LMFDB - Embedded newform 950.2.bb.a.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.1
Character	$\chi$	$=$	950.257
Dual form			950.2.bb.a.743.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(-2.17648 - 0.190417i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.431262 + 0.115556i) q^{7} +(0.258819 - 0.965926i) q^{8} +(1.74638 + 0.307934i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(-2.17648 - 0.190417i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.431262 + 0.115556i) q^{7} +(0.258819 - 0.965926i) q^{8} +(1.74638 + 0.307934i) q^{9} +(2.37939 + 4.12122i) q^{11} +(-0.565466 - 2.11035i) q^{12} +(-0.210174 - 2.40230i) q^{13} +(0.419550 + 0.152704i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.392349 + 0.560333i) q^{17} +(-1.25393 - 1.25393i) q^{18} +(-2.15160 - 3.79086i) q^{19} +(0.960637 - 0.169386i) q^{21} +(0.414754 - 4.74066i) q^{22} +(0.188689 - 0.404644i) q^{23} +(-0.747243 + 2.05303i) q^{24} +(-1.20574 + 2.08840i) q^{26} +(2.58872 + 0.693647i) q^{27} +(-0.256088 - 0.365731i) q^{28} +(0.892951 - 5.06418i) q^{29} +(2.27332 + 1.31250i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-4.39393 - 9.42282i) q^{33} +(0.642788 - 0.233956i) q^{34} +(0.307934 + 1.74638i) q^{36} +(-1.48921 + 1.48921i) q^{37} +(-0.411860 + 4.33940i) q^{38} +5.26857i q^{39} +(-0.333626 - 0.397600i) q^{41} +(-0.884064 - 0.412246i) q^{42} +(-8.46881 + 3.94907i) q^{43} +(-3.05888 + 3.64543i) q^{44} +(-0.386659 + 0.223238i) q^{46} +(-4.32402 + 3.02771i) q^{47} +(1.78968 - 1.25315i) q^{48} +(-5.88954 + 3.40033i) q^{49} +(0.960637 - 1.14484i) q^{51} +(2.18554 - 1.01913i) q^{52} +(-7.35361 - 3.42904i) q^{53} +(-1.72270 - 2.05303i) q^{54} +0.446476i q^{56} +(3.96107 + 8.66043i) q^{57} +(-3.63616 + 3.63616i) q^{58} +(-0.0555796 - 0.315207i) q^{59} +(-7.77244 + 2.82894i) q^{61} +(-1.10937 - 2.37906i) q^{62} +(-0.788731 + 0.0690050i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-1.80541 + 10.2390i) q^{66} +(6.44380 + 9.20270i) q^{67} +(-0.660732 - 0.177043i) q^{68} +(-0.487728 + 0.844770i) q^{69} +(0.879385 - 2.41609i) q^{71} +(0.749437 - 1.60717i) q^{72} +(-0.378413 + 4.32528i) q^{73} +(2.07407 - 0.365715i) q^{74} +(2.82635 - 3.31839i) q^{76} +(-1.50237 - 1.50237i) q^{77} +(3.02193 - 4.31576i) q^{78} +(-12.3274 + 10.3439i) q^{79} +(-10.5013 - 3.82218i) q^{81} +(0.0452364 + 0.517055i) q^{82} +(-0.224591 - 0.838185i) q^{83} +(0.487728 + 0.844770i) q^{84} +(9.20233 + 1.62262i) q^{86} +(-2.90780 + 10.8520i) q^{87} +(4.59662 - 1.23166i) q^{88} +(-12.7545 - 10.7023i) q^{89} +(0.368241 + 1.01173i) q^{91} +(0.444777 + 0.0389129i) q^{92} +(-4.69791 - 3.28951i) q^{93} +5.27866 q^{94} -2.18479 q^{96} +(-2.46380 - 1.72517i) q^{97} +(6.77478 + 0.592717i) q^{98} +(2.88624 + 7.92989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	−2.17648	−	0.190417i	−1.25659	−	0.109937i	−0.560660	−	0.828046i	$-0.689452\pi$
$3$	−2.17648	−	0.190417i	−1.25659	−	0.109937i	−0.695931	+	0.718109i	$0.745008\pi$
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$		0			0
$5$		0			0
$6$	1.67365	+	1.40436i	0.683264	+	0.573327i
$7$	−0.431262	+	0.115556i	−0.163002	+	0.0436762i	−0.339397	−	0.940643i	$-0.610223\pi$
$7$	−0.431262	+	0.115556i	−0.163002	+	0.0436762i	0.176395	+	0.984319i	$0.443556\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	1.74638	+	0.307934i	0.582126	+	0.102645i
$10$		0			0
$11$	2.37939	+	4.12122i	0.717412	+	1.24259i	0.962022	+	0.272972i	$0.0880066\pi$
$11$	2.37939	+	4.12122i	0.717412	+	1.24259i	−0.244610	+	0.969621i	$0.578660\pi$
$12$	−0.565466	−	2.11035i	−0.163236	−	0.609205i
$13$	−0.210174	−	2.40230i	−0.0582917	−	0.666278i	−0.967987	−	0.251001i	$-0.919240\pi$
$13$	−0.210174	−	2.40230i	−0.0582917	−	0.666278i	0.909695	−	0.415277i	$-0.136315\pi$
$14$	0.419550	+	0.152704i	0.112129	+	0.0408118i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.392349	+	0.560333i	−0.0951587	+	0.135901i	−0.863908	−	0.503649i	$-0.831990\pi$
$17$	−0.392349	+	0.560333i	−0.0951587	+	0.135901i	0.768750	+	0.639550i	$0.220879\pi$
$18$	−1.25393	−	1.25393i	−0.295553	−	0.295553i
$19$	−2.15160	−	3.79086i	−0.493611	−	0.869683i
$19$	−2.15160	−	3.79086i	−0.493611	−	0.869683i
$20$		0			0
$21$	0.960637	−	0.169386i	0.209628	−	0.0369631i
$22$	0.414754	−	4.74066i	0.0884259	−	1.01071i
$23$	0.188689	−	0.404644i	0.0393443	−	0.0843742i	−0.885653	−	0.464347i	$-0.846289\pi$
$23$	0.188689	−	0.404644i	0.0393443	−	0.0843742i	0.924998	+	0.379973i	$0.124067\pi$
$24$	−0.747243	+	2.05303i	−0.152530	+	0.419074i
$25$		0			0
$26$	−1.20574	+	2.08840i	−0.236464	+	0.409569i
$27$	2.58872	+	0.693647i	0.498200	+	0.133492i
$28$	−0.256088	−	0.365731i	−0.0483961	−	0.0691167i
$29$	0.892951	−	5.06418i	0.165817	−	0.940394i	−0.782401	−	0.622775i	$-0.786005\pi$
$29$	0.892951	−	5.06418i	0.165817	−	0.940394i	0.948218	−	0.317620i	$-0.102884\pi$
$30$		0			0
$31$	2.27332	+	1.31250i	0.408300	+	0.235732i	0.690059	−	0.723753i	$-0.257585\pi$
$31$	2.27332	+	1.31250i	0.408300	+	0.235732i	−0.281759	+	0.959485i	$0.590918\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	−4.39393	−	9.42282i	−0.764885	−	1.64030i
$34$	0.642788	−	0.233956i	0.110237	−	0.0401230i
$35$		0			0
$36$	0.307934	+	1.74638i	0.0513223	+	0.291063i
$37$	−1.48921	+	1.48921i	−0.244825	+	0.244825i	−0.818843	−	0.574018i	$-0.805384\pi$
$37$	−1.48921	+	1.48921i	−0.244825	+	0.244825i	0.574018	+	0.818843i	$0.305384\pi$
$38$	−0.411860	+	4.33940i	−0.0668124	+	0.703943i
$39$			5.26857i			0.843646i
$40$		0			0
$41$	−0.333626	−	0.397600i	−0.0521036	−	0.0620946i	0.739363	−	0.673307i	$-0.235127\pi$
$41$	−0.333626	−	0.397600i	−0.0521036	−	0.0620946i	−0.791467	+	0.611212i	$0.790682\pi$
$42$	−0.884064	−	0.412246i	−0.136414	−	0.0636109i
$43$	−8.46881	+	3.94907i	−1.29148	+	0.602227i	−0.942282	−	0.334821i	$-0.891324\pi$
$43$	−8.46881	+	3.94907i	−1.29148	+	0.602227i	−0.349199	+	0.937049i	$0.613546\pi$
$44$	−3.05888	+	3.64543i	−0.461143	+	0.549569i
$45$		0			0
$46$	−0.386659	+	0.223238i	−0.0570098	+	0.0329146i
$47$	−4.32402	+	3.02771i	−0.630724	+	0.441637i	−0.844728	−	0.535195i	$-0.820238\pi$
$47$	−4.32402	+	3.02771i	−0.630724	+	0.441637i	0.214005	+	0.976833i	$0.431349\pi$
$48$	1.78968	−	1.25315i	0.258318	−	0.180876i
$49$	−5.88954	+	3.40033i	−0.841363	+	0.485761i
$50$		0			0
$51$	0.960637	−	1.14484i	0.134516	−	0.160310i
$52$	2.18554	−	1.01913i	0.303080	−	0.141328i
$53$	−7.35361	−	3.42904i	−1.01010	−	0.471015i	−0.154131	−	0.988050i	$-0.549258\pi$
$53$	−7.35361	−	3.42904i	−1.01010	−	0.471015i	−0.855964	+	0.517035i	$0.827036\pi$
$54$	−1.72270	−	2.05303i	−0.234430	−	0.279382i
$55$		0			0
$56$			0.446476i			0.0596628i
$57$	3.96107	+	8.66043i	0.524656	+	1.14710i
$58$	−3.63616	+	3.63616i	−0.477451	+	0.477451i
$59$	−0.0555796	−	0.315207i	−0.00723585	−	0.0410365i	0.980976	−	0.194129i	$-0.0621880\pi$
$59$	−0.0555796	−	0.315207i	−0.00723585	−	0.0410365i	−0.988212	+	0.153092i	$0.951077\pi$
$60$		0			0
$61$	−7.77244	+	2.82894i	−0.995159	+	0.362208i	−0.787716	−	0.616039i	$-0.788736\pi$
$61$	−7.77244	+	2.82894i	−0.995159	+	0.362208i	−0.207443	+	0.978247i	$0.566514\pi$
$62$	−1.10937	−	2.37906i	−0.140891	−	0.302141i
$63$	−0.788731	+	0.0690050i	−0.0993707	+	0.00869381i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$		0			0
$66$	−1.80541	+	10.2390i	−0.222230	+	1.26033i
$67$	6.44380	+	9.20270i	0.787235	+	1.12429i	0.989440	+	0.144945i	$0.0463006\pi$
$67$	6.44380	+	9.20270i	0.787235	+	1.12429i	−0.202204	+	0.979343i	$0.564810\pi$
$68$	−0.660732	−	0.177043i	−0.0801255	−	0.0214696i
$69$	−0.487728	+	0.844770i	−0.0587156	+	0.101698i
$70$		0			0
$71$	0.879385	−	2.41609i	0.104364	−	0.286737i	−0.876509	−	0.481385i	$-0.840134\pi$
$71$	0.879385	−	2.41609i	0.104364	−	0.286737i	0.980873	+	0.194647i	$0.0623563\pi$
$72$	0.749437	−	1.60717i	0.0883220	−	0.189407i
$73$	−0.378413	+	4.32528i	−0.0442899	+	0.506236i	0.941357	+	0.337414i	$0.109552\pi$
$73$	−0.378413	+	4.32528i	−0.0442899	+	0.506236i	−0.985646	+	0.168823i	$0.946003\pi$
$74$	2.07407	−	0.365715i	0.241106	−	0.0425135i
$75$		0			0
$76$	2.82635	−	3.31839i	0.324205	−	0.380646i
$77$	−1.50237	−	1.50237i	−0.171211	−	0.171211i
$78$	3.02193	−	4.31576i	0.342166	−	0.488664i
$79$	−12.3274	+	10.3439i	−1.38694	+	1.16378i	−0.420374	+	0.907351i	$0.638101\pi$
$79$	−12.3274	+	10.3439i	−1.38694	+	1.16378i	−0.966563	+	0.256428i	$0.917454\pi$
$80$		0			0
$81$	−10.5013	−	3.82218i	−1.16682	−	0.424686i
$82$	0.0452364	+	0.517055i	0.00499553	+	0.0570991i
$83$	−0.224591	−	0.838185i	−0.0246521	−	0.0920028i	0.952504	−	0.304527i	$-0.0984983\pi$
$83$	−0.224591	−	0.838185i	−0.0246521	−	0.0920028i	−0.977156	+	0.212524i	$0.931832\pi$
$84$	0.487728	+	0.844770i	0.0532155	+	0.0921720i
$85$		0			0
$86$	9.20233	+	1.62262i	0.992313	+	0.174972i
$87$	−2.90780	+	10.8520i	−0.311748	+	1.16346i
$88$	4.59662	−	1.23166i	0.490001	−	0.131295i
$89$	−12.7545	−	10.7023i	−1.35198	−	1.13445i	−0.978371	−	0.206858i	$-0.933676\pi$
$89$	−12.7545	−	10.7023i	−1.35198	−	1.13445i	−0.373608	−	0.927587i	$-0.621880\pi$
$90$		0			0
$91$	0.368241	+	1.01173i	0.0386021	+	0.106058i
$92$	0.444777	+	0.0389129i	0.0463712	+	0.00405695i
$93$	−4.69791	−	3.28951i	−0.487150	−	0.341106i
$94$	5.27866			0.544452
$95$		0			0
$96$	−2.18479			−0.222984
$97$	−2.46380	−	1.72517i	−0.250161	−	0.175164i	0.441770	−	0.897128i	$-0.354351\pi$
$97$	−2.46380	−	1.72517i	−0.250161	−	0.175164i	−0.691931	+	0.721964i	$0.743240\pi$
$98$	6.77478	+	0.592717i	0.684356	+	0.0598734i
$99$	2.88624	+	7.92989i	0.290079	+	0.796984i
$100$		0			0
$101$	−3.75490	−	3.15074i	−0.373627	−	0.313510i	0.436568	−	0.899671i	$-0.356194\pi$
$101$	−3.75490	−	3.15074i	−0.373627	−	0.313510i	−0.810194	+	0.586162i	$0.800638\pi$
$102$	−1.44356	+	0.386801i	−0.142934	+	0.0382991i
$103$	−2.65770	+	9.91868i	−0.261871	+	0.977316i	0.702267	+	0.711914i	$0.252171\pi$
$103$	−2.65770	+	9.91868i	−0.261871	+	0.977316i	−0.964138	+	0.265402i	$0.914495\pi$
$104$	−2.37484	−	0.418748i	−0.232872	−	0.0410616i
$105$		0			0
$106$	4.05690	+	7.02676i	0.394041	+	0.682500i
$107$	1.52546	+	5.69310i	0.147472	+	0.550373i	0.999633	+	0.0270932i	$0.00862507\pi$
$107$	1.52546	+	5.69310i	0.147472	+	0.550373i	−0.852161	+	0.523280i	$0.824708\pi$
$108$	0.233581	+	2.66985i	0.0224764	+	0.256906i
$109$	7.27195	+	2.64677i	0.696527	+	0.253515i	0.665927	−	0.746017i	$-0.268036\pi$
$109$	7.27195	+	2.64677i	0.696527	+	0.253515i	0.0305995	+	0.999532i	$0.490258\pi$
$110$		0			0
$111$	3.52481	−	2.95767i	0.334561	−	0.280730i
$112$	0.256088	−	0.365731i	0.0241980	−	0.0345584i
$113$	8.92624	+	8.92624i	0.839710	+	0.839710i	0.988821	−	0.149111i	$-0.0476411\pi$
$113$	8.92624	+	8.92624i	0.839710	+	0.839710i	−0.149111	+	0.988821i	$0.547641\pi$
$114$	1.72270	−	9.36618i	0.161346	−	0.877223i
$115$		0			0
$116$	5.06418	−	0.892951i	0.470197	−	0.0829084i
$117$	0.372705	−	4.26004i	0.0344566	−	0.393841i
$118$	−0.135267	+	0.290082i	−0.0124524	+	0.0267042i
$119$	0.104455	−	0.286989i	0.00957541	−	0.0263082i
$120$		0			0
$121$	−5.82295	+	10.0856i	−0.529359	+	0.916877i
$122$	7.98942	+	2.14076i	0.723328	+	0.193815i
$123$	0.650420	+	0.928895i	0.0586464	+	0.0837557i
$124$	−0.455827	+	2.58512i	−0.0409345	+	0.232151i
$125$		0			0
$126$	0.685670	+	0.395872i	0.0610843	+	0.0352671i
$127$	−20.3193	+	1.77771i	−1.80305	+	0.157746i	−0.938607	−	0.344989i	$-0.887883\pi$
$127$	−20.3193	+	1.77771i	−1.80305	+	0.157746i	−0.864440	+	0.502735i	$0.832327\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	19.1841	−	6.98246i	1.68907	−	0.614771i
$130$		0			0
$131$	−0.804530	−	4.56272i	−0.0702921	−	0.398646i	−0.999572	−	0.0292689i	$-0.990682\pi$
$131$	−0.804530	−	4.56272i	−0.0702921	−	0.398646i	0.929279	−	0.369377i	$-0.120429\pi$
$132$	7.35174	−	7.35174i	0.639887	−	0.639887i
$133$	1.36596	+	1.38622i	0.118444	+	0.120201i
$134$		−	11.2344i		−	0.970506i
$135$		0			0
$136$	0.439693	+	0.524005i	0.0377033	+	0.0449331i
$137$	−15.1418	−	7.06076i	−1.29366	−	0.603241i	−0.350802	−	0.936450i	$-0.614091\pi$
$137$	−15.1418	−	7.06076i	−1.29366	−	0.603241i	−0.942853	+	0.333208i	$0.891869\pi$
$138$	0.884064	−	0.412246i	0.0752565	−	0.0350927i
$139$	−12.1085	+	14.4304i	−1.02703	+	1.22397i	−0.0527547	+	0.998608i	$0.516800\pi$
$139$	−12.1085	+	14.4304i	−1.02703	+	1.22397i	−0.974276	+	0.225360i	$0.927644\pi$
$140$		0			0
$141$	9.98767	−	5.76639i	0.841114	−	0.485617i
$142$	−2.10616	+	1.47475i	−0.176745	+	0.123758i
$143$	9.40030	−	6.58216i	0.786093	−	0.550428i
$144$	−1.53574	+	0.886659i	−0.127978	+	0.0738883i
$145$		0			0
$146$	2.79086	−	3.32602i	0.230973	−	0.275263i
$147$	13.4659	−	6.27927i	1.11065	−	0.517906i
$148$	−1.90874	−	0.890062i	−0.156898	−	0.0731627i
$149$	−8.53882	−	10.1762i	−0.699528	−	0.833665i	0.292945	−	0.956129i	$-0.405365\pi$
$149$	−8.53882	−	10.1762i	−0.699528	−	0.833665i	−0.992473	+	0.122465i	$0.960920\pi$
$150$		0			0
$151$		−	12.3520i		−	1.00519i	−0.864522	−	0.502594i	$-0.832379\pi$
$151$		−	12.3520i		−	1.00519i	0.864522	−	0.502594i	$-0.167621\pi$
$152$	−4.21856	+	1.09714i	−0.342171	+	0.0889898i
$153$	−0.857736	+	0.857736i	−0.0693438	+	0.0693438i
$154$	0.368946	+	2.09240i	0.0297305	+	0.168610i
$155$		0			0
$156$	−4.95084	+	1.80196i	−0.396384	+	0.144272i
$157$	−7.08996	−	15.2045i	−0.565841	−	1.21345i	−0.956180	−	0.292778i	$-0.905420\pi$
$157$	−7.08996	−	15.2045i	−0.565841	−	1.21345i	0.390340	−	0.920671i	$-0.372358\pi$
$158$	16.0310	−	1.40253i	1.27536	−	0.111579i
$159$	15.3520	+	8.86349i	1.21749	+	0.702921i
$160$		0			0
$161$	−0.0346151	+	0.196312i	−0.00272805	+	0.0154716i
$162$	6.40989	+	9.15427i	0.503608	+	0.719227i
$163$	23.3280	+	6.25073i	1.82719	+	0.489595i	0.997629	−	0.0688176i	$-0.0219226\pi$
$163$	23.3280	+	6.25073i	1.82719	+	0.489595i	0.829564	+	0.558412i	$0.188589\pi$
$164$	0.259515	−	0.449493i	0.0202647	−	0.0350995i
$165$		0			0
$166$	−0.296789	+	0.815422i	−0.0230353	+	0.0632890i
$167$	6.18635	−	13.2667i	0.478714	−	1.02661i	−0.507579	−	0.861605i	$-0.669460\pi$
$167$	6.18635	−	13.2667i	0.478714	−	1.02661i	0.986293	−	0.165001i	$-0.0527627\pi$
$168$	0.0850166	−	0.971745i	0.00655918	−	0.0749717i
$169$	7.07564	−	1.24763i	0.544280	−	0.0959712i
$170$		0			0
$171$	−2.59017	−	7.28282i	−0.198076	−	0.556931i
$172$	−6.60741	−	6.60741i	−0.503811	−	0.503811i
$173$	6.98346	−	9.97342i	0.530943	−	0.758265i	−0.460661	−	0.887576i	$-0.652388\pi$
$173$	6.98346	−	9.97342i	0.530943	−	0.758265i	0.991604	+	0.129311i	$0.0412766\pi$
$174$	8.60640	−	7.22163i	0.652450	−	0.547470i
$175$		0			0
$176$	−4.47178	−	1.62760i	−0.337073	−	0.122685i
$177$	0.0609468	+	0.696626i	0.00458105	+	0.0523616i
$178$	4.30930	+	16.0825i	0.322996	+	1.20544i
$179$	−2.13230	−	3.69325i	−0.159375	−	0.276046i	0.775268	−	0.631632i	$-0.217615\pi$
$179$	−2.13230	−	3.69325i	−0.159375	−	0.276046i	−0.934644	+	0.355586i	$0.884281\pi$
$180$		0			0
$181$	−14.8871	−	2.62500i	−1.10655	−	0.195115i	−0.409622	−	0.912255i	$-0.634340\pi$
$181$	−14.8871	−	2.62500i	−1.10655	−	0.195115i	−0.696929	+	0.717140i	$0.745451\pi$
$182$	0.278661	−	1.03998i	0.0206557	−	0.0770883i
$183$	17.4552	−	4.67712i	1.29033	−	0.345742i
$184$	−0.342020	−	0.286989i	−0.0252141	−	0.0211571i
$185$		0			0
$186$	1.96151	+	5.38922i	0.143825	+	0.395157i
$187$	−3.24280	−	0.283709i	−0.237137	−	0.0207468i
$188$	−4.32402	−	3.02771i	−0.315362	−	0.220819i
$189$	−1.19657			−0.0870380
$190$		0			0
$191$	18.5107			1.33939			0.669695	−	0.742636i	$-0.266425\pi$
$191$	18.5107			1.33939			0.669695	+	0.742636i	$0.266425\pi$
$192$	1.78968	+	1.25315i	0.129159	+	0.0904380i
$193$	−10.9514	−	0.958120i	−0.788296	−	0.0689670i	−0.314104	−	0.949388i	$-0.601704\pi$
$193$	−10.9514	−	0.958120i	−0.788296	−	0.0689670i	−0.474192	+	0.880422i	$0.657260\pi$
$194$	1.02871	+	2.82635i	0.0738569	+	0.202920i
$195$		0			0
$196$	−5.20961	−	4.37138i	−0.372115	−	0.312241i
$197$	−0.890202	+	0.238529i	−0.0634243	+	0.0169945i	−0.290392	−	0.956908i	$-0.593786\pi$
$197$	−0.890202	+	0.238529i	−0.0634243	+	0.0169945i	0.226967	+	0.973902i	$0.427119\pi$
$198$	2.18413	−	8.15127i	0.155219	−	0.579286i
$199$	15.8807	+	2.80019i	1.12575	+	0.198500i	0.705365	−	0.708845i	$-0.250783\pi$
$199$	15.8807	+	2.80019i	1.12575	+	0.198500i	0.420387	+	0.907345i	$0.361894\pi$
$200$		0			0
$201$	−12.2724	−	21.2565i	−0.865631	−	1.49932i
$202$	1.26865	+	4.73465i	0.0892617	+	0.333129i
$203$	0.200102	+	2.28718i	0.0140444	+	0.160528i
$204$	1.40436	+	0.511144i	0.0983247	+	0.0357873i
$205$		0			0
$206$	7.86618	−	6.60051i	0.548063	−	0.459879i
$207$	0.454125	−	0.648558i	0.0315639	−	0.0450779i
$208$	1.70517	+	1.70517i	0.118232	+	0.118232i
$209$	10.5035	−	17.8871i	0.726540	−	1.23728i
$210$		0			0
$211$	5.19846	−	0.916629i	0.357877	−	0.0631034i	0.00818081	−	0.999967i	$-0.497396\pi$
$211$	5.19846	−	0.916629i	0.357877	−	0.0631034i	0.349696	+	0.936863i	$0.386285\pi$
$212$	0.707165	−	8.08293i	0.0485683	−	0.555138i
$213$	−2.37403	+	5.09112i	−0.162666	+	0.348838i
$214$	2.01584	−	5.53849i	0.137800	−	0.378603i
$215$		0			0
$216$	1.34002	−	2.32099i	0.0911770	−	0.157923i
$217$	−1.13206	−	0.303336i	−0.0768495	−	0.0205918i
$218$	−4.43871	−	6.33913i	−0.300627	−	0.429340i
$219$	1.64722	−	9.34183i	0.111309	−	0.631263i
$220$		0			0
$221$	1.42855	+	0.824773i	0.0960946	+	0.0554802i
$222$	−4.58381	+	0.401031i	−0.307645	+	0.0269155i
$223$	−8.82113	−	18.9170i	−0.590707	−	1.26677i	−0.943593	−	0.331108i	$-0.892577\pi$
$223$	−8.82113	−	18.9170i	−0.590707	−	1.26677i	0.352886	−	0.935666i	$-0.385200\pi$
$224$	−0.419550	+	0.152704i	−0.0280324	+	0.0102029i
$225$		0			0
$226$	−2.19207	−	12.4318i	−0.145814	−	0.826953i
$227$	5.83838	−	5.83838i	0.387507	−	0.387507i	−0.486291	−	0.873797i	$-0.661650\pi$
$227$	5.83838	−	5.83838i	0.387507	−	0.387507i	0.873797	+	0.486291i	$0.161650\pi$
$228$	−6.78337	+	6.68423i	−0.449240	+	0.442674i
$229$			6.31996i			0.417634i	0.977955	+	0.208817i	$0.0669614\pi$
$229$			6.31996i			0.417634i	−0.977955	+	0.208817i	$0.933039\pi$
$230$		0			0
$231$	2.98380	+	3.55596i	0.196320	+	0.233965i
$232$	−4.66051	−	2.17323i	−0.305977	−	0.142680i
$233$	−22.0685	+	10.2907i	−1.44576	+	0.674168i	−0.977792	−	0.209579i	$-0.932791\pi$
$233$	−22.0685	+	10.2907i	−1.44576	+	0.674168i	−0.467965	+	0.883747i	$0.655013\pi$
$234$	−2.74876	+	3.27584i	−0.179692	+	0.214149i
$235$		0			0
$236$	0.277189	−	0.160035i	0.0180435	−	0.0104174i
$237$	28.7999	−	20.1659i	1.87076	−	1.30992i
$238$	−0.250175	+	0.175174i	−0.0162164	+	0.0113549i
$239$	−23.7182	+	13.6937i	−1.53420	+	0.885773i	−0.535042	+	0.844825i	$0.679704\pi$
$239$	−23.7182	+	13.6937i	−1.53420	+	0.885773i	−0.999161	+	0.0409475i	$0.986962\pi$
$240$		0			0
$241$	−5.85591	+	6.97881i	−0.377213	+	0.449544i	−0.920932	−	0.389722i	$-0.872571\pi$
$241$	−5.85591	+	6.97881i	−0.377213	+	0.449544i	0.543720	+	0.839267i	$0.317015\pi$
$242$	10.5548	−	4.92177i	0.678486	−	0.316383i
$243$	14.8413	+	6.92062i	0.952070	+	0.443958i
$244$	−5.31666	−	6.33615i	−0.340364	−	0.405631i
$245$		0			0
$246$		−	1.13397i		−	0.0722994i
$247$	−8.65456	+	5.96552i	−0.550677	+	0.379577i
$248$	1.85616	−	1.85616i	0.117866	−	0.117866i
$249$	0.329213	+	1.86706i	0.0208630	+	0.118320i
$250$		0			0
$251$	12.6236	−	4.59462i	0.796795	−	0.290010i	0.0886373	−	0.996064i	$-0.471749\pi$
$251$	12.6236	−	4.59462i	0.796795	−	0.290010i	0.708158	+	0.706054i	$0.249527\pi$
$252$	−0.334605	−	0.717563i	−0.0210781	−	0.0452022i
$253$	2.11659	−	0.185178i	0.133069	−	0.0116420i
$254$	17.6643	+	10.1985i	1.10835	+	0.639908i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	9.51923	+	13.5949i	0.593793	+	0.848024i	0.997770	−	0.0667447i	$-0.0212613\pi$
$257$	9.51923	+	13.5949i	0.593793	+	0.848024i	−0.403977	+	0.914769i	$0.632372\pi$
$258$	−19.7197	−	5.28388i	−1.22770	−	0.328960i
$259$	0.470154	−	0.814330i	0.0292139	−	0.0506000i
$260$		0			0
$261$	3.11886	−	8.56900i	0.193053	−	0.530408i
$262$	−1.95803	+	4.19902i	−0.120968	+	0.259416i
$263$	−2.35086	+	26.8704i	−0.144960	+	1.65690i	0.480758	+	0.876853i	$0.340362\pi$
$263$	−2.35086	+	26.8704i	−0.144960	+	1.65690i	−0.625718	+	0.780049i	$0.715194\pi$
$264$	−10.2390	+	1.80541i	−0.630165	+	0.111115i
$265$		0			0
$266$	−0.323826	−	1.91901i	−0.0198550	−	0.117662i
$267$	25.7221	+	25.7221i	1.57417	+	1.57417i
$268$	−6.44380	+	9.20270i	−0.393618	+	0.562144i
$269$	20.8858	−	17.5253i	1.27343	−	1.06854i	0.279316	−	0.960199i	$-0.409892\pi$
$269$	20.8858	−	17.5253i	1.27343	−	1.06854i	0.994114	−	0.108336i	$-0.0345523\pi$
$270$		0			0
$271$	−23.8862	−	8.69388i	−1.45099	−	0.528116i	−0.508120	−	0.861286i	$-0.669659\pi$
$271$	−23.8862	−	8.69388i	−1.45099	−	0.528116i	−0.942867	+	0.333171i	$0.891881\pi$
$272$	−0.0596180	−	0.681437i	−0.00361487	−	0.0413182i
$273$	−0.608817	−	2.27214i	−0.0368473	−	0.137516i
$274$	8.35359	+	14.4688i	0.504659	+	0.874095i
$275$		0			0
$276$	−0.960637	−	0.169386i	−0.0578236	−	0.0101959i
$277$	2.94703	−	10.9985i	0.177070	−	0.660835i	−0.819120	−	0.573623i	$-0.805538\pi$
$277$	2.94703	−	10.9985i	0.177070	−	0.660835i	0.996190	−	0.0872119i	$-0.0277957\pi$
$278$	18.1956	−	4.87550i	1.09130	−	0.292413i
$279$	3.56591	+	2.99215i	0.213485	+	0.179136i
$280$		0			0
$281$	−0.414878	−	1.13987i	−0.0247495	−	0.0679988i	0.926703	−	0.375796i	$-0.122631\pi$
$281$	−0.414878	−	1.13987i	−0.0247495	−	0.0679988i	−0.951452	+	0.307797i	$0.900408\pi$
$282$	−11.4889	−	1.00515i	−0.684153	−	0.0598557i
$283$	−13.7452	−	9.62446i	−0.817065	−	0.572115i	0.0886206	−	0.996065i	$-0.471754\pi$
$283$	−13.7452	−	9.62446i	−0.817065	−	0.572115i	−0.905685	+	0.423951i	$0.860643\pi$
$284$	2.57115			0.152570
$285$		0			0
$286$	−11.4757			−0.678570
$287$	0.189825	+	0.132917i	0.0112050	+	0.00784585i
$288$	1.76657	+	0.154555i	0.104096	+	0.00910723i
$289$	5.65431	+	15.5351i	0.332606	+	0.913828i
$290$		0			0
$291$	5.03390	+	4.22394i	0.295092	+	0.247612i
$292$	−4.19386	+	1.12374i	−0.245427	+	0.0657620i
$293$	2.70823	−	10.1072i	0.158216	−	0.590472i	−0.840592	−	0.541669i	$-0.817793\pi$
$293$	2.70823	−	10.1072i	0.158216	−	0.590472i	0.998808	−	0.0488029i	$-0.0155406\pi$
$294$	−14.6323	−	2.58007i	−0.853373	−	0.150473i
$295$		0			0
$296$	1.05303	+	1.82391i	0.0612063	+	0.106012i
$297$	3.30091	+	12.3191i	0.191538	+	0.714829i
$298$	1.15778	+	13.2335i	0.0670685	+	0.766596i
$299$	−1.01173	−	0.368241i	−0.0585101	−	0.0212959i
$300$		0			0
$301$	3.19594	−	2.68171i	0.184211	−	0.154571i
$302$	−7.08480	+	10.1181i	−0.407684	+	0.582234i
$303$	7.57251	+	7.57251i	0.435029	+	0.435029i
$304$	4.08494	+	1.52094i	0.234287	+	0.0872322i
$305$		0			0
$306$	1.19459	−	0.210639i	0.0682903	−	0.0120414i
$307$	−0.0486762	+	0.556371i	−0.00277810	+	0.0317538i	−0.997457	−	0.0712678i	$-0.977296\pi$
$307$	−0.0486762	+	0.556371i	−0.00277810	+	0.0317538i	0.994679	+	0.103022i	$0.0328511\pi$
$308$	0.897926	−	1.92561i	0.0511641	−	0.109722i
$309$	7.67312	−	21.0817i	0.436508	−	1.19930i
$310$		0			0
$311$	−15.4179	+	26.7045i	−0.874267	+	1.51428i	−0.0167260	+	0.999860i	$0.505324\pi$
$311$	−15.4179	+	26.7045i	−0.874267	+	1.51428i	−0.857541	+	0.514415i	$0.828009\pi$
$312$	5.08905	+	1.36361i	0.288111	+	0.0771990i
$313$	4.85822	+	6.93826i	0.274603	+	0.392173i	0.932638	−	0.360814i	$-0.117501\pi$
$313$	4.85822	+	6.93826i	0.274603	+	0.392173i	−0.658035	+	0.752987i	$0.728612\pi$
$314$	−2.91317	+	16.5214i	−0.164400	+	0.932357i
$315$		0			0
$316$	−13.9363	−	8.04612i	−0.783978	−	0.452630i
$317$	−24.7090	+	2.16175i	−1.38779	+	0.121416i	−0.756432	−	0.654072i	$-0.773059\pi$
$317$	−24.7090	+	2.16175i	−1.38779	+	0.121416i	−0.631362	+	0.775489i	$0.717504\pi$
$318$	−7.49175	−	16.0661i	−0.420116	−	0.900942i
$319$	22.9952	−	8.36959i	1.28749	−	0.468607i
$320$		0			0
$321$	−2.23607	−	12.6814i	−0.124805	−	0.707806i
$322$	0.140955	−	0.140955i	0.00785511	−	0.00785511i
$323$	2.96832	+	0.281729i	0.165162	+	0.0156758i
$324$		−	11.1753i		−	0.620850i
$325$		0			0
$326$	−15.5239	−	18.5007i	−0.859791	−	1.02466i
$327$	−15.3233	−	7.14535i	−0.847378	−	0.395139i
$328$	−0.470401	+	0.219351i	−0.0259735	+	0.0121117i
$329$	1.51492	−	1.80541i	0.0835201	−	0.0995353i
$330$		0			0
$331$	−14.8859	+	8.59440i	−0.818205	+	0.472391i	−0.849797	−	0.527110i	$-0.823276\pi$
$331$	−14.8859	+	8.59440i	−0.818205	+	0.472391i	0.0315918	+	0.999501i	$0.489942\pi$
$332$	0.710822	−	0.497723i	0.0390114	−	0.0273161i
$333$	−3.05931	+	2.14215i	−0.167649	+	0.117389i
$334$	−12.6770	+	7.31908i	−0.693655	+	0.400482i
$335$		0			0
$336$	−0.627011	+	0.747243i	−0.0342063	+	0.0407655i
$337$	12.8962	−	6.01359i	0.702500	−	0.327581i	−0.0383379	−	0.999265i	$-0.512206\pi$
$337$	12.8962	−	6.01359i	0.702500	−	0.327581i	0.740838	+	0.671684i	$0.234429\pi$
$338$	−6.51163	−	3.03642i	−0.354186	−	0.165160i
$339$	−17.7281	−	21.1275i	−0.962856	−	1.14749i
$340$		0			0
$341$			12.4918i			0.676468i
$342$	−2.05551	+	7.45140i	−0.111149	+	0.402926i
$343$	4.35695	−	4.35695i	0.235253	−	0.235253i
$344$	1.62262	+	9.20233i	0.0874858	+	0.496157i
$345$		0			0
$346$	−11.4410	+	4.16420i	−0.615074	+	0.223869i
$347$	7.99209	+	17.1391i	0.429038	+	0.920075i	0.995390	+	0.0959116i	$0.0305766\pi$
$347$	7.99209	+	17.1391i	0.429038	+	0.920075i	−0.566352	+	0.824164i	$0.691646\pi$
$348$	−11.1921	+	0.979183i	−0.599960	+	0.0524897i
$349$	17.1013	+	9.87346i	0.915413	+	0.528514i	0.882169	−	0.470933i	$-0.156083\pi$
$349$	17.1013	+	9.87346i	0.915413	+	0.528514i	0.0332442	+	0.999447i	$0.489416\pi$
$350$		0			0
$351$	1.12226	−	6.36467i	0.0599020	−	0.339721i
$352$	2.72952	+	3.89816i	0.145484	+	0.207772i
$353$	6.97696	+	1.86947i	0.371346	+	0.0995018i	0.439665	−	0.898162i	$-0.355097\pi$
$353$	6.97696	+	1.86947i	0.371346	+	0.0995018i	−0.0683195	+	0.997663i	$0.521764\pi$
$354$	0.349643	−	0.605600i	0.0185833	−	0.0321873i
$355$		0			0
$356$	5.69459	−	15.6458i	0.301813	−	0.829224i
$357$	−0.281993	+	0.604735i	−0.0149246	+	0.0320060i
$358$	−0.371684	+	4.24837i	−0.0196441	+	0.224533i
$359$	−15.8664	+	2.79767i	−0.837394	+	0.147655i	−0.575870	−	0.817542i	$-0.695336\pi$
$359$	−15.8664	+	2.79767i	−0.837394	+	0.147655i	−0.261525	+	0.965197i	$0.584225\pi$
$360$		0			0
$361$	−9.74123	+	16.3128i	−0.512696	+	0.858570i
$362$	10.6892	+	10.6892i	0.561811	+	0.561811i
$363$	14.5940	−	20.8424i	0.765987	−	1.09394i
$364$	−0.824773	+	0.692066i	−0.0432298	+	0.0362741i
$365$		0			0
$366$	−16.9812	−	6.18064i	−0.887620	−	0.323067i
$367$	−0.813947	−	9.30346i	−0.0424877	−	0.485637i	−0.987392	−	0.158291i	$-0.949401\pi$
$367$	−0.813947	−	9.30346i	−0.0424877	−	0.485637i	0.944905	−	0.327345i	$-0.106154\pi$
$368$	0.115556	+	0.431262i	0.00602379	+	0.0224811i
$369$	−0.460202	−	0.797094i	−0.0239572	−	0.0414950i
$370$		0			0
$371$	3.56758	+	0.629061i	0.185220	+	0.0326592i
$372$	1.48435	−	5.53967i	0.0769599	−	0.287218i
$373$	1.40554	−	0.376612i	0.0727759	−	0.0195002i	−0.222247	−	0.974990i	$-0.571339\pi$
$373$	1.40554	−	0.376612i	0.0727759	−	0.0195002i	0.295023	+	0.955490i	$0.404673\pi$
$374$	2.49362	+	2.09240i	0.128942	+	0.108195i
$375$		0			0
$376$	1.80541	+	4.96032i	0.0931068	+	0.255809i
$377$	−12.3533	−	1.08078i	−0.636229	−	0.0556628i
$378$	0.980177	+	0.686327i	0.0504148	+	0.0353009i
$379$	−29.9861			−1.54028			−0.770140	−	0.637875i	$-0.779814\pi$
$379$	−29.9861			−1.54028			−0.770140	+	0.637875i	$0.779814\pi$
$380$		0			0
$381$	44.5631			2.28303
$382$	−15.1631	−	10.6173i	−0.775812	−	0.543229i
$383$	6.58566	+	0.576170i	0.336511	+	0.0294409i	0.254159	−	0.967162i	$-0.418201\pi$
$383$	6.58566	+	0.576170i	0.336511	+	0.0294409i	0.0823521	+	0.996603i	$0.473757\pi$
$384$	−0.747243	−	2.05303i	−0.0381326	−	0.104768i
$385$		0			0
$386$	8.42127	+	7.06629i	0.428632	+	0.359665i
$387$	−16.0058	+	4.28874i	−0.813620	+	0.218009i
$388$	0.778461	−	2.90525i	0.0395203	−	0.147492i
$389$	3.93161	+	0.693249i	0.199340	+	0.0351491i	0.272427	−	0.962177i	$-0.412174\pi$
$389$	3.93161	+	0.693249i	0.199340	+	0.0351491i	−0.0730863	+	0.997326i	$0.523285\pi$
$390$		0			0
$391$	0.152704	+	0.264490i	0.00772256	+	0.0133759i
$392$	1.76014	+	6.56893i	0.0889005	+	0.331781i
$393$	0.882223	+	10.0839i	0.0445022	+	0.508663i
$394$	0.866025	+	0.315207i	0.0436297	+	0.0158799i
$395$		0			0
$396$	−6.46451	+	5.42437i	−0.324854	+	0.272585i
$397$	1.87281	−	2.67465i	0.0939936	−	0.134237i	−0.769401	−	0.638766i	$-0.779445\pi$
$397$	1.87281	−	2.67465i	0.0939936	−	0.134237i	0.863394	+	0.504529i	$0.168334\pi$
$398$	−11.4026	−	11.4026i	−0.571559	−	0.571559i
$399$	−2.70903	−	3.27719i	−0.135621	−	0.164065i
$400$		0			0
$401$	33.1857	−	5.85154i	1.65722	−	0.292212i	0.734764	−	0.678323i	$-0.237293\pi$
$401$	33.1857	−	5.85154i	1.65722	−	0.292212i	0.922452	+	0.386111i	$0.126182\pi$
$402$	−2.13923	+	24.4515i	−0.106695	+	1.21953i
$403$	2.67523	−	5.73704i	0.133263	−	0.285782i
$404$	1.67647	−	4.60607i	0.0834076	−	0.229160i
$405$		0			0
$406$	1.14796	−	1.98832i	0.0569721	−	0.0986786i
$407$	−9.68079	−	2.59396i	−0.479859	−	0.128578i
$408$	−0.857202	−	1.22421i	−0.0424378	−	0.0606075i
$409$	−1.04709	+	5.93835i	−0.0517753	+	0.293632i	−0.999690	−	0.0248914i	$-0.992076\pi$
$409$	−1.04709	+	5.93835i	−0.0517753	+	0.293632i	0.947915	+	0.318524i	$0.103187\pi$
$410$		0			0
$411$	31.6114	+	18.2509i	1.55928	+	0.900249i
$412$	−10.2295	+	0.894965i	−0.503971	+	0.0440918i
$413$	0.0603936	+	0.129515i	0.00297178	+	0.00637299i
$414$	−0.743995	+	0.270792i	−0.0365654	+	0.0133087i
$415$		0			0
$416$	−0.418748	−	2.37484i	−0.0205308	−	0.116436i
$417$	29.1017	−	29.1017i	1.42512	−	1.42512i
$418$	−18.8636	+	8.62774i	−0.922647	+	0.421996i
$419$		−	30.8229i		−	1.50580i	−0.658135	−	0.752900i	$-0.728654\pi$
$419$		−	30.8229i		−	1.50580i	0.658135	−	0.752900i	$-0.271346\pi$
$420$		0			0
$421$	20.6284	+	24.5839i	1.00536	+	1.19815i	0.980108	+	0.198466i	$0.0635959\pi$
$421$	20.6284	+	24.5839i	1.00536	+	1.19815i	0.0252567	+	0.999681i	$0.491960\pi$
$422$	−4.78409	−	2.23086i	−0.232886	−	0.108596i
$423$	−8.48371	+	3.95602i	−0.412492	+	0.192348i
$424$	−5.21546	+	6.21554i	−0.253285	+	0.301853i
$425$		0			0
$426$	4.86484	−	2.80872i	0.235702	−	0.136083i
$427$	3.02506	−	2.11817i	0.146393	−	0.102505i
$428$	−4.82803	+	3.38062i	−0.233372	+	0.163408i
$429$	−21.7129	+	12.5360i	−1.04831	+	0.605242i
$430$		0			0
$431$	−24.9971	+	29.7903i	−1.20407	+	1.43495i	−0.333605	+	0.942713i	$0.608265\pi$
$431$	−24.9971	+	29.7903i	−1.20407	+	1.43495i	−0.870461	+	0.492237i	$0.836179\pi$
$432$	−2.42895	+	1.13264i	−0.116863	+	0.0544940i
$433$	−25.2504	−	11.7744i	−1.21346	−	0.565844i	−0.292783	−	0.956179i	$-0.594581\pi$
$433$	−25.2504	−	11.7744i	−1.21346	−	0.565844i	−0.920673	+	0.390335i	$0.872359\pi$
$434$	0.753347	+	0.897804i	0.0361618	+	0.0430959i
$435$		0			0
$436$			7.73865i			0.370614i
$437$	−1.93993	+	0.155340i	−0.0927996	+	0.00743094i
$438$	−6.70758	+	6.70758i	−0.320500	+	0.320500i
$439$	4.91204	+	27.8576i	0.234439	+	1.32957i	0.843792	+	0.536670i	$0.180318\pi$
$439$	4.91204	+	27.8576i	0.234439	+	1.32957i	−0.609353	+	0.792899i	$0.708571\pi$
$440$		0			0
$441$	−11.3324	+	4.12467i	−0.539640	+	0.196413i
$442$	−0.697128	−	1.49500i	−0.0331590	−	0.0711097i
$443$	27.0314	−	2.36494i	1.28430	−	0.112362i	0.575518	−	0.817789i	$-0.304801\pi$
$443$	27.0314	−	2.36494i	1.28430	−	0.112362i	0.708782	+	0.705428i	$0.249245\pi$
$444$	3.98486	+	2.30066i	0.189113	+	0.109184i
$445$		0			0
$446$	−3.62449	+	20.5555i	−0.171624	+	0.973330i
$447$	16.6469	+	23.7742i	0.787369	+	1.12448i
$448$	0.431262	+	0.115556i	0.0203752	+	0.00545953i
$449$	−5.58878	+	9.68004i	−0.263751	+	0.456830i	−0.967236	−	0.253881i	$-0.918293\pi$
$449$	−5.58878	+	9.68004i	−0.263751	+	0.456830i	0.703485	+	0.710710i	$0.251626\pi$
$450$		0			0
$451$	0.844770	−	2.32099i	0.0397787	−	0.109291i
$452$	−5.33497	+	11.4409i	−0.250936	+	0.538133i
$453$	−2.35203	+	26.8838i	−0.110508	+	1.26311i
$454$	−8.13127	+	1.43376i	−0.381620	+	0.0672898i
$455$		0			0
$456$	9.39053	−	1.58461i	0.439752	−	0.0742064i
$457$	2.08248	+	2.08248i	0.0974143	+	0.0974143i	0.754134	−	0.656720i	$-0.228057\pi$
$457$	2.08248	+	2.08248i	0.0974143	+	0.0974143i	−0.656720	+	0.754134i	$0.728057\pi$
$458$	3.62498	−	5.17700i	0.169384	−	0.241906i
$459$	−1.40436	+	1.17840i	−0.0655498	+	0.0550028i
$460$		0			0
$461$	25.2875	+	9.20388i	1.17775	+	0.428667i	0.855408	−	0.517954i	$-0.173306\pi$
$461$	25.2875	+	9.20388i	1.17775	+	0.428667i	0.322346	+	0.946622i	$0.395529\pi$
$462$	−0.404575	−	4.62431i	−0.0188225	−	0.215142i
$463$	3.85707	+	14.3948i	0.179253	+	0.668982i	0.995788	+	0.0916860i	$0.0292256\pi$
$463$	3.85707	+	14.3948i	0.179253	+	0.668982i	−0.816535	+	0.577296i	$0.804108\pi$
$464$	2.57115	+	4.45336i	0.119363	+	0.206742i
$465$		0			0
$466$	23.9800	+	4.22832i	1.11085	+	0.195873i
$467$	6.71248	−	25.0513i	0.310616	−	1.15924i	−0.617385	−	0.786661i	$-0.711808\pi$
$467$	6.71248	−	25.0513i	0.310616	−	1.15924i	0.928002	−	0.372576i	$-0.121525\pi$
$468$	4.13060	−	1.10679i	0.190937	−	0.0511614i
$469$	−3.84240	−	3.22416i	−0.177425	−	0.148878i
$470$		0			0
$471$	12.5360	+	34.4423i	0.577627	+	1.58702i
$472$	−0.318852	−	0.0278959i	−0.0146764	−	0.00128401i
$473$	−36.4255	−	25.5054i	−1.67485	−	1.17274i
$474$	−35.1582			−1.61487
$475$		0			0
$476$	0.305407			0.0139983
$477$	−11.7863	−	8.25283i	−0.539656	−	0.377871i
$478$	27.2832	+	2.38697i	1.24791	+	0.109178i
$479$	4.25838	+	11.6998i	0.194570	+	0.534578i	0.998162	−	0.0606034i	$-0.0193025\pi$
$479$	4.25838	+	11.6998i	0.194570	+	0.534578i	−0.803592	+	0.595181i	$0.797080\pi$
$480$		0			0
$481$	3.89053	+	3.26454i	0.177393	+	0.148850i
$482$	8.79976	−	2.35789i	0.400818	−	0.107399i
$483$	0.112720	−	0.420678i	0.00512895	−	0.0191415i
$484$	−11.4690	−	2.02229i	−0.521317	−	0.0919222i
$485$		0			0
$486$	−8.18779	−	14.1817i	−0.371405	−	0.643293i
$487$	−7.00497	−	26.1429i	−0.317425	−	1.18465i	−0.921710	−	0.387879i	$-0.873208\pi$
$487$	−7.00497	−	26.1429i	−0.317425	−	1.18465i	0.604285	−	0.796768i	$-0.293459\pi$
$488$	0.720888	+	8.23978i	0.0326331	+	0.372998i
$489$	−49.5827	−	18.0466i	−2.24221	−	0.816097i
$490$		0			0
$491$	12.9422	−	10.8598i	0.584074	−	0.490096i	−0.302208	−	0.953242i	$-0.597724\pi$
$491$	12.9422	−	10.8598i	0.584074	−	0.490096i	0.886282	+	0.463146i	$0.153279\pi$
$492$	−0.650420	+	0.928895i	−0.0293232	+	0.0418778i
$493$	2.48728	+	2.48728i	0.112021	+	0.112021i
$494$	10.5111	+	0.0773815i	0.472916	+	0.00348156i
$495$		0			0
$496$	−2.58512	+	0.455827i	−0.116075	+	0.0204672i
$497$	−0.100051	+	1.14359i	−0.00448790	+	0.0512969i
$498$	0.801226	−	1.71823i	0.0359038	−	0.0769959i
$499$	−8.03850	+	22.0856i	−0.359853	+	0.988687i	0.619228	+	0.785212i	$0.287446\pi$
$499$	−8.03850	+	22.0856i	−0.359853	+	0.988687i	−0.979080	+	0.203475i	$0.934776\pi$
$500$		0			0
$501$	−15.9907	+	27.6966i	−0.714410	+	1.23739i
$502$	−12.9760	−	3.47691i	−0.579148	−	0.155182i
$503$	−4.30710	−	6.15117i	−0.192044	−	0.274267i	0.711570	−	0.702615i	$-0.247985\pi$
$503$	−4.30710	−	6.15117i	−0.192044	−	0.274267i	−0.903614	+	0.428348i	$0.859096\pi$
$504$	−0.137485	+	0.779715i	−0.00612406	+	0.0347313i
$505$		0			0
$506$	−1.84002	−	1.06234i	−0.0817990	−	0.0472267i
$507$	−15.6375	+	1.36811i	−0.694488	+	0.0607598i
$508$	−8.62011	−	18.4859i	−0.382456	−	0.820179i
$509$	31.4197	−	11.4358i	1.39265	−	0.506884i	0.466663	−	0.884435i	$-0.345456\pi$
$509$	31.4197	−	11.4358i	1.39265	−	0.506884i	0.925989	+	0.377551i	$0.123234\pi$
$510$		0			0
$511$	−0.336619	−	1.90906i	−0.0148911	−	0.0844519i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.94038	−	11.3059i	−0.129821	−	0.499169i
$514$		−	16.5963i		−	0.732030i
$515$		0			0
$516$	13.1227	+	15.6391i	0.577696	+	0.688471i
$517$	−22.7664	−	10.6161i	−1.00126	−	0.466897i
$518$	−0.852208	+	0.397391i	−0.0374439	+	0.0174604i
$519$	−17.0985	+	20.3772i	−0.750540	+	0.894458i
$520$		0			0
$521$	−8.12124	+	4.68880i	−0.355798	+	0.205420i	−0.667236	−	0.744846i	$-0.732523\pi$
$521$	−8.12124	+	4.68880i	−0.355798	+	0.205420i	0.311438	+	0.950267i	$0.399189\pi$
$522$	−7.46980	+	5.23041i	−0.326944	+	0.228929i
$523$	26.7770	−	18.7495i	1.17088	−	0.819857i	0.184255	−	0.982878i	$-0.441013\pi$
$523$	26.7770	−	18.7495i	1.17088	−	0.819857i	0.986623	+	0.163021i	$0.0521238\pi$
$524$	4.01239	−	2.31655i	0.175282	−	0.101199i
$525$		0			0
$526$	17.3380	−	20.6626i	0.755971	−	0.900931i
$527$	−1.62737	+	0.758856i	−0.0708895	+	0.0330563i
$528$	9.42282	+	4.39393i	0.410075	+	0.191221i
$529$	14.6560	+	17.4663i	0.637217	+	0.759405i
$530$		0			0
$531$		−	0.567586i		−	0.0246311i
$532$	−0.835437	+	1.75770i	−0.0362208	+	0.0762060i
$533$	−0.885034	+	0.885034i	−0.0383351	+	0.0383351i
$534$	−6.31672	−	35.8239i	−0.273351	−	1.55025i
$535$		0			0
$536$	10.5569	−	3.84240i	0.455989	−	0.165966i
$537$	3.93764	+	8.44430i	0.169922	+	0.364399i
$538$	−27.1607	+	2.37626i	−1.17098	+	0.102448i
$539$	−28.0270	−	16.1814i	−1.20721	−	0.696982i
$540$		0			0
$541$	1.24850	−	7.08062i	0.0536774	−	0.304419i	−0.946135	−	0.323771i	$-0.895049\pi$
$541$	1.24850	−	7.08062i	0.0536774	−	0.304419i	0.999813	+	0.0193519i	$0.00616028\pi$
$542$	14.5799	+	20.8222i	0.626259	+	0.894390i
$543$	31.9017	+	8.54803i	1.36903	+	0.366831i
$544$	−0.342020	+	0.592396i	−0.0146640	+	0.0253988i
$545$		0			0
$546$	−0.804530	+	2.21043i	−0.0344307	+	0.0945976i
$547$	0.152527	−	0.327096i	0.00652160	−	0.0139856i	−0.903020	−	0.429598i	$-0.858655\pi$
$547$	0.152527	−	0.327096i	0.00652160	−	0.0139856i	0.909542	+	0.415613i	$0.136433\pi$
$548$	1.45613	−	16.6436i	0.0622027	−	0.710980i
$549$	−14.4447	+	2.54700i	−0.616487	+	0.108703i
$550$		0			0
$551$	−21.1189	+	7.51104i	−0.899694	+	0.319981i
$552$	0.689752	+	0.689752i	0.0293578	+	0.0293578i
$553$	4.12103	−	5.88544i	0.175244	−	0.250274i
$554$	−8.72254	+	7.31908i	−0.370585	+	0.310958i
$555$		0			0
$556$	−17.7015	−	6.44280i	−0.750709	−	0.273236i
$557$	−0.311143	−	3.55638i	−0.0131836	−	0.150689i	0.986750	−	0.162250i	$-0.0518753\pi$
$557$	−0.311143	−	3.55638i	−0.0131836	−	0.150689i	−0.999933	+	0.0115618i	$0.996320\pi$
$558$	−1.20479	−	4.49635i	−0.0510030	−	0.190346i
$559$	11.2668	+	19.5146i	0.476533	+	0.825380i
$560$		0			0
$561$	7.00387	+	1.23497i	0.295704	+	0.0521405i
$562$	−0.313953	+	1.17169i	−0.0132433	+	0.0494247i
$563$	−28.6696	+	7.68200i	−1.20828	+	0.323758i	−0.806087	−	0.591797i	$-0.798419\pi$
$563$	−28.6696	+	7.68200i	−1.20828	+	0.323758i	−0.402193	+	0.915555i	$0.631752\pi$
$564$	8.83462	+	7.41312i	0.372004	+	0.312149i
$565$		0			0
$566$	5.73901	+	15.7678i	0.241228	+	0.662770i
$567$	4.97051	+	0.434863i	0.208742	+	0.0182625i
$568$	−2.10616	−	1.47475i	−0.0883726	−	0.0618792i
$569$	−3.69637			−0.154960			−0.0774800	−	0.996994i	$-0.524687\pi$
$569$	−3.69637			−0.154960			−0.0774800	+	0.996994i	$0.524687\pi$
$570$		0			0
$571$	−13.5716			−0.567954			−0.283977	−	0.958831i	$-0.591654\pi$
$571$	−13.5716			−0.567954			−0.283977	+	0.958831i	$0.591654\pi$
$572$	9.40030	+	6.58216i	0.393046	+	0.275214i
$573$	−40.2882	−	3.52476i	−1.68306	−	0.147249i
$574$	−0.0792577	−	0.217759i	−0.00330815	−	0.00908908i
$575$		0			0
$576$	−1.35844	−	1.13987i	−0.0566017	−	0.0474945i
$577$	−2.55362	+	0.684241i	−0.106309	+	0.0284853i	−0.311581	−	0.950220i	$-0.600859\pi$
$577$	−2.55362	+	0.684241i	−0.106309	+	0.0284853i	0.205273	+	0.978705i	$0.434192\pi$
$578$	4.27882	−	15.9688i	0.177975	−	0.664213i
$579$	23.6530	+	4.17066i	0.982983	+	0.173327i
$580$		0			0
$581$	0.193715	+	0.335525i	0.00803667	+	0.0139199i
$582$	−1.70077	−	6.34738i	−0.0704994	−	0.263107i
$583$	−3.36524	−	38.4648i	−0.139374	−	1.59305i
$584$	4.07996	+	1.48499i	0.168830	+	0.0614491i
$585$		0			0
$586$	−8.01573	+	6.72600i	−0.331127	+	0.277848i
$587$	18.3790	−	26.2479i	0.758583	−	1.08337i	−0.235190	−	0.971949i	$-0.575571\pi$
$587$	18.3790	−	26.2479i	0.758583	−	1.08337i	0.993773	−	0.111419i	$-0.0355397\pi$
$588$	10.5062	+	10.5062i	0.433269	+	0.433269i
$589$	0.0842334	−	11.4418i	0.00347078	−	0.471451i
$590$		0			0
$591$	1.98293	−	0.349643i	0.0815667	−	0.0143824i
$592$	0.183556	−	2.09805i	0.00754410	−	0.0862294i
$593$	−18.9693	+	40.6798i	−0.778976	+	1.67052i	−0.0377267	+	0.999288i	$0.512012\pi$
$593$	−18.9693	+	40.6798i	−0.778976	+	1.67052i	−0.741249	+	0.671230i	$0.765766\pi$
$594$	4.36203	−	11.9846i	0.178976	−	0.491733i
$595$		0			0
$596$	6.64203	−	11.5043i	0.272068	−	0.471236i
$597$	−34.0308	−	9.11852i	−1.39279	−	0.373196i
$598$	0.617549	+	0.881952i	0.0252535	+	0.0360657i
$599$	3.59315	−	20.3778i	0.146812	−	0.832614i	−0.819082	−	0.573677i	$-0.805517\pi$
$599$	3.59315	−	20.3778i	0.146812	−	0.832614i	0.965894	−	0.258937i	$-0.0833723\pi$
$600$		0			0
$601$	−23.1668	−	13.3754i	−0.944995	−	0.545593i	−0.0534725	−	0.998569i	$-0.517029\pi$
$601$	−23.1668	−	13.3754i	−0.944995	−	0.545593i	−0.891523	+	0.452976i	$0.850362\pi$
$602$	−4.15612	+	0.363614i	−0.169391	+	0.0148198i
$603$	8.41949	+	18.0557i	0.342868	+	0.735283i
$604$	11.6071	−	4.22462i	0.472284	−	0.171897i
$605$		0			0
$606$	−1.85962	−	10.5464i	−0.0755420	−	0.428420i
$607$	−0.994490	+	0.994490i	−0.0403651	+	0.0403651i	−0.727001	−	0.686636i	$-0.759087\pi$
$607$	−0.994490	+	0.994490i	−0.0403651	+	0.0403651i	0.686636	+	0.727001i	$0.259087\pi$
$608$	−2.47381	−	3.58891i	−0.100326	−	0.145550i
$609$		−	5.01609i		−	0.203262i
$610$		0			0
$611$	8.18227	+	9.75125i	0.331019	+	0.394493i
$612$	−1.09937	−	0.512645i	−0.0444394	−	0.0207224i
$613$	−2.07094	+	0.965695i	−0.0836445	+	0.0390041i	−0.463990	−	0.885840i	$-0.653583\pi$
$613$	−2.07094	+	0.965695i	−0.0836445	+	0.0390041i	0.380346	+	0.924844i	$0.375805\pi$
$614$	0.358995	−	0.427833i	0.0144878	−	0.0172659i
$615$		0			0
$616$	−1.84002	+	1.06234i	−0.0741366	+	0.0428028i
$617$	19.1664	−	13.4204i	0.771609	−	0.540287i	−0.120172	−	0.992753i	$-0.538345\pi$
$617$	19.1664	−	13.4204i	0.771609	−	0.540287i	0.891781	+	0.452467i	$0.149456\pi$
$618$	−18.3774	+	12.8680i	−0.739249	+	0.517627i
$619$	−13.6987	+	7.90895i	−0.550597	+	0.317887i	−0.749363	−	0.662160i	$-0.769640\pi$
$619$	−13.6987	+	7.90895i	−0.550597	+	0.317887i	0.198766	+	0.980047i	$0.436307\pi$
$620$		0			0
$621$	0.769143	−	0.916629i	0.0308647	−	0.0367831i
$622$	27.9467	−	13.0317i	1.12056	−	0.522525i
$623$	6.73728	+	3.14164i	0.269923	+	0.125867i
$624$	−3.38657	−	4.03596i	−0.135571	−	0.161568i
$625$		0			0
$626$		−	8.47005i		−	0.338531i
$627$	−26.2666	+	36.9309i	−1.04899	+	1.47488i
$628$	11.8626	−	11.8626i	0.473370	−	0.473370i
$629$	−0.250164	−	1.41875i	−0.00997467	−	0.0565692i
$630$		0			0
$631$	−13.0360	+	4.74470i	−0.518953	+	0.188884i	−0.588199	−	0.808716i	$-0.700163\pi$
$631$	−13.0360	+	4.74470i	−0.518953	+	0.188884i	0.0692459	+	0.997600i	$0.477941\pi$
$632$	6.80087	+	14.5845i	0.270524	+	0.580141i
$633$	−11.4889	+	1.00515i	−0.456642	+	0.0399510i
$634$	21.4803	+	12.4017i	0.853093	+	0.492533i
$635$		0			0
$636$	−3.07826	+	17.4577i	−0.122061	+	0.692242i
$637$	9.40643	+	13.4338i	0.372696	+	0.532266i
$638$	−23.6372	−	6.33357i	−0.935806	−	0.250748i
$639$	2.27973	−	3.94862i	0.0901849	−	0.156205i
$640$		0			0
$641$	13.5462	−	37.2180i	0.535044	−	1.47002i	−0.317954	−	0.948106i	$-0.602996\pi$
$641$	13.5462	−	37.2180i	0.535044	−	1.47002i	0.852998	−	0.521915i	$-0.174782\pi$
$642$	−5.44206	+	11.6705i	−0.214781	+	0.460600i
$643$	3.16104	−	36.1308i	0.124659	−	1.42486i	−0.633980	−	0.773349i	$-0.718580\pi$
$643$	3.16104	−	36.1308i	0.124659	−	1.42486i	0.758639	−	0.651511i	$-0.225864\pi$
$644$	−0.196312	+	0.0346151i	−0.00773578	+	0.00136403i
$645$		0			0
$646$	−2.26991	−	1.93334i	−0.0893086	−	0.0760662i
$647$	23.2250	+	23.2250i	0.913070	+	0.913070i	0.996513	−	0.0834422i	$-0.0265914\pi$
$647$	23.2250	+	23.2250i	0.913070	+	0.913070i	−0.0834422	+	0.996513i	$0.526591\pi$
$648$	−6.40989	+	9.15427i	−0.251804	+	0.359614i
$649$	1.16679	−	0.979055i	0.0458006	−	0.0384313i
$650$		0			0
$651$	2.40615	+	0.875768i	0.0943046	+	0.0343241i
$652$	2.10489	+	24.0591i	0.0824340	+	0.942225i
$653$	5.49501	+	20.5077i	0.215036	+	0.802527i	0.986154	+	0.165834i	$0.0530314\pi$
$653$	5.49501	+	20.5077i	0.215036	+	0.802527i	−0.771117	+	0.636693i	$0.780302\pi$
$654$	8.45367	+	14.6422i	0.330565	+	0.572555i
$655$		0			0
$656$	0.511144	+	0.0901285i	0.0199568	+	0.00351893i
$657$	−1.99275	+	7.43705i	−0.0777447	+	0.290147i
$658$	−2.27649	+	0.609983i	−0.0887467	+	0.0237796i
$659$	−4.30320	−	3.61081i	−0.167629	−	0.140657i	0.555114	−	0.831774i	$-0.312675\pi$
$659$	−4.30320	−	3.61081i	−0.167629	−	0.140657i	−0.722743	+	0.691117i	$0.757119\pi$
$660$		0			0
$661$	7.87867	+	21.6465i	0.306445	+	0.841950i	0.993343	+	0.115196i	$0.0367497\pi$
$661$	7.87867	+	21.6465i	0.306445	+	0.841950i	−0.686898	+	0.726754i	$0.741028\pi$
$662$	17.1234	+	1.49810i	0.665520	+	0.0582254i
$663$	−2.95215	−	2.06712i	−0.114652	−	0.0802803i
$664$	−0.867753			−0.0336754
$665$		0			0
$666$	3.73473			0.144718
$667$	−1.88070	−	1.31688i	−0.0728210	−	0.0509898i
$668$	14.5825	+	1.27580i	0.564212	+	0.0493622i
$669$	15.5969	+	42.8521i	0.603011	+	1.65676i
$670$		0			0
$671$	−30.1523	−	25.3008i	−1.16402	−	0.976726i
$672$	0.942219	−	0.252467i	0.0363469	−	0.00973912i
$673$	−7.11592	+	26.5570i	−0.274299	+	1.02370i	0.682011	+	0.731342i	$0.261106\pi$
$673$	−7.11592	+	26.5570i	−0.274299	+	1.02370i	−0.956310	+	0.292355i	$0.905561\pi$
$674$	−14.0132	−	2.47090i	−0.539768	−	0.0951757i
$675$		0			0
$676$	3.59240	+	6.22221i	0.138169	+	0.239316i
$677$	−1.10278	−	4.11565i	−0.0423834	−	0.158177i	0.941491	−	0.337039i	$-0.109425\pi$
$677$	−1.10278	−	4.11565i	−0.0423834	−	0.158177i	−0.983874	+	0.178861i	$0.942759\pi$
$678$	2.40375	+	27.4750i	0.0923155	+	1.05517i
$679$	1.26190	+	0.459293i	0.0484272	+	0.0176260i
$680$		0			0
$681$	−13.8188	+	11.5954i	−0.529539	+	0.444336i
$682$	7.16499	−	10.2327i	0.274362	−	0.391829i
$683$	−25.3265	−	25.3265i	−0.969091	−	0.969091i	0.0304450	−	0.999536i	$-0.490308\pi$
$683$	−25.3265	−	25.3265i	−0.969091	−	0.969091i	−0.999536	+	0.0304450i	$0.990308\pi$
$684$	5.95772	−	4.92484i	0.227799	−	0.188306i
$685$		0			0
$686$	−6.06805	+	1.06996i	−0.231679	+	0.0408513i
$687$	1.20343	−	13.7552i	0.0459137	−	0.524795i
$688$	3.94907	−	8.46881i	0.150557	−	0.322870i
$689$	−6.69205	+	18.3862i	−0.254947	+	0.700460i
$690$		0			0
$691$	2.64930	−	4.58872i	0.100784	−	0.174563i	−0.811224	−	0.584736i	$-0.801198\pi$
$691$	2.64930	−	4.58872i	0.100784	−	0.174563i	0.912008	+	0.410173i	$0.134532\pi$
$692$	11.7604	+	3.15120i	0.447065	+	0.119791i
$693$	−2.16108	−	3.08634i	−0.0820926	−	0.117240i
$694$	3.28384	−	18.6236i	0.124653	−	0.706942i
$695$		0			0
$696$	9.72967	+	5.61743i	0.368802	+	0.212928i
$697$	0.353686	−	0.0309435i	0.0133968	−	0.00117207i
$698$	−8.34541	−	17.8968i	−0.315878	−	0.677403i
$699$	49.9912	−	18.1953i	1.89084	−	0.688210i
$700$		0			0
$701$	−5.16163	−	29.2730i	−0.194952	−	1.10563i	−0.912487	−	0.409105i	$-0.865841\pi$
$701$	−5.16163	−	29.2730i	−0.194952	−	1.10563i	0.717535	−	0.696522i	$-0.245270\pi$
$702$	−4.56993	+	4.56993i	−0.172481	+	0.172481i
$703$	8.84960	+	2.44121i	0.333769	+	0.0920719i
$704$		−	4.75877i		−	0.179353i
$705$		0			0
$706$	−4.64290	−	5.53320i	−0.174738	−	0.208245i
$707$	1.98343	+	0.924891i	0.0745947	+	0.0347841i
$708$	−0.633769	+	0.295531i	−0.0238185	+	0.0111067i
$709$	7.23832	−	8.62630i	0.271841	−	0.323967i	−0.612802	−	0.790236i	$-0.709958\pi$
$709$	7.23832	−	8.62630i	0.271841	−	0.323967i	0.884643	+	0.466269i	$0.154402\pi$
$710$		0			0
$711$	−24.7135	+	14.2683i	−0.926828	+	0.535104i
$712$	−13.6388	+	9.54998i	−0.511135	+	0.357900i
$713$	0.960046	−	0.672231i	0.0359540	−	0.0251753i
$714$	0.577857	−	0.333626i	0.0216257	−	0.0124856i
$715$		0			0
$716$	2.74123	−	3.26687i	0.102445	−	0.122089i
$717$	54.2297	−	25.2877i	2.02525	−	0.944387i
$718$	14.6016	+	6.80885i	0.544928	+	0.254104i
$719$	7.86474	+	9.37283i	0.293305	+	0.349547i	0.892493	−	0.451061i	$-0.148954\pi$
$719$	7.86474	+	9.37283i	0.293305	+	0.349547i	−0.599188	+	0.800608i	$0.704510\pi$
$720$		0			0
$721$		−	4.58467i		−	0.170742i
$722$	17.3362	−	7.77535i	0.645187	−	0.289369i
$723$	14.0742	−	14.0742i	0.523424	−	0.523424i
$724$	−2.62500	−	14.8871i	−0.0975574	−	0.553276i
$725$		0			0
$726$	−23.9094	+	8.70232i	−0.887362	+	0.322973i
$727$	−2.48009	−	5.31858i	−0.0919816	−	0.197255i	0.854935	−	0.518736i	$-0.173597\pi$
$727$	−2.48009	−	5.31858i	−0.0919816	−	0.197255i	−0.946916	+	0.321481i	$0.895819\pi$
$728$	1.07257	−	0.0938375i	0.0397520	−	0.00347785i
$729$	−1.94971	−	1.12567i	−0.0722116	−	0.0416914i
$730$		0			0
$731$	1.10994	−	6.29477i	0.0410525	−	0.232820i
$732$	10.3651	+	14.8029i	0.383105	+	0.547130i
$733$	−0.861365	−	0.230802i	−0.0318153	−	0.00852487i	0.242876	−	0.970057i	$-0.421909\pi$
$733$	−0.861365	−	0.230802i	−0.0318153	−	0.00852487i	−0.274692	+	0.961532i	$0.588576\pi$
$734$	−4.66950	+	8.08781i	−0.172354	+	0.298527i
$735$		0			0
$736$	0.152704	−	0.419550i	0.00562873	−	0.0154648i
$737$	−22.5940	+	48.4531i	−0.832262	+	1.78479i
$738$	−0.0802186	+	0.916902i	−0.00295289	+	0.0337516i
$739$	−23.7837	+	4.19372i	−0.874899	+	0.154268i	−0.593026	−	0.805183i	$-0.702067\pi$
$739$	−23.7837	+	4.19372i	−0.874899	+	0.154268i	−0.281873	+	0.959452i	$0.590956\pi$
$740$		0			0
$741$	19.9724	−	11.3359i	0.733705	−	0.416433i
$742$	−2.56158	−	2.56158i	−0.0940385	−	0.0940385i
$743$	−6.49031	+	9.26912i	−0.238106	+	0.340051i	−0.920365	−	0.391059i	$-0.872109\pi$
$743$	−6.49031	+	9.26912i	−0.238106	+	0.340051i	0.682259	+	0.731111i	$0.260998\pi$
$744$	−4.39333	+	3.68644i	−0.161067	+	0.135151i
$745$		0			0
$746$	−1.36736	−	0.497680i	−0.0500627	−	0.0182213i
$747$	−0.134116	−	1.53295i	−0.00490703	−	0.0560876i
$748$	−0.842505	−	3.14427i	−0.0308050	−	0.114966i
$749$	−1.31575	−	2.27894i	−0.0480764	−	0.0832708i
$750$		0			0
$751$	−1.85323	−	0.326774i	−0.0676252	−	0.0119241i	0.139733	−	0.990189i	$-0.455376\pi$
$751$	−1.85323	−	0.326774i	−0.0676252	−	0.0119241i	−0.207358	+	0.978265i	$0.566487\pi$
$752$	1.36622	−	5.09879i	0.0498208	−	0.185934i
$753$	−28.3499	+	7.59634i	−1.03313	+	0.276826i
$754$	9.49935	+	7.97090i	0.345946	+	0.290283i
$755$		0			0
$756$	−0.409253	−	1.12441i	−0.0148844	−	0.0408945i
$757$	−54.4043	−	4.75976i	−1.97736	−	0.172996i	−0.977994	−	0.208633i	$-0.933099\pi$
$757$	−54.4043	−	4.75976i	−1.97736	−	0.172996i	−0.999365	+	0.0356365i	$0.988654\pi$
$758$	24.5631	+	17.1993i	0.892173	+	0.624706i
$759$	−4.64197			−0.168493
$760$		0			0
$761$	−24.7273			−0.896364			−0.448182	−	0.893942i	$-0.647928\pi$
$761$	−24.7273			−0.896364			−0.448182	+	0.893942i	$0.647928\pi$
$762$	−36.5039	−	25.5603i	−1.32240	−	0.925953i
$763$	−3.44197	−	0.301133i	−0.124608	−	0.0109018i
$764$	6.33104	+	17.3944i	0.229049	+	0.629307i
$765$		0			0
$766$	−5.06418	−	4.24935i	−0.182976	−	0.153535i
$767$	−0.745541	+	0.199767i	−0.0269199	+	0.00721317i
$768$	−0.565466	+	2.11035i	−0.0204045	+	0.0761506i
$769$	49.3996	+	8.71048i	1.78140	+	0.314108i	0.964777	−	0.263069i	$-0.0847348\pi$
$769$	49.3996	+	8.71048i	1.78140	+	0.314108i	0.816619	+	0.577177i	$0.195846\pi$
$770$		0			0
$771$	−18.1297	−	31.4016i	−0.652925	−	1.13090i
$772$	−2.84525	−	10.6186i	−0.102403	−	0.382172i
$773$	−3.24973	−	37.1445i	−0.116884	−	1.33600i	−0.797484	−	0.603340i	$-0.793836\pi$
$773$	−3.24973	−	37.1445i	−0.116884	−	1.33600i	0.680599	−	0.732656i	$-0.261719\pi$
$774$	15.5711	+	5.66741i	0.559691	+	0.203711i
$775$		0			0
$776$	−2.30406	+	1.93334i	−0.0827110	+	0.0694028i
$777$	−1.17834	+	1.68285i	−0.0422728	+	0.0603718i
$778$	−2.82295	−	2.82295i	−0.101208	−	0.101208i
$779$	−0.789415	+	2.12020i	−0.0282837	+	0.0759642i
$780$		0			0
$781$	12.0496	−	2.12467i	0.431170	−	0.0760268i
$782$	0.0266180	−	0.304245i	0.000951858	−	0.0108798i
$783$	5.82435	−	12.4904i	0.208145	−	0.446369i
$784$	2.32596	−	6.39053i	0.0830701	−	0.228233i
$785$		0			0
$786$	5.06118	−	8.76623i	0.180526	−	0.312681i
$787$	27.2029	+	7.28899i	0.969678	+	0.259825i	0.708692	−	0.705518i	$-0.249286\pi$
$787$	27.2029	+	7.28899i	0.969678	+	0.259825i	0.260986	+	0.965343i	$0.415952\pi$
$788$	−0.528611	−	0.754935i	−0.0188310	−	0.0268934i
$789$	10.2332	−	58.0353i	0.364311	−	2.06611i
$790$		0			0
$791$	−4.88103	−	2.81807i	−0.173550	−	0.100199i
$792$	8.40670	−	0.735491i	0.298719	−	0.0261345i
$793$	8.42951	+	18.0771i	0.299341	+	0.641938i
$794$	−3.06823	+	1.11674i	−0.108887	+	0.0396318i
$795$		0			0
$796$	2.80019	+	15.8807i	0.0992502	+	0.562876i
$797$	27.2627	−	27.2627i	0.965695	−	0.965695i	−0.0337356	−	0.999431i	$-0.510740\pi$
$797$	27.2627	−	27.2627i	0.965695	−	0.965695i	0.999431	+	0.0337356i	$0.0107404\pi$
$798$	0.339387	+	4.23835i	0.0120142	+	0.150036i
$799$		−	3.61081i		−	0.127741i
$800$		0			0
$801$	−18.9786	−	22.6179i	−0.670577	−	0.799163i
$802$	−30.5405	−	14.2413i	−1.07842	−	0.502876i
$803$	−18.7258	+	8.73199i	−0.660820	+	0.308145i
$804$	15.7771	−	18.8025i	0.556417	−	0.663112i
$805$		0			0
$806$	−5.48205	+	3.16506i	−0.193097	+	0.111485i
$807$	−48.7947	+	34.1664i	−1.71765	+	1.20271i
$808$	−4.01522	+	2.81148i	−0.141255	+	0.0989077i
$809$	12.2836	−	7.09193i	0.431868	−	0.249339i	−0.268274	−	0.963343i	$-0.586453\pi$
$809$	12.2836	−	7.09193i	0.431868	−	0.249339i	0.700142	+	0.714004i	$0.253120\pi$
$810$		0			0
$811$	28.4183	−	33.8677i	0.997903	−	1.18925i	0.0159994	−	0.999872i	$-0.494907\pi$
$811$	28.4183	−	33.8677i	0.997903	−	1.18925i	0.981903	−	0.189382i	$-0.0606485\pi$
$812$	−2.08080	+	0.970294i	−0.0730219	+	0.0340507i
$813$	50.3324	+	23.4704i	1.76524	+	0.823143i
$814$	6.44220	+	7.67752i	0.225799	+	0.269097i
$815$		0			0
$816$			1.49449i			0.0523175i
$817$	33.1919	+	23.6072i	1.16124	+	0.825913i
$818$	4.26382	−	4.26382i	0.149081	−	0.149081i
$819$	0.331541	+	1.88026i	0.0115850	+	0.0657017i
$820$		0			0
$821$	3.16132	−	1.15063i	0.110331	−	0.0401572i	−0.286265	−	0.958151i	$-0.592414\pi$
$821$	3.16132	−	1.15063i	0.110331	−	0.0401572i	0.396596	+	0.917993i	$0.370191\pi$
$822$	−15.4263	−	33.0818i	−0.538054	−	1.15386i
$823$	−12.4629	+	1.09036i	−0.434429	+	0.0380076i	−0.302273	−	0.953221i	$-0.597745\pi$
$823$	−12.4629	+	1.09036i	−0.434429	+	0.0380076i	−0.132156	+	0.991229i	$0.542190\pi$
$824$	8.89284	+	5.13429i	0.309797	+	0.178861i
$825$		0			0
$826$	0.0248149	−	0.140732i	0.000863422	−	0.00489671i
$827$	8.46818	+	12.0938i	0.294468	+	0.420543i	0.938938	−	0.344086i	$-0.111811\pi$
$827$	8.46818	+	12.0938i	0.294468	+	0.420543i	−0.644471	+	0.764629i	$0.722922\pi$
$828$	0.764765	+	0.204918i	0.0265774	+	0.00712140i
$829$	−9.45485	+	16.3763i	−0.328381	+	0.568772i	−0.982191	−	0.187887i	$-0.939836\pi$
$829$	−9.45485	+	16.3763i	−0.328381	+	0.568772i	0.653810	+	0.756659i	$0.273170\pi$
$830$		0			0
$831$	−8.50846	+	23.3768i	−0.295155	+	0.810932i
$832$	−1.01913	+	2.18554i	−0.0353321	+	0.0757699i
$833$	0.405442	−	4.63422i	0.0140477	−	0.160566i
$834$	−40.5308	+	7.14667i	−1.40347	+	0.247469i
$835$		0			0
$836$	20.4008	+	3.75227i	0.705576	+	0.129775i
$837$	4.97458	+	4.97458i	0.171947	+	0.171947i
$838$	−17.6793	+	25.2487i	−0.610722	+	0.872201i
$839$	24.9663	−	20.9492i	0.861931	−	0.723246i	−0.100452	−	0.994942i	$-0.532029\pi$
$839$	24.9663	−	20.9492i	0.861931	−	0.723246i	0.962383	+	0.271696i	$0.0875844\pi$
$840$		0			0
$841$	2.40255	+	0.874457i	0.0828466	+	0.0301537i
$842$	−2.79700	−	31.9699i	−0.0963911	−	1.10176i
$843$	0.685922	+	2.55990i	0.0236244	+	0.0881675i
$844$	2.63933	+	4.57145i	0.0908494	+	0.157356i
$845$		0			0
$846$	9.21853	+	1.62548i	0.316940	+	0.0558850i
$847$	1.34576	−	5.02244i	0.0462408	−	0.172573i
$848$	7.83734	−	2.10001i	0.269135	−	0.0721146i
$849$	28.0834	+	23.5648i	0.963819	+	0.808740i
$850$		0			0
$851$	0.321604	+	0.883600i	0.0110244	+	0.0302894i
$852$	−5.59605	−	0.489591i	−0.191718	−	0.0167731i
$853$	21.1096	+	14.7811i	0.722778	+	0.506094i	0.876129	−	0.482078i	$-0.160118\pi$
$853$	21.1096	+	14.7811i	0.722778	+	0.506094i	−0.153351	+	0.988172i	$0.549007\pi$
$854$	−3.69292			−0.126369
$855$		0			0
$856$	5.89393			0.201450
$857$	32.8873	+	23.0279i	1.12341	+	0.786619i	0.979194	−	0.202928i	$-0.0650456\pi$
$857$	32.8873	+	23.0279i	1.12341	+	0.786619i	0.144214	+	0.989546i	$0.453935\pi$
$858$	24.9765	+	2.18516i	0.852684	+	0.0746002i
$859$	10.3209	+	28.3564i	0.352144	+	0.967507i	0.981680	+	0.190536i	$0.0610227\pi$
$859$	10.3209	+	28.3564i	0.352144	+	0.967507i	−0.629536	+	0.776971i	$0.716755\pi$
$860$		0			0
$861$	−0.387841	−	0.325437i	−0.0132176	−	0.0110909i
$862$	37.5634	−	10.0651i	1.27942	−	0.342818i
$863$	−3.29914	+	12.3126i	−0.112304	+	0.419125i	−0.999071	−	0.0430920i	$-0.986279\pi$
$863$	−3.29914	+	12.3126i	−0.112304	+	0.419125i	0.886767	+	0.462217i	$0.152946\pi$
$864$	2.63933	+	0.465385i	0.0897918	+	0.0158327i
$865$		0			0
$866$	13.9304	+	24.1281i	0.473373	+	0.819906i
$867$	−9.34833	−	34.8885i	−0.317486	−	1.18487i
$868$	−0.102146	−	1.16754i	−0.00346708	−	0.0396289i
$869$	−71.9610	−	26.1917i	−2.44111	−	0.888491i
$870$		0			0
$871$	20.7533	−	17.4141i	0.703199	−	0.590054i
$872$	4.43871	−	6.33913i	0.150314	−	0.214670i
$873$	−3.77148	−	3.77148i	−0.127645	−	0.127645i
$874$	1.67820	+	0.985452i	0.0567659	+	0.0333334i
$875$		0			0
$876$	9.34183	−	1.64722i	0.315631	−	0.0556543i
$877$	2.18239	−	24.9448i	0.0736941	−	0.842328i	−0.865940	−	0.500148i	$-0.833279\pi$
$877$	2.18239	−	24.9448i	0.0736941	−	0.842328i	0.939634	−	0.342180i	$-0.111165\pi$
$878$	11.9547	−	25.6370i	0.403453	−	0.865207i
$879$	−7.81900	+	21.4825i	−0.263728	+	0.724587i
$880$		0			0
$881$	−10.1163	+	17.5220i	−0.340828	+	0.590331i	−0.984587	−	0.174897i	$-0.944041\pi$
$881$	−10.1163	+	17.5220i	−0.340828	+	0.590331i	0.643759	+	0.765229i	$0.277374\pi$
$882$	11.6488	+	3.12129i	0.392236	+	0.105099i
$883$	17.3181	+	24.7328i	0.582799	+	0.832324i	0.996963	−	0.0778789i	$-0.0248147\pi$
$883$	17.3181	+	24.7328i	0.582799	+	0.832324i	−0.414164	+	0.910202i	$0.635926\pi$
$884$	−0.286441	+	1.62449i	−0.00963404	+	0.0546373i
$885$		0			0
$886$	−23.4993	−	13.5673i	−0.789474	−	0.455803i
$887$	12.2586	−	1.07249i	0.411603	−	0.0360106i	0.120526	−	0.992710i	$-0.461542\pi$
$887$	12.2586	−	1.07249i	0.411603	−	0.0360106i	0.291077	+	0.956700i	$0.405986\pi$
$888$	−1.94460	−	4.17021i	−0.0652566	−	0.139943i
$889$	8.55753	−	3.11468i	0.287010	−	0.104463i
$890$		0			0
$891$	−9.23473	−	52.3727i	−0.309375	−	1.75455i
$892$	14.7591	−	14.7591i	0.494173	−	0.494173i
$893$	20.7812	+	9.87733i	0.695417	+	0.330532i
$894$		−	29.0229i		−	0.970671i
$895$		0			0
$896$	−0.286989	−	0.342020i	−0.00958763	−	0.0114261i
$897$	2.13190	+	0.994120i	0.0711820	+	0.0331927i
$898$	10.1303	−	4.72384i	0.338053	−	0.157637i
$899$	8.67670	−	10.3405i	0.289384	−	0.344875i
$900$		0			0
$901$	4.80659	−	2.77509i	0.160131	−	0.0924515i
$902$	−2.02326	+	1.41670i	−0.0673671	+	0.0471710i
$903$	−7.46653	+	5.22812i	−0.248471	+	0.173981i
$904$	10.9324	−	6.31180i	0.363605	−	0.209927i
$905$		0			0
$906$	17.3466	−	20.6729i	0.576302	−	0.686809i
$907$	−35.6089	+	16.6047i	−1.18237	+	0.551350i	−0.911514	−	0.411269i	$-0.865086\pi$
$907$	−35.6089	+	16.6047i	−1.18237	+	0.551350i	−0.270859	+	0.962619i	$0.587308\pi$
$908$	7.48312	+	3.48944i	0.248336	+	0.115801i
$909$	−5.58726	−	6.65863i	−0.185318	−	0.220853i
$910$		0			0
$911$		−	57.2658i		−	1.89730i	−0.316327	−	0.948650i	$-0.602450\pi$
$911$		−	57.2658i		−	1.89730i	0.316327	−	0.948650i	$-0.397550\pi$
$912$	−8.60117	−	4.08815i	−0.284813	−	0.135372i
$913$	2.91995	−	2.91995i	0.0966364	−	0.0966364i
$914$	−0.511406	−	2.90033i	−0.0169158	−	0.0959344i
$915$		0			0
$916$	−5.93882	+	2.16155i	−0.196224	+	0.0714197i
$917$	0.874214	+	1.87476i	0.0288691	+	0.0619100i
$918$	1.82628	−	0.159779i	0.0602763	−	0.00527349i
$919$	−28.0448	−	16.1917i	−0.925112	−	0.534113i	−0.0398494	−	0.999206i	$-0.512688\pi$
$919$	−28.0448	−	16.1917i	−0.925112	−	0.534113i	−0.885262	+	0.465092i	$0.846021\pi$
$920$		0			0
$921$	0.211885	−	1.20166i	0.00698186	−	0.0395961i
$922$	−15.4351	−	22.0437i	−0.508329	−	0.725970i
$923$	−5.98899	−	1.60475i	−0.197130	−	0.0528209i
$924$	−2.32099	+	4.02007i	−0.0763549	+	0.132251i
$925$		0			0
$926$	5.09698	−	14.0038i	0.167497	−	0.460195i
$927$	−7.69564	+	16.5034i	−0.252758	+	0.542042i
$928$	0.448181	−	5.12273i	0.0147123	−	0.168162i
$929$	20.5209	−	3.61839i	0.673270	−	0.118716i	0.173447	−	0.984843i	$-0.444510\pi$
$929$	20.5209	−	3.61839i	0.673270	−	0.118716i	0.499823	+	0.866128i	$0.333398\pi$
$930$		0			0
$931$	25.5621	+	15.0103i	0.837765	+	0.491942i
$932$	−17.2180	−	17.2180i	−0.563994	−	0.563994i
$933$	38.6417	−	55.1860i	1.26507	−	1.80671i
$934$	−19.8674	+	16.6707i	−0.650081	+	0.545482i
$935$		0			0
$936$	−4.01842	−	1.46258i	−0.131346	−	0.0478061i
$937$	1.47832	+	16.8973i	0.0482946	+	0.552010i	0.981344	+	0.192261i	$0.0615821\pi$
$937$	1.47832	+	16.8973i	0.0482946	+	0.552010i	−0.933049	+	0.359749i	$0.882862\pi$
$938$	1.29821	+	4.84498i	0.0423880	+	0.158194i
$939$	−9.25265	−	16.0261i	−0.301949	−	0.522990i
$940$		0			0
$941$	1.19001	+	0.209830i	0.0387931	+	0.00684027i	0.193011	−	0.981197i	$-0.438175\pi$
$941$	1.19001	+	0.209830i	0.0387931	+	0.00684027i	−0.154218	+	0.988037i	$0.549286\pi$
$942$	9.48641	−	35.4038i	0.309084	−	1.15352i
$943$	−0.223838	+	0.0599772i	−0.00728916	+	0.00195313i
$944$	0.245188	+	0.205737i	0.00798019	+	0.00669617i
$945$		0			0
$946$	15.2087	+	41.7856i	0.494478	+	1.35857i
$947$	17.4178	+	1.52386i	0.566002	+	0.0495188i	0.366566	−	0.930392i	$-0.380533\pi$
$947$	17.4178	+	1.52386i	0.566002	+	0.0495188i	0.199436	+	0.979911i	$0.436089\pi$
$948$	28.7999	+	20.1659i	0.935378	+	0.654959i
$949$	10.4702			0.339876
$950$		0			0
$951$	54.1902			1.75724
$952$	−0.250175	−	0.175174i	−0.00810822	−	0.00567744i
$953$	19.1110	+	1.67199i	0.619065	+	0.0541612i	0.392374	−	0.919806i	$-0.371654\pi$
$953$	19.1110	+	1.67199i	0.619065	+	0.0541612i	0.226691	+	0.973967i	$0.427209\pi$
$954$	4.92111	+	13.5206i	0.159327	+	0.437747i
$955$		0			0
$956$	−20.9800	−	17.6043i	−0.678541	−	0.569364i
$957$	−51.6424	+	13.8375i	−1.66936	+	0.447304i
$958$	3.22247	−	12.0264i	0.104113	−	0.388556i
$959$	7.34603	+	1.29530i	0.237216	+	0.0418275i
$960$		0			0
$961$	−12.0547	−	20.8793i	−0.388861	−	0.673527i
$962$	−1.31447	−	4.90567i	−0.0423802	−	0.158165i
$963$	0.910936	+	10.4120i	0.0293545	+	0.335524i
$964$	−8.56077	−	3.11587i	−0.275724	−	0.100355i
$965$		0			0
$966$	−0.333626	+	0.279945i	−0.0107342	+	0.00900709i
$967$	28.5553	−	40.7812i	0.918276	−	1.31143i	−0.0318257	−	0.999493i	$-0.510132\pi$
$967$	28.5553	−	40.7812i	0.918276	−	1.31143i	0.950102	−	0.311941i	$-0.100979\pi$
$968$	8.23489	+	8.23489i	0.264679	+	0.264679i
$969$	−6.40685	−	1.17840i	−0.205818	−	0.0378555i
$970$		0			0
$971$	−39.6646	+	6.99394i	−1.27290	+	0.224446i	−0.768962	−	0.639295i	$-0.779226\pi$
$971$	−39.6646	+	6.99394i	−1.27290	+	0.224446i	−0.503936	+	0.863741i	$0.668115\pi$
$972$	−1.42723	+	16.3133i	−0.0457783	+	0.523248i
$973$	3.55442	−	7.62249i	0.113950	−	0.244366i
$974$	−9.25681	+	25.4329i	−0.296607	+	0.814922i
$975$		0			0
$976$	4.13563	−	7.16312i	0.132378	−	0.229286i
$977$	−56.1055	−	15.0334i	−1.79497	−	0.480962i	−0.801799	−	0.597593i	$-0.796124\pi$
$977$	−56.1055	−	15.0334i	−1.79497	−	0.480962i	−0.993175	+	0.116631i	$0.962790\pi$
$978$	30.2647	+	43.2224i	0.967757	+	1.38210i
$979$	13.7587	−	78.0292i	0.439729	−	2.49382i
$980$		0			0
$981$	11.8845	+	6.86154i	0.379444	+	0.219072i
$982$	−16.8306	+	1.47248i	−0.537085	+	0.0469889i
$983$	26.1102	+	55.9935i	0.832786	+	1.78592i	0.571378	+	0.820687i	$0.306409\pi$
$983$	26.1102	+	55.9935i	0.832786	+	1.78592i	0.261408	+	0.965228i	$0.415813\pi$
$984$	1.06559	−	0.387841i	0.0339696	−	0.0123639i
$985$		0			0
$986$	−0.610815	−	3.46410i	−0.0194523	−	0.110319i
$987$	−3.64096	+	3.64096i	−0.115893	+	0.115893i
$988$	−8.56579	−	6.09230i	−0.272514	−	0.193822i
$989$			4.17200i			0.132662i
$990$		0			0
$991$	10.8182	+	12.8926i	0.343651	+	0.409548i	0.909994	−	0.414622i	$-0.136086\pi$
$991$	10.8182	+	12.8926i	0.343651	+	0.409548i	−0.566342	+	0.824170i	$0.691642\pi$
$992$	2.37906	+	1.10937i	0.0755352	+	0.0352227i
$993$	34.0355	−	15.8710i	1.08008	−	0.503651i
$994$	0.737892	−	0.879385i	0.0234045	−	0.0278924i
$995$		0			0
$996$	−1.64186	+	0.947931i	−0.0520245	+	0.0300363i
$997$	23.5843	−	16.5139i	0.746922	−	0.523000i	−0.137037	−	0.990566i	$-0.543758\pi$
$997$	23.5843	−	16.5139i	0.746922	−	0.523000i	0.883958	+	0.467566i	$0.154869\pi$
$998$	19.2525	−	13.4808i	0.609428	−	0.426726i
$999$	−4.88815	+	2.82218i	−0.154654	+	0.0892897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.a.257.1	yes	24
5.2	odd	4	inner	950.2.bb.a.143.2	yes	24
5.3	odd	4	inner	950.2.bb.a.143.1	✓	24
5.4	even	2	inner	950.2.bb.a.257.2	yes	24
19.2	odd	18	inner	950.2.bb.a.857.1	yes	24
95.2	even	36	inner	950.2.bb.a.743.2	yes	24
95.59	odd	18	inner	950.2.bb.a.857.2	yes	24
95.78	even	36	inner	950.2.bb.a.743.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.a.143.1	✓	24	5.3	odd	4	inner
950.2.bb.a.143.2	yes	24	5.2	odd	4	inner
950.2.bb.a.257.1	yes	24	1.1	even	1	trivial
950.2.bb.a.257.2	yes	24	5.4	even	2	inner
950.2.bb.a.743.1	yes	24	95.78	even	36	inner
950.2.bb.a.743.2	yes	24	95.2	even	36	inner
950.2.bb.a.857.1	yes	24	19.2	odd	18	inner
950.2.bb.a.857.2	yes	24	95.59	odd	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-2.17648 - 0.190417i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.431262 + 0.115556i) q^{7} +(0.258819 - 0.965926i) q^{8} +(1.74638 + 0.307934i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-2.17648 - 0.190417i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.431262 + 0.115556i) q^{7} +(0.258819 - 0.965926i) q^{8} +(1.74638 + 0.307934i) q^{9} +(2.37939 + 4.12122i) q^{11} +(-0.565466 - 2.11035i) q^{12} +(-0.210174 - 2.40230i) q^{13} +(0.419550 + 0.152704i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.392349 + 0.560333i) q^{17} +(-1.25393 - 1.25393i) q^{18} +(-2.15160 - 3.79086i) q^{19} +(0.960637 - 0.169386i) q^{21} +(0.414754 - 4.74066i) q^{22} +(0.188689 - 0.404644i) q^{23} +(-0.747243 + 2.05303i) q^{24} +(-1.20574 + 2.08840i) q^{26} +(2.58872 + 0.693647i) q^{27} +(-0.256088 - 0.365731i) q^{28} +(0.892951 - 5.06418i) q^{29} +(2.27332 + 1.31250i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-4.39393 - 9.42282i) q^{33} +(0.642788 - 0.233956i) q^{34} +(0.307934 + 1.74638i) q^{36} +(-1.48921 + 1.48921i) q^{37} +(-0.411860 + 4.33940i) q^{38} +5.26857i q^{39} +(-0.333626 - 0.397600i) q^{41} +(-0.884064 - 0.412246i) q^{42} +(-8.46881 + 3.94907i) q^{43} +(-3.05888 + 3.64543i) q^{44} +(-0.386659 + 0.223238i) q^{46} +(-4.32402 + 3.02771i) q^{47} +(1.78968 - 1.25315i) q^{48} +(-5.88954 + 3.40033i) q^{49} +(0.960637 - 1.14484i) q^{51} +(2.18554 - 1.01913i) q^{52} +(-7.35361 - 3.42904i) q^{53} +(-1.72270 - 2.05303i) q^{54} +0.446476i q^{56} +(3.96107 + 8.66043i) q^{57} +(-3.63616 + 3.63616i) q^{58} +(-0.0555796 - 0.315207i) q^{59} +(-7.77244 + 2.82894i) q^{61} +(-1.10937 - 2.37906i) q^{62} +(-0.788731 + 0.0690050i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-1.80541 + 10.2390i) q^{66} +(6.44380 + 9.20270i) q^{67} +(-0.660732 - 0.177043i) q^{68} +(-0.487728 + 0.844770i) q^{69} +(0.879385 - 2.41609i) q^{71} +(0.749437 - 1.60717i) q^{72} +(-0.378413 + 4.32528i) q^{73} +(2.07407 - 0.365715i) q^{74} +(2.82635 - 3.31839i) q^{76} +(-1.50237 - 1.50237i) q^{77} +(3.02193 - 4.31576i) q^{78} +(-12.3274 + 10.3439i) q^{79} +(-10.5013 - 3.82218i) q^{81} +(0.0452364 + 0.517055i) q^{82} +(-0.224591 - 0.838185i) q^{83} +(0.487728 + 0.844770i) q^{84} +(9.20233 + 1.62262i) q^{86} +(-2.90780 + 10.8520i) q^{87} +(4.59662 - 1.23166i) q^{88} +(-12.7545 - 10.7023i) q^{89} +(0.368241 + 1.01173i) q^{91} +(0.444777 + 0.0389129i) q^{92} +(-4.69791 - 3.28951i) q^{93} +5.27866 q^{94} -2.18479 q^{96} +(-2.46380 - 1.72517i) q^{97} +(6.77478 + 0.592717i) q^{98} +(2.88624 + 7.92989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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