LMFDB - Embedded newform 630.2.bk.b.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.b.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.04939 - 1.37796i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.37796 + 1.04939i) q^{6} +(-0.323069 + 2.62595i) q^{7} +1.00000i q^{8} +(-0.797561 + 2.89204i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.04939 - 1.37796i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.37796 + 1.04939i) q^{6} +(-0.323069 + 2.62595i) q^{7} +1.00000i q^{8} +(-0.797561 + 2.89204i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.664943 - 0.383905i) q^{11} +(1.04939 + 1.37796i) q^{12} +(3.78024 - 2.18252i) q^{13} +(2.62595 + 0.323069i) q^{14} +(1.71805 - 0.219817i) q^{15} +1.00000 q^{16} +(1.15157 - 1.99457i) q^{17} +(2.89204 + 0.797561i) q^{18} +(4.19206 - 2.42029i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.95749 - 2.31047i) q^{21} +(-0.383905 - 0.664943i) q^{22} +(4.84784 + 2.79890i) q^{23} +(1.37796 - 1.04939i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.18252 - 3.78024i) q^{26} +(4.82207 - 1.93587i) q^{27} +(0.323069 - 2.62595i) q^{28} +(-9.12141 - 5.26625i) q^{29} +(-0.219817 - 1.71805i) q^{30} +8.05924i q^{31} -1.00000i q^{32} +(-1.22679 - 0.513400i) q^{33} +(-1.99457 - 1.15157i) q^{34} +(-2.11261 - 1.59276i) q^{35} +(0.797561 - 2.89204i) q^{36} +(4.15617 + 7.19869i) q^{37} +(-2.42029 - 4.19206i) q^{38} +(-6.97439 - 2.91871i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(2.65381 + 4.59654i) q^{41} +(-2.31047 - 3.95749i) q^{42} +(5.94724 - 10.3009i) q^{43} +(-0.664943 + 0.383905i) q^{44} +(-2.10580 - 2.13673i) q^{45} +(2.79890 - 4.84784i) q^{46} +6.46146 q^{47} +(-1.04939 - 1.37796i) q^{48} +(-6.79125 - 1.69673i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-3.95689 + 0.506269i) q^{51} +(-3.78024 + 2.18252i) q^{52} +(-6.48067 - 3.74161i) q^{53} +(-1.93587 - 4.82207i) q^{54} +0.767810i q^{55} +(-2.62595 - 0.323069i) q^{56} +(-7.73417 - 3.23668i) q^{57} +(-5.26625 + 9.12141i) q^{58} +11.4347 q^{59} +(-1.71805 + 0.219817i) q^{60} +9.49997i q^{61} +8.05924 q^{62} +(-7.33669 - 3.02868i) q^{63} -1.00000 q^{64} +4.36505i q^{65} +(-0.513400 + 1.22679i) q^{66} +13.7047 q^{67} +(-1.15157 + 1.99457i) q^{68} +(-1.23049 - 9.61728i) q^{69} +(-1.59276 + 2.11261i) q^{70} -7.50583i q^{71} +(-2.89204 - 0.797561i) q^{72} +(10.1185 + 5.84190i) q^{73} +(7.19869 - 4.15617i) q^{74} +(-0.668655 + 1.59778i) q^{75} +(-4.19206 + 2.42029i) q^{76} +(0.793294 + 1.87014i) q^{77} +(-2.91871 + 6.97439i) q^{78} -1.11044 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.72779 - 4.61315i) q^{81} +(4.59654 - 2.65381i) q^{82} +(0.254578 - 0.440942i) q^{83} +(-3.95749 + 2.31047i) q^{84} +(1.15157 + 1.99457i) q^{85} +(-10.3009 - 5.94724i) q^{86} +(2.31523 + 18.0953i) q^{87} +(0.383905 + 0.664943i) q^{88} +(-2.80167 - 4.85263i) q^{89} +(-2.13673 + 2.10580i) q^{90} +(4.50993 + 10.6318i) q^{91} +(-4.84784 - 2.79890i) q^{92} +(11.1053 - 8.45728i) q^{93} -6.46146i q^{94} +4.84057i q^{95} +(-1.37796 + 1.04939i) q^{96} +(7.61423 + 4.39608i) q^{97} +(-1.69673 + 6.79125i) q^{98} +(0.579937 + 2.22923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.04939	−	1.37796i	−0.605866	−	0.795567i
$3$	−1.04939	−	1.37796i	−0.605866	−	0.795567i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.37796	+	1.04939i	−0.562551	+	0.428412i
$7$	−0.323069	+	2.62595i	−0.122108	+	0.992517i
$7$	−0.323069	+	2.62595i	−0.122108	+	0.992517i
$8$			1.00000i			0.353553i
$9$	−0.797561	+	2.89204i	−0.265854	+	0.964013i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.664943	−	0.383905i	0.200488	−	0.115752i	−0.396395	−	0.918080i	$-0.629739\pi$
$11$	0.664943	−	0.383905i	0.200488	−	0.115752i	0.596883	+	0.802328i	$0.296406\pi$
$12$	1.04939	+	1.37796i	0.302933	+	0.397783i
$13$	3.78024	−	2.18252i	1.04845	−	0.605323i	0.126236	−	0.992000i	$-0.459710\pi$
$13$	3.78024	−	2.18252i	1.04845	−	0.605323i	0.922215	+	0.386677i	$0.126377\pi$
$14$	2.62595	+	0.323069i	0.701815	+	0.0863437i
$15$	1.71805	−	0.219817i	0.443597	−	0.0567566i
$16$	1.00000			0.250000
$17$	1.15157	−	1.99457i	0.279296	−	0.483755i	−0.691914	−	0.721980i	$-0.743232\pi$
$17$	1.15157	−	1.99457i	0.279296	−	0.483755i	0.971210	+	0.238225i	$0.0765656\pi$
$18$	2.89204	+	0.797561i	0.681660	+	0.187987i
$19$	4.19206	−	2.42029i	0.961725	−	0.555252i	0.0650212	−	0.997884i	$-0.479288\pi$
$19$	4.19206	−	2.42029i	0.961725	−	0.555252i	0.896703	+	0.442632i	$0.145955\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	3.95749	−	2.31047i	0.863595	−	0.504186i
$22$	−0.383905	−	0.664943i	−0.0818489	−	0.141766i
$23$	4.84784	+	2.79890i	1.01084	+	0.583611i	0.911439	−	0.411436i	$-0.134973\pi$
$23$	4.84784	+	2.79890i	1.01084	+	0.583611i	0.0994054	+	0.995047i	$0.468306\pi$
$24$	1.37796	−	1.04939i	0.281275	−	0.214206i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.18252	−	3.78024i	−0.428028	−	0.741367i
$27$	4.82207	−	1.93587i	0.928009	−	0.372558i
$28$	0.323069	−	2.62595i	0.0610542	−	0.496258i
$29$	−9.12141	−	5.26625i	−1.69380	−	0.977918i	−0.951397	−	0.307968i	$-0.900351\pi$
$29$	−9.12141	−	5.26625i	−1.69380	−	0.977918i	−0.742407	−	0.669949i	$-0.766316\pi$
$30$	−0.219817	−	1.71805i	−0.0401330	−	0.313671i
$31$			8.05924i			1.44748i	0.690072	+	0.723741i	$0.257579\pi$
$31$			8.05924i			1.44748i	−0.690072	+	0.723741i	$0.742421\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.22679	−	0.513400i	−0.213557	−	0.0893716i
$34$	−1.99457	−	1.15157i	−0.342066	−	0.197492i
$35$	−2.11261	−	1.59276i	−0.357096	−	0.269226i
$36$	0.797561	−	2.89204i	0.132927	−	0.482007i
$37$	4.15617	+	7.19869i	0.683269	+	1.18346i	0.973977	+	0.226645i	$0.0727759\pi$
$37$	4.15617	+	7.19869i	0.683269	+	1.18346i	−0.290708	+	0.956812i	$0.593891\pi$
$38$	−2.42029	−	4.19206i	−0.392622	−	0.680042i
$39$	−6.97439	−	2.91871i	−1.11680	−	0.467368i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	2.65381	+	4.59654i	0.414456	+	0.717859i	0.995371	−	0.0961053i	$-0.0306385\pi$
$41$	2.65381	+	4.59654i	0.414456	+	0.717859i	−0.580915	+	0.813964i	$0.697305\pi$
$42$	−2.31047	−	3.95749i	−0.356514	−	0.610654i
$43$	5.94724	−	10.3009i	0.906945	−	1.57087i	0.0886598	−	0.996062i	$-0.471742\pi$
$43$	5.94724	−	10.3009i	0.906945	−	1.57087i	0.818285	−	0.574813i	$-0.194925\pi$
$44$	−0.664943	+	0.383905i	−0.100244	+	0.0578759i
$45$	−2.10580	−	2.13673i	−0.313914	−	0.318525i
$46$	2.79890	−	4.84784i	0.412675	−	0.714775i
$47$	6.46146			0.942500			0.471250	−	0.882000i	$-0.343803\pi$
$47$	6.46146			0.942500			0.471250	+	0.882000i	$0.343803\pi$
$48$	−1.04939	−	1.37796i	−0.151466	−	0.198892i
$49$	−6.79125	−	1.69673i	−0.970179	−	0.242389i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−3.95689	+	0.506269i	−0.554075	+	0.0708918i
$52$	−3.78024	+	2.18252i	−0.524225	+	0.302662i
$53$	−6.48067	−	3.74161i	−0.890188	−	0.513950i	−0.0161839	−	0.999869i	$-0.505152\pi$
$53$	−6.48067	−	3.74161i	−0.890188	−	0.513950i	−0.874004	+	0.485919i	$0.838485\pi$
$54$	−1.93587	−	4.82207i	−0.263439	−	0.656201i
$55$			0.767810i			0.103532i
$56$	−2.62595	−	0.323069i	−0.350908	−	0.0431719i
$57$	−7.73417	−	3.23668i	−1.02442	−	0.428708i
$58$	−5.26625	+	9.12141i	−0.691492	+	1.19770i
$59$	11.4347			1.48867			0.744337	−	0.667804i	$-0.232766\pi$
$59$	11.4347			1.48867			0.744337	+	0.667804i	$0.232766\pi$
$60$	−1.71805	+	0.219817i	−0.221799	+	0.0283783i
$61$			9.49997i			1.21635i	0.793804	+	0.608174i	$0.208098\pi$
$61$			9.49997i			1.21635i	−0.793804	+	0.608174i	$0.791902\pi$
$62$	8.05924			1.02352
$63$	−7.33669	−	3.02868i	−0.924337	−	0.381578i
$64$	−1.00000			−0.125000
$65$			4.36505i			0.541418i
$66$	−0.513400	+	1.22679i	−0.0631952	+	0.151008i
$67$	13.7047			1.67430			0.837151	−	0.546972i	$-0.184220\pi$
$67$	13.7047			1.67430			0.837151	+	0.546972i	$0.184220\pi$
$68$	−1.15157	+	1.99457i	−0.139648	+	0.241877i
$69$	−1.23049	−	9.61728i	−0.148134	−	1.15778i
$70$	−1.59276	+	2.11261i	−0.190371	+	0.252505i
$71$		−	7.50583i		−	0.890779i	−0.895337	−	0.445389i	$-0.853065\pi$
$71$		−	7.50583i		−	0.890779i	0.895337	−	0.445389i	$-0.146935\pi$
$72$	−2.89204	−	0.797561i	−0.340830	−	0.0939934i
$73$	10.1185	+	5.84190i	1.18428	+	0.683742i	0.957000	−	0.290088i	$-0.0936845\pi$
$73$	10.1185	+	5.84190i	1.18428	+	0.683742i	0.227277	+	0.973830i	$0.427018\pi$
$74$	7.19869	−	4.15617i	0.836831	−	0.483144i
$75$	−0.668655	+	1.59778i	−0.0772097	+	0.184496i
$76$	−4.19206	+	2.42029i	−0.480862	+	0.277626i
$77$	0.793294	+	1.87014i	0.0904043	+	0.213122i
$78$	−2.91871	+	6.97439i	−0.330479	+	0.789694i
$79$	−1.11044			−0.124934			−0.0624669	−	0.998047i	$-0.519897\pi$
$79$	−1.11044			−0.124934			−0.0624669	+	0.998047i	$0.519897\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−7.72779	−	4.61315i	−0.858644	−	0.512573i
$82$	4.59654	−	2.65381i	0.507603	−	0.293065i
$83$	0.254578	−	0.440942i	0.0279435	−	0.0483996i	−0.851715	−	0.524005i	$-0.824437\pi$
$83$	0.254578	−	0.440942i	0.0279435	−	0.0483996i	0.879659	+	0.475605i	$0.157771\pi$
$84$	−3.95749	+	2.31047i	−0.431797	+	0.252093i
$85$	1.15157	+	1.99457i	0.124905	+	0.216342i
$86$	−10.3009	−	5.94724i	−1.11078	−	0.641307i
$87$	2.31523	+	18.0953i	0.248218	+	1.94002i
$88$	0.383905	+	0.664943i	0.0409244	+	0.0708832i
$89$	−2.80167	−	4.85263i	−0.296976	−	0.514378i	0.678467	−	0.734631i	$-0.262645\pi$
$89$	−2.80167	−	4.85263i	−0.296976	−	0.514378i	−0.975443	+	0.220254i	$0.929311\pi$
$90$	−2.13673	+	2.10580i	−0.225231	+	0.221971i
$91$	4.50993	+	10.6318i	0.472769	+	1.11452i
$92$	−4.84784	−	2.79890i	−0.505422	−	0.291806i
$93$	11.1053	−	8.45728i	1.15157	−	0.876980i
$94$		−	6.46146i		−	0.666448i
$95$			4.84057i			0.496632i
$96$	−1.37796	+	1.04939i	−0.140638	+	0.107103i
$97$	7.61423	+	4.39608i	0.773107	+	0.446354i	0.833982	−	0.551792i	$-0.186056\pi$
$97$	7.61423	+	4.39608i	0.773107	+	0.446354i	−0.0608745	+	0.998145i	$0.519389\pi$
$98$	−1.69673	+	6.79125i	−0.171395	+	0.686020i
$99$	0.579937	+	2.22923i	0.0582858	+	0.224046i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.92574	−	10.2637i	−0.589633	−	1.02127i	−0.994280	−	0.106801i	$-0.965939\pi$
$101$	−5.92574	−	10.2637i	−0.589633	−	1.02127i	0.404648	−	0.914473i	$-0.367394\pi$
$102$	0.506269	+	3.95689i	0.0501281	+	0.391790i
$103$	−0.760480	−	0.439063i	−0.0749323	−	0.0432622i	0.462066	−	0.886846i	$-0.347108\pi$
$103$	−0.760480	−	0.439063i	−0.0749323	−	0.0432622i	−0.536998	+	0.843584i	$0.680442\pi$
$104$	2.18252	+	3.78024i	0.214014	+	0.370683i
$105$	0.0221835	+	4.58252i	0.00216488	+	0.447208i
$106$	−3.74161	+	6.48067i	−0.363418	+	0.629458i
$107$	−5.55184	+	3.20536i	−0.536717	+	0.309874i	−0.743747	−	0.668461i	$-0.766953\pi$
$107$	−5.55184	+	3.20536i	−0.536717	+	0.309874i	0.207031	+	0.978334i	$0.433620\pi$
$108$	−4.82207	+	1.93587i	−0.464004	+	0.186279i
$109$	−4.36380	+	7.55832i	−0.417976	+	0.723955i	−0.995736	−	0.0922513i	$-0.970594\pi$
$109$	−4.36380	+	7.55832i	−0.417976	+	0.723955i	0.577760	+	0.816207i	$0.303927\pi$
$110$	0.767810			0.0732078
$111$	5.55808	−	13.2813i	0.527550	−	1.26060i
$112$	−0.323069	+	2.62595i	−0.0305271	+	0.248129i
$113$	−0.697613	+	0.402767i	−0.0656259	+	0.0378891i	−0.532454	−	0.846459i	$-0.678730\pi$
$113$	−0.697613	+	0.402767i	−0.0656259	+	0.0378891i	0.466828	+	0.884348i	$0.345397\pi$
$114$	−3.23668	+	7.73417i	−0.303142	+	0.724372i
$115$	−4.84784	+	2.79890i	−0.452063	+	0.260999i
$116$	9.12141	+	5.26625i	0.846902	+	0.488959i
$117$	3.29698	+	12.6733i	0.304806	+	1.17165i
$118$		−	11.4347i		−	1.05265i
$119$	4.86562	+	3.66834i	0.446031	+	0.336277i
$120$	0.219817	+	1.71805i	0.0200665	+	0.156835i
$121$	−5.20523	+	9.01573i	−0.473203	+	0.819612i
$122$	9.49997			0.860087
$123$	3.54897	−	8.48042i	0.320000	−	0.764654i
$124$		−	8.05924i		−	0.723741i
$125$	1.00000			0.0894427
$126$	−3.02868	+	7.33669i	−0.269817	+	0.653605i
$127$	−12.6479			−1.12232			−0.561162	−	0.827706i	$-0.689645\pi$
$127$	−12.6479			−1.12232			−0.561162	+	0.827706i	$0.689645\pi$
$128$			1.00000i			0.0883883i
$129$	−20.4352	+	2.61461i	−1.79922	+	0.230204i
$130$	4.36505			0.382840
$131$	−4.96301	+	8.59619i	−0.433620	+	0.751053i	−0.997182	−	0.0750215i	$-0.976097\pi$
$131$	−4.96301	+	8.59619i	−0.433620	+	0.751053i	0.563561	+	0.826074i	$0.309431\pi$
$132$	1.22679	+	0.513400i	0.106779	+	0.0446858i
$133$	5.00124	+	11.7901i	0.433662	+	1.02233i
$134$		−	13.7047i		−	1.18391i
$135$	−0.734525	+	5.14397i	−0.0632178	+	0.442723i
$136$	1.99457	+	1.15157i	0.171033	+	0.0987461i
$137$	12.4651	−	7.19674i	1.06497	−	0.614859i	0.138165	−	0.990409i	$-0.455880\pi$
$137$	12.4651	−	7.19674i	1.06497	−	0.614859i	0.926802	+	0.375550i	$0.122546\pi$
$138$	−9.61728	+	1.23049i	−0.818677	+	0.104747i
$139$	8.82052	−	5.09253i	0.748147	−	0.431943i	−0.0768772	−	0.997041i	$-0.524495\pi$
$139$	8.82052	−	5.09253i	0.748147	−	0.431943i	0.825024	+	0.565098i	$0.191162\pi$
$140$	2.11261	+	1.59276i	0.178548	+	0.134613i
$141$	−6.78059	−	8.90364i	−0.571028	−	0.749822i
$142$	−7.50583			−0.629876
$143$	1.67576	−	2.90251i	0.140135	−	0.242720i
$144$	−0.797561	+	2.89204i	−0.0664634	+	0.241003i
$145$	9.12141	−	5.26625i	0.757492	−	0.437338i
$146$	5.84190	−	10.1185i	0.483479	−	0.837410i
$147$	4.78865	+	11.1386i	0.394961	+	0.918698i
$148$	−4.15617	−	7.19869i	−0.341635	−	0.591729i
$149$	−7.75355	−	4.47651i	−0.635196	−	0.366730i	0.147566	−	0.989052i	$-0.452856\pi$
$149$	−7.75355	−	4.47651i	−0.635196	−	0.366730i	−0.782761	+	0.622322i	$0.786190\pi$
$150$	1.59778	+	0.668655i	0.130458	+	0.0545955i
$151$	2.50359	+	4.33635i	0.203739	+	0.352887i	0.949730	−	0.313069i	$-0.101357\pi$
$151$	2.50359	+	4.33635i	0.203739	+	0.352887i	−0.745991	+	0.665956i	$0.768024\pi$
$152$	2.42029	+	4.19206i	0.196311	+	0.340021i
$153$	4.84994	+	4.92117i	0.392094	+	0.397853i
$154$	1.87014	−	0.793294i	0.150700	−	0.0639255i
$155$	−6.97950	−	4.02962i	−0.560607	−	0.323667i
$156$	6.97439	+	2.91871i	0.558398	+	0.233684i
$157$		−	3.25327i		−	0.259639i	−0.991538	−	0.129819i	$-0.958560\pi$
$157$		−	3.25327i		−	0.259639i	0.991538	−	0.129819i	$-0.0414398\pi$
$158$			1.11044i			0.0883415i
$159$	1.64494	+	12.8565i	0.130452	+	1.01959i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−8.91596	+	11.8260i	−0.702676	+	0.932016i
$162$	−4.61315	+	7.72779i	−0.362444	+	0.607153i
$163$	2.40931	+	4.17306i	0.188712	+	0.326859i	0.944821	−	0.327587i	$-0.106235\pi$
$163$	2.40931	+	4.17306i	0.188712	+	0.326859i	−0.756109	+	0.654446i	$0.772902\pi$
$164$	−2.65381	−	4.59654i	−0.207228	−	0.358929i
$165$	1.05801	−	0.805733i	0.0823663	−	0.0627262i
$166$	−0.440942	−	0.254578i	−0.0342237	−	0.0197591i
$167$	4.97259	+	8.61278i	0.384791	+	0.666477i	0.991740	−	0.128263i	$-0.0409403\pi$
$167$	4.97259	+	8.61278i	0.384791	+	0.666477i	−0.606949	+	0.794740i	$0.707607\pi$
$168$	2.31047	+	3.95749i	0.178257	+	0.305327i
$169$	3.02683	−	5.24262i	0.232833	−	0.403278i
$170$	1.99457	−	1.15157i	0.152977	−	0.0883212i
$171$	3.65615	+	14.0539i	0.279592	+	1.07473i
$172$	−5.94724	+	10.3009i	−0.453472	+	0.785437i
$173$	−16.6263			−1.26408			−0.632039	−	0.774937i	$-0.717782\pi$
$173$	−16.6263			−1.26408			−0.632039	+	0.774937i	$0.717782\pi$
$174$	18.0953	−	2.31523i	1.37180	−	0.175517i
$175$	2.43568	−	1.03319i	0.184120	−	0.0781019i
$176$	0.664943	−	0.383905i	0.0501220	−	0.0289379i
$177$	−11.9995	−	15.7566i	−0.901936	−	1.18434i
$178$	−4.85263	+	2.80167i	−0.363720	+	0.209994i
$179$	−4.07453	−	2.35243i	−0.304545	−	0.175829i	0.339938	−	0.940448i	$-0.389594\pi$
$179$	−4.07453	−	2.35243i	−0.304545	−	0.175829i	−0.644483	+	0.764619i	$0.722927\pi$
$180$	2.10580	+	2.13673i	0.156957	+	0.159262i
$181$		−	8.33408i		−	0.619467i	−0.950823	−	0.309734i	$-0.899760\pi$
$181$		−	8.33408i		−	0.619467i	0.950823	−	0.309734i	$-0.100240\pi$
$182$	10.6318	−	4.50993i	0.788085	−	0.334298i
$183$	13.0906	−	9.96918i	0.967685	−	0.736943i
$184$	−2.79890	+	4.84784i	−0.206338	+	0.357387i
$185$	−8.31233			−0.611135
$186$	−8.45728	−	11.1053i	−0.620118	−	0.814282i
$187$		−	1.76837i		−	0.129316i
$188$	−6.46146			−0.471250
$189$	3.52564	+	13.2880i	0.256453	+	0.966557i
$190$	4.84057			0.351172
$191$			3.79290i			0.274444i	0.990540	+	0.137222i	$0.0438174\pi$
$191$			3.79290i			0.274444i	−0.990540	+	0.137222i	$0.956183\pi$
$192$	1.04939	+	1.37796i	0.0757332	+	0.0994459i
$193$	−21.4959			−1.54731			−0.773656	−	0.633606i	$-0.781574\pi$
$193$	−21.4959			−1.54731			−0.773656	+	0.633606i	$0.781574\pi$
$194$	4.39608	−	7.61423i	0.315620	−	0.546670i
$195$	6.01487	−	4.58064i	0.430734	−	0.328026i
$196$	6.79125	+	1.69673i	0.485090	+	0.121195i
$197$			13.3908i			0.954054i	0.878889	+	0.477027i	$0.158286\pi$
$197$			13.3908i			0.954054i	−0.878889	+	0.477027i	$0.841714\pi$
$198$	2.22923	−	0.579937i	0.158424	−	0.0412143i
$199$	0.485507	+	0.280308i	0.0344167	+	0.0198705i	0.517110	−	0.855919i	$-0.327008\pi$
$199$	0.485507	+	0.280308i	0.0344167	+	0.0198705i	−0.482693	+	0.875790i	$0.660341\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−14.3816	−	18.8846i	−1.01440	−	1.33202i
$202$	−10.2637	+	5.92574i	−0.722150	+	0.416933i
$203$	16.7758	−	22.2510i	1.17743	−	1.56172i
$204$	3.95689	−	0.506269i	0.277038	−	0.0354459i
$205$	−5.30763			−0.370701
$206$	−0.439063	+	0.760480i	−0.0305910	+	0.0529851i
$207$	−11.9610	+	11.7879i	−0.831345	+	0.819312i
$208$	3.78024	−	2.18252i	0.262113	−	0.151331i
$209$	1.85832	−	3.21871i	0.128543	−	0.222643i
$210$	4.58252	−	0.0221835i	0.316224	−	0.00153080i
$211$	1.76537	+	3.05771i	0.121533	+	0.210501i	0.920372	−	0.391043i	$-0.127886\pi$
$211$	1.76537	+	3.05771i	0.121533	+	0.210501i	−0.798839	+	0.601544i	$0.794552\pi$
$212$	6.48067	+	3.74161i	0.445094	+	0.256975i
$213$	−10.3428	+	7.87655i	−0.708674	+	0.539692i
$214$	3.20536	+	5.55184i	0.219114	+	0.379516i
$215$	5.94724	+	10.3009i	0.405598	+	0.702516i
$216$	1.93587	+	4.82207i	0.131719	+	0.328101i
$217$	−21.1632	−	2.60369i	−1.43665	−	0.176750i
$218$	7.55832	+	4.36380i	0.511914	+	0.295554i
$219$	−2.56830	−	20.0733i	−0.173550	−	1.35643i
$220$		−	0.767810i		−	0.0517658i
$221$		−	10.0533i		−	0.676258i
$222$	−13.2813	−	5.55808i	−0.891381	−	0.373034i
$223$	−22.1791	−	12.8051i	−1.48522	−	0.857495i	−0.485366	−	0.874311i	$-0.661314\pi$
$223$	−22.1791	−	12.8051i	−1.48522	−	0.857495i	−0.999859	+	0.0168159i	$0.994647\pi$
$224$	2.62595	+	0.323069i	0.175454	+	0.0215859i
$225$	2.90336	−	0.755312i	0.193557	−	0.0503542i
$226$	0.402767	+	0.697613i	0.0267917	+	0.0464045i
$227$	5.56930	+	9.64631i	0.369647	+	0.640248i	0.989510	−	0.144462i	$-0.0461452\pi$
$227$	5.56930	+	9.64631i	0.369647	+	0.640248i	−0.619863	+	0.784710i	$0.712812\pi$
$228$	7.73417	+	3.23668i	0.512208	+	0.214354i
$229$	−3.29819	−	1.90421i	−0.217951	−	0.125834i	0.387050	−	0.922059i	$-0.373494\pi$
$229$	−3.29819	−	1.90421i	−0.217951	−	0.125834i	−0.605001	+	0.796225i	$0.706827\pi$
$230$	2.79890	+	4.84784i	0.184554	+	0.319657i
$231$	1.74450	−	3.05563i	0.114780	−	0.201046i
$232$	5.26625	−	9.12141i	0.345746	−	0.598850i
$233$	−2.04230	+	1.17912i	−0.133795	+	0.0772468i	−0.565404	−	0.824814i	$-0.691280\pi$
$233$	−2.04230	+	1.17912i	−0.133795	+	0.0772468i	0.431608	+	0.902061i	$0.357946\pi$
$234$	12.6733	−	3.29698i	0.828480	−	0.215530i
$235$	−3.23073	+	5.59578i	−0.210749	+	0.365029i
$236$	−11.4347			−0.744337
$237$	1.16528	+	1.53014i	0.0756931	+	0.0993932i
$238$	3.66834	−	4.86562i	0.237783	−	0.315391i
$239$	10.1968	−	5.88712i	0.659576	−	0.380806i	−0.132540	−	0.991178i	$-0.542313\pi$
$239$	10.1968	−	5.88712i	0.659576	−	0.380806i	0.792115	+	0.610372i	$0.208980\pi$
$240$	1.71805	−	0.219817i	0.110899	−	0.0141891i
$241$	16.2931	−	9.40683i	1.04953	−	0.605947i	0.127013	−	0.991901i	$-0.459461\pi$
$241$	16.2931	−	9.40683i	1.04953	−	0.605947i	0.922518	+	0.385954i	$0.126128\pi$
$242$	9.01573	+	5.20523i	0.579553	+	0.334605i
$243$	1.75272	+	15.4896i	0.112437	+	0.993659i
$244$		−	9.49997i		−	0.608174i
$245$	4.86503	−	5.03304i	0.310816	−	0.321549i
$246$	−8.48042	−	3.54897i	−0.540692	−	0.226274i
$247$	10.5647	−	18.2986i	0.672214	−	1.16431i
$248$	−8.05924			−0.511762
$249$	−0.874752	+	0.111921i	−0.0554352	+	0.00709272i
$250$		−	1.00000i		−	0.0632456i
$251$	3.35759			0.211929			0.105965	−	0.994370i	$-0.466207\pi$
$251$	3.35759			0.211929			0.105965	+	0.994370i	$0.466207\pi$
$252$	7.33669	+	3.02868i	0.462168	+	0.190789i
$253$	4.29805			0.270216
$254$			12.6479i			0.793602i
$255$	1.54000	−	3.67990i	0.0964387	−	0.230444i
$256$	1.00000			0.0625000
$257$	5.66810	−	9.81743i	0.353566	−	0.612394i	−0.633305	−	0.773902i	$-0.718302\pi$
$257$	5.66810	−	9.81743i	0.353566	−	0.612394i	0.986871	+	0.161508i	$0.0516356\pi$
$258$	2.61461	+	20.4352i	0.162779	+	1.27224i
$259$	−20.2461	+	8.58822i	−1.25803	+	0.533646i
$260$		−	4.36505i		−	0.270709i
$261$	22.5051	−	22.1793i	1.39303	−	1.37287i
$262$	8.59619	+	4.96301i	0.531074	+	0.306616i
$263$	−22.3278	+	12.8910i	−1.37679	+	0.794892i	−0.991772	−	0.128015i	$-0.959139\pi$
$263$	−22.3278	+	12.8910i	−1.37679	+	0.794892i	−0.385022	+	0.922908i	$0.625806\pi$
$264$	0.513400	−	1.22679i	0.0315976	−	0.0755038i
$265$	6.48067	−	3.74161i	0.398104	−	0.229846i
$266$	11.7901	−	5.00124i	0.722896	−	0.306645i
$267$	−3.74670	+	8.95289i	−0.229294	+	0.547908i
$268$	−13.7047			−0.837151
$269$	−2.94884	+	5.10754i	−0.179794	+	0.311412i	−0.941810	−	0.336146i	$-0.890876\pi$
$269$	−2.94884	+	5.10754i	−0.179794	+	0.311412i	0.762016	+	0.647558i	$0.224210\pi$
$270$	5.14397	+	0.734525i	0.313052	+	0.0447017i
$271$	−8.76680	+	5.06151i	−0.532545	+	0.307465i	−0.742052	−	0.670342i	$-0.766147\pi$
$271$	−8.76680	+	5.06151i	−0.532545	+	0.307465i	0.209507	+	0.977807i	$0.432814\pi$
$272$	1.15157	−	1.99457i	0.0698240	−	0.120939i
$273$	9.91761	−	17.3715i	0.600241	−	1.05137i
$274$	−7.19674	−	12.4651i	−0.434771	−	0.753045i
$275$	−0.664943	−	0.383905i	−0.0400976	−	0.0231504i
$276$	1.23049	+	9.61728i	0.0740670	+	0.578892i
$277$	−5.19502	−	8.99804i	−0.312139	−	0.540640i	0.666686	−	0.745338i	$-0.267712\pi$
$277$	−5.19502	−	8.99804i	−0.312139	−	0.540640i	−0.978825	+	0.204698i	$0.934379\pi$
$278$	−5.09253	−	8.82052i	−0.305430	−	0.529020i
$279$	−23.3076	−	6.42773i	−1.39539	−	0.384818i
$280$	1.59276	−	2.11261i	0.0951857	−	0.126252i
$281$	−14.3149	−	8.26473i	−0.853957	−	0.493032i	0.00802696	−	0.999968i	$-0.497445\pi$
$281$	−14.3149	−	8.26473i	−0.853957	−	0.493032i	−0.861984	+	0.506935i	$0.830778\pi$
$282$	−8.90364	+	6.78059i	−0.530204	+	0.403778i
$283$		−	10.3924i		−	0.617765i	−0.951100	−	0.308882i	$-0.900045\pi$
$283$		−	10.3924i		−	0.617765i	0.951100	−	0.308882i	$-0.0999550\pi$
$284$			7.50583i			0.445389i
$285$	6.67013	−	5.07965i	0.395104	−	0.300893i
$286$	−2.90251	−	1.67576i	−0.171629	−	0.0990901i
$287$	−12.9277	+	5.48379i	−0.763095	+	0.323698i
$288$	2.89204	+	0.797561i	0.170415	+	0.0469967i
$289$	5.84779	+	10.1287i	0.343987	+	0.595804i
$290$	−5.26625	−	9.12141i	−0.309245	−	0.535628i
$291$	−1.93267	−	15.1053i	−0.113295	−	0.885489i
$292$	−10.1185	−	5.84190i	−0.592138	−	0.341871i
$293$	12.7786	+	22.1332i	0.746533	+	1.29303i	0.949475	+	0.313843i	$0.101616\pi$
$293$	12.7786	+	22.1332i	0.746533	+	1.29303i	−0.202942	+	0.979191i	$0.565050\pi$
$294$	11.1386	−	4.78865i	0.649617	−	0.279280i
$295$	−5.71736	+	9.90276i	−0.332878	+	0.576561i
$296$	−7.19869	+	4.15617i	−0.418415	+	0.241572i
$297$	2.46322	−	3.13846i	0.142930	−	0.182112i
$298$	−4.47651	+	7.75355i	−0.259318	+	0.449151i
$299$	24.4347			1.41309
$300$	0.668655	−	1.59778i	0.0386048	−	0.0922479i
$301$	25.1283	+	18.9451i	1.44837	+	1.09198i
$302$	4.33635	−	2.50359i	0.249529	−	0.144065i
$303$	−7.92455	+	18.9360i	−0.455254	+	1.08785i
$304$	4.19206	−	2.42029i	0.240431	−	0.138813i
$305$	−8.22722	−	4.74999i	−0.471089	−	0.271983i
$306$	4.92117	−	4.84994i	0.281325	−	0.277253i
$307$		−	9.33336i		−	0.532683i	−0.963879	−	0.266342i	$-0.914185\pi$
$307$		−	9.33336i		−	0.532683i	0.963879	−	0.266342i	$-0.0858149\pi$
$308$	−0.793294	−	1.87014i	−0.0452021	−	0.106561i
$309$	0.193027	+	1.50866i	0.0109809	+	0.0858247i
$310$	−4.02962	+	6.97950i	−0.228867	+	0.396409i
$311$	−5.36577			−0.304265			−0.152132	−	0.988360i	$-0.548614\pi$
$311$	−5.36577			−0.304265			−0.152132	+	0.988360i	$0.548614\pi$
$312$	2.91871	−	6.97439i	0.165240	−	0.394847i
$313$		−	25.4559i		−	1.43885i	−0.694568	−	0.719427i	$-0.744404\pi$
$313$		−	25.4559i		−	1.43885i	0.694568	−	0.719427i	$-0.255596\pi$
$314$	−3.25327			−0.183592
$315$	6.29126	−	4.83942i	0.354473	−	0.272671i
$316$	1.11044			0.0624669
$317$			7.48676i			0.420498i	0.977648	+	0.210249i	$0.0674275\pi$
$317$			7.48676i			0.420498i	−0.977648	+	0.210249i	$0.932572\pi$
$318$	12.8565	−	1.64494i	0.720958	−	0.0922438i
$319$	−8.08696			−0.452783
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	10.2429	+	4.28656i	0.571703	+	0.239252i
$322$	11.8260	+	8.91596i	0.659035	+	0.496867i
$323$		−	11.1485i		−	0.620319i
$324$	7.72779	+	4.61315i	0.429322	+	0.256286i
$325$	−3.78024	−	2.18252i	−0.209690	−	0.121065i
$326$	4.17306	−	2.40931i	0.231124	−	0.133440i
$327$	14.9944	−	1.91848i	0.829192	−	0.106092i
$328$	−4.59654	+	2.65381i	−0.253801	+	0.146532i
$329$	−2.08749	+	16.9675i	−0.115087	+	0.935447i
$330$	−0.805733	−	1.05801i	−0.0443541	−	0.0582417i
$331$	7.42867			0.408317			0.204158	−	0.978938i	$-0.434554\pi$
$331$	7.42867			0.408317			0.204158	+	0.978938i	$0.434554\pi$
$332$	−0.254578	+	0.440942i	−0.0139718	+	0.0241998i
$333$	−24.1337	+	6.27841i	−1.32252	+	0.344055i
$334$	8.61278	−	4.97259i	0.471270	−	0.272088i
$335$	−6.85237	+	11.8687i	−0.374385	+	0.648454i
$336$	3.95749	−	2.31047i	0.215899	−	0.126047i
$337$	−12.9171	−	22.3731i	−0.703641	−	1.21874i	−0.967180	−	0.254093i	$-0.918223\pi$
$337$	−12.9171	−	22.3731i	−0.703641	−	1.21874i	0.263539	−	0.964649i	$-0.415110\pi$
$338$	−5.24262	−	3.02683i	−0.285161	−	0.164638i
$339$	1.28707	+	0.538625i	0.0699038	+	0.0292541i
$340$	−1.15157	−	1.99457i	−0.0624525	−	0.108171i
$341$	3.09398	+	5.35894i	0.167549	+	0.290203i
$342$	14.0539	−	3.65615i	0.759950	−	0.197702i
$343$	6.64956	−	17.2854i	0.359043	−	0.933321i
$344$	10.3009	+	5.94724i	0.555388	+	0.320653i
$345$	8.94405	+	3.74300i	0.481532	+	0.201516i
$346$			16.6263i			0.893838i
$347$		−	18.4244i		−	0.989073i	−0.869157	−	0.494537i	$-0.835338\pi$
$347$		−	18.4244i		−	0.989073i	0.869157	−	0.494537i	$-0.164662\pi$
$348$	−2.31523	−	18.0953i	−0.124109	−	0.970010i
$349$	1.37452	+	0.793577i	0.0735761	+	0.0424792i	0.536337	−	0.844004i	$-0.319808\pi$
$349$	1.37452	+	0.793577i	0.0735761	+	0.0424792i	−0.462761	+	0.886483i	$0.653141\pi$
$350$	−1.03319	−	2.43568i	−0.0552264	−	0.130192i
$351$	14.0035	−	17.8424i	0.747453	−	0.952355i
$352$	−0.383905	−	0.664943i	−0.0204622	−	0.0354416i
$353$	−4.60268	−	7.97208i	−0.244976	−	0.424311i	0.717149	−	0.696920i	$-0.245447\pi$
$353$	−4.60268	−	7.97208i	−0.244976	−	0.424311i	−0.962125	+	0.272609i	$0.912113\pi$
$354$	−15.7566	+	11.9995i	−0.837455	+	0.637765i
$355$	6.50024	+	3.75292i	0.344997	+	0.199184i
$356$	2.80167	+	4.85263i	0.148488	+	0.257189i
$357$	−0.0510915	−	10.5542i	−0.00270405	−	0.558586i
$358$	−2.35243	+	4.07453i	−0.124330	+	0.215346i
$359$	−22.3751	+	12.9183i	−1.18091	+	0.681801i	−0.956226	−	0.292629i	$-0.905470\pi$
$359$	−22.3751	+	12.9183i	−1.18091	+	0.681801i	−0.224689	+	0.974431i	$0.572136\pi$
$360$	2.13673	−	2.10580i	0.112615	−	0.110985i
$361$	2.21558	−	3.83750i	0.116610	−	0.201974i
$362$	−8.33408			−0.438029
$363$	17.8857	−	2.28840i	0.938754	−	0.120110i
$364$	−4.50993	−	10.6318i	−0.236384	−	0.557260i
$365$	−10.1185	+	5.84190i	−0.529625	+	0.305779i
$366$	−9.96918	−	13.0906i	−0.521097	−	0.684257i
$367$	19.2746	−	11.1282i	1.00613	−	0.580888i	0.0960716	−	0.995374i	$-0.469372\pi$
$367$	19.2746	−	11.1282i	1.00613	−	0.580888i	0.910055	+	0.414487i	$0.136039\pi$
$368$	4.84784	+	2.79890i	0.252711	+	0.145903i
$369$	−15.4100	+	4.00892i	−0.802210	+	0.208696i
$370$			8.31233i			0.432137i
$371$	11.9190	−	15.8091i	0.618804	−	0.820769i
$372$	−11.1053	+	8.45728i	−0.575784	+	0.438490i
$373$	16.3900	−	28.3884i	0.848644	−	1.46989i	−0.0337752	−	0.999429i	$-0.510753\pi$
$373$	16.3900	−	28.3884i	0.848644	−	1.46989i	0.882419	−	0.470465i	$-0.155914\pi$
$374$	−1.76837			−0.0914403
$375$	−1.04939	−	1.37796i	−0.0541903	−	0.0711577i
$376$			6.46146i			0.333224i
$377$	−45.9749			−2.36783
$378$	13.2880	−	3.52564i	0.683459	−	0.181339i
$379$	−26.7133			−1.37217			−0.686085	−	0.727522i	$-0.740672\pi$
$379$	−26.7133			−1.37217			−0.686085	+	0.727522i	$0.740672\pi$
$380$		−	4.84057i		−	0.248316i
$381$	13.2726	+	17.4284i	0.679977	+	0.892883i
$382$	3.79290			0.194061
$383$	−0.908668	+	1.57386i	−0.0464307	+	0.0804204i	−0.888307	−	0.459251i	$-0.848118\pi$
$383$	−0.908668	+	1.57386i	−0.0464307	+	0.0804204i	0.841876	+	0.539671i	$0.181451\pi$
$384$	1.37796	−	1.04939i	0.0703188	−	0.0535515i
$385$	−2.01623	−	0.248055i	−0.102757	−	0.0126421i
$386$			21.4959i			1.09411i
$387$	25.0474	+	25.4152i	1.27323	+	1.29193i
$388$	−7.61423	−	4.39608i	−0.386554	−	0.223177i
$389$	25.9543	−	14.9847i	1.31593	−	0.759755i	0.332863	−	0.942975i	$-0.391985\pi$
$389$	25.9543	−	14.9847i	1.31593	−	0.759755i	0.983072	+	0.183220i	$0.0586520\pi$
$390$	−4.58064	−	6.01487i	−0.231950	−	0.304575i
$391$	11.1652	−	6.44624i	0.564650	−	0.326001i
$392$	1.69673	−	6.79125i	0.0856976	−	0.343010i
$393$	17.0534	−	2.18191i	0.860228	−	0.110063i
$394$	13.3908			0.674618
$395$	0.555218	−	0.961666i	0.0279360	−	0.0483867i
$396$	−0.579937	−	2.22923i	−0.0291429	−	0.112023i
$397$	0.811242	−	0.468371i	0.0407151	−	0.0235069i	−0.479504	−	0.877540i	$-0.659184\pi$
$397$	0.811242	−	0.468371i	0.0407151	−	0.0235069i	0.520219	+	0.854033i	$0.325850\pi$
$398$	0.280308	−	0.485507i	0.0140506	−	0.0243363i
$399$	10.9980	−	19.2639i	0.550590	−	0.964401i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−5.03054	−	2.90439i	−0.251213	−	0.145038i	0.369106	−	0.929387i	$-0.379664\pi$
$401$	−5.03054	−	2.90439i	−0.251213	−	0.145038i	−0.620320	+	0.784349i	$0.712997\pi$
$402$	−18.8846	+	14.3816i	−0.941879	+	0.717290i
$403$	17.5895	+	30.4659i	0.876195	+	1.51761i
$404$	5.92574	+	10.2637i	0.294816	+	0.510637i
$405$	7.85901	−	4.38589i	0.390517	−	0.217937i
$406$	−22.2510	−	16.7758i	−1.10430	−	0.832567i
$407$	5.52723	+	3.19115i	0.273975	+	0.158179i
$408$	−0.506269	−	3.95689i	−0.0250640	−	0.195895i
$409$		−	21.8817i		−	1.08198i	−0.841029	−	0.540990i	$-0.818050\pi$
$409$		−	21.8817i		−	1.08198i	0.841029	−	0.540990i	$-0.181950\pi$
$410$			5.30763i			0.262125i
$411$	−22.9976	−	9.62428i	−1.13439	−	0.474731i
$412$	0.760480	+	0.439063i	0.0374661	+	0.0216311i
$413$	−3.69420	+	30.0270i	−0.181780	+	1.47753i
$414$	11.7879	+	11.9610i	0.579341	+	0.587850i
$415$	0.254578	+	0.440942i	0.0124967	+	0.0216450i
$416$	−2.18252	−	3.78024i	−0.107007	−	0.185342i
$417$	−16.2735	−	6.81029i	−0.796916	−	0.333502i
$418$	−3.21871	−	1.85832i	−0.157432	−	0.0908935i
$419$	7.97218	+	13.8082i	0.389467	+	0.674576i	0.992378	−	0.123232i	$-0.0393260\pi$
$419$	7.97218	+	13.8082i	0.389467	+	0.674576i	−0.602911	+	0.797808i	$0.705993\pi$
$420$	−0.0221835	−	4.58252i	−0.00108244	−	0.223604i
$421$	8.26978	−	14.3237i	0.403044	−	0.698093i	−0.591047	−	0.806637i	$-0.701285\pi$
$421$	8.26978	−	14.3237i	0.403044	−	0.698093i	0.994092	+	0.108544i	$0.0346187\pi$
$422$	3.05771	−	1.76537i	0.148847	−	0.0859368i
$423$	−5.15340	+	18.6868i	−0.250567	+	0.908583i
$424$	3.74161	−	6.48067i	0.181709	−	0.314729i
$425$	−2.30313			−0.111718
$426$	7.87655	+	10.3428i	0.381620	+	0.501108i
$427$	−24.9465	−	3.06914i	−1.20724	−	0.148526i
$428$	5.55184	−	3.20536i	0.268358	−	0.154937i
$429$	−5.75808	+	0.736724i	−0.278003	+	0.0355694i
$430$	10.3009	−	5.94724i	0.496754	−	0.286801i
$431$	10.5417	+	6.08623i	0.507774	+	0.293163i	0.731918	−	0.681393i	$-0.238625\pi$
$431$	10.5417	+	6.08623i	0.507774	+	0.293163i	−0.224144	+	0.974556i	$0.571959\pi$
$432$	4.82207	−	1.93587i	0.232002	−	0.0931396i
$433$		−	8.54538i		−	0.410665i	−0.978692	−	0.205332i	$-0.934172\pi$
$433$		−	8.54538i		−	0.410665i	0.978692	−	0.205332i	$-0.0658276\pi$
$434$	−2.60369	+	21.1632i	−0.124981	+	1.01586i
$435$	−16.8286	−	7.04261i	−0.806870	−	0.337667i
$436$	4.36380	−	7.55832i	0.208988	−	0.361978i
$437$	27.0966			1.29620
$438$	−20.0733	+	2.56830i	−0.959139	+	0.122718i
$439$		−	6.58176i		−	0.314130i	−0.987588	−	0.157065i	$-0.949797\pi$
$439$		−	6.58176i		−	0.314130i	0.987588	−	0.157065i	$-0.0502032\pi$
$440$	−0.767810			−0.0366039
$441$	10.3234	−	18.2873i	0.491592	−	0.870826i
$442$	−10.0533			−0.478186
$443$		−	27.0738i		−	1.28631i	−0.765734	−	0.643157i	$-0.777624\pi$
$443$		−	27.0738i		−	1.28631i	0.765734	−	0.643157i	$-0.222376\pi$
$444$	−5.55808	+	13.2813i	−0.263775	+	0.630301i
$445$	5.60333			0.265623
$446$	−12.8051	+	22.1791i	−0.606341	+	1.05021i
$447$	1.96803	+	15.3817i	0.0930847	+	0.727530i
$448$	0.323069	−	2.62595i	0.0152636	−	0.124065i
$449$		−	17.9654i		−	0.847841i	−0.905700	−	0.423920i	$-0.860654\pi$
$449$		−	17.9654i		−	0.847841i	0.905700	−	0.423920i	$-0.139346\pi$
$450$	−0.755312	−	2.90336i	−0.0356058	−	0.136866i
$451$	3.52927	+	2.03763i	0.166187	+	0.0959480i
$452$	0.697613	−	0.402767i	0.0328130	−	0.0189446i
$453$	3.34808	−	8.00037i	0.157306	−	0.375890i
$454$	9.64631	−	5.56930i	0.452724	−	0.261380i
$455$	−11.4624	−	1.41021i	−0.537366	−	0.0661117i
$456$	3.23668	−	7.73417i	0.151571	−	0.362186i
$457$	−5.14932			−0.240875			−0.120438	−	0.992721i	$-0.538430\pi$
$457$	−5.14932			−0.240875			−0.120438	+	0.992721i	$0.538430\pi$
$458$	−1.90421	+	3.29819i	−0.0889780	+	0.154114i
$459$	1.69171	−	11.8473i	0.0789622	−	0.552983i
$460$	4.84784	−	2.79890i	0.226032	−	0.130499i
$461$	−5.46051	+	9.45788i	−0.254321	+	0.440498i	−0.964711	−	0.263311i	$-0.915185\pi$
$461$	−5.46051	+	9.45788i	−0.254321	+	0.440498i	0.710390	+	0.703809i	$0.248519\pi$
$462$	−3.05563	−	1.74450i	−0.142161	−	0.0811616i
$463$	14.8704	+	25.7563i	0.691088	+	1.19700i	0.971482	+	0.237114i	$0.0762015\pi$
$463$	14.8704	+	25.7563i	0.691088	+	1.19700i	−0.280394	+	0.959885i	$0.590465\pi$
$464$	−9.12141	−	5.26625i	−0.423451	−	0.244479i
$465$	1.77156	+	13.8461i	0.0821541	+	0.642099i
$466$	1.17912	+	2.04230i	0.0546217	+	0.0946076i
$467$	4.55724	+	7.89337i	0.210884	+	0.365262i	0.951991	−	0.306125i	$-0.0990324\pi$
$467$	4.55724	+	7.89337i	0.210884	+	0.365262i	−0.741107	+	0.671386i	$0.765699\pi$
$468$	−3.29698	−	12.6733i	−0.152403	−	0.585824i
$469$	−4.42757	+	35.9880i	−0.204446	+	1.66177i
$470$	5.59578	+	3.23073i	0.258114	+	0.149022i
$471$	−4.48288	+	3.41394i	−0.206560	+	0.157306i
$472$			11.4347i			0.526326i
$473$		−	9.13270i		−	0.419922i
$474$	1.53014	−	1.16528i	0.0702816	−	0.0535231i
$475$	−4.19206	−	2.42029i	−0.192345	−	0.111050i
$476$	−4.86562	−	3.66834i	−0.223015	−	0.168138i
$477$	15.9896	−	15.7582i	0.732114	−	0.721518i
$478$	−5.88712	−	10.1968i	−0.269271	−	0.466390i
$479$	−18.6486	−	32.3003i	−0.852076	−	1.47584i	−0.879332	−	0.476210i	$-0.842010\pi$
$479$	−18.6486	−	32.3003i	−0.852076	−	1.47584i	0.0272561	−	0.999628i	$-0.491323\pi$
$480$	−0.219817	−	1.71805i	−0.0100332	−	0.0784177i
$481$	31.4226	+	18.1419i	1.43275	+	0.827198i
$482$	−9.40683	−	16.2931i	−0.428469	−	0.742130i
$483$	25.6520	−	0.124179i	1.16721	−	0.00565032i
$484$	5.20523	−	9.01573i	0.236602	−	0.409806i
$485$	−7.61423	+	4.39608i	−0.345744	+	0.199615i
$486$	15.4896	−	1.75272i	0.702623	−	0.0795049i
$487$	−9.44574	+	16.3605i	−0.428027	+	0.741365i	−0.996698	−	0.0812005i	$-0.974125\pi$
$487$	−9.44574	+	16.3605i	−0.428027	+	0.741365i	0.568671	+	0.822565i	$0.307458\pi$
$488$	−9.49997			−0.430044
$489$	3.22200	−	7.69911i	0.145704	−	0.348166i
$490$	−5.03304	−	4.86503i	−0.227369	−	0.219780i
$491$	−30.1458	+	17.4047i	−1.36046	+	0.785462i	−0.989685	−	0.143260i	$-0.954241\pi$
$491$	−30.1458	+	17.4047i	−1.36046	+	0.785462i	−0.370776	+	0.928723i	$0.620908\pi$
$492$	−3.54897	+	8.48042i	−0.160000	+	0.382327i
$493$	−21.0078	+	12.1289i	−0.946145	+	0.546257i
$494$	−18.2986	−	10.5647i	−0.823291	−	0.475327i
$495$	−2.22054	−	0.612375i	−0.0998058	−	0.0275242i
$496$			8.05924i			0.361870i
$497$	19.7100	+	2.42490i	0.884113	+	0.108772i
$498$	0.111921	+	0.874752i	0.00501531	+	0.0391986i
$499$	−12.2163	+	21.1593i	−0.546878	+	0.947220i	0.451608	+	0.892216i	$0.350850\pi$
$499$	−12.2163	+	21.1593i	−0.546878	+	0.947220i	−0.998486	+	0.0550038i	$0.982483\pi$
$500$	−1.00000			−0.0447214
$501$	6.64990	−	15.8902i	0.297096	−	0.709922i
$502$		−	3.35759i		−	0.149857i
$503$	13.5009			0.601977			0.300988	−	0.953628i	$-0.402683\pi$
$503$	13.5009			0.601977			0.300988	+	0.953628i	$0.402683\pi$
$504$	3.02868	−	7.33669i	0.134908	−	0.326802i
$505$	11.8515			0.527384
$506$		−	4.29805i		−	0.191072i
$507$	−10.4005	+	1.33070i	−0.461900	+	0.0590984i
$508$	12.6479			0.561162
$509$	−13.6722	+	23.6809i	−0.606008	+	1.04964i	0.385883	+	0.922548i	$0.373897\pi$
$509$	−13.6722	+	23.6809i	−0.606008	+	1.04964i	−0.991891	+	0.127089i	$0.959437\pi$
$510$	−3.67990	−	1.54000i	−0.162949	−	0.0681925i
$511$	−18.6095	+	24.6833i	−0.823236	+	1.09192i
$512$		−	1.00000i		−	0.0441942i
$513$	15.5291	−	19.7861i	0.685625	−	0.873577i
$514$	−9.81743	−	5.66810i	−0.433028	−	0.250009i
$515$	0.760480	−	0.439063i	0.0335107	−	0.0193474i
$516$	20.4352	−	2.61461i	0.899611	−	0.115102i
$517$	4.29650	−	2.48059i	0.188960	−	0.109096i
$518$	8.58822	+	20.2461i	0.377345	+	0.889564i
$519$	17.4475	+	22.9105i	0.765861	+	1.00566i
$520$	−4.36505			−0.191420
$521$	−5.24997	+	9.09321i	−0.230005	+	0.398381i	−0.957809	−	0.287404i	$-0.907208\pi$
$521$	−5.24997	+	9.09321i	−0.230005	+	0.398381i	0.727804	+	0.685785i	$0.240541\pi$
$522$	−22.1793	−	22.5051i	−0.970763	−	0.985021i
$523$	−15.4653	+	8.92889i	−0.676250	+	0.390433i	−0.798441	−	0.602074i	$-0.794341\pi$
$523$	−15.4653	+	8.92889i	−0.676250	+	0.390433i	0.122191	+	0.992507i	$0.461008\pi$
$524$	4.96301	−	8.59619i	0.216810	−	0.375526i
$525$	−3.97967	−	2.27205i	−0.173687	−	0.0991604i
$526$	12.8910	+	22.3278i	0.562074	+	0.973540i
$527$	16.0747	+	9.28075i	0.700226	+	0.404276i
$528$	−1.22679	−	0.513400i	−0.0533893	−	0.0223429i
$529$	4.16769	+	7.21865i	0.181204	+	0.313854i
$530$	−3.74161	−	6.48067i	−0.162525	−	0.281502i
$531$	−9.11988	+	33.0697i	−0.395769	+	1.43510i
$532$	−5.00124	−	11.7901i	−0.216831	−	0.511164i
$533$	20.0641	+	11.5840i	0.869074	+	0.501760i
$534$	8.95289	+	3.74670i	0.387430	+	0.162136i
$535$		−	6.41071i		−	0.277159i
$536$			13.7047i			0.591955i
$537$	1.03421	+	8.08317i	0.0446295	+	0.348814i
$538$	5.10754	+	2.94884i	0.220202	+	0.127134i
$539$	−5.16718	+	1.47897i	−0.222566	+	0.0637038i
$540$	0.734525	−	5.14397i	0.0316089	−	0.221361i
$541$	4.16365	+	7.21166i	0.179009	+	0.310053i	0.941542	−	0.336897i	$-0.109377\pi$
$541$	4.16365	+	7.21166i	0.179009	+	0.310053i	−0.762532	+	0.646950i	$0.776044\pi$
$542$	5.06151	+	8.76680i	0.217411	+	0.376566i
$543$	−11.4840	+	8.74570i	−0.492828	+	0.375314i
$544$	−1.99457	−	1.15157i	−0.0855166	−	0.0493730i
$545$	−4.36380	−	7.55832i	−0.186924	−	0.323763i
$546$	−17.3715	−	9.91761i	−0.743430	−	0.424434i
$547$	15.3348	−	26.5606i	0.655667	−	1.13565i	−0.326059	−	0.945349i	$-0.605721\pi$
$547$	15.3348	−	26.5606i	0.655667	−	1.13565i	0.981726	−	0.190299i	$-0.0609459\pi$
$548$	−12.4651	+	7.19674i	−0.532483	+	0.307429i
$549$	−27.4743	−	7.57680i	−1.17257	−	0.323370i
$550$	−0.383905	+	0.664943i	−0.0163698	+	0.0283533i
$551$	−50.9833			−2.17196
$552$	9.61728	−	1.23049i	0.409338	−	0.0523733i
$553$	0.358747	−	2.91595i	0.0152555	−	0.123999i
$554$	−8.99804	+	5.19502i	−0.382290	+	0.220715i
$555$	8.72288	+	11.4541i	0.370266	+	0.486199i
$556$	−8.82052	+	5.09253i	−0.374073	+	0.215971i
$557$	1.82492	+	1.05362i	0.0773242	+	0.0446432i	0.538164	−	0.842840i	$-0.319118\pi$
$557$	1.82492	+	1.05362i	0.0773242	+	0.0446432i	−0.460839	+	0.887484i	$0.652452\pi$
$558$	−6.42773	+	23.3076i	−0.272107	+	0.986691i
$559$		−	51.9199i		−	2.19598i
$560$	−2.11261	−	1.59276i	−0.0892740	−	0.0673065i
$561$	−2.43675	+	1.85571i	−0.102880	+	0.0783482i
$562$	−8.26473	+	14.3149i	−0.348627	+	0.603839i
$563$	11.4883			0.484174			0.242087	−	0.970255i	$-0.422168\pi$
$563$	11.4883			0.484174			0.242087	+	0.970255i	$0.422168\pi$
$564$	6.78059	+	8.90364i	0.285514	+	0.374911i
$565$		−	0.805534i		−	0.0338891i
$566$	−10.3924			−0.436826
$567$	14.6105	−	18.8025i	0.613585	−	0.789629i
$568$	7.50583			0.314938
$569$			45.8657i			1.92279i	0.275172	+	0.961395i	$0.411265\pi$
$569$			45.8657i			1.92279i	−0.275172	+	0.961395i	$0.588735\pi$
$570$	−5.07965	−	6.67013i	−0.212763	−	0.279381i
$571$	−13.5859			−0.568552			−0.284276	−	0.958742i	$-0.591753\pi$
$571$	−13.5859			−0.568552			−0.284276	+	0.958742i	$0.591753\pi$
$572$	−1.67576	+	2.90251i	−0.0700673	+	0.121360i
$573$	5.22647	−	3.98023i	0.218339	−	0.166276i
$574$	5.48379	+	12.9277i	0.228889	+	0.539590i
$575$		−	5.59780i		−	0.233444i
$576$	0.797561	−	2.89204i	0.0332317	−	0.120502i
$577$	−17.2122	−	9.93748i	−0.716554	−	0.413703i	0.0969291	−	0.995291i	$-0.469098\pi$
$577$	−17.2122	−	9.93748i	−0.716554	−	0.413703i	−0.813483	+	0.581589i	$0.802431\pi$
$578$	10.1287	−	5.84779i	0.421297	−	0.243236i
$579$	22.5576	+	29.6206i	0.937463	+	1.23099i
$580$	−9.12141	+	5.26625i	−0.378746	+	0.218669i
$581$	1.07565	+	0.810964i	0.0446253	+	0.0336444i
$582$	−15.1053	+	1.93267i	−0.626135	+	0.0801116i
$583$	−5.74570			−0.237963
$584$	−5.84190	+	10.1185i	−0.241739	+	0.418705i
$585$	−12.6239	−	3.48139i	−0.521934	−	0.143938i
$586$	22.1332	−	12.7786i	0.914313	−	0.527879i
$587$	−11.8126	+	20.4600i	−0.487558	+	0.844475i	−0.999898	−	0.0143079i	$-0.995445\pi$
$587$	−11.8126	+	20.4600i	−0.487558	+	0.844475i	0.512340	+	0.858783i	$0.328779\pi$
$588$	−4.78865	−	11.1386i	−0.197481	−	0.459349i
$589$	19.5057	+	33.7848i	0.803717	+	1.39208i
$590$	9.90276	+	5.71736i	0.407690	+	0.235380i
$591$	18.4520	−	14.0522i	0.759014	−	0.578029i
$592$	4.15617	+	7.19869i	0.170817	+	0.295864i
$593$	23.9443	+	41.4727i	0.983274	+	1.70308i	0.649367	+	0.760475i	$0.275034\pi$
$593$	23.9443	+	41.4727i	0.983274	+	1.70308i	0.333907	+	0.942606i	$0.391633\pi$
$594$	−3.13846	−	2.46322i	−0.128773	−	0.101067i
$595$	−5.60969	+	2.37958i	−0.229975	+	0.0975531i
$596$	7.75355	+	4.47651i	0.317598	+	0.183365i
$597$	−0.123233	−	0.963163i	−0.00504359	−	0.0394196i
$598$		−	24.4347i		−	0.999208i
$599$		−	14.8968i		−	0.608669i	−0.952565	−	0.304334i	$-0.901566\pi$
$599$		−	14.8968i		−	0.608669i	0.952565	−	0.304334i	$-0.0984340\pi$
$600$	−1.59778	−	0.668655i	−0.0652291	−	0.0272977i
$601$	−13.3073	−	7.68296i	−0.542815	−	0.313394i	0.203404	−	0.979095i	$-0.434800\pi$
$601$	−13.3073	−	7.68296i	−0.542815	−	0.313394i	−0.746219	+	0.665700i	$0.768133\pi$
$602$	18.9451	−	25.1283i	0.772143	−	1.02415i
$603$	−10.9304	+	39.6347i	−0.445119	+	1.61405i
$604$	−2.50359	−	4.33635i	−0.101870	−	0.176443i
$605$	−5.20523	−	9.01573i	−0.211623	−	0.366542i
$606$	18.9360	+	7.92455i	0.769224	+	0.321913i
$607$	−7.76159	−	4.48116i	−0.315033	−	0.181885i	0.334143	−	0.942522i	$-0.391553\pi$
$607$	−7.76159	−	4.48116i	−0.315033	−	0.181885i	−0.649177	+	0.760638i	$0.724886\pi$
$608$	−2.42029	−	4.19206i	−0.0981556	−	0.170011i
$609$	−48.2654	+	0.233647i	−1.95581	+	0.00946787i
$610$	−4.74999	+	8.22722i	−0.192321	+	0.333110i
$611$	24.4259	−	14.1023i	0.988165	−	0.570517i
$612$	−4.84994	−	4.92117i	−0.196047	−	0.198927i
$613$	−10.8226	+	18.7452i	−0.437119	+	0.757113i	−0.997466	−	0.0711452i	$-0.977335\pi$
$613$	−10.8226	+	18.7452i	−0.437119	+	0.757113i	0.560347	+	0.828258i	$0.310668\pi$
$614$	−9.33336			−0.376664
$615$	5.56977	+	7.31371i	0.224595	+	0.294917i
$616$	−1.87014	+	0.793294i	−0.0753500	+	0.0319627i
$617$	−28.3642	+	16.3761i	−1.14190	+	0.659277i	−0.946901	−	0.321527i	$-0.895804\pi$
$617$	−28.3642	+	16.3761i	−1.14190	+	0.659277i	−0.195000	+	0.980803i	$0.562471\pi$
$618$	1.50866	−	0.193027i	0.0606872	−	0.00776470i
$619$	11.3946	−	6.57868i	0.457988	−	0.264420i	−0.253210	−	0.967411i	$-0.581486\pi$
$619$	11.3946	−	6.57868i	0.457988	−	0.264420i	0.711198	+	0.702992i	$0.248153\pi$
$620$	6.97950	+	4.02962i	0.280304	+	0.161833i
$621$	28.7949	+	4.11172i	1.15550	+	0.164998i
$622$			5.36577i			0.215148i
$623$	13.6479	−	5.78931i	0.546792	−	0.231944i
$624$	−6.97439	−	2.91871i	−0.279199	−	0.116842i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−25.4559			−1.01742
$627$	−6.38536	+	0.816983i	−0.255007	+	0.0326271i
$628$			3.25327i			0.129819i
$629$	19.1444			0.763338
$630$	−4.83942	−	6.29126i	−0.192807	−	0.250650i
$631$	−32.3439			−1.28759			−0.643795	−	0.765198i	$-0.722641\pi$
$631$	−32.3439			−1.28759			−0.643795	+	0.765198i	$0.722641\pi$
$632$		−	1.11044i		−	0.0441708i
$633$	2.36084	−	5.64134i	0.0938352	−	0.224223i
$634$	7.48676			0.297337
$635$	6.32397	−	10.9534i	0.250959	−	0.434674i
$636$	−1.64494	−	12.8565i	−0.0652262	−	0.509794i
$637$	−29.3757	+	8.40804i	−1.16391	+	0.333139i
$638$			8.08696i			0.320166i
$639$	21.7072	+	5.98636i	0.858723	+	0.236817i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	24.2747	−	14.0150i	0.958793	−	0.553559i	0.0629917	−	0.998014i	$-0.479936\pi$
$641$	24.2747	−	14.0150i	0.958793	−	0.553559i	0.895801	+	0.444455i	$0.146603\pi$
$642$	4.28656	−	10.2429i	0.169177	−	0.404255i
$643$	11.6003	−	6.69742i	0.457470	−	0.264121i	−0.253510	−	0.967333i	$-0.581585\pi$
$643$	11.6003	−	6.69742i	0.457470	−	0.264121i	0.710980	+	0.703212i	$0.248252\pi$
$644$	8.91596	−	11.8260i	0.351338	−	0.466008i
$645$	7.95330	−	19.0047i	0.313161	−	0.748311i
$646$	−11.1485			−0.438632
$647$	10.5813	−	18.3274i	0.415995	−	0.720524i	−0.579537	−	0.814946i	$-0.696767\pi$
$647$	10.5813	−	18.3274i	0.415995	−	0.720524i	0.995532	+	0.0944214i	$0.0301001\pi$
$648$	4.61315	−	7.72779i	0.181222	−	0.303576i
$649$	7.60344	−	4.38985i	0.298461	−	0.172317i
$650$	−2.18252	+	3.78024i	−0.0856057	+	0.148273i
$651$	18.6206	+	31.8943i	0.729801	+	1.25004i
$652$	−2.40931	−	4.17306i	−0.0943560	−	0.163429i
$653$	−18.2718	−	10.5492i	−0.715030	−	0.412823i	0.0978908	−	0.995197i	$-0.468790\pi$
$653$	−18.2718	−	10.5492i	−0.715030	−	0.412823i	−0.812921	+	0.582374i	$0.802124\pi$
$654$	−1.91848	−	14.9944i	−0.0750184	−	0.586327i
$655$	−4.96301	−	8.59619i	−0.193921	−	0.335881i
$656$	2.65381	+	4.59654i	0.103614	+	0.179465i
$657$	−24.9651	+	24.6037i	−0.973981	+	0.959883i
$658$	16.9675	+	2.08749i	0.661461	+	0.0813790i
$659$	24.0800	+	13.9026i	0.938025	+	0.541569i	0.889341	−	0.457245i	$-0.151164\pi$
$659$	24.0800	+	13.9026i	0.938025	+	0.541569i	0.0486845	+	0.998814i	$0.484497\pi$
$660$	−1.05801	+	0.805733i	−0.0411831	+	0.0313631i
$661$			10.1692i			0.395534i	0.980249	+	0.197767i	$0.0633690\pi$
$661$			10.1692i			0.395534i	−0.980249	+	0.197767i	$0.936631\pi$
$662$		−	7.42867i		−	0.288723i
$663$	−13.8531	+	10.5498i	−0.538008	+	0.409721i
$664$	0.440942	+	0.254578i	0.0171119	+	0.00987953i
$665$	−12.7111	−	1.56384i	−0.492916	−	0.0606430i
$666$	6.27841	+	24.1337i	0.243283	+	0.935162i
$667$	−29.4794	−	51.0598i	−1.14145	−	1.97704i
$668$	−4.97259	−	8.61278i	−0.192395	−	0.333238i
$669$	5.62958	+	43.9996i	0.217652	+	1.70112i
$670$	11.8687	+	6.85237i	0.458526	+	0.264730i
$671$	3.64709	+	6.31694i	0.140794	+	0.243863i
$672$	−2.31047	−	3.95749i	−0.0891284	−	0.152663i
$673$	−5.29232	+	9.16657i	−0.204004	+	0.353345i	−0.949815	−	0.312812i	$-0.898729\pi$
$673$	−5.29232	+	9.16657i	−0.204004	+	0.353345i	0.745811	+	0.666158i	$0.232062\pi$
$674$	−22.3731	+	12.9171i	−0.861781	+	0.497549i
$675$	−4.08755	−	3.20810i	−0.157330	−	0.123480i
$676$	−3.02683	+	5.24262i	−0.116416	+	0.201639i
$677$	−33.1306			−1.27331			−0.636657	−	0.771147i	$-0.719683\pi$
$677$	−33.1306			−1.27331			−0.636657	+	0.771147i	$0.719683\pi$
$678$	0.538625	−	1.28707i	0.0206858	−	0.0494295i
$679$	−14.0038	+	18.5744i	−0.537417	+	0.712819i
$680$	−1.99457	+	1.15157i	−0.0764884	+	0.0441606i
$681$	7.44788	−	17.7970i	0.285403	−	0.681983i
$682$	5.35894	−	3.09398i	0.205204	−	0.118475i
$683$	15.1376	+	8.73972i	0.579225	+	0.334416i	0.760826	−	0.648957i	$-0.224794\pi$
$683$	15.1376	+	8.73972i	0.579225	+	0.334416i	−0.181600	+	0.983372i	$0.558128\pi$
$684$	−3.65615	−	14.0539i	−0.139796	−	0.537366i
$685$			14.3935i			0.549947i
$686$	−17.2854	−	6.64956i	−0.659958	−	0.253881i
$687$	0.837158	+	6.54305i	0.0319396	+	0.249633i
$688$	5.94724	−	10.3009i	0.226736	−	0.392719i
$689$	−32.6647			−1.24442
$690$	3.74300	−	8.94405i	0.142494	−	0.340494i
$691$		−	19.0857i		−	0.726054i	−0.931779	−	0.363027i	$-0.881743\pi$
$691$		−	19.0857i		−	0.726054i	0.931779	−	0.363027i	$-0.118257\pi$
$692$	16.6263			0.632039
$693$	−6.04121	+	0.802692i	−0.229487	+	0.0304917i
$694$	−18.4244			−0.699380
$695$			10.1851i			0.386341i
$696$	−18.0953	+	2.31523i	−0.685901	+	0.0877584i
$697$	12.2242			0.463024
$698$	0.793577	−	1.37452i	0.0300373	−	0.0520262i
$699$	3.76795	+	1.57685i	0.142517	+	0.0596420i
$700$	−2.43568	+	1.03319i	−0.0920599	+	0.0390509i
$701$		−	14.4247i		−	0.544815i	−0.962182	−	0.272407i	$-0.912180\pi$
$701$		−	14.4247i		−	0.544815i	0.962182	−	0.272407i	$-0.0878198\pi$
$702$	−17.8424	−	14.0035i	−0.673416	−	0.528529i
$703$	34.8458	+	20.1182i	1.31423	+	0.758773i
$704$	−0.664943	+	0.383905i	−0.0250610	+	0.0144690i
$705$	11.1011	−	1.42034i	0.418091	−	0.0534931i
$706$	−7.97208	+	4.60268i	−0.300033	+	0.173224i
$707$	28.8663	−	12.2448i	1.08563	−	0.460514i
$708$	11.9995	+	15.7566i	0.450968	+	0.592170i
$709$	23.9438			0.899229			0.449615	−	0.893223i	$-0.351561\pi$
$709$	23.9438			0.899229			0.449615	+	0.893223i	$0.351561\pi$
$710$	3.75292	−	6.50024i	0.140844	−	0.243950i
$711$	0.885640	−	3.21143i	0.0332141	−	0.120438i
$712$	4.85263	−	2.80167i	0.181860	−	0.104997i
$713$	−22.5570	+	39.0699i	−0.844766	+	1.46318i
$714$	−10.5542	+	0.0510915i	−0.394980	+	0.00191205i
$715$	1.67576	+	2.90251i	0.0626701	+	0.108548i
$716$	4.07453	+	2.35243i	0.152272	+	0.0879145i
$717$	−18.8126	−	7.87291i	−0.702571	−	0.294019i
$718$	12.9183	+	22.3751i	0.482106	+	0.835033i
$719$	7.04096	+	12.1953i	0.262584	+	0.454808i	0.966928	−	0.255051i	$-0.0820921\pi$
$719$	7.04096	+	12.1953i	0.262584	+	0.454808i	−0.704344	+	0.709859i	$0.748759\pi$
$720$	−2.10580	−	2.13673i	−0.0784785	−	0.0796311i
$721$	1.39865	−	1.85514i	0.0520883	−	0.0690889i
$722$	−3.83750	−	2.21558i	−0.142817	−	0.0824554i
$723$	−30.0601	−	12.5798i	−1.11795	−	0.467850i
$724$			8.33408i			0.309734i
$725$			10.5325i			0.391167i
$726$	−2.28840	−	17.8857i	−0.0849305	−	0.663799i
$727$	−10.6031	−	6.12171i	−0.393248	−	0.227042i	0.290319	−	0.956930i	$-0.406239\pi$
$727$	−10.6031	−	6.12171i	−0.393248	−	0.227042i	−0.683566	+	0.729888i	$0.739572\pi$
$728$	−10.6318	+	4.50993i	−0.394042	+	0.167149i
$729$	19.5048	−	18.6698i	0.722400	−	0.691475i
$730$	5.84190	+	10.1185i	0.216218	+	0.374501i
$731$	−13.6973	−	23.7244i	−0.506612	−	0.877478i
$732$	−13.0906	+	9.96918i	−0.483843	+	0.368471i
$733$	−27.7009	−	15.9931i	−1.02316	−	0.590720i	−0.108140	−	0.994136i	$-0.534489\pi$
$733$	−27.7009	−	15.9931i	−1.02316	−	0.590720i	−0.915017	+	0.403416i	$0.867823\pi$
$734$	−11.1282	−	19.2746i	−0.410750	−	0.711439i
$735$	−12.0407	−	1.42222i	−0.444126	−	0.0524592i
$736$	2.79890	−	4.84784i	0.103169	−	0.178694i
$737$	9.11288	−	5.26132i	0.335677	−	0.193803i
$738$	4.00892	+	15.4100i	0.147570	+	0.567248i
$739$	−17.7732	+	30.7841i	−0.653798	+	1.13241i	0.328396	+	0.944540i	$0.393492\pi$
$739$	−17.7732	+	30.7841i	−0.653798	+	1.13241i	−0.982194	+	0.187871i	$0.939841\pi$
$740$	8.31233			0.305567
$741$	−36.3012	+	4.64460i	−1.33356	+	0.170624i
$742$	−15.8091	−	11.9190i	−0.580371	−	0.437560i
$743$	19.6903	−	11.3682i	0.722366	−	0.417058i	−0.0932570	−	0.995642i	$-0.529728\pi$
$743$	19.6903	−	11.3682i	0.722366	−	0.417058i	0.815623	+	0.578584i	$0.196394\pi$
$744$	8.45728	+	11.1053i	0.310059	+	0.407141i
$745$	7.75355	−	4.47651i	0.284068	−	0.164007i
$746$	−28.3884	−	16.3900i	−1.03937	−	0.600082i
$747$	1.07218	+	1.08793i	0.0392290	+	0.0398052i
$748$			1.76837i			0.0646580i
$749$	−6.62349	−	15.6144i	−0.242017	−	0.570539i
$750$	−1.37796	+	1.04939i	−0.0503161	+	0.0383183i
$751$	−7.22595	+	12.5157i	−0.263678	+	0.456705i	−0.967217	−	0.253953i	$-0.918269\pi$
$751$	−7.22595	+	12.5157i	−0.263678	+	0.456705i	0.703538	+	0.710658i	$0.251602\pi$
$752$	6.46146			0.235625
$753$	−3.52342	−	4.62663i	−0.128401	−	0.168604i
$754$			45.9749i			1.67431i
$755$	−5.00718			−0.182230
$756$	−3.52564	−	13.2880i	−0.128226	−	0.483278i
$757$	29.2971			1.06482			0.532410	−	0.846487i	$-0.321287\pi$
$757$	29.2971			1.06482			0.532410	+	0.846487i	$0.321287\pi$
$758$			26.7133i			0.970270i
$759$	−4.51033	−	5.92255i	−0.163715	−	0.214975i
$760$	−4.84057			−0.175586
$761$	24.4664	−	42.3770i	0.886906	−	1.53617i	0.0433933	−	0.999058i	$-0.486183\pi$
$761$	24.4664	−	42.3770i	0.886906	−	1.53617i	0.843513	−	0.537109i	$-0.180484\pi$
$762$	17.4284	−	13.2726i	0.631364	−	0.480816i
$763$	−18.4380	−	13.9010i	−0.667500	−	0.503249i
$764$		−	3.79290i		−	0.137222i
$765$	−6.68683	+	1.73959i	−0.241763	+	0.0628949i
$766$	1.57386	+	0.908668i	0.0568658	+	0.0328315i
$767$	43.2260	−	24.9566i	1.56080	−	0.901129i
$768$	−1.04939	−	1.37796i	−0.0378666	−	0.0497229i
$769$	−44.0886	+	25.4546i	−1.58988	+	0.917915i	−0.596549	+	0.802577i	$0.703462\pi$
$769$	−44.0886	+	25.4546i	−1.58988	+	0.917915i	−0.993326	+	0.115339i	$0.963205\pi$
$770$	−0.248055	+	2.01623i	−0.00893930	+	0.0726600i
$771$	−19.4761	+	2.49189i	−0.701414	+	0.0897433i
$772$	21.4959			0.773656
$773$	10.7757	−	18.6640i	0.387574	−	0.671297i	−0.604549	−	0.796568i	$-0.706647\pi$
$773$	10.7757	−	18.6640i	0.387574	−	0.671297i	0.992123	+	0.125271i	$0.0399800\pi$
$774$	25.4152	−	25.0474i	0.913532	−	0.900309i
$775$	6.97950	−	4.02962i	0.250711	−	0.144748i
$776$	−4.39608	+	7.61423i	−0.157810	+	0.273335i
$777$	33.0804	+	18.8860i	1.18675	+	0.677532i
$778$	−14.9847	−	25.9543i	−0.537228	−	0.930507i
$779$	22.2499	+	12.8460i	0.797185	+	0.460255i
$780$	−6.01487	+	4.58064i	−0.215367	+	0.164013i
$781$	−2.88153	−	4.99095i	−0.103109	−	0.178590i
$782$	−6.44624	−	11.1652i	−0.230517	−	0.399268i
$783$	−54.1789	−	7.73638i	−1.93620	−	0.276476i
$784$	−6.79125	−	1.69673i	−0.242545	−	0.0605973i
$785$	2.81741	+	1.62663i	0.100558	+	0.0580570i
$786$	−2.18191	−	17.0534i	−0.0778263	−	0.608273i
$787$		−	24.6504i		−	0.878693i	−0.898318	−	0.439347i	$-0.855210\pi$
$787$		−	24.6504i		−	0.878693i	0.898318	−	0.439347i	$-0.144790\pi$
$788$		−	13.3908i		−	0.477027i
$789$	41.1939	+	17.2393i	1.46654	+	0.613734i
$790$	−0.961666	−	0.555218i	−0.0342145	−	0.0197538i
$791$	−0.832270	−	1.96202i	−0.0295921	−	0.0697614i
$792$	−2.22923	+	0.579937i	−0.0792122	+	0.0206072i
$793$	20.7339	+	35.9122i	0.736283	+	1.27528i
$794$	−0.468371	−	0.811242i	−0.0166219	−	0.0287899i
$795$	−11.9566	−	5.00370i	−0.424055	−	0.177463i
$796$	−0.485507	−	0.280308i	−0.0172083	−	0.00993524i
$797$	−1.27405	−	2.20672i	−0.0451293	−	0.0781662i	0.842578	−	0.538574i	$-0.181037\pi$
$797$	−1.27405	−	2.20672i	−0.0451293	−	0.0781662i	−0.887708	+	0.460407i	$0.847703\pi$
$798$	−19.2639	−	10.9980i	−0.681935	−	0.389326i
$799$	7.44080	−	12.8878i	0.263237	−	0.455939i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	16.2685	−	4.23227i	0.574819	−	0.149540i
$802$	−2.90439	+	5.03054i	−0.102557	+	0.177635i
$803$	8.97094			0.316578
$804$	14.3816	+	18.8846i	0.507201	+	0.666009i
$805$	−5.78360	−	13.6344i	−0.203845	−	0.480550i
$806$	30.4659	−	17.5895i	1.07311	−	0.619563i
$807$	10.1325	−	1.29641i	0.356680	−	0.0456359i
$808$	10.2637	−	5.92574i	0.361075	−	0.208467i
$809$	3.56339	+	2.05733i	0.125282	+	0.0723318i	0.561331	−	0.827591i	$-0.310289\pi$
$809$	3.56339	+	2.05733i	0.125282	+	0.0723318i	−0.436049	+	0.899923i	$0.643623\pi$
$810$	−4.38589	−	7.85901i	−0.154104	−	0.276137i
$811$		−	36.4586i		−	1.28024i	−0.768277	−	0.640118i	$-0.778885\pi$
$811$		−	36.4586i		−	1.28024i	0.768277	−	0.640118i	$-0.221115\pi$
$812$	−16.7758	+	22.2510i	−0.588714	+	0.780858i
$813$	16.1744	+	6.76882i	0.567260	+	0.237393i
$814$	3.19115	−	5.52723i	0.111850	−	0.193729i
$815$	−4.81863			−0.168789
$816$	−3.95689	+	0.506269i	−0.138519	+	0.0177230i
$817$		−	57.5761i		−	2.01433i
$818$	−21.8817			−0.765076
$819$	−34.3447	+	4.56335i	−1.20010	+	0.159456i
$820$	5.30763			0.185350
$821$			32.3659i			1.12958i	0.825236	+	0.564789i	$0.191042\pi$
$821$			32.3659i			1.12958i	−0.825236	+	0.564789i	$0.808958\pi$
$822$	−9.62428	+	22.9976i	−0.335685	+	0.802134i
$823$	−7.68356			−0.267832			−0.133916	−	0.990993i	$-0.542755\pi$
$823$	−7.68356			−0.267832			−0.133916	+	0.990993i	$0.542755\pi$
$824$	0.439063	−	0.760480i	0.0152955	−	0.0264926i
$825$	0.168778	+	1.31913i	0.00587610	+	0.0459263i
$826$	30.0270	+	3.69420i	1.04477	+	0.128538i
$827$		−	8.88863i		−	0.309088i	−0.987986	−	0.154544i	$-0.950609\pi$
$827$		−	8.88863i		−	0.309088i	0.987986	−	0.154544i	$-0.0493908\pi$
$828$	11.9610	−	11.7879i	0.415673	−	0.409656i
$829$	15.5068	+	8.95287i	0.538574	+	0.310946i	0.744501	−	0.667621i	$-0.232688\pi$
$829$	15.5068	+	8.95287i	0.538574	+	0.310946i	−0.205927	+	0.978567i	$0.566021\pi$
$830$	0.440942	−	0.254578i	0.0153053	−	0.00883652i
$831$	−6.94736	+	16.6010i	−0.241001	+	0.575883i
$832$	−3.78024	+	2.18252i	−0.131056	+	0.0756654i
$833$	−11.2048	+	11.5918i	−0.388224	+	0.401631i
$834$	−6.81029	+	16.2735i	−0.235821	+	0.563505i
$835$	−9.94518			−0.344167
$836$	−1.85832	+	3.21871i	−0.0642714	+	0.111321i
$837$	15.6016	+	38.8622i	0.539271	+	1.34328i
$838$	13.8082	−	7.97218i	0.476997	−	0.275395i
$839$	15.0745	−	26.1098i	0.520430	−	0.901412i	−0.479287	−	0.877658i	$-0.659105\pi$
$839$	15.0745	−	26.1098i	0.520430	−	0.901412i	0.999718	−	0.0237538i	$-0.00756179\pi$
$840$	−4.58252	+	0.0221835i	−0.158112	+	0.000765402i
$841$	40.9667	+	70.9565i	1.41265	+	2.44678i
$842$	−14.3237	−	8.26978i	−0.493627	−	0.284995i
$843$	3.63346	+	28.3984i	0.125143	+	0.978091i
$844$	−1.76537	−	3.05771i	−0.0607665	−	0.105251i
$845$	3.02683	+	5.24262i	0.104126	+	0.180352i
$846$	18.6868	+	5.15340i	0.642465	+	0.177178i
$847$	−21.9932	−	16.5814i	−0.755696	−	0.569743i
$848$	−6.48067	−	3.74161i	−0.222547	−	0.128488i
$849$	−14.3204	+	10.9057i	−0.491473	+	0.374283i
$850$			2.30313i			0.0789969i
$851$			46.5308i			1.59505i
$852$	10.3428	−	7.87655i	0.354337	−	0.269846i
$853$	11.2347	+	6.48634i	0.384668	+	0.222088i	0.679847	−	0.733354i	$-0.262046\pi$
$853$	11.2347	+	6.48634i	0.384668	+	0.222088i	−0.295180	+	0.955442i	$0.595379\pi$
$854$	−3.06914	+	24.9465i	−0.105024	+	0.853651i
$855$	−13.9991	−	3.86065i	−0.478760	−	0.132031i
$856$	−3.20536	−	5.55184i	−0.109557	−	0.189758i
$857$	−13.2292	−	22.9136i	−0.451900	−	0.782714i	0.546604	−	0.837391i	$-0.315920\pi$
$857$	−13.2292	−	22.9136i	−0.451900	−	0.782714i	−0.998504	+	0.0546774i	$0.982587\pi$
$858$	0.736724	+	5.75808i	0.0251514	+	0.196578i
$859$	26.4968	+	15.2980i	0.904060	+	0.521959i	0.878515	−	0.477714i	$-0.158535\pi$
$859$	26.4968	+	15.2980i	0.904060	+	0.521959i	0.0255448	+	0.999674i	$0.491868\pi$
$860$	−5.94724	−	10.3009i	−0.202799	−	0.351258i
$861$	21.1226	+	12.0592i	0.719857	+	0.410976i
$862$	6.08623	−	10.5417i	0.207298	−	0.359050i
$863$	42.9051	−	24.7713i	1.46051	−	0.843223i	0.461471	−	0.887155i	$-0.347322\pi$
$863$	42.9051	−	24.7713i	1.46051	−	0.843223i	0.999035	+	0.0439320i	$0.0139885\pi$
$864$	−1.93587	−	4.82207i	−0.0658596	−	0.164050i
$865$	8.31317	−	14.3988i	0.282656	−	0.489575i
$866$	−8.54538			−0.290384
$867$	7.82031	−	18.6869i	0.265592	−	0.634642i
$868$	21.1632	+	2.60369i	0.718325	+	0.0883749i
$869$	−0.738377	+	0.426302i	−0.0250477	+	0.0144613i
$870$	−7.04261	+	16.8286i	−0.238767	+	0.570543i
$871$	51.8073	−	29.9109i	1.75542	−	1.01349i
$872$	−7.55832	−	4.36380i	−0.255957	−	0.147777i
$873$	−18.7864	+	18.5145i	−0.635824	+	0.626621i
$874$		−	27.0966i		−	0.916555i
$875$	−0.323069	+	2.62595i	−0.0109217	+	0.0887734i
$876$	2.56830	+	20.0733i	0.0867748	+	0.678214i
$877$	22.0621	−	38.2126i	0.744983	−	1.29035i	−0.205219	−	0.978716i	$-0.565791\pi$
$877$	22.0621	−	38.2126i	0.744983	−	1.29035i	0.950203	−	0.311633i	$-0.100876\pi$
$878$	−6.58176			−0.222124
$879$	17.0889	−	40.8347i	0.576396	−	1.37732i
$880$			0.767810i			0.0258829i
$881$	−14.2789			−0.481068			−0.240534	−	0.970641i	$-0.577323\pi$
$881$	−14.2789			−0.481068			−0.240534	+	0.970641i	$0.577323\pi$
$882$	−18.2873	−	10.3234i	−0.615767	−	0.347608i
$883$	−2.99831			−0.100901			−0.0504505	−	0.998727i	$-0.516066\pi$
$883$	−2.99831			−0.100901			−0.0504505	+	0.998727i	$0.516066\pi$
$884$			10.0533i			0.338129i
$885$	19.6454	−	2.51355i	0.660372	−	0.0844921i
$886$	−27.0738			−0.909561
$887$	18.0122	−	31.1981i	0.604791	−	1.04753i	−0.387293	−	0.921957i	$-0.626590\pi$
$887$	18.0122	−	31.1981i	0.604791	−	1.04753i	0.992084	−	0.125572i	$-0.0400767\pi$
$888$	13.2813	+	5.55808i	0.445690	+	0.186517i
$889$	4.08615	−	33.2129i	0.137045	−	1.11392i
$890$		−	5.60333i		−	0.187824i
$891$	−6.90956	−	0.100746i	−0.231479	−	0.00337511i
$892$	22.1791	+	12.8051i	0.742612	+	0.428748i
$893$	27.0868	−	15.6386i	0.906426	−	0.523325i
$894$	15.3817	−	1.96803i	0.514441	−	0.0658208i
$895$	4.07453	−	2.35243i	0.136197	−	0.0786331i
$896$	−2.62595	−	0.323069i	−0.0877269	−	0.0107930i
$897$	−25.6415	−	33.6701i	−0.856145	−	1.12421i
$898$	−17.9654			−0.599514
$899$	42.4419	−	73.5116i	1.41552	−	2.45175i
$900$	−2.90336	+	0.755312i	−0.0967787	+	0.0251771i
$901$	−14.9258	+	8.61744i	−0.497252	+	0.287089i
$902$	2.03763	−	3.52927i	0.0678455	−	0.117512i
$903$	−0.263861	−	54.5067i	−0.00878073	−	1.81387i
$904$	−0.402767	−	0.697613i	−0.0133958	−	0.0232023i
$905$	7.21752	+	4.16704i	0.239919	+	0.138517i
$906$	−8.00037	−	3.34808i	−0.265795	−	0.111232i
$907$	−10.5464	−	18.2670i	−0.350189	−	0.606545i	0.636093	−	0.771612i	$-0.280549\pi$
$907$	−10.5464	−	18.2670i	−0.350189	−	0.606545i	−0.986282	+	0.165067i	$0.947216\pi$
$908$	−5.56930	−	9.64631i	−0.184824	−	0.320124i
$909$	34.4091	−	8.95156i	1.14128	−	0.296905i
$910$	−1.41021	+	11.4624i	−0.0467480	+	0.379975i
$911$	−23.7590	−	13.7172i	−0.787169	−	0.454472i	0.0517958	−	0.998658i	$-0.483505\pi$
$911$	−23.7590	−	13.7172i	−0.787169	−	0.454472i	−0.838965	+	0.544185i	$0.816839\pi$
$912$	−7.73417	−	3.23668i	−0.256104	−	0.107177i
$913$		−	0.390935i		−	0.0129381i
$914$			5.14932i			0.170324i
$915$	2.08826	+	16.3214i	0.0690357	+	0.539568i
$916$	3.29819	+	1.90421i	0.108975	+	0.0629169i
$917$	−20.9698	−	15.8098i	−0.692484	−	0.522085i
$918$	−11.8473	−	1.69171i	−0.391018	−	0.0558347i
$919$	2.13518	+	3.69824i	0.0704332	+	0.121994i	0.899091	−	0.437761i	$-0.144229\pi$
$919$	2.13518	+	3.69824i	0.0704332	+	0.121994i	−0.828658	+	0.559755i	$0.810895\pi$
$920$	−2.79890	−	4.84784i	−0.0922770	−	0.159828i
$921$	−12.8610	+	9.79434i	−0.423785	+	0.322734i
$922$	9.45788	+	5.46051i	0.311479	+	0.179832i
$923$	−16.3817	−	28.3739i	−0.539209	−	0.933938i
$924$	−1.74450	+	3.05563i	−0.0573899	+	0.100523i
$925$	4.15617	−	7.19869i	0.136654	−	0.236691i
$926$	25.7563	−	14.8704i	0.846406	−	0.488673i
$927$	1.87632	−	1.84916i	0.0616263	−	0.0607343i
$928$	−5.26625	+	9.12141i	−0.172873	+	0.299425i
$929$	11.8008			0.387171			0.193585	−	0.981083i	$-0.437988\pi$
$929$	11.8008			0.387171			0.193585	+	0.981083i	$0.437988\pi$
$930$	13.8461	−	1.77156i	0.454033	−	0.0580917i
$931$	−32.5759	+	9.32401i	−1.06763	+	0.305582i
$932$	2.04230	−	1.17912i	0.0668977	−	0.0386234i
$933$	5.63079	+	7.39383i	0.184344	+	0.242063i
$934$	7.89337	−	4.55724i	0.258279	−	0.149117i
$935$	1.53145	+	0.884185i	0.0500839	+	0.0289159i
$936$	−12.6733	+	3.29698i	−0.414240	+	0.107765i
$937$			52.8223i			1.72563i	0.505520	+	0.862815i	$0.331301\pi$
$937$			52.8223i			1.72563i	−0.505520	+	0.862815i	$0.668699\pi$
$938$	35.9880	+	4.42757i	1.17505	+	0.144565i
$939$	−35.0773	+	26.7132i	−1.14470	+	0.871752i
$940$	3.23073	−	5.59578i	0.105375	−	0.182514i
$941$	−41.3578			−1.34823			−0.674113	−	0.738629i	$-0.735474\pi$
$941$	−41.3578			−1.34823			−0.674113	+	0.738629i	$0.735474\pi$
$942$	3.41394	+	4.48288i	0.111232	+	0.146060i
$943$			29.7110i			0.967524i
$944$	11.4347			0.372168
$945$	−13.2705	−	3.59068i	−0.431690	−	0.116805i
$946$	−9.13270			−0.296930
$947$			19.1358i			0.621829i	0.950438	+	0.310914i	$0.100635\pi$
$947$			19.1358i			0.621829i	−0.950438	+	0.310914i	$0.899365\pi$
$948$	−1.16528	−	1.53014i	−0.0378466	−	0.0496966i
$949$	51.0003			1.65554
$950$	−2.42029	+	4.19206i	−0.0785245	+	0.136008i
$951$	10.3165	−	7.85653i	0.334535	−	0.254765i
$952$	−3.66834	+	4.86562i	−0.118892	+	0.157696i
$953$		−	16.1271i		−	0.522407i	−0.965284	−	0.261203i	$-0.915881\pi$
$953$		−	16.1271i		−	0.522407i	0.965284	−	0.261203i	$-0.0841193\pi$
$954$	−15.7582	−	15.9896i	−0.510190	−	0.517683i
$955$	−3.28474	−	1.89645i	−0.106292	−	0.0613676i
$956$	−10.1968	+	5.88712i	−0.329788	+	0.190403i
$957$	8.48638	+	11.1435i	0.274326	+	0.360219i
$958$	−32.3003	+	18.6486i	−1.04358	+	0.602508i
$959$	14.8712	+	35.0578i	0.480216	+	1.13208i
$960$	−1.71805	+	0.219817i	−0.0554497	+	0.00709457i
$961$	−33.9513			−1.09520
$962$	18.1419	−	31.4226i	0.584917	−	1.01311i
$963$	−4.84209	−	18.6126i	−0.156034	−	0.599783i
$964$	−16.2931	+	9.40683i	−0.524765	+	0.302973i
$965$	10.7480	−	18.6160i	0.345989	−	0.599271i
$966$	−0.124179	−	25.6520i	−0.00399538	−	0.825341i
$967$	23.6109	+	40.8952i	0.759274	+	1.31510i	0.943221	+	0.332165i	$0.107779\pi$
$967$	23.6109	+	40.8952i	0.759274	+	1.31510i	−0.183948	+	0.982936i	$0.558888\pi$
$968$	−9.01573	−	5.20523i	−0.289777	−	0.167303i
$969$	−15.3622	+	11.6991i	−0.493505	+	0.375830i
$970$	4.39608	+	7.61423i	0.141149	+	0.244478i
$971$	−12.0076	−	20.7978i	−0.385343	−	0.667434i	0.606474	−	0.795104i	$-0.292584\pi$
$971$	−12.0076	−	20.7978i	−0.385343	−	0.667434i	−0.991817	+	0.127670i	$0.959250\pi$
$972$	−1.75272	−	15.4896i	−0.0562185	−	0.496829i
$973$	10.5231	+	24.8075i	0.337355	+	0.795292i
$974$	16.3605	+	9.44574i	0.524224	+	0.302661i
$975$	0.959514	+	7.49935i	0.0307290	+	0.240172i
$976$			9.49997i			0.304087i
$977$		−	10.7320i		−	0.343348i	−0.985154	−	0.171674i	$-0.945082\pi$
$977$		−	10.7320i		−	0.343348i	0.985154	−	0.171674i	$-0.0549176\pi$
$978$	−7.69911	−	3.22200i	−0.246190	−	0.103028i
$979$	−3.72590	−	2.15115i	−0.119080	−	0.0687510i
$980$	−4.86503	+	5.03304i	−0.155408	+	0.160774i
$981$	−18.3786	−	18.6485i	−0.586782	−	0.595400i
$982$	17.4047	+	30.1458i	0.555406	+	0.961991i
$983$	27.1880	+	47.0910i	0.867162	+	1.50197i	0.864885	+	0.501971i	$0.167391\pi$
$983$	27.1880	+	47.0910i	0.867162	+	1.50197i	0.00227708	+	0.999997i	$0.499275\pi$
$984$	8.48042	+	3.54897i	0.270346	+	0.113137i
$985$	−11.5968	−	6.69540i	−0.369504	−	0.213333i
$986$	12.1289	+	21.0078i	0.386262	+	0.669026i
$987$	25.5711	−	14.9290i	0.813938	−	0.475196i
$988$	−10.5647	+	18.2986i	−0.336107	+	0.582154i
$989$	57.6625	−	33.2914i	1.83356	−	1.05861i
$990$	−0.612375	+	2.22054i	−0.0194626	+	0.0705733i
$991$	1.44414	−	2.50132i	0.0458746	−	0.0794571i	−0.842176	−	0.539202i	$-0.818726\pi$
$991$	1.44414	−	2.50132i	0.0458746	−	0.0794571i	0.888051	+	0.459745i	$0.152059\pi$
$992$	8.05924			0.255881
$993$	−7.79557	−	10.2364i	−0.247385	−	0.324843i
$994$	2.42490	−	19.7100i	0.0769131	−	0.625162i
$995$	−0.485507	+	0.280308i	−0.0153916	+	0.00888635i
$996$	0.874752	−	0.111921i	0.0277176	−	0.00354636i
$997$	−8.67758	+	5.01001i	−0.274822	+	0.158668i	−0.631077	−	0.775720i	$-0.717387\pi$
$997$	−8.67758	+	5.01001i	−0.274822	+	0.158668i	0.356255	+	0.934389i	$0.384053\pi$
$998$	21.1593	+	12.2163i	0.669786	+	0.386701i
$999$	33.9771	+	26.6668i	1.07499	+	0.843701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.101.3	yes	28
3.2	odd	2		1890.2.bk.b.521.6		28
7.5	odd	6		630.2.t.b.551.1	yes	28
9.4	even	3		1890.2.t.b.1151.11		28
9.5	odd	6		630.2.t.b.311.1	✓	28
21.5	even	6		1890.2.t.b.1601.11		28
63.5	even	6	inner	630.2.bk.b.131.10	yes	28
63.40	odd	6		1890.2.bk.b.341.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.1	✓	28	9.5	odd	6
630.2.t.b.551.1	yes	28	7.5	odd	6
630.2.bk.b.101.3	yes	28	1.1	even	1	trivial
630.2.bk.b.131.10	yes	28	63.5	even	6	inner
1890.2.t.b.1151.11		28	9.4	even	3
1890.2.t.b.1601.11		28	21.5	even	6
1890.2.bk.b.341.6		28	63.40	odd	6
1890.2.bk.b.521.6		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.04939 - 1.37796i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.37796 + 1.04939i) q^{6} +(-0.323069 + 2.62595i) q^{7} +1.00000i q^{8} +(-0.797561 + 2.89204i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.04939 - 1.37796i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.37796 + 1.04939i) q^{6} +(-0.323069 + 2.62595i) q^{7} +1.00000i q^{8} +(-0.797561 + 2.89204i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.664943 - 0.383905i) q^{11} +(1.04939 + 1.37796i) q^{12} +(3.78024 - 2.18252i) q^{13} +(2.62595 + 0.323069i) q^{14} +(1.71805 - 0.219817i) q^{15} +1.00000 q^{16} +(1.15157 - 1.99457i) q^{17} +(2.89204 + 0.797561i) q^{18} +(4.19206 - 2.42029i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.95749 - 2.31047i) q^{21} +(-0.383905 - 0.664943i) q^{22} +(4.84784 + 2.79890i) q^{23} +(1.37796 - 1.04939i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.18252 - 3.78024i) q^{26} +(4.82207 - 1.93587i) q^{27} +(0.323069 - 2.62595i) q^{28} +(-9.12141 - 5.26625i) q^{29} +(-0.219817 - 1.71805i) q^{30} +8.05924i q^{31} -1.00000i q^{32} +(-1.22679 - 0.513400i) q^{33} +(-1.99457 - 1.15157i) q^{34} +(-2.11261 - 1.59276i) q^{35} +(0.797561 - 2.89204i) q^{36} +(4.15617 + 7.19869i) q^{37} +(-2.42029 - 4.19206i) q^{38} +(-6.97439 - 2.91871i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(2.65381 + 4.59654i) q^{41} +(-2.31047 - 3.95749i) q^{42} +(5.94724 - 10.3009i) q^{43} +(-0.664943 + 0.383905i) q^{44} +(-2.10580 - 2.13673i) q^{45} +(2.79890 - 4.84784i) q^{46} +6.46146 q^{47} +(-1.04939 - 1.37796i) q^{48} +(-6.79125 - 1.69673i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-3.95689 + 0.506269i) q^{51} +(-3.78024 + 2.18252i) q^{52} +(-6.48067 - 3.74161i) q^{53} +(-1.93587 - 4.82207i) q^{54} +0.767810i q^{55} +(-2.62595 - 0.323069i) q^{56} +(-7.73417 - 3.23668i) q^{57} +(-5.26625 + 9.12141i) q^{58} +11.4347 q^{59} +(-1.71805 + 0.219817i) q^{60} +9.49997i q^{61} +8.05924 q^{62} +(-7.33669 - 3.02868i) q^{63} -1.00000 q^{64} +4.36505i q^{65} +(-0.513400 + 1.22679i) q^{66} +13.7047 q^{67} +(-1.15157 + 1.99457i) q^{68} +(-1.23049 - 9.61728i) q^{69} +(-1.59276 + 2.11261i) q^{70} -7.50583i q^{71} +(-2.89204 - 0.797561i) q^{72} +(10.1185 + 5.84190i) q^{73} +(7.19869 - 4.15617i) q^{74} +(-0.668655 + 1.59778i) q^{75} +(-4.19206 + 2.42029i) q^{76} +(0.793294 + 1.87014i) q^{77} +(-2.91871 + 6.97439i) q^{78} -1.11044 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.72779 - 4.61315i) q^{81} +(4.59654 - 2.65381i) q^{82} +(0.254578 - 0.440942i) q^{83} +(-3.95749 + 2.31047i) q^{84} +(1.15157 + 1.99457i) q^{85} +(-10.3009 - 5.94724i) q^{86} +(2.31523 + 18.0953i) q^{87} +(0.383905 + 0.664943i) q^{88} +(-2.80167 - 4.85263i) q^{89} +(-2.13673 + 2.10580i) q^{90} +(4.50993 + 10.6318i) q^{91} +(-4.84784 - 2.79890i) q^{92} +(11.1053 - 8.45728i) q^{93} -6.46146i q^{94} +4.84057i q^{95} +(-1.37796 + 1.04939i) q^{96} +(7.61423 + 4.39608i) q^{97} +(-1.69673 + 6.79125i) q^{98} +(0.579937 + 2.22923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

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