LMFDB - Embedded newform 252.2.ba.a.155.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.7
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18583 - 0.770594i) q^{2} +(-0.953579 + 1.44592i) q^{3} +(0.812371 + 1.82758i) q^{4} +(0.898347 - 0.518661i) q^{5} +(2.24500 - 0.979790i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +O(q^{10})$	\(q+(-1.18583 - 0.770594i) q^{2} +(-0.953579 + 1.44592i) q^{3} +(0.812371 + 1.82758i) q^{4} +(0.898347 - 0.518661i) q^{5} +(2.24500 - 0.979790i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +(-1.46496 - 0.0772186i) q^{10} +(-1.75133 + 3.03339i) q^{11} +(-3.41720 - 0.568120i) q^{12} +(2.39811 + 4.15365i) q^{13} +(-0.641659 - 1.26027i) q^{14} +(-0.106702 + 1.79352i) q^{15} +(-2.68011 + 2.96935i) q^{16} -1.35469i q^{17} +(-0.724085 + 4.18039i) q^{18} +5.14106i q^{19} +(1.67769 + 1.22046i) q^{20} +(-1.54878 + 0.775415i) q^{21} +(4.41428 - 2.24751i) q^{22} +(1.66445 + 2.88291i) q^{23} +(3.61441 + 3.30696i) q^{24} +(-1.96198 + 3.39825i) q^{25} +(0.357033 - 6.77349i) q^{26} +(5.11380 + 0.921417i) q^{27} +(-0.210257 + 1.98892i) q^{28} +(-0.188235 - 0.108677i) q^{29} +(1.50861 - 2.04458i) q^{30} +(0.738509 - 0.426379i) q^{31} +(5.46630 - 1.45586i) q^{32} +(-2.71601 - 5.42485i) q^{33} +(-1.04392 + 1.60643i) q^{34} +1.03732 q^{35} +(4.08003 - 4.39925i) q^{36} +3.25692 q^{37} +(3.96167 - 6.09641i) q^{38} +(-8.29264 - 0.493356i) q^{39} +(-1.04897 - 2.74007i) q^{40} +(-1.19014 + 0.687125i) q^{41} +(2.43412 + 0.273976i) q^{42} +(-6.70351 - 3.87028i) q^{43} +(-6.96649 - 0.736458i) q^{44} +(-2.49154 - 1.86455i) q^{45} +(0.247804 - 4.70124i) q^{46} +(2.08223 - 3.60653i) q^{47} +(-1.73774 - 6.70673i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.94524 - 2.51785i) q^{50} +(1.95878 + 1.29181i) q^{51} +(-5.64298 + 7.75705i) q^{52} +13.4415i q^{53} +(-5.35405 - 5.03331i) q^{54} +3.63338i q^{55} +(1.78198 - 2.19649i) q^{56} +(-7.43356 - 4.90241i) q^{57} +(0.139468 + 0.273925i) q^{58} +(-2.77105 - 4.79960i) q^{59} +(-3.36449 + 1.26200i) q^{60} +(5.65678 - 9.79783i) q^{61} +(-1.20431 - 0.0634795i) q^{62} +(0.355700 - 2.97884i) q^{63} +(-7.60396 - 2.48591i) q^{64} +(4.30868 + 2.48761i) q^{65} +(-0.959643 + 8.52588i) q^{66} +(12.8327 - 7.40894i) q^{67} +(2.47581 - 1.10051i) q^{68} +(-5.75563 - 0.342421i) q^{69} +(-1.23008 - 0.799354i) q^{70} -12.5490 q^{71} +(-8.22824 + 2.07271i) q^{72} +14.5146 q^{73} +(-3.86215 - 2.50977i) q^{74} +(-3.04270 - 6.07737i) q^{75} +(-9.39571 + 4.17645i) q^{76} +(-3.03339 + 1.75133i) q^{77} +(9.45346 + 6.97530i) q^{78} +(-12.2513 - 7.07327i) q^{79} +(-0.867583 + 4.05757i) q^{80} +(-6.20871 + 6.51551i) q^{81} +(1.94079 + 0.102300i) q^{82} +(6.05157 - 10.4816i) q^{83} +(-2.67532 - 2.20061i) q^{84} +(-0.702626 - 1.21698i) q^{85} +(4.96680 + 9.75516i) q^{86} +(0.336635 - 0.168540i) q^{87} +(7.69354 + 6.24164i) q^{88} -5.72707i q^{89} +(1.51773 + 4.13100i) q^{90} +4.79623i q^{91} +(-3.91660 + 5.38390i) q^{92} +(-0.0877175 + 1.47441i) q^{93} +(-5.24833 + 2.67216i) q^{94} +(2.66647 + 4.61846i) q^{95} +(-3.10750 + 9.29212i) q^{96} +(4.52430 - 7.83631i) q^{97} +(0.0744403 - 1.41225i) q^{98} +(10.4338 + 1.24589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.18583	−	0.770594i	−0.838506	−	0.544892i
$2$	−1.18583	−	0.770594i	−0.838506	−	0.544892i
$3$	−0.953579	+	1.44592i	−0.550549	+	0.834803i
$3$	−0.953579	+	1.44592i	−0.550549	+	0.834803i
$4$	0.812371	+	1.82758i	0.406185	+	0.913791i
$5$	0.898347	−	0.518661i	0.401753	−	0.231952i	−0.285487	−	0.958383i	$-0.592155\pi$
$5$	0.898347	−	0.518661i	0.401753	−	0.231952i	0.687240	+	0.726430i	$0.258822\pi$
$6$	2.24500	−	0.979790i	0.916516	−	0.399997i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	0.444992	−	2.79320i	0.157328	−	0.987546i
$9$	−1.18137	−	2.75760i	−0.393791	−	0.919200i
$10$	−1.46496	−	0.0772186i	−0.463261	−	0.0244187i
$11$	−1.75133	+	3.03339i	−0.528045	+	0.914601i	0.471421	+	0.881909i	$0.343741\pi$
$11$	−1.75133	+	3.03339i	−0.528045	+	0.914601i	−0.999465	+	0.0326921i	$0.989592\pi$
$12$	−3.41720	−	0.568120i	−0.986460	−	0.164002i
$13$	2.39811	+	4.15365i	0.665117	+	1.15202i	0.979254	+	0.202639i	$0.0649516\pi$
$13$	2.39811	+	4.15365i	0.665117	+	1.15202i	−0.314137	+	0.949378i	$0.601715\pi$
$14$	−0.641659	−	1.26027i	−0.171491	−	0.336821i
$15$	−0.106702	+	1.79352i	−0.0275504	+	0.463086i
$16$	−2.68011	+	2.96935i	−0.670027	+	0.742337i
$17$		−	1.35469i		−	0.328561i	−0.986414	−	0.164281i	$-0.947470\pi$
$17$		−	1.35469i		−	0.328561i	0.986414	−	0.164281i	$-0.0525303\pi$
$18$	−0.724085	+	4.18039i	−0.170668	+	0.985329i
$19$			5.14106i			1.17944i	0.807608	+	0.589720i	$0.200762\pi$
$19$			5.14106i			1.17944i	−0.807608	+	0.589720i	$0.799238\pi$
$20$	1.67769	+	1.22046i	0.375142	+	0.272903i
$21$	−1.54878	+	0.775415i	−0.337972	+	0.169209i
$22$	4.41428	−	2.24751i	0.941128	−	0.479171i
$23$	1.66445	+	2.88291i	0.347061	+	0.601127i	0.985726	−	0.168358i	$-0.0538463\pi$
$23$	1.66445	+	2.88291i	0.347061	+	0.601127i	−0.638665	+	0.769485i	$0.720513\pi$
$24$	3.61441	+	3.30696i	0.737789	+	0.675031i
$25$	−1.96198	+	3.39825i	−0.392396	+	0.679650i
$26$	0.357033	−	6.77349i	0.0700199	−	1.32839i
$27$	5.11380	+	0.921417i	0.984152	+	0.177327i
$28$	−0.210257	+	1.98892i	−0.0397349	+	0.375870i
$29$	−0.188235	−	0.108677i	−0.0349543	−	0.0201809i	0.482421	−	0.875939i	$-0.339758\pi$
$29$	−0.188235	−	0.108677i	−0.0349543	−	0.0201809i	−0.517375	+	0.855759i	$0.673091\pi$
$30$	1.50861	−	2.04458i	0.275433	−	0.373288i
$31$	0.738509	−	0.426379i	0.132640	−	0.0765799i	−0.432212	−	0.901772i	$-0.642267\pi$
$31$	0.738509	−	0.426379i	0.132640	−	0.0765799i	0.564852	+	0.825192i	$0.308933\pi$
$32$	5.46630	−	1.45586i	0.966315	−	0.257362i
$33$	−2.71601	−	5.42485i	−0.472796	−	0.944346i
$34$	−1.04392	+	1.60643i	−0.179030	+	0.275501i
$35$	1.03732			0.175339
$36$	4.08003	−	4.39925i	0.680004	−	0.733208i
$37$	3.25692			0.535435			0.267718	−	0.963497i	$-0.413731\pi$
$37$	3.25692			0.535435			0.267718	+	0.963497i	$0.413731\pi$
$38$	3.96167	−	6.09641i	0.642667	−	0.988968i
$39$	−8.29264	−	0.493356i	−1.32789	−	0.0790002i
$40$	−1.04897	−	2.74007i	−0.165856	−	0.433242i
$41$	−1.19014	+	0.687125i	−0.185868	+	0.107311i	−0.590047	−	0.807369i	$-0.700891\pi$
$41$	−1.19014	+	0.687125i	−0.185868	+	0.107311i	0.404179	+	0.914680i	$0.367557\pi$
$42$	2.43412	+	0.273976i	0.375593	+	0.0422754i
$43$	−6.70351	−	3.87028i	−1.02228	−	0.590212i	−0.107514	−	0.994204i	$-0.534289\pi$
$43$	−6.70351	−	3.87028i	−1.02228	−	0.590212i	−0.914762	+	0.403992i	$0.867622\pi$
$44$	−6.96649	−	0.736458i	−1.05024	−	0.111025i
$45$	−2.49154	−	1.86455i	−0.371417	−	0.277951i
$46$	0.247804	−	4.70124i	0.0365367	−	0.693160i
$47$	2.08223	−	3.60653i	0.303724	−	0.526066i	−0.673252	−	0.739413i	$-0.735103\pi$
$47$	2.08223	−	3.60653i	0.303724	−	0.526066i	0.976976	+	0.213347i	$0.0684365\pi$
$48$	−1.73774	−	6.70673i	−0.250822	−	0.968033i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	4.94524	−	2.51785i	0.699363	−	0.356077i
$51$	1.95878	+	1.29181i	0.274284	+	0.180889i
$52$	−5.64298	+	7.75705i	−0.782541	+	1.07571i
$53$			13.4415i			1.84634i	0.384395	+	0.923169i	$0.374410\pi$
$53$			13.4415i			1.84634i	−0.384395	+	0.923169i	$0.625590\pi$
$54$	−5.35405	−	5.03331i	−0.728594	−	0.684946i
$55$			3.63338i			0.489925i
$56$	1.78198	−	2.19649i	0.238127	−	0.293518i
$57$	−7.43356	−	4.90241i	−0.984600	−	0.649340i
$58$	0.139468	+	0.273925i	0.0183130	+	0.0359681i
$59$	−2.77105	−	4.79960i	−0.360760	−	0.624854i	0.627326	−	0.778757i	$-0.284149\pi$
$59$	−2.77105	−	4.79960i	−0.360760	−	0.624854i	−0.988086	+	0.153902i	$0.950816\pi$
$60$	−3.36449	+	1.26200i	−0.434354	+	0.162923i
$61$	5.65678	−	9.79783i	0.724276	−	1.25448i	−0.234995	−	0.971997i	$-0.575507\pi$
$61$	5.65678	−	9.79783i	0.724276	−	1.25448i	0.959271	−	0.282487i	$-0.0911594\pi$
$62$	−1.20431	−	0.0634795i	−0.152947	−	0.00806191i
$63$	0.355700	−	2.97884i	0.0448140	−	0.375298i
$64$	−7.60396	−	2.48591i	−0.950496	−	0.310738i
$65$	4.30868	+	2.48761i	0.534425	+	0.308551i
$66$	−0.959643	+	8.52588i	−0.118124	+	1.04946i
$67$	12.8327	−	7.40894i	1.56776	−	0.905146i	0.571329	−	0.820721i	$-0.306428\pi$
$67$	12.8327	−	7.40894i	1.56776	−	0.905146i	0.996430	−	0.0844247i	$-0.0269053\pi$
$68$	2.47581	−	1.10051i	0.300236	−	0.133457i
$69$	−5.75563	−	0.342421i	−0.692897	−	0.0412227i
$70$	−1.23008	−	0.799354i	−0.147023	−	0.0955410i
$71$	−12.5490			−1.48929			−0.744645	−	0.667460i	$-0.767381\pi$
$71$	−12.5490			−1.48929			−0.744645	+	0.667460i	$0.767381\pi$
$72$	−8.22824	+	2.07271i	−0.969707	+	0.244271i
$73$	14.5146			1.69881			0.849405	−	0.527741i	$-0.176961\pi$
$73$	14.5146			1.69881			0.849405	+	0.527741i	$0.176961\pi$
$74$	−3.86215	−	2.50977i	−0.448966	−	0.291754i
$75$	−3.04270	−	6.07737i	−0.351341	−	0.701755i
$76$	−9.39571	+	4.17645i	−1.07776	+	0.479071i
$77$	−3.03339	+	1.75133i	−0.345687	+	0.199582i
$78$	9.45346	+	6.97530i	1.07039	+	0.789797i
$79$	−12.2513	−	7.07327i	−1.37838	−	0.795806i	−0.386412	−	0.922326i	$-0.626286\pi$
$79$	−12.2513	−	7.07327i	−1.37838	−	0.795806i	−0.991964	+	0.126521i	$0.959619\pi$
$80$	−0.867583	+	4.05757i	−0.0969987	+	0.453650i
$81$	−6.20871	+	6.51551i	−0.689857	+	0.723946i
$82$	1.94079	+	0.102300i	0.214324	+	0.0112971i
$83$	6.05157	−	10.4816i	0.664246	−	1.15051i	−0.315243	−	0.949011i	$-0.602086\pi$
$83$	6.05157	−	10.4816i	0.664246	−	1.15051i	0.979489	−	0.201497i	$-0.0645805\pi$
$84$	−2.67532	−	2.20061i	−0.291901	−	0.240106i
$85$	−0.702626	−	1.21698i	−0.0762105	−	0.132000i
$86$	4.96680	+	9.75516i	0.535583	+	1.05193i
$87$	0.336635	−	0.168540i	0.0360911	−	0.0180694i
$88$	7.69354	+	6.24164i	0.820134	+	0.665362i
$89$		−	5.72707i		−	0.607068i	−0.952821	−	0.303534i	$-0.901833\pi$
$89$		−	5.72707i		−	0.607068i	0.952821	−	0.303534i	$-0.0981667\pi$
$90$	1.51773	+	4.13100i	0.159983	+	0.435446i
$91$			4.79623i			0.502781i
$92$	−3.91660	+	5.38390i	−0.408334	+	0.561310i
$93$	−0.0877175	+	1.47441i	−0.00909588	+	0.152889i
$94$	−5.24833	+	2.67216i	−0.541324	+	0.275613i
$95$	2.66647	+	4.61846i	0.273574	+	0.473844i
$96$	−3.10750	+	9.29212i	−0.317158	+	0.948373i
$97$	4.52430	−	7.83631i	0.459373	−	0.795657i	−0.539555	−	0.841950i	$-0.681408\pi$
$97$	4.52430	−	7.83631i	0.459373	−	0.795657i	0.998928	+	0.0462932i	$0.0147408\pi$
$98$	0.0744403	−	1.41225i	0.00751961	−	0.142659i
$99$	10.4338	+	1.24589i	1.04864	+	0.125217i
$100$	−7.80444	−	0.825042i	−0.780444	−	0.0825042i
$101$	5.65839	+	3.26687i	0.563031	+	0.325066i	0.754361	−	0.656460i	$-0.227947\pi$
$101$	5.65839	+	3.26687i	0.563031	+	0.325066i	−0.191330	+	0.981526i	$0.561280\pi$
$102$	−1.32731	−	3.04128i	−0.131424	−	0.301132i
$103$	8.31662	−	4.80160i	0.819460	−	0.473116i	−0.0307699	−	0.999526i	$-0.509796\pi$
$103$	8.31662	−	4.80160i	0.819460	−	0.473116i	0.850230	+	0.526411i	$0.176463\pi$
$104$	12.6691	−	4.85007i	1.24231	−	0.475589i
$105$	−0.989168	+	1.49988i	−0.0965329	+	0.146374i
$106$	10.3580	−	15.9393i	1.00605	−	1.54817i
$107$	13.6334			1.31799			0.658997	−	0.752145i	$-0.270981\pi$
$107$	13.6334			1.31799			0.658997	+	0.752145i	$0.270981\pi$
$108$	2.47034	+	10.0944i	0.237709	+	0.971337i
$109$	−0.139445			−0.0133564			−0.00667821	−	0.999978i	$-0.502126\pi$
$109$	−0.139445			−0.0133564			−0.00667821	+	0.999978i	$0.502126\pi$
$110$	2.79986	−	4.30856i	0.266956	−	0.410805i
$111$	−3.10574	+	4.70925i	−0.294783	+	0.446983i
$112$	−3.80572	+	1.23148i	−0.359606	+	0.116364i
$113$	−7.31774	+	4.22490i	−0.688395	+	0.397445i	−0.803010	−	0.595965i	$-0.796770\pi$
$113$	−7.31774	+	4.22490i	−0.688395	+	0.397445i	0.114616	+	0.993410i	$0.463436\pi$
$114$	5.03716	+	11.5417i	0.471773	+	1.08098i
$115$	2.99050	+	1.72657i	0.278866	+	0.161003i
$116$	0.0457004	−	0.432300i	0.00424317	−	0.0401381i
$117$	8.62105	−	11.5201i	0.797016	−	1.06503i
$118$	−0.412556	+	7.82684i	−0.0379788	+	0.720519i
$119$	0.677346	−	1.17320i	0.0620922	−	0.107547i
$120$	4.96219	+	1.09614i	0.452984	+	0.100064i
$121$	−0.634293	−	1.09863i	−0.0576630	−	0.0998752i
$122$	−14.2581	+	7.25945i	−1.29087	+	0.657240i
$123$	0.141360	−	2.37607i	0.0127460	−	0.214243i
$124$	1.37919	+	1.00331i	0.123854	+	0.0900998i
$125$			9.25702i			0.827973i
$126$	−2.71727	+	3.25829i	−0.242074	+	0.290271i
$127$		−	5.70398i		−	0.506146i	−0.967447	−	0.253073i	$-0.918559\pi$
$127$		−	5.70398i		−	0.506146i	0.967447	−	0.253073i	$-0.0814413\pi$
$128$	7.10136	+	8.80742i	0.627678	+	0.778473i
$129$	11.9884	−	6.00214i	1.05552	−	0.528459i
$130$	−3.19240	−	6.27012i	−0.279992	−	0.549926i
$131$	10.2385	+	17.7336i	0.894542	+	1.54939i	0.834370	+	0.551204i	$0.185832\pi$
$131$	10.2385	+	17.7336i	0.894542	+	1.54939i	0.0601718	+	0.998188i	$0.480835\pi$
$132$	7.70796	−	9.37072i	0.670892	−	0.815616i
$133$	−2.57053	+	4.45229i	−0.222893	+	0.386062i
$134$	−20.9266	−	1.10305i	−1.80778	−	0.0952888i
$135$	5.07187	−	1.82458i	0.436517	−	0.157035i
$136$	−3.78393	−	0.602827i	−0.324469	−	0.0516920i
$137$	−9.77658	−	5.64451i	−0.835270	−	0.482243i	0.0203840	−	0.999792i	$-0.493511\pi$
$137$	−9.77658	−	5.64451i	−0.835270	−	0.482243i	−0.855653	+	0.517549i	$0.826844\pi$
$138$	6.56132	+	4.84131i	0.558536	+	0.412119i
$139$	−9.25578	+	5.34382i	−0.785065	+	0.453257i	−0.838222	−	0.545329i	$-0.816405\pi$
$139$	−9.25578	+	5.34382i	−0.785065	+	0.453257i	0.0531575	+	0.998586i	$0.483071\pi$
$140$	0.842690	+	1.89579i	0.0712203	+	0.160223i
$141$	3.22918	+	6.44985i	0.271946	+	0.543175i
$142$	14.8809	+	9.67017i	1.24878	+	0.811503i
$143$	−16.7995			−1.40485
$144$	11.3545	+	3.88276i	0.946207	+	0.323563i
$145$	−0.225467			−0.0187240
$146$	−17.2119	−	11.1849i	−1.42446	−	0.925669i
$147$	−1.72899	−	0.102863i	−0.142605	−	0.00848403i
$148$	2.64583	+	5.95230i	0.217486	+	0.489276i
$149$	−5.65372	+	3.26417i	−0.463170	+	0.267412i	−0.713376	−	0.700781i	$-0.752835\pi$
$149$	−5.65372	+	3.26417i	−0.463170	+	0.267412i	0.250206	+	0.968193i	$0.419502\pi$
$150$	−1.07507	+	9.55140i	−0.0877793	+	0.779868i
$151$	2.81463	+	1.62503i	0.229051	+	0.132243i	0.610134	−	0.792298i	$-0.291115\pi$
$151$	2.81463	+	1.62503i	0.229051	+	0.132243i	−0.381083	+	0.924541i	$0.624449\pi$
$152$	14.3600	+	2.28773i	1.16475	+	0.185559i
$153$	−3.73570	+	1.60040i	−0.302013	+	0.129385i
$154$	4.94663	+	0.260739i	0.398611	+	0.0210109i
$155$	0.442292	−	0.766072i	0.0355257	−	0.0615324i
$156$	−5.83505	−	15.5563i	−0.467178	−	1.24550i
$157$	−8.13937	−	14.0978i	−0.649592	−	1.12513i	−0.983220	−	0.182422i	$-0.941606\pi$
$157$	−8.13937	−	14.0978i	−0.649592	−	1.12513i	0.333628	−	0.942705i	$-0.391727\pi$
$158$	9.07727	+	17.8284i	0.722148	+	1.41835i
$159$	−19.4354	−	12.8176i	−1.54133	−	1.01650i
$160$	4.15554	−	4.14302i	0.328524	−	0.327535i
$161$			3.32889i			0.262353i
$162$	12.3833	−	2.94187i	0.972922	−	0.231135i
$163$			6.05547i			0.474301i	0.971473	+	0.237151i	$0.0762135\pi$
$163$			6.05547i			0.474301i	−0.971473	+	0.237151i	$0.923787\pi$
$164$	−2.22261	−	1.61687i	−0.173557	−	0.126256i
$165$	−5.25358	−	3.46471i	−0.408991	−	0.269728i
$166$	−15.2532	+	7.76609i	−1.18388	+	0.602765i
$167$	−2.63025	−	4.55572i	−0.203534	−	0.352532i	0.746130	−	0.665800i	$-0.231910\pi$
$167$	−2.63025	−	4.55572i	−0.203534	−	0.352532i	−0.949665	+	0.313268i	$0.898576\pi$
$168$	1.47669	+	4.67112i	0.113929	+	0.360385i
$169$	−5.00189	+	8.66353i	−0.384761	+	0.666426i
$170$	−0.104607	+	1.98457i	−0.00802302	+	0.152210i
$171$	14.1770	−	6.07351i	1.08414	−	0.464453i
$172$	1.62751	−	15.3953i	0.124096	−	1.17388i
$173$	1.85192	+	1.06921i	0.140799	+	0.0812903i	0.568745	−	0.822514i	$-0.307429\pi$
$173$	1.85192	+	1.06921i	0.140799	+	0.0812903i	−0.427946	+	0.903804i	$0.640763\pi$
$174$	−0.529067	−	0.0595500i	−0.0401085	−	0.00451447i
$175$	−3.39825	+	1.96198i	−0.256884	+	0.148312i
$176$	−4.31343	−	13.3301i	−0.325137	−	1.00479i
$177$	9.58225	+	0.570079i	0.720246	+	0.0428497i
$178$	−4.41325	+	6.79131i	−0.330787	+	0.509031i
$179$	−6.85809			−0.512598			−0.256299	−	0.966598i	$-0.582503\pi$
$179$	−6.85809			−0.512598			−0.256299	+	0.966598i	$0.582503\pi$
$180$	1.38356	−	6.06820i	0.103124	−	0.452297i
$181$	−20.0689			−1.49171			−0.745855	−	0.666108i	$-0.767959\pi$
$181$	−20.0689			−1.49171			−0.745855	+	0.666108i	$0.767959\pi$
$182$	3.69594	−	5.68749i	0.273961	−	0.421585i
$183$	8.77270	+	17.5223i	0.648497	+	1.29528i
$184$	8.79321	−	3.36627i	0.648244	−	0.248164i
$185$	2.92585	−	1.68924i	0.215113	−	0.124195i
$186$	1.24019	−	1.68080i	0.0909352	−	0.123242i
$187$	4.10931	+	2.37251i	0.300502	+	0.173495i
$188$	8.28276	+	0.875607i	0.604083	+	0.0638602i
$189$	3.96798	+	3.35487i	0.288628	+	0.244031i
$190$	0.396985	−	7.53145i	0.0288003	−	0.546389i
$191$	12.3006	−	21.3053i	0.890040	−	1.54159i	0.0502147	−	0.998738i	$-0.484009\pi$
$191$	12.3006	−	21.3053i	0.890040	−	1.54159i	0.839826	−	0.542856i	$-0.182657\pi$
$192$	10.8454	−	8.62422i	0.782700	−	0.622400i
$193$	−1.04725	−	1.81389i	−0.0753829	−	0.130567i	0.825870	−	0.563861i	$-0.190685\pi$
$193$	−1.04725	−	1.81389i	−0.0753829	−	0.130567i	−0.901253	+	0.433294i	$0.857351\pi$
$194$	−11.4036	+	5.80612i	−0.818734	+	0.416855i
$195$	−7.70556	+	3.85787i	−0.551806	+	0.276267i
$196$	−1.17655	+	1.61732i	−0.0840391	+	0.115523i
$197$			14.3561i			1.02283i	0.859334	+	0.511415i	$0.170878\pi$
$197$			14.3561i			1.02283i	−0.859334	+	0.511415i	$0.829122\pi$
$198$	−11.4126	−	9.51767i	−0.811062	−	0.676391i
$199$			3.06244i			0.217090i	0.994092	+	0.108545i	$0.0346192\pi$
$199$			3.06244i			0.217090i	−0.994092	+	0.108545i	$0.965381\pi$
$200$	8.61894	+	6.99241i	0.609451	+	0.494438i
$201$	−1.52422	+	25.6200i	−0.107510	+	1.80710i
$202$	−4.19244	−	8.23426i	−0.294979	−	0.579361i
$203$	−0.108677	−	0.188235i	−0.00762765	−	0.0132115i
$204$	−0.769628	+	4.62925i	−0.0538847	+	0.324112i
$205$	−0.712770	+	1.23455i	−0.0497820	+	0.0862250i
$206$	−13.5621	−	0.714866i	−0.944920	−	0.0498070i
$207$	5.98357	−	7.99567i	0.415887	−	0.555737i
$208$	−18.7608	−	4.01141i	−1.30083	−	0.278141i
$209$	−15.5948	−	9.00368i	−1.07872	−	0.622797i
$210$	2.32878	−	1.01636i	0.160701	−	0.0701353i
$211$	14.8672	−	8.58359i	1.02350	−	0.590918i	0.108385	−	0.994109i	$-0.465432\pi$
$211$	14.8672	−	8.58359i	1.02350	−	0.590918i	0.915116	+	0.403191i	$0.132099\pi$
$212$	−24.5655	+	10.9195i	−1.68717	+	0.749955i
$213$	11.9665	−	18.1448i	0.819928	−	1.24326i
$214$	−16.1669	−	10.5058i	−1.10515	−	0.718165i
$215$	−8.02944			−0.547603
$216$	4.84931	−	13.8739i	0.329953	−	0.943997i
$217$	0.852757			0.0578889
$218$	0.165358	+	0.107455i	0.0111994	+	0.00727780i
$219$	−13.8409	+	20.9870i	−0.935279	+	1.41817i
$220$	−6.64030	+	2.95165i	−0.447689	+	0.199000i
$221$	5.62692	−	3.24871i	0.378508	−	0.218532i
$222$	7.31179	−	3.19110i	0.490735	−	0.214173i
$223$	−15.2826	−	8.82341i	−1.02340	−	0.590860i	−0.108312	−	0.994117i	$-0.534545\pi$
$223$	−15.2826	−	8.82341i	−1.02340	−	0.590860i	−0.915087	+	0.403257i	$0.867878\pi$
$224$	5.46189	+	1.47234i	0.364938	+	0.0983751i
$225$	11.6889	+	1.39575i	0.779257	+	0.0930503i
$226$	11.9332	+	0.629006i	0.793788	+	0.0418408i
$227$	−9.52462	+	16.4971i	−0.632171	+	1.09495i	0.354936	+	0.934891i	$0.384503\pi$
$227$	−9.52462	+	16.4971i	−0.632171	+	1.09495i	−0.987107	+	0.160062i	$0.948831\pi$
$228$	2.92074	−	17.5680i	0.193431	−	1.16347i
$229$	3.50925	+	6.07820i	0.231898	+	0.401659i	0.958367	−	0.285541i	$-0.0921732\pi$
$229$	3.50925	+	6.07820i	0.231898	+	0.401659i	−0.726469	+	0.687199i	$0.758840\pi$
$230$	−2.21573	−	4.35187i	−0.146101	−	0.286954i
$231$	0.360295	−	6.05607i	0.0237057	−	0.398460i
$232$	−0.387321	+	0.477417i	−0.0254289	+	0.0313440i
$233$		−	20.0883i		−	1.31603i	−0.753006	−	0.658013i	$-0.771397\pi$
$233$		−	20.0883i		−	1.31603i	0.753006	−	0.658013i	$-0.228603\pi$
$234$	−19.1003	+	7.01746i	−1.24863	+	0.458746i
$235$		−	4.31988i		−	0.281798i
$236$	6.52054	−	8.96337i	0.424451	−	0.583466i
$237$	21.9100	−	10.9694i	1.42320	−	0.712542i
$238$	−1.70727	+	0.869251i	−0.110666	+	0.0563452i
$239$	−0.563997	−	0.976872i	−0.0364820	−	0.0631886i	0.847208	−	0.531261i	$-0.178282\pi$
$239$	−0.563997	−	0.976872i	−0.0364820	−	0.0631886i	−0.883690	+	0.468073i	$0.844948\pi$
$240$	−5.03962	−	5.12367i	−0.325306	−	0.330732i
$241$	4.67470	−	8.09682i	0.301124	−	0.521562i	−0.675267	−	0.737573i	$-0.735972\pi$
$241$	4.67470	−	8.09682i	0.301124	−	0.521562i	0.976391	+	0.216012i	$0.0693049\pi$
$242$	−0.0944339	+	1.79156i	−0.00607044	+	0.115166i
$243$	−3.50041	−	15.1904i	−0.224552	−	0.974462i
$244$	22.5017	+	2.37876i	1.44053	+	0.152284i
$245$	0.898347	+	0.518661i	0.0573933	+	0.0331360i
$246$	−1.99861	+	2.70868i	−0.127427	+	0.172699i
$247$	−21.3542	+	12.3288i	−1.35873	+	0.784465i
$248$	−0.862331	−	2.25254i	−0.0547581	−	0.143037i
$249$	9.38495	+	18.7451i	0.594747	+	1.18793i
$250$	7.13340	−	10.9772i	0.451156	−	0.694261i
$251$	20.3965			1.28741			0.643707	−	0.765272i	$-0.277396\pi$
$251$	20.3965			1.28741			0.643707	+	0.765272i	$0.277396\pi$
$252$	5.73303	−	1.76985i	0.361147	−	0.111490i
$253$	−11.6600			−0.733055
$254$	−4.39545	+	6.76393i	−0.275795	+	0.424407i
$255$	2.42967	+	0.144549i	0.152152	+	0.00905201i
$256$	−1.63404	−	15.9163i	−0.102128	−	0.994771i
$257$	4.36914	−	2.52253i	0.272540	−	0.157351i	−0.357502	−	0.933913i	$-0.616371\pi$
$257$	4.36914	−	2.52253i	0.272540	−	0.157351i	0.630041	+	0.776562i	$0.283038\pi$
$258$	−18.8414	−	2.12073i	−1.17302	−	0.132031i
$259$	2.82058	+	1.62846i	0.175262	+	0.101188i
$260$	−1.04608	+	9.89532i	−0.0648750	+	0.613682i
$261$	−0.0773131	+	0.647464i	−0.00478556	+	0.0400770i
$262$	1.52432	−	28.9187i	0.0941725	−	1.78660i
$263$	−12.0228	+	20.8241i	−0.741357	+	1.28407i	0.210520	+	0.977590i	$0.432484\pi$
$263$	−12.0228	+	20.8241i	−0.741357	+	1.28407i	−0.951877	+	0.306479i	$0.900849\pi$
$264$	−16.3613	+	5.17235i	−1.00697	+	0.318336i
$265$	6.97160	+	12.0752i	0.428262	+	0.741772i
$266$	6.47911	−	3.29881i	0.397260	−	0.202263i
$267$	8.28089	+	5.46122i	0.506782	+	0.334221i
$268$	23.9653	+	17.4339i	1.46391	+	1.06495i
$269$		−	28.5815i		−	1.74264i	−0.490712	−	0.871322i	$-0.663263\pi$
$269$		−	28.5815i		−	1.74264i	0.490712	−	0.871322i	$-0.336737\pi$
$270$	−7.42037	−	1.74472i	−0.451589	−	0.106180i
$271$			16.5138i			1.00314i	0.865117	+	0.501570i	$0.167244\pi$
$271$			16.5138i			1.00314i	−0.865117	+	0.501570i	$0.832756\pi$
$272$	4.02255	+	3.63072i	0.243903	+	0.220145i
$273$	−6.93496	−	4.57358i	−0.419723	−	0.276806i
$274$	7.24371	+	14.2272i	0.437608	+	0.859496i
$275$	−6.87214	−	11.9029i	−0.414406	−	0.717772i
$276$	−4.04991	−	10.7971i	−0.243776	−	0.649907i
$277$	−3.71718	+	6.43834i	−0.223344	+	0.386842i	−0.955821	−	0.293949i	$-0.905031\pi$
$277$	−3.71718	+	6.43834i	−0.223344	+	0.386842i	0.732478	+	0.680791i	$0.238364\pi$
$278$	15.0937	+	0.795592i	0.905258	+	0.0477165i
$279$	−2.04824	−	1.53280i	−0.122625	−	0.0917664i
$280$	0.461600	−	2.89745i	0.0275859	−	0.173156i
$281$	−3.33471	−	1.92530i	−0.198932	−	0.114854i	0.397225	−	0.917721i	$-0.369973\pi$
$281$	−3.33471	−	1.92530i	−0.198932	−	0.114854i	−0.596157	+	0.802868i	$0.703307\pi$
$282$	1.14096	−	10.1368i	0.0679433	−	0.603637i
$283$	25.6543	−	14.8115i	1.52499	−	0.880455i	0.525431	−	0.850836i	$-0.323904\pi$
$283$	25.6543	−	14.8115i	1.52499	−	0.880455i	0.999561	−	0.0296181i	$-0.00942912\pi$
$284$	−10.1944	−	22.9343i	−0.604928	−	1.36090i
$285$	−9.22061	−	0.548563i	−0.546182	−	0.0324941i
$286$	19.9213	+	12.9456i	1.17797	+	0.765490i
$287$	−1.37425			−0.0811194
$288$	−10.4724	−	13.3540i	−0.617093	−	0.786890i
$289$	15.1648			0.892048
$290$	0.267364	+	0.173743i	0.0157002	+	0.0102026i
$291$	7.01641	+	14.0143i	0.411309	+	0.821534i
$292$	11.7913	+	26.5267i	0.690032	+	1.55236i
$293$	11.7995	−	6.81242i	0.689332	−	0.397986i	−0.114030	−	0.993477i	$-0.536376\pi$
$293$	11.7995	−	6.81242i	0.689332	−	0.397986i	0.803362	+	0.595491i	$0.203043\pi$
$294$	1.97102	+	1.45433i	0.114952	+	0.0848182i
$295$	−4.97873	−	2.87447i	−0.289873	−	0.167358i
$296$	1.44931	−	9.09725i	0.0842392	−	0.528767i
$297$	−11.7510	+	13.8984i	−0.681860	+	0.806470i
$298$	9.21968	+	0.485972i	0.534082	+	0.0281516i
$299$	−7.98306	+	13.8271i	−0.461672	+	0.799640i
$300$	8.63510	−	10.4979i	0.498547	−	0.606094i
$301$	−3.87028	−	6.70351i	−0.223079	−	0.386384i
$302$	−2.08543	−	4.09593i	−0.120003	−	0.235694i
$303$	−10.1194	+	5.06636i	−0.581342	+	0.291055i
$304$	−15.2656	−	13.7786i	−0.875542	−	0.790257i
$305$		−	11.7358i		−	0.671990i
$306$	5.66315	+	0.980912i	0.323741	+	0.0560750i
$307$			28.8685i			1.64761i	0.566872	+	0.823806i	$0.308153\pi$
$307$			28.8685i			1.64761i	−0.566872	+	0.823806i	$0.691847\pi$
$308$	−5.66493	−	4.12104i	−0.322789	−	0.234818i
$309$	−0.987818	+	16.6039i	−0.0561950	+	0.944561i
$310$	−1.11481	+	0.567601i	−0.0633170	+	0.0322376i
$311$	7.99815	+	13.8532i	0.453534	+	0.785544i	0.998603	−	0.0528478i	$-0.0168298\pi$
$311$	7.99815	+	13.8532i	0.453534	+	0.785544i	−0.545069	+	0.838391i	$0.683496\pi$
$312$	−5.06820	+	22.9435i	−0.286931	+	1.29892i
$313$	−5.03324	+	8.71782i	−0.284495	+	0.492761i	−0.972487	−	0.232958i	$-0.925159\pi$
$313$	−5.03324	+	8.71782i	−0.284495	+	0.492761i	0.687991	+	0.725719i	$0.258493\pi$
$314$	−1.21179	+	22.9897i	−0.0683855	+	1.29738i
$315$	−1.22546	−	2.86052i	−0.0690471	−	0.161172i
$316$	2.97441	−	28.1363i	0.167324	−	1.58279i
$317$	5.18429	+	2.99315i	0.291179	+	0.168112i	0.638473	−	0.769644i	$-0.279566\pi$
$317$	5.18429	+	2.99315i	0.291179	+	0.168112i	−0.347295	+	0.937756i	$0.612900\pi$
$318$	13.1699	+	30.1762i	0.738530	+	1.69220i
$319$	0.659321	−	0.380659i	0.0369149	−	0.0213128i
$320$	−8.12034	+	1.71067i	−0.453941	+	0.0956295i
$321$	−13.0006	+	19.7129i	−0.725621	+	1.10027i
$322$	2.56522	−	3.94749i	0.142954	−	0.219985i
$323$	6.96455			0.387518
$324$	−16.9514	−	6.05392i	−0.941745	−	0.336329i
$325$	−18.8202			−1.04396
$326$	4.66631	−	7.18074i	0.258443	−	0.397704i
$327$	0.132972	−	0.201626i	0.00735336	−	0.0111500i
$328$	1.38968	+	3.63006i	0.0767322	+	0.200436i
$329$	3.60653	−	2.08223i	0.198834	−	0.114797i
$330$	3.55995	+	8.15693i	0.195969	+	0.449024i
$331$	−7.64092	−	4.41149i	−0.419983	−	0.242477i	0.275087	−	0.961419i	$-0.411293\pi$
$331$	−7.64092	−	4.41149i	−0.419983	−	0.242477i	−0.695070	+	0.718942i	$0.744627\pi$
$332$	24.0721	+	2.54477i	1.32113	+	0.139662i
$333$	−3.84764	−	8.98129i	−0.210850	−	0.492172i
$334$	−0.391593	+	7.42914i	−0.0214270	+	0.406505i
$335$	7.68545	−	13.3116i	0.419901	−	0.727290i
$336$	1.84843	−	6.67707i	0.100840	−	0.364264i
$337$	−0.0365288	−	0.0632698i	−0.00198985	−	0.00344652i	0.865029	−	0.501722i	$-0.167300\pi$
$337$	−0.0365288	−	0.0632698i	−0.00198985	−	0.00344652i	−0.867019	+	0.498276i	$0.833967\pi$
$338$	12.6074	−	6.41902i	0.685755	−	0.349149i
$339$	0.869174	−	14.6096i	0.0472071	−	0.793487i
$340$	1.65334	−	2.27275i	0.0896652	−	0.123257i
$341$			2.98691i			0.161750i
$342$	−21.4917	−	3.72256i	−1.16214	−	0.201293i
$343$			1.00000i			0.0539949i
$344$	−13.7935	+	17.0020i	−0.743694	+	0.916688i
$345$	−5.34816	+	2.67761i	−0.287935	+	0.144158i
$346$	−1.37213	−	2.69497i	−0.0737663	−	0.144883i
$347$	−3.09654	−	5.36336i	−0.166231	−	0.287920i	0.770861	−	0.637004i	$-0.219826\pi$
$347$	−3.09654	−	5.36336i	−0.166231	−	0.287920i	−0.937092	+	0.349083i	$0.886493\pi$
$348$	0.581493	+	0.478312i	0.0311713	+	0.0256402i
$349$	−3.08486	+	5.34314i	−0.165129	+	0.286012i	−0.936701	−	0.350130i	$-0.886137\pi$
$349$	−3.08486	+	5.34314i	−0.165129	+	0.286012i	0.771572	+	0.636142i	$0.219471\pi$
$350$	5.54163	+	0.292101i	0.296213	+	0.0156135i
$351$	8.43623	+	23.4506i	0.450293	+	1.25170i
$352$	−5.15711	+	19.1311i	−0.274875	+	1.01969i
$353$	20.5409	+	11.8593i	1.09328	+	0.631207i	0.934449	−	0.356098i	$-0.115893\pi$
$353$	20.5409	+	11.8593i	1.09328	+	0.631207i	0.158835	+	0.987305i	$0.449226\pi$
$354$	−10.9236	−	8.06004i	−0.580582	−	0.428386i
$355$	−11.2733	+	6.50867i	−0.598327	+	0.345444i
$356$	10.4667	−	4.65250i	0.554733	−	0.246582i
$357$	1.05045	+	2.09813i	0.0555956	+	0.111045i
$358$	8.13251	+	5.28480i	0.429817	+	0.279311i
$359$	19.5103			1.02971			0.514856	−	0.857277i	$-0.327845\pi$
$359$	19.5103			1.02971			0.514856	+	0.857277i	$0.327845\pi$
$360$	−6.31678	+	6.12967i	−0.332924	+	0.323062i
$361$	−7.43049			−0.391079
$362$	23.7983	+	15.4650i	1.25081	+	0.812821i
$363$	2.19338	+	0.130491i	0.115122	+	0.00684900i
$364$	−8.76549	+	3.89631i	−0.459437	+	0.204222i
$365$	13.0392	−	7.52818i	0.682502	−	0.394043i
$366$	3.09964	−	27.5386i	0.162021	−	1.43946i
$367$	6.01843	+	3.47474i	0.314160	+	0.181380i	0.648786	−	0.760971i	$-0.275277\pi$
$367$	6.01843	+	3.47474i	0.314160	+	0.181380i	−0.334627	+	0.942351i	$0.608610\pi$
$368$	−13.0212	−	2.78418i	−0.678779	−	0.145135i
$369$	3.30081	+	2.47017i	0.171833	+	0.128592i
$370$	−4.77127	−	0.251495i	−0.248046	−	0.0130746i
$371$	−6.72077	+	11.6407i	−0.348925	+	0.604356i
$372$	−2.76587	+	1.03746i	−0.143404	+	0.0537897i
$373$	−12.3478	−	21.3871i	−0.639347	−	1.10738i	−0.985576	−	0.169232i	$-0.945871\pi$
$373$	−12.3478	−	21.3871i	−0.639347	−	1.10738i	0.346229	−	0.938150i	$-0.387462\pi$
$374$	−3.04469	−	5.97999i	−0.157437	−	0.309218i
$375$	−13.3849	−	8.82730i	−0.691194	−	0.455840i
$376$	−9.14718	−	7.42096i	−0.471730	−	0.382707i
$377$		−	1.04248i		−	0.0536906i
$378$	−2.12009	−	7.03599i	−0.109046	−	0.361893i
$379$		−	21.9062i		−	1.12524i	−0.826714	−	0.562622i	$-0.809793\pi$
$379$		−	21.9062i		−	1.12524i	0.826714	−	0.562622i	$-0.190207\pi$
$380$	−6.27444	+	8.62508i	−0.321872	+	0.442457i
$381$	8.24750	+	5.43920i	0.422532	+	0.278658i
$382$	−31.0041	+	15.7856i	−1.58631	+	0.807661i
$383$	−12.7967	−	22.1646i	−0.653882	−	1.13256i	−0.982173	−	0.187980i	$-0.939806\pi$
$383$	−12.7967	−	22.1646i	−0.653882	−	1.13256i	0.328291	−	0.944577i	$-0.393528\pi$
$384$	−19.5065	+	1.86943i	−0.995439	+	0.0953991i
$385$	−1.81669	+	3.14660i	−0.0925871	+	0.160366i
$386$	−0.155916	+	2.95797i	−0.00793590	+	0.150557i
$387$	−2.75332	+	23.0579i	−0.139959	+	1.17210i
$388$	17.9969	+	1.90253i	0.913655	+	0.0965865i
$389$	−2.81098	−	1.62292i	−0.142522	−	0.0822853i	0.427043	−	0.904231i	$-0.359555\pi$
$389$	−2.81098	−	1.62292i	−0.142522	−	0.0822853i	−0.569566	+	0.821946i	$0.692889\pi$
$390$	12.1103	+	1.36309i	0.613229	+	0.0690229i
$391$	3.90545	−	2.25481i	0.197507	−	0.114031i
$392$	2.64148	−	1.01123i	0.133415	−	0.0510747i
$393$	−35.4046	−	2.10633i	−1.78593	−	0.106250i
$394$	11.0627	−	17.0238i	0.557332	−	0.857649i
$395$	−14.6745			−0.738355
$396$	6.19917	+	20.0808i	0.311520	+	1.00910i
$397$	−20.0197			−1.00476			−0.502380	−	0.864647i	$-0.667542\pi$
$397$	−20.0197			−1.00476			−0.502380	+	0.864647i	$0.667542\pi$
$398$	2.35989	−	3.63152i	0.118291	−	0.182032i
$399$	−3.98645	−	7.96239i	−0.199572	−	0.398618i
$400$	−4.83227	−	14.9335i	−0.241613	−	0.746674i
$401$	15.7412	−	9.08820i	0.786079	−	0.453843i	−0.0525012	−	0.998621i	$-0.516719\pi$
$401$	15.7412	−	9.08820i	0.786079	−	0.453843i	0.838580	+	0.544778i	$0.183386\pi$
$402$	21.5501	−	29.2064i	1.07482	−	1.45668i
$403$	3.54206	+	2.04501i	0.176442	+	0.101869i
$404$	−1.37377	+	12.9951i	−0.0683474	+	0.646529i
$405$	−2.19824	+	9.07341i	−0.109231	+	0.450861i
$406$	−0.0161800	+	0.306960i	−0.000802998	+	0.0152342i
$407$	−5.70394	+	9.87951i	−0.282734	+	0.489709i
$408$	4.47992	−	4.89642i	0.221789	−	0.242409i
$409$	14.6559	+	25.3847i	0.724687	+	1.25519i	0.959103	+	0.283058i	$0.0913490\pi$
$409$	14.6559	+	25.3847i	0.724687	+	1.25519i	−0.234416	+	0.972136i	$0.575318\pi$
$410$	1.79656	−	0.914711i	0.0887258	−	0.0451744i
$411$	17.4843	−	8.75367i	0.862435	−	0.431787i
$412$	15.5315	+	11.2986i	0.765182	+	0.556643i
$413$		−	5.54210i		−	0.272709i
$414$	−13.2569	+	4.87058i	−0.651540	+	0.239376i
$415$		−	12.5548i		−	0.616293i
$416$	19.1559	+	19.2138i	0.939197	+	0.942035i
$417$	1.09937	−	18.4789i	0.0538363	−	0.904915i
$418$	11.5546	+	22.6941i	0.565153	+	1.11000i
$419$	−1.13615	−	1.96786i	−0.0555043	−	0.0961363i	0.836938	−	0.547297i	$-0.184343\pi$
$419$	−1.13615	−	1.96786i	−0.0555043	−	0.0961363i	−0.892443	+	0.451161i	$0.851010\pi$
$420$	−3.54473	−	0.589323i	−0.172965	−	0.0287560i
$421$	−4.74134	+	8.21225i	−0.231079	+	0.400240i	−0.958126	−	0.286347i	$-0.907559\pi$
$421$	−4.74134	+	8.21225i	−0.231079	+	0.400240i	0.727047	+	0.686588i	$0.240892\pi$
$422$	−24.2444	−	1.27793i	−1.18020	−	0.0622087i
$423$	−12.4052	−	1.48130i	−0.603164	−	0.0720232i
$424$	37.5450	+	5.98138i	1.82334	+	0.290481i
$425$	4.60359	+	2.65788i	0.223307	+	0.128926i
$426$	−28.1724	+	12.2954i	−1.36496	+	0.595712i
$427$	9.79783	−	5.65678i	0.474150	−	0.273751i
$428$	11.0754	+	24.9162i	0.535350	+	1.20437i
$429$	16.0197	−	24.2908i	0.773437	−	1.17277i
$430$	9.52153	+	6.18744i	0.459169	+	0.298385i
$431$	1.41743			0.0682751			0.0341376	−	0.999417i	$-0.489132\pi$
$431$	1.41743			0.0682751			0.0341376	+	0.999417i	$0.489132\pi$
$432$	−16.4416	+	12.7152i	−0.791045	+	0.611758i
$433$	0.663345			0.0318783			0.0159392	−	0.999873i	$-0.494926\pi$
$433$	0.663345			0.0318783			0.0159392	+	0.999873i	$0.494926\pi$
$434$	−1.01122	−	0.657129i	−0.0485402	−	0.0315432i
$435$	0.215000	−	0.326007i	0.0103085	−	0.0156308i
$436$	−0.113281	−	0.254847i	−0.00542518	−	0.0122050i
$437$	−14.8212	+	8.55702i	−0.708994	+	0.409338i
$438$	32.5853	−	14.2213i	1.55699	−	0.679520i
$439$	15.7489	+	9.09265i	0.751656	+	0.433969i	0.826292	−	0.563242i	$-0.190446\pi$
$439$	15.7489	+	9.09265i	0.751656	+	0.433969i	−0.0746362	+	0.997211i	$0.523780\pi$
$440$	10.1488	+	1.61682i	0.483823	+	0.0770791i
$441$	1.79746	−	2.40190i	0.0855936	−	0.114376i
$442$	−9.17599	−	0.483670i	−0.436457	−	0.0230058i
$443$	19.6157	−	33.9754i	0.931969	−	1.61422i	0.152018	−	0.988378i	$-0.451423\pi$
$443$	19.6157	−	33.9754i	0.931969	−	1.61422i	0.779951	−	0.625841i	$-0.215244\pi$
$444$	−11.1296	−	1.85032i	−0.528185	−	0.0878125i
$445$	−2.97041	−	5.14490i	−0.140811	−	0.243892i
$446$	11.3233	+	22.2397i	0.536172	+	1.05308i
$447$	0.671528	−	11.2875i	0.0317622	−	0.533879i
$448$	−5.34227	−	5.95484i	−0.252399	−	0.281340i
$449$		−	21.5206i		−	1.01562i	−0.861469	−	0.507810i	$-0.830455\pi$
$449$		−	21.5206i		−	1.01562i	0.861469	−	0.507810i	$-0.169545\pi$
$450$	−12.7854	−	10.6625i	−0.602709	−	0.502634i
$451$		−	4.81352i		−	0.226660i
$452$	−13.6661	−	9.94158i	−0.642797	−	0.467613i
$453$	−5.03363	+	2.52014i	−0.236501	+	0.118406i
$454$	24.0071	−	12.2231i	1.12671	−	0.573659i
$455$	2.48761	+	4.30868i	0.116621	+	0.201994i
$456$	−17.0013	+	18.5819i	−0.796159	+	0.870178i
$457$	−10.9063	+	18.8903i	−0.510175	+	0.883650i	0.489755	+	0.871860i	$0.337086\pi$
$457$	−10.9063	+	18.8903i	−0.510175	+	0.883650i	−0.999931	+	0.0117896i	$0.996247\pi$
$458$	0.522459	−	9.91190i	0.0244129	−	0.463152i
$459$	1.24824	−	6.92763i	0.0582627	−	0.323354i
$460$	−0.726046	+	6.86799i	−0.0338521	+	0.320222i
$461$	12.2310	+	7.06156i	0.569653	+	0.328889i	0.757011	−	0.653402i	$-0.226659\pi$
$461$	12.2310	+	7.06156i	0.569653	+	0.328889i	−0.187358	+	0.982292i	$0.559992\pi$
$462$	−5.09401	+	6.90381i	−0.236995	+	0.321194i
$463$	1.08348	−	0.625550i	0.0503538	−	0.0290718i	−0.474612	−	0.880195i	$-0.657412\pi$
$463$	1.08348	−	0.625550i	0.0503538	−	0.0290718i	0.524966	+	0.851123i	$0.324078\pi$
$464$	0.827190	−	0.267667i	0.0384013	−	0.0124261i
$465$	0.685919	+	1.37003i	0.0318087	+	0.0635336i
$466$	−15.4799	+	23.8212i	−0.717092	+	1.10350i
$467$	9.78040			0.452583			0.226292	−	0.974060i	$-0.427340\pi$
$467$	9.78040			0.452583			0.226292	+	0.974060i	$0.427340\pi$
$468$	28.0573	+	6.39711i	1.29695	+	0.295707i
$469$	14.8179			0.684226
$470$	−3.32887	+	5.12263i	−0.153550	+	0.236289i
$471$	28.1458	+	1.67449i	1.29689	+	0.0771562i
$472$	−14.6393	+	5.60432i	−0.673830	+	0.257960i
$473$	23.4801	−	13.5562i	1.07962	−	0.623316i
$474$	−34.4344	−	3.87582i	−1.58162	−	0.178022i
$475$	−17.4706	−	10.0867i	−0.801607	−	0.462808i
$476$	2.69437	+	0.284834i	0.123496	+	0.0130553i
$477$	37.0664	−	15.8795i	1.69715	−	0.727072i
$478$	−0.0839683	+	1.59301i	−0.00384062	+	0.0728628i
$479$	−10.8984	+	18.8765i	−0.497960	+	0.862491i	−0.999997	−	0.00235456i	$-0.999251\pi$
$479$	−10.8984	+	18.8765i	−0.497960	+	0.862491i	0.502038	+	0.864846i	$0.332584\pi$
$480$	2.02784	+	9.95928i	0.0925580	+	0.454577i
$481$	7.81047	+	13.5281i	0.356127	+	0.616830i
$482$	−11.7827	+	5.99913i	−0.536689	+	0.273253i
$483$	−4.81331	−	3.17436i	−0.219013	−	0.144438i
$484$	1.49255	−	2.05171i	0.0678432	−	0.0932597i
$485$		−	9.38631i		−	0.426210i
$486$	−7.55471	+	20.7105i	−0.342689	+	0.939449i
$487$			6.60927i			0.299495i	0.988724	+	0.149747i	$0.0478460\pi$
$487$			6.60927i			0.299495i	−0.988724	+	0.149747i	$0.952154\pi$
$488$	−24.8501	−	20.1605i	−1.12491	−	0.912623i
$489$	−8.75573	−	5.77437i	−0.395948	−	0.261126i
$490$	−0.665607	−	1.30730i	−0.0300691	−	0.0590579i
$491$	−15.6065	−	27.0312i	−0.704310	−	1.21990i	−0.966940	−	0.255004i	$-0.917923\pi$
$491$	−15.6065	−	27.0312i	−0.704310	−	1.21990i	0.262630	−	0.964897i	$-0.415410\pi$
$492$	4.45730	−	1.67190i	0.200951	−	0.0753752i
$493$	−0.147224	+	0.255000i	−0.00663065	+	0.0114846i
$494$	34.8229	+	1.83553i	1.56676	+	0.0825842i
$495$	10.0194	−	4.29238i	0.450339	−	0.192928i
$496$	−0.713219	+	3.33563i	−0.0320245	+	0.149774i
$497$	−10.8677	−	6.27449i	−0.487485	−	0.281449i
$498$	3.31597	−	29.4605i	0.148592	−	1.32016i
$499$	−7.57908	+	4.37578i	−0.339286	+	0.195887i	−0.659956	−	0.751304i	$-0.729425\pi$
$499$	−7.57908	+	4.37578i	−0.339286	+	0.195887i	0.320670	+	0.947191i	$0.396092\pi$
$500$	−16.9180	+	7.52013i	−0.756594	+	0.336311i
$501$	9.09535	+	0.541112i	0.406350	+	0.0241751i
$502$	−24.1867	−	15.7174i	−1.07950	−	0.701502i
$503$	23.2222			1.03543			0.517713	−	0.855555i	$-0.326784\pi$
$503$	23.2222			1.03543			0.517713	+	0.855555i	$0.326784\pi$
$504$	−8.16222	−	2.31910i	−0.363574	−	0.103301i
$505$	6.77759			0.301599
$506$	13.8267	+	8.98509i	0.614671	+	0.399436i
$507$	−7.75708	−	15.4937i	−0.344504	−	0.688100i
$508$	10.4245	−	4.63374i	0.462512	−	0.205589i
$509$	−24.9560	+	14.4083i	−1.10615	+	0.638638i	−0.937830	−	0.347094i	$-0.887168\pi$
$509$	−24.9560	+	14.4083i	−1.10615	+	0.638638i	−0.168323	+	0.985732i	$0.553835\pi$
$510$	−2.76978	−	2.04370i	−0.122648	−	0.0904965i
$511$	12.5701	+	7.25732i	0.556066	+	0.321045i
$512$	−10.3273	+	20.1332i	−0.456408	+	0.889770i
$513$	−4.73706	+	26.2904i	−0.209146	+	1.16075i
$514$	−7.12489	−	0.375555i	−0.314265	−	0.0165650i
$515$	4.98080	−	8.62701i	0.219480	−	0.380151i
$516$	20.7085	+	17.0339i	0.911639	+	0.749876i
$517$	7.29333	+	12.6324i	0.320760	+	0.555573i
$518$	−2.08984	−	4.10460i	−0.0918221	−	0.180346i
$519$	−3.31194	+	1.65816i	−0.145378	+	0.0727850i
$520$	8.86574	−	10.9280i	0.388788	−	0.479226i
$521$		−	12.0996i		−	0.530094i	−0.964235	−	0.265047i	$-0.914612\pi$
$521$		−	12.0996i		−	0.530094i	0.964235	−	0.265047i	$-0.0853875\pi$
$522$	0.590612	−	0.708204i	0.0258504	−	0.0309972i
$523$			7.58603i			0.331714i	0.986150	+	0.165857i	$0.0530390\pi$
$523$			7.58603i			0.331714i	−0.986150	+	0.165857i	$0.946961\pi$
$524$	−24.0922	+	33.1180i	−1.05247	+	1.44676i
$525$	0.403632	−	6.78451i	0.0176160	−	0.296100i
$526$	30.3039	−	15.4291i	1.32131	−	0.672740i
$527$	−0.577612	−	1.00045i	−0.0251612	−	0.0435804i
$528$	23.3875	+	6.47443i	1.01781	+	0.281763i
$529$	5.95924	−	10.3217i	0.259097	−	0.448770i
$530$	1.03794	−	19.6913i	0.0450851	−	0.855337i
$531$	−9.96172	+	13.3116i	−0.432302	+	0.577673i
$532$	−10.2251	−	1.08094i	−0.443316	−	0.0468649i
$533$	−5.70816	−	3.29561i	−0.247248	−	0.142749i
$534$	−5.61132	−	12.8573i	−0.242826	−	0.556388i
$535$	12.2476	−	7.07113i	0.529508	−	0.305712i
$536$	−14.9842	−	39.1411i	−0.647221	−	1.69064i
$537$	6.53974	−	9.91626i	0.282210	−	0.427918i
$538$	−22.0247	+	33.8927i	−0.949553	+	1.46122i
$539$	−3.50265			−0.150870
$540$	7.45481	+	7.78703i	0.320804	+	0.335100i
$541$	−1.63666			−0.0703654			−0.0351827	−	0.999381i	$-0.511201\pi$
$541$	−1.63666			−0.0703654			−0.0351827	+	0.999381i	$0.511201\pi$
$542$	12.7254	−	19.5825i	0.546603	−	0.841139i
$543$	19.1373	−	29.0181i	0.821260	−	1.24528i
$544$	−1.97224	−	7.40516i	−0.0845590	−	0.317494i
$545$	−0.125270	+	0.0723247i	−0.00536598	+	0.00309805i
$546$	4.69929	+	10.7675i	0.201111	+	0.460807i
$547$	−8.45182	−	4.87966i	−0.361374	−	0.208639i	0.308310	−	0.951286i	$-0.400237\pi$
$547$	−8.45182	−	4.87966i	−0.361374	−	0.208639i	−0.669683	+	0.742647i	$0.733570\pi$
$548$	2.37360	−	22.4529i	0.101395	−	0.959142i
$549$	−33.7013	−	4.02424i	−1.43834	−	0.171750i
$550$	−1.02313	+	19.4104i	−0.0436264	+	0.827663i
$551$	0.558717	−	0.967726i	0.0238021	−	0.0412265i
$552$	−3.51766	+	15.9243i	−0.149722	+	0.677782i
$553$	−7.07327	−	12.2513i	−0.300786	−	0.520977i
$554$	9.36927	−	4.77032i	0.398062	−	0.202672i
$555$	−0.347522	+	5.84137i	−0.0147515	+	0.247952i
$556$	−17.2854	−	12.5745i	−0.733064	−	0.533278i
$557$			43.1522i			1.82842i	0.405243	+	0.914209i	$0.367187\pi$
$557$			43.1522i			1.82842i	−0.405243	+	0.914209i	$0.632813\pi$
$558$	1.24769	+	3.39600i	0.0528188	+	0.143764i
$559$		−	37.1254i		−	1.57024i
$560$	−2.78013	+	3.08017i	−0.117482	+	0.130161i
$561$	−7.34901	+	3.67936i	−0.310275	+	0.155343i
$562$	2.47077	+	4.85278i	0.104223	+	0.204702i
$563$	−1.30493	−	2.26020i	−0.0549961	−	0.0952560i	0.837217	−	0.546871i	$-0.184181\pi$
$563$	−1.30493	−	2.26020i	−0.0549961	−	0.0952560i	−0.892213	+	0.451615i	$0.850848\pi$
$564$	−9.16433	+	11.1413i	−0.385888	+	0.469132i
$565$	−4.38258	+	7.59085i	−0.184376	+	0.319349i
$566$	−41.8353	−	2.20515i	−1.75847	−	0.0926894i
$567$	−8.63466	+	2.53824i	−0.362622	+	0.106596i
$568$	−5.58420	+	35.0519i	−0.234308	+	1.47074i
$569$	−19.6204	−	11.3278i	−0.822529	−	0.474888i	0.0287586	−	0.999586i	$-0.490845\pi$
$569$	−19.6204	−	11.3278i	−0.822529	−	0.474888i	−0.851288	+	0.524699i	$0.824178\pi$
$570$	10.5113	+	7.75584i	0.440271	+	0.324857i
$571$	−14.1425	+	8.16520i	−0.591847	+	0.341703i	−0.765828	−	0.643046i	$-0.777670\pi$
$571$	−14.1425	+	8.16520i	−0.591847	+	0.341703i	0.173980	+	0.984749i	$0.444337\pi$
$572$	−13.6474	−	30.7025i	−0.570628	−	1.28374i
$573$	19.0761	+	38.1020i	0.796917	+	1.59173i
$574$	1.62962	+	1.05899i	0.0680192	+	0.0442013i
$575$	−13.0625			−0.544742
$576$	2.12799	+	23.9055i	0.0886662	+	0.996061i
$577$	−3.85191			−0.160357			−0.0801786	−	0.996781i	$-0.525549\pi$
$577$	−3.85191			−0.160357			−0.0801786	+	0.996781i	$0.525549\pi$
$578$	−17.9828	−	11.6859i	−0.747987	−	0.486070i
$579$	3.62138	+	0.215448i	0.150500	+	0.00895371i
$580$	−0.183163	−	0.412059i	−0.00760541	−	0.0171098i
$581$	10.4816	−	6.05157i	0.434851	−	0.251061i
$582$	2.47910	−	22.0254i	0.102762	−	0.912981i
$583$	−40.7734	−	23.5405i	−1.68866	−	0.974949i
$584$	6.45890	−	40.5424i	0.267271	−	1.67765i
$585$	1.76969	−	14.8204i	0.0731677	−	0.612748i
$586$	−19.2417	−	1.01424i	−0.794868	−	0.0418978i
$587$	−11.3059	+	19.5823i	−0.466643	+	0.808250i	−0.999274	−	0.0380980i	$-0.987870\pi$
$587$	−11.3059	+	19.5823i	−0.466643	+	0.808250i	0.532631	+	0.846348i	$0.321203\pi$
$588$	−1.21659	−	3.24344i	−0.0501714	−	0.133757i
$589$	2.19204	+	3.79672i	0.0903214	+	0.156441i
$590$	3.68886	+	7.24520i	0.151868	+	0.298280i
$591$	−20.7578	−	13.6897i	−0.853861	−	0.563118i
$592$	−8.72891	+	9.67094i	−0.358756	+	0.397473i
$593$			0.678737i			0.0278724i	0.999903	+	0.0139362i	$0.00443617\pi$
$593$			0.678737i			0.0278724i	−0.999903	+	0.0139362i	$0.995564\pi$
$594$	24.6447	−	7.42594i	1.01118	−	0.304690i
$595$		−	1.40525i		−	0.0576097i
$596$	−10.5585	−	7.68091i	−0.432491	−	0.314622i
$597$	−4.42804	−	2.92028i	−0.181228	−	0.119519i
$598$	20.1216	−	10.2448i	0.822833	−	0.418941i
$599$	−9.15979	−	15.8652i	−0.374259	−	0.648235i	0.615957	−	0.787780i	$-0.288769\pi$
$599$	−9.15979	−	15.8652i	−0.374259	−	0.648235i	−0.990216	+	0.139545i	$0.955436\pi$
$600$	−18.3293	+	5.79449i	−0.748291	+	0.236559i
$601$	16.3104	−	28.2504i	0.665314	−	1.15236i	−0.313886	−	0.949461i	$-0.601631\pi$
$601$	16.3104	−	28.2504i	0.665314	−	1.15236i	0.979200	−	0.202897i	$-0.0650357\pi$
$602$	−0.576209	+	10.9316i	−0.0234845	+	0.445539i
$603$	−35.5911	−	26.6346i	−1.44938	−	1.08465i
$604$	−0.683347	+	6.46408i	−0.0278050	+	0.263020i
$605$	−1.13963	−	0.657965i	−0.0463325	−	0.0267501i
$606$	15.9039	+	1.79009i	0.646052	+	0.0727174i
$607$	30.1157	−	17.3873i	1.22236	−	0.705728i	0.256937	−	0.966428i	$-0.417287\pi$
$607$	30.1157	−	17.3873i	1.22236	−	0.705728i	0.965420	+	0.260700i	$0.0839533\pi$
$608$	7.48465	+	28.1026i	0.303542	+	1.13971i
$609$	0.375805	+	0.0223578i	0.0152284	+	0.000905985i
$610$	−9.04354	+	13.9166i	−0.366162	+	0.563468i
$611$	19.9737			0.808049
$612$	−5.95963	−	5.52718i	−0.240904	−	0.223423i
$613$	13.6778			0.552443			0.276221	−	0.961094i	$-0.410918\pi$
$613$	13.6778			0.552443			0.276221	+	0.961094i	$0.410918\pi$
$614$	22.2459	−	34.2330i	0.897770	−	1.38153i
$615$	−1.10538	−	2.20785i	−0.0445734	−	0.0890293i
$616$	3.54198	+	9.25219i	0.142710	+	0.372781i
$617$	4.95281	−	2.85951i	0.199393	−	0.115119i	−0.396980	−	0.917827i	$-0.629942\pi$
$617$	4.95281	−	2.85951i	0.199393	−	0.115119i	0.596372	+	0.802708i	$0.296608\pi$
$618$	13.9662	−	18.9281i	0.561804	−	0.761400i
$619$	7.04976	+	4.07018i	0.283354	+	0.163594i	0.634941	−	0.772561i	$-0.281025\pi$
$619$	7.04976	+	4.07018i	0.283354	+	0.163594i	−0.351587	+	0.936155i	$0.614358\pi$
$620$	1.75936	+	0.185990i	0.0706577	+	0.00746954i
$621$	5.85529	+	16.2763i	0.234965	+	0.653144i
$622$	1.19077	−	22.5908i	0.0477456	−	0.905810i
$623$	2.86354	−	4.95979i	0.114725	−	0.198710i
$624$	23.6901	−	23.3015i	0.948364	−	0.932806i
$625$	−5.00865	−	8.67524i	−0.200346	−	0.347010i
$626$	12.6864	−	6.45925i	0.507053	−	0.258163i
$627$	27.8895	−	13.9632i	1.11380	−	0.557635i
$628$	19.1527	−	26.3280i	0.764276	−	1.05060i
$629$		−	4.41213i		−	0.175923i
$630$	−0.751109	+	4.33641i	−0.0299249	+	0.172767i
$631$			21.8309i			0.869075i	0.900654	+	0.434538i	$0.143088\pi$
$631$			21.8309i			0.869075i	−0.900654	+	0.434538i	$0.856912\pi$
$632$	−25.2088	+	31.0727i	−1.00275	+	1.23601i
$633$	−1.76587	+	29.6819i	−0.0701872	+	1.17975i
$634$	−3.84117	−	7.54434i	−0.152552	−	0.299624i
$635$	−2.95843	−	5.12415i	−0.117402	−	0.203346i
$636$	7.63641	−	45.9324i	0.302803	−	1.82134i
$637$	−2.39811	+	4.15365i	−0.0950167	+	0.164574i
$638$	−1.07517	−	0.0566728i	−0.0425665	−	0.00224370i
$639$	14.8250	+	34.6051i	0.586470	+	1.36896i
$640$	10.9476	+	4.22892i	0.432740	+	0.167163i
$641$	−20.0771	−	11.5915i	−0.792998	−	0.457838i	0.0480189	−	0.998846i	$-0.484709\pi$
$641$	−20.0771	−	11.5915i	−0.792998	−	0.457838i	−0.841017	+	0.541009i	$0.818043\pi$
$642$	30.6070	−	13.3579i	1.20796	−	0.527194i
$643$	−9.84261	+	5.68263i	−0.388155	+	0.224101i	−0.681360	−	0.731948i	$-0.738611\pi$
$643$	−9.84261	+	5.68263i	−0.388155	+	0.224101i	0.293206	+	0.956049i	$0.405278\pi$
$644$	−6.08382	+	2.70429i	−0.239736	+	0.106564i
$645$	7.65671	−	11.6099i	0.301483	−	0.457141i
$646$	−8.25876	−	5.36684i	−0.324936	−	0.211156i
$647$	4.43372			0.174307			0.0871537	−	0.996195i	$-0.472223\pi$
$647$	4.43372			0.174307			0.0871537	+	0.996195i	$0.472223\pi$
$648$	15.4363	+	20.2415i	0.606396	+	0.795163i
$649$	19.4120			0.761990
$650$	22.3175	+	14.5027i	0.875365	+	0.568844i
$651$	−0.813172	+	1.23302i	−0.0318707	+	0.0483258i
$652$	−11.0669	+	4.91929i	−0.433412	+	0.192654i
$653$	−38.6732	+	22.3280i	−1.51340	+	0.873761i	−0.513521	+	0.858077i	$0.671659\pi$
$653$	−38.6732	+	22.3280i	−1.51340	+	0.873761i	−0.999877	+	0.0156838i	$0.995007\pi$
$654$	−0.313054	+	0.136627i	−0.0122414	+	0.00534253i
$655$	18.3955	+	10.6206i	0.718770	+	0.414982i
$656$	1.14938	−	5.37550i	0.0448757	−	0.209878i
$657$	−17.1472	−	40.0256i	−0.668977	−	1.56155i
$658$	−5.88127	−	0.310004i	−0.229276	−	0.0120852i
$659$	−5.15687	+	8.93196i	−0.200883	+	0.347940i	−0.948813	−	0.315838i	$-0.897714\pi$
$659$	−5.15687	+	8.93196i	−0.200883	+	0.347940i	0.747930	+	0.663778i	$0.231048\pi$
$660$	2.06420	−	12.4160i	0.0803487	−	0.483291i
$661$	−8.31721	−	14.4058i	−0.323502	−	0.560322i	0.657706	−	0.753275i	$-0.271527\pi$
$661$	−8.31721	−	14.4058i	−0.323502	−	0.560322i	−0.981208	+	0.192953i	$0.938194\pi$
$662$	5.66135	+	11.1193i	0.220035	+	0.432164i
$663$	−0.668346	+	11.2340i	−0.0259564	+	0.436292i
$664$	−26.5844	−	21.5675i	−1.03167	−	0.836981i
$665$			5.33293i			0.206802i
$666$	−2.35829	+	13.6152i	−0.0913818	+	0.527579i
$667$		−	0.723550i		−	0.0280160i
$668$	6.18921	−	8.50792i	0.239468	−	0.329181i
$669$	27.3311	−	13.6836i	1.05668	−	0.529039i
$670$	−19.3714	+	9.86288i	−0.748384	+	0.381036i
$671$	19.8137	+	34.3184i	0.764901	+	1.32485i
$672$	−7.33723	+	6.49346i	−0.283040	+	0.250491i
$673$	21.3572	−	36.9917i	0.823258	−	1.42592i	−0.0799851	−	0.996796i	$-0.525487\pi$
$673$	21.3572	−	36.9917i	0.823258	−	1.42592i	0.903243	−	0.429129i	$-0.141179\pi$
$674$	−0.00543844	+	0.103176i	−0.000209481	+	0.00397419i
$675$	−13.1644	+	15.5702i	−0.506698	+	0.599297i
$676$	−19.8967	−	2.10337i	−0.765258	−	0.0808988i
$677$	7.25220	+	4.18706i	0.278725	+	0.160922i	0.632846	−	0.774278i	$-0.281887\pi$
$677$	7.25220	+	4.18706i	0.278725	+	0.160922i	−0.354121	+	0.935200i	$0.615220\pi$
$678$	−12.2888	+	16.6547i	−0.471948	+	0.639621i
$679$	7.83631	−	4.52430i	0.300730	−	0.173627i
$680$	−3.71195	+	1.42103i	−0.142347	+	0.0544940i
$681$	−14.7711	−	29.5032i	−0.566028	−	1.13056i
$682$	2.30170	−	3.54196i	0.0881365	−	0.135629i
$683$	−30.2783			−1.15857			−0.579283	−	0.815127i	$-0.696667\pi$
$683$	−30.2783			−1.15857			−0.579283	+	0.815127i	$0.696667\pi$
$684$	22.6168	+	20.9757i	0.864775	+	0.802024i
$685$	−11.7103			−0.447429
$686$	0.770594	−	1.18583i	0.0294214	−	0.0452751i
$687$	−12.1349	−	0.721946i	−0.462977	−	0.0275440i
$688$	29.4583	−	9.53230i	1.12309	−	0.363416i
$689$	−55.8315	+	32.2343i	−2.12701	+	1.22803i
$690$	8.40534	+	0.946075i	0.319986	+	0.0360165i
$691$	12.9887	+	7.49902i	0.494113	+	0.285276i	0.726279	−	0.687400i	$-0.241248\pi$
$691$	12.9887	+	7.49902i	0.494113	+	0.285276i	−0.232166	+	0.972676i	$0.574581\pi$
$692$	−0.449617	+	4.25313i	−0.0170919	+	0.161680i
$693$	8.41302	+	6.29590i	0.319584	+	0.239161i
$694$	−0.461015	+	8.74619i	−0.0174999	+	0.332001i
$695$	−5.54327	+	9.60122i	−0.210268	+	0.364195i
$696$	−0.320966	−	1.01529i	−0.0121662	−	0.0384845i
$697$	0.930843	+	1.61227i	0.0352582	+	0.0610690i
$698$	7.77550	−	3.95886i	0.294307	−	0.149845i
$699$	29.0461	+	19.1558i	1.09862	+	0.724537i
$700$	−6.34632	−	4.61673i	−0.239868	−	0.174496i
$701$			50.3732i			1.90257i	0.308316	+	0.951284i	$0.400235\pi$
$701$			50.3732i			1.90257i	−0.308316	+	0.951284i	$0.599765\pi$
$702$	8.06700	−	34.3093i	0.304469	−	1.29492i
$703$			16.7440i			0.631514i
$704$	20.8577	−	18.7121i	0.786106	−	0.705240i
$705$	6.24621	+	4.11935i	0.235246	+	0.155144i
$706$	−15.2193	−	29.8918i	−0.572785	−	1.12499i
$707$	3.26687	+	5.65839i	0.122863	+	0.212806i
$708$	6.74247	+	17.9755i	0.253398	+	0.675559i
$709$	−19.7109	+	34.1403i	−0.740258	+	1.28217i	0.212119	+	0.977244i	$0.431964\pi$
$709$	−19.7109	+	34.1403i	−0.740258	+	1.28217i	−0.952378	+	0.304921i	$0.901370\pi$
$710$	18.3838	+	0.969015i	0.689931	+	0.0363665i
$711$	−5.03193	+	42.1403i	−0.188712	+	1.58038i
$712$	−15.9969	−	2.54850i	−0.599508	−	0.0955091i
$713$	2.45842	+	1.41937i	0.0920685	+	0.0531558i
$714$	0.371153	−	3.29748i	0.0138901	−	0.123405i
$715$	−15.0918	+	8.71325i	−0.564401	+	0.325857i
$716$	−5.57131	−	12.5337i	−0.208210	−	0.468407i
$717$	1.95030	+	0.116029i	0.0728351	+	0.00433320i
$718$	−23.1358	−	15.0345i	−0.863420	−	0.561082i
$719$	5.11873			0.190896			0.0954482	−	0.995434i	$-0.469572\pi$
$719$	5.11873			0.190896			0.0954482	+	0.995434i	$0.469572\pi$
$720$	12.2141	−	2.40106i	0.455192	−	0.0894822i
$721$	9.60320			0.357642
$722$	8.81128	+	5.72589i	0.327922	+	0.213096i
$723$	7.24966	+	14.4802i	0.269618	+	0.538524i
$724$	−16.3034	−	36.6776i	−0.605911	−	1.36311i
$725$	0.738626	−	0.426446i	0.0274319	−	0.0158378i
$726$	−2.50041	−	1.84494i	−0.0927989	−	0.0684722i
$727$	16.2868	+	9.40317i	0.604043	+	0.348744i	0.770630	−	0.637282i	$-0.219942\pi$
$727$	16.2868	+	9.40317i	0.604043	+	0.348744i	−0.166588	+	0.986027i	$0.553275\pi$
$728$	13.3968	+	2.13428i	0.496520	+	0.0791018i
$729$	25.3020	+	9.42389i	0.937110	+	0.349033i
$730$	−21.2634	−	1.12080i	−0.786993	−	0.0414827i
$731$	−5.24303	+	9.08120i	−0.193921	+	0.335880i
$732$	−24.8967	+	30.2674i	−0.920208	+	1.11872i
$733$	−17.9418	−	31.0762i	−0.662697	−	1.14782i	−0.979904	−	0.199468i	$-0.936079\pi$
$733$	−17.9418	−	31.0762i	−0.662697	−	1.14782i	0.317208	−	0.948356i	$-0.397255\pi$
$734$	−4.45920	−	8.75821i	−0.164592	−	0.323271i
$735$	−1.60659	+	0.804354i	−0.0592599	+	0.0296691i
$736$	13.2955	+	13.3356i	0.490077	+	0.491558i
$737$			51.9019i			1.91183i
$738$	−2.01070	−	5.47277i	−0.0740147	−	0.201456i
$739$			36.4538i			1.34097i	0.741922	+	0.670486i	$0.233915\pi$
$739$			36.4538i			1.34097i	−0.741922	+	0.670486i	$0.766085\pi$
$740$	5.46410	+	3.97494i	0.200864	+	0.146122i
$741$	2.53637	−	42.6330i	0.0931760	−	1.56616i
$742$	16.9399	−	8.62489i	0.621885	−	0.316630i
$743$	16.8124	+	29.1198i	0.616785	+	1.06830i	0.990068	+	0.140586i	$0.0448987\pi$
$743$	16.8124	+	29.1198i	0.616785	+	1.06830i	−0.373283	+	0.927717i	$0.621768\pi$
$744$	4.07930	+	0.901114i	0.149554	+	0.0330365i
$745$	−3.38600	+	5.86472i	−0.124053	+	0.214867i
$746$	−1.83836	+	34.8766i	−0.0673070	+	1.27692i
$747$	−36.0533	−	4.30509i	−1.31912	−	0.157515i
$748$	−0.997674	+	9.43745i	−0.0364786	+	0.345067i
$749$	11.8069	+	6.81672i	0.431415	+	0.249078i
$750$	9.06993	+	20.7820i	0.331187	+	0.758851i
$751$	−20.3676	+	11.7593i	−0.743225	+	0.429101i	−0.823241	−	0.567692i	$-0.807836\pi$
$751$	−20.3676	+	11.7593i	−0.743225	+	0.429101i	0.0800155	+	0.996794i	$0.474503\pi$
$752$	5.12843	+	15.8487i	0.187015	+	0.577944i
$753$	−19.4496	+	29.4917i	−0.708785	+	1.07474i
$754$	−0.803330	+	1.23620i	−0.0292556	+	0.0450199i
$755$	3.37135			0.122696
$756$	−2.90784	+	9.97720i	−0.105757	+	0.362867i
$757$	29.6018			1.07590			0.537948	−	0.842978i	$-0.319200\pi$
$757$	29.6018			1.07590			0.537948	+	0.842978i	$0.319200\pi$
$758$	−16.8808	+	25.9769i	−0.613137	+	0.943524i
$759$	11.1187	−	16.8594i	0.403583	−	0.611957i
$760$	14.0868	−	5.39281i	0.510983	−	0.195618i
$761$	10.7836	−	6.22589i	0.390904	−	0.225688i	−0.291648	−	0.956526i	$-0.594204\pi$
$761$	10.7836	−	6.22589i	0.390904	−	0.225688i	0.682552	+	0.730837i	$0.260870\pi$
$762$	−5.58870	−	12.8054i	−0.202457	−	0.463891i
$763$	−0.120763	−	0.0697225i	−0.00437191	−	0.00252412i
$764$	48.9298	+	5.17258i	1.77022	+	0.187137i
$765$	−2.52589	+	3.37527i	−0.0913238	+	0.122033i
$766$	−1.90519	+	36.1444i	−0.0688372	+	1.30595i
$767$	13.2906	−	23.0200i	0.479895	−	0.831202i
$768$	24.5720	+	12.8148i	0.886664	+	0.462414i
$769$	4.89062	+	8.47080i	0.176360	+	0.305465i	0.940631	−	0.339431i	$-0.110234\pi$
$769$	4.89062	+	8.47080i	0.176360	+	0.305465i	−0.764271	+	0.644895i	$0.776901\pi$
$770$	4.57903	−	2.33139i	0.165017	−	0.0840175i
$771$	−0.518951	+	8.72286i	−0.0186896	+	0.314146i
$772$	2.46428	−	3.38749i	0.0886915	−	0.121919i
$773$			27.6321i			0.993857i	0.867792	+	0.496928i	$0.165539\pi$
$773$			27.6321i			0.993857i	−0.867792	+	0.496928i	$0.834461\pi$
$774$	21.0332	−	25.2209i	0.756022	−	0.906548i
$775$			3.34619i			0.120199i
$776$	−19.8751	−	16.1244i	−0.713476	−	0.578832i
$777$	−5.04427	+	2.52547i	−0.180962	+	0.0906006i
$778$	2.08272	+	4.09062i	0.0746692	+	0.146656i
$779$	−3.53255	−	6.11856i	−0.126567	−	0.219220i
$780$	−13.3103	−	10.9485i	−0.476586	−	0.392020i
$781$	21.9774	−	38.0659i	0.786412	−	1.36211i
$782$	−6.36873	−	0.335698i	−0.227745	−	0.0120045i
$783$	−0.862458	−	0.729197i	−0.0308217	−	0.0260594i
$784$	−3.91158	−	0.836368i	−0.139699	−	0.0298703i
$785$	−14.6240	−	8.44314i	−0.521951	−	0.301349i
$786$	40.3606	+	29.7803i	1.43962	+	1.06223i
$787$	−27.3188	+	15.7725i	−0.973810	+	0.562229i	−0.900396	−	0.435072i	$-0.856723\pi$
$787$	−27.3188	+	15.7725i	−0.973810	+	0.562229i	−0.0734143	+	0.997302i	$0.523390\pi$
$788$	−26.2369	+	11.6625i	−0.934652	+	0.415458i
$789$	−18.6453	−	37.2414i	−0.663790	−	1.32583i
$790$	17.4014	+	11.3081i	0.619116	+	0.402324i
$791$	−8.44980			−0.300440
$792$	8.12301	−	28.5894i	0.288639	−	1.01588i
$793$	54.2624			1.92691
$794$	23.7399	+	15.4271i	0.842497	+	0.547486i
$795$	−24.1077	−	1.43424i	−0.855012	−	0.0508674i
$796$	−5.59685	+	2.48783i	−0.198375	+	0.0881789i
$797$	−16.7768	+	9.68607i	−0.594264	+	0.343098i	−0.766782	−	0.641908i	$-0.778143\pi$
$797$	−16.7768	+	9.68607i	−0.594264	+	0.343098i	0.172518	+	0.985006i	$0.444810\pi$
$798$	−1.40853	+	12.5140i	−0.0498613	+	0.442989i
$799$	−4.88573	−	2.82078i	−0.172845	−	0.0997920i
$800$	−5.77742	+	21.4322i	−0.204263	+	0.757744i
$801$	−15.7930	+	6.76581i	−0.558017	+	0.239058i
$802$	−25.6697	−	1.35306i	−0.906428	−	0.0477781i
$803$	−25.4199	+	44.0285i	−0.897049	+	1.55373i
$804$	−48.0609	+	18.0273i	−1.69498	+	0.635774i
$805$	1.72657	+	2.99050i	0.0608535	+	0.105401i
$806$	−2.62440	−	5.15451i	−0.0924405	−	0.181560i
$807$	41.3266	+	27.2547i	1.45476	+	0.959411i
$808$	11.6430	−	14.3513i	0.409598	−	0.504877i
$809$		−	21.4126i		−	0.752828i	−0.926452	−	0.376414i	$-0.877157\pi$
$809$		−	21.4126i		−	0.752828i	0.926452	−	0.376414i	$-0.122843\pi$
$810$	9.59864	−	9.06554i	0.337262	−	0.318531i
$811$		−	32.7084i		−	1.14855i	−0.818663	−	0.574274i	$-0.805285\pi$
$811$		−	32.7084i		−	1.14855i	0.818663	−	0.574274i	$-0.194715\pi$
$812$	0.255728	−	0.351533i	0.00897429	−	0.0123364i
$813$	−23.8776	−	15.7472i	−0.837424	−	0.552278i
$814$	14.3770	−	7.31997i	0.503913	−	0.256565i
$815$	3.14074	+	5.43991i	0.110015	+	0.190552i
$816$	−9.08556	+	2.35411i	−0.318058	+	0.0824103i
$817$	19.8973	−	34.4632i	0.696119	−	1.20571i
$818$	2.18198	−	41.3956i	0.0762911	−	1.44736i
$819$	13.2261	−	5.66614i	0.462156	−	0.197991i
$820$	−2.83528	−	0.299730i	−0.0990123	−	0.0104670i
$821$	38.1467	+	22.0240i	1.33133	+	0.768644i	0.985504	−	0.169654i	$-0.0542651\pi$
$821$	38.1467	+	22.0240i	1.33133	+	0.768644i	0.345827	+	0.938298i	$0.387598\pi$
$822$	−27.4788	−	3.09292i	−0.958434	−	0.107878i
$823$	−15.5963	+	9.00455i	−0.543654	+	0.313879i	−0.746559	−	0.665320i	$-0.768295\pi$
$823$	−15.5963	+	9.00455i	−0.543654	+	0.313879i	0.202904	+	0.979199i	$0.434962\pi$
$824$	−9.71102	−	25.3667i	−0.338299	−	0.883690i
$825$	23.7638	+	1.41378i	0.827349	+	0.0492216i
$826$	−4.27071	+	6.57197i	−0.148597	+	0.228668i
$827$	48.5077			1.68678			0.843389	−	0.537303i	$-0.180557\pi$
$827$	48.5077			1.68678			0.843389	+	0.537303i	$0.180557\pi$
$828$	19.4736	+	4.44001i	0.676754	+	0.154301i
$829$	−27.8358			−0.966777			−0.483389	−	0.875406i	$-0.660594\pi$
$829$	−27.8358			−0.966777			−0.483389	+	0.875406i	$0.660594\pi$
$830$	−9.67468	+	14.8879i	−0.335813	+	0.516766i
$831$	−5.76471	−	11.5142i	−0.199975	−	0.399424i
$832$	−7.90957	−	37.5457i	−0.274215	−	1.30166i
$833$	1.17320	−	0.677346i	0.0406489	−	0.0234687i
$834$	−15.5434	+	21.0656i	−0.538223	+	0.729441i
$835$	−4.72575	−	2.72841i	−0.163541	−	0.0944205i
$836$	3.78618	−	35.8151i	0.130948	−	1.23869i
$837$	4.16947	−	1.49994i	0.144118	−	0.0518456i
$838$	−0.169150	+	3.20905i	−0.00584319	+	0.110855i
$839$	3.69402	−	6.39822i	0.127532	−	0.220891i	−0.795188	−	0.606363i	$-0.792628\pi$
$839$	3.69402	−	6.39822i	0.127532	−	0.220891i	0.922720	+	0.385472i	$0.125961\pi$
$840$	3.74931	+	3.43038i	0.129364	+	0.118360i
$841$	−14.4764	−	25.0738i	−0.499185	−	0.864615i
$842$	11.9507	−	6.08465i	0.411849	−	0.209691i
$843$	5.96374	−	2.98581i	0.205402	−	0.102837i
$844$	27.7649	+	20.1980i	0.955707	+	0.695243i
$845$			10.3771i			0.356985i
$846$	13.5690	+	11.3160i	0.466512	+	0.389051i
$847$		−	1.26859i		−	0.0435891i
$848$	−39.9126	−	36.0248i	−1.37060	−	1.23710i
$849$	−3.04713	+	51.2181i	−0.104577	+	1.75780i
$850$	−3.41091	−	6.69928i	−0.116993	−	0.229784i
$851$	5.42098	+	9.38941i	0.185829	+	0.321865i
$852$	42.8824	+	7.12933i	1.46913	+	0.244247i
$853$	26.8805	−	46.5584i	0.920371	−	1.59413i	0.121529	−	0.992588i	$-0.461220\pi$
$853$	26.8805	−	46.5584i	0.920371	−	1.59413i	0.798842	−	0.601541i	$-0.205446\pi$
$854$	−15.9776	−	0.842185i	−0.546743	−	0.0288190i
$855$	9.58576	−	12.8092i	0.327826	−	0.438064i
$856$	6.06677	−	38.0810i	0.207358	−	1.30158i
$857$	43.9316	+	25.3639i	1.50068	+	0.866416i	1.00000		0.000781209i	$0.000248666\pi$
$857$	43.9316	+	25.3639i	1.50068	+	0.866416i	0.500676	+	0.865635i	$0.333085\pi$
$858$	−37.7149	+	16.4600i	−1.28756	+	0.561935i
$859$	−1.97520	+	1.14038i	−0.0673930	+	0.0389094i	−0.533318	−	0.845915i	$-0.679055\pi$
$859$	−1.97520	+	1.14038i	−0.0673930	+	0.0389094i	0.465925	+	0.884824i	$0.345722\pi$
$860$	−6.52288	−	14.6745i	−0.222428	−	0.500395i
$861$	1.31046	−	1.98706i	0.0446602	−	0.0677187i
$862$	−1.68082	−	1.09226i	−0.0572491	−	0.0372026i
$863$	−12.2604			−0.417350			−0.208675	−	0.977985i	$-0.566915\pi$
$863$	−12.2604			−0.417350			−0.208675	+	0.977985i	$0.566915\pi$
$864$	29.2951	−	2.40822i	0.996638	−	0.0819293i
$865$	2.21822			0.0754219
$866$	−0.786612	−	0.511170i	−0.0267302	−	0.0173702i
$867$	−14.4608	+	21.9271i	−0.491116	+	0.744684i
$868$	0.692755	+	1.55848i	0.0235136	+	0.0528984i
$869$	42.9120	−	24.7752i	1.45569	−	0.840442i
$870$	−0.506172	+	0.220910i	−0.0171608	+	0.00748955i
$871$	61.5483	+	35.5349i	2.08549	+	1.20406i
$872$	−0.0620519	+	0.389498i	−0.00210134	+	0.0131901i
$873$	−26.9543	−	3.21859i	−0.912265	−	0.108933i
$874$	24.1693	+	1.27397i	0.817540	+	0.0430928i
$875$	−4.62851	+	8.01682i	−0.156472	+	0.271018i
$876$	−49.5994	−	8.24606i	−1.67581	−	0.278609i
$877$	−7.38684	−	12.7944i	−0.249436	−	0.432036i	0.713933	−	0.700214i	$-0.246912\pi$
$877$	−7.38684	−	12.7944i	−0.249436	−	0.432036i	−0.963369	+	0.268178i	$0.913579\pi$
$878$	−11.6688	−	22.9183i	−0.393802	−	0.773456i
$879$	−1.40150	+	23.5573i	−0.0472713	+	0.794567i
$880$	−10.7888	−	9.73785i	−0.363689	−	0.328263i
$881$		−	23.5253i		−	0.792589i	−0.918124	−	0.396294i	$-0.870296\pi$
$881$		−	23.5253i		−	0.792589i	0.918124	−	0.396294i	$-0.129704\pi$
$882$	−3.98237	+	1.46312i	−0.134093	+	0.0492659i
$883$		−	13.0569i		−	0.439401i	−0.975567	−	0.219700i	$-0.929492\pi$
$883$		−	13.0569i		−	0.439401i	0.975567	−	0.219700i	$-0.0705080\pi$
$884$	10.5084	+	7.64451i	0.353436	+	0.257113i
$885$	8.90386	−	4.45781i	0.299300	−	0.149848i
$886$	−49.4420	+	25.1732i	−1.66104	+	0.845709i
$887$	5.09668	+	8.82771i	0.171130	+	0.296405i	0.938815	−	0.344422i	$-0.111925\pi$
$887$	5.09668	+	8.82771i	0.171130	+	0.296405i	−0.767685	+	0.640827i	$0.778592\pi$
$888$	11.7719	+	10.7705i	0.395038	+	0.361435i
$889$	2.85199	−	4.93979i	0.0956527	−	0.165675i
$890$	−0.442236	+	8.38993i	−0.0148238	+	0.281231i
$891$	−8.89058	−	30.2442i	−0.297846	−	1.01322i
$892$	3.71037	−	35.0981i	0.124232	−	1.17517i
$893$	18.5414	+	10.7049i	0.620463	+	0.358225i
$894$	−9.49437	+	12.8675i	−0.317539	+	0.430354i
$895$	−6.16095	+	3.55703i	−0.205938	+	0.118898i
$896$	1.74625	+	11.1781i	0.0583381	+	0.373435i
$897$	−12.3804	−	24.7281i	−0.413368	−	0.825646i
$898$	−16.5837	+	25.5197i	−0.553404	+	0.851604i
$899$	−0.185351			−0.00618179
$900$	6.94482	+	22.4962i	0.231494	+	0.749873i
$901$	18.2092			0.606635
$902$	−3.70927	+	5.70801i	−0.123505	+	0.190056i
$903$	13.3834	+	0.796219i	0.445370	+	0.0264965i
$904$	8.54466	+	22.3200i	0.284191	+	0.742351i
$905$	−18.0288	+	10.4090i	−0.599299	+	0.346006i
$906$	7.91101	+	0.890436i	0.262826	+	0.0295828i
$907$	−25.7954	−	14.8930i	−0.856523	−	0.494514i	0.00632328	−	0.999980i	$-0.497987\pi$
$907$	−25.7954	−	14.8930i	−0.856523	−	0.494514i	−0.862846	+	0.505466i	$0.831321\pi$
$908$	−37.8873	−	4.00524i	−1.25734	−	0.132919i
$909$	2.32405	−	19.4630i	0.0770840	−	0.645546i
$910$	0.370358	−	7.02628i	0.0122772	−	0.232919i
$911$	18.7781	−	32.5246i	0.622146	−	1.07759i	−0.366939	−	0.930245i	$-0.619594\pi$
$911$	18.7781	−	32.5246i	0.622146	−	1.07759i	0.989085	−	0.147344i	$-0.0470723\pi$
$912$	34.4797	−	8.93385i	1.14174	−	0.295829i
$913$	21.1965	+	36.7135i	0.701503	+	1.21504i
$914$	27.4897	−	13.9963i	0.909279	−	0.462955i
$915$	16.9690	+	11.1910i	0.560979	+	0.369964i
$916$	−8.25759	+	11.3512i	−0.272838	+	0.375054i
$917$			20.4770i			0.676210i
$918$	−6.81858	+	7.25309i	−0.225047	+	0.239388i
$919$		−	39.5435i		−	1.30442i	−0.758038	−	0.652210i	$-0.773842\pi$
$919$		−	39.5435i		−	1.30442i	0.758038	−	0.652210i	$-0.226158\pi$
$920$	6.15340	−	7.58477i	0.202872	−	0.250062i
$921$	−41.7415	−	27.5284i	−1.37543	−	0.907091i
$922$	−9.06223	−	17.7989i	−0.298448	−	0.586175i
$923$	−30.0939	−	52.1241i	−0.990552	−	1.71569i
$924$	11.3606	−	4.26130i	0.373738	−	0.140187i
$925$	−6.39003	+	11.0679i	−0.210103	+	0.363909i
$926$	−1.76687	−	0.0931323i	−0.0580630	−	0.00306052i
$927$	−23.0659	−	17.2614i	−0.757584	−	0.566939i
$928$	−1.18717	−	0.320021i	−0.0389706	−	0.0105052i
$929$	−27.7644	−	16.0298i	−0.910920	−	0.525920i	−0.0301929	−	0.999544i	$-0.509612\pi$
$929$	−27.7644	−	16.0298i	−0.910920	−	0.525920i	−0.880727	+	0.473624i	$0.842946\pi$
$930$	0.242355	−	2.15318i	0.00794712	−	0.0706056i
$931$	−4.45229	+	2.57053i	−0.145918	+	0.0842457i
$932$	36.7130	−	16.3191i	1.20257	−	0.534551i
$933$	−27.6575	−	1.64543i	−0.905467	−	0.0538691i
$934$	−11.5979	−	7.53672i	−0.379494	−	0.246609i
$935$	4.92211			0.160970
$936$	−28.3415	−	29.2067i	−0.926372	−	0.954650i
$937$	−41.0972			−1.34259			−0.671294	−	0.741191i	$-0.734261\pi$
$937$	−41.0972			−1.34259			−0.671294	+	0.741191i	$0.734261\pi$
$938$	−17.5714	−	11.4186i	−0.573728	−	0.372829i
$939$	−7.80569	−	15.5908i	−0.254729	−	0.508786i
$940$	7.89494	−	3.50935i	0.257504	−	0.114462i
$941$	−28.3042	+	16.3415i	−0.922692	+	0.532716i	−0.884493	−	0.466554i	$-0.845495\pi$
$941$	−28.3042	+	16.3415i	−0.922692	+	0.532716i	−0.0381990	+	0.999270i	$0.512162\pi$
$942$	−32.0857	−	23.6747i	−1.04541	−	0.771362i
$943$	−3.96183	−	2.28737i	−0.129015	−	0.0744869i
$944$	21.6784	+	4.63523i	0.705571	+	0.150864i
$945$	5.30466	+	0.955806i	0.172561	+	0.0310924i
$946$	−38.2897	−	2.01826i	−1.24490	−	0.0656194i
$947$	5.32129	−	9.21675i	0.172919	−	0.299504i	−0.766520	−	0.642220i	$-0.778014\pi$
$947$	5.32129	−	9.21675i	0.172919	−	0.299504i	0.939439	+	0.342716i	$0.111347\pi$
$948$	37.8465	+	31.1310i	1.22920	+	1.01109i
$949$	34.8078	+	60.2888i	1.12991	+	1.95706i
$950$	12.9444	+	25.4238i	0.419972	+	0.824857i
$951$	−9.27149	+	4.64186i	−0.300649	+	0.150523i
$952$	−2.97557	−	2.41403i	−0.0964387	−	0.0782391i
$953$		−	12.8664i		−	0.416782i	−0.978046	−	0.208391i	$-0.933177\pi$
$953$		−	12.8664i		−	0.416782i	0.978046	−	0.208391i	$-0.0668227\pi$
$954$	−56.1910	−	9.73281i	−1.81925	−	0.315111i
$955$		−	25.5194i		−	0.825787i
$956$	1.32714	−	1.82433i	0.0429227	−	0.0590032i
$957$	−0.0783118	+	1.31631i	−0.00253146	+	0.0425504i
$958$	27.4697	−	13.9861i	0.887507	−	0.451870i
$959$	−5.64451	−	9.77658i	−0.182271	−	0.315702i
$960$	5.26989	−	13.3726i	0.170085	−	0.431600i
$961$	−15.1364	+	26.2170i	−0.488271	+	0.845710i
$962$	1.16283	−	22.0607i	0.0374911	−	0.711266i
$963$	−16.1062	−	37.5956i	−0.519015	−	1.21150i
$964$	18.5952	+	1.96578i	0.598910	+	0.0633135i
$965$	−1.88159	−	1.08634i	−0.0605706	−	0.0349704i
$966$	3.26161	+	7.47335i	0.104941	+	0.240451i
$967$	−32.3882	+	18.6994i	−1.04154	+	0.601331i	−0.920268	−	0.391289i	$-0.872029\pi$
$967$	−32.3882	+	18.6994i	−1.04154	+	0.601331i	−0.121268	+	0.992620i	$0.538696\pi$
$968$	−3.35094	+	1.28283i	−0.107703	+	0.0412316i
$969$	−6.64125	+	10.0702i	−0.213348	+	0.323501i
$970$	−7.23303	+	11.1305i	−0.232239	+	0.357380i
$971$	−45.2767			−1.45300			−0.726500	−	0.687167i	$-0.758854\pi$
$971$	−45.2767			−1.45300			−0.726500	+	0.687167i	$0.758854\pi$
$972$	24.9180	−	18.7375i	0.799245	−	0.601005i
$973$	−10.6876			−0.342630
$974$	5.09306	−	7.83745i	0.163192	−	0.251128i
$975$	17.9466	−	27.2125i	0.574750	−	0.871499i
$976$	13.9324	+	43.0562i	0.445964	+	1.37819i
$977$	−24.9988	+	14.4331i	−0.799782	+	0.461755i	−0.843395	−	0.537294i	$-0.819447\pi$
$977$	−24.9988	+	14.4331i	−0.799782	+	0.461755i	0.0436127	+	0.999049i	$0.486113\pi$
$978$	5.93309	+	13.5945i	0.189719	+	0.434705i
$979$	17.3724	+	10.0300i	0.555225	+	0.320559i
$980$	−0.218104	+	2.06315i	−0.00696709	+	0.0659048i
$981$	0.164737	+	0.384534i	0.00525964	+	0.0122772i
$982$	−2.32350	+	44.0805i	−0.0741459	+	1.40667i
$983$	28.6347	−	49.5967i	0.913304	−	1.58189i	0.103937	−	0.994584i	$-0.466856\pi$
$983$	28.6347	−	49.5967i	0.913304	−	1.58189i	0.809366	−	0.587304i	$-0.199811\pi$
$984$	−6.57394	−	1.45218i	−0.209570	−	0.0462938i
$985$	7.44594	+	12.8968i	0.237248	+	0.410925i
$986$	0.371084	−	0.188936i	0.0118177	−	0.00601694i
$987$	−0.428370	+	7.20032i	−0.0136352	+	0.229189i
$988$	−39.8795	−	29.0109i	−1.26874	−	0.922960i
$989$		−	25.7675i		−	0.819358i
$990$	−15.1890	−	2.63087i	−0.482737	−	0.0836146i
$991$		−	33.6933i		−	1.07030i	−0.844756	−	0.535152i	$-0.820255\pi$
$991$		−	33.6933i		−	1.07030i	0.844756	−	0.535152i	$-0.179745\pi$
$992$	3.41617	−	3.40588i	0.108464	−	0.108137i
$993$	13.6649	−	6.84147i	0.433642	−	0.217107i
$994$	8.05217	+	15.8151i	0.255399	+	0.501624i
$995$	1.58837	+	2.75113i	0.0503546	+	0.0872167i
$996$	−26.6342	+	32.3798i	−0.843938	+	1.02599i
$997$	−11.9494	+	20.6969i	−0.378440	+	0.655478i	−0.990836	−	0.135074i	$-0.956873\pi$
$997$	−11.9494	+	20.6969i	−0.378440	+	0.655478i	0.612395	+	0.790552i	$0.290206\pi$
$998$	12.3594	+	0.651470i	0.391231	+	0.0206219i
$999$	16.6553	+	3.00099i	0.526950	+	0.0949470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.7	yes	72
3.2	odd	2		756.2.ba.a.575.30		72
4.3	odd	2	inner	252.2.ba.a.155.5	✓	72
9.4	even	3		756.2.ba.a.71.32		72
9.5	odd	6	inner	252.2.ba.a.239.5	yes	72
12.11	even	2		756.2.ba.a.575.32		72
36.23	even	6	inner	252.2.ba.a.239.7	yes	72
36.31	odd	6		756.2.ba.a.71.30		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.5	✓	72	4.3	odd	2	inner
252.2.ba.a.155.7	yes	72	1.1	even	1	trivial
252.2.ba.a.239.5	yes	72	9.5	odd	6	inner
252.2.ba.a.239.7	yes	72	36.23	even	6	inner
756.2.ba.a.71.30		72	36.31	odd	6
756.2.ba.a.71.32		72	9.4	even	3
756.2.ba.a.575.30		72	3.2	odd	2
756.2.ba.a.575.32		72	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18583 - 0.770594i) q^{2} +(-0.953579 + 1.44592i) q^{3} +(0.812371 + 1.82758i) q^{4} +(0.898347 - 0.518661i) q^{5} +(2.24500 - 0.979790i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +O(q^{10})\)	\(q+(-1.18583 - 0.770594i) q^{2} +(-0.953579 + 1.44592i) q^{3} +(0.812371 + 1.82758i) q^{4} +(0.898347 - 0.518661i) q^{5} +(2.24500 - 0.979790i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +(-1.46496 - 0.0772186i) q^{10} +(-1.75133 + 3.03339i) q^{11} +(-3.41720 - 0.568120i) q^{12} +(2.39811 + 4.15365i) q^{13} +(-0.641659 - 1.26027i) q^{14} +(-0.106702 + 1.79352i) q^{15} +(-2.68011 + 2.96935i) q^{16} -1.35469i q^{17} +(-0.724085 + 4.18039i) q^{18} +5.14106i q^{19} +(1.67769 + 1.22046i) q^{20} +(-1.54878 + 0.775415i) q^{21} +(4.41428 - 2.24751i) q^{22} +(1.66445 + 2.88291i) q^{23} +(3.61441 + 3.30696i) q^{24} +(-1.96198 + 3.39825i) q^{25} +(0.357033 - 6.77349i) q^{26} +(5.11380 + 0.921417i) q^{27} +(-0.210257 + 1.98892i) q^{28} +(-0.188235 - 0.108677i) q^{29} +(1.50861 - 2.04458i) q^{30} +(0.738509 - 0.426379i) q^{31} +(5.46630 - 1.45586i) q^{32} +(-2.71601 - 5.42485i) q^{33} +(-1.04392 + 1.60643i) q^{34} +1.03732 q^{35} +(4.08003 - 4.39925i) q^{36} +3.25692 q^{37} +(3.96167 - 6.09641i) q^{38} +(-8.29264 - 0.493356i) q^{39} +(-1.04897 - 2.74007i) q^{40} +(-1.19014 + 0.687125i) q^{41} +(2.43412 + 0.273976i) q^{42} +(-6.70351 - 3.87028i) q^{43} +(-6.96649 - 0.736458i) q^{44} +(-2.49154 - 1.86455i) q^{45} +(0.247804 - 4.70124i) q^{46} +(2.08223 - 3.60653i) q^{47} +(-1.73774 - 6.70673i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.94524 - 2.51785i) q^{50} +(1.95878 + 1.29181i) q^{51} +(-5.64298 + 7.75705i) q^{52} +13.4415i q^{53} +(-5.35405 - 5.03331i) q^{54} +3.63338i q^{55} +(1.78198 - 2.19649i) q^{56} +(-7.43356 - 4.90241i) q^{57} +(0.139468 + 0.273925i) q^{58} +(-2.77105 - 4.79960i) q^{59} +(-3.36449 + 1.26200i) q^{60} +(5.65678 - 9.79783i) q^{61} +(-1.20431 - 0.0634795i) q^{62} +(0.355700 - 2.97884i) q^{63} +(-7.60396 - 2.48591i) q^{64} +(4.30868 + 2.48761i) q^{65} +(-0.959643 + 8.52588i) q^{66} +(12.8327 - 7.40894i) q^{67} +(2.47581 - 1.10051i) q^{68} +(-5.75563 - 0.342421i) q^{69} +(-1.23008 - 0.799354i) q^{70} -12.5490 q^{71} +(-8.22824 + 2.07271i) q^{72} +14.5146 q^{73} +(-3.86215 - 2.50977i) q^{74} +(-3.04270 - 6.07737i) q^{75} +(-9.39571 + 4.17645i) q^{76} +(-3.03339 + 1.75133i) q^{77} +(9.45346 + 6.97530i) q^{78} +(-12.2513 - 7.07327i) q^{79} +(-0.867583 + 4.05757i) q^{80} +(-6.20871 + 6.51551i) q^{81} +(1.94079 + 0.102300i) q^{82} +(6.05157 - 10.4816i) q^{83} +(-2.67532 - 2.20061i) q^{84} +(-0.702626 - 1.21698i) q^{85} +(4.96680 + 9.75516i) q^{86} +(0.336635 - 0.168540i) q^{87} +(7.69354 + 6.24164i) q^{88} -5.72707i q^{89} +(1.51773 + 4.13100i) q^{90} +4.79623i q^{91} +(-3.91660 + 5.38390i) q^{92} +(-0.0877175 + 1.47441i) q^{93} +(-5.24833 + 2.67216i) q^{94} +(2.66647 + 4.61846i) q^{95} +(-3.10750 + 9.29212i) q^{96} +(4.52430 - 7.83631i) q^{97} +(0.0744403 - 1.41225i) q^{98} +(10.4338 + 1.24589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more