LMFDB - Embedded newform 820.2.k.c.247.31

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			247.31
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.31

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

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

Coefficient data

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

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

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

$2$	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	0.886454	+	0.462816i	$0.153161\pi$
$3$	2.33700	+	2.33700i	1.34927	+	1.34927i	0.462816	+	0.886454i	$0.346839\pi$
$4$	−1.67240	−	1.09685i	−0.836199	−	0.548426i
$5$	−1.95358	+	1.08790i	−0.873668	+	0.486523i
$5$	−1.95358	+	1.08790i	−0.873668	+	0.486523i
$6$	4.11263	−	2.22095i	1.67897	−	0.906700i
$7$	3.18120	−	3.18120i	1.20238	−	1.20238i	0.228940	−	0.973440i	$-0.426474\pi$
$7$	3.18120	−	3.18120i	1.20238	−	1.20238i	0.973440	−	0.228940i	$-0.0735261\pi$
$8$	−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	$0.149991\pi$
$11$			3.01127i			0.907933i	−0.891019	+	0.453966i	$0.850009\pi$
$12$	−1.34506	−	6.47175i	−0.388284	−	1.86823i
$13$	−1.94762	+	1.94762i	−0.540172	+	0.540172i	−0.923579	−	0.383407i	$-0.874751\pi$
$13$	−1.94762	+	1.94762i	−0.540172	+	0.540172i	0.383407	+	0.923579i	$0.374751\pi$
$14$	−3.02323	−	5.59824i	−0.807991	−	1.49619i
$15$	−7.10795	−	2.02310i	−1.83527	−	0.522363i
$16$	1.59383	+	3.66875i	0.398458	+	0.917186i
$17$	2.51915	+	2.51915i	0.610985	+	0.610985i	0.943203	−	0.332218i	$-0.107797\pi$
$17$	2.51915	+	2.51915i	0.610985	+	0.610985i	−0.332218	+	0.943203i	$0.607797\pi$
$18$	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	0.568278	−	0.822837i	$-0.307610\pi$
$23$	−1.22082	−	1.22082i	−0.254559	−	0.254559i	−0.822837	+	0.568278i	$0.807610\pi$
$24$	−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	$0.161349\pi$
$29$			5.22860i			0.970927i	−0.874257	+	0.485464i	$0.838651\pi$
$30$	−5.61819	+	8.81293i	−1.02574	+	1.60901i
$31$		−	6.16828i		−	1.10786i	−0.832565	−	0.553928i	$-0.813128\pi$
$31$		−	6.16828i		−	1.10786i	0.832565	−	0.553928i	$-0.186872\pi$
$32$	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	0.00966187	−	0.999953i	$-0.496924\pi$
$37$	−6.02371	−	6.02371i	−0.990291	−	0.990291i	−0.999953	+	0.00966187i	$0.996924\pi$
$38$	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	0.999374	+	0.0353737i	$0.0112621\pi$
$43$	6.78530	+	6.78530i	1.03475	+	1.03475i	0.0353737	+	0.999374i	$0.488738\pi$
$44$	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	$-0.680795\pi$
$47$	2.09134	−	2.09134i	0.305054	−	0.305054i	0.842987	+	0.537934i	$0.180795\pi$
$48$	−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	−0.833909	−	0.551903i	$-0.813902\pi$
$53$	−2.05303	+	2.05303i	−0.282006	+	0.282006i	0.551903	+	0.833909i	$0.313902\pi$
$54$	10.9342	+	20.2472i	1.48795	+	2.75530i
$55$	−3.27596	−	5.88276i	−0.441730	−	0.793232i
$56$	−1.08439	+	12.6785i	−0.144908	+	1.69424i
$57$	13.5124	+	13.5124i	1.78976	+	1.78976i
$58$	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	−0.654386	−	0.756161i	$-0.727073\pi$
$67$	0.833062	−	0.833062i	0.101775	−	0.101775i	0.756161	+	0.654386i	$0.227073\pi$
$68$	−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	$-0.976595\pi$
$71$		−	1.23803i		−	0.146927i	0.997298	−	0.0734634i	$-0.0234052\pi$
$72$	−14.4383	−	17.1391i	−1.70157	−	2.01987i
$73$	3.56604	−	3.56604i	0.417373	−	0.417373i	−0.466924	−	0.884297i	$-0.654638\pi$
$73$	3.56604	−	3.56604i	0.417373	−	0.417373i	0.884297	+	0.466924i	$0.154638\pi$
$74$	−10.6004	+	5.72458i	−1.23228	+	0.665469i
$75$	16.0869	−	3.78044i	1.85755	−	0.436527i
$76$	−9.66971	−	6.34193i	−1.10919	−	0.727469i
$77$	9.57946	+	9.57946i	1.09168	+	1.09168i
$78$	−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	0.105984	−	0.994368i	$-0.466201\pi$
$83$	−8.09356	−	8.09356i	−0.888383	−	0.888383i	−0.994368	+	0.105984i	$0.966201\pi$
$84$	−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	$-0.839385\pi$
$89$		−	9.12162i		−	0.966890i	0.875375	−	0.483445i	$-0.160615\pi$
$90$	−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	0.488280	−	0.872687i	$-0.337625\pi$
$97$	−3.78598	−	3.78598i	−0.384408	−	0.384408i	−0.872687	+	0.488280i	$0.837625\pi$
$98$	−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	0.758528	−	0.651640i	$-0.225919\pi$
$103$	1.08480	+	1.08480i	0.106888	+	0.106888i	−0.651640	+	0.758528i	$0.725919\pi$
$104$	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	$-0.824420\pi$
$107$	−3.38909	+	3.38909i	−0.327636	+	0.327636i	0.524051	+	0.851687i	$0.324420\pi$
$108$	31.8616	−	6.62196i	3.06588	−	0.637198i
$109$		−	3.90535i		−	0.374064i	−0.982354	−	0.187032i	$-0.940113\pi$
$109$		−	3.90535i		−	0.374064i	0.982354	−	0.187032i	$-0.0598869\pi$
$110$	−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	−0.368109	−	0.929783i	$-0.619995\pi$
$113$	5.97067	−	5.97067i	0.561674	−	0.561674i	0.929783	+	0.368109i	$0.119995\pi$
$114$	23.7790	−	12.8414i	2.22711	−	1.20271i
$115$	3.71311	+	1.05684i	0.346249	+	0.0985512i
$116$	5.73500	−	8.74431i	0.532481	−	0.811889i
$117$	−15.4313	−	15.4313i	−1.42663	−	1.42663i
$118$	−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	−0.0963329	+	0.995349i	$0.530711\pi$
$127$	−12.3026	+	12.3026i	−1.09168	+	1.09168i	−0.995349	+	0.0963329i	$0.969289\pi$
$128$	−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	$-0.790061\pi$
$131$		−	14.0266i		−	1.22551i	0.790272	−	0.612757i	$-0.209939\pi$
$132$	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	0.359424	−	0.933174i	$-0.382973\pi$
$137$	−6.71558	−	6.71558i	−0.573750	−	0.573750i	−0.933174	+	0.359424i	$0.882973\pi$
$138$	−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	$-0.818398\pi$
$149$		−	13.1848i		−	1.08014i	0.841620	−	0.540070i	$-0.181602\pi$
$150$	1.38800	−	23.3288i	0.113329	−	1.90479i
$151$		−	5.46128i		−	0.444432i	−0.974997	−	0.222216i	$-0.928671\pi$
$151$		−	5.46128i		−	0.444432i	0.974997	−	0.222216i	$-0.0713291\pi$
$152$	−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	0.268681	−	0.963229i	$-0.413412\pi$
$157$	−8.70266	−	8.70266i	−0.694548	−	0.694548i	−0.963229	+	0.268681i	$0.913412\pi$
$158$	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	−0.998242	−	0.0592635i	$-0.981125\pi$
$163$	−13.5013	−	13.5013i	−1.05751	−	1.05751i	−0.0592635	−	0.998242i	$-0.518875\pi$
$164$	−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	$-0.699714\pi$
$167$	2.87517	−	2.87517i	0.222487	−	0.222487i	0.809545	+	0.587058i	$0.199714\pi$
$168$	−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	−0.157799	−	0.987471i	$-0.550440\pi$
$173$	10.9126	−	10.9126i	0.829672	−	0.829672i	0.987471	+	0.157799i	$0.0504399\pi$
$174$	11.6125	+	21.5033i	0.880340	+	1.63016i
$175$	−5.14604	−	21.8979i	−0.389004	−	1.65533i
$176$	−11.0476	+	4.79947i	−0.832744	+	0.361773i
$177$	−2.84060	−	2.84060i	−0.213512	−	0.213512i
$178$	−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	$0.0752309\pi$
$191$			6.47206i			0.468302i	−0.972200	+	0.234151i	$0.924769\pi$
$192$	21.5994	−	15.2496i	1.55880	−	1.10054i
$193$	12.8013	−	12.8013i	0.921456	−	0.921456i	−0.0756762	−	0.997132i	$-0.524112\pi$
$193$	12.8013	−	12.8013i	0.921456	−	0.921456i	0.997132	+	0.0756762i	$0.0241115\pi$
$194$	−6.66251	+	3.59797i	−0.478341	+	0.258319i
$195$	17.7838	−	9.90334i	1.27352	−	0.709193i
$196$	−14.5224	+	22.1427i	−1.03731	+	1.58162i
$197$	8.26931	+	8.26931i	0.589164	+	0.589164i	0.937405	−	0.348241i	$-0.113221\pi$
$197$	8.26931	+	8.26931i	0.589164	+	0.589164i	−0.348241	+	0.937405i	$0.613221\pi$
$198$	−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	$0.0456640\pi$
$211$			4.15341i			0.285932i	−0.989728	+	0.142966i	$0.954336\pi$
$212$	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	0.133502	−	0.991048i	$-0.457378\pi$
$223$	−12.8059	−	12.8059i	−0.857546	−	0.857546i	−0.991048	+	0.133502i	$0.957378\pi$
$224$	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	$-0.821658\pi$
$227$	−4.75627	+	4.75627i	−0.315685	+	0.315685i	0.531422	+	0.847107i	$0.321658\pi$
$228$	−7.77704	−	37.4193i	−0.515047	−	2.47815i
$229$			13.5341i			0.894358i	0.894445	+	0.447179i	$0.147571\pi$
$229$			13.5341i			0.894358i	−0.894445	+	0.447179i	$0.852429\pi$
$230$	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	−0.415266	−	0.909700i	$-0.636312\pi$
$233$	7.54721	−	7.54721i	0.494434	−	0.494434i	0.909700	+	0.415266i	$0.136312\pi$
$234$	−27.1559	+	14.6650i	−1.77523	+	0.958683i
$235$	−1.81044	+	6.36077i	−0.118100	+	0.414931i
$236$	2.03278	+	1.33321i	0.132323	+	0.0867844i
$237$	4.33858	+	4.33858i	0.281821	+	0.281821i
$238$	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	$0.285662\pi$
$251$			24.7699i			1.56346i	−0.623618	+	0.781730i	$0.714338\pi$
$252$	−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	0.615369	−	0.788239i	$-0.289007\pi$
$257$	−2.77132	−	2.77132i	−0.172870	−	0.172870i	−0.788239	+	0.615369i	$0.789007\pi$
$258$	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	0.710367	−	0.703832i	$-0.248529\pi$
$263$	0.105987	+	0.105987i	0.00653544	+	0.00653544i	−0.703832	+	0.710367i	$0.748529\pi$
$264$	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	$0.251702\pi$
$269$			23.3185i			1.42175i	−0.703316	+	0.710877i	$0.748298\pi$
$270$	−43.3877	−	27.6593i	−2.64049	−	1.68329i
$271$			7.66973i			0.465903i	0.972488	+	0.232951i	$0.0748383\pi$
$271$			7.66973i			0.465903i	−0.972488	+	0.232951i	$0.925162\pi$
$272$	−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	0.998171	−	0.0604483i	$-0.0192530\pi$
$277$	15.6068	+	15.6068i	0.937723	+	0.937723i	−0.0604483	+	0.998171i	$0.519253\pi$
$278$	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	0.890589	−	0.454810i	$-0.150293\pi$
$283$	7.33094	+	7.33094i	0.435779	+	0.435779i	−0.454810	+	0.890589i	$0.650293\pi$
$284$	−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	−0.726133	−	0.687555i	$-0.758684\pi$
$293$	−0.660349	+	0.660349i	−0.0385780	+	0.0385780i	0.687555	+	0.726133i	$0.258684\pi$
$294$	−29.4056	−	54.4515i	−1.71497	−	3.17568i
$295$	2.37455	−	1.32233i	0.138252	−	0.0769888i
$296$	24.0072	+	2.05334i	1.39539	+	0.119348i
$297$	−34.6462	−	34.6462i	−2.01038	−	2.01038i
$298$	−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	−0.827340	−	0.561702i	$-0.810147\pi$
$307$	−4.65435	+	4.65435i	−0.265638	+	0.265638i	0.561702	+	0.827340i	$0.310147\pi$
$308$	−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	$0.337819\pi$
$311$			30.7905i			1.74597i	−0.487746	+	0.872986i	$0.662181\pi$
$312$	19.6917	−	16.5886i	1.11482	−	0.939145i
$313$	−16.7368	+	16.7368i	−0.946022	+	0.946022i	−0.998616	−	0.0525940i	$-0.983251\pi$
$313$	−16.7368	+	16.7368i	−0.946022	+	0.946022i	0.0525940	+	0.998616i	$0.483251\pi$
$314$	−15.3148	+	8.27050i	−0.864266	+	0.466731i
$315$	−76.6612	−	21.8197i	−4.31937	−	1.22940i
$316$	−3.10476	−	2.03627i	−0.174656	−	0.114549i
$317$	1.71755	+	1.71755i	0.0964673	+	0.0964673i	0.753693	−	0.657226i	$-0.228270\pi$
$317$	1.71755	+	1.71755i	0.0964673	+	0.0964673i	−0.657226	+	0.753693i	$0.728270\pi$
$318$	−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	$-0.792317\pi$
$331$		−	22.0919i		−	1.21428i	0.794595	−	0.607139i	$-0.207683\pi$
$332$	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	0.996479	−	0.0838407i	$-0.0267187\pi$
$337$	16.7538	+	16.7538i	0.912638	+	0.912638i	−0.0838407	+	0.996479i	$0.526719\pi$
$338$	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	−0.282940	−	0.959138i	$-0.591310\pi$
$347$	12.5962	−	12.5962i	0.676197	−	0.676197i	0.959138	+	0.282940i	$0.0913098\pi$
$348$	33.8382	−	7.03277i	1.81392	−	0.376996i
$349$			27.4748i			1.47069i	0.677692	+	0.735346i	$0.262980\pi$
$349$			27.4748i			1.47069i	−0.677692	+	0.735346i	$0.737020\pi$
$350$	−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	−0.828308	−	0.560272i	$-0.810696\pi$
$353$	−5.03594	+	5.03594i	−0.268036	+	0.268036i	0.560272	+	0.828308i	$0.310696\pi$
$354$	−4.99885	+	2.69954i	−0.265686	+	0.143479i
$355$	1.34685	+	2.41858i	0.0714833	+	0.128365i
$356$	−10.0051	+	15.2550i	−0.530267	+	0.808512i
$357$	37.4572	+	37.4572i	1.98245	+	1.98245i
$358$	−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	−0.393315	−	0.919404i	$-0.628672\pi$
$367$	10.0784	−	10.0784i	0.526088	−	0.526088i	0.919404	+	0.393315i	$0.128672\pi$
$368$	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	−0.236855	−	0.971545i	$-0.576116\pi$
$373$	14.1892	−	14.1892i	0.734691	−	0.734691i	0.971545	+	0.236855i	$0.0761165\pi$
$374$	7.20915	+	13.3495i	0.372776	+	0.690286i
$375$	−27.3143	+	24.8863i	−1.41050	+	1.28512i
$376$	−0.712888	+	8.33494i	−0.0367644	+	0.429842i
$377$	−10.1833	−	10.1833i	−0.524468	−	0.524468i
$378$	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	0.774216	−	0.632922i	$-0.218145\pi$
$383$	2.76517	+	2.76517i	0.141294	+	0.141294i	−0.632922	+	0.774216i	$0.718145\pi$
$384$	−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	$-0.814679\pi$
$389$		−	21.6900i		−	1.09973i	0.835254	−	0.549864i	$-0.185321\pi$
$390$	−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	0.268453	−	0.963293i	$-0.413488\pi$
$397$	−13.8446	−	13.8446i	−0.694840	−	0.694840i	−0.963293	+	0.268453i	$0.913488\pi$
$398$	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	$0.175040\pi$
$409$			21.1381i			1.04521i	−0.852574	+	0.522606i	$0.824960\pi$
$410$	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	$0.0551752\pi$
$431$			7.16120i			0.344943i	−0.985015	+	0.172471i	$0.944825\pi$
$432$	−60.5486	−	23.8729i	−2.91315	−	1.14859i
$433$	9.47183	−	9.47183i	0.455187	−	0.455187i	−0.441885	−	0.897072i	$-0.645690\pi$
$433$	9.47183	−	9.47183i	0.455187	−	0.455187i	0.897072	+	0.441885i	$0.145690\pi$
$434$	−34.5315	+	18.6481i	−1.65756	+	0.895138i
$435$	10.5780	−	37.1647i	0.507176	−	1.78191i
$436$	−4.28358	+	6.53130i	−0.205147	+	0.312792i
$437$	−7.05872	−	7.05872i	−0.337665	−	0.337665i
$438$	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	0.848079	−	0.529869i	$-0.177759\pi$
$443$	6.69755	+	6.69755i	0.318210	+	0.318210i	−0.529869	+	0.848079i	$0.677759\pi$
$444$	−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	$-0.870564\pi$
$449$		−	16.7618i		−	0.791040i	0.918457	−	0.395520i	$-0.129436\pi$
$450$	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	−0.992548	−	0.121853i	$-0.961116\pi$
$457$	−23.8232	−	23.8232i	−1.11440	−	1.11440i	−0.121853	−	0.992548i	$-0.538884\pi$
$458$	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	0.999172	+	0.0406893i	$0.0129554\pi$
$463$	22.3751	+	22.3751i	1.03986	+	1.03986i	0.0406893	+	0.999172i	$0.487045\pi$
$464$	−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	$-0.711915\pi$
$467$	3.64786	−	3.64786i	0.168803	−	0.168803i	0.786453	+	0.617650i	$0.211915\pi$
$468$	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	−0.896796	−	0.442445i	$-0.854111\pi$
$487$	−10.0266	+	10.0266i	−0.454350	+	0.454350i	0.442445	+	0.896796i	$0.354111\pi$
$488$	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	$0.300061\pi$
$491$			35.8582i			1.61826i	−0.587630	+	0.809130i	$0.699939\pi$
$492$	−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	0.489794	−	0.871838i	$-0.337072\pi$
$503$	−8.56836	−	8.56836i	−0.382044	−	0.382044i	−0.871838	+	0.489794i	$0.837072\pi$
$504$	−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	$0.122574\pi$
$509$			16.9492i			0.751261i	−0.926769	+	0.375631i	$0.877426\pi$
$510$	−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	0.482080	−	0.876127i	$-0.339881\pi$
$523$	−9.01153	−	9.01153i	−0.394047	−	0.394047i	−0.876127	+	0.482080i	$0.839881\pi$
$524$	−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	0.446198	−	0.894934i	$-0.352778\pi$
$547$	31.3664	−	31.3664i	1.34113	−	1.34113i	0.894934	−	0.446198i	$-0.147222\pi$
$548$	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	−0.919653	−	0.392733i	$-0.871530\pi$
$557$	−30.9734	−	30.9734i	−1.31239	−	1.31239i	−0.392733	−	0.919653i	$-0.628470\pi$
$558$	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	0.0109339	−	0.999940i	$-0.496520\pi$
$563$	−23.4668	−	23.4668i	−0.989006	−	0.989006i	−0.999940	+	0.0109339i	$0.996520\pi$
$564$	−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	$0.240403\pi$
$569$			32.7019i			1.37094i	−0.728102	+	0.685468i	$0.759597\pi$
$570$	−32.4840	+	50.9559i	−1.36061	+	2.13431i
$571$		−	2.32916i		−	0.0974724i	−0.998812	−	0.0487362i	$-0.984481\pi$
$571$		−	2.32916i		−	0.0974724i	0.998812	−	0.0487362i	$-0.0155194\pi$
$572$	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	0.993451	−	0.114261i	$-0.0364501\pi$
$577$	21.1189	+	21.1189i	0.879190	+	0.879190i	−0.114261	+	0.993451i	$0.536450\pi$
$578$	−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	−0.524932	−	0.851144i	$-0.675909\pi$
$587$	7.90351	−	7.90351i	0.326213	−	0.326213i	0.851144	+	0.524932i	$0.175909\pi$
$588$	−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	−0.920287	−	0.391245i	$-0.872045\pi$
$593$	−12.8830	+	12.8830i	−0.529042	+	0.529042i	0.391245	+	0.920287i	$0.372045\pi$
$594$	−60.9699	+	32.9257i	−2.50163	+	1.35096i
$595$	−31.3117	+	17.4367i	−1.28366	+	0.714835i
$596$	−14.4618	+	22.0502i	−0.592377	+	0.903213i
$597$	22.9311	+	22.9311i	0.938509	+	0.938509i
$598$	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	−0.910354	−	0.413829i	$-0.864191\pi$
$607$	−12.2331	+	12.2331i	−0.496525	+	0.496525i	0.413829	+	0.910354i	$0.364191\pi$
$608$	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	−0.610387	−	0.792103i	$-0.708986\pi$
$613$	4.49907	−	4.49907i	0.181716	−	0.181716i	0.792103	+	0.610387i	$0.208986\pi$
$614$	4.42322	+	8.19067i	0.178507	+	0.330549i
$615$	−7.10795	−	2.02310i	−0.286620	−	0.0815794i
$616$	−38.1785	−	3.26541i	−1.53825	−	0.131567i
$617$	−30.2366	−	30.2366i	−1.21728	−	1.21728i	−0.968580	−	0.248701i	$-0.919996\pi$
$617$	−30.2366	−	30.2366i	−1.21728	−	1.21728i	−0.248701	−	0.968580i	$-0.580004\pi$
$618$	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	$0.284474\pi$
$631$			39.1564i			1.55879i	−0.626531	+	0.779396i	$0.715526\pi$
$632$	−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	0.983980	−	0.178280i	$-0.0570531\pi$
$643$	20.4305	+	20.4305i	0.805700	+	0.805700i	−0.178280	+	0.983980i	$0.557053\pi$
$644$	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	$-0.672602\pi$
$647$	8.66078	−	8.66078i	0.340490	−	0.340490i	0.856552	+	0.516061i	$0.172602\pi$
$648$	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	−0.935284	−	0.353898i	$-0.884856\pi$
$653$	−14.8567	+	14.8567i	−0.581386	+	0.581386i	0.353898	+	0.935284i	$0.384856\pi$
$654$	−8.67359	−	16.0612i	−0.339164	−	0.628045i
$655$	15.2596	+	27.4022i	0.596241	+	1.07069i
$656$	1.59383	+	3.66875i	0.0622288	+	0.143240i
$657$	28.2544	+	28.2544i	1.10231	+	1.10231i
$658$	−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	0.251248	−	0.967923i	$-0.419159\pi$
$673$	31.6280	−	31.6280i	1.21917	−	1.21917i	0.967923	−	0.251248i	$-0.0808409\pi$
$674$	29.4832	−	15.9218i	1.13565	−	0.613286i
$675$	18.6118	+	79.1987i	0.716368	+	3.04836i
$676$	5.93789	−	9.05365i	0.228380	−	0.348217i
$677$	24.1394	+	24.1394i	0.927754	+	0.927754i	0.997561	−	0.0698064i	$-0.0222382\pi$
$677$	24.1394	+	24.1394i	0.927754	+	0.927754i	−0.0698064	+	0.997561i	$0.522238\pi$
$678$	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	0.552908	−	0.833242i	$-0.313518\pi$
$683$	−7.32634	−	7.32634i	−0.280335	−	0.280335i	−0.833242	+	0.552908i	$0.813518\pi$
$684$	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	$-0.793554\pi$
$691$		−	31.7570i		−	1.20809i	0.796948	−	0.604047i	$-0.206446\pi$
$692$	−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	$0.0247412\pi$
$709$			4.13510i			0.155297i	−0.996981	+	0.0776485i	$0.975259\pi$
$710$	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	−0.852097	−	0.523384i	$-0.824669\pi$
$727$	−8.86305	+	8.86305i	−0.328712	+	0.328712i	0.523384	+	0.852097i	$0.324669\pi$
$728$	−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	−0.807691	−	0.589605i	$-0.799283\pi$
$733$	−5.90445	+	5.90445i	−0.218086	+	0.218086i	0.589605	+	0.807691i	$0.299283\pi$
$734$	−9.57792	−	17.7358i	−0.353527	−	0.654642i
$735$	−26.7860	+	94.1098i	−0.988017	+	3.47129i
$736$	−7.68065	−	6.03273i	−0.283112	−	0.222369i
$737$	2.50858	+	2.50858i	0.0924047	+	0.0924047i
$738$	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	−0.881621	−	0.471958i	$-0.843547\pi$
$743$	−36.8959	−	36.8959i	−1.35358	−	1.35358i	−0.471958	−	0.881621i	$-0.656453\pi$
$744$	−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	$0.111451\pi$
$751$			18.8007i			0.686048i	−0.939327	+	0.343024i	$0.888549\pi$
$752$	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	0.118956	−	0.992900i	$-0.462045\pi$
$757$	−24.0454	−	24.0454i	−0.873943	−	0.873943i	−0.992900	+	0.118956i	$0.962045\pi$
$758$	−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	$-0.995151\pi$
$769$		−	0.844874i		−	0.0304669i	0.999884	−	0.0152335i	$-0.00484915\pi$
$770$	−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	−0.608093	−	0.793866i	$-0.708065\pi$
$773$	5.16500	−	5.16500i	0.185772	−	0.185772i	0.793866	+	0.608093i	$0.208065\pi$
$774$	51.0914	+	94.6082i	1.83644	+	3.40062i
$775$	−26.2189	−	16.2408i	−0.941809	−	0.583386i
$776$	15.0888	+	1.29055i	0.541657	+	0.0463280i
$777$	−89.5663	−	89.5663i	−3.21317	−	3.21317i
$778$	−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	−0.286236	−	0.958159i	$-0.592404\pi$
$787$	18.8498	−	18.8498i	0.671923	−	0.671923i	0.958159	+	0.286236i	$0.0924041\pi$
$788$	−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	0.744012	−	0.668166i	$-0.232920\pi$
$797$	2.14124	+	2.14124i	0.0758466	+	0.0758466i	−0.668166	+	0.744012i	$0.732920\pi$
$798$	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	$0.0276932\pi$
$809$			4.94286i			0.173782i	−0.996218	+	0.0868909i	$0.972307\pi$
$810$	−20.5104	−	92.6482i	−0.720661	−	3.25533i
$811$			24.8926i			0.874099i	0.899437	+	0.437050i	$0.143977\pi$
$811$			24.8926i			0.874099i	−0.899437	+	0.437050i	$0.856023\pi$
$812$	−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	0.632645	−	0.774442i	$-0.281969\pi$
$823$	−4.06784	−	4.06784i	−0.141796	−	0.141796i	−0.774442	+	0.632645i	$0.781969\pi$
$824$	−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	$-0.779431\pi$
$827$	−3.75497	+	3.75497i	−0.130573	+	0.130573i	0.638800	+	0.769373i	$0.279431\pi$
$828$	−26.7864	+	5.56715i	−0.930892	+	0.193472i
$829$		−	46.9114i		−	1.62930i	−0.579952	−	0.814651i	$-0.696929\pi$
$829$		−	46.9114i		−	1.62930i	0.579952	−	0.814651i	$-0.303071\pi$
$830$	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	−0.470244	−	0.882536i	$-0.655834\pi$
$853$	12.0415	−	12.0415i	0.412292	−	0.412292i	0.882536	+	0.470244i	$0.155834\pi$
$854$	15.7211	+	29.1114i	0.537965	+	0.996173i
$855$	−49.8381	−	89.4962i	−1.70443	−	3.06070i
$856$	1.15526	−	13.5071i	0.0394860	−	0.461662i
$857$	15.1688	+	15.1688i	0.518156	+	0.518156i	0.917013	−	0.398857i	$-0.130593\pi$
$857$	15.1688	+	15.1688i	0.518156	+	0.518156i	−0.398857	+	0.917013i	$0.630593\pi$
$858$	−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	0.975059	+	0.221946i	$0.0712410\pi$
$863$	35.1643	+	35.1643i	1.19701	+	1.19701i	0.221946	+	0.975059i	$0.428759\pi$
$864$	−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	0.533674	−	0.845690i	$-0.320811\pi$
$877$	−9.24009	−	9.24009i	−0.312016	−	0.312016i	−0.845690	+	0.533674i	$0.820811\pi$
$878$	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	0.901710	−	0.432342i	$-0.142313\pi$
$883$	13.9474	+	13.9474i	0.469368	+	0.469368i	−0.432342	+	0.901710i	$0.642313\pi$
$884$	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	$-0.576397\pi$
$887$	21.8492	−	21.8492i	0.733626	−	0.733626i	0.971336	+	0.237710i	$0.0763969\pi$
$888$	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	−0.0197657	−	0.999805i	$-0.506292\pi$
$907$	29.5153	−	29.5153i	0.980039	−	0.980039i	0.999805	+	0.0197657i	$0.00629204\pi$
$908$	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	$0.0212797\pi$
$911$			4.03257i			0.133605i	−0.997766	+	0.0668024i	$0.978720\pi$
$912$	−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	$0.0503751\pi$
$929$			9.60703i			0.315196i	−0.987503	+	0.157598i	$0.949625\pi$
$930$	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	0.222320	−	0.974974i	$-0.428637\pi$
$937$	−23.0391	−	23.0391i	−0.752654	−	0.752654i	−0.974974	+	0.222320i	$0.928637\pi$
$938$	−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	−0.192988	−	0.981201i	$-0.561818\pi$
$947$	24.2560	−	24.2560i	0.788213	−	0.788213i	0.981201	+	0.192988i	$0.0618180\pi$
$948$	−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	−0.732920	−	0.680315i	$-0.761843\pi$
$953$	−1.62397	+	1.62397i	−0.0526056	+	0.0526056i	0.680315	+	0.732920i	$0.261843\pi$
$954$	−28.6257	+	15.4588i	−0.926791	+	0.500497i
$955$	−7.04094	−	12.6437i	−0.227840	−	0.409140i
$956$	−33.3290	−	21.8590i	−1.07794	−	0.706970i
$957$	−36.7955	−	36.7955i	−1.18943	−	1.18943i
$958$	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	−0.206863	+	0.978370i	$0.566325\pi$
$967$	−36.8567	+	36.8567i	−1.18523	+	1.18523i	−0.978370	+	0.206863i	$0.933675\pi$
$968$	−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	$0.134185\pi$
$971$			25.5008i			0.818360i	−0.912454	+	0.409180i	$0.865815\pi$
$972$	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	0.821124	−	0.570750i	$-0.193347\pi$
$977$	7.82593	+	7.82593i	0.250374	+	0.250374i	−0.570750	+	0.821124i	$0.693347\pi$
$978$	−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	0.644503	−	0.764602i	$-0.277064\pi$
$983$	−3.76545	−	3.76545i	−0.120099	−	0.120099i	−0.764602	+	0.644503i	$0.777064\pi$
$984$	−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	$0.294874\pi$
$991$			50.3334i			1.59889i	−0.600736	+	0.799447i	$0.705126\pi$
$992$	−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	0.995342	+	0.0964040i	$0.0307341\pi$
$997$	34.4722	+	34.4722i	1.09175	+	1.09175i	0.0964040	+	0.995342i	$0.469266\pi$
$998$	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.247.31	yes	108
4.3	odd	2	inner	820.2.k.c.247.6	yes	108
5.3	odd	4	inner	820.2.k.c.83.6	✓	108
20.3	even	4	inner	820.2.k.c.83.31	yes	108

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

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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