LMFDB - Embedded newform 357.2.bl.a.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(10,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 8, 9]))

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

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

chi := DirichletCharacter("357.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.79328 + 0.236090i) q^{2} +(0.442289 + 0.896873i) q^{3} +(1.22827 - 0.329115i) q^{4} +(0.723589 - 0.634571i) q^{5} +(-1.00489 - 1.50393i) q^{6} +(-2.30150 - 1.30502i) q^{7} +(1.21721 - 0.504184i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-1.14778 + 1.30880i) q^{10} +(2.35430 - 0.154309i) q^{11} +(0.838425 + 0.956041i) q^{12} +(-4.23736 - 4.23736i) q^{13} +(4.43535 + 1.79691i) q^{14} +(0.889164 + 0.368304i) q^{15} +(-4.26624 + 2.46312i) q^{16} +(-1.17306 - 3.95271i) q^{17} +(0.904379 - 1.56643i) q^{18} +(-0.426740 - 3.24141i) q^{19} +(0.679919 - 1.01757i) q^{20} +(0.152507 - 2.64135i) q^{21} +(-4.18550 + 0.832548i) q^{22} +(5.05716 + 2.49392i) q^{23} +(0.990545 + 0.868685i) q^{24} +(-0.531730 + 4.03889i) q^{25} +(8.59918 + 6.59838i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-3.25638 - 0.845461i) q^{28} +(-0.871966 - 4.38367i) q^{29} +(-1.68148 - 0.450550i) q^{30} +(7.42551 - 3.66186i) q^{31} +(4.97858 - 3.82020i) q^{32} +(1.17968 + 2.04326i) q^{33} +(3.03682 + 6.81138i) q^{34} +(-2.49347 + 0.516169i) q^{35} +(-0.486621 + 1.17481i) q^{36} +(0.411484 - 6.27804i) q^{37} +(1.53053 + 5.71202i) q^{38} +(1.92624 - 5.67451i) q^{39} +(0.560817 - 1.13723i) q^{40} +(1.15543 - 5.80875i) q^{41} +(0.350109 + 4.77270i) q^{42} +(-3.88360 - 9.37584i) q^{43} +(2.84094 - 0.964370i) q^{44} +(0.0629456 + 0.960364i) q^{45} +(-9.65772 - 3.27835i) q^{46} +(1.23309 - 4.60194i) q^{47} +(-4.09601 - 2.73687i) q^{48} +(3.59385 + 6.00702i) q^{49} -7.36840i q^{50} +(3.02625 - 2.80032i) q^{51} +(-6.59921 - 3.81006i) q^{52} +(8.42427 + 10.9787i) q^{53} +(1.80488 + 0.118298i) q^{54} +(1.60563 - 1.60563i) q^{55} +(-3.45938 - 0.428098i) q^{56} +(2.71839 - 1.81637i) q^{57} +(2.59862 + 7.65529i) q^{58} +(-7.27849 - 0.958232i) q^{59} +(1.21335 + 0.159741i) q^{60} +(3.48342 + 10.2618i) q^{61} +(-12.4515 + 8.31984i) q^{62} +(2.43641 - 1.03146i) q^{63} +(-1.05935 + 1.05935i) q^{64} +(-5.75501 - 0.377203i) q^{65} +(-2.59789 - 3.38564i) q^{66} +(-8.19595 - 4.73193i) q^{67} +(-2.74173 - 4.46894i) q^{68} +5.63867i q^{69} +(4.34964 - 1.51432i) q^{70} +(-1.68212 - 1.12396i) q^{71} +(-0.340993 + 1.27260i) q^{72} +(-0.793083 - 0.269215i) q^{73} +(0.744275 + 11.3554i) q^{74} +(-3.85755 + 1.30946i) q^{75} +(-1.59095 - 3.84089i) q^{76} +(-5.61982 - 2.71727i) q^{77} +(-2.11459 + 10.6308i) q^{78} +(-5.72381 + 11.6067i) q^{79} +(-1.52399 + 4.48952i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.700628 + 10.6895i) q^{82} +(1.35248 - 3.26517i) q^{83} +(-0.681988 - 3.29449i) q^{84} +(-3.35709 - 2.11575i) q^{85} +(9.17794 + 15.8967i) q^{86} +(3.54593 - 2.72089i) q^{87} +(2.78788 - 1.37483i) q^{88} +(4.20089 + 1.12562i) q^{89} +(-0.339612 - 1.70734i) q^{90} +(4.22246 + 15.2821i) q^{91} +(7.03237 + 1.39882i) q^{92} +(6.56844 + 5.04014i) q^{93} +(-1.12480 + 8.54371i) q^{94} +(-2.36569 - 2.07465i) q^{95} +(5.62821 + 2.77552i) q^{96} +(-14.5413 + 2.89245i) q^{97} +(-7.86298 - 9.92381i) q^{98} +(-1.31079 + 1.96173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.79328	+	0.236090i	−1.26804	+	0.166941i	−0.734369	−	0.678750i	$-0.762522\pi$
$2$	−1.79328	+	0.236090i	−1.26804	+	0.166941i	−0.533673	+	0.845691i	$0.679189\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	1.22827	−	0.329115i	0.614137	−	0.164557i
$5$	0.723589	−	0.634571i	0.323599	−	0.283789i	−0.482097	−	0.876118i	$-0.660125\pi$
$5$	0.723589	−	0.634571i	0.323599	−	0.283789i	0.805696	+	0.592329i	$0.201791\pi$
$6$	−1.00489	−	1.50393i	−0.410245	−	0.613975i
$7$	−2.30150	−	1.30502i	−0.869887	−	0.493251i
$7$	−2.30150	−	1.30502i	−0.869887	−	0.493251i
$8$	1.21721	−	0.504184i	0.430348	−	0.178256i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−1.14778	+	1.30880i	−0.362961	+	0.413878i
$11$	2.35430	−	0.154309i	0.709850	−	0.0465260i	0.293799	−	0.955867i	$-0.405080\pi$
$11$	2.35430	−	0.154309i	0.709850	−	0.0465260i	0.416051	+	0.909341i	$0.363414\pi$
$12$	0.838425	+	0.956041i	0.242033	+	0.275985i
$13$	−4.23736	−	4.23736i	−1.17523	−	1.17523i	−0.980945	−	0.194287i	$-0.937761\pi$
$13$	−4.23736	−	4.23736i	−1.17523	−	1.17523i	−0.194287	−	0.980945i	$-0.562239\pi$
$14$	4.43535	+	1.79691i	1.18540	+	0.480244i
$15$	0.889164	+	0.368304i	0.229581	+	0.0950957i
$16$	−4.26624	+	2.46312i	−1.06656	+	0.615779i
$17$	−1.17306	−	3.95271i	−0.284508	−	0.958674i
$17$	−1.17306	−	3.95271i	−0.284508	−	0.958674i
$18$	0.904379	−	1.56643i	0.213164	−	0.369211i
$19$	−0.426740	−	3.24141i	−0.0979008	−	0.743630i	−0.968035	−	0.250815i	$-0.919301\pi$
$19$	−0.426740	−	3.24141i	−0.0979008	−	0.743630i	0.870134	−	0.492815i	$-0.164032\pi$
$20$	0.679919	−	1.01757i	0.152034	−	0.227536i
$21$	0.152507	−	2.64135i	0.0332798	−	0.576390i
$22$	−4.18550	+	0.832548i	−0.892352	+	0.177500i
$23$	5.05716	+	2.49392i	1.05449	+	0.520018i	0.885037	−	0.465520i	$-0.154133\pi$
$23$	5.05716	+	2.49392i	1.05449	+	0.520018i	0.169455	+	0.985538i	$0.445799\pi$
$24$	0.990545	+	0.868685i	0.202194	+	0.177320i
$25$	−0.531730	+	4.03889i	−0.106346	+	0.807777i
$26$	8.59918	+	6.59838i	1.68644	+	1.29405i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−3.25638	−	0.845461i	−0.615398	−	0.159777i
$29$	−0.871966	−	4.38367i	−0.161920	−	0.814027i	−0.973305	−	0.229515i	$-0.926286\pi$
$29$	−0.871966	−	4.38367i	−0.161920	−	0.814027i	0.811385	−	0.584512i	$-0.198714\pi$
$30$	−1.68148	−	0.450550i	−0.306994	−	0.0822588i
$31$	7.42551	−	3.66186i	1.33366	−	0.657689i	0.371060	−	0.928609i	$-0.378995\pi$
$31$	7.42551	−	3.66186i	1.33366	−	0.657689i	0.962602	+	0.270920i	$0.0873279\pi$
$32$	4.97858	−	3.82020i	0.880098	−	0.675323i
$33$	1.17968	+	2.04326i	0.205356	+	0.355686i
$34$	3.03682	+	6.81138i	0.520810	+	1.16814i
$35$	−2.49347	+	0.516169i	−0.421474	+	0.0872485i
$36$	−0.486621	+	1.17481i	−0.0811035	+	0.195801i
$37$	0.411484	−	6.27804i	0.0676476	−	1.03210i	−0.820233	−	0.572029i	$-0.806156\pi$
$37$	0.411484	−	6.27804i	0.0676476	−	1.03210i	0.887881	−	0.460073i	$-0.152177\pi$
$38$	1.53053	+	5.71202i	0.248285	+	0.926611i
$39$	1.92624	−	5.67451i	0.308444	−	0.908648i
$40$	0.560817	−	1.13723i	0.0886730	−	0.179811i
$41$	1.15543	−	5.80875i	0.180448	−	0.907174i	−0.779373	−	0.626561i	$-0.784462\pi$
$41$	1.15543	−	5.80875i	0.180448	−	0.907174i	0.959821	−	0.280613i	$-0.0905379\pi$
$42$	0.350109	+	4.77270i	0.0540230	+	0.736443i
$43$	−3.88360	−	9.37584i	−0.592243	−	1.42980i	−0.881331	−	0.472499i	$-0.843352\pi$
$43$	−3.88360	−	9.37584i	−0.592243	−	1.42980i	0.289088	−	0.957303i	$-0.406648\pi$
$44$	2.84094	−	0.964370i	0.428288	−	0.145384i
$45$	0.0629456	+	0.960364i	0.00938337	+	0.143163i
$46$	−9.65772	−	3.27835i	−1.42395	−	0.483367i
$47$	1.23309	−	4.60194i	0.179864	−	0.671263i	−0.815808	−	0.578324i	$-0.803707\pi$
$47$	1.23309	−	4.60194i	0.179864	−	0.671263i	0.995672	−	0.0929391i	$-0.0296262\pi$
$48$	−4.09601	−	2.73687i	−0.591208	−	0.395033i
$49$	3.59385	+	6.00702i	0.513407	+	0.858145i
$50$		−	7.36840i		−	1.04205i
$51$	3.02625	−	2.80032i	0.423760	−	0.392124i
$52$	−6.59921	−	3.81006i	−0.915146	−	0.528360i
$53$	8.42427	+	10.9787i	1.15716	+	1.50804i	0.825281	+	0.564722i	$0.191016\pi$
$53$	8.42427	+	10.9787i	1.15716	+	1.50804i	0.331881	+	0.943321i	$0.392317\pi$
$54$	1.80488	+	0.118298i	0.245614	+	0.0160984i
$55$	1.60563	−	1.60563i	0.216503	−	0.216503i
$56$	−3.45938	−	0.428098i	−0.462279	−	0.0572070i
$57$	2.71839	−	1.81637i	0.360060	−	0.240584i
$58$	2.59862	+	7.65529i	0.341216	+	1.00519i
$59$	−7.27849	−	0.958232i	−0.947579	−	0.124751i	−0.359132	−	0.933287i	$-0.616927\pi$
$59$	−7.27849	−	0.958232i	−0.947579	−	0.124751i	−0.588447	+	0.808536i	$0.700261\pi$
$60$	1.21335	+	0.159741i	0.156643	+	0.0206224i
$61$	3.48342	+	10.2618i	0.446006	+	1.31389i	0.904985	+	0.425444i	$0.139882\pi$
$61$	3.48342	+	10.2618i	0.446006	+	1.31389i	−0.458979	+	0.888447i	$0.651785\pi$
$62$	−12.4515	+	8.31984i	−1.58134	+	1.05662i
$63$	2.43641	−	1.03146i	0.306959	−	0.129952i
$64$	−1.05935	+	1.05935i	−0.132419	+	0.132419i
$65$	−5.75501	−	0.377203i	−0.713821	−	0.0467863i
$66$	−2.59789	−	3.38564i	−0.319778	−	0.416743i
$67$	−8.19595	−	4.73193i	−1.00129	−	0.578098i	−0.0926634	−	0.995697i	$-0.529538\pi$
$67$	−8.19595	−	4.73193i	−1.00129	−	0.578098i	−0.908631	+	0.417600i	$0.862871\pi$
$68$	−2.74173	−	4.46894i	−0.332484	−	0.541939i
$69$			5.63867i			0.678815i
$70$	4.34964	−	1.51432i	0.519881	−	0.180996i
$71$	−1.68212	−	1.12396i	−0.199631	−	0.133389i	0.451737	−	0.892151i	$-0.350805\pi$
$71$	−1.68212	−	1.12396i	−0.199631	−	0.133389i	−0.651368	+	0.758762i	$0.725805\pi$
$72$	−0.340993	+	1.27260i	−0.0401864	+	0.149978i
$73$	−0.793083	−	0.269215i	−0.0928233	−	0.0315093i	0.274641	−	0.961547i	$-0.411441\pi$
$73$	−0.793083	−	0.269215i	−0.0928233	−	0.0315093i	−0.367465	+	0.930037i	$0.619774\pi$
$74$	0.744275	+	11.3554i	0.0865202	+	1.32004i
$75$	−3.85755	+	1.30946i	−0.445431	+	0.151203i
$76$	−1.59095	−	3.84089i	−0.182494	−	0.440580i
$77$	−5.61982	−	2.71727i	−0.640438	−	0.309662i
$78$	−2.11459	+	10.6308i	−0.239430	+	1.20370i
$79$	−5.72381	+	11.6067i	−0.643979	+	1.30586i	0.292880	+	0.956149i	$0.405387\pi$
$79$	−5.72381	+	11.6067i	−0.643979	+	1.30586i	−0.936858	+	0.349710i	$0.886280\pi$
$80$	−1.52399	+	4.48952i	−0.170387	+	0.501943i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.700628	+	10.6895i	−0.0773714	+	1.18046i
$83$	1.35248	−	3.26517i	0.148454	−	0.358399i	−0.832107	−	0.554615i	$-0.812865\pi$
$83$	1.35248	−	3.26517i	0.148454	−	0.358399i	0.980561	+	0.196216i	$0.0628654\pi$
$84$	−0.681988	−	3.29449i	−0.0744110	−	0.359459i
$85$	−3.35709	−	2.11575i	−0.364127	−	0.229486i
$86$	9.17794	+	15.8967i	0.989682	+	1.71418i
$87$	3.54593	−	2.72089i	0.380164	−	0.291710i
$88$	2.78788	−	1.37483i	0.297188	−	0.146557i
$89$	4.20089	+	1.12562i	0.445293	+	0.119316i	0.474496	−	0.880258i	$-0.342630\pi$
$89$	4.20089	+	1.12562i	0.445293	+	0.119316i	−0.0292030	+	0.999574i	$0.509297\pi$
$90$	−0.339612	−	1.70734i	−0.0357982	−	0.179970i
$91$	4.22246	+	15.2821i	0.442634	+	1.60200i
$92$	7.03237	+	1.39882i	0.733175	+	0.145838i
$93$	6.56844	+	5.04014i	0.681116	+	0.522638i
$94$	−1.12480	+	8.54371i	−0.116014	+	0.881216i
$95$	−2.36569	−	2.07465i	−0.242714	−	0.212855i
$96$	5.62821	+	2.77552i	0.574426	+	0.283276i
$97$	−14.5413	+	2.89245i	−1.47645	+	0.293684i	−0.866668	−	0.498886i	$-0.833743\pi$
$97$	−14.5413	+	2.89245i	−1.47645	+	0.293684i	−0.609781	+	0.792570i	$0.708743\pi$
$98$	−7.86298	−	9.92381i	−0.794281	−	1.00246i
$99$	−1.31079	+	1.96173i	−0.131739	+	0.197162i
$100$	0.676148	+	5.13586i	0.0676148	+	0.513586i
$101$	−7.73464	+	13.3968i	−0.769626	+	1.33303i	0.168140	+	0.985763i	$0.446224\pi$
$101$	−7.73464	+	13.3968i	−0.769626	+	1.33303i	−0.937766	+	0.347268i	$0.887109\pi$
$102$	−4.76579	+	5.73624i	−0.471884	+	0.567972i
$103$	13.4872	−	7.78685i	1.32894	−	0.767261i	0.343800	−	0.939043i	$-0.388286\pi$
$103$	13.4872	−	7.78685i	1.32894	−	0.767261i	0.985135	+	0.171782i	$0.0549524\pi$
$104$	−7.29415	−	3.02133i	−0.715250	−	0.296266i
$105$	−1.56577	−	2.00803i	−0.152804	−	0.195964i
$106$	−17.6991	−	17.6991i	−1.71908	−	1.71908i
$107$	−7.75115	−	8.83849i	−0.749332	−	0.854449i	0.243996	−	0.969776i	$-0.421542\pi$
$107$	−7.75115	−	8.83849i	−0.749332	−	0.854449i	−0.993328	+	0.115327i	$0.963208\pi$
$108$	−1.26888	+	0.0831667i	−0.122098	+	0.00800272i
$109$	−2.69904	+	3.07767i	−0.258521	+	0.294787i	−0.866511	−	0.499158i	$-0.833643\pi$
$109$	−2.69904	+	3.07767i	−0.258521	+	0.294787i	0.607990	+	0.793945i	$0.291976\pi$
$110$	−2.50027	+	3.25842i	−0.238392	+	0.310678i
$111$	5.81259	−	2.40766i	0.551707	−	0.228525i
$112$	13.0332	−	0.101343i	1.23152	−	0.00957602i
$113$	−3.46905	−	5.19180i	−0.326341	−	0.488404i	0.631630	−	0.775270i	$-0.282386\pi$
$113$	−3.46905	−	5.19180i	−0.326341	−	0.488404i	−0.957971	+	0.286867i	$0.907386\pi$
$114$	−4.44602	+	3.89905i	−0.416407	+	0.365180i
$115$	5.24188	−	1.40456i	0.488808	−	0.130976i
$116$	−2.51374	−	5.09737i	−0.233395	−	0.473278i
$117$	5.94126	−	0.782182i	0.549270	−	0.0723127i
$118$	13.2786			1.22240
$119$	−2.45857	+	10.6280i	−0.225377	+	0.974272i
$120$	1.26799			0.115751
$121$	−5.38695	+	0.709206i	−0.489723	+	0.0644733i
$122$	−8.66946	−	17.5799i	−0.784896	−	1.59161i
$123$	5.72074	−	1.53287i	0.515822	−	0.138214i
$124$	7.91539	−	6.94161i	0.710823	−	0.623375i
$125$	4.85168	+	7.26105i	0.433947	+	0.649448i
$126$	−4.12565	+	2.42491i	−0.367542	+	0.216028i
$127$	−0.810646	+	0.335780i	−0.0719332	+	0.0297957i	−0.418360	−	0.908281i	$-0.637395\pi$
$127$	−0.810646	+	0.335780i	−0.0719332	+	0.0297957i	0.346427	+	0.938077i	$0.387395\pi$
$128$	−5.99079	+	7.80735i	−0.529516	+	0.690078i
$129$	6.69126	−	7.62992i	0.589133	−	0.671777i
$130$	10.4094	−	0.682269i	0.912966	−	0.0598389i
$131$	0.632528	+	0.721260i	0.0552642	+	0.0630168i	0.778811	−	0.627258i	$-0.215823\pi$
$131$	0.632528	+	0.721260i	0.0552642	+	0.0630168i	−0.723547	+	0.690275i	$0.757490\pi$
$132$	2.12143	+	2.12143i	0.184647	+	0.184647i
$133$	−3.24796	+	8.01702i	−0.281634	+	0.695164i
$134$	15.8148	+	6.55071i	1.36619	+	0.565895i
$135$	−0.833484	+	0.481212i	−0.0717349	+	0.0414162i
$136$	−3.42075	−	4.21983i	−0.293327	−	0.361848i
$137$	−1.50551	+	2.60762i	−0.128624	+	0.222784i	−0.923144	−	0.384455i	$-0.874389\pi$
$137$	−1.50551	+	2.60762i	−0.128624	+	0.222784i	0.794520	+	0.607239i	$0.207723\pi$
$138$	−1.33123	−	10.1117i	−0.113322	−	0.860767i
$139$	9.80727	−	14.6776i	0.831841	−	1.24494i	−0.135327	−	0.990801i	$-0.543208\pi$
$139$	9.80727	−	14.6776i	0.831841	−	1.24494i	0.967168	−	0.254138i	$-0.0817916\pi$
$140$	−2.89278	+	1.45464i	−0.244485	+	0.122939i
$141$	4.67274	−	0.929466i	0.393516	−	0.0782751i
$142$	3.28188	+	1.61844i	0.275409	+	0.135817i
$143$	−10.6299	−	9.32217i	−0.888916	−	0.779559i
$144$	0.643002	−	4.88409i	0.0535835	−	0.407007i
$145$	−3.41269	−	2.61865i	−0.283409	−	0.217467i
$146$	1.48578	+	0.295540i	0.122964	+	0.0244591i
$147$	−3.79801	+	5.88006i	−0.313255	+	0.484979i
$148$	−1.56078	−	7.84657i	−0.128295	−	0.644984i
$149$	14.0111	+	3.75426i	1.14783	+	0.307561i	0.782096	−	0.623158i	$-0.214151\pi$
$149$	14.0111	+	3.75426i	1.14783	+	0.307561i	0.365736	+	0.930719i	$0.380817\pi$
$150$	6.60852	−	3.25896i	0.539583	−	0.266093i
$151$	−5.46454	+	4.19309i	−0.444698	+	0.341229i	−0.806713	−	0.590943i	$-0.798756\pi$
$151$	−5.46454	+	4.19309i	−0.444698	+	0.341229i	0.362015	+	0.932172i	$0.382089\pi$
$152$	−2.15370	−	3.73031i	−0.174688	−	0.302568i
$153$	3.85001	+	1.47561i	0.311255	+	0.119296i
$154$	10.7194	+	3.54605i	0.863798	+	0.285749i
$155$	3.04931	−	7.36169i	0.244927	−	0.591305i
$156$	0.498379	−	7.60380i	0.0399023	−	0.608791i
$157$	−1.82049	−	6.79415i	−0.145291	−	0.542233i	−0.999742	−	0.0227014i	$-0.992773\pi$
$157$	−1.82049	−	6.79415i	−0.145291	−	0.542233i	0.854452	−	0.519531i	$-0.173893\pi$
$158$	7.52417	−	22.1655i	0.598591	−	1.76339i
$159$	−6.12056	+	12.4113i	−0.485392	+	0.984277i
$160$	1.17826	−	5.92352i	0.0931497	−	0.468295i
$161$	−8.38448	−	12.3395i	−0.660789	−	0.972486i
$162$	0.692181	+	1.67107i	0.0543829	+	0.131292i
$163$	−2.63440	+	0.894258i	−0.206342	+	0.0700437i	−0.422697	−	0.906271i	$-0.638917\pi$
$163$	−2.63440	+	0.894258i	−0.206342	+	0.0700437i	0.216355	+	0.976315i	$0.430583\pi$
$164$	−0.492559	−	7.51500i	−0.0384624	−	0.586823i
$165$	2.15020	+	0.729893i	0.167393	+	0.0568221i
$166$	−1.65450	+	6.17469i	−0.128414	+	0.479249i
$167$	11.1522	+	7.45169i	0.862987	+	0.576629i	0.906397	−	0.422428i	$-0.138822\pi$
$167$	11.1522	+	7.45169i	0.862987	+	0.576629i	−0.0434096	+	0.999057i	$0.513822\pi$
$168$	−1.14609	−	3.29196i	−0.0884230	−	0.253980i
$169$			22.9104i			1.76234i
$170$	6.51971	+	3.00157i	0.500039	+	0.230210i
$171$	2.83137	+	1.63469i	0.216520	+	0.125008i
$172$	−7.85585	−	10.2379i	−0.599003	−	0.780636i
$173$	1.31999	+	0.0865168i	0.100357	+	0.00657775i	0.115499	−	0.993308i	$-0.463153\pi$
$173$	1.31999	+	0.0865168i	0.100357	+	0.00657775i	−0.0151419	+	0.999885i	$0.504820\pi$
$174$	−5.71648	+	5.71648i	−0.433365	+	0.433365i
$175$	6.49461	−	8.60160i	0.490946	−	0.650220i
$176$	−9.66395	+	6.45725i	−0.728448	+	0.486733i
$177$	−2.35978	−	6.95170i	−0.177372	−	0.522522i
$178$	−7.79913	−	1.02677i	−0.584569	−	0.0769600i
$179$	12.6872	+	1.67030i	0.948285	+	0.124844i	0.588775	−	0.808297i	$-0.299610\pi$
$179$	12.6872	+	1.67030i	0.948285	+	0.124844i	0.359510	+	0.933141i	$0.382944\pi$
$180$	0.393384	+	1.15887i	0.0293211	+	0.0863773i
$181$	3.43135	−	2.29276i	0.255050	−	0.170419i	−0.421472	−	0.906842i	$-0.638486\pi$
$181$	3.43135	−	2.29276i	0.255050	−	0.170419i	0.676522	+	0.736422i	$0.263486\pi$
$182$	−11.1800	−	26.4083i	−0.828719	−	1.95751i
$183$	−7.66286	+	7.66286i	−0.566455	+	0.566455i
$184$	7.41301	+	0.485874i	0.546494	+	0.0358191i
$185$	−3.68611	−	4.80383i	−0.271008	−	0.353185i
$186$	−12.9690	−	7.48766i	−0.950933	−	0.549022i
$187$	−3.37167	−	9.12488i	−0.246561	−	0.667277i
$188$		−	6.05827i		−	0.441845i
$189$	2.00269	+	1.72895i	0.145674	+	0.125762i
$190$	4.73215	+	3.16192i	0.343306	+	0.229390i
$191$	4.01400	−	14.9805i	0.290443	−	1.08395i	−0.654326	−	0.756212i	$-0.727048\pi$
$191$	4.01400	−	14.9805i	0.290443	−	1.08395i	0.944769	−	0.327736i	$-0.106286\pi$
$192$	−1.41864	−	0.481565i	−0.102382	−	0.0347539i
$193$	−0.241772	−	3.68873i	−0.0174031	−	0.265521i	−0.997689	−	0.0679387i	$-0.978358\pi$
$193$	−0.241772	−	3.68873i	−0.0174031	−	0.265521i	0.980286	−	0.197582i	$-0.0633089\pi$
$194$	25.3939	−	8.62005i	1.82317	−	0.618884i
$195$	−2.20707	−	5.32834i	−0.158052	−	0.381571i
$196$	6.39122	+	6.19547i	0.456516	+	0.442534i
$197$	−1.73393	+	8.71708i	−0.123538	+	0.621066i	0.868559	+	0.495587i	$0.165047\pi$
$197$	−1.73393	+	8.71708i	−0.123538	+	0.621066i	−0.992096	+	0.125479i	$0.959953\pi$
$198$	1.88747	−	3.82741i	0.134136	−	0.272002i
$199$	2.54566	−	7.49927i	0.180457	−	0.531609i	−0.818630	−	0.574321i	$-0.805266\pi$
$199$	2.54566	−	7.49927i	0.180457	−	0.531609i	0.999087	+	0.0427114i	$0.0135996\pi$
$200$	1.38912	+	5.18425i	0.0982253	+	0.366582i
$201$	0.618966	−	9.44360i	0.0436585	−	0.666100i
$202$	10.7076	−	25.8503i	0.753381	−	1.81882i
$203$	−3.71394	+	11.2270i	−0.260667	+	0.787978i
$204$	2.79543	−	4.43555i	0.195720	−	0.310550i
$205$	−2.85000	−	4.93635i	−0.199053	−	0.344770i
$206$	−22.3480	+	17.1482i	−1.55706	+	1.19477i
$207$	−5.05716	+	2.49392i	−0.351497	+	0.173339i
$208$	28.5147	+	7.64049i	1.97714	+	0.529773i
$209$	−1.50485	−	7.56542i	−0.104093	−	0.523311i
$210$	3.28195	+	3.23130i	0.226476	+	0.222981i
$211$	10.5861	+	2.10571i	0.728777	+	0.144963i	0.545515	−	0.838101i	$-0.316334\pi$
$211$	10.5861	+	2.10571i	0.728777	+	0.144963i	0.183262	+	0.983064i	$0.441334\pi$
$212$	13.9606	+	10.7123i	0.958815	+	0.735725i
$213$	0.264064	−	2.00577i	0.0180934	−	0.137433i
$214$	15.9867	+	14.0199i	1.09283	+	0.958383i
$215$	−8.75976	−	4.31984i	−0.597411	−	0.294610i
$216$	−1.29218	+	0.257031i	−0.0879217	+	0.0174887i
$217$	−21.8686	−	1.26266i	−1.48454	−	0.0857148i
$218$	4.11354	−	6.15634i	0.278604	−	0.416960i
$219$	−0.109320	−	0.830365i	−0.00738714	−	0.0561109i
$220$	1.44371	−	2.50059i	0.0973352	−	0.168590i
$221$	−11.7784	+	21.7197i	−0.792300	+	1.46103i
$222$	−9.85520	+	5.68990i	−0.661438	+	0.381881i
$223$	9.09156	+	3.76585i	0.608816	+	0.252180i	0.665722	−	0.746200i	$-0.268124\pi$
$223$	9.09156	+	3.76585i	0.608816	+	0.252180i	−0.0569064	+	0.998380i	$0.518124\pi$
$224$	−16.4437	+	2.29506i	−1.09869	+	0.153345i
$225$	−2.88057	−	2.88057i	−0.192038	−	0.192038i
$226$	7.44672	+	8.49136i	0.495349	+	0.564837i
$227$	10.5342	−	0.690447i	0.699178	−	0.0458266i	0.288331	−	0.957531i	$-0.406900\pi$
$227$	10.5342	−	0.690447i	0.699178	−	0.0458266i	0.410847	+	0.911704i	$0.365233\pi$
$228$	2.74113	−	3.12566i	0.181536	−	0.207002i
$229$	2.92359	−	3.81010i	0.193196	−	0.251778i	−0.686704	−	0.726938i	$-0.740943\pi$
$229$	2.92359	−	3.81010i	0.193196	−	0.251778i	0.879900	+	0.475159i	$0.157610\pi$
$230$	−9.06857	+	3.75632i	−0.597964	+	0.247685i
$231$	−0.0485370	−	6.24208i	−0.00319350	−	0.410699i
$232$	−3.27154	−	4.89620i	−0.214787	−	0.321451i
$233$	−2.29993	+	2.01698i	−0.150673	+	0.132137i	−0.731364	−	0.681987i	$-0.761116\pi$
$233$	−2.29993	+	2.01698i	−0.150673	+	0.132137i	0.580691	+	0.814124i	$0.302783\pi$
$234$	−10.4697	+	2.80535i	−0.684425	+	0.183391i
$235$	−2.02801	−	4.11240i	−0.132293	−	0.268263i
$236$	−9.25535	+	1.21849i	−0.602472	+	0.0793169i
$237$	−12.9413			−0.840630
$238$	1.89973	−	19.6395i	0.123142	−	1.27304i
$239$	14.7081			0.951390			0.475695	−	0.879610i	$-0.342197\pi$
$239$	14.7081			0.951390			0.475695	+	0.879610i	$0.342197\pi$
$240$	−4.70057	+	0.618841i	−0.303420	+	0.0399460i
$241$	2.79146	+	5.66053i	0.179814	+	0.364627i	0.968054	−	0.250741i	$-0.0806742\pi$
$241$	2.79146	+	5.66053i	0.179814	+	0.364627i	−0.788240	+	0.615368i	$0.789008\pi$
$242$	9.49290	−	2.54361i	0.610227	−	0.163510i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	7.65590	+	11.4579i	0.490119	+	0.733515i
$245$	6.41235	+	2.06606i	0.409670	+	0.131996i
$246$	−9.89701	+	4.09948i	−0.631010	+	0.261373i
$247$	−11.9268	+	15.5433i	−0.758882	+	0.988994i
$248$	7.19214	−	8.20106i	0.456701	−	0.520768i
$249$	3.52663	−	0.231148i	0.223491	−	0.0146484i
$250$	−10.4147	−	11.8757i	−0.658683	−	0.751084i
$251$	−2.29036	−	2.29036i	−0.144567	−	0.144567i	0.631119	−	0.775686i	$-0.282596\pi$
$251$	−2.29036	−	2.29036i	−0.144567	−	0.144567i	−0.775686	+	0.631119i	$0.782596\pi$
$252$	2.65311	−	2.06877i	0.167130	−	0.130321i
$253$	12.2909	+	5.09107i	0.772725	+	0.320073i
$254$	1.37444	−	0.793535i	0.0862402	−	0.0497908i
$255$	0.412759	−	3.94665i	0.0258480	−	0.247149i
$256$	10.3981	−	18.0100i	0.649881	−	1.12563i
$257$	−2.18077	−	16.5646i	−0.136032	−	1.03327i	−0.914215	−	0.405230i	$-0.867191\pi$
$257$	−2.18077	−	16.5646i	−0.136032	−	1.03327i	0.778182	−	0.628039i	$-0.216142\pi$
$258$	−10.1980	+	15.2624i	−0.634898	+	0.950192i
$259$	−9.13999	+	13.9119i	−0.567931	+	0.864445i
$260$	−7.19287	+	1.43075i	−0.446083	+	0.0887313i
$261$	4.00862	+	1.97683i	0.248127	+	0.122363i
$262$	−1.30458	−	1.14409i	−0.0805975	−	0.0706821i
$263$	−3.89596	+	29.5928i	−0.240235	+	1.82477i	0.267848	+	0.963461i	$0.413688\pi$
$263$	−3.89596	+	29.5928i	−0.240235	+	1.82477i	−0.508083	+	0.861308i	$0.669646\pi$
$264$	2.46609	+	1.89230i	0.151777	+	0.116463i
$265$	13.0625	+	2.59829i	0.802422	+	0.159612i
$266$	3.93177	−	15.1436i	0.241072	−	0.928514i
$267$	0.848463	+	4.26551i	0.0519251	+	0.261045i
$268$	−11.6242	−	3.11470i	−0.710062	−	0.190260i
$269$	−7.94113	+	3.91613i	−0.484179	+	0.238771i	−0.667961	−	0.744196i	$-0.732833\pi$
$269$	−7.94113	+	3.91613i	−0.484179	+	0.238771i	0.183782	+	0.982967i	$0.441166\pi$
$270$	1.38106	−	1.05973i	0.0840488	−	0.0644929i
$271$	−7.86366	−	13.6203i	−0.477683	−	0.827372i	0.521989	−	0.852952i	$-0.325190\pi$
$271$	−7.86366	−	13.6203i	−0.477683	−	0.827372i	−0.999673	+	0.0255800i	$0.991857\pi$
$272$	14.7405	+	13.9739i	0.893776	+	0.847289i
$273$	−11.8386	+	10.5461i	−0.716503	+	0.638281i
$274$	2.08417	−	5.03163i	0.125909	−	0.303972i
$275$	−0.628616	+	9.59082i	−0.0379070	+	0.578348i
$276$	1.85577	+	6.92582i	0.111704	+	0.416885i
$277$	−0.471997	+	1.39046i	−0.0283596	+	0.0835446i	−0.960188	−	0.279354i	$-0.909880\pi$
$277$	−0.471997	+	1.39046i	−0.0283596	+	0.0835446i	0.931829	+	0.362899i	$0.118213\pi$
$278$	−14.1220	+	28.6365i	−0.846979	+	1.71750i
$279$	−1.61522	+	8.12025i	−0.0967006	+	0.486147i
$280$	−2.77483	+	1.88545i	−0.165828	+	0.112677i
$281$	12.1660	+	29.3712i	0.725760	+	1.75214i	0.656232	+	0.754559i	$0.272149\pi$
$281$	12.1660	+	29.3712i	0.725760	+	1.75214i	0.0695281	+	0.997580i	$0.477851\pi$
$282$	−8.16011	+	2.76998i	−0.485927	+	0.164950i
$283$	1.51308	+	23.0852i	0.0899433	+	1.37227i	0.769500	+	0.638647i	$0.220506\pi$
$283$	1.51308	+	23.0852i	0.0899433	+	1.37227i	−0.679557	+	0.733623i	$0.737828\pi$
$284$	−2.43602	−	0.826918i	−0.144551	−	0.0490685i
$285$	0.814382	−	3.03932i	0.0482398	−	0.180034i
$286$	21.2633	+	14.2077i	1.25732	+	0.840117i
$287$	−10.2398	+	11.8610i	−0.604434	+	0.700133i
$288$			6.27537i			0.369780i
$289$	−14.2479	+	9.27352i	−0.838110	+	0.545501i
$290$	6.73816	+	3.89028i	0.395678	+	0.228445i
$291$	−9.02563	−	11.7624i	−0.529092	−	0.689526i
$292$	−1.06273	−	0.0696547i	−0.0621913	−	0.00407623i
$293$	8.74129	−	8.74129i	0.510671	−	0.510671i	−0.404061	−	0.914732i	$-0.632402\pi$
$293$	8.74129	−	8.74129i	0.510671	−	0.510671i	0.914732	+	0.404061i	$0.132402\pi$
$294$	5.42269	−	11.4413i	0.316257	−	0.667269i
$295$	−5.87470	+	3.92535i	−0.342039	+	0.228543i
$296$	−2.66442	−	7.84913i	−0.154866	−	0.456221i
$297$	−2.33917	−	0.307958i	−0.135732	−	0.0178695i
$298$	−26.0122	−	3.42457i	−1.50684	−	0.198380i
$299$	−10.8614	−	31.9966i	−0.628131	−	1.85041i
$300$	−4.30716	+	2.87795i	−0.248674	+	0.166159i
$301$	−3.29753	+	26.6467i	−0.190067	+	1.53589i
$302$	8.80953	−	8.80953i	0.506931	−	0.506931i
$303$	−15.4362	−	1.01174i	−0.886785	−	0.0581229i
$304$	9.80454	+	12.7775i	0.562329	+	0.732842i
$305$	9.03241	+	5.21486i	0.517194	+	0.298602i
$306$	−7.25253	−	1.73724i	−0.414600	−	0.0993112i
$307$		−	13.9139i		−	0.794106i	−0.917796	−	0.397053i	$-0.870033\pi$
$307$		−	13.9139i		−	0.794106i	0.917796	−	0.397053i	$-0.129967\pi$
$308$	−7.79697	−	1.48798i	−0.444273	−	0.0847858i
$309$	12.9491	+	8.65228i	0.736646	+	0.492211i
$310$	−3.73026	+	13.9215i	−0.211864	+	0.790689i
$311$	13.1175	+	4.45280i	0.743827	+	0.252495i	0.667523	−	0.744589i	$-0.267355\pi$
$311$	13.1175	+	4.45280i	0.743827	+	0.252495i	0.0763044	+	0.997085i	$0.475688\pi$
$312$	−0.516366	−	7.87822i	−0.0292335	−	0.446016i
$313$	−29.5492	+	10.0306i	−1.67022	+	0.566962i	−0.986640	−	0.162915i	$-0.947910\pi$
$313$	−29.5492	+	10.0306i	−1.67022	+	0.566962i	−0.683578	+	0.729878i	$0.739577\pi$
$314$	4.86868	+	11.7540i	0.274756	+	0.663319i
$315$	1.10842	−	2.29243i	0.0624526	−	0.129164i
$316$	−3.21045	+	16.1400i	−0.180602	+	0.907947i
$317$	11.3103	−	22.9351i	0.635251	−	1.28816i	−0.306507	−	0.951868i	$-0.599160\pi$
$317$	11.3103	−	22.9351i	0.635251	−	1.28816i	0.941758	−	0.336292i	$-0.109173\pi$
$318$	8.04571	−	23.7019i	0.451181	−	1.32914i
$319$	−2.72931	−	10.1859i	−0.152812	−	0.570303i
$320$	−0.0943019	+	1.43877i	−0.00527164	+	0.0804297i
$321$	4.49876	−	10.8610i	0.251096	−	0.606199i
$322$	17.9490	+	20.1487i	1.00026	+	1.12284i
$323$	−12.3118	+	5.48914i	−0.685045	+	0.305424i
$324$	−0.635801	−	1.10124i	−0.0353223	−	0.0611800i
$325$	19.3673	−	14.8611i	1.07431	−	0.824344i
$326$	4.51310	−	2.22561i	0.249957	−	0.123265i
$327$	−3.95403	−	1.05948i	−0.218658	−	0.0585893i
$328$	−1.52228	−	7.65300i	−0.0840536	−	0.422566i
$329$	−8.84359	+	8.98219i	−0.487563	+	0.495204i
$330$	−4.02823	−	0.801265i	−0.221747	−	0.0441082i
$331$	5.82306	+	4.46819i	0.320064	+	0.245594i	0.756280	−	0.654248i	$-0.227015\pi$
$331$	5.82306	+	4.46819i	0.320064	+	0.245594i	−0.436216	+	0.899842i	$0.643681\pi$
$332$	0.586597	−	4.45565i	0.0321937	−	0.244535i
$333$	4.73020	+	4.14828i	0.259214	+	0.227324i
$334$	−21.7584	−	10.7301i	−1.19057	−	0.587123i
$335$	−8.93324	+	1.77693i	−0.488075	+	0.0970842i
$336$	5.85533	+	11.6443i	0.319434	+	0.635248i
$337$	−7.90873	+	11.8362i	−0.430816	+	0.644762i	−0.981836	−	0.189730i	$-0.939239\pi$
$337$	−7.90873	+	11.8362i	−0.430816	+	0.644762i	0.551020	+	0.834492i	$0.314239\pi$
$338$	−5.40892	−	41.0848i	−0.294206	−	2.23472i
$339$	3.12206	−	5.40757i	0.169567	−	0.293699i
$340$	−4.81975	−	1.49385i	−0.261387	−	0.0810156i
$341$	16.9169	−	9.76695i	0.916099	−	0.528910i
$342$	−5.46337	−	2.26300i	−0.295425	−	0.122369i
$343$	−0.431980	−	18.5152i	−0.0233247	−	0.999728i
$344$	−9.45429	−	9.45429i	−0.509741	−	0.509741i
$345$	3.57813	+	4.08008i	0.192640	+	0.219664i
$346$	−2.38754	+	0.156488i	−0.128355	+	0.00841284i
$347$	−14.3254	+	16.3350i	−0.769030	+	0.876910i	−0.995269	−	0.0971615i	$-0.969024\pi$
$347$	−14.3254	+	16.3350i	−0.769030	+	0.876910i	0.226239	+	0.974072i	$0.427357\pi$
$348$	3.45989	−	4.50901i	0.185469	−	0.241709i
$349$	−4.33319	+	1.79487i	−0.231951	+	0.0960771i	−0.495632	−	0.868533i	$-0.665063\pi$
$349$	−4.33319	+	1.79487i	−0.231951	+	0.0960771i	0.263681	+	0.964610i	$0.415063\pi$
$350$	−9.61591	+	16.9584i	−0.513992	+	0.906465i
$351$	3.32927	+	4.98261i	0.177703	+	0.265952i
$352$	11.1316	−	9.76216i	0.593317	−	0.520325i
$353$	24.6114	−	6.59461i	1.30993	−	0.350996i	0.464736	−	0.885449i	$-0.346149\pi$
$353$	24.6114	−	6.59461i	1.30993	−	0.350996i	0.845198	+	0.534454i	$0.179483\pi$
$354$	5.87299	+	11.9092i	0.312146	+	0.632969i
$355$	−1.93040	+	0.254142i	−0.102455	+	0.0134884i
$356$	5.53030			0.293105
$357$	−10.6194	+	2.49564i	−0.562039	+	0.132083i
$358$	−23.1461			−1.22331
$359$	21.2665	−	2.79979i	1.12240	−	0.147767i	0.453599	−	0.891206i	$-0.350140\pi$
$359$	21.2665	−	2.79979i	1.12240	−	0.147767i	0.668804	+	0.743439i	$0.266807\pi$
$360$	0.560817	+	1.13723i	0.0295577	+	0.0599370i
$361$	8.02796	−	2.15108i	0.422524	−	0.113215i
$362$	−5.61209	+	4.92167i	−0.294965	+	0.258677i
$363$	−3.01866	−	4.51774i	−0.158438	−	0.237120i
$364$	10.2159	+	17.3810i	0.535459	+	0.911010i
$365$	−0.744702	+	0.308466i	−0.0389795	+	0.0161458i
$366$	11.9326	−	15.5508i	0.623725	−	0.812854i
$367$	17.0157	−	19.4027i	0.888215	−	1.01281i	−0.111604	−	0.993753i	$-0.535599\pi$
$367$	17.0157	−	19.4027i	0.888215	−	1.01281i	0.999818	−	0.0190618i	$-0.00606791\pi$
$368$	−27.7179	+	1.81673i	−1.44490	+	0.0947035i
$369$	3.90501	+	4.45281i	0.203287	+	0.231804i
$370$	7.74438	+	7.74438i	0.402611	+	0.402611i
$371$	−5.06105	−	36.2614i	−0.262756	−	1.88260i
$372$	9.72662	+	4.02890i	0.504302	+	0.208889i
$373$	9.22519	−	5.32616i	0.477662	−	0.275778i	−0.241780	−	0.970331i	$-0.577731\pi$
$373$	9.22519	−	5.32616i	0.477662	−	0.275778i	0.719442	+	0.694553i	$0.244398\pi$
$374$	8.20066	+	15.5675i	0.424046	+	0.804974i
$375$	−4.36639	+	7.56282i	−0.225480	+	0.390542i
$376$	−0.819303	−	6.22322i	−0.0422523	−	0.320938i
$377$	−14.8803	+	22.2700i	−0.766376	+	1.14696i
$378$	−3.99957	−	2.62767i	−0.205716	−	0.135153i
$379$	−10.7888	+	2.14603i	−0.554185	+	0.110234i	−0.464235	−	0.885712i	$-0.653671\pi$
$379$	−10.7888	+	2.14603i	−0.554185	+	0.110234i	−0.0899500	+	0.995946i	$0.528671\pi$
$380$	−3.58851	−	1.76966i	−0.184087	−	0.0907815i
$381$	−0.659692	−	0.578534i	−0.0337970	−	0.0296392i
$382$	−3.66150	+	27.8119i	−0.187339	+	1.42298i
$383$	15.6159	+	11.9825i	0.797937	+	0.612279i	0.925152	−	0.379597i	$-0.123937\pi$
$383$	15.6159	+	11.9825i	0.797937	+	0.612279i	−0.127215	+	0.991875i	$0.540604\pi$
$384$	−9.65185	−	1.91987i	−0.492544	−	0.0979731i
$385$	−5.79074	+	1.59999i	−0.295123	+	0.0815428i
$386$	1.30444	+	6.55786i	0.0663942	+	0.333786i
$387$	9.80254	+	2.62658i	0.498291	+	0.133517i
$388$	−16.9088	+	8.33849i	−0.858414	+	0.423323i
$389$	5.57118	−	4.27491i	0.282470	−	0.216747i	−0.457802	−	0.889054i	$-0.651363\pi$
$389$	5.57118	−	4.27491i	0.282470	−	0.216747i	0.740272	+	0.672307i	$0.234697\pi$
$390$	5.21587	+	9.03416i	0.264116	+	0.457462i
$391$	3.92540	−	22.9150i	0.198516	−	1.15886i
$392$	7.40309	+	5.49982i	0.373913	+	0.277783i
$393$	−0.367118	+	0.886302i	−0.0185187	+	0.0447080i
$394$	1.05142	−	16.0415i	0.0529697	−	0.808162i
$395$	3.22361	+	12.0307i	0.162197	+	0.605328i
$396$	−0.964370	+	2.84094i	−0.0484614	+	0.142763i
$397$	−8.90249	+	18.0525i	−0.446803	+	0.906028i	0.550652	+	0.834735i	$0.314379\pi$
$397$	−8.90249	+	18.0525i	−0.446803	+	0.906028i	−0.997455	+	0.0712927i	$0.977288\pi$
$398$	−2.79458	+	14.0493i	−0.140080	+	0.704229i
$399$	−8.62679	+	0.632832i	−0.431880	+	0.0316812i
$400$	−7.67976	−	18.5406i	−0.383988	−	0.927029i
$401$	−2.34874	+	0.797291i	−0.117291	+	0.0398148i	−0.379468	−	0.925205i	$-0.623893\pi$
$401$	−2.34874	+	0.797291i	−0.117291	+	0.0398148i	0.262177	+	0.965020i	$0.415560\pi$
$402$	1.11956	+	17.0812i	0.0558386	+	0.851932i
$403$	−46.9811	−	15.9480i	−2.34030	−	0.794424i
$404$	−5.09117	+	19.0005i	−0.253295	+	0.945311i
$405$	−0.800227	−	0.534694i	−0.0397636	−	0.0265692i
$406$	4.00957	−	21.0099i	0.198992	−	1.04271i
$407$		−	14.8439i		−	0.735785i
$408$	2.27170	−	4.93436i	0.112466	−	0.244287i
$409$	18.9878	+	10.9626i	0.938888	+	0.542067i	0.889611	−	0.456718i	$-0.150975\pi$
$409$	18.9878	+	10.9626i	0.938888	+	0.542067i	0.0492762	+	0.998785i	$0.484309\pi$
$410$	6.27628	+	8.17941i	0.309964	+	0.403952i
$411$	−3.00457	−	0.196930i	−0.148204	−	0.00971384i
$412$	14.0032	−	14.0032i	0.689889	−	0.689889i
$413$	15.5010	+	11.7040i	0.762753	+	0.575914i
$414$	8.48014	−	5.66625i	0.416776	−	0.278481i
$415$	−1.09334	−	3.22089i	−0.0536701	−	0.158107i
$416$	−37.2836	−	4.90848i	−1.82798	−	0.240658i
$417$	17.5016	+	2.30413i	0.857057	+	0.112834i
$418$	4.48475	+	13.2117i	0.219356	+	0.646203i
$419$	1.05254	−	0.703287i	0.0514201	−	0.0343578i	−0.529595	−	0.848251i	$-0.677656\pi$
$419$	1.05254	−	0.703287i	0.0514201	−	0.0343578i	0.581015	+	0.813893i	$0.302656\pi$
$420$	−2.58407	−	1.95109i	−0.126090	−	0.0952035i
$421$	4.24036	−	4.24036i	0.206662	−	0.206662i	−0.596185	−	0.802847i	$-0.703317\pi$
$421$	4.24036	−	4.24036i	0.206662	−	0.206662i	0.802847	+	0.596185i	$0.203317\pi$
$422$	−19.4810	−	1.27685i	−0.948320	−	0.0621562i
$423$	2.90031	+	3.77976i	0.141018	+	0.183778i
$424$	15.7894	+	9.11599i	0.766799	+	0.442712i
$425$	16.5883	−	2.63607i	0.804651	−	0.127868i
$426$			3.65925i			0.177291i
$427$	5.37477	−	28.1635i	0.260103	−	1.36293i
$428$	−12.4294	−	8.30506i	−0.600798	−	0.401440i
$429$	3.65932	−	13.6567i	0.176673	−	0.659354i
$430$	16.7286	+	5.67860i	0.806725	+	0.273846i
$431$	−1.41078	−	21.5243i	−0.0679547	−	1.03679i	−0.886615	−	0.462509i	$-0.846949\pi$
$431$	−1.41078	−	21.5243i	−0.0679547	−	1.03679i	0.818660	−	0.574279i	$-0.194717\pi$
$432$	4.66480	−	1.58349i	0.224435	−	0.0761855i
$433$	−4.36406	−	10.5358i	−0.209723	−	0.506317i	0.783656	−	0.621195i	$-0.213352\pi$
$433$	−4.36406	−	10.5358i	−0.209723	−	0.506317i	−0.993380	+	0.114878i	$0.963352\pi$
$434$	39.5148	−	2.89867i	1.89677	−	0.139141i
$435$	0.839201	−	4.21895i	0.0402366	−	0.202283i
$436$	−2.30225	+	4.66851i	−0.110258	+	0.223581i
$437$	5.92572	−	17.4566i	0.283465	−	0.835062i
$438$	0.392082	+	1.46327i	0.0187344	+	0.0699178i
$439$	−0.368901	+	5.62835i	−0.0176067	+	0.268626i	0.979975	+	0.199121i	$0.0638087\pi$
$439$	−0.368901	+	5.62835i	−0.0176067	+	0.268626i	−0.997582	+	0.0695052i	$0.977858\pi$
$440$	1.14485	−	2.76391i	0.0545786	−	0.131764i
$441$	−6.95348	−	0.805650i	−0.331118	−	0.0383643i
$442$	15.9942	−	41.7304i	0.760765	−	1.98491i
$443$	−14.8702	−	25.7560i	−0.706506	−	1.22370i	−0.966145	−	0.257998i	$-0.916937\pi$
$443$	−14.8702	−	25.7560i	−0.706506	−	1.22370i	0.259640	−	0.965706i	$-0.416396\pi$
$444$	6.34706	−	4.87027i	0.301218	−	0.231133i
$445$	3.75400	−	1.85127i	0.177957	−	0.0877586i
$446$	−17.1928	−	4.60680i	−0.814103	−	0.218138i
$447$	2.82985	+	14.2266i	0.133847	+	0.672896i
$448$	3.82058	−	1.05563i	0.180505	−	0.0498738i
$449$	25.7072	+	5.11348i	1.21320	+	0.241320i	0.759900	−	0.650040i	$-0.225248\pi$
$449$	25.7072	+	5.11348i	1.21320	+	0.241320i	0.453297	+	0.891360i	$0.350248\pi$
$450$	5.84575	+	4.48560i	0.275571	+	0.211453i
$451$	1.82389	−	13.8539i	0.0858838	−	0.652353i
$452$	−5.96964	−	5.23524i	−0.280788	−	0.246245i
$453$	−6.17758	−	3.04644i	−0.290248	−	0.143134i
$454$	−18.7278	+	3.72518i	−0.878937	+	0.174832i
$455$	12.7529	+	8.37853i	0.597866	+	0.392792i
$456$	2.39306	−	3.58147i	0.112065	−	0.167717i
$457$	1.63781	+	12.4404i	0.0766134	+	0.581936i	0.986094	+	0.166190i	$0.0531464\pi$
$457$	1.63781	+	12.4404i	0.0766134	+	0.581936i	−0.909480	+	0.415747i	$0.863520\pi$
$458$	−4.34330	+	7.52281i	−0.202949	+	0.351518i
$459$	0.379381	+	4.10561i	0.0177080	+	0.191634i
$460$	5.97620	−	3.45036i	0.278642	−	0.160874i
$461$	−12.6561	−	5.24231i	−0.589451	−	0.244159i	0.0679632	−	0.997688i	$-0.478350\pi$
$461$	−12.6561	−	5.24231i	−0.589451	−	0.244159i	−0.657415	+	0.753529i	$0.728350\pi$
$462$	1.56073	+	11.1824i	0.0726119	+	0.520250i
$463$	−1.99105	−	1.99105i	−0.0925320	−	0.0925320i	0.659326	−	0.751858i	$-0.270842\pi$
$463$	−1.99105	−	1.99105i	−0.0925320	−	0.0925320i	−0.751858	+	0.659326i	$0.770842\pi$
$464$	14.5175	+	16.5540i	0.673958	+	0.768502i
$465$	7.95118	−	0.521148i	0.368727	−	0.0241676i
$466$	3.64823	−	4.16001i	0.169001	−	0.192709i
$467$	1.02451	−	1.33517i	0.0474088	−	0.0617844i	−0.769047	−	0.639192i	$-0.779269\pi$
$467$	1.02451	−	1.33517i	0.0474088	−	0.0617844i	0.816456	+	0.577408i	$0.195936\pi$
$468$	7.04006	−	2.91609i	0.325427	−	0.134796i
$469$	12.6877	+	21.5864i	0.585866	+	0.996769i
$470$	4.60769	+	6.89590i	0.212537	+	0.318084i
$471$	5.28831	−	4.63772i	0.243672	−	0.213695i
$472$	−9.34256	+	2.50333i	−0.430026	+	0.115225i
$473$	−10.5900	−	21.4743i	−0.486927	−	0.987390i
$474$	23.2075	−	3.05532i	1.06595	−	0.140336i
$475$	13.3186			0.611099
$476$	0.478052	+	13.8633i	0.0219115	+	0.635423i
$477$	−13.8384			−0.633616
$478$	−26.3758	+	3.47245i	−1.20640	+	0.158826i
$479$	−2.33432	−	4.73352i	−0.106658	−	0.216280i	0.837001	−	0.547202i	$-0.184307\pi$
$479$	−2.33432	−	4.73352i	−0.106658	−	0.216280i	−0.943658	+	0.330922i	$0.892640\pi$
$480$	5.83377	−	1.56316i	0.266274	−	0.0713479i
$481$	−28.3459	+	24.8587i	−1.29246	+	1.13346i
$482$	−6.34228	−	9.49189i	−0.288883	−	0.432344i
$483$	7.35857	−	12.9774i	0.334826	−	0.590493i
$484$	−6.38324	+	2.64403i	−0.290147	+	0.120183i
$485$	−8.68649	+	11.3205i	−0.394433	+	0.514035i
$486$	−1.19260	+	1.35990i	−0.0540973	+	0.0616861i
$487$	23.1025	−	1.51422i	1.04687	−	0.0686158i	0.467755	−	0.883858i	$-0.345063\pi$
$487$	23.1025	−	1.51422i	1.04687	−	0.0686158i	0.579120	+	0.815242i	$0.303396\pi$
$488$	9.41387	+	10.7345i	0.426146	+	0.485926i
$489$	−1.96720	−	1.96720i	−0.0889599	−	0.0889599i
$490$	−11.9869	−	2.19114i	−0.541514	−	0.0989858i
$491$	13.4391	+	5.56666i	0.606498	+	0.251220i	0.664730	−	0.747083i	$-0.268546\pi$
$491$	13.4391	+	5.56666i	0.606498	+	0.251220i	−0.0582323	+	0.998303i	$0.518546\pi$
$492$	6.52214	−	3.76556i	0.294041	−	0.169765i
$493$	−16.3045	+	8.58892i	−0.734318	+	0.386826i
$494$	17.7185	−	30.6893i	0.797191	−	1.38077i
$495$	0.296386	+	2.25128i	0.0133216	+	0.101187i
$496$	−22.6595	+	33.9123i	−1.01744	+	1.52271i
$497$	2.40463	+	4.78200i	0.107862	+	0.214502i
$498$	−6.26968	+	1.24712i	−0.280951	+	0.0558846i
$499$	18.9681	+	9.35404i	0.849130	+	0.418744i	0.814158	−	0.580644i	$-0.197199\pi$
$499$	18.9681	+	9.35404i	0.849130	+	0.418744i	0.0349720	+	0.999388i	$0.488866\pi$
$500$	8.34890	+	7.32179i	0.373374	+	0.327441i
$501$	−1.75071	+	13.2979i	−0.0782159	+	0.594108i
$502$	4.64800	+	3.56654i	0.207451	+	0.159182i
$503$	−12.3960	−	2.46572i	−0.552711	−	0.109941i	−0.0891698	−	0.996016i	$-0.528421\pi$
$503$	−12.3960	−	2.46572i	−0.552711	−	0.109941i	−0.463541	+	0.886075i	$0.653421\pi$
$504$	2.44557	−	2.48390i	0.108934	−	0.110642i
$505$	2.90451	+	14.6020i	0.129249	+	0.649778i
$506$	−23.2431	−	6.22797i	−1.03328	−	0.276867i
$507$	−20.5477	+	10.1330i	−0.912556	+	0.450023i
$508$	−0.885184	+	0.679226i	−0.0392737	+	0.0301358i
$509$	−2.30124	−	3.98586i	−0.102001	−	0.176670i	0.810508	−	0.585727i	$-0.199191\pi$
$509$	−2.30124	−	3.98586i	−0.102001	−	0.176670i	−0.912509	+	0.409057i	$0.865858\pi$
$510$	0.191573	+	7.17491i	0.00848298	+	0.317711i
$511$	1.47395	+	1.65459i	0.0652038	+	0.0731947i
$512$	−6.86279	+	16.5683i	−0.303296	+	0.732220i
$513$	−0.213828	+	3.26238i	−0.00944072	+	0.144038i
$514$	7.82146	+	29.1901i	0.344990	+	1.28752i
$515$	4.81790	−	14.1931i	0.212302	−	0.625422i
$516$	5.70758	−	11.5738i	0.251262	−	0.509509i
$517$	2.19294	−	11.0247i	0.0964454	−	0.484864i
$518$	13.1061	−	27.1059i	0.575850	−	1.19096i
$519$	0.506222	+	1.22213i	0.0222207	+	0.0536455i
$520$	−7.19521	+	2.44245i	−0.315531	+	0.107108i
$521$	1.03961	+	15.8614i	0.0455461	+	0.694899i	0.958188	+	0.286139i	$0.0923719\pi$
$521$	1.03961	+	15.8614i	0.0455461	+	0.694899i	−0.912642	+	0.408760i	$0.865961\pi$
$522$	−7.65529	−	2.59862i	−0.335063	−	0.113739i
$523$	0.550195	−	2.05336i	0.0240584	−	0.0897871i	−0.952853	−	0.303433i	$-0.901867\pi$
$523$	0.550195	−	2.05336i	0.0240584	−	0.0897871i	0.976911	+	0.213646i	$0.0685339\pi$
$524$	1.01429	+	0.677730i	0.0443097	+	0.0296068i
$525$	10.5870	+	2.02044i	0.462056	+	0.0881794i
$526$		−	53.9880i		−	2.35399i
$527$	−23.1848	−	25.0553i	−1.00995	−	1.09143i
$528$	−10.0656	−	5.81137i	−0.438048	−	0.252907i
$529$	5.35378	+	6.97718i	0.232773	+	0.303356i
$530$	−24.0382	−	1.57554i	−1.04415	−	0.0684373i
$531$	5.19108	−	5.19108i	0.225274	−	0.225274i
$532$	−1.35086	+	10.9160i	−0.0585673	+	0.473271i
$533$	−29.5097	+	19.7178i	−1.27821	+	0.854071i
$534$	−2.52858	−	7.44896i	−0.109422	−	0.322348i
$535$	−11.2173	−	1.47678i	−0.484966	−	0.0638470i
$536$	−12.3619	−	1.62748i	−0.533954	−	0.0702964i
$537$	4.11335	+	12.1175i	0.177504	+	0.522911i
$538$	13.3161	−	8.89756i	0.574099	−	0.383601i
$539$	9.38795	+	13.5878i	0.404368	+	0.585267i
$540$	−0.865372	+	0.865372i	−0.0372397	+	0.0372397i
$541$	−10.2812	−	0.673866i	−0.442023	−	0.0289717i	−0.157233	−	0.987562i	$-0.550257\pi$
$541$	−10.2812	−	0.673866i	−0.442023	−	0.0289717i	−0.284790	+	0.958590i	$0.591924\pi$
$542$	17.3174	+	22.5684i	0.743845	+	0.969398i
$543$	3.57396	+	2.06343i	0.153373	+	0.0885501i
$544$	−20.9403	−	15.1976i	−0.897809	−	0.651591i
$545$			3.93970i			0.168758i
$546$	18.7401	−	21.7072i	0.802002	−	0.928981i
$547$	19.9542	+	13.3329i	0.853178	+	0.570075i	0.903466	−	0.428659i	$-0.141014\pi$
$547$	19.9542	+	13.3329i	0.853178	+	0.570075i	−0.0502881	+	0.998735i	$0.516014\pi$
$548$	−0.990970	+	3.69835i	−0.0423321	+	0.157986i
$549$	−10.2618	−	3.48342i	−0.437964	−	0.148669i
$550$	−1.13701	−	17.3475i	−0.0484824	−	0.739698i
$551$	−13.8372	+	4.69708i	−0.589483	+	0.200103i
$552$	2.84292	+	6.86342i	0.121003	+	0.292127i
$553$	28.3204	−	19.2433i	1.20431	−	0.818307i
$554$	0.518151	−	2.60492i	0.0220141	−	0.110672i
$555$	2.67810	−	5.43065i	0.113679	−	0.230518i
$556$	7.21538	−	21.2558i	0.306000	−	0.901448i
$557$	3.59940	+	13.4331i	0.152511	+	0.569180i	0.999306	+	0.0372595i	$0.0118628\pi$
$557$	3.59940	+	13.4331i	0.152511	+	0.569180i	−0.846794	+	0.531920i	$0.821471\pi$
$558$	0.979432	−	14.9432i	0.0414627	−	0.632598i
$559$	−23.2726	+	56.1850i	−0.984325	+	2.37637i
$560$	9.36637	−	8.34381i	0.395801	−	0.352590i
$561$	6.69260	−	7.05979i	0.282562	−	0.298065i
$562$	−28.7512	−	49.7986i	−1.21280	−	2.10063i
$563$	−18.7030	+	14.3513i	−0.788239	+	0.604837i	−0.922450	−	0.386116i	$-0.873817\pi$
$563$	−18.7030	+	14.3513i	−0.788239	+	0.604837i	0.134211	+	0.990953i	$0.457150\pi$
$564$	5.43350	−	2.67951i	0.228792	−	0.112828i
$565$	−5.80473	−	1.55537i	−0.244207	−	0.0654351i
$566$	−8.16356	−	41.0410i	−0.343140	−	1.72508i
$567$	−0.664879	+	2.56085i	−0.0279223	+	0.107545i
$568$	−2.61418	−	0.519992i	−0.109688	−	0.0218184i
$569$	17.3875	+	13.3419i	0.728924	+	0.559323i	0.905184	−	0.425021i	$-0.139733\pi$
$569$	17.3875	+	13.3419i	0.728924	+	0.559323i	−0.176260	+	0.984344i	$0.556400\pi$
$570$	−0.742865	+	5.64262i	−0.0311152	+	0.236343i
$571$	−8.16759	−	7.16279i	−0.341803	−	0.299753i	0.471184	−	0.882035i	$-0.343827\pi$
$571$	−8.16759	−	7.16279i	−0.341803	−	0.299753i	−0.812987	+	0.582282i	$0.802160\pi$
$572$	−16.1245	−	7.95171i	−0.674198	−	0.332478i
$573$	15.2109	−	3.02564i	0.635445	−	0.126398i
$574$	15.5625	−	23.6876i	0.649567	−	0.988703i
$575$	−12.7617	+	19.0992i	−0.532200	+	0.796493i
$576$	−0.195548	−	1.48533i	−0.00814783	−	0.0618889i
$577$	−10.1021	+	17.4973i	−0.420556	+	0.728424i	−0.995994	−	0.0894214i	$-0.971498\pi$
$577$	−10.1021	+	17.4973i	−0.420556	+	0.728424i	0.575438	+	0.817845i	$0.304832\pi$
$578$	23.3611	−	19.9938i	0.971693	−	0.831633i
$579$	3.20139	−	1.84832i	0.133045	−	0.0768137i
$580$	−5.05355	−	2.09325i	−0.209837	−	0.0869175i
$581$	−7.37385	+	5.74980i	−0.305919	+	0.238542i
$582$	18.9625	+	18.9625i	0.786021	+	0.786021i
$583$	21.5274	+	24.5473i	0.891574	+	1.01665i
$584$	−1.10108	+	0.0721686i	−0.0455630	+	0.00298636i
$585$	3.80268	−	4.33613i	0.157222	−	0.179277i
$586$	−13.6119	+	17.7393i	−0.562301	+	0.732805i
$587$	33.9161	−	14.0485i	1.39987	−	0.579844i	0.450150	−	0.892953i	$-0.351370\pi$
$587$	33.9161	−	14.0485i	1.39987	−	0.579844i	0.949717	+	0.313109i	$0.101370\pi$
$588$	−2.72978	+	8.47230i	−0.112574	+	0.349392i
$589$	−15.0383	−	22.5065i	−0.619644	−	0.927363i
$590$	9.60827	−	8.42623i	0.395566	−	0.346902i
$591$	−8.58501	+	2.30035i	−0.353140	+	0.0946236i
$592$	13.7080	+	27.7972i	0.563397	+	1.14246i
$593$	10.8470	−	1.42803i	0.445431	−	0.0586421i	0.0955252	−	0.995427i	$-0.469547\pi$
$593$	10.8470	−	1.42803i	0.445431	−	0.0586421i	0.349906	+	0.936785i	$0.386214\pi$
$594$	4.26750			0.175098
$595$	4.96525	+	9.25048i	0.203556	+	0.379233i
$596$	18.4450			0.755537
$597$	7.85181	−	1.03371i	0.321353	−	0.0423069i
$598$	27.0316	+	54.8147i	1.10541	+	2.24154i
$599$	−12.7616	+	3.41946i	−0.521425	+	0.139715i	−0.509926	−	0.860218i	$-0.670327\pi$
$599$	−12.7616	+	3.41946i	−0.521425	+	0.139715i	−0.0114994	+	0.999934i	$0.503660\pi$
$600$	−4.03522	+	3.53880i	−0.164737	+	0.144471i
$601$	−21.6256	−	32.3649i	−0.882125	−	1.32019i	−0.946645	−	0.322277i	$-0.895552\pi$
$601$	−21.6256	−	32.3649i	−0.882125	−	1.32019i	0.0645206	−	0.997916i	$-0.479448\pi$
$602$	−0.377620	−	48.5636i	−0.0153906	−	1.97930i
$603$	8.74347	−	3.62166i	0.356062	−	0.147486i
$604$	−5.33194	+	6.94873i	−0.216954	+	0.282740i
$605$	−3.44790	+	3.93158i	−0.140177	+	0.159841i
$606$	27.9203	−	1.82999i	1.13418	−	0.0743383i
$607$	−4.76763	−	5.43644i	−0.193512	−	0.220658i	0.646945	−	0.762537i	$-0.276047\pi$
$607$	−4.76763	−	5.43644i	−0.193512	−	0.220658i	−0.840457	+	0.541879i	$0.817713\pi$
$608$	−14.5074	−	14.5074i	−0.588353	−	0.588353i
$609$	−11.7118	+	1.63463i	−0.474586	+	0.0662385i
$610$	−17.4288	−	7.21926i	−0.705673	−	0.292299i
$611$	−24.7251	+	14.2751i	−1.00027	+	0.577507i
$612$	5.21451	+	0.545357i	0.210784	+	0.0220447i
$613$	15.3354	−	26.5617i	0.619391	−	1.07282i	−0.370206	−	0.928950i	$-0.620713\pi$
$613$	15.3354	−	26.5617i	0.619391	−	1.07282i	0.989597	−	0.143867i	$-0.0459536\pi$
$614$	3.28493	+	24.9515i	0.132569	+	1.00696i
$615$	3.16675	−	4.73938i	0.127696	−	0.191110i
$616$	−8.21048	−	0.474059i	−0.330810	−	0.0191004i
$617$	2.65320	−	0.527755i	0.106814	−	0.0212466i	−0.141394	−	0.989953i	$-0.545158\pi$
$617$	2.65320	−	0.527755i	0.106814	−	0.0212466i	0.248208	+	0.968707i	$0.420158\pi$
$618$	−25.2640	−	12.4588i	−1.01627	−	0.501168i
$619$	−22.8792	−	20.0645i	−0.919591	−	0.806460i	0.0618770	−	0.998084i	$-0.480291\pi$
$619$	−22.8792	−	20.0645i	−0.919591	−	0.806460i	−0.981468	+	0.191624i	$0.938625\pi$
$620$	1.32255	−	10.0457i	0.0531148	−	0.403447i
$621$	−4.47345	−	3.43260i	−0.179514	−	0.137746i
$622$	−24.5747	−	4.88822i	−0.985356	−	0.196000i
$623$	−8.19940	−	8.07287i	−0.328502	−	0.323433i
$624$	5.75918	+	28.9534i	0.230552	+	1.15906i
$625$	−11.5564	−	3.09652i	−0.462255	−	0.123861i
$626$	50.6219	−	24.9640i	2.02326	−	0.997760i
$627$	6.11964	−	4.69576i	0.244395	−	0.187531i
$628$	−4.47211	−	7.74593i	−0.178457	−	0.309096i
$629$	−25.2980	+	5.73802i	−1.00870	+	0.228790i
$630$	−1.44650	+	4.37266i	−0.0576299	+	0.174211i
$631$	11.6768	−	28.1904i	0.464847	−	1.12224i	−0.501537	−	0.865136i	$-0.667232\pi$
$631$	11.6768	−	28.1904i	0.464847	−	1.12224i	0.966384	−	0.257104i	$-0.0827682\pi$
$632$	−1.11513	+	17.0136i	−0.0443576	+	0.676766i
$633$	2.79356	+	10.4257i	0.111034	+	0.414385i
$634$	−14.8679	+	43.7993i	−0.590478	+	1.73949i
$635$	−0.373498	+	0.757379i	−0.0148218	+	0.0300557i
$636$	−3.43299	+	17.2588i	−0.136127	+	0.684355i
$637$	10.2255	−	40.6823i	0.405148	−	1.61189i
$638$	7.29923	+	17.6219i	0.288979	+	0.697658i
$639$	1.91571	−	0.650296i	0.0757843	−	0.0257253i
$640$	0.619444	+	9.45089i	0.0244857	+	0.373579i
$641$	19.5645	+	6.64126i	0.772752	+	0.262314i	0.679840	−	0.733360i	$-0.262049\pi$
$641$	19.5645	+	6.64126i	0.772752	+	0.262314i	0.0929121	+	0.995674i	$0.470382\pi$
$642$	−5.50338	+	20.5389i	−0.217201	+	0.810605i
$643$	27.4324	+	18.3298i	1.08183	+	0.722856i	0.962849	−	0.270041i	$-0.0870372\pi$
$643$	27.4324	+	18.3298i	1.08183	+	0.722856i	0.118981	+	0.992897i	$0.462037\pi$
$644$	−14.3595	−	12.3968i	−0.565845	−	0.488501i
$645$		−	9.76701i		−	0.384576i
$646$	20.7826	−	12.7503i	0.817679	−	0.501653i
$647$	16.1360	+	9.31612i	0.634372	+	0.366255i	0.782443	−	0.622722i	$-0.213973\pi$
$647$	16.1360	+	9.31612i	0.634372	+	0.366255i	−0.148072	+	0.988977i	$0.547307\pi$
$648$	−0.802040	−	1.04524i	−0.0315071	−	0.0410609i
$649$	−17.2837	−	1.13283i	−0.678443	−	0.0444675i
$650$	−31.2226	+	31.2226i	−1.22465	+	1.22465i
$651$	−8.53981	−	20.1719i	−0.334702	−	0.790597i
$652$	−2.94145	+	1.96541i	−0.115196	+	0.0769715i
$653$	−2.68662	−	7.91452i	−0.105135	−	0.309719i	0.881614	−	0.471971i	$-0.156457\pi$
$653$	−2.68662	−	7.91452i	−0.105135	−	0.309719i	−0.986749	+	0.162252i	$0.948124\pi$
$654$	7.34083	+	0.966438i	0.287049	+	0.0377907i
$655$	0.915381	+	0.120512i	0.0357669	+	0.00470880i
$656$	9.37827	+	27.6275i	0.366160	+	1.07867i
$657$	0.696381	−	0.465307i	0.0271684	−	0.0181534i
$658$	13.7384	−	18.1955i	0.535580	−	0.709334i
$659$	31.9391	−	31.9391i	1.24417	−	1.24417i	0.285916	−	0.958255i	$-0.407702\pi$
$659$	31.9391	−	31.9391i	1.24417	−	1.24417i	0.958255	−	0.285916i	$-0.0922977\pi$
$660$	2.88125	+	0.188847i	0.112152	+	0.00735086i
$661$	−10.6687	−	13.9037i	−0.414963	−	0.540791i	0.538371	−	0.842708i	$-0.319040\pi$
$661$	−10.6687	−	13.9037i	−0.414963	−	0.540791i	−0.953334	+	0.301917i	$0.902373\pi$
$662$	−11.4973	−	6.63797i	−0.446855	−	0.257992i
$663$	−24.6893	−	0.957333i	−0.958852	−	0.0371797i
$664$		−	4.65629i		−	0.180699i
$665$	2.73718	+	7.86209i	0.106143	+	0.304879i
$666$	−9.46196	−	6.32228i	−0.366644	−	0.244983i
$667$	6.52283	−	24.3435i	0.252565	−	0.942586i
$668$	16.1505	+	5.48235i	0.624880	+	0.212118i
$669$	0.643608	+	9.81956i	0.0248833	+	0.379646i
$670$	15.6003	−	5.29559i	0.602693	−	0.204587i
$671$	9.78452	+	23.6219i	0.377727	+	0.911914i
$672$	−9.33123	−	13.7328i	−0.359960	−	0.529754i
$673$	−0.547465	+	2.75229i	−0.0211032	+	0.106093i	−0.989901	−	0.141758i	$-0.954724\pi$
$673$	−0.547465	+	2.75229i	−0.0211032	+	0.106093i	0.968798	+	0.247851i	$0.0797244\pi$
$674$	11.3882	−	23.0929i	0.438656	−	0.889506i
$675$	1.30946	−	3.85755i	0.0504012	−	0.148477i
$676$	7.54015	+	28.1402i	0.290006	+	1.08232i
$677$	2.11889	−	32.3280i	0.0814354	−	1.24246i	−0.740175	−	0.672415i	$-0.765257\pi$
$677$	2.11889	−	32.3280i	0.0814354	−	1.24246i	0.821610	−	0.570050i	$-0.193076\pi$
$678$	−4.32207	+	10.4344i	−0.165988	+	0.400731i
$679$	37.2417	+	12.3197i	1.42920	+	0.472788i
$680$	−5.15300	−	0.882720i	−0.197608	−	0.0338508i
$681$	5.27839	+	9.14245i	0.202268	+	0.350339i
$682$	−28.0308	+	21.5088i	−1.07336	+	0.823615i
$683$	−1.67550	+	0.826264i	−0.0641111	+	0.0316161i	−0.474062	−	0.880492i	$-0.657213\pi$
$683$	−1.67550	+	0.826264i	−0.0641111	+	0.0316161i	0.409951	+	0.912108i	$0.365546\pi$
$684$	4.01569	+	1.07600i	0.153544	+	0.0411419i
$685$	0.565348	+	2.84219i	0.0216008	+	0.108595i
$686$	5.14592	+	33.1010i	0.196472	+	1.26380i
$687$	4.71024	+	0.936925i	0.179707	+	0.0357459i
$688$	39.6622	+	30.4338i	1.51211	+	1.16028i
$689$	10.8241	−	82.2174i	0.412366	−	3.13223i
$690$	−7.37987	−	6.47197i	−0.280947	−	0.246384i
$691$	10.6092	+	5.23186i	0.403592	+	0.199029i	0.632744	−	0.774361i	$-0.281929\pi$
$691$	10.6092	+	5.23186i	0.403592	+	0.199029i	−0.229152	+	0.973391i	$0.573595\pi$
$692$	1.64978	−	0.328162i	0.0627153	−	0.0124749i
$693$	5.57688	−	2.80433i	0.211848	−	0.106528i
$694$	21.8330	−	32.6754i	0.828770	−	1.24034i
$695$	−2.21755	−	16.8440i	−0.0841165	−	0.638928i
$696$	2.94430	−	5.09968i	0.111604	−	0.193303i
$697$	−24.3157	+	2.24690i	−0.921023	+	0.0851076i
$698$	7.34689	−	4.24173i	0.278084	−	0.160552i
$699$	−2.82621	−	1.17065i	−0.106897	−	0.0442782i
$700$	5.14624	−	12.7026i	0.194509	−	0.480113i
$701$	−32.5347	−	32.5347i	−1.22882	−	1.22882i	−0.964411	−	0.264408i	$-0.914823\pi$
$701$	−32.5347	−	32.5347i	−1.22882	−	1.22882i	−0.264408	−	0.964411i	$-0.585177\pi$
$702$	−7.14667	−	8.14921i	−0.269734	−	0.307572i
$703$	−20.5253	+	1.34530i	−0.774126	+	0.0507389i
$704$	−2.33057	+	2.65751i	−0.0878366	+	0.100159i
$705$	2.79133	−	3.63773i	0.105128	−	0.137005i
$706$	−42.5783	+	17.6365i	−1.60246	+	0.663759i
$707$	35.2844	−	20.7389i	1.32701	−	0.779968i
$708$	−5.18636	−	7.76194i	−0.194916	−	0.291712i
$709$	−23.2792	+	20.4153i	−0.874269	+	0.766714i	−0.973581	−	0.228343i	$-0.926669\pi$
$709$	−23.2792	+	20.4153i	−0.874269	+	0.766714i	0.0993115	+	0.995056i	$0.468336\pi$
$710$	3.40175	−	0.911497i	0.127665	−	0.0342079i
$711$	−5.72381	−	11.6067i	−0.214660	−	0.435286i
$712$	5.68087	−	0.747901i	0.212900	−	0.0280288i
$713$	46.6844			1.74835
$714$	18.4544	−	6.98253i	0.690639	−	0.261315i
$715$	−13.6072			−0.508882
$716$	16.1331	−	2.12396i	0.602921	−	0.0793760i
$717$	6.50524	+	13.1913i	0.242943	+	0.492639i
$718$	−37.4758	+	10.0416i	−1.39859	+	0.374750i
$719$	−12.5566	+	11.0118i	−0.468280	+	0.410671i	−0.860698	−	0.509116i	$-0.829972\pi$
$719$	−12.5566	+	11.0118i	−0.468280	+	0.410671i	0.392417	+	0.919787i	$0.371639\pi$
$720$	−2.63403	−	3.94210i	−0.0981645	−	0.146914i
$721$	−41.2029	+	0.320384i	−1.53448	+	0.0119317i
$722$	−13.8885	+	5.75283i	−0.516878	+	0.214098i
$723$	−3.84214	+	5.00718i	−0.142891	+	0.186219i
$724$	3.46006	−	3.94544i	0.128592	−	0.146631i
$725$	18.1688	−	1.19085i	0.674772	−	0.0442269i
$726$	6.47990	+	7.38891i	0.240492	+	0.274228i
$727$	23.2424	+	23.2424i	0.862012	+	0.862012i	0.991572	−	0.129560i	$-0.0413564\pi$
$727$	23.2424	+	23.2424i	0.862012	+	0.862012i	−0.129560	+	0.991572i	$0.541356\pi$
$728$	12.8446	+	16.4726i	0.476053	+	0.610516i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	1.26264	−	0.728983i	0.0467323	−	0.0269809i
$731$	−32.5043	+	26.3492i	−1.20222	+	0.974559i
$732$	−6.89013	+	11.9341i	−0.254667	+	0.441095i
$733$	1.16531	+	8.85140i	0.0430417	+	0.326934i	0.999397	+	0.0347271i	$0.0110562\pi$
$733$	1.16531	+	8.85140i	0.0430417	+	0.326934i	−0.956355	+	0.292207i	$0.905610\pi$
$734$	−25.9332	+	38.8118i	−0.957214	+	1.43257i
$735$	0.983113	+	6.66485i	0.0362627	+	0.245837i
$736$	34.7048	−	6.90321i	1.27924	−	0.254456i
$737$	−20.0259	−	9.87570i	−0.737665	−	0.363776i
$738$	−8.05405	−	7.06321i	−0.296474	−	0.260000i
$739$	−1.31352	+	9.97714i	−0.0483184	+	0.367015i	0.950155	+	0.311778i	$0.100925\pi$
$739$	−1.31352	+	9.97714i	−0.0483184	+	0.367015i	−0.998473	+	0.0552366i	$0.982409\pi$
$740$	−6.10856	−	4.68727i	−0.224555	−	0.172307i
$741$	−19.2154	−	3.82218i	−0.705895	−	0.140411i
$742$	17.6368	+	63.8321i	0.647469	+	2.34335i
$743$	2.55979	+	12.8689i	0.0939095	+	0.472115i	0.998909	+	0.0467019i	$0.0148711\pi$
$743$	2.55979	+	12.8689i	0.0939095	+	0.472115i	−0.904999	+	0.425413i	$0.860129\pi$
$744$	10.5363	+	2.82319i	0.386280	+	0.103503i
$745$	12.5206	−	6.17448i	0.458719	−	0.226215i
$746$	−15.2859	+	11.7293i	−0.559657	+	0.429440i
$747$	1.76710	+	3.06071i	0.0646548	+	0.111985i
$748$	−7.14447	−	10.0982i	−0.261228	−	0.369226i
$749$	6.30490	+	30.4572i	0.230376	+	1.11288i
$750$	6.04467	−	14.5931i	0.220720	−	0.532866i
$751$	0.344343	−	5.25367i	0.0125653	−	0.191709i	−0.986962	−	0.160955i	$-0.948543\pi$
$751$	0.344343	−	5.25367i	0.0125653	−	0.191709i	0.999527	−	0.0307538i	$-0.00979079\pi$
$752$	6.07448	+	22.6702i	0.221513	+	0.826699i
$753$	1.04116	−	3.06717i	0.0379421	−	0.111774i
$754$	21.4269	−	43.4495i	0.780323	−	1.58234i
$755$	−1.29327	+	6.50172i	−0.0470670	+	0.236622i
$756$	3.02887	+	1.46450i	0.110159	+	0.0532635i
$757$	6.42088	+	15.5014i	0.233371	+	0.563407i	0.996570	−	0.0827563i	$-0.0263723\pi$
$757$	6.42088	+	15.5014i	0.233371	+	0.563407i	−0.763199	+	0.646164i	$0.776372\pi$
$758$	18.8408	−	6.39558i	0.684328	−	0.232298i
$759$	0.870098	+	13.2751i	0.0315826	+	0.481857i
$760$	−3.92554	−	1.33254i	−0.142394	−	0.0483363i
$761$	−10.2260	+	38.1639i	−0.370692	+	1.38344i	0.488847	+	0.872370i	$0.337418\pi$
$761$	−10.2260	+	38.1639i	−0.370692	+	1.38344i	−0.859539	+	0.511071i	$0.829249\pi$
$762$	1.31960	+	0.881728i	0.0478041	+	0.0319417i
$763$	10.2283	−	3.56096i	0.370288	−	0.128915i
$764$		−	19.7212i		−	0.713487i
$765$	3.72220	−	1.37537i	0.134577	−	0.0497265i
$766$	−30.8327	−	17.8013i	−1.11403	−	0.643187i
$767$	26.7812	+	34.9019i	0.967013	+	1.26024i
$768$	20.7517	+	1.36014i	0.748811	+	0.0490797i
$769$	5.90321	−	5.90321i	0.212875	−	0.212875i	−0.592613	−	0.805488i	$-0.701903\pi$
$769$	5.90321	−	5.90321i	0.212875	−	0.212875i	0.805488	+	0.592613i	$0.201903\pi$
$770$	10.0067	−	4.23636i	0.360616	−	0.152668i
$771$	13.8918	−	9.28219i	0.500300	−	0.334290i
$772$	−1.51098	−	4.45120i	−0.0543813	−	0.160202i
$773$	7.84465	+	1.03277i	0.282153	+	0.0371461i	0.270274	−	0.962783i	$-0.412886\pi$
$773$	7.84465	+	1.03277i	0.282153	+	0.0371461i	0.0118783	+	0.999929i	$0.496219\pi$
$774$	−18.1988	−	2.39592i	−0.654144	−	0.0861196i
$775$	10.8415	+	31.9379i	0.389437	+	1.14724i
$776$	−16.2415	+	10.8522i	−0.583035	+	0.389572i
$777$	−16.5197	−	2.04432i	−0.592643	−	0.0733396i
$778$	−8.98143	+	8.98143i	−0.322000	+	0.322000i
$779$	−19.3216	−	1.26640i	−0.692268	−	0.0453737i
$780$	−4.46452	−	5.81828i	−0.159856	−	0.208328i
$781$	−4.13367	−	2.38658i	−0.147914	−	0.0853984i
$782$	−1.62933	+	42.0199i	−0.0582648	+	1.50263i
$783$			4.46955i			0.159729i
$784$	−30.1282	−	16.7753i	−1.07601	−	0.599119i
$785$	−5.62866	−	3.76095i	−0.200895	−	0.134234i
$786$	0.449100	−	1.67606i	0.0160189	−	0.0597832i
$787$	−28.3888	−	9.63668i	−1.01195	−	0.343511i	−0.234270	−	0.972172i	$-0.575270\pi$
$787$	−28.3888	−	9.63668i	−1.01195	−	0.343511i	−0.777680	+	0.628661i	$0.783603\pi$
$788$	0.739174	+	11.2776i	0.0263320	+	0.401748i
$789$	−28.2641	+	9.59437i	−1.00623	+	0.341569i
$790$	−8.62116	−	20.8133i	−0.306727	−	0.740505i
$791$	1.20863	+	16.4761i	0.0429741	+	0.585824i
$792$	−0.606427	+	3.04871i	−0.0215484	+	0.108331i
$793$	28.7225	−	58.2434i	1.01997	−	2.06829i
$794$	11.7027	−	34.4750i	0.415313	−	1.22347i
$795$	3.44705	+	12.8646i	0.122254	+	0.456260i
$796$	0.658644	−	10.0490i	0.0233450	−	0.356176i
$797$	−3.56943	+	8.61737i	−0.126436	+	0.305243i	−0.974404	−	0.224804i	$-0.927826\pi$
$797$	−3.56943	+	8.61737i	−0.126436	+	0.305243i	0.847968	+	0.530047i	$0.177826\pi$
$798$	15.3209	−	3.17155i	0.542353	−	0.112272i
$799$	−19.6366	+	0.524305i	−0.694695	+	0.0185486i
$800$	12.7821	+	22.1393i	0.451916	+	0.782741i
$801$	−3.45036	+	2.64755i	−0.121912	+	0.0935466i
$802$	4.02373	−	1.98428i	0.142083	−	0.0700675i
$803$	−1.90870	−	0.511435i	−0.0673566	−	0.0180481i
$804$	−2.34777	−	11.8030i	−0.0827995	−	0.416261i
$805$	−13.8972	−	3.60816i	−0.489811	−	0.127171i
$806$	88.0156	+	17.5074i	3.10022	+	0.616672i
$807$	−7.02455	−	5.39012i	−0.247276	−	0.189741i
$808$	−2.66022	+	20.2063i	−0.0935861	+	0.710857i
$809$	−36.2836	−	31.8199i	−1.27566	−	1.11873i	−0.986901	−	0.161326i	$-0.948423\pi$
$809$	−36.2836	−	31.8199i	−1.27566	−	1.11873i	−0.288762	−	0.957401i	$-0.593244\pi$
$810$	1.56127	+	0.769933i	0.0548574	+	0.0270527i
$811$	15.5910	−	3.10125i	0.547475	−	0.108899i	0.0863996	−	0.996261i	$-0.472464\pi$
$811$	15.5910	−	3.10125i	0.547475	−	0.108899i	0.461075	+	0.887361i	$0.347464\pi$
$812$	−0.866772	+	15.0121i	−0.0304177	+	0.526821i
$813$	8.73763	−	13.0768i	0.306442	−	0.458623i
$814$	3.50450	+	26.6193i	0.122833	+	0.933007i
$815$	−1.33875	+	2.31879i	−0.0468945	+	0.0812236i
$816$	−6.01320	+	19.4009i	−0.210504	+	0.679166i
$817$	−28.7337	+	16.5894i	−1.00526	+	0.580389i
$818$	−36.6387	−	15.1763i	−1.28104	−	0.530625i
$819$	−14.6946	−	5.95327i	−0.513471	−	0.208024i
$820$	−5.12521	−	5.12521i	−0.178980	−	0.178980i
$821$	3.53088	+	4.02619i	0.123228	+	0.140515i	0.810164	−	0.586203i	$-0.199378\pi$
$821$	3.53088	+	4.02619i	0.123228	+	0.140515i	−0.686936	+	0.726718i	$0.741045\pi$
$822$	5.43454	−	0.356198i	0.189551	−	0.0124238i
$823$	−19.9373	+	22.7341i	−0.694970	+	0.792461i	−0.986441	−	0.164118i	$-0.947522\pi$
$823$	−19.9373	+	22.7341i	−0.694970	+	0.792461i	0.291471	+	0.956580i	$0.405855\pi$
$824$	12.4907	−	16.2782i	0.435135	−	0.567079i
$825$	−8.87978	+	3.67812i	−0.309154	+	0.128056i
$826$	−30.5608	−	17.3289i	−1.06335	−	0.602948i
$827$	−6.37935	−	9.54737i	−0.221832	−	0.331995i	0.703815	−	0.710383i	$-0.251478\pi$
$827$	−6.37935	−	9.54737i	−0.221832	−	0.331995i	−0.925647	+	0.378389i	$0.876478\pi$
$828$	−5.39079	+	4.72760i	−0.187343	+	0.164295i
$829$	37.8703	−	10.1473i	1.31529	−	0.352431i	0.468078	−	0.883687i	$-0.344947\pi$
$829$	37.8703	−	10.1473i	1.31529	−	0.352431i	0.847211	+	0.531256i	$0.178280\pi$
$830$	2.72109	+	5.51783i	0.0944506	+	0.191527i
$831$	−1.45582	+	0.191663i	−0.0505020	+	0.00664871i
$832$	8.97771			0.311246
$833$	19.5282	−	21.2520i	0.676613	−	0.736339i
$834$	−31.9293			−1.10562
$835$	12.7983	−	1.68492i	0.442902	−	0.0583092i
$836$	−4.33826	−	8.79713i	−0.150042	−	0.304255i
$837$	−7.99723	+	2.14285i	−0.276425	+	0.0740677i
$838$	−1.72147	+	1.50969i	−0.0594672	+	0.0521513i
$839$	−13.8417	−	20.7156i	−0.477869	−	0.715182i	0.511712	−	0.859157i	$-0.329011\pi$
$839$	−13.8417	−	20.7156i	−0.477869	−	0.715182i	−0.989581	+	0.143975i	$0.954011\pi$
$840$	−2.91828	−	1.65475i	−0.100690	−	0.0570943i
$841$	8.33629	−	3.45300i	0.287458	−	0.119069i
$842$	−6.60305	+	8.60527i	−0.227556	+	0.296557i
$843$	−20.9614	+	23.9019i	−0.721948	+	0.823224i
$844$	13.6956	−	0.897660i	0.471423	−	0.0308987i
$845$	14.5383	+	16.5777i	0.500131	+	0.570291i
$846$	−6.09344	−	6.09344i	−0.209497	−	0.209497i
$847$	13.3236	+	5.39784i	0.457805	+	0.185472i
$848$	−62.9818	−	26.0879i	−2.16280	−	0.895863i
$849$	−20.0352	+	11.5673i	−0.687607	+	0.396990i
$850$	−29.1252	+	8.64356i	−0.998986	+	0.296472i
$851$	17.7378	−	30.7229i	0.608046	−	1.05317i
$852$	−0.335785	−	2.55054i	−0.0115038	−	0.0873799i
$853$	10.6715	−	15.9710i	0.365385	−	0.546837i	−0.602536	−	0.798091i	$-0.705843\pi$
$853$	10.6715	−	15.9710i	0.365385	−	0.546837i	0.967921	+	0.251255i	$0.0808432\pi$
$854$	−2.98935	+	51.7741i	−0.102293	+	1.77167i
$855$	3.08607	−	0.613858i	0.105541	−	0.0209935i
$856$	−13.8910	−	6.85027i	−0.474783	−	0.234137i
$857$	32.4762	+	28.4808i	1.10937	+	0.972887i	0.999778	−	0.0210900i	$-0.00671365\pi$
$857$	32.4762	+	28.4808i	1.10937	+	0.972887i	0.109588	+	0.993977i	$0.465047\pi$
$858$	−3.33796	+	25.3543i	−0.113956	+	0.865583i
$859$	−16.9512	−	13.0071i	−0.578366	−	0.443796i	0.277696	−	0.960669i	$-0.410429\pi$
$859$	−16.9512	−	13.0071i	−0.578366	−	0.443796i	−0.856062	+	0.516873i	$0.827096\pi$
$860$	−12.1811	−	2.42297i	−0.415372	−	0.0826227i
$861$	−15.1667	−	3.93778i	−0.516881	−	0.134199i
$862$	7.61159	+	38.2660i	0.259252	+	1.30335i
$863$	38.4863	+	10.3124i	1.31009	+	0.351037i	0.845256	−	0.534361i	$-0.179448\pi$
$863$	38.4863	+	10.3124i	1.31009	+	0.351037i	0.464833	+	0.885398i	$0.346114\pi$
$864$	−5.62821	+	2.77552i	−0.191475	+	0.0944252i
$865$	1.01003	−	0.775025i	0.0343421	−	0.0263516i
$866$	10.3134	+	17.8633i	0.350463	+	0.607020i
$867$	−14.6188	−	8.67696i	−0.496482	−	0.294685i
$868$	−27.2762	+	5.64641i	−0.925816	+	0.191652i
$869$	−11.6846	+	28.2090i	−0.396371	+	0.956925i
$870$	−0.508873	+	7.76390i	−0.0172524	+	0.263221i
$871$	14.6783	+	54.7801i	0.497354	+	1.85615i
$872$	−1.73358	+	5.10697i	−0.0587065	+	0.172944i
$873$	6.55747	−	13.2972i	0.221937	−	0.450043i
$874$	−6.50516	+	32.7036i	−0.220040	+	1.10622i
$875$	−1.69035	−	23.0429i	−0.0571442	−	0.778991i
$876$	−0.407560	−	0.983937i	−0.0137702	−	0.0332441i
$877$	−22.3235	+	7.57782i	−0.753812	+	0.255885i	−0.671786	−	0.740745i	$-0.734473\pi$
$877$	−22.3235	+	7.57782i	−0.753812	+	0.255885i	−0.0820264	+	0.996630i	$0.526139\pi$
$878$	−0.667253	−	10.1803i	−0.0225187	−	0.343569i
$879$	11.7060	+	3.97365i	0.394833	+	0.134028i
$880$	−2.89515	+	10.8049i	−0.0975955	+	0.364232i
$881$	−2.04934	−	1.36933i	−0.0690441	−	0.0461338i	0.520569	−	0.853820i	$-0.325720\pi$
$881$	−2.04934	−	1.36933i	−0.0690441	−	0.0461338i	−0.589613	+	0.807686i	$0.700720\pi$
$882$	12.6598	−	0.196891i	0.426277	−	0.00662966i
$883$			19.0173i			0.639983i	0.947420	+	0.319992i	$0.103680\pi$
$883$			19.0173i			0.639983i	−0.947420	+	0.319992i	$0.896320\pi$
$884$	−7.31880	+	30.5542i	−0.246158	+	1.02765i
$885$	−6.11886	−	3.53272i	−0.205683	−	0.118751i
$886$	32.7473	+	42.6771i	1.10017	+	1.43376i
$887$	−8.83283	−	0.578934i	−0.296577	−	0.0194387i	−0.0836117	−	0.996498i	$-0.526646\pi$
$887$	−8.83283	−	0.578934i	−0.296577	−	0.0194387i	−0.212966	+	0.977060i	$0.568312\pi$
$888$	5.86123	−	5.86123i	0.196690	−	0.196690i
$889$	2.30390	+	0.285108i	0.0772705	+	0.00956223i
$890$	−6.29493	+	4.20613i	−0.211006	+	0.140990i
$891$	−0.758390	−	2.23415i	−0.0254070	−	0.0748467i
$892$	12.4063	+	1.63332i	0.415394	+	0.0546877i
$893$	−15.4430	−	2.03311i	−0.516780	−	0.0680354i
$894$	−8.43349	−	24.8442i	−0.282058	−	0.830916i
$895$	10.2402	−	6.84231i	0.342293	−	0.228713i
$896$	23.9766	−	10.1505i	0.801001	−	0.339106i
$897$	23.8930	−	23.8930i	0.797765	−	0.797765i
$898$	−47.3075	−	3.10070i	−1.57867	−	0.103472i
$899$	−22.5272	−	29.3580i	−0.751323	−	0.979143i
$900$	−4.48616	−	2.59009i	−0.149539	−	0.0863362i
$901$	33.5136	−	46.1774i	1.11650	−	1.53839i
$902$			25.2745i			0.841548i
$903$	−25.3572	+	8.82807i	−0.843834	+	0.293780i
$904$	−6.84017	−	4.57046i	−0.227501	−	0.152011i
$905$	1.02797	−	3.83645i	0.0341710	−	0.127528i
$906$	11.7974	+	4.00467i	0.391942	+	0.133046i
$907$	−2.42380	−	36.9800i	−0.0804809	−	1.22790i	−0.826871	−	0.562392i	$-0.809881\pi$
$907$	−2.42380	−	36.9800i	−0.0804809	−	1.22790i	0.746390	−	0.665509i	$-0.231786\pi$
$908$	12.7116	−	4.31501i	0.421850	−	0.143199i
$909$	−5.91984	−	14.2918i	−0.196349	−	0.474028i
$910$	−24.8477	−	12.0142i	−0.823693	−	0.398268i
$911$	−10.4374	+	52.4724i	−0.345807	+	1.73849i	0.281360	+	0.959602i	$0.409214\pi$
$911$	−10.4374	+	52.4724i	−0.345807	+	1.73849i	−0.627167	+	0.778885i	$0.715786\pi$
$912$	−7.12338	+	14.4448i	−0.235879	+	0.478315i
$913$	2.68030	−	7.89591i	0.0887050	−	0.261317i
$914$	−5.87410	−	21.9224i	−0.194298	−	0.725130i
$915$	−0.682137	+	10.4074i	−0.0225507	+	0.344058i
$916$	2.33701	−	5.64203i	0.0772169	−	0.186418i
$917$	−0.514508	−	2.48544i	−0.0169905	−	0.0820766i
$918$	−1.64963	−	7.27296i	−0.0544460	−	0.240043i
$919$	11.7553	+	20.3608i	0.387772	+	0.671641i	0.992150	−	0.125057i	$-0.0399115\pi$
$919$	11.7553	+	20.3608i	0.387772	+	0.671641i	−0.604378	+	0.796698i	$0.706578\pi$
$920$	5.67229	−	4.35250i	0.187010	−	0.143498i
$921$	12.4790	−	6.15395i	0.411196	−	0.202779i
$922$	23.9336	+	6.41298i	0.788210	+	0.211200i
$923$	2.36514	+	11.8904i	0.0778497	+	0.391377i
$924$	−2.11398	−	7.65101i	−0.0695448	−	0.251700i
$925$	25.1375	+	5.00016i	0.826515	+	0.164404i
$926$	4.04059	+	3.10045i	0.132782	+	0.101887i
$927$	−2.03278	+	15.4405i	−0.0667651	+	0.507131i
$928$	−21.0877	−	18.4934i	−0.692236	−	0.607075i
$929$	−32.8794	−	16.2143i	−1.07874	−	0.531976i	−0.186001	−	0.982550i	$-0.559553\pi$
$929$	−32.8794	−	16.2143i	−1.07874	−	0.531976i	−0.892739	+	0.450574i	$0.851219\pi$
$930$	−14.1357	+	2.81176i	−0.463527	+	0.0922013i
$931$	17.9376	−	14.2126i	0.587880	−	0.465798i
$932$	−2.16112	+	3.23435i	−0.0707899	+	0.105945i
$933$	1.80814	+	13.7342i	0.0591958	+	0.449637i
$934$	−1.52202	+	2.63622i	−0.0498021	+	0.0862597i
$935$	−8.23009	−	4.46310i	−0.269153	−	0.145959i
$936$	6.83738	−	3.94756i	0.223487	−	0.129030i
$937$	18.4828	+	7.65584i	0.603808	+	0.250105i	0.663578	−	0.748107i	$-0.269037\pi$
$937$	18.4828	+	7.65584i	0.603808	+	0.250105i	−0.0597707	+	0.998212i	$0.519037\pi$
$938$	−27.8491	−	35.7151i	−0.909304	−	1.16614i
$939$	−22.0654	−	22.0654i	−0.720078	−	0.720078i
$940$	−3.84440	−	4.38370i	−0.125391	−	0.142981i
$941$	31.7790	−	2.08291i	1.03597	−	0.0679008i	0.462082	−	0.886837i	$-0.347103\pi$
$941$	31.7790	−	2.08291i	1.03597	−	0.0679008i	0.573884	+	0.818937i	$0.305436\pi$
$942$	−8.38851	+	9.56527i	−0.273313	+	0.311653i
$943$	20.3297	−	26.4942i	0.662028	−	0.862771i
$944$	33.4121	−	13.8397i	1.08747	−	0.450445i
$945$	2.54626	−	0.0197991i	0.0828298	−	0.000644066i
$946$	24.0607	+	36.0093i	0.782279	+	1.17076i
$947$	−27.8123	+	24.3908i	−0.903780	+	0.792593i	−0.978849	−	0.204585i	$-0.934416\pi$
$947$	−27.8123	+	24.3908i	−0.903780	+	0.792593i	0.0750692	+	0.997178i	$0.476082\pi$
$948$	−15.8955	+	4.25919i	−0.516262	+	0.138332i
$949$	2.21981	+	4.50134i	0.0720582	+	0.146120i
$950$	−23.8840	+	3.14439i	−0.774900	+	0.102018i
$951$	25.5722			0.829237
$952$	2.36590	+	14.1761i	0.0766792	+	0.459450i
$953$	18.2040			0.589685			0.294842	−	0.955546i	$-0.404733\pi$
$953$	18.2040			0.589685			0.294842	+	0.955546i	$0.404733\pi$
$954$	24.8161	−	3.26710i	0.803451	−	0.105776i
$955$	−6.60167	−	13.3869i	−0.213625	−	0.433189i
$956$	18.0656	−	4.84067i	0.584284	−	0.156558i
$957$	7.92834	−	6.95297i	0.256287	−	0.224758i
$958$	5.30363	+	7.93744i	0.171352	+	0.256447i
$959$	6.86793	−	4.03672i	0.221777	−	0.130353i
$960$	−1.33210	+	0.551775i	−0.0429934	+	0.0178084i
$961$	22.8574	−	29.7884i	0.737337	−	0.960916i
$962$	44.9633	−	51.2708i	1.44967	−	1.65304i
$963$	11.7306	−	0.768867i	0.378015	−	0.0247764i
$964$	5.29164	+	6.03396i	0.170432	+	0.194341i
$965$	−2.51570	−	2.51570i	−0.0809834	−	0.0809834i
$966$	−10.1322	+	25.0095i	−0.325997	+	0.804666i
$967$	−11.4887	−	4.75876i	−0.369450	−	0.153031i	0.190231	−	0.981739i	$-0.439076\pi$
$967$	−11.4887	−	4.75876i	−0.369450	−	0.153031i	−0.559681	+	0.828708i	$0.689076\pi$
$968$	−6.19947	+	3.57926i	−0.199258	+	0.115042i
$969$	−10.3684	−	8.61431i	−0.333082	−	0.276731i
$970$	12.9047	−	22.3516i	0.414344	−	0.717666i
$971$	3.13041	+	23.7778i	0.100460	+	0.763066i	0.965323	+	0.261059i	$0.0840717\pi$
$971$	3.13041	+	23.7778i	0.100460	+	0.763066i	−0.864863	+	0.502008i	$0.832595\pi$
$972$	0.706464	−	1.05730i	0.0226599	−	0.0339129i
$973$	−41.7260	+	20.9819i	−1.33768	+	0.672649i
$974$	−41.0718	+	8.16970i	−1.31603	+	0.261774i
$975$	21.8945	+	10.7971i	0.701184	+	0.345786i
$976$	−40.1371	−	35.1993i	−1.28476	−	1.12670i
$977$	−1.33073	+	10.1079i	−0.0425738	+	0.323380i	0.956884	+	0.290469i	$0.0938113\pi$
$977$	−1.33073	+	10.1079i	−0.0425738	+	0.323380i	−0.999458	+	0.0329114i	$0.989522\pi$
$978$	3.99219	+	3.06331i	0.127656	+	0.0979539i
$979$	10.0639	+	2.00183i	0.321642	+	0.0639787i
$980$	8.55608	+	0.427291i	0.273314	+	0.0136493i
$981$	−0.798605	−	4.01486i	−0.0254975	−	0.128185i
$982$	−25.4143	−	6.80975i	−0.811004	−	0.217308i
$983$	−50.5392	+	24.9232i	−1.61195	+	0.794926i	−0.611960	+	0.790889i	$0.709618\pi$
$983$	−50.5392	+	24.9232i	−1.61195	+	0.794926i	−0.999992	+	0.00403734i	$0.998715\pi$
$984$	6.19048	−	4.75012i	0.197345	−	0.151428i
$985$	4.27694	+	7.40789i	0.136275	+	0.236035i
$986$	27.2108	−	19.2517i	0.866570	−	0.613099i
$987$	−11.9673	−	3.95885i	−0.380923	−	0.126012i
$988$	−9.53381	+	23.0166i	−0.303311	+	0.732257i
$989$	3.74257	−	57.1005i	0.119007	−	1.81569i
$990$	−1.06301	−	3.96720i	−0.0337846	−	0.126086i
$991$	12.6980	−	37.4070i	0.403364	−	1.18827i	−0.535663	−	0.844432i	$-0.679938\pi$
$991$	12.6980	−	37.4070i	0.403364	−	1.18827i	0.939028	−	0.343842i	$-0.111728\pi$
$992$	22.9795	−	46.5978i	0.729600	−	1.47948i
$993$	−1.43193	+	7.19878i	−0.0454408	+	0.228446i
$994$	−5.44116	−	8.00778i	−0.172583	−	0.253991i
$995$	−2.91681	−	7.04179i	−0.0924690	−	0.223240i
$996$	4.25559	−	1.44458i	0.134844	−	0.0457732i
$997$	−0.399276	−	6.09178i	−0.0126452	−	0.192929i	−0.999508	−	0.0313675i	$-0.990014\pi$
$997$	−0.399276	−	6.09178i	−0.0126452	−	0.192929i	0.986863	−	0.161561i	$-0.0516529\pi$
$998$	−36.2236	−	12.2963i	−1.14664	−	0.389231i
$999$	−1.62836	+	6.07713i	−0.0515191	+	0.192272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.5	✓	384
7.5	odd	6	inner	357.2.bl.a.61.20	yes	384
17.12	odd	16	inner	357.2.bl.a.199.20	yes	384
119.12	even	48	inner	357.2.bl.a.250.5	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.5	✓	384	1.1	even	1	trivial
357.2.bl.a.61.20	yes	384	7.5	odd	6	inner
357.2.bl.a.199.20	yes	384	17.12	odd	16	inner
357.2.bl.a.250.5	yes	384	119.12	even	48	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79328 + 0.236090i) q^{2} +(0.442289 + 0.896873i) q^{3} +(1.22827 - 0.329115i) q^{4} +(0.723589 - 0.634571i) q^{5} +(-1.00489 - 1.50393i) q^{6} +(-2.30150 - 1.30502i) q^{7} +(1.21721 - 0.504184i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-1.14778 + 1.30880i) q^{10} +(2.35430 - 0.154309i) q^{11} +(0.838425 + 0.956041i) q^{12} +(-4.23736 - 4.23736i) q^{13} +(4.43535 + 1.79691i) q^{14} +(0.889164 + 0.368304i) q^{15} +(-4.26624 + 2.46312i) q^{16} +(-1.17306 - 3.95271i) q^{17} +(0.904379 - 1.56643i) q^{18} +(-0.426740 - 3.24141i) q^{19} +(0.679919 - 1.01757i) q^{20} +(0.152507 - 2.64135i) q^{21} +(-4.18550 + 0.832548i) q^{22} +(5.05716 + 2.49392i) q^{23} +(0.990545 + 0.868685i) q^{24} +(-0.531730 + 4.03889i) q^{25} +(8.59918 + 6.59838i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-3.25638 - 0.845461i) q^{28} +(-0.871966 - 4.38367i) q^{29} +(-1.68148 - 0.450550i) q^{30} +(7.42551 - 3.66186i) q^{31} +(4.97858 - 3.82020i) q^{32} +(1.17968 + 2.04326i) q^{33} +(3.03682 + 6.81138i) q^{34} +(-2.49347 + 0.516169i) q^{35} +(-0.486621 + 1.17481i) q^{36} +(0.411484 - 6.27804i) q^{37} +(1.53053 + 5.71202i) q^{38} +(1.92624 - 5.67451i) q^{39} +(0.560817 - 1.13723i) q^{40} +(1.15543 - 5.80875i) q^{41} +(0.350109 + 4.77270i) q^{42} +(-3.88360 - 9.37584i) q^{43} +(2.84094 - 0.964370i) q^{44} +(0.0629456 + 0.960364i) q^{45} +(-9.65772 - 3.27835i) q^{46} +(1.23309 - 4.60194i) q^{47} +(-4.09601 - 2.73687i) q^{48} +(3.59385 + 6.00702i) q^{49} -7.36840i q^{50} +(3.02625 - 2.80032i) q^{51} +(-6.59921 - 3.81006i) q^{52} +(8.42427 + 10.9787i) q^{53} +(1.80488 + 0.118298i) q^{54} +(1.60563 - 1.60563i) q^{55} +(-3.45938 - 0.428098i) q^{56} +(2.71839 - 1.81637i) q^{57} +(2.59862 + 7.65529i) q^{58} +(-7.27849 - 0.958232i) q^{59} +(1.21335 + 0.159741i) q^{60} +(3.48342 + 10.2618i) q^{61} +(-12.4515 + 8.31984i) q^{62} +(2.43641 - 1.03146i) q^{63} +(-1.05935 + 1.05935i) q^{64} +(-5.75501 - 0.377203i) q^{65} +(-2.59789 - 3.38564i) q^{66} +(-8.19595 - 4.73193i) q^{67} +(-2.74173 - 4.46894i) q^{68} +5.63867i q^{69} +(4.34964 - 1.51432i) q^{70} +(-1.68212 - 1.12396i) q^{71} +(-0.340993 + 1.27260i) q^{72} +(-0.793083 - 0.269215i) q^{73} +(0.744275 + 11.3554i) q^{74} +(-3.85755 + 1.30946i) q^{75} +(-1.59095 - 3.84089i) q^{76} +(-5.61982 - 2.71727i) q^{77} +(-2.11459 + 10.6308i) q^{78} +(-5.72381 + 11.6067i) q^{79} +(-1.52399 + 4.48952i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.700628 + 10.6895i) q^{82} +(1.35248 - 3.26517i) q^{83} +(-0.681988 - 3.29449i) q^{84} +(-3.35709 - 2.11575i) q^{85} +(9.17794 + 15.8967i) q^{86} +(3.54593 - 2.72089i) q^{87} +(2.78788 - 1.37483i) q^{88} +(4.20089 + 1.12562i) q^{89} +(-0.339612 - 1.70734i) q^{90} +(4.22246 + 15.2821i) q^{91} +(7.03237 + 1.39882i) q^{92} +(6.56844 + 5.04014i) q^{93} +(-1.12480 + 8.54371i) q^{94} +(-2.36569 - 2.07465i) q^{95} +(5.62821 + 2.77552i) q^{96} +(-14.5413 + 2.89245i) q^{97} +(-7.86298 - 9.92381i) q^{98} +(-1.31079 + 1.96173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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