LMFDB - Embedded newform 230.2.l.a.217.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.11
Character	$\chi$	$=$	230.217
Dual form			230.2.l.a.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(0.846041 - 0.184045i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(0.896501 + 2.04848i) q^{5} +(-0.123220 - 0.857015i) q^{6} +(3.89809 - 2.12852i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-2.04698 + 0.934826i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(0.846041 - 0.184045i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(0.896501 + 2.04848i) q^{5} +(-0.123220 - 0.857015i) q^{6} +(3.89809 - 2.12852i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-2.04698 + 0.934826i) q^{9} +(2.10722 - 0.748080i) q^{10} +(0.483957 + 0.419351i) q^{11} +(-0.863622 + 0.0617674i) q^{12} +(0.634258 - 1.16156i) q^{13} +(-1.84501 - 4.04000i) q^{14} +(1.13549 + 1.56810i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.30942 + 0.980222i) q^{17} +(0.786414 + 2.10846i) q^{18} +(0.660894 - 4.59662i) q^{19} +(-0.595846 - 2.15522i) q^{20} +(2.90620 - 2.51823i) q^{21} +(0.452808 - 0.452808i) q^{22} +(-4.44729 - 1.79488i) q^{23} +0.865828i q^{24} +(-3.39257 + 3.67294i) q^{25} +(-1.11335 - 0.715507i) q^{26} +(-3.63917 + 2.72425i) q^{27} +(-4.16133 + 1.55210i) q^{28} +(-2.76504 + 0.397553i) q^{29} +(1.64511 - 1.02073i) q^{30} +(-0.176248 + 0.113268i) q^{31} +(0.349464 - 0.936950i) q^{32} +(0.486627 + 0.265718i) q^{33} +(1.07114 - 1.23616i) q^{34} +(7.85487 + 6.07695i) q^{35} +(2.15919 - 0.633995i) q^{36} +(-8.78046 - 3.27494i) q^{37} +(-4.53776 - 0.987129i) q^{38} +(0.322830 - 1.09946i) q^{39} +(-2.19223 + 0.440577i) q^{40} +(-0.793335 + 1.73716i) q^{41} +(-2.30449 - 3.07844i) q^{42} +(2.66167 + 12.2355i) q^{43} +(-0.419351 - 0.483957i) q^{44} +(-3.75010 - 3.35514i) q^{45} +(-2.10758 + 4.30791i) q^{46} +(5.65253 + 5.65253i) q^{47} +(0.863622 + 0.0617674i) q^{48} +(6.88001 - 10.7055i) q^{49} +(3.42155 + 3.64595i) q^{50} +(1.28823 + 0.588315i) q^{51} +(-0.793109 + 1.05947i) q^{52} +(3.58501 + 6.56546i) q^{53} +(2.45769 + 3.82425i) q^{54} +(-0.425166 + 1.36733i) q^{55} +(1.25128 + 4.26145i) q^{56} +(-0.286841 - 4.01056i) q^{57} +(0.199284 + 2.78635i) q^{58} +(-0.421120 - 1.43420i) q^{59} +(-0.900767 - 1.71374i) q^{60} +(-2.82825 - 4.40084i) q^{61} +(0.100406 + 0.183879i) q^{62} +(-5.98953 + 8.00107i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(2.94804 + 0.257930i) q^{65} +(0.299757 - 0.466431i) q^{66} +(-10.3906 - 0.743153i) q^{67} +(-1.15660 - 1.15660i) q^{68} +(-4.09293 - 0.700044i) q^{69} +(6.62183 - 7.40133i) q^{70} +(-5.23180 - 6.03781i) q^{71} +(-0.478345 - 2.19892i) q^{72} +(-3.39429 - 4.53424i) q^{73} +(-3.89299 + 8.52446i) q^{74} +(-2.19427 + 3.73184i) q^{75} +(-1.30833 + 4.45578i) q^{76} +(2.77910 + 0.604557i) q^{77} +(-1.07362 - 0.400441i) q^{78} +(-0.0648320 + 0.0190364i) q^{79} +(0.283062 + 2.21808i) q^{80} +(1.84348 - 2.12749i) q^{81} +(1.67614 + 0.915241i) q^{82} +(-2.38302 + 6.38913i) q^{83} +(-3.23500 + 2.07901i) q^{84} +(-0.834070 + 3.56110i) q^{85} +(12.3942 - 1.78202i) q^{86} +(-2.26617 + 0.845237i) q^{87} +(-0.512640 + 0.383758i) q^{88} +(-0.562341 - 0.361394i) q^{89} +(-3.61412 + 3.50119i) q^{90} -5.87788i q^{91} +(4.14658 + 2.40953i) q^{92} +(-0.128266 + 0.128266i) q^{93} +(6.04138 - 5.23488i) q^{94} +(10.0086 - 2.76704i) q^{95} +(0.123220 - 0.857015i) q^{96} +(-6.52900 - 17.5049i) q^{97} +(-10.1874 - 7.62621i) q^{98} +(-1.38267 - 0.405989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	0.846041	−	0.184045i	0.488462	−	0.106258i	0.0384123	−	0.999262i	$-0.487770\pi$
$3$	0.846041	−	0.184045i	0.488462	−	0.106258i	0.450050	+	0.893004i	$0.351406\pi$
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	0.896501	+	2.04848i	0.400927	+	0.916110i
$5$	0.896501	+	2.04848i	0.400927	+	0.916110i
$6$	−0.123220	−	0.857015i	−0.0503044	−	0.349875i
$7$	3.89809	−	2.12852i	1.47334	−	0.804504i	0.476145	−	0.879367i	$-0.342034\pi$
$7$	3.89809	−	2.12852i	1.47334	−	0.804504i	0.997194	+	0.0748635i	$0.0238521\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	−2.04698	+	0.934826i	−0.682328	+	0.311609i
$10$	2.10722	−	0.748080i	0.666362	−	0.236564i
$11$	0.483957	+	0.419351i	0.145919	+	0.126439i	0.724761	−	0.689000i	$-0.241950\pi$
$11$	0.483957	+	0.419351i	0.145919	+	0.126439i	−0.578843	+	0.815439i	$0.696495\pi$
$12$	−0.863622	+	0.0617674i	−0.249306	+	0.0178307i
$13$	0.634258	−	1.16156i	0.175912	−	0.322158i	−0.774815	−	0.632188i	$-0.782157\pi$
$13$	0.634258	−	1.16156i	0.175912	−	0.322158i	0.950727	+	0.310030i	$0.100339\pi$
$14$	−1.84501	−	4.04000i	−0.493099	−	1.07974i
$15$	1.13549	+	1.56810i	0.293182	+	0.404883i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	1.30942	+	0.980222i	0.317582	+	0.237739i	0.746161	−	0.665765i	$-0.231895\pi$
$17$	1.30942	+	0.980222i	0.317582	+	0.237739i	−0.428579	+	0.903504i	$0.640986\pi$
$18$	0.786414	+	2.10846i	0.185360	+	0.496968i
$19$	0.660894	−	4.59662i	0.151619	−	1.05454i	−0.761886	−	0.647711i	$-0.775727\pi$
$19$	0.660894	−	4.59662i	0.151619	−	1.05454i	0.913506	−	0.406826i	$-0.133364\pi$
$20$	−0.595846	−	2.15522i	−0.133235	−	0.481922i
$21$	2.90620	−	2.51823i	0.634184	−	0.549524i
$22$	0.452808	−	0.452808i	0.0965389	−	0.0965389i
$23$	−4.44729	−	1.79488i	−0.927324	−	0.374259i
$23$	−4.44729	−	1.79488i	−0.927324	−	0.374259i
$24$			0.865828i			0.176736i
$25$	−3.39257	+	3.67294i	−0.678514	+	0.734587i
$26$	−1.11335	−	0.715507i	−0.218346	−	0.140322i
$27$	−3.63917	+	2.72425i	−0.700359	+	0.524282i
$28$	−4.16133	+	1.55210i	−0.786417	+	0.293318i
$29$	−2.76504	+	0.397553i	−0.513455	+	0.0738237i	−0.394172	−	0.919037i	$-0.628969\pi$
$29$	−2.76504	+	0.397553i	−0.513455	+	0.0738237i	−0.119283	+	0.992860i	$0.538059\pi$
$30$	1.64511	−	1.02073i	0.300355	−	0.186359i
$31$	−0.176248	+	0.113268i	−0.0316550	+	0.0203435i	−0.556373	−	0.830933i	$-0.687807\pi$
$31$	−0.176248	+	0.113268i	−0.0316550	+	0.0203435i	0.524718	+	0.851276i	$0.324171\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	0.486627	+	0.265718i	0.0847108	+	0.0462556i
$34$	1.07114	−	1.23616i	0.183699	−	0.212000i
$35$	7.85487	+	6.07695i	1.32772	+	1.02719i
$36$	2.15919	−	0.633995i	0.359865	−	0.105666i
$37$	−8.78046	−	3.27494i	−1.44350	−	0.538397i	−0.498910	−	0.866654i	$-0.666266\pi$
$37$	−8.78046	−	3.27494i	−1.44350	−	0.538397i	−0.944589	+	0.328257i	$0.893539\pi$
$38$	−4.53776	−	0.987129i	−0.736122	−	0.160133i
$39$	0.322830	−	1.09946i	0.0516941	−	0.176054i
$40$	−2.19223	+	0.440577i	−0.346623	+	0.0696613i
$41$	−0.793335	+	1.73716i	−0.123898	+	0.271299i	−0.961410	−	0.275120i	$-0.911282\pi$
$41$	−0.793335	+	1.73716i	−0.123898	+	0.271299i	0.837512	+	0.546419i	$0.184010\pi$
$42$	−2.30449	−	3.07844i	−0.355591	−	0.475014i
$43$	2.66167	+	12.2355i	0.405901	+	1.86590i	0.493506	+	0.869742i	$0.335715\pi$
$43$	2.66167	+	12.2355i	0.405901	+	1.86590i	−0.0876049	+	0.996155i	$0.527921\pi$
$44$	−0.419351	−	0.483957i	−0.0632196	−	0.0729593i
$45$	−3.75010	−	3.35514i	−0.559032	−	0.500155i
$46$	−2.10758	+	4.30791i	−0.310745	+	0.635167i
$47$	5.65253	+	5.65253i	0.824506	+	0.824506i	0.986751	−	0.162244i	$-0.0518733\pi$
$47$	5.65253	+	5.65253i	0.824506	+	0.824506i	−0.162244	+	0.986751i	$0.551873\pi$
$48$	0.863622	+	0.0617674i	0.124653	+	0.00891536i
$49$	6.88001	−	10.7055i	0.982859	−	1.52936i
$50$	3.42155	+	3.64595i	0.483881	+	0.515615i
$51$	1.28823	+	0.588315i	0.180388	+	0.0823806i
$52$	−0.793109	+	1.05947i	−0.109984	+	0.146922i
$53$	3.58501	+	6.56546i	0.492440	+	0.901836i	0.999209	+	0.0397544i	$0.0126575\pi$
$53$	3.58501	+	6.56546i	0.492440	+	0.901836i	−0.506770	+	0.862081i	$0.669161\pi$
$54$	2.45769	+	3.82425i	0.334450	+	0.520414i
$55$	−0.425166	+	1.36733i	−0.0573294	+	0.184370i
$56$	1.25128	+	4.26145i	0.167209	+	0.569460i
$57$	−0.286841	−	4.01056i	−0.0379930	−	0.531212i
$58$	0.199284	+	2.78635i	0.0261673	+	0.365866i
$59$	−0.421120	−	1.43420i	−0.0548252	−	0.186717i	0.927528	−	0.373754i	$-0.121930\pi$
$59$	−0.421120	−	1.43420i	−0.0548252	−	0.186717i	−0.982353	+	0.187037i	$0.940112\pi$
$60$	−0.900767	−	1.71374i	−0.116289	−	0.221243i
$61$	−2.82825	−	4.40084i	−0.362120	−	0.563470i	0.611614	−	0.791156i	$-0.290520\pi$
$61$	−2.82825	−	4.40084i	−0.362120	−	0.563470i	−0.973735	+	0.227686i	$0.926884\pi$
$62$	0.100406	+	0.183879i	0.0127515	+	0.0233527i
$63$	−5.98953	+	8.00107i	−0.754609	+	1.00804i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	2.94804	+	0.257930i	0.365660	+	0.0319923i
$66$	0.299757	−	0.466431i	0.0368975	−	0.0574137i
$67$	−10.3906	−	0.743153i	−1.26942	−	0.0907906i	−0.579677	−	0.814846i	$-0.696821\pi$
$67$	−10.3906	−	0.743153i	−1.26942	−	0.0907906i	−0.689741	+	0.724056i	$0.742276\pi$
$68$	−1.15660	−	1.15660i	−0.140258	−	0.140258i
$69$	−4.09293	−	0.700044i	−0.492731	−	0.0842754i
$70$	6.62183	−	7.40133i	0.791460	−	0.884628i
$71$	−5.23180	−	6.03781i	−0.620900	−	0.716557i	0.354978	−	0.934875i	$-0.384488\pi$
$71$	−5.23180	−	6.03781i	−0.620900	−	0.716557i	−0.975878	+	0.218318i	$0.929943\pi$
$72$	−0.478345	−	2.19892i	−0.0563735	−	0.259145i
$73$	−3.39429	−	4.53424i	−0.397271	−	0.530692i	0.556651	−	0.830747i	$-0.312086\pi$
$73$	−3.39429	−	4.53424i	−0.397271	−	0.530692i	−0.953922	+	0.300054i	$0.902995\pi$
$74$	−3.89299	+	8.52446i	−0.452551	+	0.990948i
$75$	−2.19427	+	3.73184i	−0.253372	+	0.430916i
$76$	−1.30833	+	4.45578i	−0.150076	+	0.511112i
$77$	2.77910	+	0.604557i	0.316708	+	0.0688956i
$78$	−1.07362	−	0.400441i	−0.121564	−	0.0453411i
$79$	−0.0648320	+	0.0190364i	−0.00729418	+	0.00214176i	−0.285378	−	0.958415i	$-0.592119\pi$
$79$	−0.0648320	+	0.0190364i	−0.00729418	+	0.00214176i	0.278083	+	0.960557i	$0.410301\pi$
$80$	0.283062	+	2.21808i	0.0316473	+	0.247989i
$81$	1.84348	−	2.12749i	0.204831	−	0.236388i
$82$	1.67614	+	0.915241i	0.185099	+	0.101072i
$83$	−2.38302	+	6.38913i	−0.261571	+	0.701298i	0.738076	+	0.674718i	$0.235735\pi$
$83$	−2.38302	+	6.38913i	−0.261571	+	0.701298i	−0.999647	+	0.0265807i	$0.991538\pi$
$84$	−3.23500	+	2.07901i	−0.352967	+	0.226838i
$85$	−0.834070	+	3.56110i	−0.0904675	+	0.386256i
$86$	12.3942	−	1.78202i	1.33650	−	0.192160i
$87$	−2.26617	+	0.845237i	−0.242959	+	0.0906189i
$88$	−0.512640	+	0.383758i	−0.0546476	+	0.0409087i
$89$	−0.562341	−	0.361394i	−0.0596080	−	0.0383077i	0.510497	−	0.859879i	$-0.329461\pi$
$89$	−0.562341	−	0.361394i	−0.0596080	−	0.0383077i	−0.570105	+	0.821572i	$0.693098\pi$
$90$	−3.61412	+	3.50119i	−0.380962	+	0.369058i
$91$		−	5.87788i		−	0.616169i
$92$	4.14658	+	2.40953i	0.432311	+	0.251211i
$93$	−0.128266	+	0.128266i	−0.0133006	+	0.0133006i
$94$	6.04138	−	5.23488i	0.623120	−	0.539937i
$95$	10.0086	−	2.76704i	1.02686	−	0.283893i
$96$	0.123220	−	0.857015i	0.0125761	−	0.0874687i
$97$	−6.52900	−	17.5049i	−0.662920	−	1.77736i	−0.628319	−	0.777956i	$-0.716257\pi$
$97$	−6.52900	−	17.5049i	−0.662920	−	1.77736i	−0.0346011	−	0.999401i	$-0.511016\pi$
$98$	−10.1874	−	7.62621i	−1.02908	−	0.770363i
$99$	−1.38267	−	0.405989i	−0.138964	−	0.0408035i
$100$	3.88075	−	3.15274i	0.388075	−	0.315274i
$101$	2.53058	+	5.54119i	0.251802	+	0.551369i	0.992751	−	0.120192i	$-0.0383512\pi$
$101$	2.53058	+	5.54119i	0.251802	+	0.551369i	−0.740949	+	0.671562i	$0.765624\pi$
$102$	0.678717	−	1.24298i	0.0672030	−	0.123073i
$103$	15.2639	−	1.09170i	1.50400	−	0.107568i	0.705132	−	0.709076i	$-0.250888\pi$
$103$	15.2639	−	1.09170i	1.50400	−	0.107568i	0.798867	+	0.601507i	$0.205433\pi$
$104$	1.00019	+	0.866670i	0.0980768	+	0.0849840i
$105$	7.76397	+	3.69570i	0.757686	+	0.360663i
$106$	6.80449	−	3.10751i	0.660910	−	0.301828i
$107$	−1.26225	+	5.80246i	−0.122026	+	0.560945i	0.875016	+	0.484093i	$0.160850\pi$
$107$	−1.26225	+	5.80246i	−0.122026	+	0.560945i	−0.997043	+	0.0768517i	$0.975513\pi$
$108$	3.98983	−	2.17861i	0.383922	−	0.209637i
$109$	1.08696	+	7.55997i	0.104112	+	0.724114i	0.973284	+	0.229605i	$0.0737433\pi$
$109$	1.08696	+	7.55997i	0.104112	+	0.724114i	−0.869172	+	0.494510i	$0.835348\pi$
$110$	1.33351	+	0.521627i	0.127145	+	0.0497351i
$111$	−8.03136	−	1.15474i	−0.762303	−	0.109603i
$112$	4.33986	−	0.944079i	0.410078	−	0.0892070i
$113$	1.29323	−	18.0818i	0.121657	−	1.70099i	−0.460295	−	0.887766i	$-0.652256\pi$
$113$	1.29323	−	18.0818i	0.121657	−	1.70099i	0.581952	−	0.813223i	$-0.302289\pi$
$114$	−4.02080			−0.376583
$115$	−0.310209	−	10.7193i	−0.0289271	−	0.999582i
$116$	2.79347			0.259367
$117$	−0.212462	+	2.97061i	−0.0196421	+	0.274633i
$118$	−1.46059	+	0.317732i	−0.134458	+	0.0292496i
$119$	7.19067	+	1.03386i	0.659167	+	0.0947739i
$120$	−1.77363	+	0.776215i	−0.161910	+	0.0708584i
$121$	−1.50710	−	10.4821i	−0.137009	−	0.952922i
$122$	−4.59140	+	2.50709i	−0.415686	+	0.226981i
$123$	−0.351478	+	1.61572i	−0.0316917	+	0.145684i
$124$	0.190573	−	0.0870320i	0.0171140	−	0.00781570i
$125$	−10.5654	−	3.65684i	−0.944998	−	0.327077i
$126$	7.55340	+	6.54506i	0.672910	+	0.583080i
$127$	12.7835	−	0.914294i	1.13435	−	0.0811305i	0.508493	−	0.861066i	$-0.330203\pi$
$127$	12.7835	−	0.914294i	1.13435	−	0.0811305i	0.625859	+	0.779936i	$0.284748\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	4.50377	+	9.86187i	0.396534	+	0.868289i
$130$	0.467584	−	2.92213i	0.0410098	−	0.256288i
$131$	−1.56010	−	0.458088i	−0.136307	−	0.0400233i	0.212867	−	0.977081i	$-0.431720\pi$
$131$	−1.56010	−	0.458088i	−0.136307	−	0.0400233i	−0.349174	+	0.937058i	$0.613538\pi$
$132$	−0.443858	−	0.332268i	−0.0386329	−	0.0289202i
$133$	−7.20775	−	19.3247i	−0.624992	−	1.67567i
$134$	−1.48252	+	10.3111i	−0.128070	+	0.890748i
$135$	−8.84311	−	5.01249i	−0.761094	−	0.431407i
$136$	−1.23616	+	1.07114i	−0.106000	+	0.0918493i
$137$	−9.66832	+	9.66832i	−0.826020	+	0.826020i	−0.986964	−	0.160943i	$-0.948546\pi$
$137$	−9.66832	+	9.66832i	−0.826020	+	0.826020i	0.160943	+	0.986964i	$0.448546\pi$
$138$	−0.990247	+	4.03256i	−0.0842954	+	0.343274i
$139$		−	22.4821i		−	1.90691i	−0.301540	−	0.953453i	$-0.597501\pi$
$139$		−	22.4821i		−	1.90691i	0.301540	−	0.953453i	$-0.402499\pi$
$140$	−6.91008	−	7.13296i	−0.584008	−	0.602845i
$141$	5.82259	+	3.74195i	0.490351	+	0.315129i
$142$	−6.39566	+	4.78773i	−0.536712	+	0.401778i
$143$	0.794054	−	0.296167i	0.0664021	−	0.0247667i
$144$	−2.22744	+	0.320257i	−0.185620	+	0.0266881i
$145$	−3.29324	−	5.30773i	−0.273489	−	0.440783i
$146$	−4.76483	+	3.06217i	−0.394340	+	0.253427i
$147$	3.85048	−	10.3235i	0.317582	−	0.851470i
$148$	8.22501	+	4.49120i	0.676092	+	0.369174i
$149$	13.7976	−	15.9233i	1.13035	−	1.30449i	0.183421	−	0.983035i	$-0.441283\pi$
$149$	13.7976	−	15.9233i	1.13035	−	1.30449i	0.946925	−	0.321454i	$-0.104172\pi$
$150$	3.56579	+	2.45490i	0.291146	+	0.200442i
$151$	4.47832	−	1.31495i	0.364440	−	0.107009i	−0.0943851	−	0.995536i	$-0.530088\pi$
$151$	4.47832	−	1.31495i	0.364440	−	0.107009i	0.458826	+	0.888526i	$0.348270\pi$
$152$	4.35109	+	1.62287i	0.352920	+	0.131632i
$153$	−3.59671	−	0.782415i	−0.290776	−	0.0632545i
$154$	0.801275	−	2.72889i	0.0645686	−	0.219900i
$155$	−0.390033	−	0.259496i	−0.0313282	−	0.0208432i
$156$	−0.476013	+	1.04232i	−0.0381115	+	0.0834526i
$157$	13.7564	+	18.3764i	1.09788	+	1.46660i	0.870094	+	0.492886i	$0.164058\pi$
$157$	13.7564	+	18.3764i	1.09788	+	1.46660i	0.227787	+	0.973711i	$0.426851\pi$
$158$	0.0143628	+	0.0660249i	0.00114265	+	0.00525266i
$159$	4.24141	+	4.89485i	0.336366	+	0.388187i
$160$	2.23262	−	0.124105i	0.176504	−	0.00981134i
$161$	−21.1564	+	2.46951i	−1.66736	+	0.194625i
$162$	−1.99055	−	1.99055i	−0.156393	−	0.156393i
$163$	15.3524	+	1.09802i	1.20249	+	0.0860037i	0.658167	−	0.752872i	$-0.271332\pi$
$163$	15.3524	+	1.09802i	1.20249	+	0.0860037i	0.544322	+	0.838876i	$0.316787\pi$
$164$	1.03248	−	1.60658i	0.0806235	−	0.125453i
$165$	−0.108058	+	1.23506i	−0.00841232	+	0.0961496i
$166$	6.20285	+	2.83275i	0.481435	+	0.219864i
$167$	−6.96760	+	9.30762i	−0.539169	+	0.720245i	−0.984552	−	0.175095i	$-0.943977\pi$
$167$	−6.96760	+	9.30762i	−0.539169	+	0.720245i	0.445383	+	0.895340i	$0.353068\pi$
$168$	1.84293	+	3.37507i	0.142185	+	0.260392i
$169$	6.08140	+	9.46284i	0.467800	+	0.727911i
$170$	3.49253	+	1.08599i	0.267865	+	0.0832917i
$171$	2.94420	+	10.0270i	0.225149	+	0.766785i
$172$	−0.893286	−	12.4898i	−0.0681124	−	0.952336i
$173$	0.333147	+	4.65800i	0.0253287	+	0.354141i	0.994274	+	0.106865i	$0.0340811\pi$
$173$	0.333147	+	4.65800i	0.0253287	+	0.354141i	−0.968945	+	0.247277i	$0.920464\pi$
$174$	0.681417	+	2.32069i	0.0516581	+	0.175931i
$175$	−5.40663	+	21.5386i	−0.408703	+	1.62816i
$176$	0.346208	+	0.538711i	0.0260964	+	0.0406069i
$177$	−0.620242	−	1.13589i	−0.0466203	−	0.0853787i
$178$	−0.400591	+	0.535126i	−0.0300255	+	0.0401094i
$179$	9.03577	+	4.12650i	0.675365	+	0.308429i	0.723412	−	0.690416i	$-0.242573\pi$
$179$	9.03577	+	4.12650i	0.675365	+	0.308429i	−0.0480473	+	0.998845i	$0.515300\pi$
$180$	3.23444	+	3.85468i	0.241081	+	0.287311i
$181$	−10.0747	+	15.6766i	−0.748849	+	1.16523i	0.232425	+	0.972614i	$0.425334\pi$
$181$	−10.0747	+	15.6766i	−0.748849	+	1.16523i	−0.981274	+	0.192617i	$0.938302\pi$
$182$	−5.86290	−	0.419323i	−0.434587	−	0.0310823i
$183$	−3.20277	−	3.20277i	−0.236755	−	0.236755i
$184$	2.69921	−	3.96413i	0.198988	−	0.292239i
$185$	−1.16303	−	20.9226i	−0.0855074	−	1.53826i
$186$	0.118789	+	0.137090i	0.00871005	+	0.0100519i
$187$	0.222647	+	1.02349i	0.0162816	+	0.0748453i
$188$	−4.79056	−	6.39944i	−0.349387	−	0.466727i
$189$	−8.38720	+	18.3654i	−0.610079	+	1.33589i
$190$	−2.04599	−	10.1805i	−0.148432	−	0.738570i
$191$	−3.92260	+	13.3592i	−0.283830	+	0.966635i	0.686958	+	0.726697i	$0.258945\pi$
$191$	−3.92260	+	13.3592i	−0.283830	+	0.966635i	−0.970788	+	0.239938i	$0.922873\pi$
$192$	−0.846041	−	0.184045i	−0.0610577	−	0.0132823i
$193$	12.1125	+	4.51772i	0.871875	+	0.325192i	0.745272	−	0.666761i	$-0.232320\pi$
$193$	12.1125	+	4.51772i	0.871875	+	0.325192i	0.126603	+	0.991953i	$0.459593\pi$
$194$	−17.9261	+	5.26358i	−1.28702	+	0.377903i
$195$	2.54164	−	0.324353i	0.182010	−	0.0232274i
$196$	−8.33354	+	9.61741i	−0.595253	+	0.686958i
$197$	2.80183	+	1.52992i	0.199622	+	0.109002i	0.575951	−	0.817484i	$-0.304632\pi$
$197$	2.80183	+	1.52992i	0.199622	+	0.109002i	−0.376329	+	0.926486i	$0.622814\pi$
$198$	−0.503593	+	1.35019i	−0.0357888	+	0.0959536i
$199$	−17.2379	+	11.0781i	−1.22196	+	0.785307i	−0.982620	−	0.185629i	$-0.940568\pi$
$199$	−17.2379	+	11.0781i	−1.22196	+	0.785307i	−0.239341	+	0.970936i	$0.576931\pi$
$200$	−2.86785	−	4.09578i	−0.202788	−	0.289615i
$201$	−8.92768	+	1.28361i	−0.629710	+	0.0905386i
$202$	5.70760	−	2.12883i	0.401586	−	0.149784i
$203$	−9.93216	+	7.43512i	−0.697101	+	0.521843i
$204$	−1.19139	−	0.765661i	−0.0834141	−	0.0536070i
$205$	−4.26977	−	0.0677668i	−0.298214	−	0.00473304i
$206$		−	15.3029i		−	1.06620i
$207$	10.7814	−	0.483344i	0.749362	−	0.0335947i
$208$	0.935815	−	0.935815i	0.0648871	−	0.0648871i
$209$	2.24744	−	1.94742i	0.155459	−	0.134706i
$210$	4.24016	−	7.48054i	0.292599	−	0.516206i
$211$	0.953001	−	6.62827i	0.0656073	−	0.456309i	−0.930364	−	0.366637i	$-0.880509\pi$
$211$	0.953001	−	6.62827i	0.0656073	−	0.456309i	0.995971	−	0.0896717i	$-0.0285818\pi$
$212$	−2.61416	−	7.00884i	−0.179541	−	0.481369i
$213$	−5.53754	−	4.14535i	−0.379426	−	0.284035i
$214$	5.69763	+	1.67297i	0.389482	+	0.114362i
$215$	−22.6780	+	16.4215i	−1.54663	+	1.11994i
$216$	−1.88843	−	4.13509i	−0.128491	−	0.281357i
$217$	−0.445937	+	0.816673i	−0.0302722	+	0.0554394i
$218$	7.61826	−	0.544868i	0.515973	−	0.0369031i
$219$	−3.70621	−	3.21145i	−0.250442	−	0.217010i
$220$	0.615429	−	1.29290i	0.0414922	−	0.0871674i
$221$	1.96910	−	0.899256i	0.132456	−	0.0604905i
$222$	−1.72474	+	7.92852i	−0.115757	+	0.532128i
$223$	7.57867	−	4.13827i	0.507505	−	0.277119i	−0.205029	−	0.978756i	$-0.565729\pi$
$223$	7.57867	−	4.13827i	0.507505	−	0.277119i	0.712535	+	0.701637i	$0.247547\pi$
$224$	−0.632071	−	4.39615i	−0.0422320	−	0.293730i
$225$	3.51098	−	10.6899i	0.234065	−	0.712660i
$226$	−17.9434	−	2.57988i	−1.19358	−	0.171611i
$227$	19.8350	−	4.31485i	1.31650	−	0.286386i	0.501151	−	0.865360i	$-0.332910\pi$
$227$	19.8350	−	4.31485i	1.31650	−	0.286386i	0.815346	+	0.578973i	$0.196547\pi$
$228$	−0.286841	+	4.01056i	−0.0189965	+	0.265606i
$229$	−1.47455			−0.0974410			−0.0487205	−	0.998812i	$-0.515514\pi$
$229$	−1.47455			−0.0974410			−0.0487205	+	0.998812i	$0.515514\pi$
$230$	−10.7141	−	0.455289i	−0.706469	−	0.0300209i
$231$	2.46250			0.162021
$232$	0.199284	−	2.78635i	0.0130836	−	0.182933i
$233$	6.46366	−	1.40608i	0.423448	−	0.0921155i	0.00420857	−	0.999991i	$-0.498660\pi$
$233$	6.46366	−	1.40608i	0.423448	−	0.0921155i	0.419240	+	0.907876i	$0.362297\pi$
$234$	2.94788	+	0.423842i	0.192709	+	0.0277074i
$235$	−6.51162	+	16.6466i	−0.424771	+	1.08591i
$236$	0.212725	+	1.47954i	0.0138472	+	0.0963096i
$237$	−0.0513470	+	0.0280376i	−0.00333535	+	0.00182124i
$238$	1.54420	−	7.09859i	0.100096	−	0.460133i
$239$	12.0165	−	5.48776i	0.777284	−	0.354974i	0.0130520	−	0.999915i	$-0.495845\pi$
$239$	12.0165	−	5.48776i	0.777284	−	0.354974i	0.764232	+	0.644941i	$0.223118\pi$
$240$	0.647708	+	1.82449i	0.0418094	+	0.117770i
$241$	−13.9561	−	12.0930i	−0.898989	−	0.778979i	0.0769470	−	0.997035i	$-0.475483\pi$
$241$	−13.9561	−	12.0930i	−0.898989	−	0.778979i	−0.975936	+	0.218057i	$0.930028\pi$
$242$	−10.5629	+	0.755477i	−0.679012	+	0.0485639i
$243$	7.70395	−	14.1087i	0.494208	−	0.905075i
$244$	2.17316	+	4.75855i	0.139122	+	0.304635i
$245$	28.0980	+	4.49609i	1.79512	+	0.287245i
$246$	1.58653	+	0.465847i	0.101153	+	0.0297013i
$247$	−4.92006	−	3.68311i	−0.313056	−	0.234351i
$248$	−0.0732149	−	0.196297i	−0.00464915	−	0.0124649i
$249$	−0.840247	+	5.84405i	−0.0532485	+	0.370352i
$250$	−4.40125	+	10.2776i	−0.278359	+	0.650012i
$251$	21.8782	−	18.9575i	1.38094	−	1.19659i	0.424224	−	0.905557i	$-0.360547\pi$
$251$	21.8782	−	18.9575i	1.38094	−	1.19659i	0.956713	−	0.291032i	$-0.0939986\pi$
$252$	7.06723	−	7.06723i	0.445194	−	0.445194i
$253$	−1.39961	−	2.73362i	−0.0879927	−	0.171861i
$254$		−	12.8162i		−	0.804157i
$255$	−0.0502540	+	3.16634i	−0.00314703	+	0.198284i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−3.78676	+	2.83473i	−0.236212	+	0.176826i	−0.710826	−	0.703368i	$-0.751679\pi$
$257$	−3.78676	+	2.83473i	−0.236212	+	0.176826i	0.474614	+	0.880194i	$0.342588\pi$
$258$	10.1580	−	3.78875i	0.632412	−	0.235877i
$259$	−41.1978	+	5.92334i	−2.55990	+	0.368059i
$260$	−2.88133	−	0.674855i	−0.178692	−	0.0418528i
$261$	5.28835	−	3.39861i	0.327340	−	0.210369i
$262$	−0.568218	+	1.52345i	−0.0351046	+	0.0941191i
$263$	−4.60113	−	2.51241i	−0.283718	−	0.154922i	0.331089	−	0.943600i	$-0.392584\pi$
$263$	−4.60113	−	2.51241i	−0.283718	−	0.154922i	−0.614806	+	0.788678i	$0.710766\pi$
$264$	−0.363086	+	0.419023i	−0.0223464	+	0.0257891i
$265$	−10.2353	+	13.2298i	−0.628748	+	0.812699i
$266$	−19.7897	+	5.81078i	−1.21338	+	0.356282i
$267$	−0.542276	−	0.202258i	−0.0331867	−	0.0123780i
$268$	10.1791	+	2.21433i	0.621788	+	0.135262i
$269$	−6.10994	+	20.8086i	−0.372530	+	1.26872i	0.533606	+	0.845733i	$0.320837\pi$
$269$	−6.10994	+	20.8086i	−0.372530	+	1.26872i	−0.906136	+	0.422987i	$0.860982\pi$
$270$	−5.63058	+	8.46299i	−0.342666	+	0.515041i
$271$	−1.82164	+	3.98883i	−0.110657	+	0.242304i	−0.956856	−	0.290562i	$-0.906158\pi$
$271$	−1.82164	+	3.98883i	−0.110657	+	0.242304i	0.846200	+	0.532866i	$0.178885\pi$
$272$	0.980222	+	1.30942i	0.0594347	+	0.0793955i
$273$	−1.08179	−	4.97292i	−0.0654731	−	0.300975i
$274$	8.95396	+	10.3334i	0.540928	+	0.624265i
$275$	−3.18211	+	0.354864i	−0.191888	+	0.0213991i
$276$	3.95164	+	1.27540i	0.237861	+	0.0767703i
$277$	14.2868	+	14.2868i	0.858408	+	0.858408i	0.991151	−	0.132743i	$-0.0423784\pi$
$277$	14.2868	+	14.2868i	0.858408	+	0.858408i	−0.132743	+	0.991151i	$0.542378\pi$
$278$	−22.4248	−	1.60385i	−1.34495	−	0.0961928i
$279$	0.254891	−	0.396618i	0.0152599	−	0.0237449i
$280$	−7.60775	+	6.38361i	−0.454650	+	0.381494i
$281$	−19.9836	−	9.12619i	−1.19212	−	0.544423i	−0.282259	−	0.959338i	$-0.591084\pi$
$281$	−19.9836	−	9.12619i	−1.19212	−	0.544423i	−0.909860	+	0.414916i	$0.863811\pi$
$282$	4.14780	−	5.54081i	0.246998	−	0.329950i
$283$	4.82727	+	8.84049i	0.286952	+	0.525512i	0.980900	−	0.194512i	$-0.0623123\pi$
$283$	4.82727	+	8.84049i	0.286952	+	0.525512i	−0.693949	+	0.720025i	$0.744131\pi$
$284$	4.31927	+	6.72092i	0.256302	+	0.398813i
$285$	7.95841	−	4.18306i	0.471416	−	0.247783i
$286$	−0.238765	−	0.813159i	−0.0141185	−	0.0480831i
$287$	0.605088	+	8.46023i	0.0357172	+	0.499392i
$288$	0.160538	+	2.24461i	0.00945977	+	0.132265i
$289$	−4.03570	−	13.7443i	−0.237394	−	0.808490i
$290$	−5.52914	+	2.90620i	−0.324683	+	0.170658i
$291$	−8.74550	−	13.6083i	−0.512670	−	0.797730i
$292$	2.71445	+	4.97114i	0.158851	+	0.290914i
$293$	2.17081	−	2.89986i	0.126820	−	0.169412i	−0.732637	−	0.680619i	$-0.761711\pi$
$293$	2.17081	−	2.89986i	0.126820	−	0.169412i	0.859457	+	0.511208i	$0.170802\pi$
$294$	−10.0225	−	4.57714i	−0.584526	−	0.266944i
$295$	2.56041	−	2.14842i	0.149073	−	0.125086i
$296$	5.06652	−	7.88366i	0.294486	−	0.458228i
$297$	−2.90362	−	0.207671i	−0.168485	−	0.0120503i
$298$	−14.8984	−	14.8984i	−0.863043	−	0.863043i
$299$	−4.90559	+	4.02736i	−0.283698	+	0.232908i
$300$	2.70303	−	3.38158i	0.156060	−	0.195235i
$301$	36.4189	+	42.0297i	2.09915	+	2.42255i
$302$	−0.992123	−	4.56072i	−0.0570903	−	0.262440i
$303$	3.16080	+	4.22233i	0.181583	+	0.242567i
$304$	1.92914	−	4.22423i	0.110644	−	0.242276i
$305$	6.47953	−	9.73899i	0.371017	−	0.557653i
$306$	−1.03701	+	3.53172i	−0.0592818	+	0.201895i
$307$	14.1382	+	3.07558i	0.806911	+	0.175533i	0.597056	−	0.802200i	$-0.296337\pi$
$307$	14.1382	+	3.07558i	0.806911	+	0.175533i	0.209855	+	0.977732i	$0.432701\pi$
$308$	−2.66478	−	0.993910i	−0.151840	−	0.0566333i
$309$	12.7130	−	3.73287i	0.723216	−	0.212356i
$310$	−0.286660	+	0.370527i	−0.0162812	+	0.0210445i
$311$	15.2800	−	17.6341i	0.866449	−	0.999936i	−0.133511	−	0.991047i	$-0.542625\pi$
$311$	15.2800	−	17.6341i	0.866449	−	0.999936i	0.999960	−	0.00888825i	$-0.00282925\pi$
$312$	1.00571	+	0.549158i	0.0569370	+	0.0310900i
$313$	−1.67405	+	4.48829i	−0.0946227	+	0.253693i	−0.975635	−	0.219400i	$-0.929590\pi$
$313$	−1.67405	+	4.48829i	−0.0946227	+	0.253693i	0.881012	+	0.473093i	$0.156863\pi$
$314$	19.3110	−	12.4104i	1.08978	−	0.700360i
$315$	−21.7597	−	5.09648i	−1.22602	−	0.287154i
$316$	0.0668813	−	0.00961608i	0.00376237	−	0.000540947i
$317$	−20.3356	+	7.58479i	−1.14216	+	0.426004i	−0.848129	−	0.529791i	$-0.822271\pi$
$317$	−20.3356	+	7.58479i	−1.14216	+	0.426004i	−0.294034	+	0.955795i	$0.594998\pi$
$318$	5.18495	−	3.88141i	0.290758	−	0.217658i
$319$	−1.50487	−	0.967124i	−0.0842567	−	0.0541485i
$320$	0.0354848	−	2.23579i	0.00198366	−	0.124984i
$321$			5.14143i			0.286967i
$322$	0.953945	+	21.2786i	0.0531613	+	1.18581i
$323$	5.37110	−	5.37110i	0.298856	−	0.298856i
$324$	−2.12749	+	1.84348i	−0.118194	+	0.102415i
$325$	2.11456	+	6.27025i	0.117295	+	0.347811i
$326$	2.19045	−	15.2349i	0.121318	−	0.843783i
$327$	2.31099	+	6.19600i	0.127798	+	0.342639i
$328$	−1.52883	−	1.14447i	−0.0844153	−	0.0631925i
$329$	34.0656	+	10.0026i	1.87810	+	0.551458i
$330$	1.22421	+	0.195891i	0.0673904	+	0.0107835i
$331$	−6.89284	−	15.0932i	−0.378865	−	0.829598i	−0.998983	−	0.0450899i	$-0.985643\pi$
$331$	−6.89284	−	15.0932i	−0.378865	−	0.829598i	0.620118	−	0.784509i	$-0.287085\pi$
$332$	3.26804	−	5.98496i	0.179357	−	0.328467i
$333$	21.0350	−	1.50445i	1.15271	−	0.0824433i
$334$	8.78684	+	7.61384i	0.480795	+	0.416611i
$335$	−7.79288	−	21.9513i	−0.425771	−	1.19933i
$336$	3.49794	−	1.59746i	0.190829	−	0.0871485i
$337$	2.85668	−	13.1319i	0.155613	−	0.715342i	−0.831527	−	0.555484i	$-0.812533\pi$
$337$	2.85668	−	13.1319i	0.155613	−	0.715342i	0.987140	−	0.159858i	$-0.0511035\pi$
$338$	9.87257	−	5.39083i	0.536997	−	0.293223i
$339$	−2.23373	−	15.5359i	−0.121319	−	0.843796i
$340$	1.33238	−	3.40616i	0.0722583	−	0.184725i
$341$	−0.132795	−	0.0190931i	−0.00719126	−	0.00103395i
$342$	10.2115	−	2.22138i	0.552175	−	0.120118i
$343$	1.81414	−	25.3649i	0.0979541	−	1.36958i
$344$	−12.5217			−0.675123
$345$	−2.23528	−	9.01189i	−0.120344	−	0.485184i
$346$	4.66990			0.251055
$347$	−0.248159	+	3.46971i	−0.0133219	+	0.186264i	0.986434	+	0.164159i	$0.0524912\pi$
$347$	−0.248159	+	3.46971i	−0.0133219	+	0.186264i	−0.999756	+	0.0221044i	$0.992963\pi$
$348$	2.36339	−	0.514124i	0.126691	−	0.0275600i
$349$	−4.68836	−	0.674084i	−0.250962	−	0.0360829i	0.0156856	−	0.999877i	$-0.495007\pi$
$349$	−4.68836	−	0.674084i	−0.250962	−	0.0360829i	−0.266648	+	0.963794i	$0.585916\pi$
$350$	21.0980	+	6.92940i	1.12773	+	0.370392i
$351$	0.856198	+	5.95499i	0.0457005	+	0.317854i
$352$	0.562036	−	0.306895i	0.0299566	−	0.0163576i
$353$	−7.37233	+	33.8900i	−0.392389	+	1.80378i	0.179845	+	0.983695i	$0.442440\pi$
$353$	−7.37233	+	33.8900i	−0.392389	+	1.80378i	−0.572235	+	0.820090i	$0.693923\pi$
$354$	−1.17724	+	0.537629i	−0.0625697	+	0.0285746i
$355$	7.67805	−	16.1302i	0.407509	−	0.856100i
$356$	0.505185	+	0.437745i	0.0267748	+	0.0232005i
$357$	6.27387	−	0.448716i	0.332049	−	0.0237486i
$358$	4.76059	−	8.71837i	0.251605	−	0.460780i
$359$	−8.63206	−	18.9016i	−0.455583	−	0.997587i	−0.988472	−	0.151402i	$-0.951621\pi$
$359$	−8.63206	−	18.9016i	−0.455583	−	0.997587i	0.532889	−	0.846185i	$-0.321106\pi$
$360$	4.07561	−	2.95121i	0.214803	−	0.155542i
$361$	−2.46174	−	0.722833i	−0.129565	−	0.0380438i
$362$	14.9179	+	11.1674i	0.784068	+	0.586946i
$363$	−3.20426	−	8.59094i	−0.168180	−	0.450908i
$364$	−0.836509	+	5.81805i	−0.0438450	+	0.304949i
$365$	6.24533	−	11.0181i	0.326895	−	0.576713i
$366$	−3.42309	+	2.96613i	−0.178928	+	0.155042i
$367$	4.80283	−	4.80283i	0.250706	−	0.250706i	−0.570554	−	0.821260i	$-0.693272\pi$
$367$	4.80283	−	4.80283i	0.250706	−	0.250706i	0.821260	+	0.570554i	$0.193272\pi$
$368$	−3.76147	−	2.97513i	−0.196080	−	0.155089i
$369$		−	4.29757i		−	0.223723i
$370$	−20.9523	−	0.332540i	−1.08926	−	0.0172879i
$371$	27.9494	+	17.9620i	1.45106	+	0.932540i
$372$	0.145215	−	0.108707i	0.00752905	−	0.00563618i
$373$	−20.9615	+	7.81824i	−1.08535	+	0.404813i	−0.827553	−	0.561387i	$-0.810268\pi$
$373$	−20.9615	+	7.81824i	−1.08535	+	0.404813i	−0.257792	+	0.966200i	$0.582995\pi$
$374$	1.03677	−	0.149065i	0.0536101	−	0.00770796i
$375$	−9.61178	−	1.14933i	−0.496350	−	0.0593509i
$376$	−6.72488	+	4.32182i	−0.346809	+	0.222881i
$377$	−1.29197	+	3.46390i	−0.0665398	+	0.178400i
$378$	17.7203	+	9.67600i	0.911433	+	0.497680i
$379$	−9.98086	+	11.5185i	−0.512682	+	0.591667i	−0.951783	−	0.306771i	$-0.900751\pi$
$379$	−9.98086	+	11.5185i	−0.512682	+	0.591667i	0.439101	+	0.898438i	$0.355297\pi$
$380$	−10.3005	+	1.31451i	−0.528405	+	0.0674328i
$381$	10.6471	−	3.12627i	0.545467	−	0.160164i
$382$	13.0453	+	4.86564i	0.667455	+	0.248948i
$383$	−5.94535	−	1.29333i	−0.303793	−	0.0660861i	0.0580848	−	0.998312i	$-0.481501\pi$
$383$	−5.94535	−	1.29333i	−0.303793	−	0.0660861i	−0.361878	+	0.932226i	$0.617864\pi$
$384$	−0.243932	+	0.830755i	−0.0124481	+	0.0423943i
$385$	1.25304	+	6.23493i	0.0638610	+	0.317761i
$386$	5.37030	−	11.7593i	0.273341	−	0.598533i
$387$	−16.8865	−	22.5577i	−0.858388	−	1.14667i
$388$	3.97134	+	18.2559i	0.201614	+	0.926805i
$389$	14.2608	+	16.4579i	0.723052	+	0.834446i	0.991671	−	0.128800i	$-0.0411126\pi$
$389$	14.2608	+	16.4579i	0.723052	+	0.834446i	−0.268619	+	0.963247i	$0.586567\pi$
$390$	−0.142208	−	2.55830i	−0.00720099	−	0.129545i
$391$	−4.06400	−	6.70960i	−0.205525	−	0.339319i
$392$	8.99840	+	8.99840i	0.454488	+	0.454488i
$393$	−1.40422	−	0.100432i	−0.0708336	−	0.00506612i
$394$	1.72590	−	2.68555i	0.0869495	−	0.135296i
$395$	−0.0971178	−	0.115741i	−0.00488653	−	0.00582357i
$396$	1.31082	+	0.598632i	0.0658712	+	0.0300824i
$397$	11.8796	−	15.8694i	0.596222	−	0.796460i	−0.396352	−	0.918099i	$-0.629724\pi$
$397$	11.8796	−	15.8694i	0.596222	−	0.796460i	0.992574	+	0.121639i	$0.0388149\pi$
$398$	9.82015	+	17.9843i	0.492240	+	0.901470i
$399$	−9.65467	−	15.0230i	−0.483338	−	0.752089i
$400$	−4.28993	+	2.56836i	−0.214497	+	0.128418i
$401$	−5.72622	−	19.5017i	−0.285954	−	0.973869i	−0.969730	−	0.244178i	$-0.921482\pi$
$401$	−5.72622	−	19.5017i	−0.285954	−	0.973869i	0.683777	−	0.729691i	$-0.260336\pi$
$402$	0.643442	+	8.99650i	0.0320920	+	0.448705i
$403$	0.0197802	+	0.276563i	0.000985320	+	0.0137766i
$404$	−1.71623	−	5.84493i	−0.0853854	−	0.290796i
$405$	6.01080	+	1.86904i	0.298679	+	0.0928734i
$406$	6.70763	+	10.4373i	0.332894	+	0.517993i
$407$	−2.87601	−	5.26703i	−0.142559	−	0.261077i
$408$	−0.848703	+	1.13373i	−0.0420171	+	0.0561282i
$409$	27.6390	+	12.6223i	1.36666	+	0.624133i	0.957527	−	0.288342i	$-0.0931040\pi$
$409$	27.6390	+	12.6223i	1.36666	+	0.624133i	0.409133	+	0.912475i	$0.365831\pi$
$410$	−0.372196	+	4.25406i	−0.0183815	+	0.210093i
$411$	−6.40039	+	9.95920i	−0.315708	+	0.491251i
$412$	−15.2639	−	1.09170i	−0.752000	−	0.0537841i
$413$	−4.69429	−	4.69429i	−0.230991	−	0.230991i
$414$	0.287026	−	10.7884i	0.0141066	−	0.530223i
$415$	−15.2244	+	0.846280i	−0.747337	+	0.0415422i
$416$	−0.866670	−	1.00019i	−0.0424920	−	0.0490384i
$417$	−4.13772	−	19.0208i	−0.202625	−	0.931451i
$418$	−1.78213	−	2.38064i	−0.0871666	−	0.116441i
$419$	−9.90423	+	21.6872i	−0.483853	+	1.05949i	0.497533	+	0.867445i	$0.334239\pi$
$419$	−9.90423	+	21.6872i	−0.483853	+	1.05949i	−0.981386	+	0.192046i	$0.938488\pi$
$420$	−7.15899	−	4.76301i	−0.349323	−	0.232411i
$421$	−1.17415	+	3.99878i	−0.0572245	+	0.194889i	−0.983144	−	0.182831i	$-0.941474\pi$
$421$	−1.17415	+	3.99878i	−0.0572245	+	0.194889i	0.925920	+	0.377720i	$0.123292\pi$
$422$	−6.54339	−	1.42343i	−0.318527	−	0.0692914i
$423$	−16.8548	−	6.28650i	−0.819507	−	0.305660i
$424$	−7.17747	+	2.10750i	−0.348569	+	0.102349i
$425$	−8.04261	+	1.48395i	−0.390124	+	0.0719824i
$426$	−4.52983	+	5.22771i	−0.219471	+	0.253283i
$427$	−20.3920	−	11.1349i	−0.986840	−	0.538855i
$428$	2.07518	−	5.56376i	0.100307	−	0.268935i
$429$	0.617294	−	0.396711i	0.0298032	−	0.0191534i
$430$	14.7619	+	23.7918i	0.711880	+	1.14734i
$431$	22.2829	−	3.20379i	1.07333	−	0.154321i	0.417082	−	0.908869i	$-0.363053\pi$
$431$	22.2829	−	3.20379i	1.07333	−	0.154321i	0.656245	+	0.754548i	$0.272144\pi$
$432$	−4.25927	+	1.58863i	−0.204924	+	0.0764328i
$433$	6.97024	−	5.21785i	0.334968	−	0.250754i	−0.418531	−	0.908202i	$-0.637455\pi$
$433$	6.97024	−	5.21785i	0.334968	−	0.250754i	0.753500	+	0.657448i	$0.228364\pi$
$434$	0.782779	+	0.503062i	0.0375746	+	0.0241477i
$435$	−3.76308	−	3.88445i	−0.180426	−	0.186245i
$436$		−	7.63772i		−	0.365780i
$437$	−11.1896	+	19.2563i	−0.535270	+	0.921152i
$438$	−3.46766	+	3.46766i	−0.165691	+	0.165691i
$439$	−2.91323	+	2.52433i	−0.139041	+	0.120479i	−0.721605	−	0.692306i	$-0.756595\pi$
$439$	−2.91323	+	2.52433i	−0.139041	+	0.120479i	0.582564	+	0.812785i	$0.302050\pi$
$440$	−1.24570	−	0.706096i	−0.0593866	−	0.0336618i
$441$	−4.07548	+	28.3456i	−0.194071	+	1.34979i
$442$	−0.756491	−	2.02823i	−0.0359826	−	0.0964731i
$443$	15.9379	+	11.9309i	0.757231	+	0.566856i	0.906633	−	0.421920i	$-0.138644\pi$
$443$	15.9379	+	11.9309i	0.757231	+	0.566856i	−0.149402	+	0.988777i	$0.547735\pi$
$444$	7.78528	+	2.28596i	0.369473	+	0.108487i
$445$	0.236172	−	1.47594i	0.0111956	−	0.0699661i
$446$	−3.58707	−	7.85458i	−0.169853	−	0.371925i
$447$	8.74275	−	16.0112i	0.413518	−	0.757302i
$448$	−4.43004	+	0.316843i	−0.209300	+	0.0149694i
$449$	−13.3628	−	11.5790i	−0.630631	−	0.546445i	0.279825	−	0.960051i	$-0.409724\pi$
$449$	−13.3628	−	11.5790i	−0.630631	−	0.546445i	−0.910456	+	0.413606i	$0.864269\pi$
$450$	−10.4122	−	4.26465i	−0.490836	−	0.201037i
$451$	−1.11242	+	0.508025i	−0.0523818	+	0.0239220i
$452$	−3.85337	+	17.7137i	−0.181247	+	0.833181i
$453$	3.54683	−	1.93672i	0.166645	−	0.0909948i
$454$	−2.88884	−	20.0923i	−0.135580	−	0.942979i
$455$	12.0407	−	5.26953i	0.564479	−	0.247039i
$456$	3.97988	+	0.572220i	0.186375	+	0.0267967i
$457$	0.166193	−	0.0361530i	0.00777417	−	0.00169117i	−0.208677	−	0.977985i	$-0.566916\pi$
$457$	0.166193	−	0.0361530i	0.00777417	−	0.00169117i	0.216451	+	0.976294i	$0.430552\pi$
$458$	−0.105193	+	1.47079i	−0.00491535	+	0.0687256i
$459$	−7.43559			−0.347064
$460$	−1.21847	+	10.6544i	−0.0568113	+	0.496762i
$461$	−13.3460			−0.621587			−0.310794	−	0.950477i	$-0.600595\pi$
$461$	−13.3460			−0.621587			−0.310794	+	0.950477i	$0.600595\pi$
$462$	0.175673	−	2.45622i	0.00817303	−	0.114274i
$463$	−15.6144	+	3.39671i	−0.725664	+	0.157859i	−0.560200	−	0.828357i	$-0.689276\pi$
$463$	−15.6144	+	3.39671i	−0.725664	+	0.157859i	−0.165464	+	0.986216i	$0.552912\pi$
$464$	−2.76504	−	0.397553i	−0.128364	−	0.0184559i
$465$	−0.377743	−	0.147761i	−0.0175174	−	0.00685224i
$466$	−0.941388	−	6.54750i	−0.0436089	−	0.303307i
$467$	−9.31759	+	5.08779i	−0.431167	+	0.235435i	−0.680150	−	0.733073i	$-0.738085\pi$
$467$	−9.31759	+	5.08779i	−0.431167	+	0.235435i	0.248983	+	0.968508i	$0.419904\pi$
$468$	0.633061	−	2.91014i	0.0292633	−	0.134521i
$469$	−42.0854	+	19.2198i	−1.94332	+	0.887486i
$470$	16.1397	+	7.68258i	0.744467	+	0.354371i
$471$	15.0206	+	13.0154i	0.692111	+	0.599718i
$472$	1.49094	−	0.106634i	0.0686262	−	0.00490824i
$473$	−3.84284	+	7.03763i	−0.176694	+	0.323591i
$474$	0.0243031	+	0.0532163i	0.00111628	+	0.00244431i
$475$	14.6410	+	18.0218i	0.671773	+	0.826896i
$476$	−6.97034	−	2.04668i	−0.319485	−	0.0938093i
$477$	−13.4760	−	10.0880i	−0.617025	−	0.461899i
$478$	−4.61653	−	12.3774i	−0.211155	−	0.566129i
$479$	0.231166	−	1.60779i	0.0105622	−	0.0734619i	−0.983859	−	0.178948i	$-0.942731\pi$
$479$	0.231166	−	1.60779i	0.0105622	−	0.0734619i	0.994421	+	0.105486i	$0.0336398\pi$
$480$	1.86605	−	0.515900i	0.0851730	−	0.0235475i
$481$	−9.37311	+	8.12185i	−0.427377	+	0.370324i
$482$	−13.0578	+	13.0578i	−0.594767	+	0.594767i
$483$	−17.4446	+	5.98303i	−0.793759	+	0.272237i
$484$			10.5899i			0.481360i
$485$	30.0053	−	29.0678i	1.36247	−	1.31990i
$486$	−13.5232	−	8.69082i	−0.613424	−	0.394224i
$487$	23.7024	−	17.7434i	1.07406	−	0.804029i	0.0925982	−	0.995704i	$-0.470483\pi$
$487$	23.7024	−	17.7434i	1.07406	−	0.804029i	0.981458	+	0.191675i	$0.0613919\pi$
$488$	4.90146	−	1.82815i	0.221879	−	0.0827565i
$489$	13.1908	−	1.89655i	0.596509	−	0.0857650i
$490$	6.48913	−	27.7057i	0.293149	−	1.25161i
$491$	−10.8550	+	6.97610i	−0.489880	+	0.314827i	−0.762157	−	0.647392i	$-0.775860\pi$
$491$	−10.8550	+	6.97610i	−0.489880	+	0.314827i	0.272277	+	0.962219i	$0.412223\pi$
$492$	0.577841	−	1.54925i	0.0260511	−	0.0698457i
$493$	−4.01030	−	2.18979i	−0.180615	−	0.0986231i
$494$	−4.02472	+	4.64477i	−0.181081	+	0.208978i
$495$	−0.407905	−	3.19635i	−0.0183340	−	0.143665i
$496$	−0.201020	+	0.0590247i	−0.00902605	+	0.00265029i
$497$	−33.2456	−	12.4000i	−1.49127	−	0.556214i
$498$	5.76922	+	1.25502i	0.258525	+	0.0562386i
$499$	7.74097	−	26.3633i	0.346533	−	1.18018i	−0.583317	−	0.812245i	$-0.698245\pi$
$499$	7.74097	−	26.3633i	0.346533	−	1.18018i	0.929850	−	0.367939i	$-0.119936\pi$
$500$	9.93743	+	5.12323i	0.444415	+	0.229118i
$501$	−4.18185	+	9.15698i	−0.186831	+	0.409103i
$502$	−17.3485	−	23.1748i	−0.774300	−	1.03434i
$503$	−3.43045	−	15.7695i	−0.152956	−	0.703128i	−0.988190	−	0.153233i	$-0.951031\pi$
$503$	−3.43045	−	15.7695i	−0.152956	−	0.703128i	0.835234	−	0.549895i	$-0.185332\pi$
$504$	−6.54506	−	7.55340i	−0.291540	−	0.336455i
$505$	−9.08238	+	10.1515i	−0.404160	+	0.451737i
$506$	−2.82650	+	1.20103i	−0.125653	+	0.0533923i
$507$	6.88670	+	6.88670i	0.305849	+	0.305849i
$508$	−12.7835	−	0.914294i	−0.567176	−	0.0405652i
$509$	1.06094	−	1.65085i	0.0470253	−	0.0731728i	−0.816945	−	0.576716i	$-0.804334\pi$
$509$	1.06094	−	1.65085i	0.0470253	−	0.0731728i	0.863970	+	0.503543i	$0.167970\pi$
$510$	3.15469	+	0.276010i	0.139692	+	0.0122219i
$511$	−22.8824	−	10.4501i	−1.01226	−	0.462283i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	10.1172	+	18.5283i	0.446687	+	0.818046i
$514$	2.55737	+	3.97934i	0.112801	+	0.175521i
$515$	15.9205	+	30.2892i	0.701539	+	1.33470i
$516$	−3.05443	−	10.4024i	−0.134464	−	0.457942i
$517$	0.365187	+	5.10598i	0.0160609	+	0.224561i
$518$	2.96924	+	41.5154i	0.130461	+	1.82408i
$519$	1.13914	+	3.87955i	0.0500026	+	0.170293i
$520$	−0.878688	+	2.82584i	−0.0385330	+	0.123921i
$521$	−14.5543	−	22.6469i	−0.637636	−	0.992180i	−0.998231	−	0.0594579i	$-0.981063\pi$
$521$	−14.5543	−	22.6469i	−0.637636	−	0.992180i	0.360595	−	0.932722i	$-0.382574\pi$
$522$	−3.01269	−	5.51733i	−0.131862	−	0.241487i
$523$	−19.6632	+	26.2670i	−0.859813	+	1.14858i	0.127821	+	0.991797i	$0.459202\pi$
$523$	−19.6632	+	26.2670i	−0.859813	+	1.14858i	−0.987634	+	0.156778i	$0.949889\pi$
$524$	1.47903	+	0.675452i	0.0646118	+	0.0295072i
$525$	−0.610169	+	19.2176i	−0.0266300	+	0.838723i
$526$	−2.83424	+	4.41017i	−0.123579	+	0.192293i
$527$	−0.341810	−	0.0244468i	−0.0148895	−	0.00106492i
$528$	0.392053	+	0.392053i	0.0170619	+	0.0170619i
$529$	16.5568	+	15.9647i	0.719860	+	0.694119i
$530$	12.4659	+	11.1530i	0.541484	+	0.484455i
$531$	2.20276	+	2.54212i	0.0955915	+	0.110318i
$532$	4.38419	+	20.1538i	0.190079	+	0.873778i
$533$	1.51463	+	2.02331i	0.0656060	+	0.0876394i
$534$	−0.240429	+	0.526465i	−0.0104044	+	0.0227824i
$535$	−13.0179	+	2.61622i	−0.562811	+	0.113109i
$536$	2.93486	−	9.99521i	0.126767	−	0.431727i
$537$	8.40409	+	1.82820i	0.362663	+	0.0788926i
$538$	20.3197	+	7.57884i	0.876043	+	0.326747i
$539$	7.81900	−	2.29586i	0.336788	−	0.0988899i
$540$	8.03975	+	6.21998i	0.345976	+	0.267665i
$541$	−4.16906	+	4.81135i	−0.179242	+	0.206856i	−0.838260	−	0.545271i	$-0.816427\pi$
$541$	−4.16906	+	4.81135i	−0.179242	+	0.206856i	0.659018	+	0.752127i	$0.270972\pi$
$542$	3.84871	+	2.10155i	0.165316	+	0.0902695i
$543$	−5.63844	+	15.1172i	−0.241968	+	0.648742i
$544$	1.37602	−	0.884311i	0.0589962	−	0.0379145i
$545$	−14.5120	+	9.00415i	−0.621627	+	0.385695i
$546$	−5.03743	+	0.724273i	−0.215582	+	0.0309960i
$547$	−13.9975	+	5.22080i	−0.598490	+	0.223225i	−0.630406	−	0.776265i	$-0.717112\pi$
$547$	−13.9975	+	5.22080i	−0.598490	+	0.223225i	0.0319164	+	0.999491i	$0.489839\pi$
$548$	10.9459	−	8.19397i	0.467584	−	0.350029i
$549$	9.90341	+	6.36453i	0.422667	+	0.271632i
$550$	0.126951	+	3.19932i	0.00541322	+	0.136419i
$551$			12.9726i			0.552650i
$552$	1.55406	−	3.85059i	0.0661452	−	0.163892i
$553$	−0.212202	+	0.212202i	−0.00902373	+	0.00902373i
$554$	15.2696	−	13.2311i	0.648741	−	0.562138i
$555$	−4.83467	−	17.4873i	−0.205220	−	0.742296i
$556$	−3.19954	+	22.2533i	−0.135691	+	0.943749i
$557$	−10.7778	−	28.8964i	−0.456670	−	1.22438i	−0.937629	−	0.347637i	$-0.886984\pi$
$557$	−10.7778	−	28.8964i	−0.456670	−	1.22438i	0.480959	−	0.876743i	$-0.340288\pi$
$558$	−0.377424	−	0.282536i	−0.0159776	−	0.0119607i
$559$	15.9004	+	4.66879i	0.672516	+	0.197469i
$560$	5.82462	+	8.04376i	0.246135	+	0.339911i
$561$	0.376737	+	0.824940i	0.0159059	+	0.0348290i
$562$	−10.5285	+	19.2816i	−0.444120	+	0.813345i
$563$	−33.8977	+	2.42441i	−1.42862	+	0.102177i	−0.764101	−	0.645096i	$-0.776817\pi$
$563$	−33.8977	+	2.42441i	−1.42862	+	0.102177i	−0.664517	+	0.747273i	$0.731363\pi$
$564$	−5.23079	−	4.53251i	−0.220256	−	0.190853i
$565$	38.1996	−	13.5612i	1.60707	−	0.570522i
$566$	9.16234	−	4.18430i	0.385122	−	0.175879i
$567$	2.65765	−	12.2170i	0.111611	−	0.513066i
$568$	7.01193	−	3.82880i	0.294214	−	0.160653i
$569$	−5.06940	−	35.2585i	−0.212520	−	1.47811i	−0.764700	−	0.644386i	$-0.777113\pi$
$569$	−5.06940	−	35.2585i	−0.212520	−	1.47811i	0.552180	−	0.833725i	$-0.313796\pi$
$570$	−3.60466	−	8.23655i	−0.150982	−	0.344991i
$571$	31.9169	+	4.58896i	1.33568	+	0.192042i	0.772881	−	0.634551i	$-0.218815\pi$
$571$	31.9169	+	4.58896i	1.33568	+	0.192042i	0.562800	+	0.826593i	$0.309724\pi$
$572$	−0.828120	+	0.180147i	−0.0346255	+	0.00753231i
$573$	−0.859997	+	12.0243i	−0.0359269	+	0.502324i
$574$	8.48184			0.354025
$575$	21.6802	−	10.2453i	0.904129	−	0.427260i
$576$	2.25034			0.0937643
$577$	−0.810326	+	11.3298i	−0.0337343	+	0.471667i	0.952304	+	0.305150i	$0.0987066\pi$
$577$	−0.810326	+	11.3298i	−0.0337343	+	0.471667i	−0.986039	+	0.166517i	$0.946748\pi$
$578$	−13.9972	+	3.04491i	−0.582207	+	0.126651i
$579$	11.0791	+	1.59293i	0.460432	+	0.0662001i
$580$	2.50435	+	5.72238i	0.103988	+	0.237609i
$581$	4.31014	+	29.9777i	0.178815	+	1.24368i
$582$	−14.1975	+	7.75241i	−0.588505	+	0.321348i
$583$	−1.01824	+	4.68078i	−0.0421713	+	0.193858i
$584$	5.15212	−	2.35290i	0.213196	−	0.0973635i
$585$	−6.27572	+	2.22793i	−0.259469	+	0.0921135i
$586$	−2.73761	−	2.37215i	−0.113090	−	0.0979928i
$587$	21.9885	−	1.57265i	0.907563	−	0.0649102i	0.390252	−	0.920708i	$-0.372388\pi$
$587$	21.9885	−	1.57265i	0.907563	−	0.0649102i	0.517311	+	0.855798i	$0.326933\pi$
$588$	−5.28048	+	9.67047i	−0.217763	+	0.398803i
$589$	0.404167	+	0.885001i	0.0166534	+	0.0364658i
$590$	−1.96029	−	2.70715i	−0.0807039	−	0.111452i
$591$	2.65204	+	0.778708i	0.109090	+	0.0320318i
$592$	−7.50213	−	5.61603i	−0.308336	−	0.230817i
$593$	−13.6530	−	36.6050i	−0.560659	−	1.50319i	−0.839778	−	0.542930i	$-0.817315\pi$
$593$	−13.6530	−	36.6050i	−0.560659	−	1.50319i	0.279119	−	0.960257i	$-0.409958\pi$
$594$	−0.414284	+	2.88141i	−0.0169983	+	0.118226i
$595$	4.32859	+	15.6568i	0.177455	+	0.641867i
$596$	−15.9233	+	13.7976i	−0.652244	+	0.565173i
$597$	−12.5451	+	12.5451i	−0.513436	+	0.513436i
$598$	3.66714	+	5.18040i	0.149960	+	0.211842i
$599$		−	25.5351i		−	1.04334i	−0.853148	−	0.521669i	$-0.825310\pi$
$599$		−	25.5351i		−	1.04334i	0.853148	−	0.521669i	$-0.174690\pi$
$600$	−3.18013	−	2.93738i	−0.129828	−	0.119918i
$601$	17.4019	+	11.1835i	0.709838	+	0.456185i	0.845089	−	0.534626i	$-0.179548\pi$
$601$	17.4019	+	11.1835i	0.709838	+	0.456185i	−0.135250	+	0.990811i	$0.543184\pi$
$602$	44.5207	−	33.3278i	1.81453	−	1.35834i
$603$	21.9642	−	8.19222i	0.894451	−	0.333613i
$604$	−4.61987	+	0.664238i	−0.187980	+	0.0270274i
$605$	20.1214	−	12.4845i	0.818050	−	0.507568i
$606$	4.43706	−	2.85153i	0.180243	−	0.115835i
$607$	−12.4071	+	33.2647i	−0.503588	+	1.35017i	0.397924	+	0.917418i	$0.369731\pi$
$607$	−12.4071	+	33.2647i	−0.503588	+	1.35017i	−0.901512	+	0.432754i	$0.857542\pi$
$608$	−4.07584	−	2.22558i	−0.165297	−	0.0902591i
$609$	−7.03462	+	8.11838i	−0.285057	+	0.328973i
$610$	−9.25193	−	7.15779i	−0.374600	−	0.289811i
$611$	10.1509	−	2.98057i	0.410661	−	0.120581i
$612$	3.44875	+	1.28632i	0.139407	+	0.0519962i
$613$	−2.64155	−	0.574635i	−0.106691	−	0.0232093i	0.158903	−	0.987294i	$-0.449204\pi$
$613$	−2.64155	−	0.574635i	−0.106691	−	0.0232093i	−0.265594	+	0.964085i	$0.585568\pi$
$614$	4.07635	−	13.8828i	0.164508	−	0.560264i
$615$	−3.62487	+	0.728496i	−0.146169	+	0.0293758i
$616$	−1.18148	+	2.58708i	−0.0476032	+	0.104237i
$617$	−14.5337	−	19.4148i	−0.585106	−	0.781609i	0.406116	−	0.913822i	$-0.366883\pi$
$617$	−14.5337	−	19.4148i	−0.585106	−	0.781609i	−0.991221	+	0.132212i	$0.957792\pi$
$618$	−2.81642	−	12.9469i	−0.113293	−	0.520800i
$619$	2.13986	+	2.46953i	0.0860082	+	0.0992588i	0.797122	−	0.603818i	$-0.206355\pi$
$619$	2.13986	+	2.46953i	0.0860082	+	0.0992588i	−0.711114	+	0.703077i	$0.751809\pi$
$620$	0.349133	+	0.312362i	0.0140215	+	0.0125448i
$621$	21.0742	−	5.58364i	0.845678	−	0.224064i
$622$	−16.4991	−	16.4991i	−0.661552	−	0.661552i
$623$	−2.96129	−	0.211795i	−0.118641	−	0.00848540i
$624$	0.619505	−	0.963969i	0.0248001	−	0.0385897i
$625$	−1.98092	−	24.9214i	−0.0792367	−	0.996856i
$626$	4.35743	+	1.98997i	0.174158	+	0.0795353i
$627$	1.54301	−	2.06123i	0.0616220	−	0.0823174i
$628$	−11.0012	−	20.1471i	−0.438994	−	0.803957i
$629$	−8.28717	−	12.8951i	−0.330431	−	0.514161i
$630$	−6.63581	+	21.3407i	−0.264377	+	0.850232i
$631$	−1.11462	−	3.79606i	−0.0443725	−	0.151119i	0.934327	−	0.356417i	$-0.116002\pi$
$631$	−1.11462	−	3.79606i	−0.0443725	−	0.151119i	−0.978699	+	0.205298i	$0.934184\pi$
$632$	−0.00482032	−	0.0673969i	−0.000191742	−	0.00268091i
$633$	−0.413621	−	5.78318i	−0.0164400	−	0.229861i
$634$	6.11474	+	20.8249i	0.242847	+	0.827062i
$635$	13.3333	+	25.3671i	0.529117	+	1.00666i
$636$	−3.50163	−	5.44864i	−0.138849	−	0.216053i
$637$	−8.07136	−	14.7816i	−0.319799	−	0.585668i
$638$	−1.07202	+	1.43205i	−0.0424415	+	0.0566952i
$639$	16.3537	+	7.46849i	0.646943	+	0.295449i
$640$	−2.22756	−	0.194894i	−0.0880520	−	0.00770385i
$641$	2.40679	−	3.74504i	0.0950626	−	0.147920i	−0.790465	−	0.612508i	$-0.790161\pi$
$641$	2.40679	−	3.74504i	0.0950626	−	0.147920i	0.885527	+	0.464587i	$0.153797\pi$
$642$	5.12833	+	0.366785i	0.202399	+	0.0144759i
$643$	−9.24567	−	9.24567i	−0.364614	−	0.364614i	0.500895	−	0.865508i	$-0.333004\pi$
$643$	−9.24567	−	9.24567i	−0.364614	−	0.364614i	−0.865508	+	0.500895i	$0.833004\pi$
$644$	21.2925	+	0.566486i	0.839041	+	0.0223227i
$645$	−16.1643	+	18.0671i	−0.636467	+	0.711390i
$646$	−4.97424	−	5.74058i	−0.195709	−	0.225860i
$647$	8.38787	+	38.5584i	0.329761	+	1.51589i	0.781595	+	0.623786i	$0.214406\pi$
$647$	8.38787	+	38.5584i	0.329761	+	1.51589i	−0.451834	+	0.892102i	$0.649230\pi$
$648$	1.68701	+	2.25358i	0.0662719	+	0.0885290i
$649$	0.397631	−	0.870690i	0.0156084	−	0.0341776i
$650$	6.40513	−	1.66186i	0.251230	−	0.0651834i
$651$	−0.226977	+	0.773011i	−0.00889591	+	0.0302967i
$652$	−15.0398	−	3.27171i	−0.589005	−	0.128130i
$653$	−31.5732	−	11.7762i	−1.23556	−	0.460838i	−0.355038	−	0.934852i	$-0.615532\pi$
$653$	−31.5732	−	11.7762i	−1.23556	−	0.460838i	−0.880518	+	0.474013i	$0.842805\pi$
$654$	6.34507	−	1.86308i	0.248112	−	0.0728523i
$655$	−0.460250	−	3.60653i	−0.0179834	−	0.140919i
$656$	−1.25061	+	1.44329i	−0.0488283	+	0.0563509i
$657$	11.1868	+	6.10844i	0.436438	+	0.238313i
$658$	12.4073	−	33.2652i	0.483686	−	1.29681i
$659$	−19.4189	+	12.4798i	−0.756453	+	0.486143i	−0.861144	−	0.508362i	$-0.830251\pi$
$659$	−19.4189	+	12.4798i	−0.756453	+	0.486143i	0.104690	+	0.994505i	$0.466615\pi$
$660$	0.282726	−	1.20711i	0.0110051	−	0.0469869i
$661$	5.09759	−	0.732922i	0.198273	−	0.0285074i	−0.0424627	−	0.999098i	$-0.513520\pi$
$661$	5.09759	−	0.732922i	0.198273	−	0.0285074i	0.240736	+	0.970591i	$0.422611\pi$
$662$	−15.5465	+	5.79854i	−0.604232	+	0.225367i
$663$	1.50043	−	1.12321i	0.0582720	−	0.0436218i
$664$	−5.73657	−	3.68667i	−0.222622	−	0.143071i
$665$	33.1246	−	32.0896i	1.28452	−	1.24438i
$666$		−	21.0887i		−	0.817170i
$667$	13.0105	+	3.19489i	0.503768	+	0.123707i
$668$	8.22129	−	8.22129i	0.318091	−	0.318091i
$669$	5.65024	−	4.89596i	0.218451	−	0.189289i
$670$	−22.4513	+	6.20704i	−0.867369	+	0.239799i
$671$	0.476747	−	3.31585i	0.0184046	−	0.128007i
$672$	−1.34385	−	3.60299i	−0.0518400	−	0.138989i
$673$	38.3584	+	28.7147i	1.47861	+	1.10687i	0.969179	+	0.246358i	$0.0792340\pi$
$673$	38.3584	+	28.7147i	1.47861	+	1.10687i	0.509428	+	0.860513i	$0.329857\pi$
$674$	−12.8947	−	3.78622i	−0.496685	−	0.145840i
$675$	2.34016	−	22.6087i	0.0900727	−	0.870208i
$676$	−4.67280	−	10.2320i	−0.179723	−	0.393538i
$677$	−15.4962	+	28.3792i	−0.595568	+	1.09070i	0.389903	+	0.920856i	$0.372508\pi$
$677$	−15.4962	+	28.3792i	−0.595568	+	1.09070i	−0.985471	+	0.169845i	$0.945673\pi$
$678$	−15.6557	+	1.11972i	−0.601253	+	0.0430025i
$679$	−62.7102	−	54.3387i	−2.40660	−	2.08533i
$680$	−3.30243	−	1.57198i	−0.126642	−	0.0602825i
$681$	15.9871	−	7.30107i	0.612628	−	0.279778i
$682$	−0.0285179	+	0.131095i	−0.00109201	+	0.00501988i
$683$	4.44760	−	2.42858i	0.170183	−	0.0929269i	−0.391900	−	0.920008i	$-0.628182\pi$
$683$	4.44760	−	2.42858i	0.170183	−	0.0929269i	0.562083	+	0.827081i	$0.310000\pi$
$684$	−1.48724	−	10.3440i	−0.0568659	−	0.395511i
$685$	−28.4731	−	11.1377i	−1.08790	−	0.425551i
$686$	−25.1709	−	3.61903i	−0.961029	−	0.138175i
$687$	−1.24753	+	0.271383i	−0.0475962	+	0.0103539i
$688$	−0.893286	+	12.4898i	−0.0340562	+	0.476168i
$689$	9.89998			0.377159
$690$	−9.14839	+	1.58669i	−0.348273	+	0.0604042i
$691$	−0.0185681			−0.000706364			−0.000353182	−	1.00000i	$-0.500112\pi$
$691$	−0.0185681			−0.000706364			−0.000353182		1.00000i	$0.500112\pi$
$692$	0.333147	−	4.65800i	0.0126643	−	0.177071i
$693$	−6.25393	+	1.36046i	−0.237567	+	0.0516796i
$694$	3.44317	+	0.495053i	0.130701	+	0.0187919i
$695$	46.0542	−	20.1552i	1.74694	−	0.764531i
$696$	−0.344212	−	2.39405i	−0.0130473	−	0.0907461i
$697$	−2.74162	+	1.49704i	−0.103846	+	0.0567043i
$698$	−1.00683	+	4.62832i	−0.0381091	+	0.175185i
$699$	5.20973	−	2.37921i	0.197050	−	0.0899898i
$700$	8.41686	−	20.5499i	0.318127	−	0.776713i
$701$	18.8681	+	16.3493i	0.712638	+	0.617504i	0.933826	−	0.357727i	$-0.116448\pi$
$701$	18.8681	+	16.3493i	0.712638	+	0.617504i	−0.221188	+	0.975231i	$0.570994\pi$
$702$	6.00089	−	0.429192i	0.226489	−	0.0161988i
$703$	−20.8566	+	38.1960i	−0.786622	+	1.44059i
$704$	−0.266018	−	0.582498i	−0.0100259	−	0.0219537i
$705$	−2.44537	+	15.2821i	−0.0920979	+	0.575559i
$706$	33.2778	+	9.77123i	1.25242	+	0.367745i
$707$	21.6589	+	16.2137i	0.814568	+	0.609778i
$708$	0.452275	+	1.21260i	0.0169975	+	0.0455722i
$709$	−4.28341	+	29.7917i	−0.160867	+	1.11885i	0.736138	+	0.676831i	$0.236647\pi$
$709$	−4.28341	+	29.7917i	−0.160867	+	1.11885i	−0.897005	+	0.442021i	$0.854262\pi$
$710$	−15.5413	−	8.80920i	−0.583255	−	0.330603i
$711$	0.114914	−	0.0995739i	0.00430963	−	0.00373431i
$712$	0.472670	−	0.472670i	0.0177140	−	0.0177140i
$713$	0.987127	−	0.187389i	0.0369682	−	0.00701779i
$714$		−	6.28990i		−	0.235394i
$715$	1.31856	+	1.36109i	0.0493115	+	0.0509020i
$716$	−8.35654	−	5.37042i	−0.312298	−	0.200702i
$717$	9.15647	−	6.85445i	0.341955	−	0.255984i
$718$	−19.4692	+	7.26165i	−0.726585	+	0.271002i
$719$	14.6266	−	2.10298i	0.545479	−	0.0784281i	0.135934	−	0.990718i	$-0.456596\pi$
$719$	14.6266	−	2.10298i	0.545479	−	0.0784281i	0.409545	+	0.912290i	$0.365687\pi$
$720$	−2.65294	−	4.27576i	−0.0988693	−	0.159348i
$721$	57.1764	−	36.7451i	2.12936	−	1.36846i
$722$	−0.896610	+	2.40390i	−0.0333684	+	0.0894640i
$723$	−14.0331	−	7.66263i	−0.521895	−	0.284976i
$724$	12.2032	−	14.0832i	0.453528	−	0.523399i
$725$	7.92041	−	11.5045i	0.294156	−	0.427268i
$726$	−8.79764	+	2.58322i	−0.326511	+	0.0958723i
$727$	6.15274	+	2.29485i	0.228192	+	0.0851114i	0.460960	−	0.887421i	$-0.347505\pi$
$727$	6.15274	+	2.29485i	0.228192	+	0.0851114i	−0.232767	+	0.972532i	$0.574778\pi$
$728$	5.74355	+	1.24943i	0.212870	+	0.0463071i
$729$	1.54192	−	5.25131i	0.0571083	−	0.194493i
$730$	−10.5445	−	7.01544i	−0.390269	−	0.259653i
$731$	−8.50826	+	18.6305i	−0.314689	+	0.689074i
$732$	2.71437	+	3.62597i	0.100326	+	0.134020i
$733$	3.64792	+	16.7692i	0.134739	+	0.619384i	0.994142	+	0.108085i	$0.0344719\pi$
$733$	3.64792	+	16.7692i	0.134739	+	0.619384i	−0.859403	+	0.511299i	$0.829164\pi$
$734$	−4.44796	−	5.13322i	−0.164177	−	0.189471i
$735$	24.5995	−	1.36741i	0.907368	−	0.0504379i
$736$	−3.23589	+	3.53964i	−0.119276	+	0.130473i
$737$	−4.71698	−	4.71698i	−0.173752	−	0.173752i
$738$	−4.28662	−	0.306585i	−0.157793	−	0.0112856i
$739$	8.70552	−	13.5461i	0.320238	−	0.498300i	−0.643393	−	0.765536i	$-0.722474\pi$
$739$	8.70552	−	13.5461i	0.320238	−	0.498300i	0.963631	+	0.267236i	$0.0861104\pi$
$740$	−1.82641	+	20.8752i	−0.0671402	+	0.767387i
$741$	−4.84042	−	2.21055i	−0.177817	−	0.0812065i
$742$	19.9101	−	26.5968i	0.730923	−	0.976399i
$743$	−14.4414	−	26.4475i	−0.529805	−	0.970266i	−0.996317	−	0.0857505i	$-0.972671\pi$
$743$	−14.4414	−	26.4475i	−0.529805	−	0.970266i	0.466512	−	0.884515i	$-0.345511\pi$
$744$	−0.0980702	−	0.152600i	−0.00359543	−	0.00559459i
$745$	44.9882	+	13.9890i	1.64824	+	0.512516i
$746$	6.30294	+	21.4658i	0.230767	+	0.785920i
$747$	−1.09472	−	15.3062i	−0.0400536	−	0.560023i
$748$	−0.0747228	−	1.04476i	−0.00273214	−	0.0382003i
$749$	7.43028	+	25.3052i	0.271496	+	0.924632i
$750$	−1.83209	+	9.50529i	−0.0668986	+	0.347084i
$751$	0.941316	+	1.46472i	0.0343491	+	0.0534483i	0.858004	−	0.513644i	$-0.171705\pi$
$751$	0.941316	+	1.46472i	0.0343491	+	0.0534483i	−0.823654	+	0.567092i	$0.808068\pi$
$752$	3.83106	+	7.01607i	0.139704	+	0.255850i
$753$	15.0208	−	20.0654i	0.547388	−	0.731224i
$754$	3.36291	+	1.53579i	0.122470	+	0.0559301i
$755$	6.70848	+	7.99491i	0.244147	+	0.290964i
$756$	10.9155	−	16.9849i	0.396993	−	0.617733i
$757$	4.28835	+	0.306709i	0.155863	+	0.0111475i	0.149052	−	0.988829i	$-0.452378\pi$
$757$	4.28835	+	0.306709i	0.155863	+	0.0111475i	0.00681020	+	0.999977i	$0.497832\pi$
$758$	10.7771	+	10.7771i	0.391444	+	0.391444i
$759$	−1.68724	−	2.05516i	−0.0612428	−	0.0745978i
$760$	0.576328	+	10.3680i	0.0209056	+	0.376088i
$761$	−25.0554	−	28.9155i	−0.908257	−	1.04818i	−0.998633	−	0.0522769i	$-0.983352\pi$
$761$	−25.0554	−	28.9155i	−0.908257	−	1.04818i	0.0903754	−	0.995908i	$-0.471193\pi$
$762$	−2.35875	−	10.8430i	−0.0854484	−	0.392800i
$763$	20.3286	+	27.1558i	0.735945	+	0.983107i
$764$	5.78388	−	12.6649i	0.209254	−	0.458201i
$765$	−1.62169	−	8.06923i	−0.0586322	−	0.291744i
$766$	−1.71417	+	5.83793i	−0.0619355	+	0.210933i
$767$	−1.93301	−	0.420500i	−0.0697969	−	0.0151834i
$768$	0.811237	+	0.302576i	0.0292730	+	0.0109183i
$769$	−43.1597	+	12.6728i	−1.55638	+	0.456994i	−0.942999	−	0.332795i	$-0.892008\pi$
$769$	−43.1597	+	12.6728i	−1.55638	+	0.456994i	−0.613379	+	0.789789i	$0.710190\pi$
$770$	6.30844	−	0.805056i	0.227340	−	0.0290122i
$771$	−2.68204	+	3.09523i	−0.0965911	+	0.111472i
$772$	−11.3462	−	6.19552i	−0.408360	−	0.222982i
$773$	−10.0864	+	27.0428i	−0.362784	+	0.972661i	0.619456	+	0.785031i	$0.287353\pi$
$773$	−10.0864	+	27.0428i	−0.362784	+	0.972661i	−0.982240	+	0.187629i	$0.939920\pi$
$774$	−23.7049	+	15.2342i	−0.852054	+	0.547582i
$775$	0.181909	−	1.03162i	0.00653435	−	0.0370567i
$776$	18.4927	−	2.65885i	0.663850	−	0.0954473i
$777$	−33.7648	+	12.5936i	−1.21131	+	0.451794i
$778$	17.4333	−	13.0504i	0.625013	−	0.467879i
$779$	7.46076	+	4.79474i	0.267309	+	0.171789i
$780$	−2.56193	−	0.0406611i	−0.0917317	−	0.00145590i
$781$		−	5.11600i		−	0.183065i
$782$	−6.98242	+	3.57499i	−0.249691	+	0.127841i
$783$	8.97942	−	8.97942i	0.320898	−	0.320898i
$784$	9.61741	−	8.33354i	0.343479	−	0.297626i
$785$	−25.3111	+	44.6543i	−0.903394	+	1.59378i
$786$	−0.200352	+	1.39348i	−0.00714632	+	0.0497037i
$787$	1.58420	+	4.24741i	0.0564707	+	0.151404i	0.962122	−	0.272620i	$-0.0878901\pi$
$787$	1.58420	+	4.24741i	0.0564707	+	0.151404i	−0.905651	+	0.424024i	$0.860617\pi$
$788$	−2.55558	−	1.91308i	−0.0910388	−	0.0681508i
$789$	−4.35514	−	1.27878i	−0.155047	−	0.0455259i
$790$	−0.122375	+	0.0886134i	−0.00435389	+	0.00315272i
$791$	−33.4462	−	73.2370i	−1.18921	−	2.60401i
$792$	0.690619	−	1.26477i	0.0245401	−	0.0449418i
$793$	−6.90567	+	0.493904i	−0.245228	+	0.0175390i
$794$	−14.9814	−	12.9815i	−0.531671	−	0.460696i
$795$	−6.22458	+	13.0767i	−0.220763	+	0.463782i
$796$	18.6390	−	8.51215i	0.660642	−	0.301705i
$797$	9.59733	−	44.1182i	0.339955	−	1.56275i	−0.416769	−	0.909013i	$-0.636837\pi$
$797$	9.59733	−	44.1182i	0.339955	−	1.56275i	0.756723	−	0.653735i	$-0.226799\pi$
$798$	−15.6734	+	8.55835i	−0.554834	+	0.302962i
$799$	1.86082	+	12.9423i	0.0658311	+	0.457865i
$800$	2.25577	+	4.46223i	0.0797537	+	0.157764i
$801$	1.48894	+	0.214078i	0.0526092	+	0.00756406i
$802$	−19.8605	+	4.32039i	−0.701300	+	0.152558i
$803$	0.258748	−	3.61777i	0.00913103	−	0.127668i
$804$	9.01948			0.318093
$805$	−24.0255	−	41.1245i	−0.846786	−	1.44945i
$806$	0.277269			0.00976639
$807$	−1.33955	+	18.7294i	−0.0471545	+	0.659306i
$808$	−5.95247	+	1.29488i	−0.209407	+	0.0455537i
$809$	−43.3227	−	6.22886i	−1.52314	−	0.218995i	−0.670667	−	0.741759i	$-0.733992\pi$
$809$	−43.3227	−	6.22886i	−1.52314	−	0.218995i	−0.852478	+	0.522764i	$0.824901\pi$
$810$	2.29308	−	5.86215i	0.0805708	−	0.205975i
$811$	−0.844780	−	5.87558i	−0.0296642	−	0.206319i	0.969599	−	0.244699i	$-0.0786893\pi$
$811$	−0.844780	−	5.87558i	−0.0296642	−	0.206319i	−0.999263	+	0.0383801i	$0.987780\pi$
$812$	10.8892	−	5.94595i	0.382136	−	0.208662i
$813$	−0.807055	+	3.70997i	−0.0283047	+	0.130114i
$814$	−5.45878	+	2.49294i	−0.191330	+	0.0873775i
$815$	11.5141	+	32.4334i	0.403322	+	1.13609i
$816$	1.07030	+	0.927421i	0.0374680	+	0.0324662i
$817$	58.0010	−	4.14832i	2.02920	−	0.145131i
$818$	14.5619	−	26.6681i	0.509144	−	0.932428i
$819$	5.49479	+	12.0319i	0.192004	+	0.420429i
$820$	4.21667	+	0.674729i	0.147252	+	0.0235626i
$821$	−17.5582	−	5.15556i	−0.612786	−	0.179930i	−0.0394106	−	0.999223i	$-0.512548\pi$
$821$	−17.5582	−	5.15556i	−0.612786	−	0.179930i	−0.573375	+	0.819293i	$0.694366\pi$
$822$	9.47723	+	7.09456i	0.330556	+	0.247451i
$823$	11.5399	+	30.9397i	0.402256	+	1.07849i	0.967346	+	0.253461i	$0.0815688\pi$
$823$	11.5399	+	30.9397i	0.402256	+	1.07849i	−0.565090	+	0.825029i	$0.691158\pi$
$824$	−2.17783	+	15.1472i	−0.0758684	+	0.527676i
$825$	−2.62688	+	0.885880i	−0.0914563	+	0.0308424i
$826$	−5.01721	+	4.34744i	−0.174571	+	0.151267i
$827$	−10.7227	+	10.7227i	−0.372864	+	0.372864i	−0.868519	−	0.495655i	$-0.834928\pi$
$827$	−10.7227	+	10.7227i	−0.372864	+	0.372864i	0.495655	+	0.868519i	$0.334928\pi$
$828$	−10.7405	−	1.05593i	−0.373258	−	0.0366962i
$829$			25.9627i			0.901722i	0.892594	+	0.450861i	$0.148883\pi$
$829$			25.9627i			0.901722i	−0.892594	+	0.450861i	$0.851117\pi$
$830$	−0.241974	+	15.2460i	−0.00839903	+	0.529196i
$831$	14.7166	+	9.45777i	0.510513	+	0.328086i
$832$	−1.05947	+	0.793109i	−0.0367305	+	0.0274961i
$833$	19.5026	−	7.27410i	0.675726	−	0.252033i
$834$	−19.2675	+	2.77025i	−0.667179	+	0.0959258i
$835$	−25.3130	−	5.92872i	−0.875991	−	0.205172i
$836$	−2.50171	+	1.60775i	−0.0865235	+	0.0556053i
$837$	0.332827	−	0.892343i	0.0115042	−	0.0308439i
$838$	20.9254	+	11.4261i	0.722857	+	0.394710i
$839$	−4.99582	+	5.76549i	−0.172475	+	0.199047i	−0.835405	−	0.549634i	$-0.814767\pi$
$839$	−4.99582	+	5.76549i	−0.172475	+	0.199047i	0.662930	+	0.748681i	$0.269313\pi$
$840$	−5.26159	+	6.80096i	−0.181542	+	0.234656i
$841$	−20.3379	+	5.97175i	−0.701307	+	0.205922i
$842$	3.90483	+	1.45643i	0.134569	+	0.0501918i
$843$	−18.5865	−	4.04325i	−0.640154	−	0.139257i
$844$	−1.88660	+	6.42517i	−0.0649395	+	0.221164i
$845$	−13.9325	+	20.9411i	−0.479292	+	0.720396i
$846$	−7.47289	+	16.3634i	−0.256923	+	0.562584i
$847$	−28.1862	−	37.6524i	−0.968490	−	1.29375i
$848$	1.59009	+	7.30953i	0.0546040	+	0.251010i
$849$	5.71112	+	6.59098i	0.196005	+	0.226202i
$850$	0.906421	+	8.12798i	0.0310900	+	0.278787i
$851$	33.1711	+	30.3245i	1.13709	+	1.03951i
$852$	4.89123	+	4.89123i	0.167571	+	0.167571i
$853$	−1.83730	−	0.131406i	−0.0629078	−	0.00449926i	0.0398498	−	0.999206i	$-0.487312\pi$
$853$	−1.83730	−	0.131406i	−0.0629078	−	0.00449926i	−0.102758	+	0.994706i	$0.532767\pi$
$854$	−12.5613	+	19.5457i	−0.429838	+	0.668841i
$855$	−17.9007	+	15.0204i	−0.612191	+	0.513686i
$856$	−5.40155	−	2.46680i	−0.184621	−	0.0843136i
$857$	−0.140079	+	0.187124i	−0.00478500	+	0.00639202i	−0.802927	−	0.596077i	$-0.796725\pi$
$857$	−0.140079	+	0.187124i	−0.00478500	+	0.00639202i	0.798142	+	0.602469i	$0.205816\pi$
$858$	−0.351663	−	0.644022i	−0.0120056	−	0.0219866i
$859$	−13.2769	−	20.6592i	−0.453001	−	0.704883i	0.537366	−	0.843349i	$-0.319419\pi$
$859$	−13.2769	−	20.6592i	−0.453001	−	0.704883i	−0.990367	+	0.138466i	$0.955783\pi$
$860$	24.7842	−	13.0270i	0.845136	−	0.444216i
$861$	2.06899	+	7.04634i	0.0705110	+	0.240139i
$862$	−1.60599	−	22.4546i	−0.0547002	−	0.764808i
$863$	0.733939	+	10.2618i	0.0249836	+	0.349316i	0.994533	+	0.104421i	$0.0332989\pi$
$863$	0.733939	+	10.2618i	0.0249836	+	0.349316i	−0.969550	+	0.244895i	$0.921247\pi$
$864$	1.28073	+	4.36175i	0.0435712	+	0.148390i
$865$	−9.24318	+	4.85835i	−0.314277	+	0.165189i
$866$	−4.70731	−	7.32472i	−0.159961	−	0.248904i
$867$	−5.94394	−	10.8855i	−0.201867	−	0.369691i
$868$	0.557623	−	0.744897i	0.0189270	−	0.0252835i
$869$	−0.0393589	−	0.0179746i	−0.00133516	−	0.000609746i
$870$	−4.14301	+	3.47637i	−0.140461	+	0.117860i
$871$	−7.45356	+	11.5980i	−0.252554	+	0.392982i
$872$	−7.61826	−	0.544868i	−0.257987	−	0.0184516i
$873$	29.7288	+	29.7288i	1.00617	+	1.00617i
$874$	18.4089	+	12.5348i	0.622692	+	0.423996i
$875$	−48.9685	+	8.23395i	−1.65544	+	0.278358i
$876$	3.21145	+	3.70621i	0.108505	+	0.125221i
$877$	−3.87453	−	17.8109i	−0.130833	−	0.601432i	−0.995140	−	0.0984669i	$-0.968606\pi$
$877$	−3.87453	−	17.8109i	−0.130833	−	0.601432i	0.864307	−	0.502965i	$-0.167757\pi$
$878$	2.31007	+	3.08589i	0.0779610	+	0.104144i
$879$	1.30289	−	2.85293i	0.0439454	−	0.0962269i
$880$	−0.793164	+	1.19216i	−0.0267376	+	0.0401876i
$881$	−4.62296	+	15.7444i	−0.155752	+	0.530441i	−0.999985	−	0.00553503i	$-0.998238\pi$
$881$	−4.62296	+	15.7444i	−0.155752	+	0.530441i	0.844233	+	0.535976i	$0.180056\pi$
$882$	27.9827	+	6.08725i	0.942225	+	0.204968i
$883$	32.6348	+	12.1721i	1.09825	+	0.409625i	0.832279	−	0.554357i	$-0.187036\pi$
$883$	32.6348	+	12.1721i	1.09825	+	0.409625i	0.265968	+	0.963982i	$0.414308\pi$
$884$	−2.07703	+	0.609871i	−0.0698581	+	0.0205122i
$885$	1.77080	−	2.28888i	0.0595249	−	0.0769399i
$886$	13.0375	−	15.0461i	0.438005	−	0.505484i
$887$	21.0048	+	11.4695i	0.705271	+	0.385107i	0.791501	−	0.611168i	$-0.209300\pi$
$887$	21.0048	+	11.4695i	0.705271	+	0.385107i	−0.0862298	+	0.996275i	$0.527482\pi$
$888$	2.83554	−	7.60236i	0.0951543	−	0.255119i
$889$	47.8851	−	30.7739i	1.60601	−	1.03212i
$890$	−1.45533	−	0.340862i	−0.0487827	−	0.0114257i
$891$	1.78433	−	0.256548i	0.0597773	−	0.00859467i
$892$	−8.09047	+	3.01759i	−0.270889	+	0.101036i
$893$	29.7182	−	22.2468i	0.994483	−	0.744461i
$894$	−15.3467	−	9.86270i	−0.513269	−	0.329858i
$895$	−0.352486	+	22.2090i	−0.0117823	+	0.742366i
$896$			4.44136i			0.148375i
$897$	−3.40911	+	4.31016i	−0.113827	+	0.143912i
$898$	−12.5027	+	12.5027i	−0.417222	+	0.417222i
$899$	0.442302	−	0.383257i	0.0147516	−	0.0127823i
$900$	−4.99658	+	10.0814i	−0.166553	+	0.336048i
$901$	−1.74131	+	12.1111i	−0.0580115	+	0.403479i
$902$	0.427372	+	1.14583i	0.0142299	+	0.0381519i
$903$	38.5472	+	28.8561i	1.28277	+	0.960271i
$904$	17.3936	+	5.10724i	0.578504	+	0.169864i
$905$	−41.1452	−	6.58384i	−1.36771	−	0.218854i
$906$	−1.67875	−	3.67596i	−0.0557728	−	0.122125i
$907$	20.7242	−	37.9535i	0.688136	−	1.26023i	−0.266897	−	0.963725i	$-0.585998\pi$
$907$	20.7242	−	37.9535i	0.688136	−	1.26023i	0.955033	−	0.296501i	$-0.0958198\pi$
$908$	−20.2472	+	1.44811i	−0.671927	+	0.0480572i
$909$	−10.3601	−	8.97708i	−0.343623	−	0.297751i
$910$	−4.39712	−	12.3860i	−0.145763	−	0.410591i
$911$	−26.5616	+	12.1303i	−0.880024	+	0.401894i	−0.803592	−	0.595181i	$-0.797080\pi$
$911$	−26.5616	+	12.1303i	−0.880024	+	0.401894i	−0.0764326	+	0.997075i	$0.524353\pi$
$912$	0.854683	−	3.92892i	0.0283014	−	0.130099i
$913$	−3.83257	+	2.09274i	−0.126840	+	0.0692596i
$914$	−0.0242049	−	0.168348i	−0.000800625	−	0.00556847i
$915$	3.68953	−	9.43211i	0.121972	−	0.311816i
$916$	1.45954	+	0.209850i	0.0482246	+	0.00693365i
$917$	−7.05647	+	1.53504i	−0.233025	+	0.0506915i
$918$	−0.530449	+	7.41665i	−0.0175074	+	0.244786i
$919$	35.9123			1.18464			0.592318	−	0.805704i	$-0.298213\pi$
$919$	35.9123			1.18464			0.592318	+	0.805704i	$0.298213\pi$
$920$	10.5403	+	1.97544i	0.347503	+	0.0651282i
$921$	12.5276			0.412797
$922$	−0.952096	+	13.3120i	−0.0313556	+	0.438409i
$923$	−10.3316	+	2.24750i	−0.340068	+	0.0739772i
$924$	−2.43743	−	0.350450i	−0.0801857	−	0.0115290i
$925$	41.8170	−	21.1396i	1.37493	−	0.695065i
$926$	2.27414	+	15.8170i	0.0747328	+	0.519778i
$927$	−30.2245	+	16.5038i	−0.992702	+	0.542056i
$928$	−0.593795	+	2.72963i	−0.0194923	+	0.0896046i
$929$	11.6918	−	5.33948i	0.383597	−	0.175183i	−0.214277	−	0.976773i	$-0.568740\pi$
$929$	11.6918	−	5.33948i	0.383597	−	0.175183i	0.597874	+	0.801590i	$0.296012\pi$
$930$	−0.174332	+	0.366239i	−0.00571658	+	0.0120095i
$931$	−44.6622	−	38.7000i	−1.46374	−	1.26834i
$932$	−6.59797	+	0.471896i	−0.216124	+	0.0154575i
$933$	9.68204	−	17.7313i	0.316976	−	0.580498i
$934$	4.41012	+	9.65681i	0.144303	+	0.315980i
$935$	−1.89701	+	1.37365i	−0.0620387	+	0.0449232i
$936$	−2.85756	−	0.839055i	−0.0934023	−	0.0274254i
$937$	4.32464	+	3.23738i	0.141280	+	0.105761i	0.667580	−	0.744538i	$-0.267330\pi$
$937$	4.32464	+	3.23738i	0.141280	+	0.105761i	−0.526300	+	0.850299i	$0.676421\pi$
$938$	16.1685	+	43.3493i	0.527919	+	1.41541i
$939$	−0.590264	+	4.10538i	−0.0192625	+	0.133974i
$940$	8.81440	−	15.5505i	0.287494	−	0.507201i
$941$	−20.2062	+	17.5088i	−0.658703	+	0.570769i	−0.918756	−	0.394825i	$-0.870805\pi$
$941$	−20.2062	+	17.5088i	−0.658703	+	0.570769i	0.260054	+	0.965594i	$0.416260\pi$
$942$	14.0538	−	14.0538i	0.457897	−	0.457897i
$943$	6.64620	−	6.30172i	0.216430	−	0.205212i
$944$		−	1.49475i		−	0.0486500i
$945$	−45.1404	−	0.716436i	−1.46842	−	0.0233057i
$946$	6.74556	+	4.33511i	0.219317	+	0.140946i
$947$	−1.93847	+	1.45112i	−0.0629917	+	0.0471550i	−0.630310	−	0.776344i	$-0.717072\pi$
$947$	−1.93847	+	1.45112i	−0.0629917	+	0.0471550i	0.567318	+	0.823499i	$0.307981\pi$
$948$	0.0548145	−	0.0204448i	0.00178029	−	0.000664015i
$949$	−7.41963	+	1.06678i	−0.240851	+	0.0346292i
$950$	19.0203	−	13.3180i	0.617101	−	0.432093i
$951$	−15.8088	+	10.1597i	−0.512636	+	0.329451i
$952$	−2.53872	+	6.80657i	−0.0822804	+	0.220602i
$953$	−33.3113	−	18.1893i	−1.07906	−	0.589211i	−0.161525	−	0.986869i	$-0.551641\pi$
$953$	−33.3113	−	18.1893i	−1.07906	−	0.589211i	−0.917534	+	0.397658i	$0.869823\pi$
$954$	−11.0237	+	12.7220i	−0.356905	+	0.411891i
$955$	−30.8826	+	3.94111i	−0.999339	+	0.127531i
$956$	−12.6752	+	3.72178i	−0.409945	+	0.120371i
$957$	−1.45118	−	0.541262i	−0.0469099	−	0.0174965i
$958$	−1.58720	−	0.345275i	−0.0512802	−	0.0111553i
$959$	−17.1088	+	58.2671i	−0.552471	+	1.88154i
$960$	−0.381463	−	1.89810i	−0.0123117	−	0.0612608i
$961$	−12.8596	+	28.1587i	−0.414827	+	0.908344i
$962$	7.43248	+	9.92863i	0.239633	+	0.320112i
$963$	−2.84049	−	13.0575i	−0.0915335	−	0.420773i
$964$	12.0930	+	13.9561i	0.389489	+	0.449495i
$965$	1.60437	+	28.8623i	0.0516465	+	0.929111i
$966$	4.72330	+	17.8270i	0.151970	+	0.573575i
$967$	6.00616	+	6.00616i	0.193145	+	0.193145i	0.797054	−	0.603908i	$-0.206391\pi$
$967$	6.00616	+	6.00616i	0.193145	+	0.193145i	−0.603908	+	0.797054i	$0.706391\pi$
$968$	10.5629	+	0.755477i	0.339506	+	0.0242819i
$969$	3.55564	−	5.53269i	0.114224	−	0.177736i
$970$	−26.8531	−	32.0025i	−0.862202	−	1.02754i
$971$	−28.9927	−	13.2405i	−0.930421	−	0.424909i	−0.108233	−	0.994126i	$-0.534519\pi$
$971$	−28.9927	−	13.2405i	−0.930421	−	0.424909i	−0.822188	+	0.569217i	$0.807247\pi$
$972$	−9.63341	+	12.8687i	−0.308992	+	0.412765i
$973$	−47.8535	−	87.6372i	−1.53411	−	2.80952i
$974$	−16.0073	−	24.9078i	−0.512905	−	0.798096i
$975$	2.94301	+	4.91572i	0.0942518	+	0.157429i
$976$	−1.47383	−	5.01939i	−0.0471760	−	0.160667i
$977$	3.85874	+	53.9523i	0.123452	+	1.72609i	0.561793	+	0.827278i	$0.310112\pi$
$977$	3.85874	+	53.9523i	0.123452	+	1.72609i	−0.438341	+	0.898809i	$0.644434\pi$
$978$	−0.950698	−	13.2925i	−0.0304000	−	0.425047i
$979$	−0.120598	−	0.410718i	−0.00385431	−	0.0131266i
$980$	−27.1721	−	8.44909i	−0.867982	−	0.269896i
$981$	−9.29225	−	14.4590i	−0.296679	−	0.461641i
$982$	6.18394	+	11.3250i	0.197337	+	0.361396i
$983$	−17.2550	+	23.0500i	−0.550349	+	0.735180i	−0.986331	−	0.164775i	$-0.947310\pi$
$983$	−17.2550	+	23.0500i	−0.550349	+	0.735180i	0.435982	+	0.899955i	$0.356401\pi$
$984$	−1.50408	−	0.686891i	−0.0479484	−	0.0218973i
$985$	−0.622162	+	7.11107i	−0.0198237	+	0.226578i
$986$	−2.47030	+	3.84386i	−0.0786704	+	0.122413i
$987$	30.6618	+	2.19297i	0.975975	+	0.0698031i
$988$	4.34582	+	4.34582i	0.138259	+	0.138259i
$989$	10.1241	−	59.1923i	0.321928	−	1.88220i
$990$	−3.21731	+	0.178841i	−0.102253	+	0.00568392i
$991$	5.67864	+	6.55350i	0.180388	+	0.208179i	0.838741	−	0.544530i	$-0.183292\pi$
$991$	5.67864	+	6.55350i	0.180388	+	0.208179i	−0.658353	+	0.752709i	$0.728747\pi$
$992$	0.0445337	+	0.204718i	0.00141395	+	0.00649981i
$993$	−8.60946	−	11.5009i	−0.273213	−	0.364970i
$994$	−14.7401	+	32.2763i	−0.467527	+	1.02374i
$995$	−38.1471	−	25.3800i	−1.20934	−	0.804599i
$996$	1.66339	−	5.66499i	0.0527065	−	0.179502i
$997$	4.65575	+	1.01280i	0.147449	+	0.0320756i	0.285684	−	0.958324i	$-0.407779\pi$
$997$	4.65575	+	1.01280i	0.147449	+	0.0320756i	−0.138235	+	0.990399i	$0.544143\pi$
$998$	−25.7439	−	9.60198i	−0.814909	−	0.303945i
$999$	40.8754	−	12.0021i	1.29324	−	0.379729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.217.11	yes	240
5.3	odd	4	inner	230.2.l.a.33.5	yes	240
23.7	odd	22	inner	230.2.l.a.7.5	✓	240
115.53	even	44	inner	230.2.l.a.53.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.5	✓	240	23.7	odd	22	inner
230.2.l.a.33.5	yes	240	5.3	odd	4	inner
230.2.l.a.53.11	yes	240	115.53	even	44	inner
230.2.l.a.217.11	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.846041 - 0.184045i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(0.896501 + 2.04848i) q^{5} +(-0.123220 - 0.857015i) q^{6} +(3.89809 - 2.12852i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-2.04698 + 0.934826i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.846041 - 0.184045i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(0.896501 + 2.04848i) q^{5} +(-0.123220 - 0.857015i) q^{6} +(3.89809 - 2.12852i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-2.04698 + 0.934826i) q^{9} +(2.10722 - 0.748080i) q^{10} +(0.483957 + 0.419351i) q^{11} +(-0.863622 + 0.0617674i) q^{12} +(0.634258 - 1.16156i) q^{13} +(-1.84501 - 4.04000i) q^{14} +(1.13549 + 1.56810i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.30942 + 0.980222i) q^{17} +(0.786414 + 2.10846i) q^{18} +(0.660894 - 4.59662i) q^{19} +(-0.595846 - 2.15522i) q^{20} +(2.90620 - 2.51823i) q^{21} +(0.452808 - 0.452808i) q^{22} +(-4.44729 - 1.79488i) q^{23} +0.865828i q^{24} +(-3.39257 + 3.67294i) q^{25} +(-1.11335 - 0.715507i) q^{26} +(-3.63917 + 2.72425i) q^{27} +(-4.16133 + 1.55210i) q^{28} +(-2.76504 + 0.397553i) q^{29} +(1.64511 - 1.02073i) q^{30} +(-0.176248 + 0.113268i) q^{31} +(0.349464 - 0.936950i) q^{32} +(0.486627 + 0.265718i) q^{33} +(1.07114 - 1.23616i) q^{34} +(7.85487 + 6.07695i) q^{35} +(2.15919 - 0.633995i) q^{36} +(-8.78046 - 3.27494i) q^{37} +(-4.53776 - 0.987129i) q^{38} +(0.322830 - 1.09946i) q^{39} +(-2.19223 + 0.440577i) q^{40} +(-0.793335 + 1.73716i) q^{41} +(-2.30449 - 3.07844i) q^{42} +(2.66167 + 12.2355i) q^{43} +(-0.419351 - 0.483957i) q^{44} +(-3.75010 - 3.35514i) q^{45} +(-2.10758 + 4.30791i) q^{46} +(5.65253 + 5.65253i) q^{47} +(0.863622 + 0.0617674i) q^{48} +(6.88001 - 10.7055i) q^{49} +(3.42155 + 3.64595i) q^{50} +(1.28823 + 0.588315i) q^{51} +(-0.793109 + 1.05947i) q^{52} +(3.58501 + 6.56546i) q^{53} +(2.45769 + 3.82425i) q^{54} +(-0.425166 + 1.36733i) q^{55} +(1.25128 + 4.26145i) q^{56} +(-0.286841 - 4.01056i) q^{57} +(0.199284 + 2.78635i) q^{58} +(-0.421120 - 1.43420i) q^{59} +(-0.900767 - 1.71374i) q^{60} +(-2.82825 - 4.40084i) q^{61} +(0.100406 + 0.183879i) q^{62} +(-5.98953 + 8.00107i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(2.94804 + 0.257930i) q^{65} +(0.299757 - 0.466431i) q^{66} +(-10.3906 - 0.743153i) q^{67} +(-1.15660 - 1.15660i) q^{68} +(-4.09293 - 0.700044i) q^{69} +(6.62183 - 7.40133i) q^{70} +(-5.23180 - 6.03781i) q^{71} +(-0.478345 - 2.19892i) q^{72} +(-3.39429 - 4.53424i) q^{73} +(-3.89299 + 8.52446i) q^{74} +(-2.19427 + 3.73184i) q^{75} +(-1.30833 + 4.45578i) q^{76} +(2.77910 + 0.604557i) q^{77} +(-1.07362 - 0.400441i) q^{78} +(-0.0648320 + 0.0190364i) q^{79} +(0.283062 + 2.21808i) q^{80} +(1.84348 - 2.12749i) q^{81} +(1.67614 + 0.915241i) q^{82} +(-2.38302 + 6.38913i) q^{83} +(-3.23500 + 2.07901i) q^{84} +(-0.834070 + 3.56110i) q^{85} +(12.3942 - 1.78202i) q^{86} +(-2.26617 + 0.845237i) q^{87} +(-0.512640 + 0.383758i) q^{88} +(-0.562341 - 0.361394i) q^{89} +(-3.61412 + 3.50119i) q^{90} -5.87788i q^{91} +(4.14658 + 2.40953i) q^{92} +(-0.128266 + 0.128266i) q^{93} +(6.04138 - 5.23488i) q^{94} +(10.0086 - 2.76704i) q^{95} +(0.123220 - 0.857015i) q^{96} +(-6.52900 - 17.5049i) q^{97} +(-10.1874 - 7.62621i) q^{98} +(-1.38267 - 0.405989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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