LMFDB - Embedded newform 416.2.bg.a.77.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(77,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.6
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37688 - 0.322781i) q^{2} +(0.0930705 - 0.224692i) q^{3} +(1.79162 + 0.888865i) q^{4} +(-0.454046 - 1.09616i) q^{5} +(-0.200674 + 0.279334i) q^{6} +(-0.425170 - 0.425170i) q^{7} +(-2.17995 - 1.80217i) q^{8} +(2.07950 + 2.07950i) q^{9} +(0.271348 + 1.65585i) q^{10} +(4.27595 - 1.77116i) q^{11} +(0.366469 - 0.319837i) q^{12} +(-3.49256 + 0.895567i) q^{13} +(0.448173 + 0.722647i) q^{14} -0.288558 q^{15} +(2.41984 + 3.18503i) q^{16} -6.57858i q^{17} +(-2.19200 - 3.53445i) q^{18} +(0.183362 - 0.442675i) q^{19} +(0.160862 - 2.36750i) q^{20} +(-0.135103 + 0.0559615i) q^{21} +(-6.45919 + 1.05848i) q^{22} +(3.23409 + 3.23409i) q^{23} +(-0.607822 + 0.322089i) q^{24} +(2.54012 - 2.54012i) q^{25} +(5.09792 - 0.105761i) q^{26} +(1.33486 - 0.552918i) q^{27} +(-0.383826 - 1.13966i) q^{28} +(0.844664 - 2.03920i) q^{29} +(0.397311 + 0.0931410i) q^{30} +2.39149i q^{31} +(-2.30377 - 5.16649i) q^{32} -1.12562i q^{33} +(-2.12344 + 9.05795i) q^{34} +(-0.273009 + 0.659102i) q^{35} +(1.87728 + 5.57407i) q^{36} +(-1.75704 - 4.24186i) q^{37} +(-0.395355 + 0.550326i) q^{38} +(-0.123827 + 0.868101i) q^{39} +(-0.985673 + 3.20785i) q^{40} +(3.69384 - 3.69384i) q^{41} +(0.204085 - 0.0334438i) q^{42} +(-3.23451 - 7.80879i) q^{43} +(9.23522 + 0.627497i) q^{44} +(1.33528 - 3.22365i) q^{45} +(-3.40907 - 5.49687i) q^{46} +9.76106 q^{47} +(0.940866 - 0.247286i) q^{48} -6.63846i q^{49} +(-4.31735 + 2.67755i) q^{50} +(-1.47816 - 0.612272i) q^{51} +(-7.05339 - 1.49989i) q^{52} +(-1.93465 - 4.67066i) q^{53} +(-2.01642 + 0.330436i) q^{54} +(-3.88296 - 3.88296i) q^{55} +(0.160622 + 1.69308i) q^{56} +(-0.0823999 - 0.0823999i) q^{57} +(-1.82122 + 2.53510i) q^{58} +(0.218556 + 0.527640i) q^{59} +(-0.516987 - 0.256489i) q^{60} +(-0.932946 + 2.25233i) q^{61} +(0.771927 - 3.29280i) q^{62} -1.76828i q^{63} +(1.50438 + 7.85728i) q^{64} +(2.56747 + 3.42179i) q^{65} +(-0.363328 + 1.54984i) q^{66} +(6.87260 + 2.84673i) q^{67} +(5.84747 - 11.7863i) q^{68} +(1.02767 - 0.425676i) q^{69} +(0.588648 - 0.819386i) q^{70} +(2.79396 + 2.79396i) q^{71} +(-0.785600 - 8.28080i) q^{72} +(-9.55168 + 9.55168i) q^{73} +(1.05004 + 6.40770i) q^{74} +(-0.334334 - 0.807154i) q^{75} +(0.721994 - 0.630123i) q^{76} +(-2.57105 - 1.06496i) q^{77} +(0.450703 - 1.15531i) q^{78} +13.1352i q^{79} +(2.39259 - 4.09869i) q^{80} +8.47116i q^{81} +(-6.27829 + 3.89369i) q^{82} +(-1.54014 + 3.71824i) q^{83} +(-0.291796 - 0.0198264i) q^{84} +(-7.21120 + 2.98698i) q^{85} +(1.93301 + 11.7958i) q^{86} +(-0.379579 - 0.379579i) q^{87} +(-12.5133 - 3.84495i) q^{88} +(-6.23303 - 6.23303i) q^{89} +(-2.87906 + 4.00760i) q^{90} +(1.86570 + 1.10416i) q^{91} +(2.91960 + 8.66894i) q^{92} +(0.537349 + 0.222577i) q^{93} +(-13.4399 - 3.15069i) q^{94} -0.568499 q^{95} +(-1.37528 + 0.0367910i) q^{96} +16.8065i q^{97} +(-2.14277 + 9.14040i) q^{98} +(12.5749 + 5.20871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	−1.37688	−	0.322781i	−0.973605	−	0.228241i
$2$	−1.37688	−	0.322781i	−0.973605	−	0.228241i
$3$	0.0930705	−	0.224692i	0.0537343	−	0.129726i	−0.894733	−	0.446602i	$-0.852634\pi$
$3$	0.0930705	−	0.224692i	0.0537343	−	0.129726i	0.948467	+	0.316876i	$0.102634\pi$
$4$	1.79162	+	0.888865i	0.895812	+	0.444433i
$5$	−0.454046	−	1.09616i	−0.203056	−	0.490219i	0.789244	−	0.614080i	$-0.210473\pi$
$5$	−0.454046	−	1.09616i	−0.203056	−	0.490219i	−0.992300	+	0.123860i	$0.960473\pi$
$6$	−0.200674	+	0.279334i	−0.0819248	+	0.114038i
$7$	−0.425170	−	0.425170i	−0.160699	−	0.160699i	0.622177	−	0.782876i	$-0.286248\pi$
$7$	−0.425170	−	0.425170i	−0.160699	−	0.160699i	−0.782876	+	0.622177i	$0.786248\pi$
$8$	−2.17995	−	1.80217i	−0.770729	−	0.637163i
$9$	2.07950	+	2.07950i	0.693165	+	0.693165i
$10$	0.271348	+	1.65585i	0.0858077	+	0.523625i
$11$	4.27595	−	1.77116i	1.28925	−	0.534024i	0.370487	−	0.928838i	$-0.379191\pi$
$11$	4.27595	−	1.77116i	1.28925	−	0.534024i	0.918761	+	0.394813i	$0.129191\pi$
$12$	0.366469	−	0.319837i	0.105790	−	0.0923289i
$13$	−3.49256	+	0.895567i	−0.968661	+	0.248386i
$13$	−3.49256	+	0.895567i	−0.968661	+	0.248386i
$14$	0.448173	+	0.722647i	0.119779	+	0.193135i
$15$	−0.288558			−0.0745053
$16$	2.41984	+	3.18503i	0.604959	+	0.796256i
$17$		−	6.57858i		−	1.59554i	−0.602962	−	0.797770i	$-0.706013\pi$
$17$		−	6.57858i		−	1.59554i	0.602962	−	0.797770i	$-0.293987\pi$
$18$	−2.19200	−	3.53445i	−0.516660	−	0.833078i
$19$	0.183362	−	0.442675i	0.0420661	−	0.101557i	−0.901450	−	0.432883i	$-0.857496\pi$
$19$	0.183362	−	0.442675i	0.0420661	−	0.101557i	0.943516	+	0.331327i	$0.107496\pi$
$20$	0.160862	−	2.36750i	0.0359699	−	0.529389i
$21$	−0.135103	+	0.0559615i	−0.0294819	+	0.0122118i
$22$	−6.45919	+	1.05848i	−1.37710	+	0.225669i
$23$	3.23409	+	3.23409i	0.674354	+	0.674354i	0.958717	−	0.284363i	$-0.0917820\pi$
$23$	3.23409	+	3.23409i	0.674354	+	0.674354i	−0.284363	+	0.958717i	$0.591782\pi$
$24$	−0.607822	+	0.322089i	−0.124071	+	0.0657462i
$25$	2.54012	−	2.54012i	0.508023	−	0.508023i
$26$	5.09792	−	0.105761i	0.999785	−	0.0207414i
$27$	1.33486	−	0.552918i	0.256894	−	0.106409i
$28$	−0.383826	−	1.13966i	−0.0725363	−	0.215376i
$29$	0.844664	−	2.03920i	0.156850	−	0.378670i	−0.825846	−	0.563896i	$-0.809302\pi$
$29$	0.844664	−	2.03920i	0.156850	−	0.378670i	0.982696	+	0.185226i	$0.0593018\pi$
$30$	0.397311	+	0.0931410i	0.0725387	+	0.0170051i
$31$			2.39149i			0.429524i	0.976666	+	0.214762i	$0.0688976\pi$
$31$			2.39149i			0.429524i	−0.976666	+	0.214762i	$0.931102\pi$
$32$	−2.30377	−	5.16649i	−0.407253	−	0.913315i
$33$		−	1.12562i		−	0.195945i
$34$	−2.12344	+	9.05795i	−0.364167	+	1.55343i
$35$	−0.273009	+	0.659102i	−0.0461470	+	0.111409i
$36$	1.87728	+	5.57407i	0.312881	+	0.929011i
$37$	−1.75704	−	4.24186i	−0.288855	−	0.697358i	0.711129	−	0.703062i	$-0.248184\pi$
$37$	−1.75704	−	4.24186i	−0.288855	−	0.697358i	−0.999984	+	0.00570390i	$0.998184\pi$
$38$	−0.395355	+	0.550326i	−0.0641351	+	0.0892747i
$39$	−0.123827	+	0.868101i	−0.0198282	+	0.139007i
$40$	−0.985673	+	3.20785i	−0.155849	+	0.507206i
$41$	3.69384	−	3.69384i	0.576881	−	0.576881i	−0.357162	−	0.934042i	$-0.616256\pi$
$41$	3.69384	−	3.69384i	0.576881	−	0.576881i	0.934042	+	0.357162i	$0.116256\pi$
$42$	0.204085	−	0.0334438i	0.0314910	−	0.00516050i
$43$	−3.23451	−	7.80879i	−0.493258	−	1.19083i	−0.953053	−	0.302804i	$-0.902077\pi$
$43$	−3.23451	−	7.80879i	−0.493258	−	1.19083i	0.459795	−	0.888025i	$-0.347923\pi$
$44$	9.23522	+	0.627497i	1.39226	+	0.0945987i
$45$	1.33528	−	3.22365i	0.199052	−	0.480554i
$46$	−3.40907	−	5.49687i	−0.502639	−	0.810470i
$47$	9.76106			1.42380			0.711898	−	0.702282i	$-0.247836\pi$
$47$	9.76106			1.42380			0.711898	+	0.702282i	$0.247836\pi$
$48$	0.940866	−	0.247286i	0.135802	−	0.0356927i
$49$		−	6.63846i		−	0.948352i
$50$	−4.31735	+	2.67755i	−0.610566	+	0.378662i
$51$	−1.47816	−	0.612272i	−0.206983	−	0.0857352i
$52$	−7.05339	−	1.49989i	−0.978129	−	0.207998i
$53$	−1.93465	−	4.67066i	−0.265744	−	0.641564i	0.733530	−	0.679657i	$-0.237872\pi$
$53$	−1.93465	−	4.67066i	−0.265744	−	0.641564i	−0.999274	+	0.0380935i	$0.987872\pi$
$54$	−2.01642	+	0.330436i	−0.274401	+	0.0449667i
$55$	−3.88296	−	3.88296i	−0.523578	−	0.523578i
$56$	0.160622	+	1.69308i	0.0214640	+	0.226247i
$57$	−0.0823999	−	0.0823999i	−0.0109141	−	0.0109141i
$58$	−1.82122	+	2.53510i	−0.239138	+	0.332875i
$59$	0.218556	+	0.527640i	0.0284535	+	0.0686929i	0.937468	−	0.348072i	$-0.113164\pi$
$59$	0.218556	+	0.527640i	0.0284535	+	0.0686929i	−0.909014	+	0.416765i	$0.863164\pi$
$60$	−0.516987	−	0.256489i	−0.0667427	−	0.0331126i
$61$	−0.932946	+	2.25233i	−0.119451	+	0.288381i	−0.972284	−	0.233803i	$-0.924883\pi$
$61$	−0.932946	+	2.25233i	−0.119451	+	0.288381i	0.852832	+	0.522185i	$0.174883\pi$
$62$	0.771927	−	3.29280i	0.0980349	−	0.418187i
$63$		−	1.76828i		−	0.222782i
$64$	1.50438	+	7.85728i	0.188048	+	0.982160i
$65$	2.56747	+	3.42179i	0.318455	+	0.424420i
$66$	−0.363328	+	1.54984i	−0.0447225	+	0.190773i
$67$	6.87260	+	2.84673i	0.839622	+	0.347783i	0.760705	−	0.649098i	$-0.224854\pi$
$67$	6.87260	+	2.84673i	0.839622	+	0.347783i	0.0789175	+	0.996881i	$0.474854\pi$
$68$	5.84747	−	11.7863i	0.709110	−	1.42930i
$69$	1.02767	−	0.425676i	0.123717	−	0.0512454i
$70$	0.588648	−	0.819386i	0.0703569	−	0.0979353i
$71$	2.79396	+	2.79396i	0.331582	+	0.331582i	0.853187	−	0.521605i	$-0.174666\pi$
$71$	2.79396	+	2.79396i	0.331582	+	0.331582i	−0.521605	+	0.853187i	$0.674666\pi$
$72$	−0.785600	−	8.28080i	−0.0925838	−	0.975902i
$73$	−9.55168	+	9.55168i	−1.11794	+	1.11794i	−0.125896	+	0.992043i	$0.540181\pi$
$73$	−9.55168	+	9.55168i	−1.11794	+	1.11794i	−0.992043	+	0.125896i	$0.959819\pi$
$74$	1.05004	+	6.40770i	0.122065	+	0.744880i
$75$	−0.334334	−	0.807154i	−0.0386056	−	0.0932021i
$76$	0.721994	−	0.630123i	0.0828184	−	0.0722801i
$77$	−2.57105	−	1.06496i	−0.292998	−	0.121364i
$78$	0.450703	−	1.15531i	0.0510320	−	0.130813i
$79$			13.1352i			1.47782i	0.673804	+	0.738910i	$0.264659\pi$
$79$			13.1352i			1.47782i	−0.673804	+	0.738910i	$0.735341\pi$
$80$	2.39259	−	4.09869i	0.267500	−	0.458247i
$81$			8.47116i			0.941240i
$82$	−6.27829	+	3.89369i	−0.693321	+	0.429986i
$83$	−1.54014	+	3.71824i	−0.169053	+	0.408130i	−0.985587	−	0.169167i	$-0.945892\pi$
$83$	−1.54014	+	3.71824i	−0.169053	+	0.408130i	0.816535	+	0.577297i	$0.195892\pi$
$84$	−0.291796	−	0.0198264i	−0.0318376	−	0.00216324i
$85$	−7.21120	+	2.98698i	−0.782165	+	0.323983i
$86$	1.93301	+	11.7958i	0.208442	+	1.27198i
$87$	−0.379579	−	0.379579i	−0.0406951	−	0.0406951i
$88$	−12.5133	−	3.84495i	−1.33392	−	0.409873i
$89$	−6.23303	−	6.23303i	−0.660699	−	0.660699i	0.294846	−	0.955545i	$-0.404732\pi$
$89$	−6.23303	−	6.23303i	−0.660699	−	0.660699i	−0.955545	+	0.294846i	$0.904732\pi$
$90$	−2.87906	+	4.00760i	−0.303480	+	0.422438i
$91$	1.86570	+	1.10416i	0.195578	+	0.115748i
$92$	2.91960	+	8.66894i	0.304390	+	0.903800i
$93$	0.537349	+	0.222577i	0.0557205	+	0.0230802i
$94$	−13.4399	−	3.15069i	−1.38622	−	0.324969i
$95$	−0.568499			−0.0583267
$96$	−1.37528	+	0.0367910i	−0.140364	+	0.00375496i
$97$			16.8065i			1.70644i	0.521553	+	0.853219i	$0.325353\pi$
$97$			16.8065i			1.70644i	−0.521553	+	0.853219i	$0.674647\pi$
$98$	−2.14277	+	9.14040i	−0.216453	+	0.923320i
$99$	12.5749	+	5.20871i	1.26383	+	0.523495i
$100$	6.80876	−	2.29311i	0.680876	−	0.229311i
$101$	−5.96185	+	2.46948i	−0.593227	+	0.245723i	−0.659038	−	0.752110i	$-0.729036\pi$
$101$	−5.96185	+	2.46948i	−0.593227	+	0.245723i	0.0658114	+	0.997832i	$0.479036\pi$
$102$	1.83762	+	1.32015i	0.181951	+	0.130714i
$103$	−10.6408	+	10.6408i	−1.04847	+	1.04847i	−0.0497078	+	0.998764i	$0.515829\pi$
$103$	−10.6408	+	10.6408i	−1.04847	+	1.04847i	−0.998764	+	0.0497078i	$0.984171\pi$
$104$	9.22757	+	4.34188i	0.904838	+	0.425757i
$105$	0.122686	+	0.122686i	0.0119729	+	0.0119729i
$106$	1.15619	+	7.05542i	0.112299	+	0.685283i
$107$	2.37166	+	5.72570i	0.229277	+	0.553524i	0.996090	−	0.0883469i	$-0.0281584\pi$
$107$	2.37166	+	5.72570i	0.229277	+	0.553524i	−0.766813	+	0.641871i	$0.778158\pi$
$108$	2.88304	+	0.195891i	0.277421	+	0.0188496i
$109$	5.71105	−	13.7877i	0.547019	−	1.32062i	−0.372666	−	0.927965i	$-0.621556\pi$
$109$	5.71105	−	13.7877i	0.547019	−	1.32062i	0.919686	−	0.392656i	$-0.128444\pi$
$110$	4.09304	+	6.59973i	0.390256	+	0.629260i
$111$	−1.11664			−0.105987
$112$	0.325335	−	2.38302i	0.0307413	−	0.225174i
$113$			5.05726i			0.475747i	0.971296	+	0.237874i	$0.0764504\pi$
$113$			5.05726i			0.475747i	−0.971296	+	0.237874i	$0.923550\pi$
$114$	0.0868581	+	0.140052i	0.00813501	+	0.0131171i
$115$	2.07667	−	5.01352i	0.193650	−	0.467513i
$116$	3.32589	−	2.90269i	0.308801	−	0.269508i
$117$	−9.12509	−	5.40043i	−0.843615	−	0.499270i
$118$	−0.130614	−	0.797046i	−0.0120240	−	0.0733740i
$119$	−2.79701	+	2.79701i	−0.256402	+	0.256402i
$120$	0.629042	+	0.520030i	0.0574234	+	0.0474720i
$121$	7.36860	−	7.36860i	0.669873	−	0.669873i
$122$	2.01157	−	2.80006i	0.182119	−	0.253506i
$123$	−0.486189	−	1.17376i	−0.0438382	−	0.105835i
$124$	−2.12571	+	4.28465i	−0.190894	+	0.384773i
$125$	−9.41853	−	3.90128i	−0.842419	−	0.348941i
$126$	−0.570767	+	2.43471i	−0.0508479	+	0.216902i
$127$	16.8414			1.49443			0.747216	−	0.664581i	$-0.231390\pi$
$127$	16.8414			1.49443			0.747216	+	0.664581i	$0.231390\pi$
$128$	0.464824	−	11.3042i	0.0410850	−	0.999156i
$129$	−2.05561			−0.180986
$130$	−2.43062	−	5.54014i	−0.213180	−	0.485902i
$131$	−3.33210	+	8.04439i	−0.291127	+	0.702842i	−0.999997	−	0.00249702i	$-0.999205\pi$
$131$	−3.33210	+	8.04439i	−0.291127	+	0.702842i	0.708870	+	0.705339i	$0.249205\pi$
$132$	1.00052	−	2.01668i	0.0870842	−	0.175530i
$133$	−0.266172	+	0.110252i	−0.0230800	+	0.00956006i
$134$	−8.54391	−	6.13796i	−0.738082	−	0.530239i
$135$	−1.21218	−	1.21218i	−0.104328	−	0.104328i
$136$	−11.8557	+	14.3410i	−1.01662	+	1.22973i
$137$	5.69529	−	5.69529i	0.486581	−	0.486581i	−0.420644	−	0.907226i	$-0.638196\pi$
$137$	5.69529	−	5.69529i	0.486581	−	0.486581i	0.907226	+	0.420644i	$0.138196\pi$
$138$	−1.55239	+	0.254393i	−0.132148	+	0.0216554i
$139$	−2.42765	−	5.86088i	−0.205911	−	0.497113i	0.786861	−	0.617131i	$-0.211705\pi$
$139$	−2.42765	−	5.86088i	−0.205911	−	0.497113i	−0.992772	+	0.120017i	$0.961705\pi$
$140$	−1.07498	+	0.938195i	−0.0908526	+	0.0792920i
$141$	0.908467	−	2.19323i	0.0765067	−	0.184704i
$142$	−2.94513	−	4.74880i	−0.247149	−	0.398511i
$143$	−13.3478	+	10.0153i	−1.11620	+	0.837519i
$144$	−1.59121	+	11.6553i	−0.132601	+	0.971274i
$145$	−2.61881			−0.217481
$146$	16.2347	−	10.0685i	1.34359	−	0.833272i
$147$	−1.49161	−	0.617845i	−0.123026	−	0.0509590i
$148$	0.622494	−	9.16160i	0.0511687	−	0.753079i
$149$	−4.64622	+	1.92453i	−0.380633	+	0.157664i	−0.564793	−	0.825233i	$-0.691044\pi$
$149$	−4.64622	+	1.92453i	−0.380633	+	0.157664i	0.184159	+	0.982896i	$0.441044\pi$
$150$	0.199806	+	1.21928i	0.0163141	+	0.0995534i
$151$	−15.6885	+	15.6885i	−1.27671	+	1.27671i	−0.334214	+	0.942497i	$0.608471\pi$
$151$	−15.6885	+	15.6885i	−1.27671	+	1.27671i	−0.942497	+	0.334214i	$0.891529\pi$
$152$	−1.19749	+	0.634561i	−0.0971296	+	0.0514697i
$153$	13.6801	−	13.6801i	1.10597	−	1.10597i
$154$	3.19629	+	2.29622i	0.257564	+	0.185035i
$155$	2.62146	−	1.08585i	0.210561	−	0.0872172i
$156$	−0.993477	+	1.44525i	−0.0795418	+	0.115712i
$157$	−6.69968	+	16.1745i	−0.534692	+	1.29086i	0.393693	+	0.919242i	$0.371197\pi$
$157$	−6.69968	+	16.1745i	−0.534692	+	1.29086i	−0.928385	+	0.371620i	$0.878803\pi$
$158$	4.23978	−	18.0856i	0.337299	−	1.43881i
$159$	−1.22952			−0.0975072
$160$	−4.61730	+	4.87113i	−0.365030	+	0.385097i
$161$		−	2.75007i		−	0.216736i
$162$	2.73433	−	11.6638i	0.214829	−	0.916396i
$163$	16.0282	+	6.63911i	1.25543	+	0.520015i	0.908503	−	0.417877i	$-0.137226\pi$
$163$	16.0282	+	6.63911i	1.25543	+	0.520015i	0.346925	+	0.937893i	$0.387226\pi$
$164$	9.90130	−	3.33465i	0.773161	−	0.260392i
$165$	−1.23386	+	0.511081i	−0.0960558	+	0.0397876i
$166$	3.32078	−	4.62246i	0.257742	−	0.358772i
$167$	−7.80291	−	7.80291i	−0.603807	−	0.603807i	0.337513	−	0.941321i	$-0.390414\pi$
$167$	−7.80291	−	7.80291i	−0.603807	−	0.603807i	−0.941321	+	0.337513i	$0.890414\pi$
$168$	0.395370	+	0.121485i	0.0305035	+	0.00937277i
$169$	11.3959	−	6.25564i	0.876609	−	0.481203i
$170$	10.8931	−	1.78508i	0.835465	−	0.136910i
$171$	1.30184	−	0.539240i	0.0995542	−	0.0412367i
$172$	1.14594	−	16.8655i	0.0873772	−	1.28598i
$173$	3.31965	+	1.37504i	0.252388	+	0.104543i	0.505291	−	0.862949i	$-0.331385\pi$
$173$	3.31965	+	1.37504i	0.252388	+	0.104543i	−0.252903	+	0.967492i	$0.581385\pi$
$174$	0.400115	+	0.645157i	0.0303327	+	0.0489092i
$175$	−2.15996			−0.163278
$176$	15.9883	+	9.33311i	1.20516	+	0.703510i
$177$	0.138898			0.0104402
$178$	6.57026	+	10.5941i	0.492461	+	0.794059i
$179$	−18.9384	−	7.84454i	−1.41552	−	0.586328i	−0.461791	−	0.886989i	$-0.652793\pi$
$179$	−18.9384	−	7.84454i	−1.41552	−	0.586328i	−0.953731	+	0.300660i	$0.902793\pi$
$180$	5.25772	−	4.58869i	0.391887	−	0.342021i
$181$	1.99049	+	4.80547i	0.147952	+	0.357188i	0.980429	−	0.196871i	$-0.0630781\pi$
$181$	1.99049	+	4.80547i	0.147952	+	0.357188i	−0.832477	+	0.554059i	$0.813078\pi$
$182$	−2.21245	−	2.12252i	−0.163998	−	0.157331i
$183$	0.419251	+	0.419251i	0.0309919	+	0.0309919i
$184$	−1.22179	−	12.8785i	−0.0900713	−	0.949418i
$185$	−3.85200	+	3.85200i	−0.283205	+	0.283205i
$186$	−0.668023	−	0.479909i	−0.0489819	−	0.0351886i
$187$	−11.6517	−	28.1297i	−0.852057	−	2.05705i
$188$	17.4882	+	8.67627i	1.27545	+	0.632782i
$189$	−0.802627	−	0.332459i	−0.0583825	−	0.0241828i
$190$	0.782757	+	0.183501i	0.0567872	+	0.0133125i
$191$	3.27097			0.236679			0.118340	−	0.992973i	$-0.462243\pi$
$191$	3.27097			0.236679			0.118340	+	0.992973i	$0.462243\pi$
$192$	1.90548	+	0.393259i	0.137516	+	0.0283810i
$193$			21.8752i			1.57461i	0.616561	+	0.787307i	$0.288525\pi$
$193$			21.8752i			1.57461i	−0.616561	+	0.787307i	$0.711475\pi$
$194$	5.42481	−	23.1406i	0.389479	−	1.66140i
$195$	1.00780	−	0.258423i	0.0721704	−	0.0185060i
$196$	5.90070	−	11.8936i	0.421478	−	0.849545i
$197$	−7.30875	−	17.6449i	−0.520727	−	1.25715i	−0.937452	−	0.348114i	$-0.886822\pi$
$197$	−7.30875	−	17.6449i	−0.520727	−	1.25715i	0.416725	−	0.909032i	$-0.363178\pi$
$198$	−15.6330	−	11.2308i	−1.11099	−	0.798135i
$199$	10.1173	−	10.1173i	0.717199	−	0.717199i	−0.250832	−	0.968031i	$-0.580704\pi$
$199$	10.1173	−	10.1173i	0.717199	−	0.717199i	0.968031	+	0.250832i	$0.0807042\pi$
$200$	−10.1150	+	0.959615i	−0.715242	+	0.0678550i
$201$	1.27927	−	1.27927i	0.0902330	−	0.0902330i
$202$	9.00589	−	1.47582i	0.633652	−	0.103838i
$203$	−1.22613	+	0.507880i	−0.0860575	+	0.0356462i
$204$	−2.10407	−	2.41084i	−0.147315	−	0.168793i
$205$	−5.72622	−	2.37188i	−0.399937	−	0.165659i
$206$	18.0858	−	11.2165i	1.26010	−	0.781493i
$207$			13.4505i			0.934878i
$208$	−11.3038	−	8.95676i	−0.783779	−	0.621040i
$209$		−	2.21762i		−	0.153396i
$210$	−0.129324	−	0.208525i	−0.00892419	−	0.0143896i
$211$	3.93500	+	1.62993i	0.270897	+	0.112209i	0.513997	−	0.857792i	$-0.328164\pi$
$211$	3.93500	+	1.62993i	0.270897	+	0.112209i	−0.243100	+	0.970001i	$0.578164\pi$
$212$	0.685419	−	10.0877i	0.0470748	−	0.692826i
$213$	0.887817	−	0.367746i	0.0608322	−	0.0251975i
$214$	−1.41736	−	8.64916i	−0.0968886	−	0.591244i
$215$	−7.09110	+	7.09110i	−0.483609	+	0.483609i
$216$	−3.90639	−	1.20031i	−0.265796	−	0.0816709i
$217$	1.01679	−	1.01679i	0.0690241	−	0.0690241i
$218$	−12.3139	+	17.1406i	−0.834000	+	1.16091i
$219$	1.25721	+	3.03517i	0.0849542	+	0.205098i
$220$	−3.50538	−	10.4082i	−0.236332	−	0.701723i
$221$	5.89156	+	22.9761i	0.396309	+	1.54554i
$222$	1.53749	+	0.360431i	0.103189	+	0.0241906i
$223$		−	24.1751i		−	1.61888i	−0.587200	−	0.809442i	$-0.699770\pi$
$223$		−	24.1751i		−	1.61888i	0.587200	−	0.809442i	$-0.300230\pi$
$224$	−1.21714	+	3.17613i	−0.0813238	+	0.212214i
$225$	10.5643			0.704288
$226$	1.63239	−	6.96327i	0.108585	−	0.463190i
$227$	−10.9999	−	4.55633i	−0.730092	−	0.302414i	−0.0135021	−	0.999909i	$-0.504298\pi$
$227$	−10.9999	−	4.55633i	−0.730092	−	0.302414i	−0.716590	+	0.697495i	$0.754298\pi$
$228$	−0.0743873	−	0.220872i	−0.00492642	−	0.0146276i
$229$	−1.06780	−	2.57789i	−0.0705620	−	0.170352i	0.884664	−	0.466229i	$-0.154388\pi$
$229$	−1.06780	−	2.57789i	−0.0705620	−	0.170352i	−0.955226	+	0.295878i	$0.904388\pi$
$230$	−4.47760	+	6.23273i	−0.295244	+	0.410974i
$231$	−0.478578	+	0.478578i	−0.0314881	+	0.0314881i
$232$	−5.51631	+	2.92313i	−0.362163	+	0.191913i
$233$	17.8514	+	17.8514i	1.16949	+	1.16949i	0.982330	+	0.187156i	$0.0599270\pi$
$233$	17.8514	+	17.8514i	1.16949	+	1.16949i	0.187156	+	0.982330i	$0.440073\pi$
$234$	10.8210	+	10.3812i	0.707393	+	0.678639i
$235$	−4.43197	−	10.6997i	−0.289110	−	0.697973i
$236$	−0.0774313	+	1.13960i	−0.00504035	+	0.0741816i
$237$	2.95137	+	1.22250i	0.191712	+	0.0794096i
$238$	4.75399	−	2.94834i	0.308155	−	0.191113i
$239$	25.0865			1.62271			0.811355	−	0.584553i	$-0.198730\pi$
$239$	25.0865			1.62271			0.811355	+	0.584553i	$0.198730\pi$
$240$	−0.698263	−	0.919064i	−0.0450727	−	0.0593253i
$241$	−5.44989			−0.351058			−0.175529	−	0.984474i	$-0.556164\pi$
$241$	−5.44989			−0.351058			−0.175529	+	0.984474i	$0.556164\pi$
$242$	−12.5242	+	7.76727i	−0.805084	+	0.499299i
$243$	5.90799	+	2.44717i	0.378998	+	0.156986i
$244$	−3.67351	+	3.20607i	−0.235172	+	0.205247i
$245$	−7.27684	+	3.01417i	−0.464900	+	0.192568i
$246$	0.290557	+	1.77307i	0.0185253	+	0.113047i
$247$	−0.243957	+	1.71028i	−0.0155226	+	0.108823i
$248$	4.30986	−	5.21333i	0.273677	−	0.331047i
$249$	0.692117	+	0.692117i	0.0438611	+	0.0438611i
$250$	11.7090	+	8.41175i	0.740541	+	0.532005i
$251$	4.04951	−	1.67736i	0.255603	−	0.105874i	−0.251203	−	0.967934i	$-0.580826\pi$
$251$	4.04951	−	1.67736i	0.255603	−	0.105874i	0.506806	+	0.862060i	$0.330826\pi$
$252$	1.57176	−	3.16809i	0.0990116	−	0.199571i
$253$	19.5569	+	8.10073i	1.22953	+	0.509289i
$254$	−23.1887	−	5.43609i	−1.45499	−	0.341090i
$255$			1.89830i			0.118876i
$256$	−4.28878	+	15.4145i	−0.268049	+	0.963405i
$257$	−10.6948			−0.667124			−0.333562	−	0.942728i	$-0.608251\pi$
$257$	−10.6948			−0.667124			−0.333562	+	0.942728i	$0.608251\pi$
$258$	2.83034	+	0.663513i	0.176209	+	0.0413085i
$259$	−1.05647	+	2.55055i	−0.0656460	+	0.158484i
$260$	1.55843	+	8.41269i	0.0966500	+	0.521733i
$261$	5.99698	−	2.48403i	0.371204	−	0.153758i
$262$	7.18449	−	10.0007i	0.443859	−	0.617843i
$263$	−8.70691	+	8.70691i	−0.536891	+	0.536891i	−0.922614	−	0.385724i	$-0.873952\pi$
$263$	−8.70691	+	8.70691i	−0.536891	+	0.536891i	0.385724	+	0.922614i	$0.373952\pi$
$264$	−2.02855	+	2.45379i	−0.124849	+	0.151020i
$265$	−4.24138	+	4.24138i	−0.260546	+	0.260546i
$266$	0.402075	−	0.0658890i	0.0246528	−	0.00403991i
$267$	−1.98062	+	0.820401i	−0.121212	+	0.0502077i
$268$	9.78277	+	11.2091i	0.597578	+	0.684704i
$269$	2.45545	+	1.01708i	0.149712	+	0.0620126i	0.456281	−	0.889836i	$-0.349181\pi$
$269$	2.45545	+	1.01708i	0.149712	+	0.0620126i	−0.306569	+	0.951848i	$0.599181\pi$
$270$	1.27776	+	2.06030i	0.0777621	+	0.125386i
$271$	−10.4812			−0.636688			−0.318344	−	0.947975i	$-0.603127\pi$
$271$	−10.4812			−0.636688			−0.318344	+	0.947975i	$0.603127\pi$
$272$	20.9529	−	15.9191i	1.27046	−	0.965237i
$273$	0.421738	−	0.316443i	0.0255247	−	0.0191520i
$274$	−9.68009	+	6.00342i	−0.584795	+	0.362680i
$275$	6.36247	−	15.3604i	0.383671	−	0.926265i
$276$	2.21957	+	0.150811i	0.133603	+	0.00907776i
$277$	−7.86921	−	18.9980i	−0.472815	−	1.14148i	−0.962914	−	0.269810i	$-0.913039\pi$
$277$	−7.86921	−	18.9980i	−0.472815	−	1.14148i	0.490099	−	0.871667i	$-0.336961\pi$
$278$	1.45082	+	8.85335i	0.0870144	+	0.530989i
$279$	−4.97309	+	4.97309i	−0.297731	+	0.297731i
$280$	1.78296	−	0.944803i	0.106552	−	0.0564628i
$281$	−4.16285	−	4.16285i	−0.248335	−	0.248335i	0.571952	−	0.820287i	$-0.306186\pi$
$281$	−4.16285	−	4.16285i	−0.248335	−	0.248335i	−0.820287	+	0.571952i	$0.806186\pi$
$282$	−1.95879	+	2.72659i	−0.116644	+	0.162366i
$283$	21.7542	−	9.01087i	1.29315	−	0.535641i	0.373228	−	0.927740i	$-0.378251\pi$
$283$	21.7542	−	9.01087i	1.29315	−	0.535641i	0.919923	+	0.392099i	$0.128251\pi$
$284$	2.52228	+	7.48919i	0.149669	+	0.444402i
$285$	−0.0529105	+	0.127737i	−0.00313415	+	0.00756650i
$286$	21.6112	−	9.48145i	1.27789	−	0.560650i
$287$	−3.14102			−0.185408
$288$	5.95302	−	15.5344i	0.350785	−	0.915372i
$289$	−26.2777			−1.54575
$290$	3.60580	+	0.845303i	0.211740	+	0.0496379i
$291$	3.77628	+	1.56419i	0.221369	+	0.0916942i
$292$	−25.6032	+	8.62287i	−1.49831	+	0.504615i
$293$	−2.31884	−	5.59817i	−0.135468	−	0.327049i	0.841559	−	0.540166i	$-0.181638\pi$
$293$	−2.31884	−	5.59817i	−0.135468	−	0.327049i	−0.977027	+	0.213117i	$0.931638\pi$
$294$	1.85435	+	1.33217i	0.108148	+	0.0776935i
$295$	0.479146	−	0.479146i	0.0278969	−	0.0278969i
$296$	−3.81429	+	12.4135i	−0.221701	+	0.721522i
$297$	4.72850	−	4.72850i	0.274376	−	0.274376i
$298$	7.01852	−	1.15014i	0.406572	−	0.0666259i
$299$	−14.1916	−	8.39890i	−0.820721	−	0.485721i
$300$	0.118450	−	1.74330i	0.00683871	−	0.100649i
$301$	−1.94485	+	4.69527i	−0.112099	+	0.270631i
$302$	26.6652	−	16.5373i	1.53441	−	0.951614i
$303$			1.56942i			0.0901607i
$304$	1.85364	−	0.487188i	0.106313	−	0.0279422i
$305$	2.89252			0.165625
$306$	−23.2517	+	14.4203i	−1.32921	+	0.824352i
$307$	−9.55718	+	23.0731i	−0.545457	+	1.31685i	0.375369	+	0.926875i	$0.377516\pi$
$307$	−9.55718	+	23.0731i	−0.545457	+	1.31685i	−0.920826	+	0.389974i	$0.872484\pi$
$308$	−3.65974	−	4.19333i	−0.208533	−	0.238937i
$309$	1.40056	+	3.38126i	0.0796752	+	0.192353i
$310$	−3.95994	+	0.648925i	−0.224910	+	0.0368565i
$311$	5.93429	+	5.93429i	0.336503	+	0.336503i	0.855049	−	0.518547i	$-0.173527\pi$
$311$	5.93429	+	5.93429i	0.336503	+	0.336503i	−0.518547	+	0.855049i	$0.673527\pi$
$312$	1.83440	−	1.66926i	0.103853	−	0.0945033i
$313$	−4.77840	+	4.77840i	−0.270091	+	0.270091i	−0.829137	−	0.559046i	$-0.811168\pi$
$313$	−4.77840	+	4.77840i	−0.270091	+	0.270091i	0.559046	+	0.829137i	$0.311168\pi$
$314$	14.4455	−	20.1078i	0.815206	−	1.13475i
$315$	−1.93832	+	0.802879i	−0.109212	+	0.0452371i
$316$	−11.6754	+	23.5333i	−0.656792	+	1.32385i
$317$	−11.3640	−	4.70714i	−0.638268	−	0.264379i	0.0399933	−	0.999200i	$-0.487266\pi$
$317$	−11.3640	−	4.70714i	−0.638268	−	0.264379i	−0.678262	+	0.734821i	$0.737266\pi$
$318$	1.69291	+	0.396866i	0.0949334	+	0.0222551i
$319$		−	10.2156i		−	0.571961i
$320$	7.92981	−	5.21661i	0.443290	−	0.291618i
$321$	1.50725			0.0841266
$322$	−0.887672	+	3.78653i	−0.0494680	+	0.211015i
$323$	−2.91217	−	1.20626i	−0.162038	−	0.0671181i
$324$	−7.52972	+	15.1771i	−0.418318	+	0.843174i
$325$	−6.59666	+	11.1463i	−0.365917	+	0.618288i
$326$	−19.9261	−	14.3149i	−1.10360	−	0.792830i
$327$	−2.56646	−	2.56646i	−0.141925	−	0.141925i
$328$	−14.7093	+	1.39547i	−0.812186	+	0.0770521i
$329$	−4.15011	−	4.15011i	−0.228803	−	0.228803i
$330$	1.86385	−	0.305433i	0.102602	−	0.0168136i
$331$	−18.0894	+	7.49287i	−0.994283	+	0.411845i	−0.819697	−	0.572797i	$-0.805858\pi$
$331$	−18.0894	+	7.49287i	−0.994283	+	0.411845i	−0.174585	+	0.984642i	$0.555858\pi$
$332$	−6.06437	+	5.29271i	−0.332826	+	0.290475i
$333$	5.16719	−	12.4747i	0.283160	−	0.683609i
$334$	8.22508	+	13.2623i	0.450056	+	0.725683i
$335$		−	8.82604i		−	0.482218i
$336$	−0.505166	−	0.294889i	−0.0275591	−	0.0160875i
$337$			7.18948i			0.391636i	0.980640	+	0.195818i	$0.0627362\pi$
$337$			7.18948i			0.391636i	−0.980640	+	0.195818i	$0.937264\pi$
$338$	−17.7101	+	4.93491i	−0.963301	+	0.268424i
$339$	1.13633	+	0.470682i	0.0617168	+	0.0255639i
$340$	−15.5748	−	1.05824i	−0.844661	−	0.0573914i
$341$	4.23570	+	10.2259i	0.229376	+	0.553763i
$342$	−1.96654	+	0.322262i	−0.106338	+	0.0174259i
$343$	−5.79866	+	5.79866i	−0.313098	+	0.313098i
$344$	−7.02168	+	22.8519i	−0.378584	+	1.23209i
$345$	−0.933221	−	0.933221i	−0.0502429	−	0.0502429i
$346$	−4.12694	−	2.96480i	−0.221865	−	0.159388i
$347$	11.5539	−	4.78579i	0.620247	−	0.256915i	−0.0503560	−	0.998731i	$-0.516036\pi$
$347$	11.5539	−	4.78579i	0.620247	−	0.256915i	0.670603	+	0.741817i	$0.266036\pi$
$348$	−0.342668	−	1.01746i	−0.0183689	−	0.0545414i
$349$	33.0289	+	13.6810i	1.76800	+	0.732328i	0.995221	+	0.0976504i	$0.0311327\pi$
$349$	33.0289	+	13.6810i	1.76800	+	0.732328i	0.772777	+	0.634678i	$0.218867\pi$
$350$	2.97402	+	0.697195i	0.158968	+	0.0372666i
$351$	−4.16691	+	3.12656i	−0.222413	+	0.166883i
$352$	−19.0015	−	18.0113i	−1.01278	−	0.960008i
$353$			4.18065i			0.222513i	0.993792	+	0.111257i	$0.0354876\pi$
$353$			4.18065i			0.222513i	−0.993792	+	0.111257i	$0.964512\pi$
$354$	−0.191246	−	0.0448336i	−0.0101646	−	0.00238288i
$355$	1.79405	−	4.33123i	0.0952185	−	0.229878i
$356$	−5.62692	−	16.7076i	−0.298226	−	0.885499i
$357$	0.368147	+	0.888786i	0.0194844	+	0.0470396i
$358$	23.5439	+	16.9140i	1.24433	+	0.893932i
$359$	3.79623	+	3.79623i	0.200357	+	0.200357i	0.800153	−	0.599796i	$-0.204751\pi$
$359$	3.79623	+	3.79623i	0.200357	+	0.200357i	−0.599796	+	0.800153i	$0.704751\pi$
$360$	−8.72042	+	4.62101i	−0.459606	+	0.243549i
$361$	13.2727	+	13.2727i	0.698563	+	0.698563i
$362$	−1.18956	−	7.25907i	−0.0625220	−	0.381528i
$363$	−0.969867	−	2.34147i	−0.0509048	−	0.122895i
$364$	2.36118	+	3.63660i	0.123759	+	0.190609i
$365$	14.8071	+	6.13330i	0.775039	+	0.321032i
$366$	−0.441934	−	0.712587i	−0.0231003	−	0.0372475i
$367$		−	13.5124i		−	0.705341i	−0.935748	−	0.352671i	$-0.885274\pi$
$367$		−	13.5124i		−	0.705341i	0.935748	−	0.352671i	$-0.114726\pi$
$368$	−2.47469	+	18.1266i	−0.129002	+	0.944916i
$369$	15.3626			0.799747
$370$	6.54712	−	4.06041i	0.340368	−	0.211091i
$371$	−1.16327	+	2.80838i	−0.0603938	+	0.145804i
$372$	0.764886	+	0.876405i	0.0396575	+	0.0454395i
$373$	−7.24591	−	17.4932i	−0.375179	−	0.905763i	−0.992855	−	0.119330i	$-0.961926\pi$
$373$	−7.24591	−	17.4932i	−0.375179	−	0.905763i	0.617676	−	0.786433i	$-0.288074\pi$
$374$	6.96332	+	42.4923i	0.360065	+	2.19723i
$375$	−1.75318	+	1.75318i	−0.0905336	+	0.0905336i
$376$	−21.2786	−	17.5911i	−1.09736	−	0.907190i
$377$	−1.12380	+	7.87847i	−0.0578785	+	0.405762i
$378$	0.997814	+	0.716831i	0.0513220	+	0.0368698i
$379$	−1.96879	−	4.75307i	−0.101130	−	0.244149i	0.865214	−	0.501402i	$-0.167182\pi$
$379$	−1.96879	−	4.75307i	−0.101130	−	0.244149i	−0.966344	+	0.257254i	$0.917182\pi$
$380$	−1.01854	−	0.505319i	−0.0522498	−	0.0259223i
$381$	1.56744	−	3.78413i	0.0803023	−	0.193867i
$382$	−4.50375	−	1.05581i	−0.230432	−	0.0540199i
$383$		−	3.53949i		−	0.180860i	−0.995903	−	0.0904299i	$-0.971176\pi$
$383$		−	3.53949i		−	0.180860i	0.995903	−	0.0904299i	$-0.0288241\pi$
$384$	−2.49669	−	1.15653i	−0.127409	−	0.0590187i
$385$			3.30183i			0.168277i
$386$	7.06092	−	30.1197i	0.359391	−	1.53305i
$387$	9.51220	−	22.9645i	0.483532	−	1.16735i
$388$	−14.9387	+	30.1109i	−0.758397	+	1.52865i
$389$	−24.2724	+	10.0539i	−1.23066	+	0.509755i	−0.900783	−	0.434270i	$-0.857006\pi$
$389$	−24.2724	+	10.0539i	−1.23066	+	0.509755i	−0.329875	+	0.944025i	$0.607006\pi$
$390$	−1.47104	+	0.0305181i	−0.0744893	+	0.00154535i
$391$	21.2757	−	21.2757i	1.07596	−	1.07596i
$392$	−11.9636	+	14.4715i	−0.604254	+	0.730922i
$393$	1.49739	+	1.49739i	0.0755334	+	0.0755334i
$394$	4.36787	+	26.6541i	0.220050	+	1.34281i
$395$	14.3983	−	5.96396i	0.724456	−	0.300080i
$396$	17.8997	+	20.5095i	0.899495	+	1.03064i
$397$	−6.09509	+	14.7149i	−0.305904	+	0.738518i	0.693925	+	0.720047i	$0.255880\pi$
$397$	−6.09509	+	14.7149i	−0.305904	+	0.738518i	−0.999829	+	0.0184707i	$0.994120\pi$
$398$	−17.1961	+	10.6647i	−0.861962	+	0.534574i
$399$			0.0700679i			0.00350778i
$400$	14.2370	+	1.94367i	0.711850	+	0.0971834i
$401$	20.0101			0.999254			0.499627	−	0.866241i	$-0.333470\pi$
$401$	20.0101			0.999254			0.499627	+	0.866241i	$0.333470\pi$
$402$	−2.17434	+	1.34849i	−0.108446	+	0.0672564i
$403$	−2.14174	−	8.35241i	−0.106688	−	0.416063i
$404$	−12.8764	−	0.874903i	−0.640627	−	0.0435280i
$405$	9.28578	−	3.84630i	0.461414	−	0.191124i
$406$	1.85218	−	0.303520i	0.0919219	−	0.0150635i
$407$	−15.0260	−	15.0260i	−0.744812	−	0.744812i
$408$	2.11889	+	3.99861i	0.104901	+	0.197961i
$409$	18.8625	+	18.8625i	0.932691	+	0.932691i	0.997873	−	0.0651826i	$-0.0207630\pi$
$409$	18.8625	+	18.8625i	0.932691	+	0.932691i	−0.0651826	+	0.997873i	$0.520763\pi$
$410$	7.11875	+	5.11412i	0.351570	+	0.252569i
$411$	−0.749623	−	1.80975i	−0.0369762	−	0.0892684i
$412$	−28.5226	+	9.60610i	−1.40521	+	0.473259i
$413$	0.131413	−	0.317260i	0.00646643	−	0.0156113i
$414$	4.34159	−	18.5199i	0.213377	−	0.910201i
$415$	4.77509			0.234400
$416$	12.6730	+	15.9811i	0.621345	+	0.783537i
$417$	−1.54284			−0.0755530
$418$	−0.715806	+	3.05341i	−0.0350112	+	0.149347i
$419$	−15.1528	+	36.5821i	−0.740263	+	1.78715i	−0.135455	+	0.990784i	$0.543249\pi$
$419$	−15.1528	+	36.5821i	−0.740263	+	1.78715i	−0.604809	+	0.796371i	$0.706751\pi$
$420$	0.110756	+	0.328859i	0.00540434	+	0.0160467i
$421$	6.62434	+	15.9926i	0.322850	+	0.779430i	0.999086	+	0.0427444i	$0.0136101\pi$
$421$	6.62434	+	15.9926i	0.322850	+	0.779430i	−0.676236	+	0.736685i	$0.736390\pi$
$422$	−4.89193	−	3.51437i	−0.238136	−	0.171077i
$423$	20.2981	+	20.2981i	0.986927	+	0.986927i
$424$	−4.19986	+	13.6684i	−0.203963	+	0.663795i
$425$	−16.7104	−	16.7104i	−0.810572	−	0.810572i
$426$	−1.34112	+	0.219773i	−0.0649776	+	0.0106480i
$427$	1.35428	−	0.560962i	0.0655383	−	0.0271469i
$428$	−0.840247	+	12.3664i	−0.0406149	+	0.597752i
$429$	1.00806	+	3.93128i	0.0486698	+	0.189804i
$430$	12.0525	−	7.47475i	0.581223	−	0.360465i
$431$	−15.6394			−0.753324			−0.376662	−	0.926351i	$-0.622928\pi$
$431$	−15.6394			−0.753324			−0.376662	+	0.926351i	$0.622928\pi$
$432$	4.99121	+	2.91360i	0.240140	+	0.140181i
$433$			5.19031i			0.249430i	0.992193	+	0.124715i	$0.0398017\pi$
$433$			5.19031i			0.249430i	−0.992193	+	0.124715i	$0.960198\pi$
$434$	−1.72820	+	1.07180i	−0.0829563	+	0.0514481i
$435$	−0.243734	+	0.588427i	−0.0116862	+	0.0282129i
$436$	22.4875	−	19.6260i	1.07695	−	0.939915i
$437$	2.02466	−	0.838641i	0.0968525	−	0.0401176i
$438$	−0.751335	−	4.58488i	−0.0359002	−	0.219074i
$439$	−25.1881	−	25.1881i	−1.20216	−	1.20216i	−0.973508	−	0.228653i	$-0.926568\pi$
$439$	−25.1881	−	25.1881i	−1.20216	−	1.20216i	−0.228653	−	0.973508i	$-0.573432\pi$
$440$	1.46692	+	15.4624i	0.0699326	+	0.737141i
$441$	13.8047	−	13.8047i	0.657364	−	0.657364i
$442$	−0.695757	−	33.5371i	−0.0330938	−	1.59520i
$443$	−14.0680	+	5.82715i	−0.668390	+	0.276856i	−0.690964	−	0.722889i	$-0.742814\pi$
$443$	−14.0680	+	5.82715i	−0.668390	+	0.276856i	0.0225744	+	0.999745i	$0.492814\pi$
$444$	−2.00060	−	0.992544i	−0.0949444	−	0.0471041i
$445$	−4.00234	+	9.66250i	−0.189729	+	0.458046i
$446$	−7.80327	+	33.2863i	−0.369495	+	1.57615i
$447$			1.22309i			0.0578500i
$448$	2.70106	−	3.98029i	0.127613	−	0.188051i
$449$		−	5.19259i		−	0.245054i	−0.992465	−	0.122527i	$-0.960900\pi$
$449$		−	5.19259i		−	0.245054i	0.992465	−	0.122527i	$-0.0390998\pi$
$450$	−14.5459	−	3.40997i	−0.685698	−	0.160747i
$451$	9.25231	−	22.3370i	0.435674	−	1.05181i
$452$	−4.49523	+	9.06072i	−0.211438	+	0.426180i
$453$	2.06494	+	4.98522i	0.0970195	+	0.234226i
$454$	13.6750	+	9.82411i	0.641798	+	0.461068i
$455$	0.363230	−	2.54645i	0.0170285	−	0.119379i
$456$	0.0311294	+	0.328126i	0.00145777	+	0.0153659i
$457$	21.4978	−	21.4978i	1.00563	−	1.00563i	0.00564242	−	0.999984i	$-0.498204\pi$
$457$	21.4978	−	21.4978i	1.00563	−	1.00563i	0.999984	−	0.00564242i	$-0.00179605\pi$
$458$	0.638139	+	3.89412i	0.0298183	+	0.181960i
$459$	−3.63742	−	8.78150i	−0.169780	−	0.409885i
$460$	8.17695	−	7.13646i	0.381252	−	0.332739i
$461$	−2.37945	+	5.74451i	−0.110822	+	0.267548i	−0.969554	−	0.244876i	$-0.921253\pi$
$461$	−2.37945	+	5.74451i	−0.110822	+	0.267548i	0.858732	+	0.512425i	$0.171253\pi$
$462$	0.813422	−	0.504471i	0.0378438	−	0.0234701i
$463$	16.0054			0.743834			0.371917	−	0.928266i	$-0.378701\pi$
$463$	16.0054			0.743834			0.371917	+	0.928266i	$0.378701\pi$
$464$	8.53885	−	2.24425i	0.396406	−	0.104187i
$465$		−	0.690082i		−	0.0320018i
$466$	−18.8173	−	30.3415i	−0.871693	−	1.40554i
$467$	−33.6782	−	13.9500i	−1.55844	−	0.645527i	−0.573623	−	0.819120i	$-0.694462\pi$
$467$	−33.6782	−	13.9500i	−1.55844	−	0.645527i	−0.984818	+	0.173592i	$0.944462\pi$
$468$	−11.5485	−	17.7865i	−0.533828	−	0.822182i
$469$	−1.71168	−	4.13236i	−0.0790381	−	0.190815i
$470$	2.64864	+	16.1628i	0.122173	+	0.745536i
$471$	3.01073	+	3.01073i	0.138727	+	0.138727i
$472$	0.474455	−	1.54410i	0.0218386	−	0.0710732i
$473$	−27.6612	−	27.6612i	−1.27186	−	1.27186i
$474$	−3.66909	−	2.63588i	−0.168527	−	0.121070i
$475$	−0.658685	−	1.59021i	−0.0302225	−	0.0729636i
$476$	−7.49736	+	2.52503i	−0.343641	+	0.115735i
$477$	5.68951	−	13.7357i	0.260505	−	0.628915i
$478$	−34.5412	−	8.09745i	−1.57988	−	0.370369i
$479$		−	8.46632i		−	0.386836i	−0.981116	−	0.193418i	$-0.938043\pi$
$479$		−	8.46632i		−	0.386836i	0.981116	−	0.193418i	$-0.0619574\pi$
$480$	0.664771	+	1.49083i	0.0303425	+	0.0680468i
$481$	9.93543	+	13.2414i	0.453017	+	0.603756i
$482$	7.50387	+	1.75912i	0.341792	+	0.0801258i
$483$	−0.617920	−	0.255951i	−0.0281163	−	0.0116462i
$484$	19.7515	−	6.65207i	0.897794	−	0.302367i
$485$	18.4226	−	7.63091i	0.836529	−	0.346502i
$486$	−7.34472	−	5.27646i	−0.333163	−	0.239345i
$487$	−17.4545	−	17.4545i	−0.790940	−	0.790940i	0.190707	−	0.981647i	$-0.438922\pi$
$487$	−17.4545	−	17.4545i	−0.790940	−	0.790940i	−0.981647	+	0.190707i	$0.938922\pi$
$488$	6.09285	−	3.22865i	0.275811	−	0.146154i
$489$	2.98351	−	2.98351i	0.134919	−	0.134919i
$490$	10.9923	−	1.80133i	0.496581	−	0.0813759i
$491$	5.01627	+	12.1103i	0.226381	+	0.546532i	0.995732	−	0.0922945i	$-0.0294201\pi$
$491$	5.01627	+	12.1103i	0.226381	+	0.546532i	−0.769351	+	0.638827i	$0.779420\pi$
$492$	0.172250	−	2.53510i	0.00776563	−	0.114291i
$493$	−13.4150	−	5.55669i	−0.604183	−	0.250261i
$494$	0.887947	−	2.27611i	0.0399506	−	0.102407i
$495$		−	16.1492i		−	0.725852i
$496$	−7.61695	+	5.78701i	−0.342011	+	0.259844i
$497$		−	2.37582i		−	0.106570i
$498$	−0.729563	−	1.17637i	−0.0326925	−	0.0527143i
$499$	−9.54144	+	23.0351i	−0.427134	+	1.03119i	0.553058	+	0.833143i	$0.313461\pi$
$499$	−9.54144	+	23.0351i	−0.427134	+	1.03119i	−0.980192	+	0.198049i	$0.936539\pi$
$500$	−13.4068	−	15.3614i	−0.599568	−	0.686985i
$501$	−2.47947	+	1.02703i	−0.110775	+	0.0458844i
$502$	−6.11714	+	1.00243i	−0.273021	+	0.0447406i
$503$	−0.833986	−	0.833986i	−0.0371856	−	0.0371856i	0.688269	−	0.725455i	$-0.258371\pi$
$503$	−0.833986	−	0.833986i	−0.0371856	−	0.0371856i	−0.725455	+	0.688269i	$0.758371\pi$
$504$	−3.18673	+	3.85476i	−0.141948	+	0.171705i
$505$	5.41391	+	5.41391i	0.240916	+	0.240916i
$506$	−24.3128	−	17.4664i	−1.08084	−	0.776475i
$507$	−0.344969	−	3.14279i	−0.0153206	−	0.139576i
$508$	30.1735	+	14.9697i	1.33873	+	0.664175i
$509$	22.0499	+	9.13338i	0.977346	+	0.404830i	0.813442	−	0.581646i	$-0.197591\pi$
$509$	22.0499	+	9.13338i	0.977346	+	0.404830i	0.163904	+	0.986476i	$0.447591\pi$
$510$	0.612736	−	2.61374i	0.0271324	−	0.115738i
$511$	8.12217			0.359304
$512$	10.8807	−	19.8396i	0.480862	−	0.876796i
$513$		−	0.692294i		−	0.0305655i
$514$	14.7255	+	3.45209i	0.649515	+	0.152265i
$515$	16.4955	+	6.83266i	0.726879	+	0.301083i
$516$	−3.68288	−	1.82716i	−0.162130	−	0.0804363i
$517$	41.7378	−	17.2884i	1.83563	−	0.760342i
$518$	2.27791	−	3.17081i	0.100086	−	0.139317i
$519$	0.617923	−	0.617923i	0.0271238	−	0.0271238i
$520$	0.569674	−	12.0863i	0.0249819	−	0.530021i
$521$	−13.0996	−	13.0996i	−0.573905	−	0.573905i	0.359312	−	0.933217i	$-0.383011\pi$
$521$	−13.0996	−	13.0996i	−0.573905	−	0.573905i	−0.933217	+	0.359312i	$0.883011\pi$
$522$	−9.05895	+	1.48451i	−0.396499	+	0.0649753i
$523$	12.3708	+	29.8657i	0.540937	+	1.30594i	0.924063	+	0.382241i	$0.124847\pi$
$523$	12.3708	+	29.8657i	0.540937	+	1.30594i	−0.383126	+	0.923696i	$0.625153\pi$
$524$	−13.1202	+	11.4507i	−0.573161	+	0.500228i
$525$	−0.201029	+	0.485326i	−0.00877361	+	0.0211814i
$526$	14.7988	−	9.17798i	0.645260	−	0.400179i
$527$	15.7326			0.685323
$528$	3.58512	−	2.72381i	0.156022	−	0.118538i
$529$		−	2.08134i		−	0.0904929i
$530$	7.20894	−	4.47086i	0.313136	−	0.194202i
$531$	−0.642740	+	1.55171i	−0.0278925	+	0.0673385i
$532$	−0.574879	−	0.0390607i	−0.0249242	−	0.00169350i
$533$	−9.59286	+	16.2090i	−0.415513	+	0.702091i
$534$	2.99190	−	0.490290i	0.129472	−	0.0212169i
$535$	5.19946	−	5.19946i	0.224792	−	0.224792i
$536$	−9.85167	−	18.5913i	−0.425527	−	0.803022i
$537$	−3.52521	+	3.52521i	−0.152124	+	0.152124i
$538$	−3.05258	−	2.19298i	−0.131606	−	0.0945461i
$539$	−11.7578	−	28.3858i	−0.506443	−	1.22266i
$540$	−1.09430	−	3.24923i	−0.0470914	−	0.139825i
$541$	−5.82370	−	2.41226i	−0.250380	−	0.103711i	0.253964	−	0.967214i	$-0.418266\pi$
$541$	−5.82370	−	2.41226i	−0.250380	−	0.103711i	−0.504344	+	0.863503i	$0.668266\pi$
$542$	14.4314	+	3.38314i	0.619883	+	0.145318i
$543$	1.26501			0.0542867
$544$	−33.9882	+	15.1555i	−1.45723	+	0.649788i
$545$	−17.7066			−0.758469
$546$	−0.682826	+	0.299576i	−0.0292223	+	0.0128207i
$547$	−5.85648	+	14.1388i	−0.250405	+	0.604531i	−0.998237	−	0.0593572i	$-0.981095\pi$
$547$	−5.85648	+	14.1388i	−0.250405	+	0.604531i	0.747832	+	0.663888i	$0.231095\pi$
$548$	15.2662	−	5.14147i	0.652138	−	0.219633i
$549$	−6.62377	+	2.74365i	−0.282695	+	0.117096i
$550$	−13.7184	+	19.0958i	−0.584956	+	0.814246i
$551$	−0.747823	−	0.747823i	−0.0318583	−	0.0318583i
$552$	−3.00742	−	0.924086i	−0.128004	−	0.0393317i
$553$	5.58467	−	5.58467i	0.237484	−	0.237484i
$554$	4.70281	+	28.6980i	0.199803	+	1.21926i
$555$	0.507007	+	1.22402i	0.0215212	+	0.0519569i
$556$	0.860084	−	12.6583i	0.0364757	−	0.536834i
$557$	9.73990	−	23.5142i	0.412693	−	0.996328i	−0.571719	−	0.820449i	$-0.693723\pi$
$557$	9.73990	−	23.5142i	0.412693	−	0.996328i	0.984412	−	0.175879i	$-0.0562767\pi$
$558$	8.45259	−	5.24215i	0.357827	−	0.221918i
$559$	18.2900	+	24.3759i	0.773584	+	1.03099i
$560$	−2.75990	+	0.725379i	−0.116627	+	0.0306529i
$561$	−7.40495			−0.312637
$562$	4.38808	+	7.07546i	0.185100	+	0.298460i
$563$	39.1485	+	16.2159i	1.64991	+	0.683417i	0.997242	−	0.0742238i	$-0.0236479\pi$
$563$	39.1485	+	16.2159i	1.64991	+	0.683417i	0.652672	+	0.757640i	$0.273648\pi$
$564$	3.57712	−	3.12195i	0.150624	−	0.131458i
$565$	5.54359	−	2.29623i	0.233221	−	0.0966031i
$566$	−32.8615	+	5.38509i	−1.38127	+	0.226352i
$567$	3.60168	−	3.60168i	0.151256	−	0.151256i
$568$	−1.05551	−	11.1259i	−0.0442884	−	0.466832i
$569$	−1.35740	+	1.35740i	−0.0569051	+	0.0569051i	−0.734987	−	0.678082i	$-0.762812\pi$
$569$	−1.35740	+	1.35740i	−0.0569051	+	0.0569051i	0.678082	+	0.734987i	$0.262812\pi$
$570$	0.114083	−	0.158801i	0.00477840	−	0.00665144i
$571$	13.6426	−	5.65096i	0.570926	−	0.236485i	−0.0784947	−	0.996915i	$-0.525011\pi$
$571$	13.6426	−	5.65096i	0.570926	−	0.236485i	0.649421	+	0.760429i	$0.275011\pi$
$572$	−32.8165	+	6.07920i	−1.37213	+	0.254184i
$573$	0.304431	−	0.734962i	0.0127178	−	0.0307035i
$574$	4.32482	+	1.01386i	0.180514	+	0.0423177i
$575$	16.4299			0.685175
$576$	−13.2108	+	19.4675i	−0.550451	+	0.811147i
$577$		−	12.4882i		−	0.519890i	−0.965623	−	0.259945i	$-0.916296\pi$
$577$		−	12.4882i		−	0.519890i	0.965623	−	0.259945i	$-0.0837044\pi$
$578$	36.1814	+	8.48195i	1.50495	+	0.352803i
$579$	4.91520	+	2.03594i	0.204269	+	0.0846108i
$580$	−4.69193	−	2.32777i	−0.194822	−	0.0966554i
$581$	2.23570	−	0.926059i	0.0927527	−	0.0384194i
$582$	−4.69461	−	3.37262i	−0.194598	−	0.139799i
$583$	−16.5449	−	16.5449i	−0.685221	−	0.685221i
$584$	38.0359	−	3.60847i	1.57394	−	0.149320i
$585$	−1.77655	+	12.4546i	−0.0734512	+	0.514936i
$586$	1.38579	+	8.45652i	0.0572464	+	0.349336i
$587$	−35.2166	+	14.5872i	−1.45354	+	0.602077i	−0.963039	−	0.269361i	$-0.913187\pi$
$587$	−35.2166	+	14.5872i	−1.45354	+	0.602077i	−0.490504	+	0.871439i	$0.663187\pi$
$588$	−2.12322	−	2.43279i	−0.0875603	−	0.100326i
$589$	1.05865	+	0.438508i	0.0436210	+	0.0180684i
$590$	−0.814388	+	0.505069i	−0.0335278	+	0.0207934i
$591$	−4.64490			−0.191066
$592$	9.25870	−	15.8608i	0.380530	−	0.651876i
$593$	−15.3638			−0.630914			−0.315457	−	0.948940i	$-0.602158\pi$
$593$	−15.3638			−0.630914			−0.315457	+	0.948940i	$0.602158\pi$
$594$	−8.03688	+	4.98433i	−0.329757	+	0.204510i
$595$	4.33596	+	1.79601i	0.177757	+	0.0736293i
$596$	−10.0349	−	0.681834i	−0.411047	−	0.0279290i
$597$	−1.33166	−	3.21491i	−0.0545012	−	0.131578i
$598$	16.8292	+	16.1451i	0.688196	+	0.660222i
$599$	−20.6739	−	20.6739i	−0.844712	−	0.844712i	0.144755	−	0.989468i	$-0.453761\pi$
$599$	−20.6739	−	20.6739i	−0.844712	−	0.844712i	−0.989468	+	0.144755i	$0.953761\pi$
$600$	−0.725795	+	2.36208i	−0.0296305	+	0.0964317i
$601$	−12.5576	+	12.5576i	−0.512234	+	0.512234i	−0.915210	−	0.402976i	$-0.867976\pi$
$601$	−12.5576	+	12.5576i	−0.512234	+	0.512234i	0.402976	+	0.915210i	$0.367976\pi$
$602$	4.19338	−	5.83709i	0.170909	−	0.237902i
$603$	8.37180	+	20.2113i	0.340926	+	0.823068i
$604$	−42.0528	+	14.1629i	−1.71111	+	0.576281i
$605$	−11.4229	−	4.73151i	−0.464406	−	0.192363i
$606$	0.506579	−	2.16091i	0.0205784	−	0.0877809i
$607$	1.48312			0.0601981			0.0300991	−	0.999547i	$-0.490418\pi$
$607$	1.48312			0.0601981			0.0300991	+	0.999547i	$0.490418\pi$
$608$	−2.70950	+	0.0724833i	−0.109885	+	0.00293959i
$609$			0.322771i			0.0130793i
$610$	−3.98267	−	0.933652i	−0.161254	−	0.0378025i
$611$	−34.0911	+	8.74169i	−1.37918	+	0.353651i
$612$	36.6695	−	12.3499i	1.48227	−	0.499214i
$613$	−0.933693	−	2.25413i	−0.0377115	−	0.0910436i	0.903902	−	0.427740i	$-0.140690\pi$
$613$	−0.933693	−	2.25413i	−0.0377115	−	0.0910436i	−0.941613	+	0.336697i	$0.890690\pi$
$614$	20.6067	−	28.6841i	0.831618	−	1.15760i
$615$	−1.06589	+	1.06589i	−0.0429807	+	0.0429807i
$616$	3.68552	+	6.95503i	0.148494	+	0.280226i
$617$	0.416385	−	0.416385i	0.0167630	−	0.0167630i	−0.698676	−	0.715439i	$-0.746227\pi$
$617$	0.416385	−	0.416385i	0.0167630	−	0.0167630i	0.715439	+	0.698676i	$0.246227\pi$
$618$	−0.837007	−	5.10768i	−0.0336694	−	0.205461i
$619$	20.6420	−	8.55018i	0.829670	−	0.343661i	0.0728982	−	0.997339i	$-0.476775\pi$
$619$	20.6420	−	8.55018i	0.829670	−	0.343661i	0.756772	+	0.653679i	$0.226775\pi$
$620$	5.66185	+	0.384700i	0.227385	+	0.0154499i
$621$	6.10525	+	2.52888i	0.244995	+	0.101480i
$622$	−6.25536	−	10.0863i	−0.250817	−	0.404424i
$623$			5.30019i			0.212348i
$624$	−3.06457	+	1.70627i	−0.122681	+	0.0683055i
$625$		−	5.86572i		−	0.234629i
$626$	8.12168	−	5.03693i	0.324608	−	0.201316i
$627$	−0.498282	−	0.206395i	−0.0198995	−	0.00824262i
$628$	−26.3802	+	23.0234i	−1.05269	+	0.918735i
$629$	−27.9054	+	11.5588i	−1.11266	+	0.460880i
$630$	2.92800	−	0.479818i	0.116654	−	0.0191164i
$631$	11.2041	−	11.2041i	0.446028	−	0.446028i	−0.448004	−	0.894032i	$-0.647865\pi$
$631$	11.2041	−	11.2041i	0.446028	−	0.446028i	0.894032	+	0.448004i	$0.147865\pi$
$632$	23.6718	−	28.6340i	0.941612	−	1.13900i
$633$	0.732466	−	0.732466i	0.0291129	−	0.0291129i
$634$	14.1276	+	10.1493i	0.561079	+	0.403080i
$635$	−7.64677	−	18.4609i	−0.303453	−	0.732600i
$636$	−2.20284	−	1.09288i	−0.0873481	−	0.0433354i
$637$	5.94519	+	23.1852i	0.235557	+	0.918631i
$638$	−3.29739	+	14.0656i	−0.130545	+	0.556864i
$639$			11.6201i			0.459683i
$640$	−12.6023	+	4.62308i	−0.498148	+	0.182743i
$641$	−0.474897			−0.0187573			−0.00937865	−	0.999956i	$-0.502985\pi$
$641$	−0.474897			−0.0187573			−0.00937865	+	0.999956i	$0.502985\pi$
$642$	−2.07531	−	0.486513i	−0.0819060	−	0.0192011i
$643$	14.1793	+	5.87327i	0.559178	+	0.231619i	0.644329	−	0.764749i	$-0.277137\pi$
$643$	14.1793	+	5.87327i	0.559178	+	0.231619i	−0.0851500	+	0.996368i	$0.527137\pi$
$644$	2.44444	−	4.92710i	0.0963246	−	0.194155i
$645$	0.933342	+	2.25329i	0.0367503	+	0.0887231i
$646$	3.62037	+	2.60088i	0.142441	+	0.102330i
$647$	0.659262	−	0.659262i	0.0259183	−	0.0259183i	−0.694029	−	0.719947i	$-0.744166\pi$
$647$	0.659262	−	0.659262i	0.0259183	−	0.0259183i	0.719947	+	0.694029i	$0.244166\pi$
$648$	15.2665	−	18.4667i	0.599723	−	0.725441i
$649$	1.86907	+	1.86907i	0.0733673	+	0.0733673i
$650$	12.6807	−	13.2180i	0.497377	−	0.518451i
$651$	−0.133831	−	0.323097i	−0.00524526	−	0.0126632i
$652$	22.8153	+	26.1417i	0.893516	+	1.02379i
$653$	32.0297	+	13.2671i	1.25342	+	0.519183i	0.907883	−	0.419223i	$-0.137697\pi$
$653$	32.0297	+	13.2671i	1.25342	+	0.519183i	0.345535	+	0.938406i	$0.387697\pi$
$654$	2.70531	+	4.36212i	0.105786	+	0.170572i
$655$	10.3309			0.403662
$656$	20.7035	+	2.82648i	0.808334	+	0.110356i
$657$	−39.7254			−1.54983
$658$	4.37464	+	7.05380i	0.170541	+	0.274986i
$659$	5.21785	+	2.16130i	0.203258	+	0.0841924i	0.481990	−	0.876177i	$-0.339914\pi$
$659$	5.21785	+	2.16130i	0.203258	+	0.0841924i	−0.278732	+	0.960369i	$0.589914\pi$
$660$	−2.66490	−	0.181069i	−0.103731	−	0.00704810i
$661$	8.30835	−	3.44143i	0.323157	−	0.133856i	−0.215207	−	0.976569i	$-0.569043\pi$
$661$	8.30835	−	3.44143i	0.323157	−	0.133856i	0.538364	+	0.842712i	$0.319043\pi$
$662$	27.3256	−	4.47790i	1.06204	−	0.174039i
$663$	5.71087	+	0.814608i	0.221792	+	0.0316367i
$664$	10.0583	−	5.32998i	0.390339	−	0.206843i
$665$	0.241708	+	0.241708i	0.00937305	+	0.00937305i
$666$	−11.1412	+	15.5083i	−0.431713	+	0.600936i
$667$	9.32667	−	3.86323i	0.361130	−	0.149585i
$668$	−7.04415	−	20.9156i	−0.272546	−	0.809250i
$669$	−5.43196	−	2.24999i	−0.210012	−	0.0869896i
$670$	−2.84888	+	12.1524i	−0.110062	+	0.469490i
$671$			11.2833i			0.435585i
$672$	0.600371	+	0.569086i	0.0231598	+	0.0219530i
$673$	−37.3434			−1.43948			−0.719742	−	0.694242i	$-0.755740\pi$
$673$	−37.3434			−1.43948			−0.719742	+	0.694242i	$0.755740\pi$
$674$	2.32063	−	9.89909i	0.0893874	−	0.381299i
$675$	1.98623	−	4.79518i	0.0764500	−	0.184567i
$676$	25.9776	−	1.07832i	0.999140	−	0.0414739i
$677$	37.1722	−	15.3972i	1.42865	−	0.591764i	0.471629	−	0.881797i	$-0.343666\pi$
$677$	37.1722	−	15.3972i	1.42865	−	0.591764i	0.957017	+	0.290033i	$0.0936663\pi$
$678$	−1.41266	−	1.01486i	−0.0542531	−	0.0389755i
$679$	7.14560	−	7.14560i	0.274223	−	0.274223i
$680$	21.1031	+	6.48433i	0.809267	+	0.248663i
$681$	−2.04754	+	2.04754i	−0.0784619	+	0.0784619i
$682$	−2.53135	−	15.4471i	−0.0969304	−	0.591499i
$683$	−21.2605	+	8.80637i	−0.813509	+	0.336966i	−0.750353	−	0.661037i	$-0.770116\pi$
$683$	−21.2605	+	8.80637i	−0.813509	+	0.336966i	−0.0631556	+	0.998004i	$0.520116\pi$
$684$	2.81172	+	0.191045i	0.107509	+	0.00730480i
$685$	−8.82889	−	3.65705i	−0.337335	−	0.139729i
$686$	9.85579	−	6.11239i	0.376296	−	0.233372i
$687$	−0.678612			−0.0258907
$688$	17.0442	−	29.1980i	0.649805	−	1.11316i
$689$	10.9398	+	14.5799i	0.416772	+	0.555451i
$690$	0.983712	+	1.58616i	0.0374493	+	0.0603843i
$691$	−4.31390	+	10.4147i	−0.164109	+	0.396193i	−0.984446	−	0.175686i	$-0.943786\pi$
$691$	−4.31390	+	10.4147i	−0.164109	+	0.396193i	0.820338	+	0.571880i	$0.193786\pi$
$692$	4.72533	+	5.41428i	0.179630	+	0.205820i
$693$	−3.13190	−	7.56107i	−0.118971	−	0.287221i
$694$	−17.4532	+	2.86009i	−0.662513	+	0.108568i
$695$	−5.32221	+	5.32221i	−0.201883	+	0.201883i
$696$	0.143399	+	1.51153i	0.00543551	+	0.0572943i
$697$	−24.3002	−	24.3002i	−0.920436	−	0.920436i
$698$	−41.0610	−	29.4983i	−1.55418	−	1.11653i
$699$	5.67252	−	2.34963i	0.214554	−	0.0888713i
$700$	−3.86984	−	1.91991i	−0.146266	−	0.0725659i
$701$	−1.90705	+	4.60402i	−0.0720283	+	0.173892i	−0.955793	−	0.294039i	$-0.905000\pi$
$701$	−1.90705	+	4.60402i	−0.0720283	+	0.173892i	0.883765	+	0.467931i	$0.155000\pi$
$702$	6.74655	−	2.95991i	0.254632	−	0.111715i
$703$	−2.19994			−0.0829723
$704$	20.3491	+	30.9329i	0.766937	+	1.16583i
$705$	−2.81663			−0.106080
$706$	1.34943	−	5.75627i	0.0507866	−	0.216640i
$707$	3.58475	+	1.48485i	0.134818	+	0.0558436i
$708$	0.248853	+	0.123461i	0.00935245	+	0.00463996i
$709$	−15.9485	−	38.5031i	−0.598959	−	1.44601i	−0.874644	−	0.484767i	$-0.838905\pi$
$709$	−15.9485	−	38.5031i	−0.598959	−	1.44601i	0.275685	−	0.961248i	$-0.411095\pi$
$710$	−3.86824	+	5.38452i	−0.145173	+	0.202077i
$711$	−27.3145	+	27.3145i	−1.02437	+	1.02437i
$712$	2.35474	+	24.8207i	0.0882475	+	0.930193i
$713$	−7.73428	+	7.73428i	−0.289651	+	0.289651i
$714$	−0.220013	−	1.34259i	−0.00823378	−	0.0502451i
$715$	17.0389	+	10.0840i	0.637219	+	0.377120i
$716$	−26.9578	−	30.8882i	−1.00746	−	1.15434i
$717$	2.33481	−	5.63674i	0.0871952	−	0.210508i
$718$	−4.00162	−	6.45233i	−0.149339	−	0.240799i
$719$		−	25.9547i		−	0.967947i	−0.875083	−	0.483973i	$-0.839193\pi$
$719$		−	25.9547i		−	0.967947i	0.875083	−	0.483973i	$-0.160807\pi$
$720$	13.4986	−	3.54781i	0.503063	−	0.132219i
$721$	9.04831			0.336977
$722$	−13.9908	−	22.5591i	−0.520683	−	0.839564i
$723$	−0.507224	+	1.22455i	−0.0188639	+	0.0455414i
$724$	−0.705203	+	10.3789i	−0.0262087	+	0.385728i
$725$	−3.03426	−	7.32535i	−0.112690	−	0.272057i
$726$	0.579614	+	3.53699i	0.0215115	+	0.131270i
$727$	−3.96279	−	3.96279i	−0.146972	−	0.146972i	0.629792	−	0.776764i	$-0.283140\pi$
$727$	−3.96279	−	3.96279i	−0.146972	−	0.146972i	−0.776764	+	0.629792i	$0.783140\pi$
$728$	−2.07725	−	5.76932i	−0.0769879	−	0.213825i
$729$	−16.8703	+	16.8703i	−0.624827	+	0.624827i
$730$	−18.4080	−	13.2243i	−0.681309	−	0.489454i
$731$	−51.3707	+	21.2785i	−1.90002	+	0.787012i
$732$	0.378483	+	1.12380i	0.0139891	+	0.0415368i
$733$	−6.81166	−	2.82148i	−0.251594	−	0.104214i	0.253322	−	0.967382i	$-0.418477\pi$
$733$	−6.81166	−	2.82148i	−0.251594	−	0.104214i	−0.504916	+	0.863168i	$0.668477\pi$
$734$	−4.36155	+	18.6050i	−0.160988	+	0.686724i
$735$			1.91558i			0.0706572i
$736$	9.25830	−	24.1595i	0.341265	−	0.890531i
$737$	34.4289			1.26821
$738$	−21.1526	−	4.95877i	−0.778638	−	0.182535i
$739$	−19.5548	−	8.09986i	−0.719335	−	0.297958i	−0.00717352	−	0.999974i	$-0.502283\pi$
$739$	−19.5548	−	8.09986i	−0.719335	−	0.297958i	−0.712161	+	0.702016i	$0.752283\pi$
$740$	−10.3253	+	3.47743i	−0.379564	+	0.127833i
$741$	0.361581	+	0.213992i	0.0132830	+	0.00786119i
$742$	2.50818	−	3.49133i	0.0920780	−	0.128171i
$743$	35.1004	+	35.1004i	1.28771	+	1.28771i	0.936175	+	0.351534i	$0.114340\pi$
$743$	35.1004	+	35.1004i	1.28771	+	1.28771i	0.351534	+	0.936175i	$0.385660\pi$
$744$	−0.770273	−	1.45360i	−0.0282396	−	0.0532916i
$745$	4.21920	+	4.21920i	0.154579	+	0.154579i
$746$	4.33032	+	26.4249i	0.158544	+	0.967486i
$747$	−10.9348	+	4.52934i	−0.400083	+	0.165720i
$748$	4.12804	−	60.7547i	0.150936	−	2.22141i
$749$	1.42603	−	3.44275i	0.0521062	−	0.125795i
$750$	2.97981	−	1.84803i	0.108807	−	0.0674805i
$751$		−	19.4457i		−	0.709583i	−0.934945	−	0.354792i	$-0.884552\pi$
$751$		−	19.4457i		−	0.709583i	0.934945	−	0.354792i	$-0.115448\pi$
$752$	23.6202	+	31.0892i	0.861339	+	1.13371i
$753$		−	1.06601i		−	0.0388475i
$754$	4.09036	−	10.4850i	0.148962	−	0.381842i
$755$	24.3205	+	10.0739i	0.885112	+	0.366625i
$756$	−1.14250	−	1.30907i	−0.0415522	−	0.0476104i
$757$	13.5982	+	32.8291i	0.494236	+	1.19319i	0.952545	+	0.304399i	$0.0984556\pi$
$757$	13.5982	+	32.8291i	0.494236	+	1.19319i	−0.458308	+	0.888793i	$0.651544\pi$
$758$	1.17659	+	7.17992i	0.0427357	+	0.260786i
$759$	3.64034	−	3.64034i	0.132136	−	0.132136i
$760$	1.23930	+	1.02453i	0.0449541	+	0.0371636i
$761$	−20.3566	−	20.3566i	−0.737926	−	0.737926i	0.234250	−	0.972176i	$-0.424736\pi$
$761$	−20.3566	−	20.3566i	−0.737926	−	0.737926i	−0.972176	+	0.234250i	$0.924736\pi$
$762$	−3.37963	+	4.70437i	−0.122431	+	0.170421i
$763$	−8.29027	+	3.43394i	−0.300128	+	0.124317i
$764$	5.86035	+	2.90745i	0.212020	+	0.105188i
$765$	−21.2071	−	8.78426i	−0.766743	−	0.317595i
$766$	−1.14248	+	4.87348i	−0.0412796	+	0.176086i
$767$	−1.23586	−	1.64708i	−0.0446242	−	0.0594727i
$768$	3.06436	+	2.39829i	0.110575	+	0.0865408i
$769$			7.94374i			0.286458i	0.989690	+	0.143229i	$0.0457486\pi$
$769$			7.94374i			0.286458i	−0.989690	+	0.143229i	$0.954251\pi$
$770$	1.06577	−	4.54624i	0.0384077	−	0.163835i
$771$	−0.995372	+	2.40304i	−0.0358475	+	0.0865434i
$772$	−19.4441	+	39.1922i	−0.699810	+	1.41056i
$773$	12.3047	+	29.7063i	0.442571	+	1.06846i	0.975044	+	0.222014i	$0.0712630\pi$
$773$	12.3047	+	29.7063i	0.442571	+	1.06846i	−0.532472	+	0.846447i	$0.678737\pi$
$774$	−20.5097	+	28.5491i	−0.737206	+	1.02618i
$775$	6.07466	+	6.07466i	0.218208	+	0.218208i
$776$	30.2881	−	36.6373i	1.08728	−	1.31520i
$777$	0.474762	+	0.474762i	0.0170320	+	0.0170320i
$778$	36.6655	−	6.00846i	1.31452	−	0.215414i
$779$	−0.957860	−	2.31248i	−0.0343189	−	0.0828531i
$780$	2.03531	+	0.432806i	0.0728758	+	0.0154969i
$781$	16.8954	+	6.99830i	0.604565	+	0.250419i
$782$	−36.1616	+	22.4268i	−1.29314	+	0.801981i
$783$		−	3.18908i		−	0.113968i
$784$	21.1437	−	16.0640i	0.755131	−	0.573714i
$785$	20.7718			0.741378
$786$	−1.57841	−	2.54507i	−0.0562999	−	0.0907795i
$787$	11.9018	−	28.7335i	0.424253	−	1.02424i	−0.556825	−	0.830630i	$-0.687981\pi$
$787$	11.9018	−	28.7335i	0.424253	−	1.02424i	0.981079	−	0.193609i	$-0.0620192\pi$
$788$	2.58939	−	38.1095i	0.0922432	−	1.35760i
$789$	1.14602	+	2.76673i	0.0407993	+	0.0984982i
$790$	−21.7498	+	3.56420i	−0.773824	+	0.126808i
$791$	2.15019	−	2.15019i	0.0764521	−	0.0764521i
$792$	−18.0258	−	34.0169i	−0.640519	−	1.20874i
$793$	1.24125	−	8.70191i	0.0440782	−	0.309014i
$794$	13.1419	−	18.2933i	0.466389	−	0.649204i
$795$	0.558258	+	1.34775i	0.0197994	+	0.0477999i
$796$	27.1194	−	9.13351i	0.961222	−	0.323729i
$797$	9.09882	−	21.9665i	0.322297	−	0.778093i	−0.676823	−	0.736146i	$-0.736644\pi$
$797$	9.09882	−	21.9665i	0.322297	−	0.778093i	0.999120	−	0.0419474i	$-0.0133562\pi$
$798$	0.0226166	−	0.0964755i	0.000800619	−	0.00341519i
$799$		−	64.2139i		−	2.27173i
$800$	−18.9753	−	7.27165i	−0.670879	−	0.257092i
$801$		−	25.9231i		−	0.915948i
$802$	−27.5515	−	6.45887i	−0.972879	−	0.228071i
$803$	−23.9250	+	57.7601i	−0.844295	+	2.03831i
$804$	3.42908	−	1.15488i	0.120934	−	0.0407293i
$805$	−3.01453	+	1.24866i	−0.106248	+	0.0440095i
$806$	0.252926	+	12.1916i	0.00890894	+	0.429432i
$807$	0.457061	−	0.457061i	0.0160893	−	0.0160893i
$808$	17.4470	+	5.36091i	0.613782	+	0.188596i
$809$	−30.4095	−	30.4095i	−1.06914	−	1.06914i	−0.997425	−	0.0717163i	$-0.977152\pi$
$809$	−30.4095	−	30.4095i	−1.06914	−	1.06914i	−0.0717163	−	0.997425i	$-0.522848\pi$
$810$	−14.0270	+	2.29863i	−0.492857	+	0.0807657i
$811$	15.8147	−	6.55068i	0.555331	−	0.230026i	−0.0873259	−	0.996180i	$-0.527832\pi$
$811$	15.8147	−	6.55068i	0.555331	−	0.230026i	0.642657	+	0.766154i	$0.277832\pi$
$812$	−2.64820	−	0.179935i	−0.0929337	−	0.00631448i
$813$	−0.975492	+	2.35505i	−0.0342120	+	0.0825950i
$814$	15.8390	+	25.5392i	0.555156	+	0.895149i
$815$		−	20.5840i		−	0.721027i
$816$	−1.62679	−	6.18956i	−0.0569491	−	0.216678i
$817$	−4.04984			−0.141686
$818$	−19.8830	−	32.0600i	−0.695194	−	1.12095i
$819$	1.58361	+	6.17581i	0.0553359	+	0.215800i
$820$	−8.15096	−	9.33936i	−0.284644	−	0.326145i
$821$	−6.56851	+	2.72077i	−0.229243	+	0.0949555i	−0.494348	−	0.869264i	$-0.664593\pi$
$821$	−6.56851	+	2.72077i	−0.229243	+	0.0949555i	0.265105	+	0.964219i	$0.414593\pi$
$822$	0.447991	+	2.73378i	0.0156255	+	0.0953516i
$823$	22.9372	+	22.9372i	0.799541	+	0.799541i	0.983023	−	0.183482i	$-0.0587369\pi$
$823$	22.9372	+	22.9372i	0.799541	+	0.799541i	−0.183482	+	0.983023i	$0.558737\pi$
$824$	42.3730	−	4.01993i	1.47613	−	0.140041i
$825$	−2.85920	−	2.85920i	−0.0995444	−	0.0995444i
$826$	−0.283347	+	0.394413i	−0.00985889	+	0.0137234i
$827$	17.8125	+	43.0031i	0.619400	+	1.49536i	0.852402	+	0.522888i	$0.175145\pi$
$827$	17.8125	+	43.0031i	0.619400	+	1.49536i	−0.233002	+	0.972476i	$0.574855\pi$
$828$	−11.9557	+	24.0983i	−0.415490	+	0.837475i
$829$	12.6076	−	30.4375i	0.437881	−	1.05714i	−0.538799	−	0.842435i	$-0.681122\pi$
$829$	12.6076	−	30.4375i	0.437881	−	1.05714i	0.976679	−	0.214703i	$-0.0688784\pi$
$830$	−6.57476	−	1.54131i	−0.228213	−	0.0534997i
$831$	−5.00108			−0.173486
$832$	−12.2909	−	26.0947i	−0.426109	−	0.904672i
$833$	−43.6717			−1.51313
$834$	2.12431	+	0.497999i	0.0735588	+	0.0172443i
$835$	−5.01039	+	12.0961i	−0.173392	+	0.418605i
$836$	1.97116	−	3.97314i	0.0681742	−	0.137414i
$837$	1.32230	+	3.19231i	0.0457053	+	0.110342i
$838$	32.6717	−	45.4783i	1.12863	−	1.57102i
$839$	30.6901	+	30.6901i	1.05954	+	1.05954i	0.998112	+	0.0614269i	$0.0195651\pi$
$839$	30.6901	+	30.6901i	1.05954	+	1.05954i	0.0614269	+	0.998112i	$0.480435\pi$
$840$	−0.0463488	−	0.488550i	−0.00159918	−	0.0168566i
$841$	17.0612	+	17.0612i	0.588318	+	0.588318i
$842$	−3.95885	−	24.1581i	−0.136431	−	0.832544i
$843$	−1.32280	+	0.547921i	−0.0455596	+	0.0188714i
$844$	5.60126	+	6.41791i	0.192803	+	0.220914i
$845$	−12.0315	−	9.65145i	−0.413895	−	0.332020i
$846$	−21.3963	−	34.5000i	−0.735619	−	1.18613i
$847$	−6.26581			−0.215296
$848$	10.1946	−	17.4641i	0.350085	−	0.599721i
$849$		−	5.72664i		−	0.196538i
$850$	17.6145	+	28.4020i	0.604171	+	0.974182i
$851$	8.03615	−	19.4010i	0.275476	−	0.665057i
$852$	1.91751	+	0.130287i	0.0656928	+	0.00446357i
$853$	−50.9907	+	21.1210i	−1.74589	+	0.723170i	−0.747633	+	0.664112i	$0.768810\pi$
$853$	−50.9907	+	21.1210i	−1.74589	+	0.723170i	−0.998255	+	0.0590587i	$0.981190\pi$
$854$	−2.04576	+	0.335243i	−0.0700044	+	0.0114718i
$855$	−1.18219	−	1.18219i	−0.0404301	−	0.0404301i
$856$	5.14856	−	16.7559i	0.175974	−	0.572704i
$857$	−14.4300	+	14.4300i	−0.492919	+	0.492919i	−0.909225	−	0.416306i	$-0.863325\pi$
$857$	−14.4300	+	14.4300i	−0.492919	+	0.492919i	0.416306	+	0.909225i	$0.363325\pi$
$858$	−0.119046	−	5.73830i	−0.00406417	−	0.195902i
$859$	14.0491	−	5.81931i	0.479348	−	0.198552i	−0.129908	−	0.991526i	$-0.541468\pi$
$859$	14.0491	−	5.81931i	0.479348	−	0.198552i	0.609256	+	0.792974i	$0.291468\pi$
$860$	−19.0076	+	6.40155i	−0.648154	+	0.218291i
$861$	−0.292336	+	0.705762i	−0.00996279	+	0.0240523i
$862$	21.5337	+	5.04811i	0.733440	+	0.171939i
$863$			24.2094i			0.824099i	0.911161	+	0.412050i	$0.135187\pi$
$863$			24.2094i			0.824099i	−0.911161	+	0.412050i	$0.864813\pi$
$864$	−5.93187	−	5.62276i	−0.201806	−	0.191290i
$865$		−	4.26321i		−	0.144954i
$866$	1.67533	−	7.14645i	0.0569301	−	0.242846i
$867$	−2.44568	+	5.90440i	−0.0830597	+	0.200524i
$868$	2.72549	−	0.917915i	0.0925092	−	0.0311561i
$869$	23.2644	+	56.1653i	0.789192	+	1.90528i
$870$	0.525527	−	0.731523i	0.0178170	−	0.0248009i
$871$	−26.5524	−	3.78747i	−0.899694	−	0.128334i
$872$	−37.2975	+	19.7642i	−1.26305	+	0.669301i
$873$	−34.9490	+	34.9490i	−1.18284	+	1.18284i
$874$	−3.05842	+	0.501190i	−0.103453	+	0.0169530i
$875$	2.34577	+	5.66318i	0.0793014	+	0.191451i
$876$	−0.445411	+	6.55537i	−0.0150490	+	0.221485i
$877$	−21.7267	+	52.4528i	−0.733657	+	1.77121i	−0.103653	+	0.994613i	$0.533053\pi$
$877$	−21.7267	+	52.4528i	−0.733657	+	1.77121i	−0.630004	+	0.776592i	$0.716947\pi$
$878$	26.5508	+	42.8113i	0.896048	+	1.44481i
$879$	−1.47368			−0.0497060
$880$	2.97120	−	21.7634i	0.100159	−	0.733646i
$881$		−	25.2735i		−	0.851485i	−0.904844	−	0.425742i	$-0.860013\pi$
$881$		−	25.2735i		−	0.851485i	0.904844	−	0.425742i	$-0.139987\pi$
$882$	−23.4633	+	14.5515i	−0.790051	+	0.489976i
$883$	43.0366	+	17.8263i	1.44830	+	0.599904i	0.961794	−	0.273776i	$-0.0882725\pi$
$883$	43.0366	+	17.8263i	1.44830	+	0.599904i	0.486502	+	0.873679i	$0.338273\pi$
$884$	−9.86717	+	46.4013i	−0.331869	+	1.56064i
$885$	−0.0630659	−	0.152255i	−0.00211994	−	0.00511798i
$886$	21.2509	−	3.48243i	0.713937	−	0.116995i
$887$	−7.37765	−	7.37765i	−0.247717	−	0.247717i	0.572316	−	0.820033i	$-0.306045\pi$
$887$	−7.37765	−	7.37765i	−0.247717	−	0.247717i	−0.820033	+	0.572316i	$0.806045\pi$
$888$	2.43423	+	2.01238i	0.0816873	+	0.0675309i
$889$	−7.16045	−	7.16045i	−0.240154	−	0.240154i
$890$	8.62963	−	12.0123i	0.289266	−	0.402652i
$891$	15.0038	+	36.2223i	0.502645	+	1.21349i
$892$	21.4884	−	43.3127i	0.719485	−	1.45022i
$893$	1.78981	−	4.32097i	0.0598936	−	0.144596i
$894$	0.394789	−	1.68405i	0.0132037	−	0.0563230i
$895$			24.3214i			0.812974i
$896$	−5.00381	+	4.60856i	−0.167166	+	0.153961i
$897$	−3.20799	+	2.40705i	−0.107112	+	0.0803690i
$898$	−1.67607	+	7.14960i	−0.0559312	+	0.238585i
$899$	4.87672	+	2.02000i	0.162648	+	0.0673709i
$900$	18.9273	+	9.39026i	0.630910	+	0.313009i
$901$	−30.7263	+	12.7272i	−1.02364	+	0.424006i
$902$	−19.9493	+	27.7691i	−0.664241	+	0.924609i
$903$	0.873983	+	0.873983i	0.0290843	+	0.0290843i
$904$	9.11404	−	11.0246i	0.303128	−	0.366672i
$905$	4.36381	−	4.36381i	0.145058	−	0.145058i
$906$	−1.23406	−	7.53060i	−0.0409988	−	0.250187i
$907$	11.4825	+	27.7212i	0.381271	+	0.920469i	0.991721	+	0.128414i	$0.0409887\pi$
$907$	11.4825	+	27.7212i	0.381271	+	0.920469i	−0.610450	+	0.792055i	$0.709011\pi$
$908$	−15.6578	−	17.9407i	−0.519623	−	0.595383i
$909$	−17.5329	−	7.26238i	−0.581530	−	0.240878i
$910$	−1.32207	+	3.38893i	−0.0438263	+	0.112342i
$911$			6.83844i			0.226568i	0.993563	+	0.113284i	$0.0361369\pi$
$911$			6.83844i			0.226568i	−0.993563	+	0.113284i	$0.963863\pi$
$912$	0.0630515	−	0.461840i	0.00208784	−	0.0152931i
$913$			18.6269i			0.616459i
$914$	−36.5392	+	22.6610i	−1.20861	+	0.749558i
$915$	0.269209	−	0.649927i	0.00889976	−	0.0214859i
$916$	0.378305	−	5.56774i	0.0124996	−	0.183963i
$917$	4.83694	−	2.00353i	0.159730	−	0.0661622i
$918$	2.17380	+	13.2652i	0.0717461	+	0.437817i
$919$	23.2469	+	23.2469i	0.766844	+	0.766844i	0.977550	−	0.210705i	$-0.0675761\pi$
$919$	23.2469	+	23.2469i	0.766844	+	0.766844i	−0.210705	+	0.977550i	$0.567576\pi$
$920$	−13.5622	+	7.18672i	−0.447134	+	0.236939i
$921$	4.29484	+	4.29484i	0.141520	+	0.141520i
$922$	5.13045	−	7.14148i	0.168962	−	0.235192i
$923$	−12.2603	−	7.25589i	−0.403551	−	0.238831i
$924$	−1.28282	+	0.432040i	−0.0422018	+	0.0142131i
$925$	−15.2379	−	6.31175i	−0.501019	−	0.207529i
$926$	−22.0376	−	5.16625i	−0.724201	−	0.169773i
$927$	−44.2551			−1.45353
$928$	−12.4814	+	0.333897i	−0.409723	+	0.0109607i
$929$		−	49.2847i		−	1.61698i	−0.588511	−	0.808489i	$-0.700286\pi$
$929$		−	49.2847i		−	1.61698i	0.588511	−	0.808489i	$-0.299714\pi$
$930$	−0.222746	+	0.950164i	−0.00730412	+	0.0311571i
$931$	−2.93868	−	1.21724i	−0.0963113	−	0.0398935i
$932$	16.1155	+	47.8506i	0.527882	+	1.56740i
$933$	1.88570	−	0.781081i	0.0617349	−	0.0255714i
$934$	41.8682	+	30.0782i	1.36997	+	0.984188i
$935$	−25.5444	+	25.5444i	−0.835390	+	0.835390i
$936$	10.1598	+	28.2176i	0.332082	+	0.922322i
$937$	−0.235755	−	0.235755i	−0.00770178	−	0.00770178i	0.703245	−	0.710947i	$-0.251734\pi$
$937$	−0.235755	−	0.235755i	−0.00770178	−	0.00770178i	−0.710947	+	0.703245i	$0.751734\pi$
$938$	1.02294	+	6.24229i	0.0334001	+	0.203818i
$939$	0.628940	+	1.51840i	0.0205247	+	0.0495510i
$940$	1.57019	−	23.1093i	0.0512138	−	0.753742i
$941$	−5.62154	+	13.5716i	−0.183257	+	0.442421i	−0.988634	−	0.150341i	$-0.951963\pi$
$941$	−5.62154	+	13.5716i	−0.183257	+	0.442421i	0.805377	+	0.592763i	$0.201963\pi$
$942$	−3.17362	−	5.11724i	−0.103402	−	0.166729i
$943$	23.8924			0.778044
$944$	−1.15168	+	1.97291i	−0.0374839	+	0.0642127i
$945$			1.03076i			0.0335307i
$946$	29.1578	+	47.0148i	0.948001	+	1.52858i
$947$	−22.9158	+	55.3237i	−0.744665	+	1.79778i	−0.158907	+	0.987294i	$0.550797\pi$
$947$	−22.9158	+	55.3237i	−0.744665	+	1.79778i	−0.585758	+	0.810486i	$0.699203\pi$
$948$	4.20111	+	4.81362i	0.136446	+	0.156339i
$949$	24.8056	−	41.9140i	0.805224	−	1.36058i
$950$	0.393645	+	2.40214i	0.0127715	+	0.0779358i
$951$	−2.11532	+	2.11532i	−0.0685938	+	0.0685938i
$952$	11.1380	−	1.05667i	0.360986	−	0.0342467i
$953$	5.87640	−	5.87640i	0.190355	−	0.190355i	−0.605494	−	0.795850i	$-0.707025\pi$
$953$	5.87640	−	5.87640i	0.190355	−	0.190355i	0.795850	+	0.605494i	$0.207025\pi$
$954$	−12.2674	+	17.0760i	−0.397173	+	0.552856i
$955$	−1.48517	−	3.58552i	−0.0480590	−	0.116025i
$956$	44.9456	+	22.2985i	1.45364	+	0.721186i
$957$	−2.29535	−	0.950767i	−0.0741983	−	0.0307339i
$958$	−2.73277	+	11.6572i	−0.0882918	+	0.376625i
$959$	−4.84293			−0.156386
$960$	−0.434101	−	2.26728i	−0.0140105	−	0.0731761i
$961$	25.2808			0.815509
$962$	−9.40586	−	21.4389i	−0.303257	−	0.691217i
$963$	−6.97471	+	16.8384i	−0.224757	+	0.542611i
$964$	−9.76416	−	4.84422i	−0.314482	−	0.156022i
$965$	23.9788	−	9.93236i	0.771906	−	0.319734i
$966$	0.768188	+	0.551868i	0.0247161	+	0.0177561i
$967$	−14.5151	−	14.5151i	−0.466776	−	0.466776i	0.434093	−	0.900868i	$-0.357069\pi$
$967$	−14.5151	−	14.5151i	−0.466776	−	0.466776i	−0.900868	+	0.434093i	$0.857069\pi$
$968$	−29.3427	+	2.78374i	−0.943109	+	0.0894727i
$969$	−0.542075	+	0.542075i	−0.0174139	+	0.0174139i
$970$	−27.8290	+	4.56040i	−0.893534	+	0.146426i
$971$	−18.4053	−	44.4344i	−0.590655	−	1.42597i	−0.882871	−	0.469615i	$-0.844393\pi$
$971$	−18.4053	−	44.4344i	−0.590655	−	1.42597i	0.292216	−	0.956352i	$-0.405607\pi$
$972$	8.40970	+	9.63582i	0.269741	+	0.309069i
$973$	−1.45970	+	3.52403i	−0.0467959	+	0.112975i
$974$	18.3989	+	29.6669i	0.589538	+	0.950588i
$975$	1.89054	+	2.51961i	0.0605458	+	0.0806922i
$976$	−9.43130	+	2.47882i	−0.301889	+	0.0793449i
$977$	−26.9194			−0.861229			−0.430615	−	0.902536i	$-0.641703\pi$
$977$	−26.9194			−0.861229			−0.430615	+	0.902536i	$0.641703\pi$
$978$	−5.07098	+	3.14493i	−0.162152	+	0.100564i
$979$	−37.6918	−	15.6125i	−1.20464	−	0.498976i
$980$	−15.7166	−	1.06788i	−0.502047	−	0.0341121i
$981$	40.5475	−	16.7953i	1.29458	−	0.536234i
$982$	−2.99783	−	18.2937i	−0.0956647	−	0.583776i
$983$	37.0092	−	37.0092i	1.18041	−	1.18041i	0.200771	−	0.979638i	$-0.435655\pi$
$983$	37.0092	−	37.0092i	1.18041	−	1.18041i	0.979638	−	0.200771i	$-0.0643447\pi$
$984$	−1.05545	+	3.43494i	−0.0336466	+	0.109502i
$985$	−16.0232	+	16.0232i	−0.510541	+	0.510541i
$986$	16.6774	+	11.9810i	0.531115	+	0.381554i
$987$	−1.31875	+	0.546244i	−0.0419762	+	0.0173871i
$988$	−1.95729	+	2.84733i	−0.0622696	+	0.0905858i
$989$	14.7936	−	35.7150i	0.470410	−	1.13567i
$990$	−5.21266	+	22.2356i	−0.165669	+	0.706693i
$991$	−23.5054			−0.746675			−0.373338	−	0.927696i	$-0.621787\pi$
$991$	−23.5054			−0.746675			−0.373338	+	0.927696i	$0.621787\pi$
$992$	12.3556	−	5.50944i	0.392291	−	0.174925i
$993$			4.76191i			0.151115i
$994$	−0.766869	+	3.27123i	−0.0243236	+	0.103757i
$995$	−15.6840	−	6.49652i	−0.497216	−	0.205954i
$996$	0.624815	+	1.85521i	0.0197980	+	0.0587846i
$997$	−24.1281	+	9.99417i	−0.764144	+	0.316519i	−0.730498	−	0.682915i	$-0.760712\pi$
$997$	−24.1281	+	9.99417i	−0.764144	+	0.316519i	−0.0336459	+	0.999434i	$0.510712\pi$
$998$	20.5728	−	28.6369i	0.651219	−	0.906484i
$999$	−4.69081	−	4.69081i	−0.148411	−	0.148411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.6	✓	216
13.12	even	2	inner	416.2.bg.a.77.49	yes	216
32.5	even	8	inner	416.2.bg.a.389.49	yes	216
416.389	even	8	inner	416.2.bg.a.389.6	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.6	✓	216	1.1	even	1	trivial
416.2.bg.a.77.49	yes	216	13.12	even	2	inner
416.2.bg.a.389.6	yes	216	416.389	even	8	inner
416.2.bg.a.389.49	yes	216	32.5	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37688 - 0.322781i) q^{2} +(0.0930705 - 0.224692i) q^{3} +(1.79162 + 0.888865i) q^{4} +(-0.454046 - 1.09616i) q^{5} +(-0.200674 + 0.279334i) q^{6} +(-0.425170 - 0.425170i) q^{7} +(-2.17995 - 1.80217i) q^{8} +(2.07950 + 2.07950i) q^{9} +(0.271348 + 1.65585i) q^{10} +(4.27595 - 1.77116i) q^{11} +(0.366469 - 0.319837i) q^{12} +(-3.49256 + 0.895567i) q^{13} +(0.448173 + 0.722647i) q^{14} -0.288558 q^{15} +(2.41984 + 3.18503i) q^{16} -6.57858i q^{17} +(-2.19200 - 3.53445i) q^{18} +(0.183362 - 0.442675i) q^{19} +(0.160862 - 2.36750i) q^{20} +(-0.135103 + 0.0559615i) q^{21} +(-6.45919 + 1.05848i) q^{22} +(3.23409 + 3.23409i) q^{23} +(-0.607822 + 0.322089i) q^{24} +(2.54012 - 2.54012i) q^{25} +(5.09792 - 0.105761i) q^{26} +(1.33486 - 0.552918i) q^{27} +(-0.383826 - 1.13966i) q^{28} +(0.844664 - 2.03920i) q^{29} +(0.397311 + 0.0931410i) q^{30} +2.39149i q^{31} +(-2.30377 - 5.16649i) q^{32} -1.12562i q^{33} +(-2.12344 + 9.05795i) q^{34} +(-0.273009 + 0.659102i) q^{35} +(1.87728 + 5.57407i) q^{36} +(-1.75704 - 4.24186i) q^{37} +(-0.395355 + 0.550326i) q^{38} +(-0.123827 + 0.868101i) q^{39} +(-0.985673 + 3.20785i) q^{40} +(3.69384 - 3.69384i) q^{41} +(0.204085 - 0.0334438i) q^{42} +(-3.23451 - 7.80879i) q^{43} +(9.23522 + 0.627497i) q^{44} +(1.33528 - 3.22365i) q^{45} +(-3.40907 - 5.49687i) q^{46} +9.76106 q^{47} +(0.940866 - 0.247286i) q^{48} -6.63846i q^{49} +(-4.31735 + 2.67755i) q^{50} +(-1.47816 - 0.612272i) q^{51} +(-7.05339 - 1.49989i) q^{52} +(-1.93465 - 4.67066i) q^{53} +(-2.01642 + 0.330436i) q^{54} +(-3.88296 - 3.88296i) q^{55} +(0.160622 + 1.69308i) q^{56} +(-0.0823999 - 0.0823999i) q^{57} +(-1.82122 + 2.53510i) q^{58} +(0.218556 + 0.527640i) q^{59} +(-0.516987 - 0.256489i) q^{60} +(-0.932946 + 2.25233i) q^{61} +(0.771927 - 3.29280i) q^{62} -1.76828i q^{63} +(1.50438 + 7.85728i) q^{64} +(2.56747 + 3.42179i) q^{65} +(-0.363328 + 1.54984i) q^{66} +(6.87260 + 2.84673i) q^{67} +(5.84747 - 11.7863i) q^{68} +(1.02767 - 0.425676i) q^{69} +(0.588648 - 0.819386i) q^{70} +(2.79396 + 2.79396i) q^{71} +(-0.785600 - 8.28080i) q^{72} +(-9.55168 + 9.55168i) q^{73} +(1.05004 + 6.40770i) q^{74} +(-0.334334 - 0.807154i) q^{75} +(0.721994 - 0.630123i) q^{76} +(-2.57105 - 1.06496i) q^{77} +(0.450703 - 1.15531i) q^{78} +13.1352i q^{79} +(2.39259 - 4.09869i) q^{80} +8.47116i q^{81} +(-6.27829 + 3.89369i) q^{82} +(-1.54014 + 3.71824i) q^{83} +(-0.291796 - 0.0198264i) q^{84} +(-7.21120 + 2.98698i) q^{85} +(1.93301 + 11.7958i) q^{86} +(-0.379579 - 0.379579i) q^{87} +(-12.5133 - 3.84495i) q^{88} +(-6.23303 - 6.23303i) q^{89} +(-2.87906 + 4.00760i) q^{90} +(1.86570 + 1.10416i) q^{91} +(2.91960 + 8.66894i) q^{92} +(0.537349 + 0.222577i) q^{93} +(-13.4399 - 3.15069i) q^{94} -0.568499 q^{95} +(-1.37528 + 0.0367910i) q^{96} +16.8065i q^{97} +(-2.14277 + 9.14040i) q^{98} +(12.5749 + 5.20871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

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