LMFDB - Embedded newform 630.2.t.b.311.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 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("630.311");

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.t (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			311.1
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.71805 - 0.219817i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.37796 + 1.04939i) q^{6} +(-2.11261 - 1.59276i) q^{7} -1.00000i q^{8} +(2.90336 + 0.755312i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.71805 - 0.219817i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.37796 + 1.04939i) q^{6} +(-2.11261 - 1.59276i) q^{7} -1.00000i q^{8} +(2.90336 + 0.755312i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.767810i q^{11} +(-0.668655 - 1.59778i) q^{12} +(-3.78024 - 2.18252i) q^{13} +(1.03319 + 2.43568i) q^{14} +(1.71805 + 0.219817i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.15157 + 1.99457i) q^{17} +(-2.13673 - 2.10580i) q^{18} +(4.19206 - 2.42029i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(3.27944 + 3.20083i) q^{21} +(-0.383905 + 0.664943i) q^{22} +5.59780i q^{23} +(-0.219817 + 1.71805i) q^{24} +1.00000 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} +(-1.37796 - 1.04939i) q^{30} +(6.97950 - 4.02962i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.168778 + 1.31913i) 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} -4.84057 q^{38} +(6.01487 + 4.58064i) q^{39} +1.00000i q^{40} +(-2.65381 + 4.59654i) q^{41} +(-1.23966 - 4.41172i) q^{42} +(5.94724 + 10.3009i) q^{43} +(0.664943 - 0.383905i) q^{44} +(-2.90336 - 0.755312i) q^{45} +(2.79890 - 4.84784i) q^{46} +(3.23073 - 5.59578i) q^{47} +(1.04939 - 1.37796i) q^{48} +(1.92622 + 6.72976i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.41689 - 3.17363i) q^{51} -4.36505i q^{52} +(6.48067 + 3.74161i) q^{53} +(3.20810 + 4.08755i) q^{54} +0.767810i q^{55} +(-1.59276 + 2.11261i) q^{56} +(-7.73417 + 3.23668i) q^{57} +10.5325 q^{58} +(5.71736 + 9.90276i) q^{59} +(0.668655 + 1.59778i) q^{60} +(-8.22722 - 4.74999i) q^{61} -8.05924 q^{62} +(-4.93063 - 6.22004i) q^{63} -1.00000 q^{64} +(3.78024 + 2.18252i) q^{65} +(0.805733 - 1.05801i) q^{66} +(-6.85237 - 11.8687i) q^{67} -2.30313 q^{68} +(1.23049 - 9.61728i) q^{69} +(-1.03319 - 2.43568i) q^{70} +7.50583i q^{71} +(0.755312 - 2.90336i) q^{72} +(10.1185 + 5.84190i) q^{73} -8.31233i q^{74} +(-1.71805 - 0.219817i) q^{75} +(4.19206 + 2.42029i) q^{76} +(-1.22294 + 1.62208i) q^{77} +(-2.91871 - 6.97439i) q^{78} +(0.555218 - 0.961666i) q^{79} +(0.500000 - 0.866025i) q^{80} +(7.85901 + 4.38589i) q^{81} +(4.59654 - 2.65381i) q^{82} +(-0.254578 - 0.440942i) q^{83} +(-1.13228 + 4.44049i) q^{84} +(1.15157 - 1.99457i) q^{85} -11.8945i q^{86} +(16.8286 - 7.04261i) q^{87} -0.767810 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} +(-12.8769 + 5.38885i) q^{93} +(-5.59578 + 3.23073i) q^{94} +(-4.19206 + 2.42029i) q^{95} +(-1.59778 + 0.668655i) 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} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.71805	−	0.219817i	−0.991914	−	0.126912i
$3$	−1.71805	−	0.219817i	−0.991914	−	0.126912i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.37796	+	1.04939i	0.562551	+	0.428412i
$7$	−2.11261	−	1.59276i	−0.798491	−	0.602007i
$7$	−2.11261	−	1.59276i	−0.798491	−	0.602007i
$8$		−	1.00000i		−	0.353553i
$9$	2.90336	+	0.755312i	0.967787	+	0.251771i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	0.767810i		−	0.231504i	−0.993278	−	0.115752i	$-0.963072\pi$
$11$		−	0.767810i		−	0.231504i	0.993278	−	0.115752i	$-0.0369277\pi$
$12$	−0.668655	−	1.59778i	−0.193024	−	0.461239i
$13$	−3.78024	−	2.18252i	−1.04845	−	0.605323i	−0.126236	−	0.992000i	$-0.540290\pi$
$13$	−3.78024	−	2.18252i	−1.04845	−	0.605323i	−0.922215	+	0.386677i	$0.873623\pi$
$14$	1.03319	+	2.43568i	0.276132	+	0.650962i
$15$	1.71805	+	0.219817i	0.443597	+	0.0567566i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.15157	+	1.99457i	−0.279296	+	0.483755i	−0.971210	−	0.238225i	$-0.923434\pi$
$17$	−1.15157	+	1.99457i	−0.279296	+	0.483755i	0.691914	+	0.721980i	$0.256768\pi$
$18$	−2.13673	−	2.10580i	−0.503632	−	0.496342i
$19$	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
$21$	3.27944	+	3.20083i	0.715632	+	0.698477i
$22$	−0.383905	+	0.664943i	−0.0818489	+	0.141766i
$23$			5.59780i			1.16722i	0.812033	+	0.583611i	$0.198361\pi$
$23$			5.59780i			1.16722i	−0.812033	+	0.583611i	$0.801639\pi$
$24$	−0.219817	+	1.71805i	−0.0448700	+	0.350695i
$25$	1.00000			0.200000
$26$	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	−0.742407	+	0.669949i	$0.766316\pi$
$29$	−9.12141	+	5.26625i	−1.69380	+	0.977918i	−0.951397	+	0.307968i	$0.900351\pi$
$30$	−1.37796	−	1.04939i	−0.251580	−	0.191592i
$31$	6.97950	−	4.02962i	1.25356	−	0.723741i	0.281742	−	0.959490i	$-0.409088\pi$
$31$	6.97950	−	4.02962i	1.25356	−	0.723741i	0.971814	+	0.235749i	$0.0757544\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.168778	+	1.31913i	−0.0293805	+	0.229632i
$34$	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	$0.593891\pi$
$38$	−4.84057			−0.785245
$39$	6.01487	+	4.58064i	0.963151	+	0.733489i
$40$			1.00000i			0.158114i
$41$	−2.65381	+	4.59654i	−0.414456	+	0.717859i	−0.995371	−	0.0961053i	$-0.969361\pi$
$41$	−2.65381	+	4.59654i	−0.414456	+	0.717859i	0.580915	+	0.813964i	$0.302695\pi$
$42$	−1.23966	−	4.41172i	−0.191284	−	0.680742i
$43$	5.94724	+	10.3009i	0.906945	+	1.57087i	0.818285	+	0.574813i	$0.194925\pi$
$43$	5.94724	+	10.3009i	0.906945	+	1.57087i	0.0886598	+	0.996062i	$0.471742\pi$
$44$	0.664943	−	0.383905i	0.100244	−	0.0578759i
$45$	−2.90336	−	0.755312i	−0.432807	−	0.112595i
$46$	2.79890	−	4.84784i	0.412675	−	0.714775i
$47$	3.23073	−	5.59578i	0.471250	−	0.816229i	−0.528209	−	0.849114i	$-0.677136\pi$
$47$	3.23073	−	5.59578i	0.471250	−	0.816229i	0.999459	+	0.0328853i	$0.0104696\pi$
$48$	1.04939	−	1.37796i	0.151466	−	0.198892i
$49$	1.92622	+	6.72976i	0.275174	+	0.961394i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	2.41689	−	3.17363i	0.338432	−	0.444397i
$52$		−	4.36505i		−	0.605323i
$53$	6.48067	+	3.74161i	0.890188	+	0.513950i	0.874004	−	0.485919i	$-0.161515\pi$
$53$	6.48067	+	3.74161i	0.890188	+	0.513950i	0.0161839	+	0.999869i	$0.494848\pi$
$54$	3.20810	+	4.08755i	0.436568	+	0.556245i
$55$			0.767810i			0.103532i
$56$	−1.59276	+	2.11261i	−0.212842	+	0.282309i
$57$	−7.73417	+	3.23668i	−1.02442	+	0.428708i
$58$	10.5325			1.38298
$59$	5.71736	+	9.90276i	0.744337	+	1.28923i	0.950504	+	0.310712i	$0.100568\pi$
$59$	5.71736	+	9.90276i	0.744337	+	1.28923i	−0.206167	+	0.978517i	$0.566099\pi$
$60$	0.668655	+	1.59778i	0.0863230	+	0.206272i
$61$	−8.22722	−	4.74999i	−1.05339	−	0.608174i	−0.129792	−	0.991541i	$-0.541431\pi$
$61$	−8.22722	−	4.74999i	−1.05339	−	0.608174i	−0.923596	+	0.383368i	$0.874764\pi$
$62$	−8.05924			−1.02352
$63$	−4.93063	−	6.22004i	−0.621201	−	0.783651i
$64$	−1.00000			−0.125000
$65$	3.78024	+	2.18252i	0.468881	+	0.270709i
$66$	0.805733	−	1.05801i	0.0991788	−	0.130232i
$67$	−6.85237	−	11.8687i	−0.837151	−	1.44999i	−0.892267	−	0.451507i	$-0.850886\pi$
$67$	−6.85237	−	11.8687i	−0.837151	−	1.44999i	0.0551168	−	0.998480i	$-0.482447\pi$
$68$	−2.30313			−0.279296
$69$	1.23049	−	9.61728i	0.148134	−	1.15778i
$70$	−1.03319	−	2.43568i	−0.123490	−	0.291119i
$71$			7.50583i			0.890779i	0.895337	+	0.445389i	$0.146935\pi$
$71$			7.50583i			0.890779i	−0.895337	+	0.445389i	$0.853065\pi$
$72$	0.755312	−	2.90336i	0.0890144	−	0.342164i
$73$	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	$0.427018\pi$
$74$		−	8.31233i		−	0.966289i
$75$	−1.71805	−	0.219817i	−0.198383	−	0.0253823i
$76$	4.19206	+	2.42029i	0.480862	+	0.277626i
$77$	−1.22294	+	1.62208i	−0.139367	+	0.184853i
$78$	−2.91871	−	6.97439i	−0.330479	−	0.789694i
$79$	0.555218	−	0.961666i	0.0624669	−	0.108196i	−0.833101	−	0.553121i	$-0.813437\pi$
$79$	0.555218	−	0.961666i	0.0624669	−	0.108196i	0.895568	+	0.444926i	$0.146770\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	7.85901	+	4.38589i	0.873223	+	0.487321i
$82$	4.59654	−	2.65381i	0.507603	−	0.293065i
$83$	−0.254578	−	0.440942i	−0.0279435	−	0.0483996i	0.851715	−	0.524005i	$-0.175563\pi$
$83$	−0.254578	−	0.440942i	−0.0279435	−	0.0483996i	−0.879659	+	0.475605i	$0.842229\pi$
$84$	−1.13228	+	4.44049i	−0.123541	+	0.484497i
$85$	1.15157	−	1.99457i	0.124905	−	0.216342i
$86$		−	11.8945i		−	1.28261i
$87$	16.8286	−	7.04261i	1.80422	−	0.755047i
$88$	−0.767810			−0.0818489
$89$	2.80167	+	4.85263i	0.296976	+	0.514378i	0.975443	−	0.220254i	$-0.0706885\pi$
$89$	2.80167	+	4.85263i	0.296976	+	0.514378i	−0.678467	+	0.734631i	$0.737355\pi$
$90$	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
$93$	−12.8769	+	5.38885i	−1.33527	+	0.558798i
$94$	−5.59578	+	3.23073i	−0.577161	+	0.333224i
$95$	−4.19206	+	2.42029i	−0.430096	+	0.248316i
$96$	−1.59778	+	0.668655i	−0.163073	+	0.0682443i
$97$	−7.61423	+	4.39608i	−0.773107	+	0.446354i	−0.833982	−	0.551792i	$-0.813944\pi$
$97$	−7.61423	+	4.39608i	−0.773107	+	0.446354i	0.0608745	+	0.998145i	$0.480611\pi$
$98$	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
$101$	−11.8515			−1.17927			−0.589633	−	0.807671i	$-0.700728\pi$
$101$	−11.8515			−1.17927			−0.589633	+	0.807671i	$0.700728\pi$
$102$	−3.67990	+	1.54000i	−0.364365	+	0.152483i
$103$			0.878126i			0.0865244i	0.999064	+	0.0432622i	$0.0137751\pi$
$103$			0.878126i			0.0865244i	−0.999064	+	0.0432622i	$0.986225\pi$
$104$	−2.18252	+	3.78024i	−0.214014	+	0.370683i
$105$	−3.27944	−	3.20083i	−0.320040	−	0.312369i
$106$	−3.74161	−	6.48067i	−0.363418	−	0.629458i
$107$	5.55184	−	3.20536i	0.536717	−	0.309874i	−0.207031	−	0.978334i	$-0.566380\pi$
$107$	5.55184	−	3.20536i	0.536717	−	0.309874i	0.743747	+	0.668461i	$0.233047\pi$
$108$	−0.734525	−	5.14397i	−0.0706797	−	0.494979i
$109$	−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	$0.303927\pi$
$110$	0.383905	−	0.664943i	0.0366039	−	0.0633999i
$111$	−5.55808	−	13.2813i	−0.527550	−	1.26060i
$112$	2.43568	−	1.03319i	0.230150	−	0.0976273i
$113$	−0.697613	−	0.402767i	−0.0656259	−	0.0378891i	0.466828	−	0.884348i	$-0.345397\pi$
$113$	−0.697613	−	0.402767i	−0.0656259	−	0.0378891i	−0.532454	+	0.846459i	$0.678730\pi$
$114$	8.31633	+	1.06404i	0.778895	+	0.0996567i
$115$		−	5.59780i		−	0.521998i
$116$	−9.12141	−	5.26625i	−0.846902	−	0.488959i
$117$	−9.32692	−	9.19192i	−0.862274	−	0.849793i
$118$		−	11.4347i		−	1.05265i
$119$	5.60969	−	2.37958i	0.514239	−	0.218135i
$120$	0.219817	−	1.71805i	0.0200665	−	0.156835i
$121$	10.4105			0.946406
$122$	4.74999	+	8.22722i	0.430044	+	0.744857i
$123$	5.56977	−	7.31371i	0.502209	−	0.659455i
$124$	6.97950	+	4.02962i	0.626778	+	0.361870i
$125$	−1.00000			−0.0894427
$126$	1.16003	+	7.85203i	0.103344	+	0.699514i
$127$	−12.6479			−1.12232			−0.561162	−	0.827706i	$-0.689645\pi$
$127$	−12.6479			−1.12232			−0.561162	+	0.827706i	$0.689645\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−7.95330	−	19.0047i	−0.700249	−	1.67327i
$130$	−2.18252	−	3.78024i	−0.191420	−	0.331549i
$131$	−9.92603			−0.867241			−0.433620	−	0.901096i	$-0.642764\pi$
$131$	−9.92603			−0.867241			−0.433620	+	0.901096i	$0.642764\pi$
$132$	−1.22679	+	0.513400i	−0.106779	+	0.0446858i
$133$	−12.7111	−	1.56384i	−1.10219	−	0.135602i
$134$			13.7047i			1.18391i
$135$	4.82207	+	1.93587i	0.415018	+	0.166613i
$136$	1.99457	+	1.15157i	0.171033	+	0.0987461i
$137$		−	14.3935i		−	1.22972i	−0.788637	−	0.614859i	$-0.789213\pi$
$137$		−	14.3935i		−	1.22972i	0.788637	−	0.614859i	$-0.210787\pi$
$138$	−5.87428	+	7.71356i	−0.500052	+	0.656622i
$139$	−8.82052	−	5.09253i	−0.748147	−	0.431943i	0.0768772	−	0.997041i	$-0.475505\pi$
$139$	−8.82052	−	5.09253i	−0.748147	−	0.431943i	−0.825024	+	0.565098i	$0.808838\pi$
$140$	−0.323069	+	2.62595i	−0.0273043	+	0.221933i
$141$	−6.78059	+	8.90364i	−0.571028	+	0.749822i
$142$	3.75292	−	6.50024i	0.314938	−	0.545488i
$143$	−1.67576	+	2.90251i	−0.140135	+	0.242720i
$144$	−2.10580	+	2.13673i	−0.175483	+	0.178061i
$145$	9.12141	−	5.26625i	0.757492	−	0.437338i
$146$	−5.84190	−	10.1185i	−0.483479	−	0.837410i
$147$	−1.83001	−	11.9855i	−0.150937	−	0.988543i
$148$	−4.15617	+	7.19869i	−0.341635	+	0.591729i
$149$		−	8.95303i		−	0.733461i	−0.930327	−	0.366730i	$-0.880477\pi$
$149$		−	8.95303i		−	0.733461i	0.930327	−	0.366730i	$-0.119523\pi$
$150$	1.37796	+	1.04939i	0.112510	+	0.0856823i
$151$	−5.00718			−0.407479			−0.203739	−	0.979025i	$-0.565310\pi$
$151$	−5.00718			−0.407479			−0.203739	+	0.979025i	$0.565310\pi$
$152$	−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
$156$	−0.959514	+	7.49935i	−0.0768226	+	0.600429i
$157$	−2.81741	+	1.62663i	−0.224854	+	0.129819i	−0.608196	−	0.793787i	$-0.708106\pi$
$157$	−2.81741	+	1.62663i	−0.224854	+	0.129819i	0.383342	+	0.923607i	$0.374773\pi$
$158$	−0.961666	+	0.555218i	−0.0765060	+	0.0441708i
$159$	−10.3116	−	7.85283i	−0.817764	−	0.622770i
$160$	−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	$0.772902\pi$
$164$	−5.30763			−0.414456
$165$	0.168778	−	1.31913i	0.0131394	−	0.102694i
$166$			0.509156i			0.0395181i
$167$	−4.97259	+	8.61278i	−0.384791	+	0.666477i	−0.991740	−	0.128263i	$-0.959060\pi$
$167$	−4.97259	+	8.61278i	−0.384791	+	0.666477i	0.606949	+	0.794740i	$0.292393\pi$
$168$	3.20083	−	3.27944i	0.246949	−	0.253014i
$169$	3.02683	+	5.24262i	0.232833	+	0.403278i
$170$	−1.99457	+	1.15157i	−0.152977	+	0.0883212i
$171$	13.9991	−	3.86065i	1.07054	−	0.295231i
$172$	−5.94724	+	10.3009i	−0.453472	+	0.785437i
$173$	−8.31317	+	14.3988i	−0.632039	+	1.09472i	0.355096	+	0.934830i	$0.384448\pi$
$173$	−8.31317	+	14.3988i	−0.632039	+	1.09472i	−0.987134	+	0.159893i	$0.948885\pi$
$174$	−18.0953	−	2.31523i	−1.37180	−	0.175517i
$175$	−2.11261	−	1.59276i	−0.159698	−	0.120401i
$176$	0.664943	+	0.383905i	0.0501220	+	0.0289379i
$177$	−7.64589	−	18.2702i	−0.574700	−	1.37327i
$178$		−	5.60333i		−	0.419988i
$179$	4.07453	+	2.35243i	0.304545	+	0.175829i	0.644483	−	0.764619i	$-0.277073\pi$
$179$	4.07453	+	2.35243i	0.304545	+	0.175829i	−0.339938	+	0.940448i	$0.610406\pi$
$180$	−0.797561	−	2.89204i	−0.0594467	−	0.215560i
$181$		−	8.33408i		−	0.619467i	−0.950823	−	0.309734i	$-0.899760\pi$
$181$		−	8.33408i		−	0.619467i	0.950823	−	0.309734i	$-0.100240\pi$
$182$	1.41021	−	11.4624i	0.104532	−	0.849650i
$183$	13.0906	+	9.96918i	0.967685	+	0.736943i
$184$	5.59780			0.412675
$185$	−4.15617	−	7.19869i	−0.305567	−	0.529258i
$186$	13.8461	+	1.77156i	1.01525	+	0.129897i
$187$	1.53145	+	0.884185i	0.111991	+	0.0646580i
$188$	6.46146			0.471250
$189$	7.10377	+	11.7702i	0.516723	+	0.856152i
$190$	4.84057			0.351172
$191$	3.28474	+	1.89645i	0.237676	+	0.137222i	0.614108	−	0.789222i	$-0.289516\pi$
$191$	3.28474	+	1.89645i	0.237676	+	0.137222i	−0.376432	+	0.926444i	$0.622849\pi$
$192$	1.71805	+	0.219817i	0.123989	+	0.0158640i
$193$	10.7480	+	18.6160i	0.773656	+	1.34001i	0.935547	+	0.353202i	$0.114907\pi$
$193$	10.7480	+	18.6160i	0.773656	+	1.34001i	−0.161892	+	0.986809i	$0.551759\pi$
$194$	8.79215			0.631240
$195$	−6.01487	−	4.58064i	−0.430734	−	0.328026i
$196$	−4.86503	+	5.03304i	−0.347502	+	0.359503i
$197$		−	13.3908i		−	0.954054i	−0.878889	−	0.477027i	$-0.841714\pi$
$197$		−	13.3908i		−	0.954054i	0.878889	−	0.477027i	$-0.158286\pi$
$198$	−1.61686	+	1.64060i	−0.114905	+	0.116592i
$199$	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	$0.660341\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	9.16375	+	21.8972i	0.646361	+	1.54451i
$202$	10.2637	+	5.92574i	0.722150	+	0.416933i
$203$	27.6578	+	3.40272i	1.94120	+	0.238824i
$204$	3.95689	+	0.506269i	0.277038	+	0.0354459i
$205$	2.65381	−	4.59654i	0.185350	−	0.321036i
$206$	0.439063	−	0.760480i	0.0305910	−	0.0529851i
$207$	−4.22809	+	16.2524i	−0.293872	+	1.12962i
$208$	3.78024	−	2.18252i	0.262113	−	0.151331i
$209$	−1.85832	−	3.21871i	−0.128543	−	0.222643i
$210$	1.23966	+	4.41172i	0.0855450	+	0.304437i
$211$	1.76537	−	3.05771i	0.121533	−	0.210501i	−0.798839	−	0.601544i	$-0.794552\pi$
$211$	1.76537	−	3.05771i	0.121533	−	0.210501i	0.920372	+	0.391043i	$0.127886\pi$
$212$			7.48323i			0.513950i
$213$	1.64991	−	12.8954i	0.113050	−	0.883576i
$214$	−6.41071			−0.438227
$215$	−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
$219$	−16.0998	−	12.2609i	−1.08793	−	0.828512i
$220$	−0.664943	+	0.383905i	−0.0448305	+	0.0258829i
$221$	8.70641	−	5.02665i	0.585656	−	0.338129i
$222$	−1.82719	+	14.2810i	−0.122633	+	0.958475i
$223$	22.1791	−	12.8051i	1.48522	−	0.857495i	0.485366	−	0.874311i	$-0.338686\pi$
$223$	22.1791	−	12.8051i	1.48522	−	0.857495i	0.999859	+	0.0168159i	$0.00535291\pi$
$224$	−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
$227$	11.1386			0.739295			0.369647	−	0.929172i	$-0.379479\pi$
$227$	11.1386			0.739295			0.369647	+	0.929172i	$0.379479\pi$
$228$	−6.67013	−	5.07965i	−0.441740	−	0.336408i
$229$			3.80842i			0.251668i	0.992051	+	0.125834i	$0.0401606\pi$
$229$			3.80842i			0.251668i	−0.992051	+	0.125834i	$0.959839\pi$
$230$	−2.79890	+	4.84784i	−0.184554	+	0.319657i
$231$	2.45763	−	2.51799i	0.161700	−	0.165671i
$232$	5.26625	+	9.12141i	0.345746	+	0.598850i
$233$	2.04230	−	1.17912i	0.133795	−	0.0772468i	−0.431608	−	0.902061i	$-0.642054\pi$
$233$	2.04230	−	1.17912i	0.133795	−	0.0772468i	0.565404	+	0.824814i	$0.308720\pi$
$234$	3.48139	+	12.6239i	0.227586	+	0.825250i
$235$	−3.23073	+	5.59578i	−0.210749	+	0.365029i
$236$	−5.71736	+	9.90276i	−0.372168	+	0.644615i
$237$	−1.16528	+	1.53014i	−0.0756931	+	0.0993932i
$238$	−6.04792	−	0.744070i	−0.392029	−	0.0482309i
$239$	10.1968	+	5.88712i	0.659576	+	0.380806i	0.792115	−	0.610372i	$-0.208980\pi$
$239$	10.1968	+	5.88712i	0.659576	+	0.380806i	−0.132540	+	0.991178i	$0.542313\pi$
$240$	−1.04939	+	1.37796i	−0.0677378	+	0.0889471i
$241$			18.8137i			1.21189i	0.795505	+	0.605947i	$0.207206\pi$
$241$			18.8137i			1.21189i	−0.795505	+	0.605947i	$0.792794\pi$
$242$	−9.01573	−	5.20523i	−0.579553	−	0.334605i
$243$	−12.5380	−	9.26270i	−0.804315	−	0.594203i
$244$		−	9.49997i		−	0.608174i
$245$	−1.92622	−	6.72976i	−0.123062	−	0.429949i
$246$	−8.48042	+	3.54897i	−0.540692	+	0.226274i
$247$	−21.1293			−1.34443
$248$	−4.02962	−	6.97950i	−0.255881	−	0.443199i
$249$	0.340450	+	0.813518i	0.0215751	+	0.0515546i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−3.35759			−0.211929			−0.105965	−	0.994370i	$-0.533793\pi$
$251$	−3.35759			−0.211929			−0.105965	+	0.994370i	$0.533793\pi$
$252$	2.92140	−	7.38007i	0.184031	−	0.464901i
$253$	4.29805			0.270216
$254$	10.9534	+	6.32397i	0.687280	+	0.396801i
$255$	−2.41689	+	3.17363i	−0.151351	+	0.198741i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.3362			0.707132			0.353566	−	0.935410i	$-0.384969\pi$
$257$	11.3362			0.707132			0.353566	+	0.935410i	$0.384969\pi$
$258$	−2.61461	+	20.4352i	−0.162779	+	1.27224i
$259$	2.68545	−	21.8278i	0.166866	−	1.35631i
$260$			4.36505i			0.270709i
$261$	−30.4604	+	8.40030i	−1.88545	+	0.519966i
$262$	8.59619	+	4.96301i	0.531074	+	0.306616i
$263$			25.7820i			1.58978i	0.606750	+	0.794892i	$0.292473\pi$
$263$			25.7820i			1.58978i	−0.606750	+	0.794892i	$0.707527\pi$
$264$	1.31913	+	0.168778i	0.0811870	+	0.0103876i
$265$	−6.48067	−	3.74161i	−0.398104	−	0.229846i
$266$	10.2262	+	7.70988i	0.627011	+	0.472723i
$267$	−3.74670	−	8.95289i	−0.229294	−	0.547908i
$268$	6.85237	−	11.8687i	0.418575	−	0.724994i
$269$	2.94884	−	5.10754i	0.179794	−	0.311412i	−0.762016	−	0.647558i	$-0.775790\pi$
$269$	2.94884	−	5.10754i	0.179794	−	0.311412i	0.941810	+	0.336146i	$0.109124\pi$
$270$	−3.20810	−	4.08755i	−0.195239	−	0.248760i
$271$	−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
$273$	−5.41120	−	19.2574i	−0.327501	−	1.16551i
$274$	−7.19674	+	12.4651i	−0.434771	+	0.753045i
$275$		−	0.767810i		−	0.0463007i
$276$	8.94405	−	3.74300i	0.538369	−	0.225302i
$277$	10.3900			0.624277			0.312139	−	0.950037i	$-0.398955\pi$
$277$	10.3900			0.624277			0.312139	+	0.950037i	$0.398955\pi$
$278$	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	−0.861984	−	0.506935i	$-0.830778\pi$
$281$	−14.3149	+	8.26473i	−0.853957	+	0.493032i	0.00802696	+	0.999968i	$0.497445\pi$
$282$	10.3240	−	4.32049i	0.614784	−	0.257281i
$283$	−9.00009	+	5.19621i	−0.535000	+	0.308882i	−0.743050	−	0.669236i	$-0.766622\pi$
$283$	−9.00009	+	5.19621i	−0.535000	+	0.308882i	0.208050	+	0.978118i	$0.433288\pi$
$284$	−6.50024	+	3.75292i	−0.385718	+	0.222695i
$285$	7.73417	−	3.23668i	0.458133	−	0.191724i
$286$	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
$290$	−10.5325			−0.618490
$291$	14.0479	−	5.87892i	0.823504	−	0.344628i
$292$			11.6838i			0.683742i
$293$	−12.7786	+	22.1332i	−0.746533	+	1.29303i	0.202942	+	0.979191i	$0.434950\pi$
$293$	−12.7786	+	22.1332i	−0.746533	+	1.29303i	−0.949475	+	0.313843i	$0.898384\pi$
$294$	−4.40789	+	11.2947i	−0.257073	+	0.658721i
$295$	−5.71736	−	9.90276i	−0.332878	−	0.576561i
$296$	7.19869	−	4.15617i	0.418415	−	0.241572i
$297$	−1.48638	+	3.70244i	−0.0862486	+	0.214837i
$298$	−4.47651	+	7.75355i	−0.259318	+	0.449151i
$299$	12.2173	−	21.1611i	0.706547	−	1.22378i
$300$	−0.668655	−	1.59778i	−0.0386048	−	0.0922479i
$301$	3.84273	−	31.2343i	0.221491	−	1.80032i
$302$	4.33635	+	2.50359i	0.249529	+	0.144065i
$303$	20.3614	+	2.60516i	1.16973	+	0.149662i
$304$			4.84057i			0.277626i
$305$	8.22722	+	4.74999i	0.471089	+	0.271983i
$306$	6.66076	−	1.83689i	0.380770	−	0.105008i
$307$		−	9.33336i		−	0.532683i	−0.963879	−	0.266342i	$-0.914185\pi$
$307$		−	9.33336i		−	0.532683i	0.963879	−	0.266342i	$-0.0858149\pi$
$308$	−2.01623	−	0.248055i	−0.114886	−	0.0141343i
$309$	0.193027	−	1.50866i	0.0109809	−	0.0858247i
$310$	8.05924			0.457734
$311$	−2.68289	−	4.64689i	−0.152132	−	0.263501i	0.779879	−	0.625931i	$-0.215281\pi$
$311$	−2.68289	−	4.64689i	−0.152132	−	0.263501i	−0.932011	+	0.362429i	$0.881947\pi$
$312$	4.58064	−	6.01487i	0.259328	−	0.340525i
$313$	22.0455	+	12.7280i	1.24608	+	0.719427i	0.970326	−	0.241800i	$-0.0777378\pi$
$313$	22.0455	+	12.7280i	1.24608	+	0.719427i	0.275758	+	0.961227i	$0.411071\pi$
$314$	3.25327			0.183592
$315$	4.93063	+	6.22004i	0.277809	+	0.350460i
$316$	1.11044			0.0624669
$317$	6.48372	+	3.74338i	0.364162	+	0.210249i	0.670905	−	0.741543i	$-0.265906\pi$
$317$	6.48372	+	3.74338i	0.364162	+	0.210249i	−0.306743	+	0.951792i	$0.599239\pi$
$318$	5.00370	+	11.9566i	0.280594	+	0.670490i
$319$	4.04348	+	7.00351i	0.226391	+	0.392121i
$320$	1.00000			0.0559017
$321$	−10.2429	+	4.28656i	−0.571703	+	0.239252i
$322$	−13.6344	+	5.78360i	−0.759817	+	0.322307i
$323$			11.1485i			0.620319i
$324$	0.131212	+	8.99904i	0.00728955	+	0.499947i
$325$	−3.78024	−	2.18252i	−0.209690	−	0.121065i
$326$		−	4.81863i		−	0.266879i
$327$	9.15865	−	12.0263i	0.506474	−	0.665056i
$328$	4.59654	+	2.65381i	0.253801	+	0.146532i
$329$	−15.7380	+	6.67592i	−0.867665	+	0.368055i
$330$	−0.805733	+	1.05801i	−0.0443541	+	0.0582417i
$331$	−3.71433	+	6.43342i	−0.204158	+	0.353613i	−0.949864	−	0.312663i	$-0.898779\pi$
$331$	−3.71433	+	6.43342i	−0.204158	+	0.353613i	0.745706	+	0.666275i	$0.232112\pi$
$332$	0.254578	−	0.440942i	0.0139718	−	0.0241998i
$333$	6.62959	+	24.0396i	0.363299	+	1.31736i
$334$	8.61278	−	4.97259i	0.471270	−	0.272088i
$335$	6.85237	+	11.8687i	0.374385	+	0.648454i
$336$	−4.41172	+	1.23966i	−0.240679	+	0.0676293i
$337$	−12.9171	+	22.3731i	−0.703641	+	1.21874i	0.263539	+	0.964649i	$0.415110\pi$
$337$	−12.9171	+	22.3731i	−0.703641	+	1.21874i	−0.967180	+	0.254093i	$0.918223\pi$
$338$		−	6.05365i		−	0.329275i
$339$	1.11000	+	0.845320i	0.0602867	+	0.0459115i
$340$	2.30313			0.124905
$341$	−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
$345$	−1.23049	+	9.61728i	−0.0662476	+	0.517777i
$346$	14.3988	−	8.31317i	0.774086	−	0.446919i
$347$	15.9560	−	9.21220i	0.856562	−	0.494537i	−0.00629718	−	0.999980i	$-0.502004\pi$
$347$	15.9560	−	9.21220i	0.856562	−	0.494537i	0.862860	+	0.505444i	$0.168671\pi$
$348$	14.5134	+	11.0527i	0.777999	+	0.592487i
$349$	−1.37452	+	0.793577i	−0.0735761	+	0.0424792i	−0.536337	−	0.844004i	$-0.680192\pi$
$349$	−1.37452	+	0.793577i	−0.0735761	+	0.0424792i	0.462761	+	0.886483i	$0.346859\pi$
$350$	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
$353$	−9.20537			−0.489952			−0.244976	−	0.969529i	$-0.578780\pi$
$353$	−9.20537			−0.489952			−0.244976	+	0.969529i	$0.578780\pi$
$354$	−2.51355	+	19.6454i	−0.133594	+	1.04414i
$355$		−	7.50583i		−	0.398368i
$356$	−2.80167	+	4.85263i	−0.148488	+	0.257189i
$357$	−10.1608	+	2.85511i	−0.537765	+	0.151109i
$358$	−2.35243	−	4.07453i	−0.124330	−	0.215346i
$359$	22.3751	−	12.9183i	1.18091	−	0.681801i	0.224689	−	0.974431i	$-0.427864\pi$
$359$	22.3751	−	12.9183i	1.18091	−	0.681801i	0.956226	+	0.292629i	$0.0945302\pi$
$360$	−0.755312	+	2.90336i	−0.0398085	+	0.153021i
$361$	2.21558	−	3.83750i	0.116610	−	0.201974i
$362$	−4.16704	+	7.21752i	−0.219015	+	0.379345i
$363$	−17.8857	−	2.28840i	−0.938754	−	0.120110i
$364$	−6.95248	+	9.22163i	−0.364409	+	0.483345i
$365$	−10.1185	−	5.84190i	−0.529625	−	0.305779i
$366$	−6.35221	−	15.1789i	−0.332035	−	0.793412i
$367$			22.2564i			1.16178i	0.813984	+	0.580888i	$0.197294\pi$
$367$			22.2564i			1.16178i	−0.813984	+	0.580888i	$0.802706\pi$
$368$	−4.84784	−	2.79890i	−0.252711	−	0.145903i
$369$	−11.1768	+	11.3410i	−0.581841	+	0.590386i
$370$			8.31233i			0.432137i
$371$	−7.73160	−	18.2267i	−0.401405	−	0.946284i
$372$	−11.1053	−	8.45728i	−0.575784	−	0.438490i
$373$	−32.7801			−1.69729			−0.848644	−	0.528965i	$-0.822580\pi$
$373$	−32.7801			−1.69729			−0.848644	+	0.528965i	$0.822580\pi$
$374$	−0.884185	−	1.53145i	−0.0457201	−	0.0791896i
$375$	1.71805	+	0.219817i	0.0887195	+	0.0113513i
$376$	−5.59578	−	3.23073i	−0.288581	−	0.166612i
$377$	45.9749			2.36783
$378$	−0.266971	−	13.7451i	−0.0137315	−	0.706973i
$379$	−26.7133			−1.37217			−0.686085	−	0.727522i	$-0.740672\pi$
$379$	−26.7133			−1.37217			−0.686085	+	0.727522i	$0.740672\pi$
$380$	−4.19206	−	2.42029i	−0.215048	−	0.124158i
$381$	21.7297	+	2.78024i	1.11325	+	0.142436i
$382$	−1.89645	−	3.28474i	−0.0970307	−	0.168062i
$383$	−1.81734			−0.0928615			−0.0464307	−	0.998922i	$-0.514785\pi$
$383$	−1.81734			−0.0928615			−0.0464307	+	0.998922i	$0.514785\pi$
$384$	−1.37796	−	1.04939i	−0.0703188	−	0.0535515i
$385$	1.22294	−	1.62208i	0.0623267	−	0.0826689i
$386$		−	21.4959i		−	1.09411i
$387$	9.48656	+	34.3993i	0.482229	+	1.74861i
$388$	−7.61423	−	4.39608i	−0.386554	−	0.223177i
$389$		−	29.9694i		−	1.51951i	−0.650209	−	0.759755i	$-0.725319\pi$
$389$		−	29.9694i		−	1.51951i	0.650209	−	0.759755i	$-0.274681\pi$
$390$	2.91871	+	6.97439i	0.147795	+	0.353162i
$391$	−11.1652	−	6.44624i	−0.564650	−	0.326001i
$392$	6.72976	−	1.92622i	0.339904	−	0.0972888i
$393$	17.0534	+	2.18191i	0.860228	+	0.110063i
$394$	−6.69540	+	11.5968i	−0.337309	+	0.584237i
$395$	−0.555218	+	0.961666i	−0.0279360	+	0.0483867i
$396$	2.22054	−	0.612375i	0.111586	−	0.0307730i
$397$	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
$399$	21.4945	+	5.48087i	1.07607	+	0.274387i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	5.80877i		−	0.290076i	−0.989426	−	0.145038i	$-0.953670\pi$
$401$		−	5.80877i		−	0.290076i	0.989426	−	0.145038i	$-0.0463305\pi$
$402$	3.01254	−	23.5454i	0.150252	−	1.17434i
$403$	−35.1790			−1.75239
$404$	−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
$408$	−3.17363	−	2.41689i	−0.157118	−	0.119654i
$409$	−18.9501	+	10.9409i	−0.937023	+	0.540990i	−0.889026	−	0.457857i	$-0.848617\pi$
$409$	−18.9501	+	10.9409i	−0.937023	+	0.540990i	−0.0479969	+	0.998847i	$0.515284\pi$
$410$	−4.59654	+	2.65381i	−0.227007	+	0.131062i
$411$	−3.16394	+	24.7286i	−0.156065	+	1.21977i
$412$	−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
$416$	−4.36505			−0.214014
$417$	14.0346	+	10.6881i	0.687279	+	0.523399i
$418$			3.71664i			0.181787i
$419$	−7.97218	+	13.8082i	−0.389467	+	0.674576i	−0.992378	−	0.123232i	$-0.960674\pi$
$419$	−7.97218	+	13.8082i	−0.389467	+	0.674576i	0.602911	+	0.797808i	$0.294007\pi$
$420$	1.13228	−	4.44049i	0.0552494	−	0.216674i
$421$	8.26978	+	14.3237i	0.403044	+	0.698093i	0.994092	−	0.108544i	$-0.0346187\pi$
$421$	8.26978	+	14.3237i	0.403044	+	0.698093i	−0.591047	+	0.806637i	$0.701285\pi$
$422$	−3.05771	+	1.76537i	−0.148847	+	0.0859368i
$423$	13.6065	−	13.8064i	0.661572	−	0.671289i
$424$	3.74161	−	6.48067i	0.181709	−	0.314729i
$425$	−1.15157	+	1.99457i	−0.0558592	+	0.0967510i
$426$	−7.87655	+	10.3428i	−0.381620	+	0.501108i
$427$	9.81528	+	23.1389i	0.474995	+	1.11977i
$428$	5.55184	+	3.20536i	0.268358	+	0.154937i
$429$	3.51706	−	4.61828i	0.169805	−	0.222973i
$430$			11.8945i			0.573602i
$431$	−10.5417	−	6.08623i	−0.507774	−	0.293163i	0.224144	−	0.974556i	$-0.428041\pi$
$431$	−10.5417	−	6.08623i	−0.507774	−	0.293163i	−0.731918	+	0.681393i	$0.761375\pi$
$432$	4.08755	−	3.20810i	0.196662	−	0.154350i
$433$		−	8.54538i		−	0.410665i	−0.978692	−	0.205332i	$-0.934172\pi$
$433$		−	8.54538i		−	0.410665i	0.978692	−	0.205332i	$-0.0658276\pi$
$434$	17.0260	+	12.8364i	0.817274	+	0.616169i
$435$	−16.8286	+	7.04261i	−0.806870	+	0.337667i
$436$	−8.72759			−0.417976
$437$	13.5483	+	23.4663i	0.648102	+	1.12255i
$438$	7.81243	+	18.6681i	0.373292	+	0.891998i
$439$	5.69997	+	3.29088i	0.272045	+	0.157065i	0.629816	−	0.776744i	$-0.283130\pi$
$439$	5.69997	+	3.29088i	0.272045	+	0.157065i	−0.357772	+	0.933809i	$0.616463\pi$
$440$	0.767810			0.0366039
$441$	0.509438	+	20.9938i	0.0242589	+	0.999706i
$442$	−10.0533			−0.478186
$443$	−23.4466	−	13.5369i	−1.11398	−	0.643157i	−0.174123	−	0.984724i	$-0.555709\pi$
$443$	−23.4466	−	13.5369i	−1.11398	−	0.643157i	−0.939857	+	0.341567i	$0.889042\pi$
$444$	8.72288	−	11.4541i	0.413969	−	0.543587i
$445$	−2.80167	−	4.85263i	−0.132812	−	0.230037i
$446$	−25.6103			−1.21268
$447$	−1.96803	+	15.3817i	−0.0930847	+	0.727530i
$448$	2.11261	+	1.59276i	0.0998113	+	0.0752509i
$449$			17.9654i			0.847841i	0.905700	+	0.423920i	$0.139346\pi$
$449$			17.9654i			0.847841i	−0.905700	+	0.423920i	$0.860654\pi$
$450$	−2.13673	−	2.10580i	−0.100726	−	0.0992684i
$451$	3.52927	+	2.03763i	0.166187	+	0.0959480i
$452$		−	0.805534i		−	0.0378891i
$453$	8.60257	+	1.10067i	0.404184	+	0.0517138i
$454$	−9.64631	−	5.56930i	−0.452724	−	0.261380i
$455$	−4.50993	−	10.6318i	−0.211429	−	0.498429i
$456$	3.23668	+	7.73417i	0.151571	+	0.362186i
$457$	2.57466	−	4.45944i	0.120438	−	0.208604i	−0.799503	−	0.600662i	$-0.794904\pi$
$457$	2.57466	−	4.45944i	0.120438	−	0.208604i	0.919940	+	0.392058i	$0.128237\pi$
$458$	1.90421	−	3.29819i	0.0889780	−	0.154114i
$459$	9.41418	−	7.38870i	0.439416	−	0.344875i
$460$	4.84784	−	2.79890i	0.226032	−	0.130499i
$461$	5.46051	+	9.45788i	0.254321	+	0.440498i	0.964711	−	0.263311i	$-0.0848146\pi$
$461$	5.46051	+	9.45788i	0.254321	+	0.440498i	−0.710390	+	0.703809i	$0.751481\pi$
$462$	−3.38736	+	0.951827i	−0.157594	+	0.0442830i
$463$	14.8704	−	25.7563i	0.691088	−	1.19700i	−0.280394	−	0.959885i	$-0.590465\pi$
$463$	14.8704	−	25.7563i	0.691088	−	1.19700i	0.971482	−	0.237114i	$-0.0762015\pi$
$464$		−	10.5325i		−	0.488959i
$465$	12.8769	−	5.38885i	0.597151	−	0.249902i
$466$	−2.35824			−0.109243
$467$	−4.55724	−	7.89337i	−0.210884	−	0.365262i	0.741107	−	0.671386i	$-0.234301\pi$
$467$	−4.55724	−	7.89337i	−0.210884	−	0.365262i	−0.951991	+	0.306125i	$0.900968\pi$
$468$	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
$471$	5.19800	−	2.17531i	0.239511	−	0.100233i
$472$	9.90276	−	5.71736i	0.455811	−	0.263163i
$473$	7.90915	−	4.56635i	0.363663	−	0.209961i
$474$	1.77423	−	0.742499i	0.0814932	−	0.0341041i
$475$	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
$479$	−37.2972			−1.70415			−0.852076	−	0.523419i	$-0.824656\pi$
$479$	−37.2972			−1.70415			−0.852076	+	0.523419i	$0.824656\pi$
$480$	1.59778	−	0.668655i	0.0729283	−	0.0305198i
$481$		−	36.2837i		−	1.65440i
$482$	9.40683	−	16.2931i	0.428469	−	0.742130i
$483$	−17.9176	+	18.3576i	−0.815278	+	0.835302i
$484$	5.20523	+	9.01573i	0.236602	+	0.409806i
$485$	7.61423	−	4.39608i	0.345744	−	0.199615i
$486$	6.22691	+	14.2908i	0.282458	+	0.648242i
$487$	−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	$0.307458\pi$
$488$	−4.74999	+	8.22722i	−0.215022	+	0.372429i
$489$	−3.22200	−	7.69911i	−0.145704	−	0.348166i
$490$	−1.69673	+	6.79125i	−0.0766502	+	0.306798i
$491$	−30.1458	−	17.4047i	−1.36046	−	0.785462i	−0.370776	−	0.928723i	$-0.620908\pi$
$491$	−30.1458	−	17.4047i	−1.36046	−	0.785462i	−0.989685	+	0.143260i	$0.954241\pi$
$492$	9.11874	+	1.16671i	0.411105	+	0.0525993i
$493$		−	24.2578i		−	1.09251i
$494$	18.2986	+	10.5647i	0.823291	+	0.475327i
$495$	−0.579937	+	2.22923i	−0.0260662	+	0.100196i
$496$			8.05924i			0.361870i
$497$	11.9550	−	15.8569i	0.536255	−	0.711278i
$498$	0.111921	−	0.874752i	0.00501531	−	0.0391986i
$499$	24.4326			1.09376			0.546878	−	0.837212i	$-0.315816\pi$
$499$	24.4326			1.09376			0.546878	+	0.837212i	$0.315816\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	10.4364	−	13.7041i	0.466263	−	0.612253i
$502$	2.90776	+	1.67879i	0.129780	+	0.0749283i
$503$	−13.5009			−0.601977			−0.300988	−	0.953628i	$-0.597317\pi$
$503$	−13.5009			−0.601977			−0.300988	+	0.953628i	$0.597317\pi$
$504$	−6.22004	+	4.93063i	−0.277063	+	0.219628i
$505$	11.8515			0.527384
$506$	−3.72222	−	2.14902i	−0.165473	−	0.0955358i
$507$	−4.04781	−	9.67241i	−0.179769	−	0.429567i
$508$	−6.32397	−	10.9534i	−0.280581	−	0.485980i
$509$	−27.3443			−1.21202			−0.606008	−	0.795459i	$-0.707230\pi$
$509$	−27.3443			−1.21202			−0.606008	+	0.795459i	$0.707230\pi$
$510$	3.67990	−	1.54000i	0.162949	−	0.0681925i
$511$	−12.0716	−	28.4579i	−0.534016	−	1.25891i
$512$			1.00000i			0.0441942i
$513$	−24.8998	+	3.55552i	−1.09935	+	0.156980i
$514$	−9.81743	−	5.66810i	−0.433028	−	0.250009i
$515$		−	0.878126i		−	0.0386949i
$516$	12.4819	−	16.3901i	0.549487	−	0.721535i
$517$	−4.29650	−	2.48059i	−0.188960	−	0.109096i
$518$	−13.2396	+	17.5607i	−0.581713	+	0.771572i
$519$	17.4475	−	22.9105i	0.765861	−	1.00566i
$520$	2.18252	−	3.78024i	0.0957100	−	0.165775i
$521$	5.24997	−	9.09321i	0.230005	−	0.398381i	−0.727804	−	0.685785i	$-0.759459\pi$
$521$	5.24997	−	9.09321i	0.230005	−	0.398381i	0.957809	+	0.287404i	$0.0927923\pi$
$522$	30.5796	+	7.95533i	1.33843	+	0.348195i
$523$	−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
$525$	3.27944	+	3.20083i	0.143126	+	0.139695i
$526$	12.8910	−	22.3278i	0.562074	−	0.973540i
$527$			18.5615i			0.808552i
$528$	−1.05801	−	0.805733i	−0.0460441	−	0.0350650i
$529$	−8.33538			−0.362408
$530$	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
$534$	−1.23171	+	9.62678i	−0.0533013	+	0.416592i
$535$	−5.55184	+	3.20536i	−0.240027	+	0.138580i
$536$	−11.8687	+	6.85237i	−0.512648	+	0.295977i
$537$	−6.48312	−	4.93724i	−0.279767	−	0.213057i
$538$	−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	$0.776044\pi$
$542$	10.1230			0.434821
$543$	−1.83198	+	14.3183i	−0.0786176	+	0.614458i
$544$			2.30313i			0.0987461i
$545$	4.36380	−	7.55832i	0.186924	−	0.323763i
$546$	−4.94244	+	19.3830i	−0.211517	+	0.829514i
$547$	15.3348	+	26.5606i	0.655667	+	1.13565i	0.981726	+	0.190299i	$0.0609459\pi$
$547$	15.3348	+	26.5606i	0.655667	+	1.13565i	−0.326059	+	0.945349i	$0.605721\pi$
$548$	12.4651	−	7.19674i	0.532483	−	0.307429i
$549$	−20.2989	−	20.0050i	−0.866334	−	0.853795i
$550$	−0.383905	+	0.664943i	−0.0163698	+	0.0283533i
$551$	−25.4917	+	44.1529i	−1.08598	+	1.88098i
$552$	−9.61728	−	1.23049i	−0.409338	−	0.0523733i
$553$	−2.70466	+	1.14729i	−0.115014	+	0.0487878i
$554$	−8.99804	−	5.19502i	−0.382290	−	0.220715i
$555$	5.55808	+	13.2813i	0.235928	+	0.563759i
$556$		−	10.1851i		−	0.431943i
$557$	−1.82492	−	1.05362i	−0.0773242	−	0.0446432i	0.460839	−	0.887484i	$-0.347548\pi$
$557$	−1.82492	−	1.05362i	−0.0773242	−	0.0446432i	−0.538164	+	0.842840i	$0.680882\pi$
$558$	−23.3989	−	6.08724i	−0.990553	−	0.257694i
$559$		−	51.9199i		−	2.19598i
$560$	−2.43568	+	1.03319i	−0.102926	+	0.0436603i
$561$	−2.43675	−	1.85571i	−0.102880	−	0.0783482i
$562$	16.5295			0.697253
$563$	5.74415	+	9.94915i	0.242087	+	0.419307i	0.961309	−	0.275474i	$-0.0888347\pi$
$563$	5.74415	+	9.94915i	0.242087	+	0.419307i	−0.719222	+	0.694781i	$0.755501\pi$
$564$	−11.1011	−	1.42034i	−0.467440	−	0.0598071i
$565$	0.697613	+	0.402767i	0.0293488	+	0.0169445i
$566$	10.3924			0.436826
$567$	−9.61732	−	21.7832i	−0.403889	−	0.914808i
$568$	7.50583			0.314938
$569$	39.7209	+	22.9329i	1.66519	+	0.961395i	0.970178	+	0.242392i	$0.0779320\pi$
$569$	39.7209	+	22.9329i	1.66519	+	0.961395i	0.695007	+	0.719003i	$0.255401\pi$
$570$	−8.31633	−	1.06404i	−0.348333	−	0.0445678i
$571$	6.79295	+	11.7657i	0.284276	+	0.492381i	0.972433	−	0.233181i	$-0.0749134\pi$
$571$	6.79295	+	11.7657i	0.284276	+	0.492381i	−0.688157	+	0.725562i	$0.741580\pi$
$572$	−3.35153			−0.140135
$573$	−5.22647	−	3.98023i	−0.218339	−	0.166276i
$574$	−13.9376	−	1.71473i	−0.581743	−	0.0715713i
$575$			5.59780i			0.233444i
$576$	−2.90336	−	0.755312i	−0.120973	−	0.0314714i
$577$	−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	$0.802431\pi$
$578$		−	11.6956i		−	0.486472i
$579$	−14.3734	−	34.3458i	−0.597337	−	1.42736i
$580$	9.12141	+	5.26625i	0.378746	+	0.218669i
$581$	−0.164492	+	1.33702i	−0.00682428	+	0.0554689i
$582$	−15.1053	−	1.93267i	−0.626135	−	0.0801116i
$583$	2.87285	−	4.97592i	0.118981	−	0.206082i
$584$	5.84190	−	10.1185i	0.241739	−	0.418705i
$585$	9.32692	+	9.19192i	0.385621	+	0.380039i
$586$	22.1332	−	12.7786i	0.914313	−	0.527879i
$587$	11.8126	+	20.4600i	0.487558	+	0.844475i	0.999898	−	0.0143079i	$-0.00455451\pi$
$587$	11.8126	+	20.4600i	0.487558	+	0.844475i	−0.512340	+	0.858783i	$0.671221\pi$
$588$	9.46470	−	7.57756i	0.390318	−	0.312494i
$589$	19.5057	−	33.7848i	0.803717	−	1.39208i
$590$			11.4347i			0.470760i
$591$	−2.94353	+	23.0060i	−0.121081	+	0.946340i
$592$	−8.31233			−0.341635
$593$	−23.9443	−	41.4727i	−0.983274	−	1.70308i	−0.649367	−	0.760475i	$-0.724966\pi$
$593$	−23.9443	−	41.4727i	−0.983274	−	1.70308i	−0.333907	−	0.942606i	$-0.608367\pi$
$594$	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
$597$	−0.772507	−	0.588304i	−0.0316166	−	0.0240777i
$598$	−21.1611	+	12.2173i	−0.865340	+	0.499604i
$599$	12.9010	−	7.44842i	0.527123	−	0.304334i	−0.212721	−	0.977113i	$-0.568233\pi$
$599$	12.9010	−	7.44842i	0.527123	−	0.304334i	0.739844	+	0.672779i	$0.234899\pi$
$600$	−0.219817	+	1.71805i	−0.00897401	+	0.0701389i
$601$	13.3073	−	7.68296i	0.542815	−	0.313394i	−0.203404	−	0.979095i	$-0.565200\pi$
$601$	13.3073	−	7.68296i	0.542815	−	0.313394i	0.746219	+	0.665700i	$0.231867\pi$
$602$	−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
$605$	−10.4105			−0.423246
$606$	−16.3309	−	12.4368i	−0.663397	−	0.505211i
$607$			8.96232i			0.363769i	0.983320	+	0.181885i	$0.0582197\pi$
$607$			8.96232i			0.363769i	−0.983320	+	0.181885i	$0.941780\pi$
$608$	2.42029	−	4.19206i	0.0981556	−	0.170011i
$609$	−46.7694	−	11.9257i	−1.89519	−	0.483254i
$610$	−4.74999	−	8.22722i	−0.192321	−	0.333110i
$611$	−24.4259	+	14.1023i	−0.988165	+	0.570517i
$612$	−6.68683	−	1.73959i	−0.270299	−	0.0703186i
$613$	−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	$0.310668\pi$
$614$	−4.66668	+	8.08293i	−0.188332	+	0.326200i
$615$	−5.56977	+	7.31371i	−0.224595	+	0.294917i
$616$	1.62208	+	1.22294i	0.0653555	+	0.0492736i
$617$	−28.3642	−	16.3761i	−1.14190	−	0.659277i	−0.195000	−	0.980803i	$-0.562471\pi$
$617$	−28.3642	−	16.3761i	−1.14190	−	0.659277i	−0.946901	+	0.321527i	$0.895804\pi$
$618$	−0.921497	+	1.21003i	−0.0370681	+	0.0486743i
$619$			13.1574i			0.528839i	0.964408	+	0.264420i	$0.0851804\pi$
$619$			13.1574i			0.528839i	−0.964408	+	0.264420i	$0.914820\pi$
$620$	−6.97950	−	4.02962i	−0.280304	−	0.161833i
$621$	10.8366	−	26.9930i	0.434858	−	1.08319i
$622$			5.36577i			0.215148i
$623$	1.81026	−	14.7141i	0.0725266	−	0.589507i
$624$	−6.97439	+	2.91871i	−0.279199	+	0.116842i
$625$	1.00000			0.0400000
$626$	−12.7280	−	22.0455i	−0.508712	−	0.881115i
$627$	2.48515	+	5.93838i	0.0992475	+	0.237156i
$628$	−2.81741	−	1.62663i	−0.112427	−	0.0649097i
$629$	−19.1444			−0.763338
$630$	−1.16003	−	7.85203i	−0.0462167	−	0.312832i
$631$	−32.3439			−1.28759			−0.643795	−	0.765198i	$-0.722641\pi$
$631$	−32.3439			−1.28759			−0.643795	+	0.765198i	$0.722641\pi$
$632$	−0.961666	−	0.555218i	−0.0382530	−	0.0220854i
$633$	−3.70512	+	4.86522i	−0.147265	+	0.193375i
$634$	−3.74338	−	6.48372i	−0.148669	−	0.257502i
$635$	12.6479			0.501918
$636$	1.64494	−	12.8565i	0.0652262	−	0.509794i
$637$	7.40629	−	29.6442i	0.293448	−	1.17454i
$638$		−	8.08696i		−	0.320166i
$639$	−5.66925	+	21.7921i	−0.224272	+	0.862084i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	28.0300i		−	1.10712i	−0.832810	−	0.553559i	$-0.813269\pi$
$641$		−	28.0300i		−	1.10712i	0.832810	−	0.553559i	$-0.186731\pi$
$642$	11.0139	+	1.40919i	0.434684	+	0.0556161i
$643$	−11.6003	−	6.69742i	−0.457470	−	0.264121i	0.253510	−	0.967333i	$-0.418415\pi$
$643$	−11.6003	−	6.69742i	−0.457470	−	0.264121i	−0.710980	+	0.703212i	$0.751748\pi$
$644$	14.6996	+	1.80847i	0.579244	+	0.0712638i
$645$	7.95330	+	19.0047i	0.313161	+	0.748311i
$646$	5.57425	−	9.65488i	0.219316	−	0.379866i
$647$	−10.5813	+	18.3274i	−0.415995	+	0.720524i	−0.995532	−	0.0944214i	$-0.969900\pi$
$647$	−10.5813	+	18.3274i	−0.415995	+	0.720524i	0.579537	+	0.814946i	$0.303233\pi$
$648$	4.38589	−	7.85901i	0.172294	−	0.308731i
$649$	7.60344	−	4.38985i	0.298461	−	0.172317i
$650$	2.18252	+	3.78024i	0.0856057	+	0.148273i
$651$	35.7870	+	9.12528i	1.40260	+	0.357648i
$652$	−2.40931	+	4.17306i	−0.0943560	+	0.163429i
$653$		−	21.0984i		−	0.825645i	−0.910811	−	0.412823i	$-0.864543\pi$
$653$		−	21.0984i		−	0.825645i	0.910811	−	0.412823i	$-0.135457\pi$
$654$	−13.9448	+	5.83575i	−0.545284	+	0.228196i
$655$	9.92603			0.387842
$656$	−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	0.0486845	−	0.998814i	$-0.484497\pi$
$659$	24.0800	−	13.9026i	0.938025	−	0.541569i	0.889341	+	0.457245i	$0.151164\pi$
$660$	1.22679	−	0.513400i	0.0477528	−	0.0199841i
$661$	8.80674	−	5.08458i	0.342543	−	0.197767i	−0.318853	−	0.947804i	$-0.603298\pi$
$661$	8.80674	−	5.08458i	0.342543	−	0.197767i	0.661396	+	0.750037i	$0.269964\pi$
$662$	6.43342	−	3.71433i	0.250042	−	0.144362i
$663$	−16.0630	+	6.72219i	−0.623833	+	0.261068i
$664$	−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
$668$	−9.94518			−0.384791
$669$	−40.9196	+	17.1244i	−1.58204	+	0.662069i
$670$		−	13.7047i		−	0.529461i
$671$	−3.64709	+	6.31694i	−0.140794	+	0.243863i
$672$	4.44049	+	1.13228i	0.171296	+	0.0436785i
$673$	−5.29232	−	9.16657i	−0.204004	−	0.353345i	0.745811	−	0.666158i	$-0.232062\pi$
$673$	−5.29232	−	9.16657i	−0.204004	−	0.353345i	−0.949815	+	0.312812i	$0.898729\pi$
$674$	22.3731	−	12.9171i	0.861781	−	0.497549i
$675$	−4.82207	−	1.93587i	−0.185602	−	0.0745117i
$676$	−3.02683	+	5.24262i	−0.116416	+	0.201639i
$677$	−16.5653	+	28.6920i	−0.636657	+	1.10272i	0.349505	+	0.936935i	$0.386350\pi$
$677$	−16.5653	+	28.6920i	−0.636657	+	1.10272i	−0.986162	+	0.165787i	$0.946983\pi$
$678$	−0.538625	−	1.28707i	−0.0206858	−	0.0494295i
$679$	23.0878	+	2.84047i	0.886027	+	0.109007i
$680$	−1.99457	−	1.15157i	−0.0764884	−	0.0441606i
$681$	−19.1366	−	2.44846i	−0.733317	−	0.0938251i
$682$			6.18797i			0.236949i
$683$	−15.1376	−	8.73972i	−0.579225	−	0.334416i	0.181600	−	0.983372i	$-0.441872\pi$
$683$	−15.1376	−	8.73972i	−0.579225	−	0.334416i	−0.760826	+	0.648957i	$0.775206\pi$
$684$	10.3430	+	10.1933i	0.395474	+	0.389750i
$685$			14.3935i			0.549947i
$686$	−14.4014	+	11.6448i	−0.549847	+	0.444599i
$687$	0.837158	−	6.54305i	0.0319396	−	0.249633i
$688$	−11.8945			−0.453472
$689$	−16.3323	−	28.2884i	−0.622212	−	1.07770i
$690$	5.87428	−	7.71356i	0.223630	−	0.293650i
$691$	16.5287	+	9.54285i	0.628782	+	0.363027i	0.780280	−	0.625430i	$-0.215077\pi$
$691$	16.5287	+	9.54285i	0.628782	+	0.363027i	−0.151498	+	0.988457i	$0.548410\pi$
$692$	−16.6263			−0.632039
$693$	−4.77581	+	3.78579i	−0.181418	+	0.143810i
$694$	−18.4244			−0.699380
$695$	8.82052	+	5.09253i	0.334581	+	0.193171i
$696$	−7.04261	−	16.8286i	−0.266949	−	0.637887i
$697$	−6.11209	−	10.5864i	−0.231512	−	0.400990i
$698$	1.58715			0.0600747
$699$	−3.76795	+	1.57685i	−0.142517	+	0.0596420i
$700$	0.323069	−	2.62595i	0.0122108	−	0.0992517i
$701$			14.4247i			0.544815i	0.962182	+	0.272407i	$0.0878198\pi$
$701$			14.4247i			0.544815i	−0.962182	+	0.272407i	$0.912180\pi$
$702$	−3.20624	−	22.4537i	−0.121012	−	0.847460i
$703$	34.8458	+	20.1182i	1.31423	+	0.758773i
$704$			0.767810i			0.0289379i
$705$	6.78059	−	8.90364i	0.255372	−	0.335331i
$706$	7.97208	+	4.60268i	0.300033	+	0.173224i
$707$	25.0375	+	18.8766i	0.941632	+	0.709927i
$708$	11.9995	−	15.7566i	0.450968	−	0.592170i
$709$	−11.9719	+	20.7360i	−0.449615	+	0.778755i	−0.998361	−	0.0572336i	$-0.981772\pi$
$709$	−11.9719	+	20.7360i	−0.449615	+	0.778755i	0.548746	+	0.835989i	$0.315105\pi$
$710$	−3.75292	+	6.50024i	−0.140844	+	0.243950i
$711$	2.33836	−	2.37270i	0.0876952	−	0.0889832i
$712$	4.85263	−	2.80167i	0.181860	−	0.104997i
$713$	22.5570	+	39.0699i	0.844766	+	1.46318i
$714$	10.2270	+	2.60778i	0.382738	+	0.0975939i
$715$	1.67576	−	2.90251i	0.0626701	−	0.108548i
$716$			4.70486i			0.175829i
$717$	−16.2245	−	12.3558i	−0.605914	−	0.461435i
$718$	−25.8366			−0.964213
$719$	−7.04096	−	12.1953i	−0.262584	−	0.454808i	0.704344	−	0.709859i	$-0.251241\pi$
$719$	−7.04096	−	12.1953i	−0.262584	−	0.454808i	−0.966928	+	0.255051i	$0.917908\pi$
$720$	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
$723$	4.13557	−	32.3227i	0.153803	−	1.20209i
$724$	7.21752	−	4.16704i	0.268237	−	0.154867i
$725$	−9.12141	+	5.26625i	−0.338761	+	0.195584i
$726$	14.3452	+	10.9246i	0.532402	+	0.405451i
$727$	10.6031	−	6.12171i	0.393248	−	0.227042i	−0.290319	−	0.956930i	$-0.593761\pi$
$727$	10.6031	−	6.12171i	0.393248	−	0.227042i	0.683566	+	0.729888i	$0.260428\pi$
$728$	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
$731$	−27.3946			−1.01322
$732$	−2.08826	+	16.3214i	−0.0771843	+	0.603256i
$733$			31.9863i			1.18144i	0.806877	+	0.590720i	$0.201156\pi$
$733$			31.9863i			1.18144i	−0.806877	+	0.590720i	$0.798844\pi$
$734$	11.1282	−	19.2746i	0.410750	−	0.711439i
$735$	1.83001	+	11.9855i	0.0675011	+	0.442090i
$736$	2.79890	+	4.84784i	0.103169	+	0.178694i
$737$	−9.11288	+	5.26132i	−0.335677	+	0.193803i
$738$	15.3499	−	4.23315i	0.565037	−	0.155825i
$739$	−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	$0.939841\pi$
$740$	4.15617	−	7.19869i	0.152784	−	0.264629i
$741$	36.3012	+	4.64460i	1.33356	+	0.170624i
$742$	−2.41760	+	19.6506i	−0.0887527	+	0.721396i
$743$	19.6903	+	11.3682i	0.722366	+	0.417058i	0.815623	−	0.578584i	$-0.196394\pi$
$743$	19.6903	+	11.3682i	0.722366	+	0.417058i	−0.0932570	+	0.995642i	$0.529728\pi$
$744$	5.38885	+	12.8769i	0.197565	+	0.472090i
$745$			8.95303i			0.328014i
$746$	28.3884	+	16.3900i	1.03937	+	0.600082i
$747$	−0.406082	−	1.47250i	−0.0148578	−	0.0538759i
$748$			1.76837i			0.0646580i
$749$	−16.8342	−	2.07110i	−0.615109	−	0.0756763i
$750$	−1.37796	−	1.04939i	−0.0503161	−	0.0383183i
$751$	14.4519			0.527357			0.263678	−	0.964611i	$-0.415064\pi$
$751$	14.4519			0.527357			0.263678	+	0.964611i	$0.415064\pi$
$752$	3.23073	+	5.59578i	0.117813	+	0.204057i
$753$	5.76849	+	0.738056i	0.210215	+	0.0268963i
$754$	−39.8154	−	22.9874i	−1.44999	−	0.837153i
$755$	5.00718			0.182230
$756$	−6.64136	+	12.0371i	−0.241544	+	0.437786i
$757$	29.2971			1.06482			0.532410	−	0.846487i	$-0.321287\pi$
$757$	29.2971			1.06482			0.532410	+	0.846487i	$0.321287\pi$
$758$	23.1344	+	13.3566i	0.840278	+	0.485135i
$759$	−7.38424	−	0.944786i	−0.268031	−	0.0342936i
$760$	2.42029	+	4.19206i	0.0877930	+	0.152062i
$761$	48.9328			1.77381			0.886906	−	0.461949i	$-0.152850\pi$
$761$	48.9328			1.77381			0.886906	+	0.461949i	$0.152850\pi$
$762$	−17.4284	−	13.2726i	−0.631364	−	0.480816i
$763$	21.2576	−	9.01727i	0.769576	−	0.326447i
$764$			3.79290i			0.137222i
$765$	4.84994	−	4.92117i	0.175350	−	0.177925i
$766$	1.57386	+	0.908668i	0.0568658	+	0.0328315i
$767$		−	49.9131i		−	1.80226i
$768$	0.668655	+	1.59778i	0.0241280	+	0.0576549i
$769$	44.0886	+	25.4546i	1.58988	+	0.917915i	0.993326	+	0.115339i	$0.0367953\pi$
$769$	44.0886	+	25.4546i	1.58988	+	0.917915i	0.596549	+	0.802577i	$0.296538\pi$
$770$	−1.87014	+	0.793294i	−0.0673951	+	0.0285883i
$771$	−19.4761	−	2.49189i	−0.701414	−	0.0897433i
$772$	−10.7480	+	18.6160i	−0.386828	+	0.670005i
$773$	−10.7757	+	18.6640i	−0.387574	+	0.671297i	−0.992123	−	0.125271i	$-0.960020\pi$
$773$	−10.7757	+	18.6640i	−0.387574	+	0.671297i	0.604549	+	0.796568i	$0.293353\pi$
$774$	8.98404	−	34.5339i	0.322925	−	1.24130i
$775$	6.97950	−	4.02962i	0.250711	−	0.144748i
$776$	4.39608	+	7.61423i	0.157810	+	0.273335i
$777$	−9.41186	+	36.9108i	−0.337648	+	1.32417i
$778$	−14.9847	+	25.9543i	−0.537228	+	0.930507i
$779$			25.6920i			0.920510i
$780$	0.959514	−	7.49935i	0.0343561	−	0.268520i
$781$	5.76306			0.206218
$782$	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
$786$	−13.6777	−	10.4163i	−0.487867	−	0.371536i
$787$	−21.3479	+	12.3252i	−0.760971	+	0.439347i	−0.829644	−	0.558293i	$-0.811457\pi$
$787$	−21.3479	+	12.3252i	−0.760971	+	0.439347i	0.0686734	+	0.997639i	$0.478123\pi$
$788$	11.5968	−	6.69540i	0.413118	−	0.238514i
$789$	5.66733	−	44.2946i	0.201762	−	1.57693i
$790$	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
$794$	−0.936742			−0.0332437
$795$	10.3116	+	7.85283i	0.365715	+	0.278511i
$796$			0.560615i			0.0198705i
$797$	1.27405	−	2.20672i	0.0451293	−	0.0781662i	−0.842578	−	0.538574i	$-0.818963\pi$
$797$	1.27405	−	2.20672i	0.0451293	−	0.0781662i	0.887708	+	0.460407i	$0.152297\pi$
$798$	−15.8744	−	15.4938i	−0.561947	−	0.548476i
$799$	7.44080	+	12.8878i	0.263237	+	0.455939i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	4.46900	+	16.2051i	0.157904	+	0.572578i
$802$	−2.90439	+	5.03054i	−0.102557	+	0.177635i
$803$	4.48547	−	7.76906i	0.158289	−	0.274164i
$804$	−14.3816	+	18.8846i	−0.507201	+	0.666009i
$805$	−8.91596	+	11.8260i	−0.314246	+	0.416810i
$806$	30.4659	+	17.5895i	1.07311	+	0.619563i
$807$	−6.18897	+	8.12678i	−0.217862	+	0.286076i
$808$			11.8515i			0.416933i
$809$	−3.56339	−	2.05733i	−0.125282	−	0.0723318i	0.436049	−	0.899923i	$-0.356377\pi$
$809$	−3.56339	−	2.05733i	−0.125282	−	0.0723318i	−0.561331	+	0.827591i	$0.689711\pi$
$810$	4.61315	+	7.72779i	0.162090	+	0.271527i
$811$		−	36.4586i		−	1.28024i	−0.768277	−	0.640118i	$-0.778885\pi$
$811$		−	36.4586i		−	1.28024i	0.768277	−	0.640118i	$-0.221115\pi$
$812$	10.8821	+	25.6537i	0.381886	+	0.900270i
$813$	16.1744	−	6.76882i	0.567260	−	0.237393i
$814$	−6.38229			−0.223699
$815$	−2.40931	−	4.17306i	−0.0843946	−	0.146176i
$816$	1.54000	+	3.67990i	0.0539109	+	0.128822i
$817$	49.8623	+	28.7880i	1.74446	+	1.00717i
$818$	21.8817			0.765076
$819$	5.06358	+	34.2745i	0.176936	+	1.19765i
$820$	5.30763			0.185350
$821$	28.0297	+	16.1829i	0.978243	+	0.564789i	0.901739	−	0.432281i	$-0.142291\pi$
$821$	28.0297	+	16.1829i	0.978243	+	0.564789i	0.0765035	+	0.997069i	$0.475624\pi$
$822$	15.1044	−	19.8337i	0.526826	−	0.691779i
$823$	3.84178	+	6.65416i	0.133916	+	0.231949i	0.925183	−	0.379522i	$-0.123911\pi$
$823$	3.84178	+	6.65416i	0.133916	+	0.231949i	−0.791267	+	0.611471i	$0.790578\pi$
$824$	0.878126			0.0305910
$825$	−0.168778	+	1.31913i	−0.00587610	+	0.0459263i
$826$	−18.2128	+	24.1571i	−0.633704	+	0.840532i
$827$			8.88863i			0.309088i	0.987986	+	0.154544i	$0.0493908\pi$
$827$			8.88863i			0.309088i	−0.987986	+	0.154544i	$0.950609\pi$
$828$	−16.1891	+	4.46459i	−0.562609	+	0.155155i
$829$	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	$0.566021\pi$
$830$		−	0.509156i		−	0.0176730i
$831$	−17.8506	−	2.28391i	−0.619230	−	0.0792281i
$832$	3.78024	+	2.18252i	0.131056	+	0.0756654i
$833$	−15.6412	−	3.90779i	−0.541934	−	0.135397i
$834$	−6.81029	−	16.2735i	−0.235821	−	0.563505i
$835$	4.97259	−	8.61278i	0.172084	−	0.298058i
$836$	1.85832	−	3.21871i	0.0642714	−	0.111321i
$837$	−41.4565	+	5.91971i	−1.43295	+	0.204615i
$838$	13.8082	−	7.97218i	0.476997	−	0.275395i
$839$	−15.0745	−	26.1098i	−0.520430	−	0.901412i	−0.999718	−	0.0237538i	$-0.992438\pi$
$839$	−15.0745	−	26.1098i	−0.520430	−	0.901412i	0.479287	−	0.877658i	$-0.340895\pi$
$840$	−3.20083	+	3.27944i	−0.110439	+	0.113151i
$841$	40.9667	−	70.9565i	1.41265	−	2.44678i
$842$		−	16.5396i		−	0.569991i
$843$	26.4104	−	11.0525i	0.909624	−	0.380669i
$844$	3.53074			0.121533
$845$	−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
$849$	16.6048	−	6.94894i	0.569875	−	0.238487i
$850$	1.99457	−	1.15157i	0.0684133	−	0.0394984i
$851$	−40.2968	+	23.2654i	−1.38136	+	0.797527i
$852$	11.9927	−	5.01882i	0.410862	−	0.171942i
$853$	−11.2347	+	6.48634i	−0.384668	+	0.222088i	−0.679847	−	0.733354i	$-0.737954\pi$
$853$	−11.2347	+	6.48634i	−0.384668	+	0.222088i	0.295180	+	0.955442i	$0.404621\pi$
$854$	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
$857$	−26.4584			−0.903800			−0.451900	−	0.892069i	$-0.649254\pi$
$857$	−26.4584			−0.903800			−0.451900	+	0.892069i	$0.649254\pi$
$858$	−5.35501	+	2.24102i	−0.182817	+	0.0765071i
$859$		−	30.5959i		−	1.04392i	−0.852970	−	0.521959i	$-0.825201\pi$
$859$		−	30.5959i		−	1.04392i	0.852970	−	0.521959i	$-0.174799\pi$
$860$	5.94724	−	10.3009i	0.202799	−	0.351258i
$861$	−23.4157	+	6.57968i	−0.798006	+	0.224235i
$862$	6.08623	+	10.5417i	0.207298	+	0.359050i
$863$	−42.9051	+	24.7713i	−1.46051	+	0.843223i	−0.999035	−	0.0439320i	$-0.986012\pi$
$863$	−42.9051	+	24.7713i	−1.46051	+	0.843223i	−0.461471	+	0.887155i	$0.652678\pi$
$864$	−5.14397	+	0.734525i	−0.175002	+	0.0249890i
$865$	8.31317	−	14.3988i	0.282656	−	0.489575i
$866$	−4.27269	+	7.40052i	−0.145192	+	0.251480i
$867$	−7.82031	−	18.6869i	−0.265592	−	0.634642i
$868$	−8.32673	−	19.6297i	−0.282628	−	0.666275i
$869$	−0.738377	−	0.426302i	−0.0250477	−	0.0144613i
$870$	18.0953	+	2.31523i	0.613488	+	0.0784935i
$871$			59.8219i			2.02699i
$872$	7.55832	+	4.36380i	0.255957	+	0.147777i
$873$	−25.4273	+	7.01227i	−0.860582	+	0.237329i
$874$		−	27.0966i		−	0.916555i
$875$	2.11261	+	1.59276i	0.0714192	+	0.0538452i
$876$	2.56830	−	20.0733i	0.0867748	−	0.678214i
$877$	−44.1241			−1.48997			−0.744983	−	0.667083i	$-0.767543\pi$
$877$	−44.1241			−1.48997			−0.744983	+	0.667083i	$0.767543\pi$
$878$	−3.29088	−	5.69997i	−0.111062	−	0.192365i
$879$	26.8195	−	35.2168i	0.904598	−	1.18783i
$880$	−0.664943	−	0.383905i	−0.0224152	−	0.0129414i
$881$	14.2789			0.481068			0.240534	−	0.970641i	$-0.422677\pi$
$881$	14.2789			0.481068			0.240534	+	0.970641i	$0.422677\pi$
$882$	10.0557	−	18.4359i	0.338594	−	0.620769i
$883$	−2.99831			−0.100901			−0.0504505	−	0.998727i	$-0.516066\pi$
$883$	−2.99831			−0.100901			−0.0504505	+	0.998727i	$0.516066\pi$
$884$	8.70641	+	5.02665i	0.292828	+	0.169064i
$885$	7.64589	+	18.2702i	0.257014	+	0.614145i
$886$	13.5369	+	23.4466i	0.454781	+	0.787703i
$887$	36.0244			1.20958			0.604791	−	0.796384i	$-0.293257\pi$
$887$	36.0244			1.20958			0.604791	+	0.796384i	$0.293257\pi$
$888$	−13.2813	+	5.55808i	−0.445690	+	0.186517i
$889$	26.7201	+	20.1452i	0.896164	+	0.675647i
$890$			5.60333i			0.187824i
$891$	3.36753	−	6.03423i	0.112817	−	0.202154i
$892$	22.1791	+	12.8051i	0.742612	+	0.428748i
$893$		−	31.2772i		−	1.04665i
$894$	9.39522	−	12.3369i	0.314223	−	0.412609i
$895$	−4.07453	−	2.35243i	−0.136197	−	0.0786331i
$896$	−1.03319	−	2.43568i	−0.0345165	−	0.0813702i
$897$	−25.6415	+	33.6701i	−0.856145	+	1.12421i
$898$	8.98271	−	15.5585i	0.299757	−	0.519194i
$899$	−42.4419	+	73.5116i	−1.41552	+	2.45175i
$900$	0.797561	+	2.89204i	0.0265854	+	0.0964013i
$901$	−14.9258	+	8.61744i	−0.497252	+	0.287089i
$902$	−2.03763	−	3.52927i	−0.0678455	−	0.117512i
$903$	−13.4678	+	52.8173i	−0.448181	+	1.75765i
$904$	−0.402767	+	0.697613i	−0.0133958	+	0.0232023i
$905$			8.33408i			0.277034i
$906$	−6.89971	−	5.25449i	−0.229227	−	0.174569i
$907$	21.0929			0.700378			0.350189	−	0.936679i	$-0.386117\pi$
$907$	21.0929			0.700378			0.350189	+	0.936679i	$0.386117\pi$
$908$	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	−0.838965	−	0.544185i	$-0.816839\pi$
$911$	−23.7590	+	13.7172i	−0.787169	+	0.454472i	0.0517958	+	0.998658i	$0.483505\pi$
$912$	1.06404	−	8.31633i	0.0352340	−	0.275381i
$913$	−0.338560	+	0.195467i	−0.0112047	+	0.00646903i
$914$	−4.45944	+	2.57466i	−0.147505	+	0.0851622i
$915$	−13.0906	−	9.96918i	−0.432762	−	0.329571i
$916$	−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	$0.810895\pi$
$920$	−5.59780			−0.184554
$921$	−2.05164	+	16.0351i	−0.0676037	+	0.528376i
$922$		−	10.9210i		−	0.359665i
$923$	16.3817	−	28.3739i	0.539209	−	0.933938i
$924$	3.40945	+	0.869374i	0.112163	+	0.0286003i
$925$	4.15617	+	7.19869i	0.136654	+	0.236691i
$926$	−25.7563	+	14.8704i	−0.846406	+	0.488673i
$927$	−0.663260	+	2.54952i	−0.0217843	+	0.0837371i
$928$	−5.26625	+	9.12141i	−0.172873	+	0.299425i
$929$	5.90039	−	10.2198i	0.193585	−	0.335300i	−0.752850	−	0.658192i	$-0.771322\pi$
$929$	5.90039	−	10.2198i	0.193585	−	0.335300i	0.946436	+	0.322892i	$0.104655\pi$
$930$	−13.8461	−	1.77156i	−0.454033	−	0.0580917i
$931$	24.3628	+	23.5496i	0.798458	+	0.771806i
$932$	2.04230	+	1.17912i	0.0668977	+	0.0386234i
$933$	3.58785	+	8.57332i	0.117461	+	0.280678i
$934$			9.11448i			0.298235i
$935$	−1.53145	−	0.884185i	−0.0500839	−	0.0289159i
$936$	−9.19192	+	9.32692i	−0.300447	+	0.304860i
$937$			52.8223i			1.72563i	0.505520	+	0.862815i	$0.331301\pi$
$937$			52.8223i			1.72563i	−0.505520	+	0.862815i	$0.668699\pi$
$938$	21.8284	−	28.9527i	0.712722	−	0.945341i
$939$	−35.0773	−	26.7132i	−1.14470	−	0.871752i
$940$	−6.46146			−0.210749
$941$	−20.6789	−	35.8169i	−0.674113	−	1.16760i	−0.976727	−	0.214484i	$-0.931193\pi$
$941$	−20.6789	−	35.8169i	−0.674113	−	1.16760i	0.302615	−	0.953113i	$-0.402140\pi$
$942$	−5.58926	−	0.715124i	−0.182108	−	0.0233000i
$943$	−25.7305	−	14.8555i	−0.837901	−	0.483762i
$944$	−11.4347			−0.372168
$945$	−7.10377	−	11.7702i	−0.231086	−	0.382883i
$946$	−9.13270			−0.296930
$947$	16.5721	+	9.56789i	0.538520	+	0.310914i	0.744479	−	0.667646i	$-0.232698\pi$
$947$	16.5721	+	9.56789i	0.538520	+	0.310914i	−0.205959	+	0.978561i	$0.566031\pi$
$948$	−1.90778	−	0.244093i	−0.0619618	−	0.00792778i
$949$	−25.5002	−	44.1676i	−0.827771	−	1.43374i
$950$	−4.84057			−0.157049
$951$	−10.3165	−	7.85653i	−0.334535	−	0.254765i
$952$	−2.37958	−	5.60969i	−0.0771225	−	0.181811i
$953$			16.1271i			0.522407i	0.965284	+	0.261203i	$0.0841193\pi$
$953$			16.1271i			0.522407i	−0.965284	+	0.261203i	$0.915881\pi$
$954$	−5.96833	−	21.6418i	−0.193232	−	0.700679i
$955$	−3.28474	−	1.89645i	−0.106292	−	0.0613676i
$956$			11.7742i			0.380806i
$957$	−5.40739	−	12.9212i	−0.174796	−	0.417682i
$958$	32.3003	+	18.6486i	1.04358	+	0.602508i
$959$	−22.9254	+	30.4078i	−0.740299	+	0.981918i
$960$	−1.71805	−	0.219817i	−0.0554497	−	0.00709457i
$961$	16.9757	−	29.4027i	0.547602	−	0.948474i
$962$	−18.1419	+	31.4226i	−0.584917	+	1.01311i
$963$	18.5400	−	5.11293i	0.597445	−	0.164762i
$964$	−16.2931	+	9.40683i	−0.524765	+	0.302973i
$965$	−10.7480	−	18.6160i	−0.345989	−	0.599271i
$966$	24.6959	−	6.93940i	0.794578	−	0.223271i
$967$	23.6109	−	40.8952i	0.759274	−	1.31510i	−0.183948	−	0.982936i	$-0.558888\pi$
$967$	23.6109	−	40.8952i	0.759274	−	1.31510i	0.943221	−	0.332165i	$-0.107779\pi$
$968$		−	10.4105i		−	0.334605i
$969$	2.45063	−	19.1536i	0.0787257	−	0.615303i
$970$	−8.79215			−0.282299
$971$	12.0076	+	20.7978i	0.385343	+	0.667434i	0.991817	−	0.127670i	$-0.0407497\pi$
$971$	12.0076	+	20.7978i	0.385343	+	0.667434i	−0.606474	+	0.795104i	$0.707416\pi$
$972$	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
$975$	6.01487	+	4.58064i	0.192630	+	0.146698i
$976$	8.22722	−	4.74999i	0.263347	−	0.152043i
$977$	9.29422	−	5.36602i	0.297348	−	0.171674i	−0.343903	−	0.939005i	$-0.611749\pi$
$977$	9.29422	−	5.36602i	0.297348	−	0.171674i	0.641251	+	0.767331i	$0.278416\pi$
$978$	−1.05922	+	8.27862i	−0.0338701	+	0.264721i
$979$	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
$983$	54.3759			1.73432			0.867162	−	0.498027i	$-0.165942\pi$
$983$	54.3759			1.73432			0.867162	+	0.498027i	$0.165942\pi$
$984$	−7.31371	−	5.56977i	−0.233153	−	0.177558i
$985$			13.3908i			0.426666i
$986$	−12.1289	+	21.0078i	−0.386262	+	0.669026i
$987$	28.5061	−	8.01004i	0.907359	−	0.254962i
$988$	−10.5647	−	18.2986i	−0.336107	−	0.582154i
$989$	−57.6625	+	33.2914i	−1.83356	+	1.05861i
$990$	1.61686	−	1.64060i	0.0513870	−	0.0521417i
$991$	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	$0.152059\pi$
$992$	4.02962	−	6.97950i	0.127941	−	0.221599i
$993$	7.79557	−	10.2364i	0.247385	−	0.324843i
$994$	−18.2818	+	7.75496i	−0.579863	+	0.245972i
$995$	−0.485507	−	0.280308i	−0.0153916	−	0.00888635i
$996$	−0.534303	+	0.701597i	−0.0169300	+	0.0222310i
$997$		−	10.0200i		−	0.317337i	−0.987332	−	0.158668i	$-0.949280\pi$
$997$		−	10.0200i		−	0.317337i	0.987332	−	0.158668i	$-0.0507201\pi$
$998$	−21.1593	−	12.2163i	−0.669786	−	0.386701i
$999$	−6.10561	−	42.7584i	−0.193173	−	1.35282i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.1	✓	28	1.1	even	1	trivial
630.2.t.b.551.1	yes	28	63.47	even	6	inner
630.2.bk.b.101.3	yes	28	9.2	odd	6
630.2.bk.b.131.10	yes	28	7.5	odd	6
1890.2.t.b.1151.11		28	3.2	odd	2
1890.2.t.b.1601.11		28	63.61	odd	6
1890.2.bk.b.341.6		28	21.5	even	6
1890.2.bk.b.521.6		28	9.7	even	3

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.71805 - 0.219817i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.37796 + 1.04939i) q^{6} +(-2.11261 - 1.59276i) q^{7} -1.00000i q^{8} +(2.90336 + 0.755312i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.71805 - 0.219817i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.37796 + 1.04939i) q^{6} +(-2.11261 - 1.59276i) q^{7} -1.00000i q^{8} +(2.90336 + 0.755312i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.767810i q^{11} +(-0.668655 - 1.59778i) q^{12} +(-3.78024 - 2.18252i) q^{13} +(1.03319 + 2.43568i) q^{14} +(1.71805 + 0.219817i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.15157 + 1.99457i) q^{17} +(-2.13673 - 2.10580i) q^{18} +(4.19206 - 2.42029i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(3.27944 + 3.20083i) q^{21} +(-0.383905 + 0.664943i) q^{22} +5.59780i q^{23} +(-0.219817 + 1.71805i) q^{24} +1.00000 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} +(-1.37796 - 1.04939i) q^{30} +(6.97950 - 4.02962i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.168778 + 1.31913i) 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} -4.84057 q^{38} +(6.01487 + 4.58064i) q^{39} +1.00000i q^{40} +(-2.65381 + 4.59654i) q^{41} +(-1.23966 - 4.41172i) q^{42} +(5.94724 + 10.3009i) q^{43} +(0.664943 - 0.383905i) q^{44} +(-2.90336 - 0.755312i) q^{45} +(2.79890 - 4.84784i) q^{46} +(3.23073 - 5.59578i) q^{47} +(1.04939 - 1.37796i) q^{48} +(1.92622 + 6.72976i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.41689 - 3.17363i) q^{51} -4.36505i q^{52} +(6.48067 + 3.74161i) q^{53} +(3.20810 + 4.08755i) q^{54} +0.767810i q^{55} +(-1.59276 + 2.11261i) q^{56} +(-7.73417 + 3.23668i) q^{57} +10.5325 q^{58} +(5.71736 + 9.90276i) q^{59} +(0.668655 + 1.59778i) q^{60} +(-8.22722 - 4.74999i) q^{61} -8.05924 q^{62} +(-4.93063 - 6.22004i) q^{63} -1.00000 q^{64} +(3.78024 + 2.18252i) q^{65} +(0.805733 - 1.05801i) q^{66} +(-6.85237 - 11.8687i) q^{67} -2.30313 q^{68} +(1.23049 - 9.61728i) q^{69} +(-1.03319 - 2.43568i) q^{70} +7.50583i q^{71} +(0.755312 - 2.90336i) q^{72} +(10.1185 + 5.84190i) q^{73} -8.31233i q^{74} +(-1.71805 - 0.219817i) q^{75} +(4.19206 + 2.42029i) q^{76} +(-1.22294 + 1.62208i) q^{77} +(-2.91871 - 6.97439i) q^{78} +(0.555218 - 0.961666i) q^{79} +(0.500000 - 0.866025i) q^{80} +(7.85901 + 4.38589i) q^{81} +(4.59654 - 2.65381i) q^{82} +(-0.254578 - 0.440942i) q^{83} +(-1.13228 + 4.44049i) q^{84} +(1.15157 - 1.99457i) q^{85} -11.8945i q^{86} +(16.8286 - 7.04261i) q^{87} -0.767810 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} +(-12.8769 + 5.38885i) q^{93} +(-5.59578 + 3.23073i) q^{94} +(-4.19206 + 2.42029i) q^{95} +(-1.59778 + 0.668655i) q^{96} +(-7.61423 + 4.39608i) q^{97} +(1.69673 - 6.79125i) q^{98} +(0.579937 - 2.22923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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