LMFDB - Embedded newform 950.2.bb.a.743.1

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			743.1
Character	$\chi$	$=$	950.743
Dual form			950.2.bb.a.257.1

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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	−0.695931	−	0.718109i	$-0.745008\pi$
$3$	−2.17648	+	0.190417i	−1.25659	+	0.109937i	−0.560660	+	0.828046i	$0.689452\pi$
$4$	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	0.176395	−	0.984319i	$-0.443556\pi$
$7$	−0.431262	−	0.115556i	−0.163002	−	0.0436762i	−0.339397	+	0.940643i	$0.610223\pi$
$8$	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	−0.244610	−	0.969621i	$-0.578660\pi$
$11$	2.37939	−	4.12122i	0.717412	−	1.24259i	0.962022	−	0.272972i	$-0.0880066\pi$
$12$	−0.565466	+	2.11035i	−0.163236	+	0.609205i
$13$	−0.210174	+	2.40230i	−0.0582917	+	0.666278i	0.909695	+	0.415277i	$0.136315\pi$
$13$	−0.210174	+	2.40230i	−0.0582917	+	0.666278i	−0.967987	+	0.251001i	$0.919240\pi$
$14$	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	0.768750	−	0.639550i	$-0.220879\pi$
$17$	−0.392349	−	0.560333i	−0.0951587	−	0.135901i	−0.863908	+	0.503649i	$0.831990\pi$
$18$	−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	0.924998	−	0.379973i	$-0.124067\pi$
$23$	0.188689	+	0.404644i	0.0393443	+	0.0843742i	−0.885653	+	0.464347i	$0.846289\pi$
$24$	−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	0.948218	+	0.317620i	$0.102884\pi$
$29$	0.892951	+	5.06418i	0.165817	+	0.940394i	−0.782401	+	0.622775i	$0.786005\pi$
$30$		0			0
$31$	2.27332	−	1.31250i	0.408300	−	0.235732i	−0.281759	−	0.959485i	$-0.590918\pi$
$31$	2.27332	−	1.31250i	0.408300	−	0.235732i	0.690059	+	0.723753i	$0.257585\pi$
$32$	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	0.574018	−	0.818843i	$-0.305384\pi$
$37$	−1.48921	−	1.48921i	−0.244825	−	0.244825i	−0.818843	+	0.574018i	$0.805384\pi$
$38$	−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	−0.791467	−	0.611212i	$-0.790682\pi$
$41$	−0.333626	+	0.397600i	−0.0521036	+	0.0620946i	0.739363	+	0.673307i	$0.235127\pi$
$42$	−0.884064	+	0.412246i	−0.136414	+	0.0636109i
$43$	−8.46881	−	3.94907i	−1.29148	−	0.602227i	−0.349199	−	0.937049i	$-0.613546\pi$
$43$	−8.46881	−	3.94907i	−1.29148	−	0.602227i	−0.942282	+	0.334821i	$0.891324\pi$
$44$	−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	0.214005	−	0.976833i	$-0.431349\pi$
$47$	−4.32402	−	3.02771i	−0.630724	−	0.441637i	−0.844728	+	0.535195i	$0.820238\pi$
$48$	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	−0.855964	−	0.517035i	$-0.827036\pi$
$53$	−7.35361	+	3.42904i	−1.01010	+	0.471015i	−0.154131	+	0.988050i	$0.549258\pi$
$54$	−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	−0.988212	−	0.153092i	$-0.951077\pi$
$59$	−0.0555796	+	0.315207i	−0.00723585	+	0.0410365i	0.980976	+	0.194129i	$0.0621880\pi$
$60$		0			0
$61$	−7.77244	−	2.82894i	−0.995159	−	0.362208i	−0.207443	−	0.978247i	$-0.566514\pi$
$61$	−7.77244	−	2.82894i	−0.995159	−	0.362208i	−0.787716	+	0.616039i	$0.788736\pi$
$62$	−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	−0.202204	−	0.979343i	$-0.564810\pi$
$67$	6.44380	−	9.20270i	0.787235	−	1.12429i	0.989440	−	0.144945i	$-0.0463006\pi$
$68$	−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	0.980873	−	0.194647i	$-0.0623563\pi$
$71$	0.879385	+	2.41609i	0.104364	+	0.286737i	−0.876509	+	0.481385i	$0.840134\pi$
$72$	0.749437	+	1.60717i	0.0883220	+	0.189407i
$73$	−0.378413	−	4.32528i	−0.0442899	−	0.506236i	−0.985646	−	0.168823i	$-0.946003\pi$
$73$	−0.378413	−	4.32528i	−0.0442899	−	0.506236i	0.941357	−	0.337414i	$-0.109552\pi$
$74$	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	−0.966563	−	0.256428i	$-0.917454\pi$
$79$	−12.3274	−	10.3439i	−1.38694	−	1.16378i	−0.420374	−	0.907351i	$-0.638101\pi$
$80$		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	−0.977156	−	0.212524i	$-0.931832\pi$
$83$	−0.224591	+	0.838185i	−0.0246521	+	0.0920028i	0.952504	+	0.304527i	$0.0984983\pi$
$84$	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	−0.373608	+	0.927587i	$0.621880\pi$
$89$	−12.7545	+	10.7023i	−1.35198	+	1.13445i	−0.978371	+	0.206858i	$0.933676\pi$
$90$		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	−0.691931	−	0.721964i	$-0.743240\pi$
$97$	−2.46380	+	1.72517i	−0.250161	+	0.175164i	0.441770	+	0.897128i	$0.354351\pi$
$98$	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	−0.810194	−	0.586162i	$-0.800638\pi$
$101$	−3.75490	+	3.15074i	−0.373627	+	0.313510i	0.436568	+	0.899671i	$0.356194\pi$
$102$	−1.44356	−	0.386801i	−0.142934	−	0.0382991i
$103$	−2.65770	−	9.91868i	−0.261871	−	0.977316i	−0.964138	−	0.265402i	$-0.914495\pi$
$103$	−2.65770	−	9.91868i	−0.261871	−	0.977316i	0.702267	−	0.711914i	$-0.252171\pi$
$104$	−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	−0.852161	−	0.523280i	$-0.824708\pi$
$107$	1.52546	−	5.69310i	0.147472	−	0.550373i	0.999633	−	0.0270932i	$-0.00862507\pi$
$108$	0.233581	−	2.66985i	0.0224764	−	0.256906i
$109$	7.27195	−	2.64677i	0.696527	−	0.253515i	0.0305995	−	0.999532i	$-0.490258\pi$
$109$	7.27195	−	2.64677i	0.696527	−	0.253515i	0.665927	+	0.746017i	$0.268036\pi$
$110$		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	−0.149111	−	0.988821i	$-0.547641\pi$
$113$	8.92624	−	8.92624i	0.839710	−	0.839710i	0.988821	+	0.149111i	$0.0476411\pi$
$114$	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	−0.864440	−	0.502735i	$-0.832327\pi$
$127$	−20.3193	−	1.77771i	−1.80305	−	0.157746i	−0.938607	+	0.344989i	$0.887883\pi$
$128$	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	0.929279	+	0.369377i	$0.120429\pi$
$131$	−0.804530	+	4.56272i	−0.0702921	+	0.398646i	−0.999572	+	0.0292689i	$0.990682\pi$
$132$	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	−0.942853	−	0.333208i	$-0.891869\pi$
$137$	−15.1418	+	7.06076i	−1.29366	+	0.603241i	−0.350802	+	0.936450i	$0.614091\pi$
$138$	0.884064	+	0.412246i	0.0752565	+	0.0350927i
$139$	−12.1085	−	14.4304i	−1.02703	−	1.22397i	−0.974276	−	0.225360i	$-0.927644\pi$
$139$	−12.1085	−	14.4304i	−1.02703	−	1.22397i	−0.0527547	−	0.998608i	$-0.516800\pi$
$140$		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	−0.992473	−	0.122465i	$-0.960920\pi$
$149$	−8.53882	+	10.1762i	−0.699528	+	0.833665i	0.292945	+	0.956129i	$0.405365\pi$
$150$		0			0
$151$			12.3520i			1.00519i	0.864522	+	0.502594i	$0.167621\pi$
$151$			12.3520i			1.00519i	−0.864522	+	0.502594i	$0.832379\pi$
$152$	−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	0.390340	+	0.920671i	$0.372358\pi$
$157$	−7.08996	+	15.2045i	−0.565841	+	1.21345i	−0.956180	+	0.292778i	$0.905420\pi$
$158$	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	0.829564	−	0.558412i	$-0.188589\pi$
$163$	23.3280	−	6.25073i	1.82719	−	0.489595i	0.997629	+	0.0688176i	$0.0219226\pi$
$164$	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	0.986293	+	0.165001i	$0.0527627\pi$
$167$	6.18635	+	13.2667i	0.478714	+	1.02661i	−0.507579	+	0.861605i	$0.669460\pi$
$168$	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	0.991604	−	0.129311i	$-0.0412766\pi$
$173$	6.98346	+	9.97342i	0.530943	+	0.758265i	−0.460661	+	0.887576i	$0.652388\pi$
$174$	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	−0.934644	−	0.355586i	$-0.884281\pi$
$179$	−2.13230	+	3.69325i	−0.159375	+	0.276046i	0.775268	+	0.631632i	$0.217615\pi$
$180$		0			0
$181$	−14.8871	+	2.62500i	−1.10655	+	0.195115i	−0.696929	−	0.717140i	$-0.745451\pi$
$181$	−14.8871	+	2.62500i	−1.10655	+	0.195115i	−0.409622	+	0.912255i	$0.634340\pi$
$182$	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	−0.474192	−	0.880422i	$-0.657260\pi$
$193$	−10.9514	+	0.958120i	−0.788296	+	0.0689670i	−0.314104	+	0.949388i	$0.601704\pi$
$194$	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	0.226967	−	0.973902i	$-0.427119\pi$
$197$	−0.890202	−	0.238529i	−0.0634243	−	0.0169945i	−0.290392	+	0.956908i	$0.593786\pi$
$198$	2.18413	+	8.15127i	0.155219	+	0.579286i
$199$	15.8807	−	2.80019i	1.12575	−	0.198500i	0.420387	−	0.907345i	$-0.361894\pi$
$199$	15.8807	−	2.80019i	1.12575	−	0.198500i	0.705365	+	0.708845i	$0.250783\pi$
$200$		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	0.349696	−	0.936863i	$-0.386285\pi$
$211$	5.19846	+	0.916629i	0.357877	+	0.0631034i	0.00818081	+	0.999967i	$0.497396\pi$
$212$	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	0.352886	+	0.935666i	$0.385200\pi$
$223$	−8.82113	+	18.9170i	−0.590707	+	1.26677i	−0.943593	+	0.331108i	$0.892577\pi$
$224$	−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	0.873797	−	0.486291i	$-0.161650\pi$
$227$	5.83838	+	5.83838i	0.387507	+	0.387507i	−0.486291	+	0.873797i	$0.661650\pi$
$228$	−6.78337	−	6.68423i	−0.449240	−	0.442674i
$229$		−	6.31996i		−	0.417634i	−0.977955	−	0.208817i	$-0.933039\pi$
$229$		−	6.31996i		−	0.417634i	0.977955	−	0.208817i	$-0.0669614\pi$
$230$		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	−0.467965	−	0.883747i	$-0.655013\pi$
$233$	−22.0685	−	10.2907i	−1.44576	−	0.674168i	−0.977792	+	0.209579i	$0.932791\pi$
$234$	−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	−0.999161	−	0.0409475i	$-0.986962\pi$
$239$	−23.7182	−	13.6937i	−1.53420	−	0.885773i	−0.535042	−	0.844825i	$-0.679704\pi$
$240$		0			0
$241$	−5.85591	−	6.97881i	−0.377213	−	0.449544i	0.543720	−	0.839267i	$-0.317015\pi$
$241$	−5.85591	−	6.97881i	−0.377213	−	0.449544i	−0.920932	+	0.389722i	$0.872571\pi$
$242$	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	0.708158	−	0.706054i	$-0.249527\pi$
$251$	12.6236	+	4.59462i	0.796795	+	0.290010i	0.0886373	+	0.996064i	$0.471749\pi$
$252$	−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	−0.403977	−	0.914769i	$-0.632372\pi$
$257$	9.51923	−	13.5949i	0.593793	−	0.848024i	0.997770	+	0.0667447i	$0.0212613\pi$
$258$	−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	−0.625718	−	0.780049i	$-0.715194\pi$
$263$	−2.35086	−	26.8704i	−0.144960	−	1.65690i	0.480758	−	0.876853i	$-0.340362\pi$
$264$	−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	0.994114	+	0.108336i	$0.0345523\pi$
$269$	20.8858	+	17.5253i	1.27343	+	1.06854i	0.279316	+	0.960199i	$0.409892\pi$
$270$		0			0
$271$	−23.8862	+	8.69388i	−1.45099	+	0.528116i	−0.942867	−	0.333171i	$-0.891881\pi$
$271$	−23.8862	+	8.69388i	−1.45099	+	0.528116i	−0.508120	+	0.861286i	$0.669659\pi$
$272$	−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	0.996190	+	0.0872119i	$0.0277957\pi$
$277$	2.94703	+	10.9985i	0.177070	+	0.660835i	−0.819120	+	0.573623i	$0.805538\pi$
$278$	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	−0.951452	−	0.307797i	$-0.900408\pi$
$281$	−0.414878	+	1.13987i	−0.0247495	+	0.0679988i	0.926703	+	0.375796i	$0.122631\pi$
$282$	−11.4889	+	1.00515i	−0.684153	+	0.0598557i
$283$	−13.7452	+	9.62446i	−0.817065	+	0.572115i	−0.905685	−	0.423951i	$-0.860643\pi$
$283$	−13.7452	+	9.62446i	−0.817065	+	0.572115i	0.0886206	+	0.996065i	$0.471754\pi$
$284$	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	0.998808	+	0.0488029i	$0.0155406\pi$
$293$	2.70823	+	10.1072i	0.158216	+	0.590472i	−0.840592	+	0.541669i	$0.817793\pi$
$294$	−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	0.994679	−	0.103022i	$-0.0328511\pi$
$307$	−0.0486762	−	0.556371i	−0.00277810	−	0.0317538i	−0.997457	+	0.0712678i	$0.977296\pi$
$308$	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	−0.857541	−	0.514415i	$-0.828009\pi$
$311$	−15.4179	−	26.7045i	−0.874267	−	1.51428i	−0.0167260	−	0.999860i	$-0.505324\pi$
$312$	5.08905	−	1.36361i	0.288111	−	0.0771990i
$313$	4.85822	−	6.93826i	0.274603	−	0.392173i	−0.658035	−	0.752987i	$-0.728612\pi$
$313$	4.85822	−	6.93826i	0.274603	−	0.392173i	0.932638	+	0.360814i	$0.117501\pi$
$314$	−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	−0.631362	−	0.775489i	$-0.717504\pi$
$317$	−24.7090	−	2.16175i	−1.38779	−	0.121416i	−0.756432	+	0.654072i	$0.773059\pi$
$318$	−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	0.0315918	−	0.999501i	$-0.489942\pi$
$331$	−14.8859	−	8.59440i	−0.818205	−	0.472391i	−0.849797	+	0.527110i	$0.823276\pi$
$332$	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	0.740838	−	0.671684i	$-0.234429\pi$
$337$	12.8962	+	6.01359i	0.702500	+	0.327581i	−0.0383379	+	0.999265i	$0.512206\pi$
$338$	−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	−0.566352	−	0.824164i	$-0.691646\pi$
$347$	7.99209	−	17.1391i	0.429038	−	0.920075i	0.995390	−	0.0959116i	$-0.0305766\pi$
$348$	−11.1921	−	0.979183i	−0.599960	−	0.0524897i
$349$	17.1013	−	9.87346i	0.915413	−	0.528514i	0.0332442	−	0.999447i	$-0.489416\pi$
$349$	17.1013	−	9.87346i	0.915413	−	0.528514i	0.882169	+	0.470933i	$0.156083\pi$
$350$		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	−0.0683195	−	0.997663i	$-0.521764\pi$
$353$	6.97696	−	1.86947i	0.371346	−	0.0995018i	0.439665	+	0.898162i	$0.355097\pi$
$354$	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	−0.261525	−	0.965197i	$-0.584225\pi$
$359$	−15.8664	−	2.79767i	−0.837394	−	0.147655i	−0.575870	+	0.817542i	$0.695336\pi$
$360$		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	0.944905	+	0.327345i	$0.106154\pi$
$367$	−0.813947	+	9.30346i	−0.0424877	+	0.485637i	−0.987392	+	0.158291i	$0.949401\pi$
$368$	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	0.295023	−	0.955490i	$-0.404673\pi$
$373$	1.40554	+	0.376612i	0.0727759	+	0.0195002i	−0.222247	+	0.974990i	$0.571339\pi$
$374$	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	0.0823521	−	0.996603i	$-0.473757\pi$
$383$	6.58566	−	0.576170i	0.336511	−	0.0294409i	0.254159	+	0.967162i	$0.418201\pi$
$384$	−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	−0.0730863	−	0.997326i	$-0.523285\pi$
$389$	3.93161	−	0.693249i	0.199340	−	0.0351491i	0.272427	+	0.962177i	$0.412174\pi$
$390$		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	0.863394	−	0.504529i	$-0.168334\pi$
$397$	1.87281	+	2.67465i	0.0939936	+	0.134237i	−0.769401	+	0.638766i	$0.779445\pi$
$398$	−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	0.922452	−	0.386111i	$-0.126182\pi$
$401$	33.1857	+	5.85154i	1.65722	+	0.292212i	0.734764	+	0.678323i	$0.237293\pi$
$402$	−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	0.947915	−	0.318524i	$-0.103187\pi$
$409$	−1.04709	−	5.93835i	−0.0517753	−	0.293632i	−0.999690	+	0.0248914i	$0.992076\pi$
$410$		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	$0.271346\pi$
$419$			30.8229i			1.50580i	−0.658135	+	0.752900i	$0.728654\pi$
$420$		0			0
$421$	20.6284	−	24.5839i	1.00536	−	1.19815i	0.0252567	−	0.999681i	$-0.491960\pi$
$421$	20.6284	−	24.5839i	1.00536	−	1.19815i	0.980108	−	0.198466i	$-0.0635959\pi$
$422$	−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	−0.870461	−	0.492237i	$-0.836179\pi$
$431$	−24.9971	−	29.7903i	−1.20407	−	1.43495i	−0.333605	−	0.942713i	$-0.608265\pi$
$432$	−2.42895	−	1.13264i	−0.116863	−	0.0544940i
$433$	−25.2504	+	11.7744i	−1.21346	+	0.565844i	−0.920673	−	0.390335i	$-0.872359\pi$
$433$	−25.2504	+	11.7744i	−1.21346	+	0.565844i	−0.292783	+	0.956179i	$0.594581\pi$
$434$	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	−0.609353	−	0.792899i	$-0.708571\pi$
$439$	4.91204	−	27.8576i	0.234439	−	1.32957i	0.843792	−	0.536670i	$-0.180318\pi$
$440$		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	0.708782	−	0.705428i	$-0.249245\pi$
$443$	27.0314	+	2.36494i	1.28430	+	0.112362i	0.575518	+	0.817789i	$0.304801\pi$
$444$	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	0.703485	−	0.710710i	$-0.251626\pi$
$449$	−5.58878	−	9.68004i	−0.263751	−	0.456830i	−0.967236	+	0.253881i	$0.918293\pi$
$450$		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	−0.656720	−	0.754134i	$-0.728057\pi$
$457$	2.08248	−	2.08248i	0.0974143	−	0.0974143i	0.754134	+	0.656720i	$0.228057\pi$
$458$	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	0.322346	−	0.946622i	$-0.395529\pi$
$461$	25.2875	−	9.20388i	1.17775	−	0.428667i	0.855408	+	0.517954i	$0.173306\pi$
$462$	−0.404575	+	4.62431i	−0.0188225	+	0.215142i
$463$	3.85707	−	14.3948i	0.179253	−	0.668982i	−0.816535	−	0.577296i	$-0.804108\pi$
$463$	3.85707	−	14.3948i	0.179253	−	0.668982i	0.995788	−	0.0916860i	$-0.0292256\pi$
$464$	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	0.928002	+	0.372576i	$0.121525\pi$
$467$	6.71248	+	25.0513i	0.310616	+	1.15924i	−0.617385	+	0.786661i	$0.711808\pi$
$468$	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	−0.803592	−	0.595181i	$-0.797080\pi$
$479$	4.25838	−	11.6998i	0.194570	−	0.534578i	0.998162	+	0.0606034i	$0.0193025\pi$
$480$		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	0.604285	+	0.796768i	$0.293459\pi$
$487$	−7.00497	+	26.1429i	−0.317425	+	1.18465i	−0.921710	+	0.387879i	$0.873208\pi$
$488$	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	0.886282	−	0.463146i	$-0.153279\pi$
$491$	12.9422	+	10.8598i	0.584074	+	0.490096i	−0.302208	+	0.953242i	$0.597724\pi$
$492$	−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	−0.979080	−	0.203475i	$-0.934776\pi$
$499$	−8.03850	−	22.0856i	−0.359853	−	0.988687i	0.619228	−	0.785212i	$-0.287446\pi$
$500$		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	−0.903614	−	0.428348i	$-0.859096\pi$
$503$	−4.30710	+	6.15117i	−0.192044	+	0.274267i	0.711570	+	0.702615i	$0.247985\pi$
$504$	−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	0.925989	−	0.377551i	$-0.123234\pi$
$509$	31.4197	+	11.4358i	1.39265	+	0.506884i	0.466663	+	0.884435i	$0.345456\pi$
$510$		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	0.311438	−	0.950267i	$-0.399189\pi$
$521$	−8.12124	−	4.68880i	−0.355798	−	0.205420i	−0.667236	+	0.744846i	$0.732523\pi$
$522$	−7.46980	−	5.23041i	−0.326944	−	0.228929i
$523$	26.7770	+	18.7495i	1.17088	+	0.819857i	0.986623	−	0.163021i	$-0.0521238\pi$
$523$	26.7770	+	18.7495i	1.17088	+	0.819857i	0.184255	+	0.982878i	$0.441013\pi$
$524$	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	0.999813	−	0.0193519i	$-0.00616028\pi$
$541$	1.24850	+	7.08062i	0.0536774	+	0.304419i	−0.946135	+	0.323771i	$0.895049\pi$
$542$	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	0.909542	−	0.415613i	$-0.136433\pi$
$547$	0.152527	+	0.327096i	0.00652160	+	0.0139856i	−0.903020	+	0.429598i	$0.858655\pi$
$548$	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	−0.999933	−	0.0115618i	$-0.996320\pi$
$557$	−0.311143	+	3.55638i	−0.0131836	+	0.150689i	0.986750	+	0.162250i	$0.0518753\pi$
$558$	−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	−0.402193	−	0.915555i	$-0.631752\pi$
$563$	−28.6696	−	7.68200i	−1.20828	−	0.323758i	−0.806087	+	0.591797i	$0.798419\pi$
$564$	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	0.205273	−	0.978705i	$-0.434192\pi$
$577$	−2.55362	−	0.684241i	−0.106309	−	0.0284853i	−0.311581	+	0.950220i	$0.600859\pi$
$578$	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	0.993773	+	0.111419i	$0.0355397\pi$
$587$	18.3790	+	26.2479i	0.758583	+	1.08337i	−0.235190	+	0.971949i	$0.575571\pi$
$588$	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	−0.741249	−	0.671230i	$-0.765766\pi$
$593$	−18.9693	−	40.6798i	−0.778976	−	1.67052i	−0.0377267	−	0.999288i	$-0.512012\pi$
$594$	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	0.965894	+	0.258937i	$0.0833723\pi$
$599$	3.59315	+	20.3778i	0.146812	+	0.832614i	−0.819082	+	0.573677i	$0.805517\pi$
$600$		0			0
$601$	−23.1668	+	13.3754i	−0.944995	+	0.545593i	−0.891523	−	0.452976i	$-0.850362\pi$
$601$	−23.1668	+	13.3754i	−0.944995	+	0.545593i	−0.0534725	+	0.998569i	$0.517029\pi$
$602$	−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	0.686636	−	0.727001i	$-0.259087\pi$
$607$	−0.994490	−	0.994490i	−0.0403651	−	0.0403651i	−0.727001	+	0.686636i	$0.759087\pi$
$608$	−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	0.380346	−	0.924844i	$-0.375805\pi$
$613$	−2.07094	−	0.965695i	−0.0836445	−	0.0390041i	−0.463990	+	0.885840i	$0.653583\pi$
$614$	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	0.891781	−	0.452467i	$-0.149456\pi$
$617$	19.1664	+	13.4204i	0.771609	+	0.540287i	−0.120172	+	0.992753i	$0.538345\pi$
$618$	−18.3774	−	12.8680i	−0.739249	−	0.517627i
$619$	−13.6987	−	7.90895i	−0.550597	−	0.317887i	0.198766	−	0.980047i	$-0.436307\pi$
$619$	−13.6987	−	7.90895i	−0.550597	−	0.317887i	−0.749363	+	0.662160i	$0.769640\pi$
$620$		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	0.0692459	−	0.997600i	$-0.477941\pi$
$631$	−13.0360	−	4.74470i	−0.518953	−	0.188884i	−0.588199	+	0.808716i	$0.700163\pi$
$632$	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	0.852998	+	0.521915i	$0.174782\pi$
$641$	13.5462	+	37.2180i	0.535044	+	1.47002i	−0.317954	+	0.948106i	$0.602996\pi$
$642$	−5.44206	−	11.6705i	−0.214781	−	0.460600i
$643$	3.16104	+	36.1308i	0.124659	+	1.42486i	0.758639	+	0.651511i	$0.225864\pi$
$643$	3.16104	+	36.1308i	0.124659	+	1.42486i	−0.633980	+	0.773349i	$0.718580\pi$
$644$	−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	−0.0834422	−	0.996513i	$-0.526591\pi$
$647$	23.2250	−	23.2250i	0.913070	−	0.913070i	0.996513	+	0.0834422i	$0.0265914\pi$
$648$	−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	−0.771117	−	0.636693i	$-0.780302\pi$
$653$	5.49501	−	20.5077i	0.215036	−	0.802527i	0.986154	−	0.165834i	$-0.0530314\pi$
$654$	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	−0.722743	−	0.691117i	$-0.757119\pi$
$659$	−4.30320	+	3.61081i	−0.167629	+	0.140657i	0.555114	+	0.831774i	$0.312675\pi$
$660$		0			0
$661$	7.87867	−	21.6465i	0.306445	−	0.841950i	−0.686898	−	0.726754i	$-0.741028\pi$
$661$	7.87867	−	21.6465i	0.306445	−	0.841950i	0.993343	−	0.115196i	$-0.0367497\pi$
$662$	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	−0.956310	−	0.292355i	$-0.905561\pi$
$673$	−7.11592	−	26.5570i	−0.274299	−	1.02370i	0.682011	−	0.731342i	$-0.261106\pi$
$674$	−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	−0.983874	−	0.178861i	$-0.942759\pi$
$677$	−1.10278	+	4.11565i	−0.0423834	+	0.158177i	0.941491	+	0.337039i	$0.109425\pi$
$678$	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	−0.999536	−	0.0304450i	$-0.990308\pi$
$683$	−25.3265	+	25.3265i	−0.969091	+	0.969091i	0.0304450	+	0.999536i	$0.490308\pi$
$684$	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	0.912008	−	0.410173i	$-0.134532\pi$
$691$	2.64930	+	4.58872i	0.100784	+	0.174563i	−0.811224	+	0.584736i	$0.801198\pi$
$692$	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	0.717535	+	0.696522i	$0.245270\pi$
$701$	−5.16163	+	29.2730i	−0.194952	+	1.10563i	−0.912487	+	0.409105i	$0.865841\pi$
$702$	−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	0.884643	−	0.466269i	$-0.154402\pi$
$709$	7.23832	+	8.62630i	0.271841	+	0.323967i	−0.612802	+	0.790236i	$0.709958\pi$
$710$		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	−0.599188	−	0.800608i	$-0.704510\pi$
$719$	7.86474	−	9.37283i	0.293305	−	0.349547i	0.892493	+	0.451061i	$0.148954\pi$
$720$		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	−0.946916	−	0.321481i	$-0.895819\pi$
$727$	−2.48009	+	5.31858i	−0.0919816	+	0.197255i	0.854935	+	0.518736i	$0.173597\pi$
$728$	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	−0.274692	−	0.961532i	$-0.588576\pi$
$733$	−0.861365	+	0.230802i	−0.0318153	+	0.00852487i	0.242876	+	0.970057i	$0.421909\pi$
$734$	−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	−0.281873	−	0.959452i	$-0.590956\pi$
$739$	−23.7837	−	4.19372i	−0.874899	−	0.154268i	−0.593026	+	0.805183i	$0.702067\pi$
$740$		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	0.682259	−	0.731111i	$-0.260998\pi$
$743$	−6.49031	−	9.26912i	−0.238106	−	0.340051i	−0.920365	+	0.391059i	$0.872109\pi$
$744$	−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	−0.207358	−	0.978265i	$-0.566487\pi$
$751$	−1.85323	+	0.326774i	−0.0676252	+	0.0119241i	0.139733	+	0.990189i	$0.455376\pi$
$752$	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	−0.999365	−	0.0356365i	$-0.988654\pi$
$757$	−54.4043	+	4.75976i	−1.97736	+	0.172996i	−0.977994	+	0.208633i	$0.933099\pi$
$758$	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	0.816619	−	0.577177i	$-0.195846\pi$
$769$	49.3996	−	8.71048i	1.78140	−	0.314108i	0.964777	+	0.263069i	$0.0847348\pi$
$770$		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	0.680599	+	0.732656i	$0.261719\pi$
$773$	−3.24973	+	37.1445i	−0.116884	+	1.33600i	−0.797484	+	0.603340i	$0.793836\pi$
$774$	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	0.260986	−	0.965343i	$-0.415952\pi$
$787$	27.2029	−	7.28899i	0.969678	−	0.259825i	0.708692	+	0.705518i	$0.249286\pi$
$788$	−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	0.999431	−	0.0337356i	$-0.0107404\pi$
$797$	27.2627	+	27.2627i	0.965695	+	0.965695i	−0.0337356	+	0.999431i	$0.510740\pi$
$798$	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	0.700142	−	0.714004i	$-0.253120\pi$
$809$	12.2836	+	7.09193i	0.431868	+	0.249339i	−0.268274	+	0.963343i	$0.586453\pi$
$810$		0			0
$811$	28.4183	+	33.8677i	0.997903	+	1.18925i	0.981903	+	0.189382i	$0.0606485\pi$
$811$	28.4183	+	33.8677i	0.997903	+	1.18925i	0.0159994	+	0.999872i	$0.494907\pi$
$812$	−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	0.396596	−	0.917993i	$-0.370191\pi$
$821$	3.16132	+	1.15063i	0.110331	+	0.0401572i	−0.286265	+	0.958151i	$0.592414\pi$
$822$	−15.4263	+	33.0818i	−0.538054	+	1.15386i
$823$	−12.4629	−	1.09036i	−0.434429	−	0.0380076i	−0.132156	−	0.991229i	$-0.542190\pi$
$823$	−12.4629	−	1.09036i	−0.434429	−	0.0380076i	−0.302273	+	0.953221i	$0.597745\pi$
$824$	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	−0.644471	−	0.764629i	$-0.722922\pi$
$827$	8.46818	−	12.0938i	0.294468	−	0.420543i	0.938938	+	0.344086i	$0.111811\pi$
$828$	0.764765	−	0.204918i	0.0265774	−	0.00712140i
$829$	−9.45485	−	16.3763i	−0.328381	−	0.568772i	0.653810	−	0.756659i	$-0.273170\pi$
$829$	−9.45485	−	16.3763i	−0.328381	−	0.568772i	−0.982191	+	0.187887i	$0.939836\pi$
$830$		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	0.962383	−	0.271696i	$-0.0875844\pi$
$839$	24.9663	+	20.9492i	0.861931	+	0.723246i	−0.100452	+	0.994942i	$0.532029\pi$
$840$		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	−0.153351	−	0.988172i	$-0.549007\pi$
$853$	21.1096	−	14.7811i	0.722778	−	0.506094i	0.876129	+	0.482078i	$0.160118\pi$
$854$	−3.69292			−0.126369
$855$		0			0
$856$	5.89393			0.201450
$857$	32.8873	−	23.0279i	1.12341	−	0.786619i	0.144214	−	0.989546i	$-0.453935\pi$
$857$	32.8873	−	23.0279i	1.12341	−	0.786619i	0.979194	+	0.202928i	$0.0650456\pi$
$858$	24.9765	−	2.18516i	0.852684	−	0.0746002i
$859$	10.3209	−	28.3564i	0.352144	−	0.967507i	−0.629536	−	0.776971i	$-0.716755\pi$
$859$	10.3209	−	28.3564i	0.352144	−	0.967507i	0.981680	−	0.190536i	$-0.0610227\pi$
$860$		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	0.886767	−	0.462217i	$-0.152946\pi$
$863$	−3.29914	−	12.3126i	−0.112304	−	0.419125i	−0.999071	+	0.0430920i	$0.986279\pi$
$864$	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	0.939634	+	0.342180i	$0.111165\pi$
$877$	2.18239	+	24.9448i	0.0736941	+	0.842328i	−0.865940	+	0.500148i	$0.833279\pi$
$878$	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	0.643759	−	0.765229i	$-0.277374\pi$
$881$	−10.1163	−	17.5220i	−0.340828	−	0.590331i	−0.984587	+	0.174897i	$0.944041\pi$
$882$	11.6488	−	3.12129i	0.392236	−	0.105099i
$883$	17.3181	−	24.7328i	0.582799	−	0.832324i	−0.414164	−	0.910202i	$-0.635926\pi$
$883$	17.3181	−	24.7328i	0.582799	−	0.832324i	0.996963	+	0.0778789i	$0.0248147\pi$
$884$	−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	0.291077	−	0.956700i	$-0.405986\pi$
$887$	12.2586	+	1.07249i	0.411603	+	0.0360106i	0.120526	+	0.992710i	$0.461542\pi$
$888$	−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	−0.270859	−	0.962619i	$-0.587308\pi$
$907$	−35.6089	−	16.6047i	−1.18237	−	0.551350i	−0.911514	+	0.411269i	$0.865086\pi$
$908$	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	$0.397550\pi$
$911$			57.2658i			1.89730i	−0.316327	+	0.948650i	$0.602450\pi$
$912$	−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	−0.885262	−	0.465092i	$-0.846021\pi$
$919$	−28.0448	+	16.1917i	−0.925112	+	0.534113i	−0.0398494	+	0.999206i	$0.512688\pi$
$920$		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	0.499823	−	0.866128i	$-0.333398\pi$
$929$	20.5209	+	3.61839i	0.673270	+	0.118716i	0.173447	+	0.984843i	$0.444510\pi$
$930$		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	−0.933049	−	0.359749i	$-0.882862\pi$
$937$	1.47832	−	16.8973i	0.0482946	−	0.552010i	0.981344	−	0.192261i	$-0.0615821\pi$
$938$	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	−0.154218	−	0.988037i	$-0.549286\pi$
$941$	1.19001	−	0.209830i	0.0387931	−	0.00684027i	0.193011	+	0.981197i	$0.438175\pi$
$942$	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	0.199436	−	0.979911i	$-0.436089\pi$
$947$	17.4178	−	1.52386i	0.566002	−	0.0495188i	0.366566	+	0.930392i	$0.380533\pi$
$948$	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	0.226691	−	0.973967i	$-0.427209\pi$
$953$	19.1110	−	1.67199i	0.619065	−	0.0541612i	0.392374	+	0.919806i	$0.371654\pi$
$954$	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	0.950102	+	0.311941i	$0.100979\pi$
$967$	28.5553	+	40.7812i	0.918276	+	1.31143i	−0.0318257	+	0.999493i	$0.510132\pi$
$968$	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	−0.503936	−	0.863741i	$-0.668115\pi$
$971$	−39.6646	−	6.99394i	−1.27290	−	0.224446i	−0.768962	+	0.639295i	$0.779226\pi$
$972$	−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	−0.993175	−	0.116631i	$-0.962790\pi$
$977$	−56.1055	+	15.0334i	−1.79497	+	0.480962i	−0.801799	+	0.597593i	$0.796124\pi$
$978$	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	0.261408	−	0.965228i	$-0.415813\pi$
$983$	26.1102	−	55.9935i	0.832786	−	1.78592i	0.571378	−	0.820687i	$-0.306409\pi$
$984$	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	−0.566342	−	0.824170i	$-0.691642\pi$
$991$	10.8182	−	12.8926i	0.343651	−	0.409548i	0.909994	+	0.414622i	$0.136086\pi$
$992$	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	0.883958	−	0.467566i	$-0.154869\pi$
$997$	23.5843	+	16.5139i	0.746922	+	0.523000i	−0.137037	+	0.990566i	$0.543758\pi$
$998$	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.743.1	yes	24
5.2	odd	4	inner	950.2.bb.a.857.1	yes	24
5.3	odd	4	inner	950.2.bb.a.857.2	yes	24
5.4	even	2	inner	950.2.bb.a.743.2	yes	24
19.10	odd	18	inner	950.2.bb.a.143.1	✓	24
95.29	odd	18	inner	950.2.bb.a.143.2	yes	24
95.48	even	36	inner	950.2.bb.a.257.2	yes	24
95.67	even	36	inner	950.2.bb.a.257.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.a.143.1	✓	24	19.10	odd	18	inner
950.2.bb.a.143.2	yes	24	95.29	odd	18	inner
950.2.bb.a.257.1	yes	24	95.67	even	36	inner
950.2.bb.a.257.2	yes	24	95.48	even	36	inner
950.2.bb.a.743.1	yes	24	1.1	even	1	trivial
950.2.bb.a.743.2	yes	24	5.4	even	2	inner
950.2.bb.a.857.1	yes	24	5.2	odd	4	inner
950.2.bb.a.857.2	yes	24	5.3	odd	4	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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