LMFDB - Embedded newform 145.2.t.a.108.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(3,145)] 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("145.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.t (of order $28$, degree $12$, 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:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			108.9
Character	$\chi$	$=$	145.108
Dual form			145.2.t.a.47.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.443182 + 0.920277i) q^{2} +(-0.973467 - 1.22069i) q^{3} +(0.596480 - 0.747962i) q^{4} +(0.100511 - 2.23381i) q^{5} +(0.691949 - 1.43685i) q^{6} +(-3.19267 - 0.359728i) q^{7} +(2.94432 + 0.672023i) q^{8} +(0.125119 - 0.548181i) q^{9} +(2.10027 - 0.897485i) q^{10} +(-0.282265 - 0.177359i) q^{11} -1.49368 q^{12} +(3.66774 + 2.30460i) q^{13} +(-1.08389 - 3.09757i) q^{14} +(-2.82463 + 2.05185i) q^{15} +(0.260662 + 1.14204i) q^{16} +7.42290i q^{17} +(0.559929 - 0.127800i) q^{18} +(5.42486 - 0.611234i) q^{19} +(-1.61085 - 1.40760i) q^{20} +(2.66885 + 4.24744i) q^{21} +(0.0381244 - 0.338364i) q^{22} +(-1.34116 - 3.83282i) q^{23} +(-2.04587 - 4.24830i) q^{24} +(-4.97979 - 0.449046i) q^{25} +(-0.495389 + 4.39670i) q^{26} +(-5.01106 + 2.41320i) q^{27} +(-2.17343 + 2.17343i) q^{28} +(-0.0218780 + 5.38512i) q^{29} +(-3.14009 - 1.69010i) q^{30} +(0.716676 - 2.04814i) q^{31} +(3.78686 - 3.01992i) q^{32} +(0.0582756 + 0.517210i) q^{33} +(-6.83113 + 3.28970i) q^{34} +(-1.12446 + 7.09566i) q^{35} +(-0.335388 - 0.420563i) q^{36} +(1.62587 - 7.12342i) q^{37} +(2.96670 + 4.72148i) q^{38} +(-0.757232 - 6.72062i) q^{39} +(1.79711 - 6.50951i) q^{40} +(1.70982 + 1.70982i) q^{41} +(-2.72604 + 4.33847i) q^{42} +(-6.20526 - 2.98830i) q^{43} +(-0.301023 + 0.105332i) q^{44} +(-1.21196 - 0.334590i) q^{45} +(2.93288 - 2.93288i) q^{46} +(2.16272 + 9.47549i) q^{47} +(1.14032 - 1.42992i) q^{48} +(3.23926 + 0.739339i) q^{49} +(-1.79371 - 4.78180i) q^{50} +(9.06106 - 7.22595i) q^{51} +(3.91149 - 1.36869i) q^{52} +(6.89339 + 2.41210i) q^{53} +(-4.44163 - 3.54208i) q^{54} +(-0.424556 + 0.612698i) q^{55} +(-9.15852 - 3.20470i) q^{56} +(-6.02705 - 6.02705i) q^{57} +(-4.96550 + 2.36646i) q^{58} +6.55260i q^{59} +(-0.150132 + 3.33660i) q^{60} +(6.95855 + 0.784041i) q^{61} +(2.20248 - 0.248159i) q^{62} +(-0.596659 + 1.70515i) q^{63} +(6.56823 + 3.16309i) q^{64} +(5.51667 - 7.96139i) q^{65} +(-0.450150 + 0.282848i) q^{66} +(-6.35336 + 3.99208i) q^{67} +(5.55205 + 4.42761i) q^{68} +(-3.37311 + 5.36827i) q^{69} +(-7.02831 + 2.10985i) q^{70} +(-3.19119 + 0.728367i) q^{71} +(0.736780 - 1.52994i) q^{72} +(1.83366 - 3.80763i) q^{73} +(7.27608 - 1.66072i) q^{74} +(4.29952 + 6.51592i) q^{75} +(2.77864 - 4.42218i) q^{76} +(0.837377 + 0.667786i) q^{77} +(5.84924 - 3.67532i) q^{78} +(1.68732 - 1.06021i) q^{79} +(2.57729 - 0.467481i) q^{80} +(6.30409 + 3.03589i) q^{81} +(-0.815745 + 2.33127i) q^{82} +(-7.58032 + 0.854097i) q^{83} +(4.76884 + 0.537319i) q^{84} +(16.5813 + 0.746086i) q^{85} -7.03492i q^{86} +(6.59486 - 5.21553i) q^{87} +(-0.711889 - 0.711889i) q^{88} +(-9.71523 - 3.39950i) q^{89} +(-0.229202 - 1.26362i) q^{90} +(-10.8809 - 8.67721i) q^{91} +(-3.66678 - 1.28306i) q^{92} +(-3.19781 + 1.11896i) q^{93} +(-7.76160 + 6.18967i) q^{94} +(-0.820120 - 12.1795i) q^{95} +(-7.37277 - 1.68279i) q^{96} +(0.740965 - 0.929141i) q^{97} +(0.755184 + 3.30868i) q^{98} +(-0.132541 + 0.132541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 14 q^{2} - 10 q^{3} + 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} - 14 q^{8} - 10 q^{9} - 6 q^{10} - 20 q^{11} - 20 q^{12} - 28 q^{13} - 4 q^{14} - 4 q^{15} - 34 q^{16} + 84 q^{18} + 6 q^{20} - 16 q^{21}+ \cdots - 76 q^{99}+O(q^{100}) $ 156 * q - 14 * q^2 - 10 * q^3 + 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 - 14 * q^8 - 10 * q^9 - 6 * q^10 - 20 * q^11 - 20 * q^12 - 28 * q^13 - 4 * q^14 - 4 * q^15 - 34 * q^16 + 84 * q^18 + 6 * q^20 - 16 * q^21 - 22 * q^22 - 10 * q^23 - 56 * q^24 - 108 * q^25 + 36 * q^26 + 32 * q^27 - 8 * q^28 - 44 * q^30 - 8 * q^31 - 14 * q^32 - 14 * q^33 + 24 * q^34 + 26 * q^35 + 78 * q^36 - 72 * q^37 - 120 * q^38 - 16 * q^39 - 46 * q^40 - 22 * q^41 - 18 * q^42 + 2 * q^43 + 112 * q^44 + 30 * q^45 + 4 * q^46 + 22 * q^47 + 38 * q^48 - 84 * q^49 - 24 * q^50 - 28 * q^51 + 86 * q^52 + 56 * q^53 - 60 * q^55 + 4 * q^56 - 12 * q^57 + 96 * q^58 + 14 * q^60 - 46 * q^61 - 112 * q^62 + 158 * q^63 + 30 * q^64 + 4 * q^65 - 48 * q^66 + 18 * q^67 + 140 * q^68 + 124 * q^69 + 94 * q^70 - 28 * q^71 - 98 * q^72 - 84 * q^73 - 112 * q^74 + 54 * q^75 - 48 * q^76 + 28 * q^77 + 70 * q^78 + 4 * q^79 + 170 * q^80 + 58 * q^81 + 16 * q^82 + 46 * q^83 - 120 * q^84 + 76 * q^85 + 68 * q^87 + 40 * q^88 - 46 * q^89 + 120 * q^90 - 28 * q^91 - 14 * q^92 - 22 * q^93 + 84 * q^94 + 190 * q^95 - 28 * q^96 - 76 * q^97 - 160 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.443182	+	0.920277i	0.313377	+	0.650734i	0.996856	−	0.0792362i	$-0.0252481\pi$
$2$	0.443182	+	0.920277i	0.313377	+	0.650734i	−0.683479	+	0.729970i	$0.739534\pi$
$3$	−0.973467	−	1.22069i	−0.562032	−	0.704765i	0.416900	−	0.908952i	$-0.363116\pi$
$3$	−0.973467	−	1.22069i	−0.562032	−	0.704765i	−0.978932	+	0.204187i	$0.934545\pi$
$4$	0.596480	−	0.747962i	0.298240	−	0.373981i
$5$	0.100511	−	2.23381i	0.0449501	−	0.998989i
$5$	0.100511	−	2.23381i	0.0449501	−	0.998989i
$6$	0.691949	−	1.43685i	0.282487	−	0.586591i
$7$	−3.19267	−	0.359728i	−1.20672	−	0.135964i	−0.514395	−	0.857553i	$-0.671983\pi$
$7$	−3.19267	−	0.359728i	−1.20672	−	0.135964i	−0.692322	+	0.721589i	$0.743412\pi$
$8$	2.94432	+	0.672023i	1.04098	+	0.237596i
$9$	0.125119	−	0.548181i	0.0417063	−	0.182727i
$10$	2.10027	−	0.897485i	0.664163	−	0.283810i
$11$	−0.282265	−	0.177359i	−0.0851060	−	0.0534756i	0.488807	−	0.872392i	$-0.337432\pi$
$11$	−0.282265	−	0.177359i	−0.0851060	−	0.0534756i	−0.573913	+	0.818916i	$0.694575\pi$
$12$	−1.49368			−0.431189
$13$	3.66774	+	2.30460i	1.01725	+	0.639180i	0.933972	−	0.357347i	$-0.116319\pi$
$13$	3.66774	+	2.30460i	1.01725	+	0.639180i	0.0832770	+	0.996526i	$0.473461\pi$
$14$	−1.08389	−	3.09757i	−0.289681	−	0.827860i
$15$	−2.82463	+	2.05185i	−0.729316	+	0.529784i
$16$	0.260662	+	1.14204i	0.0651655	+	0.285509i
$17$			7.42290i			1.80032i	0.435561	+	0.900159i	$0.356550\pi$
$17$			7.42290i			1.80032i	−0.435561	+	0.900159i	$0.643450\pi$
$18$	0.559929	−	0.127800i	0.131977	−	0.0301228i
$19$	5.42486	−	0.611234i	1.24455	−	0.140227i	0.534980	−	0.844865i	$-0.320319\pi$
$19$	5.42486	−	0.611234i	1.24455	−	0.140227i	0.709567	+	0.704638i	$0.248890\pi$
$20$	−1.61085	−	1.40760i	−0.360197	−	0.314749i
$21$	2.66885	+	4.24744i	0.582390	+	0.926868i
$22$	0.0381244	−	0.338364i	0.00812816	−	0.0721394i
$23$	−1.34116	−	3.83282i	−0.279652	−	0.799199i	−0.994949	−	0.100379i	$-0.967995\pi$
$23$	−1.34116	−	3.83282i	−0.279652	−	0.799199i	0.715297	−	0.698820i	$-0.246291\pi$
$24$	−2.04587	−	4.24830i	−0.417612	−	0.867180i
$25$	−4.97979	−	0.449046i	−0.995959	−	0.0898093i
$26$	−0.495389	+	4.39670i	−0.0971537	+	0.862263i
$27$	−5.01106	+	2.41320i	−0.964379	+	0.464421i
$28$	−2.17343	+	2.17343i	−0.410739	+	0.410739i
$29$	−0.0218780	+	5.38512i	−0.00406265	+	0.999992i
$29$	−0.0218780	+	5.38512i	−0.00406265	+	0.999992i
$30$	−3.14009	−	1.69010i	−0.573300	−	0.308569i
$31$	0.716676	−	2.04814i	0.128719	−	0.367857i	−0.861430	−	0.507876i	$-0.830431\pi$
$31$	0.716676	−	2.04814i	0.128719	−	0.367857i	0.990149	+	0.140019i	$0.0447164\pi$
$32$	3.78686	−	3.01992i	0.669429	−	0.533852i
$33$	0.0582756	+	0.517210i	0.0101445	+	0.0900347i
$34$	−6.83113	+	3.28970i	−1.17153	+	0.564178i
$35$	−1.12446	+	7.09566i	−0.190069	+	1.19939i
$36$	−0.335388	−	0.420563i	−0.0558980	−	0.0700939i
$37$	1.62587	−	7.12342i	0.267292	−	1.17108i	−0.645857	−	0.763458i	$-0.723500\pi$
$37$	1.62587	−	7.12342i	0.267292	−	1.17108i	0.913149	−	0.407625i	$-0.133643\pi$
$38$	2.96670	+	4.72148i	0.481263	+	0.765926i
$39$	−0.757232	−	6.72062i	−0.121254	−	1.07616i
$40$	1.79711	−	6.50951i	0.284148	−	1.02924i
$41$	1.70982	+	1.70982i	0.267029	+	0.267029i	0.827902	−	0.560873i	$-0.189534\pi$
$41$	1.70982	+	1.70982i	0.267029	+	0.267029i	−0.560873	+	0.827902i	$0.689534\pi$
$42$	−2.72604	+	4.33847i	−0.420637	+	0.669440i
$43$	−6.20526	−	2.98830i	−0.946294	−	0.455711i	−0.103908	−	0.994587i	$-0.533135\pi$
$43$	−6.20526	−	2.98830i	−0.946294	−	0.455711i	−0.842385	+	0.538876i	$0.818849\pi$
$44$	−0.301023	+	0.105332i	−0.0453809	+	0.0158795i
$45$	−1.21196	−	0.334590i	−0.180668	−	0.0498777i
$46$	2.93288	−	2.93288i	0.432430	−	0.432430i
$47$	2.16272	+	9.47549i	0.315465	+	1.38214i	0.845414	+	0.534112i	$0.179354\pi$
$47$	2.16272	+	9.47549i	0.315465	+	1.38214i	−0.529949	+	0.848030i	$0.677789\pi$
$48$	1.14032	−	1.42992i	0.164592	−	0.206391i
$49$	3.23926	+	0.739339i	0.462751	+	0.105620i
$50$	−1.79371	−	4.78180i	−0.253669	−	0.676249i
$51$	9.06106	−	7.22595i	1.26880	−	1.01184i
$52$	3.91149	−	1.36869i	0.542425	−	0.189803i
$53$	6.89339	+	2.41210i	0.946880	+	0.331328i	0.759167	−	0.650896i	$-0.225607\pi$
$53$	6.89339	+	2.41210i	0.946880	+	0.331328i	0.187713	+	0.982224i	$0.439892\pi$
$54$	−4.44163	−	3.54208i	−0.604429	−	0.482016i
$55$	−0.424556	+	0.612698i	−0.0572471	+	0.0826162i
$56$	−9.15852	−	3.20470i	−1.22386	−	0.428247i
$57$	−6.02705	−	6.02705i	−0.798302	−	0.798302i
$58$	−4.96550	+	2.36646i	−0.652002	+	0.310731i
$59$			6.55260i			0.853075i	0.904470	+	0.426538i	$0.140267\pi$
$59$			6.55260i			0.853075i	−0.904470	+	0.426538i	$0.859733\pi$
$60$	−0.150132	+	3.33660i	−0.0193820	+	0.430753i
$61$	6.95855	+	0.784041i	0.890952	+	0.100386i	0.545559	−	0.838072i	$-0.316317\pi$
$61$	6.95855	+	0.784041i	0.890952	+	0.100386i	0.345392	+	0.938458i	$0.387746\pi$
$62$	2.20248	−	0.248159i	0.279715	−	0.0315163i
$63$	−0.596659	+	1.70515i	−0.0751720	+	0.214829i
$64$	6.56823	+	3.16309i	0.821029	+	0.395387i
$65$	5.51667	−	7.96139i	0.684259	−	0.987489i
$66$	−0.450150	+	0.282848i	−0.0554096	+	0.0348162i
$67$	−6.35336	+	3.99208i	−0.776186	+	0.487710i	−0.860949	−	0.508691i	$-0.830130\pi$
$67$	−6.35336	+	3.99208i	−0.776186	+	0.487710i	0.0847630	+	0.996401i	$0.472987\pi$
$68$	5.55205	+	4.42761i	0.673285	+	0.536927i
$69$	−3.37311	+	5.36827i	−0.406075	+	0.646264i
$70$	−7.02831	+	2.10985i	−0.840044	+	0.252176i
$71$	−3.19119	+	0.728367i	−0.378724	+	0.0864413i	−0.407645	−	0.913140i	$-0.633650\pi$
$71$	−3.19119	+	0.728367i	−0.378724	+	0.0864413i	0.0289212	+	0.999582i	$0.490793\pi$
$72$	0.736780	−	1.52994i	0.0868304	−	0.180305i
$73$	1.83366	−	3.80763i	0.214614	−	0.445650i	−0.765673	−	0.643230i	$-0.777594\pi$
$73$	1.83366	−	3.80763i	0.214614	−	0.445650i	0.980287	+	0.197580i	$0.0633083\pi$
$74$	7.27608	−	1.66072i	0.845827	−	0.193055i
$75$	4.29952	+	6.51592i	0.496466	+	0.752393i
$76$	2.77864	−	4.42218i	0.318732	−	0.507258i
$77$	0.837377	+	0.667786i	0.0954280	+	0.0761013i
$78$	5.84924	−	3.67532i	0.662296	−	0.416148i
$79$	1.68732	−	1.06021i	0.189838	−	0.119283i	−0.433760	−	0.901029i	$-0.642813\pi$
$79$	1.68732	−	1.06021i	0.189838	−	0.119283i	0.623598	+	0.781746i	$0.285670\pi$
$80$	2.57729	−	0.467481i	0.288149	−	0.0522660i
$81$	6.30409	+	3.03589i	0.700454	+	0.337321i
$82$	−0.815745	+	2.33127i	−0.0900840	+	0.257445i
$83$	−7.58032	+	0.854097i	−0.832048	+	0.0937493i	−0.517704	−	0.855560i	$-0.673213\pi$
$83$	−7.58032	+	0.854097i	−0.832048	+	0.0937493i	−0.314344	+	0.949309i	$0.601785\pi$
$84$	4.76884	+	0.537319i	0.520323	+	0.0586264i
$85$	16.5813	+	0.746086i	1.79850	+	0.0809244i
$86$		−	7.03492i		−	0.758595i
$87$	6.59486	−	5.21553i	0.707043	−	0.559164i
$88$	−0.711889	−	0.711889i	−0.0758877	−	0.0758877i
$89$	−9.71523	−	3.39950i	−1.02981	−	0.360347i	−0.238100	−	0.971241i	$-0.576524\pi$
$89$	−9.71523	−	3.39950i	−1.02981	−	0.360347i	−0.791712	+	0.610894i	$0.790810\pi$
$90$	−0.229202	−	1.26362i	−0.0241600	−	0.133197i
$91$	−10.8809	−	8.67721i	−1.14063	−	0.909618i
$92$	−3.66678	−	1.28306i	−0.382289	−	0.133769i
$93$	−3.19781	+	1.11896i	−0.331597	+	0.116031i
$94$	−7.76160	+	6.18967i	−0.800547	+	0.638415i
$95$	−0.820120	−	12.1795i	−0.0841426	−	1.24959i
$96$	−7.37277	−	1.68279i	−0.752480	−	0.171749i
$97$	0.740965	−	0.929141i	0.0752336	−	0.0943400i	−0.742790	−	0.669524i	$-0.766498\pi$
$97$	0.740965	−	0.929141i	0.0752336	−	0.0943400i	0.818024	+	0.575184i	$0.195070\pi$
$98$	0.755184	+	3.30868i	0.0762851	+	0.334227i
$99$	−0.132541	+	0.132541i	−0.0133209	+	0.0133209i
$100$	−3.30622	+	3.45685i	−0.330622	+	0.345685i
$101$	−8.62410	+	3.01770i	−0.858130	+	0.300273i	−0.723247	−	0.690589i	$-0.757351\pi$
$101$	−8.62410	+	3.01770i	−0.858130	+	0.300273i	−0.134882	+	0.990862i	$0.543066\pi$
$102$	10.6656	+	5.13627i	1.05605	+	0.508567i
$103$	5.62139	−	8.94639i	0.553892	−	0.881514i	−0.446017	−	0.895025i	$-0.647158\pi$
$103$	5.62139	−	8.94639i	0.553892	−	0.881514i	0.999909	+	0.0135104i	$0.00430061\pi$
$104$	9.25028	+	9.25028i	0.907065	+	0.907065i
$105$	9.75622	−	5.53477i	0.952110	−	0.540139i
$106$	0.835225	+	7.41283i	0.0811242	+	0.719997i
$107$	−4.63405	−	7.37505i	−0.447990	−	0.712973i	0.544028	−	0.839067i	$-0.316899\pi$
$107$	−4.63405	−	7.37505i	−0.447990	−	0.712973i	−0.992018	+	0.126094i	$0.959756\pi$
$108$	−1.18402	+	5.18751i	−0.113932	+	0.499168i
$109$	−3.50666	−	4.39721i	−0.335877	−	0.421177i	0.584998	−	0.811035i	$-0.301095\pi$
$109$	−3.50666	−	4.39721i	−0.335877	−	0.421177i	−0.920875	+	0.389858i	$0.872524\pi$
$110$	−0.752008	−	0.119172i	−0.0717011	−	0.0113626i
$111$	−10.2782	+	4.94973i	−0.975566	+	0.469808i
$112$	−0.421387	−	3.73991i	−0.0398173	−	0.353388i
$113$	−0.182774	+	0.145757i	−0.0171939	+	0.0137117i	−0.632049	−	0.774928i	$-0.717786\pi$
$113$	−0.182774	+	0.145757i	−0.0171939	+	0.0137117i	0.614855	+	0.788640i	$0.289214\pi$
$114$	2.87547	−	8.21763i	0.269313	−	0.769652i
$115$	−8.69659	+	2.61066i	−0.810962	+	0.243445i
$116$	4.01482	+	3.22848i	0.372766	+	0.299757i
$117$	1.72224	−	1.72224i	0.159221	−	0.159221i
$118$	−6.03020	+	2.90399i	−0.555125	+	0.267334i
$119$	2.67022	−	23.6989i	0.244779	−	2.17247i
$120$	−9.69551	+	4.14308i	−0.885075	+	0.378210i
$121$	−4.72450	−	9.81053i	−0.429500	−	0.891867i
$122$	2.36237	+	6.75127i	0.213879	+	0.611231i
$123$	0.422705	−	3.75161i	0.0381140	−	0.338271i
$124$	−1.10445	−	1.75772i	−0.0991826	−	0.157848i
$125$	−1.50361	+	11.0788i	−0.134487	+	0.990915i
$126$	−1.83364	+	0.206602i	−0.163354	+	0.0184056i
$127$	5.26685	−	1.20212i	0.467358	−	0.106671i	0.0176444	−	0.999844i	$-0.494383\pi$
$127$	5.26685	−	1.20212i	0.467358	−	0.106671i	0.449713	+	0.893173i	$0.351526\pi$
$128$		−	2.24073i		−	0.198055i
$129$	2.39284	+	10.4837i	0.210678	+	0.923039i
$130$	9.77158	+	1.54852i	0.857024	+	0.135814i
$131$	2.90820	+	8.31115i	0.254091	+	0.726149i	0.998304	+	0.0582077i	$0.0185386\pi$
$131$	2.90820	+	8.31115i	0.254091	+	0.726149i	−0.744214	+	0.667941i	$0.767176\pi$
$132$	0.421614	+	0.264918i	0.0366968	+	0.0230581i
$133$	−17.5397			−1.52088
$134$	−6.48951	−	4.07763i	−0.560609	−	0.352254i
$135$	4.88696	+	11.4363i	0.420602	+	0.984280i
$136$	−4.98836	+	21.8554i	−0.427748	+	1.87409i
$137$	5.93617	+	1.35489i	0.507161	+	0.115756i	0.468443	−	0.883494i	$-0.344815\pi$
$137$	5.93617	+	1.35489i	0.507161	+	0.115756i	0.0387184	+	0.999250i	$0.487672\pi$
$138$	−6.43520	−	0.725073i	−0.547801	−	0.0617223i
$139$	−8.13195	+	16.8862i	−0.689743	+	1.43227i	0.201845	+	0.979418i	$0.435306\pi$
$139$	−8.13195	+	16.8862i	−0.689743	+	1.43227i	−0.891588	+	0.452848i	$0.850408\pi$
$140$	4.63657	+	5.07347i	0.391861	+	0.428787i
$141$	9.46129	−	11.8641i	0.796784	−	0.999136i
$142$	−2.08458	−	2.61398i	−0.174934	−	0.219360i
$143$	−0.626534	−	1.30101i	−0.0523934	−	0.108796i
$144$	0.658656			0.0548880
$145$	12.0271	+	0.590137i	0.998798	+	0.0490082i
$146$	4.31672			0.357255
$147$	−2.25081	−	4.67385i	−0.185643	−	0.385493i
$148$	−4.35825	−	5.46507i	−0.358246	−	0.449226i
$149$	−12.0345	+	15.0908i	−0.985904	+	1.23628i	−0.0142448	+	0.999899i	$0.504534\pi$
$149$	−12.0345	+	15.0908i	−0.985904	+	1.23628i	−0.971659	+	0.236386i	$0.924037\pi$
$150$	−4.09098	+	6.84449i	−0.334027	+	0.558850i
$151$	−7.58945	+	15.7597i	−0.617621	+	1.28250i	0.324073	+	0.946032i	$0.394948\pi$
$151$	−7.58945	+	15.7597i	−0.617621	+	1.28250i	−0.941694	+	0.336471i	$0.890767\pi$
$152$	16.3833	+	1.84595i	1.32886	+	0.149727i
$153$	4.06909	+	0.928744i	0.328967	+	0.0750845i
$154$	−0.243438	+	1.06657i	−0.0196168	+	0.0859467i
$155$	−4.50312	−	1.80678i	−0.361699	−	0.145124i
$156$	−5.47845	−	3.44234i	−0.438627	−	0.275607i
$157$	−18.5421			−1.47982			−0.739910	−	0.672706i	$-0.765132\pi$
$157$	−18.5421			−1.47982			−0.739910	+	0.672706i	$0.765132\pi$
$158$	1.72348	+	1.08293i	0.137112	+	0.0861534i
$159$	−3.76606	−	10.7628i	−0.298668	−	0.853545i
$160$	−6.36530	−	8.76266i	−0.503221	−	0.692749i
$161$	2.90312	+	12.7194i	0.228798	+	1.00243i
$162$			7.14696i			0.561518i
$163$	1.92140	−	0.438548i	0.150496	−	0.0343497i	−0.146609	−	0.989195i	$-0.546836\pi$
$163$	1.92140	−	0.438548i	0.150496	−	0.0343497i	0.297105	+	0.954845i	$0.403979\pi$
$164$	2.29875	−	0.259007i	0.179502	−	0.0202250i
$165$	1.16121	−	0.0781909i	0.0903997	−	0.00608716i
$166$	−4.14547	−	6.59747i	−0.321751	−	0.512063i
$167$	1.08881	−	9.66345i	0.0842546	−	0.747780i	−0.878563	−	0.477627i	$-0.841497\pi$
$167$	1.08881	−	9.66345i	0.0842546	−	0.747780i	0.962817	−	0.270153i	$-0.0870743\pi$
$168$	5.00357	+	14.2994i	0.386034	+	1.10322i
$169$	2.50069	+	5.19273i	0.192361	+	0.399441i
$170$	6.66195	+	15.5901i	0.510948	+	1.19570i
$171$	0.343684	−	3.05028i	0.0262822	−	0.233261i
$172$	−5.93645	+	2.85884i	−0.452650	+	0.217985i
$173$	0.563496	−	0.563496i	0.0428418	−	0.0428418i	−0.685361	−	0.728203i	$-0.740356\pi$
$173$	0.563496	−	0.563496i	0.0428418	−	0.0428418i	0.728203	+	0.685361i	$0.240356\pi$
$174$	7.72246	+	3.75767i	0.585438	+	0.284868i
$175$	15.7373	+	3.22503i	1.18963	+	0.243789i
$176$	0.128974	−	0.368587i	0.00972179	−	0.0277833i
$177$	7.99868	−	6.37874i	0.601218	−	0.479455i
$178$	−1.17713	−	10.4473i	−0.0882295	−	0.783058i
$179$	1.04193	−	0.501769i	0.0778778	−	0.0375040i	−0.394539	−	0.918879i	$-0.629096\pi$
$179$	1.04193	−	0.501769i	0.0778778	−	0.0375040i	0.472417	+	0.881375i	$0.343382\pi$
$180$	−0.973168	+	0.706921i	−0.0725356	+	0.0526908i
$181$	−8.53309	−	10.7002i	−0.634260	−	0.795337i	0.356012	−	0.934481i	$-0.384136\pi$
$181$	−8.53309	−	10.7002i	−0.634260	−	0.795337i	−0.990272	+	0.139145i	$0.955565\pi$
$182$	3.16323	−	13.8590i	0.234474	−	1.02730i
$183$	−5.81685	−	9.25747i	−0.429994	−	0.684332i
$184$	−1.37307	−	12.1864i	−0.101224	−	0.898391i
$185$	−15.7489	−	4.34788i	−1.15788	−	0.319662i
$186$	−2.44696	−	2.44696i	−0.179420	−	0.179420i
$187$	1.31652	−	2.09522i	0.0962731	−	0.153218i
$188$	8.37732	+	4.03431i	0.610979	+	0.294232i
$189$	16.8668	−	5.90194i	1.22688	−	0.429303i
$190$	10.8451	−	6.15248i	0.786784	−	0.446348i
$191$	10.1739	−	10.1739i	0.736156	−	0.736156i	−0.235676	−	0.971832i	$-0.575730\pi$
$191$	10.1739	−	10.1739i	0.736156	−	0.736156i	0.971832	+	0.235676i	$0.0757304\pi$
$192$	−2.53280	−	11.0969i	−0.182789	−	0.800853i
$193$	0.132503	−	0.166154i	0.00953779	−	0.0119600i	−0.777040	−	0.629452i	$-0.783280\pi$
$193$	0.132503	−	0.166154i	0.00953779	−	0.0119600i	0.786578	+	0.617492i	$0.211851\pi$
$194$	1.18345	+	0.270115i	0.0849667	+	0.0193931i
$195$	−15.0887	+	1.01601i	−1.08052	+	0.0727581i
$196$	2.48515	−	1.98184i	0.177511	−	0.141560i
$197$	−1.29341	+	0.452582i	−0.0921514	+	0.0322452i	−0.375961	−	0.926635i	$-0.622687\pi$
$197$	−1.29341	+	0.452582i	−0.0921514	+	0.0322452i	0.283810	+	0.958881i	$0.408402\pi$
$198$	−0.180715	−	0.0632348i	−0.0128428	−	0.00449390i
$199$	16.6181	+	13.2525i	1.17802	+	0.939443i	0.999014	−	0.0444042i	$-0.0141389\pi$
$199$	16.6181	+	13.2525i	1.17802	+	0.939443i	0.179011	+	0.983847i	$0.442710\pi$
$200$	−14.3604	−	4.66867i	−1.01543	−	0.330125i
$201$	11.0579	+	3.86932i	0.779962	+	0.272921i
$202$	−6.59917	−	6.59917i	−0.464316	−	0.464316i
$203$	2.00703	−	17.1851i	0.140866	−	1.20615i
$204$		−	11.0875i		−	0.776278i
$205$	3.99126	−	3.64755i	0.278762	−	0.254756i
$206$	10.7245	+	1.20836i	0.747209	+	0.0841902i
$207$	−2.26889	+	0.255642i	−0.157699	+	0.0177684i
$208$	−1.67589	+	4.78941i	−0.116202	+	0.332086i
$209$	−1.63965	−	0.789615i	−0.113417	−	0.0546188i
$210$	9.41731	+	6.52552i	0.649856	+	0.450303i
$211$	0.0410704	−	0.0258062i	0.00282740	−	0.00177657i	−0.530618	−	0.847611i	$-0.678040\pi$
$211$	0.0410704	−	0.0258062i	0.00282740	−	0.00177657i	0.533445	+	0.845835i	$0.320897\pi$
$212$	5.91593	−	3.71722i	0.406308	−	0.255300i
$213$	3.99562	+	3.18640i	0.273776	+	0.218329i
$214$	4.73336	−	7.53310i	0.323566	−	0.514952i
$215$	−7.29898	+	13.5610i	−0.497786	+	0.924853i
$216$	−16.3759	+	3.73770i	−1.11424	+	0.254318i
$217$	−3.02488	+	6.28124i	−0.205343	+	0.426398i
$218$	2.49257	−	5.17587i	0.168818	−	0.350554i
$219$	−6.43295	+	1.46828i	−0.434698	+	0.0992170i
$220$	0.205036	+	0.683014i	0.0138235	+	0.0460488i
$221$	−17.1068	+	27.2253i	−1.15073	+	1.83137i
$222$	−9.11025	−	7.26518i	−0.611440	−	0.487607i
$223$	10.4384	−	6.55891i	0.699010	−	0.439217i	−0.135088	−	0.990834i	$-0.543132\pi$
$223$	10.4384	−	6.55891i	0.699010	−	0.439217i	0.834098	+	0.551616i	$0.185989\pi$
$224$	−13.1766	+	8.27938i	−0.880396	+	0.553189i
$225$	−0.869225	+	2.67365i	−0.0579483	+	0.178243i
$226$	−0.215139	−	0.103606i	−0.0143108	−	0.00689174i
$227$	3.37134	−	9.63473i	0.223764	−	0.639480i	−0.776196	−	0.630492i	$-0.782853\pi$
$227$	3.37134	−	9.63473i	0.223764	−	0.639480i	0.999960	−	0.00898794i	$-0.00286099\pi$
$228$	−8.10302	+	0.912991i	−0.536635	+	0.0604643i
$229$	20.6689	+	2.32882i	1.36584	+	0.153893i	0.764253	−	0.644917i	$-0.223108\pi$
$229$	20.6689	+	2.32882i	1.36584	+	0.153893i	0.601584	+	0.798810i	$0.294537\pi$
$230$	−6.25670	−	6.84628i	−0.412555	−	0.451430i
$231$		−	1.67225i		−	0.110026i
$232$	−3.68334	+	15.8408i	−0.241823	+	1.04000i
$233$	−15.9794	−	15.9794i	−1.04684	−	1.04684i	−0.998848	−	0.0479964i	$-0.984716\pi$
$233$	−15.9794	−	15.9794i	−1.04684	−	1.04684i	−0.0479964	−	0.998848i	$-0.515284\pi$
$234$	2.34820	+	0.821672i	0.153507	+	0.0537144i
$235$	21.3838	−	3.87870i	1.39492	−	0.253019i
$236$	4.90109	+	3.90849i	0.319034	+	0.254421i
$237$	−2.93674	−	1.02761i	−0.190761	−	0.0667503i
$238$	22.9929	−	8.04558i	1.49041	−	0.521517i
$239$	−10.5217	+	8.39081i	−0.680595	+	0.542757i	−0.901629	−	0.432509i	$-0.857628\pi$
$239$	−10.5217	+	8.39081i	−0.680595	+	0.542757i	0.221034	+	0.975266i	$0.429057\pi$
$240$	−3.07955	−	2.69099i	−0.198784	−	0.173703i
$241$	7.37877	+	1.68416i	0.475309	+	0.108486i	0.453463	−	0.891275i	$-0.350189\pi$
$241$	7.37877	+	1.68416i	0.475309	+	0.108486i	0.0218459	+	0.999761i	$0.493046\pi$
$242$	6.93459	−	8.69571i	0.445773	−	0.558981i
$243$	1.28194	+	5.61656i	0.0822368	+	0.360303i
$244$	4.73707	−	4.73707i	0.303260	−	0.303260i
$245$	1.97712	−	7.16156i	0.126314	−	0.457536i
$246$	3.63985	−	1.27364i	0.232069	−	0.0812043i
$247$	21.3056	+	10.2602i	1.35564	+	0.652844i
$248$	3.48652	−	5.54877i	0.221395	−	0.352347i
$249$	8.42178	+	8.42178i	0.533709	+	0.533709i
$250$	−10.8619	+	3.52618i	−0.686968	+	0.223015i
$251$	−2.50604	−	22.2418i	−0.158180	−	1.40389i	−0.782467	−	0.622692i	$-0.786039\pi$
$251$	−2.50604	−	22.2418i	−0.158180	−	1.40389i	0.624287	−	0.781195i	$-0.285390\pi$
$252$	0.919496	+	1.46337i	0.0579228	+	0.0921836i
$253$	−0.301221	+	1.31974i	−0.0189376	+	0.0829712i
$254$	3.44046	+	4.31420i	0.215874	+	0.270697i
$255$	−15.2306	−	20.9670i	−0.953780	−	1.31300i
$256$	15.1986	−	7.31924i	0.949910	−	0.457453i
$257$	−1.87619	−	16.6517i	−0.117034	−	1.03870i	−0.905711	−	0.423895i	$-0.860662\pi$
$257$	−1.87619	−	16.6517i	−0.117034	−	1.03870i	0.788677	−	0.614807i	$-0.210766\pi$
$258$	−8.58745	+	6.84827i	−0.534632	+	0.426354i
$259$	−7.75338	+	22.1579i	−0.481771	+	1.37682i
$260$	−2.66424	−	8.87508i	−0.165229	−	0.550409i
$261$	2.94928	+	0.685773i	0.182556	+	0.0424483i
$262$	−6.35970	+	6.35970i	−0.392904	+	0.392904i
$263$	8.21450	−	3.95590i	0.506528	−	0.243931i	−0.163125	−	0.986605i	$-0.552157\pi$
$263$	8.21450	−	3.95590i	0.506528	−	0.243931i	0.669653	+	0.742674i	$0.266443\pi$
$264$	−0.175995	+	1.56200i	−0.0108317	+	0.0961343i
$265$	6.08103	−	15.1561i	0.373555	−	0.931029i
$266$	−7.77327	−	16.1414i	−0.476610	−	0.989690i
$267$	5.30772	+	15.1686i	0.324827	+	0.928302i
$268$	−0.803726	+	7.13327i	−0.0490954	+	0.435734i
$269$	2.83114	+	4.50574i	0.172618	+	0.274720i	0.921817	−	0.387625i	$-0.126704\pi$
$269$	2.83114	+	4.50574i	0.172618	+	0.274720i	−0.749199	+	0.662344i	$0.769562\pi$
$270$	−8.35876	+	9.56572i	−0.508698	+	0.582151i
$271$	1.33774	−	0.150727i	0.0812619	−	0.00915602i	−0.0712399	−	0.997459i	$-0.522696\pi$
$271$	1.33774	−	0.150727i	0.0812619	−	0.00915602i	0.152502	+	0.988303i	$0.451267\pi$
$272$	−8.47722	+	1.93487i	−0.514007	+	0.117319i
$273$			21.7291i			1.31511i
$274$	1.38393	+	6.06338i	0.0836061	+	0.366302i
$275$	1.32598	+	1.00996i	0.0799595	+	0.0609028i
$276$	2.00327	+	5.72503i	0.120583	+	0.344606i
$277$	18.9088	+	11.8812i	1.13612	+	0.713871i	0.962591	−	0.270958i	$-0.0873404\pi$
$277$	18.9088	+	11.8812i	1.13612	+	0.713871i	0.173528	+	0.984829i	$0.444483\pi$
$278$	−19.1439			−1.14817
$279$	−1.03308	−	0.649129i	−0.0618491	−	0.0388624i
$280$	−8.07923	+	20.1363i	−0.482826	+	1.20337i
$281$	−1.16627	+	5.10977i	−0.0695739	+	0.304823i	−0.997728	−	0.0673733i	$-0.978538\pi$
$281$	−1.16627	+	5.10977i	−0.0695739	+	0.304823i	0.928154	+	0.372197i	$0.121395\pi$
$282$	15.1113	+	3.44906i	0.899866	+	0.205389i
$283$	−25.7594	−	2.90239i	−1.53124	−	0.172529i	−0.694244	−	0.719739i	$-0.744261\pi$
$283$	−25.7594	−	2.90239i	−1.53124	−	0.172529i	−0.836995	+	0.547210i	$0.815690\pi$
$284$	−1.35869	+	2.82134i	−0.0806232	+	0.167416i
$285$	−14.0691	+	12.8575i	−0.833379	+	0.761611i
$286$	0.919622	−	1.15317i	0.0543784	−	0.0681884i
$287$	−4.84382	−	6.07395i	−0.285921	−	0.358534i
$288$	−1.18166	−	2.45373i	−0.0696298	−	0.144588i
$289$	−38.0995			−2.24115
$290$	4.78712	+	11.3298i	0.281109	+	0.665310i
$291$	−1.85550			−0.108771
$292$	−1.75422	−	3.64269i	−0.102658	−	0.213172i
$293$	14.2954	+	17.9259i	0.835149	+	1.04724i	0.998161	+	0.0606195i	$0.0193076\pi$
$293$	14.2954	+	17.9259i	0.835149	+	1.04724i	−0.163012	+	0.986624i	$0.552121\pi$
$294$	3.30372	−	4.14273i	0.192677	−	0.241609i
$295$	14.6372	+	0.658611i	0.852213	+	0.0383458i
$296$	9.57420	−	19.8810i	0.556489	−	1.15556i
$297$	1.84245	+	0.207594i	0.106910	+	0.0120458i
$298$	−19.2212	−	4.38711i	−1.11345	−	0.254138i
$299$	3.91407	−	17.1487i	0.226356	−	0.991732i
$300$	7.43824	+	0.670733i	0.429447	+	0.0387248i
$301$	18.7364	+	11.7729i	1.07995	+	0.678576i
$302$	−17.8668			−1.02812
$303$	12.0790	+	7.58971i	0.693918	+	0.436017i
$304$	2.11211	+	6.03605i	0.121138	+	0.346191i
$305$	2.45081	−	15.4653i	0.140333	−	0.885539i
$306$	0.948648	+	4.15630i	0.0542306	+	0.237600i
$307$			31.7559i			1.81240i	0.422844	+	0.906202i	$0.361032\pi$
$307$			31.7559i			1.81240i	−0.422844	+	0.906202i	$0.638968\pi$
$308$	0.998958	−	0.228006i	0.0569209	−	0.0129918i
$309$	−16.3930	+	1.84705i	−0.932566	+	0.105075i
$310$	−0.332967	−	4.94485i	−0.0189112	−	0.280849i
$311$	−1.19084	−	1.89521i	−0.0675263	−	0.107468i	0.811254	−	0.584693i	$-0.198785\pi$
$311$	−1.19084	−	1.89521i	−0.0675263	−	0.107468i	−0.878781	+	0.477226i	$0.841642\pi$
$312$	2.28687	−	20.2966i	0.129469	−	1.14907i
$313$	−3.53606	−	10.1055i	−0.199870	−	0.571196i	0.799704	−	0.600395i	$-0.204990\pi$
$313$	−3.53606	−	10.1055i	−0.199870	−	0.571196i	−0.999574	+	0.0291992i	$0.990704\pi$
$314$	−8.21752	−	17.0639i	−0.463741	−	0.962969i
$315$	3.74902	+	1.50421i	0.211233	+	0.0847526i
$316$	0.213453	−	1.89444i	0.0120076	−	0.106571i
$317$	−20.1277	+	9.69299i	−1.13048	+	0.544413i	−0.903116	−	0.429396i	$-0.858726\pi$
$317$	−20.1277	+	9.69299i	−1.13048	+	0.544413i	−0.227368	+	0.973809i	$0.573012\pi$
$318$	8.23570	−	8.23570i	0.461835	−	0.461835i
$319$	0.961273	−	1.51615i	0.0538209	−	0.0848880i
$320$	7.72593	−	14.3542i	0.431892	−	0.802426i
$321$	−4.49155	+	12.8361i	−0.250694	+	0.716441i
$322$	−10.4188	+	8.30869i	−0.580615	+	0.463025i
$323$	4.53713	+	40.2682i	0.252453	+	2.24058i
$324$	6.03099	−	2.90437i	0.335055	−	0.161354i
$325$	−17.2297	−	13.1234i	−0.955734	−	0.727955i
$326$	1.25512	+	1.57387i	0.0695146	+	0.0871685i
$327$	−1.95401	+	8.56109i	−0.108057	+	0.473429i
$328$	3.88522	+	6.18329i	0.214525	+	0.341415i
$329$	−3.49625	−	31.0301i	−0.192755	−	1.71075i
$330$	0.586583	+	1.03398i	0.0322903	+	0.0569186i
$331$	−8.77860	−	8.77860i	−0.482516	−	0.482516i	0.423418	−	0.905934i	$-0.360830\pi$
$331$	−8.77860	−	8.77860i	−0.482516	−	0.482516i	−0.905934	+	0.423418i	$0.860830\pi$
$332$	−3.88268	+	6.17924i	−0.213090	+	0.339130i
$333$	−3.70150	−	1.78255i	−0.202841	−	0.0976830i
$334$	9.37559	−	3.28066i	0.513009	−	0.179510i
$335$	8.27895	+	14.5934i	0.452328	+	0.797324i
$336$	−4.15506	+	4.15506i	−0.226677	+	0.226677i
$337$	−0.316965	−	1.38871i	−0.0172662	−	0.0756481i	0.965561	−	0.260177i	$-0.0837811\pi$
$337$	−0.316965	−	1.38871i	−0.0172662	−	0.0756481i	−0.982827	+	0.184529i	$0.940924\pi$
$338$	−3.67049	+	4.60265i	−0.199648	+	0.250351i
$339$	0.355849	+	0.0812201i	0.0193270	+	0.00441127i
$340$	10.4485	−	11.9572i	0.566648	−	0.648470i
$341$	−0.565548	+	0.451009i	−0.0306261	+	0.0244235i
$342$	2.95942	−	1.03555i	0.160027	−	0.0559959i
$343$	11.1521	+	3.90230i	0.602158	+	0.210704i
$344$	−16.2621	−	12.9686i	−0.876794	−	0.699220i
$345$	11.6527	+	8.07445i	0.627358	+	0.434714i
$346$	0.768304	+	0.268841i	0.0413043	+	0.0144530i
$347$	14.4583	+	14.4583i	0.776163	+	0.776163i	0.979176	−	0.203013i	$-0.0650733\pi$
$347$	14.4583	+	14.4583i	0.776163	+	0.776163i	−0.203013	+	0.979176i	$0.565073\pi$
$348$	0.0326789	−	8.04366i	0.00175177	−	0.431186i
$349$		−	28.1957i		−	1.50928i	−0.656138	−	0.754641i	$-0.727811\pi$
$349$		−	28.1957i		−	1.50928i	0.656138	−	0.754641i	$-0.272189\pi$
$350$	4.00658	+	15.9120i	0.214161	+	0.850531i
$351$	−23.9407	−	2.69747i	−1.27786	−	0.143980i
$352$	−1.60451	+	0.180784i	−0.0855204	+	0.00963584i
$353$	−1.86690	+	5.33528i	−0.0993648	+	0.283968i	−0.982826	−	0.184537i	$-0.940922\pi$
$353$	−1.86690	+	5.33528i	−0.0993648	+	0.283968i	0.883461	+	0.468505i	$0.155207\pi$
$354$	9.41508	+	4.53406i	0.500406	+	0.240983i
$355$	1.30628	+	7.20170i	0.0693302	+	0.382227i
$356$	−8.33764	+	5.23889i	−0.441894	+	0.277660i
$357$	−31.5284	+	19.8106i	−1.66866	+	1.04849i
$358$	0.923533	+	0.736493i	0.0488103	+	0.0389249i
$359$	−0.405361	+	0.645128i	−0.0213941	+	0.0340486i	−0.857250	−	0.514900i	$-0.827829\pi$
$359$	−0.405361	+	0.645128i	−0.0213941	+	0.0340486i	0.835856	+	0.548949i	$0.184972\pi$
$360$	−3.34354	−	1.79960i	−0.176220	−	0.0948474i
$361$	10.5318	−	2.40382i	0.554307	−	0.126517i
$362$	6.06540	−	12.5949i	0.318790	−	0.661975i
$363$	−7.37646	+	15.3174i	−0.387164	+	0.803954i
$364$	−12.9804	+	2.96270i	−0.680360	+	0.155288i
$365$	−8.32122	−	4.47875i	−0.435552	−	0.234429i
$366$	5.94151	−	9.45586i	0.310568	−	0.494266i
$367$	−1.86997	−	1.49125i	−0.0976119	−	0.0778429i	0.573468	−	0.819228i	$-0.305598\pi$
$367$	−1.86997	−	1.49125i	−0.0976119	−	0.0778429i	−0.671080	+	0.741385i	$0.734169\pi$
$368$	4.02763	−	2.53073i	0.209955	−	0.131923i
$369$	1.15122	−	0.723359i	0.0599301	−	0.0376566i
$370$	−2.97840	−	16.4203i	−0.154839	−	0.853650i
$371$	−21.1406	−	10.1808i	−1.09757	−	0.528560i
$372$	−1.07049	+	3.05928i	−0.0555022	+	0.158616i
$373$	15.9897	−	1.80161i	0.827916	−	0.0932837i	0.312171	−	0.950026i	$-0.398944\pi$
$373$	15.9897	−	1.80161i	0.827916	−	0.0932837i	0.515745	+	0.856742i	$0.327515\pi$
$374$	2.51164	+	0.282994i	0.129874	+	0.0146333i
$375$	14.9875	−	8.94938i	0.773949	−	0.462144i
$376$			29.3523i			1.51373i
$377$	−12.4908	+	19.7008i	−0.643307	+	1.01464i
$378$	12.9065	+	12.9065i	0.663837	+	0.663837i
$379$	−15.5819	−	5.45235i	−0.800390	−	0.280069i	−0.101072	−	0.994879i	$-0.532227\pi$
$379$	−15.5819	−	5.45235i	−0.800390	−	0.280069i	−0.699318	+	0.714811i	$0.746513\pi$
$380$	−9.59901	−	6.65142i	−0.492419	−	0.341211i
$381$	−6.59453	−	5.25896i	−0.337848	−	0.269425i
$382$	13.8717	+	4.85391i	0.709736	+	0.248347i
$383$	−4.41190	+	1.54379i	−0.225437	+	0.0788840i	−0.440634	−	0.897687i	$-0.645246\pi$
$383$	−4.41190	+	1.54379i	−0.225437	+	0.0788840i	0.215197	+	0.976571i	$0.430961\pi$
$384$	−2.73524	+	2.18128i	−0.139582	+	0.111313i
$385$	1.57587	−	1.80342i	0.0803139	−	0.0919108i
$386$	0.211631	+	0.0483033i	0.0107717	+	0.00245857i
$387$	−2.41452	+	3.02772i	−0.122737	+	0.153907i
$388$	−0.252991	−	1.10843i	−0.0128437	−	0.0562719i
$389$	26.3154	−	26.3154i	1.33424	−	1.33424i	0.432711	−	0.901533i	$-0.357557\pi$
$389$	26.3154	−	26.3154i	1.33424	−	1.33424i	0.901533	−	0.432711i	$-0.142443\pi$
$390$	−7.62205	−	13.4355i	−0.385958	−	0.680333i
$391$	28.4507	−	9.95532i	1.43881	−	0.503462i
$392$	9.04057	+	4.35371i	0.456618	+	0.219895i
$393$	7.31430	−	11.6406i	0.368958	−	0.587193i
$394$	−0.989716	−	0.989716i	−0.0498612	−	0.0498612i
$395$	−2.19871	−	3.87570i	−0.110629	−	0.195008i
$396$	0.0200776	+	0.178194i	0.00100894	+	0.00895459i
$397$	−16.0938	−	25.6132i	−0.807726	−	1.28549i	−0.955063	−	0.296402i	$-0.904213\pi$
$397$	−16.0938	−	25.6132i	−0.807726	−	1.28549i	0.147337	−	0.989086i	$-0.452930\pi$
$398$	−4.83111	+	21.1665i	−0.242162	+	1.06098i
$399$	17.0743	+	21.4105i	0.854784	+	1.07186i
$400$	−0.785217	−	5.80415i	−0.0392608	−	0.290208i
$401$	−2.42926	+	1.16987i	−0.121311	+	0.0584205i	−0.493555	−	0.869715i	$-0.664303\pi$
$401$	−2.42926	+	1.16987i	−0.121311	+	0.0584205i	0.372244	+	0.928135i	$0.378589\pi$
$402$	1.33981	+	11.8911i	0.0668235	+	0.593075i
$403$	7.34872	−	5.86041i	0.366066	−	0.291928i
$404$	−2.88697	+	8.25050i	−0.143632	+	0.410478i
$405$	7.41522	−	13.7770i	0.368465	−	0.684583i
$406$	16.7045	−	5.76909i	0.829030	−	0.286315i
$407$	−1.72233	+	1.72233i	−0.0853726	+	0.0853726i
$408$	31.5347	−	15.1863i	1.56120	−	0.751834i
$409$	−1.94353	+	17.2493i	−0.0961013	+	0.852922i	0.849499	+	0.527591i	$0.176905\pi$
$409$	−1.94353	+	17.2493i	−0.0961013	+	0.852922i	−0.945600	+	0.325332i	$0.894524\pi$
$410$	5.12561	+	2.05654i	0.253136	+	0.101565i
$411$	−4.12476	−	8.56516i	−0.203460	−	0.422488i
$412$	−3.33852	−	9.54093i	−0.164477	−	0.470048i
$413$	2.35715	−	20.9203i	0.115988	−	1.02942i
$414$	−1.24079	−	1.97471i	−0.0609816	−	0.0970516i
$415$	1.14598	+	17.0188i	0.0562539	+	0.835421i
$416$	20.8489	−	2.34911i	1.02220	−	0.115175i
$417$	28.5290	−	6.51155i	1.39707	−	0.318872i
$418$		−	1.85888i		−	0.0909207i
$419$	1.52289	+	6.67222i	0.0743981	+	0.325960i	0.998408	−	0.0564098i	$-0.0179653\pi$
$419$	1.52289	+	6.67222i	0.0743981	+	0.325960i	−0.924010	+	0.382369i	$0.875108\pi$
$420$	1.67959	−	10.5987i	0.0819557	−	0.517162i
$421$	2.91469	+	8.32970i	0.142053	+	0.405965i	0.992826	−	0.119569i	$-0.0381513\pi$
$421$	2.91469	+	8.32970i	0.142053	+	0.405965i	−0.850773	+	0.525534i	$0.823866\pi$
$422$	0.0419505	+	0.0263593i	0.00204212	+	0.00128315i
$423$	5.46488			0.265712
$424$	18.6754	+	11.7345i	0.906957	+	0.569879i
$425$	3.33323	−	36.9645i	0.161685	−	1.79304i
$426$	−1.16159	+	5.08924i	−0.0562790	+	0.246574i
$427$	−21.9343	−	5.00637i	−1.06148	−	0.242275i
$428$	−8.28037	−	0.932974i	−0.400247	−	0.0450970i
$429$	−0.978220	+	2.03130i	−0.0472289	+	0.0980719i
$430$	−15.7147	−	0.707090i	−0.757828	−	0.0340989i
$431$	10.0620	−	12.6174i	0.484671	−	0.607758i	−0.478024	−	0.878347i	$-0.658647\pi$
$431$	10.0620	−	12.6174i	0.484671	−	0.607758i	0.962695	+	0.270589i	$0.0872183\pi$
$432$	−4.06215	−	5.09378i	−0.195440	−	0.245075i
$433$	1.77627	+	3.68847i	0.0853622	+	0.177257i	0.939280	−	0.343151i	$-0.111494\pi$
$433$	1.77627	+	3.68847i	0.0853622	+	0.177257i	−0.853918	+	0.520408i	$0.825780\pi$
$434$	−7.12105			−0.341822
$435$	−10.9876	−	15.2559i	−0.526817	−	0.731463i
$436$	−5.38060			−0.257684
$437$	−9.61837	−	19.9728i	−0.460109	−	0.955426i
$438$	−4.20219	−	5.26938i	−0.200788	−	0.251781i
$439$	−11.9256	+	14.9542i	−0.569177	+	0.713725i	−0.980224	−	0.197889i	$-0.936592\pi$
$439$	−11.9256	+	14.9542i	−0.569177	+	0.713725i	0.411048	+	0.911614i	$0.365163\pi$
$440$	−1.66178	+	1.51867i	−0.0792221	+	0.0723998i
$441$	0.810583	−	1.68319i	0.0385992	−	0.0801521i
$442$	−32.6362	−	3.67722i	−1.55235	−	0.174908i
$443$	29.1934	+	6.66320i	1.38702	+	0.316578i	0.849908	−	0.526932i	$-0.176658\pi$
$443$	29.1934	+	6.66320i	1.38702	+	0.316578i	0.537113	+	0.843510i	$0.319515\pi$
$444$	−2.42854	+	10.6401i	−0.115254	+	0.504959i
$445$	−8.57033	+	21.3603i	−0.406273	+	1.01257i
$446$	10.6621	+	6.69947i	0.504867	+	0.317229i
$447$	30.1363			1.42540
$448$	−19.8324	−	12.4615i	−0.936991	−	0.588750i
$449$	0.137280	+	0.392324i	0.00647865	+	0.0185149i	0.947077	−	0.321006i	$-0.104021\pi$
$449$	0.137280	+	0.392324i	0.00647865	+	0.0185149i	−0.940599	+	0.339521i	$0.889735\pi$
$450$	−2.84572	+	0.384984i	−0.134149	+	0.0181483i
$451$	−0.179370	−	0.785871i	−0.00844621	−	0.0370052i
$452$			0.223649i			0.0105196i
$453$	26.6257	−	6.07715i	1.25099	−	0.285529i
$454$	10.3607	−	1.16738i	0.486254	−	0.0547876i
$455$	−20.4769	+	23.4336i	−0.959970	+	1.09859i
$456$	−13.6953	−	21.7959i	−0.641340	−	1.02069i
$457$	−3.15663	+	28.0159i	−0.147661	+	1.31053i	0.673226	+	0.739437i	$0.264908\pi$
$457$	−3.15663	+	28.0159i	−0.147661	+	1.31053i	−0.820887	+	0.571091i	$0.806520\pi$
$458$	7.01691	+	20.0532i	0.327879	+	0.937023i
$459$	−17.9129	−	37.1966i	−0.836105	−	1.73619i
$460$	−3.23467	+	8.06193i	−0.150817	+	0.375889i
$461$	−1.94340	+	17.2482i	−0.0905133	+	0.803328i	0.863660	+	0.504074i	$0.168166\pi$
$461$	−1.94340	+	17.2482i	−0.0905133	+	0.803328i	−0.954174	+	0.299254i	$0.903262\pi$
$462$	1.53893	−	0.741109i	0.0715975	−	0.0344795i
$463$	10.1426	−	10.1426i	0.471365	−	0.471365i	−0.430991	−	0.902356i	$-0.641836\pi$
$463$	10.1426	−	10.1426i	0.471365	−	0.471365i	0.902356	+	0.430991i	$0.141836\pi$
$464$	−6.15570	+	1.37871i	−0.285771	+	0.0640051i
$465$	2.17813	+	7.25575i	0.101008	+	0.336477i
$466$	7.62368	−	21.7872i	0.353160	−	1.00927i
$467$	−4.24669	+	3.38662i	−0.196513	+	0.156714i	−0.716803	−	0.697276i	$-0.754395\pi$
$467$	−4.24669	+	3.38662i	−0.196513	+	0.156714i	0.520290	+	0.853990i	$0.325824\pi$
$468$	−0.260889	−	2.31545i	−0.0120596	−	0.107032i
$469$	21.7202	−	10.4599i	1.00295	−	0.482994i
$470$	13.0464	+	17.9600i	0.601785	+	0.828435i
$471$	18.0501	+	22.6341i	0.831705	+	1.04293i
$472$	−4.40349	+	19.2930i	−0.202687	+	0.888031i
$473$	1.22153	+	1.94405i	0.0561658	+	0.0893874i
$474$	−0.355824	−	3.15803i	−0.0163436	−	0.145053i
$475$	−27.2891	+	0.607810i	−1.25211	+	0.0278882i
$476$	−16.1331	−	16.1331i	−0.739461	−	0.739461i
$477$	2.18476	−	3.47703i	0.100033	−	0.159202i
$478$	−12.3849	−	5.96427i	−0.566473	−	0.272799i
$479$	−7.85928	+	2.75008i	−0.359100	+	0.125654i	−0.503798	−	0.863821i	$-0.668064\pi$
$479$	−7.85928	+	2.75008i	−0.359100	+	0.125654i	0.144698	+	0.989476i	$0.453779\pi$
$480$	−4.50007	+	16.3002i	−0.205399	+	0.744000i
$481$	22.3799	−	22.3799i	1.02044	−	1.02044i
$482$	1.72025	+	7.53690i	0.0783552	+	0.343297i
$483$	12.7003	−	15.9257i	0.577886	−	0.724646i
$484$	−10.1560	−	2.31804i	−0.461635	−	0.105365i
$485$	−2.00105	−	1.74856i	−0.0908629	−	0.0793982i
$486$	−4.60066	+	3.66890i	−0.208690	+	0.166425i
$487$	18.1215	−	6.34097i	0.821161	−	0.287337i	0.113186	−	0.993574i	$-0.463894\pi$
$487$	18.1215	−	6.34097i	0.821161	−	0.287337i	0.707975	+	0.706237i	$0.249609\pi$
$488$	19.9613	+	6.98478i	0.903608	+	0.316186i
$489$	−2.40576	−	1.91853i	−0.108792	−	0.0867588i
$490$	7.46685	−	1.35438i	0.337318	−	0.0611844i
$491$	9.42610	+	3.29834i	0.425394	+	0.148852i	0.534481	−	0.845180i	$-0.320507\pi$
$491$	9.42610	+	3.29834i	0.425394	+	0.148852i	−0.109087	+	0.994032i	$0.534793\pi$
$492$	−2.55393	−	2.55393i	−0.115140	−	0.115140i
$493$	−39.9732	−	0.162399i	−1.80030	−	0.00731406i
$494$			24.1542i			1.08675i
$495$	0.282750	+	0.309394i	0.0127087	+	0.0139062i
$496$	2.52586	+	0.284596i	0.113415	+	0.0127787i
$497$	10.4504	−	1.17748i	0.468766	−	0.0528172i
$498$	−4.01799	+	11.4828i	−0.180050	+	0.514555i
$499$	6.72572	+	3.23894i	0.301085	+	0.144995i	0.578326	−	0.815805i	$-0.303706\pi$
$499$	6.72572	+	3.23894i	0.301085	+	0.144995i	−0.277242	+	0.960800i	$0.589420\pi$
$500$	7.38963	+	7.73291i	0.330474	+	0.345826i
$501$	−12.8560	+	8.07795i	−0.574363	+	0.360896i
$502$	19.3579	−	12.1634i	0.863987	−	0.542879i
$503$	−29.7509	−	23.7256i	−1.32653	−	1.05787i	−0.993365	−	0.115001i	$-0.963313\pi$
$503$	−29.7509	−	23.7256i	−1.32653	−	1.05787i	−0.333163	−	0.942869i	$-0.608116\pi$
$504$	−2.90266	+	4.61956i	−0.129295	+	0.205771i
$505$	5.87415	+	19.5679i	0.261396	+	0.870760i
$506$	−1.34802	+	0.307677i	−0.0599268	+	0.0136779i
$507$	3.90438	−	8.10752i	0.173399	−	0.360068i
$508$	2.24243	−	4.65645i	0.0994917	−	0.206597i
$509$	17.5133	−	3.99729i	0.776263	−	0.177177i	0.184005	−	0.982925i	$-0.441094\pi$
$509$	17.5133	−	3.99729i	0.776263	−	0.177177i	0.592258	+	0.805748i	$0.298237\pi$
$510$	12.5455	−	23.3086i	0.555522	−	1.03212i
$511$	−7.22399	+	11.4969i	−0.319570	+	0.508593i
$512$	9.96771	+	7.94898i	0.440515	+	0.351299i
$513$	−25.7093	+	16.1542i	−1.13509	+	0.713225i
$514$	14.4927	−	9.10634i	0.639244	−	0.401663i
$515$	−19.4195	−	13.4563i	−0.855726	−	0.592956i
$516$	9.26870	+	4.46357i	0.408032	+	0.196498i
$517$	1.07010	−	3.05817i	0.0470630	−	0.134498i
$518$	−23.8275	+	2.68472i	−1.04692	+	0.117960i
$519$	−1.23640	−	0.139309i	−0.0542719	−	0.00611498i
$520$	21.5931	−	19.7336i	0.946921	−	0.865375i
$521$		−	15.7501i		−	0.690024i	−0.938598	−	0.345012i	$-0.887875\pi$
$521$		−	15.7501i		−	0.690024i	0.938598	−	0.345012i	$-0.112125\pi$
$522$	0.675969	+	3.01808i	0.0295864	+	0.132098i
$523$	−8.21538	−	8.21538i	−0.359233	−	0.359233i	0.504297	−	0.863530i	$-0.331752\pi$
$523$	−8.21538	−	8.21538i	−0.359233	−	0.359233i	−0.863530	+	0.504297i	$0.831752\pi$
$524$	7.95111	+	2.78221i	0.347346	+	0.121542i
$525$	−11.3830	−	22.3498i	−0.496795	−	0.975427i
$526$	7.28104	+	5.80644i	0.317468	+	0.253173i
$527$	15.2032	+	5.31982i	0.662260	+	0.231735i
$528$	−0.575482	+	0.201370i	−0.0250446	+	0.00876350i
$529$	5.09030	−	4.05938i	0.221318	−	0.176495i
$530$	16.6428	−	1.12066i	0.722916	−	0.0486783i
$531$	3.59201	+	0.819853i	0.155880	+	0.0355786i
$532$	−10.4621	+	13.1190i	−0.453588	+	0.568781i
$533$	2.33073	+	10.2116i	0.100955	+	0.442314i
$534$	−11.6070	+	11.6070i	−0.502285	+	0.502285i
$535$	−16.9402	+	9.61030i	−0.732389	+	0.415489i
$536$	−21.3891	+	7.48437i	−0.923869	+	0.323276i
$537$	−1.62679	−	0.783422i	−0.0702013	−	0.0338072i
$538$	−2.89181	+	4.60230i	−0.124675	+	0.198419i
$539$	−0.783199	−	0.783199i	−0.0337348	−	0.0337348i
$540$	11.4689	+	3.16627i	0.493543	+	0.136254i
$541$	3.67537	+	32.6198i	0.158016	+	1.40243i	0.783109	+	0.621884i	$0.213633\pi$
$541$	3.67537	+	32.6198i	0.158016	+	1.40243i	−0.625093	+	0.780551i	$0.714939\pi$
$542$	0.731573	+	1.16429i	0.0314238	+	0.0500106i
$543$	−4.75488	+	20.8325i	−0.204052	+	0.894009i
$544$	22.4166	+	28.1095i	0.961103	+	1.20518i
$545$	−10.1750	+	7.39124i	−0.435849	+	0.316606i
$546$	−19.9968	+	9.62997i	−0.855786	+	0.412125i
$547$	−1.12606	−	9.99406i	−0.0481468	−	0.427315i	−0.994545	−	0.104312i	$-0.966736\pi$
$547$	−1.12606	−	9.99406i	−0.0481468	−	0.427315i	0.946398	−	0.323003i	$-0.104693\pi$
$548$	4.55421	−	3.63186i	0.194546	−	0.155145i
$549$	1.30044	−	3.71645i	0.0555015	−	0.158614i
$550$	−0.341793	+	1.66786i	−0.0145741	+	0.0711179i
$551$	3.17289	+	29.2269i	0.135169	+	1.24511i
$552$	−13.5391	+	13.5391i	−0.576264	+	0.576264i
$553$	−5.76843	+	2.77793i	−0.245299	+	0.118130i
$554$	−2.55394	+	22.6669i	−0.108507	+	0.963023i
$555$	10.0237	+	23.4571i	0.425481	+	0.995698i
$556$	7.77967	+	16.1547i	0.329931	+	0.685110i
$557$	−12.4775	−	35.6586i	−0.528688	−	1.51090i	−0.830213	−	0.557446i	$-0.811781\pi$
$557$	−12.4775	−	35.6586i	−0.528688	−	1.51090i	0.301525	−	0.953458i	$-0.402504\pi$
$558$	0.139535	−	1.23841i	0.00590698	−	0.0524259i
$559$	−15.8725	−	25.2609i	−0.671335	−	1.06842i
$560$	−8.39660	+	0.565393i	−0.354821	+	0.0238922i
$561$	−3.83920	+	0.432574i	−0.162091	+	0.0182633i
$562$	−5.21927	+	1.19127i	−0.220162	+	0.0502505i
$563$		−	0.0469315i		−	0.00197793i	−1.00000		0.000988963i	$-0.999685\pi$
$563$		−	0.0469315i		−	0.00197793i	1.00000		0.000988963i	$-0.000314797\pi$
$564$	−3.23042	−	14.1534i	−0.136025	−	0.595965i
$565$	0.307223	+	0.422932i	0.0129250	+	0.0177929i
$566$	−8.74512	−	24.9921i	−0.367585	−	1.05050i
$567$	−19.0348	−	11.9603i	−0.799386	−	0.502287i
$568$	−9.88536			−0.414781
$569$	−24.4344	−	15.3531i	−1.02434	−	0.643637i	−0.0885075	−	0.996076i	$-0.528210\pi$
$569$	−24.4344	−	15.3531i	−1.02434	−	0.643637i	−0.935835	+	0.352438i	$0.885353\pi$
$570$	−18.0676	−	7.24922i	−0.756768	−	0.303637i
$571$	9.57895	−	41.9681i	0.400867	−	1.75631i	−0.223036	−	0.974810i	$-0.571597\pi$
$571$	9.57895	−	41.9681i	0.400867	−	1.75631i	0.623903	−	0.781502i	$-0.285546\pi$
$572$	−1.34682	−	0.307403i	−0.0563135	−	0.0128532i
$573$	−22.3231	−	2.51521i	−0.932560	−	0.105074i
$574$	3.44303	−	7.14952i	0.143709	−	0.298415i
$575$	4.95760	+	19.6889i	0.206746	+	0.821085i
$576$	2.55576	−	3.20482i	0.106490	−	0.133534i
$577$	−17.0518	−	21.3823i	−0.709875	−	0.890155i	0.287843	−	0.957678i	$-0.407062\pi$
$577$	−17.0518	−	21.3823i	−0.709875	−	0.890155i	−0.997718	+	0.0675225i	$0.978491\pi$
$578$	−16.8850	−	35.0621i	−0.702324	−	1.45839i
$579$	−0.331810			−0.0137895
$580$	7.61534	−	8.64383i	0.316210	−	0.358916i
$581$	24.5087			1.01679
$582$	−0.822324	−	1.70757i	−0.0340864	−	0.0707812i
$583$	−1.51795	−	1.90345i	−0.0628672	−	0.0788329i
$584$	7.95770	−	9.97865i	0.329292	−	0.412919i
$585$	−3.67405	−	4.02026i	−0.151903	−	0.166217i
$586$	−10.1613	+	21.1002i	−0.419761	+	0.871642i
$587$	−2.19250	−	0.247035i	−0.0904941	−	0.0101962i	0.0666013	−	0.997780i	$-0.478784\pi$
$587$	−2.19250	−	0.247035i	−0.0904941	−	0.0101962i	−0.157095	+	0.987583i	$0.550213\pi$
$588$	−4.83842	−	1.10434i	−0.199533	−	0.0455422i
$589$	2.63597	−	11.5489i	0.108613	−	0.475866i
$590$	5.88086	+	13.7622i	0.242111	+	0.566581i
$591$	1.81155	+	1.13827i	0.0745173	+	0.0468223i
$592$	8.55900			0.351773
$593$	1.33905	+	0.841384i	0.0549884	+	0.0345515i	0.559246	−	0.829002i	$-0.311091\pi$
$593$	1.33905	+	0.841384i	0.0549884	+	0.0345515i	−0.504257	+	0.863553i	$0.668234\pi$
$594$	0.625496	+	1.78756i	0.0256644	+	0.0733446i
$595$	−52.6704	−	8.34678i	−2.15928	−	0.342184i
$596$	4.10900	+	18.0027i	0.168311	+	0.737419i
$597$		−	33.1864i		−	1.35823i
$598$	17.5162	−	3.99795i	0.716289	−	0.163488i
$599$	25.1241	−	2.83081i	1.02654	−	0.115664i	0.417399	−	0.908723i	$-0.362942\pi$
$599$	25.1241	−	2.83081i	1.02654	−	0.115664i	0.609144	+	0.793060i	$0.291513\pi$
$600$	8.28034	+	22.0743i	0.338044	+	0.901181i
$601$	−14.9382	−	23.7740i	−0.609342	−	0.969762i	−0.998812	−	0.0487229i	$-0.984485\pi$
$601$	−14.9382	−	23.7740i	−0.609342	−	0.969762i	0.389471	−	0.921039i	$-0.372658\pi$
$602$	−2.53066	+	22.4602i	−0.103142	+	0.915409i
$603$	1.39346	+	3.98227i	0.0567460	+	0.162171i
$604$	7.26068	+	15.0769i	0.295433	+	0.613472i
$605$	−22.3897	+	9.56756i	−0.910271	+	0.388977i
$606$	−1.63146	+	14.4796i	−0.0662735	+	0.588194i
$607$	30.3818	−	14.6311i	1.23316	−	0.593859i	0.300213	−	0.953872i	$-0.402942\pi$
$607$	30.3818	−	14.6311i	1.23316	−	0.593859i	0.932947	+	0.360013i	$0.117228\pi$
$608$	18.6973	−	18.6973i	0.758276	−	0.758276i
$609$	−22.9314	+	14.2791i	−0.929227	+	0.578620i
$610$	15.3185	−	4.59850i	0.620227	−	0.186188i
$611$	−13.9049	+	39.7378i	−0.562531	+	1.60762i
$612$	3.12180	−	2.48955i	0.126191	−	0.100634i
$613$	−4.15227	−	36.8524i	−0.167709	−	1.48846i	−0.742329	−	0.670036i	$-0.766279\pi$
$613$	−4.15227	−	36.8524i	−0.167709	−	1.48846i	0.574620	−	0.818420i	$-0.305150\pi$
$614$	−29.2242	+	14.0736i	−1.17939	+	0.567966i
$615$	−8.33788	−	1.32132i	−0.336216	−	0.0532808i
$616$	2.01674	+	2.52892i	0.0812569	+	0.101893i
$617$	−5.39870	+	23.6532i	−0.217343	+	0.952243i	0.742088	+	0.670302i	$0.233835\pi$
$617$	−5.39870	+	23.6532i	−0.217343	+	0.952243i	−0.959432	+	0.281941i	$0.909022\pi$
$618$	−8.96488	−	14.2675i	−0.360621	−	0.573924i
$619$	4.24442	+	37.6702i	0.170598	+	1.51410i	0.728994	+	0.684521i	$0.239988\pi$
$619$	4.24442	+	37.6702i	0.170598	+	1.51410i	−0.558396	+	0.829574i	$0.688583\pi$
$620$	−4.03742	+	2.29046i	−0.162147	+	0.0919870i
$621$	15.9700	+	15.9700i	0.640855	+	0.640855i
$622$	1.21636	−	1.93583i	0.0487716	−	0.0776195i
$623$	29.7946	+	14.3483i	1.19370	+	0.574854i
$624$	7.47781	−	2.61660i	0.299352	−	0.104748i
$625$	24.5967	+	4.47232i	0.983869	+	0.178893i
$626$	7.73273	−	7.73273i	0.309062	−	0.309062i
$627$	0.632273	+	2.77017i	0.0252506	+	0.110630i
$628$	−11.0600	+	13.8688i	−0.441341	+	0.553424i
$629$	52.8765	+	12.0687i	2.10832	+	0.481211i
$630$	0.277207	+	4.11677i	0.0110442	+	0.164016i
$631$	15.9303	−	12.7040i	0.634175	−	0.505737i	−0.252822	−	0.967513i	$-0.581359\pi$
$631$	15.9303	−	12.7040i	0.634175	−	0.505737i	0.886997	+	0.461775i	$0.152787\pi$
$632$	5.68049	−	1.98769i	0.225958	−	0.0790661i
$633$	−0.0714821	−	0.0250127i	−0.00284116	−	0.000994164i
$634$	−17.8405	−	14.2273i	−0.708536	−	0.565038i
$635$	−2.15594	−	11.8860i	−0.0855557	−	0.471680i
$636$	−10.2965	−	3.60291i	−0.408284	−	0.142865i
$637$	10.1769	+	10.1769i	0.403223	+	0.403223i
$638$	1.82130	+	0.212707i	0.0721058	+	0.00842117i
$639$			1.84048i			0.0728083i
$640$	−5.00537	−	0.225219i	−0.197855	−	0.00890258i
$641$	−20.0334	−	2.25723i	−0.791273	−	0.0891550i	−0.292929	−	0.956134i	$-0.594630\pi$
$641$	−20.0334	−	2.25723i	−0.791273	−	0.0891550i	−0.498344	+	0.866979i	$0.666058\pi$
$642$	−13.8033	+	1.55526i	−0.544775	+	0.0613813i
$643$	−14.5417	+	41.5577i	−0.573467	+	1.63887i	0.181709	+	0.983352i	$0.441837\pi$
$643$	−14.5417	+	41.5577i	−0.573467	+	1.63887i	−0.755176	+	0.655522i	$0.772449\pi$
$644$	11.2453	+	5.41544i	0.443126	+	0.213398i
$645$	23.6591	−	4.29141i	0.931576	−	0.168974i
$646$	−35.0471	+	22.0216i	−1.37891	+	0.866426i
$647$	34.5951	−	21.7375i	1.36007	−	0.854591i	0.363056	−	0.931767i	$-0.381733\pi$
$647$	34.5951	−	21.7375i	1.36007	−	0.854591i	0.997017	+	0.0771768i	$0.0245906\pi$
$648$	16.5211	+	13.1751i	0.649010	+	0.517568i
$649$	1.16216	−	1.84957i	0.0456187	−	0.0726018i
$650$	4.44125	−	21.6722i	0.174200	−	0.850053i
$651$	10.6121	−	2.42214i	0.415920	−	0.0949310i
$652$	0.818062	−	1.69872i	0.0320378	−	0.0665271i
$653$	−18.4814	+	38.3770i	−0.723233	+	1.50181i	0.136266	+	0.990672i	$0.456490\pi$
$653$	−18.4814	+	38.3770i	−0.723233	+	1.50181i	−0.859499	+	0.511137i	$0.829224\pi$
$654$	−8.74456	+	1.99589i	−0.341939	+	0.0780454i
$655$	18.8578	−	5.66099i	0.736836	−	0.221193i
$656$	−1.50699	+	2.39836i	−0.0588379	+	0.0936401i
$657$	−1.85785	−	1.48158i	−0.0724815	−	0.0578021i
$658$	27.0068	−	16.9695i	1.05284	−	0.661540i
$659$	29.0653	−	18.2629i	1.13222	−	0.711423i	0.170476	−	0.985362i	$-0.445470\pi$
$659$	29.0653	−	18.2629i	1.13222	−	0.711423i	0.961747	+	0.273939i	$0.0883267\pi$
$660$	0.634152	−	0.915177i	0.0246843	−	0.0356232i
$661$	−42.5571	−	20.4944i	−1.65528	−	0.797141i	−0.999095	−	0.0425427i	$-0.986454\pi$
$661$	−42.5571	−	20.4944i	−1.65528	−	0.797141i	−0.656187	−	0.754599i	$-0.727832\pi$
$662$	4.18823	−	11.9693i	0.162780	−	0.465199i
$663$	49.8865	−	5.62086i	1.93743	−	0.218296i
$664$	−22.8929	−	2.57941i	−0.888417	−	0.100100i
$665$	−1.76294	+	39.1802i	−0.0683638	+	1.51934i
$666$		−	4.19640i		−	0.162607i
$667$	20.6696	−	7.13847i	0.800329	−	0.276403i
$668$	−6.57844	−	6.57844i	−0.254528	−	0.254528i
$669$	−18.1679	−	6.35722i	−0.702411	−	0.245784i
$670$	−9.76092	+	14.0865i	−0.377097	+	0.544208i
$671$	−1.82510	−	1.45547i	−0.0704571	−	0.0561877i
$672$	22.9335	+	8.02478i	0.884679	+	0.309563i
$673$	−34.5971	+	12.1061i	−1.33362	+	0.466654i	−0.900569	−	0.434714i	$-0.856849\pi$
$673$	−34.5971	+	12.1061i	−1.33362	+	0.466654i	−0.433053	+	0.901368i	$0.642564\pi$
$674$	1.13753	−	0.907149i	0.0438160	−	0.0349421i
$675$	26.0377	−	9.76704i	1.00219	−	0.375934i
$676$	5.37558	+	1.22694i	0.206753	+	0.0471900i
$677$	−16.8329	+	21.1078i	−0.646942	+	0.811240i	−0.991852	−	0.127396i	$-0.959338\pi$
$677$	−16.8329	+	21.1078i	−0.646942	+	0.811240i	0.344910	+	0.938636i	$0.387910\pi$
$678$	0.0829607	+	0.363475i	0.00318609	+	0.0139592i
$679$	−2.69990	+	2.69990i	−0.103613	+	0.103613i
$680$	48.3194	+	13.3398i	1.85297	+	0.511556i
$681$	−15.0429	+	5.26374i	−0.576445	+	0.201707i
$682$	−0.665694	−	0.320581i	−0.0254908	−	0.0122757i
$683$	−6.09521	+	9.70047i	−0.233227	+	0.371178i	−0.942748	−	0.333506i	$-0.891768\pi$
$683$	−6.09521	+	9.70047i	−0.233227	+	0.371178i	0.709521	+	0.704684i	$0.248911\pi$
$684$	−2.07649	−	2.07649i	−0.0793967	−	0.0793967i
$685$	3.62322	−	13.1241i	0.138436	−	0.501445i
$686$	1.35123	+	11.9925i	0.0515901	+	0.457875i
$687$	−17.2777	−	27.4973i	−0.659185	−	1.04909i
$688$	1.79526	−	7.86556i	0.0684438	−	0.299872i
$689$	19.7243	+	24.7334i	0.751434	+	0.942269i
$690$	−2.26648	+	14.3021i	−0.0862836	+	0.544472i
$691$	−15.3535	+	7.39386i	−0.584075	+	0.281276i	−0.702496	−	0.711688i	$-0.747931\pi$
$691$	−15.3535	+	7.39386i	−0.584075	+	0.281276i	0.118421	+	0.992964i	$0.462217\pi$
$692$	−0.0853597	−	0.757588i	−0.00324489	−	0.0287992i
$693$	0.470839	−	0.375482i	0.0178857	−	0.0142634i
$694$	−6.89799	+	19.7133i	−0.261844	+	0.748308i
$695$	36.9031	+	19.8625i	1.39981	+	0.753426i
$696$	22.9224	−	10.9243i	0.868870	−	0.414085i
$697$	−12.6918	+	12.6918i	−0.480736	+	0.480736i
$698$	25.9479	−	12.4958i	0.982141	−	0.472974i
$699$	−3.95046	+	35.0613i	−0.149420	+	1.32614i
$700$	11.7992	−	9.84725i	0.445968	−	0.372191i
$701$	−9.35305	−	19.4218i	−0.353260	−	0.733552i	0.646304	−	0.763080i	$-0.276314\pi$
$701$	−9.35305	−	19.4218i	−0.353260	−	0.733552i	−0.999564	+	0.0295282i	$0.990600\pi$
$702$	−8.12768	−	23.2276i	−0.306760	−	0.876669i
$703$	4.46605	−	39.6373i	0.168440	−	1.49495i
$704$	−1.29298	−	2.05776i	−0.0487309	−	0.0775548i
$705$	−25.5511	−	22.3272i	−0.962311	−	0.840890i
$706$	−5.73731	+	0.646440i	−0.215927	+	0.0243291i
$707$	28.6195	−	6.53221i	1.07635	−	0.245669i
$708$		−	9.78750i		−	0.367837i
$709$	−5.43528	−	23.8135i	−0.204126	−	0.894336i	−0.968392	−	0.249434i	$-0.919755\pi$
$709$	−5.43528	−	23.8135i	−0.204126	−	0.894336i	0.764266	−	0.644902i	$-0.223102\pi$
$710$	−6.04864	+	4.39381i	−0.227002	+	0.164897i
$711$	−0.370073	−	1.05761i	−0.0138788	−	0.0396634i
$712$	−26.3202	−	16.5381i	−0.986392	−	0.619791i
$713$	−8.81135			−0.329988
$714$	−32.2040	−	20.2351i	−1.20521	−	0.757281i
$715$	−2.96918	+	1.26879i	−0.111041	+	0.0474501i
$716$	0.246189	−	1.07862i	0.00920050	−	0.0403100i
$717$	20.4852	+	4.67560i	0.765032	+	0.174614i
$718$	−0.773345	−	0.0871351i	−0.0288610	−	0.00325185i
$719$	12.1135	−	25.1540i	0.451758	−	0.938086i	−0.543369	−	0.839494i	$-0.682852\pi$
$719$	12.1135	−	25.1540i	0.451758	−	0.938086i	0.995128	−	0.0985924i	$-0.0314340\pi$
$720$	0.0662024	−	1.47131i	0.00246722	−	0.0548325i
$721$	−21.1655	+	26.5407i	−0.788245	+	0.988428i
$722$	6.87970	+	8.62687i	0.256036	+	0.321059i
$723$	−5.12716	−	10.6467i	−0.190681	−	0.395954i
$724$	−13.0931			−0.486602
$725$	2.52712	−	26.8070i	0.0938548	−	0.995586i
$726$	−17.3654			−0.644489
$727$	1.90781	+	3.96162i	0.0707569	+	0.146928i	0.933347	−	0.358975i	$-0.116874\pi$
$727$	1.90781	+	3.96162i	0.0707569	+	0.146928i	−0.862590	+	0.505903i	$0.831159\pi$
$728$	−26.2055	−	32.8607i	−0.971242	−	1.21790i
$729$	18.6958	−	23.4438i	0.692438	−	0.868290i
$730$	0.433880	−	9.64273i	0.0160586	−	0.356893i
$731$	22.1818	−	46.0611i	0.820425	−	1.70363i
$732$	−10.3939	−	1.17111i	−0.384169	−	0.0432854i
$733$	25.3994	+	5.79725i	0.938149	+	0.214126i	0.664146	−	0.747603i	$-0.268795\pi$
$733$	25.3994	+	5.79725i	0.938149	+	0.214126i	0.274003	+	0.961729i	$0.411652\pi$
$734$	0.543629	−	2.38179i	0.0200657	−	0.0879136i
$735$	−10.6667	+	4.55809i	−0.393448	+	0.168128i
$736$	−16.6536	−	10.4642i	−0.613861	−	0.385714i
$737$	2.50136			0.0921387
$738$	1.17589	+	0.738861i	0.0432851	+	0.0271979i
$739$	1.95496	+	5.58694i	0.0719142	+	0.205519i	0.974230	−	0.225556i	$-0.0724200\pi$
$739$	1.95496	+	5.58694i	0.0719142	+	0.205519i	−0.902316	+	0.431075i	$0.858134\pi$
$740$	−12.6460	+	9.18619i	−0.464875	+	0.337691i
$741$	−8.21575	−	35.9956i	−0.301813	−	1.32233i
$742$		−	23.9672i		−	0.879863i
$743$	6.86085	−	1.56594i	0.251700	−	0.0574489i	−0.0948090	−	0.995495i	$-0.530224\pi$
$743$	6.86085	−	1.56594i	0.251700	−	0.0574489i	0.346509	+	0.938047i	$0.387367\pi$
$744$	−10.1673	+	1.14558i	−0.372753	+	0.0419992i
$745$	32.5003	+	28.3995i	1.19072	+	1.04048i
$746$	8.74433	+	13.9165i	0.320153	+	0.509520i
$747$	−0.480240	+	4.26225i	−0.0175711	+	0.155948i
$748$	−0.781872	−	2.23446i	−0.0285881	−	0.0817000i
$749$	12.1420	+	25.2131i	0.443659	+	0.921267i
$750$	14.8781	+	9.82640i	0.543271	+	0.358810i
$751$	5.32203	−	47.2343i	0.194203	−	1.72360i	−0.397632	−	0.917545i	$-0.630168\pi$
$751$	5.32203	−	47.2343i	0.194203	−	1.72360i	0.591836	−	0.806059i	$-0.298403\pi$
$752$	−10.2576	+	4.93980i	−0.374056	+	0.180136i
$753$	−24.7107	+	24.7107i	−0.900509	+	0.900509i
$754$	−23.6659	−	2.76392i	−0.861861	−	0.100656i
$755$	34.4412	+	18.5374i	1.25344	+	0.674645i
$756$	5.64626	−	16.1361i	0.205353	−	0.586864i
$757$	14.3815	−	11.4688i	0.522704	−	0.416842i	−0.326271	−	0.945276i	$-0.605792\pi$
$757$	14.3815	−	11.4688i	0.522704	−	0.416842i	0.848974	+	0.528434i	$0.177221\pi$
$758$	−1.88796	−	16.7561i	−0.0685737	−	0.608608i
$759$	1.90422	−	0.917023i	0.0691188	−	0.0332858i
$760$	5.77022	−	36.4116i	0.209308	−	1.32079i
$761$	−12.2089	−	15.3094i	−0.442571	−	0.554966i	0.509648	−	0.860383i	$-0.329776\pi$
$761$	−12.2089	−	15.3094i	−0.442571	−	0.554966i	−0.952219	+	0.305417i	$0.901204\pi$
$762$	1.91713	−	8.39947i	0.0694501	−	0.304281i
$763$	9.61382	+	15.3003i	0.348044	+	0.553908i
$764$	−1.54116	−	13.6782i	−0.0557573	−	0.494860i
$765$	2.48363	−	8.99623i	0.0897957	−	0.325259i
$766$	−3.37599	−	3.37599i	−0.121979	−	0.121979i
$767$	−15.1011	+	24.0332i	−0.545268	+	0.867790i
$768$	−23.7298	−	11.4277i	−0.856276	−	0.412361i
$769$	15.5886	−	5.45470i	0.562141	−	0.196702i	−0.0342253	−	0.999414i	$-0.510896\pi$
$769$	15.5886	−	5.45470i	0.562141	−	0.196702i	0.596366	+	0.802713i	$0.296611\pi$
$770$	2.35804	+	0.650996i	0.0849780	+	0.0234603i
$771$	−18.5001	+	18.5001i	−0.666265	+	0.666265i
$772$	−0.0452412	−	0.198215i	−0.00162827	−	0.00713391i
$773$	12.7969	−	16.0469i	0.460274	−	0.577166i	−0.496486	−	0.868045i	$-0.665376\pi$
$773$	12.7969	−	16.0469i	0.460274	−	0.577166i	0.956760	+	0.290879i	$0.0939478\pi$
$774$	−3.85641	−	0.880201i	−0.138616	−	0.0316382i
$775$	−4.48861	+	9.87751i	−0.161236	+	0.354811i
$776$	2.80605	−	2.23775i	0.100731	−	0.0803304i
$777$	34.5956	−	12.1055i	1.24111	−	0.434283i
$778$	35.8800	+	12.5549i	1.28636	+	0.450117i
$779$	10.3206	+	8.23041i	0.369774	+	0.294885i
$780$	−8.24016	+	11.8918i	−0.295045	+	0.425795i
$781$	1.02994	+	0.360392i	0.0368542	+	0.0128958i
$782$	21.7705	+	21.7705i	0.778511	+	0.778511i
$783$	−12.8857	−	27.0380i	−0.460499	−	0.966258i
$784$			3.89206i			0.139002i
$785$	−1.86369	+	41.4194i	−0.0665180	+	1.47832i
$786$	13.9542	+	1.57226i	0.497729	+	0.0560806i
$787$	34.1359	−	3.84619i	1.21681	−	0.137102i	0.519880	−	0.854239i	$-0.325977\pi$
$787$	34.1359	−	3.84619i	1.21681	−	0.137102i	0.696932	+	0.717137i	$0.254548\pi$
$788$	−0.432976	+	1.23738i	−0.0154241	+	0.0440797i
$789$	−12.8255	−	6.17642i	−0.456599	−	0.219886i
$790$	2.59229	−	3.74107i	0.0922296	−	0.133101i
$791$	0.635969	−	0.399606i	0.0226125	−	0.0142084i
$792$	−0.479315	+	0.301174i	−0.0170317	+	0.0107017i
$793$	23.7153	+	18.9123i	0.842155	+	0.671596i
$794$	16.4387	−	26.1621i	0.583388	−	0.928457i
$795$	−24.4205	+	7.33088i	−0.866107	+	0.259999i
$796$	19.8247	−	4.52486i	0.702668	−	0.160379i
$797$	−5.98688	+	12.4319i	−0.212066	+	0.440360i	−0.979684	−	0.200548i	$-0.935728\pi$
$797$	−5.98688	+	12.4319i	−0.212066	+	0.440360i	0.767618	+	0.640908i	$0.221442\pi$
$798$	−12.1366	+	25.2018i	−0.429630	+	0.892135i
$799$	−70.3356	+	16.0536i	−2.48829	+	0.567937i
$800$	−20.2139	+	13.3381i	−0.714668	+	0.471573i
$801$	−3.07910	+	4.90036i	−0.108795	+	0.173146i
$802$	−2.15321	−	1.71713i	−0.0760324	−	0.0606338i
$803$	−1.19289	+	0.749545i	−0.0420963	+	0.0264509i
$804$	9.48990	−	5.96290i	0.334683	−	0.210295i
$805$	28.7045	−	5.20657i	1.01170	−	0.183507i
$806$	8.65002	+	4.16563i	0.304684	+	0.146728i
$807$	2.74408	−	7.84213i	0.0965962	−	0.276056i
$808$	−27.4201	+	3.08950i	−0.964636	+	0.108688i
$809$	−19.1241	−	2.15477i	−0.672367	−	0.0757576i	−0.230821	−	0.972996i	$-0.574141\pi$
$809$	−19.1241	−	2.15477i	−0.672367	−	0.0757576i	−0.441546	+	0.897239i	$0.645570\pi$
$810$	15.9649	+	0.718351i	0.560950	+	0.0252403i
$811$			46.6872i			1.63941i	0.572787	+	0.819704i	$0.305862\pi$
$811$			46.6872i			1.63941i	−0.572787	+	0.819704i	$0.694138\pi$
$812$	−11.6566	−	11.7517i	−0.409067	−	0.412405i
$813$	−1.48624	−	1.48624i	−0.0521246	−	0.0521246i
$814$	−2.34832	−	0.821714i	−0.0823087	−	0.0288010i
$815$	−0.786509	−	4.33613i	−0.0275502	−	0.151888i
$816$	10.6142	+	8.46452i	0.371570	+	0.296317i
$817$	−35.4892	−	12.4182i	−1.24161	−	0.434458i
$818$	−16.7355	+	5.85599i	−0.585142	+	0.204750i
$819$	−6.11808	+	4.87901i	−0.213783	+	0.170486i
$820$	−0.347521	−	5.16100i	−0.0121360	−	0.180230i
$821$	−8.38107	−	1.91292i	−0.292501	−	0.0667615i	0.0737522	−	0.997277i	$-0.476503\pi$
$821$	−8.38107	−	1.91292i	−0.292501	−	0.0667615i	−0.366254	+	0.930515i	$0.619360\pi$
$822$	6.05430	−	7.59185i	0.211168	−	0.264796i
$823$	3.81633	+	16.7204i	0.133029	+	0.582838i	0.996869	+	0.0790717i	$0.0251956\pi$
$823$	3.81633	+	16.7204i	0.133029	+	0.582838i	−0.863840	+	0.503766i	$0.831947\pi$
$824$	22.5634	−	22.5634i	0.786033	−	0.786033i
$825$	−0.0579491	−	2.60177i	−0.00201753	−	0.0905820i
$826$	20.2971	−	7.10227i	0.706227	−	0.247119i
$827$	−23.3648	−	11.2519i	−0.812474	−	0.391267i	−0.0189613	−	0.999820i	$-0.506036\pi$
$827$	−23.3648	−	11.2519i	−0.812474	−	0.391267i	−0.793513	+	0.608553i	$0.791750\pi$
$828$	−1.16213	+	1.84953i	−0.0403870	+	0.0642755i
$829$	8.01072	+	8.01072i	0.278224	+	0.278224i	0.832400	−	0.554176i	$-0.186966\pi$
$829$	8.01072	+	8.01072i	0.278224	+	0.278224i	−0.554176	+	0.832400i	$0.686966\pi$
$830$	−15.1542	+	8.59706i	−0.526008	+	0.298408i
$831$	−3.90386	−	34.6477i	−0.135423	−	1.20192i
$832$	16.8009	+	26.7385i	0.582468	+	0.926992i
$833$	−5.48804	+	24.0447i	−0.190149	+	0.833099i
$834$	18.6359	+	23.3687i	0.645310	+	0.809193i
$835$	−21.4768	−	3.40348i	−0.743237	−	0.117782i
$836$	−1.56862	+	0.755409i	−0.0542519	+	0.0261264i
$837$	1.35127	+	11.9928i	0.0467067	+	0.414533i
$838$	−5.46538	+	4.35849i	−0.188798	+	0.150562i
$839$	1.26460	−	3.61402i	0.0436588	−	0.124770i	−0.919990	−	0.391942i	$-0.871803\pi$
$839$	1.26460	−	3.61402i	0.0436588	−	0.124770i	0.963649	+	0.267172i	$0.0860892\pi$
$840$	32.4450	−	9.73976i	1.11946	−	0.336054i
$841$	−28.9990	−	0.235632i	−0.999967	−	0.00812523i
$842$	−6.37389	+	6.37389i	−0.219659	+	0.219659i
$843$	7.37277	−	3.55054i	0.253932	−	0.122287i
$844$	0.00519557	−	0.0461120i	0.000178839	−	0.00158724i
$845$	11.8509	−	5.06413i	0.407684	−	0.174211i
$846$	2.42194	+	5.02920i	0.0832679	+	0.172908i
$847$	11.5547	+	33.0214i	0.397023	+	1.13463i
$848$	−0.957859	+	8.50124i	−0.0328930	+	0.291934i
$849$	21.5331	+	34.2697i	0.739013	+	1.17613i
$850$	35.4948	−	13.3145i	1.21746	−	0.456684i
$851$	−29.4834	+	3.32198i	−1.01068	+	0.113876i
$852$	4.76662	−	1.08795i	0.163302	−	0.0372726i
$853$			39.2828i			1.34502i	0.740089	+	0.672509i	$0.234783\pi$
$853$			39.2828i			1.34502i	−0.740089	+	0.672509i	$0.765217\pi$
$854$	−5.11366	−	22.4044i	−0.174986	−	0.766663i
$855$	−6.77920	−	1.07431i	−0.231844	−	0.0367407i
$856$	−8.68794	−	24.8287i	−0.296948	−	0.848628i
$857$	−47.4255	−	29.7994i	−1.62002	−	1.01793i	−0.964975	−	0.262341i	$-0.915505\pi$
$857$	−47.4255	−	29.7994i	−1.62002	−	1.01793i	−0.655048	−	0.755587i	$-0.727352\pi$
$858$	−2.30288			−0.0786192
$859$	3.31692	+	2.08416i	0.113172	+	0.0711105i	0.587429	−	0.809276i	$-0.300140\pi$
$859$	3.31692	+	2.08416i	0.113172	+	0.0711105i	−0.474257	+	0.880387i	$0.657283\pi$
$860$	5.78942	+	13.5482i	0.197418	+	0.461991i
$861$	−2.69911	+	11.8256i	−0.0919856	+	0.403015i
$862$	16.0708	+	3.66805i	0.547374	+	0.124934i
$863$	−34.7264	−	3.91273i	−1.18210	−	0.133191i	−0.501045	−	0.865421i	$-0.667051\pi$
$863$	−34.7264	−	3.91273i	−1.18210	−	0.133191i	−0.681057	+	0.732231i	$0.738479\pi$
$864$	−11.6885	+	24.2715i	−0.397652	+	0.825732i
$865$	−1.20210	−	1.31538i	−0.0408728	−	0.0447243i
$866$	−2.60720	+	3.26933i	−0.0885963	+	0.111096i
$867$	37.0886	+	46.5076i	1.25959	+	1.57948i
$868$	2.89385	+	6.00913i	0.0982235	+	0.203963i
$869$	−0.664307			−0.0225351
$870$	9.17010	−	16.8728i	0.310895	−	0.572041i
$871$	−32.5026			−1.10131
$872$	−7.36972	−	15.3034i	−0.249570	−	0.518238i
$873$	−0.416629	−	0.522436i	−0.0141008	−	0.0176818i
$874$	14.1178	−	17.7031i	0.477541	−	0.598817i
$875$	8.78587	−	34.8300i	0.297017	−	1.17747i
$876$	−2.73891	+	5.68740i	−0.0925391	+	0.192159i
$877$	10.1148	+	1.13966i	0.341553	+	0.0384837i	0.281075	−	0.959686i	$-0.409309\pi$
$877$	10.1148	+	1.13966i	0.341553	+	0.0384837i	0.0604776	+	0.998170i	$0.480738\pi$
$878$	−19.0472	−	4.34740i	−0.642812	−	0.146718i
$879$	7.96583	−	34.9006i	0.268681	−	1.17717i
$880$	−0.810389	−	0.325151i	−0.0273182	−	0.0109608i
$881$	−10.5567	−	6.63321i	−0.355664	−	0.223479i	0.342334	−	0.939578i	$-0.388783\pi$
$881$	−10.5567	−	6.63321i	−0.355664	−	0.223479i	−0.697998	+	0.716100i	$0.745925\pi$
$882$	1.90824			0.0642538
$883$	−8.92134	−	5.60565i	−0.300227	−	0.188645i	0.373491	−	0.927634i	$-0.378161\pi$
$883$	−8.92134	−	5.60565i	−0.300227	−	0.188645i	−0.673718	+	0.738989i	$0.735304\pi$
$884$	10.1596	+	29.0346i	0.341706	+	0.976538i
$885$	−13.4449	−	18.5087i	−0.451946	−	0.622162i
$886$	6.80600	+	29.8190i	0.228652	+	1.00179i
$887$			10.4690i			0.351515i	0.984433	+	0.175758i	$0.0562375\pi$
$887$			10.4690i			0.351515i	−0.984433	+	0.175758i	$0.943763\pi$
$888$	−33.5888	+	7.66641i	−1.12716	+	0.257268i
$889$	−17.2478	+	1.94336i	−0.578472	+	0.0651781i
$890$	−23.4556	+	1.57940i	−0.786233	+	0.0529418i
$891$	−1.24098	−	1.97501i	−0.0415744	−	0.0661652i
$892$	1.32051	−	11.7198i	0.0442138	−	0.392409i
$893$	17.5242	+	50.0812i	0.586424	+	1.67590i
$894$	13.3559	+	27.7338i	0.446688	+	0.927556i
$895$	−1.01613	−	2.37791i	−0.0339655	−	0.0794849i
$896$	−0.806054	+	7.15393i	−0.0269284	+	0.238996i
$897$	−24.7434	+	11.9158i	−0.826158	+	0.397857i
$898$	−0.300207	+	0.300207i	−0.0100180	+	0.0100180i
$899$	11.0138	+	3.90420i	0.367331	+	0.130212i
$900$	1.48131	+	2.24492i	0.0493770	+	0.0748308i
$901$	−17.9048	+	51.1689i	−0.596495	+	1.70468i
$902$	0.643726	−	0.513354i	0.0214337	−	0.0170928i
$903$	−3.86827	−	34.3318i	−0.128728	−	1.14249i
$904$	−0.636097	+	0.306328i	−0.0211563	+	0.0101883i
$905$	−24.7598	+	17.9858i	−0.823043	+	0.597868i
$906$	17.3927	+	21.8098i	0.577834	+	0.724581i
$907$	−8.36134	+	36.6334i	−0.277634	+	1.21639i	0.623142	+	0.782109i	$0.285856\pi$
$907$	−8.36134	+	36.6334i	−0.277634	+	1.21639i	−0.900776	+	0.434284i	$0.857001\pi$
$908$	−5.19548	−	8.26856i	−0.172418	−	0.274402i
$909$	0.575211	+	5.10514i	0.0190785	+	0.169327i
$910$	−30.6404	−	8.45903i	−1.01572	−	0.280414i
$911$	27.7673	+	27.7673i	0.919972	+	0.919972i	0.997027	−	0.0770545i	$-0.0245516\pi$
$911$	27.7673	+	27.7673i	0.919972	+	0.919972i	−0.0770545	+	0.997027i	$0.524552\pi$
$912$	5.31208	−	8.45412i	0.175900	−	0.279944i
$913$	2.29114	+	1.10335i	0.0758256	+	0.0365157i
$914$	−27.1813	+	9.51116i	−0.899079	+	0.314601i
$915$	−21.2641	+	12.0633i	−0.702969	+	0.398799i
$916$	14.0704	−	14.0704i	0.464900	−	0.464900i
$917$	−6.29517	−	27.5810i	−0.207885	−	0.910803i
$918$	26.2925	−	32.9697i	0.867782	−	1.08816i
$919$	−26.5398	−	6.05753i	−0.875466	−	0.199819i	−0.238902	−	0.971044i	$-0.576788\pi$
$919$	−26.5398	−	6.05753i	−0.875466	−	0.199819i	−0.636564	+	0.771224i	$0.719645\pi$
$920$	−27.3600	+	1.84231i	−0.902033	+	0.0607393i
$921$	38.7641	−	30.9133i	1.27732	−	1.01863i
$922$	−16.7344	+	5.85561i	−0.551118	+	0.192844i
$923$	−13.3830	−	4.68293i	−0.440508	−	0.154140i
$924$	−1.25078	−	0.997461i	−0.0411475	−	0.0328141i
$925$	−11.2953	+	34.7431i	−0.371386	+	1.14235i
$926$	13.8290	+	4.83896i	0.454448	+	0.159018i
$927$	−4.20090	−	4.20090i	−0.137976	−	0.137976i
$928$	16.1798	+	20.4588i	0.531128	+	0.671592i
$929$			42.3538i			1.38958i	0.719211	+	0.694792i	$0.244504\pi$
$929$			42.3538i			1.38958i	−0.719211	+	0.694792i	$0.755496\pi$
$930$	−5.71200	+	5.22010i	−0.187304	+	0.171174i
$931$	18.0244	+	2.03086i	0.590726	+	0.0665588i
$932$	−21.4834	+	2.42059i	−0.703711	+	0.0792891i
$933$	−1.15422	+	3.29857i	−0.0377875	+	0.107990i
$934$	−4.99869	−	2.40724i	−0.163562	−	0.0787674i
$935$	−4.54800	−	3.15144i	−0.148735	−	0.103063i
$936$	6.22821	−	3.91345i	0.203576	−	0.127915i
$937$	5.38668	−	3.38468i	0.175975	−	0.110573i	−0.441164	−	0.897426i	$-0.645434\pi$
$937$	5.38668	−	3.38468i	0.175975	−	0.110573i	0.617139	+	0.786854i	$0.288291\pi$
$938$	19.2521	+	15.3530i	0.628602	+	0.501293i
$939$	−8.89342	+	14.1538i	−0.290226	+	0.461892i
$940$	9.85388	−	18.3078i	0.321398	−	0.597136i
$941$	43.5932	−	9.94986i	1.42110	−	0.324356i	0.558188	−	0.829715i	$-0.311497\pi$
$941$	43.5932	−	9.94986i	1.42110	−	0.324356i	0.862910	+	0.505358i	$0.168640\pi$
$942$	−12.8302	+	26.6421i	−0.418030	+	0.868048i
$943$	4.26028	−	8.84657i	0.138734	−	0.288084i
$944$	−7.48330	+	1.70801i	−0.243561	+	0.0555911i
$945$	−11.4885	−	38.2703i	−0.373721	−	1.24493i
$946$	−1.24770	+	1.98571i	−0.0405663	+	0.0645610i
$947$	−15.8121	−	12.6098i	−0.513825	−	0.409762i	0.331954	−	0.943296i	$-0.392292\pi$
$947$	−15.8121	−	12.6098i	−0.513825	−	0.409762i	−0.845779	+	0.533534i	$0.820864\pi$
$948$	−2.52032	+	1.58362i	−0.0818561	+	0.0514336i
$949$	15.5004	−	9.73958i	0.503166	−	0.316160i
$950$	−12.6534	−	24.8442i	−0.410531	−	0.806052i
$951$	31.4258	+	15.1339i	1.01905	+	0.490749i
$952$	23.7882	−	67.9828i	0.770980	−	2.20333i
$953$	37.0553	−	4.17513i	1.20034	−	0.135246i	0.510933	−	0.859621i	$-0.329300\pi$
$953$	37.0553	−	4.17513i	1.20034	−	0.135246i	0.689406	+	0.724375i	$0.257872\pi$
$954$	4.16807	+	0.469629i	0.134946	+	0.0152048i
$955$	−21.7039	−	23.7491i	−0.702322	−	0.768502i
$956$			12.8748i			0.416402i
$957$	−2.78651	+	0.302506i	−0.0900752	+	0.00977862i
$958$	−6.01393	−	6.01393i	−0.194301	−	0.194301i
$959$	−18.4648	−	6.46113i	−0.596261	−	0.208641i
$960$	−25.0430	+	4.54243i	−0.808260	+	0.146606i
$961$	20.5555	+	16.3925i	0.663081	+	0.528790i
$962$	30.5141	+	10.6773i	0.983813	+	0.344251i
$963$	−4.62267	+	1.61754i	−0.148963	+	0.0521245i
$964$	5.66098	−	4.51448i	0.182328	−	0.145402i
$965$	−0.357838	−	0.312687i	−0.0115192	−	0.0100658i
$966$	20.2847	+	4.62984i	0.652648	+	0.148963i
$967$	23.5211	−	29.4946i	0.756389	−	0.948482i	−0.243381	−	0.969931i	$-0.578257\pi$
$967$	23.5211	−	29.4946i	0.756389	−	0.948482i	0.999770	+	0.0214491i	$0.00682797\pi$
$968$	−7.31757	−	32.0604i	−0.235196	−	1.03046i
$969$	44.7382	−	44.7382i	1.43720	−	1.43720i
$970$	0.722335	−	2.61645i	0.0231928	−	0.0840091i
$971$	−37.0487	+	12.9639i	−1.18895	+	0.416031i	−0.851016	−	0.525139i	$-0.824013\pi$
$971$	−37.0487	+	12.9639i	−1.18895	+	0.416031i	−0.337933	+	0.941170i	$0.609728\pi$
$972$	4.96563	+	2.39132i	0.159273	+	0.0767017i
$973$	32.0371	−	50.9867i	1.02706	−	1.63456i
$974$	13.8666	+	13.8666i	0.444313	+	0.444313i
$975$	0.752990	+	33.8074i	0.0241150	+	1.08270i
$976$	0.918429	+	8.15128i	0.0293982	+	0.260916i
$977$	−10.3799	−	16.5196i	−0.332083	−	0.528508i	0.638391	−	0.769712i	$-0.279600\pi$
$977$	−10.3799	−	16.5196i	−0.332083	−	0.528508i	−0.970474	+	0.241205i	$0.922457\pi$
$978$	0.699388	−	3.06422i	0.0223640	−	0.0979829i
$979$	2.13933	+	2.68264i	0.0683734	+	0.0857375i
$980$	−4.17726	−	5.75054i	−0.133438	−	0.183694i
$981$	−2.84922	+	1.37211i	−0.0909686	+	0.0438081i
$982$	1.14210	+	10.1364i	0.0364458	+	0.323465i
$983$	−13.1719	+	10.5042i	−0.420118	+	0.335033i	−0.810624	−	0.585568i	$-0.800872\pi$
$983$	−13.1719	+	10.5042i	−0.420118	+	0.335033i	0.390505	+	0.920601i	$0.372300\pi$
$984$	3.76574	−	10.7619i	0.120048	−	0.343076i
$985$	0.880980	+	2.93471i	0.0280704	+	0.0935077i
$986$	−17.5660	−	36.8584i	−0.559414	−	1.17381i
$987$	−34.4746	+	34.4746i	−1.09734	+	1.09734i
$988$	20.3827	−	9.81577i	0.648459	−	0.312281i
$989$	−3.13135	+	27.7915i	−0.0995710	+	0.883717i
$990$	−0.159418	+	0.397326i	−0.00506664	+	0.0126278i
$991$	−1.37219	−	2.84939i	−0.0435892	−	0.0905139i	0.878037	−	0.478593i	$-0.158853\pi$
$991$	−1.37219	−	2.84939i	−0.0435892	−	0.0905139i	−0.921626	+	0.388079i	$0.873139\pi$
$992$	−3.47128	−	9.92033i	−0.110213	−	0.314971i
$993$	−2.17026	+	19.2616i	−0.0688713	+	0.611249i
$994$	5.71505	+	9.09545i	0.181270	+	0.288490i
$995$	31.2738	−	35.7896i	0.991446	−	1.13461i
$996$	11.3226	−	1.27575i	0.358770	−	0.0404237i
$997$	−13.9139	+	3.17575i	−0.440657	+	0.100577i	−0.437092	−	0.899417i	$-0.643992\pi$
$997$	−13.9139	+	3.17575i	−0.440657	+	0.100577i	−0.00356433	+	0.999994i	$0.501135\pi$
$998$			7.62497i			0.241364i
$999$	9.04288	+	39.6195i	0.286104	+	1.25350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.t.a.108.9	yes	156
5.2	odd	4		145.2.o.a.137.5	yes	156
5.3	odd	4		725.2.y.b.282.9		156
5.4	even	2		725.2.bd.b.543.5		156
29.18	odd	28		145.2.o.a.18.5	✓	156
145.18	even	28		725.2.bd.b.482.5		156
145.47	even	28	inner	145.2.t.a.47.9	yes	156
145.134	odd	28		725.2.y.b.18.9		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.5	✓	156	29.18	odd	28
145.2.o.a.137.5	yes	156	5.2	odd	4
145.2.t.a.47.9	yes	156	145.47	even	28	inner
145.2.t.a.108.9	yes	156	1.1	even	1	trivial
725.2.y.b.18.9		156	145.134	odd	28
725.2.y.b.282.9		156	5.3	odd	4
725.2.bd.b.482.5		156	145.18	even	28
725.2.bd.b.543.5		156	5.4	even	2

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.t (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.443182 + 0.920277i) q^{2} +(-0.973467 - 1.22069i) q^{3} +(0.596480 - 0.747962i) q^{4} +(0.100511 - 2.23381i) q^{5} +(0.691949 - 1.43685i) q^{6} +(-3.19267 - 0.359728i) q^{7} +(2.94432 + 0.672023i) q^{8} +(0.125119 - 0.548181i) q^{9} +(2.10027 - 0.897485i) q^{10} +(-0.282265 - 0.177359i) q^{11} -1.49368 q^{12} +(3.66774 + 2.30460i) q^{13} +(-1.08389 - 3.09757i) q^{14} +(-2.82463 + 2.05185i) q^{15} +(0.260662 + 1.14204i) q^{16} +7.42290i q^{17} +(0.559929 - 0.127800i) q^{18} +(5.42486 - 0.611234i) q^{19} +(-1.61085 - 1.40760i) q^{20} +(2.66885 + 4.24744i) q^{21} +(0.0381244 - 0.338364i) q^{22} +(-1.34116 - 3.83282i) q^{23} +(-2.04587 - 4.24830i) q^{24} +(-4.97979 - 0.449046i) q^{25} +(-0.495389 + 4.39670i) q^{26} +(-5.01106 + 2.41320i) q^{27} +(-2.17343 + 2.17343i) q^{28} +(-0.0218780 + 5.38512i) q^{29} +(-3.14009 - 1.69010i) q^{30} +(0.716676 - 2.04814i) q^{31} +(3.78686 - 3.01992i) q^{32} +(0.0582756 + 0.517210i) q^{33} +(-6.83113 + 3.28970i) q^{34} +(-1.12446 + 7.09566i) q^{35} +(-0.335388 - 0.420563i) q^{36} +(1.62587 - 7.12342i) q^{37} +(2.96670 + 4.72148i) q^{38} +(-0.757232 - 6.72062i) q^{39} +(1.79711 - 6.50951i) q^{40} +(1.70982 + 1.70982i) q^{41} +(-2.72604 + 4.33847i) q^{42} +(-6.20526 - 2.98830i) q^{43} +(-0.301023 + 0.105332i) q^{44} +(-1.21196 - 0.334590i) q^{45} +(2.93288 - 2.93288i) q^{46} +(2.16272 + 9.47549i) q^{47} +(1.14032 - 1.42992i) q^{48} +(3.23926 + 0.739339i) q^{49} +(-1.79371 - 4.78180i) q^{50} +(9.06106 - 7.22595i) q^{51} +(3.91149 - 1.36869i) q^{52} +(6.89339 + 2.41210i) q^{53} +(-4.44163 - 3.54208i) q^{54} +(-0.424556 + 0.612698i) q^{55} +(-9.15852 - 3.20470i) q^{56} +(-6.02705 - 6.02705i) q^{57} +(-4.96550 + 2.36646i) q^{58} +6.55260i q^{59} +(-0.150132 + 3.33660i) q^{60} +(6.95855 + 0.784041i) q^{61} +(2.20248 - 0.248159i) q^{62} +(-0.596659 + 1.70515i) q^{63} +(6.56823 + 3.16309i) q^{64} +(5.51667 - 7.96139i) q^{65} +(-0.450150 + 0.282848i) q^{66} +(-6.35336 + 3.99208i) q^{67} +(5.55205 + 4.42761i) q^{68} +(-3.37311 + 5.36827i) q^{69} +(-7.02831 + 2.10985i) q^{70} +(-3.19119 + 0.728367i) q^{71} +(0.736780 - 1.52994i) q^{72} +(1.83366 - 3.80763i) q^{73} +(7.27608 - 1.66072i) q^{74} +(4.29952 + 6.51592i) q^{75} +(2.77864 - 4.42218i) q^{76} +(0.837377 + 0.667786i) q^{77} +(5.84924 - 3.67532i) q^{78} +(1.68732 - 1.06021i) q^{79} +(2.57729 - 0.467481i) q^{80} +(6.30409 + 3.03589i) q^{81} +(-0.815745 + 2.33127i) q^{82} +(-7.58032 + 0.854097i) q^{83} +(4.76884 + 0.537319i) q^{84} +(16.5813 + 0.746086i) q^{85} -7.03492i q^{86} +(6.59486 - 5.21553i) q^{87} +(-0.711889 - 0.711889i) q^{88} +(-9.71523 - 3.39950i) q^{89} +(-0.229202 - 1.26362i) q^{90} +(-10.8809 - 8.67721i) q^{91} +(-3.66678 - 1.28306i) q^{92} +(-3.19781 + 1.11896i) q^{93} +(-7.76160 + 6.18967i) q^{94} +(-0.820120 - 12.1795i) q^{95} +(-7.37277 - 1.68279i) q^{96} +(0.740965 - 0.929141i) q^{97} +(0.755184 + 3.30868i) q^{98} +(-0.132541 + 0.132541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 14 q^{2} - 10 q^{3} + 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} - 14 q^{8} - 10 q^{9} - 6 q^{10} - 20 q^{11} - 20 q^{12} - 28 q^{13} - 4 q^{14} - 4 q^{15} - 34 q^{16} + 84 q^{18} + 6 q^{20} - 16 q^{21}+ \cdots - 76 q^{99}+O(q^{100}) \) 156 * q - 14 * q^2 - 10 * q^3 + 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 - 14 * q^8 - 10 * q^9 - 6 * q^10 - 20 * q^11 - 20 * q^12 - 28 * q^13 - 4 * q^14 - 4 * q^15 - 34 * q^16 + 84 * q^18 + 6 * q^20 - 16 * q^21 - 22 * q^22 - 10 * q^23 - 56 * q^24 - 108 * q^25 + 36 * q^26 + 32 * q^27 - 8 * q^28 - 44 * q^30 - 8 * q^31 - 14 * q^32 - 14 * q^33 + 24 * q^34 + 26 * q^35 + 78 * q^36 - 72 * q^37 - 120 * q^38 - 16 * q^39 - 46 * q^40 - 22 * q^41 - 18 * q^42 + 2 * q^43 + 112 * q^44 + 30 * q^45 + 4 * q^46 + 22 * q^47 + 38 * q^48 - 84 * q^49 - 24 * q^50 - 28 * q^51 + 86 * q^52 + 56 * q^53 - 60 * q^55 + 4 * q^56 - 12 * q^57 + 96 * q^58 + 14 * q^60 - 46 * q^61 - 112 * q^62 + 158 * q^63 + 30 * q^64 + 4 * q^65 - 48 * q^66 + 18 * q^67 + 140 * q^68 + 124 * q^69 + 94 * q^70 - 28 * q^71 - 98 * q^72 - 84 * q^73 - 112 * q^74 + 54 * q^75 - 48 * q^76 + 28 * q^77 + 70 * q^78 + 4 * q^79 + 170 * q^80 + 58 * q^81 + 16 * q^82 + 46 * q^83 - 120 * q^84 + 76 * q^85 + 68 * q^87 + 40 * q^88 - 46 * q^89 + 120 * q^90 - 28 * q^91 - 14 * q^92 - 22 * q^93 + 84 * q^94 + 190 * q^95 - 28 * q^96 - 76 * q^97 - 160 * q^98 - 76 * q^99

Introduction

L-functions

Modular forms

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Database

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