LMFDB - Embedded newform 378.2.z.a.293.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			293.22
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(1.41810 - 0.994487i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.622684 - 3.53142i) q^{5} +(-0.449494 - 1.67271i) q^{6} +(2.42952 + 1.04757i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.02199 - 2.82055i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(1.41810 - 0.994487i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.622684 - 3.53142i) q^{5} +(-0.449494 - 1.67271i) q^{6} +(2.42952 + 1.04757i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.02199 - 2.82055i) q^{9} +(-3.10547 - 1.79295i) q^{10} +(-4.15407 + 0.732474i) q^{11} +(-1.72557 - 0.149714i) q^{12} +(2.25831 + 6.20466i) q^{13} +(1.81534 - 1.92471i) q^{14} +(-2.62892 - 5.62714i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.59771 + 4.49937i) q^{17} +(-2.30091 - 1.92505i) q^{18} +(3.98919 - 2.30316i) q^{19} +(-2.74695 + 2.30497i) q^{20} +(4.48710 - 0.930567i) q^{21} +(-0.732474 + 4.15407i) q^{22} +(-2.69373 + 3.21026i) q^{23} +(-0.730864 + 1.57030i) q^{24} +(-7.38470 - 2.68781i) q^{25} +6.60286 q^{26} +(-1.35572 - 5.01618i) q^{27} +(-1.18776 - 2.36416i) q^{28} +(1.58469 - 4.35390i) q^{29} +(-6.18692 + 0.545782i) q^{30} +(1.80493 - 2.15103i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-5.16243 + 5.16989i) q^{33} +(3.33955 + 3.97993i) q^{34} +(5.21225 - 7.92735i) q^{35} +(-2.59591 + 1.50375i) q^{36} +(-2.76078 + 4.78181i) q^{37} +(-0.799879 - 4.53634i) q^{38} +(9.37296 + 6.55295i) q^{39} +(1.22645 + 3.36964i) q^{40} +(3.08382 - 1.12242i) q^{41} +(0.660231 - 4.53477i) q^{42} +(-0.856484 - 4.85736i) q^{43} +(3.65303 + 2.10908i) q^{44} +(-9.32417 - 5.36540i) q^{45} +(2.09535 + 3.62925i) q^{46} +(0.00676417 - 0.00567581i) q^{47} +(1.22563 + 1.22386i) q^{48} +(4.80517 + 5.09022i) q^{49} +(-5.05143 + 6.02006i) q^{50} +(0.790757 + 8.96393i) q^{51} +(2.25831 - 6.20466i) q^{52} +3.95587i q^{53} +(-5.17735 - 0.441674i) q^{54} +15.1258i q^{55} +(-2.62782 + 0.307535i) q^{56} +(3.36659 - 7.23330i) q^{57} +(-3.54933 - 2.97824i) q^{58} +(0.405440 - 2.29937i) q^{59} +(-1.60318 + 6.00047i) q^{60} +(-1.23272 - 1.46910i) q^{61} +(-1.40399 - 2.43177i) q^{62} +(5.43770 - 5.78199i) q^{63} +(0.500000 - 0.866025i) q^{64} +(23.3175 - 4.11150i) q^{65} +(3.09245 + 6.61931i) q^{66} +(1.97624 - 0.719293i) q^{67} +(4.88210 - 1.77694i) q^{68} +(-0.627405 + 7.23134i) q^{69} +(-5.66658 - 7.60922i) q^{70} +(-2.82464 - 1.63080i) q^{71} +(0.525205 + 2.95367i) q^{72} +(-8.15237 + 4.70677i) q^{73} +(3.54919 + 4.22976i) q^{74} +(-13.1452 + 3.53241i) q^{75} +(-4.53634 - 0.799879i) q^{76} +(-10.8597 - 2.57213i) q^{77} +(9.36350 - 6.56646i) q^{78} +(-10.5357 - 3.83468i) q^{79} +3.58589 q^{80} +(-6.91106 - 5.76518i) q^{81} -3.28173i q^{82} +(1.26125 + 0.459057i) q^{83} +(-4.03547 - 2.17140i) q^{84} +(14.2716 + 11.9753i) q^{85} +(-4.85736 - 0.856484i) q^{86} +(-2.08265 - 7.75020i) q^{87} +(3.23129 - 2.71138i) q^{88} +(5.76444 + 9.98431i) q^{89} +(-8.23088 + 6.92678i) q^{90} +(-1.01323 + 17.4401i) q^{91} +(4.12703 - 0.727707i) q^{92} +(0.420392 - 4.84535i) q^{93} +(-0.00302003 - 0.00829748i) q^{94} +(-5.64941 - 15.5216i) q^{95} +(1.56924 - 0.733128i) q^{96} +(2.42324 - 0.427283i) q^{97} +(6.42671 - 2.77443i) q^{98} +(-2.17945 + 12.4654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	1.41810	−	0.994487i	0.818738	−	0.574167i
$3$	1.41810	−	0.994487i	0.818738	−	0.574167i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.622684	−	3.53142i	0.278473	−	1.57930i	−0.449238	−	0.893412i	$-0.648304\pi$
$5$	0.622684	−	3.53142i	0.278473	−	1.57930i	0.727710	−	0.685885i	$-0.240585\pi$
$6$	−0.449494	−	1.67271i	−0.183505	−	0.682881i
$7$	2.42952	+	1.04757i	0.918274	+	0.395946i
$7$	2.42952	+	1.04757i	0.918274	+	0.395946i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	1.02199	−	2.82055i	0.340664	−	0.940185i
$10$	−3.10547	−	1.79295i	−0.982037	−	0.566979i
$11$	−4.15407	+	0.732474i	−1.25250	+	0.220849i	−0.760265	−	0.649613i	$-0.774931\pi$
$11$	−4.15407	+	0.732474i	−1.25250	+	0.220849i	−0.492234	+	0.870463i	$0.663820\pi$
$12$	−1.72557	−	0.149714i	−0.498129	−	0.0432186i
$13$	2.25831	+	6.20466i	0.626343	+	1.72086i	0.690900	+	0.722950i	$0.257214\pi$
$13$	2.25831	+	6.20466i	0.626343	+	1.72086i	−0.0645571	+	0.997914i	$0.520563\pi$
$14$	1.81534	−	1.92471i	0.485171	−	0.514401i
$15$	−2.62892	−	5.62714i	−0.678784	−	1.45292i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.59771	+	4.49937i	−0.630038	+	1.09126i	0.357506	+	0.933911i	$0.383627\pi$
$17$	−2.59771	+	4.49937i	−0.630038	+	1.09126i	−0.987543	+	0.157346i	$0.949706\pi$
$18$	−2.30091	−	1.92505i	−0.542330	−	0.453738i
$19$	3.98919	−	2.30316i	0.915183	−	0.528381i	0.0330879	−	0.999452i	$-0.489466\pi$
$19$	3.98919	−	2.30316i	0.915183	−	0.528381i	0.882095	+	0.471071i	$0.156133\pi$
$20$	−2.74695	+	2.30497i	−0.614237	+	0.515406i
$21$	4.48710	−	0.930567i	0.979165	−	0.203066i
$22$	−0.732474	+	4.15407i	−0.156164	+	0.885651i
$23$	−2.69373	+	3.21026i	−0.561681	+	0.669386i	−0.969901	−	0.243498i	$-0.921705\pi$
$23$	−2.69373	+	3.21026i	−0.561681	+	0.669386i	0.408220	+	0.912884i	$0.366150\pi$
$24$	−0.730864	+	1.57030i	−0.149187	+	0.320536i
$25$	−7.38470	−	2.68781i	−1.47694	−	0.537562i
$26$	6.60286			1.29493
$27$	−1.35572	−	5.01618i	−0.260908	−	0.965364i
$28$	−1.18776	−	2.36416i	−0.224465	−	0.446784i
$29$	1.58469	−	4.35390i	0.294269	−	0.808498i	−0.701161	−	0.713003i	$-0.747334\pi$
$29$	1.58469	−	4.35390i	0.294269	−	0.808498i	0.995430	−	0.0954950i	$-0.0304434\pi$
$30$	−6.18692	+	0.545782i	−1.12957	+	0.0996457i
$31$	1.80493	−	2.15103i	0.324175	−	0.386337i	−0.579202	−	0.815184i	$-0.696636\pi$
$31$	1.80493	−	2.15103i	0.324175	−	0.386337i	0.903377	+	0.428847i	$0.141080\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−5.16243	+	5.16989i	−0.898664	+	0.899961i
$34$	3.33955	+	3.97993i	0.572729	+	0.682552i
$35$	5.21225	−	7.92735i	0.881031	−	1.33997i
$36$	−2.59591	+	1.50375i	−0.432652	+	0.250624i
$37$	−2.76078	+	4.78181i	−0.453869	+	0.786125i	−0.998622	−	0.0524717i	$-0.983290\pi$
$37$	−2.76078	+	4.78181i	−0.453869	+	0.786125i	0.544753	+	0.838597i	$0.316623\pi$
$38$	−0.799879	−	4.53634i	−0.129758	−	0.735891i
$39$	9.37296	+	6.55295i	1.50087	+	1.04931i
$40$	1.22645	+	3.36964i	0.193918	+	0.532786i
$41$	3.08382	−	1.12242i	0.481611	−	0.175292i	−0.0897937	−	0.995960i	$-0.528621\pi$
$41$	3.08382	−	1.12242i	0.481611	−	0.175292i	0.571405	+	0.820668i	$0.306399\pi$
$42$	0.660231	−	4.53477i	0.101876	−	0.699729i
$43$	−0.856484	−	4.85736i	−0.130613	−	0.740741i	−0.977815	−	0.209470i	$-0.932826\pi$
$43$	−0.856484	−	4.85736i	−0.130613	−	0.740741i	0.847202	−	0.531270i	$-0.178285\pi$
$44$	3.65303	+	2.10908i	0.550715	+	0.317955i
$45$	−9.32417	−	5.36540i	−1.38997	−	0.799826i
$46$	2.09535	+	3.62925i	0.308942	+	0.535104i
$47$	0.00676417	−	0.00567581i	0.000986655	−	0.000827902i	−0.642294	−	0.766458i	$-0.722017\pi$
$47$	0.00676417	−	0.00567581i	0.000986655	−	0.000827902i	0.643281	+	0.765630i	$0.277573\pi$
$48$	1.22563	+	1.22386i	0.176904	+	0.176649i
$49$	4.80517	+	5.09022i	0.686453	+	0.727174i
$50$	−5.05143	+	6.02006i	−0.714380	+	0.851365i
$51$	0.790757	+	8.96393i	0.110728	+	1.25520i
$52$	2.25831	−	6.20466i	0.313172	−	0.860432i
$53$			3.95587i			0.543380i	0.962385	+	0.271690i	$0.0875825\pi$
$53$			3.95587i			0.543380i	−0.962385	+	0.271690i	$0.912417\pi$
$54$	−5.17735	−	0.441674i	−0.704548	−	0.0601042i
$55$			15.1258i			2.03957i
$56$	−2.62782	+	0.307535i	−0.351157	+	0.0410961i
$57$	3.36659	−	7.23330i	0.445916	−	0.958074i
$58$	−3.54933	−	2.97824i	−0.466050	−	0.391062i
$59$	0.405440	−	2.29937i	0.0527838	−	0.299352i	−0.946975	−	0.321307i	$-0.895878\pi$
$59$	0.405440	−	2.29937i	0.0527838	−	0.299352i	0.999759	+	0.0219549i	$0.00698901\pi$
$60$	−1.60318	+	6.00047i	−0.206970	+	0.774658i
$61$	−1.23272	−	1.46910i	−0.157834	−	0.188099i	0.681332	−	0.731974i	$-0.261401\pi$
$61$	−1.23272	−	1.46910i	−0.157834	−	0.188099i	−0.839166	+	0.543875i	$0.816956\pi$
$62$	−1.40399	−	2.43177i	−0.178306	−	0.308836i
$63$	5.43770	−	5.78199i	0.685086	−	0.728462i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	23.3175	−	4.11150i	2.89217	−	0.509968i
$66$	3.09245	+	6.61931i	0.380654	+	0.814780i
$67$	1.97624	−	0.719293i	0.241436	−	0.0878756i	−0.218468	−	0.975844i	$-0.570106\pi$
$67$	1.97624	−	0.719293i	0.241436	−	0.0878756i	0.459904	+	0.887969i	$0.347884\pi$
$68$	4.88210	−	1.77694i	0.592042	−	0.215486i
$69$	−0.627405	+	7.23134i	−0.0755307	+	0.870551i
$70$	−5.66658	−	7.60922i	−0.677286	−	0.909476i
$71$	−2.82464	−	1.63080i	−0.335223	−	0.193541i	0.322935	−	0.946421i	$-0.395331\pi$
$71$	−2.82464	−	1.63080i	−0.335223	−	0.193541i	−0.658157	+	0.752880i	$0.728664\pi$
$72$	0.525205	+	2.95367i	0.0618961	+	0.348093i
$73$	−8.15237	+	4.70677i	−0.954163	+	0.550886i	−0.894372	−	0.447325i	$-0.852377\pi$
$73$	−8.15237	+	4.70677i	−0.954163	+	0.550886i	−0.0597914	+	0.998211i	$0.519044\pi$
$74$	3.54919	+	4.22976i	0.412585	+	0.491700i
$75$	−13.1452	+	3.53241i	−1.51788	+	0.407887i
$76$	−4.53634	−	0.799879i	−0.520354	−	0.0917524i
$77$	−10.8597	−	2.57213i	−1.23758	−	0.293122i
$78$	9.36350	−	6.56646i	1.06021	−	0.743505i
$79$	−10.5357	−	3.83468i	−1.18536	−	0.431435i	−0.327266	−	0.944932i	$-0.606127\pi$
$79$	−10.5357	−	3.83468i	−1.18536	−	0.431435i	−0.858091	+	0.513497i	$0.828350\pi$
$80$	3.58589			0.400915
$81$	−6.91106	−	5.76518i	−0.767896	−	0.640575i
$82$		−	3.28173i		−	0.362406i
$83$	1.26125	+	0.459057i	0.138440	+	0.0503881i	0.410311	−	0.911946i	$-0.365420\pi$
$83$	1.26125	+	0.459057i	0.138440	+	0.0503881i	−0.271871	+	0.962334i	$0.587642\pi$
$84$	−4.03547	−	2.17140i	−0.440306	−	0.236919i
$85$	14.2716	+	11.9753i	1.54797	+	1.29890i
$86$	−4.85736	−	0.856484i	−0.523783	−	0.0923570i
$87$	−2.08265	−	7.75020i	−0.223284	−	0.830908i
$88$	3.23129	−	2.71138i	0.344457	−	0.289034i
$89$	5.76444	+	9.98431i	0.611030	+	1.05833i	0.991067	+	0.133364i	$0.0425778\pi$
$89$	5.76444	+	9.98431i	0.611030	+	1.05833i	−0.380037	+	0.924971i	$0.624089\pi$
$90$	−8.23088	+	6.92678i	−0.867611	+	0.730147i
$91$	−1.01323	+	17.4401i	−0.106215	+	1.82822i
$92$	4.12703	−	0.727707i	0.430273	−	0.0758687i
$93$	0.420392	−	4.84535i	0.0435926	−	0.502439i
$94$	−0.00302003	−	0.00829748i	−0.000311493	−	0.000855819i
$95$	−5.64941	−	15.5216i	−0.579617	−	1.59249i
$96$	1.56924	−	0.733128i	0.160160	−	0.0748246i
$97$	2.42324	−	0.427283i	0.246043	−	0.0433840i	−0.0492664	−	0.998786i	$-0.515688\pi$
$97$	2.42324	−	0.427283i	0.246043	−	0.0433840i	0.295310	+	0.955402i	$0.404577\pi$
$98$	6.42671	−	2.77443i	0.649195	−	0.280260i
$99$	−2.17945	+	12.4654i	−0.219043	+	1.25282i
$100$	3.92932	+	6.80577i	0.392932	+	0.680577i
$101$	10.1194	−	8.49116i	1.00692	−	0.844902i	0.0189881	−	0.999820i	$-0.493956\pi$
$101$	10.1194	−	8.49116i	1.00692	−	0.844902i	0.987927	+	0.154917i	$0.0495111\pi$
$102$	8.69379	+	2.32278i	0.860814	+	0.229989i
$103$	−3.25286	−	0.573568i	−0.320514	−	0.0565153i	0.0110765	−	0.999939i	$-0.496474\pi$
$103$	−3.25286	−	0.573568i	−0.320514	−	0.0565153i	−0.331591	+	0.943423i	$0.607585\pi$
$104$	−5.05809	−	4.24424i	−0.495986	−	0.416182i
$105$	−0.492175	−	16.4253i	−0.0480314	−	1.60294i
$106$	3.71730	+	1.35299i	0.361056	+	0.131414i
$107$			14.2685i			1.37939i	0.724102	+	0.689693i	$0.242255\pi$
$107$			14.2685i			1.37939i	−0.724102	+	0.689693i	$0.757745\pi$
$108$	−2.18579	+	4.71405i	−0.210328	+	0.453610i
$109$	15.2110			1.45695			0.728475	−	0.685073i	$-0.240230\pi$
$109$	15.2110			1.45695			0.728475	+	0.685073i	$0.240230\pi$
$110$	14.2136	+	5.17334i	1.35522	+	0.493259i
$111$	0.840395	+	9.52662i	0.0797668	+	0.904227i
$112$	−0.609778	+	2.57452i	−0.0576186	+	0.243270i
$113$	9.60817	+	1.69418i	0.903860	+	0.159375i	0.606214	−	0.795301i	$-0.292687\pi$
$113$	9.60817	+	1.69418i	0.903860	+	0.159375i	0.297646	+	0.954676i	$0.403798\pi$
$114$	−5.64563	−	5.63750i	−0.528762	−	0.528000i
$115$	9.65942	+	11.5117i	0.900746	+	1.07347i
$116$	−4.01257	+	2.31666i	−0.372558	+	0.215097i
$117$	19.8086	−	0.0285722i	1.83130	−	0.00264150i
$118$	−2.02203	−	1.16742i	−0.186143	−	0.107470i
$119$	−11.0246	+	8.21003i	−1.01063	+	0.752612i
$120$	5.09028	+	3.55878i	0.464677	+	0.324871i
$121$	6.38315	−	2.32328i	0.580287	−	0.211207i
$122$	−1.80212	+	0.655917i	−0.163156	+	0.0593839i
$123$	3.25692	−	4.65851i	0.293667	−	0.420044i
$124$	−2.76531	+	0.487599i	−0.248332	+	0.0437877i
$125$	−5.12537	+	8.87740i	−0.458427	+	0.794019i
$126$	−3.57349	−	7.08732i	−0.318352	−	0.631389i
$127$	−2.75651	−	4.77441i	−0.244600	−	0.423660i	0.717419	−	0.696642i	$-0.245323\pi$
$127$	−2.75651	−	4.77441i	−0.244600	−	0.423660i	−0.962019	+	0.272982i	$0.911990\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−6.04516	−	6.03644i	−0.532246	−	0.531479i
$130$	4.11150	−	23.3175i	0.360602	−	2.04508i
$131$	−6.75981	−	5.67215i	−0.590607	−	0.495578i	0.297804	−	0.954627i	$-0.403746\pi$
$131$	−6.75981	−	5.67215i	−0.590607	−	0.495578i	−0.888411	+	0.459049i	$0.848190\pi$
$132$	7.27779	−	0.642014i	0.633450	−	0.0558801i
$133$	12.1046	−	1.41661i	1.04960	−	0.122835i
$134$		−	2.10307i		−	0.181678i
$135$	−18.5584	+	1.66412i	−1.59725	+	0.143224i
$136$		−	5.19542i		−	0.445504i
$137$	−5.14782	+	14.1435i	−0.439808	+	1.20836i	0.499810	+	0.866135i	$0.333403\pi$
$137$	−5.14782	+	14.1435i	−0.439808	+	1.20836i	−0.939617	+	0.342227i	$0.888819\pi$
$138$	6.58065	+	3.06283i	0.560182	+	0.260725i
$139$	−7.92841	+	9.44872i	−0.672479	+	0.801430i	−0.989119	−	0.147116i	$-0.953001\pi$
$139$	−7.92841	+	9.44872i	−0.672479	+	0.801430i	0.316640	+	0.948546i	$0.397445\pi$
$140$	−9.08842	+	2.72233i	−0.768111	+	0.230079i
$141$	0.00394772	−	0.0147757i	0.000332458	−	0.00124434i
$142$	−2.49854	+	2.09652i	−0.209673	+	0.175936i
$143$	−13.9259	−	24.1204i	−1.16455	−	2.01705i
$144$	2.95517	+	0.516682i	0.246264	+	0.0430569i
$145$	−14.3887	−	8.30730i	−1.19491	−	0.689883i
$146$	1.63465	+	9.27054i	0.135284	+	0.767235i
$147$	11.8763	+	2.43974i	0.979545	+	0.201226i
$148$	5.18857	−	1.88848i	0.426498	−	0.155232i
$149$	−3.89647	−	10.7055i	−0.319211	−	0.877026i	−0.990707	−	0.136017i	$-0.956570\pi$
$149$	−3.89647	−	10.7055i	−0.319211	−	0.877026i	0.671495	−	0.741009i	$-0.265652\pi$
$150$	−1.17654	+	13.5606i	−0.0960645	+	1.10722i
$151$	−3.24945	−	18.4285i	−0.264436	−	1.49969i	−0.770635	−	0.637276i	$-0.780061\pi$
$151$	−3.24945	−	18.4285i	−0.264436	−	1.49969i	0.506199	−	0.862417i	$-0.331050\pi$
$152$	−2.30316	+	3.98919i	−0.186811	+	0.323566i
$153$	10.0359	+	11.9253i	0.811352	+	0.964104i
$154$	−6.13126	+	9.32509i	−0.494071	+	0.751437i
$155$	−6.47228	−	7.71337i	−0.519866	−	0.619553i
$156$	−2.96795	−	11.0447i	−0.237626	−	0.884281i
$157$	−16.2708	−	2.86898i	−1.29855	−	0.228969i	−0.518711	−	0.854950i	$-0.673588\pi$
$157$	−16.2708	−	2.86898i	−1.29855	−	0.228969i	−0.779839	+	0.625981i	$0.784699\pi$
$158$	−7.20684	+	8.58877i	−0.573345	+	0.683286i
$159$	3.93405	+	5.60980i	0.311991	+	0.444886i
$160$	1.22645	−	3.36964i	0.0969592	−	0.266393i
$161$	−9.90747	+	4.97752i	−0.780818	+	0.392284i
$162$	−7.78121	+	4.52247i	−0.611350	+	0.355319i
$163$	−12.8760			−1.00853			−0.504265	−	0.863549i	$-0.668237\pi$
$163$	−12.8760			−1.00853			−0.504265	+	0.863549i	$0.668237\pi$
$164$	−3.08382	−	1.12242i	−0.240806	−	0.0876461i
$165$	15.0424	+	21.4499i	1.17105	+	1.66987i
$166$	0.862746	−	1.02818i	0.0669620	−	0.0798023i
$167$	−1.16696	+	6.61818i	−0.0903023	+	0.512130i	0.905784	+	0.423740i	$0.139283\pi$
$167$	−1.16696	+	6.61818i	−0.0903023	+	0.512130i	−0.996086	+	0.0883895i	$0.971828\pi$
$168$	−3.42066	+	3.04944i	−0.263909	+	0.235270i
$169$	−23.4393	+	19.6679i	−1.80302	+	1.51292i
$170$	16.1343	−	9.31512i	1.23744	−	0.714437i
$171$	−2.41926	−	13.6055i	−0.185006	−	1.04044i
$172$	−2.46615	+	4.27149i	−0.188042	+	0.325698i
$173$	0.419094	+	2.37680i	0.0318631	+	0.180705i	0.996586	−	0.0825635i	$-0.0263107\pi$
$173$	0.419094	+	2.37680i	0.0318631	+	0.180705i	−0.964723	+	0.263268i	$0.915200\pi$
$174$	−7.99511	−	0.693672i	−0.606108	−	0.0525871i
$175$	−15.1256	−	14.2661i	−1.14339	−	1.07842i
$176$	−1.44269	−	3.96377i	−0.108747	−	0.298780i
$177$	−1.71174	−	3.66393i	−0.128662	−	0.275398i
$178$	11.3537	−	2.00197i	0.850999	−	0.150054i
$179$	5.81264	+	3.35593i	0.434457	+	0.250834i	0.701244	−	0.712922i	$-0.252629\pi$
$179$	5.81264	+	3.35593i	0.434457	+	0.250834i	−0.266787	+	0.963756i	$0.585962\pi$
$180$	3.69392	+	10.1036i	0.275329	+	0.753077i
$181$	14.7147	−	8.49554i	1.09374	−	0.631469i	0.159167	−	0.987252i	$-0.449119\pi$
$181$	14.7147	−	8.49554i	1.09374	−	0.631469i	0.934569	+	0.355783i	$0.115786\pi$
$182$	16.0418	+	6.91700i	1.18910	+	0.512722i
$183$	−3.20912	−	0.857400i	−0.237225	−	0.0633808i
$184$	0.727707	−	4.12703i	0.0536473	−	0.304249i
$185$	15.1675	+	12.7270i	1.11513	+	0.935709i
$186$	−4.40935	−	2.05225i	−0.323309	−	0.150478i
$187$	7.49540	−	20.5934i	0.548118	−	1.50594i
$188$	−0.00882999			−0.000643993
$189$	1.96107	−	13.6071i	0.142647	−	0.989774i
$190$	−16.5178			−1.19833
$191$	5.90333	−	16.2193i	0.427150	−	1.17359i	−0.520384	−	0.853932i	$-0.674211\pi$
$191$	5.90333	−	16.2193i	0.427150	−	1.17359i	0.947535	−	0.319653i	$-0.103566\pi$
$192$	−0.152203	−	1.72535i	−0.0109843	−	0.124516i
$193$	−12.1718	−	10.2133i	−0.876142	−	0.735171i	0.0892398	−	0.996010i	$-0.471556\pi$
$193$	−12.1718	−	10.2133i	−0.876142	−	0.735171i	−0.965382	+	0.260839i	$0.916001\pi$
$194$	0.427283	−	2.42324i	0.0306771	−	0.173979i
$195$	28.9776	−	29.0194i	2.07513	−	2.07812i
$196$	−0.409048	−	6.98804i	−0.0292177	−	0.499146i
$197$	−14.5556	+	8.40367i	−1.03704	+	0.598736i	−0.918994	−	0.394271i	$-0.870997\pi$
$197$	−14.5556	+	8.40367i	−1.03704	+	0.598736i	−0.118048	+	0.993008i	$0.537664\pi$
$198$	10.9682	+	6.31141i	0.779476	+	0.448533i
$199$	−1.49599	−	0.863712i	−0.106048	−	0.0612269i	0.446038	−	0.895014i	$-0.352835\pi$
$199$	−1.49599	−	0.863712i	−0.106048	−	0.0612269i	−0.552086	+	0.833787i	$0.686168\pi$
$200$	7.73924	−	1.36464i	0.547247	−	0.0964944i
$201$	2.08717	−	2.98537i	0.147218	−	0.210572i
$202$	−4.51805	−	12.4133i	−0.317889	−	0.873393i
$203$	8.41107	−	8.91782i	0.590342	−	0.625908i
$204$	5.15615	−	7.37505i	0.361002	−	0.516357i
$205$	−2.04348	−	11.5891i	−0.142723	−	0.809421i
$206$	−1.65152	+	2.86052i	−0.115067	+	0.199302i
$207$	6.30175	+	10.8787i	0.438002	+	0.756120i
$208$	−5.71825	+	3.30143i	−0.396489	+	0.228913i
$209$	−14.8844	+	12.4895i	−1.02957	+	0.863914i
$210$	−15.6030	−	5.15527i	−1.07671	−	0.355748i
$211$	3.01360	−	17.0910i	0.207465	−	1.17659i	−0.686049	−	0.727555i	$-0.740657\pi$
$211$	3.01360	−	17.0910i	0.207465	−	1.17659i	0.893514	−	0.449035i	$-0.148232\pi$
$212$	2.54278	−	3.03037i	0.174639	−	0.208127i
$213$	−5.62742	+	0.496425i	−0.385584	+	0.0340145i
$214$	13.4080	+	4.88011i	0.916551	+	0.333597i
$215$	−17.6867			−1.20622
$216$	3.68218	+	3.66628i	0.250540	+	0.249459i
$217$	6.63848	−	3.33518i	0.450650	−	0.226407i
$218$	5.20247	−	14.2937i	0.352356	−	0.968089i
$219$	−6.88002	+	14.7821i	−0.464909	+	0.998881i
$220$	9.72271	−	11.5871i	0.655505	−	0.781200i
$221$	−33.7835	−	5.95695i	−2.27253	−	0.400707i
$222$	9.23953	+	2.46858i	0.620117	+	0.165681i
$223$	−5.62615	−	6.70498i	−0.376755	−	0.448999i	0.544032	−	0.839064i	$-0.316897\pi$
$223$	−5.62615	−	6.70498i	−0.376755	−	0.448999i	−0.920787	+	0.390065i	$0.872452\pi$
$224$	2.21070	+	1.45354i	0.147709	+	0.0971189i
$225$	−15.1282	+	18.0820i	−1.00855	+	1.20547i
$226$	4.87819	−	8.44928i	0.324493	−	0.562038i
$227$	0.832707	+	4.72251i	0.0552687	+	0.313444i	0.999892	−	0.0147131i	$-0.00468349\pi$
$227$	0.832707	+	4.72251i	0.0552687	+	0.313444i	−0.944623	+	0.328157i	$0.893572\pi$
$228$	−7.22843	+	3.37702i	−0.478715	+	0.223649i
$229$	8.35330	+	22.9505i	0.552002	+	1.51661i	0.830973	+	0.556313i	$0.187784\pi$
$229$	8.35330	+	22.9505i	0.552002	+	1.51661i	−0.278971	+	0.960300i	$0.589993\pi$
$230$	14.1211	−	5.13967i	0.931120	−	0.338900i
$231$	−17.9581	+	7.15232i	−1.18156	+	0.470588i
$232$	0.804568	+	4.56293i	0.0528225	+	0.299571i
$233$	10.1701	+	5.87170i	0.666264	+	0.384668i	0.794659	−	0.607055i	$-0.207649\pi$
$233$	10.1701	+	5.87170i	0.666264	+	0.384668i	−0.128396	+	0.991723i	$0.540983\pi$
$234$	6.74808	−	18.6237i	0.441136	−	1.21747i
$235$	−0.0158317	−	0.0274213i	−0.00103275	−	0.00178877i
$236$	−1.78859	+	1.50080i	−0.116427	+	0.0976941i
$237$	−18.7542	+	5.03966i	−1.21821	+	0.327361i
$238$	3.94426	+	13.1678i	0.255668	+	0.853539i
$239$	−8.48982	+	10.1178i	−0.549161	+	0.654464i	−0.967215	−	0.253958i	$-0.918268\pi$
$239$	−8.48982	+	10.1178i	−0.549161	+	0.654464i	0.418055	+	0.908422i	$0.362712\pi$
$240$	5.08514	−	3.56612i	0.328244	−	0.230192i
$241$	5.46630	−	15.0185i	0.352115	−	0.967429i	−0.629574	−	0.776940i	$-0.716771\pi$
$241$	5.46630	−	15.0185i	0.352115	−	0.967429i	0.981689	−	0.190489i	$-0.0610072\pi$
$242$		−	6.79281i		−	0.436658i
$243$	−15.5339	−	1.30262i	−0.996503	−	0.0835629i
$244$			1.91777i			0.122773i
$245$	20.9678	−	13.7995i	1.33958	−	0.881616i
$246$	−3.26364	−	4.65381i	−0.208082	−	0.296716i
$247$	23.2992	+	19.5503i	1.48249	+	1.24396i
$248$	−0.487599	+	2.76531i	−0.0309626	+	0.175597i
$249$	2.24510	−	0.603308i	0.142277	−	0.0382331i
$250$	6.58905	+	7.85252i	0.416728	+	0.496637i
$251$	−0.268322	−	0.464747i	−0.0169363	−	0.0293346i	0.857433	−	0.514596i	$-0.172058\pi$
$251$	−0.268322	−	0.464747i	−0.0169363	−	0.0293346i	−0.874369	+	0.485261i	$0.838725\pi$
$252$	−7.88211	+	0.933976i	−0.496526	+	0.0588350i
$253$	8.83850	−	15.3087i	0.555672	−	0.962452i
$254$	−5.42926	+	0.957325i	−0.340662	+	0.0600679i
$255$	32.1477	+	2.78920i	2.01317	+	0.174667i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−29.7428	+	10.8255i	−1.85531	+	0.675277i	−0.873081	+	0.487575i	$0.837881\pi$
$257$	−29.7428	+	10.8255i	−1.85531	+	0.675277i	−0.982226	+	0.187701i	$0.939896\pi$
$258$	−7.73997	+	3.61600i	−0.481869	+	0.225123i
$259$	−11.7167	+	8.72540i	−0.728039	+	0.542170i
$260$	−20.5050	−	11.8386i	−1.27167	−	0.734198i
$261$	−10.6609	−	8.91935i	−0.659891	−	0.552094i
$262$	−7.64207	+	4.41215i	−0.472129	+	0.272584i
$263$	−17.3177	−	20.6384i	−1.06785	−	1.27262i	−0.960465	−	0.278402i	$-0.910195\pi$
$263$	−17.3177	−	20.6384i	−1.06785	−	1.27262i	−0.107390	−	0.994217i	$-0.534249\pi$
$264$	1.88586	−	7.05847i	0.116066	−	0.434419i
$265$	13.9698	+	2.46325i	0.858158	+	0.151316i
$266$	2.80883	−	11.8591i	0.172220	−	0.727127i
$267$	18.1038	+	8.42605i	1.10793	+	0.515666i
$268$	−1.97624	−	0.719293i	−0.120718	−	0.0439378i
$269$	23.1181			1.40954			0.704768	−	0.709438i	$-0.251051\pi$
$269$	23.1181			1.40954			0.704768	+	0.709438i	$0.251051\pi$
$270$	−4.78358	+	18.0083i	−0.291120	+	1.09595i
$271$			8.06136i			0.489693i	0.969562	+	0.244846i	$0.0787375\pi$
$271$			8.06136i			0.489693i	−0.969562	+	0.244846i	$0.921262\pi$
$272$	−4.88210	−	1.77694i	−0.296021	−	0.107743i
$273$	15.9071	+	25.7394i	0.962743	+	1.55782i
$274$	11.5299	+	9.67473i	0.696547	+	0.584472i
$275$	32.6453	+	5.75625i	1.96859	+	0.347115i
$276$	5.12883	−	5.13624i	0.308719	−	0.309165i
$277$	16.6877	−	14.0027i	1.00267	−	0.841338i	0.0153161	−	0.999883i	$-0.495125\pi$
$277$	16.6877	−	14.0027i	1.00267	−	0.841338i	0.987352	+	0.158544i	$0.0506801\pi$
$278$	6.16721	+	10.6819i	0.369885	+	0.640659i
$279$	−4.22248	−	7.28924i	−0.252793	−	0.436395i
$280$	−0.550264	+	9.47141i	−0.0328846	+	0.566025i
$281$	−6.69515	+	1.18054i	−0.399399	+	0.0704248i	−0.369740	−	0.929135i	$-0.620553\pi$
$281$	−6.69515	+	1.18054i	−0.399399	+	0.0704248i	−0.0296590	+	0.999560i	$0.509442\pi$
$282$	−0.0125344	−	0.00876324i	−0.000746414	−	0.000521843i
$283$	8.92435	+	24.5195i	0.530498	+	1.45753i	0.858480	+	0.512846i	$0.171409\pi$
$283$	8.92435	+	24.5195i	0.530498	+	1.45753i	−0.327983	+	0.944684i	$0.606369\pi$
$284$	1.11554	+	3.06491i	0.0661949	+	0.181869i
$285$	−23.4475	−	16.3929i	−1.38891	−	0.971031i
$286$	−27.4288	+	4.83643i	−1.62190	+	0.285984i
$287$	8.66802	+	0.503589i	0.511657	+	0.0297259i
$288$	1.49625	−	2.60024i	0.0881674	−	0.153220i
$289$	−4.99621	−	8.65369i	−0.293895	−	0.509041i
$290$	−12.7275	+	10.6797i	−0.747385	+	0.627131i
$291$	3.01146	−	3.01581i	0.176535	−	0.176790i
$292$	9.27054	+	1.63465i	0.542517	+	0.0956604i
$293$	14.9324	+	12.5298i	0.872361	+	0.731998i	0.964594	−	0.263740i	$-0.0849560\pi$
$293$	14.9324	+	12.5298i	0.872361	+	0.731998i	−0.0922330	+	0.995737i	$0.529400\pi$
$294$	6.35455	−	10.3257i	0.370605	−	0.602206i
$295$	−7.86756	−	2.86356i	−0.458067	−	0.166723i
$296$		−	5.52156i		−	0.320934i
$297$	9.30597	+	19.8445i	0.539987	+	1.15150i
$298$	−11.3925			−0.659951
$299$	−26.0019	−	9.46391i	−1.50373	−	0.547312i
$300$	12.3404	+	5.74359i	0.712473	+	0.331606i
$301$	3.00760	−	12.6983i	0.173355	−	0.731918i
$302$	−18.4285	−	3.24945i	−1.06044	−	0.186985i
$303$	5.90590	−	22.1049i	0.339285	−	1.26989i
$304$	2.96089	+	3.52865i	0.169818	+	0.202382i
$305$	−5.95560	+	3.43846i	−0.341016	+	0.196886i
$306$	14.6386	−	5.35194i	0.836833	−	0.305950i
$307$	0.500675	+	0.289065i	0.0285751	+	0.0164978i	0.514219	−	0.857659i	$-0.328082\pi$
$307$	0.500675	+	0.289065i	0.0285751	+	0.0164978i	−0.485644	+	0.874156i	$0.661415\pi$
$308$	6.66570	+	8.95087i	0.379814	+	0.510023i
$309$	−5.18328	+	2.42156i	−0.294866	+	0.137757i
$310$	−9.46185	+	3.44383i	−0.537397	+	0.195596i
$311$	−19.5012	+	7.09785i	−1.10581	+	0.402482i	−0.829455	−	0.558573i	$-0.811349\pi$
$311$	−19.5012	+	7.09785i	−1.10581	+	0.402482i	−0.276355	+	0.961056i	$0.589127\pi$
$312$	−11.3937	−	0.988539i	−0.645041	−	0.0559650i
$313$	−5.16640	+	0.910976i	−0.292022	+	0.0514914i	−0.317740	−	0.948178i	$-0.602924\pi$
$313$	−5.16640	+	0.910976i	−0.292022	+	0.0514914i	0.0257179	+	0.999669i	$0.491813\pi$
$314$	−8.26089	+	14.3083i	−0.466189	+	0.807463i
$315$	−17.0326	−	22.8031i	−0.959681	−	1.28481i
$316$	5.60592	+	9.70974i	0.315358	+	0.546216i
$317$	−2.11255	−	2.51764i	−0.118653	−	0.141405i	0.703448	−	0.710746i	$-0.251643\pi$
$317$	−2.11255	−	2.51764i	−0.118653	−	0.141405i	−0.822101	+	0.569342i	$0.807198\pi$
$318$	6.61701	−	1.77814i	0.371064	−	0.0997131i
$319$	−3.39379	+	19.2471i	−0.190016	+	1.07763i
$320$	−2.74695	−	2.30497i	−0.153559	−	0.128852i
$321$	14.1898	+	20.2341i	0.791998	+	1.12936i
$322$	1.28879	+	11.0124i	0.0718214	+	0.613696i
$323$			23.9318i			1.33160i
$324$	1.58840	+	8.85872i	0.0882442	+	0.492151i
$325$		−	51.8895i		−	2.87831i
$326$	−4.40387	+	12.0995i	−0.243908	+	0.670131i
$327$	21.5707	−	15.1271i	1.19286	−	0.836533i
$328$	−2.10945	+	2.51395i	−0.116475	+	0.138810i
$329$	0.0223795	−	0.00670354i	0.00123382	−	0.000369578i
$330$	25.3011	−	6.79898i	1.39278	−	0.374272i
$331$	−11.4563	+	9.61296i	−0.629694	+	0.528376i	−0.900834	−	0.434164i	$-0.857044\pi$
$331$	−11.4563	+	9.61296i	−0.629694	+	0.528376i	0.271140	+	0.962540i	$0.412599\pi$
$332$	−0.671097	−	1.16237i	−0.0368312	−	0.0637936i
$333$	10.6659	+	12.6739i	0.584486	+	0.694526i
$334$	5.81993	+	3.36014i	0.318452	+	0.183858i
$335$	−1.30955	−	7.42682i	−0.0715483	−	0.405770i
$336$	1.69561	+	4.25734i	0.0925029	+	0.232257i
$337$	29.9586	−	10.9040i	1.63195	−	0.593981i	0.646345	−	0.763045i	$-0.276297\pi$
$337$	29.9586	−	10.9040i	1.63195	−	0.593981i	0.985605	+	0.169064i	$0.0540744\pi$
$338$	10.4651	+	28.7526i	0.569225	+	1.56393i
$339$	15.3101	−	7.15268i	0.831533	−	0.388480i
$340$	−3.23511	−	18.3472i	−0.175448	−	0.995017i
$341$	−5.92223	+	10.2576i	−0.320706	+	0.555480i
$342$	−13.6125	−	2.38000i	−0.736078	−	0.128696i
$343$	6.34190	+	17.4006i	0.342430	+	0.939543i
$344$	3.17042	+	3.77836i	0.170937	+	0.203715i
$345$	25.1462	+	6.71846i	1.35382	+	0.361710i
$346$	2.37680	+	0.419094i	0.127777	+	0.0225306i
$347$	11.2762	−	13.4384i	0.605336	−	0.721411i	−0.373139	−	0.927775i	$-0.621719\pi$
$347$	11.2762	−	13.4384i	0.605336	−	0.721411i	0.978475	+	0.206364i	$0.0661632\pi$
$348$	−3.38633	+	7.27570i	−0.181526	+	0.390018i
$349$	7.51728	−	20.6536i	0.402391	−	1.10556i	−0.558711	−	0.829363i	$-0.688704\pi$
$349$	7.51728	−	20.6536i	0.402391	−	1.10556i	0.961101	−	0.276197i	$-0.0890741\pi$
$350$	−18.5790	+	9.33413i	−0.993091	+	0.498930i
$351$	28.0620	−	19.7399i	1.49784	−	1.05364i
$352$	−4.21815			−0.224828
$353$	2.04763	+	0.745275i	0.108984	+	0.0396670i	0.395937	−	0.918278i	$-0.370420\pi$
$353$	2.04763	+	0.745275i	0.108984	+	0.0396670i	−0.286953	+	0.957945i	$0.592642\pi$
$354$	−4.02841	+	0.355368i	−0.214108	+	0.0188876i
$355$	−7.51790	+	8.95949i	−0.399009	+	0.475520i
$356$	2.00197	−	11.3537i	0.106104	−	0.601747i
$357$	−7.46922	+	22.6065i	−0.395313	+	1.19646i
$358$	5.14158	−	4.31430i	0.271741	−	0.228018i
$359$	−8.81315	+	5.08827i	−0.465140	+	0.268549i	−0.714203	−	0.699938i	$-0.753211\pi$
$359$	−8.81315	+	5.08827i	−0.465140	+	0.268549i	0.249063	+	0.968487i	$0.419877\pi$
$360$	10.7577	−	0.0155170i	0.566979	−	0.000817819i
$361$	1.10909	−	1.92100i	0.0583733	−	0.101106i
$362$	−2.95047	−	16.7330i	−0.155073	−	0.879465i
$363$	6.74146	−	9.64259i	0.353835	−	0.506105i
$364$	11.9865	−	12.7086i	0.628262	−	0.666113i
$365$	11.5452	+	31.7202i	0.604305	+	1.66031i
$366$	−1.90327	+	2.72233i	−0.0994858	+	0.142299i
$367$	−25.3414	+	4.46836i	−1.32281	+	0.233247i	−0.790061	−	0.613028i	$-0.789951\pi$
$367$	−25.3414	+	4.46836i	−1.32281	+	0.233247i	−0.532747	+	0.846275i	$0.678840\pi$
$368$	−3.62925	−	2.09535i	−0.189188	−	0.109228i
$369$	−0.0142008	−	9.84518i	−0.000739266	−	0.512519i
$370$	17.1471	−	9.89986i	0.891433	−	0.514669i
$371$	−4.14407	+	9.61087i	−0.215149	+	0.498971i
$372$	−3.43657	+	3.44153i	−0.178178	+	0.178435i
$373$	−2.86169	+	16.2295i	−0.148173	+	0.840330i	0.816592	+	0.577216i	$0.195861\pi$
$373$	−2.86169	+	16.2295i	−0.148173	+	0.840330i	−0.964765	+	0.263115i	$0.915250\pi$
$374$	−16.7879	−	14.0867i	−0.868083	−	0.728408i
$375$	1.56019	+	17.6861i	0.0805678	+	0.913307i
$376$	−0.00302003	+	0.00829748i	−0.000155746	+	0.000427910i
$377$	30.5932			1.57563
$378$	−12.1158	−	6.49672i	−0.623170	−	0.334155i
$379$	32.5089			1.66987			0.834935	−	0.550349i	$-0.185505\pi$
$379$	32.5089			1.66987			0.834935	+	0.550349i	$0.185505\pi$
$380$	−5.64941	+	15.5216i	−0.289809	+	0.796243i
$381$	−8.65708	−	4.02926i	−0.443515	−	0.206425i
$382$	−13.2221	−	11.0946i	−0.676500	−	0.567651i
$383$	4.22063	−	23.9364i	0.215664	−	1.22309i	−0.664087	−	0.747656i	$-0.731179\pi$
$383$	4.22063	−	23.9364i	0.215664	−	1.22309i	0.879751	−	0.475435i	$-0.157709\pi$
$384$	−1.67336	−	0.447081i	−0.0853931	−	0.0228150i
$385$	−15.8455	+	36.7486i	−0.807559	+	1.87288i
$386$	−13.7604	+	7.94455i	−0.700384	+	0.404367i
$387$	−14.5758	−	2.54843i	−0.740928	−	0.129544i
$388$	−2.13096	−	1.23031i	−0.108183	−	0.0624597i
$389$	−9.11231	+	1.60675i	−0.462013	+	0.0814653i	−0.399810	−	0.916598i	$-0.630924\pi$
$389$	−9.11231	+	1.60675i	−0.462013	+	0.0814653i	−0.0622031	+	0.998064i	$0.519813\pi$
$390$	−17.3584	−	37.1552i	−0.878977	−	1.88143i
$391$	−7.44662	−	20.4594i	−0.376592	−	1.03468i
$392$	−6.70651	−	2.00567i	−0.338730	−	0.101302i
$393$	−15.2269	−	1.32112i	−0.768097	−	0.0666416i
$394$	2.91856	+	16.5520i	0.147035	+	0.833877i
$395$	−20.1022	+	34.8181i	−1.01145	+	1.75189i
$396$	9.68213	−	8.14810i	0.486546	−	0.409458i
$397$	−8.97804	+	5.18347i	−0.450595	+	0.260151i	−0.708081	−	0.706131i	$-0.750439\pi$
$397$	−8.97804	+	5.18347i	−0.450595	+	0.260151i	0.257487	+	0.966282i	$0.417106\pi$
$398$	−1.32328	+	1.11037i	−0.0663302	+	0.0556577i
$399$	15.7566	−	14.0467i	0.788819	−	0.703215i
$400$	1.36464	−	7.73924i	0.0682318	−	0.386962i
$401$	15.3621	−	18.3078i	0.767145	−	0.914247i	−0.231133	−	0.972922i	$-0.574243\pi$
$401$	15.3621	−	18.3078i	0.767145	−	0.914247i	0.998277	+	0.0586749i	$0.0186875\pi$
$402$	−2.09148	−	2.98236i	−0.104313	−	0.148746i
$403$	17.4225	+	6.34128i	0.867877	+	0.315882i
$404$	−13.2099			−0.657217
$405$	−24.6626	+	20.8159i	−1.22550	+	1.03435i
$406$	−5.50325	−	10.9539i	−0.273122	−	0.543633i
$407$	7.96592	−	21.8862i	0.394856	−	1.08486i
$408$	−5.16678	−	7.36761i	−0.255794	−	0.364751i
$409$	−7.12862	+	8.49555i	−0.352487	+	0.420078i	−0.912931	−	0.408115i	$-0.866186\pi$
$409$	−7.12862	+	8.49555i	−0.352487	+	0.420078i	0.560443	+	0.828193i	$0.310631\pi$
$410$	−11.5891	−	2.04348i	−0.572347	−	0.100920i
$411$	6.76543	+	25.1763i	0.333714	+	1.24185i
$412$	2.12316	+	2.53028i	0.104600	+	0.124658i
$413$	3.39379	−	5.16164i	0.166997	−	0.253988i
$414$	12.3779	−	2.20098i	0.608342	−	0.108172i
$415$	2.40648	−	4.16815i	0.118130	−	0.204606i
$416$	1.14658	+	6.50255i	0.0562155	+	0.318814i
$417$	−1.84663	+	21.2839i	−0.0904300	+	1.04228i
$418$	6.64551	+	18.2584i	0.325042	+	0.893046i
$419$	18.9190	−	6.88595i	0.924254	−	0.336401i	0.164324	−	0.986406i	$-0.447456\pi$
$419$	18.9190	−	6.88595i	0.924254	−	0.336401i	0.759929	+	0.650006i	$0.225233\pi$
$420$	−10.1809	+	12.8988i	−0.496778	+	0.629399i
$421$	−0.773686	−	4.38779i	−0.0377071	−	0.213848i	0.960132	−	0.279546i	$-0.0901838\pi$
$421$	−0.773686	−	4.38779i	−0.0377071	−	0.213848i	−0.997840	+	0.0656977i	$0.979073\pi$
$422$	−15.0295	−	8.67731i	−0.731626	−	0.422405i
$423$	−0.00909600	−	0.0248793i	−0.000442263	−	0.00120967i
$424$	−1.97793	−	3.42588i	−0.0960569	−	0.166375i
$425$	31.2768	−	26.2443i	1.51715	−	1.27304i
$426$	−1.45820	+	5.45783i	−0.0706502	+	0.264433i
$427$	−1.45593	−	4.86058i	−0.0704575	−	0.235220i
$428$	9.17161	−	10.9303i	0.443326	−	0.528336i
$429$	−43.7358	−	20.3559i	−2.11158	−	0.982794i
$430$	−6.04920	+	16.6200i	−0.291718	+	0.801490i
$431$			12.9448i			0.623528i	0.950160	+	0.311764i	$0.100920\pi$
$431$			12.9448i			0.623528i	−0.950160	+	0.311764i	$0.899080\pi$
$432$	4.70455	−	2.20617i	0.226348	−	0.106145i
$433$			5.59339i			0.268801i	0.990927	+	0.134401i	$0.0429109\pi$
$433$			5.59339i			0.268801i	−0.990927	+	0.134401i	$0.957089\pi$
$434$	−0.863551	−	7.37883i	−0.0414518	−	0.354195i
$435$	−28.6660	+	2.52878i	−1.37443	+	0.121246i
$436$	−11.6523	−	9.77744i	−0.558044	−	0.468255i
$437$	−3.35205	+	19.0104i	−0.160350	+	0.909392i
$438$	11.5375	+	11.5209i	0.551283	+	0.550489i
$439$	19.1723	+	22.8487i	0.915046	+	1.09051i	0.995595	+	0.0937587i	$0.0298882\pi$
$439$	19.1723	+	22.8487i	0.915046	+	1.09051i	−0.0805489	+	0.996751i	$0.525667\pi$
$440$	−7.56292	−	13.0994i	−0.360548	−	0.624488i
$441$	19.2681	−	8.35109i	0.917528	−	0.397671i
$442$	−17.1523	+	29.7087i	−0.815854	+	1.41310i
$443$	−2.28813	+	0.403459i	−0.108712	+	0.0191689i	−0.227740	−	0.973722i	$-0.573134\pi$
$443$	−2.28813	+	0.403459i	−0.108712	+	0.0191689i	0.119027	+	0.992891i	$0.462022\pi$
$444$	5.47982	−	7.83801i	0.260061	−	0.371976i
$445$	38.8482	−	14.1396i	1.84158	−	0.670280i
$446$	−8.22488	+	2.99361i	−0.389459	+	0.141752i
$447$	−16.1720	−	11.3064i	−0.764910	−	0.534774i
$448$	2.12199	−	1.58024i	0.100255	−	0.0746594i
$449$	−4.71434	−	2.72182i	−0.222483	−	0.128451i	0.384616	−	0.923077i	$-0.374334\pi$
$449$	−4.71434	−	2.72182i	−0.222483	−	0.128451i	−0.607100	+	0.794626i	$0.707667\pi$
$450$	11.8174	+	20.4003i	0.557077	+	0.961679i
$451$	−11.9882	+	6.92142i	−0.564504	+	0.325917i
$452$	−6.27129	−	7.47383i	−0.294976	−	0.351539i
$453$	−22.9350	−	22.9019i	−1.07758	−	1.07603i
$454$	4.72251	+	0.832707i	0.221639	+	0.0390809i
$455$	60.9574	+	14.4378i	2.85773	+	0.676855i
$456$	0.701094	+	7.94752i	0.0328317	+	0.372177i
$457$	26.6722	+	9.70788i	1.24767	+	0.454115i	0.879614	−	0.475688i	$-0.157801\pi$
$457$	26.6722	+	9.70788i	1.24767	+	0.454115i	0.368057	+	0.929803i	$0.380023\pi$
$458$	24.4234			1.14123
$459$	26.0914	+	6.93070i	1.21784	+	0.323497i
$460$		−	15.0274i		−	0.700656i
$461$	7.69582	+	2.80105i	0.358430	+	0.130458i	0.514957	−	0.857216i	$-0.327808\pi$
$461$	7.69582	+	2.80105i	0.358430	+	0.130458i	−0.156527	+	0.987674i	$0.550030\pi$
$462$	0.578954	+	19.3213i	0.0269354	+	0.898910i
$463$	−17.3944	−	14.5956i	−0.808386	−	0.678316i	0.141836	−	0.989890i	$-0.454699\pi$
$463$	−17.3944	−	14.5956i	−0.808386	−	0.678316i	−0.950222	+	0.311574i	$0.899144\pi$
$464$	4.56293	+	0.804568i	0.211829	+	0.0373511i
$465$	−16.8492	−	4.50170i	−0.781361	−	0.208761i
$466$	8.99596	−	7.54851i	0.416730	−	0.349678i
$467$	12.4156	+	21.5045i	0.574527	+	0.995110i	0.996093	+	0.0883121i	$0.0281473\pi$
$467$	12.4156	+	21.5045i	0.574527	+	0.995110i	−0.421566	+	0.906798i	$0.638519\pi$
$468$	−15.1926	−	12.7108i	−0.702279	−	0.587558i
$469$	5.55484	+	0.322721i	0.256498	+	0.0149019i
$470$	−0.0311824	+	0.00549829i	−0.00143834	+	0.000253617i
$471$	−25.9267	+	12.1126i	−1.19464	+	0.558118i
$472$	0.798562	+	2.19403i	0.0367568	+	0.100988i
$473$	7.11579	+	19.5505i	0.327184	+	0.898931i
$474$	−1.67857	+	19.3468i	−0.0770991	+	0.888628i
$475$	−35.6494	+	6.28595i	−1.63571	+	0.288419i
$476$	13.7227	+	0.797250i	0.628977	+	0.0365419i
$477$	11.1577	+	4.04287i	0.510878	+	0.185110i
$478$	6.60391	+	11.4383i	0.302056	+	0.523176i
$479$	20.0535	−	16.8269i	0.916268	−	0.768840i	−0.0570331	−	0.998372i	$-0.518164\pi$
$479$	20.0535	−	16.8269i	0.916268	−	0.768840i	0.973301	+	0.229532i	$0.0737196\pi$
$480$	−1.61184	−	5.99816i	−0.0735700	−	0.273777i
$481$	−35.9042	−	6.33088i	−1.63709	−	0.288663i
$482$	−12.2432	−	10.2733i	−0.557664	−	0.467935i
$483$	−9.09966	+	16.9115i	−0.414049	+	0.769498i
$484$	−6.38315	−	2.32328i	−0.290143	−	0.105604i
$485$		−	8.82354i		−	0.400656i
$486$	−6.53698	+	14.1516i	−0.296523	+	0.641930i
$487$	−30.4886			−1.38157			−0.690784	−	0.723061i	$-0.742735\pi$
$487$	−30.4886			−1.38157			−0.690784	+	0.723061i	$0.742735\pi$
$488$	1.80212	+	0.655917i	0.0815780	+	0.0296920i
$489$	−18.2595	+	12.8051i	−0.825722	+	0.579065i
$490$	−5.79586	−	24.4230i	−0.261830	−	1.10332i
$491$	13.7523	+	2.42490i	0.620633	+	0.109434i	0.475119	−	0.879922i	$-0.342405\pi$
$491$	13.7523	+	2.42490i	0.620633	+	0.109434i	0.145514	+	0.989356i	$0.453516\pi$
$492$	−5.48938	+	1.47512i	−0.247480	+	0.0665035i
$493$	15.4732	+	18.4403i	0.696879	+	0.830508i
$494$	26.3401	−	15.2075i	1.18510	−	0.684216i
$495$	42.6633	+	15.4585i	1.91757	+	0.694808i
$496$	2.43177	+	1.40399i	0.109190	+	0.0630408i
$497$	−5.15413	−	6.92110i	−0.231194	−	0.310454i
$498$	0.200945	−	2.31605i	0.00900455	−	0.103785i
$499$	−21.5827	+	7.85546i	−0.966174	+	0.351659i	−0.776450	−	0.630179i	$-0.782982\pi$
$499$	−21.5827	+	7.85546i	−0.966174	+	0.351659i	−0.189724	+	0.981837i	$0.560759\pi$
$500$	9.63255	−	3.50596i	0.430781	−	0.156791i
$501$	4.92682	+	10.5457i	0.220114	+	0.471149i
$502$	−0.528491	+	0.0931873i	−0.0235877	+	0.00415915i
$503$	18.3920	−	31.8560i	0.820061	−	1.42039i	−0.0855753	−	0.996332i	$-0.527273\pi$
$503$	18.3920	−	31.8560i	0.820061	−	1.42039i	0.905636	−	0.424055i	$-0.139394\pi$
$504$	−1.81819	+	7.72620i	−0.0809886	+	0.344152i
$505$	−23.6847	−	41.0230i	−1.05395	−	1.82550i
$506$	−11.3626	−	13.5414i	−0.505127	−	0.601987i
$507$	−13.6797	+	51.2010i	−0.607537	+	2.27392i
$508$	−0.957325	+	5.42926i	−0.0424744	+	0.240884i
$509$	4.79692	+	4.02509i	0.212620	+	0.178409i	0.742878	−	0.669427i	$-0.233460\pi$
$509$	4.79692	+	4.02509i	0.212620	+	0.178409i	−0.530258	+	0.847836i	$0.677905\pi$
$510$	13.6162	−	29.2550i	0.602934	−	1.29543i
$511$	−24.7371	+	2.89500i	−1.09430	+	0.128067i
$512$			1.00000i			0.0441942i
$513$	−16.9613	−	16.8880i	−0.748859	−	0.745625i
$514$			31.6517i			1.39610i
$515$	−4.05101	+	11.1301i	−0.178509	+	0.490449i
$516$	0.750708	+	8.50993i	0.0330481	+	0.374629i
$517$	−0.0239414	+	0.0285323i	−0.00105294	+	0.00125485i
$518$	4.19185	+	13.9943i	0.184179	+	0.614876i
$519$	2.95801	+	2.95374i	0.129842	+	0.129655i
$520$	−18.1378	+	15.2194i	−0.795394	+	0.667414i
$521$	−19.9559	−	34.5646i	−0.874284	−	1.51430i	−0.857524	−	0.514444i	$-0.827998\pi$
$521$	−19.9559	−	34.5646i	−0.874284	−	1.51430i	−0.0167601	−	0.999860i	$-0.505335\pi$
$522$	−12.0277	+	6.96734i	−0.526437	+	0.304952i
$523$	−8.06742	−	4.65773i	−0.352764	−	0.203668i	0.313138	−	0.949708i	$-0.398620\pi$
$523$	−8.06742	−	4.65773i	−0.352764	−	0.203668i	−0.665902	+	0.746039i	$0.731953\pi$
$524$	1.53232	+	8.69024i	0.0669399	+	0.379635i
$525$	−35.6370	−	5.18851i	−1.55533	−	0.226445i
$526$	−25.3168	+	9.21455i	−1.10386	+	0.401773i
$527$	4.98960	+	13.7088i	0.217350	+	0.597165i
$528$	−5.98779	−	4.18626i	−0.260585	−	0.182184i
$529$	0.944307	+	5.35543i	0.0410568	+	0.232845i
$530$	7.09266	−	12.2848i	0.308085	−	0.533619i
$531$	−6.07113	−	3.49350i	−0.263465	−	0.151605i
$532$	−10.1832	−	6.69548i	−0.441498	−	0.290286i
$533$	13.9284	+	16.5993i	0.603308	+	0.718994i
$534$	14.1098	−	14.1301i	0.610589	−	0.611470i
$535$	50.3879	+	8.88475i	2.17846	+	0.384121i
$536$	−1.35183	+	1.61105i	−0.0583901	+	0.0695866i
$537$	11.5803	−	1.02156i	0.499727	−	0.0440836i
$538$	7.90685	−	21.7239i	0.340889	−	0.936584i
$539$	−23.6895	−	17.6254i	−1.02038	−	0.759182i
$540$	15.2862	+	10.6543i	0.657814	+	0.458489i
$541$	−35.4039			−1.52213			−0.761066	−	0.648674i	$-0.775324\pi$
$541$	−35.4039			−1.52213			−0.761066	+	0.648674i	$0.775324\pi$
$542$	7.57520	+	2.75715i	0.325383	+	0.118430i
$543$	12.4182	−	26.6811i	0.532915	−	1.14499i
$544$	−3.33955	+	3.97993i	−0.143182	+	0.170638i
$545$	9.47164	−	53.7164i	0.405721	−	2.30096i
$546$	29.6277	−	6.14441i	1.26795	−	0.262956i
$547$	16.6699	−	13.9877i	0.712753	−	0.598071i	−0.212617	−	0.977136i	$-0.568199\pi$
$547$	16.6699	−	13.9877i	0.712753	−	0.598071i	0.925370	+	0.379065i	$0.123754\pi$
$548$	13.0347	−	7.52561i	0.556816	−	0.321478i
$549$	−5.40351	+	1.97555i	−0.230616	+	0.0843143i
$550$	16.5744	−	28.7078i	0.706737	−	1.22410i
$551$	−3.70610	−	21.0183i	−0.157885	−	0.895410i
$552$	−3.07232	−	6.57622i	−0.130767	−	0.279903i
$553$	−21.5796	−	20.3534i	−0.917658	−	0.865513i
$554$	−7.45066	−	20.4705i	−0.316548	−	0.869709i
$555$	34.1658	+	2.96429i	1.45026	+	0.125827i
$556$	12.1470	−	2.14185i	0.515149	−	0.0908347i
$557$	−21.8679	−	12.6255i	−0.926574	−	0.534958i	−0.0408478	−	0.999165i	$-0.513006\pi$
$557$	−21.8679	−	12.6255i	−0.926574	−	0.534958i	−0.885726	+	0.464207i	$0.846339\pi$
$558$	−8.29382	+	1.47476i	−0.351105	+	0.0624317i
$559$	28.2041	−	16.2836i	1.19291	−	0.688724i
$560$	8.71201	+	3.75649i	0.368150	+	0.158741i
$561$	−9.85071	−	36.6576i	−0.415897	−	1.54768i
$562$	−1.18054	+	6.69515i	−0.0497979	+	0.282418i
$563$	−5.59522	−	4.69494i	−0.235810	−	0.197868i	0.517223	−	0.855851i	$-0.326966\pi$
$563$	−5.59522	−	4.69494i	−0.235810	−	0.197868i	−0.753033	+	0.657982i	$0.771410\pi$
$564$	−0.0125218	+	0.00878131i	−0.000527262	+	0.000369760i
$565$	11.9657	−	32.8755i	0.503401	−	1.38308i
$566$	26.0931			1.09677
$567$	−10.7511	−	21.2465i	−0.451505	−	0.892269i
$568$	3.26161			0.136854
$569$	−12.0347	+	33.0652i	−0.504523	+	1.38616i	0.382293	+	0.924041i	$0.375134\pi$
$569$	−12.0347	+	33.0652i	−0.504523	+	1.38616i	−0.886816	+	0.462123i	$0.847088\pi$
$570$	−23.4238	+	16.4267i	−0.981115	+	0.688039i
$571$	10.2370	+	8.58987i	0.428405	+	0.359475i	0.831350	−	0.555750i	$-0.187569\pi$
$571$	10.2370	+	8.58987i	0.428405	+	0.359475i	−0.402944	+	0.915224i	$0.632013\pi$
$572$	−4.83643	+	27.4288i	−0.202221	+	1.14685i
$573$	−7.75836	−	28.8713i	−0.324110	−	1.20611i
$574$	3.43786	−	7.97304i	0.143493	−	0.332788i
$575$	28.5209	−	16.4666i	1.18941	−	0.686704i
$576$	−1.93168	−	2.29535i	−0.0804865	−	0.0956396i
$577$	12.3547	+	7.13297i	0.514332	+	0.296949i	0.734612	−	0.678487i	$-0.237364\pi$
$577$	12.3547	+	7.13297i	0.514332	+	0.296949i	−0.220281	+	0.975437i	$0.570697\pi$
$578$	−9.84062	+	1.73517i	−0.409316	+	0.0721734i
$579$	−27.4177	−	2.37882i	−1.13944	−	0.0988602i
$580$	5.68253	+	15.6126i	0.235954	+	0.648278i
$581$	2.58334	+	2.43654i	0.107175	+	0.101085i
$582$	−1.80395	−	3.86132i	−0.0747763	−	0.160057i
$583$	−2.89757	−	16.4329i	−0.120005	−	0.680583i
$584$	4.70677	−	8.15237i	0.194768	−	0.337348i
$585$	12.2336	−	69.9701i	0.505796	−	2.89291i
$586$	16.8813	−	9.74644i	0.697361	−	0.402622i
$587$	−14.8498	+	12.4605i	−0.612918	+	0.514299i	−0.895568	−	0.444924i	$-0.853231\pi$
$587$	−14.8498	+	12.4605i	−0.612918	+	0.514299i	0.282651	+	0.959223i	$0.408786\pi$
$588$	−7.52958	−	9.50292i	−0.310515	−	0.391894i
$589$	2.24604	−	12.7379i	0.0925464	−	0.524857i
$590$	−5.38173	+	6.41369i	−0.221562	+	0.264047i
$591$	−12.2839	+	26.3925i	−0.505291	+	1.08564i
$592$	−5.18857	−	1.88848i	−0.213249	−	0.0776162i
$593$	31.4456			1.29132			0.645659	−	0.763626i	$-0.276583\pi$
$593$	31.4456			1.29132			0.645659	+	0.763626i	$0.276583\pi$
$594$	21.8306	−	1.95753i	0.895719	−	0.0803185i
$595$	22.1282	+	44.0448i	0.907166	+	1.80566i
$596$	−3.89647	+	10.7055i	−0.159606	+	0.438513i
$597$	−2.98041	+	0.262918i	−0.121980	+	0.0107605i
$598$	−17.7863	+	21.1969i	−0.727337	+	0.866807i
$599$	7.24030	+	1.27666i	0.295831	+	0.0521629i	0.319594	−	0.947555i	$-0.396454\pi$
$599$	7.24030	+	1.27666i	0.295831	+	0.0521629i	−0.0237630	+	0.999718i	$0.507565\pi$
$600$	9.61787	−	9.63176i	0.392648	−	0.393215i
$601$	−13.1436	−	15.6640i	−0.536140	−	0.638947i	0.428178	−	0.903695i	$-0.359156\pi$
$601$	−13.1436	−	15.6640i	−0.536140	−	0.638947i	−0.964318	+	0.264748i	$0.914711\pi$
$602$	−10.9038	−	7.16930i	−0.444407	−	0.292199i
$603$	−0.00910050	−	6.30921i	−0.000370601	−	0.256931i
$604$	−9.35641	+	16.2058i	−0.380707	+	0.659404i
$605$	−4.22977	−	23.9882i	−0.171965	−	0.975260i
$606$	−18.7518	−	13.1100i	−0.761742	−	0.532559i
$607$	−5.87208	−	16.1334i	−0.238341	−	0.654835i	−0.999977	−	0.00683029i	$-0.997826\pi$
$607$	−5.87208	−	16.1334i	−0.238341	−	0.654835i	0.761636	−	0.648005i	$-0.224396\pi$
$608$	4.32853	−	1.57545i	0.175545	−	0.0638931i
$609$	3.05906	−	21.0110i	0.123959	−	0.851409i
$610$	1.19417	+	6.77245i	0.0483504	+	0.274209i
$611$	0.0504921	+	0.0291516i	0.00204269	+	0.00117935i
$612$	−0.0224819	−	15.5863i	−0.000908775	−	0.630037i
$613$	−4.09367	−	7.09045i	−0.165342	−	0.286381i	0.771435	−	0.636308i	$-0.219539\pi$
$613$	−4.09367	−	7.09045i	−0.165342	−	0.286381i	−0.936777	+	0.349928i	$0.886206\pi$
$614$	0.442873	−	0.371615i	0.0178729	−	0.0149972i
$615$	−14.4231	−	14.4023i	−0.581596	−	0.580757i
$616$	10.6909	−	3.20233i	0.430747	−	0.129026i
$617$	−3.27774	+	3.90625i	−0.131957	+	0.157260i	−0.827977	−	0.560763i	$-0.810508\pi$
$617$	−3.27774	+	3.90625i	−0.131957	+	0.157260i	0.696020	+	0.718022i	$0.254952\pi$
$618$	0.502732	+	5.69891i	0.0202228	+	0.229244i
$619$	4.36707	−	11.9984i	0.175527	−	0.482258i	−0.820465	−	0.571697i	$-0.806285\pi$
$619$	4.36707	−	11.9984i	0.175527	−	0.482258i	0.995992	+	0.0894394i	$0.0285075\pi$
$620$			10.0691i			0.404384i
$621$	19.7552	+	9.16001i	0.792748	+	0.367578i
$622$			20.7527i			0.832108i
$623$	3.54554	+	30.2958i	0.142049	+	1.21378i
$624$	−4.82580	+	10.3685i	−0.193186	+	0.415071i
$625$	−1.94199	−	1.62952i	−0.0776795	−	0.0651808i
$626$	−0.910976	+	5.16640i	−0.0364099	+	0.206491i
$627$	−8.68686	+	32.5136i	−0.346920	+	1.29847i
$628$	10.6200	+	12.6564i	0.423784	+	0.505046i
$629$	−14.3434	−	24.8435i	−0.571910	−	0.990576i
$630$	−27.2534	+	8.20632i	−1.08580	+	0.326948i
$631$	16.8767	−	29.2313i	0.671850	−	1.16368i	−0.305529	−	0.952183i	$-0.598833\pi$
$631$	16.8767	−	29.2313i	0.671850	−	1.16368i	0.977379	−	0.211496i	$-0.0678335\pi$
$632$	11.0415	−	1.94692i	0.439208	−	0.0774442i
$633$	−12.7232	−	27.2336i	−0.505700	−	1.08244i
$634$	−3.08834	+	1.12407i	−0.122654	+	0.0446423i
$635$	−18.5769	+	6.76142i	−0.737200	+	0.268319i
$636$	0.592247	−	6.82612i	0.0234841	−	0.270673i
$637$	−20.7315	+	41.3098i	−0.821412	+	1.63675i
$638$	16.9256	+	9.77203i	0.670093	+	0.386878i
$639$	−7.48653	+	6.30037i	−0.296163	+	0.249239i
$640$	−3.10547	+	1.79295i	−0.122755	+	0.0708724i
$641$	−14.9821	−	17.8550i	−0.591759	−	0.705231i	0.384184	−	0.923256i	$-0.374483\pi$
$641$	−14.9821	−	17.8550i	−0.591759	−	0.705231i	−0.975943	+	0.218026i	$0.930038\pi$
$642$	23.8670	−	6.41360i	0.941956	−	0.253125i
$643$	−30.4244	−	5.36465i	−1.19982	−	0.211561i	−0.462201	−	0.886775i	$-0.652940\pi$
$643$	−30.4244	−	5.36465i	−1.19982	−	0.211561i	−0.737622	+	0.675214i	$0.764051\pi$
$644$	10.7891	+	2.55539i	0.425148	+	0.100697i
$645$	−25.0814	+	17.5892i	−0.987579	+	0.692573i
$646$	22.4885	+	8.18515i	0.884799	+	0.322041i
$647$	19.1842			0.754207			0.377104	−	0.926171i	$-0.376920\pi$
$647$	19.1842			0.754207			0.377104	+	0.926171i	$0.376920\pi$
$648$	8.86774	+	1.53726i	0.348358	+	0.0603892i
$649$			9.84870i			0.386595i
$650$	−48.7602	−	17.7472i	−1.91253	−	0.696104i
$651$	6.09722	−	11.3315i	0.238969	−	0.444116i
$652$	9.86363	+	8.27657i	0.386289	+	0.324135i
$653$	−14.4209	−	2.54279i	−0.564333	−	0.0995071i	−0.115798	−	0.993273i	$-0.536943\pi$
$653$	−14.4209	−	2.54279i	−0.564333	−	0.0995071i	−0.448534	+	0.893766i	$0.648054\pi$
$654$	−6.83726	−	25.4436i	−0.267358	−	0.994923i
$655$	−24.2399	+	20.3397i	−0.947133	+	0.794739i
$656$	1.64086	+	2.84206i	0.0640650	+	0.110964i
$657$	4.94405	+	27.8045i	0.192886	+	1.08476i
$658$	0.00135498	−	0.0233226i	5.28227e−5	−	0.000909211i
$659$	−18.8908	+	3.33097i	−0.735883	+	0.129756i	−0.529014	−	0.848613i	$-0.677438\pi$
$659$	−18.8908	+	3.33097i	−0.735883	+	0.129756i	−0.206868	+	0.978369i	$0.566327\pi$
$660$	2.26455	−	26.1007i	0.0881473	−	1.01597i
$661$	−4.47825	−	12.3039i	−0.174184	−	0.478566i	0.821625	−	0.570029i	$-0.193068\pi$
$661$	−4.47825	−	12.3039i	−0.174184	−	0.478566i	−0.995808	+	0.0914630i	$0.970846\pi$
$662$	5.11495	+	14.0532i	0.198798	+	0.546194i
$663$	−53.8324	+	25.1497i	−2.09068	+	0.976735i
$664$	−1.32180	+	0.233070i	−0.0512959	+	0.00904485i
$665$	2.53469	−	43.6283i	0.0982911	−	1.69183i
$666$	15.5575	−	5.68790i	0.602842	−	0.220402i
$667$	9.70842	+	16.8155i	0.375912	+	0.651098i
$668$	5.14803	−	4.31971i	0.199183	−	0.167135i
$669$	−14.6464	−	3.91318i	−0.566264	−	0.151292i
$670$	−7.42682	−	1.30955i	−0.286923	−	0.0505923i
$671$	6.19689	+	5.19980i	0.239228	+	0.200736i
$672$	4.58052	−	0.137253i	0.176697	−	0.00529465i
$673$	18.9165	+	6.88503i	0.729176	+	0.265398i	0.679816	−	0.733383i	$-0.262060\pi$
$673$	18.9165	+	6.88503i	0.729176	+	0.265398i	0.0493601	+	0.998781i	$0.484282\pi$
$674$		−	31.8813i		−	1.22802i
$675$	−3.47095	+	40.6869i	−0.133597	+	1.56604i
$676$	30.5978			1.17684
$677$	35.5798	+	12.9500i	1.36744	+	0.497709i	0.918348	−	0.395774i	$-0.129524\pi$
$677$	35.5798	+	12.9500i	1.36744	+	0.497709i	0.449097	+	0.893483i	$0.351746\pi$
$678$	−1.48495	−	16.8332i	−0.0570291	−	0.646475i
$679$	6.33494	+	1.50043i	0.243113	+	0.0575814i
$680$	−18.3472	−	3.23511i	−0.703583	−	0.124061i
$681$	5.87733	+	5.86886i	0.225220	+	0.224895i
$682$	7.61347	+	9.07338i	0.291535	+	0.347438i
$683$	−25.0411	+	14.4575i	−0.958170	+	0.553200i	−0.895609	−	0.444842i	$-0.853260\pi$
$683$	−25.0411	+	14.4575i	−0.958170	+	0.553200i	−0.0625605	+	0.998041i	$0.519927\pi$
$684$	−6.89221	+	11.9775i	−0.263530	+	0.457972i
$685$	46.7412	+	26.9860i	1.78589	+	1.03108i
$686$	18.5203	−	0.00808594i	0.707107	−	0.000308723i
$687$	34.6698	+	24.2388i	1.32273	+	0.924767i
$688$	4.63484	−	1.68694i	0.176702	−	0.0643141i
$689$	−24.5448	+	8.93358i	−0.935083	+	0.340342i
$690$	14.9138	−	21.3318i	0.567758	−	0.812089i
$691$	50.8391	−	8.96431i	1.93401	−	0.341018i	0.934137	−	0.356914i	$-0.116171\pi$
$691$	50.8391	−	8.96431i	1.93401	−	0.341018i	0.999874	+	0.0158960i	$0.00506008\pi$
$692$	1.20673	−	2.09012i	0.0458731	−	0.0794545i
$693$	−18.3534	+	28.0018i	−0.697189	+	1.06370i
$694$	−8.77129	−	15.1923i	−0.332954	−	0.576693i
$695$	28.4304	+	33.8821i	1.07843	+	1.28522i
$696$	5.67873	+	5.67054i	0.215252	+	0.214941i
$697$	−2.96070	+	16.7909i	−0.112144	+	0.636002i
$698$	−16.8369	−	14.1279i	−0.637287	−	0.534747i
$699$	20.2615	−	1.78737i	0.766359	−	0.0676047i
$700$	2.41681	+	20.6510i	0.0913467	+	0.780536i
$701$		−	25.2591i		−	0.954022i	−0.878897	−	0.477011i	$-0.841720\pi$
$701$		−	25.2591i		−	0.954022i	0.878897	−	0.477011i	$-0.158280\pi$
$702$	−8.95163	−	33.1211i	−0.337858	−	1.25008i
$703$			25.4341i			0.959264i
$704$	−1.44269	+	3.96377i	−0.0543735	+	0.149390i
$705$	−0.0497210	−	0.0231416i	−0.00187260	−	0.000871565i
$706$	1.40066	−	1.66924i	0.0527145	−	0.0628227i
$707$	33.4804	−	10.0287i	1.25916	−	0.377167i
$708$	−1.04386	+	3.90701i	−0.0392307	+	0.146835i
$709$	−1.41763	+	1.18953i	−0.0532401	+	0.0446737i	−0.669019	−	0.743245i	$-0.733286\pi$
$709$	−1.41763	+	1.18953i	−0.0532401	+	0.0446737i	0.615779	+	0.787919i	$0.288841\pi$
$710$	5.84789	+	10.1288i	0.219467	+	0.380129i
$711$	−21.5833	+	25.7975i	−0.809438	+	0.967481i
$712$	−9.98431	−	5.76444i	−0.374178	−	0.216032i
$713$	2.04338	+	11.5886i	0.0765252	+	0.433996i
$714$	18.6885	+	14.7506i	0.699399	+	0.552029i
$715$	−93.8508	+	34.1589i	−3.50982	+	1.27747i
$716$	−2.29559	−	6.30708i	−0.0857902	−	0.235707i
$717$	−1.97739	+	22.7910i	−0.0738470	+	0.851145i
$718$	1.76714	+	10.0219i	0.0659490	+	0.374016i
$719$	17.0508	−	29.5328i	0.635887	−	1.10139i	−0.350440	−	0.936585i	$-0.613968\pi$
$719$	17.0508	−	29.5328i	0.635887	−	1.10139i	0.986327	−	0.164803i	$-0.0526988\pi$
$720$	3.66476	−	10.1142i	0.136577	−	0.376934i
$721$	−7.30206	−	4.80111i	−0.271943	−	0.178803i
$722$	−1.42582	−	1.69923i	−0.0530636	−	0.0632387i
$723$	−7.18399	−	26.7339i	−0.267176	−	0.994244i
$724$	−16.7330	−	2.95047i	−0.621875	−	0.109653i
$725$	−23.4049	+	27.8929i	−0.869236	+	1.03592i
$726$	−6.75536	−	9.63286i	−0.250715	−	0.357509i
$727$	−6.23779	+	17.1382i	−0.231347	+	0.635621i	−0.999992	−	0.00405528i	$-0.998709\pi$
$727$	−6.23779	+	17.1382i	−0.231347	+	0.635621i	0.768645	+	0.639676i	$0.220931\pi$
$728$	−7.84259	−	15.6102i	−0.290666	−	0.578553i
$729$	−23.3240	+	13.6011i	−0.863854	+	0.503743i
$730$	33.7560			1.24936
$731$	24.0800	+	8.76439i	0.890629	+	0.324163i
$732$	1.90720	+	2.71959i	0.0704921	+	0.100519i
$733$	−0.548447	+	0.653614i	−0.0202574	+	0.0241418i	−0.776078	−	0.630637i	$-0.782794\pi$
$733$	−0.548447	+	0.653614i	−0.0202574	+	0.0241418i	0.755821	+	0.654779i	$0.227238\pi$
$734$	−4.46836	+	25.3414i	−0.164930	+	0.935366i
$735$	16.0109	−	40.4211i	0.590572	−	1.49096i
$736$	−3.21026	+	2.69373i	−0.118332	+	0.0992922i
$737$	−7.68258	+	4.43554i	−0.282991	+	0.163385i
$738$	−9.25630	−	3.35390i	−0.340729	−	0.123459i
$739$	8.57846	−	14.8583i	0.315564	−	0.546573i	−0.663993	−	0.747739i	$-0.731140\pi$
$739$	8.57846	−	14.8583i	0.315564	−	0.546573i	0.979557	+	0.201166i	$0.0644730\pi$
$740$	−3.43819	−	19.4989i	−0.126390	−	0.716795i
$741$	52.4830	+	4.55353i	1.92801	+	0.167278i
$742$	7.61391	+	7.18126i	0.279515	+	0.263632i
$743$	−9.19167	−	25.2539i	−0.337210	−	0.926476i	−0.986182	−	0.165664i	$-0.947023\pi$
$743$	−9.19167	−	25.2539i	−0.337210	−	0.926476i	0.648973	−	0.760812i	$-0.275199\pi$
$744$	2.05860	+	4.40639i	0.0754721	+	0.161546i
$745$	−40.2317	+	7.09394i	−1.47398	+	0.259902i
$746$	14.2720	+	8.23992i	0.522534	+	0.301685i
$747$	2.58378	−	3.08827i	0.0945357	−	0.112994i
$748$	−18.9790	+	10.9575i	−0.693942	+	0.400647i
$749$	−14.9473	+	34.6656i	−0.546163	+	1.26665i
$750$	17.1531	+	4.58291i	0.626344	+	0.167344i
$751$	3.60946	−	20.4703i	0.131711	−	0.746971i	−0.845383	−	0.534161i	$-0.820628\pi$
$751$	3.60946	−	20.4703i	0.131711	−	0.746971i	0.977094	−	0.212809i	$-0.0682613\pi$
$752$	0.00676417	+	0.00567581i	0.000246664	+	0.000206975i
$753$	−0.842691	−	0.392214i	−0.0307094	−	0.0142931i
$754$	10.4635	−	28.7482i	0.381058	−	1.04695i
$755$	−67.1022			−2.44210
$756$	−10.2488	+	9.16312i	−0.372744	+	0.333260i
$757$	−6.20156			−0.225399			−0.112700	−	0.993629i	$-0.535950\pi$
$757$	−6.20156			−0.225399			−0.112700	+	0.993629i	$0.535950\pi$
$758$	11.1187	−	30.5484i	0.403849	−	1.10957i
$759$	−2.69049	−	30.4990i	−0.0976584	−	1.10704i
$760$	12.6533	+	10.6174i	0.458985	+	0.385134i
$761$	−1.00939	+	5.72454i	−0.0365904	+	0.207514i	−0.997622	−	0.0689246i	$-0.978043\pi$
$761$	−1.00939	+	5.72454i	−0.0365904	+	0.207514i	0.961032	+	0.276439i	$0.0891543\pi$
$762$	−6.74716	+	6.75690i	−0.244424	+	0.244777i
$763$	36.9555	+	15.9347i	1.33788	+	0.576874i
$764$	−14.9478	+	8.63010i	−0.540791	+	0.312226i
$765$	48.3624	−	28.0151i	1.74855	−	1.01289i
$766$	−21.0493	−	12.1528i	−0.760541	−	0.439099i
$767$	15.1824	−	2.67707i	0.548205	−	0.0966633i
$768$	−0.992440	+	1.41953i	−0.0358116	+	0.0512228i
$769$	−9.11397	−	25.0404i	−0.328658	−	0.902981i	−0.988452	−	0.151535i	$-0.951579\pi$
$769$	−9.11397	−	25.0404i	−0.328658	−	0.902981i	0.659794	−	0.751447i	$-0.270644\pi$
$770$	29.1129	+	27.4586i	1.04916	+	0.989540i
$771$	−31.4124	+	44.9305i	−1.13129	+	1.61813i
$772$	2.75911	+	15.6477i	0.0993027	+	0.563173i
$773$	−1.72348	+	2.98515i	−0.0619892	+	0.107369i	−0.895354	−	0.445354i	$-0.853078\pi$
$773$	−1.72348	+	2.98515i	−0.0619892	+	0.107369i	0.833365	+	0.552723i	$0.186411\pi$
$774$	−7.37995	+	12.8251i	−0.265267	+	0.460990i
$775$	−19.1104	+	11.0334i	−0.686466	+	0.396332i
$776$	−1.88495	+	1.58166i	−0.0676657	+	0.0567783i
$777$	−7.93809	+	24.0255i	−0.284778	+	0.861911i
$778$	−1.60675	+	9.11231i	−0.0576047	+	0.326692i
$779$	9.71682	−	11.5801i	0.348141	−	0.414899i
$780$	−40.8514	+	3.60373i	−1.46272	+	0.129034i
$781$	12.9283	+	4.70550i	0.462609	+	0.168376i
$782$	−21.7725			−0.778581
$783$	−23.9883	−	2.04642i	−0.857272	−	0.0731329i
$784$	−4.17848	+	5.61608i	−0.149231	+	0.200574i
$785$	−20.2631	+	55.6724i	−0.723221	+	1.98703i
$786$	−6.44936	+	13.8568i	−0.230041	+	0.494255i
$787$	1.52718	−	1.82003i	0.0544382	−	0.0648770i	−0.738138	−	0.674650i	$-0.764295\pi$
$787$	1.52718	−	1.82003i	0.0544382	−	0.0648770i	0.792576	+	0.609773i	$0.208739\pi$
$788$	16.5520	+	2.91856i	0.589640	+	0.103969i
$789$	−45.0828	−	12.0450i	−1.60499	−	0.428815i
$790$	25.8429	+	30.7984i	0.919451	+	1.09576i
$791$	21.5685	+	14.1813i	0.766887	+	0.504230i
$792$	−4.34523	−	11.8850i	−0.154401	−	0.422317i
$793$	6.33140	−	10.9663i	0.224835	−	0.389425i
$794$	1.80020	+	10.2094i	0.0638867	+	0.362320i
$795$	22.2602	−	10.3997i	0.789488	−	0.368838i
$796$	0.590814	+	1.62325i	0.0209408	+	0.0575345i
$797$	−0.841055	+	0.306119i	−0.0297917	+	0.0108433i	−0.356873	−	0.934153i	$-0.616157\pi$
$797$	−0.841055	+	0.306119i	−0.0297917	+	0.0108433i	0.327081	+	0.944996i	$0.393935\pi$
$798$	−7.81050	−	19.6107i	−0.276489	−	0.694210i
$799$	0.00796620	+	0.0451786i	0.000281824	+	0.00159830i
$800$	−6.80577	−	3.92932i	−0.240620	−	0.138922i
$801$	34.0525	−	6.05503i	1.20319	−	0.213944i
$802$	−11.9496	−	20.6972i	−0.421954	−	0.730845i
$803$	30.4179	−	25.5237i	1.07343	−	0.900711i
$804$	−3.51783	+	0.945318i	−0.124064	+	0.0333388i
$805$	11.4085	+	38.0868i	0.402096	+	1.34238i
$806$	11.9177	−	14.2030i	0.419783	−	0.500278i
$807$	32.7837	−	22.9906i	1.15404	−	0.809309i
$808$	−4.51805	+	12.4133i	−0.158945	+	0.436697i
$809$		−	24.7123i		−	0.868838i	−0.900711	−	0.434419i	$-0.856954\pi$
$809$		−	24.7123i		−	0.868838i	0.900711	−	0.434419i	$-0.143046\pi$
$810$	11.1255	+	30.2948i	0.390909	+	1.06445i
$811$		−	14.3118i		−	0.502554i	−0.967915	−	0.251277i	$-0.919149\pi$
$811$		−	14.3118i		−	0.502554i	0.967915	−	0.251277i	$-0.0808505\pi$
$812$	−12.1755	+	1.42491i	−0.427277	+	0.0500045i
$813$	8.01691	+	11.4318i	0.281165	+	0.400930i
$814$	−17.8418	−	14.9710i	−0.625354	−	0.524734i
$815$	−8.01771	+	45.4707i	−0.280848	+	1.59277i
$816$	−8.69043	+	2.33531i	−0.304226	+	0.0817523i
$817$	−14.6040	−	17.4043i	−0.510928	−	0.608900i
$818$	5.54508	+	9.60436i	0.193879	+	0.335808i
$819$	48.1553	+	20.6816i	1.68268	+	0.722672i
$820$	−5.88397	+	10.1913i	−0.205477	+	0.355897i
$821$	−24.8777	+	4.38661i	−0.868238	+	0.153094i	−0.589985	−	0.807414i	$-0.700866\pi$
$821$	−24.8777	+	4.38661i	−0.868238	+	0.153094i	−0.278253	+	0.960508i	$0.589755\pi$
$822$	25.9719	+	2.25337i	0.905874	+	0.0785954i
$823$	−9.90583	+	3.60543i	−0.345296	+	0.125677i	−0.508846	−	0.860858i	$-0.669928\pi$
$823$	−9.90583	+	3.60543i	−0.345296	+	0.125677i	0.163550	+	0.986535i	$0.447705\pi$
$824$	3.10385	−	1.12971i	0.108128	−	0.0393552i
$825$	52.0187	−	24.3024i	1.81106	−	0.846101i
$826$	−3.68961	−	4.95450i	−0.128378	−	0.172389i
$827$	42.7413	+	24.6767i	1.48626	+	0.858093i	0.999877	−	0.0156532i	$-0.00498279\pi$
$827$	42.7413	+	24.6767i	1.48626	+	0.858093i	0.486383	+	0.873746i	$0.338316\pi$
$828$	2.16526	−	12.3842i	0.0752480	−	0.430382i
$829$	24.9643	−	14.4132i	0.867047	−	0.500590i	0.000680876	−	1.00000i	$-0.499783\pi$
$829$	24.9643	−	14.4132i	0.867047	−	0.500590i	0.866366	+	0.499410i	$0.166450\pi$
$830$	−3.09371	−	3.68694i	−0.107384	−	0.127976i
$831$	9.73933	−	36.4528i	0.337854	−	1.26453i
$832$	6.50255	+	1.14658i	0.225435	+	0.0397504i
$833$	−35.3852	+	8.39733i	−1.22603	+	0.290950i
$834$	19.3687	+	9.01479i	0.670684	+	0.312157i
$835$	22.6449	+	8.24206i	0.783658	+	0.285228i
$836$	19.4302			0.672006
$837$	−13.2369	−	6.13765i	−0.457535	−	0.212148i
$838$		−	20.1332i		−	0.695489i
$839$	−45.7476	−	16.6508i	−1.57938	−	0.574848i	−0.604312	−	0.796748i	$-0.706552\pi$
$839$	−45.7476	−	16.6508i	−1.57938	−	0.574848i	−0.975069	+	0.221900i	$0.928774\pi$
$840$	8.63886	+	13.9786i	0.298069	+	0.482308i
$841$	5.77011	+	4.84170i	0.198969	+	0.166955i
$842$	−4.38779	−	0.773686i	−0.151213	−	0.0266630i
$843$	−8.32034	+	8.33235i	−0.286568	+	0.286981i
$844$	−13.2944	+	11.1553i	−0.457612	+	0.383982i
$845$	54.8603	+	95.0208i	1.88725	+	3.26881i
$846$	−0.0264899		3.82095e-5i	−0.000910743		1.31367e-6i
$847$	17.9418	+	1.04237i	0.616489	+	0.0358164i
$848$	−3.89577	+	0.686929i	−0.133781	+	0.0235892i
$849$	37.0399	+	25.8958i	1.27120	+	0.888741i
$850$	−13.9643	−	38.3666i	−0.478972	−	1.31596i
$851$	−7.91407	−	21.7437i	−0.271291	−	0.745365i
$852$	4.62995	+	3.23695i	0.158619	+	0.110896i
$853$	−24.2646	+	4.27851i	−0.830805	+	0.146493i	−0.572847	−	0.819663i	$-0.694161\pi$
$853$	−24.2646	+	4.27851i	−0.830805	+	0.146493i	−0.257958	+	0.966156i	$0.583050\pi$
$854$	−5.06541	−	0.294287i	−0.173335	−	0.0100703i
$855$	−49.5533	+	0.0714764i	−1.69469	+	0.00244444i
$856$	−7.13424	−	12.3569i	−0.243843	−	0.422349i
$857$	−28.1799	+	23.6458i	−0.962608	+	0.807724i	−0.981375	−	0.192100i	$-0.938470\pi$
$857$	−28.1799	+	23.6458i	−0.962608	+	0.807724i	0.0187672	+	0.999824i	$0.494026\pi$
$858$	−34.0869	+	34.1361i	−1.16371	+	1.16539i
$859$	13.6957	+	2.41492i	0.467291	+	0.0823961i	0.402336	−	0.915492i	$-0.368198\pi$
$859$	13.6957	+	2.41492i	0.467291	+	0.0823961i	0.0649554	+	0.997888i	$0.479309\pi$
$860$	13.5488	+	11.3688i	0.462010	+	0.387672i
$861$	12.7929	−	7.90609i	0.435981	−	0.269439i
$862$	12.1641	+	4.42738i	0.414312	+	0.150797i
$863$		−	0.167383i		−	0.00569778i	−0.999996	−	0.00284889i	$-0.999093\pi$
$863$		−	0.167383i		−	0.00569778i	0.999996	−	0.00284889i	$-0.000906831\pi$
$864$	−0.464073	−	5.17539i	−0.0157881	−	0.176070i
$865$	8.65442			0.294259
$866$	5.25607	+	1.91305i	0.178608	+	0.0650081i
$867$	−15.6911	−	7.30310i	−0.532897	−	0.248026i
$868$	−7.22919	−	1.71224i	−0.245375	−	0.0581171i
$869$	46.5748	+	8.21239i	1.57994	+	0.278586i
$870$	−7.42807	+	27.8021i	−0.251835	+	0.942580i
$871$	8.92594	+	10.6375i	0.302444	+	0.360439i
$872$	−13.1731	+	7.60550i	−0.446098	+	0.257555i
$873$	1.27136	−	7.27157i	0.0430291	−	0.246105i
$874$	16.7175	+	9.65185i	0.565478	+	0.326479i
$875$	−21.7520	+	16.1987i	−0.735350	+	0.547614i
$876$	14.7721	−	6.90134i	0.499104	−	0.233175i
$877$	−24.5086	+	8.92040i	−0.827597	+	0.301221i	−0.720872	−	0.693068i	$-0.756259\pi$
$877$	−24.5086	+	8.92040i	−0.827597	+	0.301221i	−0.106725	+	0.994289i	$0.534036\pi$
$878$	28.0281	−	10.2014i	0.945902	−	0.344280i
$879$	33.6363	+	2.91835i	1.13452	+	0.0984336i
$880$	−14.8960	+	2.62658i	−0.502146	+	0.0885418i
$881$	−13.2148	+	22.8887i	−0.445217	+	0.771138i	−0.998067	−	0.0621422i	$-0.980207\pi$
$881$	−13.2148	+	22.8887i	−0.445217	+	0.771138i	0.552850	+	0.833281i	$0.313540\pi$
$882$	−1.25738	−	20.9623i	−0.0423382	−	0.705838i
$883$	16.3252	+	28.2761i	0.549387	+	0.951566i	0.998317	+	0.0579992i	$0.0184721\pi$
$883$	16.3252	+	28.2761i	0.549387	+	0.951566i	−0.448930	+	0.893567i	$0.648195\pi$
$884$	22.0506	+	26.2789i	0.741643	+	0.883855i
$885$	−14.0047	+	3.76338i	−0.470764	+	0.126505i
$886$	−0.403459	+	2.28813i	−0.0135545	+	0.0768713i
$887$	−19.9860	−	16.7702i	−0.671063	−	0.563089i	0.242317	−	0.970197i	$-0.422093\pi$
$887$	−19.9860	−	16.7702i	−0.671063	−	0.563089i	−0.913380	+	0.407109i	$0.866537\pi$
$888$	−5.49112	−	7.83010i	−0.184270	−	0.262761i
$889$	−1.69545	−	14.4872i	−0.0568635	−	0.485885i
$890$		−	41.3414i		−	1.38577i
$891$	32.9319	+	18.8868i	1.10326	+	0.632730i
$892$			8.75273i			0.293063i
$893$	0.0139112	−	0.0382208i	0.000465522	−	0.00127901i
$894$	−16.1557	+	11.3297i	−0.540327	+	0.378922i
$895$	15.4706	−	18.4372i	0.517125	−	0.616286i
$896$	−0.759179	−	2.53449i	−0.0253624	−	0.0846714i
$897$	−46.2849	+	12.4378i	−1.54541	+	0.415285i
$898$	−4.17008	+	3.49911i	−0.139157	+	0.116767i
$899$	−6.50512	−	11.2672i	−0.216958	−	0.375782i
$900$	23.2118	−	4.12740i	0.773726	−	0.137580i
$901$	−17.7989	−	10.2762i	−0.592967	−	0.342350i
$902$	2.40378	+	13.6325i	0.0800372	+	0.453914i
$903$	−8.36323	−	20.9984i	−0.278311	−	0.698784i
$904$	−9.16801	+	3.33688i	−0.304923	+	0.110983i
$905$	−20.8387	−	57.2538i	−0.692701	−	1.90318i
$906$	−29.3650	+	13.7189i	−0.975586	+	0.455780i
$907$	−2.70382	−	15.3341i	−0.0897788	−	0.509161i	−0.996223	−	0.0868348i	$-0.972325\pi$
$907$	−2.70382	−	15.3341i	−0.0897788	−	0.509161i	0.906444	−	0.422326i	$-0.138786\pi$
$908$	2.39768	−	4.15291i	0.0795699	−	0.137819i
$909$	−13.6079	−	37.2202i	−0.451344	−	1.23452i
$910$	34.4158	−	52.3432i	1.14087	−	1.73516i
$911$	−1.68724	−	2.01077i	−0.0559007	−	0.0666199i	0.737370	−	0.675490i	$-0.236068\pi$
$911$	−1.68724	−	2.01077i	−0.0559007	−	0.0666199i	−0.793270	+	0.608870i	$0.791623\pi$
$912$	7.70801	+	2.05940i	0.255238	+	0.0681935i
$913$	−5.57557	−	0.983123i	−0.184524	−	0.0325366i
$914$	18.2448	−	21.7434i	0.603486	−	0.719206i
$915$	−5.02610	+	10.7988i	−0.166158	+	0.356998i
$916$	8.35330	−	22.9505i	0.276001	−	0.758306i
$917$	−10.4811	−	20.8620i	−0.346117	−	0.688925i
$918$	15.4365	−	22.1475i	0.509481	−	0.730975i
$919$	54.9948			1.81411			0.907056	−	0.421010i	$-0.138324\pi$
$919$	54.9948			1.81411			0.907056	+	0.421010i	$0.138324\pi$
$920$	−14.1211	−	5.13967i	−0.465560	−	0.169450i
$921$	0.997477	−	0.0879929i	0.0328680	−	0.00289946i
$922$	5.26425	−	6.27369i	0.173369	−	0.206613i
$923$	3.73968	−	21.2088i	0.123093	−	0.698095i
$924$	18.3541	+	6.06425i	0.603806	+	0.199499i
$925$	33.2401	−	27.8918i	1.09293	−	0.917076i
$926$	−19.6646	+	11.3534i	−0.646220	+	0.373095i
$927$	−4.94218	+	8.58870i	−0.162323	+	0.282090i
$928$	2.31666	−	4.01257i	0.0760481	−	0.131719i
$929$	1.68371	+	9.54879i	0.0552407	+	0.313286i	0.999891	−	0.0147946i	$-0.00470945\pi$
$929$	1.68371	+	9.54879i	0.0552407	+	0.313286i	−0.944650	+	0.328080i	$0.893598\pi$
$930$	−9.99296	+	14.2934i	−0.327682	+	0.468698i
$931$	30.8923	+	9.23876i	1.01246	+	0.302788i
$932$	−4.01648	−	11.0352i	−0.131564	−	0.361469i
$933$	−20.5958	+	29.4591i	−0.674277	+	0.964447i
$934$	24.4540	−	4.31190i	0.800160	−	0.141090i
$935$	−68.0567	−	39.2926i	−2.22569	−	1.28500i
$936$	−17.1404	+	9.92903i	−0.560253	+	0.324541i
$937$	5.91074	−	3.41257i	0.193095	−	0.111484i	−0.400335	−	0.916369i	$-0.631106\pi$
$937$	5.91074	−	3.41257i	0.193095	−	0.111484i	0.593431	+	0.804885i	$0.297773\pi$
$938$	2.20312	−	5.10946i	0.0719346	−	0.166830i
$939$	−6.42050	+	6.42977i	−0.209525	+	0.209827i
$940$	−0.00549829	+	0.0311824i	−0.000179335	+	0.00101706i
$941$	10.7796	+	9.04514i	0.351404	+	0.294863i	0.801354	−	0.598191i	$-0.204114\pi$
$941$	10.7796	+	9.04514i	0.351404	+	0.294863i	−0.449949	+	0.893054i	$0.648558\pi$
$942$	2.51466	+	28.5059i	0.0819319	+	0.928771i
$943$	−4.70371	+	12.9233i	−0.153174	+	0.420842i
$944$	2.33484			0.0759925
$945$	−46.8313	−	15.3983i	−1.52342	−	0.500906i
$946$	20.8052			0.676434
$947$	12.2282	−	33.5966i	0.397362	−	1.09174i	−0.566202	−	0.824267i	$-0.691588\pi$
$947$	12.2282	−	33.5966i	0.397362	−	1.09174i	0.963564	−	0.267478i	$-0.0861901\pi$
$948$	17.6059	+	8.19433i	0.571815	+	0.266140i
$949$	−47.6146	−	39.9534i	−1.54563	−	1.29694i
$950$	−6.28595	+	35.6494i	−0.203943	+	1.15662i
$951$	−5.49956	−	1.46935i	−0.178336	−	0.0476470i
$952$	5.44260	−	12.6224i	0.176396	−	0.409095i
$953$	50.7631	−	29.3081i	1.64438	−	0.949383i	0.665128	−	0.746729i	$-0.268377\pi$
$953$	50.7631	−	29.3081i	1.64438	−	0.949383i	0.979251	−	0.202653i	$-0.0649565\pi$
$954$	7.61522	−	9.10210i	0.246552	−	0.294691i
$955$	−53.6011	−	30.9466i	−1.73449	−	1.00141i
$956$	13.0072	−	2.29351i	0.420682	−	0.0741775i
$957$	14.3283	+	30.6694i	0.463168	+	0.991400i
$958$	−8.95340	−	24.5993i	−0.289271	−	0.794766i
$959$	−27.3231	+	28.9693i	−0.882310	+	0.935467i
$960$	−6.18770	−	0.536857i	−0.199707	−	0.0173270i
$961$	4.01393	+	22.7641i	0.129482	+	0.734327i
$962$	−18.2291	+	31.5736i	−0.587728	+	1.01798i
$963$	40.2450	+	14.5823i	1.29688	+	0.469908i
$964$	−13.8412	+	7.99120i	−0.445794	+	0.257379i
$965$	−43.6466	+	36.6239i	−1.40503	+	1.17896i
$966$	12.7793	+	14.3349i	0.411167	+	0.461219i
$967$	6.41509	−	36.3818i	0.206295	−	1.16996i	−0.689093	−	0.724673i	$-0.741991\pi$
$967$	6.41509	−	36.3818i	0.206295	−	1.16996i	0.895389	−	0.445286i	$-0.146898\pi$
$968$	−4.36633	+	5.20359i	−0.140339	+	0.167250i
$969$	23.7998	+	33.9376i	0.764561	+	1.09023i
$970$	−8.29142	−	3.01783i	−0.266221	−	0.0968966i
$971$	9.70405			0.311418			0.155709	−	0.987803i	$-0.450234\pi$
$971$	9.70405			0.311418			0.155709	+	0.987803i	$0.450234\pi$
$972$	11.0624	+	10.9829i	0.354826	+	0.352276i
$973$	−29.1605	+	14.6503i	−0.934843	+	0.469666i
$974$	−10.4277	+	28.6499i	−0.334125	+	0.918001i
$975$	−51.6034	−	73.5843i	−1.65263	−	2.35658i
$976$	1.23272	−	1.46910i	0.0394584	−	0.0470247i
$977$	52.2350	+	9.21043i	1.67114	+	0.294668i	0.927476	−	0.373882i	$-0.121973\pi$
$977$	52.2350	+	9.21043i	1.67114	+	0.294668i	0.743668	+	0.668549i	$0.233084\pi$
$978$	5.78771	+	21.5379i	0.185071	+	0.688706i
$979$	−31.2591	−	37.2532i	−0.999047	−	1.19062i
$980$	−24.9324	−	2.90682i	−0.796435	−	0.0928550i
$981$	15.5455	−	42.9035i	0.496331	−	1.36980i
$982$	6.98223	−	12.0936i	0.222812	−	0.385922i
$983$	−2.35276	−	13.3432i	−0.0750415	−	0.425581i	−0.999065	−	0.0432446i	$-0.986231\pi$
$983$	−2.35276	−	13.3432i	−0.0750415	−	0.425581i	0.924023	−	0.382337i	$-0.124881\pi$
$984$	−0.491320	+	5.66285i	−0.0156627	+	0.180525i
$985$	20.6133	+	56.6346i	0.656795	+	1.80453i
$986$	22.6203	−	8.23313i	0.720378	−	0.262196i
$987$	0.0250698	−	0.0317624i	0.000797979	−	0.00101101i
$988$	−5.28149	−	29.9528i	−0.168027	−	0.952927i
$989$	17.9005	+	10.3349i	0.569204	+	0.328630i
$990$	29.1179	−	34.8032i	0.925429	−	1.10612i
$991$	8.27017	+	14.3244i	0.262711	+	0.455028i	0.966961	−	0.254923i	$-0.0820502\pi$
$991$	8.27017	+	14.3244i	0.262711	+	0.455028i	−0.704251	+	0.709951i	$0.748717\pi$
$992$	2.15103	−	1.80493i	0.0682953	−	0.0573066i
$993$	−6.68615	+	25.0252i	−0.212178	+	0.794151i
$994$	−8.26652	+	2.47614i	−0.262198	+	0.0785385i
$995$	−3.98166	+	4.74515i	−0.126227	+	0.150431i
$996$	−2.10765	−	0.980961i	−0.0667833	−	0.0310829i
$997$	−0.781840	+	2.14809i	−0.0247611	+	0.0680306i	−0.951457	−	0.307781i	$-0.900414\pi$
$997$	−0.781840	+	2.14809i	−0.0247611	+	0.0680306i	0.926696	+	0.375811i	$0.122636\pi$
$998$			22.9678i			0.727034i
$999$	27.7292	+	7.36576i	0.877315	+	0.233042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.22	yes	144
7.6	odd	2	inner	378.2.z.a.293.15	yes	144
27.20	odd	18	inner	378.2.z.a.209.15	✓	144
189.20	even	18	inner	378.2.z.a.209.22	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.15	✓	144	27.20	odd	18	inner
378.2.z.a.209.22	yes	144	189.20	even	18	inner
378.2.z.a.293.15	yes	144	7.6	odd	2	inner
378.2.z.a.293.22	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(1.41810 - 0.994487i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.622684 - 3.53142i) q^{5} +(-0.449494 - 1.67271i) q^{6} +(2.42952 + 1.04757i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.02199 - 2.82055i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(1.41810 - 0.994487i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.622684 - 3.53142i) q^{5} +(-0.449494 - 1.67271i) q^{6} +(2.42952 + 1.04757i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.02199 - 2.82055i) q^{9} +(-3.10547 - 1.79295i) q^{10} +(-4.15407 + 0.732474i) q^{11} +(-1.72557 - 0.149714i) q^{12} +(2.25831 + 6.20466i) q^{13} +(1.81534 - 1.92471i) q^{14} +(-2.62892 - 5.62714i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.59771 + 4.49937i) q^{17} +(-2.30091 - 1.92505i) q^{18} +(3.98919 - 2.30316i) q^{19} +(-2.74695 + 2.30497i) q^{20} +(4.48710 - 0.930567i) q^{21} +(-0.732474 + 4.15407i) q^{22} +(-2.69373 + 3.21026i) q^{23} +(-0.730864 + 1.57030i) q^{24} +(-7.38470 - 2.68781i) q^{25} +6.60286 q^{26} +(-1.35572 - 5.01618i) q^{27} +(-1.18776 - 2.36416i) q^{28} +(1.58469 - 4.35390i) q^{29} +(-6.18692 + 0.545782i) q^{30} +(1.80493 - 2.15103i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-5.16243 + 5.16989i) q^{33} +(3.33955 + 3.97993i) q^{34} +(5.21225 - 7.92735i) q^{35} +(-2.59591 + 1.50375i) q^{36} +(-2.76078 + 4.78181i) q^{37} +(-0.799879 - 4.53634i) q^{38} +(9.37296 + 6.55295i) q^{39} +(1.22645 + 3.36964i) q^{40} +(3.08382 - 1.12242i) q^{41} +(0.660231 - 4.53477i) q^{42} +(-0.856484 - 4.85736i) q^{43} +(3.65303 + 2.10908i) q^{44} +(-9.32417 - 5.36540i) q^{45} +(2.09535 + 3.62925i) q^{46} +(0.00676417 - 0.00567581i) q^{47} +(1.22563 + 1.22386i) q^{48} +(4.80517 + 5.09022i) q^{49} +(-5.05143 + 6.02006i) q^{50} +(0.790757 + 8.96393i) q^{51} +(2.25831 - 6.20466i) q^{52} +3.95587i q^{53} +(-5.17735 - 0.441674i) q^{54} +15.1258i q^{55} +(-2.62782 + 0.307535i) q^{56} +(3.36659 - 7.23330i) q^{57} +(-3.54933 - 2.97824i) q^{58} +(0.405440 - 2.29937i) q^{59} +(-1.60318 + 6.00047i) q^{60} +(-1.23272 - 1.46910i) q^{61} +(-1.40399 - 2.43177i) q^{62} +(5.43770 - 5.78199i) q^{63} +(0.500000 - 0.866025i) q^{64} +(23.3175 - 4.11150i) q^{65} +(3.09245 + 6.61931i) q^{66} +(1.97624 - 0.719293i) q^{67} +(4.88210 - 1.77694i) q^{68} +(-0.627405 + 7.23134i) q^{69} +(-5.66658 - 7.60922i) q^{70} +(-2.82464 - 1.63080i) q^{71} +(0.525205 + 2.95367i) q^{72} +(-8.15237 + 4.70677i) q^{73} +(3.54919 + 4.22976i) q^{74} +(-13.1452 + 3.53241i) q^{75} +(-4.53634 - 0.799879i) q^{76} +(-10.8597 - 2.57213i) q^{77} +(9.36350 - 6.56646i) q^{78} +(-10.5357 - 3.83468i) q^{79} +3.58589 q^{80} +(-6.91106 - 5.76518i) q^{81} -3.28173i q^{82} +(1.26125 + 0.459057i) q^{83} +(-4.03547 - 2.17140i) q^{84} +(14.2716 + 11.9753i) q^{85} +(-4.85736 - 0.856484i) q^{86} +(-2.08265 - 7.75020i) q^{87} +(3.23129 - 2.71138i) q^{88} +(5.76444 + 9.98431i) q^{89} +(-8.23088 + 6.92678i) q^{90} +(-1.01323 + 17.4401i) q^{91} +(4.12703 - 0.727707i) q^{92} +(0.420392 - 4.84535i) q^{93} +(-0.00302003 - 0.00829748i) q^{94} +(-5.64941 - 15.5216i) q^{95} +(1.56924 - 0.733128i) q^{96} +(2.42324 - 0.427283i) q^{97} +(6.42671 - 2.77443i) q^{98} +(-2.17945 + 12.4654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more