LMFDB - Embedded newform 483.2.r.a.181.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.17
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0271614 + 0.188911i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.88404 - 0.553203i) q^{4} +(1.98963 - 2.29616i) q^{5} +(0.0537698 - 0.183123i) q^{6} +(-2.47239 - 0.941954i) q^{7} +(0.314247 + 0.688104i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.0271614 + 0.188911i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.88404 - 0.553203i) q^{4} +(1.98963 - 2.29616i) q^{5} +(0.0537698 - 0.183123i) q^{6} +(-2.47239 - 0.941954i) q^{7} +(0.314247 + 0.688104i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.487811 + 0.313497i) q^{10} +(3.07921 + 0.442724i) q^{11} +(-1.94359 - 0.279446i) q^{12} +(1.29479 - 2.01474i) q^{13} +(0.110792 - 0.492648i) q^{14} +(-2.76369 + 1.26213i) q^{15} +(3.18227 - 2.04512i) q^{16} +(-6.24490 - 1.83367i) q^{17} +(-0.124983 + 0.144238i) q^{18} +(-1.82387 + 0.535536i) q^{19} +(2.47830 - 5.42671i) q^{20} +(1.85767 + 1.88390i) q^{21} +0.593724i q^{22} +(-0.644774 + 4.75229i) q^{23} -0.756464i q^{24} +(-0.602129 - 4.18790i) q^{25} +(0.415776 + 0.189878i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-5.17917 - 0.406941i) q^{28} +(-5.49276 - 1.61282i) q^{29} +(-0.313497 - 0.487811i) q^{30} +(7.97823 - 3.64354i) q^{31} +(1.46354 + 1.68901i) q^{32} +(-2.61704 - 1.68187i) q^{33} +(0.176781 - 1.22954i) q^{34} +(-7.08202 + 3.80286i) q^{35} +(1.65186 + 1.06159i) q^{36} +(6.32267 - 5.47863i) q^{37} +(-0.150708 - 0.330003i) q^{38} +(-2.01474 + 1.29479i) q^{39} +(2.20523 + 0.647514i) q^{40} +(4.97801 + 4.31347i) q^{41} +(-0.305434 + 0.402103i) q^{42} +(-2.26776 - 1.03565i) q^{43} +(6.04627 - 0.869322i) q^{44} +3.03825 q^{45} +(-0.915275 + 0.00727351i) q^{46} +4.70188i q^{47} +(-3.74427 + 0.538345i) q^{48} +(5.22544 + 4.65776i) q^{49} +(0.774787 - 0.227498i) q^{50} +(4.91883 + 4.26219i) q^{51} +(1.32488 - 4.51212i) q^{52} +(-4.94290 - 7.69131i) q^{53} +(0.173607 - 0.0792836i) q^{54} +(7.14306 - 6.18950i) q^{55} +(-0.128778 - 1.99727i) q^{56} +(1.88152 + 0.270521i) q^{57} +(0.155489 - 1.08145i) q^{58} +(-1.62895 + 2.53469i) q^{59} +(-4.50867 + 3.90679i) q^{60} +(0.0813133 + 0.178051i) q^{61} +(0.905006 + 1.40822i) q^{62} +(-0.907191 - 2.48536i) q^{63} +(4.67506 - 5.39531i) q^{64} +(-2.04999 - 6.98164i) q^{65} +(0.246642 - 0.540070i) q^{66} +(12.0444 - 1.73172i) q^{67} -12.7800 q^{68} +(2.56068 - 4.05499i) q^{69} +(-0.910761 - 1.23458i) q^{70} +(1.06927 + 7.43690i) q^{71} +(-0.314247 + 0.688104i) q^{72} +(0.328156 + 1.11760i) q^{73} +(1.20671 + 1.04562i) q^{74} +(-1.19200 + 4.05958i) q^{75} +(-3.13997 + 2.01794i) q^{76} +(-7.19600 - 3.99506i) q^{77} +(-0.299324 - 0.345439i) q^{78} +(-8.23775 + 12.8182i) q^{79} +(1.63563 - 11.3760i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.679654 + 1.05756i) q^{82} +(7.53178 + 8.69214i) q^{83} +(4.54209 + 2.52167i) q^{84} +(-16.6354 + 10.6909i) q^{85} +(0.134051 - 0.456536i) q^{86} +(4.32640 + 3.74885i) q^{87} +(0.662992 + 2.25794i) q^{88} +(-2.14463 + 4.69608i) q^{89} +(0.0825230 + 0.573960i) q^{90} +(-5.09903 + 3.76159i) q^{91} +(1.41420 + 9.31018i) q^{92} -8.77084 q^{93} +(-0.888240 + 0.127710i) q^{94} +(-2.39915 + 5.25340i) q^{95} +(-0.629640 - 2.14436i) q^{96} +(-8.54184 + 9.85781i) q^{97} +(-0.737974 + 1.11366i) q^{98} +(1.68187 + 2.61704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.0271614	+	0.188911i	0.0192060	+	0.133581i	0.997168	−	0.0752002i	$-0.0239596\pi$
$2$	0.0271614	+	0.188911i	0.0192060	+	0.133581i	−0.977962	+	0.208781i	$0.933050\pi$
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	1.88404	−	0.553203i	0.942018	−	0.276601i
$5$	1.98963	−	2.29616i	0.889790	−	1.02687i	−0.109669	−	0.993968i	$-0.534979\pi$
$5$	1.98963	−	2.29616i	0.889790	−	1.02687i	0.999459	−	0.0329041i	$-0.0104756\pi$
$6$	0.0537698	−	0.183123i	0.0219514	−	0.0747597i
$7$	−2.47239	−	0.941954i	−0.934476	−	0.356025i
$7$	−2.47239	−	0.941954i	−0.934476	−	0.356025i
$8$	0.314247	+	0.688104i	0.111103	+	0.243282i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	0.487811	+	0.313497i	0.154259	+	0.0991365i
$11$	3.07921	+	0.442724i	0.928418	+	0.133486i	0.589902	−	0.807475i	$-0.299166\pi$
$11$	3.07921	+	0.442724i	0.928418	+	0.133486i	0.338515	+	0.940961i	$0.390075\pi$
$12$	−1.94359	−	0.279446i	−0.561066	−	0.0806691i
$13$	1.29479	−	2.01474i	0.359111	−	0.558788i	−0.613947	−	0.789347i	$-0.710419\pi$
$13$	1.29479	−	2.01474i	0.359111	−	0.558788i	0.973058	+	0.230559i	$0.0740555\pi$
$14$	0.110792	−	0.492648i	0.0296105	−	0.131666i
$15$	−2.76369	+	1.26213i	−0.713582	+	0.325882i
$16$	3.18227	−	2.04512i	0.795568	−	0.511281i
$17$	−6.24490	−	1.83367i	−1.51461	−	0.444730i	−0.584311	−	0.811530i	$-0.698635\pi$
$17$	−6.24490	−	1.83367i	−1.51461	−	0.444730i	−0.930300	+	0.366800i	$0.880453\pi$
$18$	−0.124983	+	0.144238i	−0.0294587	+	0.0339972i
$19$	−1.82387	+	0.535536i	−0.418424	+	0.122860i	−0.484166	−	0.874976i	$-0.660877\pi$
$19$	−1.82387	+	0.535536i	−0.418424	+	0.122860i	0.0657418	+	0.997837i	$0.479059\pi$
$20$	2.47830	−	5.42671i	0.554164	−	1.21345i
$21$	1.85767	+	1.88390i	0.405376	+	0.411101i
$22$			0.593724i			0.126582i
$23$	−0.644774	+	4.75229i	−0.134445	+	0.990921i
$23$	−0.644774	+	4.75229i	−0.134445	+	0.990921i
$24$		−	0.756464i		−	0.154413i
$25$	−0.602129	−	4.18790i	−0.120426	−	0.837580i
$26$	0.415776	+	0.189878i	0.0815403	+	0.0372382i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−5.17917	−	0.406941i	−0.978771	−	0.0769047i
$29$	−5.49276	−	1.61282i	−1.01998	−	0.299493i	−0.271350	−	0.962481i	$-0.587470\pi$
$29$	−5.49276	−	1.61282i	−1.01998	−	0.299493i	−0.748631	+	0.662987i	$0.769288\pi$
$30$	−0.313497	−	0.487811i	−0.0572365	−	0.0890617i
$31$	7.97823	−	3.64354i	1.43293	−	0.654399i	0.460517	−	0.887651i	$-0.347664\pi$
$31$	7.97823	−	3.64354i	1.43293	−	0.654399i	0.972416	+	0.233252i	$0.0749368\pi$
$32$	1.46354	+	1.68901i	0.258720	+	0.298578i
$33$	−2.61704	−	1.68187i	−0.455568	−	0.292776i
$34$	0.176781	−	1.22954i	0.0303177	−	0.210864i
$35$	−7.08202	+	3.80286i	−1.19708	+	0.642800i
$36$	1.65186	+	1.06159i	0.275311	+	0.176931i
$37$	6.32267	−	5.47863i	1.03944	−	0.900681i	0.0442878	−	0.999019i	$-0.485898\pi$
$37$	6.32267	−	5.47863i	1.03944	−	0.900681i	0.995153	+	0.0983382i	$0.0313527\pi$
$38$	−0.150708	−	0.330003i	−0.0244480	−	0.0535336i
$39$	−2.01474	+	1.29479i	−0.322616	+	0.207333i
$40$	2.20523	+	0.647514i	0.348677	+	0.102381i
$41$	4.97801	+	4.31347i	0.777434	+	0.673650i	0.950314	−	0.311292i	$-0.100762\pi$
$41$	4.97801	+	4.31347i	0.777434	+	0.673650i	−0.172880	+	0.984943i	$0.555307\pi$
$42$	−0.305434	+	0.402103i	−0.0471294	+	0.0620459i
$43$	−2.26776	−	1.03565i	−0.345831	−	0.157936i	0.234925	−	0.972014i	$-0.424516\pi$
$43$	−2.26776	−	1.03565i	−0.345831	−	0.157936i	−0.580756	+	0.814078i	$0.697243\pi$
$44$	6.04627	−	0.869322i	0.911509	−	0.131055i
$45$	3.03825			0.452916
$46$	−0.915275	+	0.00727351i	−0.134950	+	0.00107242i
$47$			4.70188i			0.685840i	0.939365	+	0.342920i	$0.111416\pi$
$47$			4.70188i			0.685840i	−0.939365	+	0.342920i	$0.888584\pi$
$48$	−3.74427	+	0.538345i	−0.540439	+	0.0777034i
$49$	5.22544	+	4.65776i	0.746492	+	0.665394i
$50$	0.774787	−	0.227498i	0.109571	−	0.0321731i
$51$	4.91883	+	4.26219i	0.688773	+	0.596826i
$52$	1.32488	−	4.51212i	0.183728	−	0.625719i
$53$	−4.94290	−	7.69131i	−0.678960	−	1.05648i	−0.994208	−	0.107473i	$-0.965724\pi$
$53$	−4.94290	−	7.69131i	−0.678960	−	1.05648i	0.315248	−	0.949009i	$-0.397912\pi$
$54$	0.173607	−	0.0792836i	0.0236249	−	0.0107891i
$55$	7.14306	−	6.18950i	0.963170	−	0.834592i
$56$	−0.128778	−	1.99727i	−0.0172087	−	0.266896i
$57$	1.88152	+	0.270521i	0.249213	+	0.0358314i
$58$	0.155489	−	1.08145i	0.0204168	−	0.142002i
$59$	−1.62895	+	2.53469i	−0.212071	+	0.329989i	−0.930950	−	0.365146i	$-0.881019\pi$
$59$	−1.62895	+	2.53469i	−0.212071	+	0.329989i	0.718879	+	0.695135i	$0.244655\pi$
$60$	−4.50867	+	3.90679i	−0.582067	+	0.504364i
$61$	0.0813133	+	0.178051i	0.0104111	+	0.0227971i	0.914766	−	0.403984i	$-0.132375\pi$
$61$	0.0813133	+	0.178051i	0.0104111	+	0.0227971i	−0.904355	+	0.426781i	$0.859648\pi$
$62$	0.905006	+	1.40822i	0.114936	+	0.178844i
$63$	−0.907191	−	2.48536i	−0.114295	−	0.313126i
$64$	4.67506	−	5.39531i	0.584382	−	0.674413i
$65$	−2.04999	−	6.98164i	−0.254270	−	0.865965i
$66$	0.246642	−	0.540070i	0.0303595	−	0.0664780i
$67$	12.0444	−	1.73172i	1.47146	−	0.211563i	0.640524	−	0.767938i	$-0.278717\pi$
$67$	12.0444	−	1.73172i	1.47146	−	0.211563i	0.830932	+	0.556374i	$0.187808\pi$
$68$	−12.7800			−1.54980
$69$	2.56068	−	4.05499i	0.308270	−	0.488163i
$70$	−0.910761	−	1.23458i	−0.108857	−	0.147561i
$71$	1.06927	+	7.43690i	0.126898	+	0.882598i	0.949452	+	0.313911i	$0.101639\pi$
$71$	1.06927	+	7.43690i	0.126898	+	0.882598i	−0.822554	+	0.568687i	$0.807452\pi$
$72$	−0.314247	+	0.688104i	−0.0370343	+	0.0810938i
$73$	0.328156	+	1.11760i	0.0384077	+	0.130805i	0.976465	−	0.215675i	$-0.0691952\pi$
$73$	0.328156	+	1.11760i	0.0384077	+	0.130805i	−0.938057	+	0.346480i	$0.887377\pi$
$74$	1.20671	+	1.04562i	0.140277	+	0.121551i
$75$	−1.19200	+	4.05958i	−0.137640	+	0.468760i
$76$	−3.13997	+	2.01794i	−0.360179	+	0.231473i
$77$	−7.19600	−	3.99506i	−0.820060	−	0.455280i
$78$	−0.299324	−	0.345439i	−0.0338918	−	0.0391132i
$79$	−8.23775	+	12.8182i	−0.926819	+	1.44216i	−0.0301065	+	0.999547i	$0.509585\pi$
$79$	−8.23775	+	12.8182i	−0.926819	+	1.44216i	−0.896713	+	0.442613i	$0.854052\pi$
$80$	1.63563	−	11.3760i	0.182869	−	1.27188i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.679654	+	1.05756i	−0.0750552	+	0.116788i
$83$	7.53178	+	8.69214i	0.826721	+	0.954087i	0.999523	−	0.0308699i	$-0.00982776\pi$
$83$	7.53178	+	8.69214i	0.826721	+	0.954087i	−0.172803	+	0.984956i	$0.555282\pi$
$84$	4.54209	+	2.52167i	0.495582	+	0.275137i
$85$	−16.6354	+	10.6909i	−1.80437	+	1.15960i
$86$	0.134051	−	0.456536i	0.0144551	−	0.0492296i
$87$	4.32640	+	3.74885i	0.463839	+	0.401919i
$88$	0.662992	+	2.25794i	0.0706752	+	0.240698i
$89$	−2.14463	+	4.69608i	−0.227330	+	0.497784i	−0.988584	−	0.150670i	$-0.951857\pi$
$89$	−2.14463	+	4.69608i	−0.227330	+	0.497784i	0.761254	+	0.648454i	$0.224584\pi$
$90$	0.0825230	+	0.573960i	0.00869869	+	0.0605007i
$91$	−5.09903	+	3.76159i	−0.534524	+	0.394322i
$92$	1.41420	+	9.31018i	0.147441	+	0.970653i
$93$	−8.77084			−0.909494
$94$	−0.888240	+	0.127710i	−0.0916149	+	0.0131722i
$95$	−2.39915	+	5.25340i	−0.246147	+	0.538988i
$96$	−0.629640	−	2.14436i	−0.0642624	−	0.218858i
$97$	−8.54184	+	9.85781i	−0.867293	+	1.00091i	0.132660	+	0.991162i	$0.457648\pi$
$97$	−8.54184	+	9.85781i	−0.867293	+	1.00091i	−0.999952	+	0.00974770i	$0.996897\pi$
$98$	−0.737974	+	1.11366i	−0.0745466	+	0.112496i
$99$	1.68187	+	2.61704i	0.169034	+	0.263022i
$100$	−3.45119	−	7.55705i	−0.345119	−	0.755705i
$101$	6.94547	−	6.01829i	0.691101	−	0.598842i	−0.236850	−	0.971546i	$-0.576115\pi$
$101$	6.94547	−	6.01829i	0.691101	−	0.598842i	0.927950	+	0.372704i	$0.121569\pi$
$102$	−0.671574	+	1.04499i	−0.0664957	+	0.103469i
$103$	−2.44672	+	17.0173i	−0.241082	+	1.67676i	0.405636	+	0.914035i	$0.367050\pi$
$103$	−2.44672	+	17.0173i	−0.241082	+	1.67676i	−0.646718	+	0.762729i	$0.723859\pi$
$104$	1.79323	+	0.257828i	0.175841	+	0.0252821i
$105$	8.02180	−	0.517223i	0.782847	−	0.0504758i
$106$	1.31872	−	1.14268i	0.128085	−	0.110987i
$107$	−17.1449	+	7.82982i	−1.65746	+	0.756937i	−0.657468	+	0.753483i	$0.728372\pi$
$107$	−17.1449	+	7.82982i	−1.65746	+	0.756937i	−0.999994	+	0.00345449i	$0.998900\pi$
$108$	−1.06159	−	1.65186i	−0.102151	−	0.158951i
$109$	3.78640	−	12.8953i	0.362671	−	1.23514i	−0.552989	−	0.833189i	$-0.686513\pi$
$109$	3.78640	−	12.8953i	0.362671	−	1.23514i	0.915659	−	0.401955i	$-0.131669\pi$
$110$	1.36328	+	1.18129i	0.129984	+	0.112632i
$111$	−8.02721	+	2.35700i	−0.761909	+	0.223717i
$112$	−9.79424	+	2.05879i	−0.925469	+	0.194537i
$113$	1.56418	−	0.224895i	0.147146	−	0.0211564i	−0.0683483	−	0.997662i	$-0.521773\pi$
$113$	1.56418	−	0.224895i	0.147146	−	0.0211564i	0.215494	+	0.976505i	$0.430864\pi$
$114$			0.362788i			0.0339782i
$115$	9.62914	+	10.9358i	0.897922	+	1.01977i
$116$	−11.2408			−1.04368
$117$	2.37055	−	0.340833i	0.219157	−	0.0315100i
$118$	−0.523077	−	0.238881i	−0.0481531	−	0.0219908i
$119$	13.7126	+	10.4160i	1.25703	+	0.954829i
$120$	−1.73696	−	1.50508i	−0.158562	−	0.137395i
$121$	−1.26887	−	0.372575i	−0.115352	−	0.0338704i
$122$	−0.0314274	+	0.0201971i	−0.00284530	+	0.00182856i
$123$	−2.73627	−	5.99161i	−0.246722	−	0.540245i
$124$	13.0157	−	11.2781i	1.16884	−	1.01281i
$125$	1.96561	+	1.26322i	0.175809	+	0.112986i
$126$	0.444872	−	0.238884i	0.0396323	−	0.0212815i
$127$	−0.0684842	+	0.476318i	−0.00607699	+	0.0422664i	−0.992634	−	0.121149i	$-0.961342\pi$
$127$	−0.0684842	+	0.476318i	−0.00607699	+	0.0422664i	0.986557	+	0.163416i	$0.0522511\pi$
$128$	4.90643	+	3.15317i	0.433671	+	0.278703i
$129$	1.63260	+	1.88413i	0.143743	+	0.165888i
$130$	1.26323	−	0.576898i	0.110793	−	0.0505973i
$131$	4.45815	+	6.93701i	0.389510	+	0.606089i	0.979530	−	0.201299i	$-0.0645164\pi$
$131$	4.45815	+	6.93701i	0.389510	+	0.606089i	−0.590020	+	0.807389i	$0.700880\pi$
$132$	−5.86101	−	1.72095i	−0.510135	−	0.149789i
$133$	5.01376	+	0.393945i	0.434749	+	0.0341594i
$134$	0.654284	+	2.22829i	0.0565215	+	0.192495i
$135$	−2.76369	−	1.26213i	−0.237861	−	0.108627i
$136$	−0.700684	−	4.87336i	−0.0600832	−	0.417888i
$137$			6.38459i			0.545473i	0.962089	+	0.272736i	$0.0879287\pi$
$137$			6.38459i			0.545473i	−0.962089	+	0.272736i	$0.912071\pi$
$138$	0.835585	+	0.373603i	0.0711297	+	0.0318032i
$139$		−	8.48730i		−	0.719883i	−0.932975	−	0.359942i	$-0.882797\pi$
$139$		−	8.48730i		−	0.719883i	0.932975	−	0.359942i	$-0.117203\pi$
$140$	−11.2390	+	11.0825i	−0.949872	+	0.936644i
$141$	1.95323	−	4.27698i	0.164492	−	0.360187i
$142$	−1.37587	+	0.403993i	−0.115461	+	0.0339023i
$143$	4.87892	−	5.63057i	0.407996	−	0.470852i
$144$	3.62955	+	1.06573i	0.302462	+	0.0888109i
$145$	−14.6319	+	9.40333i	−1.21511	+	0.780904i
$146$	−0.202213	+	0.0923478i	−0.0167353	+	0.00764276i
$147$	−2.81833	−	6.40758i	−0.232452	−	0.528488i
$148$	8.88135	−	13.8197i	0.730042	−	1.13597i
$149$	−4.72606	−	0.679504i	−0.387174	−	0.0556672i	−0.0540203	−	0.998540i	$-0.517204\pi$
$149$	−4.72606	−	0.679504i	−0.387174	−	0.0556672i	−0.333153	+	0.942873i	$0.608113\pi$
$150$	−0.799278	−	0.114919i	−0.0652607	−	0.00938308i
$151$	−0.921173	−	0.592002i	−0.0749640	−	0.0481764i	0.502622	−	0.864506i	$-0.332369\pi$
$151$	−0.921173	−	0.592002i	−0.0749640	−	0.0481764i	−0.577586	+	0.816330i	$0.696005\pi$
$152$	−0.941648	−	1.08672i	−0.0763778	−	0.0881447i
$153$	−2.70375	−	5.92038i	−0.218585	−	0.478634i
$154$	0.559260	−	1.46792i	0.0450665	−	0.118288i
$155$	7.50761	−	25.5686i	0.603026	−	2.05372i
$156$	−3.07956	+	3.55400i	−0.246562	+	0.284548i
$157$	15.2897	−	4.48946i	1.22025	−	0.358298i	0.392688	−	0.919672i	$-0.371545\pi$
$157$	15.2897	−	4.48946i	1.22025	−	0.358298i	0.827562	+	0.561374i	$0.189727\pi$
$158$	−2.64525	−	1.20805i	−0.210445	−	0.0961070i
$159$	1.30114	+	9.04962i	0.103187	+	0.717681i
$160$	6.79014			0.536808
$161$	6.07057	−	11.1422i	0.478428	−	0.878127i
$162$	−0.190854			−0.0149949
$163$	−2.47568	−	17.2187i	−0.193910	−	1.34867i	−0.821535	−	0.570158i	$-0.806882\pi$
$163$	−2.47568	−	17.2187i	−0.193910	−	1.34867i	0.627625	−	0.778516i	$-0.284027\pi$
$164$	11.7650	+	5.37288i	0.918690	+	0.419551i
$165$	−9.06877	+	2.66283i	−0.706003	+	0.207301i
$166$	−1.43747	+	1.65893i	−0.111569	+	0.128758i
$167$	3.48135	−	11.8564i	0.269395	−	0.917474i	−0.708029	−	0.706184i	$-0.750415\pi$
$167$	3.48135	−	11.8564i	0.269395	−	0.917474i	0.977423	−	0.211290i	$-0.0677666\pi$
$168$	−0.712555	+	1.87028i	−0.0549748	+	0.144295i
$169$	3.01771	+	6.60787i	0.232132	+	0.508298i
$170$	−2.47148	−	2.85224i	−0.189554	−	0.218757i
$171$	−1.59911	−	1.02769i	−0.122287	−	0.0785891i
$172$	−4.84548	−	0.696674i	−0.369464	−	0.0531209i
$173$	−5.45178	−	0.783848i	−0.414492	−	0.0595949i	−0.0680853	−	0.997680i	$-0.521689\pi$
$173$	−5.45178	−	0.783848i	−0.414492	−	0.0595949i	−0.346406	+	0.938085i	$0.612598\pi$
$174$	−0.590690	+	0.919131i	−0.0447801	+	0.0696791i
$175$	−2.45611	+	10.9213i	−0.185664	+	0.825573i
$176$	10.7043	−	4.88850i	0.806869	−	0.368485i
$177$	2.53469	−	1.62895i	0.190519	−	0.122439i
$178$	−0.945395	−	0.277593i	−0.0708603	−	0.0208065i
$179$	−6.29324	+	7.26278i	−0.470379	+	0.542846i	−0.940517	−	0.339747i	$-0.889659\pi$
$179$	−6.29324	+	7.26278i	−0.470379	+	0.542846i	0.470138	+	0.882593i	$0.344204\pi$
$180$	5.72417	−	1.68077i	0.426655	−	0.125277i
$181$	0.371494	−	0.813459i	0.0276129	−	0.0604639i	−0.895323	−	0.445417i	$-0.853055\pi$
$181$	0.371494	−	0.813459i	0.0276129	−	0.0604639i	0.922936	+	0.384954i	$0.125783\pi$
$182$	−0.849103	−	0.861095i	−0.0629397	−	0.0638286i
$183$		−	0.195740i		−	0.0144695i
$184$	−3.47269	+	1.04972i	−0.256010	+	0.0773864i
$185$		−	25.4183i		−	1.86879i
$186$	−0.238228	−	1.65691i	−0.0174677	−	0.121491i
$187$	−18.4176	−	8.41102i	−1.34683	−	0.615075i
$188$	2.60110	+	8.85852i	0.189704	+	0.646074i
$189$	−0.207245	+	2.63762i	−0.0150749	+	0.191859i
$190$	−1.05759	−	0.310537i	−0.0767258	−	0.0225287i
$191$	11.9034	+	18.5221i	0.861301	+	1.34021i	0.939243	+	0.343252i	$0.111529\pi$
$191$	11.9034	+	18.5221i	0.861301	+	1.34021i	−0.0779426	+	0.996958i	$0.524835\pi$
$192$	−6.49387	+	2.96565i	−0.468655	+	0.214028i
$193$	15.7408	+	18.1658i	1.13305	+	1.30761i	0.945600	+	0.325332i	$0.105476\pi$
$193$	15.7408	+	18.1658i	1.13305	+	1.30761i	0.187448	+	0.982275i	$0.439979\pi$
$194$	−2.09426	−	1.34590i	−0.150359	−	0.0966300i
$195$	−1.03554	+	7.20232i	−0.0741563	+	0.515769i
$196$	12.4216	+	5.88466i	0.887258	+	0.420333i
$197$	3.33106	+	2.14074i	0.237328	+	0.152521i	0.653899	−	0.756582i	$-0.273132\pi$
$197$	3.33106	+	2.14074i	0.237328	+	0.152521i	−0.416571	+	0.909103i	$0.636768\pi$
$198$	−0.448706	+	0.388806i	−0.0318882	+	0.0276313i
$199$	−6.27353	−	13.7371i	−0.444719	−	0.973798i	−0.990708	−	0.136006i	$-0.956573\pi$
$199$	−6.27353	−	13.7371i	−0.444719	−	0.973798i	0.545989	−	0.837792i	$-0.316154\pi$
$200$	2.69249	−	1.73036i	0.190388	−	0.122355i
$201$	−11.6753	−	3.42819i	−0.823515	−	0.241806i
$202$	1.32557	+	1.14861i	0.0932669	+	0.0808162i
$203$	12.0611	+	9.16146i	0.846521	+	0.643008i
$204$	11.6251	+	5.30901i	0.813920	+	0.371705i
$205$	19.8088	−	2.84807i	1.38351	−	0.198918i
$206$	−3.28122			−0.228613
$207$	−4.01378	+	2.62480i	−0.278977	+	0.182436i
$208$		−	9.05946i		−	0.628161i
$209$	−5.85317	+	0.841559i	−0.404872	+	0.0582118i
$210$	0.315592	+	1.50136i	0.0217779	+	0.103604i
$211$	−12.2871	+	3.60782i	−0.845880	+	0.248373i	−0.675825	−	0.737062i	$-0.736213\pi$
$211$	−12.2871	+	3.60782i	−0.845880	+	0.248373i	−0.170055	+	0.985435i	$0.554394\pi$
$212$	−13.5675	−	11.7563i	−0.931817	−	0.807424i
$213$	2.11676	−	7.20903i	0.145038	−	0.493955i
$214$	−1.94482	−	3.02620i	−0.132945	−	0.206867i
$215$	−6.89003	+	3.14657i	−0.469896	+	0.214595i
$216$	0.571698	−	0.495379i	0.0388991	−	0.0337063i
$217$	−23.1574	+	1.49312i	−1.57202	+	0.101360i
$218$	2.53891	+	0.365040i	0.171957	+	0.0247236i
$219$	0.165765	−	1.15292i	0.0112014	−	0.0779072i
$220$	10.0337	−	15.6128i	0.676474	−	1.05261i
$221$	−11.7802	+	10.2076i	−0.792423	+	0.686639i
$222$	−0.663294	−	1.45241i	−0.0445174	−	0.0974795i
$223$	3.16358	+	4.92263i	0.211849	+	0.329644i	0.930874	−	0.365341i	$-0.119048\pi$
$223$	3.16358	+	4.92263i	0.211849	+	0.329644i	−0.719025	+	0.694985i	$0.755411\pi$
$224$	−2.02747	−	5.55449i	−0.135466	−	0.371125i
$225$	2.77069	−	3.19755i	0.184713	−	0.213170i
$226$	0.0849705	+	0.289383i	0.00565215	+	0.0192495i
$227$	1.49180	−	3.26658i	0.0990140	−	0.216810i	−0.853642	−	0.520860i	$-0.825611\pi$
$227$	1.49180	−	3.26658i	0.0990140	−	0.216810i	0.952656	+	0.304049i	$0.0983388\pi$
$228$	3.69450	−	0.531189i	0.244674	−	0.0351788i
$229$	−15.5322			−1.02640			−0.513198	−	0.858270i	$-0.671539\pi$
$229$	−15.5322			−1.02640			−0.513198	+	0.858270i	$0.671539\pi$
$230$	−1.80436	+	2.11609i	−0.118976	+	0.139531i
$231$	4.88610	+	6.62336i	0.321482	+	0.435785i
$232$	−0.616294	−	4.28642i	−0.0404617	−	0.281417i
$233$	1.71859	−	3.76318i	0.112588	−	0.246534i	−0.844947	−	0.534850i	$-0.820368\pi$
$233$	1.71859	−	3.76318i	0.112588	−	0.246534i	0.957535	+	0.288316i	$0.0930953\pi$
$234$	0.128775	+	0.438566i	0.00841826	+	0.0286700i
$235$	10.7963	+	9.35501i	0.704271	+	0.610254i
$236$	−1.66680	+	5.67659i	−0.108499	+	0.369514i
$237$	12.8182	−	8.23775i	0.832631	−	0.535099i
$238$	−1.59524	+	2.87338i	−0.103404	+	0.186254i
$239$	1.25929	+	1.45329i	0.0814565	+	0.0940058i	0.795015	−	0.606590i	$-0.207463\pi$
$239$	1.25929	+	1.45329i	0.0814565	+	0.0940058i	−0.713558	+	0.700596i	$0.752918\pi$
$240$	−6.21359	+	9.66854i	−0.401086	+	0.624102i
$241$	1.05454	−	7.33446i	0.0679287	−	0.472454i	−0.927255	−	0.374430i	$-0.877839\pi$
$241$	1.05454	−	7.33446i	0.0679287	−	0.472454i	0.995184	−	0.0980246i	$-0.0312524\pi$
$242$	0.0359193	−	0.249824i	0.00230898	−	0.0160593i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	0.251696	+	0.290472i	0.0161132	+	0.0185956i
$245$	21.0917	−	2.73122i	1.34750	−	0.174491i
$246$	1.05756	−	0.679654i	0.0674277	−	0.0433331i
$247$	−1.28257	+	4.36802i	−0.0816078	+	0.277931i
$248$	5.01427	+	4.34489i	0.318406	+	0.275901i
$249$	−3.24031	−	11.0355i	−0.205346	−	0.699344i
$250$	−0.185248	+	0.405636i	−0.0117161	+	0.0256547i
$251$	−2.58208	−	17.9588i	−0.162980	−	1.13355i	−0.892978	−	0.450100i	$-0.851388\pi$
$251$	−2.58208	−	17.9588i	−0.162980	−	1.13355i	0.729999	−	0.683449i	$-0.239521\pi$
$252$	−3.08409	−	4.18064i	−0.194279	−	0.263356i
$253$	−4.08935	+	14.3479i	−0.257095	+	0.902042i
$254$	−0.0918421			−0.00576269
$255$	19.5733	−	2.81422i	1.22573	−	0.176233i
$256$	5.46890	−	11.9752i	0.341806	−	0.748452i
$257$	4.86780	+	16.5782i	0.303645	+	1.03412i	0.960077	+	0.279735i	$0.0902465\pi$
$257$	4.86780	+	16.5782i	0.303645	+	1.03412i	−0.656432	+	0.754385i	$0.727935\pi$
$258$	−0.311589	+	0.359593i	−0.0193987	+	0.0223873i
$259$	−20.7927	+	7.58964i	−1.29200	+	0.471598i
$260$	−7.72452	−	12.0196i	−0.479055	−	0.745423i
$261$	−2.37811	−	5.20733i	−0.147201	−	0.322325i
$262$	−1.18939	+	1.03061i	−0.0734808	+	0.0636715i
$263$	9.92661	−	15.4461i	0.612101	−	0.952448i	−0.387432	−	0.921898i	$-0.626638\pi$
$263$	9.92661	−	15.4461i	0.612101	−	0.952448i	0.999533	−	0.0305496i	$-0.00972576\pi$
$264$	0.334905	−	2.32931i	0.0206120	−	0.143359i
$265$	−27.4950	−	3.95319i	−1.68900	−	0.242842i
$266$	0.0617600	+	0.957858i	0.00378675	+	0.0587300i
$267$	3.90165	−	3.38080i	0.238777	−	0.206901i
$268$	21.7341	−	9.92562i	1.32762	−	0.606304i
$269$	4.17392	+	6.49475i	0.254489	+	0.395992i	0.944866	−	0.327457i	$-0.106192\pi$
$269$	4.17392	+	6.49475i	0.254489	+	0.395992i	−0.690377	+	0.723450i	$0.742555\pi$
$270$	0.163366	−	0.556374i	0.00994214	−	0.0338598i
$271$	21.5391	+	18.6637i	1.30841	+	1.13374i	0.982076	+	0.188486i	$0.0603581\pi$
$271$	21.5391	+	18.6637i	1.30841	+	1.13374i	0.326332	+	0.945255i	$0.394187\pi$
$272$	−23.6230	+	6.93635i	−1.43236	+	0.420578i
$273$	6.20086	−	1.30345i	0.375293	−	0.0788882i
$274$	−1.20612	+	0.173414i	−0.0728645	+	0.0104763i
$275$		−	13.1620i		−	0.793699i
$276$	2.58118	−	9.05632i	0.155369	−	0.545126i
$277$	13.8216			0.830458			0.415229	−	0.909717i	$-0.363701\pi$
$277$	13.8216			0.830458			0.415229	+	0.909717i	$0.363701\pi$
$278$	1.60335	−	0.230527i	0.0961624	−	0.0138261i
$279$	7.97823	+	3.64354i	0.477644	+	0.218133i
$280$	−4.84226	−	3.67813i	−0.289381	−	0.219810i
$281$	−18.8951	−	16.3727i	−1.12719	−	0.976715i	−0.127304	−	0.991864i	$-0.540632\pi$
$281$	−18.8951	−	16.3727i	−1.12719	−	0.976715i	−0.999885	+	0.0151490i	$0.995178\pi$
$282$	0.861024	+	0.252819i	0.0512732	+	0.0150552i
$283$	1.62288	−	1.04296i	0.0964704	−	0.0619978i	−0.491516	−	0.870868i	$-0.663557\pi$
$283$	1.62288	−	1.04296i	0.0964704	−	0.0619978i	0.587987	+	0.808871i	$0.299921\pi$
$284$	6.12865	+	13.4199i	0.363669	+	0.796323i
$285$	4.36468	−	3.78202i	0.258542	−	0.224028i
$286$	1.19620	+	0.768750i	0.0707327	+	0.0454571i
$287$	−8.24450	−	15.3536i	−0.486657	−	0.906296i
$288$	−0.318058	+	2.21214i	−0.0187417	+	0.130352i
$289$	21.3351	+	13.7112i	1.25501	+	0.806544i
$290$	−2.17382	−	2.50872i	−0.127651	−	0.147317i
$291$	11.8650	−	5.41857i	0.695540	−	0.317642i
$292$	1.23651	+	1.92405i	0.0723615	+	0.112597i
$293$	−10.9898	−	3.22690i	−0.642032	−	0.188518i	−0.0555192	−	0.998458i	$-0.517681\pi$
$293$	−10.9898	−	3.22690i	−0.642032	−	0.188518i	−0.586513	+	0.809940i	$0.699500\pi$
$294$	1.13391	−	0.706453i	0.0661312	−	0.0412012i
$295$	2.57904	+	8.78342i	0.150158	+	0.511390i
$296$	5.75674	+	2.62902i	0.334604	+	0.152808i
$297$	−0.442724	−	3.07921i	−0.0256895	−	0.178674i
$298$		−	0.911262i		−	0.0527880i
$299$	8.73977	+	7.45229i	0.505434	+	0.430977i
$300$			8.30782i			0.479652i
$301$	4.63126	+	4.69667i	0.266942	+	0.270712i
$302$	0.0868156	−	0.190100i	0.00499568	−	0.0109390i
$303$	−8.81791	+	2.58917i	−0.506576	+	0.148744i
$304$	−4.70881	+	5.43425i	−0.270069	+	0.311676i
$305$	0.570617	+	0.167548i	0.0326734	+	0.00959379i
$306$	1.04499	−	0.671574i	0.0597381	−	0.0383913i
$307$	−5.11167	+	2.33442i	−0.291738	+	0.133232i	−0.555908	−	0.831244i	$-0.687629\pi$
$307$	−5.11167	+	2.33442i	−0.291738	+	0.133232i	0.264170	+	0.964476i	$0.414902\pi$
$308$	−15.7676	−	3.54600i	−0.898442	−	0.202052i
$309$	9.29485	−	14.4631i	0.528766	−	0.822775i
$310$	5.03411	+	0.723796i	0.285918	+	0.0411089i
$311$	−8.82360	−	1.26864i	−0.500340	−	0.0719381i	−0.112476	−	0.993654i	$-0.535878\pi$
$311$	−8.82360	−	1.26864i	−0.500340	−	0.0719381i	−0.387865	+	0.921716i	$0.626787\pi$
$312$	−1.52408	−	0.979465i	−0.0862839	−	0.0554513i
$313$	−20.8631	−	24.0773i	−1.17925	−	1.36093i	−0.918450	−	0.395536i	$-0.870559\pi$
$313$	−20.8631	−	24.0773i	−1.17925	−	1.36093i	−0.260801	−	0.965393i	$-0.583987\pi$
$314$	1.26340	+	2.76646i	0.0712977	+	0.156120i
$315$	−7.51175	−	2.86189i	−0.423239	−	0.161249i
$316$	−8.42916	+	28.7071i	−0.474177	+	1.61490i
$317$	6.18282	−	7.13536i	0.347262	−	0.400762i	−0.555070	−	0.831804i	$-0.687308\pi$
$317$	6.18282	−	7.13536i	0.347262	−	0.400762i	0.902332	+	0.431042i	$0.141854\pi$
$318$	−1.67424	+	0.491600i	−0.0938865	+	0.0275676i
$319$	−16.1994	−	7.39800i	−0.906990	−	0.414208i
$320$	−3.08682	−	21.4693i	−0.172559	−	1.20017i
$321$	18.8482			1.05200
$322$	2.26977	+	0.844164i	0.126489	+	0.0470434i
$323$	12.3719			0.688389
$324$	0.279446	+	1.94359i	0.0155248	+	0.107977i
$325$	−9.21716	−	4.20933i	−0.511276	−	0.233492i
$326$	3.18557	−	0.935368i	0.176432	−	0.0518052i
$327$	−8.80112	+	10.1570i	−0.486703	+	0.561685i
$328$	−1.40379	+	4.78088i	−0.0775115	+	0.263980i
$329$	4.42896	−	11.6249i	0.244176	−	0.640902i
$330$	−0.749359	−	1.64087i	−0.0412509	−	0.0903268i
$331$	2.75065	+	3.17442i	0.151189	+	0.174482i	0.826292	−	0.563242i	$-0.190446\pi$
$331$	2.75065	+	3.17442i	0.151189	+	0.174482i	−0.675103	+	0.737724i	$0.735901\pi$
$332$	18.9987	+	12.2097i	1.04269	+	0.670095i
$333$	8.28094	+	1.19062i	0.453793	+	0.0652455i
$334$	2.33436	+	0.335631i	0.127731	+	0.0183649i
$335$	19.9876	−	31.1013i	1.09204	−	1.69924i
$336$	9.76440	+	2.19593i	0.532692	+	0.119798i
$337$	0.340674	−	0.155581i	0.0185577	−	0.00847502i	−0.406115	−	0.913822i	$-0.633117\pi$
$337$	0.340674	−	0.155581i	0.0185577	−	0.00847502i	0.424672	+	0.905347i	$0.360389\pi$
$338$	−1.16634	+	0.749560i	−0.0634404	+	0.0407707i
$339$	−1.51625	−	0.445212i	−0.0823515	−	0.0241806i
$340$	−25.4275	+	29.3449i	−1.37900	+	1.59145i
$341$	26.1798	−	7.68707i	1.41771	−	0.416278i
$342$	0.150708	−	0.330003i	0.00814933	−	0.0178445i
$343$	−8.53195	−	16.4379i	−0.460682	−	0.887565i
$344$		−	1.88591i		−	0.101681i
$345$	−4.21608	−	13.9476i	−0.226986	−	0.750916i
$346$		−	1.05119i		−	0.0565126i
$347$	−3.39164	−	23.5894i	−0.182073	−	1.26634i	−0.851852	−	0.523783i	$-0.824520\pi$
$347$	−3.39164	−	23.5894i	−0.182073	−	1.26634i	0.669779	−	0.742561i	$-0.266389\pi$
$348$	10.2250	+	4.66959i	0.548116	+	0.250316i
$349$	−3.20852	−	10.9272i	−0.171748	−	0.584921i	−0.999709	−	0.0241345i	$-0.992317\pi$
$349$	−3.20852	−	10.9272i	−0.171748	−	0.584921i	0.827960	−	0.560787i	$-0.189501\pi$
$350$	−2.12987	−	0.167350i	−0.113846	−	0.00894522i
$351$	−2.29791	−	0.674728i	−0.122654	−	0.0360143i
$352$	3.75878	+	5.84878i	0.200344	+	0.311741i
$353$	−10.3813	+	4.74097i	−0.552539	+	0.252336i	−0.672062	−	0.740495i	$-0.734591\pi$
$353$	−10.3813	+	4.74097i	−0.552539	+	0.252336i	0.119522	+	0.992832i	$0.461864\pi$
$354$	0.376572	+	0.434588i	0.0200146	+	0.0230981i
$355$	19.2037	+	12.3415i	1.01923	+	0.655018i
$356$	−1.44267	+	10.0340i	−0.0764615	+	0.531801i
$357$	−8.14648	−	15.1711i	−0.431158	−	0.802940i
$358$	−1.54296	−	0.991597i	−0.0815477	−	0.0524075i
$359$	10.7048	−	9.27573i	0.564976	−	0.489554i	−0.324906	−	0.945746i	$-0.605333\pi$
$359$	10.7048	−	9.27573i	0.564976	−	0.489554i	0.889881	+	0.456192i	$0.150787\pi$
$360$	0.954760	+	2.09063i	0.0503203	+	0.110186i
$361$	−12.9441	+	8.31868i	−0.681270	+	0.437825i
$362$	0.163762	+	0.0480848i	0.00860714	+	0.00252728i
$363$	0.999435	+	0.866015i	0.0524567	+	0.0454540i
$364$	−7.52584	+	9.90777i	−0.394461	+	0.519308i
$365$	3.21908	+	1.47011i	0.168494	+	0.0769488i
$366$	0.0369775	−	0.00531656i	0.00193285	−	0.000277901i
$367$	−28.0585			−1.46464			−0.732321	−	0.680960i	$-0.761563\pi$
$367$	−28.0585			−1.46464			−0.732321	+	0.680960i	$0.761563\pi$
$368$	7.66717	+	16.4417i	0.399679	+	0.857084i
$369$			6.58685i			0.342898i
$370$	4.80180	−	0.690395i	0.249634	−	0.0358919i
$371$	4.97594	+	23.6719i	0.258338	+	1.22899i
$372$	−16.5246	+	4.85205i	−0.856759	+	0.251567i
$373$	7.22522	+	6.26069i	0.374108	+	0.324166i	0.821539	−	0.570152i	$-0.193116\pi$
$373$	7.22522	+	6.26069i	0.374108	+	0.324166i	−0.447432	+	0.894318i	$0.647661\pi$
$374$	1.08869	−	3.70774i	0.0562949	−	0.191723i
$375$	−1.26322	−	1.96561i	−0.0652324	−	0.101504i
$376$	−3.23539	+	1.47755i	−0.166852	+	0.0761989i
$377$	−10.3614	+	8.97821i	−0.533640	+	0.462402i
$378$	−0.503906	+	0.0324904i	−0.0259181	+	0.00167113i
$379$	−32.3352	−	4.64909i	−1.66095	−	0.238808i	−0.753037	−	0.657978i	$-0.771412\pi$
$379$	−32.3352	−	4.64909i	−1.66095	−	0.238808i	−0.907908	+	0.419170i	$0.862321\pi$
$380$	−1.61389	+	11.2248i	−0.0827906	+	0.575821i
$381$	0.260165	−	0.404825i	0.0133287	−	0.0207398i
$382$	−3.17572	+	2.75178i	−0.162484	+	0.140793i
$383$	−11.9571	−	26.1823i	−0.610978	−	1.33785i	−0.921903	−	0.387420i	$-0.873366\pi$
$383$	−11.9571	−	26.1823i	−0.610978	−	1.33785i	0.310926	−	0.950434i	$-0.399361\pi$
$384$	−3.15317	−	4.90643i	−0.160910	−	0.250380i
$385$	−23.4907	+	8.57443i	−1.19720	+	0.436993i
$386$	−3.00420	+	3.46703i	−0.152910	+	0.176467i
$387$	−0.702375	−	2.39207i	−0.0357037	−	0.121596i
$388$	−10.6398	+	23.2979i	−0.540153	+	1.18277i
$389$	3.29758	−	0.474121i	0.167194	−	0.0240389i	−0.0582094	−	0.998304i	$-0.518539\pi$
$389$	3.29758	−	0.474121i	0.167194	−	0.0240389i	0.225403	+	0.974266i	$0.427630\pi$
$390$	−1.38873			−0.0703209
$391$	12.7407	−	28.4953i	0.644323	−	1.44107i
$392$	−1.56295	+	5.05934i	−0.0789407	+	0.255535i
$393$	−1.17353	−	8.16211i	−0.0591970	−	0.411724i
$394$	−0.313934	+	0.687420i	−0.0158158	+	0.0346317i
$395$	13.0425	+	44.4186i	0.656239	+	2.23494i
$396$	4.61645	+	4.00018i	0.231985	+	0.201016i
$397$	−4.61746	+	15.7256i	−0.231744	+	0.789247i	0.758713	+	0.651425i	$0.225828\pi$
$397$	−4.61746	+	15.7256i	−0.231744	+	0.789247i	−0.990457	+	0.137822i	$0.955990\pi$
$398$	2.42470	−	1.55826i	0.121539	−	0.0781085i
$399$	−4.39703	−	2.44114i	−0.220127	−	0.122210i
$400$	−10.4809	−	12.0956i	−0.524045	−	0.604781i
$401$	−11.2094	+	17.4421i	−0.559769	+	0.871017i	−0.999634	−	0.0270467i	$-0.991390\pi$
$401$	−11.2094	+	17.4421i	−0.559769	+	0.871017i	0.439866	+	0.898064i	$0.355026\pi$
$402$	0.330506	−	2.29872i	0.0164841	−	0.114650i
$403$	2.98939	−	20.7917i	0.148912	−	1.03571i
$404$	9.75619	−	15.1809i	0.485389	−	0.755279i
$405$	1.98963	+	2.29616i	0.0988655	+	0.114097i
$406$	−1.40311	+	2.52731i	−0.0696351	+	0.125428i
$407$	21.8944	−	14.0707i	1.08526	−	0.697457i
$408$	−1.38710	+	4.72404i	−0.0686719	+	0.233875i
$409$	−16.6488	−	14.4262i	−0.823229	−	0.713332i	0.137596	−	0.990488i	$-0.456063\pi$
$409$	−16.6488	−	14.4262i	−0.823229	−	0.713332i	−0.960825	+	0.277156i	$0.910608\pi$
$410$	1.07607	+	3.66475i	0.0531432	+	0.180989i
$411$	2.65226	−	5.80763i	0.130826	−	0.286469i
$412$	4.80431	+	33.4147i	0.236692	+	1.64623i
$413$	6.41496	−	4.73236i	0.315660	−	0.232864i
$414$	−0.604875	−	0.686956i	−0.0297280	−	0.0337620i
$415$	34.9440			1.71533
$416$	5.29791	−	0.761724i	0.259751	−	0.0373466i
$417$	−3.52575	+	7.72032i	−0.172657	+	0.378066i
$418$	−0.317960	−	1.08287i	−0.0155519	−	0.0529650i
$419$	2.62911	−	3.03415i	0.128440	−	0.148228i	−0.687887	−	0.725818i	$-0.741461\pi$
$419$	2.62911	−	3.03415i	0.128440	−	0.148228i	0.816327	+	0.577590i	$0.196007\pi$
$420$	14.8272	−	5.41215i	0.723495	−	0.264086i
$421$	3.57138	+	5.55717i	0.174058	+	0.270840i	0.917312	−	0.398170i	$-0.130355\pi$
$421$	3.57138	+	5.55717i	0.174058	+	0.270840i	−0.743253	+	0.669010i	$0.766718\pi$
$422$	−1.01529	−	2.22318i	−0.0494237	−	0.108223i
$423$	−3.55345	+	3.07908i	−0.172775	+	0.149710i
$424$	3.73913	−	5.81820i	0.181588	−	0.282557i
$425$	−3.91898	+	27.2571i	−0.190099	+	1.32216i
$426$	1.41936	+	0.204074i	0.0687684	+	0.00988740i
$427$	−0.0333222	−	0.516806i	−0.00161257	−	0.0250100i
$428$	−27.9702	+	24.2363i	−1.35199	+	1.17150i
$429$	−6.77705	+	3.09497i	−0.327199	+	0.149427i
$430$	−0.781566	−	1.21614i	−0.0376905	−	0.0586475i
$431$	7.67874	−	26.1514i	0.369872	−	1.25967i	−0.538898	−	0.842371i	$-0.681159\pi$
$431$	7.67874	−	26.1514i	0.369872	−	1.25967i	0.908770	−	0.417297i	$-0.137023\pi$
$432$	−2.85883	−	2.47719i	−0.137546	−	0.119184i
$433$	24.3585	−	7.15232i	1.17060	−	0.343718i	0.362055	−	0.932157i	$-0.382075\pi$
$433$	24.3585	−	7.15232i	1.17060	−	0.343718i	0.808542	+	0.588438i	$0.200257\pi$
$434$	−0.911054	−	4.33414i	−0.0437320	−	0.208045i
$435$	17.2159	−	2.47527i	0.825439	−	0.118680i
$436$		−	26.3898i		−	1.26384i
$437$	−1.36904	−	9.01285i	−0.0654900	−	0.431143i
$438$	0.222302			0.0106220
$439$	−14.4724	+	2.08082i	−0.690730	+	0.0993119i	−0.478736	−	0.877959i	$-0.658905\pi$
$439$	−14.4724	+	2.08082i	−0.690730	+	0.0993119i	−0.211994	+	0.977271i	$0.567996\pi$
$440$	6.50370	+	2.97014i	0.310052	+	0.141596i
$441$	−0.0981615	+	6.99931i	−0.00467436	+	0.333301i
$442$	−2.24830	−	1.94817i	−0.106941	−	0.0926648i
$443$	−28.4358	−	8.34950i	−1.35102	−	0.396697i	−0.475434	−	0.879751i	$-0.657709\pi$
$443$	−28.4358	−	8.34950i	−1.35102	−	0.396697i	−0.875590	+	0.483055i	$0.839527\pi$
$444$	−13.8197	+	8.88135i	−0.655852	+	0.421490i
$445$	6.51592	+	14.2679i	0.308884	+	0.676362i
$446$	−0.844014	+	0.731343i	−0.0399652	+	0.0346301i
$447$	4.01670	+	2.58137i	0.189983	+	0.122095i
$448$	−16.6407	+	8.93562i	−0.786200	+	0.422168i
$449$	3.06454	−	21.3143i	0.144624	−	1.00588i	−0.780211	−	0.625517i	$-0.784888\pi$
$449$	3.06454	−	21.3143i	0.144624	−	1.00588i	0.924835	−	0.380368i	$-0.124203\pi$
$450$	0.679309	+	0.436566i	0.0320230	+	0.0205799i
$451$	13.4187	+	15.4860i	0.631860	+	0.729206i
$452$	2.82256	−	1.28902i	0.132762	−	0.0606304i
$453$	0.592002	+	0.921173i	0.0278147	+	0.0432805i
$454$	0.657613	+	0.193093i	0.0308633	+	0.00906229i
$455$	−1.50799	+	19.1923i	−0.0706958	+	0.899751i
$456$	0.405114	+	1.37969i	0.0189712	+	0.0646099i
$457$	7.35391	+	3.35842i	0.344001	+	0.157100i	0.579922	−	0.814672i	$-0.303083\pi$
$457$	7.35391	+	3.35842i	0.344001	+	0.157100i	−0.235920	+	0.971772i	$0.575810\pi$
$458$	−0.421875	−	2.93421i	−0.0197129	−	0.137106i
$459$			6.50854i			0.303793i
$460$	24.1914	+	15.2766i	1.12793	+	0.712274i
$461$			18.9743i			0.883720i	0.897084	+	0.441860i	$0.145681\pi$
$461$			18.9743i			0.883720i	−0.897084	+	0.441860i	$0.854319\pi$
$462$	−1.11852	+	1.10294i	−0.0520381	+	0.0513134i
$463$	−8.91523	+	19.5216i	−0.414326	+	0.907247i	0.581289	+	0.813697i	$0.302549\pi$
$463$	−8.91523	+	19.5216i	−0.414326	+	0.907247i	−0.995615	+	0.0935497i	$0.970179\pi$
$464$	−20.7779	+	6.10094i	−0.964589	+	0.283229i
$465$	−17.4507	+	20.1392i	−0.809258	+	0.933934i
$466$	0.757588	+	0.222448i	0.0350946	+	0.0103047i
$467$	−24.1860	+	15.5434i	−1.11920	+	0.719263i	−0.963278	−	0.268507i	$-0.913470\pi$
$467$	−24.1860	+	15.5434i	−1.11920	+	0.719263i	−0.155918	+	0.987770i	$0.549834\pi$
$468$	4.27765	−	1.95354i	0.197734	−	0.0903022i
$469$	−31.4097	−	7.06377i	−1.45036	−	0.326174i
$470$	−1.47403	+	2.29363i	−0.0679918	+	0.105797i
$471$	−15.7730	−	2.26781i	−0.726781	−	0.104495i
$472$	−2.25602	−	0.324367i	−0.103842	−	0.0149302i
$473$	−6.52442	−	4.19299i	−0.299993	−	0.192794i
$474$	1.90437	+	2.19775i	0.0874704	+	0.100946i
$475$	3.34097	+	7.31571i	0.153294	+	0.335668i
$476$	31.5972	+	12.0382i	1.44825	+	0.551769i
$477$	2.57579	−	8.77234i	0.117937	−	0.401658i
$478$	−0.240340	+	0.277367i	−0.0109929	+	0.0126865i
$479$	−13.3157	+	3.90984i	−0.608409	+	0.178645i	−0.571402	−	0.820670i	$-0.693600\pi$
$479$	−13.3157	+	3.90984i	−0.608409	+	0.178645i	−0.0370067	+	0.999315i	$0.511782\pi$
$480$	−6.17653	−	2.82073i	−0.281919	−	0.128748i
$481$	−2.85144	−	19.8322i	−0.130015	−	0.904272i
$482$	1.41421			0.0644153
$483$	−10.1506	+	7.61347i	−0.461869	+	0.346425i
$484$	−2.59671			−0.118032
$485$	5.63997	+	39.2268i	0.256098	+	1.78120i
$486$	0.173607	+	0.0792836i	0.00787497	+	0.00359638i
$487$	−15.6744	+	4.60243i	−0.710277	+	0.208556i	−0.616862	−	0.787071i	$-0.711596\pi$
$487$	−15.6744	+	4.60243i	−0.710277	+	0.208556i	−0.0934148	+	0.995627i	$0.529778\pi$
$488$	−0.0969654	+	0.111904i	−0.00438942	+	0.00506566i
$489$	−4.90096	+	16.6911i	−0.221629	+	0.754799i
$490$	1.08884	+	3.91027i	0.0491886	+	0.176648i
$491$	10.2642	+	22.4755i	0.463217	+	1.01430i	0.986742	+	0.162294i	$0.0518893\pi$
$491$	10.2642	+	22.4755i	0.463217	+	1.01430i	−0.523525	+	0.852010i	$0.675383\pi$
$492$	−8.46982	−	9.77469i	−0.381849	−	0.440677i
$493$	31.3444	+	20.1438i	1.41168	+	0.907231i
$494$	−0.860006	−	0.123650i	−0.0386935	−	0.00556329i
$495$	9.35542	+	1.34511i	0.420495	+	0.0604580i
$496$	17.9374	−	27.9112i	0.805415	−	1.25325i
$497$	4.36158	−	19.3941i	0.195644	−	0.869946i
$498$	1.99671	−	0.911869i	0.0894749	−	0.0408618i
$499$	24.6030	−	15.8114i	1.10138	−	0.707815i	0.141984	−	0.989869i	$-0.454652\pi$
$499$	24.6030	−	15.8114i	1.10138	−	0.707815i	0.959399	+	0.282054i	$0.0910156\pi$
$500$	4.40209	+	1.29257i	0.196868	+	0.0578055i
$501$	−8.09206	+	9.33874i	−0.361527	+	0.417224i
$502$	3.32249	−	0.975570i	0.148290	−	0.0435418i
$503$	10.1265	−	22.1740i	0.451519	−	0.988688i	−0.537821	−	0.843059i	$-0.680752\pi$
$503$	10.1265	−	22.1740i	0.451519	−	0.988688i	0.989339	−	0.145629i	$-0.0465205\pi$
$504$	1.42510	−	1.40526i	0.0634792	−	0.0625951i
$505$		−	27.9221i		−	1.24252i
$506$	−2.82155	−	0.382818i	−0.125433	−	0.0170183i
$507$		−	7.26434i		−	0.322621i
$508$	0.134474	+	0.935287i	0.00596632	+	0.0414966i
$509$	−5.96539	−	2.72430i	−0.264411	−	0.120753i	0.278798	−	0.960350i	$-0.410064\pi$
$509$	−5.96539	−	2.72430i	−0.264411	−	0.120753i	−0.543210	+	0.839597i	$0.682791\pi$
$510$	1.06327	+	3.62118i	0.0470826	+	0.160349i
$511$	0.241394	−	3.07224i	0.0106787	−	0.135908i
$512$	13.6029	+	3.99416i	0.601168	+	0.176519i
$513$	1.02769	+	1.59911i	0.0453734	+	0.0706024i
$514$	−2.99959	+	1.36987i	−0.132306	+	0.0604223i
$515$	34.2063	+	39.4762i	1.50731	+	1.73953i
$516$	4.11819	+	2.64660i	0.181293	+	0.116510i
$517$	−2.08164	+	14.4781i	−0.0915503	+	0.636746i
$518$	−1.99853	−	3.72184i	−0.0878104	−	0.163528i
$519$	4.63350	+	2.97777i	0.203388	+	0.130709i
$520$	4.15989	−	3.60456i	0.182423	−	0.158071i
$521$	−2.75307	−	6.02839i	−0.120614	−	0.264109i	0.839688	−	0.543069i	$-0.182738\pi$
$521$	−2.75307	−	6.02839i	−0.120614	−	0.264109i	−0.960303	+	0.278960i	$0.910010\pi$
$522$	0.919131	−	0.590690i	0.0402293	−	0.0258538i
$523$	35.4685	+	10.4145i	1.55093	+	0.455394i	0.941379	−	0.337352i	$-0.109531\pi$
$523$	35.4685	+	10.4145i	1.55093	+	0.455394i	0.609552	+	0.792746i	$0.291349\pi$
$524$	12.2369	+	10.6033i	0.534571	+	0.463208i
$525$	6.77103	−	8.91407i	0.295512	−	0.389042i
$526$	3.18757	+	1.45571i	0.138985	+	0.0634721i
$527$	−56.5043	+	8.12409i	−2.46137	+	0.353891i
$528$	−11.7677			−0.512126
$529$	−22.1685	−	6.12831i	−0.963849	−	0.266448i
$530$		−	5.30150i		−	0.230282i
$531$	−2.98233	+	0.428794i	−0.129422	+	0.0186081i
$532$	9.66405	−	2.03142i	0.418990	−	0.0880733i
$533$	15.1360	−	4.44433i	0.655613	−	0.192505i
$534$	0.744645	+	0.645239i	0.0322239	+	0.0279222i
$535$	−16.1336	+	54.9459i	−0.697515	+	2.37552i
$536$	4.97651	+	7.74361i	0.214953	+	0.334473i
$537$	8.74160	−	3.99215i	0.377228	−	0.172274i
$538$	−1.11356	+	0.964908i	−0.0480091	+	0.0416002i
$539$	14.0282	+	16.6557i	0.604235	+	0.717410i
$540$	−5.90511	−	0.849026i	−0.254115	−	0.0365363i
$541$	−1.50540	+	10.4703i	−0.0647221	+	0.450152i	0.931531	+	0.363663i	$0.118474\pi$
$541$	−1.50540	+	10.4703i	−0.0647221	+	0.450152i	−0.996253	+	0.0864894i	$0.972435\pi$
$542$	−2.94076	+	4.57592i	−0.126317	+	0.196552i
$543$	−0.675846	+	0.585624i	−0.0290033	+	0.0251315i
$544$	−6.04256	−	13.2314i	−0.259073	−	0.567290i
$545$	−22.0760	−	34.3510i	−0.945634	−	1.47144i
$546$	0.414660	+	1.13601i	0.0177458	+	0.0486167i
$547$	−22.1723	+	25.5882i	−0.948019	+	1.09407i	0.0474391	+	0.998874i	$0.484894\pi$
$547$	−22.1723	+	25.5882i	−0.948019	+	1.09407i	−0.995458	+	0.0951984i	$0.969651\pi$
$548$	3.53198	+	12.0288i	0.150879	+	0.513845i
$549$	−0.0813133	+	0.178051i	−0.00347037	+	0.00759905i
$550$	2.48645	−	0.357498i	0.106023	−	0.0152438i
$551$	10.8818			0.463580
$552$	3.59494	+	0.487749i	0.153011	+	0.0207600i
$553$	32.4411	−	23.9320i	1.37954	−	1.01769i
$554$	0.375413	+	2.61105i	0.0159498	+	0.110933i
$555$	−10.5591	+	23.1213i	−0.448210	+	0.981444i
$556$	−4.69520	−	15.9904i	−0.199121	−	0.678143i
$557$	−32.3996	−	28.0744i	−1.37282	−	1.18955i	−0.960423	−	0.278546i	$-0.910147\pi$
$557$	−32.3996	−	28.0744i	−1.37282	−	1.18955i	−0.412394	−	0.911006i	$-0.635307\pi$
$558$	−0.471606	+	1.60614i	−0.0199647	+	0.0679935i
$559$	−5.02286	+	3.22799i	−0.212444	+	0.136530i
$560$	−14.7596	+	26.5853i	−0.623708	+	1.12344i
$561$	13.2591	+	15.3019i	0.559801	+	0.646045i
$562$	2.57978	−	4.01421i	0.108821	−	0.169329i
$563$	−3.89781	+	27.1099i	−0.164273	+	1.14255i	0.726191	+	0.687493i	$0.241289\pi$
$563$	−3.89781	+	27.1099i	−0.164273	+	1.14255i	−0.890465	+	0.455053i	$0.849620\pi$
$564$	1.31392	−	9.13853i	0.0553261	−	0.384801i
$565$	2.59575	−	4.03906i	0.109204	−	0.169925i
$566$	0.241108	+	0.278253i	0.0101345	+	0.0116958i
$567$	1.28422	−	2.31317i	0.0539324	−	0.0971441i
$568$	−4.78135	+	3.07279i	−0.200621	+	0.128931i
$569$	9.40647	−	32.0355i	0.394340	−	1.34300i	−0.488188	−	0.872738i	$-0.662342\pi$
$569$	9.40647	−	32.0355i	0.394340	−	1.34300i	0.882528	−	0.470260i	$-0.155840\pi$
$570$	0.833018	+	0.721814i	0.0348913	+	0.0302335i
$571$	−1.63413	−	5.56534i	−0.0683863	−	0.232902i	0.918207	−	0.396101i	$-0.129637\pi$
$571$	−1.63413	−	5.56534i	−0.0683863	−	0.232902i	−0.986593	+	0.163199i	$0.947819\pi$
$572$	6.07721	−	13.3072i	0.254101	−	0.556404i
$573$	−3.13338	−	21.7931i	−0.130899	−	0.910421i
$574$	2.67655	−	1.97451i	0.111717	−	0.0824142i
$575$	20.2904	−	0.161243i	0.846166	−	0.00672432i
$576$	7.13901			0.297459
$577$	−12.1796	+	1.75117i	−0.507044	+	0.0729020i	−0.391090	−	0.920353i	$-0.627902\pi$
$577$	−12.1796	+	1.75117i	−0.507044	+	0.0729020i	−0.115955	+	0.993255i	$0.536993\pi$
$578$	−2.01072	+	4.40286i	−0.0836349	+	0.183135i
$579$	−6.77197	−	23.0632i	−0.281433	−	0.958474i
$580$	−22.3650	+	25.8106i	−0.928656	+	1.07173i
$581$	−10.4339	−	28.5850i	−0.432872	−	1.18590i
$582$	1.34590	+	2.09426i	0.0557894	+	0.0868099i
$583$	−11.8151	−	25.8715i	−0.489333	−	1.07149i
$584$	−0.665900	+	0.577006i	−0.0275551	+	0.0238767i
$585$	3.93391	−	6.12128i	0.162647	−	0.253084i
$586$	0.311100	−	2.16375i	0.0128514	−	0.0893836i
$587$	−14.2296	−	2.04590i	−0.587317	−	0.0844435i	−0.157751	−	0.987479i	$-0.550424\pi$
$587$	−14.2296	−	2.04590i	−0.587317	−	0.0844435i	−0.429566	+	0.903035i	$0.641334\pi$
$588$	−8.85452	−	10.5130i	−0.365154	−	0.433549i
$589$	−12.6000	+	10.9180i	−0.519174	+	0.449867i
$590$	−1.58924	+	0.725781i	−0.0654279	+	0.0298799i
$591$	−2.14074	−	3.33106i	−0.0880583	−	0.137021i
$592$	8.91600	−	30.3651i	0.366446	−	1.24800i
$593$	−28.8602	−	25.0075i	−1.18514	−	1.02693i	−0.999013	−	0.0444088i	$-0.985860\pi$
$593$	−28.8602	−	25.0075i	−1.18514	−	1.02693i	−0.186131	−	0.982525i	$-0.559595\pi$
$594$	0.569674	−	0.167271i	0.0233740	−	0.00686322i
$595$	51.1997	−	10.7624i	2.09898	−	0.441215i
$596$	−9.27996	+	1.33426i	−0.380122	+	0.0546533i
$597$			15.1018i			0.618077i
$598$	−1.17044	+	1.85346i	−0.0478628	+	0.0757935i
$599$	−24.6481			−1.00710			−0.503548	−	0.863968i	$-0.667972\pi$
$599$	−24.6481			−1.00710			−0.503548	+	0.863968i	$0.667972\pi$
$600$	−3.16800	+	0.455489i	−0.129333	+	0.0185953i
$601$	9.58037	+	4.37521i	0.390791	+	0.178468i	0.601113	−	0.799164i	$-0.294724\pi$
$601$	9.58037	+	4.37521i	0.390791	+	0.178468i	−0.210322	+	0.977632i	$0.567451\pi$
$602$	−0.761463	+	1.00247i	−0.0310349	+	0.0408575i
$603$	9.19614	+	7.96850i	0.374496	+	0.324503i
$604$	−2.06302	−	0.605758i	−0.0839431	−	0.0246479i
$605$	−3.38008	+	2.17225i	−0.137420	+	0.0883144i
$606$	−0.728631	−	1.59548i	−0.0295986	−	0.0648119i
$607$	14.4769	−	12.5443i	0.587598	−	0.509157i	−0.309552	−	0.950883i	$-0.600179\pi$
$607$	14.4769	−	12.5443i	0.587598	−	0.509157i	0.897150	+	0.441726i	$0.145634\pi$
$608$	−3.57383	−	2.29676i	−0.144938	−	0.0931459i
$609$	−7.16532	−	13.3439i	−0.290353	−	0.540722i
$610$	−0.0161531	+	0.112347i	−0.000654018	+	0.00454880i
$611$	9.47307	+	6.08797i	0.383239	+	0.246293i
$612$	−8.36912	−	9.65848i	−0.338302	−	0.390421i
$613$	2.25219	−	1.02854i	0.0909651	−	0.0415424i	−0.369413	−	0.929265i	$-0.620441\pi$
$613$	2.25219	−	1.02854i	0.0909651	−	0.0415424i	0.460378	+	0.887723i	$0.347714\pi$
$614$	−0.579839	−	0.902246i	−0.0234004	−	0.0364117i
$615$	−19.2018	−	5.63817i	−0.774293	−	0.227353i
$616$	0.487703	−	6.20703i	0.0196501	−	0.250088i
$617$	1.99184	+	6.78360i	0.0801886	+	0.273097i	0.989821	−	0.142316i	$-0.0454550\pi$
$617$	1.99184	+	6.78360i	0.0801886	+	0.273097i	−0.909633	+	0.415414i	$0.863637\pi$
$618$	2.98470	+	1.36307i	0.120062	+	0.0548306i
$619$	−5.45228	−	37.9214i	−0.219146	−	1.52419i	−0.741203	−	0.671281i	$-0.765744\pi$
$619$	−5.45228	−	37.9214i	−0.219146	−	1.52419i	0.522057	−	0.852910i	$-0.325165\pi$
$620$		−	52.3253i		−	2.10144i
$621$	4.74144	−	0.720219i	0.190268	−	0.0289014i
$622$		−	1.70134i		−	0.0682174i
$623$	9.72586	−	9.59042i	0.389658	−	0.384232i
$624$	−3.76344	+	8.24078i	−0.150658	+	0.329895i
$625$	27.1093	−	7.96000i	1.08437	−	0.318400i
$626$	3.98181	−	4.59525i	0.159145	−	0.183663i
$627$	5.67383	+	1.66599i	0.226591	+	0.0665331i
$628$	26.3228	−	16.9166i	1.05039	−	0.675046i
$629$	−49.5304	+	22.6198i	−1.97491	+	0.901910i
$630$	0.336615	−	1.49679i	0.0134111	−	0.0596334i
$631$	−15.1269	+	23.5379i	−0.602192	+	0.937029i	0.397619	+	0.917551i	$0.369837\pi$
$631$	−15.1269	+	23.5379i	−0.602192	+	0.937029i	−0.999810	+	0.0194777i	$0.993800\pi$
$632$	−11.4089	−	1.64036i	−0.453823	−	0.0652499i
$633$	12.6755	+	1.82246i	0.503806	+	0.0724363i
$634$	1.51588	+	0.974200i	0.0602035	+	0.0386904i
$635$	0.957443	+	1.10495i	0.0379950	+	0.0438485i
$636$	7.45767	+	16.3300i	0.295716	+	0.647527i
$637$	16.1500	−	4.49707i	0.639888	−	0.178180i
$638$	0.957570	−	3.26118i	0.0379106	−	0.129111i
$639$	−4.92022	+	5.67823i	−0.194641	+	0.224627i
$640$	17.0022	−	4.99228i	0.672069	−	0.197337i
$641$	31.7269	+	14.4892i	1.25314	+	0.572288i	0.927718	−	0.373282i	$-0.121767\pi$
$641$	31.7269	+	14.4892i	1.25314	+	0.572288i	0.325419	+	0.945570i	$0.394495\pi$
$642$	0.511943	+	3.56064i	0.0202048	+	0.140527i
$643$	5.94685			0.234521			0.117261	−	0.993101i	$-0.462589\pi$
$643$	5.94685			0.234521			0.117261	+	0.993101i	$0.462589\pi$
$644$	5.27330	−	24.3505i	0.207797	−	0.959545i
$645$	7.57453			0.298247
$646$	0.336037	+	2.33719i	0.0132212	+	0.0919554i
$647$	−4.29049	−	1.95940i	−0.168677	−	0.0770321i	0.329287	−	0.944230i	$-0.393192\pi$
$647$	−4.29049	−	1.95940i	−0.168677	−	0.0770321i	−0.497964	+	0.867198i	$0.665919\pi$
$648$	−0.725822	+	0.213121i	−0.0285130	+	0.00837217i
$649$	−6.13805	+	7.08368i	−0.240939	+	0.278059i
$650$	0.544841	−	1.85556i	0.0213704	−	0.0727810i
$651$	21.6849	+	8.26173i	0.849900	+	0.323803i
$652$	−14.1897	−	31.0711i	−0.555712	−	1.21684i
$653$	−4.02357	−	4.64345i	−0.157455	−	0.181712i	0.671541	−	0.740967i	$-0.265633\pi$
$653$	−4.02357	−	4.64345i	−0.157455	−	0.181712i	−0.828996	+	0.559255i	$0.811087\pi$
$654$	−2.15783	−	1.38675i	−0.0843778	−	0.0542263i
$655$	24.7985	+	3.56549i	0.968959	+	0.139315i
$656$	24.6629	+	3.54600i	0.962926	+	0.138448i
$657$	−0.629726	+	0.979873i	−0.0245680	+	0.0382285i
$658$	2.31637	+	0.520933i	0.0903016	+	0.0203081i
$659$	−13.5388	+	6.18296i	−0.527396	+	0.240854i	−0.661274	−	0.750144i	$-0.729984\pi$
$659$	−13.5388	+	6.18296i	−0.527396	+	0.240854i	0.133878	+	0.990998i	$0.457257\pi$
$660$	−15.6128	+	10.0337i	−0.607727	+	0.390563i
$661$	−34.2941	−	10.0697i	−1.33389	−	0.391664i	−0.464402	−	0.885625i	$-0.653731\pi$
$661$	−34.2941	−	10.0697i	−1.33389	−	0.391664i	−0.869485	+	0.493960i	$0.835549\pi$
$662$	−0.524973	+	0.605851i	−0.0204036	+	0.0235471i
$663$	14.9561	−	4.39150i	0.580845	−	0.170552i
$664$	−3.61426	+	7.91413i	−0.140261	+	0.307128i
$665$	10.8801	−	10.7286i	0.421912	−	0.416037i
$666$			1.59670i			0.0618710i
$667$	11.2062	−	25.0633i	0.433905	−	0.970455i
$668$		−	24.2637i		−	0.938792i
$669$	−0.832762	−	5.79199i	−0.0321964	−	0.223931i
$670$	6.41828	+	2.93113i	0.247960	+	0.113239i
$671$	0.171553	+	0.584257i	0.00662275	+	0.0225550i
$672$	−0.463169	+	5.89479i	−0.0178671	+	0.227396i
$673$	32.8145	+	9.63521i	1.26491	+	0.371410i	0.844318	−	0.535842i	$-0.180006\pi$
$673$	32.8145	+	9.63521i	1.26491	+	0.371410i	0.420588	+	0.907252i	$0.361824\pi$
$674$	0.0386441	+	0.0601314i	0.00148852	+	0.00231618i
$675$	−3.84862	+	1.75761i	−0.148133	+	0.0676503i
$676$	9.34098	+	10.7801i	0.359268	+	0.414618i
$677$	23.6920	+	15.2259i	0.910557	+	0.585180i	0.909903	−	0.414820i	$-0.136155\pi$
$677$	23.6920	+	15.2259i	0.910557	+	0.585180i	0.000653966		1.00000i	$0.499792\pi$
$678$	0.0429221	−	0.298530i	0.00164841	−	0.0114650i
$679$	30.4044	−	16.3264i	1.16681	−	0.626548i
$680$	−12.5841	−	8.08732i	−0.482579	−	0.310134i
$681$	−2.71397	+	2.35167i	−0.104000	+	0.0901162i
$682$	2.16325	+	4.73687i	0.0828353	+	0.181384i
$683$	−20.6531	+	13.2729i	−0.790268	+	0.507875i	−0.872427	−	0.488745i	$-0.837455\pi$
$683$	−20.6531	+	13.2729i	−0.790268	+	0.507875i	0.0821586	+	0.996619i	$0.473819\pi$
$684$	−3.58130	−	1.05156i	−0.136934	−	0.0402076i
$685$	14.6600	+	12.7030i	0.560131	+	0.485356i
$686$	2.87357	−	2.05826i	0.109714	−	0.0785847i
$687$	14.1286	+	6.45230i	0.539039	+	0.246171i
$688$	−9.33468	+	1.34212i	−0.355881	+	0.0511680i
$689$	−21.8960			−0.834172
$690$	2.52036	−	1.17530i	0.0959483	−	0.0447430i
$691$		−	41.5705i		−	1.58142i	−0.612192	−	0.790709i	$-0.709712\pi$
$691$		−	41.5705i		−	1.58142i	0.612192	−	0.790709i	$-0.290288\pi$
$692$	−10.7050	+	1.53914i	−0.406943	+	0.0585095i
$693$	−1.69311	−	8.05458i	−0.0643158	−	0.305968i
$694$	4.36418	−	1.28144i	0.165662	−	0.0486428i
$695$	−19.4882	−	16.8866i	−0.739228	−	0.640545i
$696$	−1.22004	+	4.15508i	−0.0462456	+	0.157498i
$697$	−23.1777	−	36.0652i	−0.877917	−	1.36607i
$698$	1.97713	−	0.902925i	0.0748355	−	0.0341762i
$699$	−3.12657	+	2.70918i	−0.118258	+	0.102471i
$700$	1.41430	+	21.9349i	0.0534555	+	0.829060i
$701$	22.3557	+	3.21426i	0.844362	+	0.121401i	0.550902	−	0.834570i	$-0.314284\pi$
$701$	22.3557	+	3.21426i	0.844362	+	0.121401i	0.293461	+	0.955971i	$0.405193\pi$
$702$	0.0650494	−	0.452429i	0.00245513	−	0.0170758i
$703$	−8.59771	+	13.3783i	−0.324269	+	0.504572i
$704$	16.7841	−	14.5435i	0.632576	−	0.548130i
$705$	−5.93441	−	12.9946i	−0.223503	−	0.489403i
$706$	−1.17759	−	1.83237i	−0.0443193	−	0.0689622i
$707$	−22.8409	+	8.33725i	−0.859020	+	0.313554i
$708$	3.87431	−	4.47119i	0.145606	−	0.168038i
$709$	−2.23064	−	7.59688i	−0.0837736	−	0.285307i	0.906942	−	0.421255i	$-0.138410\pi$
$709$	−2.23064	−	7.59688i	−0.0837736	−	0.285307i	−0.990716	+	0.135948i	$0.956592\pi$
$710$	−1.80985	+	3.96302i	−0.0679224	+	0.148729i
$711$	−15.0819	+	2.16845i	−0.565616	+	0.0813233i
$712$	−3.90534			−0.146359
$713$	12.1710	+	40.2641i	0.455807	+	1.50790i
$714$	2.64473	−	1.95103i	0.0989764	−	0.0730155i
$715$	−3.22143	−	22.4055i	−0.120475	−	0.837919i
$716$	−7.83889	+	17.1648i	−0.292953	+	0.641478i
$717$	−0.541767	−	1.84509i	−0.0202327	−	0.0689061i
$718$	2.04305	+	1.77031i	0.0762458	+	0.0660674i
$719$	−7.42067	+	25.2725i	−0.276744	+	0.942504i	0.697420	+	0.716663i	$0.254331\pi$
$719$	−7.42067	+	25.2725i	−0.276744	+	0.942504i	−0.974164	+	0.225841i	$0.927487\pi$
$720$	9.66854	−	6.21359i	0.360325	−	0.231567i
$721$	22.0788	−	39.7687i	0.822256	−	1.48106i
$722$	−1.92307	−	2.21935i	−0.0715694	−	0.0825955i
$723$	−4.00609	+	6.23359i	−0.148988	+	0.231830i
$724$	0.249901	−	1.73810i	0.00928748	−	0.0645959i
$725$	−3.44698	+	23.9743i	−0.128018	+	0.890382i
$726$	−0.136454	+	0.212327i	−0.00506429	+	0.00788019i
$727$	−0.216206	−	0.249515i	−0.00801865	−	0.00925401i	0.751726	−	0.659475i	$-0.229222\pi$
$727$	−0.216206	−	0.249515i	−0.00801865	−	0.00925401i	−0.759745	+	0.650221i	$0.774676\pi$
$728$	−4.19072	−	2.32660i	−0.155318	−	0.0862294i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−0.190285	+	0.648052i	−0.00704277	+	0.0239855i
$731$	12.2629	+	10.6259i	0.453560	+	0.393012i
$732$	−0.108284	−	0.368781i	−0.00400229	−	0.0136305i
$733$	−14.5201	+	31.7946i	−0.536312	+	1.17436i	0.426574	+	0.904452i	$0.359720\pi$
$733$	−14.5201	+	31.7946i	−0.536312	+	1.17436i	−0.962886	+	0.269907i	$0.913007\pi$
$734$	−0.762107	−	5.30057i	−0.0281299	−	0.195648i
$735$	−20.3202	−	6.27739i	−0.749523	−	0.231545i
$736$	−8.97034	+	5.86613i	−0.330651	+	0.216229i
$737$	37.8539			1.39437
$738$	−1.24433	+	0.178908i	−0.0458044	+	0.00658568i
$739$	−1.70501	+	3.73345i	−0.0627198	+	0.137337i	−0.938396	−	0.345561i	$-0.887689\pi$
$739$	−1.70501	+	3.73345i	−0.0627198	+	0.137337i	0.875677	+	0.482898i	$0.160416\pi$
$740$	−14.0615	−	47.8890i	−0.516910	−	1.76043i
$741$	2.98121	−	3.44050i	0.109517	−	0.126390i
$742$	−4.33674	+	1.58297i	−0.159207	+	0.0581128i
$743$	7.79059	+	12.1224i	0.285809	+	0.444728i	0.954238	−	0.299048i	$-0.0966692\pi$
$743$	7.79059	+	12.1224i	0.285809	+	0.444728i	−0.668429	+	0.743776i	$0.733033\pi$
$744$	−2.75621	−	6.03525i	−0.101047	−	0.221263i
$745$	−10.9634	+	9.49980i	−0.401666	+	0.348046i
$746$	−0.986469	+	1.53498i	−0.0361172	+	0.0561994i
$747$	−1.63681	+	11.3843i	−0.0598879	+	0.416529i
$748$	−39.3524	−	5.65802i	−1.43886	−	0.206878i
$749$	49.7643	−	3.20866i	1.81835	−	0.117242i
$750$	0.337015	−	0.292025i	0.0123060	−	0.0106632i
$751$	−12.3963	+	5.66118i	−0.452346	+	0.206579i	−0.628542	−	0.777776i	$-0.716348\pi$
$751$	−12.3963	+	5.66118i	−0.452346	+	0.206579i	0.176196	+	0.984355i	$0.443621\pi$
$752$	9.61593	+	14.9627i	0.350657	+	0.545633i
$753$	−5.11160	+	17.4085i	−0.186277	+	0.634402i
$754$	−1.97752	−	1.71353i	−0.0720169	−	0.0624030i
$755$	−3.19212	+	0.937292i	−0.116173	+	0.0341116i
$756$	1.06868	+	5.08402i	0.0388676	+	0.184904i
$757$	4.40815	−	0.633796i	0.160217	−	0.0230357i	−0.0617396	−	0.998092i	$-0.519665\pi$
$757$	4.40815	−	0.633796i	0.160217	−	0.0230357i	0.221956	+	0.975057i	$0.428756\pi$
$758$		−	6.23476i		−	0.226457i
$759$	9.68012	−	11.3525i	0.351366	−	0.412069i
$760$	−4.36881			−0.158473
$761$	13.0811	−	1.88077i	0.474188	−	0.0681779i	0.0989220	−	0.995095i	$-0.468461\pi$
$761$	13.0811	−	1.88077i	0.474188	−	0.0681779i	0.375266	+	0.926917i	$0.377551\pi$
$762$	0.0835425	+	0.0381526i	0.00302643	+	0.00138212i
$763$	−21.5082	+	28.3156i	−0.778650	+	1.02509i
$764$	32.6729	+	28.3112i	1.18206	+	1.02427i
$765$	−18.9736	−	5.57114i	−0.685991	−	0.201425i
$766$	4.62137	−	2.96997i	0.166977	−	0.107310i
$767$	2.99759	+	6.56381i	0.108237	+	0.237005i
$768$	−9.94938	+	8.62118i	−0.359017	+	0.311090i
$769$	4.76841	+	3.06447i	0.171953	+	0.110508i	0.623787	−	0.781595i	$-0.285593\pi$
$769$	4.76841	+	3.06447i	0.171953	+	0.110508i	−0.451833	+	0.892102i	$0.649230\pi$
$770$	−2.25785	−	4.20476i	−0.0813671	−	0.151529i
$771$	2.45893	−	17.1022i	0.0885561	−	0.615921i
$772$	39.7056	+	25.5173i	1.42904	+	0.918386i
$773$	7.30555	+	8.43105i	0.262762	+	0.303244i	0.871765	−	0.489924i	$-0.162976\pi$
$773$	7.30555	+	8.43105i	0.262762	+	0.303244i	−0.609003	+	0.793168i	$0.708430\pi$
$774$	0.432812	−	0.197659i	0.0155571	−	0.00710469i
$775$	−20.0627	−	31.2182i	−0.720673	−	1.12139i
$776$	−9.46745	−	2.77989i	−0.339862	−	0.0997924i
$777$	22.0666	+	1.73383i	0.791635	+	0.0622009i
$778$	0.179134	+	0.610073i	0.00642225	+	0.0218722i
$779$	−11.3892	−	5.20129i	−0.408062	−	0.186356i
$780$	2.03335	+	14.1423i	0.0728058	+	0.506375i
$781$			23.3732i			0.836359i
$782$	5.72914	+	1.63289i	0.204874	+	0.0583920i
$783$			5.72465i			0.204582i
$784$	26.1545	+	4.13559i	0.934089	+	0.147700i
$785$	20.1123	−	44.0399i	0.717840	−	1.57185i
$786$	1.51004	−	0.443388i	0.0538614	−	0.0158151i
$787$	2.32630	−	2.68470i	0.0829238	−	0.0956992i	−0.712771	−	0.701396i	$-0.752560\pi$
$787$	2.32630	−	2.68470i	0.0829238	−	0.0956992i	0.795695	+	0.605697i	$0.207106\pi$
$788$	7.46010	+	2.19048i	0.265755	+	0.0780327i
$789$	−15.4461	+	9.92661i	−0.549896	+	0.353397i
$790$	−8.03694	+	3.67035i	−0.285941	+	0.130585i
$791$	−4.07911	−	0.917357i	−0.145036	−	0.0326175i
$792$	−1.27227	+	1.97969i	−0.0452082	+	0.0703454i
$793$	0.464011	+	0.0667147i	0.0164775	+	0.00236911i
$794$	−3.09617	−	0.445162i	−0.109879	−	0.0157982i
$795$	23.3681	+	15.0178i	0.828782	+	0.532626i
$796$	−19.4190	−	22.4107i	−0.688287	−	0.794326i
$797$	−15.7538	−	34.4960i	−0.558028	−	1.22191i	−0.952931	−	0.303187i	$-0.901949\pi$
$797$	−15.7538	−	34.4960i	−0.558028	−	1.22191i	0.394903	−	0.918723i	$-0.370778\pi$
$798$	0.341730	−	0.896954i	0.0120971	−	0.0317518i
$799$	8.62169	−	29.3628i	0.305014	−	1.03878i
$800$	6.19218	−	7.14616i	0.218927	−	0.252655i
$801$	−4.95350	+	1.45448i	−0.175023	+	0.0513914i
$802$	−3.59947	−	1.64382i	−0.127102	−	0.0580455i
$803$	0.515675	+	3.58660i	0.0181978	+	0.126568i
$804$	−23.8933			−0.842650
$805$	−13.5060	−	36.1078i	−0.476023	−	1.27263i
$806$	4.00898			0.141210
$807$	−1.09872	−	7.64175i	−0.0386767	−	0.269002i
$808$	6.32380	+	2.88798i	0.222471	+	0.101599i
$809$	−5.07671	+	1.49066i	−0.178487	+	0.0524087i	−0.369755	−	0.929129i	$-0.620558\pi$
$809$	−5.07671	+	1.49066i	−0.178487	+	0.0524087i	0.191268	+	0.981538i	$0.438740\pi$
$810$	−0.379729	+	0.438231i	−0.0133423	+	0.0153979i
$811$	5.00423	−	17.0428i	0.175722	−	0.598455i	−0.823780	−	0.566909i	$-0.808139\pi$
$811$	5.00423	−	17.0428i	0.175722	−	0.598455i	0.999502	−	0.0315455i	$-0.0100429\pi$
$812$	27.7916	+	10.5883i	0.975295	+	0.371577i
$813$	−11.8395	−	25.9248i	−0.415228	−	0.909223i
$814$	3.25279	+	3.75392i	0.114010	+	0.131575i
$815$	−44.4626	−	28.5744i	−1.55746	−	1.00092i
$816$	24.3697	+	3.50384i	0.853112	+	0.122659i
$817$	4.69073	+	0.674425i	0.164108	+	0.0235951i
$818$	2.27308	−	3.53698i	0.0794764	−	0.123668i
$819$	−6.18197	−	1.39027i	−0.216016	−	0.0485801i
$820$	35.7449	−	16.3242i	1.24827	−	0.570064i
$821$	16.1726	−	10.3935i	0.564429	−	0.362736i	−0.227097	−	0.973872i	$-0.572923\pi$
$821$	16.1726	−	10.3935i	0.564429	−	0.362736i	0.791526	+	0.611136i	$0.209287\pi$
$822$	1.16917	+	0.343298i	0.0407794	+	0.0119739i
$823$	31.8450	−	36.7511i	1.11005	−	1.28106i	0.153931	−	0.988082i	$-0.450807\pi$
$823$	31.8450	−	36.7511i	1.11005	−	1.28106i	0.956118	−	0.292983i	$-0.0946479\pi$
$824$	−12.4785	+	3.66403i	−0.434711	+	0.127643i
$825$	−5.46770	+	11.9726i	−0.190361	+	0.416832i
$826$	1.06824	+	1.08332i	0.0371687	+	0.0376936i
$827$			12.7332i			0.442778i	0.975186	+	0.221389i	$0.0710590\pi$
$827$			12.7332i			0.442778i	−0.975186	+	0.221389i	$0.928941\pi$
$828$	−6.11006	+	7.16565i	−0.212339	+	0.249024i
$829$			24.4748i			0.850045i	0.905183	+	0.425022i	$0.139734\pi$
$829$			24.4748i			0.850045i	−0.905183	+	0.425022i	$0.860266\pi$
$830$	0.949126	+	6.60132i	0.0329447	+	0.229135i
$831$	−12.5725	−	5.74169i	−0.436137	−	0.199177i
$832$	−4.81689	−	16.4048i	−0.166996	−	0.568735i
$833$	−24.0916	−	38.6690i	−0.834724	−	1.33980i
$834$	−1.55422	−	0.456360i	−0.0538182	−	0.0158025i
$835$	−20.2975	−	31.5835i	−0.702424	−	1.09299i
$836$	−10.5620	+	4.82352i	−0.365296	+	0.166825i
$837$	−5.74368	−	6.62856i	−0.198531	−	0.229116i
$838$	0.644597	+	0.414257i	0.0222672	+	0.0143103i
$839$	−4.81555	+	33.4929i	−0.166251	+	1.15630i	0.720296	+	0.693666i	$0.244006\pi$
$839$	−4.81555	+	33.4929i	−0.166251	+	1.15630i	−0.886548	+	0.462637i	$0.846903\pi$
$840$	2.87673	+	5.35730i	0.0992565	+	0.184844i
$841$	3.17291	+	2.03911i	0.109411	+	0.0703140i
$842$	−0.952809	+	0.825614i	−0.0328360	+	0.0284525i
$843$	10.3861	+	22.7425i	0.357718	+	0.783292i
$844$	−21.1535	+	13.5945i	−0.728134	+	0.467943i
$845$	21.1768	+	6.21808i	0.728506	+	0.213909i
$846$	−0.678190	−	0.587655i	−0.0233166	−	0.0202040i
$847$	2.78620	+	2.11637i	0.0957351	+	0.0727194i
$848$	−31.4593	−	14.3670i	−1.08032	−	0.493365i
$849$	−1.90949	+	0.274543i	−0.0655335	+	0.00942230i
$850$	−5.25563			−0.180266
$851$	21.9593	+	33.5796i	0.752756	+	1.15110i
$852$		−	14.7531i		−	0.505432i
$853$	38.6872	−	5.56239i	1.32463	−	0.190452i	0.556552	−	0.830813i	$-0.312124\pi$
$853$	38.6872	−	5.56239i	1.32463	−	0.190452i	0.768074	+	0.640361i	$0.221215\pi$
$854$	0.0967255	−	0.0203321i	0.00330988	−	0.000695750i
$855$	−5.54137	+	1.62709i	−0.189511	+	0.0556454i
$856$	−10.7755	−	9.33699i	−0.368298	−	0.319132i
$857$	−9.15856	+	31.1912i	−0.312850	+	1.06547i	0.641585	+	0.767052i	$0.278277\pi$
$857$	−9.15856	+	31.1912i	−0.312850	+	1.06547i	−0.954435	+	0.298419i	$0.903541\pi$
$858$	−0.768750	−	1.19620i	−0.0262447	−	0.0408375i
$859$	10.2224	−	4.66841i	0.348784	−	0.159284i	−0.233317	−	0.972401i	$-0.574958\pi$
$859$	10.2224	−	4.66841i	0.348784	−	0.159284i	0.582101	+	0.813116i	$0.302231\pi$
$860$	−11.2404	+	9.73985i	−0.383294	+	0.332126i
$861$	1.12133	+	17.3910i	0.0382147	+	0.592685i
$862$	5.14886	+	0.740295i	0.175371	+	0.0252145i
$863$	−5.41663	+	37.6735i	−0.184384	+	1.28242i	0.661861	+	0.749626i	$0.269767\pi$
$863$	−5.41663	+	37.6735i	−0.184384	+	1.28242i	−0.846245	+	0.532793i	$0.821142\pi$
$864$	1.20827	−	1.88011i	0.0411062	−	0.0639625i
$865$	−12.6469	+	10.9586i	−0.430007	+	0.372603i
$866$	2.01277	+	4.40734i	0.0683966	+	0.149768i
$867$	−13.7112	−	21.3351i	−0.465658	−	0.724578i
$868$	−42.8033	+	15.6238i	−1.45284	+	0.530307i
$869$	−31.0407	+	35.8229i	−1.05298	+	1.21521i
$870$	0.935214	+	3.18505i	0.0317067	+	0.107983i
$871$	12.1060	−	26.5085i	0.410197	−	0.898207i
$872$	10.0632	−	1.44686i	0.340781	−	0.0489970i
$873$	−13.0438			−0.441464
$874$	1.66544	−	0.503428i	0.0563345	−	0.0170287i
$875$	−3.66986	−	4.97468i	−0.124064	−	0.168175i
$876$	−0.325492	−	2.26385i	−0.0109974	−	0.0764883i
$877$	−11.8693	+	25.9902i	−0.400799	+	0.877627i	0.596390	+	0.802695i	$0.296601\pi$
$877$	−11.8693	+	25.9902i	−0.400799	+	0.877627i	−0.997189	+	0.0749318i	$0.976126\pi$
$878$	−0.786180	−	2.67748i	−0.0265323	−	0.0903607i
$879$	8.65618	+	7.50063i	0.291966	+	0.252990i
$880$	10.0729	−	34.3051i	0.339557	−	1.15642i
$881$	39.5165	−	25.3957i	1.33135	−	0.855604i	0.335101	−	0.942182i	$-0.391230\pi$
$881$	39.5165	−	25.3957i	1.33135	−	0.855604i	0.996245	+	0.0865779i	$0.0275931\pi$
$882$	−1.32492	+	0.171567i	−0.0446122	+	0.00577696i
$883$	19.3382	+	22.3174i	0.650781	+	0.751041i	0.981242	−	0.192778i	$-0.0617498\pi$
$883$	19.3382	+	22.3174i	0.650781	+	0.751041i	−0.330462	+	0.943819i	$0.607204\pi$
$884$	−16.5475	+	25.7484i	−0.556552	+	0.866011i
$885$	1.30278	−	9.06105i	0.0437926	−	0.304584i
$886$	0.804961	−	5.59863i	0.0270432	−	0.188090i
$887$	14.0722	−	21.8968i	0.472499	−	0.735223i	−0.520434	−	0.853902i	$-0.674230\pi$
$887$	14.0722	−	21.8968i	0.472499	−	0.735223i	0.992933	+	0.118679i	$0.0378660\pi$
$888$	−4.14439	−	4.78288i	−0.139076	−	0.160503i
$889$	0.617990	−	1.11314i	0.0207267	−	0.0373334i
$890$	−2.51838	+	1.61847i	−0.0844164	+	0.0542511i
$891$	−0.876435	+	2.98486i	−0.0293617	+	0.0999967i
$892$	8.68352	+	7.52432i	0.290746	+	0.251933i
$893$	−2.51803	−	8.57561i	−0.0842626	−	0.286972i
$894$	−0.378552	+	0.828913i	−0.0126607	+	0.0277230i
$895$	4.15527	+	28.9005i	0.138895	+	0.966037i
$896$	−9.16047	−	12.4175i	−0.306030	−	0.414840i
$897$	−4.85419	−	10.4095i	−0.162077	−	0.347562i
$898$	4.10975			0.137144
$899$	−49.6989	+	7.14563i	−1.65755	+	0.238320i
$900$	3.45119	−	7.55705i	0.115040	−	0.251902i
$901$	16.7646	+	57.0951i	0.558511	+	1.90211i
$902$	−2.56101	+	2.95556i	−0.0852722	+	0.0984094i
$903$	−2.26168	−	6.19614i	−0.0752639	−	0.206195i
$904$	0.646289	+	1.00565i	0.0214953	+	0.0334473i
$905$	−1.12869	−	2.47149i	−0.0375190	−	0.0821551i
$906$	−0.157941	+	0.136856i	−0.00524722	+	0.00454675i
$907$	19.1319	−	29.7698i	0.635263	−	0.988488i	−0.363126	−	0.931740i	$-0.618290\pi$
$907$	19.1319	−	29.7698i	0.635263	−	0.988488i	0.998389	−	0.0567482i	$-0.0180732\pi$
$908$	1.00352	−	6.97962i	0.0333029	−	0.231627i
$909$	9.09664	+	1.30790i	0.301716	+	0.0433803i
$910$	−3.66661	+	0.236413i	−0.121547	+	0.00783701i
$911$	10.5229	−	9.11814i	0.348639	−	0.302097i	−0.462883	−	0.886419i	$-0.653185\pi$
$911$	10.5229	−	9.11814i	0.348639	−	0.302097i	0.811522	+	0.584322i	$0.198639\pi$
$912$	6.54075	−	2.98706i	0.216586	−	0.0989115i
$913$	19.3437	+	30.0995i	0.640185	+	0.996147i
$914$	−0.434701	+	1.48046i	−0.0143786	+	0.0489692i
$915$	−0.449450	−	0.389450i	−0.0148583	−	0.0128748i
$916$	−29.2632	+	8.59245i	−0.966883	+	0.283902i
$917$	−4.48794	−	21.3504i	−0.148205	−	0.705052i
$918$	−1.22954	+	0.176781i	−0.0405808	+	0.00583464i
$919$			6.46673i			0.213318i	0.994296	+	0.106659i	$0.0340153\pi$
$919$			6.46673i			0.213318i	−0.994296	+	0.106659i	$0.965985\pi$
$920$	−4.49905	+	10.0624i	−0.148329	+	0.331747i
$921$	5.61949			0.185168
$922$	−3.58446	+	0.515367i	−0.118048	+	0.0169727i
$923$	16.3679	+	7.47497i	0.538756	+	0.246042i
$924$	12.8697	+	9.77565i	0.423380	+	0.321595i
$925$	−26.7510	−	23.1799i	−0.879567	−	0.762150i
$926$	−3.93001	−	1.15395i	−0.129148	−	0.0379213i
$927$	−14.4631	+	9.29485i	−0.475030	+	0.305283i
$928$	−5.31480	−	11.6378i	−0.174467	−	0.382029i
$929$	34.9539	−	30.2877i	1.14680	−	0.993707i	0.146809	−	0.989165i	$-0.453100\pi$
$929$	34.9539	−	30.2877i	1.14680	−	0.993707i	0.999990	−	0.00454191i	$-0.00144574\pi$
$930$	−4.27851	−	2.74963i	−0.140298	−	0.0901640i
$931$	−12.0249	−	5.69672i	−0.394101	−	0.186703i
$932$	1.15608	−	8.04070i	0.0378686	−	0.263382i
$933$	7.49922	+	4.81945i	0.245513	+	0.157782i
$934$	−3.59325	−	4.14684i	−0.117575	−	0.135689i
$935$	−55.9572	+	25.5548i	−1.83000	+	0.835731i
$936$	0.979465	+	1.52408i	0.0320148	+	0.0498160i
$937$	−57.0430	−	16.7493i	−1.86351	−	0.547177i	−0.999007	−	0.0445557i	$-0.985813\pi$
$937$	−57.0430	−	16.7493i	−1.86351	−	0.547177i	−0.864507	−	0.502621i	$-0.832369\pi$
$938$	0.481297	−	6.12550i	0.0157149	−	0.200005i
$939$	8.97567	+	30.5683i	0.292910	+	0.997559i
$940$	25.5158	+	11.6527i	0.832233	+	0.380068i
$941$	3.13266	+	21.7881i	0.102122	+	0.710272i	0.974979	+	0.222297i	$0.0713553\pi$
$941$	3.13266	+	21.7881i	0.102122	+	0.710272i	−0.872857	+	0.487975i	$0.837736\pi$
$942$		−	3.04129i		−	0.0990907i
$943$	−23.7085	+	20.8757i	−0.772056	+	0.679807i
$944$			11.3975i			0.370956i
$945$	5.64405	+	5.72376i	0.183601	+	0.186194i
$946$	0.614892	−	1.34642i	0.0199919	−	0.0437761i
$947$	56.7113	−	16.6519i	1.84287	−	0.541115i	0.842873	−	0.538112i	$-0.180862\pi$
$947$	56.7113	−	16.6519i	1.84287	−	0.541115i	0.999995	−	0.00300292i	$-0.000955859\pi$
$948$	19.5928	−	22.6113i	0.636344	−	0.734380i
$949$	2.67656	+	0.785908i	0.0868847	+	0.0255117i
$950$	−1.29128	+	0.829853i	−0.0418945	+	0.0269240i
$951$	−8.58823	+	3.92211i	−0.278492	+	0.127183i
$952$	−2.85812	+	12.7089i	−0.0926322	+	0.411897i
$953$	−22.6342	+	35.2196i	−0.733195	+	1.14087i	0.251714	+	0.967802i	$0.419006\pi$
$953$	−22.6342	+	35.2196i	−0.733195	+	1.14087i	−0.984909	+	0.173072i	$0.944631\pi$
$954$	1.72716	+	0.248328i	0.0559188	+	0.00803990i
$955$	66.2130	+	9.51999i	2.14260	+	0.308060i
$956$	3.17651	+	2.04142i	0.102736	+	0.0660242i
$957$	11.6622	+	13.4589i	0.376986	+	0.435065i
$958$	−1.10029	−	2.40929i	−0.0355486	−	0.0778406i
$959$	6.01399	−	15.7852i	0.194202	−	0.509731i
$960$	−6.11081	+	20.8115i	−0.197226	+	0.671688i
$961$	30.0762	−	34.7098i	0.970199	−	1.11967i
$962$	3.66908	−	1.07734i	0.118296	−	0.0347349i
$963$	−17.1449	−	7.82982i	−0.552487	−	0.252312i
$964$	−2.07066	−	14.4018i	−0.0666915	−	0.463850i
$965$	73.0300			2.35092
$966$	−1.71398	−	1.71078i	−0.0551463	−	0.0550433i
$967$	−37.8330			−1.21663			−0.608313	−	0.793697i	$-0.708154\pi$
$967$	−37.8330			−1.21663			−0.608313	+	0.793697i	$0.708154\pi$
$968$	−0.142369	−	0.990198i	−0.00457591	−	0.0318262i
$969$	−11.2538	−	5.13946i	−0.361525	−	0.165103i
$970$	−7.25721	+	2.13091i	−0.233015	+	0.0684193i
$971$	−12.8561	+	14.8367i	−0.412572	+	0.476133i	−0.923560	−	0.383455i	$-0.874734\pi$
$971$	−12.8561	+	14.8367i	−0.412572	+	0.476133i	0.510988	+	0.859588i	$0.329280\pi$
$972$	0.553203	−	1.88404i	0.0177440	−	0.0604305i
$973$	−7.99464	+	20.9839i	−0.256297	+	0.672714i
$974$	−1.29519	−	2.83607i	−0.0415006	−	0.0908737i
$975$	6.63560	+	7.65789i	0.212509	+	0.245249i
$976$	0.622898	+	0.400312i	0.0199385	+	0.0128137i
$977$	13.7435	+	1.97601i	0.439693	+	0.0632183i	0.358607	−	0.933489i	$-0.383252\pi$
$977$	13.7435	+	1.97601i	0.439693	+	0.0632183i	0.0810863	+	0.996707i	$0.474161\pi$
$978$	−3.28626	−	0.472493i	−0.105083	−	0.0151087i
$979$	−8.68284	+	13.5108i	−0.277505	+	0.431806i
$980$	38.2265	−	16.8137i	1.22110	−	0.537093i
$981$	12.2252	−	5.58304i	0.390319	−	0.178253i
$982$	−3.96708	+	2.54949i	−0.126595	+	0.0813575i
$983$	16.3333	+	4.79589i	0.520951	+	0.152965i	0.531628	−	0.846978i	$-0.321580\pi$
$983$	16.3333	+	4.79589i	0.520951	+	0.152965i	−0.0106768	+	0.999943i	$0.503399\pi$
$984$	3.26298	−	3.76568i	0.104020	−	0.120046i
$985$	11.5431	−	3.38935i	0.367792	−	0.107994i
$986$	−2.95404	+	6.46844i	−0.0940758	+	0.205997i
$987$	−8.85788	+	8.73453i	−0.281950	+	0.278023i
$988$			8.93904i			0.284389i
$989$	6.38392	−	10.1093i	0.202997	−	0.321457i
$990$			1.80388i			0.0573311i
$991$	0.520711	+	3.62162i	0.0165409	+	0.115045i	0.996419	−	0.0845520i	$-0.0269459\pi$
$991$	0.520711	+	3.62162i	0.0165409	+	0.115045i	−0.979878	+	0.199597i	$0.936037\pi$
$992$	17.8304	+	8.14289i	0.566117	+	0.258537i
$993$	−1.18338	−	4.03021i	−0.0375533	−	0.127895i
$994$	3.78224	+	0.297181i	0.119965	+	0.00942601i
$995$	−44.0246	−	12.9268i	−1.39567	−	0.409807i
$996$	−12.2097	−	18.9987i	−0.386879	−	0.601996i
$997$	8.07369	−	3.68713i	0.255696	−	0.116773i	−0.283443	−	0.958989i	$-0.591477\pi$
$997$	8.07369	−	3.68713i	0.255696	−	0.116773i	0.539140	+	0.842216i	$0.318750\pi$
$998$	3.65521	+	4.21833i	0.115703	+	0.133529i
$999$	−7.03801	−	4.52305i	−0.222673	−	0.143103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.17	✓	320
7.6	odd	2	inner	483.2.r.a.181.18	yes	320
23.15	odd	22	inner	483.2.r.a.475.18	yes	320
161.153	even	22	inner	483.2.r.a.475.17	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.17	✓	320	1.1	even	1	trivial
483.2.r.a.181.18	yes	320	7.6	odd	2	inner
483.2.r.a.475.17	yes	320	161.153	even	22	inner
483.2.r.a.475.18	yes	320	23.15	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0271614 + 0.188911i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.88404 - 0.553203i) q^{4} +(1.98963 - 2.29616i) q^{5} +(0.0537698 - 0.183123i) q^{6} +(-2.47239 - 0.941954i) q^{7} +(0.314247 + 0.688104i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.0271614 + 0.188911i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.88404 - 0.553203i) q^{4} +(1.98963 - 2.29616i) q^{5} +(0.0537698 - 0.183123i) q^{6} +(-2.47239 - 0.941954i) q^{7} +(0.314247 + 0.688104i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.487811 + 0.313497i) q^{10} +(3.07921 + 0.442724i) q^{11} +(-1.94359 - 0.279446i) q^{12} +(1.29479 - 2.01474i) q^{13} +(0.110792 - 0.492648i) q^{14} +(-2.76369 + 1.26213i) q^{15} +(3.18227 - 2.04512i) q^{16} +(-6.24490 - 1.83367i) q^{17} +(-0.124983 + 0.144238i) q^{18} +(-1.82387 + 0.535536i) q^{19} +(2.47830 - 5.42671i) q^{20} +(1.85767 + 1.88390i) q^{21} +0.593724i q^{22} +(-0.644774 + 4.75229i) q^{23} -0.756464i q^{24} +(-0.602129 - 4.18790i) q^{25} +(0.415776 + 0.189878i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-5.17917 - 0.406941i) q^{28} +(-5.49276 - 1.61282i) q^{29} +(-0.313497 - 0.487811i) q^{30} +(7.97823 - 3.64354i) q^{31} +(1.46354 + 1.68901i) q^{32} +(-2.61704 - 1.68187i) q^{33} +(0.176781 - 1.22954i) q^{34} +(-7.08202 + 3.80286i) q^{35} +(1.65186 + 1.06159i) q^{36} +(6.32267 - 5.47863i) q^{37} +(-0.150708 - 0.330003i) q^{38} +(-2.01474 + 1.29479i) q^{39} +(2.20523 + 0.647514i) q^{40} +(4.97801 + 4.31347i) q^{41} +(-0.305434 + 0.402103i) q^{42} +(-2.26776 - 1.03565i) q^{43} +(6.04627 - 0.869322i) q^{44} +3.03825 q^{45} +(-0.915275 + 0.00727351i) q^{46} +4.70188i q^{47} +(-3.74427 + 0.538345i) q^{48} +(5.22544 + 4.65776i) q^{49} +(0.774787 - 0.227498i) q^{50} +(4.91883 + 4.26219i) q^{51} +(1.32488 - 4.51212i) q^{52} +(-4.94290 - 7.69131i) q^{53} +(0.173607 - 0.0792836i) q^{54} +(7.14306 - 6.18950i) q^{55} +(-0.128778 - 1.99727i) q^{56} +(1.88152 + 0.270521i) q^{57} +(0.155489 - 1.08145i) q^{58} +(-1.62895 + 2.53469i) q^{59} +(-4.50867 + 3.90679i) q^{60} +(0.0813133 + 0.178051i) q^{61} +(0.905006 + 1.40822i) q^{62} +(-0.907191 - 2.48536i) q^{63} +(4.67506 - 5.39531i) q^{64} +(-2.04999 - 6.98164i) q^{65} +(0.246642 - 0.540070i) q^{66} +(12.0444 - 1.73172i) q^{67} -12.7800 q^{68} +(2.56068 - 4.05499i) q^{69} +(-0.910761 - 1.23458i) q^{70} +(1.06927 + 7.43690i) q^{71} +(-0.314247 + 0.688104i) q^{72} +(0.328156 + 1.11760i) q^{73} +(1.20671 + 1.04562i) q^{74} +(-1.19200 + 4.05958i) q^{75} +(-3.13997 + 2.01794i) q^{76} +(-7.19600 - 3.99506i) q^{77} +(-0.299324 - 0.345439i) q^{78} +(-8.23775 + 12.8182i) q^{79} +(1.63563 - 11.3760i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.679654 + 1.05756i) q^{82} +(7.53178 + 8.69214i) q^{83} +(4.54209 + 2.52167i) q^{84} +(-16.6354 + 10.6909i) q^{85} +(0.134051 - 0.456536i) q^{86} +(4.32640 + 3.74885i) q^{87} +(0.662992 + 2.25794i) q^{88} +(-2.14463 + 4.69608i) q^{89} +(0.0825230 + 0.573960i) q^{90} +(-5.09903 + 3.76159i) q^{91} +(1.41420 + 9.31018i) q^{92} -8.77084 q^{93} +(-0.888240 + 0.127710i) q^{94} +(-2.39915 + 5.25340i) q^{95} +(-0.629640 - 2.14436i) q^{96} +(-8.54184 + 9.85781i) q^{97} +(-0.737974 + 1.11366i) q^{98} +(1.68187 + 2.61704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more