LMFDB - Embedded newform 950.2.bb.a.143.2

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			143.2
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.a.857.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(-0.190417 + 2.17648i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.115556 - 0.431262i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.74638 - 0.307934i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(-0.190417 + 2.17648i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.67365 + 1.40436i) q^{6} +(-0.115556 - 0.431262i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.74638 - 0.307934i) q^{9} +(2.37939 + 4.12122i) q^{11} +(2.11035 - 0.565466i) q^{12} +(-2.40230 + 0.210174i) q^{13} +(-0.419550 - 0.152704i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.560333 - 0.392349i) q^{17} +(-1.25393 + 1.25393i) q^{18} +(2.15160 + 3.79086i) q^{19} +(0.960637 - 0.169386i) q^{21} +(4.74066 + 0.414754i) q^{22} +(-0.404644 - 0.188689i) q^{23} +(0.747243 - 2.05303i) q^{24} +(-1.20574 + 2.08840i) q^{26} +(-0.693647 + 2.58872i) q^{27} +(-0.365731 + 0.256088i) q^{28} +(-0.892951 + 5.06418i) q^{29} +(2.27332 + 1.31250i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-9.42282 + 4.39393i) q^{33} +(-0.642788 + 0.233956i) q^{34} +(0.307934 + 1.74638i) q^{36} +(-1.48921 - 1.48921i) q^{37} +(4.33940 + 0.411860i) q^{38} -5.26857i q^{39} +(-0.333626 - 0.397600i) q^{41} +(0.412246 - 0.884064i) q^{42} +(3.94907 + 8.46881i) q^{43} +(3.05888 - 3.64543i) q^{44} +(-0.386659 + 0.223238i) q^{46} +(-3.02771 - 4.32402i) q^{47} +(-1.25315 - 1.78968i) q^{48} +(5.88954 - 3.40033i) q^{49} +(0.960637 - 1.14484i) q^{51} +(1.01913 + 2.18554i) q^{52} +(-3.42904 + 7.35361i) q^{53} +(1.72270 + 2.05303i) q^{54} +0.446476i q^{56} +(-8.66043 + 3.96107i) q^{57} +(3.63616 + 3.63616i) q^{58} +(0.0555796 + 0.315207i) q^{59} +(-7.77244 + 2.82894i) q^{61} +(2.37906 - 1.10937i) q^{62} +(0.0690050 + 0.788731i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.80541 + 10.2390i) q^{66} +(-9.20270 + 6.44380i) q^{67} +(-0.177043 + 0.660732i) q^{68} +(0.487728 - 0.844770i) q^{69} +(0.879385 - 2.41609i) q^{71} +(1.60717 + 0.749437i) q^{72} +(4.32528 + 0.378413i) q^{73} +(-2.07407 + 0.365715i) q^{74} +(2.82635 - 3.31839i) q^{76} +(1.50237 - 1.50237i) q^{77} +(-4.31576 - 3.02193i) q^{78} +(12.3274 - 10.3439i) q^{79} +(-10.5013 - 3.82218i) q^{81} +(-0.517055 + 0.0452364i) q^{82} +(-0.838185 + 0.224591i) q^{83} +(-0.487728 - 0.844770i) q^{84} +(9.20233 + 1.62262i) q^{86} +(-10.8520 - 2.90780i) q^{87} +(-1.23166 - 4.59662i) q^{88} +(12.7545 + 10.7023i) q^{89} +(0.368241 + 1.01173i) q^{91} +(-0.0389129 + 0.444777i) q^{92} +(-3.28951 + 4.69791i) q^{93} -5.27866 q^{94} -2.18479 q^{96} +(1.72517 - 2.46380i) q^{97} +(0.592717 - 6.77478i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	−0.190417	+	2.17648i	−0.109937	+	1.25659i	0.718109	+	0.695931i	$0.245008\pi$
$3$	−0.190417	+	2.17648i	−0.109937	+	1.25659i	−0.828046	+	0.560660i	$0.810548\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	1.67365	+	1.40436i	0.683264	+	0.573327i
$7$	−0.115556	−	0.431262i	−0.0436762	−	0.163002i	0.940643	−	0.339397i	$-0.110223\pi$
$7$	−0.115556	−	0.431262i	−0.0436762	−	0.163002i	−0.984319	+	0.176395i	$0.943556\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−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	$0.578660\pi$
$12$	2.11035	−	0.565466i	0.609205	−	0.163236i
$13$	−2.40230	+	0.210174i	−0.666278	+	0.0582917i	−0.415277	−	0.909695i	$-0.636315\pi$
$13$	−2.40230	+	0.210174i	−0.666278	+	0.0582917i	−0.251001	+	0.967987i	$0.580760\pi$
$14$	−0.419550	−	0.152704i	−0.112129	−	0.0408118i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.560333	−	0.392349i	−0.135901	−	0.0951587i	0.503649	−	0.863908i	$-0.331990\pi$
$17$	−0.560333	−	0.392349i	−0.135901	−	0.0951587i	−0.639550	+	0.768750i	$0.720879\pi$
$18$	−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
$22$	4.74066	+	0.414754i	1.01071	+	0.0884259i
$23$	−0.404644	−	0.188689i	−0.0843742	−	0.0393443i	0.379973	−	0.924998i	$-0.375933\pi$
$23$	−0.404644	−	0.188689i	−0.0843742	−	0.0393443i	−0.464347	+	0.885653i	$0.653711\pi$
$24$	0.747243	−	2.05303i	0.152530	−	0.419074i
$25$		0			0
$26$	−1.20574	+	2.08840i	−0.236464	+	0.409569i
$27$	−0.693647	+	2.58872i	−0.133492	+	0.498200i
$28$	−0.365731	+	0.256088i	−0.0691167	+	0.0483961i
$29$	−0.892951	+	5.06418i	−0.165817	+	0.940394i	0.782401	+	0.622775i	$0.213995\pi$
$29$	−0.892951	+	5.06418i	−0.165817	+	0.940394i	−0.948218	+	0.317620i	$0.897116\pi$
$30$		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	$0.590918\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	−9.42282	+	4.39393i	−1.64030	+	0.764885i
$34$	−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	$0.805384\pi$
$38$	4.33940	+	0.411860i	0.703943	+	0.0668124i
$39$		−	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	$0.790682\pi$
$42$	0.412246	−	0.884064i	0.0636109	−	0.136414i
$43$	3.94907	+	8.46881i	0.602227	+	1.29148i	0.937049	+	0.349199i	$0.113546\pi$
$43$	3.94907	+	8.46881i	0.602227	+	1.29148i	−0.334821	+	0.942282i	$0.608676\pi$
$44$	3.05888	−	3.64543i	0.461143	−	0.549569i
$45$		0			0
$46$	−0.386659	+	0.223238i	−0.0570098	+	0.0329146i
$47$	−3.02771	−	4.32402i	−0.441637	−	0.630724i	0.535195	−	0.844728i	$-0.320238\pi$
$47$	−3.02771	−	4.32402i	−0.441637	−	0.630724i	−0.976833	+	0.214005i	$0.931349\pi$
$48$	−1.25315	−	1.78968i	−0.180876	−	0.258318i
$49$	5.88954	−	3.40033i	0.841363	−	0.485761i
$50$		0			0
$51$	0.960637	−	1.14484i	0.134516	−	0.160310i
$52$	1.01913	+	2.18554i	0.141328	+	0.303080i
$53$	−3.42904	+	7.35361i	−0.471015	+	1.01010i	0.517035	+	0.855964i	$0.327036\pi$
$53$	−3.42904	+	7.35361i	−0.471015	+	1.01010i	−0.988050	+	0.154131i	$0.950742\pi$
$54$	1.72270	+	2.05303i	0.234430	+	0.279382i
$55$		0			0
$56$			0.446476i			0.0596628i
$57$	−8.66043	+	3.96107i	−1.14710	+	0.524656i
$58$	3.63616	+	3.63616i	0.477451	+	0.477451i
$59$	0.0555796	+	0.315207i	0.00723585	+	0.0410365i	0.988212	−	0.153092i	$-0.0489232\pi$
$59$	0.0555796	+	0.315207i	0.00723585	+	0.0410365i	−0.980976	+	0.194129i	$0.937812\pi$
$60$		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	$0.566514\pi$
$62$	2.37906	−	1.10937i	0.302141	−	0.140891i
$63$	0.0690050	+	0.788731i	0.00869381	+	0.0993707i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−1.80541	+	10.2390i	−0.222230	+	1.26033i
$67$	−9.20270	+	6.44380i	−1.12429	+	0.787235i	−0.979343	−	0.202204i	$-0.935190\pi$
$67$	−9.20270	+	6.44380i	−1.12429	+	0.787235i	−0.144945	+	0.989440i	$0.546301\pi$
$68$	−0.177043	+	0.660732i	−0.0214696	+	0.0801255i
$69$	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	$0.0623563\pi$
$72$	1.60717	+	0.749437i	0.189407	+	0.0883220i
$73$	4.32528	+	0.378413i	0.506236	+	0.0442899i	0.337414	−	0.941357i	$-0.390448\pi$
$73$	4.32528	+	0.378413i	0.506236	+	0.0442899i	0.168823	+	0.985646i	$0.446003\pi$
$74$	−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
$78$	−4.31576	−	3.02193i	−0.488664	−	0.342166i
$79$	12.3274	−	10.3439i	1.38694	−	1.16378i	0.420374	−	0.907351i	$-0.361899\pi$
$79$	12.3274	−	10.3439i	1.38694	−	1.16378i	0.966563	−	0.256428i	$-0.0825457\pi$
$80$		0			0
$81$	−10.5013	−	3.82218i	−1.16682	−	0.424686i
$82$	−0.517055	+	0.0452364i	−0.0570991	+	0.00499553i
$83$	−0.838185	+	0.224591i	−0.0920028	+	0.0246521i	−0.304527	−	0.952504i	$-0.598498\pi$
$83$	−0.838185	+	0.224591i	−0.0920028	+	0.0246521i	0.212524	+	0.977156i	$0.431832\pi$
$84$	−0.487728	−	0.844770i	−0.0532155	−	0.0921720i
$85$		0			0
$86$	9.20233	+	1.62262i	0.992313	+	0.174972i
$87$	−10.8520	−	2.90780i	−1.16346	−	0.311748i
$88$	−1.23166	−	4.59662i	−0.131295	−	0.490001i
$89$	12.7545	+	10.7023i	1.35198	+	1.13445i	0.978371	+	0.206858i	$0.0663240\pi$
$89$	12.7545	+	10.7023i	1.35198	+	1.13445i	0.373608	+	0.927587i	$0.378120\pi$
$90$		0			0
$91$	0.368241	+	1.01173i	0.0386021	+	0.106058i
$92$	−0.0389129	+	0.444777i	−0.00405695	+	0.0463712i
$93$	−3.28951	+	4.69791i	−0.341106	+	0.487150i
$94$	−5.27866			−0.544452
$95$		0			0
$96$	−2.18479			−0.222984
$97$	1.72517	−	2.46380i	0.175164	−	0.250161i	−0.721964	−	0.691931i	$-0.756760\pi$
$97$	1.72517	−	2.46380i	0.175164	−	0.250161i	0.897128	+	0.441770i	$0.145649\pi$
$98$	0.592717	−	6.77478i	0.0598734	−	0.684356i
$99$	−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	$0.800638\pi$
$102$	−0.386801	−	1.44356i	−0.0382991	−	0.142934i
$103$	9.91868	+	2.65770i	0.977316	+	0.261871i	0.711914	−	0.702267i	$-0.247829\pi$
$103$	9.91868	+	2.65770i	0.977316	+	0.261871i	0.265402	+	0.964138i	$0.414495\pi$
$104$	2.37484	+	0.418748i	0.232872	+	0.0410616i
$105$		0			0
$106$	4.05690	+	7.02676i	0.394041	+	0.682500i
$107$	−5.69310	+	1.52546i	−0.550373	+	0.147472i	−0.523280	−	0.852161i	$-0.675292\pi$
$107$	−5.69310	+	1.52546i	−0.550373	+	0.147472i	−0.0270932	+	0.999633i	$0.508625\pi$
$108$	2.66985	−	0.233581i	0.256906	−	0.0224764i
$109$	−7.27195	−	2.64677i	−0.696527	−	0.253515i	−0.0305995	−	0.999532i	$-0.509742\pi$
$109$	−7.27195	−	2.64677i	−0.696527	−	0.253515i	−0.665927	+	0.746017i	$0.731964\pi$
$110$		0			0
$111$	3.52481	−	2.95767i	0.334561	−	0.280730i
$112$	0.365731	+	0.256088i	0.0345584	+	0.0241980i
$113$	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
$117$	4.26004	+	0.372705i	0.393841	+	0.0344566i
$118$	0.290082	+	0.135267i	0.0267042	+	0.0124524i
$119$	−0.104455	+	0.286989i	−0.00957541	+	0.0263082i
$120$		0			0
$121$	−5.82295	+	10.0856i	−0.529359	+	0.916877i
$122$	−2.14076	+	7.98942i	−0.193815	+	0.723328i
$123$	0.928895	−	0.650420i	0.0837557	−	0.0586464i
$124$	0.455827	−	2.58512i	0.0409345	−	0.232151i
$125$		0			0
$126$	0.685670	+	0.395872i	0.0610843	+	0.0352671i
$127$	−1.77771	−	20.3193i	−0.157746	−	1.80305i	−0.502735	−	0.864440i	$-0.667673\pi$
$127$	−1.77771	−	20.3193i	−0.157746	−	1.80305i	0.344989	−	0.938607i	$-0.387883\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	−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
$133$	1.38622	−	1.36596i	0.120201	−	0.118444i
$134$			11.2344i			0.970506i
$135$		0			0
$136$	0.439693	+	0.524005i	0.0377033	+	0.0449331i
$137$	7.06076	−	15.1418i	0.603241	−	1.29366i	−0.333208	−	0.942853i	$-0.608131\pi$
$137$	7.06076	−	15.1418i	0.603241	−	1.29366i	0.936450	−	0.350802i	$-0.114091\pi$
$138$	−0.412246	−	0.884064i	−0.0350927	−	0.0752565i
$139$	12.1085	−	14.4304i	1.02703	−	1.22397i	0.0527547	−	0.998608i	$-0.483200\pi$
$139$	12.1085	−	14.4304i	1.02703	−	1.22397i	0.974276	−	0.225360i	$-0.0723557\pi$
$140$		0			0
$141$	9.98767	−	5.76639i	0.841114	−	0.485617i
$142$	−1.47475	−	2.10616i	−0.123758	−	0.176745i
$143$	−6.58216	−	9.40030i	−0.550428	−	0.786093i
$144$	1.53574	−	0.886659i	0.127978	−	0.0738883i
$145$		0			0
$146$	2.79086	−	3.32602i	0.230973	−	0.275263i
$147$	6.27927	+	13.4659i	0.517906	+	1.11065i
$148$	−0.890062	+	1.90874i	−0.0731627	+	0.156898i
$149$	8.53882	+	10.1762i	0.699528	+	0.833665i	0.992473	−	0.122465i	$-0.0390798\pi$
$149$	8.53882	+	10.1762i	0.699528	+	0.833665i	−0.292945	+	0.956129i	$0.594635\pi$
$150$		0			0
$151$		−	12.3520i		−	1.00519i	−0.864522	−	0.502594i	$-0.832379\pi$
$151$		−	12.3520i		−	1.00519i	0.864522	−	0.502594i	$-0.167621\pi$
$152$	−1.09714	−	4.21856i	−0.0889898	−	0.342171i
$153$	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
$157$	15.2045	−	7.08996i	1.21345	−	0.565841i	0.292778	−	0.956180i	$-0.405420\pi$
$157$	15.2045	−	7.08996i	1.21345	−	0.565841i	0.920671	+	0.390340i	$0.127642\pi$
$158$	−1.40253	−	16.0310i	−0.111579	−	1.27536i
$159$	−15.3520	−	8.86349i	−1.21749	−	0.702921i
$160$		0			0
$161$	−0.0346151	+	0.196312i	−0.00272805	+	0.0154716i
$162$	−9.15427	+	6.40989i	−0.719227	+	0.503608i
$163$	6.25073	−	23.3280i	0.489595	−	1.82719i	−0.0688176	−	0.997629i	$-0.521923\pi$
$163$	6.25073	−	23.3280i	0.489595	−	1.82719i	0.558412	−	0.829564i	$-0.311411\pi$
$164$	−0.259515	+	0.449493i	−0.0202647	+	0.0350995i
$165$		0			0
$166$	−0.296789	+	0.815422i	−0.0230353	+	0.0632890i
$167$	13.2667	+	6.18635i	1.02661	+	0.478714i	0.861605	−	0.507579i	$-0.169460\pi$
$167$	13.2667	+	6.18635i	1.02661	+	0.478714i	0.165001	+	0.986293i	$0.447237\pi$
$168$	−0.971745	−	0.0850166i	−0.0749717	−	0.00655918i
$169$	−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
$173$	−9.97342	−	6.98346i	−0.758265	−	0.530943i	0.129311	−	0.991604i	$-0.458723\pi$
$173$	−9.97342	−	6.98346i	−0.758265	−	0.530943i	−0.887576	+	0.460661i	$0.847612\pi$
$174$	−8.60640	+	7.22163i	−0.652450	+	0.547470i
$175$		0			0
$176$	−4.47178	−	1.62760i	−0.337073	−	0.122685i
$177$	−0.696626	+	0.0609468i	−0.0523616	+	0.00458105i
$178$	16.0825	−	4.30930i	1.20544	−	0.322996i
$179$	2.13230	+	3.69325i	0.159375	+	0.276046i	0.934644	−	0.355586i	$-0.115719\pi$
$179$	2.13230	+	3.69325i	0.159375	+	0.276046i	−0.775268	+	0.631632i	$0.782385\pi$
$180$		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	$0.745451\pi$
$182$	1.03998	+	0.278661i	0.0770883	+	0.0206557i
$183$	−4.67712	−	17.4552i	−0.345742	−	1.29033i
$184$	0.342020	+	0.286989i	0.0252141	+	0.0211571i
$185$		0			0
$186$	1.96151	+	5.38922i	0.143825	+	0.395157i
$187$	0.283709	−	3.24280i	0.0207468	−	0.237137i
$188$	−3.02771	+	4.32402i	−0.220819	+	0.315362i
$189$	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	$0.266425\pi$
$192$	−1.25315	+	1.78968i	−0.0904380	+	0.129159i
$193$	−0.958120	+	10.9514i	−0.0689670	+	0.788296i	0.880422	+	0.474192i	$0.157260\pi$
$193$	−0.958120	+	10.9514i	−0.0689670	+	0.788296i	−0.949388	+	0.314104i	$0.898296\pi$
$194$	−1.02871	−	2.82635i	−0.0738569	−	0.202920i
$195$		0			0
$196$	−5.20961	−	4.37138i	−0.372115	−	0.312241i
$197$	−0.238529	−	0.890202i	−0.0169945	−	0.0634243i	0.956908	−	0.290392i	$-0.0937856\pi$
$197$	−0.238529	−	0.890202i	−0.0169945	−	0.0634243i	−0.973902	+	0.226967i	$0.927119\pi$
$198$	−8.15127	−	2.18413i	−0.579286	−	0.155219i
$199$	−15.8807	−	2.80019i	−1.12575	−	0.198500i	−0.420387	−	0.907345i	$-0.638106\pi$
$199$	−15.8807	−	2.80019i	−1.12575	−	0.198500i	−0.705365	+	0.708845i	$0.749217\pi$
$200$		0			0
$201$	−12.2724	−	21.2565i	−0.865631	−	1.49932i
$202$	−4.73465	+	1.26865i	−0.333129	+	0.0892617i
$203$	2.28718	−	0.200102i	0.160528	−	0.0140444i
$204$	−1.40436	−	0.511144i	−0.0983247	−	0.0357873i
$205$		0			0
$206$	7.86618	−	6.60051i	0.548063	−	0.459879i
$207$	0.648558	+	0.454125i	0.0450779	+	0.0315639i
$208$	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	$0.386285\pi$
$212$	8.08293	+	0.707165i	0.555138	+	0.0485683i
$213$	5.09112	+	2.37403i	0.348838	+	0.162666i
$214$	−2.01584	+	5.53849i	−0.137800	+	0.378603i
$215$		0			0
$216$	1.34002	−	2.32099i	0.0911770	−	0.157923i
$217$	0.303336	−	1.13206i	0.0205918	−	0.0768495i
$218$	−6.33913	+	4.43871i	−0.429340	+	0.300627i
$219$	−1.64722	+	9.34183i	−0.111309	+	0.631263i
$220$		0			0
$221$	1.42855	+	0.824773i	0.0960946	+	0.0554802i
$222$	−0.401031	−	4.58381i	−0.0269155	−	0.307645i
$223$	−18.9170	+	8.82113i	−1.26677	+	0.590707i	−0.935666	−	0.352886i	$-0.885200\pi$
$223$	−18.9170	+	8.82113i	−1.26677	+	0.590707i	−0.331108	+	0.943593i	$0.607423\pi$
$224$	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	$0.661650\pi$
$228$	6.68423	+	6.78337i	0.442674	+	0.449240i
$229$		−	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
$232$	2.17323	−	4.66051i	0.142680	−	0.305977i
$233$	10.2907	+	22.0685i	0.674168	+	1.44576i	0.883747	+	0.467965i	$0.155013\pi$
$233$	10.2907	+	22.0685i	0.674168	+	1.44576i	−0.209579	+	0.977792i	$0.567209\pi$
$234$	2.74876	−	3.27584i	0.179692	−	0.214149i
$235$		0			0
$236$	0.277189	−	0.160035i	0.0180435	−	0.0104174i
$237$	20.1659	+	28.7999i	1.30992	+	1.87076i
$238$	0.175174	+	0.250175i	0.0113549	+	0.0162164i
$239$	23.7182	−	13.6937i	1.53420	−	0.885773i	0.535042	−	0.844825i	$-0.320296\pi$
$239$	23.7182	−	13.6937i	1.53420	−	0.885773i	0.999161	−	0.0409475i	$-0.0130376\pi$
$240$		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	$0.317015\pi$
$242$	4.92177	+	10.5548i	0.316383	+	0.678486i
$243$	6.92062	−	14.8413i	0.443958	−	0.952070i
$244$	5.31666	+	6.33615i	0.340364	+	0.405631i
$245$		0			0
$246$		−	1.13397i		−	0.0722994i
$247$	−5.96552	−	8.65456i	−0.379577	−	0.550677i
$248$	−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	$0.249527\pi$
$252$	0.717563	−	0.334605i	0.0452022	−	0.0210781i
$253$	−0.185178	−	2.11659i	−0.0116420	−	0.133069i
$254$	−17.6643	−	10.1985i	−1.10835	−	0.639908i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−13.5949	+	9.51923i	−0.848024	+	0.593793i	−0.914769	−	0.403977i	$-0.867628\pi$
$257$	−13.5949	+	9.51923i	−0.848024	+	0.593793i	0.0667447	+	0.997770i	$0.478739\pi$
$258$	−5.28388	+	19.7197i	−0.328960	+	1.22770i
$259$	−0.470154	+	0.814330i	−0.0292139	+	0.0506000i
$260$		0			0
$261$	3.11886	−	8.56900i	0.193053	−	0.530408i
$262$	−4.19902	−	1.95803i	−0.259416	−	0.120968i
$263$	26.8704	+	2.35086i	1.65690	+	0.144960i	0.876853	−	0.480758i	$-0.159638\pi$
$263$	26.8704	+	2.35086i	1.65690	+	0.144960i	0.780049	+	0.625718i	$0.215194\pi$
$264$	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
$268$	9.20270	+	6.44380i	0.562144	+	0.393618i
$269$	−20.8858	+	17.5253i	−1.27343	+	1.06854i	−0.279316	+	0.960199i	$0.590108\pi$
$269$	−20.8858	+	17.5253i	−1.27343	+	1.06854i	−0.994114	+	0.108336i	$0.965448\pi$
$270$		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	$0.891881\pi$
$272$	0.681437	−	0.0596180i	0.0413182	−	0.00361487i
$273$	−2.27214	+	0.608817i	−0.137516	+	0.0368473i
$274$	−8.35359	−	14.4688i	−0.504659	−	0.874095i
$275$		0			0
$276$	−0.960637	−	0.169386i	−0.0578236	−	0.0101959i
$277$	10.9985	+	2.94703i	0.660835	+	0.177070i	0.573623	−	0.819120i	$-0.305538\pi$
$277$	10.9985	+	2.94703i	0.660835	+	0.177070i	0.0872119	+	0.996190i	$0.472204\pi$
$278$	−4.87550	−	18.1956i	−0.292413	−	1.09130i
$279$	−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	$0.900408\pi$
$282$	1.00515	−	11.4889i	0.0598557	−	0.684153i
$283$	−9.62446	+	13.7452i	−0.572115	+	0.817065i	−0.996065	−	0.0886206i	$-0.971754\pi$
$283$	−9.62446	+	13.7452i	−0.572115	+	0.817065i	0.423951	+	0.905685i	$0.360643\pi$
$284$	−2.57115			−0.152570
$285$		0			0
$286$	−11.4757			−0.678570
$287$	−0.132917	+	0.189825i	−0.00784585	+	0.0112050i
$288$	0.154555	−	1.76657i	0.00910723	−	0.104096i
$289$	−5.65431	−	15.5351i	−0.332606	−	0.913828i
$290$		0			0
$291$	5.03390	+	4.22394i	0.295092	+	0.247612i
$292$	−1.12374	−	4.19386i	−0.0657620	−	0.245427i
$293$	−10.1072	−	2.70823i	−0.590472	−	0.158216i	−0.0488029	−	0.998808i	$-0.515541\pi$
$293$	−10.1072	−	2.70823i	−0.590472	−	0.158216i	−0.541669	+	0.840592i	$0.682207\pi$
$294$	14.6323	+	2.58007i	0.853373	+	0.150473i
$295$		0			0
$296$	1.05303	+	1.82391i	0.0612063	+	0.106012i
$297$	−12.3191	+	3.30091i	−0.714829	+	0.191538i
$298$	13.2335	−	1.15778i	0.766596	−	0.0670685i
$299$	1.01173	+	0.368241i	0.0585101	+	0.0212959i
$300$		0			0
$301$	3.19594	−	2.68171i	0.184211	−	0.154571i
$302$	−10.1181	−	7.08480i	−0.582234	−	0.407684i
$303$	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
$307$	−0.556371	−	0.0486762i	−0.0317538	−	0.00277810i	0.0712678	−	0.997457i	$-0.477296\pi$
$307$	−0.556371	−	0.0486762i	−0.0317538	−	0.00277810i	−0.103022	+	0.994679i	$0.532851\pi$
$308$	−1.92561	−	0.897926i	−0.109722	−	0.0511641i
$309$	−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	$0.828009\pi$
$312$	−1.36361	+	5.08905i	−0.0771990	+	0.288111i
$313$	6.93826	−	4.85822i	0.392173	−	0.274603i	−0.360814	−	0.932638i	$-0.617501\pi$
$313$	6.93826	−	4.85822i	0.392173	−	0.274603i	0.752987	+	0.658035i	$0.228612\pi$
$314$	2.91317	−	16.5214i	0.164400	−	0.932357i
$315$		0			0
$316$	−13.9363	−	8.04612i	−0.783978	−	0.452630i
$317$	−2.16175	−	24.7090i	−0.121416	−	1.38779i	−0.775489	−	0.631362i	$-0.782496\pi$
$317$	−2.16175	−	24.7090i	−0.121416	−	1.38779i	0.654072	−	0.756432i	$-0.273059\pi$
$318$	−16.0661	+	7.49175i	−0.900942	+	0.420116i
$319$	−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
$323$	0.281729	−	2.96832i	0.0156758	−	0.165162i
$324$			11.1753i			0.620850i
$325$		0			0
$326$	−15.5239	−	18.5007i	−0.859791	−	1.02466i
$327$	7.14535	−	15.3233i	0.395139	−	0.847378i
$328$	0.219351	+	0.470401i	0.0121117	+	0.0259735i
$329$	−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	$0.489942\pi$
$332$	0.497723	+	0.710822i	0.0273161	+	0.0390114i
$333$	2.14215	+	3.05931i	0.117389	+	0.167649i
$334$	12.6770	−	7.31908i	0.693655	−	0.400482i
$335$		0			0
$336$	−0.627011	+	0.747243i	−0.0342063	+	0.0407655i
$337$	6.01359	+	12.8962i	0.327581	+	0.702500i	0.999265	−	0.0383379i	$-0.0122063\pi$
$337$	6.01359	+	12.8962i	0.327581	+	0.702500i	−0.671684	+	0.740838i	$0.734429\pi$
$338$	−3.03642	+	6.51163i	−0.165160	+	0.354186i
$339$	17.7281	+	21.1275i	0.962856	+	1.14749i
$340$		0			0
$341$			12.4918i			0.676468i
$342$	−7.45140	−	2.05551i	−0.402926	−	0.111149i
$343$	−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
$347$	−17.1391	+	7.99209i	−0.920075	+	0.429038i	−0.824164	−	0.566352i	$-0.808354\pi$
$347$	−17.1391	+	7.99209i	−0.920075	+	0.429038i	−0.0959116	+	0.995390i	$0.530577\pi$
$348$	0.979183	+	11.1921i	0.0524897	+	0.599960i
$349$	−17.1013	−	9.87346i	−0.915413	−	0.528514i	−0.0332442	−	0.999447i	$-0.510584\pi$
$349$	−17.1013	−	9.87346i	−0.915413	−	0.528514i	−0.882169	+	0.470933i	$0.843917\pi$
$350$		0			0
$351$	1.12226	−	6.36467i	0.0599020	−	0.339721i
$352$	−3.89816	+	2.72952i	−0.207772	+	0.145484i
$353$	1.86947	−	6.97696i	0.0995018	−	0.371346i	−0.898162	−	0.439665i	$-0.855097\pi$
$353$	1.86947	−	6.97696i	0.0995018	−	0.371346i	0.997663	+	0.0683195i	$0.0217637\pi$
$354$	−0.349643	+	0.605600i	−0.0185833	+	0.0321873i
$355$		0			0
$356$	5.69459	−	15.6458i	0.301813	−	0.829224i
$357$	−0.604735	−	0.281993i	−0.0320060	−	0.0149246i
$358$	4.24837	+	0.371684i	0.224533	+	0.0196441i
$359$	15.8664	−	2.79767i	0.837394	−	0.147655i	0.261525	−	0.965197i	$-0.415775\pi$
$359$	15.8664	−	2.79767i	0.837394	−	0.147655i	0.575870	+	0.817542i	$0.304664\pi$
$360$		0			0
$361$	−9.74123	+	16.3128i	−0.512696	+	0.858570i
$362$	−10.6892	+	10.6892i	−0.561811	+	0.561811i
$363$	−20.8424	−	14.5940i	−1.09394	−	0.765987i
$364$	0.824773	−	0.692066i	0.0432298	−	0.0362741i
$365$		0			0
$366$	−16.9812	−	6.18064i	−0.887620	−	0.323067i
$367$	9.30346	−	0.813947i	0.485637	−	0.0424877i	0.158291	−	0.987392i	$-0.449401\pi$
$367$	9.30346	−	0.813947i	0.485637	−	0.0424877i	0.327345	+	0.944905i	$0.393846\pi$
$368$	0.431262	−	0.115556i	0.0224811	−	0.00602379i
$369$	0.460202	+	0.797094i	0.0239572	+	0.0414950i
$370$		0			0
$371$	3.56758	+	0.629061i	0.185220	+	0.0326592i
$372$	5.53967	+	1.48435i	0.287218	+	0.0769599i
$373$	−0.376612	−	1.40554i	−0.0195002	−	0.0727759i	0.955490	−	0.295023i	$-0.0953274\pi$
$373$	−0.376612	−	1.40554i	−0.0195002	−	0.0727759i	−0.974990	+	0.222247i	$0.928661\pi$
$374$	−2.49362	−	2.09240i	−0.128942	−	0.108195i
$375$		0			0
$376$	1.80541	+	4.96032i	0.0931068	+	0.255809i
$377$	1.08078	−	12.3533i	0.0556628	−	0.636229i
$378$	0.686327	−	0.980177i	0.0353009	−	0.0504148i
$379$	29.9861			1.54028			0.770140	−	0.637875i	$-0.220186\pi$
$379$	29.9861			1.54028			0.770140	+	0.637875i	$0.220186\pi$
$380$		0			0
$381$	44.5631			2.28303
$382$	10.6173	−	15.1631i	0.543229	−	0.775812i
$383$	0.576170	−	6.58566i	0.0294409	−	0.336511i	−0.967162	−	0.254159i	$-0.918201\pi$
$383$	0.576170	−	6.58566i	0.0294409	−	0.336511i	0.996603	−	0.0823521i	$-0.0262432\pi$
$384$	0.747243	+	2.05303i	0.0381326	+	0.104768i
$385$		0			0
$386$	8.42127	+	7.06629i	0.428632	+	0.359665i
$387$	−4.28874	−	16.0058i	−0.218009	−	0.813620i
$388$	−2.90525	−	0.778461i	−0.147492	−	0.0395203i
$389$	−3.93161	−	0.693249i	−0.199340	−	0.0351491i	0.0730863	−	0.997326i	$-0.476715\pi$
$389$	−3.93161	−	0.693249i	−0.199340	−	0.0351491i	−0.272427	+	0.962177i	$0.587826\pi$
$390$		0			0
$391$	0.152704	+	0.264490i	0.00772256	+	0.0133759i
$392$	−6.56893	+	1.76014i	−0.331781	+	0.0889005i
$393$	10.0839	−	0.882223i	0.508663	−	0.0445022i
$394$	−0.866025	−	0.315207i	−0.0436297	−	0.0158799i
$395$		0			0
$396$	−6.46451	+	5.42437i	−0.324854	+	0.272585i
$397$	2.67465	+	1.87281i	0.134237	+	0.0939936i	0.638766	−	0.769401i	$-0.279445\pi$
$397$	2.67465	+	1.87281i	0.134237	+	0.0939936i	−0.504529	+	0.863394i	$0.668334\pi$
$398$	−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	$0.126182\pi$
$402$	−24.4515	−	2.13923i	−1.21953	−	0.106695i
$403$	−5.73704	−	2.67523i	−0.285782	−	0.133263i
$404$	−1.67647	+	4.60607i	−0.0834076	+	0.229160i
$405$		0			0
$406$	1.14796	−	1.98832i	0.0569721	−	0.0986786i
$407$	2.59396	−	9.68079i	0.128578	−	0.479859i
$408$	−1.22421	+	0.857202i	−0.0606075	+	0.0424378i
$409$	1.04709	−	5.93835i	0.0517753	−	0.293632i	−0.947915	−	0.318524i	$-0.896813\pi$
$409$	1.04709	−	5.93835i	0.0517753	−	0.293632i	0.999690	+	0.0248914i	$0.00792401\pi$
$410$		0			0
$411$	31.6114	+	18.2509i	1.55928	+	0.900249i
$412$	−0.894965	−	10.2295i	−0.0440918	−	0.503971i
$413$	0.129515	−	0.0603936i	0.00637299	−	0.00297178i
$414$	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
$418$	8.62774	+	18.8636i	0.421996	+	0.922647i
$419$			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	0.980108	+	0.198466i	$0.0635959\pi$
$421$	20.6284	+	24.5839i	1.00536	+	1.19815i	0.0252567	+	0.999681i	$0.491960\pi$
$422$	2.23086	−	4.78409i	0.108596	−	0.232886i
$423$	3.95602	+	8.48371i	0.192348	+	0.412492i
$424$	5.21546	−	6.21554i	0.253285	−	0.301853i
$425$		0			0
$426$	4.86484	−	2.80872i	0.235702	−	0.136083i
$427$	2.11817	+	3.02506i	0.102505	+	0.146393i
$428$	3.38062	+	4.82803i	0.163408	+	0.233372i
$429$	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	$0.836179\pi$
$432$	−1.13264	−	2.42895i	−0.0544940	−	0.116863i
$433$	−11.7744	+	25.2504i	−0.565844	+	1.21346i	0.390335	+	0.920673i	$0.372359\pi$
$433$	−11.7744	+	25.2504i	−0.565844	+	1.21346i	−0.956179	+	0.292783i	$0.905419\pi$
$434$	−0.753347	−	0.897804i	−0.0361618	−	0.0430959i
$435$		0			0
$436$			7.73865i			0.370614i
$437$	−0.155340	−	1.93993i	−0.00743094	−	0.0927996i
$438$	6.70758	+	6.70758i	0.320500	+	0.320500i
$439$	−4.91204	−	27.8576i	−0.234439	−	1.32957i	−0.843792	−	0.536670i	$-0.819682\pi$
$439$	−4.91204	−	27.8576i	−0.234439	−	1.32957i	0.609353	−	0.792899i	$-0.291429\pi$
$440$		0			0
$441$	−11.3324	+	4.12467i	−0.539640	+	0.196413i
$442$	1.49500	−	0.697128i	0.0711097	−	0.0331590i
$443$	−2.36494	−	27.0314i	−0.112362	−	1.28430i	−0.817789	−	0.575518i	$-0.804801\pi$
$443$	−2.36494	−	27.0314i	−0.112362	−	1.28430i	0.705428	−	0.708782i	$-0.250755\pi$
$444$	−3.98486	−	2.30066i	−0.189113	−	0.109184i
$445$		0			0
$446$	−3.62449	+	20.5555i	−0.171624	+	0.973330i
$447$	−23.7742	+	16.6469i	−1.12448	+	0.787369i
$448$	0.115556	−	0.431262i	0.00545953	−	0.0203752i
$449$	5.58878	−	9.68004i	0.263751	−	0.456830i	−0.703485	−	0.710710i	$-0.748374\pi$
$449$	5.58878	−	9.68004i	0.263751	−	0.456830i	0.967236	+	0.253881i	$0.0817071\pi$
$450$		0			0
$451$	0.844770	−	2.32099i	0.0397787	−	0.109291i
$452$	−11.4409	−	5.33497i	−0.538133	−	0.250936i
$453$	26.8838	+	2.35203i	1.26311	+	0.110508i
$454$	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	$-0.771943\pi$
$457$	−2.08248	+	2.08248i	−0.0974143	+	0.0974143i	0.656720	+	0.754134i	$0.271943\pi$
$458$	−5.17700	−	3.62498i	−0.241906	−	0.169384i
$459$	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	$0.395529\pi$
$462$	4.62431	−	0.404575i	0.215142	−	0.0188225i
$463$	14.3948	−	3.85707i	0.668982	−	0.179253i	0.0916860	−	0.995788i	$-0.470774\pi$
$463$	14.3948	−	3.85707i	0.668982	−	0.179253i	0.577296	+	0.816535i	$0.304108\pi$
$464$	−2.57115	−	4.45336i	−0.119363	−	0.206742i
$465$		0			0
$466$	23.9800	+	4.22832i	1.11085	+	0.195873i
$467$	25.0513	+	6.71248i	1.15924	+	0.310616i	0.786661	−	0.617385i	$-0.211808\pi$
$467$	25.0513	+	6.71248i	1.15924	+	0.310616i	0.372576	+	0.928002i	$0.378475\pi$
$468$	−1.10679	−	4.13060i	−0.0511614	−	0.190937i
$469$	3.84240	+	3.22416i	0.177425	+	0.148878i
$470$		0			0
$471$	12.5360	+	34.4423i	0.577627	+	1.58702i
$472$	0.0278959	−	0.318852i	0.00128401	−	0.0146764i
$473$	−25.5054	+	36.4255i	−1.17274	+	1.67485i
$474$	35.1582			1.61487
$475$		0			0
$476$	0.305407			0.0139983
$477$	8.25283	−	11.7863i	0.377871	−	0.539656i
$478$	2.38697	−	27.2832i	0.109178	−	1.24791i
$479$	−4.25838	−	11.6998i	−0.194570	−	0.534578i	0.803592	−	0.595181i	$-0.202920\pi$
$479$	−4.25838	−	11.6998i	−0.194570	−	0.534578i	−0.998162	+	0.0606034i	$0.980698\pi$
$480$		0			0
$481$	3.89053	+	3.26454i	0.177393	+	0.148850i
$482$	2.35789	+	8.79976i	0.107399	+	0.400818i
$483$	−0.420678	−	0.112720i	−0.0191415	−	0.00512895i
$484$	11.4690	+	2.02229i	0.521317	+	0.0919222i
$485$		0			0
$486$	−8.18779	−	14.1817i	−0.371405	−	0.643293i
$487$	26.1429	−	7.00497i	1.18465	−	0.317425i	0.387879	−	0.921710i	$-0.373208\pi$
$487$	26.1429	−	7.00497i	1.18465	−	0.317425i	0.796768	+	0.604285i	$0.206541\pi$
$488$	8.23978	−	0.720888i	0.372998	−	0.0326331i
$489$	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	$0.153279\pi$
$492$	−0.928895	−	0.650420i	−0.0418778	−	0.0293232i
$493$	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
$497$	−1.14359	−	0.100051i	−0.0512969	−	0.00448790i
$498$	−1.71823	−	0.801226i	−0.0769959	−	0.0359038i
$499$	8.03850	−	22.0856i	0.359853	−	0.988687i	−0.619228	−	0.785212i	$-0.712554\pi$
$499$	8.03850	−	22.0856i	0.359853	−	0.988687i	0.979080	−	0.203475i	$-0.0652236\pi$
$500$		0			0
$501$	−15.9907	+	27.6966i	−0.714410	+	1.23739i
$502$	3.47691	−	12.9760i	0.155182	−	0.579148i
$503$	−6.15117	+	4.30710i	−0.274267	+	0.192044i	−0.702615	−	0.711570i	$-0.747985\pi$
$503$	−6.15117	+	4.30710i	−0.274267	+	0.192044i	0.428348	+	0.903614i	$0.359096\pi$
$504$	0.137485	−	0.779715i	0.00612406	−	0.0347313i
$505$		0			0
$506$	−1.84002	−	1.06234i	−0.0817990	−	0.0472267i
$507$	−1.36811	−	15.6375i	−0.0607598	−	0.694488i
$508$	−18.4859	+	8.62011i	−0.820179	+	0.382456i
$509$	−31.4197	+	11.4358i	−1.39265	+	0.506884i	−0.925989	−	0.377551i	$-0.876766\pi$
$509$	−31.4197	+	11.4358i	−1.39265	+	0.506884i	−0.466663	+	0.884435i	$0.654544\pi$
$510$		0			0
$511$	−0.336619	−	1.90906i	−0.0148911	−	0.0844519i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−11.3059	+	2.94038i	−0.499169	+	0.129821i
$514$			16.5963i			0.732030i
$515$		0			0
$516$	13.1227	+	15.6391i	0.577696	+	0.688471i
$517$	10.6161	−	22.7664i	0.466897	−	1.00126i
$518$	0.397391	+	0.852208i	0.0174604	+	0.0374439i
$519$	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	$0.399189\pi$
$522$	−5.23041	−	7.46980i	−0.228929	−	0.326944i
$523$	−18.7495	−	26.7770i	−0.819857	−	1.17088i	−0.982878	−	0.184255i	$-0.941013\pi$
$523$	−18.7495	−	26.7770i	−0.819857	−	1.17088i	0.163021	−	0.986623i	$-0.447876\pi$
$524$	−4.01239	+	2.31655i	−0.175282	+	0.101199i
$525$		0			0
$526$	17.3380	−	20.6626i	0.755971	−	0.900931i
$527$	−0.758856	−	1.62737i	−0.0330563	−	0.0708895i
$528$	4.39393	−	9.42282i	0.191221	−	0.410075i
$529$	−14.6560	−	17.4663i	−0.637217	−	0.759405i
$530$		0			0
$531$		−	0.567586i		−	0.0246311i
$532$	−1.75770	−	0.835437i	−0.0762060	−	0.0362208i
$533$	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
$537$	−8.44430	+	3.93764i	−0.364399	+	0.169922i
$538$	2.37626	+	27.1607i	0.102448	+	1.17098i
$539$	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	$0.00616028\pi$
$542$	−20.8222	+	14.5799i	−0.894390	+	0.626259i
$543$	8.54803	−	31.9017i	0.366831	−	1.36903i
$544$	0.342020	−	0.592396i	0.0146640	−	0.0253988i
$545$		0			0
$546$	−0.804530	+	2.21043i	−0.0344307	+	0.0945976i
$547$	0.327096	+	0.152527i	0.0139856	+	0.00652160i	0.429598	−	0.903020i	$-0.358655\pi$
$547$	0.327096	+	0.152527i	0.0139856	+	0.00652160i	−0.415613	+	0.909542i	$0.636433\pi$
$548$	−16.6436	−	1.45613i	−0.710980	−	0.0622027i
$549$	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
$553$	−5.88544	−	4.12103i	−0.250274	−	0.175244i
$554$	8.72254	−	7.31908i	0.370585	−	0.310958i
$555$		0			0
$556$	−17.7015	−	6.44280i	−0.750709	−	0.273236i
$557$	3.55638	−	0.311143i	0.150689	−	0.0131836i	−0.0115618	−	0.999933i	$-0.503680\pi$
$557$	3.55638	−	0.311143i	0.150689	−	0.0131836i	0.162250	+	0.986750i	$0.448125\pi$
$558$	−4.49635	+	1.20479i	−0.190346	+	0.0510030i
$559$	−11.2668	−	19.5146i	−0.476533	−	0.825380i
$560$		0			0
$561$	7.00387	+	1.23497i	0.295704	+	0.0521405i
$562$	−1.17169	−	0.313953i	−0.0494247	−	0.0132433i
$563$	7.68200	+	28.6696i	0.323758	+	1.20828i	0.915555	+	0.402193i	$0.131752\pi$
$563$	7.68200	+	28.6696i	0.323758	+	1.20828i	−0.591797	+	0.806087i	$0.701581\pi$
$564$	−8.83462	−	7.41312i	−0.372004	−	0.312149i
$565$		0			0
$566$	5.73901	+	15.7678i	0.241228	+	0.662770i
$567$	−0.434863	+	4.97051i	−0.0182625	+	0.208742i
$568$	−1.47475	+	2.10616i	−0.0618792	+	0.0883726i
$569$	3.69637			0.154960			0.0774800	−	0.996994i	$-0.475313\pi$
$569$	3.69637			0.154960			0.0774800	+	0.996994i	$0.475313\pi$
$570$		0			0
$571$	−13.5716			−0.567954			−0.283977	−	0.958831i	$-0.591654\pi$
$571$	−13.5716			−0.567954			−0.283977	+	0.958831i	$0.591654\pi$
$572$	−6.58216	+	9.40030i	−0.275214	+	0.393046i
$573$	−3.52476	+	40.2882i	−0.147249	+	1.68306i
$574$	0.0792577	+	0.217759i	0.00330815	+	0.00908908i
$575$		0			0
$576$	−1.35844	−	1.13987i	−0.0566017	−	0.0474945i
$577$	−0.684241	−	2.55362i	−0.0284853	−	0.106309i	0.950220	−	0.311581i	$-0.100859\pi$
$577$	−0.684241	−	2.55362i	−0.0284853	−	0.106309i	−0.978705	+	0.205273i	$0.934192\pi$
$578$	−15.9688	−	4.27882i	−0.664213	−	0.177975i
$579$	−23.6530	−	4.17066i	−0.982983	−	0.173327i
$580$		0			0
$581$	0.193715	+	0.335525i	0.00803667	+	0.0139199i
$582$	6.34738	−	1.70077i	0.263107	−	0.0704994i
$583$	−38.4648	+	3.36524i	−1.59305	+	0.139374i
$584$	−4.07996	−	1.48499i	−0.168830	−	0.0614491i
$585$		0			0
$586$	−8.01573	+	6.72600i	−0.331127	+	0.277848i
$587$	26.2479	+	18.3790i	1.08337	+	0.758583i	0.971949	−	0.235190i	$-0.0755714\pi$
$587$	26.2479	+	18.3790i	1.08337	+	0.758583i	0.111419	+	0.993773i	$0.464460\pi$
$588$	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
$592$	2.09805	+	0.183556i	0.0862294	+	0.00754410i
$593$	40.6798	+	18.9693i	1.67052	+	0.778976i	0.999288	+	0.0377267i	$0.0120116\pi$
$593$	40.6798	+	18.9693i	1.67052	+	0.778976i	0.671230	+	0.741249i	$0.265766\pi$
$594$	−4.36203	+	11.9846i	−0.178976	+	0.491733i
$595$		0			0
$596$	6.64203	−	11.5043i	0.272068	−	0.471236i
$597$	9.11852	−	34.0308i	0.373196	−	1.39279i
$598$	0.881952	−	0.617549i	0.0360657	−	0.0252535i
$599$	−3.59315	+	20.3778i	−0.146812	+	0.832614i	0.819082	+	0.573677i	$0.194483\pi$
$599$	−3.59315	+	20.3778i	−0.146812	+	0.832614i	−0.965894	+	0.258937i	$0.916628\pi$
$600$		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	$0.850362\pi$
$602$	−0.363614	−	4.15612i	−0.0148198	−	0.169391i
$603$	18.0557	−	8.41949i	0.735283	−	0.342868i
$604$	−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	$0.759087\pi$
$608$	−3.58891	+	2.47381i	−0.145550	+	0.100326i
$609$			5.01609i			0.203262i
$610$		0			0
$611$	8.18227	+	9.75125i	0.331019	+	0.394493i
$612$	0.512645	−	1.09937i	0.0207224	−	0.0444394i
$613$	0.965695	+	2.07094i	0.0390041	+	0.0836445i	0.924844	−	0.380346i	$-0.124195\pi$
$613$	0.965695	+	2.07094i	0.0390041	+	0.0836445i	−0.885840	+	0.463990i	$0.846417\pi$
$614$	−0.358995	+	0.427833i	−0.0144878	+	0.0172659i
$615$		0			0
$616$	−1.84002	+	1.06234i	−0.0741366	+	0.0428028i
$617$	13.4204	+	19.1664i	0.540287	+	0.771609i	0.992753	−	0.120172i	$-0.0383447\pi$
$617$	13.4204	+	19.1664i	0.540287	+	0.771609i	−0.452467	+	0.891781i	$0.649456\pi$
$618$	12.8680	+	18.3774i	0.517627	+	0.739249i
$619$	13.6987	−	7.90895i	0.550597	−	0.317887i	−0.198766	−	0.980047i	$-0.563693\pi$
$619$	13.6987	−	7.90895i	0.550597	−	0.317887i	0.749363	+	0.662160i	$0.230360\pi$
$620$		0			0
$621$	0.769143	−	0.916629i	0.0308647	−	0.0367831i
$622$	13.0317	+	27.9467i	0.522525	+	1.12056i
$623$	3.14164	−	6.73728i	0.125867	−	0.269923i
$624$	3.38657	+	4.03596i	0.135571	+	0.161568i
$625$		0			0
$626$		−	8.47005i		−	0.338531i
$627$	−36.9309	−	26.2666i	−1.47488	−	1.04899i
$628$	−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	$0.477941\pi$
$632$	−14.5845	+	6.80087i	−0.580141	+	0.270524i
$633$	1.00515	+	11.4889i	0.0399510	+	0.456642i
$634$	−21.4803	−	12.4017i	−0.853093	−	0.492533i
$635$		0			0
$636$	−3.07826	+	17.4577i	−0.122061	+	0.692242i
$637$	−13.4338	+	9.40643i	−0.532266	+	0.372696i
$638$	−6.33357	+	23.6372i	−0.250748	+	0.935806i
$639$	−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	$-0.174782\pi$
$642$	−11.6705	−	5.44206i	−0.460600	−	0.214781i
$643$	−36.1308	−	3.16104i	−1.42486	−	0.124659i	−0.651511	−	0.758639i	$-0.725864\pi$
$643$	−36.1308	−	3.16104i	−1.42486	−	0.124659i	−0.773349	+	0.633980i	$0.781420\pi$
$644$	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	$-0.973409\pi$
$647$	−23.2250	+	23.2250i	−0.913070	+	0.913070i	0.0834422	+	0.996513i	$0.473409\pi$
$648$	9.15427	+	6.40989i	0.359614	+	0.251804i
$649$	−1.16679	+	0.979055i	−0.0458006	+	0.0384313i
$650$		0			0
$651$	2.40615	+	0.875768i	0.0943046	+	0.0343241i
$652$	−24.0591	+	2.10489i	−0.942225	+	0.0824340i
$653$	20.5077	−	5.49501i	0.802527	−	0.215036i	0.165834	−	0.986154i	$-0.446969\pi$
$653$	20.5077	−	5.49501i	0.802527	−	0.215036i	0.636693	+	0.771117i	$0.280302\pi$
$654$	−8.45367	−	14.6422i	−0.330565	−	0.572555i
$655$		0			0
$656$	0.511144	+	0.0901285i	0.0199568	+	0.00351893i
$657$	−7.43705	−	1.99275i	−0.290147	−	0.0777447i
$658$	0.609983	+	2.27649i	0.0237796	+	0.0887467i
$659$	4.30320	+	3.61081i	0.167629	+	0.140657i	0.722743	−	0.691117i	$-0.242881\pi$
$659$	4.30320	+	3.61081i	0.167629	+	0.140657i	−0.555114	+	0.831774i	$0.687325\pi$
$660$		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	$0.741028\pi$
$662$	−1.49810	+	17.1234i	−0.0582254	+	0.665520i
$663$	−2.06712	+	2.95215i	−0.0802803	+	0.114652i
$664$	0.867753			0.0336754
$665$		0			0
$666$	3.73473			0.144718
$667$	1.31688	−	1.88070i	0.0509898	−	0.0728210i
$668$	1.27580	−	14.5825i	0.0493622	−	0.564212i
$669$	−15.5969	−	42.8521i	−0.603011	−	1.65676i
$670$		0			0
$671$	−30.1523	−	25.3008i	−1.16402	−	0.976726i
$672$	0.252467	+	0.942219i	0.00973912	+	0.0363469i
$673$	26.5570	+	7.11592i	1.02370	+	0.274299i	0.731342	−	0.682011i	$-0.238894\pi$
$673$	26.5570	+	7.11592i	1.02370	+	0.274299i	0.292355	+	0.956310i	$0.405561\pi$
$674$	14.0132	+	2.47090i	0.539768	+	0.0951757i
$675$		0			0
$676$	3.59240	+	6.22221i	0.138169	+	0.239316i
$677$	4.11565	−	1.10278i	0.158177	−	0.0423834i	−0.178861	−	0.983874i	$-0.557241\pi$
$677$	4.11565	−	1.10278i	0.158177	−	0.0423834i	0.337039	+	0.941491i	$0.390575\pi$
$678$	27.4750	−	2.40375i	1.05517	−	0.0923155i
$679$	−1.26190	−	0.459293i	−0.0484272	−	0.0176260i
$680$		0			0
$681$	−13.8188	+	11.5954i	−0.529539	+	0.444336i
$682$	10.2327	+	7.16499i	0.391829	+	0.274362i
$683$	−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
$687$	13.7552	+	1.20343i	0.524795	+	0.0459137i
$688$	−8.46881	−	3.94907i	−0.322870	−	0.150557i
$689$	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	$0.134532\pi$
$692$	−3.15120	+	11.7604i	−0.119791	+	0.447065i
$693$	−3.08634	+	2.16108i	−0.117240	+	0.0820926i
$694$	−3.28384	+	18.6236i	−0.124653	+	0.706942i
$695$		0			0
$696$	9.72967	+	5.61743i	0.368802	+	0.212928i
$697$	0.0309435	+	0.353686i	0.00117207	+	0.0133968i
$698$	−17.8968	+	8.34541i	−0.677403	+	0.315878i
$699$	−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
$703$	2.44121	−	8.84960i	0.0920719	−	0.333769i
$704$			4.75877i			0.179353i
$705$		0			0
$706$	−4.64290	−	5.53320i	−0.174738	−	0.208245i
$707$	−0.924891	+	1.98343i	−0.0347841	+	0.0745947i
$708$	0.295531	+	0.633769i	0.0111067	+	0.0238185i
$709$	−7.23832	+	8.62630i	−0.271841	+	0.323967i	−0.884643	−	0.466269i	$-0.845598\pi$
$709$	−7.23832	+	8.62630i	−0.271841	+	0.323967i	0.612802	+	0.790236i	$0.290042\pi$
$710$		0			0
$711$	−24.7135	+	14.2683i	−0.926828	+	0.535104i
$712$	−9.54998	−	13.6388i	−0.357900	−	0.511135i
$713$	−0.672231	−	0.960046i	−0.0251753	−	0.0359540i
$714$	−0.577857	+	0.333626i	−0.0216257	+	0.0124856i
$715$		0			0
$716$	2.74123	−	3.26687i	0.102445	−	0.122089i
$717$	25.2877	+	54.2297i	0.944387	+	2.02525i
$718$	6.80885	−	14.6016i	0.254104	−	0.544928i
$719$	−7.86474	−	9.37283i	−0.293305	−	0.349547i	0.599188	−	0.800608i	$-0.295490\pi$
$719$	−7.86474	−	9.37283i	−0.293305	−	0.349547i	−0.892493	+	0.451061i	$0.851046\pi$
$720$		0			0
$721$		−	4.58467i		−	0.170742i
$722$	7.77535	+	17.3362i	0.289369	+	0.645187i
$723$	−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
$727$	5.31858	−	2.48009i	0.197255	−	0.0919816i	−0.321481	−	0.946916i	$-0.604181\pi$
$727$	5.31858	−	2.48009i	0.197255	−	0.0919816i	0.518736	+	0.854935i	$0.326403\pi$
$728$	−0.0938375	−	1.07257i	−0.00347785	−	0.0397520i
$729$	1.94971	+	1.12567i	0.0722116	+	0.0416914i
$730$		0			0
$731$	1.10994	−	6.29477i	0.0410525	−	0.232820i
$732$	−14.8029	+	10.3651i	−0.547130	+	0.383105i
$733$	−0.230802	+	0.861365i	−0.00852487	+	0.0318153i	−0.970057	−	0.242876i	$-0.921909\pi$
$733$	−0.230802	+	0.861365i	−0.00852487	+	0.0318153i	0.961532	+	0.274692i	$0.0885757\pi$
$734$	4.66950	−	8.08781i	0.172354	−	0.298527i
$735$		0			0
$736$	0.152704	−	0.419550i	0.00562873	−	0.0154648i
$737$	−48.4531	−	22.5940i	−1.78479	−	0.832262i
$738$	0.916902	+	0.0802186i	0.0337516	+	0.00295289i
$739$	23.7837	−	4.19372i	0.874899	−	0.154268i	0.281873	−	0.959452i	$-0.409044\pi$
$739$	23.7837	−	4.19372i	0.874899	−	0.154268i	0.593026	+	0.805183i	$0.297933\pi$
$740$		0			0
$741$	19.9724	−	11.3359i	0.733705	−	0.416433i
$742$	2.56158	−	2.56158i	0.0940385	−	0.0940385i
$743$	9.26912	+	6.49031i	0.340051	+	0.238106i	0.731111	−	0.682259i	$-0.239002\pi$
$743$	9.26912	+	6.49031i	0.340051	+	0.238106i	−0.391059	+	0.920365i	$0.627891\pi$
$744$	4.39333	−	3.68644i	0.161067	−	0.135151i
$745$		0			0
$746$	−1.36736	−	0.497680i	−0.0500627	−	0.0182213i
$747$	1.53295	−	0.134116i	0.0560876	−	0.00490703i
$748$	−3.14427	+	0.842505i	−0.114966	+	0.0308050i
$749$	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	$0.566487\pi$
$752$	5.09879	+	1.36622i	0.185934	+	0.0498208i
$753$	7.59634	+	28.3499i	0.276826	+	1.03313i
$754$	−9.49935	−	7.97090i	−0.345946	−	0.290283i
$755$		0			0
$756$	−0.409253	−	1.12441i	−0.0148844	−	0.0408945i
$757$	4.75976	−	54.4043i	0.172996	−	1.97736i	−0.0356365	−	0.999365i	$-0.511346\pi$
$757$	4.75976	−	54.4043i	0.172996	−	1.97736i	0.208633	−	0.977994i	$-0.433099\pi$
$758$	17.1993	−	24.5631i	0.624706	−	0.892173i
$759$	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	$0.647928\pi$
$762$	25.5603	−	36.5039i	0.925953	−	1.32240i
$763$	−0.301133	+	3.44197i	−0.0109018	+	0.124608i
$764$	−6.33104	−	17.3944i	−0.229049	−	0.629307i
$765$		0			0
$766$	−5.06418	−	4.24935i	−0.182976	−	0.153535i
$767$	−0.199767	−	0.745541i	−0.00721317	−	0.0269199i
$768$	2.11035	+	0.565466i	0.0761506	+	0.0204045i
$769$	−49.3996	−	8.71048i	−1.78140	−	0.314108i	−0.816619	−	0.577177i	$-0.804154\pi$
$769$	−49.3996	−	8.71048i	−1.78140	−	0.314108i	−0.964777	+	0.263069i	$0.915265\pi$
$770$		0			0
$771$	−18.1297	−	31.4016i	−0.652925	−	1.13090i
$772$	10.6186	−	2.84525i	0.382172	−	0.102403i
$773$	−37.1445	+	3.24973i	−1.33600	+	0.116884i	−0.732656	−	0.680599i	$-0.761719\pi$
$773$	−37.1445	+	3.24973i	−1.33600	+	0.116884i	−0.603340	+	0.797484i	$0.706164\pi$
$774$	−15.5711	−	5.66741i	−0.559691	−	0.203711i
$775$		0			0
$776$	−2.30406	+	1.93334i	−0.0827110	+	0.0694028i
$777$	−1.68285	−	1.17834i	−0.0603718	−	0.0422728i
$778$	−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
$782$	0.304245	+	0.0266180i	0.0108798	+	0.000951858i
$783$	−12.4904	−	5.82435i	−0.446369	−	0.208145i
$784$	−2.32596	+	6.39053i	−0.0830701	+	0.228233i
$785$		0			0
$786$	5.06118	−	8.76623i	0.180526	−	0.312681i
$787$	−7.28899	+	27.2029i	−0.259825	+	0.969678i	0.705518	+	0.708692i	$0.250714\pi$
$787$	−7.28899	+	27.2029i	−0.259825	+	0.969678i	−0.965343	+	0.260986i	$0.915952\pi$
$788$	−0.754935	+	0.528611i	−0.0268934	+	0.0188310i
$789$	−10.2332	+	58.0353i	−0.364311	+	2.06611i
$790$		0			0
$791$	−4.88103	−	2.81807i	−0.173550	−	0.100199i
$792$	0.735491	+	8.40670i	0.0261345	+	0.298719i
$793$	18.0771	−	8.42951i	0.641938	−	0.299341i
$794$	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	$0.510740\pi$
$798$	4.23835	−	0.339387i	0.150036	−	0.0120142i
$799$			3.61081i			0.127741i
$800$		0			0
$801$	−18.9786	−	22.6179i	−0.670577	−	0.799163i
$802$	14.2413	−	30.5405i	0.502876	−	1.07842i
$803$	8.73199	+	18.7258i	0.308145	+	0.660820i
$804$	−15.7771	+	18.8025i	−0.556417	+	0.663112i
$805$		0			0
$806$	−5.48205	+	3.16506i	−0.193097	+	0.111485i
$807$	−34.1664	−	48.7947i	−1.20271	−	1.71765i
$808$	2.81148	+	4.01522i	0.0989077	+	0.141255i
$809$	−12.2836	+	7.09193i	−0.431868	+	0.249339i	−0.700142	−	0.714004i	$-0.746880\pi$
$809$	−12.2836	+	7.09193i	−0.431868	+	0.249339i	0.268274	+	0.963343i	$0.413547\pi$
$810$		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	$-0.0606485\pi$
$812$	−0.970294	−	2.08080i	−0.0340507	−	0.0730219i
$813$	23.4704	−	50.3324i	0.823143	−	1.76524i
$814$	−6.44220	−	7.67752i	−0.225799	−	0.269097i
$815$		0			0
$816$			1.49449i			0.0523175i
$817$	−23.6072	+	33.1919i	−0.825913	+	1.16124i
$818$	−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	$0.370191\pi$
$822$	33.0818	−	15.4263i	1.15386	−	0.538054i
$823$	1.09036	+	12.4629i	0.0380076	+	0.434429i	0.991229	+	0.132156i	$0.0421899\pi$
$823$	1.09036	+	12.4629i	0.0380076	+	0.434429i	−0.953221	+	0.302273i	$0.902255\pi$
$824$	−8.89284	−	5.13429i	−0.309797	−	0.178861i
$825$		0			0
$826$	0.0248149	−	0.140732i	0.000863422	−	0.00489671i
$827$	−12.0938	+	8.46818i	−0.420543	+	0.294468i	−0.764629	−	0.644471i	$-0.777078\pi$
$827$	−12.0938	+	8.46818i	−0.420543	+	0.294468i	0.344086	+	0.938938i	$0.388189\pi$
$828$	0.204918	−	0.764765i	0.00712140	−	0.0265774i
$829$	9.45485	−	16.3763i	0.328381	−	0.568772i	−0.653810	−	0.756659i	$-0.726830\pi$
$829$	9.45485	−	16.3763i	0.328381	−	0.568772i	0.982191	+	0.187887i	$0.0601638\pi$
$830$		0			0
$831$	−8.50846	+	23.3768i	−0.295155	+	0.810932i
$832$	−2.18554	−	1.01913i	−0.0757699	−	0.0353321i
$833$	−4.63422	−	0.405442i	−0.160566	−	0.0140477i
$834$	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
$838$	25.2487	+	17.6793i	0.872201	+	0.610722i
$839$	−24.9663	+	20.9492i	−0.861931	+	0.723246i	−0.962383	−	0.271696i	$-0.912416\pi$
$839$	−24.9663	+	20.9492i	−0.861931	+	0.723246i	0.100452	+	0.994942i	$0.467971\pi$
$840$		0			0
$841$	2.40255	+	0.874457i	0.0828466	+	0.0301537i
$842$	31.9699	−	2.79700i	1.10176	−	0.0963911i
$843$	2.55990	−	0.685922i	0.0881675	−	0.0236244i
$844$	−2.63933	−	4.57145i	−0.0908494	−	0.157356i
$845$		0			0
$846$	9.21853	+	1.62548i	0.316940	+	0.0558850i
$847$	5.02244	+	1.34576i	0.172573	+	0.0462408i
$848$	−2.10001	−	7.83734i	−0.0721146	−	0.269135i
$849$	−28.0834	−	23.5648i	−0.963819	−	0.808740i
$850$		0			0
$851$	0.321604	+	0.883600i	0.0110244	+	0.0302894i
$852$	0.489591	−	5.59605i	0.0167731	−	0.191718i
$853$	14.7811	−	21.1096i	0.506094	−	0.722778i	−0.482078	−	0.876129i	$-0.660118\pi$
$853$	14.7811	−	21.1096i	0.506094	−	0.722778i	0.988172	+	0.153351i	$0.0490065\pi$
$854$	3.69292			0.126369
$855$		0			0
$856$	5.89393			0.201450
$857$	−23.0279	+	32.8873i	−0.786619	+	1.12341i	0.202928	+	0.979194i	$0.434954\pi$
$857$	−23.0279	+	32.8873i	−0.786619	+	1.12341i	−0.989546	+	0.144214i	$0.953935\pi$
$858$	2.18516	−	24.9765i	0.0746002	−	0.852684i
$859$	−10.3209	−	28.3564i	−0.352144	−	0.967507i	−0.981680	−	0.190536i	$-0.938977\pi$
$859$	−10.3209	−	28.3564i	−0.352144	−	0.967507i	0.629536	−	0.776971i	$-0.283245\pi$
$860$		0			0
$861$	−0.387841	−	0.325437i	−0.0132176	−	0.0110909i
$862$	10.0651	+	37.5634i	0.342818	+	1.27942i
$863$	12.3126	+	3.29914i	0.419125	+	0.112304i	0.462217	−	0.886767i	$-0.347054\pi$
$863$	12.3126	+	3.29914i	0.419125	+	0.112304i	−0.0430920	+	0.999071i	$0.513721\pi$
$864$	−2.63933	−	0.465385i	−0.0897918	−	0.0158327i
$865$		0			0
$866$	13.9304	+	24.1281i	0.473373	+	0.819906i
$867$	34.8885	−	9.34833i	1.18487	−	0.317486i
$868$	−1.16754	+	0.102146i	−0.0396289	+	0.00346708i
$869$	71.9610	+	26.1917i	2.44111	+	0.888491i
$870$		0			0
$871$	20.7533	−	17.4141i	0.703199	−	0.590054i
$872$	6.33913	+	4.43871i	0.214670	+	0.150314i
$873$	−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
$877$	24.9448	+	2.18239i	0.842328	+	0.0736941i	0.500148	−	0.865940i	$-0.333279\pi$
$877$	24.9448	+	2.18239i	0.842328	+	0.0736941i	0.342180	+	0.939634i	$0.388835\pi$
$878$	−25.6370	−	11.9547i	−0.865207	−	0.403453i
$879$	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	$0.277374\pi$
$882$	−3.12129	+	11.6488i	−0.105099	+	0.392236i
$883$	24.7328	−	17.3181i	0.832324	−	0.582799i	−0.0778789	−	0.996963i	$-0.524815\pi$
$883$	24.7328	−	17.3181i	0.832324	−	0.582799i	0.910202	+	0.414164i	$0.135926\pi$
$884$	0.286441	−	1.62449i	0.00963404	−	0.0546373i
$885$		0			0
$886$	−23.4993	−	13.5673i	−0.789474	−	0.455803i
$887$	1.07249	+	12.2586i	0.0360106	+	0.411603i	0.992710	+	0.120526i	$0.0384581\pi$
$887$	1.07249	+	12.2586i	0.0360106	+	0.411603i	−0.956700	+	0.291077i	$0.905986\pi$
$888$	−4.17021	+	1.94460i	−0.139943	+	0.0652566i
$889$	−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
$893$	9.87733	−	20.7812i	0.330532	−	0.695417i
$894$			29.0229i			0.970671i
$895$		0			0
$896$	−0.286989	−	0.342020i	−0.00958763	−	0.0114261i
$897$	−0.994120	+	2.13190i	−0.0331927	+	0.0711820i
$898$	−4.72384	−	10.1303i	−0.157637	−	0.338053i
$899$	−8.67670	+	10.3405i	−0.289384	+	0.344875i
$900$		0			0
$901$	4.80659	−	2.77509i	0.160131	−	0.0924515i
$902$	−1.41670	−	2.02326i	−0.0471710	−	0.0673671i
$903$	5.22812	+	7.46653i	0.173981	+	0.248471i
$904$	−10.9324	+	6.31180i	−0.363605	+	0.209927i
$905$		0			0
$906$	17.3466	−	20.6729i	0.576302	−	0.686809i
$907$	−16.6047	−	35.6089i	−0.551350	−	1.18237i	−0.962619	−	0.270859i	$-0.912692\pi$
$907$	−16.6047	−	35.6089i	−0.551350	−	1.18237i	0.411269	−	0.911514i	$-0.365086\pi$
$908$	3.48944	−	7.48312i	0.115801	−	0.248336i
$909$	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	$-0.397550\pi$
$912$	4.08815	−	8.60117i	0.135372	−	0.284813i
$913$	−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
$917$	−1.87476	+	0.874214i	−0.0619100	+	0.0288691i
$918$	−0.159779	−	1.82628i	−0.00527349	−	0.0602763i
$919$	28.0448	+	16.1917i	0.925112	+	0.534113i	0.885262	−	0.465092i	$-0.153979\pi$
$919$	28.0448	+	16.1917i	0.925112	+	0.534113i	0.0398494	+	0.999206i	$0.487312\pi$
$920$		0			0
$921$	0.211885	−	1.20166i	0.00698186	−	0.0395961i
$922$	22.0437	−	15.4351i	0.725970	−	0.508329i
$923$	−1.60475	+	5.98899i	−0.0528209	+	0.197130i
$924$	2.32099	−	4.02007i	0.0763549	−	0.132251i
$925$		0			0
$926$	5.09698	−	14.0038i	0.167497	−	0.460195i
$927$	−16.5034	−	7.69564i	−0.542042	−	0.252758i
$928$	−5.12273	−	0.448181i	−0.168162	−	0.0147123i
$929$	−20.5209	+	3.61839i	−0.673270	+	0.118716i	−0.499823	−	0.866128i	$-0.666602\pi$
$929$	−20.5209	+	3.61839i	−0.673270	+	0.118716i	−0.173447	+	0.984843i	$0.555490\pi$
$930$		0			0
$931$	25.5621	+	15.0103i	0.837765	+	0.491942i
$932$	17.2180	−	17.2180i	0.563994	−	0.563994i
$933$	−55.1860	−	38.6417i	−1.80671	−	1.26507i
$934$	19.8674	−	16.6707i	0.650081	−	0.545482i
$935$		0			0
$936$	−4.01842	−	1.46258i	−0.131346	−	0.0478061i
$937$	−16.8973	+	1.47832i	−0.552010	+	0.0482946i	−0.359749	−	0.933049i	$-0.617138\pi$
$937$	−16.8973	+	1.47832i	−0.552010	+	0.0482946i	−0.192261	+	0.981344i	$0.561582\pi$
$938$	4.84498	−	1.29821i	0.158194	−	0.0423880i
$939$	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	$0.549286\pi$
$942$	35.4038	+	9.48641i	1.15352	+	0.309084i
$943$	0.0599772	+	0.223838i	0.00195313	+	0.00728916i
$944$	−0.245188	−	0.205737i	−0.00798019	−	0.00669617i
$945$		0			0
$946$	15.2087	+	41.7856i	0.494478	+	1.35857i
$947$	−1.52386	+	17.4178i	−0.0495188	+	0.566002i	0.930392	+	0.366566i	$0.119467\pi$
$947$	−1.52386	+	17.4178i	−0.0495188	+	0.566002i	−0.979911	+	0.199436i	$0.936089\pi$
$948$	20.1659	−	28.7999i	0.654959	−	0.935378i
$949$	−10.4702			−0.339876
$950$		0			0
$951$	54.1902			1.75724
$952$	0.175174	−	0.250175i	0.00567744	−	0.00810822i
$953$	1.67199	−	19.1110i	0.0541612	−	0.619065i	−0.919806	−	0.392374i	$-0.871654\pi$
$953$	1.67199	−	19.1110i	0.0541612	−	0.619065i	0.973967	−	0.226691i	$-0.0727907\pi$
$954$	−4.92111	−	13.5206i	−0.159327	−	0.437747i
$955$		0			0
$956$	−20.9800	−	17.6043i	−0.678541	−	0.569364i
$957$	−13.8375	−	51.6424i	−0.447304	−	1.66936i
$958$	−12.0264	−	3.22247i	−0.388556	−	0.104113i
$959$	−7.34603	−	1.29530i	−0.237216	−	0.0418275i
$960$		0			0
$961$	−12.0547	−	20.8793i	−0.388861	−	0.673527i
$962$	4.90567	−	1.31447i	0.158165	−	0.0423802i
$963$	10.4120	−	0.910936i	0.335524	−	0.0293545i
$964$	8.56077	+	3.11587i	0.275724	+	0.100355i
$965$		0			0
$966$	−0.333626	+	0.279945i	−0.0107342	+	0.00900709i
$967$	40.7812	+	28.5553i	1.31143	+	0.918276i	0.999493	−	0.0318257i	$-0.0101321\pi$
$967$	40.7812	+	28.5553i	1.31143	+	0.918276i	0.311941	+	0.950102i	$0.399021\pi$
$968$	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	$0.668115\pi$
$972$	−16.3133	−	1.42723i	−0.523248	−	0.0457783i
$973$	−7.62249	−	3.55442i	−0.244366	−	0.113950i
$974$	9.25681	−	25.4329i	0.296607	−	0.814922i
$975$		0			0
$976$	4.13563	−	7.16312i	0.132378	−	0.229286i
$977$	15.0334	−	56.1055i	0.480962	−	1.79497i	−0.116631	−	0.993175i	$-0.537210\pi$
$977$	15.0334	−	56.1055i	0.480962	−	1.79497i	0.597593	−	0.801799i	$-0.296124\pi$
$978$	43.2224	−	30.2647i	1.38210	−	0.967757i
$979$	−13.7587	+	78.0292i	−0.439729	+	2.49382i
$980$		0			0
$981$	11.8845	+	6.86154i	0.379444	+	0.219072i
$982$	−1.47248	−	16.8306i	−0.0469889	−	0.537085i
$983$	55.9935	−	26.1102i	1.78592	−	0.832786i	0.820687	−	0.571378i	$-0.193591\pi$
$983$	55.9935	−	26.1102i	1.78592	−	0.832786i	0.965228	−	0.261408i	$-0.0841867\pi$
$984$	−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
$988$	−6.09230	+	8.56579i	−0.193822	+	0.272514i
$989$		−	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	$0.691642\pi$
$992$	−1.10937	+	2.37906i	−0.0352227	+	0.0755352i
$993$	−15.8710	−	34.0355i	−0.503651	−	1.08008i
$994$	−0.737892	+	0.879385i	−0.0234045	+	0.0278924i
$995$		0			0
$996$	−1.64186	+	0.947931i	−0.0520245	+	0.0300363i
$997$	16.5139	+	23.5843i	0.523000	+	0.746922i	0.990566	−	0.137037i	$-0.0437578\pi$
$997$	16.5139	+	23.5843i	0.523000	+	0.746922i	−0.467566	+	0.883958i	$0.654869\pi$
$998$	−13.4808	−	19.2525i	−0.426726	−	0.609428i
$999$	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.143.2	yes	24
5.2	odd	4	inner	950.2.bb.a.257.2	yes	24
5.3	odd	4	inner	950.2.bb.a.257.1	yes	24
5.4	even	2	inner	950.2.bb.a.143.1	✓	24
19.2	odd	18	inner	950.2.bb.a.743.2	yes	24
95.2	even	36	inner	950.2.bb.a.857.2	yes	24
95.59	odd	18	inner	950.2.bb.a.743.1	yes	24
95.78	even	36	inner	950.2.bb.a.857.1	yes	24

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

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