LMFDB - Embedded newform 462.2.y.d.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	462.25
Dual form			462.2.y.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.0415637 + 0.395452i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.168521 + 2.64038i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.198815 + 0.344358i) q^{10} +(-2.37271 + 2.31738i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.60680 + 1.89395i) q^{13} +(-1.22789 + 2.34356i) q^{14} +(-0.122875 + 0.378169i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.72165 - 2.54744i) q^{17} +(0.669131 + 0.743145i) q^{18} +(3.36660 - 3.73899i) q^{19} +(-0.321690 + 0.233721i) q^{20} +(-0.713804 + 2.54764i) q^{21} +(-3.11014 + 1.15196i) q^{22} +(-3.00849 - 5.21086i) q^{23} +(0.104528 + 0.994522i) q^{24} +(4.73608 + 1.00669i) q^{25} +(-3.15177 + 0.669930i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.07495 + 1.64152i) q^{28} +(1.61120 - 4.95877i) q^{29} +(-0.266067 + 0.295497i) q^{30} +(0.0330720 + 0.314659i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.80267 + 1.77342i) q^{33} +6.26312 q^{34} +(-1.03714 - 0.176386i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-3.19633 + 0.679401i) q^{37} +(4.59633 - 2.04642i) q^{38} +(-2.94361 + 1.31058i) q^{39} +(-0.388941 + 0.0826720i) q^{40} +(2.86189 + 8.80800i) q^{41} +(-1.68831 + 2.03706i) q^{42} -2.62440 q^{43} +(-3.30980 - 0.212643i) q^{44} +(-0.198815 + 0.344358i) q^{45} +(-0.628946 - 5.98402i) q^{46} +(5.26550 - 5.84793i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-6.94320 - 0.889920i) q^{49} +(3.91717 + 2.84599i) q^{50} +(6.12626 - 1.30218i) q^{51} +(-3.15177 - 0.669930i) q^{52} +(-1.22064 - 11.6136i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.817793 - 1.03461i) q^{55} +(-2.56323 + 0.655649i) q^{56} +(4.07042 - 2.95733i) q^{57} +(3.48882 - 3.87473i) q^{58} +(-5.29985 - 5.88608i) q^{59} +(-0.363254 + 0.161731i) q^{60} +(0.383995 - 3.65347i) q^{61} +(-0.0977705 + 0.300907i) q^{62} +(-1.22789 + 2.34356i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.640620 - 1.10959i) q^{65} +(-3.28168 + 0.480151i) q^{66} +(-7.15234 + 12.3882i) q^{67} +(5.72165 + 2.54744i) q^{68} +(-1.85935 - 5.72249i) q^{69} +(-0.875731 - 0.582979i) q^{70} +(-4.67285 - 3.39502i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(5.49108 + 6.09846i) q^{73} +(-3.19633 - 0.679401i) q^{74} +(4.42329 + 1.96937i) q^{75} +5.03131 q^{76} +(-5.71890 - 6.65539i) q^{77} -3.22219 q^{78} +(-0.608200 - 0.270788i) q^{79} +(-0.388941 - 0.0826720i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.968067 + 9.21054i) q^{82} +(7.09793 + 5.15695i) q^{83} +(-2.37090 + 1.17425i) q^{84} +(0.769579 + 2.36852i) q^{85} +(-2.39751 - 1.06744i) q^{86} +(2.60698 - 4.51542i) q^{87} +(-2.93716 - 1.54048i) q^{88} +(2.97452 + 5.15202i) q^{89} +(-0.321690 + 0.233721i) q^{90} +(-4.56145 - 7.20212i) q^{91} +(1.85935 - 5.72249i) q^{92} +(-0.0330720 + 0.314659i) q^{93} +(7.18884 - 3.20068i) q^{94} +(1.33866 + 1.48674i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(12.7158 - 9.23855i) q^{97} +(-5.98097 - 3.63704i) q^{98} +(-3.11014 + 1.15196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	−0.0415637	+	0.395452i	−0.0185879	+	0.176852i	−0.999877	−	0.0156886i	$-0.995006\pi$
$5$	−0.0415637	+	0.395452i	−0.0185879	+	0.176852i	0.981289	+	0.192540i	$0.0616726\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−0.168521	+	2.64038i	−0.0636951	+	0.997969i
$7$	−0.168521	+	2.64038i	−0.0636951	+	0.997969i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−0.198815	+	0.344358i	−0.0628709	+	0.108896i
$11$	−2.37271	+	2.31738i	−0.715400	+	0.698715i
$11$	−2.37271	+	2.31738i	−0.715400	+	0.698715i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.60680	+	1.89395i	−0.722997	+	0.525288i	−0.887340	−	0.461115i	$-0.847450\pi$
$13$	−2.60680	+	1.89395i	−0.722997	+	0.525288i	0.164343	+	0.986403i	$0.447450\pi$
$14$	−1.22789	+	2.34356i	−0.328168	+	0.626343i
$15$	−0.122875	+	0.378169i	−0.0317261	+	0.0976429i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	5.72165	−	2.54744i	1.38770	−	0.617845i	0.429274	−	0.903174i	$-0.358770\pi$
$17$	5.72165	−	2.54744i	1.38770	−	0.617845i	0.958430	+	0.285329i	$0.0921029\pi$
$18$	0.669131	+	0.743145i	0.157716	+	0.175161i
$19$	3.36660	−	3.73899i	0.772352	−	0.857784i	−0.220715	−	0.975338i	$-0.570839\pi$
$19$	3.36660	−	3.73899i	0.772352	−	0.857784i	0.993066	+	0.117555i	$0.0375056\pi$
$20$	−0.321690	+	0.233721i	−0.0719321	+	0.0522617i
$21$	−0.713804	+	2.54764i	−0.155765	+	0.555941i
$22$	−3.11014	+	1.15196i	−0.663085	+	0.245598i
$23$	−3.00849	−	5.21086i	−0.627314	−	1.08654i	−0.988089	−	0.153887i	$-0.950821\pi$
$23$	−3.00849	−	5.21086i	−0.627314	−	1.08654i	0.360775	−	0.932653i	$-0.382512\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	4.73608	+	1.00669i	0.947217	+	0.201337i
$26$	−3.15177	+	0.669930i	−0.618114	+	0.131384i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.07495	+	1.64152i	−0.392128	+	0.310219i
$29$	1.61120	−	4.95877i	0.299193	−	0.920821i	−0.682588	−	0.730804i	$-0.739146\pi$
$29$	1.61120	−	4.95877i	0.299193	−	0.920821i	0.981781	−	0.190018i	$-0.0608545\pi$
$30$	−0.266067	+	0.295497i	−0.0485769	+	0.0539501i
$31$	0.0330720	+	0.314659i	0.00593990	+	0.0565144i	0.997090	−	0.0762291i	$-0.0242880\pi$
$31$	0.0330720	+	0.314659i	0.00593990	+	0.0565144i	−0.991150	+	0.132743i	$0.957621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.80267	+	1.77342i	−0.487883	+	0.308713i
$34$	6.26312			1.07412
$35$	−1.03714	−	0.176386i	−0.175309	−	0.0298147i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−3.19633	+	0.679401i	−0.525473	+	0.111693i	−0.463008	−	0.886354i	$-0.653230\pi$
$37$	−3.19633	+	0.679401i	−0.525473	+	0.111693i	−0.0624657	+	0.998047i	$0.519896\pi$
$38$	4.59633	−	2.04642i	0.745623	−	0.331973i
$39$	−2.94361	+	1.31058i	−0.471355	+	0.209861i
$40$	−0.388941	+	0.0826720i	−0.0614970	+	0.0130716i
$41$	2.86189	+	8.80800i	0.446952	+	1.37558i	0.880328	+	0.474365i	$0.157322\pi$
$41$	2.86189	+	8.80800i	0.446952	+	1.37558i	−0.433376	+	0.901213i	$0.642678\pi$
$42$	−1.68831	+	2.03706i	−0.260512	+	0.314325i
$43$	−2.62440			−0.400218			−0.200109	−	0.979774i	$-0.564130\pi$
$43$	−2.62440			−0.400218			−0.200109	+	0.979774i	$0.564130\pi$
$44$	−3.30980	−	0.212643i	−0.498971	−	0.0320571i
$45$	−0.198815	+	0.344358i	−0.0296376	+	0.0513339i
$46$	−0.628946	−	5.98402i	−0.0927330	−	0.882296i
$47$	5.26550	−	5.84793i	0.768052	−	0.853008i	−0.224545	−	0.974464i	$-0.572089\pi$
$47$	5.26550	−	5.84793i	0.768052	−	0.853008i	0.992597	+	0.121455i	$0.0387562\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−6.94320	−	0.889920i	−0.991886	−	0.127131i
$50$	3.91717	+	2.84599i	0.553972	+	0.402484i
$51$	6.12626	−	1.30218i	0.857848	−	0.182341i
$52$	−3.15177	−	0.669930i	−0.437072	−	0.0929026i
$53$	−1.22064	−	11.6136i	−0.167668	−	1.59526i	−0.677857	−	0.735194i	$-0.737091\pi$
$53$	−1.22064	−	11.6136i	−0.167668	−	1.59526i	0.510189	−	0.860062i	$-0.329576\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−0.817793	−	1.03461i	−0.110271	−	0.139507i
$56$	−2.56323	+	0.655649i	−0.342525	+	0.0876147i
$57$	4.07042	−	2.95733i	0.539140	−	0.391708i
$58$	3.48882	−	3.87473i	0.458105	−	0.508777i
$59$	−5.29985	−	5.88608i	−0.689982	−	0.766302i	0.291766	−	0.956490i	$-0.405757\pi$
$59$	−5.29985	−	5.88608i	−0.689982	−	0.766302i	−0.981748	+	0.190188i	$0.939090\pi$
$60$	−0.363254	+	0.161731i	−0.0468958	+	0.0208794i
$61$	0.383995	−	3.65347i	0.0491655	−	0.467779i	−0.942045	−	0.335486i	$-0.891099\pi$
$61$	0.383995	−	3.65347i	0.0491655	−	0.467779i	0.991211	−	0.132293i	$-0.0422338\pi$
$62$	−0.0977705	+	0.300907i	−0.0124169	+	0.0382152i
$63$	−1.22789	+	2.34356i	−0.154700	+	0.295261i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.640620	−	1.10959i	−0.0794591	−	0.137627i
$66$	−3.28168	+	0.480151i	−0.403947	+	0.0591024i
$67$	−7.15234	+	12.3882i	−0.873797	+	1.51346i	−0.0157579	+	0.999876i	$0.505016\pi$
$67$	−7.15234	+	12.3882i	−0.873797	+	1.51346i	−0.858039	+	0.513585i	$0.828317\pi$
$68$	5.72165	+	2.54744i	0.693852	+	0.308923i
$69$	−1.85935	−	5.72249i	−0.223839	−	0.688907i
$70$	−0.875731	−	0.582979i	−0.104670	−	0.0696794i
$71$	−4.67285	−	3.39502i	−0.554565	−	0.402915i	0.274901	−	0.961473i	$-0.411355\pi$
$71$	−4.67285	−	3.39502i	−0.554565	−	0.402915i	−0.829466	+	0.558558i	$0.811355\pi$
$72$	−0.104528	+	0.994522i	−0.0123188	+	0.117206i
$73$	5.49108	+	6.09846i	0.642682	+	0.713771i	0.973182	−	0.230035i	$-0.0738842\pi$
$73$	5.49108	+	6.09846i	0.642682	+	0.713771i	−0.330500	+	0.943806i	$0.607217\pi$
$74$	−3.19633	−	0.679401i	−0.371566	−	0.0789787i
$75$	4.42329	+	1.96937i	0.510757	+	0.227404i
$76$	5.03131			0.577131
$77$	−5.71890	−	6.65539i	−0.651729	−	0.758452i
$78$	−3.22219			−0.364841
$79$	−0.608200	−	0.270788i	−0.0684278	−	0.0304660i	0.372237	−	0.928138i	$-0.378591\pi$
$79$	−0.608200	−	0.270788i	−0.0684278	−	0.0304660i	−0.440665	+	0.897672i	$0.645257\pi$
$80$	−0.388941	−	0.0826720i	−0.0434850	−	0.00924302i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.968067	+	9.21054i	−0.106905	+	1.01713i
$83$	7.09793	+	5.15695i	0.779100	+	0.566049i	0.904709	−	0.426031i	$-0.140089\pi$
$83$	7.09793	+	5.15695i	0.779100	+	0.566049i	−0.125609	+	0.992080i	$0.540089\pi$
$84$	−2.37090	+	1.17425i	−0.258686	+	0.128121i
$85$	0.769579	+	2.36852i	0.0834725	+	0.256902i
$86$	−2.39751	−	1.06744i	−0.258530	−	0.115105i
$87$	2.60698	−	4.51542i	0.279498	−	0.484104i
$88$	−2.93716	−	1.54048i	−0.313103	−	0.164215i
$89$	2.97452	+	5.15202i	0.315298	+	0.546113i	0.979501	−	0.201440i	$-0.0645621\pi$
$89$	2.97452	+	5.15202i	0.315298	+	0.546113i	−0.664202	+	0.747553i	$0.731229\pi$
$90$	−0.321690	+	0.233721i	−0.0339091	+	0.0246364i
$91$	−4.56145	−	7.20212i	−0.478170	−	0.754987i
$92$	1.85935	−	5.72249i	0.193851	−	0.596611i
$93$	−0.0330720	+	0.314659i	−0.00342940	+	0.0326286i
$94$	7.18884	−	3.20068i	0.741472	−	0.330125i
$95$	1.33866	+	1.48674i	0.137344	+	0.152536i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	12.7158	−	9.23855i	1.29109	−	0.938033i	0.291265	−	0.956642i	$-0.405924\pi$
$97$	12.7158	−	9.23855i	1.29109	−	0.938033i	0.999827	+	0.0186093i	$0.00592386\pi$
$98$	−5.98097	−	3.63704i	−0.604169	−	0.367396i
$99$	−3.11014	+	1.15196i	−0.312581	+	0.115776i
$100$	2.42094	+	4.19320i	0.242094	+	0.419320i
$101$	−1.45592	−	13.8521i	−0.144869	−	1.37834i	−0.789455	−	0.613808i	$-0.789637\pi$
$101$	−1.45592	−	13.8521i	−0.144869	−	1.37834i	0.644586	−	0.764532i	$-0.277030\pi$
$102$	6.12626	+	1.30218i	0.606590	+	0.128935i
$103$	−7.76389	+	1.65027i	−0.764998	+	0.162605i	−0.573855	−	0.818957i	$-0.694553\pi$
$103$	−7.76389	+	1.65027i	−0.764998	+	0.162605i	−0.191143	+	0.981562i	$0.561219\pi$
$104$	−2.60680	−	1.89395i	−0.255618	−	0.185717i
$105$	−0.977803	−	0.388165i	−0.0954238	−	0.0378810i
$106$	3.60858	−	11.1061i	0.350496	−	1.07872i
$107$	3.89993	−	4.33131i	0.377020	−	0.418723i	−0.524534	−	0.851389i	$-0.675760\pi$
$107$	3.89993	−	4.33131i	0.377020	−	0.418723i	0.901554	+	0.432666i	$0.142427\pi$
$108$	0.104528	+	0.994522i	0.0100583	+	0.0956979i
$109$	−6.50107	+	11.2602i	−0.622690	+	1.07853i	0.366293	+	0.930500i	$0.380627\pi$
$109$	−6.50107	+	11.2602i	−0.622690	+	1.07853i	−0.988983	+	0.148031i	$0.952706\pi$
$110$	−0.326276	−	1.27779i	−0.0311092	−	0.121833i
$111$	−3.26774			−0.310160
$112$	−2.60830	−	0.443593i	−0.246461	−	0.0419156i
$113$	−3.90848	−	12.0291i	−0.367679	−	1.13160i	−0.948286	−	0.317416i	$-0.897185\pi$
$113$	−3.90848	−	12.0291i	−0.367679	−	1.13160i	0.580607	−	0.814184i	$-0.302815\pi$
$114$	4.92136	−	1.04607i	0.460928	−	0.0979733i
$115$	2.18569	−	0.973132i	0.203817	−	0.0907451i
$116$	4.76319	−	2.12071i	0.442251	−	0.196903i
$117$	−3.15177	+	0.669930i	−0.291382	+	0.0619351i
$118$	−2.44757	−	7.53284i	−0.225317	−	0.693454i
$119$	5.76199	+	15.5366i	0.528201	+	1.42424i
$120$	−0.397631			−0.0362985
$121$	0.259538	−	10.9969i	0.0235943	−	0.999722i
$122$	1.83680	−	3.18142i	0.166296	−	0.288033i
$123$	0.968067	+	9.21054i	0.0872877	+	0.830487i
$124$	−0.211708	+	0.235125i	−0.0190119	+	0.0211149i
$125$	−1.20932	+	3.72190i	−0.108165	+	0.332897i
$126$	−2.07495	+	1.64152i	−0.184851	+	0.146238i
$127$	6.02970	+	4.38083i	0.535049	+	0.388736i	0.822243	−	0.569137i	$-0.192722\pi$
$127$	6.02970	+	4.38083i	0.535049	+	0.388736i	−0.287194	+	0.957872i	$0.592722\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	−2.56705	−	0.545644i	−0.226016	−	0.0480413i
$130$	−0.133926	−	1.27422i	−0.0117461	−	0.111757i
$131$	−2.74662	−	4.75728i	−0.239973	−	0.415646i	0.720733	−	0.693213i	$-0.243805\pi$
$131$	−2.74662	−	4.75728i	−0.239973	−	0.415646i	−0.960706	+	0.277567i	$0.910472\pi$
$132$	−3.19326	−	0.896142i	−0.277938	−	0.0779992i
$133$	9.30501	+	9.51921i	0.806847	+	0.825420i
$134$	−11.5727	+	8.40807i	−0.999731	+	0.726347i
$135$	−0.266067	+	0.295497i	−0.0228994	+	0.0254323i
$136$	4.19085	+	4.65441i	0.359362	+	0.399112i
$137$	−17.5484	+	7.81306i	−1.49926	+	0.667515i	−0.982098	−	0.188371i	$-0.939679\pi$
$137$	−17.5484	+	7.81306i	−1.49926	+	0.667515i	−0.517165	+	0.855886i	$0.673013\pi$
$138$	0.628946	−	5.98402i	0.0535394	−	0.509394i
$139$	−3.89057	+	11.9740i	−0.329994	+	1.01562i	0.639142	+	0.769089i	$0.279290\pi$
$139$	−3.89057	+	11.9740i	−0.329994	+	1.01562i	−0.969136	+	0.246528i	$0.920710\pi$
$140$	−0.562901	−	0.888770i	−0.0475739	−	0.0751148i
$141$	6.36629	−	4.62538i	0.536138	−	0.389527i
$142$	−2.88798	−	5.00213i	−0.242354	−	0.419769i
$143$	1.79619	−	10.5348i	0.150205	−	0.880960i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.89399	+	0.843259i	0.157287	+	0.0700289i
$146$	2.53588	+	7.80464i	0.209871	+	0.645917i
$147$	−6.60645	−	2.31405i	−0.544891	−	0.190859i
$148$	−2.64365	−	1.92073i	−0.217307	−	0.157883i
$149$	1.04344	−	9.92765i	0.0854818	−	0.813305i	−0.864843	−	0.502043i	$-0.832582\pi$
$149$	1.04344	−	9.92765i	0.0854818	−	0.813305i	0.950324	−	0.311261i	$-0.100751\pi$
$150$	3.23986	+	3.59823i	0.264533	+	0.293794i
$151$	−4.36034	−	0.926820i	−0.354840	−	0.0754235i	0.0270430	−	0.999634i	$-0.491391\pi$
$151$	−4.36034	−	0.926820i	−0.354840	−	0.0754235i	−0.381883	+	0.924211i	$0.624724\pi$
$152$	4.59633	+	2.04642i	0.372812	+	0.165986i
$153$	6.26312			0.506344
$154$	−2.51748	−	8.40609i	−0.202864	−	0.677382i
$155$	−0.125807			−0.0101051
$156$	−2.94361	−	1.31058i	−0.235678	−	0.104930i
$157$	11.5427	+	2.45347i	0.921204	+	0.195808i	0.644020	−	0.765009i	$-0.277265\pi$
$157$	11.5427	+	2.45347i	0.921204	+	0.195808i	0.277184	+	0.960817i	$0.410599\pi$
$158$	−0.445479	−	0.494754i	−0.0354404	−	0.0393605i
$159$	1.22064	−	11.6136i	0.0968033	−	0.921022i
$160$	−0.321690	−	0.233721i	−0.0254318	−	0.0184773i
$161$	14.2656	−	7.06542i	1.12429	−	0.556833i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−18.5786	−	8.27172i	−1.45519	−	0.647891i	−0.481638	−	0.876370i	$-0.659958\pi$
$163$	−18.5786	−	8.27172i	−1.45519	−	0.647891i	−0.973549	+	0.228479i	$0.926625\pi$
$164$	−4.63064	+	8.02050i	−0.361592	+	0.626296i
$165$	−0.584814	−	1.18203i	−0.0455277	−	0.0920212i
$166$	4.38677	+	7.59810i	0.340479	+	0.589727i
$167$	1.76999	−	1.28597i	0.136966	−	0.0995113i	−0.517193	−	0.855869i	$-0.673023\pi$
$167$	1.76999	−	1.28597i	0.136966	−	0.0995113i	0.654158	+	0.756358i	$0.273023\pi$
$168$	−2.64353	+	0.108397i	−0.203953	+	0.00836298i
$169$	−0.808858	+	2.48941i	−0.0622199	+	0.191493i
$170$	−0.260319	+	2.47677i	−0.0199655	+	0.189959i
$171$	4.59633	−	2.04642i	0.351490	−	0.156493i
$172$	−1.75607	−	1.95031i	−0.133899	−	0.148710i
$173$	−4.00765	+	4.45095i	−0.304696	+	0.338399i	−0.875975	−	0.482357i	$-0.839781\pi$
$173$	−4.00765	+	4.45095i	−0.304696	+	0.338399i	0.571279	+	0.820756i	$0.306448\pi$
$174$	4.21819	−	3.06469i	0.319780	−	0.232334i
$175$	−3.45616	+	12.3354i	−0.261261	+	0.932469i
$176$	−2.05667	−	2.60195i	−0.155027	−	0.196129i
$177$	−3.96025	−	6.85935i	−0.297671	−	0.515581i
$178$	0.621844	+	5.91645i	0.0466092	+	0.443457i
$179$	−1.32957	−	0.282609i	−0.0993767	−	0.0211232i	0.157955	−	0.987446i	$-0.449510\pi$
$179$	−1.32957	−	0.282609i	−0.0993767	−	0.0211232i	−0.257332	+	0.966323i	$0.582843\pi$
$180$	−0.388941	+	0.0826720i	−0.0289900	+	0.00616201i
$181$	20.5349	+	14.9195i	1.52635	+	1.10896i	0.958225	+	0.286017i	$0.0923313\pi$
$181$	20.5349	+	14.9195i	1.52635	+	1.10896i	0.568126	+	0.822942i	$0.307669\pi$
$182$	−1.23773	−	8.43477i	−0.0917465	−	0.625227i
$183$	1.13520	−	3.49379i	0.0839166	−	0.258269i
$184$	4.02615	−	4.47149i	0.296812	−	0.329643i
$185$	−0.135819	−	1.29223i	−0.00998563	−	0.0950069i
$186$	−0.158196	+	0.274003i	−0.0115995	+	0.0200909i
$187$	−7.67245	+	19.3036i	−0.561065	+	1.41162i
$188$	7.86917			0.573918
$189$	−1.68831	+	2.03706i	−0.122807	+	0.148174i
$190$	0.618220	+	1.90269i	0.0448504	+	0.138035i
$191$	−18.1836	+	3.86505i	−1.31572	+	0.279665i	−0.811725	−	0.584040i	$-0.801471\pi$
$191$	−18.1836	+	3.86505i	−1.31572	+	0.279665i	−0.503997	+	0.863706i	$0.668138\pi$
$192$	−0.913545	+	0.406737i	−0.0659295	+	0.0293537i
$193$	18.4383	−	8.20928i	1.32722	−	0.590917i	0.384077	−	0.923301i	$-0.374520\pi$
$193$	18.4383	−	8.20928i	1.32722	−	0.590917i	0.943144	+	0.332384i	$0.107853\pi$
$194$	15.3741	−	3.26787i	1.10380	−	0.234619i
$195$	−0.395925	−	1.21853i	−0.0283528	−	0.0872608i
$196$	−3.98457	−	5.75528i	−0.284612	−	0.411091i
$197$	13.3412			0.950520			0.475260	−	0.879845i	$-0.342354\pi$
$197$	13.3412			0.950520			0.475260	+	0.879845i	$0.342354\pi$
$198$	−3.30980	−	0.212643i	−0.235217	−	0.0151118i
$199$	−9.47838	+	16.4170i	−0.671904	+	1.16377i	0.305459	+	0.952205i	$0.401190\pi$
$199$	−9.47838	+	16.4170i	−0.671904	+	1.16377i	−0.977363	+	0.211567i	$0.932143\pi$
$200$	0.506115	+	4.81537i	0.0357878	+	0.340498i
$201$	−9.57169	+	10.6304i	−0.675135	+	0.749814i
$202$	4.30413	−	13.2467i	0.302837	−	0.932038i
$203$	12.8215	+	5.08985i	0.899894	+	0.357237i
$204$	5.06697	+	3.68137i	0.354759	+	0.257748i
$205$	−3.60209	+	0.765649i	−0.251581	+	0.0534752i
$206$	−7.76389	−	1.65027i	−0.540936	−	0.114979i
$207$	−0.628946	−	5.98402i	−0.0437148	−	0.415918i
$208$	−1.61109	−	2.79049i	−0.111709	−	0.193486i
$209$	0.676665	+	16.6732i	0.0468059	+	1.15331i
$210$	−0.735386	−	0.752315i	−0.0507465	−	0.0519146i
$211$	−7.03436	+	5.11076i	−0.484265	+	0.351839i	−0.802975	−	0.596013i	$-0.796751\pi$
$211$	−7.03436	+	5.11076i	−0.484265	+	0.351839i	0.318709	+	0.947852i	$0.396751\pi$
$212$	7.81385	−	8.67816i	0.536657	−	0.596018i
$213$	−3.86487	−	4.29237i	−0.264816	−	0.294109i
$214$	5.32446	−	2.37060i	0.363973	−	0.162051i
$215$	0.109080	−	1.03783i	0.00743919	−	0.0707791i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−0.836392	+	0.0342958i	−0.0567780	+	0.00232815i
$218$	−10.5190	+	7.64247i	−0.712434	+	0.517613i
$219$	4.10314	+	7.10685i	0.277265	+	0.480237i
$220$	0.221658	−	1.30003i	0.0149442	−	0.0876480i
$221$	−10.0905	+	17.4772i	−0.678759	+	1.17564i
$222$	−2.98523	−	1.32911i	−0.200355	−	0.0892039i
$223$	−4.25602	−	13.0987i	−0.285004	−	0.877154i	−0.986397	−	0.164379i	$-0.947438\pi$
$223$	−4.25602	−	13.0987i	−0.285004	−	0.877154i	0.701393	−	0.712775i	$-0.252562\pi$
$224$	−2.20237	−	1.46613i	−0.147152	−	0.0979601i
$225$	3.91717	+	2.84599i	0.261145	+	0.189733i
$226$	1.32209	−	12.5788i	0.0879440	−	0.836731i
$227$	10.9162	+	12.1236i	0.724532	+	0.804674i	0.987077	−	0.160245i	$-0.0512285\pi$
$227$	10.9162	+	12.1236i	0.724532	+	0.804674i	−0.262545	+	0.964920i	$0.584562\pi$
$228$	4.92136	+	1.04607i	0.325925	+	0.0692776i
$229$	−19.0047	−	8.46144i	−1.25587	−	0.559147i	−0.332512	−	0.943099i	$-0.607896\pi$
$229$	−19.0047	−	8.46144i	−1.25587	−	0.559147i	−0.923353	+	0.383952i	$0.874563\pi$
$230$	2.39254			0.157759
$231$	−4.21019	−	7.69898i	−0.277010	−	0.506556i
$232$	5.21396			0.342313
$233$	−4.63920	−	2.06551i	−0.303924	−	0.135316i	0.249108	−	0.968476i	$-0.419863\pi$
$233$	−4.63920	−	2.06551i	−0.303924	−	0.135316i	−0.553032	+	0.833160i	$0.686529\pi$
$234$	−3.15177	−	0.669930i	−0.206038	−	0.0437947i
$235$	2.09372	+	2.32532i	0.136579	+	0.151687i
$236$	0.827918	−	7.87711i	0.0538928	−	0.512756i
$237$	−0.538609	−	0.391322i	−0.0349864	−	0.0254191i
$238$	−1.05547	+	16.5370i	−0.0684159	+	1.07194i
$239$	5.78426	+	17.8021i	0.374153	+	1.15152i	0.944049	+	0.329807i	$0.106984\pi$
$239$	5.78426	+	17.8021i	0.374153	+	1.15152i	−0.569896	+	0.821717i	$0.693016\pi$
$240$	−0.363254	−	0.161731i	−0.0234479	−	0.0104397i
$241$	6.18350	−	10.7101i	0.398314	−	0.689901i	−0.595204	−	0.803575i	$-0.702929\pi$
$241$	6.18350	−	10.7101i	0.398314	−	0.689901i	0.993518	+	0.113674i	$0.0362619\pi$
$242$	4.70996	−	9.94064i	0.302768	−	0.639008i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.97200	−	2.15928i	0.190263	−	0.138234i
$245$	0.640506	−	2.70872i	0.0409204	−	0.173054i
$246$	−2.86189	+	8.80800i	−0.182468	+	0.561577i
$247$	−1.69460	+	16.1230i	−0.107825	+	1.02588i
$248$	−0.289038	+	0.128688i	−0.0183540	+	0.00817171i
$249$	5.87064	+	6.52000i	0.372037	+	0.413188i
$250$	−2.61860	+	2.90825i	−0.165615	+	0.183934i
$251$	−6.61755	+	4.80793i	−0.417696	+	0.303474i	−0.776710	−	0.629858i	$-0.783113\pi$
$251$	−6.61755	+	4.80793i	−0.417696	+	0.303474i	0.359014	+	0.933332i	$0.383113\pi$
$252$	−2.56323	+	0.655649i	−0.161468	+	0.0413020i
$253$	19.2138	+	5.39207i	1.20796	+	0.338997i
$254$	3.72656	+	6.45459i	0.233825	+	0.404997i
$255$	0.260319	+	2.47677i	0.0163018	+	0.155101i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	6.29294	−	1.33761i	0.392543	−	0.0834376i	−0.00741167	−	0.999973i	$-0.502359\pi$
$257$	6.29294	−	1.33761i	0.392543	−	0.0834376i	0.399955	+	0.916535i	$0.369026\pi$
$258$	−2.12319	−	1.54258i	−0.132184	−	0.0960371i
$259$	−1.25523	−	8.55401i	−0.0779959	−	0.531520i
$260$	0.395925	−	1.21853i	0.0245542	−	0.0755701i
$261$	3.48882	−	3.87473i	0.215953	−	0.239840i
$262$	−0.574199	−	5.46314i	−0.0354742	−	0.337514i
$263$	−12.9098	+	22.3605i	−0.796054	+	1.37881i	0.126114	+	0.992016i	$0.459749\pi$
$263$	−12.9098	+	22.3605i	−0.796054	+	1.37881i	−0.922168	+	0.386790i	$0.873584\pi$
$264$	−2.55270	−	2.11748i	−0.157108	−	0.130322i
$265$	4.64338			0.285240
$266$	4.62874	+	12.4809i	0.283806	+	0.765254i
$267$	1.83835	+	5.65787i	0.112505	+	0.346256i
$268$	−13.9921	+	2.97411i	−0.854702	+	0.181673i
$269$	−11.2372	+	5.00314i	−0.685146	+	0.305047i	−0.719629	−	0.694359i	$-0.755688\pi$
$269$	−11.2372	+	5.00314i	−0.685146	+	0.305047i	0.0344833	+	0.999405i	$0.489021\pi$
$270$	−0.363254	+	0.161731i	−0.0221069	+	0.00984263i
$271$	−4.55626	+	0.968463i	−0.276773	+	0.0588299i	−0.344207	−	0.938894i	$-0.611852\pi$
$271$	−4.55626	+	0.968463i	−0.276773	+	0.0588299i	0.0674338	+	0.997724i	$0.478519\pi$
$272$	1.93541	+	5.95658i	0.117352	+	0.361171i
$273$	−2.96437	−	7.99311i	−0.179412	−	0.483765i
$274$	−19.2091			−1.16047
$275$	−13.5702	+	8.58671i	−0.818316	+	0.517798i
$276$	3.00849	−	5.21086i	0.181090	−	0.313657i
$277$	−0.687049	−	6.53683i	−0.0412808	−	0.392760i	−0.995581	−	0.0939097i	$-0.970064\pi$
$277$	−0.687049	−	6.53683i	−0.0412808	−	0.392760i	0.954300	−	0.298850i	$-0.0966032\pi$
$278$	−8.42446	+	9.35631i	−0.505265	+	0.561154i
$279$	−0.0977705	+	0.300907i	−0.00585337	+	0.0180148i
$280$	−0.152741	−	1.04088i	−0.00912800	−	0.0622048i
$281$	11.7993	+	8.57267i	0.703885	+	0.511403i	0.881195	−	0.472752i	$-0.156740\pi$
$281$	11.7993	+	8.57267i	0.703885	+	0.511403i	−0.177310	+	0.984155i	$0.556740\pi$
$282$	7.69721	−	1.63609i	0.458362	−	0.0974278i
$283$	10.5358	+	2.23946i	0.626291	+	0.133122i	0.510115	−	0.860106i	$-0.329603\pi$
$283$	10.5358	+	2.23946i	0.626291	+	0.133122i	0.116176	+	0.993229i	$0.462936\pi$
$284$	−0.603752	−	5.74432i	−0.0358261	−	0.340862i
$285$	1.00030	+	1.73257i	0.0592527	+	0.102629i
$286$	5.92577	−	8.89340i	0.350398	−	0.525877i
$287$	−23.7387	+	6.07214i	−1.40125	+	0.358427i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	14.8726	−	16.5177i	0.874857	−	0.971628i
$290$	1.38726	+	1.54071i	0.0814629	+	0.0904737i
$291$	14.3587	−	6.39291i	0.841723	−	0.374759i
$292$	−0.857790	+	8.16133i	−0.0501984	+	0.477606i
$293$	−3.41332	+	10.5051i	−0.199408	+	0.613715i	0.800489	+	0.599348i	$0.204573\pi$
$293$	−3.41332	+	10.5051i	−0.199408	+	0.613715i	−0.999897	+	0.0143673i	$0.995427\pi$
$294$	−5.09409	−	4.80107i	−0.297093	−	0.280004i
$295$	2.54794	−	1.85119i	0.148347	−	0.107780i
$296$	−1.63387	−	2.82994i	−0.0949667	−	0.164487i
$297$	−3.28168	+	0.480151i	−0.190423	+	0.0278612i
$298$	4.99117	−	8.64495i	0.289131	−	0.500789i
$299$	17.7117	+	7.88574i	1.02429	+	0.456044i
$300$	1.49623	+	4.60491i	0.0863847	+	0.265865i
$301$	0.442268	−	6.92941i	0.0254919	−	0.399405i
$302$	−3.60640	−	2.62020i	−0.207525	−	0.150776i
$303$	1.45592	−	13.8521i	0.0836404	−	0.795785i
$304$	3.36660	+	3.73899i	0.193088	+	0.214446i
$305$	1.42881	+	0.303703i	0.0818135	+	0.0173900i
$306$	5.72165	+	2.54744i	0.327085	+	0.145628i
$307$	−8.80164			−0.502336			−0.251168	−	0.967944i	$-0.580815\pi$
$307$	−8.80164			−0.502336			−0.251168	+	0.967944i	$0.580815\pi$
$308$	1.11923	−	8.70329i	0.0637740	−	0.495916i
$309$	−7.93734			−0.451539
$310$	−0.114931	−	0.0511704i	−0.00652762	−	0.00290628i
$311$	11.0114	+	2.34055i	0.624401	+	0.132721i	0.509238	−	0.860626i	$-0.329927\pi$
$311$	11.0114	+	2.34055i	0.624401	+	0.132721i	0.115164	+	0.993347i	$0.463261\pi$
$312$	−2.15606	−	2.39455i	−0.122063	−	0.135565i
$313$	2.54847	−	24.2470i	0.144048	−	1.37052i	−0.648733	−	0.761016i	$-0.724701\pi$
$313$	2.54847	−	24.2470i	0.144048	−	1.37052i	0.792781	−	0.609507i	$-0.208633\pi$
$314$	9.54682	+	6.93617i	0.538758	+	0.391431i
$315$	−0.875731	−	0.582979i	−0.0493419	−	0.0328472i
$316$	−0.205730	−	0.633173i	−0.0115732	−	0.0356188i
$317$	25.5472	+	11.3743i	1.43487	+	0.638846i	0.969237	−	0.246131i	$-0.0791592\pi$
$317$	25.5472	+	11.3743i	1.43487	+	0.638846i	0.465635	+	0.884977i	$0.345826\pi$
$318$	5.83881	−	10.1131i	0.327424	−	0.567115i
$319$	7.66842	+	15.4995i	0.429349	+	0.867806i
$320$	−0.198815	−	0.344358i	−0.0111141	−	0.0192502i
$321$	4.71523	−	3.42582i	0.263179	−	0.191210i
$322$	15.9061	−	0.652221i	0.886411	−	0.0363468i
$323$	9.73766	−	29.9694i	0.541818	−	1.66754i
$324$	−0.104528	+	0.994522i	−0.00580714	+	0.0552512i
$325$	−14.2527	+	6.34569i	−0.790595	+	0.351995i
$326$	−13.6080	−	15.1132i	−0.753676	−	0.837042i
$327$	−8.70014	+	9.66248i	−0.481119	+	0.534336i
$328$	−7.49253	+	5.44364i	−0.413706	+	0.300575i
$329$	14.5534	+	14.8884i	0.802355	+	0.820825i
$330$	−0.0534776	−	1.31771i	−0.00294385	−	0.0725374i
$331$	−2.05987	−	3.56780i	−0.113221	−	0.196104i	0.803846	−	0.594837i	$-0.202783\pi$
$331$	−2.05987	−	3.56780i	−0.113221	−	0.196104i	−0.917067	+	0.398733i	$0.869450\pi$
$332$	0.917084	+	8.72547i	0.0503315	+	0.478872i
$333$	−3.19633	−	0.679401i	−0.175158	−	0.0372309i
$334$	2.14001	−	0.454874i	0.117096	−	0.0248896i
$335$	−4.60167	−	3.34331i	−0.251416	−	0.182664i
$336$	−2.45907	−	0.976195i	−0.134153	−	0.0532558i
$337$	−10.8990	+	33.5435i	−0.593704	+	1.82723i	−0.0326280	+	0.999468i	$0.510388\pi$
$337$	−10.8990	+	33.5435i	−0.593704	+	1.82723i	−0.561076	+	0.827764i	$0.689612\pi$
$338$	−1.75146	+	1.94520i	−0.0952670	+	0.105805i
$339$	−1.32209	−	12.5788i	−0.0718060	−	0.683188i
$340$	−1.24520	+	2.15676i	−0.0675307	+	0.116967i
$341$	−0.807653	−	0.669955i	−0.0437369	−	0.0362801i
$342$	5.03131			0.272062
$343$	3.51980	−	18.1827i	0.190052	−	0.981774i
$344$	−0.810985	−	2.49595i	−0.0437254	−	0.134573i
$345$	2.34025	−	0.497436i	0.125995	−	0.0267811i
$346$	−5.47153	+	2.43608i	−0.294152	+	0.130965i
$347$	−13.2716	+	5.90888i	−0.712455	+	0.317206i	−0.730767	−	0.682627i	$-0.760838\pi$
$347$	−13.2716	+	5.90888i	−0.712455	+	0.317206i	0.0183118	+	0.999832i	$0.494171\pi$
$348$	5.10003	−	1.08404i	0.273390	−	0.0581109i
$349$	−9.60127	−	29.5497i	−0.513944	−	1.58176i	−0.785195	−	0.619249i	$-0.787437\pi$
$349$	−9.60127	−	29.5497i	−0.513944	−	1.58176i	0.271250	−	0.962509i	$-0.412563\pi$
$350$	−8.17462	+	9.86321i	−0.436952	+	0.527211i
$351$	−3.22219			−0.171988
$352$	−0.820550	−	3.21352i	−0.0437354	−	0.171281i
$353$	−4.14946	+	7.18708i	−0.220854	+	0.382530i	−0.955067	−	0.296389i	$-0.904218\pi$
$353$	−4.14946	+	7.18708i	−0.220854	+	0.382530i	0.734214	+	0.678918i	$0.237551\pi$
$354$	−0.827918	−	7.87711i	−0.0440033	−	0.418664i
$355$	1.53679	−	1.70678i	0.0815644	−	0.0905864i
$356$	−1.83835	+	5.65787i	−0.0974326	+	0.299867i
$357$	2.40583	+	16.3951i	0.127330	+	0.867720i
$358$	−1.09967	−	0.798960i	−0.0581196	−	0.0422264i
$359$	14.9577	−	3.17935i	0.789436	−	0.167800i	0.204486	−	0.978869i	$-0.434448\pi$
$359$	14.9577	−	3.17935i	0.789436	−	0.167800i	0.584950	+	0.811070i	$0.301114\pi$
$360$	−0.388941	−	0.0826720i	−0.0204990	−	0.00435720i
$361$	−0.660001	−	6.27949i	−0.0347369	−	0.330499i
$362$	12.6913	+	21.9820i	0.667040	+	1.15535i
$363$	2.54026	−	10.7027i	0.133329	−	0.561744i
$364$	2.30001	−	8.20898i	0.120553	−	0.430267i
$365$	−2.63988	+	1.91798i	−0.138178	+	0.100392i
$366$	2.45811	−	2.73001i	0.128488	−	0.142700i
$367$	−12.3959	−	13.7671i	−0.647061	−	0.718634i	0.326973	−	0.945034i	$-0.393971\pi$
$367$	−12.3959	−	13.7671i	−0.647061	−	0.718634i	−0.974035	+	0.226399i	$0.927305\pi$
$368$	5.49679	−	2.44733i	0.286540	−	0.127576i
$369$	−0.968067	+	9.21054i	−0.0503956	+	0.479482i
$370$	0.401522	−	1.23576i	0.0208741	−	0.0642440i
$371$	30.8701	−	1.26581i	1.60270	−	0.0657178i
$372$	−0.255966	+	0.185971i	−0.0132712	+	0.00964212i
$373$	−8.67070	−	15.0181i	−0.448952	−	0.777607i	0.549366	−	0.835582i	$-0.314869\pi$
$373$	−8.67070	−	15.0181i	−0.448952	−	0.777607i	−0.998318	+	0.0579743i	$0.981536\pi$
$374$	−14.8606	+	14.5140i	−0.768423	+	0.750502i
$375$	−1.95672	+	3.38914i	−0.101044	+	0.175014i
$376$	7.18884	+	3.20068i	0.370736	+	0.165062i
$377$	5.19160	+	15.9781i	0.267381	+	0.822914i
$378$	−2.37090	+	1.17425i	−0.121946	+	0.0603967i
$379$	15.9478	+	11.5868i	0.819183	+	0.595172i	0.916478	−	0.400084i	$-0.131019\pi$
$379$	15.9478	+	11.5868i	0.819183	+	0.595172i	−0.0972951	+	0.995256i	$0.531019\pi$
$380$	−0.209120	+	1.98964i	−0.0107276	+	0.102067i
$381$	4.98711	+	5.53874i	0.255497	+	0.283758i
$382$	−18.1836	−	3.86505i	−0.930355	−	0.197753i
$383$	−16.2875	−	7.25168i	−0.832254	−	0.370543i	−0.0540372	−	0.998539i	$-0.517209\pi$
$383$	−16.2875	−	7.25168i	−0.832254	−	0.370543i	−0.778217	+	0.627995i	$0.783876\pi$
$384$	−1.00000			−0.0510310
$385$	2.86959	−	1.98493i	0.146248	−	0.101161i
$386$	20.1833			1.02730
$387$	−2.39751	−	1.06744i	−0.121872	−	0.0542610i
$388$	15.3741	+	3.26787i	0.780502	+	0.165901i
$389$	−17.5200	−	19.4579i	−0.888297	−	0.986554i	0.111677	−	0.993745i	$-0.464378\pi$
$389$	−17.5200	−	19.4579i	−0.888297	−	0.986554i	−0.999974	+	0.00719038i	$0.997711\pi$
$390$	0.133926	−	1.27422i	0.00678161	−	0.0645227i
$391$	−30.4879	−	22.1508i	−1.54184	−	1.12021i
$392$	−1.29920	−	6.87838i	−0.0656196	−	0.347411i
$393$	−1.69750	−	5.22438i	−0.0856277	−	0.263535i
$394$	12.1878	+	5.42635i	0.614011	+	0.273375i
$395$	0.132363	−	0.229259i	0.00665989	−	0.0115353i
$396$	−2.93716	−	1.54048i	−0.147598	−	0.0774118i
$397$	−6.48629	−	11.2346i	−0.325538	−	0.563848i	0.656083	−	0.754688i	$-0.272212\pi$
$397$	−6.48629	−	11.2346i	−0.325538	−	0.563848i	−0.981621	+	0.190841i	$0.938879\pi$
$398$	−15.3363	+	11.1425i	−0.768741	+	0.558523i
$399$	7.12252	+	11.2458i	0.356572	+	0.562995i
$400$	−1.49623	+	4.60491i	−0.0748113	+	0.230246i
$401$	1.28138	−	12.1915i	0.0639890	−	0.608814i	−0.914795	−	0.403919i	$-0.867648\pi$
$401$	1.28138	−	12.1915i	0.0639890	−	0.608814i	0.978784	−	0.204896i	$-0.0656855\pi$
$402$	−13.0680	+	5.81823i	−0.651771	+	0.290187i
$403$	−0.682161	−	0.757617i	−0.0339809	−	0.0377396i
$404$	9.31995	−	10.3509i	0.463685	−	0.514974i
$405$	−0.321690	+	0.233721i	−0.0159849	+	0.0116137i
$406$	9.64281	+	9.86479i	0.478565	+	0.489581i
$407$	6.00955	−	9.01912i	0.297882	−	0.447061i
$408$	3.13156	+	5.42402i	0.155035	+	0.268529i
$409$	2.90320	+	27.6221i	0.143554	+	1.36583i	0.794759	+	0.606925i	$0.207597\pi$
$409$	2.90320	+	27.6221i	0.143554	+	1.36583i	−0.651205	+	0.758902i	$0.725736\pi$
$410$	−3.60209	−	0.765649i	−0.177895	−	0.0378127i
$411$	−18.7894	+	3.99381i	−0.926812	+	0.197000i
$412$	−6.42144	−	4.66545i	−0.316362	−	0.229850i
$413$	16.4346	−	13.0017i	0.808694	−	0.639771i
$414$	1.85935	−	5.72249i	0.0913821	−	0.281245i
$415$	−2.33435	+	2.59255i	−0.114588	+	0.127263i
$416$	−0.336810	−	3.20453i	−0.0165135	−	0.157115i
$417$	−6.29508	+	10.9034i	−0.308271	+	0.533942i
$418$	−6.16345	+	15.5070i	−0.301464	+	0.758472i
$419$	−6.13229			−0.299582			−0.149791	−	0.988718i	$-0.547860\pi$
$419$	−6.13229			−0.299582			−0.149791	+	0.988718i	$0.547860\pi$
$420$	−0.365815	−	0.986382i	−0.0178499	−	0.0481305i
$421$	−7.70987	−	23.7285i	−0.375756	−	1.15646i	−0.942967	−	0.332886i	$-0.891978\pi$
$421$	−7.70987	−	23.7285i	−0.375756	−	1.15646i	0.567211	−	0.823572i	$-0.308022\pi$
$422$	−8.50494	+	1.80778i	−0.414014	+	0.0880014i
$423$	7.18884	−	3.20068i	0.349533	−	0.155622i
$424$	10.6680	−	4.74971i	0.518085	−	0.230666i
$425$	29.6627	−	6.30500i	1.43885	−	0.305837i
$426$	−1.78487	−	5.49326i	−0.0864772	−	0.266149i
$427$	9.58183	+	1.62958i	0.463697	+	0.0788609i
$428$	5.82835			0.281724
$429$	3.94724	−	9.93109i	0.190575	−	0.479478i
$430$	0.521771	−	0.903734i	0.0251620	−	0.0435819i
$431$	−0.795768	−	7.57123i	−0.0383308	−	0.364693i	−0.996828	−	0.0795902i	$-0.974639\pi$
$431$	−0.795768	−	7.57123i	−0.0383308	−	0.364693i	0.958497	−	0.285103i	$-0.0920278\pi$
$432$	−0.669131	+	0.743145i	−0.0321936	+	0.0357546i
$433$	7.51787	−	23.1376i	0.361286	−	1.11192i	−0.590989	−	0.806680i	$-0.701262\pi$
$433$	7.51787	−	23.1376i	0.361286	−	1.11192i	0.952274	−	0.305243i	$-0.0987378\pi$
$434$	−0.778031	−	0.308860i	−0.0373467	−	0.0148258i
$435$	1.67728	+	1.21861i	0.0804194	+	0.0584281i
$436$	−12.7180	+	2.70330i	−0.609083	+	0.129465i
$437$	−29.6118	−	6.29417i	−1.41652	−	0.301091i
$438$	0.857790	+	8.16133i	0.0409868	+	0.389963i
$439$	0.970029	+	1.68014i	0.0462970	+	0.0801887i	0.888245	−	0.459370i	$-0.151925\pi$
$439$	0.970029	+	1.68014i	0.0462970	+	0.0801887i	−0.841948	+	0.539558i	$0.818591\pi$
$440$	0.731264	−	1.09748i	0.0348617	−	0.0523203i
$441$	−5.98097	−	3.63704i	−0.284808	−	0.173192i
$442$	−16.3267	+	11.8621i	−0.776583	+	0.564221i
$443$	−14.5611	+	16.1717i	−0.691819	+	0.768342i	−0.982051	−	0.188614i	$-0.939601\pi$
$443$	−14.5611	+	16.1717i	−0.691819	+	0.768342i	0.290233	+	0.956956i	$0.406267\pi$
$444$	−2.18654	−	2.42840i	−0.103769	−	0.115247i
$445$	−2.16101	+	0.962143i	−0.102442	+	0.0456100i
$446$	1.43965	−	13.6973i	0.0681693	−	0.648588i
$447$	3.08471	−	9.49376i	0.145902	−	0.449040i
$448$	−1.41564	−	2.23517i	−0.0668827	−	0.105602i
$449$	−10.2057	+	7.41489i	−0.481638	+	0.349930i	−0.801959	−	0.597378i	$-0.796209\pi$
$449$	−10.2057	+	7.41489i	−0.481638	+	0.349930i	0.320322	+	0.947309i	$0.396209\pi$
$450$	2.42094	+	4.19320i	0.114124	+	0.197669i
$451$	−27.2019	−	14.2668i	−1.28089	−	0.671796i
$452$	6.32406	−	10.9536i	0.297459	−	0.515214i
$453$	−4.07236	−	1.81313i	−0.191336	−	0.0851884i
$454$	5.04129	+	15.5155i	0.236600	+	0.728179i
$455$	3.03769	−	1.50449i	0.142409	−	0.0705316i
$456$	4.07042	+	2.95733i	0.190615	+	0.138490i
$457$	2.21412	−	21.0659i	0.103572	−	0.985422i	−0.812106	−	0.583510i	$-0.801679\pi$
$457$	2.21412	−	21.0659i	0.103572	−	0.985422i	0.915678	−	0.401912i	$-0.131654\pi$
$458$	−13.9201	−	15.4598i	−0.650442	−	0.722390i
$459$	6.12626	+	1.30218i	0.285949	+	0.0607804i
$460$	2.18569	+	0.973132i	0.101908	+	0.0453725i
$461$	−22.6341			−1.05417			−0.527087	−	0.849811i	$-0.676716\pi$
$461$	−22.6341			−1.05417			−0.527087	+	0.849811i	$0.676716\pi$
$462$	−0.714746	−	8.74581i	−0.0332530	−	0.406892i
$463$	17.5540			0.815804			0.407902	−	0.913026i	$-0.366261\pi$
$463$	17.5540			0.815804			0.407902	+	0.913026i	$0.366261\pi$
$464$	4.76319	+	2.12071i	0.221126	+	0.0984515i
$465$	−0.123058	−	0.0261568i	−0.00570668	−	0.00121299i
$466$	−3.39801	−	3.77387i	−0.157410	−	0.174821i
$467$	1.47691	−	14.0518i	0.0683431	−	0.650241i	−0.905706	−	0.423906i	$-0.860659\pi$
$467$	1.47691	−	14.0518i	0.0683431	−	0.650241i	0.974049	−	0.226335i	$-0.0726746\pi$
$468$	−2.60680	−	1.89395i	−0.120500	−	0.0875480i
$469$	−31.5042	−	20.9726i	−1.45473	−	0.968422i
$470$	0.966921	+	2.97588i	0.0446007	+	0.137267i
$471$	10.7803	+	4.79970i	0.496731	+	0.221159i
$472$	3.96025	−	6.85935i	0.182285	−	0.315727i
$473$	6.22695	−	6.08173i	0.286316	−	0.279638i
$474$	−0.332879	−	0.576563i	−0.0152896	−	0.0264824i
$475$	19.7085	−	14.3191i	0.904288	−	0.657004i
$476$	−7.69043	+	14.6780i	−0.352490	+	0.672766i
$477$	3.60858	−	11.1061i	0.165226	−	0.508512i
$478$	−1.95659	+	18.6157i	−0.0894924	+	0.851463i
$479$	2.55498	−	1.13755i	0.116740	−	0.0519759i	−0.347536	−	0.937667i	$-0.612981\pi$
$479$	2.55498	−	1.13755i	0.116740	−	0.0519759i	0.464275	+	0.885691i	$0.346315\pi$
$480$	−0.266067	−	0.295497i	−0.0121442	−	0.0134875i
$481$	7.04545	−	7.82476i	0.321245	−	0.356778i
$482$	10.0051	−	7.26914i	0.455721	−	0.331100i
$483$	15.4229	−	3.94503i	0.701766	−	0.179505i
$484$	8.34598	−	7.16551i	0.379363	−	0.325705i
$485$	3.12489	+	5.41247i	0.141894	+	0.245768i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	14.7188	+	3.12857i	0.666972	+	0.141769i	0.528941	−	0.848659i	$-0.322589\pi$
$487$	14.7188	+	3.12857i	0.666972	+	0.141769i	0.138031	+	0.990428i	$0.455923\pi$
$488$	3.59331	−	0.763783i	0.162662	−	0.0345748i
$489$	−16.4528	−	11.9537i	−0.744022	−	0.540564i
$490$	1.68687	−	2.21402i	0.0762048	−	0.100019i
$491$	4.56029	−	14.0351i	0.205803	−	0.633397i	−0.793876	−	0.608079i	$-0.791940\pi$
$491$	4.56029	−	14.0351i	0.205803	−	0.633397i	0.999679	−	0.0253176i	$-0.00805971\pi$
$492$	−6.19700	+	6.88247i	−0.279383	+	0.310286i
$493$	−3.41345	−	32.4768i	−0.153734	−	1.46268i
$494$	−8.10591	+	14.0398i	−0.364702	+	0.631682i
$495$	−0.326276	−	1.27779i	−0.0146650	−	0.0574325i
$496$	−0.316392			−0.0142064
$497$	9.75162	−	11.7660i	0.437420	−	0.527775i
$498$	2.71117	+	8.34412i	0.121490	+	0.373909i
$499$	−5.41663	+	1.15134i	−0.242482	+	0.0515411i	−0.327549	−	0.944834i	$-0.606223\pi$
$499$	−5.41663	+	1.15134i	−0.242482	+	0.0515411i	0.0850676	+	0.996375i	$0.472889\pi$
$500$	−3.57510	+	1.59174i	−0.159883	+	0.0711847i
$501$	1.99867	−	0.889867i	0.0892942	−	0.0397563i
$502$	−8.00099	+	1.70066i	−0.357102	+	0.0759043i
$503$	−1.30086	−	4.00364i	−0.0580026	−	0.178514i	0.917858	−	0.396910i	$-0.129917\pi$
$503$	−1.30086	−	4.00364i	−0.0580026	−	0.178514i	−0.975860	+	0.218396i	$0.929917\pi$
$504$	−2.60830	−	0.443593i	−0.116183	−	0.0197592i
$505$	5.53838			0.246455
$506$	15.3595	+	12.7409i	0.682815	+	0.566401i
$507$	−1.30876	+	2.26684i	−0.0581241	+	0.100674i
$508$	0.779062	+	7.41228i	0.0345653	+	0.328867i
$509$	−22.3611	+	24.8345i	−0.991140	+	1.10077i	0.00376919	+	0.999993i	$0.498800\pi$
$509$	−22.3611	+	24.8345i	−0.991140	+	1.10077i	−0.994909	+	0.100779i	$0.967866\pi$
$510$	−0.769579	+	2.36852i	−0.0340775	+	0.104880i
$511$	−17.0276	+	13.4708i	−0.753257	+	0.595913i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	4.92136	−	1.04607i	0.217284	−	0.0461850i
$514$	6.29294	+	1.33761i	0.277570	+	0.0589993i
$515$	−0.329905	−	3.13884i	−0.0145374	−	0.138314i
$516$	−1.31220	−	2.27280i	−0.0577664	−	0.100054i
$517$	1.05833	+	26.0776i	0.0465453	+	1.14689i
$518$	2.33252	−	8.32503i	0.102485	−	0.365781i
$519$	−4.84548	+	3.52045i	−0.212693	+	0.154530i
$520$	0.857317	−	0.952147i	0.0375958	−	0.0417544i
$521$	8.08546	+	8.97982i	0.354231	+	0.393413i	0.893754	−	0.448558i	$-0.148062\pi$
$521$	8.08546	+	8.97982i	0.354231	+	0.393413i	−0.539523	+	0.841971i	$0.681395\pi$
$522$	4.76319	−	2.12071i	0.208479	−	0.0928210i
$523$	3.02242	−	28.7564i	0.132161	−	1.25743i	−0.704499	−	0.709705i	$-0.748828\pi$
$523$	3.02242	−	28.7564i	0.132161	−	1.25743i	0.836660	−	0.547723i	$-0.184505\pi$
$524$	1.69750	−	5.22438i	0.0741558	−	0.228228i
$525$	−5.94531	+	11.3473i	−0.259475	+	0.495235i
$526$	−20.8885	+	15.1764i	−0.910783	+	0.661723i
$527$	0.990801	+	1.71612i	0.0431600	+	0.0747553i
$528$	−1.47075	−	2.97269i	−0.0640060	−	0.129370i
$529$	−6.60205	+	11.4351i	−0.287045	+	0.497177i
$530$	4.24194	+	1.88863i	0.184258	+	0.0820369i
$531$	−2.44757	−	7.53284i	−0.106215	−	0.326898i
$532$	−0.847883	+	13.2846i	−0.0367604	+	0.575959i
$533$	−24.1423	−	17.5404i	−1.04572	−	0.759760i
$534$	−0.621844	+	5.91645i	−0.0269098	+	0.256030i
$535$	1.55073	+	1.72226i	0.0670439	+	0.0744598i
$536$	−13.9921	−	2.97411i	−0.604366	−	0.128462i
$537$	−1.24176	−	0.552866i	−0.0535858	−	0.0238579i
$538$	−12.3007			−0.530320
$539$	18.5365	−	13.9785i	0.798424	−	0.602096i
$540$	−0.397631			−0.0171113
$541$	35.5441	+	15.8253i	1.52816	+	0.680381i	0.987027	−	0.160556i	$-0.0513287\pi$
$541$	35.5441	+	15.8253i	1.52816	+	0.680381i	0.541133	+	0.840937i	$0.317995\pi$
$542$	−4.55626	−	0.968463i	−0.195708	−	0.0415990i
$543$	16.9843	+	18.8629i	0.728865	+	0.809486i
$544$	−0.654675	+	6.22881i	−0.0280689	+	0.267058i
$545$	−4.18266	−	3.03888i	−0.179165	−	0.130171i
$546$	0.543007	−	8.50779i	0.0232386	−	0.364100i
$547$	4.89671	+	15.0705i	0.209368	+	0.644369i	0.999506	+	0.0314395i	$0.0100092\pi$
$547$	4.89671	+	15.0705i	0.209368	+	0.644369i	−0.790137	+	0.612930i	$0.789991\pi$
$548$	−17.5484	−	7.81306i	−0.749632	−	0.333757i
$549$	1.83680	−	3.18142i	0.0783925	−	0.135780i
$550$	−15.8896	+	2.32484i	−0.677533	+	0.0991313i
$551$	−13.1165	−	22.7185i	−0.558783	−	0.967841i
$552$	4.86784	−	3.53669i	0.207189	−	0.150532i
$553$	0.817477	−	1.56024i	0.0347627	−	0.0663483i
$554$	2.03112	−	6.25114i	0.0862940	−	0.265585i
$555$	0.135819	−	1.29223i	0.00576521	−	0.0548523i
$556$	−11.5017	+	5.12088i	−0.487780	+	0.217174i
$557$	−13.5379	−	15.0353i	−0.573618	−	0.637068i	0.384608	−	0.923080i	$-0.374337\pi$
$557$	−13.5379	−	15.0353i	−0.573618	−	0.637068i	−0.958226	+	0.286013i	$0.907670\pi$
$558$	−0.211708	+	0.235125i	−0.00896230	+	0.00995364i
$559$	6.84130	−	4.97049i	0.289356	−	0.210229i
$560$	0.283830	−	1.01302i	0.0119940	−	0.0428079i
$561$	−11.5182	+	17.2865i	−0.486300	+	0.729838i
$562$	7.29235	+	12.6307i	0.307609	+	0.532795i
$563$	−1.76765	−	16.8181i	−0.0744978	−	0.708799i	−0.966482	−	0.256733i	$-0.917354\pi$
$563$	−1.76765	−	16.8181i	−0.0744978	−	0.708799i	0.891985	−	0.452066i	$-0.149313\pi$
$564$	7.69721	+	1.63609i	0.324111	+	0.0688919i
$565$	4.91938	−	1.04565i	0.206960	−	0.0439906i
$566$	8.71410	+	6.33116i	0.366281	+	0.266119i
$567$	−2.07495	+	1.64152i	−0.0871396	+	0.0689375i
$568$	1.78487	−	5.49326i	0.0748914	−	0.230492i
$569$	−8.77435	+	9.74490i	−0.367840	+	0.408528i	−0.898441	−	0.439094i	$-0.855300\pi$
$569$	−8.77435	+	9.74490i	−0.367840	+	0.408528i	0.530601	+	0.847622i	$0.321966\pi$
$570$	0.209120	+	1.98964i	0.00875907	+	0.0833370i
$571$	9.12708	−	15.8086i	0.381956	−	0.661568i	−0.609385	−	0.792874i	$-0.708584\pi$
$571$	9.12708	−	15.8086i	0.381956	−	0.661568i	0.991342	+	0.131306i	$0.0419171\pi$
$572$	9.03073	−	5.71429i	0.377594	−	0.238927i
$573$	−18.5899			−0.776603
$574$	−24.1562	−	4.10824i	−1.00826	−	0.171474i
$575$	−9.00277	−	27.7077i	−0.375441	−	1.15549i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	27.3724	−	12.1870i	1.13953	−	0.507350i	0.251827	−	0.967772i	$-0.418969\pi$
$577$	27.3724	−	12.1870i	1.13953	−	0.507350i	0.887700	+	0.460422i	$0.152302\pi$
$578$	20.3051	−	9.04042i	0.844581	−	0.376032i
$579$	19.7422	−	4.19634i	0.820459	−	0.174394i
$580$	0.640664	+	1.97176i	0.0266021	+	0.0818729i
$581$	−14.8125	+	17.8722i	−0.614524	+	0.741463i
$582$	15.7176			0.651514
$583$	29.8094	+	24.7272i	1.23458	+	1.02409i
$584$	−4.10314	+	7.10685i	−0.169789	+	0.294084i
$585$	−0.133926	−	1.27422i	−0.00553716	−	0.0526825i
$586$	−7.39104	+	8.20858i	−0.305321	+	0.339093i
$587$	−4.11520	+	12.6653i	−0.169853	+	0.522752i	−0.999361	−	0.0357417i	$-0.988621\pi$
$587$	−4.11520	+	12.6653i	−0.169853	+	0.522752i	0.829509	+	0.558494i	$0.188621\pi$
$588$	−2.70091	−	6.45795i	−0.111384	−	0.266321i
$589$	1.28785	+	0.935675i	0.0530648	+	0.0385538i
$590$	3.08061	−	0.654804i	0.126827	−	0.0269579i
$591$	13.0496	+	2.77379i	0.536791	+	0.114098i
$592$	−0.341571	−	3.24984i	−0.0140385	−	0.133567i
$593$	−4.66083	−	8.07280i	−0.191397	−	0.331510i	0.754316	−	0.656511i	$-0.227969\pi$
$593$	−4.66083	−	8.07280i	−0.191397	−	0.331510i	−0.945714	+	0.325001i	$0.894635\pi$
$594$	−3.19326	−	0.896142i	−0.131021	−	0.0367692i
$595$	−6.38348	+	1.63283i	−0.261697	+	0.0669397i
$596$	8.07588	−	5.86747i	0.330801	−	0.240341i
$597$	−12.6845	+	14.0876i	−0.519144	+	0.576568i
$598$	12.9730	+	14.4080i	0.530505	+	0.589186i
$599$	26.1119	−	11.6258i	1.06690	−	0.475016i	0.203262	−	0.979124i	$-0.434846\pi$
$599$	26.1119	−	11.6258i	1.06690	−	0.475016i	0.863640	+	0.504109i	$0.168179\pi$
$600$	−0.506115	+	4.81537i	−0.0206621	+	0.196586i
$601$	−13.3442	+	41.0693i	−0.544323	+	1.67525i	0.178272	+	0.983981i	$0.442949\pi$
$601$	−13.3442	+	41.0693i	−0.544323	+	1.67525i	−0.722594	+	0.691272i	$0.757051\pi$
$602$	3.22248	−	6.15045i	0.131338	−	0.250674i
$603$	−11.5727	+	8.40807i	−0.471278	+	0.342403i
$604$	−2.22888	−	3.86053i	−0.0906918	−	0.157083i
$605$	4.33798	+	0.559708i	0.176364	+	0.0227554i
$606$	6.96423	−	12.0624i	0.282902	−	0.490001i
$607$	17.4327	+	7.76155i	0.707573	+	0.315032i	0.728784	−	0.684743i	$-0.240086\pi$
$607$	17.4327	+	7.76155i	0.707573	+	0.315032i	−0.0212117	+	0.999775i	$0.506752\pi$
$608$	1.55476	+	4.78506i	0.0630539	+	0.194060i
$609$	11.4831	+	7.64437i	0.465319	+	0.309765i
$610$	1.18176	+	0.858597i	0.0478480	+	0.0347636i
$611$	−2.65041	+	25.2170i	−0.107224	+	1.02017i
$612$	4.19085	+	4.65441i	0.169405	+	0.188143i
$613$	2.23927	+	0.475970i	0.0904431	+	0.0192243i	0.252911	−	0.967490i	$-0.418612\pi$
$613$	2.23927	+	0.475970i	0.0904431	+	0.0192243i	−0.162468	+	0.986714i	$0.551945\pi$
$614$	−8.04070	−	3.57995i	−0.324496	−	0.144475i
$615$	−3.68257			−0.148495
$616$	4.56242	−	7.49562i	0.183825	−	0.302007i
$617$	−25.5472			−1.02849			−0.514246	−	0.857643i	$-0.671928\pi$
$617$	−25.5472			−1.02849			−0.514246	+	0.857643i	$0.671928\pi$
$618$	−7.25112	−	3.22841i	−0.291683	−	0.129866i
$619$	−32.1127	−	6.82577i	−1.29072	−	0.274351i	−0.489122	−	0.872215i	$-0.662683\pi$
$619$	−32.1127	−	6.82577i	−1.29072	−	0.274351i	−0.801597	+	0.597865i	$0.796016\pi$
$620$	−0.0841814	−	0.0934929i	−0.00338081	−	0.00375477i
$621$	0.628946	−	5.98402i	0.0252387	−	0.240131i
$622$	9.10746	+	6.61696i	0.365176	+	0.265316i
$623$	−14.1045	+	6.98563i	−0.565087	+	0.279873i
$624$	−0.995710	−	3.06448i	−0.0398603	−	0.122677i
$625$	20.6949	+	9.21395i	0.827795	+	0.368558i
$626$	12.1903	−	21.1142i	0.487222	−	0.843894i
$627$	−2.80468	+	16.4496i	−0.112008	+	0.656933i
$628$	5.90026	+	10.2196i	0.235446	+	0.407804i
$629$	−16.5575	+	12.0298i	−0.660192	+	0.479658i
$630$	−0.562901	−	0.888770i	−0.0224265	−	0.0354095i
$631$	0.0427691	−	0.131630i	0.00170261	−	0.00524009i	−0.950202	−	0.311636i	$-0.899123\pi$
$631$	0.0427691	−	0.131630i	0.00170261	−	0.00524009i	0.951904	+	0.306396i	$0.0991231\pi$
$632$	0.0695906	−	0.662110i	0.00276817	−	0.0263373i
$633$	−7.94323	+	3.53655i	−0.315715	+	0.140565i
$634$	18.7121	+	20.7819i	0.743154	+	0.825356i
$635$	−1.98303	+	2.20237i	−0.0786940	+	0.0873985i
$636$	9.44739	−	6.86393i	0.374613	−	0.272172i
$637$	19.7850	−	10.8303i	0.783911	−	0.429110i
$638$	0.701230	+	17.2785i	0.0277620	+	0.684064i
$639$	−2.88798	−	5.00213i	−0.114247	−	0.197881i
$640$	−0.0415637	−	0.395452i	−0.00164295	−	0.0156316i
$641$	8.78167	+	1.86660i	0.346855	+	0.0737263i	0.378045	−	0.925787i	$-0.376596\pi$
$641$	8.78167	+	1.86660i	0.346855	+	0.0737263i	−0.0311901	+	0.999513i	$0.509930\pi$
$642$	5.70098	−	1.21178i	0.225000	−	0.0478252i
$643$	−18.0299	−	13.0995i	−0.711031	−	0.516594i	0.172475	−	0.985014i	$-0.444823\pi$
$643$	−18.0299	−	13.0995i	−0.711031	−	0.516594i	−0.883506	+	0.468420i	$0.844823\pi$
$644$	14.7962	+	5.87375i	0.583052	+	0.231458i
$645$	0.322472	−	0.992468i	0.0126973	−	0.0390784i
$646$	21.0855	−	23.4178i	0.829596	−	0.921360i
$647$	−1.77126	−	16.8524i	−0.0696353	−	0.662536i	−0.972546	−	0.232709i	$-0.925241\pi$
$647$	−1.77126	−	16.8524i	−0.0696353	−	0.662536i	0.902911	−	0.429827i	$-0.141426\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	26.2153	+	1.68424i	1.02904	+	0.0661120i
$650$	−15.6015			−0.611940
$651$	−0.825245	−	0.140349i	−0.0323439	−	0.00550072i
$652$	−6.28441	−	19.3414i	−0.246117	−	0.757469i
$653$	−4.74665	+	1.00893i	−0.185751	+	0.0394826i	−0.299848	−	0.953987i	$-0.596936\pi$
$653$	−4.74665	+	1.00893i	−0.185751	+	0.0394826i	0.114097	+	0.993470i	$0.463603\pi$
$654$	−11.8781	+	5.28845i	−0.464469	+	0.206795i
$655$	1.99544	−	0.888426i	0.0779682	−	0.0347137i
$656$	−9.05890	+	1.92553i	−0.353690	+	0.0751792i
$657$	2.53588	+	7.80464i	0.0989342	+	0.304488i
$658$	7.23953	+	19.5206i	0.282226	+	0.760994i
$659$	−1.59901			−0.0622887			−0.0311443	−	0.999515i	$-0.509915\pi$
$659$	−1.59901			−0.0622887			−0.0311443	+	0.999515i	$0.509915\pi$
$660$	0.487105	−	1.22554i	0.0189606	−	0.0477039i
$661$	−11.9610	+	20.7170i	−0.465229	+	0.805800i	−0.999212	−	0.0396955i	$-0.987361\pi$
$661$	−11.9610	+	20.7170i	−0.465229	+	0.805800i	0.533983	+	0.845495i	$0.320695\pi$
$662$	−0.430630	−	4.09717i	−0.0167369	−	0.159241i
$663$	−13.5037	+	14.9974i	−0.524440	+	0.582449i
$664$	−2.71117	+	8.34412i	−0.105214	+	0.323815i
$665$	−4.15114	+	3.28403i	−0.160974	+	0.127349i
$666$	−2.64365	−	1.92073i	−0.102440	−	0.0744267i
$667$	−30.6868	+	6.52267i	−1.18820	+	0.252559i
$668$	2.14001	+	0.454874i	0.0827996	+	0.0175996i
$669$	−1.43965	−	13.6973i	−0.0556600	−	0.529570i
$670$	−2.84399	−	4.92593i	−0.109873	−	0.190305i
$671$	7.55535	+	9.55849i	0.291671	+	0.369001i
$672$	−1.84942	−	1.89199i	−0.0713430	−	0.0729853i
$673$	15.4530	−	11.2273i	0.595669	−	0.432779i	−0.248670	−	0.968588i	$-0.579993\pi$
$673$	15.4530	−	11.2273i	0.595669	−	0.432779i	0.844339	+	0.535810i	$0.179993\pi$
$674$	−23.6001	+	26.2105i	−0.909041	+	1.00959i
$675$	3.23986	+	3.59823i	0.124702	+	0.138496i
$676$	−2.39122	+	1.06464i	−0.0919701	+	0.0409477i
$677$	0.261626	−	2.48920i	0.0100551	−	0.0956679i	−0.988343	−	0.152241i	$-0.951351\pi$
$677$	0.261626	−	2.48920i	0.0100551	−	0.0956679i	0.998398	+	0.0565735i	$0.0180175\pi$
$678$	3.90848	−	12.0291i	0.150104	−	0.461974i
$679$	22.2504	+	35.1314i	0.853892	+	1.34822i
$680$	−2.01478	+	1.46383i	−0.0772634	+	0.0561352i
$681$	8.15698	+	14.1283i	0.312576	+	0.541398i
$682$	−0.465332	−	0.940536i	−0.0178185	−	0.0360150i
$683$	12.5142	−	21.6752i	0.478842	−	0.829379i	−0.520863	−	0.853640i	$-0.674390\pi$
$683$	12.5142	−	21.6752i	0.478842	−	0.829379i	0.999706	+	0.0242607i	$0.00772319\pi$
$684$	4.59633	+	2.04642i	0.175745	+	0.0782467i
$685$	−2.36032	−	7.26431i	−0.0901830	−	0.277555i
$686$	10.6111	−	15.1791i	0.405133	−	0.579541i
$687$	−16.8302	−	12.2278i	−0.642111	−	0.466521i
$688$	0.274325	−	2.61002i	0.0104585	−	0.0995063i
$689$	25.1777	+	27.9626i	0.959193	+	1.06529i
$690$	2.34025	+	0.497436i	0.0890920	+	0.0189371i
$691$	7.16190	+	3.18868i	0.272451	+	0.121303i	0.538415	−	0.842680i	$-0.319023\pi$
$691$	7.16190	+	3.18868i	0.272451	+	0.121303i	−0.265963	+	0.963983i	$0.585690\pi$
$692$	−5.98934			−0.227681
$693$	−2.51748	−	8.40609i	−0.0956312	−	0.319321i
$694$	−14.5275			−0.551458
$695$	−4.57342	−	2.03622i	−0.173480	−	0.0772381i
$696$	5.10003	+	1.08404i	0.193316	+	0.0410906i
$697$	38.8126	+	43.1058i	1.47013	+	1.63275i
$698$	3.24774	−	30.9002i	0.122929	−	1.16959i
$699$	−4.10838	−	2.98491i	−0.155393	−	0.112900i
$700$	−11.4796	+	5.68557i	−0.433889	+	0.214894i
$701$	13.8853	+	42.7344i	0.524439	+	1.61406i	0.765423	+	0.643527i	$0.222530\pi$
$701$	13.8853	+	42.7344i	0.524439	+	1.61406i	−0.240984	+	0.970529i	$0.577470\pi$
$702$	−2.94361	−	1.31058i	−0.111100	−	0.0494647i
$703$	−8.22050	+	14.2383i	−0.310042	+	0.537008i
$704$	0.557446	−	3.26944i	0.0210095	−	0.123222i
$705$	1.56451	+	2.70981i	0.0589229	+	0.102057i
$706$	−6.71397	+	4.87799i	−0.252684	+	0.183585i
$707$	36.8203	−	1.50980i	1.38477	−	0.0567818i
$708$	2.44757	−	7.53284i	0.0919853	−	0.283102i
$709$	−5.39648	+	51.3441i	−0.202669	+	1.92827i	0.142634	+	0.989775i	$0.454443\pi$
$709$	−5.39648	+	51.3441i	−0.202669	+	1.92827i	−0.345303	+	0.938491i	$0.612224\pi$
$710$	2.09814	−	0.934151i	0.0787417	−	0.0350581i
$711$	−0.445479	−	0.494754i	−0.0167068	−	0.0185547i
$712$	−3.98068	+	4.42100i	−0.149182	+	0.165684i
$713$	1.54015	−	1.11898i	0.0576789	−	0.0419062i
$714$	−4.47064	+	15.9562i	−0.167310	+	0.597146i
$715$	4.09134	+	1.14817i	0.153007	+	0.0429392i
$716$	−0.679636	−	1.17716i	−0.0253992	−	0.0439927i
$717$	1.95659	+	18.6157i	0.0730702	+	0.695217i
$718$	14.9577	+	3.17935i	0.558215	+	0.118652i
$719$	20.3822	−	4.33237i	0.760128	−	0.161570i	0.188489	−	0.982075i	$-0.439641\pi$
$719$	20.3822	−	4.33237i	0.760128	−	0.161570i	0.571639	+	0.820505i	$0.306308\pi$
$720$	−0.321690	−	0.233721i	−0.0119887	−	0.00871028i
$721$	−3.04894	−	20.7777i	−0.113549	−	0.773802i
$722$	1.95116	−	6.00504i	0.0726145	−	0.223485i
$723$	8.27514	−	9.19048i	0.307756	−	0.341798i
$724$	2.65320	+	25.2435i	0.0986055	+	0.938169i
$725$	12.6227	−	21.8632i	0.468796	−	0.811979i
$726$	6.67381	−	8.74416i	0.247688	−	0.324526i
$727$	29.6889			1.10110			0.550551	−	0.834802i	$-0.314418\pi$
$727$	29.6889			1.10110			0.550551	+	0.834802i	$0.314418\pi$
$728$	5.44006	−	6.56378i	0.201622	−	0.243270i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.19176	+	0.678430i	−0.118132	+	0.0251098i
$731$	−15.0159	+	6.68551i	−0.555383	+	0.247273i
$732$	3.35599	−	1.49418i	0.124041	−	0.0552266i
$733$	−36.1912	+	7.69268i	−1.33675	+	0.284136i	−0.820179	−	0.572107i	$-0.806126\pi$
$733$	−36.1912	+	7.69268i	−1.33675	+	0.284136i	−0.516574	+	0.856243i	$0.672793\pi$
$734$	−5.72466	−	17.6187i	−0.211301	−	0.650318i
$735$	1.18968	−	2.51636i	0.0438821	−	0.0928172i
$736$	6.01698			0.221789
$737$	−11.7377	−	45.9683i	−0.432363	−	1.69326i
$738$	−4.63064	+	8.02050i	−0.170456	+	0.295239i
$739$	0.540832	+	5.14567i	0.0198948	+	0.189286i	0.999956	−	0.00941084i	$-0.00299561\pi$
$739$	0.540832	+	5.14567i	0.0198948	+	0.189286i	−0.980061	+	0.198697i	$0.936329\pi$
$740$	0.869436	−	0.965607i	0.0319611	−	0.0354964i
$741$	−5.00973	+	15.4184i	−0.184037	+	0.566407i
$742$	28.7161	+	11.3996i	1.05420	+	0.418494i
$743$	15.4796	+	11.2466i	0.567893	+	0.412598i	0.834339	−	0.551251i	$-0.185849\pi$
$743$	15.4796	+	11.2466i	0.567893	+	0.412598i	−0.266446	+	0.963850i	$0.585849\pi$
$744$	−0.309478	+	0.0657816i	−0.0113460	+	0.00241167i
$745$	3.88254	+	0.825260i	0.142245	+	0.0302352i
$746$	−1.81267	−	17.2464i	−0.0663666	−	0.631436i
$747$	4.38677	+	7.59810i	0.160503	+	0.278000i
$748$	−19.4792	+	7.21486i	−0.712230	+	0.263801i
$749$	10.7791	+	11.0272i	0.393859	+	0.402925i
$750$	−3.16604	+	2.30026i	−0.115607	+	0.0839936i
$751$	−23.2738	+	25.8481i	−0.849272	+	0.943212i	−0.998963	−	0.0455210i	$-0.985505\pi$
$751$	−23.2738	+	25.8481i	−0.849272	+	0.943212i	0.149692	+	0.988733i	$0.452172\pi$
$752$	5.26550	+	5.84793i	0.192013	+	0.213252i
$753$	−7.47256	+	3.32700i	−0.272315	+	0.121243i
$754$	−1.75612	+	16.7083i	−0.0639540	+	0.608481i
$755$	0.547745	−	1.68579i	0.0199345	−	0.0613520i
$756$	−2.64353	+	0.108397i	−0.0961443	+	0.00394235i
$757$	−30.6253	+	22.2506i	−1.11310	+	0.808711i	−0.983148	−	0.182810i	$-0.941481\pi$
$757$	−30.6253	+	22.2506i	−1.11310	+	0.808711i	−0.129947	+	0.991521i	$0.541481\pi$
$758$	9.85628	+	17.0716i	0.357996	+	0.620068i
$759$	17.6729	+	9.26902i	0.641485	+	0.336444i
$760$	−1.00030	+	1.73257i	−0.0362847	+	0.0628470i
$761$	−16.4314	−	7.31573i	−0.595638	−	0.265195i	0.0866973	−	0.996235i	$-0.472369\pi$
$761$	−16.4314	−	7.31573i	−0.595638	−	0.265195i	−0.682335	+	0.731040i	$0.739035\pi$
$762$	2.30314	+	7.08833i	0.0834339	+	0.256783i
$763$	−28.6356	−	19.0629i	−1.03668	−	0.690123i
$764$	−15.0395	−	10.9268i	−0.544111	−	0.395319i
$765$	−0.260319	+	2.47677i	−0.00941184	+	0.0895477i
$766$	−11.9299	−	13.2495i	−0.431044	−	0.478723i
$767$	24.9636	+	5.30618i	0.901384	+	0.191595i
$768$	−0.913545	−	0.406737i	−0.0329647	−	0.0146768i
$769$	−15.6386			−0.563942			−0.281971	−	0.959423i	$-0.590988\pi$
$769$	−15.6386			−0.563942			−0.281971	+	0.959423i	$0.590988\pi$
$770$	3.42884	−	0.646156i	0.123567	−	0.0232858i
$771$	6.43353			0.231698
$772$	18.4383	+	8.20928i	0.663610	+	0.295458i
$773$	11.3223	+	2.40664i	0.407236	+	0.0865607i	0.406975	−	0.913439i	$-0.366584\pi$
$773$	11.3223	+	2.40664i	0.407236	+	0.0865607i	0.000260994		1.00000i	$0.499917\pi$
$774$	−1.75607	−	1.95031i	−0.0631205	−	0.0701025i
$775$	−0.160131	+	1.52354i	−0.00575207	+	0.0547273i
$776$	12.7158	+	9.23855i	0.456470	+	0.331645i
$777$	0.550683	−	8.62806i	0.0197557	−	0.309530i
$778$	−8.09105	−	24.9017i	−0.290078	−	0.892768i
$779$	42.5679	+	18.9524i	1.52515	+	0.679042i
$780$	0.640620	−	1.10959i	0.0229379	−	0.0397296i
$781$	18.9549	−	2.77333i	0.678259	−	0.0992375i
$782$	−18.8426	−	32.6363i	−0.673808	−	1.16707i
$783$	4.21819	−	3.06469i	0.150746	−	0.109523i
$784$	1.61081	−	6.81214i	0.0575288	−	0.243291i
$785$	−1.44998	+	4.46259i	−0.0517522	+	0.159277i
$786$	0.574199	−	5.46314i	0.0204810	−	0.194864i
$787$	−20.5210	+	9.13655i	−0.731495	+	0.325683i	−0.738464	−	0.674293i	$-0.764448\pi$
$787$	−20.5210	+	9.13655i	−0.731495	+	0.325683i	0.00696857	+	0.999976i	$0.497782\pi$
$788$	8.92700	+	9.91443i	0.318011	+	0.353187i
$789$	−17.2767	+	19.1877i	−0.615067	+	0.683101i
$790$	0.214167	−	0.155602i	0.00761974	−	0.00553606i
$791$	32.4200	−	8.29272i	1.15272	−	0.294855i
$792$	−2.05667	−	2.60195i	−0.0730804	−	0.0924562i
$793$	5.91850	+	10.2511i	0.210172	+	0.364029i
$794$	−1.35600	−	12.9015i	−0.0481228	−	0.457858i
$795$	4.54191	+	0.965412i	0.161085	+	0.0342396i
$796$	−18.5425	+	3.94133i	−0.657222	+	0.139697i
$797$	−3.96008	−	2.87717i	−0.140273	−	0.101915i	0.515436	−	0.856928i	$-0.327630\pi$
$797$	−3.96008	−	2.87717i	−0.140273	−	0.101915i	−0.655709	+	0.755014i	$0.727630\pi$
$798$	1.93266	+	13.1705i	0.0684155	+	0.466232i
$799$	15.2301	−	46.8734i	0.538801	−	1.65826i
$800$	−3.23986	+	3.59823i	−0.114546	+	0.127216i
$801$	0.621844	+	5.91645i	0.0219718	+	0.209047i
$802$	6.12933	−	10.6163i	0.216434	−	0.374875i
$803$	−27.1612	−	1.74501i	−0.958497	−	0.0615799i
$804$	−14.3047			−0.504487
$805$	2.20110	+	5.93505i	0.0775787	+	0.209183i
$806$	−0.315035	−	0.969577i	−0.0110966	−	0.0341519i
$807$	−12.0319	+	2.55745i	−0.423542	+	0.0900267i
$808$	12.7243	−	5.66521i	0.447638	−	0.199301i
$809$	−46.0211	+	20.4899i	−1.61802	+	0.720387i	−0.997940	−	0.0641542i	$-0.979565\pi$
$809$	−46.0211	+	20.4899i	−1.61802	+	0.720387i	−0.620076	+	0.784542i	$0.712898\pi$
$810$	−0.388941	+	0.0826720i	−0.0136660	+	0.00290480i
$811$	−9.79672	−	30.1512i	−0.344009	−	1.05875i	−0.962112	−	0.272654i	$-0.912098\pi$
$811$	−9.79672	−	30.1512i	−0.344009	−	1.05875i	0.618103	−	0.786097i	$-0.287902\pi$
$812$	4.79678	+	12.9340i	0.168334	+	0.453895i
$813$	−4.65805			−0.163365
$814$	9.15840	−	5.79507i	0.321002	−	0.203117i
$815$	4.04327	−	7.00314i	0.141629	−	0.245309i
$816$	0.654675	+	6.22881i	0.0229182	+	0.218052i
$817$	−8.83532	+	9.81262i	−0.309109	+	0.343300i
$818$	−8.58272	+	26.4149i	−0.300088	+	0.923576i
$819$	−1.23773	−	8.43477i	−0.0432497	−	0.294735i
$820$	−2.97926	−	2.16456i	−0.104040	−	0.0755897i
$821$	−26.7676	+	5.68963i	−0.934196	+	0.198569i	−0.649772	−	0.760129i	$-0.725136\pi$
$821$	−26.7676	+	5.68963i	−0.934196	+	0.198569i	−0.284424	+	0.958699i	$0.591802\pi$
$822$	−18.7894	−	3.99381i	−0.655355	−	0.139300i
$823$	−2.65432	−	25.2541i	−0.0925237	−	0.880304i	−0.938080	−	0.346418i	$-0.887398\pi$
$823$	−2.65432	−	25.2541i	−0.0925237	−	0.880304i	0.845557	−	0.533886i	$-0.179269\pi$
$824$	−3.96867	−	6.87394i	−0.138255	−	0.239465i
$825$	−15.0590	+	5.57766i	−0.524286	+	0.194189i
$826$	20.3020	−	5.19306i	0.706398	−	0.180690i
$827$	11.0845	−	8.05334i	0.385445	−	0.280042i	−0.378141	−	0.925748i	$-0.623437\pi$
$827$	11.0845	−	8.05334i	0.385445	−	0.280042i	0.763586	+	0.645706i	$0.223437\pi$
$828$	4.02615	−	4.47149i	0.139918	−	0.155395i
$829$	28.9748	+	32.1797i	1.00633	+	1.11765i	0.993045	+	0.117736i	$0.0375637\pi$
$829$	28.9748	+	32.1797i	1.00633	+	1.11765i	0.0132898	+	0.999912i	$0.495770\pi$
$830$	−3.18702	+	1.41895i	−0.110623	+	0.0492525i
$831$	0.687049	−	6.53683i	0.0238335	−	0.226760i
$832$	0.995710	−	3.06448i	0.0345200	−	0.106242i
$833$	−41.9936	+	12.5956i	−1.45499	+	0.436411i
$834$	−10.1857	+	7.40031i	−0.352700	+	0.256252i
$835$	0.434972	+	0.753394i	0.0150528	+	0.0260723i
$836$	−11.9379	+	11.6594i	−0.412879	+	0.403250i
$837$	−0.158196	+	0.274003i	−0.00546805	+	0.00947095i
$838$	−5.60213	−	2.49423i	−0.193522	−	0.0861616i
$839$	6.90690	+	21.2573i	0.238453	+	0.733882i	0.996645	+	0.0818507i	$0.0260831\pi$
$839$	6.90690	+	21.2573i	0.238453	+	0.733882i	−0.758192	+	0.652032i	$0.773917\pi$
$840$	0.0670092	−	1.04990i	0.00231204	−	0.0362248i
$841$	1.46803	+	1.06659i	0.0506217	+	0.0367788i
$842$	2.60795	−	24.8130i	0.0898759	−	0.855112i
$843$	9.75907	+	10.8385i	0.336120	+	0.373299i
$844$	−8.50494	−	1.80778i	−0.292752	−	0.0622264i
$845$	−0.950824	−	0.423334i	−0.0327093	−	0.0145631i
$846$	7.86917			0.270548
$847$	28.9923	+	2.53850i	0.996189	+	0.0872238i
$848$	11.6776			0.401011
$849$	9.84000	+	4.38105i	0.337708	+	0.150357i
$850$	29.6627	+	6.30500i	1.01742	+	0.216260i
$851$	13.1564	+	14.6117i	0.450995	+	0.500881i
$852$	0.603752	−	5.74432i	0.0206842	−	0.196797i
$853$	6.43021	+	4.67182i	0.220166	+	0.159960i	0.692401	−	0.721512i	$-0.256553\pi$
$853$	6.43021	+	4.67182i	0.220166	+	0.159960i	−0.472235	+	0.881473i	$0.656553\pi$
$854$	8.09062	+	5.38597i	0.276855	+	0.184304i
$855$	0.618220	+	1.90269i	0.0211427	+	0.0650705i
$856$	5.32446	+	2.37060i	0.181986	+	0.0810255i
$857$	24.9355	−	43.1896i	0.851782	−	1.47533i	−0.0278164	−	0.999613i	$-0.508855\pi$
$857$	24.9355	−	43.1896i	0.851782	−	1.47533i	0.879599	−	0.475717i	$-0.157811\pi$
$858$	7.64532	−	7.46702i	0.261007	−	0.254920i
$859$	14.8401	+	25.7038i	0.506338	+	0.877003i	0.999973	+	0.00733380i	$0.00233444\pi$
$859$	14.8401	+	25.7038i	0.506338	+	0.877003i	−0.493635	+	0.869669i	$0.664332\pi$
$860$	0.844244	−	0.613379i	0.0287885	−	0.0209160i
$861$	−24.4825	+	1.00389i	−0.834360	+	0.0342125i
$862$	2.35253	−	7.24033i	0.0801273	−	0.246607i
$863$	−3.51149	+	33.4096i	−0.119533	+	1.13728i	0.756153	+	0.654395i	$0.227076\pi$
$863$	−3.51149	+	33.4096i	−0.119533	+	1.13728i	−0.875686	+	0.482881i	$0.839590\pi$
$864$	−0.913545	+	0.406737i	−0.0310794	+	0.0138375i
$865$	−1.59356	−	1.76983i	−0.0541828	−	0.0601761i
$866$	16.2788	−	18.0795i	0.553177	−	0.614366i
$867$	17.9818	−	13.0645i	0.610694	−	0.443695i
$868$	−0.585142	−	0.598612i	−0.0198610	−	0.0203182i
$869$	2.07060	−	0.766925i	0.0702403	−	0.0260162i
$870$	1.03662	+	1.79547i	0.0351446	+	0.0608722i
$871$	−4.81796	−	45.8398i	−0.163250	−	1.55322i
$872$	−12.7180	−	2.70330i	−0.430687	−	0.0915452i
$873$	15.3741	−	3.26787i	0.520335	−	0.110601i
$874$	−24.4916	−	17.7942i	−0.828441	−	0.601898i
$875$	−9.62343	−	3.82028i	−0.325331	−	0.129149i
$876$	−2.53588	+	7.80464i	−0.0856795	+	0.263694i
$877$	6.05297	−	6.72250i	0.204394	−	0.227003i	−0.632229	−	0.774782i	$-0.717860\pi$
$877$	6.05297	−	6.72250i	0.204394	−	0.227003i	0.836623	+	0.547779i	$0.184526\pi$
$878$	0.202791	+	1.92943i	0.00684387	+	0.0651151i
$879$	−5.52286	+	9.56588i	−0.186282	+	0.322649i
$880$	1.11443	−	0.705166i	0.0375674	−	0.0237712i
$881$	3.78457			0.127505			0.0637527	−	0.997966i	$-0.479693\pi$
$881$	3.78457			0.127505			0.0637527	+	0.997966i	$0.479693\pi$
$882$	−3.98457	−	5.75528i	−0.134167	−	0.193790i
$883$	−8.51736	−	26.2138i	−0.286632	−	0.882163i	−0.985905	−	0.167308i	$-0.946493\pi$
$883$	−8.51736	−	26.2138i	−0.286632	−	0.882163i	0.699273	−	0.714855i	$-0.253507\pi$
$884$	−19.7399	+	4.19585i	−0.663926	+	0.141122i
$885$	2.87715	−	1.28099i	0.0967143	−	0.0430600i
$886$	−19.8799	+	8.85109i	−0.667877	+	0.297358i
$887$	−6.69235	+	1.42250i	−0.224707	+	0.0477629i	−0.318889	−	0.947792i	$-0.603310\pi$
$887$	−6.69235	+	1.42250i	−0.224707	+	0.0477629i	0.0941821	+	0.995555i	$0.469976\pi$
$888$	−1.00979	−	3.10780i	−0.0338862	−	0.104291i
$889$	−12.5832	+	15.1824i	−0.422026	+	0.509202i
$890$	−2.36552			−0.0792924
$891$	−3.30980	−	0.212643i	−0.110883	−	0.00712379i
$892$	6.88639	−	11.9276i	0.230573	−	0.399365i
$893$	−4.13851	−	39.3753i	−0.138490	−	1.31764i
$894$	6.67948	−	7.41832i	0.223395	−	0.248106i
$895$	0.167020	−	0.514035i	0.00558287	−	0.0171823i
$896$	−0.384127	−	2.61772i	−0.0128328	−	0.0874518i
$897$	15.6851	+	11.3959i	0.523710	+	0.380498i
$898$	−12.3393	+	2.62280i	−0.411768	+	0.0875240i
$899$	1.61361	+	0.342983i	0.0538168	+	0.0114391i
$900$	0.506115	+	4.81537i	0.0168705	+	0.160512i
$901$	−36.5692	−	63.3397i	−1.21830	−	2.11015i
$902$	−19.0473	−	24.0974i	−0.634207	−	0.802354i
$903$	1.87331	−	6.68604i	0.0623398	−	0.222497i
$904$	10.2325	−	7.43438i	0.340329	−	0.247264i
$905$	−6.75346	+	7.50048i	−0.224493	+	0.249324i
$906$	−2.98282	−	3.31276i	−0.0990976	−	0.110059i
$907$	12.2224	−	5.44176i	0.405838	−	0.180691i	−0.193657	−	0.981069i	$-0.562035\pi$
$907$	12.2224	−	5.44176i	0.405838	−	0.180691i	0.599495	+	0.800379i	$0.295368\pi$
$908$	−1.70527	+	16.2246i	−0.0565915	+	0.538432i
$909$	4.30413	−	13.2467i	0.142759	−	0.439367i
$910$	3.38700	−	0.138882i	0.112278	−	0.00460389i
$911$	−22.3112	+	16.2101i	−0.739205	+	0.537064i	−0.892462	−	0.451123i	$-0.851024\pi$
$911$	−22.3112	+	16.2101i	−0.739205	+	0.537064i	0.153257	+	0.988186i	$0.451024\pi$
$912$	2.51565	+	4.35724i	0.0833017	+	0.144283i
$913$	−28.7920	+	4.21262i	−0.952875	+	0.139417i
$914$	10.5910	−	18.3441i	0.350318	−	0.606769i
$915$	1.33445	+	0.594133i	0.0441154	+	0.0196414i
$916$	−6.42855	−	19.7850i	−0.212405	−	0.653716i
$917$	13.0239	−	6.45041i	0.430087	−	0.213011i
$918$	5.06697	+	3.68137i	0.167235	+	0.121503i
$919$	−5.59003	+	53.1856i	−0.184398	+	1.75443i	0.376380	+	0.926465i	$0.377169\pi$
$919$	−5.59003	+	53.1856i	−0.184398	+	1.75443i	−0.560778	+	0.827966i	$0.689498\pi$
$920$	1.60092	+	1.77800i	0.0527808	+	0.0586190i
$921$	−8.60930	−	1.82996i	−0.283686	−	0.0602993i
$922$	−20.6773	−	9.20611i	−0.680969	−	0.303187i
$923$	18.6112			0.612595
$924$	2.90429	−	8.28041i	0.0955440	−	0.272405i
$925$	−15.8220			−0.520225
$926$	16.0364	+	7.13986i	0.526988	+	0.234630i
$927$	−7.76389	−	1.65027i	−0.254999	−	0.0542018i
$928$	3.48882	+	3.87473i	0.114526	+	0.127194i
$929$	−0.432352	+	4.11355i	−0.0141850	+	0.134961i	−0.999322	−	0.0368069i	$-0.988281\pi$
$929$	−0.432352	+	4.11355i	−0.0141850	+	0.134961i	0.985137	+	0.171768i	$0.0549480\pi$
$930$	−0.101780	−	0.0739476i	−0.00333750	−	0.00242484i
$931$	−26.7024	+	22.9646i	−0.875136	+	0.752633i
$932$	−1.56926	−	4.82969i	−0.0514029	−	0.158202i
$933$	10.2842	+	4.57881i	0.336689	+	0.149904i
$934$	7.06462	−	12.2363i	0.231161	−	0.400383i
$935$	−7.31474	−	3.83642i	−0.239218	−	0.125464i
$936$	−1.61109	−	2.79049i	−0.0526602	−	0.0912102i
$937$	−10.9603	+	7.96309i	−0.358056	+	0.260143i	−0.752241	−	0.658888i	$-0.771027\pi$
$937$	−10.9603	+	7.96309i	−0.358056	+	0.260143i	0.394185	+	0.919031i	$0.371027\pi$
$938$	−20.2503	−	31.9733i	−0.661194	−	1.04397i
$939$	7.53402	−	23.1873i	0.245863	−	0.756690i
$940$	−0.327072	+	3.11188i	−0.0106679	+	0.101498i
$941$	−48.8404	+	21.7451i	−1.59215	+	0.708871i	−0.995600	−	0.0937051i	$-0.970129\pi$
$941$	−48.8404	+	21.7451i	−1.59215	+	0.708871i	−0.596550	+	0.802576i	$0.703462\pi$
$942$	7.89609	+	8.76950i	0.257269	+	0.285726i
$943$	37.2873	−	41.4117i	1.21424	−	1.34855i
$944$	6.40782	−	4.65555i	0.208557	−	0.151525i
$945$	−0.735386	−	0.752315i	−0.0239221	−	0.0244728i
$946$	8.16227	−	3.02320i	0.265378	−	0.0982928i
$947$	−24.9856	−	43.2763i	−0.811922	−	1.40629i	−0.911517	−	0.411263i	$-0.865088\pi$
$947$	−24.9856	−	43.2763i	−0.811922	−	1.40629i	0.0995943	−	0.995028i	$-0.468246\pi$
$948$	−0.0695906	−	0.662110i	−0.00226020	−	0.0215043i
$949$	−25.8644	−	5.49764i	−0.839592	−	0.178461i
$950$	23.8287	−	5.06495i	0.773105	−	0.164329i
$951$	22.6240	+	16.4373i	0.733635	+	0.533017i
$952$	−12.9956	+	10.2811i	−0.421191	+	0.333211i
$953$	17.7883	−	54.7468i	0.576220	−	1.77342i	−0.0557659	−	0.998444i	$-0.517760\pi$
$953$	17.7883	−	54.7468i	0.576220	−	1.77342i	0.631986	−	0.774980i	$-0.282240\pi$
$954$	7.81385	−	8.67816i	0.252983	−	0.280966i
$955$	−0.772664	−	7.35141i	−0.0250028	−	0.237886i
$956$	−9.35913	+	16.2105i	−0.302696	+	0.524285i
$957$	4.27832	+	16.7552i	0.138298	+	0.541618i
$958$	2.79677			0.0903595
$959$	−17.6722	−	47.6512i	−0.570664	−	1.53874i
$960$	−0.122875	−	0.378169i	−0.00396576	−	0.0122054i
$961$	30.2247	−	6.42445i	0.974989	−	0.207240i
$962$	9.61895	−	4.28263i	0.310127	−	0.138078i
$963$	5.32446	−	2.37060i	0.171578	−	0.0763916i
$964$	12.0968	−	2.57125i	0.389610	−	0.0828142i
$965$	2.48001	+	7.63269i	0.0798344	+	0.245705i
$966$	15.6941	+	2.66909i	0.504949	+	0.0858766i
$967$	−38.0100			−1.22232			−0.611160	−	0.791507i	$-0.709297\pi$
$967$	−38.0100			−1.22232			−0.611160	+	0.791507i	$0.709297\pi$
$968$	10.5389	−	3.15141i	0.338733	−	0.101290i
$969$	15.7559	−	27.2899i	0.506151	−	0.876679i
$970$	0.653281	+	6.21555i	0.0209756	+	0.199569i
$971$	25.9114	−	28.7776i	0.831538	−	0.923516i	−0.166506	−	0.986040i	$-0.553248\pi$
$971$	25.9114	−	28.7776i	0.831538	−	0.923516i	0.998043	+	0.0625244i	$0.0199151\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−30.9601	−	12.2905i	−0.992536	−	0.394014i
$974$	12.1738	+	8.84476i	0.390073	+	0.283404i
$975$	−15.2605	+	3.24373i	−0.488728	+	0.103882i
$976$	3.59331	+	0.763783i	0.115019	+	0.0244481i
$977$	−2.08502	−	19.8377i	−0.0667057	−	0.634663i	−0.975889	−	0.218267i	$-0.929960\pi$
$977$	−2.08502	−	19.8377i	−0.0667057	−	0.634663i	0.909183	−	0.416396i	$-0.136707\pi$
$978$	−10.1684	−	17.6122i	−0.325149	−	0.563175i
$979$	−18.9968	−	5.33118i	−0.607142	−	0.170385i
$980$	2.44155	−	1.33650i	0.0779925	−	0.0426928i
$981$	−10.5190	+	7.64247i	−0.335845	+	0.244005i
$982$	9.87464	−	10.9669i	0.315112	−	0.349968i
$983$	−20.8974	−	23.2089i	−0.666524	−	0.740250i	0.311153	−	0.950360i	$-0.399285\pi$
$983$	−20.8974	−	23.2089i	−0.666524	−	0.740250i	−0.977678	+	0.210109i	$0.932618\pi$
$984$	−8.46060	+	3.76690i	−0.269714	+	0.120084i
$985$	−0.554509	+	5.27580i	−0.0176681	+	0.168101i
$986$	10.0912	−	31.0574i	0.321368	−	0.989070i
$987$	11.1399	+	17.5889i	0.354587	+	0.559861i
$988$	−13.1156	+	9.52906i	−0.417264	+	0.303160i
$989$	7.89549	+	13.6754i	0.251062	+	0.434852i
$990$	0.221658	−	1.30003i	0.00704474	−	0.0413177i
$991$	22.8906	−	39.6477i	0.727145	−	1.25945i	−0.230940	−	0.972968i	$-0.574180\pi$
$991$	22.8906	−	39.6477i	0.727145	−	1.25945i	0.958085	−	0.286484i	$-0.0924865\pi$
$992$	−0.289038	−	0.128688i	−0.00917698	−	0.00408585i
$993$	−1.27307	−	3.91811i	−0.0403997	−	0.124337i
$994$	13.6942	−	6.78239i	0.434353	−	0.215124i
$995$	−6.09820	−	4.43060i	−0.193326	−	0.140459i
$996$	−0.917084	+	8.72547i	−0.0290589	+	0.276477i
$997$	7.52837	+	8.36110i	0.238426	+	0.264799i	0.850468	−	0.526026i	$-0.176319\pi$
$997$	7.52837	+	8.36110i	0.238426	+	0.264799i	−0.612043	+	0.790825i	$0.709652\pi$
$998$	−5.41663	−	1.15134i	−0.171460	−	0.0364450i
$999$	−2.98523	−	1.32911i	−0.0944484	−	0.0420511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.25.2	✓	40
7.2	even	3	inner	462.2.y.d.289.4	yes	40
11.4	even	5	inner	462.2.y.d.235.4	yes	40
77.37	even	15	inner	462.2.y.d.37.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.2	✓	40	1.1	even	1	trivial
462.2.y.d.37.2	yes	40	77.37	even	15	inner
462.2.y.d.235.4	yes	40	11.4	even	5	inner
462.2.y.d.289.4	yes	40	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.0415637 + 0.395452i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.168521 + 2.64038i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.198815 + 0.344358i) q^{10} +(-2.37271 + 2.31738i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.60680 + 1.89395i) q^{13} +(-1.22789 + 2.34356i) q^{14} +(-0.122875 + 0.378169i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.72165 - 2.54744i) q^{17} +(0.669131 + 0.743145i) q^{18} +(3.36660 - 3.73899i) q^{19} +(-0.321690 + 0.233721i) q^{20} +(-0.713804 + 2.54764i) q^{21} +(-3.11014 + 1.15196i) q^{22} +(-3.00849 - 5.21086i) q^{23} +(0.104528 + 0.994522i) q^{24} +(4.73608 + 1.00669i) q^{25} +(-3.15177 + 0.669930i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.07495 + 1.64152i) q^{28} +(1.61120 - 4.95877i) q^{29} +(-0.266067 + 0.295497i) q^{30} +(0.0330720 + 0.314659i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.80267 + 1.77342i) q^{33} +6.26312 q^{34} +(-1.03714 - 0.176386i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-3.19633 + 0.679401i) q^{37} +(4.59633 - 2.04642i) q^{38} +(-2.94361 + 1.31058i) q^{39} +(-0.388941 + 0.0826720i) q^{40} +(2.86189 + 8.80800i) q^{41} +(-1.68831 + 2.03706i) q^{42} -2.62440 q^{43} +(-3.30980 - 0.212643i) q^{44} +(-0.198815 + 0.344358i) q^{45} +(-0.628946 - 5.98402i) q^{46} +(5.26550 - 5.84793i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-6.94320 - 0.889920i) q^{49} +(3.91717 + 2.84599i) q^{50} +(6.12626 - 1.30218i) q^{51} +(-3.15177 - 0.669930i) q^{52} +(-1.22064 - 11.6136i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.817793 - 1.03461i) q^{55} +(-2.56323 + 0.655649i) q^{56} +(4.07042 - 2.95733i) q^{57} +(3.48882 - 3.87473i) q^{58} +(-5.29985 - 5.88608i) q^{59} +(-0.363254 + 0.161731i) q^{60} +(0.383995 - 3.65347i) q^{61} +(-0.0977705 + 0.300907i) q^{62} +(-1.22789 + 2.34356i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.640620 - 1.10959i) q^{65} +(-3.28168 + 0.480151i) q^{66} +(-7.15234 + 12.3882i) q^{67} +(5.72165 + 2.54744i) q^{68} +(-1.85935 - 5.72249i) q^{69} +(-0.875731 - 0.582979i) q^{70} +(-4.67285 - 3.39502i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(5.49108 + 6.09846i) q^{73} +(-3.19633 - 0.679401i) q^{74} +(4.42329 + 1.96937i) q^{75} +5.03131 q^{76} +(-5.71890 - 6.65539i) q^{77} -3.22219 q^{78} +(-0.608200 - 0.270788i) q^{79} +(-0.388941 - 0.0826720i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.968067 + 9.21054i) q^{82} +(7.09793 + 5.15695i) q^{83} +(-2.37090 + 1.17425i) q^{84} +(0.769579 + 2.36852i) q^{85} +(-2.39751 - 1.06744i) q^{86} +(2.60698 - 4.51542i) q^{87} +(-2.93716 - 1.54048i) q^{88} +(2.97452 + 5.15202i) q^{89} +(-0.321690 + 0.233721i) q^{90} +(-4.56145 - 7.20212i) q^{91} +(1.85935 - 5.72249i) q^{92} +(-0.0330720 + 0.314659i) q^{93} +(7.18884 - 3.20068i) q^{94} +(1.33866 + 1.48674i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(12.7158 - 9.23855i) q^{97} +(-5.98097 - 3.63704i) q^{98} +(-3.11014 + 1.15196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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