LMFDB - Embedded newform 585.2.bt.b.571.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.1
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39334 + 1.38179i) q^{2} +(-0.969577 + 1.43524i) q^{3} +(2.81871 - 4.88215i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.337317 - 4.77477i) q^{6} +(-0.814209 + 0.470084i) q^{7} +10.0523i q^{8} +(-1.11984 - 2.78316i) q^{9} +O(q^{10})$	\(q+(-2.39334 + 1.38179i) q^{2} +(-0.969577 + 1.43524i) q^{3} +(2.81871 - 4.88215i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.337317 - 4.77477i) q^{6} +(-0.814209 + 0.470084i) q^{7} +10.0523i q^{8} +(-1.11984 - 2.78316i) q^{9} -2.76359 q^{10} +(1.21522 - 0.701610i) q^{11} +(4.27411 + 8.77915i) q^{12} +(-0.345136 - 3.58899i) q^{13} +(1.29912 - 2.25014i) q^{14} +(-1.55730 + 0.758168i) q^{15} +(-8.25283 - 14.2943i) q^{16} +4.46696 q^{17} +(6.52590 + 5.11364i) q^{18} +4.15403i q^{19} +(4.88215 - 2.81871i) q^{20} +(0.114754 - 1.62437i) q^{21} +(-1.93896 + 3.35838i) q^{22} +(-3.91930 + 6.78842i) q^{23} +(-14.4275 - 9.74651i) q^{24} +(0.500000 + 0.866025i) q^{25} +(5.78528 + 8.11277i) q^{26} +(5.08027 + 1.09124i) q^{27} +5.30012i q^{28} +(4.28503 + 7.42189i) q^{29} +(2.67951 - 3.96642i) q^{30} +(6.20587 + 3.58296i) q^{31} +(22.0925 + 12.7551i) q^{32} +(-0.171273 + 2.42440i) q^{33} +(-10.6909 + 6.17241i) q^{34} -0.940168 q^{35} +(-16.7443 - 2.37768i) q^{36} -5.11958i q^{37} +(-5.74002 - 9.94200i) q^{38} +(5.48571 + 2.98445i) q^{39} +(-5.02616 + 8.70557i) q^{40} +(-5.13782 - 2.96632i) q^{41} +(1.96990 + 4.04623i) q^{42} +(0.366759 + 0.635244i) q^{43} -7.91053i q^{44} +(0.421768 - 2.97020i) q^{45} -21.6626i q^{46} +(-3.03656 + 1.75316i) q^{47} +(28.5176 + 2.01464i) q^{48} +(-3.05804 + 5.29668i) q^{49} +(-2.39334 - 1.38179i) q^{50} +(-4.33106 + 6.41116i) q^{51} +(-18.4948 - 8.43133i) q^{52} -5.13246 q^{53} +(-13.6667 + 4.40818i) q^{54} +1.40322 q^{55} +(-4.72544 - 8.18470i) q^{56} +(-5.96204 - 4.02766i) q^{57} +(-20.5110 - 11.8421i) q^{58} +(-1.86109 - 1.07450i) q^{59} +(-0.688089 + 9.74002i) q^{60} +(3.62363 + 6.27631i) q^{61} -19.8036 q^{62} +(2.22010 + 1.73965i) q^{63} -37.4883 q^{64} +(1.49560 - 3.28073i) q^{65} +(-2.94011 - 6.03908i) q^{66} +(9.82249 + 5.67102i) q^{67} +(12.5911 - 21.8083i) q^{68} +(-5.94297 - 12.2070i) q^{69} +(2.25014 - 1.29912i) q^{70} -2.61002i q^{71} +(27.9772 - 11.2570i) q^{72} -2.38236i q^{73} +(7.07420 + 12.2529i) q^{74} +(-1.72774 - 0.122057i) q^{75} +(20.2806 + 11.7090i) q^{76} +(-0.659631 + 1.14251i) q^{77} +(-17.2531 + 0.437318i) q^{78} +(-3.36957 - 5.83626i) q^{79} -16.5057i q^{80} +(-6.49192 + 6.23338i) q^{81} +16.3954 q^{82} +(-13.1087 + 7.56831i) q^{83} +(-7.60695 - 5.13887i) q^{84} +(3.86850 + 2.23348i) q^{85} +(-1.75555 - 1.01357i) q^{86} +(-14.8069 - 1.04604i) q^{87} +(7.05281 + 12.2158i) q^{88} -5.36781i q^{89} +(3.09478 + 7.69150i) q^{90} +(1.96814 + 2.75995i) q^{91} +(22.0947 + 38.2692i) q^{92} +(-11.1595 + 5.43297i) q^{93} +(4.84501 - 8.39181i) q^{94} +(-2.07702 + 3.59750i) q^{95} +(-39.7270 + 19.3410i) q^{96} +(-2.13066 + 1.23014i) q^{97} -16.9023i q^{98} +(-3.31355 - 2.59647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.39334	+	1.38179i	−1.69235	+	0.977076i	−0.739727	+	0.672907i	$0.765045\pi$
$2$	−2.39334	+	1.38179i	−1.69235	+	0.977076i	−0.952618	+	0.304169i	$0.901621\pi$
$3$	−0.969577	+	1.43524i	−0.559786	+	0.828637i
$3$	−0.969577	+	1.43524i	−0.559786	+	0.828637i
$4$	2.81871	−	4.88215i	1.40935	−	2.44107i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	0.337317	−	4.77477i	0.137709	−	1.94929i
$7$	−0.814209	+	0.470084i	−0.307742	+	0.177675i	−0.645916	−	0.763409i	$-0.723524\pi$
$7$	−0.814209	+	0.470084i	−0.307742	+	0.177675i	0.338174	+	0.941084i	$0.390191\pi$
$8$			10.0523i			3.55403i
$9$	−1.11984	−	2.78316i	−0.373280	−	0.927719i
$10$	−2.76359			−0.873923
$11$	1.21522	−	0.701610i	0.366404	−	0.211543i	−0.305482	−	0.952198i	$-0.598818\pi$
$11$	1.21522	−	0.701610i	0.366404	−	0.211543i	0.671886	+	0.740654i	$0.265484\pi$
$12$	4.27411	+	8.77915i	1.23383	+	2.53432i
$13$	−0.345136	−	3.58899i	−0.0957234	−	0.995408i
$13$	−0.345136	−	3.58899i	−0.0957234	−	0.995408i
$14$	1.29912	−	2.25014i	0.347204	−	0.601375i
$15$	−1.55730	+	0.758168i	−0.402093	+	0.195758i
$16$	−8.25283	−	14.2943i	−2.06321	−	3.57358i
$17$	4.46696			1.08340			0.541698	−	0.840573i	$-0.317782\pi$
$17$	4.46696			1.08340			0.541698	+	0.840573i	$0.317782\pi$
$18$	6.52590	+	5.11364i	1.53817	+	1.20530i
$19$			4.15403i			0.953001i	0.879174	+	0.476500i	$0.158095\pi$
$19$			4.15403i			0.953001i	−0.879174	+	0.476500i	$0.841905\pi$
$20$	4.88215	−	2.81871i	1.09168	−	0.630283i
$21$	0.114754	−	1.62437i	0.0250415	−	0.354467i
$22$	−1.93896	+	3.35838i	−0.413388	+	0.716008i
$23$	−3.91930	+	6.78842i	−0.817230	+	1.41548i	0.0904860	+	0.995898i	$0.471158\pi$
$23$	−3.91930	+	6.78842i	−0.817230	+	1.41548i	−0.907716	+	0.419586i	$0.862175\pi$
$24$	−14.4275	−	9.74651i	−2.94501	−	1.98950i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	5.78528	+	8.11277i	1.13459	+	1.59104i
$27$	5.08027	+	1.09124i	0.977699	+	0.210010i
$28$			5.30012i			1.00163i
$29$	4.28503	+	7.42189i	0.795710	+	1.37821i	0.922387	+	0.386266i	$0.126235\pi$
$29$	4.28503	+	7.42189i	0.795710	+	1.37821i	−0.126677	+	0.991944i	$0.540431\pi$
$30$	2.67951	−	3.96642i	0.489210	−	0.724166i
$31$	6.20587	+	3.58296i	1.11461	+	0.643519i	0.940019	−	0.341123i	$-0.110807\pi$
$31$	6.20587	+	3.58296i	1.11461	+	0.643519i	0.174588	+	0.984642i	$0.444141\pi$
$32$	22.0925	+	12.7551i	3.90543	+	2.25480i
$33$	−0.171273	+	2.42440i	−0.0298149	+	0.422035i
$34$	−10.6909	+	6.17241i	−1.83348	+	1.05856i
$35$	−0.940168			−0.158917
$36$	−16.7443	−	2.37768i	−2.79071	−	0.396281i
$37$		−	5.11958i		−	0.841653i	−0.907141	−	0.420827i	$-0.861740\pi$
$37$		−	5.11958i		−	0.841653i	0.907141	−	0.420827i	$-0.138260\pi$
$38$	−5.74002	−	9.94200i	−0.931154	−	1.61281i
$39$	5.48571	+	2.98445i	0.878417	+	0.477895i
$40$	−5.02616	+	8.70557i	−0.794706	+	1.37647i
$41$	−5.13782	−	2.96632i	−0.802392	−	0.463261i	0.0419147	−	0.999121i	$-0.486654\pi$
$41$	−5.13782	−	2.96632i	−0.802392	−	0.463261i	−0.844307	+	0.535860i	$0.819988\pi$
$42$	1.96990	+	4.04623i	0.303962	+	0.624347i
$43$	0.366759	+	0.635244i	0.0559302	+	0.0968739i	0.892635	−	0.450780i	$-0.148854\pi$
$43$	0.366759	+	0.635244i	0.0559302	+	0.0968739i	−0.836705	+	0.547654i	$0.815521\pi$
$44$		−	7.91053i		−	1.19256i
$45$	0.421768	−	2.97020i	0.0628735	−	0.442772i
$46$		−	21.6626i		−	3.19398i
$47$	−3.03656	+	1.75316i	−0.442928	+	0.255725i	−0.704839	−	0.709367i	$-0.748981\pi$
$47$	−3.03656	+	1.75316i	−0.442928	+	0.255725i	0.261911	+	0.965092i	$0.415647\pi$
$48$	28.5176	+	2.01464i	4.11615	+	0.290788i
$49$	−3.05804	+	5.29668i	−0.436863	+	0.756669i
$50$	−2.39334	−	1.38179i	−0.338469	−	0.195415i
$51$	−4.33106	+	6.41116i	−0.606470	+	0.897743i
$52$	−18.4948	−	8.43133i	−2.56477	−	1.16921i
$53$	−5.13246			−0.704998			−0.352499	−	0.935812i	$-0.614668\pi$
$53$	−5.13246			−0.704998			−0.352499	+	0.935812i	$0.614668\pi$
$54$	−13.6667	+	4.40818i	−1.85980	+	0.599877i
$55$	1.40322			0.189210
$56$	−4.72544	−	8.18470i	−0.631463	−	1.09373i
$57$	−5.96204	−	4.02766i	−0.789692	−	0.533476i
$58$	−20.5110	−	11.8421i	−2.69323	−	1.55494i
$59$	−1.86109	−	1.07450i	−0.242293	−	0.139888i	0.373937	−	0.927454i	$-0.378008\pi$
$59$	−1.86109	−	1.07450i	−0.242293	−	0.139888i	−0.616230	+	0.787566i	$0.711341\pi$
$60$	−0.688089	+	9.74002i	−0.0888319	+	1.25743i
$61$	3.62363	+	6.27631i	0.463959	+	0.803600i	0.999154	−	0.0411286i	$-0.0130953\pi$
$61$	3.62363	+	6.27631i	0.463959	+	0.803600i	−0.535195	+	0.844728i	$0.679762\pi$
$62$	−19.8036			−2.51507
$63$	2.22010	+	1.73965i	0.279706	+	0.219176i
$64$	−37.4883			−4.68604
$65$	1.49560	−	3.28073i	0.185506	−	0.406924i
$66$	−2.94011	−	6.03908i	−0.361903	−	0.743360i
$67$	9.82249	+	5.67102i	1.20001	+	0.692825i	0.960557	−	0.278083i	$-0.0896991\pi$
$67$	9.82249	+	5.67102i	1.20001	+	0.692825i	0.239452	+	0.970908i	$0.423032\pi$
$68$	12.5911	−	21.8083i	1.52689	−	2.64465i
$69$	−5.94297	−	12.2070i	−0.715449	−	1.46955i
$70$	2.25014	−	1.29912i	0.268943	−	0.155274i
$71$		−	2.61002i		−	0.309753i	−0.987934	−	0.154876i	$-0.950502\pi$
$71$		−	2.61002i		−	0.309753i	0.987934	−	0.154876i	$-0.0494979\pi$
$72$	27.9772	−	11.2570i	3.29714	−	1.32665i
$73$		−	2.38236i		−	0.278835i	−0.990234	−	0.139417i	$-0.955477\pi$
$73$		−	2.38236i		−	0.278835i	0.990234	−	0.139417i	$-0.0445229\pi$
$74$	7.07420	+	12.2529i	0.822359	+	1.42437i
$75$	−1.72774	−	0.122057i	−0.199503	−	0.0140940i
$76$	20.2806	+	11.7090i	2.32635	+	1.34312i
$77$	−0.659631	+	1.14251i	−0.0751719	+	0.130202i
$78$	−17.2531	+	0.437318i	−1.95352	+	0.0495165i
$79$	−3.36957	−	5.83626i	−0.379106	−	0.656631i	0.611826	−	0.790992i	$-0.290435\pi$
$79$	−3.36957	−	5.83626i	−0.379106	−	0.656631i	−0.990932	+	0.134361i	$0.957102\pi$
$80$		−	16.5057i		−	1.84539i
$81$	−6.49192	+	6.23338i	−0.721324	+	0.692598i
$82$	16.3954			1.81057
$83$	−13.1087	+	7.56831i	−1.43887	+	0.830730i	−0.997771	−	0.0667310i	$-0.978743\pi$
$83$	−13.1087	+	7.56831i	−1.43887	+	0.830730i	−0.441095	+	0.897461i	$0.645410\pi$
$84$	−7.60695	−	5.13887i	−0.829987	−	0.560697i
$85$	3.86850	+	2.23348i	0.419598	+	0.242255i
$86$	−1.75555	−	1.01357i	−0.189306	−	0.109296i
$87$	−14.8069	−	1.04604i	−1.58746	−	0.112147i
$88$	7.05281	+	12.2158i	0.751832	+	1.30221i
$89$		−	5.36781i		−	0.568987i	−0.958678	−	0.284493i	$-0.908175\pi$
$89$		−	5.36781i		−	0.568987i	0.958678	−	0.284493i	$-0.0918254\pi$
$90$	3.09478	+	7.69150i	0.326218	+	0.810755i
$91$	1.96814	+	2.75995i	0.206317	+	0.289321i
$92$	22.0947	+	38.2692i	2.30353	+	3.98984i
$93$	−11.1595	+	5.43297i	−1.15718	+	0.563372i
$94$	4.84501	−	8.39181i	0.499725	−	0.865549i
$95$	−2.07702	+	3.59750i	−0.213097	+	0.369096i
$96$	−39.7270	+	19.3410i	−4.05462	+	1.97398i
$97$	−2.13066	+	1.23014i	−0.216336	+	0.124902i	−0.604253	−	0.796793i	$-0.706528\pi$
$97$	−2.13066	+	1.23014i	−0.216336	+	0.124902i	0.387917	+	0.921694i	$0.373195\pi$
$98$		−	16.9023i		−	1.70739i
$99$	−3.31355	−	2.59647i	−0.333024	−	0.260955i
$100$	5.63742			0.563742
$101$	7.72313	+	13.3769i	0.768480	+	1.33105i	0.938387	+	0.345586i	$0.112320\pi$
$101$	7.72313	+	13.3769i	0.768480	+	1.33105i	−0.169907	+	0.985460i	$0.554347\pi$
$102$	1.50678	−	21.3287i	0.149193	−	2.11186i
$103$	−3.13526	+	5.43043i	−0.308926	+	0.535076i	−0.978128	−	0.208005i	$-0.933303\pi$
$103$	−3.13526	+	5.43043i	−0.308926	+	0.535076i	0.669202	+	0.743081i	$0.266636\pi$
$104$	36.0777	−	3.46942i	3.53771	−	0.340204i
$105$	0.911565	−	1.34937i	0.0889596	−	0.131685i
$106$	12.2837	−	7.09200i	1.19310	−	0.688836i
$107$	1.87714			0.181470			0.0907348	−	0.995875i	$-0.471078\pi$
$107$	1.87714			0.181470			0.0907348	+	0.995875i	$0.471078\pi$
$108$	19.6474	−	21.7268i	1.89057	−	2.09066i
$109$			4.00285i			0.383404i	0.981453	+	0.191702i	$0.0614007\pi$
$109$			4.00285i			0.383404i	−0.981453	+	0.191702i	$0.938599\pi$
$110$	−3.35838	+	1.93896i	−0.320209	+	0.184873i
$111$	7.34783	+	4.96383i	0.697425	+	0.471145i
$112$	13.4391	+	7.75904i	1.26987	+	0.733160i
$113$	1.10512	−	1.91412i	0.103961	−	0.180065i	−0.809352	−	0.587323i	$-0.800182\pi$
$113$	1.10512	−	1.91412i	0.103961	−	0.180065i	0.913313	+	0.407258i	$0.133515\pi$
$114$	19.8346	+	1.40122i	1.85768	+	0.131237i
$115$	−6.78842	+	3.91930i	−0.633023	+	0.365476i
$116$	48.3130			4.48575
$117$	−9.60224	+	4.97967i	−0.887727	+	0.460370i
$118$	5.93895			0.546725
$119$	−3.63704	+	2.09984i	−0.333407	+	0.192492i
$120$	−7.62135	−	15.6545i	−0.695731	−	1.42905i
$121$	−4.51549	+	7.82105i	−0.410499	+	0.711005i
$122$	−17.3451	−	10.0142i	−1.57036	−	0.906645i
$123$	9.23890	−	4.49794i	0.833043	−	0.405565i
$124$	34.9851	−	20.1986i	3.14175	−	1.81389i
$125$			1.00000i			0.0894427i
$126$	−7.71729	−	1.09585i	−0.687511	−	0.0976264i
$127$	8.59217			0.762432			0.381216	−	0.924486i	$-0.375505\pi$
$127$	8.59217			0.762432			0.381216	+	0.924486i	$0.375505\pi$
$128$	45.5372	−	26.2909i	4.02496	−	2.32381i
$129$	−1.26733	−	0.0895312i	−0.111582	−	0.00788279i
$130$	0.953813	+	9.91850i	0.0836549	+	0.869910i
$131$	−1.96246	+	3.39908i	−0.171461	+	0.296979i	−0.938931	−	0.344106i	$-0.888182\pi$
$131$	−1.96246	+	3.39908i	−0.171461	+	0.296979i	0.767470	+	0.641085i	$0.221515\pi$
$132$	11.3535	+	7.66987i	0.988198	+	0.667577i
$133$	−1.95274	−	3.38225i	−0.169324	−	0.293278i
$134$	−31.3447			−2.70777
$135$	3.85402	+	3.48518i	0.331702	+	0.299957i
$136$			44.9033i			3.85043i
$137$	−9.46701	+	5.46578i	−0.808822	+	0.466973i	−0.846546	−	0.532315i	$-0.821322\pi$
$137$	−9.46701	+	5.46578i	−0.808822	+	0.466973i	0.0377249	+	0.999288i	$0.487989\pi$
$138$	31.0911	+	21.0036i	2.64665	+	1.78795i
$139$	1.52565	−	2.64251i	0.129404	−	0.224134i	−0.794042	−	0.607863i	$-0.792027\pi$
$139$	1.52565	−	2.64251i	0.129404	−	0.224134i	0.923446	+	0.383729i	$0.125360\pi$
$140$	−2.65006	+	4.59004i	−0.223971	+	0.387929i
$141$	0.427973	−	6.05803i	0.0360418	−	0.510178i
$142$	3.60652	+	6.24667i	0.302652	+	0.524209i
$143$	−2.93749	−	4.11928i	−0.245645	−	0.344472i
$144$	−30.5415	+	38.9762i	−2.54512	+	3.24802i
$145$			8.57006i			0.711705i
$146$	3.29193	+	5.70180i	0.272442	+	0.471884i
$147$	−4.63702	−	9.52458i	−0.382455	−	0.785574i
$148$	−24.9945	−	14.4306i	−2.05454	−	1.18619i
$149$	2.46587	+	1.42367i	0.202012	+	0.116631i	0.597593	−	0.801799i	$-0.296124\pi$
$149$	2.46587	+	1.42367i	0.202012	+	0.116631i	−0.395582	+	0.918431i	$0.629457\pi$
$150$	4.30373	−	2.09526i	0.351398	−	0.171077i
$151$	7.48190	−	4.31968i	0.608868	−	0.351530i	−0.163654	−	0.986518i	$-0.552328\pi$
$151$	7.48190	−	4.31968i	0.608868	−	0.351530i	0.772522	+	0.634988i	$0.218995\pi$
$152$	−41.7577			−3.38700
$153$	−5.00228	−	12.4322i	−0.404410	−	1.00509i
$154$		−	3.64589i		−	0.293795i
$155$	3.58296	+	6.20587i	0.287790	+	0.498467i
$156$	30.0332	−	18.3697i	2.40458	−	1.47076i
$157$	8.19349	−	14.1915i	0.653912	−	1.13261i	−0.328254	−	0.944590i	$-0.606460\pi$
$157$	8.19349	−	14.1915i	0.653912	−	1.13261i	0.982165	−	0.188019i	$-0.0602066\pi$
$158$	16.1290	+	9.31210i	1.28316	+	0.740831i
$159$	4.97632	−	7.36632i	0.394648	−	0.584187i
$160$	12.7551	+	22.0925i	1.00838	+	1.74656i
$161$		−	7.36959i		−	0.580805i
$162$	6.92410	−	23.8891i	0.544009	−	1.87690i
$163$			15.3374i			1.20132i	0.799504	+	0.600661i	$0.205096\pi$
$163$			15.3374i			1.20132i	−0.799504	+	0.600661i	$0.794904\pi$
$164$	−28.9640	+	16.7224i	−2.26171	+	1.30580i
$165$	−1.36053	+	2.01396i	−0.105917	+	0.156787i
$166$	20.9157	−	36.2270i	1.62337	−	2.81176i
$167$	18.7608	+	10.8316i	1.45175	+	0.838171i	0.998581	−	0.0532517i	$-0.0169586\pi$
$167$	18.7608	+	10.8316i	1.45175	+	0.838171i	0.453173	+	0.891422i	$0.350292\pi$
$168$	16.3287	+	1.15355i	1.25979	+	0.0889983i
$169$	−12.7618	+	2.47738i	−0.981674	+	0.190568i
$170$	−12.3448			−0.946805
$171$	11.5613	−	4.65185i	0.884117	−	0.355736i
$172$	4.13514			0.315302
$173$	−9.26888	−	16.0542i	−0.704700	−	1.22058i	−0.966800	−	0.255535i	$-0.917748\pi$
$173$	−9.26888	−	16.0542i	−0.704700	−	1.22058i	0.262100	−	0.965041i	$-0.415585\pi$
$174$	36.8833	−	17.9565i	2.79611	−	1.36128i
$175$	−0.814209	−	0.470084i	−0.0615484	−	0.0355350i
$176$	−20.0581	−	11.5805i	−1.51193	−	0.872915i
$177$	3.34664	−	1.62930i	0.251549	−	0.122466i
$178$	7.41721	+	12.8470i	0.555943	+	0.962922i
$179$	−13.7008			−1.02405			−0.512023	−	0.858972i	$-0.671104\pi$
$179$	−13.7008			−1.02405			−0.512023	+	0.858972i	$0.671104\pi$
$180$	−13.3121	−	10.4313i	−0.992228	−	0.777501i
$181$	9.90097			0.735933			0.367966	−	0.929839i	$-0.380054\pi$
$181$	9.90097			0.735933			0.367966	+	0.929839i	$0.380054\pi$
$182$	−8.52411	−	3.88592i	−0.631849	−	0.288044i
$183$	−12.5214	−	0.884583i	−0.925610	−	0.0653902i
$184$	−68.2394	−	39.3980i	−5.03068	−	2.90446i
$185$	2.55979	−	4.43368i	0.188199	−	0.325971i
$186$	19.2012	−	28.4230i	1.40790	−	2.08408i
$187$	5.42835	−	3.13406i	0.396960	−	0.229185i
$188$			19.7666i			1.44163i
$189$	−4.64938	+	1.49965i	−0.338193	+	0.109084i
$190$		−	11.4800i		−	0.832850i
$191$	5.23461	+	9.06661i	0.378763	+	0.656037i	0.990883	−	0.134728i	$-0.0430162\pi$
$191$	5.23461	+	9.06661i	0.378763	+	0.656037i	−0.612120	+	0.790765i	$0.709683\pi$
$192$	36.3478	−	53.8048i	2.62318	−	3.88303i
$193$	23.9152	+	13.8075i	1.72145	+	0.993882i	0.915950	+	0.401292i	$0.131439\pi$
$193$	23.9152	+	13.8075i	1.72145	+	0.993882i	0.805504	+	0.592590i	$0.201895\pi$
$194$	3.39960	−	5.88827i	0.244077	−	0.422753i
$195$	3.25854	+	5.32747i	0.233349	+	0.381508i
$196$	17.2395	+	29.8596i	1.23139	+	2.13283i
$197$		−	3.17899i		−	0.226494i	−0.993567	−	0.113247i	$-0.963875\pi$
$197$		−	3.17899i		−	0.226494i	0.993567	−	0.113247i	$-0.0361251\pi$
$198$	11.5182	+	1.63558i	0.818564	+	0.116236i
$199$	8.27536			0.586624			0.293312	−	0.956017i	$-0.405242\pi$
$199$	8.27536			0.586624			0.293312	+	0.956017i	$0.405242\pi$
$200$	−8.70557	+	5.02616i	−0.615577	+	0.355403i
$201$	−17.6630	+	8.59916i	−1.24585	+	0.606538i
$202$	−36.9681	−	21.3435i	−2.60107	−	1.50173i
$203$	−6.97782	−	4.02865i	−0.489747	−	0.282756i
$204$	19.0923	+	39.2161i	1.33673	+	2.74568i
$205$	−2.96632	−	5.13782i	−0.207177	−	0.358841i
$206$		−	17.3291i		−	1.20738i
$207$	23.2822	+	3.30607i	1.61823	+	0.229788i
$208$	−48.4539	+	34.5528i	−3.35967	+	2.39581i
$209$	2.91451	+	5.04808i	0.201601	+	0.349183i
$210$	−0.317134	+	4.48909i	−0.0218843	+	0.309777i
$211$	1.31199	−	2.27244i	0.0903214	−	0.156441i	−0.817325	−	0.576177i	$-0.804544\pi$
$211$	1.31199	−	2.27244i	0.0903214	−	0.156441i	0.907646	+	0.419736i	$0.137877\pi$
$212$	−14.4669	+	25.0574i	−0.993592	+	1.72095i
$213$	3.74602	+	2.53062i	0.256673	+	0.173395i
$214$	−4.49262	+	2.59382i	−0.307109	+	0.177310i
$215$			0.733517i			0.0500254i
$216$	−10.9695	+	51.0686i	−0.746382	+	3.47478i
$217$	−6.73716			−0.457349
$218$	−5.53112	−	9.58018i	−0.374615	−	0.648852i
$219$	3.41927	+	2.30988i	0.231053	+	0.156088i
$220$	3.95527	−	6.85072i	0.266664	−	0.461876i
$221$	−1.54171	−	16.0319i	−0.103706	−	1.07842i
$222$	−24.4448	−	1.72692i	−1.64063	−	0.115903i
$223$	−15.0867	+	8.71029i	−1.01028	+	0.583284i	−0.911273	−	0.411802i	$-0.864899\pi$
$223$	−15.0867	+	8.71029i	−1.01028	+	0.583284i	−0.0990052	+	0.995087i	$0.531566\pi$
$224$	−23.9838			−1.60249
$225$	1.85036	−	2.36139i	0.123358	−	0.157426i
$226$			6.10817i			0.406310i
$227$	19.1103	−	11.0333i	1.26839	−	0.732307i	0.293709	−	0.955895i	$-0.405110\pi$
$227$	19.1103	−	11.0333i	1.26839	−	0.732307i	0.974684	+	0.223588i	$0.0717769\pi$
$228$	−36.4689	+	17.7548i	−2.41521	+	1.17584i
$229$	−0.226938	−	0.131023i	−0.0149965	−	0.00865823i	0.492483	−	0.870322i	$-0.336089\pi$
$229$	−0.226938	−	0.131023i	−0.0149965	−	0.00865823i	−0.507480	+	0.861664i	$0.669423\pi$
$230$	10.8313	−	18.7604i	0.714196	−	1.23702i
$231$	−1.00022	−	2.05449i	−0.0658097	−	0.135175i
$232$	−74.6073	+	43.0745i	−4.89821	+	2.82798i
$233$	−0.554346			−0.0363164			−0.0181582	−	0.999835i	$-0.505780\pi$
$233$	−0.554346			−0.0363164			−0.0181582	+	0.999835i	$0.505780\pi$
$234$	16.1005	−	25.1863i	1.05252	−	1.64648i
$235$	−3.50632			−0.228727
$236$	−10.4917	+	6.05741i	−0.682954	+	0.394304i
$237$	11.6435	+	0.822562i	0.756327	+	0.0534311i
$238$	5.80310	−	10.0513i	0.376159	−	0.651527i
$239$	24.7211	+	14.2727i	1.59907	+	0.923225i	0.991666	+	0.128835i	$0.0411237\pi$
$239$	24.7211	+	14.2727i	1.59907	+	0.923225i	0.607407	+	0.794391i	$0.292210\pi$
$240$	23.6896	+	16.0035i	1.52916	+	1.03302i
$241$	7.86079	−	4.53843i	0.506358	−	0.292346i	−0.224977	−	0.974364i	$-0.572231\pi$
$241$	7.86079	−	4.53843i	0.506358	−	0.292346i	0.731335	+	0.682018i	$0.238897\pi$
$242$		−	24.9579i		−	1.60435i
$243$	−2.65199	−	15.3612i	−0.170125	−	0.985422i
$244$	40.8559			2.61553
$245$	−5.29668	+	3.05804i	−0.338393	+	0.195371i
$246$	−15.8966	+	23.5313i	−1.01353	+	1.50030i
$247$	14.9088	−	1.43371i	0.948625	−	0.0912245i
$248$	−36.0171	+	62.3834i	−2.28709	+	3.96135i
$249$	1.84754	−	26.1522i	0.117083	−	1.65733i
$250$	−1.38179	−	2.39334i	−0.0873923	−	0.151368i
$251$	−17.9008			−1.12989			−0.564945	−	0.825129i	$-0.691103\pi$
$251$	−17.9008			−1.12989			−0.564945	+	0.825129i	$0.691103\pi$
$252$	14.7511	−	5.93528i	0.929229	−	0.373888i
$253$			10.9993i			0.691518i
$254$	−20.5640	+	11.8726i	−1.29030	+	0.744954i
$255$	−6.95639	+	3.38670i	−0.435626	+	0.212083i
$256$	−35.1690	+	60.9145i	−2.19806	+	3.80716i
$257$	3.01865	−	5.22846i	0.188298	−	0.326142i	−0.756385	−	0.654127i	$-0.773036\pi$
$257$	3.01865	−	5.22846i	0.188298	−	0.326142i	0.944683	+	0.327985i	$0.106369\pi$
$258$	3.15686	−	1.53691i	0.196538	−	0.0956839i
$259$	2.40663	+	4.16841i	0.149541	+	0.259012i
$260$	−11.8013	−	16.5492i	−0.731888	−	1.02634i
$261$	15.8577	−	20.2372i	0.981569	−	1.25265i
$262$		−	10.8469i		−	0.670122i
$263$	12.7170	+	22.0265i	0.784164	+	1.35821i	0.929497	+	0.368830i	$0.120241\pi$
$263$	12.7170	+	22.0265i	0.784164	+	1.35821i	−0.145332	+	0.989383i	$0.546425\pi$
$264$	−24.3709	−	1.72170i	−1.49993	−	0.105963i
$265$	−4.44484	−	2.56623i	−0.273044	−	0.157642i
$266$	9.34715	+	5.39658i	0.573111	+	0.330886i
$267$	7.70411	+	5.20451i	0.471484	+	0.318511i
$268$	55.3735	−	31.9699i	3.38248	−	1.95287i
$269$	−3.71647			−0.226597			−0.113298	−	0.993561i	$-0.536142\pi$
$269$	−3.71647			−0.226597			−0.113298	+	0.993561i	$0.536142\pi$
$270$	−14.0398	−	3.01575i	−0.854434	−	0.183533i
$271$		−	18.5902i		−	1.12927i	−0.825340	−	0.564636i	$-0.809016\pi$
$271$		−	18.5902i		−	1.12927i	0.825340	−	0.564636i	$-0.190984\pi$
$272$	−36.8650	−	63.8521i	−2.23527	−	3.87160i
$273$	−5.86946	+	0.148775i	−0.355236	+	0.00900426i
$274$	15.1052	−	26.1629i	0.912537	−	1.58056i
$275$	1.21522	+	0.701610i	0.0732807	+	0.0423087i
$276$	−76.3481	−	5.39365i	−4.59561	−	0.324660i
$277$	−14.3726	−	24.8941i	−0.863566	−	1.49574i	−0.868464	−	0.495752i	$-0.834893\pi$
$277$	−14.3726	−	24.8941i	−0.863566	−	1.49574i	0.00489863	−	0.999988i	$-0.498441\pi$
$278$			8.43255i			0.505750i
$279$	3.02236	−	21.2842i	0.180944	−	1.27425i
$280$		−	9.45087i		−	0.564798i
$281$	4.82295	−	2.78453i	0.287713	−	0.166111i	−0.349197	−	0.937049i	$-0.613546\pi$
$281$	4.82295	−	2.78453i	0.287713	−	0.166111i	0.636910	+	0.770938i	$0.280212\pi$
$282$	7.34667	+	15.0903i	0.437488	+	0.898613i
$283$	−6.34111	+	10.9831i	−0.376940	+	0.652879i	−0.990615	−	0.136679i	$-0.956357\pi$
$283$	−6.34111	+	10.9831i	−0.376940	+	0.652879i	0.613675	+	0.789559i	$0.289690\pi$
$284$	−12.7425	−	7.35690i	−0.756130	−	0.436552i
$285$	−3.14945	−	6.46908i	−0.186558	−	0.383195i
$286$	12.7224	+	5.79982i	0.752291	+	0.342951i
$287$	5.57768			0.329240
$288$	10.7594	−	75.7704i	0.634003	−	4.46481i
$289$	2.95370			0.173747
$290$	−11.8421	−	20.5110i	−0.695390	−	1.20445i
$291$	0.300295	−	4.25073i	0.0176036	−	0.249182i
$292$	−11.6310	−	6.71519i	−0.680656	−	0.392977i
$293$	−27.6460	−	15.9614i	−1.61510	−	0.932477i	−0.988163	−	0.153406i	$-0.950976\pi$
$293$	−27.6460	−	15.9614i	−1.61510	−	0.932477i	−0.626935	−	0.779071i	$-0.715691\pi$
$294$	24.2589	+	16.3881i	1.41481	+	0.955775i
$295$	−1.07450	−	1.86109i	−0.0625598	−	0.108357i
$296$	51.4637			2.99126
$297$	6.93930	−	2.23826i	0.402659	−	0.129877i
$298$	−7.86887			−0.455831
$299$	25.7163	+	11.7234i	1.48721	+	0.677982i
$300$	−5.46591	+	8.09106i	−0.315575	+	0.467138i
$301$	−0.597236	−	0.344814i	−0.0344241	−	0.0198748i
$302$	−11.9378	+	20.6769i	−0.686943	+	1.18982i
$303$	−26.6872	−	1.88533i	−1.53314	−	0.108309i
$304$	59.3791	−	34.2825i	3.40562	−	1.96624i
$305$			7.24726i			0.414977i
$306$	29.1509	+	22.8424i	1.66645	+	1.30581i
$307$		−	1.59309i		−	0.0909227i	−0.998966	−	0.0454614i	$-0.985524\pi$
$307$		−	1.59309i		−	0.0909227i	0.998966	−	0.0454614i	$-0.0144758\pi$
$308$	3.71861	+	6.44083i	0.211888	+	0.367000i
$309$	−4.75410	−	9.76507i	−0.270451	−	0.555515i
$310$	−17.1505	−	9.90182i	−0.974081	−	0.562386i
$311$	−5.65092	+	9.78768i	−0.320434	+	0.555009i	−0.980578	−	0.196131i	$-0.937162\pi$
$311$	−5.65092	+	9.78768i	−0.320434	+	0.555009i	0.660143	+	0.751140i	$0.270496\pi$
$312$	−30.0007	+	55.1442i	−1.69846	+	3.12192i
$313$	6.19960	+	10.7380i	0.350422	+	0.606949i	0.986323	−	0.164821i	$-0.0527048\pi$
$313$	6.19960	+	10.7380i	0.350422	+	0.606949i	−0.635901	+	0.771770i	$0.719371\pi$
$314$			45.2869i			2.55569i
$315$	1.05284	+	2.61663i	0.0593207	+	0.147431i
$316$	−37.9913			−2.13718
$317$	4.77057	−	2.75429i	0.267942	−	0.154696i	−0.360010	−	0.932948i	$-0.617227\pi$
$317$	4.77057	−	2.75429i	0.267942	−	0.154696i	0.627952	+	0.778252i	$0.283893\pi$
$318$	−1.73126	+	24.5063i	−0.0970844	+	1.37425i
$319$	10.4145	+	6.01284i	0.583102	+	0.336654i
$320$	−32.4658	−	18.7441i	−1.81489	−	1.04783i
$321$	−1.82003	+	2.69415i	−0.101584	+	0.150373i
$322$	10.1833	+	17.6379i	0.567491	+	0.982923i
$323$			18.5559i			1.03248i
$324$	12.1335	+	49.2646i	0.674081	+	2.73692i
$325$	2.93559	−	2.09339i	0.162837	−	0.116121i
$326$	−21.1932	−	36.7077i	−1.17378	−	2.03305i
$327$	−5.74507	−	3.88108i	−0.317703	−	0.214624i
$328$	29.8184	−	51.6470i	1.64645	−	2.85173i
$329$	1.64827	−	2.85488i	0.0908718	−	0.157395i
$330$	0.473329	−	6.70006i	0.0260559	−	0.368826i
$331$	−2.49540	+	1.44072i	−0.137160	+	0.0791891i	−0.567010	−	0.823711i	$-0.691900\pi$
$331$	−2.49540	+	1.44072i	−0.137160	+	0.0791891i	0.429850	+	0.902900i	$0.358566\pi$
$332$			85.3314i			4.68317i
$333$	−14.2486	+	5.73311i	−0.780818	+	0.314172i
$334$	−59.8679			−3.27583
$335$	5.67102	+	9.82249i	0.309841	+	0.536660i
$336$	−24.1663	+	11.7653i	−1.31838	+	0.641850i
$337$	−12.4695	+	21.5978i	−0.679258	+	1.17651i	0.295946	+	0.955205i	$0.404365\pi$
$337$	−12.4695	+	21.5978i	−0.679258	+	1.17651i	−0.975205	+	0.221305i	$0.928968\pi$
$338$	27.1200	−	23.5633i	1.47513	−	1.28168i
$339$	1.67573	+	3.44199i	0.0910130	+	0.186943i
$340$	21.8083	−	12.5911i	1.18272	−	0.682846i
$341$	10.0554			0.544528
$342$	−21.2423	+	27.1088i	−1.14865	+	1.46588i
$343$		−	12.3313i		−	0.665829i
$344$	−6.38568	+	3.68678i	−0.344293	+	0.198778i
$345$	0.956759	−	13.5431i	0.0515102	−	0.729135i
$346$	44.3671	+	25.6154i	2.38519	+	1.37709i
$347$	7.98579	−	13.8318i	0.428700	−	0.742530i	−0.568058	−	0.822988i	$-0.692305\pi$
$347$	7.98579	−	13.8318i	0.428700	−	0.742530i	0.996758	+	0.0804587i	$0.0256385\pi$
$348$	−46.8432	+	69.3409i	−2.51106	+	3.71706i
$349$	−15.5244	+	8.96300i	−0.831000	+	0.479778i	−0.854195	−	0.519953i	$-0.825950\pi$
$349$	−15.5244	+	8.96300i	−0.831000	+	0.479778i	0.0231946	+	0.999731i	$0.492616\pi$
$350$	2.59824			0.138882
$351$	2.16308	−	18.6097i	0.115457	−	0.993312i
$352$	35.7964			1.90795
$353$	14.0533	−	8.11371i	0.747984	−	0.431849i	−0.0769808	−	0.997033i	$-0.524528\pi$
$353$	14.0533	−	8.11371i	0.747984	−	0.431849i	0.824965	+	0.565184i	$0.191195\pi$
$354$	−5.75827	+	8.52383i	−0.306049	+	0.453037i
$355$	1.30501	−	2.26035i	0.0692629	−	0.119967i
$356$	−26.2064	−	15.1303i	−1.38894	−	0.801904i
$357$	0.512603	−	7.25599i	0.0271298	−	0.384028i
$358$	32.7906	−	18.9317i	1.73304	−	1.00057i
$359$		−	8.77458i		−	0.463104i	−0.972822	−	0.231552i	$-0.925620\pi$
$359$		−	8.77458i		−	0.463104i	0.972822	−	0.231552i	$-0.0743804\pi$
$360$	29.8575	+	4.23975i	1.57363	+	0.223455i
$361$	1.74400			0.0917896
$362$	−23.6964	+	13.6811i	−1.24545	+	0.719062i
$363$	−6.84699	−	14.0639i	−0.359374	−	0.738165i
$364$	19.0221	−	1.82926i	0.997029	−	0.0958793i
$365$	1.19118	−	2.06319i	0.0623493	−	0.107992i
$366$	31.1903	−	15.1849i	1.63034	−	0.793729i
$367$	6.27655	+	10.8713i	0.327633	+	0.567477i	0.982042	−	0.188664i	$-0.0604156\pi$
$367$	6.27655	+	10.8713i	0.327633	+	0.567477i	−0.654409	+	0.756141i	$0.727082\pi$
$368$	129.381			6.74446
$369$	−2.50220	+	17.6212i	−0.130259	+	0.917321i
$370$			14.1484i			0.735540i
$371$	4.17889	−	2.41269i	0.216957	−	0.125260i
$372$	−4.93079	+	69.7962i	−0.255650	+	3.61876i
$373$	15.6255	−	27.0642i	0.809059	−	1.40133i	−0.104457	−	0.994529i	$-0.533311\pi$
$373$	15.6255	−	27.0642i	0.809059	−	1.40133i	0.913516	−	0.406802i	$-0.133356\pi$
$374$	−8.66125	+	15.0017i	−0.447863	+	0.775721i
$375$	−1.43524	−	0.969577i	−0.0741156	−	0.0500688i
$376$	−17.6233	−	30.5245i	−0.908855	−	1.57418i
$377$	25.1582	−	17.9405i	1.29571	−	0.923983i
$378$	9.05532	−	10.0137i	0.465756	−	0.515047i
$379$			20.8786i			1.07246i	0.844071	+	0.536232i	$0.180153\pi$
$379$			20.8786i			1.07246i	−0.844071	+	0.536232i	$0.819847\pi$
$380$	11.7090	+	20.2806i	0.600660	+	1.04037i
$381$	−8.33077	+	12.3318i	−0.426799	+	0.631780i
$382$	−25.0564	−	14.4663i	−1.28200	−	0.740160i
$383$	−4.28958	−	2.47659i	−0.219187	−	0.126548i	0.386387	−	0.922337i	$-0.373723\pi$
$383$	−4.28958	−	2.47659i	−0.219187	−	0.126548i	−0.605574	+	0.795789i	$0.707056\pi$
$384$	−6.41801	+	90.8480i	−0.327518	+	4.63607i
$385$	−1.14251	+	0.659631i	−0.0582279	+	0.0336179i
$386$	−76.3162			−3.88439
$387$	1.35727	−	1.73212i	0.0689941	−	0.0880485i
$388$			13.8696i			0.704123i
$389$	−2.65062	−	4.59101i	−0.134392	−	0.232773i	0.790973	−	0.611851i	$-0.209575\pi$
$389$	−2.65062	−	4.59101i	−0.134392	−	0.232773i	−0.925365	+	0.379078i	$0.876241\pi$
$390$	−15.1602	−	8.24780i	−0.767669	−	0.417644i
$391$	−17.5073	+	30.3236i	−0.885384	+	1.53353i
$392$	−53.2440	−	30.7404i	−2.68923	−	1.55263i
$393$	−2.97575	−	6.11228i	−0.150107	−	0.308324i
$394$	4.39271	+	7.60839i	0.221301	+	0.383305i
$395$		−	6.73913i		−	0.339083i
$396$	−22.0163	+	8.85853i	−1.10636	+	0.445158i
$397$			8.13319i			0.408193i	0.978951	+	0.204097i	$0.0654257\pi$
$397$			8.13319i			0.408193i	−0.978951	+	0.204097i	$0.934574\pi$
$398$	−19.8057	+	11.4348i	−0.992771	+	0.573177i
$399$	6.74769	+	0.476694i	0.337807	+	0.0238645i
$400$	8.25283	−	14.2943i	0.412641	−	0.714716i
$401$	10.0017	+	5.77447i	0.499459	+	0.288363i	0.728490	−	0.685056i	$-0.240222\pi$
$401$	10.0017	+	5.77447i	0.499459	+	0.288363i	−0.229031	+	0.973419i	$0.573556\pi$
$402$	30.3911	−	44.9873i	1.51577	−	2.24376i
$403$	10.7174	−	23.5094i	0.533869	−	1.17109i
$404$	87.0770			4.33224
$405$	−8.73885	+	2.15231i	−0.434237	+	0.106949i
$406$	22.2670			1.10509
$407$	−3.59194	−	6.22143i	−0.178046	−	0.308385i
$408$	−64.4471	−	43.5372i	−3.19061	−	2.15541i
$409$	18.1368	+	10.4713i	0.896809	+	0.517773i	0.876163	−	0.482014i	$-0.160095\pi$
$409$	18.1368	+	10.4713i	0.896809	+	0.517773i	0.0206452	+	0.999787i	$0.493428\pi$
$410$	14.1988	+	8.19769i	0.701229	+	0.404855i
$411$	1.33428	−	18.8870i	0.0658151	−	0.931625i
$412$	17.6748	+	30.6136i	0.870773	+	1.50822i
$413$	2.02042			0.0994184
$414$	−60.2905	+	24.2587i	−2.96312	+	1.19225i
$415$	−15.1366			−0.743027
$416$	38.1530	−	83.6919i	1.87061	−	4.10333i
$417$	2.31340	+	4.75179i	0.113288	+	0.232696i
$418$	−13.9508	−	8.05451i	−0.682357	−	0.393959i
$419$	−12.0859	+	20.9334i	−0.590435	+	1.02266i	0.403738	+	0.914874i	$0.367711\pi$
$419$	−12.0859	+	20.9334i	−0.590435	+	1.02266i	−0.994174	+	0.107789i	$0.965623\pi$
$420$	−4.01838	−	8.25387i	−0.196077	−	0.402748i
$421$	−21.6880	+	12.5216i	−1.05701	+	0.610265i	−0.924604	−	0.380930i	$-0.875604\pi$
$421$	−21.6880	+	12.5216i	−1.05701	+	0.610265i	−0.132407	+	0.991195i	$0.542270\pi$
$422$			7.25162i			0.353004i
$423$	8.27979	+	6.48797i	0.402577	+	0.315456i
$424$		−	51.5932i		−	2.50559i
$425$	2.23348	+	3.86850i	0.108340	+	0.187650i
$426$	−12.4623	−	0.880404i	−0.603799	−	0.0426557i
$427$	−5.90079	−	3.40682i	−0.285559	−	0.164868i
$428$	5.29110	−	9.16446i	0.255755	−	0.442981i
$429$	8.76029	−	0.222049i	0.422951	−	0.0107206i
$430$	−1.01357	−	1.75555i	−0.0488787	−	0.0846603i
$431$		−	36.5394i		−	1.76004i	−0.474934	−	0.880021i	$-0.657528\pi$
$431$		−	36.5394i		−	1.76004i	0.474934	−	0.880021i	$-0.342472\pi$
$432$	−26.3280	−	81.6249i	−1.26671	−	3.92718i
$433$	−5.44159			−0.261506			−0.130753	−	0.991415i	$-0.541739\pi$
$433$	−5.44159			−0.261506			−0.130753	+	0.991415i	$0.541739\pi$
$434$	16.1243	−	9.30937i	0.773992	−	0.446864i
$435$	−12.3001	−	8.30934i	−0.589745	−	0.398402i
$436$	19.5425	+	11.2829i	0.935917	+	0.540352i
$437$	−28.1993	−	16.2809i	−1.34896	−	0.778821i
$438$	−11.3752	−	0.803610i	−0.543530	−	0.0383980i
$439$	−10.8326	−	18.7626i	−0.517010	−	0.895488i	−0.999805	−	0.0197542i	$-0.993712\pi$
$439$	−10.8326	−	18.7626i	−0.517010	−	0.895488i	0.482795	−	0.875734i	$-0.339622\pi$
$440$			14.1056i			0.672459i
$441$	18.1660	+	2.57957i	0.865049	+	0.122837i
$442$	25.8426	+	36.2394i	1.22921	+	1.72373i
$443$	−11.6711	−	20.2149i	−0.554510	−	0.960440i	−0.997941	−	0.0641315i	$-0.979572\pi$
$443$	−11.6711	−	20.2149i	−0.554510	−	0.960440i	0.443431	−	0.896308i	$-0.353761\pi$
$444$	44.9455	−	21.8816i	2.13302	−	1.03846i
$445$	2.68391	−	4.64866i	0.127229	−	0.220368i
$446$	24.0717	−	41.6933i	1.13983	−	1.97424i
$447$	−4.43416	+	2.15876i	−0.209728	+	0.102106i
$448$	30.5233	−	17.6226i	1.44209	−	0.832592i
$449$		−	38.0975i		−	1.79793i	−0.438017	−	0.898967i	$-0.644319\pi$
$449$		−	38.0975i		−	1.79793i	0.438017	−	0.898967i	$-0.355681\pi$
$450$	−1.16559	+	8.20842i	−0.0549466	+	0.386949i
$451$	−8.32480			−0.391999
$452$	−6.23000	−	10.7907i	−0.293035	−	0.507551i
$453$	−1.05450	+	14.9266i	−0.0495446	+	0.701313i
$454$	−30.4915	+	52.8129i	−1.43104	+	2.47863i
$455$	0.324485	+	3.37426i	0.0152121	+	0.158188i
$456$	40.4873	−	59.9324i	1.89599	−	2.80659i
$457$	27.7372	−	16.0141i	1.29749	−	0.749107i	0.317521	−	0.948251i	$-0.397149\pi$
$457$	27.7372	−	16.0141i	1.29749	−	0.749107i	0.979970	+	0.199144i	$0.0638162\pi$
$458$	0.724186			0.0338390
$459$	22.6934	+	4.87454i	1.05924	+	0.227524i
$460$			44.1894i			2.06034i
$461$	−5.01318	+	2.89436i	−0.233487	+	0.134804i	−0.612180	−	0.790719i	$-0.709707\pi$
$461$	−5.01318	+	2.89436i	−0.233487	+	0.134804i	0.378693	+	0.925522i	$0.376374\pi$
$462$	5.23274	+	3.53498i	0.243449	+	0.164462i
$463$	−16.4158	−	9.47766i	−0.762906	−	0.440464i	0.0674320	−	0.997724i	$-0.478519\pi$
$463$	−16.4158	−	9.47766i	−0.762906	−	0.440464i	−0.830338	+	0.557260i	$0.811853\pi$
$464$	70.7272	−	122.503i	3.28343	−	5.68707i
$465$	−12.3809	−	0.874654i	−0.574150	−	0.0405611i
$466$	1.32674	−	0.765992i	0.0614599	−	0.0354839i
$467$	−17.8196			−0.824594			−0.412297	−	0.911050i	$-0.635273\pi$
$467$	−17.8196			−0.824594			−0.412297	+	0.911050i	$0.635273\pi$
$468$	−2.75445	+	60.9158i	−0.127324	+	2.81583i
$469$	−10.6634			−0.492391
$470$	8.39181	−	4.84501i	0.387085	−	0.223484i
$471$	12.4241	+	25.5194i	0.572471	+	1.17587i
$472$	10.8012	−	18.7083i	0.497167	−	0.861118i
$473$	0.891387	+	0.514643i	0.0409860	+	0.0236633i
$474$	−29.0034	+	14.1203i	−1.33217	+	0.648565i
$475$	−3.59750	+	2.07702i	−0.165065	+	0.0953001i
$476$			23.6754i			1.08516i
$477$	5.74753	+	14.2844i	0.263161	+	0.654039i
$478$	−78.8878			−3.60825
$479$	22.1315	−	12.7776i	1.01121	−	0.583825i	0.0996673	−	0.995021i	$-0.468222\pi$
$479$	22.1315	−	12.7776i	1.01121	−	0.583825i	0.911547	+	0.411196i	$0.134889\pi$
$480$	−44.0751	−	3.11371i	−2.01174	−	0.142121i
$481$	−18.3741	+	1.76695i	−0.837788	+	0.0805659i
$482$	−12.5423	+	21.7240i	−0.571288	+	0.989500i
$483$	10.5771	+	7.14539i	0.481277	+	0.325126i
$484$	25.4557	+	44.0906i	1.15708	+	2.00412i
$485$	−2.46028			−0.111715
$486$	27.5731	+	33.1001i	1.25074	+	1.50145i
$487$			1.02317i			0.0463641i	0.999731	+	0.0231821i	$0.00737974\pi$
$487$			1.02317i			0.0463641i	−0.999731	+	0.0231821i	$0.992620\pi$
$488$	−63.0916	+	36.4259i	−2.85602	+	1.64892i
$489$	−22.0129	−	14.8708i	−0.995460	−	0.672482i
$490$	8.45117	−	14.6379i	0.381785	−	0.661271i
$491$	17.8296	−	30.8817i	0.804638	−	1.39367i	−0.111898	−	0.993720i	$-0.535693\pi$
$491$	17.8296	−	30.8817i	0.804638	−	1.39367i	0.916535	−	0.399953i	$-0.130974\pi$
$492$	4.08218	−	57.7840i	0.184039	−	2.60511i
$493$	19.1410	+	33.1533i	0.862069	+	1.49315i
$494$	−33.7007	+	24.0322i	−1.51627	+	1.08126i
$495$	−1.57138	−	3.90538i	−0.0706283	−	0.175534i
$496$		−	118.278i		−	5.31085i
$497$	1.22693	+	2.12511i	0.0550353	+	0.0953240i
$498$	31.7152	+	65.1440i	1.42119	+	2.91917i
$499$	−16.9361	−	9.77806i	−0.758164	−	0.437726i	0.0704724	−	0.997514i	$-0.477549\pi$
$499$	−16.9361	−	9.77806i	−0.758164	−	0.437726i	−0.828636	+	0.559788i	$0.810883\pi$
$500$	4.88215	+	2.81871i	0.218336	+	0.126057i
$501$	−33.7359	+	16.4243i	−1.50721	+	0.733782i
$502$	42.8427	−	24.7353i	1.91216	−	1.10399i
$503$	−0.0328439			−0.00146444			−0.000732219	−	1.00000i	$-0.500233\pi$
$503$	−0.0328439			−0.00146444			−0.000732219		1.00000i	$0.500233\pi$
$504$	−17.4876	+	22.3172i	−0.778958	+	0.994086i
$505$			15.4463i			0.687349i
$506$	−15.1987	−	26.3250i	−0.675665	−	1.17029i
$507$	8.81787	−	20.7182i	0.391616	−	0.920129i
$508$	24.2188	−	41.9483i	1.07454	−	1.86115i
$509$	26.4775	+	15.2868i	1.17359	+	0.677574i	0.954524	−	0.298136i	$-0.0963647\pi$
$509$	26.4775	+	15.2868i	1.17359	+	0.677574i	0.219069	+	0.975709i	$0.429698\pi$
$510$	11.9693	−	17.7178i	0.530008	−	0.784558i
$511$	1.11991	+	1.93974i	0.0495419	+	0.0858091i
$512$		−	89.2216i		−	3.94307i
$513$	−4.53306	+	21.1036i	−0.200140	+	0.931748i
$514$			16.6846i			0.735927i
$515$	−5.43043	+	3.13526i	−0.239293	+	0.138156i
$516$	−4.00934	+	5.93493i	−0.176501	+	0.261271i
$517$	−2.46007	+	4.26096i	−0.108194	+	0.187397i
$518$	−11.5198	−	6.65093i	−0.506149	−	0.292225i
$519$	32.0285	+	2.26267i	1.40590	+	0.0993203i
$520$	32.9790	+	15.0343i	1.44622	+	0.659296i
$521$	16.9685			0.743404			0.371702	−	0.928352i	$-0.378774\pi$
$521$	16.9685			0.743404			0.371702	+	0.928352i	$0.378774\pi$
$522$	−9.98921	+	70.3467i	−0.437216	+	3.07899i
$523$	39.1230			1.71073			0.855365	−	0.518025i	$-0.173333\pi$
$523$	39.1230			1.71073			0.855365	+	0.518025i	$0.173333\pi$
$524$	11.0632	+	19.1621i	0.483299	+	0.837098i
$525$	1.46412	−	0.712805i	0.0638995	−	0.0311093i
$526$	−60.8722	−	35.1446i	−2.65415	−	1.53238i
$527$	27.7213	+	16.0049i	1.20756	+	0.697185i
$528$	36.0687	−	17.5600i	1.56969	−	0.764199i
$529$	−19.2218	−	33.2931i	−0.835729	−	1.44752i
$530$	14.1840			0.616114
$531$	−0.906380	+	6.38297i	−0.0393335	+	0.276997i
$532$	−22.0169			−0.954552
$533$	−8.87286	+	19.4634i	−0.384326	+	0.843053i
$534$	−25.6301	−	1.81065i	−1.10912	−	0.0783546i
$535$	1.62565	+	0.938568i	0.0702829	+	0.0405778i
$536$	−57.0069	+	98.7389i	−2.46232	+	4.26487i
$537$	13.2840	−	19.6640i	0.573246	−	0.848563i
$538$	8.89476	−	5.13539i	0.383480	−	0.221402i
$539$			8.58221i			0.369662i
$540$	27.8785	−	8.99221i	1.19970	−	0.386963i
$541$		−	34.2098i		−	1.47079i	−0.677637	−	0.735397i	$-0.736996\pi$
$541$		−	34.2098i		−	1.47079i	0.677637	−	0.735397i	$-0.263004\pi$
$542$	25.6878	+	44.4926i	1.10338	+	1.91112i
$543$	−9.59975	+	14.2103i	−0.411965	+	0.609822i
$544$	98.6861	+	56.9764i	4.23113	+	2.44284i
$545$	−2.00143	+	3.46657i	−0.0857317	+	0.148492i
$546$	13.8420	−	8.46645i	0.592384	−	0.362331i
$547$	0.907849	+	1.57244i	0.0388168	+	0.0672327i	0.884781	−	0.466007i	$-0.154308\pi$
$547$	0.907849	+	1.57244i	0.0388168	+	0.0672327i	−0.845964	+	0.533240i	$0.820974\pi$
$548$			61.6258i			2.63252i
$549$	13.4101	−	17.1136i	0.572328	−	0.730391i
$550$	−3.87792			−0.165355
$551$	−30.8308	+	17.8002i	−1.31344	+	0.758312i
$552$	122.709	−	59.7406i	5.22285	−	2.54273i
$553$	5.48706	+	3.16796i	0.233334	+	0.134715i
$554$	68.7970	+	39.7199i	2.92290	+	1.68754i
$555$	3.88150	+	7.97272i	0.164760	+	0.338423i
$556$	−8.60074	−	14.8969i	−0.364753	−	0.631770i
$557$			8.40849i			0.356279i	0.984005	+	0.178140i	$0.0570078\pi$
$557$			8.40849i			0.356279i	−0.984005	+	0.178140i	$0.942992\pi$
$558$	22.1769	+	55.1166i	0.938824	+	2.33327i
$559$	2.15331	−	1.53554i	0.0910752	−	0.0649464i
$560$	7.75904	+	13.4391i	0.327879	+	0.567904i
$561$	−0.765071	+	10.8297i	−0.0323013	+	0.457231i
$562$	−7.69530	+	13.3286i	−0.324607	+	0.562235i
$563$	1.50627	−	2.60894i	0.0634817	−	0.109954i	−0.832538	−	0.553968i	$-0.813113\pi$
$563$	1.50627	−	2.60894i	0.0634817	−	0.109954i	0.896019	+	0.444015i	$0.146446\pi$
$564$	−28.3699	−	19.1652i	−1.19459	−	0.807003i
$565$	1.91412	−	1.10512i	0.0805275	−	0.0464926i
$566$		−	35.0485i		−	1.47320i
$567$	2.35557	−	8.12702i	0.0989245	−	0.341303i
$568$	26.2368			1.10087
$569$	−1.56915	−	2.71784i	−0.0657820	−	0.113938i	0.831259	−	0.555886i	$-0.187621\pi$
$569$	−1.56915	−	2.71784i	−0.0657820	−	0.113938i	−0.897041	+	0.441948i	$0.854288\pi$
$570$	16.4766	+	11.1308i	0.690130	+	0.466217i
$571$	−0.656430	+	1.13697i	−0.0274708	+	0.0475807i	−0.879434	−	0.476021i	$-0.842079\pi$
$571$	−0.656430	+	1.13697i	−0.0274708	+	0.0475807i	0.851963	+	0.523602i	$0.175412\pi$
$572$	−28.3909	+	2.73021i	−1.18708	+	0.114156i
$573$	−18.0881	−	1.27785i	−0.755643	−	0.0533828i
$574$	−13.3493	+	7.70720i	−0.557187	+	0.321692i
$575$	−7.83859			−0.326892
$576$	41.9809	+	104.336i	1.74920	+	4.34732i
$577$		−	0.958966i		−	0.0399223i	−0.999801	−	0.0199611i	$-0.993646\pi$
$577$		−	0.958966i		−	0.0399223i	0.999801	−	0.0199611i	$-0.00635425\pi$
$578$	−7.06921	+	4.08141i	−0.294040	+	0.169764i
$579$	−43.0047	+	20.9367i	−1.78721	+	0.870101i
$580$	41.8403	+	24.1565i	1.73732	+	1.00304i
$581$	7.11548	−	12.3244i	0.295200	−	0.511301i
$582$	5.15493	+	10.5884i	0.213679	+	0.438902i
$583$	−6.23709	+	3.60098i	−0.258314	+	0.149137i
$584$	23.9483			0.990987
$585$	−10.8056	−	0.488601i	−0.446757	−	0.0202012i
$586$	88.2217			3.64441
$587$	1.95240	−	1.12722i	0.0805840	−	0.0465252i	−0.459167	−	0.888350i	$-0.651852\pi$
$587$	1.95240	−	1.12722i	0.0805840	−	0.0465252i	0.539751	+	0.841825i	$0.318519\pi$
$588$	−59.5708	−	4.20841i	−2.45666	−	0.173552i
$589$	−14.8837	+	25.7794i	−0.613274	+	1.06222i
$590$	5.14328	+	2.96948i	0.211746	+	0.122251i
$591$	4.56262	+	3.08227i	0.187681	+	0.126788i
$592$	−73.1808	+	42.2510i	−3.00771	+	1.73650i
$593$			27.3356i			1.12254i	0.827633	+	0.561270i	$0.189687\pi$
$593$			27.3356i			1.12254i	−0.827633	+	0.561270i	$0.810313\pi$
$594$	−13.5153	+	14.9456i	−0.554538	+	0.613225i
$595$	−4.19969			−0.172170
$596$	13.9011	−	8.02582i	0.569412	−	0.328750i
$597$	−8.02360	+	11.8771i	−0.328384	+	0.486099i
$598$	−77.7471	+	7.47655i	−3.17932	+	0.305739i
$599$	6.79637	−	11.7717i	0.277692	−	0.480977i	−0.693119	−	0.720824i	$-0.743764\pi$
$599$	6.79637	−	11.7717i	0.277692	−	0.480977i	0.970811	+	0.239847i	$0.0770972\pi$
$600$	1.22696	−	17.3679i	0.0500905	−	0.709040i
$601$	14.2702	+	24.7167i	0.582094	+	1.00822i	0.995231	+	0.0975469i	$0.0310996\pi$
$601$	14.2702	+	24.7167i	0.582094	+	1.00822i	−0.413137	+	0.910669i	$0.635567\pi$
$602$	1.90585			0.0776767
$603$	4.78371	−	33.6882i	0.194808	−	1.37189i
$604$		−	48.7036i		−	1.98172i
$605$	−7.82105	+	4.51549i	−0.317971	+	0.183581i
$606$	66.4766	−	32.3640i	2.70043	−	1.31470i
$607$	0.672883	−	1.16547i	0.0273115	−	0.0473048i	−0.852047	−	0.523466i	$-0.824639\pi$
$607$	0.672883	−	1.16547i	0.0273115	−	0.0473048i	0.879358	+	0.476161i	$0.157972\pi$
$608$	−52.9851	+	91.7728i	−2.14883	+	3.72188i
$609$	12.5476	−	6.10878i	0.508455	−	0.247540i
$610$	−10.0142	−	17.3451i	−0.405464	−	0.702285i
$611$	7.34011	+	10.2931i	0.296949	+	0.416416i
$612$	−74.7960	−	10.6210i	−3.02345	−	0.429329i
$613$		−	48.1040i		−	1.94290i	−0.237243	−	0.971450i	$-0.576244\pi$
$613$		−	48.1040i		−	1.94290i	0.237243	−	0.971450i	$-0.423756\pi$
$614$	2.20133	+	3.81281i	0.0888384	+	0.153873i
$615$	10.2501	+	0.724123i	0.413323	+	0.0291995i
$616$	−11.4849	−	6.63082i	−0.462741	−	0.267163i
$617$	22.4778	+	12.9776i	0.904923	+	0.522457i	0.878794	−	0.477201i	$-0.158349\pi$
$617$	22.4778	+	12.9776i	0.904923	+	0.522457i	0.0261287	+	0.999659i	$0.491682\pi$
$618$	24.8715	+	16.8019i	1.00048	+	0.675872i
$619$	−33.5563	+	19.3737i	−1.34874	+	0.778697i	−0.988071	−	0.153997i	$-0.950786\pi$
$619$	−33.5563	+	19.3737i	−1.34874	+	0.778697i	−0.360671	+	0.932693i	$0.617452\pi$
$620$	40.3973			1.62239
$621$	−27.3189	+	30.2101i	−1.09627	+	1.21229i
$622$		−	31.2336i		−	1.25235i
$623$	2.52332	+	4.37052i	0.101095	+	0.175101i
$624$	−2.61190	−	103.045i	−0.104560	−	4.12509i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−29.6755	−	17.1331i	−1.18607	−	0.684778i
$627$	−10.0711	−	0.711475i	−0.402199	−	0.0284136i
$628$	−46.1901	−	80.0037i	−1.84319	−	3.19249i
$629$		−	22.8689i		−	0.911844i
$630$	−6.13544	−	4.80768i	−0.244442	−	0.191543i
$631$		−	4.70806i		−	0.187425i	−0.995599	−	0.0937124i	$-0.970127\pi$
$631$		−	4.70806i		−	0.187425i	0.995599	−	0.0937124i	$-0.0298734\pi$
$632$	58.6680	−	33.8720i	2.33369	−	1.34736i
$633$	1.98942	+	4.08634i	0.0790725	+	0.162417i
$634$	−7.61172	+	13.1839i	−0.302300	+	0.523599i
$635$	7.44104	+	4.29609i	0.295289	+	0.170485i
$636$	−21.9367	−	45.0586i	−0.869846	−	1.78669i
$637$	20.0652	+	9.14722i	0.795013	+	0.362426i
$638$	−33.2340			−1.31575
$639$	−7.26411	+	2.92281i	−0.287364	+	0.115625i
$640$	52.5819			2.07848
$641$	−10.2802	−	17.8059i	−0.406045	−	0.703291i	0.588397	−	0.808572i	$-0.299759\pi$
$641$	−10.2802	−	17.8059i	−0.406045	−	0.703291i	−0.994443	+	0.105281i	$0.966426\pi$
$642$	0.633189	−	8.96291i	0.0249900	−	0.353738i
$643$	20.7509	+	11.9805i	0.818336	+	0.472467i	0.849842	−	0.527037i	$-0.176697\pi$
$643$	20.7509	+	11.9805i	0.818336	+	0.472467i	−0.0315062	+	0.999504i	$0.510030\pi$
$644$	−35.9794	−	20.7727i	−1.41779	−	0.818560i
$645$	−1.05277	−	0.711201i	−0.0414530	−	0.0280035i
$646$	−25.6404	−	44.4105i	−1.00881	−	1.74731i
$647$	−13.3974			−0.526705			−0.263353	−	0.964700i	$-0.584828\pi$
$647$	−13.3974			−0.526705			−0.263353	+	0.964700i	$0.584828\pi$
$648$	−62.6600	−	65.2589i	−2.46152	−	2.56361i
$649$	−3.01552			−0.118369
$650$	−4.13323	+	9.06658i	−0.162118	+	0.355621i
$651$	6.53220	−	9.66946i	0.256017	−	0.378976i
$652$	74.8797	+	43.2318i	2.93251	+	1.69309i
$653$	15.5616	−	26.9534i	0.608972	−	1.05477i	−0.382439	−	0.923981i	$-0.624916\pi$
$653$	15.5616	−	26.9534i	0.608972	−	1.05477i	0.991410	−	0.130789i	$-0.0417510\pi$
$654$	19.1127	+	1.35023i	0.747367	+	0.0527981i
$655$	−3.39908	+	1.96246i	−0.132813	+	0.0766797i
$656$			97.9221i			3.82322i
$657$	−6.63049	+	2.66787i	−0.258680	+	0.104083i
$658$			9.11025i			0.355155i
$659$	16.3755	+	28.3632i	0.637899	+	1.10487i	0.985893	+	0.167377i	$0.0535296\pi$
$659$	16.3755	+	28.3632i	0.637899	+	1.10487i	−0.347994	+	0.937497i	$0.613137\pi$
$660$	5.99751	+	12.3191i	0.233453	+	0.479519i
$661$	0.856192	+	0.494323i	0.0333020	+	0.0192269i	0.516559	−	0.856252i	$-0.327213\pi$
$661$	0.856192	+	0.494323i	0.0333020	+	0.0192269i	−0.483257	+	0.875479i	$0.660546\pi$
$662$	3.98156	−	6.89626i	0.154748	−	0.268031i
$663$	24.5044	+	13.3314i	0.951674	+	0.517750i
$664$	−76.0791	−	131.773i	−2.95244	−	5.11378i
$665$		−	3.90549i		−	0.151448i
$666$	26.1797	−	33.4099i	1.01444	−	1.29461i
$667$	−67.1772			−2.60111
$668$	105.762	−	61.0620i	4.09207	−	2.36256i
$669$	2.12631	−	30.0983i	0.0822080	−	1.16367i
$670$	−27.1453	−	15.6724i	−1.04872	−	0.605476i
$671$	8.80705	+	5.08475i	0.339992	+	0.196295i
$672$	23.2542	−	34.4226i	0.897050	−	1.32788i
$673$	−16.9228	−	29.3112i	−0.652327	−	1.12986i	−0.982557	−	0.185963i	$-0.940459\pi$
$673$	−16.9228	−	29.3112i	−0.652327	−	1.12986i	0.330229	−	0.943901i	$-0.392874\pi$
$674$		−	68.9212i		−	2.65475i
$675$	1.59509	+	4.94527i	0.0613951	+	0.190343i
$676$	−23.8768	+	69.2878i	−0.918337	+	2.66492i
$677$	−4.26394	−	7.38536i	−0.163876	−	0.283842i	0.772379	−	0.635162i	$-0.219067\pi$
$677$	−4.26394	−	7.38536i	−0.163876	−	0.283842i	−0.936256	+	0.351319i	$0.885733\pi$
$678$	−8.76671	−	5.92234i	−0.336683	−	0.227446i
$679$	1.15654	−	2.00318i	0.0443838	−	0.0768750i
$680$	−22.4517	+	38.8874i	−0.860982	+	1.49126i
$681$	−2.69340	+	38.1255i	−0.103211	+	1.46097i
$682$	−24.0659	+	13.8944i	−0.921529	+	0.532045i
$683$			14.2430i			0.544992i	0.962157	+	0.272496i	$0.0878492\pi$
$683$			14.2430i			0.544992i	−0.962157	+	0.272496i	$0.912151\pi$
$684$	9.87698	−	69.5563i	0.377656	−	2.65955i
$685$	−10.9316			−0.417674
$686$	17.0393	+	29.5130i	0.650565	+	1.12681i
$687$	0.408084	−	0.198675i	0.0155694	−	0.00757991i
$688$	6.05359	−	10.4851i	0.230791	−	0.399742i
$689$	1.77139	+	18.4204i	0.0674848	+	0.701760i
$690$	16.4239	+	33.7352i	0.625248	+	1.28428i
$691$	−25.0299	+	14.4510i	−0.952182	+	0.549742i	−0.893758	−	0.448549i	$-0.851941\pi$
$691$	−25.0299	+	14.4510i	−0.952182	+	0.549742i	−0.0584238	+	0.998292i	$0.518607\pi$
$692$	−104.505			−3.97269
$693$	3.91848	+	0.556423i	0.148851	+	0.0211367i
$694$			44.1389i			1.67549i
$695$	2.64251	−	1.52565i	0.100236	−	0.0578713i
$696$	10.5151	−	148.844i	0.398575	−	5.64190i
$697$	−22.9504	−	13.2504i	−0.869309	−	0.501896i
$698$	24.7700	−	42.9030i	0.937560	−	1.62390i
$699$	0.537482	−	0.795621i	0.0203294	−	0.0300932i
$700$	−4.59004	+	2.65006i	−0.173487	+	0.100163i
$701$	−11.3665			−0.429307			−0.214654	−	0.976690i	$-0.568862\pi$
$701$	−11.3665			−0.429307			−0.214654	+	0.976690i	$0.568862\pi$
$702$	20.5378	+	47.5282i	0.775149	+	1.79384i
$703$	21.2669			0.802096
$704$	−45.5567	+	26.3022i	−1.71698	+	0.991300i
$705$	3.39965	−	5.03242i	0.128038	−	0.189532i
$706$	−22.4229	+	38.8377i	−0.843898	+	1.46167i
$707$	−12.5765	−	7.26104i	−0.472987	−	0.273079i
$708$	1.47870	−	20.9313i	0.0555731	−	0.786647i
$709$	−10.7632	+	6.21412i	−0.404220	+	0.233376i	−0.688303	−	0.725423i	$-0.741644\pi$
$709$	−10.7632	+	6.21412i	−0.404220	+	0.233376i	0.284083	+	0.958800i	$0.408311\pi$
$710$			7.21303i			0.270700i
$711$	−12.4699	+	15.9137i	−0.467656	+	0.596811i
$712$	53.9590			2.02220
$713$	−48.6453	+	28.0854i	−1.82178	+	1.05180i
$714$	8.79945	+	18.0743i	0.329311	+	0.676415i
$715$	−0.484301	−	5.03615i	−0.0181118	−	0.188341i
$716$	−38.6186	+	66.8894i	−1.44324	+	2.49977i
$717$	−44.4538	+	21.6422i	−1.66016	+	0.808244i
$718$	12.1247	+	21.0005i	0.452488	+	0.783732i
$719$	−24.9731			−0.931339			−0.465670	−	0.884959i	$-0.654186\pi$
$719$	−24.9731			−0.931339			−0.465670	+	0.884959i	$0.654186\pi$
$720$	−45.9378	+	18.4837i	−1.71200	+	0.688846i
$721$		−	5.89534i		−	0.219554i
$722$	−4.17399	+	2.40985i	−0.155340	+	0.0896854i
$723$	−1.10790	+	15.6825i	−0.0412032	+	0.583238i
$724$	27.9079	−	48.3380i	1.03719	−	1.79647i
$725$	−4.28503	+	7.42189i	−0.159142	+	0.275642i
$726$	35.8206	+	24.1986i	1.32943	+	0.898095i
$727$	12.4131	+	21.5002i	0.460378	+	0.797398i	0.998980	−	0.0451624i	$-0.0143805\pi$
$727$	12.4131	+	21.5002i	0.460378	+	0.797398i	−0.538602	+	0.842561i	$0.681047\pi$
$728$	−27.7439	+	19.7844i	−1.02826	+	0.733258i
$729$	24.6184	+	11.0876i	0.911792	+	0.410653i
$730$			6.58387i			0.243680i
$731$	1.63829	+	2.83761i	0.0605945	+	0.104953i
$732$	−39.6129	+	58.6381i	−1.46414	+	2.16732i
$733$	32.5827	+	18.8116i	1.20347	+	0.694823i	0.961325	−	0.275417i	$-0.0888161\pi$
$733$	32.5827	+	18.8116i	1.20347	+	0.694823i	0.242144	+	0.970240i	$0.422149\pi$
$734$	−30.0438	−	17.3458i	−1.10894	−	0.640245i
$735$	0.746514	−	10.5670i	0.0275356	−	0.389771i
$736$	−173.174	+	99.9819i	−6.38327	+	3.68538i
$737$	15.9154			0.586250
$738$	−18.3602	−	45.6309i	−0.675848	−	1.67970i
$739$		−	33.7094i		−	1.24002i	−0.784594	−	0.620009i	$-0.787129\pi$
$739$		−	33.7094i		−	1.24002i	0.784594	−	0.620009i	$-0.212871\pi$
$740$	−14.4306	−	24.9945i	−0.530479	−	0.918817i
$741$	−12.3975	+	22.7878i	−0.455434	+	0.837132i
$742$	−6.66767	+	11.5487i	−0.244778	+	0.423968i
$743$	−25.8146	−	14.9041i	−0.947046	−	0.546777i	−0.0548841	−	0.998493i	$-0.517479\pi$
$743$	−25.8146	−	14.9041i	−0.947046	−	0.546777i	−0.892162	+	0.451715i	$0.850812\pi$
$744$	−54.6140	−	112.179i	−2.00224	−	4.11267i
$745$	1.42367	+	2.46587i	0.0521592	+	0.0903423i
$746$			86.3650i			3.16205i
$747$	35.7434	+	28.0082i	1.30778	+	1.02477i
$748$		−	35.3360i		−	1.29201i
$749$	−1.52838	+	0.882412i	−0.0558459	+	0.0322426i
$750$	4.77477	+	0.337317i	0.174350	+	0.0123171i
$751$	12.3434	−	21.3793i	0.450416	−	0.780143i	−0.547996	−	0.836481i	$-0.684609\pi$
$751$	12.3434	−	21.3793i	0.450416	−	0.780143i	0.998412	+	0.0563380i	$0.0179424\pi$
$752$	50.1205	+	28.9371i	1.82771	+	1.05523i
$753$	17.3562	−	25.6920i	0.632496	−	0.936269i
$754$	−35.4220	+	77.7011i	−1.28999	+	2.82971i
$755$	8.63935			0.314418
$756$	−5.78372	+	26.9261i	−0.210352	+	0.979291i
$757$	8.67812			0.315412			0.157706	−	0.987486i	$-0.449590\pi$
$757$	8.67812			0.315412			0.157706	+	0.987486i	$0.449590\pi$
$758$	−28.8500	−	49.9696i	−1.04788	−	1.81498i
$759$	−15.7866	−	10.6646i	−0.573018	−	0.387102i
$760$	−36.1632	−	20.8789i	−1.31178	−	0.757356i
$761$	3.55858	+	2.05455i	0.128999	+	0.0744773i	0.563111	−	0.826382i	$-0.309604\pi$
$761$	3.55858	+	2.05455i	0.128999	+	0.0744773i	−0.434112	+	0.900859i	$0.642938\pi$
$762$	2.89828	−	41.0257i	0.104994	−	1.48620i
$763$	−1.88168	−	3.25916i	−0.0681213	−	0.117990i
$764$	59.0194			2.13525
$765$	1.88402	−	13.2678i	0.0681169	−	0.479697i
$766$	13.6886			0.494588
$767$	−3.21405	+	7.05029i	−0.116053	+	0.254571i
$768$	−53.3280	−	109.537i	−1.92431	−	3.95259i
$769$	20.4103	+	11.7839i	0.736013	+	0.424937i	0.820618	−	0.571477i	$-0.193629\pi$
$769$	20.4103	+	11.7839i	0.736013	+	0.424937i	−0.0846050	+	0.996415i	$0.526963\pi$
$770$	1.82295	−	3.15744i	0.0656945	−	0.113786i
$771$	4.57729	+	9.40189i	0.164847	+	0.338601i
$772$	134.820	−	77.8384i	4.85228	−	2.80146i

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39334 + 1.38179i) q^{2} +(-0.969577 + 1.43524i) q^{3} +(2.81871 - 4.88215i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.337317 - 4.77477i) q^{6} +(-0.814209 + 0.470084i) q^{7} +10.0523i q^{8} +(-1.11984 - 2.78316i) q^{9} +O(q^{10})\)	\(q+(-2.39334 + 1.38179i) q^{2} +(-0.969577 + 1.43524i) q^{3} +(2.81871 - 4.88215i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.337317 - 4.77477i) q^{6} +(-0.814209 + 0.470084i) q^{7} +10.0523i q^{8} +(-1.11984 - 2.78316i) q^{9} -2.76359 q^{10} +(1.21522 - 0.701610i) q^{11} +(4.27411 + 8.77915i) q^{12} +(-0.345136 - 3.58899i) q^{13} +(1.29912 - 2.25014i) q^{14} +(-1.55730 + 0.758168i) q^{15} +(-8.25283 - 14.2943i) q^{16} +4.46696 q^{17} +(6.52590 + 5.11364i) q^{18} +4.15403i q^{19} +(4.88215 - 2.81871i) q^{20} +(0.114754 - 1.62437i) q^{21} +(-1.93896 + 3.35838i) q^{22} +(-3.91930 + 6.78842i) q^{23} +(-14.4275 - 9.74651i) q^{24} +(0.500000 + 0.866025i) q^{25} +(5.78528 + 8.11277i) q^{26} +(5.08027 + 1.09124i) q^{27} +5.30012i q^{28} +(4.28503 + 7.42189i) q^{29} +(2.67951 - 3.96642i) q^{30} +(6.20587 + 3.58296i) q^{31} +(22.0925 + 12.7551i) q^{32} +(-0.171273 + 2.42440i) q^{33} +(-10.6909 + 6.17241i) q^{34} -0.940168 q^{35} +(-16.7443 - 2.37768i) q^{36} -5.11958i q^{37} +(-5.74002 - 9.94200i) q^{38} +(5.48571 + 2.98445i) q^{39} +(-5.02616 + 8.70557i) q^{40} +(-5.13782 - 2.96632i) q^{41} +(1.96990 + 4.04623i) q^{42} +(0.366759 + 0.635244i) q^{43} -7.91053i q^{44} +(0.421768 - 2.97020i) q^{45} -21.6626i q^{46} +(-3.03656 + 1.75316i) q^{47} +(28.5176 + 2.01464i) q^{48} +(-3.05804 + 5.29668i) q^{49} +(-2.39334 - 1.38179i) q^{50} +(-4.33106 + 6.41116i) q^{51} +(-18.4948 - 8.43133i) q^{52} -5.13246 q^{53} +(-13.6667 + 4.40818i) q^{54} +1.40322 q^{55} +(-4.72544 - 8.18470i) q^{56} +(-5.96204 - 4.02766i) q^{57} +(-20.5110 - 11.8421i) q^{58} +(-1.86109 - 1.07450i) q^{59} +(-0.688089 + 9.74002i) q^{60} +(3.62363 + 6.27631i) q^{61} -19.8036 q^{62} +(2.22010 + 1.73965i) q^{63} -37.4883 q^{64} +(1.49560 - 3.28073i) q^{65} +(-2.94011 - 6.03908i) q^{66} +(9.82249 + 5.67102i) q^{67} +(12.5911 - 21.8083i) q^{68} +(-5.94297 - 12.2070i) q^{69} +(2.25014 - 1.29912i) q^{70} -2.61002i q^{71} +(27.9772 - 11.2570i) q^{72} -2.38236i q^{73} +(7.07420 + 12.2529i) q^{74} +(-1.72774 - 0.122057i) q^{75} +(20.2806 + 11.7090i) q^{76} +(-0.659631 + 1.14251i) q^{77} +(-17.2531 + 0.437318i) q^{78} +(-3.36957 - 5.83626i) q^{79} -16.5057i q^{80} +(-6.49192 + 6.23338i) q^{81} +16.3954 q^{82} +(-13.1087 + 7.56831i) q^{83} +(-7.60695 - 5.13887i) q^{84} +(3.86850 + 2.23348i) q^{85} +(-1.75555 - 1.01357i) q^{86} +(-14.8069 - 1.04604i) q^{87} +(7.05281 + 12.2158i) q^{88} -5.36781i q^{89} +(3.09478 + 7.69150i) q^{90} +(1.96814 + 2.75995i) q^{91} +(22.0947 + 38.2692i) q^{92} +(-11.1595 + 5.43297i) q^{93} +(4.84501 - 8.39181i) q^{94} +(-2.07702 + 3.59750i) q^{95} +(-39.7270 + 19.3410i) q^{96} +(-2.13066 + 1.23014i) q^{97} -16.9023i q^{98} +(-3.31355 - 2.59647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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