LMFDB - Embedded newform 616.2.bi.c.13.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.15
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26637 + 0.629539i) q^{2} +(-0.250134 + 0.181733i) q^{3} +(1.20736 - 1.59445i) q^{4} +(-0.645803 - 1.98758i) q^{5} +(0.202353 - 0.387610i) q^{6} +(-1.50618 - 2.17518i) q^{7} +(-0.525193 + 2.77924i) q^{8} +(-0.897511 + 2.76225i) q^{9} +O(q^{10})$	\(q+(-1.26637 + 0.629539i) q^{2} +(-0.250134 + 0.181733i) q^{3} +(1.20736 - 1.59445i) q^{4} +(-0.645803 - 1.98758i) q^{5} +(0.202353 - 0.387610i) q^{6} +(-1.50618 - 2.17518i) q^{7} +(-0.525193 + 2.77924i) q^{8} +(-0.897511 + 2.76225i) q^{9} +(2.06908 + 2.11044i) q^{10} +(3.24758 - 0.673199i) q^{11} +(-0.0122379 + 0.618245i) q^{12} +(1.29671 + 0.421327i) q^{13} +(3.27674 + 1.80637i) q^{14} +(0.522747 + 0.379798i) q^{15} +(-1.08455 - 3.85016i) q^{16} +(-1.65570 - 5.09571i) q^{17} +(-0.602369 - 4.06304i) q^{18} +(2.18971 + 3.01388i) q^{19} +(-3.94882 - 1.37002i) q^{20} +(0.772051 + 0.270364i) q^{21} +(-3.68882 + 2.89700i) q^{22} -8.02255 q^{23} +(-0.373712 - 0.790629i) q^{24} +(0.511679 - 0.371756i) q^{25} +(-1.90735 + 0.282776i) q^{26} +(-0.564124 - 1.73619i) q^{27} +(-5.28673 - 0.224695i) q^{28} +(-3.45950 - 2.51347i) q^{29} +(-0.901086 - 0.151873i) q^{30} +(-8.84725 - 2.87465i) q^{31} +(3.79727 + 4.19294i) q^{32} +(-0.689990 + 0.758584i) q^{33} +(5.30467 + 5.41071i) q^{34} +(-3.35065 + 4.39840i) q^{35} +(3.32066 + 4.76608i) q^{36} +(-0.711193 + 0.978873i) q^{37} +(-4.67033 - 2.43816i) q^{38} +(-0.400921 + 0.130267i) q^{39} +(5.86313 - 0.750980i) q^{40} +(-2.23713 + 1.62537i) q^{41} +(-1.14790 + 0.143656i) q^{42} -3.36702 q^{43} +(2.84763 - 5.99091i) q^{44} +6.06981 q^{45} +(10.1595 - 5.05050i) q^{46} +(-5.65972 - 7.78994i) q^{47} +(0.970987 + 0.765959i) q^{48} +(-2.46283 + 6.55244i) q^{49} +(-0.413937 + 0.792901i) q^{50} +(1.34021 + 0.973718i) q^{51} +(2.23739 - 1.55885i) q^{52} +(-2.50565 - 0.814137i) q^{53} +(1.80739 + 1.84352i) q^{54} +(-3.43534 - 6.02007i) q^{55} +(6.83639 - 3.04365i) q^{56} +(-1.09544 - 0.355932i) q^{57} +(5.96332 + 1.00509i) q^{58} +(-11.2387 - 8.16539i) q^{59} +(1.23671 - 0.374941i) q^{60} +(12.2195 - 3.97035i) q^{61} +(13.0135 - 1.92933i) q^{62} +(7.36022 - 2.20821i) q^{63} +(-7.44835 - 2.91927i) q^{64} -2.84941i q^{65} +(0.396221 - 1.39502i) q^{66} -7.78089i q^{67} +(-10.1239 - 3.51244i) q^{68} +(2.00672 - 1.45796i) q^{69} +(1.47418 - 7.67934i) q^{70} +(2.99110 + 9.20567i) q^{71} +(-7.20560 - 3.94511i) q^{72} +(7.28939 + 5.29605i) q^{73} +(0.284392 - 1.68733i) q^{74} +(-0.0604279 + 0.185978i) q^{75} +(7.44926 + 0.147455i) q^{76} +(-6.35579 - 6.05012i) q^{77} +(0.425705 - 0.417361i) q^{78} +(-3.23744 - 1.05191i) q^{79} +(-6.95209 + 4.64208i) q^{80} +(-6.59251 - 4.78974i) q^{81} +(1.80979 - 3.46667i) q^{82} +(-8.97086 + 2.91481i) q^{83} +(1.36323 - 0.904571i) q^{84} +(-9.05887 + 6.58166i) q^{85} +(4.26388 - 2.11967i) q^{86} +1.32212 q^{87} +(0.165373 + 9.37937i) q^{88} +4.89989i q^{89} +(-7.68660 + 3.82118i) q^{90} +(-1.03662 - 3.45518i) q^{91} +(-9.68612 + 12.7916i) q^{92} +(2.73542 - 0.888792i) q^{93} +(12.0713 + 6.30189i) q^{94} +(4.57620 - 6.29860i) q^{95} +(-1.71182 - 0.358710i) q^{96} +(-5.78175 - 1.87861i) q^{97} +(-1.00618 - 9.84823i) q^{98} +(-1.05520 + 9.57486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.26637	+	0.629539i	−0.895456	+	0.445151i
$2$	−1.26637	+	0.629539i	−0.895456	+	0.445151i
$3$	−0.250134	+	0.181733i	−0.144415	+	0.104924i	−0.657647	−	0.753326i	$-0.728448\pi$
$3$	−0.250134	+	0.181733i	−0.144415	+	0.104924i	0.513232	+	0.858250i	$0.328448\pi$
$4$	1.20736	−	1.59445i	0.603681	−	0.797226i
$5$	−0.645803	−	1.98758i	−0.288812	−	0.888872i	−0.985230	−	0.171236i	$-0.945224\pi$
$5$	−0.645803	−	1.98758i	−0.288812	−	0.888872i	0.696418	−	0.717636i	$-0.254776\pi$
$6$	0.202353	−	0.387610i	0.0826104	−	0.158241i
$7$	−1.50618	−	2.17518i	−0.569284	−	0.822141i
$7$	−1.50618	−	2.17518i	−0.569284	−	0.822141i
$8$	−0.525193	+	2.77924i	−0.185684	+	0.982610i
$9$	−0.897511	+	2.76225i	−0.299170	+	0.920751i
$10$	2.06908	+	2.11044i	0.654301	+	0.667380i
$11$	3.24758	−	0.673199i	0.979183	−	0.202977i
$11$	3.24758	−	0.673199i	0.979183	−	0.202977i
$12$	−0.0122379	+	0.618245i	−0.00353278	+	0.178472i
$13$	1.29671	+	0.421327i	0.359643	+	0.116855i	0.483265	−	0.875474i	$-0.339451\pi$
$13$	1.29671	+	0.421327i	0.359643	+	0.116855i	−0.123622	+	0.992329i	$0.539451\pi$
$14$	3.27674	+	1.80637i	0.875745	+	0.482774i
$15$	0.522747	+	0.379798i	0.134973	+	0.0980634i
$16$	−1.08455	−	3.85016i	−0.271138	−	0.962540i
$17$	−1.65570	−	5.09571i	−0.401566	−	1.23589i	−0.923729	−	0.383046i	$-0.874875\pi$
$17$	−1.65570	−	5.09571i	−0.401566	−	1.23589i	0.522164	−	0.852845i	$-0.325125\pi$
$18$	−0.602369	−	4.06304i	−0.141980	−	0.957668i
$19$	2.18971	+	3.01388i	0.502354	+	0.691431i	0.982607	−	0.185699i	$-0.0594549\pi$
$19$	2.18971	+	3.01388i	0.502354	+	0.691431i	−0.480252	+	0.877130i	$0.659455\pi$
$20$	−3.94882	−	1.37002i	−0.882982	−	0.306347i
$21$	0.772051	+	0.270364i	0.168475	+	0.0589983i
$22$	−3.68882	+	2.89700i	−0.786460	+	0.617641i
$23$	−8.02255			−1.67282			−0.836408	−	0.548107i	$-0.815349\pi$
$23$	−8.02255			−1.67282			−0.836408	+	0.548107i	$0.815349\pi$
$24$	−0.373712	−	0.790629i	−0.0762836	−	0.161386i
$25$	0.511679	−	0.371756i	0.102336	−	0.0743512i
$26$	−1.90735	+	0.282776i	−0.374062	+	0.0554569i
$27$	−0.564124	−	1.73619i	−0.108566	−	0.334131i
$28$	−5.28673	−	0.224695i	−0.999098	−	0.0424634i
$29$	−3.45950	−	2.51347i	−0.642413	−	0.466741i	0.218265	−	0.975889i	$-0.429960\pi$
$29$	−3.45950	−	2.51347i	−0.642413	−	0.466741i	−0.860678	+	0.509149i	$0.829960\pi$
$30$	−0.901086	−	0.151873i	−0.164515	−	0.0277282i
$31$	−8.84725	−	2.87465i	−1.58901	−	0.516302i	−0.624654	−	0.780901i	$-0.714760\pi$
$31$	−8.84725	−	2.87465i	−1.58901	−	0.516302i	−0.964358	+	0.264600i	$0.914760\pi$
$32$	3.79727	+	4.19294i	0.671268	+	0.741215i
$33$	−0.689990	+	0.758584i	−0.120112	+	0.132053i
$34$	5.30467	+	5.41071i	0.909743	+	0.927929i
$35$	−3.35065	+	4.39840i	−0.566362	+	0.743465i
$36$	3.32066	+	4.76608i	0.553443	+	0.794346i
$37$	−0.711193	+	0.978873i	−0.116919	+	0.160926i	−0.863465	−	0.504408i	$-0.831711\pi$
$37$	−0.711193	+	0.978873i	−0.116919	+	0.160926i	0.746546	+	0.665334i	$0.231711\pi$
$38$	−4.67033	−	2.43816i	−0.757627	−	0.395523i
$39$	−0.400921	+	0.130267i	−0.0641988	+	0.0208594i
$40$	5.86313	−	0.750980i	0.927042	−	0.118740i
$41$	−2.23713	+	1.62537i	−0.349381	+	0.253840i	−0.748609	−	0.663011i	$-0.769278\pi$
$41$	−2.23713	+	1.62537i	−0.349381	+	0.253840i	0.399228	+	0.916852i	$0.369278\pi$
$42$	−1.14790	+	0.143656i	−0.177125	+	0.0221666i
$43$	−3.36702			−0.513466			−0.256733	−	0.966482i	$-0.582646\pi$
$43$	−3.36702			−0.513466			−0.256733	+	0.966482i	$0.582646\pi$
$44$	2.84763	−	5.99091i	0.429296	−	0.903164i
$45$	6.06981			0.904834
$46$	10.1595	−	5.05050i	1.49793	−	0.744656i
$47$	−5.65972	−	7.78994i	−0.825555	−	1.13628i	−0.988734	−	0.149682i	$-0.952175\pi$
$47$	−5.65972	−	7.78994i	−0.825555	−	1.13628i	0.163179	−	0.986596i	$-0.447825\pi$
$48$	0.970987	+	0.765959i	0.140150	+	0.110557i
$49$	−2.46283	+	6.55244i	−0.351832	+	0.936063i
$50$	−0.413937	+	0.792901i	−0.0585395	+	0.112133i
$51$	1.34021	+	0.973718i	0.187667	+	0.136348i
$52$	2.23739	−	1.55885i	0.310270	−	0.216173i
$53$	−2.50565	−	0.814137i	−0.344178	−	0.111830i	0.131827	−	0.991273i	$-0.457916\pi$
$53$	−2.50565	−	0.814137i	−0.344178	−	0.111830i	−0.476005	+	0.879442i	$0.657916\pi$
$54$	1.80739	+	1.84352i	0.245954	+	0.250871i
$55$	−3.43534	−	6.02007i	−0.463221	−	0.811747i
$56$	6.83639	−	3.04365i	0.913550	−	0.406725i
$57$	−1.09544	−	0.355932i	−0.145095	−	0.0471443i
$58$	5.96332	+	1.00509i	0.783023	+	0.131974i
$59$	−11.2387	−	8.16539i	−1.46315	−	1.06304i	−0.982527	−	0.186118i	$-0.940409\pi$
$59$	−11.2387	−	8.16539i	−1.46315	−	1.06304i	−0.480627	−	0.876925i	$-0.659591\pi$
$60$	1.23671	−	0.374941i	0.159659	−	0.0484047i
$61$	12.2195	−	3.97035i	1.56454	−	0.508351i	0.606527	−	0.795063i	$-0.292562\pi$
$61$	12.2195	−	3.97035i	1.56454	−	0.508351i	0.958017	+	0.286711i	$0.0925620\pi$
$62$	13.0135	−	1.92933i	1.65272	−	0.245026i
$63$	7.36022	−	2.20821i	0.927300	−	0.278209i
$64$	−7.44835	−	2.91927i	−0.931043	−	0.364909i
$65$		−	2.84941i		−	0.353426i
$66$	0.396221	−	1.39502i	0.0487715	−	0.171715i
$67$		−	7.78089i		−	0.950587i	−0.879827	−	0.475293i	$-0.842342\pi$
$67$		−	7.78089i		−	0.950587i	0.879827	−	0.475293i	$-0.157658\pi$
$68$	−10.1239	−	3.51244i	−1.22770	−	0.425946i
$69$	2.00672	−	1.45796i	0.241580	−	0.175518i
$70$	1.47418	−	7.67934i	0.176198	−	0.917856i
$71$	2.99110	+	9.20567i	0.354979	+	1.09251i	0.956022	+	0.293296i	$0.0947521\pi$
$71$	2.99110	+	9.20567i	0.354979	+	1.09251i	−0.601043	+	0.799217i	$0.705248\pi$
$72$	−7.20560	−	3.94511i	−0.849188	−	0.464936i
$73$	7.28939	+	5.29605i	0.853159	+	0.619856i	0.926015	−	0.377486i	$-0.123211\pi$
$73$	7.28939	+	5.29605i	0.853159	+	0.619856i	−0.0728562	+	0.997342i	$0.523211\pi$
$74$	0.284392	−	1.68733i	0.0330599	−	0.196149i
$75$	−0.0604279	+	0.185978i	−0.00697762	+	0.0214749i
$76$	7.44926	+	0.147455i	0.854489	+	0.0169142i
$77$	−6.35579	−	6.05012i	−0.724309	−	0.689475i
$78$	0.425705	−	0.417361i	0.0482016	−	0.0472569i
$79$	−3.23744	−	1.05191i	−0.364240	−	0.118349i	0.121178	−	0.992631i	$-0.461333\pi$
$79$	−3.23744	−	1.05191i	−0.364240	−	0.118349i	−0.485418	+	0.874282i	$0.661333\pi$
$80$	−6.95209	+	4.64208i	−0.777267	+	0.519000i
$81$	−6.59251	−	4.78974i	−0.732501	−	0.532193i
$82$	1.80979	−	3.46667i	0.199858	−	0.382830i
$83$	−8.97086	+	2.91481i	−0.984679	+	0.319942i	−0.756727	−	0.653731i	$-0.773203\pi$
$83$	−8.97086	+	2.91481i	−0.984679	+	0.319942i	−0.227952	+	0.973672i	$0.573203\pi$
$84$	1.36323	−	0.904571i	0.148740	−	0.0986968i
$85$	−9.05887	+	6.58166i	−0.982573	+	0.713881i
$86$	4.26388	−	2.11967i	0.459786	−	0.228570i
$87$	1.32212			0.141746
$88$	0.165373	+	9.37937i	0.0176288	+	0.999845i
$89$			4.89989i			0.519388i	0.965691	+	0.259694i	$0.0836216\pi$
$89$			4.89989i			0.519388i	−0.965691	+	0.259694i	$0.916378\pi$
$90$	−7.68660	+	3.82118i	−0.810239	+	0.402788i
$91$	−1.03662	−	3.45518i	−0.108668	−	0.362201i
$92$	−9.68612	+	12.7916i	−1.00985	+	1.33361i
$93$	2.73542	−	0.888792i	0.283650	−	0.0921634i
$94$	12.0713	+	6.30189i	1.24506	+	0.649991i
$95$	4.57620	−	6.29860i	0.469508	−	0.646223i
$96$	−1.71182	−	0.358710i	−0.174712	−	0.0366107i
$97$	−5.78175	−	1.87861i	−0.587048	−	0.190743i	0.000407524	−	1.00000i	$-0.499870\pi$
$97$	−5.78175	−	1.87861i	−0.587048	−	0.190743i	−0.587456	+	0.809256i	$0.699870\pi$
$98$	−1.00618	−	9.84823i	−0.101639	−	0.994821i
$99$	−1.05520	+	9.57486i	−0.106051	+	0.962309i
$100$	0.0250340	−	1.26469i	0.00250340	−	0.126469i
$101$	8.55322	+	2.77911i	0.851077	+	0.276532i	0.701897	−	0.712278i	$-0.252337\pi$
$101$	8.55322	+	2.77911i	0.851077	+	0.276532i	0.149180	+	0.988810i	$0.452337\pi$
$102$	−2.31019	−	0.389370i	−0.228742	−	0.0385534i
$103$	5.02394	−	6.91486i	0.495024	−	0.681342i	−0.486281	−	0.873803i	$-0.661647\pi$
$103$	5.02394	−	6.91486i	0.495024	−	0.681342i	0.981305	+	0.192461i	$0.0616468\pi$
$104$	−1.85199	+	3.38259i	−0.181603	+	0.331691i
$105$	0.0387766	−	1.70911i	0.00378421	−	0.166792i
$106$	3.68560	−	0.546412i	0.357978	−	0.0530722i
$107$	3.29329	−	2.39271i	0.318374	−	0.231312i	−0.417107	−	0.908857i	$-0.636956\pi$
$107$	3.29329	−	2.39271i	0.318374	−	0.231312i	0.735481	+	0.677545i	$0.236956\pi$
$108$	−3.44938	−	1.19675i	−0.331917	−	0.115157i
$109$	19.1074			1.83016			0.915080	−	0.403271i	$-0.132127\pi$
$109$	19.1074			1.83016			0.915080	+	0.403271i	$0.132127\pi$
$110$	8.14026	+	5.46094i	0.776143	+	0.520680i
$111$		−	0.374097i		−	0.0355077i
$112$	−6.74126	+	8.15815i	−0.636990	+	0.770872i
$113$	5.19449	−	3.77401i	0.488656	−	0.355029i	−0.316011	−	0.948755i	$-0.602344\pi$
$113$	5.19449	−	3.77401i	0.488656	−	0.355029i	0.804667	+	0.593726i	$0.202344\pi$
$114$	1.61131	−	0.238885i	0.150913	−	0.0223737i
$115$	5.18099	+	15.9454i	0.483130	+	1.48692i
$116$	−8.18449	+	2.48133i	−0.759910	+	0.230386i
$117$	−2.32762	+	3.20370i	−0.215189	+	0.296182i
$118$	19.3727	+	3.26518i	1.78340	+	0.300584i
$119$	−8.59031	+	11.2765i	−0.787473	+	1.03372i
$120$	−1.33009	+	1.25337i	−0.121420	+	0.114417i
$121$	10.0936	−	4.37254i	0.917601	−	0.397504i
$122$	−12.9748	+	12.7206i	−1.17469	+	1.15166i
$123$	0.264199	−	0.813122i	0.0238221	−	0.0733167i
$124$	−15.2653	+	10.6358i	−1.37087	+	0.955121i
$125$	−9.52301	−	6.91888i	−0.851764	−	0.618843i
$126$	−7.93057	+	7.42994i	−0.706511	+	0.661912i
$127$	0.285205	−	0.0926688i	0.0253079	−	0.00822303i	−0.296336	−	0.955084i	$-0.595765\pi$
$127$	0.285205	−	0.0926688i	0.0253079	−	0.00822303i	0.321644	+	0.946861i	$0.395765\pi$
$128$	11.2701	−	0.992154i	0.996147	−	0.0876949i
$129$	0.842209	−	0.611900i	0.0741523	−	0.0538748i
$130$	1.79381	+	3.60839i	0.157328	+	0.316477i
$131$			16.2748i			1.42193i	0.703225	+	0.710967i	$0.251743\pi$
$131$			16.2748i			1.42193i	−0.703225	+	0.710967i	$0.748257\pi$
$132$	0.376458	+	2.01604i	0.0327665	+	0.175474i
$133$	3.25763	−	9.30248i	0.282472	−	0.806627i
$134$	4.89837	+	9.85344i	0.423155	+	0.851208i
$135$	−3.08651	+	2.24248i	−0.265644	+	0.193002i
$136$	15.0318	−	1.92535i	1.28896	−	0.165097i
$137$	−1.03761	−	3.19342i	−0.0886487	−	0.272833i	0.896898	−	0.442238i	$-0.145815\pi$
$137$	−1.03761	−	3.19342i	−0.0886487	−	0.272833i	−0.985546	+	0.169405i	$0.945815\pi$
$138$	−1.62339	+	3.10962i	−0.138192	+	0.264708i
$139$	−5.05030	+	6.95114i	−0.428361	+	0.589588i	−0.967576	−	0.252580i	$-0.918721\pi$
$139$	−5.05030	+	6.95114i	−0.428361	+	0.589588i	0.539215	+	0.842168i	$0.318721\pi$
$140$	2.96759	+	10.6529i	0.250807	+	0.900334i
$141$	2.83138	+	0.919972i	0.238445	+	0.0774756i
$142$	−9.58316	−	9.77473i	−0.804201	−	0.820277i
$143$	4.49482	+	0.495350i	0.375875	+	0.0414233i
$144$	11.6085	+	0.459752i	0.967377	+	0.0383126i
$145$	−2.76157	+	8.49924i	−0.229336	+	0.705824i
$146$	−12.5651	−	2.11779i	−1.03990	−	0.175269i
$147$	−0.574759	−	2.08657i	−0.0474054	−	0.172097i
$148$	0.702098	+	2.31582i	0.0577121	+	0.190359i
$149$	−3.32443	−	10.2315i	−0.272348	−	0.838201i	−0.989909	−	0.141705i	$-0.954742\pi$
$149$	−3.32443	−	10.2315i	−0.272348	−	0.838201i	0.717561	−	0.696496i	$-0.245258\pi$
$150$	−0.0405565	−	0.273558i	−0.00331143	−	0.0223359i
$151$	−9.62623	−	13.2494i	−0.783372	−	1.07822i	−0.994902	−	0.100847i	$-0.967845\pi$
$151$	−9.62623	−	13.2494i	−0.783372	−	1.07822i	0.211530	−	0.977371i	$-0.432155\pi$
$152$	−9.52632	+	4.50287i	−0.772686	+	0.365231i
$153$	15.5617			1.25809
$154$	11.8575	+	3.66045i	0.955507	+	0.294968i
$155$			19.4411i			1.56154i
$156$	−0.276352	+	0.796529i	−0.0221259	+	0.0637734i
$157$	3.18690	−	2.31542i	0.254342	−	0.184790i	−0.453307	−	0.891355i	$-0.649756\pi$
$157$	3.18690	−	2.31542i	0.254342	−	0.184790i	0.707649	+	0.706564i	$0.249756\pi$
$158$	4.76199	−	0.705993i	0.378844	−	0.0561658i
$159$	0.774706	−	0.251717i	0.0614382	−	0.0199625i
$160$	5.88152	−	10.2552i	0.464975	−	0.810743i
$161$	12.0834	+	17.4505i	0.952307	+	1.37529i
$162$	11.3639	+	1.91532i	0.892828	+	0.150482i
$163$	18.1417	+	5.89459i	1.42097	+	0.461700i	0.915909	−	0.401387i	$-0.131472\pi$
$163$	18.1417	+	5.89459i	1.42097	+	0.461700i	0.505056	+	0.863086i	$0.331472\pi$
$164$	−0.109452	+	5.52941i	−0.00854679	+	0.431774i
$165$	1.95334	+	0.881513i	0.152068	+	0.0686257i
$166$	9.52540	−	9.33871i	0.739314	−	0.724825i
$167$	−3.01517	+	9.27973i	−0.233321	+	0.718087i	0.764019	+	0.645194i	$0.223223\pi$
$167$	−3.01517	+	9.27973i	−0.233321	+	0.718087i	−0.997340	+	0.0728936i	$0.976777\pi$
$168$	−1.15688	+	2.00372i	−0.0892554	+	0.154590i
$169$	−9.01328	−	6.54853i	−0.693329	−	0.503733i
$170$	7.32844	−	14.0377i	0.562065	−	1.07664i
$171$	−10.2904	+	3.34355i	−0.786926	+	0.255688i
$172$	−4.06522	+	5.36856i	−0.309970	+	0.409349i
$173$	−3.80263	−	5.23387i	−0.289108	−	0.397924i	0.639616	−	0.768695i	$-0.279093\pi$
$173$	−3.80263	−	5.23387i	−0.289108	−	0.397924i	−0.928724	+	0.370771i	$0.879093\pi$
$174$	−1.67429	+	0.832327i	−0.126928	+	0.0630986i
$175$	−1.57932	−	0.553061i	−0.119385	−	0.0418075i
$176$	−6.11410	−	11.7736i	−0.460868	−	0.887469i
$177$	4.29511			0.322840
$178$	−3.08467	−	6.20506i	−0.231206	−	0.465089i
$179$	−7.43342	−	10.2312i	−0.555600	−	0.764717i	0.435159	−	0.900354i	$-0.356692\pi$
$179$	−7.43342	−	10.2312i	−0.555600	−	0.764717i	−0.990759	+	0.135636i	$0.956692\pi$
$180$	7.32846	−	9.67802i	0.546231	−	0.721357i
$181$	6.65327	+	20.4767i	0.494534	+	1.52202i	0.817682	+	0.575670i	$0.195259\pi$
$181$	6.65327	+	20.4767i	0.494534	+	1.52202i	−0.323149	+	0.946348i	$0.604741\pi$
$182$	3.48791	+	3.72292i	0.258541	+	0.275961i
$183$	−2.33497	+	3.21381i	−0.172606	+	0.237572i
$184$	4.21338	−	22.2966i	0.310615	−	1.64373i
$185$	2.40488	+	0.781392i	0.176810	+	0.0574491i
$186$	−2.90451	+	2.84759i	−0.212969	+	0.208795i
$187$	−8.80744	−	15.4341i	−0.644064	−	1.12866i
$188$	−19.2540	−	0.381125i	−1.40424	−	0.0277964i
$189$	−2.92686	+	3.84210i	−0.212898	+	0.279471i
$190$	−1.82993	+	10.8572i	−0.132757	+	0.787666i
$191$	12.3532	+	8.97515i	0.893849	+	0.649419i	0.936879	−	0.349654i	$-0.113701\pi$
$191$	12.3532	+	8.97515i	0.893849	+	0.649419i	−0.0430297	+	0.999074i	$0.513701\pi$
$192$	2.39362	−	0.623402i	0.172744	−	0.0449901i
$193$	4.43101	−	1.43972i	0.318951	−	0.103634i	−0.145166	−	0.989407i	$-0.546372\pi$
$193$	4.43101	−	1.43972i	0.318951	−	0.103634i	0.464117	+	0.885774i	$0.346372\pi$
$194$	8.50446	−	1.26084i	0.610585	−	0.0905227i
$195$	0.517833	+	0.712736i	0.0370828	+	0.0510401i
$196$	7.47403	+	11.8380i	0.533859	+	0.845573i
$197$	−12.9371			−0.921733			−0.460867	−	0.887469i	$-0.652461\pi$
$197$	−12.9371			−0.921733			−0.460867	+	0.887469i	$0.652461\pi$
$198$	−4.69148	−	12.7896i	−0.333409	−	0.908914i
$199$			11.8041i			0.836774i	0.908269	+	0.418387i	$0.137404\pi$
$199$			11.8041i			0.836774i	−0.908269	+	0.418387i	$0.862596\pi$
$200$	0.764470	+	1.61732i	0.0540562	+	0.114362i
$201$	1.41405	+	1.94627i	0.0997391	+	0.137279i
$202$	−12.5811	+	1.86521i	−0.885200	+	0.131236i
$203$	−0.256621	+	11.3108i	−0.0180112	+	0.793862i
$204$	3.17066	−	0.961266i	0.221991	−	0.0673021i
$205$	4.67530	+	3.39680i	0.326537	+	0.237243i
$206$	−2.00897	+	11.9195i	−0.139972	+	0.830471i
$207$	7.20032	−	22.1603i	0.500457	−	1.54025i
$208$	0.215826	−	5.44950i	0.0149648	−	0.377855i
$209$	9.14021	+	8.31372i	0.632242	+	0.575072i
$210$	1.02685	+	2.18877i	0.0708592	+	0.151040i
$211$	3.20245	−	9.85611i	0.220465	−	0.678523i	−0.778255	−	0.627949i	$-0.783895\pi$
$211$	3.20245	−	9.85611i	0.220465	−	0.678523i	0.998720	−	0.0505743i	$-0.0161052\pi$
$212$	−4.32333	+	3.01219i	−0.296928	+	0.206878i
$213$	−2.42116	−	1.75907i	−0.165895	−	0.120530i
$214$	−2.66420	+	5.10330i	−0.182121	+	0.348855i
$215$	2.17444	+	6.69223i	0.148295	+	0.456406i
$216$	5.12157	−	0.655998i	0.348479	−	0.0446350i
$217$	7.07270	+	23.5741i	0.480126	+	1.60031i
$218$	−24.1970	+	12.0289i	−1.63883	+	0.814698i
$219$	−2.78580			−0.188247
$220$	−13.7464	−	1.79093i	−0.926783	−	0.120745i
$221$		−	7.30526i		−	0.491405i
$222$	0.235509	+	0.473744i	0.0158063	+	0.0317956i
$223$	−4.75690	−	6.54731i	−0.318545	−	0.438440i	0.619477	−	0.785015i	$-0.287345\pi$
$223$	−4.75690	−	6.54731i	−0.318545	−	0.438440i	−0.938022	+	0.346575i	$0.887345\pi$
$224$	3.40103	−	14.5751i	0.227241	−	0.973839i
$225$	0.567648	+	1.74704i	0.0378432	+	0.116469i
$226$	−4.20223	+	8.04941i	−0.279528	+	0.535439i
$227$	12.4515	−	17.1380i	0.826434	−	1.13749i	−0.162142	−	0.986767i	$-0.551840\pi$
$227$	12.4515	−	17.1380i	0.826434	−	1.13749i	0.988576	−	0.150722i	$-0.0481597\pi$
$228$	−1.89011	+	1.31690i	−0.125176	+	0.0872135i
$229$	−1.78468	+	5.49267i	−0.117935	+	0.362966i	−0.992548	−	0.121856i	$-0.961115\pi$
$229$	−1.78468	+	5.49267i	−0.117935	+	0.362966i	0.874613	+	0.484822i	$0.161115\pi$
$230$	−16.5993	−	16.9311i	−1.09453	−	1.11641i
$231$	2.68931	+	0.358286i	0.176944	+	0.0235735i
$232$	8.80245	−	8.29472i	0.577909	−	0.544575i
$233$	−5.71622	−	1.85731i	−0.374482	−	0.121677i	0.115728	−	0.993281i	$-0.463080\pi$
$233$	−5.71622	−	1.85731i	−0.374482	−	0.121677i	−0.490210	+	0.871604i	$0.663080\pi$
$234$	0.930770	−	5.52238i	0.0608463	−	0.361010i
$235$	−11.8280	+	16.2799i	−0.771576	+	1.06198i
$236$	−26.5885	+	8.06098i	−1.73076	+	0.524725i
$237$	1.00096	−	0.325232i	0.0650194	−	0.0211261i
$238$	3.77947	−	19.6881i	0.244987	−	1.27619i
$239$	−2.76276	−	3.80261i	−0.178708	−	0.245971i	0.710260	−	0.703939i	$-0.248577\pi$
$239$	−2.76276	−	3.80261i	−0.178708	−	0.245971i	−0.888968	+	0.457969i	$0.848577\pi$
$240$	0.895337	−	2.42457i	0.0577937	−	0.156505i
$241$	−2.94190			−0.189505			−0.0947523	−	0.995501i	$-0.530206\pi$
$241$	−2.94190			−0.189505			−0.0947523	+	0.995501i	$0.530206\pi$
$242$	−10.0295	+	11.8915i	−0.644721	+	0.764418i
$243$	7.99610			0.512950
$244$	8.42281	−	24.2770i	0.539215	−	1.55418i
$245$	14.6140	+	0.663469i	0.933654	+	0.0423875i
$246$	0.177319	+	1.19603i	0.0113054	+	0.0762563i
$247$	1.56960	+	4.83072i	0.0998709	+	0.307371i
$248$	12.6358	−	23.0789i	0.802377	−	1.46551i
$249$	1.71420	−	2.35940i	0.108633	−	0.149521i
$250$	16.4153	+	2.76672i	1.03820	+	0.174983i
$251$	2.25458	−	6.93888i	0.142308	−	0.437978i	−0.854347	−	0.519703i	$-0.826043\pi$
$251$	2.25458	−	6.93888i	0.142308	−	0.437978i	0.996655	+	0.0817244i	$0.0260427\pi$
$252$	5.36556	−	14.4016i	0.337999	−	0.907217i
$253$	−26.0539	+	5.40077i	−1.63799	+	0.339543i
$254$	−0.302835	+	0.296900i	−0.0190016	+	0.0186292i
$255$	1.06983	−	3.29260i	0.0669953	−	0.206190i
$256$	−13.6475	+	8.35141i	−0.852968	+	0.521963i
$257$	8.19083	−	11.2737i	0.510930	−	0.703235i	−0.473146	−	0.880984i	$-0.656882\pi$
$257$	8.19083	−	11.2737i	0.510930	−	0.703235i	0.984076	+	0.177749i	$0.0568817\pi$
$258$	−0.681329	+	1.30509i	−0.0424177	+	0.0812515i
$259$	3.20041	+	0.0726113i	0.198864	+	0.00451185i
$260$	−4.54325	−	3.44027i	−0.281760	−	0.213356i
$261$	10.0478	−	7.30015i	0.621943	−	0.451868i
$262$	−10.2456	−	20.6098i	−0.632975	−	1.27328i
$263$		−	20.5078i		−	1.26456i	−0.774738	−	0.632282i	$-0.782118\pi$
$263$		−	20.5078i		−	1.26456i	0.774738	−	0.632282i	$-0.217882\pi$
$264$	−1.74591	−	2.31605i	−0.107453	−	0.142543i
$265$			5.50596i			0.338228i
$266$	1.73092	+	13.8311i	0.106130	+	0.848041i
$267$	−0.890474	−	1.22563i	−0.0544961	−	0.0750075i
$268$	−12.4062	−	9.39435i	−0.757832	−	0.573851i
$269$	0.343205	+	1.05628i	0.0209256	+	0.0644023i	0.960974	−	0.276639i	$-0.0892205\pi$
$269$	0.343205	+	1.05628i	0.0209256	+	0.0644023i	−0.940048	+	0.341041i	$0.889221\pi$
$270$	2.49692	−	4.78288i	0.151958	−	0.291077i
$271$	18.5992	+	13.5131i	1.12982	+	0.820865i	0.985669	−	0.168690i	$-0.0539538\pi$
$271$	18.5992	+	13.5131i	1.12982	+	0.820865i	0.144154	+	0.989555i	$0.453954\pi$
$272$	−17.8236	+	11.9013i	−1.08072	+	0.721620i
$273$	0.887216	+	0.675870i	0.0536967	+	0.0409055i
$274$	3.32437	+	3.39083i	0.200833	+	0.204847i
$275$	1.41145	−	1.55177i	0.0851138	−	0.0935753i
$276$	0.0981791	−	4.95990i	0.00590969	−	0.298551i
$277$	−3.27351	+	10.0748i	−0.196686	+	0.605338i	0.803267	+	0.595620i	$0.203093\pi$
$277$	−3.27351	+	10.0748i	−0.196686	+	0.605338i	−0.999953	+	0.00971800i	$0.996907\pi$
$278$	2.01951	−	11.9820i	0.121122	−	0.718635i
$279$	15.8810	−	21.8583i	0.950771	−	1.30862i
$280$	−10.4645	−	11.6223i	−0.625371	−	0.694562i
$281$	20.8560	−	6.77654i	1.24417	−	0.404254i	0.388340	−	0.921516i	$-0.373049\pi$
$281$	20.8560	−	6.77654i	1.24417	−	0.404254i	0.855827	+	0.517262i	$0.173049\pi$
$282$	−4.16472	+	0.617444i	−0.248006	+	0.0367682i
$283$	−7.78705	−	10.7180i	−0.462892	−	0.637116i	0.512213	−	0.858858i	$-0.328826\pi$
$283$	−7.78705	−	10.7180i	−0.462892	−	0.637116i	−0.975105	+	0.221742i	$0.928826\pi$
$284$	18.2893	+	6.34541i	1.08527	+	0.376531i
$285$			2.40714i			0.142587i
$286$	−6.00392	+	2.20237i	−0.355019	+	0.130229i
$287$	6.90500	+	2.41806i	0.407589	+	0.142733i
$288$	−14.9901	+	6.72580i	−0.883298	+	0.396322i
$289$	−9.47166	+	6.88156i	−0.557156	+	0.404798i
$290$	−1.85344	−	12.5017i	−0.108838	−	0.734123i
$291$	1.78762	−	0.580833i	0.104792	−	0.0340490i
$292$	17.2452	−	5.22833i	1.00920	−	0.305965i
$293$	18.6020	−	25.6035i	1.08674	−	1.49577i	0.234869	−	0.972027i	$-0.424534\pi$
$293$	18.6020	−	25.6035i	1.08674	−	1.49577i	0.851874	−	0.523747i	$-0.175466\pi$
$294$	2.04143	+	2.28052i	0.119059	+	0.133003i
$295$	−8.97137	+	27.6110i	−0.522333	+	1.60758i
$296$	−2.34701	−	2.49067i	−0.136417	−	0.144767i
$297$	−3.00084	−	5.25867i	−0.174127	−	0.305139i
$298$	10.6511	+	10.8640i	0.617001	+	0.629335i
$299$	−10.4029	−	3.38012i	−0.601617	−	0.195477i
$300$	0.223575	+	0.320892i	0.0129081	+	0.0185267i
$301$	5.07135	+	7.32389i	0.292308	+	0.422142i
$302$	20.5313	+	10.7185i	1.18144	+	0.616778i
$303$	−2.64451	+	0.859254i	−0.151923	+	0.0493629i
$304$	9.22907	−	11.6995i	0.529323	−	0.671010i
$305$	−15.7828	−	21.7231i	−0.903719	−	1.24386i
$306$	−19.7067	+	9.79666i	−1.12656	+	0.560038i
$307$		−	5.59203i		−	0.319154i	−0.987186	−	0.159577i	$-0.948987\pi$
$307$		−	5.59203i		−	0.319154i	0.987186	−	0.159577i	$-0.0510130\pi$
$308$	−17.3204	+	2.82930i	−0.986919	+	0.161215i
$309$			2.64266i			0.150336i
$310$	−12.2389	−	24.6195i	−0.695123	−	1.39829i
$311$	1.28439	+	1.76782i	0.0728313	+	0.100244i	0.843879	−	0.536534i	$-0.180267\pi$
$311$	1.28439	+	1.76782i	0.0728313	+	0.100244i	−0.771047	+	0.636778i	$0.780267\pi$
$312$	−0.151483	−	1.18267i	−0.00857603	−	0.0669556i
$313$	−11.8612	+	3.85393i	−0.670433	+	0.217837i	−0.624402	−	0.781103i	$-0.714657\pi$
$313$	−11.8612	+	3.85393i	−0.670433	+	0.217837i	−0.0460307	+	0.998940i	$0.514657\pi$
$314$	−2.57813	+	4.93844i	−0.145492	+	0.278692i
$315$	−9.14225	−	13.2029i	−0.515107	−	0.743901i
$316$	−5.58597	+	3.89190i	−0.314236	+	0.218937i
$317$	−14.9342	−	4.85240i	−0.838785	−	0.272538i	−0.142044	−	0.989860i	$-0.545367\pi$
$317$	−14.9342	−	4.85240i	−0.838785	−	0.272538i	−0.696741	+	0.717322i	$0.745367\pi$
$318$	−0.822595	+	0.806474i	−0.0461289	+	0.0452248i
$319$	−12.9271	−	5.83379i	−0.723778	−	0.326629i
$320$	−0.992118	+	16.6894i	−0.0554611	+	0.932968i
$321$	−0.388929	+	1.19700i	−0.0217079	+	0.0668101i
$322$	−26.2878	−	14.4917i	−1.46496	−	0.807592i
$323$	11.7324	−	16.1482i	0.652806	−	0.898511i
$324$	−15.5966	+	4.72849i	−0.866475	+	0.262694i
$325$	0.820130	−	0.266477i	0.0454926	−	0.0147815i
$326$	−26.6848	+	3.95618i	−1.47794	+	0.219113i
$327$	−4.77943	+	3.47246i	−0.264303	+	0.192027i
$328$	−3.34237	−	7.07115i	−0.184551	−	0.390439i
$329$	−8.41995	+	24.0440i	−0.464207	+	1.32559i
$330$	−3.02859	+	0.113388i	−0.166719	+	0.00624181i
$331$		−	13.1488i		−	0.722725i	−0.932425	−	0.361362i	$-0.882312\pi$
$331$		−	13.1488i		−	0.722725i	0.932425	−	0.361362i	$-0.117688\pi$
$332$	−6.18355	+	17.8228i	−0.339367	+	0.978155i
$333$	−2.06559	−	2.84305i	−0.113194	−	0.155798i
$334$	−2.02365	−	13.6497i	−0.110729	−	0.746878i
$335$	−15.4651	+	5.02492i	−0.844950	+	0.274541i
$336$	0.203615	−	3.26575i	0.0111081	−	0.178161i
$337$	1.56439	−	2.15320i	0.0852178	−	0.117292i	−0.764280	−	0.644885i	$-0.776905\pi$
$337$	1.56439	−	2.15320i	0.0852178	−	0.117292i	0.849497	+	0.527593i	$0.176905\pi$
$338$	15.5367	+	2.61862i	0.845083	+	0.142434i
$339$	−0.613455	+	1.88802i	−0.0333183	+	0.102543i
$340$	−0.443208	+	22.3904i	−0.0240363	+	1.21429i
$341$	−30.6674	−	3.37969i	−1.66073	−	0.183021i
$342$	10.9265	−	10.7124i	0.590838	−	0.579258i
$343$	17.9622	−	4.51209i	0.969868	−	0.243630i
$344$	1.76834	−	9.35777i	0.0953423	−	0.504537i
$345$	−4.19376	−	3.04695i	−0.225785	−	0.164042i
$346$	8.11044	+	4.23409i	0.436020	+	0.227626i
$347$	7.54226	+	23.2127i	0.404889	+	1.24612i	0.920987	+	0.389592i	$0.127384\pi$
$347$	7.54226	+	23.2127i	0.404889	+	1.24612i	−0.516098	+	0.856530i	$0.672616\pi$
$348$	1.59628	−	2.10806i	0.0855696	−	0.113004i
$349$	−4.25079	−	5.85071i	−0.227540	−	0.313182i	0.679948	−	0.733260i	$-0.262002\pi$
$349$	−4.25079	−	5.85071i	−0.227540	−	0.313182i	−0.907488	+	0.420079i	$0.862002\pi$
$350$	2.34817	−	0.293865i	0.125515	−	0.0157078i
$351$		−	2.48902i		−	0.132854i
$352$	15.1546	+	11.0606i	0.807744	+	0.589533i
$353$			21.4543i			1.14190i	0.820986	+	0.570948i	$0.193424\pi$
$353$			21.4543i			1.14190i	−0.820986	+	0.570948i	$0.806576\pi$
$354$	−5.43918	+	2.70394i	−0.289089	+	0.143713i
$355$	16.3653	−	11.8901i	0.868582	−	0.631062i
$356$	7.81264	+	5.91595i	0.414069	+	0.313545i
$357$	0.0994145	−	4.38179i	0.00526158	−	0.231909i
$358$	15.8544	+	8.27684i	0.837929	+	0.437445i
$359$	9.99780	−	13.7608i	0.527664	−	0.726267i	−0.459108	−	0.888380i	$-0.651831\pi$
$359$	9.99780	−	13.7608i	0.527664	−	0.726267i	0.986772	+	0.162113i	$0.0518310\pi$
$360$	−3.18782	+	16.8695i	−0.168013	+	0.889099i
$361$	1.58269	−	4.87102i	0.0832994	−	0.256369i
$362$	−21.3163	−	21.7424i	−1.12036	−	1.14276i
$363$	−1.73012	+	2.92807i	−0.0908079	+	0.153684i
$364$	−6.76069	−	2.51881i	−0.354357	−	0.132021i
$365$	5.81881	−	17.9085i	0.304570	−	0.937371i
$366$	0.933707	−	5.53981i	0.0488056	−	0.289570i
$367$	−12.0647	+	16.6056i	−0.629772	+	0.866807i	−0.998018	−	0.0629216i	$-0.979958\pi$
$367$	−12.0647	+	16.6056i	−0.629772	+	0.866807i	0.368247	+	0.929728i	$0.379958\pi$
$368$	8.70087	+	30.8881i	0.453564	+	1.61015i
$369$	−2.48184	−	7.63831i	−0.129199	−	0.397634i
$370$	−3.53737	+	0.524436i	−0.183899	+	0.0272641i
$371$	2.00308	+	6.67649i	0.103995	+	0.346626i
$372$	1.88551	−	5.43459i	0.0977590	−	0.281770i
$373$	22.5795			1.16912			0.584560	−	0.811350i	$-0.301267\pi$
$373$	22.5795			1.16912			0.584560	+	0.811350i	$0.301267\pi$
$374$	20.8698	+	14.0006i	1.07915	+	0.723956i
$375$	3.63942			0.187939
$376$	24.6225	−	11.6385i	1.26981	−	0.600210i
$377$	−3.42698	−	4.71683i	−0.176498	−	0.242929i
$378$	1.28773	−	6.70807i	0.0662337	−	0.345026i
$379$	34.6790	−	11.2679i	1.78134	−	0.578793i	0.782313	−	0.622885i	$-0.214040\pi$
$379$	34.6790	−	11.2679i	1.78134	−	0.578793i	0.999027	+	0.0440925i	$0.0140396\pi$
$380$	−4.51768	−	14.9012i	−0.231752	−	0.764416i
$381$	−0.0544986	+	0.0750110i	−0.00279205	+	0.00384293i
$382$	−21.2939	−	3.58898i	−1.08949	−	0.183628i
$383$	−2.31238	−	0.751338i	−0.118157	−	0.0383916i	0.249342	−	0.968416i	$-0.419786\pi$
$383$	−2.31238	−	0.751338i	−0.118157	−	0.0383916i	−0.367499	+	0.930024i	$0.619786\pi$
$384$	−2.63874	+	2.29633i	−0.134658	+	0.117184i
$385$	−7.92051	+	16.5398i	−0.403666	+	0.842947i
$386$	−4.70492	+	4.61271i	−0.239474	+	0.234781i
$387$	3.02194	−	9.30058i	0.153614	−	0.472775i
$388$	−9.97601	+	6.95057i	−0.506455	+	0.352862i
$389$	−2.86883	+	3.94861i	−0.145456	+	0.200202i	−0.875528	−	0.483167i	$-0.839486\pi$
$389$	−2.86883	+	3.94861i	−0.145456	+	0.200202i	0.730072	+	0.683370i	$0.239486\pi$
$390$	−1.10446	−	0.576588i	−0.0559265	−	0.0291967i
$391$	13.2829	+	40.8806i	0.671746	+	2.06742i
$392$	−16.9173	−	10.2861i	−0.854455	−	0.519525i
$393$	−2.95767	−	4.07088i	−0.149195	−	0.205349i
$394$	16.3831	−	8.14443i	0.825371	−	0.410311i
$395$			7.11398i			0.357943i
$396$	13.9926	+	13.2428i	0.703157	+	0.665475i
$397$	3.77969			0.189697			0.0948487	−	0.995492i	$-0.469763\pi$
$397$	3.77969			0.189697			0.0948487	+	0.995492i	$0.469763\pi$
$398$	−7.43117	−	14.9484i	−0.372491	−	0.749294i
$399$	0.875725	+	2.91889i	0.0438411	+	0.146127i
$400$	−1.98626	−	1.56686i	−0.0993132	−	0.0783428i
$401$	1.78685	+	5.49935i	0.0892309	+	0.274624i	0.985707	−	0.168467i	$-0.0538817\pi$
$401$	1.78685	+	5.49935i	0.0892309	+	0.274624i	−0.896476	+	0.443091i	$0.853882\pi$
$402$	−3.01595	−	1.57449i	−0.150422	−	0.0785284i
$403$	−10.2612	−	7.45517i	−0.511145	−	0.371368i
$404$	14.7580	−	10.2823i	0.734238	−	0.511564i
$405$	−5.26252	+	16.1964i	−0.261497	+	0.804804i
$406$	−6.79561	−	14.4852i	−0.337260	−	0.718886i
$407$	−1.65068	+	3.65775i	−0.0818213	+	0.181308i
$408$	−3.41006	+	3.21337i	−0.168823	+	0.159085i
$409$	9.60979	−	29.5759i	0.475173	−	1.46243i	−0.370550	−	0.928812i	$-0.620831\pi$
$409$	9.60979	−	29.5759i	0.475173	−	1.46243i	0.845724	−	0.533621i	$-0.179169\pi$
$410$	−8.05905	−	1.35831i	−0.398008	−	0.0670823i
$411$	0.839892	+	0.610217i	0.0414288	+	0.0300998i
$412$	−4.95970	−	16.3592i	−0.244347	−	0.805959i
$413$	−0.833670	+	36.7448i	−0.0410222	+	1.80809i
$414$	4.83253	+	32.5959i	0.237506	+	1.60200i
$415$	11.5868	+	15.9479i	0.568775	+	0.782851i
$416$	3.15736	+	7.03693i	0.154802	+	0.345014i
$417$		−	2.65653i		−	0.130091i
$418$	−16.8087	−	4.77409i	−0.822138	−	0.233508i
$419$	35.1393			1.71667			0.858333	−	0.513093i	$-0.171500\pi$
$419$	35.1393			1.71667			0.858333	+	0.513093i	$0.171500\pi$
$420$	−2.67828	−	2.12535i	−0.130687	−	0.103706i
$421$	0.406800	+	0.559913i	0.0198262	+	0.0272885i	0.818815	−	0.574057i	$-0.194631\pi$
$421$	0.406800	+	0.559913i	0.0198262	+	0.0272885i	−0.798989	+	0.601346i	$0.794631\pi$
$422$	2.14934	+	14.4975i	0.104628	+	0.705727i
$423$	26.5974	−	8.64203i	1.29321	−	0.420190i
$424$	3.57863	−	6.53624i	0.173794	−	0.317428i
$425$	−2.74155	−	1.99185i	−0.132985	−	0.0966190i
$426$	4.17347	+	0.703418i	0.202205	+	0.0340807i
$427$	−27.0410	−	20.5995i	−1.30861	−	0.996880i
$428$	0.161125	−	8.13986i	0.00778828	−	0.393455i
$429$	−1.21433	+	0.692954i	−0.0586284	+	0.0334561i
$430$	−6.96664	−	7.10591i	−0.335961	−	0.342677i
$431$	−10.1313	−	3.29185i	−0.488007	−	0.158563i	0.0546702	−	0.998504i	$-0.482589\pi$
$431$	−10.1313	−	3.29185i	−0.488007	−	0.158563i	−0.542677	+	0.839941i	$0.682589\pi$
$432$	−6.07281	+	4.05496i	−0.292178	+	0.195094i
$433$	−0.714395	+	0.983280i	−0.0343316	+	0.0472534i	−0.825838	−	0.563908i	$-0.809297\pi$
$433$	−0.714395	+	0.983280i	−0.0343316	+	0.0472534i	0.791506	+	0.611161i	$0.209297\pi$
$434$	−23.7974	−	25.4009i	−1.14231	−	1.21928i
$435$	−0.853831	−	2.62782i	−0.0409381	−	0.125994i
$436$	23.0696	−	30.4659i	1.10483	−	1.45905i
$437$	−17.5671	−	24.1790i	−0.840347	−	1.15664i
$438$	3.52784	−	1.75377i	0.168567	−	0.0837982i
$439$	−22.4050			−1.06933			−0.534667	−	0.845063i	$-0.679563\pi$
$439$	−22.4050			−1.06933			−0.534667	+	0.845063i	$0.679563\pi$
$440$	18.5354	−	6.38592i	0.883643	−	0.304437i
$441$	−15.8891	−	12.6838i	−0.756624	−	0.603992i
$442$	4.59894	+	9.25112i	0.218749	+	0.440031i
$443$	−1.22714	−	1.68902i	−0.0583034	−	0.0802478i	0.778870	−	0.627186i	$-0.215793\pi$
$443$	−1.22714	−	1.68902i	−0.0583034	−	0.0802478i	−0.837173	+	0.546938i	$0.815793\pi$
$444$	−0.596480	−	0.451671i	−0.0283077	−	0.0214354i
$445$	9.73892	−	3.16437i	0.461669	−	0.150005i
$446$	10.1458	+	5.29663i	0.480415	+	0.250803i
$447$	2.69097	+	1.95510i	0.127278	+	0.0924731i
$448$	4.86862	+	20.5985i	0.230021	+	0.973186i
$449$	11.3001	−	34.7782i	0.533286	−	1.64128i	−0.214039	−	0.976825i	$-0.568662\pi$
$449$	11.3001	−	34.7782i	0.533286	−	1.64128i	0.747325	−	0.664459i	$-0.231338\pi$
$450$	−1.81868	−	1.85504i	−0.0857334	−	0.0874472i
$451$	−6.17107	+	6.78456i	−0.290584	+	0.319472i
$452$	0.254142	−	12.8390i	0.0119538	−	0.603894i
$453$	4.81570	+	1.56472i	0.226262	+	0.0735168i
$454$	−4.97910	+	29.5417i	−0.233681	+	1.38646i
$455$	−6.19798	+	4.29173i	−0.290566	+	0.201200i
$456$	1.56454	−	2.85757i	0.0732662	−	0.133818i
$457$	−30.1324	+	9.79060i	−1.40953	+	0.457985i	−0.912261	−	0.409609i	$-0.865665\pi$
$457$	−30.1324	+	9.79060i	−1.40953	+	0.457985i	−0.497272	+	0.867594i	$0.665665\pi$
$458$	−1.19780	−	8.07925i	−0.0559693	−	0.377519i
$459$	−7.91313	+	5.74922i	−0.369353	+	0.268351i
$460$	31.6796	+	10.9911i	1.47707	+	0.512462i
$461$			39.9848i			1.86228i	0.364662	+	0.931140i	$0.381184\pi$
$461$			39.9848i			1.86228i	−0.364662	+	0.931140i	$0.618816\pi$
$462$	−3.63120	+	1.23930i	−0.168939	+	0.0576576i
$463$	6.27434			0.291593			0.145797	−	0.989315i	$-0.453426\pi$
$463$	6.27434			0.291593			0.145797	+	0.989315i	$0.453426\pi$
$464$	−5.92527	+	16.0456i	−0.275074	+	0.744900i
$465$	−3.53309	−	4.86288i	−0.163843	−	0.225511i
$466$	8.40807	−	1.24654i	0.389496	−	0.0577451i
$467$	7.13339	+	21.9543i	0.330094	+	1.01592i	0.969088	+	0.246714i	$0.0793507\pi$
$467$	7.13339	+	21.9543i	0.330094	+	1.01592i	−0.638994	+	0.769211i	$0.720649\pi$
$468$	2.29786	+	7.57931i	0.106219	+	0.350354i
$469$	−16.9248	+	11.7194i	−0.781516	+	0.541153i
$470$	4.72979	−	28.0625i	0.218169	−	1.29443i
$471$	−0.376364	+	1.15833i	−0.0173420	+	0.0533731i
$472$	28.5961	−	26.9466i	1.31624	−	1.24032i
$473$	−10.9347	+	2.26668i	−0.502778	+	0.104222i
$474$	−1.06284	+	1.04201i	−0.0488177	+	0.0478609i
$475$	2.24086	+	0.728099i	0.102818	+	0.0334075i
$476$	7.60824	+	27.3117i	0.348723	+	1.25183i
$477$	4.49770	−	6.19056i	0.205936	−	0.283446i
$478$	5.89255	+	3.07623i	0.269519	+	0.140704i
$479$	0.495356	+	1.52455i	0.0226334	+	0.0696584i	0.961735	−	0.273981i	$-0.0883404\pi$
$479$	0.495356	+	1.52455i	0.0226334	+	0.0696584i	−0.939102	+	0.343639i	$0.888340\pi$
$480$	0.392538	+	3.63404i	0.0179168	+	0.165871i
$481$	−1.33464	+	0.969671i	−0.0608542	+	0.0442132i
$482$	3.72552	−	1.85204i	0.169693	−	0.0843581i
$483$	−6.19382	−	2.16901i	−0.281828	−	0.0986933i
$484$	5.21484	−	21.3730i	0.237038	−	0.971500i
$485$			12.7049i			0.576900i
$486$	−10.1260	+	5.03385i	−0.459324	+	0.228340i
$487$	9.94775	−	7.22747i	0.450776	−	0.327508i	−0.339126	−	0.940741i	$-0.610131\pi$
$487$	9.94775	−	7.22747i	0.450776	−	0.327508i	0.789902	+	0.613233i	$0.210131\pi$
$488$	4.61697	+	36.0461i	0.209000	+	1.63173i
$489$	−5.60910	+	1.82251i	−0.253652	+	0.0824166i
$490$	−18.9243	+	8.35988i	−0.854914	+	0.377661i
$491$	7.34633	+	5.33742i	0.331535	+	0.240875i	0.741082	−	0.671415i	$-0.234313\pi$
$491$	7.34633	+	5.33742i	0.331535	+	0.240875i	−0.409546	+	0.912289i	$0.634313\pi$
$492$	−0.977500	−	1.40299i	−0.0440691	−	0.0632515i
$493$	−7.08006	+	21.7902i	−0.318870	+	0.981380i
$494$	−5.02880	−	5.12933i	−0.226257	−	0.230780i
$495$	19.7122	−	4.08619i	0.885999	−	0.183661i
$496$	−1.47254	+	37.1810i	−0.0661191	+	1.66948i
$497$	15.5189	−	20.3716i	0.696116	−	0.913792i
$498$	−0.685475	+	4.06702i	−0.0307169	+	0.182247i
$499$	−13.0153	+	17.9140i	−0.582645	+	0.801943i	−0.993982	−	0.109541i	$-0.965062\pi$
$499$	−13.0153	+	17.9140i	−0.582645	+	0.801943i	0.411337	+	0.911483i	$0.365062\pi$
$500$	−22.5295	+	6.83040i	−1.00755	+	0.305465i
$501$	−0.932239	−	2.86914i	−0.0416494	−	0.128184i
$502$	1.51317	+	10.2065i	0.0675362	+	0.455539i
$503$	−8.81886	+	6.40728i	−0.393214	+	0.285686i	−0.766771	−	0.641921i	$-0.778138\pi$
$503$	−8.81886	+	6.40728i	−0.393214	+	0.285686i	0.373557	+	0.927607i	$0.378138\pi$
$504$	2.27162	+	21.6155i	0.101186	+	0.962833i
$505$		−	18.7950i		−	0.836365i
$506$	29.5938	−	23.2413i	1.31560	−	1.03320i
$507$	3.44462			0.152981
$508$	0.196590	−	0.566631i	0.00872228	−	0.0251402i
$509$	13.2976	−	9.66126i	0.589405	−	0.428228i	−0.252698	−	0.967545i	$-0.581318\pi$
$509$	13.2976	−	9.66126i	0.589405	−	0.428228i	0.842102	+	0.539318i	$0.181318\pi$
$510$	0.718022	+	4.84313i	0.0317945	+	0.214457i
$511$	0.540716	−	23.8326i	0.0239199	−	1.05429i
$512$	12.0252	−	19.1676i	0.531443	−	0.847094i
$513$	3.99741	−	5.50197i	0.176490	−	0.242918i
$514$	−3.27535	+	19.4331i	−0.144469	+	0.857156i
$515$	−16.9883	−	5.51984i	−0.748594	−	0.243233i
$516$	0.0412053	−	2.08165i	0.00181396	−	0.0916394i
$517$	−23.6246	−	21.4884i	−1.03901	−	0.945057i
$518$	−4.09860	+	1.92283i	−0.180082	+	0.0844844i
$519$	1.90234	+	0.618107i	0.0835033	+	0.0271319i
$520$	7.91919	+	1.49649i	0.347280	+	0.0656254i
$521$	7.70305	−	10.6023i	0.337477	−	0.464497i	−0.606225	−	0.795293i	$-0.707317\pi$
$521$	7.70305	−	10.6023i	0.337477	−	0.464497i	0.943702	+	0.330796i	$0.107317\pi$
$522$	−8.12845	+	15.5701i	−0.355773	+	0.681486i
$523$	−39.6868	+	12.8950i	−1.73538	+	0.563860i	−0.994210	−	0.107455i	$-0.965730\pi$
$523$	−39.6868	+	12.8950i	−1.73538	+	0.563860i	−0.741173	+	0.671315i	$0.765730\pi$
$524$	25.9494	+	19.6496i	1.13360	+	0.858395i
$525$	0.495552	−	0.148675i	0.0216276	−	0.00648872i
$526$	12.9104	+	25.9704i	0.562922	+	1.13236i
$527$			49.8426i			2.17118i
$528$	3.66900	+	1.83385i	0.159673	+	0.0798080i
$529$	41.3613			1.79832
$530$	−3.46621	−	6.97255i	−0.150563	−	0.302868i
$531$	32.6417	−	23.7156i	1.41653	−	1.02917i
$532$	−10.8992	−	16.4256i	−0.472541	−	0.712140i
$533$	−3.58572	+	1.16507i	−0.155315	+	0.0504649i
$534$	1.89925	+	0.991510i	0.0821885	+	0.0429068i
$535$	−6.88253	−	5.00045i	−0.297558	−	0.216188i
$536$	21.6249	+	4.08647i	0.934055	+	0.176508i
$537$	3.71871	+	1.20828i	0.160474	+	0.0521412i
$538$	−1.09959	−	1.12157i	−0.0474067	−	0.0483544i
$539$	−3.58714	+	22.9376i	−0.154509	+	0.987991i
$540$	−0.151008	+	7.62878i	−0.00649837	+	0.328290i
$541$	0.0603527	−	0.185747i	0.00259477	−	0.00798587i	−0.949751	−	0.313007i	$-0.898664\pi$
$541$	0.0603527	−	0.185747i	0.00259477	−	0.00798587i	0.952346	+	0.305021i	$0.0986636\pi$
$542$	−32.0605	−	5.40363i	−1.37712	−	0.232106i
$543$	−5.38550	−	3.91280i	−0.231114	−	0.167914i
$544$	15.0789	−	26.2920i	0.646503	−	1.12726i
$545$	−12.3397	−	37.9775i	−0.528573	−	1.62678i
$546$	−1.54903	−	0.297362i	−0.0662922	−	0.0127259i
$547$	−0.837808	+	0.608703i	−0.0358221	+	0.0260263i	−0.605552	−	0.795806i	$-0.707048\pi$
$547$	−0.837808	+	0.608703i	−0.0358221	+	0.0260263i	0.569730	+	0.821832i	$0.307048\pi$
$548$	−6.34452	−	2.20121i	−0.271025	−	0.0940308i
$549$			37.3167i			1.59264i
$550$	−0.810516	+	2.85367i	−0.0345605	+	0.121681i
$551$		−	15.9303i		−	0.678654i
$552$	2.99812	+	6.34285i	0.127608	+	0.269970i
$553$	2.58808	+	8.62637i	0.110057	+	0.366831i
$554$	−2.19703	−	14.8192i	−0.0933430	−	0.629608i
$555$	−0.743548	+	0.241593i	−0.0315618	+	0.0102551i
$556$	4.98572	+	16.4450i	0.211442	+	0.697424i
$557$	18.7331	+	13.6104i	0.793749	+	0.576692i	0.909074	−	0.416636i	$-0.136791\pi$
$557$	18.7331	+	13.6104i	0.793749	+	0.576692i	−0.115325	+	0.993328i	$0.536791\pi$
$558$	−6.35049	+	37.6783i	−0.268838	+	1.59505i
$559$	−4.36606	−	1.41862i	−0.184665	−	0.0600012i
$560$	20.5685	+	8.13023i	0.869177	+	0.343565i
$561$	5.00794	+	2.26000i	0.211435	+	0.0954174i
$562$	−22.1453	+	21.7113i	−0.934142	+	0.915834i
$563$	18.3780	+	5.97138i	0.774541	+	0.251663i	0.669508	−	0.742805i	$-0.266505\pi$
$563$	18.3780	+	5.97138i	0.774541	+	0.251663i	0.105033	+	0.994469i	$0.466505\pi$
$564$	4.88535	−	3.40376i	0.205710	−	0.143324i
$565$	−10.8558	−	7.88718i	−0.456706	−	0.331816i
$566$	16.6086	+	8.67059i	0.698112	+	0.364452i
$567$	−0.489022	+	21.5541i	−0.0205370	+	0.905188i
$568$	−27.1557	+	3.47824i	−1.13943	+	0.145944i
$569$	18.6977	+	25.7351i	0.783847	+	1.07887i	0.994847	+	0.101387i	$0.0323281\pi$
$569$	18.6977	+	25.7351i	0.783847	+	1.07887i	−0.211000	+	0.977486i	$0.567672\pi$
$570$	−1.51539	−	3.04832i	−0.0634727	−	0.127680i
$571$	−21.9188			−0.917272			−0.458636	−	0.888624i	$-0.651662\pi$
$571$	−21.9188			−0.917272			−0.458636	+	0.888624i	$0.651662\pi$
$572$	6.21668	−	6.56870i	0.259933	−	0.274651i
$573$	−4.72105			−0.197225
$574$	−10.2665	+	1.28482i	−0.428516	+	0.0536274i
$575$	−4.10497	+	2.98243i	−0.171189	+	0.124376i
$576$	14.7487	−	17.9541i	0.614531	−	0.748089i
$577$	−26.4757	+	8.60248i	−1.10220	+	0.358126i	−0.802948	−	0.596049i	$-0.796736\pi$
$577$	−26.4757	+	8.60248i	−1.10220	+	0.358126i	−0.299250	+	0.954175i	$0.596736\pi$
$578$	7.66237	−	14.6773i	0.318713	−	0.610497i
$579$	−0.846703	+	1.16539i	−0.0351878	+	0.0484318i
$580$	10.2174	+	14.6649i	0.424255	+	0.608925i
$581$	19.8520	+	15.1230i	0.823599	+	0.627408i
$582$	−1.89812	+	1.86092i	−0.0786798	+	0.0771377i
$583$	−8.68540	−	0.957173i	−0.359713	−	0.0396421i
$584$	−18.5473	+	17.4775i	−0.767495	+	0.723225i
$585$	7.87079	+	2.55738i	0.325417	+	0.105734i
$586$	−7.43858	+	44.1341i	−0.307285	+	1.82316i
$587$	−25.8200	−	18.7593i	−1.06570	−	0.774279i	−0.0905686	−	0.995890i	$-0.528868\pi$
$587$	−25.8200	−	18.7593i	−1.06570	−	0.774279i	−0.975135	+	0.221611i	$0.928868\pi$
$588$	−4.02088	−	1.60282i	−0.165818	−	0.0660991i
$589$	−10.7091	−	32.9592i	−0.441260	−	1.35806i
$590$	−6.02118	−	40.6135i	−0.247888	−	1.67203i
$591$	3.23602	−	2.35111i	0.133112	−	0.0967117i
$592$	4.54015	+	1.67657i	0.186599	+	0.0689065i
$593$	34.6434			1.42264			0.711318	−	0.702871i	$-0.248099\pi$
$593$	34.6434			1.42264			0.711318	+	0.702871i	$0.248099\pi$
$594$	7.11070	+	4.77025i	0.291756	+	0.195726i
$595$	27.9606	+	9.79151i	1.14627	+	0.401413i
$596$	−20.3275	−	7.05254i	−0.832647	−	0.288883i
$597$	−2.14521	−	2.95262i	−0.0877975	−	0.120843i
$598$	15.3018	−	2.26858i	0.625738	−	0.0927692i
$599$	−8.77903	−	27.0191i	−0.358701	−	1.10397i	−0.953832	−	0.300340i	$-0.902900\pi$
$599$	−8.77903	−	27.0191i	−0.358701	−	1.10397i	0.595131	−	0.803629i	$-0.297100\pi$
$600$	−0.485141	−	0.265618i	−0.0198058	−	0.0108438i
$601$	−36.2678	−	26.3501i	−1.47939	−	1.07484i	−0.977751	−	0.209767i	$-0.932729\pi$
$601$	−36.2678	−	26.3501i	−1.47939	−	1.07484i	−0.501642	−	0.865075i	$-0.667271\pi$
$602$	−11.0329	−	6.08210i	−0.449666	−	0.247888i
$603$	21.4928	+	6.98343i	0.875254	+	0.284387i
$604$	−32.7478	−	0.648229i	−1.33249	−	0.0263761i
$605$	−15.2093	−	17.2380i	−0.618344	−	0.700826i
$606$	2.80798	−	2.75295i	0.114067	−	0.111831i
$607$	−4.50096	+	13.8525i	−0.182688	+	0.562257i	−0.999901	−	0.0140794i	$-0.995518\pi$
$607$	−4.50096	+	13.8525i	−0.182688	+	0.562257i	0.817212	+	0.576337i	$0.195518\pi$
$608$	−4.32211	+	20.6258i	−0.175285	+	0.836488i
$609$	−1.99136	−	2.87586i	−0.0806939	−	0.116536i
$610$	33.6623	+	17.5735i	1.36295	+	0.711532i
$611$	−4.05691	−	12.4859i	−0.164125	−	0.505125i
$612$	18.7886	−	24.8123i	0.759482	−	1.00298i
$613$	12.6100	−	9.16170i	0.509313	−	0.370038i	−0.303250	−	0.952911i	$-0.598072\pi$
$613$	12.6100	−	9.16170i	0.509313	−	0.370038i	0.812563	+	0.582873i	$0.198072\pi$
$614$	3.52040	+	7.08155i	0.142072	+	0.285788i
$615$	−1.78676			−0.0720493
$616$	20.1528	−	14.4868i	0.811978	−	0.583689i
$617$	−22.9667			−0.924606			−0.462303	−	0.886722i	$-0.652977\pi$
$617$	−22.9667			−0.924606			−0.462303	+	0.886722i	$0.652977\pi$
$618$	−1.66366	−	3.34658i	−0.0669221	−	0.134619i
$619$	19.3074	−	14.0276i	0.776029	−	0.563818i	−0.127756	−	0.991806i	$-0.540777\pi$
$619$	19.3074	−	14.0276i	0.776029	−	0.563818i	0.903785	+	0.427988i	$0.140777\pi$
$620$	30.9978	+	23.4724i	1.24490	+	0.942674i
$621$	4.52571	+	13.9287i	0.181610	+	0.558940i
$622$	−2.73942	−	1.43013i	−0.109841	−	0.0573428i
$623$	10.6582	−	7.38014i	0.427010	−	0.295679i
$624$	0.936370	+	1.40233i	0.0374848	+	0.0561381i
$625$	−6.62459	+	20.3884i	−0.264984	+	0.815536i
$626$	12.5944	−	12.3475i	0.503372	−	0.493507i
$627$	−3.79716	−	0.418466i	−0.151644	−	0.0167119i
$628$	0.155920	−	7.87690i	0.00622188	−	0.314323i
$629$	6.16558	+	2.00332i	0.245838	+	0.0798775i
$630$	19.8892	+	10.9643i	0.792404	+	0.436830i
$631$	−1.34409	−	0.976537i	−0.0535073	−	0.0388753i	0.560710	−	0.828012i	$-0.310528\pi$
$631$	−1.34409	−	0.976537i	−0.0535073	−	0.0388753i	−0.614217	+	0.789137i	$0.710528\pi$
$632$	4.62378	−	8.44516i	0.183924	−	0.335930i
$633$	0.990142	+	3.04734i	0.0393546	+	0.121121i
$634$	21.9669	−	3.25671i	0.872416	−	0.129341i
$635$	−0.368373	−	0.507022i	−0.0146184	−	0.0201206i
$636$	0.534000	−	1.53915i	0.0211745	−	0.0610311i
$637$	−5.95429	+	7.45897i	−0.235918	+	0.295535i
$638$	20.0430	−	0.750394i	0.793511	−	0.0297084i
$639$	−28.1130			−1.11213
$640$	−9.25027	−	21.7595i	−0.365649	−	0.860120i
$641$	−39.8256	+	28.9350i	−1.57302	+	1.14286i	−0.648822	+	0.760940i	$0.724738\pi$
$641$	−39.8256	+	28.9350i	−1.57302	+	1.14286i	−0.924194	+	0.381923i	$0.875262\pi$
$642$	−0.261032	−	1.76069i	−0.0103021	−	0.0694887i
$643$	10.9444	+	33.6835i	0.431606	+	1.32835i	0.896525	+	0.442993i	$0.146083\pi$
$643$	10.9444	+	33.6835i	0.431606	+	1.32835i	−0.464919	+	0.885353i	$0.653917\pi$
$644$	42.4130	+	1.80263i	1.67131	+	0.0710335i
$645$	−1.76010	−	1.27879i	−0.0693039	−	0.0503522i
$646$	−4.69154	+	27.8355i	−0.184586	+	1.09517i
$647$	−13.7169	−	4.45689i	−0.539267	−	0.175218i	0.0267044	−	0.999643i	$-0.491499\pi$
$647$	−13.7169	−	4.45689i	−0.539267	−	0.175218i	−0.565971	+	0.824425i	$0.691499\pi$
$648$	16.7742	−	15.8066i	0.658952	−	0.620943i
$649$	−41.9956	−	18.9519i	−1.64847	−	0.743928i
$650$	−0.870827	+	0.853760i	−0.0341567	+	0.0334872i
$651$	−6.05333	−	4.61135i	−0.237249	−	0.180733i
$652$	31.3022	−	21.8091i	1.22589	−	0.854111i
$653$	−28.2362	+	38.8638i	−1.10497	+	1.52086i	−0.276335	+	0.961061i	$0.589120\pi$
$653$	−28.2362	+	38.8638i	−1.10497	+	1.52086i	−0.828631	+	0.559795i	$0.810880\pi$
$654$	3.86646	−	7.40624i	0.151190	−	0.289607i
$655$	32.3474	−	10.5103i	1.26392	−	0.410672i
$656$	8.68422	+	6.85051i	0.339062	+	0.267468i
$657$	−21.1714	+	15.3819i	−0.825973	+	0.600105i
$658$	−4.47389	−	35.7491i	−0.174410	−	1.39365i
$659$	34.6456			1.34960			0.674800	−	0.738001i	$-0.264230\pi$
$659$	34.6456			1.34960			0.674800	+	0.738001i	$0.264230\pi$
$660$	3.76392	−	2.05021i	0.146511	−	0.0798042i
$661$	−23.6953			−0.921641			−0.460820	−	0.887493i	$-0.652445\pi$
$661$	−23.6953			−0.921641			−0.460820	+	0.887493i	$0.652445\pi$
$662$	8.27769	+	16.6512i	0.321722	+	0.647168i
$663$	1.32761	+	1.82730i	0.0515600	+	0.0709663i
$664$	−3.38952	−	26.4630i	−0.131539	−	1.02696i
$665$	−20.5932	−	0.467220i	−0.798570	−	0.0181180i
$666$	4.40560	+	2.29996i	0.170714	+	0.0891218i
$667$	27.7540	+	20.1645i	1.07464	+	0.780771i
$668$	11.1557	+	16.0115i	0.431626	+	0.619505i
$669$	2.37973	+	0.773220i	0.0920056	+	0.0298944i
$670$	16.4211	−	16.0993i	0.634403	−	0.621969i
$671$	37.0110	−	21.1202i	1.42879	−	0.815336i
$672$	1.79806	+	4.26381i	0.0693617	+	0.164480i
$673$	−24.4565	−	7.94640i	−0.942729	−	0.306311i	−0.202972	−	0.979185i	$-0.565060\pi$
$673$	−24.4565	−	7.94640i	−0.942729	−	0.306311i	−0.739758	+	0.672873i	$0.765060\pi$
$674$	−0.625568	+	3.71158i	−0.0240960	+	0.142965i
$675$	−0.934091	−	0.678657i	−0.0359532	−	0.0261215i
$676$	−21.3236	+	6.46479i	−0.820139	+	0.248646i
$677$	10.1960	−	3.31288i	0.391864	−	0.127324i	−0.106456	−	0.994317i	$-0.533950\pi$
$677$	10.1960	−	3.31288i	0.391864	−	0.127324i	0.498320	+	0.866993i	$0.333950\pi$
$678$	−0.411724	−	2.77712i	−0.0158122	−	0.106655i
$679$	4.62207	+	15.4059i	0.177379	+	0.591223i
$680$	−13.5343	−	28.6334i	−0.519018	−	1.09804i
$681$			6.54965i			0.250983i
$682$	40.9638	−	15.0264i	1.56858	−	0.575390i
$683$		−	39.5464i		−	1.51320i	−0.653878	−	0.756600i	$-0.726859\pi$
$683$		−	39.5464i		−	1.51320i	0.653878	−	0.756600i	$-0.273141\pi$
$684$	−7.09310	+	20.4444i	−0.271211	+	0.781712i
$685$	−5.67709	+	4.12465i	−0.216910	+	0.157595i
$686$	−19.9062	+	17.0219i	−0.760022	+	0.649897i
$687$	−0.551792	−	1.69824i	−0.0210522	−	0.0647919i
$688$	3.65171	+	12.9636i	0.139220	+	0.494232i
$689$	−2.90609	−	2.11140i	−0.110713	−	0.0804379i
$690$	7.22900	+	1.21841i	0.275203	+	0.0463842i
$691$	12.1045	−	37.2538i	0.460476	−	1.41720i	−0.404108	−	0.914711i	$-0.632418\pi$
$691$	12.1045	−	37.2538i	0.460476	−	1.41720i	0.864584	−	0.502489i	$-0.167582\pi$
$692$	−12.9363	−	0.256069i	−0.491764	−	0.00973427i
$693$	22.4164	−	12.1262i	0.851527	−	0.460638i
$694$	−24.1645	−	24.6476i	−0.917273	−	0.935610i
$695$	17.0774	+	5.54880i	0.647784	+	0.210478i
$696$	−0.694369	+	3.67449i	−0.0263200	+	0.139281i
$697$	11.9864	+	8.70865i	0.454018	+	0.329864i
$698$	9.06631	+	4.73310i	0.343165	+	0.179151i
$699$	1.76736	−	0.574250i	0.0668476	−	0.0217201i
$700$	−2.78864	+	1.85040i	−0.105401	+	0.0699387i
$701$	−20.9445	+	15.2171i	−0.791064	+	0.574742i	−0.908279	−	0.418365i	$-0.862603\pi$
$701$	−20.9445	+	15.2171i	−0.791064	+	0.574742i	0.117215	+	0.993107i	$0.462603\pi$
$702$	1.56694	+	3.15201i	0.0591402	+	0.118965i
$703$	−4.50751			−0.170004
$704$	−26.1544	−	4.46637i	−0.985730	−	0.168333i
$705$		−	6.22171i		−	0.234323i
$706$	−13.5063	−	27.1690i	−0.508317	−	1.02252i
$707$	−6.83765	−	22.7907i	−0.257156	−	0.857131i
$708$	5.18575	−	6.84834i	0.194893	−	0.257377i
$709$	−15.6935	+	5.09912i	−0.589381	+	0.191502i	−0.588499	−	0.808498i	$-0.700281\pi$
$709$	−15.6935	+	5.09912i	−0.589381	+	0.191502i	−0.000882425		1.00000i	$0.500281\pi$
$710$	−13.2392	+	25.3598i	−0.496859	+	0.951738i
$711$	5.81127	−	7.99852i	0.217940	−	0.299968i
$712$	−13.6180	−	2.57339i	−0.510355	−	0.0964418i
$713$	70.9775	+	23.0620i	2.65813	+	0.863678i
$714$	2.63261	+	5.61153i	0.0985230	+	0.210006i
$715$	−1.91822	−	9.25370i	−0.0717373	−	0.346069i
$716$	−25.2880	−	0.500565i	−0.945057	−	0.0187070i
$717$	1.38212	+	0.449079i	0.0516163	+	0.0167712i
$718$	−3.99792	+	23.7202i	−0.149201	+	0.885230i
$719$	−22.4482	+	30.8973i	−0.837176	+	1.15227i	0.149368	+	0.988782i	$0.452276\pi$
$719$	−22.4482	+	30.8973i	−0.837176	+	1.15227i	−0.986545	+	0.163493i	$0.947724\pi$
$720$	−6.58303	−	23.3698i	−0.245335	−	0.870940i
$721$	−22.6081	−	0.512934i	−0.841968	−	0.0191027i
$722$	1.06223	+	7.16485i	0.0395321	+	0.266648i
$723$	0.735871	−	0.534641i	0.0273673	−	0.0198835i
$724$	40.6820	+	14.1144i	1.51193	+	0.524559i
$725$	−2.70455			−0.100445
$726$	0.347636	−	4.79718i	0.0129020	−	0.178040i
$727$		−	20.3361i		−	0.754226i	−0.926167	−	0.377113i	$-0.876917\pi$
$727$		−	20.3361i		−	0.754226i	0.926167	−	0.377113i	$-0.123083\pi$
$728$	10.1472	−	1.06639i	0.376080	−	0.0395229i
$729$	17.7774	−	12.9161i	0.658423	−	0.478373i
$730$	3.90532	+	26.3418i	0.144543	+	0.974954i
$731$	5.57477	+	17.1574i	0.206190	+	0.634589i
$732$	2.30511	+	7.60323i	0.0851993	+	0.281023i
$733$	−3.37351	+	4.64323i	−0.124603	+	0.171502i	−0.866761	−	0.498723i	$-0.833802\pi$
$733$	−3.37351	+	4.64323i	−0.124603	+	0.171502i	0.742158	+	0.670225i	$0.233802\pi$
$734$	4.82443	−	28.6240i	0.178073	−	1.05653i
$735$	−3.77604	+	2.48989i	−0.139281	+	0.0918411i
$736$	−30.4637	−	33.6381i	−1.12291	−	1.23992i
$737$	−5.23808	−	25.2691i	−0.192947	−	0.930799i
$738$	7.95152	+	8.11048i	0.292700	+	0.298551i
$739$	−0.814111	+	2.50558i	−0.0299476	+	0.0921691i	−0.964913	−	0.262569i	$-0.915430\pi$
$739$	−0.814111	+	2.50558i	−0.0299476	+	0.0921691i	0.934966	+	0.354739i	$0.115430\pi$
$740$	4.14945	−	2.89104i	0.152537	−	0.106277i
$741$	−1.27051	−	0.923081i	−0.0466734	−	0.0339102i
$742$	−6.73974	−	7.19386i	−0.247424	−	0.264095i
$743$	11.5063	−	3.73863i	0.422126	−	0.137157i	−0.0902481	−	0.995919i	$-0.528766\pi$
$743$	11.5063	−	3.73863i	0.422126	−	0.137157i	0.512374	+	0.858762i	$0.328766\pi$
$744$	1.03354	+	8.06917i	0.0378915	+	0.295830i
$745$	−18.1891	+	13.2151i	−0.666396	+	0.484165i
$746$	−28.5939	+	14.2146i	−1.04690	+	0.520435i
$747$		−	27.3959i		−	1.00236i
$748$	−35.2428	−	4.59156i	−1.28860	−	0.167884i
$749$	−10.1649	−	3.55963i	−0.371417	−	0.130066i
$750$	−4.60884	+	2.29116i	−0.168291	+	0.0836613i
$751$	2.47439	−	1.79775i	0.0902917	−	0.0656007i	−0.541724	−	0.840557i	$-0.682228\pi$
$751$	2.47439	−	1.79775i	0.0902917	−	0.0656007i	0.632015	+	0.774956i	$0.282228\pi$
$752$	−23.8542	+	30.2394i	−0.869875	+	1.10272i
$753$	0.697078	+	2.14539i	0.0254029	+	0.0781822i
$754$	7.30924	+	3.81582i	0.266187	+	0.138964i
$755$	−20.1175	+	27.6894i	−0.732151	+	1.00772i
$756$	2.59225	+	9.30555i	0.0942794	+	0.338439i
$757$	16.9102	+	5.49446i	0.614612	+	0.199699i	0.599746	−	0.800190i	$-0.295268\pi$
$757$	16.9102	+	5.49446i	0.614612	+	0.199699i	0.0148651	+	0.999890i	$0.495268\pi$
$758$	−36.8227	+	36.1010i	−1.33746	+	1.31125i
$759$	5.53548	−	6.08578i	0.200925	−	0.220900i
$760$	15.1019	+	16.0263i	0.547804	+	0.581336i
$761$	6.91334	−	21.2771i	0.250608	−	0.771293i	−0.744055	−	0.668118i	$-0.767100\pi$
$761$	6.91334	−	21.2771i	0.250608	−	0.771293i	0.994663	−	0.103175i	$-0.0329000\pi$
$762$	0.0217929	−	0.129300i	0.000789474	−	0.00468405i
$763$	−28.7793	−	41.5621i	−1.04188	−	1.50465i
$764$	29.2253	−	8.86038i	1.05733	−	0.320557i
$765$	−10.0498	−	30.9300i	−0.363350	−	1.11828i
$766$	3.40131	−	0.504264i	0.122894	−	0.0182198i
$767$	−11.1330	−	15.3233i	−0.401991	−	0.553293i
$768$	1.89598	−	4.56918i	0.0684152	−	0.164876i
$769$	−14.6502			−0.528298			−0.264149	−	0.964482i	$-0.585091\pi$
$769$	−14.6502			−0.528298			−0.264149	+	0.964482i	$0.585091\pi$
$770$	−0.382196	−	25.9317i	−0.0137734	−	0.934514i
$771$			4.30849i			0.155166i
$772$	3.05427	−	8.80330i	0.109925	−	0.316838i
$773$	17.7763	−	12.9152i	0.639368	−	0.464528i	−0.220265	−	0.975440i	$-0.570692\pi$
$773$	17.7763	−	12.9152i	0.639368	−	0.464528i	0.859633	+	0.510912i	$0.170692\pi$
$774$	2.02819	+	13.6804i	0.0729018	+	0.491730i
$775$	−5.59561	+	1.81813i	−0.201000	+	0.0653090i
$776$	8.25763	−	15.0822i	0.296432	−	0.541421i
$777$	−0.813729	+	0.563459i	−0.0291924	+	0.0202140i
$778$	1.14719	−	6.80642i	0.0411287	−	0.244022i
$779$	−9.79734	−	3.18335i	−0.351026	−	0.114055i
$780$	1.76163	+	0.0348708i	0.0630766	+	0.00124857i
$781$	15.9111	+	27.8826i	0.569344	+	0.997718i
$782$	−42.5569	−	43.4077i	−1.52183	−	1.55225i
$783$	−2.41229	+	7.42428i	−0.0862084	+	0.265322i
$784$	27.8990	+	2.37581i	0.996394	+	0.0848503i
$785$	−6.66018	−	4.83890i	−0.237712	−	0.172708i
$786$	6.30827	+	3.29326i	0.225008	+	0.117467i
$787$	8.22863	−	2.67364i	0.293319	−	0.0953051i	−0.158661	−	0.987333i	$-0.550718\pi$
$787$	8.22863	−	2.67364i	0.293319	−	0.0953051i	0.451980	+	0.892028i	$0.350718\pi$
$788$	−15.6198	+	20.6277i	−0.556433	+	0.734830i
$789$	3.72695	+	5.12970i	0.132683	+	0.182622i
$790$	−4.47853	−	9.00890i	−0.159339	−	0.320522i
$791$	−16.0330	−	5.61459i	−0.570068	−	0.199632i
$792$	−26.0566	−	7.96129i	−0.925882	−	0.282892i
$793$	17.5180			0.622081
$794$	−4.78647	+	2.37946i	−0.169866	+	0.0844440i
$795$	−1.00062	−	1.37723i	−0.0354882	−	0.0488453i
$796$	18.8211	+	14.2519i	0.667098	+	0.505145i
$797$	−12.1365	−	37.3523i	−0.429896	−	1.32309i	−0.898227	−	0.439532i	$-0.855144\pi$
$797$	−12.1365	−	37.3523i	−0.429896	−	1.32309i	0.468331	−	0.883553i	$-0.344856\pi$
$798$	−2.94654	−	3.14508i	−0.104306	−	0.111335i
$799$	−30.3245	+	41.7381i	−1.07280	+	1.47659i
$800$	3.50173	+	0.733782i	0.123805	+	0.0259431i
$801$	−13.5348	−	4.39771i	−0.478227	−	0.155385i
$802$	−5.72485	−	5.83930i	−0.202152	−	0.206193i
$803$	27.2382	+	12.2922i	0.961216	+	0.433781i
$804$	4.81050	+	0.0952217i	0.169653	+	0.00335821i
$805$	26.8807	−	35.2863i	0.947420	−	1.24368i
$806$	17.6877	+	2.98117i	0.623023	+	0.105007i
$807$	−0.277808	−	0.201839i	−0.00977930	−	0.00710508i
$808$	−12.2159	+	22.3119i	−0.429754	+	0.784929i
$809$	−37.9986	+	12.3465i	−1.33596	+	0.434080i	−0.887947	−	0.459946i	$-0.847869\pi$
$809$	−37.9986	+	12.3465i	−1.33596	+	0.434080i	−0.448014	+	0.894026i	$0.647869\pi$
$810$	−3.53197	−	23.8235i	−0.124101	−	0.837071i
$811$	−25.2982	−	34.8200i	−0.888341	−	1.22270i	−0.974040	−	0.226375i	$-0.927313\pi$
$811$	−25.2982	−	34.8200i	−0.888341	−	1.22270i	0.0856996	−	0.996321i	$-0.472687\pi$
$812$	17.7247	+	14.0654i	0.622014	+	0.493599i
$813$	−7.10810			−0.249292
$814$	−0.212326	−	5.67121i	−0.00744201	−	0.198776i
$815$		−	39.8647i		−	1.39640i
$816$	2.29545	−	6.21606i	0.0803567	−	0.217606i
$817$	−7.37281	−	10.1478i	−0.257942	−	0.355027i
$818$	6.44966	+	43.5036i	0.225507	+	1.52107i
$819$	10.4745	+	0.237646i	0.366007	+	0.00830401i
$820$	11.0608	−	3.35336i	0.386260	−	0.117105i
$821$	−8.48204	−	6.16256i	−0.296025	−	0.215075i	0.429852	−	0.902899i	$-0.358566\pi$
$821$	−8.48204	−	6.16256i	−0.296025	−	0.215075i	−0.725877	+	0.687825i	$0.758566\pi$
$822$	−1.44777	−	0.244014i	−0.0504966	−	0.00851095i
$823$	13.1660	−	40.5207i	0.458937	−	1.41246i	−0.407512	−	0.913200i	$-0.633604\pi$
$823$	13.1660	−	40.5207i	0.458937	−	1.41246i	0.866450	−	0.499265i	$-0.166396\pi$
$824$	16.5795	+	17.5944i	0.577575	+	0.612929i
$825$	−0.0710446	+	0.644659i	−0.00247346	+	0.0224442i
$826$	−22.0765	−	47.0571i	−0.768141	−	1.63733i
$827$	−7.35219	+	22.6277i	−0.255661	+	0.786843i	0.738038	+	0.674759i	$0.235752\pi$
$827$	−7.35219	+	22.6277i	−0.255661	+	0.786843i	−0.993699	+	0.112084i	$0.964248\pi$
$828$	−26.6402	−	38.2361i	−0.925809	−	1.32880i
$829$	−7.94613	−	5.77320i	−0.275981	−	0.200512i	0.441182	−	0.897418i	$-0.354559\pi$
$829$	−7.94613	−	5.77320i	−0.275981	−	0.200512i	−0.717162	+	0.696906i	$0.754559\pi$
$830$	−24.7130	−	12.9015i	−0.857799	−	0.447818i
$831$	−1.01211	−	3.11497i	−0.0351098	−	0.108057i
$832$	−8.42838	−	6.92364i	−0.292202	−	0.240034i
$833$	37.4670	+	1.70099i	1.29816	+	0.0589358i
$834$	1.67239	+	3.36413i	0.0579100	+	0.116490i
$835$	20.3914			0.705674
$836$	24.2914	−	4.53596i	0.840135	−	0.156880i
$837$			16.9822i			0.586991i
$838$	−44.4992	+	22.1215i	−1.53720	+	0.764176i
$839$	−13.3635	−	18.3932i	−0.461358	−	0.635005i	0.513431	−	0.858131i	$-0.328374\pi$
$839$	−13.3635	−	18.3932i	−0.461358	−	0.635005i	−0.974790	+	0.223125i	$0.928374\pi$
$840$	4.72967	+	1.00538i	0.163189	+	0.0346890i
$841$	−3.31090	−	10.1899i	−0.114169	−	0.351376i
$842$	−0.867644	−	0.452957i	−0.0299010	−	0.0156099i
$843$	−3.98529	+	5.48528i	−0.137261	+	0.188923i
$844$	−11.8486	−	17.0060i	−0.407845	−	0.585372i
$845$	−7.19491	+	22.1437i	−0.247512	+	0.761765i
$846$	−28.2416	+	27.6881i	−0.970966	+	0.951936i
$847$	−24.7139	−	15.3696i	−0.849179	−	0.528105i
$848$	−0.417043	+	10.5302i	−0.0143213	+	0.361607i
$849$	3.89562	+	1.26576i	0.133697	+	0.0434409i
$850$	4.72575	+	0.796501i	0.162092	+	0.0273198i
$851$	5.70558	−	7.85306i	0.195585	−	0.269199i
$852$	−5.72797	+	1.73658i	−0.196237	+	0.0594942i
$853$	12.8228	−	4.16637i	0.439043	−	0.142654i	−0.0811511	−	0.996702i	$-0.525860\pi$
$853$	12.8228	−	4.16637i	0.439043	−	0.142654i	0.520194	+	0.854048i	$0.325860\pi$
$854$	47.2120	+	9.06315i	1.61556	+	0.310135i
$855$	13.2911	+	18.2937i	0.454547	+	0.625631i
$856$	4.92032	+	10.4095i	0.168173	+	0.355789i
$857$	17.7713			0.607056			0.303528	−	0.952823i	$-0.401835\pi$
$857$	17.7713			0.607056			0.303528	+	0.952823i	$0.401835\pi$
$858$	1.10154	−	1.64200i	0.0376061	−	0.0560570i
$859$	19.3459			0.660075			0.330037	−	0.943968i	$-0.392939\pi$
$859$	19.3459			0.660075			0.330037	+	0.943968i	$0.392939\pi$
$860$	13.2958	+	4.61291i	0.453382	+	0.157299i
$861$	−2.16662	+	0.650029i	−0.0738382	+	0.0221529i
$862$	14.9023	−	2.20935i	0.507573	−	0.0752506i
$863$	6.69009	+	20.5900i	0.227733	+	0.700891i	0.998003	+	0.0631725i	$0.0201218\pi$
$863$	6.69009	+	20.5900i	0.227733	+	0.700891i	−0.770269	+	0.637719i	$0.779878\pi$
$864$	5.13764	−	8.95813i	0.174786	−	0.304762i
$865$	−7.94698	+	10.9381i	−0.270205	+	0.371906i
$866$	0.285672	−	1.69493i	0.00970753	−	0.0575961i
$867$	1.11858	−	3.44263i	0.0379889	−	0.116918i
$868$	46.1271	+	17.1854i	1.56566	+	0.583311i
$869$	−11.2220	−	1.23672i	−0.380680	−	0.0419528i
$870$	2.73558	+	2.79026i	0.0927448	+	0.0945988i
$871$	3.27830	−	10.0896i	0.111081	−	0.341872i
$872$	−10.0351	+	53.1042i	−0.339831	+	1.79833i
$873$	10.3784	−	14.2846i	0.351255	−	0.483460i
$874$	37.4679	+	19.5603i	1.26737	+	0.661637i
$875$	−0.706403	+	31.1354i	−0.0238808	+	1.05257i
$876$	−3.36347	+	4.44182i	−0.113641	+	0.150075i
$877$	−39.4788	+	28.6830i	−1.33310	+	0.968557i	−0.333436	+	0.942773i	$0.608208\pi$
$877$	−39.4788	+	28.6830i	−1.33310	+	0.968557i	−0.999668	+	0.0257839i	$0.991792\pi$
$878$	28.3730	−	14.1048i	0.957542	−	0.476015i
$879$			9.78493i			0.330038i
$880$	−19.4525	+	19.7557i	−0.655742	+	0.665964i
$881$		−	20.8237i		−	0.701569i	−0.936456	−	0.350784i	$-0.885915\pi$
$881$		−	20.8237i		−	0.701569i	0.936456	−	0.350784i	$-0.114085\pi$
$882$	28.1064	+	6.05957i	0.946391	+	0.204036i
$883$	9.10196	+	12.5278i	0.306305	+	0.421593i	0.934225	−	0.356685i	$-0.116093\pi$
$883$	9.10196	+	12.5278i	0.306305	+	0.421593i	−0.627919	+	0.778279i	$0.716093\pi$
$884$	−11.6479	−	8.82009i	−0.391761	−	0.296652i
$885$	−2.77380	−	8.53687i	−0.0932401	−	0.286964i
$886$	2.61732	+	1.36638i	0.0879305	+	0.0459045i
$887$	3.92888	+	2.85450i	0.131919	+	0.0958447i	0.651788	−	0.758401i	$-0.274019\pi$
$887$	3.92888	+	2.85450i	0.131919	+	0.0958447i	−0.519869	+	0.854246i	$0.674019\pi$
$888$	1.03971	+	0.196473i	0.0348903	+	0.00659321i
$889$	−0.631143	−	0.480797i	−0.0211678	−	0.0161254i
$890$	−10.3409	+	10.1383i	−0.346629	+	0.339836i
$891$	−24.6342	−	11.1170i	−0.825276	−	0.372434i
$892$	−16.1827	−	0.320329i	−0.541836	−	0.0107254i
$893$	11.0848	−	34.1154i	0.370938	−	1.14163i
$894$	−4.63856	−	0.781806i	−0.155137	−	0.0261475i
$895$	−15.5348	+	21.3819i	−0.519272	+	0.714717i
$896$	−19.1330	−	23.0202i	−0.639188	−	0.769051i
$897$	3.21641	−	1.04507i	0.107393	−	0.0348940i
$898$	7.58413	+	51.1558i	0.253086	+	1.70709i
$899$	23.3817	+	32.1822i	0.779824	+	1.07334i
$900$	3.47093	+	1.20422i	0.115698	+	0.0401408i
$901$			14.1161i			0.470274i
$902$	3.54369	−	12.4767i	0.117992	−	0.415427i
$903$	−2.59951	−	0.910322i	−0.0865064	−	0.0302936i
$904$	7.76078	+	16.4188i	0.258120	+	0.546081i
$905$	36.4023	−	26.4478i	1.21005	−	0.879154i
$906$	−7.08349	+	1.05017i	−0.235333	+	0.0348895i
$907$	−34.1933	+	11.1101i	−1.13537	+	0.368905i	−0.815615	−	0.578595i	$-0.803601\pi$
$907$	−34.1933	+	11.1101i	−1.13537	+	0.368905i	−0.319757	+	0.947500i	$0.603601\pi$
$908$	−12.2923	−	40.5451i	−0.407933	−	1.34554i
$909$	−15.3532	+	21.1319i	−0.509234	+	0.700901i
$910$	5.14710	−	9.33677i	0.170625	−	0.309511i
$911$	−4.68329	+	14.4137i	−0.155164	+	0.477546i	−0.998177	−	0.0603465i	$-0.980779\pi$
$911$	−4.68329	+	14.4137i	−0.155164	+	0.477546i	0.843013	+	0.537893i	$0.180779\pi$
$912$	−0.182327	+	4.60367i	−0.00603744	+	0.152443i
$913$	−27.1714	+	15.5053i	−0.899241	+	0.513149i
$914$	31.9950	−	31.3680i	1.05830	−	1.03756i
$915$	7.89563	+	2.56544i	0.261021	+	0.0848110i
$916$	6.60305	+	9.47722i	0.218171	+	0.313136i
$917$	35.4006	−	24.5128i	1.16903	−	0.809484i
$918$	6.40155	−	12.2622i	0.211283	−	0.404714i
$919$	−3.71705	+	1.20774i	−0.122614	+	0.0398397i	−0.369681	−	0.929159i	$-0.620533\pi$
$919$	−3.71705	+	1.20774i	−0.122614	+	0.0398397i	0.247067	+	0.968998i	$0.420533\pi$
$920$	−47.0372	+	6.02478i	−1.55077	+	0.198631i
$921$	1.01626	+	1.39876i	0.0334868	+	0.0460907i
$922$	−25.1720	−	50.6354i	−0.828996	−	1.66759i
$923$			13.1973i			0.434396i
$924$	3.81824	−	3.85539i	0.125611	−	0.126833i
$925$			0.765259i			0.0251616i
$926$	−7.94560	+	3.94994i	−0.261109	+	0.129803i
$927$	14.5916	+	20.0836i	0.479250	+	0.659631i
$928$	−2.59779	−	24.0498i	−0.0852765	−	0.789474i
$929$	3.27798	−	1.06508i	0.107547	−	0.0349441i	−0.254749	−	0.967007i	$-0.581993\pi$
$929$	3.27798	−	1.06508i	0.107547	−	0.0349441i	0.362296	+	0.932063i	$0.381993\pi$
$930$	7.53555	+	3.93396i	0.247100	+	0.129000i
$931$	−25.1412	+	6.92530i	−0.823968	+	0.226968i
$932$	−9.86294	+	6.87179i	−0.323071	+	0.225093i
$933$	−0.642542	−	0.208775i	−0.0210359	−	0.00683498i
$934$	−22.8546	−	23.3114i	−0.747825	−	0.762774i
$935$	−24.9887	+	27.4729i	−0.817218	+	0.898460i
$936$	−7.68140	−	8.15159i	−0.251074	−	0.266443i
$937$	−8.11799	+	24.9846i	−0.265203	+	0.816212i	0.726443	+	0.687226i	$0.241172\pi$
$937$	−8.11799	+	24.9846i	−0.265203	+	0.816212i	−0.991647	+	0.128985i	$0.958828\pi$
$938$	14.0552	−	25.4959i	0.458918	−	0.832472i
$939$	2.26650	−	3.11957i	0.0739644	−	0.101803i
$940$	11.6768	+	38.5150i	0.380855	+	1.25622i
$941$	29.3513	−	9.53682i	0.956825	−	0.310891i	0.211339	−	0.977413i	$-0.432218\pi$
$941$	29.3513	−	9.53682i	0.956825	−	0.310891i	0.745486	+	0.666521i	$0.232218\pi$
$942$	−0.252599	−	1.70381i	−0.00823012	−	0.0555130i
$943$	17.9475	−	13.0396i	0.584450	−	0.424628i
$944$	−19.2491	+	52.1266i	−0.626506	+	1.69658i
$945$	9.52665	+	3.33613i	0.309902	+	0.108524i
$946$	12.4204	−	9.75425i	0.403821	−	0.317138i
$947$		−	39.2249i		−	1.27464i	−0.770600	−	0.637319i	$-0.780044\pi$
$947$		−	39.2249i		−	1.27464i	0.770600	−	0.637319i	$-0.219956\pi$
$948$	0.689956	−	1.98866i	0.0224087	−	0.0645885i
$949$	7.22087	+	9.93867i	0.234399	+	0.322623i
$950$	−3.29611	+	0.488667i	−0.106940	+	0.0158545i
$951$	4.61739	−	1.50028i	0.149729	−	0.0486499i
$952$	−26.8286	−	29.7969i	−0.869519	−	0.965723i
$953$	10.7470	−	14.7919i	0.348128	−	0.479157i	−0.598665	−	0.800999i	$-0.704302\pi$
$953$	10.7470	−	14.7919i	0.348128	−	0.479157i	0.946793	+	0.321842i	$0.104302\pi$
$954$	−1.79854	+	10.6710i	−0.0582299	+	0.345486i
$955$	9.86106	−	30.3492i	0.319096	−	0.982078i
$956$	−9.39873	−	0.186044i	−0.303977	−	0.00601709i
$957$	4.29370	−	0.890051i	0.138796	−	0.0287713i
$958$	−1.58706	−	1.61879i	−0.0512757	−	0.0523007i
$959$	−5.38345	+	7.06686i	−0.173841	+	0.228201i
$960$	−2.78487	−	4.35491i	−0.0898811	−	0.140554i
$961$	44.9307	+	32.6441i	1.44938	+	1.05303i
$962$	1.07969	−	2.06816i	0.0348107	−	0.0666803i
$963$	3.65352	+	11.2444i	0.117733	+	0.362345i
$964$	−3.55194	+	4.69072i	−0.114400	+	0.151078i
$965$	−5.72312	−	7.87720i	−0.184234	−	0.253576i
$966$	9.20911	−	1.15249i	0.296298	−	0.0370807i
$967$		−	13.0476i		−	0.419581i	−0.977746	−	0.209791i	$-0.932722\pi$
$967$		−	13.0476i		−	0.419581i	0.977746	−	0.209791i	$-0.0672782\pi$
$968$	6.85125	+	30.3490i	0.220207	+	0.975453i
$969$			6.17139i			0.198253i
$970$	−7.99822	−	16.0890i	−0.256807	−	0.516588i
$971$	−1.86331	+	1.35377i	−0.0597964	+	0.0434446i	−0.617282	−	0.786742i	$-0.711766\pi$
$971$	−1.86331	+	1.35377i	−0.0597964	+	0.0434446i	0.557486	+	0.830187i	$0.311766\pi$
$972$	9.65419	−	12.7494i	0.309658	−	0.408937i
$973$	22.7267	+	0.515625i	0.728583	+	0.0165302i
$974$	−8.04752	+	15.4151i	−0.257859	+	0.493932i
$975$	−0.156715	+	0.215700i	−0.00501890	+	0.00690793i
$976$	−28.5392	−	42.7409i	−0.913516	−	1.36810i
$977$	−1.17260	+	3.60888i	−0.0375147	+	0.115458i	−0.968060	−	0.250718i	$-0.919333\pi$
$977$	−1.17260	+	3.60888i	−0.0375147	+	0.115458i	0.930545	+	0.366176i	$0.119333\pi$
$978$	5.95583	−	5.83910i	0.190446	−	0.186714i
$979$	3.29860	+	15.9128i	0.105424	+	0.508576i
$980$	18.7023	−	22.5003i	0.597422	−	0.718744i
$981$	−17.1491	+	52.7796i	−0.547530	+	1.68512i
$982$	−12.6633	−	2.13433i	−0.404101	−	0.0681091i
$983$	−18.7627	+	25.8247i	−0.598438	+	0.823679i	−0.995564	−	0.0940849i	$-0.970008\pi$
$983$	−18.7627	+	25.8247i	−0.598438	+	0.823679i	0.397126	+	0.917764i	$0.370008\pi$
$984$	2.12111	+	1.16132i	0.0676184	+	0.0370215i
$985$	8.35485	+	25.7136i	0.266208	+	0.819303i
$986$	−4.75182	−	32.0515i	−0.151329	−	1.02073i
$987$	−2.26347	−	7.54441i	−0.0720472	−	0.240141i
$988$	9.59742	+	3.32978i	0.305334	+	0.105934i
$989$	27.0121			0.858935
$990$	−22.3905	+	17.5842i	−0.711616	+	0.558863i
$991$	30.5241			0.969630			0.484815	−	0.874617i	$-0.338887\pi$
$991$	30.5241			0.969630			0.484815	+	0.874617i	$0.338887\pi$
$992$	−21.5421	−	48.0118i	−0.683963	−	1.52438i
$993$	2.38958	+	3.28897i	0.0758310	+	0.104372i
$994$	−6.82782	+	35.5676i	−0.216565	+	1.12814i
$995$	23.4617	−	7.62316i	0.743785	−	0.241670i
$996$	−1.69228	−	5.58186i	−0.0536220	−	0.176868i
$997$	−19.2982	+	26.5617i	−0.611179	+	0.841216i	−0.996674	−	0.0814940i	$-0.974031\pi$
$997$	−19.2982	+	26.5617i	−0.611179	+	0.841216i	0.385495	+	0.922710i	$0.374031\pi$
$998$	5.20456	−	30.8794i	0.164747	−	0.977469i
$999$	2.10072	+	0.682564i	0.0664637	+	0.0215954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.c.13.15	✓	352
7.6	odd	2	inner	616.2.bi.c.13.16	yes	352
8.5	even	2	inner	616.2.bi.c.13.34	yes	352
11.6	odd	10	inner	616.2.bi.c.237.33	yes	352
56.13	odd	2	inner	616.2.bi.c.13.33	yes	352
77.6	even	10	inner	616.2.bi.c.237.34	yes	352
88.61	odd	10	inner	616.2.bi.c.237.16	yes	352
616.237	even	10	inner	616.2.bi.c.237.15	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.15	✓	352	1.1	even	1	trivial
616.2.bi.c.13.16	yes	352	7.6	odd	2	inner
616.2.bi.c.13.33	yes	352	56.13	odd	2	inner
616.2.bi.c.13.34	yes	352	8.5	even	2	inner
616.2.bi.c.237.15	yes	352	616.237	even	10	inner
616.2.bi.c.237.16	yes	352	88.61	odd	10	inner
616.2.bi.c.237.33	yes	352	11.6	odd	10	inner
616.2.bi.c.237.34	yes	352	77.6	even	10	inner

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26637 + 0.629539i) q^{2} +(-0.250134 + 0.181733i) q^{3} +(1.20736 - 1.59445i) q^{4} +(-0.645803 - 1.98758i) q^{5} +(0.202353 - 0.387610i) q^{6} +(-1.50618 - 2.17518i) q^{7} +(-0.525193 + 2.77924i) q^{8} +(-0.897511 + 2.76225i) q^{9} +O(q^{10})\)	\(q+(-1.26637 + 0.629539i) q^{2} +(-0.250134 + 0.181733i) q^{3} +(1.20736 - 1.59445i) q^{4} +(-0.645803 - 1.98758i) q^{5} +(0.202353 - 0.387610i) q^{6} +(-1.50618 - 2.17518i) q^{7} +(-0.525193 + 2.77924i) q^{8} +(-0.897511 + 2.76225i) q^{9} +(2.06908 + 2.11044i) q^{10} +(3.24758 - 0.673199i) q^{11} +(-0.0122379 + 0.618245i) q^{12} +(1.29671 + 0.421327i) q^{13} +(3.27674 + 1.80637i) q^{14} +(0.522747 + 0.379798i) q^{15} +(-1.08455 - 3.85016i) q^{16} +(-1.65570 - 5.09571i) q^{17} +(-0.602369 - 4.06304i) q^{18} +(2.18971 + 3.01388i) q^{19} +(-3.94882 - 1.37002i) q^{20} +(0.772051 + 0.270364i) q^{21} +(-3.68882 + 2.89700i) q^{22} -8.02255 q^{23} +(-0.373712 - 0.790629i) q^{24} +(0.511679 - 0.371756i) q^{25} +(-1.90735 + 0.282776i) q^{26} +(-0.564124 - 1.73619i) q^{27} +(-5.28673 - 0.224695i) q^{28} +(-3.45950 - 2.51347i) q^{29} +(-0.901086 - 0.151873i) q^{30} +(-8.84725 - 2.87465i) q^{31} +(3.79727 + 4.19294i) q^{32} +(-0.689990 + 0.758584i) q^{33} +(5.30467 + 5.41071i) q^{34} +(-3.35065 + 4.39840i) q^{35} +(3.32066 + 4.76608i) q^{36} +(-0.711193 + 0.978873i) q^{37} +(-4.67033 - 2.43816i) q^{38} +(-0.400921 + 0.130267i) q^{39} +(5.86313 - 0.750980i) q^{40} +(-2.23713 + 1.62537i) q^{41} +(-1.14790 + 0.143656i) q^{42} -3.36702 q^{43} +(2.84763 - 5.99091i) q^{44} +6.06981 q^{45} +(10.1595 - 5.05050i) q^{46} +(-5.65972 - 7.78994i) q^{47} +(0.970987 + 0.765959i) q^{48} +(-2.46283 + 6.55244i) q^{49} +(-0.413937 + 0.792901i) q^{50} +(1.34021 + 0.973718i) q^{51} +(2.23739 - 1.55885i) q^{52} +(-2.50565 - 0.814137i) q^{53} +(1.80739 + 1.84352i) q^{54} +(-3.43534 - 6.02007i) q^{55} +(6.83639 - 3.04365i) q^{56} +(-1.09544 - 0.355932i) q^{57} +(5.96332 + 1.00509i) q^{58} +(-11.2387 - 8.16539i) q^{59} +(1.23671 - 0.374941i) q^{60} +(12.2195 - 3.97035i) q^{61} +(13.0135 - 1.92933i) q^{62} +(7.36022 - 2.20821i) q^{63} +(-7.44835 - 2.91927i) q^{64} -2.84941i q^{65} +(0.396221 - 1.39502i) q^{66} -7.78089i q^{67} +(-10.1239 - 3.51244i) q^{68} +(2.00672 - 1.45796i) q^{69} +(1.47418 - 7.67934i) q^{70} +(2.99110 + 9.20567i) q^{71} +(-7.20560 - 3.94511i) q^{72} +(7.28939 + 5.29605i) q^{73} +(0.284392 - 1.68733i) q^{74} +(-0.0604279 + 0.185978i) q^{75} +(7.44926 + 0.147455i) q^{76} +(-6.35579 - 6.05012i) q^{77} +(0.425705 - 0.417361i) q^{78} +(-3.23744 - 1.05191i) q^{79} +(-6.95209 + 4.64208i) q^{80} +(-6.59251 - 4.78974i) q^{81} +(1.80979 - 3.46667i) q^{82} +(-8.97086 + 2.91481i) q^{83} +(1.36323 - 0.904571i) q^{84} +(-9.05887 + 6.58166i) q^{85} +(4.26388 - 2.11967i) q^{86} +1.32212 q^{87} +(0.165373 + 9.37937i) q^{88} +4.89989i q^{89} +(-7.68660 + 3.82118i) q^{90} +(-1.03662 - 3.45518i) q^{91} +(-9.68612 + 12.7916i) q^{92} +(2.73542 - 0.888792i) q^{93} +(12.0713 + 6.30189i) q^{94} +(4.57620 - 6.29860i) q^{95} +(-1.71182 - 0.358710i) q^{96} +(-5.78175 - 1.87861i) q^{97} +(-1.00618 - 9.84823i) q^{98} +(-1.05520 + 9.57486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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