LMFDB - Embedded newform 820.2.k.c.247.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.6
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35506 + 0.404723i) q^{2} +(-2.33700 - 2.33700i) q^{3} +(1.67240 - 1.09685i) q^{4} +(-1.95358 + 1.08790i) q^{5} +(4.11263 + 2.22095i) q^{6} +(-3.18120 + 3.18120i) q^{7} +(-1.82229 + 2.16316i) q^{8} +7.92318i q^{9} +(2.20693 - 2.26483i) q^{10} -3.01127i q^{11} +(-6.47175 - 1.34506i) q^{12} +(-1.94762 + 1.94762i) q^{13} +(3.02323 - 5.59824i) q^{14} +(7.10795 + 2.02310i) q^{15} +(1.59383 - 3.66875i) q^{16} +(2.51915 + 2.51915i) q^{17} +(-3.20669 - 10.7364i) q^{18} -5.78194 q^{19} +(-2.07390 + 3.96219i) q^{20} +14.8690 q^{21} +(1.21873 + 4.08047i) q^{22} +(1.22082 + 1.22082i) q^{23} +(9.31401 - 0.796628i) q^{24} +(2.63295 - 4.25060i) q^{25} +(1.85090 - 3.42739i) q^{26} +(11.5055 - 11.5055i) q^{27} +(-1.83093 + 8.80954i) q^{28} +5.22860i q^{29} +(-10.4505 + 0.135318i) q^{30} +6.16828i q^{31} +(-0.674922 + 5.61645i) q^{32} +(-7.03736 + 7.03736i) q^{33} +(-4.43318 - 2.39406i) q^{34} +(2.75391 - 9.67556i) q^{35} +(8.69055 + 13.2507i) q^{36} +(-6.02371 - 6.02371i) q^{37} +(7.83490 - 2.34008i) q^{38} +9.10318 q^{39} +(1.20668 - 6.20837i) q^{40} +1.00000 q^{41} +(-20.1484 + 6.01781i) q^{42} +(-6.78530 - 6.78530i) q^{43} +(-3.30292 - 5.03605i) q^{44} +(-8.61962 - 15.4786i) q^{45} +(-2.14839 - 1.16020i) q^{46} +(-2.09134 + 2.09134i) q^{47} +(-12.2987 + 4.84908i) q^{48} -13.2401i q^{49} +(-1.84751 + 6.82545i) q^{50} -11.7745i q^{51} +(-1.12095 + 5.39344i) q^{52} +(-2.05303 + 2.05303i) q^{53} +(-10.9342 + 20.2472i) q^{54} +(3.27596 + 5.88276i) q^{55} +(-1.08439 - 12.6785i) q^{56} +(13.5124 + 13.5124i) q^{57} +(-2.11614 - 7.08509i) q^{58} +1.21549 q^{59} +(14.1064 - 4.41293i) q^{60} -5.20011 q^{61} +(-2.49644 - 8.35842i) q^{62} +(-25.2052 - 25.2052i) q^{63} +(-1.35854 - 7.88380i) q^{64} +(1.68602 - 5.92364i) q^{65} +(6.68789 - 12.3843i) q^{66} +(-0.833062 + 0.833062i) q^{67} +(6.97617 + 1.44989i) q^{68} -5.70614i q^{69} +(0.184198 + 14.2256i) q^{70} +1.23803i q^{71} +(-17.1391 - 14.4383i) q^{72} +(3.56604 - 3.56604i) q^{73} +(10.6004 + 5.72458i) q^{74} +(-16.0869 + 3.78044i) q^{75} +(-9.66971 + 6.34193i) q^{76} +(9.57946 + 9.57946i) q^{77} +(-12.3354 + 3.68427i) q^{78} -1.85647 q^{79} +(0.877541 + 8.90112i) q^{80} -30.0073 q^{81} +(-1.35506 + 0.404723i) q^{82} +(8.09356 + 8.09356i) q^{83} +(24.8668 - 16.3090i) q^{84} +(-7.66195 - 2.18079i) q^{85} +(11.9407 + 6.44835i) q^{86} +(12.2193 - 12.2193i) q^{87} +(6.51387 + 5.48740i) q^{88} -9.12162i q^{89} +(17.9447 + 17.4859i) q^{90} -12.3915i q^{91} +(3.38076 + 0.702641i) q^{92} +(14.4153 - 14.4153i) q^{93} +(1.98749 - 3.68032i) q^{94} +(11.2955 - 6.29016i) q^{95} +(14.7030 - 11.5484i) q^{96} +(-3.78598 - 3.78598i) q^{97} +(5.35856 + 17.9412i) q^{98} +23.8589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.35506	+	0.404723i	−0.958175	+	0.286182i
$2$	−1.35506	+	0.404723i	−0.958175	+	0.286182i
$3$	−2.33700	−	2.33700i	−1.34927	−	1.34927i	−0.886454	−	0.462816i	$-0.846839\pi$
$3$	−2.33700	−	2.33700i	−1.34927	−	1.34927i	−0.462816	−	0.886454i	$-0.653161\pi$
$4$	1.67240	−	1.09685i	0.836199	−	0.548426i
$5$	−1.95358	+	1.08790i	−0.873668	+	0.486523i
$5$	−1.95358	+	1.08790i	−0.873668	+	0.486523i
$6$	4.11263	+	2.22095i	1.67897	+	0.906700i
$7$	−3.18120	+	3.18120i	−1.20238	+	1.20238i	−0.228940	+	0.973440i	$0.573526\pi$
$7$	−3.18120	+	3.18120i	−1.20238	+	1.20238i	−0.973440	+	0.228940i	$0.926474\pi$
$8$	−1.82229	+	2.16316i	−0.644276	+	0.764793i
$9$			7.92318i			2.64106i
$10$	2.20693	−	2.26483i	0.697892	−	0.716203i
$11$		−	3.01127i		−	0.907933i	−0.891019	−	0.453966i	$-0.850009\pi$
$11$		−	3.01127i		−	0.907933i	0.891019	−	0.453966i	$-0.149991\pi$
$12$	−6.47175	−	1.34506i	−1.86823	−	0.388284i
$13$	−1.94762	+	1.94762i	−0.540172	+	0.540172i	−0.923579	−	0.383407i	$-0.874751\pi$
$13$	−1.94762	+	1.94762i	−0.540172	+	0.540172i	0.383407	+	0.923579i	$0.374751\pi$
$14$	3.02323	−	5.59824i	0.807991	−	1.49619i
$15$	7.10795	+	2.02310i	1.83527	+	0.522363i
$16$	1.59383	−	3.66875i	0.398458	−	0.917186i
$17$	2.51915	+	2.51915i	0.610985	+	0.610985i	0.943203	−	0.332218i	$-0.107797\pi$
$17$	2.51915	+	2.51915i	0.610985	+	0.610985i	−0.332218	+	0.943203i	$0.607797\pi$
$18$	−3.20669	−	10.7364i	−0.755825	−	2.53060i
$19$	−5.78194			−1.32647			−0.663234	−	0.748412i	$-0.730817\pi$
$19$	−5.78194			−1.32647			−0.663234	+	0.748412i	$0.730817\pi$
$20$	−2.07390	+	3.96219i	−0.463739	+	0.885972i
$21$	14.8690			3.24467
$22$	1.21873	+	4.08047i	0.259834	+	0.869959i
$23$	1.22082	+	1.22082i	0.254559	+	0.254559i	0.822837	−	0.568278i	$-0.192390\pi$
$23$	1.22082	+	1.22082i	0.254559	+	0.254559i	−0.568278	+	0.822837i	$0.692390\pi$
$24$	9.31401	−	0.796628i	1.90121	−	0.162611i
$25$	2.63295	−	4.25060i	0.526591	−	0.850119i
$26$	1.85090	−	3.42739i	0.362992	−	0.672167i
$27$	11.5055	−	11.5055i	2.21423	−	2.21423i
$28$	−1.83093	+	8.80954i	−0.346013	+	1.66485i
$29$			5.22860i			0.970927i	0.874257	+	0.485464i	$0.161349\pi$
$29$			5.22860i			0.970927i	−0.874257	+	0.485464i	$0.838651\pi$
$30$	−10.4505	+	0.135318i	−1.90800	+	0.0247055i
$31$			6.16828i			1.10786i	0.832565	+	0.553928i	$0.186872\pi$
$31$			6.16828i			1.10786i	−0.832565	+	0.553928i	$0.813128\pi$
$32$	−0.674922	+	5.61645i	−0.119310	+	0.992857i
$33$	−7.03736	+	7.03736i	−1.22505	+	1.22505i
$34$	−4.43318	−	2.39406i	−0.760283	−	0.410577i
$35$	2.75391	−	9.67556i	0.465495	−	1.63547i
$36$	8.69055	+	13.2507i	1.44843	+	2.20845i
$37$	−6.02371	−	6.02371i	−0.990291	−	0.990291i	0.00966187	−	0.999953i	$-0.496924\pi$
$37$	−6.02371	−	6.02371i	−0.990291	−	0.990291i	−0.999953	+	0.00966187i	$0.996924\pi$
$38$	7.83490	−	2.34008i	1.27099	−	0.379612i
$39$	9.10318			1.45768
$40$	1.20668	−	6.20837i	0.190793	−	0.981630i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−20.1484	+	6.01781i	−3.10897	+	0.928568i
$43$	−6.78530	−	6.78530i	−1.03475	−	1.03475i	−0.999374	−	0.0353737i	$-0.988738\pi$
$43$	−6.78530	−	6.78530i	−1.03475	−	1.03475i	−0.0353737	−	0.999374i	$-0.511262\pi$
$44$	−3.30292	−	5.03605i	−0.497934	−	0.759213i
$45$	−8.61962	−	15.4786i	−1.28494	−	2.30741i
$46$	−2.14839	−	1.16020i	−0.316763	−	0.171062i
$47$	−2.09134	+	2.09134i	−0.305054	+	0.305054i	−0.842987	−	0.537934i	$-0.819205\pi$
$47$	−2.09134	+	2.09134i	−0.305054	+	0.305054i	0.537934	+	0.842987i	$0.319205\pi$
$48$	−12.2987	+	4.84908i	−1.77516	+	0.699904i
$49$		−	13.2401i		−	1.89144i
$50$	−1.84751	+	6.82545i	−0.261277	+	0.965264i
$51$		−	11.7745i		−	1.64877i
$52$	−1.12095	+	5.39344i	−0.155447	+	0.747935i
$53$	−2.05303	+	2.05303i	−0.282006	+	0.282006i	−0.833909	−	0.551903i	$-0.813902\pi$
$53$	−2.05303	+	2.05303i	−0.282006	+	0.282006i	0.551903	+	0.833909i	$0.313902\pi$
$54$	−10.9342	+	20.2472i	−1.48795	+	2.75530i
$55$	3.27596	+	5.88276i	0.441730	+	0.793232i
$56$	−1.08439	−	12.6785i	−0.144908	−	1.69424i
$57$	13.5124	+	13.5124i	1.78976	+	1.78976i
$58$	−2.11614	−	7.08509i	−0.277862	−	0.930318i
$59$	1.21549			0.158243			0.0791214	−	0.996865i	$-0.474789\pi$
$59$	1.21549			0.158243			0.0791214	+	0.996865i	$0.474789\pi$
$60$	14.1064	−	4.41293i	1.82112	−	0.569707i
$61$	−5.20011			−0.665806			−0.332903	−	0.942961i	$-0.608028\pi$
$61$	−5.20011			−0.665806			−0.332903	+	0.942961i	$0.608028\pi$
$62$	−2.49644	−	8.35842i	−0.317049	−	1.06152i
$63$	−25.2052	−	25.2052i	−3.17556	−	3.17556i
$64$	−1.35854	−	7.88380i	−0.169818	−	0.985475i
$65$	1.68602	−	5.92364i	0.209125	−	0.734737i
$66$	6.68789	−	12.3843i	0.823223	−	1.52440i
$67$	−0.833062	+	0.833062i	−0.101775	+	0.101775i	−0.756161	−	0.654386i	$-0.772927\pi$
$67$	−0.833062	+	0.833062i	−0.101775	+	0.101775i	0.654386	+	0.756161i	$0.272927\pi$
$68$	6.97617	+	1.44989i	0.845985	+	0.175825i
$69$		−	5.70614i		−	0.686938i
$70$	0.184198	+	14.2256i	0.0220159	+	1.70028i
$71$			1.23803i			0.146927i	0.997298	+	0.0734634i	$0.0234052\pi$
$71$			1.23803i			0.146927i	−0.997298	+	0.0734634i	$0.976595\pi$
$72$	−17.1391	−	14.4383i	−2.01987	−	1.70157i
$73$	3.56604	−	3.56604i	0.417373	−	0.417373i	−0.466924	−	0.884297i	$-0.654638\pi$
$73$	3.56604	−	3.56604i	0.417373	−	0.417373i	0.884297	+	0.466924i	$0.154638\pi$
$74$	10.6004	+	5.72458i	1.23228	+	0.665469i
$75$	−16.0869	+	3.78044i	−1.85755	+	0.436527i
$76$	−9.66971	+	6.34193i	−1.10919	+	0.727469i
$77$	9.57946	+	9.57946i	1.09168	+	1.09168i
$78$	−12.3354	+	3.68427i	−1.39671	+	0.417161i
$79$	−1.85647			−0.208869			−0.104435	−	0.994532i	$-0.533303\pi$
$79$	−1.85647			−0.208869			−0.104435	+	0.994532i	$0.533303\pi$
$80$	0.877541	+	8.90112i	0.0981120	+	0.995175i
$81$	−30.0073			−3.33414
$82$	−1.35506	+	0.404723i	−0.149642	+	0.0446942i
$83$	8.09356	+	8.09356i	0.888383	+	0.888383i	0.994368	−	0.105984i	$-0.0337994\pi$
$83$	8.09356	+	8.09356i	0.888383	+	0.888383i	−0.105984	+	0.994368i	$0.533799\pi$
$84$	24.8668	−	16.3090i	2.71319	−	1.77946i
$85$	−7.66195	−	2.18079i	−0.831056	−	0.236539i
$86$	11.9407	+	6.44835i	1.28760	+	0.695343i
$87$	12.2193	−	12.2193i	1.31004	−	1.31004i
$88$	6.51387	+	5.48740i	0.694381	+	0.584959i
$89$		−	9.12162i		−	0.966890i	−0.875375	−	0.483445i	$-0.839385\pi$
$89$		−	9.12162i		−	0.966890i	0.875375	−	0.483445i	$-0.160615\pi$
$90$	17.9447	+	17.4859i	1.89153	+	1.84318i
$91$		−	12.3915i		−	1.29898i
$92$	3.38076	+	0.702641i	0.352469	+	0.0732554i
$93$	14.4153	−	14.4153i	1.49480	−	1.49480i
$94$	1.98749	−	3.68032i	0.204994	−	0.379596i
$95$	11.2955	−	6.29016i	1.15889	−	0.645357i
$96$	14.7030	−	11.5484i	1.50061	−	1.17865i
$97$	−3.78598	−	3.78598i	−0.384408	−	0.384408i	0.488280	−	0.872687i	$-0.337625\pi$
$97$	−3.78598	−	3.78598i	−0.384408	−	0.384408i	−0.872687	+	0.488280i	$0.837625\pi$
$98$	5.35856	+	17.9412i	0.541297	+	1.81233i
$99$	23.8589			2.39791
$100$	−0.258925	−	9.99665i	−0.0258925	−	0.999665i
$101$	3.99668			0.397685			0.198842	−	0.980031i	$-0.436282\pi$
$101$	3.99668			0.397685			0.198842	+	0.980031i	$0.436282\pi$
$102$	4.76543	+	15.9553i	0.471848	+	1.57981i
$103$	−1.08480	−	1.08480i	−0.106888	−	0.106888i	0.651640	−	0.758528i	$-0.274081\pi$
$103$	−1.08480	−	1.08480i	−0.106888	−	0.106888i	−0.758528	+	0.651640i	$0.774081\pi$
$104$	−0.663896	−	7.76213i	−0.0651003	−	0.761139i
$105$	−29.0477	+	16.1759i	−2.83477	+	1.57861i
$106$	1.95108	−	3.61290i	0.189506	−	0.350916i
$107$	3.38909	−	3.38909i	0.327636	−	0.327636i	−0.524051	−	0.851687i	$-0.675580\pi$
$107$	3.38909	−	3.38909i	0.327636	−	0.327636i	0.851687	+	0.524051i	$0.175580\pi$
$108$	6.62196	−	31.8616i	0.637198	−	3.06588i
$109$		−	3.90535i		−	0.374064i	−0.982354	−	0.187032i	$-0.940113\pi$
$109$		−	3.90535i		−	0.374064i	0.982354	−	0.187032i	$-0.0598869\pi$
$110$	−6.82002	−	6.64567i	−0.650264	−	0.633639i
$111$			28.1549i			2.67234i
$112$	6.60071	+	16.7413i	0.623708	+	1.58191i
$113$	5.97067	−	5.97067i	0.561674	−	0.561674i	−0.368109	−	0.929783i	$-0.619995\pi$
$113$	5.97067	−	5.97067i	0.561674	−	0.561674i	0.929783	+	0.368109i	$0.119995\pi$
$114$	−23.7790	−	12.8414i	−2.22711	−	1.20271i
$115$	−3.71311	−	1.05684i	−0.346249	−	0.0985512i
$116$	5.73500	+	8.74431i	0.532481	+	0.811889i
$117$	−15.4313	−	15.4313i	−1.42663	−	1.42663i
$118$	−1.64706	+	0.491935i	−0.151624	+	0.0452863i
$119$	−16.0279			−1.46927
$120$	−17.3290	+	11.6890i	−1.58192	+	1.06705i
$121$	1.93224			0.175658
$122$	7.04648	−	2.10460i	0.637958	−	0.190542i
$123$	−2.33700	−	2.33700i	−0.210721	−	0.210721i
$124$	6.76569	+	10.3158i	0.607577	+	0.926388i
$125$	−0.519469	+	11.1683i	−0.0464627	+	0.998920i
$126$	44.3558	+	23.9536i	3.95153	+	2.13395i
$127$	12.3026	−	12.3026i	1.09168	−	1.09168i	0.0963329	−	0.995349i	$-0.469289\pi$
$127$	12.3026	−	12.3026i	1.09168	−	1.09168i	0.995349	−	0.0963329i	$-0.0307113\pi$
$128$	5.03167	+	10.1332i	0.444741	+	0.895659i
$129$			31.7145i			2.79231i
$130$	0.112771	+	8.70928i	0.00989069	+	0.763854i
$131$			14.0266i			1.22551i	0.790272	+	0.612757i	$0.209939\pi$
$131$			14.0266i			1.22551i	−0.790272	+	0.612757i	$0.790061\pi$
$132$	−4.05033	+	19.4882i	−0.352536	+	1.69623i
$133$	18.3935	−	18.3935i	1.59492	−	1.59492i
$134$	0.791694	−	1.46601i	0.0683919	−	0.126644i
$135$	−9.96010	+	34.9937i	−0.857229	+	3.01178i
$136$	−10.0400	+	0.858719i	−0.860919	+	0.0736345i
$137$	−6.71558	−	6.71558i	−0.573750	−	0.573750i	0.359424	−	0.933174i	$-0.382973\pi$
$137$	−6.71558	−	6.71558i	−0.573750	−	0.573750i	−0.933174	+	0.359424i	$0.882973\pi$
$138$	2.30940	+	7.73218i	0.196590	+	0.658207i
$139$	−6.90952			−0.586058			−0.293029	−	0.956104i	$-0.594663\pi$
$139$	−6.90952			−0.586058			−0.293029	+	0.956104i	$0.594663\pi$
$140$	−6.00702	−	19.2020i	−0.507686	−	1.62287i
$141$	9.77495			0.823200
$142$	−0.501058	−	1.67761i	−0.0420478	−	0.140782i
$143$	5.86481	+	5.86481i	0.490440	+	0.490440i
$144$	29.0681	+	12.6282i	2.42234	+	1.05235i
$145$	−5.68819	−	10.2145i	−0.472378	−	0.848268i
$146$	−3.38895	+	6.27547i	−0.280472	+	0.519361i
$147$	−30.9421	+	30.9421i	−2.55206	+	2.55206i
$148$	−16.6812	−	3.46693i	−1.37118	−	0.284980i
$149$		−	13.1848i		−	1.08014i	−0.841620	−	0.540070i	$-0.818398\pi$
$149$		−	13.1848i		−	1.08014i	0.841620	−	0.540070i	$-0.181602\pi$
$150$	20.2687	−	11.6335i	1.65494	−	0.949869i
$151$			5.46128i			0.444432i	0.974997	+	0.222216i	$0.0713291\pi$
$151$			5.46128i			0.444432i	−0.974997	+	0.222216i	$0.928671\pi$
$152$	10.5364	−	12.5073i	0.854611	−	1.01447i
$153$	−19.9597	+	19.9597i	−1.61365	+	1.61365i
$154$	−16.8578	−	9.10376i	−1.35844	−	0.733602i
$155$	−6.71046	−	12.0502i	−0.538997	−	0.967898i
$156$	15.2241	−	9.98484i	1.21891	−	0.799427i
$157$	−8.70266	−	8.70266i	−0.694548	−	0.694548i	0.268681	−	0.963229i	$-0.413412\pi$
$157$	−8.70266	−	8.70266i	−0.694548	−	0.694548i	−0.963229	+	0.268681i	$0.913412\pi$
$158$	2.51564	−	0.751356i	0.200133	−	0.0597747i
$159$	9.59590			0.761004
$160$	−4.79161	−	11.7064i	−0.378810	−	0.925474i
$161$	−7.76736			−0.612154
$162$	40.6618	−	12.1446i	3.19469	−	0.954172i
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.998242	+	0.0592635i	$0.0188752\pi$
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.0592635	+	0.998242i	$0.481125\pi$
$164$	1.67240	−	1.09685i	0.130592	−	0.0856497i
$165$	6.09211	−	21.4040i	0.474270	−	1.66630i
$166$	−14.2429	−	7.69164i	−1.10547	−	0.596987i
$167$	−2.87517	+	2.87517i	−0.222487	+	0.222487i	−0.809545	−	0.587058i	$-0.800286\pi$
$167$	−2.87517	+	2.87517i	−0.222487	+	0.222487i	0.587058	+	0.809545i	$0.300286\pi$
$168$	−27.0955	+	32.1640i	−2.09046	+	2.48150i
$169$			5.41357i			0.416429i
$170$	11.2651	−	0.145864i	0.863990	−	0.0111873i
$171$		−	45.8114i		−	3.50328i
$172$	−18.7902	−	3.90526i	−1.43274	−	0.297773i
$173$	10.9126	−	10.9126i	0.829672	−	0.829672i	−0.157799	−	0.987471i	$-0.550440\pi$
$173$	10.9126	−	10.9126i	0.829672	−	0.829672i	0.987471	+	0.157799i	$0.0504399\pi$
$174$	−11.6125	+	21.5033i	−0.880340	+	1.63016i
$175$	5.14604	+	21.8979i	0.389004	+	1.65533i
$176$	−11.0476	−	4.79947i	−0.832744	−	0.361773i
$177$	−2.84060	−	2.84060i	−0.213512	−	0.213512i
$178$	3.69173	+	12.3604i	0.276707	+	0.926450i
$179$	11.6172			0.868309			0.434154	−	0.900839i	$-0.357047\pi$
$179$	11.6172			0.868309			0.434154	+	0.900839i	$0.357047\pi$
$180$	−31.3931	−	16.4319i	−2.33991	−	1.22476i
$181$	7.08888			0.526912			0.263456	−	0.964671i	$-0.415138\pi$
$181$	7.08888			0.526912			0.263456	+	0.964671i	$0.415138\pi$
$182$	5.01513	+	16.7913i	0.371747	+	1.24465i
$183$	12.1527	+	12.1527i	0.898352	+	0.898352i
$184$	−4.86553	+	0.416149i	−0.358691	+	0.0306789i
$185$	18.3210	+	5.21461i	1.34699	+	0.383386i
$186$	−13.6995	+	25.3679i	−1.00449	+	1.86006i
$187$	7.58586	−	7.58586i	0.554733	−	0.554733i
$188$	−1.20367	+	5.79145i	−0.0877864	+	0.422385i
$189$			73.2026i			5.32471i
$190$	−12.7603	+	13.0951i	−0.925732	+	0.950020i
$191$		−	6.47206i		−	0.468302i	−0.972200	−	0.234151i	$-0.924769\pi$
$191$		−	6.47206i		−	0.468302i	0.972200	−	0.234151i	$-0.0752309\pi$
$192$	−15.2496	+	21.5994i	−1.10054	+	1.55880i
$193$	12.8013	−	12.8013i	0.921456	−	0.921456i	−0.0756762	−	0.997132i	$-0.524112\pi$
$193$	12.8013	−	12.8013i	0.921456	−	0.921456i	0.997132	+	0.0756762i	$0.0241115\pi$
$194$	6.66251	+	3.59797i	0.478341	+	0.258319i
$195$	−17.7838	+	9.90334i	−1.27352	+	0.709193i
$196$	−14.5224	−	22.1427i	−1.03731	−	1.58162i
$197$	8.26931	+	8.26931i	0.589164	+	0.589164i	0.937405	−	0.348241i	$-0.113221\pi$
$197$	8.26931	+	8.26931i	0.589164	+	0.589164i	−0.348241	+	0.937405i	$0.613221\pi$
$198$	−32.3303	+	9.65623i	−2.29761	+	0.686238i
$199$	−9.81219			−0.695567			−0.347784	−	0.937575i	$-0.613066\pi$
$199$	−9.81219			−0.695567			−0.347784	+	0.937575i	$0.613066\pi$
$200$	4.39673	+	13.4413i	0.310896	+	0.950444i
$201$	3.89374			0.274643
$202$	−5.41576	+	1.61755i	−0.381052	+	0.113810i
$203$	−16.6332	−	16.6332i	−1.16742	−	1.16742i
$204$	−12.9149	−	19.6917i	−0.904226	−	1.37870i
$205$	−1.95358	+	1.08790i	−0.136444	+	0.0759821i
$206$	1.90902	+	1.03093i	0.133007	+	0.0718283i
$207$	−9.67280	+	9.67280i	−0.672306	+	0.672306i
$208$	4.04113	+	10.2495i	0.280202	+	0.710674i
$209$			17.4110i			1.20434i
$210$	32.8147	−	33.6757i	2.26443	−	2.32384i
$211$		−	4.15341i		−	0.285932i	−0.989728	−	0.142966i	$-0.954336\pi$
$211$		−	4.15341i		−	0.285932i	0.989728	−	0.142966i	$-0.0456640\pi$
$212$	−1.18162	+	5.68536i	−0.0811538	+	0.390472i
$213$	2.89327	−	2.89327i	0.198244	−	0.198244i
$214$	−3.22080	+	5.96408i	−0.220169	+	0.407696i
$215$	20.6373	+	5.87391i	1.40745	+	0.400597i
$216$	3.92195	+	45.8546i	0.266855	+	3.12001i
$217$	−19.6225	−	19.6225i	−1.33206	−	1.33206i
$218$	1.58058	+	5.29200i	0.107051	+	0.358419i
$219$	−16.6677			−1.12630
$220$	11.9312	+	6.24508i	0.804403	+	0.421043i
$221$	−9.81270			−0.660073
$222$	−11.3949	−	38.1517i	−0.764777	−	2.56057i
$223$	12.8059	+	12.8059i	0.857546	+	0.857546i	0.991048	−	0.133502i	$-0.0426224\pi$
$223$	12.8059	+	12.8059i	0.857546	+	0.857546i	−0.133502	+	0.991048i	$0.542622\pi$
$224$	−15.7200	−	20.0141i	−1.05034	−	1.33725i
$225$	33.6782	+	20.8614i	2.24522	+	1.39076i
$226$	−5.67418	+	10.5071i	−0.377441	+	0.698923i
$227$	4.75627	−	4.75627i	0.315685	−	0.315685i	−0.531422	−	0.847107i	$-0.678342\pi$
$227$	4.75627	−	4.75627i	0.315685	−	0.315685i	0.847107	+	0.531422i	$0.178342\pi$
$228$	37.4193	+	7.77704i	2.47815	+	0.515047i
$229$			13.5341i			0.894358i	0.894445	+	0.447179i	$0.147571\pi$
$229$			13.5341i			0.894358i	−0.894445	+	0.447179i	$0.852429\pi$
$230$	5.45923	−	0.0706882i	0.359971	−	0.00466104i
$231$		−	44.7745i		−	2.94595i
$232$	−11.3103	−	9.52801i	−0.742559	−	0.625545i
$233$	7.54721	−	7.54721i	0.494434	−	0.494434i	−0.415266	−	0.909700i	$-0.636312\pi$
$233$	7.54721	−	7.54721i	0.494434	−	0.494434i	0.909700	+	0.415266i	$0.136312\pi$
$234$	27.1559	+	14.6650i	1.77523	+	0.958683i
$235$	1.81044	−	6.36077i	0.118100	−	0.414931i
$236$	2.03278	−	1.33321i	0.132323	−	0.0867844i
$237$	4.33858	+	4.33858i	0.281821	+	0.281821i
$238$	21.7188	−	6.48685i	1.40782	−	0.420480i
$239$	−19.9288			−1.28909			−0.644545	−	0.764567i	$-0.722953\pi$
$239$	−19.9288			−1.28909			−0.644545	+	0.764567i	$0.722953\pi$
$240$	18.7511	−	22.8528i	1.21038	−	1.47514i
$241$	−14.0234			−0.903330			−0.451665	−	0.892188i	$-0.649170\pi$
$241$	−14.0234			−0.903330			−0.451665	+	0.892188i	$0.649170\pi$
$242$	−2.61831	+	0.782022i	−0.168311	+	0.0502703i
$243$	35.6106	+	35.6106i	2.28442	+	2.28442i
$244$	−8.69665	+	5.70375i	−0.556746	+	0.365145i
$245$	14.4039	+	25.8656i	0.920229	+	1.65249i
$246$	4.11263	+	2.22095i	0.262212	+	0.141603i
$247$	11.2610	−	11.2610i	0.716521	−	0.716521i
$248$	−13.3430	−	11.2404i	−0.847281	−	0.713764i
$249$		−	37.8294i		−	2.39734i
$250$	−3.81614	−	15.3440i	−0.241354	−	0.970437i
$251$		−	24.7699i		−	1.56346i	−0.623618	−	0.781730i	$-0.714338\pi$
$251$		−	24.7699i		−	1.56346i	0.623618	−	0.781730i	$-0.285662\pi$
$252$	−69.7996	−	14.5068i	−4.39696	−	0.913842i
$253$	3.67623	−	3.67623i	0.231123	−	0.231123i
$254$	−11.6917	+	21.6500i	−0.733602	+	1.35844i
$255$	12.8095	+	23.0025i	0.802163	+	1.44047i
$256$	−10.9194	−	11.6947i	−0.682462	−	0.730921i
$257$	−2.77132	−	2.77132i	−0.172870	−	0.172870i	0.615369	−	0.788239i	$-0.289007\pi$
$257$	−2.77132	−	2.77132i	−0.172870	−	0.172870i	−0.788239	+	0.615369i	$0.789007\pi$
$258$	−12.8356	−	42.9752i	−0.799110	−	2.67552i
$259$	38.3252			2.38141
$260$	−3.67766	−	11.7560i	−0.228079	−	0.729076i
$261$	−41.4272			−2.56428
$262$	−5.67691	−	19.0070i	−0.350720	−	1.17426i
$263$	−0.105987	−	0.105987i	−0.00653544	−	0.00653544i	0.703832	−	0.710367i	$-0.251471\pi$
$263$	−0.105987	−	0.105987i	−0.00653544	−	0.00653544i	−0.710367	+	0.703832i	$0.751471\pi$
$264$	−2.39887	−	28.0470i	−0.147640	−	1.72618i
$265$	1.77727	−	6.24426i	0.109177	−	0.383582i
$266$	−17.4801	+	32.3687i	−1.07177	+	1.98465i
$267$	−21.3173	+	21.3173i	−1.30460	+	1.30460i
$268$	−0.479467	+	2.30696i	−0.0292881	+	0.140920i
$269$			23.3185i			1.42175i	0.703316	+	0.710877i	$0.251702\pi$
$269$			23.3185i			1.42175i	−0.703316	+	0.710877i	$0.748298\pi$
$270$	−0.666193	−	51.4498i	−0.0405432	−	3.13114i
$271$		−	7.66973i		−	0.465903i	−0.972488	−	0.232951i	$-0.925162\pi$
$271$		−	7.66973i		−	0.465903i	0.972488	−	0.232951i	$-0.0748383\pi$
$272$	13.2572	−	5.22702i	0.803839	−	0.316935i
$273$	−28.9590	+	28.9590i	−1.75268	+	1.75268i
$274$	11.8180	+	6.38209i	0.713951	+	0.385556i
$275$	−12.7997	−	7.92854i	−0.771851	−	0.478109i
$276$	−6.25878	−	9.54293i	−0.376735	−	0.574417i
$277$	15.6068	+	15.6068i	0.937723	+	0.937723i	0.998171	−	0.0604483i	$-0.0192530\pi$
$277$	15.6068	+	15.6068i	0.937723	+	0.937723i	−0.0604483	+	0.998171i	$0.519253\pi$
$278$	9.36285	−	2.79644i	0.561546	−	0.167720i
$279$	−48.8724			−2.92591
$280$	15.9114	+	23.5888i	0.950887	+	1.40970i
$281$	26.0228			1.55239			0.776195	−	0.630493i	$-0.217147\pi$
$281$	26.0228			1.55239			0.776195	+	0.630493i	$0.217147\pi$
$282$	−13.2457	+	3.95615i	−0.788769	+	0.235585i
$283$	−7.33094	−	7.33094i	−0.435779	−	0.435779i	0.454810	−	0.890589i	$-0.349707\pi$
$283$	−7.33094	−	7.33094i	−0.435779	−	0.435779i	−0.890589	+	0.454810i	$0.849707\pi$
$284$	1.35793	+	2.07047i	0.0805784	+	0.122860i
$285$	−41.0977	−	11.6975i	−2.43442	−	0.692898i
$286$	−10.3208	−	5.57357i	−0.610282	−	0.329572i
$287$	−3.18120	+	3.18120i	−0.187780	+	0.187780i
$288$	−44.5001	−	5.34753i	−2.62220	−	0.315106i
$289$		−	4.30773i		−	0.253396i
$290$	11.8419	+	11.5392i	0.695381	+	0.677603i
$291$			17.6957i			1.03734i
$292$	2.05242	−	9.87525i	0.120109	−	0.577905i
$293$	−0.660349	+	0.660349i	−0.0385780	+	0.0385780i	−0.726133	−	0.687555i	$-0.758684\pi$
$293$	−0.660349	+	0.660349i	−0.0385780	+	0.0385780i	0.687555	+	0.726133i	$0.258684\pi$
$294$	29.4056	−	54.4515i	1.71497	−	3.17568i
$295$	−2.37455	+	1.32233i	−0.138252	+	0.0769888i
$296$	24.0072	−	2.05334i	1.39539	−	0.119348i
$297$	−34.6462	−	34.6462i	−2.01038	−	2.01038i
$298$	5.33619	+	17.8662i	0.309117	+	1.03496i
$299$	−4.75539			−0.275011
$300$	−22.7571	+	23.9673i	−1.31388	+	1.38375i
$301$	43.1708			2.48832
$302$	−2.21030	−	7.40038i	−0.127189	−	0.425844i
$303$	−9.34027	−	9.34027i	−0.536584	−	0.536584i
$304$	−9.21545	+	21.2125i	−0.528542	+	1.21662i
$305$	10.1588	−	5.65719i	0.581693	−	0.323930i
$306$	18.9685	−	35.1249i	1.08436	−	2.00795i
$307$	4.65435	−	4.65435i	0.265638	−	0.265638i	−0.561702	−	0.827340i	$-0.689853\pi$
$307$	4.65435	−	4.65435i	0.265638	−	0.265638i	0.827340	+	0.561702i	$0.189853\pi$
$308$	26.5279	+	5.51343i	1.51157	+	0.314157i
$309$			5.07036i			0.288443i
$310$	13.9701	+	13.6130i	0.793449	+	0.773164i
$311$		−	30.7905i		−	1.74597i	−0.487746	−	0.872986i	$-0.662181\pi$
$311$		−	30.7905i		−	1.74597i	0.487746	−	0.872986i	$-0.337819\pi$
$312$	−16.5886	+	19.6917i	−0.939145	+	1.11482i
$313$	−16.7368	+	16.7368i	−0.946022	+	0.946022i	−0.998616	−	0.0525940i	$-0.983251\pi$
$313$	−16.7368	+	16.7368i	−0.946022	+	0.946022i	0.0525940	+	0.998616i	$0.483251\pi$
$314$	15.3148	+	8.27050i	0.864266	+	0.466731i
$315$	76.6612	+	21.8197i	4.31937	+	1.22940i
$316$	−3.10476	+	2.03627i	−0.174656	+	0.114549i
$317$	1.71755	+	1.71755i	0.0964673	+	0.0964673i	0.753693	−	0.657226i	$-0.228270\pi$
$317$	1.71755	+	1.71755i	0.0964673	+	0.0964673i	−0.657226	+	0.753693i	$0.728270\pi$
$318$	−13.0031	+	3.88368i	−0.729175	+	0.217786i
$319$	15.7447			0.881537
$320$	11.2308	+	13.9237i	0.627821	+	0.778358i
$321$	−15.8407			−0.884139
$322$	10.5253	−	3.14363i	0.586551	−	0.175188i
$323$	−14.5656	−	14.5656i	−0.810451	−	0.810451i
$324$	−50.1841	+	32.9135i	−2.78801	+	1.82853i
$325$	3.15055	+	13.4065i	0.174761	+	0.743660i
$326$	−23.7595	−	12.8309i	−1.31592	−	0.710636i
$327$	−9.12681	+	9.12681i	−0.504714	+	0.504714i
$328$	−1.82229	+	2.16316i	−0.100619	+	0.119441i
$329$		−	13.3060i		−	0.733581i
$330$	0.407478	+	31.4694i	0.0224309	+	1.73233i
$331$			22.0919i			1.21428i	0.794595	+	0.607139i	$0.207683\pi$
$331$			22.0919i			1.21428i	−0.794595	+	0.607139i	$0.792317\pi$
$332$	22.4131	+	4.65822i	1.23008	+	0.255653i
$333$	47.7269	−	47.7269i	2.61542	−	2.61542i
$334$	2.73239	−	5.05968i	0.149510	−	0.276854i
$335$	0.721167	−	2.53374i	0.0394016	−	0.138433i
$336$	23.6987	−	54.5504i	1.29287	−	2.97597i
$337$	16.7538	+	16.7538i	0.912638	+	0.912638i	0.996479	−	0.0838407i	$-0.0267187\pi$
$337$	16.7538	+	16.7538i	0.912638	+	0.912638i	−0.0838407	+	0.996479i	$0.526719\pi$
$338$	−2.19100	−	7.33574i	−0.119175	−	0.399012i
$339$	−27.9070			−1.51570
$340$	−15.2058	+	4.75688i	−0.824652	+	0.257978i
$341$	18.5744			1.00586
$342$	18.5409	+	62.0773i	1.00258	+	3.35676i
$343$	19.8509	+	19.8509i	1.07185	+	1.07185i
$344$	27.0424	−	2.31294i	1.45803	−	0.124706i
$345$	6.20770	+	11.1474i	0.334211	+	0.600156i
$346$	−10.3707	+	19.2039i	−0.557533	+	1.03241i
$347$	−12.5962	+	12.5962i	−0.676197	+	0.676197i	−0.959138	−	0.282940i	$-0.908690\pi$
$347$	−12.5962	+	12.5962i	−0.676197	+	0.676197i	0.282940	+	0.959138i	$0.408690\pi$
$348$	7.03277	−	33.8382i	0.376996	−	1.81392i
$349$			27.4748i			1.47069i	0.677692	+	0.735346i	$0.262980\pi$
$349$			27.4748i			1.47069i	−0.677692	+	0.735346i	$0.737020\pi$
$350$	−15.8358	−	27.5904i	−0.846460	−	1.47477i
$351$			44.8166i			2.39213i
$352$	16.9127	+	2.03237i	0.901447	+	0.108326i
$353$	−5.03594	+	5.03594i	−0.268036	+	0.268036i	−0.828308	−	0.560272i	$-0.810696\pi$
$353$	−5.03594	+	5.03594i	−0.268036	+	0.268036i	0.560272	+	0.828308i	$0.310696\pi$
$354$	4.99885	+	2.69954i	0.265686	+	0.143479i
$355$	−1.34685	−	2.41858i	−0.0714833	−	0.128365i
$356$	−10.0051	−	15.2550i	−0.530267	−	0.808512i
$357$	37.4572	+	37.4572i	1.98245	+	1.98245i
$358$	−15.7420	+	4.70174i	−0.831992	+	0.248495i
$359$	25.1352			1.32658			0.663292	−	0.748360i	$-0.269159\pi$
$359$	25.1352			1.32658			0.663292	+	0.748360i	$0.269159\pi$
$360$	49.1901	+	9.56076i	2.59255	+	0.503896i
$361$	14.4308			0.759517
$362$	−9.60589	+	2.86903i	−0.504874	+	0.150793i
$363$	−4.51565	−	4.51565i	−0.237010	−	0.237010i
$364$	−13.5917	−	20.7236i	−0.712397	−	1.08621i
$365$	−3.08705	+	10.8460i	−0.161584	+	0.567707i
$366$	−21.3861	−	11.5492i	−1.11787	−	0.603686i
$367$	−10.0784	+	10.0784i	−0.526088	+	0.526088i	−0.919404	−	0.393315i	$-0.871328\pi$
$367$	−10.0784	+	10.0784i	−0.526088	+	0.526088i	0.393315	+	0.919404i	$0.371328\pi$
$368$	6.42468	−	2.53310i	0.334909	−	0.132047i
$369$			7.92318i			0.412464i
$370$	−26.9366	+	0.348786i	−1.40037	+	0.0181325i
$371$		−	13.0622i		−	0.678157i
$372$	8.29668	−	39.9196i	0.430163	−	2.06973i
$373$	14.1892	−	14.1892i	0.734691	−	0.734691i	−0.236855	−	0.971545i	$-0.576116\pi$
$373$	14.1892	−	14.1892i	0.734691	−	0.734691i	0.971545	+	0.236855i	$0.0761165\pi$
$374$	−7.20915	+	13.3495i	−0.372776	+	0.690286i
$375$	27.3143	−	24.8863i	1.41050	−	1.28512i
$376$	−0.712888	−	8.33494i	−0.0367644	−	0.429842i
$377$	−10.1833	−	10.1833i	−0.524468	−	0.524468i
$378$	−29.6268	−	99.1942i	−1.52384	−	5.10200i
$379$	15.3174			0.786804			0.393402	−	0.919367i	$-0.371298\pi$
$379$	15.3174			0.786804			0.393402	+	0.919367i	$0.371298\pi$
$380$	11.9912	−	22.9091i	0.615134	−	1.17521i
$381$	−57.5026			−2.94595
$382$	2.61939	+	8.77005i	0.134020	+	0.448715i
$383$	−2.76517	−	2.76517i	−0.141294	−	0.141294i	0.632922	−	0.774216i	$-0.281855\pi$
$383$	−2.76517	−	2.76517i	−0.141294	−	0.141294i	−0.774216	+	0.632922i	$0.781855\pi$
$384$	11.9224	−	35.4404i	0.608411	−	1.80856i
$385$	−29.1357	−	8.29276i	−1.48489	−	0.422638i
$386$	−12.1656	+	22.5275i	−0.619212	+	1.14662i
$387$	53.7611	−	53.7611i	2.73283	−	2.73283i
$388$	−10.4843	−	2.17901i	−0.532260	−	0.110622i
$389$		−	21.6900i		−	1.09973i	−0.835254	−	0.549864i	$-0.814679\pi$
$389$		−	21.6900i		−	1.09973i	0.835254	−	0.549864i	$-0.185321\pi$
$390$	20.0901	−	20.6172i	1.01730	−	1.04399i
$391$			6.15088i			0.311063i
$392$	28.6404	+	24.1272i	1.44656	+	1.21861i
$393$	32.7803	−	32.7803i	1.65355	−	1.65355i
$394$	−14.5522	−	7.85867i	−0.733130	−	0.395914i
$395$	3.62676	−	2.01965i	0.182482	−	0.101620i
$396$	39.9015	−	26.1696i	2.00513	−	1.31507i
$397$	−13.8446	−	13.8446i	−0.694840	−	0.694840i	0.268453	−	0.963293i	$-0.413488\pi$
$397$	−13.8446	−	13.8446i	−0.694840	−	0.694840i	−0.963293	+	0.268453i	$0.913488\pi$
$398$	13.2961	−	3.97122i	0.666475	−	0.199059i
$399$	−85.9714			−4.30396
$400$	−11.3979	−	16.4344i	−0.569893	−	0.821719i
$401$	−28.3914			−1.41780			−0.708900	−	0.705309i	$-0.750808\pi$
$401$	−28.3914			−1.41780			−0.708900	+	0.705309i	$0.750808\pi$
$402$	−5.27627	+	1.57589i	−0.263156	+	0.0785981i
$403$	−12.0134	−	12.0134i	−0.598433	−	0.598433i
$404$	6.68405	−	4.38377i	0.332544	−	0.218101i
$405$	58.6216	−	32.6449i	2.91293	−	1.62214i
$406$	29.2710	+	15.8072i	1.45269	+	0.784501i
$407$	−18.1390	+	18.1390i	−0.899118	+	0.899118i
$408$	25.4703	+	21.4566i	1.26097	+	1.06226i
$409$			21.1381i			1.04521i	0.852574	+	0.522606i	$0.175040\pi$
$409$			21.1381i			1.04521i	−0.852574	+	0.522606i	$0.824960\pi$
$410$	2.20693	−	2.26483i	0.108992	−	0.111852i
$411$			31.3887i			1.54829i
$412$	−3.00408	−	0.624353i	−0.148000	−	0.0307597i
$413$	−3.86671	+	3.86671i	−0.190268	+	0.190268i
$414$	9.19246	−	17.0221i	0.451785	−	0.836589i
$415$	−24.6164	−	7.00645i	−1.20837	−	0.343933i
$416$	−9.62420	−	12.2532i	−0.471865	−	0.600762i
$417$	16.1476	+	16.1476i	0.790751	+	0.790751i
$418$	−7.04663	−	23.5930i	−0.344662	−	1.15397i
$419$	22.3383			1.09130			0.545649	−	0.838014i	$-0.316283\pi$
$419$	22.3383			1.09130			0.545649	+	0.838014i	$0.316283\pi$
$420$	−30.8368	+	58.9136i	−1.50468	+	2.87469i
$421$	−7.25093			−0.353389			−0.176694	−	0.984266i	$-0.556540\pi$
$421$	−7.25093			−0.353389			−0.176694	+	0.984266i	$0.556540\pi$
$422$	1.68098	+	5.62813i	0.0818288	+	0.273973i
$423$	−16.5701	−	16.5701i	−0.805665	−	0.805665i
$424$	−0.699830	−	8.18226i	−0.0339867	−	0.397366i
$425$	17.3407	−	4.07509i	0.841148	−	0.197671i
$426$	−2.74960	+	5.09155i	−0.133218	+	0.246686i
$427$	16.5426	−	16.5426i	0.800552	−	0.800552i
$428$	1.95058	−	9.38525i	0.0942850	−	0.453653i
$429$		−	27.4122i		−	1.32347i
$430$	−30.3422	+	0.392883i	−1.46323	+	0.0189465i
$431$		−	7.16120i		−	0.344943i	−0.985015	−	0.172471i	$-0.944825\pi$
$431$		−	7.16120i		−	0.344943i	0.985015	−	0.172471i	$-0.0551752\pi$
$432$	−23.8729	−	60.5486i	−1.14859	−	2.91315i
$433$	9.47183	−	9.47183i	0.455187	−	0.455187i	−0.441885	−	0.897072i	$-0.645690\pi$
$433$	9.47183	−	9.47183i	0.455187	−	0.455187i	0.897072	+	0.441885i	$0.145690\pi$
$434$	34.5315	+	18.6481i	1.65756	+	0.895138i
$435$	−10.5780	+	37.1647i	−0.507176	+	1.78191i
$436$	−4.28358	−	6.53130i	−0.205147	−	0.312792i
$437$	−7.05872	−	7.05872i	−0.337665	−	0.337665i
$438$	22.5858	−	6.74580i	1.07919	−	0.322327i
$439$	−11.5201			−0.549824			−0.274912	−	0.961469i	$-0.588649\pi$
$439$	−11.5201			−0.549824			−0.274912	+	0.961469i	$0.588649\pi$
$440$	−18.6951	−	3.63365i	−0.891254	−	0.173227i
$441$	104.904			4.99541
$442$	13.2968	−	3.97142i	0.632466	−	0.188901i
$443$	−6.69755	−	6.69755i	−0.318210	−	0.318210i	0.529869	−	0.848079i	$-0.322241\pi$
$443$	−6.69755	−	6.69755i	−0.318210	−	0.318210i	−0.848079	+	0.529869i	$0.822241\pi$
$444$	30.8817	+	47.0862i	1.46558	+	2.23461i
$445$	9.92340	+	17.8198i	0.470414	+	0.844740i
$446$	−22.5356	−	12.1700i	−1.06709	−	0.576265i
$447$	−30.8129	+	30.8129i	−1.45740	+	1.45740i
$448$	29.4018	+	20.7582i	1.38910	+	0.980731i
$449$		−	16.7618i		−	0.791040i	−0.918457	−	0.395520i	$-0.870564\pi$
$449$		−	16.7618i		−	0.791040i	0.918457	−	0.395520i	$-0.129436\pi$
$450$	−54.0793	−	14.6381i	−2.54932	−	0.690048i
$451$		−	3.01127i		−	0.141795i
$452$	3.43640	−	16.5343i	0.161635	−	0.777707i
$453$	12.7630	−	12.7630i	0.599659	−	0.599659i
$454$	−4.52008	+	8.37002i	−0.212138	+	0.392824i
$455$	13.4807	+	24.2078i	0.631986	+	1.13488i
$456$	−53.8531	+	4.60606i	−2.52190	+	0.215698i
$457$	−23.8232	−	23.8232i	−1.11440	−	1.11440i	−0.992548	−	0.121853i	$-0.961116\pi$
$457$	−23.8232	−	23.8232i	−1.11440	−	1.11440i	−0.121853	−	0.992548i	$-0.538884\pi$
$458$	−5.47756	−	18.3396i	−0.255949	−	0.856951i
$459$	57.9682			2.70573
$460$	−7.36900	+	2.30526i	−0.343581	+	0.107483i
$461$	23.3344			1.08679			0.543395	−	0.839477i	$-0.317139\pi$
$461$	23.3344			1.08679			0.543395	+	0.839477i	$0.317139\pi$
$462$	18.1213	+	60.6723i	0.843078	+	2.82273i
$463$	−22.3751	−	22.3751i	−1.03986	−	1.03986i	−0.999172	−	0.0406893i	$-0.987045\pi$
$463$	−22.3751	−	22.3751i	−1.03986	−	1.03986i	−0.0406893	−	0.999172i	$-0.512955\pi$
$464$	19.1824	+	8.33352i	0.890521	+	0.386874i
$465$	−12.4791	+	43.8438i	−0.578703	+	2.03321i
$466$	−7.17242	+	13.2815i	−0.332256	+	0.615253i
$467$	−3.64786	+	3.64786i	−0.168803	+	0.168803i	−0.786453	−	0.617650i	$-0.788085\pi$
$467$	−3.64786	+	3.64786i	−0.168803	+	0.168803i	0.617650	+	0.786453i	$0.288085\pi$
$468$	−42.7332	−	8.88146i	−1.97534	−	0.410545i
$469$		−	5.30028i		−	0.244744i
$470$	0.121093	+	9.35198i	0.00558561	+	0.431375i
$471$			40.6763i			1.87427i
$472$	−2.21496	+	2.62929i	−0.101952	+	0.121023i
$473$	−20.4324	+	20.4324i	−0.939481	+	0.939481i
$474$	−7.63498	−	4.12313i	−0.350686	−	0.189382i
$475$	−15.2236	+	24.5767i	−0.698506	+	1.12766i
$476$	−26.8050	+	17.5802i	−1.22860	+	0.805787i
$477$	−16.2666	−	16.2666i	−0.744795	−	0.744795i
$478$	27.0049	−	8.06566i	1.23517	−	0.368915i
$479$	−37.5765			−1.71691			−0.858456	−	0.512887i	$-0.828576\pi$
$479$	−37.5765			−1.71691			−0.858456	+	0.512887i	$0.828576\pi$
$480$	−16.1600	+	38.5560i	−0.737598	+	1.75983i
$481$	23.4638			1.06986
$482$	19.0027	−	5.67561i	0.865548	−	0.258517i
$483$	18.1524	+	18.1524i	0.825961	+	0.825961i
$484$	3.23147	−	2.11938i	0.146885	−	0.0963354i
$485$	11.5150	+	3.27745i	0.522868	+	0.148821i
$486$	−62.6671	−	33.8422i	−2.84264	−	1.53512i
$487$	10.0266	−	10.0266i	0.454350	−	0.454350i	−0.442445	−	0.896796i	$-0.645889\pi$
$487$	10.0266	−	10.0266i	0.454350	−	0.454350i	0.896796	+	0.442445i	$0.145889\pi$
$488$	9.47609	−	11.2487i	0.428962	−	0.509204i
$489$		−	63.1054i		−	2.85372i
$490$	−29.9865	−	29.2199i	−1.35465	−	1.32002i
$491$		−	35.8582i		−	1.61826i	−0.587630	−	0.809130i	$-0.699939\pi$
$491$		−	35.8582i		−	1.61826i	0.587630	−	0.809130i	$-0.300061\pi$
$492$	−6.47175	−	1.34506i	−0.291769	−	0.0606398i
$493$	−13.1717	+	13.1717i	−0.593222	+	0.593222i
$494$	−10.7018	+	19.8170i	−0.481497	+	0.891608i
$495$	−46.6102	+	25.9560i	−2.09497	+	1.16664i
$496$	22.6298	+	9.83121i	1.01611	+	0.441435i
$497$	−3.93841	−	3.93841i	−0.176662	−	0.176662i
$498$	15.3104	+	51.2612i	0.686076	+	2.29707i
$499$	−24.3435			−1.08976			−0.544882	−	0.838513i	$-0.683425\pi$
$499$	−24.3435			−1.08976			−0.544882	+	0.838513i	$0.683425\pi$
$500$	11.3812	+	19.2476i	0.508981	+	0.860778i
$501$	13.4386			0.600391
$502$	10.0249	+	33.5647i	0.447434	+	1.49807i
$503$	8.56836	+	8.56836i	0.382044	+	0.382044i	0.871838	−	0.489794i	$-0.162928\pi$
$503$	8.56836	+	8.56836i	0.382044	+	0.382044i	−0.489794	+	0.871838i	$0.662928\pi$
$504$	100.454	−	8.59185i	4.47458	−	0.382712i
$505$	−7.80784	+	4.34799i	−0.347444	+	0.193483i
$506$	−3.49367	+	6.46938i	−0.155313	+	0.287599i
$507$	12.6515	−	12.6515i	0.561875	−	0.561875i
$508$	7.08074	−	34.0691i	0.314157	−	1.51157i
$509$			16.9492i			0.751261i	0.926769	+	0.375631i	$0.122574\pi$
$509$			16.9492i			0.751261i	−0.926769	+	0.375631i	$0.877426\pi$
$510$	−26.6674	−	25.9856i	−1.18085	−	1.15066i
$511$			22.6886i			1.00368i
$512$	19.5296	+	11.4278i	0.863095	+	0.505042i
$513$	−66.5241	+	66.5241i	−2.93711	+	2.93711i
$514$	4.87693	+	2.63370i	0.215112	+	0.116167i
$515$	3.29940	+	0.939091i	0.145389	+	0.0413813i
$516$	34.7861	+	53.0393i	1.53137	+	2.33493i
$517$	6.29760	+	6.29760i	0.276968	+	0.276968i
$518$	−51.9332	+	15.5111i	−2.28181	+	0.681519i
$519$	−51.0057			−2.23890
$520$	9.74138	+	14.4417i	0.427188	+	0.633310i
$521$	−26.8387			−1.17583			−0.587913	−	0.808924i	$-0.700050\pi$
$521$	−26.8387			−1.17583			−0.587913	+	0.808924i	$0.700050\pi$
$522$	56.1365	−	16.7665i	2.45703	−	0.733851i
$523$	9.01153	+	9.01153i	0.394047	+	0.394047i	0.876127	−	0.482080i	$-0.160119\pi$
$523$	9.01153	+	9.01153i	0.394047	+	0.394047i	−0.482080	+	0.876127i	$0.660119\pi$
$524$	15.3851	+	23.4581i	0.672103	+	1.02477i
$525$	39.1493	−	63.2019i	1.70861	−	2.75836i
$526$	0.186515	+	0.100724i	0.00813242	+	0.00439177i
$527$	−15.5388	+	15.5388i	−0.676883	+	0.676883i
$528$	14.6019	+	37.0347i	0.635466	+	1.61173i
$529$		−	20.0192i		−	0.870399i
$530$	0.118875	+	9.18068i	0.00516360	+	0.398783i
$531$			9.63052i			0.417929i
$532$	10.5863	−	50.9362i	0.458976	−	2.20837i
$533$	−1.94762	+	1.94762i	−0.0843607	+	0.0843607i
$534$	20.2587	−	37.5139i	0.876679	−	1.62338i
$535$	−2.93388	+	10.3079i	−0.126843	+	0.445648i
$536$	−0.283971	−	3.32013i	−0.0122657	−	0.143408i
$537$	−27.1494	−	27.1494i	−1.17158	−	1.17158i
$538$	−9.43753	−	31.5981i	−0.406881	−	1.36229i
$539$	−39.8695			−1.71730
$540$	21.7257	+	69.4482i	0.934924	+	2.98858i
$541$	−31.1907			−1.34099			−0.670496	−	0.741914i	$-0.733918\pi$
$541$	−31.1907			−1.34099			−0.670496	+	0.741914i	$0.733918\pi$
$542$	3.10412	+	10.3930i	0.133333	+	0.446417i
$543$	−16.5667	−	16.5667i	−0.710947	−	0.710947i
$544$	−15.8489	+	12.4485i	−0.679517	+	0.533723i
$545$	4.24862	+	7.62941i	0.181991	+	0.326808i
$546$	27.5210	−	50.9618i	1.17779	−	2.18096i
$547$	−31.3664	+	31.3664i	−1.34113	+	1.34113i	−0.446198	+	0.894934i	$0.647222\pi$
$547$	−31.3664	+	31.3664i	−1.34113	+	1.34113i	−0.894934	+	0.446198i	$0.852778\pi$
$548$	−18.5971	−	3.86513i	−0.794429	−	0.165110i
$549$		−	41.2014i		−	1.75843i
$550$	20.5533	+	5.56335i	0.876395	+	0.237222i
$551$		−	30.2315i		−	1.28790i
$552$	12.3433	+	10.3982i	0.525366	+	0.442577i
$553$	5.90580	−	5.90580i	0.251140	−	0.251140i
$554$	−27.4647	−	14.8318i	−1.16686	−	0.630143i
$555$	−30.6296	−	55.0028i	−1.30016	−	2.33474i
$556$	−11.5555	+	7.57872i	−0.490061	+	0.321409i
$557$	−30.9734	−	30.9734i	−1.31239	−	1.31239i	−0.919653	−	0.392733i	$-0.871530\pi$
$557$	−30.9734	−	30.9734i	−1.31239	−	1.31239i	−0.392733	−	0.919653i	$-0.628470\pi$
$558$	66.2253	−	19.7798i	2.80354	−	0.837345i
$559$	26.4303			1.11788
$560$	−31.1079	−	25.5246i	−1.31455	−	1.07861i
$561$	−35.4564			−1.49697
$562$	−35.2626	+	10.5320i	−1.48746	+	0.444267i
$563$	23.4668	+	23.4668i	0.989006	+	0.989006i	0.999940	−	0.0109339i	$-0.00348044\pi$
$563$	23.4668	+	23.4668i	0.989006	+	0.989006i	−0.0109339	+	0.999940i	$0.503480\pi$
$564$	16.3476	−	10.7217i	0.688359	−	0.451464i
$565$	−5.16870	+	18.1597i	−0.217449	+	0.763983i
$566$	12.9009	+	6.96689i	0.542265	+	0.292840i
$567$	95.4591	−	95.4591i	4.00891	−	4.00891i
$568$	−2.67805	−	2.25604i	−0.112369	−	0.0946613i
$569$			32.7019i			1.37094i	0.728102	+	0.685468i	$0.240403\pi$
$569$			32.7019i			1.37094i	−0.728102	+	0.685468i	$0.759597\pi$
$570$	60.4243	−	0.782398i	2.53090	−	0.0327710i
$571$			2.32916i			0.0974724i	0.998812	+	0.0487362i	$0.0155194\pi$
$571$			2.32916i			0.0974724i	−0.998812	+	0.0487362i	$0.984481\pi$
$572$	16.2411	+	3.37547i	0.679075	+	0.141136i
$573$	−15.1252	+	15.1252i	−0.631865	+	0.631865i
$574$	3.02323	−	5.59824i	0.126187	−	0.233666i
$575$	8.40359	−	1.97485i	0.350454	−	0.0823571i
$576$	62.4648	−	10.7640i	2.60270	−	0.448499i
$577$	21.1189	+	21.1189i	0.879190	+	0.879190i	0.993451	−	0.114261i	$-0.0364501\pi$
$577$	21.1189	+	21.1189i	0.879190	+	0.879190i	−0.114261	+	0.993451i	$0.536450\pi$
$578$	1.74344	+	5.83725i	0.0725174	+	0.242797i
$579$	−59.8333			−2.48659
$580$	−20.7167	−	10.8436i	−0.860214	−	0.450256i
$581$	−51.4945			−2.13635
$582$	−7.16185	−	23.9788i	−0.296868	−	0.993953i
$583$	6.18224	+	6.18224i	0.256042	+	0.256042i
$584$	1.21558	+	14.2123i	0.0503009	+	0.588107i
$585$	46.9341	+	13.3586i	1.94048	+	0.552311i
$586$	0.627557	−	1.16207i	0.0259241	−	0.0480048i
$587$	−7.90351	+	7.90351i	−0.326213	+	0.326213i	−0.851144	−	0.524932i	$-0.824091\pi$
$587$	−7.90351	+	7.90351i	−0.326213	+	0.326213i	0.524932	+	0.851144i	$0.324091\pi$
$588$	−17.8086	+	85.6865i	−0.734416	+	3.53365i
$589$		−	35.6646i		−	1.46954i
$590$	2.68249	−	2.75287i	0.110436	−	0.113334i
$591$		−	38.6508i		−	1.58988i
$592$	−31.7002	+	12.4987i	−1.30287	+	0.513692i
$593$	−12.8830	+	12.8830i	−0.529042	+	0.529042i	−0.920287	−	0.391245i	$-0.872045\pi$
$593$	−12.8830	+	12.8830i	−0.529042	+	0.529042i	0.391245	+	0.920287i	$0.372045\pi$
$594$	60.9699	+	32.9257i	2.50163	+	1.35096i
$595$	31.3117	−	17.4367i	1.28366	−	0.714835i
$596$	−14.4618	−	22.0502i	−0.592377	−	0.903213i
$597$	22.9311	+	22.9311i	0.938509	+	0.938509i
$598$	6.44386	−	1.92462i	0.263509	−	0.0787034i
$599$	37.3899			1.52771			0.763855	−	0.645388i	$-0.223304\pi$
$599$	37.3899			1.52771			0.763855	+	0.645388i	$0.223304\pi$
$600$	21.1372	−	41.6876i	0.862923	−	1.70189i
$601$	−27.0507			−1.10342			−0.551710	−	0.834036i	$-0.686025\pi$
$601$	−27.0507			−1.10342			−0.551710	+	0.834036i	$0.686025\pi$
$602$	−58.4992	+	17.4722i	−2.38425	+	0.712114i
$603$	−6.60051	−	6.60051i	−0.268793	−	0.268793i
$604$	5.99021	+	9.13343i	0.243738	+	0.371634i
$605$	−3.77478	+	2.10208i	−0.153467	+	0.0854617i
$606$	16.4369	+	8.87644i	0.667703	+	0.360581i
$607$	12.2331	−	12.2331i	0.496525	−	0.496525i	−0.413829	−	0.910354i	$-0.635809\pi$
$607$	12.2331	−	12.2331i	0.496525	−	0.496525i	0.910354	+	0.413829i	$0.135809\pi$
$608$	3.90236	−	32.4740i	0.158261	−	1.31699i
$609$			77.7439i			3.15034i
$610$	−11.4763	+	11.7774i	−0.464661	+	0.476852i
$611$		−	8.14627i		−	0.329563i
$612$	−11.4878	+	55.2734i	−0.464365	+	2.23430i
$613$	4.49907	−	4.49907i	0.181716	−	0.181716i	−0.610387	−	0.792103i	$-0.708986\pi$
$613$	4.49907	−	4.49907i	0.181716	−	0.181716i	0.792103	+	0.610387i	$0.208986\pi$
$614$	−4.42322	+	8.19067i	−0.178507	+	0.330549i
$615$	7.10795	+	2.02310i	0.286620	+	0.0815794i
$616$	−38.1785	+	3.26541i	−1.53825	+	0.131567i
$617$	−30.2366	−	30.2366i	−1.21728	−	1.21728i	−0.968580	−	0.248701i	$-0.919996\pi$
$617$	−30.2366	−	30.2366i	−1.21728	−	1.21728i	−0.248701	−	0.968580i	$-0.580004\pi$
$618$	−2.05209	−	6.87067i	−0.0825473	−	0.276379i
$619$	−27.5236			−1.10627			−0.553134	−	0.833093i	$-0.686568\pi$
$619$	−27.5236			−1.10627			−0.553134	+	0.833093i	$0.686568\pi$
$620$	−24.4399	−	12.7924i	−0.981529	−	0.513755i
$621$	28.0923			1.12731
$622$	12.4616	+	41.7232i	0.499666	+	1.67295i
$623$	29.0177	+	29.0177i	1.16257	+	1.16257i
$624$	14.5090	−	33.3973i	0.580823	−	1.33696i
$625$	−11.1351	−	22.3832i	−0.445405	−	0.895329i
$626$	15.9057	−	29.4533i	0.635720	−	1.17719i
$627$	40.6896	−	40.6896i	1.62499	−	1.62499i
$628$	−24.0998	−	5.00879i	−0.961688	−	0.199872i
$629$		−	30.3493i		−	1.21011i
$630$	−112.712	+	1.45944i	−4.49054	+	0.0581454i
$631$		−	39.1564i		−	1.55879i	−0.626531	−	0.779396i	$-0.715526\pi$
$631$		−	39.1564i		−	1.55879i	0.626531	−	0.779396i	$-0.284474\pi$
$632$	3.38302	−	4.01585i	0.134569	−	0.159742i
$633$	−9.70653	+	9.70653i	−0.385800	+	0.385800i
$634$	−3.02252	−	1.63226i	−0.120040	−	0.0648253i
$635$	−10.6502	+	37.4182i	−0.422639	+	1.48490i
$636$	16.0482	−	10.5253i	0.636351	−	0.417354i
$637$	25.7866	+	25.7866i	1.02170	+	1.02170i
$638$	−21.3351	+	6.37226i	−0.844666	+	0.252280i
$639$	−9.80911			−0.388042
$640$	−20.8537	−	14.3221i	−0.824315	−	0.566132i
$641$	−0.646836			−0.0255485			−0.0127742	−	0.999918i	$-0.504066\pi$
$641$	−0.646836			−0.0255485			−0.0127742	+	0.999918i	$0.504066\pi$
$642$	21.4651	−	6.41108i	0.847160	−	0.253025i
$643$	−20.4305	−	20.4305i	−0.805700	−	0.805700i	0.178280	−	0.983980i	$-0.442947\pi$
$643$	−20.4305	−	20.4305i	−0.805700	−	0.805700i	−0.983980	+	0.178280i	$0.942947\pi$
$644$	−12.9901	+	8.51964i	−0.511883	+	0.335721i
$645$	−34.5022	−	61.9569i	−1.35852	−	2.43955i
$646$	25.6324	+	13.8423i	1.00849	+	0.544618i
$647$	−8.66078	+	8.66078i	−0.340490	+	0.340490i	−0.856552	−	0.516061i	$-0.827398\pi$
$647$	−8.66078	+	8.66078i	−0.340490	+	0.340490i	0.516061	+	0.856552i	$0.327398\pi$
$648$	54.6818	−	64.9106i	2.14811	−	2.54993i
$649$		−	3.66016i		−	0.143674i
$650$	−9.69512	−	16.8916i	−0.380274	−	0.662543i
$651$			91.7159i			3.59463i
$652$	37.3886	+	7.77065i	1.46425	+	0.304322i
$653$	−14.8567	+	14.8567i	−0.581386	+	0.581386i	−0.935284	−	0.353898i	$-0.884856\pi$
$653$	−14.8567	+	14.8567i	−0.581386	+	0.581386i	0.353898	+	0.935284i	$0.384856\pi$
$654$	8.67359	−	16.0612i	0.339164	−	0.628045i
$655$	−15.2596	−	27.4022i	−0.596241	−	1.07069i
$656$	1.59383	−	3.66875i	0.0622288	−	0.143240i
$657$	28.2544	+	28.2544i	1.10231	+	1.10231i
$658$	5.38523	+	18.0304i	0.209938	+	0.702899i
$659$	25.9600			1.01126			0.505630	−	0.862751i	$-0.331260\pi$
$659$	25.9600			1.01126			0.505630	+	0.862751i	$0.331260\pi$
$660$	−13.2885	−	42.4781i	−0.517256	−	1.65346i
$661$	1.95766			0.0761442			0.0380721	−	0.999275i	$-0.487878\pi$
$661$	1.95766			0.0761442			0.0380721	+	0.999275i	$0.487878\pi$
$662$	−8.94109	−	29.9359i	−0.347505	−	1.16349i
$663$	22.9323	+	22.9323i	0.890617	+	0.890617i
$664$	−32.2565	+	2.75890i	−1.25179	+	0.107066i
$665$	−15.9229	+	55.9435i	−0.617465	+	2.16940i
$666$	−45.3569	+	83.9893i	−1.75754	+	3.25452i
$667$	−6.38320	+	6.38320i	−0.247158	+	0.247158i
$668$	−1.65479	+	7.96206i	−0.0640259	+	0.308061i
$669$		−	59.8549i		−	2.31412i
$670$	0.0482361	+	3.72526i	0.00186352	+	0.143919i
$671$			15.6589i			0.604507i
$672$	−10.0354	+	83.5107i	−0.387123	+	3.22150i
$673$	31.6280	−	31.6280i	1.21917	−	1.21917i	0.251248	−	0.967923i	$-0.419159\pi$
$673$	31.6280	−	31.6280i	1.21917	−	1.21917i	0.967923	−	0.251248i	$-0.0808409\pi$
$674$	−29.4832	−	15.9218i	−1.13565	−	0.613286i
$675$	−18.6118	−	79.1987i	−0.716368	−	3.04836i
$676$	5.93789	+	9.05365i	0.228380	+	0.348217i
$677$	24.1394	+	24.1394i	0.927754	+	0.927754i	0.997561	−	0.0698064i	$-0.0222382\pi$
$677$	24.1394	+	24.1394i	0.927754	+	0.927754i	−0.0698064	+	0.997561i	$0.522238\pi$
$678$	37.8158	−	11.2946i	1.45231	−	0.433766i
$679$	24.0879			0.924409
$680$	18.6797	−	12.6000i	0.716333	−	0.483189i
$681$	−22.2308			−0.851888
$682$	−25.1695	+	7.51748i	−0.963789	+	0.287859i
$683$	7.32634	+	7.32634i	0.280335	+	0.280335i	0.833242	−	0.552908i	$-0.186482\pi$
$683$	7.32634	+	7.32634i	0.280335	+	0.280335i	−0.552908	+	0.833242i	$0.686482\pi$
$684$	−50.2483	−	76.6149i	−1.92129	−	2.92944i
$685$	20.4253	+	5.81355i	0.780410	+	0.222124i
$686$	−34.9334	−	18.8652i	−1.33376	−	0.720275i
$687$	31.6292	−	31.6292i	1.20673	−	1.20673i
$688$	−35.7082	+	14.0789i	−1.36136	+	0.536753i
$689$		−	7.99705i		−	0.304663i
$690$	−12.9234	−	12.5930i	−0.491987	−	0.479409i
$691$			31.7570i			1.20809i	0.796948	+	0.604047i	$0.206446\pi$
$691$			31.7570i			1.20809i	−0.796948	+	0.604047i	$0.793554\pi$
$692$	6.28073	−	30.2198i	0.238758	−	1.14878i
$693$	−75.8998	+	75.8998i	−2.88320	+	2.88320i
$694$	11.9707	−	22.1666i	0.454400	−	0.841431i
$695$	13.4983	−	7.51686i	0.512020	−	0.285131i
$696$	4.16525	+	48.6993i	0.157884	+	1.84594i
$697$	2.51915	+	2.51915i	0.0954198	+	0.0954198i
$698$	−11.1197	−	37.2301i	−0.420886	−	1.40918i
$699$	−35.2757			−1.33425
$700$	32.6250	+	30.9777i	1.23311	+	1.17085i
$701$	−11.5623			−0.436703			−0.218351	−	0.975870i	$-0.570068\pi$
$701$	−11.5623			−0.436703			−0.218351	+	0.975870i	$0.570068\pi$
$702$	−18.1383	−	60.7294i	−0.684587	−	2.29208i
$703$	34.8287	+	34.8287i	1.31359	+	1.31359i
$704$	−23.7403	+	4.09094i	−0.894745	+	0.154183i
$705$	−19.0962	+	10.6342i	−0.719203	+	0.400506i
$706$	4.78586	−	8.86218i	0.180118	−	0.333532i
$707$	−12.7143	+	12.7143i	−0.478169	+	0.478169i
$708$	−7.86632	−	1.63490i	−0.295635	−	0.0614432i
$709$			4.13510i			0.155297i	0.996981	+	0.0776485i	$0.0247412\pi$
$709$			4.13510i			0.155297i	−0.996981	+	0.0776485i	$0.975259\pi$
$710$	2.80392	+	2.73224i	0.105229	+	0.102539i
$711$		−	14.7091i		−	0.551636i
$712$	19.7315	+	16.6222i	0.739471	+	0.622943i
$713$	−7.53038	+	7.53038i	−0.282015	+	0.282015i
$714$	−65.9167	−	35.5971i	−2.46687	−	1.33219i
$715$	−17.8377	−	5.07706i	−0.667092	−	0.189871i
$716$	19.4286	−	12.7423i	0.726079	−	0.476203i
$717$	46.5738	+	46.5738i	1.73933	+	1.73933i
$718$	−34.0598	+	10.1728i	−1.27110	+	0.379645i
$719$	51.6984			1.92802			0.964012	−	0.265859i	$-0.0856556\pi$
$719$	51.6984			1.92802			0.964012	+	0.265859i	$0.0856556\pi$
$720$	−70.5252	+	6.95291i	−2.62832	+	0.259120i
$721$	6.90193			0.257041
$722$	−19.5547	+	5.84049i	−0.727751	+	0.217360i
$723$	32.7729	+	32.7729i	1.21884	+	1.21884i
$724$	11.8554	−	7.77545i	0.440604	−	0.288972i
$725$	22.2247	+	13.7667i	0.825404	+	0.511281i
$726$	7.94659	+	4.29141i	0.294926	+	0.159269i
$727$	8.86305	−	8.86305i	0.328712	−	0.328712i	−0.523384	−	0.852097i	$-0.675331\pi$
$727$	8.86305	−	8.86305i	0.328712	−	0.328712i	0.852097	+	0.523384i	$0.175331\pi$
$728$	26.8049	+	22.5809i	0.993455	+	0.836904i
$729$		−	76.4226i		−	2.83047i
$730$	−0.206481	−	15.9465i	−0.00764221	−	0.590205i
$731$		−	34.1864i		−	1.26443i
$732$	33.6538	+	6.99444i	1.24388	+	0.258522i
$733$	−5.90445	+	5.90445i	−0.218086	+	0.218086i	−0.807691	−	0.589605i	$-0.799283\pi$
$733$	−5.90445	+	5.90445i	−0.218086	+	0.218086i	0.589605	+	0.807691i	$0.299283\pi$
$734$	9.57792	−	17.7358i	0.353527	−	0.654642i
$735$	26.7860	−	94.1098i	0.988017	−	3.47129i
$736$	−7.68065	+	6.03273i	−0.283112	+	0.222369i
$737$	2.50858	+	2.50858i	0.0924047	+	0.0924047i
$738$	−3.20669	−	10.7364i	−0.118040	−	0.395213i
$739$	47.0284			1.72997			0.864984	−	0.501799i	$-0.167328\pi$
$739$	47.0284			1.72997			0.864984	+	0.501799i	$0.167328\pi$
$740$	36.3596	−	11.3745i	1.33661	−	0.418134i
$741$	−52.6341			−1.93356
$742$	5.28658	+	17.7002i	0.194077	+	0.649793i
$743$	36.8959	+	36.8959i	1.35358	+	1.35358i	0.881621	+	0.471958i	$0.156453\pi$
$743$	36.8959	+	36.8959i	1.35358	+	1.35358i	0.471958	+	0.881621i	$0.343547\pi$
$744$	4.91383	+	57.4514i	0.180150	+	2.10627i
$745$	14.3437	+	25.7576i	0.525513	+	0.943684i
$746$	−13.4846	+	24.9700i	−0.493707	+	0.914218i
$747$	−64.1267	+	64.1267i	−2.34627	+	2.34627i
$748$	4.36602	−	21.0071i	0.159637	−	0.768097i
$749$			21.5628i			0.787887i
$750$	−26.9406	+	44.7772i	−0.983730	+	1.63503i
$751$		−	18.8007i		−	0.686048i	−0.939327	−	0.343024i	$-0.888549\pi$
$751$		−	18.8007i		−	0.686048i	0.939327	−	0.343024i	$-0.111451\pi$
$752$	4.33935	+	11.0059i	0.158240	+	0.401342i
$753$	−57.8873	+	57.8873i	−2.10953	+	2.10953i
$754$	17.9205	+	9.67763i	0.652625	+	0.352438i
$755$	−5.94132	−	10.6690i	−0.216227	−	0.388286i
$756$	80.2924	+	122.424i	2.92021	+	4.45252i
$757$	−24.0454	−	24.0454i	−0.873943	−	0.873943i	0.118956	−	0.992900i	$-0.462045\pi$
$757$	−24.0454	−	24.0454i	−0.873943	−	0.873943i	−0.992900	+	0.118956i	$0.962045\pi$
$758$	−20.7561	+	6.19932i	−0.753896	+	0.225169i
$759$	−17.1827			−0.623694
$760$	−6.97696	+	35.8965i	−0.253081	+	1.30210i
$761$	2.45207			0.0888874			0.0444437	−	0.999012i	$-0.485848\pi$
$761$	2.45207			0.0888874			0.0444437	+	0.999012i	$0.485848\pi$
$762$	77.9197	−	23.2726i	2.82273	−	0.843079i
$763$	12.4237	+	12.4237i	0.449768	+	0.449768i
$764$	−7.09888	−	10.8239i	−0.256829	−	0.391593i
$765$	17.2788	−	60.7071i	0.624715	−	2.19487i
$766$	4.86612	+	2.62786i	0.175820	+	0.0949484i
$767$	−2.36730	+	2.36730i	−0.0854783	+	0.0854783i
$768$	−1.81201	+	52.8493i	−0.0653852	+	1.90704i
$769$		−	0.844874i		−	0.0304669i	−0.999884	−	0.0152335i	$-0.995151\pi$
$769$		−	0.844874i		−	0.0304669i	0.999884	−	0.0152335i	$-0.00484915\pi$
$770$	42.8371	−	0.554671i	1.54374	−	0.0199890i
$771$			12.9532i			0.466496i
$772$	7.36774	−	35.4499i	0.265171	−	1.27587i
$773$	5.16500	−	5.16500i	0.185772	−	0.185772i	−0.608093	−	0.793866i	$-0.708065\pi$
$773$	5.16500	−	5.16500i	0.185772	−	0.185772i	0.793866	+	0.608093i	$0.208065\pi$
$774$	−51.0914	+	94.6082i	−1.83644	+	3.40062i
$775$	26.2189	+	16.2408i	0.941809	+	0.583386i
$776$	15.0888	−	1.29055i	0.541657	−	0.0463280i
$777$	−89.5663	−	89.5663i	−3.21317	−	3.21317i
$778$	8.77845	+	29.3914i	0.314723	+	1.05373i
$779$	−5.78194			−0.207159
$780$	−18.8791	+	36.0685i	−0.675980	+	1.29146i
$781$	3.72804			0.133400
$782$	−2.48940	−	8.33484i	−0.0890209	−	0.298053i
$783$	60.1577	+	60.1577i	2.14986	+	2.14986i
$784$	−48.5745	−	21.1025i	−1.73480	−	0.753660i
$785$	26.4690	+	7.53373i	0.944717	+	0.268890i
$786$	−31.1525	+	57.6864i	−1.11117	+	2.05761i
$787$	−18.8498	+	18.8498i	−0.671923	+	0.671923i	−0.958159	−	0.286236i	$-0.907596\pi$
$787$	−18.8498	+	18.8498i	−0.671923	+	0.671923i	0.286236	+	0.958159i	$0.407596\pi$
$788$	22.8998	+	4.75938i	0.815771	+	0.169546i
$789$			0.495384i			0.0176361i
$790$	−4.09710	+	4.20459i	−0.145768	+	0.149593i
$791$			37.9878i			1.35069i
$792$	−43.4777	+	51.6106i	−1.54491	+	1.83390i
$793$	10.1278	−	10.1278i	0.359649	−	0.359649i
$794$	24.3635	+	13.1571i	0.864629	+	0.466927i
$795$	−18.7464	+	10.4394i	−0.664865	+	0.370246i
$796$	−16.4099	+	10.7625i	−0.581633	+	0.381467i
$797$	2.14124	+	2.14124i	0.0758466	+	0.0758466i	0.744012	−	0.668166i	$-0.232920\pi$
$797$	2.14124	+	2.14124i	0.0758466	+	0.0758466i	−0.668166	+	0.744012i	$0.732920\pi$
$798$	116.497	−	34.7946i	4.12394	−	1.23172i
$799$	−10.5368			−0.372766
$800$	22.0962	+	17.6567i	0.781219	+	0.624257i
$801$	72.2722			2.55361
$802$	38.4722	−	11.4907i	1.35850	−	0.405750i
$803$	−10.7383	−	10.7383i	−0.378947	−	0.378947i
$804$	6.51189	−	4.27086i	0.229657	−	0.150621i
$805$	15.1742	−	8.45010i	0.534819	−	0.297827i
$806$	21.1411	+	11.4169i	0.744664	+	0.402142i
$807$	54.4954	−	54.4954i	1.91833	−	1.91833i
$808$	−7.28310	+	8.64547i	−0.256219	+	0.304147i
$809$			4.94286i			0.173782i	0.996218	+	0.0868909i	$0.0276932\pi$
$809$			4.94286i			0.173782i	−0.996218	+	0.0868909i	$0.972307\pi$
$810$	−66.2239	+	67.9614i	−2.32687	+	2.38792i
$811$		−	24.8926i		−	0.874099i	−0.899437	−	0.437050i	$-0.856023\pi$
$811$		−	24.8926i		−	0.874099i	0.899437	−	0.437050i	$-0.143977\pi$
$812$	−46.0616	−	9.57321i	−1.61644	−	0.335954i
$813$	−17.9242	+	17.9242i	−0.628629	+	0.628629i
$814$	17.2383	−	31.9208i	0.604201	−	1.11882i
$815$	−41.0640	−	11.6879i	−1.43841	−	0.409408i
$816$	−43.1978	−	18.7667i	−1.51223	−	0.656965i
$817$	39.2322	+	39.2322i	1.37256	+	1.37256i
$818$	−8.55508	−	28.6435i	−0.299122	−	1.00150i
$819$	98.1803			3.43070
$820$	−2.07390	+	3.96219i	−0.0724238	+	0.138366i
$821$	3.69769			0.129050			0.0645251	−	0.997916i	$-0.479447\pi$
$821$	3.69769			0.129050			0.0645251	+	0.997916i	$0.479447\pi$
$822$	−12.7037	−	42.5337i	−0.443093	−	1.48353i
$823$	4.06784	+	4.06784i	0.141796	+	0.141796i	0.774442	−	0.632645i	$-0.218031\pi$
$823$	4.06784	+	4.06784i	0.141796	+	0.141796i	−0.632645	+	0.774442i	$0.718031\pi$
$824$	4.32341	−	0.369782i	0.150613	−	0.0128820i
$825$	11.3839	+	48.4420i	0.396337	+	1.68653i
$826$	3.67469	−	6.80458i	0.127859	−	0.236762i
$827$	3.75497	−	3.75497i	0.130573	−	0.130573i	−0.638800	−	0.769373i	$-0.720569\pi$
$827$	3.75497	−	3.75497i	0.130573	−	0.130573i	0.769373	+	0.638800i	$0.220569\pi$
$828$	−5.56715	+	26.7864i	−0.193472	+	0.930892i
$829$		−	46.9114i		−	1.62930i	−0.579952	−	0.814651i	$-0.696929\pi$
$829$		−	46.9114i		−	1.62930i	0.579952	−	0.814651i	$-0.303071\pi$
$830$	36.1925	−	0.468634i	1.25626	−	0.0162665i
$831$		−	72.9464i		−	2.53048i
$832$	18.0006	+	12.7087i	0.624057	+	0.440595i
$833$	33.3538	−	33.3538i	1.15564	−	1.15564i
$834$	−28.4163	−	15.3457i	−0.983977	−	0.531379i
$835$	2.48898	−	8.74476i	0.0861347	−	0.302625i
$836$	19.0973	+	29.1181i	0.660493	+	1.00707i
$837$	70.9691	+	70.9691i	2.45305	+	2.45305i
$838$	−30.2698	+	9.04083i	−1.04565	+	0.312310i
$839$	−24.3808			−0.841717			−0.420859	−	0.907126i	$-0.638271\pi$
$839$	−24.3808			−0.841717			−0.420859	+	0.907126i	$0.638271\pi$
$840$	17.9421	−	92.3121i	0.619061	−	3.18507i
$841$	1.66171			0.0573004
$842$	9.82547	−	2.93462i	0.338608	−	0.101134i
$843$	−60.8154	−	60.8154i	−2.09459	−	2.09459i
$844$	−4.55567	−	6.94615i	−0.156813	−	0.239096i
$845$	−5.88942	−	10.5759i	−0.202602	−	0.363820i
$846$	29.1598	+	15.7472i	1.00254	+	0.541401i
$847$	−6.14684	+	6.14684i	−0.211208	+	0.211208i
$848$	4.25986	+	10.8043i	0.146284	+	0.371020i
$849$			34.2649i			1.17597i
$850$	−21.8485	+	12.5402i	−0.749398	+	0.430125i
$851$		−	14.7078i		−	0.504175i
$852$	1.66522	−	8.01220i	0.0570494	−	0.274493i
$853$	12.0415	−	12.0415i	0.412292	−	0.412292i	−0.470244	−	0.882536i	$-0.655834\pi$
$853$	12.0415	−	12.0415i	0.412292	−	0.412292i	0.882536	+	0.470244i	$0.155834\pi$
$854$	−15.7211	+	29.1114i	−0.537965	+	0.996173i
$855$	49.8381	+	89.4962i	1.70443	+	3.06070i
$856$	1.15526	+	13.5071i	0.0394860	+	0.461662i
$857$	15.1688	+	15.1688i	0.518156	+	0.518156i	0.917013	−	0.398857i	$-0.130593\pi$
$857$	15.1688	+	15.1688i	0.518156	+	0.518156i	−0.398857	+	0.917013i	$0.630593\pi$
$858$	11.0943	+	37.1452i	0.378754	+	1.26812i
$859$	46.7493			1.59507			0.797533	−	0.603276i	$-0.206138\pi$
$859$	46.7493			1.59507			0.797533	+	0.603276i	$0.206138\pi$
$860$	40.9567	−	12.8126i	1.39661	−	0.436905i
$861$	14.8690			0.506733
$862$	2.89830	+	9.70389i	0.0987166	+	0.330516i
$863$	−35.1643	−	35.1643i	−1.19701	−	1.19701i	−0.975059	−	0.221946i	$-0.928759\pi$
$863$	−35.1643	−	35.1643i	−1.19701	−	1.19701i	−0.221946	−	0.975059i	$-0.571241\pi$
$864$	56.8547	+	72.3853i	1.93424	+	2.46260i
$865$	−9.44686	+	33.1905i	−0.321203	+	1.12851i
$866$	−9.00147	+	16.6684i	−0.305882	+	0.566415i
$867$	−10.0672	+	10.0672i	−0.341899	+	0.341899i
$868$	−54.3397	−	11.2937i	−1.84441	−	0.383333i
$869$			5.59034i			0.189639i
$870$	−0.707522	−	54.6417i	−0.0239872	−	1.85253i
$871$		−	3.24497i		−	0.109952i
$872$	8.44790	+	7.11666i	0.286082	+	0.241001i
$873$	29.9970	−	29.9970i	1.01524	−	1.01524i
$874$	12.4219	+	6.70820i	0.420175	+	0.226908i
$875$	−33.8760	−	37.1810i	−1.14522	−	1.25695i
$876$	−27.8750	+	18.2820i	−0.941810	+	0.617691i
$877$	−9.24009	−	9.24009i	−0.312016	−	0.312016i	0.533674	−	0.845690i	$-0.320811\pi$
$877$	−9.24009	−	9.24009i	−0.312016	−	0.312016i	−0.845690	+	0.533674i	$0.820811\pi$
$878$	15.6105	−	4.66245i	0.526828	−	0.157350i
$879$	3.08648			0.104104
$880$	26.8037	−	2.64251i	0.903552	−	0.0890791i
$881$	41.6557			1.40341			0.701707	−	0.712465i	$-0.252421\pi$
$881$	41.6557			1.40341			0.701707	+	0.712465i	$0.252421\pi$
$882$	−142.151	+	42.4569i	−4.78647	+	1.42960i
$883$	−13.9474	−	13.9474i	−0.469368	−	0.469368i	0.432342	−	0.901710i	$-0.357687\pi$
$883$	−13.9474	−	13.9474i	−0.469368	−	0.469368i	−0.901710	+	0.432342i	$0.857687\pi$
$884$	−16.4107	+	10.7631i	−0.551953	+	0.362001i
$885$	8.63962	+	2.45905i	0.290418	+	0.0826602i
$886$	11.7863	+	6.36496i	0.395967	+	0.213835i
$887$	−21.8492	+	21.8492i	−0.733626	+	0.733626i	−0.971336	−	0.237710i	$-0.923603\pi$
$887$	−21.8492	+	21.8492i	−0.733626	+	0.733626i	0.237710	+	0.971336i	$0.423603\pi$
$888$	−60.9035	−	51.3062i	−2.04379	−	1.72172i
$889$			78.2743i			2.62524i
$890$	−20.6589	−	20.1308i	−0.692489	−	0.674785i
$891$			90.3600i			3.02718i
$892$	35.4627	+	7.37040i	1.18738	+	0.246779i
$893$	12.0920	−	12.0920i	0.404644	−	0.404644i
$894$	29.2828	−	54.2242i	0.979363	−	1.81353i
$895$	−22.6951	+	12.6383i	−0.758613	+	0.422452i
$896$	−48.2426	−	16.2291i	−1.61167	−	0.542175i
$897$	11.1134	+	11.1134i	0.371065	+	0.371065i
$898$	6.78390	+	22.7134i	0.226382	+	0.757954i
$899$	−32.2515			−1.07565
$900$	79.2053	−	2.05151i	2.64018	−	0.0683835i
$901$	−10.3438			−0.344602
$902$	1.21873	+	4.08047i	0.0405793	+	0.135865i
$903$	−100.890	−	100.890i	−3.35742	−	3.35742i
$904$	2.03526	+	23.7958i	0.0676917	+	0.791437i
$905$	−13.8487	+	7.71198i	−0.460346	+	0.256355i
$906$	−12.1292	+	22.4602i	−0.402967	+	0.746191i
$907$	−29.5153	+	29.5153i	−0.980039	+	0.980039i	−0.999805	−	0.0197657i	$-0.993708\pi$
$907$	−29.5153	+	29.5153i	−0.980039	+	0.980039i	0.0197657	+	0.999805i	$0.493708\pi$
$908$	2.73746	−	13.1713i	0.0908457	−	0.437105i
$909$			31.6664i			1.05031i
$910$	−28.0647	−	27.3472i	−0.930336	−	0.906551i
$911$		−	4.03257i		−	0.133605i	−0.997766	−	0.0668024i	$-0.978720\pi$
$911$		−	4.03257i		−	0.133605i	0.997766	−	0.0668024i	$-0.0212797\pi$
$912$	71.1102	−	28.0371i	2.35469	−	0.928400i
$913$	24.3719	−	24.3719i	0.806592	−	0.806592i
$914$	41.9237	+	22.6401i	1.38671	+	0.748870i
$915$	−36.9621	−	10.5203i	−1.22193	−	0.347792i
$916$	14.8449	+	22.6344i	0.490489	+	0.747861i
$917$	−44.6216	−	44.6216i	−1.47353	−	1.47353i
$918$	−78.5507	+	23.4611i	−2.59256	+	0.774331i
$919$	9.38703			0.309650			0.154825	−	0.987942i	$-0.450519\pi$
$919$	9.38703			0.309650			0.154825	+	0.987942i	$0.450519\pi$
$920$	9.05247	−	6.10618i	0.298451	−	0.201315i
$921$	−21.7545			−0.716835
$922$	−31.6196	+	9.44396i	−1.04134	+	0.311020i
$923$	−2.41120	−	2.41120i	−0.0793657	−	0.0793657i
$924$	−49.1110	−	74.8808i	−1.61563	−	2.46340i
$925$	−41.4645	+	9.74420i	−1.36334	+	0.320387i
$926$	39.3755	+	21.2640i	1.29396	+	0.698779i
$927$	8.59506	−	8.59506i	0.282299	−	0.282299i
$928$	−29.3662	−	3.52890i	−0.963992	−	0.115842i
$929$			9.60703i			0.315196i	0.987503	+	0.157598i	$0.0503751\pi$
$929$			9.60703i			0.315196i	−0.987503	+	0.157598i	$0.949625\pi$
$930$	−0.834677	−	64.4618i	−0.0273701	−	2.11378i
$931$			76.5533i			2.50893i
$932$	4.34377	−	20.9001i	0.142285	−	0.684606i
$933$	−71.9576	+	71.9576i	−2.35579	+	2.35579i
$934$	3.46671	−	6.41946i	0.113434	−	0.210051i
$935$	−6.56694	+	23.0722i	−0.214762	+	0.754543i
$936$	61.5008	−	5.26017i	2.01022	−	0.171934i
$937$	−23.0391	−	23.0391i	−0.752654	−	0.752654i	0.222320	−	0.974974i	$-0.428637\pi$
$937$	−23.0391	−	23.0391i	−0.752654	−	0.752654i	−0.974974	+	0.222320i	$0.928637\pi$
$938$	2.14514	+	7.18222i	0.0700414	+	0.234508i
$939$	78.2281			2.55288
$940$	−3.94905	−	12.6235i	−0.128804	−	0.411734i
$941$	10.8604			0.354038			0.177019	−	0.984207i	$-0.443355\pi$
$941$	10.8604			0.354038			0.177019	+	0.984207i	$0.443355\pi$
$942$	−16.4626	−	55.1190i	−0.536382	−	1.79587i
$943$	1.22082	+	1.22082i	0.0397555	+	0.0397555i
$944$	1.93728	−	4.45931i	0.0630532	−	0.145138i
$945$	−79.6370	−	143.007i	−2.59059	−	4.65202i
$946$	19.4177	−	35.9566i	0.631325	−	1.16905i
$947$	−24.2560	+	24.2560i	−0.788213	+	0.788213i	−0.981201	−	0.192988i	$-0.938182\pi$
$947$	−24.2560	+	24.2560i	−0.788213	+	0.788213i	0.192988	+	0.981201i	$0.438182\pi$
$948$	12.0146	+	2.49706i	0.390216	+	0.0811006i
$949$			13.8905i			0.450906i
$950$	10.6822	−	39.4643i	0.346575	−	1.28039i
$951$		−	8.02785i		−	0.260321i
$952$	29.2074	−	34.6709i	0.946616	−	1.12369i
$953$	−1.62397	+	1.62397i	−0.0526056	+	0.0526056i	−0.732920	−	0.680315i	$-0.761843\pi$
$953$	−1.62397	+	1.62397i	−0.0526056	+	0.0526056i	0.680315	+	0.732920i	$0.261843\pi$
$954$	28.6257	+	15.4588i	0.926791	+	0.500497i
$955$	7.04094	+	12.6437i	0.227840	+	0.409140i
$956$	−33.3290	+	21.8590i	−1.07794	+	0.706970i
$957$	−36.7955	−	36.7955i	−1.18943	−	1.18943i
$958$	50.9185	−	15.2081i	1.64510	−	0.491350i
$959$	42.7272			1.37973
$960$	6.29328	−	58.7862i	0.203115	−	1.89732i
$961$	−7.04768			−0.227345
$962$	−31.7949	+	9.49632i	−1.02511	+	0.306174i
$963$	26.8524	+	26.8524i	0.865307	+	0.865307i
$964$	−23.4528	+	15.3816i	−0.755364	+	0.495409i
$965$	−11.0818	+	38.9348i	−0.356737	+	1.25336i
$966$	−31.9443	−	17.2509i	−1.02779	−	0.555040i
$967$	36.8567	−	36.8567i	1.18523	−	1.18523i	0.206863	−	0.978370i	$-0.433675\pi$
$967$	36.8567	−	36.8567i	1.18523	−	1.18523i	0.978370	−	0.206863i	$-0.0663255\pi$
$968$	−3.52109	+	4.17975i	−0.113172	+	0.134342i
$969$			68.0797i			2.18704i
$970$	−16.9300	+	0.219216i	−0.543589	+	0.00703860i
$971$		−	25.5008i		−	0.818360i	−0.912454	−	0.409180i	$-0.865815\pi$
$971$		−	25.5008i		−	0.818360i	0.912454	−	0.409180i	$-0.134185\pi$
$972$	98.6147	+	20.4956i	3.16307	+	0.657396i
$973$	21.9806	−	21.9806i	0.704665	−	0.704665i
$974$	−9.52873	+	17.6448i	−0.305320	+	0.565374i
$975$	23.9682	−	38.6939i	0.767598	−	1.23920i
$976$	−8.28811	+	19.0779i	−0.265296	+	0.610668i
$977$	7.82593	+	7.82593i	0.250374	+	0.250374i	0.821124	−	0.570750i	$-0.193347\pi$
$977$	7.82593	+	7.82593i	0.250374	+	0.250374i	−0.570750	+	0.821124i	$0.693347\pi$
$978$	25.5402	+	85.5118i	0.816685	+	2.73437i
$979$	−27.4677			−0.877871
$980$	52.4597	+	27.4586i	1.67576	+	0.877133i
$981$	30.9428			0.987927
$982$	14.5127	+	48.5902i	0.463117	+	1.55058i
$983$	3.76545	+	3.76545i	0.120099	+	0.120099i	0.764602	−	0.644503i	$-0.222936\pi$
$983$	3.76545	+	3.76545i	0.120099	+	0.120099i	−0.644503	+	0.764602i	$0.722936\pi$
$984$	9.31401	−	0.796628i	0.296920	−	0.0253956i
$985$	−25.1509	−	7.15859i	−0.801375	−	0.228092i
$986$	12.5176	−	23.1793i	0.398641	−	0.738180i
$987$	−31.0961	+	31.0961i	−0.989799	+	0.989799i
$988$	6.48124	−	31.1845i	0.206196	−	0.992112i
$989$		−	16.5673i		−	0.526809i
$990$	52.6548	−	54.0363i	1.67348	−	1.71739i
$991$		−	50.3334i		−	1.59889i	−0.600736	−	0.799447i	$-0.705126\pi$
$991$		−	50.3334i		−	1.59889i	0.600736	−	0.799447i	$-0.294874\pi$
$992$	−34.6438	−	4.16311i	−1.09994	−	0.132179i
$993$	51.6288	−	51.6288i	1.63839	−	1.63839i
$994$	6.93077	+	3.74284i	0.219831	+	0.118716i
$995$	19.1689	−	10.6747i	0.607695	−	0.338410i
$996$	−41.4932	−	63.2658i	−1.31476	−	2.00465i
$997$	34.4722	+	34.4722i	1.09175	+	1.09175i	0.995342	+	0.0964040i	$0.0307341\pi$
$997$	34.4722	+	34.4722i	1.09175	+	1.09175i	0.0964040	+	0.995342i	$0.469266\pi$
$998$	32.9870	−	9.85236i	1.04418	−	0.311871i
$999$	−138.612			−4.38547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.247.6	yes	108
4.3	odd	2	inner	820.2.k.c.247.31	yes	108
5.3	odd	4	inner	820.2.k.c.83.31	yes	108
20.3	even	4	inner	820.2.k.c.83.6	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.6	✓	108	20.3	even	4	inner
820.2.k.c.83.31	yes	108	5.3	odd	4	inner
820.2.k.c.247.6	yes	108	1.1	even	1	trivial
820.2.k.c.247.31	yes	108	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35506 + 0.404723i) q^{2} +(-2.33700 - 2.33700i) q^{3} +(1.67240 - 1.09685i) q^{4} +(-1.95358 + 1.08790i) q^{5} +(4.11263 + 2.22095i) q^{6} +(-3.18120 + 3.18120i) q^{7} +(-1.82229 + 2.16316i) q^{8} +7.92318i q^{9} +(2.20693 - 2.26483i) q^{10} -3.01127i q^{11} +(-6.47175 - 1.34506i) q^{12} +(-1.94762 + 1.94762i) q^{13} +(3.02323 - 5.59824i) q^{14} +(7.10795 + 2.02310i) q^{15} +(1.59383 - 3.66875i) q^{16} +(2.51915 + 2.51915i) q^{17} +(-3.20669 - 10.7364i) q^{18} -5.78194 q^{19} +(-2.07390 + 3.96219i) q^{20} +14.8690 q^{21} +(1.21873 + 4.08047i) q^{22} +(1.22082 + 1.22082i) q^{23} +(9.31401 - 0.796628i) q^{24} +(2.63295 - 4.25060i) q^{25} +(1.85090 - 3.42739i) q^{26} +(11.5055 - 11.5055i) q^{27} +(-1.83093 + 8.80954i) q^{28} +5.22860i q^{29} +(-10.4505 + 0.135318i) q^{30} +6.16828i q^{31} +(-0.674922 + 5.61645i) q^{32} +(-7.03736 + 7.03736i) q^{33} +(-4.43318 - 2.39406i) q^{34} +(2.75391 - 9.67556i) q^{35} +(8.69055 + 13.2507i) q^{36} +(-6.02371 - 6.02371i) q^{37} +(7.83490 - 2.34008i) q^{38} +9.10318 q^{39} +(1.20668 - 6.20837i) q^{40} +1.00000 q^{41} +(-20.1484 + 6.01781i) q^{42} +(-6.78530 - 6.78530i) q^{43} +(-3.30292 - 5.03605i) q^{44} +(-8.61962 - 15.4786i) q^{45} +(-2.14839 - 1.16020i) q^{46} +(-2.09134 + 2.09134i) q^{47} +(-12.2987 + 4.84908i) q^{48} -13.2401i q^{49} +(-1.84751 + 6.82545i) q^{50} -11.7745i q^{51} +(-1.12095 + 5.39344i) q^{52} +(-2.05303 + 2.05303i) q^{53} +(-10.9342 + 20.2472i) q^{54} +(3.27596 + 5.88276i) q^{55} +(-1.08439 - 12.6785i) q^{56} +(13.5124 + 13.5124i) q^{57} +(-2.11614 - 7.08509i) q^{58} +1.21549 q^{59} +(14.1064 - 4.41293i) q^{60} -5.20011 q^{61} +(-2.49644 - 8.35842i) q^{62} +(-25.2052 - 25.2052i) q^{63} +(-1.35854 - 7.88380i) q^{64} +(1.68602 - 5.92364i) q^{65} +(6.68789 - 12.3843i) q^{66} +(-0.833062 + 0.833062i) q^{67} +(6.97617 + 1.44989i) q^{68} -5.70614i q^{69} +(0.184198 + 14.2256i) q^{70} +1.23803i q^{71} +(-17.1391 - 14.4383i) q^{72} +(3.56604 - 3.56604i) q^{73} +(10.6004 + 5.72458i) q^{74} +(-16.0869 + 3.78044i) q^{75} +(-9.66971 + 6.34193i) q^{76} +(9.57946 + 9.57946i) q^{77} +(-12.3354 + 3.68427i) q^{78} -1.85647 q^{79} +(0.877541 + 8.90112i) q^{80} -30.0073 q^{81} +(-1.35506 + 0.404723i) q^{82} +(8.09356 + 8.09356i) q^{83} +(24.8668 - 16.3090i) q^{84} +(-7.66195 - 2.18079i) q^{85} +(11.9407 + 6.44835i) q^{86} +(12.2193 - 12.2193i) q^{87} +(6.51387 + 5.48740i) q^{88} -9.12162i q^{89} +(17.9447 + 17.4859i) q^{90} -12.3915i q^{91} +(3.38076 + 0.702641i) q^{92} +(14.4153 - 14.4153i) q^{93} +(1.98749 - 3.68032i) q^{94} +(11.2955 - 6.29016i) q^{95} +(14.7030 - 11.5484i) q^{96} +(-3.78598 - 3.78598i) q^{97} +(5.35856 + 17.9412i) q^{98} +23.8589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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