LMFDB - Embedded newform 185.2.p.a.103.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.13
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.13

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.659061 + 1.14153i) q^{2} +(-0.318379 - 1.18821i) q^{3} +(0.131277 - 0.227378i) q^{4} +(-1.74856 - 1.39375i) q^{5} +(1.14654 - 1.14654i) q^{6} +(-1.10683 - 4.13076i) q^{7} +2.98232 q^{8} +(1.28760 - 0.743399i) q^{9} +(0.438595 - 2.91460i) q^{10} +4.89589i q^{11} +(-0.311968 - 0.0835914i) q^{12} +(-1.48771 + 2.57679i) q^{13} +(3.98591 - 3.98591i) q^{14} +(-1.09936 + 2.52139i) q^{15} +(1.70298 + 2.94965i) q^{16} +(3.65256 - 2.10881i) q^{17} +(1.69722 + 0.979891i) q^{18} +(-4.90693 + 1.31481i) q^{19} +(-0.546452 + 0.214617i) q^{20} +(-4.55581 + 2.63030i) q^{21} +(-5.58880 + 3.22669i) q^{22} +6.57051 q^{23} +(-0.949509 - 3.54362i) q^{24} +(1.11493 + 4.87411i) q^{25} -3.92197 q^{26} +(-3.90274 - 3.90274i) q^{27} +(-1.08454 - 0.290603i) q^{28} +(0.417950 - 0.417950i) q^{29} +(-3.60278 + 0.406805i) q^{30} +(3.03803 + 3.03803i) q^{31} +(0.737586 - 1.27754i) q^{32} +(5.81734 - 1.55875i) q^{33} +(4.81453 + 2.77967i) q^{34} +(-3.82188 + 8.76554i) q^{35} -0.390363i q^{36} +(6.07879 - 0.219784i) q^{37} +(-4.73486 - 4.73486i) q^{38} +(3.53541 + 0.947311i) q^{39} +(-5.21477 - 4.15661i) q^{40} +(-0.897477 - 0.518158i) q^{41} +(-6.00512 - 3.46706i) q^{42} -3.17618 q^{43} +(1.11322 + 0.642716i) q^{44} +(-3.28757 - 0.494720i) q^{45} +(4.33037 + 7.50041i) q^{46} +(-4.44958 + 4.44958i) q^{47} +(2.96260 - 2.96260i) q^{48} +(-9.77595 + 5.64415i) q^{49} +(-4.82913 + 4.48505i) q^{50} +(-3.66860 - 3.66860i) q^{51} +(0.390602 + 0.676543i) q^{52} +(1.71709 - 6.40827i) q^{53} +(1.88294 - 7.02724i) q^{54} +(6.82365 - 8.56076i) q^{55} +(-3.30094 - 12.3193i) q^{56} +(3.12453 + 5.41184i) q^{57} +(0.752555 + 0.201647i) q^{58} +(-1.57132 + 5.86425i) q^{59} +(0.428988 + 0.580969i) q^{60} +(1.68182 - 0.450642i) q^{61} +(-1.46575 + 5.47024i) q^{62} +(-4.49597 - 4.49597i) q^{63} +8.75638 q^{64} +(6.19274 - 2.43217i) q^{65} +(5.61334 + 5.61334i) q^{66} +(-11.5327 + 3.09017i) q^{67} -1.10735i q^{68} +(-2.09191 - 7.80712i) q^{69} +(-12.5250 + 1.41424i) q^{70} +(-1.78413 + 3.09021i) q^{71} +(3.84005 - 2.21705i) q^{72} +(-2.50291 + 2.50291i) q^{73} +(4.25718 + 6.79426i) q^{74} +(5.43648 - 2.87658i) q^{75} +(-0.345207 + 1.28833i) q^{76} +(20.2238 - 5.41895i) q^{77} +(1.24867 + 4.66011i) q^{78} +(3.97409 - 1.06485i) q^{79} +(1.13331 - 7.53116i) q^{80} +(-1.16452 + 2.01701i) q^{81} -1.36599i q^{82} +(-0.688684 + 2.57020i) q^{83} +1.38119i q^{84} +(-9.32588 - 1.40338i) q^{85} +(-2.09329 - 3.62569i) q^{86} +(-0.629677 - 0.363544i) q^{87} +14.6011i q^{88} +(11.4703 + 3.07346i) q^{89} +(-1.60197 - 4.07890i) q^{90} +(12.2907 + 3.29330i) q^{91} +(0.862553 - 1.49399i) q^{92} +(2.64257 - 4.57706i) q^{93} +(-8.01187 - 2.14677i) q^{94} +(10.4126 + 4.54001i) q^{95} +(-1.75281 - 0.469664i) q^{96} +10.2570i q^{97} +(-12.8859 - 7.43968i) q^{98} +(3.63960 + 6.30397i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	0.659061	+	1.14153i	0.466027	+	0.807182i	0.999247	−	0.0387944i	$-0.0123517\pi$
$2$	0.659061	+	1.14153i	0.466027	+	0.807182i	−0.533221	+	0.845976i	$0.679018\pi$
$3$	−0.318379	−	1.18821i	−0.183816	−	0.686012i	−0.994881	−	0.101055i	$-0.967778\pi$
$3$	−0.318379	−	1.18821i	−0.183816	−	0.686012i	0.811064	−	0.584957i	$-0.198889\pi$
$4$	0.131277	−	0.227378i	0.0656383	−	0.113689i
$5$	−1.74856	−	1.39375i	−0.781980	−	0.623304i
$5$	−1.74856	−	1.39375i	−0.781980	−	0.623304i
$6$	1.14654	−	1.14654i	0.468073	−	0.468073i
$7$	−1.10683	−	4.13076i	−0.418344	−	1.56128i	−0.778041	−	0.628213i	$-0.783787\pi$
$7$	−1.10683	−	4.13076i	−0.418344	−	1.56128i	0.359697	−	0.933069i	$-0.382880\pi$
$8$	2.98232			1.05441
$9$	1.28760	−	0.743399i	0.429201	−	0.247800i
$10$	0.438595	−	2.91460i	0.138696	−	0.921676i
$11$			4.89589i			1.47617i	0.674709	+	0.738084i	$0.264269\pi$
$11$			4.89589i			1.47617i	−0.674709	+	0.738084i	$0.735731\pi$
$12$	−0.311968	−	0.0835914i	−0.0900573	−	0.0241308i
$13$	−1.48771	+	2.57679i	−0.412616	+	0.714672i	−0.995175	−	0.0981164i	$-0.968718\pi$
$13$	−1.48771	+	2.57679i	−0.412616	+	0.714672i	0.582559	+	0.812789i	$0.302052\pi$
$14$	3.98591	−	3.98591i	1.06528	−	1.06528i
$15$	−1.09936	+	2.52139i	−0.283853	+	0.651021i
$16$	1.70298	+	2.94965i	0.425745	+	0.737412i
$17$	3.65256	−	2.10881i	0.885877	−	0.511461i	0.0132853	−	0.999912i	$-0.495771\pi$
$17$	3.65256	−	2.10881i	0.885877	−	0.511461i	0.872592	+	0.488450i	$0.162438\pi$
$18$	1.69722	+	0.979891i	0.400039	+	0.230962i
$19$	−4.90693	+	1.31481i	−1.12573	+	0.301638i	−0.773199	−	0.634164i	$-0.781345\pi$
$19$	−4.90693	+	1.31481i	−1.12573	+	0.301638i	−0.352528	+	0.935801i	$0.614678\pi$
$20$	−0.546452	+	0.214617i	−0.122190	+	0.0479898i
$21$	−4.55581	+	2.63030i	−0.994160	+	0.573978i
$22$	−5.58880	+	3.22669i	−1.19154	+	0.687933i
$23$	6.57051			1.37005			0.685023	−	0.728522i	$-0.259792\pi$
$23$	6.57051			1.37005			0.685023	+	0.728522i	$0.259792\pi$
$24$	−0.949509	−	3.54362i	−0.193818	−	0.723338i
$25$	1.11493	+	4.87411i	0.222985	+	0.974822i
$26$	−3.92197			−0.769161
$27$	−3.90274	−	3.90274i	−0.751083	−	0.751083i
$28$	−1.08454	−	0.290603i	−0.204960	−	0.0549188i
$29$	0.417950	−	0.417950i	0.0776113	−	0.0776113i	−0.667236	−	0.744847i	$-0.732523\pi$
$29$	0.417950	−	0.417950i	0.0776113	−	0.0776113i	0.744847	+	0.667236i	$0.232523\pi$
$30$	−3.60278	+	0.406805i	−0.657775	+	0.0742721i
$31$	3.03803	+	3.03803i	0.545646	+	0.545646i	0.925179	−	0.379532i	$-0.123915\pi$
$31$	3.03803	+	3.03803i	0.545646	+	0.545646i	−0.379532	+	0.925179i	$0.623915\pi$
$32$	0.737586	−	1.27754i	0.130388	−	0.225839i
$33$	5.81734	−	1.55875i	1.01267	−	0.271344i
$34$	4.81453	+	2.77967i	0.825685	+	0.476709i
$35$	−3.82188	+	8.76554i	−0.646016	+	1.48165i
$36$		−	0.390363i		−	0.0650605i
$37$	6.07879	−	0.219784i	0.999347	−	0.0361323i
$37$	6.07879	−	0.219784i	0.999347	−	0.0361323i
$38$	−4.73486	−	4.73486i	−0.768095	−	0.768095i
$39$	3.53541	+	0.947311i	0.566119	+	0.151691i
$40$	−5.21477	−	4.15661i	−0.824527	−	0.657218i
$41$	−0.897477	−	0.518158i	−0.140162	−	0.0809228i	0.428279	−	0.903647i	$-0.359120\pi$
$41$	−0.897477	−	0.518158i	−0.140162	−	0.0809228i	−0.568441	+	0.822724i	$0.692453\pi$
$42$	−6.00512	−	3.46706i	−0.926610	−	0.534978i
$43$	−3.17618			−0.484362			−0.242181	−	0.970231i	$-0.577863\pi$
$43$	−3.17618			−0.484362			−0.242181	+	0.970231i	$0.577863\pi$
$44$	1.11322	+	0.642716i	0.167824	+	0.0968931i
$45$	−3.28757	−	0.494720i	−0.490081	−	0.0737486i
$46$	4.33037	+	7.50041i	0.638478	+	1.10588i
$47$	−4.44958	+	4.44958i	−0.649038	+	0.649038i	−0.952761	−	0.303722i	$-0.901770\pi$
$47$	−4.44958	+	4.44958i	−0.649038	+	0.649038i	0.303722	+	0.952761i	$0.401770\pi$
$48$	2.96260	−	2.96260i	0.427615	−	0.427615i
$49$	−9.77595	+	5.64415i	−1.39656	+	0.806307i
$50$	−4.82913	+	4.48505i	−0.682942	+	0.634283i
$51$	−3.66860	−	3.66860i	−0.513707	−	0.513707i
$52$	0.390602	+	0.676543i	0.0541668	+	0.0938197i
$53$	1.71709	−	6.40827i	0.235861	−	0.880243i	−0.741899	−	0.670512i	$-0.766074\pi$
$53$	1.71709	−	6.40827i	0.235861	−	0.880243i	0.977759	−	0.209731i	$-0.0672589\pi$
$54$	1.88294	−	7.02724i	0.256236	−	0.956286i
$55$	6.82365	−	8.56076i	0.920101	−	1.15433i
$56$	−3.30094	−	12.3193i	−0.441106	−	1.64623i
$57$	3.12453	+	5.41184i	0.413854	+	0.716816i
$58$	0.752555	+	0.201647i	0.0988154	+	0.0264775i
$59$	−1.57132	+	5.86425i	−0.204568	+	0.763460i	0.785012	+	0.619480i	$0.212657\pi$
$59$	−1.57132	+	5.86425i	−0.204568	+	0.763460i	−0.989581	+	0.143979i	$0.954010\pi$
$60$	0.428988	+	0.580969i	0.0553822	+	0.0750028i
$61$	1.68182	−	0.450642i	0.215335	−	0.0576988i	−0.149539	−	0.988756i	$-0.547779\pi$
$61$	1.68182	−	0.450642i	0.215335	−	0.0576988i	0.364874	+	0.931057i	$0.381112\pi$
$62$	−1.46575	+	5.47024i	−0.186150	+	0.694722i
$63$	−4.49597	−	4.49597i	−0.566439	−	0.566439i
$64$	8.75638			1.09455
$65$	6.19274	−	2.43217i	0.768115	−	0.301674i
$66$	5.61334	+	5.61334i	0.690954	+	0.690954i
$67$	−11.5327	+	3.09017i	−1.40894	+	0.377524i	−0.881547	−	0.472097i	$-0.843497\pi$
$67$	−11.5327	+	3.09017i	−1.40894	+	0.377524i	−0.527394	+	0.849621i	$0.676831\pi$
$68$		−	1.10735i		−	0.134286i
$69$	−2.09191	−	7.80712i	−0.251837	−	0.939867i
$70$	−12.5250	+	1.41424i	−1.49702	+	0.169034i
$71$	−1.78413	+	3.09021i	−0.211738	+	0.366741i	−0.952258	−	0.305293i	$-0.901246\pi$
$71$	−1.78413	+	3.09021i	−0.211738	+	0.366741i	0.740521	+	0.672034i	$0.234579\pi$
$72$	3.84005	−	2.21705i	0.452554	−	0.261282i
$73$	−2.50291	+	2.50291i	−0.292943	+	0.292943i	−0.838242	−	0.545298i	$-0.816416\pi$
$73$	−2.50291	+	2.50291i	−0.292943	+	0.292943i	0.545298	+	0.838242i	$0.316416\pi$
$74$	4.25718	+	6.79426i	0.494888	+	0.789816i
$75$	5.43648	−	2.87658i	0.627751	−	0.332159i
$76$	−0.345207	+	1.28833i	−0.0395979	+	0.147781i
$77$	20.2238	−	5.41895i	2.30471	−	0.617546i
$78$	1.24867	+	4.66011i	0.141384	+	0.527653i
$79$	3.97409	−	1.06485i	0.447120	−	0.119805i	−0.0282316	−	0.999601i	$-0.508988\pi$
$79$	3.97409	−	1.06485i	0.447120	−	0.119805i	0.475351	+	0.879796i	$0.342321\pi$
$80$	1.13331	−	7.53116i	0.126708	−	0.842010i
$81$	−1.16452	+	2.01701i	−0.129391	+	0.224112i
$82$		−	1.36599i		−	0.150849i
$83$	−0.688684	+	2.57020i	−0.0755929	+	0.282117i	−0.993367	−	0.114986i	$-0.963318\pi$
$83$	−0.688684	+	2.57020i	−0.0755929	+	0.282117i	0.917774	+	0.397103i	$0.129984\pi$
$84$			1.38119i			0.150700i
$85$	−9.32588	−	1.40338i	−1.01153	−	0.152218i
$86$	−2.09329	−	3.62569i	−0.225726	−	0.390968i
$87$	−0.629677	−	0.363544i	−0.0675085	−	0.0389760i
$88$			14.6011i			1.55649i
$89$	11.4703	+	3.07346i	1.21585	+	0.325786i	0.809055	−	0.587734i	$-0.199980\pi$
$89$	11.4703	+	3.07346i	1.21585	+	0.325786i	0.406795	+	0.913519i	$0.366646\pi$
$90$	−1.60197	−	4.07890i	−0.168862	−	0.429954i
$91$	12.2907	+	3.29330i	1.28842	+	0.345231i
$92$	0.862553	−	1.49399i	0.0899274	−	0.155759i
$93$	2.64257	−	4.57706i	0.274021	−	0.474619i
$94$	−8.01187	−	2.14677i	−0.826361	−	0.221423i
$95$	10.4126	+	4.54001i	1.06831	+	0.465795i
$96$	−1.75281	−	0.469664i	−0.178895	−	0.0479349i
$97$			10.2570i			1.04144i	0.853728	+	0.520719i	$0.174336\pi$
$97$			10.2570i			1.04144i	−0.853728	+	0.520719i	$0.825664\pi$
$98$	−12.8859	−	7.43968i	−1.30167	−	0.751521i
$99$	3.63960	+	6.30397i	0.365794	+	0.633573i
$100$	1.25463	+	0.386347i	0.125463	+	0.0386347i
$101$			19.0134i			1.89190i	0.324311	+	0.945951i	$0.394868\pi$
$101$			19.0134i			1.89190i	−0.324311	+	0.945951i	$0.605132\pi$
$102$	1.76998	−	6.60565i	0.175254	−	0.654056i
$103$		−	18.1801i		−	1.79133i	−0.444724	−	0.895667i	$-0.646698\pi$
$103$		−	18.1801i		−	1.79133i	0.444724	−	0.895667i	$-0.353302\pi$
$104$	−4.43683	+	7.68481i	−0.435067	+	0.753558i
$105$	11.6321	+	1.75042i	1.13518	+	0.170824i
$106$	8.44688	−	2.26334i	0.820434	−	0.219835i
$107$	−1.69532	−	6.32701i	−0.163893	−	0.611656i	−0.998179	−	0.0603240i	$-0.980787\pi$
$107$	−1.69532	−	6.32701i	−0.163893	−	0.611656i	0.834286	−	0.551332i	$-0.185880\pi$
$108$	−1.39974	+	0.375058i	−0.134690	+	0.0360900i
$109$	1.79221	−	6.68861i	0.171662	−	0.640652i	−0.825434	−	0.564499i	$-0.809069\pi$
$109$	1.79221	−	6.68861i	0.171662	−	0.640652i	0.997096	−	0.0761534i	$-0.0242639\pi$
$110$	14.2696	+	2.14731i	1.36055	+	0.204738i
$111$	−2.19651	−	7.15289i	−0.208483	−	0.678922i
$112$	10.2994	−	10.2994i	0.973200	−	0.973200i
$113$	−1.34597	+	0.777094i	−0.126618	+	0.0731029i	−0.561971	−	0.827157i	$-0.689957\pi$
$113$	−1.34597	+	0.777094i	−0.126618	+	0.0731029i	0.435353	+	0.900260i	$0.356623\pi$
$114$	−4.11851	+	7.13347i	−0.385734	+	0.668111i
$115$	−11.4889	−	9.15764i	−1.07135	−	0.853954i
$116$	−0.0401654	−	0.149899i	−0.00372926	−	0.0139178i
$117$			4.42384i			0.408984i
$118$	−7.72979	+	2.07119i	−0.711585	+	0.190669i
$119$	−12.7538	−	12.7538i	−1.16914	−	1.16914i
$120$	−3.27864	+	7.51961i	−0.299298	+	0.686443i
$121$	−12.9698			−1.17907
$122$	1.62284	+	1.62284i	0.146925	+	0.146925i
$123$	−0.329942	+	1.23136i	−0.0297498	+	0.111028i
$124$	1.08960	−	0.291958i	0.0978492	−	0.0262186i
$125$	4.84377	−	10.0766i	0.433240	−	0.901278i
$126$	2.16915	−	8.09539i	0.193244	−	0.721195i
$127$	−15.7291	−	4.21459i	−1.39573	−	0.373984i	−0.518920	−	0.854823i	$-0.673666\pi$
$127$	−15.7291	−	4.21459i	−1.39573	−	0.373984i	−0.876809	+	0.480839i	$0.840332\pi$
$128$	4.29582	+	7.44057i	0.379700	+	0.657660i
$129$	1.01123	+	3.77396i	0.0890337	+	0.332278i
$130$	6.85779	+	5.46624i	0.601468	+	0.479421i
$131$	3.68624	−	13.7572i	0.322068	−	1.20197i	−0.595158	−	0.803608i	$-0.702911\pi$
$131$	3.68624	−	13.7572i	0.322068	−	1.20197i	0.917227	−	0.398366i	$-0.130423\pi$
$132$	0.409255	−	1.52736i	0.0356211	−	0.132940i
$133$	10.8623	+	18.8141i	0.941883	+	1.63139i
$134$	−11.1283	−	11.1283i	−0.961335	−	0.961335i
$135$	1.38474	+	12.2636i	0.119179	+	1.05549i
$136$	10.8931	−	6.28915i	0.934078	−	0.539290i
$137$	−7.34260	+	7.34260i	−0.627321	+	0.627321i	−0.947393	−	0.320072i	$-0.896293\pi$
$137$	−7.34260	+	7.34260i	−0.627321	+	0.627321i	0.320072	+	0.947393i	$0.396293\pi$
$138$	7.53335	−	7.53335i	0.641281	−	0.641281i
$139$	−4.37561	−	7.57878i	−0.371135	−	0.642824i	0.618606	−	0.785702i	$-0.287698\pi$
$139$	−4.37561	−	7.57878i	−0.371135	−	0.642824i	−0.989740	+	0.142877i	$0.954365\pi$
$140$	1.49136	+	2.01972i	0.126043	+	0.170698i
$141$	6.70368	+	3.87037i	0.564552	+	0.325944i
$142$	−4.70341			−0.394702
$143$	−12.6157	−	7.28366i	−1.05498	−	0.609091i
$144$	4.38553	+	2.53199i	0.365461	+	0.210999i
$145$	−1.31333	+	0.148293i	−0.109066	+	0.0123151i
$146$	−4.50671	−	1.20757i	−0.372978	−	0.0999392i
$147$	9.81888	+	9.81888i	0.809848	+	0.809848i
$148$	0.748029	−	1.41103i	0.0614876	−	0.115986i
$149$		−	16.7086i		−	1.36883i	−0.729095	−	0.684413i	$-0.760059\pi$
$149$		−	16.7086i		−	1.36883i	0.729095	−	0.684413i	$-0.239941\pi$
$150$	6.86667	+	4.31006i	0.560661	+	0.351915i
$151$	−3.85044	−	2.22305i	−0.313344	−	0.180909i	0.335078	−	0.942190i	$-0.391237\pi$
$151$	−3.85044	−	2.22305i	−0.313344	−	0.180909i	−0.648422	+	0.761281i	$0.724571\pi$
$152$	−14.6340	+	3.92118i	−1.18698	+	0.318050i
$153$	3.13537	−	5.43062i	0.253480	−	0.439040i
$154$	19.5146	+	19.5146i	1.57253	+	1.57253i
$155$	−1.07793	−	9.54643i	−0.0865811	−	0.766788i
$156$	0.679514	−	0.679514i	0.0544047	−	0.0544047i
$157$	−9.34877	−	2.50499i	−0.746113	−	0.199920i	−0.134320	−	0.990938i	$-0.542885\pi$
$157$	−9.34877	−	2.50499i	−0.746113	−	0.199920i	−0.611793	+	0.791018i	$0.709552\pi$
$158$	3.83473	+	3.83473i	0.305075	+	0.305075i
$159$	−8.16104			−0.647213
$160$	−3.07028	+	1.20584i	−0.242727	+	0.0953300i
$161$	−7.27247	−	27.1412i	−0.573151	−	2.13903i
$162$	−3.06996			−0.241199
$163$	−14.1737	+	8.18322i	−1.11017	+	0.640959i	−0.938874	−	0.344260i	$-0.888130\pi$
$163$	−14.1737	+	8.18322i	−1.11017	+	0.640959i	−0.171299	+	0.985219i	$0.554797\pi$
$164$	−0.235635	+	0.136044i	−0.0184000	+	0.0106233i
$165$	−12.3445	−	5.38234i	−0.961016	−	0.419015i
$166$	−3.38784	+	0.907770i	−0.262948	+	0.0704566i
$167$	8.53712	+	4.92891i	0.660623	+	0.381411i	0.792514	−	0.609854i	$-0.208772\pi$
$167$	8.53712	+	4.92891i	0.660623	+	0.381411i	−0.131892	+	0.991264i	$0.542105\pi$
$168$	−13.5869	+	7.84440i	−1.04825	+	0.605209i
$169$	2.07344	+	3.59131i	0.159496	+	0.276255i
$170$	−4.54433	−	11.5707i	−0.348534	−	0.887429i
$171$	−5.34076	+	5.34076i	−0.408418	+	0.408418i
$172$	−0.416957	+	0.722191i	−0.0317927	+	0.0550666i
$173$	7.28794	+	1.95280i	0.554092	+	0.148468i	0.524991	−	0.851108i	$-0.324069\pi$
$173$	7.28794	+	1.95280i	0.554092	+	0.148468i	0.0291012	+	0.999576i	$0.490735\pi$
$174$		−	0.958392i		−	0.0726555i
$175$	18.8998	−	10.0003i	1.42869	−	0.755954i
$176$	−14.4412	+	8.33761i	−1.08854	+	0.628471i
$177$	7.46822			0.561346
$178$	4.05119	+	15.1193i	0.303650	+	1.13324i
$179$	−15.1099	+	15.1099i	−1.12937	+	1.12937i	−0.139089	+	0.990280i	$0.544417\pi$
$179$	−15.1099	+	15.1099i	−1.12937	+	1.12937i	−0.990280	+	0.139089i	$0.955583\pi$
$180$	−0.544068	+	0.682574i	−0.0405525	+	0.0508760i
$181$	−0.167025	+	0.289295i	−0.0124148	+	0.0215032i	−0.872166	−	0.489210i	$-0.837285\pi$
$181$	−0.167025	+	0.289295i	−0.0124148	+	0.0215032i	0.859751	+	0.510713i	$0.170619\pi$
$182$	4.34097	+	16.2007i	0.321774	+	1.20088i
$183$	−1.07091	−	1.85487i	−0.0791641	−	0.137116i
$184$	19.5954			1.44459
$185$	−10.9355	−	8.08801i	−0.803991	−	0.594642i
$186$	6.96645			0.510805
$187$	10.3245	+	17.8826i	0.755003	+	1.30770i
$188$	0.427610	+	1.59586i	0.0311866	+	0.116390i
$189$	−11.8016	+	20.4410i	−0.858442	+	1.48686i
$190$	1.67998	+	14.8784i	0.121878	+	1.07939i
$191$	−2.98486	+	2.98486i	−0.215977	+	0.215977i	−0.806801	−	0.590824i	$-0.798803\pi$
$191$	−2.98486	+	2.98486i	−0.215977	+	0.215977i	0.590824	+	0.806801i	$0.298803\pi$
$192$	−2.78785	−	10.4044i	−0.201196	−	0.750872i
$193$	7.99715			0.575648			0.287824	−	0.957683i	$-0.407068\pi$
$193$	7.99715			0.575648			0.287824	+	0.957683i	$0.407068\pi$
$194$	−11.7086	+	6.75997i	−0.840629	+	0.485338i
$195$	−4.86157	−	6.58391i	−0.348144	−	0.471484i
$196$			2.96378i			0.211698i
$197$	4.74803	+	1.27223i	0.338283	+	0.0906426i	0.423962	−	0.905680i	$-0.360639\pi$
$197$	4.74803	+	1.27223i	0.338283	+	0.0906426i	−0.0856786	+	0.996323i	$0.527306\pi$
$198$	−4.79744	+	8.30941i	−0.340939	+	0.590524i
$199$	−7.98996	+	7.98996i	−0.566393	+	0.566393i	−0.931116	−	0.364723i	$-0.881164\pi$
$199$	−7.98996	+	7.98996i	−0.566393	+	0.566393i	0.364723	+	0.931116i	$0.381164\pi$
$200$	3.32507	+	14.5362i	0.235118	+	1.02786i
$201$	7.34353	+	12.7194i	0.517973	+	0.897155i
$202$	−21.7043	+	12.5310i	−1.52711	+	0.881676i
$203$	−2.18905	−	1.26385i	−0.153641	−	0.0887049i
$204$	−1.31576	+	0.352557i	−0.0921216	+	0.0246839i
$205$	0.847109	+	2.15689i	0.0591647	+	0.150644i
$206$	20.7530	−	11.9818i	1.44593	−	0.834810i
$207$	8.46021	−	4.88451i	0.588025	−	0.339497i
$208$	−10.1342			−0.702677
$209$	−6.43716	−	24.0238i	−0.445268	−	1.66176i
$210$	5.66810	+	14.4320i	0.391136	+	0.995902i
$211$	−16.1514			−1.11191			−0.555955	−	0.831213i	$-0.687647\pi$
$211$	−16.1514			−1.11191			−0.555955	+	0.831213i	$0.687647\pi$
$212$	−1.23168	−	1.23168i	−0.0845923	−	0.0845923i
$213$	4.23984	+	1.13606i	0.290509	+	0.0778417i
$214$	6.10514	−	6.10514i	0.417339	−	0.417339i
$215$	5.55373	+	4.42679i	0.378762	+	0.301905i
$216$	−11.6392	−	11.6392i	−0.791950	−	0.791950i
$217$	9.18679	−	15.9120i	0.623640	−	1.08018i
$218$	8.81640	−	2.36235i	0.597122	−	0.159998i
$219$	3.77085	+	2.17710i	0.254811	+	0.147115i
$220$	−1.05074	−	2.67537i	−0.0708410	−	0.180374i
$221$			12.5492i			0.844149i
$222$	6.71759	−	7.22157i	0.450855	−	0.484680i
$223$	−2.37166	−	2.37166i	−0.158818	−	0.158818i	0.623225	−	0.782043i	$-0.285822\pi$
$223$	−2.37166	−	2.37166i	−0.158818	−	0.158818i	−0.782043	+	0.623225i	$0.785822\pi$
$224$	−6.09359	−	1.63277i	−0.407145	−	0.109094i
$225$	5.05899	+	5.44709i	0.337266	+	0.363139i
$226$	−1.77415	−	1.02431i	−0.118015	−	0.0681358i
$227$	3.72482	+	2.15053i	0.247225	+	0.142735i	0.618493	−	0.785790i	$-0.287744\pi$
$227$	3.72482	+	2.15053i	0.247225	+	0.142735i	−0.371268	+	0.928526i	$0.621077\pi$
$228$	1.64071			0.108659
$229$	6.37880	+	3.68280i	0.421523	+	0.243366i	0.695729	−	0.718305i	$-0.255082\pi$
$229$	6.37880	+	3.68280i	0.421523	+	0.243366i	−0.274206	+	0.961671i	$0.588415\pi$
$230$	2.88179	−	19.1504i	0.190020	−	1.26274i
$231$	−12.8777	−	22.3048i	−0.847288	−	1.46755i
$232$	1.24646	−	1.24646i	0.0818341	−	0.0818341i
$233$	−2.31125	+	2.31125i	−0.151415	+	0.151415i	−0.778750	−	0.627335i	$-0.784146\pi$
$233$	−2.31125	+	2.31125i	−0.151415	+	0.151415i	0.627335	+	0.778750i	$0.284146\pi$
$234$	−5.04994	+	2.91558i	−0.330125	+	0.190598i
$235$	13.9820	−	1.57876i	0.912083	−	0.102987i
$236$	1.12712	+	1.12712i	0.0733693	+	0.0733693i
$237$	−2.53053	−	4.38301i	−0.164376	−	0.284707i
$238$	6.15327	−	22.9643i	0.398857	−	1.48856i
$239$	4.53201	−	16.9137i	0.293151	−	1.09406i	−0.649523	−	0.760342i	$-0.725032\pi$
$239$	4.53201	−	16.9137i	0.293151	−	1.09406i	0.942675	−	0.333713i	$-0.108302\pi$
$240$	−9.30941	+	1.05116i	−0.600920	+	0.0678523i
$241$	−5.49887	−	20.5221i	−0.354213	−	1.32194i	−0.881472	−	0.472237i	$-0.843447\pi$
$241$	−5.49887	−	20.5221i	−0.354213	−	1.32194i	0.527258	−	0.849705i	$-0.323220\pi$
$242$	−8.54788	−	14.8054i	−0.549478	−	0.951724i
$243$	−13.2264	−	3.54399i	−0.848471	−	0.227347i
$244$	0.118317	−	0.441567i	0.00757450	−	0.0282684i
$245$	24.9604	+	3.75609i	1.59466	+	0.239968i
$246$	−1.62308	+	0.434904i	−0.103484	+	0.0277284i
$247$	3.91210	−	14.6002i	0.248921	−	0.928986i
$248$	9.06039	+	9.06039i	0.575335	+	0.575335i
$249$	3.27320			0.207431
$250$	14.6951	−	1.11180i	0.929397	−	0.0703162i
$251$	17.7562	+	17.7562i	1.12076	+	1.12076i	0.991627	+	0.129136i	$0.0412203\pi$
$251$	17.7562	+	17.7562i	1.12076	+	1.12076i	0.129136	+	0.991627i	$0.458780\pi$
$252$	−1.61250	+	0.432068i	−0.101578	+	0.0272177i
$253$			32.1685i			2.02242i
$254$	−5.55535	−	20.7328i	−0.348573	−	1.30089i
$255$	1.30166	+	11.5279i	0.0815131	+	0.721904i
$256$	3.09396	−	5.35890i	0.193373	−	0.334931i
$257$	−4.57311	+	2.64029i	−0.285263	+	0.164696i	−0.635803	−	0.771851i	$-0.719331\pi$
$257$	−4.57311	+	2.64029i	−0.285263	+	0.164696i	0.350541	+	0.936547i	$0.385998\pi$
$258$	−3.64161	+	3.64161i	−0.226717	+	0.226717i
$259$	−7.63609	−	24.8668i	−0.474484	−	1.54515i
$260$	0.259940	−	1.72738i	0.0161208	−	0.107127i
$261$	0.227451	−	0.848857i	0.0140788	−	0.0525429i
$262$	18.1337	−	4.85891i	1.12030	−	0.300185i
$263$	4.47743	+	16.7100i	0.276090	+	1.03038i	0.955107	+	0.296261i	$0.0957397\pi$
$263$	4.47743	+	16.7100i	0.276090	+	1.03038i	−0.679017	+	0.734123i	$0.737594\pi$
$264$	17.3492	−	4.64870i	1.06777	−	0.286108i
$265$	−11.9340	+	8.81205i	−0.733097	+	0.541320i
$266$	−14.3179	+	24.7993i	−0.877885	+	1.52054i
$267$		−	14.6076i		−	0.893972i
$268$	−0.811334	+	3.02794i	−0.0495601	+	0.184961i
$269$		−	0.173030i		−	0.0105498i	−0.999986	−	0.00527492i	$-0.998321\pi$
$269$		−	0.173030i		−	0.0105498i	0.999986	−	0.00527492i	$-0.00167907\pi$
$270$	−13.0866	+	9.66320i	−0.796428	+	0.588083i
$271$	−9.17400	−	15.8898i	−0.557281	−	0.965239i	−0.997722	−	0.0674574i	$-0.978511\pi$
$271$	−9.17400	−	15.8898i	−0.557281	−	0.965239i	0.440441	−	0.897781i	$-0.354822\pi$
$272$	12.4405	+	7.18252i	0.754315	+	0.435504i
$273$		−	15.6525i		−	0.947331i
$274$	−13.2210	−	3.54256i	−0.798710	−	0.214014i
$275$	−23.8631	+	5.45856i	−1.43900	+	0.329163i
$276$	−2.04978	−	0.549238i	−0.123383	−	0.0330602i
$277$	−0.919384	+	1.59242i	−0.0552405	+	0.0956793i	−0.892323	−	0.451397i	$-0.850926\pi$
$277$	−0.919384	+	1.59242i	−0.0552405	+	0.0956793i	0.837083	+	0.547076i	$0.184259\pi$
$278$	5.76759	−	9.98977i	0.345917	−	0.599146i
$279$	6.17025	+	1.65331i	0.369403	+	0.0989813i
$280$	−11.3981	+	26.1417i	−0.681166	+	1.56226i
$281$	3.28246	+	0.879533i	0.195815	+	0.0524686i	0.355394	−	0.934717i	$-0.384347\pi$
$281$	3.28246	+	0.879533i	0.195815	+	0.0524686i	−0.159578	+	0.987185i	$0.551013\pi$
$282$			10.2032i			0.607595i
$283$	10.8904	+	6.28759i	0.647369	+	0.373758i	0.787447	−	0.616382i	$-0.211402\pi$
$283$	10.8904	+	6.28759i	0.647369	+	0.373758i	−0.140079	+	0.990140i	$0.544736\pi$
$284$	0.468430	+	0.811344i	0.0277962	+	0.0481444i
$285$	2.07933	−	13.8177i	0.123169	−	0.818492i
$286$		−	19.2015i		−	1.13541i
$287$	−1.14703	+	4.28078i	−0.0677071	+	0.252686i
$288$		−	2.19328i		−	0.129240i
$289$	0.394151	−	0.682690i	0.0231854	−	0.0401582i
$290$	−1.03484	−	1.40146i	−0.0607681	−	0.0822968i
$291$	12.1874	−	3.26561i	0.714438	−	0.191433i
$292$	0.240532	+	0.897679i	0.0140761	+	0.0525327i
$293$	10.1828	−	2.72847i	0.594885	−	0.159399i	0.0512000	−	0.998688i	$-0.483695\pi$
$293$	10.1828	−	2.72847i	0.594885	−	0.159399i	0.543685	+	0.839290i	$0.317029\pi$
$294$	−4.73728	+	17.6798i	−0.276284	+	1.03110i
$295$	10.9208	−	8.06396i	0.635836	−	0.469502i
$296$	18.1289	−	0.655467i	1.05372	−	0.0380982i
$297$	19.1074	−	19.1074i	1.10872	−	1.10872i
$298$	19.0734	−	11.0120i	1.10489	−	0.637909i
$299$	−9.77500	+	16.9308i	−0.565303	+	0.979133i
$300$	0.0596133	−	1.61376i	0.00344178	−	0.0931706i
$301$	3.51550	+	13.1200i	0.202630	+	0.756226i
$302$		−	5.86051i		−	0.337234i
$303$	22.5918	−	6.05346i	1.29787	−	0.347762i
$304$	−12.2346	−	12.2346i	−0.701704	−	0.701704i
$305$	−3.56884	−	1.55606i	−0.204351	−	0.0890997i
$306$	8.26561			0.472513
$307$	−7.96428	−	7.96428i	−0.454546	−	0.454546i	0.442314	−	0.896860i	$-0.354158\pi$
$307$	−7.96428	−	7.96428i	−0.454546	−	0.454546i	−0.896860	+	0.442314i	$0.854158\pi$
$308$	1.42276	−	5.30982i	0.0810693	−	0.302555i
$309$	−21.6017	+	5.78816i	−1.22888	+	0.329277i
$310$	10.1871	−	7.52217i	0.578588	−	0.427230i
$311$	0.179038	−	0.668180i	0.0101523	−	0.0378890i	−0.960664	−	0.277714i	$-0.910423\pi$
$311$	0.179038	−	0.668180i	0.0101523	−	0.0378890i	0.970816	+	0.239825i	$0.0770900\pi$
$312$	10.5437	+	2.82519i	0.596922	+	0.159945i
$313$	−11.6249	−	20.1350i	−0.657081	−	1.13810i	−0.981368	−	0.192139i	$-0.938458\pi$
$313$	−11.6249	−	20.1350i	−0.657081	−	1.13810i	0.324287	−	0.945959i	$-0.394876\pi$
$314$	−3.30189	−	12.3228i	−0.186336	−	0.695417i
$315$	1.59522	+	14.1277i	0.0898804	+	0.796007i
$316$	0.279581	−	1.04341i	0.0157276	−	0.0586963i
$317$	−8.41276	+	31.3969i	−0.472508	+	1.76342i	0.158205	+	0.987406i	$0.449429\pi$
$317$	−8.41276	+	31.3969i	−0.472508	+	1.76342i	−0.630713	+	0.776017i	$0.717237\pi$
$318$	−5.37862	−	9.31605i	−0.301618	−	0.522418i
$319$	2.04624	+	2.04624i	0.114567	+	0.114567i
$320$	−15.3111	−	12.2042i	−0.855914	−	0.682235i
$321$	−6.97805	+	4.02878i	−0.389477	+	0.224865i
$322$	26.1894	−	26.1894i	1.45948	−	1.45948i
$323$	−15.1502	+	15.1502i	−0.842979	+	0.842979i
$324$	0.305748	+	0.529572i	0.0169860	+	0.0294207i
$325$	−14.2182	−	4.37833i	−0.788685	−	0.242866i
$326$	−18.6827	−	10.7865i	−1.03474	−	0.597408i
$327$	−8.51805			−0.471049
$328$	−2.67656	−	1.54532i	−0.147789	−	0.0853258i
$329$	23.3051	+	13.4552i	1.28485	+	0.741810i
$330$	−1.99167	−	17.6388i	−0.109638	−	0.970987i
$331$	20.5568	+	5.50817i	1.12990	+	0.302757i	0.774885	−	0.632103i	$-0.217808\pi$
$331$	20.5568	+	5.50817i	1.12990	+	0.302757i	0.355018	+	0.934859i	$0.384475\pi$
$332$	0.493999	+	0.493999i	0.0271117	+	0.0271117i
$333$	7.66369	−	4.80196i	0.419968	−	0.263146i
$334$			12.9938i			0.710990i
$335$	24.4725	+	10.6703i	1.33708	+	0.582981i
$336$	−15.5169	−	8.95869i	−0.846517	−	0.488737i
$337$	−1.82172	+	0.488128i	−0.0992352	+	0.0265900i	−0.308095	−	0.951356i	$-0.599691\pi$
$337$	−1.82172	+	0.488128i	−0.0992352	+	0.0265900i	0.208860	+	0.977946i	$0.433025\pi$
$338$	−2.73305	+	4.73379i	−0.148659	+	0.257484i
$339$	1.35188	+	1.35188i	0.0734239	+	0.0734239i
$340$	−1.54337	+	1.93627i	−0.0837008	+	0.105009i
$341$	−14.8739	+	14.8739i	−0.805466	+	0.805466i
$342$	−9.61651	−	2.57674i	−0.520001	−	0.139334i
$343$	12.9675	+	12.9675i	0.700179	+	0.700179i
$344$	−9.47238			−0.510716
$345$	−7.22334	+	16.5668i	−0.388892	+	0.891928i
$346$	2.57403	+	9.60640i	0.138381	+	0.516443i
$347$	6.76364			0.363091			0.181546	−	0.983383i	$-0.441890\pi$
$347$	6.76364			0.363091			0.181546	+	0.983383i	$0.441890\pi$
$348$	−0.165324	+	0.0954497i	−0.00886228	+	0.00511664i
$349$	12.1596	−	7.02035i	0.650888	−	0.375790i	−0.137908	−	0.990445i	$-0.544038\pi$
$349$	12.1596	−	7.02035i	0.650888	−	0.375790i	0.788796	+	0.614655i	$0.210705\pi$
$350$	23.8717	+	14.9838i	1.27600	+	0.800916i
$351$	15.8627	−	4.25039i	0.846688	−	0.226869i
$352$	6.25468	+	3.61114i	0.333376	+	0.192475i
$353$	−12.4891	+	7.21056i	−0.664725	+	0.383779i	−0.794075	−	0.607820i	$-0.792044\pi$
$353$	−12.4891	+	7.21056i	−0.664725	+	0.383779i	0.129350	+	0.991599i	$0.458711\pi$
$354$	4.92201	+	8.52517i	0.261602	+	0.453108i
$355$	7.42664	−	2.91678i	0.394165	−	0.154807i
$356$	2.20462	−	2.20462i	0.116844	−	0.116844i
$357$	−11.0936	+	19.2147i	−0.587135	+	1.01695i
$358$	−27.2068	−	7.29003i	−1.43792	−	0.385290i
$359$			2.87625i			0.151803i	0.997115	+	0.0759013i	$0.0241834\pi$
$359$			2.87625i			0.151803i	−0.997115	+	0.0759013i	$0.975817\pi$
$360$	−9.80458	−	1.47542i	−0.516747	−	0.0777612i
$361$	5.89475	−	3.40334i	0.310250	−	0.179123i
$362$	−0.440318			−0.0231426
$363$	4.12931	+	15.4108i	0.216732	+	0.808856i
$364$	2.36231	−	2.36231i	0.123819	−	0.123819i
$365$	7.86492	−	0.888060i	0.411669	−	0.0464832i
$366$	1.41159	−	2.44495i	0.0737852	−	0.127800i
$367$	6.77750	+	25.2940i	0.353783	+	1.32033i	0.882010	+	0.471231i	$0.156190\pi$
$367$	6.77750	+	25.2940i	0.353783	+	1.32033i	−0.528227	+	0.849103i	$0.677143\pi$
$368$	11.1894	+	19.3807i	0.583290	+	1.01029i
$369$	−1.54079			−0.0802105
$370$	2.02555	−	17.8136i	0.105303	−	0.926086i
$371$	−28.3716			−1.47298
$372$	−0.693814	−	1.20172i	−0.0359726	−	0.0623063i
$373$	−8.90222	−	33.2235i	−0.460939	−	1.72025i	−0.670013	−	0.742349i	$-0.733712\pi$
$373$	−8.90222	−	33.2235i	−0.460939	−	1.72025i	0.209074	−	0.977900i	$-0.432955\pi$
$374$	−13.6090	+	23.5714i	−0.703703	+	1.21885i
$375$	−13.5152	−	2.54723i	−0.697924	−	0.131538i
$376$	−13.2701	+	13.2701i	−0.684352	+	0.684352i
$377$	0.455180	+	1.69875i	0.0234430	+	0.0874903i
$378$	−31.1120			−1.60023
$379$	−1.99724	+	1.15311i	−0.102591	+	0.0592312i	−0.550418	−	0.834889i	$-0.685532\pi$
$379$	−1.99724	+	1.15311i	−0.102591	+	0.0592312i	0.447826	+	0.894121i	$0.352198\pi$
$380$	2.39922	−	1.77159i	0.123078	−	0.0908806i
$381$			20.0312i			1.02623i
$382$	−5.37450	−	1.44009i	−0.274983	−	0.0736816i
$383$	−0.0702694	+	0.121710i	−0.00359060	+	0.00621910i	−0.867815	−	0.496887i	$-0.834476\pi$
$383$	−0.0702694	+	0.121710i	−0.00359060	+	0.00621910i	0.864225	+	0.503106i	$0.167810\pi$
$384$	7.47325	−	7.47325i	0.381367	−	0.381367i
$385$	−42.9152	−	18.7115i	−2.18716	−	0.953628i
$386$	5.27061	+	9.12897i	0.268267	+	0.464652i
$387$	−4.08966	+	2.36116i	−0.207889	+	0.120025i
$388$	2.33220	+	1.34650i	0.118400	+	0.0683581i
$389$	5.08702	−	1.36306i	0.257922	−	0.0691101i	−0.127541	−	0.991833i	$-0.540708\pi$
$389$	5.08702	−	1.36306i	0.257922	−	0.0691101i	0.385463	+	0.922723i	$0.374042\pi$
$390$	4.31164	−	9.88882i	0.218329	−	0.500740i
$391$	23.9992	−	13.8559i	1.21369	−	0.700725i
$392$	−29.1550	+	16.8327i	−1.47255	+	0.850178i
$393$	−17.5201			−0.883770
$394$	1.67696	+	6.25848i	0.0844838	+	0.315298i
$395$	−8.43307	−	3.67692i	−0.424314	−	0.185006i
$396$	1.91118			0.0960402
$397$	−3.01599	−	3.01599i	−0.151368	−	0.151368i	0.627361	−	0.778729i	$-0.284135\pi$
$397$	−3.01599	−	3.01599i	−0.151368	−	0.151368i	−0.778729	+	0.627361i	$0.784135\pi$
$398$	−14.3866	−	3.85489i	−0.721137	−	0.193228i
$399$	18.8967	−	18.8967i	0.946019	−	0.946019i
$400$	−12.4782	+	11.5891i	−0.623910	+	0.579457i
$401$	−6.97260	−	6.97260i	−0.348195	−	0.348195i	0.511242	−	0.859437i	$-0.329186\pi$
$401$	−6.97260	−	6.97260i	−0.348195	−	0.348195i	−0.859437	+	0.511242i	$0.829186\pi$
$402$	−9.67967	+	16.7657i	−0.482778	+	0.836196i
$403$	−12.3481	+	3.30865i	−0.615101	+	0.164816i
$404$	4.32321	+	2.49601i	0.215088	+	0.124181i
$405$	4.84744	−	1.90381i	0.240871	−	0.0946012i
$406$		−	3.33182i		−	0.165355i
$407$	1.07604	+	29.7611i	0.0533373	+	1.47520i
$408$	−10.9410	−	10.9410i	−0.541658	−	0.541658i
$409$	8.95729	+	2.40010i	0.442910	+	0.118677i	0.473380	−	0.880858i	$-0.343034\pi$
$409$	8.95729	+	2.40010i	0.442910	+	0.118677i	−0.0304703	+	0.999536i	$0.509700\pi$
$410$	−1.90385	+	2.38852i	−0.0940245	+	0.117961i
$411$	11.0623	+	6.38680i	0.545661	+	0.315038i
$412$	−4.13374	−	2.38662i	−0.203655	−	0.117580i
$413$	25.9630			1.27756
$414$	11.1516	+	6.43838i	0.548071	+	0.316429i
$415$	4.78643	−	3.53430i	0.234956	−	0.173492i
$416$	2.19463	+	3.80120i	0.107600	+	0.186369i
$417$	−7.61206	+	7.61206i	−0.372764	+	0.372764i
$418$	23.1814	−	23.1814i	1.13384	−	1.13384i
$419$	29.2106	−	16.8648i	1.42703	−	0.823898i	0.430147	−	0.902759i	$-0.358462\pi$
$419$	29.2106	−	16.8648i	1.42703	−	0.823898i	0.996886	+	0.0788607i	$0.0251282\pi$
$420$	1.92503	−	2.41509i	0.0939317	−	0.117844i
$421$	6.17988	+	6.17988i	0.301189	+	0.301189i	0.841479	−	0.540290i	$-0.181685\pi$
$421$	6.17988	+	6.17988i	0.301189	+	0.301189i	−0.540290	+	0.841479i	$0.681685\pi$
$422$	−10.6448	−	18.4373i	−0.518179	−	0.897513i
$423$	−2.42149	+	9.03711i	−0.117737	+	0.439400i
$424$	5.12092	−	19.1115i	0.248694	−	0.928138i
$425$	14.3509	+	15.4518i	0.696121	+	0.749524i
$426$	1.49747	+	5.58863i	0.0725526	+	0.270770i
$427$	−3.72299	−	6.44841i	−0.180168	−	0.312060i
$428$	−1.66118	−	0.445111i	−0.0802960	−	0.0215153i
$429$	−4.63794	+	17.3090i	−0.223922	+	0.835687i
$430$	−1.39305	+	9.25727i	−0.0671791	+	0.446425i
$431$	3.98861	−	1.06874i	0.192124	−	0.0514796i	−0.161474	−	0.986877i	$-0.551625\pi$
$431$	3.98861	−	1.06874i	0.192124	−	0.0514796i	0.353598	+	0.935397i	$0.384958\pi$
$432$	4.86542	−	18.1580i	0.234088	−	0.873628i
$433$	−2.42155	−	2.42155i	−0.116372	−	0.116372i	0.646523	−	0.762895i	$-0.276223\pi$
$433$	−2.42155	−	2.42155i	−0.116372	−	0.116372i	−0.762895	+	0.646523i	$0.776223\pi$
$434$	24.2186			1.16253
$435$	0.594339	+	1.51329i	0.0284964	+	0.0725568i
$436$	−1.28556	−	1.28556i	−0.0615674	−	0.0615674i
$437$	−32.2410	+	8.63895i	−1.54230	+	0.413257i
$438$			5.73937i			0.274238i
$439$	2.19354	+	8.18640i	0.104692	+	0.390716i	0.998310	−	0.0581125i	$-0.0185082\pi$
$439$	2.19354	+	8.18640i	0.104692	+	0.390716i	−0.893618	+	0.448828i	$0.851842\pi$
$440$	20.3503	−	25.5310i	0.970163	−	1.21714i
$441$	−8.39170	+	14.5349i	−0.399605	+	0.692136i
$442$	−14.3252	+	8.27068i	−0.681382	+	0.393396i
$443$	21.9112	−	21.9112i	1.04103	−	1.04103i	0.0419105	−	0.999121i	$-0.486656\pi$
$443$	21.9112	−	21.9112i	1.04103	−	1.04103i	0.999121	−	0.0419105i	$-0.0133444\pi$
$444$	−1.91476	−	0.439569i	−0.0908704	−	0.0208610i
$445$	−15.7729	−	21.3609i	−0.747706	−	1.01260i
$446$	1.14425	−	4.27038i	0.0541816	−	0.202209i
$447$	−19.8533	+	5.31969i	−0.939031	+	0.251613i
$448$	−9.69186	−	36.1705i	−0.457898	−	1.70890i
$449$	−24.7248	+	6.62498i	−1.16683	+	0.312652i	−0.789692	−	0.613503i	$-0.789760\pi$
$449$	−24.7248	+	6.62498i	−1.16683	+	0.312652i	−0.377142	+	0.926155i	$0.623093\pi$
$450$	−2.88382	+	9.36494i	−0.135945	+	0.441468i
$451$	2.53685	−	4.39395i	0.119456	−	0.206903i
$452$			0.408057i			0.0191934i
$453$	−1.41555	+	5.28289i	−0.0665082	+	0.248212i
$454$			5.66931i			0.266074i
$455$	−16.9011	−	22.8888i	−0.792335	−	1.07304i
$456$	9.31835	+	16.1399i	0.436372	+	0.755818i
$457$	−23.0907	−	13.3314i	−1.08014	−	0.623617i	−0.149203	−	0.988807i	$-0.547671\pi$
$457$	−23.0907	−	13.3314i	−1.08014	−	0.623617i	−0.930933	+	0.365190i	$0.881004\pi$
$458$			9.70877i			0.453661i
$459$	−22.4852	−	6.02488i	−1.04952	−	0.281217i
$460$	−3.59047	+	1.41014i	−0.167406	+	0.0657482i
$461$	28.6141	+	7.66712i	1.33269	+	0.357094i	0.853718	−	0.520736i	$-0.174342\pi$
$461$	28.6141	+	7.66712i	1.33269	+	0.357094i	0.478973	+	0.877829i	$0.341009\pi$
$462$	16.9743	−	29.4004i	0.789718	−	1.36783i
$463$	−9.41385	+	16.3053i	−0.437499	+	0.757770i	−0.997496	−	0.0707245i	$-0.977469\pi$
$463$	−9.41385	+	16.3053i	−0.437499	+	0.757770i	0.559997	+	0.828495i	$0.310802\pi$
$464$	1.94456	+	0.521044i	0.0902741	+	0.0241889i
$465$	−11.0000	+	4.32019i	−0.510111	+	0.200344i
$466$	−4.16161	−	1.11510i	−0.192783	−	0.0516560i
$467$		−	22.1604i		−	1.02546i	−0.858549	−	0.512731i	$-0.828634\pi$
$467$		−	22.1604i		−	1.02546i	0.858549	−	0.512731i	$-0.171366\pi$
$468$	1.00588	+	0.580747i	0.0464970	+	0.0268450i
$469$	25.5295	+	44.2185i	1.17884	+	2.04182i
$470$	11.0172	+	14.9203i	0.508184	+	0.688222i
$471$			11.9058i			0.548591i
$472$	−4.68618	+	17.4891i	−0.215699	+	0.805000i
$473$		−	15.5502i		−	0.715000i
$474$	3.33555	−	5.77735i	0.153207	−	0.265362i
$475$	−11.8794	−	22.4510i	−0.545063	−	1.03012i
$476$	−4.57420	+	1.22565i	−0.209658	+	0.0561777i
$477$	−2.55297	−	9.52780i	−0.116892	−	0.436248i
$478$	22.2943	−	5.97374i	1.01972	−	0.273233i
$479$	−1.61172	+	6.01501i	−0.0736412	+	0.274833i	−0.992922	−	0.118770i	$-0.962105\pi$
$479$	−1.61172	+	6.01501i	−0.0736412	+	0.274833i	0.919281	+	0.393603i	$0.128772\pi$
$480$	2.41030	+	3.26421i	0.110015	+	0.148990i
$481$	−8.47713	+	15.9907i	−0.386524	+	0.729114i
$482$	19.8024	−	19.8024i	0.901975	−	0.901975i
$483$	−29.9340	+	17.2824i	−1.36204	+	0.786376i
$484$	−1.70263	+	2.94904i	−0.0773921	+	0.134047i
$485$	14.2956	−	17.9349i	0.649132	−	0.814383i
$486$	−4.67141	−	17.4340i	−0.211900	−	0.790820i
$487$		−	13.1383i		−	0.595352i	−0.954667	−	0.297676i	$-0.903788\pi$
$487$		−	13.1383i		−	0.595352i	0.954667	−	0.297676i	$-0.0962115\pi$
$488$	5.01572	−	1.34396i	0.227051	−	0.0608382i
$489$	14.2360	+	14.2360i	0.643774	+	0.643774i
$490$	12.1627	+	30.9684i	0.549456	+	1.39901i
$491$	−1.90585			−0.0860099			−0.0430050	−	0.999075i	$-0.513693\pi$
$491$	−1.90585			−0.0860099			−0.0430050	+	0.999075i	$0.513693\pi$
$492$	0.236670	+	0.236670i	0.0106699	+	0.0106699i
$493$	0.645212	−	2.40796i	0.0290589	−	0.108449i
$494$	19.2448	−	5.15663i	0.865865	−	0.232008i
$495$	2.42210	−	16.0956i	0.108865	−	0.723442i
$496$	−3.78742	+	14.1348i	−0.170060	+	0.634672i
$497$	14.7397	+	3.94948i	0.661165	+	0.177159i
$498$	2.15724	+	3.73645i	0.0966682	+	0.167434i
$499$	5.11290	+	19.0816i	0.228885	+	0.854210i	0.980811	+	0.194962i	$0.0624584\pi$
$499$	5.11290	+	19.0816i	0.228885	+	0.854210i	−0.751926	+	0.659248i	$0.770875\pi$
$500$	−1.65532	−	2.42419i	−0.0740281	−	0.108413i
$501$	3.13853	−	11.7131i	0.140219	−	0.523304i
$502$	−8.56678	+	31.9717i	−0.382354	+	1.42696i
$503$	6.40682	+	11.0969i	0.285666	+	0.494788i	0.972770	−	0.231770i	$-0.0744518\pi$
$503$	6.40682	+	11.0969i	0.285666	+	0.494788i	−0.687104	+	0.726559i	$0.741118\pi$
$504$	−13.4084	−	13.4084i	−0.597259	−	0.597259i
$505$	26.4999	−	33.2460i	1.17923	−	1.47943i
$506$	−36.7212	+	21.2010i	−1.63246	+	0.942500i
$507$	3.60708	−	3.60708i	0.160196	−	0.160196i
$508$	−3.02316	+	3.02316i	−0.134131	+	0.134131i
$509$	−16.2560	−	28.1562i	−0.720534	−	1.24800i	−0.960786	−	0.277291i	$-0.910563\pi$
$509$	−16.2560	−	28.1562i	−0.720534	−	1.24800i	0.240252	−	0.970711i	$-0.422770\pi$
$510$	−12.3015	+	9.08347i	−0.544721	+	0.402223i
$511$	13.1092	+	7.56862i	0.579919	+	0.334816i
$512$	25.3397			1.11987
$513$	24.2818	+	14.0191i	1.07207	+	0.618960i
$514$	−6.02792	−	3.48022i	−0.265880	−	0.153506i
$515$	−25.3385	+	31.7889i	−1.11655	+	1.40079i
$516$	0.990864	+	0.265501i	0.0436203	+	0.0116880i
$517$	−21.7847	−	21.7847i	−0.958089	−	0.958089i
$518$	23.3535	−	25.1055i	1.02609	−	1.10307i
$519$		−	9.28132i		−	0.407405i
$520$	18.4688	−	7.25353i	0.809909	−	0.318088i
$521$	24.6860	+	14.2524i	1.08151	+	0.624411i	0.931304	−	0.364244i	$-0.118672\pi$
$521$	24.6860	+	14.2524i	1.08151	+	0.624411i	0.150208	+	0.988654i	$0.452006\pi$
$522$	1.11890	−	0.299808i	0.0489728	−	0.0131222i
$523$	13.3720	−	23.1609i	0.584716	−	1.01276i	−0.410195	−	0.911998i	$-0.634539\pi$
$523$	13.3720	−	23.1609i	0.584716	−	1.01276i	0.994911	−	0.100760i	$-0.0321273\pi$
$524$	−2.64417	−	2.64417i	−0.115511	−	0.115511i
$525$	−17.8998	−	19.2729i	−0.781209	−	0.841140i
$526$	−16.1240	+	16.1240i	−0.703041	+	0.703041i
$527$	17.5032	+	4.68998i	0.762453	+	0.204299i
$528$	14.5046	+	14.5046i	0.631231	+	0.631231i
$529$	20.1715			0.877024
$530$	−17.9244	−	7.81526i	−0.778586	−	0.339473i
$531$	2.33623	+	8.71894i	0.101384	+	0.378370i
$532$	5.70387			0.247294
$533$	2.67037	−	1.54174i	0.115666	−	0.0667801i
$534$	16.6750	−	9.62732i	0.721598	−	0.416615i
$535$	−5.85391	+	13.4260i	−0.253086	+	0.580457i
$536$	−34.3942	+	9.21589i	−1.48560	+	0.398066i
$537$	22.7644	+	13.1430i	0.982357	+	0.567164i
$538$	0.197519	−	0.114037i	0.00851563	−	0.00491650i
$539$	−27.6331	−	47.8620i	−1.19024	−	2.06156i
$540$	2.97026	+	1.29507i	0.127820	+	0.0557309i
$541$	17.2856	−	17.2856i	0.743165	−	0.743165i	−0.230021	−	0.973186i	$-0.573879\pi$
$541$	17.2856	−	17.2856i	0.743165	−	0.743165i	0.973186	+	0.230021i	$0.0738794\pi$
$542$	12.0925	−	20.9448i	0.519416	−	0.899654i
$543$	0.396920	+	0.106354i	0.0170335	+	0.00456410i
$544$		−	6.22171i		−	0.266754i
$545$	−12.4560	+	9.19754i	−0.533557	+	0.393979i
$546$	17.8677	−	10.3159i	0.764669	−	0.441482i
$547$	13.5842			0.580818			0.290409	−	0.956903i	$-0.406209\pi$
$547$	13.5842			0.580818			0.290409	+	0.956903i	$0.406209\pi$
$548$	0.705632	+	2.63345i	0.0301431	+	0.112496i
$549$	1.83051	−	1.83051i	0.0781243	−	0.0781243i
$550$	−21.9584	−	23.6429i	−0.936307	−	1.00814i
$551$	−1.50133	+	2.60037i	−0.0639586	+	0.110780i
$552$	−6.23876	−	23.2834i	−0.265539	−	0.991006i
$553$	−8.79732	−	15.2374i	−0.374100	−	0.647960i
$554$	−2.42372			−0.102974
$555$	−6.12861	+	15.5686i	−0.260145	+	0.660852i
$556$	−2.29766			−0.0974425
$557$	−20.4323	−	35.3898i	−0.865744	−	1.49951i	−0.866307	−	0.499513i	$-0.833512\pi$
$557$	−20.4323	−	35.3898i	−0.865744	−	1.49951i	0.000562636	−	1.00000i	$-0.499821\pi$
$558$	2.17927	+	8.13315i	0.0922558	+	0.344303i
$559$	4.72522	−	8.18433i	0.199856	−	0.346160i
$560$	−32.3638	+	3.65433i	−1.36762	+	0.154424i
$561$	17.9611	−	17.9611i	0.758318	−	0.758318i
$562$	1.15933	+	4.32669i	0.0489035	+	0.182510i
$563$	−27.8829			−1.17512			−0.587561	−	0.809180i	$-0.699912\pi$
$563$	−27.8829			−1.17512			−0.587561	+	0.809180i	$0.699912\pi$
$564$	1.76007	−	1.01618i	0.0741124	−	0.0427888i
$565$	3.43658	+	0.517144i	0.144578	+	0.0217564i
$566$			16.5756i			0.696726i
$567$	9.62072	+	2.57786i	0.404032	+	0.108260i
$568$	−5.32086	+	9.21600i	−0.223258	+	0.386695i
$569$	−10.7860	+	10.7860i	−0.452173	+	0.452173i	−0.896075	−	0.443902i	$-0.853594\pi$
$569$	−10.7860	+	10.7860i	−0.452173	+	0.452173i	0.443902	+	0.896075i	$0.353594\pi$
$570$	17.1437	−	6.73313i	0.718072	−	0.282020i
$571$	16.7650	+	29.0378i	0.701594	+	1.21520i	0.967907	+	0.251310i	$0.0808612\pi$
$571$	16.7650	+	29.0378i	0.701594	+	1.21520i	−0.266313	+	0.963887i	$0.585805\pi$
$572$	−3.31228	+	1.91235i	−0.138494	+	0.0799593i
$573$	4.49695	+	2.59631i	0.187863	+	0.108463i
$574$	−5.64259	+	1.51193i	−0.235517	+	0.0631067i
$575$	7.32562	+	32.0254i	0.305500	+	1.33555i
$576$	11.2747	−	6.50948i	0.469781	−	0.271228i
$577$	15.5106	−	8.95508i	0.645717	−	0.372805i	−0.141097	−	0.989996i	$-0.545063\pi$
$577$	15.5106	−	8.95508i	0.645717	−	0.372805i	0.786813	+	0.617191i	$0.211729\pi$
$578$	1.03908			0.0432200
$579$	−2.54613	−	9.50228i	−0.105813	−	0.394901i
$580$	−0.138690	+	0.318089i	−0.00575881	+	0.0132079i
$581$	11.3792			0.472087
$582$	11.7600	+	11.7600i	0.487469	+	0.487469i
$583$	31.3742	+	8.40669i	1.29939	+	0.348170i
$584$	−7.46448	+	7.46448i	−0.308883	+	0.308883i
$585$	6.16573	−	7.73536i	0.254922	−	0.319818i
$586$	9.82570	+	9.82570i	0.405896	+	0.405896i
$587$	−18.7207	+	32.4251i	−0.772684	+	1.33833i	0.163402	+	0.986560i	$0.447753\pi$
$587$	−18.7207	+	32.4251i	−0.772684	+	1.33833i	−0.936087	+	0.351769i	$0.885580\pi$
$588$	3.52158	−	0.943605i	0.145228	−	0.0389136i
$589$	−18.9018	−	10.9130i	−0.778836	−	0.449661i
$590$	16.4027	+	7.15179i	0.675290	+	0.294435i
$591$		−	6.04669i		−	0.248728i
$592$	11.0003	+	17.5560i	0.452111	+	0.721547i
$593$	8.22207	+	8.22207i	0.337640	+	0.337640i	0.855478	−	0.517839i	$-0.173263\pi$
$593$	8.22207	+	8.22207i	0.337640	+	0.337640i	−0.517839	+	0.855478i	$0.673263\pi$
$594$	34.4046	+	9.21869i	1.41164	+	0.378247i
$595$	4.52518	+	40.0763i	0.185514	+	1.64297i
$596$	−3.79917	−	2.19345i	−0.155620	−	0.0898473i
$597$	12.0376	+	6.94990i	0.492665	+	0.284440i
$598$	−25.7693			−1.05378
$599$	−15.7152	−	9.07320i	−0.642107	−	0.370721i	0.143318	−	0.989677i	$-0.454223\pi$
$599$	−15.7152	−	9.07320i	−0.642107	−	0.370721i	−0.785426	+	0.618956i	$0.787556\pi$
$600$	16.2133	−	8.57888i	0.661907	−	0.350231i
$601$	−21.7617	−	37.6924i	−0.887679	−	1.53751i	−0.842612	−	0.538521i	$-0.818983\pi$
$601$	−21.7617	−	37.6924i	−0.887679	−	1.53751i	−0.0450671	−	0.998984i	$-0.514350\pi$
$602$	−12.6599	+	12.6599i	−0.515981	+	0.515981i
$603$	−12.5523	+	12.5523i	−0.511169	+	0.511169i
$604$	−1.01094	+	0.583669i	−0.0411347	+	0.0237492i
$605$	22.6784	+	18.0766i	0.922009	+	0.734919i
$606$	21.7996	+	21.7996i	0.885548	+	0.885548i
$607$	−7.16138	−	12.4039i	−0.290671	−	0.503458i	0.683297	−	0.730140i	$-0.260545\pi$
$607$	−7.16138	−	12.4039i	−0.290671	−	0.503458i	−0.973969	+	0.226683i	$0.927212\pi$
$608$	−1.93957	+	7.23856i	−0.0786598	+	0.293563i
$609$	−0.804767	+	3.00343i	−0.0326108	+	0.121705i
$610$	−0.575802	−	5.09947i	−0.0233135	−	0.206472i
$611$	−4.84594	−	18.0853i	−0.196046	−	0.731653i
$612$	−0.823201	−	1.42583i	−0.0332759	−	0.0576356i
$613$	0.324630	+	0.0869843i	0.0131117	+	0.00351326i	0.265369	−	0.964147i	$-0.414506\pi$
$613$	0.324630	+	0.0869843i	0.0131117	+	0.00351326i	−0.252257	+	0.967660i	$0.581173\pi$
$614$	3.84250	−	14.3404i	0.155071	−	0.578731i
$615$	2.29313	−	1.69325i	0.0924679	−	0.0682784i
$616$	60.3138	−	16.1610i	2.43011	−	0.651147i
$617$	−6.94555	+	25.9211i	−0.279617	+	1.04355i	0.673066	+	0.739582i	$0.264977\pi$
$617$	−6.94555	+	25.9211i	−0.279617	+	1.04355i	−0.952684	+	0.303964i	$0.901690\pi$
$618$	−20.8442	−	20.8442i	−0.838476	−	0.838476i
$619$	45.2493			1.81872			0.909361	−	0.416008i	$-0.136571\pi$
$619$	45.2493			1.81872			0.909361	+	0.416008i	$0.136571\pi$
$620$	−2.31215	−	1.00813i	−0.0928582	−	0.0404873i
$621$	−25.6430	−	25.6430i	−1.02902	−	1.02902i
$622$	0.880744	−	0.235995i	0.0353146	−	0.00946252i
$623$		−	50.7829i		−	2.03457i
$624$	3.22650	+	12.0415i	0.129164	+	0.482045i
$625$	−22.5139	+	10.8685i	−0.900555	+	0.434741i
$626$	15.3231	−	26.5404i	0.612434	−	1.06077i
$627$	−26.4958	+	15.2974i	−1.05814	+	0.610918i
$628$	−1.79685	+	1.79685i	−0.0717023	+	0.0717023i
$629$	21.7397	−	13.6218i	0.866818	−	0.543136i
$630$	−15.0758	+	11.1320i	−0.600636	+	0.443511i
$631$	−8.96677	+	33.4644i	−0.356961	+	1.33220i	0.521037	+	0.853534i	$0.325545\pi$
$631$	−8.96677	+	33.4644i	−0.356961	+	1.33220i	−0.877998	+	0.478664i	$0.841121\pi$
$632$	11.8520	−	3.17574i	0.471448	−	0.126324i
$633$	5.14227	+	19.1912i	0.204387	+	0.762783i
$634$	−41.3849	+	11.0890i	−1.64360	+	0.440402i
$635$	21.6291	+	29.2918i	0.858326	+	1.16241i
$636$	−1.07135	+	1.85564i	−0.0424819	+	0.0735808i
$637$		−	33.5874i		−	1.33078i
$638$	−0.987240	+	3.68443i	−0.0390852	+	0.145868i
$639$			5.30529i			0.209874i
$640$	2.85880	−	18.9976i	0.113004	−	0.750945i
$641$	−5.16086	−	8.93888i	−0.203842	−	0.353065i	0.745921	−	0.666034i	$-0.232010\pi$
$641$	−5.16086	−	8.93888i	−0.203842	−	0.353065i	−0.949763	+	0.312970i	$0.898676\pi$
$642$	−9.19793	−	5.31043i	−0.363013	−	0.209586i
$643$		−	9.55874i		−	0.376960i	−0.982077	−	0.188480i	$-0.939644\pi$
$643$		−	9.55874i		−	0.376960i	0.982077	−	0.188480i	$-0.0603561\pi$
$644$	−7.12601	−	1.90941i	−0.280804	−	0.0752412i
$645$	3.49175	−	8.00839i	0.137488	−	0.315330i
$646$	−27.2793	−	7.30946i	−1.07329	−	0.287587i
$647$	0.852572	−	1.47670i	0.0335181	−	0.0580550i	−0.848780	−	0.528747i	$-0.822662\pi$
$647$	0.852572	−	1.47670i	0.0335181	−	0.0580550i	0.882298	+	0.470692i	$0.155996\pi$
$648$	−3.47298	+	6.01537i	−0.136431	+	0.236306i
$649$	−28.7107	−	7.69301i	−1.12699	−	0.301977i
$650$	−4.37270	−	19.1161i	−0.171511	−	0.749795i
$651$	−21.8316	−	5.84977i	−0.855649	−	0.229270i
$652$			4.29706i			0.168286i
$653$	−24.9960	−	14.4314i	−0.978168	−	0.564746i	−0.0764516	−	0.997073i	$-0.524359\pi$
$653$	−24.9960	−	14.4314i	−0.978168	−	0.564746i	−0.901717	+	0.432328i	$0.857692\pi$
$654$	−5.61392	−	9.72359i	−0.219522	−	0.380223i
$655$	−25.6197	+	18.9176i	−1.00105	+	0.739174i
$656$		−	3.52965i		−	0.137810i
$657$	−1.36210	+	5.08342i	−0.0531405	+	0.198323i
$658$			35.4713i			1.38281i
$659$	−11.5673	+	20.0352i	−0.450598	+	0.780459i	−0.998423	−	0.0561341i	$-0.982123\pi$
$659$	−11.5673	+	20.0352i	−0.450598	+	0.780459i	0.547825	+	0.836593i	$0.315456\pi$
$660$	−2.84436	+	2.10028i	−0.110717	+	0.0817534i
$661$	−32.1200	+	8.60652i	−1.24932	+	0.334755i	−0.822074	−	0.569380i	$-0.807183\pi$
$661$	−32.1200	+	8.60652i	−1.24932	+	0.334755i	−0.427247	+	0.904135i	$0.640517\pi$
$662$	7.26045	+	27.0964i	0.282185	+	1.05313i
$663$	14.9110	−	3.99540i	0.579096	−	0.155168i
$664$	−2.05388	+	7.66518i	−0.0797059	+	0.297466i
$665$	7.22871	−	48.0369i	0.280317	−	1.86279i
$666$	10.5324	+	5.58353i	0.408123	+	0.216357i
$667$	2.74614	−	2.74614i	0.106331	−	0.106331i
$668$	2.24145	−	1.29410i	0.0867242	−	0.0500703i
$669$	−2.06294	+	3.57311i	−0.0797577	+	0.138144i
$670$	3.94843	+	34.9684i	0.152541	+	1.35095i
$671$	2.20629	+	8.23400i	0.0851731	+	0.317870i
$672$			7.76029i			0.299360i
$673$	33.8290	−	9.06446i	1.30401	−	0.349409i	0.461047	−	0.887376i	$-0.347474\pi$
$673$	33.8290	−	9.06446i	1.30401	−	0.349409i	0.842966	+	0.537966i	$0.180807\pi$
$674$	−1.75783	−	1.75783i	−0.0677092	−	0.0677092i
$675$	14.6711	−	23.3737i	0.564692	−	0.899653i
$676$	1.08878			0.0418761
$677$	−9.71006	−	9.71006i	−0.373188	−	0.373188i	0.495449	−	0.868637i	$-0.335004\pi$
$677$	−9.71006	−	9.71006i	−0.373188	−	0.373188i	−0.868637	+	0.495449i	$0.835004\pi$
$678$	−0.652235	+	2.43418i	−0.0250489	+	0.0934839i
$679$	42.3691	−	11.3528i	1.62598	−	0.435679i
$680$	−27.8128	−	4.18533i	−1.06657	−	0.160500i
$681$	1.36937	−	5.11054i	0.0524742	−	0.195836i
$682$	−26.7817	−	7.17614i	−1.02553	−	0.274789i
$683$	−2.83069	−	4.90289i	−0.108313	−	0.187604i	0.806774	−	0.590860i	$-0.201212\pi$
$683$	−2.83069	−	4.90289i	−0.108313	−	0.187604i	−0.915087	+	0.403256i	$0.867878\pi$
$684$	0.513253	+	1.91548i	0.0196247	+	0.0732404i
$685$	23.0727	−	2.60523i	0.881563	−	0.0995409i
$686$	−6.25638	+	23.3491i	−0.238870	+	0.891474i
$687$	2.34506	−	8.75186i	0.0894694	−	0.333904i
$688$	−5.40896	−	9.36860i	−0.206215	−	0.357174i
$689$	13.9582	+	13.9582i	0.531766	+	0.531766i
$690$	−23.6721	+	2.67291i	−0.901182	+	0.101756i
$691$	27.9652	−	16.1457i	1.06385	−	0.614212i	0.137353	−	0.990522i	$-0.456141\pi$
$691$	27.9652	−	16.1457i	1.06385	−	0.614212i	0.926494	+	0.376310i	$0.122807\pi$
$692$	1.40076	−	1.40076i	0.0532488	−	0.0532488i
$693$	22.0118	−	22.0118i	0.836159	−	0.836159i
$694$	4.45765	+	7.72088i	0.169210	+	0.293081i
$695$	−2.91190	+	19.3505i	−0.110455	+	0.734005i
$696$	−1.87790	−	1.08421i	−0.0711816	−	0.0410967i
$697$	−4.37079			−0.165555
$698$	16.0278	+	9.25368i	0.606663	+	0.350257i
$699$	3.48210	+	2.01039i	0.131705	+	0.0760399i
$700$	0.207244	−	5.61019i	0.00783308	−	0.212045i
$701$	−45.2722	−	12.1306i	−1.70991	−	0.458168i	−0.734505	−	0.678603i	$-0.762586\pi$
$701$	−45.2722	−	12.1306i	−1.70991	−	0.458168i	−0.975402	+	0.220435i	$0.929252\pi$
$702$	15.3064	+	15.3064i	0.577704	+	0.577704i
$703$	−29.5392	+	9.07091i	−1.11409	+	0.342116i
$704$			42.8703i			1.61573i
$705$	−6.32746	−	16.1108i	−0.238306	−	0.606769i
$706$	−16.4621	−	9.50440i	−0.619559	−	0.357703i
$707$	78.5397	−	21.0447i	2.95379	−	0.791466i
$708$	0.980401	−	1.69811i	0.0368457	−	0.0638187i
$709$	−21.6799	−	21.6799i	−0.814204	−	0.814204i	0.171057	−	0.985261i	$-0.445282\pi$
$709$	−21.6799	−	21.6799i	−0.814204	−	0.814204i	−0.985261	+	0.171057i	$0.945282\pi$
$710$	8.22420	+	6.55538i	0.308649	+	0.246019i
$711$	4.32544	−	4.32544i	0.162217	−	0.162217i
$712$	34.2081	+	9.16604i	1.28200	+	0.343512i
$713$	19.9614	+	19.9614i	0.747560	+	0.747560i
$714$	−29.2454			−1.09448
$715$	11.9077	+	30.3190i	0.445322	+	1.13387i
$716$	1.45208	+	5.41924i	0.0542668	+	0.202526i
$717$	−21.5399			−0.804421
$718$	−3.28332	+	1.89562i	−0.122532	+	0.0707440i
$719$	−4.69821	+	2.71251i	−0.175214	+	0.101160i	−0.585042	−	0.811003i	$-0.698922\pi$
$719$	−4.69821	+	2.71251i	−0.175214	+	0.101160i	0.409828	+	0.912163i	$0.365589\pi$
$720$	−4.13941	−	10.5397i	−0.154267	−	0.392790i
$721$	−75.0976	+	20.1223i	−2.79678	+	0.749395i
$722$	7.77001	+	4.48602i	0.289170	+	0.166952i
$723$	−22.6337	+	13.0676i	−0.841758	+	0.485989i
$724$	0.0438528	+	0.0759554i	0.00162978	+	0.00282286i
$725$	2.50311	+	1.57115i	0.0929633	+	0.0583510i
$726$	−14.8704	+	14.8704i	−0.551891	+	0.551891i
$727$	−12.7814	+	22.1381i	−0.474037	+	0.821057i	−0.999558	−	0.0297241i	$-0.990537\pi$
$727$	−12.7814	+	22.1381i	−0.474037	+	0.821057i	0.525521	+	0.850781i	$0.323870\pi$
$728$	36.6550	+	9.82167i	1.35852	+	0.364015i
$729$			23.8311i			0.882634i
$730$	6.19721	+	8.39274i	0.229369	+	0.310629i
$731$	−11.6012	+	6.69795i	−0.429085	+	0.247733i
$732$	−0.562343			−0.0207848
$733$	5.41101	+	20.1942i	0.199860	+	0.745889i	0.990955	+	0.134195i	$0.0428448\pi$
$733$	5.41101	+	20.1942i	0.199860	+	0.745889i	−0.791095	+	0.611694i	$0.790489\pi$
$734$	−24.4070	+	24.4070i	−0.900878	+	0.900878i
$735$	−3.48384	−	30.8540i	−0.128504	−	1.13807i
$736$	4.84631	−	8.39406i	0.178637	−	0.309409i
$737$	−15.1291	−	56.4628i	−0.557289	−	2.07983i
$738$	−1.01548	−	1.75886i	−0.0373802	−	0.0647445i
$739$	−23.1549			−0.851767			−0.425884	−	0.904778i	$-0.640037\pi$
$739$	−23.1549			−0.851767			−0.425884	+	0.904778i	$0.640037\pi$
$740$	−3.27460	+	1.42471i	−0.120377	+	0.0523735i
$741$	−18.5936			−0.683051
$742$	−18.6986	−	32.3869i	−0.686448	−	1.18896i
$743$	−6.50787	−	24.2877i	−0.238750	−	0.891029i	−0.976422	−	0.215869i	$-0.930741\pi$
$743$	−6.50787	−	24.2877i	−0.238750	−	0.891029i	0.737672	−	0.675159i	$-0.235925\pi$
$744$	7.88098	−	13.6503i	0.288931	−	0.500443i
$745$	−23.2877	+	29.2161i	−0.853194	+	1.07039i
$746$	32.0585	−	32.0585i	1.17374	−	1.17374i
$747$	1.02393	+	3.82137i	0.0374638	+	0.139817i
$748$	5.42146			0.198228
$749$	−24.2590	+	14.0059i	−0.886403	+	0.511765i
$750$	−5.99965	−	17.1068i	−0.219076	−	0.624652i
$751$		−	49.5019i		−	1.80635i	−0.429272	−	0.903175i	$-0.641230\pi$
$751$		−	49.5019i		−	1.80635i	0.429272	−	0.903175i	$-0.358770\pi$
$752$	−20.7022	−	5.54715i	−0.754933	−	0.202284i
$753$	15.4449	−	26.7513i	0.562842	−	0.974871i
$754$	−1.63918	+	1.63918i	−0.0596955	+	0.0596955i
$755$	3.63435	+	9.25368i	0.132267	+	0.336776i
$756$	3.09855	+	5.36685i	0.112693	+	0.195190i
$757$	30.8365	−	17.8035i	1.12077	−	0.647078i	0.179174	−	0.983817i	$-0.442658\pi$
$757$	30.8365	−	17.8035i	1.12077	−	0.647078i	0.941598	+	0.336740i	$0.109324\pi$
$758$	−2.63261	−	1.51994i	−0.0956207	−	0.0552067i
$759$	38.2229	−	10.2418i	1.38740	−	0.371753i
$760$	31.0536	+	13.5398i	1.12643	+	0.491139i
$761$	9.14549	−	5.28015i	0.331524	−	0.191405i	−0.324994	−	0.945716i	$-0.605362\pi$
$761$	9.14549	−	5.28015i	0.331524	−	0.191405i	0.656517	+	0.754311i	$0.272029\pi$
$762$	−22.8662	+	13.2018i	−0.828355	+	0.478251i
$763$	−29.6127			−1.07205
$764$	0.286848	+	1.07053i	0.0103778	+	0.0387305i
$765$	−13.0513	+	5.12585i	−0.471871	+	0.185325i
$766$	−0.185247			−0.00669326
$767$	−12.7732	−	12.7732i	−0.461215	−	0.461215i
$768$	−7.35254	−	1.97011i	−0.265312	−	0.0710901i
$769$	10.0805	−	10.0805i	0.363511	−	0.363511i	−0.501593	−	0.865104i	$-0.667252\pi$
$769$	10.0805	−	10.0805i	0.363511	−	0.363511i	0.865104	+	0.501593i	$0.167252\pi$
$770$	−6.92399	−	61.3209i	−0.249523	−	2.20985i
$771$	4.59319	+	4.59319i	0.165420	+	0.165420i
$772$	1.04984	−	1.81837i	0.0377845	−	0.0654447i
$773$	3.01172	−	0.806988i	0.108324	−	0.0290253i	−0.204250	−	0.978919i	$-0.565475\pi$
$773$	3.01172	−	0.806988i	0.108324	−	0.0290253i	0.312574	+	0.949893i	$0.398809\pi$
$774$	−5.39067	−	3.11230i	−0.193764	−	0.111869i
$775$	−11.4205	+	18.1949i	−0.410237	+	0.653579i
$776$			30.5896i			1.09810i
$777$	−27.1157	+	16.9903i	−0.972771	+	0.609525i
$778$	4.90864	+	4.90864i	0.175983	+	0.175983i
$779$	5.08513	+	1.36256i	0.182194	+	0.0488187i
$780$	−2.13524	+	0.241099i	−0.0764540	+	0.00863273i
$781$	−15.1293	−	8.73493i	−0.541370	−	0.312560i
$782$	31.6339	+	18.2638i	1.13123	+	0.653113i
$783$	−3.26230			−0.116585
$784$	−33.2965	−	19.2237i	−1.18916	−	0.686562i
$785$	12.8555	+	17.4100i	0.458834	+	0.621389i
$786$	−11.5468	−	19.9996i	−0.411861	−	0.713363i
$787$	14.6240	−	14.6240i	0.521288	−	0.521288i	−0.396673	−	0.917960i	$-0.629835\pi$
$787$	14.6240	−	14.6240i	0.521288	−	0.521288i	0.917960	+	0.396673i	$0.129835\pi$
$788$	0.912581	−	0.912581i	0.0325094	−	0.0325094i
$789$	18.4294	−	10.6402i	0.656105	−	0.378803i
$790$	−1.36060	−	12.0499i	−0.0484081	−	0.428716i
$791$	4.69976	+	4.69976i	0.167104	+	0.167104i
$792$	10.8545	+	18.8005i	0.385697	+	0.668046i
$793$	−1.34085	+	5.00411i	−0.0476149	+	0.177701i
$794$	1.45512	−	5.43057i	0.0516401	−	0.192724i
$795$	14.2701	+	11.3744i	0.506107	+	0.403410i
$796$	0.767844	+	2.86563i	0.0272155	+	0.101570i
$797$	4.72156	+	8.17798i	0.167246	+	0.289679i	0.937451	−	0.348118i	$-0.113179\pi$
$797$	4.72156	+	8.17798i	0.167246	+	0.289679i	−0.770204	+	0.637797i	$0.779846\pi$
$798$	34.0252	+	9.11703i	1.20448	+	0.322739i
$799$	−6.86907	+	25.6357i	−0.243010	+	0.906926i
$800$	7.04921	+	2.17072i	0.249227	+	0.0767464i
$801$	17.0540	−	4.56961i	0.602574	−	0.161459i
$802$	3.36405	−	12.5548i	0.118789	−	0.443325i
$803$	−12.2540	−	12.2540i	−0.432434	−	0.432434i
$804$	3.85613			0.135995
$805$	−25.1117	+	57.5940i	−0.885071	+	2.02992i
$806$	−11.9151	−	11.9151i	−0.419690	−	0.419690i
$807$	−0.205596	+	0.0550892i	−0.00723731	+	0.00193923i
$808$			56.7040i			1.99484i
$809$	−0.700060	−	2.61266i	−0.0246128	−	0.0918562i	0.952527	−	0.304454i	$-0.0984741\pi$
$809$	−0.700060	−	2.61266i	−0.0246128	−	0.0918562i	−0.977140	+	0.212598i	$0.931807\pi$
$810$	5.36801	+	4.27876i	0.188613	+	0.150340i
$811$	−6.24691	+	10.8200i	−0.219359	+	0.379940i	−0.954612	−	0.297852i	$-0.903730\pi$
$811$	−6.24691	+	10.8200i	−0.219359	+	0.379940i	0.735253	+	0.677792i	$0.237063\pi$
$812$	−0.574742	+	0.331828i	−0.0201695	+	0.0116449i
$813$	−15.9596	+	15.9596i	−0.559728	+	0.559728i
$814$	−33.2640	+	20.8427i	−1.16590	+	0.730537i
$815$	36.1890	+	5.44580i	1.26765	+	0.190758i
$816$	4.57353	−	17.0686i	0.160106	−	0.597522i
$817$	15.5853	−	4.17606i	0.545260	−	0.146102i
$818$	3.16362	+	11.8068i	0.110614	+	0.412815i
$819$	18.2739	−	4.89646i	0.638540	−	0.171096i
$820$	0.601634	+	0.0905352i	0.0210100	+	0.00316163i
$821$	−12.5053	+	21.6598i	−0.436438	+	0.755932i	−0.997412	−	0.0719010i	$-0.977093\pi$
$821$	−12.5053	+	21.6598i	−0.436438	+	0.755932i	0.560974	+	0.827833i	$0.310427\pi$
$822$			16.8372i			0.587264i
$823$	−0.352784	+	1.31661i	−0.0122973	+	0.0458940i	−0.971802	−	0.235799i	$-0.924229\pi$
$823$	−0.352784	+	1.31661i	−0.0122973	+	0.0458940i	0.959505	+	0.281693i	$0.0908960\pi$
$824$		−	54.2188i		−	1.88880i
$825$	14.0834	+	26.6164i	0.490322	+	0.926666i
$826$	17.1112	+	29.6375i	0.595375	+	1.03122i
$827$	−28.5764	−	16.4986i	−0.993698	−	0.573712i	−0.0873203	−	0.996180i	$-0.527830\pi$
$827$	−28.5764	−	16.4986i	−0.993698	−	0.573712i	−0.906378	+	0.422469i	$0.861164\pi$
$828$		−	2.56488i		−	0.0891359i
$829$	37.2077	+	9.96978i	1.29228	+	0.346265i	0.838525	−	0.544863i	$-0.183418\pi$
$829$	37.2077	+	9.96978i	1.29228	+	0.346265i	0.453752	+	0.891128i	$0.350085\pi$
$830$	7.18905	+	3.13451i	0.249536	+	0.108801i
$831$	2.18484	+	0.585426i	0.0757912	+	0.0203082i
$832$	−13.0269	+	22.5633i	−0.451628	+	0.782242i
$833$	−23.8049	+	41.2312i	−0.824790	+	1.42858i
$834$	−13.7062	−	3.67256i	−0.474607	−	0.127171i
$835$	−8.05801	−	20.5171i	−0.278859	−	0.710024i
$836$	−6.30752	−	1.69010i	−0.218150	−	0.0584532i
$837$		−	23.7133i		−	0.819652i
$838$	38.5032	+	22.2298i	1.33007	+	0.767917i
$839$	−21.2111	−	36.7387i	−0.732288	−	1.26836i	−0.955903	−	0.293683i	$-0.905119\pi$
$839$	−21.2111	−	36.7387i	−0.732288	−	1.26836i	0.223614	−	0.974678i	$-0.428214\pi$
$840$	34.6906	+	5.22033i	1.19694	+	0.180118i
$841$			28.6506i			0.987953i
$842$	−2.98158	+	11.1274i	−0.102752	+	0.383476i
$843$		−	4.18027i		−	0.143976i
$844$	−2.12030	+	3.67247i	−0.0729838	+	0.126412i
$845$	1.37985	−	9.16949i	0.0474681	−	0.315440i
$846$	−11.9120	+	3.19182i	−0.409544	+	0.109737i
$847$	14.3554	+	53.5751i	0.493257	+	1.84086i
$848$	21.8263	−	5.84834i	0.749518	−	0.200833i
$849$	4.00368	−	14.9419i	0.137406	−	0.512806i
$850$	−8.18057	+	26.5657i	−0.280591	+	0.911194i
$851$	39.9407	−	1.44409i	1.36915	−	0.0495028i
$852$	0.814907	−	0.814907i	0.0279183	−	0.0279183i
$853$	−36.3664	+	20.9962i	−1.24516	+	0.718895i	−0.970141	−	0.242543i	$-0.922019\pi$
$853$	−36.3664	+	20.9962i	−1.24516	+	0.718895i	−0.275022	+	0.961438i	$0.588685\pi$
$854$	4.90736	−	8.49979i	0.167926	−	0.290857i
$855$	16.7823	−	1.89496i	0.573943	−	0.0648062i
$856$	−5.05599	−	18.8692i	−0.172810	−	0.644936i
$857$			26.5861i			0.908164i	0.890960	+	0.454082i	$0.150033\pi$
$857$			26.5861i			0.908164i	−0.890960	+	0.454082i	$0.849967\pi$
$858$	−22.8154	+	6.11337i	−0.778905	+	0.208707i
$859$	−8.37407	−	8.37407i	−0.285720	−	0.285720i	0.549665	−	0.835385i	$-0.314755\pi$
$859$	−8.37407	−	8.37407i	−0.285720	−	0.285720i	−0.835385	+	0.549665i	$0.814755\pi$
$860$	1.73563	−	0.681661i	0.0591844	−	0.0232444i
$861$	5.45165			0.185792
$862$	3.84874	+	3.84874i	0.131089	+	0.131089i
$863$	7.87417	−	29.3868i	0.268040	−	1.00034i	−0.692324	−	0.721587i	$-0.743413\pi$
$863$	7.87417	−	29.3868i	0.268040	−	1.00034i	0.960363	−	0.278751i	$-0.0899204\pi$
$864$	−7.86451	+	2.10729i	−0.267556	+	0.0716914i
$865$	−10.0217	−	13.5721i	−0.340748	−	0.461467i
$866$	1.16831	−	4.36021i	0.0397009	−	0.148166i
$867$	−0.936666	−	0.250979i	−0.0318109	−	0.00852369i
$868$	−2.41202	−	4.17774i	−0.0818693	−	0.141802i
$869$	5.21341	+	19.4567i	0.176853	+	0.660024i
$870$	−1.33576	+	1.67581i	−0.0452864	+	0.0568151i
$871$	9.19455	−	34.3145i	0.311545	−	1.16270i
$872$	5.34494	−	19.9476i	0.181002	−	0.675510i
$873$	7.62502	+	13.2069i	0.258068	+	0.446986i
$874$	−31.1104	−	31.1104i	−1.05233	−	1.05233i
$875$	−46.9853	−	8.85535i	−1.58839	−	0.299365i
$876$	0.990049	−	0.571605i	0.0334506	−	0.0193127i
$877$	29.7086	−	29.7086i	1.00319	−	1.00319i	0.00319179	−	0.999995i	$-0.498984\pi$
$877$	29.7086	−	29.7086i	1.00319	−	1.00319i	0.999995	−	0.00319179i	$-0.00101598\pi$
$878$	−7.89932	+	7.89932i	−0.266589	+	0.266589i
$879$	−6.48398	−	11.2306i	−0.218699	−	0.378798i
$880$	36.8718	+	5.54855i	1.24295	+	0.187042i
$881$	32.3408	+	18.6720i	1.08959	+	0.629074i	0.933467	−	0.358664i	$-0.116767\pi$
$881$	32.3408	+	18.6720i	1.08959	+	0.629074i	0.156122	+	0.987738i	$0.450101\pi$
$882$	−22.1226			−0.744906
$883$	38.8484	+	22.4292i	1.30735	+	0.754801i	0.981654	−	0.190672i	$-0.0610666\pi$
$883$	38.8484	+	22.4292i	1.30735	+	0.754801i	0.325700	+	0.945473i	$0.394400\pi$
$884$	2.85340	+	1.64741i	0.0959703	+	0.0554085i
$885$	−13.0586	−	10.4088i	−0.438961	−	0.349889i
$886$	39.4530	+	10.5714i	1.32545	+	0.355153i
$887$	24.0980	+	24.0980i	0.809132	+	0.809132i	0.984503	−	0.175370i	$-0.0561122\pi$
$887$	24.0980	+	24.0980i	0.809132	+	0.809132i	−0.175370	+	0.984503i	$0.556112\pi$
$888$	−6.55070	−	21.3322i	−0.219827	−	0.715863i
$889$			69.6379i			2.33558i
$890$	13.9887	−	32.0833i	0.468903	−	1.07543i
$891$	−9.87506	−	5.70137i	−0.330827	−	0.191003i
$892$	−0.850605	+	0.227919i	−0.0284804	+	0.00763129i
$893$	15.9834	−	27.6841i	0.534865	−	0.926414i
$894$	−19.1571	−	19.1571i	−0.640710	−	0.640710i
$895$	47.4801	−	5.36116i	1.58708	−	0.179204i
$896$	25.9805	−	25.9805i	0.867947	−	0.867947i
$897$	23.2295	+	6.22431i	0.775609	+	0.207824i
$898$	−23.8577	−	23.8577i	−0.796143	−	0.796143i
$899$	2.53949			0.0846966
$900$	1.90267	−	0.435226i	0.0634224	−	0.0145075i
$901$	−7.24203	−	27.0276i	−0.241267	−	0.900421i
$902$	6.68775			0.222678
$903$	14.4701	−	8.35429i	0.481533	−	0.278013i
$904$	−4.01411	+	2.31755i	−0.133507	+	0.0770804i
$905$	0.695258	−	0.273060i	0.0231112	−	0.00907681i
$906$	−6.96350	+	1.86586i	−0.231347	+	0.0619892i
$907$	−6.32376	−	3.65102i	−0.209977	−	0.121230i	0.391324	−	0.920253i	$-0.372017\pi$
$907$	−6.32376	−	3.65102i	−0.209977	−	0.121230i	−0.601301	+	0.799023i	$0.705351\pi$
$908$	0.977963	−	0.564627i	0.0324548	−	0.0187378i
$909$	14.1345	+	24.4817i	0.468812	+	0.812007i
$910$	14.9893	−	34.3781i	0.496890	−	1.13962i
$911$	38.5071	−	38.5071i	1.27580	−	1.27580i	0.332797	−	0.942998i	$-0.392008\pi$
$911$	38.5071	−	38.5071i	1.27580	−	1.27580i	0.942998	−	0.332797i	$-0.107992\pi$
$912$	−10.6420	+	18.4325i	−0.352392	+	0.610362i
$913$	−12.5834	−	3.37172i	−0.416451	−	0.111588i
$914$		−	35.1449i		−	1.16249i
$915$	−0.712676	+	4.73594i	−0.0235603	+	0.156565i
$916$	1.67477	−	0.966931i	0.0553361	−	0.0319483i
$917$	−60.9079			−2.01136
$918$	−7.94153	−	29.6382i	−0.262110	−	0.978206i
$919$	9.38503	−	9.38503i	0.309583	−	0.309583i	−0.535164	−	0.844748i	$-0.679750\pi$
$919$	9.38503	−	9.38503i	0.309583	−	0.309583i	0.844748	+	0.535164i	$0.179750\pi$
$920$	−34.2637	−	27.3110i	−1.12964	−	0.900418i
$921$	−6.92756	+	11.9989i	−0.228271	+	0.395377i
$922$	10.1062	+	37.7169i	0.332830	+	1.24214i
$923$	−5.30854	−	9.19467i	−0.174733	−	0.302646i
$924$	−6.76214			−0.222458
$925$	7.84865	+	29.3836i	0.258062	+	0.966128i
$926$	−24.8172			−0.815544
$927$	−13.5150	−	23.4087i	−0.443892	−	0.768844i
$928$	−0.225672	−	0.842219i	−0.00740805	−	0.0276472i
$929$	−3.03772	+	5.26148i	−0.0996643	+	0.172624i	−0.911546	−	0.411199i	$-0.865110\pi$
$929$	−3.03772	+	5.26148i	−0.0996643	+	0.172624i	0.811881	+	0.583822i	$0.198444\pi$
$930$	−12.1813	−	9.70948i	−0.399439	−	0.318387i
$931$	40.5489	−	40.5489i	1.32894	−	1.32894i
$932$	0.222113	+	0.828939i	0.00727557	+	0.0271528i
$933$	−0.850939			−0.0278585
$934$	25.2967	−	14.6051i	0.827734	−	0.477892i
$935$	6.87080	−	45.6585i	0.224699	−	1.49319i
$936$			13.1933i			0.431237i
$937$	33.2324	+	8.90460i	1.08566	+	0.290901i	0.756911	−	0.653518i	$-0.226708\pi$
$937$	33.2324	+	8.90460i	1.08566	+	0.290901i	0.328745	+	0.944419i	$0.393374\pi$
$938$	−33.6511	+	58.2853i	−1.09875	+	1.90308i
$939$	−20.2234	+	20.2234i	−0.659966	+	0.659966i
$940$	1.47653	−	3.38644i	0.0481591	−	0.110453i
$941$	−27.4941	−	47.6211i	−0.896281	−	1.55240i	−0.832211	−	0.554459i	$-0.812925\pi$
$941$	−27.4941	−	47.6211i	−0.896281	−	1.55240i	−0.0640700	−	0.997945i	$-0.520408\pi$
$942$	−13.5908	+	7.84666i	−0.442813	+	0.255658i
$943$	−5.89688	−	3.40456i	−0.192029	−	0.110868i
$944$	−19.9734	+	5.35185i	−0.650078	+	0.174188i
$945$	49.1255	−	19.2938i	1.59805	−	0.627628i
$946$	17.7510	−	10.2485i	0.577135	−	0.333209i
$947$	33.5806	−	19.3878i	1.09122	−	0.630018i	0.157321	−	0.987548i	$-0.449714\pi$
$947$	33.5806	−	19.3878i	1.09122	−	0.630018i	0.933902	+	0.357530i	$0.116381\pi$
$948$	−1.32880			−0.0431574
$949$	−2.72587	−	10.1731i	−0.0884853	−	0.330232i
$950$	17.7992	−	28.3572i	0.577482	−	0.920030i
$951$	39.9844			1.29658
$952$	−38.0359	−	38.0359i	−1.23275	−	1.23275i
$953$	−39.3428	−	10.5419i	−1.27444	−	0.341485i	−0.442708	−	0.896666i	$-0.645982\pi$
$953$	−39.3428	−	10.5419i	−1.27444	−	0.341485i	−0.831729	+	0.555181i	$0.812649\pi$
$954$	9.19368	−	9.19368i	0.297656	−	0.297656i
$955$	9.37935	−	1.05906i	0.303509	−	0.0342704i
$956$	−3.25085	−	3.25085i	−0.105140	−	0.105140i
$957$	1.77987	−	3.08283i	0.0575352	−	0.0996538i
$958$	−7.92852	+	2.12444i	−0.256159	+	0.0686375i
$959$	38.4576	+	22.2035i	1.24186	+	0.716988i
$960$	−9.62640	+	22.0783i	−0.310691	+	0.712573i
$961$		−	12.5407i		−	0.404540i
$962$	−23.8408	+	0.861985i	−0.768658	+	0.0277915i
$963$	−6.88639	−	6.88639i	−0.221911	−	0.221911i
$964$	−5.38813	−	1.44374i	−0.173540	−	0.0464999i
$965$	−13.9835	−	11.1460i	−0.450145	−	0.358803i
$966$	−39.4567	−	22.7803i	−1.26950	−	0.732945i
$967$	39.9757	+	23.0800i	1.28553	+	0.742202i	0.977854	−	0.209288i	$-0.0671147\pi$
$967$	39.9757	+	23.0800i	1.28553	+	0.742202i	0.307678	+	0.951491i	$0.400448\pi$
$968$	−38.6800			−1.24322
$969$	22.8251	+	13.1781i	0.733247	+	0.423341i
$970$	29.8949	+	4.49866i	0.959868	+	0.144443i
$971$	−2.87600	−	4.98139i	−0.0922954	−	0.159860i	0.816181	−	0.577796i	$-0.196087\pi$
$971$	−2.87600	−	4.98139i	−0.0922954	−	0.159860i	−0.908477	+	0.417936i	$0.862754\pi$
$972$	−2.54213	+	2.54213i	−0.0815390	+	0.0815390i
$973$	−26.4631	+	26.4631i	−0.848368	+	0.848368i
$974$	14.9977	−	8.65893i	0.480557	−	0.277450i
$975$	−0.675576	+	18.2882i	−0.0216358	+	0.585690i
$976$	4.19334	+	4.19334i	0.134225	+	0.134225i
$977$	−24.1361	−	41.8050i	−0.772184	−	1.33746i	−0.936364	−	0.351031i	$-0.885831\pi$
$977$	−24.1361	−	41.8050i	−0.772184	−	1.33746i	0.164180	−	0.986430i	$-0.447502\pi$
$978$	−6.86838	+	25.6332i	−0.219627	+	0.819658i
$979$	−15.0473	+	56.1574i	−0.480915	+	1.79480i
$980$	4.13076	−	5.18234i	0.131952	−	0.165544i
$981$	−2.66465	−	9.94460i	−0.0850757	−	0.317507i
$982$	−1.25607	−	2.17558i	−0.0400829	−	0.0694257i
$983$	−29.7867	−	7.98131i	−0.950047	−	0.254564i	−0.249665	−	0.968332i	$-0.580320\pi$
$983$	−29.7867	−	7.98131i	−0.950047	−	0.254564i	−0.700382	+	0.713768i	$0.746987\pi$
$984$	−0.983993	+	3.67231i	−0.0313685	+	0.117069i
$985$	−6.52904	−	8.84213i	−0.208033	−	0.281734i
$986$	3.17399	−	0.850468i	0.101080	−	0.0270844i
$987$	8.56773	−	31.9752i	0.272714	−	1.01778i
$988$	−2.80618	−	2.80618i	−0.0892766	−	0.0892766i
$989$	−20.8691			−0.663598
$990$	19.9698	−	7.84307i	0.634683	−	0.249269i
$991$	−18.7066	−	18.7066i	−0.594235	−	0.594235i	0.344537	−	0.938773i	$-0.388036\pi$
$991$	−18.7066	−	18.7066i	−0.594235	−	0.594235i	−0.938773	+	0.344537i	$0.888036\pi$
$992$	6.12200	−	1.64039i	0.194374	−	0.0520823i
$993$		−	26.1794i		−	0.830778i
$994$	5.20590	+	19.4287i	0.165121	+	0.616241i
$995$	25.1069	−	2.83493i	0.795943	−	0.0898732i
$996$	0.429694	−	0.744252i	0.0136154	−	0.0235825i
$997$	27.7475	−	16.0200i	0.878771	−	0.507359i	0.00851805	−	0.999964i	$-0.497289\pi$
$997$	27.7475	−	16.0200i	0.878771	−	0.507359i	0.870253	+	0.492605i	$0.163955\pi$
$998$	−18.4125	+	18.4125i	−0.582836	+	0.582836i
$999$	−24.5817	−	22.8662i	−0.777731	−	0.723455i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.13	yes	68
5.2	odd	4		185.2.u.a.177.5	yes	68
5.3	odd	4		925.2.y.b.732.13		68
5.4	even	2		925.2.t.b.843.5		68
37.23	odd	12		185.2.u.a.23.5	yes	68
185.23	even	12		925.2.t.b.282.5		68
185.97	even	12	inner	185.2.p.a.97.13	✓	68
185.134	odd	12		925.2.y.b.393.13		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.13	✓	68	185.97	even	12	inner
185.2.p.a.103.13	yes	68	1.1	even	1	trivial
185.2.u.a.23.5	yes	68	37.23	odd	12
185.2.u.a.177.5	yes	68	5.2	odd	4
925.2.t.b.282.5		68	185.23	even	12
925.2.t.b.843.5		68	5.4	even	2
925.2.y.b.393.13		68	185.134	odd	12
925.2.y.b.732.13		68	5.3	odd	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.13

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$