LMFDB - Embedded newform 140.2.w.b.23.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(23,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.883367 + 1.10438i) q^{2} +(0.807254 + 0.216303i) q^{3} +(-0.439327 + 1.95115i) q^{4} +(-0.780454 + 2.09545i) q^{5} +(0.474220 + 1.08259i) q^{6} +(0.335905 - 2.62434i) q^{7} +(-2.54291 + 1.23840i) q^{8} +(-1.99320 - 1.15078i) q^{9} +(-3.00360 + 0.989126i) q^{10} +(4.21811 - 2.43533i) q^{11} +(-0.776689 + 1.48005i) q^{12} +(0.247904 + 0.247904i) q^{13} +(3.19501 - 1.94729i) q^{14} +(-1.08328 + 1.52274i) q^{15} +(-3.61398 - 1.71439i) q^{16} +(5.83537 + 1.56358i) q^{17} +(-0.489830 - 3.21782i) q^{18} +(-1.48858 + 2.57830i) q^{19} +(-3.74566 - 2.44337i) q^{20} +(0.838814 - 2.04585i) q^{21} +(6.41567 + 2.50713i) q^{22} +(-1.70618 - 6.36754i) q^{23} +(-2.32064 + 0.449662i) q^{24} +(-3.78178 - 3.27080i) q^{25} +(-0.0547911 + 0.492771i) q^{26} +(-3.13296 - 3.13296i) q^{27} +(4.97292 + 1.80835i) q^{28} +4.67111i q^{29} +(-2.63862 + 0.148788i) q^{30} +(-5.75848 + 3.32466i) q^{31} +(-1.29913 - 5.50566i) q^{32} +(3.93186 - 1.05354i) q^{33} +(3.42797 + 7.82570i) q^{34} +(5.23701 + 2.75205i) q^{35} +(3.12101 - 3.38347i) q^{36} +(-0.641729 - 2.39496i) q^{37} +(-4.16240 + 0.633619i) q^{38} +(0.146499 + 0.253744i) q^{39} +(-0.610370 - 6.29503i) q^{40} -1.15345 q^{41} +(3.00039 - 0.880866i) q^{42} +(3.23212 - 3.23212i) q^{43} +(2.89856 + 9.30008i) q^{44} +(3.96699 - 3.27852i) q^{45} +(5.52503 - 7.50914i) q^{46} +(-4.74443 + 1.27127i) q^{47} +(-2.54658 - 2.16566i) q^{48} +(-6.77434 - 1.76306i) q^{49} +(0.271513 - 7.06585i) q^{50} +(4.37242 + 2.52442i) q^{51} +(-0.592609 + 0.374787i) q^{52} +(0.0828048 - 0.309032i) q^{53} +(0.692438 - 6.22754i) q^{54} +(1.81106 + 10.7395i) q^{55} +(2.39580 + 7.08944i) q^{56} +(-1.75936 + 1.75936i) q^{57} +(-5.15869 + 4.12630i) q^{58} +(0.423416 + 0.733378i) q^{59} +(-2.49519 - 2.78262i) q^{60} +(-5.04573 + 8.73945i) q^{61} +(-8.75855 - 3.42268i) q^{62} +(-3.68956 + 4.84429i) q^{63} +(4.93275 - 6.29825i) q^{64} +(-0.712947 + 0.325992i) q^{65} +(4.63678 + 3.41162i) q^{66} +(-0.721946 + 2.69434i) q^{67} +(-5.61442 + 10.6988i) q^{68} -5.50928i q^{69} +(1.58688 + 8.21473i) q^{70} +6.49911i q^{71} +(6.49365 + 0.457943i) q^{72} +(-0.321006 + 1.19801i) q^{73} +(2.07808 - 2.82435i) q^{74} +(-2.34538 - 3.45838i) q^{75} +(-4.37668 - 4.03717i) q^{76} +(-4.97424 - 11.8878i) q^{77} +(-0.150818 + 0.385940i) q^{78} +(-4.44724 + 7.70284i) q^{79} +(6.41295 - 6.23490i) q^{80} +(1.60090 + 2.77285i) q^{81} +(-1.01892 - 1.27385i) q^{82} +(10.8443 - 10.8443i) q^{83} +(3.62326 + 2.53545i) q^{84} +(-7.83063 + 11.0074i) q^{85} +(6.42465 + 0.714354i) q^{86} +(-1.01038 + 3.77077i) q^{87} +(-7.71036 + 11.4165i) q^{88} +(8.26789 + 4.77347i) q^{89} +(7.12505 + 1.48495i) q^{90} +(0.733857 - 0.567313i) q^{91} +(13.1736 - 0.531576i) q^{92} +(-5.36769 + 1.43827i) q^{93} +(-5.59504 - 4.11668i) q^{94} +(-4.24092 - 5.13149i) q^{95} +(0.142163 - 4.72547i) q^{96} +(-2.35897 + 2.35897i) q^{97} +(-4.03713 - 9.03889i) q^{98} -11.2101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.883367	+	1.10438i	0.624634	+	0.780917i
$2$	0.883367	+	1.10438i	0.624634	+	0.780917i
$3$	0.807254	+	0.216303i	0.466069	+	0.124883i	0.484208	−	0.874953i	$-0.339108\pi$
$3$	0.807254	+	0.216303i	0.466069	+	0.124883i	−0.0181397	+	0.999835i	$0.505774\pi$
$4$	−0.439327	+	1.95115i	−0.219664	+	0.975576i
$5$	−0.780454	+	2.09545i	−0.349030	+	0.937112i
$5$	−0.780454	+	2.09545i	−0.349030	+	0.937112i
$6$	0.474220	+	1.08259i	0.193599	+	0.441967i
$7$	0.335905	−	2.62434i	0.126960	−	0.991908i
$7$	0.335905	−	2.62434i	0.126960	−	0.991908i
$8$	−2.54291	+	1.23840i	−0.899053	+	0.437839i
$9$	−1.99320	−	1.15078i	−0.664401	−	0.383592i
$10$	−3.00360	+	0.989126i	−0.949823	+	0.312789i
$11$	4.21811	−	2.43533i	1.27181	−	0.734279i	0.296480	−	0.955039i	$-0.404187\pi$
$11$	4.21811	−	2.43533i	1.27181	−	0.734279i	0.975328	+	0.220760i	$0.0708539\pi$
$12$	−0.776689	+	1.48005i	−0.224211	+	0.427253i
$13$	0.247904	+	0.247904i	0.0687562	+	0.0687562i	0.740649	−	0.671892i	$-0.234518\pi$
$13$	0.247904	+	0.247904i	0.0687562	+	0.0687562i	−0.671892	+	0.740649i	$0.734518\pi$
$14$	3.19501	−	1.94729i	0.853902	−	0.520434i
$15$	−1.08328	+	1.52274i	−0.279701	+	0.393171i
$16$	−3.61398	−	1.71439i	−0.903496	−	0.428597i
$17$	5.83537	+	1.56358i	1.41528	+	0.379224i	0.883808	−	0.467849i	$-0.154971\pi$
$17$	5.83537	+	1.56358i	1.41528	+	0.379224i	0.531476	+	0.847073i	$0.321638\pi$
$18$	−0.489830	−	3.21782i	−0.115454	−	0.758447i
$19$	−1.48858	+	2.57830i	−0.341505	+	0.591503i	−0.984712	−	0.174188i	$-0.944270\pi$
$19$	−1.48858	+	2.57830i	−0.341505	+	0.591503i	0.643208	+	0.765692i	$0.277603\pi$
$20$	−3.74566	−	2.44337i	−0.837554	−	0.546354i
$21$	0.838814	−	2.04585i	0.183044	−	0.446442i
$22$	6.41567	+	2.50713i	1.36783	+	0.534521i
$23$	−1.70618	−	6.36754i	−0.355762	−	1.32772i	−0.879522	−	0.475858i	$-0.842138\pi$
$23$	−1.70618	−	6.36754i	−0.355762	−	1.32772i	0.523760	−	0.851866i	$-0.324529\pi$
$24$	−2.32064	+	0.449662i	−0.473699	+	0.0917868i
$25$	−3.78178	−	3.27080i	−0.756357	−	0.654159i
$26$	−0.0547911	+	0.492771i	−0.0107454	+	0.0966404i
$27$	−3.13296	−	3.13296i	−0.602938	−	0.602938i
$28$	4.97292	+	1.80835i	0.939793	+	0.341745i
$29$			4.67111i			0.867403i	0.901057	+	0.433701i	$0.142793\pi$
$29$			4.67111i			0.867403i	−0.901057	+	0.433701i	$0.857207\pi$
$30$	−2.63862	+	0.148788i	−0.481744	+	0.0271648i
$31$	−5.75848	+	3.32466i	−1.03425	+	0.597127i	−0.918200	−	0.396116i	$-0.870358\pi$
$31$	−5.75848	+	3.32466i	−1.03425	+	0.597127i	−0.116053	+	0.993243i	$0.537024\pi$
$32$	−1.29913	−	5.50566i	−0.229656	−	0.973272i
$33$	3.93186	−	1.05354i	0.684448	−	0.183397i
$34$	3.42797	+	7.82570i	0.587892	+	1.34210i
$35$	5.23701	+	2.75205i	0.885216	+	0.465181i
$36$	3.12101	−	3.38347i	0.520168	−	0.563912i
$37$	−0.641729	−	2.39496i	−0.105500	−	0.393730i	0.892902	−	0.450251i	$-0.148666\pi$
$37$	−0.641729	−	2.39496i	−0.105500	−	0.393730i	−0.998401	+	0.0565217i	$0.981999\pi$
$38$	−4.16240	+	0.633619i	−0.675231	+	0.102787i
$39$	0.146499	+	0.253744i	0.0234587	+	0.0406316i
$40$	−0.610370	−	6.29503i	−0.0965080	−	0.995332i
$41$	−1.15345			−0.180138			−0.0900692	−	0.995936i	$-0.528709\pi$
$41$	−1.15345			−0.180138			−0.0900692	+	0.995936i	$0.528709\pi$
$42$	3.00039	−	0.880866i	0.462970	−	0.135921i
$43$	3.23212	−	3.23212i	0.492894	−	0.492894i	−0.416323	−	0.909217i	$-0.636682\pi$
$43$	3.23212	−	3.23212i	0.492894	−	0.492894i	0.909217	+	0.416323i	$0.136682\pi$
$44$	2.89856	+	9.30008i	0.436974	+	1.40204i
$45$	3.96699	−	3.27852i	0.591364	−	0.488733i
$46$	5.52503	−	7.50914i	0.814621	−	1.10716i
$47$	−4.74443	+	1.27127i	−0.692047	+	0.185433i	−0.587666	−	0.809104i	$-0.699953\pi$
$47$	−4.74443	+	1.27127i	−0.692047	+	0.185433i	−0.104381	+	0.994537i	$0.533286\pi$
$48$	−2.54658	−	2.16566i	−0.367567	−	0.312587i
$49$	−6.77434	−	1.76306i	−0.967762	−	0.251866i
$50$	0.271513	−	7.06585i	0.0383978	−	0.999263i
$51$	4.37242	+	2.52442i	0.612261	+	0.353489i
$52$	−0.592609	+	0.374787i	−0.0821801	+	0.0519737i
$53$	0.0828048	−	0.309032i	0.0113741	−	0.0424488i	−0.960006	−	0.279981i	$-0.909672\pi$
$53$	0.0828048	−	0.309032i	0.0113741	−	0.0424488i	0.971380	+	0.237532i	$0.0763385\pi$
$54$	0.692438	−	6.22754i	0.0942289	−	0.847461i
$55$	1.81106	+	10.7395i	0.244203	+	1.44811i
$56$	2.39580	+	7.08944i	0.320152	+	0.947366i
$57$	−1.75936	+	1.75936i	−0.233033	+	0.233033i
$58$	−5.15869	+	4.12630i	−0.677370	+	0.541810i
$59$	0.423416	+	0.733378i	0.0551240	+	0.0954776i	0.892271	−	0.451501i	$-0.149111\pi$
$59$	0.423416	+	0.733378i	0.0551240	+	0.0954776i	−0.837147	+	0.546979i	$0.815778\pi$
$60$	−2.49519	−	2.78262i	−0.322128	−	0.359235i
$61$	−5.04573	+	8.73945i	−0.646039	+	1.11897i	0.338021	+	0.941138i	$0.390242\pi$
$61$	−5.04573	+	8.73945i	−0.646039	+	1.11897i	−0.984060	+	0.177834i	$0.943091\pi$
$62$	−8.75855	−	3.42268i	−1.11234	−	0.434681i
$63$	−3.68956	+	4.84429i	−0.464841	+	0.610324i
$64$	4.93275	−	6.29825i	0.616594	−	0.787281i
$65$	−0.712947	+	0.325992i	−0.0884302	+	0.0404343i
$66$	4.63678	+	3.41162i	0.570748	+	0.419941i
$67$	−0.721946	+	2.69434i	−0.0881998	+	0.329166i	−0.995901	−	0.0904513i	$-0.971169\pi$
$67$	−0.721946	+	2.69434i	−0.0881998	+	0.329166i	0.907701	+	0.419617i	$0.137836\pi$
$68$	−5.61442	+	10.6988i	−0.680848	+	1.29742i
$69$		−	5.50928i		−	0.663239i
$70$	1.58688	+	8.21473i	0.189668	+	0.981848i
$71$			6.49911i			0.771303i	0.922645	+	0.385651i	$0.126023\pi$
$71$			6.49911i			0.771303i	−0.922645	+	0.385651i	$0.873977\pi$
$72$	6.49365	+	0.457943i	0.765284	+	0.0539691i
$73$	−0.321006	+	1.19801i	−0.0375710	+	0.140217i	−0.982164	−	0.188028i	$-0.939790\pi$
$73$	−0.321006	+	1.19801i	−0.0375710	+	0.140217i	0.944593	+	0.328245i	$0.106457\pi$
$74$	2.07808	−	2.82435i	0.241572	−	0.328324i
$75$	−2.34538	−	3.45838i	−0.270821	−	0.399339i
$76$	−4.37668	−	4.03717i	−0.502040	−	0.463095i
$77$	−4.97424	−	11.8878i	−0.566868	−	1.35474i
$78$	−0.150818	+	0.385940i	−0.0170768	+	0.0436991i
$79$	−4.44724	+	7.70284i	−0.500353	+	0.866637i	0.499647	+	0.866229i	$0.333463\pi$
$79$	−4.44724	+	7.70284i	−0.500353	+	0.866637i	−1.00000		0.000408067i	$0.999870\pi$
$80$	6.41295	−	6.23490i	0.716990	−	0.697084i
$81$	1.60090	+	2.77285i	0.177878	+	0.308094i
$82$	−1.01892	−	1.27385i	−0.112521	−	0.140673i
$83$	10.8443	−	10.8443i	1.19032	−	1.19032i	0.213343	−	0.976977i	$-0.431565\pi$
$83$	10.8443	−	10.8443i	1.19032	−	1.19032i	0.976977	−	0.213343i	$-0.0684351\pi$
$84$	3.62326	+	2.53545i	0.395330	+	0.276641i
$85$	−7.83063	+	11.0074i	−0.849351	+	1.19392i
$86$	6.42465	+	0.714354i	0.692787	+	0.0770308i
$87$	−1.01038	+	3.77077i	−0.108324	+	0.404269i
$88$	−7.71036	+	11.4165i	−0.821927	+	1.21700i
$89$	8.26789	+	4.77347i	0.876395	+	0.505987i	0.869468	−	0.493989i	$-0.164462\pi$
$89$	8.26789	+	4.77347i	0.876395	+	0.505987i	0.00692697	+	0.999976i	$0.497795\pi$
$90$	7.12505	+	1.48495i	0.751047	+	0.156527i
$91$	0.733857	−	0.567313i	0.0769291	−	0.0594705i
$92$	13.1736	−	0.531576i	1.37344	−	0.0554207i
$93$	−5.36769	+	1.43827i	−0.556604	+	0.149142i
$94$	−5.59504	−	4.11668i	−0.577084	−	0.424603i
$95$	−4.24092	−	5.13149i	−0.435110	−	0.526480i
$96$	0.142163	−	4.72547i	0.0145094	−	0.482292i
$97$	−2.35897	+	2.35897i	−0.239518	+	0.239518i	−0.816650	−	0.577133i	$-0.804172\pi$
$97$	−2.35897	+	2.35897i	−0.239518	+	0.239518i	0.577133	+	0.816650i	$0.304172\pi$
$98$	−4.03713	−	9.03889i	−0.407811	−	0.913066i
$99$	−11.2101			−1.12665
$100$	8.04326	−	5.94188i	0.804326	−	0.594188i
$101$	−0.729492	−	1.26352i	−0.0725872	−	0.125725i	0.827447	−	0.561543i	$-0.189792\pi$
$101$	−0.729492	−	1.26352i	−0.0725872	−	0.125725i	−0.900034	+	0.435819i	$0.856459\pi$
$102$	1.07452	+	7.05881i	0.106394	+	0.698927i
$103$	0.142820	+	0.533010i	0.0140724	+	0.0525190i	0.972605	−	0.232464i	$-0.0746787\pi$
$103$	0.142820	+	0.533010i	0.0140724	+	0.0525190i	−0.958533	+	0.284983i	$0.908012\pi$
$104$	−0.937400	−	0.323394i	−0.0919197	−	0.0317113i
$105$	3.63232	+	3.35438i	0.354478	+	0.327354i
$106$	0.414437	−	0.181540i	0.0402536	−	0.0176327i
$107$	4.80344	−	1.28708i	0.464366	−	0.124426i	−0.0190477	−	0.999819i	$-0.506063\pi$
$107$	4.80344	−	1.28708i	0.464366	−	0.124426i	0.483414	+	0.875392i	$0.339397\pi$
$108$	7.48927	−	4.73648i	0.720656	−	0.455768i
$109$	9.70303	−	5.60205i	0.929382	−	0.536579i	0.0427659	−	0.999085i	$-0.486383\pi$
$109$	9.70303	−	5.60205i	0.929382	−	0.536579i	0.886616	+	0.462506i	$0.153050\pi$
$110$	−10.2607	+	11.4870i	−0.978318	+	1.09524i
$111$		−	2.07215i		−	0.196680i
$112$	−5.71309	+	8.90845i	−0.539837	+	0.841770i
$113$	5.88750	+	5.88750i	0.553850	+	0.553850i	0.927550	−	0.373700i	$-0.121911\pi$
$113$	5.88750	+	5.88750i	0.553850	+	0.553850i	−0.373700	+	0.927550i	$0.621911\pi$
$114$	−3.49717	−	0.388849i	−0.327540	−	0.0364191i
$115$	14.6744	+	1.39437i	1.36840	+	0.130026i
$116$	−9.11404	−	2.05214i	−0.846217	−	0.190537i
$117$	−0.208841	−	0.779405i	−0.0193074	−	0.0720561i
$118$	−0.435899	+	1.11545i	−0.0401278	+	0.102686i
$119$	6.06350	−	14.7888i	0.555840	−	1.35568i
$120$	0.868912	−	5.21372i	0.0793204	−	0.475945i
$121$	6.36163	−	11.0187i	0.578330	−	1.00170i
$122$	−14.1089	+	2.14772i	−1.27736	+	0.194446i
$123$	−0.931126	−	0.249494i	−0.0839568	−	0.0224962i
$124$	−3.95706	−	12.6963i	−0.355354	−	1.14016i
$125$	9.80528	−	5.37182i	0.877011	−	0.480470i
$126$	−8.60919	+	0.204600i	−0.766968	+	0.0182272i
$127$	−5.47059	−	5.47059i	−0.485436	−	0.485436i	0.421426	−	0.906863i	$-0.361530\pi$
$127$	−5.47059	−	5.47059i	−0.485436	−	0.485436i	−0.906863	+	0.421426i	$0.861530\pi$
$128$	11.3131	−	0.116014i	0.999947	−	0.0102543i
$129$	3.30826	−	1.91002i	0.291276	−	0.168168i
$130$	−0.989814	−	0.499397i	−0.0868124	−	0.0438000i
$131$	−4.93009	−	2.84639i	−0.430744	−	0.248690i	0.268920	−	0.963163i	$-0.413333\pi$
$131$	−4.93009	−	2.84639i	−0.430744	−	0.248690i	−0.699663	+	0.714473i	$0.746667\pi$
$132$	0.328240	+	8.13450i	0.0285696	+	0.708017i
$133$	6.26632	+	4.77262i	0.543359	+	0.413838i
$134$	−3.61333	+	1.58278i	−0.312144	+	0.136732i
$135$	9.01008	−	4.11982i	0.775464	−	0.354577i
$136$	−16.7751	+	3.25045i	−1.43846	+	0.278724i
$137$	−0.479505	−	0.128483i	−0.0409668	−	0.0109770i	0.238277	−	0.971197i	$-0.423417\pi$
$137$	−0.479505	−	0.128483i	−0.0409668	−	0.0109770i	−0.279244	+	0.960220i	$0.590084\pi$
$138$	6.08435	−	4.86671i	0.517935	−	0.414282i
$139$	−6.37368			−0.540608			−0.270304	−	0.962775i	$-0.587124\pi$
$139$	−6.37368			−0.540608			−0.270304	+	0.962775i	$0.587124\pi$
$140$	−7.67042	+	9.00914i	−0.648269	+	0.761411i
$141$	−4.10494			−0.345699
$142$	−7.17752	+	5.74110i	−0.602324	+	0.481782i
$143$	1.64941	+	0.441959i	0.137931	+	0.0369585i
$144$	5.23053	+	7.57601i	0.435877	+	0.631334i
$145$	−9.78805	−	3.64558i	−0.812853	−	0.302749i
$146$	−1.60663	+	0.703770i	−0.132966	+	0.0582444i
$147$	−5.08726	−	2.88855i	−0.419590	−	0.238243i
$148$	4.95487	−	0.199937i	0.407288	−	0.0164347i
$149$	−5.05558	−	2.91884i	−0.414169	−	0.239121i	0.278410	−	0.960462i	$-0.410192\pi$
$149$	−5.05558	−	2.91884i	−0.414169	−	0.239121i	−0.692579	+	0.721342i	$0.743526\pi$
$150$	1.74755	−	5.64521i	0.142687	−	0.460930i
$151$	−3.20930	+	1.85289i	−0.261169	+	0.150786i	−0.624868	−	0.780731i	$-0.714847\pi$
$151$	−3.20930	+	1.85289i	−0.261169	+	0.150786i	0.363699	+	0.931517i	$0.381514\pi$
$152$	0.592370	−	8.39984i	0.0480476	−	0.681317i
$153$	−9.83174	−	9.83174i	−0.794849	−	0.794849i
$154$	8.73461	−	15.9948i	0.703855	−	1.28889i
$155$	−2.47242	−	14.6613i	−0.198589	−	1.17763i
$156$	−0.559454	+	0.174365i	−0.0447922	+	0.0139604i
$157$	10.6646	+	2.85757i	0.851127	+	0.228059i	0.657909	−	0.753097i	$-0.271441\pi$
$157$	10.6646	+	2.85757i	0.851127	+	0.228059i	0.193218	+	0.981156i	$0.438108\pi$
$158$	−12.4354	+	1.89298i	−0.989310	+	0.150597i
$159$	0.133689	−	0.231556i	0.0106022	−	0.0183636i
$160$	12.5507	+	1.57466i	0.992221	+	0.124487i
$161$	−17.2837	+	2.33870i	−1.36215	+	0.184316i
$162$	−1.64810	+	4.21745i	−0.129487	+	0.331354i
$163$	−0.187432	−	0.699506i	−0.0146808	−	0.0547896i	0.958197	−	0.286110i	$-0.0923622\pi$
$163$	−0.187432	−	0.699506i	−0.0146808	−	0.0547896i	−0.972878	+	0.231320i	$0.925696\pi$
$164$	0.506741	−	2.25055i	0.0395698	−	0.175739i
$165$	−0.861001	+	9.06123i	−0.0670288	+	0.705416i
$166$	21.5558	+	2.39679i	1.67306	+	0.186027i
$167$	−2.79303	−	2.79303i	−0.216131	−	0.216131i	0.590735	−	0.806866i	$-0.298838\pi$
$167$	−2.79303	−	2.79303i	−0.216131	−	0.216131i	−0.806866	+	0.590735i	$0.798838\pi$
$168$	0.400551	+	6.24120i	0.0309031	+	0.481519i
$169$		−	12.8771i		−	0.990545i
$170$	−19.0737	+	1.07553i	−1.46289	+	0.0824897i
$171$	5.93410	−	3.42606i	0.453792	−	0.261997i
$172$	4.88640	+	7.72631i	0.372584	+	0.589126i
$173$	21.8113	−	5.84433i	1.65828	−	0.444336i	0.696369	−	0.717684i	$-0.254798\pi$
$173$	21.8113	−	5.84433i	1.65828	−	0.444336i	0.961915	+	0.273348i	$0.0881310\pi$
$174$	−5.05691	+	2.21513i	−0.383363	+	0.167929i
$175$	−9.85401	+	8.82602i	−0.744893	+	0.667184i
$176$	−19.4193	+	1.56975i	−1.46378	+	0.118325i
$177$	0.183172	+	0.683609i	0.0137681	+	0.0513832i
$178$	2.03184	+	13.3477i	0.152293	+	1.00045i
$179$	4.66406	+	8.07838i	0.348608	+	0.603807i	0.986002	−	0.166731i	$-0.0533211\pi$
$179$	4.66406	+	8.07838i	0.348608	+	0.603807i	−0.637394	+	0.770538i	$0.719988\pi$
$180$	4.65408	+	9.18055i	0.346895	+	0.684278i
$181$	13.7888			1.02492			0.512458	−	0.858712i	$-0.328735\pi$
$181$	13.7888			1.02492			0.512458	+	0.858712i	$0.328735\pi$
$182$	1.27480	+	0.309315i	0.0944941	+	0.0229279i
$183$	−5.96356	+	5.96356i	−0.440839	+	0.440839i
$184$	12.2242	+	14.0791i	0.901179	+	1.03793i
$185$	5.51936	+	0.524451i	0.405791	+	0.0385584i
$186$	−6.33004	−	4.65747i	−0.464141	−	0.341503i
$187$	28.4220	−	7.61566i	2.07843	−	0.556913i
$188$	−0.396076	−	9.81561i	−0.0288868	−	0.715877i
$189$	−9.27433	+	7.16958i	−0.674608	+	0.521510i
$190$	1.92085	−	9.21660i	0.139353	−	0.668642i
$191$	0.149824	+	0.0865011i	0.0108409	+	0.00625900i	0.505411	−	0.862879i	$-0.331341\pi$
$191$	0.149824	+	0.0865011i	0.0108409	+	0.00625900i	−0.494570	+	0.869138i	$0.664674\pi$
$192$	5.34432	−	4.01732i	0.385693	−	0.289925i
$193$	−2.43607	+	9.09154i	−0.175352	+	0.654423i	0.821139	+	0.570728i	$0.193339\pi$
$193$	−2.43607	+	9.09154i	−0.175352	+	0.654423i	−0.996491	+	0.0836952i	$0.973328\pi$
$194$	−4.68905	−	0.521374i	−0.336654	−	0.0374325i
$195$	−0.646043	+	0.108946i	−0.0462641	+	0.00780176i
$196$	6.41615	−	12.4432i	0.458296	−	0.888800i
$197$	−10.6666	+	10.6666i	−0.759966	+	0.759966i	−0.976316	−	0.216350i	$-0.930585\pi$
$197$	−10.6666	+	10.6666i	−0.759966	+	0.759966i	0.216350	+	0.976316i	$0.430585\pi$
$198$	−9.90260	−	12.3802i	−0.703747	−	0.879824i
$199$	−8.58014	−	14.8612i	−0.608230	−	1.05349i	−0.991532	−	0.129862i	$-0.958547\pi$
$199$	−8.58014	−	14.8612i	−0.608230	−	1.05349i	0.383302	−	0.923623i	$-0.374787\pi$
$200$	13.6673	+	3.63399i	0.966422	+	0.256962i
$201$	−1.16559	+	2.01886i	−0.0822143	+	0.142399i
$202$	0.750999	−	1.92179i	0.0528401	−	0.135217i
$203$	12.2586	+	1.56905i	0.860384	+	0.110126i
$204$	−6.84644	+	7.42220i	−0.479347	+	0.519658i
$205$	0.900213	−	2.41699i	0.0628736	−	0.168810i
$206$	−0.462486	+	0.628571i	−0.0322229	+	0.0437946i
$207$	−3.92686	+	14.6552i	−0.272935	+	1.01861i
$208$	−0.470917	−	1.32092i	−0.0326523	−	0.0915897i
$209$			14.5008i			1.00304i
$210$	−0.495858	+	6.97463i	−0.0342174	+	0.481295i
$211$		−	2.47386i		−	0.170307i	−0.996368	−	0.0851536i	$-0.972862\pi$
$211$		−	2.47386i		−	0.170307i	0.996368	−	0.0851536i	$-0.0271381\pi$
$212$	0.566589	+	0.297331i	0.0389135	+	0.0204208i
$213$	−1.40578	+	5.24644i	−0.0963224	+	0.359480i
$214$	5.66462	+	4.16788i	0.387226	+	0.284910i
$215$	4.25021	+	9.29525i	0.289862	+	0.633931i
$216$	11.8467	+	4.08698i	0.806064	+	0.278084i
$217$	6.79074	+	16.2290i	0.460985	+	1.10170i
$218$	14.7581	+	5.76721i	0.999548	+	0.390605i
$219$	−0.518268	+	0.897666i	−0.0350213	+	0.0606587i
$220$	−21.7500	−	1.18450i	−1.46638	−	0.0798591i
$221$	1.05899	+	1.83423i	0.0712356	+	0.123384i
$222$	2.28845	−	1.83047i	0.153591	−	0.122853i
$223$	−7.05641	+	7.05641i	−0.472532	+	0.472532i	−0.902733	−	0.430201i	$-0.858443\pi$
$223$	−7.05641	+	7.05641i	−0.472532	+	0.472532i	0.430201	+	0.902733i	$0.358443\pi$
$224$	−14.8851	+	1.55998i	−0.994553	+	0.104231i
$225$	3.77391	+	10.8714i	0.251594	+	0.724757i
$226$	−1.30124	+	11.7029i	−0.0865572	+	0.778464i
$227$	−5.27268	+	19.6779i	−0.349960	+	1.30607i	0.536750	+	0.843742i	$0.319652\pi$
$227$	−5.27268	+	19.6779i	−0.349960	+	1.30607i	−0.886710	+	0.462327i	$0.847015\pi$
$228$	−2.65984	−	4.20572i	−0.176153	−	0.278530i
$229$	−8.26790	−	4.77347i	−0.546358	−	0.315440i	0.201294	−	0.979531i	$-0.435485\pi$
$229$	−8.26790	−	4.77347i	−0.546358	−	0.315440i	−0.747652	+	0.664091i	$0.768819\pi$
$230$	11.4230	+	17.4379i	0.753209	+	1.14982i
$231$	−1.44411	−	10.6724i	−0.0950156	−	0.702194i
$232$	−5.78468	−	11.8782i	−0.379783	−	0.779841i
$233$	−19.7757	+	5.29887i	−1.29555	+	0.347141i	−0.839765	−	0.542951i	$-0.817307\pi$
$233$	−19.7757	+	5.29887i	−1.29555	+	0.347141i	−0.455782	+	0.890091i	$0.650640\pi$
$234$	0.676280	−	0.919141i	0.0442098	−	0.0600861i
$235$	1.03894	−	10.9339i	0.0677730	−	0.713247i
$236$	−1.61695	+	0.503956i	−0.105254	+	0.0328047i
$237$	−5.25620	+	5.25620i	−0.341427	+	0.341427i
$238$	21.6888	−	6.36748i	1.40587	−	0.412742i
$239$	25.5833			1.65484			0.827422	−	0.561581i	$-0.189807\pi$
$239$	25.5833			1.65484			0.827422	+	0.561581i	$0.189807\pi$
$240$	6.52551	−	3.64601i	0.421220	−	0.235349i
$241$	−8.01250	−	13.8781i	−0.516131	−	0.893965i	−0.999825	−	0.0187274i	$-0.994039\pi$
$241$	−8.01250	−	13.8781i	−0.516131	−	0.893965i	0.483694	−	0.875237i	$-0.339295\pi$
$242$	17.7885	−	2.70784i	1.14349	−	0.174067i
$243$	4.13279	+	15.4238i	0.265119	+	0.989436i
$244$	−14.8353	−	13.6845i	−0.949731	−	0.876057i
$245$	8.98145	−	12.8193i	0.573804	−	0.818993i
$246$	−0.546988	−	1.24872i	−0.0348747	−	0.0796152i
$247$	−1.00820	+	0.270146i	−0.0641501	+	0.0171890i
$248$	10.5260	−	15.5856i	0.668404	−	0.989685i
$249$	11.0998	−	6.40847i	0.703421	−	0.406120i
$250$	14.5942	+	6.08351i	0.923019	+	0.384755i
$251$			28.9444i			1.82696i	0.406889	+	0.913478i	$0.366614\pi$
$251$			28.9444i			1.82696i	−0.406889	+	0.913478i	$0.633386\pi$
$252$	−7.83103	−	9.32712i	−0.493308	−	0.587553i
$253$	−22.7039	−	22.7039i	−1.42738	−	1.42738i
$254$	1.20909	−	10.8742i	0.0758654	−	0.682306i
$255$	−8.70225	+	7.19197i	−0.544956	+	0.450379i
$256$	10.1217	+	12.3915i	0.632609	+	0.774471i
$257$	−5.33306	−	19.9032i	−0.332667	−	1.24153i	−0.906376	−	0.422471i	$-0.861163\pi$
$257$	−5.33306	−	19.9032i	−0.332667	−	1.24153i	0.573709	−	0.819059i	$-0.305504\pi$
$258$	5.03181	+	1.96634i	0.313267	+	0.122419i
$259$	−6.50076	+	0.879634i	−0.403938	+	0.0546578i
$260$	−0.322842	−	1.53428i	−0.0200218	−	0.0951523i
$261$	5.37540	−	9.31047i	0.332729	−	0.576303i
$262$	−1.21157	−	7.95911i	−0.0748511	−	0.491716i
$263$	−12.2013	−	3.26932i	−0.752362	−	0.201595i	−0.137796	−	0.990461i	$-0.544002\pi$
$263$	−12.2013	−	3.26932i	−0.752362	−	0.201595i	−0.614566	+	0.788866i	$0.710669\pi$
$264$	−8.69365	+	7.54824i	−0.535057	+	0.464562i
$265$	0.582934	+	0.414698i	0.0358093	+	0.0254747i
$266$	0.264660	+	11.1364i	0.0162273	+	0.682816i
$267$	5.64178	+	5.64178i	0.345271	+	0.345271i
$268$	−4.93989	−	2.59232i	−0.301752	−	0.158351i
$269$	−9.69903	+	5.59974i	−0.591360	+	0.341422i	−0.765635	−	0.643275i	$-0.777575\pi$
$269$	−9.69903	+	5.59974i	−0.591360	+	0.341422i	0.174275	+	0.984697i	$0.444242\pi$
$270$	12.5091	+	6.31127i	0.761277	+	0.384092i
$271$	−20.6434	−	11.9184i	−1.25399	−	0.723994i	−0.282094	−	0.959387i	$-0.591029\pi$
$271$	−20.6434	−	11.9184i	−1.25399	−	0.723994i	−0.971900	+	0.235392i	$0.924362\pi$
$272$	−18.4083	−	15.6548i	−1.11617	−	0.949214i
$273$	0.715121	−	0.299230i	0.0432811	−	0.0181102i
$274$	−0.281684	−	0.643054i	−0.0170171	−	0.0388483i
$275$	−23.9174	−	4.58670i	−1.44228	−	0.276588i
$276$	10.7494	+	2.42037i	0.647040	+	0.145689i
$277$	5.30858	+	1.42243i	0.318962	+	0.0854656i	0.414748	−	0.909936i	$-0.363870\pi$
$277$	5.30858	+	1.42243i	0.318962	+	0.0854656i	−0.0957860	+	0.995402i	$0.530536\pi$
$278$	−5.63029	−	7.03899i	−0.337683	−	0.422170i
$279$	15.3038			0.916212
$280$	−16.7253	−	0.512715i	−0.999530	−	0.0306406i
$281$	29.7858			1.77687			0.888436	−	0.459001i	$-0.151793\pi$
$281$	29.7858			1.77687			0.888436	+	0.459001i	$0.151793\pi$
$282$	−3.62617	−	4.53343i	−0.215935	−	0.269962i
$283$	−20.9364	−	5.60990i	−1.24454	−	0.333474i	−0.424316	−	0.905514i	$-0.639485\pi$
$283$	−20.9364	−	5.60990i	−1.24454	−	0.333474i	−0.820225	+	0.572041i	$0.806152\pi$
$284$	−12.6808	−	2.85524i	−0.752464	−	0.169427i
$285$	−2.31355	−	5.05975i	−0.137043	−	0.299713i
$286$	0.968945	+	2.21200i	0.0572949	+	0.130798i
$287$	−0.387449	+	3.02704i	−0.0228704	+	0.178681i
$288$	−3.74635	+	12.4689i	−0.220756	+	0.734737i
$289$	16.8843	+	9.74814i	0.993193	+	0.573420i
$290$	−4.62031	−	14.0301i	−0.271314	−	0.823879i
$291$	−2.41455	+	1.39404i	−0.141543	+	0.0817200i
$292$	−2.19648	−	1.15265i	−0.128539	−	0.0674538i
$293$	−2.85175	−	2.85175i	−0.166601	−	0.166601i	0.618883	−	0.785484i	$-0.287586\pi$
$293$	−2.85175	−	2.85175i	−0.166601	−	0.166601i	−0.785484	+	0.618883i	$0.787586\pi$
$294$	−1.30385	−	8.16993i	−0.0760419	−	0.476480i
$295$	−1.86721	+	0.314877i	−0.108713	+	0.0183329i
$296$	4.59777	+	5.29546i	0.267240	+	0.307792i
$297$	−20.8449	−	5.58539i	−1.20955	−	0.324097i
$298$	−1.24241	−	8.16170i	−0.0719709	−	0.472795i
$299$	1.15557	−	2.00151i	0.0668284	−	0.115750i
$300$	7.77821	−	3.05683i	0.449075	−	0.176486i
$301$	−7.39650	−	9.56787i	−0.426327	−	0.551483i
$302$	−4.88129	−	1.90752i	−0.280887	−	0.109765i
$303$	−0.315583	−	1.17777i	−0.0181298	−	0.0676612i
$304$	9.79993	−	6.76593i	0.562064	−	0.388053i
$305$	−14.3751	−	17.3938i	−0.823116	−	0.995965i
$306$	2.17298	−	19.5430i	0.124221	−	1.11720i
$307$	3.58241	+	3.58241i	0.204459	+	0.204459i	0.801907	−	0.597448i	$-0.203819\pi$
$307$	3.58241	+	3.58241i	0.204459	+	0.204459i	−0.597448	+	0.801907i	$0.703819\pi$
$308$	25.3802	−	4.48287i	1.44617	−	0.255435i
$309$			0.461167i			0.0262349i
$310$	14.0077	−	15.6818i	0.795583	−	0.890668i
$311$	21.3073	−	12.3018i	1.20822	−	0.697569i	0.245854	−	0.969307i	$-0.420932\pi$
$311$	21.3073	−	12.3018i	1.20822	−	0.697569i	0.962371	+	0.271738i	$0.0875984\pi$
$312$	−0.686770	−	0.463824i	−0.0388807	−	0.0262588i
$313$	6.49513	−	1.74036i	0.367126	−	0.0983712i	−0.0705393	−	0.997509i	$-0.522472\pi$
$313$	6.49513	−	1.74036i	0.367126	−	0.0983712i	0.437666	+	0.899138i	$0.355805\pi$
$314$	6.26489	+	14.3021i	0.353548	+	0.807113i
$315$	−7.27143	−	11.5120i	−0.409698	−	0.648629i
$316$	−13.0756	−	12.0613i	−0.735561	−	0.678501i
$317$	3.57664	+	13.3482i	0.200884	+	0.749709i	0.990665	+	0.136320i	$0.0435275\pi$
$317$	3.57664	+	13.3482i	0.200884	+	0.749709i	−0.789781	+	0.613389i	$0.789806\pi$
$318$	0.373823	−	0.0569050i	0.0209630	−	0.00319107i
$319$	11.3757	+	19.7032i	0.636915	+	1.10317i
$320$	9.34786	+	15.2518i	0.522561	+	0.852602i
$321$	4.15600			0.231965
$322$	−17.8507	−	17.0219i	−0.994779	−	0.948594i
$323$	−12.7178	+	12.7178i	−0.707638	+	0.707638i
$324$	−6.11356	+	1.90542i	−0.339642	+	0.105857i
$325$	−0.126676	−	1.74836i	−0.00702671	−	0.0969818i
$326$	0.606952	−	0.824917i	0.0336160	−	0.0456879i
$327$	9.04456	−	2.42348i	0.500165	−	0.134019i
$328$	2.93311	−	1.42843i	0.161954	−	0.0788716i
$329$	1.74256	+	12.8780i	0.0960704	+	0.709989i
$330$	−10.7677	+	7.05351i	−0.592740	+	0.388283i
$331$	1.62048	+	0.935587i	0.0890699	+	0.0514245i	0.543873	−	0.839167i	$-0.316957\pi$
$331$	1.62048	+	0.935587i	0.0890699	+	0.0514245i	−0.454804	+	0.890592i	$0.650291\pi$
$332$	16.3947	+	25.9231i	0.899777	+	1.42272i
$333$	−1.47697	+	5.51214i	−0.0809376	+	0.302063i
$334$	0.617308	−	5.55185i	0.0337776	−	0.303784i
$335$	−5.08240	−	3.61561i	−0.277681	−	0.197542i
$336$	−6.53885	+	5.95563i	−0.356723	+	0.324906i
$337$	15.5089	−	15.5089i	0.844825	−	0.844825i	−0.144657	−	0.989482i	$-0.546208\pi$
$337$	15.5089	−	15.5089i	0.844825	−	0.844825i	0.989482	+	0.144657i	$0.0462078\pi$
$338$	14.2212	−	11.3752i	0.773534	−	0.618729i
$339$	3.47923	+	6.02620i	0.188966	+	0.327298i
$340$	−18.0369	−	20.1146i	−0.978187	−	1.09087i
$341$	−16.1933	+	28.0476i	−0.876915	+	1.51886i
$342$	9.02567	+	3.52706i	0.488052	+	0.190722i
$343$	−6.90240	+	17.1859i	−0.372695	+	0.927954i
$344$	−4.21633	+	12.2216i	−0.227330	+	0.658946i
$345$	11.5444	+	4.29973i	0.621529	+	0.231490i
$346$	25.7218	+	18.9254i	1.38281	+	1.01744i
$347$	2.72992	−	10.1882i	0.146550	−	0.546931i	−0.853132	−	0.521696i	$-0.825300\pi$
$347$	2.72992	−	10.1882i	0.146550	−	0.546931i	0.999682	−	0.0252358i	$-0.00803366\pi$
$348$	−6.91346	−	3.62800i	−0.370600	−	0.194481i
$349$			7.92462i			0.424195i	0.977249	+	0.212098i	$0.0680295\pi$
$349$			7.92462i			0.424195i	−0.977249	+	0.212098i	$0.931971\pi$
$350$	−18.4520	−	3.08600i	−0.986301	−	0.164954i
$351$		−	1.55335i		−	0.0829115i
$352$	−18.8879	−	20.0597i	−1.00673	−	1.06918i
$353$	−2.32090	+	8.66171i	−0.123529	+	0.461016i	−0.999783	−	0.0208332i	$-0.993368\pi$
$353$	−2.32090	+	8.66171i	−0.123529	+	0.461016i	0.876254	+	0.481849i	$0.160035\pi$
$354$	−0.593158	+	0.806170i	−0.0315260	+	0.0428474i
$355$	−13.6185	−	5.07226i	−0.722797	−	0.269207i
$356$	−12.9461	+	14.0348i	−0.686141	+	0.743843i
$357$	8.09365	−	10.6268i	0.428361	−	0.562427i
$358$	−4.80156	+	12.2871i	−0.253771	+	0.649392i
$359$	11.6112	−	20.1111i	0.612814	−	1.06143i	−0.377950	−	0.925826i	$-0.623371\pi$
$359$	11.6112	−	20.1111i	0.612814	−	1.06143i	0.990764	−	0.135599i	$-0.0432960\pi$
$360$	−6.02759	+	13.2497i	−0.317682	+	0.698320i
$361$	5.06824	+	8.77844i	0.266749	+	0.462023i
$362$	12.1806	+	15.2282i	0.640198	+	0.800375i
$363$	7.51883	−	7.51883i	0.394636	−	0.394636i
$364$	0.784509	+	1.68110i	0.0411195	+	0.0881137i
$365$	−2.25984	−	1.60764i	−0.118285	−	0.0841480i
$366$	−11.8541	−	1.31805i	−0.619622	−	0.0688955i
$367$	8.07404	−	30.1327i	0.421462	−	1.57292i	−0.350069	−	0.936724i	$-0.613842\pi$
$367$	8.07404	−	30.1327i	0.421462	−	1.57292i	0.771530	−	0.636192i	$-0.219492\pi$
$368$	−4.75034	+	25.9372i	−0.247628	+	1.35207i
$369$	2.29906	+	1.32736i	0.119684	+	0.0690997i
$370$	4.29642	+	6.55877i	0.223360	+	0.340974i
$371$	−0.783190	−	0.321113i	−0.0406612	−	0.0166714i
$372$	−0.448107	−	11.1051i	−0.0232333	−	0.575770i
$373$	17.9985	−	4.82267i	0.931925	−	0.249709i	0.239250	−	0.970958i	$-0.423099\pi$
$373$	17.9985	−	4.82267i	0.931925	−	0.249709i	0.692675	+	0.721250i	$0.256432\pi$
$374$	33.5177	+	24.6614i	1.73316	+	1.27521i
$375$	9.07730	−	2.21551i	0.468750	−	0.114408i
$376$	10.4903	−	9.10820i	0.540997	−	0.469720i
$377$	−1.15799	+	1.15799i	−0.0596393	+	0.0596393i
$378$	−16.1106	−	3.90906i	−0.828640	−	0.201060i
$379$	18.6149			0.956182			0.478091	−	0.878310i	$-0.341329\pi$
$379$	18.6149			0.956182			0.478091	+	0.878310i	$0.341329\pi$
$380$	11.8755	−	6.02028i	0.609199	−	0.308834i
$381$	−3.23285	−	5.59946i	−0.165624	−	0.286869i
$382$	0.0368194	+	0.241876i	0.00188384	+	0.0123754i
$383$	8.07570	+	30.1389i	0.412649	+	1.54003i	0.789498	+	0.613753i	$0.210341\pi$
$383$	8.07570	+	30.1389i	0.412649	+	1.54003i	−0.376849	+	0.926275i	$0.622992\pi$
$384$	9.15766	+	2.35341i	0.467325	+	0.120097i
$385$	28.7924	−	1.14538i	1.46740	−	0.0583740i
$386$	−12.1925	+	5.34080i	−0.620581	+	0.271840i
$387$	−10.1617	+	2.72282i	−0.516549	+	0.138409i
$388$	−3.56636	−	5.63908i	−0.181054	−	0.286281i
$389$	−3.21806	+	1.85795i	−0.163162	+	0.0942017i	−0.579358	−	0.815073i	$-0.696697\pi$
$389$	−3.21806	+	1.85795i	−0.163162	+	0.0942017i	0.416196	+	0.909275i	$0.363363\pi$
$390$	−0.691010	−	0.617240i	−0.0349907	−	0.0312552i
$391$		−	39.8247i		−	2.01402i
$392$	19.4099	−	3.90601i	0.980346	−	0.197283i
$393$	−3.36415	−	3.36415i	−0.169699	−	0.169699i
$394$	−21.2026	−	2.35751i	−1.06817	−	0.118770i
$395$	−12.6700	−	15.3307i	−0.637498	−	0.771369i
$396$	4.92489	−	21.8725i	0.247485	−	1.09914i
$397$	−1.15071	−	4.29450i	−0.0577524	−	0.215535i	0.931019	−	0.364971i	$-0.118921\pi$
$397$	−1.15071	−	4.29450i	−0.0577524	−	0.215535i	−0.988771	+	0.149436i	$0.952254\pi$
$398$	8.83310	−	22.6037i	0.442763	−	1.13302i
$399$	4.02619	+	5.20814i	0.201561	+	0.260733i
$400$	8.05989	+	18.3040i	0.402995	+	0.915202i
$401$	−17.5463	+	30.3911i	−0.876220	+	1.51766i	−0.0207625	+	0.999784i	$0.506609\pi$
$401$	−17.5463	+	30.3911i	−0.876220	+	1.51766i	−0.855457	+	0.517873i	$0.826724\pi$
$402$	−3.25924	+	0.496135i	−0.162556	+	0.0247450i
$403$	−2.25175	−	0.603354i	−0.112168	−	0.0300552i
$404$	2.78580	−	0.868252i	0.138599	−	0.0431971i
$405$	−7.05978	+	1.19053i	−0.350803	+	0.0591578i
$406$	9.09599	+	14.9242i	0.451426	+	0.740677i
$407$	−8.53940	−	8.53940i	−0.423282	−	0.423282i
$408$	−14.2449	−	1.00457i	−0.705227	−	0.0497337i
$409$	−31.9026	+	18.4190i	−1.57748	+	0.910759i	−0.582272	+	0.812994i	$0.697836\pi$
$409$	−31.9026	+	18.4190i	−1.57748	+	0.910759i	−0.995210	+	0.0977650i	$0.968831\pi$
$410$	3.46450	−	1.14091i	0.171099	−	0.0563453i
$411$	−0.359291	−	0.207437i	−0.0177225	−	0.0102321i
$412$	−1.10273	+	0.0444969i	−0.0543275	+	0.00219220i
$413$	2.06686	−	0.864842i	0.101704	−	0.0425561i
$414$	−19.6538	+	8.60918i	−0.965934	+	0.423118i
$415$	14.2602	+	31.1872i	0.700006	+	1.53092i
$416$	1.04282	−	1.68693i	0.0511282	−	0.0827088i
$417$	−5.14518	−	1.37865i	−0.251961	−	0.0675126i
$418$	−16.0144	+	12.8095i	−0.783290	+	0.626532i
$419$	−31.8030			−1.55368			−0.776840	−	0.629699i	$-0.783178\pi$
$419$	−31.8030			−1.55368			−0.776840	+	0.629699i	$0.783178\pi$
$420$	−8.14069	+	5.61353i	−0.397225	+	0.273912i
$421$	13.1193			0.639396			0.319698	−	0.947519i	$-0.396418\pi$
$421$	13.1193			0.639396			0.319698	+	0.947519i	$0.396418\pi$
$422$	2.73209	−	2.18532i	0.132996	−	0.106380i
$423$	10.9196	+	2.92589i	0.530928	+	0.142262i
$424$	0.172139	+	0.888384i	0.00835980	+	0.0431437i
$425$	−16.9539	−	24.9994i	−0.822387	−	1.21265i
$426$	−7.03590	+	3.08201i	−0.340890	+	0.149324i
$427$	21.2404	+	16.1773i	1.02790	+	0.782876i
$428$	0.401002	+	9.93768i	0.0193831	+	0.480356i
$429$	1.23590	+	0.713547i	0.0596698	+	0.0344504i
$430$	−6.51103	+	12.9050i	−0.313990	+	0.622333i
$431$	17.0409	−	9.83859i	0.820833	−	0.473908i	−0.0298705	−	0.999554i	$-0.509509\pi$
$431$	17.0409	−	9.83859i	0.820833	−	0.473908i	0.850704	+	0.525646i	$0.176176\pi$
$432$	5.95136	+	16.6936i	0.286335	+	0.803170i
$433$	−12.6198	−	12.6198i	−0.606466	−	0.606466i	0.335554	−	0.942021i	$-0.391076\pi$
$433$	−12.6198	−	12.6198i	−0.606466	−	0.606466i	−0.942021	+	0.335554i	$0.891076\pi$
$434$	−11.9243	+	21.8357i	−0.572386	+	1.04815i
$435$	−7.11290	−	5.06010i	−0.341037	−	0.242613i
$436$	6.66764	+	21.3932i	0.319322	+	1.02455i
$437$	18.9572	+	5.07957i	0.906847	+	0.242989i
$438$	−1.44919	+	0.220602i	−0.0692449	+	0.0105408i
$439$	2.34778	−	4.06648i	0.112054	−	0.194082i	−0.804545	−	0.593892i	$-0.797591\pi$
$439$	2.34778	−	4.06648i	0.112054	−	0.194082i	0.916598	+	0.399810i	$0.130924\pi$
$440$	−17.9051	−	25.0667i	−0.853591	−	1.19501i
$441$	11.4737	+	11.3099i	0.546369	+	0.538566i
$442$	−1.09021	+	2.78983i	−0.0518562	+	0.132699i
$443$	1.07698	+	4.01934i	0.0511688	+	0.190965i	0.986779	−	0.162069i	$-0.0518168\pi$
$443$	1.07698	+	4.01934i	0.0511688	+	0.190965i	−0.935611	+	0.353034i	$0.885150\pi$
$444$	4.04309	+	0.910353i	0.191876	+	0.0432035i
$445$	−16.4553	+	13.5994i	−0.780054	+	0.644676i
$446$	−14.0264	−	1.55959i	−0.664168	−	0.0738486i
$447$	−3.44978	−	3.44978i	−0.163169	−	0.163169i
$448$	−14.8718	−	15.0608i	−0.702628	−	0.711558i
$449$		−	41.3539i		−	1.95161i	−0.218641	−	0.975805i	$-0.570163\pi$
$449$		−	41.3539i		−	1.95161i	0.218641	−	0.975805i	$-0.429837\pi$
$450$	−8.67240	+	13.7712i	−0.408821	+	0.649182i
$451$	−4.86537	+	2.80902i	−0.229101	+	0.132272i
$452$	−14.0739	+	8.90087i	−0.661983	+	0.418662i
$453$	−2.99151	+	0.801572i	−0.140553	+	0.0376612i
$454$	−26.3897	+	11.5597i	−1.23853	+	0.542526i
$455$	0.616031	+	1.98052i	0.0288800	+	0.0928482i
$456$	2.29511	−	6.65268i	0.107478	−	0.311540i
$457$	5.99940	+	22.3901i	0.280640	+	1.04736i	0.951967	+	0.306202i	$0.0990582\pi$
$457$	5.99940	+	22.3901i	0.280640	+	1.04736i	−0.671326	+	0.741162i	$0.734275\pi$
$458$	−2.03184	−	13.3477i	−0.0949416	−	0.623695i
$459$	−13.3833	−	23.1806i	−0.624680	−	1.08198i
$460$	−9.16750	+	28.0194i	−0.427437	+	1.30641i
$461$	16.9131			0.787723			0.393861	−	0.919170i	$-0.371139\pi$
$461$	16.9131			0.787723			0.393861	+	0.919170i	$0.371139\pi$
$462$	10.5108	−	11.0225i	0.489005	−	0.512814i
$463$	22.3542	−	22.3542i	1.03889	−	1.03889i	0.0396749	−	0.999213i	$-0.487368\pi$
$463$	22.3542	−	22.3542i	1.03889	−	1.03889i	0.999213	−	0.0396749i	$-0.0126322\pi$
$464$	8.00809	−	16.8813i	0.371766	−	0.783695i
$465$	1.17542	−	12.3702i	0.0545089	−	0.573655i
$466$	−23.3212	−	17.1591i	−1.08033	−	0.794879i
$467$	−8.28849	+	2.22089i	−0.383546	+	0.102771i	−0.445440	−	0.895312i	$-0.646953\pi$
$467$	−8.28849	+	2.22089i	−0.383546	+	0.102771i	0.0618940	+	0.998083i	$0.480286\pi$
$468$	1.61249	−	0.0650665i	0.0745373	−	0.00300770i
$469$	6.82836	+	2.79968i	0.315305	+	0.129277i
$470$	12.9930	−	8.51123i	0.599320	−	0.392594i
$471$	7.99094	+	4.61357i	0.368203	+	0.212582i
$472$	−1.98492	−	1.34055i	−0.0913633	−	0.0617040i
$473$	5.76217	−	21.5047i	0.264945	−	0.988787i
$474$	−10.4480	−	1.16171i	−0.479893	−	0.0533592i
$475$	14.0626	−	4.88173i	0.645237	−	0.223989i
$476$	26.1913	+	18.3279i	1.20048	+	0.840059i
$477$	−0.520673	+	0.520673i	−0.0238400	+	0.0238400i
$478$	22.5994	+	28.2537i	1.03367	+	1.29230i
$479$	12.0963	+	20.9514i	0.552694	+	0.957294i	0.998079	+	0.0619545i	$0.0197334\pi$
$479$	12.0963	+	20.9514i	0.552694	+	0.957294i	−0.445385	+	0.895339i	$0.646933\pi$
$480$	9.79102	+	3.98591i	0.446897	+	0.181931i
$481$	0.434634	−	0.752808i	0.0198176	−	0.0343251i
$482$	8.24873	−	21.1083i	0.375719	−	0.961457i
$483$	−14.4582	−	1.85059i	−0.657872	−	0.0842049i
$484$	18.7043	+	17.2533i	0.850194	+	0.784241i
$485$	−3.10203	−	6.78417i	−0.140856	−	0.308053i
$486$	−13.3830	+	18.1890i	−0.607065	+	0.825071i
$487$	4.79710	−	17.9030i	0.217377	−	0.811263i	−0.767939	−	0.640523i	$-0.778718\pi$
$487$	4.79710	−	17.9030i	0.217377	−	0.811263i	0.985316	−	0.170740i	$-0.0546157\pi$
$488$	2.00791	−	28.4722i	0.0908937	−	1.28888i
$489$		−	0.605222i		−	0.0273691i
$490$	22.0913	−	1.40514i	0.997983	−	0.0634778i
$491$			26.3306i			1.18828i	0.804360	+	0.594142i	$0.202508\pi$
$491$			26.3306i			1.18828i	−0.804360	+	0.594142i	$0.797492\pi$
$492$	0.895871	−	1.70716i	0.0403890	−	0.0769646i
$493$	−7.30366	+	27.2576i	−0.328940	+	1.22762i
$494$	−1.18895	−	0.874800i	−0.0534935	−	0.0393591i
$495$	8.74894	−	23.4901i	0.393236	−	1.05580i
$496$	26.5108	−	2.14300i	1.19037	−	0.0962235i
$497$	17.0559	+	2.18309i	0.765061	+	0.0979248i
$498$	16.8826	+	6.59741i	0.756528	+	0.295637i
$499$	−5.41316	+	9.37586i	−0.242326	+	0.419721i	−0.961376	−	0.275237i	$-0.911244\pi$
$499$	−5.41316	+	9.37586i	−0.242326	+	0.419721i	0.719050	+	0.694958i	$0.244577\pi$
$500$	6.17350	+	21.4916i	0.276087	+	0.961133i
$501$	−1.65055	−	2.85883i	−0.0737409	−	0.127723i
$502$	−31.9657	+	25.5685i	−1.42670	+	1.14118i
$503$	−1.75566	+	1.75566i	−0.0782809	+	0.0782809i	−0.745163	−	0.666882i	$-0.767628\pi$
$503$	−1.75566	+	1.75566i	−0.0782809	+	0.0782809i	0.666882	+	0.745163i	$0.267628\pi$
$504$	3.38305	−	16.8877i	0.150693	−	0.752239i
$505$	3.21697	−	0.542494i	0.143153	−	0.0241407i
$506$	5.01795	−	45.1296i	0.223075	−	2.00626i
$507$	2.78535	−	10.3951i	0.123702	−	0.461662i
$508$	13.0773	−	8.27057i	0.580213	−	0.366947i
$509$	27.6605	+	15.9698i	1.22603	+	0.707849i	0.966197	−	0.257804i	$-0.0829989\pi$
$509$	27.6605	+	15.9698i	1.22603	+	0.707849i	0.259834	+	0.965653i	$0.416332\pi$
$510$	−15.6300	−	3.25747i	−0.692107	−	0.144243i
$511$	3.03617	+	1.24485i	0.134312	+	0.0550689i
$512$	−4.74380	+	22.1246i	−0.209648	+	0.977777i
$513$	12.7414	−	3.41405i	0.562546	−	0.150734i
$514$	17.2698	−	23.4716i	0.761737	−	1.03529i
$515$	−1.22836	−	0.116719i	−0.0541279	−	0.00514325i
$516$	2.27334	+	7.29404i	0.100078	+	0.321102i
$517$	−16.9166	+	16.9166i	−0.743991	+	0.743991i
$518$	−6.71401	−	6.40230i	−0.294997	−	0.281301i
$519$	18.8714			0.828364
$520$	1.40925	−	1.71188i	0.0617998	−	0.0750708i
$521$	−16.3491	−	28.3174i	−0.716265	−	1.24061i	−0.962469	−	0.271390i	$-0.912517\pi$
$521$	−16.3491	−	28.3174i	−0.716265	−	1.24061i	0.246204	−	0.969218i	$-0.420817\pi$
$522$	15.0308	−	2.28805i	0.657879	−	0.100145i
$523$	−9.21055	−	34.3742i	−0.402749	−	1.50308i	−0.808170	−	0.588950i	$-0.799542\pi$
$523$	−9.21055	−	34.3742i	−0.402749	−	1.50308i	0.405421	−	0.914130i	$-0.367125\pi$
$524$	7.71966	−	8.36885i	0.337235	−	0.365595i
$525$	−9.86379	+	4.99339i	−0.430491	+	0.217929i
$526$	−7.16760	−	16.3629i	−0.312522	−	0.713456i
$527$	−38.8012	+	10.3968i	−1.69021	+	0.452890i
$528$	−16.0158	−	2.93326i	−0.697000	−	0.127654i
$529$	−17.7159	+	10.2283i	−0.770257	+	0.444708i
$530$	0.0569586	+	1.01011i	0.00247412	+	0.0438765i
$531$		−	1.94903i		−	0.0845806i
$532$	−12.0651	+	10.1298i	−0.523087	+	0.439183i
$533$	−0.285944	−	0.285944i	−0.0123856	−	0.0123856i
$534$	−1.24693	+	11.2144i	−0.0539600	+	0.485297i
$535$	−1.05186	+	11.0698i	−0.0454759	+	0.478591i
$536$	−1.50082	−	7.74551i	−0.0648255	−	0.334555i
$537$	2.01770	+	7.53016i	0.0870702	+	0.324950i
$538$	−14.7521	−	5.76483i	−0.636006	−	0.248540i
$539$	−32.8685	+	9.06094i	−1.41575	+	0.390282i
$540$	4.08001	+	19.3900i	0.175576	+	0.834411i
$541$	18.6970	−	32.3842i	0.803848	−	1.39231i	−0.113218	−	0.993570i	$-0.536116\pi$
$541$	18.6970	−	32.3842i	0.803848	−	1.39231i	0.917066	−	0.398736i	$-0.130551\pi$
$542$	−5.07311	−	33.3266i	−0.217909	−	1.43150i
$543$	11.1311	+	2.98257i	0.477681	+	0.127994i
$544$	1.02765	−	34.1588i	0.0440600	−	1.46455i
$545$	4.16602	+	24.7043i	0.178453	+	1.05822i
$546$	0.962179	+	0.525438i	0.0411774	+	0.0224867i
$547$	27.0715	+	27.0715i	1.15749	+	1.15749i	0.985013	+	0.172480i	$0.0551781\pi$
$547$	27.0715	+	27.0715i	1.15749	+	1.15749i	0.172480	+	0.985013i	$0.444822\pi$
$548$	0.461349	−	0.879140i	0.0197078	−	0.0375550i
$549$	20.1143	−	11.6130i	0.858458	−	0.495631i
$550$	−16.0624	−	30.4658i	−0.684903	−	1.29906i
$551$	−12.0435	−	6.95334i	−0.513072	−	0.296222i
$552$	6.82266	+	14.0096i	0.290392	+	0.596287i
$553$	18.7210	+	14.2585i	0.796099	+	0.606333i
$554$	3.11852	+	7.11924i	0.132493	+	0.302468i
$555$	4.34208	+	1.61722i	0.184311	+	0.0686472i
$556$	2.80013	−	12.4360i	0.118752	−	0.527404i
$557$	−15.8098	−	4.23623i	−0.669884	−	0.179495i	−0.0921814	−	0.995742i	$-0.529384\pi$
$557$	−15.8098	−	4.23623i	−0.669884	−	0.179495i	−0.577703	+	0.816247i	$0.696051\pi$
$558$	13.5188	+	16.9012i	0.572298	+	0.715486i
$559$	1.60251			0.0677790
$560$	−14.2084	−	18.9241i	−0.600413	−	0.799690i
$561$	24.5911			1.03824
$562$	26.3118	+	32.8949i	1.10989	+	1.38759i
$563$	−22.6700	−	6.07440i	−0.955425	−	0.256005i	−0.252762	−	0.967528i	$-0.581339\pi$
$563$	−22.6700	−	6.07440i	−0.955425	−	0.256005i	−0.702663	+	0.711523i	$0.748006\pi$
$564$	1.80341	−	8.00937i	0.0759374	−	0.337255i
$565$	−16.9319	+	7.74202i	−0.712329	+	0.325709i
$566$	−12.2991	−	28.0774i	−0.516968	−	1.18018i
$567$	7.81464	−	3.26990i	0.328184	−	0.137323i
$568$	−8.04848	−	16.5266i	−0.337707	−	0.693443i
$569$	−16.8334	−	9.71879i	−0.705694	−	0.407433i	0.103770	−	0.994601i	$-0.466909\pi$
$569$	−16.8334	−	9.71879i	−0.705694	−	0.407433i	−0.809465	+	0.587168i	$0.800243\pi$
$570$	3.54419	−	7.02465i	0.148450	−	0.294230i
$571$	−40.3258	+	23.2821i	−1.68758	+	0.974327i	−0.731223	+	0.682138i	$0.761050\pi$
$571$	−40.3258	+	23.2821i	−1.68758	+	0.974327i	−0.956361	+	0.292189i	$0.905616\pi$
$572$	−1.58696	+	3.02409i	−0.0663542	+	0.126444i
$573$	0.102236	+	0.102236i	0.00427097	+	0.00427097i
$574$	−3.68528	+	2.24609i	−0.153820	+	0.0937502i
$575$	−14.3745	+	29.6612i	−0.599459	+	1.23696i
$576$	−17.0799	+	6.87720i	−0.711661	+	0.286550i
$577$	−23.5105	−	6.29961i	−0.978754	−	0.262256i	−0.266234	−	0.963908i	$-0.585779\pi$
$577$	−23.5105	−	6.29961i	−0.978754	−	0.262256i	−0.712520	+	0.701652i	$0.752446\pi$
$578$	4.14931	+	27.2579i	0.172589	+	1.13378i
$579$	−3.93306	+	6.81225i	−0.163452	+	0.283108i
$580$	11.4132	−	17.4964i	0.473909	−	0.726497i
$581$	−24.8166	−	32.1019i	−1.02956	−	1.33181i
$582$	−3.67248	−	1.43514i	−0.152229	−	0.0594884i
$583$	−0.403313	−	1.50519i	−0.0167035	−	0.0623385i
$584$	−0.667324	−	3.44397i	−0.0276141	−	0.142512i
$585$	1.79619	+	0.170675i	0.0742634	+	0.00705653i
$586$	0.630286	−	5.66857i	0.0260369	−	0.234166i
$587$	−0.195894	−	0.195894i	−0.00808542	−	0.00808542i	0.703053	−	0.711138i	$-0.251820\pi$
$587$	−0.195894	−	0.195894i	−0.00808542	−	0.00808542i	−0.711138	+	0.703053i	$0.751820\pi$
$588$	7.87096	−	8.65699i	0.324593	−	0.357008i
$589$		−	19.7961i		−	0.815686i
$590$	−1.99718	−	1.78396i	−0.0822224	−	0.0734446i
$591$	−10.9179	+	6.30346i	−0.449103	+	0.259290i
$592$	−1.78670	+	9.75553i	−0.0734329	+	0.400950i
$593$	4.03218	−	1.08042i	0.165582	−	0.0443676i	−0.175076	−	0.984555i	$-0.556017\pi$
$593$	4.03218	−	1.08042i	0.165582	−	0.0443676i	0.340658	+	0.940187i	$0.389350\pi$
$594$	−12.2453	−	27.9548i	−0.502432	−	1.14700i
$595$	26.2568	+	24.2477i	1.07642	+	0.994058i
$596$	7.91615	−	8.58187i	0.324258	−	0.351527i
$597$	−3.71182	−	13.8527i	−0.151915	−	0.566954i
$598$	3.23122	−	0.491871i	0.132135	−	0.0201141i
$599$	−8.35085	−	14.4641i	−0.341206	−	0.590987i	0.643451	−	0.765488i	$-0.277502\pi$
$599$	−8.35085	−	14.4641i	−0.341206	−	0.590987i	−0.984657	+	0.174501i	$0.944169\pi$
$600$	10.2469	+	5.88982i	0.418329	+	0.240451i
$601$	−38.4209			−1.56722			−0.783610	−	0.621253i	$-0.786624\pi$
$601$	−38.4209			−1.56722			−0.783610	+	0.621253i	$0.786624\pi$
$602$	4.03278	−	16.6205i	0.164364	−	0.677401i
$603$	4.53957	−	4.53957i	0.184866	−	0.184866i
$604$	−2.20534	−	7.07586i	−0.0897339	−	0.287913i
$605$	18.1241	+	21.9300i	0.736848	+	0.891582i
$606$	1.02194	−	1.38893i	0.0415133	−	0.0564214i
$607$	−30.8579	+	8.26835i	−1.25248	+	0.335602i	−0.823295	−	0.567613i	$-0.807867\pi$
$607$	−30.8579	+	8.26835i	−1.25248	+	0.335602i	−0.429188	+	0.903215i	$0.641200\pi$
$608$	16.1291	+	4.84608i	0.654122	+	0.196535i
$609$	9.55640	+	3.91819i	0.387245	+	0.158773i
$610$	6.51094	−	31.2407i	0.263620	−	1.26490i
$611$	−1.49132	−	0.861012i	−0.0603322	−	0.0348328i
$612$	23.5026	−	14.8639i	0.950035	−	0.600836i
$613$	7.17171	−	26.7652i	0.289663	−	1.08104i	−0.655702	−	0.755020i	$-0.727627\pi$
$613$	7.17171	−	26.7652i	0.289663	−	1.08104i	0.945364	−	0.326016i	$-0.105706\pi$
$614$	−0.791775	+	7.12094i	−0.0319534	+	0.287378i
$615$	1.24950	−	1.75641i	0.0503848	−	0.0708251i
$616$	27.3708	+	24.0695i	1.10280	+	0.969787i
$617$	10.6961	−	10.6961i	0.430610	−	0.430610i	−0.458226	−	0.888836i	$-0.651515\pi$
$617$	10.6961	−	10.6961i	0.430610	−	0.430610i	0.888836	+	0.458226i	$0.151515\pi$
$618$	−0.509305	+	0.407380i	−0.0204873	+	0.0163872i
$619$	1.43357	+	2.48301i	0.0576199	+	0.0998006i	0.893397	−	0.449269i	$-0.148316\pi$
$619$	1.43357	+	2.48301i	0.0576199	+	0.0998006i	−0.835777	+	0.549070i	$0.814982\pi$
$620$	29.6927	+	1.61706i	1.19249	+	0.0649427i
$621$	−14.6039	+	25.2946i	−0.586033	+	1.01504i
$622$	32.4080	+	12.6644i	1.29944	+	0.507798i
$623$	15.3044	−	20.0943i	0.613160	−	0.805063i
$624$	−0.0944300	−	1.16818i	−0.00378022	−	0.0467648i
$625$	3.60378	+	24.7389i	0.144151	+	0.989556i
$626$	7.65961	+	5.63573i	0.306140	+	0.225249i
$627$	−3.13656	+	11.7058i	−0.125262	+	0.467485i
$628$	−10.2608	+	19.5528i	−0.409450	+	0.780242i
$629$		−	14.9789i		−	0.597247i
$630$	6.29035	−	18.1998i	0.250613	−	0.725096i
$631$		−	0.116828i		−	0.00465086i	−0.999997	−	0.00232543i	$-0.999260\pi$
$631$		−	0.116828i		−	0.00465086i	0.999997	−	0.00232543i	$-0.000740209\pi$
$632$	1.76974	−	25.0951i	0.0703966	−	0.998228i
$633$	0.535103	−	1.99703i	0.0212684	−	0.0793748i
$634$	−11.5820	+	15.7413i	−0.459982	+	0.625168i
$635$	15.7329	−	7.19378i	0.624340	−	0.285476i
$636$	0.393068	+	0.362577i	0.0155862	+	0.0143771i
$637$	−1.24232	−	2.11645i	−0.0492223	−	0.0838570i
$638$	−11.7111	+	29.9683i	−0.463645	+	1.18646i
$639$	7.47903	−	12.9541i	0.295866	−	0.512455i
$640$	−8.58626	+	23.7966i	−0.339402	+	0.940642i
$641$	−3.64503	−	6.31338i	−0.143970	−	0.249364i	0.785018	−	0.619473i	$-0.212654\pi$
$641$	−3.64503	−	6.31338i	−0.143970	−	0.249364i	−0.928988	+	0.370109i	$0.879320\pi$
$642$	3.67127	+	4.58981i	0.144893	+	0.181146i
$643$	−2.55764	+	2.55764i	−0.100863	+	0.100863i	−0.755738	−	0.654874i	$-0.772722\pi$
$643$	−2.55764	+	2.55764i	−0.100863	+	0.100863i	0.654874	+	0.755738i	$0.272722\pi$
$644$	3.03004	−	34.7506i	0.119400	−	1.36936i
$645$	1.42041	+	8.42297i	0.0559286	+	0.331654i
$646$	−25.2799	−	2.81086i	−0.994622	−	0.110592i
$647$	−3.58712	+	13.3873i	−0.141024	+	0.526309i	0.858876	+	0.512183i	$0.171163\pi$
$647$	−3.58712	+	13.3873i	−0.141024	+	0.526309i	−0.999900	+	0.0141258i	$0.995503\pi$
$648$	−7.50483	−	5.06854i	−0.294817	−	0.199111i
$649$	3.57203	+	2.06231i	0.140214	+	0.0809528i
$650$	1.81896	−	1.68434i	0.0713456	−	0.0660654i
$651$	1.97147	+	14.5698i	0.0772681	+	0.571035i
$652$	1.44719	−	0.0583963i	0.0566762	−	0.00228698i
$653$	−28.5901	+	7.66070i	−1.11882	+	0.299786i	−0.770405	−	0.637555i	$-0.779946\pi$
$653$	−28.5901	+	7.66070i	−1.11882	+	0.299786i	−0.348413	+	0.937341i	$0.613279\pi$
$654$	10.6661	+	7.84784i	0.417078	+	0.306875i
$655$	9.81216	−	8.10926i	0.383393	−	0.316855i
$656$	4.16854	+	1.97746i	0.162754	+	0.0772067i
$657$	2.01848	−	2.01848i	0.0787482	−	0.0787482i
$658$	−12.6830	+	13.3005i	−0.494434	+	0.518507i
$659$	−41.1139			−1.60157			−0.800784	−	0.598953i	$-0.795584\pi$
$659$	−41.1139			−1.60157			−0.800784	+	0.598953i	$0.795584\pi$
$660$	−17.3016	−	5.66079i	−0.673463	−	0.220346i
$661$	7.77799	+	13.4719i	0.302529	+	0.523995i	0.976708	−	0.214572i	$-0.0688358\pi$
$661$	7.77799	+	13.4719i	0.302529	+	0.523995i	−0.674179	+	0.738568i	$0.735502\pi$
$662$	0.398234	+	2.61610i	0.0154778	+	0.101678i
$663$	0.458127	+	1.70975i	0.0177922	+	0.0664013i
$664$	−14.1466	+	41.0057i	−0.548993	+	1.59133i
$665$	−14.8913	+	9.40593i	−0.577461	+	0.364747i
$666$	−7.39222	+	3.23809i	−0.286443	+	0.125474i
$667$	29.7435	−	7.96973i	1.15167	−	0.308589i
$668$	6.67668	−	4.22257i	0.258329	−	0.163376i
$669$	−7.22264	+	4.16999i	−0.279243	+	0.161221i
$670$	−0.496602	−	8.80682i	−0.0191854	−	0.340237i
$671$			49.1520i			1.89749i
$672$	−12.3535	−	1.96039i	−0.476547	−	0.0756239i
$673$	2.25638	+	2.25638i	0.0869771	+	0.0869771i	0.749257	−	0.662280i	$-0.230411\pi$
$673$	2.25638	+	2.25638i	0.0869771	+	0.0869771i	−0.662280	+	0.749257i	$0.730411\pi$
$674$	30.8279	+	3.42774i	1.18745	+	0.132032i
$675$	1.60090	+	22.0955i	0.0616188	+	0.850454i
$676$	25.1251	+	5.65725i	0.966352	+	0.217587i
$677$	−10.7790	−	40.2278i	−0.414271	−	1.54608i	−0.786292	−	0.617855i	$-0.788002\pi$
$677$	−10.7790	−	40.2278i	−0.414271	−	1.54608i	0.372022	−	0.928224i	$-0.378665\pi$
$678$	−3.58180	+	9.16574i	−0.137558	+	0.352008i
$679$	5.39836	+	6.98315i	0.207170	+	0.267989i
$680$	6.28107	−	37.6882i	0.240868	−	1.44528i
$681$	−8.51279	+	14.7446i	−0.326211	+	0.565014i
$682$	−45.2799	+	6.89269i	−1.73386	+	0.263935i
$683$	41.8335	+	11.2093i	1.60072	+	0.428910i	0.945259	−	0.326322i	$-0.105810\pi$
$683$	41.8335	+	11.2093i	1.60072	+	0.428910i	0.655457	+	0.755233i	$0.272476\pi$
$684$	4.07774	+	13.0835i	0.155916	+	0.500260i
$685$	0.643460	−	0.904501i	0.0245853	−	0.0345592i
$686$	−25.0772	+	7.55859i	−0.957453	+	0.288588i
$687$	−5.64178	−	5.64178i	−0.215247	−	0.215247i
$688$	−17.2219	+	6.13972i	−0.656580	+	0.234075i
$689$	0.0971379	−	0.0560826i	0.00370066	−	0.00213658i
$690$	5.44937	+	16.5477i	0.207454	+	0.629959i
$691$	37.3091	+	21.5404i	1.41930	+	0.819436i	0.996238	−	0.0866626i	$-0.0276202\pi$
$691$	37.3091	+	21.5404i	1.41930	+	0.819436i	0.423067	+	0.906098i	$0.360954\pi$
$692$	1.82086	+	45.1248i	0.0692186	+	1.71539i
$693$	−3.76552	+	29.4190i	−0.143040	+	1.11754i
$694$	13.6632	−	5.98504i	0.518648	−	0.227189i
$695$	4.97436	−	13.3557i	0.188688	−	0.506610i
$696$	−2.10042	−	10.8400i	−0.0796162	−	0.410888i
$697$	−6.73079	−	1.80351i	−0.254947	−	0.0683128i
$698$	−8.75182	+	7.00034i	−0.331261	+	0.264967i
$699$	−17.1102			−0.647166
$700$	−12.8918	−	23.1042i	−0.487263	−	0.873255i
$701$	−13.3256			−0.503300			−0.251650	−	0.967818i	$-0.580973\pi$
$701$	−13.3256			−0.503300			−0.251650	+	0.967818i	$0.580973\pi$
$702$	1.71549	−	1.37217i	0.0647470	−	0.0517894i
$703$	7.13021	+	1.91053i	0.268921	+	0.0720572i
$704$	5.46859	−	38.5796i	0.206105	−	1.45402i
$705$	3.20372	−	8.60169i	0.120659	−	0.323958i
$706$	−11.6161	+	5.08830i	−0.437176	+	0.191501i
$707$	−3.56094	+	1.49001i	−0.133923	+	0.0560378i
$708$	−1.41430	+	0.0570692i	−0.0531525	+	0.00214479i
$709$	−3.81245	−	2.20112i	−0.143180	−	0.0826648i	0.426699	−	0.904394i	$-0.359676\pi$
$709$	−3.81245	−	2.20112i	−0.143180	−	0.0826648i	−0.569879	+	0.821729i	$0.693010\pi$
$710$	−6.42844	−	19.5208i	−0.241255	−	0.732601i
$711$	17.7285	−	10.2356i	0.664871	−	0.383863i
$712$	−26.9359	−	1.89957i	−1.00947	−	0.0711892i
$713$	30.9949	+	30.9949i	1.16077	+	1.16077i
$714$	18.8857	−	0.448823i	0.706778	−	0.0167968i
$715$	−2.21339	+	3.11133i	−0.0827762	+	0.116357i
$716$	−17.8112	+	5.55123i	−0.665636	+	0.207459i
$717$	20.6522	+	5.53374i	0.771271	+	0.206661i
$718$	32.4673	−	4.94232i	1.21167	−	0.184446i
$719$	0.144472	−	0.250232i	0.00538788	−	0.00933208i	−0.863319	−	0.504659i	$-0.831618\pi$
$719$	0.144472	−	0.250232i	0.00538788	−	0.00933208i	0.868707	+	0.495327i	$0.164952\pi$
$720$	−19.9573	+	5.04756i	−0.743765	+	0.188111i
$721$	1.44677	−	0.195767i	0.0538807	−	0.00729073i
$722$	−5.21766	+	13.3519i	−0.194181	+	0.496905i
$723$	−3.46626	−	12.9363i	−0.128912	−	0.481105i
$724$	−6.05781	+	26.9041i	−0.225137	+	0.999884i
$725$	15.2782	−	17.6651i	0.567420	−	0.656066i
$726$	14.9456	+	1.66179i	0.554682	+	0.0616749i
$727$	−4.87969	−	4.87969i	−0.180978	−	0.180978i	0.610804	−	0.791782i	$-0.290846\pi$
$727$	−4.87969	−	4.87969i	−0.180978	−	0.180978i	−0.791782	+	0.610804i	$0.790846\pi$
$728$	−1.16357	+	2.35143i	−0.0431249	+	0.0871498i
$729$			3.73943i			0.138497i
$730$	−0.220809	−	3.91587i	−0.00817252	−	0.144933i
$731$	23.9143	−	13.8069i	0.884502	−	0.510667i
$732$	−9.01585	−	14.2558i	−0.333235	−	0.526908i
$733$	21.9180	−	5.87292i	0.809561	−	0.216921i	0.169783	−	0.985481i	$-0.445693\pi$
$733$	21.9180	−	5.87292i	0.809561	−	0.216921i	0.639777	+	0.768560i	$0.279027\pi$
$734$	40.4105	−	17.7014i	1.49158	−	0.653371i
$735$	10.0232	−	8.40569i	0.369710	−	0.310049i
$736$	−32.8409	+	17.6659i	−1.21053	+	0.651173i
$737$	3.51635	+	13.1232i	0.129526	+	0.483399i
$738$	0.564994	+	3.71159i	0.0207977	+	0.136625i
$739$	2.90840	+	5.03750i	0.106987	+	0.185307i	0.914548	−	0.404477i	$-0.132546\pi$
$739$	2.90840	+	5.03750i	0.106987	+	0.185307i	−0.807561	+	0.589784i	$0.799213\pi$
$740$	−3.44809	+	10.5387i	−0.126754	+	0.387410i
$741$	−0.872306			−0.0320449
$742$	−0.337212	−	1.14860i	−0.0123794	−	0.0421666i
$743$	5.70591	−	5.70591i	0.209329	−	0.209329i	−0.594653	−	0.803982i	$-0.702711\pi$
$743$	5.70591	−	5.70591i	0.209329	−	0.209329i	0.803982	+	0.594653i	$0.202711\pi$
$744$	11.8684	−	10.3047i	0.435117	−	0.377789i
$745$	10.0619	−	8.31567i	0.368640	−	0.304663i
$746$	21.2253	+	15.6170i	0.777114	+	0.571780i
$747$	−34.0944	+	9.13556i	−1.24745	+	0.334253i
$748$	2.37274	+	58.8015i	0.0867558	+	2.15000i
$749$	−1.76423	−	13.0382i	−0.0644636	−	0.476405i
$750$	10.4654	+	8.06772i	0.382141	+	0.294591i
$751$	−36.3916	−	21.0107i	−1.32795	−	0.766690i	−0.342965	−	0.939348i	$-0.611431\pi$
$751$	−36.3916	−	21.0107i	−1.32795	−	0.766690i	−0.984982	+	0.172658i	$0.944764\pi$
$752$	19.3258	+	3.53946i	0.704738	+	0.129071i
$753$	−6.26077	+	23.3655i	−0.228155	+	0.851486i
$754$	−2.30179	−	0.255935i	−0.0838262	−	0.00932060i
$755$	−1.37792	−	8.17101i	−0.0501477	−	0.297374i
$756$	−9.91447	−	21.2454i	−0.360586	−	0.772688i
$757$	−36.1581	+	36.1581i	−1.31419	+	1.31419i	−0.395891	+	0.918298i	$0.629564\pi$
$757$	−36.1581	+	36.1581i	−1.31419	+	1.31419i	−0.918298	+	0.395891i	$0.870436\pi$
$758$	16.4438	+	20.5580i	0.597264	+	0.746699i
$759$	−13.4169	−	23.2387i	−0.487002	−	0.843512i
$760$	17.1391	+	7.79697i	0.621700	+	0.282826i
$761$	−0.178655	+	0.309439i	−0.00647623	+	0.0112172i	−0.869245	−	0.494381i	$-0.835395\pi$
$761$	−0.178655	+	0.309439i	−0.00647623	+	0.0112172i	0.862769	+	0.505598i	$0.168728\pi$
$762$	3.32816	−	8.51669i	0.120567	−	0.308527i
$763$	−11.4424	−	27.3458i	−0.414242	−	0.989985i
$764$	−0.234599	+	0.254328i	−0.00848748	+	0.00920125i
$765$	28.2751	−	12.9287i	1.02229	−	0.467437i
$766$	−26.1511	+	35.5424i	−0.944879	+	1.28420i
$767$	−0.0768408	+	0.286774i	−0.00277456	+	0.0103548i
$768$	5.49050	+	12.1925i	0.198121	+	0.439959i
$769$		−	23.4758i		−	0.846559i	−0.905999	−	0.423279i	$-0.860879\pi$
$769$		−	23.4758i		−	0.846559i	0.905999	−	0.423279i	$-0.139121\pi$
$770$	26.6992	+	30.7861i	0.962172	+	1.10945i
$771$		−	17.2205i		−	0.620183i
$772$	−16.6687	−	8.74730i	−0.599921	−	0.314822i
$773$	−6.57570	+	24.5409i	−0.236512	+	0.882673i	0.740950	+	0.671560i	$0.234376\pi$
$773$	−6.57570	+	24.5409i	−0.236512	+	0.882673i	−0.977462	+	0.211113i	$0.932291\pi$
$774$	−11.9836	−	8.81719i	−0.430740	−	0.316927i
$775$	32.6516	+	6.26167i	1.17288	+	0.224926i
$776$	3.07731	−	8.92000i	0.110469	−	0.320209i
$777$	−5.43804	−	0.696047i	−0.195089	−	0.0249705i
$778$	−4.89461	−	1.91272i	−0.175480	−	0.0685745i
$779$	1.71700	−	2.97394i	0.0615181	−	0.106552i
$780$	0.0712548	−	1.30839i	0.00255133	−	0.0468479i
$781$	15.8275	+	27.4140i	0.566351	+	0.980949i
$782$	43.9817	−	35.1798i	1.57278	−	1.25803i
$783$	14.6344	−	14.6344i	0.522990	−	0.522990i
$784$	21.4598	+	17.9855i	0.766420	+	0.642339i
$785$	−14.3111	+	20.1169i	−0.510785	+	0.718002i
$786$	0.743536	−	6.68710i	0.0265211	−	0.238521i
$787$	−0.657725	+	2.45466i	−0.0234454	+	0.0874993i	−0.976657	−	0.214804i	$-0.931089\pi$
$787$	−0.657725	+	2.45466i	−0.0234454	+	0.0874993i	0.953212	+	0.302303i	$0.0977555\pi$
$788$	−16.1261	−	25.4984i	−0.574468	−	0.908342i
$789$	−9.14236	−	5.27834i	−0.325477	−	0.187914i
$790$	5.73866	−	27.5352i	0.204172	−	0.979657i
$791$	17.4285	−	13.4732i	0.619685	−	0.479051i
$792$	28.5062	−	13.8825i	1.01292	−	0.493293i
$793$	−3.41740	+	0.915690i	−0.121356	+	0.0325171i
$794$	3.72628	−	5.06444i	0.132241	−	0.179730i
$795$	0.380875	+	0.460857i	0.0135083	+	0.0163449i
$796$	32.7660	−	10.2122i	1.16136	−	0.361962i
$797$	31.6762	−	31.6762i	1.12203	−	1.12203i	0.130593	−	0.991436i	$-0.458312\pi$
$797$	31.6762	−	31.6762i	1.12203	−	1.12203i	0.991436	−	0.130593i	$-0.0416882\pi$
$798$	−2.19519	+	9.04715i	−0.0777089	+	0.320266i
$799$	−29.6732			−1.04976
$800$	−13.0949	+	25.0704i	−0.462973	+	0.886372i
$801$	−10.9864	−	19.0290i	−0.388185	−	0.672357i
$802$	−49.0632	+	7.46861i	−1.73248	+	0.263726i
$803$	1.56351	+	5.83510i	0.0551751	+	0.205916i
$804$	−3.42702	−	3.16118i	−0.120862	−	0.111486i
$805$	8.58851	−	38.0423i	0.302705	−	1.34082i
$806$	−1.32278	−	3.01978i	−0.0465931	−	0.106367i
$807$	−9.04083	+	2.42248i	−0.318252	+	0.0852754i
$808$	3.41977	+	2.30961i	0.120307	+	0.0812517i
$809$	40.9623	−	23.6496i	1.44016	−	0.831475i	0.442298	−	0.896868i	$-0.354163\pi$
$809$	40.9623	−	23.6496i	1.44016	−	0.831475i	0.997860	+	0.0653930i	$0.0208301\pi$
$810$	−7.55117	−	6.74503i	−0.265321	−	0.236996i
$811$			5.30651i			0.186337i	0.995650	+	0.0931683i	$0.0296995\pi$
$811$			5.30651i			0.186337i	−0.995650	+	0.0931683i	$0.970301\pi$
$812$	−8.44698	+	23.2290i	−0.296431	+	0.815179i
$813$	−14.0864	−	14.0864i	−0.494033	−	0.494033i
$814$	1.88736	−	16.9742i	0.0661518	−	0.594945i
$815$	1.61206	+	0.153178i	0.0564680	+	0.00536561i
$816$	−11.4740	−	16.6192i	−0.401671	−	0.581789i
$817$	3.52210	+	13.1447i	0.123223	+	0.459874i
$818$	−48.5233	−	18.9620i	−1.69658	−	0.662991i
$819$	−2.11558	+	0.286264i	−0.0739242	+	0.0100029i
$820$	4.32042	+	2.81830i	0.150876	+	0.0984193i
$821$	3.34048	−	5.78588i	0.116584	−	0.201929i	−0.801828	−	0.597555i	$-0.796139\pi$
$821$	3.34048	−	5.78588i	0.116584	−	0.201929i	0.918412	+	0.395626i	$0.129472\pi$
$822$	−0.0882958	−	0.580038i	−0.00307967	−	0.0202311i
$823$	−29.6750	−	7.95140i	−1.03441	−	0.277168i	−0.298613	−	0.954374i	$-0.596524\pi$
$823$	−29.6750	−	7.95140i	−1.03441	−	0.277168i	−0.735794	+	0.677206i	$0.763191\pi$
$824$	−1.02325	−	1.17853i	−0.0356468	−	0.0410560i
$825$	−18.3153	−	8.87605i	−0.637658	−	0.309024i
$826$	2.78091	+	1.51863i	0.0967604	+	0.0528401i
$827$	−34.0292	−	34.0292i	−1.18331	−	1.18331i	−0.978882	−	0.204428i	$-0.934467\pi$
$827$	−34.0292	−	34.0292i	−1.18331	−	1.18331i	−0.204428	−	0.978882i	$-0.565533\pi$
$828$	−26.8694	−	14.1003i	−0.933776	−	0.490020i
$829$	3.90921	−	2.25698i	0.135773	−	0.0783883i	−0.430575	−	0.902555i	$-0.641689\pi$
$829$	3.90921	−	2.25698i	0.135773	−	0.0783883i	0.566348	+	0.824166i	$0.308356\pi$
$830$	−21.8457	+	43.2985i	−0.758274	+	1.50291i
$831$	3.97770	+	2.29653i	0.137985	+	0.0796657i
$832$	2.78421	−	0.338513i	0.0965252	−	0.0117358i
$833$	−36.7740	−	20.8803i	−1.27414	−	0.723460i
$834$	−3.02252	−	6.90010i	−0.104661	−	0.238931i
$835$	8.03248	−	3.67281i	0.277975	−	0.127103i
$836$	−28.2932	−	6.37058i	−0.978540	−	0.220331i
$837$	28.4571	+	7.62506i	0.983622	+	0.263561i
$838$	−28.0937	−	35.1227i	−0.970481	−	1.21329i
$839$	28.1768			0.972772			0.486386	−	0.873744i	$-0.338315\pi$
$839$	28.1768			0.972772			0.486386	+	0.873744i	$0.338315\pi$
$840$	−13.3907	−	4.03164i	−0.462023	−	0.139105i
$841$	7.18076			0.247612
$842$	11.5892	+	14.4888i	0.399389	+	0.499316i
$843$	24.0447	+	6.44276i	0.828144	+	0.221900i
$844$	4.82687	+	1.08683i	0.166148	+	0.0374103i
$845$	26.9832	+	10.0500i	0.928251	+	0.345729i
$846$	6.41468	+	14.6440i	0.220541	+	0.503472i
$847$	−26.7799	−	20.3963i	−0.920167	−	0.700826i
$848$	−0.829055	+	0.974876i	−0.0284699	+	0.0334774i
$849$	−15.6876	−	9.05723i	−0.538396	−	0.310843i
$850$	12.6324	−	40.8073i	0.433288	−	1.39968i
$851$	−14.1551	+	8.17246i	−0.485231	+	0.280148i
$852$	−9.61900	−	5.04779i	−0.329541	−	0.172934i
$853$	7.11404	+	7.11404i	0.243580	+	0.243580i	0.818329	−	0.574749i	$-0.194900\pi$
$853$	7.11404	+	7.11404i	0.243580	+	0.243580i	−0.574749	+	0.818329i	$0.694900\pi$
$854$	0.897094	+	37.7481i	0.0306979	+	1.29171i
$855$	2.54782	+	15.1085i	0.0871336	+	0.516699i
$856$	−10.6208	+	9.22148i	−0.363011	+	0.315184i
$857$	−21.4508	−	5.74773i	−0.732746	−	0.196339i	−0.126894	−	0.991916i	$-0.540501\pi$
$857$	−21.4508	−	5.74773i	−0.732746	−	0.196339i	−0.605852	+	0.795578i	$0.707168\pi$
$858$	0.303723	+	1.99523i	0.0103689	+	0.0681161i
$859$	−9.63913	+	16.6955i	−0.328883	+	0.569642i	−0.982290	−	0.187364i	$-0.940005\pi$
$859$	−9.63913	+	16.6955i	−0.328883	+	0.569642i	0.653408	+	0.757006i	$0.273339\pi$
$860$	−20.0037	+	4.20915i	−0.682120	+	0.143531i
$861$	−0.967529	+	2.35979i	−0.0329733	+	0.0804213i
$862$	25.9190	+	10.1287i	0.882804	+	0.344983i
$863$	4.28964	+	16.0091i	0.146021	+	0.544958i	0.999708	+	0.0241711i	$0.00769465\pi$
$863$	4.28964	+	16.0091i	0.146021	+	0.544958i	−0.853687	+	0.520787i	$0.825639\pi$
$864$	−13.1789	+	21.3191i	−0.448355	+	0.725291i
$865$	−4.77626	+	50.2657i	−0.162398	+	1.70908i
$866$	2.78918	−	25.0849i	0.0947803	−	0.852420i
$867$	11.5214	+	11.5214i	0.391286	+	0.391286i
$868$	−34.6486	+	6.11993i	−1.17605	+	0.207724i
$869$			43.3219i			1.46960i
$870$	−0.695002	−	12.3253i	−0.0235628	−	0.417866i
$871$	−0.846911	+	0.488964i	−0.0286965	+	0.0165679i
$872$	−17.7364	+	26.2617i	−0.600629	+	0.889333i
$873$	7.41657	−	1.98726i	0.251013	−	0.0672587i
$874$	11.1364	+	25.4232i	0.376694	+	0.859952i
$875$	−10.8038	−	27.5368i	−0.365236	−	0.930915i
$876$	−1.52379	−	1.40559i	−0.0514842	−	0.0474904i
$877$	−10.0222	−	37.4032i	−0.338424	−	1.26302i	−0.900109	−	0.435665i	$-0.856513\pi$
$877$	−10.0222	−	37.4032i	−0.338424	−	1.26302i	0.561685	−	0.827351i	$-0.310153\pi$
$878$	6.56491	−	0.999338i	0.221555	−	0.0337260i
$879$	−1.68525	−	2.91893i	−0.0568419	−	0.0984531i
$880$	11.8665	−	41.9171i	0.400020	−	1.41303i
$881$	34.3504			1.15729			0.578647	−	0.815578i	$-0.303581\pi$
$881$	34.3504			1.15729			0.578647	+	0.815578i	$0.303581\pi$
$882$	−2.35493	+	22.6622i	−0.0792947	+	0.763076i
$883$	34.1114	−	34.1114i	1.14794	−	1.14794i	0.160984	−	0.986957i	$-0.448533\pi$
$883$	34.1114	−	34.1114i	1.14794	−	1.14794i	0.986957	−	0.160984i	$-0.0514666\pi$
$884$	−4.04410	+	1.26043i	−0.136018	+	0.0423928i
$885$	−1.57542	−	0.149697i	−0.0529572	−	0.00503201i
$886$	−3.48753	+	4.73995i	−0.117166	+	0.159242i
$887$	40.4245	−	10.8317i	1.35732	−	0.363693i	0.494490	−	0.869184i	$-0.335355\pi$
$887$	40.4245	−	10.8317i	1.35732	−	0.363693i	0.862832	+	0.505490i	$0.168688\pi$
$888$	2.56615	+	5.26929i	0.0861142	+	0.176826i
$889$	−16.1943	+	12.5191i	−0.543139	+	0.419877i
$890$	−29.5550	−	6.15962i	−0.990687	−	0.206471i
$891$	13.5056	+	7.79744i	0.452454	+	0.261224i
$892$	−10.6680	−	16.8682i	−0.357193	−	0.564789i
$893$	3.78478	−	14.1250i	0.126653	−	0.472674i
$894$	0.762462	−	6.85731i	0.0255005	−	0.229343i
$895$	−20.5679	+	3.46847i	−0.687509	+	0.115938i
$896$	3.49567	−	29.7284i	0.116782	−	0.993158i
$897$	1.36577	−	1.36577i	0.0456018	−	0.0456018i
$898$	45.6706	−	36.5306i	1.52405	−	1.21904i
$899$	−15.5298	−	26.8985i	−0.517949	−	0.897114i
$900$	−22.8696	+	2.58739i	−0.762321	+	0.0862462i
$901$	0.966393	−	1.67384i	0.0321952	−	0.0557637i
$902$	−7.40015	−	2.89184i	−0.246398	−	0.0962877i
$903$	−3.90130	−	9.32359i	−0.129827	−	0.310270i
$904$	−22.2624	−	7.68031i	−0.740437	−	0.255443i
$905$	−10.7616	+	28.8938i	−0.357726	+	0.960461i
$906$	−3.52784	−	2.59569i	−0.117205	−	0.0862361i
$907$	7.45963	−	27.8397i	0.247693	−	0.924403i	−0.724318	−	0.689466i	$-0.757845\pi$
$907$	7.45963	−	27.8397i	0.247693	−	0.924403i	0.972011	−	0.234936i	$-0.0754882\pi$
$908$	−36.0781	−	18.9328i	−1.19730	−	0.628308i
$909$			3.35793i			0.111375i
$910$	−1.64307	+	2.42986i	−0.0544673	+	0.0805490i
$911$		−	19.1234i		−	0.633586i	−0.948495	−	0.316793i	$-0.897394\pi$
$911$		−	19.1234i		−	0.633586i	0.948495	−	0.316793i	$-0.102606\pi$
$912$	9.37453	−	3.34207i	0.310422	−	0.110667i
$913$	19.3331	−	72.1521i	0.639832	−	2.38789i
$914$	−19.4276	+	26.4043i	−0.642607	+	0.873376i
$915$	−7.84203	−	17.1506i	−0.259249	−	0.566981i
$916$	12.9461	−	14.0348i	0.427751	−	0.463723i
$917$	−9.12594	+	11.9821i	−0.301365	+	0.395684i
$918$	13.7779	−	35.2573i	0.454738	−	1.16366i
$919$	−13.6744	+	23.6848i	−0.451077	+	0.781289i	−0.998453	−	0.0555980i	$-0.982293\pi$
$919$	−13.6744	+	23.6848i	−0.451077	+	0.781289i	0.547376	+	0.836887i	$0.315627\pi$
$920$	−39.0425	+	14.6270i	−1.28719	+	0.482238i
$921$	2.11703	+	3.66680i	0.0697585	+	0.120825i
$922$	14.9405	+	18.6786i	0.492039	+	0.615146i
$923$	−1.61116	+	1.61116i	−0.0530319	+	0.0530319i
$924$	21.4580	+	1.87100i	0.705915	+	0.0615515i
$925$	−5.40656	+	11.1562i	−0.177767	+	0.366814i
$926$	44.4346	+	4.94066i	1.46021	+	0.162360i
$927$	0.328707	−	1.22675i	0.0107962	−	0.0402918i
$928$	25.7175	−	6.06837i	0.844219	−	0.199204i
$929$	12.9501	+	7.47676i	0.424880	+	0.245305i	0.697163	−	0.716913i	$-0.254445\pi$
$929$	12.9501	+	7.47676i	0.424880	+	0.245305i	−0.272283	+	0.962217i	$0.587779\pi$
$930$	14.6998	−	9.62931i	0.482025	−	0.315758i
$931$	14.6299	−	14.8418i	0.479475	−	0.486421i
$932$	−1.65092	−	40.9133i	−0.0540776	−	1.34016i
$933$	19.8613	−	5.32182i	0.650230	−	0.174229i
$934$	−9.77450	−	7.19181i	−0.319831	−	0.235323i
$935$	−6.22388	+	65.5005i	−0.203543	+	2.14210i
$936$	1.49628	+	1.72333i	0.0489073	+	0.0563287i
$937$	22.4138	−	22.4138i	0.732226	−	0.732226i	−0.238835	−	0.971060i	$-0.576765\pi$
$937$	22.4138	−	22.4138i	0.732226	−	0.732226i	0.971060	+	0.238835i	$0.0767653\pi$
$938$	2.94003	+	10.0143i	0.0959954	+	0.326978i
$939$	5.61967			0.183391
$940$	20.8772	+	6.83067i	0.680939	+	0.222792i
$941$	12.6079	+	21.8376i	0.411007	+	0.711884i	0.995000	−	0.0998741i	$-0.0318440\pi$
$941$	12.6079	+	21.8376i	0.411007	+	0.711884i	−0.583994	+	0.811758i	$0.698511\pi$
$942$	1.96377	+	12.9005i	0.0639832	+	0.420322i
$943$	1.96799	+	7.34462i	0.0640864	+	0.239174i
$944$	−0.272924	−	3.37631i	−0.00888292	−	0.109890i
$945$	−7.78527	−	25.0294i	−0.253255	−	0.814206i
$946$	28.8395	−	12.6329i	0.937655	−	0.410731i
$947$	20.9252	−	5.60688i	0.679976	−	0.182199i	0.0977318	−	0.995213i	$-0.468841\pi$
$947$	20.9252	−	5.60688i	0.679976	−	0.182199i	0.582245	+	0.813014i	$0.302175\pi$
$948$	−7.94645	−	12.5648i	−0.258089	−	0.408087i
$949$	−0.376571	+	0.217413i	−0.0122240	+	0.00705754i
$950$	17.8137	+	11.2182i	0.577954	+	0.363965i
$951$			11.5490i			0.374503i
$952$	2.89544	+	45.1155i	0.0938418	+	1.46220i
$953$	22.8157	+	22.8157i	0.739074	+	0.739074i	0.972399	−	0.233325i	$-0.0749605\pi$
$953$	22.8157	+	22.8157i	0.739074	+	0.739074i	−0.233325	+	0.972399i	$0.574960\pi$
$954$	−1.03497	−	0.115078i	−0.0335083	−	0.00372578i
$955$	−0.298189	+	0.246439i	−0.00964918	+	0.00797457i
$956$	−11.2394	+	49.9168i	−0.363509	+	1.61443i
$957$	4.92119	+	18.3661i	0.159079	+	0.593692i
$958$	−12.4529	+	31.8667i	−0.402336	+	1.02957i
$959$	−0.498251	+	1.21523i	−0.0160894	+	0.0392417i
$960$	4.24709	+	14.3341i	0.137074	+	0.462630i
$961$	6.60673	−	11.4432i	0.213120	−	0.369135i
$962$	1.21533	−	0.185003i	0.0391838	−	0.00596473i
$963$	−11.0554	−	2.96228i	−0.356254	−	0.0954580i
$964$	30.5983	−	9.53660i	0.985505	−	0.307153i
$965$	−17.1496	−	12.2002i	−0.552064	−	0.392737i
$966$	−10.7281	−	17.6022i	−0.345172	−	0.566341i
$967$	−11.0053	−	11.0053i	−0.353908	−	0.353908i	0.507654	−	0.861561i	$-0.330513\pi$
$967$	−11.0053	−	11.0053i	−0.353908	−	0.353908i	−0.861561	+	0.507654i	$0.830513\pi$
$968$	−2.53156	+	35.8977i	−0.0813675	+	1.15380i
$969$	−13.0174	+	7.51561i	−0.418180	+	0.241436i
$970$	4.75210	−	9.41875i	0.152581	−	0.302418i
$971$	−15.7328	−	9.08331i	−0.504888	−	0.291497i	0.225842	−	0.974164i	$-0.427487\pi$
$971$	−15.7328	−	9.08331i	−0.504888	−	0.291497i	−0.730730	+	0.682667i	$0.760820\pi$
$972$	−31.9098	+	1.28761i	−1.02351	+	0.0413002i
$973$	−2.14095	+	16.7267i	−0.0686357	+	0.536234i
$974$	24.0094	−	10.5171i	0.769310	−	0.336989i
$975$	0.275917	−	1.43877i	0.00883641	−	0.0460777i
$976$	33.2180	−	22.9339i	1.06328	−	0.734097i
$977$	−0.733186	−	0.196456i	−0.0234567	−	0.00628520i	0.247072	−	0.968997i	$-0.420532\pi$
$977$	−0.733186	−	0.196456i	−0.0234567	−	0.00628520i	−0.270528	+	0.962712i	$0.587198\pi$
$978$	0.668397	−	0.534633i	0.0213730	−	0.0170957i
$979$	46.4999			1.48614
$980$	21.0665	+	23.1560i	0.672946	+	0.739692i
$981$	−25.7868			−0.823310
$982$	−29.0791	+	23.2596i	−0.927951	+	0.742243i
$983$	−32.5127	−	8.71176i	−1.03699	−	0.277862i	−0.300127	−	0.953899i	$-0.597029\pi$
$983$	−32.5127	−	8.71176i	−1.03699	−	0.277862i	−0.736867	+	0.676037i	$0.763696\pi$
$984$	2.67674	−	0.518662i	0.0853314	−	0.0165343i
$985$	−14.0265	−	30.6762i	−0.446923	−	0.977424i
$986$	−36.5547	+	16.0124i	−1.16414	+	0.509940i
$987$	−1.37887	+	10.7728i	−0.0438900	+	0.342901i
$988$	−0.0841666	−	2.08583i	−0.00267770	−	0.0663591i
$989$	−26.0952	−	15.0661i	−0.829779	−	0.479073i
$990$	33.6706	−	11.0882i	1.07012	−	0.352405i
$991$	−25.1531	+	14.5222i	−0.799016	+	0.461312i	−0.843127	−	0.537715i	$-0.819288\pi$
$991$	−25.1531	+	14.5222i	−0.799016	+	0.461312i	0.0441111	+	0.999027i	$0.485954\pi$
$992$	25.7855	+	27.3851i	0.818689	+	0.869476i
$993$	1.10577	+	1.10577i	0.0350906	+	0.0350906i
$994$	12.6556	+	20.7647i	0.401413	+	0.658617i
$995$	37.8373	−	6.38071i	1.19952	−	0.202282i
$996$	7.62746	+	24.4728i	0.241685	+	0.775451i
$997$	45.9271	+	12.3061i	1.45453	+	0.389739i	0.897596	−	0.440820i	$-0.145312\pi$
$997$	45.9271	+	12.3061i	1.45453	+	0.389739i	0.556931	+	0.830559i	$0.311979\pi$
$998$	−15.1364	+	2.30412i	−0.479133	+	0.0729357i
$999$	−5.49282	+	9.51384i	−0.173785	+	0.301004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.12	yes	72
4.3	odd	2	inner	140.2.w.b.23.9	✓	72
5.2	odd	4	inner	140.2.w.b.107.4	yes	72
5.3	odd	4		700.2.be.e.107.15		72
5.4	even	2		700.2.be.e.443.7		72
7.2	even	3		980.2.k.k.883.12		36
7.3	odd	6		980.2.x.m.263.1		72
7.4	even	3	inner	140.2.w.b.123.1	yes	72
7.5	odd	6		980.2.k.j.883.12		36
7.6	odd	2		980.2.x.m.863.12		72
20.3	even	4		700.2.be.e.107.18		72
20.7	even	4	inner	140.2.w.b.107.1	yes	72
20.19	odd	2		700.2.be.e.443.10		72
28.3	even	6		980.2.x.m.263.4		72
28.11	odd	6	inner	140.2.w.b.123.4	yes	72
28.19	even	6		980.2.k.j.883.16		36
28.23	odd	6		980.2.k.k.883.16		36
28.27	even	2		980.2.x.m.863.9		72
35.2	odd	12		980.2.k.k.687.16		36
35.4	even	6		700.2.be.e.543.18		72
35.12	even	12		980.2.k.j.687.16		36
35.17	even	12		980.2.x.m.67.9		72
35.18	odd	12		700.2.be.e.207.10		72
35.27	even	4		980.2.x.m.667.4		72
35.32	odd	12	inner	140.2.w.b.67.9	yes	72
140.27	odd	4		980.2.x.m.667.1		72
140.39	odd	6		700.2.be.e.543.15		72
140.47	odd	12		980.2.k.j.687.12		36
140.67	even	12	inner	140.2.w.b.67.12	yes	72
140.87	odd	12		980.2.x.m.67.12		72
140.107	even	12		980.2.k.k.687.12		36
140.123	even	12		700.2.be.e.207.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.9	✓	72	4.3	odd	2	inner
140.2.w.b.23.12	yes	72	1.1	even	1	trivial
140.2.w.b.67.9	yes	72	35.32	odd	12	inner
140.2.w.b.67.12	yes	72	140.67	even	12	inner
140.2.w.b.107.1	yes	72	20.7	even	4	inner
140.2.w.b.107.4	yes	72	5.2	odd	4	inner
140.2.w.b.123.1	yes	72	7.4	even	3	inner
140.2.w.b.123.4	yes	72	28.11	odd	6	inner
700.2.be.e.107.15		72	5.3	odd	4
700.2.be.e.107.18		72	20.3	even	4
700.2.be.e.207.7		72	140.123	even	12
700.2.be.e.207.10		72	35.18	odd	12
700.2.be.e.443.7		72	5.4	even	2
700.2.be.e.443.10		72	20.19	odd	2
700.2.be.e.543.15		72	140.39	odd	6
700.2.be.e.543.18		72	35.4	even	6
980.2.k.j.687.12		36	140.47	odd	12
980.2.k.j.687.16		36	35.12	even	12
980.2.k.j.883.12		36	7.5	odd	6
980.2.k.j.883.16		36	28.19	even	6
980.2.k.k.687.12		36	140.107	even	12
980.2.k.k.687.16		36	35.2	odd	12
980.2.k.k.883.12		36	7.2	even	3
980.2.k.k.883.16		36	28.23	odd	6
980.2.x.m.67.9		72	35.17	even	12
980.2.x.m.67.12		72	140.87	odd	12
980.2.x.m.263.1		72	7.3	odd	6
980.2.x.m.263.4		72	28.3	even	6
980.2.x.m.667.1		72	140.27	odd	4
980.2.x.m.667.4		72	35.27	even	4
980.2.x.m.863.9		72	28.27	even	2
980.2.x.m.863.12		72	7.6	odd	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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.883367 + 1.10438i) q^{2} +(0.807254 + 0.216303i) q^{3} +(-0.439327 + 1.95115i) q^{4} +(-0.780454 + 2.09545i) q^{5} +(0.474220 + 1.08259i) q^{6} +(0.335905 - 2.62434i) q^{7} +(-2.54291 + 1.23840i) q^{8} +(-1.99320 - 1.15078i) q^{9} +(-3.00360 + 0.989126i) q^{10} +(4.21811 - 2.43533i) q^{11} +(-0.776689 + 1.48005i) q^{12} +(0.247904 + 0.247904i) q^{13} +(3.19501 - 1.94729i) q^{14} +(-1.08328 + 1.52274i) q^{15} +(-3.61398 - 1.71439i) q^{16} +(5.83537 + 1.56358i) q^{17} +(-0.489830 - 3.21782i) q^{18} +(-1.48858 + 2.57830i) q^{19} +(-3.74566 - 2.44337i) q^{20} +(0.838814 - 2.04585i) q^{21} +(6.41567 + 2.50713i) q^{22} +(-1.70618 - 6.36754i) q^{23} +(-2.32064 + 0.449662i) q^{24} +(-3.78178 - 3.27080i) q^{25} +(-0.0547911 + 0.492771i) q^{26} +(-3.13296 - 3.13296i) q^{27} +(4.97292 + 1.80835i) q^{28} +4.67111i q^{29} +(-2.63862 + 0.148788i) q^{30} +(-5.75848 + 3.32466i) q^{31} +(-1.29913 - 5.50566i) q^{32} +(3.93186 - 1.05354i) q^{33} +(3.42797 + 7.82570i) q^{34} +(5.23701 + 2.75205i) q^{35} +(3.12101 - 3.38347i) q^{36} +(-0.641729 - 2.39496i) q^{37} +(-4.16240 + 0.633619i) q^{38} +(0.146499 + 0.253744i) q^{39} +(-0.610370 - 6.29503i) q^{40} -1.15345 q^{41} +(3.00039 - 0.880866i) q^{42} +(3.23212 - 3.23212i) q^{43} +(2.89856 + 9.30008i) q^{44} +(3.96699 - 3.27852i) q^{45} +(5.52503 - 7.50914i) q^{46} +(-4.74443 + 1.27127i) q^{47} +(-2.54658 - 2.16566i) q^{48} +(-6.77434 - 1.76306i) q^{49} +(0.271513 - 7.06585i) q^{50} +(4.37242 + 2.52442i) q^{51} +(-0.592609 + 0.374787i) q^{52} +(0.0828048 - 0.309032i) q^{53} +(0.692438 - 6.22754i) q^{54} +(1.81106 + 10.7395i) q^{55} +(2.39580 + 7.08944i) q^{56} +(-1.75936 + 1.75936i) q^{57} +(-5.15869 + 4.12630i) q^{58} +(0.423416 + 0.733378i) q^{59} +(-2.49519 - 2.78262i) q^{60} +(-5.04573 + 8.73945i) q^{61} +(-8.75855 - 3.42268i) q^{62} +(-3.68956 + 4.84429i) q^{63} +(4.93275 - 6.29825i) q^{64} +(-0.712947 + 0.325992i) q^{65} +(4.63678 + 3.41162i) q^{66} +(-0.721946 + 2.69434i) q^{67} +(-5.61442 + 10.6988i) q^{68} -5.50928i q^{69} +(1.58688 + 8.21473i) q^{70} +6.49911i q^{71} +(6.49365 + 0.457943i) q^{72} +(-0.321006 + 1.19801i) q^{73} +(2.07808 - 2.82435i) q^{74} +(-2.34538 - 3.45838i) q^{75} +(-4.37668 - 4.03717i) q^{76} +(-4.97424 - 11.8878i) q^{77} +(-0.150818 + 0.385940i) q^{78} +(-4.44724 + 7.70284i) q^{79} +(6.41295 - 6.23490i) q^{80} +(1.60090 + 2.77285i) q^{81} +(-1.01892 - 1.27385i) q^{82} +(10.8443 - 10.8443i) q^{83} +(3.62326 + 2.53545i) q^{84} +(-7.83063 + 11.0074i) q^{85} +(6.42465 + 0.714354i) q^{86} +(-1.01038 + 3.77077i) q^{87} +(-7.71036 + 11.4165i) q^{88} +(8.26789 + 4.77347i) q^{89} +(7.12505 + 1.48495i) q^{90} +(0.733857 - 0.567313i) q^{91} +(13.1736 - 0.531576i) q^{92} +(-5.36769 + 1.43827i) q^{93} +(-5.59504 - 4.11668i) q^{94} +(-4.24092 - 5.13149i) q^{95} +(0.142163 - 4.72547i) q^{96} +(-2.35897 + 2.35897i) q^{97} +(-4.03713 - 9.03889i) q^{98} -11.2101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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