LMFDB - Embedded newform 820.2.k.c.83.31

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			83.31
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.404723 + 1.35506i) 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} +(-2.16316 - 1.82229i) q^{8} -7.92318i q^{9} +(0.683514 - 3.08752i) q^{10} -3.01127i q^{11} +(-1.34506 + 6.47175i) 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} +(10.7364 - 3.20669i) q^{18} +5.78194 q^{19} +(4.46043 - 0.323387i) q^{20} +14.8690 q^{21} +(4.08047 - 1.21873i) 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} +(-8.80954 - 1.83093i) q^{28} -5.22860i q^{29} +(-5.61819 - 8.81293i) q^{30} +6.16828i q^{31} +(5.61645 + 0.674922i) 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} +(2.34008 + 7.83490i) q^{38} -9.10318 q^{39} +(2.24345 + 5.91328i) q^{40} +1.00000 q^{41} +(6.01781 + 20.1484i) 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} +(-4.84908 - 12.2987i) q^{48} +13.2401i q^{49} +(-4.69421 + 5.28813i) q^{50} -11.7745i q^{51} +(5.39344 + 1.12095i) 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} +(7.08509 - 2.11614i) q^{58} -1.21549 q^{59} +(9.66828 - 11.1798i) q^{60} -5.20011 q^{61} +(-8.35842 + 2.49644i) 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} +(-1.44989 + 6.97617i) q^{68} +5.70614i q^{69} +(11.9964 - 7.64764i) q^{70} +1.23803i q^{71} +(-14.4383 + 17.1391i) 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} +(-3.68427 - 12.3354i) q^{78} +1.85647 q^{79} +(-7.10491 + 5.43326i) q^{80} -30.0073 q^{81} +(0.404723 + 1.35506i) 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} +(-5.48740 + 6.51387i) q^{88} +9.12162i q^{89} +(-24.4630 - 5.41560i) q^{90} -12.3915i q^{91} +(0.702641 - 3.38076i) 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} +(-17.9412 + 5.35856i) 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 $

$2$	0.404723	+	1.35506i	0.286182	+	0.958175i
$2$	0.404723	+	1.35506i	0.286182	+	0.958175i
$3$	2.33700	−	2.33700i	1.34927	−	1.34927i	0.462816	−	0.886454i	$-0.346839\pi$
$3$	2.33700	−	2.33700i	1.34927	−	1.34927i	0.886454	−	0.462816i	$-0.153161\pi$
$4$	−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	$0.0735261\pi$
$7$	3.18120	+	3.18120i	1.20238	+	1.20238i	0.228940	+	0.973440i	$0.426474\pi$
$8$	−2.16316	−	1.82229i	−0.764793	−	0.644276i
$9$		−	7.92318i		−	2.64106i
$10$	0.683514	−	3.08752i	0.216146	−	0.976361i
$11$		−	3.01127i		−	0.907933i	−0.891019	−	0.453966i	$-0.850009\pi$
$11$		−	3.01127i		−	0.907933i	0.891019	−	0.453966i	$-0.149991\pi$
$12$	−1.34506	+	6.47175i	−0.388284	+	1.86823i
$13$	−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	$0.107797\pi$
$18$	10.7364	−	3.20669i	2.53060	−	0.755825i
$19$	5.78194			1.32647			0.663234	−	0.748412i	$-0.269183\pi$
$19$	5.78194			1.32647			0.663234	+	0.748412i	$0.269183\pi$
$20$	4.46043	−	0.323387i	0.997382	−	0.0723116i
$21$	14.8690			3.24467
$22$	4.08047	−	1.21873i	0.869959	−	0.259834i
$23$	−1.22082	+	1.22082i	−0.254559	+	0.254559i	−0.822837	−	0.568278i	$-0.807610\pi$
$23$	−1.22082	+	1.22082i	−0.254559	+	0.254559i	0.568278	+	0.822837i	$0.307610\pi$
$24$	−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
$28$	−8.80954	−	1.83093i	−1.66485	−	0.346013i
$29$		−	5.22860i		−	0.970927i	−0.874257	−	0.485464i	$-0.838651\pi$
$29$		−	5.22860i		−	0.970927i	0.874257	−	0.485464i	$-0.161349\pi$
$30$	−5.61819	−	8.81293i	−1.02574	−	1.60901i
$31$			6.16828i			1.10786i	0.832565	+	0.553928i	$0.186872\pi$
$31$			6.16828i			1.10786i	−0.832565	+	0.553928i	$0.813128\pi$
$32$	5.61645	+	0.674922i	0.992857	+	0.119310i
$33$	−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	$0.496924\pi$
$38$	2.34008	+	7.83490i	0.379612	+	1.27099i
$39$	−9.10318			−1.45768
$40$	2.24345	+	5.91328i	0.354720	+	0.934972i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	6.01781	+	20.1484i	0.928568	+	3.10897i
$43$	6.78530	−	6.78530i	1.03475	−	1.03475i	0.0353737	−	0.999374i	$-0.488738\pi$
$43$	6.78530	−	6.78530i	1.03475	−	1.03475i	0.999374	−	0.0353737i	$-0.0112621\pi$
$44$	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	$-0.180795\pi$
$47$	2.09134	+	2.09134i	0.305054	+	0.305054i	−0.537934	+	0.842987i	$0.680795\pi$
$48$	−4.84908	−	12.2987i	−0.699904	−	1.77516i
$49$			13.2401i			1.89144i
$50$	−4.69421	+	5.28813i	−0.663862	+	0.747855i
$51$		−	11.7745i		−	1.64877i
$52$	5.39344	+	1.12095i	0.747935	+	0.155447i
$53$	−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
$58$	7.08509	−	2.11614i	0.930318	−	0.277862i
$59$	−1.21549			−0.158243			−0.0791214	−	0.996865i	$-0.525211\pi$
$59$	−1.21549			−0.158243			−0.0791214	+	0.996865i	$0.525211\pi$
$60$	9.66828	−	11.1798i	1.24817	−	1.44331i
$61$	−5.20011			−0.665806			−0.332903	−	0.942961i	$-0.608028\pi$
$61$	−5.20011			−0.665806			−0.332903	+	0.942961i	$0.608028\pi$
$62$	−8.35842	+	2.49644i	−1.06152	+	0.317049i
$63$	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	$-0.227073\pi$
$67$	0.833062	+	0.833062i	0.101775	+	0.101775i	−0.654386	+	0.756161i	$0.727073\pi$
$68$	−1.44989	+	6.97617i	−0.175825	+	0.845985i
$69$			5.70614i			0.686938i
$70$	11.9964	−	7.64764i	1.43385	−	0.914068i
$71$			1.23803i			0.146927i	0.997298	+	0.0734634i	$0.0234052\pi$
$71$			1.23803i			0.146927i	−0.997298	+	0.0734634i	$0.976595\pi$
$72$	−14.4383	+	17.1391i	−1.70157	+	2.01987i
$73$	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
$78$	−3.68427	−	12.3354i	−0.417161	−	1.39671i
$79$	1.85647			0.208869			0.104435	−	0.994532i	$-0.466697\pi$
$79$	1.85647			0.208869			0.104435	+	0.994532i	$0.466697\pi$
$80$	−7.10491	+	5.43326i	−0.794353	+	0.607457i
$81$	−30.0073			−3.33414
$82$	0.404723	+	1.35506i	0.0446942	+	0.149642i
$83$	−8.09356	+	8.09356i	−0.888383	+	0.888383i	−0.994368	−	0.105984i	$-0.966201\pi$
$83$	−8.09356	+	8.09356i	−0.888383	+	0.888383i	0.105984	+	0.994368i	$0.466201\pi$
$84$	−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
$88$	−5.48740	+	6.51387i	−0.584959	+	0.694381i
$89$			9.12162i			0.966890i	0.875375	+	0.483445i	$0.160615\pi$
$89$			9.12162i			0.966890i	−0.875375	+	0.483445i	$0.839385\pi$
$90$	−24.4630	−	5.41560i	−2.57863	−	0.570855i
$91$		−	12.3915i		−	1.29898i
$92$	0.702641	−	3.38076i	0.0732554	−	0.352469i
$93$	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	$0.337625\pi$
$98$	−17.9412	+	5.35856i	−1.81233	+	0.541297i
$99$	−23.8589			−2.39791
$100$	−9.06562	−	4.22073i	−0.906562	−	0.422073i
$101$	3.99668			0.397685			0.198842	−	0.980031i	$-0.436282\pi$
$101$	3.99668			0.397685			0.198842	+	0.980031i	$0.436282\pi$
$102$	15.9553	−	4.76543i	1.57981	−	0.471848i
$103$	1.08480	−	1.08480i	0.106888	−	0.106888i	−0.651640	−	0.758528i	$-0.725919\pi$
$103$	1.08480	−	1.08480i	0.106888	−	0.106888i	0.758528	+	0.651640i	$0.225919\pi$
$104$	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	$-0.324420\pi$
$107$	−3.38909	−	3.38909i	−0.327636	−	0.327636i	−0.851687	+	0.524051i	$0.824420\pi$
$108$	31.8616	+	6.62196i	3.06588	+	0.637198i
$109$			3.90535i			0.374064i	0.982354	+	0.187032i	$0.0598869\pi$
$109$			3.90535i			0.374064i	−0.982354	+	0.187032i	$0.940113\pi$
$110$	−9.29738	−	2.05825i	−0.886470	−	0.196246i
$111$			28.1549i			2.67234i
$112$	16.7413	−	6.60071i	1.58191	−	0.623708i
$113$	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
$118$	−0.491935	−	1.64706i	−0.0452863	−	0.151624i
$119$	16.0279			1.46927
$120$	19.0623	+	8.57642i	1.74014	+	0.782917i
$121$	1.93224			0.175658
$122$	−2.10460	−	7.04648i	−0.190542	−	0.637958i
$123$	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	$-0.969289\pi$
$127$	−12.3026	−	12.3026i	−1.09168	−	1.09168i	−0.0963329	−	0.995349i	$-0.530711\pi$
$128$	−10.1332	+	5.03167i	−0.895659	+	0.444741i
$129$		−	31.7145i		−	2.79231i
$130$	−7.34454	+	4.68209i	−0.644159	+	0.410647i
$131$			14.0266i			1.22551i	0.790272	+	0.612757i	$0.209939\pi$
$131$			14.0266i			1.22551i	−0.790272	+	0.612757i	$0.790061\pi$
$132$	19.4882	+	4.05033i	1.69623	+	0.352536i
$133$	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	$0.382973\pi$
$138$	−7.73218	+	2.30940i	−0.658207	+	0.196590i
$139$	6.90952			0.586058			0.293029	−	0.956104i	$-0.405337\pi$
$139$	6.90952			0.586058			0.293029	+	0.956104i	$0.405337\pi$
$140$	15.2183	+	13.1608i	1.28618	+	1.11229i
$141$	9.77495			0.823200
$142$	−1.67761	+	0.501058i	−0.140782	+	0.0420478i
$143$	−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
$148$	3.46693	−	16.6812i	0.284980	−	1.37118i
$149$			13.1848i			1.08014i	0.841620	+	0.540070i	$0.181602\pi$
$149$			13.1848i			1.08014i	−0.841620	+	0.540070i	$0.818398\pi$
$150$	1.38800	+	23.3288i	0.113329	+	1.90479i
$151$			5.46128i			0.444432i	0.974997	+	0.222216i	$0.0713291\pi$
$151$			5.46128i			0.444432i	−0.974997	+	0.222216i	$0.928671\pi$
$152$	−12.5073	−	10.5364i	−1.01447	−	0.854611i
$153$	−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	$0.413412\pi$
$158$	0.751356	+	2.51564i	0.0597747	+	0.200133i
$159$	−9.59590			−0.761004
$160$	−10.2379	−	7.42864i	−0.809380	−	0.587286i
$161$	−7.76736			−0.612154
$162$	−12.1446	−	40.6618i	−0.954172	−	3.19469i
$163$	−13.5013	+	13.5013i	−1.05751	+	1.05751i	−0.0592635	+	0.998242i	$0.518875\pi$
$163$	−13.5013	+	13.5013i	−1.05751	+	1.05751i	−0.998242	+	0.0592635i	$0.981125\pi$
$164$	−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	$-0.199714\pi$
$167$	2.87517	+	2.87517i	0.222487	+	0.222487i	−0.587058	+	0.809545i	$0.699714\pi$
$168$	−32.1640	−	27.0955i	−2.48150	−	2.09046i
$169$		−	5.41357i		−	0.416429i
$170$	−6.05607	−	9.49983i	−0.464480	−	0.728603i
$171$		−	45.8114i		−	3.50328i
$172$	−3.90526	+	18.7902i	−0.297773	+	1.43274i
$173$	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
$178$	−12.3604	+	3.69173i	−0.926450	+	0.276707i
$179$	−11.6172			−0.868309			−0.434154	−	0.900839i	$-0.642953\pi$
$179$	−11.6172			−0.868309			−0.434154	+	0.900839i	$0.642953\pi$
$180$	−2.56226	−	35.3408i	−0.190979	−	2.63415i
$181$	7.08888			0.526912			0.263456	−	0.964671i	$-0.415138\pi$
$181$	7.08888			0.526912			0.263456	+	0.964671i	$0.415138\pi$
$182$	16.7913	−	5.01513i	1.24465	−	0.371747i
$183$	−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
$188$	−5.79145	−	1.20367i	−0.422385	−	0.0877864i
$189$		−	73.2026i		−	5.32471i
$190$	3.95204	−	17.8519i	0.286711	−	1.29511i
$191$		−	6.47206i		−	0.468302i	−0.972200	−	0.234151i	$-0.924769\pi$
$191$		−	6.47206i		−	0.468302i	0.972200	−	0.234151i	$-0.0752309\pi$
$192$	21.5994	+	15.2496i	1.55880	+	1.10054i
$193$	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	$0.113221\pi$
$198$	−9.65623	−	32.3303i	−0.686238	−	2.29761i
$199$	9.81219			0.695567			0.347784	−	0.937575i	$-0.386934\pi$
$199$	9.81219			0.695567			0.347784	+	0.937575i	$0.386934\pi$
$200$	2.05030	−	13.9927i	0.144978	−	0.989435i
$201$	3.89374			0.274643
$202$	1.61755	+	5.41576i	0.113810	+	0.381052i
$203$	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
$208$	−10.2495	+	4.04113i	−0.710674	+	0.280202i
$209$		−	17.4110i		−	1.20434i
$210$	10.1631	−	45.9083i	0.701323	−	3.16797i
$211$		−	4.15341i		−	0.285932i	−0.989728	−	0.142966i	$-0.954336\pi$
$211$		−	4.15341i		−	0.285932i	0.989728	−	0.142966i	$-0.0456640\pi$
$212$	5.68536	+	1.18162i	0.390472	+	0.0811538i
$213$	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
$218$	−5.29200	+	1.58058i	−0.358419	+	0.107051i
$219$	16.6677			1.12630
$220$	−0.973807	−	13.4316i	−0.0656541	−	0.905556i
$221$	−9.81270			−0.660073
$222$	−38.1517	+	11.3949i	−2.56057	+	0.764777i
$223$	−12.8059	+	12.8059i	−0.857546	+	0.857546i	−0.991048	−	0.133502i	$-0.957378\pi$
$223$	−12.8059	+	12.8059i	−0.857546	+	0.857546i	0.133502	+	0.991048i	$0.457378\pi$
$224$	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	$-0.321658\pi$
$227$	−4.75627	−	4.75627i	−0.315685	−	0.315685i	−0.847107	+	0.531422i	$0.821658\pi$
$228$	−7.77704	+	37.4193i	−0.515047	+	2.47815i
$229$		−	13.5341i		−	0.894358i	−0.894445	−	0.447179i	$-0.852429\pi$
$229$		−	13.5341i		−	0.894358i	0.894445	−	0.447179i	$-0.147571\pi$
$230$	2.93487	+	4.60377i	0.193520	+	0.303564i
$231$		−	44.7745i		−	2.94595i
$232$	−9.52801	+	11.3103i	−0.625545	+	0.742559i
$233$	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
$238$	6.48685	+	21.7188i	0.420480	+	1.40782i
$239$	19.9288			1.28909			0.644545	−	0.764567i	$-0.277047\pi$
$239$	19.9288			1.28909			0.644545	+	0.764567i	$0.277047\pi$
$240$	−3.90665	+	29.3018i	−0.252173	+	1.89142i
$241$	−14.0234			−0.903330			−0.451665	−	0.892188i	$-0.649170\pi$
$241$	−14.0234			−0.903330			−0.451665	+	0.892188i	$0.649170\pi$
$242$	0.782022	+	2.61831i	0.0502703	+	0.168311i
$243$	−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
$248$	11.2404	−	13.3430i	0.713764	−	0.847281i
$249$			37.8294i			2.39734i
$250$	14.9235	−	5.22397i	0.943844	−	0.330393i
$251$		−	24.7699i		−	1.56346i	−0.623618	−	0.781730i	$-0.714338\pi$
$251$		−	24.7699i		−	1.56346i	0.623618	−	0.781730i	$-0.285662\pi$
$252$	−14.5068	+	69.7996i	−0.913842	+	4.39696i
$253$	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	$0.289007\pi$
$258$	42.9752	−	12.8356i	2.67552	−	0.799110i
$259$	−38.3252			−2.38141
$260$	−9.31704	−	8.05737i	−0.577818	−	0.499697i
$261$	−41.4272			−2.56428
$262$	−19.0070	+	5.67691i	−1.17426	+	0.350720i
$263$	0.105987	−	0.105987i	0.00653544	−	0.00653544i	−0.703832	−	0.710367i	$-0.748529\pi$
$263$	0.105987	−	0.105987i	0.00653544	−	0.00653544i	0.710367	+	0.703832i	$0.248529\pi$
$264$	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
$268$	−2.30696	−	0.479467i	−0.140920	−	0.0292881i
$269$		−	23.3185i		−	1.42175i	−0.703316	−	0.710877i	$-0.748298\pi$
$269$		−	23.3185i		−	1.42175i	0.703316	−	0.710877i	$-0.251702\pi$
$270$	−43.3877	+	27.6593i	−2.64049	+	1.68329i
$271$		−	7.66973i		−	0.465903i	−0.972488	−	0.232951i	$-0.925162\pi$
$271$		−	7.66973i		−	0.465903i	0.972488	−	0.232951i	$-0.0748383\pi$
$272$	−5.22702	−	13.2572i	−0.316935	−	0.803839i
$273$	−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	$0.0192530\pi$
$278$	2.79644	+	9.36285i	0.167720	+	0.561546i
$279$	48.8724			2.92591
$280$	−11.6745	+	25.9482i	−0.697684	+	1.55070i
$281$	26.0228			1.55239			0.776195	−	0.630493i	$-0.217147\pi$
$281$	26.0228			1.55239			0.776195	+	0.630493i	$0.217147\pi$
$282$	3.95615	+	13.2457i	0.235585	+	0.788769i
$283$	7.33094	−	7.33094i	0.435779	−	0.435779i	−0.454810	−	0.890589i	$-0.650293\pi$
$283$	7.33094	−	7.33094i	0.435779	−	0.435779i	0.890589	+	0.454810i	$0.150293\pi$
$284$	−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
$288$	5.34753	−	44.5001i	0.315106	−	2.62220i
$289$			4.30773i			0.253396i
$290$	−16.1434	−	3.57382i	−0.947975	−	0.209862i
$291$			17.6957i			1.03734i
$292$	−9.87525	−	2.05242i	−0.577905	−	0.120109i
$293$	−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
$298$	−17.8662	+	5.33619i	−1.03496	+	0.309117i
$299$	4.75539			0.275011
$300$	−31.0503	+	11.3225i	−1.79269	+	0.653706i
$301$	43.1708			2.48832
$302$	−7.40038	+	2.21030i	−0.425844	+	0.127189i
$303$	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	$-0.310147\pi$
$307$	−4.65435	−	4.65435i	−0.265638	−	0.265638i	−0.827340	+	0.561702i	$0.810147\pi$
$308$	−5.51343	+	26.5279i	−0.314157	+	1.51157i
$309$		−	5.07036i		−	0.288443i
$310$	19.0447	+	4.21610i	1.08167	+	0.239459i
$311$		−	30.7905i		−	1.74597i	−0.487746	−	0.872986i	$-0.662181\pi$
$311$		−	30.7905i		−	1.74597i	0.487746	−	0.872986i	$-0.337819\pi$
$312$	19.6917	+	16.5886i	1.11482	+	0.939145i
$313$	−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	$0.228270\pi$
$318$	−3.88368	−	13.0031i	−0.217786	−	0.729175i
$319$	−15.7447			−0.881537
$320$	5.92276	−	16.8796i	0.331092	−	0.943598i
$321$	−15.8407			−0.884139
$322$	−3.14363	−	10.5253i	−0.175188	−	0.586551i
$323$	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
$328$	−2.16316	−	1.82229i	−0.119441	−	0.100619i
$329$			13.3060i			0.733581i
$330$	−26.5381	+	16.9179i	−1.46088	+	0.931299i
$331$			22.0919i			1.21428i	0.794595	+	0.607139i	$0.207683\pi$
$331$			22.0919i			1.21428i	−0.794595	+	0.607139i	$0.792317\pi$
$332$	4.65822	−	22.4131i	0.255653	−	1.23008i
$333$	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	$0.0267187\pi$
$338$	7.33574	−	2.19100i	0.399012	−	0.119175i
$339$	27.9070			1.51570
$340$	10.4218	−	12.0512i	0.565204	−	0.653566i
$341$	18.5744			1.00586
$342$	62.0773	−	18.5409i	3.35676	−	1.00258i
$343$	−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	$-0.0913098\pi$
$347$	12.5962	+	12.5962i	0.676197	+	0.676197i	−0.282940	+	0.959138i	$0.591310\pi$
$348$	33.8382	+	7.03277i	1.81392	+	0.376996i
$349$		−	27.4748i		−	1.47069i	−0.677692	−	0.735346i	$-0.737020\pi$
$349$		−	27.4748i		−	1.47069i	0.677692	−	0.735346i	$-0.262980\pi$
$350$	−31.7558	+	1.88938i	−1.69742	+	0.100992i
$351$			44.8166i			2.39213i
$352$	2.03237	−	16.9127i	0.108326	−	0.901447i
$353$	−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
$358$	−4.70174	−	15.7420i	−0.248495	−	0.831992i
$359$	−25.1352			−1.32658			−0.663292	−	0.748360i	$-0.730841\pi$
$359$	−25.1352			−1.32658			−0.663292	+	0.748360i	$0.730841\pi$
$360$	46.8520	−	17.7753i	2.46932	−	0.936838i
$361$	14.4308			0.759517
$362$	2.86903	+	9.60589i	0.150793	+	0.504874i
$363$	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	$-0.128672\pi$
$367$	10.0784	+	10.0784i	0.526088	+	0.526088i	−0.393315	+	0.919404i	$0.628672\pi$
$368$	2.53310	+	6.42468i	0.132047	+	0.334909i
$369$		−	7.92318i		−	0.412464i
$370$	14.4811	+	22.7156i	0.752834	+	1.18093i
$371$		−	13.0622i		−	0.678157i
$372$	−39.9196	−	8.29668i	−2.06973	−	0.430163i
$373$	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
$378$	99.1942	−	29.6268i	5.10200	−	1.52384i
$379$	−15.3174			−0.786804			−0.393402	−	0.919367i	$-0.628702\pi$
$379$	−15.3174			−0.786804			−0.393402	+	0.919367i	$0.628702\pi$
$380$	25.7899	−	1.86981i	1.32300	−	0.0959190i
$381$	−57.5026			−2.94595
$382$	8.77005	−	2.61939i	0.448715	−	0.134020i
$383$	2.76517	−	2.76517i	0.141294	−	0.141294i	−0.632922	−	0.774216i	$-0.718145\pi$
$383$	2.76517	−	2.76517i	0.141294	−	0.141294i	0.774216	+	0.632922i	$0.218145\pi$
$384$	−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
$388$	2.17901	−	10.4843i	0.110622	−	0.532260i
$389$			21.6900i			1.09973i	0.835254	+	0.549864i	$0.185321\pi$
$389$			21.6900i			1.09973i	−0.835254	+	0.549864i	$0.814679\pi$
$390$	−6.22215	+	28.1063i	−0.315071	+	1.42322i
$391$			6.15088i			0.311063i
$392$	24.1272	−	28.6404i	1.21861	−	1.44656i
$393$	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	$0.413488\pi$
$398$	3.97122	+	13.2961i	0.199059	+	0.666475i
$399$	85.9714			4.30396
$400$	19.7908	−	2.88489i	0.989542	−	0.144245i
$401$	−28.3914			−1.41780			−0.708900	−	0.705309i	$-0.750808\pi$
$401$	−28.3914			−1.41780			−0.708900	+	0.705309i	$0.750808\pi$
$402$	1.57589	+	5.27627i	0.0785981	+	0.263156i
$403$	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
$408$	−21.4566	+	25.4703i	−1.06226	+	1.26097i
$409$		−	21.1381i		−	1.04521i	−0.852574	−	0.522606i	$-0.824960\pi$
$409$		−	21.1381i		−	1.04521i	0.852574	−	0.522606i	$-0.175040\pi$
$410$	0.683514	−	3.08752i	0.0337563	−	0.152482i
$411$			31.3887i			1.54829i
$412$	−0.624353	+	3.00408i	−0.0307597	+	0.148000i
$413$	−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
$418$	23.5930	−	7.04663i	1.15397	−	0.344662i
$419$	−22.3383			−1.09130			−0.545649	−	0.838014i	$-0.683717\pi$
$419$	−22.3383			−1.09130			−0.545649	+	0.838014i	$0.683717\pi$
$420$	66.3219	−	4.80843i	3.23618	−	0.234628i
$421$	−7.25093			−0.353389			−0.176694	−	0.984266i	$-0.556540\pi$
$421$	−7.25093			−0.353389			−0.176694	+	0.984266i	$0.556540\pi$
$422$	5.62813	−	1.68098i	0.273973	−	0.0818288i
$423$	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
$428$	9.38525	+	1.95058i	0.453653	+	0.0942850i
$429$			27.4122i			1.32347i
$430$	−16.3119	−	25.5876i	−0.786631	−	1.23394i
$431$		−	7.16120i		−	0.344943i	−0.985015	−	0.172471i	$-0.944825\pi$
$431$		−	7.16120i		−	0.344943i	0.985015	−	0.172471i	$-0.0551752\pi$
$432$	−60.5486	+	23.8729i	−2.91315	+	1.14859i
$433$	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
$438$	6.74580	+	22.5858i	0.322327	+	1.07919i
$439$	11.5201			0.549824			0.274912	−	0.961469i	$-0.411351\pi$
$439$	11.5201			0.549824			0.274912	+	0.961469i	$0.411351\pi$
$440$	17.8065	−	6.75563i	0.848892	−	0.322062i
$441$	104.904			4.99541
$442$	−3.97142	−	13.2968i	−0.188901	−	0.632466i
$443$	6.69755	−	6.69755i	0.318210	−	0.318210i	−0.529869	−	0.848079i	$-0.677759\pi$
$443$	6.69755	−	6.69755i	0.318210	−	0.318210i	0.848079	+	0.529869i	$0.177759\pi$
$444$	−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
$448$	−20.7582	+	29.4018i	−0.980731	+	1.38910i
$449$			16.7618i			0.791040i	0.918457	+	0.395520i	$0.129436\pi$
$449$			16.7618i			0.791040i	−0.918457	+	0.395520i	$0.870564\pi$
$450$	41.8988	+	37.1931i	1.97513	+	1.75330i
$451$		−	3.01127i		−	0.141795i
$452$	−16.5343	−	3.43640i	−0.777707	−	0.161635i
$453$	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	$0.961116\pi$
$458$	18.3396	−	5.47756i	0.856951	−	0.255949i
$459$	−57.9682			−2.70573
$460$	−5.05059	+	5.84019i	−0.235485	+	0.272300i
$461$	23.3344			1.08679			0.543395	−	0.839477i	$-0.317139\pi$
$461$	23.3344			1.08679			0.543395	+	0.839477i	$0.317139\pi$
$462$	60.6723	−	18.1213i	2.82273	−	0.843078i
$463$	22.3751	−	22.3751i	1.03986	−	1.03986i	0.0406893	−	0.999172i	$-0.487045\pi$
$463$	22.3751	−	22.3751i	1.03986	−	1.03986i	0.999172	−	0.0406893i	$-0.0129554\pi$
$464$	−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	$-0.211915\pi$
$467$	3.64786	+	3.64786i	0.168803	+	0.168803i	−0.617650	+	0.786453i	$0.711915\pi$
$468$	8.88146	−	42.7332i	0.410545	−	1.97534i
$469$			5.30028i			0.244744i
$470$	7.88653	−	5.02761i	0.363779	−	0.231906i
$471$			40.6763i			1.87427i
$472$	2.62929	+	2.21496i	0.121023	+	0.101952i
$473$	−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
$478$	8.06566	+	27.0049i	0.368915	+	1.23517i
$479$	37.5765			1.71691			0.858456	−	0.512887i	$-0.171424\pi$
$479$	37.5765			1.71691			0.858456	+	0.512887i	$0.171424\pi$
$480$	−41.2869	+	6.56534i	−1.88448	+	0.299665i
$481$	23.4638			1.06986
$482$	−5.67561	−	19.0027i	−0.258517	−	0.865548i
$483$	−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	$-0.354111\pi$
$487$	−10.0266	−	10.0266i	−0.454350	−	0.454350i	−0.896796	+	0.442445i	$0.854111\pi$
$488$	11.2487	+	9.47609i	0.509204	+	0.428962i
$489$			63.1054i			2.85372i
$490$	40.8791	+	9.04977i	1.84673	+	0.408827i
$491$		−	35.8582i		−	1.61826i	−0.587630	−	0.809130i	$-0.699939\pi$
$491$		−	35.8582i		−	1.61826i	0.587630	−	0.809130i	$-0.300061\pi$
$492$	−1.34506	+	6.47175i	−0.0606398	+	0.291769i
$493$	−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
$498$	−51.2612	+	15.3104i	−2.29707	+	0.686076i
$499$	24.3435			1.08976			0.544882	−	0.838513i	$-0.316575\pi$
$499$	24.3435			1.08976			0.544882	+	0.838513i	$0.316575\pi$
$500$	13.1187	+	18.1080i	0.586685	+	0.809815i
$501$	13.4386			0.600391
$502$	33.5647	−	10.0249i	1.49807	−	0.447434i
$503$	−8.56836	+	8.56836i	−0.382044	+	0.382044i	−0.871838	−	0.489794i	$-0.837072\pi$
$503$	−8.56836	+	8.56836i	−0.382044	+	0.382044i	0.489794	+	0.871838i	$0.337072\pi$
$504$	−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
$508$	34.0691	+	7.08074i	1.51157	+	0.314157i
$509$		−	16.9492i		−	0.751261i	−0.926769	−	0.375631i	$-0.877426\pi$
$509$		−	16.9492i		−	0.751261i	0.926769	−	0.375631i	$-0.122574\pi$
$510$	−36.3542	−	8.04807i	−1.60979	−	0.356374i
$511$			22.6886i			1.00368i
$512$	11.4278	−	19.5296i	0.505042	−	0.863095i
$513$	−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
$518$	−15.5111	−	51.9332i	−0.681519	−	2.28181i
$519$	51.0057			2.23890
$520$	7.14744	−	15.8862i	0.313436	−	0.696656i
$521$	−26.8387			−1.17583			−0.587913	−	0.808924i	$-0.700050\pi$
$521$	−26.8387			−1.17583			−0.587913	+	0.808924i	$0.700050\pi$
$522$	−16.7665	−	56.1365i	−0.733851	−	2.45703i
$523$	−9.01153	+	9.01153i	−0.394047	+	0.394047i	−0.876127	−	0.482080i	$-0.839881\pi$
$523$	−9.01153	+	9.01153i	−0.394047	+	0.394047i	0.482080	+	0.876127i	$0.339881\pi$
$524$	−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
$528$	−37.0347	+	14.6019i	−1.61173	+	0.635466i
$529$			20.0192i			0.870399i
$530$	−7.74207	+	4.93552i	−0.336294	+	0.214385i
$531$			9.63052i			0.417929i
$532$	−50.9362	−	10.5863i	−2.20837	−	0.458976i
$533$	−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
$538$	31.5981	−	9.43753i	1.36229	−	0.406881i
$539$	39.8695			1.71730
$540$	−55.0402	−	47.5987i	−2.36855	−	2.04832i
$541$	−31.1907			−1.34099			−0.670496	−	0.741914i	$-0.733918\pi$
$541$	−31.1907			−1.34099			−0.670496	+	0.741914i	$0.733918\pi$
$542$	10.3930	−	3.10412i	0.446417	−	0.133333i
$543$	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	$0.147222\pi$
$547$	31.3664	+	31.3664i	1.34113	+	1.34113i	0.446198	+	0.894934i	$0.352778\pi$
$548$	3.86513	−	18.5971i	0.165110	−	0.794429i
$549$			41.2014i			1.75843i
$550$	15.9240	+	14.1356i	0.679002	+	0.602742i
$551$		−	30.2315i		−	1.28790i
$552$	10.3982	−	12.3433i	0.442577	−	0.525366i
$553$	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	$0.871530\pi$
$558$	19.7798	+	66.2253i	0.837345	+	2.80354i
$559$	−26.4303			−1.11788
$560$	−39.8864	−	5.31784i	−1.68551	−	0.224720i
$561$	−35.4564			−1.49697
$562$	10.5320	+	35.2626i	0.444267	+	1.48746i
$563$	−23.4668	+	23.4668i	−0.989006	+	0.989006i	−0.999940	−	0.0109339i	$-0.996520\pi$
$563$	−23.4668	+	23.4668i	−0.989006	+	0.989006i	0.0109339	+	0.999940i	$0.496520\pi$
$564$	−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
$568$	2.25604	−	2.67805i	0.0946613	−	0.112369i
$569$		−	32.7019i		−	1.37094i	−0.728102	−	0.685468i	$-0.759597\pi$
$569$		−	32.7019i		−	1.37094i	0.728102	−	0.685468i	$-0.240403\pi$
$570$	−32.4840	−	50.9559i	−1.36061	−	2.13431i
$571$			2.32916i			0.0974724i	0.998812	+	0.0487362i	$0.0155194\pi$
$571$			2.32916i			0.0974724i	−0.998812	+	0.0487362i	$0.984481\pi$
$572$	3.37547	−	16.2411i	0.141136	−	0.679075i
$573$	−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	$0.0364501\pi$
$578$	−5.83725	+	1.74344i	−0.242797	+	0.0725174i
$579$	59.8333			2.48659
$580$	−1.69086	−	23.3218i	−0.0702093	−	0.968385i
$581$	−51.4945			−2.13635
$582$	−23.9788	+	7.16185i	−0.993953	+	0.296868i
$583$	−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	$-0.175909\pi$
$587$	7.90351	+	7.90351i	0.326213	+	0.326213i	−0.524932	+	0.851144i	$0.675909\pi$
$588$	−85.6865	−	17.8086i	−3.53365	−	0.734416i
$589$			35.6646i			1.46954i
$590$	−0.830801	+	3.75284i	−0.0342036	+	0.154502i
$591$		−	38.6508i		−	1.58988i
$592$	12.4987	+	31.7002i	0.513692	+	1.30287i
$593$	−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
$598$	1.92462	+	6.44386i	0.0787034	+	0.263509i
$599$	−37.3899			−1.52771			−0.763855	−	0.645388i	$-0.776696\pi$
$599$	−37.3899			−1.52771			−0.763855	+	0.645388i	$0.776696\pi$
$600$	−27.9095	−	37.4926i	−1.13940	−	1.53063i
$601$	−27.0507			−1.10342			−0.551710	−	0.834036i	$-0.686025\pi$
$601$	−27.0507			−1.10342			−0.551710	+	0.834036i	$0.686025\pi$
$602$	17.4722	+	58.4992i	0.712114	+	2.38425i
$603$	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	$-0.364191\pi$
$607$	−12.2331	−	12.2331i	−0.496525	−	0.496525i	−0.910354	+	0.413829i	$0.864191\pi$
$608$	32.4740	+	3.90236i	1.31699	+	0.158261i
$609$		−	77.7439i		−	3.15034i
$610$	−3.55434	+	16.0555i	−0.143911	+	0.650067i
$611$		−	8.14627i		−	0.329563i
$612$	55.2734	+	11.4878i	2.23430	+	0.464365i
$613$	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	$0.919996\pi$
$618$	6.87067	−	2.05209i	0.276379	−	0.0825473i
$619$	27.5236			1.10627			0.553134	−	0.833093i	$-0.313432\pi$
$619$	27.5236			1.10627			0.553134	+	0.833093i	$0.313432\pi$
$620$	1.99474	+	27.5132i	0.0801108	+	1.10496i
$621$	28.0923			1.12731
$622$	41.7232	−	12.4616i	1.67295	−	0.499666i
$623$	−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
$628$	5.00879	−	24.0998i	0.199872	−	0.961688i
$629$			30.3493i			1.21011i
$630$	−60.5937	−	95.0499i	−2.41411	−	3.78688i
$631$		−	39.1564i		−	1.55879i	−0.626531	−	0.779396i	$-0.715526\pi$
$631$		−	39.1564i		−	1.55879i	0.626531	−	0.779396i	$-0.284474\pi$
$632$	−4.01585	−	3.38302i	−0.159742	−	0.134569i
$633$	−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
$638$	−6.37226	−	21.3351i	−0.252280	−	0.844666i
$639$	9.80911			0.388042
$640$	25.2700	+	1.19415i	0.998885	+	0.0472030i
$641$	−0.646836			−0.0255485			−0.0127742	−	0.999918i	$-0.504066\pi$
$641$	−0.646836			−0.0255485			−0.0127742	+	0.999918i	$0.504066\pi$
$642$	−6.41108	−	21.4651i	−0.253025	−	0.847160i
$643$	20.4305	−	20.4305i	0.805700	−	0.805700i	−0.178280	−	0.983980i	$-0.557053\pi$
$643$	20.4305	−	20.4305i	0.805700	−	0.805700i	0.983980	+	0.178280i	$0.0570531\pi$
$644$	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	$-0.172602\pi$
$647$	8.66078	+	8.66078i	0.340490	+	0.340490i	−0.516061	+	0.856552i	$0.672602\pi$
$648$	64.9106	+	54.6818i	2.54993	+	2.14811i
$649$			3.66016i			0.143674i
$650$	19.4418	−	1.15673i	0.762570	−	0.0453707i
$651$			91.7159i			3.59463i
$652$	7.77065	−	37.3886i	0.304322	−	1.46425i
$653$	−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
$658$	−18.0304	+	5.38523i	−0.702899	+	0.209938i
$659$	−25.9600			−1.01126			−0.505630	−	0.862751i	$-0.668740\pi$
$659$	−25.9600			−1.01126			−0.505630	+	0.862751i	$0.668740\pi$
$660$	−33.6654	−	29.1138i	−1.31042	−	1.13325i
$661$	1.95766			0.0761442			0.0380721	−	0.999275i	$-0.487878\pi$
$661$	1.95766			0.0761442			0.0380721	+	0.999275i	$0.487878\pi$
$662$	−29.9359	+	8.94109i	−1.16349	+	0.347505i
$663$	−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
$668$	−7.96206	−	1.65479i	−0.308061	−	0.0640259i
$669$			59.8549i			2.31412i
$670$	3.14151	−	2.00269i	0.121367	−	0.0773707i
$671$			15.6589i			0.604507i
$672$	83.5107	+	10.0354i	3.22150	+	0.387123i
$673$	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	$0.0222382\pi$
$678$	11.2946	+	37.8158i	0.433766	+	1.45231i
$679$	−24.0879			−0.924409
$680$	20.5481	+	9.24488i	0.787982	+	0.354525i
$681$	−22.2308			−0.851888
$682$	7.51748	+	25.1695i	0.287859	+	0.963789i
$683$	−7.32634	+	7.32634i	−0.280335	+	0.280335i	−0.833242	−	0.552908i	$-0.813518\pi$
$683$	−7.32634	+	7.32634i	−0.280335	+	0.280335i	0.552908	+	0.833242i	$0.313518\pi$
$684$	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
$688$	−14.0789	−	35.7082i	−0.536753	−	1.36136i
$689$			7.99705i			0.304663i
$690$	17.6178	+	3.90022i	0.670700	+	0.148479i
$691$			31.7570i			1.20809i	0.796948	+	0.604047i	$0.206446\pi$
$691$			31.7570i			1.20809i	−0.796948	+	0.604047i	$0.793554\pi$
$692$	−30.2198	−	6.28073i	−1.14878	−	0.238758i
$693$	−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
$698$	37.2301	−	11.1197i	1.40918	−	0.420886i
$699$	35.2757			1.33425
$700$	−15.4126	−	42.2665i	−0.582540	−	1.59753i
$701$	−11.5623			−0.436703			−0.218351	−	0.975870i	$-0.570068\pi$
$701$	−11.5623			−0.436703			−0.218351	+	0.975870i	$0.570068\pi$
$702$	−60.7294	+	18.1383i	−2.29208	+	0.684587i
$703$	−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
$708$	1.63490	−	7.86632i	0.0614432	−	0.295635i
$709$		−	4.13510i		−	0.155297i	−0.996981	−	0.0776485i	$-0.975259\pi$
$709$		−	4.13510i		−	0.155297i	0.996981	−	0.0776485i	$-0.0247412\pi$
$710$	3.82244	+	0.846208i	0.143454	+	0.0317576i
$711$		−	14.7091i		−	0.551636i
$712$	16.6222	−	19.7315i	0.622943	−	0.739471i
$713$	−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
$718$	−10.1728	−	34.0598i	−0.379645	−	1.27110i
$719$	−51.6984			−1.92802			−0.964012	−	0.265859i	$-0.914344\pi$
$719$	−51.6984			−1.92802			−0.964012	+	0.265859i	$0.914344\pi$
$720$	43.0487	+	56.2935i	1.60433	+	2.09793i
$721$	6.90193			0.257041
$722$	5.84049	+	19.5547i	0.217360	+	0.727751i
$723$	−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	$-0.324669\pi$
$727$	−8.86305	−	8.86305i	−0.328712	−	0.328712i	−0.852097	+	0.523384i	$0.824669\pi$
$728$	−22.5809	+	26.8049i	−0.836904	+	0.993455i
$729$			76.4226i			2.83047i
$730$	13.4477	−	8.57279i	0.497720	−	0.317293i
$731$		−	34.1864i		−	1.26443i
$732$	6.99444	−	33.6538i	0.258522	−	1.24388i
$733$	−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
$738$	10.7364	−	3.20669i	0.395213	−	0.118040i
$739$	−47.0284			−1.72997			−0.864984	−	0.501799i	$-0.832672\pi$
$739$	−47.0284			−1.72997			−0.864984	+	0.501799i	$0.832672\pi$
$740$	−24.9203	+	28.8163i	−0.916089	+	1.05931i
$741$	−52.6341			−1.93356
$742$	17.7002	−	5.28658i	0.649793	−	0.194077i
$743$	−36.8959	+	36.8959i	−1.35358	+	1.35358i	−0.471958	+	0.881621i	$0.656453\pi$
$743$	−36.8959	+	36.8959i	−1.35358	+	1.35358i	−0.881621	+	0.471958i	$0.843547\pi$
$744$	−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
$748$	21.0071	+	4.36602i	0.768097	+	0.159637i
$749$		−	21.5628i		−	0.787887i
$750$	22.6678	−	47.0847i	0.827711	−	1.71929i
$751$		−	18.8007i		−	0.686048i	−0.939327	−	0.343024i	$-0.888549\pi$
$751$		−	18.8007i		−	0.686048i	0.939327	−	0.343024i	$-0.111451\pi$
$752$	11.0059	−	4.33935i	0.401342	−	0.158240i
$753$	−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	$0.462045\pi$
$758$	−6.19932	−	20.7561i	−0.225169	−	0.753896i
$759$	17.1827			0.623694
$760$	12.9715	+	34.1903i	0.470525	+	1.24021i
$761$	2.45207			0.0888874			0.0444437	−	0.999012i	$-0.485848\pi$
$761$	2.45207			0.0888874			0.0444437	+	0.999012i	$0.485848\pi$
$762$	−23.2726	−	77.9197i	−0.843079	−	2.82273i
$763$	−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
$768$	−52.8493	−	1.81201i	−1.90704	−	0.0653852i
$769$			0.844874i			0.0304669i	0.999884	+	0.0152335i	$0.00484915\pi$
$769$			0.844874i			0.0304669i	−0.999884	+	0.0152335i	$0.995151\pi$
$770$	−23.0291	−	36.1245i	−0.829912	−	1.30184i
$771$			12.9532i			0.466496i
$772$	−35.4499	−	7.36774i	−1.27587	−	0.265171i
$773$	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
$778$	−29.3914	+	8.77845i	−1.05373	+	0.314723i
$779$	5.78194			0.207159
$780$	−40.6041	+	2.94385i	−1.45386	+	0.105407i
$781$	3.72804			0.133400
$782$	−8.33484	+	2.48940i	−0.298053	+	0.0890209i
$783$	−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	$-0.0924041\pi$
$787$	18.8498	+	18.8498i	0.671923	+	0.671923i	−0.286236	+	0.958159i	$0.592404\pi$
$788$	−4.75938	+	22.8998i	−0.169546	+	0.815771i
$789$		−	0.495384i		−	0.0176361i
$790$	1.26892	−	5.73190i	0.0451462	−	0.203932i
$791$			37.9878i			1.35069i
$792$	51.6106	+	43.4777i	1.83390	+	1.54491i
$793$	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	$0.232920\pi$
$798$	34.7946	+	116.497i	1.23172	+	4.12394i
$799$	10.5368			0.372766
$800$	11.9190	+	25.6503i	0.421401	+	0.906874i
$801$	72.2722			2.55361
$802$	−11.4907	−	38.4722i	−0.405750	−	1.35850i
$803$	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
$808$	−8.64547	−	7.28310i	−0.304147	−	0.256219i
$809$		−	4.94286i		−	0.173782i	−0.996218	−	0.0868909i	$-0.972307\pi$
$809$		−	4.94286i		−	0.173782i	0.996218	−	0.0868909i	$-0.0276932\pi$
$810$	−20.5104	+	92.6482i	−0.720661	+	3.25533i
$811$		−	24.8926i		−	0.874099i	−0.899437	−	0.437050i	$-0.856023\pi$
$811$		−	24.8926i		−	0.874099i	0.899437	−	0.437050i	$-0.143977\pi$
$812$	−9.57321	+	46.0616i	−0.335954	+	1.61644i
$813$	−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
$818$	28.6435	−	8.55508i	1.00150	−	0.299122i
$819$	−98.1803			−3.43070
$820$	4.46043	−	0.323387i	0.155765	−	0.0112932i
$821$	3.69769			0.129050			0.0645251	−	0.997916i	$-0.479447\pi$
$821$	3.69769			0.129050			0.0645251	+	0.997916i	$0.479447\pi$
$822$	−42.5337	+	12.7037i	−1.48353	+	0.443093i
$823$	−4.06784	+	4.06784i	−0.141796	+	0.141796i	−0.774442	−	0.632645i	$-0.781969\pi$
$823$	−4.06784	+	4.06784i	−0.141796	+	0.141796i	0.632645	+	0.774442i	$0.281969\pi$
$824$	−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	$-0.279431\pi$
$827$	−3.75497	−	3.75497i	−0.130573	−	0.130573i	−0.769373	+	0.638800i	$0.779431\pi$
$828$	−26.7864	−	5.56715i	−0.930892	−	0.193472i
$829$			46.9114i			1.62930i	0.579952	+	0.814651i	$0.303071\pi$
$829$			46.9114i			1.62930i	−0.579952	+	0.814651i	$0.696929\pi$
$830$	19.4570	+	30.5211i	0.675362	+	1.05940i
$831$		−	72.9464i		−	2.53048i
$832$	12.7087	−	18.0006i	0.440595	−	0.624057i
$833$	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
$838$	−9.04083	−	30.2698i	−0.312310	−	1.04565i
$839$	24.3808			0.841717			0.420859	−	0.907126i	$-0.361729\pi$
$839$	24.3808			0.841717			0.420859	+	0.907126i	$0.361729\pi$
$840$	33.3578	+	87.9244i	1.15095	+	3.03368i
$841$	1.66171			0.0573004
$842$	−2.93462	−	9.82547i	−0.101134	−	0.338608i
$843$	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
$848$	−10.8043	+	4.25986i	−0.371020	+	0.146284i
$849$		−	34.2649i		−	1.17597i
$850$	1.49618	+	25.1471i	0.0513185	+	0.862537i
$851$		−	14.7078i		−	0.504175i
$852$	−8.01220	−	1.66522i	−0.274493	−	0.0570494i
$853$	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	$0.130593\pi$
$858$	−37.1452	+	11.0943i	−1.26812	+	0.378754i
$859$	−46.7493			−1.59507			−0.797533	−	0.603276i	$-0.793862\pi$
$859$	−46.7493			−1.59507			−0.797533	+	0.603276i	$0.793862\pi$
$860$	28.0710	−	32.4596i	0.957215	−	1.10686i
$861$	14.8690			0.506733
$862$	9.70389	−	2.89830i	0.330516	−	0.0987166i
$863$	35.1643	−	35.1643i	1.19701	−	1.19701i	0.221946	−	0.975059i	$-0.428759\pi$
$863$	35.1643	−	35.1643i	1.19701	−	1.19701i	0.975059	−	0.221946i	$-0.0712410\pi$
$864$	−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
$868$	11.2937	−	54.3397i	0.383333	−	1.84441i
$869$		−	5.59034i		−	0.189639i
$870$	−46.0793	+	29.3753i	−1.56224	+	0.995915i
$871$		−	3.24497i		−	0.109952i
$872$	7.11666	−	8.44790i	0.241001	−	0.286082i
$873$	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	$0.320811\pi$
$878$	4.66245	+	15.6105i	0.157350	+	0.526828i
$879$	−3.08648			−0.104104
$880$	16.3610	+	21.3948i	0.551530	+	0.721219i
$881$	41.6557			1.40341			0.701707	−	0.712465i	$-0.252421\pi$
$881$	41.6557			1.40341			0.701707	+	0.712465i	$0.252421\pi$
$882$	42.4569	+	142.151i	1.42960	+	4.78647i
$883$	13.9474	−	13.9474i	0.469368	−	0.469368i	−0.432342	−	0.901710i	$-0.642313\pi$
$883$	13.9474	−	13.9474i	0.469368	−	0.469368i	0.901710	+	0.432342i	$0.142313\pi$
$884$	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	$-0.0763969\pi$
$887$	21.8492	+	21.8492i	0.733626	+	0.733626i	−0.237710	+	0.971336i	$0.576397\pi$
$888$	51.3062	−	60.9035i	1.72172	−	2.04379i
$889$		−	78.2743i		−	2.62524i
$890$	28.1632	+	6.23475i	0.944033	+	0.208989i
$891$			90.3600i			3.02718i
$892$	7.37040	−	35.4627i	0.246779	−	1.18738i
$893$	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
$898$	−22.7134	+	6.78390i	−0.757954	+	0.226382i
$899$	32.2515			1.07565
$900$	−33.4416	+	71.8285i	−1.11472	+	2.39428i
$901$	−10.3438			−0.344602
$902$	4.08047	−	1.21873i	0.135865	−	0.0405793i
$903$	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	$-0.00629204\pi$
$907$	29.5153	+	29.5153i	0.980039	+	0.980039i	−0.0197657	+	0.999805i	$0.506292\pi$
$908$	13.1713	+	2.73746i	0.437105	+	0.0908457i
$909$		−	31.6664i		−	1.05031i
$910$	−38.2591	−	8.46978i	−1.26828	−	0.280770i
$911$		−	4.03257i		−	0.133605i	−0.997766	−	0.0668024i	$-0.978720\pi$
$911$		−	4.03257i		−	0.133605i	0.997766	−	0.0668024i	$-0.0212797\pi$
$912$	−28.0371	−	71.1102i	−0.928400	−	2.35469i
$913$	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
$918$	−23.4611	−	78.5507i	−0.774331	−	2.59256i
$919$	−9.38703			−0.309650			−0.154825	−	0.987942i	$-0.549481\pi$
$919$	−9.38703			−0.309650			−0.154825	+	0.987942i	$0.549481\pi$
$920$	−9.95793	−	4.48022i	−0.328303	−	0.147708i
$921$	−21.7545			−0.716835
$922$	9.44396	+	31.6196i	0.311020	+	1.04134i
$923$	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
$928$	3.52890	−	29.3662i	0.115842	−	0.963992i
$929$		−	9.60703i		−	0.315196i	−0.987503	−	0.157598i	$-0.949625\pi$
$929$		−	9.60703i		−	0.315196i	0.987503	−	0.157598i	$-0.0503751\pi$
$930$	54.3606	−	34.6545i	1.78256	−	1.13637i
$931$			76.5533i			2.50893i
$932$	−20.9001	−	4.34377i	−0.684606	−	0.142285i
$933$	−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	$0.428637\pi$
$938$	−7.18222	+	2.14514i	−0.234508	+	0.0700414i
$939$	−78.2281			−2.55288
$940$	10.0046	+	8.65197i	0.326314	+	0.282196i
$941$	10.8604			0.354038			0.177019	−	0.984207i	$-0.443355\pi$
$941$	10.8604			0.354038			0.177019	+	0.984207i	$0.443355\pi$
$942$	−55.1190	+	16.4626i	−1.79587	+	0.536382i
$943$	−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	$-0.0618180\pi$
$947$	24.2560	+	24.2560i	0.788213	+	0.788213i	−0.192988	+	0.981201i	$0.561818\pi$
$948$	−2.49706	+	12.0146i	−0.0811006	+	0.390216i
$949$		−	13.8905i		−	0.450906i
$950$	−27.1417	+	30.5757i	−0.880592	+	0.992006i
$951$		−	8.02785i		−	0.260321i
$952$	−34.6709	−	29.2074i	−1.12369	−	0.946616i
$953$	−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
$958$	15.2081	+	50.9185i	0.491350	+	1.64510i
$959$	−42.7272			−1.37973
$960$	−25.6062	−	53.2892i	−0.826437	−	1.71990i
$961$	−7.04768			−0.227345
$962$	9.49632	+	31.7949i	0.306174	+	1.02511i
$963$	−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	$-0.933675\pi$
$967$	−36.8567	−	36.8567i	−1.18523	−	1.18523i	−0.206863	−	0.978370i	$-0.566325\pi$
$968$	−4.17975	−	3.52109i	−0.134342	−	0.113172i
$969$		−	68.0797i		−	2.18704i
$970$	9.10153	+	14.2771i	0.292232	+	0.458409i
$971$		−	25.5008i		−	0.818360i	−0.912454	−	0.409180i	$-0.865815\pi$
$971$		−	25.5008i		−	0.818360i	0.912454	−	0.409180i	$-0.134185\pi$
$972$	20.4956	−	98.6147i	0.657396	−	3.16307i
$973$	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	$0.193347\pi$
$978$	−85.5118	+	25.5402i	−2.73437	+	0.816685i
$979$	27.4677			0.877871
$980$	4.28167	+	59.0564i	0.136773	+	1.88649i
$981$	30.9428			0.987927
$982$	48.5902	−	14.5127i	1.55058	−	0.463117i
$983$	−3.76545	+	3.76545i	−0.120099	+	0.120099i	−0.764602	−	0.644503i	$-0.777064\pi$
$983$	−3.76545	+	3.76545i	−0.120099	+	0.120099i	0.644503	+	0.764602i	$0.277064\pi$
$984$	−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
$988$	31.1845	+	6.48124i	0.992112	+	0.206196i
$989$			16.5673i			0.526809i
$990$	−16.3079	+	73.6648i	−0.518298	+	2.34122i
$991$		−	50.3334i		−	1.59889i	−0.600736	−	0.799447i	$-0.705126\pi$
$991$		−	50.3334i		−	1.59889i	0.600736	−	0.799447i	$-0.294874\pi$
$992$	−4.16311	+	34.6438i	−0.132179	+	1.09994i
$993$	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	$-0.0307341\pi$
$998$	9.85236	+	32.9870i	0.311871	+	1.04418i
$999$	138.612			4.38547

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.6	✓	108	4.3	odd	2	inner
820.2.k.c.83.31	yes	108	1.1	even	1	trivial
820.2.k.c.247.6	yes	108	5.2	odd	4	inner
820.2.k.c.247.31	yes	108	20.7	even	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+(0.404723 + 1.35506i) 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} +(-2.16316 - 1.82229i) q^{8} -7.92318i q^{9} +(0.683514 - 3.08752i) q^{10} -3.01127i q^{11} +(-1.34506 + 6.47175i) 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} +(10.7364 - 3.20669i) q^{18} +5.78194 q^{19} +(4.46043 - 0.323387i) q^{20} +14.8690 q^{21} +(4.08047 - 1.21873i) 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} +(-8.80954 - 1.83093i) q^{28} -5.22860i q^{29} +(-5.61819 - 8.81293i) q^{30} +6.16828i q^{31} +(5.61645 + 0.674922i) 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} +(2.34008 + 7.83490i) q^{38} -9.10318 q^{39} +(2.24345 + 5.91328i) q^{40} +1.00000 q^{41} +(6.01781 + 20.1484i) 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} +(-4.84908 - 12.2987i) q^{48} +13.2401i q^{49} +(-4.69421 + 5.28813i) q^{50} -11.7745i q^{51} +(5.39344 + 1.12095i) 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} +(7.08509 - 2.11614i) q^{58} -1.21549 q^{59} +(9.66828 - 11.1798i) q^{60} -5.20011 q^{61} +(-8.35842 + 2.49644i) 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} +(-1.44989 + 6.97617i) q^{68} +5.70614i q^{69} +(11.9964 - 7.64764i) q^{70} +1.23803i q^{71} +(-14.4383 + 17.1391i) 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} +(-3.68427 - 12.3354i) q^{78} +1.85647 q^{79} +(-7.10491 + 5.43326i) q^{80} -30.0073 q^{81} +(0.404723 + 1.35506i) 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} +(-5.48740 + 6.51387i) q^{88} +9.12162i q^{89} +(-24.4630 - 5.41560i) q^{90} -12.3915i q^{91} +(0.702641 - 3.38076i) 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} +(-17.9412 + 5.35856i) 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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