LMFDB - Embedded newform 950.2.l.k.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.3
Character	$\chi$	$=$	950.301
Dual form			950.2.l.k.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.0801377 - 0.0291678i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-0.920368 - 1.59412i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29256 + 1.92369i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.0801377 - 0.0291678i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-0.920368 - 1.59412i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29256 + 1.92369i) q^{9} +(-1.21024 + 2.09620i) q^{11} +(0.0426404 + 0.0738553i) q^{12} +(-2.84986 - 1.03726i) q^{13} +(0.319640 - 1.81277i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(5.22645 + 4.38551i) q^{17} -2.99273 q^{18} +(-3.15879 + 3.00368i) q^{19} +(-0.120253 - 0.100904i) q^{21} +(-2.27451 + 0.827855i) q^{22} +(1.39392 + 7.90530i) q^{23} +(-0.0148089 + 0.0839852i) q^{24} +(-1.51638 - 2.62644i) q^{26} +(-0.255532 + 0.442595i) q^{27} +(1.41009 - 1.18320i) q^{28} +(-7.77809 + 6.52659i) q^{29} +(-2.41863 - 4.18918i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0358446 + 0.203285i) q^{33} +(1.18474 + 6.71899i) q^{34} +(-2.29256 - 1.92369i) q^{36} -0.202139 q^{37} +(-4.35050 + 0.270521i) q^{38} -0.258636 q^{39} +(5.41537 - 1.97103i) q^{41} +(-0.0272592 - 0.154595i) q^{42} +(0.365228 - 2.07131i) q^{43} +(-2.27451 - 0.827855i) q^{44} +(-4.01363 + 6.95180i) q^{46} +(7.53443 - 6.32214i) q^{47} +(-0.0653289 + 0.0548174i) q^{48} +(1.80585 - 3.12782i) q^{49} +(0.546751 + 0.199001i) q^{51} +(0.526632 - 2.98668i) q^{52} +(1.08918 + 6.17705i) q^{53} +(-0.480244 + 0.174794i) q^{54} +1.84074 q^{56} +(-0.165527 + 0.332843i) q^{57} -10.1536 q^{58} +(-4.62264 - 3.87886i) q^{59} +(0.741860 + 4.20730i) q^{61} +(0.839980 - 4.76376i) q^{62} +(5.17660 + 1.88413i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.158128 + 0.132685i) q^{66} +(2.39061 - 2.00596i) q^{67} +(-3.41132 + 5.90858i) q^{68} +(0.342285 + 0.592856i) q^{69} +(-1.94076 + 11.0066i) q^{71} +(-0.519682 - 2.94726i) q^{72} +(7.33739 - 2.67059i) q^{73} +(-0.154847 - 0.129932i) q^{74} +(-3.50656 - 2.58921i) q^{76} +4.45548 q^{77} +(-0.198126 - 0.166248i) q^{78} +(-9.87176 + 3.59303i) q^{79} +(1.55148 - 8.79886i) q^{81} +(5.41537 + 1.97103i) q^{82} +(-6.37710 - 11.0455i) q^{83} +(0.0784897 - 0.135948i) q^{84} +(1.61119 - 1.35195i) q^{86} +(-0.432953 + 0.749896i) q^{87} +(-1.21024 - 2.09620i) q^{88} +(-1.21570 - 0.442480i) q^{89} +(0.969391 + 5.49769i) q^{91} +(-7.54315 + 2.74548i) q^{92} +(-0.316012 - 0.265166i) q^{93} +9.83551 q^{94} -0.0852808 q^{96} +(-6.28244 - 5.27159i) q^{97} +(3.39388 - 1.23527i) q^{98} +(-1.25788 - 7.13381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * 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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.0801377	−	0.0291678i	0.0462676	−	0.0168400i	−0.318783	−	0.947828i	$-0.603274\pi$
$3$	0.0801377	−	0.0291678i	0.0462676	−	0.0168400i	0.365050	+	0.930988i	$0.381052\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	0.0801377	+	0.0291678i	0.0327161	+	0.0119077i
$7$	−0.920368	−	1.59412i	−0.347866	−	0.602522i	0.638004	−	0.770033i	$-0.279760\pi$
$7$	−0.920368	−	1.59412i	−0.347866	−	0.602522i	−0.985870	+	0.167511i	$0.946427\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−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	$0.285564\pi$
$12$	0.0426404	+	0.0738553i	0.0123092	+	0.0213202i
$13$	−2.84986	−	1.03726i	−0.790408	−	0.287685i	−0.0849022	−	0.996389i	$-0.527058\pi$
$13$	−2.84986	−	1.03726i	−0.790408	−	0.287685i	−0.705506	+	0.708704i	$0.749280\pi$
$14$	0.319640	−	1.81277i	0.0854275	−	0.484483i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	5.22645	+	4.38551i	1.26760	+	1.06364i	0.994829	+	0.101564i	$0.0323845\pi$
$17$	5.22645	+	4.38551i	1.26760	+	1.06364i	0.272771	+	0.962079i	$0.412060\pi$
$18$	−2.99273			−0.705393
$19$	−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
$22$	−2.27451	+	0.827855i	−0.484928	+	0.176499i
$23$	1.39392	+	7.90530i	0.290652	+	1.64837i	0.684368	+	0.729137i	$0.260078\pi$
$23$	1.39392	+	7.90530i	0.290652	+	1.64837i	−0.393716	+	0.919232i	$0.628811\pi$
$24$	−0.0148089	+	0.0839852i	−0.00302285	+	0.0171434i
$25$		0			0
$26$	−1.51638	−	2.62644i	−0.297386	−	0.515087i
$27$	−0.255532	+	0.442595i	−0.0491772	+	0.0851774i
$28$	1.41009	−	1.18320i	0.266481	−	0.223604i
$29$	−7.77809	+	6.52659i	−1.44436	+	1.21196i	−0.507782	+	0.861486i	$0.669534\pi$
$29$	−7.77809	+	6.52659i	−1.44436	+	1.21196i	−0.936573	+	0.350472i	$0.886021\pi$
$30$		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	$0.976372\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.0358446	+	0.203285i	−0.00623975	+	0.0353874i
$34$	1.18474	+	6.71899i	0.203181	+	1.15230i
$35$		0			0
$36$	−2.29256	−	1.92369i	−0.382094	−	0.320615i
$37$	−0.202139			−0.0332314			−0.0166157	−	0.999862i	$-0.505289\pi$
$37$	−0.202139			−0.0332314			−0.0166157	+	0.999862i	$0.505289\pi$
$38$	−4.35050	+	0.270521i	−0.705744	+	0.0438843i
$39$	−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	$0.240310\pi$
$42$	−0.0272592	−	0.154595i	−0.00420619	−	0.0238545i
$43$	0.365228	−	2.07131i	0.0556967	−	0.315872i	−0.944213	−	0.329336i	$-0.893175\pi$
$43$	0.365228	−	2.07131i	0.0556967	−	0.315872i	0.999909	+	0.0134647i	$0.00428609\pi$
$44$	−2.27451	−	0.827855i	−0.342896	−	0.124804i
$45$		0			0
$46$	−4.01363	+	6.95180i	−0.591777	+	1.02499i
$47$	7.53443	−	6.32214i	1.09901	−	0.922179i	0.101652	−	0.994820i	$-0.467587\pi$
$47$	7.53443	−	6.32214i	1.09901	−	0.922179i	0.997358	+	0.0726409i	$0.0231427\pi$
$48$	−0.0653289	+	0.0548174i	−0.00942941	+	0.00791222i
$49$	1.80585	−	3.12782i	0.257978	−	0.446831i
$50$		0			0
$51$	0.546751	+	0.199001i	0.0765605	+	0.0278657i
$52$	0.526632	−	2.98668i	0.0730307	−	0.414178i
$53$	1.08918	+	6.17705i	0.149610	+	0.848483i	0.963549	+	0.267532i	$0.0862080\pi$
$53$	1.08918	+	6.17705i	0.149610	+	0.848483i	−0.813939	+	0.580951i	$0.802681\pi$
$54$	−0.480244	+	0.174794i	−0.0653529	+	0.0237865i
$55$		0			0
$56$	1.84074			0.245979
$57$	−0.165527	+	0.332843i	−0.0219247	+	0.0440861i
$58$	−10.1536			−1.33323
$59$	−4.62264	−	3.87886i	−0.601817	−	0.504984i	0.290212	−	0.956962i	$-0.406274\pi$
$59$	−4.62264	−	3.87886i	−0.601817	−	0.504984i	−0.892029	+	0.451978i	$0.850719\pi$
$60$		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	$0.856263\pi$
$62$	0.839980	−	4.76376i	0.106678	−	0.604999i
$63$	5.17660	+	1.88413i	0.652190	+	0.237378i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.158128	+	0.132685i	−0.0194642	+	0.0163324i
$67$	2.39061	−	2.00596i	0.292059	−	0.245067i	−0.484971	−	0.874530i	$-0.661170\pi$
$67$	2.39061	−	2.00596i	0.292059	−	0.245067i	0.777030	+	0.629463i	$0.216725\pi$
$68$	−3.41132	+	5.90858i	−0.413684	+	0.716521i
$69$	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	$0.824754\pi$
$72$	−0.519682	−	2.94726i	−0.0612451	−	0.347338i
$73$	7.33739	−	2.67059i	0.858777	−	0.312569i	0.125163	−	0.992136i	$-0.460055\pi$
$73$	7.33739	−	2.67059i	0.858777	−	0.312569i	0.733613	+	0.679567i	$0.237832\pi$
$74$	−0.154847	−	0.129932i	−0.0180006	−	0.0151043i
$75$		0			0
$76$	−3.50656	−	2.58921i	−0.402230	−	0.297003i
$77$	4.45548			0.507749
$78$	−0.198126	−	0.166248i	−0.0224334	−	0.0188239i
$79$	−9.87176	+	3.59303i	−1.11066	+	0.404247i	−0.831236	−	0.555920i	$-0.812366\pi$
$79$	−9.87176	+	3.59303i	−1.11066	+	0.404247i	−0.279425	+	0.960168i	$0.590144\pi$
$80$		0			0
$81$	1.55148	−	8.79886i	0.172386	−	0.977651i
$82$	5.41537	+	1.97103i	0.598028	+	0.217664i
$83$	−6.37710	−	11.0455i	−0.699978	−	1.21240i	−0.968474	−	0.249116i	$-0.919860\pi$
$83$	−6.37710	−	11.0455i	−0.699978	−	1.21240i	0.268496	−	0.963281i	$-0.413473\pi$
$84$	0.0784897	−	0.135948i	0.00856393	−	0.0148332i
$85$		0			0
$86$	1.61119	−	1.35195i	0.173739	−	0.145785i
$87$	−0.432953	+	0.749896i	−0.0464174	+	0.0803973i
$88$	−1.21024	−	2.09620i	−0.129012	−	0.223456i
$89$	−1.21570	−	0.442480i	−0.128864	−	0.0469028i	0.276783	−	0.960932i	$-0.410732\pi$
$89$	−1.21570	−	0.442480i	−0.128864	−	0.0469028i	−0.405647	+	0.914030i	$0.632954\pi$
$90$		0			0
$91$	0.969391	+	5.49769i	0.101620	+	0.576314i
$92$	−7.54315	+	2.74548i	−0.786428	+	0.286236i
$93$	−0.316012	−	0.265166i	−0.0327690	−	0.0274964i
$94$	9.83551			1.01445
$95$		0			0
$96$	−0.0852808			−0.00870394
$97$	−6.28244	−	5.27159i	−0.637885	−	0.535249i	0.265483	−	0.964116i	$-0.414469\pi$
$97$	−6.28244	−	5.27159i	−0.637885	−	0.535249i	−0.903368	+	0.428866i	$0.858913\pi$
$98$	3.39388	−	1.23527i	0.342834	−	0.124781i
$99$	−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	$0.741341\pi$
$102$	0.290920	+	0.503889i	0.0288054	+	0.0498924i
$103$	−1.69681	+	2.93896i	−0.167192	+	0.289584i	−0.937431	−	0.348170i	$-0.886803\pi$
$103$	−1.69681	+	2.93896i	−0.167192	+	0.289584i	0.770240	+	0.637754i	$0.220137\pi$
$104$	2.32322	−	1.94942i	0.227811	−	0.191156i
$105$		0			0
$106$	−3.13617	+	5.43200i	−0.304612	+	0.527603i
$107$	−5.76673	−	9.98827i	−0.557491	−	0.965603i	−0.997705	−	0.0677099i	$-0.978431\pi$
$107$	−5.76673	−	9.98827i	−0.557491	−	0.965603i	0.440214	−	0.897893i	$-0.354903\pi$
$108$	−0.480244	−	0.174794i	−0.0462115	−	0.0168196i
$109$	−1.87490	+	10.6331i	−0.179583	+	1.01847i	0.753136	+	0.657865i	$0.228540\pi$
$109$	−1.87490	+	10.6331i	−0.179583	+	1.01847i	−0.932719	+	0.360603i	$0.882571\pi$
$110$		0			0
$111$	−0.0161990	+	0.00589594i	−0.00153754	+	0.000559618i
$112$	1.41009	+	1.18320i	0.133241	+	0.111802i
$113$	11.9087			1.12028			0.560139	−	0.828399i	$-0.310748\pi$
$113$	11.9087			1.12028			0.560139	+	0.828399i	$0.310748\pi$
$114$	−0.340748	+	0.148573i	−0.0319140	+	0.0139152i
$115$		0			0
$116$	−7.77809	−	6.52659i	−0.722178	−	0.605979i
$117$	8.52884	−	3.10424i	0.788492	−	0.286987i
$118$	−1.04787	−	5.94276i	−0.0964641	−	0.547075i
$119$	2.18079	−	12.3679i	0.199913	−	1.13376i
$120$		0			0
$121$	2.57062	+	4.45245i	0.233693	+	0.404768i
$122$	−2.13610	+	3.69983i	−0.193393	+	0.334967i
$123$	0.376485	−	0.315908i	0.0339465	−	0.0284845i
$124$	3.70555	−	3.10933i	0.332768	−	0.279226i
$125$		0			0
$126$	2.75441	+	4.77078i	0.245382	+	0.425015i
$127$	4.49504	+	1.63606i	0.398870	+	0.145177i	0.533664	−	0.845697i	$-0.320815\pi$
$127$	4.49504	+	1.63606i	0.398870	+	0.145177i	−0.134793	+	0.990874i	$0.543037\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−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	$0.531085\pi$
$132$	−0.206421			−0.0179666
$133$	7.69548	+	2.27101i	0.667283	+	0.196921i
$134$	3.12072			0.269589
$135$		0			0
$136$	−6.41119	+	2.33348i	−0.549755	+	0.200094i
$137$	0.460196	+	2.60990i	0.0393172	+	0.222979i	0.998135	−	0.0610423i	$-0.0194425\pi$
$137$	0.460196	+	2.60990i	0.0393172	+	0.222979i	−0.958818	+	0.284021i	$0.908331\pi$
$138$	−0.118874	+	0.674170i	−0.0101193	+	0.0573892i
$139$	10.8366	+	3.94420i	0.919149	+	0.334543i	0.757900	−	0.652371i	$-0.226225\pi$
$139$	10.8366	+	3.94420i	0.919149	+	0.334543i	0.161249	+	0.986914i	$0.448448\pi$
$140$		0			0
$141$	0.419390	−	0.726405i	0.0353190	−	0.0611743i
$142$	−8.56163	+	7.18406i	−0.718476	+	0.602873i
$143$	5.62333	−	4.71854i	0.470247	−	0.394584i
$144$	1.49636	−	2.59178i	0.124697	−	0.215981i
$145$		0			0
$146$	7.33739	+	2.67059i	0.607247	+	0.221020i
$147$	0.0534850	−	0.303329i	0.00441137	−	0.0250181i
$148$	−0.0351010	−	0.199068i	−0.00288529	−	0.0163633i
$149$	11.4325	−	4.16108i	0.936585	−	0.340889i	0.171769	−	0.985137i	$-0.445052\pi$
$149$	11.4325	−	4.16108i	0.936585	−	0.340889i	0.764817	+	0.644248i	$0.222830\pi$
$150$		0			0
$151$	17.4621			1.42104			0.710521	−	0.703676i	$-0.248459\pi$
$151$	17.4621			1.42104			0.710521	+	0.703676i	$0.248459\pi$
$152$	−1.02187	−	4.23743i	−0.0828844	−	0.343701i
$153$	−20.4183			−1.65072
$154$	3.41309	+	2.86393i	0.275035	+	0.230782i
$155$		0			0
$156$	−0.0449116	−	0.254706i	−0.00359581	−	0.0203928i
$157$	−3.89857	+	22.1099i	−0.311140	+	1.76456i	0.281952	+	0.959428i	$0.409018\pi$
$157$	−3.89857	+	22.1099i	−0.311140	+	1.76456i	−0.593092	+	0.805134i	$0.702093\pi$
$158$	−9.87176	−	3.59303i	−0.785355	−	0.285846i
$159$	0.267455	+	0.463246i	0.0212106	+	0.0367378i
$160$		0			0
$161$	11.3191	−	9.49786i	0.892071	−	0.748536i
$162$	6.84430	−	5.74305i	0.537739	−	0.451217i
$163$	4.75414	−	8.23440i	0.372373	−	0.644968i	−0.617557	−	0.786526i	$-0.711878\pi$
$163$	4.75414	−	8.23440i	0.372373	−	0.644968i	0.989930	+	0.141558i	$0.0452110\pi$
$164$	2.88146	+	4.99083i	0.225004	+	0.389719i
$165$		0			0
$166$	2.21474	−	12.5604i	0.171897	−	0.974879i
$167$	0.0476307	+	0.270127i	0.00368577	+	0.0209030i	0.986595	−	0.163187i	$-0.0521773\pi$
$167$	0.0476307	+	0.270127i	0.00368577	+	0.0209030i	−0.982909	+	0.184090i	$0.941066\pi$
$168$	0.147512	−	0.0536901i	0.0113808	−	0.00414228i
$169$	−2.91281	−	2.44414i	−0.224063	−	0.188011i
$170$		0			0
$171$	1.46358	−	12.9626i	0.111922	−	0.991277i
$172$	2.10326			0.160372
$173$	8.95459	+	7.51380i	0.680805	+	0.571263i	0.916241	−	0.400626i	$-0.131207\pi$
$173$	8.95459	+	7.51380i	0.680805	+	0.571263i	−0.235436	+	0.971890i	$0.575652\pi$
$174$	−0.813685	+	0.296157i	−0.0616853	+	0.0224516i
$175$		0			0
$176$	0.420313	−	2.38371i	0.0316823	−	0.179679i
$177$	−0.483586	−	0.176011i	−0.0363485	−	0.0132298i
$178$	−0.646862	−	1.12040i	−0.0484844	−	0.0839774i
$179$	8.22436	−	14.2450i	0.614718	−	1.06472i	−0.375716	−	0.926735i	$-0.622603\pi$
$179$	8.22436	−	14.2450i	0.614718	−	1.06472i	0.990434	−	0.137987i	$-0.0440633\pi$
$180$		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	$0.973985\pi$
$182$	−2.79125	+	4.83458i	−0.206901	+	0.358363i
$183$	0.182168	+	0.315525i	0.0134663	+	0.0233243i
$184$	−7.54315	−	2.74548i	−0.556088	−	0.202400i
$185$		0			0
$186$	−0.0716342	−	0.406258i	−0.00525247	−	0.0297883i
$187$	−15.5182	+	5.64816i	−1.13480	+	0.413034i
$188$	7.53443	+	6.32214i	0.549505	+	0.461090i
$189$	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	$0.556132\pi$
$192$	−0.0653289	−	0.0548174i	−0.00471471	−	0.00395611i
$193$	9.24069	−	3.36334i	0.665160	−	0.242098i	0.0126972	−	0.999919i	$-0.495958\pi$
$193$	9.24069	−	3.36334i	0.665160	−	0.242098i	0.652462	+	0.757821i	$0.273736\pi$
$194$	−1.42411	−	8.07655i	−0.102245	−	0.579862i
$195$		0			0
$196$	3.39388	+	1.23527i	0.242420	+	0.0882336i
$197$	4.90346	+	8.49304i	0.349357	+	0.605104i	0.986135	−	0.165943i	$-0.0530667\pi$
$197$	4.90346	+	8.49304i	0.349357	+	0.605104i	−0.636778	+	0.771047i	$0.719733\pi$
$198$	3.62193	−	6.27336i	0.257399	−	0.445828i
$199$	1.06106	−	0.890332i	0.0752163	−	0.0631140i	−0.604404	−	0.796678i	$-0.706589\pi$
$199$	1.06106	−	0.890332i	0.0752163	−	0.0631140i	0.679621	+	0.733564i	$0.262144\pi$
$200$		0			0
$201$	0.133069	−	0.230482i	0.00938594	−	0.0162569i
$202$	−3.99795	−	6.92466i	−0.281295	−	0.487217i
$203$	17.5629	+	6.39237i	1.23267	+	0.448657i
$204$	−0.101036	+	0.573001i	−0.00707390	+	0.0401181i
$205$		0			0
$206$	−3.18896	+	1.16069i	−0.222185	+	0.0808689i
$207$	−18.4030	−	15.4419i	−1.27910	−	1.07329i
$208$	3.03275			0.210284
$209$	−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	$0.774259\pi$
$212$	−5.89407	+	2.14527i	−0.404806	+	0.147337i
$213$	0.165510	+	0.938653i	0.0113406	+	0.0643155i
$214$	2.00277	−	11.3582i	0.136906	−	0.776434i
$215$		0			0
$216$	−0.255532	−	0.442595i	−0.0173868	−	0.0301148i
$217$	−4.45205	+	7.71118i	−0.302225	+	0.523469i
$218$	−8.27109	+	6.94027i	−0.560189	+	0.470054i
$219$	0.510107	−	0.428031i	0.0344698	−	0.0289236i
$220$		0			0
$221$	−10.3457	−	17.9193i	−0.695927	−	1.20538i
$222$	−0.0161990	−	0.00589594i	−0.00108720	−	0.000395709i
$223$	4.49724	−	25.5051i	0.301157	−	1.70795i	−0.339906	−	0.940459i	$-0.610395\pi$
$223$	4.49724	−	25.5051i	0.301157	−	1.70795i	0.641064	−	0.767488i	$-0.278494\pi$
$224$	0.319640	+	1.81277i	0.0213569	+	0.121121i
$225$		0			0
$226$	9.12261	+	7.65478i	0.606827	+	0.509188i
$227$	11.0277			0.731932			0.365966	−	0.930628i	$-0.380739\pi$
$227$	11.0277			0.731932			0.365966	+	0.930628i	$0.380739\pi$
$228$	−0.356529	−	0.105215i	−0.0236117	−	0.00696805i
$229$	24.1631			1.59674			0.798370	−	0.602167i	$-0.205696\pi$
$229$	24.1631			1.59674			0.798370	+	0.602167i	$0.205696\pi$
$230$		0			0
$231$	0.357052	−	0.129956i	0.0234923	−	0.00855049i
$232$	−1.76315	−	9.99932i	−0.115756	−	0.656487i
$233$	−3.45540	+	19.5965i	−0.226371	+	1.28381i	0.633677	+	0.773598i	$0.281545\pi$
$233$	−3.45540	+	19.5965i	−0.226371	+	1.28381i	−0.860048	+	0.510214i	$0.829566\pi$
$234$	8.52884	+	3.10424i	0.557548	+	0.202931i
$235$		0			0
$236$	3.01722	−	5.22597i	0.196404	−	0.340182i
$237$	−0.686300	+	0.575874i	−0.0445800	+	0.0374071i
$238$	9.62051	−	8.07257i	0.623605	−	0.523267i
$239$	−9.00250	+	15.5928i	−0.582323	+	1.00861i	0.412880	+	0.910785i	$0.364523\pi$
$239$	−9.00250	+	15.5928i	−0.582323	+	1.00861i	−0.995203	+	0.0978282i	$0.968810\pi$
$240$		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	$0.519273\pi$
$242$	−0.892768	+	5.06314i	−0.0573893	+	0.325471i
$243$	−0.398548	−	2.26028i	−0.0255668	−	0.144997i
$244$	−4.01456	+	1.46118i	−0.257006	+	0.0935424i
$245$		0			0
$246$	0.491466			0.0313347
$247$	12.1177	−	5.28355i	0.771030	−	0.336184i
$248$	4.83725			0.307166
$249$	−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	$-0.204425\pi$
$252$	−0.956597	+	5.42513i	−0.0602599	+	0.341751i
$253$	−18.2581	−	6.64540i	−1.14788	−	0.417793i
$254$	2.39176	+	4.14265i	0.150072	+	0.259933i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−22.4360	+	18.8261i	−1.39952	+	1.17434i	−0.438210	+	0.898873i	$0.644387\pi$
$257$	−22.4360	+	18.8261i	−1.39952	+	1.17434i	−0.961311	+	0.275465i	$0.911168\pi$
$258$	0.0896840	−	0.155337i	0.00558348	−	0.00967087i
$259$	0.186042	+	0.322234i	0.0115601	+	0.0200227i
$260$		0			0
$261$	5.27663	−	29.9252i	0.326615	−	1.85233i
$262$	2.24601	+	12.7377i	0.138759	+	0.786940i
$263$	0.0138755	−	0.00505025i	0.000855598	−	0.000311412i	−0.341592	−	0.939848i	$-0.610966\pi$
$263$	0.0138755	−	0.00505025i	0.000855598	−	0.000311412i	0.342448	+	0.939537i	$0.388744\pi$
$264$	−0.158128	−	0.132685i	−0.00973209	−	0.00816619i
$265$		0			0
$266$	4.43530	+	6.68625i	0.271946	+	0.409960i
$267$	−0.110330			−0.00675208
$268$	2.39061	+	2.00596i	0.146030	+	0.122533i
$269$	11.7330	−	4.27045i	0.715371	−	0.260374i	0.0414116	−	0.999142i	$-0.486815\pi$
$269$	11.7330	−	4.27045i	0.715371	−	0.260374i	0.673959	+	0.738768i	$0.264592\pi$
$270$		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	$0.0596249\pi$
$272$	−6.41119	−	2.33348i	−0.388735	−	0.141488i
$273$	0.238040	+	0.412297i	0.0144068	+	0.0249534i
$274$	−1.32508	+	2.29511i	−0.0800511	+	0.138653i
$275$		0			0
$276$	−0.524412	+	0.440033i	−0.0315659	+	0.0264869i
$277$	−15.2888	+	26.4810i	−0.918616	+	1.59109i	−0.117098	+	0.993120i	$0.537359\pi$
$277$	−15.2888	+	26.4810i	−0.918616	+	1.59109i	−0.801519	+	0.597970i	$0.795974\pi$
$278$	5.76604	+	9.98707i	0.345824	+	0.598985i
$279$	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	$0.837299\pi$
$282$	0.788195	−	0.286880i	0.0469363	−	0.0170834i
$283$	−0.610978	−	0.512672i	−0.0363189	−	0.0304752i	0.624448	−	0.781067i	$-0.285324\pi$
$283$	−0.610978	−	0.512672i	−0.0363189	−	0.0304752i	−0.660766	+	0.750592i	$0.729769\pi$
$284$	−11.1764			−0.663198
$285$		0			0
$286$	7.34074			0.434067
$287$	−8.12621	−	6.81870i	−0.479675	−	0.402495i
$288$	2.81224	−	1.02357i	0.165713	−	0.0603146i
$289$	5.13104	+	29.0996i	0.301826	+	1.71174i
$290$		0			0
$291$	−0.657221	−	0.239209i	−0.0385270	−	0.0140227i
$292$	3.90414	+	6.76218i	0.228473	+	0.395726i
$293$	−6.86939	+	11.8981i	−0.401314	+	0.695096i	−0.993885	−	0.110422i	$-0.964780\pi$
$293$	−6.86939	+	11.8981i	−0.401314	+	0.695096i	0.592571	+	0.805518i	$0.298113\pi$
$294$	0.235948	−	0.197984i	0.0137608	−	0.0115466i
$295$		0			0
$296$	0.101069	−	0.175057i	0.00587454	−	0.0101750i
$297$	−0.618513	−	1.07130i	−0.0358897	−	0.0621628i
$298$	11.4325	+	4.16108i	0.662266	+	0.241045i
$299$	4.22741	−	23.9748i	0.244477	−	1.38650i
$300$		0			0
$301$	−3.63807	+	1.32415i	−0.209695	+	0.0763226i
$302$	13.3767	+	11.2244i	0.769744	+	0.645892i
$303$	−0.681898			−0.0391740
$304$	1.94097	−	3.90290i	0.111322	−	0.223847i
$305$		0			0
$306$	−15.6413	−	13.1246i	−0.894156	−	0.750286i
$307$	−0.624954	+	0.227465i	−0.0356680	+	0.0129821i	−0.359793	−	0.933032i	$-0.617153\pi$
$307$	−0.624954	+	0.227465i	−0.0356680	+	0.0129821i	0.324125	+	0.946014i	$0.394930\pi$
$308$	0.773685	+	4.38779i	0.0440848	+	0.250017i
$309$	−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	$0.533389\pi$
$312$	0.129318	−	0.223985i	0.00732118	−	0.0126807i
$313$	7.65401	−	6.42248i	0.432630	−	0.363020i	−0.400313	−	0.916379i	$-0.631099\pi$
$313$	7.65401	−	6.42248i	0.432630	−	0.363020i	0.832943	+	0.553359i	$0.186654\pi$
$314$	−17.1985	+	14.4312i	−0.970565	+	0.814401i
$315$		0			0
$316$	−5.25266	−	9.09787i	−0.295485	−	0.511795i
$317$	10.9305	+	3.97837i	0.613918	+	0.223448i	0.630217	−	0.776419i	$-0.282966\pi$
$317$	10.9305	+	3.97837i	0.613918	+	0.223448i	−0.0162989	+	0.999867i	$0.505188\pi$
$318$	−0.0928861	+	0.526784i	−0.00520880	+	0.0295406i
$319$	−4.26768	−	24.2032i	−0.238944	−	1.35512i
$320$		0			0
$321$	−0.753468	−	0.632235i	−0.0420545	−	0.0352879i
$322$	14.7761			0.823437
$323$	−29.6819	+	1.84567i	−1.65154	+	0.102696i
$324$	8.93460			0.496367
$325$		0			0
$326$	8.93485	−	3.25202i	0.494856	−	0.180113i
$327$	0.159893	+	0.906800i	0.00884212	+	0.0501462i
$328$	−1.00072	+	5.67537i	−0.0552555	+	0.313370i
$329$	−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	$0.923432\pi$
$332$	9.77028	−	8.19824i	0.536214	−	0.449937i
$333$	0.463416	−	0.388852i	0.0253950	−	0.0213090i
$334$	−0.137147	+	0.237546i	−0.00750435	+	0.0129979i
$335$		0			0
$336$	0.147512	+	0.0536901i	0.00804746	+	0.00292904i
$337$	−0.245540	+	1.39253i	−0.0133754	+	0.0758559i	−0.990765	−	0.135591i	$-0.956707\pi$
$337$	−0.245540	+	1.39253i	−0.0133754	+	0.0758559i	0.977389	+	0.211447i	$0.0678177\pi$
$338$	−0.660281	−	3.74464i	−0.0359146	−	0.203682i
$339$	0.954338	−	0.347351i	0.0518325	−	0.0188655i
$340$		0			0
$341$	11.7085			0.634051
$342$	9.45338	−	8.98918i	0.511180	−	0.486079i
$343$	−19.5333			−1.05470
$344$	1.61119	+	1.35195i	0.0868697	+	0.0728923i
$345$		0			0
$346$	2.02984	+	11.5118i	0.109125	+	0.618878i
$347$	5.57910	−	31.6406i	0.299502	−	1.69856i	−0.348818	−	0.937190i	$-0.613417\pi$
$347$	5.57910	−	31.6406i	0.299502	−	1.69856i	0.648320	−	0.761368i	$-0.275472\pi$
$348$	−0.813685	−	0.296157i	−0.0436181	−	0.0158757i
$349$	0.908473	+	1.57352i	0.0486295	+	0.0842287i	0.889316	−	0.457294i	$-0.151181\pi$
$349$	0.908473	+	1.57352i	0.0486295	+	0.0842287i	−0.840686	+	0.541523i	$0.817848\pi$
$350$		0			0
$351$	1.18732	−	0.996278i	0.0633743	−	0.0531774i
$352$	1.85420	−	1.55586i	0.0988292	−	0.0829275i
$353$	13.5160	−	23.4104i	0.719385	−	1.24601i	−0.241859	−	0.970311i	$-0.577757\pi$
$353$	13.5160	−	23.4104i	0.719385	−	1.24601i	0.961244	−	0.275699i	$-0.0889094\pi$
$354$	−0.257311	−	0.445675i	−0.0136759	−	0.0236874i
$355$		0			0
$356$	0.224653	−	1.27407i	0.0119066	−	0.0675256i
$357$	−0.185980	−	1.05474i	−0.00984309	−	0.0558230i
$358$	15.4567	−	5.62579i	0.816914	−	0.297332i
$359$	17.9055	+	15.0245i	0.945017	+	0.792963i	0.978451	−	0.206478i	$-0.0662001\pi$
$359$	17.9055	+	15.0245i	0.945017	+	0.792963i	−0.0334346	+	0.999441i	$0.510645\pi$
$360$		0			0
$361$	0.955856	−	18.9759i	0.0503082	−	0.998734i
$362$	−21.9553			−1.15395
$363$	0.335872	+	0.281830i	0.0176287	+	0.0147922i
$364$	−5.24583	+	1.90933i	−0.274956	+	0.100076i
$365$		0			0
$366$	−0.0632664	+	0.358802i	−0.00330699	+	0.0187549i
$367$	−7.40612	−	2.69561i	−0.386596	−	0.140710i	0.141408	−	0.989951i	$-0.454837\pi$
$367$	−7.40612	−	2.69561i	−0.386596	−	0.140710i	−0.528004	+	0.849242i	$0.677059\pi$
$368$	−4.01363	−	6.95180i	−0.209225	−	0.362388i
$369$	−8.62342	+	14.9362i	−0.448917	+	0.777548i
$370$		0			0
$371$	8.84453	−	7.42144i	0.459185	−	0.385302i
$372$	0.206262	−	0.357257i	0.0106942	−	0.0185229i
$373$	−6.85652	−	11.8758i	−0.355017	−	0.614907i	0.632104	−	0.774884i	$-0.282192\pi$
$373$	−6.85652	−	11.8758i	−0.355017	−	0.614907i	−0.987121	+	0.159976i	$0.948858\pi$
$374$	−15.5182	−	5.64816i	−0.802427	−	0.292059i
$375$		0			0
$376$	1.70792	+	9.68608i	0.0880791	+	0.499522i
$377$	28.9362	−	10.5319i	1.49029	−	0.542422i
$378$	0.720645	+	0.604693i	0.0370660	+	0.0311020i
$379$	−14.9079			−0.765766			−0.382883	−	0.923797i	$-0.625069\pi$
$379$	−14.9079			−0.765766			−0.382883	+	0.923797i	$0.625069\pi$
$380$		0			0
$381$	0.407942			0.0208995
$382$	−3.71453	−	3.11686i	−0.190052	−	0.159473i
$383$	−9.48923	+	3.45380i	−0.484877	+	0.176481i	−0.572880	−	0.819639i	$-0.694174\pi$
$383$	−9.48923	+	3.45380i	−0.484877	+	0.176481i	0.0880027	+	0.996120i	$0.471952\pi$
$384$	−0.0148089	−	0.0839852i	−0.000755711	−	0.00428585i
$385$		0			0
$386$	9.24069	+	3.36334i	0.470339	+	0.171189i
$387$	3.14725	+	5.45119i	0.159983	+	0.277099i
$388$	4.10057	−	7.10240i	0.208175	−	0.360570i
$389$	4.69733	−	3.94153i	0.238164	−	0.199844i	−0.515891	−	0.856654i	$-0.672539\pi$
$389$	4.69733	−	3.94153i	0.238164	−	0.199844i	0.754056	+	0.656810i	$0.228095\pi$
$390$		0			0
$391$	−27.3835	+	47.4297i	−1.38485	+	2.39862i
$392$	1.80585	+	3.12782i	0.0912090	+	0.157979i
$393$	1.03652	+	0.377262i	0.0522855	+	0.0190304i
$394$	−1.70295	+	9.65793i	−0.0857936	+	0.486560i
$395$		0			0
$396$	6.80700	−	2.47754i	0.342064	−	0.124501i
$397$	−1.19313	−	1.00116i	−0.0598817	−	0.0502467i	0.612356	−	0.790582i	$-0.290222\pi$
$397$	−1.19313	−	1.00116i	−0.0598817	−	0.0502467i	−0.672237	+	0.740336i	$0.734667\pi$
$398$	1.38511			0.0694293
$399$	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	$-0.630544\pi$
$402$	0.250087	−	0.0910244i	0.0124732	−	0.00453988i
$403$	2.54745	+	14.4473i	0.126898	+	0.719672i
$404$	1.38847	−	7.87443i	0.0690792	−	0.391768i
$405$		0			0
$406$	9.34503	+	16.1861i	0.463786	+	0.803301i
$407$	0.244637	−	0.423724i	0.0121262	−	0.0210032i
$408$	−0.445716	+	0.374000i	−0.0220662	+	0.0185158i
$409$	−26.8662	+	22.5434i	−1.32845	+	1.11470i	−0.344013	+	0.938965i	$0.611786\pi$
$409$	−26.8662	+	22.5434i	−1.32845	+	1.11470i	−0.984437	+	0.175737i	$0.943769\pi$
$410$		0			0
$411$	0.113004	+	0.195729i	0.00557408	+	0.00965459i
$412$	−3.18896	−	1.16069i	−0.157109	−	0.0571829i
$413$	−1.92885	+	10.9390i	−0.0949124	+	0.538275i
$414$	−4.17162	−	23.6584i	−0.205024	−	1.16275i
$415$		0			0
$416$	2.32322	+	1.94942i	0.113905	+	0.0955780i
$417$	0.983465			0.0481605
$418$	4.69809	−	9.44692i	0.229791	−	0.462064i
$419$	12.6047			0.615780			0.307890	−	0.951422i	$-0.400377\pi$
$419$	12.6047			0.615780			0.307890	+	0.951422i	$0.400377\pi$
$420$		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	$0.614363\pi$
$422$	−0.821042	−	4.65636i	−0.0399677	−	0.226668i
$423$	−5.11133	+	28.9878i	−0.248521	+	1.40944i
$424$	−5.89407	−	2.14527i	−0.286241	−	0.104183i
$425$		0			0
$426$	−0.476567	+	0.825438i	−0.0230897	+	0.0399926i
$427$	6.02417	−	5.05488i	0.291530	−	0.244623i
$428$	8.83515	−	7.41357i	0.427063	−	0.358348i
$429$	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	$0.673663\pi$
$432$	0.0887454	−	0.503300i	0.00426977	−	0.0242151i
$433$	3.96602	+	22.4924i	0.190595	+	1.08092i	0.918554	+	0.395296i	$0.129358\pi$
$433$	3.96602	+	22.4924i	0.190595	+	1.08092i	−0.727959	+	0.685620i	$0.759531\pi$
$434$	−8.36712	+	3.04538i	−0.401635	+	0.146183i
$435$		0			0
$436$	−10.7971			−0.517089
$437$	−28.1481	−	20.7843i	−1.34650	−	0.994247i
$438$	0.665897			0.0318178
$439$	−10.8652	−	9.11699i	−0.518568	−	0.435130i	0.345564	−	0.938395i	$-0.387688\pi$
$439$	−10.8652	−	9.11699i	−0.518568	−	0.435130i	−0.864132	+	0.503265i	$0.832132\pi$
$440$		0			0
$441$	1.87693	+	10.6446i	0.0893776	+	0.506886i
$442$	3.59302	−	20.3770i	0.170903	−	0.969237i
$443$	−29.5868	−	10.7687i	−1.40571	−	0.511637i	−0.475843	−	0.879530i	$-0.657857\pi$
$443$	−29.5868	−	10.7687i	−1.40571	−	0.511637i	−0.929868	+	0.367894i	$0.880079\pi$
$444$	−0.00861928	−	0.0149290i	−0.000409053	−	0.000708501i
$445$		0			0
$446$	19.8394	−	16.6473i	0.939425	−	0.788271i
$447$	0.794804	−	0.666920i	0.0375929	−	0.0315442i
$448$	−0.920368	+	1.59412i	−0.0434833	+	0.0753153i
$449$	13.6115	+	23.5758i	0.642366	+	1.11261i	0.984903	+	0.173106i	$0.0553804\pi$
$449$	13.6115	+	23.5758i	0.642366	+	1.11261i	−0.342537	+	0.939504i	$0.611286\pi$
$450$		0			0
$451$	−2.42223	+	13.7371i	−0.114058	+	0.646857i
$452$	2.06793	+	11.7278i	0.0972671	+	0.551629i
$453$	1.39937	−	0.509329i	0.0657482	−	0.0239304i
$454$	8.44769	+	7.08845i	0.396470	+	0.332678i
$455$		0			0
$456$	−0.205486	−	0.309772i	−0.00962278	−	0.0145064i
$457$	27.4781			1.28537			0.642687	−	0.766129i	$-0.277820\pi$
$457$	27.4781			1.28537			0.642687	+	0.766129i	$0.277820\pi$
$458$	18.5100	+	15.5317i	0.864915	+	0.725750i
$459$	−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	$0.0134817\pi$
$462$	0.357052	+	0.129956i	0.0166116	+	0.00604611i
$463$	−11.0325	−	19.1089i	−0.512726	−	0.888067i	−0.999891	−	0.0147575i	$-0.995302\pi$
$463$	−11.0325	−	19.1089i	−0.512726	−	0.888067i	0.487165	−	0.873310i	$-0.338031\pi$
$464$	5.07679	−	8.79325i	0.235684	−	0.408217i
$465$		0			0
$466$	−15.2434	+	12.7907i	−0.706137	+	0.592519i
$467$	10.6841	−	18.5055i	0.494403	−	0.856331i	−0.505576	−	0.862782i	$-0.668720\pi$
$467$	10.6841	−	18.5055i	0.494403	−	0.856331i	0.999979	+	0.00645068i	$0.00205333\pi$
$468$	4.53810	+	7.86022i	0.209774	+	0.363339i
$469$	−5.39799	−	1.96471i	−0.249256	−	0.0907218i
$470$		0			0
$471$	0.332474	+	1.88555i	0.0153196	+	0.0868816i
$472$	5.67051	−	2.06390i	0.261006	−	0.0949986i
$473$	3.89987	+	3.27238i	0.179316	+	0.150464i
$474$	−0.895901			−0.0411501
$475$		0			0
$476$	12.5587			0.575626
$477$	−14.3797	−	12.0660i	−0.658402	−	0.552465i
$478$	−16.9192	+	6.15807i	−0.773865	+	0.281664i
$479$	−3.34220	−	18.9545i	−0.152709	−	0.866055i	−0.960851	−	0.277067i	$-0.910638\pi$
$479$	−3.34220	−	18.9545i	−0.152709	−	0.866055i	0.808142	−	0.588988i	$-0.200474\pi$
$480$		0			0
$481$	0.576067	+	0.209671i	0.0262664	+	0.00956018i
$482$	4.41711	+	7.65066i	0.201194	+	0.348478i
$483$	0.630057	−	1.09129i	0.0286686	−	0.0496554i
$484$	−3.93842	+	3.30473i	−0.179019	+	0.150215i
$485$		0			0
$486$	1.14757	−	1.98765i	0.0520549	−	0.0901618i
$487$	−7.35793	−	12.7443i	−0.333420	−	0.577500i	0.649760	−	0.760139i	$-0.274869\pi$
$487$	−7.35793	−	12.7443i	−0.333420	−	0.577500i	−0.983180	+	0.182639i	$0.941536\pi$
$488$	−4.01456	−	1.46118i	−0.181730	−	0.0661445i
$489$	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	$0.737966\pi$
$492$	0.376485	+	0.315908i	0.0169733	+	0.0142423i
$493$	−69.2742			−3.11995
$494$	12.6789	+	3.74166i	0.570450	+	0.168345i
$495$		0			0
$496$	3.70555	+	3.10933i	0.166384	+	0.139613i
$497$	19.3321	−	7.03632i	0.867165	−	0.315622i
$498$	−0.188875	−	1.07116i	−0.00846370	−	0.0480000i
$499$	−0.814770	+	4.62079i	−0.0364741	+	0.206855i	−0.997599	−	0.0692604i	$-0.977936\pi$
$499$	−0.814770	+	4.62079i	−0.0364741	+	0.206855i	0.961125	+	0.276115i	$0.0890472\pi$
$500$		0			0
$501$	0.0116960	+	0.0202581i	0.000522539	+	0.000905064i
$502$	7.14238	−	12.3710i	0.318780	−	0.552143i
$503$	6.66619	−	5.59360i	0.297231	−	0.249406i	−0.481960	−	0.876193i	$-0.660075\pi$
$503$	6.66619	−	5.59360i	0.297231	−	0.249406i	0.779191	+	0.626787i	$0.215630\pi$
$504$	−4.22000	+	3.54100i	−0.187974	+	0.157729i
$505$		0			0
$506$	−9.71493	−	16.8267i	−0.431881	−	0.748040i
$507$	−0.304717	−	0.110908i	−0.0135329	−	0.00492559i
$508$	−0.830649	+	4.71085i	−0.0368541	+	0.209010i
$509$	0.971085	+	5.50730i	0.0430426	+	0.244107i	0.998736	−	0.0502560i	$-0.0160037\pi$
$509$	0.971085	+	5.50730i	0.0430426	+	0.244107i	−0.955694	+	0.294363i	$0.904893\pi$
$510$		0			0
$511$	−11.0104	−	9.23879i	−0.487069	−	0.408700i
$512$	1.00000			0.0441942
$513$	−0.522240	−	2.16560i	−0.0230575	−	0.0956135i
$514$	−29.2882			−1.29185
$515$		0			0
$516$	0.168551	−	0.0613474i	0.00742003	−	0.00270067i
$517$	4.13399	+	23.4450i	0.181813	+	1.03111i
$518$	−0.0646118	+	0.366431i	−0.00283888	+	0.0161001i
$519$	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	$0.244481\pi$
$522$	23.2777	−	19.5323i	1.01884	−	0.854906i
$523$	28.3456	−	23.7848i	1.23947	−	1.04004i	0.241900	−	0.970301i	$-0.422229\pi$
$523$	28.3456	−	23.7848i	1.23947	−	1.04004i	0.997566	−	0.0697344i	$-0.0222152\pi$
$524$	−6.46712	+	11.2014i	−0.282517	+	0.489334i
$525$		0			0
$526$	0.0138755	+	0.00505025i	0.000604999	+	0.000220202i
$527$	5.73089	−	32.5015i	0.249641	−	1.41579i
$528$	−0.0358446	−	0.203285i	−0.00155994	−	0.00884685i
$529$	−38.9378	+	14.1722i	−1.69295	+	0.616183i
$530$		0			0
$531$	18.0594			0.783712
$532$	−0.900202	+	7.97292i	−0.0390287	+	0.345670i
$533$	−17.4775			−0.757035
$534$	−0.0845176	−	0.0709187i	−0.00365743	−	0.00306895i
$535$		0			0
$536$	0.541907	+	3.07331i	0.0234068	+	0.132747i
$537$	0.243587	−	1.38145i	0.0105115	−	0.0596139i
$538$	11.7330	+	4.27045i	0.505844	+	0.184112i
$539$	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	$-0.00303534\pi$
$542$	−0.322423	+	0.270545i	−0.0138493	+	0.0116209i
$543$	−0.936184	+	1.62152i	−0.0401755	+	0.0695860i
$544$	−3.41132	−	5.90858i	−0.146259	−	0.253328i
$545$		0			0
$546$	−0.0826704	+	0.468847i	−0.00353797	+	0.0200648i
$547$	4.63156	+	26.2669i	0.198031	+	1.12309i	0.908036	+	0.418893i	$0.137582\pi$
$547$	4.63156	+	26.2669i	0.198031	+	1.12309i	−0.710005	+	0.704197i	$0.751307\pi$
$548$	−2.49034	+	0.906409i	−0.106382	+	0.0387199i
$549$	−9.79429	−	8.21838i	−0.418010	−	0.350752i
$550$		0			0
$551$	4.96555	−	43.9790i	0.211540	−	1.87357i
$552$	−0.684571			−0.0291373
$553$	14.8134	+	12.4299i	0.629929	+	0.528573i
$554$	−28.7336	+	10.4582i	−1.22077	+	0.444325i
$555$		0			0
$556$	−2.00252	+	11.3569i	−0.0849260	+	0.481639i
$557$	12.3655	+	4.50069i	0.523945	+	0.190700i	0.590433	−	0.807087i	$-0.298957\pi$
$557$	12.3655	+	4.50069i	0.523945	+	0.190700i	−0.0664876	+	0.997787i	$0.521179\pi$
$558$	7.23829	+	12.5371i	0.306421	+	0.530737i
$559$	−3.18934	+	5.52409i	−0.134895	+	0.233644i
$560$		0			0
$561$	−1.07885	+	0.905262i	−0.0455490	+	0.0382202i
$562$	−5.53661	+	9.58968i	−0.233548	+	0.404516i
$563$	9.12041	+	15.7970i	0.384379	+	0.665765i	0.991683	−	0.128705i	$-0.0410821\pi$
$563$	9.12041	+	15.7970i	0.384379	+	0.665765i	−0.607304	+	0.794470i	$0.707749\pi$
$564$	0.788195	+	0.286880i	0.0331890	+	0.0120798i
$565$		0			0
$566$	−0.138497	−	0.785458i	−0.00582148	−	0.0330153i
$567$	−15.4544	+	5.62494i	−0.649024	+	0.236225i
$568$	−8.56163	−	7.18406i	−0.359238	−	0.301436i
$569$	27.5994			1.15703			0.578514	−	0.815672i	$-0.303633\pi$
$569$	27.5994			1.15703			0.578514	+	0.815672i	$0.303633\pi$
$570$		0			0
$571$	29.8138			1.24767			0.623835	−	0.781556i	$-0.285574\pi$
$571$	29.8138			1.24767			0.623835	+	0.781556i	$0.285574\pi$
$572$	5.62333	+	4.71854i	0.235123	+	0.197292i
$573$	−0.388586	+	0.141434i	−0.0162334	+	0.00590848i
$574$	−1.84206	−	10.4468i	−0.0768862	−	0.436043i
$575$		0			0
$576$	2.81224	+	1.02357i	0.117177	+	0.0426489i
$577$	7.15498	+	12.3928i	0.297866	+	0.515918i	0.975647	−	0.219345i	$-0.0703919\pi$
$577$	7.15498	+	12.3928i	0.297866	+	0.515918i	−0.677782	+	0.735263i	$0.737059\pi$
$578$	−14.7742	+	25.5897i	−0.614527	+	1.06439i
$579$	0.642427	−	0.539061i	0.0266984	−	0.0224026i
$580$		0			0
$581$	−11.7386	+	20.3318i	−0.486997	+	0.843504i
$582$	−0.349700	−	0.605698i	−0.0144955	−	0.0251070i
$583$	−14.2665	−	5.19259i	−0.590859	−	0.215055i
$584$	−1.35590	+	7.68966i	−0.0561073	+	0.318201i
$585$		0			0
$586$	−12.9102	+	4.69894i	−0.533317	+	0.194111i
$587$	4.38558	+	3.67994i	0.181012	+	0.151887i	0.728792	−	0.684735i	$-0.240082\pi$
$587$	4.38558	+	3.67994i	0.181012	+	0.151887i	−0.547779	+	0.836623i	$0.684527\pi$
$588$	0.308008			0.0127020
$589$	20.2229	+	5.96796i	0.833269	+	0.245906i
$590$		0			0
$591$	0.640675	+	0.537590i	0.0263539	+	0.0221135i
$592$	0.189948	−	0.0691356i	0.00780683	−	0.00284145i
$593$	1.89256	+	10.7332i	0.0777182	+	0.440762i	0.998692	+	0.0511364i	$0.0162843\pi$
$593$	1.89256	+	10.7332i	0.0777182	+	0.440762i	−0.920974	+	0.389625i	$0.872605\pi$
$594$	0.214807	−	1.21823i	0.00881364	−	0.0499847i
$595$		0			0
$596$	6.08310	+	10.5362i	0.249173	+	0.431581i
$597$	0.0590617	−	0.102298i	0.00241723	−	0.00418677i
$598$	18.6491	−	15.6485i	0.762618	−	0.639913i
$599$	−8.33800	+	6.99641i	−0.340681	+	0.285866i	−0.797035	−	0.603933i	$-0.793600\pi$
$599$	−8.33800	+	6.99641i	−0.340681	+	0.285866i	0.456354	+	0.889798i	$0.349155\pi$
$600$		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	$0.876282\pi$
$602$	−3.63807	−	1.32415i	−0.148277	−	0.0539683i
$603$	−1.62178	+	9.19757i	−0.0660440	+	0.374554i
$604$	3.03226	+	17.1968i	0.123381	+	0.699727i
$605$		0			0
$606$	−0.522364	−	0.438315i	−0.0212196	−	0.0178053i
$607$	−8.03380			−0.326082			−0.163041	−	0.986619i	$-0.552130\pi$
$607$	−8.03380			−0.326082			−0.163041	+	0.986619i	$0.552130\pi$
$608$	3.99561	−	1.74216i	0.162043	−	0.0706541i
$609$	1.59390			0.0645882
$610$		0			0
$611$	−28.0298	+	10.2020i	−1.13396	+	0.412729i
$612$	−3.54560	−	20.1081i	−0.143322	−	0.812822i
$613$	−2.52835	+	14.3390i	−0.102119	+	0.579145i	0.890213	+	0.455544i	$0.150555\pi$
$613$	−2.52835	+	14.3390i	−0.102119	+	0.579145i	−0.992332	+	0.123601i	$0.960556\pi$
$614$	−0.624954	−	0.227465i	−0.0252211	−	0.00917973i
$615$		0			0
$616$	−2.22774	+	3.85856i	−0.0897581	+	0.155466i
$617$	−4.72364	+	3.96361i	−0.190167	+	0.159569i	−0.732900	−	0.680336i	$-0.761834\pi$
$617$	−4.72364	+	3.96361i	−0.190167	+	0.159569i	0.542734	+	0.839905i	$0.317389\pi$
$618$	−0.221701	+	0.186030i	−0.00891814	+	0.00748321i
$619$	−5.14294	+	8.90783i	−0.206712	+	0.358036i	−0.950677	−	0.310183i	$-0.899610\pi$
$619$	−5.14294	+	8.90783i	−0.206712	+	0.358036i	0.743965	+	0.668219i	$0.232943\pi$
$620$		0			0
$621$	−3.85504	−	1.40312i	−0.154697	−	0.0563052i
$622$	−4.95430	+	28.0972i	−0.198649	+	1.12660i
$623$	0.413527	+	2.34523i	0.0165676	+	0.0939595i
$624$	0.243038	−	0.0884586i	0.00972931	−	0.00354118i
$625$		0			0
$626$	9.99160			0.399345
$627$	−0.497377	−	0.749800i	−0.0198633	−	0.0299441i
$628$	−22.4510			−0.895892
$629$	−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	$-0.165223\pi$
$632$	1.82423	−	10.3457i	0.0725639	−	0.411530i
$633$	−0.378907	−	0.137911i	−0.0150602	−	0.00548146i
$634$	5.81599	+	10.0736i	0.230983	+	0.400074i
$635$		0			0
$636$	−0.409765	+	0.343834i	−0.0162482	+	0.0136339i
$637$	−8.39077	+	7.04069i	−0.332454	+	0.278962i
$638$	12.2883	−	21.2840i	0.486498	−	0.842640i
$639$	−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	$0.992309\pi$
$642$	−0.170797	−	0.968640i	−0.00674084	−	0.0382292i
$643$	13.8304	−	5.03384i	0.545417	−	0.198515i	−0.0545923	−	0.998509i	$-0.517386\pi$
$643$	13.8304	−	5.03384i	0.545417	−	0.198515i	0.600009	+	0.799993i	$0.295164\pi$
$644$	11.3191	+	9.49786i	0.446036	+	0.374268i
$645$		0			0
$646$	−23.9240	−	17.6653i	−0.941278	−	0.695031i
$647$	21.6933			0.852852			0.426426	−	0.904522i	$-0.359772\pi$
$647$	21.6933			0.852852			0.426426	+	0.904522i	$0.359772\pi$
$648$	6.84430	+	5.74305i	0.268869	+	0.225608i
$649$	13.7254	−	4.99564i	0.538769	−	0.196096i
$650$		0			0
$651$	−0.131860	+	0.747813i	−0.00516799	+	0.0293091i
$652$	8.93485	+	3.25202i	0.349916	+	0.127359i
$653$	0.299256	+	0.518327i	0.0117108	+	0.0202837i	0.871821	−	0.489824i	$-0.162939\pi$
$653$	0.299256	+	0.518327i	0.0117108	+	0.0202837i	−0.860111	+	0.510108i	$0.829606\pi$
$654$	−0.460395	+	0.797427i	−0.0180029	+	0.0311819i
$655$		0			0
$656$	−4.41465	+	3.70433i	−0.172363	+	0.144630i
$657$	−11.6840	+	20.2374i	−0.455838	+	0.789534i
$658$	−9.05228	−	15.6790i	−0.352895	−	0.611232i
$659$	−26.5885	−	9.67743i	−1.03574	−	0.376979i	−0.232478	−	0.972602i	$-0.574683\pi$
$659$	−26.5885	−	9.67743i	−1.03574	−	0.376979i	−0.803265	+	0.595622i	$0.796905\pi$
$660$		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	$0.692485\pi$
$662$	−23.6584	+	8.61094i	−0.919509	+	0.334674i
$663$	−1.35175	−	1.13425i	−0.0524975	−	0.0440506i
$664$	12.7542			0.494959
$665$		0			0
$666$	0.604946			0.0234412
$667$	−62.4367	−	52.3906i	−2.41756	−	2.02857i
$668$	−0.257752	+	0.0938141i	−0.00997273	+	0.00362978i
$669$	−0.383528	−	2.17509i	−0.0148280	−	0.0840940i
$670$		0			0
$671$	−9.71718	−	3.53676i	−0.375127	−	0.136535i
$672$	0.0784897	+	0.135948i	0.00302781	+	0.00524432i
$673$	7.34858	−	12.7281i	0.283267	−	0.490633i	−0.688920	−	0.724837i	$-0.741915\pi$
$673$	7.34858	−	12.7281i	0.283267	−	0.490633i	0.972187	+	0.234204i	$0.0752484\pi$
$674$	−1.08320	+	0.908909i	−0.0417231	+	0.0350099i
$675$		0			0
$676$	1.90120	−	3.29298i	0.0731233	−	0.126653i
$677$	−11.7886	−	20.4185i	−0.453075	−	0.784748i	0.545501	−	0.838110i	$-0.316340\pi$
$677$	−11.7886	−	20.4185i	−0.453075	−	0.784748i	−0.998575	+	0.0533622i	$0.983006\pi$
$678$	0.954338	+	0.347351i	0.0366511	+	0.0133399i
$679$	−2.62142	+	14.8668i	−0.100601	+	0.570535i
$680$		0			0
$681$	0.883733	−	0.321653i	0.0338647	−	0.0123258i
$682$	8.96924	+	7.52608i	0.343450	+	0.288189i
$683$	−5.85445			−0.224014			−0.112007	−	0.993707i	$-0.535728\pi$
$683$	−5.85445			−0.224014			−0.112007	+	0.993707i	$0.535728\pi$
$684$	13.0198	−	0.809596i	0.497826	−	0.0309557i
$685$		0			0
$686$	−14.9634	−	12.5558i	−0.571305	−	0.479382i
$687$	1.93637	−	0.704783i	0.0738773	−	0.0268891i
$688$	0.365228	+	2.07131i	0.0139242	+	0.0789679i
$689$	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	$0.774649\pi$
$692$	−5.84470	+	10.1233i	−0.222182	+	0.384831i
$693$	−10.2145	+	8.57095i	−0.388015	+	0.325583i
$694$	24.6120	−	20.6520i	0.934261	−	0.783938i
$695$		0			0
$696$	−0.432953	−	0.749896i	−0.0164110	−	0.0284247i
$697$	36.9471	+	13.4477i	1.39947	+	0.509367i
$698$	−0.315510	+	1.78934i	−0.0119422	+	0.0677276i
$699$	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	$0.534678\pi$
$702$	1.54993			0.0584984
$703$	0.638513	−	0.607160i	0.0240820	−	0.0228995i
$704$	2.42049			0.0912255
$705$		0			0
$706$	25.4018	−	9.24549i	0.956009	−	0.347959i
$707$	2.55582	+	14.4948i	0.0961213	+	0.545131i
$708$	0.0893630	−	0.506803i	0.00335847	−	0.0190468i
$709$	19.2050	+	6.99003i	0.721257	+	0.262516i	0.676459	−	0.736480i	$-0.263513\pi$
$709$	19.2050	+	6.99003i	0.721257	+	0.262516i	0.0447979	+	0.998996i	$0.485736\pi$
$710$		0			0
$711$	15.7198	−	27.2274i	0.589537	−	1.02111i
$712$	0.991050	−	0.831590i	0.0371412	−	0.0311651i
$713$	29.7454	−	24.9593i	1.11397	−	0.934735i
$714$	0.535507	−	0.927526i	0.0200409	−	0.0347118i
$715$		0			0
$716$	15.4567	+	5.62579i	0.577646	+	0.210246i
$717$	−0.266634	+	1.51215i	−0.00995761	+	0.0564724i
$718$	4.05885	+	23.0189i	0.151475	+	0.859057i
$719$	−22.5450	+	8.20572i	−0.840788	+	0.306022i	−0.726279	−	0.687400i	$-0.758752\pi$
$719$	−22.5450	+	8.20572i	−0.840788	+	0.306022i	−0.114509	+	0.993422i	$0.536530\pi$
$720$		0			0
$721$	6.24676			0.232641
$722$	12.9297	−	13.9220i	0.481195	−	0.518123i
$723$	0.753390			0.0280189
$724$	−16.8188	−	14.1126i	−0.625064	−	0.524491i
$725$		0			0
$726$	0.0761360	+	0.431789i	0.00282567	+	0.0160252i
$727$	−4.81172	+	27.2886i	−0.178457	+	1.01208i	0.755621	+	0.655010i	$0.227335\pi$
$727$	−4.81172	+	27.2886i	−0.178457	+	1.01208i	−0.934078	+	0.357070i	$0.883776\pi$
$728$	−5.24583	−	1.90933i	−0.194423	−	0.0707644i
$729$	13.3040	+	23.0433i	0.492742	+	0.853454i
$730$		0			0
$731$	10.9926	−	9.22388i	0.406576	−	0.341158i
$732$	−0.279098	+	0.234191i	−0.0103158	+	0.00865595i
$733$	−3.26440	+	5.65411i	−0.120573	+	0.208839i	−0.919994	−	0.391933i	$-0.871807\pi$
$733$	−3.26440	+	5.65411i	−0.120573	+	0.208839i	0.799421	+	0.600772i	$0.205140\pi$
$734$	−3.94071	−	6.82552i	−0.145454	−	0.251934i
$735$		0			0
$736$	1.39392	−	7.90530i	0.0513805	−	0.291393i
$737$	1.31168	+	7.43890i	0.0483163	+	0.274015i
$738$	−16.2067	+	5.89877i	−0.596578	+	0.217137i
$739$	−10.5758	−	8.87419i	−0.389039	−	0.326442i	0.427200	−	0.904157i	$-0.359500\pi$
$739$	−10.5758	−	8.87419i	−0.389039	−	0.326442i	−0.816239	+	0.577715i	$0.803945\pi$
$740$		0			0
$741$	0.816975	−	0.776858i	0.0300123	−	0.0285386i
$742$	11.5457			0.423857
$743$	−7.03012	−	5.89897i	−0.257910	−	0.216412i	0.504660	−	0.863318i	$-0.331618\pi$
$743$	−7.03012	−	5.89897i	−0.257910	−	0.216412i	−0.762569	+	0.646906i	$0.776062\pi$
$744$	0.387647	−	0.141092i	0.0142118	−	0.00517268i
$745$		0			0
$746$	2.38124	−	13.5047i	0.0871835	−	0.494442i
$747$	35.8679	+	13.0549i	1.31234	+	0.477652i
$748$	−8.25706	−	14.3016i	−0.301908	−	0.522920i
$749$	−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	$0.417735\pi$
$752$	−4.91775	+	8.51780i	−0.179332	+	0.310612i
$753$	−0.609108	−	1.05501i	−0.0221971	−	0.0384466i
$754$	28.9362	+	10.5319i	1.05380	+	0.383550i
$755$		0			0
$756$	0.163357	+	0.926443i	0.00594123	+	0.0336944i
$757$	−19.2741	+	7.01518i	−0.700527	+	0.254971i	−0.667636	−	0.744488i	$-0.732694\pi$
$757$	−19.2741	+	7.01518i	−0.700527	+	0.254971i	−0.0328914	+	0.999459i	$0.510472\pi$
$758$	−11.4201	−	9.58260i	−0.414796	−	0.348056i
$759$	−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	$0.307408\pi$
$762$	0.312502	+	0.262220i	0.0113208	+	0.00949924i
$763$	18.6761	−	6.79755i	0.676120	−	0.246088i
$764$	−0.842016	−	4.77531i	−0.0304631	−	0.172765i
$765$		0			0
$766$	−9.48923	−	3.45380i	−0.342860	−	0.124791i
$767$	9.15047	+	15.8491i	0.330404	+	0.572277i
$768$	0.0426404	−	0.0738553i	0.00153865	−	0.00266503i
$769$	−2.75633	+	2.31283i	−0.0993957	+	0.0834029i	−0.691131	−	0.722729i	$-0.742887\pi$
$769$	−2.75633	+	2.31283i	−0.0993957	+	0.0834029i	0.591736	+	0.806132i	$0.298443\pi$
$770$		0			0
$771$	−1.24886	+	2.16309i	−0.0449766	+	0.0779017i
$772$	4.91687	+	8.51627i	0.176962	+	0.306507i
$773$	13.5301	+	4.92456i	0.486644	+	0.177124i	0.573677	−	0.819081i	$-0.305516\pi$
$773$	13.5301	+	4.92456i	0.486644	+	0.177124i	−0.0870330	+	0.996205i	$0.527739\pi$
$774$	−1.09303	+	6.19886i	−0.0392880	+	0.222814i
$775$		0			0
$776$	7.70655	−	2.80496i	0.276649	−	0.100692i
$777$	0.0243079	+	0.0203967i	0.000872039	+	0.000731728i
$778$	6.13194			0.219841
$779$	−11.1856	+	22.4921i	−0.400767	+	0.805863i
$780$		0			0
$781$	−20.7233	−	17.3889i	−0.741538	−	0.622224i
$782$	−51.4642	+	18.7314i	−1.84036	+	0.669835i
$783$	−0.901084	−	5.11030i	−0.0322021	−	0.182627i
$784$	−0.627164	+	3.55682i	−0.0223987	+	0.127029i
$785$		0			0
$786$	0.551521	+	0.955262i	0.0196721	+	0.0340731i
$787$	−24.4550	+	42.3573i	−0.871727	+	1.50988i	−0.0115176	+	0.999934i	$0.503666\pi$
$787$	−24.4550	+	42.3573i	−0.871727	+	1.50988i	−0.860209	+	0.509941i	$0.829667\pi$
$788$	−7.51254	+	6.30377i	−0.267623	+	0.224562i
$789$	0.000964644	0	0.000809432i	3.43422e−5	0	2.88165e-5i
$790$		0			0
$791$	−10.9604	−	18.9840i	−0.389707	−	0.674993i
$792$	6.80700	+	2.47754i	0.241876	+	0.0880357i
$793$	2.24988	−	12.7597i	0.0798955	−	0.453110i
$794$	−0.270461	−	1.53386i	−0.00959832	−	0.0544348i
$795$		0			0
$796$	1.06106	+	0.890332i	0.0376082	+	0.0315570i
$797$	−1.34326			−0.0475809			−0.0237904	−	0.999717i	$-0.507573\pi$
$797$	−1.34326			−0.0475809			−0.0237904	+	0.999717i	$0.507573\pi$
$798$	0.550458	+	0.406453i	0.0194860	+	0.0143883i
$799$	67.1042			2.37397
$800$		0			0
$801$	3.63827	−	1.32422i	0.128552	−	0.0467891i
$802$	−6.22380	−	35.2969i	−0.219770	−	1.24638i
$803$	−3.28193	+	18.6127i	−0.115817	+	0.656829i
$804$	0.250087	+	0.0910244i	0.00881990	+	0.00321018i
$805$		0			0
$806$	−7.33510	+	12.7048i	−0.258368	+	0.447506i
$807$	0.815693	−	0.684448i	0.0287138	−	0.0240937i
$808$	6.12522	−	5.13967i	0.215485	−	0.180813i
$809$	14.2421	−	24.6681i	0.500726	−	0.867283i	−0.499273	−	0.866445i	$-0.666400\pi$
$809$	14.2421	−	24.6681i	0.500726	−	0.867283i	1.00000		0.000838933i	$-0.000267041\pi$
$810$		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	$0.265637\pi$
$812$	−3.24549	+	18.4061i	−0.113894	+	0.645928i
$813$	0.00623296	+	0.0353489i	0.000218599	+	0.00123974i
$814$	0.459767	−	0.167342i	0.0161148	−	0.00586532i
$815$		0			0
$816$	−0.581841			−0.0203685
$817$	5.06787	+	7.63985i	0.177302	+	0.267284i
$818$	−35.0714			−1.22624
$819$	−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	$-0.320945\pi$
$822$	−0.0392459	+	0.222575i	−0.00136886	+	0.00776318i
$823$	47.1499	+	17.1612i	1.64354	+	0.598201i	0.987653	−	0.156656i	$-0.0500715\pi$
$823$	47.1499	+	17.1612i	1.64354	+	0.598201i	0.655889	+	0.754857i	$0.272294\pi$
$824$	−1.69681	−	2.93896i	−0.0591112	−	0.102384i
$825$		0			0
$826$	−8.50907	+	7.13995i	−0.296068	+	0.248431i
$827$	−1.42533	+	1.19599i	−0.0495635	+	0.0415887i	−0.667233	−	0.744849i	$-0.732521\pi$
$827$	−1.42533	+	1.19599i	−0.0495635	+	0.0415887i	0.617669	+	0.786438i	$0.288077\pi$
$828$	12.0117	−	20.8049i	0.417435	−	0.723019i
$829$	−9.83821	−	17.0403i	−0.341695	−	0.591833i	0.643052	−	0.765822i	$-0.277668\pi$
$829$	−9.83821	−	17.0403i	−0.341695	−	0.591833i	−0.984748	+	0.173989i	$0.944334\pi$
$830$		0			0
$831$	−0.452820	+	2.56807i	−0.0157082	+	0.0890854i
$832$	0.526632	+	2.98668i	0.0182577	+	0.103544i
$833$	23.1552	−	8.42781i	0.802281	−	0.292006i
$834$	0.753378	+	0.632159i	0.0260873	+	0.0218899i
$835$		0			0
$836$	9.67131	−	4.21688i	0.334489	−	0.145844i
$837$	2.47215			0.0854500
$838$	9.65576	+	8.10214i	0.333553	+	0.279884i
$839$	43.1880	−	15.7191i	1.49102	−	0.542685i	0.537299	−	0.843392i	$-0.319445\pi$
$839$	43.1880	−	15.7191i	1.49102	−	0.542685i	0.953717	+	0.300707i	$0.0972225\pi$
$840$		0			0
$841$	12.8665	−	72.9694i	0.443672	−	2.51619i
$842$	−25.0875	−	9.13109i	−0.864571	−	0.314678i
$843$	0.472166	+	0.817816i	0.0162623	+	0.0281671i
$844$	2.36410	−	4.09473i	0.0813755	−	0.140947i
$845$		0			0
$846$	−22.5485	+	18.9204i	−0.775234	+	0.650498i
$847$	4.73184	−	8.19578i	0.162588	−	0.281610i
$848$	−3.13617	−	5.43200i	−0.107696	−	0.186536i
$849$	−0.0639159	−	0.0232635i	−0.00219359	−	0.000798401i
$850$		0			0
$851$	−0.281765	−	1.59797i	−0.00965878	−	0.0547777i
$852$	−0.895653	+	0.325991i	−0.0306845	+	0.0111683i
$853$	−20.9800	−	17.6043i	−0.718340	−	0.602759i	0.208585	−	0.978004i	$-0.433114\pi$
$853$	−20.9800	−	17.6043i	−0.718340	−	0.602759i	−0.926926	+	0.375245i	$0.877559\pi$
$854$	7.86399			0.269100
$855$		0			0
$856$	11.5335			0.394206
$857$	14.3363	+	12.0296i	0.489718	+	0.410922i	0.853925	−	0.520396i	$-0.174216\pi$
$857$	14.3363	+	12.0296i	0.489718	+	0.410922i	−0.364207	+	0.931318i	$0.618660\pi$
$858$	0.588270	−	0.214113i	0.0200832	−	0.00730969i
$859$	2.55291	+	14.4783i	0.0871042	+	0.493993i	0.996883	+	0.0788984i	$0.0251403\pi$
$859$	2.55291	+	14.4783i	0.0871042	+	0.493993i	−0.909778	+	0.415094i	$0.863749\pi$
$860$		0			0
$861$	−0.850102	−	0.309412i	−0.0289714	−	0.0105447i
$862$	−4.05351	−	7.02088i	−0.138063	−	0.239132i
$863$	23.3533	−	40.4491i	0.794956	−	1.37690i	−0.127912	−	0.991786i	$-0.540827\pi$
$863$	23.3533	−	40.4491i	0.794956	−	1.37690i	0.922867	−	0.385118i	$-0.125839\pi$
$864$	0.391498	−	0.328506i	0.0133190	−	0.0111760i
$865$		0			0
$866$	−11.4197	+	19.7795i	−0.388057	+	0.672135i
$867$	1.25996	+	2.18231i	0.0427904	+	0.0741152i
$868$	−8.36712	−	3.04538i	−0.283999	−	0.103367i
$869$	4.41552	−	25.0417i	0.149786	−	0.849480i
$870$		0			0
$871$	−8.89360	+	3.23701i	−0.301348	+	0.109682i
$872$	−8.27109	−	6.94027i	−0.280095	−	0.235027i
$873$	24.5438			0.830681
$874$	−8.20279	−	34.0149i	−0.277463	−	1.15057i
$875$		0			0
$876$	0.510107	+	0.428031i	0.0172349	+	0.0144618i
$877$	−20.3788	+	7.41727i	−0.688143	+	0.250463i	−0.662340	−	0.749204i	$-0.730436\pi$
$877$	−20.3788	+	7.41727i	−0.688143	+	0.250463i	−0.0258029	+	0.999667i	$0.508214\pi$
$878$	−2.46294	−	13.9680i	−0.0831202	−	0.471398i
$879$	−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	$0.662031\pi$
$882$	−5.40440	+	9.36070i	−0.181976	+	0.315191i
$883$	−42.5570	+	35.7095i	−1.43216	+	1.20172i	−0.487730	+	0.872994i	$0.662175\pi$
$883$	−42.5570	+	35.7095i	−1.43216	+	1.20172i	−0.944425	+	0.328727i	$0.893380\pi$
$884$	15.8505	−	13.3002i	0.533111	−	0.447333i
$885$		0			0
$886$	−15.7428	−	27.2673i	−0.528890	−	0.916064i
$887$	−7.50631	−	2.73207i	−0.252037	−	0.0917340i	0.212912	−	0.977071i	$-0.431705\pi$
$887$	−7.50631	−	2.73207i	−0.252037	−	0.0917340i	−0.464949	+	0.885337i	$0.653927\pi$
$888$	0.00299345	−	0.0169767i	0.000100453	−	0.000569700i
$889$	−1.52901	−	8.67142i	−0.0512812	−	0.290830i
$890$		0			0
$891$	16.5665	+	13.9010i	0.555000	+	0.465700i
$892$	25.8985			0.867147
$893$	−4.81000	+	42.6013i	−0.160960	+	1.42560i
$894$	1.03754			0.0347006
$895$		0			0
$896$	−1.72973	+	0.629569i	−0.0577861	+	0.0210324i
$897$	−0.360517	−	2.04459i	−0.0120373	−	0.0682670i
$898$	−4.72722	+	26.8094i	−0.157749	+	0.894641i
$899$	46.1534	+	16.7985i	1.53930	+	0.560260i
$900$		0			0
$901$	−21.3970	+	37.0606i	−0.712836	+	1.23467i
$902$	−10.6856	+	8.96628i	−0.355792	+	0.298545i
$903$	−0.252924	+	0.212229i	−0.00841679	+	0.00706252i
$904$	−5.95436	+	10.3133i	−0.198039	+	0.343014i
$905$		0			0
$906$	1.39937	+	0.509329i	0.0464910	+	0.0169213i
$907$	6.31036	−	35.7878i	0.209532	−	1.18831i	−0.680615	−	0.732641i	$-0.738287\pi$
$907$	6.31036	−	35.7878i	0.209532	−	1.18831i	0.890147	−	0.455674i	$-0.150602\pi$
$908$	1.91494	+	10.8601i	0.0635494	+	0.360406i
$909$	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	$0.133217\pi$
$912$	0.0417061	−	0.369383i	0.00138103	−	0.0122315i
$913$	30.8714			1.02169
$914$	21.0495	+	17.6626i	0.696255	+	0.584227i
$915$		0			0
$916$	4.19587	+	23.7960i	0.138636	+	0.786241i
$917$	4.13430	−	23.4468i	0.136527	−	0.774282i
$918$	−3.27653	−	1.19256i	−0.108142	−	0.0393603i
$919$	−11.9007	−	20.6125i	−0.392566	−	0.679945i	0.600221	−	0.799834i	$-0.295079\pi$
$919$	−11.9007	−	20.6125i	−0.392566	−	0.679945i	−0.992787	+	0.119889i	$0.961746\pi$
$920$		0			0
$921$	−0.0434478	+	0.0364570i	−0.00143165	+	0.00120130i
$922$	4.33542	−	3.63785i	0.142779	−	0.119806i
$923$	16.9476	−	29.3542i	0.557839	−	0.966205i
$924$	0.189983	+	0.329061i	0.00624999	+	0.0108253i
$925$		0			0
$926$	3.83156	−	21.7299i	0.125913	−	0.714088i
$927$	−1.76360	−	10.0019i	−0.0579243	−	0.328505i
$928$	9.54124	−	3.47273i	0.313207	−	0.113998i
$929$	−39.8007	−	33.3968i	−1.30582	−	1.09571i	−0.989108	−	0.147191i	$-0.952977\pi$
$929$	−39.8007	−	33.3968i	−1.30582	−	1.09571i	−0.316711	−	0.948522i	$-0.602579\pi$
$930$		0			0
$931$	3.69067	+	15.3043i	0.120957	+	0.501577i
$932$	−19.8988			−0.651808
$933$	1.86388	+	1.56398i	0.0610206	+	0.0512024i
$934$	20.0796	−	7.30838i	0.657025	−	0.239138i
$935$		0			0
$936$	−1.57607	+	8.93831i	−0.0515153	+	0.292158i
$937$	−50.2023	−	18.2722i	−1.64004	−	0.596925i	−0.652993	−	0.757364i	$-0.726487\pi$
$937$	−50.2023	−	18.2722i	−1.64004	−	0.596925i	−0.987046	+	0.160438i	$0.948709\pi$
$938$	−2.87221	−	4.97481i	−0.0937810	−	0.162433i
$939$	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	$0.345772\pi$
$942$	−0.957319	+	1.65813i	−0.0311911	+	0.0540247i
$943$	23.1302	+	40.0627i	0.753223	+	1.30462i
$944$	5.67051	+	2.06390i	0.184559	+	0.0671741i
$945$		0			0
$946$	0.884029	+	5.01358i	0.0287422	+	0.163005i
$947$	−11.8246	+	4.30379i	−0.384246	+	0.139854i	−0.526919	−	0.849916i	$-0.676653\pi$
$947$	−11.8246	+	4.30379i	−0.384246	+	0.139854i	0.142672	+	0.989770i	$0.454431\pi$
$948$	−0.686300	−	0.575874i	−0.0222900	−	0.0187035i
$949$	−23.6806			−0.768705
$950$		0			0
$951$	0.991985			0.0321673
$952$	9.62051	+	8.07257i	0.311803	+	0.261633i
$953$	50.7655	−	18.4771i	1.64446	−	0.598533i	0.656647	−	0.754198i	$-0.271974\pi$
$953$	50.7655	−	18.4771i	1.64446	−	0.598533i	0.987810	+	0.155665i	$0.0497521\pi$
$954$	−3.25962	−	18.4862i	−0.105534	−	0.598513i
$955$		0			0
$956$	−16.9192	−	6.15807i	−0.547205	−	0.199166i
$957$	−1.04796	−	1.81511i	−0.0338756	−	0.0586743i
$958$	9.62348	−	16.6684i	0.310920	−	0.538530i
$959$	3.73696	−	3.13568i	0.120673	−	0.101256i
$960$		0			0
$961$	3.80049	−	6.58264i	0.122596	−	0.212343i
$962$	0.306519	+	0.530906i	0.00988256	+	0.0171171i
$963$	32.4349	+	11.8053i	1.04520	+	0.380422i
$964$	−1.53405	+	8.70001i	−0.0494083	+	0.280209i
$965$		0			0
$966$	1.18412	−	0.430984i	0.0380984	−	0.0138667i
$967$	30.3684	+	25.4821i	0.976582	+	0.819449i	0.983570	−	0.180526i	$-0.0577800\pi$
$967$	30.3684	+	25.4821i	0.976582	+	0.819449i	−0.00698833	+	0.999976i	$0.502224\pi$
$968$	−5.14125			−0.165246
$969$	−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	$-0.678711\pi$
$972$	2.15673	−	0.784985i	0.0691771	−	0.0251784i
$973$	−3.68612	−	20.9050i	−0.118172	−	0.670184i
$974$	2.55538	−	14.4923i	0.0818797	−	0.464363i
$975$		0			0
$976$	−2.13610	−	3.69983i	−0.0683749	−	0.118429i
$977$	7.73546	−	13.3982i	0.247479	−	0.428647i	−0.715346	−	0.698770i	$-0.753731\pi$
$977$	7.73546	−	13.3982i	0.247479	−	0.428647i	0.962826	+	0.270123i	$0.0870644\pi$
$978$	0.621165	−	0.521219i	0.0198627	−	0.0166667i
$979$	2.39882	−	2.01285i	0.0766667	−	0.0643310i
$980$		0			0
$981$	−16.1565	−	27.9838i	−0.515836	−	0.893454i
$982$	−37.0504	−	13.4853i	−1.18233	−	0.430332i
$983$	9.25575	−	52.4920i	0.295213	−	1.67423i	−0.371125	−	0.928583i	$-0.621028\pi$
$983$	9.25575	−	52.4920i	0.295213	−	1.67423i	0.666337	−	0.745651i	$-0.267861\pi$
$984$	0.0853422	+	0.484000i	0.00272061	+	0.0154293i
$985$		0			0
$986$	−53.0671	−	44.5286i	−1.69000	−	1.41808i
$987$	−1.54397			−0.0491452
$988$	7.30750	+	11.0161i	0.232482	+	0.350469i
$989$	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	$0.257516\pi$
$992$	0.839980	+	4.76376i	0.0266694	+	0.151250i
$993$	−0.372838	+	2.11447i	−0.0118317	+	0.0671007i
$994$	19.3321	+	7.03632i	0.613178	+	0.223179i
$995$		0			0
$996$	0.543844	−	0.941966i	0.0172324	−	0.0298473i
$997$	22.3783	−	18.7776i	0.708727	−	0.594692i	−0.215515	−	0.976501i	$-0.569143\pi$
$997$	22.3783	−	18.7776i	0.708727	−	0.594692i	0.924242	+	0.381808i	$0.124699\pi$
$998$	−3.59434	+	3.01601i	−0.113777	+	0.0954700i
$999$	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.l.k.301.3	yes	24
5.2	odd	4		950.2.u.h.149.2		48
5.3	odd	4		950.2.u.h.149.7		48
5.4	even	2		950.2.l.j.301.2	yes	24
19.6	even	9	inner	950.2.l.k.101.3	yes	24
95.44	even	18		950.2.l.j.101.2	✓	24
95.63	odd	36		950.2.u.h.899.2		48
95.82	odd	36		950.2.u.h.899.7		48

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

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.0801377 - 0.0291678i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-0.920368 - 1.59412i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29256 + 1.92369i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.0801377 - 0.0291678i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0801377 + 0.0291678i) q^{6} +(-0.920368 - 1.59412i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.29256 + 1.92369i) q^{9} +(-1.21024 + 2.09620i) q^{11} +(0.0426404 + 0.0738553i) q^{12} +(-2.84986 - 1.03726i) q^{13} +(0.319640 - 1.81277i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(5.22645 + 4.38551i) q^{17} -2.99273 q^{18} +(-3.15879 + 3.00368i) q^{19} +(-0.120253 - 0.100904i) q^{21} +(-2.27451 + 0.827855i) q^{22} +(1.39392 + 7.90530i) q^{23} +(-0.0148089 + 0.0839852i) q^{24} +(-1.51638 - 2.62644i) q^{26} +(-0.255532 + 0.442595i) q^{27} +(1.41009 - 1.18320i) q^{28} +(-7.77809 + 6.52659i) q^{29} +(-2.41863 - 4.18918i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0358446 + 0.203285i) q^{33} +(1.18474 + 6.71899i) q^{34} +(-2.29256 - 1.92369i) q^{36} -0.202139 q^{37} +(-4.35050 + 0.270521i) q^{38} -0.258636 q^{39} +(5.41537 - 1.97103i) q^{41} +(-0.0272592 - 0.154595i) q^{42} +(0.365228 - 2.07131i) q^{43} +(-2.27451 - 0.827855i) q^{44} +(-4.01363 + 6.95180i) q^{46} +(7.53443 - 6.32214i) q^{47} +(-0.0653289 + 0.0548174i) q^{48} +(1.80585 - 3.12782i) q^{49} +(0.546751 + 0.199001i) q^{51} +(0.526632 - 2.98668i) q^{52} +(1.08918 + 6.17705i) q^{53} +(-0.480244 + 0.174794i) q^{54} +1.84074 q^{56} +(-0.165527 + 0.332843i) q^{57} -10.1536 q^{58} +(-4.62264 - 3.87886i) q^{59} +(0.741860 + 4.20730i) q^{61} +(0.839980 - 4.76376i) q^{62} +(5.17660 + 1.88413i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.158128 + 0.132685i) q^{66} +(2.39061 - 2.00596i) q^{67} +(-3.41132 + 5.90858i) q^{68} +(0.342285 + 0.592856i) q^{69} +(-1.94076 + 11.0066i) q^{71} +(-0.519682 - 2.94726i) q^{72} +(7.33739 - 2.67059i) q^{73} +(-0.154847 - 0.129932i) q^{74} +(-3.50656 - 2.58921i) q^{76} +4.45548 q^{77} +(-0.198126 - 0.166248i) q^{78} +(-9.87176 + 3.59303i) q^{79} +(1.55148 - 8.79886i) q^{81} +(5.41537 + 1.97103i) q^{82} +(-6.37710 - 11.0455i) q^{83} +(0.0784897 - 0.135948i) q^{84} +(1.61119 - 1.35195i) q^{86} +(-0.432953 + 0.749896i) q^{87} +(-1.21024 - 2.09620i) q^{88} +(-1.21570 - 0.442480i) q^{89} +(0.969391 + 5.49769i) q^{91} +(-7.54315 + 2.74548i) q^{92} +(-0.316012 - 0.265166i) q^{93} +9.83551 q^{94} -0.0852808 q^{96} +(-6.28244 - 5.27159i) q^{97} +(3.39388 - 1.23527i) q^{98} +(-1.25788 - 7.13381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Introduction

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