LMFDB - Embedded newform 630.2.t.b.311.12

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			311.12
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.0350998 + 1.73170i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.835450 + 1.51724i) q^{6} +(-1.17997 + 2.36805i) q^{7} +1.00000i q^{8} +(-2.99754 + 0.121564i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.0350998 + 1.73170i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.835450 + 1.51724i) q^{6} +(-1.17997 + 2.36805i) q^{7} +1.00000i q^{8} +(-2.99754 + 0.121564i) q^{9} +(-0.866025 - 0.500000i) q^{10} +0.751037i q^{11} +(-1.48214 + 0.896245i) q^{12} +(-2.72204 - 1.57157i) q^{13} +(-2.20591 + 1.46081i) q^{14} +(-0.0350998 - 1.73170i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.433117 - 0.750180i) q^{17} +(-2.65672 - 1.39349i) q^{18} +(1.23551 - 0.713322i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-4.14216 - 1.96023i) q^{21} +(-0.375518 + 0.650417i) q^{22} +5.06153i q^{23} +(-1.73170 + 0.0350998i) q^{24} +1.00000 q^{25} +(-1.57157 - 2.72204i) q^{26} +(-0.315725 - 5.18655i) q^{27} +(-2.64078 + 0.162142i) q^{28} +(-5.23368 + 3.02167i) q^{29} +(0.835450 - 1.51724i) q^{30} +(5.38301 - 3.10788i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.30057 + 0.0263612i) q^{33} +(0.750180 - 0.433117i) q^{34} +(1.17997 - 2.36805i) q^{35} +(-1.60405 - 2.53516i) q^{36} +(3.60391 + 6.24216i) q^{37} +1.42664 q^{38} +(2.62594 - 4.76891i) q^{39} -1.00000i q^{40} +(-2.08432 + 3.61015i) q^{41} +(-2.60710 - 3.76869i) q^{42} +(3.69510 + 6.40010i) q^{43} +(-0.650417 + 0.375518i) q^{44} +(2.99754 - 0.121564i) q^{45} +(-2.53076 + 4.38341i) q^{46} +(-1.72922 + 2.99510i) q^{47} +(-1.51724 - 0.835450i) q^{48} +(-4.21534 - 5.58846i) q^{49} +(0.866025 + 0.500000i) q^{50} +(1.31429 + 0.723695i) q^{51} -3.14314i q^{52} +(-0.790248 - 0.456250i) q^{53} +(2.31985 - 4.64955i) q^{54} -0.751037i q^{55} +(-2.36805 - 1.17997i) q^{56} +(1.27862 + 2.11449i) q^{57} -6.04334 q^{58} +(-4.21910 - 7.30769i) q^{59} +(1.48214 - 0.896245i) q^{60} +(9.30244 + 5.37077i) q^{61} +6.21576 q^{62} +(3.24913 - 7.24176i) q^{63} -1.00000 q^{64} +(2.72204 + 1.57157i) q^{65} +(-1.13950 - 0.627454i) q^{66} +(5.44637 + 9.43339i) q^{67} +0.866234 q^{68} +(-8.76502 + 0.177659i) q^{69} +(2.20591 - 1.46081i) q^{70} -5.43339i q^{71} +(-0.121564 - 2.99754i) q^{72} +(0.539702 + 0.311597i) q^{73} +7.20782i q^{74} +(0.0350998 + 1.73170i) q^{75} +(1.23551 + 0.713322i) q^{76} +(-1.77849 - 0.886201i) q^{77} +(4.65858 - 2.81702i) q^{78} +(-0.00292607 + 0.00506811i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.97044 - 0.728787i) q^{81} +(-3.61015 + 2.08432i) q^{82} +(1.01834 + 1.76381i) q^{83} +(-0.373471 - 4.56733i) q^{84} +(-0.433117 + 0.750180i) q^{85} +7.39020i q^{86} +(-5.41631 - 8.95708i) q^{87} -0.751037 q^{88} +(-1.22452 - 2.12093i) q^{89} +(2.65672 + 1.39349i) q^{90} +(6.93349 - 4.59153i) q^{91} +(-4.38341 + 2.53076i) q^{92} +(5.57084 + 9.21264i) q^{93} +(-2.99510 + 1.72922i) q^{94} +(-1.23551 + 0.713322i) q^{95} +(-0.896245 - 1.48214i) q^{96} +(9.23519 - 5.33194i) q^{97} +(-0.856363 - 6.94742i) q^{98} +(-0.0912993 - 2.25126i) 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
$3$	0.0350998	+	1.73170i	0.0202649	+	0.999795i
$3$	0.0350998	+	1.73170i	0.0202649	+	0.999795i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.835450	+	1.51724i	−0.341071	+	0.619411i
$7$	−1.17997	+	2.36805i	−0.445987	+	0.895040i
$7$	−1.17997	+	2.36805i	−0.445987	+	0.895040i
$8$			1.00000i			0.353553i
$9$	−2.99754	+	0.121564i	−0.999179	+	0.0405214i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			0.751037i			0.226446i	0.993570	+	0.113223i	$0.0361175\pi$
$11$			0.751037i			0.226446i	−0.993570	+	0.113223i	$0.963883\pi$
$12$	−1.48214	+	0.896245i	−0.427858	+	0.258724i
$13$	−2.72204	−	1.57157i	−0.754958	−	0.435875i	0.0725244	−	0.997367i	$-0.476894\pi$
$13$	−2.72204	−	1.57157i	−0.754958	−	0.435875i	−0.827483	+	0.561491i	$0.810228\pi$
$14$	−2.20591	+	1.46081i	−0.589554	+	0.390417i
$15$	−0.0350998	−	1.73170i	−0.00906273	−	0.447122i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.433117	−	0.750180i	0.105046	−	0.181945i	−0.808711	−	0.588206i	$-0.799834\pi$
$17$	0.433117	−	0.750180i	0.105046	−	0.181945i	0.913757	+	0.406261i	$0.133168\pi$
$18$	−2.65672	−	1.39349i	−0.626196	−	0.328449i
$19$	1.23551	−	0.713322i	0.283446	−	0.163647i	−0.351537	−	0.936174i	$-0.614341\pi$
$19$	1.23551	−	0.713322i	0.283446	−	0.163647i	0.634982	+	0.772527i	$0.281007\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−4.14216	−	1.96023i	−0.903894	−	0.427757i
$22$	−0.375518	+	0.650417i	−0.0800608	+	0.138669i
$23$			5.06153i			1.05540i	0.849430	+	0.527701i	$0.176946\pi$
$23$			5.06153i			1.05540i	−0.849430	+	0.527701i	$0.823054\pi$
$24$	−1.73170	+	0.0350998i	−0.353481	+	0.00716472i
$25$	1.00000			0.200000
$26$	−1.57157	−	2.72204i	−0.308210	−	0.533836i
$27$	−0.315725	−	5.18655i	−0.0607613	−	0.998152i
$28$	−2.64078	+	0.162142i	−0.499060	+	0.0306420i
$29$	−5.23368	+	3.02167i	−0.971870	+	0.561110i	−0.899806	−	0.436290i	$-0.856292\pi$
$29$	−5.23368	+	3.02167i	−0.971870	+	0.561110i	−0.0720645	+	0.997400i	$0.522959\pi$
$30$	0.835450	−	1.51724i	0.152532	−	0.277009i
$31$	5.38301	−	3.10788i	0.966817	−	0.558192i	0.0685524	−	0.997648i	$-0.478162\pi$
$31$	5.38301	−	3.10788i	0.966817	−	0.558192i	0.898264	+	0.439456i	$0.144829\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.30057	+	0.0263612i	−0.226400	+	0.00458890i
$34$	0.750180	−	0.433117i	0.128655	−	0.0742789i
$35$	1.17997	−	2.36805i	0.199451	−	0.400274i
$36$	−1.60405	−	2.53516i	−0.267341	−	0.422527i
$37$	3.60391	+	6.24216i	0.592479	+	1.02620i	0.993897	+	0.110309i	$0.0351842\pi$
$37$	3.60391	+	6.24216i	0.592479	+	1.02620i	−0.401418	+	0.915895i	$0.631482\pi$
$38$	1.42664			0.231432
$39$	2.62594	−	4.76891i	0.420487	−	0.763636i
$40$		−	1.00000i		−	0.158114i
$41$	−2.08432	+	3.61015i	−0.325516	+	0.563811i	−0.981617	−	0.190863i	$-0.938871\pi$
$41$	−2.08432	+	3.61015i	−0.325516	+	0.563811i	0.656101	+	0.754673i	$0.272205\pi$
$42$	−2.60710	−	3.76869i	−0.402285	−	0.581521i
$43$	3.69510	+	6.40010i	0.563497	+	0.976006i	0.997188	+	0.0749440i	$0.0238778\pi$
$43$	3.69510	+	6.40010i	0.563497	+	0.976006i	−0.433690	+	0.901062i	$0.642789\pi$
$44$	−0.650417	+	0.375518i	−0.0980540	+	0.0566115i
$45$	2.99754	−	0.121564i	0.446846	−	0.0181217i
$46$	−2.53076	+	4.38341i	−0.373141	+	0.646299i
$47$	−1.72922	+	2.99510i	−0.252233	+	0.436880i	−0.964140	−	0.265393i	$-0.914498\pi$
$47$	−1.72922	+	2.99510i	−0.252233	+	0.436880i	0.711907	+	0.702273i	$0.247832\pi$
$48$	−1.51724	−	0.835450i	−0.218995	−	0.120587i
$49$	−4.21534	−	5.58846i	−0.602192	−	0.798352i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	1.31429	+	0.723695i	0.184037	+	0.101338i
$52$		−	3.14314i		−	0.435875i
$53$	−0.790248	−	0.456250i	−0.108549	−	0.0626707i	0.444743	−	0.895658i	$-0.353295\pi$
$53$	−0.790248	−	0.456250i	−0.108549	−	0.0626707i	−0.553292	+	0.832988i	$0.686628\pi$
$54$	2.31985	−	4.64955i	0.315692	−	0.632723i
$55$		−	0.751037i		−	0.101270i
$56$	−2.36805	−	1.17997i	−0.316444	−	0.157680i
$57$	1.27862	+	2.11449i	0.169358	+	0.280071i
$58$	−6.04334			−0.793529
$59$	−4.21910	−	7.30769i	−0.549280	−	0.951381i	−0.998324	−	0.0578710i	$-0.981569\pi$
$59$	−4.21910	−	7.30769i	−0.549280	−	0.951381i	0.449044	−	0.893510i	$-0.351765\pi$
$60$	1.48214	−	0.896245i	0.191344	−	0.115705i
$61$	9.30244	+	5.37077i	1.19106	+	0.687656i	0.958546	−	0.284938i	$-0.0919729\pi$
$61$	9.30244	+	5.37077i	1.19106	+	0.687656i	0.232510	+	0.972594i	$0.425306\pi$
$62$	6.21576			0.789403
$63$	3.24913	−	7.24176i	0.409352	−	0.912376i
$64$	−1.00000			−0.125000
$65$	2.72204	+	1.57157i	0.337628	+	0.194929i
$66$	−1.13950	−	0.627454i	−0.140263	−	0.0772342i
$67$	5.44637	+	9.43339i	0.665380	+	1.15247i	0.979182	+	0.202984i	$0.0650639\pi$
$67$	5.44637	+	9.43339i	0.665380	+	1.15247i	−0.313802	+	0.949489i	$0.601603\pi$
$68$	0.866234			0.105046
$69$	−8.76502	+	0.177659i	−1.05518	+	0.0213876i
$70$	2.20591	−	1.46081i	0.263657	−	0.174600i
$71$		−	5.43339i		−	0.644825i	−0.946599	−	0.322413i	$-0.895506\pi$
$71$		−	5.43339i		−	0.644825i	0.946599	−	0.322413i	$-0.104494\pi$
$72$	−0.121564	−	2.99754i	−0.0143265	−	0.353263i
$73$	0.539702	+	0.311597i	0.0631673	+	0.0364697i	0.531251	−	0.847214i	$-0.321722\pi$
$73$	0.539702	+	0.311597i	0.0631673	+	0.0364697i	−0.468084	+	0.883684i	$0.655055\pi$
$74$			7.20782i			0.837892i
$75$	0.0350998	+	1.73170i	0.00405298	+	0.199959i
$76$	1.23551	+	0.713322i	0.141723	+	0.0818237i
$77$	−1.77849	−	0.886201i	−0.202678	−	0.100992i
$78$	4.65858	−	2.81702i	0.527481	−	0.318965i
$79$	−0.00292607	+	0.00506811i	−0.000329209	+	0.000570206i	−0.866190	−	0.499715i	$-0.833438\pi$
$79$	−0.00292607	+	0.00506811i	−0.000329209	+	0.000570206i	0.865861	+	0.500285i	$0.166771\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	8.97044	−	0.728787i	0.996716	−	0.0809763i
$82$	−3.61015	+	2.08432i	−0.398674	+	0.230175i
$83$	1.01834	+	1.76381i	0.111777	+	0.193603i	0.916487	−	0.400065i	$-0.131012\pi$
$83$	1.01834	+	1.76381i	0.111777	+	0.193603i	−0.804710	+	0.593668i	$0.797679\pi$
$84$	−0.373471	−	4.56733i	−0.0407491	−	0.498337i
$85$	−0.433117	+	0.750180i	−0.0469781	+	0.0813685i
$86$			7.39020i			0.796905i
$87$	−5.41631	−	8.95708i	−0.580689	−	0.960300i
$88$	−0.751037			−0.0800608
$89$	−1.22452	−	2.12093i	−0.129799	−	0.224819i	0.793800	−	0.608179i	$-0.208100\pi$
$89$	−1.22452	−	2.12093i	−0.129799	−	0.224819i	−0.923599	+	0.383361i	$0.874767\pi$
$90$	2.65672	+	1.39349i	0.280043	+	0.146887i
$91$	6.93349	−	4.59153i	0.726827	−	0.481323i
$92$	−4.38341	+	2.53076i	−0.457002	+	0.263850i
$93$	5.57084	+	9.21264i	0.577670	+	0.955307i
$94$	−2.99510	+	1.72922i	−0.308921	+	0.178355i
$95$	−1.23551	+	0.713322i	−0.126761	+	0.0731853i
$96$	−0.896245	−	1.48214i	−0.0914726	−	0.151270i
$97$	9.23519	−	5.33194i	0.937692	−	0.541377i	0.0484558	−	0.998825i	$-0.484570\pi$
$97$	9.23519	−	5.33194i	0.937692	−	0.541377i	0.889236	+	0.457449i	$0.151237\pi$
$98$	−0.856363	−	6.94742i	−0.0865057	−	0.701795i
$99$	−0.0912993	−	2.25126i	−0.00917592	−	0.226260i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.74239			−0.571389			−0.285695	−	0.958321i	$-0.592224\pi$
$101$	−5.74239			−0.571389			−0.285695	+	0.958321i	$0.592224\pi$
$102$	0.776357	+	1.28388i	0.0768708	+	0.127123i
$103$			15.6548i			1.54251i	0.636526	+	0.771255i	$0.280371\pi$
$103$			15.6548i			1.54251i	−0.636526	+	0.771255i	$0.719629\pi$
$104$	1.57157	−	2.72204i	0.154105	−	0.266918i
$105$	4.14216	+	1.96023i	0.404234	+	0.191299i
$106$	−0.456250	−	0.790248i	−0.0443149	−	0.0767557i
$107$	11.6558	−	6.72947i	1.12681	−	0.650562i	0.183677	−	0.982987i	$-0.441200\pi$
$107$	11.6558	−	6.72947i	1.12681	−	0.650562i	0.943130	+	0.332425i	$0.107867\pi$
$108$	4.33382	−	2.86670i	0.417022	−	0.275849i
$109$	−6.28955	+	10.8938i	−0.602430	+	1.04344i	0.390022	+	0.920806i	$0.372467\pi$
$109$	−6.28955	+	10.8938i	−0.602430	+	1.04344i	−0.992452	+	0.122634i	$0.960866\pi$
$110$	0.375518	−	0.650417i	0.0358043	−	0.0620148i
$111$	−10.6830	+	6.45997i	−1.01399	+	0.613154i
$112$	−1.46081	−	2.20591i	−0.138033	−	0.208439i
$113$	−2.91695	−	1.68410i	−0.274404	−	0.158427i	0.356484	−	0.934302i	$-0.383976\pi$
$113$	−2.91695	−	1.68410i	−0.274404	−	0.158427i	−0.630887	+	0.775875i	$0.717309\pi$
$114$	0.0500750	+	2.47051i	0.00468995	+	0.231385i
$115$		−	5.06153i		−	0.471990i
$116$	−5.23368	−	3.02167i	−0.485935	−	0.280555i
$117$	8.35046	+	4.37994i	0.772000	+	0.404925i
$118$		−	8.43820i		−	0.776799i
$119$	1.26540	+	1.91083i	0.115999	+	0.175166i
$120$	1.73170	−	0.0350998i	0.158081	−	0.00320416i
$121$	10.4359			0.948722
$122$	5.37077	+	9.30244i	0.486246	+	0.842204i
$123$	−6.32484	−	3.48269i	−0.570291	−	0.314024i
$124$	5.38301	+	3.10788i	0.483408	+	0.279096i
$125$	−1.00000			−0.0894427
$126$	6.43471	−	4.64699i	0.573250	−	0.413986i
$127$	6.31880			0.560703			0.280352	−	0.959897i	$-0.409549\pi$
$127$	6.31880			0.560703			0.280352	+	0.959897i	$0.409549\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−10.9533	+	6.62343i	−0.964386	+	0.583160i
$130$	1.57157	+	2.72204i	0.137836	+	0.238739i
$131$	10.9728			0.958699			0.479350	−	0.877624i	$-0.340873\pi$
$131$	10.9728			0.958699			0.479350	+	0.877624i	$0.340873\pi$
$132$	−0.673113	−	1.11314i	−0.0585870	−	0.0968867i
$133$	0.231319	+	3.76745i	0.0200579	+	0.326680i
$134$			10.8927i			0.940990i
$135$	0.315725	+	5.18655i	0.0271733	+	0.446387i
$136$	0.750180	+	0.433117i	0.0643274	+	0.0371395i
$137$			21.2377i			1.81446i	0.420637	+	0.907229i	$0.361807\pi$
$137$			21.2377i			1.81446i	−0.420637	+	0.907229i	$0.638193\pi$
$138$	−7.67956	−	4.22866i	−0.653728	−	0.359967i
$139$	−8.99525	−	5.19341i	−0.762967	−	0.440499i	0.0673930	−	0.997727i	$-0.478532\pi$
$139$	−8.99525	−	5.19341i	−0.762967	−	0.440499i	−0.830360	+	0.557227i	$0.811865\pi$
$140$	2.64078	−	0.162142i	0.223187	−	0.0137035i
$141$	−5.24729	−	2.88936i	−0.441902	−	0.243328i
$142$	2.71670	−	4.70546i	0.227980	−	0.394873i
$143$	1.18031	−	2.04435i	0.0987023	−	0.170957i
$144$	1.39349	−	2.65672i	0.116124	−	0.221394i
$145$	5.23368	−	3.02167i	0.434634	−	0.250936i
$146$	0.311597	+	0.539702i	0.0257880	+	0.0446660i
$147$	9.52955	−	7.49584i	0.785984	−	0.618247i
$148$	−3.60391	+	6.24216i	−0.296240	+	0.513102i
$149$			12.9684i			1.06241i	0.847242	+	0.531207i	$0.178261\pi$
$149$			12.9684i			1.06241i	−0.847242	+	0.531207i	$0.821739\pi$
$150$	−0.835450	+	1.51724i	−0.0682142	+	0.123882i
$151$	22.9105			1.86443			0.932217	−	0.361900i	$-0.117872\pi$
$151$	22.9105			1.86443			0.932217	+	0.361900i	$0.117872\pi$
$152$	0.713322	+	1.23551i	0.0578581	+	0.100213i
$153$	−1.20709	+	2.30134i	−0.0975873	+	0.186053i
$154$	−1.09712	−	1.65672i	−0.0884085	−	0.133502i
$155$	−5.38301	+	3.10788i	−0.432374	+	0.249631i
$156$	5.44296	−	0.110324i	0.435786	−	0.00883296i
$157$	7.74720	−	4.47285i	0.618294	−	0.356972i	−0.157911	−	0.987453i	$-0.550476\pi$
$157$	7.74720	−	4.47285i	0.618294	−	0.356972i	0.776204	+	0.630481i	$0.217143\pi$
$158$	−0.00506811	+	0.00292607i	−0.000403197	+	0.000232786i
$159$	0.762348	−	1.38448i	0.0604581	−	0.109797i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−11.9860	−	5.97245i	−0.944626	−	0.470695i
$162$	8.13303	+	3.85407i	0.638991	+	0.302805i
$163$	−8.68748	−	15.0472i	−0.680456	−	1.17858i	−0.974842	−	0.222898i	$-0.928448\pi$
$163$	−8.68748	−	15.0472i	−0.680456	−	1.17858i	0.294386	−	0.955687i	$-0.404885\pi$
$164$	−4.16864			−0.325516
$165$	1.30057	−	0.0263612i	0.101249	−	0.00205222i
$166$			2.03667i			0.158076i
$167$	8.49076	−	14.7064i	0.657035	−	1.13802i	−0.324345	−	0.945939i	$-0.605144\pi$
$167$	8.49076	−	14.7064i	0.657035	−	1.13802i	0.981380	−	0.192079i	$-0.0615229\pi$
$168$	1.96023	−	4.14216i	0.151235	−	0.319575i
$169$	−1.56033	−	2.70257i	−0.120025	−	0.207890i
$170$	−0.750180	+	0.433117i	−0.0575362	+	0.0332185i
$171$	−3.61677	+	2.28840i	−0.276582	+	0.174999i
$172$	−3.69510	+	6.40010i	−0.281749	+	0.488003i
$173$	−4.57540	+	7.92483i	−0.347861	+	0.602514i	−0.985869	−	0.167516i	$-0.946425\pi$
$173$	−4.57540	+	7.92483i	−0.347861	+	0.602514i	0.638008	+	0.770030i	$0.279759\pi$
$174$	−0.212120	−	10.4652i	−0.0160808	−	0.793366i
$175$	−1.17997	+	2.36805i	−0.0891973	+	0.179008i
$176$	−0.650417	−	0.375518i	−0.0490270	−	0.0283058i
$177$	12.5066	−	7.56269i	0.940054	−	0.568447i
$178$		−	2.44904i		−	0.183564i
$179$	−17.2805	−	9.97688i	−1.29160	−	0.745707i	−0.312664	−	0.949864i	$-0.601221\pi$
$179$	−17.2805	−	9.97688i	−1.29160	−	0.745707i	−0.978938	+	0.204157i	$0.934555\pi$
$180$	1.60405	+	2.53516i	0.119559	+	0.188960i
$181$		−	21.6898i		−	1.61219i	−0.591784	−	0.806097i	$-0.701576\pi$
$181$		−	21.6898i		−	1.61219i	0.591784	−	0.806097i	$-0.298424\pi$
$182$	8.30034	−	0.509636i	0.615262	−	0.0377767i
$183$	−8.97402	+	16.2975i	−0.663378	+	1.20475i
$184$	−5.06153			−0.373141
$185$	−3.60391	−	6.24216i	−0.264965	−	0.458933i
$186$	0.218172	+	10.7638i	0.0159971	+	0.789240i
$187$	0.563413	+	0.325287i	0.0412008	+	0.0237873i
$188$	−3.45844			−0.252233
$189$	12.6546	+	5.37232i	0.920485	+	0.390779i
$190$	−1.42664			−0.103500
$191$	−6.10266	−	3.52337i	−0.441573	−	0.254942i	0.262692	−	0.964880i	$-0.415390\pi$
$191$	−6.10266	−	3.52337i	−0.441573	−	0.254942i	−0.704265	+	0.709938i	$0.748723\pi$
$192$	−0.0350998	−	1.73170i	−0.00253311	−	0.124974i
$193$	1.20239	+	2.08260i	0.0865498	+	0.149909i	0.906051	−	0.423169i	$-0.139083\pi$
$193$	1.20239	+	2.08260i	0.0865498	+	0.149909i	−0.819501	+	0.573078i	$0.805749\pi$
$194$	10.6639			0.765622
$195$	−2.62594	+	4.76891i	−0.188047	+	0.341508i
$196$	2.73208	−	6.44482i	0.195148	−	0.460345i
$197$		−	1.58424i		−	0.112873i	−0.998406	−	0.0564364i	$-0.982026\pi$
$197$		−	1.58424i		−	0.112873i	0.998406	−	0.0564364i	$-0.0179738\pi$
$198$	1.04656	−	1.99530i	0.0743759	−	0.141800i
$199$	6.71297	+	3.87574i	0.475870	+	0.274744i	0.718694	−	0.695327i	$-0.244740\pi$
$199$	6.71297	+	3.87574i	0.475870	+	0.274744i	−0.242824	+	0.970070i	$0.578074\pi$
$200$			1.00000i			0.0707107i
$201$	−16.1446	+	9.76257i	−1.13875	+	0.688598i
$202$	−4.97305	−	2.87119i	−0.349903	−	0.202017i
$203$	−0.979879	−	15.9591i	−0.0687740	−	1.12011i
$204$	0.0304046	+	1.50005i	0.00212875	+	0.105025i
$205$	2.08432	−	3.61015i	0.145575	−	0.252144i
$206$	−7.82738	+	13.5574i	−0.545360	+	0.944591i
$207$	−0.615301	−	15.1721i	−0.0427664	−	1.05453i
$208$	2.72204	−	1.57157i	0.188740	−	0.108969i
$209$	0.535731	+	0.927914i	0.0370573	+	0.0641851i
$210$	2.60710	+	3.76869i	0.179907	+	0.260064i
$211$	6.64182	−	11.5040i	0.457242	−	0.791966i	−0.541572	−	0.840654i	$-0.682171\pi$
$211$	6.64182	−	11.5040i	0.457242	−	0.791966i	0.998814	+	0.0486881i	$0.0155040\pi$
$212$		−	0.912500i		−	0.0626707i
$213$	9.40898	−	0.190711i	0.644693	−	0.0130673i
$214$	13.4589			0.920034
$215$	−3.69510	−	6.40010i	−0.252004	−	0.436483i
$216$	5.18655	−	0.315725i	0.352900	−	0.0214824i
$217$	1.00784	+	16.4144i	0.0684164	+	1.11429i
$218$	−10.8938	+	6.28955i	−0.737823	+	0.425982i
$219$	−0.520648	+	0.945536i	−0.0351821	+	0.0638934i
$220$	0.650417	−	0.375518i	0.0438511	−	0.0253174i
$221$	−2.35792	+	1.36135i	−0.158611	+	0.0915742i
$222$	−12.4818	+	0.252993i	−0.837720	+	0.0169798i
$223$	−13.8018	+	7.96848i	−0.924237	+	0.533609i	−0.884984	−	0.465621i	$-0.845831\pi$
$223$	−13.8018	+	7.96848i	−0.924237	+	0.533609i	−0.0392529	+	0.999229i	$0.512498\pi$
$224$	−0.162142	−	2.64078i	−0.0108336	−	0.176444i
$225$	−2.99754	+	0.121564i	−0.199836	+	0.00810429i
$226$	−1.68410	−	2.91695i	−0.112025	−	0.194033i
$227$	−13.1879			−0.875314			−0.437657	−	0.899142i	$-0.644192\pi$
$227$	−13.1879			−0.875314			−0.437657	+	0.899142i	$0.644192\pi$
$228$	−1.19189	+	2.16457i	−0.0789349	+	0.143352i
$229$		−	19.7537i		−	1.30536i	−0.757633	−	0.652681i	$-0.773644\pi$
$229$		−	19.7537i		−	1.30536i	0.757633	−	0.652681i	$-0.226356\pi$
$230$	2.53076	−	4.38341i	0.166874	−	0.289034i
$231$	1.47220	−	3.11092i	0.0968640	−	0.204683i
$232$	−3.02167	−	5.23368i	−0.198382	−	0.343608i
$233$	23.8501	−	13.7699i	1.56247	−	0.902094i	0.565467	−	0.824771i	$-0.308696\pi$
$233$	23.8501	−	13.7699i	1.56247	−	0.902094i	0.997006	−	0.0773231i	$-0.0246373\pi$
$234$	5.04174	+	7.96837i	0.329589	+	0.520909i
$235$	1.72922	−	2.99510i	0.112802	−	0.195379i
$236$	4.21910	−	7.30769i	0.274640	−	0.475690i
$237$	−0.00887912	−	0.00488918i	−0.000576761	−	0.000317586i
$238$	0.140453	+	2.28753i	0.00910421	+	0.148279i
$239$	6.52234	+	3.76567i	0.421895	+	0.243581i	0.695888	−	0.718151i	$-0.255011\pi$
$239$	6.52234	+	3.76567i	0.421895	+	0.243581i	−0.273993	+	0.961732i	$0.588344\pi$
$240$	1.51724	+	0.835450i	0.0979375	+	0.0539281i
$241$		−	11.9813i		−	0.771785i	−0.922544	−	0.385892i	$-0.873894\pi$
$241$		−	11.9813i		−	0.771785i	0.922544	−	0.385892i	$-0.126106\pi$
$242$	9.03779	+	5.21797i	0.580971	+	0.335424i
$243$	1.57690	+	15.5085i	0.101158	+	0.994870i
$244$			10.7415i			0.687656i
$245$	4.21534	+	5.58846i	0.269308	+	0.357034i
$246$	−3.73612	−	6.17852i	−0.238206	−	0.393928i
$247$	−4.48415			−0.285319
$248$	3.10788	+	5.38301i	0.197351	+	0.341821i
$249$	−3.01864	+	1.82536i	−0.191298	+	0.115677i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	−30.3694			−1.91690			−0.958449	−	0.285265i	$-0.907918\pi$
$251$	−30.3694			−1.91690			−0.958449	+	0.285265i	$0.907918\pi$
$252$	7.89612	−	0.807051i	0.497409	−	0.0508394i
$253$	−3.80139			−0.238992
$254$	5.47224	+	3.15940i	0.343359	+	0.198238i
$255$	−1.31429	−	0.723695i	−0.0823038	−	0.0453195i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.800054			−0.0499060			−0.0249530	−	0.999689i	$-0.507944\pi$
$257$	−0.800054			−0.0499060			−0.0249530	+	0.999689i	$0.507944\pi$
$258$	−12.7976	+	0.259394i	−0.796742	+	0.0161492i
$259$	−19.0343	+	1.16869i	−1.18273	+	0.0726190i
$260$			3.14314i			0.194929i
$261$	15.3208	−	9.69379i	0.948335	−	0.600030i
$262$	9.50274	+	5.48641i	0.587081	+	0.338951i
$263$		−	20.8541i		−	1.28592i	−0.765900	−	0.642960i	$-0.777706\pi$
$263$		−	20.8541i		−	1.28592i	0.765900	−	0.642960i	$-0.222294\pi$
$264$	−0.0263612	−	1.30057i	−0.00162242	−	0.0800443i
$265$	0.790248	+	0.456250i	0.0485445	+	0.0280272i
$266$	−1.68340	+	3.37837i	−0.103216	+	0.207141i
$267$	3.62983	−	2.19494i	0.222142	−	0.134328i
$268$	−5.44637	+	9.43339i	−0.332690	+	0.576236i
$269$	−15.0545	+	26.0752i	−0.917889	+	1.58983i	−0.115273	+	0.993334i	$0.536774\pi$
$269$	−15.0545	+	26.0752i	−0.917889	+	1.58983i	−0.802616	+	0.596497i	$0.796559\pi$
$270$	−2.31985	+	4.64955i	−0.141182	+	0.282962i
$271$	−12.3296	+	7.11850i	−0.748970	+	0.432418i	−0.825322	−	0.564663i	$-0.809006\pi$
$271$	−12.3296	+	7.11850i	−0.748970	+	0.432418i	0.0763514	+	0.997081i	$0.475673\pi$
$272$	0.433117	+	0.750180i	0.0262616	+	0.0454864i
$273$	8.19449	+	11.8455i	0.495953	+	0.716924i
$274$	−10.6188	+	18.3924i	−0.641508	+	1.11112i
$275$			0.751037i			0.0452892i
$276$	−4.53637	−	7.50190i	−0.273057	−	0.451562i
$277$	−16.9306			−1.01726			−0.508631	−	0.860985i	$-0.669848\pi$
$277$	−16.9306			−1.01726			−0.508631	+	0.860985i	$0.669848\pi$
$278$	−5.19341	−	8.99525i	−0.311480	−	0.539499i
$279$	−15.7580	+	9.97037i	−0.943404	+	0.596910i
$280$	2.36805	+	1.17997i	0.141518	+	0.0705167i
$281$	−16.7637	+	9.67853i	−1.00004	+	0.577373i	−0.908260	−	0.418407i	$-0.862589\pi$
$281$	−16.7637	+	9.67853i	−1.00004	+	0.577373i	−0.0917791	+	0.995779i	$0.529255\pi$
$282$	−3.09961	−	5.12590i	−0.184579	−	0.305243i
$283$	26.4542	−	15.2734i	1.57254	−	0.907907i	0.576685	−	0.816966i	$-0.304346\pi$
$283$	26.4542	−	15.2734i	1.57254	−	0.907907i	0.995856	−	0.0909409i	$-0.0289874\pi$
$284$	4.70546	−	2.71670i	0.279218	−	0.161206i
$285$	−1.27862	−	2.11449i	−0.0757391	−	0.125252i
$286$	2.04435	−	1.18031i	0.120885	−	0.0697930i
$287$	−6.08958	−	9.19565i	−0.359457	−	0.542802i
$288$	2.53516	−	1.60405i	0.149386	−	0.0945193i
$289$	8.12482	+	14.0726i	0.477931	+	0.827800i
$290$	6.04334			0.354877
$291$	9.55745	+	15.8054i	0.560268	+	0.926528i
$292$			0.623194i			0.0364697i
$293$	0.844143	−	1.46210i	0.0493154	−	0.0854167i	−0.840314	−	0.542100i	$-0.817629\pi$
$293$	0.844143	−	1.46210i	0.0493154	−	0.0854167i	0.889629	+	0.456683i	$0.150963\pi$
$294$	12.0008	−	1.72681i	0.699898	−	0.100710i
$295$	4.21910	+	7.30769i	0.245645	+	0.425470i
$296$	−6.24216	+	3.60391i	−0.362818	+	0.209473i
$297$	3.89529	−	0.237121i	0.226028	−	0.0137592i
$298$	−6.48421	+	11.2310i	−0.375620	+	0.650593i
$299$	7.95455	−	13.7777i	0.460024	−	0.796784i
$300$	−1.48214	+	0.896245i	−0.0855715	+	0.0517447i
$301$	−19.5159	+	1.19826i	−1.12488	+	0.0690667i
$302$	19.8411	+	11.4553i	1.14173	+	0.659177i
$303$	−0.201557	−	9.94407i	−0.0115791	−	0.571272i
$304$			1.42664i			0.0818237i
$305$	−9.30244	−	5.37077i	−0.532656	−	0.307529i
$306$	−2.19604	+	1.38948i	−0.125539	+	0.0794312i
$307$		−	7.15873i		−	0.408570i	−0.978911	−	0.204285i	$-0.934513\pi$
$307$		−	7.15873i		−	0.408570i	0.978911	−	0.204285i	$-0.0654869\pi$
$308$	−0.121775	−	1.98332i	−0.00693876	−	0.113010i
$309$	−27.1093	+	0.549479i	−1.54219	+	0.0312588i
$310$	−6.21576			−0.353032
$311$	12.3177	+	21.3350i	0.698475	+	1.20979i	0.968995	+	0.247080i	$0.0794711\pi$
$311$	12.3177	+	21.3350i	0.698475	+	1.20979i	−0.270520	+	0.962714i	$0.587196\pi$
$312$	4.76891	+	2.62594i	0.269986	+	0.148665i
$313$	−11.0002	−	6.35095i	−0.621766	−	0.358977i	0.155790	−	0.987790i	$-0.450208\pi$
$313$	−11.0002	−	6.35095i	−0.621766	−	0.358977i	−0.777556	+	0.628813i	$0.783541\pi$
$314$	8.94569			0.504835
$315$	−3.24913	+	7.24176i	−0.183068	+	0.408027i
$316$	−0.00585214			−0.000329209
$317$	22.1158	+	12.7685i	1.24214	+	0.717152i	0.969530	−	0.244971i	$-0.0787784\pi$
$317$	22.1158	+	12.7685i	1.24214	+	0.717152i	0.272614	+	0.962123i	$0.412112\pi$
$318$	1.35245	−	0.817823i	0.0758419	−	0.0458612i
$319$	−2.26938	−	3.93069i	−0.127061	−	0.220076i
$320$	1.00000			0.0559017
$321$	12.0625	+	19.9480i	0.673263	+	1.11339i
$322$	−7.39392	−	11.1653i	−0.412047	−	0.622217i
$323$		−	1.23581i		−	0.0687622i
$324$	5.11637	+	7.40424i	0.284243	+	0.411347i
$325$	−2.72204	−	1.57157i	−0.150992	−	0.0871751i
$326$		−	17.3750i		−	0.962310i
$327$	−19.0855	−	10.5092i	−1.05543	−	0.581161i
$328$	−3.61015	−	2.08432i	−0.199337	−	0.115087i
$329$	−5.05212	−	7.62901i	−0.278532	−	0.420601i
$330$	1.13950	+	0.627454i	0.0627277	+	0.0345402i
$331$	7.01463	−	12.1497i	0.385559	−	0.667807i	−0.606288	−	0.795245i	$-0.707342\pi$
$331$	7.01463	−	12.1497i	0.385559	−	0.667807i	0.991847	+	0.127438i	$0.0406754\pi$
$332$	−1.01834	+	1.76381i	−0.0558884	+	0.0968016i
$333$	−11.5617	−	18.2730i	−0.633576	−	1.00135i
$334$	14.7064	−	8.49076i	0.804700	−	0.464594i
$335$	−5.44637	−	9.43339i	−0.297567	−	0.515401i
$336$	3.76869	−	2.60710i	0.205599	−	0.142229i
$337$	13.7946	−	23.8930i	0.751442	−	1.30154i	−0.195682	−	0.980667i	$-0.562692\pi$
$337$	13.7946	−	23.8930i	0.751442	−	1.30154i	0.947124	−	0.320868i	$-0.103975\pi$
$338$		−	3.12066i		−	0.169741i
$339$	2.81397	−	5.11038i	0.152834	−	0.277558i
$340$	−0.866234			−0.0469781
$341$	2.33413	+	4.04284i	0.126400	+	0.218932i
$342$	−4.27642	+	0.173429i	−0.231242	+	0.00937797i
$343$	18.2077	−	3.38793i	0.983126	−	0.182931i
$344$	−6.40010	+	3.69510i	−0.345070	+	0.199226i
$345$	8.76502	−	0.177659i	0.471893	−	0.00956482i
$346$	−7.92483	+	4.57540i	−0.426041	+	0.245975i
$347$	−10.1962	+	5.88676i	−0.547359	+	0.316018i	−0.748056	−	0.663635i	$-0.769013\pi$
$347$	−10.1962	+	5.88676i	−0.547359	+	0.316018i	0.200697	+	0.979653i	$0.435679\pi$
$348$	5.04891	−	9.16920i	0.270650	−	0.491521i
$349$	−25.3085	+	14.6119i	−1.35473	+	0.782155i	−0.988908	−	0.148530i	$-0.952546\pi$
$349$	−25.3085	+	14.6119i	−1.35473	+	0.782155i	−0.365824	+	0.930684i	$0.619213\pi$
$350$	−2.20591	+	1.46081i	−0.117911	+	0.0780835i
$351$	−7.29162	+	14.6142i	−0.389198	+	0.780048i
$352$	−0.375518	−	0.650417i	−0.0200152	−	0.0346673i
$353$	0.301856			0.0160662			0.00803309	−	0.999968i	$-0.497443\pi$
$353$	0.301856			0.0160662			0.00803309	+	0.999968i	$0.497443\pi$
$354$	14.6124	−	0.296179i	0.776639	−	0.0157417i
$355$			5.43339i			0.288375i
$356$	1.22452	−	2.12093i	0.0648995	−	0.112409i
$357$	−3.26457	+	2.25836i	−0.172779	+	0.119525i
$358$	−9.97688	−	17.2805i	−0.527294	−	0.913301i
$359$	22.8586	−	13.1974i	1.20643	−	0.696534i	0.244455	−	0.969661i	$-0.421391\pi$
$359$	22.8586	−	13.1974i	1.20643	−	0.696534i	0.961978	+	0.273126i	$0.0880577\pi$
$360$	0.121564	+	2.99754i	0.00640700	+	0.157984i
$361$	−8.48234	+	14.6918i	−0.446439	+	0.773255i
$362$	10.8449	−	18.7840i	0.569996	−	0.987263i
$363$	0.366300	+	18.0719i	0.0192257	+	0.948527i
$364$	7.44312	+	3.70881i	0.390126	+	0.194395i
$365$	−0.539702	−	0.311597i	−0.0282493	−	0.0163097i
$366$	−15.9205	+	9.62705i	−0.832177	+	0.503214i
$367$			9.73338i			0.508079i	0.967194	+	0.254039i	$0.0817592\pi$
$367$			9.73338i			0.508079i	−0.967194	+	0.254039i	$0.918241\pi$
$368$	−4.38341	−	2.53076i	−0.228501	−	0.131925i
$369$	5.80896	−	11.0749i	0.302402	−	0.576538i
$370$		−	7.20782i		−	0.374717i
$371$	2.01289	−	1.33299i	0.104504	−	0.0692052i
$372$	−5.19296	+	9.43081i	−0.269242	+	0.488965i
$373$	−19.2585			−0.997168			−0.498584	−	0.866841i	$-0.666146\pi$
$373$	−19.2585			−0.997168			−0.498584	+	0.866841i	$0.666146\pi$
$374$	0.325287	+	0.563413i	0.0168202	+	0.0291334i
$375$	−0.0350998	−	1.73170i	−0.00181255	−	0.0894244i
$376$	−2.99510	−	1.72922i	−0.154460	−	0.0891777i
$377$	18.9951			0.978296
$378$	8.27302	+	10.9799i	0.425518	+	0.564743i
$379$	−29.4361			−1.51203			−0.756015	−	0.654554i	$-0.772856\pi$
$379$	−29.4361			−1.51203			−0.756015	+	0.654554i	$0.772856\pi$
$380$	−1.23551	−	0.713322i	−0.0633804	−	0.0365927i
$381$	0.221789	+	10.9422i	0.0113626	+	0.560588i
$382$	−3.52337	−	6.10266i	−0.180271	−	0.312239i
$383$	17.8073			0.909912			0.454956	−	0.890514i	$-0.349655\pi$
$383$	17.8073			0.909912			0.454956	+	0.890514i	$0.349655\pi$
$384$	0.835450	−	1.51724i	0.0426339	−	0.0774264i
$385$	1.77849	+	0.886201i	0.0906405	+	0.0451650i
$386$			2.40478i			0.122400i
$387$	−11.8542	−	18.7353i	−0.602584	−	0.952371i
$388$	9.23519	+	5.33194i	0.468846	+	0.270688i
$389$			12.5302i			0.635306i	0.948207	+	0.317653i	$0.102895\pi$
$389$			12.5302i			0.635306i	−0.948207	+	0.317653i	$0.897105\pi$
$390$	−4.65858	+	2.81702i	−0.235897	+	0.142646i
$391$	3.79706	+	2.19223i	0.192026	+	0.110866i
$392$	5.58846	−	4.21534i	0.282260	−	0.212907i
$393$	0.385144	+	19.0016i	0.0194279	+	0.958502i
$394$	0.792122	−	1.37200i	0.0399066	−	0.0691202i
$395$	0.00292607	−	0.00506811i	0.000147227	−	0.000255004i
$396$	1.90400	−	1.20470i	0.0956795	−	0.0605383i
$397$	−26.6549	+	15.3892i	−1.33777	+	0.772361i	−0.986476	−	0.163905i	$-0.947591\pi$
$397$	−26.6549	+	15.3892i	−1.33777	+	0.772361i	−0.351293	+	0.936266i	$0.614258\pi$
$398$	3.87574	+	6.71297i	0.194273	+	0.336491i
$399$	−6.51596	+	0.532811i	−0.326206	+	0.0266739i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	7.17154i		−	0.358129i	−0.983837	−	0.179065i	$-0.942693\pi$
$401$		−	7.17154i		−	0.358129i	0.983837	−	0.179065i	$-0.0573071\pi$
$402$	−18.8629	+	0.382333i	−0.940797	+	0.0190690i
$403$	−19.5370			−0.973208
$404$	−2.87119	−	4.97305i	−0.142847	−	0.247419i
$405$	−8.97044	+	0.728787i	−0.445745	+	0.0362137i
$406$	7.13096	−	14.3109i	0.353903	−	0.710240i
$407$	−4.68809	+	2.70667i	−0.232380	+	0.134165i
$408$	−0.723695	+	1.31429i	−0.0358282	+	0.0650669i
$409$	23.0919	−	13.3321i	1.14182	−	0.659232i	0.194942	−	0.980815i	$-0.437548\pi$
$409$	23.0919	−	13.3321i	1.14182	−	0.659232i	0.946881	+	0.321583i	$0.104215\pi$
$410$	3.61015	−	2.08432i	0.178293	−	0.102937i
$411$	−36.7772	+	0.745439i	−1.81409	+	0.0367698i
$412$	−13.5574	+	7.82738i	−0.667926	+	0.385627i
$413$	22.2834	−	1.36819i	1.09649	−	0.0673241i
$414$	7.05319	−	13.4471i	0.346645	−	0.660888i
$415$	−1.01834	−	1.76381i	−0.0499881	−	0.0865820i
$416$	3.14314			0.154105
$417$	8.67767	−	15.7593i	0.424947	−	0.771737i
$418$			1.07146i			0.0524070i
$419$	12.2128	−	21.1533i	0.596636	−	1.03340i	−0.396677	−	0.917958i	$-0.629837\pi$
$419$	12.2128	−	21.1533i	0.596636	−	1.03340i	0.993314	−	0.115446i	$-0.0368298\pi$
$420$	0.373471	+	4.56733i	0.0182235	+	0.222863i
$421$	8.84702	+	15.3235i	0.431177	+	0.746821i	0.996975	−	0.0777229i	$-0.0247649\pi$
$421$	8.84702	+	15.3235i	0.431177	+	0.746821i	−0.565798	+	0.824544i	$0.691432\pi$
$422$	11.5040	−	6.64182i	0.560005	−	0.323319i
$423$	4.81930	−	9.18813i	0.234323	−	0.446742i
$424$	0.456250	−	0.790248i	0.0221574	−	0.0383778i
$425$	0.433117	−	0.750180i	0.0210093	−	0.0363891i
$426$	8.24377	+	4.53933i	0.399412	+	0.219931i
$427$	−23.6949	+	15.6913i	−1.14667	+	0.759356i
$428$	11.6558	+	6.72947i	0.563403	+	0.325281i
$429$	3.58162	+	1.97218i	0.172922	+	0.0952176i
$430$		−	7.39020i		−	0.356387i
$431$	−20.5184	−	11.8463i	−0.988335	−	0.570616i	−0.0835591	−	0.996503i	$-0.526629\pi$
$431$	−20.5184	−	11.8463i	−0.988335	−	0.570616i	−0.904776	+	0.425887i	$0.859962\pi$
$432$	4.64955	+	2.31985i	0.223701	+	0.111614i
$433$		−	24.1077i		−	1.15854i	−0.815135	−	0.579271i	$-0.803337\pi$
$433$		−	24.1077i		−	1.15854i	0.815135	−	0.579271i	$-0.196663\pi$
$434$	−7.33441	+	14.7192i	−0.352063	+	0.706547i
$435$	5.41631	+	8.95708i	0.259692	+	0.429459i
$436$	−12.5791			−0.602430
$437$	3.61050	+	6.25357i	0.172714	+	0.299149i
$438$	−0.923662	+	0.558534i	−0.0441343	+	0.0266878i
$439$	−0.925536	−	0.534359i	−0.0441734	−	0.0255035i	0.477751	−	0.878495i	$-0.341452\pi$
$439$	−0.925536	−	0.534359i	−0.0441734	−	0.0255035i	−0.521924	+	0.852992i	$0.674786\pi$
$440$	0.751037			0.0358043
$441$	13.3150	+	16.2392i	0.634047	+	0.773294i
$442$	−2.72270			−0.129505
$443$	−26.8115	−	15.4796i	−1.27385	−	0.735459i	−0.298142	−	0.954522i	$-0.596367\pi$
$443$	−26.8115	−	15.4796i	−1.27385	−	0.735459i	−0.975711	+	0.219062i	$0.929700\pi$
$444$	−10.9360	−	6.02178i	−0.519000	−	0.285781i
$445$	1.22452	+	2.12093i	0.0580479	+	0.100542i
$446$	−15.9370			−0.754637
$447$	−22.4574	+	0.455189i	−1.06220	+	0.0215297i
$448$	1.17997	−	2.36805i	0.0557483	−	0.111880i
$449$		−	22.4824i		−	1.06101i	−0.847682	−	0.530505i	$-0.822002\pi$
$449$		−	22.4824i		−	1.06101i	0.847682	−	0.530505i	$-0.177998\pi$
$450$	−2.65672	−	1.39349i	−0.125239	−	0.0656898i
$451$	−2.71135	−	1.56540i	−0.127673	−	0.0737119i
$452$		−	3.36820i		−	0.158427i
$453$	0.804155	+	39.6741i	0.0377825	+	1.86405i
$454$	−11.4211	−	6.59397i	−0.536018	−	0.309470i
$455$	−6.93349	+	4.59153i	−0.325047	+	0.215254i
$456$	−2.11449	+	1.27862i	−0.0990201	+	0.0598770i
$457$	−20.6626	+	35.7886i	−0.966554	+	1.67412i	−0.261174	+	0.965292i	$0.584110\pi$
$457$	−20.6626	+	35.7886i	−0.966554	+	1.67412i	−0.705380	+	0.708829i	$0.749224\pi$
$458$	9.87685	−	17.1072i	0.461515	−	0.799367i
$459$	−4.02760	−	2.00953i	−0.187992	−	0.0937969i
$460$	4.38341	−	2.53076i	0.204378	−	0.117997i
$461$	−13.0109	−	22.5356i	−0.605979	−	1.04959i	−0.991896	−	0.127052i	$-0.959448\pi$
$461$	−13.0109	−	22.5356i	−0.605979	−	1.04959i	0.385917	−	0.922533i	$-0.373885\pi$
$462$	2.83042	−	1.95803i	0.131683	−	0.0910958i
$463$	−5.54762	+	9.60876i	−0.257820	+	0.446557i	−0.965658	−	0.259818i	$-0.916337\pi$
$463$	−5.54762	+	9.60876i	−0.257820	+	0.446557i	0.707838	+	0.706375i	$0.249671\pi$
$464$		−	6.04334i		−	0.280555i
$465$	−5.57084	−	9.21264i	−0.258342	−	0.427226i
$466$	27.5397			1.27575
$467$	18.7366	+	32.4527i	0.867025	+	1.50173i	0.865022	+	0.501734i	$0.167304\pi$
$467$	18.7366	+	32.4527i	0.867025	+	1.50173i	0.00200339	+	0.999998i	$0.499362\pi$
$468$	0.382094	+	9.42168i	0.0176623	+	0.435517i
$469$	−28.7653	+	1.76617i	−1.32826	+	0.0815543i
$470$	2.99510	−	1.72922i	0.138154	−	0.0797630i
$471$	8.01753	+	13.2588i	0.369428	+	0.610933i
$472$	7.30769	−	4.21910i	0.336364	−	0.194200i
$473$	−4.80671	+	2.77515i	−0.221013	+	0.127602i
$474$	−0.00524495	−	0.00867371i	−0.000240909	−	0.000398397i
$475$	1.23551	−	0.713322i	0.0566891	−	0.0327295i
$476$	−1.02213	+	2.05129i	−0.0468492	+	0.0940206i
$477$	2.42426	+	1.27156i	0.110999	+	0.0582207i
$478$	3.76567	+	6.52234i	0.172238	+	0.298325i
$479$	13.9632			0.637996			0.318998	−	0.947755i	$-0.396654\pi$
$479$	13.9632			0.637996			0.318998	+	0.947755i	$0.396654\pi$
$480$	0.896245	+	1.48214i	0.0409078	+	0.0676502i
$481$		−	22.6552i		−	1.03299i
$482$	5.99066	−	10.3761i	0.272867	−	0.472620i
$483$	9.92176	−	20.9657i	0.451456	−	0.953971i
$484$	5.21797	+	9.03779i	0.237181	+	0.410809i
$485$	−9.23519	+	5.33194i	−0.419349	+	0.242111i
$486$	−6.38861	+	14.2192i	−0.289793	+	0.644996i
$487$	1.90704	−	3.30309i	0.0864163	−	0.149677i	−0.819578	−	0.572968i	$-0.805792\pi$
$487$	1.90704	−	3.30309i	0.0864163	−	0.149677i	0.905994	+	0.423291i	$0.139125\pi$
$488$	−5.37077	+	9.30244i	−0.243123	+	0.421102i
$489$	25.7522	−	15.5722i	1.16455	−	0.704200i
$490$	0.856363	+	6.94742i	0.0386865	+	0.313852i
$491$	23.7383	+	13.7053i	1.07129	+	0.618512i	0.928535	−	0.371245i	$-0.121069\pi$
$491$	23.7383	+	13.7053i	1.07129	+	0.618512i	0.142760	+	0.989757i	$0.454402\pi$
$492$	−0.146318	−	7.21881i	−0.00659655	−	0.325449i
$493$			5.23494i			0.235770i
$494$	−3.88339	−	2.24207i	−0.174722	−	0.100876i
$495$	0.0912993	+	2.25126i	0.00410360	+	0.101187i
$496$			6.21576i			0.279096i
$497$	12.8666	+	6.41124i	0.577144	+	0.287584i
$498$	−3.52689	+	0.0714868i	−0.158044	+	0.00320340i
$499$	25.7894			1.15449			0.577247	−	0.816570i	$-0.304127\pi$
$499$	25.7894			1.15449			0.577247	+	0.816570i	$0.304127\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	25.7651	+	14.1872i	1.15110	+	0.633838i
$502$	−26.3006	−	15.1847i	−1.17386	−	0.677726i
$503$	17.3517			0.773675			0.386838	−	0.922148i	$-0.373567\pi$
$503$	17.3517			0.773675			0.386838	+	0.922148i	$0.373567\pi$
$504$	7.24176	+	3.24913i	0.322574	+	0.144728i
$505$	5.74239			0.255533
$506$	−3.29210	−	1.90070i	−0.146352	−	0.0844963i
$507$	4.62526	−	2.79687i	0.205415	−	0.124214i
$508$	3.15940	+	5.47224i	0.140176	+	0.242792i
$509$	28.1334			1.24699			0.623497	−	0.781826i	$-0.285712\pi$
$509$	28.1334			1.24699			0.623497	+	0.781826i	$0.285712\pi$
$510$	−0.776357	−	1.28388i	−0.0343777	−	0.0568512i
$511$	−1.37471	+	0.910367i	−0.0608136	+	0.0402723i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.08977	−	6.18283i	−0.180568	−	0.272978i
$514$	−0.692867	−	0.400027i	−0.0305611	−	0.0176444i
$515$		−	15.6548i		−	0.689831i
$516$	−11.2127	−	6.17414i	−0.493612	−	0.271801i
$517$	−2.24943	−	1.29871i	−0.0989298	−	0.0571171i
$518$	−17.0685	−	8.50501i	−0.749947	−	0.373689i
$519$	−13.8840	−	7.64504i	−0.609439	−	0.335580i
$520$	−1.57157	+	2.72204i	−0.0689179	+	0.119369i
$521$	3.97534	−	6.88549i	0.174163	−	0.301659i	−0.765708	−	0.643188i	$-0.777611\pi$
$521$	3.97534	−	6.88549i	0.174163	−	0.301659i	0.939871	+	0.341529i	$0.110945\pi$
$522$	18.1151	−	0.734654i	0.792877	−	0.0321549i
$523$	0.614490	−	0.354776i	0.0268698	−	0.0155133i	−0.486505	−	0.873678i	$-0.661728\pi$
$523$	0.614490	−	0.354776i	0.0268698	−	0.0155133i	0.513375	+	0.858165i	$0.328395\pi$
$524$	5.48641	+	9.50274i	0.239675	+	0.415129i
$525$	−4.14216	−	1.96023i	−0.180779	−	0.0855515i
$526$	10.4271	−	18.0602i	0.454641	−	0.787462i
$527$		−	5.38430i		−	0.234544i
$528$	0.627454	−	1.13950i	0.0273064	−	0.0495906i
$529$	−2.61907			−0.113873
$530$	0.456250	+	0.790248i	0.0198182	+	0.0343262i
$531$	13.5353	+	21.3922i	0.587380	+	0.928342i
$532$	−3.14705	+	2.08405i	−0.136442	+	0.0903552i
$533$	11.3472	−	6.55131i	0.491502	−	0.283769i
$534$	4.24100	−	0.0859610i	0.183526	−	0.00371989i
$535$	−11.6558	+	6.72947i	−0.503923	+	0.290940i
$536$	−9.43339	+	5.44637i	−0.407461	+	0.235247i
$537$	16.6704	−	30.2747i	0.719380	−	1.30645i
$538$	−26.0752	+	15.0545i	−1.12418	+	0.649046i
$539$	4.19714	−	3.16588i	0.180784	−	0.136364i
$540$	−4.33382	+	2.86670i	−0.186498	+	0.123363i
$541$	−0.152089	−	0.263426i	−0.00653882	−	0.0113256i	0.862737	−	0.505652i	$-0.168748\pi$
$541$	−0.152089	−	0.263426i	−0.00653882	−	0.0113256i	−0.869276	+	0.494327i	$0.835415\pi$
$542$	−14.2370			−0.611532
$543$	37.5602	−	0.761309i	1.61186	−	0.0326709i
$544$			0.866234i			0.0371395i
$545$	6.28955	−	10.8938i	0.269415	−	0.466640i
$546$	1.17387	+	14.3558i	0.0502372	+	0.614370i
$547$	4.14876	+	7.18586i	0.177388	+	0.307245i	0.940985	−	0.338448i	$-0.109902\pi$
$547$	4.14876	+	7.18586i	0.177388	+	0.307245i	−0.763597	+	0.645693i	$0.776569\pi$
$548$	−18.3924	+	10.6188i	−0.785684	+	0.453615i
$549$	−28.5373	−	14.9682i	−1.21794	−	0.638828i
$550$	−0.375518	+	0.650417i	−0.0160122	+	0.0277339i
$551$	−4.31085	+	7.46661i	−0.183648	+	0.318088i
$552$	−0.177659	−	8.76502i	−0.00756165	−	0.373064i
$553$	−0.00854886	−	0.0129093i	−0.000363535	−	0.000548959i
$554$	−14.6623	−	8.46531i	−0.622943	−	0.359657i
$555$	10.6830	−	6.45997i	0.453469	−	0.274211i
$556$		−	10.3868i		−	0.440499i
$557$	−2.70966	−	1.56442i	−0.114812	−	0.0662867i	0.441494	−	0.897264i	$-0.354449\pi$
$557$	−2.70966	−	1.56442i	−0.114812	−	0.0662867i	−0.556306	+	0.830977i	$0.687782\pi$
$558$	−18.6320	+	0.755615i	−0.788754	+	0.0319877i
$559$		−	23.2284i		−	0.982458i
$560$	1.46081	+	2.20591i	0.0617304	+	0.0932167i
$561$	−0.543522	+	0.987077i	−0.0229475	+	0.0416744i
$562$	−19.3571			−0.816528
$563$	10.4373	+	18.0780i	0.439881	+	0.761897i	0.997680	−	0.0680796i	$-0.0216872\pi$
$563$	10.4373	+	18.0780i	0.439881	+	0.761897i	−0.557799	+	0.829976i	$0.688354\pi$
$564$	−0.121391	−	5.98897i	−0.00511147	−	0.252181i
$565$	2.91695	+	1.68410i	0.122717	+	0.0708507i
$566$	30.5467			1.28397
$567$	−8.85905	+	22.1024i	−0.372045	+	0.928215i
$568$	5.43339			0.227980
$569$	20.0446	+	11.5727i	0.840313	+	0.485155i	0.857371	−	0.514700i	$-0.172097\pi$
$569$	20.0446	+	11.5727i	0.840313	+	0.485155i	−0.0170577	+	0.999855i	$0.505430\pi$
$570$	−0.0500750	−	2.47051i	−0.00209741	−	0.103478i
$571$	12.3844	+	21.4504i	0.518271	+	0.897671i	0.999775	+	0.0212272i	$0.00675732\pi$
$571$	12.3844	+	21.4504i	0.518271	+	0.897671i	−0.481504	+	0.876444i	$0.659909\pi$
$572$	2.36061			0.0987023
$573$	5.88720	−	10.6916i	0.245941	−	0.446649i
$574$	−0.675912	−	11.0085i	−0.0282120	−	0.459484i
$575$			5.06153i			0.211080i
$576$	2.99754	−	0.121564i	0.124897	−	0.00506518i
$577$	31.6396	+	18.2671i	1.31717	+	0.760470i	0.983273	−	0.182138i	$-0.0583019\pi$
$577$	31.6396	+	18.2671i	1.31717	+	0.760470i	0.333900	+	0.942609i	$0.391635\pi$
$578$			16.2496i			0.675896i
$579$	−3.56422	+	2.15527i	−0.148124	+	0.0895699i
$580$	5.23368	+	3.02167i	0.217317	+	0.125468i
$581$	−5.37840	+	0.330230i	−0.223134	+	0.0137003i
$582$	0.374300	+	18.4666i	0.0155152	+	0.765465i
$583$	0.342660	−	0.593505i	0.0141915	−	0.0245805i
$584$	−0.311597	+	0.539702i	−0.0128940	+	0.0223330i
$585$	−8.35046	−	4.37994i	−0.345249	−	0.181088i
$586$	1.46210	−	0.844143i	0.0603987	−	0.0348712i
$587$	−12.1405	−	21.0280i	−0.501092	−	0.867918i	−0.999999	−	0.00126186i	$-0.999598\pi$
$587$	−12.1405	−	21.0280i	−0.501092	−	0.867918i	0.498907	−	0.866656i	$-0.333735\pi$
$588$	11.2564	+	4.50491i	0.464205	+	0.185780i
$589$	4.43384	−	7.67964i	0.182693	−	0.316434i
$590$			8.43820i			0.347395i
$591$	2.74343	−	0.0556067i	0.112850	−	0.00228735i
$592$	−7.20782			−0.296240
$593$	19.7837	+	34.2664i	0.812419	+	1.40715i	0.911166	+	0.412039i	$0.135183\pi$
$593$	19.7837	+	34.2664i	0.812419	+	1.40715i	−0.0987467	+	0.995113i	$0.531483\pi$
$594$	3.49198	+	1.74229i	0.143278	+	0.0714871i
$595$	−1.26540	−	1.91083i	−0.0518764	−	0.0783365i
$596$	−11.2310	+	6.48421i	−0.460039	+	0.265604i
$597$	−6.47597	+	11.7609i	−0.265044	+	0.481340i
$598$	13.7777	−	7.95455i	0.563411	−	0.325286i
$599$	35.4500	−	20.4671i	1.44845	−	0.836263i	0.450060	−	0.892998i	$-0.351402\pi$
$599$	35.4500	−	20.4671i	1.44845	−	0.836263i	0.998389	+	0.0567354i	$0.0180691\pi$
$600$	−1.73170	+	0.0350998i	−0.0706962	+	0.00143294i
$601$	4.48642	−	2.59023i	0.183005	−	0.105658i	−0.405699	−	0.914007i	$-0.632972\pi$
$601$	4.48642	−	2.59023i	0.183005	−	0.105658i	0.588704	+	0.808349i	$0.299639\pi$
$602$	−17.5004	−	8.72021i	−0.713262	−	0.355409i
$603$	−17.4725	−	27.6149i	−0.711534	−	1.12456i
$604$	11.4553	+	19.8411i	0.466108	+	0.807323i
$605$	−10.4359			−0.424281
$606$	4.79748	−	8.71259i	0.194884	−	0.353925i
$607$		−	3.09536i		−	0.125637i	−0.998025	−	0.0628183i	$-0.979991\pi$
$607$		−	3.09536i		−	0.125637i	0.998025	−	0.0628183i	$-0.0200089\pi$
$608$	−0.713322	+	1.23551i	−0.0289290	+	0.0501066i
$609$	27.6019	−	2.25701i	1.11849	−	0.0914588i
$610$	−5.37077	−	9.30244i	−0.217456	−	0.376645i
$611$	9.41402	−	5.43519i	0.380850	−	0.219884i
$612$	−2.59657	+	0.105303i	−0.104960	+	0.00425663i
$613$	−1.39906	+	2.42324i	−0.0565075	+	0.0978739i	−0.892895	−	0.450264i	$-0.851330\pi$
$613$	−1.39906	+	2.42324i	−0.0565075	+	0.0978739i	0.836388	+	0.548138i	$0.184663\pi$
$614$	3.57936	−	6.19964i	0.144451	−	0.250197i
$615$	6.32484	+	3.48269i	0.255042	+	0.140436i
$616$	0.886201	−	1.77849i	0.0357060	−	0.0716576i
$617$	−20.0878	−	11.5977i	−0.808706	−	0.466906i	0.0378006	−	0.999285i	$-0.487965\pi$
$617$	−20.0878	−	11.5977i	−0.808706	−	0.466906i	−0.846506	+	0.532379i	$0.821298\pi$
$618$	−23.7521	−	13.0788i	−0.955448	−	0.526106i
$619$		−	9.82235i		−	0.394793i	−0.980324	−	0.197397i	$-0.936751\pi$
$619$		−	9.82235i		−	0.394793i	0.980324	−	0.197397i	$-0.0632487\pi$
$620$	−5.38301	−	3.10788i	−0.216187	−	0.124816i
$621$	26.2519	−	1.59805i	1.05345	−	0.0641276i
$622$			24.6355i			0.987793i
$623$	6.46738	−	0.397093i	0.259110	−	0.0159092i
$624$	2.81702	+	4.65858i	0.112771	+	0.186493i
$625$	1.00000			0.0400000
$626$	−6.35095	−	11.0002i	−0.253835	−	0.439655i
$627$	−1.58806	+	0.960293i	−0.0634210	+	0.0383504i
$628$	7.74720	+	4.47285i	0.309147	+	0.178486i
$629$	6.24366			0.248951
$630$	−6.43471	+	4.64699i	−0.256365	+	0.185140i
$631$	26.4402			1.05257			0.526285	−	0.850308i	$-0.323585\pi$
$631$	26.4402			1.05257			0.526285	+	0.850308i	$0.323585\pi$
$632$	−0.00506811	−	0.00292607i	−0.000201598	−	0.000116393i
$633$	20.1545	+	11.0978i	0.801070	+	0.441099i
$634$	12.7685	+	22.1158i	0.507103	+	0.878329i
$635$	−6.31880			−0.250754
$636$	1.58017	−	0.0320286i	0.0626579	−	0.00127001i
$637$	2.69167	+	21.8367i	0.106648	+	0.865203i
$638$		−	4.53877i		−	0.179692i
$639$	0.660507	+	16.2868i	0.0261292	+	0.644296i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$		−	27.8267i		−	1.09909i	−0.835465	−	0.549543i	$-0.814802\pi$
$641$		−	27.8267i		−	1.09909i	0.835465	−	0.549543i	$-0.185198\pi$
$642$	0.472406	+	23.3068i	0.0186444	+	0.919845i
$643$	36.4628	+	21.0518i	1.43795	+	0.830203i	0.997707	−	0.0676745i	$-0.0215580\pi$
$643$	36.4628	+	21.0518i	1.43795	+	0.830203i	0.440246	+	0.897877i	$0.354891\pi$
$644$	−0.820687	−	13.3664i	−0.0323396	−	0.526709i
$645$	10.9533	−	6.62343i	0.431287	−	0.260797i
$646$	0.617904	−	1.07024i	0.0243111	−	0.0421081i
$647$	−11.5301	+	19.9708i	−0.453296	+	0.785132i	−0.998588	−	0.0531139i	$-0.983085\pi$
$647$	−11.5301	+	19.9708i	−0.453296	+	0.785132i	0.545292	+	0.838246i	$0.316419\pi$
$648$	0.728787	+	8.97044i	0.0286294	+	0.352392i
$649$	5.48835	−	3.16870i	0.215436	−	0.124382i
$650$	−1.57157	−	2.72204i	−0.0616421	−	0.106767i
$651$	−28.3894	+	2.32141i	−1.11267	+	0.0909832i
$652$	8.68748	−	15.0472i	0.340228	−	0.589292i
$653$			25.7997i			1.00962i	0.863230	+	0.504810i	$0.168437\pi$
$653$			25.7997i			1.00962i	−0.863230	+	0.504810i	$0.831563\pi$
$654$	−11.2740	−	18.6440i	−0.440847	−	0.729039i
$655$	−10.9728			−0.428743
$656$	−2.08432	−	3.61015i	−0.0813790	−	0.140953i
$657$	−1.65565	−	0.868415i	−0.0645932	−	0.0338801i
$658$	−0.560759	−	9.13298i	−0.0218607	−	0.356040i
$659$	25.3231	−	14.6203i	0.986447	−	0.569525i	0.0822364	−	0.996613i	$-0.473794\pi$
$659$	25.3231	−	14.6203i	0.986447	−	0.569525i	0.904210	+	0.427088i	$0.140460\pi$
$660$	0.673113	+	1.11314i	0.0262009	+	0.0433290i
$661$	22.4429	−	12.9574i	0.872926	−	0.503984i	0.00460675	−	0.999989i	$-0.498534\pi$
$661$	22.4429	−	12.9574i	0.872926	−	0.503984i	0.868320	+	0.496005i	$0.165200\pi$
$662$	12.1497	−	7.01463i	0.472211	−	0.272631i
$663$	−2.44020	−	4.03542i	−0.0947696	−	0.156723i
$664$	−1.76381	+	1.01834i	−0.0684491	+	0.0395191i
$665$	−0.231319	−	3.76745i	−0.00897017	−	0.146096i
$666$	−0.876214	−	21.6057i	−0.0339526	−	0.837204i
$667$	−15.2943	−	26.4904i	−0.592196	−	1.02571i
$668$	16.9815			0.657035
$669$	−14.2834	−	23.6208i	−0.552229	−	0.913234i
$670$		−	10.8927i		−	0.420823i
$671$	−4.03364	+	6.98648i	−0.155717	+	0.269710i
$672$	4.56733	−	0.373471i	0.176189	−	0.0144070i
$673$	−4.62323	−	8.00767i	−0.178212	−	0.308673i	0.763056	−	0.646332i	$-0.223698\pi$
$673$	−4.62323	−	8.00767i	−0.178212	−	0.308673i	−0.941268	+	0.337660i	$0.890365\pi$
$674$	23.8930	−	13.7946i	0.920325	−	0.531350i
$675$	−0.315725	−	5.18655i	−0.0121523	−	0.199630i
$676$	1.56033	−	2.70257i	0.0600127	−	0.103945i
$677$	−12.3613	+	21.4103i	−0.475082	+	0.822866i	−0.999593	−	0.0285376i	$-0.990915\pi$
$677$	−12.3613	+	21.4103i	−0.475082	+	0.822866i	0.524511	+	0.851404i	$0.324248\pi$
$678$	4.99216	−	3.01874i	0.191723	−	0.115934i
$679$	1.72906	+	28.1610i	0.0663554	+	1.08072i
$680$	−0.750180	−	0.433117i	−0.0287681	−	0.0166093i
$681$	−0.462894	−	22.8375i	−0.0177381	−	0.875134i
$682$			4.66827i			0.178757i
$683$	−26.9472	−	15.5580i	−1.03111	−	0.595309i	−0.113804	−	0.993503i	$-0.536304\pi$
$683$	−26.9472	−	15.5580i	−1.03111	−	0.595309i	−0.917301	+	0.398194i	$0.869637\pi$
$684$	−3.79020	−	1.98802i	−0.144922	−	0.0760137i
$685$		−	21.2377i		−	0.811451i
$686$	17.4623	+	6.16984i	0.666715	+	0.235565i
$687$	34.2074	−	0.693351i	1.30509	−	0.0264530i
$688$	−7.39020			−0.281749
$689$	1.43406	+	2.48386i	0.0546333	+	0.0946276i
$690$	7.67956	+	4.22866i	0.292356	+	0.160982i
$691$	27.9609	+	16.1432i	1.06368	+	0.614118i	0.926449	−	0.376421i	$-0.122845\pi$
$691$	27.9609	+	16.1432i	1.06368	+	0.614118i	0.137235	+	0.990539i	$0.456179\pi$
$692$	−9.15080			−0.347861
$693$	5.43883	+	2.44022i	0.206604	+	0.0926962i
$694$	−11.7735			−0.446917
$695$	8.99525	+	5.19341i	0.341209	+	0.196997i
$696$	8.95708	−	5.41631i	0.339517	−	0.205305i
$697$	1.80551	+	3.12723i	0.0683885	+	0.118452i
$698$	−29.2237			−1.10613
$699$	24.6824	+	40.8178i	0.933572	+	1.54387i
$700$	−2.64078	+	0.162142i	−0.0998120	+	0.00612839i
$701$		−	26.3883i		−	0.996673i	−0.866984	−	0.498337i	$-0.833944\pi$
$701$		−	26.3883i		−	0.996673i	0.866984	−	0.498337i	$-0.166056\pi$
$702$	−13.6218	+	9.01045i	−0.514122	+	0.340078i
$703$	8.90534	+	5.14150i	0.335871	+	0.193915i
$704$		−	0.751037i		−	0.0283058i
$705$	5.24729	+	2.88936i	0.197624	+	0.108819i
$706$	0.261415	+	0.150928i	0.00983849	+	0.00568025i
$707$	6.77585	−	13.5983i	0.254832	−	0.511416i
$708$	12.8028	+	7.04969i	0.481158	+	0.264944i
$709$	4.53937	−	7.86242i	0.170480	−	0.295279i	−0.768108	−	0.640320i	$-0.778802\pi$
$709$	4.53937	−	7.86242i	0.170480	−	0.295279i	0.938588	+	0.345041i	$0.112135\pi$
$710$	−2.71670	+	4.70546i	−0.101956	+	0.176593i
$711$	0.00815491	−	0.0155475i	0.000305833	−	0.000583078i
$712$	2.12093	−	1.22452i	0.0794854	−	0.0458909i
$713$	15.7306	+	27.2462i	0.589117	+	1.02038i
$714$	−3.95638	+	0.323514i	−0.148064	+	0.0121072i
$715$	−1.18031	+	2.04435i	−0.0441410	+	0.0764545i
$716$		−	19.9538i		−	0.745707i
$717$	−6.29207	+	11.4269i	−0.234981	+	0.426744i
$718$	26.3949			0.985048
$719$	19.1759	+	33.2136i	0.715140	+	1.23866i	0.962906	+	0.269839i	$0.0869703\pi$
$719$	19.1759	+	33.2136i	0.715140	+	1.23866i	−0.247766	+	0.968820i	$0.579696\pi$
$720$	−1.39349	+	2.65672i	−0.0519323	+	0.0990103i
$721$	−37.0713	−	18.4722i	−1.38061	−	0.687939i
$722$	−14.6918	+	8.48234i	−0.546774	+	0.315680i
$723$	20.7480	−	0.420542i	0.771626	−	0.0156401i
$724$	18.7840	−	10.8449i	0.698100	−	0.403048i
$725$	−5.23368	+	3.02167i	−0.194374	+	0.112222i
$726$	−8.71871	+	15.8339i	−0.323582	+	0.587649i
$727$	8.55880	−	4.94142i	0.317428	−	0.183267i	−0.332817	−	0.942991i	$-0.607999\pi$
$727$	8.55880	−	4.94142i	0.317428	−	0.183267i	0.650246	+	0.759724i	$0.274666\pi$
$728$	4.59153	+	6.93349i	0.170173	+	0.256972i
$729$	−26.8006	+	3.27505i	−0.992616	+	0.121298i
$730$	−0.311597	−	0.539702i	−0.0115327	−	0.0199753i
$731$	6.40164			0.236773
$732$	−18.6011	+	0.377026i	−0.687515	+	0.0139353i
$733$		−	6.99187i		−	0.258251i	−0.991628	−	0.129125i	$-0.958783\pi$
$733$		−	6.99187i		−	0.258251i	0.991628	−	0.129125i	$-0.0412169\pi$
$734$	−4.86669	+	8.42936i	−0.179633	+	0.311133i
$735$	−9.52955	+	7.49584i	−0.351503	+	0.276488i
$736$	−2.53076	−	4.38341i	−0.0932852	−	0.161575i
$737$	−7.08483	+	4.09043i	−0.260973	+	0.150673i
$738$	10.5682	−	6.68669i	0.389020	−	0.246140i
$739$	9.75535	−	16.8968i	0.358856	−	0.621558i	−0.628914	−	0.777475i	$-0.716500\pi$
$739$	9.75535	−	16.8968i	0.358856	−	0.621558i	0.987770	+	0.155918i	$0.0498334\pi$
$740$	3.60391	−	6.24216i	0.132482	−	0.229466i
$741$	−0.157393	−	7.76518i	−0.00578196	−	0.285261i
$742$	2.40971	−	0.147955i	0.0884632	−	0.00543158i
$743$	33.4098	+	19.2892i	1.22569	+	0.707651i	0.966125	−	0.258075i	$-0.0830883\pi$
$743$	33.4098	+	19.2892i	1.22569	+	0.707651i	0.259563	+	0.965726i	$0.416422\pi$
$744$	−9.21264	+	5.57084i	−0.337752	+	0.204237i
$745$		−	12.9684i		−	0.475126i
$746$	−16.6784	−	9.62926i	−0.610638	−	0.352552i
$747$	−3.26691	−	5.16329i	−0.119530	−	0.188915i
$748$			0.650573i			0.0237873i
$749$	2.18226	+	35.5421i	0.0797380	+	1.29868i
$750$	0.835450	−	1.51724i	0.0305063	−	0.0554018i
$751$	−19.7427			−0.720423			−0.360211	−	0.932871i	$-0.617295\pi$
$751$	−19.7427			−0.720423			−0.360211	+	0.932871i	$0.617295\pi$
$752$	−1.72922	−	2.99510i	−0.0630582	−	0.109220i
$753$	−1.06596	−	52.5905i	−0.0388457	−	1.91650i
$754$	16.4502	+	9.49753i	0.599081	+	0.345880i
$755$	−22.9105			−0.833800
$756$	1.67472	+	13.6453i	0.0609089	+	0.496276i
$757$	−21.2004			−0.770540			−0.385270	−	0.922804i	$-0.625892\pi$
$757$	−21.2004			−0.770540			−0.385270	+	0.922804i	$0.625892\pi$
$758$	−25.4924	−	14.7180i	−0.925926	−	0.534584i
$759$	−0.133428	−	6.58285i	−0.00484314	−	0.238942i
$760$	−0.713322	−	1.23551i	−0.0258749	−	0.0448167i
$761$	1.39505			0.0505706			0.0252853	−	0.999680i	$-0.491951\pi$
$761$	1.39505			0.0505706			0.0252853	+	0.999680i	$0.491951\pi$
$762$	−5.27904	+	9.58715i	−0.191240	+	0.347306i
$763$	−18.3757	−	27.7484i	−0.665244	−	1.00456i
$764$		−	7.04674i		−	0.254942i
$765$	1.20709	−	2.30134i	0.0436424	−	0.0832053i
$766$	15.4216	+	8.90367i	0.557205	+	0.321703i
$767$			26.5224i			0.957670i
$768$	1.48214	−	0.896245i	0.0534822	−	0.0323405i
$769$	−10.8209	−	6.24747i	−0.390213	−	0.225289i	0.292040	−	0.956406i	$-0.405666\pi$
$769$	−10.8209	−	6.24747i	−0.390213	−	0.225289i	−0.682252	+	0.731117i	$0.738999\pi$
$770$	1.09712	+	1.65672i	0.0395375	+	0.0597040i
$771$	−0.0280817	−	1.38545i	−0.00101134	−	0.0498958i
$772$	−1.20239	+	2.08260i	−0.0432749	+	0.0749543i
$773$	−19.4887	+	33.7554i	−0.700960	+	1.21410i	0.267169	+	0.963650i	$0.413912\pi$
$773$	−19.4887	+	33.7554i	−0.700960	+	1.21410i	−0.968130	+	0.250449i	$0.919422\pi$
$774$	−0.898384	−	22.1524i	−0.0322918	−	0.796251i
$775$	5.38301	−	3.10788i	0.193363	−	0.111638i
$776$	5.33194	+	9.23519i	0.191406	+	0.331524i
$777$	−2.69192	−	32.9205i	−0.0965719	−	1.18102i
$778$	−6.26510	+	10.8515i	−0.224615	+	0.389044i
$779$			5.94717i			0.213079i
$780$	−5.44296	+	0.110324i	−0.194889	+	0.00395022i
$781$	4.08068			0.146018
$782$	2.19223	+	3.79706i	0.0783941	+	0.135783i
$783$	17.3244	+	26.1907i	0.619125	+	0.935981i
$784$	6.94742	−	0.856363i	0.248122	−	0.0305844i
$785$	−7.74720	+	4.47285i	−0.276509	+	0.159643i
$786$	−9.16724	+	16.6484i	−0.326985	+	0.593829i
$787$	−24.6682	+	14.2422i	−0.879326	+	0.507679i	−0.870436	−	0.492281i	$-0.836163\pi$
$787$	−24.6682	+	14.2422i	−0.879326	+	0.507679i	−0.00888998	+	0.999960i	$0.502830\pi$
$788$	1.37200	−	0.792122i	0.0488753	−	0.0282182i
$789$	36.1130	−	0.731975i	1.28566	−	0.0260590i
$790$	0.00506811	−	0.00292607i	0.000180315	−	0.000104105i
$791$	7.42996	−	4.92030i	0.264179	−	0.174946i
$792$	2.25126	−	0.0912993i	0.0799950	−	0.00324418i
$793$	−16.8811	−	29.2389i	−0.599465	−	1.03830i
$794$	−30.7784			−1.09228
$795$	−0.762348	+	1.38448i	−0.0270377	+	0.0491025i
$796$			7.75147i			0.274744i
$797$	3.94399	−	6.83119i	0.139703	−	0.241973i	−0.787681	−	0.616083i	$-0.788718\pi$
$797$	3.94399	−	6.83119i	0.139703	−	0.241973i	0.927384	+	0.374110i	$0.122052\pi$
$798$	−5.90939	−	2.79655i	−0.209190	−	0.0989969i
$799$	1.49791	+	2.59445i	0.0529922	+	0.0917852i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	3.92838	+	6.20872i	0.138802	+	0.219374i
$802$	3.58577	−	6.21073i	0.126618	−	0.219309i
$803$	−0.234021	+	0.405336i	−0.00825841	+	0.0143040i
$804$	−16.5269	−	9.10035i	−0.582860	−	0.320944i
$805$	11.9860	+	5.97245i	0.422450	+	0.210501i
$806$	−16.9196	−	9.76851i	−0.595966	−	0.344081i
$807$	−45.6826	−	25.1546i	−1.60810	−	0.885483i
$808$		−	5.74239i		−	0.202017i
$809$	2.59994	+	1.50108i	0.0914092	+	0.0527751i	0.545008	−	0.838431i	$-0.316527\pi$
$809$	2.59994	+	1.50108i	0.0914092	+	0.0527751i	−0.453599	+	0.891206i	$0.649860\pi$
$810$	−8.13303	−	3.85407i	−0.285765	−	0.135418i
$811$		−	7.71594i		−	0.270943i	−0.990781	−	0.135472i	$-0.956745\pi$
$811$		−	7.71594i		−	0.270943i	0.990781	−	0.135472i	$-0.0432549\pi$
$812$	13.3311	−	8.82816i	0.467828	−	0.309808i
$813$	−12.7598	−	21.1013i	−0.447507	−	0.740054i
$814$	−5.41334			−0.189737
$815$	8.68748	+	15.0472i	0.304309	+	0.527079i
$816$	−1.28388	+	0.776357i	−0.0449448	+	0.0271779i
$817$	9.13067	+	5.27159i	0.319442	+	0.184430i
$818$	26.6643			0.932295
$819$	−20.2252	+	14.6061i	−0.706726	+	0.510380i
$820$	4.16864			0.145575
$821$	−42.1560	−	24.3388i	−1.47125	−	0.849429i	−0.471775	−	0.881719i	$-0.656387\pi$
$821$	−42.1560	−	24.3388i	−1.47125	−	0.849429i	−0.999479	+	0.0322902i	$0.989720\pi$
$822$	−32.2227	−	17.7430i	−1.12390	−	0.618859i
$823$	24.3935	+	42.2508i	0.850304	+	1.47277i	0.880934	+	0.473238i	$0.156915\pi$
$823$	24.3935	+	42.2508i	0.850304	+	1.47277i	−0.0306307	+	0.999531i	$0.509752\pi$
$824$	−15.6548			−0.545360
$825$	−1.30057	+	0.0263612i	−0.0452799	+	0.000917781i
$826$	19.9821	+	9.95682i	0.695266	+	0.346442i
$827$		−	28.6190i		−	0.995181i	−0.867412	−	0.497591i	$-0.834218\pi$
$827$		−	28.6190i		−	0.995181i	0.867412	−	0.497591i	$-0.165782\pi$
$828$	12.8318	−	8.11892i	0.445935	−	0.282152i
$829$	−22.2964	−	12.8728i	−0.774386	−	0.447092i	0.0600511	−	0.998195i	$-0.480874\pi$
$829$	−22.2964	−	12.8728i	−0.774386	−	0.447092i	−0.834437	+	0.551103i	$0.814207\pi$
$830$		−	2.03667i		−	0.0706939i
$831$	−0.594261	−	29.3187i	−0.0206147	−	1.01705i
$832$	2.72204	+	1.57157i	0.0943698	+	0.0544844i
$833$	−6.01809	+	0.741810i	−0.208514	+	0.0257022i
$834$	15.3947	−	9.30913i	0.533076	−	0.322349i
$835$	−8.49076	+	14.7064i	−0.293835	+	0.508937i
$836$	−0.535731	+	0.927914i	−0.0185287	+	0.0320926i
$837$	−17.8187	−	26.9380i	−0.615906	−	0.931114i
$838$	21.1533	−	12.2128i	0.730727	−	0.421886i
$839$	16.6271	+	28.7990i	0.574032	+	0.994252i	0.996146	+	0.0877095i	$0.0279547\pi$
$839$	16.6271	+	28.7990i	0.574032	+	0.994252i	−0.422114	+	0.906543i	$0.638712\pi$
$840$	−1.96023	+	4.14216i	−0.0676344	+	0.142918i
$841$	3.76096	−	6.51417i	0.129688	−	0.224626i
$842$			17.6940i			0.609777i
$843$	−17.3487	−	28.6899i	−0.597520	−	0.988133i
$844$	13.2836			0.457242
$845$	1.56033	+	2.70257i	0.0536770	+	0.0929712i
$846$	8.76770	−	5.54750i	0.301440	−	0.190727i
$847$	−12.3141	+	24.7129i	−0.423117	+	0.849144i
$848$	0.790248	−	0.456250i	0.0271372	−	0.0156677i
$849$	27.3774	+	45.2746i	0.939588	+	1.55382i
$850$	0.750180	−	0.433117i	0.0257310	−	0.0148558i
$851$	−31.5949	+	18.2413i	−1.08306	+	0.625304i
$852$	4.86965	+	8.05306i	0.166832	+	0.275893i
$853$	0.801658	−	0.462837i	0.0274482	−	0.0158473i	−0.486213	−	0.873840i	$-0.661622\pi$
$853$	0.801658	−	0.462837i	0.0274482	−	0.0158473i	0.513661	+	0.857993i	$0.328289\pi$
$854$	−28.3660	+	1.74165i	−0.970665	+	0.0595982i
$855$	3.61677	−	2.28840i	0.123691	−	0.0782618i
$856$	6.72947	+	11.6558i	0.230008	+	0.398386i
$857$	−16.2250			−0.554236			−0.277118	−	0.960836i	$-0.589379\pi$
$857$	−16.2250			−0.554236			−0.277118	+	0.960836i	$0.589379\pi$
$858$	2.11569	+	3.49877i	0.0722284	+	0.119446i
$859$			22.9123i			0.781759i	0.920442	+	0.390880i	$0.127829\pi$
$859$			22.9123i			0.781759i	−0.920442	+	0.390880i	$0.872171\pi$
$860$	3.69510	−	6.40010i	0.126002	−	0.218242i
$861$	15.7103	−	10.8681i	0.535406	−	0.370383i
$862$	−11.8463	−	20.5184i	−0.403486	−	0.698859i
$863$	−1.28485	+	0.741810i	−0.0437369	+	0.0252515i	−0.521709	−	0.853123i	$-0.674705\pi$
$863$	−1.28485	+	0.741810i	−0.0437369	+	0.0252515i	0.477972	+	0.878375i	$0.341372\pi$
$864$	2.86670	+	4.33382i	0.0975272	+	0.147440i
$865$	4.57540	−	7.92483i	0.155568	−	0.269452i
$866$	12.0538	−	20.8779i	0.409606	−	0.709459i
$867$	−24.0843	+	14.5637i	−0.817945	+	0.494608i
$868$	−13.7114	+	9.08004i	−0.465396	+	0.308197i
$869$	−0.00380633	−	0.00219759i	−0.000129121	−	7.45481e-5i
$870$	0.212120	+	10.4652i	0.00719154	+	0.354804i
$871$		−	34.2374i		−	1.16009i
$872$	−10.8938	−	6.28955i	−0.368911	−	0.212991i
$873$	−27.0347	+	17.1054i	−0.914984	+	0.578929i
$874$			7.22100i			0.244254i
$875$	1.17997	−	2.36805i	0.0398903	−	0.0800548i
$876$	−1.07918	+	0.0218740i	−0.0364622	+	0.000739053i
$877$	−40.6373			−1.37222			−0.686112	−	0.727496i	$-0.740684\pi$
$877$	−40.6373			−1.37222			−0.686112	+	0.727496i	$0.740684\pi$
$878$	−0.534359	−	0.925536i	−0.0180337	−	0.0312353i
$879$	2.56154	+	1.41048i	0.0863985	+	0.0475743i
$880$	0.650417	+	0.375518i	0.0219255	+	0.0126587i
$881$	5.36428			0.180727			0.0903636	−	0.995909i	$-0.471197\pi$
$881$	5.36428			0.180727			0.0903636	+	0.995909i	$0.471197\pi$
$882$	3.41154	+	20.7210i	0.114872	+	0.697714i
$883$	9.15422			0.308064			0.154032	−	0.988066i	$-0.450774\pi$
$883$	9.15422			0.308064			0.154032	+	0.988066i	$0.450774\pi$
$884$	−2.35792	−	1.36135i	−0.0793055	−	0.0457871i
$885$	−12.5066	+	7.56269i	−0.420405	+	0.254217i
$886$	−15.4796	−	26.8115i	−0.520048	−	0.900750i
$887$	−36.1166			−1.21268			−0.606338	−	0.795207i	$-0.707362\pi$
$887$	−36.1166			−1.21268			−0.606338	+	0.795207i	$0.707362\pi$
$888$	−6.45997	−	10.6830i	−0.216783	−	0.358499i
$889$	−7.45600	+	14.9633i	−0.250066	+	0.501851i
$890$			2.44904i			0.0820921i
$891$	0.547346	+	6.73713i	0.0183368	+	0.225702i
$892$	−13.8018	−	7.96848i	−0.462119	−	0.266804i
$893$			4.93397i			0.165109i
$894$	−19.6762	−	10.8345i	−0.658072	−	0.362359i
$895$	17.2805	+	9.97688i	0.577622	+	0.333490i
$896$	2.20591	−	1.46081i	0.0736943	−	0.0488022i
$897$	24.1380	+	13.2913i	0.805943	+	0.443782i
$898$	11.2412	−	19.4703i	0.375123	−	0.649733i
$899$	−18.7820	+	32.5313i	−0.626414	+	1.08498i
$900$	−1.60405	−	2.53516i	−0.0534682	−	0.0845053i
$901$	−0.684539	+	0.395219i	−0.0228053	+	0.0131667i
$902$	−1.56540	−	2.71135i	−0.0521222	−	0.0902782i
$903$	−2.76003	−	33.7535i	−0.0918480	−	1.12325i
$904$	1.68410	−	2.91695i	0.0560124	−	0.0970163i
$905$			21.6898i			0.720995i
$906$	−19.1406	+	34.7608i	−0.635904	+	1.15485i
$907$	23.0774			0.766272			0.383136	−	0.923692i	$-0.374844\pi$
$907$	23.0774			0.766272			0.383136	+	0.923692i	$0.374844\pi$
$908$	−6.59397	−	11.4211i	−0.218828	−	0.379022i
$909$	17.2130	−	0.698070i	0.570920	−	0.0231535i
$910$	−8.30034	+	0.509636i	−0.275154	+	0.0168943i
$911$	30.4817	−	17.5986i	1.00990	−	0.583068i	0.0987403	−	0.995113i	$-0.468519\pi$
$911$	30.4817	−	17.5986i	1.00990	−	0.583068i	0.911163	+	0.412045i	$0.135185\pi$
$912$	−2.47051	+	0.0500750i	−0.0818069	+	0.00165815i
$913$	−1.32469	+	0.764808i	−0.0438407	+	0.0253114i
$914$	−35.7886	+	20.6626i	−1.18378	+	0.683457i
$915$	8.97402	−	16.2975i	0.296672	−	0.538779i
$916$	17.1072	−	9.87685i	0.565238	−	0.326340i
$917$	−12.9476	+	25.9842i	−0.427567	+	0.858074i
$918$	−2.48323	−	3.75410i	−0.0819589	−	0.123904i
$919$	9.86747	+	17.0910i	0.325498	+	0.563779i	0.981613	−	0.190882i	$-0.0611348\pi$
$919$	9.86747	+	17.0910i	0.325498	+	0.563779i	−0.656115	+	0.754661i	$0.727801\pi$
$920$	5.06153			0.166874
$921$	12.3967	−	0.251270i	0.408486	−	0.00827962i
$922$		−	26.0218i		−	0.856983i
$923$	−8.53897	+	14.7899i	−0.281063	+	0.486816i
$924$	3.43023	−	0.280491i	0.112846	−	0.00922747i
$925$	3.60391	+	6.24216i	0.118496	+	0.205241i
$926$	−9.60876	+	5.54762i	−0.315763	+	0.182306i
$927$	−1.90306	−	46.9257i	−0.0625047	−	1.54124i
$928$	3.02167	−	5.23368i	0.0991911	−	0.171804i
$929$	26.1679	−	45.3241i	0.858540	−	1.48703i	−0.0147821	−	0.999891i	$-0.504705\pi$
$929$	26.1679	−	45.3241i	0.858540	−	1.48703i	0.873322	−	0.487144i	$-0.161961\pi$
$930$	−0.218172	−	10.7638i	−0.00715414	−	0.352959i
$931$	−9.19447	−	3.89771i	−0.301337	−	0.127742i
$932$	23.8501	+	13.7699i	0.781236	+	0.451047i
$933$	−36.5133	+	22.0794i	−1.19539	+	0.722848i
$934$			37.4732i			1.22616i
$935$	−0.563413	−	0.325287i	−0.0184256	−	0.0106380i
$936$	−4.37994	+	8.35046i	−0.143163	+	0.272943i
$937$		−	36.5989i		−	1.19563i	−0.801633	−	0.597816i	$-0.796035\pi$
$937$		−	36.5989i		−	1.19563i	0.801633	−	0.597816i	$-0.203965\pi$
$938$	−25.7946	−	12.8531i	−0.842223	−	0.419669i
$939$	10.6118	−	19.2719i	0.346303	−	0.628913i
$940$	3.45844			0.112802
$941$	6.92046	+	11.9866i	0.225601	+	0.390752i	0.956499	−	0.291734i	$-0.0942322\pi$
$941$	6.92046	+	11.9866i	0.225601	+	0.390752i	−0.730899	+	0.682486i	$0.760899\pi$
$942$	0.313992	+	15.4912i	0.0102304	+	0.504731i
$943$	−18.2729	−	10.5498i	−0.595047	−	0.343550i
$944$	8.43820			0.274640
$945$	−12.6546	−	5.37232i	−0.411653	−	0.174762i
$946$	−5.55031			−0.180456
$947$	−18.8005	−	10.8545i	−0.610935	−	0.352724i	0.162396	−	0.986726i	$-0.448078\pi$
$947$	−18.8005	−	10.8545i	−0.610935	−	0.352724i	−0.773331	+	0.634002i	$0.781411\pi$
$948$	−0.000205409	−	0.0101341i	−6.67138e−6	−	0.000329141i
$949$	−0.979394	−	1.69636i	−0.0317925	−	0.0550662i
$950$	1.42664			0.0462865
$951$	−21.3350	+	38.7459i	−0.691833	+	1.25642i
$952$	−1.91083	+	1.26540i	−0.0619305	+	0.0410119i
$953$		−	7.37332i		−	0.238845i	−0.992844	−	0.119423i	$-0.961896\pi$
$953$		−	7.37332i		−	0.238845i	0.992844	−	0.119423i	$-0.0381043\pi$
$954$	1.46369	+	2.31333i	0.0473887	+	0.0748969i
$955$	6.10266	+	3.52337i	0.197477	+	0.114014i
$956$			7.53135i			0.243581i
$957$	6.72710	−	4.06785i	0.217456	−	0.131495i
$958$	12.0925	+	6.98162i	0.390691	+	0.225566i
$959$	−50.2920	−	25.0598i	−1.62401	−	0.809224i
$960$	0.0350998	+	1.73170i	0.00113284	+	0.0558902i
$961$	3.81785	−	6.61271i	0.123156	−	0.213313i
$962$	11.3276	−	19.6200i	0.365217	−	0.632574i
$963$	−34.1205	+	21.5887i	−1.09952	+	0.695687i
$964$	10.3761	−	5.99066i	0.334193	−	0.192946i
$965$	−1.20239	−	2.08260i	−0.0387062	−	0.0670412i
$966$	19.0753	−	13.1959i	0.613739	−	0.424572i
$967$	3.66184	−	6.34250i	0.117757	−	0.203961i	−0.801122	−	0.598502i	$-0.795763\pi$
$967$	3.66184	−	6.34250i	0.117757	−	0.203961i	0.918878	+	0.394541i	$0.129096\pi$
$968$			10.4359i			0.335424i
$969$	2.14004	−	0.0433766i	0.0687481	−	0.00139346i
$970$	−10.6639			−0.342397
$971$	25.1933	+	43.6361i	0.808491	+	1.40035i	0.913909	+	0.405920i	$0.133049\pi$
$971$	25.1933	+	43.6361i	0.808491	+	1.40035i	−0.105418	+	0.994428i	$0.533618\pi$
$972$	−12.6423	+	9.11988i	−0.405502	+	0.292520i
$973$	22.9124	−	15.1731i	0.734537	−	0.486429i
$974$	3.30309	−	1.90704i	0.105838	−	0.0611055i
$975$	2.62594	−	4.76891i	0.0840973	−	0.152727i
$976$	−9.30244	+	5.37077i	−0.297764	+	0.171914i
$977$	−51.0807	+	29.4915i	−1.63422	+	0.943515i	−0.651444	+	0.758697i	$0.725836\pi$
$977$	−51.0807	+	29.4915i	−1.63422	+	0.943515i	−0.982773	+	0.184818i	$0.940830\pi$
$978$	30.0881	−	0.609858i	0.962113	−	0.0195011i
$979$	1.59290	−	0.919661i	0.0509093	−	0.0293925i
$980$	−2.73208	+	6.44482i	−0.0872730	+	0.205872i
$981$	17.5289	−	33.4192i	0.559653	−	1.06699i
$982$	13.7053	+	23.7383i	0.437354	+	0.757520i
$983$	−10.7629			−0.343284			−0.171642	−	0.985159i	$-0.554907\pi$
$983$	−10.7629			−0.343284			−0.171642	+	0.985159i	$0.554907\pi$
$984$	3.48269	−	6.32484i	0.111024	−	0.201628i
$985$			1.58424i			0.0504782i
$986$	−2.61747	+	4.53359i	−0.0833572	+	0.144379i
$987$	13.0338	−	9.01651i	0.414870	−	0.286999i
$988$	−2.24207	−	3.88339i	−0.0713299	−	0.123547i
$989$	−32.3943	+	18.7028i	−1.03008	+	0.594716i
$990$	−1.04656	+	1.99530i	−0.0332619	+	0.0634147i
$991$	−23.9427	+	41.4700i	−0.760566	+	1.31734i	0.181993	+	0.983300i	$0.441745\pi$
$991$	−23.9427	+	41.4700i	−0.760566	+	1.31734i	−0.942559	+	0.334039i	$0.891588\pi$
$992$	−3.10788	+	5.38301i	−0.0986753	+	0.170911i
$993$	21.2858	+	11.7207i	0.675484	+	0.371947i
$994$	7.93715	+	11.9856i	0.251751	+	0.380160i
$995$	−6.71297	−	3.87574i	−0.212816	−	0.122869i
$996$	−3.09012	−	1.70154i	−0.0979143	−	0.0539153i
$997$			27.4211i			0.868435i	0.900808	+	0.434217i	$0.142975\pi$
$997$			27.4211i			0.868435i	−0.900808	+	0.434217i	$0.857025\pi$
$998$	22.3343	+	12.8947i	0.706980	+	0.408175i
$999$	31.2374	−	20.6627i	0.988308	−	0.653738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.311.12	✓	28
3.2	odd	2		1890.2.t.b.1151.4		28
7.5	odd	6		630.2.bk.b.131.6	yes	28
9.2	odd	6		630.2.bk.b.101.13	yes	28
9.7	even	3		1890.2.bk.b.521.10		28
21.5	even	6		1890.2.bk.b.341.10		28
63.47	even	6	inner	630.2.t.b.551.12	yes	28
63.61	odd	6		1890.2.t.b.1601.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.12	✓	28	1.1	even	1	trivial
630.2.t.b.551.12	yes	28	63.47	even	6	inner
630.2.bk.b.101.13	yes	28	9.2	odd	6
630.2.bk.b.131.6	yes	28	7.5	odd	6
1890.2.t.b.1151.4		28	3.2	odd	2
1890.2.t.b.1601.4		28	63.61	odd	6
1890.2.bk.b.341.10		28	21.5	even	6
1890.2.bk.b.521.10		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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0350998 + 1.73170i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.835450 + 1.51724i) q^{6} +(-1.17997 + 2.36805i) q^{7} +1.00000i q^{8} +(-2.99754 + 0.121564i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0350998 + 1.73170i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.835450 + 1.51724i) q^{6} +(-1.17997 + 2.36805i) q^{7} +1.00000i q^{8} +(-2.99754 + 0.121564i) q^{9} +(-0.866025 - 0.500000i) q^{10} +0.751037i q^{11} +(-1.48214 + 0.896245i) q^{12} +(-2.72204 - 1.57157i) q^{13} +(-2.20591 + 1.46081i) q^{14} +(-0.0350998 - 1.73170i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.433117 - 0.750180i) q^{17} +(-2.65672 - 1.39349i) q^{18} +(1.23551 - 0.713322i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-4.14216 - 1.96023i) q^{21} +(-0.375518 + 0.650417i) q^{22} +5.06153i q^{23} +(-1.73170 + 0.0350998i) q^{24} +1.00000 q^{25} +(-1.57157 - 2.72204i) q^{26} +(-0.315725 - 5.18655i) q^{27} +(-2.64078 + 0.162142i) q^{28} +(-5.23368 + 3.02167i) q^{29} +(0.835450 - 1.51724i) q^{30} +(5.38301 - 3.10788i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.30057 + 0.0263612i) q^{33} +(0.750180 - 0.433117i) q^{34} +(1.17997 - 2.36805i) q^{35} +(-1.60405 - 2.53516i) q^{36} +(3.60391 + 6.24216i) q^{37} +1.42664 q^{38} +(2.62594 - 4.76891i) q^{39} -1.00000i q^{40} +(-2.08432 + 3.61015i) q^{41} +(-2.60710 - 3.76869i) q^{42} +(3.69510 + 6.40010i) q^{43} +(-0.650417 + 0.375518i) q^{44} +(2.99754 - 0.121564i) q^{45} +(-2.53076 + 4.38341i) q^{46} +(-1.72922 + 2.99510i) q^{47} +(-1.51724 - 0.835450i) q^{48} +(-4.21534 - 5.58846i) q^{49} +(0.866025 + 0.500000i) q^{50} +(1.31429 + 0.723695i) q^{51} -3.14314i q^{52} +(-0.790248 - 0.456250i) q^{53} +(2.31985 - 4.64955i) q^{54} -0.751037i q^{55} +(-2.36805 - 1.17997i) q^{56} +(1.27862 + 2.11449i) q^{57} -6.04334 q^{58} +(-4.21910 - 7.30769i) q^{59} +(1.48214 - 0.896245i) q^{60} +(9.30244 + 5.37077i) q^{61} +6.21576 q^{62} +(3.24913 - 7.24176i) q^{63} -1.00000 q^{64} +(2.72204 + 1.57157i) q^{65} +(-1.13950 - 0.627454i) q^{66} +(5.44637 + 9.43339i) q^{67} +0.866234 q^{68} +(-8.76502 + 0.177659i) q^{69} +(2.20591 - 1.46081i) q^{70} -5.43339i q^{71} +(-0.121564 - 2.99754i) q^{72} +(0.539702 + 0.311597i) q^{73} +7.20782i q^{74} +(0.0350998 + 1.73170i) q^{75} +(1.23551 + 0.713322i) q^{76} +(-1.77849 - 0.886201i) q^{77} +(4.65858 - 2.81702i) q^{78} +(-0.00292607 + 0.00506811i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.97044 - 0.728787i) q^{81} +(-3.61015 + 2.08432i) q^{82} +(1.01834 + 1.76381i) q^{83} +(-0.373471 - 4.56733i) q^{84} +(-0.433117 + 0.750180i) q^{85} +7.39020i q^{86} +(-5.41631 - 8.95708i) q^{87} -0.751037 q^{88} +(-1.22452 - 2.12093i) q^{89} +(2.65672 + 1.39349i) q^{90} +(6.93349 - 4.59153i) q^{91} +(-4.38341 + 2.53076i) q^{92} +(5.57084 + 9.21264i) q^{93} +(-2.99510 + 1.72922i) q^{94} +(-1.23551 + 0.713322i) q^{95} +(-0.896245 - 1.48214i) q^{96} +(9.23519 - 5.33194i) q^{97} +(-0.856363 - 6.94742i) q^{98} +(-0.0912993 - 2.25126i) 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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