LMFDB - Embedded newform 380.2.bb.a.59.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.17
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777543 + 1.18128i) q^{2} +(-1.85226 + 2.20744i) q^{3} +(-0.790854 - 1.83699i) q^{4} +(-0.543418 - 2.16903i) q^{5} +(-1.16739 - 3.90441i) q^{6} +(0.0958109 + 0.165949i) q^{7} +(2.78493 + 0.494121i) q^{8} +(-0.920966 - 5.22306i) q^{9} +O(q^{10})$	\(q+(-0.777543 + 1.18128i) q^{2} +(-1.85226 + 2.20744i) q^{3} +(-0.790854 - 1.83699i) q^{4} +(-0.543418 - 2.16903i) q^{5} +(-1.16739 - 3.90441i) q^{6} +(0.0958109 + 0.165949i) q^{7} +(2.78493 + 0.494121i) q^{8} +(-0.920966 - 5.22306i) q^{9} +(2.98477 + 1.04458i) q^{10} +(0.219953 + 0.126990i) q^{11} +(5.51991 + 1.65683i) q^{12} +(1.99715 - 1.67581i) q^{13} +(-0.270530 - 0.0158531i) q^{14} +(5.79455 + 2.81804i) q^{15} +(-2.74910 + 2.90559i) q^{16} +(2.07502 + 0.365881i) q^{17} +(6.88599 + 2.97323i) q^{18} +(4.07719 - 1.54161i) q^{19} +(-3.55473 + 2.71364i) q^{20} +(-0.543789 - 0.0958847i) q^{21} +(-0.321034 + 0.161086i) q^{22} +(-4.63707 - 1.68775i) q^{23} +(-6.24915 + 5.23232i) q^{24} +(-4.40939 + 2.35738i) q^{25} +(0.426732 + 3.66221i) q^{26} +(5.74881 + 3.31907i) q^{27} +(0.229076 - 0.307246i) q^{28} +(6.52866 - 1.15118i) q^{29} +(-7.83441 + 4.65384i) q^{30} +(1.47566 + 2.55592i) q^{31} +(-1.29478 - 5.50668i) q^{32} +(-0.687731 + 0.250314i) q^{33} +(-2.04562 + 2.16669i) q^{34} +(0.307884 - 0.297997i) q^{35} +(-8.86638 + 5.82248i) q^{36} +6.57793 q^{37} +(-1.34912 + 6.01497i) q^{38} +7.51261i q^{39} +(-0.441619 - 6.30912i) q^{40} +(-7.06401 + 8.41856i) q^{41} +(0.536086 - 0.567814i) q^{42} +(6.67333 - 2.42889i) q^{43} +(0.0593291 - 0.504483i) q^{44} +(-10.8285 + 4.83591i) q^{45} +(5.59923 - 4.16538i) q^{46} +(-0.936863 - 5.31322i) q^{47} +(-1.32186 - 11.4504i) q^{48} +(3.48164 - 6.03038i) q^{49} +(0.643758 - 7.04170i) q^{50} +(-4.65112 + 3.90276i) q^{51} +(-4.65791 - 2.34344i) q^{52} +(4.80209 + 1.74782i) q^{53} +(-8.39071 + 4.21024i) q^{54} +(0.155918 - 0.546093i) q^{55} +(0.184828 + 0.509500i) q^{56} +(-4.14901 + 11.8556i) q^{57} +(-3.71644 + 8.60727i) q^{58} +(2.04472 - 11.5962i) q^{59} +(0.594093 - 12.8732i) q^{60} +(11.1808 + 4.06946i) q^{61} +(-4.16665 - 0.244166i) q^{62} +(0.778525 - 0.653260i) q^{63} +(7.51169 + 2.75219i) q^{64} +(-4.72017 - 3.42122i) q^{65} +(0.239050 - 1.00703i) q^{66} +(2.04302 - 0.360240i) q^{67} +(-0.968912 - 4.10115i) q^{68} +(12.3147 - 7.10987i) q^{69} +(0.112625 + 0.595403i) q^{70} +(9.44807 - 3.43882i) q^{71} +(0.0159957 - 15.0009i) q^{72} +(2.30448 - 2.74637i) q^{73} +(-5.11462 + 7.77038i) q^{74} +(2.96356 - 14.0999i) q^{75} +(-6.05638 - 6.27059i) q^{76} +0.0486681i q^{77} +(-8.87451 - 5.84138i) q^{78} +(-5.82732 - 4.88970i) q^{79} +(7.79623 + 4.38393i) q^{80} +(-3.02357 + 1.10049i) q^{81} +(-4.45212 - 14.8904i) q^{82} +(1.59925 + 2.76998i) q^{83} +(0.253918 + 1.07477i) q^{84} +(-0.333994 - 4.69960i) q^{85} +(-2.31959 + 9.77165i) q^{86} +(-9.55160 + 16.5439i) q^{87} +(0.549805 + 0.462341i) q^{88} +(-8.40523 - 10.0170i) q^{89} +(2.70705 - 16.5516i) q^{90} +(0.469448 + 0.170865i) q^{91} +(0.566846 + 9.85304i) q^{92} +(-8.37534 - 1.47680i) q^{93} +(7.00486 + 3.02455i) q^{94} +(-5.55941 - 8.00581i) q^{95} +(14.5539 + 7.34166i) q^{96} +(2.46221 - 13.9639i) q^{97} +(4.41645 + 8.80168i) q^{98} +(0.460706 - 1.26578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

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 $

$2$	−0.777543	+	1.18128i	−0.549806	+	0.835292i
$2$	−0.777543	+	1.18128i	−0.549806	+	0.835292i
$3$	−1.85226	+	2.20744i	−1.06940	+	1.27446i	−0.109542	+	0.993982i	$0.534939\pi$
$3$	−1.85226	+	2.20744i	−1.06940	+	1.27446i	−0.959859	+	0.280481i	$0.909506\pi$
$4$	−0.790854	−	1.83699i	−0.395427	−	0.918497i
$5$	−0.543418	−	2.16903i	−0.243024	−	0.970020i
$5$	−0.543418	−	2.16903i	−0.243024	−	0.970020i
$6$	−1.16739	−	3.90441i	−0.476586	−	1.59397i
$7$	0.0958109	+	0.165949i	0.0362131	+	0.0627230i	0.883564	−	0.468311i	$-0.155137\pi$
$7$	0.0958109	+	0.165949i	0.0362131	+	0.0627230i	−0.847351	+	0.531034i	$0.821804\pi$
$8$	2.78493	+	0.494121i	0.984622	+	0.174698i
$9$	−0.920966	−	5.22306i	−0.306989	−	1.74102i
$10$	2.98477	+	1.04458i	0.943867	+	0.330327i
$11$	0.219953	+	0.126990i	0.0663183	+	0.0382889i	0.532792	−	0.846246i	$-0.321143\pi$
$11$	0.219953	+	0.126990i	0.0663183	+	0.0382889i	−0.466474	+	0.884535i	$0.654476\pi$
$12$	5.51991	+	1.65683i	1.59346	+	0.478286i
$13$	1.99715	−	1.67581i	0.553910	−	0.464786i	−0.322352	−	0.946620i	$-0.604474\pi$
$13$	1.99715	−	1.67581i	0.553910	−	0.464786i	0.876263	+	0.481834i	$0.160029\pi$
$14$	−0.270530	−	0.0158531i	−0.0723022	−	0.00423691i
$15$	5.79455	+	2.81804i	1.49615	+	0.727616i
$16$	−2.74910	+	2.90559i	−0.687275	+	0.726397i
$17$	2.07502	+	0.365881i	0.503265	+	0.0887392i	0.419517	−	0.907748i	$-0.362200\pi$
$17$	2.07502	+	0.365881i	0.503265	+	0.0887392i	0.0837487	+	0.996487i	$0.473311\pi$
$18$	6.88599	+	2.97323i	1.62304	+	0.700797i
$19$	4.07719	−	1.54161i	0.935371	−	0.353669i
$19$	4.07719	−	1.54161i	0.935371	−	0.353669i
$20$	−3.55473	+	2.71364i	−0.794863	+	0.606789i
$21$	−0.543789	−	0.0958847i	−0.118665	−	0.0209238i
$22$	−0.321034	+	0.161086i	−0.0684446	+	0.0343437i
$23$	−4.63707	−	1.68775i	−0.966896	−	0.351921i	−0.190164	−	0.981752i	$-0.560902\pi$
$23$	−4.63707	−	1.68775i	−0.966896	−	0.351921i	−0.776732	+	0.629831i	$0.783124\pi$
$24$	−6.24915	+	5.23232i	−1.27560	+	1.06804i
$25$	−4.40939	+	2.35738i	−0.881879	+	0.471477i
$26$	0.426732	+	3.66221i	0.0836890	+	0.718219i
$27$	5.74881	+	3.31907i	1.10636	+	0.638756i
$28$	0.229076	−	0.307246i	0.0432913	−	0.0580640i
$29$	6.52866	−	1.15118i	1.21234	−	0.213768i	0.469315	−	0.883031i	$-0.344501\pi$
$29$	6.52866	−	1.15118i	1.21234	−	0.213768i	0.743026	+	0.669263i	$0.233390\pi$
$30$	−7.83441	+	4.65384i	−1.43036	+	0.849672i
$31$	1.47566	+	2.55592i	0.265037	+	0.459057i	0.967573	−	0.252591i	$-0.0812826\pi$
$31$	1.47566	+	2.55592i	0.265037	+	0.459057i	−0.702537	+	0.711648i	$0.747949\pi$
$32$	−1.29478	−	5.50668i	−0.228886	−	0.973453i
$33$	−0.687731	+	0.250314i	−0.119719	+	0.0435740i
$34$	−2.04562	+	2.16669i	−0.350821	+	0.371584i
$35$	0.307884	−	0.297997i	0.0520419	−	0.0503707i
$36$	−8.86638	+	5.82248i	−1.47773	+	0.970414i
$37$	6.57793			1.08140			0.540702	−	0.841214i	$-0.318159\pi$
$37$	6.57793			1.08140			0.540702	+	0.841214i	$0.318159\pi$
$38$	−1.34912	+	6.01497i	−0.218856	+	0.975757i
$39$			7.51261i			1.20298i
$40$	−0.441619	−	6.30912i	−0.0698261	−	0.997559i
$41$	−7.06401	+	8.41856i	−1.10321	+	1.31476i	−0.158316	+	0.987389i	$0.550606\pi$
$41$	−7.06401	+	8.41856i	−1.10321	+	1.31476i	−0.944897	+	0.327369i	$0.893838\pi$
$42$	0.536086	−	0.567814i	0.0827199	−	0.0876156i
$43$	6.67333	−	2.42889i	1.01767	−	0.370403i	0.221298	−	0.975206i	$-0.428971\pi$
$43$	6.67333	−	2.42889i	1.01767	−	0.370403i	0.796375	+	0.604803i	$0.206748\pi$
$44$	0.0593291	−	0.504483i	0.00894420	−	0.0760536i
$45$	−10.8285	+	4.83591i	−1.61422	+	0.720895i
$46$	5.59923	−	4.16538i	0.825562	−	0.614152i
$47$	−0.936863	−	5.31322i	−0.136656	−	0.775012i	−0.973693	−	0.227866i	$-0.926825\pi$
$47$	−0.936863	−	5.31322i	−0.136656	−	0.775012i	0.837037	−	0.547146i	$-0.184286\pi$
$48$	−1.32186	−	11.4504i	−0.190794	−	1.65272i
$49$	3.48164	−	6.03038i	0.497377	−	0.861483i
$50$	0.643758	−	7.04170i	0.0910411	−	0.995847i
$51$	−4.65112	+	3.90276i	−0.651288	+	0.546495i
$52$	−4.65791	−	2.34344i	−0.645935	−	0.324976i
$53$	4.80209	+	1.74782i	0.659618	+	0.240081i	0.650071	−	0.759873i	$-0.274739\pi$
$53$	4.80209	+	1.74782i	0.659618	+	0.240081i	0.00954631	+	0.999954i	$0.496961\pi$
$54$	−8.39071	+	4.21024i	−1.14183	+	0.572941i
$55$	0.155918	−	0.546093i	0.0210240	−	0.0736352i
$56$	0.184828	+	0.509500i	0.0246987	+	0.0680848i
$57$	−4.14901	+	11.8556i	−0.549549	+	1.57031i
$58$	−3.71644	+	8.60727i	−0.487993	+	1.13019i
$59$	2.04472	−	11.5962i	0.266200	−	1.50970i	−0.499396	−	0.866374i	$-0.666445\pi$
$59$	2.04472	−	11.5962i	0.266200	−	1.50970i	0.765596	−	0.643322i	$-0.222444\pi$
$60$	0.594093	−	12.8732i	0.0766971	−	1.66193i
$61$	11.1808	+	4.06946i	1.43155	+	0.521041i	0.937375	−	0.348321i	$-0.113248\pi$
$61$	11.1808	+	4.06946i	1.43155	+	0.521041i	0.494174	+	0.869363i	$0.335470\pi$
$62$	−4.16665	−	0.244166i	−0.529165	−	0.0310091i
$63$	0.778525	−	0.653260i	0.0980849	−	0.0823030i
$64$	7.51169	+	2.75219i	0.938961	+	0.344023i
$65$	−4.72017	−	3.42122i	−0.585465	−	0.424350i
$66$	0.239050	−	1.00703i	0.0294250	−	0.123957i
$67$	2.04302	−	0.360240i	0.249595	−	0.0440103i	−0.0474508	−	0.998874i	$-0.515110\pi$
$67$	2.04302	−	0.360240i	0.249595	−	0.0440103i	0.297046	+	0.954863i	$0.403999\pi$
$68$	−0.968912	−	4.10115i	−0.117498	−	0.497338i
$69$	12.3147	−	7.10987i	1.48251	−	0.855928i
$70$	0.112625	+	0.595403i	0.0134613	+	0.0711643i
$71$	9.44807	−	3.43882i	1.12128	−	0.408112i	0.286160	−	0.958182i	$-0.407621\pi$
$71$	9.44807	−	3.43882i	1.12128	−	0.408112i	0.835119	+	0.550069i	$0.185399\pi$
$72$	0.0159957	−	15.0009i	0.00188512	−	1.76788i
$73$	2.30448	−	2.74637i	0.269719	−	0.321438i	−0.614136	−	0.789200i	$-0.710495\pi$
$73$	2.30448	−	2.74637i	0.269719	−	0.321438i	0.883854	+	0.467762i	$0.154940\pi$
$74$	−5.11462	+	7.77038i	−0.594562	+	0.903289i
$75$	2.96356	−	14.0999i	0.342203	−	1.62812i
$76$	−6.05638	−	6.27059i	−0.694715	−	0.719285i
$77$			0.0486681i			0.00554624i
$78$	−8.87451	−	5.84138i	−1.00484	−	0.661406i
$79$	−5.82732	−	4.88970i	−0.655625	−	0.550135i	0.253147	−	0.967428i	$-0.418534\pi$
$79$	−5.82732	−	4.88970i	−0.655625	−	0.550135i	−0.908772	+	0.417293i	$0.862979\pi$
$80$	7.79623	+	4.38393i	0.871644	+	0.490139i
$81$	−3.02357	+	1.10049i	−0.335952	+	0.122277i
$82$	−4.45212	−	14.8904i	−0.491654	−	1.64437i
$83$	1.59925	+	2.76998i	0.175540	+	0.304045i	0.940348	−	0.340214i	$-0.110499\pi$
$83$	1.59925	+	2.76998i	0.175540	+	0.304045i	−0.764808	+	0.644259i	$0.777166\pi$
$84$	0.253918	+	1.07477i	0.0277047	+	0.117267i
$85$	−0.333994	−	4.69960i	−0.0362267	−	0.509743i
$86$	−2.31959	+	9.77165i	−0.250128	+	1.05370i
$87$	−9.55160	+	16.5439i	−1.02404	+	1.77369i
$88$	0.549805	+	0.462341i	0.0586094	+	0.0492858i
$89$	−8.40523	−	10.0170i	−0.890953	−	1.06180i	−0.997718	−	0.0675121i	$-0.978494\pi$
$89$	−8.40523	−	10.0170i	−0.890953	−	1.06180i	0.106766	−	0.994284i	$-0.465951\pi$
$90$	2.70705	−	16.5516i	0.285349	−	1.74470i
$91$	0.469448	+	0.170865i	0.0492116	+	0.0179115i
$92$	0.566846	+	9.85304i	0.0590978	+	1.02725i
$93$	−8.37534	−	1.47680i	−0.868482	−	0.153137i
$94$	7.00486	+	3.02455i	0.722496	+	0.311959i
$95$	−5.55941	−	8.00581i	−0.570384	−	0.821379i
$96$	14.5539	+	7.34166i	1.48540	+	0.749305i
$97$	2.46221	−	13.9639i	0.250000	−	1.41782i	−0.558590	−	0.829444i	$-0.688657\pi$
$97$	2.46221	−	13.9639i	0.250000	−	1.41782i	0.808589	−	0.588374i	$-0.200232\pi$
$98$	4.41645	+	8.80168i	0.446129	+	0.889104i
$99$	0.460706	−	1.26578i	0.0463027	−	0.127216i
$100$	7.81769	+	6.23569i	0.781769	+	0.623569i
$101$	−10.1766	+	8.53922i	−1.01261	+	0.849684i	−0.988682	−	0.150029i	$-0.952063\pi$
$101$	−10.1766	+	8.53922i	−1.01261	+	0.849684i	−0.0239326	+	0.999714i	$0.507619\pi$
$102$	−0.993807	−	8.52885i	−0.0984015	−	0.844482i
$103$	13.3173	+	7.68877i	1.31220	+	0.757597i	0.982459	−	0.186476i	$-0.0597068\pi$
$103$	13.3173	+	7.68877i	1.31220	+	0.757597i	0.329736	+	0.944073i	$0.393040\pi$
$104$	6.38998	−	3.68018i	0.626589	−	0.360871i
$105$	0.0875282	+	1.23160i	0.00854188	+	0.120192i
$106$	−5.79849	+	4.31362i	−0.563200	+	0.418976i
$107$	−8.80846	+	5.08557i	−0.851546	+	0.491640i	−0.861172	−	0.508313i	$-0.830269\pi$
$107$	−8.80846	+	5.08557i	−0.851546	+	0.491640i	0.00962624	+	0.999954i	$0.496936\pi$
$108$	1.55066	−	13.1854i	0.149212	−	1.26877i
$109$	2.76832	+	7.60589i	0.265157	+	0.728512i	0.998800	+	0.0489773i	$0.0155962\pi$
$109$	2.76832	+	7.60589i	0.265157	+	0.728512i	−0.733643	+	0.679535i	$0.762182\pi$
$110$	0.523857	+	0.608795i	0.0499478	+	0.0580463i
$111$	−12.1840	+	14.5203i	−1.15646	+	1.37821i
$112$	−0.745575	−	0.177824i	−0.0704502	−	0.0168028i
$113$	−6.60225			−0.621088			−0.310544	−	0.950559i	$-0.600511\pi$
$113$	−6.60225			−0.621088			−0.310544	+	0.950559i	$0.600511\pi$
$114$	−10.7788	−	14.1194i	−1.00952	−	1.32240i
$115$	−1.14092	+	10.9751i	−0.106392	+	1.02343i
$116$	−7.27792	−	11.0827i	−0.675738	−	1.02900i
$117$	−10.5922	−	8.88787i	−0.979245	−	0.821684i
$118$	12.1085	+	11.4319i	1.11468	+	1.05239i
$119$	0.138091	+	0.379403i	0.0126588	+	0.0347798i
$120$	14.7450	+	10.7113i	1.34602	+	0.977801i
$121$	−5.46775	−	9.47042i	−0.497068	−	0.860947i
$122$	−13.5007	+	10.0434i	−1.22230	+	0.909291i
$123$	−5.49905	−	31.1867i	−0.495833	−	2.81201i
$124$	3.52818	−	4.73214i	0.316840	−	0.424959i
$125$	7.50938	+	8.28306i	0.671660	+	0.740860i
$126$	0.166348	+	1.42759i	0.0148194	+	0.127180i
$127$	2.41341	+	2.87619i	0.214155	+	0.255220i	0.862418	−	0.506196i	$-0.168949\pi$
$127$	2.41341	+	2.87619i	0.214155	+	0.255220i	−0.648263	+	0.761416i	$0.724504\pi$
$128$	−9.09177	+	6.73348i	−0.803606	+	0.595161i
$129$	−6.99910	+	19.2299i	−0.616237	+	1.69310i
$130$	7.71156	−	2.91571i	0.676348	−	0.255725i
$131$	−21.2428	−	3.74567i	−1.85599	−	0.327261i	−0.869867	−	0.493286i	$-0.835796\pi$
$131$	−21.2428	−	3.74567i	−1.85599	−	0.327261i	−0.986122	+	0.166025i	$0.946907\pi$
$132$	1.00372	+	1.06540i	0.0873626	+	0.0927309i
$133$	0.646468	+	0.528904i	0.0560559	+	0.0458618i
$134$	−1.16299	+	2.69349i	−0.100467	+	0.232682i
$135$	4.07517	−	14.2730i	0.350735	−	1.22842i
$136$	5.59799	+	2.04426i	0.480024	+	0.175294i
$137$	−1.62948	+	4.47695i	−0.139215	+	0.382491i	−0.989633	−	0.143616i	$-0.954127\pi$
$137$	−1.62948	+	4.47695i	−0.139215	+	0.382491i	0.850418	+	0.526108i	$0.176349\pi$
$138$	−1.17641	+	20.0753i	−0.100143	+	1.70892i
$139$	2.89532	+	3.45051i	0.245578	+	0.292668i	0.874727	−	0.484617i	$-0.161041\pi$
$139$	2.89532	+	3.45051i	0.245578	+	0.292668i	−0.629149	+	0.777285i	$0.716596\pi$
$140$	−0.790910	−	0.329909i	−0.0668441	−	0.0278824i
$141$	13.4639	+	7.77338i	1.13386	+	0.654637i
$142$	−3.28407	+	13.8347i	−0.275593	+	1.16098i
$143$	0.652090	−	0.114981i	0.0545305	−	0.00961520i
$144$	17.7079	+	11.6828i	1.47566	+	0.973563i
$145$	−6.04473	−	13.5353i	−0.501988	−	1.12404i
$146$	1.45241	+	4.85766i	0.120202	+	0.402023i
$147$	6.86277	+	18.8553i	0.566032	+	1.55516i
$148$	−5.20218	−	12.0836i	−0.427616	−	0.993267i
$149$	0.0188513	+	0.0158181i	0.00154436	+	0.00129587i	0.643559	−	0.765396i	$-0.277457\pi$
$149$	0.0188513	+	0.0158181i	0.00154436	+	0.00129587i	−0.642015	+	0.766692i	$0.721901\pi$
$150$	14.3517	+	14.4641i	1.17181	+	1.18099i
$151$	1.21023			0.0984867			0.0492434	−	0.998787i	$-0.484319\pi$
$151$	1.21023			0.0984867			0.0492434	+	0.998787i	$0.484319\pi$
$152$	12.1164	−	2.27864i	0.982772	−	0.184822i
$153$		−	11.1749i		−	0.903436i
$154$	−0.0574907	−	0.0378415i	−0.00463273	−	0.00304936i
$155$	4.74197	−	4.58969i	0.380884	−	0.368653i
$156$	13.8006	−	5.94138i	1.10493	−	0.475691i
$157$	−6.83282	−	18.7730i	−0.545318	−	1.49825i	−0.839964	−	0.542643i	$-0.817424\pi$
$157$	−6.83282	−	18.7730i	−0.545318	−	1.49825i	0.294645	−	0.955607i	$-0.404798\pi$
$158$	10.3071	−	3.08176i	0.819990	−	0.245171i
$159$	−12.7529	+	7.36289i	−1.01137	+	0.583915i
$160$	−11.2406	+	5.80084i	−0.888644	+	0.458597i
$161$	−0.164200	−	0.931224i	−0.0129408	−	0.0733908i
$162$	1.05097	−	4.42736i	0.0825717	−	0.347846i
$163$	5.76941	−	9.99291i	0.451895	−	0.782705i	−0.546609	−	0.837388i	$-0.684081\pi$
$163$	5.76941	−	9.99291i	0.451895	−	0.782705i	0.998504	+	0.0546830i	$0.0174148\pi$
$164$	21.0514	+	6.31870i	1.64384	+	0.493407i
$165$	0.916664	+	1.35569i	0.0713622	+	0.105540i
$166$	−4.51561	−	0.264615i	−0.350480	−	0.0205381i
$167$	−7.10931	+	19.5327i	−0.550135	+	1.51148i	0.283391	+	0.959004i	$0.408541\pi$
$167$	−7.10931	+	19.5327i	−0.550135	+	1.51148i	−0.833526	+	0.552480i	$0.813682\pi$
$168$	−1.46704	−	0.535730i	−0.113184	−	0.0413325i
$169$	−1.07715	+	6.10881i	−0.0828576	+	0.469909i
$170$	5.81125	+	3.25960i	0.445702	+	0.250000i
$171$	−11.8068	−	19.8756i	−0.902892	−	1.51993i
$172$	−9.73949	−	10.3380i	−0.742629	−	0.788263i
$173$	−0.948110	+	5.37700i	−0.0720835	+	0.408806i	0.927320	+	0.374270i	$0.122107\pi$
$173$	−0.948110	+	5.37700i	−0.0720835	+	0.408806i	−0.999403	+	0.0345363i	$0.989005\pi$
$174$	−12.1162	−	24.1467i	−0.918526	−	1.83056i
$175$	−0.813674	−	0.505873i	−0.0615080	−	0.0382404i
$176$	−0.973653	+	0.289985i	−0.0733918	+	0.0218584i
$177$	21.8105	+	25.9927i	1.63938	+	1.95373i
$178$	18.3683	−	2.14033i	1.37676	−	0.160424i
$179$	5.97553	−	10.3499i	0.446632	−	0.773589i	−0.551532	−	0.834154i	$-0.685957\pi$
$179$	5.97553	−	10.3499i	0.446632	−	0.773589i	0.998164	+	0.0605641i	$0.0192900\pi$
$180$	17.4473	+	16.0674i	1.30045	+	1.19759i
$181$	1.91519	−	0.337700i	0.142355	−	0.0251010i	−0.102017	−	0.994783i	$-0.532529\pi$
$181$	1.91519	−	0.337700i	0.142355	−	0.0251010i	0.244371	+	0.969682i	$0.421418\pi$
$182$	−0.566856	+	0.421696i	−0.0420182	+	0.0312582i
$183$	−29.6927	+	17.1431i	−2.19495	+	1.26725i
$184$	−12.0800	−	6.99156i	−0.890547	−	0.515424i
$185$	−3.57457	−	14.2677i	−0.262807	−	1.04898i
$186$	8.25670	−	8.74536i	0.605410	−	0.641241i
$187$	0.409942	+	0.343983i	0.0299780	+	0.0251545i
$188$	−9.01943	+	5.92299i	−0.657810	+	0.431979i
$189$			1.27201i			0.0925255i
$190$	13.7798	−	0.342372i	0.999691	−	0.0248383i
$191$		−	22.4077i		−	1.62137i	−0.585486	−	0.810683i	$-0.699096\pi$
$191$		−	22.4077i		−	1.62137i	0.585486	−	0.810683i	$-0.300904\pi$
$192$	−19.9889	+	11.4838i	−1.44257	+	0.828772i
$193$	2.58774	+	2.17137i	0.186270	+	0.156299i	0.731154	−	0.682212i	$-0.238982\pi$
$193$	2.58774	+	2.17137i	0.186270	+	0.156299i	−0.544884	+	0.838511i	$0.683426\pi$
$194$	14.5808	+	13.7661i	1.04684	+	0.988347i
$195$	16.2951	−	4.08249i	1.16692	−	0.292353i
$196$	−13.8312	−	1.62661i	−0.987946	−	0.116186i
$197$	19.7720	−	11.4154i	1.40870	−	0.813311i	0.413433	−	0.910534i	$-0.364329\pi$
$197$	19.7720	−	11.4154i	1.40870	−	0.813311i	0.995263	+	0.0972234i	$0.0309961\pi$
$198$	1.13702	+	1.52842i	0.0808048	+	0.108620i
$199$	−17.6314	+	3.10890i	−1.24986	+	0.220384i	−0.759136	−	0.650932i	$-0.774378\pi$
$199$	−17.6314	+	3.10890i	−1.24986	+	0.220384i	−0.490723	+	0.871316i	$0.663267\pi$
$200$	−13.4447	+	4.38638i	−0.950683	+	0.310164i
$201$	−2.98900	+	5.17710i	−0.210828	+	0.365164i
$202$	−2.17445	−	18.6611i	−0.152994	−	1.31299i
$203$	0.816554	+	0.973131i	0.0573109	+	0.0683004i
$204$	10.8477	+	5.45758i	0.759491	+	0.382107i
$205$	22.0988	+	10.7473i	1.54345	+	0.750621i
$206$	−19.4374	+	9.75318i	−1.35427	+	0.679536i
$207$	−4.54466	+	25.7740i	−0.315876	+	1.79142i
$208$	−0.621157	+	10.4099i	−0.0430695	+	0.721794i
$209$	1.09256	+	0.178681i	0.0755738	+	0.0123596i
$210$	−1.52293	−	0.854227i	−0.105092	−	0.0589473i
$211$	−1.67355	+	9.49116i	−0.115212	+	0.653398i	0.871433	+	0.490514i	$0.163191\pi$
$211$	−1.67355	+	9.49116i	−0.115212	+	0.653398i	−0.986645	+	0.162884i	$0.947920\pi$
$212$	−0.587019	−	10.2037i	−0.0403166	−	0.700792i
$213$	−9.90930	+	27.2256i	−0.678974	+	1.86547i
$214$	0.841468	−	14.3595i	0.0575216	−	0.981597i
$215$	−8.89476	−	13.1548i	−0.606617	−	0.897147i
$216$	14.3700	+	12.0840i	0.977755	+	0.822212i
$217$	−0.282769	+	0.489770i	−0.0191956	+	0.0332478i
$218$	−11.1372	−	2.64374i	−0.754306	−	0.179057i
$219$	1.79395	+	10.1740i	0.121224	+	0.687493i
$220$	−1.12648	+	0.145458i	−0.0759472	+	0.00980681i
$221$	4.75727	−	2.74661i	0.320008	−	0.184757i
$222$	−7.67902	−	25.6829i	−0.515382	−	1.72373i
$223$	−1.20429	−	3.30877i	−0.0806454	−	0.221572i	0.892816	−	0.450421i	$-0.148726\pi$
$223$	−1.20429	−	3.30877i	−0.0806454	−	0.221572i	−0.973462	+	0.228849i	$0.926504\pi$
$224$	0.789777	−	0.742468i	0.0527692	−	0.0496082i
$225$	16.3736	+	20.8594i	1.09158	+	1.39063i
$226$	5.13354	−	7.79912i	0.341478	−	0.518790i
$227$		−	15.8038i		−	1.04893i	−0.851431	−	0.524467i	$-0.824265\pi$
$227$		−	15.8038i		−	1.04893i	0.851431	−	0.524467i	$-0.175735\pi$
$228$	25.0599	−	1.75433i	1.65963	−	0.116183i
$229$	−16.4726			−1.08854			−0.544268	−	0.838911i	$-0.683193\pi$
$229$	−16.4726			−1.08854			−0.544268	+	0.838911i	$0.683193\pi$
$230$	−12.0776	−	9.88137i	−0.796372	−	0.651558i
$231$	−0.107432	−	0.0901458i	−0.00706848	−	0.00593116i
$232$	18.7507	+	0.0199942i	1.23104	+	0.00131268i
$233$	3.51094	+	9.64624i	0.230009	+	0.631946i	0.999981	−	0.00613213i	$-0.00195193\pi$
$233$	3.51094	+	9.64624i	0.230009	+	0.631946i	−0.769972	+	0.638078i	$0.779730\pi$
$234$	18.7349	−	5.60162i	1.22474	−	0.366189i
$235$	−11.0154	+	4.91939i	−0.718567	+	0.320905i
$236$	−22.9192	+	5.41475i	−1.49191	+	0.352470i
$237$	21.5874	−	3.80644i	1.40225	−	0.247255i
$238$	−0.555554	−	0.131877i	−0.0360112	−	0.00854834i
$239$	18.9539	+	10.9430i	1.22603	+	0.707846i	0.966196	−	0.257809i	$-0.0830004\pi$
$239$	18.9539	+	10.9430i	1.22603	+	0.707846i	0.259829	+	0.965655i	$0.416334\pi$
$240$	−24.1179	+	9.08949i	−1.55680	+	0.586724i
$241$	14.3132	+	17.0578i	0.921993	+	1.09879i	0.994841	+	0.101445i	$0.0323467\pi$
$241$	14.3132	+	17.0578i	0.921993	+	1.09879i	−0.0728483	+	0.997343i	$0.523209\pi$
$242$	15.4386	+	0.904705i	0.992433	+	0.0581566i
$243$	−3.63997	+	10.0007i	−0.233504	+	0.641548i
$244$	−1.36676	−	23.7573i	−0.0874980	−	1.52091i
$245$	−14.9721	−	4.27477i	−0.956530	−	0.273105i
$246$	41.1160	+	17.7530i	2.62146	+	1.13189i
$247$	5.55932	−	9.91141i	0.353731	−	0.630648i
$248$	2.84668	+	7.84722i	0.180764	+	0.498299i
$249$	−9.07678	−	1.60048i	−0.575217	−	0.101426i
$250$	−15.6235	+	2.43026i	−0.988117	+	0.153703i
$251$	0.238781	−	0.656046i	0.0150717	−	0.0414092i	−0.931929	−	0.362642i	$-0.881875\pi$
$251$	0.238781	−	0.656046i	0.0150717	−	0.0414092i	0.947000	+	0.321232i	$0.104097\pi$
$252$	−1.81573	−	0.913513i	−0.114381	−	0.0575459i
$253$	−0.805609	−	0.960087i	−0.0506482	−	0.0603602i
$254$	−5.27411	+	0.614555i	−0.330927	+	0.0385606i
$255$	10.9927	+	7.96760i	0.688390	+	0.498951i
$256$	−0.884894	−	15.9755i	−0.0553059	−	0.998469i
$257$	4.39595	+	24.9307i	0.274212	+	1.55513i	0.741454	+	0.671003i	$0.234136\pi$
$257$	4.39595	+	24.9307i	0.274212	+	1.55513i	−0.467243	+	0.884129i	$0.654753\pi$
$258$	−17.2738	−	23.2200i	−1.07542	−	1.44561i
$259$	0.630237	+	1.09160i	0.0391610	+	0.0678289i
$260$	−2.55179	+	11.3766i	−0.158256	+	0.705548i
$261$	−12.0253	−	33.0393i	−0.744350	−	2.04508i
$262$	20.9419	−	22.1813i	1.29379	−	1.37036i
$263$	−2.76507	−	2.32017i	−0.170502	−	0.143068i	0.553544	−	0.832820i	$-0.313275\pi$
$263$	−2.76507	−	2.32017i	−0.170502	−	0.143068i	−0.724046	+	0.689752i	$0.757719\pi$
$264$	−2.03897	+	0.357284i	−0.125490	+	0.0219893i
$265$	1.18153	−	11.3657i	0.0725806	−	0.698188i
$266$	−1.12744	+	0.352415i	−0.0691279	+	0.0216080i
$267$	37.6805			2.30601
$268$	−2.27749	−	3.46812i	−0.139120	−	0.211849i
$269$	−0.966795	+	1.15218i	−0.0589465	+	0.0702497i	−0.794712	−	0.606987i	$-0.792378\pi$
$269$	−0.966795	+	1.15218i	−0.0589465	+	0.0702497i	0.735765	+	0.677236i	$0.236823\pi$
$270$	13.6918	+	15.9118i	0.833257	+	0.968360i
$271$	5.94257	+	16.3271i	0.360985	+	0.991799i	0.978682	+	0.205382i	$0.0658438\pi$
$271$	5.94257	+	16.3271i	0.360985	+	0.991799i	−0.617696	+	0.786417i	$0.711934\pi$
$272$	−6.76753	+	5.02330i	−0.410342	+	0.304582i
$273$	−1.24671	+	0.719791i	−0.0754545	+	0.0435637i
$274$	−4.02155	−	5.40589i	−0.242951	−	0.326582i
$275$	−1.26922	−	0.0414349i	−0.0765370	−	0.00249862i
$276$	−22.7999	−	16.9991i	−1.37239	−	1.02323i
$277$	−12.7706	−	7.37314i	−0.767314	−	0.443009i	0.0646017	−	0.997911i	$-0.479422\pi$
$277$	−12.7706	−	7.37314i	−0.767314	−	0.443009i	−0.831916	+	0.554902i	$0.812756\pi$
$278$	−6.32726	+	0.737270i	−0.379484	+	0.0442185i
$279$	11.9907	−	10.0614i	0.717864	−	0.602359i
$280$	1.00468	−	0.677769i	0.0600413	−	0.0405044i
$281$	0.243968	−	0.670298i	0.0145539	−	0.0399866i	−0.932203	−	0.361936i	$-0.882116\pi$
$281$	0.243968	−	0.670298i	0.0145539	−	0.0399866i	0.946757	+	0.321949i	$0.104338\pi$
$282$	−19.6513	+	9.86052i	−1.17022	+	0.587185i
$283$	−0.0957935	+	0.543272i	−0.00569433	+	0.0322942i	−0.987523	−	0.157478i	$-0.949664\pi$
$283$	−0.0957935	+	0.543272i	−0.00569433	+	0.0322942i	0.981828	+	0.189772i	$0.0607749\pi$
$284$	−13.7891	−	14.6365i	−0.818234	−	0.868514i
$285$	27.9698	+	2.55678i	1.65679	+	0.151451i
$286$	−0.371203	+	0.859705i	−0.0219497	+	0.0508354i
$287$	−2.07386	−	0.365678i	−0.122416	−	0.0215853i
$288$	−27.5693	+	11.8342i	−1.62454	+	0.697334i
$289$	−11.8030	−	4.29592i	−0.694291	−	0.252701i
$290$	20.6890	+	3.38373i	1.21490	+	0.198700i
$291$	26.2637	+	31.2999i	1.53961	+	1.83483i
$292$	−6.86757	−	2.06134i	−0.401894	−	0.120631i
$293$	−1.26930	+	2.19849i	−0.0741532	+	0.128437i	−0.900718	−	0.434405i	$-0.856959\pi$
$293$	−1.26930	+	2.19849i	−0.0741532	+	0.128437i	0.826565	+	0.562842i	$0.190292\pi$
$294$	−27.6095	−	6.55395i	−1.61022	−	0.382234i
$295$	−26.2636	+	1.86652i	−1.52913	+	0.108673i
$296$	18.3191	+	3.25029i	1.06477	+	0.188919i
$297$	0.842978	+	1.46008i	0.0489145	+	0.0847224i
$298$	−0.0333433	+	0.00996943i	−0.00193153	+	0.000577513i
$299$	−12.0893	+	4.40014i	−0.699141	+	0.254467i
$300$	−28.2452	+	5.70694i	−1.63074	+	0.329490i
$301$	1.04245	+	0.874721i	0.0600859	+	0.0504181i
$302$	−0.941002	+	1.42962i	−0.0541486	+	0.0822652i
$303$		−	38.2811i		−	2.19919i
$304$	−6.72932	+	16.0847i	−0.385953	+	0.922518i
$305$	2.75096	−	26.4628i	0.157520	−	1.51526i
$306$	13.2007	+	8.68896i	0.754634	+	0.496715i
$307$	−10.4012	+	12.3957i	−0.593630	+	0.707461i	−0.976299	−	0.216425i	$-0.930560\pi$
$307$	−10.4012	+	12.3957i	−0.593630	+	0.707461i	0.382669	+	0.923885i	$0.375005\pi$
$308$	0.0894030	−	0.0384893i	0.00509421	−	0.00219313i
$309$	−41.6396	+	15.1556i	−2.36879	+	0.862170i
$310$	1.73463	+	9.17028i	0.0985205	+	0.520837i
$311$	22.3213	−	12.8872i	1.26572	−	0.730766i	0.291549	−	0.956556i	$-0.405829\pi$
$311$	22.3213	−	12.8872i	1.26572	−	0.730766i	0.974176	+	0.225790i	$0.0724962\pi$
$312$	−3.71214	+	20.9221i	−0.210159	+	1.18448i
$313$	−24.7407	+	4.36245i	−1.39843	+	0.246580i	−0.821497	−	0.570213i	$-0.806861\pi$
$313$	−24.7407	+	4.36245i	−1.39843	+	0.246580i	−0.576930	+	0.816793i	$0.695750\pi$
$314$	27.4890	+	6.52534i	1.55130	+	0.368246i
$315$	−1.84001	−	1.33365i	−0.103673	−	0.0751427i
$316$	−4.37380	+	14.5718i	−0.246046	+	0.819728i
$317$	−8.87066	+	7.44337i	−0.498226	+	0.418061i	−0.856963	−	0.515377i	$-0.827652\pi$
$317$	−8.87066	+	7.44337i	−0.498226	+	0.418061i	0.358738	+	0.933438i	$0.383207\pi$
$318$	1.21828	−	20.7897i	0.0683177	−	1.16583i
$319$	1.58218	+	0.575868i	0.0885853	+	0.0322424i
$320$	1.88759	−	17.7887i	0.105519	−	0.994417i
$321$	5.08948	−	28.8639i	0.284067	−	1.61103i
$322$	1.22771	+	0.530100i	0.0684177	+	0.0295413i
$323$	9.02427	−	1.70709i	0.502124	−	0.0949851i
$324$	4.41279	+	4.68395i	0.245155	+	0.260220i
$325$	−4.85570	+	12.0973i	−0.269346	+	0.671040i
$326$	7.31848	+	14.5852i	0.405333	+	0.807800i
$327$	−21.9172	−	7.97719i	−1.21202	−	0.441140i
$328$	−23.8326	+	19.9546i	−1.31593	+	1.10181i
$329$	0.791963	−	0.664536i	0.0436624	−	0.0366371i
$330$	−2.31419	+	0.0287350i	−0.127392	+	0.00158181i
$331$	6.55680	−	11.3567i	0.360394	−	0.624221i	−0.627631	−	0.778511i	$-0.715976\pi$
$331$	6.55680	−	11.3567i	0.360394	−	0.624221i	0.988026	+	0.154290i	$0.0493088\pi$
$332$	3.82367	−	5.12846i	0.209851	−	0.281461i
$333$	−6.05805	−	34.3569i	−0.331979	−	1.88275i
$334$	−17.5458	−	23.5856i	−0.960064	−	1.29055i
$335$	−1.89159	−	4.23562i	−0.103348	−	0.231417i
$336$	1.77353	−	1.31643i	0.0967541	−	0.0718172i
$337$	5.07189	−	1.84602i	0.276284	−	0.100559i	−0.200162	−	0.979763i	$-0.564147\pi$
$337$	5.07189	−	1.84602i	0.276284	−	0.100559i	0.476446	+	0.879204i	$0.341925\pi$
$338$	−6.37870	−	6.02228i	−0.346956	−	0.327569i
$339$	12.2291	−	14.5740i	0.664192	−	0.791554i
$340$	−8.36900	+	4.33024i	−0.453873	+	0.234840i
$341$			0.749576i			0.0405918i
$342$	32.6590	+	1.50693i	1.76600	+	0.0814853i
$343$	2.67567			0.144473
$344$	19.7849	−	3.46687i	1.06673	−	0.186921i
$345$	−22.1135	−	22.8472i	−1.19055	−	1.23005i
$346$	−5.61456	−	5.30084i	−0.301841	−	0.284975i
$347$	23.3819	−	8.51031i	1.25521	−	0.456858i	0.373048	−	0.927812i	$-0.378313\pi$
$347$	23.3819	−	8.51031i	1.25521	−	0.456858i	0.882158	+	0.470954i	$0.156090\pi$
$348$	37.9449	+	4.46247i	2.03406	+	0.239213i
$349$	−4.38247	−	7.59066i	−0.234588	−	0.406319i	0.724565	−	0.689207i	$-0.242041\pi$
$349$	−4.38247	−	7.59066i	−0.234588	−	0.406319i	−0.959153	+	0.282888i	$0.908708\pi$
$350$	1.23025	−	0.567841i	0.0657594	−	0.0303524i
$351$	17.0434	−	3.00521i	0.909708	−	0.160406i
$352$	0.414503	−	1.37563i	0.0220931	−	0.0733215i
$353$	−22.9267	−	13.2368i	−1.22027	−	0.704522i	−0.255293	−	0.966864i	$-0.582172\pi$
$353$	−22.9267	−	13.2368i	−1.22027	−	0.704522i	−0.964975	+	0.262342i	$0.915505\pi$
$354$	−47.6634	+	5.55387i	−2.53328	+	0.295185i
$355$	−12.5932	−	18.6244i	−0.668375	−	0.988482i
$356$	−11.7538	+	23.3623i	−0.622950	+	1.23820i
$357$	−1.09329	−	0.397925i	−0.0578630	−	0.0210604i
$358$	7.57994	+	15.1063i	0.400612	+	0.798392i
$359$	−4.23581	−	0.746887i	−0.223557	−	0.0394192i	0.0607473	−	0.998153i	$-0.480652\pi$
$359$	−4.23581	−	0.746887i	−0.223557	−	0.0394192i	−0.284305	+	0.958734i	$0.591763\pi$
$360$	−32.5462	+	8.11709i	−1.71533	+	0.427808i
$361$	14.2469	−	12.5708i	0.749837	−	0.661623i
$362$	−1.09022	+	2.52495i	−0.0573009	+	0.132709i
$363$	31.0330	+	5.47196i	1.62881	+	0.287203i
$364$	−0.0573865	−	0.997504i	−0.00300787	−	0.0522834i
$365$	−7.20925	−	3.50605i	−0.377350	−	0.183515i
$366$	2.83653	−	48.4050i	0.148268	−	2.53017i
$367$	5.83396	−	4.89527i	0.304530	−	0.255531i	−0.477697	−	0.878525i	$-0.658528\pi$
$367$	5.83396	−	4.89527i	0.304530	−	0.255531i	0.782227	+	0.622994i	$0.214084\pi$
$368$	17.6517	−	8.83361i	0.920158	−	0.460484i
$369$	50.4763	+	29.1425i	2.62769	+	1.51710i
$370$	19.6336	+	6.87120i	1.02070	+	0.357217i
$371$	0.170043	+	0.964364i	0.00882821	+	0.0500673i
$372$	3.91080	+	16.5534i	0.202765	+	0.858253i
$373$	6.70564	+	11.6145i	0.347205	+	0.601376i	0.985752	−	0.168207i	$-0.0537976\pi$
$373$	6.70564	+	11.6145i	0.347205	+	0.601376i	−0.638547	+	0.769583i	$0.720464\pi$
$374$	−0.725088	+	0.216796i	−0.0374934	+	0.0112103i
$375$	−32.1936	+	1.23410i	−1.66247	+	0.0637289i
$376$	0.0162718	−	15.2599i	0.000839156	−	0.786968i
$377$	11.1096	−	13.2399i	0.572171	−	0.681887i
$378$	−1.50261	−	0.989046i	−0.0772858	−	0.0508710i
$379$	12.9096			0.663121			0.331560	−	0.943434i	$-0.392425\pi$
$379$	12.9096			0.663121			0.331560	+	0.943434i	$0.392425\pi$
$380$	−10.3099	+	16.5440i	−0.528889	+	0.848691i
$381$	−10.8192			−0.554287
$382$	26.4698	+	17.4230i	1.35431	+	0.891436i
$383$	−12.4196	+	14.8011i	−0.634612	+	0.756301i	−0.983509	−	0.180860i	$-0.942112\pi$
$383$	−12.4196	+	14.8011i	−0.634612	+	0.756301i	0.348897	+	0.937161i	$0.386556\pi$
$384$	1.97659	−	32.5416i	0.100867	−	1.66063i
$385$	0.105563	−	0.0264471i	0.00537997	−	0.00134787i
$386$	−4.57709	+	1.36852i	−0.232968	+	0.0696557i
$387$	−18.8322	−	32.6183i	−0.957292	−	1.65808i
$388$	−27.5988	+	6.52033i	−1.40112	+	0.331019i
$389$	1.76945	+	10.0350i	0.0897145	+	0.508796i	0.996239	+	0.0866438i	$0.0276142\pi$
$389$	1.76945	+	10.0350i	0.0897145	+	0.508796i	−0.906525	+	0.422152i	$0.861275\pi$
$390$	−7.84756	+	22.4234i	−0.397377	+	1.13545i
$391$	−9.00447	−	5.19874i	−0.455376	−	0.262911i
$392$	12.6759	−	15.0738i	0.640228	−	0.761344i
$393$	47.6154	−	39.9541i	2.40188	−	2.01542i
$394$	−1.88881	+	32.2322i	−0.0951568	+	1.62384i
$395$	−7.43925	+	15.2968i	−0.374309	+	0.769665i
$396$	−2.68958	+	0.154732i	−0.135157	+	0.00777557i
$397$	−13.6668	−	2.40983i	−0.685917	−	0.120946i	−0.180181	−	0.983634i	$-0.557668\pi$
$397$	−13.6668	−	2.40983i	−0.685917	−	0.120946i	−0.505737	+	0.862688i	$0.668779\pi$
$398$	10.0367	−	23.2450i	0.503095	−	1.16517i
$399$	−2.36495	+	0.447369i	−0.118395	+	0.0223965i
$400$	5.27228	−	19.2926i	0.263614	−	0.964628i
$401$	19.1441	+	3.37562i	0.956011	+	0.168571i	0.629827	−	0.776736i	$-0.283126\pi$
$401$	19.1441	+	3.37562i	0.956011	+	0.168571i	0.326184	+	0.945306i	$0.394237\pi$
$402$	−3.79154	−	7.55627i	−0.189105	−	0.376872i
$403$	7.23035	+	2.63163i	0.360170	+	0.131091i
$404$	23.7347	+	11.9412i	1.18085	+	0.594096i
$405$	4.03006	+	5.96019i	0.200255	+	0.296164i
$406$	−1.78445	+	0.207929i	−0.0885607	+	0.0103194i
$407$	1.44683	+	0.835330i	0.0717169	+	0.0414058i
$408$	−14.8815	+	8.57069i	−0.736744	+	0.424313i
$409$	−4.27875	+	0.754459i	−0.211571	+	0.0373056i	−0.278429	−	0.960457i	$-0.589814\pi$
$409$	−4.27875	+	0.754459i	−0.211571	+	0.0373056i	0.0668582	+	0.997762i	$0.478702\pi$
$410$	−29.8783	+	17.7485i	−1.47558	+	0.876535i
$411$	−6.86436	−	11.8894i	−0.338594	−	0.586462i
$412$	3.59216	−	30.5446i	0.176973	−	1.50482i
$413$	2.12029	−	0.771722i	0.104333	−	0.0379740i
$414$	−26.9127	−	25.4089i	−1.32269	−	1.24878i
$415$	5.13911	−	4.97408i	0.252269	−	0.244168i
$416$	−11.8140	−	8.82788i	−0.579230	−	0.432822i
$417$	−12.9796			−0.635616
$418$	−1.06058	+	1.15169i	−0.0518748	+	0.0563308i
$419$			28.8611i			1.40996i	0.709229	+	0.704978i	$0.249043\pi$
$419$			28.8611i			1.40996i	−0.709229	+	0.704978i	$0.750957\pi$
$420$	2.19322	−	1.13481i	0.107018	−	0.0553728i
$421$	−2.74345	+	3.26952i	−0.133708	+	0.159347i	−0.828744	−	0.559628i	$-0.810944\pi$
$421$	−2.74345	+	3.26952i	−0.133708	+	0.159347i	0.695036	+	0.718975i	$0.255388\pi$
$422$	−9.91048	−	9.35671i	−0.482434	−	0.455478i
$423$	−26.8884	+	9.78658i	−1.30736	+	0.475840i
$424$	12.5099	+	7.24036i	0.607532	+	0.351623i
$425$	−10.0121	+	3.27829i	−0.485657	+	0.159021i
$426$	−24.4562	−	32.8747i	−1.18491	−	1.59279i
$427$	0.395914	+	2.24534i	0.0191596	+	0.108660i
$428$	16.3084	+	12.1592i	0.788295	+	0.587735i
$429$	−0.954025	+	1.65242i	−0.0460608	+	0.0797796i
$430$	22.4555	−	0.278827i	1.08290	−	0.0134463i
$431$	−8.33990	+	6.99800i	−0.401719	+	0.337082i	−0.821158	−	0.570702i	$-0.806671\pi$
$431$	−8.33990	+	6.99800i	−0.401719	+	0.337082i	0.419439	+	0.907784i	$0.362227\pi$
$432$	−25.4479	+	7.57920i	−1.22436	+	0.364654i
$433$	−6.90980	−	2.51496i	−0.332064	−	0.120861i	0.170607	−	0.985339i	$-0.445427\pi$
$433$	−6.90980	−	2.51496i	−0.332064	−	0.120861i	−0.502671	+	0.864478i	$0.667649\pi$
$434$	−0.358692	−	0.714847i	−0.0172178	−	0.0343138i
$435$	41.0747	+	11.7275i	1.96938	+	0.562290i
$436$	11.7826	−	11.1005i	0.564287	−	0.531619i
$437$	−21.5080	+	0.267242i	−1.02887	+	0.0127839i
$438$	−13.4132	−	5.79154i	−0.640907	−	0.276731i
$439$	−4.74163	+	26.8911i	−0.226306	+	1.28344i	0.633868	+	0.773442i	$0.281466\pi$
$439$	−4.74163	+	26.8911i	−0.226306	+	1.28344i	−0.860173	+	0.510002i	$0.829645\pi$
$440$	0.704058	−	1.44379i	0.0335647	−	0.0688300i
$441$	−34.7035	−	12.6310i	−1.65255	−	0.601478i
$442$	−0.454460	+	7.75528i	−0.0216164	+	0.368881i
$443$	5.94567	−	4.98901i	0.282487	−	0.237035i	−0.490523	−	0.871428i	$-0.663194\pi$
$443$	5.94567	−	4.98901i	0.282487	−	0.237035i	0.773011	+	0.634393i	$0.218750\pi$
$444$	36.3096	+	10.8985i	1.72318	+	0.517220i
$445$	−17.1596	+	23.6746i	−0.813441	+	1.12228i
$446$	4.84498	+	1.15010i	0.229416	+	0.0544588i
$447$	−0.0698349	+	0.0123138i	−0.00330308	+	0.000582422i
$448$	0.262978	+	1.51025i	0.0124245	+	0.0713526i
$449$	20.0039	−	11.5493i	0.944042	−	0.545043i	0.0528169	−	0.998604i	$-0.483180\pi$
$449$	20.0039	−	11.5493i	0.944042	−	0.545043i	0.891225	+	0.453561i	$0.149847\pi$
$450$	−37.3721	+	3.12278i	−1.76174	+	0.147209i
$451$	−2.62282	+	0.954628i	−0.123504	+	0.0449517i
$452$	5.22142	+	12.1283i	0.245595	+	0.570468i
$453$	−2.24165	+	2.67149i	−0.105322	+	0.125518i
$454$	18.6687	+	12.2881i	0.876167	+	0.576710i
$455$	0.115505	−	1.11110i	0.00541496	−	0.0520892i
$456$	−17.4128	+	30.9669i	−0.815429	+	1.45016i
$457$			31.7508i			1.48524i	0.669713	+	0.742620i	$0.266417\pi$
$457$			31.7508i			1.48524i	−0.669713	+	0.742620i	$0.733583\pi$
$458$	12.8081	−	19.4587i	0.598484	−	0.909247i
$459$	10.7145	+	8.99051i	0.500109	+	0.419641i
$460$	21.0635	−	6.58383i	0.982091	−	0.306973i
$461$	−3.26610	+	1.18876i	−0.152117	+	0.0553662i	−0.416957	−	0.908926i	$-0.636903\pi$
$461$	−3.26610	+	1.18876i	−0.152117	+	0.0553662i	0.264839	+	0.964293i	$0.414681\pi$
$462$	0.190020	−	0.0568148i	0.00884055	−	0.00264326i
$463$	18.3179	+	31.7276i	0.851307	+	1.47451i	0.880029	+	0.474919i	$0.157523\pi$
$463$	18.3179	+	31.7276i	0.851307	+	1.47451i	−0.0287227	+	0.999587i	$0.509144\pi$
$464$	−14.6031	+	22.1343i	−0.677931	+	1.02756i
$465$	1.34809	+	18.9689i	0.0625163	+	0.879661i
$466$	−14.1248	−	3.35295i	−0.654320	−	0.155322i
$467$	−12.5471	+	21.7322i	−0.580610	+	1.00565i	0.414797	+	0.909914i	$0.363853\pi$
$467$	−12.5471	+	21.7322i	−0.580610	+	1.00565i	−0.995407	+	0.0957321i	$0.969481\pi$
$468$	−7.95013	+	26.4867i	−0.367495	+	1.22435i
$469$	0.255526	+	0.304523i	0.0117991	+	0.0140616i
$470$	2.75378	−	16.8374i	0.127023	−	0.776649i
$471$	54.0964	+	19.6895i	2.49263	+	0.907243i
$472$	11.4243	−	31.2843i	0.525848	−	1.43998i
$473$	1.77626	+	0.313203i	0.0816726	+	0.0144011i
$474$	−12.2887	+	28.4605i	−0.564437	+	1.30723i
$475$	−14.3438	+	16.4090i	−0.658137	+	0.752898i
$476$	0.587751	−	0.553726i	0.0269395	−	0.0253800i
$477$	4.70639	−	26.6913i	0.215491	−	1.22211i
$478$	−27.6643	+	13.8812i	−1.26533	+	0.634912i
$479$	−0.294696	+	0.809670i	−0.0134650	+	0.0369948i	−0.946243	−	0.323456i	$-0.895155\pi$
$479$	−0.294696	+	0.809670i	−0.0134650	+	0.0369948i	0.932778	+	0.360451i	$0.117377\pi$
$480$	8.01544	−	35.5575i	0.365853	−	1.62297i
$481$	13.1371	−	11.0233i	0.599001	−	0.502621i
$482$	−31.2792	+	3.64474i	−1.42473	+	0.166013i
$483$	2.35976	+	1.36241i	0.107373	+	0.0619917i
$484$	−13.0729	+	17.5339i	−0.594223	+	0.796997i
$485$	−31.6261	+	2.24762i	−1.43607	+	0.102059i
$486$	−8.98346	−	12.0758i	−0.407498	−	0.547771i
$487$	−0.0141149	+	0.00814923i	−0.000639606	+	0.000369277i	−0.500320	−	0.865841i	$-0.666784\pi$
$487$	−0.0141149	+	0.00814923i	−0.000639606	+	0.000369277i	0.499680	+	0.866210i	$0.333451\pi$
$488$	29.1268	+	16.8578i	1.31851	+	0.763118i
$489$	11.3723	+	31.2450i	0.514272	+	1.41295i
$490$	16.6911	−	14.3624i	0.754028	−	0.648828i
$491$	21.8209	−	26.0051i	0.984762	−	1.17359i	−5.49353e−5	−	1.00000i	$-0.500017\pi$
$491$	21.8209	−	26.0051i	0.984762	−	1.17359i	0.984817	−	0.173594i	$-0.0555381\pi$
$492$	−52.9408	+	34.7658i	−2.38676	+	1.56736i
$493$	13.9683			0.629099
$494$	7.38555	+	14.2737i	0.332292	+	0.642203i
$495$	−2.99587	−	0.311438i	−0.134654	−	0.0139981i
$496$	−11.4832	−	2.73882i	−0.515611	−	0.122976i
$497$	1.47590	+	1.23843i	0.0662031	+	0.0555510i
$498$	8.94820	−	9.47779i	0.400979	−	0.424710i
$499$	−2.40577	−	6.60979i	−0.107697	−	0.295895i	0.874125	−	0.485702i	$-0.161436\pi$
$499$	−2.40577	−	6.60979i	−0.107697	−	0.295895i	−0.981821	+	0.189807i	$0.939214\pi$
$500$	9.27712	−	20.3454i	0.414886	−	0.909874i
$501$	−29.9488	−	51.8729i	−1.33802	−	2.31751i
$502$	0.589312	+	0.792171i	0.0263023	+	0.0353563i
$503$	−1.76407	−	10.0045i	−0.0786560	−	0.446080i	−0.998546	−	0.0539040i	$-0.982833\pi$
$503$	−1.76407	−	10.0045i	−0.0786560	−	0.446080i	0.919890	−	0.392176i	$-0.128278\pi$
$504$	2.49093	−	1.43460i	0.110955	−	0.0639021i
$505$	24.0520	+	17.4331i	1.07030	+	0.775762i
$506$	1.76053	−	0.205142i	0.0782651	−	0.00911968i
$507$	−11.4897	−	13.6928i	−0.510273	−	0.608120i
$508$	3.37489	−	6.70806i	0.149736	−	0.297622i
$509$	0.0483110	−	0.132733i	0.00214135	−	0.00588330i	−0.938617	−	0.344960i	$-0.887892\pi$
$509$	0.0483110	−	0.132733i	0.00214135	−	0.00588330i	0.940759	+	0.339077i	$0.110115\pi$
$510$	−17.9593	+	6.79033i	−0.795251	+	0.300681i
$511$	0.676552	+	0.119294i	0.0299289	+	0.00527728i
$512$	19.5596	+	11.3763i	0.864422	+	0.502768i
$513$	28.5557	+	4.67009i	1.26076	+	0.206190i
$514$	−32.8682	−	14.1918i	−1.44975	−	0.625974i
$515$	9.44029	−	33.0639i	0.415989	−	1.45697i
$516$	40.8605	−	2.35071i	1.79878	−	0.103484i
$517$	0.468659	−	1.28763i	0.0206116	−	0.0566299i
$518$	−1.77953	−	0.104280i	−0.0781879	−	0.00458181i
$519$	−10.1132	−	12.0525i	−0.443922	−	0.529046i
$520$	−11.4549	−	11.8602i	−0.502329	−	0.520104i
$521$	10.5164	+	6.07163i	0.460731	+	0.266003i	0.712351	−	0.701823i	$-0.247630\pi$
$521$	10.5164	+	6.07163i	0.460731	+	0.266003i	−0.251621	+	0.967826i	$0.580964\pi$
$522$	48.3790	+	11.4842i	2.11749	+	0.502650i
$523$	12.8118	−	2.25907i	0.560223	−	0.0987824i	0.113636	−	0.993522i	$-0.463750\pi$
$523$	12.8118	−	2.25907i	0.560223	−	0.0987824i	0.446587	+	0.894740i	$0.352639\pi$
$524$	9.91914	+	41.9851i	0.433320	+	1.83413i
$525$	2.62382	−	0.859126i	0.114513	−	0.0374953i
$526$	4.89073	−	1.46230i	0.213246	−	0.0637591i
$527$	2.12686	+	5.84349i	0.0926474	+	0.254547i
$528$	1.16333	−	2.68640i	0.0506276	−	0.116911i
$529$	1.03487	+	0.868356i	0.0449942	+	0.0377546i
$530$	12.5074	+	10.2330i	0.543286	+	0.444494i
$531$	−62.4507			−2.71013
$532$	0.460332	−	1.60584i	0.0199579	−	0.0696222i
$533$			28.6511i			1.24101i
$534$	−29.2982	+	44.5113i	−1.26786	+	1.92619i
$535$	15.8174	+	16.3422i	0.683847	+	0.706536i
$536$	5.86768	+	0.00625680i	0.253445	+	0.000270253i
$537$	11.7786	+	32.3613i	0.508282	+	1.39649i
$538$	−0.609326	−	2.03793i	−0.0262699	−	0.0878613i
$539$	1.53159	−	0.884266i	0.0659704	−	0.0380880i
$540$	−29.4423	+	3.80178i	−1.26699	+	0.163603i
$541$	6.57080	+	37.2649i	0.282501	+	1.60214i	0.714078	+	0.700066i	$0.246846\pi$
$541$	6.57080	+	37.2649i	0.282501	+	1.60214i	−0.431577	+	0.902076i	$0.642043\pi$
$542$	−23.9075	−	5.67515i	−1.02691	−	0.243769i
$543$	−2.80198	+	4.85316i	−0.120244	+	0.208269i
$544$	−0.671889	−	11.9002i	−0.0288070	−	0.510216i
$545$	14.9931	−	10.1378i	0.642232	−	0.434254i
$546$	0.119098	−	2.03239i	0.00509692	−	0.0869782i
$547$	9.91750	−	27.2481i	0.424042	−	1.16504i	−0.525333	−	0.850897i	$-0.676059\pi$
$547$	9.91750	−	27.2481i	0.424042	−	1.16504i	0.949374	−	0.314148i	$-0.101719\pi$
$548$	9.51281	−	0.547273i	0.406367	−	0.0233783i
$549$	10.9579	−	62.1456i	0.467674	−	2.65231i
$550$	1.03582	−	1.46709i	0.0441676	−	0.0625570i
$551$	24.8439	−	14.7582i	1.05838	−	0.628720i
$552$	37.8086	−	13.7156i	1.60924	−	0.583774i
$553$	0.253122	−	1.43553i	0.0107639	−	0.0610449i
$554$	18.6395	−	9.35280i	0.791916	−	0.397363i
$555$	38.1161	+	18.5369i	1.61794	+	0.786847i
$556$	4.04879	−	8.04753i	0.171707	−	0.341291i
$557$	0.188721	+	0.224908i	0.00799635	+	0.00952968i	0.770028	−	0.638010i	$-0.220242\pi$
$557$	0.188721	+	0.224908i	0.00799635	+	0.00952968i	−0.762031	+	0.647540i	$0.775798\pi$
$558$	2.56205	+	21.9875i	0.108460	+	0.930807i
$559$	9.25729	−	16.0341i	0.391541	−	0.678170i
$560$	0.0194524	+	1.71381i	0.000822015	+	0.0724216i
$561$	−1.51864	+	0.267777i	−0.0641170	+	0.0113056i
$562$	0.602115	+	0.809381i	0.0253987	+	0.0341417i
$563$	−8.23177	+	4.75261i	−0.346928	+	0.200299i	−0.663331	−	0.748326i	$-0.730858\pi$
$563$	−8.23177	+	4.75261i	−0.346928	+	0.200299i	0.316404	+	0.948625i	$0.397525\pi$
$564$	3.63169	−	30.8807i	0.152922	−	1.30031i
$565$	3.58779	+	14.3205i	0.150939	+	0.602468i
$566$	−0.567274	−	0.535576i	−0.0238443	−	0.0225119i
$567$	−0.472316	−	0.396320i	−0.0198354	−	0.0166439i
$568$	28.0114	−	4.90838i	1.17533	−	0.205951i
$569$		−	35.3359i		−	1.48136i	−0.671860	−	0.740678i	$-0.734504\pi$
$569$		−	35.3359i		−	1.48136i	0.671860	−	0.740678i	$-0.265496\pi$
$570$	−24.7680	+	31.0522i	−1.03742	+	1.30063i
$571$		−	22.5979i		−	0.945693i	−0.881145	−	0.472846i	$-0.843227\pi$
$571$		−	22.5979i		−	0.945693i	0.881145	−	0.472846i	$-0.156773\pi$
$572$	−0.726927	−	1.10695i	−0.0303944	−	0.0462840i
$573$	49.4636	+	41.5049i	2.06637	+	1.73389i
$574$	2.04449	−	2.16549i	0.0853352	−	0.0903857i
$575$	24.4253	−	3.48937i	1.01861	−	0.145517i
$576$	7.45682	−	41.7687i	0.310701	−	1.74036i
$577$	−17.8228	+	10.2900i	−0.741973	+	0.428378i	−0.822786	−	0.568351i	$-0.807582\pi$
$577$	−17.8228	+	10.2900i	−0.741973	+	0.428378i	0.0808134	+	0.996729i	$0.474248\pi$
$578$	14.2520	−	10.6023i	0.592805	−	0.441000i
$579$	−9.58634	+	1.69033i	−0.398395	+	0.0702477i
$580$	−20.0837	+	21.8086i	−0.833932	+	0.905552i
$581$	−0.306451	+	0.530789i	−0.0127137	+	0.0220208i
$582$	−57.3952	+	6.68786i	−2.37911	+	0.277221i
$583$	0.834278	+	0.994254i	0.0345523	+	0.0411778i
$584$	7.77485	−	6.50976i	0.321726	−	0.269376i
$585$	−13.5221	+	27.8045i	−0.559070	+	1.14958i
$586$	−1.61010	−	3.20882i	−0.0665127	−	0.132555i
$587$	1.22130	−	6.92636i	0.0504086	−	0.285881i	−0.949175	−	0.314750i	$-0.898079\pi$
$587$	1.22130	−	6.92636i	0.0504086	−	0.285881i	0.999583	+	0.0288686i	$0.00919043\pi$
$588$	29.2097	−	27.5187i	1.20459	−	1.13485i
$589$	9.95677	+	8.14608i	0.410262	+	0.335653i
$590$	18.2162	−	32.4761i	0.749950	−	1.33702i
$591$	−11.4242	+	64.7896i	−0.469927	+	2.66509i
$592$	−18.0834	+	19.1127i	−0.743222	+	0.785529i
$593$	−9.24887	+	25.4111i	−0.379806	+	1.04351i	0.591631	+	0.806209i	$0.298484\pi$
$593$	−9.24887	+	25.4111i	−0.379806	+	1.04351i	−0.971437	+	0.237298i	$0.923738\pi$
$594$	−2.38022	−	0.139481i	−0.0976615	−	0.00572297i
$595$	0.747896	−	0.505699i	0.0306607	−	0.0207317i
$596$	0.0141492	−	0.0471395i	0.000579573	−	0.00193091i
$597$	25.7953	−	44.6787i	1.05573	−	1.82858i
$598$	4.20213	−	17.7021i	0.171838	−	0.723895i
$599$	−7.08750	−	40.1952i	−0.289587	−	1.64233i	−0.688423	−	0.725310i	$-0.741697\pi$
$599$	−7.08750	−	40.1952i	−0.289587	−	1.64233i	0.398835	−	0.917023i	$-0.369414\pi$
$600$	15.2204	−	37.8030i	0.621370	−	1.54330i
$601$	0.850544	−	0.491062i	0.0346944	−	0.0200308i	−0.482552	−	0.875867i	$-0.660290\pi$
$601$	0.850544	−	0.491062i	0.0346944	−	0.0200308i	0.517247	+	0.855836i	$0.326957\pi$
$602$	−1.84384	+	0.551296i	−0.0751494	+	0.0224692i
$603$	−3.76311	−	10.3391i	−0.153246	−	0.421039i
$604$	−0.957111	−	2.22318i	−0.0389443	−	0.0904598i
$605$	−17.5704	+	17.0061i	−0.714336	+	0.691397i
$606$	45.2208	+	29.7652i	1.83697	+	1.20913i
$607$			37.2092i			1.51027i	0.655567	+	0.755137i	$0.272430\pi$
$607$			37.2092i			1.51027i	−0.655567	+	0.755137i	$0.727570\pi$
$608$	−13.7682	−	20.4557i	−0.558373	−	0.829590i
$609$	−3.66059			−0.148335
$610$	29.1211	+	23.8257i	1.17908	+	0.964673i
$611$	−10.7750	−	9.04129i	−0.435910	−	0.365772i
$612$	−20.5282	+	8.83771i	−0.829804	+	0.357243i
$613$	−4.30413	−	11.8255i	−0.173842	−	0.477628i	0.821919	−	0.569605i	$-0.192904\pi$
$613$	−4.30413	−	11.8255i	−0.173842	−	0.477628i	−0.995761	+	0.0919768i	$0.970681\pi$
$614$	−6.55542	−	21.9250i	−0.264555	−	0.884820i
$615$	−64.6566	+	28.8750i	−2.60721	+	1.16435i
$616$	−0.0240479	+	0.135537i	−0.000968918	+	0.00546095i
$617$	−13.0886	+	2.30787i	−0.526927	+	0.0929115i	−0.430782	−	0.902456i	$-0.641762\pi$
$617$	−13.0886	+	2.30787i	−0.526927	+	0.0929115i	−0.0961449	+	0.995367i	$0.530651\pi$
$618$	14.4736	−	60.9722i	0.582212	−	2.45266i
$619$	−3.50644	−	2.02445i	−0.140936	−	0.0813694i	0.427874	−	0.903838i	$-0.359263\pi$
$619$	−3.50644	−	2.02445i	−0.140936	−	0.0813694i	−0.568810	+	0.822469i	$0.692596\pi$
$620$	−12.1814	−	5.08120i	−0.489218	−	0.204066i
$621$	−21.0558	−	25.0934i	−0.844941	−	1.00696i
$622$	−2.13234	+	36.3881i	−0.0854992	+	1.45903i
$623$	0.856996	−	2.35458i	0.0343348	−	0.0943342i
$624$	−21.8286	−	20.6529i	−0.873842	−	0.826779i
$625$	13.8855	−	20.7893i	0.555420	−	0.831570i
$626$	14.0837	−	32.6177i	0.562897	−	1.30367i
$627$	−2.41812	+	2.08079i	−0.0965706	+	0.0830986i
$628$	−29.0822	+	27.3986i	−1.16050	+	1.09332i
$629$	13.6493	+	2.40674i	0.544233	+	0.0959630i
$630$	3.00610	−	1.13659i	0.119766	−	0.0452830i
$631$	−0.233424	+	0.641327i	−0.00929246	+	0.0255308i	−0.944252	−	0.329223i	$-0.893213\pi$
$631$	−0.233424	+	0.641327i	−0.00929246	+	0.0255308i	0.934960	+	0.354754i	$0.115435\pi$
$632$	−13.8126	−	16.4969i	−0.549435	−	0.656211i
$633$	−17.8513	−	21.2743i	−0.709524	−	0.845578i
$634$	−1.89540	−	16.2663i	−0.0752758	−	0.646017i
$635$	4.92705	−	6.79773i	0.195524	−	0.269760i
$636$	23.6113	+	17.6040i	0.936248	+	0.698046i
$637$	−3.15240	−	17.8781i	−0.124903	−	0.708358i
$638$	−1.91048	+	1.42124i	−0.0756366	+	0.0562676i
$639$	−26.6625	−	46.1808i	−1.05475	−	1.82688i
$640$	19.5458	+	16.0612i	0.772614	+	0.634876i
$641$	5.28242	+	14.5133i	0.208643	+	0.573242i	0.999235	−	0.0391011i	$-0.0124494\pi$
$641$	5.28242	+	14.5133i	0.208643	+	0.573242i	−0.790592	+	0.612343i	$0.790227\pi$
$642$	30.1391	+	28.4550i	1.18950	+	1.12303i
$643$	−21.0675	−	17.6777i	−0.830821	−	0.697141i	0.124659	−	0.992200i	$-0.460216\pi$
$643$	−21.0675	−	17.6777i	−0.830821	−	0.697141i	−0.955479	+	0.295058i	$0.904661\pi$
$644$	−1.58080	+	1.03810i	−0.0622921	+	0.0409067i
$645$	45.5137	+	4.73140i	1.79210	+	0.186299i
$646$	−5.00020	+	11.9875i	−0.196730	+	0.471644i
$647$	15.3177			0.602202			0.301101	−	0.953592i	$-0.402646\pi$
$647$	15.3177			0.602202			0.301101	+	0.953592i	$0.402646\pi$
$648$	−8.96420	+	1.57078i	−0.352147	+	0.0617059i
$649$	1.92234	−	2.29096i	0.0754585	−	0.0899279i
$650$	−10.5149	−	15.1422i	−0.412427	−	0.593924i
$651$	−0.557375	−	1.53138i	−0.0218453	−	0.0600193i
$652$	−22.9197	−	2.69544i	−0.897604	−	0.105562i
$653$	21.1784	−	12.2274i	0.828777	−	0.478494i	−0.0246570	−	0.999696i	$-0.507849\pi$
$653$	21.1784	−	12.2274i	0.828777	−	0.478494i	0.853434	+	0.521202i	$0.174516\pi$
$654$	26.4648	−	19.6877i	1.03486	−	0.769851i
$655$	3.41923	+	48.1117i	0.133600	+	1.87988i
$656$	−5.04120	−	43.6686i	−0.196826	−	1.70497i
$657$	−16.4668	−	9.50710i	−0.642431	−	0.370907i
$658$	0.169219	+	1.45224i	0.00659684	+	0.0566141i
$659$	−21.7171	+	18.2228i	−0.845977	+	0.709859i	−0.958900	−	0.283745i	$-0.908423\pi$
$659$	−21.7171	+	18.2228i	−0.845977	+	0.709859i	0.112923	+	0.993604i	$0.463979\pi$
$660$	1.76544	−	2.75606i	0.0687197	−	0.107279i
$661$	−9.40873	+	25.8503i	−0.365957	+	1.00546i	0.610927	+	0.791687i	$0.290797\pi$
$661$	−9.40873	+	25.8503i	−0.365957	+	1.00546i	−0.976884	+	0.213772i	$0.931425\pi$
$662$	8.31728	+	16.5758i	0.323260	+	0.644235i
$663$	−2.74872	+	15.5888i	−0.106752	+	0.605418i
$664$	3.08509	+	8.50443i	0.119725	+	0.330036i
$665$	0.795907	−	1.68962i	0.0308639	−	0.0655208i
$666$	45.2956	+	19.5577i	1.75517	+	0.757845i
$667$	−32.2167	−	5.68068i	−1.24744	−	0.219957i
$668$	41.5039	−	2.38772i	1.60583	−	0.0923837i
$669$	9.53455	+	3.47029i	0.368627	+	0.134169i
$670$	6.47425	+	1.05888i	0.250122	+	0.0409080i
$671$	1.94246	+	2.31493i	0.0749878	+	0.0893670i
$672$	0.176079	+	3.11862i	0.00679238	+	0.120304i
$673$	−10.0526	+	17.4115i	−0.387497	+	0.671165i	−0.992112	−	0.125353i	$-0.959994\pi$
$673$	−10.0526	+	17.4115i	−0.387497	+	0.671165i	0.604615	+	0.796518i	$0.293327\pi$
$674$	−1.76295	+	7.42669i	−0.0679062	+	0.286066i
$675$	−33.1731	−	1.08296i	−1.27683	−	0.0416833i
$676$	12.0737	−	2.85246i	0.464374	−	0.109710i
$677$	−13.4615	−	23.3160i	−0.517369	−	0.896109i	−0.999797	−	0.0201729i	$-0.993578\pi$
$677$	−13.4615	−	23.3160i	−0.517369	−	0.896109i	0.482428	−	0.875936i	$-0.339755\pi$
$678$	7.70743	+	25.7779i	0.296002	+	0.989996i
$679$	2.55321	−	0.929291i	0.0979830	−	0.0356629i
$680$	1.39202	−	13.2531i	0.0533816	−	0.508233i
$681$	34.8858	+	29.2727i	1.33683	+	1.12173i
$682$	−0.885460	−	0.582828i	−0.0339060	−	0.0223176i
$683$			39.9412i			1.52831i	0.645034	+	0.764154i	$0.276843\pi$
$683$			39.9412i			1.52831i	−0.645034	+	0.764154i	$0.723157\pi$
$684$	−27.1739	+	37.4078i	−1.03902	+	1.43032i
$685$	10.5961	+	1.10153i	0.404857	+	0.0420872i
$686$	−2.08045	+	3.16072i	−0.0794319	+	0.120677i
$687$	30.5114	−	36.3621i	1.16408	−	1.38730i
$688$	−11.2883	+	26.0672i	−0.430362	+	0.993803i
$689$	12.5195	−	4.55673i	0.476955	−	0.173597i
$690$	44.1833	−	8.35762i	1.68203	−	0.318169i
$691$	32.0313	−	18.4933i	1.21853	−	0.703517i	0.253924	−	0.967224i	$-0.418279\pi$
$691$	32.0313	−	18.4933i	1.21853	−	0.703517i	0.964603	+	0.263707i	$0.0849453\pi$
$692$	10.6273	−	2.51075i	0.403991	−	0.0954443i
$693$	0.254196	−	0.0448216i	0.00965611	−	0.00170263i
$694$	−8.12735	+	34.2377i	−0.308510	+	1.29965i
$695$	5.91089	−	8.15511i	0.224213	−	0.309341i
$696$	−34.7752	+	41.3539i	−1.31815	+	1.56751i
$697$	−17.7381	+	14.8840i	−0.671879	+	0.563774i
$698$	12.3743	+	0.725132i	0.468373	+	0.0274467i
$699$	−27.7966	−	10.1171i	−1.05136	−	0.382665i
$700$	−0.285789	+	1.89479i	−0.0108018	+	0.0716162i
$701$	−3.84939	+	21.8310i	−0.145389	+	0.824544i	0.821664	+	0.569972i	$0.193046\pi$
$701$	−3.84939	+	21.8310i	−0.145389	+	0.824544i	−0.967054	+	0.254572i	$0.918065\pi$
$702$	−9.70196	+	22.4697i	−0.366177	+	0.848064i
$703$	26.8194	−	10.1406i	1.01151	−	0.382459i
$704$	1.30272	+	1.55926i	0.0490980	+	0.0587668i
$705$	9.54418	−	33.4278i	0.359455	−	1.25896i
$706$	33.4629	−	16.7908i	1.25939	−	0.631930i
$707$	−2.39211	−	0.870658i	−0.0899647	−	0.0327445i
$708$	30.4996	−	60.6222i	1.14625	−	2.27832i
$709$	−13.7969	+	11.5770i	−0.518154	+	0.434783i	−0.863988	−	0.503513i	$-0.832041\pi$
$709$	−13.7969	+	11.5770i	−0.518154	+	0.434783i	0.345833	+	0.938296i	$0.387596\pi$
$710$	31.7924	−	0.394763i	1.19315	−	0.0148152i
$711$	−20.1724	+	34.9397i	−0.756526	+	1.31034i
$712$	−18.4584	−	32.0498i	−0.691758	−	1.20112i
$713$	−2.52898	−	14.3425i	−0.0947109	−	0.537132i
$714$	1.32014	−	0.982079i	0.0494050	−	0.0367534i
$715$	−0.603755	−	1.35192i	−0.0225792	−	0.0505589i
$716$	−23.7385	−	2.79174i	−0.887150	−	0.104332i
$717$	−59.2635	+	21.5702i	−2.21324	+	0.805553i
$718$	4.17581	−	4.42295i	0.155840	−	0.165063i
$719$	11.8451	−	14.1164i	0.441746	−	0.526453i	−0.498526	−	0.866874i	$-0.666125\pi$
$719$	11.8451	−	14.1164i	0.441746	−	0.526453i	0.940273	+	0.340422i	$0.110570\pi$
$720$	15.7175	−	44.7576i	0.585756	−	1.66802i
$721$			2.94667i			0.109740i
$722$	3.77212	+	26.6040i	0.140384	+	0.990097i
$723$	−64.1656			−2.38635
$724$	−2.13499	−	3.25112i	−0.0793462	−	0.120827i
$725$	−26.0736	+	20.4665i	−0.968351	+	0.760108i
$726$	−30.5934	+	32.4041i	−1.13543	+	1.20263i
$727$	−23.1678	+	8.43240i	−0.859247	+	0.312740i	−0.733805	−	0.679360i	$-0.762257\pi$
$727$	−23.1678	+	8.43240i	−0.859247	+	0.312740i	−0.125443	+	0.992101i	$0.540035\pi$
$728$	1.22295	+	0.707812i	0.0453257	+	0.0262333i
$729$	−20.1602	−	34.9186i	−0.746676	−	1.29328i
$730$	9.74714	−	5.79005i	0.360758	−	0.214300i
$731$	14.7360	−	2.59835i	0.545029	−	0.0961033i
$732$	54.9744	+	40.9877i	2.03191	+	1.51495i
$733$	−27.5618	−	15.9128i	−1.01802	−	0.587754i	−0.104490	−	0.994526i	$-0.533321\pi$
$733$	−27.5618	−	15.9128i	−1.01802	−	0.587754i	−0.913530	+	0.406772i	$0.866654\pi$
$734$	1.24654	+	10.6978i	0.0460107	+	0.394864i
$735$	37.1684	−	25.1319i	1.37098	−	0.927004i
$736$	−3.28997	+	27.7201i	−0.121270	+	1.02178i
$737$	0.495115	+	0.180207i	0.0182378	+	0.00663802i
$738$	−73.6730	+	36.9672i	−2.71194	+	1.36078i
$739$	−18.4313	−	3.24994i	−0.678008	−	0.119551i	−0.175968	−	0.984396i	$-0.556306\pi$
$739$	−18.4313	−	3.24994i	−0.678008	−	0.119551i	−0.502039	+	0.864845i	$0.667417\pi$
$740$	−23.3828	+	17.8501i	−0.859568	+	0.656184i
$741$	11.5815	+	30.6303i	0.425457	+	1.12523i
$742$	−1.27140	−	0.548965i	−0.0466746	−	0.0201531i
$743$	−22.5077	−	3.96871i	−0.825727	−	0.145598i	−0.255212	−	0.966885i	$-0.582145\pi$
$743$	−22.5077	−	3.96871i	−0.825727	−	0.145598i	−0.570515	+	0.821287i	$0.693256\pi$
$744$	−22.5950	−	8.25121i	−0.828374	−	0.302504i
$745$	0.0240658	−	0.0494849i	0.000881704	−	0.00181299i
$746$	−18.9339	−	1.10953i	−0.693220	−	0.0406227i
$747$	12.9949	−	10.9040i	0.475459	−	0.398958i
$748$	0.307690	−	1.02510i	0.0112502	−	0.0374814i
$749$	−1.68789	−	0.974506i	−0.0616743	−	0.0356077i
$750$	23.5741	−	38.9893i	0.860805	−	1.42369i
$751$	3.41796	+	19.3842i	0.124723	+	0.707341i	0.981472	+	0.191606i	$0.0613697\pi$
$751$	3.41796	+	19.3842i	0.124723	+	0.707341i	−0.856749	+	0.515734i	$0.827519\pi$
$752$	18.0136	+	11.8844i	0.656887	+	0.433380i
$753$	1.00589	+	1.74226i	0.0366568	+	0.0634915i
$754$	7.00184	+	23.4181i	0.254992	+	0.852836i
$755$	−0.657659	−	2.62502i	−0.0239347	−	0.0955341i
$756$	2.33668	−	1.00598i	0.0849844	−	0.0365871i
$757$	2.12976	−	2.53815i	0.0774075	−	0.0922506i	−0.725951	−	0.687747i	$-0.758600\pi$
$757$	2.12976	−	2.53815i	0.0774075	−	0.0922506i	0.803358	+	0.595496i	$0.203044\pi$
$758$	−10.0378	+	15.2499i	−0.364588	+	0.553900i
$759$	3.61153			0.131090
$760$	−11.5267	−	25.0426i	−0.418119	−	0.908392i
$761$	−44.5713			−1.61571			−0.807854	−	0.589383i	$-0.799371\pi$
$761$	−44.5713			−1.61571			−0.807854	+	0.589383i	$0.799371\pi$
$762$	8.41243	−	12.7806i	0.304750	−	0.462992i
$763$	−0.996958	+	1.18813i	−0.0360923	+	0.0430131i
$764$	−41.1629	+	17.7212i	−1.48922	+	0.641131i
$765$	−24.2387	+	6.07264i	−0.876352	+	0.219557i
$766$	−7.82750	−	26.1796i	−0.282819	−	0.945906i
$767$	−15.3494	−	26.5859i	−0.554234	−	0.959962i
$768$	36.9040	+	27.6374i	1.33166	+	0.997280i
$769$	−2.67500	−	15.1707i	−0.0964628	−	0.547068i	−0.994289	−	0.106718i	$-0.965966\pi$
$769$	−2.67500	−	15.1707i	−0.0964628	−	0.547068i	0.897827	−	0.440349i	$-0.145145\pi$
$770$	−0.0508379	+	0.145263i	−0.00183207	+	0.00523491i
$771$	−63.1753	−	36.4743i	−2.27520	−	1.31359i
$772$	1.94228	−	6.47091i	0.0699041	−	0.232893i
$773$	4.49806	−	3.77432i	0.161784	−	0.135753i	−0.558302	−	0.829638i	$-0.688547\pi$
$773$	4.49806	−	3.77432i	0.161784	−	0.135753i	0.720086	+	0.693885i	$0.244102\pi$
$774$	53.1742	+	3.11601i	1.91131	+	0.112003i
$775$	−12.5321	−	7.79136i	−0.450165	−	0.279874i
$776$	13.7569	−	37.6718i	0.493845	−	1.35234i
$777$	−3.57700	−	0.630722i	−0.128324	−	0.0226270i
$778$	−13.2300	−	5.71245i	−0.474319	−	0.204801i
$779$	−15.8232	+	45.2139i	−0.566924	+	1.61996i
$780$	−20.3866	−	26.7053i	−0.729956	−	0.956205i
$781$	2.51482	+	0.443431i	0.0899875	+	0.0158672i
$782$	13.1425	−	6.59458i	0.469976	−	0.235822i
$783$	41.3528	+	15.0512i	1.47783	+	0.537886i
$784$	7.95042	+	26.6943i	0.283944	+	0.953369i
$785$	−37.0062	+	25.0222i	−1.32081	+	0.893080i
$786$	10.1740	+	87.3132i	0.362894	+	3.11436i
$787$	−31.7249	−	18.3164i	−1.13087	−	0.652909i	−0.186717	−	0.982414i	$-0.559785\pi$
$787$	−31.7249	−	18.3164i	−1.13087	−	0.652909i	−0.944154	+	0.329505i	$0.893118\pi$
$788$	−36.6067	−	27.2932i	−1.30406	−	0.972279i
$789$	10.2432	−	1.80616i	0.364669	−	0.0643010i
$790$	−12.2855	−	20.6818i	−0.437098	−	0.735824i
$791$	−0.632568	−	1.09564i	−0.0224915	−	0.0389565i
$792$	1.90848	−	3.29747i	0.0678150	−	0.117170i
$793$	29.1493	−	10.6095i	1.03512	−	0.376754i
$794$	13.4732	−	14.2706i	0.478147	−	0.506445i
$795$	22.9005	+	23.6603i	0.812197	+	0.839145i
$796$	19.6549	+	29.9302i	0.696650	+	1.06085i
$797$	19.1943			0.679899			0.339949	−	0.940444i	$-0.389590\pi$
$797$	19.1943			0.679899			0.339949	+	0.940444i	$0.389590\pi$
$798$	1.31038	−	3.14152i	0.0463869	−	0.111209i
$799$		−	11.3678i		−	0.402163i
$800$	18.6905	+	21.2288i	0.660810	+	0.750553i
$801$	−44.5783	+	53.1263i	−1.57510	+	1.87713i
$802$	−18.8729	+	19.9899i	−0.666426	+	0.705868i
$803$	0.855637	−	0.311426i	0.0301948	−	0.0109900i
$804$	11.8742	+	1.39645i	0.418769	+	0.0492489i
$805$	−1.93063	+	0.862199i	−0.0680456	+	0.0303885i
$806$	−8.73061	+	6.49488i	−0.307523	+	0.228772i
$807$	−0.752612	−	4.26827i	−0.0264932	−	0.150250i
$808$	−32.5607	+	18.7526i	−1.14548	+	0.659716i
$809$	−6.42832	+	11.1342i	−0.226008	+	0.391457i	−0.956621	−	0.291334i	$-0.905901\pi$
$809$	−6.42832	+	11.1342i	−0.226008	+	0.391457i	0.730614	+	0.682791i	$0.239234\pi$
$810$	−10.1742	+	0.126332i	−0.357485	+	0.00443885i
$811$	−37.5339	+	31.4947i	−1.31799	+	1.10593i	−0.331267	+	0.943537i	$0.607476\pi$
$811$	−37.5339	+	31.4947i	−1.31799	+	1.10593i	−0.986726	+	0.162391i	$0.948079\pi$
$812$	1.14186	−	2.26961i	0.0400715	−	0.0796477i
$813$	−47.0481	−	17.1241i	−1.65005	−	0.600569i
$814$	−2.11173	+	1.05961i	−0.0740163	+	0.0371394i
$815$	−24.8101	−	7.08370i	−0.869061	−	0.248131i
$816$	1.44660	−	24.2433i	0.0506412	−	0.848686i
$817$	23.4640	−	20.1907i	0.820902	−	0.706383i
$818$	2.43568	−	5.64103i	0.0851616	−	0.197234i
$819$	0.460093	−	2.60932i	0.0160770	−	0.0911769i
$820$	2.26571	−	49.0949i	0.0791220	−	1.71447i
$821$	10.2289	+	3.72300i	0.356990	+	0.129934i	0.514288	−	0.857618i	$-0.328056\pi$
$821$	10.2289	+	3.72300i	0.356990	+	0.129934i	−0.157298	+	0.987551i	$0.550278\pi$
$822$	19.3821	+	1.13579i	0.676028	+	0.0396153i
$823$	11.8165	−	9.91522i	0.411897	−	0.345623i	−0.413173	−	0.910652i	$-0.635580\pi$
$823$	11.8165	−	9.91522i	0.411897	−	0.345623i	0.825071	+	0.565030i	$0.191135\pi$
$824$	33.2887	+	27.9931i	1.15967	+	0.975185i
$825$	2.44239	−	2.72498i	0.0850332	−	0.0948716i
$826$	−0.736994	+	3.10471i	−0.0256433	+	0.108027i
$827$	33.9340	−	5.98348i	1.18000	−	0.208066i	0.450965	−	0.892542i	$-0.351080\pi$
$827$	33.9340	−	5.98348i	1.18000	−	0.208066i	0.729036	+	0.684476i	$0.239969\pi$
$828$	50.9409	−	12.0350i	1.77032	−	0.418245i
$829$	24.6183	−	14.2134i	0.855027	−	0.493650i	−0.00731663	−	0.999973i	$-0.502329\pi$
$829$	24.6183	−	14.2134i	0.855027	−	0.493650i	0.862344	+	0.506323i	$0.168996\pi$
$830$	1.87991	+	9.93830i	0.0652526	+	0.344964i
$831$	39.9303	−	14.5334i	1.38517	−	0.504159i
$832$	19.6141	−	7.09162i	0.679997	−	0.245858i
$833$	9.43086	−	11.2393i	0.326760	−	0.389417i
$834$	10.0922	−	15.3326i	0.349465	−	0.530925i
$835$	46.2303	+	4.80590i	1.59987	+	0.166315i
$836$	−0.535818	−	2.14833i	−0.0185316	−	0.0743016i
$837$			19.5913i			0.677175i
$838$	−34.0931	−	22.4407i	−1.17773	−	0.775202i
$839$	31.7996	+	26.6830i	1.09784	+	0.921200i	0.997278	−	0.0737304i	$-0.0234904\pi$
$839$	31.7996	+	26.6830i	1.09784	+	0.921200i	0.100565	+	0.994930i	$0.467935\pi$
$840$	−0.364800	+	3.47318i	−0.0125868	+	0.119836i
$841$	14.0470	−	5.11271i	0.484381	−	0.176300i
$842$	−1.72907	−	5.78299i	−0.0595878	−	0.199295i
$843$	1.02775	+	1.78011i	0.0353975	+	0.0613102i
$844$	18.7587	−	4.43182i	0.645702	−	0.152550i
$845$	13.8356	−	0.983273i	0.475957	−	0.0338256i
$846$	9.34619	−	39.3723i	0.321328	−	1.35365i
$847$	1.04774	−	1.81474i	0.0360008	−	0.0623552i
$848$	−18.2799	+	9.14797i	−0.627733	+	0.314143i
$849$	−1.02180	−	1.21774i	−0.0350682	−	0.0417926i
$850$	3.91224	−	14.3761i	0.134189	−	0.493096i
$851$	−30.5023	−	11.1019i	−1.04561	−	0.380569i
$852$	57.8500	−	3.32812i	1.98191	−	0.114019i
$853$	4.87147	+	0.858972i	0.166796	+	0.0294106i	0.256422	−	0.966565i	$-0.417456\pi$
$853$	4.87147	+	0.858972i	0.166796	+	0.0294106i	−0.0896264	+	0.995975i	$0.528567\pi$
$854$	−2.96022	−	1.27816i	−0.101297	−	0.0437378i
$855$	−36.6948	+	36.4102i	−1.25493	+	1.24520i
$856$	−27.0438	+	9.81051i	−0.924340	+	0.335316i
$857$	−1.41770	+	8.04016i	−0.0484276	+	0.274647i	−0.999400	−	0.0346284i	$-0.988975\pi$
$857$	−1.41770	+	8.04016i	−0.0484276	+	0.274647i	0.950973	+	0.309275i	$0.100086\pi$
$858$	−1.21018	−	2.41180i	−0.0413148	−	0.0823375i
$859$	−4.77963	+	13.1319i	−0.163079	+	0.448056i	−0.994137	−	0.108130i	$-0.965514\pi$
$859$	−4.77963	+	13.1319i	−0.163079	+	0.448056i	0.831058	+	0.556186i	$0.187736\pi$
$860$	−17.1308	+	26.7431i	−0.584154	+	0.911932i
$861$	4.64854	−	3.90059i	0.158422	−	0.132932i
$862$	−1.78199	−	15.2930i	−0.0606947	−	0.520882i
$863$	−10.4797	−	6.05048i	−0.356735	−	0.205961i	0.310913	−	0.950438i	$-0.399365\pi$
$863$	−10.4797	−	6.05048i	−0.356735	−	0.205961i	−0.667647	+	0.744478i	$0.732699\pi$
$864$	10.8337	−	35.9543i	0.368569	−	1.22319i
$865$	12.1781	−	0.865481i	0.414068	−	0.0294272i
$866$	8.34355	−	6.20693i	0.283525	−	0.210920i
$867$	31.3451	−	18.0971i	1.06454	−	0.614610i
$868$	1.12333	+	0.132108i	0.0381285	+	0.00448405i
$869$	−0.660793	−	1.81551i	−0.0224159	−	0.0615871i
$870$	−45.7908	+	39.4021i	−1.55245	+	1.33586i
$871$	3.47653	−	4.14317i	0.117798	−	0.140386i
$872$	3.95135	+	22.5498i	0.133809	+	0.763632i
$873$	−75.2018			−2.54520
$874$	16.4077	−	25.6149i	0.555000	−	0.866436i
$875$	−0.655089	+	2.03979i	−0.0221460	+	0.0689574i
$876$	17.2708	−	11.3416i	0.583526	−	0.383197i
$877$	14.3653	+	12.0539i	0.485080	+	0.407031i	0.852259	−	0.523120i	$-0.175232\pi$
$877$	14.3653	+	12.0539i	0.485080	+	0.407031i	−0.367179	+	0.930150i	$0.619676\pi$
$878$	−28.0792	−	26.5102i	−0.947626	−	0.894676i
$879$	−2.50195	−	6.87406i	−0.0843888	−	0.231856i
$880$	1.15809	+	1.95430i	0.0390391	+	0.0658794i
$881$	−7.59692	−	13.1583i	−0.255947	−	0.443313i	0.709205	−	0.705002i	$-0.249054\pi$
$881$	−7.59692	−	13.1583i	−0.255947	−	0.443313i	−0.965152	+	0.261689i	$0.915721\pi$
$882$	41.9043	−	31.1734i	1.41099	−	1.04966i
$883$	4.36952	+	24.7808i	0.147046	+	0.833940i	0.965702	+	0.259655i	$0.0836087\pi$
$883$	4.36952	+	24.7808i	0.147046	+	0.833940i	−0.818656	+	0.574285i	$0.805280\pi$
$884$	−8.80781	−	6.56691i	−0.296239	−	0.220869i
$885$	44.5268	−	61.4326i	1.49675	−	2.06503i
$886$	1.27041	+	10.9027i	0.0426804	+	0.366283i
$887$	−35.0086	−	41.7216i	−1.17547	−	1.40088i	−0.897916	−	0.440166i	$-0.854919\pi$
$887$	−35.0086	−	41.7216i	−1.17547	−	1.40088i	−0.277558	−	0.960709i	$-0.589525\pi$
$888$	−41.1065	+	34.4178i	−1.37944	+	1.15499i
$889$	−0.246071	+	0.676074i	−0.00825295	+	0.0226748i
$890$	−14.6241	−	38.6783i	−0.490201	−	1.29650i
$891$	−0.804793	−	0.141907i	−0.0269616	−	0.00475405i
$892$	−5.12577	+	4.82903i	−0.171624	+	0.161688i
$893$	−12.0107	−	20.2187i	−0.401921	−	0.676593i
$894$	0.0397536	−	0.0920692i	0.00132956	−	0.00307926i
$895$	−25.6965	−	7.33677i	−0.858940	−	0.245241i
$896$	−1.98851	−	0.863633i	−0.0664314	−	0.0288520i
$897$	12.6794	−	34.8365i	0.423354	−	1.16316i
$898$	−1.91096	+	32.6103i	−0.0637696	+	1.08822i
$899$	12.5764	+	14.9880i	0.419447	+	0.499877i
$900$	25.3695	−	46.5751i	0.845651	−	1.55250i
$901$	9.32492	+	5.38374i	0.310658	+	0.179358i
$902$	0.911670	−	3.84055i	0.0303553	−	0.127876i
$903$	−3.86178	+	0.680936i	−0.128512	+	0.0226601i
$904$	−18.3868	−	3.26231i	−0.611537	−	0.108503i
$905$	−1.77323	−	3.97059i	−0.0589442	−	0.131987i
$906$	−1.41281	−	4.72522i	−0.0469374	−	0.156985i
$907$	0.879664	+	2.41686i	0.0292088	+	0.0802504i	0.953440	−	0.301583i	$-0.0975150\pi$
$907$	0.879664	+	2.41686i	0.0292088	+	0.0802504i	−0.924231	+	0.381833i	$0.875293\pi$
$908$	−29.0315	+	12.4985i	−0.963444	+	0.414777i
$909$	53.9732	+	45.2889i	1.79018	+	1.50214i
$910$	1.22271	+	1.00037i	0.0405325	+	0.0331620i
$911$	−52.2477			−1.73104			−0.865522	−	0.500871i	$-0.833013\pi$
$911$	−52.2477			−1.73104			−0.865522	+	0.500871i	$0.833013\pi$
$912$	−23.0414	−	44.6475i	−0.762977	−	1.47843i
$913$			0.812354i			0.0268850i
$914$	−37.5066	−	24.6876i	−1.24061	−	0.816594i
$915$	53.3195	+	55.0886i	1.76269	+	1.82117i
$916$	13.0274	+	30.2600i	0.430437	+	0.999818i
$917$	−1.41370	−	3.88410i	−0.0466844	−	0.128264i
$918$	−18.9513	+	5.66631i	−0.625486	+	0.187016i
$919$	−42.7717	+	24.6942i	−1.41091	+	0.814588i	−0.995474	−	0.0950359i	$-0.969703\pi$
$919$	−42.7717	+	24.6942i	−1.41091	+	0.814588i	−0.415433	+	0.909624i	$0.636370\pi$
$920$	−8.60043	+	30.0012i	−0.283548	+	0.989109i
$921$	−8.09695	−	45.9201i	−0.266804	−	1.51312i
$922$	1.13527	−	4.78250i	0.0373881	−	0.157503i
$923$	13.1064	−	22.7010i	0.431403	−	0.747212i
$924$	−0.0806347	+	0.268643i	−0.00265269	+	0.00883772i
$925$	−29.0047	+	15.5067i	−0.953667	+	0.509857i
$926$	−51.7222	−	3.03092i	−1.69970	−	0.0996023i
$927$	27.8941	−	76.6383i	0.916161	−	2.51713i
$928$	−14.7923	−	34.4607i	−0.485582	−	1.13123i
$929$	3.68391	−	20.8925i	0.120865	−	0.685460i	−0.862813	−	0.505523i	$-0.831300\pi$
$929$	3.68391	−	20.8925i	0.120865	−	0.685460i	0.983678	−	0.179937i	$-0.0575894\pi$
$930$	−23.4558	−	13.1566i	−0.769146	−	0.431423i
$931$	4.89883	−	29.9543i	0.160553	−	0.981712i
$932$	14.9434	−	14.0783i	0.489489	−	0.461152i
$933$	−12.8971	+	73.1433i	−0.422233	+	2.39460i
$934$	−15.9159	−	31.7194i	−0.520786	−	1.03789i
$935$	0.523339	−	1.07610i	0.0171150	−	0.0351924i
$936$	−25.1067	−	29.9859i	−0.820639	−	0.980121i
$937$	12.7989	+	15.2531i	0.418122	+	0.498298i	0.933456	−	0.358691i	$-0.116777\pi$
$937$	12.7989	+	15.2531i	0.418122	+	0.498298i	−0.515335	+	0.856989i	$0.672332\pi$
$938$	−0.558410	+	0.0650676i	−0.0182327	+	0.00212453i
$939$	36.1963	−	62.6939i	1.18122	−	2.04594i
$940$	17.7485	+	16.3448i	0.578892	+	0.533107i
$941$	43.7669	−	7.71729i	1.42676	−	0.251576i	0.593668	−	0.804710i	$-0.297679\pi$
$941$	43.7669	−	7.71729i	1.42676	−	0.251576i	0.833093	+	0.553133i	$0.186568\pi$
$942$	−65.3210	+	48.5936i	−2.12827	+	1.58327i
$943$	46.9647	−	27.1151i	1.52938	−	0.882989i
$944$	28.0726	+	37.8202i	0.913686	+	1.23094i
$945$	2.75904	−	0.691236i	0.0897516	−	0.0224859i
$946$	−1.75110	+	1.85474i	−0.0569332	+	0.0603027i
$947$	12.7746	+	10.7192i	0.415119	+	0.348326i	0.826303	−	0.563226i	$-0.190440\pi$
$947$	12.7746	+	10.7192i	0.415119	+	0.348326i	−0.411184	+	0.911552i	$0.634885\pi$
$948$	−24.0649	−	36.6456i	−0.781592	−	1.19019i
$949$		−	9.34678i		−	0.303409i
$950$	−8.23081	−	29.7028i	−0.267043	−	0.963685i
$951$		−	33.3684i		−	1.08205i
$952$	0.197104	+	1.12485i	0.00638818	+	0.0364565i
$953$	5.32713	+	4.46999i	0.172563	+	0.144797i	0.724979	−	0.688771i	$-0.241850\pi$
$953$	5.32713	+	4.46999i	0.172563	+	0.144797i	−0.552416	+	0.833568i	$0.686294\pi$
$954$	27.8705	+	26.3132i	0.902340	+	0.851921i
$955$	−48.6030	+	12.1768i	−1.57276	+	0.394031i
$956$	5.11254	−	43.4725i	0.165351	−	1.40600i
$957$	−4.20181	+	2.42591i	−0.135825	+	0.0784186i
$958$	−0.727310	−	0.977672i	−0.0234983	−	0.0315871i
$959$	−0.899068	+	0.158530i	−0.0290324	+	0.00511920i
$960$	35.7711	+	37.1160i	1.15451	+	1.19791i
$961$	11.1448	−	19.3034i	0.359511	−	0.622692i
$962$	2.80701	+	24.0898i	0.0905016	+	0.776685i
$963$	34.6745	+	41.3235i	1.11737	+	1.33163i
$964$	20.0154	−	39.7834i	0.644653	−	1.28134i
$965$	3.30355	−	6.79286i	0.106345	−	0.218670i
$966$	−3.44420	+	1.72821i	−0.110815	+	0.0556042i
$967$	6.60027	−	37.4320i	0.212250	−	1.20373i	−0.673364	−	0.739311i	$-0.735151\pi$
$967$	6.60027	−	37.4320i	0.212250	−	1.20373i	0.885615	−	0.464421i	$-0.153737\pi$
$968$	−10.5478	−	29.0762i	−0.339018	−	0.934544i
$969$	−12.9470	+	23.0825i	−0.415917	+	0.741516i
$970$	21.9356	−	39.1070i	0.704309	−	1.25565i
$971$	1.26442	−	7.17088i	0.0405772	−	0.230125i	−0.957774	−	0.287521i	$-0.907169\pi$
$971$	1.26442	−	7.17088i	0.0405772	−	0.230125i	0.998351	+	0.0573966i	$0.0182800\pi$
$972$	21.2500	−	1.22251i	0.681594	−	0.0392122i
$973$	−0.295206	+	0.811073i	−0.00946388	+	0.0260018i
$974$	0.00134839	−	0.0230100i	4.32051e−5	−	0.000737289i
$975$	−17.7101	−	33.1261i	−0.567177	−	1.06088i
$976$	−42.5612	+	21.2993i	−1.36235	+	0.681775i
$977$	−19.7220	+	34.1595i	−0.630962	+	1.09286i	0.356393	+	0.934336i	$0.384006\pi$
$977$	−19.7220	+	34.1595i	−0.630962	+	1.09286i	−0.987355	+	0.158523i	$0.949327\pi$
$978$	−45.7516	−	10.8605i	−1.46298	−	0.347281i
$979$	−0.576702	−	3.27064i	−0.0184315	−	0.104530i
$980$	3.98799	+	30.8843i	0.127392	+	0.986564i
$981$	37.1765	−	21.4639i	1.18695	−	0.685288i
$982$	13.7527	+	45.9967i	0.438866	+	1.46781i
$983$	0.774239	+	2.12721i	0.0246944	+	0.0678473i	0.951427	−	0.307874i	$-0.0996174\pi$
$983$	0.774239	+	2.12721i	0.0246944	+	0.0678473i	−0.926733	+	0.375721i	$0.877395\pi$
$984$	0.0955099	−	89.5700i	0.00304474	−	2.85539i
$985$	−35.5047	−	36.6827i	−1.13128	−	1.16881i
$986$	−10.8609	+	16.5005i	−0.345882	+	0.525481i
$987$			2.97910i			0.0948258i
$988$	−22.6038	−	2.37397i	−0.719123	−	0.0755260i
$989$	−35.0441			−1.11434
$990$	2.69731	−	3.29681i	0.0857263	−	0.104780i
$991$	−13.9481	−	11.7038i	−0.443075	−	0.371784i	0.393784	−	0.919203i	$-0.371166\pi$
$991$	−13.9481	−	11.7038i	−0.443075	−	0.371784i	−0.836858	+	0.547419i	$0.815610\pi$
$992$	12.1640	−	11.4353i	0.386207	−	0.363073i
$993$	12.9243	+	35.5093i	0.410141	+	1.12685i
$994$	−2.61050	+	0.780522i	−0.0828001	+	0.0247567i
$995$	16.3245	+	36.5537i	0.517523	+	1.15883i
$996$	4.23833	+	17.9397i	0.134297	+	0.568442i
$997$	−4.84182	+	0.853743i	−0.153342	+	0.0270383i	−0.249792	−	0.968300i	$-0.580362\pi$
$997$	−4.84182	+	0.853743i	−0.153342	+	0.0270383i	0.0964502	+	0.995338i	$0.469251\pi$
$998$	9.67861	+	2.29751i	0.306371	+	0.0727263i
$999$	37.8152	+	21.8326i	1.19642	+	0.690754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.17	✓	336
4.3	odd	2	inner	380.2.bb.a.59.32	yes	336
5.4	even	2	inner	380.2.bb.a.59.40	yes	336
19.10	odd	18	inner	380.2.bb.a.219.25	yes	336
20.19	odd	2	inner	380.2.bb.a.59.25	yes	336
76.67	even	18	inner	380.2.bb.a.219.40	yes	336
95.29	odd	18	inner	380.2.bb.a.219.32	yes	336
380.219	even	18	inner	380.2.bb.a.219.17	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.17	✓	336	1.1	even	1	trivial
380.2.bb.a.59.25	yes	336	20.19	odd	2	inner
380.2.bb.a.59.32	yes	336	4.3	odd	2	inner
380.2.bb.a.59.40	yes	336	5.4	even	2	inner
380.2.bb.a.219.17	yes	336	380.219	even	18	inner
380.2.bb.a.219.25	yes	336	19.10	odd	18	inner
380.2.bb.a.219.32	yes	336	95.29	odd	18	inner
380.2.bb.a.219.40	yes	336	76.67	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777543 + 1.18128i) q^{2} +(-1.85226 + 2.20744i) q^{3} +(-0.790854 - 1.83699i) q^{4} +(-0.543418 - 2.16903i) q^{5} +(-1.16739 - 3.90441i) q^{6} +(0.0958109 + 0.165949i) q^{7} +(2.78493 + 0.494121i) q^{8} +(-0.920966 - 5.22306i) q^{9} +O(q^{10})\)	\(q+(-0.777543 + 1.18128i) q^{2} +(-1.85226 + 2.20744i) q^{3} +(-0.790854 - 1.83699i) q^{4} +(-0.543418 - 2.16903i) q^{5} +(-1.16739 - 3.90441i) q^{6} +(0.0958109 + 0.165949i) q^{7} +(2.78493 + 0.494121i) q^{8} +(-0.920966 - 5.22306i) q^{9} +(2.98477 + 1.04458i) q^{10} +(0.219953 + 0.126990i) q^{11} +(5.51991 + 1.65683i) q^{12} +(1.99715 - 1.67581i) q^{13} +(-0.270530 - 0.0158531i) q^{14} +(5.79455 + 2.81804i) q^{15} +(-2.74910 + 2.90559i) q^{16} +(2.07502 + 0.365881i) q^{17} +(6.88599 + 2.97323i) q^{18} +(4.07719 - 1.54161i) q^{19} +(-3.55473 + 2.71364i) q^{20} +(-0.543789 - 0.0958847i) q^{21} +(-0.321034 + 0.161086i) q^{22} +(-4.63707 - 1.68775i) q^{23} +(-6.24915 + 5.23232i) q^{24} +(-4.40939 + 2.35738i) q^{25} +(0.426732 + 3.66221i) q^{26} +(5.74881 + 3.31907i) q^{27} +(0.229076 - 0.307246i) q^{28} +(6.52866 - 1.15118i) q^{29} +(-7.83441 + 4.65384i) q^{30} +(1.47566 + 2.55592i) q^{31} +(-1.29478 - 5.50668i) q^{32} +(-0.687731 + 0.250314i) q^{33} +(-2.04562 + 2.16669i) q^{34} +(0.307884 - 0.297997i) q^{35} +(-8.86638 + 5.82248i) q^{36} +6.57793 q^{37} +(-1.34912 + 6.01497i) q^{38} +7.51261i q^{39} +(-0.441619 - 6.30912i) q^{40} +(-7.06401 + 8.41856i) q^{41} +(0.536086 - 0.567814i) q^{42} +(6.67333 - 2.42889i) q^{43} +(0.0593291 - 0.504483i) q^{44} +(-10.8285 + 4.83591i) q^{45} +(5.59923 - 4.16538i) q^{46} +(-0.936863 - 5.31322i) q^{47} +(-1.32186 - 11.4504i) q^{48} +(3.48164 - 6.03038i) q^{49} +(0.643758 - 7.04170i) q^{50} +(-4.65112 + 3.90276i) q^{51} +(-4.65791 - 2.34344i) q^{52} +(4.80209 + 1.74782i) q^{53} +(-8.39071 + 4.21024i) q^{54} +(0.155918 - 0.546093i) q^{55} +(0.184828 + 0.509500i) q^{56} +(-4.14901 + 11.8556i) q^{57} +(-3.71644 + 8.60727i) q^{58} +(2.04472 - 11.5962i) q^{59} +(0.594093 - 12.8732i) q^{60} +(11.1808 + 4.06946i) q^{61} +(-4.16665 - 0.244166i) q^{62} +(0.778525 - 0.653260i) q^{63} +(7.51169 + 2.75219i) q^{64} +(-4.72017 - 3.42122i) q^{65} +(0.239050 - 1.00703i) q^{66} +(2.04302 - 0.360240i) q^{67} +(-0.968912 - 4.10115i) q^{68} +(12.3147 - 7.10987i) q^{69} +(0.112625 + 0.595403i) q^{70} +(9.44807 - 3.43882i) q^{71} +(0.0159957 - 15.0009i) q^{72} +(2.30448 - 2.74637i) q^{73} +(-5.11462 + 7.77038i) q^{74} +(2.96356 - 14.0999i) q^{75} +(-6.05638 - 6.27059i) q^{76} +0.0486681i q^{77} +(-8.87451 - 5.84138i) q^{78} +(-5.82732 - 4.88970i) q^{79} +(7.79623 + 4.38393i) q^{80} +(-3.02357 + 1.10049i) q^{81} +(-4.45212 - 14.8904i) q^{82} +(1.59925 + 2.76998i) q^{83} +(0.253918 + 1.07477i) q^{84} +(-0.333994 - 4.69960i) q^{85} +(-2.31959 + 9.77165i) q^{86} +(-9.55160 + 16.5439i) q^{87} +(0.549805 + 0.462341i) q^{88} +(-8.40523 - 10.0170i) q^{89} +(2.70705 - 16.5516i) q^{90} +(0.469448 + 0.170865i) q^{91} +(0.566846 + 9.85304i) q^{92} +(-8.37534 - 1.47680i) q^{93} +(7.00486 + 3.02455i) q^{94} +(-5.55941 - 8.00581i) q^{95} +(14.5539 + 7.34166i) q^{96} +(2.46221 - 13.9639i) q^{97} +(4.41645 + 8.80168i) q^{98} +(0.460706 - 1.26578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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