LMFDB - Embedded newform 630.2.t.b.311.10

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			311.10
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.22158 - 1.22791i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.443962 - 1.67419i) q^{6} +(2.64030 + 0.169721i) q^{7} +1.00000i q^{8} +(-0.0155088 + 2.99996i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.22158 - 1.22791i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.443962 - 1.67419i) q^{6} +(2.64030 + 0.169721i) q^{7} +1.00000i q^{8} +(-0.0155088 + 2.99996i) q^{9} +(-0.866025 - 0.500000i) q^{10} +0.207763i q^{11} +(0.452611 - 1.67187i) q^{12} +(1.22567 + 0.707642i) q^{13} +(2.20171 + 1.46713i) q^{14} +(1.22158 + 1.22791i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.680447 - 1.17857i) q^{17} +(-1.51341 + 2.59029i) q^{18} +(5.73160 - 3.30914i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.01693 - 3.44937i) q^{21} +(-0.103881 + 0.179928i) q^{22} +6.39482i q^{23} +(1.22791 - 1.22158i) q^{24} +1.00000 q^{25} +(0.707642 + 1.22567i) q^{26} +(3.70262 - 3.64563i) q^{27} +(1.17317 + 2.37143i) q^{28} +(6.11758 - 3.53199i) q^{29} +(0.443962 + 1.67419i) q^{30} +(4.10937 - 2.37255i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.255113 - 0.253798i) q^{33} +(1.17857 - 0.680447i) q^{34} +(-2.64030 - 0.169721i) q^{35} +(-2.60580 + 1.48655i) q^{36} +(1.32889 + 2.30171i) q^{37} +6.61828 q^{38} +(-0.628332 - 2.36945i) q^{39} -1.00000i q^{40} +(-1.41245 + 2.44643i) q^{41} +(-0.888048 - 4.49571i) q^{42} +(1.06723 + 1.84849i) q^{43} +(-0.179928 + 0.103881i) q^{44} +(0.0155088 - 2.99996i) q^{45} +(-3.19741 + 5.53808i) q^{46} +(-0.0573414 + 0.0993182i) q^{47} +(1.67419 - 0.443962i) q^{48} +(6.94239 + 0.896231i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-2.27839 + 0.604185i) q^{51} +1.41528i q^{52} +(-8.40507 - 4.85267i) q^{53} +(5.02938 - 1.30590i) q^{54} -0.207763i q^{55} +(-0.169721 + 2.64030i) q^{56} +(-11.0649 - 2.99551i) q^{57} +7.06398 q^{58} +(4.34473 + 7.52530i) q^{59} +(-0.452611 + 1.67187i) q^{60} +(-1.85102 - 1.06869i) q^{61} +4.74509 q^{62} +(-0.550105 + 7.91817i) q^{63} -1.00000 q^{64} +(-1.22567 - 0.707642i) q^{65} +(0.347833 - 0.0922387i) q^{66} +(-0.0235223 - 0.0407418i) q^{67} +1.36089 q^{68} +(7.85224 - 7.81175i) q^{69} +(-2.20171 - 1.46713i) q^{70} +3.45539i q^{71} +(-2.99996 - 0.0155088i) q^{72} +(-11.5793 - 6.68529i) q^{73} +2.65778i q^{74} +(-1.22158 - 1.22791i) q^{75} +(5.73160 + 3.30914i) q^{76} +(-0.0352617 + 0.548556i) q^{77} +(0.640573 - 2.36617i) q^{78} +(-7.97657 + 13.8158i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99952 - 0.0930513i) q^{81} +(-2.44643 + 1.41245i) q^{82} +(-8.06016 - 13.9606i) q^{83} +(1.47878 - 4.33742i) q^{84} +(-0.680447 + 1.17857i) q^{85} +2.13446i q^{86} +(-11.8100 - 3.19723i) q^{87} -0.207763 q^{88} +(-1.40976 - 2.44178i) q^{89} +(1.51341 - 2.59029i) q^{90} +(3.11604 + 2.07641i) q^{91} +(-5.53808 + 3.19741i) q^{92} +(-7.93317 - 2.14768i) q^{93} +(-0.0993182 + 0.0573414i) q^{94} +(-5.73160 + 3.30914i) q^{95} +(1.67187 + 0.452611i) q^{96} +(1.39248 - 0.803947i) q^{97} +(5.56417 + 4.24735i) q^{98} +(-0.623280 - 0.00322214i) 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
$3$	−1.22158	−	1.22791i	−0.705277	−	0.708932i
$3$	−1.22158	−	1.22791i	−0.705277	−	0.708932i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.443962	−	1.67419i	−0.181247	−	0.683483i
$7$	2.64030	+	0.169721i	0.997940	+	0.0641486i
$7$	2.64030	+	0.169721i	0.997940	+	0.0641486i
$8$			1.00000i			0.353553i
$9$	−0.0155088	+	2.99996i	−0.00516958	+	0.999987i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			0.207763i			0.0626428i	0.999509	+	0.0313214i	$0.00997154\pi$
$11$			0.207763i			0.0626428i	−0.999509	+	0.0313214i	$0.990028\pi$
$12$	0.452611	−	1.67187i	0.130657	−	0.482627i
$13$	1.22567	+	0.707642i	0.339940	+	0.196265i	0.660246	−	0.751050i	$-0.270452\pi$
$13$	1.22567	+	0.707642i	0.339940	+	0.196265i	−0.320305	+	0.947314i	$0.603786\pi$
$14$	2.20171	+	1.46713i	0.588431	+	0.392108i
$15$	1.22158	+	1.22791i	0.315409	+	0.317044i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.680447	−	1.17857i	0.165033	−	0.285845i	−0.771634	−	0.636067i	$-0.780560\pi$
$17$	0.680447	−	1.17857i	0.165033	−	0.285845i	0.936667	+	0.350222i	$0.113894\pi$
$18$	−1.51341	+	2.59029i	−0.356714	+	0.610537i
$19$	5.73160	−	3.30914i	1.31492	−	0.759169i	0.332013	−	0.943275i	$-0.392272\pi$
$19$	5.73160	−	3.30914i	1.31492	−	0.759169i	0.982906	+	0.184106i	$0.0589389\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−3.01693	−	3.44937i	−0.658347	−	0.752715i
$22$	−0.103881	+	0.179928i	−0.0221476	+	0.0383607i
$23$			6.39482i			1.33341i	0.745321	+	0.666706i	$0.232296\pi$
$23$			6.39482i			1.33341i	−0.745321	+	0.666706i	$0.767704\pi$
$24$	1.22791	−	1.22158i	0.250645	−	0.249353i
$25$	1.00000			0.200000
$26$	0.707642	+	1.22567i	0.138780	+	0.240374i
$27$	3.70262	−	3.64563i	0.712569	−	0.701602i
$28$	1.17317	+	2.37143i	0.221708	+	0.448158i
$29$	6.11758	−	3.53199i	1.13601	−	0.655874i	0.190568	−	0.981674i	$-0.438967\pi$
$29$	6.11758	−	3.53199i	1.13601	−	0.655874i	0.945439	+	0.325800i	$0.105634\pi$
$30$	0.443962	+	1.67419i	0.0810560	+	0.305663i
$31$	4.10937	−	2.37255i	0.738065	−	0.426122i	−0.0833006	−	0.996524i	$-0.526546\pi$
$31$	4.10937	−	2.37255i	0.738065	−	0.426122i	0.821365	+	0.570403i	$0.193213\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.255113	−	0.253798i	0.0444095	−	0.0441805i
$34$	1.17857	−	0.680447i	0.202123	−	0.116696i
$35$	−2.64030	−	0.169721i	−0.446292	−	0.0286881i
$36$	−2.60580	+	1.48655i	−0.434299	+	0.247758i
$37$	1.32889	+	2.30171i	0.218468	+	0.378398i	0.954340	−	0.298723i	$-0.0965607\pi$
$37$	1.32889	+	2.30171i	0.218468	+	0.378398i	−0.735872	+	0.677121i	$0.763227\pi$
$38$	6.61828			1.07363
$39$	−0.628332	−	2.36945i	−0.100614	−	0.379415i
$40$		−	1.00000i		−	0.158114i
$41$	−1.41245	+	2.44643i	−0.220587	+	0.382068i	−0.954986	−	0.296650i	$-0.904131\pi$
$41$	−1.41245	+	2.44643i	−0.220587	+	0.382068i	0.734399	+	0.678718i	$0.237464\pi$
$42$	−0.888048	−	4.49571i	−0.137029	−	0.693702i
$43$	1.06723	+	1.84849i	0.162751	+	0.281893i	0.935854	−	0.352387i	$-0.114630\pi$
$43$	1.06723	+	1.84849i	0.162751	+	0.281893i	−0.773103	+	0.634280i	$0.781297\pi$
$44$	−0.179928	+	0.103881i	−0.0271251	+	0.0156607i
$45$	0.0155088	−	2.99996i	0.00231191	−	0.447208i
$46$	−3.19741	+	5.53808i	−0.471432	+	0.816545i
$47$	−0.0573414	+	0.0993182i	−0.00836410	+	0.0144870i	−0.870177	−	0.492739i	$-0.835996\pi$
$47$	−0.0573414	+	0.0993182i	−0.00836410	+	0.0144870i	0.861813	+	0.507226i	$0.169329\pi$
$48$	1.67419	−	0.443962i	0.241648	−	0.0640804i
$49$	6.94239	+	0.896231i	0.991770	+	0.128033i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−2.27839	+	0.604185i	−0.319038	+	0.0846028i
$52$			1.41528i			0.196265i
$53$	−8.40507	−	4.85267i	−1.15452	−	0.666565i	−0.204539	−	0.978858i	$-0.565570\pi$
$53$	−8.40507	−	4.85267i	−1.15452	−	0.666565i	−0.949986	+	0.312293i	$0.898903\pi$
$54$	5.02938	−	1.30590i	0.684411	−	0.177711i
$55$		−	0.207763i		−	0.0280147i
$56$	−0.169721	+	2.64030i	−0.0226800	+	0.352825i
$57$	−11.0649	−	2.99551i	−1.46558	−	0.396764i
$58$	7.06398			0.927546
$59$	4.34473	+	7.52530i	0.565636	+	0.979711i	0.996990	+	0.0775280i	$0.0247027\pi$
$59$	4.34473	+	7.52530i	0.565636	+	0.979711i	−0.431354	+	0.902183i	$0.641964\pi$
$60$	−0.452611	+	1.67187i	−0.0584318	+	0.215837i
$61$	−1.85102	−	1.06869i	−0.236999	−	0.136832i	0.376798	−	0.926296i	$-0.377025\pi$
$61$	−1.85102	−	1.06869i	−0.236999	−	0.136832i	−0.613797	+	0.789464i	$0.710359\pi$
$62$	4.74509			0.602627
$63$	−0.550105	+	7.91817i	−0.0693067	+	0.997595i
$64$	−1.00000			−0.125000
$65$	−1.22567	−	0.707642i	−0.152026	−	0.0877722i
$66$	0.347833	−	0.0922387i	0.0428153	−	0.0113538i
$67$	−0.0235223	−	0.0407418i	−0.00287371	−	0.00497740i	0.864585	−	0.502487i	$-0.167581\pi$
$67$	−0.0235223	−	0.0407418i	−0.00287371	−	0.00497740i	−0.867459	+	0.497509i	$0.834248\pi$
$68$	1.36089			0.165033
$69$	7.85224	−	7.81175i	0.945299	−	0.940424i
$70$	−2.20171	−	1.46713i	−0.263154	−	0.175356i
$71$			3.45539i			0.410079i	0.978754	+	0.205040i	$0.0657323\pi$
$71$			3.45539i			0.410079i	−0.978754	+	0.205040i	$0.934268\pi$
$72$	−2.99996	−	0.0155088i	−0.353549	−	0.00182772i
$73$	−11.5793	−	6.68529i	−1.35525	−	0.782454i	−0.366271	−	0.930508i	$-0.619366\pi$
$73$	−11.5793	−	6.68529i	−1.35525	−	0.782454i	−0.988979	+	0.148054i	$0.952699\pi$
$74$			2.65778i			0.308961i
$75$	−1.22158	−	1.22791i	−0.141055	−	0.141786i
$76$	5.73160	+	3.30914i	0.657460	+	0.379585i
$77$	−0.0352617	+	0.548556i	−0.00401845	+	0.0625138i
$78$	0.640573	−	2.36617i	0.0725306	−	0.267916i
$79$	−7.97657	+	13.8158i	−0.897434	+	1.55440i	−0.0666713	+	0.997775i	$0.521238\pi$
$79$	−7.97657	+	13.8158i	−0.897434	+	1.55440i	−0.830763	+	0.556627i	$0.812095\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.99952	−	0.0930513i	−0.999947	−	0.0103390i
$82$	−2.44643	+	1.41245i	−0.270163	+	0.155979i
$83$	−8.06016	−	13.9606i	−0.884717	−	1.53237i	−0.846038	−	0.533123i	$-0.821018\pi$
$83$	−8.06016	−	13.9606i	−0.884717	−	1.53237i	−0.0386794	−	0.999252i	$-0.512315\pi$
$84$	1.47878	−	4.33742i	0.161348	−	0.473251i
$85$	−0.680447	+	1.17857i	−0.0738048	+	0.127834i
$86$			2.13446i			0.230164i
$87$	−11.8100	−	3.19723i	−1.26617	−	0.342779i
$88$	−0.207763			−0.0221476
$89$	−1.40976	−	2.44178i	−0.149435	−	0.258828i	0.781584	−	0.623800i	$-0.214412\pi$
$89$	−1.40976	−	2.44178i	−0.149435	−	0.258828i	−0.931019	+	0.364972i	$0.881079\pi$
$90$	1.51341	−	2.59029i	0.159528	−	0.273040i
$91$	3.11604	+	2.07641i	0.326650	+	0.217667i
$92$	−5.53808	+	3.19741i	−0.577384	+	0.333353i
$93$	−7.93317	−	2.14768i	−0.822631	−	0.222704i
$94$	−0.0993182	+	0.0573414i	−0.0102439	+	0.00591431i
$95$	−5.73160	+	3.30914i	−0.588050	+	0.339511i
$96$	1.67187	+	0.452611i	0.170634	+	0.0461944i
$97$	1.39248	−	0.803947i	0.141385	−	0.0816284i	−0.427639	−	0.903950i	$-0.640655\pi$
$97$	1.39248	−	0.803947i	0.141385	−	0.0816284i	0.569024	+	0.822321i	$0.307321\pi$
$98$	5.56417	+	4.24735i	0.562066	+	0.429047i
$99$	−0.623280	−	0.00322214i	−0.0626420	−	0.000323837i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−6.10803			−0.607772			−0.303886	−	0.952708i	$-0.598284\pi$
$101$	−6.10803			−0.607772			−0.303886	+	0.952708i	$0.598284\pi$
$102$	−2.27524	−	0.615955i	−0.225282	−	0.0609886i
$103$			6.61641i			0.651934i	0.945381	+	0.325967i	$0.105690\pi$
$103$			6.61641i			0.651934i	−0.945381	+	0.325967i	$0.894310\pi$
$104$	−0.707642	+	1.22567i	−0.0693900	+	0.120187i
$105$	3.01693	+	3.44937i	0.294422	+	0.336624i
$106$	−4.85267	−	8.40507i	−0.471333	−	0.816372i
$107$	−4.64917	+	2.68420i	−0.449452	+	0.259491i	−0.707599	−	0.706614i	$-0.750222\pi$
$107$	−4.64917	+	2.68420i	−0.449452	+	0.259491i	0.258147	+	0.966106i	$0.416888\pi$
$108$	5.00852	+	1.38374i	0.481945	+	0.133151i
$109$	9.12274	−	15.8011i	0.873800	−	1.51347i	0.0157652	−	0.999876i	$-0.494982\pi$
$109$	9.12274	−	15.8011i	0.873800	−	1.51347i	0.858035	−	0.513591i	$-0.171685\pi$
$110$	0.103881	−	0.179928i	0.00990470	−	0.0171554i
$111$	1.20294	−	4.44346i	0.114178	−	0.421755i
$112$	−1.46713	+	2.20171i	−0.138631	+	0.208042i
$113$	−3.64375	−	2.10372i	−0.342775	−	0.197901i	0.318723	−	0.947848i	$-0.396746\pi$
$113$	−3.64375	−	2.10372i	−0.342775	−	0.197901i	−0.661498	+	0.749947i	$0.730079\pi$
$114$	−8.08473	−	8.12663i	−0.757204	−	0.761129i
$115$		−	6.39482i		−	0.596320i
$116$	6.11758	+	3.53199i	0.568003	+	0.327937i
$117$	−2.14191	+	3.66599i	−0.198019	+	0.338921i
$118$			8.68947i			0.799930i
$119$	1.99661	−	2.99629i	0.183029	−	0.274670i
$120$	−1.22791	+	1.22158i	−0.112092	+	0.111514i
$121$	10.9568			0.996076
$122$	−1.06869	−	1.85102i	−0.0967546	−	0.167584i
$123$	4.72940	−	1.25414i	0.426435	−	0.113082i
$124$	4.10937	+	2.37255i	0.369032	+	0.213061i
$125$	−1.00000			−0.0894427
$126$	−4.43549	+	6.58228i	−0.395145	+	0.586396i
$127$	−14.9591			−1.32741			−0.663704	−	0.747995i	$-0.731017\pi$
$127$	−14.9591			−1.32741			−0.663704	+	0.747995i	$0.731017\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.966078	−	3.56853i	0.0850584	−	0.314192i
$130$	−0.707642	−	1.22567i	−0.0620643	−	0.107499i
$131$	−16.7931			−1.46722			−0.733609	−	0.679572i	$-0.762166\pi$
$131$	−16.7931			−1.46722			−0.733609	+	0.679572i	$0.762166\pi$
$132$	0.347352	+	0.0940356i	0.0302331	+	0.00818475i
$133$	15.6948	−	7.76436i	1.36091	−	0.673255i
$134$		−	0.0470446i		−	0.00406403i
$135$	−3.70262	+	3.64563i	−0.318670	+	0.313766i
$136$	1.17857	+	0.680447i	0.101061	+	0.0583478i
$137$		−	3.39189i		−	0.289789i	−0.989447	−	0.144894i	$-0.953716\pi$
$137$		−	3.39189i		−	0.289789i	0.989447	−	0.144894i	$-0.0462842\pi$
$138$	10.7061	−	2.83906i	0.911365	−	0.241676i
$139$	5.07662	+	2.93099i	0.430593	+	0.248603i	0.699599	−	0.714535i	$-0.253362\pi$
$139$	5.07662	+	2.93099i	0.430593	+	0.248603i	−0.269006	+	0.963138i	$0.586695\pi$
$140$	−1.17317	−	2.37143i	−0.0991508	−	0.200422i
$141$	0.192000	−	0.0509148i	0.0161693	−	0.00428780i
$142$	−1.72769	+	2.99245i	−0.144985	+	0.251121i
$143$	−0.147022	+	0.254649i	−0.0122946	+	0.0212948i
$144$	−2.59029	−	1.51341i	−0.215857	−	0.126118i
$145$	−6.11758	+	3.53199i	−0.508038	+	0.293316i
$146$	−6.68529	−	11.5793i	−0.553279	−	0.958307i
$147$	−7.38016	−	9.61942i	−0.608706	−	0.793396i
$148$	−1.32889	+	2.30171i	−0.109234	+	0.189199i
$149$			22.3632i			1.83207i	0.401104	+	0.916033i	$0.368627\pi$
$149$			22.3632i			1.83207i	−0.401104	+	0.916033i	$0.631373\pi$
$150$	−0.443962	−	1.67419i	−0.0362493	−	0.136697i
$151$	12.6238			1.02731			0.513656	−	0.857996i	$-0.328291\pi$
$151$	12.6238			1.02731			0.513656	+	0.857996i	$0.328291\pi$
$152$	3.30914	+	5.73160i	0.268407	+	0.464894i
$153$	3.52511	+	2.05959i	0.284988	+	0.166508i
$154$	−0.304816	+	0.457433i	−0.0245627	+	0.0368610i
$155$	−4.10937	+	2.37255i	−0.330072	+	0.190567i
$156$	1.73784	−	1.72888i	0.139138	−	0.138421i
$157$	−5.02485	+	2.90110i	−0.401027	+	0.231533i	−0.686927	−	0.726727i	$-0.741041\pi$
$157$	−5.02485	+	2.90110i	−0.401027	+	0.231533i	0.285900	+	0.958259i	$0.407707\pi$
$158$	−13.8158	+	7.97657i	−1.09913	+	0.634582i
$159$	4.30880	+	16.2485i	0.341710	+	1.28859i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−1.08534	+	16.8843i	−0.0855365	+	1.33067i
$162$	−7.74729	−	4.58034i	−0.608684	−	0.359866i
$163$	8.98690	+	15.5658i	0.703908	+	1.21920i	0.967084	+	0.254457i	$0.0818967\pi$
$163$	8.98690	+	15.5658i	0.703908	+	1.21920i	−0.263176	+	0.964748i	$0.584770\pi$
$164$	−2.82489			−0.220587
$165$	−0.255113	+	0.253798i	−0.0198605	+	0.0197581i
$166$		−	16.1203i		−	1.25118i
$167$	−5.00537	+	8.66956i	−0.387327	+	0.670870i	−0.992089	−	0.125536i	$-0.959935\pi$
$167$	−5.00537	+	8.66956i	−0.387327	+	0.670870i	0.604762	+	0.796406i	$0.293268\pi$
$168$	3.44937	−	3.01693i	0.266125	−	0.232761i
$169$	−5.49849	−	9.52366i	−0.422960	−	0.732589i
$170$	−1.17857	+	0.680447i	−0.0903921	+	0.0521879i
$171$	9.83840	+	17.2459i	0.752361	+	1.31883i
$172$	−1.06723	+	1.84849i	−0.0813754	+	0.140946i
$173$	3.60215	−	6.23910i	0.273866	−	0.474350i	−0.695982	−	0.718059i	$-0.745031\pi$
$173$	3.60215	−	6.23910i	0.273866	−	0.474350i	0.969848	+	0.243709i	$0.0783642\pi$
$174$	−8.62918	−	8.67390i	−0.654176	−	0.657567i
$175$	2.64030	+	0.169721i	0.199588	+	0.0128297i
$176$	−0.179928	−	0.103881i	−0.0135626	−	0.00783035i
$177$	3.93295	−	14.5276i	0.295618	−	1.09196i
$178$		−	2.81953i		−	0.211333i
$179$	12.7104	+	7.33833i	0.950016	+	0.548492i	0.893086	−	0.449886i	$-0.148535\pi$
$179$	12.7104	+	7.33833i	0.950016	+	0.548492i	0.0569303	+	0.998378i	$0.481869\pi$
$180$	2.60580	−	1.48655i	0.194225	−	0.110801i
$181$		−	20.6504i		−	1.53493i	−0.641090	−	0.767465i	$-0.721518\pi$
$181$		−	20.6504i		−	1.53493i	0.641090	−	0.767465i	$-0.278482\pi$
$182$	1.66037	+	3.35625i	0.123075	+	0.248782i
$183$	0.948914	+	3.57837i	0.0701458	+	0.264521i
$184$	−6.39482			−0.471432
$185$	−1.32889	−	2.30171i	−0.0977020	−	0.169225i
$186$	−5.79648	−	5.82653i	−0.425019	−	0.427222i
$187$	0.244863	+	0.141371i	0.0179061	+	0.0103381i
$188$	−0.114683			−0.00836410
$189$	10.3948	−	8.99716i	0.756108	−	0.654447i
$190$	−6.61828			−0.480141
$191$	−19.0114	−	10.9763i	−1.37562	−	0.794214i	−0.383990	−	0.923337i	$-0.625450\pi$
$191$	−19.0114	−	10.9763i	−1.37562	−	0.794214i	−0.991629	+	0.129124i	$0.958784\pi$
$192$	1.22158	+	1.22791i	0.0881596	+	0.0886165i
$193$	−10.3050	−	17.8488i	−0.741772	−	1.28479i	−0.951688	−	0.307068i	$-0.900652\pi$
$193$	−10.3050	−	17.8488i	−0.741772	−	1.28479i	0.209915	−	0.977720i	$-0.432681\pi$
$194$	1.60789			0.115440
$195$	0.628332	+	2.36945i	0.0449958	+	0.169680i
$196$	2.69504	+	6.46040i	0.192503	+	0.461457i
$197$		−	9.49837i		−	0.676731i	−0.941015	−	0.338365i	$-0.890126\pi$
$197$		−	9.49837i		−	0.676731i	0.941015	−	0.338365i	$-0.109874\pi$
$198$	−0.538165	−	0.314430i	−0.0382457	−	0.0223456i
$199$	1.57005	+	0.906467i	0.111298	+	0.0642578i	0.554616	−	0.832107i	$-0.312865\pi$
$199$	1.57005	+	0.906467i	0.111298	+	0.0642578i	−0.443318	+	0.896365i	$0.646199\pi$
$200$			1.00000i			0.0707107i
$201$	−0.0212929	+	0.0786524i	−0.00150188	+	0.00554771i
$202$	−5.28971	−	3.05401i	−0.372183	−	0.214880i
$203$	16.7517	−	8.28723i	1.17574	−	0.581650i
$204$	−1.66243	−	1.67105i	−0.116394	−	0.116997i
$205$	1.41245	−	2.44643i	0.0986496	−	0.170866i
$206$	−3.30820	+	5.72998i	−0.230493	+	0.399226i
$207$	−19.1842	−	0.0991757i	−1.33339	−	0.00689319i
$208$	−1.22567	+	0.707642i	−0.0849851	+	0.0490661i
$209$	0.687516	+	1.19081i	0.0475565	+	0.0823702i
$210$	0.888048	+	4.49571i	0.0612812	+	0.310233i
$211$	11.3768	−	19.7053i	0.783214	−	1.35657i	−0.146847	−	0.989159i	$-0.546912\pi$
$211$	11.3768	−	19.7053i	0.783214	−	1.35657i	0.930060	−	0.367407i	$-0.119754\pi$
$212$		−	9.70533i		−	0.666565i
$213$	4.24289	−	4.22102i	0.290718	−	0.289219i
$214$	−5.36840			−0.366976
$215$	−1.06723	−	1.84849i	−0.0727844	−	0.126066i
$216$	3.64563	+	3.70262i	0.248054	+	0.251931i
$217$	11.2526	−	5.56679i	0.763879	−	0.377898i
$218$	15.8011	−	9.12274i	1.07018	−	0.617870i
$219$	5.93603	+	22.3848i	0.401120	+	1.51263i
$220$	0.179928	−	0.103881i	0.0121307	−	0.00700368i
$221$	1.66801	−	0.963026i	0.112202	−	0.0647801i
$222$	3.26351	−	3.24668i	0.219032	−	0.217903i
$223$	−8.80329	+	5.08258i	−0.589512	+	0.340355i	−0.764904	−	0.644144i	$-0.777214\pi$
$223$	−8.80329	+	5.08258i	−0.589512	+	0.340355i	0.175393	+	0.984499i	$0.443881\pi$
$224$	−2.37143	+	1.17317i	−0.158448	+	0.0783856i
$225$	−0.0155088	+	2.99996i	−0.00103392	+	0.199997i
$226$	−2.10372	−	3.64375i	−0.139937	−	0.242379i
$227$	17.1927			1.14112			0.570560	−	0.821256i	$-0.306726\pi$
$227$	17.1927			1.14112			0.570560	+	0.821256i	$0.306726\pi$
$228$	−2.93826	−	11.0802i	−0.194591	−	0.733806i
$229$			3.59285i			0.237423i	0.992929	+	0.118711i	$0.0378763\pi$
$229$			3.59285i			0.237423i	−0.992929	+	0.118711i	$0.962124\pi$
$230$	3.19741	−	5.53808i	0.210831	−	0.365170i
$231$	0.716650	−	0.626804i	0.0471521	−	0.0412407i
$232$	3.53199	+	6.11758i	0.231886	+	0.401639i
$233$	18.4117	−	10.6300i	1.20619	−	0.696396i	0.244268	−	0.969708i	$-0.421452\pi$
$233$	18.4117	−	10.6300i	1.20619	−	0.696396i	0.961926	+	0.273312i	$0.0881191\pi$
$234$	−3.68794	+	2.10389i	−0.241088	+	0.137536i
$235$	0.0573414	−	0.0993182i	0.00374054	−	0.00647881i
$236$	−4.34473	+	7.52530i	−0.282818	+	0.489855i
$237$	26.7085	−	7.08258i	1.73490	−	0.460063i
$238$	3.22726	−	1.59656i	0.209192	−	0.103489i
$239$	−4.18867	−	2.41833i	−0.270943	−	0.156429i	0.358373	−	0.933578i	$-0.383331\pi$
$239$	−4.18867	−	2.41833i	−0.270943	−	0.156429i	−0.629316	+	0.777150i	$0.716665\pi$
$240$	−1.67419	+	0.443962i	−0.108068	+	0.0286576i
$241$			1.60992i			0.103704i	0.998655	+	0.0518522i	$0.0165125\pi$
$241$			1.60992i			0.103704i	−0.998655	+	0.0518522i	$0.983488\pi$
$242$	9.48890	+	5.47842i	0.609969	+	0.352166i
$243$	10.8793	+	11.1642i	0.697909	+	0.716186i
$244$		−	2.13738i		−	0.136832i
$245$	−6.94239	−	0.896231i	−0.443533	−	0.0572581i
$246$	4.72285	+	1.27858i	0.301118	+	0.0815191i
$247$	9.36675			0.595992
$248$	2.37255	+	4.10937i	0.150657	+	0.260945i
$249$	−7.29623	+	26.9510i	−0.462379	+	1.70795i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	2.86313			0.180719			0.0903596	−	0.995909i	$-0.471198\pi$
$251$	2.86313			0.180719			0.0903596	+	0.995909i	$0.471198\pi$
$252$	−7.13239	+	3.48268i	−0.449298	+	0.219388i
$253$	−1.32860			−0.0835287
$254$	−12.9550	−	7.47957i	−0.812869	−	0.469310i
$255$	2.27839	−	0.604185i	0.142678	−	0.0378355i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−31.4714			−1.96313			−0.981567	−	0.191118i	$-0.938789\pi$
$257$	−31.4714			−1.96313			−0.981567	+	0.191118i	$0.938789\pi$
$258$	2.62091	−	2.60740i	0.163171	−	0.162330i
$259$	3.11802	+	6.30274i	0.193745	+	0.391633i
$260$		−	1.41528i		−	0.0877722i
$261$	10.5009	+	18.4073i	0.649992	+	1.13938i
$262$	−14.5432	−	8.39654i	−0.898484	−	0.518740i
$263$			3.29302i			0.203056i	0.994833	+	0.101528i	$0.0323732\pi$
$263$			3.29302i			0.203056i	−0.994833	+	0.101528i	$0.967627\pi$
$264$	0.253798	+	0.255113i	0.0156202	+	0.0157011i
$265$	8.40507	+	4.85267i	0.516319	+	0.298097i
$266$	17.4743	+	1.12326i	1.07142	+	0.0688717i
$267$	−1.27615	+	4.71388i	−0.0780990	+	0.288485i
$268$	0.0235223	−	0.0407418i	0.00143685	−	0.00248870i
$269$	9.44456	−	16.3585i	0.575845	−	0.997393i	−0.420104	−	0.907476i	$-0.638006\pi$
$269$	9.44456	−	16.3585i	0.575845	−	0.997393i	0.995949	−	0.0899173i	$-0.0286603\pi$
$270$	−5.02938	+	1.30590i	−0.306078	+	0.0794747i
$271$	2.78962	−	1.61059i	0.169457	−	0.0978362i	−0.412873	−	0.910789i	$-0.635475\pi$
$271$	2.78962	−	1.61059i	0.169457	−	0.0978362i	0.582330	+	0.812953i	$0.302141\pi$
$272$	0.680447	+	1.17857i	0.0412582	+	0.0714612i
$273$	−1.25684	−	6.36270i	−0.0760675	−	0.385088i
$274$	1.69594	−	2.93746i	0.102456	−	0.177459i
$275$			0.207763i			0.0125286i
$276$	10.6913	+	2.89436i	0.643540	+	0.174220i
$277$	0.118953			0.00714722			0.00357361	−	0.999994i	$-0.498862\pi$
$277$	0.118953			0.00714722			0.00357361	+	0.999994i	$0.498862\pi$
$278$	2.93099	+	5.07662i	0.175789	+	0.304475i
$279$	7.05381	+	12.3647i	0.422301	+	0.740258i
$280$	0.169721	−	2.64030i	0.0101428	−	0.157788i
$281$	−11.3489	+	6.55231i	−0.677021	+	0.390878i	−0.798732	−	0.601688i	$-0.794495\pi$
$281$	−11.3489	+	6.55231i	−0.677021	+	0.390878i	0.121711	+	0.992566i	$0.461162\pi$
$282$	0.191735	+	0.0519067i	0.0114176	+	0.00309100i
$283$	−21.6963	+	12.5264i	−1.28971	+	0.744617i	−0.978603	−	0.205757i	$-0.934034\pi$
$283$	−21.6963	+	12.5264i	−1.28971	+	0.744617i	−0.311111	+	0.950374i	$0.600701\pi$
$284$	−2.99245	+	1.72769i	−0.177569	+	0.102520i
$285$	11.0649	+	2.99551i	0.655428	+	0.177438i
$286$	−0.254649	+	0.147022i	−0.0150577	+	0.00869357i
$287$	−4.14450	+	6.21959i	−0.244642	+	0.367131i
$288$	−1.48655	−	2.60580i	−0.0875957	−	0.153548i
$289$	7.57398	+	13.1185i	0.445528	+	0.771678i
$290$	−7.06398			−0.414811
$291$	−2.68819	−	0.727750i	−0.157584	−	0.0426614i
$292$		−	13.3706i		−	0.782454i
$293$	−0.727716	+	1.26044i	−0.0425136	+	0.0736358i	−0.886499	−	0.462730i	$-0.846870\pi$
$293$	−0.727716	+	1.26044i	−0.0425136	+	0.0736358i	0.843986	+	0.536366i	$0.180203\pi$
$294$	−1.58170	−	12.0207i	−0.0922465	−	0.701064i
$295$	−4.34473	−	7.52530i	−0.252960	−	0.438140i
$296$	−2.30171	+	1.32889i	−0.133784	+	0.0772402i
$297$	0.757426	+	0.769265i	0.0439503	+	0.0446373i
$298$	−11.1816	+	19.3671i	−0.647733	+	1.12191i
$299$	−4.52524	+	7.83795i	−0.261702	+	0.453280i
$300$	0.452611	−	1.67187i	0.0261315	−	0.0965254i
$301$	2.50408	+	5.06171i	0.144333	+	0.291752i
$302$	10.9325	+	6.31191i	0.629097	+	0.363209i
$303$	7.46142	+	7.50009i	0.428647	+	0.430869i
$304$			6.61828i			0.379585i
$305$	1.85102	+	1.06869i	0.105989	+	0.0611930i
$306$	2.02304	+	3.54621i	0.115649	+	0.202723i
$307$			0.302317i			0.0172541i	0.999963	+	0.00862706i	$0.00274611\pi$
$307$			0.302317i			0.0172541i	−0.999963	+	0.00862706i	$0.997254\pi$
$308$	−0.492694	+	0.243740i	−0.0280739	+	0.0138884i
$309$	8.12433	−	8.08244i	0.462177	−	0.459794i
$310$	−4.74509			−0.269503
$311$	0.158581	+	0.274670i	0.00899228	+	0.0155751i	0.870487	−	0.492192i	$-0.163804\pi$
$311$	0.158581	+	0.274670i	0.00899228	+	0.0155751i	−0.861494	+	0.507767i	$0.830471\pi$
$312$	2.36945	−	0.628332i	0.134144	−	0.0355723i
$313$	−18.3001	−	10.5656i	−1.03438	−	0.597201i	−0.116146	−	0.993232i	$-0.537054\pi$
$313$	−18.3001	−	10.5656i	−1.03438	−	0.597201i	−0.918237	+	0.396031i	$0.870387\pi$
$314$	−5.80220			−0.327437
$315$	0.550105	−	7.91817i	0.0309949	−	0.446138i
$316$	−15.9531			−0.897434
$317$	8.81472	+	5.08918i	0.495084	+	0.285837i	0.726681	−	0.686975i	$-0.241062\pi$
$317$	8.81472	+	5.08918i	0.495084	+	0.285837i	−0.231597	+	0.972812i	$0.574395\pi$
$318$	−4.39274	+	16.2260i	−0.246333	+	0.909911i
$319$	0.733815	+	1.27101i	0.0410858	+	0.0711626i
$320$	1.00000			0.0559017
$321$	8.97526	+	2.42980i	0.500950	+	0.135618i
$322$	−9.38206	+	14.0795i	−0.522842	+	0.784621i
$323$		−	9.00678i		−	0.501151i
$324$	−4.41917	−	7.84034i	−0.245510	−	0.435574i
$325$	1.22567	+	0.707642i	0.0679880	+	0.0392529i
$326$			17.9738i			0.995476i
$327$	−30.5463	+	8.10030i	−1.68922	+	0.447948i
$328$	−2.44643	−	1.41245i	−0.135081	−	0.0779893i
$329$	−0.168255	+	0.252498i	−0.00927620	+	0.0139207i
$330$	−0.347833	+	0.0922387i	−0.0191476	+	0.00507757i
$331$	11.0901	−	19.2086i	0.609566	−	1.05580i	−0.381746	−	0.924267i	$-0.624677\pi$
$331$	11.0901	−	19.2086i	0.609566	−	1.05580i	0.991312	−	0.131531i	$-0.0419894\pi$
$332$	8.06016	−	13.9606i	0.442359	−	0.766187i
$333$	−6.92564	+	3.95092i	−0.379522	+	0.216509i
$334$	−8.66956	+	5.00537i	−0.474377	+	0.273882i
$335$	0.0235223	+	0.0407418i	0.00128516	+	0.00222596i
$336$	4.49571	−	0.888048i	0.245261	−	0.0484470i
$337$	−13.9347	+	24.1356i	−0.759070	+	1.31475i	0.184256	+	0.982878i	$0.441013\pi$
$337$	−13.9347	+	24.1356i	−0.759070	+	1.31475i	−0.943325	+	0.331869i	$0.892321\pi$
$338$		−	10.9970i		−	0.598156i
$339$	1.86794	+	7.04403i	0.101453	+	0.382579i
$340$	−1.36089			−0.0738048
$341$	0.492926	+	0.853773i	0.0266935	+	0.0462344i
$342$	−0.102641	+	19.8546i	−0.00555021	+	1.07361i
$343$	18.1779	+	3.54459i	0.981514	+	0.191390i
$344$	−1.84849	+	1.06723i	−0.0996641	+	0.0575411i
$345$	−7.85224	+	7.81175i	−0.422750	+	0.420571i
$346$	6.23910	−	3.60215i	0.335416	−	0.193653i
$347$	7.70036	−	4.44581i	0.413377	−	0.238663i	−0.278863	−	0.960331i	$-0.589957\pi$
$347$	7.70036	−	4.44581i	0.413377	−	0.238663i	0.692240	+	0.721668i	$0.256624\pi$
$348$	−3.13614	−	11.8264i	−0.168115	−	0.633962i
$349$	−22.9898	+	13.2732i	−1.23062	+	0.710497i	−0.967159	−	0.254173i	$-0.918197\pi$
$349$	−22.9898	+	13.2732i	−1.23062	+	0.710497i	−0.263459	+	0.964671i	$0.584863\pi$
$350$	2.20171	+	1.46713i	0.117686	+	0.0784216i
$351$	7.11800	−	1.84822i	0.379930	−	0.0986509i
$352$	−0.103881	−	0.179928i	−0.00553689	−	0.00959018i
$353$	29.8048			1.58635			0.793175	−	0.608994i	$-0.208427\pi$
$353$	29.8048			1.58635			0.793175	+	0.608994i	$0.208427\pi$
$354$	10.6699	−	10.6148i	0.567096	−	0.564172i
$355$		−	3.45539i		−	0.183393i
$356$	1.40976	−	2.44178i	0.0747173	−	0.129414i
$357$	−6.11818	+	1.20854i	−0.323808	+	0.0639627i
$358$	7.33833	+	12.7104i	0.387843	+	0.671763i
$359$	14.6722	−	8.47101i	0.774370	−	0.447083i	−0.0600612	−	0.998195i	$-0.519130\pi$
$359$	14.6722	−	8.47101i	0.774370	−	0.447083i	0.834431	+	0.551112i	$0.185796\pi$
$360$	2.99996	+	0.0155088i	0.158112	+	0.000817383i
$361$	12.4008	−	21.4789i	0.652675	−	1.13047i
$362$	10.3252	−	17.8838i	0.542680	−	0.939949i
$363$	−13.3846	−	13.4540i	−0.702509	−	0.706150i
$364$	−0.240204	+	3.73678i	−0.0125901	+	0.195860i
$365$	11.5793	+	6.68529i	0.606086	+	0.349924i
$366$	−0.967400	+	3.57341i	−0.0505668	+	0.186785i
$367$			21.0437i			1.09847i	0.835667	+	0.549236i	$0.185081\pi$
$367$			21.0437i			1.09847i	−0.835667	+	0.549236i	$0.814919\pi$
$368$	−5.53808	−	3.19741i	−0.288692	−	0.166677i
$369$	−7.31728	−	4.27522i	−0.380923	−	0.222559i
$370$		−	2.65778i		−	0.138171i
$371$	−21.3683	−	14.2390i	−1.10939	−	0.739253i
$372$	−2.10664	−	7.94416i	−0.109224	−	0.411886i
$373$	−11.2313			−0.581535			−0.290768	−	0.956794i	$-0.593911\pi$
$373$	−11.2313			−0.581535			−0.290768	+	0.956794i	$0.593911\pi$
$374$	0.141371	+	0.244863i	0.00731014	+	0.0126615i
$375$	1.22158	+	1.22791i	0.0630819	+	0.0634088i
$376$	−0.0993182	−	0.0573414i	−0.00512195	−	0.00295716i
$377$	9.99753			0.514899
$378$	13.5007	−	2.59439i	0.694402	−	0.133441i
$379$	2.41836			0.124223			0.0621113	−	0.998069i	$-0.480217\pi$
$379$	2.41836			0.124223			0.0621113	+	0.998069i	$0.480217\pi$
$380$	−5.73160	−	3.30914i	−0.294025	−	0.169755i
$381$	18.2737	+	18.3684i	0.936191	+	0.941043i
$382$	−10.9763	−	19.0114i	−0.561594	−	0.972709i
$383$	−17.5017			−0.894293			−0.447146	−	0.894461i	$-0.647560\pi$
$383$	−17.5017			−0.894293			−0.447146	+	0.894461i	$0.647560\pi$
$384$	0.443962	+	1.67419i	0.0226558	+	0.0854354i
$385$	0.0352617	−	0.548556i	0.00179710	−	0.0279570i
$386$		−	20.6101i		−	1.04902i
$387$	−5.56196	+	3.17297i	−0.282730	+	0.161291i
$388$	1.39248	+	0.803947i	0.0706923	+	0.0408142i
$389$			6.70962i			0.340191i	0.985428	+	0.170096i	$0.0544076\pi$
$389$			6.70962i			0.340191i	−0.985428	+	0.170096i	$0.945592\pi$
$390$	−0.640573	+	2.36617i	−0.0324367	+	0.119816i
$391$	7.53673	+	4.35134i	0.381149	+	0.220057i
$392$	−0.896231	+	6.94239i	−0.0452665	+	0.350644i
$393$	20.5140	+	20.6203i	1.03479	+	1.04016i
$394$	4.74918	−	8.22583i	0.239260	−	0.414411i
$395$	7.97657	−	13.8158i	0.401345	−	0.695149i
$396$	−0.308849	−	0.541387i	−0.0155203	−	0.0272057i
$397$	6.02981	−	3.48131i	0.302628	−	0.174722i	−0.340995	−	0.940065i	$-0.610764\pi$
$397$	6.02981	−	3.48131i	0.302628	−	0.174722i	0.643623	+	0.765343i	$0.277431\pi$
$398$	0.906467	+	1.57005i	0.0454371	+	0.0786994i
$399$	−28.7063	−	9.78699i	−1.43711	−	0.489962i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	11.5760i		−	0.578076i	−0.957318	−	0.289038i	$-0.906665\pi$
$401$		−	11.5760i		−	0.578076i	0.957318	−	0.289038i	$-0.0933354\pi$
$402$	−0.0577664	+	0.0574685i	−0.00288112	+	0.00286627i
$403$	6.71565			0.334530
$404$	−3.05401	−	5.28971i	−0.151943	−	0.263173i
$405$	8.99952	+	0.0930513i	0.447190	+	0.00462376i
$406$	18.6510	+	1.19891i	0.925635	+	0.0595008i
$407$	−0.478209	+	0.276094i	−0.0237039	+	0.0136855i
$408$	−0.604185	−	2.27839i	−0.0299116	−	0.112797i
$409$	−31.4609	+	18.1640i	−1.55564	+	0.898151i	−0.557979	+	0.829855i	$0.688423\pi$
$409$	−31.4609	+	18.1640i	−1.55564	+	0.898151i	−0.997665	+	0.0682960i	$0.978244\pi$
$410$	2.44643	−	1.41245i	0.120821	−	0.0697558i
$411$	−4.16492	+	4.14345i	−0.205440	+	0.204381i
$412$	−5.72998	+	3.30820i	−0.282296	+	0.162983i
$413$	10.1942	+	20.6065i	0.501624	+	1.01398i
$414$	−16.5644	−	9.67799i	−0.814097	−	0.475647i
$415$	8.06016	+	13.9606i	0.395657	+	0.685299i
$416$	−1.41528			−0.0693900
$417$	−2.60249	−	9.81403i	−0.127445	−	0.480595i
$418$			1.37503i			0.0672550i
$419$	16.0393	−	27.7808i	0.783570	−	1.35718i	−0.146280	−	0.989243i	$-0.546730\pi$
$419$	16.0393	−	27.7808i	0.783570	−	1.35718i	0.929850	−	0.367939i	$-0.119937\pi$
$420$	−1.47878	+	4.33742i	−0.0721571	+	0.211644i
$421$	−5.92162	−	10.2565i	−0.288602	−	0.499873i	0.684874	−	0.728661i	$-0.259857\pi$
$421$	−5.92162	−	10.2565i	−0.288602	−	0.499873i	−0.973476	+	0.228788i	$0.926524\pi$
$422$	19.7053	−	11.3768i	0.959237	−	0.553816i
$423$	−0.297061	−	0.173562i	−0.0144436	−	0.00843888i
$424$	4.85267	−	8.40507i	0.235666	−	0.408186i
$425$	0.680447	−	1.17857i	0.0330065	−	0.0571690i
$426$	5.78496	−	1.53406i	0.280282	−	0.0743254i
$427$	−4.70588	−	3.13582i	−0.227734	−	0.151753i
$428$	−4.64917	−	2.68420i	−0.224726	−	0.129746i
$429$	0.492283	−	0.130544i	0.0237676	−	0.00630272i
$430$		−	2.13446i		−	0.102933i
$431$	28.2466	+	16.3082i	1.36059	+	0.785538i	0.989703	−	0.143139i	$-0.0457195\pi$
$431$	28.2466	+	16.3082i	1.36059	+	0.785538i	0.370890	+	0.928677i	$0.379053\pi$
$432$	1.30590	+	5.02938i	0.0628303	+	0.241976i
$433$		−	1.82172i		−	0.0875462i	−0.999041	−	0.0437731i	$-0.986062\pi$
$433$		−	1.82172i		−	0.0875462i	0.999041	−	0.0437731i	$-0.0139379\pi$
$434$	12.5285	+	0.805343i	0.601386	+	0.0386577i
$435$	11.8100	+	3.19723i	0.566248	+	0.153296i
$436$	18.2455			0.873800
$437$	21.1614	+	36.6526i	1.01229	+	1.75333i
$438$	−6.05167	+	22.3539i	−0.289160	+	1.06811i
$439$	20.6763	+	11.9375i	0.986825	+	0.569744i	0.904324	−	0.426847i	$-0.140376\pi$
$439$	20.6763	+	11.9375i	0.986825	+	0.569744i	0.0825012	+	0.996591i	$0.473709\pi$
$440$	0.207763			0.00990470
$441$	−2.79632	+	20.8130i	−0.133158	+	0.991095i
$442$	1.92605			0.0916129
$443$	−20.4555	−	11.8100i	−0.971868	−	0.561109i	−0.0720631	−	0.997400i	$-0.522958\pi$
$443$	−20.4555	−	11.8100i	−0.971868	−	0.561109i	−0.899805	+	0.436292i	$0.856292\pi$
$444$	4.44962	−	1.17995i	0.211170	−	0.0559981i
$445$	1.40976	+	2.44178i	0.0668292	+	0.115752i
$446$	−10.1652			−0.481334
$447$	27.4599	−	27.3183i	1.29881	−	1.29211i
$448$	−2.64030	−	0.169721i	−0.124743	−	0.00801858i
$449$		−	33.6640i		−	1.58870i	−0.607459	−	0.794351i	$-0.707811\pi$
$449$		−	33.6640i		−	1.58870i	0.607459	−	0.794351i	$-0.292189\pi$
$450$	−1.51341	+	2.59029i	−0.0713429	+	0.122107i
$451$	−0.508277	−	0.293454i	−0.0239338	−	0.0138182i
$452$		−	4.20744i		−	0.197901i
$453$	−15.4209	−	15.5009i	−0.724539	−	0.728294i
$454$	14.8893	+	8.59635i	0.698790	+	0.403447i
$455$	−3.11604	−	2.07641i	−0.146082	−	0.0973437i
$456$	2.99551	−	11.0649i	0.140277	−	0.518161i
$457$	−9.09952	+	15.7608i	−0.425658	+	0.737261i	−0.996482	−	0.0838116i	$-0.973291\pi$
$457$	−9.09952	+	15.7608i	−0.425658	+	0.737261i	0.570824	+	0.821073i	$0.306624\pi$
$458$	−1.79643	+	3.11150i	−0.0839415	+	0.145391i
$459$	−1.77720	−	6.84445i	−0.0829524	−	0.319471i
$460$	5.53808	−	3.19741i	0.258214	−	0.149080i
$461$	−7.33169	−	12.6989i	−0.341471	−	0.591445i	0.643235	−	0.765669i	$-0.277592\pi$
$461$	−7.33169	−	12.6989i	−0.341471	−	0.591445i	−0.984706	+	0.174224i	$0.944258\pi$
$462$	0.934040	−	0.184503i	0.0434555	−	0.00858387i
$463$	−3.20796	+	5.55635i	−0.149087	+	0.258226i	−0.930890	−	0.365299i	$-0.880967\pi$
$463$	−3.20796	+	5.55635i	−0.149087	+	0.258226i	0.781804	+	0.623525i	$0.214300\pi$
$464$			7.06398i			0.327937i
$465$	7.93317	+	2.14768i	0.367892	+	0.0995962i
$466$	21.2600			0.984853
$467$	−13.0712	−	22.6399i	−0.604862	−	1.04765i	−0.992073	−	0.125660i	$-0.959895\pi$
$467$	−13.0712	−	22.6399i	−0.604862	−	1.04765i	0.387212	−	0.921991i	$-0.373438\pi$
$468$	−4.24580	−	0.0219493i	−0.196262	−	0.00101461i
$469$	−0.0551912	−	0.111563i	−0.00254849	−	0.00515150i
$470$	0.0993182	−	0.0573414i	0.00458121	−	0.00264496i
$471$	9.70051	+	2.62614i	0.446976	+	0.121006i
$472$	−7.52530	+	4.34473i	−0.346380	+	0.199983i
$473$	−0.384048	+	0.221730i	−0.0176585	+	0.0101952i
$474$	26.6715	+	7.22056i	1.22506	+	0.331651i
$475$	5.73160	−	3.30914i	0.262984	−	0.151834i
$476$	3.59317	+	0.230973i	0.164693	+	0.0105866i
$477$	14.6882	−	25.1396i	0.672525	−	1.15106i
$478$	−2.41833	−	4.18867i	−0.110612	−	0.191585i
$479$	33.7251			1.54094			0.770470	−	0.637476i	$-0.220021\pi$
$479$	33.7251			1.54094			0.770470	+	0.637476i	$0.220021\pi$
$480$	−1.67187	−	0.452611i	−0.0763100	−	0.0206588i
$481$			3.76152i			0.171510i
$482$	−0.804962	+	1.39424i	−0.0366650	+	0.0635057i
$483$	22.0581	−	19.2927i	1.00368	−	0.877848i
$484$	5.47842	+	9.48890i	0.249019	+	0.431314i
$485$	−1.39248	+	0.803947i	−0.0632291	+	0.0365053i
$486$	3.83966	+	15.1082i	0.174170	+	0.685321i
$487$	3.38529	−	5.86349i	0.153402	−	0.265700i	−0.779074	−	0.626932i	$-0.784310\pi$
$487$	3.38529	−	5.86349i	0.153402	−	0.265700i	0.932476	+	0.361232i	$0.117644\pi$
$488$	1.06869	−	1.85102i	0.0483773	−	0.0837919i
$489$	8.13513	−	30.0498i	0.367883	−	1.35890i
$490$	−5.56417	−	4.24735i	−0.251364	−	0.191876i
$491$	−7.86871	−	4.54300i	−0.355110	−	0.205023i	0.311824	−	0.950140i	$-0.399060\pi$
$491$	−7.86871	−	4.54300i	−0.355110	−	0.205023i	−0.666934	+	0.745117i	$0.732393\pi$
$492$	3.45082	+	3.46870i	0.155575	+	0.156381i
$493$		−	9.61332i		−	0.432962i
$494$	8.11184	+	4.68338i	0.364969	+	0.210715i
$495$	0.623280	+	0.00322214i	0.0280143	+	0.000144824i
$496$			4.74509i			0.213061i
$497$	−0.586453	+	9.12327i	−0.0263060	+	0.409234i
$498$	−19.7942	+	19.6922i	−0.887001	+	0.882427i
$499$	−42.0589			−1.88281			−0.941407	−	0.337274i	$-0.890495\pi$
$499$	−42.0589			−1.88281			−0.941407	+	0.337274i	$0.890495\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	16.7598	−	4.44439i	0.748774	−	0.198561i
$502$	2.47954	+	1.43157i	0.110667	+	0.0638939i
$503$	−19.9162			−0.888021			−0.444011	−	0.896021i	$-0.646445\pi$
$503$	−19.9162			−0.888021			−0.444011	+	0.896021i	$0.646445\pi$
$504$	−7.91817	−	0.550105i	−0.352703	−	0.0245036i
$505$	6.10803			0.271804
$506$	−1.15061	−	0.664302i	−0.0511506	−	0.0295318i
$507$	−4.97735	+	18.3855i	−0.221052	+	0.816528i
$508$	−7.47957	−	12.9550i	−0.331852	−	0.574785i
$509$	24.0286			1.06505			0.532524	−	0.846415i	$-0.321244\pi$
$509$	24.0286			1.06505			0.532524	+	0.846415i	$0.321244\pi$
$510$	2.27524	+	0.615955i	0.100749	+	0.0272750i
$511$	−29.4381	−	19.6164i	−1.30227	−	0.867780i
$512$		−	1.00000i		−	0.0441942i
$513$	9.15800	−	33.1478i	0.404336	−	1.46351i
$514$	−27.2551	−	15.7357i	−1.20217	−	0.694073i
$515$		−	6.61641i		−	0.291554i
$516$	3.57348	−	0.947617i	0.157314	−	0.0417165i
$517$	−0.0206346	−	0.0119134i	−0.000907509	−	0.000523951i
$518$	−0.451082	+	7.01735i	−0.0198194	+	0.308324i
$519$	−12.0613	+	3.19843i	−0.529433	+	0.140395i
$520$	0.707642	−	1.22567i	0.0310322	−	0.0537493i
$521$	−16.5020	+	28.5823i	−0.722965	+	1.25221i	0.236841	+	0.971548i	$0.423888\pi$
$521$	−16.5020	+	28.5823i	−0.722965	+	1.25221i	−0.959806	+	0.280663i	$0.909446\pi$
$522$	−0.109553	+	21.1916i	−0.00479503	+	0.927533i
$523$	−26.4518	+	15.2720i	−1.15666	+	0.667797i	−0.950501	−	0.310722i	$-0.899429\pi$
$523$	−26.4518	+	15.2720i	−1.15666	+	0.667797i	−0.206157	+	0.978519i	$0.566096\pi$
$524$	−8.39654	−	14.5432i	−0.366805	−	0.635324i
$525$	−3.01693	−	3.44937i	−0.131669	−	0.150543i
$526$	−1.64651	+	2.85184i	−0.0717912	+	0.124346i
$527$		−	6.45757i		−	0.281296i
$528$	0.0922387	+	0.347833i	0.00401417	+	0.0151375i
$529$	−17.8937			−0.777988
$530$	4.85267	+	8.40507i	0.210786	+	0.365093i
$531$	−22.6430	+	12.9173i	−0.982622	+	0.560564i
$532$	14.5715	+	9.70991i	0.631756	+	0.420978i
$533$	−3.46239	+	1.99901i	−0.149973	+	0.0865869i
$534$	−3.46212	+	3.44427i	−0.149820	+	0.149048i
$535$	4.64917	−	2.68420i	0.201001	−	0.116048i
$536$	0.0407418	−	0.0235223i	0.00175978	−	0.00101601i
$537$	−6.51587	−	24.5714i	−0.281181	−	1.06034i
$538$	16.3585	−	9.44456i	0.705264	−	0.407184i
$539$	−0.186203	+	1.44237i	−0.00802034	+	0.0621272i
$540$	−5.00852	−	1.38374i	−0.215532	−	0.0595468i
$541$	−14.4385	−	25.0082i	−0.620760	−	1.07519i	−0.989345	−	0.145593i	$-0.953491\pi$
$541$	−14.4385	−	25.0082i	−0.620760	−	1.07519i	0.368585	−	0.929594i	$-0.379842\pi$
$542$	3.22117			0.138361
$543$	−25.3567	+	25.2260i	−1.08816	+	1.08255i
$544$			1.36089i			0.0583478i
$545$	−9.12274	+	15.8011i	−0.390775	+	0.676843i
$546$	2.09289	−	6.13868i	0.0895676	−	0.262711i
$547$	14.0094	+	24.2650i	0.598999	+	1.03750i	0.992969	+	0.118374i	$0.0377681\pi$
$547$	14.0094	+	24.2650i	0.598999	+	1.03750i	−0.393970	+	0.919123i	$0.628899\pi$
$548$	2.93746	−	1.69594i	0.125482	−	0.0724472i
$549$	3.23473	−	5.53642i	0.138055	−	0.236289i
$550$	−0.103881	+	0.179928i	−0.00442951	+	0.00767214i
$551$	23.3757	−	40.4879i	0.995838	−	1.72484i
$552$	7.81175	+	7.85224i	0.332490	+	0.334214i
$553$	−23.4054	+	35.1242i	−0.995298	+	1.49363i
$554$	0.103017	+	0.0594767i	0.00437676	+	0.00252692i
$555$	−1.20294	+	4.44346i	−0.0510620	+	0.188614i
$556$			5.86197i			0.248603i
$557$	8.62658	+	4.98056i	0.365520	+	0.211033i	0.671499	−	0.741005i	$-0.265651\pi$
$557$	8.62658	+	4.98056i	0.365520	+	0.211033i	−0.305980	+	0.952038i	$0.598984\pi$
$558$	−0.0735905	+	14.2351i	−0.00311533	+	0.602619i
$559$			3.02086i			0.127769i
$560$	1.46713	−	2.20171i	0.0619977	−	0.0930391i
$561$	−0.125527	−	0.473364i	−0.00529976	−	0.0199855i
$562$	−13.1046			−0.552785
$563$	−19.2619	−	33.3626i	−0.811794	−	1.40607i	−0.911608	−	0.411062i	$-0.865158\pi$
$563$	−19.2619	−	33.3626i	−0.811794	−	1.40607i	0.0998141	−	0.995006i	$-0.468175\pi$
$564$	0.140094	+	0.140820i	0.00589901	+	0.00592958i
$565$	3.64375	+	2.10372i	0.153294	+	0.0885041i
$566$	−25.0528			−1.05305
$567$	−23.7457	−	1.77309i	−0.997224	−	0.0744629i
$568$	−3.45539			−0.144985
$569$	−13.3337	−	7.69820i	−0.558977	−	0.322725i	0.193758	−	0.981049i	$-0.437932\pi$
$569$	−13.3337	−	7.69820i	−0.558977	−	0.322725i	−0.752735	+	0.658324i	$0.771266\pi$
$570$	8.08473	+	8.12663i	0.338632	+	0.340387i
$571$	−2.32196	−	4.02175i	−0.0971709	−	0.168305i	0.813342	−	0.581786i	$-0.197646\pi$
$571$	−2.32196	−	4.02175i	−0.0971709	−	0.168305i	−0.910513	+	0.413481i	$0.864313\pi$
$572$	−0.294043			−0.0122946
$573$	9.74607	+	36.7526i	0.407148	+	1.53536i
$574$	−6.69903	+	3.31407i	−0.279612	+	0.138327i
$575$			6.39482i			0.266682i
$576$	0.0155088	−	2.99996i	0.000646198	−	0.124998i
$577$	−16.2075	−	9.35741i	−0.674727	−	0.389554i	0.123138	−	0.992390i	$-0.460704\pi$
$577$	−16.2075	−	9.35741i	−0.674727	−	0.389554i	−0.797865	+	0.602836i	$0.794037\pi$
$578$			15.1480i			0.630072i
$579$	−9.32834	+	34.4573i	−0.387672	+	1.43200i
$580$	−6.11758	−	3.53199i	−0.254019	−	0.146658i
$581$	−18.9118	−	38.2282i	−0.784595	−	1.58597i
$582$	−1.96416	−	1.97434i	−0.0814172	−	0.0818391i
$583$	1.00820	−	1.74626i	0.0417555	−	0.0723226i
$584$	6.68529	−	11.5793i	0.276639	−	0.479153i
$585$	2.14191	−	3.66599i	0.0885569	−	0.151570i
$586$	−1.26044	+	0.727716i	−0.0520684	+	0.0300617i
$587$	5.45638	+	9.45073i	0.225209	+	0.390073i	0.956382	−	0.292119i	$-0.0943602\pi$
$587$	5.45638	+	9.45073i	0.225209	+	0.390073i	−0.731173	+	0.682192i	$0.761027\pi$
$588$	4.64058	−	11.2011i	0.191374	−	0.461926i
$589$	15.7022	−	27.1970i	0.646997	−	1.12063i
$590$		−	8.68947i		−	0.357740i
$591$	−11.6631	+	11.6030i	−0.479756	+	0.477282i
$592$	−2.65778			−0.109234
$593$	−9.60114	−	16.6297i	−0.394272	−	0.682899i	0.598736	−	0.800946i	$-0.295670\pi$
$593$	−9.60114	−	16.6297i	−0.394272	−	0.682899i	−0.993008	+	0.118048i	$0.962336\pi$
$594$	0.271318	+	1.04492i	0.0111323	+	0.0428734i
$595$	−1.99661	+	2.99629i	−0.0818532	+	0.122836i
$596$	−19.3671	+	11.1816i	−0.793307	+	0.458016i
$597$	−0.804874	−	3.03519i	−0.0329413	−	0.124222i
$598$	−7.83795	+	4.52524i	−0.320518	+	0.185051i
$599$	18.9751	−	10.9553i	0.775301	−	0.447620i	−0.0594613	−	0.998231i	$-0.518938\pi$
$599$	18.9751	−	10.9553i	0.775301	−	0.447620i	0.834762	+	0.550610i	$0.185605\pi$
$600$	1.22791	−	1.22158i	0.0501291	−	0.0498706i
$601$	−38.2477	+	22.0823i	−1.56016	+	0.900756i	−0.562915	+	0.826515i	$0.690320\pi$
$601$	−38.2477	+	22.0823i	−1.56016	+	0.900756i	−0.997240	+	0.0742412i	$0.976347\pi$
$602$	−0.362263	+	5.63561i	−0.0147647	+	0.229690i
$603$	0.122589	−	0.0699341i	0.00499219	−	0.00284794i
$604$	6.31191	+	10.9325i	0.256828	+	0.444839i
$605$	−10.9568			−0.445459
$606$	2.71173	+	10.2260i	0.110157	+	0.415402i
$607$			25.8388i			1.04876i	0.851483	+	0.524382i	$0.175704\pi$
$607$			25.8388i			1.04876i	−0.851483	+	0.524382i	$0.824296\pi$
$608$	−3.30914	+	5.73160i	−0.134203	+	0.232447i
$609$	−30.6394	−	10.4461i	−1.24157	−	0.423296i
$610$	1.06869	+	1.85102i	0.0432700	+	0.0749458i
$611$	−0.140563	+	0.0811544i	−0.00568659	+	0.00328315i
$612$	−0.0211058	+	4.08263i	−0.000853150	+	0.165030i
$613$	20.3696	−	35.2812i	0.822720	−	1.42499i	−0.0809298	−	0.996720i	$-0.525789\pi$
$613$	20.3696	−	35.2812i	0.822720	−	1.42499i	0.903650	−	0.428273i	$-0.140878\pi$
$614$	−0.151158	+	0.261814i	−0.00610025	+	0.0105659i
$615$	−4.72940	+	1.25414i	−0.190708	+	0.0505720i
$616$	−0.548556	−	0.0352617i	−0.0221020	−	0.00142074i
$617$	18.7258	+	10.8114i	0.753874	+	0.435249i	0.827092	−	0.562067i	$-0.189994\pi$
$617$	18.7258	+	10.8114i	0.753874	+	0.435249i	−0.0732181	+	0.997316i	$0.523327\pi$
$618$	11.0771	−	2.93743i	0.445586	−	0.118161i
$619$		−	41.5576i		−	1.67034i	−0.549992	−	0.835170i	$-0.685369\pi$
$619$		−	41.5576i		−	1.67034i	0.549992	−	0.835170i	$-0.314631\pi$
$620$	−4.10937	−	2.37255i	−0.165036	−	0.0952837i
$621$	23.3132	+	23.6776i	0.935525	+	0.950148i
$622$			0.317161i			0.0127170i
$623$	−3.30778	−	6.68631i	−0.132523	−	0.267881i
$624$	2.36617	+	0.640573i	0.0947226	+	0.0256434i
$625$	1.00000			0.0400000
$626$	−10.5656	−	18.3001i	−0.422285	−	0.731419i
$627$	0.622354	−	2.29887i	0.0248544	−	0.0918081i
$628$	−5.02485	−	2.90110i	−0.200513	−	0.115766i
$629$	3.61696			0.144218
$630$	4.43549	−	6.58228i	0.176714	−	0.262244i
$631$	−24.7896			−0.986860			−0.493430	−	0.869785i	$-0.664257\pi$
$631$	−24.7896			−0.986860			−0.493430	+	0.869785i	$0.664257\pi$
$632$	−13.8158	−	7.97657i	−0.549564	−	0.317291i
$633$	−38.0939	+	10.1018i	−1.51410	+	0.401509i
$634$	5.08918	+	8.81472i	0.202117	+	0.350077i
$635$	14.9591			0.593635
$636$	−11.9172	+	11.8558i	−0.472549	+	0.470113i
$637$	7.87488	+	6.01121i	0.312014	+	0.238173i
$638$			1.46763i			0.0581040i
$639$	−10.3660	−	0.0535888i	−0.410074	−	0.00211994i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$			35.4280i			1.39932i	0.714476	+	0.699660i	$0.246665\pi$
$641$			35.4280i			1.39932i	−0.714476	+	0.699660i	$0.753335\pi$
$642$	6.55790	+	6.59189i	0.258820	+	0.260161i
$643$	−25.1223	−	14.5043i	−0.990726	−	0.571996i	−0.0852345	−	0.996361i	$-0.527164\pi$
$643$	−25.1223	−	14.5043i	−0.990726	−	0.571996i	−0.905491	+	0.424365i	$0.860497\pi$
$644$	−15.1649	+	7.50220i	−0.597579	+	0.295628i
$645$	−0.966078	+	3.56853i	−0.0380393	+	0.140511i
$646$	4.50339	−	7.80010i	0.177184	−	0.306891i
$647$	14.2851	−	24.7426i	0.561607	−	0.972731i	−0.435750	−	0.900068i	$-0.643517\pi$
$647$	14.2851	−	24.7426i	0.561607	−	0.972731i	0.997357	−	0.0726633i	$-0.0231498\pi$
$648$	0.0930513	−	8.99952i	0.00365540	−	0.353534i
$649$	−1.56348	+	0.902674i	−0.0613718	+	0.0354330i
$650$	0.707642	+	1.22567i	0.0277560	+	0.0480748i
$651$	−20.5815	−	7.01695i	−0.806651	−	0.275016i
$652$	−8.98690	+	15.5658i	−0.351954	+	0.609602i
$653$			23.3202i			0.912588i	0.889829	+	0.456294i	$0.150823\pi$
$653$			23.3202i			0.912588i	−0.889829	+	0.456294i	$0.849177\pi$
$654$	−30.5041	−	8.25810i	−1.19280	−	0.322917i
$655$	16.7931			0.656160
$656$	−1.41245	−	2.44643i	−0.0551468	−	0.0955170i
$657$	20.2352	−	34.6336i	0.789450	−	1.35119i
$658$	−0.271962	+	0.134542i	−0.0106022	+	0.00524500i
$659$	−41.6998	+	24.0754i	−1.62440	+	0.937845i	−0.638670	+	0.769481i	$0.720515\pi$
$659$	−41.6998	+	24.0754i	−1.62440	+	0.937845i	−0.985725	+	0.168364i	$0.946151\pi$
$660$	−0.347352	−	0.0940356i	−0.0135206	−	0.00366033i
$661$	−37.5132	+	21.6582i	−1.45909	+	0.842408i	−0.998967	−	0.0454452i	$-0.985529\pi$
$661$	−37.5132	+	21.6582i	−1.45909	+	0.842408i	−0.460127	+	0.887853i	$0.652196\pi$
$662$	19.2086	−	11.0901i	0.746562	−	0.431028i
$663$	−3.22010	−	0.871752i	−0.125058	−	0.0338560i
$664$	13.9606	−	8.06016i	0.541776	−	0.312795i
$665$	−15.6948	+	7.76436i	−0.608618	+	0.301089i
$666$	−7.97324	−	0.0412189i	−0.308957	−	0.00159720i
$667$	22.5864	+	39.1208i	0.874550	+	1.51476i
$668$	−10.0107			−0.387327
$669$	16.9948	+	4.60086i	0.657057	+	0.177880i
$670$			0.0470446i			0.00181749i
$671$	0.222034	−	0.384574i	0.00857151	−	0.0148463i
$672$	4.33742	+	1.47878i	0.167320	+	0.0570452i
$673$	−10.7910	−	18.6906i	−0.415964	−	0.720471i	0.579565	−	0.814926i	$-0.303222\pi$
$673$	−10.7910	−	18.6906i	−0.415964	−	0.720471i	−0.995529	+	0.0944550i	$0.969889\pi$
$674$	−24.1356	+	13.9347i	−0.929667	+	0.536743i
$675$	3.70262	−	3.64563i	0.142514	−	0.140320i
$676$	5.49849	−	9.52366i	0.211480	−	0.366294i
$677$	18.2704	−	31.6452i	0.702188	−	1.21623i	−0.265509	−	0.964108i	$-0.585540\pi$
$677$	18.2704	−	31.6452i	0.702188	−	1.21623i	0.967697	−	0.252117i	$-0.0811268\pi$
$678$	−1.90433	+	7.03428i	−0.0731354	+	0.270150i
$679$	3.81301	−	1.88633i	0.146330	−	0.0723907i
$680$	−1.17857	−	0.680447i	−0.0451960	−	0.0260940i
$681$	−21.0022	−	21.1110i	−0.804805	−	0.808976i
$682$			0.985853i			0.0377502i
$683$	36.6115	+	21.1377i	1.40090	+	0.808811i	0.994485	−	0.104878i	$-0.0334451\pi$
$683$	36.6115	+	21.1377i	1.40090	+	0.808811i	0.406416	+	0.913688i	$0.366778\pi$
$684$	−10.0162	+	17.1433i	−0.382978	+	0.655489i
$685$			3.39189i			0.129597i
$686$	13.9702	+	12.1587i	0.533386	+	0.464220i
$687$	4.41169	−	4.38894i	0.168316	−	0.167449i
$688$	−2.13446			−0.0813754
$689$	−6.86790	−	11.8956i	−0.261646	−	0.453185i
$690$	−10.7061	+	2.83906i	−0.407575	+	0.108081i
$691$	−26.9067	−	15.5346i	−1.02358	−	0.590964i	−0.108441	−	0.994103i	$-0.534586\pi$
$691$	−26.9067	−	15.5346i	−1.02358	−	0.590964i	−0.915139	+	0.403139i	$0.867919\pi$
$692$	7.20429			0.273866
$693$	−1.64510	−	0.114291i	−0.0624922	−	0.00434156i
$694$	8.89161			0.337521
$695$	−5.07662	−	2.93099i	−0.192567	−	0.111179i
$696$	3.19723	−	11.8100i	0.121191	−	0.447658i
$697$	1.92219	+	3.32933i	0.0728081	+	0.126107i
$698$	−26.5464			−1.00480
$699$	−35.5440	−	9.62253i	−1.34440	−	0.363957i
$700$	1.17317	+	2.37143i	0.0443416	+	0.0896316i
$701$			27.7518i			1.04817i	0.851666	+	0.524085i	$0.175593\pi$
$701$			27.7518i			1.04817i	−0.851666	+	0.524085i	$0.824407\pi$
$702$	7.08848	+	1.95839i	0.267537	+	0.0739146i
$703$	15.2333	+	8.79497i	0.574536	+	0.331709i
$704$		−	0.207763i		−	0.00783035i
$705$	−0.192000	+	0.0509148i	−0.00723115	+	0.00191756i
$706$	25.8117	+	14.9024i	0.971437	+	0.560859i
$707$	−16.1270	−	1.03666i	−0.606520	−	0.0389877i
$708$	14.5478	−	3.85779i	0.546739	−	0.144985i
$709$	−7.10868	+	12.3126i	−0.266972	+	0.462409i	−0.968078	−	0.250648i	$-0.919356\pi$
$709$	−7.10868	+	12.3126i	−0.266972	+	0.462409i	0.701106	+	0.713057i	$0.252690\pi$
$710$	1.72769	−	2.99245i	0.0648392	−	0.112305i
$711$	−41.3232	−	24.1437i	−1.54974	−	0.905458i
$712$	2.44178	−	1.40976i	0.0915097	−	0.0528331i
$713$	15.1720	+	26.2787i	0.568196	+	0.984144i
$714$	−5.90277	−	2.01246i	−0.220906	−	0.0753146i
$715$	0.147022	−	0.254649i	0.00549830	−	0.00952333i
$716$			14.6767i			0.548492i
$717$	2.14729	+	8.09747i	0.0801921	+	0.302405i
$718$	16.9420			0.632271
$719$	21.6234	+	37.4528i	0.806415	+	1.39675i	0.915332	+	0.402701i	$0.131929\pi$
$719$	21.6234	+	37.4528i	0.806415	+	1.39675i	−0.108916	+	0.994051i	$0.534738\pi$
$720$	2.59029	+	1.51341i	0.0965343	+	0.0564015i
$721$	−1.12294	+	17.4693i	−0.0418207	+	0.650591i
$722$	21.4789	−	12.4008i	0.799361	−	0.461511i
$723$	1.97684	−	1.96664i	0.0735194	−	0.0731403i
$724$	17.8838	−	10.3252i	0.664645	−	0.383733i
$725$	6.11758	−	3.53199i	0.227201	−	0.131175i
$726$	−4.86442	−	18.3438i	−0.180535	−	0.680801i
$727$	−2.32159	+	1.34037i	−0.0861032	+	0.0497117i	−0.542433	−	0.840099i	$-0.682497\pi$
$727$	−2.32159	+	1.34037i	−0.0861032	+	0.0497117i	0.456330	+	0.889811i	$0.349164\pi$
$728$	−2.07641	+	3.11604i	−0.0769569	+	0.115488i
$729$	0.418721	−	26.9968i	0.0155082	−	0.999880i
$730$	6.68529	+	11.5793i	0.247434	+	0.428568i
$731$	2.90477			0.107437
$732$	−2.62450	+	2.61097i	−0.0970043	+	0.0965041i
$733$		−	21.7022i		−	0.801588i	−0.916168	−	0.400794i	$-0.868734\pi$
$733$		−	21.7022i		−	0.801588i	0.916168	−	0.400794i	$-0.131266\pi$
$734$	−10.5218	+	18.2244i	−0.388368	+	0.672674i
$735$	7.38016	+	9.61942i	0.272221	+	0.354818i
$736$	−3.19741	−	5.53808i	−0.117858	−	0.204136i
$737$	0.00846463	−	0.00488705i	0.000311799	−	0.000180017i
$738$	−4.19934	−	7.36110i	−0.154580	−	0.270966i
$739$	−0.779082	+	1.34941i	−0.0286590	+	0.0496389i	−0.879999	−	0.474975i	$-0.842457\pi$
$739$	−0.779082	+	1.34941i	−0.0286590	+	0.0496389i	0.851340	+	0.524614i	$0.175790\pi$
$740$	1.32889	−	2.30171i	0.0488510	−	0.0846124i
$741$	−11.4422	−	11.5015i	−0.420339	−	0.422518i
$742$	−11.3860	−	23.0155i	−0.417993	−	0.844926i
$743$	−5.56936	−	3.21547i	−0.204320	−	0.117964i	0.394349	−	0.918961i	$-0.370970\pi$
$743$	−5.56936	−	3.21547i	−0.204320	−	0.117964i	−0.598669	+	0.800997i	$0.704303\pi$
$744$	2.14768	−	7.93317i	0.0787377	−	0.290844i
$745$		−	22.3632i		−	0.819324i
$746$	−9.72660	−	5.61566i	−0.356116	−	0.205604i
$747$	42.0062	−	23.9636i	1.53693	−	0.876783i
$748$			0.282743i			0.0103381i
$749$	−12.7308	+	6.29804i	−0.465173	+	0.230125i
$750$	0.443962	+	1.67419i	0.0162112	+	0.0611326i
$751$	54.6839			1.99544			0.997722	−	0.0674569i	$-0.0214885\pi$
$751$	54.6839			1.99544			0.997722	+	0.0674569i	$0.0214885\pi$
$752$	−0.0573414	−	0.0993182i	−0.00209103	−	0.00362176i
$753$	−3.49753	−	3.51566i	−0.127457	−	0.128118i
$754$	8.65812	+	4.99877i	0.315310	+	0.182044i
$755$	−12.6238			−0.459427
$756$	12.9892	+	4.50355i	0.472411	+	0.163793i
$757$	6.88087			0.250089			0.125045	−	0.992151i	$-0.460093\pi$
$757$	6.88087			0.250089			0.125045	+	0.992151i	$0.460093\pi$
$758$	2.09436	+	1.20918i	0.0760705	+	0.0439193i
$759$	1.62299	+	1.63140i	0.0589108	+	0.0592161i
$760$	−3.30914	−	5.73160i	−0.120035	−	0.207907i
$761$	−20.3654			−0.738246			−0.369123	−	0.929380i	$-0.620342\pi$
$761$	−20.3654			−0.738246			−0.369123	+	0.929380i	$0.620342\pi$
$762$	6.64129	+	25.0444i	0.240588	+	0.907262i
$763$	26.7686	−	40.1712i	0.969087	−	1.45430i
$764$		−	21.9525i		−	0.794214i
$765$	−3.52511	−	2.05959i	−0.127450	−	0.0744647i
$766$	−15.1569	−	8.75083i	−0.547640	−	0.316180i
$767$			12.2981i			0.444057i
$768$	−0.452611	+	1.67187i	−0.0163322	+	0.0603284i
$769$	17.8787	+	10.3223i	0.644721	+	0.372230i	0.786431	−	0.617678i	$-0.211927\pi$
$769$	17.8787	+	10.3223i	0.644721	+	0.372230i	−0.141710	+	0.989908i	$0.545260\pi$
$770$	0.304816	−	0.457433i	0.0109848	−	0.0164847i
$771$	38.4447	+	38.6440i	1.38455	+	1.39173i
$772$	10.3050	−	17.8488i	0.370886	−	0.642394i
$773$	−13.4607	+	23.3145i	−0.484146	+	0.838566i	−0.999834	−	0.0182107i	$-0.994203\pi$
$773$	−13.4607	+	23.3145i	−0.484146	+	0.838566i	0.515688	+	0.856776i	$0.327536\pi$
$774$	−6.40328	−	0.0331028i	−0.230161	−	0.00118985i
$775$	4.10937	−	2.37255i	0.147613	−	0.0852244i
$776$	0.803947	+	1.39248i	0.0288600	+	0.0499870i
$777$	3.93028	−	11.5279i	0.140998	−	0.413562i
$778$	−3.35481	+	5.81070i	−0.120276	+	0.208324i
$779$			18.6959i			0.669852i
$780$	−1.73784	+	1.72888i	−0.0622245	+	0.0619037i
$781$	−0.717900			−0.0256885
$782$	4.35134	+	7.53673i	0.155603	+	0.269513i
$783$	9.77472	−	35.3801i	0.349320	−	1.26438i
$784$	−4.24735	+	5.56417i	−0.151691	+	0.198720i
$785$	5.02485	−	2.90110i	0.179345	−	0.103545i
$786$	7.45549	+	28.1147i	0.265928	+	1.00282i
$787$	23.5840	−	13.6162i	0.840677	−	0.485365i	−0.0168171	−	0.999859i	$-0.505353\pi$
$787$	23.5840	−	13.6162i	0.840677	−	0.485365i	0.857494	+	0.514493i	$0.172020\pi$
$788$	8.22583	−	4.74918i	0.293033	−	0.169183i
$789$	4.04352	−	4.02267i	0.143953	−	0.143211i
$790$	13.8158	−	7.97657i	0.491545	−	0.283794i
$791$	−9.26355	−	6.17287i	−0.329374	−	0.219482i
$792$	0.00322214	−	0.623280i	0.000114494	−	0.0221473i
$793$	−1.51250	−	2.61972i	−0.0537104	−	0.0930291i
$794$	6.96263			0.247094
$795$	−4.30880	−	16.2485i	−0.152817	−	0.576276i
$796$			1.81293i			0.0642578i
$797$	−12.9468	+	22.4246i	−0.458601	+	0.794319i	−0.998887	−	0.0471616i	$-0.984982\pi$
$797$	−12.9468	+	22.4246i	−0.458601	+	0.794319i	0.540287	+	0.841481i	$0.318316\pi$
$798$	−19.9669	−	22.8289i	−0.706819	−	0.808135i
$799$	0.0780356	+	0.135162i	0.00276070	+	0.00478167i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	7.34711	−	4.19137i	0.259598	−	0.148095i
$802$	5.78798	−	10.0251i	0.204381	−	0.353998i
$803$	1.38895	−	2.40574i	0.0490151	−	0.0848967i
$804$	−0.0787614	+	0.0208860i	−0.00277770	+	0.000736592i
$805$	1.08534	−	16.8843i	0.0382531	−	0.595092i
$806$	5.81593	+	3.35783i	0.204857	+	0.118274i
$807$	−31.6239	+	8.38605i	−1.11321	+	0.295203i
$808$		−	6.10803i		−	0.214880i
$809$	−20.9833	−	12.1147i	−0.737734	−	0.425931i	0.0835110	−	0.996507i	$-0.473387\pi$
$809$	−20.9833	−	12.1147i	−0.737734	−	0.425931i	−0.821245	+	0.570576i	$0.806720\pi$
$810$	7.74729	+	4.58034i	0.272212	+	0.160937i
$811$			26.9699i			0.947040i	0.880783	+	0.473520i	$0.157017\pi$
$811$			26.9699i			0.947040i	−0.880783	+	0.473520i	$0.842983\pi$
$812$	15.5528	+	10.3638i	0.545797	+	0.363698i
$813$	−5.38538	−	1.45794i	−0.188873	−	0.0511321i
$814$	−0.552188			−0.0193542
$815$	−8.98690	−	15.5658i	−0.314797	−	0.545245i
$816$	0.615955	−	2.27524i	0.0215627	−	0.0796492i
$817$	12.2339	+	7.06322i	0.428008	+	0.247111i
$818$	−36.3280			−1.27018
$819$	−6.27748	+	9.31580i	−0.219353	+	0.325520i
$820$	2.82489			0.0986496
$821$	−1.73135	−	0.999595i	−0.0604245	−	0.0348861i	0.469483	−	0.882941i	$-0.344440\pi$
$821$	−1.73135	−	0.999595i	−0.0604245	−	0.0348861i	−0.529908	+	0.848055i	$0.677774\pi$
$822$	−5.67865	+	1.50587i	−0.198066	+	0.0525232i
$823$	3.14423	+	5.44597i	0.109601	+	0.189835i	0.915609	−	0.402071i	$-0.131709\pi$
$823$	3.14423	+	5.44597i	0.109601	+	0.189835i	−0.806008	+	0.591905i	$0.798376\pi$
$824$	−6.61641			−0.230493
$825$	0.255113	−	0.253798i	0.00888190	−	0.00883610i
$826$	−1.47479	+	22.9428i	−0.0513144	+	0.798283i
$827$			43.5204i			1.51335i	0.653789	+	0.756677i	$0.273178\pi$
$827$			43.5204i			1.51335i	−0.653789	+	0.756677i	$0.726822\pi$
$828$	−9.50621	−	16.6636i	−0.330364	−	0.579100i
$829$	−28.3927	−	16.3926i	−0.986120	−	0.569337i	−0.0820080	−	0.996632i	$-0.526133\pi$
$829$	−28.3927	−	16.3926i	−0.986120	−	0.569337i	−0.904112	+	0.427295i	$0.859467\pi$
$830$			16.1203i			0.559544i
$831$	−0.145310	−	0.146064i	−0.00504076	−	0.00506689i
$832$	−1.22567	−	0.707642i	−0.0424925	−	0.0245331i
$833$	5.78020	−	7.57225i	0.200272	−	0.262363i
$834$	2.65319	−	9.80044i	0.0918725	−	0.339362i
$835$	5.00537	−	8.66956i	0.173218	−	0.300022i
$836$	−0.687516	+	1.19081i	−0.0237782	+	0.0411851i
$837$	6.56598	−	23.7659i	0.226954	−	0.821469i
$838$	27.7808	−	16.0393i	0.959673	−	0.554067i
$839$	−4.60486	−	7.97586i	−0.158978	−	0.275357i	0.775523	−	0.631320i	$-0.217486\pi$
$839$	−4.60486	−	7.97586i	−0.158978	−	0.275357i	−0.934500	+	0.355962i	$0.884153\pi$
$840$	−3.44937	+	3.01693i	−0.119015	+	0.104094i
$841$	10.4499	−	18.0997i	0.360341	−	0.624128i
$842$		−	11.8432i		−	0.408145i
$843$	21.9092	+	5.93129i	0.754593	+	0.204284i
$844$	22.7537			0.783214
$845$	5.49849	+	9.52366i	0.189154	+	0.327624i
$846$	−0.170482	−	0.298840i	−0.00586128	−	0.0102743i
$847$	28.9294	+	1.85961i	0.994024	+	0.0638969i
$848$	8.40507	−	4.85267i	0.288631	−	0.166641i
$849$	41.8850	+	11.3392i	1.43749	+	0.389159i
$850$	1.17857	−	0.680447i	0.0404246	−	0.0233391i
$851$	−14.7190	+	8.49802i	−0.504561	+	0.291308i
$852$	5.77695	+	1.56395i	0.197915	+	0.0535799i
$853$	−34.0668	+	19.6685i	−1.16642	+	0.673435i	−0.952835	−	0.303489i	$-0.901849\pi$
$853$	−34.0668	+	19.6685i	−1.16642	+	0.673435i	−0.213589	+	0.976924i	$0.568515\pi$
$854$	−2.50750	−	5.06864i	−0.0858050	−	0.173445i
$855$	−9.83840	−	17.2459i	−0.336466	−	0.589797i
$856$	−2.68420	−	4.64917i	−0.0917441	−	0.158905i
$857$	32.4112			1.10715			0.553573	−	0.832801i	$-0.313264\pi$
$857$	32.4112			1.10715			0.553573	+	0.832801i	$0.313264\pi$
$858$	0.491601	+	0.133087i	0.0167830	+	0.00454352i
$859$			26.4199i			0.901435i	0.892667	+	0.450717i	$0.148832\pi$
$859$			26.4199i			0.901435i	−0.892667	+	0.450717i	$0.851168\pi$
$860$	1.06723	−	1.84849i	0.0363922	−	0.0630331i
$861$	12.6999	−	2.50864i	0.432811	−	0.0854943i
$862$	16.3082	+	28.2466i	0.555459	+	0.962084i
$863$	24.4007	−	14.0878i	0.830610	−	0.479553i	−0.0234518	−	0.999725i	$-0.507466\pi$
$863$	24.4007	−	14.0878i	0.830610	−	0.479553i	0.854061	+	0.520172i	$0.174132\pi$
$864$	−1.38374	+	5.00852i	−0.0470759	+	0.170393i
$865$	−3.60215	+	6.23910i	−0.122477	+	0.212136i
$866$	0.910860	−	1.57766i	0.0309523	−	0.0536109i
$867$	6.85613	−	25.3254i	0.232846	−	0.860096i
$868$	10.4473	+	6.96168i	0.354605	+	0.236295i
$869$	−2.87041	−	1.65723i	−0.0973721	−	0.0562178i
$870$	8.62918	+	8.67390i	0.292557	+	0.294073i
$871$		−	0.0665815i		−	0.00225603i
$872$	15.8011	+	9.12274i	0.535091	+	0.308935i
$873$	2.39021	+	4.18984i	0.0808964	+	0.141805i
$874$			42.3227i			1.43159i
$875$	−2.64030	−	0.169721i	−0.0892585	−	0.00573763i
$876$	−16.4178	+	16.3332i	−0.554707	+	0.551847i
$877$	36.3479			1.22738			0.613691	−	0.789546i	$-0.289684\pi$
$877$	36.3479			1.22738			0.613691	+	0.789546i	$0.289684\pi$
$878$	11.9375	+	20.6763i	0.402870	+	0.697791i
$879$	2.43666	−	0.646156i	0.0821866	−	0.0217943i
$880$	0.179928	+	0.103881i	0.00606536	+	0.00350184i
$881$	0.589367			0.0198563			0.00992814	−	0.999951i	$-0.496840\pi$
$881$	0.589367			0.0198563			0.00992814	+	0.999951i	$0.496840\pi$
$882$	−12.8282	+	16.6264i	−0.431947	+	0.559841i
$883$	55.1932			1.85740			0.928700	−	0.370833i	$-0.120928\pi$
$883$	55.1932			1.85740			0.928700	+	0.370833i	$0.120928\pi$
$884$	1.66801	+	0.963026i	0.0561012	+	0.0323901i
$885$	−3.93295	+	14.5276i	−0.132205	+	0.488342i
$886$	−11.8100	−	20.4555i	−0.396764	−	0.687215i
$887$	50.8028			1.70579			0.852896	−	0.522082i	$-0.174844\pi$
$887$	50.8028			1.70579			0.852896	+	0.522082i	$0.174844\pi$
$888$	4.44346	+	1.20294i	0.149113	+	0.0403680i
$889$	−39.4966	−	2.53888i	−1.32467	−	0.0851514i
$890$			2.81953i			0.0945108i
$891$	0.0193326	−	1.86976i	0.000647666	−	0.0626394i
$892$	−8.80329	−	5.08258i	−0.294756	−	0.170177i
$893$			0.759003i			0.0253991i
$894$	37.4402	−	9.92841i	1.25219	−	0.332056i
$895$	−12.7104	−	7.33833i	−0.424860	−	0.245293i
$896$	−2.20171	−	1.46713i	−0.0735539	−	0.0490135i
$897$	15.1522	−	4.01807i	0.505917	−	0.134159i
$898$	16.8320	−	29.1539i	0.561691	−	0.972878i
$899$	16.7596	−	29.0285i	0.558964	−	0.968154i
$900$	−2.60580	+	1.48655i	−0.0868599	+	0.0495516i
$901$	−11.4384	+	6.60397i	−0.381068	+	0.220010i
$902$	−0.293454	−	0.508277i	−0.00977094	−	0.0169238i
$903$	3.15639	−	9.25803i	0.105038	−	0.308088i
$904$	2.10372	−	3.64375i	0.0699687	−	0.121189i
$905$			20.6504i			0.686442i
$906$	−5.60449	−	21.1346i	−0.186197	−	0.702150i
$907$	−19.4956			−0.647340			−0.323670	−	0.946170i	$-0.604917\pi$
$907$	−19.4956			−0.647340			−0.323670	+	0.946170i	$0.604917\pi$
$908$	8.59635	+	14.8893i	0.285280	+	0.494119i
$909$	0.0947279	−	18.3238i	0.00314193	−	0.607764i
$910$	−1.66037	−	3.35625i	−0.0550406	−	0.111258i
$911$	29.5749	−	17.0751i	0.979860	−	0.565723i	0.0776324	−	0.996982i	$-0.475264\pi$
$911$	29.5749	−	17.0751i	0.979860	−	0.565723i	0.902228	+	0.431259i	$0.141931\pi$
$912$	8.12663	−	8.08473i	0.269100	−	0.267712i
$913$	2.90049	−	1.67460i	0.0959922	−	0.0554211i
$914$	−15.7608	+	9.09952i	−0.521322	+	0.300986i
$915$	−0.948914	−	3.57837i	−0.0313701	−	0.118297i
$916$	−3.11150	+	1.79643i	−0.102807	+	0.0593556i
$917$	−44.3388	−	2.85014i	−1.46420	−	0.0941200i
$918$	1.88313	−	6.81606i	0.0621524	−	0.224964i
$919$	−8.23460	−	14.2627i	−0.271634	−	0.470484i	0.697646	−	0.716442i	$-0.254231\pi$
$919$	−8.23460	−	14.2627i	−0.271634	−	0.470484i	−0.969280	+	0.245958i	$0.920897\pi$
$920$	6.39482			0.210831
$921$	0.371216	−	0.369302i	0.0122320	−	0.0121689i
$922$		−	14.6634i		−	0.482913i
$923$	−2.44518	+	4.23517i	−0.0804840	+	0.139402i
$924$	0.901154	+	0.307235i	0.0296458	+	0.0101073i
$925$	1.32889	+	2.30171i	0.0436937	+	0.0756796i
$926$	−5.55635	+	3.20796i	−0.182593	+	0.105420i
$927$	−19.8490	−	0.102612i	−0.651925	−	0.00337023i
$928$	−3.53199	+	6.11758i	−0.115943	+	0.200820i
$929$	−5.86104	+	10.1516i	−0.192294	+	0.333064i	−0.946010	−	0.324137i	$-0.894926\pi$
$929$	−5.86104	+	10.1516i	−0.192294	+	0.333064i	0.753716	+	0.657200i	$0.228260\pi$
$930$	5.79648	+	5.82653i	0.190074	+	0.191059i
$931$	42.7568	−	17.8365i	1.40130	−	0.584568i
$932$	18.4117	+	10.6300i	0.603097	+	0.348198i
$933$	0.143550	−	0.530252i	0.00469963	−	0.0173597i
$934$		−	26.1423i		−	0.855403i
$935$	−0.244863	−	0.141371i	−0.00800786	−	0.00462334i
$936$	−3.66599	−	2.14191i	−0.119827	−	0.0700104i
$937$		−	10.5888i		−	0.345922i	−0.984929	−	0.172961i	$-0.944667\pi$
$937$		−	10.5888i		−	0.345922i	0.984929	−	0.172961i	$-0.0553334\pi$
$938$	0.00798447	−	0.124212i	0.000260702	−	0.00405566i
$939$	9.38142	+	35.3775i	0.306151	+	1.15450i
$940$	0.114683			0.00374054
$941$	5.81412	+	10.0704i	0.189535	+	0.328284i	0.945095	−	0.326795i	$-0.105969\pi$
$941$	5.81412	+	10.0704i	0.189535	+	0.328284i	−0.755560	+	0.655079i	$0.772635\pi$
$942$	7.08782	+	7.12455i	0.230934	+	0.232130i
$943$	−15.6445	−	9.03234i	−0.509454	−	0.294134i
$944$	−8.68947			−0.282818
$945$	−10.3948	+	8.99716i	−0.338142	+	0.292678i
$946$	−0.443460			−0.0144181
$947$	−1.79619	−	1.03703i	−0.0583682	−	0.0336989i	0.470532	−	0.882383i	$-0.344062\pi$
$947$	−1.79619	−	1.03703i	−0.0583682	−	0.0336989i	−0.528900	+	0.848684i	$0.677395\pi$
$948$	19.4880	+	19.5890i	0.632939	+	0.636220i
$949$	−9.46159	−	16.3879i	−0.307136	−	0.531975i
$950$	6.61828			0.214725
$951$	−4.51880	−	17.0405i	−0.146532	−	0.552575i
$952$	2.99629	+	1.99661i	0.0971104	+	0.0647106i
$953$			28.8160i			0.933442i	0.884405	+	0.466721i	$0.154565\pi$
$953$			28.8160i			0.933442i	−0.884405	+	0.466721i	$0.845435\pi$
$954$	25.2901	−	14.4275i	0.818798	−	0.467106i
$955$	19.0114	+	10.9763i	0.615195	+	0.355183i
$956$		−	4.83666i		−	0.156429i
$957$	0.664265	−	2.45368i	0.0214726	−	0.0793164i
$958$	29.2068	+	16.8626i	0.943629	+	0.544805i
$959$	0.575676	−	8.95561i	0.0185895	−	0.289192i
$960$	−1.22158	−	1.22791i	−0.0394262	−	0.0396305i
$961$	−4.24206	+	7.34746i	−0.136840	+	0.237015i
$962$	−1.88076	+	3.25757i	−0.0606381	+	0.105028i
$963$	−7.98039	−	13.9890i	−0.257165	−	0.450788i
$964$	−1.39424	+	0.804962i	−0.0449053	+	0.0259261i
$965$	10.3050	+	17.8488i	0.331731	+	0.574574i
$966$	28.7492	−	5.67891i	0.924991	−	0.182716i
$967$	−9.12278	+	15.8011i	−0.293369	+	0.508130i	−0.974604	−	0.223935i	$-0.928110\pi$
$967$	−9.12278	+	15.8011i	−0.293369	+	0.508130i	0.681235	+	0.732065i	$0.261443\pi$
$968$			10.9568i			0.352166i
$969$	−11.0595	+	11.0025i	−0.355282	+	0.353450i
$970$	−1.60789			−0.0516263
$971$	−1.09564	−	1.89770i	−0.0351606	−	0.0609000i	0.847910	−	0.530141i	$-0.177861\pi$
$971$	−1.09564	−	1.89770i	−0.0351606	−	0.0609000i	−0.883070	+	0.469241i	$0.844528\pi$
$972$	−4.22885	+	15.0039i	−0.135640	+	0.481250i
$973$	12.9063	+	8.60030i	0.413759	+	0.275713i
$974$	5.86349	−	3.38529i	0.187878	−	0.108472i
$975$	−0.628332	−	2.36945i	−0.0201227	−	0.0758831i
$976$	1.85102	−	1.06869i	0.0592498	−	0.0342079i
$977$	−0.216592	+	0.125049i	−0.00692939	+	0.00400068i	−0.503461	−	0.864018i	$-0.667940\pi$
$977$	−0.216592	+	0.125049i	−0.00692939	+	0.00400068i	0.496531	+	0.868019i	$0.334607\pi$
$978$	22.0701	−	21.9563i	0.705725	−	0.702086i
$979$	0.507311	−	0.292896i	0.0162137	−	0.00936101i
$980$	−2.69504	−	6.46040i	−0.0860898	−	0.206370i
$981$	47.2611	+	27.6129i	1.50893	+	0.881613i
$982$	−4.54300	−	7.86871i	−0.144973	−	0.251101i
$983$	−3.21720			−0.102613			−0.0513064	−	0.998683i	$-0.516339\pi$
$983$	−3.21720			−0.102613			−0.0513064	+	0.998683i	$0.516339\pi$
$984$	1.25414	+	4.72940i	0.0399807	+	0.150768i
$985$			9.49837i			0.302643i
$986$	4.80666	−	8.32538i	0.153075	−	0.265134i
$987$	0.515580	−	0.101844i	0.0164111	−	0.00324173i
$988$	4.68338	+	8.11184i	0.148998	+	0.258072i
$989$	−11.8208	+	6.82473i	−0.375879	+	0.217014i
$990$	0.538165	+	0.314430i	0.0171040	+	0.00999325i
$991$	−0.704168	+	1.21966i	−0.0223686	+	0.0387436i	−0.876993	−	0.480503i	$-0.840454\pi$
$991$	−0.704168	+	1.21966i	−0.0223686	+	0.0387436i	0.854624	+	0.519247i	$0.173787\pi$
$992$	−2.37255	+	4.10937i	−0.0753284	+	0.130473i
$993$	−37.1337	+	9.84714i	−1.17840	+	0.312489i
$994$	−5.06952	+	7.60775i	−0.160795	+	0.241303i
$995$	−1.57005	−	0.906467i	−0.0497739	−	0.0287369i
$996$	−26.9884	+	7.15680i	−0.855160	+	0.226772i
$997$		−	35.8484i		−	1.13533i	−0.823260	−	0.567664i	$-0.807847\pi$
$997$		−	35.8484i		−	1.13533i	0.823260	−	0.567664i	$-0.192153\pi$
$998$	−36.4240	−	21.0294i	−1.15298	−	0.665675i
$999$	13.3115	+	3.67768i	0.421159	+	0.116357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.311.10	✓	28
3.2	odd	2		1890.2.t.b.1151.6		28
7.5	odd	6		630.2.bk.b.131.2	yes	28
9.2	odd	6		630.2.bk.b.101.9	yes	28
9.7	even	3		1890.2.bk.b.521.7		28
21.5	even	6		1890.2.bk.b.341.7		28
63.47	even	6	inner	630.2.t.b.551.10	yes	28
63.61	odd	6		1890.2.t.b.1601.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.10	✓	28	1.1	even	1	trivial
630.2.t.b.551.10	yes	28	63.47	even	6	inner
630.2.bk.b.101.9	yes	28	9.2	odd	6
630.2.bk.b.131.2	yes	28	7.5	odd	6
1890.2.t.b.1151.6		28	3.2	odd	2
1890.2.t.b.1601.6		28	63.61	odd	6
1890.2.bk.b.341.7		28	21.5	even	6
1890.2.bk.b.521.7		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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.22158 - 1.22791i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.443962 - 1.67419i) q^{6} +(2.64030 + 0.169721i) q^{7} +1.00000i q^{8} +(-0.0155088 + 2.99996i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.22158 - 1.22791i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.443962 - 1.67419i) q^{6} +(2.64030 + 0.169721i) q^{7} +1.00000i q^{8} +(-0.0155088 + 2.99996i) q^{9} +(-0.866025 - 0.500000i) q^{10} +0.207763i q^{11} +(0.452611 - 1.67187i) q^{12} +(1.22567 + 0.707642i) q^{13} +(2.20171 + 1.46713i) q^{14} +(1.22158 + 1.22791i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.680447 - 1.17857i) q^{17} +(-1.51341 + 2.59029i) q^{18} +(5.73160 - 3.30914i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.01693 - 3.44937i) q^{21} +(-0.103881 + 0.179928i) q^{22} +6.39482i q^{23} +(1.22791 - 1.22158i) q^{24} +1.00000 q^{25} +(0.707642 + 1.22567i) q^{26} +(3.70262 - 3.64563i) q^{27} +(1.17317 + 2.37143i) q^{28} +(6.11758 - 3.53199i) q^{29} +(0.443962 + 1.67419i) q^{30} +(4.10937 - 2.37255i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.255113 - 0.253798i) q^{33} +(1.17857 - 0.680447i) q^{34} +(-2.64030 - 0.169721i) q^{35} +(-2.60580 + 1.48655i) q^{36} +(1.32889 + 2.30171i) q^{37} +6.61828 q^{38} +(-0.628332 - 2.36945i) q^{39} -1.00000i q^{40} +(-1.41245 + 2.44643i) q^{41} +(-0.888048 - 4.49571i) q^{42} +(1.06723 + 1.84849i) q^{43} +(-0.179928 + 0.103881i) q^{44} +(0.0155088 - 2.99996i) q^{45} +(-3.19741 + 5.53808i) q^{46} +(-0.0573414 + 0.0993182i) q^{47} +(1.67419 - 0.443962i) q^{48} +(6.94239 + 0.896231i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-2.27839 + 0.604185i) q^{51} +1.41528i q^{52} +(-8.40507 - 4.85267i) q^{53} +(5.02938 - 1.30590i) q^{54} -0.207763i q^{55} +(-0.169721 + 2.64030i) q^{56} +(-11.0649 - 2.99551i) q^{57} +7.06398 q^{58} +(4.34473 + 7.52530i) q^{59} +(-0.452611 + 1.67187i) q^{60} +(-1.85102 - 1.06869i) q^{61} +4.74509 q^{62} +(-0.550105 + 7.91817i) q^{63} -1.00000 q^{64} +(-1.22567 - 0.707642i) q^{65} +(0.347833 - 0.0922387i) q^{66} +(-0.0235223 - 0.0407418i) q^{67} +1.36089 q^{68} +(7.85224 - 7.81175i) q^{69} +(-2.20171 - 1.46713i) q^{70} +3.45539i q^{71} +(-2.99996 - 0.0155088i) q^{72} +(-11.5793 - 6.68529i) q^{73} +2.65778i q^{74} +(-1.22158 - 1.22791i) q^{75} +(5.73160 + 3.30914i) q^{76} +(-0.0352617 + 0.548556i) q^{77} +(0.640573 - 2.36617i) q^{78} +(-7.97657 + 13.8158i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99952 - 0.0930513i) q^{81} +(-2.44643 + 1.41245i) q^{82} +(-8.06016 - 13.9606i) q^{83} +(1.47878 - 4.33742i) q^{84} +(-0.680447 + 1.17857i) q^{85} +2.13446i q^{86} +(-11.8100 - 3.19723i) q^{87} -0.207763 q^{88} +(-1.40976 - 2.44178i) q^{89} +(1.51341 - 2.59029i) q^{90} +(3.11604 + 2.07641i) q^{91} +(-5.53808 + 3.19741i) q^{92} +(-7.93317 - 2.14768i) q^{93} +(-0.0993182 + 0.0573414i) q^{94} +(-5.73160 + 3.30914i) q^{95} +(1.67187 + 0.452611i) q^{96} +(1.39248 - 0.803947i) q^{97} +(5.56417 + 4.24735i) q^{98} +(-0.623280 - 0.00322214i) 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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