LMFDB - Embedded newform 504.2.cc.b.293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.8
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37160 + 0.344550i) q^{2} +(1.55842 - 0.755861i) q^{3} +(1.76257 - 0.945170i) q^{4} +(0.673579 + 0.388891i) q^{5} +(-1.87710 + 1.57369i) q^{6} +(-2.62122 - 0.359471i) q^{7} +(-2.09188 + 1.90369i) q^{8} +(1.85735 - 2.35590i) q^{9} +O(q^{10})$	\(q+(-1.37160 + 0.344550i) q^{2} +(1.55842 - 0.755861i) q^{3} +(1.76257 - 0.945170i) q^{4} +(0.673579 + 0.388891i) q^{5} +(-1.87710 + 1.57369i) q^{6} +(-2.62122 - 0.359471i) q^{7} +(-2.09188 + 1.90369i) q^{8} +(1.85735 - 2.35590i) q^{9} +(-1.05787 - 0.301321i) q^{10} +(1.17876 + 2.04167i) q^{11} +(2.03241 - 2.80523i) q^{12} +(1.25247 - 2.16934i) q^{13} +(3.71912 - 0.410091i) q^{14} +(1.34367 + 0.0969238i) q^{15} +(2.21331 - 3.33186i) q^{16} +7.85438 q^{17} +(-1.73581 + 3.87130i) q^{18} +1.23260 q^{19} +(1.55480 + 0.0488015i) q^{20} +(-4.35667 + 1.42107i) q^{21} +(-2.32025 - 2.39422i) q^{22} +(4.50123 + 2.59879i) q^{23} +(-1.82111 + 4.54792i) q^{24} +(-2.19753 - 3.80623i) q^{25} +(-0.970438 + 3.40700i) q^{26} +(1.11380 - 5.07538i) q^{27} +(-4.95984 + 1.84390i) q^{28} +(-3.81352 - 6.60522i) q^{29} +(-1.87637 + 0.330020i) q^{30} +(1.36702 + 0.789250i) q^{31} +(-1.88778 + 5.33257i) q^{32} +(3.38022 + 2.29081i) q^{33} +(-10.7731 + 2.70623i) q^{34} +(-1.62580 - 1.26150i) q^{35} +(1.04699 - 5.90795i) q^{36} -4.63204i q^{37} +(-1.69063 + 0.424692i) q^{38} +(0.312154 - 4.32743i) q^{39} +(-2.14938 + 0.468770i) q^{40} +(-2.21729 + 3.84046i) q^{41} +(5.48598 - 3.45023i) q^{42} +(-1.37019 + 0.791080i) q^{43} +(4.00737 + 2.48446i) q^{44} +(2.16726 - 0.864577i) q^{45} +(-7.06930 - 2.01359i) q^{46} +(1.00393 + 1.73887i) q^{47} +(0.930847 - 6.86539i) q^{48} +(6.74156 + 1.88450i) q^{49} +(4.32556 + 4.46346i) q^{50} +(12.2404 - 5.93682i) q^{51} +(0.157171 - 5.00740i) q^{52} -9.91801 q^{53} +(0.221034 + 7.34514i) q^{54} +1.83364i q^{55} +(6.16760 - 4.23801i) q^{56} +(1.92091 - 0.931674i) q^{57} +(7.50645 + 7.74576i) q^{58} +(11.0077 + 6.35529i) q^{59} +(2.45992 - 1.09916i) q^{60} +(1.25634 + 2.17605i) q^{61} +(-2.14694 - 0.611528i) q^{62} +(-5.71539 + 5.50766i) q^{63} +(0.751945 - 7.96458i) q^{64} +(1.68727 - 0.974146i) q^{65} +(-5.42561 - 1.97741i) q^{66} +(-10.5771 - 6.10669i) q^{67} +(13.8439 - 7.42372i) q^{68} +(8.97913 + 0.647699i) q^{69} +(2.66460 + 1.17010i) q^{70} +4.19502i q^{71} +(0.599538 + 8.46407i) q^{72} -2.22110i q^{73} +(1.59597 + 6.35331i) q^{74} +(-6.30165 - 4.27068i) q^{75} +(2.17254 - 1.16502i) q^{76} +(-2.35587 - 5.77540i) q^{77} +(1.06287 + 6.04305i) q^{78} +(6.28083 + 10.8787i) q^{79} +(2.78657 - 1.38353i) q^{80} +(-2.10051 - 8.75145i) q^{81} +(1.71800 - 6.03154i) q^{82} +(-8.79780 + 5.07941i) q^{83} +(-6.33578 + 6.62252i) q^{84} +(5.29054 + 3.05450i) q^{85} +(1.60679 - 1.55714i) q^{86} +(-10.9357 - 7.41121i) q^{87} +(-6.35254 - 2.02695i) q^{88} +10.6590 q^{89} +(-2.67472 + 1.93258i) q^{90} +(-4.06280 + 5.23608i) q^{91} +(10.3900 + 0.326119i) q^{92} +(2.72696 + 0.196706i) q^{93} +(-1.97612 - 2.03912i) q^{94} +(0.830253 + 0.479347i) q^{95} +(1.08872 + 9.73728i) q^{96} +(4.55061 - 2.62730i) q^{97} +(-9.89603 - 0.261975i) q^{98} +(6.99934 + 1.01506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.37160	+	0.344550i	−0.969867	+	0.243634i
$2$	−1.37160	+	0.344550i	−0.969867	+	0.243634i
$3$	1.55842	−	0.755861i	0.899754	−	0.436396i
$3$	1.55842	−	0.755861i	0.899754	−	0.436396i
$4$	1.76257	−	0.945170i	0.881285	−	0.472585i
$5$	0.673579	+	0.388891i	0.301234	+	0.173917i	0.642997	−	0.765869i	$-0.277691\pi$
$5$	0.673579	+	0.388891i	0.301234	+	0.173917i	−0.341763	+	0.939786i	$0.611024\pi$
$6$	−1.87710	+	1.57369i	−0.766322	+	0.642457i
$7$	−2.62122	−	0.359471i	−0.990727	−	0.135867i
$7$	−2.62122	−	0.359471i	−0.990727	−	0.135867i
$8$	−2.09188	+	1.90369i	−0.739592	+	0.673055i
$9$	1.85735	−	2.35590i	0.619116	−	0.785299i
$10$	−1.05787	−	0.301321i	−0.334529	−	0.0952861i
$11$	1.17876	+	2.04167i	0.355410	+	0.615587i	0.987188	−	0.159562i	$-0.0510081\pi$
$11$	1.17876	+	2.04167i	0.355410	+	0.615587i	−0.631778	+	0.775149i	$0.717675\pi$
$12$	2.03241	−	2.80523i	0.586706	−	0.809800i
$13$	1.25247	−	2.16934i	0.347372	−	0.601665i	−0.638410	−	0.769696i	$-0.720408\pi$
$13$	1.25247	−	2.16934i	0.347372	−	0.601665i	0.985782	+	0.168031i	$0.0537409\pi$
$14$	3.71912	−	0.410091i	0.993976	−	0.109601i
$15$	1.34367	+	0.0969238i	0.346933	+	0.0250256i
$16$	2.21331	−	3.33186i	0.553327	−	0.832964i
$17$	7.85438			1.90497			0.952483	−	0.304591i	$-0.0985198\pi$
$17$	7.85438			1.90497			0.952483	+	0.304591i	$0.0985198\pi$
$18$	−1.73581	+	3.87130i	−0.409135	+	0.912474i
$19$	1.23260			0.282778			0.141389	−	0.989954i	$-0.454843\pi$
$19$	1.23260			0.282778			0.141389	+	0.989954i	$0.454843\pi$
$20$	1.55480	+	0.0488015i	0.347663	+	0.0109123i
$21$	−4.35667	+	1.42107i	−0.950703	+	0.310103i
$22$	−2.32025	−	2.39422i	−0.494678	−	0.510448i
$23$	4.50123	+	2.59879i	0.938571	+	0.541884i	0.889512	−	0.456912i	$-0.151044\pi$
$23$	4.50123	+	2.59879i	0.938571	+	0.541884i	0.0490591	+	0.998796i	$0.484378\pi$
$24$	−1.82111	+	4.54792i	−0.371732	+	0.928340i
$25$	−2.19753	−	3.80623i	−0.439506	−	0.761246i
$26$	−0.970438	+	3.40700i	−0.190318	+	0.668167i
$27$	1.11380	−	5.07538i	0.214351	−	0.976757i
$28$	−4.95984	+	1.84390i	−0.937322	+	0.348465i
$29$	−3.81352	−	6.60522i	−0.708153	−	1.22656i	−0.965541	−	0.260250i	$-0.916195\pi$
$29$	−3.81352	−	6.60522i	−0.708153	−	1.22656i	0.257388	−	0.966308i	$-0.417138\pi$
$30$	−1.87637	+	0.330020i	−0.342576	+	0.0602531i
$31$	1.36702	+	0.789250i	0.245524	+	0.141753i	0.617713	−	0.786404i	$-0.288059\pi$
$31$	1.36702	+	0.789250i	0.245524	+	0.141753i	−0.372189	+	0.928157i	$0.621393\pi$
$32$	−1.88778	+	5.33257i	−0.333716	+	0.942674i
$33$	3.38022	+	2.29081i	0.588422	+	0.398778i
$34$	−10.7731	+	2.70623i	−1.84756	+	0.464114i
$35$	−1.62580	−	1.26150i	−0.274811	−	0.213232i
$36$	1.04699	−	5.90795i	0.174498	−	0.984658i
$37$		−	4.63204i		−	0.761503i	−0.924677	−	0.380751i	$-0.875665\pi$
$37$		−	4.63204i		−	0.761503i	0.924677	−	0.380751i	$-0.124335\pi$
$38$	−1.69063	+	0.424692i	−0.274257	+	0.0688942i
$39$	0.312154	−	4.32743i	0.0499846	−	0.692943i
$40$	−2.14938	+	0.468770i	−0.339846	+	0.0741190i
$41$	−2.21729	+	3.84046i	−0.346282	+	0.599779i	−0.985586	−	0.169176i	$-0.945889\pi$
$41$	−2.21729	+	3.84046i	−0.346282	+	0.599779i	0.639303	+	0.768955i	$0.279223\pi$
$42$	5.48598	−	3.45023i	0.846504	−	0.532382i
$43$	−1.37019	+	0.791080i	−0.208952	+	0.120639i	−0.600824	−	0.799381i	$-0.705161\pi$
$43$	−1.37019	+	0.791080i	−0.208952	+	0.120639i	0.391872	+	0.920020i	$0.371828\pi$
$44$	4.00737	+	2.48446i	0.604134	+	0.374547i
$45$	2.16726	−	0.864577i	0.323076	−	0.128884i
$46$	−7.06930	−	2.01359i	−1.04231	−	0.296888i
$47$	1.00393	+	1.73887i	0.146439	+	0.253640i	0.929909	−	0.367790i	$-0.119885\pi$
$47$	1.00393	+	1.73887i	0.146439	+	0.253640i	−0.783470	+	0.621430i	$0.786552\pi$
$48$	0.930847	−	6.86539i	0.134356	−	0.990933i
$49$	6.74156	+	1.88450i	0.963080	+	0.269214i
$50$	4.32556	+	4.46346i	0.611727	+	0.631229i
$51$	12.2404	−	5.93682i	1.71400	−	0.831321i
$52$	0.157171	−	5.00740i	0.0217956	−	0.694401i
$53$	−9.91801			−1.36234			−0.681172	−	0.732124i	$-0.738529\pi$
$53$	−9.91801			−1.36234			−0.681172	+	0.732124i	$0.738529\pi$
$54$	0.221034	+	7.34514i	0.0300789	+	0.999548i
$55$			1.83364i			0.247248i
$56$	6.16760	−	4.23801i	0.824180	−	0.566328i
$57$	1.92091	−	0.931674i	0.254431	−	0.123403i
$58$	7.50645	+	7.74576i	0.985646	+	1.01707i
$59$	11.0077	+	6.35529i	1.43308	+	0.827388i	0.997354	−	0.0726929i	$-0.0231593\pi$
$59$	11.0077	+	6.35529i	1.43308	+	0.827388i	0.435723	+	0.900081i	$0.356493\pi$
$60$	2.45992	−	1.09916i	0.317574	−	0.141901i
$61$	1.25634	+	2.17605i	0.160858	+	0.278614i	0.935177	−	0.354182i	$-0.115241\pi$
$61$	1.25634	+	2.17605i	0.160858	+	0.278614i	−0.774319	+	0.632796i	$0.781907\pi$
$62$	−2.14694	−	0.611528i	−0.272662	−	0.0776641i
$63$	−5.71539	+	5.50766i	−0.720072	+	0.693900i
$64$	0.751945	−	7.96458i	0.0939931	−	0.995573i
$65$	1.68727	−	0.974146i	0.209280	−	0.120828i
$66$	−5.42561	−	1.97741i	−0.667847	−	0.243403i
$67$	−10.5771	−	6.10669i	−1.29220	−	0.746051i	−0.313155	−	0.949702i	$-0.601386\pi$
$67$	−10.5771	−	6.10669i	−1.29220	−	0.746051i	−0.979044	+	0.203651i	$0.934719\pi$
$68$	13.8439	−	7.42372i	1.67882	−	0.900258i
$69$	8.97913	+	0.647699i	1.08096	+	0.0779738i
$70$	2.66460	+	1.17010i	0.318481	+	0.139854i
$71$			4.19502i			0.497857i	0.968522	+	0.248928i	$0.0800784\pi$
$71$			4.19502i			0.497857i	−0.968522	+	0.248928i	$0.919922\pi$
$72$	0.599538	+	8.46407i	0.0706563	+	0.997501i
$73$		−	2.22110i		−	0.259960i	−0.991517	−	0.129980i	$-0.958509\pi$
$73$		−	2.22110i		−	0.259960i	0.991517	−	0.129980i	$-0.0414913\pi$
$74$	1.59597	+	6.35331i	0.185528	+	0.738557i
$75$	−6.30165	−	4.27068i	−0.727652	−	0.493136i
$76$	2.17254	−	1.16502i	0.249208	−	0.133636i
$77$	−2.35587	−	5.77540i	−0.268476	−	0.658168i
$78$	1.06287	+	6.04305i	0.120346	+	0.684241i
$79$	6.28083	+	10.8787i	0.706649	+	1.22395i	0.966093	+	0.258194i	$0.0831273\pi$
$79$	6.28083	+	10.8787i	0.706649	+	1.22395i	−0.259444	+	0.965758i	$0.583539\pi$
$80$	2.78657	−	1.38353i	0.311548	−	0.154684i
$81$	−2.10051	−	8.75145i	−0.233390	−	0.972383i
$82$	1.71800	−	6.03154i	0.189722	−	0.666072i
$83$	−8.79780	+	5.07941i	−0.965684	+	0.557538i	−0.897918	−	0.440164i	$-0.854920\pi$
$83$	−8.79780	+	5.07941i	−0.965684	+	0.557538i	−0.0677660	+	0.997701i	$0.521587\pi$
$84$	−6.33578	+	6.62252i	−0.691291	+	0.722577i
$85$	5.29054	+	3.05450i	0.573840	+	0.331307i
$86$	1.60679	−	1.55714i	0.173264	−	0.167911i
$87$	−10.9357	−	7.41121i	−1.17243	−	0.794565i
$88$	−6.35254	−	2.02695i	−0.677183	−	0.216073i
$89$	10.6590			1.12985			0.564925	−	0.825142i	$-0.308905\pi$
$89$	10.6590			1.12985			0.564925	+	0.825142i	$0.308905\pi$
$90$	−2.67472	+	1.93258i	−0.281940	+	0.203712i
$91$	−4.06280	+	5.23608i	−0.425897	+	0.548890i
$92$	10.3900	+	0.326119i	1.08324	+	0.0340002i
$93$	2.72696	+	0.196706i	0.282772	+	0.0203974i
$94$	−1.97612	−	2.03912i	−0.203821	−	0.210319i
$95$	0.830253	+	0.479347i	0.0851822	+	0.0491800i
$96$	1.08872	+	9.73728i	0.111117	+	0.993807i
$97$	4.55061	−	2.62730i	0.462045	−	0.266762i	−0.250859	−	0.968024i	$-0.580713\pi$
$97$	4.55061	−	2.62730i	0.462045	−	0.266762i	0.712904	+	0.701262i	$0.247380\pi$
$98$	−9.89603	−	0.261975i	−0.999650	−	0.0264635i
$99$	6.99934	+	1.01506i	0.703460	+	0.102017i
$100$	−7.47083	−	4.63171i	−0.747083	−	0.463171i
$101$	−12.3845	+	7.15020i	−1.23231	+	0.711472i	−0.967510	−	0.252833i	$-0.918638\pi$
$101$	−12.3845	+	7.15020i	−1.23231	+	0.711472i	−0.264795	+	0.964305i	$0.585304\pi$
$102$	−14.7434	+	12.3604i	−1.45982	+	1.22386i
$103$	−3.59006	−	2.07272i	−0.353739	−	0.204231i	0.312592	−	0.949888i	$-0.398803\pi$
$103$	−3.59006	−	2.07272i	−0.353739	−	0.204231i	−0.666331	+	0.745656i	$0.732136\pi$
$104$	1.50973	+	6.92230i	0.148041	+	0.678787i
$105$	−3.48720	−	0.737067i	−0.340316	−	0.0719304i
$106$	13.6035	−	3.41725i	1.32129	−	0.331913i
$107$	−9.31583			−0.900595			−0.450298	−	0.892879i	$-0.648682\pi$
$107$	−9.31583			−0.900595			−0.450298	+	0.892879i	$0.648682\pi$
$108$	−2.83394	−	9.99844i	−0.272696	−	0.962100i
$109$			20.6091i			1.97399i	0.160754	+	0.986995i	$0.448608\pi$
$109$			20.6091i			1.97399i	−0.160754	+	0.986995i	$0.551392\pi$
$110$	−0.631780	−	2.51502i	−0.0602378	−	0.239797i
$111$	−3.50118	−	7.21867i	−0.332317	−	0.685166i
$112$	−6.99927	+	7.93790i	−0.661369	+	0.750061i
$113$	−2.97307	−	1.71650i	−0.279683	−	0.161475i	0.353597	−	0.935398i	$-0.384958\pi$
$113$	−2.97307	−	1.71650i	−0.279683	−	0.161475i	−0.633280	+	0.773923i	$0.718292\pi$
$114$	−2.31371	+	1.93973i	−0.216699	+	0.181673i
$115$	2.02129	+	3.50098i	0.188486	+	0.326468i
$116$	−12.9647	−	8.03773i	−1.20374	−	0.746285i
$117$	−2.78447	−	6.97990i	−0.257424	−	0.645292i
$118$	−17.2878	−	4.92421i	−1.59147	−	0.453310i
$119$	−20.5880	−	2.82342i	−1.88730	−	0.258822i
$120$	−2.99531	+	2.35517i	−0.273433	+	0.214997i
$121$	2.72105	−	4.71299i	0.247368	−	0.428454i
$122$	−2.47295	−	2.55179i	−0.223891	−	0.231028i
$123$	−0.552618	+	7.66101i	−0.0498279	+	0.690770i
$124$	3.15545	+	0.0990421i	0.283367	+	0.00889424i
$125$		−	7.30730i		−	0.653585i
$126$	5.94156	−	9.52354i	0.529317	−	0.848424i
$127$	−8.81750			−0.782426			−0.391213	−	0.920300i	$-0.627944\pi$
$127$	−8.81750			−0.782426			−0.391213	+	0.920300i	$0.627944\pi$
$128$	1.71283	+	11.1833i	0.151394	+	0.988473i
$129$	−1.53739	+	2.26851i	−0.135359	+	0.199731i
$130$	−1.97862	+	1.91749i	−0.173536	+	0.168175i
$131$	−6.48414	−	3.74362i	−0.566522	−	0.327081i	0.189237	−	0.981931i	$-0.439398\pi$
$131$	−6.48414	−	3.74362i	−0.566522	−	0.327081i	−0.755759	+	0.654850i	$0.772732\pi$
$132$	8.12308	+	0.842822i	0.707024	+	0.0733582i
$133$	−3.23091	−	0.443083i	−0.280156	−	0.0384202i
$134$	16.6116	+	4.73160i	1.43502	+	0.408748i
$135$	2.72400	−	2.98552i	0.234445	−	0.256953i
$136$	−16.4304	+	14.9523i	−1.40890	+	1.28215i
$137$	−11.8681	+	6.85208i	−1.01396	+	0.585412i	−0.912350	−	0.409412i	$-0.865734\pi$
$137$	−11.8681	+	6.85208i	−1.01396	+	0.585412i	−0.101614	+	0.994824i	$0.532401\pi$
$138$	−12.5389	+	2.20538i	−1.06738	+	0.187734i
$139$	−9.90315	+	17.1528i	−0.839974	+	1.45488i	0.0499413	+	0.998752i	$0.484097\pi$
$139$	−9.90315	+	17.1528i	−0.839974	+	1.45488i	−0.889915	+	0.456126i	$0.849237\pi$
$140$	−4.05792	−	0.686824i	−0.342957	−	0.0580472i
$141$	2.87889	+	1.95105i	0.242446	+	0.164308i
$142$	−1.44539	−	5.75388i	−0.121295	−	0.482855i
$143$	5.90543			0.493837
$144$	−3.73862	−	11.4027i	−0.311552	−	0.950229i
$145$		−	5.93218i		−	0.492641i
$146$	0.765279	+	3.04646i	0.0633350	+	0.252126i
$147$	11.9306	−	2.15884i	0.984020	−	0.178058i
$148$	−4.37806	−	8.16430i	−0.359875	−	0.671101i
$149$	7.60979	−	13.1805i	0.623418	−	1.07979i	−0.365426	−	0.930840i	$-0.619077\pi$
$149$	7.60979	−	13.1805i	0.623418	−	1.07979i	0.988844	−	0.148952i	$-0.0475899\pi$
$150$	10.1148	+	3.68643i	0.825870	+	0.300996i
$151$	3.55039	+	6.14945i	0.288926	+	0.500435i	0.973554	−	0.228458i	$-0.0733684\pi$
$151$	3.55039	+	6.14945i	0.288926	+	0.500435i	−0.684627	+	0.728893i	$0.740035\pi$
$152$	−2.57845	+	2.34649i	−0.209140	+	0.190325i
$153$	14.5883	−	18.5041i	1.17940	−	1.49597i
$154$	5.22122	+	7.10982i	0.420738	+	0.572926i
$155$	0.613864	+	1.06324i	0.0493068	+	0.0854019i
$156$	−3.53996	−	7.92243i	−0.283424	−	0.634302i
$157$	6.36488	−	11.0243i	0.507972	−	0.879834i	−0.491985	−	0.870604i	$-0.663729\pi$
$157$	6.36488	−	11.0243i	0.507972	−	0.879834i	0.999957	−	0.00923039i	$-0.00293817\pi$
$158$	−12.3631	−	12.7572i	−0.983552	−	1.01491i
$159$	−15.4564	+	7.49664i	−1.22577	+	0.594522i
$160$	−3.34536	+	2.85776i	−0.264474	+	0.225926i
$161$	−10.8645	−	8.43004i	−0.856244	−	0.664380i
$162$	5.89637	+	11.2798i	0.463263	+	0.886221i
$163$		−	4.95008i		−	0.387720i	−0.981029	−	0.193860i	$-0.937899\pi$
$163$		−	4.95008i		−	0.387720i	0.981029	−	0.193860i	$-0.0621008\pi$
$164$	−0.278245	+	8.86479i	−0.0217273	+	0.692224i
$165$	1.38597	+	2.85758i	0.107898	+	0.222462i
$166$	10.3169	−	9.99820i	0.800750	−	0.776011i
$167$	−9.19113	+	15.9195i	−0.711231	+	1.23189i	0.253164	+	0.967423i	$0.418529\pi$
$167$	−9.19113	+	15.9195i	−0.711231	+	1.23189i	−0.964395	+	0.264465i	$0.914805\pi$
$168$	6.40837	−	11.2664i	0.494416	−	0.869225i
$169$	3.36266	+	5.82429i	0.258666	+	0.448022i
$170$	−8.30893	−	2.36669i	−0.637266	−	0.181517i
$171$	2.28937	−	2.90388i	0.175072	−	0.222065i
$172$	−1.66735	+	2.68940i	−0.127134	+	0.205065i
$173$	−8.56186	+	4.94319i	−0.650946	+	0.375824i	−0.788819	−	0.614626i	$-0.789307\pi$
$173$	−8.56186	+	4.94319i	−0.650946	+	0.375824i	0.137873	+	0.990450i	$0.455974\pi$
$174$	17.5529	+	6.39732i	1.33068	+	0.484979i
$175$	4.39197	+	10.7669i	0.332002	+	0.813901i
$176$	9.41152	+	0.591394i	0.709420	+	0.0445780i
$177$	21.9583	+	1.58394i	1.65049	+	0.119056i
$178$	−14.6199	+	3.67255i	−1.09580	+	0.275270i
$179$	0.466406			0.0348608			0.0174304	−	0.999848i	$-0.494451\pi$
$179$	0.466406			0.0348608			0.0174304	+	0.999848i	$0.494451\pi$
$180$	3.00277	−	3.57230i	0.223814	−	0.266264i
$181$	13.8348			1.02833			0.514167	−	0.857690i	$-0.328101\pi$
$181$	13.8348			1.02833			0.514167	+	0.857690i	$0.328101\pi$
$182$	3.76844	−	8.58164i	0.279336	−	0.636113i
$183$	3.60270	+	2.44158i	0.266319	+	0.180487i
$184$	−14.3633	+	3.13258i	−1.05888	+	0.230937i
$185$	1.80136	−	3.12005i	0.132439	−	0.229390i
$186$	−3.80807	+	0.669772i	−0.279221	+	0.0491101i
$187$	9.25843	+	16.0361i	0.677043	+	1.17267i
$188$	3.41303	+	2.11598i	0.248921	+	0.154324i
$189$	−4.74396	+	12.9033i	−0.345072	+	0.938576i
$190$	−1.30393	−	0.371408i	−0.0945973	−	0.0269448i
$191$	−3.31443	+	1.91359i	−0.239824	+	0.138462i	−0.615096	−	0.788452i	$-0.710883\pi$
$191$	−3.31443	+	1.91359i	−0.239824	+	0.138462i	0.375272	+	0.926915i	$0.377549\pi$
$192$	−4.84827	−	12.9805i	−0.349894	−	0.936789i
$193$	−3.45456	+	5.98348i	−0.248665	+	0.430700i	−0.963156	−	0.268945i	$-0.913325\pi$
$193$	−3.45456	+	5.98348i	−0.248665	+	0.430700i	0.714491	+	0.699645i	$0.246658\pi$
$194$	−5.33638	+	5.17151i	−0.383130	+	0.371293i
$195$	1.89316	−	2.79347i	0.135572	−	0.200045i
$196$	13.6637	−	3.05035i	0.975975	−	0.217882i
$197$	8.72829			0.621865			0.310932	−	0.950432i	$-0.399359\pi$
$197$	8.72829			0.621865			0.310932	+	0.950432i	$0.399359\pi$
$198$	−9.95003	+	1.01937i	−0.707118	+	0.0724434i
$199$		−	6.92466i		−	0.490876i	−0.969412	−	0.245438i	$-0.921068\pi$
$199$		−	6.92466i		−	0.490876i	0.969412	−	0.245438i	$-0.0789318\pi$
$200$	11.8428	+	3.77878i	0.837415	+	0.267200i
$201$	−21.0994	−	1.52198i	−1.48824	−	0.107352i
$202$	14.5230	−	14.0743i	1.02183	−	0.990264i
$203$	7.62169	+	18.6846i	0.534938	+	1.31140i
$204$	15.9633	−	22.0333i	1.11766	−	1.54264i
$205$	−2.98704	+	1.72457i	−0.208624	+	0.120449i
$206$	5.63828	+	1.60599i	0.392838	+	0.111895i
$207$	14.4828	−	5.77758i	1.00663	−	0.401570i
$208$	−4.45582	−	8.97445i	−0.308955	−	0.622266i
$209$	1.45294	+	2.51657i	0.100502	+	0.174074i
$210$	5.03700	−	0.190555i	0.347586	−	0.0131495i
$211$	−11.6803	−	6.74361i	−0.804103	−	0.464249i	0.0408006	−	0.999167i	$-0.487009\pi$
$211$	−11.6803	−	6.74361i	−0.804103	−	0.464249i	−0.844904	+	0.534918i	$0.820342\pi$
$212$	−17.4812	+	9.37420i	−1.20061	+	0.643823i
$213$	3.17085	+	6.53760i	0.217263	+	0.447949i
$214$	12.7776	−	3.20977i	0.873458	−	0.219415i
$215$	−1.23058			−0.0839245
$216$	7.33199	+	12.7374i	0.498879	+	0.866672i
$217$	−3.29955	−	2.56020i	−0.223988	−	0.173798i
$218$	−7.10085	−	28.2674i	−0.480930	−	1.91451i
$219$	−1.67884	−	3.46140i	−0.113446	−	0.233900i
$220$	1.73310	+	3.23191i	0.116845	+	0.217896i
$221$	9.83734	−	17.0388i	0.661731	−	1.14615i
$222$	7.28941	+	8.69479i	0.489233	+	0.583556i
$223$	−1.13546	+	0.655557i	−0.0760359	+	0.0438993i	−0.537536	−	0.843241i	$-0.680645\pi$
$223$	−1.13546	+	0.655557i	−0.0760359	+	0.0438993i	0.461500	+	0.887140i	$0.347311\pi$
$224$	6.86519	−	13.2992i	0.458700	−	0.888591i
$225$	−13.0487	−	1.89235i	−0.869911	−	0.126156i
$226$	4.66928	+	1.32998i	0.310596	+	0.0884690i
$227$	−3.17145	+	1.83104i	−0.210496	+	0.121530i	−0.601542	−	0.798841i	$-0.705447\pi$
$227$	−3.17145	+	1.83104i	−0.210496	+	0.121530i	0.391046	+	0.920371i	$0.372113\pi$
$228$	2.50515	−	3.45773i	0.165907	−	0.228993i
$229$	2.90486	−	5.03137i	0.191959	−	0.332483i	−0.753940	−	0.656943i	$-0.771849\pi$
$229$	2.90486	−	5.03137i	0.191959	−	0.332483i	0.945899	+	0.324460i	$0.105183\pi$
$230$	−3.97866	−	4.10550i	−0.262345	−	0.270709i
$231$	−8.03683	−	7.21979i	−0.528784	−	0.475027i
$232$	20.5517	+	6.55758i	1.34929	+	0.430526i
$233$		−	5.53176i		−	0.362398i	−0.983446	−	0.181199i	$-0.942002\pi$
$233$		−	5.53176i		−	0.362398i	0.983446	−	0.181199i	$-0.0579978\pi$
$234$	6.22410	+	8.61423i	0.406882	+	0.563130i
$235$			1.56168i			0.101873i
$236$	25.4086	+	0.797517i	1.65396	+	0.0519140i
$237$	18.0110	+	12.2062i	1.16994	+	0.792877i
$238$	29.2113	−	3.22101i	1.89349	−	0.208787i
$239$	1.58187	+	0.913296i	0.102323	+	0.0590762i	0.550288	−	0.834975i	$-0.314518\pi$
$239$	1.58187	+	0.913296i	0.102323	+	0.0590762i	−0.447965	+	0.894051i	$0.647851\pi$
$240$	3.29689	−	4.26238i	0.212813	−	0.275136i
$241$	−16.4901	+	9.52055i	−1.06222	+	0.613272i	−0.926045	−	0.377412i	$-0.876814\pi$
$241$	−16.4901	+	9.52055i	−1.06222	+	0.613272i	−0.136174	+	0.990685i	$0.543481\pi$
$242$	−2.10833	+	7.40188i	−0.135528	+	0.475811i
$243$	−9.88835	−	12.0507i	−0.634338	−	0.773056i
$244$	4.27112	+	2.64798i	0.273431	+	0.169520i
$245$	3.80811	+	3.89109i	0.243291	+	0.248593i
$246$	−1.88163	−	10.6982i	−0.119968	−	0.682095i
$247$	1.54379	−	2.67392i	0.0982290	−	0.170138i
$248$	−4.36213	+	0.951363i	−0.276996	+	0.0604116i
$249$	−9.87134	+	14.5658i	−0.625571	+	0.923068i
$250$	2.51773	+	10.0227i	0.159235	+	0.633891i
$251$		−	5.50248i		−	0.347314i	−0.984806	−	0.173657i	$-0.944442\pi$
$251$		−	5.50248i		−	0.347314i	0.984806	−	0.173657i	$-0.0555583\pi$
$252$	−4.86811	+	15.1096i	−0.306662	+	0.951818i
$253$			12.2534i			0.770364i
$254$	12.0941	−	3.03807i	0.758850	−	0.190625i
$255$	10.5537	+	0.761276i	0.660896	+	0.0476730i
$256$	−6.20252	−	14.7489i	−0.387658	−	0.921803i
$257$	−12.0416	+	20.8566i	−0.751133	+	1.30100i	0.196141	+	0.980576i	$0.437159\pi$
$257$	−12.0416	+	20.8566i	−0.751133	+	1.30100i	−0.947274	+	0.320425i	$0.896174\pi$
$258$	1.32706	−	3.64119i	0.0826194	−	0.226691i
$259$	−1.66508	+	12.1416i	−0.103463	+	0.754442i
$260$	2.05320	−	3.31176i	0.127334	−	0.205386i
$261$	−22.6443	−	3.28392i	−1.40164	−	0.203270i
$262$	10.1835	+	2.90063i	0.629139	+	0.179202i
$263$	14.5868	−	8.42167i	0.899459	−	0.519303i	0.0224341	−	0.999748i	$-0.492858\pi$
$263$	14.5868	−	8.42167i	0.899459	−	0.519303i	0.877024	+	0.480446i	$0.159525\pi$
$264$	−11.4320	+	1.64280i	−0.703592	+	0.101107i
$265$	−6.68056	−	3.85703i	−0.410384	−	0.236935i
$266$	4.58418	−	0.505478i	0.281074	−	0.0309929i
$267$	16.6112	−	8.05671i	1.01659	−	0.493062i
$268$	−24.4148	−	0.766322i	−1.49137	−	0.0468106i
$269$			11.7987i			0.719380i	0.933072	+	0.359690i	$0.117118\pi$
$269$			11.7987i			0.719380i	−0.933072	+	0.359690i	$0.882882\pi$
$270$	−2.70758	+	5.03349i	−0.164778	+	0.306329i
$271$		−	20.7503i		−	1.26049i	−0.776397	−	0.630244i	$-0.782955\pi$
$271$		−	20.7503i		−	1.26049i	0.776397	−	0.630244i	$-0.217045\pi$
$272$	17.3842	−	26.1697i	1.05407	−	1.58677i
$273$	−2.37381	+	11.2309i	−0.143669	+	0.679726i
$274$	13.9175	−	13.4875i	0.840784	−	0.814808i
$275$	5.18072	−	8.97326i	0.312409	−	0.541108i
$276$	16.4385	−	7.34518i	0.989483	−	0.442128i
$277$	10.0712	−	5.81460i	0.605119	−	0.349366i	−0.165934	−	0.986137i	$-0.553064\pi$
$277$	10.0712	−	5.81460i	0.605119	−	0.349366i	0.771053	+	0.636771i	$0.219730\pi$
$278$	7.67317	−	26.9388i	0.460206	−	1.61568i
$279$	4.39843	−	1.75465i	0.263327	−	0.105048i
$280$	5.80249	−	0.456110i	0.346765	−	0.0272578i
$281$	−16.8811	+	9.74633i	−1.00704	+	0.581417i	−0.910325	−	0.413894i	$-0.864168\pi$
$281$	−16.8811	+	9.74633i	−1.00704	+	0.581417i	−0.0967194	+	0.995312i	$0.530835\pi$
$282$	−4.62092	−	1.68414i	−0.275172	−	0.100289i
$283$	12.9150	−	22.3694i	0.767715	−	1.32972i	−0.171084	−	0.985257i	$-0.554727\pi$
$283$	12.9150	−	22.3694i	0.767715	−	1.32972i	0.938799	−	0.344465i	$-0.111940\pi$
$284$	3.96500	+	7.39401i	0.235280	+	0.438754i
$285$	1.65620	+	0.119468i	0.0981050	+	0.00707669i
$286$	−8.09989	+	2.03472i	−0.478956	+	0.120315i
$287$	7.19253	−	9.26963i	0.424562	−	0.547169i
$288$	9.05671	+	14.3519i	0.533672	+	0.845692i
$289$	44.6913			2.62890
$290$	2.04393	+	8.13657i	0.120024	+	0.477796i
$291$	5.10589	−	7.53406i	0.299313	−	0.441654i
$292$	−2.09931	−	3.91484i	−0.122853	−	0.229099i
$293$	−23.3045	−	13.4548i	−1.36146	−	0.786040i	−0.371643	−	0.928376i	$-0.621205\pi$
$293$	−23.3045	−	13.4548i	−1.36146	−	0.786040i	−0.989818	+	0.142336i	$0.954539\pi$
$294$	−15.6202	+	7.07175i	−0.910988	+	0.412433i
$295$	4.94303	+	8.56157i	0.287794	+	0.498474i
$296$	8.81796	+	9.68969i	0.512534	+	0.563202i
$297$	11.6752	−	3.70864i	0.677462	−	0.215197i
$298$	−5.89623	+	20.7004i	−0.341559	+	1.19914i
$299$	11.2753	−	6.50978i	0.652066	−	0.376471i
$300$	−15.1436	−	1.57125i	−0.874317	−	0.0907160i
$301$	3.87594	−	1.58105i	0.223405	−	0.0911302i
$302$	−6.98850	−	7.21130i	−0.402143	−	0.414963i
$303$	−13.8957	+	20.5040i	−0.798288	+	1.17792i
$304$	2.72812	−	4.10684i	0.156469	−	0.235544i
$305$			1.95432i			0.111904i
$306$	−13.6337	+	30.4066i	−0.779389	+	1.73823i
$307$	−24.8929			−1.42071			−0.710357	−	0.703841i	$-0.751467\pi$
$307$	−24.8929			−1.42071			−0.710357	+	0.703841i	$0.751467\pi$
$308$	−9.61111	−	7.95285i	−0.547644	−	0.453156i
$309$	−7.16152	−	0.516587i	−0.407404	−	0.0293876i
$310$	−1.20832	−	1.24684i	−0.0686278	−	0.0708157i
$311$	3.31781	−	5.74661i	0.188136	−	0.325860i	−0.756493	−	0.654002i	$-0.773089\pi$
$311$	3.31781	−	5.74661i	0.188136	−	0.325860i	0.944629	+	0.328141i	$0.106422\pi$
$312$	7.58508	+	9.64671i	0.429421	+	0.546138i
$313$	18.7711	−	10.8375i	1.06101	−	0.612572i	0.135295	−	0.990805i	$-0.456802\pi$
$313$	18.7711	−	10.8375i	1.06101	−	0.612572i	0.925710	+	0.378234i	$0.123468\pi$
$314$	−4.93164	+	17.3139i	−0.278309	+	0.977082i
$315$	−5.99165	+	1.48718i	−0.337591	+	0.0837930i
$316$	21.3527	+	13.2381i	1.20118	+	0.744699i
$317$	−12.4304	−	21.5301i	−0.698162	−	1.20925i	−0.969103	−	0.246656i	$-0.920668\pi$
$317$	−12.4304	−	21.5301i	−0.698162	−	1.20925i	0.270941	−	0.962596i	$-0.412665\pi$
$318$	18.6171	−	15.6079i	1.04399	−	0.875248i
$319$	8.99046	−	15.5719i	0.503369	−	0.871861i
$320$	3.60385	−	5.07235i	0.201461	−	0.283553i
$321$	−14.5180	+	7.04147i	−0.810315	+	0.393017i
$322$	17.8063	+	7.81927i	0.992308	+	0.435751i
$323$	9.68131			0.538682
$324$	−11.9739	−	13.4397i	−0.665217	−	0.746650i
$325$	−11.0093			−0.610687
$326$	1.70555	+	6.78953i	0.0944618	+	0.376037i
$327$	15.5776	+	32.1176i	0.861442	+	1.77611i
$328$	−2.67272	−	12.2548i	−0.147577	−	0.676659i
$329$	−2.00646	−	4.91883i	−0.110620	−	0.271184i
$330$	−2.88558	−	3.44191i	−0.158846	−	0.189471i
$331$	−5.91373	+	3.41429i	−0.325048	+	0.187667i	−0.653640	−	0.756805i	$-0.726759\pi$
$331$	−5.91373	+	3.41429i	−0.325048	+	0.187667i	0.328592	+	0.944472i	$0.393426\pi$
$332$	−10.7058	+	17.2682i	−0.587559	+	0.947717i
$333$	−10.9126	−	8.60332i	−0.598008	−	0.471459i
$334$	7.12149	−	25.0020i	0.389670	−	1.36805i
$335$	−4.74968	−	8.22668i	−0.259503	−	0.449472i
$336$	−4.90786	+	17.6611i	−0.267746	+	0.963490i
$337$	−3.30338	+	5.72162i	−0.179946	+	0.311676i	−0.941862	−	0.336000i	$-0.890926\pi$
$337$	−3.30338	+	5.72162i	−0.179946	+	0.311676i	0.761916	+	0.647676i	$0.224259\pi$
$338$	−6.61898	−	6.82999i	−0.360025	−	0.371503i
$339$	−5.93072	−	0.427806i	−0.322113	−	0.0232352i
$340$	12.2120	+	0.383305i	0.662287	+	0.0207876i
$341$			3.72135i			0.201522i
$342$	−2.13956	+	4.77176i	−0.115694	+	0.258027i
$343$	−16.9937	−	7.36308i	−0.917572	−	0.397569i
$344$	1.36031	−	4.26326i	0.0733429	−	0.229860i
$345$	5.79627	+	3.92818i	0.312061	+	0.211486i
$346$	10.0403	−	9.73007i	0.539768	−	0.523092i
$347$	−2.79128	+	4.83464i	−0.149844	+	0.259537i	−0.931170	−	0.364586i	$-0.881210\pi$
$347$	−2.79128	+	4.83464i	−0.149844	+	0.259537i	0.781326	+	0.624123i	$0.214544\pi$
$348$	−26.2798	−	2.72670i	−1.40874	−	0.146166i
$349$	13.6117	+	23.5762i	0.728620	+	1.26201i	0.957467	+	0.288544i	$0.0931711\pi$
$349$	13.6117	+	23.5762i	0.728620	+	1.26201i	−0.228847	+	0.973462i	$0.573496\pi$
$350$	−9.73376	−	13.2546i	−0.520291	−	0.708489i
$351$	−9.61520	−	8.77294i	−0.513221	−	0.468265i
$352$	−13.1126	+	2.43158i	−0.698904	+	0.129604i
$353$	3.84237	+	6.65518i	0.204509	+	0.354220i	0.949976	−	0.312322i	$-0.101107\pi$
$353$	3.84237	+	6.65518i	0.204509	+	0.354220i	−0.745467	+	0.666542i	$0.767774\pi$
$354$	−30.6637	+	5.39321i	−1.62976	+	0.286646i
$355$	−1.63140	+	2.82568i	−0.0865860	+	0.149971i
$356$	18.7872	−	10.0745i	0.995720	−	0.533950i
$357$	−34.2189	+	11.1616i	−1.81106	+	0.590735i
$358$	−0.639722	+	0.160700i	−0.0338103	+	0.00849326i
$359$		−	12.1437i		−	0.640919i	−0.947262	−	0.320460i	$-0.896163\pi$
$359$		−	12.1437i		−	0.640919i	0.947262	−	0.320460i	$-0.103837\pi$
$360$	−2.88777	+	5.93438i	−0.152199	+	0.312769i
$361$	−17.4807			−0.920037
$362$	−18.9758	+	4.76679i	−0.997348	+	0.250537i
$363$	0.678170	−	9.40156i	0.0355947	−	0.493454i
$364$	−2.21199	+	13.0690i	−0.115940	+	0.685001i
$365$	0.863765	−	1.49608i	0.0452115	−	0.0783086i
$366$	−5.78270	−	2.10756i	−0.302267	−	0.110164i
$367$	−25.2607	+	14.5843i	−1.31860	+	0.761293i	−0.983503	−	0.180891i	$-0.942102\pi$
$367$	−25.2607	+	14.5843i	−1.31860	+	0.761293i	−0.335095	+	0.942184i	$0.608768\pi$
$368$	18.6214	−	9.24553i	0.970707	−	0.481957i
$369$	4.92945	+	12.3568i	0.256617	+	0.643268i
$370$	−1.39573	+	4.90011i	−0.0725606	+	0.254745i
$371$	25.9973	+	3.56523i	1.34971	+	0.185098i
$372$	4.99237	−	2.23073i	0.258843	−	0.115658i
$373$	21.6268	+	12.4862i	1.11979	+	0.646513i	0.941348	−	0.337437i	$-0.109560\pi$
$373$	21.6268	+	12.4862i	1.11979	+	0.646513i	0.178445	+	0.983950i	$0.442893\pi$
$374$	−18.2241	−	18.8051i	−0.942345	−	0.972387i
$375$	−5.52331	−	11.3879i	−0.285222	−	0.588066i
$376$	−5.41037	−	1.72632i	−0.279019	−	0.0890284i
$377$	−19.1052			−0.983970
$378$	2.06098	−	19.3327i	0.106006	−	0.994366i
$379$			4.59169i			0.235859i	0.993022	+	0.117930i	$0.0376258\pi$
$379$			4.59169i			0.235859i	−0.993022	+	0.117930i	$0.962374\pi$
$380$	1.91644	+	0.0601527i	0.0983115	+	0.00308577i
$381$	−13.7414	+	6.66480i	−0.703992	+	0.341448i
$382$	3.88675	−	3.76667i	0.198863	−	0.192719i
$383$	7.39046	−	12.8007i	0.377635	−	0.654083i	−0.613083	−	0.790019i	$-0.710071\pi$
$383$	7.39046	−	12.8007i	0.377635	−	0.654083i	0.990718	+	0.135936i	$0.0434041\pi$
$384$	11.1223	+	16.1336i	0.567584	+	0.823316i
$385$	0.659139	−	4.80636i	0.0335928	−	0.244955i
$386$	2.67667	−	9.39721i	0.136239	−	0.478305i
$387$	−0.681219	+	4.69734i	−0.0346283	+	0.238779i
$388$	5.53753	−	8.93189i	0.281126	−	0.453448i
$389$	2.80467	+	4.85784i	0.142203	+	0.246302i	0.928326	−	0.371768i	$-0.121248\pi$
$389$	2.80467	+	4.85784i	0.142203	+	0.246302i	−0.786123	+	0.618070i	$0.787915\pi$
$390$	−1.63416	+	4.48381i	−0.0827491	+	0.227047i
$391$	35.3544	+	20.4118i	1.78795	+	1.03227i
$392$	−17.6901	+	8.89167i	−0.893483	+	0.449097i
$393$	−12.9347	−	0.933026i	−0.652467	−	0.0470650i
$394$	−11.9717	+	3.00733i	−0.603126	+	0.151507i
$395$			9.77024i			0.491594i
$396$	13.2962	−	4.82645i	0.668161	−	0.242538i
$397$	0.00985613			0.000494665			0.000247333	−	1.00000i	$-0.499921\pi$
$397$	0.00985613			0.000494665			0.000247333		1.00000i	$0.499921\pi$
$398$	2.38589	+	9.49786i	0.119594	+	0.476085i
$399$	−5.37003	+	1.75161i	−0.268838	+	0.0876902i
$400$	−17.5456	−	1.10252i	−0.877281	−	0.0551259i
$401$	24.7773	+	14.3052i	1.23732	+	0.714365i	0.968545	−	0.248838i	$-0.0800488\pi$
$401$	24.7773	+	14.3052i	1.23732	+	0.714365i	0.268772	+	0.963204i	$0.413382\pi$
$402$	29.4643	−	5.18225i	1.46955	−	0.258467i
$403$	3.42430	−	1.97702i	0.170576	−	0.0984823i
$404$	−15.0704	+	24.3082i	−0.749782	+	1.20938i
$405$	1.98850	−	6.71166i	0.0988094	−	0.333505i
$406$	−16.8917	−	23.0017i	−0.838320	−	1.14155i
$407$	9.45711	−	5.46007i	0.468772	−	0.270645i
$408$	−14.3037	+	35.7211i	−0.708138	+	1.76846i
$409$	−29.2880	−	16.9094i	−1.44820	−	0.836118i	−0.449825	−	0.893117i	$-0.648514\pi$
$409$	−29.2880	−	16.9094i	−1.44820	−	0.836118i	−0.998374	+	0.0569988i	$0.981847\pi$
$410$	3.50282	−	3.39460i	0.172992	−	0.167647i
$411$	−13.3163	+	19.6491i	−0.656847	+	0.969218i
$412$	−8.28681	−	0.260104i	−0.408262	−	0.0128144i
$413$	−26.5690	−	20.6155i	−1.30737	−	1.01442i
$414$	−17.8740	+	12.9146i	−0.878458	+	0.634718i
$415$	−7.90135			−0.387862
$416$	9.20374	+	10.7741i	0.451251	+	0.528243i
$417$	−2.46817	+	34.2166i	−0.120867	+	1.67559i
$418$	−2.85993	−	2.95111i	−0.139884	−	0.144343i
$419$	−3.56884	−	2.06047i	−0.174349	−	0.100661i	0.410286	−	0.911957i	$-0.365429\pi$
$419$	−3.56884	−	2.06047i	−0.174349	−	0.100661i	−0.584635	+	0.811296i	$0.698762\pi$
$420$	−6.84309	+	1.99686i	−0.333909	+	0.0974370i
$421$	10.9947	−	6.34777i	0.535847	−	0.309371i	−0.207547	−	0.978225i	$-0.566548\pi$
$421$	10.9947	−	6.34777i	0.535847	−	0.309371i	0.743394	+	0.668854i	$0.233215\pi$
$422$	18.3442	+	5.22509i	0.892980	+	0.254354i
$423$	5.96125	+	0.864513i	0.289846	+	0.0420341i
$424$	20.7473	−	18.8808i	1.00758	−	0.916933i
$425$	−17.2602	−	29.8956i	−0.837243	−	1.45015i
$426$	−6.60167	−	7.87445i	−0.319852	−	0.381519i
$427$	−2.51092	−	6.15551i	−0.121512	−	0.297886i
$428$	−16.4198	+	8.80504i	−0.793681	+	0.425608i
$429$	9.20314	−	4.46368i	0.444332	−	0.215509i
$430$	1.68786	−	0.423995i	0.0813957	−	0.0204468i
$431$		−	7.03295i		−	0.338765i	−0.985550	−	0.169383i	$-0.945823\pi$
$431$		−	7.03295i		−	0.338765i	0.985550	−	0.169383i	$-0.0541774\pi$
$432$	−14.4452	−	14.9444i	−0.694997	−	0.719013i
$433$			19.8436i			0.953624i	0.879005	+	0.476812i	$0.158208\pi$
$433$			19.8436i			0.953624i	−0.879005	+	0.476812i	$0.841792\pi$
$434$	5.40778	+	2.37471i	0.259582	+	0.113990i
$435$	−4.48390	−	9.24483i	−0.214987	−	0.443256i
$436$	19.4790	+	36.3249i	0.932877	+	1.73965i
$437$	5.54821	+	3.20326i	0.265407	+	0.153233i
$438$	3.49532	+	4.16921i	0.167013	+	0.199213i
$439$	13.5047	−	7.79695i	0.644545	−	0.372128i	−0.141818	−	0.989893i	$-0.545295\pi$
$439$	13.5047	−	7.79695i	0.644545	−	0.372128i	0.786363	+	0.617765i	$0.211962\pi$
$440$	−3.49067	−	3.83575i	−0.166411	−	0.182862i
$441$	16.9611	−	12.3823i	0.807673	−	0.589631i
$442$	−7.62218	+	26.7598i	−0.362550	+	1.27284i
$443$	14.5689	+	25.2341i	0.692191	+	1.19891i	0.971118	+	0.238598i	$0.0766878\pi$
$443$	14.5689	+	25.2341i	0.692191	+	1.19891i	−0.278927	+	0.960312i	$0.589979\pi$
$444$	−12.9939	−	9.41420i	−0.616665	−	0.446778i
$445$	7.17967	+	4.14518i	0.340349	+	0.196500i
$446$	1.33152	−	1.29038i	0.0630494	−	0.0611014i
$447$	1.89660	−	26.2928i	0.0897060	−	1.24361i
$448$	−4.83404	+	20.6066i	−0.228387	+	0.973570i
$449$			8.62683i			0.407125i	0.979062	+	0.203563i	$0.0652521\pi$
$449$			8.62683i			0.407125i	−0.979062	+	0.203563i	$0.934748\pi$
$450$	18.5495	−	1.90038i	0.874434	−	0.0895847i
$451$	−10.4546			−0.492288
$452$	−6.86262	−	0.215402i	−0.322791	−	0.0101316i
$453$	10.1811	+	6.89983i	0.478351	+	0.324182i
$454$	3.71907	−	3.60417i	0.174545	−	0.169152i
$455$	−4.77288	+	1.94692i	−0.223756	+	0.0912732i
$456$	−2.24470	+	5.60576i	−0.105118	+	0.262514i
$457$	−7.37105	−	12.7670i	−0.344803	−	0.597216i	0.640515	−	0.767946i	$-0.278721\pi$
$457$	−7.37105	−	12.7670i	−0.344803	−	0.597216i	−0.985318	+	0.170729i	$0.945388\pi$
$458$	−2.25075	+	7.90190i	−0.105171	+	0.369232i
$459$	8.74821	−	39.8639i	0.408331	−	1.86069i
$460$	6.87168	+	4.26025i	0.320394	+	0.198635i
$461$	−11.5488	+	6.66768i	−0.537879	+	0.310545i	−0.744219	−	0.667936i	$-0.767178\pi$
$461$	−11.5488	+	6.66768i	−0.537879	+	0.310545i	0.206340	+	0.978480i	$0.433845\pi$
$462$	13.5109	+	7.13357i	0.628583	+	0.331884i
$463$	14.8848	−	25.7812i	0.691754	−	1.19815i	−0.279509	−	0.960143i	$-0.590172\pi$
$463$	14.8848	−	25.7812i	0.691754	−	1.19815i	0.971263	−	0.238009i	$-0.0764949\pi$
$464$	−30.4481	−	1.91328i	−1.41352	−	0.0888216i
$465$	1.76032	+	1.19299i	0.0816331	+	0.0553234i
$466$	1.90597	+	7.58736i	0.0882923	+	0.351478i
$467$		−	27.9931i		−	1.29537i	−0.761910	−	0.647683i	$-0.775738\pi$
$467$		−	27.9931i		−	1.29537i	0.761910	−	0.647683i	$-0.224262\pi$
$468$	−11.5050	−	9.67077i	−0.531819	−	0.447031i
$469$	25.5297	+	19.8091i	1.17885	+	0.914701i
$470$	−0.538079	−	2.14201i	−0.0248197	−	0.0988034i
$471$	1.58633	−	21.9914i	0.0730940	−	1.01331i
$472$	−35.1253	+	7.66067i	−1.61677	+	0.352611i
$473$	−3.23025	−	1.86499i	−0.148527	−	0.0857522i
$474$	−28.9095	−	10.5363i	−1.32786	−	0.483949i
$475$	−2.70867	−	4.69156i	−0.124282	−	0.215263i
$476$	−38.9565	+	14.4827i	−1.78557	+	0.663814i
$477$	−18.4212	+	23.3658i	−0.843449	+	1.06985i
$478$	−2.48437	−	0.707641i	−0.113633	−	0.0323667i
$479$	11.4972	+	19.9138i	0.525322	+	0.909884i	0.999565	+	0.0294903i	$0.00938841\pi$
$479$	11.4972	+	19.9138i	0.525322	+	0.909884i	−0.474243	+	0.880394i	$0.657278\pi$
$480$	−3.05340	+	6.98222i	−0.139368	+	0.318693i
$481$	−10.0485	−	5.80148i	−0.458170	−	0.264525i
$482$	19.3375	−	18.7400i	0.880798	−	0.853585i
$483$	−23.3034	−	4.92549i	−1.06034	−	0.224118i
$484$	0.341461	−	10.8788i	0.0155210	−	0.494493i
$485$	4.08693			0.185578
$486$	17.7149	+	13.1218i	0.803566	+	0.595215i
$487$	28.4385			1.28867			0.644335	−	0.764743i	$-0.277134\pi$
$487$	28.4385			1.28867			0.644335	+	0.764743i	$0.277134\pi$
$488$	−6.77063	−	2.16035i	−0.306492	−	0.0977946i
$489$	−3.74157	−	7.71431i	−0.169200	−	0.348853i
$490$	−6.56388	−	4.02494i	−0.296526	−	0.181828i
$491$	−18.8874	+	32.7140i	−0.852377	+	1.47636i	0.0266799	+	0.999644i	$0.491507\pi$
$491$	−18.8874	+	32.7140i	−0.852377	+	1.47636i	−0.879057	+	0.476717i	$0.841827\pi$
$492$	6.26693	+	14.0254i	0.282535	+	0.632313i
$493$	−29.9529	−	51.8799i	−1.34901	−	2.33655i
$494$	−1.19616	+	4.19946i	−0.0538178	+	0.188943i
$495$	4.31986	+	3.40570i	0.194163	+	0.153075i
$496$	5.65531	−	2.80786i	0.253931	−	0.126077i
$497$	1.50799	−	10.9961i	0.0676424	−	0.493240i
$498$	8.52089	−	23.3796i	0.381830	−	1.04766i
$499$	−14.1432	−	8.16561i	−0.633139	−	0.365543i	0.148828	−	0.988863i	$-0.452450\pi$
$499$	−14.1432	−	8.16561i	−0.633139	−	0.365543i	−0.781967	+	0.623320i	$0.785783\pi$
$500$	−6.90664	−	12.8796i	−0.308874	−	0.575995i
$501$	−2.29072	+	31.7565i	−0.102342	+	1.41878i
$502$	1.89588	+	7.54720i	0.0846173	+	0.336848i
$503$	21.8436			0.973957			0.486978	−	0.873414i	$-0.338099\pi$
$503$	21.8436			0.973957			0.486978	+	0.873414i	$0.338099\pi$
$504$	1.47107	−	22.4017i	0.0655265	−	0.997851i
$505$	−11.1226			−0.494949
$506$	−4.22190	−	16.8067i	−0.187687	−	0.747150i
$507$	9.64278	+	6.53499i	0.428251	+	0.290229i
$508$	−15.5415	+	8.33403i	−0.689541	+	0.369763i
$509$	21.3142	+	12.3057i	0.944734	+	0.545443i	0.891441	−	0.453136i	$-0.149695\pi$
$509$	21.3142	+	12.3057i	0.944734	+	0.545443i	0.0532930	+	0.998579i	$0.483028\pi$
$510$	−14.7377	+	2.59210i	−0.652596	+	0.114780i
$511$	−0.798419	+	5.82198i	−0.0353200	+	0.257549i
$512$	13.5891	+	18.0924i	0.600559	+	0.799580i
$513$	1.37287	−	6.25591i	0.0606137	−	0.276205i
$514$	9.33007	−	32.7559i	0.411532	−	1.44480i
$515$	−1.61213	−	2.79229i	−0.0710388	−	0.123043i
$516$	−0.565628	+	5.45150i	−0.0249004	+	0.239989i
$517$	−2.36680	+	4.09941i	−0.104092	+	0.180292i
$518$	−1.89956	−	17.2271i	−0.0834618	−	0.756915i
$519$	−9.60661	+	14.1751i	−0.421683	+	0.622220i
$520$	−1.67510	+	5.24983i	−0.0734580	+	0.230220i
$521$	22.1426			0.970084			0.485042	−	0.874491i	$-0.338804\pi$
$521$	22.1426			0.970084			0.485042	+	0.874491i	$0.338804\pi$
$522$	32.1903	−	3.29786i	1.40893	−	0.144343i
$523$	19.6414			0.858859			0.429429	−	0.903100i	$-0.358715\pi$
$523$	19.6414			0.858859			0.429429	+	0.903100i	$0.358715\pi$
$524$	−14.9671	−	0.469782i	−0.653841	−	0.0205225i
$525$	14.9828	+	13.4596i	0.653904	+	0.587427i
$526$	−17.1055	+	16.5770i	−0.745836	+	0.722793i
$527$	10.7371	+	6.19907i	0.467715	+	0.270036i
$528$	15.1141	−	6.19216i	0.657757	−	0.269479i
$529$	2.00738	+	3.47688i	0.0872773	+	0.151169i
$530$	10.4920	+	2.98851i	0.455743	+	0.129812i
$531$	35.4175	−	14.1290i	1.53699	−	0.613146i
$532$	−6.11350	+	2.27279i	−0.265054	+	0.0985381i
$533$	5.55416	+	9.62009i	0.240577	+	0.416692i
$534$	−20.0079	+	16.7740i	−0.865828	+	0.725880i
$535$	−6.27495	−	3.62284i	−0.271290	−	0.156629i
$536$	33.7513	−	7.36102i	1.45783	−	0.317948i
$537$	0.726856	−	0.352538i	0.0313662	−	0.0152131i
$538$	−4.06525	−	16.1831i	−0.175265	−	0.697703i
$539$	4.09915	+	15.9854i	0.176563	+	0.688542i
$540$	1.97942	−	7.83683i	0.0851807	−	0.337244i
$541$		−	29.0446i		−	1.24873i	−0.781135	−	0.624363i	$-0.785359\pi$
$541$		−	29.0446i		−	1.24873i	0.781135	−	0.624363i	$-0.214641\pi$
$542$	7.14950	+	28.4610i	0.307098	+	1.22251i
$543$	21.5605	−	10.4572i	0.925249	−	0.448761i
$544$	−14.8274	+	41.8840i	−0.635718	+	1.79576i
$545$	−8.01467	+	13.8818i	−0.343311	+	0.594632i
$546$	−0.613703	−	16.2222i	−0.0262641	−	0.694247i
$547$	5.66604	−	3.27129i	0.242262	−	0.139870i	−0.373954	−	0.927447i	$-0.621998\pi$
$547$	5.66604	−	3.27129i	0.242262	−	0.139870i	0.616216	+	0.787577i	$0.288665\pi$
$548$	−14.4421	+	23.2947i	−0.616934	+	0.995099i
$549$	7.46001	+	1.08187i	0.318385	+	0.0461729i
$550$	−4.01413	+	14.0927i	−0.171163	+	0.600916i
$551$	−4.70055	−	8.14159i	−0.200250	−	0.346843i
$552$	−20.0163	+	15.7385i	−0.851950	+	0.669877i
$553$	−12.5529	−	30.7733i	−0.533801	−	1.30861i
$554$	−11.8102	+	11.4453i	−0.501768	+	0.486266i
$555$	0.448955	−	6.22392i	0.0190571	−	0.264191i
$556$	−1.24273	+	39.5931i	−0.0527037	+	1.67912i
$557$	38.1110			1.61482			0.807408	−	0.589994i	$-0.200870\pi$
$557$	38.1110			1.61482			0.807408	+	0.589994i	$0.200870\pi$
$558$	−5.42832	+	3.92216i	−0.229799	+	0.166038i
$559$			3.96320i			0.167626i
$560$	−7.80154	+	2.62485i	−0.329675	+	0.110920i
$561$	26.5496	+	17.9929i	1.12092	+	0.759659i
$562$	19.7961	−	19.1845i	0.835046	−	0.809248i
$563$	7.45309	+	4.30304i	0.314110	+	0.181352i	0.648764	−	0.760989i	$-0.275286\pi$
$563$	7.45309	+	4.30304i	0.314110	+	0.181352i	−0.334654	+	0.942341i	$0.608619\pi$
$564$	6.91832	+	0.717820i	0.291314	+	0.0302257i
$565$	−1.33506	−	2.31240i	−0.0561665	−	0.0972833i
$566$	−10.0068	+	35.1317i	−0.420617	+	1.47670i
$567$	2.36000	+	23.6945i	0.0991108	+	0.995076i
$568$	−7.98600	−	8.77548i	−0.335085	−	0.368211i
$569$	20.5079	−	11.8402i	0.859735	−	0.496369i	−0.00418822	−	0.999991i	$-0.501333\pi$
$569$	20.5079	−	11.8402i	0.859735	−	0.496369i	0.863924	+	0.503623i	$0.168000\pi$
$570$	−2.31281	+	0.406782i	−0.0968730	+	0.0170382i
$571$	−2.43795	−	1.40755i	−0.102025	−	0.0589043i	0.448119	−	0.893974i	$-0.352094\pi$
$571$	−2.43795	−	1.40755i	−0.102025	−	0.0589043i	−0.550144	+	0.835070i	$0.685427\pi$
$572$	10.4087	−	5.58163i	0.435211	−	0.233380i
$573$	−3.71887	+	5.48743i	−0.155358	+	0.229241i
$574$	−6.67142	+	15.1924i	−0.278460	+	0.634119i
$575$		−	22.8436i		−	0.952645i
$576$	−17.3671	−	16.5645i	−0.723630	−	0.690188i
$577$			33.7274i			1.40409i	0.712132	+	0.702046i	$0.247730\pi$
$577$			33.7274i			1.40409i	−0.712132	+	0.702046i	$0.752270\pi$
$578$	−61.2985	+	15.3984i	−2.54968	+	0.640488i
$579$	−0.860985	+	11.9359i	−0.0357813	+	0.496041i
$580$	−5.60691	−	10.4559i	−0.232814	−	0.434157i
$581$	24.8868	−	10.1517i	1.03248	−	0.421163i
$582$	−4.40738	+	12.0930i	−0.182692	+	0.501269i
$583$	−11.6910	−	20.2493i	−0.484190	−	0.838642i
$584$	4.22828	+	4.64627i	0.174967	+	0.192264i
$585$	0.838861	−	5.78436i	0.0346826	−	0.239154i
$586$	36.6003	+	10.4251i	1.51194	+	0.430657i
$587$	6.99671	−	4.03955i	0.288785	−	0.166730i	−0.348609	−	0.937268i	$-0.613346\pi$
$587$	6.99671	−	4.03955i	0.288785	−	0.166730i	0.637394	+	0.770538i	$0.280012\pi$
$588$	18.9881	−	15.0815i	0.783055	−	0.621953i
$589$	1.68499	+	0.972830i	0.0694288	+	0.0400847i
$590$	−9.72974	−	10.0399i	−0.400567	−	0.413337i
$591$	13.6023	−	6.59737i	0.559526	−	0.271380i
$592$	−15.4333	−	10.2521i	−0.634304	−	0.421360i
$593$	15.3764			0.631431			0.315716	−	0.948854i	$-0.397755\pi$
$593$	15.3764			0.631431			0.315716	+	0.948854i	$0.397755\pi$
$594$	−14.7358	+	9.10944i	−0.604619	+	0.373765i
$595$	−12.7697	−	9.90830i	−0.523505	−	0.406201i
$596$	0.954944	−	30.4242i	0.0391160	−	1.24622i
$597$	−5.23408	−	10.7915i	−0.214217	−	0.441668i
$598$	−13.2222	+	12.8137i	−0.540697	+	0.523992i
$599$	21.6005	+	12.4710i	0.882571	+	0.509553i	0.871505	−	0.490386i	$-0.163144\pi$
$599$	21.6005	+	12.4710i	0.882571	+	0.509553i	0.0110658	+	0.999939i	$0.496478\pi$
$600$	21.3124	−	3.06261i	0.870073	−	0.125031i
$601$	20.8507	−	12.0381i	0.850516	−	0.491046i	−0.0103091	−	0.999947i	$-0.503282\pi$
$601$	20.8507	−	12.0381i	0.850516	−	0.491046i	0.860825	+	0.508901i	$0.169948\pi$
$602$	−4.77148	+	3.50402i	−0.194471	+	0.142813i
$603$	−34.0321	+	13.5763i	−1.38590	+	0.552870i
$604$	12.0701	+	7.48312i	0.491124	+	0.304484i
$605$	3.66568	−	2.11638i	0.149031	−	0.0860432i
$606$	11.9947	−	32.9110i	0.487252	−	1.33692i
$607$	42.1068	+	24.3104i	1.70906	+	0.986727i	0.935725	+	0.352732i	$0.114747\pi$
$607$	42.1068	+	24.3104i	1.70906	+	0.986727i	0.773337	+	0.633995i	$0.218586\pi$
$608$	−2.32688	+	6.57292i	−0.0943675	+	0.266567i
$609$	26.0007	+	23.3575i	1.05360	+	0.946492i
$610$	−0.673361	−	2.68054i	−0.0272636	−	0.108532i
$611$	5.02958			0.203475
$612$	8.22342	−	46.4032i	0.332412	−	1.87574i
$613$		−	41.8919i		−	1.69200i	−0.533185	−	0.845998i	$-0.679005\pi$
$613$		−	41.8919i		−	1.69200i	0.533185	−	0.845998i	$-0.320995\pi$
$614$	34.1431	−	8.57686i	1.37790	−	0.346134i
$615$	−3.35153	+	4.94539i	−0.135147	+	0.199417i
$616$	15.9227	+	7.59662i	0.641546	+	0.306077i
$617$	−23.3876	−	13.5028i	−0.941549	−	0.543603i	−0.0511031	−	0.998693i	$-0.516274\pi$
$617$	−23.3876	−	13.5028i	−0.941549	−	0.543603i	−0.890445	+	0.455090i	$0.849607\pi$
$618$	10.0007	−	1.75895i	0.402288	−	0.0707554i
$619$	−19.5911	−	33.9327i	−0.787432	−	1.36387i	−0.927535	−	0.373735i	$-0.878077\pi$
$619$	−19.5911	−	33.9327i	−0.787432	−	1.36387i	0.140103	−	0.990137i	$-0.455257\pi$
$620$	2.08693	+	1.29384i	0.0838130	+	0.0519618i
$621$	18.2033	−	19.9509i	0.730473	−	0.800602i
$622$	−2.57071	+	9.02520i	−0.103076	+	0.361878i
$623$	−27.9395	−	3.83159i	−1.11937	−	0.153509i
$624$	−13.7275	−	10.6180i	−0.549539	−	0.425060i
$625$	−8.14589	+	14.1091i	−0.325836	+	0.564364i
$626$	−22.0124	+	21.3323i	−0.879791	+	0.852610i
$627$	4.16646	+	2.82365i	0.166393	+	0.112766i
$628$	0.798721	−	25.4470i	0.0318724	−	1.01544i
$629$		−	36.3818i		−	1.45064i
$630$	7.70573	−	4.10424i	0.307004	−	0.163517i
$631$	−42.7248			−1.70085			−0.850423	−	0.526099i	$-0.823654\pi$
$631$	−42.7248			−1.70085			−0.850423	+	0.526099i	$0.823654\pi$
$632$	−33.8485	−	10.8003i	−1.34642	−	0.429611i
$633$	−23.3000	−	1.68072i	−0.926092	−	0.0668026i
$634$	24.4678	+	25.2478i	0.971739	+	1.00272i
$635$	−5.93928	−	3.42904i	−0.235693	−	0.136077i
$636$	−20.1575	+	27.8223i	−0.799295	+	1.10323i
$637$	12.5317	−	12.2644i	0.496524	−	0.485935i
$638$	−6.96600	+	24.4561i	−0.275787	+	0.968227i
$639$	9.88303	+	7.79161i	0.390967	+	0.308231i
$640$	−3.19536	+	8.19894i	−0.126308	+	0.324092i
$641$	−4.89304	+	2.82500i	−0.193264	+	0.111581i	−0.593509	−	0.804827i	$-0.702258\pi$
$641$	−4.89304	+	2.82500i	−0.193264	+	0.111581i	0.400246	+	0.916408i	$0.368925\pi$
$642$	17.4867	−	14.6602i	0.690146	−	0.578594i
$643$	−13.8244	+	23.9446i	−0.545181	+	0.944281i	0.453414	+	0.891300i	$0.350206\pi$
$643$	−13.8244	+	23.9446i	−0.545181	+	0.944281i	−0.998595	+	0.0529815i	$0.983128\pi$
$644$	−27.1173	−	4.58974i	−1.06857	−	0.180861i
$645$	−1.91775	+	0.930144i	−0.0755115	+	0.0366244i
$646$	−13.2789	+	3.33569i	−0.522450	+	0.131241i
$647$	22.0540			0.867032			0.433516	−	0.901146i	$-0.357273\pi$
$647$	22.0540			0.867032			0.433516	+	0.901146i	$0.357273\pi$
$648$	21.0540	+	14.3083i	0.827081	+	0.562083i
$649$			29.9654i			1.17625i
$650$	15.1004	−	3.79326i	0.592285	−	0.148784i
$651$	−7.07724	−	1.49587i	−0.277379	−	0.0586278i
$652$	−4.67867	−	8.72487i	−0.183231	−	0.341692i
$653$	−15.4791	+	26.8107i	−0.605746	+	1.04918i	0.386187	+	0.922420i	$0.373792\pi$
$653$	−15.4791	+	26.8107i	−0.605746	+	1.04918i	−0.991933	+	0.126762i	$0.959541\pi$
$654$	−32.4323	−	38.6852i	−1.26820	−	1.51271i
$655$	−2.91172	−	5.04324i	−0.113770	−	0.197056i
$656$	7.88831	+	15.8878i	0.307987	+	0.620315i
$657$	−5.23268	−	4.12535i	−0.204146	−	0.160945i
$658$	4.44684	+	6.05534i	0.173356	+	0.236062i
$659$	−8.43863	−	14.6161i	−0.328722	−	0.569364i	0.653536	−	0.756895i	$-0.273285\pi$
$659$	−8.43863	−	14.6161i	−0.328722	−	0.569364i	−0.982259	+	0.187531i	$0.939951\pi$
$660$	5.14377	+	3.72670i	0.200221	+	0.145062i
$661$	3.63378	−	6.29389i	0.141338	−	0.244804i	−0.786663	−	0.617383i	$-0.788193\pi$
$661$	3.63378	−	6.29389i	0.141338	−	0.244804i	0.928001	+	0.372579i	$0.121526\pi$
$662$	6.93487	−	6.72062i	0.269532	−	0.261204i
$663$	2.45177	−	33.9892i	0.0952190	−	1.32003i
$664$	8.73435	−	27.3738i	0.338958	−	1.06231i
$665$	−2.00396	−	1.55492i	−0.0777104	−	0.0602974i
$666$	17.9320	+	8.04036i	0.694851	+	0.311558i
$667$		−	39.6421i		−	1.53495i
$668$	−1.15338	+	36.7464i	−0.0446258	+	1.42176i
$669$	−1.27401	+	1.87988i	−0.0492561	+	0.0726804i
$670$	9.34916	+	9.64721i	0.361189	+	0.372704i
$671$	−2.96185	+	5.13007i	−0.114341	+	0.198044i
$672$	0.646497	−	25.9149i	0.0249391	−	0.999689i
$673$	−17.5434	−	30.3860i	−0.676247	−	1.17129i	−0.976103	−	0.217310i	$-0.930272\pi$
$673$	−17.5434	−	30.3860i	−0.676247	−	1.17129i	0.299855	−	0.953985i	$-0.403062\pi$
$674$	2.55953	−	8.98594i	0.0985893	−	0.346126i
$675$	−21.7657	+	6.91390i	−0.837760	+	0.266116i
$676$	11.4319	+	7.08744i	0.439687	+	0.272594i
$677$	11.0626	−	6.38699i	0.425170	−	0.245472i	−0.272117	−	0.962264i	$-0.587724\pi$
$677$	11.0626	−	6.38699i	0.425170	−	0.245472i	0.697287	+	0.716792i	$0.254390\pi$
$678$	8.28198	−	1.45665i	0.318067	−	0.0559424i
$679$	−12.8726	+	5.25090i	−0.494004	+	0.201511i
$680$	−16.8820	+	3.68190i	−0.647395	+	0.141194i
$681$	−3.55844	+	5.25070i	−0.136360	+	0.201207i
$682$	−1.28219	−	5.10420i	−0.0490976	−	0.195450i
$683$	−29.9249			−1.14504			−0.572522	−	0.819889i	$-0.694035\pi$
$683$	−29.9249			−1.14504			−0.572522	+	0.819889i	$0.694035\pi$
$684$	1.29051	−	7.28213i	0.0493440	−	0.278439i
$685$	−10.6588			−0.407253
$686$	25.8455	+	4.24403i	0.986785	+	0.162038i
$687$	0.723983	−	10.0367i	0.0276217	−	0.382923i
$688$	−0.396891	+	6.31618i	−0.0151313	+	0.240802i
$689$	−12.4220	+	21.5155i	−0.473240	+	0.819675i
$690$	−9.30361	−	3.39078i	−0.354182	−	0.129085i
$691$	17.2506	+	29.8789i	0.656243	+	1.13665i	0.981581	+	0.191049i	$0.0611889\pi$
$691$	17.2506	+	29.8789i	0.656243	+	1.13665i	−0.325337	+	0.945598i	$0.605478\pi$
$692$	−10.4187	+	16.8051i	−0.396060	+	0.638835i
$693$	−17.9819	−	5.17675i	−0.683076	−	0.196648i
$694$	2.16274	−	7.59293i	0.0820966	−	0.288224i
$695$	−13.3411	+	7.70249i	−0.506057	+	0.292172i
$696$	36.9848	−	5.31477i	1.40191	−	0.201456i
$697$	−17.4154	+	30.1644i	−0.659657	+	1.14256i
$698$	−26.7930	−	27.6472i	−1.01413	−	1.04646i
$699$	−4.18124	−	8.62081i	−0.158149	−	0.326069i
$700$	17.9177	+	14.8263i	0.677226	+	0.560380i
$701$	−2.75241			−0.103957			−0.0519785	−	0.998648i	$-0.516553\pi$
$701$	−2.75241			−0.103957			−0.0519785	+	0.998648i	$0.516553\pi$
$702$	16.2109	+	8.72005i	0.611842	+	0.329117i
$703$		−	5.70945i		−	0.215336i
$704$	17.1474	−	7.85311i	0.646268	−	0.295975i
$705$	1.18042	+	2.43376i	0.0444570	+	0.0916607i
$706$	−7.56324	−	7.80436i	−0.284646	−	0.293721i
$707$	35.0328	−	14.2904i	1.31754	−	0.537444i
$708$	40.2001	−	17.9625i	1.51081	−	0.675073i
$709$	−16.9695	+	9.79733i	−0.637302	+	0.367947i	−0.783575	−	0.621298i	$-0.786606\pi$
$709$	−16.9695	+	9.79733i	−0.637302	+	0.367947i	0.146272	+	0.989244i	$0.453272\pi$
$710$	1.26405	−	4.43780i	0.0474388	−	0.166547i
$711$	37.2949	+	5.40858i	1.39867	+	0.202838i
$712$	−22.2973	+	20.2914i	−0.835628	+	0.760451i
$713$	4.10218	+	7.10519i	0.153628	+	0.266091i
$714$	43.0889	−	27.0994i	1.61256	−	1.01417i
$715$	3.97777	+	2.29657i	0.148760	+	0.0858868i
$716$	0.822073	−	0.440832i	0.0307223	−	0.0164747i
$717$	3.15555	+	0.227622i	0.117846	+	0.00850069i
$718$	4.18411	+	16.6563i	0.156150	+	0.621607i
$719$	−36.3966			−1.35736			−0.678682	−	0.734432i	$-0.737449\pi$
$719$	−36.3966			−1.35736			−0.678682	+	0.734432i	$0.737449\pi$
$720$	1.91617	−	9.13457i	0.0714114	−	0.340425i
$721$	8.66525	+	6.72358i	0.322711	+	0.250399i
$722$	23.9765	−	6.02298i	0.892314	−	0.224152i
$723$	−18.5023	+	27.3012i	−0.688106	+	1.01534i
$724$	24.3849	−	13.0763i	0.906256	−	0.485975i
$725$	−16.7606	+	29.0303i	−0.622475	+	1.07816i
$726$	2.30913	+	13.1288i	0.0856999	+	0.487257i
$727$	−26.7682	+	15.4546i	−0.992778	+	0.573180i	−0.906103	−	0.423056i	$-0.860957\pi$
$727$	−26.7682	+	15.4546i	−0.992778	+	0.573180i	−0.0866743	+	0.996237i	$0.527624\pi$
$728$	−1.46895	−	18.6876i	−0.0544431	−	0.692607i
$729$	−24.5189	−	11.3059i	−0.908107	−	0.418737i
$730$	−0.669263	+	2.34964i	−0.0247705	+	0.0869640i
$731$	−10.7620	+	6.21344i	−0.398047	+	0.229812i
$732$	8.65771	+	0.898292i	0.319998	+	0.0332018i
$733$	−22.2144	+	38.4765i	−0.820508	+	1.42116i	0.0847973	+	0.996398i	$0.472976\pi$
$733$	−22.2144	+	38.4765i	−0.820508	+	1.42116i	−0.905305	+	0.424762i	$0.860358\pi$
$734$	29.6226	−	28.7074i	1.09339	−	1.05961i
$735$	8.87576	+	3.18556i	0.327387	+	0.117501i
$736$	−22.3555	+	19.0972i	−0.824036	+	0.703931i
$737$		−	28.7933i		−	1.06062i
$738$	−11.0188	−	15.2501i	−0.405606	−	0.561364i
$739$		−	14.5793i		−	0.536308i	−0.963376	−	0.268154i	$-0.913586\pi$
$739$		−	14.5793i		−	0.536308i	0.963376	−	0.268154i	$-0.0864135\pi$
$740$	0.226050	−	7.20189i	0.00830978	−	0.264747i
$741$	0.384761	−	5.33399i	0.0141345	−	0.195949i
$742$	−36.8862	+	4.06729i	−1.35414	+	0.149315i
$743$	−8.82597	−	5.09567i	−0.323793	−	0.186942i	0.329289	−	0.944229i	$-0.393191\pi$
$743$	−8.82597	−	5.09567i	−0.323793	−	0.186942i	−0.653082	+	0.757287i	$0.726524\pi$
$744$	−6.07894	+	4.77979i	−0.222865	+	0.175236i
$745$	10.2516	−	5.91876i	0.375589	−	0.216846i
$746$	−33.9654	−	9.67460i	−1.24356	−	0.354212i
$747$	−4.37401	+	30.1609i	−0.160037	+	1.10353i
$748$	31.4754	+	19.5139i	1.15086	+	0.713499i
$749$	24.4188	+	3.34877i	0.892244	+	0.122361i
$750$	11.4994	+	13.7165i	0.419900	+	0.500856i
$751$	−16.5719	+	28.7033i	−0.604716	+	1.04740i	0.387381	+	0.921920i	$0.373380\pi$
$751$	−16.5719	+	28.7033i	−0.604716	+	1.04740i	−0.992096	+	0.125478i	$0.959953\pi$
$752$	8.01567	+	0.503682i	0.292301	+	0.0183674i
$753$	−4.15911	−	8.57518i	−0.151566	−	0.312497i
$754$	26.2047	−	6.58271i	0.954320	−	0.239728i
$755$			5.52285i			0.200997i
$756$	3.83423	+	27.2268i	0.139450	+	0.990229i
$757$		−	6.11726i		−	0.222336i	−0.993802	−	0.111168i	$-0.964541\pi$
$757$		−	6.11726i		−	0.222336i	0.993802	−	0.111168i	$-0.0354591\pi$
$758$	−1.58207	−	6.29796i	−0.0574633	−	0.228752i
$759$	9.26185	+	19.0959i	0.336184	+	0.693138i
$760$	−2.64932	+	0.577806i	−0.0961009	+	0.0209592i
$761$	20.8125	−	36.0484i	0.754454	−	1.30675i	−0.191192	−	0.981553i	$-0.561235\pi$
$761$	20.8125	−	36.0484i	0.754454	−	1.30675i	0.945645	−	0.325200i	$-0.105431\pi$
$762$	16.5513	−	13.8760i	0.599590	−	0.502675i
$763$	7.40835	−	54.0208i	0.268200	−	1.95568i
$764$	−4.03326	+	6.50554i	−0.145918	+	0.235362i
$765$	17.0225	−	6.79071i	0.615449	−	0.245519i
$766$	−5.72629	+	20.1038i	−0.206899	+	0.726378i
$767$	27.5735	−	15.9196i	0.995621	−	0.574822i
$768$	−20.8142	−	18.2967i	−0.751069	−	0.660224i
$769$	21.3432	+	12.3225i	0.769655	+	0.444360i	0.832751	−	0.553647i	$-0.186764\pi$
$769$	21.3432	+	12.3225i	0.769655	+	0.444360i	−0.0630966	+	0.998007i	$0.520098\pi$
$770$	0.751958	+	6.81951i	0.0270987	+	0.245758i
$771$	−3.00114	+	41.6051i	−0.108083	+	1.49837i
$772$	−0.433509	+	13.8115i	−0.0156023	+	0.497085i
$773$			33.5062i			1.20513i	0.798068	+	0.602567i	$0.205855\pi$
$773$			33.5062i			1.20513i	−0.798068	+	0.602567i	$0.794145\pi$
$774$	−0.684110	−	6.67758i	−0.0245898	−	0.240021i
$775$		−	6.93760i		−	0.249206i
$776$	−4.51779	+	14.1589i	−0.162179	+	0.508276i
$777$	6.58245	+	20.1803i	0.236144	+	0.723963i
$778$	−5.52066	−	5.69666i	−0.197925	−	0.204235i
$779$	−2.73303	+	4.73375i	−0.0979210	+	0.169604i
$780$	0.696521	−	6.71304i	0.0249395	−	0.240365i
$781$	−8.56485	+	4.94492i	−0.306474	+	0.176943i
$782$	−55.5249	−	15.8155i	−1.98557	−	0.565562i
$783$	−37.7715	+	11.9982i	−1.34984	+	0.428780i
$784$	21.2000	−	18.2909i	0.757145	−	0.653247i
$785$	8.57449	−	4.95049i	0.306037	−	0.176690i
$786$	18.0627	−	3.17690i	0.644273	−	0.113316i
$787$	1.27253	−	2.20408i	0.0453607	−	0.0785670i	−0.842454	−	0.538769i	$-0.818890\pi$
$787$	1.27253	−	2.20408i	0.0453607	−	0.0785670i	0.887814	+	0.460202i	$0.152223\pi$
$788$	15.3842	−	8.24971i	0.548040	−	0.293884i
$789$	16.3667	−	24.1501i	0.582670	−	0.859765i
$790$	−3.36634	−	13.4009i	−0.119769	−	0.476781i
$791$	7.17602	+	5.56805i	0.255150	+	0.197977i
$792$	−16.5742	+	11.2012i	−0.588937	+	0.398016i
$793$	6.29410			0.223510
$794$	−0.0135187	+	0.00339593i	−0.000479760	+	0.000120517i
$795$	−13.3265	−	0.961291i	−0.472642	−	0.0340935i
$796$	−6.54498	−	12.2052i	−0.231981	−	0.432602i
$797$	−30.1642	−	17.4153i	−1.06847	−	0.616881i	−0.140707	−	0.990051i	$-0.544937\pi$
$797$	−30.1642	−	17.4153i	−1.06847	−	0.616881i	−0.927763	+	0.373170i	$0.878271\pi$
$798$	6.76201	−	4.25275i	0.239373	−	0.150546i
$799$	7.88528	+	13.6577i	0.278961	+	0.483175i
$800$	24.4454	−	4.53313i	0.864276	−	0.160270i
$801$	19.7974	−	25.1115i	0.699508	−	0.887270i
$802$	−38.9133	−	11.0839i	−1.37408	−	0.391387i
$803$	4.53475	−	2.61814i	0.160028	−	0.0923922i
$804$	−38.6277	+	17.2599i	−1.36229	+	0.608710i
$805$	−4.03974	−	9.90341i	−0.142382	−	0.349049i
$806$	−4.01558	+	3.89152i	−0.141443	+	0.137073i
$807$	8.91818	+	18.3873i	0.313935	+	0.647265i
$808$	12.2952	−	38.5336i	0.432543	−	1.35561i
$809$			12.7396i			0.447899i	0.974601	+	0.223950i	$0.0718951\pi$
$809$			12.7396i			0.447899i	−0.974601	+	0.223950i	$0.928105\pi$
$810$	−0.414923	+	9.89085i	−0.0145789	+	0.347529i
$811$	−1.93372			−0.0679021			−0.0339510	−	0.999423i	$-0.510809\pi$
$811$	−1.93372			−0.0679021			−0.0339510	+	0.999423i	$0.510809\pi$
$812$	31.0938	+	25.7291i	1.09118	+	0.902913i
$813$	−15.6843	−	32.3376i	−0.550073	−	1.13413i
$814$	−11.0901	+	10.7475i	−0.388708	+	0.376699i
$815$	1.92504	−	3.33427i	0.0674313	−	0.116794i
$816$	7.31123	−	53.9233i	0.255944	−	1.88769i
$817$	−1.68890	+	0.975085i	−0.0590870	+	0.0341139i
$818$	45.9976	+	13.1018i	1.60827	+	0.458093i
$819$	4.78962	+	19.2968i	0.167363	+	0.674283i
$820$	−3.63486	+	5.86293i	−0.126935	+	0.204742i
$821$	6.49088	+	11.2425i	0.226533	+	0.392367i	0.956778	−	0.290818i	$-0.0939274\pi$
$821$	6.49088	+	11.2425i	0.226533	+	0.392367i	−0.730245	+	0.683185i	$0.760594\pi$
$822$	11.4946	−	31.5388i	0.400920	−	1.10004i
$823$	7.72706	−	13.3837i	0.269348	−	0.466525i	−0.699345	−	0.714784i	$-0.746525\pi$
$823$	7.72706	−	13.3837i	0.269348	−	0.466525i	0.968694	+	0.248259i	$0.0798584\pi$
$824$	11.4558	−	2.49846i	0.399082	−	0.0870381i
$825$	1.29120	−	17.9000i	0.0449537	−	0.623199i
$826$	43.5451	+	19.1219i	1.51513	+	0.665336i
$827$	3.50359			0.121832			0.0609159	−	0.998143i	$-0.480598\pi$
$827$	3.50359			0.121832			0.0609159	+	0.998143i	$0.480598\pi$
$828$	20.0662	−	23.8721i	0.697349	−	0.829614i
$829$	21.0756			0.731985			0.365993	−	0.930618i	$-0.380730\pi$
$829$	21.0756			0.731985			0.365993	+	0.930618i	$0.380730\pi$
$830$	10.8375	−	2.72241i	0.376175	−	0.0944962i
$831$	11.3001	−	16.6740i	0.391997	−	0.578415i
$832$	−16.3361	−	11.6066i	−0.566351	−	0.402386i
$833$	52.9508	+	14.8016i	1.83464	+	0.512845i
$834$	−8.40399	−	47.7819i	−0.291006	−	1.65455i
$835$	−12.3819	+	7.14870i	−0.428494	+	0.247391i
$836$	4.93949	+	3.06235i	0.170836	+	0.105914i
$837$	5.52833	−	6.05908i	0.191087	−	0.209432i
$838$	5.60496	+	1.59650i	0.193620	+	0.0551501i
$839$	−7.57118	−	13.1137i	−0.261386	−	0.452734i	0.705224	−	0.708984i	$-0.250846\pi$
$839$	−7.57118	−	13.1137i	−0.261386	−	0.452734i	−0.966611	+	0.256250i	$0.917513\pi$
$840$	8.69796	−	5.09669i	0.300108	−	0.175852i
$841$	−14.5859	+	25.2635i	−0.502963	+	0.871157i
$842$	−12.8931	+	12.4948i	−0.444327	+	0.430599i
$843$	−18.9410	+	27.9487i	−0.652364	+	0.962603i
$844$	−26.9612	−	0.846248i	−0.928042	−	0.0291291i
$845$			5.23083i			0.179946i
$846$	−8.47431	+	0.868183i	−0.291353	+	0.0298487i
$847$	−8.82664	+	11.3756i	−0.303287	+	0.390872i
$848$	−21.9516	+	33.0454i	−0.753822	+	1.13478i
$849$	3.21881	−	44.6228i	0.110469	−	1.53145i
$850$	33.9746	+	35.0577i	1.16532	+	1.20247i
$851$	12.0377	−	20.8499i	0.412647	−	0.714725i
$852$	11.7680	+	8.52599i	0.403165	+	0.292096i
$853$	−2.00746	−	3.47702i	−0.0687340	−	0.119051i	0.829610	−	0.558343i	$-0.188563\pi$
$853$	−2.00746	−	3.47702i	−0.0687340	−	0.119051i	−0.898344	+	0.439292i	$0.855229\pi$
$854$	5.56486	+	7.57776i	0.190425	+	0.259305i
$855$	2.67136	−	1.06568i	0.0913587	−	0.0364454i
$856$	19.4876	−	17.7344i	0.666073	−	0.606150i
$857$	−6.04836	−	10.4761i	−0.206608	−	0.357856i	0.744036	−	0.668140i	$-0.232909\pi$
$857$	−6.04836	−	10.4761i	−0.206608	−	0.357856i	−0.950644	+	0.310284i	$0.899576\pi$
$858$	−11.0851	+	9.29333i	−0.378438	+	0.317269i
$859$	9.72267	−	16.8402i	0.331733	−	0.574579i	−0.651119	−	0.758976i	$-0.725700\pi$
$859$	9.72267	−	16.8402i	0.331733	−	0.574579i	0.982852	+	0.184397i	$0.0590333\pi$
$860$	−2.16898	+	1.16310i	−0.0739615	+	0.0396615i
$861$	4.20244	−	19.8825i	0.143219	−	0.677595i
$862$	2.42320	+	9.64639i	0.0825347	+	0.328558i
$863$			39.6886i			1.35101i	0.737353	+	0.675507i	$0.236075\pi$
$863$			39.6886i			1.35101i	−0.737353	+	0.675507i	$0.763925\pi$
$864$	24.9622	+	15.5206i	0.849231	+	0.528022i
$865$	−7.68945			−0.261449
$866$	−6.83712	−	27.2175i	−0.232335	−	0.924889i
$867$	69.6478	−	33.7804i	2.36536	−	1.14724i
$868$	−8.23551	−	1.39390i	−0.279531	−	0.0473121i
$869$	−14.8072	+	25.6468i	−0.502300	+	0.870009i
$870$	9.33542	+	11.1353i	0.316501	+	0.377521i
$871$	−26.4949	+	15.2969i	−0.897747	+	0.518314i
$872$	−39.2332	−	43.1117i	−1.32860	−	1.45995i
$873$	2.26243	−	15.6006i	0.0765717	−	0.528000i
$874$	−8.71361	−	2.48196i	−0.294742	−	0.0839534i
$875$	−2.62676	+	19.1540i	−0.0888007	+	0.647525i
$876$	−6.23069	−	4.51418i	−0.210515	−	0.152520i
$877$	−8.72927	−	5.03985i	−0.294767	−	0.170184i	0.345323	−	0.938484i	$-0.387769\pi$
$877$	−8.72927	−	5.03985i	−0.294767	−	0.170184i	−0.640089	+	0.768300i	$0.721103\pi$
$878$	−15.8366	+	15.3473i	−0.534460	+	0.517948i
$879$	−46.4881	−	3.35337i	−1.56801	−	0.113106i
$880$	6.10941	+	4.05841i	0.205948	+	0.136809i
$881$	6.69447			0.225542			0.112771	−	0.993621i	$-0.464027\pi$
$881$	6.69447			0.225542			0.112771	+	0.993621i	$0.464027\pi$
$882$	−18.9976	+	22.8275i	−0.639681	+	0.768640i
$883$			34.8152i			1.17162i	0.810447	+	0.585812i	$0.199224\pi$
$883$			34.8152i			1.17162i	−0.810447	+	0.585812i	$0.800776\pi$
$884$	1.23448	−	39.3300i	0.0415200	−	1.32281i
$885$	14.1747	+	9.60629i	0.476476	+	0.322912i
$886$	−28.6772	−	29.5914i	−0.963429	−	0.994143i
$887$	−26.8317	+	46.4738i	−0.900919	+	1.56044i	−0.0746160	+	0.997212i	$0.523773\pi$
$887$	−26.8317	+	46.4738i	−0.900919	+	1.56044i	−0.826303	+	0.563226i	$0.809560\pi$
$888$	21.0661	+	8.43546i	0.706934	+	0.283075i
$889$	23.1126	+	3.16963i	0.775171	+	0.106306i
$890$	−11.2758	−	3.21177i	−0.377967	−	0.107659i
$891$	15.3916	−	14.6044i	0.515638	−	0.489266i
$892$	−1.38171	+	2.22867i	−0.0462631	+	0.0746212i
$893$	1.23745	+	2.14333i	0.0414097	+	0.0717237i
$894$	6.45780	+	36.7166i	0.215981	+	1.22799i
$895$	0.314161	+	0.181381i	0.0105012	+	0.00606290i
$896$	−0.469633	−	29.9296i	−0.0156893	−	0.999877i
$897$	12.6511	−	18.6675i	0.422409	−	0.623290i
$898$	−2.97238	−	11.8326i	−0.0991894	−	0.394858i
$899$		−	12.0393i		−	0.401533i
$900$	−24.7878	+	8.99781i	−0.826259	+	0.299927i
$901$	−77.8998			−2.59522
$902$	14.3395	−	3.60214i	0.477455	−	0.119938i
$903$	4.84529	−	5.39361i	0.161241	−	0.179488i
$904$	9.48699	−	2.06907i	0.315533	−	0.0688163i
$905$	9.31885	+	5.38024i	0.309769	+	0.178845i
$906$	−16.3418	−	5.95590i	−0.542919	−	0.197871i
$907$	23.0426	−	13.3037i	0.765118	−	0.441741i	−0.0660125	−	0.997819i	$-0.521028\pi$
$907$	23.0426	−	13.3037i	0.765118	−	0.441741i	0.831130	+	0.556078i	$0.187694\pi$
$908$	−3.85926	+	6.22488i	−0.128074	+	0.206580i
$909$	−6.15722	+	42.4571i	−0.204222	+	1.40821i
$910$	5.87566	−	4.31490i	0.194776	−	0.143037i
$911$	2.62007	−	1.51270i	0.0868068	−	0.0501179i	−0.455968	−	0.889996i	$-0.650707\pi$
$911$	2.62007	−	1.51270i	0.0868068	−	0.0501179i	0.542775	+	0.839878i	$0.317374\pi$
$912$	1.14736	−	8.46227i	0.0379930	−	0.280214i
$913$	−20.7410	−	11.9748i	−0.686426	−	0.396308i
$914$	14.5090	+	14.9716i	0.479915	+	0.495215i
$915$	1.47719	+	3.04565i	0.0488345	+	0.100686i
$916$	0.364528	−	11.6137i	0.0120443	−	0.383729i
$917$	15.6506	+	12.1437i	0.516829	+	0.401020i
$918$	1.73609	+	57.6915i	0.0572994	+	1.90410i
$919$	−19.9020			−0.656506			−0.328253	−	0.944590i	$-0.606460\pi$
$919$	−19.9020			−0.656506			−0.328253	+	0.944590i	$0.606460\pi$
$920$	−10.8931	−	3.47573i	−0.359134	−	0.114591i
$921$	−38.7937	+	18.8156i	−1.27829	+	0.619995i
$922$	13.5429	−	13.1245i	0.446012	−	0.432233i
$923$	9.10040	+	5.25412i	0.299543	+	0.172941i
$924$	−20.9894	−	5.12923i	−0.690501	−	0.168739i
$925$	−17.6306	+	10.1790i	−0.579691	+	0.334685i
$926$	−11.5330	+	40.4900i	−0.378999	+	1.33058i
$927$	−11.5511	+	4.60805i	−0.379389	+	0.151348i
$928$	42.4219	−	7.86666i	1.39257	−	0.258236i
$929$	6.94527	+	12.0296i	0.227867	+	0.394677i	0.957176	−	0.289507i	$-0.0934915\pi$
$929$	6.94527	+	12.0296i	0.227867	+	0.394677i	−0.729309	+	0.684185i	$0.760158\pi$
$930$	−2.82550	−	1.02978i	−0.0926519	−	0.0337678i
$931$	8.30965	+	2.32284i	0.272338	+	0.0761279i
$932$	−5.22845	−	9.75012i	−0.171264	−	0.319376i
$933$	0.826901	−	11.4634i	0.0270715	−	0.375296i
$934$	9.64502	+	38.3953i	0.315595	+	1.25633i
$935$			14.4021i			0.470998i
$936$	19.1123	+	9.30037i	0.624706	+	0.303992i
$937$		−	14.7935i		−	0.483283i	−0.970366	−	0.241641i	$-0.922314\pi$
$937$		−	14.7935i		−	0.483283i	0.970366	−	0.241641i	$-0.0776858\pi$
$938$	−41.8418	−	18.3739i	−1.36618	−	0.599930i
$939$	21.0616	−	31.0777i	0.687320	−	1.01418i
$940$	1.47606	+	2.75258i	0.0481437	+	0.0897792i
$941$	39.4409	+	22.7712i	1.28574	+	0.742320i	0.977891	−	0.209117i	$-0.0670588\pi$
$941$	39.4409	+	22.7712i	1.28574	+	0.742320i	0.307845	+	0.951437i	$0.400392\pi$
$942$	5.40135	+	30.7100i	0.175985	+	1.00059i
$943$	−19.9611	+	11.5245i	−0.650022	+	0.375290i
$944$	45.5383	−	22.6098i	1.48215	−	0.735886i
$945$	−8.21340	+	6.84650i	−0.267182	+	0.222717i
$946$	5.07319	+	1.44503i	0.164944	+	0.0469820i
$947$	−1.57037	−	2.71995i	−0.0510300	−	0.0883866i	0.839382	−	0.543542i	$-0.182917\pi$
$947$	−1.57037	−	2.71995i	−0.0510300	−	0.0883866i	−0.890412	+	0.455155i	$0.849584\pi$
$948$	43.2825	+	4.49084i	1.40575	+	0.145856i
$949$	−4.81830	−	2.78185i	−0.156409	−	0.0903027i
$950$	5.33169	+	5.50167i	0.172983	+	0.178498i
$951$	−35.6456	−	24.1573i	−1.15589	−	0.783354i
$952$	48.4427	−	33.2869i	1.57004	−	1.07884i
$953$			9.40494i			0.304656i	0.988330	+	0.152328i	$0.0486770\pi$
$953$			9.40494i			0.304656i	−0.988330	+	0.152328i	$0.951323\pi$
$954$	17.2158	−	38.3956i	0.557383	−	1.24310i
$955$	−2.97671			−0.0963241
$956$	3.65138	+	0.114608i	0.118094	+	0.00370670i
$957$	2.24070	−	31.0632i	0.0724316	−	1.00413i
$958$	−22.6309	−	23.3524i	−0.731171	−	0.754481i
$959$	33.5721	−	13.6945i	1.08410	−	0.442219i
$960$	1.78232	−	10.6289i	0.0575242	−	0.343045i
$961$	−14.2542	−	24.6889i	−0.459812	−	0.796418i
$962$	15.7814	+	4.49511i	0.508811	+	0.144928i
$963$	−17.3027	+	21.9471i	−0.557573	+	0.707237i
$964$	−20.0664	+	32.3666i	−0.646295	+	1.04246i
$965$	−4.65384	+	2.68690i	−0.149812	+	0.0864943i
$966$	33.6600	−	1.27339i	1.08299	−	0.0409708i
$967$	9.21544	−	15.9616i	0.296349	−	0.513291i	−0.678949	−	0.734185i	$-0.737564\pi$
$967$	9.21544	−	15.9616i	0.296349	−	0.513291i	0.975298	+	0.220894i	$0.0708976\pi$
$968$	3.27996	+	15.0391i	0.105422	+	0.483374i
$969$	15.0875	−	7.31772i	0.484682	−	0.235079i
$970$	−5.60563	+	1.40815i	−0.179986	+	0.0452130i
$971$		−	37.9556i		−	1.21805i	−0.793150	−	0.609027i	$-0.791560\pi$
$971$		−	37.9556i		−	1.21805i	0.793150	−	0.609027i	$-0.208440\pi$
$972$	−28.8189	−	11.8941i	−0.924367	−	0.381504i
$973$	32.1242	−	41.4012i	1.02986	−	1.32726i
$974$	−39.0062	+	9.79848i	−1.24984	+	0.313964i
$975$	−17.1571	+	8.32151i	−0.549468	+	0.266502i
$976$	10.0309	+	0.630317i	0.321083	+	0.0201759i
$977$	−15.8836	−	9.17041i	−0.508162	−	0.293387i	0.223916	−	0.974608i	$-0.428116\pi$
$977$	−15.8836	−	9.17041i	−0.508162	−	0.293387i	−0.732078	+	0.681221i	$0.761449\pi$
$978$	7.78991	+	9.29178i	0.249094	+	0.297119i
$979$	12.5644	+	21.7622i	0.401559	+	0.695521i
$980$	10.3898	+	3.25902i	0.331890	+	0.104106i
$981$	48.5528	+	38.2782i	1.55017	+	1.22213i
$982$	14.6344	−	51.3781i	0.467002	−	1.63954i
$983$	−21.4210	−	37.1023i	−0.683224	−	1.18338i	−0.973991	−	0.226585i	$-0.927244\pi$
$983$	−21.4210	−	37.1023i	−0.683224	−	1.18338i	0.290768	−	0.956794i	$-0.406089\pi$
$984$	−13.4282	−	17.0779i	−0.428074	−	0.544425i
$985$	5.87919	+	3.39435i	0.187327	+	0.108153i
$986$	58.9585	+	60.8381i	1.87762	+	1.93748i
$987$	−6.84486	−	6.14900i	−0.217874	−	0.195725i
$988$	0.193728	−	6.17212i	0.00616332	−	0.196361i
$989$	−8.22339			−0.261489
$990$	−7.09856	−	3.18285i	−0.225607	−	0.101158i
$991$	19.8153			0.629453			0.314726	−	0.949182i	$-0.398087\pi$
$991$	19.8153			0.629453			0.314726	+	0.949182i	$0.398087\pi$
$992$	−6.78937	+	5.79980i	−0.215563	+	0.184144i
$993$	−6.63535	+	9.79086i	−0.210566	+	0.310704i
$994$	1.72034	+	15.6018i	0.0545658	+	0.494858i
$995$	2.69294	−	4.66431i	0.0853719	−	0.147868i
$996$	−3.63181	+	35.0033i	−0.115078	+	1.10912i
$997$	2.60366	+	4.50968i	0.0824589	+	0.142823i	0.904306	−	0.426886i	$-0.140389\pi$
$997$	2.60366	+	4.50968i	0.0824589	+	0.142823i	−0.821847	+	0.569709i	$0.807056\pi$
$998$	22.2123	+	6.32689i	0.703119	+	0.200274i
$999$	−23.5094	−	5.15917i	−0.743803	−	0.163229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.8	yes	168
7.6	odd	2	inner	504.2.cc.b.293.7	✓	168
8.5	even	2	inner	504.2.cc.b.293.21	yes	168
9.2	odd	6	inner	504.2.cc.b.461.22	yes	168
56.13	odd	2	inner	504.2.cc.b.293.22	yes	168
63.20	even	6	inner	504.2.cc.b.461.21	yes	168
72.29	odd	6	inner	504.2.cc.b.461.7	yes	168
504.461	even	6	inner	504.2.cc.b.461.8	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.7	✓	168	7.6	odd	2	inner
504.2.cc.b.293.8	yes	168	1.1	even	1	trivial
504.2.cc.b.293.21	yes	168	8.5	even	2	inner
504.2.cc.b.293.22	yes	168	56.13	odd	2	inner
504.2.cc.b.461.7	yes	168	72.29	odd	6	inner
504.2.cc.b.461.8	yes	168	504.461	even	6	inner
504.2.cc.b.461.21	yes	168	63.20	even	6	inner
504.2.cc.b.461.22	yes	168	9.2	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37160 + 0.344550i) q^{2} +(1.55842 - 0.755861i) q^{3} +(1.76257 - 0.945170i) q^{4} +(0.673579 + 0.388891i) q^{5} +(-1.87710 + 1.57369i) q^{6} +(-2.62122 - 0.359471i) q^{7} +(-2.09188 + 1.90369i) q^{8} +(1.85735 - 2.35590i) q^{9} +O(q^{10})\)	\(q+(-1.37160 + 0.344550i) q^{2} +(1.55842 - 0.755861i) q^{3} +(1.76257 - 0.945170i) q^{4} +(0.673579 + 0.388891i) q^{5} +(-1.87710 + 1.57369i) q^{6} +(-2.62122 - 0.359471i) q^{7} +(-2.09188 + 1.90369i) q^{8} +(1.85735 - 2.35590i) q^{9} +(-1.05787 - 0.301321i) q^{10} +(1.17876 + 2.04167i) q^{11} +(2.03241 - 2.80523i) q^{12} +(1.25247 - 2.16934i) q^{13} +(3.71912 - 0.410091i) q^{14} +(1.34367 + 0.0969238i) q^{15} +(2.21331 - 3.33186i) q^{16} +7.85438 q^{17} +(-1.73581 + 3.87130i) q^{18} +1.23260 q^{19} +(1.55480 + 0.0488015i) q^{20} +(-4.35667 + 1.42107i) q^{21} +(-2.32025 - 2.39422i) q^{22} +(4.50123 + 2.59879i) q^{23} +(-1.82111 + 4.54792i) q^{24} +(-2.19753 - 3.80623i) q^{25} +(-0.970438 + 3.40700i) q^{26} +(1.11380 - 5.07538i) q^{27} +(-4.95984 + 1.84390i) q^{28} +(-3.81352 - 6.60522i) q^{29} +(-1.87637 + 0.330020i) q^{30} +(1.36702 + 0.789250i) q^{31} +(-1.88778 + 5.33257i) q^{32} +(3.38022 + 2.29081i) q^{33} +(-10.7731 + 2.70623i) q^{34} +(-1.62580 - 1.26150i) q^{35} +(1.04699 - 5.90795i) q^{36} -4.63204i q^{37} +(-1.69063 + 0.424692i) q^{38} +(0.312154 - 4.32743i) q^{39} +(-2.14938 + 0.468770i) q^{40} +(-2.21729 + 3.84046i) q^{41} +(5.48598 - 3.45023i) q^{42} +(-1.37019 + 0.791080i) q^{43} +(4.00737 + 2.48446i) q^{44} +(2.16726 - 0.864577i) q^{45} +(-7.06930 - 2.01359i) q^{46} +(1.00393 + 1.73887i) q^{47} +(0.930847 - 6.86539i) q^{48} +(6.74156 + 1.88450i) q^{49} +(4.32556 + 4.46346i) q^{50} +(12.2404 - 5.93682i) q^{51} +(0.157171 - 5.00740i) q^{52} -9.91801 q^{53} +(0.221034 + 7.34514i) q^{54} +1.83364i q^{55} +(6.16760 - 4.23801i) q^{56} +(1.92091 - 0.931674i) q^{57} +(7.50645 + 7.74576i) q^{58} +(11.0077 + 6.35529i) q^{59} +(2.45992 - 1.09916i) q^{60} +(1.25634 + 2.17605i) q^{61} +(-2.14694 - 0.611528i) q^{62} +(-5.71539 + 5.50766i) q^{63} +(0.751945 - 7.96458i) q^{64} +(1.68727 - 0.974146i) q^{65} +(-5.42561 - 1.97741i) q^{66} +(-10.5771 - 6.10669i) q^{67} +(13.8439 - 7.42372i) q^{68} +(8.97913 + 0.647699i) q^{69} +(2.66460 + 1.17010i) q^{70} +4.19502i q^{71} +(0.599538 + 8.46407i) q^{72} -2.22110i q^{73} +(1.59597 + 6.35331i) q^{74} +(-6.30165 - 4.27068i) q^{75} +(2.17254 - 1.16502i) q^{76} +(-2.35587 - 5.77540i) q^{77} +(1.06287 + 6.04305i) q^{78} +(6.28083 + 10.8787i) q^{79} +(2.78657 - 1.38353i) q^{80} +(-2.10051 - 8.75145i) q^{81} +(1.71800 - 6.03154i) q^{82} +(-8.79780 + 5.07941i) q^{83} +(-6.33578 + 6.62252i) q^{84} +(5.29054 + 3.05450i) q^{85} +(1.60679 - 1.55714i) q^{86} +(-10.9357 - 7.41121i) q^{87} +(-6.35254 - 2.02695i) q^{88} +10.6590 q^{89} +(-2.67472 + 1.93258i) q^{90} +(-4.06280 + 5.23608i) q^{91} +(10.3900 + 0.326119i) q^{92} +(2.72696 + 0.196706i) q^{93} +(-1.97612 - 2.03912i) q^{94} +(0.830253 + 0.479347i) q^{95} +(1.08872 + 9.73728i) q^{96} +(4.55061 - 2.62730i) q^{97} +(-9.89603 - 0.261975i) q^{98} +(6.99934 + 1.01506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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