LMFDB - Embedded newform 630.2.cg.a.187.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(157,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("630.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cg (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.48
Character	$\chi$	$=$	630.187
Dual form			630.2.cg.a.283.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.73177 + 0.0309423i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.05295 + 0.886221i) q^{5} +(0.478104 - 1.66476i) q^{6} +(-0.374056 + 2.61918i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99809 + 0.107170i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.73177 + 0.0309423i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.05295 + 0.886221i) q^{5} +(0.478104 - 1.66476i) q^{6} +(-0.374056 + 2.61918i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99809 + 0.107170i) q^{9} +(0.324681 + 2.21237i) q^{10} +3.95117 q^{11} +(-1.48429 - 0.892684i) q^{12} +(0.976306 - 3.64363i) q^{13} +(2.43312 + 1.03920i) q^{14} +(-3.58267 + 1.47121i) q^{15} +(0.500000 + 0.866025i) q^{16} +(6.04740 + 1.62039i) q^{17} +(0.879480 - 2.86819i) q^{18} +(-0.957091 + 1.65773i) q^{19} +(2.22102 + 0.258986i) q^{20} +(-0.728824 + 4.52425i) q^{21} +(1.02264 - 3.81654i) q^{22} +(-0.0235569 + 0.0235569i) q^{23} +(-1.24643 + 1.20267i) q^{24} +(3.42922 - 3.63874i) q^{25} +(-3.26678 - 1.88608i) q^{26} +(5.18869 + 0.278362i) q^{27} +(1.63353 - 2.08124i) q^{28} +(8.65084 + 4.99457i) q^{29} +(0.493818 + 3.84137i) q^{30} +(-2.60433 - 1.50361i) q^{31} +(0.965926 - 0.258819i) q^{32} +(6.84254 + 0.122258i) q^{33} +(3.13036 - 5.42195i) q^{34} +(-1.55325 - 5.70854i) q^{35} +(-2.54283 - 1.59185i) q^{36} +(-5.00610 + 1.34138i) q^{37} +(1.35353 + 1.35353i) q^{38} +(1.80348 - 6.27973i) q^{39} +(0.825003 - 2.07831i) q^{40} +(-8.19705 + 4.73257i) q^{41} +(4.18145 + 1.87495i) q^{42} +(-0.513362 - 1.91589i) q^{43} +(-3.42181 - 1.97559i) q^{44} +(-6.24990 + 2.43695i) q^{45} +(0.0166572 + 0.0288511i) q^{46} +(-0.773256 - 0.207193i) q^{47} +(0.839090 + 1.51523i) q^{48} +(-6.72016 - 1.95944i) q^{49} +(-2.62720 - 4.25415i) q^{50} +(10.4226 + 2.99328i) q^{51} +(-2.66732 + 2.66732i) q^{52} +(-3.30076 - 0.884435i) q^{53} +(1.61181 - 4.93985i) q^{54} +(-8.11156 + 3.50161i) q^{55} +(-1.58754 - 2.11653i) q^{56} +(-1.70876 + 2.84120i) q^{57} +(7.06338 - 7.06338i) q^{58} +(3.15468 - 5.46407i) q^{59} +(3.83829 + 0.517229i) q^{60} +(-6.86064 + 3.96099i) q^{61} +(-2.12642 + 2.12642i) q^{62} +(-1.40215 + 7.81242i) q^{63} -1.00000i q^{64} +(1.22475 + 8.34541i) q^{65} +(1.88907 - 6.57774i) q^{66} +(-6.18954 + 1.65848i) q^{67} +(-4.42700 - 4.42700i) q^{68} +(-0.0415241 + 0.0400662i) q^{69} +(-5.91604 + 0.0228458i) q^{70} -3.11188 q^{71} +(-2.19575 + 2.04419i) q^{72} +(0.292904 - 1.09313i) q^{73} +5.18270i q^{74} +(6.05123 - 6.19537i) q^{75} +(1.65773 - 0.957091i) q^{76} +(-1.47796 + 10.3488i) q^{77} +(-5.59897 - 3.36735i) q^{78} +(2.11476 - 1.22095i) q^{79} +(-1.79397 - 1.33480i) q^{80} +(8.97703 + 0.642610i) q^{81} +(2.44976 + 9.14262i) q^{82} +(-15.1694 + 4.06462i) q^{83} +(2.89330 - 3.55370i) q^{84} +(-13.8510 + 2.03274i) q^{85} -1.98348 q^{86} +(14.8268 + 8.91714i) q^{87} +(-2.79390 + 2.79390i) q^{88} +(7.93473 - 13.7434i) q^{89} +(0.736320 + 6.66767i) q^{90} +(9.17810 + 3.92004i) q^{91} +(0.0321793 - 0.00862241i) q^{92} +(-4.46358 - 2.68449i) q^{93} +(-0.400267 + 0.693283i) q^{94} +(0.495746 - 4.25143i) q^{95} +(1.68077 - 0.418328i) q^{96} +(-4.61042 - 17.2063i) q^{97} +(-3.63198 + 5.98404i) q^{98} +(11.8459 + 0.423448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50} + 24 q^{51} - 40 q^{53} + 8 q^{56} - 32 q^{57} + 24 q^{58} + 8 q^{60} + 36 q^{61} - 108 q^{63} - 8 q^{65} + 16 q^{71} - 8 q^{72} + 80 q^{77} - 16 q^{78} + 4 q^{81} - 168 q^{83} - 16 q^{86} + 36 q^{90} + 8 q^{92} - 60 q^{93} + 64 q^{95} - 12 q^{96} - 48 q^{98}+O(q^{100}) $ 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.73177	+	0.0309423i	0.999840	+	0.0178645i
$3$	1.73177	+	0.0309423i	0.999840	+	0.0178645i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.05295	+	0.886221i	−0.918108	+	0.396330i
$5$	−2.05295	+	0.886221i	−0.918108	+	0.396330i
$6$	0.478104	−	1.66476i	0.195185	−	0.679634i
$7$	−0.374056	+	2.61918i	−0.141380	+	0.989955i
$7$	−0.374056	+	2.61918i	−0.141380	+	0.989955i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.99809	+	0.107170i	0.999362	+	0.0357234i
$10$	0.324681	+	2.21237i	0.102673	+	0.699613i
$11$	3.95117			1.19132			0.595661	−	0.803236i	$-0.296890\pi$
$11$	3.95117			1.19132			0.595661	+	0.803236i	$0.296890\pi$
$12$	−1.48429	−	0.892684i	−0.428477	−	0.257696i
$13$	0.976306	−	3.64363i	0.270779	−	1.01056i	−0.687839	−	0.725863i	$-0.741441\pi$
$13$	0.976306	−	3.64363i	0.270779	−	1.01056i	0.958618	−	0.284697i	$-0.0918928\pi$
$14$	2.43312	+	1.03920i	0.650278	+	0.277739i
$15$	−3.58267	+	1.47121i	−0.925042	+	0.379865i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	6.04740	+	1.62039i	1.46671	+	0.393003i	0.901801	−	0.432151i	$-0.142245\pi$
$17$	6.04740	+	1.62039i	1.46671	+	0.393003i	0.564908	+	0.825154i	$0.308912\pi$
$18$	0.879480	−	2.86819i	0.207295	−	0.676039i
$19$	−0.957091	+	1.65773i	−0.219572	+	0.380309i	−0.954677	−	0.297644i	$-0.903799\pi$
$19$	−0.957091	+	1.65773i	−0.219572	+	0.380309i	0.735105	+	0.677953i	$0.237133\pi$
$20$	2.22102	+	0.258986i	0.496635	+	0.0579110i
$21$	−0.728824	+	4.52425i	−0.159042	+	0.987272i
$22$	1.02264	−	3.81654i	0.218027	−	0.813689i
$23$	−0.0235569	+	0.0235569i	−0.00491194	+	0.00491194i	−0.709558	−	0.704647i	$-0.751106\pi$
$23$	−0.0235569	+	0.0235569i	−0.00491194	+	0.00491194i	0.704647	+	0.709558i	$0.251106\pi$
$24$	−1.24643	+	1.20267i	−0.254426	+	0.245494i
$25$	3.42922	−	3.63874i	0.685845	−	0.727748i
$26$	−3.26678	−	1.88608i	−0.640669	−	0.369891i
$27$	5.18869	+	0.278362i	0.998564	+	0.0535708i
$28$	1.63353	−	2.08124i	0.308708	−	0.393318i
$29$	8.65084	+	4.99457i	1.60642	+	0.927468i	0.990162	+	0.139924i	$0.0446860\pi$
$29$	8.65084	+	4.99457i	1.60642	+	0.927468i	0.616259	+	0.787543i	$0.288647\pi$
$30$	0.493818	+	3.84137i	0.0901584	+	0.701335i
$31$	−2.60433	−	1.50361i	−0.467751	−	0.270056i	0.247547	−	0.968876i	$-0.420376\pi$
$31$	−2.60433	−	1.50361i	−0.467751	−	0.270056i	−0.715298	+	0.698820i	$0.753709\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	6.84254	+	0.122258i	1.19113	+	0.0212824i
$34$	3.13036	−	5.42195i	0.536853	−	0.929856i
$35$	−1.55325	−	5.70854i	−0.262547	−	0.964919i
$36$	−2.54283	−	1.59185i	−0.423805	−	0.265309i
$37$	−5.00610	+	1.34138i	−0.822998	+	0.220522i	−0.645657	−	0.763628i	$-0.723416\pi$
$37$	−5.00610	+	1.34138i	−0.822998	+	0.220522i	−0.177341	+	0.984149i	$0.556750\pi$
$38$	1.35353	+	1.35353i	0.219572	+	0.219572i
$39$	1.80348	−	6.27973i	0.288789	−	1.00556i
$40$	0.825003	−	2.07831i	0.130444	−	0.328610i
$41$	−8.19705	+	4.73257i	−1.28016	+	0.739103i	−0.976878	−	0.213797i	$-0.931417\pi$
$41$	−8.19705	+	4.73257i	−1.28016	+	0.739103i	−0.303285	+	0.952900i	$0.598084\pi$
$42$	4.18145	+	1.87495i	0.645212	+	0.289311i
$43$	−0.513362	−	1.91589i	−0.0782870	−	0.292171i	0.915672	−	0.401927i	$-0.131660\pi$
$43$	−0.513362	−	1.91589i	−0.0782870	−	0.292171i	−0.993959	+	0.109756i	$0.964993\pi$
$44$	−3.42181	−	1.97559i	−0.515858	−	0.297831i
$45$	−6.24990	+	2.43695i	−0.931680	+	0.363279i
$46$	0.0166572	+	0.0288511i	0.00245597	+	0.00425387i
$47$	−0.773256	−	0.207193i	−0.112791	−	0.0302223i	0.201982	−	0.979389i	$-0.435262\pi$
$47$	−0.773256	−	0.207193i	−0.112791	−	0.0302223i	−0.314773	+	0.949167i	$0.601928\pi$
$48$	0.839090	+	1.51523i	0.121112	+	0.218705i
$49$	−6.72016	−	1.95944i	−0.960023	−	0.279919i
$50$	−2.62720	−	4.25415i	−0.371543	−	0.601628i
$51$	10.4226	+	2.99328i	1.45945	+	0.419143i
$52$	−2.66732	+	2.66732i	−0.369891	+	0.369891i
$53$	−3.30076	−	0.884435i	−0.453394	−	0.121486i	0.0248932	−	0.999690i	$-0.492075\pi$
$53$	−3.30076	−	0.884435i	−0.453394	−	0.121486i	−0.478287	+	0.878204i	$0.658742\pi$
$54$	1.61181	−	4.93985i	0.219339	−	0.672228i
$55$	−8.11156	+	3.50161i	−1.09376	+	0.472157i
$56$	−1.58754	−	2.11653i	−0.212144	−	0.282834i
$57$	−1.70876	+	2.84120i	−0.226331	+	0.376326i
$58$	7.06338	−	7.06338i	0.927468	−	0.927468i
$59$	3.15468	−	5.46407i	0.410705	−	0.711361i	−0.584262	−	0.811565i	$-0.698616\pi$
$59$	3.15468	−	5.46407i	0.410705	−	0.711361i	0.994967	+	0.100204i	$0.0319494\pi$
$60$	3.83829	+	0.517229i	0.495521	+	0.0667740i
$61$	−6.86064	+	3.96099i	−0.878415	+	0.507153i	−0.870136	−	0.492813i	$-0.835969\pi$
$61$	−6.86064	+	3.96099i	−0.878415	+	0.507153i	−0.00827960	+	0.999966i	$0.502636\pi$
$62$	−2.12642	+	2.12642i	−0.270056	+	0.270056i
$63$	−1.40215	+	7.81242i	−0.176654	+	0.984273i
$64$		−	1.00000i		−	0.125000i
$65$	1.22475	+	8.34541i	0.151911	+	1.03512i
$66$	1.88907	−	6.57774i	0.232529	−	0.809664i
$67$	−6.18954	+	1.65848i	−0.756173	+	0.202616i	−0.616254	−	0.787547i	$-0.711351\pi$
$67$	−6.18954	+	1.65848i	−0.756173	+	0.202616i	−0.139918	+	0.990163i	$0.544684\pi$
$68$	−4.42700	−	4.42700i	−0.536853	−	0.536853i
$69$	−0.0415241	+	0.0400662i	−0.00499891	+	0.00482341i
$70$	−5.91604	+	0.0228458i	−0.707102	+	0.00273059i
$71$	−3.11188			−0.369312			−0.184656	−	0.982803i	$-0.559117\pi$
$71$	−3.11188			−0.369312			−0.184656	+	0.982803i	$0.559117\pi$
$72$	−2.19575	+	2.04419i	−0.258771	+	0.240910i
$73$	0.292904	−	1.09313i	0.0342818	−	0.127942i	−0.946664	−	0.322222i	$-0.895570\pi$
$73$	0.292904	−	1.09313i	0.0342818	−	0.127942i	0.980946	+	0.194280i	$0.0622371\pi$
$74$			5.18270i			0.602476i
$75$	6.05123	−	6.19537i	0.698736	−	0.715379i
$76$	1.65773	−	0.957091i	0.190155	−	0.109786i
$77$	−1.47796	+	10.3488i	−0.168429	+	1.17936i
$78$	−5.59897	−	3.36735i	−0.633959	−	0.381277i
$79$	2.11476	−	1.22095i	0.237929	−	0.137368i	−0.376296	−	0.926500i	$-0.622802\pi$
$79$	2.11476	−	1.22095i	0.237929	−	0.137368i	0.614224	+	0.789131i	$0.289469\pi$
$80$	−1.79397	−	1.33480i	−0.200571	−	0.149235i
$81$	8.97703	+	0.642610i	0.997448	+	0.0714011i
$82$	2.44976	+	9.14262i	0.270530	+	1.00963i
$83$	−15.1694	+	4.06462i	−1.66506	+	0.446150i	−0.963771	−	0.266731i	$-0.914056\pi$
$83$	−15.1694	+	4.06462i	−1.66506	+	0.446150i	−0.701285	+	0.712881i	$0.747390\pi$
$84$	2.89330	−	3.55370i	0.315685	−	0.387741i
$85$	−13.8510	+	2.03274i	−1.50236	+	0.220481i
$86$	−1.98348			−0.213884
$87$	14.8268	+	8.91714i	1.58960	+	0.956018i
$88$	−2.79390	+	2.79390i	−0.297831	+	0.297831i
$89$	7.93473	−	13.7434i	0.841080	−	1.45679i	−0.0479025	−	0.998852i	$-0.515254\pi$
$89$	7.93473	−	13.7434i	0.841080	−	1.45679i	0.888982	−	0.457941i	$-0.151413\pi$
$90$	0.736320	+	6.66767i	0.0776150	+	0.702834i
$91$	9.17810	+	3.92004i	0.962127	+	0.410932i
$92$	0.0321793	−	0.00862241i	0.00335492	−	0.000898948i
$93$	−4.46358	−	2.68449i	−0.462852	−	0.278369i
$94$	−0.400267	+	0.693283i	−0.0412844	+	0.0715067i
$95$	0.495746	−	4.25143i	0.0508625	−	0.436188i
$96$	1.68077	−	0.418328i	0.171543	−	0.0426954i
$97$	−4.61042	−	17.2063i	−0.468117	−	1.74704i	−0.646344	−	0.763047i	$-0.723703\pi$
$97$	−4.61042	−	17.2063i	−0.468117	−	1.74704i	0.178227	−	0.983989i	$-0.442964\pi$
$98$	−3.63198	+	5.98404i	−0.366885	+	0.604479i
$99$	11.8459	+	0.423448i	1.19056	+	0.0425581i
$100$	−4.78916	+	1.43663i	−0.478916	+	0.143663i
$101$		−	5.42195i		−	0.539505i	−0.962930	−	0.269752i	$-0.913058\pi$
$101$		−	5.42195i		−	0.539505i	0.962930	−	0.269752i	$-0.0869418\pi$
$102$	5.58885	−	9.29273i	0.553379	−	0.920117i
$103$	−9.69873	−	9.69873i	−0.955644	−	0.955644i	0.0434131	−	0.999057i	$-0.486177\pi$
$103$	−9.69873	−	9.69873i	−0.955644	−	0.955644i	−0.999057	+	0.0434131i	$0.986177\pi$
$104$	1.88608	+	3.26678i	0.184945	+	0.320335i
$105$	−2.51324	−	9.93396i	−0.245267	−	0.969455i
$106$	−1.70860	+	2.95938i	−0.165954	+	0.287440i
$107$	15.2629	−	4.08968i	1.47552	−	0.395365i	0.570700	−	0.821158i	$-0.306672\pi$
$107$	15.2629	−	4.08968i	1.47552	−	0.395365i	0.904820	+	0.425794i	$0.140005\pi$
$108$	−4.35436	−	2.83541i	−0.418998	−	0.272838i
$109$	8.20738	−	4.73853i	0.786124	−	0.453869i	−0.0524723	−	0.998622i	$-0.516710\pi$
$109$	8.20738	−	4.73853i	0.786124	−	0.453869i	0.838596	+	0.544753i	$0.183377\pi$
$110$	1.28287	+	8.74145i	0.122317	+	0.833465i
$111$	−8.71094	+	2.16807i	−0.826806	+	0.205784i
$112$	−2.45530	+	0.985646i	−0.232004	+	0.0931348i
$113$	13.2455	+	3.54912i	1.24603	+	0.333873i	0.820802	−	0.571212i	$-0.193527\pi$
$113$	13.2455	+	3.54912i	1.24603	+	0.333873i	0.425229	+	0.905086i	$0.360193\pi$
$114$	2.30213	+	2.38589i	0.215614	+	0.223459i
$115$	0.0274845	−	0.0692377i	0.00256294	−	0.00645645i
$116$	−4.99457	−	8.65084i	−0.463734	−	0.803211i
$117$	3.31754	−	10.8193i	0.306706	−	1.00024i
$118$	−4.46139	−	4.46139i	−0.410705	−	0.410705i
$119$	−6.50616	+	15.2331i	−0.596419	+	1.39641i
$120$	1.49303	−	3.57364i	0.136294	−	0.326227i
$121$	4.61175			0.419250
$122$	2.05036	+	7.65205i	0.185631	+	0.692784i
$123$	−14.3419	+	7.94210i	−1.29316	+	0.716115i
$124$	1.50361	+	2.60433i	0.135028	+	0.233875i
$125$	−3.81531	+	10.5092i	−0.341251	+	0.939972i
$126$	7.18332	+	3.37638i	0.639941	+	0.300791i
$127$	−5.74938	−	5.74938i	−0.510175	−	0.510175i	0.404405	−	0.914580i	$-0.367479\pi$
$127$	−5.74938	−	5.74938i	−0.510175	−	0.510175i	−0.914580	+	0.404405i	$0.867479\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−0.829745	−	3.33378i	−0.0730550	−	0.293523i
$130$	8.37804	+	0.976937i	0.734802	+	0.0856830i
$131$			3.20096i			0.279669i	0.990175	+	0.139834i	$0.0446570\pi$
$131$			3.20096i			0.279669i	−0.990175	+	0.139834i	$0.955343\pi$
$132$	−5.86468	−	3.52715i	−0.510455	−	0.306999i
$133$	−3.98388	−	3.12687i	−0.345446	−	0.271134i
$134$			6.40788i			0.553557i
$135$	−10.8988	+	4.02686i	−0.938021	+	0.346577i
$136$	−5.42195	+	3.13036i	−0.464928	+	0.268426i
$137$	4.42993	+	4.42993i	0.378474	+	0.378474i	0.870552	−	0.492077i	$-0.163762\pi$
$137$	4.42993	+	4.42993i	0.378474	+	0.378474i	−0.492077	+	0.870552i	$0.663762\pi$
$138$	0.0279538	+	0.0504791i	0.00237959	+	0.00429706i
$139$	6.85223	+	11.8684i	0.581199	+	1.00667i	0.995338	+	0.0964518i	$0.0307494\pi$
$139$	6.85223	+	11.8684i	0.581199	+	1.00667i	−0.414139	+	0.910214i	$0.635917\pi$
$140$	−1.50912	+	5.72036i	−0.127544	+	0.483459i
$141$	−1.33269	−	0.382739i	−0.112233	−	0.0322324i
$142$	−0.805413	+	3.00584i	−0.0675887	+	0.252245i
$143$	3.85755	−	14.3966i	0.322585	−	1.20390i
$144$	1.40623	+	2.65000i	0.117186	+	0.220834i
$145$	−22.1861	−	2.58705i	−1.84245	−	0.214843i
$146$	−0.980076	−	0.565847i	−0.0811117	−	0.0468299i
$147$	−11.5772	−	3.60124i	−0.954870	−	0.297025i
$148$	5.00610	+	1.34138i	0.411499	+	0.110261i
$149$			16.0257i			1.31287i	0.754381	+	0.656437i	$0.227937\pi$
$149$			16.0257i			1.31287i	−0.754381	+	0.656437i	$0.772063\pi$
$150$	−4.41809	−	7.44852i	−0.360736	−	0.608169i
$151$	8.15466			0.663617			0.331808	−	0.943347i	$-0.392341\pi$
$151$	8.15466			0.663617			0.331808	+	0.943347i	$0.392341\pi$
$152$	−0.495427	−	1.84896i	−0.0401844	−	0.149970i
$153$	17.9569	+	5.50618i	1.45173	+	0.445148i
$154$	9.61366	+	4.10607i	0.774691	+	0.330876i
$155$	6.67909	+	0.778827i	0.536477	+	0.0625569i
$156$	−4.70173	+	4.53666i	−0.376439	+	0.363224i
$157$	−1.11210	−	4.15042i	−0.0887554	−	0.331240i	0.907243	−	0.420606i	$-0.138182\pi$
$157$	−1.11210	−	4.15042i	−0.0887554	−	0.331240i	−0.995999	+	0.0893663i	$0.971516\pi$
$158$	−0.632013	−	2.35870i	−0.0502802	−	0.187648i
$159$	−5.68880	−	1.63377i	−0.451151	−	0.129567i
$160$	−1.75363	+	1.38737i	−0.138637	+	0.109681i
$161$	−0.0528880	−	0.0705111i	−0.00416815	−	0.00555705i
$162$	2.94414	−	8.50482i	0.231313	−	0.668202i
$163$	−2.86087	−	10.6769i	−0.224081	−	0.836280i	−0.982771	−	0.184829i	$-0.940827\pi$
$163$	−2.86087	−	10.6769i	−0.224081	−	0.836280i	0.758690	−	0.651452i	$-0.225840\pi$
$164$	9.46513			0.739103
$165$	−14.1557	+	5.81301i	−1.10202	+	0.452542i
$166$			15.7045i			1.21891i
$167$	−14.2000	−	3.80488i	−1.09883	−	0.294431i	−0.336542	−	0.941668i	$-0.609257\pi$
$167$	−14.2000	−	3.80488i	−1.09883	−	0.294431i	−0.762288	+	0.647238i	$0.775924\pi$
$168$	−2.68377	−	3.71448i	−0.207057	−	0.286579i
$169$	−1.06450	−	0.614589i	−0.0818846	−	0.0472761i
$170$	−1.62144	+	13.9052i	−0.124359	+	1.06648i
$171$	−3.04710	+	4.86744i	−0.233017	+	0.372223i
$172$	−0.513362	+	1.91589i	−0.0391435	+	0.146086i
$173$	−1.10419	+	4.12088i	−0.0839497	+	0.313304i	−0.995113	−	0.0987404i	$-0.968519\pi$
$173$	−1.10419	+	4.12088i	−0.0839497	+	0.313304i	0.911164	+	0.412045i	$0.135185\pi$
$174$	12.4507	−	12.0136i	0.943889	−	0.910751i
$175$	8.24778	+	10.3428i	0.623473	+	0.781845i
$176$	1.97559	+	3.42181i	0.148915	+	0.257929i
$177$	5.63227	−	9.36492i	0.423347	−	0.703911i
$178$	−11.2214	−	11.2214i	−0.841080	−	0.841080i
$179$	−11.8636	+	6.84947i	−0.886730	+	0.511954i	−0.872871	−	0.487950i	$-0.837745\pi$
$179$	−11.8636	+	6.84947i	−0.886730	+	0.511954i	−0.0138584	+	0.999904i	$0.504411\pi$
$180$	6.63105	+	1.01449i	0.494249	+	0.0756156i
$181$			12.5435i			0.932350i	0.884693	+	0.466175i	$0.154368\pi$
$181$			12.5435i			0.932350i	−0.884693	+	0.466175i	$0.845632\pi$
$182$	6.16193	−	7.85079i	0.456753	−	0.581939i
$183$	−12.0036	+	6.64726i	−0.887335	+	0.491380i
$184$		−	0.0333144i		−	0.00245597i
$185$	9.08853	−	7.19030i	0.668202	−	0.528642i
$186$	−3.74828	+	3.61669i	−0.274837	+	0.265189i
$187$	23.8943	+	6.40246i	1.74732	+	0.468194i
$188$	0.566063	+	0.566063i	0.0412844	+	0.0412844i
$189$	−2.66994	+	13.4860i	−0.194210	+	0.980960i
$190$	−3.97826	−	1.57921i	−0.288613	−	0.114568i
$191$	−2.88213	−	4.99200i	−0.208544	−	0.361208i	0.742712	−	0.669611i	$-0.233539\pi$
$191$	−2.88213	−	4.99200i	−0.208544	−	0.361208i	−0.951256	+	0.308402i	$0.900206\pi$
$192$	0.0309423	−	1.73177i	0.00223307	−	0.124980i
$193$	−3.39132	−	12.6566i	−0.244113	−	0.911042i	−0.973827	−	0.227290i	$-0.927014\pi$
$193$	−3.39132	−	12.6566i	−0.244113	−	0.911042i	0.729714	−	0.683752i	$-0.239653\pi$
$194$	−17.8133			−1.27892
$195$	1.86276	+	14.4903i	0.133395	+	1.03767i
$196$	4.84011	+	5.05700i	0.345722	+	0.361215i
$197$	−10.3528	−	10.3528i	−0.737605	−	0.737605i	0.234509	−	0.972114i	$-0.424652\pi$
$197$	−10.3528	−	10.3528i	−0.737605	−	0.737605i	−0.972114	+	0.234509i	$0.924652\pi$
$198$	3.47498	−	11.3327i	0.246956	−	0.805381i
$199$	9.29599	+	16.1011i	0.658975	+	1.14138i	0.980881	+	0.194607i	$0.0623431\pi$
$199$	9.29599	+	16.1011i	0.658975	+	1.14138i	−0.321906	+	0.946772i	$0.604324\pi$
$200$	0.148149	+	4.99780i	0.0104757	+	0.353398i
$201$	−10.7702	+	2.68060i	−0.759671	+	0.189075i
$202$	−5.23721	−	1.40331i	−0.368489	−	0.0987362i
$203$	−16.3175	+	20.7898i	−1.14527	+	1.45916i
$204$	−7.52959	−	7.80355i	−0.527176	−	0.546358i
$205$	12.6340	−	16.9801i	0.882400	−	1.18594i
$206$	−11.8785	+	6.85804i	−0.827612	+	0.477822i
$207$	−0.0731500	+	0.0681009i	−0.00508428	+	0.00473334i
$208$	3.64363	−	0.976306i	0.252640	−	0.0676947i
$209$	−3.78163	+	6.54997i	−0.261581	+	0.453071i
$210$	−10.2459	−	0.143492i	−0.707037	−	0.00990189i
$211$	−9.18953	−	15.9167i	−0.632633	−	1.09575i	−0.987011	−	0.160651i	$-0.948641\pi$
$211$	−9.18953	−	15.9167i	−0.632633	−	1.09575i	0.354378	−	0.935102i	$-0.384693\pi$
$212$	2.41632	+	2.41632i	0.165954	+	0.165954i
$213$	−5.38907	−	0.0962885i	−0.369253	−	0.00659758i
$214$		−	15.8013i		−	1.08016i
$215$	2.75181	+	3.47829i	0.187672	+	0.237217i
$216$	−3.86579	+	3.47213i	−0.263034	+	0.236248i
$217$	4.91238	−	6.25876i	0.333474	−	0.424872i
$218$	−2.45284	−	9.15414i	−0.166128	−	0.619996i
$219$	0.541068	−	1.88400i	0.0365620	−	0.127309i
$220$	8.77563	+	1.02330i	0.591653	+	0.0689908i
$221$	11.8082	−	20.4524i	0.794307	−	1.37578i
$222$	−0.160365	+	8.97526i	−0.0107630	+	0.602380i
$223$	−23.5572	+	6.31213i	−1.57751	+	0.422692i	−0.938153	−	0.346221i	$-0.887465\pi$
$223$	−23.5572	+	6.31213i	−1.57751	+	0.422692i	−0.639354	+	0.768913i	$0.720798\pi$
$224$	0.316582	+	2.62674i	0.0211525	+	0.175507i
$225$	10.6711	−	10.5417i	0.711405	−	0.702783i
$226$	6.85637	−	11.8756i	0.456079	−	0.789952i
$227$	−4.12146	+	4.12146i	−0.273551	+	0.273551i	−0.830528	−	0.556977i	$-0.811961\pi$
$227$	−4.12146	+	4.12146i	−0.273551	+	0.273551i	0.556977	+	0.830528i	$0.311961\pi$
$228$	2.90043	−	1.60617i	0.192086	−	0.106371i
$229$	3.22080			0.212836			0.106418	−	0.994321i	$-0.466062\pi$
$229$	3.22080			0.212836			0.106418	+	0.994321i	$0.466062\pi$
$230$	−0.0597649	−	0.0444680i	−0.00394078	−	0.00293213i
$231$	−2.87971	+	17.8761i	−0.189471	+	1.17616i
$232$	−9.64876	+	2.58538i	−0.633472	+	0.169738i
$233$	−1.79952	−	6.71592i	−0.117891	−	0.439974i	0.881596	−	0.472005i	$-0.156469\pi$
$233$	−1.79952	−	6.71592i	−0.117891	−	0.439974i	−0.999487	+	0.0320302i	$0.989803\pi$
$234$	−9.59197	−	6.00473i	−0.627047	−	0.392541i
$235$	1.77108	−	0.259918i	0.115532	−	0.0169552i
$236$	−5.46407	+	3.15468i	−0.355681	+	0.205352i
$237$	3.70006	−	2.04898i	0.240345	−	0.133096i
$238$	13.0301	+	10.2271i	0.844616	+	0.662923i
$239$	−12.6853	+	7.32389i	−0.820547	+	0.473743i	−0.850605	−	0.525805i	$-0.823764\pi$
$239$	−12.6853	+	7.32389i	−0.820547	+	0.473743i	0.0300581	+	0.999548i	$0.490431\pi$
$240$	−3.06544	−	2.36708i	−0.197873	−	0.152794i
$241$		−	7.92487i		−	0.510486i	−0.966877	−	0.255243i	$-0.917845\pi$
$241$		−	7.92487i		−	0.510486i	0.966877	−	0.255243i	$-0.0821554\pi$
$242$	1.19361	−	4.45461i	0.0767281	−	0.286353i
$243$	15.5263	+	1.39063i	0.996013	+	0.0892087i
$244$	7.92199			0.507153
$245$	15.5327	−	1.93292i	0.992346	−	0.123490i
$246$	3.95953	+	15.9088i	0.252451	+	1.01430i
$247$	5.10573	+	5.10573i	0.324870	+	0.324870i
$248$	2.90475	−	0.778325i	0.184452	−	0.0494237i
$249$	−26.3957	+	6.56963i	−1.67276	+	0.416334i
$250$	9.16364	+	6.40529i	0.579560	+	0.405106i
$251$			20.3047i			1.28162i	0.767699	+	0.640810i	$0.221401\pi$
$251$			20.3047i			1.28162i	−0.767699	+	0.640810i	$0.778599\pi$
$252$	5.12051	−	6.06468i	0.322562	−	0.382039i
$253$	−0.0930771	+	0.0930771i	−0.00585171	+	0.00585171i
$254$	−7.04153	+	4.06543i	−0.441825	+	0.255088i
$255$	−24.0498	+	3.09166i	−1.50606	+	0.193607i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.24154	+	6.24154i	−0.389337	+	0.389337i	−0.874451	−	0.485114i	$-0.838778\pi$
$257$	−6.24154	+	6.24154i	−0.389337	+	0.389337i	0.485114	+	0.874451i	$0.338778\pi$
$258$	−3.43494	−	0.0613734i	−0.213850	−	0.00382094i
$259$	−1.64075	−	13.6136i	−0.101951	−	0.845909i
$260$	3.11204	−	7.83971i	0.193001	−	0.486198i
$261$	25.4007	+	15.9012i	1.57226	+	0.984263i
$262$	3.09189	+	0.828469i	0.191017	+	0.0511830i
$263$	21.8684	−	21.8684i	1.34846	−	1.34846i	0.461127	−	0.887334i	$-0.347445\pi$
$263$	21.8684	−	21.8684i	1.34846	−	1.34846i	0.887334	−	0.461127i	$-0.152555\pi$
$264$	−4.92485	+	4.75195i	−0.303104	+	0.292463i
$265$	7.56010	−	1.10950i	0.464413	−	0.0681559i
$266$	−4.05143	+	3.03884i	−0.248409	+	0.186323i
$267$	14.1664	−	23.5549i	0.866971	−	1.44154i
$268$	6.18954	+	1.65848i	0.378086	+	0.101308i
$269$	−12.1610	−	21.0635i	−0.741472	−	1.28427i	−0.951825	−	0.306641i	$-0.900795\pi$
$269$	−12.1610	−	21.0635i	−0.741472	−	1.28427i	0.210354	−	0.977625i	$-0.432538\pi$
$270$	1.06883	+	11.5697i	0.0650468	+	0.704109i
$271$	−1.25698	−	0.725715i	−0.0763558	−	0.0440841i	0.461336	−	0.887226i	$-0.347370\pi$
$271$	−1.25698	−	0.725715i	−0.0763558	−	0.0440841i	−0.537692	+	0.843141i	$0.680704\pi$
$272$	1.62039	+	6.04740i	0.0982509	+	0.366677i
$273$	15.7731	+	7.07261i	0.954632	+	0.428054i
$274$	5.42553	−	3.13243i	0.327768	−	0.189237i
$275$	13.5495	−	14.3773i	0.817063	−	0.866983i
$276$	0.0559940	−	0.0139364i	0.00337044	−	0.000838870i
$277$	6.99924	+	6.99924i	0.420543	+	0.420543i	0.885391	−	0.464847i	$-0.153891\pi$
$277$	6.99924	+	6.99924i	0.420543	+	0.420543i	−0.464847	+	0.885391i	$0.653891\pi$
$278$	13.2375	−	3.54698i	0.793932	−	0.212733i
$279$	−7.64685	−	4.78705i	−0.457805	−	0.286593i
$280$	5.13486	+	2.93823i	0.306867	+	0.175593i
$281$	12.3266	−	21.3503i	0.735343	−	1.27365i	−0.219230	−	0.975673i	$-0.570354\pi$
$281$	12.3266	−	21.3503i	0.735343	−	1.27365i	0.954573	−	0.297978i	$-0.0963122\pi$
$282$	−0.714624	+	1.18822i	−0.0425552	+	0.0707577i
$283$	−10.5766	+	2.83399i	−0.628713	+	0.168463i	−0.559086	−	0.829110i	$-0.688848\pi$
$283$	−10.5766	+	2.83399i	−0.628713	+	0.168463i	−0.0696276	+	0.997573i	$0.522181\pi$
$284$	2.69496	+	1.55594i	0.159917	+	0.0923279i
$285$	0.990070	−	7.34719i	0.0586467	−	0.435210i
$286$	−12.9076	−	7.45222i	−0.763244	−	0.440659i
$287$	−9.32927	−	23.2398i	−0.550690	−	1.37180i
$288$	2.92367	−	0.672443i	0.172279	−	0.0396241i
$289$	19.2229	+	11.0983i	1.13076	+	0.652843i
$290$	−8.24107	+	20.7605i	−0.483932	+	1.21910i
$291$	−7.45180	−	29.9401i	−0.436832	−	1.75512i
$292$	−0.800229	+	0.800229i	−0.0468299	+	0.0468299i
$293$	4.36541	−	16.2919i	0.255030	−	0.951785i	−0.713044	−	0.701119i	$-0.752684\pi$
$293$	4.36541	−	16.2919i	0.255030	−	0.951785i	0.968074	−	0.250665i	$-0.0806493\pi$
$294$	−6.47492	+	10.2506i	−0.377625	+	0.597829i
$295$	−1.63404	+	14.0132i	−0.0951373	+	0.815881i
$296$	2.59135	−	4.48835i	0.150619	−	0.260880i
$297$	20.5014	+	1.09986i	1.18961	+	0.0638201i
$298$	15.4796	+	4.14775i	0.896709	+	0.240273i
$299$	0.0628336	+	0.108831i	0.00363376	+	0.00629386i
$300$	−8.33821	+	2.33973i	−0.481407	+	0.135084i
$301$	5.21009	−	0.627934i	0.300305	−	0.0361935i
$302$	2.11058	−	7.87680i	0.121450	−	0.453259i
$303$	0.167768	−	9.38960i	0.00963800	−	0.539419i
$304$	−1.91418			−0.109786
$305$	10.5743	−	14.2118i	0.605480	−	0.813764i
$306$	9.96616	−	15.9200i	0.569728	−	0.910084i
$307$	−22.4039	+	22.4039i	−1.27866	+	1.27866i	−0.337241	+	0.941418i	$0.609494\pi$
$307$	−22.4039	+	22.4039i	−1.27866	+	1.27866i	−0.941418	+	0.337241i	$0.890506\pi$
$308$	6.45436	−	8.22335i	0.367771	−	0.468569i
$309$	−16.4959	−	17.0961i	−0.938419	−	0.972564i
$310$	2.48096	−	6.24993i	0.140909	−	0.354972i
$311$	16.6729	+	9.62610i	0.945433	+	0.545846i	0.891659	−	0.452707i	$-0.149542\pi$
$311$	16.6729	+	9.62610i	0.945433	+	0.545846i	0.0537738	+	0.998553i	$0.482875\pi$
$312$	3.16518	+	5.71569i	0.179193	+	0.323587i
$313$	1.03044	−	3.84567i	0.0582441	−	0.217370i	−0.930670	−	0.365860i	$-0.880775\pi$
$313$	1.03044	−	3.84567i	0.0582441	−	0.217370i	0.988914	+	0.148490i	$0.0474414\pi$
$314$	−4.29683			−0.242484
$315$	−4.04499	−	17.2811i	−0.227909	−	0.973682i
$316$	−2.44191			−0.137368
$317$	3.71161	−	13.8519i	0.208465	−	0.778002i	−0.779900	−	0.625904i	$-0.784730\pi$
$317$	3.71161	−	13.8519i	0.208465	−	0.778002i	0.988365	−	0.152098i	$-0.0486030\pi$
$318$	−3.05047	+	5.07211i	−0.171062	+	0.284430i
$319$	34.1810	+	19.7344i	1.91377	+	1.10491i
$320$	0.886221	+	2.05295i	0.0495413	+	0.114764i
$321$	26.5585	−	6.61014i	1.48235	−	0.368942i
$322$	−0.0817969	+	0.0328362i	−0.00455836	+	0.00182989i
$323$	−8.47408	+	8.47408i	−0.471511	+	0.471511i
$324$	−7.45303	−	5.04503i	−0.414057	−	0.280280i
$325$	−9.91023	−	16.0473i	−0.549720	−	0.890146i
$326$	−11.0536			−0.612200
$327$	14.3599	−	7.95211i	0.794107	−	0.439753i
$328$	2.44976	−	9.14262i	0.135265	−	0.504817i
$329$	0.831917	−	1.94779i	0.0458651	−	0.107385i
$330$	1.95116	+	15.1779i	0.107408	+	0.835517i
$331$	7.59490	+	13.1547i	0.417453	+	0.723050i	0.995683	−	0.0928240i	$-0.0295894\pi$
$331$	7.59490	+	13.1547i	0.417453	+	0.723050i	−0.578229	+	0.815874i	$0.696256\pi$
$332$	15.1694	+	4.06462i	0.832528	+	0.223075i
$333$	−15.1525	+	3.48507i	−0.830351	+	0.190981i
$334$	−7.35047	+	12.7314i	−0.402200	+	0.696631i
$335$	11.2370	−	8.89008i	0.613945	−	0.485717i
$336$	−4.28253	+	1.63094i	−0.233631	+	0.0889753i
$337$	−1.56258	+	5.83164i	−0.0851193	+	0.317669i	−0.995337	−	0.0964611i	$-0.969248\pi$
$337$	−1.56258	+	5.83164i	−0.0851193	+	0.317669i	0.910217	+	0.414131i	$0.135914\pi$
$338$	−0.869161	+	0.869161i	−0.0472761	+	0.0472761i
$339$	22.8284	+	6.55612i	1.23987	+	0.356080i
$340$	13.0117	+	5.16512i	0.705660	+	0.280118i
$341$	−10.2901	−	5.94101i	−0.557242	−	0.321724i
$342$	3.91294	+	4.20306i	0.211588	+	0.227275i
$343$	7.64583	−	16.8684i	0.412836	−	0.910805i
$344$	1.71774	+	0.991740i	0.0926145	+	0.0534710i
$345$	0.0497393	−	0.119054i	0.00267788	−	0.00640963i
$346$	3.69468	+	2.13312i	0.198627	+	0.114677i
$347$	−26.1770	+	7.01410i	−1.40525	+	0.376537i	−0.880229	−	0.474550i	$-0.842611\pi$
$347$	−26.1770	+	7.01410i	−1.40525	+	0.376537i	−0.525025	+	0.851087i	$0.675944\pi$
$348$	−8.38179	−	15.1359i	−0.449311	−	0.811367i
$349$	5.72139	−	9.90973i	0.306259	−	0.530456i	−0.671282	−	0.741202i	$-0.734256\pi$
$349$	5.72139	−	9.90973i	0.306259	−	0.530456i	0.977541	+	0.210746i	$0.0675894\pi$
$350$	12.1251	−	5.28982i	0.648113	−	0.282753i
$351$	6.08000	−	18.6339i	0.324526	−	0.994603i
$352$	3.81654	−	1.02264i	0.203422	−	0.0545068i
$353$	20.7801	+	20.7801i	1.10601	+	1.10601i	0.993670	+	0.112341i	$0.0358349\pi$
$353$	20.7801	+	20.7801i	1.10601	+	1.10601i	0.112341	+	0.993670i	$0.464165\pi$
$354$	−7.58808	−	7.86417i	−0.403302	−	0.417976i
$355$	6.38853	−	2.75781i	0.339068	−	0.146369i
$356$	−13.7434	+	7.93473i	−0.728397	+	0.420540i
$357$	−11.7386	+	26.1789i	−0.621270	+	1.38554i
$358$	3.54555	+	13.2322i	0.187388	+	0.699342i
$359$	17.1164	+	9.88213i	0.903367	+	0.521559i	0.878291	−	0.478126i	$-0.158684\pi$
$359$	17.1164	+	9.88213i	0.903367	+	0.521559i	0.0250758	+	0.999686i	$0.492017\pi$
$360$	2.69616	−	6.14253i	0.142100	−	0.323740i
$361$	7.66795	+	13.2813i	0.403577	+	0.699015i
$362$	12.1161	+	3.24649i	0.636807	+	0.170632i
$363$	7.98652	+	0.142698i	0.419183	+	0.00748971i
$364$	−5.98845	−	7.98390i	−0.313880	−	0.418470i
$365$	0.367439	+	2.50373i	0.0192327	+	0.131051i
$366$	3.31399	+	13.3151i	0.173225	+	0.695990i
$367$	−23.4648	+	23.4648i	−1.22485	+	1.22485i	−0.258963	+	0.965887i	$0.583381\pi$
$367$	−23.4648	+	23.4648i	−1.22485	+	1.22485i	−0.965887	+	0.258963i	$0.916619\pi$
$368$	−0.0321793	−	0.00862241i	−0.00167746	−	0.000449474i
$369$	−25.0826	+	13.3102i	−1.30575	+	0.692899i
$370$	−4.59302	−	10.6398i	−0.238780	−	0.553138i
$371$	3.55116	−	8.31443i	0.184367	−	0.431664i
$372$	2.52333	+	4.55663i	0.130828	+	0.236250i
$373$	−4.75700	+	4.75700i	−0.246308	+	0.246308i	−0.819454	−	0.573145i	$-0.805723\pi$
$373$	−4.75700	+	4.75700i	−0.246308	+	0.246308i	0.573145	+	0.819454i	$0.305723\pi$
$374$	12.3686	−	21.4230i	0.639565	−	1.10776i
$375$	−6.93243	+	18.0815i	−0.357989	+	0.933726i
$376$	0.693283	−	0.400267i	0.0357533	−	0.0206422i
$377$	26.6442	−	26.6442i	1.37225	−	1.37225i
$378$	12.3354	+	6.06939i	0.634465	+	0.312176i
$379$		−	4.82581i		−	0.247885i	−0.992289	−	0.123943i	$-0.960446\pi$
$379$		−	4.82581i		−	0.247885i	0.992289	−	0.123943i	$-0.0395538\pi$
$380$	−2.55505	+	3.43398i	−0.131071	+	0.176159i
$381$	−9.77874	−	10.1345i	−0.500980	−	0.519208i
$382$	−5.56785	+	1.49190i	−0.284876	+	0.0763323i
$383$	−9.20969	−	9.20969i	−0.470593	−	0.470593i	0.431513	−	0.902107i	$-0.357980\pi$
$383$	−9.20969	−	9.20969i	−0.470593	−	0.470593i	−0.902107	+	0.431513i	$0.857980\pi$
$384$	−1.66476	−	0.478104i	−0.0849543	−	0.0243982i
$385$	−6.13716	−	22.5554i	−0.312778	−	1.14953i
$386$	−13.1031			−0.666929
$387$	−1.33378	−	5.79903i	−0.0677997	−	0.294781i
$388$	−4.61042	+	17.2063i	−0.234058	+	0.873518i
$389$		−	17.9639i		−	0.910808i	−0.890285	−	0.455404i	$-0.849495\pi$
$389$		−	17.9639i		−	0.910808i	0.890285	−	0.455404i	$-0.150505\pi$
$390$	14.4786	+	1.95107i	0.733154	+	0.0987962i
$391$	−0.180629	+	0.104286i	−0.00913480	+	0.00527398i
$392$	6.13740	−	3.36634i	0.309986	−	0.170026i
$393$	−0.0990449	+	5.54334i	−0.00499616	+	0.279624i
$394$	−12.6795	+	7.32052i	−0.638785	+	0.368802i
$395$	−3.25946	+	4.38070i	−0.164001	+	0.220417i
$396$	−10.0472	−	6.28969i	−0.504889	−	0.316069i
$397$	−9.67082	−	36.0920i	−0.485364	−	1.81140i	−0.578415	−	0.815743i	$-0.696328\pi$
$397$	−9.67082	−	36.0920i	−0.485364	−	1.81140i	0.0930504	−	0.995661i	$-0.470338\pi$
$398$	17.9585	−	4.81196i	0.900177	−	0.241202i
$399$	−6.80243	−	5.53831i	−0.340547	−	0.277262i
$400$	4.86585	+	1.15043i	0.243293	+	0.0575213i
$401$	−3.78094			−0.188811			−0.0944054	−	0.995534i	$-0.530095\pi$
$401$	−3.78094			−0.188811			−0.0944054	+	0.995534i	$0.530095\pi$
$402$	−0.198275	+	11.0970i	−0.00988904	+	0.553468i
$403$	−8.02121	+	8.02121i	−0.399565	+	0.399565i
$404$	−2.71098	+	4.69555i	−0.134876	+	0.233612i
$405$	−18.9989	+	6.63638i	−0.944063	+	0.329765i
$406$	15.8581	+	21.1423i	0.787027	+	1.04928i
$407$	−19.7800	+	5.30003i	−0.980456	+	0.262713i
$408$	−9.48645	+	5.25331i	−0.469649	+	0.260078i
$409$	−3.25649	+	5.64040i	−0.161023	+	0.278900i	−0.935236	−	0.354025i	$-0.884813\pi$
$409$	−3.25649	+	5.64040i	−0.161023	+	0.278900i	0.774213	+	0.632925i	$0.218146\pi$
$410$	−13.1316	−	16.5983i	−0.648524	−	0.819733i
$411$	7.53457	+	7.80871i	0.371653	+	0.385175i
$412$	3.54998	+	13.2487i	0.174895	+	0.652717i
$413$	13.1313	+	10.3065i	0.646151	+	0.507151i
$414$	0.0468478	+	0.0882833i	0.00230244	+	0.00433889i
$415$	27.5399	−	21.7879i	1.35188	−	1.06953i
$416$		−	3.77216i		−	0.184945i
$417$	11.4993	+	20.7654i	0.563122	+	1.01689i
$418$	5.34803	+	5.34803i	0.261581	+	0.261581i
$419$	12.1798	+	21.0961i	0.595023	+	1.03061i	0.993544	+	0.113450i	$0.0361903\pi$
$419$	12.1798	+	21.0961i	0.595023	+	1.03061i	−0.398521	+	0.917159i	$0.630476\pi$
$420$	−2.79045	+	9.85969i	−0.136160	+	0.481103i
$421$	8.80641	−	15.2531i	0.429198	−	0.743393i	−0.567604	−	0.823302i	$-0.692130\pi$
$421$	8.80641	−	15.2531i	0.429198	−	0.743393i	0.996802	+	0.0799087i	$0.0254629\pi$
$422$	−17.7528	+	4.75685i	−0.864193	+	0.231560i
$423$	−2.29608	−	0.704054i	−0.111639	−	0.0342323i
$424$	2.95938	−	1.70860i	0.143720	−	0.0829768i
$425$	26.6341	−	16.4482i	1.29194	−	0.797855i
$426$	−1.48780	+	5.18052i	−0.0720842	+	0.250997i
$427$	−7.80827	−	19.4509i	−0.377869	−	0.941293i
$428$	−15.2629	−	4.08968i	−0.737760	−	0.197682i
$429$	7.12588	−	24.8123i	0.344041	−	1.19795i
$430$	4.07199	−	1.75780i	0.196369	−	0.0847687i
$431$	0.982273	+	1.70135i	0.0473144	+	0.0819510i	0.888713	−	0.458465i	$-0.151600\pi$
$431$	0.982273	+	1.70135i	0.0473144	+	0.0819510i	−0.841398	+	0.540416i	$0.818267\pi$
$432$	2.35328	+	4.63272i	0.113222	+	0.222892i
$433$	−21.9116	−	21.9116i	−1.05301	−	1.05301i	−0.998514	−	0.0544924i	$-0.982646\pi$
$433$	−21.9116	−	21.9116i	−1.05301	−	1.05301i	−0.0544924	−	0.998514i	$-0.517354\pi$
$434$	−4.77408	−	6.36488i	−0.229163	−	0.305524i
$435$	−38.3412	−	5.16667i	−1.83832	−	0.247723i
$436$	−9.47706			−0.453869
$437$	−0.0165049	−	0.0615969i	−0.000789534	−	0.00294658i
$438$	−1.67976	−	1.01025i	−0.0802621	−	0.0482714i
$439$	8.40704	+	14.5614i	0.401246	+	0.694979i	0.993877	−	0.110496i	$-0.0352439\pi$
$439$	8.40704	+	14.5614i	0.401246	+	0.694979i	−0.592631	+	0.805474i	$0.701911\pi$
$440$	3.25973	−	8.21176i	0.155402	−	0.391480i
$441$	−19.9376	−	6.59476i	−0.949411	−	0.314036i
$442$	−16.6993	−	16.6993i	−0.794307	−	0.794307i
$443$	−26.1227	−	6.99957i	−1.24113	−	0.332559i	−0.422225	−	0.906491i	$-0.638751\pi$
$443$	−26.1227	−	6.99957i	−1.24113	−	0.332559i	−0.818903	+	0.573931i	$0.805418\pi$
$444$	8.62793	+	2.47787i	0.409464	+	0.117594i
$445$	−4.10997	+	35.2464i	−0.194831	+	1.67084i
$446$			24.3882i			1.15481i
$447$	−0.495871	+	27.7528i	−0.0234539	+	1.31266i
$448$	2.61918	+	0.374056i	0.123744	+	0.0176725i
$449$		−	11.4017i		−	0.538081i	−0.963129	−	0.269041i	$-0.913293\pi$
$449$		−	11.4017i		−	0.538081i	0.963129	−	0.269041i	$-0.0867066\pi$
$450$	−7.42066	−	13.0359i	−0.349813	−	0.614517i
$451$	−32.3879	+	18.6992i	−1.52509	+	0.880510i
$452$	−9.69638	−	9.69638i	−0.456079	−	0.456079i
$453$	14.1220	+	0.252324i	0.663511	+	0.0118552i
$454$	2.91432	+	5.04774i	0.136776	+	0.236902i
$455$	−22.3162	+	0.0861779i	−1.04620	+	0.00404008i
$456$	−0.800756	−	3.21731i	−0.0374988	−	0.150664i
$457$	0.473160	−	1.76586i	0.0221335	−	0.0826033i	−0.953976	−	0.299884i	$-0.903052\pi$
$457$	0.473160	−	1.76586i	0.0221335	−	0.0826033i	0.976109	+	0.217281i	$0.0697187\pi$
$458$	0.833604	−	3.11105i	0.0389517	−	0.145370i
$459$	30.9270	+	10.0911i	1.44355	+	0.471012i
$460$	−0.0584211	+	0.0462193i	−0.00272390	+	0.00215499i
$461$	−28.7456	−	16.5963i	−1.33881	−	0.772965i	−0.352183	−	0.935931i	$-0.614560\pi$
$461$	−28.7456	−	16.5963i	−1.33881	−	0.772965i	−0.986632	+	0.162966i	$0.947894\pi$
$462$	16.5216	+	7.40825i	0.768656	+	0.344663i
$463$	−6.01636	−	1.61208i	−0.279604	−	0.0749196i	0.116292	−	0.993215i	$-0.462899\pi$
$463$	−6.01636	−	1.61208i	−0.279604	−	0.0749196i	−0.395896	+	0.918295i	$0.629566\pi$
$464$			9.98913i			0.463734i
$465$	11.5426	+	1.55542i	0.535274	+	0.0721309i
$466$	−6.95283			−0.322084
$467$	−0.890902	−	3.32489i	−0.0412260	−	0.153858i	0.942245	−	0.334926i	$-0.108711\pi$
$467$	−0.890902	−	3.32489i	−0.0412260	−	0.153858i	−0.983471	+	0.181068i	$0.942045\pi$
$468$	−8.28271	+	7.71099i	−0.382868	+	0.356441i
$469$	−2.02862	−	16.8319i	−0.0936731	−	0.777223i
$470$	0.207327	−	1.77800i	0.00956329	−	0.0820131i
$471$	−1.79749	−	7.22200i	−0.0828238	−	0.332772i
$472$	1.63298	+	6.09438i	0.0751642	+	0.280516i
$473$	−2.02838	−	7.57002i	−0.0932651	−	0.348070i
$474$	−1.02152	−	4.10430i	−0.0469200	−	0.188517i
$475$	2.74997	+	9.16733i	0.126177	+	0.420626i
$476$	13.2510	−	9.93915i	0.607360	−	0.455560i
$477$	−9.80116	−	3.00535i	−0.448764	−	0.137606i
$478$	3.79112	+	14.1487i	0.173402	+	0.647145i
$479$	26.6284			1.21668			0.608341	−	0.793676i	$-0.291835\pi$
$479$	26.6284			1.21668			0.608341	+	0.793676i	$0.291835\pi$
$480$	−3.07982	+	2.34835i	−0.140574	+	0.107187i
$481$			19.5500i			0.891401i
$482$	−7.65484	−	2.05111i	−0.348668	−	0.0934254i
$483$	−0.0894082	−	0.123746i	−0.00406822	−	0.00563063i
$484$	−3.99389	−	2.30588i	−0.181541	−	0.104813i
$485$	24.7136	+	31.2379i	1.12218	+	1.41844i
$486$	5.36175	−	14.6373i	0.243214	−	0.663963i
$487$	−2.79932	+	10.4472i	−0.126849	+	0.473408i	−0.999899	−	0.0142234i	$-0.995472\pi$
$487$	−2.79932	+	10.4472i	−0.126849	+	0.473408i	0.873049	+	0.487632i	$0.162139\pi$
$488$	2.05036	−	7.65205i	0.0928155	−	0.346392i
$489$	−4.62401	−	18.5785i	−0.209105	−	0.840150i
$490$	2.15309	−	15.5037i	0.0972667	−	0.700385i
$491$	9.43968	+	16.3500i	0.426007	+	0.737865i	0.996514	−	0.0834275i	$-0.0265867\pi$
$491$	9.43968	+	16.3500i	0.426007	+	0.737865i	−0.570507	+	0.821293i	$0.693253\pi$
$492$	16.3915	+	0.292873i	0.738985	+	0.0132037i
$493$	44.2219	+	44.2219i	1.99165	+	1.99165i
$494$	6.25322	−	3.61030i	0.281346	−	0.162435i
$495$	−24.6944	+	9.62881i	−1.10993	+	0.432783i
$496$		−	3.00722i		−	0.135028i
$497$	1.16402	−	8.15055i	0.0522132	−	0.365602i
$498$	−0.485933	+	27.1966i	−0.0217752	+	1.21871i
$499$			12.2488i			0.548332i	0.961682	+	0.274166i	$0.0884018\pi$
$499$			12.2488i			0.548332i	−0.961682	+	0.274166i	$0.911598\pi$
$500$	8.55876	−	7.19359i	0.382759	−	0.321707i
$501$	−24.4735	−	7.02858i	−1.09340	−	0.314014i
$502$	19.6128	+	5.25524i	0.875363	+	0.234553i
$503$	12.3368	+	12.3368i	0.550069	+	0.550069i	0.926461	−	0.376392i	$-0.122835\pi$
$503$	12.3368	+	12.3368i	0.550069	+	0.550069i	−0.376392	+	0.926461i	$0.622835\pi$
$504$	−4.53275	−	6.51569i	−0.201905	−	0.290232i
$505$	4.80505	+	11.1310i	0.213822	+	0.495324i
$506$	0.0658155	+	0.113996i	0.00292586	+	0.00506773i
$507$	−1.82446	−	1.09727i	−0.0810270	−	0.0487314i
$508$	2.10442	+	7.85380i	0.0933686	+	0.348456i
$509$	−9.89275			−0.438488			−0.219244	−	0.975670i	$-0.570359\pi$
$509$	−9.89275			−0.438488			−0.219244	+	0.975670i	$0.570359\pi$
$510$	−3.23823	+	24.0305i	−0.143391	+	1.06409i
$511$	2.75355	+	1.17606i	0.121810	+	0.0520258i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.42750	+	8.33503i	−0.239630	+	0.368001i
$514$	4.41344	+	7.64430i	0.194668	+	0.337176i
$515$	28.5062	+	11.3158i	1.25614	+	0.498634i
$516$	−0.948310	+	3.30201i	−0.0417470	+	0.145363i
$517$	−3.05527	−	0.818657i	−0.134371	−	0.0360045i
$518$	−13.5744	−	1.93862i	−0.596425	−	0.0851780i
$519$	−2.03971	+	7.10226i	−0.0895333	+	0.311755i
$520$	−6.76712	−	5.03507i	−0.296758	−	0.220802i
$521$	32.1000	−	18.5329i	1.40633	−	0.811943i	0.411295	−	0.911502i	$-0.365077\pi$
$521$	32.1000	−	18.5329i	1.40633	−	0.811943i	0.995032	+	0.0995596i	$0.0317434\pi$
$522$	21.9336	−	20.4196i	0.960008	−	0.893744i
$523$	4.46358	−	1.19601i	0.195179	−	0.0522980i	−0.159905	−	0.987132i	$-0.551119\pi$
$523$	4.46358	−	1.19601i	0.195179	−	0.0522980i	0.355084	+	0.934834i	$0.384452\pi$
$524$	1.60048	−	2.77211i	0.0699172	−	0.121100i
$525$	13.9633	+	18.1667i	0.609406	+	0.792858i
$526$	−15.4633	−	26.7832i	−0.674231	−	1.16780i
$527$	−13.3130	−	13.3130i	−0.579921	−	0.579921i
$528$	3.31539	+	5.98694i	0.144284	+	0.260548i
$529$			22.9989i			0.999952i
$530$	0.885006	−	7.58965i	0.0384422	−	0.329673i
$531$	10.0436	−	16.0437i	0.435855	−	0.696235i
$532$	1.88671	+	4.69989i	0.0817991	+	0.203766i
$533$	9.24087	+	34.4874i	0.400267	+	1.49382i
$534$	−19.0857	−	19.7802i	−0.825920	−	0.855971i
$535$	−27.7096	+	21.9222i	−1.19799	+	0.947781i
$536$	3.20394	−	5.54939i	0.138389	−	0.239697i
$537$	−20.7571	+	11.4947i	−0.895734	+	0.496031i
$538$	−23.4933	+	6.29502i	−1.01287	+	0.271397i
$539$	−26.5525	−	7.74207i	−1.14370	−	0.333474i
$540$	11.4521	+	1.96205i	0.492820	+	0.0844330i
$541$	−1.27287	+	2.20468i	−0.0547251	+	0.0947867i	−0.892090	−	0.451857i	$-0.850762\pi$
$541$	−1.27287	+	2.20468i	−0.0547251	+	0.0947867i	0.837365	+	0.546644i	$0.184095\pi$
$542$	−1.02632	+	1.02632i	−0.0440841	+	0.0440841i
$543$	−0.388124	+	21.7225i	−0.0166560	+	0.932201i
$544$	6.26072			0.268426
$545$	−12.6500	+	17.0015i	−0.541865	+	0.728265i
$546$	10.9140	−	13.4051i	0.467076	−	0.573686i
$547$	39.0666	−	10.4679i	1.67037	−	0.447573i	0.705156	−	0.709052i	$-0.250877\pi$
$547$	39.0666	−	10.4679i	1.67037	−	0.447573i	0.965209	+	0.261479i	$0.0842102\pi$
$548$	−1.62147	−	6.05140i	−0.0692656	−	0.258503i
$549$	−20.9933	+	11.1401i	−0.895972	+	0.475450i
$550$	−10.3805	−	16.8089i	−0.442627	−	0.716733i
$551$	−16.5593	+	9.56051i	−0.705449	+	0.407291i
$552$	0.00103082	−	0.0576931i	4.38748e−5	−	0.00245558i
$553$	2.40686	+	5.99562i	0.102350	+	0.254960i
$554$	8.57228	−	4.94921i	0.364201	−	0.210272i
$555$	15.9618	−	12.1708i	0.677539	−	0.516620i
$556$		−	13.7045i		−	0.581199i
$557$	−5.77269	+	21.5440i	−0.244597	+	0.912848i	0.728989	+	0.684526i	$0.239991\pi$
$557$	−5.77269	+	21.5440i	−0.244597	+	0.912848i	−0.973586	+	0.228322i	$0.926676\pi$
$558$	−6.60309	+	6.14731i	−0.279531	+	0.260236i
$559$	−7.48200			−0.316455
$560$	4.16711	−	4.19942i	0.176093	−	0.177458i
$561$	41.1814	+	11.8270i	1.73868	+	0.499334i
$562$	−17.4324	−	17.4324i	−0.735343	−	0.735343i
$563$	9.18203	−	2.46032i	0.386976	−	0.103690i	−0.0600851	−	0.998193i	$-0.519137\pi$
$563$	9.18203	−	2.46032i	0.386976	−	0.103690i	0.447061	+	0.894503i	$0.352471\pi$
$564$	0.962778	+	0.997809i	0.0405403	+	0.0420153i
$565$	−30.3377	+	4.45226i	−1.27632	+	0.187308i
$566$			10.9497i			0.460250i
$567$	−5.04102	+	23.2720i	−0.211703	+	0.977334i
$568$	2.20043	−	2.20043i	0.0923279	−	0.0923279i
$569$	−29.1233	+	16.8143i	−1.22091	+	0.704894i	−0.965112	−	0.261836i	$-0.915672\pi$
$569$	−29.1233	+	16.8143i	−1.22091	+	0.704894i	−0.255800	+	0.966730i	$0.582339\pi$
$570$	−6.84059	−	2.85793i	−0.286521	−	0.119705i
$571$	0.215517	−	0.373287i	0.00901911	−	0.0156216i	−0.861481	−	0.507790i	$-0.830462\pi$
$571$	0.215517	−	0.373287i	0.00901911	−	0.0156216i	0.870500	+	0.492169i	$0.163796\pi$
$572$	−10.5390	+	10.5390i	−0.440659	+	0.440659i
$573$	−4.83674	−	8.73420i	−0.202058	−	0.364876i
$574$	−24.8625	+	2.99649i	−1.03774	+	0.125071i
$575$	0.00493550	+	0.166499i	0.000205824	+	0.00694349i
$576$	0.107170	−	2.99809i	0.00446542	−	0.124920i
$577$	−14.8785	−	3.98668i	−0.619400	−	0.165968i	−0.0645448	−	0.997915i	$-0.520560\pi$
$577$	−14.8785	−	3.98668i	−0.619400	−	0.165968i	−0.554855	+	0.831947i	$0.687226\pi$
$578$	15.6954	−	15.6954i	0.652843	−	0.652843i
$579$	−5.48138	−	22.0233i	−0.227799	−	0.915257i
$580$	17.9202	+	13.3335i	0.744094	+	0.553643i
$581$	−4.97177	−	41.2517i	−0.206264	−	1.71141i
$582$	−30.8486	−	0.551184i	−1.27872	−	0.0228473i
$583$	−13.0419	−	3.49455i	−0.540138	−	0.144730i
$584$	0.565847	+	0.980076i	0.0234149	+	0.0405558i
$585$	2.77752	+	25.1515i	0.114836	+	1.03989i
$586$	−14.6069	−	8.43332i	−0.603407	−	0.348377i
$587$	−6.15410	−	22.9674i	−0.254007	−	0.947967i	−0.968640	−	0.248468i	$-0.920073\pi$
$587$	−6.15410	−	22.9674i	−0.254007	−	0.947967i	0.714633	−	0.699499i	$-0.246594\pi$
$588$	8.22551	+	8.90735i	0.339214	+	0.367333i
$589$	4.98515	−	2.87818i	0.205410	−	0.118593i
$590$	13.1128	+	5.20525i	0.539846	+	0.214297i
$591$	−17.6083	−	18.2490i	−0.724310	−	0.750664i
$592$	−3.66472	−	3.66472i	−0.150619	−	0.150619i
$593$	8.92036	−	2.39020i	0.366315	−	0.0981539i	−0.0709659	−	0.997479i	$-0.522608\pi$
$593$	8.92036	−	2.39020i	0.366315	−	0.0981539i	0.437281	+	0.899325i	$0.355941\pi$
$594$	6.36853	−	19.5182i	0.261304	−	0.800840i
$595$	−0.143031	−	37.0387i	−0.00586370	−	1.51844i
$596$	8.01283	−	13.8786i	0.328218	−	0.568491i
$597$	15.6004	+	28.1712i	0.638480	+	1.15297i
$598$	0.121385	−	0.0325251i	0.00496381	−	0.00133005i
$599$	−18.8125	−	10.8614i	−0.768659	−	0.443786i	0.0637368	−	0.997967i	$-0.479698\pi$
$599$	−18.8125	−	10.8614i	−0.768659	−	0.443786i	−0.832396	+	0.554181i	$0.813032\pi$
$600$	0.101917	+	8.65965i	0.00416075	+	0.353529i
$601$	−4.17275	−	2.40914i	−0.170210	−	0.0982709i	0.412475	−	0.910969i	$-0.364664\pi$
$601$	−4.17275	−	2.40914i	−0.170210	−	0.0982709i	−0.582685	+	0.812698i	$0.697998\pi$
$602$	0.741932	−	5.19508i	0.0302389	−	0.211736i
$603$	−18.7345	+	4.30894i	−0.762928	+	0.175473i
$604$	−7.06214	−	4.07733i	−0.287355	−	0.165904i
$605$	−9.46771	+	4.08703i	−0.384917	+	0.166161i
$606$	−9.02624	−	2.59226i	−0.366666	−	0.105303i
$607$	8.55045	−	8.55045i	0.347052	−	0.347052i	−0.511958	−	0.859010i	$-0.671080\pi$
$607$	8.55045	−	8.55045i	0.347052	−	0.347052i	0.859010	+	0.511958i	$0.171080\pi$
$608$	−0.495427	+	1.84896i	−0.0200922	+	0.0749851i
$609$	−28.9016	+	35.4984i	−1.17115	+	1.43847i
$610$	−10.9907	−	13.8922i	−0.445001	−	0.562480i
$611$	−1.50987	+	2.61517i	−0.0610828	+	0.105799i
$612$	−12.7981	−	13.7470i	−0.517332	−	0.555688i
$613$	34.8532	+	9.33889i	1.40771	+	0.377194i	0.881107	−	0.472918i	$-0.156799\pi$
$613$	34.8532	+	9.33889i	1.40771	+	0.377194i	0.526602	+	0.850112i	$0.323466\pi$
$614$	15.8420	+	27.4391i	0.639330	+	1.10735i
$615$	22.4047	−	29.0148i	0.903445	−	1.16999i
$616$	−6.27264	−	8.36279i	−0.252732	−	0.336946i
$617$	−0.898261	+	3.35236i	−0.0361626	+	0.134961i	−0.981647	−	0.190706i	$-0.938922\pi$
$617$	−0.898261	+	3.35236i	−0.0361626	+	0.134961i	0.945485	+	0.325667i	$0.105589\pi$
$618$	−20.7830	+	11.5090i	−0.836016	+	0.462961i
$619$	36.5534			1.46920			0.734602	−	0.678499i	$-0.237369\pi$
$619$	36.5534			1.46920			0.734602	+	0.678499i	$0.237369\pi$
$620$	−5.39485	−	4.01403i	−0.216662	−	0.161207i
$621$	−0.128787	+	0.115672i	−0.00516803	+	0.00464175i
$622$	13.6134	−	13.6134i	0.545846	−	0.545846i
$623$	33.0282	+	25.9232i	1.32325	+	1.03859i
$624$	6.34015	−	1.57800i	0.253809	−	0.0631706i
$625$	−1.48084	−	24.9561i	−0.0592336	−	0.998244i
$626$	−3.44793	−	1.99067i	−0.137807	−	0.0795630i
$627$	−6.75160	+	11.2261i	−0.269633	+	0.448326i
$628$	−1.11210	+	4.15042i	−0.0443777	+	0.165620i
$629$	−32.4474			−1.29376
$630$	−17.7392	−	0.565529i	−0.706748	−	0.0225312i
$631$	45.5398			1.81291			0.906455	−	0.422301i	$-0.138778\pi$
$631$	45.5398			1.81291			0.906455	+	0.422301i	$0.138778\pi$
$632$	−0.632013	+	2.35870i	−0.0251401	+	0.0938242i
$633$	−15.4217	−	27.8485i	−0.612957	−	1.10688i
$634$	−12.4193	−	7.17029i	−0.493234	−	0.284768i
$635$	16.8984	+	6.70798i	0.670594	+	0.266198i
$636$	4.10976	+	4.25929i	0.162962	+	0.168892i
$637$	−13.7004	+	22.5728i	−0.542829	+	0.894365i
$638$	27.9086	−	27.9086i	1.10491	−	1.10491i
$639$	−9.32967	−	0.333500i	−0.369076	−	0.0131931i
$640$	2.21237	−	0.324681i	0.0874516	−	0.0128341i
$641$	−22.2413			−0.878477			−0.439238	−	0.898371i	$-0.644752\pi$
$641$	−22.2413			−0.878477			−0.439238	+	0.898371i	$0.644752\pi$
$642$	0.488929	−	27.3643i	0.0192965	−	1.07998i
$643$	−0.122417	+	0.456867i	−0.00482767	+	0.0180171i	−0.968298	−	0.249799i	$-0.919635\pi$
$643$	−0.122417	+	0.456867i	−0.00482767	+	0.0180171i	0.963470	+	0.267816i	$0.0863020\pi$
$644$	0.0105468	+	0.0875084i	0.000415600	+	0.00344831i
$645$	4.65789	+	6.10875i	0.183404	+	0.240532i
$646$	5.99208	+	10.3786i	0.235755	+	0.408340i
$647$	6.58285	+	1.76387i	0.258799	+	0.0693449i	0.385885	−	0.922547i	$-0.373896\pi$
$647$	6.58285	+	1.76387i	0.258799	+	0.0693449i	−0.127087	+	0.991892i	$0.540563\pi$
$648$	−6.80211	+	5.89332i	−0.267212	+	0.231512i
$649$	12.4647	−	21.5895i	0.489282	−	0.847461i
$650$	−18.0655	+	5.41919i	−0.708587	+	0.212558i
$651$	8.70079	−	10.6868i	0.341011	−	0.418847i
$652$	−2.86087	+	10.6769i	−0.112040	+	0.418140i
$653$	−21.7890	+	21.7890i	−0.852669	+	0.852669i	−0.990461	−	0.137792i	$-0.955999\pi$
$653$	−21.7890	+	21.7890i	−0.852669	+	0.852669i	0.137792	+	0.990461i	$0.455999\pi$
$654$	−3.96452	−	15.9288i	−0.155025	−	0.622865i
$655$	−2.83676	−	6.57141i	−0.110841	−	0.256766i
$656$	−8.19705	−	4.73257i	−0.320041	−	0.184776i
$657$	0.995303	−	3.24592i	0.0388305	−	0.126635i
$658$	−1.66611	−	1.30770i	−0.0649516	−	0.0509793i
$659$	−40.3475	−	23.2946i	−1.57171	−	0.907429i	−0.995959	−	0.0898064i	$-0.971375\pi$
$659$	−40.3475	−	23.2946i	−1.57171	−	0.907429i	−0.575754	−	0.817623i	$-0.695292\pi$
$660$	15.1657	+	2.04366i	0.590326	+	0.0795494i
$661$	−5.33062	−	3.07763i	−0.207337	−	0.119706i	0.392736	−	0.919651i	$-0.371529\pi$
$661$	−5.33062	−	3.07763i	−0.207337	−	0.119706i	−0.600073	+	0.799945i	$0.704862\pi$
$662$	14.6722	−	3.93141i	0.570252	−	0.152799i
$663$	21.0820	−	35.0536i	0.818758	−	1.36137i
$664$	7.85225	−	13.6005i	0.304726	−	0.527801i
$665$	10.9498	+	2.88872i	0.424616	+	0.112020i
$666$	−0.555430	+	15.5382i	−0.0215225	+	0.602092i
$667$	−0.321443	+	0.0861304i	−0.0124463	+	0.00333498i
$668$	10.3951	+	10.3951i	0.402200	+	0.402200i
$669$	−40.9911	+	10.2023i	−1.58481	+	0.394443i
$670$	−5.67880	−	13.1551i	−0.219391	−	0.508225i
$671$	−27.1076	+	15.6506i	−1.04648	+	0.604183i
$672$	0.466972	+	4.55872i	0.0180138	+	0.175856i
$673$	−2.27225	−	8.48016i	−0.0875889	−	0.326886i	0.908203	−	0.418530i	$-0.137455\pi$
$673$	−2.27225	−	8.48016i	−0.0875889	−	0.326886i	−0.995792	+	0.0916439i	$0.970788\pi$
$674$	5.22850	+	3.01868i	0.201394	+	0.116275i
$675$	18.8061	−	17.9257i	0.723846	−	0.689961i
$676$	0.614589	+	1.06450i	0.0236381	+	0.0409423i
$677$	8.26661	+	2.21503i	0.317711	+	0.0851305i	0.414151	−	0.910208i	$-0.364079\pi$
$677$	8.26661	+	2.21503i	0.317711	+	0.0851305i	−0.0964392	+	0.995339i	$0.530745\pi$
$678$	12.2412	−	20.3537i	0.470119	−	0.781679i
$679$	46.7909	−	5.63937i	1.79567	−	0.216419i
$680$	8.35680	−	11.2315i	0.320469	−	0.430709i
$681$	−7.26497	+	7.00992i	−0.278394	+	0.268621i
$682$	−8.40186	+	8.40186i	−0.321724	+	0.321724i
$683$	−39.0018	−	10.4505i	−1.49236	−	0.399878i	−0.581829	−	0.813311i	$-0.697663\pi$
$683$	−39.0018	−	10.4505i	−1.49236	−	0.399878i	−0.910534	+	0.413434i	$0.864329\pi$
$684$	5.07259	−	2.69178i	0.193955	−	0.102923i
$685$	−13.0203	−	5.16854i	−0.497481	−	0.197480i
$686$	−14.3147	−	11.7512i	−0.546538	−	0.448661i
$687$	5.57769	+	0.0996588i	0.212802	+	0.00380222i
$688$	1.40253	−	1.40253i	0.0534710	−	0.0534710i
$689$	−6.44510	+	11.1632i	−0.245539	+	0.425286i
$690$	−0.102123	−	0.0788578i	−0.00388777	−	0.00300207i
$691$	−20.5187	+	11.8465i	−0.780567	+	0.450661i	−0.836631	−	0.547766i	$-0.815478\pi$
$691$	−20.5187	+	11.8465i	−0.780567	+	0.450661i	0.0560640	+	0.998427i	$0.482145\pi$
$692$	3.01669	−	3.01669i	0.114677	−	0.114677i
$693$	−5.54013	+	30.8682i	−0.210452	+	1.17259i
$694$			27.1004i			1.02872i
$695$	−24.5853	−	18.2927i	−0.932575	−	0.693881i
$696$	−16.7895	+	4.17874i	−0.636404	+	0.158395i
$697$	−57.2394	+	15.3373i	−2.16810	+	0.580940i
$698$	−8.09126	−	8.09126i	−0.306259	−	0.306259i
$699$	−2.90856	−	11.6861i	−0.110012	−	0.442010i
$700$	−1.97137	−	13.0810i	−0.0745106	−	0.494417i
$701$	−13.1510			−0.496706			−0.248353	−	0.968670i	$-0.579889\pi$
$701$	−13.1510			−0.496706			−0.248353	+	0.968670i	$0.579889\pi$
$702$	−16.4253	−	10.6956i	−0.619934	−	0.403681i
$703$	2.56765	−	9.58259i	0.0968406	−	0.361414i
$704$		−	3.95117i		−	0.148915i
$705$	3.07515	−	0.395318i	0.115817	−	0.0148885i
$706$	25.4503	−	14.6937i	0.957833	−	0.553005i
$707$	14.2011	+	2.02811i	0.534086	+	0.0762751i
$708$	−9.56015	+	5.29413i	−0.359292	+	0.198965i
$709$	−15.9133	+	9.18757i	−0.597638	+	0.345046i	−0.768112	−	0.640316i	$-0.778803\pi$
$709$	−15.9133	+	9.18757i	−0.597638	+	0.345046i	0.170474	+	0.985362i	$0.445470\pi$
$710$	−1.01037	−	6.88462i	−0.0379184	−	0.258375i
$711$	6.47107	−	3.43389i	0.242684	−	0.128781i
$712$	4.10732	+	15.3287i	0.153928	+	0.574468i
$713$	0.0967700	−	0.0259294i	0.00362407	−	0.000971065i
$714$	22.2487	+	18.1142i	0.832638	+	0.677906i
$715$	4.83919	+	32.9741i	0.180975	+	1.23316i
$716$	13.6989			0.511954
$717$	−22.1948	+	12.2908i	−0.828879	+	0.459009i
$718$	13.9754	−	13.9754i	0.521559	−	0.521559i
$719$	2.45946	−	4.25990i	0.0917223	−	0.158868i	−0.816514	−	0.577326i	$-0.804096\pi$
$719$	2.45946	−	4.25990i	0.0917223	−	0.158868i	0.908236	+	0.418459i	$0.137429\pi$
$720$	−5.23541	−	4.19410i	−0.195112	−	0.156305i
$721$	29.0305	−	21.7748i	1.08115	−	0.810936i
$722$	14.8134	−	3.96923i	0.551296	−	0.147719i
$723$	0.245214	−	13.7241i	0.00911959	−	0.510404i
$724$	6.27174	−	10.8630i	0.233087	−	0.403719i
$725$	47.8396	−	14.3507i	1.77672	−	0.532970i
$726$	2.20490	−	7.67745i	0.0818314	−	0.284937i
$727$	5.86620	+	21.8930i	0.217565	+	0.811965i	0.985248	+	0.171135i	$0.0547433\pi$
$727$	5.86620	+	21.8930i	0.217565	+	0.811965i	−0.767682	+	0.640831i	$0.778590\pi$
$728$	−9.26178	+	3.71801i	−0.343265	+	0.137799i
$729$	26.8450	+	2.88867i	0.994260	+	0.106988i
$730$	2.51352	+	0.293093i	0.0930294	+	0.0108479i
$731$		−	12.4180i		−	0.459297i
$732$	13.7191	+	0.245124i	0.507072	+	0.00906006i
$733$	−8.86124	−	8.86124i	−0.327297	−	0.327297i	0.524261	−	0.851558i	$-0.324342\pi$
$733$	−8.86124	−	8.86124i	−0.327297	−	0.327297i	−0.851558	+	0.524261i	$0.824342\pi$
$734$	16.5921	+	28.7383i	0.612425	+	1.06075i
$735$	26.9589	−	2.86677i	0.994394	−	0.105742i
$736$	−0.0166572	+	0.0288511i	−0.000613993	+	0.00106347i
$737$	−24.4559	+	6.55295i	−0.900846	+	0.241381i
$738$	6.36476	+	27.6729i	0.234290	+	1.01865i
$739$	9.16761	−	5.29292i	0.337236	−	0.194703i	−0.321813	−	0.946803i	$-0.604292\pi$
$739$	9.16761	−	5.29292i	0.337236	−	0.194703i	0.659049	+	0.752100i	$0.270959\pi$
$740$	−11.4660	+	1.68272i	−0.421500	+	0.0618581i
$741$	8.68399	+	8.99996i	0.319014	+	0.330622i
$742$	−7.11202	−	5.58209i	−0.261090	−	0.204925i
$743$	41.4015	+	11.0935i	1.51887	+	0.406981i	0.919371	−	0.393392i	$-0.128698\pi$
$743$	41.4015	+	11.0935i	1.51887	+	0.406981i	0.599503	+	0.800373i	$0.295365\pi$
$744$	5.05445	−	1.25800i	0.185305	−	0.0461207i
$745$	−14.2023	−	32.8999i	−0.520331	−	1.20536i
$746$	3.36371	+	5.82612i	0.123154	+	0.213309i
$747$	−45.9147	+	10.5604i	−1.67993	+	0.386384i
$748$	−17.4918	−	17.4918i	−0.639565	−	0.639565i
$749$	5.00242	+	41.5060i	0.182784	+	1.51660i
$750$	15.6712	+	11.3761i	0.572230	+	0.415395i
$751$	−2.68568			−0.0980020			−0.0490010	−	0.998799i	$-0.515604\pi$
$751$	−2.68568			−0.0980020			−0.0490010	+	0.998799i	$0.515604\pi$
$752$	−0.207193	−	0.773256i	−0.00755557	−	0.0281978i
$753$	−0.628274	+	35.1631i	−0.0228956	+	1.28142i
$754$	−18.8403	−	32.6324i	−0.686123	−	1.18840i
$755$	−16.7411	+	7.22683i	−0.609272	+	0.263011i
$756$	9.05522	−	10.3442i	0.329335	−	0.376216i
$757$	20.0221	+	20.0221i	0.727716	+	0.727716i	0.970164	−	0.242448i	$-0.0779505\pi$
$757$	20.0221	+	20.0221i	0.727716	+	0.727716i	−0.242448	+	0.970164i	$0.577950\pi$
$758$	−4.66137	−	1.24901i	−0.169309	−	0.0453661i
$759$	−0.164069	+	0.158309i	−0.00595531	+	0.00574624i
$760$	2.65567	+	3.35676i	0.0963314	+	0.121763i
$761$		−	20.0308i		−	0.726117i	−0.931766	−	0.363059i	$-0.881732\pi$
$761$		−	20.0308i		−	0.726117i	0.931766	−	0.363059i	$-0.118268\pi$
$762$	−12.3201	+	6.82252i	−0.446311	+	0.247154i
$763$	9.34103	+	23.2690i	0.338168	+	0.842396i
$764$			5.76426i			0.208544i
$765$	−41.7445	+	4.60990i	−1.50927	+	0.166671i
$766$	−11.2795	+	6.51224i	−0.407546	+	0.235297i
$767$	−16.8291	−	16.8291i	−0.607663	−	0.607663i
$768$	−0.892684	+	1.48429i	−0.0322120	+	0.0535597i
$769$	2.41918	+	4.19014i	0.0872379	+	0.151100i	0.906343	−	0.422544i	$-0.138863\pi$
$769$	2.41918	+	4.19014i	0.0872379	+	0.151100i	−0.819105	+	0.573644i	$0.805529\pi$
$770$	−23.3753	+	0.0902675i	−0.842386	+	0.00325302i
$771$	−11.0021	+	10.6158i	−0.396230	+	0.382319i
$772$	−3.39132	+	12.6566i	−0.122056	+	0.455521i
$773$	−8.21278	+	30.6505i	−0.295393	+	1.10242i	0.645511	+	0.763751i	$0.276644\pi$
$773$	−8.21278	+	30.6505i	−0.295393	+	1.10242i	−0.940905	+	0.338672i	$0.890022\pi$
$774$	−5.94664	−	0.212570i	−0.213748	−	0.00764066i
$775$	−14.4021	+	4.32025i	−0.517337	+	0.155188i
$776$	15.4268	+	8.90664i	0.553788	+	0.319730i
$777$	−2.42017	−	23.6265i	−0.0868232	−	0.847595i
$778$	−17.3518	−	4.64941i	−0.622094	−	0.166689i
$779$		−	18.1180i		−	0.649144i
$780$	5.63194	−	13.4803i	0.201656	−	0.482673i
$781$	−12.2956			−0.439969
$782$	0.0539825	+	0.201465i	0.00193041	+	0.00720439i
$783$	43.4963	+	28.3233i	1.55443	+	1.01219i
$784$	−1.66316	−	6.79955i	−0.0593986	−	0.242841i
$785$	5.96128	+	7.53505i	0.212767	+	0.268937i
$786$	5.32882	+	1.53039i	0.190073	+	0.0545872i
$787$	2.21135	+	8.25288i	0.0788262	+	0.294183i	0.994074	−	0.108709i	$-0.0346716\pi$
$787$	2.21135	+	8.25288i	0.0788262	+	0.294183i	−0.915247	+	0.402892i	$0.868005\pi$
$788$	3.78938	+	14.1422i	0.134991	+	0.503793i
$789$	38.5477	−	37.1944i	1.37234	−	1.32416i
$790$	3.38782	+	4.28220i	0.120533	+	0.152354i
$791$	−14.2503	+	33.3647i	−0.506683	+	1.18631i
$792$	−8.67577	+	8.07693i	−0.308280	+	0.287001i
$793$	7.73429	+	28.8647i	0.274653	+	1.02502i
$794$	−37.3652			−1.32604
$795$	13.1267	−	1.68747i	0.465557	−	0.0598485i
$796$		−	18.5920i		−	0.658975i
$797$	24.0244	+	6.43733i	0.850990	+	0.228022i	0.657850	−	0.753149i	$-0.271466\pi$
$797$	24.0244	+	6.43733i	0.850990	+	0.228022i	0.193140	+	0.981171i	$0.438133\pi$
$798$	−7.11019	+	5.13722i	−0.251698	+	0.181856i
$799$	−4.34045	−	2.50596i	−0.153554	−	0.0886545i
$800$	2.37060	−	4.40230i	0.0838134	−	0.155645i
$801$	25.2619	−	40.3534i	0.892585	−	1.42582i
$802$	−0.978578	+	3.65210i	−0.0345548	+	0.128960i
$803$	1.15731	−	4.31916i	0.0408407	−	0.152420i
$804$	10.6676	+	3.06364i	0.376216	+	0.108046i
$805$	0.171065	+	0.0978855i	0.00602924	+	0.00345001i
$806$	5.67185	+	9.82393i	0.199782	+	0.346033i
$807$	−20.4084	−	36.8536i	−0.718410	−	1.29731i
$808$	3.83390	+	3.83390i	0.134876	+	0.134876i
$809$	−4.26327	+	2.46140i	−0.149889	+	0.0865383i	−0.573069	−	0.819507i	$-0.694247\pi$
$809$	−4.26327	+	2.46140i	−0.149889	+	0.0865383i	0.423180	+	0.906046i	$0.360914\pi$
$810$	1.49298	+	20.0692i	0.0524578	+	0.705158i
$811$			16.8988i			0.593398i	0.954971	+	0.296699i	$0.0958859\pi$
$811$			16.8988i			0.593398i	−0.954971	+	0.296699i	$0.904114\pi$
$812$	24.5263	−	9.84575i	0.860705	−	0.345518i
$813$	−2.15434	−	1.29567i	−0.0755561	−	0.0454411i
$814$			20.4777i			0.717744i
$815$	15.3353	+	19.3838i	0.537173	+	0.678986i
$816$	2.61904	+	10.5229i	0.0916847	+	0.368374i
$817$	3.66737	+	0.982668i	0.128305	+	0.0343792i
$818$	4.60537	+	4.60537i	0.161023	+	0.161023i
$819$	27.0966	+	12.7362i	0.946833	+	0.445040i
$820$	−19.4315	+	8.38820i	−0.678576	+	0.292929i
$821$	23.1227	+	40.0496i	0.806986	+	1.39774i	0.914942	+	0.403586i	$0.132236\pi$
$821$	23.1227	+	40.0496i	0.806986	+	1.39774i	−0.107955	+	0.994156i	$0.534430\pi$
$822$	9.49272	−	5.25679i	0.331097	−	0.183352i
$823$	−11.4050	−	42.5640i	−0.397553	−	1.48369i	−0.817387	−	0.576088i	$-0.804578\pi$
$823$	−11.4050	−	42.5640i	−0.397553	−	1.48369i	0.419834	−	0.907601i	$-0.362088\pi$
$824$	13.7161			0.477822
$825$	23.9095	−	24.4790i	0.832421	−	0.852248i
$826$	13.3540	−	10.0164i	0.464645	−	0.348514i
$827$	10.8889	+	10.8889i	0.378644	+	0.378644i	0.870613	−	0.491969i	$-0.163723\pi$
$827$	10.8889	+	10.8889i	0.378644	+	0.378644i	−0.491969	+	0.870613i	$0.663723\pi$
$828$	0.0974002	−	0.0224021i	0.00338489	−	0.000778525i
$829$	4.16509	+	7.21414i	0.144659	+	0.250558i	0.929246	−	0.369462i	$-0.120458\pi$
$829$	4.16509	+	7.21414i	0.144659	+	0.250558i	−0.784586	+	0.620020i	$0.787125\pi$
$830$	−13.9177	−	32.2406i	−0.483089	−	1.11909i
$831$	11.9045	+	12.3377i	0.412963	+	0.427989i
$832$	−3.64363	−	0.976306i	−0.126320	−	0.0338473i
$833$	−37.4644	−	22.7388i	−1.29807	−	0.787853i
$834$	23.0341	−	5.73296i	0.797606	−	0.198516i
$835$	32.5239	−	4.77311i	1.12554	−	0.165180i
$836$	6.54997	−	3.78163i	0.226536	−	0.130790i
$837$	−13.0945	−	8.52671i	−0.452612	−	0.294726i
$838$	23.5296	−	6.30473i	0.812816	−	0.217793i
$839$	12.7370	−	22.0611i	0.439729	−	0.761633i	−0.557939	−	0.829882i	$-0.688408\pi$
$839$	12.7370	−	22.0611i	0.439729	−	0.761633i	0.997668	+	0.0682488i	$0.0217412\pi$
$840$	8.80150	+	5.24724i	0.303681	+	0.181047i
$841$	35.3914	+	61.2997i	1.22039	+	2.11378i
$842$	−12.4541	−	12.4541i	−0.429198	−	0.429198i
$843$	22.0075	−	36.5925i	0.757979	−	1.26031i
$844$			18.3791i			0.632633i
$845$	2.73003	+	0.318340i	0.0939159	+	0.0109512i
$846$	−1.27433	+	2.03562i	−0.0438125	+	0.0699862i
$847$	−1.72505	+	12.0790i	−0.0592735	+	0.415039i
$848$	−0.884435	−	3.30076i	−0.0303716	−	0.113348i
$849$	−18.4040	+	4.58057i	−0.631623	+	0.157205i
$850$	−8.99433	−	29.9836i	−0.308503	−	1.02843i
$851$	0.0863293	−	0.149527i	0.00295933	−	0.00512571i
$852$	4.61892	+	2.77792i	0.158242	+	0.0951700i
$853$	29.0613	−	7.78694i	0.995039	−	0.266620i	0.275673	−	0.961251i	$-0.411099\pi$
$853$	29.0613	−	7.78694i	0.995039	−	0.266620i	0.719366	+	0.694632i	$0.244433\pi$
$854$	−20.8090	+	2.50796i	−0.712070	+	0.0858207i
$855$	1.94192	−	12.6930i	0.0664121	−	0.434093i
$856$	−7.90066	+	13.6843i	−0.270039	+	0.467721i
$857$	0.453500	−	0.453500i	0.0154913	−	0.0154913i	−0.699319	−	0.714810i	$-0.746513\pi$
$857$	0.453500	−	0.453500i	0.0154913	−	0.0154913i	0.714810	+	0.699319i	$0.246513\pi$
$858$	−22.1225	−	13.3050i	−0.755250	−	0.454224i
$859$	−46.3077			−1.58000			−0.789999	−	0.613108i	$-0.789919\pi$
$859$	−46.3077			−1.58000			−0.789999	+	0.613108i	$0.789919\pi$
$860$	−0.643997	−	4.38819i	−0.0219601	−	0.149636i
$861$	−15.4371	−	40.5347i	−0.526095	−	1.38142i
$862$	1.89761	−	0.508462i	0.0646327	−	0.0173183i
$863$	9.98720	+	37.2727i	0.339968	+	1.26878i	0.898382	+	0.439216i	$0.144744\pi$
$863$	9.98720	+	37.2727i	0.339968	+	1.26878i	−0.558413	+	0.829563i	$0.688590\pi$
$864$	5.08394	−	1.07405i	0.172959	−	0.0365401i
$865$	−1.38517	−	9.43851i	−0.0470971	−	0.320919i
$866$	−26.8362	+	15.4939i	−0.911930	+	0.526503i
$867$	32.9463	+	19.8146i	1.11891	+	0.672940i
$868$	−7.38362	+	2.96405i	−0.250616	+	0.100606i
$869$	8.35576	−	4.82420i	0.283450	−	0.163650i
$870$	−14.9141	+	35.6975i	−0.505634	+	1.21026i
$871$			24.1715i			0.819022i
$872$	−2.45284	+	9.15414i	−0.0830638	+	0.309998i
$873$	−11.9784	−	52.0801i	−0.405408	−	1.76264i
$874$	−0.0637698			−0.00215705
$875$	−26.0983	−	13.9240i	−0.882284	−	0.470717i
$876$	−1.41058	+	1.36106i	−0.0476590	+	0.0459858i
$877$	−16.8104	−	16.8104i	−0.567648	−	0.567648i	0.363821	−	0.931469i	$-0.381472\pi$
$877$	−16.8104	−	16.8104i	−0.567648	−	0.567648i	−0.931469	+	0.363821i	$0.881472\pi$
$878$	16.2412	−	4.35180i	0.548112	−	0.146866i
$879$	8.06401	−	28.0789i	0.271992	−	0.947077i
$880$	−7.08827	−	5.27402i	−0.238945	−	0.177787i
$881$		−	52.9619i		−	1.78433i	−0.451708	−	0.892166i	$-0.649185\pi$
$881$		−	52.9619i		−	1.78433i	0.451708	−	0.892166i	$-0.350815\pi$
$882$	−11.5303	+	17.5514i	−0.388245	+	0.590987i
$883$	−25.5270	+	25.5270i	−0.859052	+	0.859052i	−0.991226	−	0.132175i	$-0.957804\pi$
$883$	−25.5270	+	25.5270i	−0.859052	+	0.859052i	0.132175	+	0.991226i	$0.457804\pi$
$884$	−20.4524	+	11.8082i	−0.687890	+	0.397154i
$885$	−3.26339	+	24.2172i	−0.109697	+	0.814051i
$886$	−13.5221	+	23.4210i	−0.454285	+	0.786844i
$887$	−3.65392	+	3.65392i	−0.122687	+	0.122687i	−0.765784	−	0.643098i	$-0.777649\pi$
$887$	−3.65392	+	3.65392i	−0.122687	+	0.122687i	0.643098	+	0.765784i	$0.277649\pi$
$888$	4.62651	−	7.69262i	0.155256	−	0.258148i
$889$	17.2092	−	12.9081i	0.577179	−	0.432922i
$890$	32.9817	+	13.0924i	1.10555	+	0.438857i
$891$	35.4698	+	2.53906i	1.18828	+	0.0850618i
$892$	23.5572	+	6.31213i	0.788753	+	0.211346i
$893$	1.08355	−	1.08355i	0.0362595	−	0.0362595i
$894$	26.6788	+	7.66194i	0.892274	+	0.256254i
$895$	18.2853	−	24.5754i	0.611211	−	0.821467i
$896$	1.03920	−	2.43312i	0.0347173	−	0.0812847i
$897$	0.105446	+	0.190415i	0.00352075	+	0.00635777i
$898$	−11.0132	−	2.95099i	−0.367516	−	0.0984757i
$899$	−15.0197	−	26.0150i	−0.500937	−	0.867648i
$900$	−14.5123	+	3.79388i	−0.483743	+	0.126463i
$901$	−18.5278	−	10.6971i	−0.617252	−	0.356371i
$902$	9.67941	+	36.1240i	0.322289	+	1.20280i
$903$	9.04213	−	0.926229i	0.300903	−	0.0308230i
$904$	−11.8756	+	6.85637i	−0.394976	+	0.228040i
$905$	−11.1163	−	25.7512i	−0.369518	−	0.855998i
$906$	3.89878	−	13.5755i	0.129528	−	0.451017i
$907$	22.3050	+	22.3050i	0.740624	+	0.740624i	0.972698	−	0.232074i	$-0.0745511\pi$
$907$	22.3050	+	22.3050i	0.740624	+	0.740624i	−0.232074	+	0.972698i	$0.574551\pi$
$908$	5.63003	−	1.50856i	0.186839	−	0.0500633i
$909$	0.581072	−	16.2555i	0.0192729	−	0.539160i
$910$	−5.69262	+	21.5781i	−0.188709	+	0.715308i
$911$	−12.7553	+	22.0928i	−0.422601	+	0.731966i	−0.996193	−	0.0871750i	$-0.972216\pi$
$911$	−12.7553	+	22.0928i	−0.422601	+	0.731966i	0.573592	+	0.819141i	$0.305549\pi$
$912$	−3.31493	−	0.0592292i	−0.109768	−	0.00196127i
$913$	−59.9368	+	16.0600i	−1.98362	+	0.531509i
$914$	−1.58322	−	0.914074i	−0.0523684	−	0.0302349i
$915$	18.7520	−	24.2844i	0.619921	−	0.802817i
$916$	−2.78929	−	1.61040i	−0.0921608	−	0.0532091i
$917$	−8.38387	−	1.19734i	−0.276860	−	0.0395395i
$918$	17.7517	−	27.2614i	0.585895	−	0.899761i
$919$	−44.5695	−	25.7322i	−1.47021	−	0.848827i	−0.470770	−	0.882256i	$-0.656024\pi$
$919$	−44.5695	−	25.7322i	−1.47021	−	0.848827i	−0.999441	+	0.0334288i	$0.989357\pi$
$920$	0.0295239	+	0.0683929i	0.000973375	+	0.00225485i
$921$	−39.4918	+	38.1053i	−1.30130	+	1.25561i
$922$	−23.4707	+	23.4707i	−0.772965	+	0.772965i
$923$	−3.03814	+	11.3385i	−0.100002	+	0.373211i
$924$	11.4319	−	14.0413i	0.376083	−	0.461924i
$925$	−12.2861	+	22.8158i	−0.403965	+	0.750179i
$926$	−3.11430	+	5.39412i	−0.102342	+	0.177262i
$927$	−28.0382	−	30.1170i	−0.920895	−	0.989173i
$928$	9.64876	+	2.58538i	0.316736	+	0.0848692i
$929$	20.1096	+	34.8308i	0.659774	+	1.14276i	0.980674	+	0.195649i	$0.0626812\pi$
$929$	20.1096	+	34.8308i	0.659774	+	1.14276i	−0.320900	+	0.947113i	$0.603985\pi$
$930$	4.48986	−	10.7467i	0.147228	−	0.352398i
$931$	9.68002	−	9.26486i	0.317250	−	0.303643i
$932$	−1.79952	+	6.71592i	−0.0589454	+	0.219987i
$933$	28.5758	+	17.1861i	0.935531	+	0.562649i
$934$	−3.44218			−0.112632
$935$	−54.7278	+	8.03169i	−1.78979	+	0.262664i
$936$	5.30452	+	9.99623i	0.173384	+	0.326737i
$937$	42.4642	−	42.4642i	1.38725	−	1.38725i	0.556193	−	0.831053i	$-0.312262\pi$
$937$	42.4642	−	42.4642i	1.38725	−	1.38725i	0.831053	−	0.556193i	$-0.187738\pi$
$938$	−16.7834	−	2.39691i	−0.547996	−	0.0782618i
$939$	1.90349	−	6.62795i	0.0621181	−	0.216295i
$940$	−1.66376	−	0.660443i	−0.0542658	−	0.0215413i
$941$	7.90367	+	4.56319i	0.257652	+	0.148756i	0.623263	−	0.782012i	$-0.285807\pi$
$941$	7.90367	+	4.56319i	0.257652	+	0.148756i	−0.365611	+	0.930768i	$0.619140\pi$
$942$	−7.44114	−	0.132954i	−0.242446	−	0.00433187i
$943$	0.0816122	−	0.304581i	0.00265766	−	0.00991852i
$944$	6.30936			0.205352
$945$	−6.47029	−	30.0522i	−0.210479	−	0.977598i
$946$	−7.83706			−0.254805
$947$	−5.04104	+	18.8134i	−0.163812	+	0.611354i	0.834377	+	0.551194i	$0.185828\pi$
$947$	−5.04104	+	18.8134i	−0.163812	+	0.611354i	−0.998189	+	0.0601599i	$0.980839\pi$
$948$	−4.22884	−	0.0755583i	−0.137346	−	0.00245402i
$949$	−3.69700	−	2.13447i	−0.120010	−	0.0692877i
$950$	9.56671	−	0.283584i	0.310385	−	0.00920068i
$951$	6.85629	−	23.8736i	0.222330	−	0.774154i
$952$	−6.17086	−	15.3720i	−0.199999	−	0.498208i
$953$	−6.52614	+	6.52614i	−0.211402	+	0.211402i	−0.804863	−	0.593461i	$-0.797761\pi$
$953$	−6.52614	+	6.52614i	−0.211402	+	0.211402i	0.593461	+	0.804863i	$0.297761\pi$
$954$	−5.43968	+	8.68935i	−0.176116	+	0.281328i
$955$	10.3409	+	7.69413i	0.334624	+	0.248976i
$956$	14.6478			0.473743
$957$	58.5831	+	35.2331i	1.89372	+	1.13893i
$958$	6.89194	−	25.7211i	0.222668	−	0.831010i
$959$	−13.2598	+	9.94572i	−0.428181	+	0.321164i
$960$	1.47121	+	3.58267i	0.0474832	+	0.115630i
$961$	−10.9783	−	19.0150i	−0.354139	−	0.613388i
$962$	18.8838	+	5.05990i	0.608838	+	0.163138i
$963$	46.1978	−	10.6255i	1.48870	−	0.342402i
$964$	−3.96244	+	6.86314i	−0.127621	+	0.221047i
$965$	18.1788	+	22.9779i	0.585195	+	0.739685i
$966$	−0.142670	+	0.0543339i	−0.00459033	+	0.00174817i
$967$	−1.97798	+	7.38193i	−0.0636076	+	0.237387i	−0.990409	−	0.138164i	$-0.955880\pi$
$967$	−1.97798	+	7.38193i	−0.0636076	+	0.237387i	0.926802	+	0.375551i	$0.122547\pi$
$968$	−3.26100	+	3.26100i	−0.104813	+	0.104813i
$969$	−14.9374	+	14.4130i	−0.479859	+	0.463012i
$970$	36.5698	−	15.7865i	1.17419	−	0.506874i
$971$	22.6494	+	13.0766i	0.726852	+	0.419648i	0.817270	−	0.576256i	$-0.195487\pi$
$971$	22.6494	+	13.0766i	0.726852	+	0.419648i	−0.0904172	+	0.995904i	$0.528820\pi$
$972$	−12.7509	−	8.96747i	−0.408984	−	0.287632i
$973$	−33.6486	+	13.5077i	−1.07872	+	0.433038i
$974$	9.36671	+	5.40787i	0.300129	+	0.173279i
$975$	−16.6657	−	28.0970i	−0.533731	−	0.899824i
$976$	−6.86064	−	3.96099i	−0.219604	−	0.126788i
$977$	48.9599	−	13.1188i	1.56637	−	0.419707i	0.631695	−	0.775217i	$-0.282360\pi$
$977$	48.9599	−	13.1188i	1.56637	−	0.419707i	0.934672	+	0.355510i	$0.115693\pi$
$978$	−19.1423	−	0.342022i	−0.612102	−	0.0109367i
$979$	31.3515	−	54.3024i	1.00200	−	1.73551i
$980$	−14.4181	−	6.09237i	−0.460571	−	0.194614i
$981$	25.1142	−	13.3269i	0.801836	−	0.425496i
$982$	18.2361	−	4.88634i	0.581936	−	0.155929i
$983$	5.99626	+	5.99626i	0.191251	+	0.191251i	0.796237	−	0.604985i	$-0.206821\pi$
$983$	5.99626	+	5.99626i	0.191251	+	0.191251i	−0.604985	+	0.796237i	$0.706821\pi$
$984$	4.52532	−	15.7571i	0.144262	−	0.502320i
$985$	30.4286	+	12.0789i	0.969536	+	0.384866i
$986$	54.1606	−	31.2696i	1.72482	−	0.995827i
$987$	1.50096	−	3.34740i	0.0477761	−	0.106549i
$988$	−1.86883	−	6.97456i	−0.0594553	−	0.221890i
$989$	0.0572256	+	0.0330392i	0.00181967	+	0.00105059i
$990$	2.90933	+	26.3451i	0.0924645	+	0.837302i
$991$	13.3193	+	23.0696i	0.423100	+	0.732831i	0.996241	−	0.0866260i	$-0.0276085\pi$
$991$	13.3193	+	23.0696i	0.423100	+	0.732831i	−0.573141	+	0.819457i	$0.694275\pi$
$992$	−2.90475	−	0.778325i	−0.0922259	−	0.0247118i
$993$	12.7456	+	23.0161i	0.404470	+	0.730393i
$994$	−7.57156	−	3.23387i	−0.240155	−	0.102572i
$995$	−33.3534	−	24.8165i	−1.05737	−	0.786737i
$996$	26.1442	+	7.50838i	0.828410	+	0.237912i
$997$	12.9125	−	12.9125i	0.408943	−	0.408943i	−0.472427	−	0.881370i	$-0.656622\pi$
$997$	12.9125	−	12.9125i	0.408943	−	0.408943i	0.881370	+	0.472427i	$0.156622\pi$
$998$	11.8314	+	3.17023i	0.374518	+	0.100352i
$999$	−26.3485	+	5.56650i	−0.833630	+	0.176116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cg.a.187.48	yes	192
5.3	odd	4	inner	630.2.cg.a.313.12	yes	192
7.3	odd	6		630.2.bw.a.367.41	yes	192
9.4	even	3		630.2.bw.a.607.29	yes	192
35.3	even	12		630.2.bw.a.493.29	yes	192
45.13	odd	12		630.2.bw.a.103.41	✓	192
63.31	odd	6	inner	630.2.cg.a.157.12	yes	192
315.283	even	12	inner	630.2.cg.a.283.48	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.41	✓	192	45.13	odd	12
630.2.bw.a.367.41	yes	192	7.3	odd	6
630.2.bw.a.493.29	yes	192	35.3	even	12
630.2.bw.a.607.29	yes	192	9.4	even	3
630.2.cg.a.157.12	yes	192	63.31	odd	6	inner
630.2.cg.a.187.48	yes	192	1.1	even	1	trivial
630.2.cg.a.283.48	yes	192	315.283	even	12	inner
630.2.cg.a.313.12	yes	192	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.73177 + 0.0309423i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.05295 + 0.886221i) q^{5} +(0.478104 - 1.66476i) q^{6} +(-0.374056 + 2.61918i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99809 + 0.107170i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.73177 + 0.0309423i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.05295 + 0.886221i) q^{5} +(0.478104 - 1.66476i) q^{6} +(-0.374056 + 2.61918i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99809 + 0.107170i) q^{9} +(0.324681 + 2.21237i) q^{10} +3.95117 q^{11} +(-1.48429 - 0.892684i) q^{12} +(0.976306 - 3.64363i) q^{13} +(2.43312 + 1.03920i) q^{14} +(-3.58267 + 1.47121i) q^{15} +(0.500000 + 0.866025i) q^{16} +(6.04740 + 1.62039i) q^{17} +(0.879480 - 2.86819i) q^{18} +(-0.957091 + 1.65773i) q^{19} +(2.22102 + 0.258986i) q^{20} +(-0.728824 + 4.52425i) q^{21} +(1.02264 - 3.81654i) q^{22} +(-0.0235569 + 0.0235569i) q^{23} +(-1.24643 + 1.20267i) q^{24} +(3.42922 - 3.63874i) q^{25} +(-3.26678 - 1.88608i) q^{26} +(5.18869 + 0.278362i) q^{27} +(1.63353 - 2.08124i) q^{28} +(8.65084 + 4.99457i) q^{29} +(0.493818 + 3.84137i) q^{30} +(-2.60433 - 1.50361i) q^{31} +(0.965926 - 0.258819i) q^{32} +(6.84254 + 0.122258i) q^{33} +(3.13036 - 5.42195i) q^{34} +(-1.55325 - 5.70854i) q^{35} +(-2.54283 - 1.59185i) q^{36} +(-5.00610 + 1.34138i) q^{37} +(1.35353 + 1.35353i) q^{38} +(1.80348 - 6.27973i) q^{39} +(0.825003 - 2.07831i) q^{40} +(-8.19705 + 4.73257i) q^{41} +(4.18145 + 1.87495i) q^{42} +(-0.513362 - 1.91589i) q^{43} +(-3.42181 - 1.97559i) q^{44} +(-6.24990 + 2.43695i) q^{45} +(0.0166572 + 0.0288511i) q^{46} +(-0.773256 - 0.207193i) q^{47} +(0.839090 + 1.51523i) q^{48} +(-6.72016 - 1.95944i) q^{49} +(-2.62720 - 4.25415i) q^{50} +(10.4226 + 2.99328i) q^{51} +(-2.66732 + 2.66732i) q^{52} +(-3.30076 - 0.884435i) q^{53} +(1.61181 - 4.93985i) q^{54} +(-8.11156 + 3.50161i) q^{55} +(-1.58754 - 2.11653i) q^{56} +(-1.70876 + 2.84120i) q^{57} +(7.06338 - 7.06338i) q^{58} +(3.15468 - 5.46407i) q^{59} +(3.83829 + 0.517229i) q^{60} +(-6.86064 + 3.96099i) q^{61} +(-2.12642 + 2.12642i) q^{62} +(-1.40215 + 7.81242i) q^{63} -1.00000i q^{64} +(1.22475 + 8.34541i) q^{65} +(1.88907 - 6.57774i) q^{66} +(-6.18954 + 1.65848i) q^{67} +(-4.42700 - 4.42700i) q^{68} +(-0.0415241 + 0.0400662i) q^{69} +(-5.91604 + 0.0228458i) q^{70} -3.11188 q^{71} +(-2.19575 + 2.04419i) q^{72} +(0.292904 - 1.09313i) q^{73} +5.18270i q^{74} +(6.05123 - 6.19537i) q^{75} +(1.65773 - 0.957091i) q^{76} +(-1.47796 + 10.3488i) q^{77} +(-5.59897 - 3.36735i) q^{78} +(2.11476 - 1.22095i) q^{79} +(-1.79397 - 1.33480i) q^{80} +(8.97703 + 0.642610i) q^{81} +(2.44976 + 9.14262i) q^{82} +(-15.1694 + 4.06462i) q^{83} +(2.89330 - 3.55370i) q^{84} +(-13.8510 + 2.03274i) q^{85} -1.98348 q^{86} +(14.8268 + 8.91714i) q^{87} +(-2.79390 + 2.79390i) q^{88} +(7.93473 - 13.7434i) q^{89} +(0.736320 + 6.66767i) q^{90} +(9.17810 + 3.92004i) q^{91} +(0.0321793 - 0.00862241i) q^{92} +(-4.46358 - 2.68449i) q^{93} +(-0.400267 + 0.693283i) q^{94} +(0.495746 - 4.25143i) q^{95} +(1.68077 - 0.418328i) q^{96} +(-4.61042 - 17.2063i) q^{97} +(-3.63198 + 5.98404i) q^{98} +(11.8459 + 0.423448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50} + 24 q^{51} - 40 q^{53} + 8 q^{56} - 32 q^{57} + 24 q^{58} + 8 q^{60} + 36 q^{61} - 108 q^{63} - 8 q^{65} + 16 q^{71} - 8 q^{72} + 80 q^{77} - 16 q^{78} + 4 q^{81} - 168 q^{83} - 16 q^{86} + 36 q^{90} + 8 q^{92} - 60 q^{93} + 64 q^{95} - 12 q^{96} - 48 q^{98}+O(q^{100}) \) 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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