LMFDB - Embedded newform 350.2.r.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-1.42631 - 0.726740i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.81867 + 1.30093i) q^{5} +(1.52243 + 0.494669i) q^{6} +(1.53413 + 2.15556i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.257154 - 0.353942i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.42631 - 0.726740i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.81867 + 1.30093i) q^{5} +(1.52243 + 0.494669i) q^{6} +(1.53413 + 2.15556i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.257154 - 0.353942i) q^{9} +(-1.99979 - 1.00041i) q^{10} +(-2.70996 - 1.96890i) q^{11} +(-1.58107 - 0.250418i) q^{12} +(-0.820317 + 5.17928i) q^{13} +(-1.85245 - 1.88903i) q^{14} +(-1.64855 - 3.17723i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.41312 - 2.24859i) q^{17} +(0.309356 + 0.309356i) q^{18} +(-0.820727 + 2.52594i) q^{19} +(2.13167 + 0.675260i) q^{20} +(-0.621614 - 4.18941i) q^{21} +(2.98460 + 1.52073i) q^{22} +(1.30534 + 8.24157i) q^{23} +1.60078 q^{24} +(1.61515 + 4.73195i) q^{25} -5.24384i q^{26} +(0.860809 + 5.43494i) q^{27} +(2.12515 + 1.57599i) q^{28} +(9.50947 - 3.08982i) q^{29} +(2.12528 + 2.88023i) q^{30} +(-0.0905199 - 0.0294117i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.43435 + 4.77769i) q^{33} +(-4.00702 + 2.91127i) q^{34} +(-0.0141528 + 5.91606i) q^{35} +(-0.353942 - 0.257154i) q^{36} +(-0.202466 + 1.27832i) q^{37} +(0.415479 - 2.62323i) q^{38} +(4.93401 - 6.79109i) q^{39} +(-2.21106 - 0.333480i) q^{40} +(3.94647 + 5.43185i) q^{41} +(1.26933 + 4.04059i) q^{42} +(-6.37353 - 6.37353i) q^{43} +(-3.18575 - 1.03511i) q^{44} +(-0.00722408 - 0.978244i) q^{45} +(-2.57853 - 7.93591i) q^{46} +(1.40495 - 2.75737i) q^{47} +(-1.58107 + 0.250418i) q^{48} +(-2.29287 + 6.61383i) q^{49} +(-2.33550 - 4.42102i) q^{50} -7.92860 q^{51} +(0.820317 + 5.17928i) q^{52} +(1.32085 - 2.59231i) q^{53} +(-1.70042 - 5.23336i) q^{54} +(-2.36712 - 7.10626i) q^{55} +(-2.34553 - 1.22414i) q^{56} +(3.00631 - 3.00631i) q^{57} +(-8.90904 + 4.53938i) q^{58} +(0.832854 - 0.605104i) q^{59} +(-2.54968 - 2.51230i) q^{60} +(-6.83675 + 9.40998i) q^{61} +(0.0940065 + 0.0148892i) q^{62} +(0.368434 - 1.09730i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-8.22978 + 8.35224i) q^{65} +(-3.15178 - 4.33805i) q^{66} +(2.22863 + 4.37394i) q^{67} +(3.50227 - 3.50227i) q^{68} +(4.12767 - 12.7037i) q^{69} +(-0.911498 - 5.84544i) q^{70} +(-2.60623 - 8.02115i) q^{71} +(0.389812 + 0.198619i) q^{72} +(-0.273027 + 0.0432433i) q^{73} -1.29426i q^{74} +(1.13520 - 7.92300i) q^{75} +2.65593i q^{76} +(0.0866458 - 8.86203i) q^{77} +(-3.81091 + 7.47933i) q^{78} +(9.33602 - 3.03346i) q^{79} +(2.23601 - 0.0165123i) q^{80} +(2.31643 - 7.12922i) q^{81} +(-4.74761 - 4.74761i) q^{82} +(-5.48037 - 10.7558i) q^{83} +(-1.88579 - 3.79227i) q^{84} +(10.9513 + 1.65171i) q^{85} +(7.29210 + 5.29802i) q^{86} +(-15.8089 - 2.50389i) q^{87} +(3.30845 + 0.524007i) q^{88} +(7.38182 + 5.36320i) q^{89} +(0.160166 + 0.965070i) q^{90} +(-12.4227 + 6.17746i) q^{91} +(3.78824 + 7.43483i) q^{92} +(0.107735 + 0.107735i) q^{93} +(-0.956306 + 2.94321i) q^{94} +(-4.77871 + 3.52615i) q^{95} +(1.52243 - 0.494669i) q^{96} +(0.525421 - 1.03120i) q^{97} +(1.23001 - 6.89109i) q^{98} +1.46548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−1.42631	−	0.726740i	−0.823479	−	0.419584i	−0.00912955	−	0.999958i	$-0.502906\pi$
$3$	−1.42631	−	0.726740i	−0.823479	−	0.419584i	−0.814349	+	0.580375i	$0.802906\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.81867	+	1.30093i	0.813335	+	0.581795i
$5$	1.81867	+	1.30093i	0.813335	+	0.581795i
$6$	1.52243	+	0.494669i	0.621531	+	0.201948i
$7$	1.53413	+	2.15556i	0.579848	+	0.814725i
$7$	1.53413	+	2.15556i	0.579848	+	0.814725i
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−0.257154	−	0.353942i	−0.0857179	−	0.117981i
$10$	−1.99979	−	1.00041i	−0.632390	−	0.316358i
$11$	−2.70996	−	1.96890i	−0.817083	−	0.593645i	0.0987925	−	0.995108i	$-0.468502\pi$
$11$	−2.70996	−	1.96890i	−0.817083	−	0.593645i	−0.915875	+	0.401463i	$0.868502\pi$
$12$	−1.58107	−	0.250418i	−0.456417	−	0.0722893i
$13$	−0.820317	+	5.17928i	−0.227515	+	1.43647i	0.564228	+	0.825619i	$0.309174\pi$
$13$	−0.820317	+	5.17928i	−0.227515	+	1.43647i	−0.791743	+	0.610854i	$0.790826\pi$
$14$	−1.85245	−	1.88903i	−0.495088	−	0.504864i
$15$	−1.64855	−	3.17723i	−0.425653	−	0.820358i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.41312	−	2.24859i	1.07034	−	0.545364i	0.172193	−	0.985063i	$-0.444915\pi$
$17$	4.41312	−	2.24859i	1.07034	−	0.545364i	0.898145	+	0.439699i	$0.144915\pi$
$18$	0.309356	+	0.309356i	0.0729160	+	0.0729160i
$19$	−0.820727	+	2.52594i	−0.188288	+	0.579490i	−0.999990	−	0.00458209i	$-0.998541\pi$
$19$	−0.820727	+	2.52594i	−0.188288	+	0.579490i	0.811702	+	0.584072i	$0.198541\pi$
$20$	2.13167	+	0.675260i	0.476656	+	0.150993i
$21$	−0.621614	−	4.18941i	−0.135647	−	0.914203i
$22$	2.98460	+	1.52073i	0.636318	+	0.324220i
$23$	1.30534	+	8.24157i	0.272182	+	1.71849i	0.623153	+	0.782100i	$0.285852\pi$
$23$	1.30534	+	8.24157i	0.272182	+	1.71849i	−0.350971	+	0.936386i	$0.614148\pi$
$24$	1.60078			0.326758
$25$	1.61515	+	4.73195i	0.323029	+	0.946389i
$26$		−	5.24384i		−	1.02840i
$27$	0.860809	+	5.43494i	0.165663	+	1.04595i
$28$	2.12515	+	1.57599i	0.401616	+	0.297833i
$29$	9.50947	−	3.08982i	1.76587	−	0.573764i	0.768084	−	0.640349i	$-0.221210\pi$
$29$	9.50947	−	3.08982i	1.76587	−	0.573764i	0.997781	+	0.0665845i	$0.0212102\pi$
$30$	2.12528	+	2.88023i	0.388021	+	0.525855i
$31$	−0.0905199	−	0.0294117i	−0.0162579	−	0.00528250i	0.300877	−	0.953663i	$-0.402721\pi$
$31$	−0.0905199	−	0.0294117i	−0.0162579	−	0.00528250i	−0.317135	+	0.948381i	$0.602721\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.43435	+	4.77769i	0.423767	+	0.831689i
$34$	−4.00702	+	2.91127i	−0.687199	+	0.499279i
$35$	−0.0141528	+	5.91606i	−0.00239227	+	0.999997i
$36$	−0.353942	−	0.257154i	−0.0589903	−	0.0428589i
$37$	−0.202466	+	1.27832i	−0.0332853	+	0.210155i	−0.998726	−	0.0504692i	$-0.983928\pi$
$37$	−0.202466	+	1.27832i	−0.0332853	+	0.210155i	0.965440	+	0.260624i	$0.0839283\pi$
$38$	0.415479	−	2.62323i	0.0673996	−	0.425544i
$39$	4.93401	−	6.79109i	0.790074	−	1.08744i
$40$	−2.21106	−	0.333480i	−0.349599	−	0.0527277i
$41$	3.94647	+	5.43185i	0.616335	+	0.848313i	0.997080	−	0.0763675i	$-0.0243322\pi$
$41$	3.94647	+	5.43185i	0.616335	+	0.848313i	−0.380744	+	0.924680i	$0.624332\pi$
$42$	1.26933	+	4.04059i	0.195862	+	0.623476i
$43$	−6.37353	−	6.37353i	−0.971954	−	0.971954i	0.0276633	−	0.999617i	$-0.491193\pi$
$43$	−6.37353	−	6.37353i	−0.971954	−	0.971954i	−0.999617	+	0.0276633i	$0.991193\pi$
$44$	−3.18575	−	1.03511i	−0.480269	−	0.156049i
$45$	−0.00722408	−	0.978244i	−0.00107690	−	0.145828i
$46$	−2.57853	−	7.93591i	−0.380184	−	1.17009i
$47$	1.40495	−	2.75737i	0.204933	−	0.402204i	−0.765549	−	0.643378i	$-0.777532\pi$
$47$	1.40495	−	2.75737i	0.204933	−	0.402204i	0.970482	+	0.241174i	$0.0775324\pi$
$48$	−1.58107	+	0.250418i	−0.228208	+	0.0361447i
$49$	−2.29287	+	6.61383i	−0.327553	+	0.944833i
$50$	−2.33550	−	4.42102i	−0.330290	−	0.625227i
$51$	−7.92860			−1.11023
$52$	0.820317	+	5.17928i	0.113758	+	0.718237i
$53$	1.32085	−	2.59231i	0.181432	−	0.356081i	−0.782321	−	0.622875i	$-0.785964\pi$
$53$	1.32085	−	2.59231i	0.181432	−	0.356081i	0.963754	+	0.266794i	$0.0859644\pi$
$54$	−1.70042	−	5.23336i	−0.231398	−	0.712170i
$55$	−2.36712	−	7.10626i	−0.319183	−	0.958208i
$56$	−2.34553	−	1.22414i	−0.313434	−	0.163582i
$57$	3.00631	−	3.00631i	0.398195	−	0.398195i
$58$	−8.90904	+	4.53938i	−1.16981	+	0.596050i
$59$	0.832854	−	0.605104i	0.108428	−	0.0787778i	−0.532250	−	0.846587i	$-0.678653\pi$
$59$	0.832854	−	0.605104i	0.108428	−	0.0787778i	0.640678	+	0.767810i	$0.278653\pi$
$60$	−2.54968	−	2.51230i	−0.329162	−	0.324336i
$61$	−6.83675	+	9.40998i	−0.875356	+	1.20482i	0.102329	+	0.994751i	$0.467370\pi$
$61$	−6.83675	+	9.40998i	−0.875356	+	1.20482i	−0.977686	+	0.210074i	$0.932630\pi$
$62$	0.0940065	+	0.0148892i	0.0119388	+	0.00189093i
$63$	0.368434	−	1.09730i	0.0464184	−	0.138247i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−8.22978	+	8.35224i	−1.02078	+	1.03597i
$66$	−3.15178	−	4.33805i	−0.387957	−	0.533977i
$67$	2.22863	+	4.37394i	0.272271	+	0.534362i	0.986140	−	0.165918i	$-0.0530587\pi$
$67$	2.22863	+	4.37394i	0.272271	+	0.534362i	−0.713869	+	0.700280i	$0.753059\pi$
$68$	3.50227	−	3.50227i	0.424712	−	0.424712i
$69$	4.12767	−	12.7037i	0.496913	−	1.52934i
$70$	−0.911498	−	5.84544i	−0.108945	−	0.698664i
$71$	−2.60623	−	8.02115i	−0.309303	−	0.951936i	−0.978036	−	0.208434i	$-0.933163\pi$
$71$	−2.60623	−	8.02115i	−0.309303	−	0.951936i	0.668734	−	0.743502i	$-0.266837\pi$
$72$	0.389812	+	0.198619i	0.0459397	+	0.0234075i
$73$	−0.273027	+	0.0432433i	−0.0319554	+	0.00506124i	−0.172392	−	0.985028i	$-0.555149\pi$
$73$	−0.273027	+	0.0432433i	−0.0319554	+	0.00506124i	0.140436	+	0.990090i	$0.455149\pi$
$74$		−	1.29426i		−	0.150454i
$75$	1.13520	−	7.92300i	0.131082	−	0.914869i
$76$			2.65593i			0.304656i
$77$	0.0866458	−	8.86203i	0.00987420	−	1.00992i
$78$	−3.81091	+	7.47933i	−0.431500	+	0.846867i
$79$	9.33602	−	3.03346i	1.05038	−	0.341291i	0.267565	−	0.963540i	$-0.413781\pi$
$79$	9.33602	−	3.03346i	1.05038	−	0.341291i	0.782819	+	0.622249i	$0.213781\pi$
$80$	2.23601	−	0.0165123i	0.249993	−	0.00184614i
$81$	2.31643	−	7.12922i	0.257381	−	0.792136i
$82$	−4.74761	−	4.74761i	−0.524286	−	0.524286i
$83$	−5.48037	−	10.7558i	−0.601549	−	1.18061i	−0.968184	−	0.250241i	$-0.919490\pi$
$83$	−5.48037	−	10.7558i	−0.601549	−	1.18061i	0.366635	−	0.930365i	$-0.380510\pi$
$84$	−1.88579	−	3.79227i	−0.205756	−	0.413771i
$85$	10.9513	+	1.65171i	1.18783	+	0.179153i
$86$	7.29210	+	5.29802i	0.786327	+	0.571300i
$87$	−15.8089	−	2.50389i	−1.69489	−	0.268445i
$88$	3.30845	+	0.524007i	0.352682	+	0.0558594i
$89$	7.38182	+	5.36320i	0.782471	+	0.568498i	0.905720	−	0.423877i	$-0.139331\pi$
$89$	7.38182	+	5.36320i	0.782471	+	0.568498i	−0.123249	+	0.992376i	$0.539331\pi$
$90$	0.160166	+	0.965070i	0.0168830	+	0.101727i
$91$	−12.4227	+	6.17746i	−1.30225	+	0.647573i
$92$	3.78824	+	7.43483i	0.394951	+	0.775135i
$93$	0.107735	+	0.107735i	0.0111716	+	0.0111716i
$94$	−0.956306	+	2.94321i	−0.0986354	+	0.303569i
$95$	−4.77871	+	3.52615i	−0.490285	+	0.361775i
$96$	1.52243	−	0.494669i	0.155383	−	0.0504869i
$97$	0.525421	−	1.03120i	0.0533484	−	0.104702i	−0.862793	−	0.505557i	$-0.831287\pi$
$97$	0.525421	−	1.03120i	0.0533484	−	0.104702i	0.916141	+	0.400855i	$0.131287\pi$
$98$	1.23001	−	6.89109i	0.124250	−	0.696105i
$99$			1.46548i			0.147286i
$100$	2.99835	+	4.00124i	0.299835	+	0.400124i
$101$		−	13.4917i		−	1.34248i	−0.741241	−	0.671239i	$-0.765763\pi$
$101$		−	13.4917i		−	1.34248i	0.741241	−	0.671239i	$-0.234237\pi$
$102$	7.83099	−	1.24031i	0.775383	−	0.122809i
$103$	−4.08511	−	2.08147i	−0.402518	−	0.205093i	0.240999	−	0.970525i	$-0.422525\pi$
$103$	−4.08511	−	2.08147i	−0.402518	−	0.205093i	−0.643516	+	0.765432i	$0.722525\pi$
$104$	−1.62044	−	4.98719i	−0.158897	−	0.489034i
$105$	4.31963	−	8.42784i	0.421552	−	0.822473i
$106$	−0.899060	+	2.76702i	−0.0873244	+	0.268757i
$107$	−10.0230	+	10.0230i	−0.968962	+	0.968962i	−0.999533	−	0.0305711i	$-0.990267\pi$
$107$	−10.0230	+	10.0230i	−0.968962	+	0.968962i	0.0305711	+	0.999533i	$0.490267\pi$
$108$	2.49817	+	4.90293i	0.240386	+	0.471784i
$109$	−0.826894	−	1.13812i	−0.0792020	−	0.109012i	0.767578	−	0.640956i	$-0.221462\pi$
$109$	−0.826894	−	1.13812i	−0.0792020	−	0.109012i	−0.846780	+	0.531944i	$0.821462\pi$
$110$	3.44964	+	6.64847i	0.328910	+	0.633907i
$111$	1.21779	−	1.67614i	0.115587	−	0.159092i
$112$	2.50815	+	0.842144i	0.236997	+	0.0795751i
$113$	−15.8119	−	2.50435i	−1.48745	−	0.235590i	−0.640790	−	0.767716i	$-0.721393\pi$
$113$	−15.8119	−	2.50435i	−1.48745	−	0.235590i	−0.846665	+	0.532127i	$0.821393\pi$
$114$	−2.49901	+	3.43959i	−0.234053	+	0.322147i
$115$	−8.34775	+	16.6869i	−0.778432	+	1.55606i
$116$	8.08924	−	5.87718i	0.751067	−	0.545682i
$117$	2.04411	−	1.04153i	0.188978	−	0.0962891i
$118$	−0.727941	+	0.727941i	−0.0670124	+	0.0670124i
$119$	11.6173	+	6.06309i	1.06495	+	0.555803i
$120$	2.91130	+	2.08251i	0.265764	+	0.190106i
$121$	0.0681178	+	0.209645i	0.00619253	+	0.0190587i
$122$	5.28053	−	10.3636i	0.478077	−	0.938279i
$123$	−1.68134	−	10.6156i	−0.151601	−	0.957172i
$124$	−0.0951783			−0.00854726
$125$	−3.21852	+	10.7071i	−0.287873	+	0.957668i
$126$	−0.192242	+	1.14143i	−0.0171263	+	0.101687i
$127$	13.6409	−	2.16050i	1.21043	−	0.191713i	0.481590	−	0.876396i	$-0.340059\pi$
$127$	13.6409	−	2.16050i	1.21043	−	0.191713i	0.728841	+	0.684683i	$0.240059\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	4.45871	+	13.7225i	0.392568	+	1.20820i
$130$	6.82188	−	9.53683i	0.598319	−	0.836435i
$131$	−2.76143	−	0.897243i	−0.241267	−	0.0783925i	0.185887	−	0.982571i	$-0.440484\pi$
$131$	−2.76143	−	0.897243i	−0.241267	−	0.0783925i	−0.427155	+	0.904179i	$0.640484\pi$
$132$	3.79160	+	3.79160i	0.330016	+	0.330016i
$133$	−6.70391	+	2.10600i	−0.581303	+	0.182613i
$134$	−2.88543	−	3.97145i	−0.249263	−	0.343081i
$135$	−5.50496	+	11.0042i	−0.473791	+	0.947093i
$136$	−2.91127	+	4.00702i	−0.249640	+	0.343600i
$137$	3.41213	−	21.5434i	0.291518	−	1.84057i	−0.212851	−	0.977085i	$-0.568275\pi$
$137$	3.41213	−	21.5434i	0.291518	−	1.84057i	0.504369	−	0.863488i	$-0.331725\pi$
$138$	−2.08956	+	13.1930i	−0.177875	+	1.12306i
$139$	−12.9776	−	9.42879i	−1.10075	−	0.799740i	−0.119565	−	0.992826i	$-0.538150\pi$
$139$	−12.9776	−	9.42879i	−1.10075	−	0.799740i	−0.981182	+	0.193087i	$0.938150\pi$
$140$	1.81470	+	5.63088i	0.153370	+	0.475897i
$141$	−4.00779	+	2.91183i	−0.337516	+	0.245220i
$142$	3.82893	+	7.51469i	0.321316	+	0.630619i
$143$	12.4205	−	12.4205i	1.03865	−	1.03865i
$144$	−0.416083	−	0.135194i	−0.0346736	−	0.0112661i
$145$	21.3143	+	6.75183i	1.77005	+	0.560709i
$146$	0.262901	−	0.0854218i	0.0217579	−	0.00706956i
$147$	8.07688	−	7.76703i	0.666170	−	0.640614i
$148$	0.202466	+	1.27832i	0.0166426	+	0.105077i
$149$		−	11.5164i		−	0.943461i	−0.881743	−	0.471730i	$-0.843630\pi$
$149$		−	11.5164i		−	0.943461i	0.881743	−	0.471730i	$-0.156370\pi$
$150$	0.118207	+	8.00304i	0.00965158	+	0.653445i
$151$	−2.62095			−0.213290			−0.106645	−	0.994297i	$-0.534011\pi$
$151$	−2.62095			−0.213290			−0.106645	+	0.994297i	$0.534011\pi$
$152$	−0.415479	−	2.62323i	−0.0336998	−	0.212772i
$153$	−1.93072	−	0.983751i	−0.156089	−	0.0795315i
$154$	1.30075	+	8.76648i	0.104817	+	0.706423i
$155$	−0.126364	−	0.171251i	−0.0101498	−	0.0137552i
$156$	2.59396	−	7.98340i	0.207683	−	0.639184i
$157$	12.7076	+	12.7076i	1.01418	+	1.01418i	0.999898	+	0.0142812i	$0.00454600\pi$
$157$	12.7076	+	12.7076i	1.01418	+	1.01418i	0.0142812	+	0.999898i	$0.495454\pi$
$158$	−8.74654	+	4.45659i	−0.695838	+	0.354547i
$159$	−3.76787	+	2.73752i	−0.298812	+	0.217099i
$160$	−2.20589	+	0.366098i	−0.174391	+	0.0289426i
$161$	−15.7626	+	15.4574i	−1.24227	+	1.21821i
$162$	−1.17265	+	7.40382i	−0.0921321	+	0.581699i
$163$	5.41750	+	0.858048i	0.424331	+	0.0672075i	0.364948	−	0.931028i	$-0.381087\pi$
$163$	5.41750	+	0.858048i	0.424331	+	0.0672075i	0.0593830	+	0.998235i	$0.481087\pi$
$164$	5.43185	+	3.94647i	0.424156	+	0.308168i
$165$	−1.78816	+	11.8560i	−0.139208	+	0.922988i
$166$	7.09548	+	9.76609i	0.550716	+	0.757996i
$167$	−7.02396	+	3.57888i	−0.543530	+	0.276942i	−0.704123	−	0.710078i	$-0.748659\pi$
$167$	−7.02396	+	3.57888i	−0.543530	+	0.276942i	0.160593	+	0.987021i	$0.448659\pi$
$168$	2.45581	+	3.45058i	0.189470	+	0.266218i
$169$	−13.7883	−	4.48008i	−1.06064	−	0.344621i
$170$	−11.0748	+	0.0817849i	−0.849402	+	0.00627262i
$171$	1.10509	−	0.359065i	0.0845081	−	0.0274584i
$172$	−8.03111	−	4.09206i	−0.612367	−	0.312016i
$173$	−14.7618	+	2.33804i	−1.12232	+	0.177758i	−0.689893	−	0.723911i	$-0.742342\pi$
$173$	−14.7618	+	2.33804i	−1.12232	+	0.177758i	−0.432426	+	0.901669i	$0.642342\pi$
$174$	16.0060			1.21341
$175$	−7.72214	+	10.7410i	−0.583739	+	0.811941i
$176$	−3.34969			−0.252493
$177$	−1.62766	+	0.257796i	−0.122342	+	0.0193771i
$178$	−8.12992	−	4.14240i	−0.609364	−	0.310486i
$179$	7.49400	−	2.43495i	0.560128	−	0.181997i	−0.0152507	−	0.999884i	$-0.504855\pi$
$179$	7.49400	−	2.43495i	0.560128	−	0.181997i	0.575379	+	0.817887i	$0.304855\pi$
$180$	−0.309164	−	0.928133i	−0.0230438	−	0.0691789i
$181$	11.5677	+	3.75857i	0.859819	+	0.279372i	0.705553	−	0.708657i	$-0.250699\pi$
$181$	11.5677	+	3.75857i	0.859819	+	0.279372i	0.154266	+	0.988029i	$0.450699\pi$
$182$	11.3034	−	8.04474i	0.837864	−	0.596316i
$183$	16.5899	−	8.45298i	1.22636	−	0.624863i
$184$	−4.90466	−	6.75068i	−0.361576	−	0.497667i
$185$	−2.03123	+	2.06146i	−0.149339	+	0.151561i
$186$	−0.123262	−	0.0895548i	−0.00903798	−	0.00656648i
$187$	−16.3866	−	2.59538i	−1.19831	−	0.189793i
$188$	0.484113	−	3.05657i	0.0353076	−	0.222923i
$189$	−10.3947	+	10.1934i	−0.756105	+	0.741463i
$190$	4.16827	−	4.23029i	0.302398	−	0.306897i
$191$	15.0499	−	10.9344i	1.08897	−	0.791183i	0.109745	−	0.993960i	$-0.464997\pi$
$191$	15.0499	−	10.9344i	1.08897	−	0.791183i	0.979225	+	0.202777i	$0.0649966\pi$
$192$	−1.42631	+	0.726740i	−0.102935	+	0.0524479i
$193$	−2.67764	−	2.67764i	−0.192741	−	0.192741i	0.604138	−	0.796879i	$-0.293517\pi$
$193$	−2.67764	−	2.67764i	−0.192741	−	0.192741i	−0.796879	+	0.604138i	$0.793517\pi$
$194$	−0.357637	+	1.10069i	−0.0256769	+	0.0790252i
$195$	17.8081	−	5.93195i	1.27526	−	0.424795i
$196$	−0.136868	+	6.99866i	−0.00977626	+	0.499904i
$197$	−4.69364	−	2.39153i	−0.334408	−	0.170389i	0.278721	−	0.960372i	$-0.410089\pi$
$197$	−4.69364	−	2.39153i	−0.334408	−	0.170389i	−0.613129	+	0.789983i	$0.710089\pi$
$198$	−0.229251	−	1.44743i	−0.0162922	−	0.102865i
$199$	11.3395			0.803835			0.401917	−	0.915676i	$-0.368344\pi$
$199$	11.3395			0.803835			0.401917	+	0.915676i	$0.368344\pi$
$200$	−3.58736	−	3.48293i	−0.253665	−	0.246281i
$201$		−	7.85822i		−	0.554276i
$202$	2.11057	+	13.3256i	0.148499	+	0.937588i
$203$	21.2491	+	15.7581i	1.49139	+	1.10600i
$204$	−7.54055	+	2.45007i	−0.527944	+	0.171539i
$205$	0.110866	+	15.0129i	0.00774323	+	1.04854i
$206$	4.36043	+	1.41679i	0.303805	+	0.0987123i
$207$	2.58136	−	2.58136i	0.179417	−	0.179417i
$208$	2.38065	+	4.67229i	0.165069	+	0.323965i
$209$	7.19745	−	5.22926i	0.497858	−	0.361715i
$210$	−2.94804	+	8.99982i	−0.203434	+	0.621046i
$211$	2.43138	+	1.76650i	0.167383	+	0.121611i	0.668323	−	0.743871i	$-0.267012\pi$
$211$	2.43138	+	1.76650i	0.167383	+	0.121611i	−0.500940	+	0.865482i	$0.667012\pi$
$212$	0.455133	−	2.87360i	0.0312587	−	0.197360i
$213$	−2.11201	+	13.3347i	−0.144712	+	0.913677i
$214$	8.33167	−	11.4676i	0.569541	−	0.783906i
$215$	−3.29983	−	19.8829i	−0.225047	−	1.35600i
$216$	−3.23440	−	4.45176i	−0.220073	−	0.302904i
$217$	−0.0754709	−	0.240243i	−0.00512330	−	0.0163087i
$218$	0.994754	+	0.994754i	0.0673733	+	0.0673733i
$219$	0.420848	+	0.136742i	0.0284382	+	0.00924014i
$220$	−4.44722	−	6.02697i	−0.299832	−	0.406338i
$221$	8.02594	+	24.7013i	0.539883	+	1.66159i
$222$	−0.940588	+	1.84601i	−0.0631282	+	0.123896i
$223$	−9.10012	+	1.44132i	−0.609389	+	0.0965178i	−0.453499	−	0.891257i	$-0.649825\pi$
$223$	−9.10012	+	1.44132i	−0.609389	+	0.0965178i	−0.155890	+	0.987774i	$0.549825\pi$
$224$	−2.60901	−	0.439415i	−0.174322	−	0.0293597i
$225$	1.25949	−	1.78850i	0.0839661	−	0.119234i
$226$	16.0090			1.06490
$227$	1.81307	+	11.4473i	0.120338	+	0.759783i	0.971877	+	0.235491i	$0.0756699\pi$
$227$	1.81307	+	11.4473i	0.120338	+	0.759783i	−0.851539	+	0.524292i	$0.824330\pi$
$228$	1.93017	−	3.78817i	0.127829	−	0.250878i
$229$	−5.10113	−	15.6997i	−0.337092	−	1.03746i	−0.965682	−	0.259726i	$-0.916368\pi$
$229$	−5.10113	−	15.6997i	−0.337092	−	1.03746i	0.628590	−	0.777737i	$-0.283632\pi$
$230$	5.63458	−	17.7873i	0.371533	−	1.17286i
$231$	−6.56397	+	12.5770i	−0.431878	+	0.827506i
$232$	−7.07026	+	7.07026i	−0.464185	+	0.464185i
$233$	18.2120	−	9.27949i	1.19311	−	0.607919i	0.259337	−	0.965787i	$-0.416496\pi$
$233$	18.2120	−	9.27949i	1.19311	−	0.607919i	0.933772	+	0.357868i	$0.116496\pi$
$234$	−1.85601	+	1.34847i	−0.121331	+	0.0881524i
$235$	6.14230	−	3.18701i	0.400680	−	0.207898i
$236$	0.605104	−	0.832854i	0.0393889	−	0.0542142i
$237$	−15.5206	−	2.45822i	−1.00817	−	0.159678i
$238$	−12.4227	−	4.17110i	−0.805246	−	0.270372i
$239$	−6.15963	+	8.47800i	−0.398433	+	0.548396i	−0.960350	−	0.278798i	$-0.910064\pi$
$239$	−6.15963	+	8.47800i	−0.398433	+	0.548396i	0.561917	+	0.827194i	$0.310064\pi$
$240$	−3.20123	−	1.60144i	−0.206639	−	0.103373i
$241$	−5.53014	−	7.61158i	−0.356227	−	0.490305i	0.592865	−	0.805302i	$-0.297997\pi$
$241$	−5.53014	−	7.61158i	−0.356227	−	0.490305i	−0.949093	+	0.314997i	$0.897997\pi$
$242$	−0.100075	−	0.196408i	−0.00643306	−	0.0126256i
$243$	3.18793	−	3.18793i	0.204505	−	0.204505i
$244$	−3.59429	+	11.0621i	−0.230101	+	0.708178i
$245$	−12.7741	+	9.04552i	−0.816110	+	0.577897i
$246$	3.32128	+	10.2218i	0.211757	+	0.651721i
$247$	−12.4093	−	6.32284i	−0.789584	−	0.402313i
$248$	0.0940065	−	0.0148892i	0.00596942	−	0.000945463i
$249$			19.3239i			1.22460i
$250$	1.50394	−	11.0787i	0.0951177	−	0.700680i
$251$			1.74242i			0.109981i	0.998487	+	0.0549904i	$0.0175128\pi$
$251$			1.74242i			0.109981i	−0.998487	+	0.0549904i	$0.982487\pi$
$252$	0.0113166	−	1.15745i	0.000712879	−	0.0729125i
$253$	12.6894	−	24.9044i	0.797777	−	1.56573i
$254$	−13.1349	+	4.26780i	−0.824160	+	0.267786i
$255$	−14.4195	−	10.3146i	−0.902987	−	0.645924i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.0089	+	15.0089i	0.936230	+	0.936230i	0.998085	−	0.0618551i	$-0.0197017\pi$
$257$	15.0089	+	15.0089i	0.936230	+	0.936230i	−0.0618551	+	0.998085i	$0.519702\pi$
$258$	−6.55049	−	12.8561i	−0.407816	−	0.800384i
$259$	−3.06611	+	1.52469i	−0.190519	+	0.0947395i
$260$	−5.24601	+	10.4866i	−0.325343	+	0.650351i
$261$	−3.53901	−	2.57124i	−0.219059	−	0.159156i
$262$	2.86779	+	0.454214i	0.177173	+	0.0280614i
$263$	16.7733	+	2.65662i	1.03428	+	0.163814i	0.650419	−	0.759575i	$-0.274593\pi$
$263$	16.7733	+	2.65662i	1.03428	+	0.163814i	0.383864	+	0.923390i	$0.374593\pi$
$264$	−4.33805	−	3.15178i	−0.266989	−	0.193979i
$265$	5.77461	−	2.99623i	0.354732	−	0.184057i
$266$	6.29193	−	3.12879i	0.385783	−	0.191839i
$267$	−6.63109	−	13.0142i	−0.405816	−	0.796459i
$268$	3.47118	+	3.47118i	0.212036	+	0.212036i
$269$	0.889732	−	2.73831i	0.0542479	−	0.166958i	−0.920262	−	0.391303i	$-0.872024\pi$
$269$	0.889732	−	2.73831i	0.0542479	−	0.166958i	0.974510	+	0.224345i	$0.0720243\pi$
$270$	3.71574	−	11.7299i	0.226133	−	0.713860i
$271$	14.9515	−	4.85805i	0.908241	−	0.295105i	0.182607	−	0.983186i	$-0.441547\pi$
$271$	14.9515	−	4.85805i	0.908241	−	0.295105i	0.725634	+	0.688081i	$0.241547\pi$
$272$	2.24859	−	4.41312i	0.136341	−	0.267584i
$273$	22.2080	+	0.217132i	1.34409	+	0.0131414i
$274$			21.8119i			1.31770i
$275$	4.93975	−	16.0034i	0.297878	−	0.965043i
$276$		−	13.3574i		−	0.804022i
$277$	1.22317	−	0.193732i	0.0734934	−	0.0116402i	−0.119579	−	0.992825i	$-0.538155\pi$
$277$	1.22317	−	0.193732i	0.0734934	−	0.0116402i	0.193073	+	0.981184i	$0.438155\pi$
$278$	14.2928	+	7.28256i	0.857227	+	0.436779i
$279$	0.0128675	+	0.0396021i	0.000770357	+	0.00237091i
$280$	−2.67323	−	5.27768i	−0.159756	−	0.315401i
$281$	0.0173682	−	0.0534539i	0.00103610	−	0.00318879i	−0.950537	−	0.310611i	$-0.899466\pi$
$281$	0.0173682	−	0.0534539i	0.00103610	−	0.00318879i	0.951573	+	0.307422i	$0.0994664\pi$
$282$	3.50293	−	3.50293i	0.208597	−	0.208597i
$283$	−2.83782	−	5.56953i	−0.168691	−	0.331074i	0.791149	−	0.611624i	$-0.209483\pi$
$283$	−2.83782	−	5.56953i	−0.168691	−	0.331074i	−0.959840	+	0.280549i	$0.909483\pi$
$284$	−4.95734	−	6.82320i	−0.294164	−	0.404882i
$285$	9.37850	−	1.55649i	0.555535	−	0.0921984i
$286$	−10.3246	+	14.2106i	−0.610506	+	0.840289i
$287$	−5.65427	+	16.8400i	−0.333761	+	0.994036i
$288$	0.432109	+	0.0684394i	0.0254623	+	0.00403283i
$289$	4.42706	−	6.09333i	0.260415	−	0.358431i
$290$	−22.1081	−	3.33441i	−1.29823	−	0.195803i
$291$	−1.49882	+	1.08896i	−0.0878626	+	0.0638359i
$292$	−0.246301	+	0.125497i	−0.0144137	+	0.00734415i
$293$	−10.8342	+	10.8342i	−0.632938	+	0.632938i	−0.948804	−	0.315866i	$-0.897705\pi$
$293$	−10.8342	+	10.8342i	−0.632938	+	0.632938i	0.315866	+	0.948804i	$0.397705\pi$
$294$	−6.76241	+	8.93491i	−0.394392	+	0.521094i
$295$	2.30189	−	0.0169989i	0.134021	−	0.000989712i
$296$	−0.399947	−	1.23091i	−0.0232465	−	0.0715453i
$297$	8.36808	−	16.4233i	0.485566	−	0.952976i
$298$	1.80156	+	11.3746i	0.104362	+	0.658914i
$299$	−43.7562			−2.53049
$300$	−1.36870	−	7.88602i	−0.0790221	−	0.455299i
$301$	3.96068	−	23.5164i	0.228290	−	1.35546i
$302$	2.58868	−	0.410007i	0.148962	−	0.0235932i
$303$	−9.80498	+	19.2434i	−0.563281	+	1.10550i
$304$	0.820727	+	2.52594i	0.0470719	+	0.144873i
$305$	−24.6756	+	8.21952i	−1.41292	+	0.470649i
$306$	2.06084	+	0.669608i	0.117810	+	0.0382789i
$307$	4.29427	+	4.29427i	0.245087	+	0.245087i	0.818951	−	0.573864i	$-0.194556\pi$
$307$	4.29427	+	4.29427i	0.245087	+	0.245087i	−0.573864	+	0.818951i	$0.694556\pi$
$308$	−2.65611	−	8.45506i	−0.151346	−	0.481772i
$309$	4.31394	+	5.93762i	0.245411	+	0.337780i
$310$	0.151597	+	0.149375i	0.00861015	+	0.00848391i
$311$	2.49114	−	3.42877i	0.141260	−	0.194427i	−0.732525	−	0.680740i	$-0.761658\pi$
$311$	2.49114	−	3.42877i	0.141260	−	0.194427i	0.873785	+	0.486313i	$0.161658\pi$
$312$	−1.31315	+	8.29090i	−0.0743424	+	0.469380i
$313$	1.27715	−	8.06359i	0.0721887	−	0.455781i	−0.924944	−	0.380104i	$-0.875888\pi$
$313$	1.27715	−	8.06359i	0.0721887	−	0.455781i	0.997132	−	0.0756771i	$-0.0241118\pi$
$314$	−14.5391	−	10.5633i	−0.820488	−	0.596120i
$315$	2.09758	−	1.51633i	0.118185	−	0.0854354i
$316$	7.94170	−	5.76998i	0.446755	−	0.324587i
$317$	−15.6145	−	30.6451i	−0.876996	−	1.72120i	−0.669278	−	0.743012i	$-0.733396\pi$
$317$	−15.6145	−	30.6451i	−0.876996	−	1.72120i	−0.207718	−	0.978189i	$-0.566604\pi$
$318$	3.29324	−	3.29324i	0.184676	−	0.184676i
$319$	−31.8538	−	10.3499i	−1.78347	−	0.579485i
$320$	2.12147	−	0.706668i	0.118594	−	0.0395040i
$321$	21.5800	−	7.01178i	1.20448	−	0.391359i
$322$	13.1505	−	17.7329i	0.732849	−	0.988216i
$323$	2.05785	+	12.9927i	0.114502	+	0.722935i
$324$		−	7.49611i		−	0.416451i
$325$	−25.8330	+	4.48359i	−1.43296	+	0.248705i
$326$	−5.48503			−0.303788
$327$	0.352286	+	2.22425i	0.0194815	+	0.123001i
$328$	−5.98234	−	3.04816i	−0.330320	−	0.168306i
$329$	8.09906	−	1.20172i	0.446516	−	0.0662529i
$330$	−0.0885413	−	11.9898i	−0.00487404	−	0.660014i
$331$	−3.66859	+	11.2908i	−0.201644	+	0.620596i	0.798191	+	0.602405i	$0.205791\pi$
$331$	−3.66859	+	11.2908i	−0.201644	+	0.620596i	−0.999835	+	0.0181913i	$0.994209\pi$
$332$	−8.53588	−	8.53588i	−0.468467	−	0.468467i
$333$	0.504516	−	0.257064i	0.0276473	−	0.0140870i
$334$	6.37762	−	4.63361i	0.348968	−	0.253540i
$335$	−1.63705	+	10.8541i	−0.0894414	+	0.593021i
$336$	−2.96537	−	3.02393i	−0.161774	−	0.164969i
$337$	−1.09314	+	6.90179i	−0.0595469	+	0.375964i	0.939861	+	0.341557i	$0.110954\pi$
$337$	−1.09314	+	6.90179i	−0.0595469	+	0.375964i	−0.999408	+	0.0344071i	$0.989046\pi$
$338$	14.3193	+	2.26796i	0.778870	+	0.123361i
$339$	20.7326	+	15.0631i	1.12604	+	0.818115i
$340$	10.9257	−	1.81327i	0.592529	−	0.0983381i
$341$	0.187396	+	0.257929i	0.0101481	+	0.0139676i
$342$	−1.03531	+	0.527518i	−0.0559833	+	0.0285249i
$343$	−17.7741	+	5.20406i	−0.959710	+	0.280993i
$344$	8.57238	+	2.78533i	0.462192	+	0.150175i
$345$	24.0335	−	17.7340i	1.29392	−	0.954766i
$346$	14.2143	−	4.61851i	0.764166	−	0.248293i
$347$	−21.7457	−	11.0800i	−1.16737	−	0.594804i	−0.240669	−	0.970607i	$-0.577367\pi$
$347$	−21.7457	−	11.0800i	−1.16737	−	0.594804i	−0.926699	+	0.375804i	$0.877367\pi$
$348$	−15.8089	+	2.50389i	−0.847447	+	0.134222i
$349$	−14.4915			−0.775715			−0.387857	−	0.921719i	$-0.626785\pi$
$349$	−14.4915			−0.775715			−0.387857	+	0.921719i	$0.626785\pi$
$350$	5.94681	−	11.8167i	0.317870	−	0.631632i
$351$	−28.8552			−1.54018
$352$	3.30845	−	0.524007i	0.176341	−	0.0279297i
$353$	−8.38191	−	4.27080i	−0.446124	−	0.227312i	0.216472	−	0.976289i	$-0.430545\pi$
$353$	−8.38191	−	4.27080i	−0.446124	−	0.227312i	−0.662596	+	0.748977i	$0.730545\pi$
$354$	1.56729	−	0.509244i	0.0833006	−	0.0270660i
$355$	5.69510	−	17.9784i	0.302265	−	0.954194i
$356$	8.67785	+	2.81960i	0.459925	+	0.149439i
$357$	−12.1635	−	17.0906i	−0.643762	−	0.904529i
$358$	−7.02083	+	3.57729i	−0.371062	+	0.189066i
$359$	9.19792	+	12.6598i	0.485447	+	0.668161i	0.979540	−	0.201248i	$-0.0644997\pi$
$359$	9.19792	+	12.6598i	0.485447	+	0.668161i	−0.494093	+	0.869409i	$0.664500\pi$
$360$	0.450550	+	0.868342i	0.0237461	+	0.0457656i
$361$	9.66455	+	7.02171i	0.508661	+	0.369564i
$362$	−12.0132	−	1.90271i	−0.631401	−	0.100004i
$363$	0.0552005	−	0.348522i	0.00289728	−	0.0182927i
$364$	−9.90577	+	9.71394i	−0.519203	+	0.509149i
$365$	−0.552804	−	0.276545i	−0.0289351	−	0.0144750i
$366$	−15.0633	+	10.9441i	−0.787373	+	0.572060i
$367$	14.9334	−	7.60893i	0.779515	−	0.397183i	−0.0184933	−	0.999829i	$-0.505887\pi$
$367$	14.9334	−	7.60893i	0.779515	−	0.397183i	0.798009	+	0.602646i	$0.205887\pi$
$368$	5.90031	+	5.90031i	0.307575	+	0.307575i
$369$	0.907709	−	2.79364i	0.0472534	−	0.145431i
$370$	1.68374	−	2.35383i	0.0875336	−	0.122370i
$371$	7.61424	−	1.12978i	0.395311	−	0.0586553i
$372$	0.135753	+	0.0691699i	0.00703849	+	0.00358629i
$373$	−3.71244	−	23.4394i	−0.192223	−	1.21365i	−0.875402	−	0.483396i	$-0.839403\pi$
$373$	−3.71244	−	23.4394i	−0.192223	−	1.21365i	0.683179	−	0.730251i	$-0.260597\pi$
$374$	16.5909			0.857894
$375$	12.3719	−	12.9325i	0.638880	−	0.667833i
$376$			3.09467i			0.159595i
$377$	8.20223	+	51.7868i	0.422436	+	2.66716i
$378$	8.67215	−	11.6940i	0.446047	−	0.601476i
$379$	12.6226	−	4.10133i	0.648379	−	0.210671i	0.0336797	−	0.999433i	$-0.489277\pi$
$379$	12.6226	−	4.10133i	0.648379	−	0.210671i	0.614699	+	0.788762i	$0.289277\pi$
$380$	−3.45519	+	4.83027i	−0.177247	+	0.247787i
$381$	−21.0262	−	6.83182i	−1.07720	−	0.350005i
$382$	−13.1541	+	13.1541i	−0.673020	+	0.673020i
$383$	−1.56544	−	3.07234i	−0.0799900	−	0.156989i	0.847547	−	0.530720i	$-0.178078\pi$
$383$	−1.56544	−	3.07234i	−0.0799900	−	0.156989i	−0.927537	+	0.373731i	$0.878078\pi$
$384$	1.29506	−	0.940916i	0.0660883	−	0.0480159i
$385$	11.6865	−	16.0044i	0.595598	−	0.815660i
$386$	3.06355	+	2.22580i	0.155931	+	0.113290i
$387$	−0.616881	+	3.89483i	−0.0313578	+	0.197985i
$388$	0.181048	−	1.14309i	0.00919130	−	0.0580316i
$389$	−11.0589	+	15.2213i	−0.560708	+	0.771749i	−0.991416	−	0.130743i	$-0.958264\pi$
$389$	−11.0589	+	15.2213i	−0.560708	+	0.771749i	0.430708	+	0.902491i	$0.358264\pi$
$390$	−16.6609	+	8.64472i	−0.843657	+	0.437742i
$391$	24.2926	+	33.4358i	1.22853	+	1.69092i
$392$	−0.959649	−	6.93391i	−0.0484696	−	0.350215i
$393$	3.28659	+	3.28659i	0.165786	+	0.165786i
$394$	5.00997	+	1.62784i	0.252399	+	0.0820093i
$395$	20.9255	+	6.62867i	1.05288	+	0.333525i
$396$	0.452857	+	1.39375i	0.0227569	+	0.0700386i
$397$	3.73201	−	7.32448i	0.187304	−	0.367605i	−0.778190	−	0.628028i	$-0.783862\pi$
$397$	3.73201	−	7.32448i	0.187304	−	0.367605i	0.965495	+	0.260423i	$0.0838621\pi$
$398$	−11.1999	+	1.77389i	−0.561399	+	0.0889169i
$399$	11.0924	+	1.86820i	0.555312	+	0.0935271i
$400$	4.08805	+	2.87887i	0.204402	+	0.143943i
$401$	19.8635			0.991937			0.495968	−	0.868341i	$-0.334813\pi$
$401$	19.8635			0.991937			0.495968	+	0.868341i	$0.334813\pi$
$402$	1.22930	+	7.76147i	0.0613117	+	0.387107i
$403$	0.226586	−	0.444701i	0.0112871	−	0.0221521i
$404$	−4.16917	−	12.8314i	−0.207424	−	0.638386i
$405$	13.4875	−	9.95222i	0.670198	−	0.494530i
$406$	−23.4526	−	12.2400i	−1.16393	−	0.607459i
$407$	3.06556	−	3.06556i	0.151954	−	0.151954i
$408$	7.06444	−	3.59951i	0.349742	−	0.178202i
$409$	−11.0058	+	7.99619i	−0.544202	+	0.395386i	−0.825643	−	0.564192i	$-0.809188\pi$
$409$	−11.0058	+	7.99619i	−0.544202	+	0.395386i	0.281441	+	0.959579i	$0.409188\pi$
$410$	−2.45803	−	14.8107i	−0.121393	−	0.731448i
$411$	−20.5232	+	28.2477i	−1.01233	+	1.39336i
$412$	−4.52838	−	0.717224i	−0.223097	−	0.0353351i
$413$	2.58205	+	0.866957i	0.127054	+	0.0426602i
$414$	−2.14577	+	2.95340i	−0.105459	+	0.145151i
$415$	4.02562	−	26.6909i	0.197610	−	1.31021i
$416$	−3.08225	−	4.24235i	−0.151120	−	0.207999i
$417$	11.6578	+	22.8797i	0.570885	+	1.12042i
$418$	−6.29081	+	6.29081i	−0.307693	+	0.307693i
$419$	8.48222	−	26.1056i	0.414384	−	1.27534i	−0.498417	−	0.866937i	$-0.666085\pi$
$419$	8.48222	−	26.1056i	0.414384	−	1.27534i	0.912801	−	0.408405i	$-0.133915\pi$
$420$	1.50386	−	9.35019i	0.0733810	−	0.456243i
$421$	4.20101	+	12.9294i	0.204745	+	0.630139i	0.999724	+	0.0235025i	$0.00748178\pi$
$421$	4.20101	+	12.9294i	0.204745	+	0.630139i	−0.794979	+	0.606637i	$0.792518\pi$
$422$	−2.67778	−	1.36440i	−0.130352	−	0.0664179i
$423$	−1.33724	+	0.211797i	−0.0650187	+	0.0102979i
$424$			2.90942i			0.141294i
$425$	17.7681	+	17.2508i	0.861877	+	0.836787i
$426$		−	13.5009i		−	0.654121i
$427$	−30.7723	−	0.300866i	−1.48917	−	0.0145599i
$428$	−6.43517	+	12.6297i	−0.311056	+	0.610481i
$429$	−26.7419	+	8.68898i	−1.29111	+	0.419508i
$430$	6.36958	+	19.1219i	0.307168	+	0.922140i
$431$	−1.59759	+	4.91689i	−0.0769534	+	0.236838i	−0.982132	−	0.188193i	$-0.939737\pi$
$431$	−1.59759	+	4.91689i	−0.0769534	+	0.236838i	0.905179	+	0.425031i	$0.139737\pi$
$432$	3.89098	+	3.89098i	0.187205	+	0.187205i
$433$	−0.850698	−	1.66959i	−0.0408819	−	0.0802353i	0.869662	−	0.493648i	$-0.164337\pi$
$433$	−0.850698	−	1.66959i	−0.0408819	−	0.0802353i	−0.910544	+	0.413412i	$0.864337\pi$
$434$	0.112124	+	0.225479i	0.00538212	+	0.0108233i
$435$	−25.4939	−	25.1201i	−1.22234	−	1.20442i
$436$	−1.13812	−	0.826894i	−0.0545061	−	0.0396010i
$437$	−21.8890	−	3.46688i	−1.04709	−	0.165843i
$438$	−0.437057	−	0.0692231i	−0.0208834	−	0.00330761i
$439$	30.2954	+	22.0109i	1.44592	+	1.05052i	0.986763	+	0.162167i	$0.0518483\pi$
$439$	30.2954	+	22.0109i	1.44592	+	1.05052i	0.459157	+	0.888355i	$0.348152\pi$
$440$	5.33529	+	5.25707i	0.254350	+	0.250621i
$441$	2.93053	−	0.889226i	0.139549	−	0.0423441i
$442$	−11.7913	−	23.1417i	−0.560853	−	1.10074i
$443$	25.5150	+	25.5150i	1.21226	+	1.21226i	0.970283	+	0.241973i	$0.0777946\pi$
$443$	25.5150	+	25.5150i	1.21226	+	1.21226i	0.241973	+	0.970283i	$0.422205\pi$
$444$	0.640229	−	1.97042i	0.0303839	−	0.0935121i
$445$	6.44794	+	19.3572i	0.305662	+	0.917618i
$446$	8.76262	−	2.84715i	0.414922	−	0.134816i
$447$	−8.36943	+	16.4259i	−0.395860	+	0.776920i
$448$	2.64562	+	0.0258668i	0.124994	+	0.00122209i
$449$			10.4838i			0.494760i	0.968919	+	0.247380i	$0.0795696\pi$
$449$			10.4838i			0.494760i	−0.968919	+	0.247380i	$0.920430\pi$
$450$	−0.964201	+	1.96351i	−0.0454529	+	0.0925608i
$451$		−	22.4903i		−	1.05903i
$452$	−15.8119	+	2.50435i	−0.743727	+	0.117795i
$453$	3.73828	+	1.90475i	0.175640	+	0.0894929i
$454$	−3.58150	−	11.0227i	−0.168088	−	0.517322i
$455$	−30.6293	−	4.92635i	−1.43592	−	0.230951i
$456$	−1.31381	+	4.04348i	−0.0615246	+	0.189353i
$457$	9.80976	−	9.80976i	0.458881	−	0.458881i	−0.439407	−	0.898288i	$-0.644811\pi$
$457$	9.80976	−	9.80976i	0.458881	−	0.458881i	0.898288	+	0.439407i	$0.144811\pi$
$458$	7.49429	+	14.7084i	0.350185	+	0.687277i
$459$	16.0198	+	22.0494i	0.747741	+	1.02918i
$460$	−2.78265	+	18.4498i	−0.129742	+	0.860225i
$461$	−1.84894	+	2.54484i	−0.0861136	+	0.118525i	−0.849900	−	0.526944i	$-0.823338\pi$
$461$	−1.84894	+	2.54484i	−0.0861136	+	0.118525i	0.763787	+	0.645469i	$0.223338\pi$
$462$	4.51568	−	13.4490i	0.210089	−	0.625704i
$463$	23.7372	+	3.75960i	1.10316	+	0.174724i	0.681348	−	0.731959i	$-0.261394\pi$
$463$	23.7372	+	3.75960i	1.10316	+	0.174724i	0.421813	+	0.906683i	$0.361394\pi$
$464$	5.87718	−	8.08924i	0.272841	−	0.375534i
$465$	0.0557785	+	0.336090i	0.00258667	+	0.0155858i
$466$	−16.5362	+	12.0142i	−0.766023	+	0.556548i
$467$	11.6466	−	5.93422i	0.538939	−	0.274603i	−0.163261	−	0.986583i	$-0.552201\pi$
$467$	11.6466	−	5.93422i	0.538939	−	0.274603i	0.702200	+	0.711980i	$0.252201\pi$
$468$	1.62221	−	1.62221i	0.0749869	−	0.0749869i
$469$	−6.00927	+	11.5141i	−0.277482	+	0.531674i
$470$	−5.56812	+	4.10864i	−0.256838	+	0.189518i
$471$	−8.88985	−	27.3601i	−0.409622	−	1.26069i
$472$	−0.467367	+	0.917259i	−0.0215123	+	0.0422203i
$473$	4.72316	+	29.8208i	0.217171	+	1.37116i
$474$	15.7140			0.721770
$475$	−13.2782	+	0.196123i	−0.609245	+	0.00899874i
$476$	12.9223	+	2.17640i	0.592292	+	0.0997553i
$477$	−1.25719	+	0.199119i	−0.0575626	+	0.00911703i
$478$	4.75754	−	9.33720i	0.217605	−	0.427074i
$479$	8.04855	+	24.7709i	0.367747	+	1.13181i	0.948243	+	0.317547i	$0.102859\pi$
$479$	8.04855	+	24.7709i	0.367747	+	1.13181i	−0.580495	+	0.814264i	$0.697141\pi$
$480$	3.41234	+	1.08094i	0.155751	+	0.0493381i
$481$	−6.45470	−	2.09726i	−0.294309	−	0.0956268i
$482$	6.65276	+	6.65276i	0.303025	+	0.303025i
$483$	33.7159	−	10.5917i	1.53413	−	0.481937i
$484$	0.129568	+	0.178335i	0.00588945	+	0.00810613i
$485$	2.29709	−	1.19187i	0.104305	−	0.0541201i
$486$	−2.64998	+	3.64738i	−0.120205	+	0.165448i
$487$	−4.28027	+	27.0246i	−0.193958	+	1.22460i	0.678016	+	0.735047i	$0.262840\pi$
$487$	−4.28027	+	27.0246i	−0.193958	+	1.22460i	−0.871974	+	0.489553i	$0.837160\pi$
$488$	1.81955	−	11.4882i	0.0823671	−	0.520045i
$489$	−7.10344	−	5.16095i	−0.321229	−	0.233386i
$490$	11.2018	−	10.9325i	0.506047	−	0.493879i
$491$	4.84166	−	3.51767i	0.218501	−	0.158750i	−0.473151	−	0.880982i	$-0.656883\pi$
$491$	4.84166	−	3.51767i	0.218501	−	0.158750i	0.691652	+	0.722231i	$0.256883\pi$
$492$	−4.87943	−	9.57643i	−0.219982	−	0.431739i
$493$	35.0187	−	35.0187i	1.57716	−	1.57716i
$494$	13.2456	+	4.30376i	0.595948	+	0.193635i
$495$	−1.90649	+	2.66522i	−0.0856902	+	0.119793i
$496$	−0.0905199	+	0.0294117i	−0.00406446	+	0.00132062i
$497$	13.2918	−	17.9234i	0.596217	−	0.803974i
$498$	−3.02293	−	19.0860i	−0.135461	−	0.855265i
$499$		−	16.4859i		−	0.738008i	−0.929428	−	0.369004i	$-0.879699\pi$
$499$		−	16.4859i		−	0.738008i	0.929428	−	0.369004i	$-0.120301\pi$
$500$	0.247667	+	11.1776i	0.0110760	+	0.499877i
$501$	12.6192			0.563786
$502$	−0.272575	−	1.72097i	−0.0121656	−	0.0768107i
$503$	−15.1677	−	7.72832i	−0.676294	−	0.344589i	0.0818792	−	0.996642i	$-0.473908\pi$
$503$	−15.1677	−	7.72832i	−0.676294	−	0.344589i	−0.758173	+	0.652053i	$0.773908\pi$
$504$	0.169888	+	1.14497i	0.00756740	+	0.0510010i
$505$	17.5518	−	24.5371i	0.781047	−	1.09188i
$506$	−8.63729	+	26.5828i	−0.383974	+	1.18175i
$507$	16.4105	+	16.4105i	0.728814	+	0.728814i
$508$	12.3056	−	6.27002i	0.545973	−	0.278187i
$509$	−2.11726	+	1.53828i	−0.0938461	+	0.0681832i	−0.633719	−	0.773563i	$-0.718472\pi$
$509$	−2.11726	+	1.53828i	−0.0938461	+	0.0681832i	0.539873	+	0.841747i	$0.318472\pi$
$510$	15.8556	+	7.93188i	0.702096	+	0.351230i
$511$	−0.512074	−	0.522186i	−0.0226528	−	0.0231001i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	−14.4348	−	2.28625i	−0.637312	−	0.100940i
$514$	−17.1720	−	12.4762i	−0.757426	−	0.550302i
$515$	−4.72163	−	9.09996i	−0.208060	−	0.400992i
$516$	8.48098	+	11.6731i	0.373354	+	0.513878i
$517$	−9.23635	+	4.70615i	−0.406214	+	0.206976i
$518$	2.78985	−	1.98556i	0.122579	−	0.0872406i
$519$	22.7540	+	7.39323i	0.998791	+	0.324527i
$520$	3.54095	−	11.1781i	0.155281	−	0.490194i
$521$	−3.84295	+	1.24865i	−0.168362	+	0.0547043i	−0.391985	−	0.919971i	$-0.628212\pi$
$521$	−3.84295	+	1.24865i	−0.168362	+	0.0547043i	0.223623	+	0.974676i	$0.428212\pi$
$522$	3.89767	+	1.98596i	0.170596	+	0.0869232i
$523$	24.9673	−	3.95443i	1.09174	−	0.172915i	0.415499	−	0.909594i	$-0.363607\pi$
$523$	24.9673	−	3.95443i	1.09174	−	0.172915i	0.676243	+	0.736679i	$0.263607\pi$
$524$	−2.90354			−0.126842
$525$	18.8200	−	9.70794i	0.821374	−	0.423689i
$526$	−16.9823			−0.740465
$527$	−0.465610	+	0.0737454i	−0.0202823	+	0.00321240i
$528$	4.77769	+	2.43435i	0.207922	+	0.105942i
$529$	−44.3453	+	14.4087i	−1.92806	+	0.626464i
$530$	−5.23481	+	3.86269i	−0.227385	+	0.167785i
$531$	−0.428343	−	0.139177i	−0.0185885	−	0.00603977i
$532$	−5.72501	+	4.07455i	−0.248211	+	0.176654i
$533$	−31.3704	+	15.9840i	−1.35880	+	0.692345i
$534$	8.58532	+	11.8167i	0.371523	+	0.511358i
$535$	−31.2679	+	5.18932i	−1.35183	+	0.224354i
$536$	−3.97145	−	2.88543i	−0.171541	−	0.124632i
$537$	−12.4583	−	1.97321i	−0.537617	−	0.0851501i
$538$	−0.450412	+	2.84379i	−0.0194186	+	0.122604i
$539$	19.2356	−	13.4088i	0.828534	−	0.577556i
$540$	−1.83503	+	12.1668i	−0.0789672	+	0.523574i
$541$	−17.2475	+	12.5310i	−0.741527	+	0.538751i	−0.893189	−	0.449681i	$-0.851538\pi$
$541$	−17.2475	+	12.5310i	−0.741527	+	0.538751i	0.151662	+	0.988432i	$0.451538\pi$
$542$	−14.0075	+	7.13717i	−0.601673	+	0.306568i
$543$	−13.7676	−	13.7676i	−0.590823	−	0.590823i
$544$	−1.53055	+	4.71054i	−0.0656217	+	0.201963i
$545$	−0.0232295	−	3.14560i	−0.000995042	−	0.134743i
$546$	−21.9686	+	3.25964i	−0.940168	+	0.139500i
$547$	12.7581	+	6.50059i	0.545498	+	0.277945i	0.704946	−	0.709261i	$-0.250971\pi$
$547$	12.7581	+	6.50059i	0.545498	+	0.277945i	−0.159448	+	0.987206i	$0.550971\pi$
$548$	−3.41213	−	21.5434i	−0.145759	−	0.920286i
$549$	5.08868			0.217179
$550$	−2.37544	+	16.5791i	−0.101289	+	0.706937i
$551$			26.5562i			1.13133i
$552$	2.08956	+	13.1930i	0.0889376	+	0.561530i
$553$	20.8615	+	15.4706i	0.887121	+	0.657878i
$554$	−1.17781	+	0.382693i	−0.0500403	+	0.0162591i
$555$	4.39531	−	1.46409i	0.186570	−	0.0621473i
$556$	−15.2561	−	4.95701i	−0.647003	−	0.210224i
$557$	2.58558	−	2.58558i	0.109555	−	0.109555i	−0.650205	−	0.759759i	$-0.725317\pi$
$557$	2.58558	−	2.58558i	0.109555	−	0.109555i	0.759759	+	0.650205i	$0.225317\pi$
$558$	−0.0189042	−	0.0371016i	−0.000800279	−	0.00157064i
$559$	38.2386	−	27.7820i	1.61732	−	1.17505i
$560$	3.46592	+	4.79451i	0.146462	+	0.202605i
$561$	21.4862	+	15.6106i	0.907147	+	0.659081i
$562$	−0.00879236	+	0.0555128i	−0.000370883	+	0.00234167i
$563$	−0.364349	+	2.30041i	−0.0153555	+	0.0969506i	−0.994176	−	0.107771i	$-0.965629\pi$
$563$	−0.364349	+	2.30041i	−0.0153555	+	0.0969506i	0.978820	+	0.204721i	$0.0656288\pi$
$564$	−2.91183	+	4.00779i	−0.122610	+	0.168758i
$565$	−25.4986	−	25.1248i	−1.07273	−	1.05701i
$566$	3.67415	+	5.05703i	0.154436	+	0.212563i
$567$	18.9212	−	5.94398i	0.794615	−	0.249624i
$568$	5.96370	+	5.96370i	0.250231	+	0.250231i
$569$	10.5656	+	3.43298i	0.442934	+	0.143918i	0.521989	−	0.852952i	$-0.325190\pi$
$569$	10.5656	+	3.43298i	0.442934	+	0.143918i	−0.0790552	+	0.996870i	$0.525190\pi$
$570$	−9.01955	+	3.00445i	−0.377787	+	0.125842i
$571$	1.62526	+	5.00203i	0.0680150	+	0.209329i	0.979287	−	0.202476i	$-0.0648987\pi$
$571$	1.62526	+	5.00203i	0.0680150	+	0.209329i	−0.911272	+	0.411804i	$0.864899\pi$
$572$	7.97445	−	15.6507i	0.333429	−	0.654390i
$573$	−29.4122	+	4.65843i	−1.22871	+	0.194609i
$574$	2.95030	−	17.5172i	0.123143	−	0.731155i
$575$	−36.8904	+	19.4881i	−1.53843	+	0.812711i
$576$	−0.437496			−0.0182290
$577$	−5.41296	−	34.1761i	−0.225344	−	1.42277i	−0.797844	−	0.602864i	$-0.794026\pi$
$577$	−5.41296	−	34.1761i	−0.225344	−	1.42277i	0.572500	−	0.819905i	$-0.305974\pi$
$578$	−3.41935	+	6.71085i	−0.142226	+	0.279135i
$579$	1.87319	+	5.76509i	0.0778472	+	0.239589i
$580$	22.3575	−	0.165105i	0.928345	−	0.00685559i
$581$	14.7772	−	28.3141i	0.613062	−	1.17467i
$582$	1.31002	−	1.31002i	0.0543020	−	0.0543020i
$583$	−8.68344	+	4.42443i	−0.359631	+	0.183241i
$584$	0.223637	−	0.162482i	0.00925417	−	0.00672355i
$585$	5.07252	+	0.765054i	0.209723	+	0.0316311i
$586$	9.00594	−	12.3956i	0.372032	−	0.512058i
$587$	−34.3444	−	5.43961i	−1.41754	−	0.224517i	−0.599824	−	0.800132i	$-0.704763\pi$
$587$	−34.3444	−	5.43961i	−1.41754	−	0.224517i	−0.817721	+	0.575615i	$0.804763\pi$
$588$	5.28142	−	9.88278i	0.217802	−	0.407559i
$589$	0.148584	−	0.204509i	0.00612231	−	0.00842664i
$590$	−2.27089	+	0.376884i	−0.0934910	+	0.0155161i
$591$	4.95655	+	6.82211i	0.203885	+	0.280624i
$592$	0.587580	+	1.15319i	0.0241494	+	0.0473959i
$593$	−20.9319	+	20.9319i	−0.859570	+	0.859570i	−0.991287	−	0.131717i	$-0.957951\pi$
$593$	−20.9319	+	20.9319i	−0.859570	+	0.859570i	0.131717	+	0.991287i	$0.457951\pi$
$594$	−5.69589	+	17.5301i	−0.233705	+	0.719271i
$595$	13.2404	+	26.1401i	0.542802	+	1.07164i
$596$	−3.55876	−	10.9528i	−0.145773	−	0.448642i
$597$	−16.1736	−	8.24085i	−0.661941	−	0.337276i
$598$	43.2175	−	6.84498i	1.76729	−	0.279912i
$599$		−	42.6803i		−	1.74387i	−0.489623	−	0.871934i	$-0.662866\pi$
$599$		−	42.6803i		−	1.74387i	0.489623	−	0.871934i	$-0.337134\pi$
$600$	2.58550	+	7.57481i	0.105552	+	0.309240i
$601$		−	1.09356i		−	0.0446073i	−0.999751	−	0.0223037i	$-0.992900\pi$
$601$		−	1.09356i		−	0.0446073i	0.999751	−	0.0223037i	$-0.00710006\pi$
$602$	−0.233151	+	23.8464i	−0.00950253	+	0.971908i
$603$	0.975017	−	1.91358i	0.0397058	−	0.0779270i
$604$	−2.49267	+	0.809917i	−0.101425	+	0.0329551i
$605$	−0.148850	+	0.469893i	−0.00605162	+	0.0191039i
$606$	6.67394	−	20.5403i	0.271110	−	0.834392i
$607$	20.1725	+	20.1725i	0.818778	+	0.818778i	0.985931	−	0.167153i	$-0.0534573\pi$
$607$	20.1725	+	20.1725i	0.818778	+	0.818778i	−0.167153	+	0.985931i	$0.553457\pi$
$608$	−1.20577	−	2.36645i	−0.0489003	−	0.0959722i
$609$	−18.8557	−	37.9184i	−0.764072	−	1.53653i
$610$	23.0860	−	11.9784i	0.934723	−	0.484993i
$611$	13.1287	+	9.53855i	0.531130	+	0.385889i
$612$	−2.14022	−	0.338977i	−0.0865132	−	0.0137023i
$613$	−24.9172	−	3.94650i	−1.00640	−	0.159398i	−0.368588	−	0.929593i	$-0.620159\pi$
$613$	−24.9172	−	3.94650i	−1.00640	−	0.159398i	−0.637808	+	0.770195i	$0.720159\pi$
$614$	−4.91318	−	3.56963i	−0.198280	−	0.144059i
$615$	10.7523	−	21.4935i	0.433575	−	0.866703i
$616$	3.94607	+	7.93546i	0.158992	+	0.319729i
$617$	−18.9654	−	37.2217i	−0.763519	−	1.49849i	−0.863968	−	0.503547i	$-0.832028\pi$
$617$	−18.9654	−	37.2217i	−0.763519	−	1.49849i	0.100449	−	0.994942i	$-0.467972\pi$
$618$	−5.18967	−	5.18967i	−0.208759	−	0.208759i
$619$	0.889049	−	2.73621i	0.0357339	−	0.109978i	−0.931599	−	0.363489i	$-0.881585\pi$
$619$	0.889049	−	2.73621i	0.0357339	−	0.109978i	0.967332	+	0.253511i	$0.0815855\pi$
$620$	−0.173098	−	0.123821i	−0.00695179	−	0.00497275i
$621$	−43.6688	+	14.1888i	−1.75237	+	0.569379i
$622$	−1.92410	+	3.77625i	−0.0771492	+	0.151414i
$623$	−0.236020	+	24.1398i	−0.00945593	+	0.967141i
$624$		−	8.39424i		−	0.336039i
$625$	−19.7826	+	15.2856i	−0.791304	+	0.611422i
$626$			8.16411i			0.326303i
$627$	−14.0661	+	2.22785i	−0.561746	+	0.0889718i
$628$	16.0125	+	8.15880i	0.638970	+	0.325572i
$629$	1.98092	+	6.09665i	0.0789845	+	0.243089i
$630$	−1.83455	+	1.82579i	−0.0730902	+	0.0727413i
$631$	−4.37645	+	13.4693i	−0.174224	+	0.536206i	−0.999597	−	0.0283814i	$-0.990965\pi$
$631$	−4.37645	+	13.4693i	−0.174224	+	0.536206i	0.825373	+	0.564587i	$0.190965\pi$
$632$	−6.94130	+	6.94130i	−0.276110	+	0.276110i
$633$	−2.18411	−	4.28655i	−0.0868104	−	0.170375i
$634$	20.2162	+	27.8252i	0.802887	+	1.10508i
$635$	27.6190	+	13.8166i	1.09602	+	0.548295i
$636$	−2.73752	+	3.76787i	−0.108550	+	0.149406i
$637$	−32.3740	−	17.3009i	−1.28270	−	0.685485i
$638$	33.0807	+	5.23947i	1.30968	+	0.207433i
$639$	−2.16882	+	2.98512i	−0.0857971	+	0.118090i
$640$	−1.98480	+	1.02984i	−0.0784561	+	0.0407079i
$641$	10.9223	−	7.93549i	0.431404	−	0.313433i	−0.350806	−	0.936448i	$-0.614092\pi$
$641$	10.9223	−	7.93549i	0.431404	−	0.313433i	0.782210	+	0.623015i	$0.214092\pi$
$642$	−20.2175	+	10.3013i	−0.797919	+	0.406560i
$643$	−23.7587	+	23.7587i	−0.936951	+	0.936951i	−0.998127	−	0.0611758i	$-0.980515\pi$
$643$	−23.7587	+	23.7587i	−0.936951	+	0.936951i	0.0611758	+	0.998127i	$0.480515\pi$
$644$	−10.2146	+	19.5718i	−0.402510	+	0.771236i
$645$	−9.74312	+	30.7573i	−0.383635	+	1.21107i
$646$	−4.06502	−	12.5109i	−0.159936	−	0.492233i
$647$	10.5181	−	20.6430i	0.413510	−	0.811560i	−0.586488	−	0.809958i	$-0.699490\pi$
$647$	10.5181	−	20.6430i	0.413510	−	0.811560i	0.999999	−	0.00160196i	$-0.000509919\pi$
$648$	1.17265	+	7.40382i	0.0460660	+	0.290850i
$649$	−3.44839			−0.135361
$650$	24.8136	−	8.46956i	0.973268	−	0.332204i
$651$	−0.0669492	+	0.397507i	−0.00262395	+	0.0155795i
$652$	5.41750	−	0.858048i	0.212166	−	0.0336037i
$653$	4.16214	−	8.16867i	0.162877	−	0.319665i	−0.795115	−	0.606459i	$-0.792590\pi$
$653$	4.16214	−	8.16867i	0.162877	−	0.319665i	0.957992	+	0.286794i	$0.0925895\pi$
$654$	−0.695898	−	2.14175i	−0.0272118	−	0.0837492i
$655$	−3.85489	−	5.22423i	−0.150623	−	0.204127i
$656$	6.38553	+	2.07478i	0.249313	+	0.0810067i
$657$	0.0855155	+	0.0855155i	0.00333628	+	0.00333628i
$658$	−7.81136	+	2.45390i	−0.304518	+	0.0956628i
$659$	−24.0785	−	33.1412i	−0.937964	−	1.29100i	−0.956671	−	0.291172i	$-0.905955\pi$
$659$	−24.0785	−	33.1412i	−0.937964	−	1.29100i	0.0187066	−	0.999825i	$-0.494045\pi$
$660$	1.96306	+	11.8283i	0.0764121	+	0.460416i
$661$	−8.66605	+	11.9278i	−0.337070	+	0.463937i	−0.943583	−	0.331136i	$-0.892568\pi$
$661$	−8.66605	+	11.9278i	−0.337070	+	0.463937i	0.606513	+	0.795074i	$0.292568\pi$
$662$	1.85716	−	11.7256i	0.0721806	−	0.455730i
$663$	6.50397	−	41.0644i	0.252593	−	1.59481i
$664$	9.76609	+	7.09548i	0.378998	+	0.275358i
$665$	−14.9320	−	4.89122i	−0.579038	−	0.189673i
$666$	−0.458091	+	0.332823i	−0.0177507	+	0.0128966i
$667$	37.8780	+	74.3398i	1.46664	+	2.87845i
$668$	−5.57424	+	5.57424i	−0.215674	+	0.215674i
$669$	14.0270	+	4.55766i	0.542317	+	0.176209i
$670$	−0.0810589	−	10.9765i	−0.00313158	−	0.424060i
$671$	37.0546	−	12.0398i	1.43048	−	0.464790i
$672$	3.40190	+	2.52281i	0.131231	+	0.0973195i
$673$	−0.164723	−	1.04002i	−0.00634962	−	0.0400899i	0.984310	−	0.176447i	$-0.0564605\pi$
$673$	−0.164723	−	1.04002i	−0.00634962	−	0.0400899i	−0.990660	+	0.136357i	$0.956460\pi$
$674$		−	6.98782i		−	0.269161i
$675$	−24.3275	+	12.8515i	−0.936365	+	0.494655i
$676$	−14.4978			−0.557609
$677$	1.38608	+	8.75138i	0.0532715	+	0.336343i	0.999902	+	0.0140212i	$0.00446324\pi$
$677$	1.38608	+	8.75138i	0.0532715	+	0.336343i	−0.946630	+	0.322322i	$0.895537\pi$
$678$	−22.8337	−	11.6343i	−0.876923	−	0.446814i
$679$	3.02887	−	0.449416i	0.116237	−	0.0172470i
$680$	−10.5075	+	3.50010i	−0.402945	+	0.134223i
$681$	5.73320	−	17.6450i	0.219697	−	0.676157i
$682$	−0.225438	−	0.225438i	−0.00863248	−	0.00863248i
$683$	−25.1802	+	12.8300i	−0.963494	+	0.490925i	−0.863657	−	0.504079i	$-0.831832\pi$
$683$	−25.1802	+	12.8300i	−0.963494	+	0.490925i	−0.0998364	+	0.995004i	$0.531832\pi$
$684$	0.940043	−	0.682982i	0.0359435	−	0.0261145i
$685$	34.2320	−	34.7414i	1.30794	−	1.32740i
$686$	16.7412	−	7.92047i	0.639180	−	0.302405i
$687$	−4.13379	+	26.0997i	−0.157714	+	0.995767i
$688$	−8.90256	−	1.41003i	−0.339407	−	0.0537568i
$689$	12.3428	+	8.96756i	0.470223	+	0.341637i
$690$	−20.9634	+	21.2753i	−0.798063	+	0.809937i
$691$	−3.67548	−	5.05886i	−0.139822	−	0.192448i	0.733363	−	0.679837i	$-0.237949\pi$
$691$	−3.67548	−	5.05886i	−0.139822	−	0.192448i	−0.873185	+	0.487389i	$0.837949\pi$
$692$	−13.3168	+	6.78526i	−0.506229	+	0.257937i
$693$	−3.15892	+	2.24823i	−0.119997	+	0.0854034i
$694$	23.2112	+	7.54178i	0.881086	+	0.286282i
$695$	−11.3358	−	34.0309i	−0.429992	−	1.29087i
$696$	15.2226	−	4.94612i	0.577011	−	0.187482i
$697$	29.6303	+	15.0974i	1.12233	+	0.571854i
$698$	14.3131	−	2.26698i	0.541760	−	0.0858064i
$699$	−32.7197			−1.23757
$700$	−4.02505	+	12.6015i	−0.152133	+	0.476294i
$701$	20.1709			0.761846			0.380923	−	0.924607i	$-0.375606\pi$
$701$	20.1709			0.761846			0.380923	+	0.924607i	$0.375606\pi$
$702$	28.4999	−	4.51394i	1.07566	−	0.170368i
$703$	−3.06279	−	1.56057i	−0.115515	−	0.0588581i
$704$	−3.18575	+	1.03511i	−0.120067	+	0.0390122i
$705$	−11.0769	+	0.0818004i	−0.417182	+	0.00308078i
$706$	8.94681	+	2.90700i	0.336718	+	0.109406i
$707$	29.0822	−	20.6981i	1.09375	−	0.778432i
$708$	−1.46833	+	0.748153i	−0.0551833	+	0.0281173i
$709$	24.5406	+	33.7772i	0.921642	+	1.26853i	0.963032	+	0.269388i	$0.0868213\pi$
$709$	24.5406	+	33.7772i	0.921642	+	1.26853i	−0.0413902	+	0.999143i	$0.513179\pi$
$710$	−2.81255	+	18.6480i	−0.105553	+	0.699845i
$711$	−3.47446	−	2.52434i	−0.130302	−	0.0946702i
$712$	−9.01209	−	1.42737i	−0.337742	−	0.0534931i
$713$	0.124240	−	0.784419i	0.00465281	−	0.0293767i
$714$	14.6873	+	14.9774i	0.549660	+	0.560514i
$715$	38.7471	−	6.43059i	1.44906	−	0.240491i
$716$	6.37478	−	4.63155i	0.238237	−	0.173089i
$717$	14.9468	−	7.61579i	0.558199	−	0.284417i
$718$	−11.0651	−	11.0651i	−0.412946	−	0.412946i
$719$	6.37070	−	19.6070i	0.237587	−	0.731218i	−0.759180	−	0.650880i	$-0.774400\pi$
$719$	6.37070	−	19.6070i	0.237587	−	0.731218i	0.996768	−	0.0803380i	$-0.0256000\pi$
$720$	−0.580842	−	0.787170i	−0.0216467	−	0.0293361i
$721$	−1.78037	−	11.9989i	−0.0663045	−	0.446864i
$722$	−10.6440	−	5.42339i	−0.396129	−	0.201838i
$723$	2.35604	+	14.8754i	0.0876219	+	0.553223i
$724$	12.1630			0.452033
$725$	29.9800	+	40.0078i	1.11343	+	1.48585i
$726$			0.352867i			0.0130961i
$727$	−6.05088	−	38.2037i	−0.224415	−	1.41690i	−0.800414	−	0.599448i	$-0.795387\pi$
$727$	−6.05088	−	38.2037i	−0.224415	−	1.41690i	0.575999	−	0.817450i	$-0.304613\pi$
$728$	8.26422	−	11.1439i	0.306292	−	0.413022i
$729$	−28.2514	+	9.17945i	−1.04635	+	0.339979i
$730$	0.589259	+	0.186663i	0.0218095	+	0.00690869i
$731$	−42.4586	−	13.7956i	−1.57039	−	0.510250i
$732$	13.1658	−	13.1658i	0.486623	−	0.486623i
$733$	−23.1529	−	45.4401i	−0.855171	−	1.67837i	−0.727025	−	0.686611i	$-0.759097\pi$
$733$	−23.1529	−	45.4401i	−0.855171	−	1.67837i	−0.128146	−	0.991755i	$-0.540903\pi$
$734$	−13.5592	+	9.85134i	−0.500480	+	0.363620i
$735$	24.7936	−	3.61821i	0.914525	−	0.133460i
$736$	−6.75068	−	4.90466i	−0.248834	−	0.180788i
$737$	2.57234	−	16.2411i	0.0947535	−	0.598250i
$738$	−0.459512	+	2.90124i	−0.0169149	+	0.106796i
$739$	6.76635	−	9.31309i	0.248904	−	0.342587i	−0.666223	−	0.745753i	$-0.732090\pi$
$739$	6.76635	−	9.31309i	0.248904	−	0.342587i	0.915127	+	0.403165i	$0.132090\pi$
$740$	−1.29479	+	2.58825i	−0.0475975	+	0.0951458i
$741$	13.1044	+	18.0366i	0.481402	+	0.662593i
$742$	−7.34376	+	2.30700i	−0.269598	+	0.0846927i
$743$	14.0731	+	14.0731i	0.516291	+	0.516291i	0.916447	−	0.400156i	$-0.131044\pi$
$743$	14.0731	+	14.0731i	0.516291	+	0.516291i	−0.400156	+	0.916447i	$0.631044\pi$
$744$	−0.144903	−	0.0470817i	−0.00531239	−	0.00172610i
$745$	14.9821	−	20.9446i	0.548901	−	0.767350i
$746$	7.33347	+	22.5701i	0.268497	+	0.826350i
$747$	−2.39764	+	4.70563i	−0.0877250	+	0.172170i
$748$	−16.3866	+	2.59538i	−0.599154	+	0.0948966i
$749$	−36.9818	−	6.22857i	−1.35129	−	0.227587i
$750$	−10.1964	+	14.7087i	−0.372321	+	0.537086i
$751$	−11.6798			−0.426203			−0.213101	−	0.977030i	$-0.568356\pi$
$751$	−11.6798			−0.426203			−0.213101	+	0.977030i	$0.568356\pi$
$752$	−0.484113	−	3.05657i	−0.0176538	−	0.111462i
$753$	1.26629	−	2.48523i	0.0461462	−	0.0905669i
$754$	−16.2025	−	49.8661i	−0.590060	−	1.81602i
$755$	−4.76665	−	3.40968i	−0.173476	−	0.124091i
$756$	−6.73603	+	12.9067i	−0.244987	+	0.469412i
$757$	−10.3428	+	10.3428i	−0.375916	+	0.375916i	−0.869626	−	0.493710i	$-0.835640\pi$
$757$	−10.3428	+	10.3428i	−0.375916	+	0.375916i	0.493710	+	0.869626i	$0.335640\pi$
$758$	−11.8256	+	6.02544i	−0.429525	+	0.218854i
$759$	−36.1980	+	26.2994i	−1.31391	+	0.954608i
$760$	2.65703	−	5.31131i	0.0963805	−	0.192661i
$761$	25.8875	−	35.6312i	0.938423	−	1.29163i	−0.0180592	−	0.999837i	$-0.505749\pi$
$761$	25.8875	−	35.6312i	0.938423	−	1.29163i	0.956482	−	0.291791i	$-0.0942513\pi$
$762$	21.8361	+	3.45849i	0.791037	+	0.125288i
$763$	1.18472	−	3.52845i	0.0428899	−	0.127738i
$764$	10.9344	−	15.0499i	0.395591	−	0.544485i
$765$	−2.23155	−	4.30086i	−0.0806820	−	0.155498i
$766$	2.02678	+	2.78963i	0.0732306	+	0.100793i
$767$	2.45080	+	4.80996i	0.0884931	+	0.173678i
$768$	−1.13192	+	1.13192i	−0.0408448	+	0.0408448i
$769$	13.4416	−	41.3690i	0.484717	−	1.49181i	−0.347673	−	0.937616i	$-0.613028\pi$
$769$	13.4416	−	41.3690i	0.484717	−	1.49181i	0.832390	−	0.554190i	$-0.186972\pi$
$770$	−9.03896	+	17.6355i	−0.325742	+	0.635541i
$771$	−10.4997	−	32.3149i	−0.378139	−	1.16379i
$772$	−3.37403	−	1.71915i	−0.121434	−	0.0618736i
$773$	−4.14531	+	0.656552i	−0.149096	+	0.0236145i	−0.230536	−	0.973064i	$-0.574048\pi$
$773$	−4.14531	+	0.656552i	−0.149096	+	0.0236145i	0.0814400	+	0.996678i	$0.474048\pi$
$774$		−	3.94338i		−	0.141742i
$775$	−0.00702829	−	0.475839i	−0.000252464	−	0.0170927i
$776$			1.15734i			0.0415460i
$777$	5.48127	+	0.0535914i	0.196639	+	0.00192258i
$778$	8.54161	−	16.7639i	0.306232	−	0.601013i
$779$	−16.9595	+	5.51048i	−0.607637	+	0.197433i
$780$	15.1034	−	11.1446i	0.540790	−	0.399042i
$781$	−8.73007	+	26.8684i	−0.312386	+	0.961426i
$782$	−29.2240	−	29.2240i	−1.04505	−	1.04505i
$783$	24.9788	+	49.0236i	0.892669	+	1.75196i
$784$	2.03254	+	6.69842i	0.0725906	+	0.239229i
$785$	6.57925	+	39.6428i	0.234824	+	1.41491i
$786$	−3.76026	−	2.73199i	−0.134124	−	0.0974468i
$787$	51.2020	+	8.10960i	1.82515	+	0.289076i	0.972414	−	0.233260i	$-0.0749392\pi$
$787$	51.2020	+	8.10960i	1.82515	+	0.289076i	0.852740	+	0.522336i	$0.174939\pi$
$788$	−5.20294	−	0.824065i	−0.185347	−	0.0293561i
$789$	−21.9931	−	15.9790i	−0.782977	−	0.568866i
$790$	−21.7048	−	3.27359i	−0.772223	−	0.116469i
$791$	−18.8592	−	37.9254i	−0.670556	−	1.34847i
$792$	−0.665312	−	1.30575i	−0.0236408	−	0.0463978i
$793$	−43.1286	−	43.1286i	−1.53154	−	1.53154i
$794$	−2.54026	+	7.81812i	−0.0901505	+	0.277455i
$795$	−10.4139	+	0.0769037i	−0.369341	+	0.00272749i
$796$	10.7845	−	3.50409i	0.382246	−	0.124199i
$797$	−0.392876	+	0.771063i	−0.0139164	+	0.0273125i	−0.897860	−	0.440281i	$-0.854879\pi$
$797$	−0.392876	+	0.771063i	−0.0139164	+	0.0273125i	0.883944	+	0.467593i	$0.154879\pi$
$798$	−11.2480	−	0.109974i	−0.398176	−	0.00389305i
$799$		−	15.3278i		−	0.542257i
$800$	−4.48807	−	2.20391i	−0.158677	−	0.0779200i
$801$		−	3.99190i		−	0.141047i
$802$	−19.6190	+	3.10734i	−0.692770	+	0.109724i
$803$	0.825034	+	0.420376i	0.0291148	+	0.0148347i
$804$	−2.42832	−	7.47361i	−0.0856403	−	0.263574i
$805$	−48.7761	+	7.60581i	−1.71913	+	0.268070i
$806$	−0.154230	+	0.474672i	−0.00543253	+	0.0167196i
$807$	−3.25908	+	3.25908i	−0.114725	+	0.114725i
$808$	6.12512	+	12.0212i	0.215481	+	0.422905i
$809$	−4.13832	−	5.69591i	−0.145496	−	0.200257i	0.730049	−	0.683395i	$-0.239497\pi$
$809$	−4.13832	−	5.69591i	−0.145496	−	0.200257i	−0.875545	+	0.483137i	$0.839497\pi$
$810$	−11.7645	+	11.9396i	−0.413364	+	0.419515i
$811$	14.7852	−	20.3500i	0.519177	−	0.714586i	−0.466256	−	0.884650i	$-0.654397\pi$
$811$	14.7852	−	20.3500i	0.519177	−	0.714586i	0.985433	+	0.170064i	$0.0543974\pi$
$812$	25.0786	+	8.42047i	0.880086	+	0.295501i
$813$	−24.8560	−	3.93681i	−0.871738	−	0.138070i
$814$	−2.54826	+	3.50738i	−0.0893165	+	0.122934i
$815$	8.73640	+	8.60831i	0.306023	+	0.301536i
$816$	−6.41437	+	4.66032i	−0.224548	+	0.163144i
$817$	21.3301	−	10.8682i	0.746245	−	0.380231i
$818$	9.61943	−	9.61943i	0.336336	−	0.336336i
$819$	5.38100	+	2.80836i	0.188028	+	0.0981321i
$820$	4.74467	+	14.2438i	0.165691	+	0.497416i
$821$	−0.790986	−	2.43440i	−0.0276056	−	0.0849613i	0.936305	−	0.351189i	$-0.114223\pi$
$821$	−0.790986	−	2.43440i	−0.0276056	−	0.0849613i	−0.963910	+	0.266228i	$0.914223\pi$
$822$	15.8516	−	31.1105i	0.552887	−	1.08510i
$823$	−2.90282	−	18.3277i	−0.101186	−	0.638863i	−0.985201	−	0.171404i	$-0.945170\pi$
$823$	−2.90282	−	18.3277i	−0.101186	−	0.638863i	0.884015	−	0.467459i	$-0.154830\pi$
$824$	4.58482			0.159720
$825$	−18.6759	+	19.2359i	−0.650212	+	0.669708i
$826$	−2.68588	−	0.452362i	−0.0934537	−	0.0157397i
$827$	−17.3280	+	2.74448i	−0.602553	+	0.0954350i	−0.450256	−	0.892900i	$-0.648667\pi$
$827$	−17.3280	+	2.74448i	−0.602553	+	0.0954350i	−0.152297	+	0.988335i	$0.548667\pi$
$828$	1.65734	−	3.25271i	0.0575964	−	0.113039i
$829$	9.49451	+	29.2211i	0.329758	+	1.01489i	0.969247	+	0.246090i	$0.0791459\pi$
$829$	9.49451	+	29.2211i	0.329758	+	1.01489i	−0.639489	+	0.768800i	$0.720854\pi$
$830$	0.199330	+	26.9921i	0.00691883	+	0.936909i
$831$	−1.88542	−	0.612609i	−0.0654043	−	0.0212512i
$832$	3.70795	+	3.70795i	0.128550	+	0.128550i
$833$	4.75310	+	34.3433i	0.164685	+	1.18993i
$834$	−15.0934	−	20.7743i	−0.522643	−	0.719357i
$835$	−17.4302	−	2.62888i	−0.603196	−	0.0909760i
$836$	5.22926	−	7.19745i	0.180858	−	0.248929i
$837$	0.0819303	−	0.517288i	0.00283193	−	0.0178801i
$838$	−4.29398	+	27.1111i	−0.148333	+	0.936538i
$839$	−39.2449	−	28.5131i	−1.35489	−	0.984382i	−0.998752	−	0.0499475i	$-0.984095\pi$
$839$	−39.2449	−	28.5131i	−1.35489	−	0.984382i	−0.356134	−	0.934435i	$-0.615905\pi$
$840$	−0.0226556	+	9.47033i	−0.000781693	+	0.326757i
$841$	57.4216	−	41.7193i	1.98006	−	1.43860i
$842$	−6.17189	−	12.1130i	−0.212697	−	0.417442i
$843$	−0.0636195	+	0.0636195i	−0.00219117	+	0.00219117i
$844$	2.85825	+	0.928703i	0.0983852	+	0.0319673i
$845$	−19.2481	−	26.0854i	−0.662154	−	0.897365i
$846$	1.28764	−	0.418380i	0.0442700	−	0.0143842i
$847$	−0.347401	+	0.468456i	−0.0119368	+	0.0160963i
$848$	−0.455133	−	2.87360i	−0.0156293	−	0.0986798i
$849$			10.0062i			0.343412i
$850$	−20.2479	−	14.2589i	−0.694498	−	0.489076i
$851$	−10.7997			−0.370208
$852$	2.11201	+	13.3347i	0.0723561	+	0.456839i
$853$	−43.8990	−	22.3676i	−1.50307	−	0.765853i	−0.507662	−	0.861557i	$-0.669490\pi$
$853$	−43.8990	−	22.3676i	−1.50307	−	0.765853i	−0.995410	+	0.0957033i	$0.969490\pi$
$854$	30.4405	−	4.51668i	1.04165	−	0.154558i
$855$	2.47691	+	0.784623i	0.0847086	+	0.0268336i
$856$	4.38022	−	13.4809i	0.149713	−	0.460769i
$857$	−14.4841	−	14.4841i	−0.494766	−	0.494766i	0.415038	−	0.909804i	$-0.363768\pi$
$857$	−14.4841	−	14.4841i	−0.494766	−	0.494766i	−0.909804	+	0.415038i	$0.863768\pi$
$858$	25.0534	−	12.7654i	0.855310	−	0.435802i
$859$	−10.4018	+	7.55732i	−0.354903	+	0.257852i	−0.750923	−	0.660390i	$-0.770391\pi$
$859$	−10.4018	+	7.55732i	−0.354903	+	0.257852i	0.396020	+	0.918242i	$0.370391\pi$
$860$	−9.28248	−	17.8901i	−0.316530	−	0.610046i
$861$	20.3031	−	19.9099i	0.691926	−	0.678527i
$862$	0.808754	−	5.10627i	0.0275463	−	0.173920i
$863$	−24.2363	−	3.83865i	−0.825012	−	0.130669i	−0.270368	−	0.962757i	$-0.587145\pi$
$863$	−24.2363	−	3.83865i	−0.825012	−	0.130669i	−0.554644	+	0.832088i	$0.687145\pi$
$864$	−4.45176	−	3.23440i	−0.151452	−	0.110036i
$865$	−29.8885	−	14.9520i	−1.01624	−	0.508383i
$866$	1.10141	+	1.51595i	0.0374273	+	0.0515142i
$867$	−10.7426	+	5.47364i	−0.364838	+	0.185894i
$868$	−0.146016	−	0.205162i	−0.00495611	−	0.00696367i
$869$	−31.2728	−	10.1611i	−1.06086	−	0.344693i
$870$	29.1097	+	20.8227i	0.986910	+	0.705956i
$871$	−24.4820	+	7.95469i	−0.829542	+	0.269534i
$872$	1.25346	+	0.638672i	0.0424476	+	0.0216282i
$873$	−0.500097	+	0.0792076i	−0.0169257	+	0.00268077i
$874$	22.1619			0.749637
$875$	−28.0173	+	9.48833i	−0.947159	+	0.320764i
$876$	0.442505			0.0149509
$877$	51.2765	−	8.12139i	1.73148	−	0.274240i	0.790443	−	0.612535i	$-0.209850\pi$
$877$	51.2765	−	8.12139i	1.73148	−	0.274240i	0.941040	+	0.338295i	$0.109850\pi$
$878$	−33.3657	−	17.0007i	−1.12604	−	0.573744i
$879$	23.3265	−	7.57923i	0.786782	−	0.255641i
$880$	−6.09200	−	4.35772i	−0.205361	−	0.146899i
$881$	−7.98607	−	2.59483i	−0.269057	−	0.0874221i	0.171381	−	0.985205i	$-0.445177\pi$
$881$	−7.98607	−	2.59483i	−0.269057	−	0.0874221i	−0.440439	+	0.897783i	$0.645177\pi$
$882$	−2.75534	+	1.33671i	−0.0927773	+	0.0450095i
$883$	0.615026	−	0.313371i	0.0206973	−	0.0105458i	−0.443611	−	0.896219i	$-0.646303\pi$
$883$	0.615026	−	0.313371i	0.0206973	−	0.0105458i	0.464309	+	0.885674i	$0.346303\pi$
$884$	15.2662	+	21.0122i	0.513460	+	0.706716i
$885$	−3.29556	−	1.64863i	−0.110779	−	0.0554181i
$886$	−29.1923	−	21.2095i	−0.980736	−	0.712546i
$887$	5.77918	+	0.915332i	0.194046	+	0.0307338i	0.252701	−	0.967544i	$-0.418681\pi$
$887$	5.77918	+	0.915332i	0.194046	+	0.0307338i	−0.0586550	+	0.998278i	$0.518681\pi$
$888$	−0.324105	+	2.04632i	−0.0108762	+	0.0686699i
$889$	25.5840	+	26.0892i	0.858059	+	0.875004i
$890$	−9.39669	−	18.1102i	−0.314978	−	0.607054i
$891$	−20.3141	+	14.7591i	−0.680549	+	0.494448i
$892$	−8.20934	+	4.18287i	−0.274869	+	0.140053i
$893$	5.81187	+	5.81187i	0.194487	+	0.194487i
$894$	5.69681	−	17.5330i	0.190530	−	0.586390i
$895$	16.7969	+	5.32082i	0.561457	+	0.177855i
$896$	−2.61710	+	0.388319i	−0.0874312	+	0.0129728i
$897$	62.4098	+	31.7994i	2.08380	+	1.06175i
$898$	−1.64002	−	10.3547i	−0.0547283	−	0.345541i
$899$	−0.951674			−0.0317401
$900$	0.645169	−	2.09017i	0.0215056	−	0.0696724i
$901$		−	14.4102i		−	0.480074i
$902$	3.51826	+	22.2134i	0.117145	+	0.739625i
$903$	−22.7394	+	30.6632i	−0.756721	+	1.02041i
$904$	15.2254	−	4.94704i	0.506390	−	0.164536i
$905$	16.1482	+	21.8844i	0.536784	+	0.727461i
$906$	−3.99022	−	1.29650i	−0.132566	−	0.0430734i
$907$	37.1917	−	37.1917i	1.23493	−	1.23493i	0.272882	−	0.962047i	$-0.412023\pi$
$907$	37.1917	−	37.1917i	1.23493	−	1.23493i	0.962047	−	0.272882i	$-0.0879770\pi$
$908$	5.26174	+	10.3267i	0.174617	+	0.342705i
$909$	−4.77528	+	3.46945i	−0.158386	+	0.115074i
$910$	31.0229	+	0.0742152i	1.02840	+	0.00246021i
$911$	−3.51042	−	2.55047i	−0.116305	−	0.0845008i	0.528112	−	0.849175i	$-0.322900\pi$
$911$	−3.51042	−	2.55047i	−0.116305	−	0.0845008i	−0.644417	+	0.764674i	$0.722900\pi$
$912$	0.665091	−	4.19922i	0.0220234	−	0.139050i
$913$	−6.32558	+	39.9381i	−0.209346	+	1.32176i
$914$	−8.15440	+	11.2236i	−0.269724	+	0.371243i
$915$	41.1684	+	6.20915i	1.36099	+	0.205268i
$916$	−9.70292	−	13.3549i	−0.320594	−	0.441259i
$917$	−2.30234	−	7.32892i	−0.0760299	−	0.242022i
$918$	−19.2719	−	19.2719i	−0.636067	−	0.636067i
$919$	−24.0969	−	7.82954i	−0.794882	−	0.258273i	−0.116700	−	0.993167i	$-0.537232\pi$
$919$	−24.0969	−	7.82954i	−0.794882	−	0.258273i	−0.678182	+	0.734894i	$0.737232\pi$
$920$	−0.137784	−	18.6579i	−0.00454261	−	0.615134i
$921$	−3.00413	−	9.24577i	−0.0989896	−	0.304659i
$922$	1.42807	−	2.80275i	0.0470311	−	0.0923037i
$923$	43.6817	−	6.91850i	1.43780	−	0.227725i
$924$	−2.35620	+	13.9898i	−0.0775133	+	0.460231i
$925$	−6.37597	+	1.10662i	−0.209640	+	0.0363854i
$926$	−24.0331			−0.789776
$927$	0.313783	+	1.98115i	0.0103060	+	0.0650694i
$928$	−4.53938	+	8.90904i	−0.149013	+	0.292454i
$929$	14.3416	+	44.1390i	0.470534	+	1.44815i	0.851887	+	0.523725i	$0.175458\pi$
$929$	14.3416	+	44.1390i	0.470534	+	1.44815i	−0.381353	+	0.924429i	$0.624542\pi$
$930$	−0.107668	−	0.323226i	−0.00353057	−	0.0105990i
$931$	−14.8243	−	11.2198i	−0.485847	−	0.367714i
$932$	14.4531	−	14.4531i	0.473428	−	0.473428i
$933$	−6.04496	+	3.08006i	−0.197903	+	0.100837i
$934$	−10.5749	+	7.68309i	−0.346020	+	0.251398i
$935$	−26.4255	−	26.0380i	−0.864205	−	0.851535i
$936$	−1.34847	+	1.85601i	−0.0440762	+	0.0606657i
$937$	−3.22135	−	0.510212i	−0.105237	−	0.0166679i	0.103594	−	0.994620i	$-0.466966\pi$
$937$	−3.22135	−	0.510212i	−0.105237	−	0.0166679i	−0.208831	+	0.977952i	$0.566966\pi$
$938$	4.13407	−	12.3124i	0.134982	−	0.402016i
$939$	−7.68174	+	10.5730i	−0.250684	+	0.345037i
$940$	4.85684	−	4.92910i	0.158413	−	0.160770i
$941$	14.8861	+	20.4889i	0.485272	+	0.667919i	0.979507	−	0.201409i	$-0.0645519\pi$
$941$	14.8861	+	20.4889i	0.485272	+	0.667919i	−0.494235	+	0.869328i	$0.664552\pi$
$942$	13.0605	+	25.6326i	0.425533	+	0.835155i
$943$	−39.6155	+	39.6155i	−1.29006	+	1.29006i
$944$	0.318122	−	0.979079i	0.0103540	−	0.0318663i
$945$	−32.1656	+	5.01568i	−1.04635	+	0.163160i
$946$	−9.33001	−	28.7148i	−0.303345	−	0.933599i
$947$	47.3980	+	24.1505i	1.54023	+	0.784785i	0.998446	−	0.0557343i	$-0.0177500\pi$
$947$	47.3980	+	24.1505i	1.54023	+	0.784785i	0.541782	+	0.840519i	$0.317750\pi$
$948$	−15.5206	+	2.45822i	−0.504085	+	0.0798392i
$949$		−	1.44956i		−	0.0470546i
$950$	13.0840	−	2.27088i	0.424502	−	0.0736769i
$951$			55.0570i			1.78535i
$952$	−13.1037	−	0.128117i	−0.424692	−	0.00415230i
$953$	−21.2360	+	41.6780i	−0.687902	+	1.35008i	0.237608	+	0.971361i	$0.423637\pi$
$953$	−21.2360	+	41.6780i	−0.687902	+	1.35008i	−0.925510	+	0.378723i	$0.876363\pi$
$954$	1.21056	−	0.393335i	0.0391933	−	0.0127347i
$955$	41.5957	−	0.307173i	1.34600	−	0.00993990i
$956$	−3.23831	+	9.96649i	−0.104734	+	0.322339i
$957$	37.9116	+	37.9116i	1.22551	+	1.22551i
$958$	−11.8245	−	23.2068i	−0.382031	−	0.749779i
$959$	51.6726	−	25.6953i	1.66860	−	0.829745i
$960$	−3.53943	−	0.533828i	−0.114235	−	0.0172292i
$961$	−25.0722	−	18.2160i	−0.808781	−	0.587613i
$962$	6.70332	+	1.06170i	0.216124	+	0.0342306i
$963$	6.12502	+	0.970107i	0.197376	+	0.0312613i
$964$	−7.61158	−	5.53014i	−0.245152	−	0.178114i
$965$	−1.38632	−	8.35319i	−0.0446273	−	0.268899i
$966$	−31.6439	+	15.7356i	−1.01813	+	0.506284i
$967$	1.52347	+	2.98999i	0.0489916	+	0.0961515i	0.914204	−	0.405253i	$-0.132817\pi$
$967$	1.52347	+	2.98999i	0.0489916	+	0.0961515i	−0.865213	+	0.501405i	$0.832817\pi$
$968$	−0.155870	−	0.155870i	−0.00500986	−	0.00500986i
$969$	6.50722	−	20.0272i	0.209042	−	0.643365i
$970$	−2.08236	+	1.53654i	−0.0668604	+	0.0493354i
$971$	24.1005	−	7.83072i	0.773421	−	0.251300i	0.104392	−	0.994536i	$-0.466710\pi$
$971$	24.1005	−	7.83072i	0.773421	−	0.251300i	0.669029	+	0.743236i	$0.266710\pi$
$972$	2.04677	−	4.01702i	0.0656503	−	0.128846i
$973$	0.414935	−	42.4390i	0.0133022	−	1.36053i
$974$		−	27.3614i		−	0.876716i
$975$	40.1042	+	12.3789i	1.28436	+	0.396442i
$976$			11.6314i			0.372311i
$977$	13.2906	−	2.10502i	0.425204	−	0.0673456i	0.0598343	−	0.998208i	$-0.480943\pi$
$977$	13.2906	−	2.10502i	0.425204	−	0.0673456i	0.365369	+	0.930863i	$0.380943\pi$
$978$	7.82334	+	3.98619i	0.250163	+	0.127464i
$979$	−9.44480	−	29.0681i	−0.301857	−	0.929021i
$980$	−9.35371	+	12.5502i	−0.298793	+	0.400902i
$981$	−0.190190	+	0.585344i	−0.00607229	+	0.0186886i
$982$	−4.23177	+	4.23177i	−0.135041	+	0.135041i
$983$	25.7366	+	50.5109i	0.820870	+	1.61105i	0.791255	+	0.611486i	$0.209428\pi$
$983$	25.7366	+	50.5109i	0.820870	+	1.61105i	0.0296150	+	0.999561i	$0.490572\pi$
$984$	6.31744	+	8.69521i	0.201393	+	0.277193i
$985$	−5.42498	−	10.4555i	−0.172854	−	0.333141i
$986$	−29.1094	+	40.0657i	−0.927032	+	1.27595i
$987$	−12.4251	−	4.17189i	−0.395495	−	0.132793i
$988$	−13.7558	−	2.17870i	−0.437630	−	0.0693138i
$989$	44.2083	−	60.8475i	1.40574	−	1.93484i
$990$	1.46608	−	2.93065i	0.0465951	−	0.0931421i
$991$	6.61975	−	4.80953i	0.210283	−	0.152780i	−0.477659	−	0.878546i	$-0.658514\pi$
$991$	6.61975	−	4.80953i	0.210283	−	0.152780i	0.687942	+	0.725766i	$0.258514\pi$
$992$	0.0848045	−	0.0432100i	0.00269254	−	0.00137192i
$993$	13.4380	−	13.4380i	0.426442	−	0.426442i
$994$	−10.3243	+	19.7820i	−0.327467	+	0.627448i
$995$	20.6228	+	14.7519i	0.653787	+	0.467667i
$996$	5.97142	+	18.3781i	0.189212	+	0.582334i
$997$	−21.7891	+	42.7635i	−0.690067	+	1.35433i	0.234050	+	0.972224i	$0.424802\pi$
$997$	−21.7891	+	42.7635i	−0.690067	+	1.35433i	−0.924118	+	0.382108i	$0.875198\pi$
$998$	2.57896	+	16.2829i	0.0816354	+	0.515426i
$999$	−7.12189			−0.225327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.13.4	✓	160
7.6	odd	2	inner	350.2.r.a.13.7	yes	160
25.2	odd	20	inner	350.2.r.a.27.7	yes	160
175.27	even	20	inner	350.2.r.a.27.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.4	✓	160	1.1	even	1	trivial
350.2.r.a.13.7	yes	160	7.6	odd	2	inner
350.2.r.a.27.4	yes	160	175.27	even	20	inner
350.2.r.a.27.7	yes	160	25.2	odd	20	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.42631 - 0.726740i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.81867 + 1.30093i) q^{5} +(1.52243 + 0.494669i) q^{6} +(1.53413 + 2.15556i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.257154 - 0.353942i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.42631 - 0.726740i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.81867 + 1.30093i) q^{5} +(1.52243 + 0.494669i) q^{6} +(1.53413 + 2.15556i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.257154 - 0.353942i) q^{9} +(-1.99979 - 1.00041i) q^{10} +(-2.70996 - 1.96890i) q^{11} +(-1.58107 - 0.250418i) q^{12} +(-0.820317 + 5.17928i) q^{13} +(-1.85245 - 1.88903i) q^{14} +(-1.64855 - 3.17723i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.41312 - 2.24859i) q^{17} +(0.309356 + 0.309356i) q^{18} +(-0.820727 + 2.52594i) q^{19} +(2.13167 + 0.675260i) q^{20} +(-0.621614 - 4.18941i) q^{21} +(2.98460 + 1.52073i) q^{22} +(1.30534 + 8.24157i) q^{23} +1.60078 q^{24} +(1.61515 + 4.73195i) q^{25} -5.24384i q^{26} +(0.860809 + 5.43494i) q^{27} +(2.12515 + 1.57599i) q^{28} +(9.50947 - 3.08982i) q^{29} +(2.12528 + 2.88023i) q^{30} +(-0.0905199 - 0.0294117i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.43435 + 4.77769i) q^{33} +(-4.00702 + 2.91127i) q^{34} +(-0.0141528 + 5.91606i) q^{35} +(-0.353942 - 0.257154i) q^{36} +(-0.202466 + 1.27832i) q^{37} +(0.415479 - 2.62323i) q^{38} +(4.93401 - 6.79109i) q^{39} +(-2.21106 - 0.333480i) q^{40} +(3.94647 + 5.43185i) q^{41} +(1.26933 + 4.04059i) q^{42} +(-6.37353 - 6.37353i) q^{43} +(-3.18575 - 1.03511i) q^{44} +(-0.00722408 - 0.978244i) q^{45} +(-2.57853 - 7.93591i) q^{46} +(1.40495 - 2.75737i) q^{47} +(-1.58107 + 0.250418i) q^{48} +(-2.29287 + 6.61383i) q^{49} +(-2.33550 - 4.42102i) q^{50} -7.92860 q^{51} +(0.820317 + 5.17928i) q^{52} +(1.32085 - 2.59231i) q^{53} +(-1.70042 - 5.23336i) q^{54} +(-2.36712 - 7.10626i) q^{55} +(-2.34553 - 1.22414i) q^{56} +(3.00631 - 3.00631i) q^{57} +(-8.90904 + 4.53938i) q^{58} +(0.832854 - 0.605104i) q^{59} +(-2.54968 - 2.51230i) q^{60} +(-6.83675 + 9.40998i) q^{61} +(0.0940065 + 0.0148892i) q^{62} +(0.368434 - 1.09730i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-8.22978 + 8.35224i) q^{65} +(-3.15178 - 4.33805i) q^{66} +(2.22863 + 4.37394i) q^{67} +(3.50227 - 3.50227i) q^{68} +(4.12767 - 12.7037i) q^{69} +(-0.911498 - 5.84544i) q^{70} +(-2.60623 - 8.02115i) q^{71} +(0.389812 + 0.198619i) q^{72} +(-0.273027 + 0.0432433i) q^{73} -1.29426i q^{74} +(1.13520 - 7.92300i) q^{75} +2.65593i q^{76} +(0.0866458 - 8.86203i) q^{77} +(-3.81091 + 7.47933i) q^{78} +(9.33602 - 3.03346i) q^{79} +(2.23601 - 0.0165123i) q^{80} +(2.31643 - 7.12922i) q^{81} +(-4.74761 - 4.74761i) q^{82} +(-5.48037 - 10.7558i) q^{83} +(-1.88579 - 3.79227i) q^{84} +(10.9513 + 1.65171i) q^{85} +(7.29210 + 5.29802i) q^{86} +(-15.8089 - 2.50389i) q^{87} +(3.30845 + 0.524007i) q^{88} +(7.38182 + 5.36320i) q^{89} +(0.160166 + 0.965070i) q^{90} +(-12.4227 + 6.17746i) q^{91} +(3.78824 + 7.43483i) q^{92} +(0.107735 + 0.107735i) q^{93} +(-0.956306 + 2.94321i) q^{94} +(-4.77871 + 3.52615i) q^{95} +(1.52243 - 0.494669i) q^{96} +(0.525421 - 1.03120i) q^{97} +(1.23001 - 6.89109i) q^{98} +1.46548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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