0.933170i	$-0.617030\pi$
$823$	17.3905	−	19.3141i	0.606195	−	0.673248i	0.965630	+	0.259922i	$0.0836969\pi$
$824$	13.1368	+	22.7536i	0.457642	+	0.792660i
$825$	−9.48758	−	16.7013i	−0.330315	−	0.581464i
$826$	3.20360	−	5.54879i	0.111467	−	0.193067i
$827$	−6.86114	−	21.1164i	−0.238585	−	0.734290i	−0.996626	−	0.0820821i	$-0.973843\pi$
$827$	−6.86114	−	21.1164i	−0.238585	−	0.734290i	0.758040	−	0.652208i	$-0.226157\pi$
$828$	−9.24229	+	8.16503i	−0.321192	+	0.283754i
$829$	6.23980	−	4.53348i	0.216717	−	0.157454i	−0.474131	−	0.880455i	$-0.657238\pi$
$829$	6.23980	−	4.53348i	0.216717	−	0.157454i	0.690848	+	0.723000i	$0.257238\pi$
$830$	−18.5392	+	16.6928i	−0.643505	+	0.579415i
$831$	17.8670	−	1.79261i	0.619798	−	0.0621850i
$832$	0.852191	−	1.91405i	0.0295444	−	0.0663578i
$833$	−0.719746	+	6.84793i	−0.0249377	+	0.237267i
$834$	−9.78610	−	3.23088i	−0.338865	−	0.111876i
$835$	−53.1314	−	30.6755i	−1.83869	−	1.06157i
$836$	−30.6657	+	9.88732i	−1.06060	+	0.341960i
$837$	−38.4928	+	7.61348i	−1.33051	+	0.263160i
$838$	2.25932	−	0.734097i	0.0780468	−	0.0253589i
$839$	−19.0618	−	42.8134i	−0.658085	−	1.47808i	−0.866055	−	0.499948i	$-0.833352\pi$
$839$	−19.0618	−	42.8134i	−0.658085	−	1.47808i	0.207970	−	0.978135i	$-0.433314\pi$
$840$	17.9558	+	0.0848132i	0.619535	+	0.00292633i
$841$	26.7005	−	5.67537i	0.920708	−	0.195702i
$842$	−16.5357	+	3.51478i	−0.569859	+	0.121127i
$843$	8.29617	−	14.2139i	0.285735	−	0.489553i
$844$	−0.671652	−	1.50855i	−0.0231192	−	0.0519266i
$845$	34.7686	−	11.2970i	1.19608	−	0.388629i
$846$	20.5254	+	18.8352i	0.705676	+	0.647569i
$847$	−13.9221	−	4.59326i	−0.478370	−	0.157826i
$848$	1.71292	+	0.988954i	0.0588219	+	0.0339608i
$849$	4.37019	+	21.0485i	0.149985	+	0.722384i
$850$	0.369651	−	3.51700i	0.0126789	−	0.120632i
$851$	4.93368	−	11.0812i	0.169124	−	0.379859i
$852$	−4.61255	+	10.2297i	−0.158023	+	0.350462i
$853$	−24.6554	+	22.1998i	−0.844185	+	0.760108i	−0.972815	−	0.231585i	$-0.925609\pi$
$853$	−24.6554	+	22.1998i	−0.844185	+	0.760108i	0.128630	+	0.991693i	$0.458942\pi$
$854$	−6.84135	+	4.97053i	−0.234106	+	0.170088i
$855$	−60.8362	+	12.3316i	−2.08055	+	0.421733i
$856$	−2.44923	−	7.53796i	−0.0837130	−	0.257642i
$857$	1.62627	−	2.81679i	0.0555524	−	0.0962196i	−0.836912	−	0.547338i	$-0.815641\pi$
$857$	1.62627	−	2.81679i	0.0555524	−	0.0962196i	0.892464	+	0.451118i	$0.148975\pi$
$858$	−2.02111	+	1.79441i	−0.0689995	+	0.0612603i
$859$	−3.97946	−	6.89262i	−0.135777	−	0.235173i	0.790117	−	0.612956i	$-0.210020\pi$
$859$	−3.97946	−	6.89262i	−0.135777	−	0.235173i	−0.925894	+	0.377783i	$0.876686\pi$
$860$	34.0109	−	37.7730i	1.15976	−	1.28805i
$861$	4.95074	−	1.58278i	0.168721	−	0.0539410i
$862$	−3.20013	−	30.4472i	−0.108997	−	1.03704i
$863$	38.4621	+	12.4971i	1.30926	+	0.425405i	0.878795	−	0.477200i	$-0.158348\pi$
$863$	38.4621	+	12.4971i	1.30926	+	0.425405i	0.430469	+	0.902605i	$0.358348\pi$
$864$	−3.59220	+	30.0720i	−0.122209	+	1.02307i
$865$	−21.0414	−	28.9610i	−0.715429	−	0.984704i
$866$	−15.5700	+	6.93221i	−0.529090	+	0.235566i
$867$	−8.28767	+	25.1027i	−0.281464	+	0.852534i
$868$	11.8206	−	6.82461i	0.401216	−	0.231642i
$869$	18.7090	−	41.7668i	0.634660	−	1.41684i
$870$	−2.10810	−	4.79571i	−0.0714713	−	0.162590i
$871$	−1.06106	+	4.99189i	−0.0359526	+	0.169144i
$872$	2.27854	−	3.13614i	0.0771611	−	0.106203i
$873$	−2.25725	+	0.979549i	−0.0763964	+	0.0331527i
$874$	5.38343	−	16.5685i	0.182097	−	0.560437i
$875$	−4.26661	−	4.73855i	−0.144238	−	0.160192i
$876$	−17.9117	+	10.2288i	−0.605180	+	0.345600i
$877$	27.9090	+	2.93335i	0.942418	+	0.0990522i	0.563260	−	0.826280i	$-0.309547\pi$
$877$	27.9090	+	2.93335i	0.942418	+	0.0990522i	0.379158	+	0.925332i	$0.376214\pi$
$878$	16.4196	+	14.7843i	0.554134	+	0.498944i
$879$	4.92540	−	44.8244i	0.166130	−	1.51189i
$880$	−3.93600	+	3.52791i	−0.132682	+	0.118926i
$881$			23.2639i			0.783780i	0.920012	+	0.391890i	$0.128179\pi$
$881$			23.2639i			0.783780i	−0.920012	+	0.391890i	$0.871821\pi$
$882$	−10.2420	+	7.29445i	−0.344867	+	0.245617i
$883$	−23.6812	−	17.2054i	−0.796937	−	0.579008i	0.113077	−	0.993586i	$-0.463929\pi$
$883$	−23.6812	−	17.2054i	−0.796937	−	0.579008i	−0.910014	+	0.414578i	$0.863929\pi$
$884$	1.04250	−	0.109571i	0.0350632	−	0.00368529i
$885$	2.99258	+	29.8271i	0.100595	+	1.00263i
$886$	4.46329	+	20.9981i	0.149947	+	0.705446i
$887$	−4.45691	−	1.98434i	−0.149648	−	0.0666278i	0.330546	−	0.943790i	$-0.392767\pi$
$887$	−4.45691	−	1.98434i	−0.149648	−	0.0666278i	−0.480194	+	0.877162i	$0.659434\pi$
$888$	−5.68406	−	17.7790i	−0.190745	−	0.596626i
$889$	6.15577	+	1.30845i	0.206458	+	0.0438840i
$890$	20.5644			0.689320
$891$	15.4683	−	25.5291i	0.518207	−	0.855255i
$892$	17.7008			0.592665
$893$	81.0893	+	17.2361i	2.71355	+	0.576783i
$894$	−2.60816	−	8.15800i	−0.0872299	−	0.272844i
$895$	29.4550	+	13.1142i	0.984572	+	0.438359i
$896$	−2.43568	−	11.4590i	−0.0813702	−	0.382817i
$897$	0.307323	+	3.06309i	0.0102612	+	0.102274i
$898$	−23.6074	+	2.48124i	−0.787789	+	0.0828000i
$899$	−7.97246	−	5.79233i	−0.265896	−	0.193185i
$900$	−11.0811	+	7.89202i	−0.369369	+	0.263067i
$901$		−	4.72544i		−	0.157427i
$902$	3.00765	−	5.18231i	0.100144	−	0.172552i
$903$	3.27140	−	29.7718i	0.108865	−	0.990745i
$904$	3.78539	+	3.40838i	0.125900	+	0.113361i
$905$	−0.0547000	−	0.00574920i	−0.00181829	−	0.000191110i
$906$	−23.7950	+	13.5886i	−0.790535	+	0.451451i
$907$	−6.84938	−	7.60701i	−0.227430	−	0.252587i	0.618620	−	0.785691i	$-0.287692\pi$
$907$	−6.84938	−	7.60701i	−0.227430	−	0.252587i	−0.846050	+	0.533104i	$0.821025\pi$
$908$	0.331524	−	1.02033i	0.0110020	−	0.0338607i
$909$	47.1885	−	20.4778i	1.56515	−	0.679205i
$910$	1.06462	−	1.46532i	0.0352918	−	0.0485749i
$911$	1.35450	−	6.37241i	0.0448765	−	0.211127i	−0.949996	−	0.312261i	$-0.898914\pi$
$911$	1.35450	−	6.37241i	0.0448765	−	0.211127i	0.994873	+	0.101134i	$0.0322470\pi$
$912$	2.75465	+	6.26655i	0.0912157	+	0.207506i
$913$	−17.7799	−	30.9570i	−0.588428	−	1.02453i
$914$	−0.228161	+	0.131729i	−0.00754689	+	0.00435720i
$915$	12.4036	−	37.5696i	0.410050	−	1.24201i
$916$	12.1014	−	5.38788i	0.399841	−	0.178021i
$917$	6.17680	+	8.50163i	0.203976	+	0.280749i
$918$	5.05164	−	2.16390i	0.166729	−	0.0714192i
$919$	22.0654	+	7.16949i	0.727871	+	0.236500i	0.649432	−	0.760419i	$-0.275007\pi$
$919$	22.0654	+	7.16949i	0.727871	+	0.236500i	0.0784385	+	0.996919i	$0.475007\pi$
$920$	−2.46452	−	23.4484i	−0.0812530	−	0.773070i
$921$	−29.7414	+	9.50850i	−0.980013	+	0.313316i
$922$	1.71057	−	1.89978i	0.0563346	−	0.0625659i
$923$	1.40058	+	2.42587i	0.0461006	+	0.0798485i
$924$	−2.22968	+	10.1410i	−0.0733510	+	0.333615i
$925$	6.69043	−	11.5882i	0.219980	−	0.381016i
$926$	6.76675	+	20.8259i	0.222369	+	0.684382i
$927$	−28.6864	+	5.81480i	−0.942185	+	0.190983i
$928$	−6.15344	+	4.47074i	−0.201997	+	0.146759i
$929$	5.52024	−	4.97045i	0.181113	−	0.163075i	−0.573587	−	0.819144i	$-0.694449\pi$
$929$	5.52024	−	4.97045i	0.181113	−	0.163075i	0.754701	+	0.656069i	$0.227782\pi$
$930$	12.4605	−	27.6346i	0.408595	−	0.906175i
$931$	−15.2196	+	34.1838i	−0.498802	+	1.12033i
$932$	−2.34929	+	22.3520i	−0.0769535	+	0.732164i
$933$	4.42750	+	21.3245i	0.144950	+	0.698134i
$934$	12.6853	+	7.32387i	0.415076	+	0.239644i
$935$	12.0011	+	3.92942i	0.392479	+	0.128506i
$936$	3.49029	+	3.20289i	0.114084	+	0.104690i
$937$	−44.2612	+	14.3813i	−1.44595	+	0.469817i	−0.923747	−	0.383004i	$-0.874890\pi$
$937$	−44.2612	+	14.3813i	−1.44595	+	0.469817i	−0.522203	+	0.852821i	$0.674890\pi$
$938$	−3.78547	−	8.50231i	−0.123600	−	0.277610i
$939$	−10.2115	+	17.4954i	−0.333238	+	0.570941i
$940$	44.3469	−	9.42623i	1.44644	−	0.307450i
$941$	17.3202	−	3.68153i	0.564623	−	0.120014i	0.0832478	−	0.996529i	$-0.473471\pi$
$941$	17.3202	−	3.68153i	0.564623	−	0.120014i	0.481375	+	0.876514i	$0.340137\pi$
$942$	6.77455	+	0.0319992i	0.220727	+	0.00104259i
$943$	−2.77590	−	6.23478i	−0.0903959	−	0.203032i
$944$	3.14396	−	1.02153i	0.102327	−	0.0332481i
$945$	−6.45044	+	18.9351i	−0.209833	+	0.615960i
$946$	−20.2318	−	27.9795i	−0.657792	−	0.909691i
$947$	24.8531	+	14.3490i	0.807618	+	0.466278i	0.846128	−	0.532980i	$-0.178928\pi$
$947$	24.8531	+	14.3490i	0.807618	+	0.466278i	−0.0385102	+	0.999258i	$0.512261\pi$
$948$	−30.7797	−	10.1619i	−0.999679	−	0.330044i
$949$	−0.538208	+	5.12071i	−0.0174710	+	0.166225i
$950$	7.81657	−	17.5563i	0.253603	−	0.569601i
$951$	−28.3510	+	2.84448i	−0.919344	+	0.0922387i
$952$	−3.51564	+	3.16550i	−0.113943	+	0.102594i
$953$	−30.0074	+	21.8016i	−0.972033	+	0.706224i	−0.955914	−	0.293646i	$-0.905131\pi$
$953$	−30.0074	+	21.8016i	−0.972033	+	0.706224i	−0.0161193	+	0.999870i	$0.505131\pi$
$954$	6.46707	−	5.71328i	0.209379	−	0.184974i
$955$	2.33443	+	7.18465i	0.0755405	+	0.232490i
$956$	0.824898	−	1.42877i	0.0266791	−	0.0462096i
$957$	7.34342	−	1.50737i	0.237379	−	0.0487263i
$958$	−5.08024	−	8.79924i	−0.164135	−	0.284290i
$959$	−6.00711	+	6.67157i	−0.193980	+	0.215436i
$960$	−13.2284	−	12.0245i	−0.426943	−	0.388089i
$961$	−2.72031	−	25.8820i	−0.0877519	−	0.834903i
$962$	−1.79066	−	0.581820i	−0.0577331	−	0.0187586i
$963$	8.82933	+	0.0834115i	0.284521	+	0.00268790i
$964$	−0.604824	−	0.832469i	−0.0194801	−	0.0268120i
$965$	−33.8955	+	15.0913i	−1.09114	+	0.485805i
$966$	−3.73682	−	4.18979i	−0.120230	−	0.134804i
$967$	−47.1454	+	27.2194i	−1.51609	+	0.875317i	−0.516272	+	0.856425i	$0.672681\pi$
$967$	−47.1454	+	27.2194i	−1.51609	+	0.875317i	−0.999822	+	0.0188923i	$0.993986\pi$
$968$	14.6949	+	25.7201i	0.472310	+	0.826674i
$969$	9.67510	−	13.1852i	0.310809	−	0.423570i
$970$	0.395235	−	1.85943i	0.0126902	−	0.0597028i
$971$	4.73162	−	6.51252i	0.151845	−	0.208997i	−0.726317	−	0.687360i	$-0.758770\pi$
$971$	4.73162	−	6.51252i	0.151845	−	0.208997i	0.878162	+	0.478363i	$0.158770\pi$
$972$	−19.1050	−	9.05260i	−0.612794	−	0.290362i
$973$	−3.05404	+	9.39936i	−0.0979080	+	0.301330i
$974$	−8.19404	−	9.10040i	−0.262554	−	0.291596i
$975$	−0.0160404	+	3.39591i	−0.000513703	+	0.108756i
$976$	−4.33912	−	0.456060i	−0.138892	−	0.0145981i
$977$	−9.44286	−	8.50239i	−0.302104	−	0.272016i	0.504110	−	0.863639i	$-0.331820\pi$
$977$	−9.44286	−	8.50239i	−0.302104	−	0.272016i	−0.806214	+	0.591624i	$0.798487\pi$
$978$	14.1218	−	6.20766i	0.451565	−	0.198499i
$979$	−6.18349	+	28.7711i	−0.197625	+	0.919527i
$980$			20.4640i			0.653698i
$981$	2.50526	+	3.51761i	0.0799869	+	0.112309i
$982$	−18.4389	−	13.3967i	−0.588409	−	0.427504i
$983$	5.25465	−	0.552286i	0.167597	−	0.0176152i	−0.0203581	−	0.999793i	$-0.506481\pi$
$983$	5.25465	−	0.552286i	0.167597	−	0.0176152i	0.187955	+	0.982178i	$0.439814\pi$
$984$	−9.57382	−	4.31684i	−0.305202	−	0.137616i
$985$	4.13278	+	19.4432i	0.131681	+	0.619512i
$986$	1.26086	+	0.561371i	0.0401539	+	0.0178777i
$987$	17.9697	−	19.7688i	0.571983	−	0.629249i
$988$	5.57202	+	1.18437i	0.177269	+	0.0376798i
$989$	−39.3279			−1.25055
$990$	9.13227	+	21.1752i	0.290243	+	0.672991i
$991$	54.4977			1.73118			0.865589	−	0.500756i	$-0.166945\pi$
$991$	54.4977			1.73118			0.865589	+	0.500756i	$0.166945\pi$
$992$	−43.0519	−	9.15096i	−1.36690	−	0.290543i
$993$	−33.2160	−	7.22443i	−1.05408	−	0.229260i
$994$	−4.66674	−	2.07777i	−0.148020	−	0.0659028i
$995$	0.0405788	+	0.190908i	0.00128643	+	0.00605220i
$996$	−20.5256	+	14.7651i	−0.650378	+	0.467849i
$997$	−7.60753	+	0.799583i	−0.240933	+	0.0253231i	−0.224225	−	0.974537i	$-0.571985\pi$
$997$	−7.60753	+	0.799583i	−0.240933	+	0.0253231i	−0.0167076	+	0.999860i	$0.505318\pi$
$998$	14.1919	+	10.3110i	0.449236	+	0.326389i
$999$	20.7920	+	0.294647i	0.657831	+	0.00932223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.83.5	yes	80
3.2	odd	2		297.2.t.a.116.6		80
9.2	odd	6		891.2.k.a.809.8		80
9.4	even	3		297.2.t.a.17.6		80
9.5	odd	6	inner	99.2.p.a.50.5	yes	80
9.7	even	3		891.2.k.a.809.13		80
11.2	odd	10	inner	99.2.p.a.2.5	✓	80
33.2	even	10		297.2.t.a.35.6		80
99.2	even	30		891.2.k.a.728.13		80
99.13	odd	30		297.2.t.a.233.6		80
99.68	even	30	inner	99.2.p.a.68.5	yes	80
99.79	odd	30		891.2.k.a.728.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.5	✓	80	11.2	odd	10	inner
99.2.p.a.50.5	yes	80	9.5	odd	6	inner
99.2.p.a.68.5	yes	80	99.68	even	30	inner
99.2.p.a.83.5	yes	80	1.1	even	1	trivial
297.2.t.a.17.6		80	9.4	even	3
297.2.t.a.35.6		80	33.2	even	10
297.2.t.a.116.6		80	3.2	odd	2
297.2.t.a.233.6		80	99.13	odd	30
891.2.k.a.728.8		80	99.79	odd	30
891.2.k.a.728.13		80	99.2	even	30
891.2.k.a.809.8		80	9.2	odd	6
891.2.k.a.809.13		80	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.784831 - 0.166821i) q^{2} +(0.527446 + 1.64979i) q^{3} +(-1.23896 - 0.551620i) q^{4} +(0.600562 + 2.82542i) q^{5} +(-0.138737 - 1.38279i) q^{6} +(-1.32545 + 0.139311i) q^{7} +(2.17861 + 1.58285i) q^{8} +(-2.44360 + 1.74035i) q^{9} -2.31767i q^{10} +(3.24258 + 0.696897i) q^{11} +(0.256572 - 2.33497i) q^{12} +(-0.435761 - 0.392361i) q^{13} +(1.06350 + 0.111778i) q^{14} +(-4.34458 + 2.48106i) q^{15} +(0.369177 + 0.410013i) q^{16} +(0.407327 - 1.25362i) q^{17} +(2.20814 - 0.958237i) q^{18} +(4.21041 - 5.79513i) q^{19} +(0.814488 - 3.83187i) q^{20} +(-0.928938 - 2.11323i) q^{21} +(-2.42862 - 1.08788i) q^{22} +(-2.62500 + 1.51554i) q^{23} +(-1.46227 + 4.42911i) q^{24} +(-3.05460 + 1.36000i) q^{25} +(0.276545 + 0.380632i) q^{26} +(-4.16008 - 3.11348i) q^{27} +(1.71903 + 0.558546i) q^{28} +(-0.136407 - 1.29783i) q^{29} +(3.82366 - 1.22244i) q^{30} +(5.05291 - 5.61183i) q^{31} +(-2.91425 - 5.04763i) q^{32} +(0.560556 + 5.71715i) q^{33} +(-0.528814 + 0.915932i) q^{34} +(-1.18963 - 3.66129i) q^{35} +(3.98754 - 0.808283i) q^{36} +(-3.23755 + 2.35222i) q^{37} +(-4.27121 + 3.84582i) q^{38} +(0.417472 - 0.925863i) q^{39} +(-3.16383 + 7.10608i) q^{40} +(-0.235357 + 2.23927i) q^{41} +(0.376527 + 1.81350i) q^{42} +(11.2365 + 6.48742i) q^{43} +(-3.63301 - 2.65210i) q^{44} +(-6.38475 - 5.85901i) q^{45} +(2.31301 - 0.751541i) q^{46} +(4.70724 + 10.5726i) q^{47} +(-0.481713 + 0.825325i) q^{48} +(-5.10962 + 1.08608i) q^{49} +(2.62423 - 0.557796i) q^{50} +(2.28306 + 0.0107839i) q^{51} +(0.323456 + 0.726494i) q^{52} +(3.40948 - 1.10781i) q^{53} +(2.74556 + 3.13755i) q^{54} +(-0.0216557 + 9.58019i) q^{55} +(-3.10815 - 1.79449i) q^{56} +(11.7815 + 3.88966i) q^{57} +(-0.109449 + 1.04133i) q^{58} +(2.43702 - 5.47364i) q^{59} +(6.75136 - 0.677371i) q^{60} +(-5.87674 + 5.29144i) q^{61} +(-4.90186 + 3.56141i) q^{62} +(2.99642 - 2.64717i) q^{63} +(1.10416 + 3.39825i) q^{64} +(0.846884 - 1.46685i) q^{65} +(0.513798 - 4.58051i) q^{66} +(-4.35166 - 7.53730i) q^{67} +(-1.19619 + 1.32850i) q^{68} +(-3.88487 - 3.53132i) q^{69} +(0.322875 + 3.07195i) q^{70} +(-4.54327 - 1.47620i) q^{71} +(-8.07836 - 0.0763170i) q^{72} +(-5.16130 - 7.10392i) q^{73} +(2.93333 - 1.30600i) q^{74} +(-3.85485 - 4.32212i) q^{75} +(-8.41325 + 4.85739i) q^{76} +(-4.39497 - 0.471977i) q^{77} +(-0.482099 + 0.657003i) q^{78} +(2.86894 - 13.4973i) q^{79} +(-0.936746 + 1.28932i) q^{80} +(2.94237 - 8.50544i) q^{81} +(0.558273 - 1.71819i) q^{82} +(-7.20241 - 7.99909i) q^{83} +(-0.0147874 + 3.13063i) q^{84} +(3.78664 + 0.397992i) q^{85} +(-7.73655 - 6.96602i) q^{86} +(2.06920 - 0.909579i) q^{87} +(5.96123 + 6.65078i) q^{88} +8.87289i q^{89} +(4.03355 + 5.66345i) q^{90} +(0.632240 + 0.459350i) q^{91} +(4.08827 - 0.429695i) q^{92} +(11.9235 + 5.37630i) q^{93} +(-1.93065 - 9.08301i) q^{94} +(18.9023 + 8.41585i) q^{95} +(6.79040 - 7.47025i) q^{96} +(0.802287 + 0.170531i) q^{97} +4.19137 q^{98} +(-9.13642 + 3.94029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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