LMFDB - Embedded newform 950.2.u.h.149.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.7
Character	$\chi$	$=$	950.149
Dual form			950.2.u.h.899.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.0291678 + 0.0801377i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-1.59412 + 0.920368i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.29256 - 1.92369i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.0291678 + 0.0801377i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-1.59412 + 0.920368i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.29256 - 1.92369i) q^{9} +(-1.21024 + 2.09620i) q^{11} +(0.0738553 - 0.0426404i) q^{12} +(1.03726 - 2.84986i) q^{13} +(-0.319640 + 1.81277i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.38551 - 5.22645i) q^{17} -2.99273i q^{18} +(3.15879 - 3.00368i) q^{19} +(-0.120253 - 0.100904i) q^{21} +(0.827855 + 2.27451i) q^{22} +(-7.90530 + 1.39392i) q^{23} +(0.0148089 - 0.0839852i) q^{24} +(-1.51638 - 2.62644i) q^{26} +(0.442595 + 0.255532i) q^{27} +(1.18320 + 1.41009i) q^{28} +(7.77809 - 6.52659i) q^{29} +(-2.41863 - 4.18918i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.203285 - 0.0358446i) q^{33} +(-1.18474 - 6.71899i) q^{34} +(-2.29256 - 1.92369i) q^{36} +0.202139i q^{37} +(-0.270521 - 4.35050i) q^{38} +0.258636 q^{39} +(5.41537 - 1.97103i) q^{41} +(-0.154595 + 0.0272592i) q^{42} +(2.07131 + 0.365228i) q^{43} +(2.27451 + 0.827855i) q^{44} +(-4.01363 + 6.95180i) q^{46} +(-6.32214 - 7.53443i) q^{47} +(-0.0548174 - 0.0653289i) q^{48} +(-1.80585 + 3.12782i) q^{49} +(0.546751 + 0.199001i) q^{51} +(-2.98668 - 0.526632i) q^{52} +(-6.17705 + 1.08918i) q^{53} +(0.480244 - 0.174794i) q^{54} +1.84074 q^{56} +(0.332843 + 0.165527i) q^{57} -10.1536i q^{58} +(4.62264 + 3.87886i) q^{59} +(0.741860 + 4.20730i) q^{61} +(-4.76376 - 0.839980i) q^{62} +(-1.88413 + 5.17660i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.158128 + 0.132685i) q^{66} +(-2.00596 - 2.39061i) q^{67} +(-5.90858 - 3.41132i) q^{68} +(-0.342285 - 0.592856i) q^{69} +(-1.94076 + 11.0066i) q^{71} +(-2.94726 + 0.519682i) q^{72} +(2.67059 + 7.33739i) q^{73} +(0.154847 + 0.129932i) q^{74} +(-3.50656 - 2.58921i) q^{76} -4.45548i q^{77} +(0.166248 - 0.198126i) q^{78} +(9.87176 - 3.59303i) q^{79} +(1.55148 - 8.79886i) q^{81} +(1.97103 - 5.41537i) q^{82} +(11.0455 - 6.37710i) q^{83} +(-0.0784897 + 0.135948i) q^{84} +(1.61119 - 1.35195i) q^{86} +(0.749896 + 0.432953i) q^{87} +(2.09620 - 1.21024i) q^{88} +(1.21570 + 0.442480i) q^{89} +(0.969391 + 5.49769i) q^{91} +(2.74548 + 7.54315i) q^{92} +(0.265166 - 0.316012i) q^{93} -9.83551 q^{94} -0.0852808 q^{96} +(-5.27159 + 6.28244i) q^{97} +(1.23527 + 3.39388i) q^{98} +(1.25788 + 7.13381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.0291678	+	0.0801377i	0.0168400	+	0.0462676i	0.947828	−	0.318783i	$-0.103274\pi$
$3$	0.0291678	+	0.0801377i	0.0168400	+	0.0462676i	−0.930988	+	0.365050i	$0.881052\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	0.0801377	+	0.0291678i	0.0327161	+	0.0119077i
$7$	−1.59412	+	0.920368i	−0.602522	+	0.347866i	−0.770033	−	0.638004i	$-0.779760\pi$
$7$	−1.59412	+	0.920368i	−0.602522	+	0.347866i	0.167511	+	0.985870i	$0.446427\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	2.29256	−	1.92369i	0.764187	−	0.641229i
$10$		0			0
$11$	−1.21024	+	2.09620i	−0.364902	+	0.632029i	−0.988760	−	0.149509i	$-0.952231\pi$
$11$	−1.21024	+	2.09620i	−0.364902	+	0.632029i	0.623858	+	0.781537i	$0.285564\pi$
$12$	0.0738553	−	0.0426404i	0.0213202	−	0.0123092i
$13$	1.03726	−	2.84986i	0.287685	−	0.790408i	−0.708704	−	0.705506i	$-0.750720\pi$
$13$	1.03726	−	2.84986i	0.287685	−	0.790408i	0.996389	−	0.0849022i	$-0.0270578\pi$
$14$	−0.319640	+	1.81277i	−0.0854275	+	0.484483i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	4.38551	−	5.22645i	1.06364	−	1.26760i	0.101564	−	0.994829i	$-0.467615\pi$
$17$	4.38551	−	5.22645i	1.06364	−	1.26760i	0.962079	−	0.272771i	$-0.0879401\pi$
$18$		−	2.99273i		−	0.705393i
$19$	3.15879	−	3.00368i	0.724675	−	0.689091i
$19$	3.15879	−	3.00368i	0.724675	−	0.689091i
$20$		0			0
$21$	−0.120253	−	0.100904i	−0.0262414	−	0.0220192i
$22$	0.827855	+	2.27451i	0.176499	+	0.484928i
$23$	−7.90530	+	1.39392i	−1.64837	+	0.290652i	−0.919232	−	0.393716i	$-0.871189\pi$
$23$	−7.90530	+	1.39392i	−1.64837	+	0.290652i	−0.729137	+	0.684368i	$0.760078\pi$
$24$	0.0148089	−	0.0839852i	0.00302285	−	0.0171434i
$25$		0			0
$26$	−1.51638	−	2.62644i	−0.297386	−	0.515087i
$27$	0.442595	+	0.255532i	0.0851774	+	0.0491772i
$28$	1.18320	+	1.41009i	0.223604	+	0.266481i
$29$	7.77809	−	6.52659i	1.44436	−	1.21196i	0.507782	−	0.861486i	$-0.330466\pi$
$29$	7.77809	−	6.52659i	1.44436	−	1.21196i	0.936573	−	0.350472i	$-0.113979\pi$
$30$		0			0
$31$	−2.41863	−	4.18918i	−0.434398	−	0.752400i	0.562848	−	0.826560i	$-0.309706\pi$
$31$	−2.41863	−	4.18918i	−0.434398	−	0.752400i	−0.997246	+	0.0741606i	$0.976372\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.203285	−	0.0358446i	−0.0353874	−	0.00623975i
$34$	−1.18474	−	6.71899i	−0.203181	−	1.15230i
$35$		0			0
$36$	−2.29256	−	1.92369i	−0.382094	−	0.320615i
$37$			0.202139i			0.0332314i	0.999862	+	0.0166157i	$0.00528919\pi$
$37$			0.202139i			0.0332314i	−0.999862	+	0.0166157i	$0.994711\pi$
$38$	−0.270521	−	4.35050i	−0.0438843	−	0.705744i
$39$	0.258636			0.0414148
$40$		0			0
$41$	5.41537	−	1.97103i	0.845739	−	0.307824i	0.117437	−	0.993080i	$-0.462532\pi$
$41$	5.41537	−	1.97103i	0.845739	−	0.307824i	0.728302	+	0.685257i	$0.240310\pi$
$42$	−0.154595	+	0.0272592i	−0.0238545	+	0.00420619i
$43$	2.07131	+	0.365228i	0.315872	+	0.0556967i	0.329336	−	0.944213i	$-0.393175\pi$
$43$	2.07131	+	0.365228i	0.315872	+	0.0556967i	−0.0134647	+	0.999909i	$0.504286\pi$
$44$	2.27451	+	0.827855i	0.342896	+	0.124804i
$45$		0			0
$46$	−4.01363	+	6.95180i	−0.591777	+	1.02499i
$47$	−6.32214	−	7.53443i	−0.922179	−	1.09901i	−0.994820	−	0.101652i	$-0.967587\pi$
$47$	−6.32214	−	7.53443i	−0.922179	−	1.09901i	0.0726409	−	0.997358i	$-0.476857\pi$
$48$	−0.0548174	−	0.0653289i	−0.00791222	−	0.00942941i
$49$	−1.80585	+	3.12782i	−0.257978	+	0.446831i
$50$		0			0
$51$	0.546751	+	0.199001i	0.0765605	+	0.0278657i
$52$	−2.98668	−	0.526632i	−0.414178	−	0.0730307i
$53$	−6.17705	+	1.08918i	−0.848483	+	0.149610i	−0.580951	−	0.813939i	$-0.697319\pi$
$53$	−6.17705	+	1.08918i	−0.848483	+	0.149610i	−0.267532	+	0.963549i	$0.586208\pi$
$54$	0.480244	−	0.174794i	0.0653529	−	0.0237865i
$55$		0			0
$56$	1.84074			0.245979
$57$	0.332843	+	0.165527i	0.0440861	+	0.0219247i
$58$		−	10.1536i		−	1.33323i
$59$	4.62264	+	3.87886i	0.601817	+	0.504984i	0.892029	−	0.451978i	$-0.149281\pi$
$59$	4.62264	+	3.87886i	0.601817	+	0.504984i	−0.290212	+	0.956962i	$0.593726\pi$
$60$		0			0
$61$	0.741860	+	4.20730i	0.0949854	+	0.538689i	0.994752	+	0.102317i	$0.0326257\pi$
$61$	0.741860	+	4.20730i	0.0949854	+	0.538689i	−0.899766	+	0.436372i	$0.856263\pi$
$62$	−4.76376	−	0.839980i	−0.604999	−	0.106678i
$63$	−1.88413	+	5.17660i	−0.237378	+	0.652190i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−0.158128	+	0.132685i	−0.0194642	+	0.0163324i
$67$	−2.00596	−	2.39061i	−0.245067	−	0.292059i	0.629463	−	0.777030i	$-0.283275\pi$
$67$	−2.00596	−	2.39061i	−0.245067	−	0.292059i	−0.874530	+	0.484971i	$0.838830\pi$
$68$	−5.90858	−	3.41132i	−0.716521	−	0.413684i
$69$	−0.342285	−	0.592856i	−0.0412063	−	0.0713714i
$70$		0			0
$71$	−1.94076	+	11.0066i	−0.230326	+	1.30625i	0.621910	+	0.783089i	$0.286357\pi$
$71$	−1.94076	+	11.0066i	−0.230326	+	1.30625i	−0.852237	+	0.523157i	$0.824754\pi$
$72$	−2.94726	+	0.519682i	−0.347338	+	0.0612451i
$73$	2.67059	+	7.33739i	0.312569	+	0.858777i	0.992136	+	0.125163i	$0.0399455\pi$
$73$	2.67059	+	7.33739i	0.312569	+	0.858777i	−0.679567	+	0.733613i	$0.737832\pi$
$74$	0.154847	+	0.129932i	0.0180006	+	0.0151043i
$75$		0			0
$76$	−3.50656	−	2.58921i	−0.402230	−	0.297003i
$77$		−	4.45548i		−	0.507749i
$78$	0.166248	−	0.198126i	0.0188239	−	0.0224334i
$79$	9.87176	−	3.59303i	1.11066	−	0.404247i	0.279425	−	0.960168i	$-0.409856\pi$
$79$	9.87176	−	3.59303i	1.11066	−	0.404247i	0.831236	+	0.555920i	$0.187634\pi$
$80$		0			0
$81$	1.55148	−	8.79886i	0.172386	−	0.977651i
$82$	1.97103	−	5.41537i	0.217664	−	0.598028i
$83$	11.0455	−	6.37710i	1.21240	−	0.699978i	0.249116	−	0.968474i	$-0.419860\pi$
$83$	11.0455	−	6.37710i	1.21240	−	0.699978i	0.963281	+	0.268496i	$0.0865266\pi$
$84$	−0.0784897	+	0.135948i	−0.00856393	+	0.0148332i
$85$		0			0
$86$	1.61119	−	1.35195i	0.173739	−	0.145785i
$87$	0.749896	+	0.432953i	0.0803973	+	0.0464174i
$88$	2.09620	−	1.21024i	0.223456	−	0.129012i
$89$	1.21570	+	0.442480i	0.128864	+	0.0469028i	0.405647	−	0.914030i	$-0.367046\pi$
$89$	1.21570	+	0.442480i	0.128864	+	0.0469028i	−0.276783	+	0.960932i	$0.589268\pi$
$90$		0			0
$91$	0.969391	+	5.49769i	0.101620	+	0.576314i
$92$	2.74548	+	7.54315i	0.286236	+	0.786428i
$93$	0.265166	−	0.316012i	0.0274964	−	0.0327690i
$94$	−9.83551			−1.01445
$95$		0			0
$96$	−0.0852808			−0.00870394
$97$	−5.27159	+	6.28244i	−0.535249	+	0.637885i	−0.964116	−	0.265483i	$-0.914469\pi$
$97$	−5.27159	+	6.28244i	−0.535249	+	0.637885i	0.428866	+	0.903368i	$0.358913\pi$
$98$	1.23527	+	3.39388i	0.124781	+	0.342834i
$99$	1.25788	+	7.13381i	0.126422	+	0.716974i
$100$		0			0
$101$	−7.51370	−	2.73476i	−0.747641	−	0.272119i	−0.0600281	−	0.998197i	$-0.519119\pi$
$101$	−7.51370	−	2.73476i	−0.747641	−	0.272119i	−0.687613	+	0.726078i	$0.741341\pi$
$102$	0.503889	−	0.290920i	0.0498924	−	0.0288054i
$103$	−2.93896	−	1.69681i	−0.289584	−	0.167192i	0.348170	−	0.937431i	$-0.386803\pi$
$103$	−2.93896	−	1.69681i	−0.289584	−	0.167192i	−0.637754	+	0.770240i	$0.720137\pi$
$104$	−2.32322	+	1.94942i	−0.227811	+	0.191156i
$105$		0			0
$106$	−3.13617	+	5.43200i	−0.304612	+	0.527603i
$107$	−9.98827	+	5.76673i	−0.965603	+	0.557491i	−0.897893	−	0.440214i	$-0.854903\pi$
$107$	−9.98827	+	5.76673i	−0.965603	+	0.557491i	−0.0677099	+	0.997705i	$0.521569\pi$
$108$	0.174794	−	0.480244i	0.0168196	−	0.0462115i
$109$	1.87490	−	10.6331i	0.179583	−	1.01847i	−0.753136	−	0.657865i	$-0.771460\pi$
$109$	1.87490	−	10.6331i	0.179583	−	1.01847i	0.932719	−	0.360603i	$-0.117429\pi$
$110$		0			0
$111$	−0.0161990	+	0.00589594i	−0.00153754	+	0.000559618i
$112$	1.18320	−	1.41009i	0.111802	−	0.133241i
$113$			11.9087i			1.12028i	0.828399	+	0.560139i	$0.189252\pi$
$113$			11.9087i			1.12028i	−0.828399	+	0.560139i	$0.810748\pi$
$114$	0.340748	−	0.148573i	0.0319140	−	0.0139152i
$115$		0			0
$116$	−7.77809	−	6.52659i	−0.722178	−	0.605979i
$117$	−3.10424	−	8.52884i	−0.286987	−	0.788492i
$118$	5.94276	−	1.04787i	0.547075	−	0.0964641i
$119$	−2.18079	+	12.3679i	−0.199913	+	1.13376i
$120$		0			0
$121$	2.57062	+	4.45245i	0.233693	+	0.404768i
$122$	3.69983	+	2.13610i	0.334967	+	0.193393i
$123$	0.315908	+	0.376485i	0.0284845	+	0.0339465i
$124$	−3.70555	+	3.10933i	−0.332768	+	0.279226i
$125$		0			0
$126$	2.75441	+	4.77078i	0.245382	+	0.425015i
$127$	1.63606	−	4.49504i	0.145177	−	0.398870i	−0.845697	−	0.533664i	$-0.820815\pi$
$127$	1.63606	−	4.49504i	0.145177	−	0.398870i	0.990874	+	0.134793i	$0.0430371\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	0.0311469	+	0.176643i	0.00274233	+	0.0155525i
$130$		0			0
$131$	9.90820	+	8.31396i	0.865683	+	0.726394i	0.963185	−	0.268841i	$-0.0866406\pi$
$131$	9.90820	+	8.31396i	0.865683	+	0.726394i	−0.0975015	+	0.995235i	$0.531085\pi$
$132$			0.206421i			0.0179666i
$133$	−2.27101	+	7.69548i	−0.196921	+	0.667283i
$134$	−3.12072			−0.269589
$135$		0			0
$136$	−6.41119	+	2.33348i	−0.549755	+	0.200094i
$137$	2.60990	−	0.460196i	0.222979	−	0.0393172i	−0.0610423	−	0.998135i	$-0.519442\pi$
$137$	2.60990	−	0.460196i	0.222979	−	0.0393172i	0.284021	+	0.958818i	$0.408331\pi$
$138$	−0.674170	−	0.118874i	−0.0573892	−	0.0101193i
$139$	−10.8366	−	3.94420i	−0.919149	−	0.334543i	−0.161249	−	0.986914i	$-0.551552\pi$
$139$	−10.8366	−	3.94420i	−0.919149	−	0.334543i	−0.757900	+	0.652371i	$0.773775\pi$
$140$		0			0
$141$	0.419390	−	0.726405i	0.0353190	−	0.0611743i
$142$	7.18406	+	8.56163i	0.602873	+	0.718476i
$143$	4.71854	+	5.62333i	0.394584	+	0.470247i
$144$	−1.49636	+	2.59178i	−0.124697	+	0.215981i
$145$		0			0
$146$	7.33739	+	2.67059i	0.607247	+	0.221020i
$147$	−0.303329	−	0.0534850i	−0.0250181	−	0.00441137i
$148$	0.199068	−	0.0351010i	0.0163633	−	0.00288529i
$149$	−11.4325	+	4.16108i	−0.936585	+	0.340889i	−0.764817	−	0.644248i	$-0.777170\pi$
$149$	−11.4325	+	4.16108i	−0.936585	+	0.340889i	−0.171769	+	0.985137i	$0.554948\pi$
$150$		0			0
$151$	17.4621			1.42104			0.710521	−	0.703676i	$-0.248459\pi$
$151$	17.4621			1.42104			0.710521	+	0.703676i	$0.248459\pi$
$152$	−4.23743	+	1.02187i	−0.343701	+	0.0828844i
$153$		−	20.4183i		−	1.65072i
$154$	−3.41309	−	2.86393i	−0.275035	−	0.230782i
$155$		0			0
$156$	−0.0449116	−	0.254706i	−0.00359581	−	0.0203928i
$157$	22.1099	+	3.89857i	1.76456	+	0.311140i	0.959428	−	0.281952i	$-0.0909820\pi$
$157$	22.1099	+	3.89857i	1.76456	+	0.311140i	0.805134	+	0.593092i	$0.202093\pi$
$158$	3.59303	−	9.87176i	0.285846	−	0.785355i
$159$	−0.267455	−	0.463246i	−0.0212106	−	0.0367378i
$160$		0			0
$161$	11.3191	−	9.49786i	0.892071	−	0.748536i
$162$	−5.74305	−	6.84430i	−0.451217	−	0.537739i
$163$	8.23440	+	4.75414i	0.644968	+	0.372373i	0.786526	−	0.617557i	$-0.211878\pi$
$163$	8.23440	+	4.75414i	0.644968	+	0.372373i	−0.141558	+	0.989930i	$0.545211\pi$
$164$	−2.88146	−	4.99083i	−0.225004	−	0.389719i
$165$		0			0
$166$	2.21474	−	12.5604i	0.171897	−	0.974879i
$167$	0.270127	−	0.0476307i	0.0209030	−	0.00368577i	−0.163187	−	0.986595i	$-0.552177\pi$
$167$	0.270127	−	0.0476307i	0.0209030	−	0.00368577i	0.184090	+	0.982909i	$0.441066\pi$
$168$	0.0536901	+	0.147512i	0.00414228	+	0.0113808i
$169$	2.91281	+	2.44414i	0.224063	+	0.188011i
$170$		0			0
$171$	1.46358	−	12.9626i	0.111922	−	0.991277i
$172$		−	2.10326i		−	0.160372i
$173$	−7.51380	+	8.95459i	−0.571263	+	0.680805i	−0.971890	−	0.235436i	$-0.924348\pi$
$173$	−7.51380	+	8.95459i	−0.571263	+	0.680805i	0.400626	+	0.916241i	$0.368793\pi$
$174$	0.813685	−	0.296157i	0.0616853	−	0.0224516i
$175$		0			0
$176$	0.420313	−	2.38371i	0.0316823	−	0.179679i
$177$	−0.176011	+	0.483586i	−0.0132298	+	0.0363485i
$178$	1.12040	−	0.646862i	0.0839774	−	0.0484844i
$179$	−8.22436	+	14.2450i	−0.614718	+	1.06472i	0.375716	+	0.926735i	$0.377397\pi$
$179$	−8.22436	+	14.2450i	−0.614718	+	1.06472i	−0.990434	+	0.137987i	$0.955937\pi$
$180$		0			0
$181$	−16.8188	+	14.1126i	−1.25013	+	1.04898i	−0.253466	+	0.967344i	$0.581571\pi$
$181$	−16.8188	+	14.1126i	−1.25013	+	1.04898i	−0.996662	+	0.0816380i	$0.973985\pi$
$182$	4.83458	+	2.79125i	0.358363	+	0.206901i
$183$	−0.315525	+	0.182168i	−0.0233243	+	0.0134663i
$184$	7.54315	+	2.74548i	0.556088	+	0.202400i
$185$		0			0
$186$	−0.0716342	−	0.406258i	−0.00525247	−	0.0297883i
$187$	5.64816	+	15.5182i	0.413034	+	1.13480i
$188$	−6.32214	+	7.53443i	−0.461090	+	0.549505i
$189$	−0.940735			−0.0684284
$190$		0			0
$191$	−4.84898			−0.350860			−0.175430	−	0.984492i	$-0.556132\pi$
$191$	−4.84898			−0.350860			−0.175430	+	0.984492i	$0.556132\pi$
$192$	−0.0548174	+	0.0653289i	−0.00395611	+	0.00471471i
$193$	3.36334	+	9.24069i	0.242098	+	0.665160i	0.999919	+	0.0126972i	$0.00404176\pi$
$193$	3.36334	+	9.24069i	0.242098	+	0.665160i	−0.757821	+	0.652462i	$0.773736\pi$
$194$	1.42411	+	8.07655i	0.102245	+	0.579862i
$195$		0			0
$196$	3.39388	+	1.23527i	0.242420	+	0.0882336i
$197$	8.49304	−	4.90346i	0.605104	−	0.349357i	−0.165943	−	0.986135i	$-0.553067\pi$
$197$	8.49304	−	4.90346i	0.605104	−	0.349357i	0.771047	+	0.636778i	$0.219733\pi$
$198$	6.27336	+	3.62193i	0.445828	+	0.257399i
$199$	−1.06106	+	0.890332i	−0.0752163	+	0.0631140i	−0.679621	−	0.733564i	$-0.737856\pi$
$199$	−1.06106	+	0.890332i	−0.0752163	+	0.0631140i	0.604404	+	0.796678i	$0.293411\pi$
$200$		0			0
$201$	0.133069	−	0.230482i	0.00938594	−	0.0162569i
$202$	−6.92466	+	3.99795i	−0.487217	+	0.281295i
$203$	−6.39237	+	17.5629i	−0.448657	+	1.23267i
$204$	0.101036	−	0.573001i	0.00707390	−	0.0401181i
$205$		0			0
$206$	−3.18896	+	1.16069i	−0.222185	+	0.0808689i
$207$	−15.4419	+	18.4030i	−1.07329	+	1.27910i
$208$			3.03275i			0.210284i
$209$	2.47342	+	10.2566i	0.171090	+	0.709466i
$210$		0			0
$211$	−3.62200	−	3.03922i	−0.249349	−	0.209229i	0.509543	−	0.860445i	$-0.329815\pi$
$211$	−3.62200	−	3.03922i	−0.249349	−	0.209229i	−0.758892	+	0.651217i	$0.774259\pi$
$212$	2.14527	+	5.89407i	0.147337	+	0.404806i
$213$	−0.938653	+	0.165510i	−0.0643155	+	0.0113406i
$214$	−2.00277	+	11.3582i	−0.136906	+	0.776434i
$215$		0			0
$216$	−0.255532	−	0.442595i	−0.0173868	−	0.0301148i
$217$	7.71118	+	4.45205i	0.523469	+	0.302225i
$218$	−6.94027	−	8.27109i	−0.470054	−	0.560189i
$219$	−0.510107	+	0.428031i	−0.0344698	+	0.0289236i
$220$		0			0
$221$	−10.3457	−	17.9193i	−0.695927	−	1.20538i
$222$	−0.00589594	+	0.0161990i	−0.000395709	+	0.00108720i
$223$	25.5051	+	4.49724i	1.70795	+	0.301157i	0.940459	−	0.339906i	$-0.110395\pi$
$223$	25.5051	+	4.49724i	1.70795	+	0.301157i	0.767488	+	0.641064i	$0.221506\pi$
$224$	−0.319640	−	1.81277i	−0.0213569	−	0.121121i
$225$		0			0
$226$	9.12261	+	7.65478i	0.606827	+	0.509188i
$227$		−	11.0277i		−	0.731932i	−0.930628	−	0.365966i	$-0.880739\pi$
$227$		−	11.0277i		−	0.731932i	0.930628	−	0.365966i	$-0.119261\pi$
$228$	0.105215	−	0.356529i	0.00696805	−	0.0236117i
$229$	−24.1631			−1.59674			−0.798370	−	0.602167i	$-0.794304\pi$
$229$	−24.1631			−1.59674			−0.798370	+	0.602167i	$0.794304\pi$
$230$		0			0
$231$	0.357052	−	0.129956i	0.0234923	−	0.00855049i
$232$	−9.99932	+	1.76315i	−0.656487	+	0.115756i
$233$	−19.5965	−	3.45540i	−1.28381	−	0.226371i	−0.510214	−	0.860048i	$-0.670434\pi$
$233$	−19.5965	−	3.45540i	−1.28381	−	0.226371i	−0.773598	+	0.633677i	$0.781545\pi$
$234$	−8.52884	−	3.10424i	−0.557548	−	0.202931i
$235$		0			0
$236$	3.01722	−	5.22597i	0.196404	−	0.340182i
$237$	0.575874	+	0.686300i	0.0374071	+	0.0445800i
$238$	8.07257	+	9.62051i	0.523267	+	0.623605i
$239$	9.00250	−	15.5928i	0.582323	−	1.00861i	−0.412880	−	0.910785i	$-0.635477\pi$
$239$	9.00250	−	15.5928i	0.582323	−	1.00861i	0.995203	−	0.0978282i	$-0.0311896\pi$
$240$		0			0
$241$	8.30146	+	3.02148i	0.534744	+	0.194631i	0.595255	−	0.803537i	$-0.297051\pi$
$241$	8.30146	+	3.02148i	0.534744	+	0.194631i	−0.0605114	+	0.998168i	$0.519273\pi$
$242$	5.06314	+	0.892768i	0.325471	+	0.0573893i
$243$	2.26028	−	0.398548i	0.144997	−	0.0255668i
$244$	4.01456	−	1.46118i	0.257006	−	0.0935424i
$245$		0			0
$246$	0.491466			0.0313347
$247$	−5.28355	−	12.1177i	−0.336184	−	0.771030i
$248$			4.83725i			0.307166i
$249$	0.833218	+	0.699153i	0.0528030	+	0.0443070i
$250$		0			0
$251$	−2.48052	−	14.0677i	−0.156569	−	0.887948i	−0.957337	−	0.288973i	$-0.906686\pi$
$251$	−2.48052	−	14.0677i	−0.156569	−	0.887948i	0.800768	−	0.598975i	$-0.204425\pi$
$252$	5.42513	+	0.956597i	0.341751	+	0.0602599i
$253$	6.64540	−	18.2581i	0.417793	−	1.14788i
$254$	−2.39176	−	4.14265i	−0.150072	−	0.259933i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	18.8261	+	22.4360i	1.17434	+	1.39952i	0.898873	+	0.438210i	$0.144387\pi$
$257$	18.8261	+	22.4360i	1.17434	+	1.39952i	0.275465	+	0.961311i	$0.411168\pi$
$258$	0.155337	+	0.0896840i	0.00967087	+	0.00558348i
$259$	−0.186042	−	0.322234i	−0.0115601	−	0.0200227i
$260$		0			0
$261$	5.27663	−	29.9252i	0.326615	−	1.85233i
$262$	12.7377	−	2.24601i	0.786940	−	0.138759i
$263$	0.00505025	+	0.0138755i	0.000311412	+	0.000855598i	0.939848	−	0.341592i	$-0.110966\pi$
$263$	0.00505025	+	0.0138755i	0.000311412	+	0.000855598i	−0.939537	+	0.342448i	$0.888744\pi$
$264$	0.158128	+	0.132685i	0.00973209	+	0.00816619i
$265$		0			0
$266$	4.43530	+	6.68625i	0.271946	+	0.409960i
$267$			0.110330i			0.00675208i
$268$	−2.00596	+	2.39061i	−0.122533	+	0.146030i
$269$	−11.7330	+	4.27045i	−0.715371	+	0.260374i	−0.673959	−	0.738768i	$-0.735408\pi$
$269$	−11.7330	+	4.27045i	−0.715371	+	0.260374i	−0.0414116	+	0.999142i	$0.513185\pi$
$270$		0			0
$271$	−0.0730874	+	0.414500i	−0.00443975	+	0.0251791i	−0.986947	−	0.161044i	$-0.948514\pi$
$271$	−0.0730874	+	0.414500i	−0.00443975	+	0.0251791i	0.982507	+	0.186224i	$0.0596249\pi$
$272$	−2.33348	+	6.41119i	−0.141488	+	0.388735i
$273$	−0.412297	+	0.238040i	−0.0249534	+	0.0144068i
$274$	1.32508	−	2.29511i	0.0800511	−	0.138653i
$275$		0			0
$276$	−0.524412	+	0.440033i	−0.0315659	+	0.0264869i
$277$	26.4810	+	15.2888i	1.59109	+	0.918616i	0.993120	+	0.117098i	$0.0373590\pi$
$277$	26.4810	+	15.2888i	1.59109	+	0.918616i	0.597970	+	0.801519i	$0.295974\pi$
$278$	−9.98707	+	5.76604i	−0.598985	+	0.345824i
$279$	−13.6035	−	4.95128i	−0.814422	−	0.296425i
$280$		0			0
$281$	1.92284	+	10.9050i	0.114707	+	0.650537i	0.986895	+	0.161365i	$0.0515897\pi$
$281$	1.92284	+	10.9050i	0.114707	+	0.650537i	−0.872188	+	0.489172i	$0.837299\pi$
$282$	−0.286880	−	0.788195i	−0.0170834	−	0.0469363i
$283$	0.512672	−	0.610978i	0.0304752	−	0.0363189i	−0.750592	−	0.660766i	$-0.770231\pi$
$283$	0.512672	−	0.610978i	0.0304752	−	0.0363189i	0.781067	+	0.624448i	$0.214676\pi$
$284$	11.1764			0.663198
$285$		0			0
$286$	7.34074			0.434067
$287$	−6.81870	+	8.12621i	−0.402495	+	0.479675i
$288$	1.02357	+	2.81224i	0.0603146	+	0.165713i
$289$	−5.13104	−	29.0996i	−0.301826	−	1.71174i
$290$		0			0
$291$	−0.657221	−	0.239209i	−0.0385270	−	0.0140227i
$292$	6.76218	−	3.90414i	0.395726	−	0.228473i
$293$	−11.8981	−	6.86939i	−0.695096	−	0.401314i	0.110422	−	0.993885i	$-0.464780\pi$
$293$	−11.8981	−	6.86939i	−0.695096	−	0.401314i	−0.805518	+	0.592571i	$0.798113\pi$
$294$	−0.235948	+	0.197984i	−0.0137608	+	0.0115466i
$295$		0			0
$296$	0.101069	−	0.175057i	0.00587454	−	0.0101750i
$297$	−1.07130	+	0.618513i	−0.0621628	+	0.0358897i
$298$	−4.16108	+	11.4325i	−0.241045	+	0.662266i
$299$	−4.22741	+	23.9748i	−0.244477	+	1.38650i
$300$		0			0
$301$	−3.63807	+	1.32415i	−0.209695	+	0.0763226i
$302$	11.2244	−	13.3767i	0.645892	−	0.769744i
$303$		−	0.681898i		−	0.0391740i
$304$	−1.94097	+	3.90290i	−0.111322	+	0.223847i
$305$		0			0
$306$	−15.6413	−	13.1246i	−0.894156	−	0.750286i
$307$	0.227465	+	0.624954i	0.0129821	+	0.0356680i	0.946014	−	0.324125i	$-0.105070\pi$
$307$	0.227465	+	0.624954i	0.0129821	+	0.0356680i	−0.933032	+	0.359793i	$0.882847\pi$
$308$	−4.38779	+	0.773685i	−0.250017	+	0.0440848i
$309$	0.0502556	−	0.285014i	0.00285894	−	0.0162139i
$310$		0			0
$311$	14.2653	+	24.7083i	0.808913	+	1.40108i	0.913617	+	0.406576i	$0.133277\pi$
$311$	14.2653	+	24.7083i	0.808913	+	1.40108i	−0.104704	+	0.994503i	$0.533389\pi$
$312$	−0.223985	−	0.129318i	−0.0126807	−	0.00732118i
$313$	6.42248	+	7.65401i	0.363020	+	0.432630i	0.916379	−	0.400313i	$-0.131099\pi$
$313$	6.42248	+	7.65401i	0.363020	+	0.432630i	−0.553359	+	0.832943i	$0.686654\pi$
$314$	17.1985	−	14.4312i	0.970565	−	0.814401i
$315$		0			0
$316$	−5.25266	−	9.09787i	−0.295485	−	0.511795i
$317$	3.97837	−	10.9305i	0.223448	−	0.613918i	−0.776419	−	0.630217i	$-0.782966\pi$
$317$	3.97837	−	10.9305i	0.223448	−	0.613918i	0.999867	+	0.0162989i	$0.00518832\pi$
$318$	−0.526784	−	0.0928861i	−0.0295406	−	0.00520880i
$319$	4.26768	+	24.2032i	0.238944	+	1.35512i
$320$		0			0
$321$	−0.753468	−	0.632235i	−0.0420545	−	0.0352879i
$322$		−	14.7761i		−	0.823437i
$323$	−1.84567	−	29.6819i	−0.102696	−	1.65154i
$324$	−8.93460			−0.496367
$325$		0			0
$326$	8.93485	−	3.25202i	0.494856	−	0.180113i
$327$	0.906800	−	0.159893i	0.0501462	−	0.00884212i
$328$	−5.67537	−	1.00072i	−0.313370	−	0.0552555i
$329$	17.0127	+	6.19213i	0.937942	+	0.341383i
$330$		0			0
$331$	−12.5884	+	21.8037i	−0.691919	+	1.19844i	0.279290	+	0.960207i	$0.409901\pi$
$331$	−12.5884	+	21.8037i	−0.691919	+	1.19844i	−0.971208	+	0.238231i	$0.923432\pi$
$332$	−8.19824	−	9.77028i	−0.449937	−	0.536214i
$333$	0.388852	+	0.463416i	0.0213090	+	0.0253950i
$334$	0.137147	−	0.237546i	0.00750435	−	0.0129979i
$335$		0			0
$336$	0.147512	+	0.0536901i	0.00804746	+	0.00292904i
$337$	1.39253	+	0.245540i	0.0758559	+	0.0133754i	0.211447	−	0.977389i	$-0.432182\pi$
$337$	1.39253	+	0.245540i	0.0758559	+	0.0133754i	−0.135591	+	0.990765i	$0.543293\pi$
$338$	3.74464	−	0.660281i	0.203682	−	0.0359146i
$339$	−0.954338	+	0.347351i	−0.0518325	+	0.0188655i
$340$		0			0
$341$	11.7085			0.634051
$342$	−8.98918	−	9.45338i	−0.486079	−	0.511180i
$343$		−	19.5333i		−	1.05470i
$344$	−1.61119	−	1.35195i	−0.0868697	−	0.0728923i
$345$		0			0
$346$	2.02984	+	11.5118i	0.109125	+	0.618878i
$347$	−31.6406	−	5.57910i	−1.69856	−	0.299502i	−0.761368	−	0.648320i	$-0.775472\pi$
$347$	−31.6406	−	5.57910i	−1.69856	−	0.299502i	−0.937190	+	0.348818i	$0.886583\pi$
$348$	0.296157	−	0.813685i	0.0158757	−	0.0436181i
$349$	−0.908473	−	1.57352i	−0.0486295	−	0.0842287i	0.840686	−	0.541523i	$-0.182152\pi$
$349$	−0.908473	−	1.57352i	−0.0486295	−	0.0842287i	−0.889316	+	0.457294i	$0.848819\pi$
$350$		0			0
$351$	1.18732	−	0.996278i	0.0633743	−	0.0531774i
$352$	−1.55586	−	1.85420i	−0.0829275	−	0.0988292i
$353$	23.4104	+	13.5160i	1.24601	+	0.719385i	0.970311	−	0.241859i	$-0.0777573\pi$
$353$	23.4104	+	13.5160i	1.24601	+	0.719385i	0.275699	+	0.961244i	$0.411091\pi$
$354$	0.257311	+	0.445675i	0.0136759	+	0.0236874i
$355$		0			0
$356$	0.224653	−	1.27407i	0.0119066	−	0.0675256i
$357$	−1.05474	+	0.185980i	−0.0558230	+	0.00984309i
$358$	5.62579	+	15.4567i	0.297332	+	0.816914i
$359$	−17.9055	−	15.0245i	−0.945017	−	0.792963i	0.0334346	−	0.999441i	$-0.489355\pi$
$359$	−17.9055	−	15.0245i	−0.945017	−	0.792963i	−0.978451	+	0.206478i	$0.933800\pi$
$360$		0			0
$361$	0.955856	−	18.9759i	0.0503082	−	0.998734i
$362$			21.9553i			1.15395i
$363$	−0.281830	+	0.335872i	−0.0147922	+	0.0176287i
$364$	5.24583	−	1.90933i	0.274956	−	0.100076i
$365$		0			0
$366$	−0.0632664	+	0.358802i	−0.00330699	+	0.0187549i
$367$	−2.69561	+	7.40612i	−0.140710	+	0.386596i	−0.989951	−	0.141408i	$-0.954837\pi$
$367$	−2.69561	+	7.40612i	−0.140710	+	0.386596i	0.849242	+	0.528004i	$0.177059\pi$
$368$	6.95180	−	4.01363i	0.362388	−	0.209225i
$369$	8.62342	−	14.9362i	0.448917	−	0.777548i
$370$		0			0
$371$	8.84453	−	7.42144i	0.459185	−	0.385302i
$372$	−0.357257	−	0.206262i	−0.0185229	−	0.0106942i
$373$	11.8758	−	6.85652i	0.614907	−	0.355017i	−0.159976	−	0.987121i	$-0.551142\pi$
$373$	11.8758	−	6.85652i	0.614907	−	0.355017i	0.774884	+	0.632104i	$0.217808\pi$
$374$	15.5182	+	5.64816i	0.802427	+	0.292059i
$375$		0			0
$376$	1.70792	+	9.68608i	0.0880791	+	0.499522i
$377$	−10.5319	−	28.9362i	−0.542422	−	1.49029i
$378$	−0.604693	+	0.720645i	−0.0311020	+	0.0370660i
$379$	14.9079			0.765766			0.382883	−	0.923797i	$-0.374931\pi$
$379$	14.9079			0.765766			0.382883	+	0.923797i	$0.374931\pi$
$380$		0			0
$381$	0.407942			0.0208995
$382$	−3.11686	+	3.71453i	−0.159473	+	0.190052i
$383$	−3.45380	−	9.48923i	−0.176481	−	0.484877i	0.819639	−	0.572880i	$-0.194174\pi$
$383$	−3.45380	−	9.48923i	−0.176481	−	0.484877i	−0.996120	+	0.0880027i	$0.971952\pi$
$384$	0.0148089	+	0.0839852i	0.000755711	+	0.00428585i
$385$		0			0
$386$	9.24069	+	3.36334i	0.470339	+	0.171189i
$387$	5.45119	−	3.14725i	0.277099	−	0.159983i
$388$	7.10240	+	4.10057i	0.360570	+	0.208175i
$389$	−4.69733	+	3.94153i	−0.238164	+	0.199844i	−0.754056	−	0.656810i	$-0.771905\pi$
$389$	−4.69733	+	3.94153i	−0.238164	+	0.199844i	0.515891	+	0.856654i	$0.327461\pi$
$390$		0			0
$391$	−27.3835	+	47.4297i	−1.38485	+	2.39862i
$392$	3.12782	−	1.80585i	0.157979	−	0.0912090i
$393$	−0.377262	+	1.03652i	−0.0190304	+	0.0522855i
$394$	1.70295	−	9.65793i	0.0857936	−	0.486560i
$395$		0			0
$396$	6.80700	−	2.47754i	0.342064	−	0.124501i
$397$	−1.00116	+	1.19313i	−0.0502467	+	0.0598817i	−0.790582	−	0.612356i	$-0.790222\pi$
$397$	−1.00116	+	1.19313i	−0.0502467	+	0.0598817i	0.740336	+	0.672237i	$0.234667\pi$
$398$			1.38511i			0.0694293i
$399$	−0.682939	+	0.0424663i	−0.0341897	+	0.00212597i
$400$		0			0
$401$	−27.4561	−	23.0384i	−1.37109	−	1.15048i	−0.972379	−	0.233409i	$-0.925012\pi$
$401$	−27.4561	−	23.0384i	−1.37109	−	1.15048i	−0.398715	−	0.917075i	$-0.630544\pi$
$402$	−0.0910244	−	0.250087i	−0.00453988	−	0.0124732i
$403$	−14.4473	+	2.54745i	−0.719672	+	0.126898i
$404$	−1.38847	+	7.87443i	−0.0690792	+	0.391768i
$405$		0			0
$406$	9.34503	+	16.1861i	0.463786	+	0.803301i
$407$	−0.423724	−	0.244637i	−0.0210032	−	0.0121262i
$408$	−0.374000	−	0.445716i	−0.0185158	−	0.0220662i
$409$	26.8662	−	22.5434i	1.32845	−	1.11470i	0.344013	−	0.938965i	$-0.388214\pi$
$409$	26.8662	−	22.5434i	1.32845	−	1.11470i	0.984437	−	0.175737i	$-0.0562307\pi$
$410$		0			0
$411$	0.113004	+	0.195729i	0.00557408	+	0.00965459i
$412$	−1.16069	+	3.18896i	−0.0571829	+	0.157109i
$413$	−10.9390	−	1.92885i	−0.538275	−	0.0949124i
$414$	4.17162	+	23.6584i	0.205024	+	1.16275i
$415$		0			0
$416$	2.32322	+	1.94942i	0.113905	+	0.0955780i
$417$		−	0.983465i		−	0.0481605i
$418$	9.44692	+	4.69809i	0.462064	+	0.229791i
$419$	−12.6047			−0.615780			−0.307890	−	0.951422i	$-0.599623\pi$
$419$	−12.6047			−0.615780			−0.307890	+	0.951422i	$0.599623\pi$
$420$		0			0
$421$	−25.0875	+	9.13109i	−1.22269	+	0.445022i	−0.871088	−	0.491128i	$-0.836585\pi$
$421$	−25.0875	+	9.13109i	−1.22269	+	0.445022i	−0.351601	+	0.936150i	$0.614363\pi$
$422$	−4.65636	+	0.821042i	−0.226668	+	0.0399677i
$423$	−28.9878	−	5.11133i	−1.40944	−	0.248521i
$424$	5.89407	+	2.14527i	0.286241	+	0.104183i
$425$		0			0
$426$	−0.476567	+	0.825438i	−0.0230897	+	0.0399926i
$427$	−5.05488	−	6.02417i	−0.244623	−	0.291530i
$428$	7.41357	+	8.83515i	0.358348	+	0.427063i
$429$	−0.313012	+	0.542153i	−0.0151124	+	0.0261754i
$430$		0			0
$431$	−7.61810	−	2.77276i	−0.366951	−	0.133559i	0.151962	−	0.988386i	$-0.451441\pi$
$431$	−7.61810	−	2.77276i	−0.366951	−	0.133559i	−0.518913	+	0.854827i	$0.673663\pi$
$432$	−0.503300	−	0.0887454i	−0.0242151	−	0.00426977i
$433$	−22.4924	+	3.96602i	−1.08092	+	0.190595i	−0.685620	−	0.727959i	$-0.740469\pi$
$433$	−22.4924	+	3.96602i	−1.08092	+	0.190595i	−0.395296	+	0.918554i	$0.629358\pi$
$434$	8.36712	−	3.04538i	0.401635	−	0.146183i
$435$		0			0
$436$	−10.7971			−0.517089
$437$	−20.7843	+	28.1481i	−0.994247	+	1.34650i
$438$			0.665897i			0.0318178i
$439$	10.8652	+	9.11699i	0.518568	+	0.435130i	0.864132	−	0.503265i	$-0.167868\pi$
$439$	10.8652	+	9.11699i	0.518568	+	0.435130i	−0.345564	+	0.938395i	$0.612312\pi$
$440$		0			0
$441$	1.87693	+	10.6446i	0.0893776	+	0.506886i
$442$	−20.3770	−	3.59302i	−0.969237	−	0.170903i
$443$	10.7687	−	29.5868i	0.511637	−	1.40571i	−0.367894	−	0.929868i	$-0.619921\pi$
$443$	10.7687	−	29.5868i	0.511637	−	1.40571i	0.879530	−	0.475843i	$-0.157857\pi$
$444$	0.00861928	+	0.0149290i	0.000409053	+	0.000708501i
$445$		0			0
$446$	19.8394	−	16.6473i	0.939425	−	0.788271i
$447$	−0.666920	−	0.794804i	−0.0315442	−	0.0375929i
$448$	−1.59412	−	0.920368i	−0.0753153	−	0.0434833i
$449$	−13.6115	−	23.5758i	−0.642366	−	1.11261i	−0.984903	−	0.173106i	$-0.944620\pi$
$449$	−13.6115	−	23.5758i	−0.642366	−	1.11261i	0.342537	−	0.939504i	$-0.388714\pi$
$450$		0			0
$451$	−2.42223	+	13.7371i	−0.114058	+	0.646857i
$452$	11.7278	−	2.06793i	0.551629	−	0.0972671i
$453$	0.509329	+	1.39937i	0.0239304	+	0.0657482i
$454$	−8.44769	−	7.08845i	−0.396470	−	0.332678i
$455$		0			0
$456$	−0.205486	−	0.309772i	−0.00962278	−	0.0145064i
$457$		−	27.4781i		−	1.28537i	−0.766129	−	0.642687i	$-0.777820\pi$
$457$		−	27.4781i		−	1.28537i	0.766129	−	0.642687i	$-0.222180\pi$
$458$	−15.5317	+	18.5100i	−0.725750	+	0.864915i
$459$	3.27653	−	1.19256i	0.152935	−	0.0556639i
$460$		0			0
$461$	0.982759	−	5.57350i	0.0457716	−	0.259584i	−0.953332	−	0.301925i	$-0.902371\pi$
$461$	0.982759	−	5.57350i	0.0457716	−	0.259584i	0.999103	+	0.0423415i	$0.0134817\pi$
$462$	0.129956	−	0.357052i	0.00604611	−	0.0166116i
$463$	19.1089	−	11.0325i	0.888067	−	0.512726i	0.0147575	−	0.999891i	$-0.495302\pi$
$463$	19.1089	−	11.0325i	0.888067	−	0.512726i	0.873310	+	0.487165i	$0.161969\pi$
$464$	−5.07679	+	8.79325i	−0.235684	+	0.408217i
$465$		0			0
$466$	−15.2434	+	12.7907i	−0.706137	+	0.592519i
$467$	−18.5055	−	10.6841i	−0.856331	−	0.494403i	0.00645068	−	0.999979i	$-0.497947\pi$
$467$	−18.5055	−	10.6841i	−0.856331	−	0.494403i	−0.862782	+	0.505576i	$0.831280\pi$
$468$	−7.86022	+	4.53810i	−0.363339	+	0.209774i
$469$	5.39799	+	1.96471i	0.249256	+	0.0907218i
$470$		0			0
$471$	0.332474	+	1.88555i	0.0153196	+	0.0868816i
$472$	−2.06390	−	5.67051i	−0.0949986	−	0.261006i
$473$	−3.27238	+	3.89987i	−0.150464	+	0.179316i
$474$	0.895901			0.0411501
$475$		0			0
$476$	12.5587			0.575626
$477$	−12.0660	+	14.3797i	−0.552465	+	0.658402i
$478$	−6.15807	−	16.9192i	−0.281664	−	0.773865i
$479$	3.34220	+	18.9545i	0.152709	+	0.866055i	0.960851	+	0.277067i	$0.0893625\pi$
$479$	3.34220	+	18.9545i	0.152709	+	0.866055i	−0.808142	+	0.588988i	$0.799526\pi$
$480$		0			0
$481$	0.576067	+	0.209671i	0.0262664	+	0.00956018i
$482$	7.65066	−	4.41711i	0.348478	−	0.201194i
$483$	1.09129	+	0.630057i	0.0496554	+	0.0286686i
$484$	3.93842	−	3.30473i	0.179019	−	0.150215i
$485$		0			0
$486$	1.14757	−	1.98765i	0.0520549	−	0.0901618i
$487$	−12.7443	+	7.35793i	−0.577500	+	0.333420i	−0.760139	−	0.649760i	$-0.774869\pi$
$487$	−12.7443	+	7.35793i	−0.577500	+	0.333420i	0.182639	+	0.983180i	$0.441536\pi$
$488$	1.46118	−	4.01456i	0.0661445	−	0.181730i
$489$	−0.140807	+	0.798554i	−0.00636750	+	0.0361119i
$490$		0			0
$491$	−37.0504	+	13.4853i	−1.67206	+	0.608581i	−0.992189	−	0.124748i	$-0.960188\pi$
$491$	−37.0504	+	13.4853i	−1.67206	+	0.608581i	−0.679874	+	0.733329i	$0.737966\pi$
$492$	0.315908	−	0.376485i	0.0142423	−	0.0169733i
$493$		−	69.2742i		−	3.11995i
$494$	−12.6789	−	3.74166i	−0.570450	−	0.168345i
$495$		0			0
$496$	3.70555	+	3.10933i	0.166384	+	0.139613i
$497$	−7.03632	−	19.3321i	−0.315622	−	0.867165i
$498$	1.07116	−	0.188875i	0.0480000	−	0.00846370i
$499$	0.814770	−	4.62079i	0.0364741	−	0.206855i	−0.961125	−	0.276115i	$-0.910953\pi$
$499$	0.814770	−	4.62079i	0.0364741	−	0.206855i	0.997599	+	0.0692604i	$0.0220639\pi$
$500$		0			0
$501$	0.0116960	+	0.0202581i	0.000522539	+	0.000905064i
$502$	−12.3710	−	7.14238i	−0.552143	−	0.318780i
$503$	5.59360	+	6.66619i	0.249406	+	0.297231i	0.876193	−	0.481960i	$-0.160075\pi$
$503$	5.59360	+	6.66619i	0.249406	+	0.297231i	−0.626787	+	0.779191i	$0.715630\pi$
$504$	4.22000	−	3.54100i	0.187974	−	0.157729i
$505$		0			0
$506$	−9.71493	−	16.8267i	−0.431881	−	0.748040i
$507$	−0.110908	+	0.304717i	−0.00492559	+	0.0135329i
$508$	−4.71085	−	0.830649i	−0.209010	−	0.0368541i
$509$	−0.971085	−	5.50730i	−0.0430426	−	0.244107i	0.955694	−	0.294363i	$-0.0951074\pi$
$509$	−0.971085	−	5.50730i	−0.0430426	−	0.244107i	−0.998736	+	0.0502560i	$0.983996\pi$
$510$		0			0
$511$	−11.0104	−	9.23879i	−0.487069	−	0.408700i
$512$		−	1.00000i		−	0.0441942i
$513$	2.16560	−	0.522240i	0.0956135	−	0.0230575i
$514$	29.2882			1.29185
$515$		0			0
$516$	0.168551	−	0.0613474i	0.00742003	−	0.00270067i
$517$	23.4450	−	4.13399i	1.03111	−	0.181813i
$518$	−0.366431	−	0.0646118i	−0.0161001	−	0.00283888i
$519$	−0.936762	−	0.340953i	−0.0411193	−	0.0149662i
$520$		0			0
$521$	−5.52450	+	9.56871i	−0.242033	+	0.419213i	−0.961293	−	0.275528i	$-0.911147\pi$
$521$	−5.52450	+	9.56871i	−0.242033	+	0.419213i	0.719261	+	0.694740i	$0.244481\pi$
$522$	−19.5323	−	23.2777i	−0.854906	−	1.01884i
$523$	23.7848	+	28.3456i	1.04004	+	1.23947i	0.970301	+	0.241900i	$0.0777707\pi$
$523$	23.7848	+	28.3456i	1.04004	+	1.23947i	0.0697344	+	0.997566i	$0.477785\pi$
$524$	6.46712	−	11.2014i	0.282517	−	0.489334i
$525$		0			0
$526$	0.0138755	+	0.00505025i	0.000604999	+	0.000220202i
$527$	−32.5015	−	5.73089i	−1.41579	−	0.249641i
$528$	0.203285	−	0.0358446i	0.00884685	−	0.00155994i
$529$	38.9378	−	14.1722i	1.69295	−	0.616183i
$530$		0			0
$531$	18.0594			0.783712
$532$	7.97292	+	0.900202i	0.345670	+	0.0390287i
$533$		−	17.4775i		−	0.757035i
$534$	0.0845176	+	0.0709187i	0.00365743	+	0.00306895i
$535$		0			0
$536$	0.541907	+	3.07331i	0.0234068	+	0.132747i
$537$	−1.38145	−	0.243587i	−0.0596139	−	0.0105115i
$538$	−4.27045	+	11.7330i	−0.184112	+	0.505844i
$539$	−4.37102	−	7.57084i	−0.188273	−	0.326099i
$540$		0			0
$541$	27.5155	−	23.0883i	1.18299	−	0.992643i	0.183031	−	0.983107i	$-0.441409\pi$
$541$	27.5155	−	23.0883i	1.18299	−	0.992643i	0.999955	−	0.00953567i	$-0.00303534\pi$
$542$	0.270545	+	0.322423i	0.0116209	+	0.0138493i
$543$	−1.62152	−	0.936184i	−0.0695860	−	0.0401755i
$544$	3.41132	+	5.90858i	0.146259	+	0.253328i
$545$		0			0
$546$	−0.0826704	+	0.468847i	−0.00353797	+	0.0200648i
$547$	26.2669	−	4.63156i	1.12309	−	0.198031i	0.418893	−	0.908036i	$-0.362418\pi$
$547$	26.2669	−	4.63156i	1.12309	−	0.198031i	0.704197	+	0.710005i	$0.251307\pi$
$548$	−0.906409	−	2.49034i	−0.0387199	−	0.106382i
$549$	9.79429	+	8.21838i	0.418010	+	0.350752i
$550$		0			0
$551$	4.96555	−	43.9790i	0.211540	−	1.87357i
$552$			0.684571i			0.0291373i
$553$	−12.4299	+	14.8134i	−0.528573	+	0.629929i
$554$	28.7336	−	10.4582i	1.22077	−	0.444325i
$555$		0			0
$556$	−2.00252	+	11.3569i	−0.0849260	+	0.481639i
$557$	4.50069	−	12.3655i	0.190700	−	0.523945i	−0.807087	−	0.590433i	$-0.798957\pi$
$557$	4.50069	−	12.3655i	0.190700	−	0.523945i	0.997787	+	0.0664876i	$0.0211793\pi$
$558$	−12.5371	+	7.23829i	−0.530737	+	0.306421i
$559$	3.18934	−	5.52409i	0.134895	−	0.233644i
$560$		0			0
$561$	−1.07885	+	0.905262i	−0.0455490	+	0.0382202i
$562$	9.58968	+	5.53661i	0.404516	+	0.233548i
$563$	−15.7970	+	9.12041i	−0.665765	+	0.384379i	−0.794470	−	0.607304i	$-0.792251\pi$
$563$	−15.7970	+	9.12041i	−0.665765	+	0.384379i	0.128705	+	0.991683i	$0.458918\pi$
$564$	−0.788195	−	0.286880i	−0.0331890	−	0.0120798i
$565$		0			0
$566$	−0.138497	−	0.785458i	−0.00582148	−	0.0330153i
$567$	5.62494	+	15.4544i	0.236225	+	0.649024i
$568$	7.18406	−	8.56163i	0.301436	−	0.359238i
$569$	−27.5994			−1.15703			−0.578514	−	0.815672i	$-0.696367\pi$
$569$	−27.5994			−1.15703			−0.578514	+	0.815672i	$0.696367\pi$
$570$		0			0
$571$	29.8138			1.24767			0.623835	−	0.781556i	$-0.285574\pi$
$571$	29.8138			1.24767			0.623835	+	0.781556i	$0.285574\pi$
$572$	4.71854	−	5.62333i	0.197292	−	0.235123i
$573$	−0.141434	−	0.388586i	−0.00590848	−	0.0162334i
$574$	1.84206	+	10.4468i	0.0768862	+	0.436043i
$575$		0			0
$576$	2.81224	+	1.02357i	0.117177	+	0.0426489i
$577$	12.3928	−	7.15498i	0.515918	−	0.297866i	−0.219345	−	0.975647i	$-0.570392\pi$
$577$	12.3928	−	7.15498i	0.515918	−	0.297866i	0.735263	+	0.677782i	$0.237059\pi$
$578$	−25.5897	−	14.7742i	−1.06439	−	0.614527i
$579$	−0.642427	+	0.539061i	−0.0266984	+	0.0224026i
$580$		0			0
$581$	−11.7386	+	20.3318i	−0.486997	+	0.843504i
$582$	−0.605698	+	0.349700i	−0.0251070	+	0.0144955i
$583$	5.19259	−	14.2665i	0.215055	−	0.590859i
$584$	1.35590	−	7.68966i	0.0561073	−	0.318201i
$585$		0			0
$586$	−12.9102	+	4.69894i	−0.533317	+	0.194111i
$587$	3.67994	−	4.38558i	0.151887	−	0.181012i	−0.684735	−	0.728792i	$-0.740082\pi$
$587$	3.67994	−	4.38558i	0.151887	−	0.181012i	0.836623	+	0.547779i	$0.184527\pi$
$588$			0.308008i			0.0127020i
$589$	−20.2229	−	5.96796i	−0.833269	−	0.245906i
$590$		0			0
$591$	0.640675	+	0.537590i	0.0263539	+	0.0221135i
$592$	−0.0691356	−	0.189948i	−0.00284145	−	0.00780683i
$593$	−10.7332	+	1.89256i	−0.440762	+	0.0777182i	−0.389625	−	0.920974i	$-0.627395\pi$
$593$	−10.7332	+	1.89256i	−0.440762	+	0.0777182i	−0.0511364	+	0.998692i	$0.516284\pi$
$594$	−0.214807	+	1.21823i	−0.00881364	+	0.0499847i
$595$		0			0
$596$	6.08310	+	10.5362i	0.249173	+	0.431581i
$597$	−0.102298	−	0.0590617i	−0.00418677	−	0.00241723i
$598$	15.6485	+	18.6491i	0.639913	+	0.762618i
$599$	8.33800	−	6.99641i	0.340681	−	0.285866i	−0.456354	−	0.889798i	$-0.650845\pi$
$599$	8.33800	−	6.99641i	0.340681	−	0.285866i	0.797035	+	0.603933i	$0.206400\pi$
$600$		0			0
$601$	−3.29773	−	5.71184i	−0.134517	−	0.232991i	0.790896	−	0.611951i	$-0.209615\pi$
$601$	−3.29773	−	5.71184i	−0.134517	−	0.232991i	−0.925413	+	0.378960i	$0.876282\pi$
$602$	−1.32415	+	3.63807i	−0.0539683	+	0.148277i
$603$	−9.19757	−	1.62178i	−0.374554	−	0.0660440i
$604$	−3.03226	−	17.1968i	−0.123381	−	0.699727i
$605$		0			0
$606$	−0.522364	−	0.438315i	−0.0212196	−	0.0178053i
$607$			8.03380i			0.326082i	0.986619	+	0.163041i	$0.0521303\pi$
$607$			8.03380i			0.326082i	−0.986619	+	0.163041i	$0.947870\pi$
$608$	1.74216	+	3.99561i	0.0706541	+	0.162043i
$609$	−1.59390			−0.0645882
$610$		0			0
$611$	−28.0298	+	10.2020i	−1.13396	+	0.412729i
$612$	−20.1081	+	3.54560i	−0.812822	+	0.143322i
$613$	−14.3390	−	2.52835i	−0.579145	−	0.102119i	−0.123601	−	0.992332i	$-0.539444\pi$
$613$	−14.3390	−	2.52835i	−0.579145	−	0.102119i	−0.455544	+	0.890213i	$0.650555\pi$
$614$	0.624954	+	0.227465i	0.0252211	+	0.00917973i
$615$		0			0
$616$	−2.22774	+	3.85856i	−0.0897581	+	0.155466i
$617$	3.96361	+	4.72364i	0.159569	+	0.190167i	0.839905	−	0.542734i	$-0.182611\pi$
$617$	3.96361	+	4.72364i	0.159569	+	0.190167i	−0.680336	+	0.732900i	$0.738166\pi$
$618$	−0.186030	−	0.221701i	−0.00748321	−	0.00891814i
$619$	5.14294	−	8.90783i	0.206712	−	0.358036i	−0.743965	−	0.668219i	$-0.767057\pi$
$619$	5.14294	−	8.90783i	0.206712	−	0.358036i	0.950677	+	0.310183i	$0.100390\pi$
$620$		0			0
$621$	−3.85504	−	1.40312i	−0.154697	−	0.0563052i
$622$	28.0972	+	4.95430i	1.12660	+	0.198649i
$623$	−2.34523	+	0.413527i	−0.0939595	+	0.0165676i
$624$	−0.243038	+	0.0884586i	−0.00972931	+	0.00354118i
$625$		0			0
$626$	9.99160			0.399345
$627$	−0.749800	+	0.497377i	−0.0299441	+	0.0198633i
$628$		−	22.4510i		−	0.895892i
$629$	1.05647	+	0.886482i	0.0421242	+	0.0353464i
$630$		0			0
$631$	−2.94657	−	16.7108i	−0.117301	−	0.665247i	−0.985585	−	0.169180i	$-0.945888\pi$
$631$	−2.94657	−	16.7108i	−0.117301	−	0.665247i	0.868284	−	0.496067i	$-0.165223\pi$
$632$	−10.3457	−	1.82423i	−0.411530	−	0.0725639i
$633$	0.137911	−	0.378907i	0.00548146	−	0.0150602i
$634$	−5.81599	−	10.0736i	−0.230983	−	0.400074i
$635$		0			0
$636$	−0.409765	+	0.343834i	−0.0162482	+	0.0136339i
$637$	7.04069	+	8.39077i	0.278962	+	0.332454i
$638$	21.2840	+	12.2883i	0.842640	+	0.486498i
$639$	16.7240	+	28.9668i	0.661590	+	1.14591i
$640$		0			0
$641$	−1.73562	+	9.84322i	−0.0685531	+	0.388784i	0.931155	+	0.364623i	$0.118802\pi$
$641$	−1.73562	+	9.84322i	−0.0685531	+	0.388784i	−0.999708	+	0.0241602i	$0.992309\pi$
$642$	−0.968640	+	0.170797i	−0.0382292	+	0.00674084i
$643$	5.03384	+	13.8304i	0.198515	+	0.545417i	0.998509	−	0.0545923i	$-0.0173859\pi$
$643$	5.03384	+	13.8304i	0.198515	+	0.545417i	−0.799993	+	0.600009i	$0.795164\pi$
$644$	−11.3191	−	9.49786i	−0.446036	−	0.374268i
$645$		0			0
$646$	−23.9240	−	17.6653i	−0.941278	−	0.695031i
$647$		−	21.6933i		−	0.852852i	−0.904522	−	0.426426i	$-0.859772\pi$
$647$		−	21.6933i		−	0.852852i	0.904522	−	0.426426i	$-0.140228\pi$
$648$	−5.74305	+	6.84430i	−0.225608	+	0.268869i
$649$	−13.7254	+	4.99564i	−0.538769	+	0.196096i
$650$		0			0
$651$	−0.131860	+	0.747813i	−0.00516799	+	0.0293091i
$652$	3.25202	−	8.93485i	0.127359	−	0.349916i
$653$	−0.518327	+	0.299256i	−0.0202837	+	0.0117108i	−0.510108	−	0.860111i	$-0.670394\pi$
$653$	−0.518327	+	0.299256i	−0.0202837	+	0.0117108i	0.489824	+	0.871821i	$0.337061\pi$
$654$	0.460395	−	0.797427i	0.0180029	−	0.0311819i
$655$		0			0
$656$	−4.41465	+	3.70433i	−0.172363	+	0.144630i
$657$	20.2374	+	11.6840i	0.789534	+	0.455838i
$658$	15.6790	−	9.05228i	0.611232	−	0.352895i
$659$	26.5885	+	9.67743i	1.03574	+	0.376979i	0.803265	−	0.595622i	$-0.203095\pi$
$659$	26.5885	+	9.67743i	1.03574	+	0.376979i	0.232478	+	0.972602i	$0.425317\pi$
$660$		0			0
$661$	6.35248	+	36.0267i	0.247083	+	1.40128i	0.815605	+	0.578609i	$0.196404\pi$
$661$	6.35248	+	36.0267i	0.247083	+	1.40128i	−0.568522	+	0.822668i	$0.692485\pi$
$662$	8.61094	+	23.6584i	0.334674	+	0.919509i
$663$	1.13425	−	1.35175i	0.0440506	−	0.0524975i
$664$	−12.7542			−0.494959
$665$		0			0
$666$	0.604946			0.0234412
$667$	−52.3906	+	62.4367i	−2.02857	+	2.41756i
$668$	−0.0938141	−	0.257752i	−0.00362978	−	0.00997273i
$669$	0.383528	+	2.17509i	0.0148280	+	0.0840940i
$670$		0			0
$671$	−9.71718	−	3.53676i	−0.375127	−	0.136535i
$672$	0.135948	−	0.0784897i	0.00524432	−	0.00302781i
$673$	12.7281	+	7.34858i	0.490633	+	0.283267i	0.724837	−	0.688920i	$-0.241915\pi$
$673$	12.7281	+	7.34858i	0.490633	+	0.283267i	−0.234204	+	0.972187i	$0.575248\pi$
$674$	1.08320	−	0.908909i	0.0417231	−	0.0350099i
$675$		0			0
$676$	1.90120	−	3.29298i	0.0731233	−	0.126653i
$677$	−20.4185	+	11.7886i	−0.784748	+	0.453075i	−0.838110	−	0.545501i	$-0.816340\pi$
$677$	−20.4185	+	11.7886i	−0.784748	+	0.453075i	0.0533622	+	0.998575i	$0.483006\pi$
$678$	−0.347351	+	0.954338i	−0.0133399	+	0.0366511i
$679$	2.62142	−	14.8668i	0.100601	−	0.570535i
$680$		0			0
$681$	0.883733	−	0.321653i	0.0338647	−	0.0123258i
$682$	7.52608	−	8.96924i	0.288189	−	0.343450i
$683$		−	5.85445i		−	0.224014i	−0.993707	−	0.112007i	$-0.964272\pi$
$683$		−	5.85445i		−	0.224014i	0.993707	−	0.112007i	$-0.0357279\pi$
$684$	−13.0198	+	0.809596i	−0.497826	+	0.0309557i
$685$		0			0
$686$	−14.9634	−	12.5558i	−0.571305	−	0.479382i
$687$	−0.704783	−	1.93637i	−0.0268891	−	0.0738773i
$688$	−2.07131	+	0.365228i	−0.0789679	+	0.0139242i
$689$	−3.30321	+	18.7335i	−0.125842	+	0.713688i
$690$		0			0
$691$	4.81892	+	8.34661i	0.183320	+	0.317520i	0.943009	−	0.332767i	$-0.107982\pi$
$691$	4.81892	+	8.34661i	0.183320	+	0.317520i	−0.759689	+	0.650287i	$0.774649\pi$
$692$	10.1233	+	5.84470i	0.384831	+	0.222182i
$693$	−8.57095	−	10.2145i	−0.325583	−	0.388015i
$694$	−24.6120	+	20.6520i	−0.934261	+	0.783938i
$695$		0			0
$696$	−0.432953	−	0.749896i	−0.0164110	−	0.0284247i
$697$	13.4477	−	36.9471i	0.509367	−	1.39947i
$698$	−1.78934	−	0.315510i	−0.0677276	−	0.0119422i
$699$	−0.294679	−	1.67121i	−0.0111458	−	0.0632109i
$700$		0			0
$701$	22.5409	+	18.9141i	0.851358	+	0.714374i	0.960088	−	0.279697i	$-0.0902340\pi$
$701$	22.5409	+	18.9141i	0.851358	+	0.714374i	−0.108730	+	0.994071i	$0.534678\pi$
$702$		−	1.54993i		−	0.0584984i
$703$	0.607160	+	0.638513i	0.0228995	+	0.0240820i
$704$	−2.42049			−0.0912255
$705$		0			0
$706$	25.4018	−	9.24549i	0.956009	−	0.347959i
$707$	14.4948	−	2.55582i	0.545131	−	0.0961213i
$708$	0.506803	+	0.0893630i	0.0190468	+	0.00335847i
$709$	−19.2050	−	6.99003i	−0.721257	−	0.262516i	−0.0447979	−	0.998996i	$-0.514264\pi$
$709$	−19.2050	−	6.99003i	−0.721257	−	0.262516i	−0.676459	+	0.736480i	$0.736487\pi$
$710$		0			0
$711$	15.7198	−	27.2274i	0.589537	−	1.02111i
$712$	−0.831590	−	0.991050i	−0.0311651	−	0.0371412i
$713$	24.9593	+	29.7454i	0.934735	+	1.11397i
$714$	−0.535507	+	0.927526i	−0.0200409	+	0.0347118i
$715$		0			0
$716$	15.4567	+	5.62579i	0.577646	+	0.210246i
$717$	1.51215	+	0.266634i	0.0564724	+	0.00995761i
$718$	−23.0189	+	4.05885i	−0.859057	+	0.151475i
$719$	22.5450	−	8.20572i	0.840788	−	0.306022i	0.114509	−	0.993422i	$-0.463470\pi$
$719$	22.5450	−	8.20572i	0.840788	−	0.306022i	0.726279	+	0.687400i	$0.241248\pi$
$720$		0			0
$721$	6.24676			0.232641
$722$	−13.9220	−	12.9297i	−0.518123	−	0.481195i
$723$			0.753390i			0.0280189i
$724$	16.8188	+	14.1126i	0.625064	+	0.524491i
$725$		0			0
$726$	0.0761360	+	0.431789i	0.00282567	+	0.0160252i
$727$	27.2886	+	4.81172i	1.01208	+	0.178457i	0.655010	−	0.755621i	$-0.272665\pi$
$727$	27.2886	+	4.81172i	1.01208	+	0.178457i	0.357070	+	0.934078i	$0.383776\pi$
$728$	1.90933	−	5.24583i	0.0707644	−	0.194423i
$729$	−13.3040	−	23.0433i	−0.492742	−	0.853454i
$730$		0			0
$731$	10.9926	−	9.22388i	0.406576	−	0.341158i
$732$	0.234191	+	0.279098i	0.00865595	+	0.0103158i
$733$	−5.65411	−	3.26440i	−0.208839	−	0.120573i	0.391933	−	0.919994i	$-0.371807\pi$
$733$	−5.65411	−	3.26440i	−0.208839	−	0.120573i	−0.600772	+	0.799421i	$0.705140\pi$
$734$	3.94071	+	6.82552i	0.145454	+	0.251934i
$735$		0			0
$736$	1.39392	−	7.90530i	0.0513805	−	0.291393i
$737$	7.43890	−	1.31168i	0.274015	−	0.0483163i
$738$	−5.89877	−	16.2067i	−0.217137	−	0.596578i
$739$	10.5758	+	8.87419i	0.389039	+	0.326442i	0.816239	−	0.577715i	$-0.196055\pi$
$739$	10.5758	+	8.87419i	0.389039	+	0.326442i	−0.427200	+	0.904157i	$0.640500\pi$
$740$		0			0
$741$	0.816975	−	0.776858i	0.0300123	−	0.0285386i
$742$		−	11.5457i		−	0.423857i
$743$	5.89897	−	7.03012i	0.216412	−	0.257910i	−0.646906	−	0.762569i	$-0.723938\pi$
$743$	5.89897	−	7.03012i	0.216412	−	0.257910i	0.863318	+	0.504660i	$0.168382\pi$
$744$	−0.387647	+	0.141092i	−0.0142118	+	0.00517268i
$745$		0			0
$746$	2.38124	−	13.5047i	0.0871835	−	0.494442i
$747$	13.0549	−	35.8679i	0.477652	−	1.31234i
$748$	14.3016	−	8.25706i	0.522920	−	0.301908i
$749$	10.6150	−	18.3858i	0.387865	−	0.671802i
$750$		0			0
$751$	−17.8717	+	14.9961i	−0.652147	+	0.547216i	−0.907722	−	0.419573i	$-0.862180\pi$
$751$	−17.8717	+	14.9961i	−0.652147	+	0.547216i	0.255574	+	0.966789i	$0.417735\pi$
$752$	8.51780	+	4.91775i	0.310612	+	0.179332i
$753$	1.05501	−	0.609108i	0.0384466	−	0.0221971i
$754$	−28.9362	−	10.5319i	−1.05380	−	0.383550i
$755$		0			0
$756$	0.163357	+	0.926443i	0.00594123	+	0.0336944i
$757$	7.01518	+	19.2741i	0.254971	+	0.700527i	0.999459	+	0.0328914i	$0.0104715\pi$
$757$	7.01518	+	19.2741i	0.254971	+	0.700527i	−0.744488	+	0.667636i	$0.767306\pi$
$758$	9.58260	−	11.4201i	0.348056	−	0.414796i
$759$	1.65699			0.0601451
$760$		0			0
$761$	31.3821			1.13760			0.568800	−	0.822476i	$-0.307408\pi$
$761$	31.3821			1.13760			0.568800	+	0.822476i	$0.307408\pi$
$762$	0.262220	−	0.312502i	0.00949924	−	0.0113208i
$763$	6.79755	+	18.6761i	0.246088	+	0.676120i
$764$	0.842016	+	4.77531i	0.0304631	+	0.172765i
$765$		0			0
$766$	−9.48923	−	3.45380i	−0.342860	−	0.124791i
$767$	15.8491	−	9.15047i	0.572277	−	0.330404i
$768$	0.0738553	+	0.0426404i	0.00266503	+	0.00153865i
$769$	2.75633	−	2.31283i	0.0993957	−	0.0834029i	−0.591736	−	0.806132i	$-0.701557\pi$
$769$	2.75633	−	2.31283i	0.0993957	−	0.0834029i	0.691131	+	0.722729i	$0.257113\pi$
$770$		0			0
$771$	−1.24886	+	2.16309i	−0.0449766	+	0.0779017i
$772$	8.51627	−	4.91687i	0.306507	−	0.176962i
$773$	−4.92456	+	13.5301i	−0.177124	+	0.486644i	−0.996205	−	0.0870330i	$-0.972261\pi$
$773$	−4.92456	+	13.5301i	−0.177124	+	0.486644i	0.819081	+	0.573677i	$0.194484\pi$
$774$	1.09303	−	6.19886i	0.0392880	−	0.222814i
$775$		0			0
$776$	7.70655	−	2.80496i	0.276649	−	0.100692i
$777$	0.0203967	−	0.0243079i	0.000731728	−	0.000872039i
$778$			6.13194i			0.219841i
$779$	11.1856	−	22.4921i	0.400767	−	0.805863i
$780$		0			0
$781$	−20.7233	−	17.3889i	−0.741538	−	0.622224i
$782$	18.7314	+	51.4642i	0.669835	+	1.84036i
$783$	5.11030	−	0.901084i	0.182627	−	0.0322021i
$784$	0.627164	−	3.55682i	0.0223987	−	0.127029i
$785$		0			0
$786$	0.551521	+	0.955262i	0.0196721	+	0.0340731i
$787$	42.3573	+	24.4550i	1.50988	+	0.871727i	0.999934	+	0.0115176i	$0.00366625\pi$
$787$	42.3573	+	24.4550i	1.50988	+	0.871727i	0.509941	+	0.860209i	$0.329667\pi$
$788$	−6.30377	−	7.51254i	−0.224562	−	0.267623i
$789$	−0.000964644	0	0.000809432i	−3.43422e−5	0	2.88165e-5i
$790$		0			0
$791$	−10.9604	−	18.9840i	−0.389707	−	0.674993i
$792$	2.47754	−	6.80700i	0.0880357	−	0.241876i
$793$	12.7597	+	2.24988i	0.453110	+	0.0798955i
$794$	0.270461	+	1.53386i	0.00959832	+	0.0544348i
$795$		0			0
$796$	1.06106	+	0.890332i	0.0376082	+	0.0315570i
$797$			1.34326i			0.0475809i	0.999717	+	0.0237904i	$0.00757345\pi$
$797$			1.34326i			0.0475809i	−0.999717	+	0.0237904i	$0.992427\pi$
$798$	−0.406453	+	0.550458i	−0.0143883	+	0.0194860i
$799$	−67.1042			−2.37397
$800$		0			0
$801$	3.63827	−	1.32422i	0.128552	−	0.0467891i
$802$	−35.2969	+	6.22380i	−1.24638	+	0.219770i
$803$	−18.6127	−	3.28193i	−0.656829	−	0.115817i
$804$	−0.250087	−	0.0910244i	−0.00881990	−	0.00321018i
$805$		0			0
$806$	−7.33510	+	12.7048i	−0.258368	+	0.447506i
$807$	−0.684448	−	0.815693i	−0.0240937	−	0.0287138i
$808$	5.13967	+	6.12522i	0.180813	+	0.215485i
$809$	−14.2421	+	24.6681i	−0.500726	+	0.867283i	0.499273	+	0.866445i	$0.333600\pi$
$809$	−14.2421	+	24.6681i	−0.500726	+	0.867283i	−1.00000		0.000838933i	$0.999733\pi$
$810$		0			0
$811$	47.3375	+	17.2294i	1.66225	+	0.605008i	0.990713	−	0.135968i	$-0.0434144\pi$
$811$	47.3375	+	17.2294i	1.66225	+	0.605008i	0.671532	+	0.740976i	$0.265637\pi$
$812$	18.4061	+	3.24549i	0.645928	+	0.113894i
$813$	−0.0353489	+	0.00623296i	−0.00123974	+	0.000218599i
$814$	−0.459767	+	0.167342i	−0.0161148	+	0.00586532i
$815$		0			0
$816$	−0.581841			−0.0203685
$817$	7.63985	−	5.06787i	0.267284	−	0.177302i
$818$		−	35.0714i		−	1.22624i
$819$	12.7982	+	10.7390i	0.447206	+	0.375250i
$820$		0			0
$821$	−7.36834	−	41.7879i	−0.257157	−	1.45841i	−0.790475	−	0.612494i	$-0.790166\pi$
$821$	−7.36834	−	41.7879i	−0.257157	−	1.45841i	0.533318	−	0.845915i	$-0.320945\pi$
$822$	0.222575	+	0.0392459i	0.00776318	+	0.00136886i
$823$	−17.1612	+	47.1499i	−0.598201	+	1.64354i	0.156656	+	0.987653i	$0.449928\pi$
$823$	−17.1612	+	47.1499i	−0.598201	+	1.64354i	−0.754857	+	0.655889i	$0.772294\pi$
$824$	1.69681	+	2.93896i	0.0591112	+	0.102384i
$825$		0			0
$826$	−8.50907	+	7.13995i	−0.296068	+	0.248431i
$827$	1.19599	+	1.42533i	0.0415887	+	0.0495635i	0.786438	−	0.617669i	$-0.211923\pi$
$827$	1.19599	+	1.42533i	0.0415887	+	0.0495635i	−0.744849	+	0.667233i	$0.767479\pi$
$828$	20.8049	+	12.0117i	0.723019	+	0.417435i
$829$	9.83821	+	17.0403i	0.341695	+	0.591833i	0.984748	−	0.173989i	$-0.0556656\pi$
$829$	9.83821	+	17.0403i	0.341695	+	0.591833i	−0.643052	+	0.765822i	$0.722332\pi$
$830$		0			0
$831$	−0.452820	+	2.56807i	−0.0157082	+	0.0890854i
$832$	2.98668	−	0.526632i	0.103544	−	0.0182577i
$833$	8.42781	+	23.1552i	0.292006	+	0.802281i
$834$	−0.753378	−	0.632159i	−0.0260873	−	0.0218899i
$835$		0			0
$836$	9.67131	−	4.21688i	0.334489	−	0.145844i
$837$		−	2.47215i		−	0.0854500i
$838$	−8.10214	+	9.65576i	−0.279884	+	0.333553i
$839$	−43.1880	+	15.7191i	−1.49102	+	0.542685i	−0.953717	−	0.300707i	$-0.902777\pi$
$839$	−43.1880	+	15.7191i	−1.49102	+	0.542685i	−0.537299	+	0.843392i	$0.680555\pi$
$840$		0			0
$841$	12.8665	−	72.9694i	0.443672	−	2.51619i
$842$	−9.13109	+	25.0875i	−0.314678	+	0.864571i
$843$	−0.817816	+	0.472166i	−0.0281671	+	0.0162623i
$844$	−2.36410	+	4.09473i	−0.0813755	+	0.140947i
$845$		0			0
$846$	−22.5485	+	18.9204i	−0.775234	+	0.650498i
$847$	−8.19578	−	4.73184i	−0.281610	−	0.162588i
$848$	5.43200	−	3.13617i	0.186536	−	0.107696i
$849$	0.0639159	+	0.0232635i	0.00219359	+	0.000798401i
$850$		0			0
$851$	−0.281765	−	1.59797i	−0.00965878	−	0.0547777i
$852$	0.325991	+	0.895653i	0.0111683	+	0.0306845i
$853$	17.6043	−	20.9800i	0.602759	−	0.718340i	−0.375245	−	0.926926i	$-0.622441\pi$
$853$	17.6043	−	20.9800i	0.602759	−	0.718340i	0.978004	+	0.208585i	$0.0668859\pi$
$854$	−7.86399			−0.269100
$855$		0			0
$856$	11.5335			0.394206
$857$	12.0296	−	14.3363i	0.410922	−	0.489718i	−0.520396	−	0.853925i	$-0.674216\pi$
$857$	12.0296	−	14.3363i	0.410922	−	0.489718i	0.931318	+	0.364207i	$0.118660\pi$
$858$	0.214113	+	0.588270i	0.00730969	+	0.0200832i
$859$	−2.55291	−	14.4783i	−0.0871042	−	0.493993i	−0.996883	−	0.0788984i	$-0.974860\pi$
$859$	−2.55291	−	14.4783i	−0.0871042	−	0.493993i	0.909778	−	0.415094i	$-0.136251\pi$
$860$		0			0
$861$	−0.850102	−	0.309412i	−0.0289714	−	0.0105447i
$862$	−7.02088	+	4.05351i	−0.239132	+	0.138063i
$863$	40.4491	+	23.3533i	1.37690	+	0.794956i	0.991786	−	0.127912i	$-0.0408274\pi$
$863$	40.4491	+	23.3533i	1.37690	+	0.794956i	0.385118	+	0.922867i	$0.374161\pi$
$864$	−0.391498	+	0.328506i	−0.0133190	+	0.0111760i
$865$		0			0
$866$	−11.4197	+	19.7795i	−0.388057	+	0.672135i
$867$	2.18231	−	1.25996i	0.0741152	−	0.0427904i
$868$	3.04538	−	8.36712i	0.103367	−	0.283999i
$869$	−4.41552	+	25.0417i	−0.149786	+	0.849480i
$870$		0			0
$871$	−8.89360	+	3.23701i	−0.301348	+	0.109682i
$872$	−6.94027	+	8.27109i	−0.235027	+	0.280095i
$873$			24.5438i			0.830681i
$874$	8.20279	+	34.0149i	0.277463	+	1.15057i
$875$		0			0
$876$	0.510107	+	0.428031i	0.0172349	+	0.0144618i
$877$	7.41727	+	20.3788i	0.250463	+	0.688143i	0.999667	+	0.0258029i	$0.00821422\pi$
$877$	7.41727	+	20.3788i	0.250463	+	0.688143i	−0.749204	+	0.662340i	$0.769564\pi$
$878$	13.9680	−	2.46294i	0.471398	−	0.0831202i
$879$	0.203456	−	1.15385i	0.00686239	−	0.0389185i
$880$		0			0
$881$	15.2136	+	26.3508i	0.512560	+	0.887780i	0.999894	+	0.0145644i	$0.00463615\pi$
$881$	15.2136	+	26.3508i	0.512560	+	0.887780i	−0.487334	+	0.873216i	$0.662031\pi$
$882$	9.36070	+	5.40440i	0.315191	+	0.181976i
$883$	−35.7095	−	42.5570i	−1.20172	−	1.43216i	−0.872994	−	0.487730i	$-0.837825\pi$
$883$	−35.7095	−	42.5570i	−1.20172	−	1.43216i	−0.328727	−	0.944425i	$-0.606620\pi$
$884$	−15.8505	+	13.3002i	−0.533111	+	0.447333i
$885$		0			0
$886$	−15.7428	−	27.2673i	−0.528890	−	0.916064i
$887$	−2.73207	+	7.50631i	−0.0917340	+	0.252037i	−0.977071	−	0.212912i	$-0.931705\pi$
$887$	−2.73207	+	7.50631i	−0.0917340	+	0.252037i	0.885337	+	0.464949i	$0.153927\pi$
$888$	0.0169767	+	0.00299345i	0.000569700	+	0.000100453i
$889$	1.52901	+	8.67142i	0.0512812	+	0.290830i
$890$		0			0
$891$	16.5665	+	13.9010i	0.555000	+	0.465700i
$892$		−	25.8985i		−	0.867147i
$893$	−42.6013	−	4.81000i	−1.42560	−	0.160960i
$894$	−1.03754			−0.0347006
$895$		0			0
$896$	−1.72973	+	0.629569i	−0.0577861	+	0.0210324i
$897$	−2.04459	+	0.360517i	−0.0682670	+	0.0120373i
$898$	−26.8094	−	4.72722i	−0.894641	−	0.157749i
$899$	−46.1534	−	16.7985i	−1.53930	−	0.560260i
$900$		0			0
$901$	−21.3970	+	37.0606i	−0.712836	+	1.23467i
$902$	8.96628	+	10.6856i	0.298545	+	0.355792i
$903$	−0.212229	−	0.252924i	−0.00706252	−	0.00841679i
$904$	5.95436	−	10.3133i	0.198039	−	0.343014i
$905$		0			0
$906$	1.39937	+	0.509329i	0.0464910	+	0.0169213i
$907$	−35.7878	−	6.31036i	−1.18831	−	0.209532i	−0.455674	−	0.890147i	$-0.650602\pi$
$907$	−35.7878	−	6.31036i	−1.18831	−	0.209532i	−0.732641	+	0.680615i	$0.761713\pi$
$908$	−10.8601	+	1.91494i	−0.360406	+	0.0635494i
$909$	−22.4864	+	8.18440i	−0.745828	+	0.271459i
$910$		0			0
$911$	55.1556			1.82739			0.913694	−	0.406404i	$-0.133217\pi$
$911$	55.1556			1.82739			0.913694	+	0.406404i	$0.133217\pi$
$912$	−0.369383	−	0.0417061i	−0.0122315	−	0.00138103i
$913$			30.8714i			1.02169i
$914$	−21.0495	−	17.6626i	−0.696255	−	0.584227i
$915$		0			0
$916$	4.19587	+	23.7960i	0.138636	+	0.786241i
$917$	−23.4468	−	4.13430i	−0.774282	−	0.136527i
$918$	1.19256	−	3.27653i	0.0393603	−	0.108142i
$919$	11.9007	+	20.6125i	0.392566	+	0.679945i	0.992787	−	0.119889i	$-0.0382540\pi$
$919$	11.9007	+	20.6125i	0.392566	+	0.679945i	−0.600221	+	0.799834i	$0.704921\pi$
$920$		0			0
$921$	−0.0434478	+	0.0364570i	−0.00143165	+	0.00120130i
$922$	−3.63785	−	4.33542i	−0.119806	−	0.142779i
$923$	29.3542	+	16.9476i	0.966205	+	0.557839i
$924$	−0.189983	−	0.329061i	−0.00624999	−	0.0108253i
$925$		0			0
$926$	3.83156	−	21.7299i	0.125913	−	0.714088i
$927$	−10.0019	+	1.76360i	−0.328505	+	0.0579243i
$928$	3.47273	+	9.54124i	0.113998	+	0.313207i
$929$	39.8007	+	33.3968i	1.30582	+	1.09571i	0.989108	+	0.147191i	$0.0470231\pi$
$929$	39.8007	+	33.3968i	1.30582	+	1.09571i	0.316711	+	0.948522i	$0.397421\pi$
$930$		0			0
$931$	3.69067	+	15.3043i	0.120957	+	0.501577i
$932$			19.8988i			0.651808i
$933$	−1.56398	+	1.86388i	−0.0512024	+	0.0610206i
$934$	−20.0796	+	7.30838i	−0.657025	+	0.239138i
$935$		0			0
$936$	−1.57607	+	8.93831i	−0.0515153	+	0.292158i
$937$	−18.2722	+	50.2023i	−0.596925	+	1.64004i	0.160438	+	0.987046i	$0.448709\pi$
$937$	−18.2722	+	50.2023i	−0.596925	+	1.64004i	−0.757364	+	0.652993i	$0.773513\pi$
$938$	4.97481	−	2.87221i	0.162433	−	0.0937810i
$939$	−0.426046	+	0.737933i	−0.0139035	+	0.0240815i
$940$		0			0
$941$	−9.96308	+	8.36002i	−0.324787	+	0.272529i	−0.790572	−	0.612369i	$-0.790217\pi$
$941$	−9.96308	+	8.36002i	−0.324787	+	0.272529i	0.465785	+	0.884898i	$0.345772\pi$
$942$	1.65813	+	0.957319i	0.0540247	+	0.0311911i
$943$	−40.0627	+	23.1302i	−1.30462	+	0.753223i
$944$	−5.67051	−	2.06390i	−0.184559	−	0.0671741i
$945$		0			0
$946$	0.884029	+	5.01358i	0.0287422	+	0.163005i
$947$	4.30379	+	11.8246i	0.139854	+	0.384246i	0.989770	−	0.142672i	$-0.0455695\pi$
$947$	4.30379	+	11.8246i	0.139854	+	0.384246i	−0.849916	+	0.526919i	$0.823347\pi$
$948$	0.575874	−	0.686300i	0.0187035	−	0.0222900i
$949$	23.6806			0.768705
$950$		0			0
$951$	0.991985			0.0321673
$952$	8.07257	−	9.62051i	0.261633	−	0.311803i
$953$	18.4771	+	50.7655i	0.598533	+	1.64446i	0.754198	+	0.656647i	$0.228026\pi$
$953$	18.4771	+	50.7655i	0.598533	+	1.64446i	−0.155665	+	0.987810i	$0.549752\pi$
$954$	3.25962	+	18.4862i	0.105534	+	0.598513i
$955$		0			0
$956$	−16.9192	−	6.15807i	−0.547205	−	0.199166i
$957$	−1.81511	+	1.04796i	−0.0586743	+	0.0338756i
$958$	16.6684	+	9.62348i	0.538530	+	0.310920i
$959$	−3.73696	+	3.13568i	−0.120673	+	0.101256i
$960$		0			0
$961$	3.80049	−	6.58264i	0.122596	−	0.212343i
$962$	0.530906	−	0.306519i	0.0171171	−	0.00988256i
$963$	−11.8053	+	32.4349i	−0.380422	+	1.04520i
$964$	1.53405	−	8.70001i	0.0494083	−	0.280209i
$965$		0			0
$966$	1.18412	−	0.430984i	0.0380984	−	0.0138667i
$967$	25.4821	−	30.3684i	0.819449	−	0.976582i	−0.180526	−	0.983570i	$-0.557780\pi$
$967$	25.4821	−	30.3684i	0.819449	−	0.976582i	0.999976	+	0.00698833i	$0.00222447\pi$
$968$		−	5.14125i		−	0.165246i
$969$	2.32481	−	1.01366i	0.0746835	−	0.0325635i
$970$		0			0
$971$	−45.4477	−	38.1351i	−1.45849	−	1.22381i	−0.926081	−	0.377324i	$-0.876844\pi$
$971$	−45.4477	−	38.1351i	−1.45849	−	1.22381i	−0.532404	−	0.846490i	$-0.678711\pi$
$972$	−0.784985	−	2.15673i	−0.0251784	−	0.0691771i
$973$	20.9050	−	3.68612i	0.670184	−	0.118172i
$974$	−2.55538	+	14.4923i	−0.0818797	+	0.464363i
$975$		0			0
$976$	−2.13610	−	3.69983i	−0.0683749	−	0.118429i
$977$	−13.3982	−	7.73546i	−0.428647	−	0.247479i	0.270123	−	0.962826i	$-0.412936\pi$
$977$	−13.3982	−	7.73546i	−0.428647	−	0.247479i	−0.698770	+	0.715346i	$0.746269\pi$
$978$	0.521219	+	0.621165i	0.0166667	+	0.0198627i
$979$	−2.39882	+	2.01285i	−0.0766667	+	0.0643310i
$980$		0			0
$981$	−16.1565	−	27.9838i	−0.515836	−	0.893454i
$982$	−13.4853	+	37.0504i	−0.430332	+	1.18233i
$983$	52.4920	+	9.25575i	1.67423	+	0.295213i	0.928583	−	0.371125i	$-0.121028\pi$
$983$	52.4920	+	9.25575i	1.67423	+	0.295213i	0.745651	+	0.666337i	$0.232139\pi$
$984$	−0.0853422	−	0.484000i	−0.00272061	−	0.0154293i
$985$		0			0
$986$	−53.0671	−	44.5286i	−1.69000	−	1.41808i
$987$			1.54397i			0.0491452i
$988$	−11.0161	+	7.30750i	−0.350469	+	0.232482i
$989$	−16.8834			−0.536861
$990$		0			0
$991$	23.7305	−	8.63720i	0.753825	−	0.274370i	0.0636105	−	0.997975i	$-0.479738\pi$
$991$	23.7305	−	8.63720i	0.753825	−	0.274370i	0.690214	+	0.723605i	$0.257516\pi$
$992$	4.76376	−	0.839980i	0.151250	−	0.0266694i
$993$	−2.11447	−	0.372838i	−0.0671007	−	0.0118317i
$994$	−19.3321	−	7.03632i	−0.613178	−	0.223179i
$995$		0			0
$996$	0.543844	−	0.941966i	0.0172324	−	0.0298473i
$997$	−18.7776	−	22.3783i	−0.594692	−	0.708727i	0.381808	−	0.924242i	$-0.375301\pi$
$997$	−18.7776	−	22.3783i	−0.594692	−	0.708727i	−0.976501	+	0.215515i	$0.930857\pi$
$998$	−3.01601	−	3.59434i	−0.0954700	−	0.113777i
$999$	−0.0516530	+	0.0894656i	−0.00163423	+	0.00283057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.149.7		48
5.2	odd	4		950.2.l.k.301.3	yes	24
5.3	odd	4		950.2.l.j.301.2	yes	24
5.4	even	2	inner	950.2.u.h.149.2		48
19.6	even	9	inner	950.2.u.h.899.2		48
95.44	even	18	inner	950.2.u.h.899.7		48
95.63	odd	36		950.2.l.j.101.2	✓	24
95.82	odd	36		950.2.l.k.101.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.2	✓	24	95.63	odd	36
950.2.l.j.301.2	yes	24	5.3	odd	4
950.2.l.k.101.3	yes	24	95.82	odd	36
950.2.l.k.301.3	yes	24	5.2	odd	4
950.2.u.h.149.2		48	5.4	even	2	inner
950.2.u.h.149.7		48	1.1	even	1	trivial
950.2.u.h.899.2		48	19.6	even	9	inner
950.2.u.h.899.7		48	95.44	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.0291678 + 0.0801377i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-1.59412 + 0.920368i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.29256 - 1.92369i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.0291678 + 0.0801377i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-1.59412 + 0.920368i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.29256 - 1.92369i) q^{9} +(-1.21024 + 2.09620i) q^{11} +(0.0738553 - 0.0426404i) q^{12} +(1.03726 - 2.84986i) q^{13} +(-0.319640 + 1.81277i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.38551 - 5.22645i) q^{17} -2.99273i q^{18} +(3.15879 - 3.00368i) q^{19} +(-0.120253 - 0.100904i) q^{21} +(0.827855 + 2.27451i) q^{22} +(-7.90530 + 1.39392i) q^{23} +(0.0148089 - 0.0839852i) q^{24} +(-1.51638 - 2.62644i) q^{26} +(0.442595 + 0.255532i) q^{27} +(1.18320 + 1.41009i) q^{28} +(7.77809 - 6.52659i) q^{29} +(-2.41863 - 4.18918i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.203285 - 0.0358446i) q^{33} +(-1.18474 - 6.71899i) q^{34} +(-2.29256 - 1.92369i) q^{36} +0.202139i q^{37} +(-0.270521 - 4.35050i) q^{38} +0.258636 q^{39} +(5.41537 - 1.97103i) q^{41} +(-0.154595 + 0.0272592i) q^{42} +(2.07131 + 0.365228i) q^{43} +(2.27451 + 0.827855i) q^{44} +(-4.01363 + 6.95180i) q^{46} +(-6.32214 - 7.53443i) q^{47} +(-0.0548174 - 0.0653289i) q^{48} +(-1.80585 + 3.12782i) q^{49} +(0.546751 + 0.199001i) q^{51} +(-2.98668 - 0.526632i) q^{52} +(-6.17705 + 1.08918i) q^{53} +(0.480244 - 0.174794i) q^{54} +1.84074 q^{56} +(0.332843 + 0.165527i) q^{57} -10.1536i q^{58} +(4.62264 + 3.87886i) q^{59} +(0.741860 + 4.20730i) q^{61} +(-4.76376 - 0.839980i) q^{62} +(-1.88413 + 5.17660i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.158128 + 0.132685i) q^{66} +(-2.00596 - 2.39061i) q^{67} +(-5.90858 - 3.41132i) q^{68} +(-0.342285 - 0.592856i) q^{69} +(-1.94076 + 11.0066i) q^{71} +(-2.94726 + 0.519682i) q^{72} +(2.67059 + 7.33739i) q^{73} +(0.154847 + 0.129932i) q^{74} +(-3.50656 - 2.58921i) q^{76} -4.45548i q^{77} +(0.166248 - 0.198126i) q^{78} +(9.87176 - 3.59303i) q^{79} +(1.55148 - 8.79886i) q^{81} +(1.97103 - 5.41537i) q^{82} +(11.0455 - 6.37710i) q^{83} +(-0.0784897 + 0.135948i) q^{84} +(1.61119 - 1.35195i) q^{86} +(0.749896 + 0.432953i) q^{87} +(2.09620 - 1.21024i) q^{88} +(1.21570 + 0.442480i) q^{89} +(0.969391 + 5.49769i) q^{91} +(2.74548 + 7.54315i) q^{92} +(0.265166 - 0.316012i) q^{93} -9.83551 q^{94} -0.0852808 q^{96} +(-5.27159 + 6.28244i) q^{97} +(1.23527 + 3.39388i) q^{98} +(1.25788 + 7.13381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

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