LMFDB - Embedded newform 690.2.i.e.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	690.47
Dual form			690.2.i.e.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +(2.23586 + 0.0307665i) q^{10} -3.84509i q^{11} +(-0.471935 - 1.66652i) q^{12} +(0.875224 - 0.875224i) q^{13} -4.87868 q^{14} +(3.35488 + 1.93514i) q^{15} -1.00000 q^{16} +(-1.35706 + 1.35706i) q^{17} +(0.694081 - 2.91860i) q^{18} +3.81508i q^{19} +(1.60274 - 1.55923i) q^{20} +(-7.37712 - 4.12100i) q^{21} +(-2.71889 - 2.71889i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.51211 - 0.844697i) q^{24} +(-0.137579 + 4.99811i) q^{25} -1.23775i q^{26} +(3.51487 - 3.82697i) q^{27} +(-3.44975 + 3.44975i) q^{28} +7.78450 q^{29} +(3.74061 - 1.00391i) q^{30} +5.58131 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.81463 - 6.40791i) q^{33} +1.91917i q^{34} +(0.150100 - 10.9080i) q^{35} +(-1.57298 - 2.55455i) q^{36} +(1.86954 + 1.86954i) q^{37} +(2.69767 + 2.69767i) q^{38} +(1.04553 - 1.87162i) q^{39} +(0.0307665 - 2.23586i) q^{40} +4.29759i q^{41} +(-8.13040 + 2.30242i) q^{42} +(0.142657 - 0.142657i) q^{43} -3.84509 q^{44} +(6.50423 + 1.64166i) q^{45} -1.00000 q^{46} +(-3.63185 + 3.63185i) q^{47} +(-1.66652 + 0.471935i) q^{48} +16.8015i q^{49} +(3.43691 + 3.63148i) q^{50} +(-1.62112 + 2.90201i) q^{51} +(-0.875224 - 0.875224i) q^{52} +(3.62512 + 3.62512i) q^{53} +(-0.220693 - 5.19146i) q^{54} +(6.16270 - 5.99540i) q^{55} +4.87868i q^{56} +(1.80047 + 6.35789i) q^{57} +(5.50447 - 5.50447i) q^{58} +3.87315 q^{59} +(1.93514 - 3.35488i) q^{60} -13.5655 q^{61} +(3.94659 - 3.94659i) q^{62} +(-14.2389 - 3.38620i) q^{63} +1.00000i q^{64} +(2.76744 + 0.0380814i) q^{65} +(-5.81422 - 3.24794i) q^{66} +(-2.77087 - 2.77087i) q^{67} +(1.35706 + 1.35706i) q^{68} +(-1.51211 - 0.844697i) q^{69} +(-7.60700 - 7.81928i) q^{70} +6.15174i q^{71} +(-2.91860 - 0.694081i) q^{72} +(-9.60788 + 9.60788i) q^{73} +2.64393 q^{74} +(2.12950 + 8.39436i) q^{75} +3.81508 q^{76} +(-13.2646 + 13.2646i) q^{77} +(-0.584139 - 2.06274i) q^{78} -17.1956i q^{79} +(-1.55923 - 1.60274i) q^{80} +(4.05150 - 8.03650i) q^{81} +(3.03885 + 3.03885i) q^{82} +(2.00448 + 2.00448i) q^{83} +(-4.12100 + 7.37712i) q^{84} +(-4.29100 - 0.0590463i) q^{85} -0.201747i q^{86} +(12.9730 - 3.67378i) q^{87} +(-2.71889 + 2.71889i) q^{88} +12.5987 q^{89} +(5.76001 - 3.43835i) q^{90} -6.03860 q^{91} +(-0.707107 + 0.707107i) q^{92} +(9.30135 - 2.63402i) q^{93} +5.13622i q^{94} +(-6.11459 + 5.94860i) q^{95} +(-0.844697 + 1.51211i) q^{96} +(-3.36602 - 3.36602i) q^{97} +(11.8805 + 11.8805i) q^{98} +(-6.04824 - 9.82250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.66652	−	0.471935i	0.962164	−	0.272472i
$3$	1.66652	−	0.471935i	0.962164	−	0.272472i
$4$		−	1.00000i		−	0.500000i
$5$	1.55923	+	1.60274i	0.697311	+	0.716769i
$5$	1.55923	+	1.60274i	0.697311	+	0.716769i
$6$	0.844697	−	1.51211i	0.344846	−	0.617318i
$7$	−3.44975	−	3.44975i	−1.30388	−	1.30388i	−0.925753	−	0.378129i	$-0.876568\pi$
$7$	−3.44975	−	3.44975i	−1.30388	−	1.30388i	−0.378129	−	0.925753i	$-0.623432\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.55455	−	1.57298i	0.851518	−	0.524325i
$10$	2.23586	+	0.0307665i	0.707040	+	0.00972923i
$11$		−	3.84509i		−	1.15934i	−0.814852	−	0.579670i	$-0.803182\pi$
$11$		−	3.84509i		−	1.15934i	0.814852	−	0.579670i	$-0.196818\pi$
$12$	−0.471935	−	1.66652i	−0.136236	−	0.481082i
$13$	0.875224	−	0.875224i	0.242743	−	0.242743i	−0.575241	−	0.817984i	$-0.695092\pi$
$13$	0.875224	−	0.875224i	0.242743	−	0.242743i	0.817984	+	0.575241i	$0.195092\pi$
$14$	−4.87868			−1.30388
$15$	3.35488	+	1.93514i	0.866226	+	0.499652i
$16$	−1.00000			−0.250000
$17$	−1.35706	+	1.35706i	−0.329135	+	0.329135i	−0.852258	−	0.523122i	$-0.824767\pi$
$17$	−1.35706	+	1.35706i	−0.329135	+	0.329135i	0.523122	+	0.852258i	$0.324767\pi$
$18$	0.694081	−	2.91860i	0.163597	−	0.687922i
$19$			3.81508i			0.875239i	0.899160	+	0.437619i	$0.144178\pi$
$19$			3.81508i			0.875239i	−0.899160	+	0.437619i	$0.855822\pi$
$20$	1.60274	−	1.55923i	0.358385	−	0.348655i
$21$	−7.37712	−	4.12100i	−1.60982	−	0.899277i
$22$	−2.71889	−	2.71889i	−0.579670	−	0.579670i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−1.51211	−	0.844697i	−0.308659	−	0.172423i
$25$	−0.137579	+	4.99811i	−0.0275158	+	0.999621i
$26$		−	1.23775i		−	0.242743i
$27$	3.51487	−	3.82697i	0.676436	−	0.736501i
$28$	−3.44975	+	3.44975i	−0.651941	+	0.651941i
$29$	7.78450			1.44554			0.722772	−	0.691086i	$-0.242867\pi$
$29$	7.78450			1.44554			0.722772	+	0.691086i	$0.242867\pi$
$30$	3.74061	−	1.00391i	0.682939	−	0.183287i
$31$	5.58131			1.00243			0.501217	−	0.865322i	$-0.332886\pi$
$31$	5.58131			1.00243			0.501217	+	0.865322i	$0.332886\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.81463	−	6.40791i	−0.315887	−	1.11547i
$34$			1.91917i			0.329135i
$35$	0.150100	−	10.9080i	0.0253715	−	1.84379i
$36$	−1.57298	−	2.55455i	−0.262163	−	0.425759i
$37$	1.86954	+	1.86954i	0.307351	+	0.307351i	0.843881	−	0.536530i	$-0.180265\pi$
$37$	1.86954	+	1.86954i	0.307351	+	0.307351i	−0.536530	+	0.843881i	$0.680265\pi$
$38$	2.69767	+	2.69767i	0.437619	+	0.437619i
$39$	1.04553	−	1.87162i	0.167418	−	0.299700i
$40$	0.0307665	−	2.23586i	0.00486461	−	0.353520i
$41$			4.29759i			0.671170i	0.942010	+	0.335585i	$0.108934\pi$
$41$			4.29759i			0.671170i	−0.942010	+	0.335585i	$0.891066\pi$
$42$	−8.13040	+	2.30242i	−1.25455	+	0.355271i
$43$	0.142657	−	0.142657i	0.0217549	−	0.0217549i	−0.696146	−	0.717901i	$-0.745103\pi$
$43$	0.142657	−	0.142657i	0.0217549	−	0.0217549i	0.717901	+	0.696146i	$0.245103\pi$
$44$	−3.84509			−0.579670
$45$	6.50423	+	1.64166i	0.969593	+	0.244724i
$46$	−1.00000			−0.147442
$47$	−3.63185	+	3.63185i	−0.529760	+	0.529760i	−0.920501	−	0.390741i	$-0.872219\pi$
$47$	−3.63185	+	3.63185i	−0.529760	+	0.529760i	0.390741	+	0.920501i	$0.372219\pi$
$48$	−1.66652	+	0.471935i	−0.240541	+	0.0681180i
$49$			16.8015i			2.40022i
$50$	3.43691	+	3.63148i	0.486053	+	0.513569i
$51$	−1.62112	+	2.90201i	−0.227002	+	0.406362i
$52$	−0.875224	−	0.875224i	−0.121372	−	0.121372i
$53$	3.62512	+	3.62512i	0.497949	+	0.497949i	0.910799	−	0.412850i	$-0.135467\pi$
$53$	3.62512	+	3.62512i	0.497949	+	0.497949i	−0.412850	+	0.910799i	$0.635467\pi$
$54$	−0.220693	−	5.19146i	−0.0300326	−	0.706469i
$55$	6.16270	−	5.99540i	0.830979	−	0.808420i
$56$			4.87868i			0.651941i
$57$	1.80047	+	6.35789i	0.238478	+	0.842123i
$58$	5.50447	−	5.50447i	0.722772	−	0.722772i
$59$	3.87315			0.504241			0.252120	−	0.967696i	$-0.418872\pi$
$59$	3.87315			0.504241			0.252120	+	0.967696i	$0.418872\pi$
$60$	1.93514	−	3.35488i	0.249826	−	0.433113i
$61$	−13.5655			−1.73688			−0.868442	−	0.495791i	$-0.834878\pi$
$61$	−13.5655			−1.73688			−0.868442	+	0.495791i	$0.834878\pi$
$62$	3.94659	−	3.94659i	0.501217	−	0.501217i
$63$	−14.2389	−	3.38620i	−1.79394	−	0.426621i
$64$			1.00000i			0.125000i
$65$	2.76744	+	0.0380814i	0.343259	+	0.00472341i
$66$	−5.81422	−	3.24794i	−0.715681	−	0.399794i
$67$	−2.77087	−	2.77087i	−0.338515	−	0.338515i	0.517293	−	0.855808i	$-0.326940\pi$
$67$	−2.77087	−	2.77087i	−0.338515	−	0.338515i	−0.855808	+	0.517293i	$0.826940\pi$
$68$	1.35706	+	1.35706i	0.164568	+	0.164568i
$69$	−1.51211	−	0.844697i	−0.182037	−	0.101690i
$70$	−7.60700	−	7.81928i	−0.909211	−	0.934582i
$71$			6.15174i			0.730077i	0.930992	+	0.365039i	$0.118944\pi$
$71$			6.15174i			0.730077i	−0.930992	+	0.365039i	$0.881056\pi$
$72$	−2.91860	−	0.694081i	−0.343961	−	0.0817983i
$73$	−9.60788	+	9.60788i	−1.12452	+	1.12452i	−0.133463	+	0.991054i	$0.542610\pi$
$73$	−9.60788	+	9.60788i	−1.12452	+	1.12452i	−0.991054	+	0.133463i	$0.957390\pi$
$74$	2.64393			0.307351
$75$	2.12950	+	8.39436i	0.245894	+	0.969297i
$76$	3.81508			0.437619
$77$	−13.2646	+	13.2646i	−1.51164	+	1.51164i
$78$	−0.584139	−	2.06274i	−0.0661408	−	0.233559i
$79$		−	17.1956i		−	1.93466i	−0.253525	−	0.967329i	$-0.581590\pi$
$79$		−	17.1956i		−	1.93466i	0.253525	−	0.967329i	$-0.418410\pi$
$80$	−1.55923	−	1.60274i	−0.174328	−	0.179192i
$81$	4.05150	−	8.03650i	0.450166	−	0.892945i
$82$	3.03885	+	3.03885i	0.335585	+	0.335585i
$83$	2.00448	+	2.00448i	0.220021	+	0.220021i	0.808507	−	0.588486i	$-0.200276\pi$
$83$	2.00448	+	2.00448i	0.220021	+	0.220021i	−0.588486	+	0.808507i	$0.700276\pi$
$84$	−4.12100	+	7.37712i	−0.449638	+	0.804910i
$85$	−4.29100	−	0.0590463i	−0.465424	−	0.00640447i
$86$		−	0.201747i		−	0.0217549i
$87$	12.9730	−	3.67378i	1.39085	−	0.393870i
$88$	−2.71889	+	2.71889i	−0.289835	+	0.289835i
$89$	12.5987			1.33546			0.667728	−	0.744406i	$-0.267267\pi$
$89$	12.5987			1.33546			0.667728	+	0.744406i	$0.267267\pi$
$90$	5.76001	−	3.43835i	0.607159	−	0.362434i
$91$	−6.03860			−0.633018
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	9.30135	−	2.63402i	0.964505	−	0.273135i
$94$			5.13622i			0.529760i
$95$	−6.11459	+	5.94860i	−0.627344	+	0.610313i
$96$	−0.844697	+	1.51211i	−0.0862115	+	0.154329i
$97$	−3.36602	−	3.36602i	−0.341767	−	0.341767i	0.515264	−	0.857032i	$-0.327694\pi$
$97$	−3.36602	−	3.36602i	−0.341767	−	0.341767i	−0.857032	+	0.515264i	$0.827694\pi$
$98$	11.8805	+	11.8805i	1.20011	+	1.20011i
$99$	−6.04824	−	9.82250i	−0.607871	−	0.987199i
$100$	4.99811	+	0.137579i	0.499811	+	0.0137579i
$101$		−	11.2944i		−	1.12383i	−0.827194	−	0.561916i	$-0.810064\pi$
$101$		−	11.2944i		−	1.12383i	0.827194	−	0.561916i	$-0.189936\pi$
$102$	0.905725	+	3.19833i	0.0896801	+	0.316682i
$103$	−8.36819	+	8.36819i	−0.824542	+	0.824542i	−0.986756	−	0.162214i	$-0.948137\pi$
$103$	−8.36819	+	8.36819i	−0.824542	+	0.824542i	0.162214	+	0.986756i	$0.448137\pi$
$104$	−1.23775			−0.121372
$105$	−4.89774	−	18.2492i	−0.477970	−	1.78094i
$106$	5.12670			0.497949
$107$	−7.21940	+	7.21940i	−0.697925	+	0.697925i	−0.963963	−	0.266037i	$-0.914286\pi$
$107$	−7.21940	+	7.21940i	−0.697925	+	0.697925i	0.266037	+	0.963963i	$0.414286\pi$
$108$	−3.82697	−	3.51487i	−0.368251	−	0.338218i
$109$		−	2.16073i		−	0.206960i	−0.994632	−	0.103480i	$-0.967002\pi$
$109$		−	2.16073i		−	0.206960i	0.994632	−	0.103480i	$-0.0329978\pi$
$110$	0.118300	−	8.59708i	0.0112795	−	0.819699i
$111$	3.99792	+	2.23332i	0.379466	+	0.211977i
$112$	3.44975	+	3.44975i	0.325971	+	0.325971i
$113$	8.63760	+	8.63760i	0.812557	+	0.812557i	0.985017	−	0.172459i	$-0.0551713\pi$
$113$	8.63760	+	8.63760i	0.812557	+	0.812557i	−0.172459	+	0.985017i	$0.555171\pi$
$114$	5.76883	+	3.22258i	0.540301	+	0.301823i
$115$	0.0307665	−	2.23586i	0.00286899	−	0.208495i
$116$		−	7.78450i		−	0.722772i
$117$	0.859102	−	3.61251i	0.0794240	−	0.333977i
$118$	2.73873	−	2.73873i	0.252120	−	0.252120i
$119$	9.36303			0.858308
$120$	−1.00391	−	3.74061i	−0.0916437	−	0.341470i
$121$	−3.78475			−0.344068
$122$	−9.59226	+	9.59226i	−0.868442	+	0.868442i
$123$	2.02818	+	7.16200i	0.182875	+	0.645775i
$124$		−	5.58131i		−	0.501217i
$125$	−8.22521	+	7.57271i	−0.735685	+	0.677324i
$126$	−12.4629	+	7.67404i	−1.11028	+	0.683658i
$127$	−10.4407	−	10.4407i	−0.926462	−	0.926462i	0.0710131	−	0.997475i	$-0.477377\pi$
$127$	−10.4407	−	10.4407i	−0.926462	−	0.926462i	−0.997475	+	0.0710131i	$0.977377\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.170415	−	0.305064i	0.0150042	−	0.0268594i
$130$	1.98380	−	1.92995i	0.173991	−	0.169268i
$131$			11.2466i			0.982617i	0.870985	+	0.491309i	$0.163481\pi$
$131$			11.2466i			0.982617i	−0.870985	+	0.491309i	$0.836519\pi$
$132$	−6.40791	+	1.81463i	−0.557737	+	0.157944i
$133$	13.1611	−	13.1611i	1.14121	−	1.14121i
$134$	−3.91860			−0.338515
$135$	11.6142	−	0.333716i	0.999587	−	0.0287217i
$136$	1.91917			0.164568
$137$	10.4263	−	10.4263i	0.890776	−	0.890776i	−0.103820	−	0.994596i	$-0.533107\pi$
$137$	10.4263	−	10.4263i	0.890776	−	0.890776i	0.994596	+	0.103820i	$0.0331066\pi$
$138$	−1.66652	+	0.471935i	−0.141863	+	0.0401738i
$139$			14.6451i			1.24218i	0.783738	+	0.621092i	$0.213311\pi$
$139$			14.6451i			1.24218i	−0.783738	+	0.621092i	$0.786689\pi$
$140$	−10.9080	−	0.150100i	−0.921897	−	0.0126858i
$141$	−4.33854	+	7.76654i	−0.365371	+	0.654061i
$142$	4.34994	+	4.34994i	0.365039	+	0.365039i
$143$	−3.36532	−	3.36532i	−0.281422	−	0.281422i
$144$	−2.55455	+	1.57298i	−0.212880	+	0.131081i
$145$	12.1379	+	12.4766i	1.00799	+	1.03612i
$146$			13.5876i			1.12452i
$147$	7.92922	+	28.0000i	0.653991	+	2.30940i
$148$	1.86954	−	1.86954i	0.153675	−	0.153675i
$149$	1.21978			0.0999285			0.0499642	−	0.998751i	$-0.484089\pi$
$149$	1.21978			0.0999285			0.0499642	+	0.998751i	$0.484089\pi$
$150$	7.44149	+	4.42992i	0.607595	+	0.361701i
$151$	6.92084			0.563210			0.281605	−	0.959530i	$-0.409133\pi$
$151$	6.92084			0.563210			0.281605	+	0.959530i	$0.409133\pi$
$152$	2.69767	−	2.69767i	0.218810	−	0.218810i
$153$	−1.33206	+	5.60131i	−0.107691	+	0.452839i
$154$			18.7590i			1.51164i
$155$	8.70257	+	8.94542i	0.699008	+	0.718513i
$156$	−1.87162	−	1.04553i	−0.149850	−	0.0837091i
$157$	1.67127	+	1.67127i	0.133382	+	0.133382i	0.770646	−	0.637264i	$-0.219934\pi$
$157$	1.67127	+	1.67127i	0.133382	+	0.133382i	−0.637264	+	0.770646i	$0.719934\pi$
$158$	−12.1591	−	12.1591i	−0.967329	−	0.967329i
$159$	7.75215	+	4.33051i	0.614786	+	0.343431i
$160$	−2.23586	−	0.0307665i	−0.176760	−	0.00243231i
$161$			4.87868i			0.384494i
$162$	−2.81782	−	8.54751i	−0.221389	−	0.671556i
$163$	9.29670	−	9.29670i	0.728173	−	0.728173i	−0.242082	−	0.970256i	$-0.577830\pi$
$163$	9.29670	−	9.29670i	0.728173	−	0.728173i	0.970256	+	0.242082i	$0.0778304\pi$
$164$	4.29759			0.335585
$165$	7.44081	−	12.8998i	0.579266	−	1.00425i
$166$	2.83477			0.220021
$167$	−10.9776	+	10.9776i	−0.849475	+	0.849475i	−0.990068	−	0.140593i	$-0.955099\pi$
$167$	−10.9776	+	10.9776i	−0.849475	+	0.849475i	0.140593	+	0.990068i	$0.455099\pi$
$168$	2.30242	+	8.13040i	0.177636	+	0.627274i
$169$			11.4680i			0.882151i
$170$	−3.07594	+	2.99244i	−0.235914	+	0.229510i
$171$	6.00102	+	9.74582i	0.458910	+	0.745282i
$172$	−0.142657	−	0.142657i	−0.0108775	−	0.0108775i
$173$	−17.3398	−	17.3398i	−1.31832	−	1.31832i	−0.915107	−	0.403212i	$-0.867894\pi$
$173$	−17.3398	−	17.3398i	−1.31832	−	1.31832i	−0.403212	−	0.915107i	$-0.632106\pi$
$174$	6.57554	−	11.7710i	0.498490	−	0.892361i
$175$	17.7168	−	16.7676i	1.33927	−	1.26751i
$176$			3.84509i			0.289835i
$177$	6.45466	−	1.82787i	0.485162	−	0.137391i
$178$	8.90860	−	8.90860i	0.667728	−	0.667728i
$179$	−1.47094			−0.109943			−0.0549715	−	0.998488i	$-0.517507\pi$
$179$	−1.47094			−0.109943			−0.0549715	+	0.998488i	$0.517507\pi$
$180$	1.64166	−	6.50423i	0.122362	−	0.484796i
$181$	−15.6852			−1.16587			−0.582936	−	0.812518i	$-0.698096\pi$
$181$	−15.6852			−1.16587			−0.582936	+	0.812518i	$0.698096\pi$
$182$	−4.26994	+	4.26994i	−0.316509	+	0.316509i
$183$	−22.6071	+	6.40203i	−1.67117	+	0.473252i
$184$			1.00000i			0.0737210i
$185$	−0.0813446	+	5.91145i	−0.00598057	+	0.434618i
$186$	4.71452	−	8.43958i	0.345685	−	0.618820i
$187$	5.21802	+	5.21802i	0.381580	+	0.381580i
$188$	3.63185	+	3.63185i	0.264880	+	0.264880i
$189$	−25.3275	+	1.07669i	−1.84230	+	0.0783179i
$190$	−0.117377	+	8.52997i	−0.00851540	+	0.618829i
$191$		−	21.7200i		−	1.57160i	−0.618480	−	0.785800i	$-0.712251\pi$
$191$		−	21.7200i		−	1.57160i	0.618480	−	0.785800i	$-0.287749\pi$
$192$	0.471935	+	1.66652i	0.0340590	+	0.120270i
$193$	17.8302	−	17.8302i	1.28345	−	1.28345i	0.344751	−	0.938694i	$-0.387963\pi$
$193$	17.8302	−	17.8302i	1.28345	−	1.28345i	0.938694	−	0.344751i	$-0.112037\pi$
$194$	−4.76027			−0.341767
$195$	4.62996	−	1.24259i	0.331558	−	0.0889836i
$196$	16.8015			1.20011
$197$	−0.806128	+	0.806128i	−0.0574342	+	0.0574342i	−0.735241	−	0.677806i	$-0.762931\pi$
$197$	−0.806128	+	0.806128i	−0.0574342	+	0.0574342i	0.677806	+	0.735241i	$0.262931\pi$
$198$	−11.2223	−	2.66881i	−0.797535	−	0.189664i
$199$			18.0493i			1.27948i	0.768590	+	0.639742i	$0.220959\pi$
$199$			18.0493i			1.27948i	−0.768590	+	0.639742i	$0.779041\pi$
$200$	3.63148	−	3.43691i	0.256784	−	0.243026i
$201$	−5.92537	−	3.31003i	−0.417943	−	0.233471i
$202$	−7.98633	−	7.98633i	−0.561916	−	0.561916i
$203$	−26.8546	−	26.8546i	−1.88482	−	1.88482i
$204$	2.90201	+	1.62112i	0.203181	+	0.113501i
$205$	−6.88793	+	6.70094i	−0.481074	+	0.468014i
$206$			11.8344i			0.824542i
$207$	−2.91860	−	0.694081i	−0.202857	−	0.0482420i
$208$	−0.875224	+	0.875224i	−0.0606859	+	0.0606859i
$209$	14.6693			1.01470
$210$	−16.3674	−	9.44094i	−1.12946	−	0.651487i
$211$	7.95847			0.547884			0.273942	−	0.961746i	$-0.411672\pi$
$211$	7.95847			0.547884			0.273942	+	0.961746i	$0.411672\pi$
$212$	3.62512	−	3.62512i	0.248975	−	0.248975i
$213$	2.90322	+	10.2520i	0.198925	+	0.702454i
$214$			10.2098i			0.697925i
$215$	0.451077	+	0.00620705i	0.0307632	+	0.000423317i
$216$	−5.19146	+	0.220693i	−0.353234	+	0.0150163i
$217$	−19.2541	−	19.2541i	−1.30706	−	1.30706i
$218$	−1.52786	−	1.52786i	−0.103480	−	0.103480i
$219$	−11.4774	+	20.5460i	−0.775570	+	1.38837i
$220$	−5.99540	−	6.16270i	−0.404210	−	0.415489i
$221$			2.37546i			0.159791i
$222$	4.40615	−	1.24776i	0.295722	−	0.0837444i
$223$	16.5940	−	16.5940i	1.11122	−	1.11122i	0.118233	−	0.992986i	$-0.462277\pi$
$223$	16.5940	−	16.5940i	1.11122	−	1.11122i	0.992986	−	0.118233i	$-0.0377228\pi$
$224$	4.87868			0.325971
$225$	7.51044	+	12.9843i	0.500696	+	0.865623i
$226$	12.2154			0.812557
$227$	4.89140	−	4.89140i	0.324653	−	0.324653i	−0.525896	−	0.850549i	$-0.676270\pi$
$227$	4.89140	−	4.89140i	0.324653	−	0.324653i	0.850549	+	0.525896i	$0.176270\pi$
$228$	6.35789	−	1.80047i	0.421062	−	0.119239i
$229$		−	4.39356i		−	0.290335i	−0.989407	−	0.145167i	$-0.953628\pi$
$229$		−	4.39356i		−	0.290335i	0.989407	−	0.145167i	$-0.0463721\pi$
$230$	−1.55923	−	1.60274i	−0.102813	−	0.105682i
$231$	−15.8456	+	28.3657i	−1.04257	+	1.86633i
$232$	−5.50447	−	5.50447i	−0.361386	−	0.361386i
$233$	8.94095	+	8.94095i	0.585741	+	0.585741i	0.936475	−	0.350734i	$-0.114068\pi$
$233$	8.94095	+	8.94095i	0.585741	+	0.585741i	−0.350734	+	0.936475i	$0.614068\pi$
$234$	−1.94696	−	3.16191i	−0.127276	−	0.206700i
$235$	−11.4838	−	0.158024i	−0.749123	−	0.0103083i
$236$		−	3.87315i		−	0.252120i
$237$	−8.11521	−	28.6568i	−0.527140	−	1.86146i
$238$	6.62066	−	6.62066i	0.429154	−	0.429154i
$239$	7.07155			0.457420			0.228710	−	0.973495i	$-0.426549\pi$
$239$	7.07155			0.457420			0.228710	+	0.973495i	$0.426549\pi$
$240$	−3.35488	−	1.93514i	−0.216557	−	0.124913i
$241$	−4.22605			−0.272224			−0.136112	−	0.990693i	$-0.543461\pi$
$241$	−4.22605			−0.272224			−0.136112	+	0.990693i	$0.543461\pi$
$242$	−2.67622	+	2.67622i	−0.172034	+	0.172034i
$243$	2.95918	−	15.3050i	0.189832	−	0.981817i
$244$			13.5655i			0.868442i
$245$	−26.9285	+	26.1975i	−1.72040	+	1.67370i
$246$	6.49844	+	3.63016i	0.414325	+	0.231450i
$247$	3.33905	+	3.33905i	0.212459	+	0.212459i
$248$	−3.94659	−	3.94659i	−0.250608	−	0.250608i
$249$	4.28649	+	2.39452i	0.271645	+	0.151747i
$250$	−0.461381	+	11.1708i	−0.0291803	+	0.706504i
$251$		−	0.318931i		−	0.0201307i	−0.999949	−	0.0100654i	$-0.996796\pi$
$251$		−	0.318931i		−	0.0201307i	0.999949	−	0.0100654i	$-0.00320396\pi$
$252$	−3.38620	+	14.2389i	−0.213311	+	0.896969i
$253$	−2.71889	+	2.71889i	−0.170935	+	0.170935i
$254$	−14.7654			−0.926462
$255$	−7.17888	+	1.92667i	−0.449559	+	0.120653i
$256$	1.00000			0.0625000
$257$	−9.89138	+	9.89138i	−0.617007	+	0.617007i	−0.944763	−	0.327755i	$-0.893708\pi$
$257$	−9.89138	+	9.89138i	−0.617007	+	0.617007i	0.327755	+	0.944763i	$0.393708\pi$
$258$	−0.0952114	−	0.336214i	−0.00592760	−	0.0209318i
$259$		−	12.8989i		−	0.801498i
$260$	0.0380814	−	2.76744i	0.00236171	−	0.171629i
$261$	19.8859	−	12.2448i	1.23091	−	0.757935i
$262$	7.95253	+	7.95253i	0.491309	+	0.491309i
$263$	6.24409	+	6.24409i	0.385027	+	0.385027i	0.872909	−	0.487882i	$-0.162231\pi$
$263$	6.24409	+	6.24409i	0.385027	+	0.385027i	−0.487882	+	0.872909i	$0.662231\pi$
$264$	−3.24794	+	5.81422i	−0.199897	+	0.357840i
$265$	−0.157731	+	11.4626i	−0.00968932	+	0.704140i
$266$		−	18.6125i		−	1.14121i
$267$	20.9959	−	5.94575i	1.28493	−	0.363874i
$268$	−2.77087	+	2.77087i	−0.169258	+	0.169258i
$269$	11.4973			0.701002			0.350501	−	0.936562i	$-0.386011\pi$
$269$	11.4973			0.701002			0.350501	+	0.936562i	$0.386011\pi$
$270$	7.97648	−	8.44842i	0.485433	−	0.514155i
$271$	14.4129			0.875519			0.437760	−	0.899092i	$-0.355772\pi$
$271$	14.4129			0.875519			0.437760	+	0.899092i	$0.355772\pi$
$272$	1.35706	−	1.35706i	0.0822839	−	0.0822839i
$273$	−10.0634	+	2.84983i	−0.609067	+	0.172479i
$274$		−	14.7450i		−	0.890776i
$275$	19.2182	+	0.529004i	1.15890	+	0.0319002i
$276$	−0.844697	+	1.51211i	−0.0508448	+	0.0910185i
$277$	−21.8386	−	21.8386i	−1.31215	−	1.31215i	−0.919827	−	0.392325i	$-0.871671\pi$
$277$	−21.8386	−	21.8386i	−1.31215	−	1.31215i	−0.392325	−	0.919827i	$-0.628329\pi$
$278$	10.3557	+	10.3557i	0.621092	+	0.621092i
$279$	14.2578	−	8.77927i	0.853590	−	0.525601i
$280$	−7.81928	+	7.60700i	−0.467291	+	0.454605i
$281$			32.5667i			1.94277i	0.237517	+	0.971383i	$0.423666\pi$
$281$			32.5667i			1.94277i	−0.237517	+	0.971383i	$0.576334\pi$
$282$	2.42396	+	8.55959i	0.144345	+	0.509716i
$283$	−18.1562	+	18.1562i	−1.07927	+	1.07927i	−0.0827000	+	0.996574i	$0.526354\pi$
$283$	−18.1562	+	18.1562i	−1.07927	+	1.07927i	−0.996574	+	0.0827000i	$0.973646\pi$
$284$	6.15174			0.365039
$285$	−7.38272	+	12.7991i	−0.437315	+	0.758155i
$286$	−4.75928			−0.281422
$287$	14.8256	−	14.8256i	0.875127	−	0.875127i
$288$	−0.694081	+	2.91860i	−0.0408991	+	0.171980i
$289$			13.3168i			0.783340i
$290$	17.4050	+	0.239502i	1.02206	+	0.0140640i
$291$	−7.19807	−	4.02098i	−0.421958	−	0.235714i
$292$	9.60788	+	9.60788i	0.562258	+	0.562258i
$293$	9.83546	+	9.83546i	0.574594	+	0.574594i	0.933409	−	0.358815i	$-0.116819\pi$
$293$	9.83546	+	9.83546i	0.574594	+	0.574594i	−0.358815	+	0.933409i	$0.616819\pi$
$294$	25.4058	+	14.1922i	1.48170	+	0.827705i
$295$	6.03914	+	6.20766i	0.351612	+	0.361424i
$296$		−	2.64393i		−	0.153675i
$297$	−14.7151	−	13.5150i	−0.853855	−	0.784219i
$298$	0.862517	−	0.862517i	0.0499642	−	0.0499642i
$299$	−1.23775			−0.0715811
$300$	8.39436	−	2.12950i	0.484648	−	0.122947i
$301$	−0.984258			−0.0567317
$302$	4.89377	−	4.89377i	0.281605	−	0.281605i
$303$	−5.33021	−	18.8223i	−0.306213	−	1.08131i
$304$		−	3.81508i		−	0.218810i
$305$	−21.1518	−	21.7420i	−1.21115	−	1.24494i
$306$	3.01881	+	4.90263i	0.172574	+	0.280265i
$307$	−16.7681	−	16.7681i	−0.957004	−	0.957004i	0.0421088	−	0.999113i	$-0.486592\pi$
$307$	−16.7681	−	16.7681i	−0.957004	−	0.957004i	−0.999113	+	0.0421088i	$0.986592\pi$
$308$	13.2646	+	13.2646i	0.755821	+	0.755821i
$309$	−9.99648	+	17.8950i	−0.568680	+	1.01801i
$310$	12.4790	+	0.171718i	0.708760	+	0.00975291i
$311$			6.36857i			0.361128i	0.983563	+	0.180564i	$0.0577924\pi$
$311$			6.36857i			0.361128i	−0.983563	+	0.180564i	$0.942208\pi$
$312$	−2.06274	+	0.584139i	−0.116779	+	0.0330704i
$313$	−16.8425	+	16.8425i	−0.951993	+	0.951993i	−0.998899	−	0.0469067i	$-0.985064\pi$
$313$	−16.8425	+	16.8425i	−0.951993	+	0.951993i	0.0469067	+	0.998899i	$0.485064\pi$
$314$	2.36353			0.133382
$315$	−16.7746	−	28.1013i	−0.945143	−	1.58333i
$316$	−17.1956			−0.967329
$317$	17.8078	−	17.8078i	1.00018	−	1.00018i	0.000184598	−	1.00000i	$-0.499941\pi$
$317$	17.8078	−	17.8078i	1.00018	−	1.00018i	1.00000		0.000184598i	$-5.87594e-5\pi$
$318$	8.54373	−	2.41947i	0.479108	−	0.135677i
$319$		−	29.9321i		−	1.67588i
$320$	−1.60274	+	1.55923i	−0.0895961	+	0.0871638i
$321$	−8.62416	+	15.4383i	−0.481353	+	0.861683i
$322$	3.44975	+	3.44975i	0.192247	+	0.192247i
$323$	−5.17729	−	5.17729i	−0.288072	−	0.288072i
$324$	−8.03650	−	4.05150i	−0.446472	−	0.225083i
$325$	4.25405	+	4.49488i	0.235972	+	0.249331i
$326$		−	13.1475i		−	0.728173i
$327$	−1.01972	−	3.60089i	−0.0563908	−	0.199129i
$328$	3.03885	−	3.03885i	0.167793	−	0.167793i
$329$	25.0580			1.38149
$330$	−3.86011	−	14.3830i	−0.212492	−	0.791758i
$331$	−5.76581			−0.316918			−0.158459	−	0.987366i	$-0.550653\pi$
$331$	−5.76581			−0.316918			−0.158459	+	0.987366i	$0.550653\pi$
$332$	2.00448	−	2.00448i	0.110010	−	0.110010i
$333$	7.71659	+	1.83510i	0.422866	+	0.100563i
$334$			15.5247i			0.849475i
$335$	0.120562	−	8.76143i	0.00658699	−	0.478688i
$336$	7.37712	+	4.12100i	0.402455	+	0.224819i
$337$	−11.3239	−	11.3239i	−0.616851	−	0.616851i	0.327871	−	0.944722i	$-0.393669\pi$
$337$	−11.3239	−	11.3239i	−0.616851	−	0.616851i	−0.944722	+	0.327871i	$0.893669\pi$
$338$	8.10908	+	8.10908i	0.441076	+	0.441076i
$339$	18.4711	+	10.3183i	1.00321	+	0.560414i
$340$	−0.0590463	+	4.29100i	−0.00320223	+	0.232712i
$341$		−	21.4607i		−	1.16216i
$342$	11.1347	+	2.64797i	0.602096	+	0.143186i
$343$	33.8128	−	33.8128i	1.82572	−	1.82572i
$344$	−0.201747			−0.0108775
$345$	−1.00391	−	3.74061i	−0.0540485	−	0.201388i
$346$	−24.5221			−1.31832
$347$	−6.47445	+	6.47445i	−0.347567	+	0.347567i	−0.859203	−	0.511636i	$-0.829040\pi$
$347$	−6.47445	+	6.47445i	−0.347567	+	0.347567i	0.511636	+	0.859203i	$0.329040\pi$
$348$	−3.67378	−	12.9730i	−0.196935	−	0.695425i
$349$			11.4593i			0.613401i	0.951806	+	0.306701i	$0.0992251\pi$
$349$			11.4593i			0.613401i	−0.951806	+	0.306701i	$0.900775\pi$
$350$	0.671204	−	24.3842i	0.0358774	−	1.30339i
$351$	−0.273164	−	6.42575i	−0.0145804	−	0.342981i
$352$	2.71889	+	2.71889i	0.144917	+	0.144917i
$353$	−14.6045	−	14.6045i	−0.777319	−	0.777319i	0.202055	−	0.979374i	$-0.435238\pi$
$353$	−14.6045	−	14.6045i	−0.777319	−	0.777319i	−0.979374	+	0.202055i	$0.935238\pi$
$354$	3.27163	−	5.85664i	0.173885	−	0.311277i
$355$	−9.85967	+	9.59200i	−0.523297	+	0.509091i
$356$		−	12.5987i		−	0.667728i
$357$	15.6036	−	4.41874i	0.825833	−	0.233865i
$358$	−1.04011	+	1.04011i	−0.0549715	+	0.0549715i
$359$	−3.30519			−0.174441			−0.0872207	−	0.996189i	$-0.527799\pi$
$359$	−3.30519			−0.174441			−0.0872207	+	0.996189i	$0.527799\pi$
$360$	−3.43835	−	5.76001i	−0.181217	−	0.303579i
$361$	4.44518			0.233957
$362$	−11.0911	+	11.0911i	−0.582936	+	0.582936i
$363$	−6.30734	+	1.78615i	−0.331050	+	0.0937488i
$364$			6.03860i			0.316509i
$365$	−30.3799	−	0.418043i	−1.59016	−	0.0218814i
$366$	−11.4587	+	20.5126i	−0.598957	+	1.07221i
$367$	−12.2911	−	12.2911i	−0.641591	−	0.641591i	0.309355	−	0.950946i	$-0.399887\pi$
$367$	−12.2911	−	12.2911i	−0.641591	−	0.641591i	−0.950946	+	0.309355i	$0.899887\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	6.75999	+	10.9784i	0.351911	+	0.571513i
$370$	4.12251	+	4.23754i	0.214319	+	0.220299i
$371$		−	25.0115i		−	1.29853i
$372$	−2.63402	−	9.30135i	−0.136567	−	0.482253i
$373$	4.21951	−	4.21951i	0.218478	−	0.218478i	−0.589379	−	0.807857i	$-0.700627\pi$
$373$	4.21951	−	4.21951i	0.218478	−	0.218478i	0.807857	+	0.589379i	$0.200627\pi$
$374$	7.37940			0.381580
$375$	−10.1336	+	16.5018i	−0.523297	+	0.852150i
$376$	5.13622			0.264880
$377$	6.81318	−	6.81318i	0.350897	−	0.350897i
$378$	−17.1479	+	18.6706i	−0.881993	+	0.960311i
$379$		−	24.7674i		−	1.27221i	−0.771601	−	0.636107i	$-0.780544\pi$
$379$		−	24.7674i		−	1.27221i	0.771601	−	0.636107i	$-0.219456\pi$
$380$	5.94860	+	6.11459i	0.305157	+	0.313672i
$381$	−22.3269	−	12.4723i	−1.14384	−	0.638974i
$382$	−15.3583	−	15.3583i	−0.785800	−	0.785800i
$383$	−12.2872	−	12.2872i	−0.627846	−	0.627846i	0.319680	−	0.947526i	$-0.396425\pi$
$383$	−12.2872	−	12.2872i	−0.627846	−	0.627846i	−0.947526	+	0.319680i	$0.896425\pi$
$384$	1.51211	+	0.844697i	0.0771647	+	0.0431057i
$385$	−41.9424	−	0.577149i	−2.13758	−	0.0294142i
$386$		−	25.2157i		−	1.28345i
$387$	0.140029	−	0.588819i	0.00711806	−	0.0299314i
$388$	−3.36602	+	3.36602i	−0.170884	+	0.170884i
$389$	−15.4882			−0.785281			−0.392640	−	0.919692i	$-0.628438\pi$
$389$	−15.4882			−0.785281			−0.392640	+	0.919692i	$0.628438\pi$
$390$	2.39523	−	4.15252i	0.121287	−	0.210271i
$391$	1.91917			0.0970568
$392$	11.8805	−	11.8805i	0.600054	−	0.600054i
$393$	5.30765	+	18.7426i	0.267736	+	0.945439i
$394$			1.14004i			0.0574342i
$395$	27.5602	−	26.8120i	1.38670	−	1.34906i
$396$	−9.82250	+	6.04824i	−0.493599	+	0.303935i
$397$	−14.2745	−	14.2745i	−0.716415	−	0.716415i	0.251454	−	0.967869i	$-0.419091\pi$
$397$	−14.2745	−	14.2745i	−0.716415	−	0.716415i	−0.967869	+	0.251454i	$0.919091\pi$
$398$	12.7628	+	12.7628i	0.639742	+	0.639742i
$399$	15.7220	−	28.1443i	0.787082	−	1.40898i
$400$	0.137579	−	4.99811i	0.00687895	−	0.249905i
$401$		−	3.26739i		−	0.163166i	−0.996667	−	0.0815829i	$-0.974002\pi$
$401$		−	3.26739i		−	0.163166i	0.996667	−	0.0815829i	$-0.0259975\pi$
$402$	−6.53041	+	1.84932i	−0.325707	+	0.0922359i
$403$	4.88490	−	4.88490i	0.243334	−	0.243334i
$404$	−11.2944			−0.561916
$405$	19.1977	−	6.03727i	0.953941	−	0.299994i
$406$	−37.9781			−1.88482
$407$	7.18856	−	7.18856i	0.356324	−	0.356324i
$408$	3.19833	−	0.905725i	0.158341	−	0.0448401i
$409$		−	33.7644i		−	1.66954i	−0.550596	−	0.834772i	$-0.685600\pi$
$409$		−	33.7644i		−	1.66954i	0.550596	−	0.834772i	$-0.314400\pi$
$410$	−0.132222	+	9.60878i	−0.00652997	+	0.474544i
$411$	12.4550	−	22.2961i	0.614361	−	1.09978i
$412$	8.36819	+	8.36819i	0.412271	+	0.412271i
$413$	−13.3614	−	13.3614i	−0.657470	−	0.657470i
$414$	−2.55455	+	1.57298i	−0.125550	+	0.0773075i
$415$	−0.0872160	+	6.33814i	−0.00428126	+	0.311127i
$416$			1.23775i			0.0606859i
$417$	6.91155	+	24.4063i	0.338460	+	1.19518i
$418$	10.3728	−	10.3728i	0.507349	−	0.507349i
$419$	−20.6323			−1.00795			−0.503977	−	0.863717i	$-0.668130\pi$
$419$	−20.6323			−1.00795			−0.503977	+	0.863717i	$0.668130\pi$
$420$	−18.2492	+	4.89774i	−0.890472	+	0.238985i
$421$	−33.8481			−1.64966			−0.824828	−	0.565383i	$-0.808728\pi$
$421$	−33.8481			−1.64966			−0.824828	+	0.565383i	$0.808728\pi$
$422$	5.62749	−	5.62749i	0.273942	−	0.273942i
$423$	−3.56495	+	14.9906i	−0.173334	+	0.728867i
$424$		−	5.12670i		−	0.248975i
$425$	−6.59603	−	6.96944i	−0.319954	−	0.338067i
$426$	9.30213	+	5.19635i	0.450690	+	0.251764i
$427$	46.7975	+	46.7975i	2.26469	+	2.26469i
$428$	7.21940	+	7.21940i	0.348963	+	0.348963i
$429$	−7.19657	−	4.02015i	−0.347454	−	0.194095i
$430$	0.323349	−	0.314570i	0.0155932	−	0.0151699i
$431$			11.9724i			0.576690i	0.957527	+	0.288345i	$0.0931051\pi$
$431$			11.9724i			0.576690i	−0.957527	+	0.288345i	$0.906895\pi$
$432$	−3.51487	+	3.82697i	−0.169109	+	0.184125i
$433$	13.6433	−	13.6433i	0.655655	−	0.655655i	−0.298694	−	0.954349i	$-0.596551\pi$
$433$	13.6433	−	13.6433i	0.655655	−	0.655655i	0.954349	+	0.298694i	$0.0965511\pi$
$434$	−27.2294			−1.30706
$435$	26.1161	+	15.0641i	1.25217	+	0.722269i
$436$	−2.16073			−0.103480
$437$	2.69767	−	2.69767i	0.129047	−	0.129047i
$438$	6.41246	+	22.6439i	0.306399	+	1.08197i
$439$		−	12.4463i		−	0.594027i	−0.954873	−	0.297014i	$-0.904009\pi$
$439$		−	12.4463i		−	0.594027i	0.954873	−	0.297014i	$-0.0959907\pi$
$440$	−8.59708	−	0.118300i	−0.409850	−	0.00563974i
$441$	26.4284	+	42.9204i	1.25849	+	2.04383i
$442$	1.67971	+	1.67971i	0.0798955	+	0.0798955i
$443$	8.23721	+	8.23721i	0.391362	+	0.391362i	0.875173	−	0.483811i	$-0.160748\pi$
$443$	8.23721	+	8.23721i	0.391362	+	0.391362i	−0.483811	+	0.875173i	$0.660748\pi$
$444$	2.23332	−	3.99792i	0.105989	−	0.189733i
$445$	19.6443	+	20.1924i	0.931227	+	0.957213i
$446$		−	23.4675i		−	1.11122i
$447$	2.03279	−	0.575658i	0.0961476	−	0.0272277i
$448$	3.44975	−	3.44975i	0.162985	−	0.162985i
$449$	−16.4715			−0.777340			−0.388670	−	0.921377i	$-0.627065\pi$
$449$	−16.4715			−0.777340			−0.388670	+	0.921377i	$0.627065\pi$
$450$	14.4920	+	3.87063i	0.683160	+	0.182463i
$451$	16.5246			0.778114
$452$	8.63760	−	8.63760i	0.406279	−	0.406279i
$453$	11.5337	−	3.26619i	0.541900	−	0.153459i
$454$		−	6.91748i		−	0.324653i
$455$	−9.41560	−	9.67834i	−0.441410	−	0.453728i
$456$	3.22258	−	5.76883i	0.150911	−	0.270150i
$457$	−8.60752	−	8.60752i	−0.402643	−	0.402643i	0.476520	−	0.879163i	$-0.341898\pi$
$457$	−8.60752	−	8.60752i	−0.402643	−	0.402643i	−0.879163	+	0.476520i	$0.841898\pi$
$458$	−3.10672	−	3.10672i	−0.145167	−	0.145167i
$459$	0.423549	+	9.96332i	0.0197696	+	0.465048i
$460$	−2.23586	−	0.0307665i	−0.104247	−	0.00143450i
$461$			37.7905i			1.76008i	0.474898	+	0.880041i	$0.342485\pi$
$461$			37.7905i			1.76008i	−0.474898	+	0.880041i	$0.657515\pi$
$462$	8.85302	+	31.2622i	0.411880	+	1.45445i
$463$	−7.64424	+	7.64424i	−0.355258	+	0.355258i	−0.862062	−	0.506804i	$-0.830827\pi$
$463$	−7.64424	+	7.64424i	−0.355258	+	0.355258i	0.506804	+	0.862062i	$0.330827\pi$
$464$	−7.78450			−0.361386
$465$	18.7246	+	10.8006i	0.868334	+	0.500868i
$466$	12.6444			0.585741
$467$	−5.24131	+	5.24131i	−0.242539	+	0.242539i	−0.817900	−	0.575361i	$-0.804862\pi$
$467$	−5.24131	+	5.24131i	−0.242539	+	0.242539i	0.575361	+	0.817900i	$0.304862\pi$
$468$	−3.61251	−	0.859102i	−0.166988	−	0.0397120i
$469$			19.1176i			0.882768i
$470$	−8.23204	+	8.00856i	−0.379716	+	0.369407i
$471$	3.57393	+	1.99647i	0.164678	+	0.0919923i
$472$	−2.73873	−	2.73873i	−0.126060	−	0.126060i
$473$	−0.548528	−	0.548528i	−0.0252213	−	0.0252213i
$474$	−26.0017	−	14.5251i	−1.19430	−	0.667159i
$475$	−19.0682	−	0.524875i	−0.874907	−	0.0240829i
$476$		−	9.36303i		−	0.429154i
$477$	14.9628	+	3.55835i	0.685100	+	0.162926i
$478$	5.00034	−	5.00034i	0.228710	−	0.228710i
$479$	−26.6043			−1.21558			−0.607790	−	0.794098i	$-0.707944\pi$
$479$	−26.6043			−1.21558			−0.607790	+	0.794098i	$0.707944\pi$
$480$	−3.74061	+	1.00391i	−0.170735	+	0.0458218i
$481$	3.27254			0.149215
$482$	−2.98827	+	2.98827i	−0.136112	+	0.136112i
$483$	2.30242	+	8.13040i	0.104764	+	0.369946i
$484$			3.78475i			0.172034i
$485$	0.146457	−	10.6433i	0.00665027	−	0.483286i
$486$	−8.72982	−	12.9147i	−0.395993	−	0.585824i
$487$	−5.61285	−	5.61285i	−0.254342	−	0.254342i	0.568406	−	0.822748i	$-0.307560\pi$
$487$	−5.61285	−	5.61285i	−0.254342	−	0.254342i	−0.822748	+	0.568406i	$0.807560\pi$
$488$	9.59226	+	9.59226i	0.434221	+	0.434221i
$489$	11.1057	−	19.8805i	0.502215	−	0.899029i
$490$	−0.516924	+	37.5658i	−0.0233523	+	1.69705i
$491$		−	35.1263i		−	1.58523i	−0.609724	−	0.792614i	$-0.708720\pi$
$491$		−	35.1263i		−	1.58523i	0.609724	−	0.792614i	$-0.291280\pi$
$492$	7.16200	−	2.02818i	0.322888	−	0.0914375i
$493$	−10.5640	+	10.5640i	−0.475780	+	0.475780i
$494$	4.72213			0.212459
$495$	6.31234	−	25.0094i	0.283719	−	1.12409i
$496$	−5.58131			−0.250608
$497$	21.2219	−	21.2219i	0.951934	−	0.951934i
$498$	4.72419	−	1.33783i	0.211696	−	0.0599495i
$499$			10.0259i			0.448822i	0.974495	+	0.224411i	$0.0720458\pi$
$499$			10.0259i			0.448822i	−0.974495	+	0.224411i	$0.927954\pi$
$500$	7.57271	+	8.22521i	0.338662	+	0.367842i
$501$	−13.1137	+	23.4751i	−0.585876	+	1.04879i
$502$	−0.225518	−	0.225518i	−0.0100654	−	0.0100654i
$503$	14.7345	+	14.7345i	0.656979	+	0.656979i	0.954664	−	0.297685i	$-0.0962145\pi$
$503$	14.7345	+	14.7345i	0.656979	+	0.656979i	−0.297685	+	0.954664i	$0.596215\pi$
$504$	7.67404	+	12.4629i	0.341829	+	0.555140i
$505$	18.1020	−	17.6106i	0.805528	−	0.783660i
$506$			3.84509i			0.170935i
$507$	5.41214	+	19.1116i	0.240361	+	0.848774i
$508$	−10.4407	+	10.4407i	−0.463231	+	0.463231i
$509$	−29.8800			−1.32441			−0.662205	−	0.749323i	$-0.730379\pi$
$509$	−29.8800			−1.32441			−0.662205	+	0.749323i	$0.730379\pi$
$510$	−3.71387	+	6.43860i	−0.164453	+	0.285106i
$511$	66.2895			2.93247
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	14.6002	+	13.4095i	0.644615	+	0.592043i
$514$			13.9885i			0.617007i
$515$	−26.4600	−	0.364103i	−1.16597	−	0.0160443i
$516$	−0.305064	−	0.170415i	−0.0134297	−	0.00750209i
$517$	13.9648	+	13.9648i	0.614172	+	0.614172i
$518$	−9.12089	−	9.12089i	−0.400749	−	0.400749i
$519$	−37.0803	−	20.7138i	−1.62764	−	0.909234i
$520$	−1.92995	−	1.98380i	−0.0846338	−	0.0869955i
$521$			1.39433i			0.0610866i	0.999533	+	0.0305433i	$0.00972375\pi$
$521$			1.39433i			0.0610866i	−0.999533	+	0.0305433i	$0.990276\pi$
$522$	5.40308	−	22.7199i	0.236486	−	0.994422i
$523$	−25.8878	+	25.8878i	−1.13199	+	1.13199i	−0.142148	+	0.989845i	$0.545401\pi$
$523$	−25.8878	+	25.8878i	−1.13199	+	1.13199i	−0.989845	+	0.142148i	$0.954599\pi$
$524$	11.2466			0.491309
$525$	21.6122	−	36.3047i	0.943232	−	1.58447i
$526$	8.83047			0.385027
$527$	−7.57418	+	7.57418i	−0.329936	+	0.329936i
$528$	1.81463	+	6.40791i	0.0789718	+	0.278869i
$529$			1.00000i			0.0434783i
$530$	7.99372	+	8.21679i	0.347225	+	0.356914i
$531$	9.89417	−	6.09236i	0.429370	−	0.264386i
$532$	−13.1611	−	13.1611i	−0.570604	−	0.570604i
$533$	3.76135	+	3.76135i	0.162922	+	0.162922i
$534$	10.6420	−	19.0506i	0.460526	−	0.824400i
$535$	−22.8276	−	0.314119i	−0.986922	−	0.0135805i
$536$			3.91860i			0.169258i
$537$	−2.45134	+	0.694187i	−0.105783	+	0.0299564i
$538$	8.12981	−	8.12981i	0.350501	−	0.350501i
$539$	64.6034			2.78267
$540$	−0.333716	−	11.6142i	−0.0143608	−	0.499794i
$541$	18.7230			0.804966			0.402483	−	0.915427i	$-0.368147\pi$
$541$	18.7230			0.804966			0.402483	+	0.915427i	$0.368147\pi$
$542$	10.1914	−	10.1914i	0.437760	−	0.437760i
$543$	−26.1396	+	7.40239i	−1.12176	+	0.317667i
$544$		−	1.91917i		−	0.0822839i
$545$	3.46309	−	3.36908i	0.148343	−	0.144315i
$546$	−5.10079	+	9.13106i	−0.218294	+	0.390773i
$547$	17.9273	+	17.9273i	0.766517	+	0.766517i	0.977492	−	0.210974i	$-0.0676636\pi$
$547$	17.9273	+	17.9273i	0.766517	+	0.766517i	−0.210974	+	0.977492i	$0.567664\pi$
$548$	−10.4263	−	10.4263i	−0.445388	−	0.445388i
$549$	−34.6538	+	21.3382i	−1.47899	+	0.910692i
$550$	13.9634	−	13.2152i	0.595400	−	0.563500i
$551$			29.6985i			1.26520i
$552$	0.471935	+	1.66652i	0.0200869	+	0.0709317i
$553$	−59.3205	+	59.3205i	−2.52257	+	2.52257i
$554$	−30.8844			−1.31215
$555$	2.65426	+	9.88992i	0.112667	+	0.419804i
$556$	14.6451			0.621092
$557$	18.5689	−	18.5689i	0.786789	−	0.786789i	−0.194178	−	0.980966i	$-0.562204\pi$
$557$	18.5689	−	18.5689i	0.786789	−	0.786789i	0.980966	+	0.194178i	$0.0622038\pi$
$558$	3.87389	−	16.2896i	0.163995	−	0.689596i
$559$		−	0.249713i		−	0.0105617i
$560$	−0.150100	+	10.9080i	−0.00634288	+	0.460948i
$561$	11.1585	+	6.23336i	0.471112	+	0.263172i
$562$	23.0281	+	23.0281i	0.971383	+	0.971383i
$563$	−9.38961	−	9.38961i	−0.395725	−	0.395725i	0.480997	−	0.876722i	$-0.340275\pi$
$563$	−9.38961	−	9.38961i	−0.395725	−	0.395725i	−0.876722	+	0.480997i	$0.840275\pi$
$564$	7.76654	+	4.33854i	0.327030	+	0.182686i
$565$	−0.375826	+	27.3119i	−0.0158111	+	1.14902i
$566$			25.6768i			1.07927i
$567$	−41.7005	+	13.7473i	−1.75126	+	0.577330i
$568$	4.34994	−	4.34994i	0.182519	−	0.182519i
$569$	9.13075			0.382781			0.191390	−	0.981514i	$-0.438700\pi$
$569$	9.13075			0.382781			0.191390	+	0.981514i	$0.438700\pi$
$570$	3.82998	+	14.2707i	0.160420	+	0.597735i
$571$	33.9459			1.42059			0.710296	−	0.703903i	$-0.248561\pi$
$571$	33.9459			1.42059			0.710296	+	0.703903i	$0.248561\pi$
$572$	−3.36532	+	3.36532i	−0.140711	+	0.140711i
$573$	−10.2504	−	36.1967i	−0.428217	−	1.51214i
$574$		−	20.9665i		−	0.875127i
$575$	3.63148	−	3.43691i	0.151443	−	0.143329i
$576$	1.57298	+	2.55455i	0.0655406	+	0.106440i
$577$	−3.14294	−	3.14294i	−0.130842	−	0.130842i	0.638653	−	0.769495i	$-0.279492\pi$
$577$	−3.14294	−	3.14294i	−0.130842	−	0.130842i	−0.769495	+	0.638653i	$0.779492\pi$
$578$	9.41638	+	9.41638i	0.391670	+	0.391670i
$579$	21.2996	−	38.1290i	0.885182	−	1.58459i
$580$	12.4766	−	12.1379i	0.518061	−	0.503997i
$581$		−	13.8299i		−	0.573762i
$582$	−7.93307	+	2.24654i	−0.328836	+	0.0931220i
$583$	13.9389	−	13.9389i	0.577292	−	0.577292i
$584$	13.5876			0.562258
$585$	7.12948	−	4.25583i	0.294768	−	0.175957i
$586$	13.9094			0.574594
$587$	15.2589	−	15.2589i	0.629804	−	0.629804i	−0.318215	−	0.948019i	$-0.603083\pi$
$587$	15.2589	−	15.2589i	0.629804	−	0.629804i	0.948019	+	0.318215i	$0.103083\pi$
$588$	28.0000	−	7.92922i	1.15470	−	0.326996i
$589$			21.2931i			0.877369i
$590$	8.65980	+	0.119163i	0.356518	+	0.00490587i
$591$	−0.962985	+	1.72387i	−0.0396119	+	0.0709103i
$592$	−1.86954	−	1.86954i	−0.0768377	−	0.0768377i
$593$	23.4549	+	23.4549i	0.963176	+	0.963176i	0.999346	−	0.0361698i	$-0.0115157\pi$
$593$	23.4549	+	23.4549i	0.963176	+	0.963176i	−0.0361698	+	0.999346i	$0.511516\pi$
$594$	−19.9617	+	0.848587i	−0.819037	+	0.0348179i
$595$	14.5992	+	15.0065i	0.598507	+	0.615208i
$596$		−	1.21978i		−	0.0499642i
$597$	8.51811	+	30.0795i	0.348623	+	1.23107i
$598$	−0.875224	+	0.875224i	−0.0357906	+	0.0357906i
$599$	−10.6390			−0.434697			−0.217349	−	0.976094i	$-0.569741\pi$
$599$	−10.6390			−0.434697			−0.217349	+	0.976094i	$0.569741\pi$
$600$	4.42992	−	7.44149i	0.180851	−	0.303798i
$601$	−24.4899			−0.998966			−0.499483	−	0.866324i	$-0.666477\pi$
$601$	−24.4899			−0.998966			−0.499483	+	0.866324i	$0.666477\pi$
$602$	−0.695975	+	0.695975i	−0.0283658	+	0.0283658i
$603$	−11.4368	−	2.71983i	−0.465744	−	0.110760i
$604$		−	6.92084i		−	0.281605i
$605$	−5.90131	−	6.06598i	−0.239922	−	0.246617i
$606$	−17.0784	−	9.54032i	−0.693761	−	0.387549i
$607$	−20.6737	−	20.6737i	−0.839120	−	0.839120i	0.149623	−	0.988743i	$-0.452194\pi$
$607$	−20.6737	−	20.6737i	−0.839120	−	0.839120i	−0.988743	+	0.149623i	$0.952194\pi$
$608$	−2.69767	−	2.69767i	−0.109405	−	0.109405i
$609$	−57.4272	−	32.0799i	−2.32707	−	1.29995i
$610$	−30.3305	−	0.417363i	−1.22805	−	0.0168985i
$611$			6.35737i			0.257192i
$612$	5.60131	+	1.33206i	0.226419	+	0.0538454i
$613$	14.6753	−	14.6753i	0.592731	−	0.592731i	−0.345637	−	0.938368i	$-0.612337\pi$
$613$	14.6753	−	14.6753i	0.592731	−	0.592731i	0.938368	+	0.345637i	$0.112337\pi$
$614$	−23.7136			−0.957004
$615$	−8.31644	+	14.4179i	−0.335351	+	0.581385i
$616$	18.7590			0.755821
$617$	9.12773	−	9.12773i	0.367469	−	0.367469i	−0.499085	−	0.866553i	$-0.666330\pi$
$617$	9.12773	−	9.12773i	0.367469	−	0.367469i	0.866553	+	0.499085i	$0.166330\pi$
$618$	5.58507	+	19.7222i	0.224664	+	0.793344i
$619$			14.8927i			0.598587i	0.954161	+	0.299294i	$0.0967510\pi$
$619$			14.8927i			0.598587i	−0.954161	+	0.299294i	$0.903249\pi$
$620$	8.94542	−	8.70257i	0.359257	−	0.349504i
$621$	−5.19146	+	0.220693i	−0.208326	+	0.00885612i
$622$	4.50326	+	4.50326i	0.180564	+	0.180564i
$623$	−43.4622	−	43.4622i	−1.74128	−	1.74128i
$624$	−1.04553	+	1.87162i	−0.0418546	+	0.0749249i
$625$	−24.9621	−	1.37527i	−0.998486	−	0.0550108i
$626$			23.8188i			0.951993i
$627$	24.4467	−	6.92297i	0.976307	−	0.276477i
$628$	1.67127	−	1.67127i	0.0666909	−	0.0666909i
$629$	−5.07416			−0.202320
$630$	−31.7320	−	8.00914i	−1.26423	−	0.319092i
$631$	−5.19423			−0.206779			−0.103390	−	0.994641i	$-0.532969\pi$
$631$	−5.19423			−0.206779			−0.103390	+	0.994641i	$0.532969\pi$
$632$	−12.1591	+	12.1591i	−0.483664	+	0.483664i
$633$	13.2629	−	3.75588i	0.527154	−	0.149283i
$634$		−	25.1840i		−	1.00018i
$635$	0.454279	−	33.0133i	0.0180275	−	1.31009i
$636$	4.33051	−	7.75215i	0.171716	−	0.307393i
$637$	14.7051	+	14.7051i	0.582637	+	0.582637i
$638$	−21.1652	−	21.1652i	−0.837939	−	0.837939i
$639$	9.67653	+	15.7150i	0.382798	+	0.621674i
$640$	−0.0307665	+	2.23586i	−0.00121615	+	0.0883800i
$641$			37.8880i			1.49649i	0.663425	+	0.748243i	$0.269102\pi$
$641$			37.8880i			1.49649i	−0.663425	+	0.748243i	$0.730898\pi$
$642$	4.81835	+	17.0147i	0.190165	+	0.671518i
$643$	−8.06700	+	8.06700i	−0.318131	+	0.318131i	−0.848049	−	0.529918i	$-0.822223\pi$
$643$	−8.06700	+	8.06700i	−0.318131	+	0.318131i	0.529918	+	0.848049i	$0.322223\pi$
$644$	4.87868			0.192247
$645$	0.754656	−	0.202535i	0.0297146	−	0.00797480i
$646$	−7.32179			−0.288072
$647$	−19.7436	+	19.7436i	−0.776203	+	0.776203i	−0.979183	−	0.202980i	$-0.934937\pi$
$647$	−19.7436	+	19.7436i	−0.776203	+	0.776203i	0.202980	+	0.979183i	$0.434937\pi$
$648$	−8.54751	+	2.81782i	−0.335778	+	0.110695i
$649$		−	14.8926i		−	0.584586i
$650$	6.18643	+	0.170289i	0.242652	+	0.00667928i
$651$	−41.1740	−	23.0006i	−1.61374	−	0.901465i
$652$	−9.29670	−	9.29670i	−0.364087	−	0.364087i
$653$	−1.55428	−	1.55428i	−0.0608235	−	0.0608235i	0.676041	−	0.736864i	$-0.263694\pi$
$653$	−1.55428	−	1.55428i	−0.0608235	−	0.0608235i	−0.736864	+	0.676041i	$0.763694\pi$
$654$	−3.26726	−	1.82516i	−0.127760	−	0.0713693i
$655$	−18.0254	+	17.5360i	−0.704310	+	0.685190i
$656$		−	4.29759i		−	0.167793i
$657$	−9.43089	+	39.6568i	−0.367934	+	1.54716i
$658$	17.7187	−	17.7187i	0.690745	−	0.690745i
$659$	10.6771			0.415921			0.207960	−	0.978137i	$-0.433318\pi$
$659$	10.6771			0.415921			0.207960	+	0.978137i	$0.433318\pi$
$660$	−12.8998	−	7.44081i	−0.502125	−	0.289633i
$661$	40.2271			1.56465			0.782326	−	0.622869i	$-0.214033\pi$
$661$	40.2271			1.56465			0.782326	+	0.622869i	$0.214033\pi$
$662$	−4.07705	+	4.07705i	−0.158459	+	0.158459i
$663$	1.12106	+	3.95875i	0.0435385	+	0.153745i
$664$		−	2.83477i		−	0.110010i
$665$	41.6150	+	0.572643i	1.61376	+	0.0222062i
$666$	6.75407	−	4.15884i	0.261715	−	0.161152i
$667$	−5.50447	−	5.50447i	−0.213134	−	0.213134i
$668$	10.9776	+	10.9776i	0.424738	+	0.424738i
$669$	19.8229	−	35.4855i	0.766398	−	1.37195i
$670$	−6.11001	−	6.28051i	−0.236050	−	0.242637i
$671$			52.1606i			2.01364i
$672$	8.13040	−	2.30242i	0.313637	−	0.0888178i
$673$	−24.3131	+	24.3131i	−0.937203	+	0.937203i	−0.998142	−	0.0609388i	$-0.980591\pi$
$673$	−24.3131	+	24.3131i	−0.937203	+	0.937203i	0.0609388	+	0.998142i	$0.480591\pi$
$674$	−16.0144			−0.616851
$675$	18.6440	+	18.0942i	0.717610	+	0.696445i
$676$	11.4680			0.441076
$677$	−32.4421	+	32.4421i	−1.24685	+	1.24685i	−0.289749	+	0.957103i	$0.593572\pi$
$677$	−32.4421	+	32.4421i	−1.24685	+	1.24685i	−0.957103	+	0.289749i	$0.906428\pi$
$678$	20.3572	−	5.76488i	0.781813	−	0.221399i
$679$			23.2238i			0.891249i
$680$	2.99244	+	3.07594i	0.114755	+	0.117957i
$681$	5.84317	−	10.4600i	0.223911	−	0.400829i
$682$	−15.1750	−	15.1750i	−0.581080	−	0.581080i
$683$	30.8958	+	30.8958i	1.18219	+	1.18219i	0.979175	+	0.203020i	$0.0650755\pi$
$683$	30.8958	+	30.8958i	1.18219	+	1.18219i	0.203020	+	0.979175i	$0.434924\pi$
$684$	9.74582	−	6.00102i	0.372641	−	0.229455i
$685$	32.9676	+	0.453651i	1.25963	+	0.0173331i
$686$		−	47.8185i		−	1.82572i
$687$	−2.07348	−	7.32194i	−0.0791081	−	0.279350i
$688$	−0.142657	+	0.142657i	−0.00543873	+	0.00543873i
$689$	6.34559			0.241748
$690$	−3.35488	−	1.93514i	−0.127718	−	0.0736696i
$691$	−4.89262			−0.186124			−0.0930620	−	0.995660i	$-0.529665\pi$
$691$	−4.89262			−0.186124			−0.0930620	+	0.995660i	$0.529665\pi$
$692$	−17.3398	+	17.3398i	−0.659159	+	0.659159i
$693$	−13.0203	+	54.7500i	−0.494599	+	2.07978i
$694$			9.15626i			0.347567i
$695$	−23.4724	+	22.8352i	−0.890359	+	0.866188i
$696$	−11.7710	−	6.57554i	−0.446180	−	0.249245i
$697$	−5.83208	−	5.83208i	−0.220906	−	0.220906i
$698$	8.10294	+	8.10294i	0.306701	+	0.306701i
$699$	19.1198	+	10.6807i	0.723177	+	0.403981i
$700$	−16.7676	−	17.7168i	−0.633755	−	0.669633i
$701$		−	12.6440i		−	0.477556i	−0.971074	−	0.238778i	$-0.923253\pi$
$701$		−	12.6440i		−	0.477556i	0.971074	−	0.238778i	$-0.0767468\pi$
$702$	−4.73685	−	4.35054i	−0.178781	−	0.164200i
$703$	−7.13245	+	7.13245i	−0.269005	+	0.269005i
$704$	3.84509			0.144917
$705$	−19.2126	+	5.15628i	−0.723588	+	0.194197i
$706$	−20.6539			−0.777319
$707$	−38.9627	+	38.9627i	−1.46534	+	1.46534i
$708$	−1.82787	−	6.45466i	−0.0686957	−	0.242581i
$709$		−	18.0882i		−	0.679317i	−0.940549	−	0.339658i	$-0.889689\pi$
$709$		−	18.0882i		−	0.679317i	0.940549	−	0.339658i	$-0.110311\pi$
$710$	−0.189268	+	13.7544i	−0.00710309	+	0.516194i
$711$	−27.0483	−	43.9271i	−1.01439	−	1.64740i
$712$	−8.90860	−	8.90860i	−0.333864	−	0.333864i
$713$	−3.94659	−	3.94659i	−0.147801	−	0.147801i
$714$	7.90892	−	14.1580i	0.295984	−	0.529849i
$715$	0.146426	−	10.6411i	0.00547604	−	0.397953i
$716$			1.47094i			0.0549715i
$717$	11.7849	−	3.33731i	0.440113	−	0.124634i
$718$	−2.33713	+	2.33713i	−0.0872207	+	0.0872207i
$719$	18.9895			0.708188			0.354094	−	0.935210i	$-0.384789\pi$
$719$	18.9895			0.708188			0.354094	+	0.935210i	$0.384789\pi$
$720$	−6.50423	−	1.64166i	−0.242398	−	0.0611811i
$721$	57.7363			2.15021
$722$	3.14322	−	3.14322i	0.116978	−	0.116978i
$723$	−7.04278	+	1.99442i	−0.261924	+	0.0741733i
$724$			15.6852i			0.582936i
$725$	−1.07098	+	38.9078i	−0.0397753	+	1.44500i
$726$	−3.19696	+	5.72297i	−0.118650	+	0.212399i
$727$	−2.21531	−	2.21531i	−0.0821613	−	0.0821613i	0.664832	−	0.746993i	$-0.268503\pi$
$727$	−2.21531	−	2.21531i	−0.0821613	−	0.0821613i	−0.746993	+	0.664832i	$0.768503\pi$
$728$	4.26994	+	4.26994i	0.158254	+	0.158254i
$729$	−2.29144	−	26.9026i	−0.0848683	−	0.996392i
$730$	−21.7774	+	21.1862i	−0.806019	+	0.784138i
$731$			0.387187i			0.0143206i
$732$	6.40203	+	22.6071i	0.236626	+	0.835583i
$733$	23.0122	−	23.0122i	0.849976	−	0.849976i	−0.140154	−	0.990130i	$-0.544760\pi$
$733$	23.0122	−	23.0122i	0.849976	−	0.849976i	0.990130	+	0.140154i	$0.0447597\pi$
$734$	−17.3823			−0.641591
$735$	−32.5133	+	56.3671i	−1.19927	+	2.07913i
$736$	1.00000			0.0368605
$737$	−10.6542	+	10.6542i	−0.392454	+	0.392454i
$738$	12.5430	+	2.98287i	0.461712	+	0.109801i
$739$		−	10.0080i		−	0.368151i	−0.982912	−	0.184076i	$-0.941071\pi$
$739$		−	10.0080i		−	0.368151i	0.982912	−	0.184076i	$-0.0589291\pi$
$740$	5.91145	+	0.0813446i	0.217309	+	0.00299029i
$741$	7.14039	+	3.98876i	0.262309	+	0.146531i
$742$	−17.6858	−	17.6858i	−0.649267	−	0.649267i
$743$	23.6306	+	23.6306i	0.866922	+	0.866922i	0.992130	−	0.125208i	$-0.0399599\pi$
$743$	23.6306	+	23.6306i	0.866922	+	0.866922i	−0.125208	+	0.992130i	$0.539960\pi$
$744$	−8.43958	−	4.71452i	−0.309410	−	0.172843i
$745$	1.90193	+	1.95500i	0.0696812	+	0.0716257i
$746$		−	5.96729i		−	0.218478i
$747$	8.27357	+	1.96756i	0.302714	+	0.0719893i
$748$	5.21802	−	5.21802i	0.190790	−	0.190790i
$749$	49.8102			1.82002
$750$	4.50300	+	18.8341i	0.164426	+	0.687724i
$751$	17.4785			0.637798			0.318899	−	0.947789i	$-0.396687\pi$
$751$	17.4785			0.637798			0.318899	+	0.947789i	$0.396687\pi$
$752$	3.63185	−	3.63185i	0.132440	−	0.132440i
$753$	−0.150515	−	0.531504i	−0.00548506	−	0.0193691i
$754$		−	9.63529i		−	0.350897i
$755$	10.7912	+	11.0923i	0.392732	+	0.403691i
$756$	1.07669	+	25.3275i	0.0391589	+	0.921152i
$757$	7.37005	+	7.37005i	0.267869	+	0.267869i	0.828241	−	0.560372i	$-0.189342\pi$
$757$	7.37005	+	7.37005i	0.267869	+	0.267869i	−0.560372	+	0.828241i	$0.689342\pi$
$758$	−17.5132	−	17.5132i	−0.636107	−	0.636107i
$759$	−3.24794	+	5.81422i	−0.117893	+	0.211043i
$760$	8.52997	+	0.117377i	0.309414	+	0.00425770i
$761$		−	49.0359i		−	1.77755i	−0.458345	−	0.888774i	$-0.651558\pi$
$761$		−	49.0359i		−	1.77755i	0.458345	−	0.888774i	$-0.348442\pi$
$762$	−24.6067	+	6.96830i	−0.891408	+	0.252435i
$763$	−7.45396	+	7.45396i	−0.269851	+	0.269851i
$764$	−21.7200			−0.785800
$765$	−11.0545	+	6.59879i	−0.399675	+	0.238580i
$766$	−17.3767			−0.627846
$767$	3.38987	−	3.38987i	0.122401	−	0.122401i
$768$	1.66652	−	0.471935i	0.0601352	−	0.0170295i
$769$		−	24.0936i		−	0.868838i	−0.900711	−	0.434419i	$-0.856954\pi$
$769$		−	24.0936i		−	0.868838i	0.900711	−	0.434419i	$-0.143046\pi$
$770$	−30.0659	+	29.2496i	−1.08350	+	1.05408i
$771$	−11.8161	+	21.1522i	−0.425545	+	0.761779i
$772$	−17.8302	−	17.8302i	−0.641723	−	0.641723i
$773$	12.6293	+	12.6293i	0.454243	+	0.454243i	0.896760	−	0.442517i	$-0.145914\pi$
$773$	12.6293	+	12.6293i	0.454243	+	0.454243i	−0.442517	+	0.896760i	$0.645914\pi$
$774$	−0.317343	−	0.515373i	−0.0114066	−	0.0185247i
$775$	−0.767872	+	27.8960i	−0.0275828	+	1.00205i
$776$			4.76027i			0.170884i
$777$	−6.08744	−	21.4962i	−0.218386	−	0.771172i
$778$	−10.9518	+	10.9518i	−0.392640	+	0.392640i
$779$	−16.3956			−0.587434
$780$	−1.24259	−	4.62996i	−0.0444918	−	0.165779i
$781$	23.6540			0.846407
$782$	1.35706	−	1.35706i	0.0485284	−	0.0485284i
$783$	27.3615	−	29.7911i	0.977819	−	1.06465i
$784$		−	16.8015i		−	0.600054i
$785$	−0.0727176	+	5.28452i	−0.00259540	+	0.188612i
$786$	17.0061	+	9.49994i	0.606587	+	0.338852i
$787$	−1.79982	−	1.79982i	−0.0641566	−	0.0641566i	0.674300	−	0.738457i	$-0.264445\pi$
$787$	−1.79982	−	1.79982i	−0.0641566	−	0.0641566i	−0.738457	+	0.674300i	$0.764445\pi$
$788$	0.806128	+	0.806128i	0.0287171	+	0.0287171i
$789$	13.3527	+	7.45907i	0.475368	+	0.265550i
$790$	0.529049	−	38.4469i	0.0188227	−	1.36788i
$791$		−	59.5951i		−	2.11896i
$792$	−2.66881	+	11.2223i	−0.0948320	+	0.398767i
$793$	−11.8729	+	11.8729i	−0.421617	+	0.421617i
$794$	−20.1872			−0.716415
$795$	5.14672	+	19.1770i	0.182535	+	0.680138i
$796$	18.0493			0.639742
$797$	30.9163	−	30.9163i	1.09511	−	1.09511i	0.100136	−	0.994974i	$-0.468072\pi$
$797$	30.9163	−	30.9163i	1.09511	−	1.09511i	0.994974	−	0.100136i	$-0.0319279\pi$
$798$	−8.78391	−	31.0181i	−0.310947	−	1.09803i
$799$		−	9.85729i		−	0.348726i
$800$	−3.43691	−	3.63148i	−0.121513	−	0.128392i
$801$	32.1840	−	19.8174i	1.13716	−	0.700213i
$802$	−2.31040	−	2.31040i	−0.0815829	−	0.0815829i
$803$	36.9432	+	36.9432i	1.30370	+	1.30370i
$804$	−3.31003	+	5.92537i	−0.116736	+	0.208972i
$805$	−7.81928	+	7.60700i	−0.275593	+	0.268112i
$806$		−	6.90829i		−	0.243334i
$807$	19.1604	−	5.42598i	0.674479	−	0.191003i
$808$	−7.98633	+	7.98633i	−0.280958	+	0.280958i
$809$	−48.5806			−1.70800			−0.854001	−	0.520272i	$-0.825831\pi$
$809$	−48.5806			−1.70800			−0.854001	+	0.520272i	$0.825831\pi$
$810$	9.30582	−	17.8438i	0.326973	−	0.626968i
$811$	12.0582			0.423419			0.211710	−	0.977333i	$-0.432097\pi$
$811$	12.0582			0.423419			0.211710	+	0.977333i	$0.432097\pi$
$812$	−26.8546	+	26.8546i	−0.942410	+	0.942410i
$813$	24.0193	−	6.80194i	0.842393	−	0.238554i
$814$		−	10.1662i		−	0.356324i
$815$	29.3960	+	0.404503i	1.02970	+	0.0141691i
$816$	1.62112	−	2.90201i	0.0567505	−	0.101591i
$817$	0.544246	+	0.544246i	0.0190407	+	0.0190407i
$818$	−23.8751	−	23.8751i	−0.834772	−	0.834772i
$819$	−15.4259	+	9.49857i	−0.539026	+	0.331907i
$820$	6.70094	+	6.88793i	0.234007	+	0.240537i
$821$			4.47010i			0.156008i	0.996953	+	0.0780038i	$0.0248546\pi$
$821$			4.47010i			0.156008i	−0.996953	+	0.0780038i	$0.975145\pi$
$822$	−6.95867	−	24.5727i	−0.242711	−	0.857072i
$823$	−12.8565	+	12.8565i	−0.448148	+	0.448148i	−0.894739	−	0.446590i	$-0.852638\pi$
$823$	−12.8565	+	12.8565i	−0.448148	+	0.448148i	0.446590	+	0.894739i	$0.352638\pi$
$824$	11.8344			0.412271
$825$	32.2771	−	8.18814i	1.12374	−	0.285075i
$826$	−18.8958			−0.657470
$827$	−19.8305	+	19.8305i	−0.689573	+	0.689573i	−0.962138	−	0.272564i	$-0.912128\pi$
$827$	−19.8305	+	19.8305i	−0.689573	+	0.689573i	0.272564	+	0.962138i	$0.412128\pi$
$828$	−0.694081	+	2.91860i	−0.0241210	+	0.101429i
$829$			32.9160i			1.14322i	0.820526	+	0.571610i	$0.193681\pi$
$829$			32.9160i			1.14322i	−0.820526	+	0.571610i	$0.806319\pi$
$830$	4.42007	+	4.54341i	0.153423	+	0.157704i
$831$	−46.7007	−	26.0879i	−1.62003	−	0.904981i
$832$	0.875224	+	0.875224i	0.0303429	+	0.0303429i
$833$	−22.8007	−	22.8007i	−0.789996	−	0.789996i
$834$	22.1451	+	12.3707i	0.766822	+	0.428362i
$835$	−34.7110	−	0.477642i	−1.20123	−	0.0165295i
$836$		−	14.6693i		−	0.507349i
$837$	19.6176	−	21.3595i	0.678082	−	0.738294i
$838$	−14.5892	+	14.5892i	−0.503977	+	0.503977i
$839$	36.9410			1.27535			0.637673	−	0.770307i	$-0.279897\pi$
$839$	36.9410			1.27535			0.637673	+	0.770307i	$0.279897\pi$
$840$	−9.44094	+	16.3674i	−0.325743	+	0.564728i
$841$	31.5984			1.08960
$842$	−23.9342	+	23.9342i	−0.824828	+	0.824828i
$843$	15.3694	+	54.2729i	0.529349	+	1.86926i
$844$		−	7.95847i		−	0.273942i
$845$	−18.3802	+	17.8812i	−0.632299	+	0.615133i
$846$	8.07914	+	13.1207i	0.277767	+	0.451101i
$847$	13.0564	+	13.0564i	0.448624	+	0.448624i
$848$	−3.62512	−	3.62512i	−0.124487	−	0.124487i
$849$	−21.6891	+	38.8262i	−0.744367	+	1.33251i
$850$	−9.59223	−	0.264038i	−0.329011	−	0.00905643i
$851$		−	2.64393i		−	0.0906328i
$852$	10.2520	−	2.90322i	0.351227	−	0.0994627i
$853$	1.30323	−	1.30323i	0.0446219	−	0.0446219i	−0.684444	−	0.729066i	$-0.739955\pi$
$853$	1.30323	−	1.30323i	0.0446219	−	0.0446219i	0.729066	+	0.684444i	$0.239955\pi$
$854$	66.1817			2.26469
$855$	−6.26307	+	24.8141i	−0.214192	+	0.848625i
$856$	10.2098			0.348963
$857$	27.5259	−	27.5259i	0.940268	−	0.940268i	−0.0580457	−	0.998314i	$-0.518487\pi$
$857$	27.5259	−	27.5259i	0.940268	−	0.940268i	0.998314	+	0.0580457i	$0.0184869\pi$
$858$	−7.93142	+	2.24607i	−0.270774	+	0.0766796i
$859$			11.6992i			0.399172i	0.979880	+	0.199586i	$0.0639597\pi$
$859$			11.6992i			0.399172i	−0.979880	+	0.199586i	$0.936040\pi$
$860$	0.00620705	−	0.451077i	0.000211659	−	0.0153816i
$861$	17.7104	−	31.7038i	0.603568	−	1.08046i
$862$	8.46577	+	8.46577i	0.288345	+	0.288345i
$863$	−25.3452	−	25.3452i	−0.862762	−	0.862762i	0.128896	−	0.991658i	$-0.458857\pi$
$863$	−25.3452	−	25.3452i	−0.862762	−	0.862762i	−0.991658	+	0.128896i	$0.958857\pi$
$864$	0.220693	+	5.19146i	0.00750814	+	0.176617i
$865$	0.754461	−	54.8280i	0.0256524	−	1.86421i
$866$		−	19.2945i		−	0.655655i
$867$	6.28465	+	22.1926i	0.213438	+	0.753701i
$868$	−19.2541	+	19.2541i	−0.653528	+	0.653528i
$869$	−66.1187			−2.24292
$870$	29.1188	−	7.81490i	0.987219	−	0.264950i
$871$	−4.85026			−0.164345
$872$	−1.52786	+	1.52786i	−0.0517400	+	0.0517400i
$873$	−13.8933	−	3.30402i	−0.470219	−	0.111824i
$874$		−	3.81508i		−	0.129047i
$875$	54.4988	+	2.25093i	1.84240	+	0.0760954i
$876$	20.5460	+	11.4774i	0.694184	+	0.387785i
$877$	−5.23787	−	5.23787i	−0.176870	−	0.176870i	0.613120	−	0.789990i	$-0.289914\pi$
$877$	−5.23787	−	5.23787i	−0.176870	−	0.176870i	−0.789990	+	0.613120i	$0.789914\pi$
$878$	−8.80083	−	8.80083i	−0.297014	−	0.297014i
$879$	21.0327	+	11.7493i	0.709414	+	0.396293i
$880$	−6.16270	+	5.99540i	−0.207745	+	0.202105i
$881$			50.3328i			1.69575i	0.530193	+	0.847877i	$0.322120\pi$
$881$			50.3328i			1.69575i	−0.530193	+	0.847877i	$0.677880\pi$
$882$	49.0370	+	11.6616i	1.65116	+	0.392667i
$883$	22.4165	−	22.4165i	0.754377	−	0.754377i	−0.220916	−	0.975293i	$-0.570905\pi$
$883$	22.4165	−	22.4165i	0.754377	−	0.754377i	0.975293	+	0.220916i	$0.0709047\pi$
$884$	2.37546			0.0798955
$885$	12.9939	+	7.49509i	0.436787	+	0.251945i
$886$	11.6492			0.391362
$887$	−7.53529	+	7.53529i	−0.253010	+	0.253010i	−0.822204	−	0.569193i	$-0.807256\pi$
$887$	−7.53529	+	7.53529i	−0.253010	+	0.253010i	0.569193	+	0.822204i	$0.307256\pi$
$888$	−1.24776	−	4.40615i	−0.0418722	−	0.147861i
$889$			72.0356i			2.41599i
$890$	28.1688	+	0.387617i	0.944220	+	0.0129929i
$891$	−30.9011	−	15.5784i	−1.03523	−	0.521896i
$892$	−16.5940	−	16.5940i	−0.555609	−	0.555609i
$893$	−13.8558	−	13.8558i	−0.463667	−	0.463667i
$894$	1.03035	−	1.84445i	0.0344599	−	0.0616876i
$895$	−2.29354	−	2.35754i	−0.0766644	−	0.0788038i
$896$		−	4.87868i		−	0.162985i
$897$	−2.06274	+	0.584139i	−0.0688728	+	0.0195038i
$898$	−11.6471	+	11.6471i	−0.388670	+	0.388670i
$899$	43.4477			1.44906
$900$	12.9843	−	7.51044i	0.432812	−	0.250348i
$901$	−9.83902			−0.327785
$902$	11.6847	−	11.6847i	0.389057	−	0.389057i
$903$	−1.64028	+	0.464506i	−0.0545852	+	0.0154578i
$904$		−	12.2154i		−	0.406279i
$905$	−24.4569	−	25.1394i	−0.812975	−	0.835661i
$906$	5.84601	−	10.4651i	0.194221	−	0.347679i
$907$	30.7230	+	30.7230i	1.02014	+	1.02014i	0.999793	+	0.0203465i	$0.00647695\pi$
$907$	30.7230	+	30.7230i	1.02014	+	1.02014i	0.0203465	+	0.999793i	$0.493523\pi$
$908$	−4.89140	−	4.89140i	−0.162327	−	0.162327i
$909$	−17.7658	−	28.8521i	−0.589253	−	0.956963i
$910$	−13.5015	−	0.185787i	−0.447569	−	0.00615877i
$911$		−	22.0603i		−	0.730892i	−0.930833	−	0.365446i	$-0.880917\pi$
$911$		−	22.0603i		−	0.730892i	0.930833	−	0.365446i	$-0.119083\pi$
$912$	−1.80047	−	6.35789i	−0.0596195	−	0.210531i
$913$	7.70743	−	7.70743i	0.255079	−	0.255079i
$914$	−12.1729			−0.402643
$915$	−45.5106	−	26.2512i	−1.50453	−	0.867837i
$916$	−4.39356			−0.145167
$917$	38.7978	−	38.7978i	1.28122	−	1.28122i
$918$	7.34462	+	6.74564i	0.242409	+	0.222639i
$919$		−	3.88895i		−	0.128285i	−0.997941	−	0.0641423i	$-0.979569\pi$
$919$		−	3.88895i		−	0.128285i	0.997941	−	0.0641423i	$-0.0204312\pi$
$920$	−1.60274	+	1.55923i	−0.0528409	+	0.0514064i
$921$	−35.8577	−	20.0308i	−1.18155	−	0.660038i
$922$	26.7220	+	26.7220i	0.880041	+	0.880041i
$923$	5.38415	+	5.38415i	0.177221	+	0.177221i
$924$	28.3657	+	15.8456i	0.933163	+	0.521284i
$925$	−9.60138	+	9.08696i	−0.315691	+	0.298777i
$926$			10.8106i			0.355258i
$927$	−8.21404	+	34.5399i	−0.269784	+	1.13444i
$928$	−5.50447	+	5.50447i	−0.180693	+	0.180693i
$929$	−23.5939			−0.774091			−0.387045	−	0.922061i	$-0.626504\pi$
$929$	−23.5939			−0.774091			−0.387045	+	0.922061i	$0.626504\pi$
$930$	20.8775	−	5.60312i	0.684601	−	0.183733i
$931$	−64.0991			−2.10076
$932$	8.94095	−	8.94095i	0.292870	−	0.292870i
$933$	3.00555	+	10.6133i	0.0983973	+	0.347465i
$934$			7.41233i			0.242539i
$935$	−0.227038	+	16.4993i	−0.00742495	+	0.539584i
$936$	−3.16191	+	1.94696i	−0.103350	+	0.0636382i
$937$	13.8791	+	13.8791i	0.453411	+	0.453411i	0.896485	−	0.443074i	$-0.146112\pi$
$937$	13.8791	+	13.8791i	0.453411	+	0.453411i	−0.443074	+	0.896485i	$0.646112\pi$
$938$	13.5182	+	13.5182i	0.441384	+	0.441384i
$939$	−20.1197	+	36.0168i	−0.656582	+	1.17536i
$940$	−0.158024	+	11.4838i	−0.00515416	+	0.374562i
$941$		−	28.8322i		−	0.939903i	−0.882692	−	0.469952i	$-0.844271\pi$
$941$		−	28.8322i		−	0.939903i	0.882692	−	0.469952i	$-0.155729\pi$
$942$	3.93886	−	1.11543i	0.128335	−	0.0363428i
$943$	3.03885	−	3.03885i	0.0989586	−	0.0989586i
$944$	−3.87315			−0.126060
$945$	−41.2171	−	38.9147i	−1.34079	−	1.26589i
$946$	−0.775735			−0.0252213
$947$	−18.6992	+	18.6992i	−0.607644	+	0.607644i	−0.942330	−	0.334686i	$-0.891370\pi$
$947$	−18.6992	+	18.6992i	−0.607644	+	0.607644i	0.334686	+	0.942330i	$0.391370\pi$
$948$	−28.6568	+	8.11521i	−0.930729	+	0.263570i
$949$			16.8181i			0.545938i
$950$	−13.8544	+	13.1121i	−0.449495	+	0.425412i
$951$	21.2728	−	38.0811i	0.689819	−	1.23486i
$952$	−6.62066	−	6.62066i	−0.214577	−	0.214577i
$953$	−20.6730	−	20.6730i	−0.669664	−	0.669664i	0.287974	−	0.957638i	$-0.407018\pi$
$953$	−20.6730	−	20.6730i	−0.669664	−	0.669664i	−0.957638	+	0.287974i	$0.907018\pi$
$954$	13.0964	−	8.06417i	0.424013	−	0.261087i
$955$	34.8115	−	33.8665i	1.12647	−	1.09589i
$956$		−	7.07155i		−	0.228710i
$957$	−14.1260	−	49.8824i	−0.456629	−	1.61247i
$958$	−18.8121	+	18.8121i	−0.607790	+	0.607790i
$959$	−71.9360			−2.32293
$960$	−1.93514	+	3.35488i	−0.0624565	+	0.108278i
$961$	0.151067			0.00487312
$962$	2.31403	−	2.31403i	0.0746074	−	0.0746074i
$963$	−7.08641	+	29.7983i	−0.228356	+	0.960236i
$964$			4.22605i			0.136112i
$965$	56.3787	+	0.775799i	1.81489	+	0.0249739i
$966$	7.37712	+	4.12100i	0.237355	+	0.132591i
$967$	−10.4942	−	10.4942i	−0.337471	−	0.337471i	0.517944	−	0.855415i	$-0.326698\pi$
$967$	−10.4942	−	10.4942i	−0.337471	−	0.337471i	−0.855415	+	0.517944i	$0.826698\pi$
$968$	2.67622	+	2.67622i	0.0860170	+	0.0860170i
$969$	−11.0714	−	6.18470i	−0.355664	−	0.198681i
$970$	−7.42238	−	7.62950i	−0.238318	−	0.244968i
$971$		−	3.41196i		−	0.109495i	−0.998500	−	0.0547475i	$-0.982565\pi$
$971$		−	3.41196i		−	0.109495i	0.998500	−	0.0547475i	$-0.0174354\pi$
$972$	−15.3050	−	2.95918i	−0.490908	−	0.0949158i
$973$	50.5220	−	50.5220i	1.61966	−	1.61966i
$974$	−7.93776			−0.254342
$975$	9.21074	+	5.48315i	0.294980	+	0.175601i
$976$	13.5655			0.434221
$977$	−2.16215	+	2.16215i	−0.0691735	+	0.0691735i	−0.740847	−	0.671674i	$-0.765576\pi$
$977$	−2.16215	+	2.16215i	−0.0691735	+	0.0691735i	0.671674	+	0.740847i	$0.265576\pi$
$978$	−6.20477	−	21.9105i	−0.198407	−	0.700622i
$979$		−	48.4430i		−	1.54825i
$980$	26.1975	+	26.9285i	0.836848	+	0.860200i
$981$	−3.39877	−	5.51969i	−0.108514	−	0.176230i
$982$	−24.8380	−	24.8380i	−0.792614	−	0.792614i
$983$	−15.0702	−	15.0702i	−0.480665	−	0.480665i	0.424679	−	0.905344i	$-0.360387\pi$
$983$	−15.0702	−	15.0702i	−0.480665	−	0.480665i	−0.905344	+	0.424679i	$0.860387\pi$
$984$	3.63016	−	6.49844i	0.115725	−	0.207163i
$985$	−2.54896	−	0.0350750i	−0.0812166	−	0.00111758i
$986$			14.9398i			0.475780i
$987$	41.7595	−	11.8257i	1.32922	−	0.376417i
$988$	3.33905	−	3.33905i	0.106229	−	0.106229i
$989$	−0.201747			−0.00641517
$990$	−13.2208	−	22.1478i	−0.420184	−	0.703903i
$991$	−38.6581			−1.22802			−0.614008	−	0.789300i	$-0.710444\pi$
$991$	−38.6581			−1.22802			−0.614008	+	0.789300i	$0.710444\pi$
$992$	−3.94659	+	3.94659i	−0.125304	+	0.125304i
$993$	−9.60883	+	2.72109i	−0.304927	+	0.0863512i
$994$		−	30.0124i		−	0.951934i
$995$	−28.9285	+	28.1431i	−0.917094	+	0.892197i
$996$	2.39452	−	4.28649i	0.0758733	−	0.135823i
$997$	9.32310	+	9.32310i	0.295266	+	0.295266i	0.839156	−	0.543891i	$-0.183049\pi$
$997$	9.32310	+	9.32310i	0.295266	+	0.295266i	−0.543891	+	0.839156i	$0.683049\pi$
$998$	7.08939	+	7.08939i	0.224411	+	0.224411i
$999$	13.7259	−	0.583498i	0.434267	−	0.0184611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.47.16	yes	32
3.2	odd	2	inner	690.2.i.e.47.5	✓	32
5.3	odd	4	inner	690.2.i.e.323.5	yes	32
15.8	even	4	inner	690.2.i.e.323.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.5	✓	32	3.2	odd	2	inner
690.2.i.e.47.16	yes	32	1.1	even	1	trivial
690.2.i.e.323.5	yes	32	5.3	odd	4	inner
690.2.i.e.323.16	yes	32	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +(2.23586 + 0.0307665i) q^{10} -3.84509i q^{11} +(-0.471935 - 1.66652i) q^{12} +(0.875224 - 0.875224i) q^{13} -4.87868 q^{14} +(3.35488 + 1.93514i) q^{15} -1.00000 q^{16} +(-1.35706 + 1.35706i) q^{17} +(0.694081 - 2.91860i) q^{18} +3.81508i q^{19} +(1.60274 - 1.55923i) q^{20} +(-7.37712 - 4.12100i) q^{21} +(-2.71889 - 2.71889i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.51211 - 0.844697i) q^{24} +(-0.137579 + 4.99811i) q^{25} -1.23775i q^{26} +(3.51487 - 3.82697i) q^{27} +(-3.44975 + 3.44975i) q^{28} +7.78450 q^{29} +(3.74061 - 1.00391i) q^{30} +5.58131 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.81463 - 6.40791i) q^{33} +1.91917i q^{34} +(0.150100 - 10.9080i) q^{35} +(-1.57298 - 2.55455i) q^{36} +(1.86954 + 1.86954i) q^{37} +(2.69767 + 2.69767i) q^{38} +(1.04553 - 1.87162i) q^{39} +(0.0307665 - 2.23586i) q^{40} +4.29759i q^{41} +(-8.13040 + 2.30242i) q^{42} +(0.142657 - 0.142657i) q^{43} -3.84509 q^{44} +(6.50423 + 1.64166i) q^{45} -1.00000 q^{46} +(-3.63185 + 3.63185i) q^{47} +(-1.66652 + 0.471935i) q^{48} +16.8015i q^{49} +(3.43691 + 3.63148i) q^{50} +(-1.62112 + 2.90201i) q^{51} +(-0.875224 - 0.875224i) q^{52} +(3.62512 + 3.62512i) q^{53} +(-0.220693 - 5.19146i) q^{54} +(6.16270 - 5.99540i) q^{55} +4.87868i q^{56} +(1.80047 + 6.35789i) q^{57} +(5.50447 - 5.50447i) q^{58} +3.87315 q^{59} +(1.93514 - 3.35488i) q^{60} -13.5655 q^{61} +(3.94659 - 3.94659i) q^{62} +(-14.2389 - 3.38620i) q^{63} +1.00000i q^{64} +(2.76744 + 0.0380814i) q^{65} +(-5.81422 - 3.24794i) q^{66} +(-2.77087 - 2.77087i) q^{67} +(1.35706 + 1.35706i) q^{68} +(-1.51211 - 0.844697i) q^{69} +(-7.60700 - 7.81928i) q^{70} +6.15174i q^{71} +(-2.91860 - 0.694081i) q^{72} +(-9.60788 + 9.60788i) q^{73} +2.64393 q^{74} +(2.12950 + 8.39436i) q^{75} +3.81508 q^{76} +(-13.2646 + 13.2646i) q^{77} +(-0.584139 - 2.06274i) q^{78} -17.1956i q^{79} +(-1.55923 - 1.60274i) q^{80} +(4.05150 - 8.03650i) q^{81} +(3.03885 + 3.03885i) q^{82} +(2.00448 + 2.00448i) q^{83} +(-4.12100 + 7.37712i) q^{84} +(-4.29100 - 0.0590463i) q^{85} -0.201747i q^{86} +(12.9730 - 3.67378i) q^{87} +(-2.71889 + 2.71889i) q^{88} +12.5987 q^{89} +(5.76001 - 3.43835i) q^{90} -6.03860 q^{91} +(-0.707107 + 0.707107i) q^{92} +(9.30135 - 2.63402i) q^{93} +5.13622i q^{94} +(-6.11459 + 5.94860i) q^{95} +(-0.844697 + 1.51211i) q^{96} +(-3.36602 - 3.36602i) q^{97} +(11.8805 + 11.8805i) q^{98} +(-6.04824 - 9.82250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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