LMFDB - Embedded newform 630.2.bt.a.347.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("630.317");

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.bt (of order $12$, degree $4$, 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:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			347.38
Character	$\chi$	$=$	630.347
Dual form			630.2.bt.a.443.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.0558589 - 1.73115i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.02346 - 0.951627i) q^{5} +(1.68662 - 0.394099i) q^{6} +(-2.58706 + 0.554174i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99376 - 0.193400i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.0558589 - 1.73115i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.02346 - 0.951627i) q^{5} +(1.68662 - 0.394099i) q^{6} +(-2.58706 + 0.554174i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99376 - 0.193400i) q^{9} +(1.44291 + 1.70822i) q^{10} -4.54436i q^{11} +(0.817200 + 1.52715i) q^{12} +(-1.13198 - 4.22459i) q^{13} +(-1.20487 - 2.35548i) q^{14} +(-1.53438 - 3.55608i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.304112 - 1.13496i) q^{17} +(-0.588032 - 2.94181i) q^{18} +(-5.35282 + 3.09045i) q^{19} +(-1.27656 + 1.83586i) q^{20} +(0.814849 + 4.50955i) q^{21} +(4.38951 - 1.17617i) q^{22} +(5.32448 + 5.32448i) q^{23} +(-1.26361 + 1.18461i) q^{24} +(3.18881 - 3.85116i) q^{25} +(3.78767 - 2.18681i) q^{26} +(-0.502033 + 5.17184i) q^{27} +(1.96337 - 1.77346i) q^{28} +(-3.13342 - 5.42724i) q^{29} +(3.03778 - 2.40248i) q^{30} +(0.179481 + 0.310870i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.86697 - 0.253843i) q^{33} +(1.01758 - 0.587499i) q^{34} +(-4.70746 + 3.58327i) q^{35} +(2.68937 - 1.32939i) q^{36} +(2.46721 - 9.20775i) q^{37} +(-4.37056 - 4.37056i) q^{38} +(-7.37664 + 1.72364i) q^{39} +(-2.10371 - 0.757903i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(-4.14499 + 1.95424i) q^{42} +(8.19545 + 2.19596i) q^{43} +(2.27218 + 3.93553i) q^{44} +(-6.24181 + 2.45760i) q^{45} +(-3.76497 + 6.52113i) q^{46} +(-0.788240 - 2.94175i) q^{47} +(-1.47129 - 0.913950i) q^{48} +(6.38578 - 2.86737i) q^{49} +(4.54527 + 2.08340i) q^{50} +(-1.98178 + 0.463066i) q^{51} +(3.09262 + 3.09262i) q^{52} +(-0.0705647 + 0.0189078i) q^{53} +(-5.12555 + 0.853645i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(2.22119 + 1.43747i) q^{56} +(5.05103 + 9.43915i) q^{57} +(4.43132 - 4.43132i) q^{58} +(4.25394 + 7.36804i) q^{59} +(3.10685 + 2.31246i) q^{60} +(2.94582 - 5.10230i) q^{61} +(-0.253824 + 0.253824i) q^{62} +(7.85222 - 1.15873i) q^{63} +1.00000i q^{64} +(-6.31075 - 7.47110i) q^{65} +(-1.79093 - 7.66461i) q^{66} +(2.47729 - 9.24538i) q^{67} +(0.830850 + 0.830850i) q^{68} +(9.51489 - 8.92005i) q^{69} +(-4.67955 - 3.61964i) q^{70} +13.2021i q^{71} +(1.98015 + 2.25366i) q^{72} +(2.45665 + 9.16835i) q^{73} +9.53256 q^{74} +(-6.48882 - 5.73544i) q^{75} +(3.09045 - 5.35282i) q^{76} +(2.51837 + 11.7565i) q^{77} +(-3.57412 - 6.67917i) q^{78} +(-4.56295 - 2.63442i) q^{79} +(0.187599 - 2.22818i) q^{80} +(8.92519 + 1.15799i) q^{81} +(2.40536 - 8.97694i) q^{82} +(0.957089 - 3.57191i) q^{83} +(-2.96045 - 3.49796i) q^{84} +(-1.69542 - 2.00715i) q^{85} +8.48456i q^{86} +(-9.57039 + 5.12126i) q^{87} +(-3.21335 + 3.21335i) q^{88} +(2.74487 + 4.75426i) q^{89} +(-3.98936 - 5.39305i) q^{90} +(5.26966 + 10.3020i) q^{91} +(-7.27337 - 1.94889i) q^{92} +(0.548188 - 0.293343i) q^{93} +(2.63750 - 1.52276i) q^{94} +(-7.89027 + 11.3473i) q^{95} +(0.502010 - 1.65770i) q^{96} +(0.903546 - 3.37208i) q^{97} +(4.42243 + 5.42606i) q^{98} +(-0.878880 + 13.6047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.0558589	−	1.73115i	0.0322501	−	0.999480i
$3$	0.0558589	−	1.73115i	0.0322501	−	0.999480i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.02346	−	0.951627i	0.904921	−	0.425580i
$5$	2.02346	−	0.951627i	0.904921	−	0.425580i
$6$	1.68662	−	0.394099i	0.688560	−	0.160890i
$7$	−2.58706	+	0.554174i	−0.977818	+	0.209458i
$7$	−2.58706	+	0.554174i	−0.977818	+	0.209458i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.99376	−	0.193400i	−0.997920	−	0.0644667i
$10$	1.44291	+	1.70822i	0.456289	+	0.540186i
$11$		−	4.54436i		−	1.37018i	−0.728460	−	0.685088i	$-0.759764\pi$
$11$		−	4.54436i		−	1.37018i	0.728460	−	0.685088i	$-0.240236\pi$
$12$	0.817200	+	1.52715i	0.235905	+	0.440850i
$13$	−1.13198	−	4.22459i	−0.313954	−	1.17169i	−0.924960	−	0.380065i	$-0.875901\pi$
$13$	−1.13198	−	4.22459i	−0.313954	−	1.17169i	0.611006	−	0.791626i	$-0.290765\pi$
$14$	−1.20487	−	2.35548i	−0.322016	−	0.629528i
$15$	−1.53438	−	3.55608i	−0.396175	−	0.918175i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.304112	−	1.13496i	−0.0737580	−	0.275269i	0.919191	−	0.393812i	$-0.128844\pi$
$17$	−0.304112	−	1.13496i	−0.0737580	−	0.275269i	−0.992949	+	0.118544i	$0.962177\pi$
$18$	−0.588032	−	2.94181i	−0.138600	−	0.693390i
$19$	−5.35282	+	3.09045i	−1.22802	+	0.708998i	−0.966615	−	0.256232i	$-0.917519\pi$
$19$	−5.35282	+	3.09045i	−1.22802	+	0.708998i	−0.261405	+	0.965229i	$0.584186\pi$
$20$	−1.27656	+	1.83586i	−0.285447	+	0.410512i
$21$	0.814849	+	4.50955i	0.177815	+	0.984064i
$22$	4.38951	−	1.17617i	0.935848	−	0.250760i
$23$	5.32448	+	5.32448i	1.11023	+	1.11023i	0.993119	+	0.117112i	$0.0373635\pi$
$23$	5.32448	+	5.32448i	1.11023	+	1.11023i	0.117112	+	0.993119i	$0.462636\pi$
$24$	−1.26361	+	1.18461i	−0.257932	+	0.241807i
$25$	3.18881	−	3.85116i	0.637763	−	0.770233i
$26$	3.78767	−	2.18681i	0.742823	−	0.428869i
$27$	−0.502033	+	5.17184i	−0.0966163	+	0.995322i
$28$	1.96337	−	1.77346i	0.371043	−	0.335152i
$29$	−3.13342	−	5.42724i	−0.581861	−	1.00781i	−0.995259	−	0.0972625i	$-0.968991\pi$
$29$	−3.13342	−	5.42724i	−0.581861	−	1.00781i	0.413398	−	0.910551i	$-0.364342\pi$
$30$	3.03778	−	2.40248i	0.554620	−	0.438630i
$31$	0.179481	+	0.310870i	0.0322357	+	0.0558338i	0.881693	−	0.471823i	$-0.156404\pi$
$31$	0.179481	+	0.310870i	0.0322357	+	0.0558338i	−0.849457	+	0.527657i	$0.823071\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−7.86697	−	0.253843i	−1.36946	−	0.0441884i
$34$	1.01758	−	0.587499i	0.174513	−	0.100755i
$35$	−4.70746	+	3.58327i	−0.795706	+	0.605683i
$36$	2.68937	−	1.32939i	0.448229	−	0.221565i
$37$	2.46721	−	9.20775i	0.405607	−	1.51374i	−0.397328	−	0.917677i	$-0.630062\pi$
$37$	2.46721	−	9.20775i	0.405607	−	1.51374i	0.802934	−	0.596068i	$-0.203271\pi$
$38$	−4.37056	−	4.37056i	−0.708998	−	0.708998i
$39$	−7.37664	+	1.72364i	−1.18121	+	0.276003i
$40$	−2.10371	−	0.757903i	−0.332625	−	0.119835i
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.284482	−	0.958681i	$-0.591822\pi$
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.972483	+	0.232972i	$0.925155\pi$
$42$	−4.14499	+	1.95424i	−0.639586	+	0.301546i
$43$	8.19545	+	2.19596i	1.24979	+	0.334881i	0.822257	−	0.569116i	$-0.192715\pi$
$43$	8.19545	+	2.19596i	1.24979	+	0.334881i	0.427537	+	0.903998i	$0.359381\pi$
$44$	2.27218	+	3.93553i	0.342544	+	0.593304i
$45$	−6.24181	+	2.45760i	−0.930474	+	0.366358i
$46$	−3.76497	+	6.52113i	−0.555115	+	0.961488i
$47$	−0.788240	−	2.94175i	−0.114977	−	0.429099i	0.884308	−	0.466903i	$-0.154630\pi$
$47$	−0.788240	−	2.94175i	−0.114977	−	0.429099i	−0.999285	+	0.0378043i	$0.987964\pi$
$48$	−1.47129	−	0.913950i	−0.212362	−	0.131917i
$49$	6.38578	−	2.86737i	0.912254	−	0.409624i
$50$	4.54527	+	2.08340i	0.642798	+	0.294638i
$51$	−1.98178	+	0.463066i	−0.277504	+	0.0648422i
$52$	3.09262	+	3.09262i	0.428869	+	0.428869i
$53$	−0.0705647	+	0.0189078i	−0.00969281	+	0.00259718i	−0.263662	−	0.964615i	$-0.584930\pi$
$53$	−0.0705647	+	0.0189078i	−0.00969281	+	0.00259718i	0.253969	+	0.967212i	$0.418264\pi$
$54$	−5.12555	+	0.853645i	−0.697499	+	0.116166i
$55$	−4.32453	−	9.19535i	−0.583120	−	1.23990i
$56$	2.22119	+	1.43747i	0.296819	+	0.192090i
$57$	5.05103	+	9.43915i	0.669025	+	1.25025i
$58$	4.43132	−	4.43132i	0.581861	−	0.581861i
$59$	4.25394	+	7.36804i	0.553816	+	0.959237i	0.997995	+	0.0632989i	$0.0201621\pi$
$59$	4.25394	+	7.36804i	0.553816	+	0.959237i	−0.444179	+	0.895938i	$0.646505\pi$
$60$	3.10685	+	2.31246i	0.401093	+	0.298538i
$61$	2.94582	−	5.10230i	0.377173	−	0.653283i	−0.613477	−	0.789713i	$-0.710230\pi$
$61$	2.94582	−	5.10230i	0.377173	−	0.653283i	0.990650	+	0.136430i	$0.0435628\pi$
$62$	−0.253824	+	0.253824i	−0.0322357	+	0.0322357i
$63$	7.85222	−	1.15873i	0.989287	−	0.145986i
$64$			1.00000i			0.125000i
$65$	−6.31075	−	7.47110i	−0.782752	−	0.926675i
$66$	−1.79093	−	7.66461i	−0.220448	−	0.943448i
$67$	2.47729	−	9.24538i	0.302649	−	1.12950i	−0.632301	−	0.774723i	$-0.717889\pi$
$67$	2.47729	−	9.24538i	0.302649	−	1.12950i	0.934950	−	0.354779i	$-0.115444\pi$
$68$	0.830850	+	0.830850i	0.100755	+	0.100755i
$69$	9.51489	−	8.92005i	1.14546	−	1.07385i
$70$	−4.67955	−	3.61964i	−0.559314	−	0.432630i
$71$			13.2021i			1.56680i	0.621520	+	0.783398i	$0.286515\pi$
$71$			13.2021i			1.56680i	−0.621520	+	0.783398i	$0.713485\pi$
$72$	1.98015	+	2.25366i	0.233363	+	0.265597i
$73$	2.45665	+	9.16835i	0.287529	+	1.07307i	0.946971	+	0.321319i	$0.104126\pi$
$73$	2.45665	+	9.16835i	0.287529	+	1.07307i	−0.659442	+	0.751756i	$0.729207\pi$
$74$	9.53256			1.10814
$75$	−6.48882	−	5.73544i	−0.749264	−	0.662271i
$76$	3.09045	−	5.35282i	0.354499	−	0.614010i
$77$	2.51837	+	11.7565i	0.286995	+	1.33978i
$78$	−3.57412	−	6.67917i	−0.404690	−	0.756267i
$79$	−4.56295	−	2.63442i	−0.513372	−	0.296395i	0.220847	−	0.975309i	$-0.429118\pi$
$79$	−4.56295	−	2.63442i	−0.513372	−	0.296395i	−0.734219	+	0.678913i	$0.762451\pi$
$80$	0.187599	−	2.22818i	0.0209742	−	0.249119i
$81$	8.92519	+	1.15799i	0.991688	+	0.128665i
$82$	2.40536	−	8.97694i	0.265628	−	0.991338i
$83$	0.957089	−	3.57191i	0.105054	−	0.392068i	−0.893297	−	0.449467i	$-0.851614\pi$
$83$	0.957089	−	3.57191i	0.105054	−	0.392068i	0.998351	+	0.0573990i	$0.0182807\pi$
$84$	−2.96045	−	3.49796i	−0.323012	−	0.381659i
$85$	−1.69542	−	2.00715i	−0.183894	−	0.217706i
$86$			8.48456i			0.914913i
$87$	−9.57039	+	5.12126i	−1.02605	+	0.549056i
$88$	−3.21335	+	3.21335i	−0.342544	+	0.342544i
$89$	2.74487	+	4.75426i	0.290956	+	0.503951i	0.974036	−	0.226393i	$-0.0726933\pi$
$89$	2.74487	+	4.75426i	0.290956	+	0.503951i	−0.683080	+	0.730344i	$0.739360\pi$
$90$	−3.98936	−	5.39305i	−0.420516	−	0.568477i
$91$	5.26966	+	10.3020i	0.552410	+	1.07994i
$92$	−7.27337	−	1.94889i	−0.758301	−	0.203186i
$93$	0.548188	−	0.293343i	0.0568444	−	0.0304183i
$94$	2.63750	−	1.52276i	0.272038	−	0.157061i
$95$	−7.89027	+	11.3473i	−0.809525	+	1.16421i
$96$	0.502010	−	1.65770i	0.0512362	−	0.169189i
$97$	0.903546	−	3.37208i	0.0917412	−	0.342383i	−0.904764	−	0.425913i	$-0.859953\pi$
$97$	0.903546	−	3.37208i	0.0917412	−	0.342383i	0.996505	+	0.0835303i	$0.0266195\pi$
$98$	4.42243	+	5.42606i	0.446733	+	0.548115i
$99$	−0.878880	+	13.6047i	−0.0883308	+	1.36733i
$100$	−0.836011	+	4.92961i	−0.0836011	+	0.492961i
$101$			9.50946i			0.946227i	0.881001	+	0.473114i	$0.156870\pi$
$101$			9.50946i			0.946227i	−0.881001	+	0.473114i	$0.843130\pi$
$102$	−0.960209	−	1.79440i	−0.0950748	−	0.177672i
$103$	2.17566	−	2.17566i	0.214375	−	0.214375i	−0.591748	−	0.806123i	$-0.701562\pi$
$103$	2.17566	−	2.17566i	0.214375	−	0.214375i	0.806123	+	0.591748i	$0.201562\pi$
$104$	−2.18681	+	3.78767i	−0.214434	+	0.371411i
$105$	5.94022	+	8.34948i	0.579706	+	0.814825i
$106$	−0.0365270	−	0.0632666i	−0.00354782	−	0.00614500i
$107$	13.1662	+	3.52788i	1.27283	+	0.341053i	0.831113	−	0.556104i	$-0.187704\pi$
$107$	13.1662	+	3.52788i	1.27283	+	0.341053i	0.441713	+	0.897156i	$0.354371\pi$
$108$	−2.15115	−	4.72996i	−0.206994	−	0.455141i
$109$	0.421534	+	0.243373i	0.0403756	+	0.0233109i	0.520052	−	0.854135i	$-0.325913\pi$
$109$	0.421534	+	0.243373i	0.0403756	+	0.0233109i	−0.479676	+	0.877446i	$0.659246\pi$
$110$	7.76275	−	6.55711i	0.740149	−	0.625196i
$111$	−15.8022	−	4.78544i	−1.49988	−	0.454214i
$112$	−0.813602	+	2.51755i	−0.0768782	+	0.237886i
$113$	2.84653	−	0.762725i	0.267779	−	0.0717511i	−0.122431	−	0.992477i	$-0.539069\pi$
$113$	2.84653	−	0.762725i	0.267779	−	0.0717511i	0.390210	+	0.920726i	$0.372402\pi$
$114$	−7.81022	+	7.32195i	−0.731494	+	0.685764i
$115$	15.8408	+	5.70697i	1.47716	+	0.532178i
$116$	5.42724	+	3.13342i	0.503907	+	0.290931i
$117$	2.57183	+	12.8663i	0.237766	+	1.18949i
$118$	−6.01598	+	6.01598i	−0.553816	+	0.553816i
$119$	1.41572	+	2.76769i	0.129779	+	0.253713i
$120$	−1.42956	+	3.59950i	−0.130500	+	0.328588i
$121$	−9.65121			−0.877382
$122$	5.69088	+	1.52487i	0.515228	+	0.138055i
$123$	−8.49390	+	13.6736i	−0.765869	+	1.23291i
$124$	−0.310870	−	0.179481i	−0.0279169	−	0.0161178i
$125$	2.78758	−	10.8273i	0.249329	−	0.968419i
$126$	3.15155	+	7.28476i	0.280762	+	0.648978i
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	0.968999	−	0.247064i	$-0.0794659\pi$
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	−0.247064	+	0.968999i	$0.579466\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	4.25933	−	14.0649i	0.375013	−	1.23834i
$130$	5.58318	−	8.02938i	0.489677	−	0.704223i
$131$		−	9.30859i		−	0.813295i	−0.913585	−	0.406648i	$-0.866698\pi$
$131$		−	9.30859i		−	0.813295i	0.913585	−	0.406648i	$-0.133302\pi$
$132$	6.93992	−	3.71365i	0.604042	−	0.323232i
$133$	12.1354	−	10.9616i	1.05227	−	0.950489i
$134$	9.57152			0.826853
$135$	3.90582	+	10.9428i	0.336159	+	0.941805i
$136$	−0.587499	+	1.01758i	−0.0503777	+	0.0872567i
$137$	−13.1600	+	13.1600i	−1.12433	+	1.12433i	−0.133253	+	0.991082i	$0.542542\pi$
$137$	−13.1600	+	13.1600i	−1.12433	+	1.12433i	−0.991082	+	0.133253i	$0.957458\pi$
$138$	11.0787	+	6.88200i	0.943085	+	0.585835i
$139$	−14.1952	−	8.19559i	−1.20402	−	0.695141i	−0.242573	−	0.970133i	$-0.577991\pi$
$139$	−14.1952	−	8.19559i	−1.20402	−	0.695141i	−0.961446	+	0.274992i	$0.911325\pi$
$140$	2.28515	−	5.45693i	0.193130	−	0.461195i
$141$	−5.13665	+	1.20024i	−0.432584	+	0.101078i
$142$	−12.7522	+	3.41694i	−1.07014	+	0.286744i
$143$	−19.1981	+	5.14411i	−1.60542	+	0.430172i
$144$	−1.66437	+	2.49597i	−0.138697	+	0.207998i
$145$	−11.5051	−	7.99998i	−0.955444	−	0.664362i
$146$	−8.22012	+	4.74589i	−0.680302	+	0.392772i
$147$	−4.60714	−	11.2149i	−0.379991	−	0.924990i
$148$	2.46721	+	9.20775i	0.202803	+	0.756872i
$149$	−4.48602			−0.367509			−0.183754	−	0.982972i	$-0.558825\pi$
$149$	−4.48602			−0.367509			−0.183754	+	0.982972i	$0.558825\pi$
$150$	3.86057	−	7.75216i	0.315215	−	0.632961i
$151$	−1.18802			−0.0966800			−0.0483400	−	0.998831i	$-0.515393\pi$
$151$	−1.18802			−0.0966800			−0.0483400	+	0.998831i	$0.515393\pi$
$152$	5.97029	+	1.59973i	0.484254	+	0.129756i
$153$	0.690937	+	3.45662i	0.0558589	+	0.279451i
$154$	−10.7041	+	5.47537i	−0.862565	+	0.441218i
$155$	0.659005	+	0.458235i	0.0529325	+	0.0368063i
$156$	5.52653	−	5.18103i	0.442477	−	0.414815i
$157$	1.13432	−	4.23335i	0.0905287	−	0.337858i	−0.905775	−	0.423759i	$-0.860710\pi$
$157$	1.13432	−	4.23335i	0.0905287	−	0.337858i	0.996304	+	0.0859013i	$0.0273770\pi$
$158$	1.36368	−	5.08931i	0.108488	−	0.404884i
$159$	0.0287905	+	0.123214i	0.00228324	+	0.00977153i
$160$	2.20082	−	0.395490i	0.173990	−	0.0312662i
$161$	−16.7254	−	10.8241i	−1.31815	−	0.853056i
$162$	1.19148	+	8.92078i	0.0936115	+	0.700883i
$163$	17.1899	+	4.60602i	1.34642	+	0.360771i	0.858811	−	0.512293i	$-0.171204\pi$
$163$	17.1899	+	4.60602i	1.34642	+	0.360771i	0.487606	+	0.873064i	$0.337870\pi$
$164$	9.29362			0.725709
$165$	−16.1601	+	6.97277i	−1.25806	+	0.542830i
$166$	3.69791			0.287013
$167$	3.33901	+	12.4613i	0.258380	+	0.964287i	0.966179	+	0.257873i	$0.0830217\pi$
$167$	3.33901	+	12.4613i	0.258380	+	0.964287i	−0.707799	+	0.706414i	$0.750312\pi$
$168$	2.61255	−	3.76492i	0.201562	−	0.290470i
$169$	−5.30750	+	3.06428i	−0.408269	+	0.235714i
$170$	1.49995	−	2.15714i	0.115041	−	0.165445i
$171$	16.6227	−	8.21683i	1.27117	−	0.628356i
$172$	−8.19545	+	2.19596i	−0.624897	+	0.167441i
$173$	14.7767	−	3.95942i	1.12346	−	0.301029i	0.351174	−	0.936310i	$-0.385782\pi$
$173$	14.7767	−	3.95942i	1.12346	−	0.301029i	0.772281	+	0.635281i	$0.219116\pi$
$174$	−7.42375	−	7.91881i	−0.562793	−	0.600324i
$175$	−6.11544	+	11.7304i	−0.462284	+	0.886732i
$176$	−3.93553	−	2.27218i	−0.296652	−	0.171272i
$177$	12.9928	−	6.95264i	0.976599	−	0.522592i
$178$	−3.88184	+	3.88184i	−0.290956	+	0.290956i
$179$	5.38279	−	9.32327i	0.402329	−	0.696854i	−0.591678	−	0.806175i	$-0.701534\pi$
$179$	5.38279	−	9.32327i	0.402329	−	0.696854i	0.994007	+	0.109321i	$0.0348675\pi$
$180$	4.17676	−	5.24925i	0.311318	−	0.391256i
$181$	0.210492			0.0156458			0.00782288	−	0.999969i	$-0.497510\pi$
$181$	0.210492			0.0156458			0.00782288	+	0.999969i	$0.497510\pi$
$182$	−8.58706	+	7.75644i	−0.636515	+	0.574946i
$183$	−8.66830	−	5.38466i	−0.640779	−	0.398045i
$184$		−	7.52995i		−	0.555115i
$185$	−3.77003	−	20.9794i	−0.277178	−	1.54244i
$186$	0.425229	+	0.453586i	0.0311793	+	0.0332585i
$187$	−5.15767	+	1.38199i	−0.377167	+	0.101061i
$188$	2.15351	+	2.15351i	0.157061	+	0.157061i
$189$	−1.56731	−	13.6581i	−0.114005	−	0.993480i
$190$	−13.0028	−	4.68452i	−0.943322	−	0.339851i
$191$	−18.7304	−	10.8140i	−1.35528	−	0.782473i	−0.366299	−	0.930497i	$-0.619375\pi$
$191$	−18.7304	−	10.8140i	−1.35528	−	0.782473i	−0.988984	+	0.148025i	$0.952709\pi$
$192$	1.73115	+	0.0558589i	0.124935	+	0.00403127i
$193$	20.8400	+	5.58407i	1.50010	+	0.401950i	0.913133	−	0.407663i	$-0.133656\pi$
$193$	20.8400	+	5.58407i	1.50010	+	0.401950i	0.586965	+	0.809613i	$0.300323\pi$
$194$	3.49103			0.250642
$195$	−13.2861	+	10.5075i	−0.951437	+	0.752460i
$196$	−4.09656	+	5.67610i	−0.292612	+	0.405436i
$197$	3.69607	−	3.69607i	0.263334	−	0.263334i	−0.563073	−	0.826407i	$-0.690381\pi$
$197$	3.69607	−	3.69607i	0.263334	−	0.263334i	0.826407	+	0.563073i	$0.190381\pi$
$198$	−13.3686	+	2.67223i	−0.950067	+	0.189907i
$199$	3.82151	+	2.20635i	0.270900	+	0.156404i	0.629296	−	0.777165i	$-0.283343\pi$
$199$	3.82151	+	2.20635i	0.270900	+	0.156404i	−0.358397	+	0.933569i	$0.616677\pi$
$200$	−4.97802	+	0.468353i	−0.351999	+	0.0331176i
$201$	−15.8668	−	4.80500i	−1.11915	−	0.338918i
$202$	−9.18544	+	2.46123i	−0.646285	+	0.173172i
$203$	11.1140	+	12.3041i	0.780049	+	0.863582i
$204$	1.48474	−	1.39191i	0.103952	−	0.0974535i
$205$	−20.7079	−	1.74347i	−1.44630	−	0.121769i
$206$	2.66463	+	1.53843i	0.185654	+	0.107187i
$207$	−14.9105	−	16.9700i	−1.03635	−	1.17949i
$208$	−4.22459	−	1.13198i	−0.292923	−	0.0784885i
$209$	14.0441	+	24.3251i	0.971452	+	1.68260i
$210$	−6.52753	+	7.89882i	−0.450442	+	0.545070i
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	−0.511618	−	0.859213i	$-0.670954\pi$
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	0.999909	+	0.0134680i	$0.00428714\pi$
$212$	0.0516570	−	0.0516570i	0.00354782	−	0.00354782i
$213$	22.8547	+	0.737452i	1.56598	+	0.0505294i
$214$			13.6307i			0.931774i
$215$	18.6729	−	3.35555i	1.27348	−	0.228847i
$216$	4.01204	−	3.30205i	0.272984	−	0.224676i
$217$	−0.636604	−	0.704776i	−0.0432155	−	0.0478433i
$218$	−0.125979	+	0.470160i	−0.00853238	+	0.0318433i
$219$	16.0090	−	3.74070i	1.08179	−	0.252773i
$220$	8.34283	+	5.80114i	0.562474	+	0.391113i
$221$	−4.45050	+	2.56950i	−0.299373	+	0.172843i
$222$	0.532478	−	16.5023i	0.0357376	−	1.10756i
$223$	−2.29046	−	0.613728i	−0.153381	−	0.0410982i	0.181312	−	0.983426i	$-0.441966\pi$
$223$	−2.29046	−	0.613728i	−0.153381	−	0.0410982i	−0.334692	+	0.942327i	$0.608632\pi$
$224$	−2.64234	−	0.134290i	−0.176549	−	0.00897260i
$225$	−10.2914	+	10.9127i	−0.686090	+	0.727516i
$226$	1.47347	+	2.55213i	0.0980139	+	0.169765i
$227$	−0.388994	+	0.388994i	−0.0258184	+	0.0258184i	−0.719898	−	0.694080i	$-0.755812\pi$
$227$	−0.388994	+	0.388994i	−0.0258184	+	0.0258184i	0.694080	+	0.719898i	$0.255812\pi$
$228$	−9.09390	−	5.64903i	−0.602258	−	0.374116i
$229$			19.6829i			1.30068i	0.759643	+	0.650340i	$0.225374\pi$
$229$			19.6829i			1.30068i	−0.759643	+	0.650340i	$0.774626\pi$
$230$	−1.41261	+	16.7781i	−0.0931449	+	1.10632i
$231$	20.4930	−	3.70297i	1.34834	−	0.243637i
$232$	−1.62198	+	6.05330i	−0.106488	+	0.397419i
$233$	−1.56548	+	5.84244i	−0.102558	+	0.382751i	−0.998057	−	0.0623128i	$-0.980152\pi$
$233$	−1.56548	+	5.84244i	−0.102558	+	0.382751i	0.895499	+	0.445064i	$0.146819\pi$
$234$	−11.7623	+	5.81425i	−0.768925	+	0.380089i
$235$	−4.39443	−	5.20242i	−0.286661	−	0.339369i
$236$	−7.36804	−	4.25394i	−0.479619	−	0.276908i
$237$	−4.81546	+	7.75199i	−0.312798	+	0.503546i
$238$	−2.30696	+	2.08381i	−0.149538	+	0.135074i
$239$	−10.1819	+	17.6355i	−0.658610	+	1.14075i	0.322365	+	0.946615i	$0.395522\pi$
$239$	−10.1819	+	17.6355i	−0.658610	+	1.14075i	−0.980976	+	0.194131i	$0.937811\pi$
$240$	−3.84684	−	0.449226i	−0.248313	−	0.0289974i
$241$	−9.48551			−0.611016			−0.305508	−	0.952190i	$-0.598826\pi$
$241$	−9.48551			−0.611016			−0.305508	+	0.952190i	$0.598826\pi$
$242$	−2.49792	−	9.32235i	−0.160572	−	0.599263i
$243$	2.50320	−	15.3862i	0.160580	−	0.987023i
$244$			5.89163i			0.377173i
$245$	10.1927	−	11.8789i	0.651190	−	0.758915i
$246$	−15.4061	−	4.66549i	−0.982255	−	0.297461i
$247$	19.1152	+	19.1152i	1.21627	+	1.21627i
$248$	0.0929061	−	0.346730i	0.00589954	−	0.0220174i
$249$	−6.13004	−	1.85639i	−0.388476	−	0.117644i
$250$	11.1798	−	0.109706i	0.707073	−	0.00693844i
$251$		−	12.4751i		−	0.787419i	−0.919235	−	0.393710i	$-0.871192\pi$
$251$		−	12.4751i		−	0.787419i	0.919235	−	0.393710i	$-0.128808\pi$
$252$	−6.22086	+	4.92960i	−0.391877	+	0.310535i
$253$	24.1963	−	24.1963i	1.52121	−	1.52121i
$254$	−5.75287	+	9.96427i	−0.360967	+	0.625214i
$255$	−3.56939	+	2.82291i	−0.223524	+	0.176777i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.74272	+	7.74272i	−0.482978	+	0.482978i	−0.906081	−	0.423104i	$-0.860941\pi$
$257$	−7.74272	+	7.74272i	−0.482978	+	0.482978i	0.423104	+	0.906081i	$0.360941\pi$
$258$	14.6880	+	0.473938i	0.914437	+	0.0295061i
$259$	−1.28012	+	25.1883i	−0.0795430	+	1.56512i
$260$	9.20082	+	3.31478i	0.570611	+	0.205574i
$261$	8.33107	+	16.8539i	0.515680	+	1.04323i
$262$	8.99141	−	2.40924i	0.555491	−	0.148843i
$263$	−6.04074	−	6.04074i	−0.372488	−	0.372488i	0.495895	−	0.868383i	$-0.334840\pi$
$263$	−6.04074	−	6.04074i	−0.372488	−	0.372488i	−0.868383	+	0.495895i	$0.834840\pi$
$264$	5.38329	+	5.74228i	0.331319	+	0.353413i
$265$	−0.124792	+	0.105410i	−0.00766592	+	0.00647531i
$266$	13.7289	+	8.88485i	0.841776	+	0.544765i
$267$	8.38366	−	4.48622i	0.513072	−	0.274552i
$268$	2.47729	+	9.24538i	0.151325	+	0.564751i
$269$	1.89941	−	3.28987i	0.115809	−	0.200587i	−0.802294	−	0.596929i	$-0.796387\pi$
$269$	1.89941	−	3.28987i	0.115809	−	0.200587i	0.918103	+	0.396342i	$0.129721\pi$
$270$	−9.55902	+	6.60493i	−0.581743	+	0.401963i
$271$	−9.26483	−	16.0472i	−0.562798	−	0.974795i	−0.997251	−	0.0741005i	$-0.976391\pi$
$271$	−9.26483	−	16.0472i	−0.562798	−	0.974795i	0.434452	−	0.900695i	$-0.356942\pi$
$272$	−1.13496	−	0.304112i	−0.0688172	−	0.0184395i
$273$	18.1286	−	8.54711i	1.09719	−	0.517294i
$274$	−16.1176	−	9.30553i	−0.973702	−	0.562167i
$275$	−17.5011	−	14.4911i	−1.05535	−	0.873847i
$276$	−3.78011	+	12.4824i	−0.227536	+	0.751354i
$277$	−14.0238	−	14.0238i	−0.842611	−	0.842611i	0.146587	−	0.989198i	$-0.453171\pi$
$277$	−14.0238	−	14.0238i	−0.842611	−	0.842611i	−0.989198	+	0.146587i	$0.953171\pi$
$278$	4.24235	−	15.8327i	0.254439	−	0.949580i
$279$	−0.477200	−	0.965381i	−0.0285692	−	0.0577958i
$280$	5.86243	+	0.794923i	0.350347	+	0.0475057i
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	−0.169079	−	0.985602i	$-0.554079\pi$
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	0.769017	+	0.639228i	$0.220746\pi$
$282$	−2.48880	−	4.65097i	−0.148206	−	0.276961i
$283$	−25.0581	−	6.71429i	−1.48955	−	0.399123i	−0.579963	−	0.814643i	$-0.696933\pi$
$283$	−25.0581	−	6.71429i	−1.48955	−	0.399123i	−0.909584	+	0.415520i	$0.863600\pi$
$284$	−6.60103	−	11.4333i	−0.391699	−	0.678443i
$285$	19.2031	+	14.2931i	1.13749	+	0.846650i
$286$	−9.93766	−	17.2125i	−0.587626	−	1.01780i
$287$	23.3971	+	7.56130i	1.38109	+	0.446330i
$288$	−2.84169	−	0.961652i	−0.167448	−	0.0566659i
$289$	13.5268	−	7.80969i	0.795693	−	0.459393i
$290$	4.74966	−	13.1836i	0.278909	−	0.774167i
$291$	−5.78711	−	1.75253i	−0.339246	−	0.102735i
$292$	−6.71170	−	6.71170i	−0.392772	−	0.392772i
$293$	6.70156	−	1.79568i	0.391510	−	0.104905i	−0.0576935	−	0.998334i	$-0.518375\pi$
$293$	6.70156	−	1.79568i	0.391510	−	0.104905i	0.449203	+	0.893430i	$0.351708\pi$
$294$	9.64036	−	7.35279i	0.562237	−	0.428823i
$295$	15.6193	+	10.8608i	0.909392	+	0.632340i
$296$	−8.25544	+	4.76628i	−0.479838	+	0.277034i
$297$	23.5027	+	2.28142i	1.36377	+	0.132381i
$298$	−1.16107	−	4.33316i	−0.0672588	−	0.251013i
$299$	16.4666	−	28.5209i	0.952287	−	1.64941i
$300$	8.48720	+	1.72262i	0.490009	+	0.0994557i
$301$	−22.4191	−	1.13939i	−1.29221	−	0.0656732i
$302$	−0.307483	−	1.14754i	−0.0176937	−	0.0660337i
$303$	16.4623	+	0.531188i	0.945735	+	0.0305160i
$304$			6.18090i			0.354499i
$305$	1.10526	−	13.1276i	0.0632873	−	0.751687i
$306$	−3.16001	+	1.56203i	−0.180646	+	0.0892954i
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	0.875333	−	0.483520i	$-0.160642\pi$
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	−0.483520	+	0.875333i	$0.660642\pi$
$308$	−8.05924	−	8.92228i	−0.459218	−	0.508394i
$309$	−3.64487	−	3.88793i	−0.207349	−	0.221177i
$310$	−0.272058	+	0.755150i	−0.0154519	+	0.0428896i
$311$	−0.815666	+	0.470925i	−0.0462522	+	0.0267037i	−0.522948	−	0.852365i	$-0.675168\pi$
$311$	−0.815666	+	0.470925i	−0.0462522	+	0.0267037i	0.476696	+	0.879068i	$0.341834\pi$
$312$	6.43487	+	3.99727i	0.364303	+	0.226301i
$313$	−4.33150	−	16.1654i	−0.244831	−	0.913720i	−0.973468	−	0.228821i	$-0.926513\pi$
$313$	−4.33150	−	16.1654i	−0.244831	−	0.913720i	0.728638	−	0.684899i	$-0.240154\pi$
$314$	4.38268			0.247329
$315$	14.7860	−	9.81702i	0.833097	−	0.553127i
$316$	5.26884			0.296395
$317$	3.13043	+	11.6829i	0.175823	+	0.656179i	0.996410	+	0.0846578i	$0.0269797\pi$
$317$	3.13043	+	11.6829i	0.175823	+	0.656179i	−0.820588	+	0.571521i	$0.806354\pi$
$318$	−0.111564	+	0.0596997i	−0.00625622	+	0.00334779i
$319$	−24.6633	+	14.2394i	−1.38088	+	0.797252i
$320$	0.951627	+	2.02346i	0.0531976	+	0.113115i
$321$	6.84273	−	22.5956i	0.381924	−	1.26117i
$322$	6.12638	−	18.9570i	0.341410	−	1.05643i
$323$	5.13540	+	5.13540i	0.285741	+	0.285741i
$324$	−8.30844	+	3.45975i	−0.461580	+	0.192208i
$325$	−19.8793	−	9.11201i	−1.10270	−	0.505444i
$326$			17.7963i			0.985645i
$327$	0.444861	−	0.716144i	0.0246009	−	0.0396029i
$328$	2.40536	+	8.97694i	0.132814	+	0.495669i
$329$	3.66947	+	7.17368i	0.202305	+	0.395498i
$330$	−10.9177	−	13.8048i	−0.601001	−	0.759927i
$331$	9.07201	−	15.7132i	0.498643	−	0.863674i	−0.501356	−	0.865241i	$-0.667165\pi$
$331$	9.07201	−	15.7132i	0.498643	−	0.863674i	0.999999	+	0.00156673i	$0.000498705\pi$
$332$	0.957089	+	3.57191i	0.0525271	+	0.196034i
$333$	−9.16701	+	27.0886i	−0.502349	+	1.48445i
$334$	−11.1725	+	6.45046i	−0.611334	+	0.352954i
$335$	−3.78544	−	21.0651i	−0.206821	−	1.15091i
$336$	4.31281	+	1.54909i	0.235283	+	0.0845100i
$337$	11.2533	−	3.01532i	0.613007	−	0.164255i	0.0610603	−	0.998134i	$-0.480552\pi$
$337$	11.2533	−	3.01532i	0.613007	−	0.164255i	0.551947	+	0.833879i	$0.313885\pi$
$338$	−4.33355	−	4.33355i	−0.235714	−	0.235714i
$339$	−1.16139	−	4.97037i	−0.0630779	−	0.269954i
$340$	2.47185	+	0.890536i	0.134055	+	0.0482961i
$341$	1.41270	−	0.815625i	0.0765022	−	0.0441686i
$342$	12.2391	+	13.9297i	0.661816	+	0.753230i
$343$	−14.9314	+	10.9569i	−0.806219	+	0.591617i
$344$	−4.24228	−	7.34784i	−0.228728	−	0.396169i
$345$	10.7645	−	27.1040i	0.579540	−	1.45923i
$346$	7.64901	+	13.2485i	0.411213	+	0.712242i
$347$	−8.08498	−	2.16636i	−0.434024	−	0.116296i	0.0351902	−	0.999381i	$-0.488796\pi$
$347$	−8.08498	−	2.16636i	−0.434024	−	0.116296i	−0.469215	+	0.883084i	$0.655463\pi$
$348$	5.72758	−	9.22034i	0.307030	−	0.494262i
$349$	13.2937	−	7.67509i	0.711593	−	0.410838i	−0.100058	−	0.994982i	$-0.531903\pi$
$349$	13.2937	−	7.67509i	0.711593	−	0.410838i	0.811651	+	0.584143i	$0.198569\pi$
$350$	−12.9135	−	2.87102i	−0.690253	−	0.153463i
$351$	22.4172	−	3.73352i	1.19654	−	0.199281i
$352$	1.17617	−	4.38951i	0.0626899	−	0.233962i
$353$	−11.9208	−	11.9208i	−0.634481	−	0.634481i	0.314708	−	0.949189i	$-0.398093\pi$
$353$	−11.9208	−	11.9208i	−0.634481	−	0.634481i	−0.949189	+	0.314708i	$0.898093\pi$
$354$	10.0785	+	10.7506i	0.535667	+	0.571388i
$355$	12.5634	+	26.7139i	0.666798	+	1.41783i
$356$	−4.75426	−	2.74487i	−0.251975	−	0.145478i
$357$	4.87036	−	2.29623i	0.257767	−	0.121529i
$358$	10.3988	+	2.78634i	0.549591	+	0.147263i
$359$	−14.1397	−	24.4907i	−0.746264	−	1.29257i	−0.949602	−	0.313459i	$-0.898512\pi$
$359$	−14.1397	−	24.4907i	−0.746264	−	1.29257i	0.203337	−	0.979109i	$-0.434821\pi$
$360$	6.15141	+	2.67584i	0.324208	+	0.141029i
$361$	9.60175	−	16.6307i	0.505355	−	0.875301i
$362$	0.0544794	+	0.203320i	0.00286337	+	0.0106863i
$363$	−0.539106	+	16.7077i	−0.0282957	+	0.876926i
$364$	−9.71464	−	6.28694i	−0.509186	−	0.329525i
$365$	13.6958	+	16.2140i	0.716871	+	0.848680i
$366$	2.95766	−	9.76659i	0.154599	−	0.510508i
$367$	−13.9010	−	13.9010i	−0.725627	−	0.725627i	0.244118	−	0.969745i	$-0.421502\pi$
$367$	−13.9010	−	13.9010i	−0.725627	−	0.725627i	−0.969745	+	0.244118i	$0.921502\pi$
$368$	7.27337	−	1.94889i	0.379151	−	0.101593i
$369$	23.1966	+	15.4680i	1.20757	+	0.805232i
$370$	19.2888	−	9.07144i	1.00278	−	0.471602i
$371$	0.172077	−	0.0880207i	0.00893380	−	0.00456981i
$372$	−0.328073	+	0.528136i	−0.0170098	+	0.0273826i
$373$	3.80852	−	3.80852i	0.197198	−	0.197198i	−0.601600	−	0.798798i	$-0.705470\pi$
$373$	3.80852	−	3.80852i	0.197198	−	0.197198i	0.798798	+	0.601600i	$0.205470\pi$
$374$	−2.66981	−	4.62424i	−0.138053	−	0.239114i
$375$	−18.5879	−	5.43051i	−0.959874	−	0.280430i
$376$	−1.52276	+	2.63750i	−0.0785305	+	0.136019i
$377$	−19.3809	+	19.3809i	−0.998169	+	0.998169i
$378$	12.7871	−	5.04888i	0.657695	−	0.259687i
$379$			19.4353i			0.998326i	0.866508	+	0.499163i	$0.166359\pi$
$379$			19.4353i			0.998326i	−0.866508	+	0.499163i	$0.833641\pi$
$380$	1.15953	−	13.7722i	0.0594827	−	0.706498i
$381$	14.5387	−	13.6298i	0.744842	−	0.698277i
$382$	5.59773	−	20.8910i	0.286405	−	1.06888i
$383$	−10.1754	−	10.1754i	−0.519938	−	0.519938i	0.397615	−	0.917553i	$-0.369838\pi$
$383$	−10.1754	−	10.1754i	−0.519938	−	0.519938i	−0.917553	+	0.397615i	$0.869838\pi$
$384$	0.394099	+	1.68662i	0.0201113	+	0.0860700i
$385$	16.2837	+	21.3924i	0.829893	+	1.09026i
$386$			21.5752i			1.09815i
$387$	−24.1105	−	8.15919i	−1.22561	−	0.414755i
$388$	0.903546	+	3.37208i	0.0458706	+	0.171191i
$389$	6.29071			0.318952			0.159476	−	0.987202i	$-0.449020\pi$
$389$	6.29071			0.318952			0.159476	+	0.987202i	$0.449020\pi$
$390$	−13.5882	−	10.1138i	−0.688065	−	0.512134i
$391$	4.42384	−	7.66232i	0.223723	−	0.387500i
$392$	−6.54296	−	2.48789i	−0.330470	−	0.125658i
$393$	−16.1146	−	0.519968i	−0.812872	−	0.0262289i
$394$	4.52674	+	2.61352i	0.228054	+	0.131667i
$395$	−11.7399	−	0.988430i	−0.590701	−	0.0497333i
$396$	−6.04123	−	12.2215i	−0.303583	−	0.614152i
$397$	4.00301	−	14.9394i	0.200905	−	0.749788i	−0.789754	−	0.613424i	$-0.789792\pi$
$397$	4.00301	−	14.9394i	0.200905	−	0.749788i	0.990659	−	0.136364i	$-0.0435417\pi$
$398$	−1.14209	+	4.26234i	−0.0572478	+	0.213652i
$399$	−18.2983	−	21.6205i	−0.916059	−	1.08238i
$400$	−1.74080	−	4.68718i	−0.0870400	−	0.234359i
$401$		−	6.08822i		−	0.304031i	−0.988378	−	0.152015i	$-0.951424\pi$
$401$		−	6.08822i		−	0.304031i	0.988378	−	0.152015i	$-0.0485764\pi$
$402$	0.534654	−	16.5697i	0.0266661	−	0.826423i
$403$	1.11013	−	1.11013i	0.0552995	−	0.0552995i
$404$	−4.75473	−	8.23544i	−0.236557	−	0.409728i
$405$	19.1618	−	6.15031i	0.952156	−	0.305611i
$406$	−9.00838	+	13.9198i	−0.447078	+	0.690830i
$407$	−41.8433	−	11.2119i	−2.07410	−	0.555752i
$408$	1.72876	+	1.07389i	0.0855866	+	0.0531655i
$409$	1.46766	−	0.847356i	0.0725713	−	0.0418991i	−0.463275	−	0.886214i	$-0.653326\pi$
$409$	1.46766	−	0.847356i	0.0725713	−	0.0418991i	0.535847	+	0.844315i	$0.319993\pi$
$410$	−3.67553	−	20.4535i	−0.181521	−	1.01013i
$411$	22.0468	+	23.5170i	1.08749	+	1.16001i
$412$	−0.796349	+	2.97201i	−0.0392333	+	0.146421i
$413$	−15.0884	−	16.7042i	−0.742451	−	0.821958i
$414$	12.5326	−	18.7945i	0.615944	−	0.923701i
$415$	−1.46249	−	8.13841i	−0.0717906	−	0.399499i
$416$		−	4.37362i		−	0.214434i
$417$	−14.9807	+	24.1162i	−0.733609	+	1.18097i
$418$	−19.8614	+	19.8614i	−0.971452	+	0.971452i
$419$	−2.28863	+	3.96402i	−0.111807	+	0.193655i	−0.916499	−	0.400037i	$-0.868997\pi$
$419$	−2.28863	+	3.96402i	−0.111807	+	0.193655i	0.804692	+	0.593693i	$0.202330\pi$
$420$	−9.31912	−	4.26075i	−0.454727	−	0.207903i
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	0.970097	−	0.242716i	$-0.0780383\pi$
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	−0.695247	+	0.718771i	$0.744705\pi$
$422$	13.7023	+	3.67152i	0.667018	+	0.178727i
$423$	1.79087	+	8.95935i	0.0870749	+	0.435618i
$424$	0.0632666	+	0.0365270i	0.00307250	+	0.00177391i
$425$	−5.34068	−	2.44800i	−0.259061	−	0.118745i
$426$	5.20292	+	22.2669i	0.252082	+	1.07883i
$427$	−4.79344	+	14.8325i	−0.231971	+	0.717794i
$428$	−13.1662	+	3.52788i	−0.636413	+	0.170526i
$429$	7.83284	+	33.5221i	0.378173	+	1.61846i
$430$	8.07413	+	17.1682i	0.389369	+	0.827924i
$431$	1.92684	+	1.11246i	0.0928126	+	0.0535854i	0.545688	−	0.837988i	$-0.316268\pi$
$431$	1.92684	+	1.11246i	0.0928126	+	0.0535854i	−0.452875	+	0.891574i	$0.649602\pi$
$432$	4.22793	+	3.02069i	0.203416	+	0.145333i
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.0446415	−	0.999003i	$-0.485785\pi$
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.999003	−	0.0446415i	$-0.0142146\pi$
$434$	0.515996	−	0.797321i	0.0247686	−	0.0382727i
$435$	−14.4918	+	19.4701i	−0.694830	+	0.933521i
$436$	−0.486746			−0.0233109
$437$	−44.9560	−	12.0459i	−2.15054	−	0.576234i
$438$	7.75668	+	14.4954i	0.370628	+	0.692615i
$439$	−12.4395	−	7.18196i	−0.593706	−	0.342776i	0.172856	−	0.984947i	$-0.444701\pi$
$439$	−12.4395	−	7.18196i	−0.593706	−	0.342776i	−0.766562	+	0.642171i	$0.778034\pi$
$440$	−3.44419	+	9.56000i	−0.164195	+	0.455755i
$441$	−19.6720	+	7.34920i	−0.936764	+	0.349962i
$442$	−3.63382	−	3.63382i	−0.172843	−	0.172843i
$443$	−9.21653	+	2.46956i	−0.437891	+	0.117332i	−0.471028	−	0.882118i	$-0.656117\pi$
$443$	−9.21653	+	2.46956i	−0.437891	+	0.117332i	0.0331371	+	0.999451i	$0.489450\pi$
$444$	16.0778	−	3.75677i	0.763019	−	0.178289i
$445$	10.0784	+	7.00798i	0.477764	+	0.332210i
$446$		−	2.37126i		−	0.112282i
$447$	−0.250584	+	7.76597i	−0.0118522	+	0.367318i
$448$	−0.554174	−	2.58706i	−0.0261823	−	0.122227i
$449$	40.8669			1.92863			0.964313	−	0.264764i	$-0.0852941\pi$
$449$	40.8669			1.92863			0.964313	+	0.264764i	$0.0852941\pi$
$450$	−13.2045	−	7.11626i	−0.622466	−	0.335464i
$451$	−21.1168	+	36.5753i	−0.994350	+	1.72226i
$452$	−2.08380	+	2.08380i	−0.0980139	+	0.0980139i
$453$	−0.0663617	+	2.05665i	−0.00311794	+	0.0966297i
$454$	−0.476418	−	0.275060i	−0.0223594	−	0.0129092i
$455$	20.4666	+	15.8309i	0.959489	+	0.742165i
$456$	3.10287	−	10.2461i	0.145305	−	0.479818i
$457$	22.4641	−	6.01924i	1.05083	−	0.281568i	0.308234	−	0.951311i	$-0.400262\pi$
$457$	22.4641	−	6.01924i	1.05083	−	0.281568i	0.742594	+	0.669742i	$0.233595\pi$
$458$	−19.0122	+	5.09430i	−0.888381	+	0.238041i
$459$	6.02252	−	1.00303i	0.281107	−	0.0468175i
$460$	−16.5720	+	2.97802i	−0.772675	+	0.138851i
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	−0.823679	−	0.567056i	$-0.808082\pi$
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	0.0792453	+	0.996855i	$0.474749\pi$
$462$	8.88077	+	18.8363i	0.413171	+	0.876345i
$463$	−4.81433	−	17.9673i	−0.223741	−	0.835012i	−0.982905	−	0.184113i	$-0.941059\pi$
$463$	−4.81433	−	17.9673i	−0.223741	−	0.835012i	0.759164	−	0.650899i	$-0.225608\pi$
$464$	−6.26684			−0.290931
$465$	0.830085	−	1.11524i	0.0384943	−	0.0517180i
$466$	−6.04854			−0.280193
$467$	2.83925	+	0.760775i	0.131385	+	0.0352045i	0.323912	−	0.946087i	$-0.395002\pi$
$467$	2.83925	+	0.760775i	0.131385	+	0.0352045i	−0.192527	+	0.981292i	$0.561668\pi$
$468$	−8.66044	−	9.85667i	−0.400329	−	0.455625i
$469$	−1.28535	+	25.2912i	−0.0593521	+	1.16784i
$470$	3.88779	−	5.59118i	0.179330	−	0.257902i
$471$	−7.26520	−	2.20015i	−0.334763	−	0.101378i
$472$	2.20200	−	8.21798i	0.101355	−	0.378263i
$473$	9.97925	−	37.2431i	0.458847	−	1.71244i
$474$	−8.73418	−	2.64501i	−0.401174	−	0.121489i
$475$	−5.16730	+	30.4694i	−0.237092	+	1.39803i
$476$	−2.60990	−	1.68902i	−0.119624	−	0.0774163i
$477$	0.214911	−	0.0429581i	0.00984008	−	0.00196691i
$478$	−19.6699	−	5.27052i	−0.899679	−	0.241068i
$479$	0.235352			0.0107535			0.00537676	−	0.999986i	$-0.498289\pi$
$479$	0.235352			0.0107535			0.00537676	+	0.999986i	$0.498289\pi$
$480$	−0.561717	−	3.83203i	−0.0256388	−	0.174908i
$481$	−41.6918			−1.90098
$482$	−2.45503	−	9.16230i	−0.111824	−	0.417331i
$483$	−19.6723	+	28.3496i	−0.895123	+	1.28995i
$484$	8.35819	−	4.82560i	0.379918	−	0.219346i
$485$	−1.38067	−	7.68312i	−0.0626929	−	0.348873i
$486$	15.5098	−	1.56433i	0.703537	−	0.0709592i
$487$	−14.6577	+	3.92751i	−0.664202	+	0.177973i	−0.575142	−	0.818054i	$-0.695053\pi$
$487$	−14.6577	+	3.92751i	−0.664202	+	0.177973i	−0.0890606	+	0.996026i	$0.528386\pi$
$488$	−5.69088	+	1.52487i	−0.257614	+	0.0690275i
$489$	8.93392	−	29.5010i	0.404006	−	1.33408i
$490$	14.1122	+	6.77094i	0.637524	+	0.305880i
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	0.445363	−	0.895350i	$-0.353075\pi$
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	−0.552715	+	0.833371i	$0.686408\pi$
$492$	0.519131	−	16.0886i	0.0234042	−	0.725332i
$493$	−5.20680	+	5.20680i	−0.234502	+	0.234502i
$494$	−13.5165	+	23.4112i	−0.608134	+	1.05332i
$495$	11.1682	+	28.3650i	0.501975	+	1.27491i
$496$	0.358961			0.0161178
$497$	−7.31624	−	34.1545i	−0.328178	−	1.53204i
$498$	0.206561	−	6.40163i	0.00925622	−	0.286864i
$499$			34.6887i			1.55288i	0.630192	+	0.776439i	$0.282976\pi$
$499$			34.6887i			1.55288i	−0.630192	+	0.776439i	$0.717024\pi$
$500$	2.99951	+	10.7705i	0.134142	+	0.481670i
$501$	21.7590	−	5.08424i	0.972119	−	0.227147i
$502$	12.0500	−	3.22879i	0.537817	−	0.144108i
$503$	23.1452	+	23.1452i	1.03199	+	1.03199i	0.999471	+	0.0325210i	$0.0103536\pi$
$503$	23.1452	+	23.1452i	1.03199	+	1.03199i	0.0325210	+	0.999471i	$0.489646\pi$
$504$	−6.37170	−	4.73301i	−0.283818	−	0.210825i
$505$	9.04946	+	19.2421i	0.402696	+	0.856260i
$506$	29.6343	+	17.1094i	1.31741	+	0.760606i
$507$	5.00826	+	9.35924i	0.222425	+	0.415658i
$508$	−11.1137	−	2.97791i	−0.493091	−	0.132123i
$509$	−37.4631			−1.66052			−0.830262	−	0.557373i	$-0.811809\pi$
$509$	−37.4631			−1.66052			−0.830262	+	0.557373i	$0.811809\pi$
$510$	−3.65055	−	2.71714i	−0.161649	−	0.120317i
$511$	−11.4364	−	22.3577i	−0.505916	−	0.989046i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−13.2960	−	29.2354i	−0.587034	−	1.29078i
$514$	−9.48286	−	5.47493i	−0.418271	−	0.241489i
$515$	2.33196	−	6.47280i	0.102758	−	0.285226i
$516$	3.34375	+	14.3102i	0.147201	+	0.629972i
$517$	−13.3684	+	3.58205i	−0.587941	+	0.157538i
$518$	−24.6613	+	5.28270i	−1.08356	+	0.232109i
$519$	−6.02893	−	25.8019i	−0.264641	−	1.13258i
$520$	−0.820487	+	9.74524i	−0.0359808	+	0.427357i
$521$	28.8826	+	16.6754i	1.26537	+	0.730562i	0.974109	−	0.226081i	$-0.0725913\pi$
$521$	28.8826	+	16.6754i	1.26537	+	0.730562i	0.291263	+	0.956643i	$0.405925\pi$
$522$	−14.1233	+	12.4093i	−0.618162	+	0.543140i
$523$	−39.0426	−	10.4614i	−1.70722	−	0.457447i	−0.732476	−	0.680793i	$-0.761635\pi$
$523$	−39.0426	−	10.4614i	−1.70722	−	0.457447i	−0.974739	+	0.223346i	$0.928302\pi$
$524$	4.65430	+	8.06148i	0.203324	+	0.352167i
$525$	19.9654	+	11.2420i	0.871362	+	0.490641i
$526$	4.27144	−	7.39836i	0.186244	−	0.322584i
$527$	0.298243	−	0.298243i	0.0129917	−	0.0129917i
$528$	−4.15332	+	6.68607i	−0.180750	+	0.290974i
$529$			33.7001i			1.46522i
$530$	−0.134117	−	0.0932576i	−0.00582568	−	0.00405085i
$531$	−11.3103	−	22.8809i	−0.490825	−	0.992944i
$532$	−5.02879	+	15.5607i	−0.218026	+	0.674642i
$533$	−10.5202	+	39.2618i	−0.455679	+	1.70062i
$534$	6.50321	+	6.93688i	0.281421	+	0.300188i
$535$	29.9986	−	5.39079i	1.29695	−	0.233064i
$536$	−8.28918	+	4.78576i	−0.358038	+	0.206713i
$537$	−15.8393	−	9.83921i	−0.683516	−	0.424593i
$538$	3.66937	+	0.983206i	0.158198	+	0.0423890i
$539$	−13.0304	−	29.0193i	−0.561257	−	1.24995i
$540$	−8.85393	−	7.52382i	−0.381013	−	0.323774i
$541$	15.8159	+	27.3939i	0.679977	+	1.17776i	0.974987	+	0.222261i	$0.0713438\pi$
$541$	15.8159	+	27.3939i	0.679977	+	1.17776i	−0.295010	+	0.955494i	$0.595323\pi$
$542$	13.1024	−	13.1024i	0.562798	−	0.562798i
$543$	0.0117579	−	0.364393i	0.000504578	−	0.0156376i
$544$		−	1.17500i		−	0.0503777i
$545$	1.08456	+	0.0913130i	0.0464574	+	0.00391142i
$546$	12.9479	+	15.2987i	0.554119	+	0.654726i
$547$	5.47211	−	20.4222i	0.233971	−	0.873190i	−0.744640	−	0.667467i	$-0.767379\pi$
$547$	5.47211	−	20.4222i	0.233971	−	0.873190i	0.978610	−	0.205723i	$-0.0659547\pi$
$548$	4.81689	−	17.9769i	0.205768	−	0.767935i
$549$	−9.80585	+	14.7053i	−0.418504	+	0.627609i
$550$	9.46773	−	20.6553i	0.403705	−	0.880746i
$551$	33.5452	+	19.3673i	1.42907	+	0.825076i
$552$	−13.0355	−	0.420615i	−0.554826	−	0.0179025i
$553$	13.2646	+	4.28674i	0.564067	+	0.182291i
$554$	9.91635	−	17.1756i	0.421305	−	0.729722i
$555$	−36.5291	+	5.35460i	−1.55057	+	0.227290i
$556$	16.3912			0.695141
$557$	−0.450534	−	1.68142i	−0.0190898	−	0.0712439i	0.955724	−	0.294265i	$-0.0950748\pi$
$557$	−0.450534	−	1.68142i	−0.0190898	−	0.0712439i	−0.974814	+	0.223021i	$0.928408\pi$
$558$	0.808978	−	0.710799i	0.0342468	−	0.0300905i
$559$		−	37.1082i		−	1.56951i
$560$	0.749473	+	5.86841i	0.0316710	+	0.247986i
$561$	2.10434	+	9.00590i	0.0888452	+	0.380230i
$562$	8.21134	+	8.21134i	0.346374	+	0.346374i
$563$	3.56920	−	13.3204i	0.150424	−	0.561390i	−0.849030	−	0.528345i	$-0.822813\pi$
$563$	3.56920	−	13.3204i	0.150424	−	0.561390i	0.999454	−	0.0330450i	$-0.0105205\pi$
$564$	3.84835	−	3.60776i	0.162045	−	0.151914i
$565$	5.03402	−	4.25218i	0.211783	−	0.178891i
$566$		−	25.9420i		−	1.09042i
$567$	−23.7318	+	1.95033i	−0.996640	+	0.0819061i
$568$	9.33527	−	9.33527i	0.391699	−	0.391699i
$569$	8.34560	−	14.4550i	0.349866	−	0.605985i	−0.636360	−	0.771393i	$-0.719561\pi$
$569$	8.34560	−	14.4550i	0.349866	−	0.605985i	0.986225	+	0.165407i	$0.0528939\pi$
$570$	−8.83594	+	22.2481i	−0.370097	+	0.931871i
$571$	−10.1607	−	17.5989i	−0.425214	−	0.736492i	0.571226	−	0.820793i	$-0.306468\pi$
$571$	−10.1607	−	17.5989i	−0.425214	−	0.736492i	−0.996440	+	0.0843004i	$0.973134\pi$
$572$	14.0540	−	14.0540i	0.587626	−	0.587626i
$573$	−19.7669	+	31.8210i	−0.825774	+	1.32934i
$574$	−1.24804	+	24.5569i	−0.0520920	+	1.02499i
$575$	37.4842	−	3.52668i	1.56320	−	0.147073i
$576$	0.193400	−	2.99376i	0.00805834	−	0.124740i
$577$	20.5594	−	5.50888i	0.855900	−	0.229338i	0.195919	−	0.980620i	$-0.437231\pi$
$577$	20.5594	−	5.50888i	0.855900	−	0.229338i	0.659981	+	0.751282i	$0.270564\pi$
$578$	11.0446	+	11.0446i	0.459393	+	0.459393i
$579$	10.8310	−	35.7653i	0.450119	−	1.48635i
$580$	13.9637	+	1.17565i	0.579810	+	0.0488163i
$581$	−0.496590	+	9.77114i	−0.0206020	+	0.405375i
$582$	0.195005	−	6.04350i	0.00808323	−	0.250511i
$583$	0.0859237	+	0.320672i	0.00355860	+	0.0132809i
$584$	4.74589	−	8.22012i	0.196386	−	0.340151i
$585$	17.4480	+	23.5872i	0.721384	+	0.975209i
$586$	3.46898	+	6.00846i	0.143302	+	0.248207i
$587$	−2.96086	−	0.793359i	−0.122208	−	0.0327455i	0.197197	−	0.980364i	$-0.436816\pi$
$587$	−2.96086	−	0.793359i	−0.122208	−	0.0327455i	−0.319405	+	0.947618i	$0.603483\pi$
$588$	9.59736	+	7.40883i	0.395788	+	0.305535i
$589$	−1.92145	−	1.10935i	−0.0791721	−	0.0457101i
$590$	−6.44815	+	17.8981i	−0.265466	+	0.736852i
$591$	−6.19199	−	6.60491i	−0.254704	−	0.271690i
$592$	−6.74054	−	6.74054i	−0.277034	−	0.277034i
$593$	6.34257	−	23.6708i	0.260458	−	0.972042i	−0.704514	−	0.709690i	$-0.748835\pi$
$593$	6.34257	−	23.6708i	0.260458	−	0.972042i	0.964972	−	0.262352i	$-0.0844983\pi$
$594$	3.87927	+	23.2924i	0.159168	+	0.955697i
$595$	5.49847	+	4.25307i	0.225415	+	0.174359i
$596$	3.88501	−	2.24301i	0.159136	−	0.0918772i
$597$	4.03299	−	6.49236i	0.165059	−	0.265715i
$598$	31.8110	+	8.52373i	1.30085	+	0.348561i
$599$	14.9433	+	25.8825i	0.610565	+	1.05753i	0.991145	+	0.132782i	$0.0423909\pi$
$599$	14.9433	+	25.8825i	0.610565	+	1.05753i	−0.380580	+	0.924748i	$0.624276\pi$
$600$	0.532723	+	8.64385i	0.0217483	+	0.352884i
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	0.866729	−	0.498779i	$-0.166218\pi$
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	−0.865320	+	0.501220i	$0.832885\pi$
$602$	−4.70192	−	21.9501i	−0.191636	−	0.894618i
$603$	−9.20447	+	27.1993i	−0.374835	+	1.10764i
$604$	1.02886	−	0.594012i	0.0418637	−	0.0241700i
$605$	−19.5289	+	9.18435i	−0.793961	+	0.373397i
$606$	3.74767	+	16.0388i	0.152239	+	0.651534i
$607$	26.6712	+	26.6712i	1.08255	+	1.08255i	0.996271	+	0.0862787i	$0.0274976\pi$
$607$	26.6712	+	26.6712i	1.08255	+	1.08255i	0.0862787	+	0.996271i	$0.472502\pi$
$608$	−5.97029	+	1.59973i	−0.242127	+	0.0648778i
$609$	21.9211	−	18.5527i	0.888289	−	0.751793i
$610$	12.9664	−	2.33008i	0.524994	−	0.0943422i
$611$	−11.5354	+	6.65999i	−0.466674	+	0.269434i
$612$	−2.32668	−	2.64805i	−0.0940504	−	0.107041i
$613$	9.75789	+	36.4169i	0.394117	+	1.47087i	0.823278	+	0.567638i	$0.192143\pi$
$613$	9.75789	+	36.4169i	0.394117	+	1.47087i	−0.429161	+	0.903228i	$0.641191\pi$
$614$	−4.85438	+	8.40804i	−0.195907	+	0.339321i
$615$	−4.17493	+	35.7511i	−0.168350	+	1.44162i
$616$	6.53237	−	10.0939i	0.263197	−	0.406694i
$617$	5.39816	+	20.1462i	0.217322	+	0.811056i	0.985336	+	0.170624i	$0.0545782\pi$
$617$	5.39816	+	20.1462i	0.217322	+	0.811056i	−0.768014	+	0.640433i	$0.778755\pi$
$618$	2.81209	−	4.52695i	0.113119	−	0.182100i
$619$		−	31.3473i		−	1.25995i	−0.776614	−	0.629977i	$-0.783064\pi$
$619$		−	31.3473i		−	1.25995i	0.776614	−	0.629977i	$-0.216936\pi$
$620$	−0.799832	−	0.0673408i	−0.0321220	−	0.00270447i
$621$	−30.2104	+	24.8643i	−1.21230	+	0.997770i
$622$	−0.665989	−	0.665989i	−0.0267037	−	0.0267037i
$623$	−9.73585	−	10.7784i	−0.390059	−	0.431829i
$624$	−2.19560	+	7.25017i	−0.0878944	+	0.290239i
$625$	−4.66294	−	24.5613i	−0.186518	−	0.982452i
$626$	14.4935	−	8.36781i	0.579276	−	0.334445i
$627$	42.8949	−	22.9537i	1.71306	−	0.916682i
$628$	1.13432	+	4.23335i	0.0452644	+	0.168929i
$629$	−11.2007			−0.446603
$630$	13.3094	+	11.7414i	0.530260	+	0.467787i
$631$	1.35271			0.0538504			0.0269252	−	0.999637i	$-0.491428\pi$
$631$	1.35271			0.0538504			0.0269252	+	0.999637i	$0.491428\pi$
$632$	1.36368	+	5.08931i	0.0542441	+	0.202442i
$633$	−20.8712	−	12.9650i	−0.829557	−	0.515312i
$634$	−10.4746	+	6.04753i	−0.416001	+	0.240178i
$635$	24.2047	+	8.72024i	0.960535	+	0.346052i
$636$	−0.0865405	−	0.0923115i	−0.00343155	−	0.00366039i
$637$	−19.3420	−	23.7315i	−0.766359	−	0.940278i
$638$	−20.1375	−	20.1375i	−0.797252	−	0.797252i
$639$	2.55328	−	39.5238i	0.101006	−	1.56354i
$640$	−1.70822	+	1.44291i	−0.0675232	+	0.0570361i
$641$			30.0591i			1.18726i	0.804737	+	0.593632i	$0.202306\pi$
$641$			30.0591i			1.18726i	−0.804737	+	0.593632i	$0.797694\pi$
$642$	23.5967	+	0.761394i	0.931289	+	0.0300498i
$643$	9.85511	+	36.7798i	0.388648	+	1.45045i	0.832336	+	0.554272i	$0.187003\pi$
$643$	9.85511	+	36.7798i	0.388648	+	1.45045i	−0.443688	+	0.896181i	$0.646330\pi$
$644$	19.8967	+	1.01119i	0.784040	+	0.0398466i
$645$	−4.76592	−	32.5131i	−0.187658	−	1.28020i
$646$	−3.63127	+	6.28955i	−0.142871	+	0.247459i
$647$	7.64948	+	28.5483i	0.300732	+	1.12235i	0.936557	+	0.350515i	$0.113993\pi$
$647$	7.64948	+	28.5483i	0.300732	+	1.12235i	−0.635825	+	0.771833i	$0.719340\pi$
$648$	−5.49224	−	7.12989i	−0.215756	−	0.280088i
$649$	33.4830	−	19.3314i	1.31432	−	0.758825i
$650$	3.65640	−	21.5603i	0.143416	−	0.845663i
$651$	−1.25563	+	1.06269i	−0.0492121	+	0.0416500i
$652$	−17.1899	+	4.60602i	−0.673208	+	0.180386i
$653$	19.4926	+	19.4926i	0.762806	+	0.762806i	0.976829	−	0.214023i	$-0.0686567\pi$
$653$	19.4926	+	19.4926i	0.762806	+	0.762806i	−0.214023	+	0.976829i	$0.568657\pi$
$654$	0.806881	+	0.244351i	0.0315515	+	0.00955489i
$655$	−8.85830	−	18.8356i	−0.346123	−	0.735968i
$656$	−8.04851	+	4.64681i	−0.314241	+	0.181427i
$657$	−5.58147	−	27.9230i	−0.217754	−	1.08938i
$658$	−5.97951	+	5.40112i	−0.233106	+	0.210558i
$659$	16.0689	+	27.8321i	0.625954	+	1.08418i	0.988356	+	0.152162i	$0.0486234\pi$
$659$	16.0689	+	27.8321i	0.625954	+	1.08418i	−0.362402	+	0.932022i	$0.618043\pi$
$660$	10.5087	−	14.1186i	0.409049	−	0.549568i
$661$	−3.58598	−	6.21110i	−0.139479	−	0.241584i	0.787821	−	0.615904i	$-0.211209\pi$
$661$	−3.58598	−	6.21110i	−0.139479	−	0.241584i	−0.927299	+	0.374321i	$0.877876\pi$
$662$	17.5258	+	4.69602i	0.681158	+	0.182516i
$663$	4.19959	+	7.84802i	0.163099	+	0.304792i
$664$	−3.20248	+	1.84895i	−0.124280	+	0.0717534i
$665$	14.1242	−	33.7287i	0.547715	−	1.30794i
$666$	−28.5382	−	1.84360i	−1.10583	−	0.0714380i
$667$	12.2134	−	45.5810i	0.472905	−	1.76490i
$668$	−9.12233	−	9.12233i	−0.352954	−	0.352954i
$669$	−1.19040	+	3.93085i	−0.0460234	+	0.151976i
$670$	19.3676	−	9.10851i	0.748236	−	0.351892i
$671$	−23.1867	−	13.3868i	−0.895113	−	0.516794i
$672$	−0.380074	+	4.56679i	−0.0146617	+	0.176168i
$673$	−43.9221	−	11.7689i	−1.69307	−	0.453658i	−0.721894	−	0.692004i	$-0.756728\pi$
$673$	−43.9221	−	11.7689i	−1.69307	−	0.453658i	−0.971180	+	0.238346i	$0.923395\pi$
$674$	5.82514	+	10.0894i	0.224376	+	0.388631i
$675$	18.3167	+	18.4255i	0.705011	+	0.709196i
$676$	3.06428	−	5.30750i	0.117857	−	0.204134i
$677$	2.67325	+	9.97669i	0.102741	+	0.383435i	0.998079	−	0.0619522i	$-0.0197326\pi$
$677$	2.67325	+	9.97669i	0.102741	+	0.383435i	−0.895338	+	0.445387i	$0.853066\pi$
$678$	4.50042	−	2.40824i	0.172838	−	0.0924879i
$679$	−0.468809	+	9.22450i	−0.0179913	+	0.354004i
$680$	−0.220429	+	2.61811i	−0.00845306	+	0.100400i
$681$	0.651677	+	0.695135i	0.0249723	+	0.0266376i
$682$	1.15347	+	1.15347i	0.0441686	+	0.0441686i
$683$	3.02083	−	0.809428i	0.115589	−	0.0309719i	−0.200561	−	0.979681i	$-0.564276\pi$
$683$	3.02083	−	0.809428i	0.115589	−	0.0309719i	0.316150	+	0.948709i	$0.397610\pi$
$684$	−10.2873	+	15.4273i	−0.393345	+	0.589879i
$685$	−14.1054	+	39.1522i	−0.538939	+	1.49593i
$686$	−14.4481	−	11.5868i	−0.551630	−	0.442385i
$687$	34.0740	+	1.09946i	1.30000	+	0.0419471i
$688$	5.99949	−	5.99949i	0.228728	−	0.228728i
$689$	0.159755	+	0.276704i	0.00608619	+	0.0105416i
$690$	28.9665	+	3.38265i	1.10274	+	0.128775i
$691$	−15.4143	+	26.6983i	−0.586386	+	1.01565i	0.408315	+	0.912841i	$0.366117\pi$
$691$	−15.4143	+	26.6983i	−0.586386	+	1.01565i	−0.994701	+	0.102809i	$0.967217\pi$
$692$	−10.8173	+	10.8173i	−0.411213	+	0.411213i
$693$	−5.26567	−	35.6833i	−0.200026	−	1.35550i
$694$		−	8.37019i		−	0.317728i
$695$	−36.5226	−	3.07497i	−1.38538	−	0.116640i
$696$	10.3886	+	3.14602i	0.393778	+	0.119249i
$697$	−2.82630	+	10.5479i	−0.107054	+	0.399530i
$698$	10.8542	+	10.8542i	0.410838	+	0.410838i
$699$	10.0267	+	3.03643i	0.379244	+	0.114848i
$700$	−0.569054	−	13.2165i	−0.0215082	−	0.499537i
$701$			40.5025i			1.52976i	0.644174	+	0.764879i	$0.277201\pi$
$701$			40.5025i			1.52976i	−0.644174	+	0.764879i	$0.722799\pi$
$702$	9.40831	+	20.6871i	0.355094	+	0.780783i
$703$	15.2496	+	56.9122i	0.575148	+	2.14648i
$704$	4.54436			0.171272
$705$	−9.25164	+	7.31681i	−0.348437	+	0.275567i
$706$	8.42929	−	14.6000i	0.317240	−	0.549477i
$707$	−5.26990	−	24.6016i	−0.198195	−	0.925237i
$708$	−7.77578	+	12.5176i	−0.292232	+	0.470439i
$709$	11.6317	+	6.71555i	0.436837	+	0.252208i	0.702255	−	0.711926i	$-0.252177\pi$
$709$	11.6317	+	6.71555i	0.436837	+	0.252208i	−0.265418	+	0.964133i	$0.585510\pi$
$710$	−22.5520	+	19.0494i	−0.846361	+	0.714912i
$711$	13.1509	+	8.76930i	0.493196	+	0.328874i
$712$	1.42085	−	5.30269i	0.0532487	−	0.198727i
$713$	−0.699578	+	2.61086i	−0.0261994	+	0.0977775i
$714$	3.47853	+	4.11010i	0.130181	+	0.153817i
$715$	−33.9513	+	28.6783i	−1.26971	+	1.07251i
$716$			10.7656i			0.402329i
$717$	29.9610	+	18.6114i	1.11891	+	0.695057i
$718$	19.9965	−	19.9965i	0.746264	−	0.746264i
$719$	2.12346	+	3.67795i	0.0791919	+	0.137164i	0.902901	−	0.429848i	$-0.141433\pi$
$719$	2.12346	+	3.67795i	0.0791919	+	0.137164i	−0.823710	+	0.567012i	$0.808099\pi$
$720$	−0.992558	+	6.63437i	−0.0369905	+	0.247248i
$721$	−4.42288	+	6.83428i	−0.164717	+	0.254522i
$722$	18.5492	+	4.97023i	0.690328	+	0.184973i
$723$	−0.529850	+	16.4208i	−0.0197053	+	0.610698i
$724$	−0.182292	+	0.105246i	−0.00677481	+	0.00391144i
$725$	−30.8931	−	5.23914i	−1.14734	−	0.194577i
$726$	−16.2779	+	3.80353i	−0.604130	+	0.141162i
$727$	−3.48815	+	13.0179i	−0.129368	+	0.482809i	−0.999958	−	0.00920135i	$-0.997071\pi$
$727$	−3.48815	+	13.0179i	−0.129368	+	0.482809i	0.870589	+	0.492010i	$0.163738\pi$
$728$	3.55839	−	11.0108i	0.131883	−	0.408088i
$729$	−26.4959	−	5.19287i	−0.981331	−	0.192329i
$730$	−12.1168	+	17.4256i	−0.448463	+	0.644951i
$731$		−	9.96934i		−	0.368729i
$732$	10.1993	+	0.329100i	0.376977	+	0.0121639i
$733$	−17.4201	+	17.4201i	−0.643427	+	0.643427i	−0.951396	−	0.307970i	$-0.900350\pi$
$733$	−17.4201	+	17.4201i	−0.643427	+	0.643427i	0.307970	+	0.951396i	$0.400350\pi$
$734$	9.82951	−	17.0252i	0.362814	−	0.628412i
$735$	−19.9948	−	18.3087i	−0.737519	−	0.675326i
$736$	3.76497	+	6.52113i	0.138779	+	0.240372i
$737$	−42.0143	−	11.2577i	−1.54762	−	0.414683i
$738$	−8.93723	+	26.4096i	−0.328984	+	0.972151i
$739$	−21.0639	−	12.1612i	−0.774847	−	0.447358i	0.0597540	−	0.998213i	$-0.480968\pi$
$739$	−21.0639	−	12.1612i	−0.774847	−	0.447358i	−0.834601	+	0.550855i	$0.814302\pi$
$740$	13.7546	+	16.2837i	0.505631	+	0.598600i
$741$	34.1589	−	32.0234i	1.25486	−	1.17641i
$742$	0.129558	+	0.143432i	0.00475624	+	0.00526557i
$743$	−19.6154	+	5.25592i	−0.719618	+	0.192821i	−0.600001	−	0.799999i	$-0.704833\pi$
$743$	−19.6154	+	5.25592i	−0.719618	+	0.192821i	−0.119617	+	0.992820i	$0.538167\pi$
$744$	−0.595052	−	0.180202i	−0.0218157	−	0.00660654i
$745$	−9.07730	+	4.26901i	−0.332566	+	0.156405i
$746$	4.66447	+	2.69303i	0.170778	+	0.0985990i
$747$	−3.55610	+	10.5083i	−0.130111	+	0.384480i
$748$	3.77568	−	3.77568i	0.138053	−	0.138053i
$749$	−36.0169	−	1.83046i	−1.31603	−	0.0668834i
$750$	0.434573	−	19.3600i	0.0158684	−	0.706929i
$751$	31.6555			1.15512			0.577562	−	0.816347i	$-0.304004\pi$
$751$	31.6555			1.15512			0.577562	+	0.816347i	$0.304004\pi$
$752$	−2.94175	−	0.788240i	−0.107275	−	0.0287442i
$753$	−21.5962	−	0.696844i	−0.787010	−	0.0253944i
$754$	−23.7367	−	13.7044i	−0.864439	−	0.499084i
$755$	−2.40392	+	1.13055i	−0.0874877	+	0.0411451i
$756$	8.18638	+	11.0446i	0.297736	+	0.401688i
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	0.614619	−	0.788824i	$-0.289310\pi$
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	−0.788824	+	0.614619i	$0.789310\pi$
$758$	−18.7731	+	5.03024i	−0.681870	+	0.182706i
$759$	−40.5359	−	43.2391i	−1.47136	−	1.56948i
$760$	13.6030	−	2.44448i	0.493433	−	0.0886707i
$761$			10.5394i			0.382054i	0.981585	+	0.191027i	$0.0611817\pi$
$761$			10.5394i			0.382054i	−0.981585	+	0.191027i	$0.938818\pi$
$762$	16.9283	+	10.5157i	0.613247	+	0.380943i
$763$	−1.22541	−	0.396017i	−0.0443627	−	0.0143368i
$764$	21.6280			0.782473
$765$	4.68750	+	6.33683i	0.169477	+	0.229108i
$766$	7.19509	−	12.4623i	0.259969	−	0.450280i
$767$	26.3116	−	26.3116i	0.950057	−	0.950057i
$768$	−1.52715	+	0.817200i	−0.0551062	+	0.0294882i
$769$	−15.0585	−	8.69401i	−0.543022	−	0.313514i	0.203281	−	0.979121i	$-0.434840\pi$
$769$	−15.0585	−	8.69401i	−0.543022	−	0.313514i	−0.746303	+	0.665607i	$0.768173\pi$
$770$	−16.4489	+	21.2656i	−0.592779	+	0.766358i
$771$	12.9713	+	13.8363i	0.467150	+	0.498303i
$772$	−20.8400	+	5.58407i	−0.750049	+	0.200975i
$773$	−29.8801	+	8.00635i	−1.07471	+	0.287968i	−0.752428	−	0.658674i	$-0.771118\pi$
$773$	−29.8801	+	8.00635i	−1.07471	+	0.287968i	−0.322285	+	0.946643i	$0.604451\pi$
$774$	1.64091	−	25.4007i	0.0589815	−	0.913010i
$775$	1.76954	+	0.300096i	0.0635638	+	0.0107798i
$776$	−3.02332	+	1.74552i	−0.108531	+	0.0626604i
$777$	43.5332	+	3.62307i	1.56174	+	0.129977i
$778$	1.62816	+	6.07636i	0.0583722	+	0.217848i
$779$	57.4429			2.05811
$780$	6.25233	−	15.7428i	0.223869	−	0.563684i
$781$	59.9949			2.14679
$782$	8.54620	+	2.28995i	0.305612	+	0.0818884i
$783$	29.6419	−	13.4809i	1.05932	−	0.481768i
$784$	0.709677	−	6.96393i	0.0253456	−	0.248712i
$785$	−1.73331	−	9.64548i	−0.0618644	−	0.344262i
$786$	−3.66851	−	15.7001i	−0.130851	−	0.560002i
$787$	−1.75278	+	6.54148i	−0.0624800	+	0.233179i	−0.990104	−	0.140337i	$-0.955181\pi$
$787$	−1.75278	+	6.54148i	−0.0624800	+	0.233179i	0.927624	+	0.373516i	$0.121848\pi$
$788$	−1.35285	+	5.04892i	−0.0481935	+	0.179860i
$789$	−10.7948	+	10.1200i	−0.384307	+	0.360281i
$790$	−2.08377	−	11.5957i	−0.0741373	−	0.412558i
$791$	−6.94146	+	3.55069i	−0.246810	+	0.126248i
$792$	10.2415	−	8.99853i	0.363914	−	0.319749i
$793$	−24.8898	−	6.66919i	−0.883861	−	0.236830i
$794$	15.4664			0.548883
$795$	0.175511	+	0.221922i	0.00622472	+	0.00787076i
$796$	−4.41270			−0.156404
$797$	−2.62468	−	9.79545i	−0.0929710	−	0.346973i	0.903733	−	0.428097i	$-0.140816\pi$
$797$	−2.62468	−	9.79545i	−0.0929710	−	0.346973i	−0.996704	+	0.0811240i	$0.974149\pi$
$798$	16.1479	−	23.2706i	0.571629	−	0.823769i
$799$	−3.09906	+	1.78925i	−0.109637	+	0.0632989i
$800$	4.07691	−	2.89461i	0.144141	−	0.102340i
$801$	−7.29802	−	14.7640i	−0.257863	−	0.521659i
$802$	5.88077	−	1.57575i	0.207657	−	0.0556415i
$803$	41.6643	−	11.1639i	1.47030	−	0.393966i
$804$	16.1435	−	3.77213i	0.569338	−	0.133033i
$805$	−44.1438	−	5.98573i	−1.55586	−	0.210969i
$806$	1.35963	+	0.784981i	0.0478908	+	0.0276498i
$807$	−5.58916	−	3.47193i	−0.196748	−	0.122218i
$808$	6.72421	−	6.72421i	0.236557	−	0.236557i
$809$	1.25982	−	2.18207i	0.0442929	−	0.0767175i	−0.843029	−	0.537868i	$-0.819230\pi$
$809$	1.25982	−	2.18207i	0.0442929	−	0.0767175i	0.887322	+	0.461151i	$0.152563\pi$
$810$	10.9002	+	16.9170i	0.382993	+	0.594404i
$811$	−6.87827			−0.241529			−0.120764	−	0.992681i	$-0.538535\pi$
$811$	−6.87827			−0.241529			−0.120764	+	0.992681i	$0.538535\pi$
$812$	−15.7771	−	5.09871i	−0.553667	−	0.178930i
$813$	−28.2976	+	15.1424i	−0.992439	+	0.531068i
$814$		−	43.3194i		−	1.51834i
$815$	39.1663	−	7.03825i	1.37194	−	0.246539i
$816$	−0.589861	+	1.94780i	−0.0206493	+	0.0681867i
$817$	−50.6552	+	13.5730i	−1.77220	+	0.474860i
$818$	1.19834	+	1.19834i	0.0418991	+	0.0418991i
$819$	−13.7837	−	31.8608i	−0.481641	−	1.11331i
$820$	18.8053	−	8.84405i	0.656709	−	0.308848i
$821$	−12.9311	−	7.46579i	−0.451300	−	0.260558i	0.257079	−	0.966390i	$-0.417240\pi$
$821$	−12.9311	−	7.46579i	−0.451300	−	0.260558i	−0.708379	+	0.705832i	$0.750573\pi$
$822$	−17.0096	+	27.3823i	−0.593277	+	0.955066i
$823$	−25.9643	−	6.95712i	−0.905060	−	0.242510i	−0.223872	−	0.974619i	$-0.571870\pi$
$823$	−25.9643	−	6.95712i	−0.905060	−	0.242510i	−0.681188	+	0.732108i	$0.738536\pi$
$824$	−3.07685			−0.107187
$825$	−26.0639	+	29.4875i	−0.907428	+	1.02662i
$826$	12.2298	−	18.8976i	0.425529	−	0.657532i
$827$	−5.42032	+	5.42032i	−0.188483	+	0.188483i	−0.795040	−	0.606557i	$-0.792550\pi$
$827$	−5.42032	+	5.42032i	−0.188483	+	0.188483i	0.606557	+	0.795040i	$0.292550\pi$
$828$	21.3978	+	7.24119i	0.743625	+	0.251649i
$829$	12.1226	+	6.99901i	0.421037	+	0.243086i	0.695521	−	0.718506i	$-0.255174\pi$
$829$	12.1226	+	6.99901i	0.421037	+	0.243086i	−0.274484	+	0.961592i	$0.588507\pi$
$830$	7.48259	−	3.51903i	0.259724	−	0.122147i
$831$	−25.0607	+	23.4940i	−0.869347	+	0.814998i
$832$	4.22459	−	1.13198i	0.146461	−	0.0392442i
$833$	−5.19635	−	6.37562i	−0.180043	−	0.220902i
$834$	−27.1717	−	8.22854i	−0.940880	−	0.284931i
$835$	18.6149	+	22.0376i	0.644195	+	0.762642i
$836$	−24.3251	−	14.0441i	−0.841302	−	0.485726i
$837$	−1.69787	+	0.772179i	−0.0586871	+	0.0266904i
$838$	−4.42129	−	1.18468i	−0.152731	−	0.0409241i
$839$	16.7773	+	29.0592i	0.579217	+	1.00323i	0.995569	+	0.0940302i	$0.0299750\pi$
$839$	16.7773	+	29.0592i	0.579217	+	1.00323i	−0.416352	+	0.909203i	$0.636692\pi$
$840$	1.70360	−	10.1043i	0.0587798	−	0.348633i
$841$	−5.13662	+	8.89689i	−0.177125	+	0.306789i
$842$	−7.97541	+	7.97541i	−0.274851	+	0.274851i
$843$	−9.48980	−	17.7341i	−0.326846	−	0.610796i
$844$			14.1857i			0.488291i
$845$	−7.82347	+	11.2512i	−0.269136	+	0.387054i
$846$	−8.19055	+	4.04869i	−0.281597	+	0.139197i
$847$	24.9683	−	5.34845i	0.857920	−	0.183775i
$848$	−0.0189078	+	0.0705647i	−0.000649295	+	0.00242320i
$849$	−13.0232	+	43.0042i	−0.446953	+	1.47590i
$850$	0.982312	−	5.79229i	0.0336930	−	0.198674i
$851$	62.1630	−	35.8899i	2.13092	−	1.23029i
$852$	−20.1615	+	10.7887i	−0.690722	+	0.369615i
$853$	−5.70488	−	1.52862i	−0.195331	−	0.0523389i	0.159827	−	0.987145i	$-0.448906\pi$
$853$	−5.70488	−	1.52862i	−0.195331	−	0.0523389i	−0.355158	+	0.934806i	$0.615573\pi$
$854$	−15.5677	−	0.791184i	−0.532716	−	0.0270738i
$855$	25.8162	−	32.4451i	0.882894	−	1.10960i
$856$	−6.81534	−	11.8045i	−0.232943	−	0.403470i
$857$	0.500131	−	0.500131i	0.0170842	−	0.0170842i	−0.698513	−	0.715597i	$-0.746155\pi$
$857$	0.500131	−	0.500131i	0.0170842	−	0.0170842i	0.715597	+	0.698513i	$0.246155\pi$
$858$	−30.3526	+	16.2421i	−1.03622	+	0.554496i
$859$		−	38.7200i		−	1.32111i	−0.750778	−	0.660555i	$-0.770321\pi$
$859$		−	38.7200i		−	1.32111i	0.750778	−	0.660555i	$-0.229679\pi$
$860$	−14.4935	+	12.2425i	−0.494223	+	0.417465i
$861$	14.3967	−	40.0816i	0.490638	−	1.36598i
$862$	−0.575852	+	2.14911i	−0.0196136	+	0.0731990i
$863$	1.27101	−	4.74346i	0.0432655	−	0.161469i	−0.940913	−	0.338648i	$-0.890030\pi$
$863$	1.27101	−	4.74346i	0.0432655	−	0.161469i	0.984179	+	0.177179i	$0.0566971\pi$
$864$	−1.82350	+	4.86568i	−0.0620367	+	0.165534i
$865$	26.1323	−	22.0737i	0.888526	−	0.750528i
$866$	26.5976	+	15.3561i	0.903823	+	0.521822i
$867$	−12.7642	−	23.8531i	−0.433493	−	0.810094i
$868$	0.903703	+	0.292052i	0.0306737	+	0.00991288i
$869$	−11.9718	+	20.7357i	−0.406114	+	0.703410i
$870$	−22.5575	−	8.95879i	−0.764769	−	0.303731i
$871$	−41.8622			−1.41845
$872$	−0.125979	−	0.470160i	−0.00426619	−	0.0159216i
$873$	−3.35716	+	9.92045i	−0.113623	+	0.335756i
$874$		−	46.5419i		−	1.57430i
$875$	−1.21145	+	29.5556i	−0.0409544	+	0.999161i
$876$	−11.9939	+	11.2440i	−0.405235	+	0.379901i
$877$	−1.29700	−	1.29700i	−0.0437966	−	0.0437966i	0.684869	−	0.728666i	$-0.259859\pi$
$877$	−1.29700	−	1.29700i	−0.0437966	−	0.0437966i	−0.728666	+	0.684869i	$0.759859\pi$
$878$	3.71766	−	13.8745i	0.125465	−	0.468241i
$879$	−2.73425	−	11.7017i	−0.0922239	−	0.394689i
$880$	−10.1257	−	0.852518i	−0.341336	−	0.0287384i
$881$			9.87338i			0.332643i	0.986072	+	0.166321i	$0.0531889\pi$
$881$			9.87338i			0.332643i	−0.986072	+	0.166321i	$0.946811\pi$
$882$	−12.1903	−	17.0996i	−0.410468	−	0.575774i
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	−0.280884	−	0.959742i	$-0.590628\pi$
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	0.959742	+	0.280884i	$0.0906277\pi$
$884$	2.56950	−	4.45050i	0.0864216	−	0.149687i
$885$	19.6741	−	26.4327i	0.661339	−	0.888526i
$886$	−4.77083	−	8.26332i	−0.160279	−	0.277612i
$887$	−8.78931	+	8.78931i	−0.295116	+	0.295116i	−0.839097	−	0.543981i	$-0.816916\pi$
$887$	−8.78931	+	8.78931i	−0.295116	+	0.295116i	0.543981	+	0.839097i	$0.316916\pi$
$888$	7.79001	+	14.5576i	0.261415	+	0.488523i
$889$	−25.5564	−	16.5392i	−0.857136	−	0.554705i
$890$	−4.16070	+	11.5488i	−0.139467	+	0.387117i
$891$	5.26231	−	40.5593i	0.176294	−	1.35879i
$892$	2.29046	−	0.613728i	0.0766904	−	0.0205491i
$893$	13.3106	+	13.3106i	0.445424	+	0.445424i
$894$	−7.56621	+	1.76794i	−0.253052	+	0.0591286i
$895$	2.01961	−	23.9877i	0.0675082	−	0.801821i
$896$	2.35548	−	1.20487i	0.0786910	−	0.0402520i
$897$	−48.4542	−	30.0993i	−1.61784	−	1.00498i
$898$	10.5771	+	39.4744i	0.352963	+	1.31728i
$899$	1.12478	−	1.94817i	0.0375134	−	0.0649751i
$900$	3.45620	−	14.5964i	0.115207	−	0.486546i
$901$	0.0429192	+	0.0743382i	0.00142985	+	0.00247656i
$902$	−40.7945	−	10.9308i	−1.35831	−	0.363957i
$903$	−3.22475	+	38.7472i	−0.107313	+	1.28942i
$904$	−2.55213	−	1.47347i	−0.0848825	−	0.0490069i
$905$	0.425923	−	0.200310i	0.0141582	−	0.00665853i
$906$	−2.00374	+	0.468199i	−0.0665699	+	0.0155549i
$907$	23.5846	+	23.5846i	0.783113	+	0.783113i	0.980355	−	0.197242i	$-0.0631983\pi$
$907$	23.5846	+	23.5846i	0.783113	+	0.783113i	−0.197242	+	0.980355i	$0.563198\pi$
$908$	0.142382	−	0.531375i	0.00472510	−	0.0176343i
$909$	1.83913	−	28.4690i	0.0610002	−	0.944259i
$910$	−9.99436	+	23.8666i	−0.331310	+	0.791169i
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	−0.777235	−	0.629210i	$-0.783379\pi$
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	0.156294	+	0.987711i	$0.450045\pi$
$912$	10.7001	+	0.345258i	0.354314	+	0.0114326i
$913$	−16.2320	−	4.34936i	−0.537202	−	0.143943i
$914$	11.6283	+	20.1408i	0.384630	+	0.666198i
$915$	−22.6642	−	2.64667i	−0.749255	−	0.0874964i
$916$	−9.84143	−	17.0459i	−0.325170	−	0.563211i
$917$	5.15858	+	24.0819i	0.170351	+	0.795255i
$918$	2.52760	+	5.55770i	0.0834231	+	0.183432i
$919$	−21.8011	+	12.5868i	−0.719150	+	0.415202i	−0.814440	−	0.580248i	$-0.802956\pi$
$919$	−21.8011	+	12.5868i	−0.719150	+	0.415202i	0.0952895	+	0.995450i	$0.469622\pi$
$920$	−7.16570	−	15.2366i	−0.236246	−	0.502335i
$921$	12.2681	−	11.5011i	0.404246	−	0.378974i
$922$	−13.0506	−	13.0506i	−0.429799	−	0.429799i
$923$	55.7733	−	14.9444i	1.83580	−	0.491902i
$924$	−15.8960	+	13.4534i	−0.522939	+	0.442583i
$925$	−27.5931	−	38.8634i	−0.907255	−	1.27782i
$926$	16.1091	−	9.30057i	0.529377	−	0.305636i
$927$	−6.93419	+	6.09264i	−0.227749	+	0.200109i
$928$	−1.62198	−	6.05330i	−0.0532440	−	0.198709i
$929$	−16.6278	+	28.8002i	−0.545541	+	0.944905i	0.453031	+	0.891495i	$0.350343\pi$
$929$	−16.6278	+	28.8002i	−0.545541	+	0.944905i	−0.998573	+	0.0534108i	$0.982991\pi$
$930$	1.29208	+	0.513155i	0.0423690	+	0.0168270i
$931$	−25.3205	+	35.0834i	−0.829844	+	1.14981i
$932$	−1.56548	−	5.84244i	−0.0512789	−	0.191376i
$933$	0.769680	+	1.43835i	0.0251982	+	0.0470893i
$934$			2.93941i			0.0961804i
$935$	−9.12123	+	7.70460i	−0.298296	+	0.251967i
$936$	7.27932	−	10.9164i	0.237932	−	0.356815i
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	0.804469	−	0.593994i	$-0.202450\pi$
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	−0.593994	+	0.804469i	$0.702450\pi$
$938$	−24.7621	+	5.30429i	−0.808512	+	0.173191i
$939$	−28.2266	+	6.59549i	−0.921141	+	0.215236i
$940$	6.40690	+	2.30822i	0.208970	+	0.0752857i
$941$	−40.4672	+	23.3637i	−1.31919	+	0.761636i	−0.983599	−	0.180370i	$-0.942270\pi$
$941$	−40.4672	+	23.3637i	−1.31919	+	0.761636i	−0.335594	+	0.942007i	$0.608937\pi$
$942$	0.244812	−	7.58708i	0.00797640	−	0.247200i
$943$	−18.1123	−	67.5959i	−0.589817	−	2.20123i
$944$	8.50788			0.276908
$945$	−16.1688	−	26.1452i	−0.525971	−	0.850502i
$946$	38.5569			1.25359
$947$	7.37361	+	27.5187i	0.239610	+	0.894237i	0.976016	+	0.217698i	$0.0698546\pi$
$947$	7.37361	+	27.5187i	0.239610	+	0.894237i	−0.736406	+	0.676540i	$0.763479\pi$
$948$	0.294312	−	9.12115i	0.00955879	−	0.296241i
$949$	35.9517	−	20.7567i	1.16704	−	0.673792i
$950$	−30.7686	+	2.89484i	−0.998266	+	0.0939212i
$951$	20.3998	−	4.76665i	0.661508	−	0.154569i
$952$	0.955981	−	2.95812i	0.0309835	−	0.0958731i
$953$	10.3138	+	10.3138i	0.334098	+	0.334098i	0.854140	−	0.520042i	$-0.174084\pi$
$953$	10.3138	+	10.3138i	0.334098	+	0.334098i	−0.520042	+	0.854140i	$0.674084\pi$
$954$	0.0971173	+	0.196469i	0.00314429	+	0.00636093i
$955$	−48.1911	−	4.05739i	−1.55943	−	0.131294i
$956$		−	20.3637i		−	0.658610i
$957$	23.2728	+	43.4913i	0.752304	+	1.40587i
$958$	0.0609136	+	0.227333i	0.00196803	+	0.00734479i
$959$	26.7528	−	41.3387i	0.863893	−	1.33490i
$960$	3.55608	−	1.53438i	0.114772	−	0.0495219i
$961$	15.4356	−	26.7352i	0.497922	−	0.862426i
$962$	−10.7906	−	40.2712i	−0.347904	−	1.29840i
$963$	−38.7342	−	13.1080i	−1.24819	−	0.422398i
$964$	8.21469	−	4.74276i	0.264577	−	0.152754i
$965$	47.4830	−	8.53276i	1.52853	−	0.274679i
$966$	−32.4752	−	11.6646i	−1.04487	−	0.375302i
$967$	45.7943	−	12.2705i	1.47265	−	0.394594i	0.568808	−	0.822470i	$-0.307405\pi$
$967$	45.7943	−	12.2705i	1.47265	−	0.394594i	0.903837	+	0.427876i	$0.140738\pi$
$968$	6.82443	+	6.82443i	0.219346	+	0.219346i
$969$	9.17700	−	8.60328i	0.294808	−	0.276377i
$970$	7.06398	−	3.32216i	0.226811	−	0.106668i
$971$	29.2801	−	16.9049i	0.939642	−	0.542503i	0.0497939	−	0.998760i	$-0.484144\pi$
$971$	29.2801	−	16.9049i	0.939642	−	0.542503i	0.889848	+	0.456257i	$0.150810\pi$
$972$	5.52525	+	14.5764i	0.177222	+	0.467538i
$973$	41.2656	+	13.3359i	1.32291	+	0.427529i
$974$	−7.58737	−	13.1417i	−0.243115	−	0.421087i
$975$	−16.8847	+	33.9050i	−0.540743	+	1.08583i
$976$	−2.94582	−	5.10230i	−0.0942933	−	0.163321i
$977$	51.3818	+	13.7677i	1.64385	+	0.440468i	0.957882	−	0.287163i	$-0.0927123\pi$
$977$	51.3818	+	13.7677i	1.64385	+	0.440468i	0.685968	+	0.727632i	$0.259379\pi$
$978$	30.8080	+	0.994081i	0.985133	+	0.0317872i
$979$	21.6051	−	12.4737i	0.690501	−	0.398661i
$980$	−2.88772	+	15.3838i	−0.0922448	+	0.491417i
$981$	−1.21490	−	0.810124i	−0.0387889	−	0.0258653i
$982$	0.710911	−	2.65316i	0.0226861	−	0.0846656i
$983$	38.2310	+	38.2310i	1.21938	+	1.21938i	0.967849	+	0.251532i	$0.0809344\pi$
$983$	38.2310	+	38.2310i	1.21938	+	1.21938i	0.251532	+	0.967849i	$0.419066\pi$
$984$	15.6748	−	3.66260i	0.499694	−	0.116760i
$985$	3.96158	−	10.9961i	0.126227	−	0.350366i
$986$	−6.37700	−	3.68176i	−0.203085	−	0.117251i
$987$	12.6237	−	5.95169i	0.401816	−	0.189444i
$988$	−26.1118	−	6.99663i	−0.830727	−	0.222593i
$989$	31.9441	+	55.3289i	1.01576	+	1.75936i
$990$	−24.5080	+	18.1291i	−0.778914	+	0.576180i
$991$	7.91050	−	13.7014i	0.251285	−	0.435239i	−0.712595	−	0.701576i	$-0.752480\pi$
$991$	7.91050	−	13.7014i	0.251285	−	0.435239i	0.963880	+	0.266337i	$0.0858134\pi$
$992$	0.0929061	+	0.346730i	0.00294977	+	0.0110087i
$993$	−26.6951	−	16.5827i	−0.847144	−	0.526237i
$994$	31.0972	−	15.9068i	0.986343	−	0.504533i
$995$	9.83230	+	0.827818i	0.311705	+	0.0262436i
$996$	6.23697	−	1.45734i	0.197626	−	0.0461777i
$997$	−34.8123	−	34.8123i	−1.10252	−	1.10252i	−0.994106	−	0.108412i	$-0.965424\pi$
$997$	−34.8123	−	34.8123i	−1.10252	−	1.10252i	−0.108412	−	0.994106i	$-0.534576\pi$
$998$	−33.5067	+	8.97809i	−1.06064	+	0.284196i
$999$	46.3824	+	17.3826i	1.46747	+	0.549961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.347.38	yes	192
5.3	odd	4	inner	630.2.bt.a.473.47	yes	192
7.2	even	3		630.2.cd.a.527.43	yes	192
9.2	odd	6		630.2.cd.a.137.7	yes	192
35.23	odd	12		630.2.cd.a.23.7	yes	192
45.38	even	12		630.2.cd.a.263.43	yes	192
63.2	odd	6	inner	630.2.bt.a.317.47	✓	192
315.128	even	12	inner	630.2.bt.a.443.38	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.47	✓	192	63.2	odd	6	inner
630.2.bt.a.347.38	yes	192	1.1	even	1	trivial
630.2.bt.a.443.38	yes	192	315.128	even	12	inner
630.2.bt.a.473.47	yes	192	5.3	odd	4	inner
630.2.cd.a.23.7	yes	192	35.23	odd	12
630.2.cd.a.137.7	yes	192	9.2	odd	6
630.2.cd.a.263.43	yes	192	45.38	even	12
630.2.cd.a.527.43	yes	192	7.2	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.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.0558589 - 1.73115i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.02346 - 0.951627i) q^{5} +(1.68662 - 0.394099i) q^{6} +(-2.58706 + 0.554174i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99376 - 0.193400i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.0558589 - 1.73115i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.02346 - 0.951627i) q^{5} +(1.68662 - 0.394099i) q^{6} +(-2.58706 + 0.554174i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99376 - 0.193400i) q^{9} +(1.44291 + 1.70822i) q^{10} -4.54436i q^{11} +(0.817200 + 1.52715i) q^{12} +(-1.13198 - 4.22459i) q^{13} +(-1.20487 - 2.35548i) q^{14} +(-1.53438 - 3.55608i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.304112 - 1.13496i) q^{17} +(-0.588032 - 2.94181i) q^{18} +(-5.35282 + 3.09045i) q^{19} +(-1.27656 + 1.83586i) q^{20} +(0.814849 + 4.50955i) q^{21} +(4.38951 - 1.17617i) q^{22} +(5.32448 + 5.32448i) q^{23} +(-1.26361 + 1.18461i) q^{24} +(3.18881 - 3.85116i) q^{25} +(3.78767 - 2.18681i) q^{26} +(-0.502033 + 5.17184i) q^{27} +(1.96337 - 1.77346i) q^{28} +(-3.13342 - 5.42724i) q^{29} +(3.03778 - 2.40248i) q^{30} +(0.179481 + 0.310870i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.86697 - 0.253843i) q^{33} +(1.01758 - 0.587499i) q^{34} +(-4.70746 + 3.58327i) q^{35} +(2.68937 - 1.32939i) q^{36} +(2.46721 - 9.20775i) q^{37} +(-4.37056 - 4.37056i) q^{38} +(-7.37664 + 1.72364i) q^{39} +(-2.10371 - 0.757903i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(-4.14499 + 1.95424i) q^{42} +(8.19545 + 2.19596i) q^{43} +(2.27218 + 3.93553i) q^{44} +(-6.24181 + 2.45760i) q^{45} +(-3.76497 + 6.52113i) q^{46} +(-0.788240 - 2.94175i) q^{47} +(-1.47129 - 0.913950i) q^{48} +(6.38578 - 2.86737i) q^{49} +(4.54527 + 2.08340i) q^{50} +(-1.98178 + 0.463066i) q^{51} +(3.09262 + 3.09262i) q^{52} +(-0.0705647 + 0.0189078i) q^{53} +(-5.12555 + 0.853645i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(2.22119 + 1.43747i) q^{56} +(5.05103 + 9.43915i) q^{57} +(4.43132 - 4.43132i) q^{58} +(4.25394 + 7.36804i) q^{59} +(3.10685 + 2.31246i) q^{60} +(2.94582 - 5.10230i) q^{61} +(-0.253824 + 0.253824i) q^{62} +(7.85222 - 1.15873i) q^{63} +1.00000i q^{64} +(-6.31075 - 7.47110i) q^{65} +(-1.79093 - 7.66461i) q^{66} +(2.47729 - 9.24538i) q^{67} +(0.830850 + 0.830850i) q^{68} +(9.51489 - 8.92005i) q^{69} +(-4.67955 - 3.61964i) q^{70} +13.2021i q^{71} +(1.98015 + 2.25366i) q^{72} +(2.45665 + 9.16835i) q^{73} +9.53256 q^{74} +(-6.48882 - 5.73544i) q^{75} +(3.09045 - 5.35282i) q^{76} +(2.51837 + 11.7565i) q^{77} +(-3.57412 - 6.67917i) q^{78} +(-4.56295 - 2.63442i) q^{79} +(0.187599 - 2.22818i) q^{80} +(8.92519 + 1.15799i) q^{81} +(2.40536 - 8.97694i) q^{82} +(0.957089 - 3.57191i) q^{83} +(-2.96045 - 3.49796i) q^{84} +(-1.69542 - 2.00715i) q^{85} +8.48456i q^{86} +(-9.57039 + 5.12126i) q^{87} +(-3.21335 + 3.21335i) q^{88} +(2.74487 + 4.75426i) q^{89} +(-3.98936 - 5.39305i) q^{90} +(5.26966 + 10.3020i) q^{91} +(-7.27337 - 1.94889i) q^{92} +(0.548188 - 0.293343i) q^{93} +(2.63750 - 1.52276i) q^{94} +(-7.89027 + 11.3473i) q^{95} +(0.502010 - 1.65770i) q^{96} +(0.903546 - 3.37208i) q^{97} +(4.42243 + 5.42606i) q^{98} +(-0.878880 + 13.6047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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