LMFDB - Embedded newform 322.2.i.c.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 41 x^{18} - 119 x^{17} + 245 x^{16} - 404 x^{15} + 623 x^{14} - 898 x^{13} + \cdots + 1 $ x^20 - 9x^19 + 41x^18 - 119x^17 + 245x^16 - 404x^15 + 623x^14 - 898x^13 + 1048x^12 - 693x^11 + 859x^10 - 935x^9 + 620x^8 + 679x^7 + 1220x^6 + 2241x^5 + 1750x^4 + 1079x^3 + 534x^2 + 38*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.2
Root			$2.47844 + 0.727734i$ of defining polynomial
Character	$\chi$	$=$	322.85
Dual form			322.2.i.c.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(1.33176 - 0.855871i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.426940 + 0.934869i) q^{5} +(-0.225294 + 1.56696i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.205171 + 0.449262i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(1.33176 - 0.855871i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.426940 + 0.934869i) q^{5} +(-0.225294 + 1.56696i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.205171 + 0.449262i) q^{9} +(-0.986114 - 0.289549i) q^{10} +(2.66816 + 3.07922i) q^{11} +(-1.03669 - 1.19640i) q^{12} +(5.08004 + 1.49163i) q^{13} +(0.415415 - 0.909632i) q^{14} +(1.36871 + 0.879617i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.323828 - 2.25227i) q^{17} +(-0.205171 - 0.449262i) q^{18} +(-0.474179 - 3.29799i) q^{19} +(0.864594 - 0.555641i) q^{20} +(-1.03669 + 1.19640i) q^{21} -4.07440 q^{22} +(4.65285 - 1.16231i) q^{23} +1.58307 q^{24} +(2.58260 - 2.98048i) q^{25} +(-4.45402 + 2.86242i) q^{26} +(0.787154 + 5.47478i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.0814920 - 0.566789i) q^{29} +(-1.56109 + 0.458376i) q^{30} +(-8.38147 - 5.38644i) q^{31} +(0.415415 - 0.909632i) q^{32} +(6.18878 + 1.81719i) q^{33} +(1.49009 + 1.71966i) q^{34} +(-0.673030 - 0.776717i) q^{35} +(0.473888 + 0.139146i) q^{36} +(-0.813758 + 1.78188i) q^{37} +(2.80297 + 1.80136i) q^{38} +(8.04205 - 2.36136i) q^{39} +(-0.146263 + 1.01728i) q^{40} +(2.46732 + 5.40267i) q^{41} +(-0.225294 - 1.56696i) q^{42} +(-9.19826 + 5.91136i) q^{43} +(2.66816 - 3.07922i) q^{44} -0.507597 q^{45} +(-2.16856 + 4.27754i) q^{46} -7.21974 q^{47} +(-1.03669 + 1.19640i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.561253 + 3.90360i) q^{50} +(-1.49640 - 3.27665i) q^{51} +(0.753486 - 5.24061i) q^{52} +(-7.15625 + 2.10126i) q^{53} +(-4.65304 - 2.99032i) q^{54} +(-1.73952 + 3.80903i) q^{55} +(-0.959493 - 0.281733i) q^{56} +(-3.45414 - 3.98630i) q^{57} +(0.374985 + 0.432756i) q^{58} +(4.02616 + 1.18219i) q^{59} +(0.675876 - 1.47996i) q^{60} +(-5.62552 - 3.61530i) q^{61} +(9.55950 - 2.80692i) q^{62} +(0.0702885 - 0.488867i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.774391 + 5.38601i) q^{65} +(-5.42613 + 3.48716i) q^{66} +(-2.06638 + 2.38473i) q^{67} -2.27544 q^{68} +(5.20171 - 5.53016i) q^{69} +1.02774 q^{70} +(6.56994 - 7.58211i) q^{71} +(-0.415491 + 0.267020i) q^{72} +(-1.30769 - 9.09520i) q^{73} +(-0.813758 - 1.78188i) q^{74} +(0.888502 - 6.17967i) q^{75} +(-3.19693 + 0.938705i) q^{76} +(-3.42760 - 2.20279i) q^{77} +(-3.48183 + 7.62413i) q^{78} +(-11.2236 - 3.29555i) q^{79} +(-0.673030 - 0.776717i) q^{80} +(4.76371 + 5.49761i) q^{81} +(-5.69881 - 1.67332i) q^{82} +(6.21437 - 13.6076i) q^{83} +(1.33176 + 0.855871i) q^{84} +(2.24384 - 0.658850i) q^{85} +(1.55607 - 10.8227i) q^{86} +(-0.376571 - 0.824575i) q^{87} +(0.579847 + 4.03293i) q^{88} +(11.6806 - 7.50667i) q^{89} +(0.332406 - 0.383616i) q^{90} -5.29450 q^{91} +(-1.81265 - 4.44008i) q^{92} -15.7722 q^{93} +(4.72793 - 5.45632i) q^{94} +(2.88074 - 1.85134i) q^{95} +(-0.225294 - 1.56696i) q^{96} +(3.04736 + 6.67279i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-1.93081 + 0.566937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	1.33176	−	0.855871i	0.768893	−	0.494138i	−0.0964376	−	0.995339i	$-0.530745\pi$
$3$	1.33176	−	0.855871i	0.768893	−	0.494138i	0.865331	+	0.501201i	$0.167108\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.426940	+	0.934869i	0.190934	+	0.418086i	0.980753	−	0.195253i	$-0.0625529\pi$
$5$	0.426940	+	0.934869i	0.190934	+	0.418086i	−0.789819	+	0.613340i	$0.789826\pi$
$6$	−0.225294	+	1.56696i	−0.0919759	+	0.639707i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	−0.205171	+	0.449262i	−0.0683904	+	0.149754i
$10$	−0.986114	−	0.289549i	−0.311837	−	0.0915635i
$11$	2.66816	+	3.07922i	0.804481	+	0.928421i	0.998618	−	0.0525536i	$-0.0167361\pi$
$11$	2.66816	+	3.07922i	0.804481	+	0.928421i	−0.194137	+	0.980974i	$0.562191\pi$
$12$	−1.03669	−	1.19640i	−0.299266	−	0.345372i
$13$	5.08004	+	1.49163i	1.40895	+	0.413705i	0.895747	−	0.444563i	$-0.146641\pi$
$13$	5.08004	+	1.49163i	1.40895	+	0.413705i	0.513202	+	0.858268i	$0.328459\pi$
$14$	0.415415	−	0.909632i	0.111024	−	0.243109i
$15$	1.36871	+	0.879617i	0.353400	+	0.227116i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.323828	−	2.25227i	0.0785399	−	0.546257i	−0.912122	−	0.409918i	$-0.865557\pi$
$17$	0.323828	−	2.25227i	0.0785399	−	0.546257i	0.990662	−	0.136339i	$-0.0435336\pi$
$18$	−0.205171	−	0.449262i	−0.0483593	−	0.105892i
$19$	−0.474179	−	3.29799i	−0.108784	−	0.756610i	−0.969068	−	0.246794i	$-0.920623\pi$
$19$	−0.474179	−	3.29799i	−0.108784	−	0.756610i	0.860284	−	0.509815i	$-0.170286\pi$
$20$	0.864594	−	0.555641i	0.193329	−	0.124245i
$21$	−1.03669	+	1.19640i	−0.226224	+	0.261077i
$22$	−4.07440			−0.868664
$23$	4.65285	−	1.16231i	0.970187	−	0.242358i
$23$	4.65285	−	1.16231i	0.970187	−	0.242358i
$24$	1.58307			0.323142
$25$	2.58260	−	2.98048i	0.516520	−	0.596096i
$26$	−4.45402	+	2.86242i	−0.873505	+	0.561368i
$27$	0.787154	+	5.47478i	0.151488	+	1.05362i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	0.0814920	−	0.566789i	0.0151327	−	0.105250i	−0.980855	−	0.194739i	$-0.937614\pi$
$29$	0.0814920	−	0.566789i	0.0151327	−	0.105250i	0.995988	+	0.0894885i	$0.0285232\pi$
$30$	−1.56109	+	0.458376i	−0.285014	+	0.0836876i
$31$	−8.38147	−	5.38644i	−1.50536	−	0.967434i	−0.994154	−	0.107973i	$-0.965564\pi$
$31$	−8.38147	−	5.38644i	−1.50536	−	0.967434i	−0.511202	−	0.859460i	$-0.670800\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	6.18878	+	1.81719i	1.07733	+	0.316332i
$34$	1.49009	+	1.71966i	0.255549	+	0.294919i
$35$	−0.673030	−	0.776717i	−0.113763	−	0.131289i
$36$	0.473888	+	0.139146i	0.0789814	+	0.0231910i
$37$	−0.813758	+	1.78188i	−0.133781	+	0.292939i	−0.964653	−	0.263525i	$-0.915115\pi$
$37$	−0.813758	+	1.78188i	−0.133781	+	0.292939i	0.830872	+	0.556464i	$0.187842\pi$
$38$	2.80297	+	1.80136i	0.454702	+	0.292219i
$39$	8.04205	−	2.36136i	1.28776	−	0.378120i
$40$	−0.146263	+	1.01728i	−0.0231263	+	0.160847i
$41$	2.46732	+	5.40267i	0.385330	+	0.843755i	0.998549	+	0.0538424i	$0.0171469\pi$
$41$	2.46732	+	5.40267i	0.385330	+	0.843755i	−0.613219	+	0.789913i	$0.710126\pi$
$42$	−0.225294	−	1.56696i	−0.0347636	−	0.241786i
$43$	−9.19826	+	5.91136i	−1.40272	+	0.901475i	−0.999905	−	0.0138058i	$-0.995605\pi$
$43$	−9.19826	+	5.91136i	−1.40272	+	0.901475i	−0.402817	+	0.915280i	$0.631969\pi$
$44$	2.66816	−	3.07922i	0.402241	−	0.464210i
$45$	−0.507597			−0.0756681
$46$	−2.16856	+	4.27754i	−0.319737	+	0.630689i
$47$	−7.21974			−1.05311			−0.526554	−	0.850142i	$-0.676516\pi$
$47$	−7.21974			−1.05311			−0.526554	+	0.850142i	$0.676516\pi$
$48$	−1.03669	+	1.19640i	−0.149633	+	0.172686i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.561253	+	3.90360i	0.0793731	+	0.552052i
$51$	−1.49640	−	3.27665i	−0.209537	−	0.458823i
$52$	0.753486	−	5.24061i	0.104490	−	0.726742i
$53$	−7.15625	+	2.10126i	−0.982987	+	0.288631i	−0.733457	−	0.679736i	$-0.762094\pi$
$53$	−7.15625	+	2.10126i	−0.982987	+	0.288631i	−0.249530	+	0.968367i	$0.580276\pi$
$54$	−4.65304	−	2.99032i	−0.633198	−	0.406932i
$55$	−1.73952	+	3.80903i	−0.234557	+	0.513609i
$56$	−0.959493	−	0.281733i	−0.128218	−	0.0376481i
$57$	−3.45414	−	3.98630i	−0.457513	−	0.527998i
$58$	0.374985	+	0.432756i	0.0492379	+	0.0568236i
$59$	4.02616	+	1.18219i	0.524161	+	0.153908i	0.533100	−	0.846052i	$-0.321027\pi$
$59$	4.02616	+	1.18219i	0.524161	+	0.153908i	−0.00893850	+	0.999960i	$0.502845\pi$
$60$	0.675876	−	1.47996i	0.0872552	−	0.191062i
$61$	−5.62552	−	3.61530i	−0.720274	−	0.462892i	0.128458	−	0.991715i	$-0.458997\pi$
$61$	−5.62552	−	3.61530i	−0.720274	−	0.462892i	−0.848732	+	0.528823i	$0.822634\pi$
$62$	9.55950	−	2.80692i	1.21406	−	0.356479i
$63$	0.0702885	−	0.488867i	0.00885552	−	0.0615915i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.774391	+	5.38601i	0.0960514	+	0.668052i
$66$	−5.42613	+	3.48716i	−0.667910	+	0.429240i
$67$	−2.06638	+	2.38473i	−0.252449	+	0.291341i	−0.867802	−	0.496910i	$-0.834468\pi$
$67$	−2.06638	+	2.38473i	−0.252449	+	0.291341i	0.615353	+	0.788251i	$0.289013\pi$
$68$	−2.27544			−0.275937
$69$	5.20171	−	5.53016i	0.626212	−	0.665753i
$70$	1.02774			0.122839
$71$	6.56994	−	7.58211i	0.779708	−	0.899831i	−0.217380	−	0.976087i	$-0.569751\pi$
$71$	6.56994	−	7.58211i	0.779708	−	0.899831i	0.997088	+	0.0762559i	$0.0242966\pi$
$72$	−0.415491	+	0.267020i	−0.0489660	+	0.0314686i
$73$	−1.30769	−	9.09520i	−0.153054	−	1.06451i	−0.911062	−	0.412268i	$-0.864737\pi$
$73$	−1.30769	−	9.09520i	−0.153054	−	1.06451i	0.758009	−	0.652245i	$-0.226172\pi$
$74$	−0.813758	−	1.78188i	−0.0945974	−	0.207139i
$75$	0.888502	−	6.17967i	0.102595	−	0.713566i
$76$	−3.19693	+	0.938705i	−0.366714	+	0.107677i
$77$	−3.42760	−	2.20279i	−0.390611	−	0.251031i
$78$	−3.48183	+	7.62413i	−0.394239	+	0.863263i
$79$	−11.2236	−	3.29555i	−1.26276	−	0.370778i	−0.419236	−	0.907877i	$-0.637702\pi$
$79$	−11.2236	−	3.29555i	−1.26276	−	0.370778i	−0.843519	+	0.537099i	$0.819520\pi$
$80$	−0.673030	−	0.776717i	−0.0752470	−	0.0868397i
$81$	4.76371	+	5.49761i	0.529301	+	0.610846i
$82$	−5.69881	−	1.67332i	−0.629329	−	0.184788i
$83$	6.21437	−	13.6076i	0.682116	−	1.49363i	−0.178269	−	0.983982i	$-0.557050\pi$
$83$	6.21437	−	13.6076i	0.682116	−	1.49363i	0.860385	−	0.509644i	$-0.170223\pi$
$84$	1.33176	+	0.855871i	0.145307	+	0.0933832i
$85$	2.24384	−	0.658850i	0.243378	−	0.0714623i
$86$	1.55607	−	10.8227i	0.167795	−	1.16704i
$87$	−0.376571	−	0.824575i	−0.0403726	−	0.0884037i
$88$	0.579847	+	4.03293i	0.0618119	+	0.429911i
$89$	11.6806	−	7.50667i	1.23814	−	0.795705i	0.253003	−	0.967466i	$-0.418582\pi$
$89$	11.6806	−	7.50667i	1.23814	−	0.795705i	0.985139	+	0.171760i	$0.0549455\pi$
$90$	0.332406	−	0.383616i	0.0350386	−	0.0404367i
$91$	−5.29450			−0.555015
$92$	−1.81265	−	4.44008i	−0.188981	−	0.462910i
$93$	−15.7722			−1.63550
$94$	4.72793	−	5.45632i	0.487648	−	0.562776i
$95$	2.88074	−	1.85134i	0.295558	−	0.189943i
$96$	−0.225294	−	1.56696i	−0.0229940	−	0.159927i
$97$	3.04736	+	6.67279i	0.309412	+	0.677519i	0.998906	−	0.0467735i	$-0.0148939\pi$
$97$	3.04736	+	6.67279i	0.309412	+	0.677519i	−0.689493	+	0.724292i	$0.742167\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	−1.93081	+	0.566937i	−0.194054	+	0.0569793i
$100$	−3.31769	−	2.13215i	−0.331769	−	0.213215i
$101$	−2.74912	+	6.01973i	−0.273547	+	0.598985i	−0.995688	−	0.0927605i	$-0.970431\pi$
$101$	−2.74912	+	6.01973i	−0.273547	+	0.598985i	0.722141	+	0.691746i	$0.243158\pi$
$102$	3.45626	+	1.01485i	0.342220	+	0.100485i
$103$	−1.32656	−	1.53093i	−0.130710	−	0.150847i	0.686622	−	0.727015i	$-0.259093\pi$
$103$	−1.32656	−	1.53093i	−0.130710	−	0.150847i	−0.817331	+	0.576168i	$0.804547\pi$
$104$	3.46716	+	4.00132i	0.339983	+	0.392361i
$105$	−1.56109	−	0.458376i	−0.152346	−	0.0447329i
$106$	3.09832	−	6.78437i	0.300935	−	0.658956i
$107$	−16.9137	−	10.8698i	−1.63511	−	1.05082i	−0.944975	−	0.327142i	$-0.893914\pi$
$107$	−16.9137	−	10.8698i	−1.63511	−	1.05082i	−0.690136	−	0.723680i	$-0.742449\pi$
$108$	5.30703	−	1.55828i	0.510669	−	0.149946i
$109$	−1.43194	+	9.95939i	−0.137155	+	0.953937i	0.798744	+	0.601670i	$0.205498\pi$
$109$	−1.43194	+	9.95939i	−0.137155	+	0.953937i	−0.935900	+	0.352266i	$0.885411\pi$
$110$	−1.73952	−	3.80903i	−0.165857	−	0.363177i
$111$	0.441329	+	3.06951i	0.0418891	+	0.291345i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	−1.24471	+	1.43647i	−0.117093	+	0.135132i	−0.811270	−	0.584672i	$-0.801223\pi$
$113$	−1.24471	+	1.43647i	−0.117093	+	0.135132i	0.694177	+	0.719804i	$0.255769\pi$
$114$	5.27462			0.494014
$115$	3.07310	+	3.85357i	0.286568	+	0.359348i
$116$	−0.572618			−0.0531662
$117$	−1.71241	+	1.97623i	−0.158313	+	0.182702i
$118$	−3.53001	+	2.26860i	−0.324964	+	0.208842i
$119$	0.323828	+	2.25227i	0.0296853	+	0.206466i
$120$	0.675876	+	1.47996i	0.0616988	+	0.135101i
$121$	−0.797064	+	5.54370i	−0.0724603	+	0.503973i
$122$	6.41620	−	1.88397i	0.580895	−	0.170566i
$123$	7.90987	+	5.08336i	0.713209	+	0.458351i
$124$	−4.13881	+	9.06273i	−0.371676	+	0.813857i
$125$	8.81955	+	2.58965i	0.788844	+	0.231626i
$126$	0.323432	+	0.373261i	0.0288136	+	0.0332527i
$127$	−5.43243	−	6.26935i	−0.482050	−	0.556315i	0.461674	−	0.887050i	$-0.347249\pi$
$127$	−5.43243	−	6.26935i	−0.482050	−	0.556315i	−0.943724	+	0.330735i	$0.892704\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	−7.19053	+	15.7451i	−0.633091	+	1.38628i
$130$	−4.57759	−	2.94184i	−0.401481	−	0.258016i
$131$	16.0262	−	4.70571i	1.40021	−	0.411140i	0.507456	−	0.861677i	$-0.330586\pi$
$131$	16.0262	−	4.70571i	1.40021	−	0.411140i	0.892758	+	0.450537i	$0.148768\pi$
$132$	0.917938	−	6.38440i	0.0798962	−	0.555690i
$133$	1.38412	+	3.03080i	0.120019	+	0.262804i
$134$	−0.449068	−	3.12333i	−0.0387935	−	0.269815i
$135$	−4.78213	+	3.07329i	−0.411580	+	0.264507i
$136$	1.49009	−	1.71966i	0.127774	−	0.147460i
$137$	−6.23224			−0.532456			−0.266228	−	0.963910i	$-0.585777\pi$
$137$	−6.23224			−0.532456			−0.266228	+	0.963910i	$0.585777\pi$
$138$	0.773021	+	7.55267i	0.0658039	+	0.642926i
$139$	5.47079			0.464026			0.232013	−	0.972713i	$-0.425469\pi$
$139$	5.47079			0.464026			0.232013	+	0.972713i	$0.425469\pi$
$140$	−0.673030	+	0.776717i	−0.0568814	+	0.0656446i
$141$	−9.61498	+	6.17917i	−0.809727	+	0.520380i
$142$	1.42778	+	9.93045i	0.119817	+	0.833345i
$143$	8.96129	+	19.6225i	0.749381	+	1.64092i
$144$	0.0702885	−	0.488867i	0.00585738	−	0.0407389i
$145$	0.564666	−	0.165801i	0.0468930	−	0.0137690i
$146$	7.73005	+	4.96780i	0.639744	+	0.411138i
$147$	0.657630	−	1.44001i	0.0542404	−	0.118770i
$148$	1.87955	+	0.551887i	0.154498	+	0.0453648i
$149$	7.87751	+	9.09114i	0.645351	+	0.744775i	0.980311	−	0.197457i	$-0.0632684\pi$
$149$	7.87751	+	9.09114i	0.645351	+	0.744775i	−0.334960	+	0.942232i	$0.608723\pi$
$150$	4.08843	+	4.71830i	0.333819	+	0.385248i
$151$	−11.8757	−	3.48703i	−0.966434	−	0.283771i	−0.239821	−	0.970817i	$-0.577089\pi$
$151$	−11.8757	−	3.48703i	−0.966434	−	0.283771i	−0.726614	+	0.687046i	$0.758907\pi$
$152$	1.38412	−	3.03080i	0.112267	−	0.245831i
$153$	0.945422	+	0.607586i	0.0764328	+	0.0491204i
$154$	3.90935	−	1.14789i	0.315025	−	0.0924996i
$155$	1.45723	−	10.1353i	0.117048	−	0.814084i
$156$	−3.48183	−	7.62413i	−0.278769	−	0.610419i
$157$	−1.12802	−	7.84556i	−0.0900259	−	0.626144i	−0.984019	−	0.178063i	$-0.943017\pi$
$157$	−1.12802	−	7.84556i	−0.0900259	−	0.626144i	0.893993	−	0.448081i	$-0.147892\pi$
$158$	9.84052	−	6.32412i	0.782869	−	0.503120i
$159$	−7.73201	+	8.92322i	−0.613188	+	0.707657i
$160$	1.02774			0.0812503
$161$	−4.13692	+	2.42608i	−0.326035	+	0.191202i
$162$	−7.27438			−0.571530
$163$	13.3731	−	15.4334i	1.04746	−	1.20884i	0.0700390	−	0.997544i	$-0.477688\pi$
$163$	13.3731	−	15.4334i	1.04746	−	1.20884i	0.977423	−	0.211291i	$-0.0677669\pi$
$164$	4.99654	−	3.21108i	0.390164	−	0.250743i
$165$	0.943405	+	6.56153i	0.0734440	+	0.510814i
$166$	6.21437	+	13.6076i	0.482329	+	1.05615i
$167$	1.06785	−	7.42705i	0.0826326	−	0.574722i	−0.905874	−	0.423547i	$-0.860785\pi$
$167$	1.06785	−	7.42705i	0.0826326	−	0.574722i	0.988507	−	0.151176i	$-0.0483059\pi$
$168$	−1.51894	+	0.446002i	−0.117189	+	0.0344098i
$169$	12.6455	+	8.12678i	0.972732	+	0.625137i
$170$	−0.971475	+	2.12723i	−0.0745088	+	0.163151i
$171$	1.57895	+	0.463621i	0.120745	+	0.0354540i
$172$	7.16024	+	8.26336i	0.545964	+	0.630075i
$173$	8.16818	+	9.42658i	0.621015	+	0.716690i	0.975900	−	0.218220i	$-0.0700252\pi$
$173$	8.16818	+	9.42658i	0.621015	+	0.716690i	−0.354884	+	0.934910i	$0.615480\pi$
$174$	0.869774	+	0.255389i	0.0659374	+	0.0193610i
$175$	−1.63829	+	3.58735i	−0.123843	+	0.271178i
$176$	−3.42760	−	2.20279i	−0.258365	−	0.166041i
$177$	6.37368	−	1.87148i	0.479075	−	0.140669i
$178$	−1.97601	+	13.7434i	−0.148108	+	1.03011i
$179$	8.38585	+	18.3625i	0.626788	+	1.37247i	0.910478	+	0.413558i	$0.135714\pi$
$179$	8.38585	+	18.3625i	0.626788	+	1.37247i	−0.283689	+	0.958916i	$0.591558\pi$
$180$	0.0722386	+	0.502431i	0.00538435	+	0.0374490i
$181$	−7.27198	+	4.67342i	−0.540522	+	0.347373i	−0.782243	−	0.622973i	$-0.785925\pi$
$181$	−7.27198	+	4.67342i	−0.540522	+	0.347373i	0.241721	+	0.970346i	$0.422288\pi$
$182$	3.46716	−	4.00132i	0.257003	−	0.296597i
$183$	−10.5861			−0.782547
$184$	4.54262	+	1.53773i	0.334886	+	0.113363i
$185$	−2.01325			−0.148017
$186$	10.3286	−	11.9198i	0.757330	−	0.874006i
$187$	7.79928	−	5.01229i	0.570340	−	0.366535i
$188$	1.02748	+	7.14626i	0.0749365	+	0.521194i
$189$	−2.29769	−	5.03124i	−0.167132	−	0.365969i
$190$	−0.487335	+	3.38949i	−0.0353550	+	0.245899i
$191$	−9.12257	+	2.67863i	−0.660086	+	0.193819i	−0.594584	−	0.804034i	$-0.702683\pi$
$191$	−9.12257	+	2.67863i	−0.660086	+	0.193819i	−0.0655023	+	0.997852i	$0.520865\pi$
$192$	1.33176	+	0.855871i	0.0961116	+	0.0617672i
$193$	2.34078	−	5.12559i	0.168493	−	0.368948i	−0.806483	−	0.591257i	$-0.798632\pi$
$193$	2.34078	−	5.12559i	0.168493	−	0.368948i	0.974976	+	0.222309i	$0.0713593\pi$
$194$	−7.03855	−	2.06671i	−0.505339	−	0.148381i
$195$	5.64104	+	6.51010i	0.403963	+	0.466198i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−1.70473	−	0.500554i	−0.121457	−	0.0356630i	0.220439	−	0.975401i	$-0.429251\pi$
$197$	−1.70473	−	0.500554i	−0.121457	−	0.0356630i	−0.341896	+	0.939738i	$0.611069\pi$
$198$	0.835949	−	1.83047i	0.0594083	−	0.130086i
$199$	1.92183	+	1.23509i	0.136235	+	0.0875530i	0.606983	−	0.794715i	$-0.292380\pi$
$199$	1.92183	+	1.23509i	0.136235	+	0.0875530i	−0.470748	+	0.882268i	$0.656016\pi$
$200$	3.78399	−	1.11108i	0.267569	−	0.0785652i
$201$	−0.710905	+	4.94445i	−0.0501433	+	0.348755i
$202$	−2.74912	−	6.01973i	−0.193427	−	0.423547i
$203$	0.0814920	+	0.566789i	0.00571962	+	0.0397808i
$204$	−3.03034	+	1.94748i	−0.212166	+	0.136351i
$205$	−3.99739	+	4.61324i	−0.279190	+	0.322202i
$206$	2.02571			0.141138
$207$	−0.432451	+	2.32882i	−0.0300574	+	0.161864i
$208$	−5.29450			−0.367108
$209$	8.89005	−	10.2597i	0.614938	−	0.709676i
$210$	1.36871	−	0.879617i	0.0944500	−	0.0606993i
$211$	−3.22643	−	22.4403i	−0.222117	−	1.54485i	−0.730011	−	0.683435i	$-0.760485\pi$
$211$	−3.22643	−	22.4403i	−0.222117	−	1.54485i	0.507894	−	0.861419i	$-0.330424\pi$
$212$	3.09832	+	6.78437i	0.212793	+	0.465952i
$213$	2.26028	−	15.7206i	0.154872	−	1.07716i
$214$	19.2910	−	5.66434i	1.31870	−	0.387206i
$215$	−9.45346	−	6.07537i	−0.644721	−	0.414337i
$216$	−2.29769	+	5.03124i	−0.156338	+	0.342333i
$217$	9.55950	+	2.80692i	0.648941	+	0.190546i
$218$	−6.58908	−	7.60421i	−0.446269	−	0.515022i
$219$	−9.52586	−	10.9934i	−0.643698	−	0.742867i
$220$	4.01782	+	1.17974i	0.270881	+	0.0795379i
$221$	5.00463	−	10.9586i	0.336648	−	0.737156i
$222$	−2.60879	−	1.67657i	−0.175091	−	0.112524i
$223$	−0.277502	+	0.0814819i	−0.0185829	+	0.00545643i	−0.291011	−	0.956720i	$-0.593992\pi$
$223$	−0.277502	+	0.0814819i	−0.0185829	+	0.00545643i	0.272428	+	0.962176i	$0.412173\pi$
$224$	−0.142315	+	0.989821i	−0.00950881	+	0.0661352i
$225$	0.809142	+	1.77177i	0.0539428	+	0.118118i
$226$	−0.270502	−	1.88138i	−0.0179935	−	0.125148i
$227$	−11.2986	+	7.26116i	−0.749913	+	0.481940i	−0.858926	−	0.512100i	$-0.828868\pi$
$227$	−11.2986	+	7.26116i	−0.749913	+	0.481940i	0.109012	+	0.994040i	$0.465231\pi$
$228$	−3.45414	+	3.98630i	−0.228756	+	0.263999i
$229$	−0.842339			−0.0556633			−0.0278317	−	0.999613i	$-0.508860\pi$
$229$	−0.842339			−0.0556633			−0.0278317	+	0.999613i	$0.508860\pi$
$230$	−4.92479	−	0.201064i	−0.324731	−	0.0132577i
$231$	−6.45005			−0.424382
$232$	0.374985	−	0.432756i	0.0246190	−	0.0284118i
$233$	−19.9137	+	12.7977i	−1.30459	+	0.838408i	−0.993704	−	0.112040i	$-0.964262\pi$
$233$	−19.9137	+	12.7977i	−1.30459	+	0.838408i	−0.310884	+	0.950448i	$0.600625\pi$
$234$	−0.372143	−	2.58831i	−0.0243277	−	0.169203i
$235$	−3.08240	−	6.74952i	−0.201074	−	0.440290i
$236$	0.597172	−	4.15342i	0.0388726	−	0.270365i
$237$	−17.7678	+	5.21708i	−1.15414	+	0.338886i
$238$	−1.91422	−	1.23019i	−0.124080	−	0.0797416i
$239$	3.42132	−	7.49165i	0.221307	−	0.484595i	−0.766115	−	0.642704i	$-0.777813\pi$
$239$	3.42132	−	7.49165i	0.221307	−	0.484595i	0.987422	+	0.158109i	$0.0505398\pi$
$240$	−1.56109	−	0.458376i	−0.100768	−	0.0295880i
$241$	15.6524	+	18.0639i	1.00826	+	1.16360i	0.986488	+	0.163832i	$0.0523855\pi$
$241$	15.6524	+	18.0639i	1.00826	+	1.16360i	0.0217726	+	0.999763i	$0.493069\pi$
$242$	−3.66768	−	4.23273i	−0.235768	−	0.272090i
$243$	−4.87170	−	1.43046i	−0.312520	−	0.0917641i
$244$	−2.77791	+	6.08278i	−0.177837	+	0.389410i
$245$	0.864594	+	0.555641i	0.0552369	+	0.0354986i
$246$	−9.02161	+	2.64898i	−0.575197	+	0.168893i
$247$	2.51054	−	17.4612i	0.159742	−	1.11103i
$248$	−4.13881	−	9.06273i	−0.262815	−	0.575484i
$249$	−3.37027	−	23.4408i	−0.213582	−	1.48550i
$250$	−7.73270	+	4.96951i	−0.489059	+	0.314299i
$251$	−0.509182	+	0.587628i	−0.0321393	+	0.0370907i	−0.771592	−	0.636118i	$-0.780539\pi$
$251$	−0.509182	+	0.587628i	−0.0321393	+	0.0370907i	0.739452	+	0.673209i	$0.235085\pi$
$252$	−0.493895			−0.0311124
$253$	15.9936	+	11.2260i	1.00551	+	0.705770i
$254$	8.29554			0.520509
$255$	2.42437	−	2.79787i	0.151820	−	0.175209i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.182604	+	1.27004i	0.0113905	+	0.0792228i	0.994724	−	0.102589i	$-0.0327128\pi$
$257$	0.182604	+	1.27004i	0.0113905	+	0.0792228i	−0.983333	+	0.181812i	$0.941804\pi$
$258$	−7.19053	−	15.7451i	−0.447663	−	0.980245i
$259$	0.278781	−	1.93896i	0.0173226	−	0.120481i
$260$	5.22098	−	1.53302i	0.323791	−	0.0950738i
$261$	0.237917	+	0.152900i	0.0147267	+	0.00946428i
$262$	−6.93858	+	15.1934i	−0.428667	+	0.938649i
$263$	−24.4335	−	7.17432i	−1.50663	−	0.442387i	−0.578827	−	0.815450i	$-0.696489\pi$
$263$	−24.4335	−	7.17432i	−1.50663	−	0.442387i	−0.927806	+	0.373063i	$0.878307\pi$
$264$	4.22388	+	4.87462i	0.259962	+	0.300012i
$265$	−5.01970	−	5.79304i	−0.308358	−	0.355864i
$266$	−3.19693	−	0.938705i	−0.196017	−	0.0575557i
$267$	9.13104	−	19.9942i	0.558811	−	1.22362i
$268$	2.65453	+	1.70597i	0.162151	+	0.104208i
$269$	15.7739	−	4.63164i	0.961753	−	0.282396i	0.237081	−	0.971490i	$-0.423809\pi$
$269$	15.7739	−	4.63164i	0.961753	−	0.282396i	0.724672	+	0.689094i	$0.241991\pi$
$270$	0.808993	−	5.62667i	0.0492338	−	0.342428i
$271$	−0.0478999	−	0.104886i	−0.00290971	−	0.00637137i	0.908172	−	0.418598i	$-0.137478\pi$
$271$	−0.0478999	−	0.104886i	−0.00290971	−	0.00637137i	−0.911081	+	0.412227i	$0.864751\pi$
$272$	0.323828	+	2.25227i	0.0196350	+	0.136564i
$273$	−7.05102	+	4.53141i	−0.426747	+	0.274254i
$274$	4.08125	−	4.71001i	0.246557	−	0.284542i
$275$	16.0684			0.968959
$276$	−6.21415	−	4.36174i	−0.374048	−	0.262546i
$277$	−29.6543			−1.78175			−0.890877	−	0.454244i	$-0.849909\pi$
$277$	−29.6543			−1.78175			−0.890877	+	0.454244i	$0.849909\pi$
$278$	−3.58260	+	4.13455i	−0.214870	+	0.247974i
$279$	4.13956	−	2.66033i	0.247829	−	0.159270i
$280$	−0.146263	−	1.01728i	−0.00874090	−	0.0607943i
$281$	8.99448	+	19.6952i	0.536566	+	1.17492i	0.962778	+	0.270292i	$0.0871203\pi$
$281$	8.99448	+	19.6952i	0.536566	+	1.17492i	−0.426212	+	0.904623i	$0.640152\pi$
$282$	1.62657	−	11.3130i	0.0968606	−	0.673680i
$283$	−11.2572	+	3.30542i	−0.669174	+	0.196487i	−0.598635	−	0.801022i	$-0.704290\pi$
$283$	−11.2572	+	3.30542i	−0.669174	+	0.196487i	−0.0705386	+	0.997509i	$0.522472\pi$
$284$	−8.43994	−	5.42402i	−0.500818	−	0.321856i
$285$	2.25195	−	4.93108i	0.133394	−	0.292092i
$286$	−20.6981	−	6.07751i	−1.22390	−	0.359371i
$287$	−3.88948	−	4.48870i	−0.229589	−	0.264960i
$288$	0.323432	+	0.373261i	0.0190584	+	0.0219946i
$289$	11.3435	+	3.33075i	0.667265	+	0.195927i
$290$	−0.244474	+	0.535323i	−0.0143560	+	0.0314352i
$291$	9.76940	+	6.27841i	0.572693	+	0.368047i
$292$	−8.81652	+	2.58876i	−0.515948	+	0.151496i
$293$	2.61100	−	18.1599i	0.152536	−	1.06091i	−0.759413	−	0.650609i	$-0.774514\pi$
$293$	2.61100	−	18.1599i	0.152536	−	1.06091i	0.911949	−	0.410303i	$-0.134577\pi$
$294$	0.657630	+	1.44001i	0.0383538	+	0.0839831i
$295$	0.613740	+	4.26866i	0.0357333	+	0.248531i
$296$	−1.64793	+	1.05906i	−0.0957842	+	0.0615568i
$297$	−14.7578	+	17.0314i	−0.856335	+	0.988263i
$298$	−12.0293			−0.696839
$299$	25.3704	+	1.03579i	1.46721	+	0.0599015i
$300$	−6.24321			−0.360452
$301$	7.16024	−	8.26336i	0.412710	−	0.476292i
$302$	10.4123	−	6.69157i	0.599160	−	0.385056i
$303$	1.49094	+	10.3697i	0.0856524	+	0.595726i
$304$	1.38412	+	3.03080i	0.0793848	+	0.173828i
$305$	0.978073	−	6.80265i	0.0560043	−	0.389519i
$306$	−1.07830	+	0.316618i	−0.0616424	+	0.0180999i
$307$	20.6845	+	13.2931i	1.18052	+	0.758677i	0.975483	−	0.220076i	$-0.0706305\pi$
$307$	20.6845	+	13.2931i	1.18052	+	0.758677i	0.205042	+	0.978753i	$0.434267\pi$
$308$	−1.69257	+	3.70620i	−0.0964429	+	0.211180i
$309$	−3.07694	−	0.903470i	−0.175041	−	0.0513966i
$310$	6.70544	+	7.73849i	0.380843	+	0.439517i
$311$	−2.91401	−	3.36295i	−0.165238	−	0.190695i	0.667092	−	0.744976i	$-0.267539\pi$
$311$	−2.91401	−	3.36295i	−0.165238	−	0.190695i	−0.832330	+	0.554280i	$0.812994\pi$
$312$	8.04205	+	2.36136i	0.455291	+	0.133686i
$313$	3.07203	−	6.72681i	0.173641	−	0.380222i	−0.802723	−	0.596352i	$-0.796616\pi$
$313$	3.07203	−	6.72681i	0.173641	−	0.380222i	0.976365	+	0.216130i	$0.0693436\pi$
$314$	6.66798	+	4.28525i	0.376296	+	0.241831i
$315$	0.487036	−	0.143007i	0.0274414	−	0.00805752i
$316$	−1.66472	+	11.5784i	−0.0936478	+	0.651335i
$317$	5.26594	+	11.5308i	0.295764	+	0.647634i	0.997925	−	0.0643847i	$-0.0205085\pi$
$317$	5.26594	+	11.5308i	0.295764	+	0.647634i	−0.702161	+	0.712019i	$0.747781\pi$
$318$	−1.68033	−	11.6869i	−0.0942280	−	0.655370i
$319$	1.96271	−	1.26135i	0.109890	−	0.0706223i
$320$	−0.673030	+	0.776717i	−0.0376235	+	0.0434198i
$321$	−31.8282			−1.77648
$322$	0.875594	−	4.71522i	0.0487950	−	0.262769i
$323$	−7.58152			−0.421847
$324$	4.76371	−	5.49761i	0.264650	−	0.305423i
$325$	17.5655	−	11.2887i	0.974358	−	0.626182i
$326$	2.90625	+	20.2134i	0.160962	+	1.11952i
$327$	6.61695	+	14.4891i	0.365918	+	0.801249i
$328$	−0.845265	+	5.87895i	−0.0466719	+	0.324610i
$329$	6.92729	−	2.03404i	0.381914	−	0.112140i
$330$	−5.57667	−	3.58391i	−0.306986	−	0.197288i
$331$	−0.215571	+	0.472034i	−0.0118488	+	0.0259453i	−0.915464	−	0.402400i	$-0.868176\pi$
$331$	−0.215571	+	0.472034i	−0.0118488	+	0.0259453i	0.903615	+	0.428345i	$0.140903\pi$
$332$	−14.3535	−	4.21456i	−0.787749	−	0.231304i
$333$	−0.633572	−	0.731181i	−0.0347195	−	0.0400685i
$334$	4.91370	+	5.67071i	0.268866	+	0.310287i
$335$	−3.11163	−	0.913658i	−0.170007	−	0.0499185i
$336$	0.657630	−	1.44001i	0.0358767	−	0.0785590i
$337$	−5.03765	−	3.23750i	−0.274418	−	0.176358i	0.396192	−	0.918168i	$-0.370331\pi$
$337$	−5.03765	−	3.23750i	−0.274418	−	0.176358i	−0.670611	+	0.741810i	$0.733968\pi$
$338$	−14.4229	+	4.23493i	−0.784500	+	0.230350i
$339$	−0.428223	+	2.97836i	−0.0232579	+	0.161762i
$340$	−0.971475	−	2.12723i	−0.0526857	−	0.115365i
$341$	−5.77706	−	40.1803i	−0.312845	−	2.17589i
$342$	−1.38437	+	0.889682i	−0.0748583	+	0.0481085i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	−10.9340			−0.589522
$345$	7.39080	+	2.50187i	0.397907	+	0.134696i
$346$	−12.4732			−0.670561
$347$	−14.8409	+	17.1274i	−0.796703	+	0.919445i	−0.998196	−	0.0600454i	$-0.980875\pi$
$347$	−14.8409	+	17.1274i	−0.796703	+	0.919445i	0.201492	+	0.979490i	$0.435421\pi$
$348$	−0.762591	+	0.490087i	−0.0408791	+	0.0262714i
$349$	−3.27218	−	22.7585i	−0.175156	−	1.21823i	−0.867785	−	0.496940i	$-0.834457\pi$
$349$	−3.27218	−	22.7585i	−0.175156	−	1.21823i	0.692629	−	0.721294i	$-0.256452\pi$
$350$	−1.63829	−	3.58735i	−0.0875702	−	0.191752i
$351$	−4.16759	+	28.9862i	−0.222449	+	1.54717i
$352$	3.90935	−	1.14789i	0.208369	−	0.0611828i
$353$	13.0806	+	8.40636i	0.696208	+	0.447425i	0.840288	−	0.542141i	$-0.182386\pi$
$353$	13.0806	+	8.40636i	0.696208	+	0.447425i	−0.144080	+	0.989566i	$0.546022\pi$
$354$	−2.75950	+	6.04247i	−0.146666	+	0.321154i
$355$	9.89326	+	2.90492i	0.525079	+	0.154177i
$356$	−9.09258	−	10.4934i	−0.481906	−	0.556149i
$357$	2.35892	+	2.72234i	0.124847	+	0.144081i
$358$	−19.3690	−	5.68725i	−1.02368	−	0.300580i
$359$	−12.8602	+	28.1599i	−0.678736	+	1.48623i	0.185240	+	0.982693i	$0.440694\pi$
$359$	−12.8602	+	28.1599i	−0.678736	+	1.48623i	−0.863977	+	0.503532i	$0.832034\pi$
$360$	−0.427018	−	0.274428i	−0.0225058	−	0.0144636i
$361$	7.57850	−	2.22525i	0.398869	−	0.117118i
$362$	1.23020	−	8.55624i	0.0646579	−	0.449706i
$363$	3.68320	+	8.06507i	0.193318	+	0.423307i
$364$	0.753486	+	5.24061i	0.0394934	+	0.274683i
$365$	7.94452	−	5.10563i	0.415835	−	0.267241i
$366$	6.93242	−	8.00044i	0.362363	−	0.418189i
$367$	−8.23517			−0.429873			−0.214936	−	0.976628i	$-0.568954\pi$
$367$	−8.23517			−0.429873			−0.214936	+	0.976628i	$0.568954\pi$
$368$	−4.13692	+	2.42608i	−0.215652	+	0.126468i
$369$	−2.93344			−0.152709
$370$	1.31840	−	1.52151i	0.0685403	−	0.0790997i
$371$	6.27438	−	4.03230i	0.325749	−	0.209346i
$372$	2.24462	+	15.6117i	0.116378	+	0.809428i
$373$	6.55146	+	14.3457i	0.339222	+	0.742793i	0.999969	−	0.00781576i	$-0.00248786\pi$
$373$	6.55146	+	14.3457i	0.339222	+	0.742793i	−0.660747	+	0.750608i	$0.729761\pi$
$374$	−1.31940	+	9.17666i	−0.0682248	+	0.474514i
$375$	13.9619	−	4.09960i	0.720992	−	0.211702i
$376$	−6.07364	−	3.90329i	−0.313224	−	0.201297i
$377$	1.25942	−	2.75776i	0.0648637	−	0.142032i
$378$	5.30703	+	1.55828i	0.272964	+	0.0801495i
$379$	12.1377	+	14.0077i	0.623472	+	0.719525i	0.976362	−	0.216140i	$-0.0693467\pi$
$379$	12.1377	+	14.0077i	0.623472	+	0.719525i	−0.352891	+	0.935665i	$0.614801\pi$
$380$	−2.24247	−	2.58794i	−0.115036	−	0.132759i
$381$	−12.6005	−	3.69983i	−0.645541	−	0.189548i
$382$	3.94964	−	8.64851i	0.202081	−	0.442496i
$383$	10.9665	+	7.04775i	0.560362	+	0.360123i	0.789956	−	0.613164i	$-0.210103\pi$
$383$	10.9665	+	7.04775i	0.560362	+	0.360123i	−0.229594	+	0.973287i	$0.573740\pi$
$384$	−1.51894	+	0.446002i	−0.0775132	+	0.0227599i
$385$	0.595935	−	4.14482i	0.0303716	−	0.211239i
$386$	2.34078	+	5.12559i	0.119142	+	0.260885i
$387$	−0.768534	−	5.34527i	−0.0390668	−	0.271716i
$388$	6.17118	−	3.96598i	0.313294	−	0.201342i
$389$	−12.1028	+	13.9674i	−0.613638	+	0.708176i	−0.974486	−	0.224448i	$-0.927942\pi$
$389$	−12.1028	+	13.9674i	−0.613638	+	0.708176i	0.360848	+	0.932625i	$0.382487\pi$
$390$	−8.61410			−0.436192
$391$	−1.11111	−	10.8559i	−0.0561911	−	0.549006i
$392$	1.00000			0.0505076
$393$	17.3156	−	19.9832i	0.873455	−	1.00802i
$394$	1.49465	−	0.960556i	0.0752996	−	0.0483921i
$395$	−1.71091	−	11.8996i	−0.0860851	−	0.598735i
$396$	0.835949	+	1.83047i	0.0420080	+	0.0919847i
$397$	−1.48434	+	10.3238i	−0.0744967	+	0.518136i	0.918068	+	0.396422i	$0.129748\pi$
$397$	−1.48434	+	10.3238i	−0.0744967	+	0.518136i	−0.992565	+	0.121714i	$0.961161\pi$
$398$	−2.19195	+	0.643614i	−0.109872	+	0.0322615i
$399$	4.43730	+	2.85168i	0.222143	+	0.142762i
$400$	−1.63829	+	3.58735i	−0.0819145	+	0.179368i
$401$	−6.90107	−	2.02634i	−0.344623	−	0.101190i	0.104841	−	0.994489i	$-0.466567\pi$
$401$	−6.90107	−	2.02634i	−0.344623	−	0.101190i	−0.449464	+	0.893299i	$0.648385\pi$
$402$	−3.27122	−	3.77519i	−0.163154	−	0.188289i
$403$	−34.5436	−	39.8654i	−1.72074	−	1.98584i
$404$	6.34970	+	1.86444i	0.315909	+	0.0927593i
$405$	−3.10573	+	6.80060i	−0.154325	+	0.337924i
$406$	−0.481717	−	0.309581i	−0.0239072	−	0.0153642i
$407$	−7.65805	+	2.24861i	−0.379595	+	0.111459i
$408$	0.512642	−	3.56550i	0.0253796	−	0.176519i
$409$	−16.0597	−	35.1657i	−0.794099	−	1.73883i	−0.664527	−	0.747264i	$-0.731367\pi$
$409$	−16.0597	−	35.1657i	−0.794099	−	1.73883i	−0.129572	−	0.991570i	$-0.541360\pi$
$410$	−0.868716	−	6.04205i	−0.0429028	−	0.298396i
$411$	−8.29986	+	5.33400i	−0.409402	+	0.263107i
$412$	−1.32656	+	1.53093i	−0.0653548	+	0.0754235i
$413$	−4.19613			−0.206478
$414$	−1.47681	−	1.85188i	−0.0725813	−	0.0910149i
$415$	15.3745			0.754703
$416$	3.46716	−	4.00132i	0.169992	−	0.196181i
$417$	7.28579	−	4.68229i	0.356786	−	0.229293i
$418$	1.93199	+	13.4373i	0.0944968	+	0.657240i
$419$	11.0364	+	24.1663i	0.539162	+	1.18060i	0.961662	+	0.274237i	$0.0884252\pi$
$419$	11.0364	+	24.1663i	0.539162	+	1.18060i	−0.422501	+	0.906363i	$0.638848\pi$
$420$	−0.231545	+	1.61043i	−0.0112982	+	0.0785809i
$421$	26.7324	−	7.84935i	1.30286	−	0.382554i	0.444581	−	0.895739i	$-0.353353\pi$
$421$	26.7324	−	7.84935i	1.30286	−	0.382554i	0.858278	+	0.513185i	$0.171535\pi$
$422$	19.0721	+	12.2569i	0.928416	+	0.596657i
$423$	1.48128	−	3.24356i	0.0720225	−	0.157707i
$424$	−7.15625	−	2.10126i	−0.347538	−	0.102046i
$425$	−5.87654	−	6.78189i	−0.285054	−	0.328970i
$426$	10.4007	+	12.0030i	0.503914	+	0.581547i
$427$	6.41620	+	1.88397i	0.310502	+	0.0911715i
$428$	−8.35208	+	18.2885i	−0.403713	+	0.884008i
$429$	28.7286	+	18.4628i	1.38703	+	0.891391i
$430$	10.7822	−	3.16593i	0.519962	−	0.152675i
$431$	−1.30395	+	9.06916i	−0.0628090	+	0.436846i	0.934017	+	0.357230i	$0.116279\pi$
$431$	−1.30395	+	9.06916i	−0.0628090	+	0.436846i	−0.996826	+	0.0796165i	$0.974630\pi$
$432$	−2.29769	−	5.03124i	−0.110548	−	0.242066i
$433$	0.268360	+	1.86648i	0.0128966	+	0.0896975i	0.995253	−	0.0973199i	$-0.0310270\pi$
$433$	0.268360	+	1.86648i	0.0128966	+	0.0896975i	−0.982357	+	0.187017i	$0.940118\pi$
$434$	−8.38147	+	5.38644i	−0.402323	+	0.258558i
$435$	0.610097	−	0.704089i	0.0292519	−	0.0337585i
$436$	10.0618			0.481873
$437$	−6.03955	−	14.7939i	−0.288911	−	0.707688i
$438$	14.5464			0.695053
$439$	2.65460	−	3.06357i	0.126697	−	0.146216i	−0.688857	−	0.724898i	$-0.741887\pi$
$439$	2.65460	−	3.06357i	0.126697	−	0.146216i	0.815554	+	0.578681i	$0.196433\pi$
$440$	−3.52270	+	2.26390i	−0.167938	+	0.107927i
$441$	0.0702885	+	0.488867i	0.00334707	+	0.0232794i
$442$	5.00463	+	10.9586i	0.238046	+	0.521248i
$443$	1.32508	−	9.21612i	0.0629563	−	0.437871i	−0.933827	−	0.357725i	$-0.883552\pi$
$443$	1.32508	−	9.21612i	0.0629563	−	0.437871i	0.996783	−	0.0801455i	$-0.0255385\pi$
$444$	2.97546	−	0.873674i	0.141209	−	0.0414627i
$445$	12.0047	+	7.71494i	0.569076	+	0.365723i
$446$	0.120145	−	0.263081i	0.00568904	−	0.0124573i
$447$	18.2718	+	5.36509i	0.864227	+	0.253760i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	−4.72494	−	5.45287i	−0.222984	−	0.257337i	0.633224	−	0.773969i	$-0.281731\pi$
$449$	−4.72494	−	5.45287i	−0.222984	−	0.257337i	−0.856208	+	0.516632i	$0.827186\pi$
$450$	−1.86889	−	0.548756i	−0.0881005	−	0.0258686i
$451$	−10.0528	+	22.0126i	−0.473369	+	1.03653i
$452$	1.59899	+	1.02761i	0.0752104	+	0.0483348i
$453$	−18.8001	+	5.52021i	−0.883307	+	0.259362i
$454$	1.91138	−	13.2939i	0.0897056	−	0.623916i
$455$	−2.26044	−	4.94967i	−0.105971	−	0.232044i
$456$	−0.750657	−	5.22094i	−0.0351528	−	0.244493i
$457$	4.43608	−	2.85090i	0.207511	−	0.133359i	−0.432758	−	0.901510i	$-0.642459\pi$
$457$	4.43608	−	2.85090i	0.207511	−	0.133359i	0.640269	+	0.768151i	$0.278823\pi$
$458$	0.551615	−	0.636597i	0.0257753	−	0.0297462i
$459$	12.5856			0.587446
$460$	3.37700	−	3.59024i	0.157454	−	0.167396i
$461$	−17.6258			−0.820916			−0.410458	−	0.911879i	$-0.634631\pi$
$461$	−17.6258			−0.820916			−0.410458	+	0.911879i	$0.634631\pi$
$462$	4.22388	−	4.87462i	0.196513	−	0.226788i
$463$	0.654465	−	0.420599i	0.0304156	−	0.0195469i	−0.525345	−	0.850890i	$-0.676064\pi$
$463$	0.654465	−	0.420599i	0.0304156	−	0.0195469i	0.555760	+	0.831343i	$0.312427\pi$
$464$	0.0814920	+	0.566789i	0.00378317	+	0.0263125i
$465$	−6.73380	−	14.7450i	−0.312272	−	0.683781i
$466$	3.36880	−	23.4305i	0.156056	−	1.08540i
$467$	1.56171	−	0.458559i	0.0722673	−	0.0212196i	−0.245399	−	0.969422i	$-0.578919\pi$
$467$	1.56171	−	0.458559i	0.0722673	−	0.0212196i	0.317666	+	0.948203i	$0.397101\pi$
$468$	2.19982	+	1.41374i	0.101687	+	0.0653499i
$469$	1.31082	−	2.87030i	0.0605281	−	0.132538i
$470$	7.11949	+	2.09047i	0.328398	+	0.0964262i
$471$	−8.21705	−	9.48298i	−0.378622	−	0.436953i
$472$	2.74788	+	3.17122i	0.126482	+	0.145967i
$473$	−42.7449	−	12.5510i	−1.96541	−	0.577097i
$474$	7.69259	−	16.8444i	0.353333	−	0.773690i
$475$	−11.0542	−	7.10410i	−0.507201	−	0.325959i
$476$	2.18326	−	0.641064i	0.100070	−	0.0293831i
$477$	0.524238	−	3.64615i	0.0240032	−	0.166946i
$478$	3.42132	+	7.49165i	0.156488	+	0.342660i
$479$	4.37139	+	30.4037i	0.199734	+	1.38918i	0.805056	+	0.593199i	$0.202135\pi$
$479$	4.37139	+	30.4037i	0.199734	+	1.38918i	−0.605322	+	0.795981i	$0.706955\pi$
$480$	1.36871	−	0.879617i	0.0624728	−	0.0401488i
$481$	−6.79183	+	7.83819i	−0.309681	+	0.357391i
$482$	−23.9019			−1.08870
$483$	−3.43298	+	6.77164i	−0.156206	+	0.308120i
$484$	5.60071			0.254578
$485$	−4.93714	+	5.69777i	−0.224184	+	0.258722i
$486$	4.27136	−	2.74504i	0.193753	−	0.124517i
$487$	5.94270	+	41.3324i	0.269290	+	1.87295i	0.455208	+	0.890385i	$0.349565\pi$
$487$	5.94270	+	41.3324i	0.269290	+	1.87295i	−0.185918	+	0.982565i	$0.559526\pi$
$488$	−2.77791	−	6.08278i	−0.125750	−	0.275354i
$489$	4.60080	−	31.9992i	0.208055	−	1.44706i
$490$	−0.986114	+	0.289549i	−0.0445481	+	0.0130805i
$491$	18.9483	+	12.1774i	0.855126	+	0.549556i	0.893170	−	0.449720i	$-0.148476\pi$
$491$	18.9483	+	12.1774i	0.855126	+	0.549556i	−0.0380436	+	0.999276i	$0.512113\pi$
$492$	3.90593	−	8.55279i	0.176093	−	0.385590i
$493$	−1.25018	−	0.367085i	−0.0563051	−	0.0165327i
$494$	11.5522	+	13.3320i	0.519760	+	0.599835i
$495$	−1.35435	−	1.56301i	−0.0608736	−	0.0702519i
$496$	9.55950	+	2.80692i	0.429234	+	0.126034i
$497$	−4.16768	+	9.12595i	−0.186946	+	0.409355i
$498$	19.9224	+	12.8034i	0.892744	+	0.573732i
$499$	36.6242	−	10.7538i	1.63952	−	0.481408i	0.673356	−	0.739319i	$-0.264852\pi$
$499$	36.6242	−	10.7538i	1.63952	−	0.481408i	0.966169	+	0.257911i	$0.0830340\pi$
$500$	1.30814	−	9.09832i	0.0585018	−	0.406889i
$501$	−4.93448	−	10.8050i	−0.220456	−	0.482732i
$502$	−0.110656	−	0.769628i	−0.00493881	−	0.0343502i
$503$	−10.8328	+	6.96183i	−0.483012	+	0.310413i	−0.759390	−	0.650636i	$-0.774502\pi$
$503$	−10.8328	+	6.96183i	−0.483012	+	0.310413i	0.276378	+	0.961049i	$0.410866\pi$
$504$	0.323432	−	0.373261i	0.0144068	−	0.0166263i
$505$	−6.80137			−0.302657
$506$	−18.9576	+	4.73570i	−0.842767	+	0.210527i
$507$	23.7963			1.05683
$508$	−5.43243	+	6.26935i	−0.241025	+	0.278158i
$509$	8.31628	−	5.34455i	0.368613	−	0.236893i	−0.343200	−	0.939262i	$-0.611511\pi$
$509$	8.31628	−	5.34455i	0.368613	−	0.236893i	0.711813	+	0.702369i	$0.247875\pi$
$510$	0.526865	+	3.66443i	0.0233300	+	0.162264i
$511$	3.81714	+	8.35836i	0.168860	+	0.369752i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	17.6825	−	5.19204i	0.780701	−	0.229234i
$514$	−1.07941	−	0.693695i	−0.0476108	−	0.0305976i
$515$	0.864857	−	1.89377i	0.0381102	−	0.0834496i
$516$	16.6081	+	4.87658i	0.731132	+	0.214680i
$517$	−19.2635	−	22.2312i	−0.847206	−	0.977727i
$518$	1.28281	+	1.48044i	0.0563634	+	0.0650468i
$519$	18.9460	+	5.56305i	0.831638	+	0.244191i
$520$	−2.26044	+	4.94967i	−0.0991267	+	0.217057i
$521$	1.78833	+	1.14929i	0.0783483	+	0.0503514i	0.579228	−	0.815165i	$-0.303354\pi$
$521$	1.78833	+	1.14929i	0.0783483	+	0.0503514i	−0.500880	+	0.865517i	$0.666990\pi$
$522$	−0.271357	+	0.0796776i	−0.0118770	+	0.00348739i
$523$	−1.55575	+	10.8204i	−0.0680280	+	0.473145i	0.927121	+	0.374763i	$0.122276\pi$
$523$	−1.55575	+	10.8204i	−0.0680280	+	0.473145i	−0.995149	+	0.0983822i	$0.968633\pi$
$524$	−6.93858	−	15.1934i	−0.303113	−	0.663725i
$525$	0.888502	+	6.17967i	0.0387774	+	0.269703i
$526$	21.4225	−	13.7674i	0.934066	−	0.600288i
$527$	−14.8459	+	17.1331i	−0.646698	+	0.746329i
$528$	−6.45005			−0.280702
$529$	20.2981	−	10.8161i	0.882526	−	0.470264i
$530$	7.66530			0.332959
$531$	−1.35716	+	1.56625i	−0.0588959	+	0.0679695i
$532$	2.80297	−	1.80136i	0.121524	−	0.0780989i
$533$	4.47526	+	31.1261i	0.193845	+	1.34822i
$534$	9.13104	+	19.9942i	0.395139	+	0.865233i
$535$	2.94068	−	20.4529i	0.127137	−	0.884255i
$536$	−3.02763	+	0.888993i	−0.130774	+	0.0383987i
$537$	26.8839	+	17.2772i	1.16012	+	0.745567i
$538$	−6.82936	+	14.9542i	−0.294435	+	0.644722i
$539$	3.90935	+	1.14789i	0.168388	+	0.0494431i
$540$	3.72258	+	4.29608i	0.160194	+	0.184874i
$541$	19.4039	+	22.3933i	0.834237	+	0.962761i	0.999725	−	0.0234505i	$-0.00746521\pi$
$541$	19.4039	+	22.3933i	0.834237	+	0.962761i	−0.165488	+	0.986212i	$0.552920\pi$
$542$	0.110635	+	0.0324855i	0.00475219	+	0.00139537i
$543$	−5.68470	+	12.4478i	−0.243954	+	0.534185i
$544$	−1.91422	−	1.23019i	−0.0820714	−	0.0527441i
$545$	−9.92208	+	2.91339i	−0.425015	+	0.124796i
$546$	1.19282	−	8.29625i	0.0510480	−	0.355047i
$547$	−10.2878	−	22.5272i	−0.439876	−	0.963195i	−0.991621	−	0.129182i	$-0.958765\pi$
$547$	−10.2878	−	22.5272i	−0.439876	−	0.963195i	0.551745	−	0.834013i	$-0.313962\pi$
$548$	0.886941	+	6.16881i	0.0378882	+	0.263518i
$549$	2.77842	−	1.78558i	0.118580	−	0.0762067i
$550$	−10.5225	+	12.1437i	−0.448683	+	0.517807i
$551$	−1.90791			−0.0812795
$552$	7.36579	−	1.84001i	0.313509	−	0.0783160i
$553$	11.6974			0.497426
$554$	19.4194	−	22.4112i	0.825053	−	0.952162i
$555$	−2.68117	+	1.72308i	−0.113809	+	0.0731409i
$556$	−0.778574	−	5.41510i	−0.0330189	−	0.229652i
$557$	0.325938	+	0.713705i	0.0138105	+	0.0302407i	0.916412	−	0.400237i	$-0.131072\pi$
$557$	0.325938	+	0.713705i	0.0138105	+	0.0302407i	−0.902601	+	0.430478i	$0.858345\pi$
$558$	−0.700289	+	4.87062i	−0.0296456	+	0.206190i
$559$	−55.5451	+	16.3095i	−2.34931	+	0.689819i
$560$	0.864594	+	0.555641i	0.0365358	+	0.0234801i
$561$	6.09691	−	13.3504i	0.257412	−	0.563653i
$562$	−20.7747	−	6.10002i	−0.876330	−	0.257314i
$563$	−9.89491	−	11.4193i	−0.417021	−	0.481268i	0.507906	−	0.861412i	$-0.330420\pi$
$563$	−9.89491	−	11.4193i	−0.417021	−	0.481268i	−0.924927	+	0.380145i	$0.875874\pi$
$564$	7.48463	+	8.63773i	0.315160	+	0.363714i
$565$	−1.87433	−	0.550354i	−0.0788538	−	0.0231536i
$566$	4.87385	−	10.6722i	0.204863	−	0.448588i
$567$	−6.11960	−	3.93283i	−0.256999	−	0.165163i
$568$	9.62618	−	2.82650i	0.403906	−	0.118597i
$569$	2.59086	−	18.0198i	0.108615	−	0.755431i	−0.860612	−	0.509261i	$-0.829919\pi$
$569$	2.59086	−	18.0198i	0.108615	−	0.755431i	0.969227	−	0.246170i	$-0.0791721\pi$
$570$	2.25195	+	4.93108i	0.0943238	+	0.206540i
$571$	6.40866	+	44.5732i	0.268194	+	1.86533i	0.465582	+	0.885005i	$0.345845\pi$
$571$	6.40866	+	44.5732i	0.268194	+	1.86533i	−0.197388	+	0.980325i	$0.563246\pi$
$572$	18.1474	−	11.6627i	0.758783	−	0.487640i
$573$	−9.85653	+	11.3750i	−0.411763	+	0.475199i
$574$	5.93940			0.247906
$575$	8.55223	−	16.8695i	0.356653	−	0.703507i
$576$	−0.493895			−0.0205789
$577$	−16.7090	+	19.2832i	−0.695604	+	0.802770i	−0.988152	−	0.153481i	$-0.950952\pi$
$577$	−16.7090	+	19.2832i	−0.695604	+	0.802770i	0.292547	+	0.956251i	$0.405497\pi$
$578$	−9.94563	+	6.39167i	−0.413684	+	0.265858i
$579$	−1.26949	−	8.82946i	−0.0527580	−	0.366940i
$580$	−0.244474	−	0.535323i	−0.0101512	−	0.0222281i
$581$	−2.12895	+	14.8072i	−0.0883237	+	0.614305i
$582$	−11.1425	+	3.27174i	−0.461872	+	0.135618i
$583$	−25.5643	−	16.4292i	−1.05877	−	0.680427i
$584$	3.81714	−	8.35836i	0.157954	−	0.345872i
$585$	−2.57861	−	0.757149i	−0.106613	−	0.0313043i
$586$	12.0145	+	13.8655i	0.496314	+	0.572777i
$587$	19.0076	+	21.9360i	0.784529	+	0.905395i	0.997428	−	0.0716796i	$-0.0228359\pi$
$587$	19.0076	+	21.9360i	0.784529	+	0.905395i	−0.212899	+	0.977074i	$0.568290\pi$
$588$	−1.51894	−	0.446002i	−0.0626402	−	0.0183928i
$589$	−13.7901	+	30.1961i	−0.568211	+	1.24421i
$590$	−3.62795	−	2.33154i	−0.149360	−	0.0959880i
$591$	−2.69871	+	0.792411i	−0.111010	+	0.0325954i
$592$	0.278781	−	1.93896i	0.0114578	−	0.0796909i
$593$	−9.85777	−	21.5855i	−0.404810	−	0.886411i	−0.996760	−	0.0804357i	$-0.974369\pi$
$593$	−9.85777	−	21.5855i	−0.404810	−	0.886411i	0.591950	−	0.805975i	$-0.298358\pi$
$594$	−3.20718	−	22.3064i	−0.131592	−	0.915243i
$595$	−1.96733	+	1.26432i	−0.0806525	+	0.0518322i
$596$	7.87751	−	9.09114i	0.322676	−	0.372387i
$597$	3.61650			0.148013
$598$	−17.3969	+	18.4954i	−0.711411	+	0.756332i
$599$	−8.37113			−0.342035			−0.171018	−	0.985268i	$-0.554705\pi$
$599$	−8.37113			−0.342035			−0.171018	+	0.985268i	$0.554705\pi$
$600$	4.08843	−	4.71830i	0.166910	−	0.192624i
$601$	11.1225	−	7.14800i	0.453696	−	0.291573i	−0.293766	−	0.955877i	$-0.594909\pi$
$601$	11.1225	−	7.14800i	0.453696	−	0.291573i	0.747462	+	0.664305i	$0.231272\pi$
$602$	1.55607	+	10.8227i	0.0634207	+	0.441100i
$603$	−0.647408	−	1.41763i	−0.0263645	−	0.0577302i
$604$	−1.76145	+	12.2511i	−0.0716722	+	0.498491i
$605$	−5.52293	+	1.62168i	−0.224539	+	0.0659307i
$606$	−8.81328	−	5.66395i	−0.358015	−	0.230082i
$607$	−2.93496	+	6.42667i	−0.119126	+	0.260851i	−0.959796	−	0.280697i	$-0.909434\pi$
$607$	−2.93496	+	6.42667i	−0.119126	+	0.260851i	0.840670	+	0.541548i	$0.182162\pi$
$608$	−3.19693	−	0.938705i	−0.129653	−	0.0380695i
$609$	0.593627	+	0.685082i	0.0240550	+	0.0277609i
$610$	4.50060	+	5.19397i	0.182224	+	0.210298i
$611$	−36.6766	−	10.7692i	−1.48378	−	0.435676i
$612$	0.466854	−	1.02227i	0.0188714	−	0.0413227i
$613$	−31.4214	−	20.1933i	−1.26910	−	0.815600i	−0.279596	−	0.960118i	$-0.590201\pi$
$613$	−31.4214	−	20.1933i	−1.26910	−	0.815600i	−0.989502	+	0.144518i	$0.953837\pi$
$614$	−23.5917	+	6.92715i	−0.952083	+	0.279557i
$615$	−1.37524	+	9.56498i	−0.0554549	+	0.385697i
$616$	−1.69257	−	3.70620i	−0.0681954	−	0.149327i
$617$	1.06838	+	7.43077i	0.0430115	+	0.299152i	0.999960	+	0.00889524i	$0.00283148\pi$
$617$	1.06838	+	7.43077i	0.0430115	+	0.299152i	−0.956949	+	0.290256i	$0.906259\pi$
$618$	2.69776	−	1.73375i	0.108520	−	0.0697415i
$619$	23.9067	−	27.5898i	0.960891	−	1.10893i	−0.0330987	−	0.999452i	$-0.510538\pi$
$619$	23.9067	−	27.5898i	0.960891	−	1.10893i	0.993990	−	0.109475i	$-0.0349170\pi$
$620$	−10.2395			−0.411228
$621$	10.0259	+	24.5584i	0.402325	+	0.985495i
$622$	4.44982			0.178422
$623$	−9.09258	+	10.4934i	−0.364287	+	0.420409i
$624$	−7.05102	+	4.53141i	−0.282267	+	0.181402i
$625$	−1.46183	−	10.1672i	−0.0584732	−	0.406690i
$626$	3.07203	+	6.72681i	0.122783	+	0.268857i
$627$	3.05848	−	21.2722i	0.122144	−	0.849529i
$628$	−7.60517	+	2.23308i	−0.303479	+	0.0891096i
$629$	3.74977	+	2.40983i	0.149513	+	0.0960862i
$630$	−0.210864	+	0.461727i	−0.00840101	+	0.0183956i
$631$	34.4292	+	10.1093i	1.37060	+	0.402446i	0.882489	−	0.470333i	$-0.155866\pi$
$631$	34.4292	+	10.1093i	1.37060	+	0.402446i	0.488116	+	0.872779i	$0.337684\pi$
$632$	−7.66020	−	8.84034i	−0.304706	−	0.351650i
$633$	−23.5029	−	27.1237i	−0.934155	−	1.07807i
$634$	−12.1628	−	3.57133i	−0.483048	−	0.141836i
$635$	3.54170	−	7.75525i	0.140548	−	0.307758i
$636$	9.93277	+	6.38340i	0.393860	+	0.253118i
$637$	5.08004	−	1.49163i	0.201278	−	0.0591007i
$638$	−0.332031	+	2.30932i	−0.0131452	+	0.0914270i
$639$	2.05839	+	4.50726i	0.0814288	+	0.178304i
$640$	−0.146263	−	1.01728i	−0.00578156	−	0.0402117i
$641$	−5.35093	+	3.43884i	−0.211349	+	0.135826i	−0.642033	−	0.766677i	$-0.721909\pi$
$641$	−5.35093	+	3.43884i	−0.211349	+	0.135826i	0.430684	+	0.902503i	$0.358272\pi$
$642$	20.8430	−	24.0541i	0.822609	−	0.949341i
$643$	−7.88681			−0.311025			−0.155513	−	0.987834i	$-0.549703\pi$
$643$	−7.88681			−0.311025			−0.155513	+	0.987834i	$0.549703\pi$
$644$	2.99014	+	3.74954i	0.117828	+	0.147753i
$645$	−17.7895			−0.700461
$646$	4.96484	−	5.72973i	0.195339	−	0.225433i
$647$	−37.7615	+	24.2678i	−1.48456	+	0.954067i	−0.487855	+	0.872925i	$0.662220\pi$
$647$	−37.7615	+	24.2678i	−1.48456	+	0.954067i	−0.996703	+	0.0811421i	$0.974143\pi$
$648$	1.03525	+	7.20034i	0.0406686	+	0.282856i
$649$	7.10223	+	15.5517i	0.278787	+	0.610458i
$650$	−2.97155	+	20.6676i	−0.116554	+	0.810651i
$651$	15.1333	−	4.44355i	0.593122	−	0.174156i
$652$	−17.1795	−	11.0406i	−0.672800	−	0.432383i
$653$	11.7291	−	25.6832i	0.458997	−	1.00506i	−0.528718	−	0.848797i	$-0.677327\pi$
$653$	11.7291	−	25.6832i	0.458997	−	1.00506i	0.987715	−	0.156265i	$-0.0499455\pi$
$654$	−15.2833	−	4.48758i	−0.597625	−	0.175478i
$655$	11.2415	+	12.9733i	0.439240	+	0.506910i
$656$	−3.88948	−	4.48870i	−0.151859	−	0.175254i
$657$	4.35443	+	1.27858i	0.169883	+	0.0498820i
$658$	−2.99919	+	6.56731i	−0.116921	+	0.256020i
$659$	−26.9244	−	17.3033i	−1.04883	−	0.674040i	−0.101672	−	0.994818i	$-0.532419\pi$
$659$	−26.9244	−	17.3033i	−1.04883	−	0.674040i	−0.947154	+	0.320778i	$0.896056\pi$
$660$	6.36048	−	1.86761i	0.247581	−	0.0726964i
$661$	6.47938	−	45.0651i	0.252019	−	1.75283i	−0.334039	−	0.942559i	$-0.608412\pi$
$661$	6.47938	−	45.0651i	0.252019	−	1.75283i	0.586058	−	0.810269i	$-0.300679\pi$
$662$	−0.215571	−	0.472034i	−0.00837839	−	0.0183461i
$663$	−2.71419	−	18.8776i	−0.105410	−	0.733144i
$664$	12.5847	−	8.08768i	0.488380	−	0.313863i
$665$	−2.24247	+	2.58794i	−0.0869591	+	0.100356i
$666$	0.967491			0.0374895
$667$	−0.279612	−	2.73191i	−0.0108266	−	0.105780i
$668$	−7.50342			−0.290316
$669$	−0.299829	+	0.346021i	−0.0115920	+	0.0133779i
$670$	2.72818	−	1.75330i	0.105399	−	0.0677358i
$671$	−3.87748	−	26.9685i	−0.149688	−	1.04111i
$672$	0.657630	+	1.44001i	0.0253686	+	0.0555496i
$673$	−2.13214	+	14.8294i	−0.0821880	+	0.571630i	0.906564	+	0.422068i	$0.138696\pi$
$673$	−2.13214	+	14.8294i	−0.0821880	+	0.571630i	−0.988752	+	0.149562i	$0.952214\pi$
$674$	5.74570	−	1.68709i	0.221316	−	0.0649843i
$675$	18.3504	+	11.7931i	0.706306	+	0.453915i
$676$	6.24442	−	13.6734i	0.240170	−	0.525899i
$677$	34.6729	+	10.1809i	1.33259	+	0.391283i	0.869019	−	0.494779i	$-0.164751\pi$
$677$	34.6729	+	10.1809i	1.33259	+	0.391283i	0.463567	+	0.886062i	$0.346569\pi$
$678$	−1.97046	−	2.27404i	−0.0756752	−	0.0873339i
$679$	−4.80386	−	5.54395i	−0.184355	−	0.212757i
$680$	2.24384	+	0.658850i	0.0860472	+	0.0252658i
$681$	−8.83240	+	19.3403i	−0.338458	+	0.741121i
$682$	34.1494	+	21.9465i	1.30765	+	0.840375i
$683$	30.6416	−	8.99719i	1.17247	−	0.344268i	0.363202	−	0.931710i	$-0.381683\pi$
$683$	30.6416	−	8.99719i	1.17247	−	0.344268i	0.809266	+	0.587443i	$0.199865\pi$
$684$	0.234194	−	1.62886i	0.00895464	−	0.0622809i
$685$	−2.66080	−	5.82633i	−0.101664	−	0.222613i
$686$	−0.142315	−	0.989821i	−0.00543361	−	0.0377916i
$687$	−1.12179	+	0.720934i	−0.0427991	+	0.0275053i
$688$	7.16024	−	8.26336i	0.272982	−	0.315038i
$689$	−39.4883			−1.50439
$690$	−6.73073	+	3.94722i	−0.256234	+	0.150268i
$691$	−37.5642			−1.42901			−0.714505	−	0.699630i	$-0.753348\pi$
$691$	−37.5642			−1.42901			−0.714505	+	0.699630i	$0.753348\pi$
$692$	8.16818	−	9.42658i	0.310508	−	0.358345i
$693$	1.69287	−	1.08794i	0.0643069	−	0.0413276i
$694$	−3.22524	−	22.4321i	−0.122429	−	0.851510i
$695$	2.33570	+	5.11447i	0.0885982	+	0.194003i
$696$	0.129007	−	0.897266i	0.00489001	−	0.0340108i
$697$	12.9673	−	3.80754i	0.491171	−	0.144221i
$698$	19.3425	+	12.4307i	0.732126	+	0.470509i
$699$	−15.5670	+	34.0871i	−0.588800	+	1.28929i
$700$	3.78399	+	1.11108i	0.143021	+	0.0419949i
$701$	−10.9086	−	12.5892i	−0.412013	−	0.475488i	0.511375	−	0.859358i	$-0.329136\pi$
$701$	−10.9086	−	12.5892i	−0.412013	−	0.475488i	−0.923387	+	0.383870i	$0.874591\pi$
$702$	−19.1771	−	22.1316i	−0.723794	−	0.835303i
$703$	6.26248	+	1.83883i	0.236194	+	0.0693528i
$704$	−1.69257	+	3.70620i	−0.0637910	+	0.139683i
$705$	−9.88174	−	6.35061i	−0.372168	−	0.239178i
$706$	−14.9190	+	4.38063i	−0.561486	+	0.164867i
$707$	0.941806	−	6.55040i	0.0354203	−	0.246353i
$708$	−2.75950	−	6.04247i	−0.103708	−	0.227090i
$709$	−3.57173	−	24.8419i	−0.134139	−	0.932957i	−0.940078	−	0.340959i	$-0.889248\pi$
$709$	−3.57173	−	24.8419i	−0.134139	−	0.932957i	0.805939	−	0.591998i	$-0.201661\pi$
$710$	−8.67410	+	5.57450i	−0.325533	+	0.209207i
$711$	3.78333	−	4.36619i	0.141886	−	0.163745i
$712$	13.8848			0.520353
$713$	−45.2584	−	15.3205i	−1.69494	−	0.573757i
$714$	−3.60217			−0.134808
$715$	−14.5185	+	16.7553i	−0.542962	+	0.626612i
$716$	16.9821	−	10.9137i	0.634652	−	0.407866i
$717$	−1.85550	−	12.9053i	−0.0692950	−	0.481958i
$718$	−12.8602	−	28.1599i	−0.479939	−	1.05092i
$719$	1.16947	−	8.13382i	0.0436138	−	0.303340i	−0.956325	−	0.292304i	$-0.905578\pi$
$719$	1.16947	−	8.13382i	0.0436138	−	0.303340i	0.999939	−	0.0110360i	$-0.00351295\pi$
$720$	0.487036	−	0.143007i	0.0181508	−	0.00532955i
$721$	1.70414	+	1.09518i	0.0634653	+	0.0407867i
$722$	−3.28113	+	7.18468i	−0.122111	+	0.267386i
$723$	36.3056	+	10.6603i	1.35022	+	0.396461i
$724$	5.66076	+	6.53287i	0.210381	+	0.242792i
$725$	−1.47884	−	1.70668i	−0.0549229	−	0.0633844i
$726$	−8.50716	−	2.49793i	−0.315730	−	0.0927067i
$727$	−1.25075	+	2.73876i	−0.0463878	+	0.101575i	−0.931407	−	0.363979i	$-0.881418\pi$
$727$	−1.25075	+	2.73876i	−0.0463878	+	0.101575i	0.885019	+	0.465555i	$0.154145\pi$
$728$	−4.45402	−	2.86242i	−0.165077	−	0.106088i
$729$	−28.6514	+	8.41281i	−1.06116	+	0.311586i
$730$	−1.34397	+	9.34754i	−0.0497427	+	0.345968i
$731$	10.3354	+	22.6313i	0.382267	+	0.837048i
$732$	1.50656	+	10.4783i	0.0556840	+	0.387291i
$733$	43.9936	−	28.2730i	1.62494	−	1.04429i	0.672261	−	0.740314i	$-0.265323\pi$
$733$	43.9936	−	28.2730i	1.62494	−	1.04429i	0.952681	−	0.303973i	$-0.0983132\pi$
$734$	5.39289	−	6.22373i	0.199055	−	0.229722i
$735$	1.62699			0.0600124
$736$	0.875594	−	4.71522i	0.0322748	−	0.173805i
$737$	−12.8566			−0.473577
$738$	1.92099	−	2.21694i	0.0707127	−	0.0816068i
$739$	29.6758	−	19.0715i	1.09164	−	0.701557i	0.134425	−	0.990924i	$-0.457081\pi$
$739$	29.6758	−	19.0715i	1.09164	−	0.701557i	0.957218	+	0.289367i	$0.0934448\pi$
$740$	0.286516	+	1.99276i	0.0105325	+	0.0732553i
$741$	−11.6011	−	25.4028i	−0.426177	−	0.933197i
$742$	−1.06144	+	7.38245i	−0.0389666	+	0.271018i
$743$	−16.4852	+	4.84050i	−0.604785	+	0.177581i	−0.569768	−	0.821806i	$-0.692967\pi$
$743$	−16.4852	+	4.84050i	−0.604785	+	0.177581i	−0.0350171	+	0.999387i	$0.511149\pi$
$744$	−13.2684	−	8.52711i	−0.486444	−	0.312619i
$745$	−5.13579	+	11.2458i	−0.188161	+	0.412015i
$746$	−15.1321	−	4.44317i	−0.554024	−	0.162676i
$747$	4.83836	+	5.58377i	0.177026	+	0.204299i
$748$	−6.07123	−	7.00657i	−0.221986	−	0.256186i
$749$	19.2910	+	5.66434i	0.704877	+	0.206970i
$750$	−6.04486	+	13.2364i	−0.220727	+	0.483325i
$751$	−30.3308	−	19.4924i	−1.10679	−	0.711288i	−0.146196	−	0.989256i	$-0.546703\pi$
$751$	−30.3308	−	19.4924i	−1.10679	−	0.711288i	−0.960590	+	0.277968i	$0.910339\pi$
$752$	6.92729	−	2.03404i	0.252612	−	0.0741737i
$753$	−0.175176	+	1.21837i	−0.00638376	+	0.0444000i
$754$	1.25942	+	2.75776i	0.0458655	+	0.100432i
$755$	−1.81032	−	12.5910i	−0.0658842	−	0.458234i
$756$	−4.65304	+	2.99032i	−0.169229	+	0.108757i
$757$	−18.0991	+	20.8875i	−0.657824	+	0.759170i	−0.982420	−	0.186683i	$-0.940226\pi$
$757$	−18.0991	+	20.8875i	−0.657824	+	0.759170i	0.324596	+	0.945853i	$0.394772\pi$
$758$	−18.5348			−0.673214
$759$	30.9076	+	1.26186i	1.12187	+	0.0458026i
$760$	3.42434			0.124214
$761$	−25.5849	+	29.5266i	−0.927454	+	1.07034i	0.0698941	+	0.997554i	$0.477734\pi$
$761$	−25.5849	+	29.5266i	−0.927454	+	1.07034i	−0.997348	+	0.0727842i	$0.976812\pi$
$762$	11.0477	−	7.09992i	0.400215	−	0.257203i
$763$	−1.43194	−	9.95939i	−0.0518399	−	0.360554i
$764$	3.94964	+	8.64851i	0.142893	+	0.312892i
$765$	−0.164374	+	1.14325i	−0.00594297	+	0.0413342i
$766$	−12.5079	+	3.67264i	−0.451928	+	0.132698i
$767$	18.6896	+	12.0111i	0.674844	+	0.433696i
$768$	0.657630	−	1.44001i	0.0237302	−	0.0519619i
$769$	−44.6283	−	13.1041i	−1.60934	−	0.472544i	−0.651213	−	0.758895i	$-0.725739\pi$
$769$	−44.6283	−	13.1041i	−1.60934	−	0.472544i	−0.958125	+	0.286351i	$0.907558\pi$
$770$	2.74219	+	3.16466i	0.0988216	+	0.114046i
$771$	1.33017	+	1.53510i	0.0479051	+	0.0552854i
$772$	−5.40654	−	1.58750i	−0.194586	−	0.0571355i
$773$	−1.08997	+	2.38669i	−0.0392034	+	0.0858434i	−0.928220	−	0.372031i	$-0.878662\pi$
$773$	−1.08997	+	2.38669i	−0.0392034	+	0.0858434i	0.889017	+	0.457874i	$0.151389\pi$
$774$	4.54297	+	2.91959i	0.163294	+	0.104943i
$775$	−37.7002	+	11.0698i	−1.35423	+	0.397638i
$776$	−1.04398	+	7.26103i	−0.0374767	+	0.260656i
$777$	−1.28823	−	2.82084i	−0.0462151	−	0.101197i
$778$	−2.63020	−	18.2934i	−0.0942972	−	0.655851i
$779$	16.6480	−	10.6990i	0.596476	−	0.383332i
$780$	5.64104	−	6.51010i	0.201982	−	0.233099i
$781$	40.8767			1.46268
$782$	8.93196	+	6.26938i	0.319406	+	0.224193i
$783$	3.16719			0.113186
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	6.85298	−	4.40414i	0.244593	−	0.157191i
$786$	3.76303	+	26.1725i	0.134223	+	0.933541i
$787$	−14.7595	−	32.3189i	−0.526121	−	1.15204i	−0.967070	−	0.254512i	$-0.918085\pi$
$787$	−14.7595	−	32.3189i	−0.526121	−	1.15204i	0.440949	−	0.897532i	$-0.354642\pi$
$788$	−0.252851	+	1.75862i	−0.00900743	+	0.0626481i
$789$	−38.6799	+	11.3574i	−1.37704	+	0.404335i
$790$	10.1135	+	6.49958i	0.359823	+	0.231245i
$791$	0.789591	−	1.72896i	0.0280746	−	0.0614749i
$792$	−1.93081	−	0.566937i	−0.0686083	−	0.0201452i
$793$	−23.1852	−	26.7571i	−0.823329	−	0.950173i
$794$	−6.83016	−	7.88243i	−0.242393	−	0.279737i
$795$	−11.6431	−	3.41874i	−0.412940	−	0.121250i
$796$	0.949010	−	2.07804i	0.0336368	−	0.0736543i
$797$	21.6035	+	13.8837i	0.765234	+	0.491786i	0.864103	−	0.503315i	$-0.167886\pi$
$797$	21.6035	+	13.8837i	0.765234	+	0.491786i	−0.0988696	+	0.995100i	$0.531523\pi$
$798$	−5.06097	+	1.48603i	−0.179156	+	0.0526050i
$799$	−2.33796	+	16.2608i	−0.0827110	+	0.575267i
$800$	−1.63829	−	3.58735i	−0.0579223	−	0.126832i
$801$	0.975939	+	6.78781i	0.0344831	+	0.239835i
$802$	6.05065	−	3.88851i	0.213656	−	0.137308i
$803$	24.5170	−	28.2942i	0.865187	−	0.998479i
$804$	4.99529			0.176170
$805$	−4.03429	−	2.83169i	−0.142190	−	0.0998038i
$806$	52.7495			1.85802
$807$	17.0430	−	19.6687i	0.599943	−	0.692371i
$808$	−5.56722	+	3.57783i	−0.195854	+	0.125868i
$809$	2.81659	+	19.5898i	0.0990260	+	0.688741i	0.977498	+	0.210946i	$0.0676545\pi$
$809$	2.81659	+	19.5898i	0.0990260	+	0.688741i	−0.878472	+	0.477794i	$0.841436\pi$
$810$	−3.10573	−	6.80060i	−0.109124	−	0.238949i
$811$	3.36905	−	23.4323i	0.118303	−	0.822818i	−0.841120	−	0.540848i	$-0.818103\pi$
$811$	3.36905	−	23.4323i	0.118303	−	0.822818i	0.959423	−	0.281969i	$-0.0909877\pi$
$812$	0.549423	−	0.161325i	0.0192810	−	0.00566140i
$813$	−0.153560	−	0.0986871i	−0.00538559	−	0.00346111i
$814$	3.31557	−	7.26009i	0.116211	−	0.254466i
$815$	20.1377	+	5.91297i	0.705393	+	0.207122i
$816$	2.35892	+	2.72234i	0.0825787	+	0.0953009i
$817$	23.8572	+	27.5327i	0.834658	+	0.963247i
$818$	37.0933	+	10.8916i	1.29694	+	0.380815i
$819$	1.08628	−	2.37862i	0.0379577	−	0.0831157i
$820$	5.13517	+	3.30017i	0.179328	+	0.115247i
$821$	2.70112	−	0.793121i	0.0942698	−	0.0276801i	−0.234258	−	0.972175i	$-0.575266\pi$
$821$	2.70112	−	0.793121i	0.0942698	−	0.0276801i	0.328527	+	0.944494i	$0.393448\pi$
$822$	1.40409	−	9.76564i	0.0489732	−	0.340616i
$823$	10.3070	+	22.5692i	0.359280	+	0.786713i	0.999823	+	0.0187912i	$0.00598178\pi$
$823$	10.3070	+	22.5692i	0.359280	+	0.786713i	−0.640544	+	0.767922i	$0.721291\pi$
$824$	−0.288289	−	2.00509i	−0.0100430	−	0.0698506i
$825$	21.3992	−	13.7525i	0.745026	−	0.478799i
$826$	2.74788	−	3.17122i	0.0956110	−	0.110341i
$827$	−18.4387			−0.641176			−0.320588	−	0.947219i	$-0.603880\pi$
$827$	−18.4387			−0.641176			−0.320588	+	0.947219i	$0.603880\pi$
$828$	2.36666	+	0.0966235i	0.0822472	+	0.00335790i
$829$	20.3691			0.707450			0.353725	−	0.935350i	$-0.384915\pi$
$829$	20.3691			0.707450			0.353725	+	0.935350i	$0.384915\pi$
$830$	−10.0681	+	11.6193i	−0.349470	+	0.403310i
$831$	−39.4925	+	25.3803i	−1.36998	+	0.880432i
$832$	0.753486	+	5.24061i	0.0261224	+	0.181686i
$833$	−0.945250	−	2.06981i	−0.0327510	−	0.0717146i
$834$	−1.23254	+	8.57248i	−0.0426792	+	0.296841i
$835$	7.39923	−	2.17261i	0.256061	−	0.0751862i
$836$	−11.4204	−	7.33946i	−0.394984	−	0.253840i
$837$	22.8921	−	50.1266i	0.791265	−	1.73263i
$838$	−25.4909	−	7.48481i	−0.880569	−	0.258559i
$839$	9.42024	+	10.8715i	0.325223	+	0.375327i	0.894691	−	0.446687i	$-0.147396\pi$
$839$	9.42024	+	10.8715i	0.325223	+	0.375327i	−0.569468	+	0.822014i	$0.692851\pi$
$840$	−1.06545	−	1.22960i	−0.0367616	−	0.0424251i
$841$	27.5107	+	8.07787i	0.948644	+	0.278547i
$842$	−11.5739	+	25.3432i	−0.398862	+	0.873386i
$843$	28.8350	+	18.5312i	0.993132	+	0.638247i
$844$	−21.7527	+	6.38718i	−0.748760	+	0.219856i
$845$	−2.19859	+	15.2916i	−0.0756339	+	0.526045i
$846$	1.48128	+	3.24356i	0.0509276	+	0.111516i
$847$	−0.797064	−	5.54370i	−0.0273874	−	0.190484i
$848$	6.27438	−	4.03230i	0.215463	−	0.138470i
$849$	−12.1629	+	14.0368i	−0.417431	+	0.481741i
$850$	8.97373			0.307796
$851$	−1.71520	+	9.23666i	−0.0587964	+	0.316629i
$852$	−15.8822			−0.544117
$853$	−31.0303	+	35.8108i	−1.06246	+	1.22614i	−0.0892970	+	0.996005i	$0.528462\pi$
$853$	−31.0303	+	35.8108i	−1.06246	+	1.22614i	−0.973159	+	0.230134i	$0.926083\pi$
$854$	−5.62552	+	3.61530i	−0.192501	+	0.123713i
$855$	0.240692	+	1.67405i	0.00823149	+	0.0572513i
$856$	−8.35208	−	18.2885i	−0.285468	−	0.625088i
$857$	−7.58353	+	52.7446i	−0.259049	+	1.80172i	0.280592	+	0.959827i	$0.409469\pi$
$857$	−7.58353	+	52.7446i	−0.259049	+	1.80172i	−0.539641	+	0.841896i	$0.681440\pi$
$858$	−32.7665	+	9.62111i	−1.11863	+	0.328459i
$859$	−13.2117	−	8.49066i	−0.450778	−	0.289697i	0.295487	−	0.955347i	$-0.404518\pi$
$859$	−13.2117	−	8.49066i	−0.450778	−	0.289697i	−0.746265	+	0.665649i	$0.768155\pi$
$860$	−4.66817	+	10.2219i	−0.159183	+	0.348562i
$861$	−9.02161	−	2.64898i	−0.307456	−	0.0902771i
$862$	−6.00011	−	6.92450i	−0.204365	−	0.235849i
$863$	−14.4910	−	16.7236i	−0.493281	−	0.569276i	0.453459	−	0.891277i	$-0.350190\pi$
$863$	−14.4910	−	16.7236i	−0.493281	−	0.569276i	−0.946739	+	0.322001i	$0.895645\pi$
$864$	5.30703	+	1.55828i	0.180549	+	0.0530139i
$865$	−5.32530	+	11.6608i	−0.181066	+	0.396478i
$866$	−1.58633	−	1.01947i	−0.0539058	−	0.0346432i
$867$	17.9575	−	5.27281i	0.609870	−	0.179074i
$868$	1.41789	−	9.86166i	0.0481264	−	0.334727i
$869$	−19.7987	−	43.3531i	−0.671625	−	1.47065i
$870$	0.132587	+	0.922161i	0.00449511	+	0.0312642i
$871$	−14.0544	+	9.03224i	−0.476216	+	0.306046i
$872$	−6.58908	+	7.60421i	−0.223134	+	0.257511i
$873$	−3.62306			−0.122622
$874$	15.1356	+	5.12356i	0.511968	+	0.173307i
$875$	−9.19188			−0.310742
$876$	−9.52586	+	10.9934i	−0.321849	+	0.371433i
$877$	45.0768	−	28.9691i	1.52213	−	0.978216i	0.530707	−	0.847555i	$-0.321926\pi$
$877$	45.0768	−	28.9691i	1.52213	−	0.978216i	0.991427	−	0.130661i	$-0.0417101\pi$
$878$	0.576899	+	4.01242i	0.0194694	+	0.135413i
$879$	−12.0653	−	26.4193i	−0.406952	−	0.891101i
$880$	0.595935	−	4.14482i	0.0200890	−	0.139722i
$881$	38.7559	−	11.3797i	1.30572	−	0.383393i	0.446399	−	0.894834i	$-0.352706\pi$
$881$	38.7559	−	11.3797i	1.30572	−	0.383393i	0.859319	+	0.511440i	$0.170888\pi$
$882$	−0.415491	−	0.267020i	−0.0139903	−	0.00899102i
$883$	−14.3633	+	31.4512i	−0.483363	+	1.05842i	0.498162	+	0.867084i	$0.334009\pi$
$883$	−14.3633	+	31.4512i	−0.483363	+	1.05842i	−0.981525	+	0.191334i	$0.938719\pi$
$884$	−11.5593	−	3.39412i	−0.388781	−	0.114156i
$885$	4.47078	+	5.15955i	0.150283	+	0.173436i
$886$	6.09733	+	7.03670i	0.204844	+	0.236403i
$887$	−38.9931	−	11.4494i	−1.30926	−	0.384433i	−0.448654	−	0.893706i	$-0.648096\pi$
$887$	−38.9931	−	11.4494i	−1.30926	−	0.384433i	−0.860605	+	0.509272i	$0.829915\pi$
$888$	−1.28823	+	2.82084i	−0.0432303	+	0.0946611i
$889$	6.97865	+	4.48491i	0.234057	+	0.150419i
$890$	−13.6919	+	4.02032i	−0.458955	+	0.134761i
$891$	−4.21803	+	29.3370i	−0.141309	+	0.982828i
$892$	0.120145	+	0.263081i	0.00402276	+	0.00880861i
$893$	3.42345	+	23.8106i	0.114561	+	0.796792i
$894$	−16.0202	+	10.2955i	−0.535794	+	0.344334i
$895$	−13.5862	+	15.6794i	−0.454138	+	0.524103i
$896$	1.00000			0.0334077
$897$	34.6738	−	20.3344i	1.15773	−	0.678945i
$898$	7.21518			0.240774
$899$	−3.73600	+	4.31158i	−0.124603	+	0.143799i
$900$	1.63859	−	1.05306i	0.0546196	−	0.0351019i
$901$	2.41523	+	16.7983i	0.0804630	+	0.559632i
$902$	−10.0528	−	22.0126i	−0.334722	−	0.732940i
$903$	2.46336	−	17.1331i	0.0819757	−	0.570153i
$904$	−1.82374	+	0.535497i	−0.0606565	+	0.0178104i
$905$	−7.47374	−	4.80308i	−0.248436	−	0.159660i
$906$	8.13956	−	17.8232i	0.270419	−	0.592135i
$907$	−14.5587	−	4.27482i	−0.483414	−	0.141943i	0.0309397	−	0.999521i	$-0.490150\pi$
$907$	−14.5587	−	4.27482i	−0.483414	−	0.141943i	−0.514354	+	0.857578i	$0.671968\pi$
$908$	8.79521	+	10.1502i	0.291879	+	0.336847i
$909$	−2.14040	−	2.47015i	−0.0709925	−	0.0819297i
$910$	5.22098	+	1.53302i	0.173074	+	0.0508191i
$911$	12.2285	−	26.7767i	0.405148	−	0.887151i	−0.591574	−	0.806251i	$-0.701493\pi$
$911$	12.2285	−	26.7767i	0.405148	−	0.887151i	0.996722	−	0.0809000i	$-0.0257794\pi$
$912$	4.43730	+	2.85168i	0.146934	+	0.0944285i
$913$	58.4817	−	17.1718i	1.93546	−	0.568303i
$914$	−0.750452	+	5.21951i	−0.0248227	+	0.172646i
$915$	−4.51963	−	9.89661i	−0.149414	−	0.327172i
$916$	0.119877	+	0.833765i	0.00396086	+	0.0275484i
$917$	−14.0513	+	9.03019i	−0.464013	+	0.298203i
$918$	−8.24182	+	9.51156i	−0.272020	+	0.313928i
$919$	15.3834			0.507452			0.253726	−	0.967276i	$-0.418344\pi$
$919$	15.3834			0.507452			0.253726	+	0.967276i	$0.418344\pi$
$920$	0.501853	+	4.90327i	0.0165456	+	0.161656i
$921$	38.9240			1.28259
$922$	11.5425	−	13.3207i	0.380131	−	0.438694i
$923$	44.6853	−	28.7175i	1.47083	−	0.945247i
$924$	0.917938	+	6.38440i	0.0301979	+	0.210031i
$925$	3.20925	+	7.02728i	0.105519	+	0.231055i
$926$	−0.110716	+	0.770046i	−0.00363835	+	0.0253053i
$927$	0.959960	−	0.281870i	0.0315292	−	0.00925782i
$928$	−0.481717	−	0.309581i	−0.0158131	−	0.0101625i
$929$	6.56781	−	14.3815i	0.215483	−	0.471842i	−0.770764	−	0.637121i	$-0.780125\pi$
$929$	6.56781	−	14.3815i	0.215483	−	0.471842i	0.986247	+	0.165279i	$0.0528525\pi$
$930$	15.5532	+	4.56683i	0.510010	+	0.149752i
$931$	−2.18193	−	2.51808i	−0.0715099	−	0.0825268i
$932$	15.5015	+	17.8897i	0.507768	+	0.585996i
$933$	−6.75902	−	1.98463i	−0.221280	−	0.0649738i
$934$	−0.676146	+	1.48055i	−0.0221242	+	0.0484452i
$935$	8.01567	+	5.15136i	0.262140	+	0.168467i
$936$	−2.50900	+	0.736710i	−0.0820093	+	0.0240801i
$937$	−1.59644	+	11.1035i	−0.0521535	+	0.362736i	0.946987	+	0.321273i	$0.104111\pi$
$937$	−1.59644	+	11.1035i	−0.0521535	+	0.362736i	−0.999140	+	0.0414625i	$0.986798\pi$
$938$	1.31082	+	2.87030i	0.0427998	+	0.0937186i
$939$	−1.66607	−	11.5878i	−0.0543701	−	0.378152i
$940$	−6.24215	+	4.01158i	−0.203596	+	0.130843i
$941$	−13.7291	+	15.8443i	−0.447557	+	0.516508i	−0.934034	−	0.357185i	$-0.883736\pi$
$941$	−13.7291	+	15.8443i	−0.447557	+	0.516508i	0.486476	+	0.873694i	$0.338282\pi$
$942$	12.5478			0.408829
$943$	17.7596	+	22.2700i	0.578333	+	0.725212i
$944$	−4.19613			−0.136572
$945$	3.72258	−	4.29608i	0.121095	−	0.139752i
$946$	37.4774	−	24.0852i	1.21849	−	0.783079i
$947$	5.99996	+	41.7306i	0.194972	+	1.35606i	0.818610	+	0.574349i	$0.194745\pi$
$947$	5.99996	+	41.7306i	0.194972	+	1.35606i	−0.623638	+	0.781713i	$0.714346\pi$
$948$	7.69259	+	16.8444i	0.249844	+	0.547082i
$949$	6.92358	−	48.1546i	0.224749	−	1.56316i
$950$	12.6079	−	3.70201i	0.409054	−	0.120109i
$951$	16.8818	+	10.8493i	0.547431	+	0.351813i
$952$	−0.945250	+	2.06981i	−0.0306357	+	0.0670829i
$953$	18.7730	+	5.51224i	0.608116	+	0.178559i	0.571270	−	0.820762i	$-0.306451\pi$
$953$	18.7730	+	5.51224i	0.608116	+	0.178559i	0.0368459	+	0.999321i	$0.488269\pi$
$954$	2.41228	+	2.78391i	0.0781003	+	0.0901326i
$955$	−6.39896	−	7.38480i	−0.207066	−	0.238966i
$956$	−7.90230	−	2.32033i	−0.255579	−	0.0750447i
$957$	1.53430	−	3.35965i	0.0495968	−	0.108602i
$958$	−25.8402	−	16.6065i	−0.834860	−	0.536532i
$959$	5.97979	−	1.75583i	0.193098	−	0.0566986i
$960$	−0.231545	+	1.61043i	−0.00747308	+	0.0519764i
$961$	28.3574	+	62.0940i	0.914754	+	2.00303i
$962$	−1.47601	−	10.2658i	−0.0475883	−	0.330984i
$963$	8.35359	−	5.36853i	0.269191	−	0.172998i
$964$	15.6524	−	18.0639i	0.504130	−	0.581798i
$965$	5.79113			0.186423
$966$	−2.86954	−	7.02895i	−0.0923260	−	0.226153i
$967$	2.31973			0.0745976			0.0372988	−	0.999304i	$-0.488125\pi$
$967$	2.31973			0.0745976			0.0372988	+	0.999304i	$0.488125\pi$
$968$	−3.66768	+	4.23273i	−0.117884	+	0.136045i
$969$	−10.0968	+	6.48881i	−0.324355	+	0.208451i
$970$	−1.07294	−	7.46249i	−0.0344501	−	0.239606i
$971$	12.6015	+	27.5934i	0.404401	+	0.885515i	0.996805	+	0.0798736i	$0.0254517\pi$
$971$	12.6015	+	27.5934i	0.404401	+	0.885515i	−0.592404	+	0.805641i	$0.701821\pi$
$972$	−0.722586	+	5.02569i	−0.0231769	+	0.161199i
$973$	−5.24918	+	1.54130i	−0.168281	+	0.0494118i
$974$	−35.1286	−	22.5758i	−1.12559	−	0.723375i
$975$	13.7314	−	30.0676i	0.439757	−	0.962934i
$976$	6.41620	+	1.88397i	0.205378	+	0.0603043i
$977$	5.89489	+	6.80307i	0.188594	+	0.217650i	0.842171	−	0.539211i	$-0.181278\pi$
$977$	5.89489	+	6.80307i	0.188594	+	0.217650i	−0.653576	+	0.756861i	$0.726732\pi$
$978$	21.1705	+	24.4321i	0.676959	+	0.781252i
$979$	54.2804	+	15.9382i	1.73481	+	0.509386i
$980$	0.426940	−	0.934869i	0.0136381	−	0.0298633i
$981$	−4.18058	−	2.68670i	−0.133476	−	0.0857797i
$982$	−21.6115	+	6.34572i	−0.689652	+	0.202500i
$983$	5.74006	−	39.9230i	0.183080	−	1.27335i	−0.666348	−	0.745641i	$-0.732143\pi$
$983$	5.74006	−	39.9230i	0.183080	−	1.27335i	0.849427	−	0.527705i	$-0.176948\pi$
$984$	3.90593	+	8.55279i	0.124516	+	0.272653i
$985$	−0.259866	−	1.80741i	−0.00828002	−	0.0575888i
$986$	1.09612	−	0.704431i	0.0349074	−	0.0224336i
$987$	7.48463	−	8.63773i	0.238238	−	0.274942i
$988$	−17.6407			−0.561227
$989$	−35.9274	+	38.1959i	−1.14242	+	1.21456i
$990$	2.06815			0.0657302
$991$	4.41376	−	5.09375i	0.140208	−	0.161808i	−0.681303	−	0.732002i	$-0.738586\pi$
$991$	4.41376	−	5.09375i	0.140208	−	0.161808i	0.821511	+	0.570193i	$0.193132\pi$
$992$	−8.38147	+	5.38644i	−0.266112	+	0.171020i
$993$	0.116911	+	0.813137i	0.00371007	+	0.0258041i
$994$	−4.16768	−	9.12595i	−0.132191	−	0.289457i
$995$	−0.334137	+	2.32397i	−0.0105928	+	0.0736748i
$996$	−22.7225	+	6.67194i	−0.719991	+	0.211408i
$997$	18.5065	+	11.8934i	0.586106	+	0.376667i	0.799830	−	0.600227i	$-0.204923\pi$
$997$	18.5065	+	11.8934i	0.586106	+	0.376667i	−0.213724	+	0.976894i	$0.568559\pi$
$998$	−15.8565	+	34.7210i	−0.501930	+	1.09907i
$999$	−10.3959	−	3.05253i	−0.328913	−	0.0965776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.c.85.2	✓	20
23.6	even	11		7406.2.a.bp.1.10		10
23.13	even	11	inner	322.2.i.c.197.2	yes	20
23.17	odd	22		7406.2.a.bo.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.c.85.2	✓	20	1.1	even	1	trivial
322.2.i.c.197.2	yes	20	23.13	even	11	inner
7406.2.a.bo.1.10		10	23.17	odd	22
7406.2.a.bp.1.10		10	23.6	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(1.33176 - 0.855871i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.426940 + 0.934869i) q^{5} +(-0.225294 + 1.56696i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.205171 + 0.449262i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(1.33176 - 0.855871i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.426940 + 0.934869i) q^{5} +(-0.225294 + 1.56696i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.205171 + 0.449262i) q^{9} +(-0.986114 - 0.289549i) q^{10} +(2.66816 + 3.07922i) q^{11} +(-1.03669 - 1.19640i) q^{12} +(5.08004 + 1.49163i) q^{13} +(0.415415 - 0.909632i) q^{14} +(1.36871 + 0.879617i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.323828 - 2.25227i) q^{17} +(-0.205171 - 0.449262i) q^{18} +(-0.474179 - 3.29799i) q^{19} +(0.864594 - 0.555641i) q^{20} +(-1.03669 + 1.19640i) q^{21} -4.07440 q^{22} +(4.65285 - 1.16231i) q^{23} +1.58307 q^{24} +(2.58260 - 2.98048i) q^{25} +(-4.45402 + 2.86242i) q^{26} +(0.787154 + 5.47478i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.0814920 - 0.566789i) q^{29} +(-1.56109 + 0.458376i) q^{30} +(-8.38147 - 5.38644i) q^{31} +(0.415415 - 0.909632i) q^{32} +(6.18878 + 1.81719i) q^{33} +(1.49009 + 1.71966i) q^{34} +(-0.673030 - 0.776717i) q^{35} +(0.473888 + 0.139146i) q^{36} +(-0.813758 + 1.78188i) q^{37} +(2.80297 + 1.80136i) q^{38} +(8.04205 - 2.36136i) q^{39} +(-0.146263 + 1.01728i) q^{40} +(2.46732 + 5.40267i) q^{41} +(-0.225294 - 1.56696i) q^{42} +(-9.19826 + 5.91136i) q^{43} +(2.66816 - 3.07922i) q^{44} -0.507597 q^{45} +(-2.16856 + 4.27754i) q^{46} -7.21974 q^{47} +(-1.03669 + 1.19640i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.561253 + 3.90360i) q^{50} +(-1.49640 - 3.27665i) q^{51} +(0.753486 - 5.24061i) q^{52} +(-7.15625 + 2.10126i) q^{53} +(-4.65304 - 2.99032i) q^{54} +(-1.73952 + 3.80903i) q^{55} +(-0.959493 - 0.281733i) q^{56} +(-3.45414 - 3.98630i) q^{57} +(0.374985 + 0.432756i) q^{58} +(4.02616 + 1.18219i) q^{59} +(0.675876 - 1.47996i) q^{60} +(-5.62552 - 3.61530i) q^{61} +(9.55950 - 2.80692i) q^{62} +(0.0702885 - 0.488867i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.774391 + 5.38601i) q^{65} +(-5.42613 + 3.48716i) q^{66} +(-2.06638 + 2.38473i) q^{67} -2.27544 q^{68} +(5.20171 - 5.53016i) q^{69} +1.02774 q^{70} +(6.56994 - 7.58211i) q^{71} +(-0.415491 + 0.267020i) q^{72} +(-1.30769 - 9.09520i) q^{73} +(-0.813758 - 1.78188i) q^{74} +(0.888502 - 6.17967i) q^{75} +(-3.19693 + 0.938705i) q^{76} +(-3.42760 - 2.20279i) q^{77} +(-3.48183 + 7.62413i) q^{78} +(-11.2236 - 3.29555i) q^{79} +(-0.673030 - 0.776717i) q^{80} +(4.76371 + 5.49761i) q^{81} +(-5.69881 - 1.67332i) q^{82} +(6.21437 - 13.6076i) q^{83} +(1.33176 + 0.855871i) q^{84} +(2.24384 - 0.658850i) q^{85} +(1.55607 - 10.8227i) q^{86} +(-0.376571 - 0.824575i) q^{87} +(0.579847 + 4.03293i) q^{88} +(11.6806 - 7.50667i) q^{89} +(0.332406 - 0.383616i) q^{90} -5.29450 q^{91} +(-1.81265 - 4.44008i) q^{92} -15.7722 q^{93} +(4.72793 - 5.45632i) q^{94} +(2.88074 - 1.85134i) q^{95} +(-0.225294 - 1.56696i) q^{96} +(3.04736 + 6.67279i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-1.93081 + 0.566937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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