LMFDB - Embedded newform 64.2.i.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	64.37
Dual form			64.2.i.a.45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35786 - 0.395231i) q^{2} +(0.443610 - 0.663909i) q^{3} +(1.68758 + 1.07334i) q^{4} +(0.154331 - 0.775873i) q^{5} +(-0.864759 + 0.726169i) q^{6} +(1.53949 - 3.71667i) q^{7} +(-1.86729 - 2.12443i) q^{8} +(0.904065 + 2.18261i) q^{9} +O(q^{10})$	\(q+(-1.35786 - 0.395231i) q^{2} +(0.443610 - 0.663909i) q^{3} +(1.68758 + 1.07334i) q^{4} +(0.154331 - 0.775873i) q^{5} +(-0.864759 + 0.726169i) q^{6} +(1.53949 - 3.71667i) q^{7} +(-1.86729 - 2.12443i) q^{8} +(0.904065 + 2.18261i) q^{9} +(-0.516209 + 0.992533i) q^{10} +(-1.83415 + 1.22554i) q^{11} +(1.46123 - 0.644259i) q^{12} +(0.559685 + 2.81373i) q^{13} +(-3.55936 + 4.43827i) q^{14} +(-0.446646 - 0.446646i) q^{15} +(1.69589 + 3.62270i) q^{16} +(-2.73419 + 2.73419i) q^{17} +(-0.364963 - 3.32099i) q^{18} +(-5.68264 + 1.13035i) q^{19} +(1.09322 - 1.14370i) q^{20} +(-1.78459 - 2.67083i) q^{21} +(2.97490 - 0.939205i) q^{22} +(2.55179 - 1.05698i) q^{23} +(-2.23878 + 0.297293i) q^{24} +(4.04124 + 1.67394i) q^{25} +(0.352096 - 4.04186i) q^{26} +(4.19950 + 0.835333i) q^{27} +(6.58727 - 4.61979i) q^{28} +(-2.96252 - 1.97949i) q^{29} +(0.429956 + 0.783013i) q^{30} -0.201957i q^{31} +(-0.870977 - 5.58940i) q^{32} +1.76137i q^{33} +(4.79329 - 2.63202i) q^{34} +(-2.64607 - 1.76805i) q^{35} +(-0.816990 + 4.65370i) q^{36} +(-8.82594 - 1.75559i) q^{37} +(8.16299 + 0.711098i) q^{38} +(2.11634 + 0.876616i) q^{39} +(-1.93647 + 1.12092i) q^{40} +(7.85196 - 3.25239i) q^{41} +(1.36764 + 4.33195i) q^{42} +(1.06440 + 1.59299i) q^{43} +(-4.41071 + 0.0995378i) q^{44} +(1.83295 - 0.364596i) q^{45} +(-3.88273 + 0.426695i) q^{46} +(-7.56082 + 7.56082i) q^{47} +(3.15746 + 0.481152i) q^{48} +(-6.49382 - 6.49382i) q^{49} +(-4.82586 - 3.87020i) q^{50} +(0.602339 + 3.02816i) q^{51} +(-2.07557 + 5.34913i) q^{52} +(11.1942 - 7.47973i) q^{53} +(-5.37220 - 2.79404i) q^{54} +(0.667799 + 1.61221i) q^{55} +(-10.7705 + 3.66955i) q^{56} +(-1.77043 + 4.27418i) q^{57} +(3.24034 + 3.85875i) q^{58} +(-1.71321 + 8.61290i) q^{59} +(-0.274351 - 1.23316i) q^{60} +(-2.32214 + 3.47533i) q^{61} +(-0.0798198 + 0.274231i) q^{62} +9.50382 q^{63} +(-1.02644 + 7.93388i) q^{64} +2.26947 q^{65} +(0.696149 - 2.39170i) q^{66} +(5.15244 - 7.71118i) q^{67} +(-7.54888 + 1.67946i) q^{68} +(0.430256 - 2.16304i) q^{69} +(2.89421 + 3.44657i) q^{70} +(1.98817 - 4.79986i) q^{71} +(2.94865 - 5.99619i) q^{72} +(-6.11102 - 14.7533i) q^{73} +(11.2906 + 5.87213i) q^{74} +(2.90407 - 1.94044i) q^{75} +(-10.8032 - 4.19184i) q^{76} +(1.73126 + 8.70365i) q^{77} +(-2.52723 - 2.02677i) q^{78} +(-2.91841 - 2.91841i) q^{79} +(3.07248 - 0.756698i) q^{80} +(-2.59396 + 2.59396i) q^{81} +(-11.9473 + 1.31296i) q^{82} +(-0.190374 + 0.0378677i) q^{83} +(-0.144944 - 6.42273i) q^{84} +(1.69941 + 2.54335i) q^{85} +(-0.815713 - 2.58375i) q^{86} +(-2.62840 + 1.08872i) q^{87} +(6.02849 + 1.60809i) q^{88} +(0.659812 + 0.273303i) q^{89} +(-2.63299 - 0.229366i) q^{90} +(11.3193 + 2.25155i) q^{91} +(5.44086 + 0.955181i) q^{92} +(-0.134081 - 0.0895903i) q^{93} +(13.2548 - 7.27829i) q^{94} +4.58345i q^{95} +(-4.09723 - 1.90126i) q^{96} +2.80442i q^{97} +(6.25116 + 11.3843i) q^{98} +(-4.33307 - 2.89527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$1$

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 $

$2$	−1.35786	−	0.395231i	−0.960154	−	0.279470i
$2$	−1.35786	−	0.395231i	−0.960154	−	0.279470i
$3$	0.443610	−	0.663909i	0.256118	−	0.383308i	−0.681021	−	0.732264i	$-0.738464\pi$
$3$	0.443610	−	0.663909i	0.256118	−	0.383308i	0.937139	+	0.348956i	$0.113464\pi$
$4$	1.68758	+	1.07334i	0.843792	+	0.536670i
$5$	0.154331	−	0.775873i	0.0690188	−	0.346981i	−0.930810	−	0.365504i	$-0.880897\pi$
$5$	0.154331	−	0.775873i	0.0690188	−	0.346981i	0.999828	+	0.0185235i	$0.00589654\pi$
$6$	−0.864759	+	0.726169i	−0.353036	+	0.296457i
$7$	1.53949	−	3.71667i	0.581874	−	1.40477i	−0.309238	−	0.950985i	$-0.600074\pi$
$7$	1.53949	−	3.71667i	0.581874	−	1.40477i	0.891112	−	0.453783i	$-0.149926\pi$
$8$	−1.86729	−	2.12443i	−0.660188	−	0.751101i
$9$	0.904065	+	2.18261i	0.301355	+	0.727535i
$10$	−0.516209	+	0.992533i	−0.163240	+	0.313866i
$11$	−1.83415	+	1.22554i	−0.553018	+	0.369515i	−0.800459	−	0.599388i	$-0.795411\pi$
$11$	−1.83415	+	1.22554i	−0.553018	+	0.369515i	0.247440	+	0.968903i	$0.420411\pi$
$12$	1.46123	−	0.644259i	0.421820	−	0.185982i
$13$	0.559685	+	2.81373i	0.155229	+	0.780387i	0.977441	+	0.211207i	$0.0677393\pi$
$13$	0.559685	+	2.81373i	0.155229	+	0.780387i	−0.822213	+	0.569180i	$0.807261\pi$
$14$	−3.55936	+	4.43827i	−0.951280	+	1.18618i
$15$	−0.446646	−	0.446646i	−0.115324	−	0.115324i
$16$	1.69589	+	3.62270i	0.423972	+	0.905676i
$17$	−2.73419	+	2.73419i	−0.663138	+	0.663138i	−0.956118	−	0.292981i	$-0.905353\pi$
$17$	−2.73419	+	2.73419i	−0.663138	+	0.663138i	0.292981	+	0.956118i	$0.405353\pi$
$18$	−0.364963	−	3.32099i	−0.0860226	−	0.782766i
$19$	−5.68264	+	1.13035i	−1.30369	+	0.259319i	−0.797612	−	0.603171i	$-0.793904\pi$
$19$	−5.68264	+	1.13035i	−1.30369	+	0.259319i	−0.506074	+	0.862490i	$0.668904\pi$
$20$	1.09322	−	1.14370i	0.244452	−	0.255740i
$21$	−1.78459	−	2.67083i	−0.389430	−	0.582823i
$22$	2.97490	−	0.939205i	0.634251	−	0.200239i
$23$	2.55179	−	1.05698i	0.532084	−	0.220396i	−0.100432	−	0.994944i	$-0.532022\pi$
$23$	2.55179	−	1.05698i	0.532084	−	0.220396i	0.632516	+	0.774548i	$0.282022\pi$
$24$	−2.23878	+	0.297293i	−0.456989	+	0.0606846i
$25$	4.04124	+	1.67394i	0.808247	+	0.334787i
$26$	0.352096	−	4.04186i	0.0690517	−	0.792674i
$27$	4.19950	+	0.835333i	0.808195	+	0.160760i
$28$	6.58727	−	4.61979i	1.24488	−	0.873058i
$29$	−2.96252	−	1.97949i	−0.550125	−	0.367582i	0.249226	−	0.968445i	$-0.419824\pi$
$29$	−2.96252	−	1.97949i	−0.550125	−	0.367582i	−0.799352	+	0.600863i	$0.794824\pi$
$30$	0.429956	+	0.783013i	0.0784989	+	0.142958i
$31$		−	0.201957i		−	0.0362726i	−0.999836	−	0.0181363i	$-0.994227\pi$
$31$		−	0.201957i		−	0.0362726i	0.999836	−	0.0181363i	$-0.00577328\pi$
$32$	−0.870977	−	5.58940i	−0.153968	−	0.988076i
$33$			1.76137i			0.306616i
$34$	4.79329	−	2.63202i	0.822042	−	0.451387i
$35$	−2.64607	−	1.76805i	−0.447267	−	0.298854i
$36$	−0.816990	+	4.65370i	−0.136165	+	0.775617i
$37$	−8.82594	−	1.75559i	−1.45098	−	0.288617i	−0.594204	−	0.804314i	$-0.702533\pi$
$37$	−8.82594	−	1.75559i	−1.45098	−	0.288617i	−0.856771	+	0.515697i	$0.827533\pi$
$38$	8.16299	+	0.711098i	1.32421	+	0.115355i
$39$	2.11634	+	0.876616i	0.338885	+	0.140371i
$40$	−1.93647	+	1.12092i	−0.306183	+	0.177232i
$41$	7.85196	−	3.25239i	1.22627	−	0.507938i	0.326872	−	0.945069i	$-0.394005\pi$
$41$	7.85196	−	3.25239i	1.22627	−	0.507938i	0.899398	+	0.437131i	$0.144005\pi$
$42$	1.36764	+	4.33195i	0.211031	+	0.668435i
$43$	1.06440	+	1.59299i	0.162320	+	0.242929i	0.903710	−	0.428146i	$-0.140833\pi$
$43$	1.06440	+	1.59299i	0.162320	+	0.242929i	−0.741390	+	0.671074i	$0.765833\pi$
$44$	−4.41071	+	0.0995378i	−0.664940	+	0.0150059i
$45$	1.83295	−	0.364596i	0.273240	−	0.0543508i
$46$	−3.88273	+	0.426695i	−0.572477	+	0.0629128i
$47$	−7.56082	+	7.56082i	−1.10286	+	1.10286i	−0.108795	+	0.994064i	$0.534699\pi$
$47$	−7.56082	+	7.56082i	−1.10286	+	1.10286i	−0.994064	+	0.108795i	$0.965301\pi$
$48$	3.15746	+	0.481152i	0.455739	+	0.0694483i
$49$	−6.49382	−	6.49382i	−0.927688	−	0.927688i
$50$	−4.82586	−	3.87020i	−0.682479	−	0.547329i
$51$	0.602339	+	3.02816i	0.0843443	+	0.424027i
$52$	−2.07557	+	5.34913i	−0.287829	+	0.741791i
$53$	11.1942	−	7.47973i	1.53764	−	1.02742i	0.557256	−	0.830341i	$-0.311854\pi$
$53$	11.1942	−	7.47973i	1.53764	−	1.02742i	0.980387	−	0.197080i	$-0.0631458\pi$
$54$	−5.37220	−	2.79404i	−0.731064	−	0.380221i
$55$	0.667799	+	1.61221i	0.0900460	+	0.217390i
$56$	−10.7705	+	3.66955i	−1.43927	+	0.490364i
$57$	−1.77043	+	4.27418i	−0.234499	+	0.566130i
$58$	3.24034	+	3.85875i	0.425477	+	0.506679i
$59$	−1.71321	+	8.61290i	−0.223041	+	1.12130i	0.693221	+	0.720725i	$0.256191\pi$
$59$	−1.71321	+	8.61290i	−0.223041	+	1.12130i	−0.916262	+	0.400579i	$0.868809\pi$
$60$	−0.274351	−	1.23316i	−0.0354185	−	0.159200i
$61$	−2.32214	+	3.47533i	−0.297320	+	0.444970i	−0.949810	−	0.312826i	$-0.898724\pi$
$61$	−2.32214	+	3.47533i	−0.297320	+	0.444970i	0.652491	+	0.757797i	$0.273724\pi$
$62$	−0.0798198	+	0.274231i	−0.0101371	+	0.0348273i
$63$	9.50382			1.19737
$64$	−1.02644	+	7.93388i	−0.128305	+	0.991735i
$65$	2.26947			0.281493
$66$	0.696149	−	2.39170i	0.0856901	−	0.294398i
$67$	5.15244	−	7.71118i	0.629471	−	0.942070i	−0.370442	−	0.928856i	$-0.620794\pi$
$67$	5.15244	−	7.71118i	0.629471	−	0.942070i	0.999913	−	0.0132144i	$-0.00420639\pi$
$68$	−7.54888	+	1.67946i	−0.915436	+	0.203665i
$69$	0.430256	−	2.16304i	0.0517967	−	0.260400i
$70$	2.89421	+	3.44657i	0.345925	+	0.411944i
$71$	1.98817	−	4.79986i	0.235952	−	0.569639i	−0.760905	−	0.648864i	$-0.775244\pi$
$71$	1.98817	−	4.79986i	0.235952	−	0.569639i	0.996857	+	0.0792247i	$0.0252445\pi$
$72$	2.94865	−	5.99619i	0.347501	−	0.706658i
$73$	−6.11102	−	14.7533i	−0.715240	−	1.72674i	−0.686472	−	0.727157i	$-0.740841\pi$
$73$	−6.11102	−	14.7533i	−0.715240	−	1.72674i	−0.0287686	−	0.999586i	$-0.509159\pi$
$74$	11.2906	+	5.87213i	1.31250	+	0.682622i
$75$	2.90407	−	1.94044i	0.335333	−	0.224063i
$76$	−10.8032	−	4.19184i	−1.23921	−	0.480837i
$77$	1.73126	+	8.70365i	0.197296	+	0.991873i
$78$	−2.52723	−	2.02677i	−0.286153	−	0.229486i
$79$	−2.91841	−	2.91841i	−0.328346	−	0.328346i	0.523611	−	0.851957i	$-0.324585\pi$
$79$	−2.91841	−	2.91841i	−0.328346	−	0.328346i	−0.851957	+	0.523611i	$0.824585\pi$
$80$	3.07248	−	0.756698i	0.343514	−	0.0846014i
$81$	−2.59396	+	2.59396i	−0.288217	+	0.288217i
$82$	−11.9473	+	1.31296i	−1.31936	+	0.144992i
$83$	−0.190374	+	0.0378677i	−0.0208962	+	0.00415652i	−0.205527	−	0.978651i	$-0.565891\pi$
$83$	−0.190374	+	0.0378677i	−0.0208962	+	0.00415652i	0.184631	+	0.982808i	$0.440891\pi$
$84$	−0.144944	−	6.42273i	−0.0158146	−	0.700777i
$85$	1.69941	+	2.54335i	0.184327	+	0.275865i
$86$	−0.815713	−	2.58375i	−0.0879606	−	0.278612i
$87$	−2.62840	+	1.08872i	−0.281794	+	0.116723i
$88$	6.02849	+	1.60809i	0.642639	+	0.171423i
$89$	0.659812	+	0.273303i	0.0699399	+	0.0289701i	0.417379	−	0.908732i	$-0.362949\pi$
$89$	0.659812	+	0.273303i	0.0699399	+	0.0289701i	−0.347439	+	0.937702i	$0.612949\pi$
$90$	−2.63299	−	0.229366i	−0.277542	−	0.0241773i
$91$	11.3193	+	2.25155i	1.18659	+	0.236027i
$92$	5.44086	+	0.955181i	0.567249	+	0.0995845i
$93$	−0.134081	−	0.0895903i	−0.0139036	−	0.00929008i
$94$	13.2548	−	7.27829i	1.36713	−	0.750699i
$95$			4.58345i			0.470252i
$96$	−4.09723	−	1.90126i	−0.418171	−	0.194047i
$97$			2.80442i			0.284746i	0.989813	+	0.142373i	$0.0454732\pi$
$97$			2.80442i			0.284746i	−0.989813	+	0.142373i	$0.954527\pi$
$98$	6.25116	+	11.3843i	0.631463	+	1.14999i
$99$	−4.33307	−	2.89527i	−0.435490	−	0.290985i
$100$	5.02323	+	7.16253i	0.502323	+	0.716253i
$101$	6.80113	+	1.35283i	0.676738	+	0.134612i	0.521481	−	0.853263i	$-0.325380\pi$
$101$	6.80113	+	1.35283i	0.676738	+	0.134612i	0.155257	+	0.987874i	$0.450380\pi$
$102$	0.378930	−	4.34989i	0.0375196	−	0.430704i
$103$	−12.7910	−	5.29822i	−1.26034	−	0.522049i	−0.350324	−	0.936629i	$-0.613929\pi$
$103$	−12.7910	−	5.29822i	−1.26034	−	0.522049i	−0.910013	+	0.414580i	$0.863929\pi$
$104$	4.93248	−	6.44306i	0.483669	−	0.631794i
$105$	−2.34764	+	0.972426i	−0.229107	+	0.0948990i
$106$	−18.1564	+	5.73216i	−1.76351	+	0.556756i
$107$	−6.64476	−	9.94459i	−0.642373	−	0.961380i	−0.999625	−	0.0273716i	$-0.991286\pi$
$107$	−6.64476	−	9.94459i	−0.642373	−	0.961380i	0.357252	−	0.934008i	$-0.383714\pi$
$108$	6.19042	+	5.91719i	0.595674	+	0.569382i
$109$	4.24802	−	0.844985i	0.406887	−	0.0809348i	0.0125963	−	0.999921i	$-0.495990\pi$
$109$	4.24802	−	0.844985i	0.406887	−	0.0809348i	0.394291	+	0.918986i	$0.370990\pi$
$110$	−0.269585	−	2.45309i	−0.0257039	−	0.233893i
$111$	−5.08082	+	5.08082i	−0.482250	+	0.482250i
$112$	16.0752	−	0.725916i	1.51896	−	0.0685926i
$113$	−4.08315	−	4.08315i	−0.384110	−	0.384110i	0.488470	−	0.872581i	$-0.337555\pi$
$113$	−4.08315	−	4.08315i	−0.384110	−	0.384110i	−0.872581	+	0.488470i	$0.837555\pi$
$114$	4.09329	−	5.10403i	0.383371	−	0.478036i
$115$	−0.426266	−	2.14299i	−0.0397496	−	0.199834i
$116$	−2.87483	−	6.52034i	−0.266922	−	0.605399i
$117$	−5.63526	+	3.76536i	−0.520980	+	0.348108i
$118$	5.73039	−	11.0180i	0.527526	−	1.01429i
$119$	5.95280	+	14.3713i	0.545692	+	1.31742i
$120$	−0.114851	+	1.78289i	−0.0104844	+	0.162755i
$121$	−2.34735	+	5.66701i	−0.213396	+	0.515182i
$122$	4.52671	−	3.80124i	0.409829	−	0.344148i
$123$	1.32392	−	6.65577i	0.119373	−	0.600131i
$124$	0.216769	−	0.340820i	0.0194664	−	0.0306066i
$125$	4.11993	−	6.16591i	0.368498	−	0.551496i
$126$	−12.9049	−	3.75620i	−1.14966	−	0.334629i
$127$	−7.68361			−0.681810			−0.340905	−	0.940098i	$-0.610733\pi$
$127$	−7.68361			−0.681810			−0.340905	+	0.940098i	$0.610733\pi$
$128$	4.52947	−	10.3674i	0.400353	−	0.916361i
$129$	1.52978			0.134689
$130$	−3.08163	−	0.896964i	−0.270277	−	0.0786690i
$131$	3.11524	−	4.66229i	0.272180	−	0.407346i	−0.670048	−	0.742318i	$-0.733727\pi$
$131$	3.11524	−	4.66229i	0.272180	−	0.407346i	0.942228	+	0.334971i	$0.108727\pi$
$132$	−1.89055	+	2.97247i	−0.164551	+	0.258720i
$133$	−4.54726	+	22.8606i	−0.394298	+	1.98227i
$134$	−10.0440	+	8.43432i	−0.867670	+	0.728614i
$135$	1.29622	−	3.12936i	0.111561	−	0.269333i
$136$	10.9141	+	0.703071i	0.935878	+	0.0602879i
$137$	3.02379	+	7.30007i	0.258339	+	0.623687i	0.998829	−	0.0483813i	$-0.0154063\pi$
$137$	3.02379	+	7.30007i	0.258339	+	0.623687i	−0.740489	+	0.672068i	$0.765406\pi$
$138$	−1.43913	+	2.76706i	−0.122507	+	0.235548i
$139$	−0.706120	+	0.471814i	−0.0598923	+	0.0400188i	−0.585156	−	0.810921i	$-0.698967\pi$
$139$	−0.706120	+	0.471814i	−0.0598923	+	0.0400188i	0.525264	+	0.850940i	$0.323967\pi$
$140$	−2.56775	−	5.82386i	−0.217015	−	0.492206i
$141$	1.66564	+	8.37375i	0.140272	+	0.705197i
$142$	−4.59672	+	5.73177i	−0.385748	+	0.481000i
$143$	−4.47489	−	4.47489i	−0.374209	−	0.374209i
$144$	−6.37374	+	6.97661i	−0.531145	+	0.581384i
$145$	−1.99304	+	1.99304i	−0.165513	+	0.165513i
$146$	2.46696	+	22.4482i	0.204167	+	1.85783i
$147$	−7.19202	+	1.43058i	−0.593188	+	0.117992i
$148$	−13.0102	−	12.4359i	−1.06943	−	1.02223i
$149$	0.819641	+	1.22668i	0.0671476	+	0.100493i	0.863524	−	0.504308i	$-0.168252\pi$
$149$	0.819641	+	1.22668i	0.0671476	+	0.100493i	−0.796376	+	0.604802i	$0.793252\pi$
$150$	−4.71025	+	1.48707i	−0.384591	+	0.121419i
$151$	−5.92201	+	2.45298i	−0.481927	+	0.199621i	−0.610401	−	0.792092i	$-0.708992\pi$
$151$	−5.92201	+	2.45298i	−0.481927	+	0.199621i	0.128475	+	0.991713i	$0.458992\pi$
$152$	13.0125	+	9.96170i	1.05545	+	0.808000i
$153$	−8.43953	−	3.49577i	−0.682296	−	0.282616i
$154$	1.08913	−	12.5026i	0.0877649	−	1.00749i
$155$	−0.156693	−	0.0311682i	−0.0125859	−	0.00250349i
$156$	2.63059	+	3.75091i	0.210616	+	0.300313i
$157$	−4.13123	−	2.76040i	−0.329708	−	0.220304i	0.379687	−	0.925115i	$-0.376032\pi$
$157$	−4.13123	−	2.76040i	−0.329708	−	0.220304i	−0.709395	+	0.704811i	$0.751032\pi$
$158$	2.80935	+	5.11624i	0.223500	+	0.407026i
$159$		−	10.7500i		−	0.852532i
$160$	−4.47108	−	0.186849i	−0.353470	−	0.0147717i
$161$		−	11.1114i		−	0.875698i
$162$	4.54745	−	2.49703i	0.357281	−	0.196185i
$163$	18.6548	+	12.4647i	1.46115	+	0.976311i	0.995836	+	0.0911673i	$0.0290598\pi$
$163$	18.6548	+	12.4647i	1.46115	+	0.976311i	0.465317	+	0.885144i	$0.345940\pi$
$164$	16.7418	+	2.93913i	1.30731	+	0.229508i
$165$	1.36660	+	0.271834i	0.106390	+	0.0211622i
$166$	0.273468	+	0.0238224i	0.0212252	+	0.00184898i
$167$	−1.14501	−	0.474279i	−0.0886036	−	0.0367008i	0.337941	−	0.941167i	$-0.390269\pi$
$167$	−1.14501	−	0.474279i	−0.0886036	−	0.0367008i	−0.426545	+	0.904466i	$0.640269\pi$
$168$	−2.34165	+	8.77847i	−0.180662	+	0.677274i
$169$	4.40663	−	1.82529i	0.338972	−	0.140407i
$170$	−1.30236	−	4.12518i	−0.0998863	−	0.316387i
$171$	−7.60457	−	11.3810i	−0.581536	−	0.870331i
$172$	0.0864500	+	3.83077i	0.00659175	+	0.292093i
$173$	−3.23710	+	0.643899i	−0.246112	+	0.0489547i	−0.316605	−	0.948558i	$-0.602543\pi$
$173$	−3.23710	+	0.643899i	−0.246112	+	0.0489547i	0.0704926	+	0.997512i	$0.477543\pi$
$174$	3.99930	−	0.439507i	0.303187	−	0.0333189i
$175$	12.4429	−	12.4429i	0.940596	−	0.940596i
$176$	−7.55029	−	4.56621i	−0.569125	−	0.344191i
$177$	4.95818	+	4.95818i	0.372680	+	0.372680i
$178$	−0.787916	−	0.631886i	−0.0590568	−	0.0473619i
$179$	1.34019	+	6.73758i	0.100170	+	0.503591i	0.997998	+	0.0632437i	$0.0201445\pi$
$179$	1.34019	+	6.73758i	0.100170	+	0.503591i	−0.897828	+	0.440347i	$0.854855\pi$
$180$	3.48459	+	1.35209i	0.259726	+	0.100779i
$181$	5.57875	−	3.72760i	0.414665	−	0.277070i	−0.330688	−	0.943740i	$-0.607281\pi$
$181$	5.57875	−	3.72760i	0.414665	−	0.277070i	0.745353	+	0.666670i	$0.232281\pi$
$182$	−14.4802	−	7.53104i	−1.07334	−	0.558238i
$183$	1.27718	+	3.08338i	0.0944117	+	0.227930i
$184$	−7.01042	−	3.44740i	−0.516815	−	0.254146i
$185$	−2.72423	+	6.57686i	−0.200289	+	0.483541i
$186$	0.146655	+	0.174644i	0.0107533	+	0.0128055i
$187$	1.66406	−	8.36578i	0.121688	−	0.611767i
$188$	−20.8749	+	4.64420i	−1.52246	+	0.338713i
$189$	9.56977	−	14.3222i	0.696098	−	1.04178i
$190$	1.81152	−	6.22370i	0.131422	−	0.451515i
$191$	12.7735			0.924258			0.462129	−	0.886813i	$-0.347086\pi$
$191$	12.7735			0.924258			0.462129	+	0.886813i	$0.347086\pi$
$192$	4.81203	+	4.20101i	0.347279	+	0.303181i
$193$	19.9599			1.43675			0.718373	−	0.695659i	$-0.244887\pi$
$193$	19.9599			1.43675			0.718373	+	0.695659i	$0.244887\pi$
$194$	1.10839	−	3.80802i	0.0795780	−	0.273400i
$195$	1.00676	−	1.50672i	0.0720955	−	0.107898i
$196$	−3.98880	−	17.9289i	−0.284914	−	1.28064i
$197$	1.38429	−	6.95930i	0.0986267	−	0.495830i	−0.899622	−	0.436670i	$-0.856158\pi$
$197$	1.38429	−	6.95930i	0.0986267	−	0.495830i	0.998249	−	0.0591600i	$-0.0188422\pi$
$198$	4.73942	+	5.64394i	0.336816	+	0.401097i
$199$	−2.35849	+	5.69389i	−0.167189	+	0.403629i	−0.985162	−	0.171627i	$-0.945098\pi$
$199$	−2.35849	+	5.69389i	−0.167189	+	0.403629i	0.817973	+	0.575256i	$0.195098\pi$
$200$	−3.99001	−	11.7111i	−0.282136	−	0.828097i
$201$	−2.83384	−	6.84150i	−0.199884	−	0.482563i
$202$	−8.70033	−	4.52498i	−0.612153	−	0.318376i
$203$	−11.9179	+	7.96327i	−0.836471	+	0.558912i
$204$	−2.23375	+	5.75679i	−0.156394	+	0.403056i
$205$	−1.31164	−	6.59406i	−0.0916090	−	0.460549i
$206$	15.2744	+	12.2497i	1.06422	+	0.853474i
$207$	4.61396	+	4.61396i	0.320692	+	0.320692i
$208$	−9.24413	+	6.79933i	−0.640965	+	0.471449i
$209$	9.03754	−	9.03754i	0.625140	−	0.625140i
$210$	3.57211	−	0.392560i	0.246499	−	0.0270892i
$211$	22.5419	−	4.48387i	1.55185	−	0.308682i	0.656599	−	0.754240i	$-0.271995\pi$
$211$	22.5419	−	4.48387i	1.55185	−	0.308682i	0.895253	+	0.445558i	$0.146995\pi$
$212$	26.9195	−	0.607499i	1.84884	−	0.0417232i
$213$	−2.30470	−	3.44923i	−0.157916	−	0.236337i
$214$	5.09227	+	16.1296i	0.348100	+	1.10260i
$215$	1.40023	−	0.579993i	0.0954947	−	0.0395552i
$216$	−6.06709	−	10.4814i	−0.412813	−	0.713168i
$217$	−0.750608	−	0.310912i	−0.0509546	−	0.0211061i
$218$	−6.10220	−	0.531577i	−0.413293	−	0.0360030i
$219$	−12.5057	−	2.48755i	−0.845060	−	0.168093i
$220$	−0.603480	+	3.43751i	−0.0406866	+	0.231757i
$221$	−9.22353	−	6.16297i	−0.620442	−	0.414566i
$222$	8.90716	−	4.89096i	0.597809	−	0.328260i
$223$			14.8044i			0.991375i	0.868501	+	0.495688i	$0.165084\pi$
$223$			14.8044i			0.991375i	−0.868501	+	0.495688i	$0.834916\pi$
$224$	−22.1148	−	5.36771i	−1.47761	−	0.358645i
$225$			10.3338i			0.688918i
$226$	3.93057	+	7.15814i	0.261458	+	0.476153i
$227$	−9.66687	−	6.45920i	−0.641613	−	0.428712i	0.191746	−	0.981445i	$-0.438585\pi$
$227$	−9.66687	−	6.45920i	−0.641613	−	0.428712i	−0.833359	+	0.552733i	$0.813585\pi$
$228$	−7.57539	+	5.31278i	−0.501693	+	0.351848i
$229$	−12.7938	−	2.54484i	−0.845435	−	0.168168i	−0.246677	−	0.969098i	$-0.579339\pi$
$229$	−12.7938	−	2.54484i	−0.845435	−	0.168168i	−0.598758	+	0.800930i	$0.704339\pi$
$230$	−0.268163	+	3.07836i	−0.0176821	+	0.202981i
$231$	6.54644	+	2.71162i	0.430724	+	0.178412i
$232$	1.32659	+	9.98995i	0.0870949	+	0.655873i
$233$	−15.7633	+	6.52939i	−1.03269	+	0.427755i	−0.833683	−	0.552243i	$-0.813772\pi$
$233$	−15.7633	+	6.52939i	−1.03269	+	0.427755i	−0.199008	+	0.979998i	$0.563772\pi$
$234$	9.14010	−	2.88562i	0.597507	−	0.188639i
$235$	4.69937	+	7.03310i	0.306553	+	0.458789i
$236$	−12.1358	+	12.6961i	−0.789971	+	0.826449i
$237$	−3.23219	+	0.642923i	−0.209953	+	0.0417623i
$238$	−2.40309	−	21.8670i	−0.155769	−	1.41743i
$239$	4.07054	−	4.07054i	0.263301	−	0.263301i	−0.563093	−	0.826394i	$-0.690389\pi$
$239$	4.07054	−	4.07054i	0.263301	−	0.263301i	0.826394	+	0.563093i	$0.190389\pi$
$240$	0.860605	−	2.37553i	0.0555518	−	0.153340i
$241$	8.38424	+	8.38424i	0.540076	+	0.540076i	0.923551	−	0.383475i	$-0.125273\pi$
$241$	8.38424	+	8.38424i	0.540076	+	0.540076i	−0.383475	+	0.923551i	$0.625273\pi$
$242$	5.42716	−	6.76727i	0.348871	−	0.435017i
$243$	3.07745	+	15.4714i	0.197418	+	0.992489i
$244$	−7.64902	+	3.37247i	−0.489678	+	0.215900i
$245$	−6.04057	+	4.03618i	−0.385918	+	0.257862i
$246$	−4.42826	+	8.51438i	−0.282336	+	0.542857i
$247$	−6.36097	−	15.3567i	−0.404739	−	0.977126i
$248$	−0.429045	+	0.377114i	−0.0272444	+	0.0239467i
$249$	−0.0593109	+	0.143189i	−0.00375868	+	0.00907425i
$250$	−8.03126	+	6.74414i	−0.507942	+	0.426537i
$251$	−3.80254	+	19.1167i	−0.240014	+	1.20663i	0.653264	+	0.757130i	$0.273399\pi$
$251$	−3.80254	+	19.1167i	−0.240014	+	1.20663i	−0.893278	+	0.449504i	$0.851601\pi$
$252$	16.0385	+	10.2008i	1.01033	+	0.642591i
$253$	−3.38499	+	5.06599i	−0.212812	+	0.318496i
$254$	10.4333	+	3.03680i	0.654643	+	0.190546i
$255$	2.44243			0.152951
$256$	−10.2479	+	12.2874i	−0.640496	+	0.767961i
$257$	−10.7354			−0.669657			−0.334828	−	0.942279i	$-0.608678\pi$
$257$	−10.7354			−0.669657			−0.334828	+	0.942279i	$0.608678\pi$
$258$	−2.07723	−	0.604616i	−0.129323	−	0.0376417i
$259$	−20.1124	+	30.1004i	−1.24972	+	1.87034i
$260$	3.82992	+	2.43591i	0.237522	+	0.151069i
$261$	1.64214	−	8.25559i	0.101646	−	0.511008i
$262$	−6.07276	+	5.09951i	−0.375176	+	0.315049i
$263$	−6.13406	+	14.8089i	−0.378242	+	0.913158i	0.614053	+	0.789265i	$0.289538\pi$
$263$	−6.13406	+	14.8089i	−0.378242	+	0.913158i	−0.992296	+	0.123893i	$0.960462\pi$
$264$	3.74192	−	3.28900i	0.230299	−	0.202424i
$265$	−4.07571	−	9.83964i	−0.250369	−	0.604444i
$266$	15.2098	−	29.2444i	0.932572	−	1.79309i
$267$	0.474147	−	0.316815i	0.0290173	−	0.0193888i
$268$	16.9719	−	7.48295i	1.03672	−	0.457094i
$269$	−6.17273	−	31.0324i	−0.376358	−	1.89208i	−0.446925	−	0.894571i	$-0.647481\pi$
$269$	−6.17273	−	31.0324i	−0.376358	−	1.89208i	0.0705674	−	0.997507i	$-0.477519\pi$
$270$	−2.99692	+	3.73694i	−0.182387	+	0.227423i
$271$	2.32497	+	2.32497i	0.141232	+	0.141232i	0.774188	−	0.632956i	$-0.218159\pi$
$271$	2.32497	+	2.32497i	0.141232	+	0.141232i	−0.632956	+	0.774188i	$0.718159\pi$
$272$	−14.5420	−	5.26827i	−0.881739	−	0.319436i
$273$	6.51618	−	6.51618i	0.394377	−	0.394377i
$274$	−1.22068	−	11.1076i	−0.0737437	−	0.671034i
$275$	−9.46373	+	1.88245i	−0.570684	+	0.113516i
$276$	3.04777	−	3.18851i	0.183454	−	0.191925i
$277$	7.64613	+	11.4432i	0.459411	+	0.687557i	0.986778	−	0.162081i	$-0.0518204\pi$
$277$	7.64613	+	11.4432i	0.459411	+	0.687557i	−0.527366	+	0.849638i	$0.676820\pi$
$278$	1.14529	−	0.361579i	0.0686899	−	0.0216860i
$279$	0.440793	−	0.182583i	0.0263896	−	0.0109309i
$280$	1.18489	+	8.92286i	0.0708106	+	0.533243i
$281$	5.95182	+	2.46532i	0.355056	+	0.147069i	0.553080	−	0.833128i	$-0.313452\pi$
$281$	5.95182	+	2.46532i	0.355056	+	0.147069i	−0.198024	+	0.980197i	$0.563452\pi$
$282$	1.04785	−	12.0287i	0.0623986	−	0.716300i
$283$	−17.8358	−	3.54776i	−1.06023	−	0.210893i	−0.365976	−	0.930624i	$-0.619265\pi$
$283$	−17.8358	−	3.54776i	−1.06023	−	0.210893i	−0.694252	+	0.719732i	$0.744265\pi$
$284$	8.50709	−	5.96620i	0.504803	−	0.354029i
$285$	3.04299	+	2.03326i	0.180251	+	0.120440i
$286$	4.30767	+	7.84490i	0.254718	+	0.463879i
$287$		−	34.1901i		−	2.01818i
$288$	11.4120	−	6.95418i	0.672461	−	0.409779i
$289$			2.04845i			0.120497i
$290$	3.49399	−	1.91856i	0.205174	−	0.112662i
$291$	1.86188	+	1.24407i	0.109145	+	0.0729285i
$292$	5.52243	−	31.4566i	0.323176	−	1.84086i
$293$	2.52796	+	0.502842i	0.147685	+	0.0293763i	0.268379	−	0.963313i	$-0.413512\pi$
$293$	2.52796	+	0.502842i	0.147685	+	0.0293763i	−0.120694	+	0.992690i	$0.538512\pi$
$294$	10.3312	+	0.899975i	0.602528	+	0.0524876i
$295$	6.41812	+	2.65847i	0.373677	+	0.154782i
$296$	12.7510	+	22.0283i	0.741136	+	1.28037i
$297$	−8.72628	+	3.61454i	−0.506350	+	0.209737i
$298$	−0.628138	−	1.98961i	−0.0363871	−	0.115255i
$299$	4.40226	+	6.58845i	0.254589	+	0.381020i
$300$	6.98362	−	0.157601i	0.403199	−	0.00909911i
$301$	7.55925	−	1.50363i	0.435708	−	0.0866677i
$302$	9.01078	−	0.990246i	0.518512	−	0.0569822i
$303$	3.91520	−	3.91520i	0.224923	−	0.224923i
$304$	−13.7320	−	18.6696i	−0.787585	−	1.07077i
$305$	2.33804	+	2.33804i	0.133876	+	0.133876i
$306$	10.0781	+	8.08234i	0.576126	+	0.462037i
$307$	1.65226	+	8.30646i	0.0942993	+	0.474075i	0.998860	+	0.0477304i	$0.0151988\pi$
$307$	1.65226	+	8.30646i	0.0942993	+	0.474075i	−0.904561	+	0.426344i	$0.859801\pi$
$308$	−6.42032	+	16.5464i	−0.365832	+	0.942818i
$309$	−9.19175	+	6.14173i	−0.522901	+	0.349391i
$310$	0.200449	+	0.104252i	0.0113848	+	0.00592113i
$311$	−0.633352	−	1.52905i	−0.0359141	−	0.0867042i	0.904905	−	0.425614i	$-0.139942\pi$
$311$	−0.633352	−	1.52905i	−0.0359141	−	0.0867042i	−0.940819	+	0.338910i	$0.889942\pi$
$312$	−2.08951	−	6.13292i	−0.118295	−	0.347208i
$313$	6.07939	−	14.6769i	0.343628	−	0.829590i	−0.653715	−	0.756740i	$-0.726791\pi$
$313$	6.07939	−	14.6769i	0.343628	−	0.829590i	0.997343	−	0.0728497i	$-0.0232094\pi$
$314$	4.51865	+	5.38104i	0.255002	+	0.303670i
$315$	1.46673	−	7.37375i	0.0826409	−	0.415464i
$316$	−1.79262	−	8.05750i	−0.100843	−	0.453270i
$317$	−8.81780	+	13.1968i	−0.495257	+	0.741204i	−0.991937	−	0.126729i	$-0.959552\pi$
$317$	−8.81780	+	13.1968i	−0.495257	+	0.741204i	0.496680	+	0.867934i	$0.334552\pi$
$318$	−4.24874	+	14.5971i	−0.238258	+	0.818562i
$319$	7.85966			0.440057
$320$	5.99727	+	2.02082i	0.335258	+	0.112968i
$321$	−9.54998			−0.533028
$322$	−4.39155	+	15.0877i	−0.244732	+	0.840805i
$323$	12.4468	−	18.6280i	0.692559	−	1.03649i
$324$	−7.16172	+	1.59333i	−0.397873	+	0.0885182i
$325$	−2.44817	+	12.3078i	−0.135800	+	0.682714i
$326$	−20.4042	−	24.2983i	−1.13008	−	1.34576i
$327$	1.32347	−	3.19514i	0.0731882	−	0.176692i
$328$	−21.5714	−	10.6078i	−1.19108	−	0.585718i
$329$	16.4612	+	39.7409i	0.907536	+	2.19099i
$330$	−1.74822	−	0.909237i	−0.0962364	−	0.0500518i
$331$	17.9691	−	12.0066i	0.987671	−	0.659941i	0.0468703	−	0.998901i	$-0.485075\pi$
$331$	17.9691	−	12.0066i	0.987671	−	0.659941i	0.940801	+	0.338960i	$0.110075\pi$
$332$	−0.361917	−	0.140431i	−0.0198628	−	0.00770713i
$333$	−4.14746	−	20.8507i	−0.227280	−	1.14261i
$334$	1.36732	+	1.09655i	0.0748164	+	0.0600005i
$335$	−5.18771	−	5.18771i	−0.283435	−	0.283435i
$336$	6.64916	−	10.9945i	0.362742	−	0.599798i
$337$	0.918442	−	0.918442i	0.0500307	−	0.0500307i	−0.681649	−	0.731680i	$-0.738737\pi$
$337$	0.918442	−	0.918442i	0.0500307	−	0.0500307i	0.731680	+	0.681649i	$0.238737\pi$
$338$	−6.70501	+	0.736852i	−0.364705	+	0.0400795i
$339$	−4.52216	+	0.899514i	−0.245610	+	0.0488549i
$340$	0.138025	+	6.11616i	0.00748547	+	0.331696i
$341$	0.247507	+	0.370421i	0.0134033	+	0.0200594i
$342$	5.82783	+	18.4595i	0.315133	+	0.998174i
$343$	−8.11589	+	3.36171i	−0.438217	+	0.181515i
$344$	1.39665	−	5.23583i	0.0753024	−	0.282297i
$345$	−1.61184	−	0.667647i	−0.0867787	−	0.0359449i
$346$	4.65003	+	0.405075i	0.249987	+	0.0217770i
$347$	−0.170754	−	0.0339651i	−0.00916656	−	0.00182334i	0.190505	−	0.981686i	$-0.438987\pi$
$347$	−0.170754	−	0.0339651i	−0.00916656	−	0.00182334i	−0.199671	+	0.979863i	$0.563987\pi$
$348$	−5.60422	−	0.983859i	−0.300417	−	0.0527404i
$349$	0.883430	+	0.590289i	0.0472889	+	0.0315974i	0.578990	−	0.815335i	$-0.303447\pi$
$349$	0.883430	+	0.590289i	0.0472889	+	0.0315974i	−0.531701	+	0.846932i	$0.678447\pi$
$350$	−21.8136	+	11.9780i	−1.16599	+	0.640249i
$351$			12.2838i			0.655659i
$352$	8.44756	+	9.18440i	0.450256	+	0.489530i
$353$		−	0.638175i		−	0.0339666i	−0.999856	−	0.0169833i	$-0.994594\pi$
$353$		−	0.638175i		−	0.0339666i	0.999856	−	0.0169833i	$-0.00540622\pi$
$354$	−4.77291	−	8.69216i	−0.253677	−	0.461983i
$355$	−3.41725	−	2.28333i	−0.181369	−	0.121187i
$356$	0.820141	+	1.16942i	0.0434674	+	0.0619793i
$357$	12.1820	+	2.42314i	0.644738	+	0.128246i
$358$	0.843109	−	9.67840i	0.0445597	−	0.511519i
$359$	14.2385	+	5.89779i	0.751480	+	0.311273i	0.725345	−	0.688385i	$-0.241680\pi$
$359$	14.2385	+	5.89779i	0.751480	+	0.311273i	0.0261347	+	0.999658i	$0.491680\pi$
$360$	−4.19721	−	3.21317i	−0.221213	−	0.169349i
$361$	13.4610	−	5.57571i	0.708472	−	0.293459i
$362$	−9.04844	+	2.85668i	−0.475575	+	0.150144i
$363$	2.72107	+	4.07237i	0.142819	+	0.213744i
$364$	16.6856	+	15.9491i	0.874564	+	0.835962i
$365$	−12.3898	+	2.46448i	−0.648512	+	0.128997i
$366$	−0.515585	−	4.69159i	−0.0269501	−	0.245233i
$367$	5.81483	−	5.81483i	0.303531	−	0.303531i	−0.538862	−	0.842394i	$-0.681146\pi$
$367$	5.81483	−	5.81483i	0.303531	−	0.303531i	0.842394	+	0.538862i	$0.181146\pi$
$368$	8.15668	+	7.45183i	0.425196	+	0.388454i
$369$	14.1974	+	14.1974i	0.739085	+	0.739085i
$370$	6.29851	−	7.85378i	0.327444	−	0.408299i
$371$	−10.5663	−	53.1202i	−0.548573	−	2.75786i
$372$	−0.130113	−	0.295106i	−0.00674604	−	0.0153005i
$373$	−4.87425	+	3.25687i	−0.252379	+	0.168634i	−0.675324	−	0.737521i	$-0.735996\pi$
$373$	−4.87425	+	3.25687i	−0.252379	+	0.168634i	0.422945	+	0.906155i	$0.360996\pi$
$374$	−5.56598	+	10.7019i	−0.287810	+	0.553382i
$375$	−2.26596	−	5.47052i	−0.117014	−	0.282496i
$376$	30.1807	+	1.94420i	1.55645	+	0.100264i
$377$	3.91167	−	9.44360i	0.201461	−	0.486370i
$378$	−18.6550	+	15.6653i	−0.959509	+	0.805735i
$379$	2.02175	−	10.1640i	0.103850	−	0.522090i	−0.893482	−	0.449098i	$-0.851745\pi$
$379$	2.02175	−	10.1640i	0.103850	−	0.522090i	0.997333	−	0.0729916i	$-0.0232546\pi$
$380$	−4.91960	+	7.73496i	−0.252370	+	0.396795i
$381$	−3.40852	+	5.10122i	−0.174624	+	0.261343i
$382$	−17.3447	−	5.04848i	−0.887430	−	0.258303i
$383$	−35.5967			−1.81890			−0.909452	−	0.415808i	$-0.863499\pi$
$383$	−35.5967			−1.81890			−0.909452	+	0.415808i	$0.863499\pi$
$384$	−4.87372	−	7.60626i	−0.248711	−	0.388155i
$385$	7.02012			0.357778
$386$	−27.1028	−	7.88877i	−1.37950	−	0.401528i
$387$	−2.51458	+	3.76333i	−0.127823	+	0.191301i
$388$	−3.01009	+	4.73269i	−0.152814	+	0.240266i
$389$	6.65141	−	33.4389i	0.337240	−	1.69542i	−0.324663	−	0.945830i	$-0.605251\pi$
$389$	6.65141	−	33.4389i	0.337240	−	1.69542i	0.661903	−	0.749590i	$-0.269749\pi$
$390$	−1.96254	+	1.64802i	−0.0993772	+	0.0834506i
$391$	−4.08707	+	9.86705i	−0.206692	+	0.498998i
$392$	−1.66983	+	25.9215i	−0.0843390	+	1.30924i
$393$	−1.71338	−	4.13647i	−0.0864288	−	0.208658i
$394$	−4.63021	+	8.90267i	−0.233267	+	0.448510i
$395$	−2.71471	+	1.81391i	−0.136592	+	0.0912679i
$396$	−4.20482	−	9.53686i	−0.211300	−	0.479245i
$397$	5.24522	+	26.3695i	0.263250	+	1.32345i	0.855546	+	0.517727i	$0.173222\pi$
$397$	5.24522	+	26.3695i	0.263250	+	1.32345i	−0.592295	+	0.805721i	$0.701778\pi$
$398$	5.45290	−	6.79938i	0.273329	−	0.340822i
$399$	13.1602	+	13.1602i	0.658832	+	0.658832i
$400$	0.789309	+	17.4790i	0.0394655	+	0.873950i
$401$	−8.87445	+	8.87445i	−0.443169	+	0.443169i	−0.893076	−	0.449907i	$-0.851457\pi$
$401$	−8.87445	+	8.87445i	−0.443169	+	0.443169i	0.449907	+	0.893076i	$0.351457\pi$
$402$	1.14400	+	10.4099i	0.0570574	+	0.519196i
$403$	0.568253	−	0.113032i	0.0283067	−	0.00563055i
$404$	10.0254	+	9.58294i	0.498784	+	0.476769i
$405$	1.61225	+	2.41291i	0.0801135	+	0.119898i
$406$	19.3302	−	6.10272i	0.959341	−	0.302873i
$407$	18.3397	−	7.59655i	0.909064	−	0.376547i
$408$	5.30839	−	6.93409i	0.262804	−	0.343289i
$409$	−10.8015	−	4.47412i	−0.534099	−	0.221231i	0.0992984	−	0.995058i	$-0.468340\pi$
$409$	−10.8015	−	4.47412i	−0.534099	−	0.221231i	−0.633398	+	0.773827i	$0.718340\pi$
$410$	−0.825149	+	9.47224i	−0.0407512	+	0.467800i
$411$	6.18796	+	1.23086i	0.305229	+	0.0607139i
$412$	−15.8992	−	22.6703i	−0.783295	−	1.11689i
$413$	29.3738	+	19.6269i	1.44539	+	0.965779i
$414$	−4.44155	−	8.08871i	−0.218290	−	0.397538i
$415$			0.153550i			0.00753747i
$416$	15.2396	−	5.57899i	0.747181	−	0.273533i
$417$			0.678100i			0.0332067i
$418$	−15.8437	+	8.69983i	−0.774939	+	0.425523i
$419$	13.3738	+	8.93607i	0.653351	+	0.436555i	0.837570	−	0.546330i	$-0.183975\pi$
$419$	13.3738	+	8.93607i	0.653351	+	0.436555i	−0.184219	+	0.982885i	$0.558975\pi$
$420$	−5.00559	−	0.878767i	−0.244248	−	0.0428794i
$421$	25.6227	+	5.09667i	1.24877	+	0.248397i	0.774836	−	0.632162i	$-0.217832\pi$
$421$	25.6227	+	5.09667i	1.24877	+	0.248397i	0.473938	+	0.880558i	$0.342832\pi$
$422$	−32.3810	−	2.82079i	−1.57628	−	0.137314i
$423$	−23.3378	−	9.66682i	−1.13472	−	0.470017i
$424$	−36.7931	−	9.81451i	−1.78683	−	0.476635i
$425$	−15.6263	+	6.47265i	−0.757989	+	0.313969i
$426$	1.76623	+	5.59447i	0.0855740	+	0.271053i
$427$	9.34172	+	13.9809i	0.452077	+	0.676582i
$428$	−0.539683	−	23.9144i	−0.0260866	−	1.15595i
$429$	−4.95602	+	0.985814i	−0.239279	+	0.0475955i
$430$	−2.13055	+	0.234138i	−0.102744	+	0.0112911i
$431$	−6.74058	+	6.74058i	−0.324682	+	0.324682i	−0.850560	−	0.525878i	$-0.823737\pi$
$431$	−6.74058	+	6.74058i	−0.324682	+	0.324682i	0.525878	+	0.850560i	$0.323737\pi$
$432$	4.09572	+	16.6302i	0.197055	+	0.800120i
$433$	−8.98452	−	8.98452i	−0.431769	−	0.431769i	0.457461	−	0.889230i	$-0.348759\pi$
$433$	−8.98452	−	8.98452i	−0.431769	−	0.431769i	−0.889230	+	0.457461i	$0.848759\pi$
$434$	0.896341	+	0.718840i	0.0430258	+	0.0345054i
$435$	0.439065	+	2.20733i	0.0210515	+	0.105833i
$436$	8.07586	+	3.13359i	0.386763	+	0.150072i
$437$	−13.3061	+	8.89086i	−0.636518	+	0.425308i
$438$	15.9979	+	8.32041i	0.764411	+	0.397564i
$439$	−12.2357	−	29.5395i	−0.583976	−	1.40984i	−0.889181	−	0.457556i	$-0.848725\pi$
$439$	−12.2357	−	29.5395i	−0.583976	−	1.40984i	0.305205	−	0.952287i	$-0.401275\pi$
$440$	2.17806	−	4.42916i	0.103835	−	0.211152i
$441$	8.30261	−	20.0443i	0.395363	−	0.954490i
$442$	10.0885	+	12.0139i	0.479861	+	0.571443i
$443$	5.01357	−	25.2049i	0.238202	−	1.19752i	−0.657704	−	0.753277i	$-0.728472\pi$
$443$	5.01357	−	25.2049i	0.238202	−	1.19752i	0.895906	−	0.444244i	$-0.146528\pi$
$444$	−14.0278	+	3.12087i	−0.665728	+	0.148110i
$445$	0.313877	−	0.469751i	0.0148792	−	0.0222683i
$446$	5.85115	−	20.1023i	0.277060	−	0.951873i
$447$	1.17800			0.0557176
$448$	27.9074	+	16.0291i	1.31850	+	0.757303i
$449$	−26.9484			−1.27177			−0.635887	−	0.771782i	$-0.719365\pi$
$449$	−26.9484			−1.27177			−0.635887	+	0.771782i	$0.719365\pi$
$450$	4.08423	−	14.0319i	0.192532	−	0.661468i
$451$	−10.4158	+	15.5883i	−0.490459	+	0.734024i
$452$	−2.50806	−	11.2733i	−0.117969	−	0.530250i
$453$	−0.998508	+	5.01984i	−0.0469140	+	0.235853i
$454$	10.5734	+	12.5914i	0.496235	+	0.590942i
$455$	3.49383	−	8.43486i	0.163793	−	0.395432i
$456$	12.3861	−	4.22000i	0.580033	−	0.197620i
$457$	4.39604	+	10.6130i	0.205638	+	0.496454i	0.992727	−	0.120385i	$-0.0384128\pi$
$457$	4.39604	+	10.6130i	0.205638	+	0.496454i	−0.787089	+	0.616839i	$0.788413\pi$
$458$	16.3664	+	8.51203i	0.764750	+	0.397741i
$459$	−13.7662	+	9.19827i	−0.642551	+	0.429339i
$460$	1.58079	−	4.07400i	0.0737047	−	0.189951i
$461$	3.51862	+	17.6893i	0.163878	+	0.823872i	0.972023	+	0.234888i	$0.0754722\pi$
$461$	3.51862	+	17.6893i	0.163878	+	0.823872i	−0.808144	+	0.588985i	$0.799528\pi$
$462$	−7.81745	−	6.26937i	−0.363701	−	0.291677i
$463$	9.97845	+	9.97845i	0.463738	+	0.463738i	0.899879	−	0.436141i	$-0.143655\pi$
$463$	9.97845	+	9.97845i	0.463738	+	0.463738i	−0.436141	+	0.899879i	$0.643655\pi$
$464$	2.14701	−	14.0893i	0.0996726	−	0.654079i
$465$	−0.0902035	+	0.0902035i	−0.00418309	+	0.00418309i
$466$	23.9851	−	2.63586i	1.11109	−	0.122104i
$467$	35.3990	−	7.04130i	1.63807	−	0.325832i	0.711711	−	0.702473i	$-0.247921\pi$
$467$	35.3990	−	7.04130i	1.63807	−	0.325832i	0.926360	+	0.376640i	$0.122921\pi$
$468$	−13.5515	+	0.305820i	−0.626418	+	0.0141366i
$469$	−20.7277	−	31.0212i	−0.957117	−	1.43243i
$470$	−3.60140	−	11.4073i	−0.166120	−	0.526181i
$471$	−3.66531	+	1.51822i	−0.168889	+	0.0699559i
$472$	21.4966	−	12.4432i	0.989462	−	0.572745i
$473$	−3.90455	−	1.61732i	−0.179531	−	0.0743644i
$474$	4.64297	+	0.404461i	0.213259	+	0.0185775i
$475$	−24.8570	−	4.94437i	−1.14052	−	0.226863i
$476$	−5.37945	+	30.6422i	−0.246567	+	1.40448i
$477$	26.4456	+	17.6704i	1.21086	+	0.809072i
$478$	−7.13604	+	3.91843i	−0.326395	+	0.179225i
$479$			37.7961i			1.72695i	0.504393	+	0.863474i	$0.331716\pi$
$479$			37.7961i			1.72695i	−0.504393	+	0.863474i	$0.668284\pi$
$480$	−2.10747	+	2.88550i	−0.0961922	+	0.131705i
$481$		−	25.8163i		−	1.17712i
$482$	−8.07094	−	14.6984i	−0.367621	−	0.669492i
$483$	−7.37693	−	4.92910i	−0.335662	−	0.224282i
$484$	−10.0440	+	7.04405i	−0.456544	+	0.320184i
$485$	2.17587	+	0.432808i	0.0988012	+	0.0196528i
$486$	1.93601	−	22.2243i	0.0878193	−	1.00811i
$487$	17.7628	+	7.35758i	0.804908	+	0.333404i	0.746920	−	0.664914i	$-0.231532\pi$
$487$	17.7628	+	7.35758i	0.804908	+	0.333404i	0.0579876	+	0.998317i	$0.481532\pi$
$488$	11.7192	−	1.55622i	0.530504	−	0.0704469i
$489$	16.5509	−	6.85559i	0.748456	−	0.310020i
$490$	9.79750	−	3.09316i	0.442606	−	0.139735i
$491$	19.8604	+	29.7231i	0.896285	+	1.34139i	0.939582	+	0.342323i	$0.111214\pi$
$491$	19.8604	+	29.7231i	0.896285	+	1.34139i	−0.0432969	+	0.999062i	$0.513786\pi$
$492$	9.37812	−	9.81117i	0.422798	−	0.442322i
$493$	13.5124	−	2.68778i	0.608566	−	0.121051i
$494$	2.56787	+	23.3664i	0.115534	+	1.05130i
$495$	−2.91508	+	2.91508i	−0.131023	+	0.131023i
$496$	0.731632	−	0.342497i	0.0328512	−	0.0153786i
$497$	−14.7787	−	14.7787i	−0.662916	−	0.662916i
$498$	0.137129	−	0.170990i	0.00614490	−	0.00766224i
$499$	−5.52124	−	27.7572i	−0.247165	−	1.24258i	−0.882488	−	0.470335i	$-0.844133\pi$
$499$	−5.52124	−	27.7572i	−0.247165	−	1.24258i	0.635323	−	0.772246i	$-0.280867\pi$
$500$	13.5708	−	5.98342i	0.606907	−	0.267587i
$501$	−0.822816	+	0.549788i	−0.0367607	+	0.0245627i
$502$	12.7188	−	24.4549i	0.567669	−	1.09148i
$503$	3.74555	+	9.04255i	0.167006	+	0.403187i	0.985120	−	0.171868i	$-0.0549804\pi$
$503$	3.74555	+	9.04255i	0.167006	+	0.403187i	−0.818114	+	0.575056i	$0.804980\pi$
$504$	−17.7464	−	20.1902i	−0.790488	−	0.899345i
$505$	2.09925	−	5.06803i	0.0934153	−	0.225524i
$506$	6.59859	−	5.54108i	0.293343	−	0.246331i
$507$	0.743001	−	3.73532i	0.0329978	−	0.165891i
$508$	−12.9667	−	8.24712i	−0.575306	−	0.365907i
$509$	−13.6199	+	20.3836i	−0.603691	+	0.903488i	−0.999892	−	0.0146761i	$-0.995328\pi$
$509$	−13.6199	+	20.3836i	−0.603691	+	0.903488i	0.396201	+	0.918164i	$0.370328\pi$
$510$	−3.31648	−	0.965323i	−0.146856	−	0.0427452i
$511$	−64.2409			−2.84185
$512$	18.7717	−	12.6343i	0.829598	−	0.558361i
$513$	−24.8085			−1.09532
$514$	14.5772	+	4.24297i	0.642974	+	0.187149i
$515$	−6.08479	+	9.10653i	−0.268128	+	0.401282i
$516$	2.58163	+	1.64197i	0.113650	+	0.0722837i
$517$	4.60160	−	23.1338i	0.202378	−	1.01742i
$518$	39.2065	−	32.9231i	1.72263	−	1.44656i
$519$	−1.00852	+	2.43478i	−0.0442690	+	0.106875i
$520$	−4.23776	−	4.82134i	−0.185838	−	0.211430i
$521$	−1.21410	−	2.93109i	−0.0531905	−	0.128413i	0.895050	−	0.445965i	$-0.147139\pi$
$521$	−1.21410	−	2.93109i	−0.0531905	−	0.128413i	−0.948241	+	0.317552i	$0.897139\pi$
$522$	−5.49267	+	10.5609i	−0.240407	+	0.462240i
$523$	32.5809	−	21.7698i	1.42466	−	0.951929i	0.425772	−	0.904830i	$-0.360003\pi$
$523$	32.5809	−	21.7698i	1.42466	−	0.951929i	0.998890	−	0.0470985i	$-0.0149975\pi$
$524$	10.2615	−	4.52430i	0.448274	−	0.197645i
$525$	−2.74116	−	13.7808i	−0.119634	−	0.601442i
$526$	14.1822	−	17.6841i	0.618372	−	0.771065i
$527$	0.552189	+	0.552189i	0.0240537	+	0.0240537i
$528$	−6.38093	+	2.98709i	−0.277694	+	0.129996i
$529$	−10.8691	+	10.8691i	−0.472568	+	0.472568i
$530$	1.64533	+	14.9717i	0.0714685	+	0.650330i
$531$	−20.3474	+	4.04736i	−0.883003	+	0.175640i
$532$	−32.2111	+	33.6985i	−1.39653	+	1.46101i
$533$	13.5459	+	20.2729i	0.586740	+	0.878118i
$534$	−0.769042	+	0.242794i	−0.0332797	+	0.0105067i
$535$	−8.74123	+	3.62073i	−0.377916	+	0.156538i
$536$	−26.0030	+	3.45300i	−1.12316	+	0.149147i
$537$	5.06766	+	2.09909i	0.218686	+	0.0905826i
$538$	−3.88324	+	44.5774i	−0.167419	+	1.92187i
$539$	19.8691	+	3.95221i	0.855824	+	0.170234i
$540$	5.54636	−	3.88978i	0.238677	−	0.167389i
$541$	−15.3762	−	10.2741i	−0.661075	−	0.441716i	0.179247	−	0.983804i	$-0.442634\pi$
$541$	−15.3762	−	10.2741i	−0.661075	−	0.441716i	−0.840322	+	0.542088i	$0.817634\pi$
$542$	−2.23809	−	4.07590i	−0.0961343	−	0.175075i
$543$		−	5.35738i		−	0.229907i
$544$	17.6639	+	12.9010i	0.757333	+	0.553128i
$545$		−	3.42633i		−	0.146768i
$546$	−11.4235	+	6.27268i	−0.488880	+	0.268446i
$547$	−12.2578	−	8.19037i	−0.524104	−	0.350195i	0.265204	−	0.964192i	$-0.414561\pi$
$547$	−12.2578	−	8.19037i	−0.524104	−	0.350195i	−0.789308	+	0.613997i	$0.789561\pi$
$548$	−2.73255	+	15.5650i	−0.116729	+	0.664905i
$549$	−9.68464	−	1.92639i	−0.413330	−	0.0822165i
$550$	13.5945	+	1.18425i	0.579670	+	0.0504964i
$551$	19.0724	+	7.90005i	0.812512	+	0.336553i
$552$	−5.39865	+	3.12498i	−0.229782	+	0.133008i
$553$	−15.3396	+	6.35388i	−0.652307	+	0.270194i
$554$	−5.85967	−	18.5603i	−0.248954	−	0.788553i
$555$	3.15794	+	4.72620i	0.134047	+	0.200616i
$556$	−1.69805	+	0.0383205i	−0.0720135	+	0.00162515i
$557$	−18.6390	+	3.70752i	−0.789758	+	0.157093i	−0.573459	−	0.819234i	$-0.694399\pi$
$557$	−18.6390	+	3.70752i	−0.789758	+	0.157093i	−0.216299	+	0.976327i	$0.569399\pi$
$558$	−0.670700	+	0.0737070i	−0.0283930	+	0.00312027i
$559$	−3.88650	+	3.88650i	−0.164382	+	0.164382i
$560$	1.91768	−	12.5843i	0.0810366	−	0.531785i
$561$	−4.81592	−	4.81592i	−0.203328	−	0.203328i
$562$	−7.10738	−	5.69992i	−0.299807	−	0.240436i
$563$	5.99694	+	30.1487i	0.252741	+	1.27061i	0.873582	+	0.486678i	$0.161791\pi$
$563$	5.99694	+	30.1487i	0.252741	+	1.27061i	−0.620841	+	0.783937i	$0.713209\pi$
$564$	−6.17696	+	15.9192i	−0.260097	+	0.670320i
$565$	−3.79816	+	2.53785i	−0.159790	+	0.106768i
$566$	22.8164	+	11.8666i	0.959045	+	0.498792i
$567$	5.64749	+	13.6343i	0.237172	+	0.572585i
$568$	−13.9095	+	4.73902i	−0.583629	+	0.198845i
$569$	1.35295	−	3.26632i	0.0567187	−	0.136931i	−0.892980	−	0.450097i	$-0.851390\pi$
$569$	1.35295	−	3.26632i	0.0567187	−	0.136931i	0.949699	+	0.313166i	$0.101390\pi$
$570$	−3.32836	−	3.96358i	−0.139410	−	0.166016i
$571$	−7.21231	+	36.2587i	−0.301826	+	1.51738i	0.470641	+	0.882325i	$0.344023\pi$
$571$	−7.21231	+	36.2587i	−0.301826	+	1.51738i	−0.772467	+	0.635055i	$0.780977\pi$
$572$	−2.74868	−	12.3548i	−0.114928	−	0.516581i
$573$	5.66645	−	8.48044i	0.236719	−	0.354275i
$574$	−13.5130	+	46.4255i	−0.564022	+	1.93776i
$575$	12.0817			0.503842
$576$	−18.2445	+	4.93244i	−0.760187	+	0.205518i
$577$	−13.4288			−0.559050			−0.279525	−	0.960138i	$-0.590177\pi$
$577$	−13.4288			−0.559050			−0.279525	+	0.960138i	$0.590177\pi$
$578$	0.809610	−	2.78151i	0.0336753	−	0.115696i
$579$	8.85440	−	13.2516i	0.367977	−	0.550716i
$580$	−5.50263	+	1.22422i	−0.228484	+	0.0508328i
$581$	−0.152338	+	0.765853i	−0.00632003	+	0.0317729i
$582$	−2.03648	−	2.42514i	−0.0844149	−	0.100525i
$583$	−11.3652	+	27.4380i	−0.470698	+	1.13636i
$584$	−19.9313	+	40.5312i	−0.824765	+	1.67719i
$585$	2.05175	+	4.95336i	0.0848293	+	0.204796i
$586$	−3.23388	−	1.68192i	−0.133590	−	0.0694793i
$587$	4.86470	−	3.25049i	0.200788	−	0.134162i	−0.451112	−	0.892467i	$-0.648972\pi$
$587$	4.86470	−	3.25049i	0.200788	−	0.134162i	0.651899	+	0.758305i	$0.273972\pi$
$588$	−13.6727	−	5.30525i	−0.563851	−	0.218785i
$589$	0.228282	+	1.14765i	0.00940619	+	0.0472881i
$590$	−7.66421	−	6.14648i	−0.315531	−	0.253046i
$591$	−4.00626	−	4.00626i	−0.164795	−	0.164795i
$592$	−8.60781	−	34.9510i	−0.353779	−	1.43648i
$593$	22.6469	−	22.6469i	0.929995	−	0.929995i	−0.0677097	−	0.997705i	$-0.521569\pi$
$593$	22.6469	−	22.6469i	0.929995	−	0.929995i	0.997705	+	0.0677097i	$0.0215692\pi$
$594$	13.2777	−	1.45916i	0.544789	−	0.0598700i
$595$	12.0690	−	2.40068i	0.494781	−	0.0984181i
$596$	0.0665707	+	2.94988i	0.00272684	+	0.120832i
$597$	2.73398	+	4.09168i	0.111894	+	0.167462i
$598$	−3.37371	−	10.6861i	−0.137961	−	0.436988i
$599$	40.9799	−	16.9744i	1.67439	−	0.693557i	0.675360	−	0.737488i	$-0.263988\pi$
$599$	40.9799	−	16.9744i	1.67439	−	0.693557i	0.999035	+	0.0439314i	$0.0139883\pi$
$600$	−9.54509	−	2.54614i	−0.389677	−	0.103946i
$601$	19.0417	+	7.88732i	0.776727	+	0.321731i	0.735594	−	0.677423i	$-0.236903\pi$
$601$	19.0417	+	7.88732i	0.776727	+	0.321731i	0.0411328	+	0.999154i	$0.486903\pi$
$602$	−10.8587	−	0.945928i	−0.442568	−	0.0385531i
$603$	21.4886	+	4.27435i	0.875084	+	0.174065i
$604$	−12.6268	−	2.21672i	−0.513776	−	0.0901970i
$605$	4.03461	+	2.69584i	0.164030	+	0.109601i
$606$	−6.86372	+	3.76890i	−0.278820	+	0.153101i
$607$			19.4092i			0.787793i	0.919155	+	0.393897i	$0.128873\pi$
$607$			19.4092i			0.787793i	−0.919155	+	0.393897i	$0.871127\pi$
$608$	11.2674	+	30.7780i	0.456954	+	1.24821i
$609$			11.4450i			0.463773i
$610$	−2.25067	−	4.09880i	−0.0911269	−	0.165955i
$611$	−25.5058	−	17.0424i	−1.03185	−	0.689462i
$612$	−10.4903	−	14.9579i	−0.424045	−	0.604637i
$613$	−17.2993	−	3.44105i	−0.698712	−	0.138983i	−0.167062	−	0.985946i	$-0.553428\pi$
$613$	−17.2993	−	3.44105i	−0.698712	−	0.138983i	−0.531650	+	0.846964i	$0.678428\pi$
$614$	1.03943	−	11.9321i	0.0419480	−	0.481539i
$615$	−4.95971	−	2.05438i	−0.199995	−	0.0828406i
$616$	15.2576	−	19.9302i	0.614745	−	0.803012i
$617$	19.6710	−	8.14801i	0.791926	−	0.328027i	0.0502085	−	0.998739i	$-0.484011\pi$
$617$	19.6710	−	8.14801i	0.791926	−	0.328027i	0.741718	+	0.670712i	$0.234011\pi$
$618$	14.9085	−	4.70677i	0.599710	−	0.189334i
$619$	−8.49755	−	12.7175i	−0.341545	−	0.511159i	0.620442	−	0.784252i	$-0.286953\pi$
$619$	−8.49755	−	12.7175i	−0.341545	−	0.511159i	−0.961987	+	0.273094i	$0.911953\pi$
$620$	−0.230979	−	0.220784i	−0.00927634	−	0.00886690i
$621$	11.5992	−	2.30722i	0.465459	−	0.0925855i
$622$	0.255678	+	2.32656i	0.0102518	+	0.0932864i
$623$	2.03155	−	2.03155i	0.0813924	−	0.0813924i
$624$	0.413350	+	9.15350i	0.0165472	+	0.366433i
$625$	11.3170	+	11.3170i	0.452681	+	0.452681i
$626$	−14.0558	+	17.5265i	−0.561781	+	0.700501i
$627$	−1.99096	−	10.0092i	−0.0795114	−	0.399731i
$628$	−4.00896	−	9.09263i	−0.159975	−	0.362835i
$629$	28.9319	−	19.3317i	1.15359	−	0.770804i
$630$	−4.90596	+	9.43285i	−0.195458	+	0.375814i
$631$	−15.2549	−	36.8286i	−0.607289	−	1.46613i	−0.865937	−	0.500153i	$-0.833277\pi$
$631$	−15.2549	−	36.8286i	−0.607289	−	1.46613i	0.258648	−	0.965972i	$-0.416723\pi$
$632$	−0.750442	+	11.6495i	−0.0298510	+	0.463392i
$633$	7.02294	−	16.9549i	0.279137	−	0.673896i
$634$	17.1891	−	14.4343i	0.682668	−	0.573261i
$635$	−1.18582	+	5.96150i	−0.0470577	+	0.236575i
$636$	11.5384	−	18.1416i	0.457528	−	0.719360i
$637$	14.6373	−	21.9063i	0.579952	−	0.867960i
$638$	−10.6723	−	3.10638i	−0.422522	−	0.122983i
$639$	12.2736			0.485538
$640$	−7.34478	−	5.11431i	−0.290328	−	0.202161i
$641$	−29.8562			−1.17925			−0.589624	−	0.807678i	$-0.700724\pi$
$641$	−29.8562			−1.17925			−0.589624	+	0.807678i	$0.700724\pi$
$642$	12.9676	+	3.77445i	0.511789	+	0.148966i
$643$	−16.7593	+	25.0820i	−0.660921	+	0.989138i	0.337928	+	0.941172i	$0.390274\pi$
$643$	−16.7593	+	25.0820i	−0.660921	+	0.989138i	−0.998849	+	0.0479657i	$0.984726\pi$
$644$	11.9263	−	18.7514i	0.469960	−	0.738907i
$645$	0.236092	−	1.18691i	0.00929610	−	0.0467347i
$646$	−24.2634	+	20.3749i	−0.954631	+	0.801638i
$647$	9.93240	−	23.9789i	0.390483	−	0.942709i	−0.599352	−	0.800486i	$-0.704575\pi$
$647$	9.93240	−	23.9789i	0.390483	−	0.942709i	0.989835	−	0.142223i	$-0.0454252\pi$
$648$	10.3544	+	0.667013i	0.406758	+	0.0262027i
$649$	−7.41318	−	17.8970i	−0.290993	−	0.702519i
$650$	8.18871	−	15.7447i	0.321188	−	0.617559i
$651$	−0.539394	+	0.360412i	−0.0211405	+	0.0141257i
$652$	18.1026	+	41.0581i	0.708953	+	1.60796i
$653$	−1.64465	−	8.26822i	−0.0643602	−	0.323560i	0.935170	−	0.354198i	$-0.115246\pi$
$653$	−1.64465	−	8.26822i	−0.0643602	−	0.323560i	−0.999531	+	0.0306378i	$0.990246\pi$
$654$	−3.05991	+	3.81549i	−0.119652	+	0.149198i
$655$	−3.13657	−	3.13657i	−0.122556	−	0.122556i
$656$	25.0985	+	22.9296i	0.979930	+	0.895251i
$657$	26.6759	−	26.6759i	1.04073	−	1.04073i
$658$	−6.64525	−	60.4687i	−0.259059	−	2.35731i
$659$	−4.11710	+	0.818941i	−0.160379	+	0.0319014i	−0.274627	−	0.961551i	$-0.588554\pi$
$659$	−4.11710	+	0.818941i	−0.160379	+	0.0319014i	0.114248	+	0.993452i	$0.463554\pi$
$660$	2.01449	+	1.92557i	0.0784138	+	0.0749527i
$661$	−16.0973	−	24.0913i	−0.626112	−	0.937043i	−0.999954	−	0.00955074i	$-0.996960\pi$
$661$	−16.0973	−	24.0913i	−0.626112	−	0.937043i	0.373842	−	0.927492i	$-0.378040\pi$
$662$	−29.1449	+	9.20133i	−1.13275	+	0.357620i
$663$	−8.18330	+	3.38963i	−0.317813	+	0.131642i
$664$	0.435931	+	0.333726i	0.0169174	+	0.0129511i
$665$	17.0352	+	7.05619i	0.660595	+	0.273627i
$666$	−2.60916	+	29.9516i	−0.101103	+	1.16060i
$667$	−9.65200	−	1.91990i	−0.373727	−	0.0743389i
$668$	−1.42324	−	2.02937i	−0.0550669	−	0.0785187i
$669$	9.82876	+	6.56737i	0.380002	+	0.253909i
$670$	4.99386	+	9.09455i	0.192930	+	0.351353i
$671$		−	9.22017i		−	0.355941i
$672$	−13.3740	+	12.3010i	−0.515914	+	0.474523i
$673$			3.38922i			0.130645i	0.997864	+	0.0653224i	$0.0208076\pi$
$673$			3.38922i			0.130645i	−0.997864	+	0.0653224i	$0.979192\pi$
$674$	−1.61012	+	0.884122i	−0.0620193	+	0.0340551i
$675$	15.5729	+	10.4055i	0.599401	+	0.400507i
$676$	9.39572	+	1.64948i	0.361374	+	0.0634417i
$677$	22.4472	+	4.46503i	0.862717	+	0.171605i	0.606568	−	0.795032i	$-0.292546\pi$
$677$	22.4472	+	4.46503i	0.862717	+	0.171605i	0.256150	+	0.966637i	$0.417546\pi$
$678$	6.49599	+	0.565881i	0.249477	+	0.0217325i
$679$	10.4231	+	4.31738i	0.400001	+	0.165686i
$680$	2.22988	−	8.35947i	0.0855119	−	0.320571i
$681$	−8.57664	+	3.55256i	−0.328657	+	0.136134i
$682$	−0.189679	−	0.600804i	−0.00726320	−	0.0230060i
$683$	−10.4891	−	15.6981i	−0.401355	−	0.600670i	0.574655	−	0.818396i	$-0.305136\pi$
$683$	−10.4891	−	15.6981i	−0.401355	−	0.600670i	−0.976010	+	0.217726i	$0.930136\pi$
$684$	−0.617639	−	27.3688i	−0.0236160	−	1.04647i
$685$	6.13059	−	1.21945i	0.234238	−	0.0465928i
$686$	12.3489	−	1.35709i	0.471484	−	0.0518141i
$687$	−7.36497	+	7.36497i	−0.280991	+	0.280991i
$688$	−3.96582	+	6.55754i	−0.151196	+	0.250004i
$689$	27.3111	+	27.3111i	1.04047	+	1.04047i
$690$	1.92479	+	1.54362i	0.0732754	+	0.0587648i
$691$	−1.70364	−	8.56476i	−0.0648094	−	0.325819i	0.934756	−	0.355290i	$-0.115618\pi$
$691$	−1.70364	−	8.56476i	−0.0648094	−	0.325819i	−0.999566	+	0.0294708i	$0.990618\pi$
$692$	−6.15400	−	2.38787i	−0.233940	−	0.0907732i
$693$	−17.4315	+	11.6473i	−0.662167	+	0.442446i
$694$	0.218437	+	0.113607i	0.00829174	+	0.00431247i
$695$	0.257092	+	0.620674i	0.00975205	+	0.0235435i
$696$	7.22091	+	3.55091i	0.273708	+	0.134597i
$697$	−12.5761	+	30.3613i	−0.476353	+	1.15002i
$698$	−0.966276	−	1.15069i	−0.0365741	−	0.0435543i
$699$	−2.65785	+	13.3619i	−0.100529	+	0.505394i
$700$	34.3539	−	7.64301i	1.29846	−	0.288879i
$701$	−26.3880	+	39.4924i	−0.996661	+	1.49161i	−0.130746	+	0.991416i	$0.541737\pi$
$701$	−26.3880	+	39.4924i	−0.996661	+	1.49161i	−0.865914	+	0.500192i	$0.833263\pi$
$702$	4.85493	−	16.6797i	0.183237	−	0.629534i
$703$	52.1390			1.96646
$704$	−7.84066	−	15.8099i	−0.295506	−	0.595858i
$705$	6.75403			0.254371
$706$	−0.252226	+	0.866554i	−0.00949267	+	0.0326132i
$707$	15.4983	−	23.1949i	0.582874	−	0.872333i
$708$	3.04554	+	13.6892i	0.114459	+	0.514471i
$709$	1.30250	−	6.54810i	0.0489163	−	0.245919i	−0.948589	−	0.316511i	$-0.897489\pi$
$709$	1.30250	−	6.54810i	0.0489163	−	0.245919i	0.997505	+	0.0705917i	$0.0224887\pi$
$710$	3.73771	+	4.45106i	0.140274	+	0.167045i
$711$	3.73130	−	9.00816i	0.139935	−	0.337833i
$712$	−0.651447	−	1.91206i	−0.0244140	−	0.0716576i
$713$	−0.213466	−	0.515352i	−0.00799436	−	0.0193001i
$714$	−15.5837	−	8.10499i	−0.583207	−	0.303321i
$715$	−4.16256	+	2.78133i	−0.155671	+	0.104016i
$716$	−4.97003	+	12.8087i	−0.185739	+	0.478684i
$717$	−0.896736	−	4.50820i	−0.0334892	−	0.168362i
$718$	−17.0030	−	13.6359i	−0.634545	−	0.508887i
$719$	−6.09983	−	6.09983i	−0.227485	−	0.227485i	0.584156	−	0.811641i	$-0.301426\pi$
$719$	−6.09983	−	6.09983i	−0.227485	−	0.227485i	−0.811641	+	0.584156i	$0.801426\pi$
$720$	4.42930	+	6.02192i	0.165070	+	0.224424i
$721$	−39.3834	+	39.3834i	−1.46671	+	1.46671i
$722$	−20.4818	+	2.25087i	−0.762255	+	0.0837686i
$723$	9.28570	−	1.84704i	0.345339	−	0.0686922i
$724$	13.4156	−	0.302753i	0.498586	−	0.0112517i
$725$	−8.65869	−	12.9586i	−0.321576	−	0.481272i
$726$	−2.08531	−	6.60516i	−0.0773932	−	0.245141i
$727$	3.50465	−	1.45167i	0.129980	−	0.0538395i	−0.316745	−	0.948511i	$-0.602590\pi$
$727$	3.50465	−	1.45167i	0.129980	−	0.0538395i	0.446725	+	0.894671i	$0.352590\pi$
$728$	−16.3532	−	28.2514i	−0.606090	−	1.04707i
$729$	1.46926	+	0.608586i	0.0544170	+	0.0225402i
$730$	17.7977	+	1.55040i	0.658722	+	0.0573829i
$731$	−7.26580	−	1.44526i	−0.268735	−	0.0534548i
$732$	−1.15417	+	6.57431i	−0.0426592	+	0.242993i
$733$	−6.66476	−	4.45325i	−0.246169	−	0.164485i	0.426365	−	0.904551i	$-0.359794\pi$
$733$	−6.66476	−	4.45325i	−0.246169	−	0.164485i	−0.672534	+	0.740067i	$0.734794\pi$
$734$	−10.1939	+	5.59754i	−0.376265	+	0.206609i
$735$			5.80088i			0.213969i
$736$	−8.13046	−	13.3423i	−0.299693	−	0.491805i
$737$			20.4580i			0.753581i
$738$	−13.6668	−	24.8893i	−0.503083	−	0.916188i
$739$	−24.1533	−	16.1387i	−0.888492	−	0.593671i	0.0253784	−	0.999678i	$-0.491921\pi$
$739$	−24.1533	−	16.1387i	−0.888492	−	0.593671i	−0.913870	+	0.406007i	$0.866921\pi$
$740$	−11.6566	+	8.17500i	−0.428504	+	0.300519i
$741$	−13.0173	−	2.58929i	−0.478201	−	0.0951201i
$742$	−6.64720	+	76.3060i	−0.244026	+	2.80128i
$743$	−27.7230	−	11.4832i	−1.01706	−	0.421279i	−0.189033	−	0.981971i	$-0.560535\pi$
$743$	−27.7230	−	11.4832i	−1.01706	−	0.421279i	−0.828025	+	0.560691i	$0.810535\pi$
$744$	0.0600405	+	0.452138i	0.00220119	+	0.0165762i
$745$	1.07824	−	0.446623i	0.0395037	−	0.0163630i
$746$	7.90579	−	2.49593i	0.289451	−	0.0913825i
$747$	−0.254760	−	0.381276i	−0.00932120	−	0.0139502i
$748$	11.7876	−	12.3319i	0.430996	−	0.450898i
$749$	−47.1903	+	9.38673i	−1.72430	+	0.342984i
$750$	0.914749	+	8.32379i	0.0334019	+	0.303942i
$751$	18.6881	−	18.6881i	0.681937	−	0.681937i	−0.278499	−	0.960436i	$-0.589837\pi$
$751$	18.6881	−	18.6881i	0.681937	−	0.681937i	0.960436	+	0.278499i	$0.0898370\pi$
$752$	−40.2129	−	14.5683i	−1.46641	−	0.531252i
$753$	11.0049	+	11.0049i	0.401040	+	0.401040i
$754$	−9.04391	+	11.2771i	−0.329360	+	0.410688i
$755$	0.989251	+	4.97330i	0.0360025	+	0.180997i
$756$	31.5223	−	13.8983i	1.14646	−	0.505475i
$757$	0.988973	−	0.660810i	0.0359448	−	0.0240176i	−0.537468	−	0.843284i	$-0.680619\pi$
$757$	0.988973	−	0.660810i	0.0359448	−	0.0240176i	0.573413	+	0.819267i	$0.305619\pi$
$758$	−6.76238	+	13.0023i	−0.245621	+	0.472264i
$759$	1.86174	+	4.49465i	0.0675770	+	0.163145i
$760$	9.73724	−	8.55864i	0.353207	−	0.310455i
$761$	−3.73816	+	9.02472i	−0.135508	+	0.327146i	−0.977038	−	0.213065i	$-0.931655\pi$
$761$	−3.73816	+	9.02472i	−0.135508	+	0.327146i	0.841530	+	0.540211i	$0.181655\pi$
$762$	6.64447	−	5.57960i	0.240704	−	0.202128i
$763$	3.39928	−	17.0893i	0.123062	−	0.618675i
$764$	21.5564	+	13.7103i	0.779882	+	0.496021i
$765$	−4.01475	+	6.00850i	−0.145154	+	0.217238i
$766$	48.3354	+	14.0689i	1.74643	+	0.508330i
$767$	−25.1932			−0.909674
$768$	3.61161	+	12.2545i	0.130323	+	0.442196i
$769$	53.0775			1.91402			0.957012	−	0.290049i	$-0.0936716\pi$
$769$	53.0775			1.91402			0.957012	+	0.290049i	$0.0936716\pi$
$770$	−9.53236	−	2.77457i	−0.343522	−	0.0999885i
$771$	−4.76233	+	7.12734i	−0.171511	+	0.256685i
$772$	33.6840	+	21.4237i	1.21231	+	0.771057i
$773$	−4.23170	+	21.2742i	−0.152204	+	0.765179i	0.826985	+	0.562225i	$0.190054\pi$
$773$	−4.23170	+	21.2742i	−0.152204	+	0.765179i	−0.979188	+	0.202955i	$0.934946\pi$
$774$	4.90184	−	4.11625i	0.176193	−	0.147956i
$775$	0.338064	−	0.816158i	0.0121436	−	0.0293173i
$776$	5.95780	−	5.23667i	0.213873	−	0.187985i
$777$	11.0618	+	26.7056i	0.396841	+	0.958059i
$778$	−22.2478	+	42.7766i	−0.797622	+	1.53362i
$779$	−40.9435	+	27.3576i	−1.46695	+	0.980187i
$780$	3.31621	−	1.46213i	0.118739	−	0.0523525i
$781$	2.23583	+	11.2403i	0.0800043	+	0.402209i
$782$	9.44944	−	11.7828i	0.337911	−	0.421351i
$783$	−10.7876	−	10.7876i	−0.385516	−	0.385516i
$784$	12.5124	−	34.5380i	0.446871	−	1.23350i
$785$	−2.77930	+	2.77930i	−0.0991974	+	0.0991974i
$786$	0.691678	+	6.29395i	0.0246713	+	0.224498i
$787$	−23.2249	+	4.61971i	−0.827877	+	0.164675i	−0.590802	−	0.806816i	$-0.701189\pi$
$787$	−23.2249	+	4.61971i	−0.827877	+	0.164675i	−0.237075	+	0.971491i	$0.576189\pi$
$788$	9.80580	−	10.2586i	0.349317	−	0.365448i
$789$	7.11065	+	10.6418i	0.253146	+	0.378859i
$790$	4.40312	−	1.39011i	0.156656	−	0.0494578i
$791$	−21.4617	+	8.88972i	−0.763089	+	0.316082i
$792$	1.94031	+	14.6116i	0.0689460	+	0.519202i
$793$	−11.0783	−	4.58878i	−0.393402	−	0.162952i
$794$	3.29976	−	37.8793i	0.117104	−	1.34429i
$795$	−8.34065	−	1.65906i	−0.295812	−	0.0588407i
$796$	−10.0916	+	7.07747i	−0.357688	+	0.250854i
$797$	−20.4305	−	13.6512i	−0.723684	−	0.483550i	0.138361	−	0.990382i	$-0.455817\pi$
$797$	−20.4305	−	13.6512i	−0.723684	−	0.483550i	−0.862045	+	0.506832i	$0.830817\pi$
$798$	−12.6684	−	23.0710i	−0.448456	−	0.816705i
$799$		−	41.3454i		−	1.46270i
$800$	5.83647	−	24.0461i	0.206350	−	0.850156i
$801$			1.68719i			0.0596140i
$802$	15.5578	−	8.54284i	0.549363	−	0.301658i
$803$	29.2893	+	19.5705i	1.03360	+	0.690628i
$804$	2.56090	−	14.5873i	0.0903161	−	0.514454i
$805$	−8.62100	−	1.71482i	−0.303850	−	0.0604396i
$806$	−0.816283	−	0.0711084i	−0.0287524	−	0.00250469i
$807$	−23.3410	−	9.66814i	−0.821641	−	0.340335i
$808$	−9.82571	−	16.9747i	−0.345667	−	0.597167i
$809$	10.0811	−	4.17573i	0.354433	−	0.146811i	−0.198361	−	0.980129i	$-0.563562\pi$
$809$	10.0811	−	4.17573i	0.354433	−	0.146811i	0.552794	+	0.833318i	$0.313562\pi$
$810$	−1.23556	−	3.91361i	−0.0434133	−	0.137510i
$811$	5.66881	+	8.48397i	0.199059	+	0.297913i	0.917548	−	0.397626i	$-0.130166\pi$
$811$	5.66881	+	8.48397i	0.199059	+	0.297913i	−0.718489	+	0.695539i	$0.755166\pi$
$812$	−28.6597	+	0.646772i	−1.00576	+	0.0226972i
$813$	2.57495	−	0.512189i	0.0903074	−	0.0179633i
$814$	−27.9052	+	3.06666i	−0.978076	+	0.107486i
$815$	12.5500	−	12.5500i	0.439608	−	0.439608i
$816$	−9.94863	+	7.31751i	−0.348272	+	0.256164i
$817$	−7.84923	−	7.84923i	−0.274610	−	0.274610i
$818$	12.8986	+	10.3443i	0.450990	+	0.361681i
$819$	5.31914	+	26.7411i	0.185866	+	0.934411i
$820$	4.86416	−	12.5359i	0.169864	−	0.437772i
$821$	−3.93484	+	2.62918i	−0.137327	+	0.0917589i	−0.622336	−	0.782750i	$-0.713816\pi$
$821$	−3.93484	+	2.62918i	−0.137327	+	0.0917589i	0.485009	+	0.874509i	$0.338816\pi$
$822$	−7.91593	−	4.11701i	−0.276100	−	0.143597i
$823$	9.96174	+	24.0498i	0.347245	+	0.838322i	0.996943	+	0.0781305i	$0.0248951\pi$
$823$	9.96174	+	24.0498i	0.347245	+	0.838322i	−0.649699	+	0.760192i	$0.725105\pi$
$824$	12.6289	+	37.0670i	0.439948	+	1.29129i
$825$	−2.94843	+	7.11813i	−0.102651	+	0.247821i
$826$	−32.1284	−	38.2601i	−1.11789	−	1.33124i
$827$	0.00652173	−	0.0327870i	0.000226783	−	0.00114011i	−0.980672	−	0.195660i	$-0.937315\pi$
$827$	0.00652173	−	0.0327870i	0.000226783	−	0.00114011i	0.980899	+	0.194520i	$0.0623150\pi$
$828$	2.83411	+	12.7388i	0.0984920	+	0.442704i
$829$	22.2612	−	33.3162i	0.773163	−	1.15712i	−0.210586	−	0.977575i	$-0.567537\pi$
$829$	22.2612	−	33.3162i	0.773163	−	1.15712i	0.983750	−	0.179546i	$-0.0574628\pi$
$830$	0.0606877	−	0.208500i	0.00210650	−	0.00723713i
$831$	10.9892			0.381210
$832$	−22.8982	+	1.55236i	−0.793853	+	0.0538184i
$833$	35.5106			1.23037
$834$	0.268006	−	0.920768i	0.00928030	−	0.0318836i
$835$	−0.544691	+	0.815187i	−0.0188498	+	0.0282107i
$836$	24.9520	−	5.55127i	0.862982	−	0.191995i
$837$	0.168702	−	0.848121i	0.00583119	−	0.0293154i
$838$	−14.6279	−	17.4197i	−0.505314	−	0.601753i
$839$	7.52166	−	18.1589i	0.259676	−	0.626914i	−0.739241	−	0.673441i	$-0.764815\pi$
$839$	7.52166	−	18.1589i	0.259676	−	0.626914i	0.998917	+	0.0465270i	$0.0148153\pi$
$840$	6.44959	+	3.17161i	0.222532	+	0.109431i
$841$	−6.23970	−	15.0640i	−0.215162	−	0.519447i
$842$	−32.7778	−	17.0475i	−1.12960	−	0.587494i
$843$	4.27703	−	2.85782i	0.147309	−	0.0984287i
$844$	42.8542	+	16.6282i	1.47510	+	0.572368i
$845$	−0.736112	−	3.70068i	−0.0253230	−	0.127307i
$846$	27.8689	+	22.3500i	0.958152	+	0.768410i
$847$	17.4486	+	17.4486i	0.599542	+	0.599542i
$848$	46.0810	+	27.8685i	1.58243	+	0.957009i
$849$	−10.2675	+	10.2675i	−0.352381	+	0.352381i
$850$	23.7766	−	2.61295i	0.815532	−	0.0896235i
$851$	−24.3775	+	4.84899i	−0.835651	+	0.166221i
$852$	−0.187186	−	8.29459i	−0.00641290	−	0.284168i
$853$	22.1961	+	33.2188i	0.759980	+	1.13739i	0.986560	+	0.163398i	$0.0522454\pi$
$853$	22.1961	+	33.2188i	0.759980	+	1.13739i	−0.226580	+	0.973992i	$0.572755\pi$
$854$	−7.15910	−	22.6762i	−0.244979	−	0.775965i
$855$	−10.0039	+	4.14374i	−0.342125	+	0.141713i
$856$	−8.71890	+	32.6858i	−0.298006	+	1.11718i
$857$	−25.2546	−	10.4608i	−0.862682	−	0.357335i	−0.0929262	−	0.995673i	$-0.529622\pi$
$857$	−25.2546	−	10.4608i	−0.862682	−	0.357335i	−0.769756	+	0.638338i	$0.779622\pi$
$858$	7.11922	+	0.620173i	0.243046	+	0.0211723i
$859$	−7.74276	−	1.54013i	−0.264179	−	0.0525486i	0.0612232	−	0.998124i	$-0.480500\pi$
$859$	−7.74276	−	1.54013i	−0.264179	−	0.0525486i	−0.325403	+	0.945576i	$0.605500\pi$
$860$	2.98553	+	0.524131i	0.101806	+	0.0178727i
$861$	−22.6991	−	15.1671i	−0.773584	−	0.516892i
$862$	11.8169	−	6.48870i	0.402484	−	0.221006i
$863$		−	18.5138i		−	0.630218i	−0.949055	−	0.315109i	$-0.897959\pi$
$863$		−	18.5138i		−	0.630218i	0.949055	−	0.315109i	$-0.102041\pi$
$864$	1.01134	−	24.2003i	0.0344065	−	0.823310i
$865$			2.61095i			0.0887750i
$866$	8.64879	+	15.7507i	0.293898	+	0.535231i
$867$	1.35998	+	0.908711i	0.0461874	+	0.0308614i
$868$	−0.933001	−	1.33035i	−0.0316681	−	0.0451550i
$869$	8.92944	+	1.77618i	0.302911	+	0.0602527i
$870$	0.276214	−	3.17078i	0.00936454	−	0.107500i
$871$	24.5809	+	10.1817i	0.832891	+	0.344995i
$872$	−9.72742	−	7.44681i	−0.329412	−	0.252181i
$873$	−6.12094	+	2.53538i	−0.207162	+	0.0858095i
$874$	21.5818	−	6.81358i	0.730016	−	0.230473i
$875$	−16.5740	−	24.8048i	−0.560304	−	0.838555i
$876$	−18.4345	−	17.6209i	−0.622845	−	0.595354i
$877$	37.1814	−	7.39584i	1.25553	−	0.249740i	0.477870	−	0.878430i	$-0.341409\pi$
$877$	37.1814	−	7.39584i	1.25553	−	0.249740i	0.777655	+	0.628691i	$0.216409\pi$
$878$	4.93942	+	44.9465i	0.166698	+	1.51687i
$879$	1.45527	−	1.45527i	0.0490849	−	0.0490849i
$880$	−4.70804	+	5.15336i	−0.158708	+	0.173720i
$881$	−38.5474	−	38.5474i	−1.29870	−	1.29870i	−0.929253	−	0.369443i	$-0.879548\pi$
$881$	−38.5474	−	38.5474i	−1.29870	−	1.29870i	−0.369443	−	0.929253i	$-0.620452\pi$
$882$	−19.1959	+	23.9359i	−0.646361	+	0.805965i
$883$	−3.56318	−	17.9133i	−0.119910	−	0.602831i	−0.993276	−	0.115766i	$-0.963068\pi$
$883$	−3.56318	−	17.9133i	−0.119910	−	0.602831i	0.873366	−	0.487064i	$-0.161932\pi$
$884$	−8.95054	−	20.3005i	−0.301039	−	0.682780i
$885$	4.61212	−	3.08172i	0.155035	−	0.103591i
$886$	−16.7695	+	32.2433i	−0.563382	+	1.08323i
$887$	17.2580	+	41.6645i	0.579467	+	1.39896i	0.893292	+	0.449477i	$0.148390\pi$
$887$	17.2580	+	41.6645i	0.579467	+	1.39896i	−0.313825	+	0.949481i	$0.601610\pi$
$888$	20.2813	+	1.30649i	0.680594	+	0.0438428i
$889$	−11.8289	+	28.5574i	−0.396728	+	0.957785i
$890$	−0.611863	+	0.513803i	−0.0205097	+	0.0172227i
$891$	1.57871	−	7.93672i	0.0528889	−	0.265890i
$892$	−15.8901	+	24.9837i	−0.532041	+	0.836515i
$893$	34.4191	−	51.5118i	1.15179	−	1.72378i
$894$	−1.59957	−	0.465583i	−0.0534975	−	0.0155714i
$895$	5.43434			0.181650
$896$	−31.5592	−	32.7952i	−1.05432	−	1.09561i
$897$	6.32701			0.211253
$898$	36.5922	+	10.6508i	1.22110	+	0.355423i
$899$	−0.399773	+	0.598302i	−0.0133332	+	0.0199545i
$900$	−11.0916	+	17.4391i	−0.369721	+	0.581304i
$901$	−10.1561	+	51.0581i	−0.338348	+	1.70099i
$902$	20.3042	−	17.0501i	0.676054	−	0.567707i
$903$	2.35508	−	5.68567i	0.0783723	−	0.189207i
$904$	−1.04994	+	16.2988i	−0.0349206	+	0.542090i
$905$	−2.03117	−	4.90368i	−0.0675184	−	0.163004i
$906$	3.33983	−	6.42162i	0.110959	−	0.213344i
$907$	−12.0798	+	8.07148i	−0.401104	+	0.268009i	−0.739719	−	0.672916i	$-0.765042\pi$
$907$	−12.0798	+	8.07148i	−0.401104	+	0.268009i	0.338615	+	0.940925i	$0.390042\pi$
$908$	−9.38076	−	21.2763i	−0.311311	−	0.706078i
$909$	3.19597	+	16.0672i	0.106004	+	0.532917i
$910$	−8.07786	+	10.0725i	−0.267779	+	0.333901i
$911$	−17.8629	−	17.8629i	−0.591824	−	0.591824i	0.346300	−	0.938124i	$-0.387438\pi$
$911$	−17.8629	−	17.8629i	−0.591824	−	0.591824i	−0.938124	+	0.346300i	$0.887438\pi$
$912$	−18.4865	+	0.834807i	−0.612150	+	0.0276432i
$913$	0.302766	−	0.302766i	0.0100201	−	0.0100201i
$914$	−1.77464	−	16.1484i	−0.0587000	−	0.534143i
$915$	2.58942	−	0.515067i	0.0856035	−	0.0170276i
$916$	−18.8591	−	18.0267i	−0.623122	−	0.595618i
$917$	−12.5323	−	18.7559i	−0.413852	−	0.619374i
$918$	22.3280	−	7.04917i	0.736935	−	0.232657i
$919$	26.6553	−	11.0410i	0.879279	−	0.364209i	0.103062	−	0.994675i	$-0.467136\pi$
$919$	26.6553	−	11.0410i	0.879279	−	0.364209i	0.776217	+	0.630466i	$0.217136\pi$
$920$	−3.75667	+	4.90716i	−0.123854	+	0.161784i
$921$	6.24769	+	2.58788i	0.205868	+	0.0852735i
$922$	2.21355	−	25.4103i	0.0728995	−	0.836844i
$923$	14.6182	+	2.90775i	0.481165	+	0.0957098i
$924$	8.13718	+	11.6026i	0.267694	+	0.381699i
$925$	−32.7290	−	21.8688i	−1.07612	−	0.719042i
$926$	−9.60558	−	17.4932i	−0.315659	−	0.574861i
$927$		−	32.7077i		−	1.07426i
$928$	−8.48388	+	18.2828i	−0.278497	+	0.600162i
$929$		−	7.79886i		−	0.255872i	−0.991782	−	0.127936i	$-0.959165\pi$
$929$		−	7.79886i		−	0.255872i	0.991782	−	0.127936i	$-0.0408353\pi$
$930$	0.158135	−	0.0868328i	0.00518546	−	0.00284736i
$931$	44.2423	+	29.5617i	1.44998	+	0.968847i
$932$	−33.6102	−	5.90051i	−1.10094	−	0.193278i
$933$	−1.29611	−	0.257812i	−0.0424327	−	0.00844038i
$934$	−50.8499	−	4.42966i	−1.66386	−	0.144943i
$935$	−6.23397	−	2.58219i	−0.203873	−	0.0844468i
$936$	18.5219	+	4.94071i	0.605409	+	0.161492i
$937$	19.8623	−	8.22722i	0.648872	−	0.268772i	−0.0338753	−	0.999426i	$-0.510785\pi$
$937$	19.8623	−	8.22722i	0.648872	−	0.268772i	0.682748	+	0.730654i	$0.260785\pi$
$938$	15.8849	+	50.3148i	0.518659	+	1.64284i
$939$	−7.04728	−	10.5470i	−0.229979	−	0.344188i
$940$	0.381680	+	16.9130i	0.0124490	+	0.551641i
$941$	23.3357	−	4.64175i	0.760721	−	0.151317i	0.200538	−	0.979686i	$-0.435731\pi$
$941$	23.3357	−	4.64175i	0.760721	−	0.151317i	0.560183	+	0.828369i	$0.310731\pi$
$942$	5.57704	−	0.612893i	0.181710	−	0.0199691i
$943$	16.5988	−	16.5988i	0.540531	−	0.540531i
$944$	−34.1074	+	8.40004i	−1.11010	+	0.273398i
$945$	−9.63527	−	9.63527i	−0.313435	−	0.313435i
$946$	4.66263	+	3.73930i	0.151595	+	0.121575i
$947$	11.0117	+	55.3597i	0.357833	+	1.79895i	0.569924	+	0.821698i	$0.306973\pi$
$947$	11.0117	+	55.3597i	0.357833	+	1.79895i	−0.212091	+	0.977250i	$0.568027\pi$
$948$	−6.14467	−	2.38425i	−0.199570	−	0.0774368i
$949$	38.0915	−	25.4519i	1.23650	−	0.826204i
$950$	31.7983	+	16.5380i	1.03167	+	0.536565i
$951$	4.84979	+	11.7084i	0.157265	+	0.379672i
$952$	19.4153	−	39.4818i	0.629254	−	1.27961i
$953$	0.127965	−	0.308934i	0.00414519	−	0.0100074i	−0.921793	−	0.387682i	$-0.873276\pi$
$953$	0.127965	−	0.308934i	0.00414519	−	0.0100074i	0.925939	+	0.377674i	$0.123276\pi$
$954$	−28.9256	−	34.4461i	−0.936502	−	1.11523i
$955$	1.97134	−	9.91061i	0.0637911	−	0.320700i
$956$	11.2385	−	2.50031i	0.363477	−	0.0808659i
$957$	3.48662	−	5.21810i	0.112706	−	0.168677i
$958$	14.9382	−	51.3220i	0.482631	−	1.65814i
$959$	31.7870			1.02646
$960$	4.00209	−	3.08518i	0.129167	−	0.0995738i
$961$	30.9592			0.998684
$962$	−10.2034	+	35.0551i	−0.328971	+	1.13022i
$963$	15.6978	−	23.4935i	0.505855	−	0.757066i
$964$	5.14998	+	23.1482i	0.165870	+	0.745555i
$965$	3.08043	−	15.4863i	0.0991624	−	0.498523i
$966$	8.06872	+	9.60864i	0.259607	+	0.309153i
$967$	−10.1992	+	24.6231i	−0.327985	+	0.791825i	0.670757	+	0.741677i	$0.265969\pi$
$967$	−10.1992	+	24.6231i	−0.327985	+	0.791825i	−0.998742	+	0.0501479i	$0.984031\pi$
$968$	16.4224	−	5.59517i	0.527835	−	0.179836i
$969$	−6.84575	−	16.5271i	−0.219917	−	0.530927i
$970$	−2.78348	−	1.44767i	−0.0893721	−	0.0464817i
$971$	21.0612	−	14.0726i	0.675885	−	0.451612i	−0.169669	−	0.985501i	$-0.554270\pi$
$971$	21.0612	−	14.0726i	0.675885	−	0.451612i	0.845555	+	0.533889i	$0.179270\pi$
$972$	−11.4126	+	29.4124i	−0.366058	+	0.943403i
$973$	0.666509	+	3.35077i	0.0213673	+	0.107421i
$974$	−21.2115	−	17.0110i	−0.679659	−	0.545067i
$975$	7.08523	+	7.08523i	0.226909	+	0.226909i
$976$	−16.5282	−	2.51866i	−0.529054	−	0.0806204i
$977$	24.9968	−	24.9968i	0.799719	−	0.799719i	−0.183332	−	0.983051i	$-0.558688\pi$
$977$	24.9968	−	24.9968i	0.799719	−	0.799719i	0.983051	+	0.183332i	$0.0586885\pi$
$978$	−25.1833	+	2.76754i	−0.805274	+	0.0884962i
$979$	−1.54514	+	0.307348i	−0.0493829	+	0.00982287i
$980$	−14.5262	+	0.327816i	−0.464022	+	0.0104717i
$981$	5.68476	+	8.50784i	0.181500	+	0.271634i
$982$	−15.2201	−	48.2094i	−0.485694	−	1.53842i
$983$	−49.9297	+	20.6816i	−1.59251	+	0.659640i	−0.990332	−	0.138721i	$-0.955701\pi$
$983$	−49.9297	+	20.6816i	−1.59251	+	0.659640i	−0.602180	+	0.798361i	$0.705701\pi$
$984$	−16.6119	+	9.61571i	−0.529568	+	0.306538i
$985$	−5.18590	−	2.14807i	−0.165236	−	0.0684431i
$986$	−19.4102	−	1.69087i	−0.618148	−	0.0538483i
$987$	33.6867	+	6.70070i	1.07226	+	0.213286i
$988$	5.74831	−	32.7433i	0.182878	−	1.04170i
$989$	4.39989	+	2.93991i	0.139908	+	0.0934837i
$990$	5.11042	−	2.80615i	0.162420	−	0.0891854i
$991$			59.9993i			1.90594i	0.303061	+	0.952971i	$0.401991\pi$
$991$			59.9993i			1.90594i	−0.303061	+	0.952971i	$0.598009\pi$
$992$	−1.12882	+	0.175900i	−0.0358401	+	0.00558484i
$993$		−	17.2561i		−	0.547605i
$994$	14.2265	+	25.9085i	0.451236	+	0.821767i
$995$	4.05375	+	2.70863i	0.128512	+	0.0858693i
$996$	−0.253783	+	0.177983i	−0.00804142	+	0.00563962i
$997$	−15.0130	−	2.98627i	−0.475466	−	0.0945761i	−0.0484607	−	0.998825i	$-0.515432\pi$
$997$	−15.0130	−	2.98627i	−0.475466	−	0.0945761i	−0.427006	+	0.904249i	$0.640432\pi$
$998$	−3.47340	+	39.8726i	−0.109948	+	1.26214i
$999$	−35.5981	−	14.7452i	−1.12627	−	0.466518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.37.1	✓	56
3.2	odd	2		576.2.bd.a.37.7		56
4.3	odd	2		256.2.i.a.241.3		56
8.3	odd	2		512.2.i.a.225.5		56
8.5	even	2		512.2.i.b.225.3		56
64.13	even	16		512.2.i.b.289.3		56
64.19	odd	16		256.2.i.a.17.3		56
64.45	even	16	inner	64.2.i.a.45.1	yes	56
64.51	odd	16		512.2.i.a.289.5		56
192.173	odd	16		576.2.bd.a.109.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.1	✓	56	1.1	even	1	trivial
64.2.i.a.45.1	yes	56	64.45	even	16	inner
256.2.i.a.17.3		56	64.19	odd	16
256.2.i.a.241.3		56	4.3	odd	2
512.2.i.a.225.5		56	8.3	odd	2
512.2.i.a.289.5		56	64.51	odd	16
512.2.i.b.225.3		56	8.5	even	2
512.2.i.b.289.3		56	64.13	even	16
576.2.bd.a.37.7		56	3.2	odd	2
576.2.bd.a.109.7		56	192.173	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35786 - 0.395231i) q^{2} +(0.443610 - 0.663909i) q^{3} +(1.68758 + 1.07334i) q^{4} +(0.154331 - 0.775873i) q^{5} +(-0.864759 + 0.726169i) q^{6} +(1.53949 - 3.71667i) q^{7} +(-1.86729 - 2.12443i) q^{8} +(0.904065 + 2.18261i) q^{9} +O(q^{10})\)	\(q+(-1.35786 - 0.395231i) q^{2} +(0.443610 - 0.663909i) q^{3} +(1.68758 + 1.07334i) q^{4} +(0.154331 - 0.775873i) q^{5} +(-0.864759 + 0.726169i) q^{6} +(1.53949 - 3.71667i) q^{7} +(-1.86729 - 2.12443i) q^{8} +(0.904065 + 2.18261i) q^{9} +(-0.516209 + 0.992533i) q^{10} +(-1.83415 + 1.22554i) q^{11} +(1.46123 - 0.644259i) q^{12} +(0.559685 + 2.81373i) q^{13} +(-3.55936 + 4.43827i) q^{14} +(-0.446646 - 0.446646i) q^{15} +(1.69589 + 3.62270i) q^{16} +(-2.73419 + 2.73419i) q^{17} +(-0.364963 - 3.32099i) q^{18} +(-5.68264 + 1.13035i) q^{19} +(1.09322 - 1.14370i) q^{20} +(-1.78459 - 2.67083i) q^{21} +(2.97490 - 0.939205i) q^{22} +(2.55179 - 1.05698i) q^{23} +(-2.23878 + 0.297293i) q^{24} +(4.04124 + 1.67394i) q^{25} +(0.352096 - 4.04186i) q^{26} +(4.19950 + 0.835333i) q^{27} +(6.58727 - 4.61979i) q^{28} +(-2.96252 - 1.97949i) q^{29} +(0.429956 + 0.783013i) q^{30} -0.201957i q^{31} +(-0.870977 - 5.58940i) q^{32} +1.76137i q^{33} +(4.79329 - 2.63202i) q^{34} +(-2.64607 - 1.76805i) q^{35} +(-0.816990 + 4.65370i) q^{36} +(-8.82594 - 1.75559i) q^{37} +(8.16299 + 0.711098i) q^{38} +(2.11634 + 0.876616i) q^{39} +(-1.93647 + 1.12092i) q^{40} +(7.85196 - 3.25239i) q^{41} +(1.36764 + 4.33195i) q^{42} +(1.06440 + 1.59299i) q^{43} +(-4.41071 + 0.0995378i) q^{44} +(1.83295 - 0.364596i) q^{45} +(-3.88273 + 0.426695i) q^{46} +(-7.56082 + 7.56082i) q^{47} +(3.15746 + 0.481152i) q^{48} +(-6.49382 - 6.49382i) q^{49} +(-4.82586 - 3.87020i) q^{50} +(0.602339 + 3.02816i) q^{51} +(-2.07557 + 5.34913i) q^{52} +(11.1942 - 7.47973i) q^{53} +(-5.37220 - 2.79404i) q^{54} +(0.667799 + 1.61221i) q^{55} +(-10.7705 + 3.66955i) q^{56} +(-1.77043 + 4.27418i) q^{57} +(3.24034 + 3.85875i) q^{58} +(-1.71321 + 8.61290i) q^{59} +(-0.274351 - 1.23316i) q^{60} +(-2.32214 + 3.47533i) q^{61} +(-0.0798198 + 0.274231i) q^{62} +9.50382 q^{63} +(-1.02644 + 7.93388i) q^{64} +2.26947 q^{65} +(0.696149 - 2.39170i) q^{66} +(5.15244 - 7.71118i) q^{67} +(-7.54888 + 1.67946i) q^{68} +(0.430256 - 2.16304i) q^{69} +(2.89421 + 3.44657i) q^{70} +(1.98817 - 4.79986i) q^{71} +(2.94865 - 5.99619i) q^{72} +(-6.11102 - 14.7533i) q^{73} +(11.2906 + 5.87213i) q^{74} +(2.90407 - 1.94044i) q^{75} +(-10.8032 - 4.19184i) q^{76} +(1.73126 + 8.70365i) q^{77} +(-2.52723 - 2.02677i) q^{78} +(-2.91841 - 2.91841i) q^{79} +(3.07248 - 0.756698i) q^{80} +(-2.59396 + 2.59396i) q^{81} +(-11.9473 + 1.31296i) q^{82} +(-0.190374 + 0.0378677i) q^{83} +(-0.144944 - 6.42273i) q^{84} +(1.69941 + 2.54335i) q^{85} +(-0.815713 - 2.58375i) q^{86} +(-2.62840 + 1.08872i) q^{87} +(6.02849 + 1.60809i) q^{88} +(0.659812 + 0.273303i) q^{89} +(-2.63299 - 0.229366i) q^{90} +(11.3193 + 2.25155i) q^{91} +(5.44086 + 0.955181i) q^{92} +(-0.134081 - 0.0895903i) q^{93} +(13.2548 - 7.27829i) q^{94} +4.58345i q^{95} +(-4.09723 - 1.90126i) q^{96} +2.80442i q^{97} +(6.25116 + 11.3843i) q^{98} +(-4.33307 - 2.89527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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