LMFDB - Embedded newform 430.2.l.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.392168 - 1.46359i) q^{3} -1.00000i q^{4} +(-2.07474 - 0.833933i) q^{5} +(0.757610 + 1.31222i) q^{6} +(1.23476 + 4.60819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.609775 + 0.352054i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.392168 - 1.46359i) q^{3} -1.00000i q^{4} +(-2.07474 - 0.833933i) q^{5} +(0.757610 + 1.31222i) q^{6} +(1.23476 + 4.60819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.609775 + 0.352054i) q^{9} +(2.05674 - 0.877385i) q^{10} -0.406610 q^{11} +(-1.46359 - 0.392168i) q^{12} +(0.411540 + 1.53589i) q^{13} +(-4.13159 - 2.38537i) q^{14} +(-2.03418 + 2.70953i) q^{15} -1.00000 q^{16} +(5.38666 - 1.44335i) q^{17} +(-0.680116 + 0.182236i) q^{18} +(-0.623534 - 1.07999i) q^{19} +(-0.833933 + 2.07474i) q^{20} +7.22874 q^{21} +(0.287517 - 0.287517i) q^{22} +(2.85984 + 0.766292i) q^{23} +(1.31222 - 0.757610i) q^{24} +(3.60911 + 3.46039i) q^{25} +(-1.37704 - 0.795034i) q^{26} +(3.96866 - 3.96866i) q^{27} +(4.60819 - 1.23476i) q^{28} +(0.822347 - 1.42435i) q^{29} +(-0.477543 - 3.35431i) q^{30} +(3.56580 + 6.17615i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.159459 + 0.595110i) q^{33} +(-2.78834 + 4.82955i) q^{34} +(1.28111 - 10.5905i) q^{35} +(0.352054 - 0.609775i) q^{36} +(6.18887 + 1.65830i) q^{37} +(1.20457 + 0.322765i) q^{38} +2.40930 q^{39} +(-0.877385 - 2.05674i) q^{40} -7.43479 q^{41} +(-5.11149 + 5.11149i) q^{42} +(-3.63469 - 5.45793i) q^{43} +0.406610i q^{44} +(-0.971537 - 1.23893i) q^{45} +(-2.56406 + 1.48036i) q^{46} +(0.817561 + 0.817561i) q^{47} +(-0.392168 + 1.46359i) q^{48} +(-13.6486 + 7.88002i) q^{49} +(-4.99889 + 0.105161i) q^{50} -8.44990i q^{51} +(1.53589 - 0.411540i) q^{52} +(4.53015 + 1.21385i) q^{53} +5.61254i q^{54} +(0.843611 + 0.339085i) q^{55} +(-2.38537 + 4.13159i) q^{56} +(-1.82520 + 0.489060i) q^{57} +(0.425678 + 1.58865i) q^{58} +10.0036i q^{59} +(2.70953 + 2.03418i) q^{60} +(-0.0709823 - 0.0409816i) q^{61} +(-6.88860 - 1.84580i) q^{62} +(-0.869404 + 3.24466i) q^{63} +1.00000i q^{64} +(0.426988 - 3.52977i) q^{65} +(-0.308052 - 0.533561i) q^{66} +(-2.61959 + 9.77645i) q^{67} +(-1.44335 - 5.38666i) q^{68} +(2.24307 - 3.88512i) q^{69} +(6.58274 + 8.39451i) q^{70} +(-9.12242 - 5.26683i) q^{71} +(0.182236 + 0.680116i) q^{72} +(-1.87778 + 0.503151i) q^{73} +(-5.54879 + 3.20359i) q^{74} +(6.47997 - 3.92521i) q^{75} +(-1.07999 + 0.623534i) q^{76} +(-0.502066 - 1.87374i) q^{77} +(-1.70363 + 1.70363i) q^{78} +(9.80286 + 5.65969i) q^{79} +(2.07474 + 0.833933i) q^{80} +(-3.19596 - 5.53556i) q^{81} +(5.25719 - 5.25719i) q^{82} +(6.04379 + 1.61943i) q^{83} -7.22874i q^{84} +(-12.3796 - 1.49753i) q^{85} +(6.42945 + 1.28923i) q^{86} +(-1.76216 - 1.76216i) q^{87} +(-0.287517 - 0.287517i) q^{88} +(-8.31721 - 14.4058i) q^{89} +(1.56304 + 0.189077i) q^{90} +(-6.56951 + 3.79291i) q^{91} +(0.766292 - 2.85984i) q^{92} +(10.4377 - 2.79679i) q^{93} -1.15621 q^{94} +(0.393031 + 2.76069i) q^{95} +(-0.757610 - 1.31222i) q^{96} +(-9.72677 - 9.72677i) q^{97} +(4.07900 - 15.2230i) q^{98} +(-0.247940 - 0.143149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.392168	−	1.46359i	0.226418	−	0.845004i	−0.755413	−	0.655249i	$-0.772564\pi$
$3$	0.392168	−	1.46359i	0.226418	−	0.845004i	0.981831	−	0.189756i	$-0.0607695\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−2.07474	−	0.833933i	−0.927853	−	0.372946i
$5$	−2.07474	−	0.833933i	−0.927853	−	0.372946i
$6$	0.757610	+	1.31222i	0.309293	+	0.535711i
$7$	1.23476	+	4.60819i	0.466696	+	1.74173i	0.651206	+	0.758901i	$0.274264\pi$
$7$	1.23476	+	4.60819i	0.466696	+	1.74173i	−0.184510	+	0.982831i	$0.559070\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.609775	+	0.352054i	0.203258	+	0.117351i
$10$	2.05674	−	0.877385i	0.650400	−	0.277453i
$11$	−0.406610			−0.122597			−0.0612987	−	0.998119i	$-0.519524\pi$
$11$	−0.406610			−0.122597			−0.0612987	+	0.998119i	$0.519524\pi$
$12$	−1.46359	−	0.392168i	−0.422502	−	0.113209i
$13$	0.411540	+	1.53589i	0.114141	+	0.425978i	0.999221	−	0.0394594i	$-0.0125636\pi$
$13$	0.411540	+	1.53589i	0.114141	+	0.425978i	−0.885081	+	0.465438i	$0.845897\pi$
$14$	−4.13159	−	2.38537i	−1.10421	−	0.637518i
$15$	−2.03418	+	2.70953i	−0.525224	+	0.699598i
$16$	−1.00000			−0.250000
$17$	5.38666	−	1.44335i	1.30646	−	0.350064i	0.462569	−	0.886583i	$-0.346928\pi$
$17$	5.38666	−	1.44335i	1.30646	−	0.350064i	0.843888	+	0.536519i	$0.180261\pi$
$18$	−0.680116	+	0.182236i	−0.160305	+	0.0429535i
$19$	−0.623534	−	1.07999i	−0.143048	−	0.247767i	0.785595	−	0.618741i	$-0.212357\pi$
$19$	−0.623534	−	1.07999i	−0.143048	−	0.247767i	−0.928643	+	0.370974i	$0.879024\pi$
$20$	−0.833933	+	2.07474i	−0.186473	+	0.463927i
$21$	7.22874			1.57744
$22$	0.287517	−	0.287517i	0.0612987	−	0.0612987i
$23$	2.85984	+	0.766292i	0.596318	+	0.159783i	0.544339	−	0.838865i	$-0.316781\pi$
$23$	2.85984	+	0.766292i	0.596318	+	0.159783i	0.0519787	+	0.998648i	$0.483447\pi$
$24$	1.31222	−	0.757610i	0.267856	−	0.154647i
$25$	3.60911	+	3.46039i	0.721822	+	0.692078i
$26$	−1.37704	−	0.795034i	−0.270059	−	0.155919i
$27$	3.96866	−	3.96866i	0.763770	−	0.763770i
$28$	4.60819	−	1.23476i	0.870866	−	0.233348i
$29$	0.822347	−	1.42435i	0.152706	−	0.264494i	−0.779515	−	0.626383i	$-0.784535\pi$
$29$	0.822347	−	1.42435i	0.152706	−	0.264494i	0.932221	+	0.361889i	$0.117868\pi$
$30$	−0.477543	−	3.35431i	−0.0871871	−	0.612411i
$31$	3.56580	+	6.17615i	0.640437	+	1.10927i	0.985335	+	0.170629i	$0.0545801\pi$
$31$	3.56580	+	6.17615i	0.640437	+	1.10927i	−0.344898	+	0.938640i	$0.612087\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.159459	+	0.595110i	−0.0277583	+	0.103595i
$34$	−2.78834	+	4.82955i	−0.478196	+	0.828261i
$35$	1.28111	−	10.5905i	0.216547	−	1.79012i
$36$	0.352054	−	0.609775i	0.0586756	−	0.101629i
$37$	6.18887	+	1.65830i	1.01744	+	0.272623i	0.728736	−	0.684794i	$-0.240108\pi$
$37$	6.18887	+	1.65830i	1.01744	+	0.272623i	0.288707	+	0.957417i	$0.406775\pi$
$38$	1.20457	+	0.322765i	0.195408	+	0.0523594i
$39$	2.40930			0.385797
$40$	−0.877385	−	2.05674i	−0.138727	−	0.325200i
$41$	−7.43479			−1.16112			−0.580560	−	0.814218i	$-0.697166\pi$
$41$	−7.43479			−1.16112			−0.580560	+	0.814218i	$0.697166\pi$
$42$	−5.11149	+	5.11149i	−0.788720	+	0.788720i
$43$	−3.63469	−	5.45793i	−0.554285	−	0.832327i
$43$	−3.63469	−	5.45793i	−0.554285	−	0.832327i
$44$			0.406610i			0.0612987i
$45$	−0.971537	−	1.23893i	−0.144828	−	0.184689i
$46$	−2.56406	+	1.48036i	−0.378050	+	0.218267i
$47$	0.817561	+	0.817561i	0.119254	+	0.119254i	0.764215	−	0.644962i	$-0.223127\pi$
$47$	0.817561	+	0.817561i	0.119254	+	0.119254i	−0.644962	+	0.764215i	$0.723127\pi$
$48$	−0.392168	+	1.46359i	−0.0566046	+	0.211251i
$49$	−13.6486	+	7.88002i	−1.94980	+	1.12572i
$50$	−4.99889	+	0.105161i	−0.706950	+	0.0148721i
$51$		−	8.44990i		−	1.18322i
$52$	1.53589	−	0.411540i	0.212989	−	0.0570703i
$53$	4.53015	+	1.21385i	0.622264	+	0.166735i	0.556157	−	0.831077i	$-0.312275\pi$
$53$	4.53015	+	1.21385i	0.622264	+	0.166735i	0.0661072	+	0.997813i	$0.478942\pi$
$54$			5.61254i			0.763770i
$55$	0.843611	+	0.339085i	0.113752	+	0.0457222i
$56$	−2.38537	+	4.13159i	−0.318759	+	0.552107i
$57$	−1.82520	+	0.489060i	−0.241753	+	0.0647776i
$58$	0.425678	+	1.58865i	0.0558942	+	0.208600i
$59$			10.0036i			1.30235i	0.758927	+	0.651176i	$0.225724\pi$
$59$			10.0036i			1.30235i	−0.758927	+	0.651176i	$0.774276\pi$
$60$	2.70953	+	2.03418i	0.349799	+	0.262612i
$61$	−0.0709823	−	0.0409816i	−0.00908835	−	0.00524716i	0.495449	−	0.868637i	$-0.335004\pi$
$61$	−0.0709823	−	0.0409816i	−0.00908835	−	0.00524716i	−0.504537	+	0.863390i	$0.668337\pi$
$62$	−6.88860	−	1.84580i	−0.874853	−	0.234416i
$63$	−0.869404	+	3.24466i	−0.109535	+	0.408789i
$64$			1.00000i			0.125000i
$65$	0.426988	−	3.52977i	0.0529613	−	0.437814i
$66$	−0.308052	−	0.533561i	−0.0379185	−	0.0656768i
$67$	−2.61959	+	9.77645i	−0.320034	+	1.19438i	0.599177	+	0.800617i	$0.295495\pi$
$67$	−2.61959	+	9.77645i	−0.320034	+	1.19438i	−0.919211	+	0.393766i	$0.871172\pi$
$68$	−1.44335	−	5.38666i	−0.175032	−	0.653228i
$69$	2.24307	−	3.88512i	0.270034	−	0.467713i
$70$	6.58274	+	8.39451i	0.786788	+	1.00334i
$71$	−9.12242	−	5.26683i	−1.08263	−	0.625058i	−0.151027	−	0.988530i	$-0.548258\pi$
$71$	−9.12242	−	5.26683i	−1.08263	−	0.625058i	−0.931605	+	0.363472i	$0.881591\pi$
$72$	0.182236	+	0.680116i	0.0214768	+	0.0801524i
$73$	−1.87778	+	0.503151i	−0.219778	+	0.0588894i	−0.367028	−	0.930210i	$-0.619625\pi$
$73$	−1.87778	+	0.503151i	−0.219778	+	0.0588894i	0.147250	+	0.989099i	$0.452958\pi$
$74$	−5.54879	+	3.20359i	−0.645033	+	0.372410i
$75$	6.47997	−	3.92521i	0.748243	−	0.453244i
$76$	−1.07999	+	0.623534i	−0.123884	+	0.0715242i
$77$	−0.502066	−	1.87374i	−0.0572157	−	0.213532i
$78$	−1.70363	+	1.70363i	−0.192899	+	0.192899i
$79$	9.80286	+	5.65969i	1.10291	+	0.636764i	0.936983	−	0.349374i	$-0.113606\pi$
$79$	9.80286	+	5.65969i	1.10291	+	0.636764i	0.165925	+	0.986138i	$0.446939\pi$
$80$	2.07474	+	0.833933i	0.231963	+	0.0932365i
$81$	−3.19596	−	5.53556i	−0.355106	−	0.615062i
$82$	5.25719	−	5.25719i	0.580560	−	0.580560i
$83$	6.04379	+	1.61943i	0.663392	+	0.177755i	0.574776	−	0.818311i	$-0.305089\pi$
$83$	6.04379	+	1.61943i	0.663392	+	0.177755i	0.0886155	+	0.996066i	$0.471756\pi$
$84$		−	7.22874i		−	0.788720i
$85$	−12.3796	−	1.49753i	−1.34276	−	0.162430i
$86$	6.42945	+	1.28923i	0.693306	+	0.139021i
$87$	−1.76216	−	1.76216i	−0.188924	−	0.188924i
$88$	−0.287517	−	0.287517i	−0.0306494	−	0.0306494i
$89$	−8.31721	−	14.4058i	−0.881623	−	1.52702i	−0.849536	−	0.527531i	$-0.823118\pi$
$89$	−8.31721	−	14.4058i	−0.881623	−	1.52702i	−0.0320869	−	0.999485i	$-0.510215\pi$
$90$	1.56304	+	0.189077i	0.164759	+	0.0199305i
$91$	−6.56951	+	3.79291i	−0.688671	+	0.397605i
$92$	0.766292	−	2.85984i	0.0798914	−	0.298159i
$93$	10.4377	−	2.79679i	1.08234	−	0.290013i
$94$	−1.15621			−0.119254
$95$	0.393031	+	2.76069i	0.0403241	+	0.283241i
$96$	−0.757610	−	1.31222i	−0.0773233	−	0.133928i
$97$	−9.72677	−	9.72677i	−0.987604	−	0.987604i	0.0123198	−	0.999924i	$-0.496078\pi$
$97$	−9.72677	−	9.72677i	−0.987604	−	0.987604i	−0.999924	+	0.0123198i	$0.996078\pi$
$98$	4.07900	−	15.2230i	0.412041	−	1.53776i
$99$	−0.247940	−	0.143149i	−0.0249190	−	0.0143870i
$100$	3.46039	−	3.60911i	0.346039	−	0.360911i
$101$	8.37106	−	14.4991i	0.832952	−	1.44272i	−0.0627351	−	0.998030i	$-0.519982\pi$
$101$	8.37106	−	14.4991i	0.832952	−	1.44272i	0.895687	−	0.444685i	$-0.146684\pi$
$102$	5.97498	+	5.97498i	0.591611	+	0.591611i
$103$	−0.768526	−	2.86818i	−0.0757251	−	0.282610i	0.917672	−	0.397340i	$-0.130066\pi$
$103$	−0.768526	−	2.86818i	−0.0757251	−	0.282610i	−0.993397	+	0.114730i	$0.963400\pi$
$104$	−0.795034	+	1.37704i	−0.0779595	+	0.135030i
$105$	−14.9978	−	6.02828i	−1.46363	−	0.588300i
$106$	−4.06162	+	2.34498i	−0.394500	+	0.227764i
$107$	1.79044	+	1.79044i	0.173089	+	0.173089i	0.788335	−	0.615246i	$-0.210943\pi$
$107$	1.79044	+	1.79044i	0.173089	+	0.173089i	−0.615246	+	0.788335i	$0.710943\pi$
$108$	−3.96866	−	3.96866i	−0.381885	−	0.381885i
$109$	−11.8460	+	6.83930i	−1.13464	+	0.655086i	−0.945098	−	0.326786i	$-0.894034\pi$
$109$	−11.8460	+	6.83930i	−1.13464	+	0.655086i	−0.189544	+	0.981872i	$0.560701\pi$
$110$	−0.836292	+	0.356753i	−0.0797373	+	0.0340151i
$111$	4.85415	−	8.40763i	0.460736	−	0.798017i
$112$	−1.23476	−	4.60819i	−0.116674	−	0.435433i
$113$	11.5494	+	11.5494i	1.08647	+	1.08647i	0.995889	+	0.0905825i	$0.0288729\pi$
$113$	11.5494	+	11.5494i	1.08647	+	1.08647i	0.0905825	+	0.995889i	$0.471127\pi$
$114$	0.944791	−	1.63643i	0.0884878	−	0.153265i
$115$	−5.29439	−	3.97477i	−0.493705	−	0.370649i
$116$	−1.42435	−	0.822347i	−0.132247	−	0.0763530i
$117$	−0.289768	+	1.08143i	−0.0267891	+	0.0999782i
$118$	−7.07358	−	7.07358i	−0.651176	−	0.651176i
$119$	13.3025	+	23.0406i	1.21944	+	2.11212i
$120$	−3.35431	+	0.477543i	−0.306205	+	0.0435935i
$121$	−10.8347			−0.984970
$122$	0.0791704	−	0.0212137i	0.00716776	−	0.00192059i
$123$	−2.91569	+	10.8815i	−0.262899	+	0.981151i
$124$	6.17615	−	3.56580i	0.554635	−	0.320219i
$125$	−4.60224	−	10.1892i	−0.411637	−	0.911348i
$126$	−1.67956	−	2.90908i	−0.149627	−	0.259162i
$127$	1.04962	+	1.04962i	0.0931388	+	0.0931388i	0.752141	−	0.659002i	$-0.229021\pi$
$127$	1.04962	+	1.04962i	0.0931388	+	0.0931388i	−0.659002	+	0.752141i	$0.729021\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−9.41359	+	3.17927i	−0.828820	+	0.279919i
$130$	2.19400	+	2.79785i	0.192426	+	0.245387i
$131$		−	15.1067i		−	1.31988i	−0.751318	−	0.659940i	$-0.770581\pi$
$131$		−	15.1067i		−	1.31988i	0.751318	−	0.659940i	$-0.229419\pi$
$132$	0.595110	+	0.159459i	0.0517977	+	0.0138792i
$133$	4.20689	−	4.20689i	0.364784	−	0.364784i
$134$	−5.06066	−	8.76532i	−0.437175	−	0.757209i
$135$	−11.5436	+	4.92436i	−0.993511	+	0.423821i
$136$	4.82955	+	2.78834i	0.414130	+	0.239098i
$137$	2.08800	−	2.08800i	0.178390	−	0.178390i	−0.612264	−	0.790653i	$-0.709741\pi$
$137$	2.08800	−	2.08800i	0.178390	−	0.178390i	0.790653	+	0.612264i	$0.209741\pi$
$138$	1.16110	+	4.33329i	0.0988394	+	0.368874i
$139$	−5.14163	+	2.96852i	−0.436107	+	0.251787i	−0.701945	−	0.712231i	$-0.747685\pi$
$139$	−5.14163	+	2.96852i	−0.436107	+	0.251787i	0.265838	+	0.964018i	$0.414351\pi$
$140$	−10.5905	−	1.28111i	−0.895062	−	0.108274i
$141$	1.51720	−	0.875953i	0.127771	−	0.0737686i
$142$	10.1747	−	2.72631i	0.853845	−	0.228787i
$143$	−0.167336	−	0.624507i	−0.0139933	−	0.0522239i
$144$	−0.609775	−	0.352054i	−0.0508146	−	0.0293378i
$145$	−2.89397	+	2.26937i	−0.240331	+	0.188461i
$146$	0.972013	−	1.68358i	0.0804444	−	0.139334i
$147$	6.18058	+	23.0663i	0.509766	+	1.90247i
$148$	1.65830	−	6.18887i	0.136312	−	0.508722i
$149$	−9.19116	−	15.9196i	−0.752969	−	1.30418i	−0.946378	−	0.323063i	$-0.895288\pi$
$149$	−9.19116	−	15.9196i	−0.752969	−	1.30418i	0.193408	−	0.981118i	$-0.438046\pi$
$150$	−1.80649	+	7.35757i	−0.147499	+	0.600743i
$151$			8.75960i			0.712846i	0.934325	+	0.356423i	$0.116004\pi$
$151$			8.75960i			0.712846i	−0.934325	+	0.356423i	$0.883996\pi$
$152$	0.322765	−	1.20457i	0.0261797	−	0.0977039i
$153$	3.79279	+	1.01627i	0.306629	+	0.0821609i
$154$	1.67995	+	0.969917i	0.135374	+	0.0781581i
$155$	−2.24763	−	15.7876i	−0.180534	−	1.26809i
$156$		−	2.40930i		−	0.192899i
$157$	−1.40304	−	5.23623i	−0.111975	−	0.417897i	0.887068	−	0.461639i	$-0.152739\pi$
$157$	−1.40304	−	5.23623i	−0.111975	−	0.417897i	−0.999043	+	0.0437426i	$0.986072\pi$
$158$	−10.9337	+	2.92967i	−0.869836	+	0.233072i
$159$	3.55316	−	6.15425i	0.281784	−	0.488064i
$160$	−2.05674	+	0.877385i	−0.162600	+	0.0693634i
$161$			14.1249i			1.11320i
$162$	6.17411	+	1.65435i	0.485084	+	0.129978i
$163$	12.8571	−	3.44504i	1.00704	−	0.269837i	0.282650	−	0.959223i	$-0.408786\pi$
$163$	12.8571	−	3.44504i	1.00704	−	0.269837i	0.724394	+	0.689386i	$0.242120\pi$
$164$			7.43479i			0.580560i
$165$	0.827119	−	1.10172i	0.0643911	−	0.0857689i
$166$	−5.41871	+	3.12849i	−0.420573	+	0.242818i
$167$	−3.18750	+	11.8959i	−0.246656	+	0.920533i	0.725888	+	0.687813i	$0.241429\pi$
$167$	−3.18750	+	11.8959i	−0.246656	+	0.920533i	−0.972544	+	0.232720i	$0.925237\pi$
$168$	5.11149	+	5.11149i	0.394360	+	0.394360i
$169$	9.06875	−	5.23584i	0.697596	−	0.402757i
$170$	9.81261	−	7.69478i	0.752593	−	0.590163i
$171$		−	0.878070i		−	0.0671477i
$172$	−5.45793	+	3.63469i	−0.416164	+	0.277142i
$173$	−1.04144	+	1.04144i	−0.0791791	+	0.0791791i	−0.745587	−	0.666408i	$-0.767831\pi$
$173$	−1.04144	+	1.04144i	−0.0791791	+	0.0791791i	0.666408	+	0.745587i	$0.267831\pi$
$174$	2.49207			0.188924
$175$	−11.4898	+	20.9042i	−0.868544	+	1.58021i
$176$	0.406610			0.0306494
$177$	14.6411	+	3.92307i	1.10049	+	0.294876i
$178$	16.0676	+	4.30531i	1.20432	+	0.322696i
$179$	7.37046	−	12.7660i	0.550894	−	0.954176i	−0.447316	−	0.894376i	$-0.647620\pi$
$179$	7.37046	−	12.7660i	0.550894	−	0.954176i	0.998210	−	0.0598007i	$-0.0190465\pi$
$180$	−1.23893	+	0.971537i	−0.0923445	+	0.0724141i
$181$	5.28694	−	9.15725i	0.392975	−	0.680653i	−0.599865	−	0.800101i	$-0.704779\pi$
$181$	5.28694	−	9.15725i	0.392975	−	0.680653i	0.992840	+	0.119448i	$0.0381125\pi$
$182$	1.96335	−	7.32733i	0.145533	−	0.543138i
$183$	−0.0878173	+	0.0878173i	−0.00649164	+	0.00649164i
$184$	1.48036	+	2.56406i	0.109134	+	0.189025i
$185$	−11.4574	−	8.60165i	−0.842364	−	0.632406i
$186$	−5.40298	+	9.35823i	−0.396165	+	0.686179i
$187$	−2.19027	+	0.586881i	−0.160168	+	0.0429170i
$188$	0.817561	−	0.817561i	0.0596268	−	0.0596268i
$189$	23.1887	+	13.3880i	1.68673	+	0.973834i
$190$	−2.23002	−	1.67419i	−0.161783	−	0.121458i
$191$	−10.8079	+	6.23996i	−0.782034	+	0.451507i	−0.837151	−	0.546973i	$-0.815780\pi$
$191$	−10.8079	+	6.23996i	−0.782034	+	0.451507i	0.0551169	+	0.998480i	$0.482447\pi$
$192$	1.46359	+	0.392168i	0.105626	+	0.0283023i
$193$	16.8719	−	16.8719i	1.21447	−	1.21447i	0.244925	−	0.969542i	$-0.421237\pi$
$193$	16.8719	−	16.8719i	1.21447	−	1.21447i	0.969542	−	0.244925i	$-0.0787634\pi$
$194$	13.7557			0.987604
$195$	−4.99868	−	2.00920i	−0.357963	−	0.143882i
$196$	7.88002	+	13.6486i	0.562859	+	0.974900i
$197$	−22.8916	+	6.13378i	−1.63096	+	0.437013i	−0.954194	−	0.299188i	$-0.903284\pi$
$197$	−22.8916	+	6.13378i	−1.63096	+	0.437013i	−0.676762	+	0.736202i	$0.736617\pi$
$198$	0.276542	−	0.0740991i	0.0196530	−	0.00526599i
$199$	20.9667			1.48629			0.743147	−	0.669129i	$-0.233332\pi$
$199$	20.9667			1.48629			0.743147	+	0.669129i	$0.233332\pi$
$200$	0.105161	+	4.99889i	0.00743603	+	0.353475i
$201$	13.2814	+	7.66802i	0.936797	+	0.540860i
$202$	4.33318	+	16.1717i	0.304882	+	1.13783i
$203$	7.57906	+	2.03080i	0.531946	+	0.142534i
$204$	−8.44990			−0.591611
$205$	15.4253	+	6.20012i	1.07735	+	0.433035i
$206$	2.57154	+	1.48468i	0.179168	+	0.103442i
$207$	1.47408	+	1.47408i	0.102456	+	0.102456i
$208$	−0.411540	−	1.53589i	−0.0285351	−	0.106495i
$209$	0.253535	+	0.439135i	0.0175374	+	0.0303756i
$210$	14.8677	−	6.34238i	1.02597	−	0.437666i
$211$		−	3.81064i		−	0.262335i	−0.991360	−	0.131168i	$-0.958127\pi$
$211$		−	3.81064i		−	0.262335i	0.991360	−	0.131168i	$-0.0418726\pi$
$212$	1.21385	−	4.53015i	0.0833676	−	0.311132i
$213$	−11.2860	+	11.2860i	−0.773304	+	0.773304i
$214$	−2.53207			−0.173089
$215$	2.98949	+	14.3549i	0.203881	+	0.978996i
$216$	5.61254			0.381885
$217$	−24.0580	+	24.0580i	−1.63316	+	1.63316i
$218$	3.54028	−	13.2125i	0.239778	−	0.894864i
$219$			2.94563i			0.199047i
$220$	0.339085	−	0.843611i	0.0228611	−	0.0568762i
$221$	4.43365	+	7.67931i	0.298239	+	0.516566i
$222$	2.51269	+	9.37750i	0.168641	+	0.629376i
$223$	2.90244	+	2.90244i	0.194362	+	0.194362i	0.797578	−	0.603216i	$-0.206114\pi$
$223$	2.90244	+	2.90244i	0.194362	+	0.194362i	−0.603216	+	0.797578i	$0.706114\pi$
$224$	4.13159	+	2.38537i	0.276053	+	0.159380i
$225$	0.982502	+	3.38066i	0.0655002	+	0.225377i
$226$	−16.3332			−1.08647
$227$	−22.7139	−	6.08618i	−1.50758	−	0.403954i	−0.591947	−	0.805977i	$-0.701641\pi$
$227$	−22.7139	−	6.08618i	−1.50758	−	0.403954i	−0.915630	+	0.402023i	$0.868307\pi$
$228$	0.489060	+	1.82520i	0.0323888	+	0.120877i
$229$	−4.10223	−	2.36842i	−0.271083	−	0.156510i	0.358297	−	0.933608i	$-0.383358\pi$
$229$	−4.10223	−	2.36842i	−0.271083	−	0.156510i	−0.629380	+	0.777098i	$0.716691\pi$
$230$	6.55429	−	0.933114i	0.432177	−	0.0615277i
$231$	−2.93928			−0.193390
$232$	1.58865	−	0.425678i	0.104300	−	0.0279471i
$233$	−21.6085	+	5.78999i	−1.41562	+	0.379315i	−0.883929	−	0.467621i	$-0.845111\pi$
$233$	−21.6085	+	5.78999i	−1.41562	+	0.379315i	−0.531694	+	0.846936i	$0.678444\pi$
$234$	−0.559789	−	0.969583i	−0.0365946	−	0.0633836i
$235$	−1.01444	−	2.37802i	−0.0661746	−	0.155125i
$236$	10.0036			0.651176
$237$	12.1278	−	12.1278i	0.787787	−	0.787787i
$238$	−25.6984	−	6.88587i	−1.66578	−	0.446344i
$239$	−8.44025	+	4.87298i	−0.545954	+	0.315207i	−0.747489	−	0.664275i	$-0.768741\pi$
$239$	−8.44025	+	4.87298i	−0.545954	+	0.315207i	0.201534	+	0.979481i	$0.435407\pi$
$240$	2.03418	−	2.70953i	0.131306	−	0.174900i
$241$	−9.12937	−	5.27085i	−0.588075	−	0.339525i	0.176261	−	0.984343i	$-0.443600\pi$
$241$	−9.12937	−	5.27085i	−0.588075	−	0.339525i	−0.764336	+	0.644818i	$0.776933\pi$
$242$	7.66127	−	7.66127i	0.492485	−	0.492485i
$243$	6.90875	−	1.85119i	0.443197	−	0.118754i
$244$	−0.0409816	+	0.0709823i	−0.00262358	+	0.00454417i
$245$	34.8887	−	4.96700i	2.22896	−	0.317330i
$246$	−5.63268	−	9.75608i	−0.359126	−	0.622025i
$247$	1.40214	−	1.40214i	0.0892159	−	0.0892159i
$248$	−1.84580	+	6.88860i	−0.117208	+	0.437427i
$249$	4.74036	−	8.21054i	0.300408	−	0.520322i
$250$	10.4591	+	3.95056i	0.661493	+	0.249855i
$251$	−11.2862	+	19.5483i	−0.712380	+	1.23388i	0.251582	+	0.967836i	$0.419049\pi$
$251$	−11.2862	+	19.5483i	−0.712380	+	1.23388i	−0.963961	+	0.266042i	$0.914284\pi$
$252$	3.24466	+	0.869404i	0.204394	+	0.0547673i
$253$	−1.16284	−	0.311582i	−0.0731070	−	0.0195890i
$254$	−1.48439			−0.0931388
$255$	−7.04665	+	17.5314i	−0.441278	+	1.09786i
$256$	1.00000			0.0625000
$257$	10.4542	−	10.4542i	0.652116	−	0.652116i	−0.301386	−	0.953502i	$-0.597449\pi$
$257$	10.4542	−	10.4542i	0.652116	−	0.652116i	0.953502	+	0.301386i	$0.0974493\pi$
$258$	4.40833	−	8.90449i	0.274451	−	0.554370i
$259$			30.5671i			1.89935i
$260$	−3.52977	−	0.426988i	−0.218907	−	0.0264807i
$261$	1.00289	−	0.579020i	0.0620775	−	0.0358405i
$262$	10.6821	+	10.6821i	0.659940	+	0.659940i
$263$	−5.01903	+	18.7313i	−0.309486	+	1.15502i	0.619528	+	0.784975i	$0.287324\pi$
$263$	−5.01903	+	18.7313i	−0.309486	+	1.15502i	−0.929014	+	0.370044i	$0.879343\pi$
$264$	−0.533561	+	0.308052i	−0.0328384	+	0.0189593i
$265$	−8.38662	−	6.29627i	−0.515186	−	0.386777i
$266$			5.94945i			0.364784i
$267$	−24.3460	+	6.52349i	−1.48995	+	0.399231i
$268$	9.77645	+	2.61959i	0.597192	+	0.160017i
$269$		−	18.5885i		−	1.13336i	−0.823938	−	0.566680i	$-0.808227\pi$
$269$		−	18.5885i		−	1.13336i	0.823938	−	0.566680i	$-0.191773\pi$
$270$	4.68048	−	11.6446i	0.284845	−	0.708666i
$271$	7.70740	−	13.3496i	0.468191	−	0.810931i	−0.531148	−	0.847279i	$-0.678239\pi$
$271$	7.70740	−	13.3496i	0.468191	−	0.810931i	0.999339	+	0.0363481i	$0.0115725\pi$
$272$	−5.38666	+	1.44335i	−0.326614	+	0.0875160i
$273$	2.97491	+	11.1025i	0.180050	+	0.671955i
$274$			2.95287i			0.178390i
$275$	−1.46750	−	1.40703i	−0.0884936	−	0.0848471i
$276$	−3.88512	−	2.24307i	−0.233857	−	0.135017i
$277$	−4.29110	−	1.14980i	−0.257827	−	0.0690847i	0.127590	−	0.991827i	$-0.459276\pi$
$277$	−4.29110	−	1.14980i	−0.257827	−	0.0690847i	−0.385417	+	0.922742i	$0.625943\pi$
$278$	1.53662	−	5.73474i	0.0921603	−	0.343947i
$279$			5.02142i			0.300624i
$280$	8.39451	−	6.58274i	0.501668	−	0.393394i
$281$	0.133766	+	0.231689i	0.00797981	+	0.0138214i	0.869988	−	0.493073i	$-0.164127\pi$
$281$	0.133766	+	0.231689i	0.00797981	+	0.0138214i	−0.862008	+	0.506895i	$0.830793\pi$
$282$	−0.453427	+	1.69221i	−0.0270012	+	0.100770i
$283$	−2.15094	−	8.02743i	−0.127860	−	0.477181i	0.872065	−	0.489390i	$-0.162780\pi$
$283$	−2.15094	−	8.02743i	−0.127860	−	0.477181i	−0.999925	+	0.0122086i	$0.996114\pi$
$284$	−5.26683	+	9.12242i	−0.312529	+	0.541316i
$285$	4.19466	+	0.507418i	0.248470	+	0.0300568i
$286$	0.559917	+	0.323268i	0.0331086	+	0.0191153i
$287$	−9.18019	−	34.2609i	−0.541890	−	2.02236i
$288$	0.680116	−	0.182236i	0.0400762	−	0.0107384i
$289$	12.2104	−	7.04969i	0.718260	−	0.414687i
$290$	0.441657	−	3.65103i	0.0259350	−	0.214396i
$291$	−18.0505	+	10.4215i	−1.05814	+	0.610918i
$292$	0.503151	+	1.87778i	0.0294447	+	0.109889i
$293$	11.3112	−	11.3112i	0.660807	−	0.660807i	−0.294763	−	0.955570i	$-0.595241\pi$
$293$	11.3112	−	11.3112i	0.660807	−	0.660807i	0.955570	+	0.294763i	$0.0952409\pi$
$294$	−20.6806	−	11.9400i	−1.20612	−	0.696353i
$295$	8.34229	−	20.7548i	0.485707	−	1.20839i
$296$	3.20359	+	5.54879i	0.186205	+	0.322517i
$297$	−1.61370	+	1.61370i	−0.0936362	+	0.0936362i
$298$	17.7560	+	4.75769i	1.02858	+	0.275606i
$299$			4.70775i			0.272256i
$300$	−3.92521	−	6.47997i	−0.226622	−	0.374121i
$301$	20.6632	−	23.4886i	1.19101	−	1.35386i
$302$	−6.19397	−	6.19397i	−0.356423	−	0.356423i
$303$	−17.9379	−	17.9379i	−1.03050	−	1.03050i
$304$	0.623534	+	1.07999i	0.0357621	+	0.0619418i
$305$	0.113094	+	0.144221i	0.00647574	+	0.00825806i
$306$	−3.40052	+	1.96329i	−0.194395	+	0.112234i
$307$	6.30950	−	23.5474i	0.360102	−	1.34392i	−0.513839	−	0.857887i	$-0.671777\pi$
$307$	6.30950	−	23.5474i	0.360102	−	1.34392i	0.873941	−	0.486032i	$-0.161556\pi$
$308$	−1.87374	+	0.502066i	−0.106766	+	0.0286079i
$309$	−4.49923			−0.255952
$310$	12.7528	+	9.57418i	0.724311	+	0.543777i
$311$	7.46482	+	12.9295i	0.423291	+	0.733162i	0.996259	−	0.0864158i	$-0.0275413\pi$
$311$	7.46482	+	12.9295i	0.423291	+	0.733162i	−0.572968	+	0.819578i	$0.694208\pi$
$312$	1.70363	+	1.70363i	0.0964493	+	0.0964493i
$313$	0.471014	−	1.75785i	0.0266233	−	0.0993595i	−0.951336	−	0.308156i	$-0.900288\pi$
$313$	0.471014	−	1.75785i	0.0266233	−	0.0993595i	0.977959	+	0.208797i	$0.0669547\pi$
$314$	4.69467	+	2.71047i	0.264936	+	0.152961i
$315$	4.50962	−	6.00681i	0.254088	−	0.338445i
$316$	5.65969	−	9.80286i	0.318382	−	0.551454i
$317$	5.31731	+	5.31731i	0.298650	+	0.298650i	0.840485	−	0.541835i	$-0.182270\pi$
$317$	5.31731	+	5.31731i	0.298650	+	0.298650i	−0.541835	+	0.840485i	$0.682270\pi$
$318$	1.83925	+	6.86418i	0.103140	+	0.384924i
$319$	−0.334374	+	0.579153i	−0.0187214	+	0.0324263i
$320$	0.833933	−	2.07474i	0.0466183	−	0.115982i
$321$	3.32263	−	1.91832i	0.185451	−	0.107070i
$322$	−9.98779	−	9.98779i	−0.556598	−	0.556598i
$323$	−4.91757	−	4.91757i	−0.273621	−	0.273621i
$324$	−5.53556	+	3.19596i	−0.307531	+	0.177553i
$325$	−3.82948	+	6.96728i	−0.212421	+	0.386475i
$326$	−6.65531	+	11.5273i	−0.368604	+	0.638440i
$327$	5.36431	+	20.0199i	0.296647	+	1.10710i
$328$	−5.25719	−	5.25719i	−0.290280	−	0.290280i
$329$	−2.75798	+	4.77697i	−0.152053	+	0.263363i
$330$	0.194174	+	1.36390i	0.0106889	+	0.0750800i
$331$	0.584128	+	0.337246i	0.0321066	+	0.0185367i	0.515967	−	0.856608i	$-0.327433\pi$
$331$	0.584128	+	0.337246i	0.0321066	+	0.0185367i	−0.483861	+	0.875145i	$0.660766\pi$
$332$	1.61943	−	6.04379i	0.0888776	−	0.331696i
$333$	3.19001	+	3.19001i	0.174811	+	0.174811i
$334$	−6.15778	−	10.6656i	−0.336938	−	0.583595i
$335$	13.5879	−	18.0990i	0.742385	−	0.988857i
$336$	−7.22874			−0.394360
$337$	−19.7092	+	5.28107i	−1.07363	+	0.287678i	−0.751984	−	0.659182i	$-0.770903\pi$
$337$	−19.7092	+	5.28107i	−1.07363	+	0.287678i	−0.321646	+	0.946860i	$0.604236\pi$
$338$	−2.71027	+	10.1149i	−0.147419	+	0.550177i
$339$	21.4328	−	12.3742i	1.16407	−	0.672076i
$340$	−1.49753	+	12.3796i	−0.0812150	+	0.671378i
$341$	−1.44989	−	2.51128i	−0.0785160	−	0.135994i
$342$	0.620889	+	0.620889i	0.0335738	+	0.0335738i
$343$	−29.5514	−	29.5514i	−1.59563	−	1.59563i
$344$	1.28923	−	6.42945i	0.0695107	−	0.346653i
$345$	−7.89373	+	6.19005i	−0.424984	+	0.333261i
$346$		−	1.47282i		−	0.0791791i
$347$	−7.76099	−	2.07955i	−0.416632	−	0.111636i	0.0444125	−	0.999013i	$-0.485858\pi$
$347$	−7.76099	−	2.07955i	−0.416632	−	0.111636i	−0.461044	+	0.887377i	$0.652525\pi$
$348$	−1.76216	+	1.76216i	−0.0944618	+	0.0944618i
$349$	6.89369	+	11.9402i	0.369011	+	0.639145i	0.989411	−	0.145140i	$-0.0463632\pi$
$349$	6.89369	+	11.9402i	0.369011	+	0.639145i	−0.620400	+	0.784285i	$0.713030\pi$
$350$	−6.65704	−	22.9060i	−0.355834	−	1.22438i
$351$	7.72868	+	4.46216i	0.412527	+	0.238172i
$352$	−0.287517	+	0.287517i	−0.0153247	+	0.0153247i
$353$	1.16063	+	4.33153i	0.0617741	+	0.230544i	0.989910	−	0.141697i	$-0.0452560\pi$
$353$	1.16063	+	4.33153i	0.0617741	+	0.230544i	−0.928136	+	0.372241i	$0.878589\pi$
$354$	−13.1269	+	7.57879i	−0.697684	+	0.402808i
$355$	14.5345	+	18.5348i	0.771411	+	0.983725i
$356$	−14.4058	+	8.31721i	−0.763508	+	0.440811i
$357$	38.9387	−	10.4336i	2.06086	−	0.552205i
$358$	3.81523	+	14.2386i	0.201641	+	0.752535i
$359$	9.07707	+	5.24065i	0.479069	+	0.276591i	0.720029	−	0.693944i	$-0.244129\pi$
$359$	9.07707	+	5.24065i	0.479069	+	0.276591i	−0.240959	+	0.970535i	$0.577462\pi$
$360$	0.189077	−	1.56304i	0.00996524	−	0.0823793i
$361$	8.72241	−	15.1077i	0.459074	−	0.795140i
$362$	2.73672	+	10.2136i	0.143839	+	0.536814i
$363$	−4.24901	+	15.8575i	−0.223015	+	0.832304i
$364$	3.79291	+	6.56951i	0.198802	+	0.344336i
$365$	4.31551	+	0.522038i	0.225884	+	0.0273247i
$366$		−	0.124192i		−	0.00649164i
$367$	8.11136	−	30.2720i	0.423409	−	1.58019i	−0.343963	−	0.938983i	$-0.611769\pi$
$367$	8.11136	−	30.2720i	0.423409	−	1.58019i	0.767372	−	0.641202i	$-0.221564\pi$
$368$	−2.85984	−	0.766292i	−0.149079	−	0.0399457i
$369$	−4.53355	−	2.61745i	−0.236007	−	0.136259i
$370$	14.1839	−	2.01932i	0.737385	−	0.104979i
$371$			22.3746i			1.16163i
$372$	−2.79679	−	10.4377i	−0.145007	−	0.541172i
$373$	−5.85356	+	1.56846i	−0.303086	+	0.0812116i	−0.407157	−	0.913358i	$-0.633480\pi$
$373$	−5.85356	+	1.56846i	−0.303086	+	0.0812116i	0.104071	+	0.994570i	$0.466813\pi$
$374$	1.13377	−	1.96374i	0.0586257	−	0.101543i
$375$	−16.7176	+	2.73993i	−0.863295	+	0.141489i
$376$			1.15621i			0.0596268i
$377$	2.52606	+	0.676857i	0.130099	+	0.0348599i
$378$	−25.8636	+	6.93014i	−1.33028	+	0.356448i
$379$		−	18.9726i		−	0.974559i	−0.873246	−	0.487280i	$-0.837989\pi$
$379$		−	18.9726i		−	0.974559i	0.873246	−	0.487280i	$-0.162011\pi$
$380$	2.76069	−	0.393031i	0.141620	−	0.0201621i
$381$	1.94784	−	1.12459i	0.0997910	−	0.0576144i
$382$	3.23004	−	12.0547i	0.165263	−	0.616771i
$383$	−18.0135	−	18.0135i	−0.920449	−	0.920449i	0.0766124	−	0.997061i	$-0.475590\pi$
$383$	−18.0135	−	18.0135i	−0.920449	−	0.920449i	−0.997061	+	0.0766124i	$0.975590\pi$
$384$	−1.31222	+	0.757610i	−0.0669639	+	0.0386616i
$385$	−0.520912	+	4.30621i	−0.0265481	+	0.219465i
$386$			23.8605i			1.21447i
$387$	−0.294855	−	4.60772i	−0.0149883	−	0.234223i
$388$	−9.72677	+	9.72677i	−0.493802	+	0.493802i
$389$	−28.1907			−1.42933			−0.714663	−	0.699469i	$-0.753420\pi$
$389$	−28.1907			−1.42933			−0.714663	+	0.699469i	$0.753420\pi$
$390$	4.95532	−	2.11389i	0.250922	−	0.107041i
$391$	16.5110			0.834998
$392$	−15.2230	−	4.07900i	−0.768879	−	0.206021i
$393$	−22.1101	−	5.92437i	−1.11531	−	0.298845i
$394$	11.8495	−	20.5240i	0.596971	−	1.03398i
$395$	−15.6186	−	19.9173i	−0.785858	−	1.00215i
$396$	−0.143149	+	0.247940i	−0.00719348	+	0.0124595i
$397$	0.392704	−	1.46559i	0.0197093	−	0.0735559i	−0.955371	−	0.295409i	$-0.904544\pi$
$397$	0.392704	−	1.46559i	0.0197093	−	0.0735559i	0.975080	+	0.221853i	$0.0712106\pi$
$398$	−14.8257	+	14.8257i	−0.743147	+	0.743147i
$399$	−4.50736	−	7.80698i	−0.225650	−	0.390838i
$400$	−3.60911	−	3.46039i	−0.180456	−	0.173020i
$401$	14.5126	−	25.1366i	0.724726	−	1.25526i	−0.234360	−	0.972150i	$-0.575299\pi$
$401$	14.5126	−	25.1366i	0.724726	−	1.25526i	0.959087	−	0.283113i	$-0.0913672\pi$
$402$	−14.8135	+	3.96926i	−0.738829	+	0.197969i
$403$	−8.01840	+	8.01840i	−0.399425	+	0.399425i
$404$	−14.4991	−	8.37106i	−0.721358	−	0.416476i
$405$	2.01450	+	14.1501i	0.100101	+	0.703122i
$406$	−6.79520	+	3.92321i	−0.337240	+	0.194706i
$407$	−2.51645	−	0.674282i	−0.124736	−	0.0334229i
$408$	5.97498	−	5.97498i	0.295806	−	0.295806i
$409$	1.42637			0.0705293			0.0352647	−	0.999378i	$-0.488773\pi$
$409$	1.42637			0.0705293			0.0352647	+	0.999378i	$0.488773\pi$
$410$	−15.2915	+	6.52318i	−0.755192	+	0.322157i
$411$	−2.23713	−	3.87482i	−0.110349	−	0.191131i
$412$	−2.86818	+	0.768526i	−0.141305	+	0.0378626i
$413$	−46.0983	+	12.3520i	−2.26835	+	0.607802i
$414$	−2.08467			−0.102456
$415$	−11.1888	−	8.40001i	−0.549237	−	0.412340i
$416$	1.37704	+	0.795034i	0.0675149	+	0.0389797i
$417$	2.32832	+	8.68939i	0.114018	+	0.425521i
$418$	−0.489792	−	0.131239i	−0.0239565	−	0.00641913i
$419$	−1.76150			−0.0860548			−0.0430274	−	0.999074i	$-0.513700\pi$
$419$	−1.76150			−0.0860548			−0.0430274	+	0.999074i	$0.513700\pi$
$420$	−6.02828	+	14.9978i	−0.294150	+	0.731816i
$421$	8.90465	+	5.14110i	0.433986	+	0.250562i	0.701043	−	0.713119i	$-0.252718\pi$
$421$	8.90465	+	5.14110i	0.433986	+	0.250562i	−0.267057	+	0.963681i	$0.586051\pi$
$422$	2.69453	+	2.69453i	0.131168	+	0.131168i
$423$	0.210703	+	0.786353i	0.0102447	+	0.0382338i
$424$	2.34498	+	4.06162i	0.113882	+	0.197250i
$425$	24.4356	+	13.4307i	1.18530	+	0.651486i
$426$		−	15.9608i		−	0.773304i
$427$	0.101205	−	0.377702i	0.00489765	−	0.0182783i
$428$	1.79044	−	1.79044i	0.0865444	−	0.0865444i
$429$	−0.979646			−0.0472978
$430$	−12.2643	−	8.03655i	−0.591439	−	0.387557i
$431$	32.3514			1.55831			0.779155	−	0.626831i	$-0.215648\pi$
$431$	32.3514			1.55831			0.779155	+	0.626831i	$0.215648\pi$
$432$	−3.96866	+	3.96866i	−0.190942	+	0.190942i
$433$	−5.05734	+	18.8743i	−0.243040	+	0.907039i	0.731318	+	0.682037i	$0.238906\pi$
$433$	−5.05734	+	18.8743i	−0.243040	+	0.907039i	−0.974358	+	0.225002i	$0.927761\pi$
$434$		−	34.0231i		−	1.63316i
$435$	2.18651	+	5.12556i	0.104835	+	0.245752i
$436$	6.83930	+	11.8460i	0.327543	+	0.567321i
$437$	−0.955617	−	3.56641i	−0.0457134	−	0.170605i
$438$	−2.08287	−	2.08287i	−0.0995235	−	0.0995235i
$439$	31.7391	+	18.3246i	1.51483	+	0.874585i	0.999849	+	0.0173809i	$0.00553280\pi$
$439$	31.7391	+	18.3246i	1.51483	+	0.874585i	0.514977	+	0.857204i	$0.327801\pi$
$440$	0.356753	+	0.836292i	0.0170075	+	0.0398687i
$441$	−11.0968			−0.528417
$442$	−8.56515	−	2.29503i	−0.407403	−	0.109163i
$443$	8.85269	+	33.0387i	0.420604	+	1.56972i	0.773340	+	0.633992i	$0.218585\pi$
$443$	8.85269	+	33.0387i	0.420604	+	1.56972i	−0.352736	+	0.935723i	$0.614749\pi$
$444$	−8.40763	−	4.85415i	−0.399009	−	0.230368i
$445$	5.24258	+	36.8244i	0.248522	+	1.74564i
$446$	−4.10467			−0.194362
$447$	−26.9042	+	7.20896i	−1.27252	+	0.340972i
$448$	−4.60819	+	1.23476i	−0.217717	+	0.0583370i
$449$	1.77362	+	3.07201i	0.0837025	+	0.144977i	0.904838	−	0.425757i	$-0.139992\pi$
$449$	1.77362	+	3.07201i	0.0837025	+	0.144977i	−0.821135	+	0.570734i	$0.806659\pi$
$450$	−3.08522	−	1.69575i	−0.145439	−	0.0799386i
$451$	3.02306			0.142350
$452$	11.5494	−	11.5494i	0.543236	−	0.543236i
$453$	12.8205	+	3.43523i	0.602358	+	0.161401i
$454$	20.3648	−	11.7576i	0.955766	−	0.551811i
$455$	16.7931	−	2.39078i	0.787271	−	0.112081i
$456$	−1.63643	−	0.944791i	−0.0766327	−	0.0442439i
$457$	−17.9598	+	17.9598i	−0.840125	+	0.840125i	−0.988875	−	0.148750i	$-0.952475\pi$
$457$	−17.9598	+	17.9598i	−0.840125	+	0.840125i	0.148750	+	0.988875i	$0.452475\pi$
$458$	4.57544	−	1.22599i	0.213796	−	0.0572865i
$459$	15.6497	−	27.1060i	0.730464	−	1.26520i
$460$	−3.97477	+	5.29439i	−0.185325	+	0.246852i
$461$	−12.3940	−	21.4670i	−0.577245	−	0.999817i	−0.995794	−	0.0916230i	$-0.970795\pi$
$461$	−12.3940	−	21.4670i	−0.577245	−	0.999817i	0.418549	−	0.908194i	$-0.362539\pi$
$462$	2.07838	−	2.07838i	0.0966950	−	0.0966950i
$463$	4.44764	−	16.5988i	0.206699	−	0.771413i	−0.782225	−	0.622996i	$-0.785915\pi$
$463$	4.44764	−	16.5988i	0.206699	−	0.771413i	0.988925	−	0.148417i	$-0.0474179\pi$
$464$	−0.822347	+	1.42435i	−0.0381765	+	0.0661236i
$465$	−23.9880	−	2.90177i	−1.11242	−	0.134566i
$466$	11.1854	−	19.3737i	0.518154	−	0.897469i
$467$	30.5190	+	8.17753i	1.41225	+	0.378411i	0.882727	−	0.469885i	$-0.155705\pi$
$467$	30.5190	+	8.17753i	1.41225	+	0.378411i	0.529522	+	0.848296i	$0.322371\pi$
$468$	1.08143	+	0.289768i	0.0499891	+	0.0133945i
$469$	−48.2863			−2.22965
$470$	2.39883	+	0.964198i	0.110650	+	0.0444751i
$471$	−8.21392			−0.378478
$472$	−7.07358	+	7.07358i	−0.325588	+	0.325588i
$473$	1.47790	+	2.21925i	0.0679539	+	0.102041i
$474$			17.1513i			0.787787i
$475$	1.48679	−	6.05548i	0.0682187	−	0.277845i
$476$	23.0406	−	13.3025i	1.05606	−	0.609718i
$477$	2.33503	+	2.33503i	0.106914	+	0.106914i
$478$	2.52244	−	9.41387i	0.115374	−	0.430581i
$479$	−2.70816	+	1.56356i	−0.123739	+	0.0714409i	−0.560592	−	0.828092i	$-0.689426\pi$
$479$	−2.70816	+	1.56356i	−0.123739	+	0.0714409i	0.436853	+	0.899533i	$0.356093\pi$
$480$	0.477543	+	3.35431i	0.0217968	+	0.153103i
$481$			10.1879i			0.464526i
$482$	10.1825	−	2.72839i	0.463800	−	0.124275i
$483$	20.6730	+	5.53932i	0.940655	+	0.252048i
$484$			10.8347i			0.492485i
$485$	12.0691	+	28.2920i	0.548028	+	1.28467i
$486$	−3.57623	+	6.19422i	−0.162221	+	0.280975i
$487$	34.7328	−	9.30662i	1.57389	−	0.421723i	0.636863	−	0.770977i	$-0.280231\pi$
$487$	34.7328	−	9.30662i	1.57389	−	0.421723i	0.937028	+	0.349254i	$0.113565\pi$
$488$	−0.0212137	−	0.0791704i	−0.000960297	−	0.00358388i
$489$		−	20.1685i		−	0.912053i
$490$	−21.1579	+	28.1823i	−0.955815	+	1.27315i
$491$	−10.6042	−	6.12234i	−0.478561	−	0.276297i	0.241256	−	0.970462i	$-0.422441\pi$
$491$	−10.6042	−	6.12234i	−0.478561	−	0.276297i	−0.719817	+	0.694164i	$0.755774\pi$
$492$	10.8815	+	2.91569i	0.490576	+	0.131449i
$493$	2.37387	−	8.85940i	0.106914	−	0.399007i
$494$			1.98292i			0.0892159i
$495$	0.395036	+	0.503762i	0.0177556	+	0.0226424i
$496$	−3.56580	−	6.17615i	−0.160109	−	0.277317i
$497$	13.0066	−	48.5411i	0.583424	−	2.17737i
$498$	2.45379	+	9.15767i	0.109957	+	0.410365i
$499$	−12.9038	+	22.3500i	−0.577653	+	1.00052i	0.418095	+	0.908404i	$0.362698\pi$
$499$	−12.9038	+	22.3500i	−0.577653	+	1.00052i	−0.995748	+	0.0921213i	$0.970635\pi$
$500$	−10.1892	+	4.60224i	−0.455674	+	0.205819i
$501$	16.1607	+	9.33039i	0.722007	+	0.416851i
$502$	−5.84218	−	21.8033i	−0.260749	−	0.973129i
$503$	−14.5345	+	3.89451i	−0.648061	+	0.173647i	−0.567852	−	0.823131i	$-0.692225\pi$
$503$	−14.5345	+	3.89451i	−0.648061	+	0.173647i	−0.0802089	+	0.996778i	$0.525559\pi$
$504$	−2.90908	+	1.67956i	−0.129581	+	0.0748136i
$505$	−29.4591	+	23.1010i	−1.31091	+	1.02798i
$506$	1.04257	−	0.601930i	0.0463480	−	0.0267590i
$507$	−4.10666	−	15.3263i	−0.182383	−	0.680663i
$508$	1.04962	−	1.04962i	0.0465694	−	0.0465694i
$509$	4.23269	+	2.44374i	0.187610	+	0.108317i	0.590863	−	0.806772i	$-0.298787\pi$
$509$	4.23269	+	2.44374i	0.187610	+	0.108317i	−0.403253	+	0.915089i	$0.632121\pi$
$510$	−7.41381	−	17.3793i	−0.328289	−	0.769568i
$511$	−4.63723	−	8.03192i	−0.205139	−	0.355311i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.76072	−	1.81153i	−0.298493	−	0.0799810i
$514$			14.7845i			0.652116i
$515$	−0.797374	+	6.59163i	−0.0351365	+	0.290462i
$516$	3.17927	+	9.41359i	0.139959	+	0.414410i
$517$	−0.332428	−	0.332428i	−0.0146202	−	0.0146202i
$518$	−21.6142	−	21.6142i	−0.949673	−	0.949673i
$519$	1.11582	+	1.93266i	0.0489791	+	0.0848343i
$520$	2.79785	−	2.19400i	0.122694	−	0.0962131i
$521$	5.45087	−	3.14706i	0.238807	−	0.137875i	−0.375821	−	0.926692i	$-0.622639\pi$
$521$	5.45087	−	3.14706i	0.238807	−	0.137875i	0.614628	+	0.788817i	$0.289306\pi$
$522$	−0.299723	+	1.11858i	−0.0131185	+	0.0489590i
$523$	28.8571	−	7.73224i	1.26183	−	0.338107i	0.434936	−	0.900461i	$-0.356771\pi$
$523$	28.8571	−	7.73224i	1.26183	−	0.338107i	0.826897	+	0.562354i	$0.190104\pi$
$524$	−15.1067			−0.659940
$525$	26.0893	+	25.0143i	1.13863	+	1.09171i
$526$	−9.69601	−	16.7940i	−0.422766	−	0.732253i
$527$	28.1221	+	28.1221i	1.22502	+	1.22502i
$528$	0.159459	−	0.595110i	0.00693958	−	0.0258988i
$529$	−12.3271	−	7.11706i	−0.535961	−	0.309437i
$530$	10.3824	−	1.47811i	0.450981	−	0.0642048i
$531$	−3.52179	+	6.09992i	−0.152833	+	0.264714i
$532$	−4.20689	−	4.20689i	−0.182392	−	0.182392i
$533$	−3.05971	−	11.4190i	−0.132531	−	0.494612i
$534$	12.6024	−	21.8280i	0.545360	−	0.944591i
$535$	−2.22160	−	5.20782i	−0.0960481	−	0.225154i
$536$	−8.76532	+	5.06066i	−0.378604	+	0.218587i
$537$	−15.7938	−	15.7938i	−0.681551	−	0.681551i
$538$	13.1441	+	13.1441i	0.566680	+	0.566680i
$539$	5.54966	−	3.20410i	0.239041	−	0.138010i
$540$	4.92436	+	11.5436i	0.211911	+	0.496756i
$541$	2.04858	−	3.54825i	0.0880754	−	0.152551i	−0.818622	−	0.574332i	$-0.805262\pi$
$541$	2.04858	−	3.54825i	0.0880754	−	0.152551i	0.906698	+	0.421781i	$0.138595\pi$
$542$	3.98964	+	14.8896i	0.171370	+	0.639561i
$543$	−11.3291	−	11.3291i	−0.486178	−	0.486178i
$544$	2.78834	−	4.82955i	0.119549	−	0.207065i
$545$	30.2810	−	4.31101i	1.29709	−	0.184663i
$546$	−9.95425	−	5.74709i	−0.426003	−	0.245953i
$547$	−7.86630	+	29.3574i	−0.336339	+	1.25523i	0.566072	+	0.824356i	$0.308462\pi$
$547$	−7.86630	+	29.3574i	−0.336339	+	1.25523i	−0.902411	+	0.430877i	$0.858204\pi$
$548$	−2.08800	−	2.08800i	−0.0891948	−	0.0891948i
$549$	−0.0288555	−	0.0499792i	−0.00123152	−	0.00213306i
$550$	2.03260	−	0.0427596i	0.0866703	−	0.00182328i
$551$	−2.05104			−0.0873774
$552$	4.33329	−	1.16110i	0.184437	−	0.0494197i
$553$	−13.9767	+	52.1618i	−0.594350	+	2.21815i
$554$	3.84730	−	2.22124i	0.163456	−	0.0943714i
$555$	−17.0825	+	13.3956i	−0.725112	+	0.568613i
$556$	2.96852	+	5.14163i	0.125893	+	0.218054i
$557$	22.9673	+	22.9673i	0.973157	+	0.973157i	0.999649	−	0.0264916i	$-0.00843352\pi$
$557$	22.9673	+	22.9673i	0.973157	+	0.973157i	−0.0264916	+	0.999649i	$0.508434\pi$
$558$	−3.55068	−	3.55068i	−0.150312	−	0.150312i
$559$	6.88695	−	7.82863i	0.291287	−	0.331116i
$560$	−1.28111	+	10.5905i	−0.0541368	+	0.447531i
$561$			3.43581i			0.145060i
$562$	−0.258416	−	0.0692424i	−0.0109006	−	0.00292081i
$563$	−4.83082	+	4.83082i	−0.203595	+	0.203595i	−0.801538	−	0.597943i	$-0.795985\pi$
$563$	−4.83082	+	4.83082i	−0.203595	+	0.203595i	0.597943	+	0.801538i	$0.295985\pi$
$564$	−0.875953	−	1.51720i	−0.0368843	−	0.0638854i
$565$	−14.3305	−	33.5933i	−0.602891	−	1.41328i
$566$	7.19720	+	4.15530i	0.302521	+	0.174660i
$567$	21.5627	−	21.5627i	0.905546	−	0.905546i
$568$	−2.72631	−	10.1747i	−0.114394	−	0.426923i
$569$	−12.6227	+	7.28772i	−0.529172	+	0.305517i	−0.740679	−	0.671859i	$-0.765496\pi$
$569$	−12.6227	+	7.28772i	−0.529172	+	0.305517i	0.211508	+	0.977376i	$0.432163\pi$
$570$	−3.32487	+	2.60727i	−0.139263	+	0.109207i
$571$	31.4193	−	18.1400i	1.31486	−	0.759134i	0.331961	−	0.943293i	$-0.392290\pi$
$571$	31.4193	−	18.1400i	1.31486	−	0.759134i	0.982896	+	0.184159i	$0.0589563\pi$
$572$	−0.624507	+	0.167336i	−0.0261119	+	0.00699667i
$573$	4.89422	+	18.2655i	0.204459	+	0.763051i
$574$	30.7175	+	17.7348i	1.28212	+	0.740235i
$575$	7.66981	+	12.6618i	0.319853	+	0.528033i
$576$	−0.352054	+	0.609775i	−0.0146689	+	0.0254073i
$577$	−1.45093	−	5.41495i	−0.0604030	−	0.225427i	0.929126	−	0.369765i	$-0.120562\pi$
$577$	−1.45093	−	5.41495i	−0.0604030	−	0.225427i	−0.989529	+	0.144337i	$0.953895\pi$
$578$	−3.64919	+	13.6189i	−0.151786	+	0.566473i
$579$	−18.0770	−	31.3102i	−0.751252	−	1.30121i
$580$	2.26937	+	2.89397i	0.0942304	+	0.120165i
$581$			29.8505i			1.23841i
$582$	5.39456	−	20.1328i	0.223612	−	0.834530i
$583$	−1.84200	−	0.493563i	−0.0762880	−	0.0204413i
$584$	−1.68358	−	0.972013i	−0.0696669	−	0.0402222i
$585$	1.50303	−	2.00204i	0.0621428	−	0.0827742i
$586$			15.9964i			0.660807i
$587$	−2.42276	−	9.04186i	−0.0999979	−	0.373197i	0.897732	−	0.440542i	$-0.145214\pi$
$587$	−2.42276	−	9.04186i	−0.0999979	−	0.373197i	−0.997730	+	0.0673450i	$0.978547\pi$
$588$	23.0663	−	6.18058i	0.951236	−	0.254883i
$589$	4.44680	−	7.70208i	0.183227	−	0.317359i
$590$	8.77697	+	20.5747i	0.361342	+	0.847049i
$591$			35.9093i			1.47711i
$592$	−6.18887	−	1.65830i	−0.254361	−	0.0681558i
$593$	25.1443	−	6.73740i	1.03255	−	0.276672i	0.297529	−	0.954713i	$-0.403837\pi$
$593$	25.1443	−	6.73740i	1.03255	−	0.276672i	0.735024	+	0.678041i	$0.237171\pi$
$594$		−	2.28211i		−	0.0936362i
$595$	−8.38493	−	58.8966i	−0.343748	−	2.41452i
$596$	−15.9196	+	9.19116i	−0.652090	+	0.376485i
$597$	8.22248	−	30.6867i	0.336524	−	1.25592i
$598$	−3.32888	−	3.32888i	−0.136128	−	0.136128i
$599$	−11.1109	+	6.41490i	−0.453980	+	0.262106i	−0.709510	−	0.704696i	$-0.751084\pi$
$599$	−11.1109	+	6.41490i	−0.453980	+	0.262106i	0.255530	+	0.966801i	$0.417750\pi$
$600$	7.35757	+	1.80649i	0.300372	+	0.0737497i
$601$		−	43.6014i		−	1.77854i	−0.457386	−	0.889268i	$-0.651214\pi$
$601$		−	43.6014i		−	1.77854i	0.457386	−	0.889268i	$-0.348786\pi$
$602$	1.99782	+	31.2200i	0.0814250	+	1.27243i
$603$	−5.03920	+	5.03920i	−0.205212	+	0.205212i
$604$	8.75960			0.356423
$605$	22.4791	+	9.03539i	0.913907	+	0.367341i
$606$	25.3680			1.03050
$607$	−46.8649	−	12.5574i	−1.90219	−	0.509689i	−0.996276	−	0.0862176i	$-0.972522\pi$
$607$	−46.8649	−	12.5574i	−1.90219	−	0.509689i	−0.905909	−	0.423472i	$-0.860811\pi$
$608$	−1.20457	−	0.322765i	−0.0488520	−	0.0130898i
$609$	5.94453	−	10.2962i	0.240884	−	0.417224i
$610$	−0.181949	−	0.0220100i	−0.00736690	−	0.000891157i
$611$	−0.919222	+	1.59214i	−0.0371878	+	0.0644111i
$612$	1.01627	−	3.79279i	0.0410805	−	0.153314i
$613$	−3.50469	+	3.50469i	−0.141553	+	0.141553i	−0.774332	−	0.632779i	$-0.781914\pi$
$613$	−3.50469	+	3.50469i	−0.141553	+	0.141553i	0.632779	+	0.774332i	$0.281914\pi$
$614$	12.1890	+	21.1120i	0.491908	+	0.852010i
$615$	15.1237	−	20.1448i	0.609848	−	0.812317i
$616$	0.969917	−	1.67995i	0.0390791	−	0.0676869i
$617$	−26.0951	+	6.99215i	−1.05055	+	0.281493i	−0.742478	−	0.669871i	$-0.766350\pi$
$617$	−26.0951	+	6.99215i	−1.05055	+	0.281493i	−0.308069	+	0.951364i	$0.599683\pi$
$618$	3.18143	−	3.18143i	0.127976	−	0.127976i
$619$	−0.416535	−	0.240487i	−0.0167419	−	0.00966597i	0.491606	−	0.870818i	$-0.336410\pi$
$619$	−0.416535	−	0.240487i	−0.0167419	−	0.00966597i	−0.508348	+	0.861152i	$0.669743\pi$
$620$	−15.7876	+	2.24763i	−0.634044	+	0.0902669i
$621$	14.3909	−	8.30859i	0.577487	−	0.333412i
$622$	−14.4209	−	3.86408i	−0.578227	−	0.154935i
$623$	56.1151	−	56.1151i	2.24820	−	2.24820i
$624$	−2.40930			−0.0964493
$625$	1.05138	+	24.9779i	0.0420552	+	0.999115i
$626$	0.909929	+	1.57604i	0.0363681	+	0.0629914i
$627$	0.742143	−	0.198857i	0.0296383	−	0.00794157i
$628$	−5.23623	+	1.40304i	−0.208948	+	0.0559875i
$629$	35.7308			1.42468
$630$	1.05867	+	7.43624i	0.0421786	+	0.296267i
$631$	−28.2822	−	16.3287i	−1.12590	−	0.650037i	−0.182997	−	0.983113i	$-0.558580\pi$
$631$	−28.2822	−	16.3287i	−1.12590	−	0.650037i	−0.942900	+	0.333076i	$0.891913\pi$
$632$	2.92967	+	10.9337i	0.116536	+	0.434918i
$633$	−5.57721	−	1.49441i	−0.221674	−	0.0593974i
$634$	−7.51981			−0.298650
$635$	−1.30238	−	3.05301i	−0.0516834	−	0.121155i
$636$	−6.15425	−	3.55316i	−0.244032	−	0.140892i
$637$	−17.7198	−	17.7198i	−0.702083	−	0.702083i
$638$	−0.173085	−	0.645961i	−0.00685249	−	0.0255739i
$639$	−3.70842	−	6.42316i	−0.146703	−	0.254096i
$640$	0.877385	+	2.05674i	0.0346817	+	0.0812999i
$641$		−	0.459697i		−	0.0181570i	−0.999959	−	0.00907848i	$-0.997110\pi$
$641$		−	0.459697i		−	0.0181570i	0.999959	−	0.00907848i	$-0.00288981\pi$
$642$	−0.992996	+	3.70591i	−0.0391904	+	0.146261i
$643$	−20.7771	+	20.7771i	−0.819368	+	0.819368i	−0.986016	−	0.166648i	$-0.946706\pi$
$643$	−20.7771	+	20.7771i	−0.819368	+	0.819368i	0.166648	+	0.986016i	$0.446706\pi$
$644$	14.1249			0.556598
$645$	22.1821	+	1.25414i	0.873418	+	0.0493817i
$646$	6.95450			0.273621
$647$	−19.2316	+	19.2316i	−0.756072	+	0.756072i	−0.975605	−	0.219533i	$-0.929547\pi$
$647$	−19.2316	+	19.2316i	−0.756072	+	0.756072i	0.219533	+	0.975605i	$0.429547\pi$
$648$	1.65435	−	6.17411i	0.0649889	−	0.242542i
$649$		−	4.06754i		−	0.159665i
$650$	−2.21876	−	7.63446i	−0.0870269	−	0.299448i
$651$	25.7762	+	44.6458i	1.01025	+	1.74981i
$652$	−3.44504	−	12.8571i	−0.134918	−	0.503522i
$653$	−28.4897	−	28.4897i	−1.11489	−	1.11489i	−0.992480	−	0.122407i	$-0.960939\pi$
$653$	−28.4897	−	28.4897i	−1.11489	−	1.11489i	−0.122407	−	0.992480i	$-0.539061\pi$
$654$	−17.9493	−	10.3630i	−0.701874	−	0.405227i
$655$	−12.5980	+	31.3426i	−0.492244	+	1.22466i
$656$	7.43479			0.290280
$657$	−1.32216	−	0.354272i	−0.0515825	−	0.0138215i
$658$	−1.42764	−	5.32802i	−0.0556551	−	0.207708i
$659$	−42.9837	−	24.8167i	−1.67441	−	0.966720i	−0.965122	−	0.261800i	$-0.915684\pi$
$659$	−42.9837	−	24.8167i	−1.67441	−	0.966720i	−0.709286	−	0.704921i	$-0.750983\pi$
$660$	−1.10172	−	0.827119i	−0.0428845	−	0.0321956i
$661$	−32.1092			−1.24890			−0.624451	−	0.781064i	$-0.714677\pi$
$661$	−32.1092			−1.24890			−0.624451	+	0.781064i	$0.714677\pi$
$662$	−0.651510	+	0.174572i	−0.0253216	+	0.00678491i
$663$	12.9781	−	3.47747i	0.504027	−	0.135054i
$664$	3.12849	+	5.41871i	0.121409	+	0.210287i
$665$	−12.2365	+	5.21996i	−0.474511	+	0.202421i
$666$	−4.51135			−0.174811
$667$	3.44324	−	3.44324i	0.133323	−	0.133323i
$668$	11.8959	+	3.18750i	0.460267	+	0.123328i
$669$	5.38623	−	3.10974i	0.208244	−	0.120229i
$670$	3.18988	+	22.4060i	0.123236	+	0.865621i
$671$	0.0288621	+	0.0166635i	0.00111421	+	0.000643289i
$672$	5.11149	−	5.11149i	0.197180	−	0.197180i
$673$	33.3972	−	8.94875i	1.28737	−	0.344949i	0.450707	−	0.892672i	$-0.351172\pi$
$673$	33.3972	−	8.94875i	1.28737	−	0.344949i	0.836660	+	0.547723i	$0.184505\pi$
$674$	10.2022	−	17.6708i	0.392976	−	0.680654i
$675$	28.0565	−	0.590222i	1.07989	−	0.0227177i
$676$	−5.23584	−	9.06875i	−0.201379	−	0.348798i
$677$	13.1780	−	13.1780i	0.506473	−	0.506473i	−0.406969	−	0.913442i	$-0.633414\pi$
$677$	13.1780	−	13.1780i	0.506473	−	0.506473i	0.913442	+	0.406969i	$0.133414\pi$
$678$	−6.40537	+	23.9052i	−0.245997	+	0.918073i
$679$	32.8126	−	56.8331i	1.25923	−	2.18105i
$680$	−7.69478	−	9.81261i	−0.295081	−	0.376296i
$681$	−17.8154	+	30.8571i	−0.682686	+	1.18245i
$682$	2.80097	+	0.750518i	0.107255	+	0.0287388i
$683$	44.3260	+	11.8771i	1.69609	+	0.454466i	0.971950	−	0.235188i	$-0.0755707\pi$
$683$	44.3260	+	11.8771i	1.69609	+	0.454466i	0.724139	+	0.689654i	$0.242237\pi$
$684$	−0.878070			−0.0335738
$685$	−6.07330	+	2.59081i	−0.232049	+	0.0989896i
$686$	41.7920			1.59563
$687$	−5.07516	+	5.07516i	−0.193629	+	0.193629i
$688$	3.63469	+	5.45793i	0.138571	+	0.208082i
$689$			7.45735i			0.284102i
$690$	1.20468	−	9.95873i	0.0458616	−	0.379122i
$691$	−15.6498	+	9.03543i	−0.595347	+	0.343724i	−0.767209	−	0.641397i	$-0.778355\pi$
$691$	−15.6498	+	9.03543i	−0.595347	+	0.343724i	0.171862	+	0.985121i	$0.445022\pi$
$692$	1.04144	+	1.04144i	0.0395896	+	0.0395896i
$693$	0.353508	−	1.31931i	0.0134287	−	0.0501165i
$694$	6.95831	−	4.01738i	0.264134	−	0.152498i
$695$	13.1431	−	1.87114i	0.498546	−	0.0709765i
$696$		−	2.49207i		−	0.0944618i
$697$	−40.0487	+	10.7310i	−1.51695	+	0.406466i
$698$	−13.3176	−	3.56844i	−0.504078	−	0.135067i
$699$			33.8967i			1.28209i
$700$	20.9042	+	11.4898i	0.790106	+	0.434272i
$701$	−14.6886	+	25.4414i	−0.554782	+	0.960910i	0.443139	+	0.896453i	$0.353865\pi$
$701$	−14.6886	+	25.4414i	−0.554782	+	0.960910i	−0.997920	+	0.0644572i	$0.979468\pi$
$702$	−8.62023	+	2.30978i	−0.325349	+	0.0871771i
$703$	−2.06802	−	7.71794i	−0.0779967	−	0.291088i
$704$		−	0.406610i		−	0.0153247i
$705$	−3.87828	+	0.552138i	−0.146064	+	0.0207947i
$706$	−3.88354	−	2.24216i	−0.146159	−	0.0843850i
$707$	77.1509	+	20.6725i	2.90156	+	0.777470i
$708$	3.92307	−	14.6411i	0.147438	−	0.550246i
$709$			27.7610i			1.04259i	0.853378	+	0.521293i	$0.174550\pi$
$709$			27.7610i			1.04259i	−0.853378	+	0.521293i	$0.825450\pi$
$710$	−23.3835	−	2.82865i	−0.877568	−	0.106157i
$711$	3.98503	+	6.90227i	0.149450	+	0.258855i
$712$	4.30531	−	16.0676i	0.161348	−	0.602160i
$713$	5.46489	+	20.3952i	0.204662	+	0.763808i
$714$	−20.1562	+	34.9115i	−0.754326	+	1.30653i
$715$	−0.173617	+	1.43524i	−0.00649292	+	0.0536748i
$716$	−12.7660	−	7.37046i	−0.477088	−	0.275447i
$717$	3.82205	+	14.2641i	0.142737	+	0.532702i
$718$	−10.1242	+	2.71276i	−0.377830	+	0.101239i
$719$	−36.0942	+	20.8390i	−1.34609	+	0.777164i	−0.987693	−	0.156407i	$-0.950009\pi$
$719$	−36.0942	+	20.8390i	−1.34609	+	0.777164i	−0.358394	+	0.933570i	$0.616676\pi$
$720$	0.971537	+	1.23893i	0.0362070	+	0.0461723i
$721$	12.2682	−	7.08303i	0.456890	−	0.263786i
$722$	4.51505	+	16.8504i	0.168033	+	0.627107i
$723$	−11.2946	+	11.2946i	−0.420051	+	0.420051i
$724$	−9.15725	−	5.28694i	−0.340326	−	0.196488i
$725$	7.89674	−	2.29498i	0.293277	−	0.0852335i
$726$	−8.20845	−	14.2175i	−0.304644	−	0.527659i
$727$	−14.6500	+	14.6500i	−0.543339	+	0.543339i	−0.924506	−	0.381167i	$-0.875522\pi$
$727$	−14.6500	+	14.6500i	−0.543339	+	0.543339i	0.381167	+	0.924506i	$0.375522\pi$
$728$	−7.32733	−	1.96335i	−0.271569	−	0.0727667i
$729$		−	30.0133i		−	1.11160i
$730$	−3.42067	+	2.68239i	−0.126604	+	0.0992798i
$731$	−27.4565	−	24.1539i	−1.01552	−	0.893365i
$732$	0.0878173	+	0.0878173i	0.00324582	+	0.00324582i
$733$	29.1594	+	29.1594i	1.07703	+	1.07703i	0.996774	+	0.0802539i	$0.0255731\pi$
$733$	29.1594	+	29.1594i	1.07703	+	1.07703i	0.0802539	+	0.996774i	$0.474427\pi$
$734$	15.6699	+	27.1411i	0.578388	+	1.00180i
$735$	6.41259	−	53.0107i	0.236532	−	1.95533i
$736$	2.56406	−	1.48036i	0.0945126	−	0.0545669i
$737$	1.06515	−	3.97520i	0.0392354	−	0.146428i
$738$	5.05652	−	1.35489i	0.186133	−	0.0498742i
$739$	−19.9423			−0.733590			−0.366795	−	0.930302i	$-0.619545\pi$
$739$	−19.9423			−0.733590			−0.366795	+	0.930302i	$0.619545\pi$
$740$	−8.60165	+	11.4574i	−0.316203	+	0.421182i
$741$	−1.50228	−	2.60203i	−0.0551877	−	0.0955879i
$742$	−15.8212	−	15.8212i	−0.580816	−	0.580816i
$743$	−4.61633	+	17.2284i	−0.169357	+	0.632048i	0.828088	+	0.560599i	$0.189429\pi$
$743$	−4.61633	+	17.2284i	−0.169357	+	0.632048i	−0.997444	+	0.0714489i	$0.977238\pi$
$744$	9.35823	+	5.40298i	0.343089	+	0.198083i
$745$	5.79345	+	40.6938i	0.212256	+	1.49091i
$746$	3.03003	−	5.24816i	0.110937	−	0.192149i
$747$	3.11522	+	3.11522i	0.113980	+	0.113980i
$748$	0.586881	+	2.19027i	0.0214585	+	0.0800842i
$749$	−6.03993	+	10.4615i	−0.220694	+	0.382254i
$750$	9.88373	−	13.7586i	0.360903	−	0.502392i
$751$	24.4815	−	14.1344i	0.893343	−	0.515772i	0.0183082	−	0.999832i	$-0.494172\pi$
$751$	24.4815	−	14.1344i	0.893343	−	0.515772i	0.875034	+	0.484061i	$0.160839\pi$
$752$	−0.817561	−	0.817561i	−0.0298134	−	0.0298134i
$753$	24.1846	+	24.1846i	0.881336	+	0.881336i
$754$	−2.26481	+	1.30759i	−0.0824794	+	0.0476195i
$755$	7.30491	−	18.1739i	0.265853	−	0.661416i
$756$	13.3880	−	23.1887i	0.486917	−	0.843365i
$757$	13.3699	+	49.8972i	0.485938	+	1.81354i	0.575801	+	0.817590i	$0.304690\pi$
$757$	13.3699	+	49.8972i	0.485938	+	1.81354i	−0.0898639	+	0.995954i	$0.528643\pi$
$758$	13.4157	+	13.4157i	0.487280	+	0.487280i
$759$	−0.912056	+	1.57973i	−0.0331055	+	0.0573405i
$760$	−1.67419	+	2.23002i	−0.0607292	+	0.0808913i
$761$	−31.9767	−	18.4617i	−1.15915	−	0.669237i	−0.208052	−	0.978118i	$-0.566712\pi$
$761$	−31.9767	−	18.4617i	−1.15915	−	0.669237i	−0.951101	+	0.308880i	$0.900046\pi$
$762$	−0.582129	+	2.17254i	−0.0210883	+	0.0787027i
$763$	−46.1438	−	46.1438i	−1.67052	−	1.67052i
$764$	6.23996	+	10.8079i	0.225754	+	0.391017i
$765$	−7.02155	−	5.27144i	−0.253865	−	0.190589i
$766$	25.4750			0.920449
$767$	−15.3643	+	4.11686i	−0.554774	+	0.148651i
$768$	0.392168	−	1.46359i	0.0141511	−	0.0528128i
$769$	22.5741	−	13.0332i	0.814044	−	0.469988i	−0.0343145	−	0.999411i	$-0.510925\pi$
$769$	22.5741	−	13.0332i	0.814044	−	0.469988i	0.848358	+	0.529423i	$0.177591\pi$
$770$	−2.67661	−	3.41329i	−0.0964583	−	0.123006i
$771$	−11.2009	−	19.4005i	−0.403390	−	0.698692i
$772$	−16.8719	−	16.8719i	−0.607234	−	0.607234i
$773$	−3.06174	−	3.06174i	−0.110123	−	0.110123i	0.649898	−	0.760021i	$-0.274812\pi$
$773$	−3.06174	−	3.06174i	−0.110123	−	0.110123i	−0.760021	+	0.649898i	$0.774812\pi$
$774$	3.46664	+	3.04965i	0.124606	+	0.109618i
$775$	−8.50252	+	34.6295i	−0.305420	+	1.24393i
$776$		−	13.7557i		−	0.493802i
$777$	44.7377	+	11.9874i	1.60496	+	0.430047i
$778$	19.9338	−	19.9338i	0.714663	−	0.714663i
$779$	4.63585	+	8.02952i	0.166096	+	0.287687i
$780$	−2.00920	+	4.99868i	−0.0719408	+	0.178982i
$781$	3.70927	+	2.14155i	0.132728	+	0.0766305i
$782$	−11.6750	+	11.6750i	−0.417499	+	0.417499i
$783$	−2.38913	−	8.91637i	−0.0853807	−	0.318645i
$784$	13.6486	−	7.88002i	0.487450	−	0.281429i
$785$	−1.45571	+	12.0339i	−0.0519565	+	0.429507i
$786$	19.8233	−	11.4450i	0.707075	−	0.408230i
$787$	−20.2809	+	5.43426i	−0.722937	+	0.193710i	−0.601482	−	0.798886i	$-0.705423\pi$
$787$	−20.2809	+	5.43426i	−0.722937	+	0.193710i	−0.121455	+	0.992597i	$0.538756\pi$
$788$	6.13378	+	22.8916i	0.218507	+	0.815478i
$789$	25.4466	+	14.6916i	0.905923	+	0.523035i
$790$	25.1277	+	3.03964i	0.894003	+	0.108146i
$791$	−38.9609	+	67.4823i	−1.38529	+	2.39939i
$792$	−0.0740991	−	0.276542i	−0.00263300	−	0.00982648i
$793$	0.0337311	−	0.125886i	0.00119783	−	0.00447035i
$794$	0.758646	+	1.31401i	0.0269233	+	0.0466326i
$795$	−12.5041	+	9.80539i	−0.443475	+	0.347761i
$796$		−	20.9667i		−	0.743147i
$797$	−3.31705	+	12.3794i	−0.117496	+	0.438501i	−0.999462	−	0.0328131i	$-0.989553\pi$
$797$	−3.31705	+	12.3794i	−0.117496	+	0.438501i	0.881966	+	0.471314i	$0.156220\pi$
$798$	8.70755	+	2.33318i	0.308244	+	0.0825938i
$799$	5.58395	+	3.22390i	0.197546	+	0.114053i
$800$	4.99889	−	0.105161i	0.176738	−	0.00371802i
$801$		−	11.7124i		−	0.413838i
$802$	7.51229	+	28.0363i	0.265268	+	0.989995i
$803$	0.763526	−	0.204586i	0.0269442	−	0.00721969i
$804$	7.66802	−	13.2814i	0.270430	−	0.468399i
$805$	11.7792	−	29.3055i	0.415162	−	1.03288i
$806$		−	11.3397i		−	0.399425i
$807$	−27.2059	−	7.28981i	−0.957695	−	0.256614i
$808$	16.1717	−	4.33318i	0.568917	−	0.152441i
$809$			20.0129i			0.703618i	0.936072	+	0.351809i	$0.114433\pi$
$809$			20.0129i			0.703618i	−0.936072	+	0.351809i	$0.885567\pi$
$810$	−11.4301	−	8.58114i	−0.401612	−	0.301511i
$811$	−6.90544	+	3.98686i	−0.242483	+	0.139998i	−0.616317	−	0.787498i	$-0.711376\pi$
$811$	−6.90544	+	3.98686i	−0.242483	+	0.139998i	0.373834	+	0.927495i	$0.378043\pi$
$812$	2.03080	−	7.57906i	0.0712672	−	0.265973i
$813$	−16.5158	−	16.5158i	−0.579233	−	0.579233i
$814$	2.25619	−	1.30261i	0.0790795	−	0.0456565i
$815$	−29.5481	−	3.57436i	−1.03502	−	0.125204i
$816$			8.44990i			0.295806i
$817$	−3.62818	+	7.32864i	−0.126934	+	0.256397i
$818$	−1.00859	+	1.00859i	−0.0352647	+	0.0352647i
$819$	−5.34123			−0.186638
$820$	6.20012	−	15.4253i	0.216518	−	0.538674i
$821$	−36.7222			−1.28161			−0.640807	−	0.767702i	$-0.721400\pi$
$821$	−36.7222			−1.28161			−0.640807	+	0.767702i	$0.721400\pi$
$822$	4.32180	+	1.15802i	0.150740	+	0.0403906i
$823$	34.8499	+	9.33801i	1.21479	+	0.325503i	0.808641	−	0.588303i	$-0.200204\pi$
$823$	34.8499	+	9.33801i	1.21479	+	0.325503i	0.406152	+	0.913806i	$0.366870\pi$
$824$	1.48468	−	2.57154i	0.0517212	−	0.0895838i
$825$	−2.63482	+	1.59603i	−0.0917327	+	0.0555666i
$826$	23.8622	−	41.3306i	0.830273	−	1.43807i
$827$	−5.39449	+	20.1325i	−0.187585	+	0.700075i	0.806478	+	0.591264i	$0.201371\pi$
$827$	−5.39449	+	20.1325i	−0.187585	+	0.700075i	−0.994062	+	0.108811i	$0.965296\pi$
$828$	1.47408	−	1.47408i	0.0512279	−	0.0512279i
$829$	−12.7117	−	22.0173i	−0.441495	−	0.764692i	0.556306	−	0.830978i	$-0.312218\pi$
$829$	−12.7117	−	22.0173i	−0.441495	−	0.764692i	−0.997801	+	0.0662861i	$0.978885\pi$
$830$	13.8514	−	1.97198i	0.480788	−	0.0684484i
$831$	−3.36567	+	5.82950i	−0.116754	+	0.202223i
$832$	−1.53589	+	0.411540i	−0.0532473	+	0.0142676i
$833$	−62.1467	+	62.1467i	−2.15326	+	2.15326i
$834$	−7.79070	−	4.49796i	−0.269770	−	0.155752i
$835$	16.5336	−	22.0228i	0.572170	−	0.762130i
$836$	0.439135	−	0.253535i	0.0151878	−	0.00876869i
$837$	38.6625	+	10.3596i	1.33637	+	0.358080i
$838$	1.24557	−	1.24557i	0.0430274	−	0.0430274i
$839$	7.27911			0.251303			0.125651	−	0.992074i	$-0.459898\pi$
$839$	7.27911			0.251303			0.125651	+	0.992074i	$0.459898\pi$
$840$	−6.34238	−	14.8677i	−0.218833	−	0.512983i
$841$	13.1475	+	22.7721i	0.453362	+	0.785246i
$842$	−9.93185	+	2.66123i	−0.342274	+	0.0917121i
$843$	0.391557	−	0.104917i	0.0134859	−	0.00361355i
$844$	−3.81064			−0.131168
$845$	−23.1817	+	3.30030i	−0.797473	+	0.113534i
$846$	−0.705025	−	0.407047i	−0.0242393	−	0.0139945i
$847$	−13.3782	−	49.9282i	−0.459681	−	1.71555i
$848$	−4.53015	−	1.21385i	−0.155566	−	0.0416838i
$849$	−12.5924			−0.432170
$850$	−26.7756	+	7.78163i	−0.918394	+	0.266908i
$851$	16.4284	+	9.48495i	0.563159	+	0.325140i
$852$	11.2860	+	11.2860i	0.386652	+	0.386652i
$853$	−9.66092	−	36.0551i	−0.330784	−	1.23450i	−0.908368	−	0.418171i	$-0.862671\pi$
$853$	−9.66092	−	36.0551i	−0.330784	−	1.23450i	0.577585	−	0.816331i	$-0.303995\pi$
$854$	0.195513	+	0.338639i	0.00669032	+	0.0115880i
$855$	−0.732251	+	1.82177i	−0.0250425	+	0.0623032i
$856$			2.53207i			0.0865444i
$857$	8.10430	−	30.2457i	0.276838	−	1.03317i	−0.677762	−	0.735281i	$-0.737050\pi$
$857$	8.10430	−	30.2457i	0.276838	−	1.03317i	0.954600	−	0.297891i	$-0.0962831\pi$
$858$	0.692714	−	0.692714i	0.0236489	−	0.0236489i
$859$	−5.30623			−0.181046			−0.0905232	−	0.995894i	$-0.528854\pi$
$859$	−5.30623			−0.181046			−0.0905232	+	0.995894i	$0.528854\pi$
$860$	14.3549	−	2.98949i	0.489498	−	0.101941i
$861$	−53.7442			−1.83160
$862$	−22.8759	+	22.8759i	−0.779155	+	0.779155i
$863$	−2.43974	+	9.10523i	−0.0830497	+	0.309946i	−0.994938	−	0.100493i	$-0.967958\pi$
$863$	−2.43974	+	9.10523i	−0.0830497	+	0.309946i	0.911888	+	0.410439i	$0.134625\pi$
$864$		−	5.61254i		−	0.190942i
$865$	3.02921	−	1.29223i	0.102996	−	0.0439371i
$866$	−9.77004	−	16.9222i	−0.331999	−	0.575040i
$867$	−5.52932	−	20.6357i	−0.187786	−	0.700825i
$868$	24.0580	+	24.0580i	0.816581	+	0.816581i
$869$	−3.98594	−	2.30128i	−0.135214	−	0.0780657i
$870$	−5.17041	−	2.07822i	−0.175293	−	0.0704583i
$871$	−16.0936			−0.545310
$872$	−13.2125	−	3.54028i	−0.447432	−	0.119889i
$873$	−2.50680	−	9.35549i	−0.0848422	−	0.316635i
$874$	3.19756	+	1.84611i	0.108159	+	0.0624456i
$875$	41.2710	−	33.7892i	1.39521	−	1.14228i
$876$	2.94563			0.0995235
$877$	36.8111	−	9.86351i	1.24302	−	0.333067i	0.423386	−	0.905949i	$-0.360841\pi$
$877$	36.8111	−	9.86351i	1.24302	−	0.333067i	0.819638	+	0.572882i	$0.194175\pi$
$878$	−35.4004	+	9.48551i	−1.19471	+	0.320120i
$879$	−12.1191	−	20.9908i	−0.408766	−	0.708003i
$880$	−0.843611	−	0.339085i	−0.0284381	−	0.0114306i
$881$	45.5356			1.53413			0.767066	−	0.641568i	$-0.221716\pi$
$881$	45.5356			1.53413			0.767066	+	0.641568i	$0.221716\pi$
$882$	7.84660	−	7.84660i	0.264209	−	0.264209i
$883$	−42.4158	−	11.3653i	−1.42740	−	0.382472i	−0.539300	−	0.842114i	$-0.681311\pi$
$883$	−42.4158	−	11.3653i	−1.42740	−	0.382472i	−0.888104	+	0.459642i	$0.847978\pi$
$884$	7.67931	−	4.43365i	0.258283	−	0.149120i
$885$	−27.1049	−	20.3491i	−0.911123	−	0.684026i
$886$	−29.6217	−	17.1021i	−0.995159	−	0.574556i
$887$	−4.95853	+	4.95853i	−0.166491	+	0.166491i	−0.785435	−	0.618944i	$-0.787561\pi$
$887$	−4.95853	+	4.95853i	−0.166491	+	0.166491i	0.618944	+	0.785435i	$0.287561\pi$
$888$	9.37750	−	2.51269i	0.314688	−	0.0843205i
$889$	−3.54082	+	6.13288i	−0.118755	+	0.205690i
$890$	−29.7458	−	22.3317i	−0.997083	−	0.748561i
$891$	1.29951	+	2.25081i	0.0435351	+	0.0754050i
$892$	2.90244	−	2.90244i	0.0971809	−	0.0971809i
$893$	0.373183	−	1.39274i	0.0124881	−	0.0466061i
$894$	13.9266	−	24.1216i	0.465776	−	0.806748i
$895$	−25.9378	+	20.3397i	−0.867005	+	0.679882i
$896$	2.38537	−	4.13159i	0.0796898	−	0.138027i
$897$	6.89022	+	1.84623i	0.230058	+	0.0616438i
$898$	−3.42638	−	0.918096i	−0.114340	−	0.0306373i
$899$	11.7293			0.391194
$900$	3.38066	−	0.982502i	0.112689	−	0.0327501i
$901$	26.1544			0.871329
$902$	−2.13763	+	2.13763i	−0.0711752	+	0.0711752i
$903$	−26.2742	−	39.4540i	−0.874350	−	1.31295i
$904$			16.3332i			0.543236i
$905$	−18.6056	+	14.5900i	−0.618470	+	0.484987i
$906$	−11.4945	+	6.63636i	−0.381880	+	0.220478i
$907$	−26.3436	−	26.3436i	−0.874724	−	0.874724i	0.118258	−	0.992983i	$-0.462269\pi$
$907$	−26.3436	−	26.3436i	−0.874724	−	0.874724i	−0.992983	+	0.118258i	$0.962269\pi$
$908$	−6.08618	+	22.7139i	−0.201977	+	0.753789i
$909$	10.2089	−	5.89413i	0.338609	−	0.195496i
$910$	−10.1840	+	13.5650i	−0.337595	+	0.449676i
$911$		−	21.6652i		−	0.717800i	−0.933376	−	0.358900i	$-0.883152\pi$
$911$		−	21.6652i		−	0.717800i	0.933376	−	0.358900i	$-0.116848\pi$
$912$	1.82520	−	0.489060i	0.0604383	−	0.0161944i
$913$	−2.45746	−	0.658475i	−0.0813301	−	0.0217923i
$914$		−	25.3990i		−	0.840125i
$915$	0.255432	−	0.108965i	0.00844432	−	0.00360226i
$916$	−2.36842	+	4.10223i	−0.0782549	+	0.135541i
$917$	69.6147	−	18.6532i	2.29888	−	0.615983i
$918$	8.10086	+	30.2328i	0.267368	+	0.997832i
$919$			17.5467i			0.578811i	0.957207	+	0.289405i	$0.0934576\pi$
$919$			17.5467i			0.578811i	−0.957207	+	0.289405i	$0.906542\pi$
$920$	−0.933114	−	6.55429i	−0.0307639	−	0.216089i
$921$	−31.9893	−	18.4690i	−1.05408	−	0.608575i
$922$	23.9433	+	6.41559i	0.788531	+	0.211286i
$923$	4.33502	−	16.1785i	0.142689	−	0.532522i
$924$			2.93928i			0.0966950i
$925$	16.5979	+	27.4009i	0.545737	+	0.900936i
$926$	8.59219	+	14.8821i	0.282357	+	0.489056i
$927$	0.541125	−	2.01951i	0.0177729	−	0.0663293i
$928$	−0.425678	−	1.58865i	−0.0139736	−	0.0521500i
$929$	−14.5216	+	25.1522i	−0.476440	+	0.825218i	−0.999636	−	0.0269949i	$-0.991406\pi$
$929$	−14.5216	+	25.1522i	−0.476440	+	0.825218i	0.523196	+	0.852212i	$0.324740\pi$
$930$	19.0139	−	14.9102i	0.623491	−	0.488925i
$931$	17.0207	+	9.82692i	0.557832	+	0.322064i
$932$	5.78999	+	21.6085i	0.189658	+	0.707812i
$933$	21.8509	−	5.85493i	0.715366	−	0.191682i
$934$	−27.3626	+	15.7978i	−0.895330	+	0.516919i
$935$	5.03366	+	0.608911i	0.164618	+	0.0199135i
$936$	−0.969583	+	0.559789i	−0.0316918	+	0.0182973i
$937$	5.96974	+	22.2794i	0.195023	+	0.727836i	0.992261	+	0.124170i	$0.0396270\pi$
$937$	5.96974	+	22.2794i	0.195023	+	0.727836i	−0.797238	+	0.603665i	$0.793706\pi$
$938$	34.1436	−	34.1436i	1.11483	−	1.11483i
$939$	−2.38805	−	1.37874i	−0.0779312	−	0.0449936i
$940$	−2.37802	+	1.01444i	−0.0775624	+	0.0330873i
$941$	0.605912	+	1.04947i	0.0197522	+	0.0342117i	0.875733	−	0.482797i	$-0.160379\pi$
$941$	0.605912	+	1.04947i	0.0197522	+	0.0342117i	−0.855980	+	0.517008i	$0.827046\pi$
$942$	5.80812	−	5.80812i	0.189239	−	0.189239i
$943$	−21.2623	−	5.69722i	−0.692396	−	0.185527i
$944$		−	10.0036i		−	0.325588i
$945$	−36.9459	−	47.1145i	−1.20185	−	1.53263i
$946$	−2.61428	−	0.524214i	−0.0849976	−	0.0170437i
$947$	7.45374	+	7.45374i	0.242214	+	0.242214i	0.817765	−	0.575552i	$-0.195213\pi$
$947$	7.45374	+	7.45374i	0.242214	+	0.242214i	−0.575552	+	0.817765i	$0.695213\pi$
$948$	−12.1278	−	12.1278i	−0.393894	−	0.393894i
$949$	−1.54557	−	2.67700i	−0.0501712	−	0.0868990i
$950$	3.23055	+	5.33320i	0.104813	+	0.173032i
$951$	9.86764	−	5.69708i	0.319980	−	0.184741i
$952$	−6.88587	+	25.6984i	−0.223172	+	0.832890i
$953$	−28.4724	+	7.62915i	−0.922310	+	0.247132i	−0.688573	−	0.725167i	$-0.741762\pi$
$953$	−28.4724	+	7.62915i	−0.922310	+	0.247132i	−0.233738	+	0.972300i	$0.575096\pi$
$954$	−3.30223			−0.106914
$955$	27.6274	−	3.93322i	0.894000	−	0.127276i
$956$	4.87298	+	8.44025i	0.157603	+	0.272977i
$957$	0.716512	+	0.716512i	0.0231615	+	0.0231615i
$958$	0.809358	−	3.02057i	0.0261492	−	0.0975900i
$959$	12.2001	+	7.04371i	0.393960	+	0.227453i
$960$	−2.70953	−	2.03418i	−0.0874498	−	0.0656530i
$961$	−9.92990	+	17.1991i	−0.320319	+	0.554809i
$962$	−7.20390	−	7.20390i	−0.232263	−	0.232263i
$963$	0.461435	+	1.72210i	0.0148695	+	0.0554939i
$964$	−5.27085	+	9.12937i	−0.169763	+	0.294037i
$965$	−49.0749	+	20.9348i	−1.57978	+	0.673916i
$966$	−18.5349	+	10.7011i	−0.596351	+	0.344304i
$967$	−22.6066	−	22.6066i	−0.726979	−	0.726979i	0.243038	−	0.970017i	$-0.421856\pi$
$967$	−22.6066	−	22.6066i	−0.726979	−	0.726979i	−0.970017	+	0.243038i	$0.921856\pi$
$968$	−7.66127	−	7.66127i	−0.246242	−	0.246242i
$969$	−9.12583	+	5.26880i	−0.293164	+	0.169258i
$970$	−28.5396	−	11.4714i	−0.916352	−	0.368323i
$971$	9.04076	−	15.6590i	0.290132	−	0.502523i	−0.683709	−	0.729755i	$-0.739634\pi$
$971$	9.04076	−	15.6590i	0.290132	−	0.502523i	0.973841	+	0.227232i	$0.0729676\pi$
$972$	−1.85119	−	6.90875i	−0.0593771	−	0.221598i
$973$	−20.0282	−	20.0282i	−0.642074	−	0.642074i
$974$	−17.9790	+	31.1405i	−0.576084	+	0.997807i
$975$	8.69544	+	8.33713i	0.278477	+	0.267002i
$976$	0.0709823	+	0.0409816i	0.00227209	+	0.00131179i
$977$	−0.0973272	+	0.363230i	−0.00311377	+	0.0116208i	−0.967465	−	0.253004i	$-0.918581\pi$
$977$	−0.0973272	+	0.363230i	−0.00311377	+	0.0116208i	0.964351	+	0.264625i	$0.0852481\pi$
$978$	14.2613	+	14.2613i	0.456026	+	0.456026i
$979$	3.38186	+	5.85755i	0.108085	+	0.187208i
$980$	−4.96700	−	34.8887i	−0.158665	−	1.11448i
$981$	−9.63121			−0.307501
$982$	11.8274	−	3.16915i	0.377429	−	0.101132i
$983$	−0.414000	+	1.54507i	−0.0132046	+	0.0492801i	−0.972214	−	0.234095i	$-0.924787\pi$
$983$	−0.414000	+	1.54507i	−0.0132046	+	0.0492801i	0.959009	+	0.283375i	$0.0914541\pi$
$984$	−9.75608	+	5.63268i	−0.311012	+	0.179563i
$985$	52.6093	+	6.36402i	1.67627	+	0.202775i
$986$	4.58596	+	7.94312i	0.146047	+	0.252961i
$987$	5.90993	+	5.90993i	0.188115	+	0.188115i
$988$	−1.40214	−	1.40214i	−0.0446079	−	0.0446079i
$989$	−6.21225	−	18.3940i	−0.197538	−	0.584897i
$990$	−0.635546	−	0.0768806i	−0.0201990	−	0.00244343i
$991$		−	49.9546i		−	1.58686i	−0.608662	−	0.793430i	$-0.708293\pi$
$991$		−	49.9546i		−	1.58686i	0.608662	−	0.793430i	$-0.291707\pi$
$992$	6.88860	+	1.84580i	0.218713	+	0.0586041i
$993$	0.722667	−	0.722667i	0.0229331	−	0.0229331i
$994$	25.1267	+	43.5208i	0.796972	+	1.38040i
$995$	−43.5006	−	17.4849i	−1.37906	−	0.554307i
$996$	−8.21054	−	4.74036i	−0.260161	−	0.150204i
$997$	−22.9108	+	22.9108i	−0.725594	+	0.725594i	−0.969739	−	0.244145i	$-0.921493\pi$
$997$	−22.9108	+	22.9108i	−0.725594	+	0.725594i	0.244145	+	0.969739i	$0.421493\pi$
$998$	−6.67950	−	24.9282i	−0.211436	−	0.789089i
$999$	31.1428	−	17.9803i	0.985314	−	0.568871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.8	✓	88
5.3	odd	4	inner	430.2.l.a.93.19	yes	88
43.37	odd	6	inner	430.2.l.a.37.19	yes	88
215.123	even	12	inner	430.2.l.a.123.8	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.8	✓	88	1.1	even	1	trivial
430.2.l.a.37.19	yes	88	43.37	odd	6	inner
430.2.l.a.93.19	yes	88	5.3	odd	4	inner
430.2.l.a.123.8	yes	88	215.123	even	12	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.392168 - 1.46359i) q^{3} -1.00000i q^{4} +(-2.07474 - 0.833933i) q^{5} +(0.757610 + 1.31222i) q^{6} +(1.23476 + 4.60819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.609775 + 0.352054i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.392168 - 1.46359i) q^{3} -1.00000i q^{4} +(-2.07474 - 0.833933i) q^{5} +(0.757610 + 1.31222i) q^{6} +(1.23476 + 4.60819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.609775 + 0.352054i) q^{9} +(2.05674 - 0.877385i) q^{10} -0.406610 q^{11} +(-1.46359 - 0.392168i) q^{12} +(0.411540 + 1.53589i) q^{13} +(-4.13159 - 2.38537i) q^{14} +(-2.03418 + 2.70953i) q^{15} -1.00000 q^{16} +(5.38666 - 1.44335i) q^{17} +(-0.680116 + 0.182236i) q^{18} +(-0.623534 - 1.07999i) q^{19} +(-0.833933 + 2.07474i) q^{20} +7.22874 q^{21} +(0.287517 - 0.287517i) q^{22} +(2.85984 + 0.766292i) q^{23} +(1.31222 - 0.757610i) q^{24} +(3.60911 + 3.46039i) q^{25} +(-1.37704 - 0.795034i) q^{26} +(3.96866 - 3.96866i) q^{27} +(4.60819 - 1.23476i) q^{28} +(0.822347 - 1.42435i) q^{29} +(-0.477543 - 3.35431i) q^{30} +(3.56580 + 6.17615i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.159459 + 0.595110i) q^{33} +(-2.78834 + 4.82955i) q^{34} +(1.28111 - 10.5905i) q^{35} +(0.352054 - 0.609775i) q^{36} +(6.18887 + 1.65830i) q^{37} +(1.20457 + 0.322765i) q^{38} +2.40930 q^{39} +(-0.877385 - 2.05674i) q^{40} -7.43479 q^{41} +(-5.11149 + 5.11149i) q^{42} +(-3.63469 - 5.45793i) q^{43} +0.406610i q^{44} +(-0.971537 - 1.23893i) q^{45} +(-2.56406 + 1.48036i) q^{46} +(0.817561 + 0.817561i) q^{47} +(-0.392168 + 1.46359i) q^{48} +(-13.6486 + 7.88002i) q^{49} +(-4.99889 + 0.105161i) q^{50} -8.44990i q^{51} +(1.53589 - 0.411540i) q^{52} +(4.53015 + 1.21385i) q^{53} +5.61254i q^{54} +(0.843611 + 0.339085i) q^{55} +(-2.38537 + 4.13159i) q^{56} +(-1.82520 + 0.489060i) q^{57} +(0.425678 + 1.58865i) q^{58} +10.0036i q^{59} +(2.70953 + 2.03418i) q^{60} +(-0.0709823 - 0.0409816i) q^{61} +(-6.88860 - 1.84580i) q^{62} +(-0.869404 + 3.24466i) q^{63} +1.00000i q^{64} +(0.426988 - 3.52977i) q^{65} +(-0.308052 - 0.533561i) q^{66} +(-2.61959 + 9.77645i) q^{67} +(-1.44335 - 5.38666i) q^{68} +(2.24307 - 3.88512i) q^{69} +(6.58274 + 8.39451i) q^{70} +(-9.12242 - 5.26683i) q^{71} +(0.182236 + 0.680116i) q^{72} +(-1.87778 + 0.503151i) q^{73} +(-5.54879 + 3.20359i) q^{74} +(6.47997 - 3.92521i) q^{75} +(-1.07999 + 0.623534i) q^{76} +(-0.502066 - 1.87374i) q^{77} +(-1.70363 + 1.70363i) q^{78} +(9.80286 + 5.65969i) q^{79} +(2.07474 + 0.833933i) q^{80} +(-3.19596 - 5.53556i) q^{81} +(5.25719 - 5.25719i) q^{82} +(6.04379 + 1.61943i) q^{83} -7.22874i q^{84} +(-12.3796 - 1.49753i) q^{85} +(6.42945 + 1.28923i) q^{86} +(-1.76216 - 1.76216i) q^{87} +(-0.287517 - 0.287517i) q^{88} +(-8.31721 - 14.4058i) q^{89} +(1.56304 + 0.189077i) q^{90} +(-6.56951 + 3.79291i) q^{91} +(0.766292 - 2.85984i) q^{92} +(10.4377 - 2.79679i) q^{93} -1.15621 q^{94} +(0.393031 + 2.76069i) q^{95} +(-0.757610 - 1.31222i) q^{96} +(-9.72677 - 9.72677i) q^{97} +(4.07900 - 15.2230i) q^{98} +(-0.247940 - 0.143149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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