LMFDB - Embedded newform 820.2.k.c.83.6

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			83.6
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.6

$q$-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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−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	−0.462816	+	0.886454i	$0.653161\pi$
$3$	−2.33700	+	2.33700i	−1.34927	+	1.34927i	−0.886454	+	0.462816i	$0.846839\pi$
$4$	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	−0.973440	−	0.228940i	$-0.926474\pi$
$7$	−3.18120	−	3.18120i	−1.20238	−	1.20238i	−0.228940	−	0.973440i	$-0.573526\pi$
$8$	−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	$0.149991\pi$
$11$			3.01127i			0.907933i	−0.891019	+	0.453966i	$0.850009\pi$
$12$	−6.47175	+	1.34506i	−1.86823	+	0.388284i
$13$	−1.94762	−	1.94762i	−0.540172	−	0.540172i	0.383407	−	0.923579i	$-0.374751\pi$
$13$	−1.94762	−	1.94762i	−0.540172	−	0.540172i	−0.923579	+	0.383407i	$0.874751\pi$
$14$	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	−0.332218	−	0.943203i	$-0.607797\pi$
$17$	2.51915	−	2.51915i	0.610985	−	0.610985i	0.943203	+	0.332218i	$0.107797\pi$
$18$	−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	−0.568278	−	0.822837i	$-0.692390\pi$
$23$	1.22082	−	1.22082i	0.254559	−	0.254559i	0.822837	+	0.568278i	$0.192390\pi$
$24$	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	$-0.838651\pi$
$29$		−	5.22860i		−	0.970927i	0.874257	−	0.485464i	$-0.161349\pi$
$30$	−10.4505	−	0.135318i	−1.90800	−	0.0247055i
$31$		−	6.16828i		−	1.10786i	−0.832565	−	0.553928i	$-0.813128\pi$
$31$		−	6.16828i		−	1.10786i	0.832565	−	0.553928i	$-0.186872\pi$
$32$	−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	−0.999953	−	0.00966187i	$-0.996924\pi$
$37$	−6.02371	+	6.02371i	−0.990291	+	0.990291i	0.00966187	+	0.999953i	$0.496924\pi$
$38$	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	−0.0353737	+	0.999374i	$0.511262\pi$
$43$	−6.78530	+	6.78530i	−1.03475	+	1.03475i	−0.999374	+	0.0353737i	$0.988738\pi$
$44$	−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	0.537934	−	0.842987i	$-0.319205\pi$
$47$	−2.09134	−	2.09134i	−0.305054	−	0.305054i	−0.842987	+	0.537934i	$0.819205\pi$
$48$	−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	0.551903	−	0.833909i	$-0.313902\pi$
$53$	−2.05303	−	2.05303i	−0.282006	−	0.282006i	−0.833909	+	0.551903i	$0.813902\pi$
$54$	−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	0.654386	−	0.756161i	$-0.272927\pi$
$67$	−0.833062	−	0.833062i	−0.101775	−	0.101775i	−0.756161	+	0.654386i	$0.772927\pi$
$68$	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	$-0.976595\pi$
$71$		−	1.23803i		−	0.146927i	0.997298	−	0.0734634i	$-0.0234052\pi$
$72$	−17.1391	+	14.4383i	−2.01987	+	1.70157i
$73$	3.56604	+	3.56604i	0.417373	+	0.417373i	0.884297	−	0.466924i	$-0.154638\pi$
$73$	3.56604	+	3.56604i	0.417373	+	0.417373i	−0.466924	+	0.884297i	$0.654638\pi$
$74$	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	−0.105984	−	0.994368i	$-0.533799\pi$
$83$	8.09356	−	8.09356i	0.888383	−	0.888383i	0.994368	+	0.105984i	$0.0337994\pi$
$84$	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	$0.160615\pi$
$89$			9.12162i			0.966890i	−0.875375	+	0.483445i	$0.839385\pi$
$90$	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	−0.872687	−	0.488280i	$-0.837625\pi$
$97$	−3.78598	+	3.78598i	−0.384408	+	0.384408i	0.488280	+	0.872687i	$0.337625\pi$
$98$	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	−0.758528	−	0.651640i	$-0.774081\pi$
$103$	−1.08480	+	1.08480i	−0.106888	+	0.106888i	0.651640	+	0.758528i	$0.274081\pi$
$104$	−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	0.851687	−	0.524051i	$-0.175580\pi$
$107$	3.38909	+	3.38909i	0.327636	+	0.327636i	−0.524051	+	0.851687i	$0.675580\pi$
$108$	6.62196	+	31.8616i	0.637198	+	3.06588i
$109$			3.90535i			0.374064i	0.982354	+	0.187032i	$0.0598869\pi$
$109$			3.90535i			0.374064i	−0.982354	+	0.187032i	$0.940113\pi$
$110$	−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	0.929783	−	0.368109i	$-0.119995\pi$
$113$	5.97067	+	5.97067i	0.561674	+	0.561674i	−0.368109	+	0.929783i	$0.619995\pi$
$114$	−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	0.995349	+	0.0963329i	$0.0307113\pi$
$127$	12.3026	+	12.3026i	1.09168	+	1.09168i	0.0963329	+	0.995349i	$0.469289\pi$
$128$	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	$-0.790061\pi$
$131$		−	14.0266i		−	1.22551i	0.790272	−	0.612757i	$-0.209939\pi$
$132$	−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	−0.933174	−	0.359424i	$-0.882973\pi$
$137$	−6.71558	+	6.71558i	−0.573750	+	0.573750i	0.359424	+	0.933174i	$0.382973\pi$
$138$	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	$0.181602\pi$
$149$			13.1848i			1.08014i	−0.841620	+	0.540070i	$0.818398\pi$
$150$	20.2687	+	11.6335i	1.65494	+	0.949869i
$151$		−	5.46128i		−	0.444432i	−0.974997	−	0.222216i	$-0.928671\pi$
$151$		−	5.46128i		−	0.444432i	0.974997	−	0.222216i	$-0.0713291\pi$
$152$	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	−0.963229	−	0.268681i	$-0.913412\pi$
$157$	−8.70266	+	8.70266i	−0.694548	+	0.694548i	0.268681	+	0.963229i	$0.413412\pi$
$158$	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	0.0592635	−	0.998242i	$-0.481125\pi$
$163$	13.5013	−	13.5013i	1.05751	−	1.05751i	0.998242	−	0.0592635i	$-0.0188752\pi$
$164$	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	0.587058	−	0.809545i	$-0.300286\pi$
$167$	−2.87517	−	2.87517i	−0.222487	−	0.222487i	−0.809545	+	0.587058i	$0.800286\pi$
$168$	−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	0.987471	−	0.157799i	$-0.0504399\pi$
$173$	10.9126	+	10.9126i	0.829672	+	0.829672i	−0.157799	+	0.987471i	$0.550440\pi$
$174$	−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	$0.0752309\pi$
$191$			6.47206i			0.468302i	−0.972200	+	0.234151i	$0.924769\pi$
$192$	−15.2496	−	21.5994i	−1.10054	−	1.55880i
$193$	12.8013	+	12.8013i	0.921456	+	0.921456i	0.997132	−	0.0756762i	$-0.0241115\pi$
$193$	12.8013	+	12.8013i	0.921456	+	0.921456i	−0.0756762	+	0.997132i	$0.524112\pi$
$194$	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	−0.348241	−	0.937405i	$-0.613221\pi$
$197$	8.26931	−	8.26931i	0.589164	−	0.589164i	0.937405	+	0.348241i	$0.113221\pi$
$198$	−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	$0.0456640\pi$
$211$			4.15341i			0.285932i	−0.989728	+	0.142966i	$0.954336\pi$
$212$	−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	−0.133502	−	0.991048i	$-0.542622\pi$
$223$	12.8059	−	12.8059i	0.857546	−	0.857546i	0.991048	+	0.133502i	$0.0426224\pi$
$224$	−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	0.847107	−	0.531422i	$-0.178342\pi$
$227$	4.75627	+	4.75627i	0.315685	+	0.315685i	−0.531422	+	0.847107i	$0.678342\pi$
$228$	37.4193	−	7.77704i	2.47815	−	0.515047i
$229$		−	13.5341i		−	0.894358i	−0.894445	−	0.447179i	$-0.852429\pi$
$229$		−	13.5341i		−	0.894358i	0.894445	−	0.447179i	$-0.147571\pi$
$230$	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	0.909700	−	0.415266i	$-0.136312\pi$
$233$	7.54721	+	7.54721i	0.494434	+	0.494434i	−0.415266	+	0.909700i	$0.636312\pi$
$234$	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	$0.285662\pi$
$251$			24.7699i			1.56346i	−0.623618	+	0.781730i	$0.714338\pi$
$252$	−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	−0.788239	−	0.615369i	$-0.789007\pi$
$257$	−2.77132	+	2.77132i	−0.172870	+	0.172870i	0.615369	+	0.788239i	$0.289007\pi$
$258$	−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	−0.710367	−	0.703832i	$-0.751471\pi$
$263$	−0.105987	+	0.105987i	−0.00653544	+	0.00653544i	0.703832	+	0.710367i	$0.251471\pi$
$264$	−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	$-0.748298\pi$
$269$		−	23.3185i		−	1.42175i	0.703316	−	0.710877i	$-0.251702\pi$
$270$	−0.666193	+	51.4498i	−0.0405432	+	3.13114i
$271$			7.66973i			0.465903i	0.972488	+	0.232951i	$0.0748383\pi$
$271$			7.66973i			0.465903i	−0.972488	+	0.232951i	$0.925162\pi$
$272$	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	−0.0604483	−	0.998171i	$-0.519253\pi$
$277$	15.6068	−	15.6068i	0.937723	−	0.937723i	0.998171	+	0.0604483i	$0.0192530\pi$
$278$	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	−0.890589	−	0.454810i	$-0.849707\pi$
$283$	−7.33094	+	7.33094i	−0.435779	+	0.435779i	0.454810	+	0.890589i	$0.349707\pi$
$284$	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	0.687555	−	0.726133i	$-0.258684\pi$
$293$	−0.660349	−	0.660349i	−0.0385780	−	0.0385780i	−0.726133	+	0.687555i	$0.758684\pi$
$294$	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	0.827340	−	0.561702i	$-0.189853\pi$
$307$	4.65435	+	4.65435i	0.265638	+	0.265638i	−0.561702	+	0.827340i	$0.689853\pi$
$308$	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	$0.337819\pi$
$311$			30.7905i			1.74597i	−0.487746	+	0.872986i	$0.662181\pi$
$312$	−16.5886	−	19.6917i	−0.939145	−	1.11482i
$313$	−16.7368	−	16.7368i	−0.946022	−	0.946022i	0.0525940	−	0.998616i	$-0.483251\pi$
$313$	−16.7368	−	16.7368i	−0.946022	−	0.946022i	−0.998616	+	0.0525940i	$0.983251\pi$
$314$	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	−0.657226	−	0.753693i	$-0.728270\pi$
$317$	1.71755	−	1.71755i	0.0964673	−	0.0964673i	0.753693	+	0.657226i	$0.228270\pi$
$318$	−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	$-0.792317\pi$
$331$		−	22.0919i		−	1.21428i	0.794595	−	0.607139i	$-0.207683\pi$
$332$	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	−0.0838407	−	0.996479i	$-0.526719\pi$
$337$	16.7538	−	16.7538i	0.912638	−	0.912638i	0.996479	+	0.0838407i	$0.0267187\pi$
$338$	−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	0.282940	−	0.959138i	$-0.408690\pi$
$347$	−12.5962	−	12.5962i	−0.676197	−	0.676197i	−0.959138	+	0.282940i	$0.908690\pi$
$348$	7.03277	+	33.8382i	0.376996	+	1.81392i
$349$		−	27.4748i		−	1.47069i	−0.677692	−	0.735346i	$-0.737020\pi$
$349$		−	27.4748i		−	1.47069i	0.677692	−	0.735346i	$-0.262980\pi$
$350$	−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	0.560272	−	0.828308i	$-0.310696\pi$
$353$	−5.03594	−	5.03594i	−0.268036	−	0.268036i	−0.828308	+	0.560272i	$0.810696\pi$
$354$	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	0.393315	−	0.919404i	$-0.371328\pi$
$367$	−10.0784	−	10.0784i	−0.526088	−	0.526088i	−0.919404	+	0.393315i	$0.871328\pi$
$368$	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	0.971545	−	0.236855i	$-0.0761165\pi$
$373$	14.1892	+	14.1892i	0.734691	+	0.734691i	−0.236855	+	0.971545i	$0.576116\pi$
$374$	−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	−0.774216	−	0.632922i	$-0.781855\pi$
$383$	−2.76517	+	2.76517i	−0.141294	+	0.141294i	0.632922	+	0.774216i	$0.281855\pi$
$384$	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	$0.185321\pi$
$389$			21.6900i			1.09973i	−0.835254	+	0.549864i	$0.814679\pi$
$390$	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	−0.963293	−	0.268453i	$-0.913488\pi$
$397$	−13.8446	+	13.8446i	−0.694840	+	0.694840i	0.268453	+	0.963293i	$0.413488\pi$
$398$	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	$-0.824960\pi$
$409$		−	21.1381i		−	1.04521i	0.852574	−	0.522606i	$-0.175040\pi$
$410$	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	$0.0551752\pi$
$431$			7.16120i			0.344943i	−0.985015	+	0.172471i	$0.944825\pi$
$432$	−23.8729	+	60.5486i	−1.14859	+	2.91315i
$433$	9.47183	+	9.47183i	0.455187	+	0.455187i	0.897072	−	0.441885i	$-0.145690\pi$
$433$	9.47183	+	9.47183i	0.455187	+	0.455187i	−0.441885	+	0.897072i	$0.645690\pi$
$434$	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	−0.848079	−	0.529869i	$-0.822241\pi$
$443$	−6.69755	+	6.69755i	−0.318210	+	0.318210i	0.529869	+	0.848079i	$0.322241\pi$
$444$	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	$0.129436\pi$
$449$			16.7618i			0.791040i	−0.918457	+	0.395520i	$0.870564\pi$
$450$	−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	−0.121853	+	0.992548i	$0.538884\pi$
$457$	−23.8232	+	23.8232i	−1.11440	+	1.11440i	−0.992548	+	0.121853i	$0.961116\pi$
$458$	−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	−0.0406893	+	0.999172i	$0.512955\pi$
$463$	−22.3751	+	22.3751i	−1.03986	+	1.03986i	−0.999172	+	0.0406893i	$0.987045\pi$
$464$	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	0.617650	−	0.786453i	$-0.288085\pi$
$467$	−3.64786	−	3.64786i	−0.168803	−	0.168803i	−0.786453	+	0.617650i	$0.788085\pi$
$468$	−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	0.896796	−	0.442445i	$-0.145889\pi$
$487$	10.0266	+	10.0266i	0.454350	+	0.454350i	−0.442445	+	0.896796i	$0.645889\pi$
$488$	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	$0.300061\pi$
$491$			35.8582i			1.61826i	−0.587630	+	0.809130i	$0.699939\pi$
$492$	−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	−0.489794	−	0.871838i	$-0.662928\pi$
$503$	8.56836	−	8.56836i	0.382044	−	0.382044i	0.871838	+	0.489794i	$0.162928\pi$
$504$	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	$-0.877426\pi$
$509$		−	16.9492i		−	0.751261i	0.926769	−	0.375631i	$-0.122574\pi$
$510$	−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	−0.482080	−	0.876127i	$-0.660119\pi$
$523$	9.01153	−	9.01153i	0.394047	−	0.394047i	0.876127	+	0.482080i	$0.160119\pi$
$524$	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	−0.894934	−	0.446198i	$-0.852778\pi$
$547$	−31.3664	−	31.3664i	−1.34113	−	1.34113i	−0.446198	−	0.894934i	$-0.647222\pi$
$548$	−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	−0.392733	+	0.919653i	$0.628470\pi$
$557$	−30.9734	+	30.9734i	−1.31239	+	1.31239i	−0.919653	+	0.392733i	$0.871530\pi$
$558$	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	−0.0109339	−	0.999940i	$-0.503480\pi$
$563$	23.4668	−	23.4668i	0.989006	−	0.989006i	0.999940	+	0.0109339i	$0.00348044\pi$
$564$	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	$-0.759597\pi$
$569$		−	32.7019i		−	1.37094i	0.728102	−	0.685468i	$-0.240403\pi$
$570$	60.4243	+	0.782398i	2.53090	+	0.0327710i
$571$		−	2.32916i		−	0.0974724i	−0.998812	−	0.0487362i	$-0.984481\pi$
$571$		−	2.32916i		−	0.0974724i	0.998812	−	0.0487362i	$-0.0155194\pi$
$572$	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	−0.114261	−	0.993451i	$-0.536450\pi$
$577$	21.1189	−	21.1189i	0.879190	−	0.879190i	0.993451	+	0.114261i	$0.0364501\pi$
$578$	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	0.524932	−	0.851144i	$-0.324091\pi$
$587$	−7.90351	−	7.90351i	−0.326213	−	0.326213i	−0.851144	+	0.524932i	$0.824091\pi$
$588$	−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	0.391245	−	0.920287i	$-0.372045\pi$
$593$	−12.8830	−	12.8830i	−0.529042	−	0.529042i	−0.920287	+	0.391245i	$0.872045\pi$
$594$	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	0.910354	−	0.413829i	$-0.135809\pi$
$607$	12.2331	+	12.2331i	0.496525	+	0.496525i	−0.413829	+	0.910354i	$0.635809\pi$
$608$	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	0.792103	−	0.610387i	$-0.208986\pi$
$613$	4.49907	+	4.49907i	0.181716	+	0.181716i	−0.610387	+	0.792103i	$0.708986\pi$
$614$	−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	−0.248701	+	0.968580i	$0.580004\pi$
$617$	−30.2366	+	30.2366i	−1.21728	+	1.21728i	−0.968580	+	0.248701i	$0.919996\pi$
$618$	−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	$0.284474\pi$
$631$			39.1564i			1.55879i	−0.626531	+	0.779396i	$0.715526\pi$
$632$	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	−0.983980	−	0.178280i	$-0.942947\pi$
$643$	−20.4305	+	20.4305i	−0.805700	+	0.805700i	0.178280	+	0.983980i	$0.442947\pi$
$644$	−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	0.516061	−	0.856552i	$-0.327398\pi$
$647$	−8.66078	−	8.66078i	−0.340490	−	0.340490i	−0.856552	+	0.516061i	$0.827398\pi$
$648$	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	0.353898	−	0.935284i	$-0.384856\pi$
$653$	−14.8567	−	14.8567i	−0.581386	−	0.581386i	−0.935284	+	0.353898i	$0.884856\pi$
$654$	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	0.967923	+	0.251248i	$0.0808409\pi$
$673$	31.6280	+	31.6280i	1.21917	+	1.21917i	0.251248	+	0.967923i	$0.419159\pi$
$674$	−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	−0.0698064	−	0.997561i	$-0.522238\pi$
$677$	24.1394	−	24.1394i	0.927754	−	0.927754i	0.997561	+	0.0698064i	$0.0222382\pi$
$678$	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	−0.552908	−	0.833242i	$-0.686482\pi$
$683$	7.32634	−	7.32634i	0.280335	−	0.280335i	0.833242	+	0.552908i	$0.186482\pi$
$684$	−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	$-0.793554\pi$
$691$		−	31.7570i		−	1.20809i	0.796948	−	0.604047i	$-0.206446\pi$
$692$	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	$-0.975259\pi$
$709$		−	4.13510i		−	0.155297i	0.996981	−	0.0776485i	$-0.0247412\pi$
$710$	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	0.852097	−	0.523384i	$-0.175331\pi$
$727$	8.86305	+	8.86305i	0.328712	+	0.328712i	−0.523384	+	0.852097i	$0.675331\pi$
$728$	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	0.589605	−	0.807691i	$-0.299283\pi$
$733$	−5.90445	−	5.90445i	−0.218086	−	0.218086i	−0.807691	+	0.589605i	$0.799283\pi$
$734$	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	0.471958	−	0.881621i	$-0.343547\pi$
$743$	36.8959	−	36.8959i	1.35358	−	1.35358i	0.881621	−	0.471958i	$-0.156453\pi$
$744$	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	$0.111451\pi$
$751$			18.8007i			0.686048i	−0.939327	+	0.343024i	$0.888549\pi$
$752$	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	−0.992900	−	0.118956i	$-0.962045\pi$
$757$	−24.0454	+	24.0454i	−0.873943	+	0.873943i	0.118956	+	0.992900i	$0.462045\pi$
$758$	−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	$0.00484915\pi$
$769$			0.844874i			0.0304669i	−0.999884	+	0.0152335i	$0.995151\pi$
$770$	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	0.793866	−	0.608093i	$-0.208065\pi$
$773$	5.16500	+	5.16500i	0.185772	+	0.185772i	−0.608093	+	0.793866i	$0.708065\pi$
$774$	−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	0.286236	−	0.958159i	$-0.407596\pi$
$787$	−18.8498	−	18.8498i	−0.671923	−	0.671923i	−0.958159	+	0.286236i	$0.907596\pi$
$788$	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	−0.668166	−	0.744012i	$-0.732920\pi$
$797$	2.14124	−	2.14124i	0.0758466	−	0.0758466i	0.744012	+	0.668166i	$0.232920\pi$
$798$	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	$-0.972307\pi$
$809$		−	4.94286i		−	0.173782i	0.996218	−	0.0868909i	$-0.0276932\pi$
$810$	−66.2239	−	67.9614i	−2.32687	−	2.38792i
$811$			24.8926i			0.874099i	0.899437	+	0.437050i	$0.143977\pi$
$811$			24.8926i			0.874099i	−0.899437	+	0.437050i	$0.856023\pi$
$812$	−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	−0.632645	−	0.774442i	$-0.718031\pi$
$823$	4.06784	−	4.06784i	0.141796	−	0.141796i	0.774442	+	0.632645i	$0.218031\pi$
$824$	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	0.769373	−	0.638800i	$-0.220569\pi$
$827$	3.75497	+	3.75497i	0.130573	+	0.130573i	−0.638800	+	0.769373i	$0.720569\pi$
$828$	−5.56715	−	26.7864i	−0.193472	−	0.930892i
$829$			46.9114i			1.62930i	0.579952	+	0.814651i	$0.303071\pi$
$829$			46.9114i			1.62930i	−0.579952	+	0.814651i	$0.696929\pi$
$830$	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	0.882536	−	0.470244i	$-0.155834\pi$
$853$	12.0415	+	12.0415i	0.412292	+	0.412292i	−0.470244	+	0.882536i	$0.655834\pi$
$854$	−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	−0.398857	−	0.917013i	$-0.630593\pi$
$857$	15.1688	−	15.1688i	0.518156	−	0.518156i	0.917013	+	0.398857i	$0.130593\pi$
$858$	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	−0.221946	+	0.975059i	$0.571241\pi$
$863$	−35.1643	+	35.1643i	−1.19701	+	1.19701i	−0.975059	+	0.221946i	$0.928759\pi$
$864$	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	−0.845690	−	0.533674i	$-0.820811\pi$
$877$	−9.24009	+	9.24009i	−0.312016	+	0.312016i	0.533674	+	0.845690i	$0.320811\pi$
$878$	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	−0.901710	−	0.432342i	$-0.857687\pi$
$883$	−13.9474	+	13.9474i	−0.469368	+	0.469368i	0.432342	+	0.901710i	$0.357687\pi$
$884$	−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	0.237710	−	0.971336i	$-0.423603\pi$
$887$	−21.8492	−	21.8492i	−0.733626	−	0.733626i	−0.971336	+	0.237710i	$0.923603\pi$
$888$	−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	0.0197657	−	0.999805i	$-0.493708\pi$
$907$	−29.5153	−	29.5153i	−0.980039	−	0.980039i	−0.999805	+	0.0197657i	$0.993708\pi$
$908$	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	$0.0212797\pi$
$911$			4.03257i			0.133605i	−0.997766	+	0.0668024i	$0.978720\pi$
$912$	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	$-0.949625\pi$
$929$		−	9.60703i		−	0.315196i	0.987503	−	0.157598i	$-0.0503751\pi$
$930$	−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	−0.974974	−	0.222320i	$-0.928637\pi$
$937$	−23.0391	+	23.0391i	−0.752654	+	0.752654i	0.222320	+	0.974974i	$0.428637\pi$
$938$	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	0.192988	−	0.981201i	$-0.438182\pi$
$947$	−24.2560	−	24.2560i	−0.788213	−	0.788213i	−0.981201	+	0.192988i	$0.938182\pi$
$948$	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	0.680315	−	0.732920i	$-0.261843\pi$
$953$	−1.62397	−	1.62397i	−0.0526056	−	0.0526056i	−0.732920	+	0.680315i	$0.761843\pi$
$954$	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	0.978370	+	0.206863i	$0.0663255\pi$
$967$	36.8567	+	36.8567i	1.18523	+	1.18523i	0.206863	+	0.978370i	$0.433675\pi$
$968$	−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	$0.134185\pi$
$971$			25.5008i			0.818360i	−0.912454	+	0.409180i	$0.865815\pi$
$972$	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	−0.570750	−	0.821124i	$-0.693347\pi$
$977$	7.82593	−	7.82593i	0.250374	−	0.250374i	0.821124	+	0.570750i	$0.193347\pi$
$978$	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	−0.644503	−	0.764602i	$-0.722936\pi$
$983$	3.76545	−	3.76545i	0.120099	−	0.120099i	0.764602	+	0.644503i	$0.222936\pi$
$984$	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	$0.294874\pi$
$991$			50.3334i			1.59889i	−0.600736	+	0.799447i	$0.705126\pi$
$992$	−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	0.0964040	−	0.995342i	$-0.469266\pi$
$997$	34.4722	−	34.4722i	1.09175	−	1.09175i	0.995342	−	0.0964040i	$-0.0307341\pi$
$998$	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.83.6	✓	108
4.3	odd	2	inner	820.2.k.c.83.31	yes	108
5.2	odd	4	inner	820.2.k.c.247.31	yes	108
20.7	even	4	inner	820.2.k.c.247.6	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.6	✓	108	1.1	even	1	trivial
820.2.k.c.83.31	yes	108	4.3	odd	2	inner
820.2.k.c.247.6	yes	108	20.7	even	4	inner
820.2.k.c.247.31	yes	108	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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