LMFDB - Embedded newform 585.2.bt.b.376.1

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			376.1
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.1

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	−0.952618	−	0.304169i	$-0.901621\pi$
$2$	−2.39334	−	1.38179i	−1.69235	−	0.977076i	−0.739727	−	0.672907i	$-0.765045\pi$
$3$	−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	0.338174	−	0.941084i	$-0.390191\pi$
$7$	−0.814209	−	0.470084i	−0.307742	−	0.177675i	−0.645916	+	0.763409i	$0.723524\pi$
$8$		−	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	0.671886	−	0.740654i	$-0.265484\pi$
$11$	1.21522	+	0.701610i	0.366404	+	0.211543i	−0.305482	+	0.952198i	$0.598818\pi$
$12$	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	$-0.841905\pi$
$19$		−	4.15403i		−	0.953001i	0.879174	−	0.476500i	$-0.158095\pi$
$20$	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	−0.907716	−	0.419586i	$-0.862175\pi$
$23$	−3.91930	−	6.78842i	−0.817230	−	1.41548i	0.0904860	−	0.995898i	$-0.471158\pi$
$24$	−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	−0.126677	−	0.991944i	$-0.540431\pi$
$29$	4.28503	−	7.42189i	0.795710	−	1.37821i	0.922387	−	0.386266i	$-0.126235\pi$
$30$	2.67951	+	3.96642i	0.489210	+	0.724166i
$31$	6.20587	−	3.58296i	1.11461	−	0.643519i	0.174588	−	0.984642i	$-0.444141\pi$
$31$	6.20587	−	3.58296i	1.11461	−	0.643519i	0.940019	+	0.341123i	$0.110807\pi$
$32$	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	$0.138260\pi$
$37$			5.11958i			0.841653i	−0.907141	+	0.420827i	$0.861740\pi$
$38$	−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	−0.844307	−	0.535860i	$-0.819988\pi$
$41$	−5.13782	+	2.96632i	−0.802392	+	0.463261i	0.0419147	+	0.999121i	$0.486654\pi$
$42$	1.96990	−	4.04623i	0.303962	−	0.624347i
$43$	0.366759	−	0.635244i	0.0559302	−	0.0968739i	−0.836705	−	0.547654i	$-0.815521\pi$
$43$	0.366759	−	0.635244i	0.0559302	−	0.0968739i	0.892635	+	0.450780i	$0.148854\pi$
$44$			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	0.261911	−	0.965092i	$-0.415647\pi$
$47$	−3.03656	−	1.75316i	−0.442928	−	0.255725i	−0.704839	+	0.709367i	$0.748981\pi$
$48$	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	−0.616230	−	0.787566i	$-0.711341\pi$
$59$	−1.86109	+	1.07450i	−0.242293	+	0.139888i	0.373937	+	0.927454i	$0.378008\pi$
$60$	−0.688089	−	9.74002i	−0.0888319	−	1.25743i
$61$	3.62363	−	6.27631i	0.463959	−	0.803600i	−0.535195	−	0.844728i	$-0.679762\pi$
$61$	3.62363	−	6.27631i	0.463959	−	0.803600i	0.999154	+	0.0411286i	$0.0130953\pi$
$62$	−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	0.239452	−	0.970908i	$-0.423032\pi$
$67$	9.82249	−	5.67102i	1.20001	−	0.692825i	0.960557	+	0.278083i	$0.0896991\pi$
$68$	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	$0.0494979\pi$
$71$			2.61002i			0.309753i	−0.987934	+	0.154876i	$0.950502\pi$
$72$	27.9772	+	11.2570i	3.29714	+	1.32665i
$73$			2.38236i			0.278835i	0.990234	+	0.139417i	$0.0445229\pi$
$73$			2.38236i			0.278835i	−0.990234	+	0.139417i	$0.955477\pi$
$74$	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	−0.990932	−	0.134361i	$-0.957102\pi$
$79$	−3.36957	+	5.83626i	−0.379106	+	0.656631i	0.611826	+	0.790992i	$0.290435\pi$
$80$			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	−0.441095	−	0.897461i	$-0.645410\pi$
$83$	−13.1087	−	7.56831i	−1.43887	−	0.830730i	−0.997771	+	0.0667310i	$0.978743\pi$
$84$	−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	$0.0918254\pi$
$89$			5.36781i			0.568987i	−0.958678	+	0.284493i	$0.908175\pi$
$90$	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	0.387917	−	0.921694i	$-0.373195\pi$
$97$	−2.13066	−	1.23014i	−0.216336	−	0.124902i	−0.604253	+	0.796793i	$0.706528\pi$
$98$			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	−0.169907	−	0.985460i	$-0.554347\pi$
$101$	7.72313	−	13.3769i	0.768480	−	1.33105i	0.938387	−	0.345586i	$-0.112320\pi$
$102$	1.50678	+	21.3287i	0.149193	+	2.11186i
$103$	−3.13526	−	5.43043i	−0.308926	−	0.535076i	0.669202	−	0.743081i	$-0.266636\pi$
$103$	−3.13526	−	5.43043i	−0.308926	−	0.535076i	−0.978128	+	0.208005i	$0.933303\pi$
$104$	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	$-0.938599\pi$
$109$		−	4.00285i		−	0.383404i	0.981453	−	0.191702i	$-0.0614007\pi$
$110$	−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	0.913313	−	0.407258i	$-0.133515\pi$
$113$	1.10512	+	1.91412i	0.103961	+	0.180065i	−0.809352	+	0.587323i	$0.800182\pi$
$114$	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	0.767470	−	0.641085i	$-0.221515\pi$
$131$	−1.96246	−	3.39908i	−0.171461	−	0.296979i	−0.938931	+	0.344106i	$0.888182\pi$
$132$	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	0.0377249	−	0.999288i	$-0.487989\pi$
$137$	−9.46701	−	5.46578i	−0.808822	−	0.466973i	−0.846546	+	0.532315i	$0.821322\pi$
$138$	31.0911	−	21.0036i	2.64665	−	1.78795i
$139$	1.52565	+	2.64251i	0.129404	+	0.224134i	0.923446	−	0.383729i	$-0.125360\pi$
$139$	1.52565	+	2.64251i	0.129404	+	0.224134i	−0.794042	+	0.607863i	$0.792027\pi$
$140$	−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	−0.395582	−	0.918431i	$-0.629457\pi$
$149$	2.46587	−	1.42367i	0.202012	−	0.116631i	0.597593	+	0.801799i	$0.296124\pi$
$150$	4.30373	+	2.09526i	0.351398	+	0.171077i
$151$	7.48190	+	4.31968i	0.608868	+	0.351530i	0.772522	−	0.634988i	$-0.218995\pi$
$151$	7.48190	+	4.31968i	0.608868	+	0.351530i	−0.163654	+	0.986518i	$0.552328\pi$
$152$	−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	0.982165	+	0.188019i	$0.0602066\pi$
$157$	8.19349	+	14.1915i	0.653912	+	1.13261i	−0.328254	+	0.944590i	$0.606460\pi$
$158$	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	$-0.794904\pi$
$163$		−	15.3374i		−	1.20132i	0.799504	−	0.600661i	$-0.205096\pi$
$164$	−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	0.453173	−	0.891422i	$-0.350292\pi$
$167$	18.7608	−	10.8316i	1.45175	−	0.838171i	0.998581	+	0.0532517i	$0.0169586\pi$
$168$	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	0.262100	+	0.965041i	$0.415585\pi$
$173$	−9.26888	+	16.0542i	−0.704700	+	1.22058i	−0.966800	+	0.255535i	$0.917748\pi$
$174$	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	−0.612120	−	0.790765i	$-0.709683\pi$
$191$	5.23461	−	9.06661i	0.378763	−	0.656037i	0.990883	+	0.134728i	$0.0430162\pi$
$192$	36.3478	+	53.8048i	2.62318	+	3.88303i
$193$	23.9152	−	13.8075i	1.72145	−	0.993882i	0.805504	−	0.592590i	$-0.201895\pi$
$193$	23.9152	−	13.8075i	1.72145	−	0.993882i	0.915950	−	0.401292i	$-0.131439\pi$
$194$	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	$0.0361251\pi$
$197$			3.17899i			0.226494i	−0.993567	+	0.113247i	$0.963875\pi$
$198$	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	0.907646	−	0.419736i	$-0.137877\pi$
$211$	1.31199	+	2.27244i	0.0903214	+	0.156441i	−0.817325	+	0.576177i	$0.804544\pi$
$212$	−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	−0.0990052	−	0.995087i	$-0.531566\pi$
$223$	−15.0867	−	8.71029i	−1.01028	−	0.583284i	−0.911273	+	0.411802i	$0.864899\pi$
$224$	−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	0.974684	−	0.223588i	$-0.0717769\pi$
$227$	19.1103	+	11.0333i	1.26839	+	0.732307i	0.293709	+	0.955895i	$0.405110\pi$
$228$	−36.4689	−	17.7548i	−2.41521	−	1.17584i
$229$	−0.226938	+	0.131023i	−0.0149965	+	0.00865823i	−0.507480	−	0.861664i	$-0.669423\pi$
$229$	−0.226938	+	0.131023i	−0.0149965	+	0.00865823i	0.492483	+	0.870322i	$0.336089\pi$
$230$	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	0.607407	−	0.794391i	$-0.292210\pi$
$239$	24.7211	−	14.2727i	1.59907	−	0.923225i	0.991666	−	0.128835i	$-0.0411237\pi$
$240$	23.6896	−	16.0035i	1.52916	−	1.03302i
$241$	7.86079	+	4.53843i	0.506358	+	0.292346i	0.731335	−	0.682018i	$-0.238897\pi$
$241$	7.86079	+	4.53843i	0.506358	+	0.292346i	−0.224977	+	0.974364i	$0.572231\pi$
$242$			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	0.944683	−	0.327985i	$-0.106369\pi$
$257$	3.01865	+	5.22846i	0.188298	+	0.326142i	−0.756385	+	0.654127i	$0.773036\pi$
$258$	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	−0.145332	−	0.989383i	$-0.546425\pi$
$263$	12.7170	−	22.0265i	0.784164	−	1.35821i	0.929497	−	0.368830i	$-0.120241\pi$
$264$	−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	$0.190984\pi$
$271$			18.5902i			1.12927i	−0.825340	+	0.564636i	$0.809016\pi$
$272$	−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	0.00489863	+	0.999988i	$0.498441\pi$
$277$	−14.3726	+	24.8941i	−0.863566	+	1.49574i	−0.868464	+	0.495752i	$0.834893\pi$
$278$		−	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	0.636910	−	0.770938i	$-0.280212\pi$
$281$	4.82295	+	2.78453i	0.287713	+	0.166111i	−0.349197	+	0.937049i	$0.613546\pi$
$282$	7.34667	−	15.0903i	0.437488	−	0.898613i
$283$	−6.34111	−	10.9831i	−0.376940	−	0.652879i	0.613675	−	0.789559i	$-0.289690\pi$
$283$	−6.34111	−	10.9831i	−0.376940	−	0.652879i	−0.990615	+	0.136679i	$0.956357\pi$
$284$	−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	−0.626935	+	0.779071i	$0.715691\pi$
$293$	−27.6460	+	15.9614i	−1.61510	+	0.932477i	−0.988163	+	0.153406i	$0.950976\pi$
$294$	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	$0.0144758\pi$
$307$			1.59309i			0.0909227i	−0.998966	+	0.0454614i	$0.985524\pi$
$308$	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	0.660143	−	0.751140i	$-0.270496\pi$
$311$	−5.65092	−	9.78768i	−0.320434	−	0.555009i	−0.980578	+	0.196131i	$0.937162\pi$
$312$	−30.0007	−	55.1442i	−1.69846	−	3.12192i
$313$	6.19960	−	10.7380i	0.350422	−	0.606949i	−0.635901	−	0.771770i	$-0.719371\pi$
$313$	6.19960	−	10.7380i	0.350422	−	0.606949i	0.986323	+	0.164821i	$0.0527048\pi$
$314$		−	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	0.627952	−	0.778252i	$-0.283893\pi$
$317$	4.77057	+	2.75429i	0.267942	+	0.154696i	−0.360010	+	0.932948i	$0.617227\pi$
$318$	−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	0.429850	−	0.902900i	$-0.358566\pi$
$331$	−2.49540	−	1.44072i	−0.137160	−	0.0791891i	−0.567010	+	0.823711i	$0.691900\pi$
$332$		−	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	−0.975205	−	0.221305i	$-0.928968\pi$
$337$	−12.4695	−	21.5978i	−0.679258	−	1.17651i	0.295946	−	0.955205i	$-0.404365\pi$
$338$	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	0.996758	−	0.0804587i	$-0.0256385\pi$
$347$	7.98579	+	13.8318i	0.428700	+	0.742530i	−0.568058	+	0.822988i	$0.692305\pi$
$348$	−46.8432	−	69.3409i	−2.51106	−	3.71706i
$349$	−15.5244	−	8.96300i	−0.831000	−	0.479778i	0.0231946	−	0.999731i	$-0.492616\pi$
$349$	−15.5244	−	8.96300i	−0.831000	−	0.479778i	−0.854195	+	0.519953i	$0.825950\pi$
$350$	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	0.824965	−	0.565184i	$-0.191195\pi$
$353$	14.0533	+	8.11371i	0.747984	+	0.431849i	−0.0769808	+	0.997033i	$0.524528\pi$
$354$	−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	$0.0743804\pi$
$359$			8.77458i			0.463104i	−0.972822	+	0.231552i	$0.925620\pi$
$360$	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	−0.654409	−	0.756141i	$-0.727082\pi$
$367$	6.27655	−	10.8713i	0.327633	−	0.567477i	0.982042	+	0.188664i	$0.0604156\pi$
$368$	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	0.913516	+	0.406802i	$0.133356\pi$
$373$	15.6255	+	27.0642i	0.809059	+	1.40133i	−0.104457	+	0.994529i	$0.533311\pi$
$374$	−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	$-0.819847\pi$
$379$		−	20.8786i		−	1.07246i	0.844071	−	0.536232i	$-0.180153\pi$
$380$	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	−0.605574	−	0.795789i	$-0.707056\pi$
$383$	−4.28958	+	2.47659i	−0.219187	+	0.126548i	0.386387	+	0.922337i	$0.373723\pi$
$384$	−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	−0.925365	−	0.379078i	$-0.876241\pi$
$389$	−2.65062	+	4.59101i	−0.134392	+	0.232773i	0.790973	+	0.611851i	$0.209575\pi$
$390$	−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	$-0.934574\pi$
$397$		−	8.13319i		−	0.408193i	0.978951	−	0.204097i	$-0.0654257\pi$
$398$	−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	−0.229031	−	0.973419i	$-0.573556\pi$
$401$	10.0017	−	5.77447i	0.499459	−	0.288363i	0.728490	+	0.685056i	$0.240222\pi$
$402$	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	0.0206452	−	0.999787i	$-0.493428\pi$
$409$	18.1368	−	10.4713i	0.896809	−	0.517773i	0.876163	+	0.482014i	$0.160095\pi$
$410$	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	−0.994174	−	0.107789i	$-0.965623\pi$
$419$	−12.0859	−	20.9334i	−0.590435	−	1.02266i	0.403738	−	0.914874i	$-0.367711\pi$
$420$	−4.01838	+	8.25387i	−0.196077	+	0.402748i
$421$	−21.6880	−	12.5216i	−1.05701	−	0.610265i	−0.132407	−	0.991195i	$-0.542270\pi$
$421$	−21.6880	−	12.5216i	−1.05701	−	0.610265i	−0.924604	+	0.380930i	$0.875604\pi$
$422$		−	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	$0.342472\pi$
$431$			36.5394i			1.76004i	−0.474934	+	0.880021i	$0.657528\pi$
$432$	−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	0.482795	+	0.875734i	$0.339622\pi$
$439$	−10.8326	+	18.7626i	−0.517010	+	0.895488i	−0.999805	+	0.0197542i	$0.993712\pi$
$440$		−	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	0.443431	+	0.896308i	$0.353761\pi$
$443$	−11.6711	+	20.2149i	−0.554510	+	0.960440i	−0.997941	+	0.0641315i	$0.979572\pi$
$444$	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	$0.355681\pi$
$449$			38.0975i			1.79793i	−0.438017	+	0.898967i	$0.644319\pi$
$450$	−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	0.979970	−	0.199144i	$-0.0638162\pi$
$457$	27.7372	+	16.0141i	1.29749	+	0.749107i	0.317521	+	0.948251i	$0.397149\pi$
$458$	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	0.378693	−	0.925522i	$-0.376374\pi$
$461$	−5.01318	−	2.89436i	−0.233487	−	0.134804i	−0.612180	+	0.790719i	$0.709707\pi$
$462$	5.23274	−	3.53498i	0.243449	−	0.164462i
$463$	−16.4158	+	9.47766i	−0.762906	+	0.440464i	−0.830338	−	0.557260i	$-0.811853\pi$
$463$	−16.4158	+	9.47766i	−0.762906	+	0.440464i	0.0674320	+	0.997724i	$0.478519\pi$
$464$	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	0.911547	−	0.411196i	$-0.134889\pi$
$479$	22.1315	+	12.7776i	1.01121	+	0.583825i	0.0996673	+	0.995021i	$0.468222\pi$
$480$	−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	$-0.992620\pi$
$487$		−	1.02317i		−	0.0463641i	0.999731	−	0.0231821i	$-0.00737974\pi$
$488$	−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	0.916535	+	0.399953i	$0.130974\pi$
$491$	17.8296	+	30.8817i	0.804638	+	1.39367i	−0.111898	+	0.993720i	$0.535693\pi$
$492$	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	−0.828636	−	0.559788i	$-0.810883\pi$
$499$	−16.9361	+	9.77806i	−0.758164	+	0.437726i	0.0704724	+	0.997514i	$0.477549\pi$
$500$	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	0.219069	−	0.975709i	$-0.429698\pi$
$509$	26.4775	−	15.2868i	1.17359	−	0.677574i	0.954524	+	0.298136i	$0.0963647\pi$
$510$	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	$0.263004\pi$
$541$			34.2098i			1.47079i	−0.677637	+	0.735397i	$0.736996\pi$
$542$	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	−0.845964	−	0.533240i	$-0.820974\pi$
$547$	0.907849	−	1.57244i	0.0388168	−	0.0672327i	0.884781	+	0.466007i	$0.154308\pi$
$548$		−	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	$-0.942992\pi$
$557$		−	8.40849i		−	0.356279i	0.984005	−	0.178140i	$-0.0570078\pi$
$558$	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	0.896019	−	0.444015i	$-0.146446\pi$
$563$	1.50627	+	2.60894i	0.0634817	+	0.109954i	−0.832538	+	0.553968i	$0.813113\pi$
$564$	−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	−0.897041	−	0.441948i	$-0.854288\pi$
$569$	−1.56915	+	2.71784i	−0.0657820	+	0.113938i	0.831259	+	0.555886i	$0.187621\pi$
$570$	16.4766	−	11.1308i	0.690130	−	0.466217i
$571$	−0.656430	−	1.13697i	−0.0274708	−	0.0475807i	0.851963	−	0.523602i	$-0.175412\pi$
$571$	−0.656430	−	1.13697i	−0.0274708	−	0.0475807i	−0.879434	+	0.476021i	$0.842079\pi$
$572$	−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	$0.00635425\pi$
$577$			0.958966i			0.0399223i	−0.999801	+	0.0199611i	$0.993646\pi$
$578$	−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	0.539751	−	0.841825i	$-0.318519\pi$
$587$	1.95240	+	1.12722i	0.0805840	+	0.0465252i	−0.459167	+	0.888350i	$0.651852\pi$
$588$	−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	$-0.810313\pi$
$593$		−	27.3356i		−	1.12254i	0.827633	−	0.561270i	$-0.189687\pi$
$594$	−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	0.970811	−	0.239847i	$-0.0770972\pi$
$599$	6.79637	+	11.7717i	0.277692	+	0.480977i	−0.693119	+	0.720824i	$0.743764\pi$
$600$	1.22696	+	17.3679i	0.0500905	+	0.709040i
$601$	14.2702	−	24.7167i	0.582094	−	1.00822i	−0.413137	−	0.910669i	$-0.635567\pi$
$601$	14.2702	−	24.7167i	0.582094	−	1.00822i	0.995231	−	0.0975469i	$-0.0310996\pi$
$602$	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	0.879358	−	0.476161i	$-0.157972\pi$
$607$	0.672883	+	1.16547i	0.0273115	+	0.0473048i	−0.852047	+	0.523466i	$0.824639\pi$
$608$	−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	$0.423756\pi$
$613$			48.1040i			1.94290i	−0.237243	+	0.971450i	$0.576244\pi$
$614$	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	0.0261287	−	0.999659i	$-0.491682\pi$
$617$	22.4778	−	12.9776i	0.904923	−	0.522457i	0.878794	+	0.477201i	$0.158349\pi$
$618$	24.8715	−	16.8019i	1.00048	−	0.675872i
$619$	−33.5563	−	19.3737i	−1.34874	−	0.778697i	−0.360671	−	0.932693i	$-0.617452\pi$
$619$	−33.5563	−	19.3737i	−1.34874	−	0.778697i	−0.988071	+	0.153997i	$0.950786\pi$
$620$	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	$0.0298734\pi$
$631$			4.70806i			0.187425i	−0.995599	+	0.0937124i	$0.970127\pi$
$632$	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	−0.994443	−	0.105281i	$-0.966426\pi$
$641$	−10.2802	+	17.8059i	−0.406045	+	0.703291i	0.588397	+	0.808572i	$0.299759\pi$
$642$	0.633189	+	8.96291i	0.0249900	+	0.353738i
$643$	20.7509	−	11.9805i	0.818336	−	0.472467i	−0.0315062	−	0.999504i	$-0.510030\pi$
$643$	20.7509	−	11.9805i	0.818336	−	0.472467i	0.849842	+	0.527037i	$0.176697\pi$
$644$	−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	0.991410	+	0.130789i	$0.0417510\pi$
$653$	15.5616	+	26.9534i	0.608972	+	1.05477i	−0.382439	+	0.923981i	$0.624916\pi$
$654$	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	−0.347994	−	0.937497i	$-0.613137\pi$
$659$	16.3755	−	28.3632i	0.637899	−	1.10487i	0.985893	−	0.167377i	$-0.0535296\pi$
$660$	5.99751	−	12.3191i	0.233453	−	0.479519i
$661$	0.856192	−	0.494323i	0.0333020	−	0.0192269i	−0.483257	−	0.875479i	$-0.660546\pi$
$661$	0.856192	−	0.494323i	0.0333020	−	0.0192269i	0.516559	+	0.856252i	$0.327213\pi$
$662$	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	0.330229	+	0.943901i	$0.392874\pi$
$673$	−16.9228	+	29.3112i	−0.652327	+	1.12986i	−0.982557	+	0.185963i	$0.940459\pi$
$674$			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	−0.936256	−	0.351319i	$-0.885733\pi$
$677$	−4.26394	+	7.38536i	−0.163876	+	0.283842i	0.772379	+	0.635162i	$0.219067\pi$
$678$	−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	$-0.912151\pi$
$683$		−	14.2430i		−	0.544992i	0.962157	−	0.272496i	$-0.0878492\pi$
$684$	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	−0.0584238	−	0.998292i	$-0.518607\pi$
$691$	−25.0299	−	14.4510i	−0.952182	−	0.549742i	−0.893758	+	0.448549i	$0.851941\pi$
$692$	−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	0.284083	−	0.958800i	$-0.408311\pi$
$709$	−10.7632	−	6.21412i	−0.404220	−	0.233376i	−0.688303	+	0.725423i	$0.741644\pi$
$710$		−	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	−0.538602	−	0.842561i	$-0.681047\pi$
$727$	12.4131	−	21.5002i	0.460378	−	0.797398i	0.998980	+	0.0451624i	$0.0143805\pi$
$728$	−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	0.242144	−	0.970240i	$-0.422149\pi$
$733$	32.5827	−	18.8116i	1.20347	−	0.694823i	0.961325	+	0.275417i	$0.0888161\pi$
$734$	−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	$0.212871\pi$
$739$			33.7094i			1.24002i	−0.784594	+	0.620009i	$0.787129\pi$
$740$	−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	−0.892162	−	0.451715i	$-0.850812\pi$
$743$	−25.8146	+	14.9041i	−0.947046	+	0.546777i	−0.0548841	+	0.998493i	$0.517479\pi$
$744$	−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	0.998412	−	0.0563380i	$-0.0179424\pi$
$751$	12.3434	+	21.3793i	0.450416	+	0.780143i	−0.547996	+	0.836481i	$0.684609\pi$
$752$	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	−0.434112	−	0.900859i	$-0.642938\pi$
$761$	3.55858	−	2.05455i	0.128999	−	0.0744773i	0.563111	+	0.826382i	$0.309604\pi$
$762$	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	−0.0846050	−	0.996415i	$-0.526963\pi$
$769$	20.4103	−	11.7839i	0.736013	−	0.424937i	0.820618	+	0.571477i	$0.193629\pi$
$770$	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
$773$			42.0316i			1.51177i	0.654704	+	0.755885i	$0.272793\pi$
$773$			42.0316i			1.51177i	−0.654704	+	0.755885i	$0.727207\pi$
$774$	−0.854983	−	6.02102i	−0.0307317	−	0.216421i
$775$		−	7.16592i		−	0.257407i
$776$	−12.3658	+	21.4181i	−0.443905	+	0.768866i
$777$	−8.31609	+	0.587494i	−0.298338	+	0.0210762i
$778$	12.6876	−	7.32522i	0.454874	−	0.262622i
$779$	12.3222	+	21.3427i	0.441488	+	0.764680i
$780$	35.1944	+	0.892081i	1.26016	+	0.0319416i
$781$	−1.83122	+	3.17176i	−0.0655261	+	0.113495i
$782$			96.7661i			3.46035i
$783$	13.6700	−	42.3812i	0.488527	−	1.51458i
$784$	100.950			3.60536
$785$	14.1915	+	8.19349i	0.506518	+	0.292438i
$786$	15.5679	−	10.5169i	0.555288	−	0.375125i
$787$	−43.0233	+	24.8395i	−1.53362	+	0.885434i	−0.534425	+	0.845216i	$0.679472\pi$
$787$	−43.0233	+	24.8395i	−1.53362	+	0.885434i	−0.999191	+	0.0402179i	$0.987195\pi$
$788$	−15.5203	+	8.96064i	−0.552888	+	0.319210i
$789$	−43.9435	+	3.10441i	−1.56443	+	0.110520i
$790$	9.31210	−	16.1290i	0.331310	−	0.573845i
$791$		−	2.07799i		−	0.0738848i
$792$	26.1005	+	33.3088i	0.927442	+	1.18358i
$793$	21.2750	+	15.1714i	0.755498	+	0.538751i
$794$	−11.2384	+	19.4655i	−0.398836	+	0.690804i
$795$	7.99278	+	3.89126i	0.283475	+	0.138009i
$796$	23.3258	+	40.4015i	0.826762	+	1.43199i
$797$	11.9721	+	20.7362i	0.424072	+	0.734515i	0.996333	−	0.0855568i	$-0.0272669\pi$
$797$	11.9721	+	20.7362i	0.424072	+	0.734515i	−0.572261	+	0.820072i	$0.693934\pi$
$798$	−16.8082	−	8.18302i	−0.595003	−	0.289676i
$799$	−13.5642	−	7.83129i	−0.479867	−	0.277051i
$800$		−	25.5102i		−	0.901921i
$801$	−14.9395	−	6.01109i	−0.527860	−	0.212391i
$802$	−31.9165			−1.12701
$803$	−1.67149	+	2.89510i	−0.0589856	+	0.102166i
$804$	−7.80433	−	110.472i	−0.275238	−	3.89604i
$805$	3.68480	+	6.38225i	0.129872	+	0.224945i
$806$	6.83494	−	71.0752i	0.240751	−	2.50352i
$807$	3.60340	+	5.33403i	0.126846	+	0.187767i
$808$	−134.468	−	77.6354i	−4.73059	−	2.73120i
$809$	−18.1585			−0.638419			−0.319210	−	0.947684i	$-0.603417\pi$
$809$	−18.1585			−0.638419			−0.319210	+	0.947684i	$0.603417\pi$
$810$	17.9410	+	17.2265i	0.630382	+	0.605277i
$811$			8.70908i			0.305817i	0.988240	+	0.152909i	$0.0488640\pi$
$811$			8.70908i			0.305817i	−0.988240	+	0.152909i	$0.951136\pi$
$812$	−39.3369	−	22.7112i	−1.38045	−	0.797006i
$813$	26.6814	−	18.0246i	0.935757	−	0.632151i
$814$	17.1935	−	9.92666i	0.602631	−	0.347929i
$815$	−7.66872	−	13.2826i	−0.268624	−	0.465270i
$816$	127.387	−	8.99930i	4.45943	−	0.315039i
$817$	−2.63883	−	1.52353i	−0.0923209	−	0.0533015i
$818$	−57.8767			−2.02361
$819$	5.47737	+	8.56834i	0.191395	+	0.299402i
$820$	−33.4448			−1.16794
$821$	0.683452	+	0.394591i	0.0238527	+	0.0137713i	0.511879	−	0.859058i	$-0.328950\pi$
$821$	0.683452	+	0.394591i	0.0238527	+	0.0137713i	−0.488026	+	0.872829i	$0.662283\pi$
$822$	22.9045	−	47.0466i	0.798886	−	1.64094i
$823$	−2.00423	−	3.47143i	−0.0698631	−	0.121006i	0.828978	−	0.559282i	$-0.188923\pi$
$823$	−2.00423	−	3.47143i	−0.0698631	−	0.121006i	−0.898841	+	0.438275i	$0.855590\pi$
$824$	−54.5884	+	31.5166i	−1.90168	+	1.09793i
$825$	−2.18523	−	1.06388i	−0.0760800	−	0.0370394i
$826$	−4.83555	−	2.79180i	−0.168250	−	0.0971393i
$827$		−	2.14581i		−	0.0746171i	−0.999304	−	0.0373085i	$-0.988122\pi$
$827$		−	2.14581i		−	0.0746171i	0.999304	−	0.0373085i	$-0.0118784\pi$
$828$	81.7665	+	104.348i	2.84158	+	3.62636i
$829$	−29.7826			−1.03439			−0.517197	−	0.855866i	$-0.673025\pi$
$829$	−29.7826			−1.03439			−0.517197	+	0.855866i	$0.673025\pi$
$830$	36.2270	+	20.9157i	1.25746	+	0.725994i
$831$	49.6644	−	3.50857i	1.72284	−	0.121711i
$832$	12.9385	−	134.545i	0.448563	−	4.66452i
$833$	−13.6601	−	23.6601i	−0.473296	−	0.819773i
$834$	−12.1027	+	8.17600i	−0.419084	+	0.283112i
$835$	10.8316	−	18.7608i	0.374841	−	0.649244i
$836$	32.8606			1.13651
$837$	27.6176	−	24.9745i	0.954605	−	0.863246i
$838$			66.8009i			2.30760i
$839$	24.9858	+	14.4256i	0.862606	+	0.498026i	0.864884	−	0.501972i	$-0.167392\pi$
$839$	24.9858	+	14.4256i	0.862606	+	0.498026i	−0.00227843	+	0.999997i	$0.500725\pi$
$840$	13.5643	−	9.16335i	0.468012	−	0.316166i
$841$	−22.2230	−	38.4913i	−0.766309	−	1.32729i
$842$	34.6045	+	59.9368i	1.19255	+	2.06556i
$843$	−0.679746	−	9.62192i	−0.0234117	−	0.331397i
$844$	−7.39626	+	12.8107i	−0.254590	+	0.440963i
$845$	−12.2907	+	4.23541i	−0.422813	+	0.145702i
$846$	−28.7814	+	4.08695i	−0.989524	+	0.140512i
$847$			8.49063i			0.291742i
$848$	42.3573	−	73.3650i	1.45456	−	2.51936i
$849$	−9.61525	+	19.7500i	−0.329995	+	0.677819i
$850$	−10.6909	+	6.17241i	−0.366696	+	0.211712i
$851$	34.7538	−	20.0651i	1.19135	−	0.687824i
$852$	22.9138	+	11.1555i	0.785014	+	0.382182i
$853$	−25.7142	−	14.8461i	−0.880437	−	0.508321i	−0.00963453	−	0.999954i	$-0.503067\pi$
$853$	−25.7142	−	14.8461i	−0.880437	−	0.508321i	−0.870802	+	0.491633i	$0.836400\pi$
$854$	18.8301			0.644353
$855$	12.3383	−	1.75204i	0.421962	−	0.0599185i
$856$		−	18.8696i		−	0.644949i
$857$	−11.6988	+	20.2628i	−0.399622	+	0.692166i	−0.993679	−	0.112257i	$-0.964192\pi$
$857$	−11.6988	+	20.2628i	−0.399622	+	0.692166i	0.594057	+	0.804423i	$0.297525\pi$
$858$	−20.6595	−	12.6364i	−0.705304	−	0.431398i
$859$	−9.81639	−	17.0025i	−0.334931	−	0.580117i	0.648541	−	0.761180i	$-0.275380\pi$
$859$	−9.81639	−	17.0025i	−0.334931	−	0.580117i	−0.983472	+	0.181063i	$0.942046\pi$
$860$	3.58114	−	2.06757i	0.122116	−	0.0705036i
$861$	−5.40799	−	8.00532i	−0.184304	−	0.272820i
$862$	50.4900	−	87.4512i	1.71970	−	2.97860i
$863$			54.8732i			1.86790i	0.357397	+	0.933952i	$0.383664\pi$
$863$			54.8732i			1.86790i	−0.357397	+	0.933952i	$0.616336\pi$
$864$	98.3168	−	88.9076i	3.34481	−	3.02470i
$865$			18.5378i			0.630303i
$866$	13.0236	+	7.51915i	0.442558	+	0.255511i
$867$	−2.86384	−	4.23928i	−0.0972613	−	0.143974i
$868$	−18.9901	−	32.8918i	−0.644566	−	1.11642i
$869$	−8.18956	+	4.72824i	−0.277812	+	0.160395i
$870$	40.9201	−	2.89082i	1.38732	−	0.0980081i
$871$	16.9632	+	37.2101i	0.574775	+	1.26082i
$872$	−40.2380			−1.36263
$873$	5.80967	−	4.55241i	0.196627	−	0.154076i
$874$	89.9873			3.04387
$875$	−0.470084	+	0.814209i	−0.0158917	+	0.0275253i
$876$	20.9151	+	10.1825i	0.706656	+	0.344034i
$877$	19.4794	−	11.2464i	0.657773	−	0.379766i	−0.133655	−	0.991028i	$-0.542671\pi$
$877$	19.4794	−	11.2464i	0.657773	−	0.379766i	0.791428	+	0.611262i	$0.209338\pi$
$878$	51.8520	−	29.9367i	1.74992	−	1.01032i
$879$	49.7135	+	24.2029i	1.67679	+	0.816343i
$880$	−11.5805	+	20.0581i	−0.390379	+	0.676157i
$881$	−29.7326			−1.00172			−0.500859	−	0.865529i	$-0.666983\pi$
$881$	−29.7326			−1.00172			−0.500859	+	0.865529i	$0.666983\pi$
$882$	−47.0418	−	18.9279i	−1.58398	−	0.637336i
$883$	−0.987923			−0.0332462			−0.0166231	−	0.999862i	$-0.505292\pi$
$883$	−0.987923			−0.0332462			−0.0166231	+	0.999862i	$0.505292\pi$
$884$	−82.6156	+	37.6624i	−2.77866	+	1.26672i
$885$	3.71292	−	0.262302i	0.124809	−	0.00881717i
$886$	55.8657	−	32.2541i	1.87685	−	1.08360i
$887$	24.4108	+	42.2807i	0.819634	+	1.41965i	0.905952	+	0.423381i	$0.139157\pi$
$887$	24.4108	+	42.2807i	0.819634	+	1.41965i	−0.0863175	+	0.996268i	$0.527510\pi$
$888$	−49.8980	−	73.8628i	−1.67447	−	2.47867i
$889$	−6.99582	−	4.03904i	−0.234632	−	0.135465i
$890$		−	14.8344i		−	0.497251i
$891$	−3.51573	−	12.1297i	−0.117781	−	0.406362i
$892$		−	98.2072i		−	3.28822i
$893$	−7.28269	+	12.6140i	−0.243706	+	0.422111i
$894$	7.62947	+	11.2937i	0.255168	+	0.377719i
$895$	−11.8652	+	6.85040i	−0.396611	+	0.228984i
$896$	−24.7179	−	42.8126i	−0.825767	−	1.43027i
$897$	−41.7599	−	25.5424i	−1.39432	−	0.852834i
$898$	52.6429	−	91.1803i	1.75672	−	3.04272i
$899$		−	61.4124i		−	2.04822i
$900$	−6.31301	+	15.6898i	−0.210434	+	0.522994i
$901$	−22.9265			−0.763792
$902$	19.9240	+	11.5032i	0.663398	+	0.383013i
$903$	1.07396	+	0.522854i	0.0357391	+	0.0173995i
$904$	19.2413	−	11.1090i	0.639957	−	0.369479i
$905$	8.57449	−	4.95048i	0.285026	−	0.164560i
$906$	−18.1017	+	37.1815i	−0.601389	+	1.23527i
$907$	−17.1992	+	29.7898i	−0.571089	+	0.989155i	0.425366	+	0.905022i	$0.360145\pi$
$907$	−17.1992	+	29.7898i	−0.571089	+	0.989155i	−0.996455	+	0.0841332i	$0.973188\pi$
$908$			124.399i			4.12832i
$909$	28.5812	+	36.4746i	0.947979	+	1.20979i
$910$	−5.43913	+	7.62736i	−0.180305	+	0.252845i
$911$	0.939177	−	1.62670i	0.0311163	−	0.0538950i	−0.850048	−	0.526705i	$-0.823427\pi$
$911$	0.939177	−	1.62670i	0.0311163	−	0.0538950i	0.881164	+	0.472810i	$0.156760\pi$
$912$	−8.36887	−	118.463i	−0.277121	−	3.92270i
$913$	−10.6200	−	18.3944i	−0.351470	−	0.608765i
$914$	−44.2563	−	76.6542i	−1.46387	−	2.53550i
$915$	−10.4016	+	7.02678i	−0.343866	+	0.232298i
$916$	−1.27935	−	0.738631i	−0.0422708	−	0.0244050i
$917$			3.69009i			0.121857i
$918$	−61.0485	−	19.6911i	−2.01490	−	0.649905i
$919$	12.3643			0.407860			0.203930	−	0.978985i	$-0.434628\pi$
$919$	12.3643			0.407860			0.203930	+	0.978985i	$0.434628\pi$
$920$	−39.3980	+	68.2394i	−1.29892	+	2.24979i
$921$	2.28648	−	1.54463i	0.0753420	−	0.0508972i
$922$	7.99881	+	13.8544i	0.263427	+	0.456269i
$923$	−9.36736	−	0.900812i	−0.308330	−	0.0296506i
$924$	−12.8496	+	0.907769i	−0.422722	+	0.0298634i
$925$	4.43368	+	2.55979i	0.145779	+	0.0841653i
$926$	52.3847			1.72147
$927$	18.6247	−	2.64470i	0.611716	−	0.0868635i
$928$		−	218.624i		−	7.17667i
$929$	14.5127	+	8.37893i	0.476147	+	0.274904i	0.718809	−	0.695207i	$-0.244687\pi$
$929$	14.5127	+	8.37893i	0.476147	+	0.274904i	−0.242662	+	0.970111i	$0.578021\pi$
$930$	30.8402	+	15.0145i	1.01129	+	0.492344i
$931$	−22.0026	+	12.7032i	−0.721106	+	0.416331i
$932$	−1.56254	−	2.70640i	−0.0511827	−	0.0886511i
$933$	−8.56869	+	17.6004i	−0.280526	+	0.576210i
$934$	42.6484	+	24.6230i	1.39550	+	0.805691i
$935$	6.26812			0.204989
$936$	−50.0572	+	96.5248i	−1.63617	+	3.15501i
$937$	−1.76649			−0.0577087			−0.0288543	−	0.999584i	$-0.509186\pi$
$937$	−1.76649			−0.0577087			−0.0288543	+	0.999584i	$0.509186\pi$
$938$	25.5212	+	14.7346i	0.833295	+	0.481103i
$939$	−21.4227	+	1.51341i	−0.699102	+	0.0493884i
$940$	−9.88330	−	17.1184i	−0.322358	−	0.558340i
$941$	−19.4606	+	11.2356i	−0.634398	+	0.366270i	−0.782453	−	0.622709i	$-0.786032\pi$
$941$	−19.4606	+	11.2356i	−0.634398	+	0.366270i	0.148055	+	0.988979i	$0.452699\pi$
$942$	−64.9976	+	43.9091i	−2.11774	+	1.43064i
$943$	40.2733	+	23.2518i	1.31148	+	0.757182i
$944$		−	35.4707i		−	1.15447i
$945$	−4.77631	+	1.02595i	−0.155373	+	0.0333742i
$946$	−2.84452			−0.0924833
$947$	18.0321	+	10.4108i	0.585963	+	0.338306i	0.763500	−	0.645808i	$-0.223479\pi$
$947$	18.0321	+	10.4108i	0.585963	+	0.338306i	−0.177536	+	0.984114i	$0.556813\pi$
$948$	36.8355	+	54.5267i	1.19636	+	1.77095i
$949$	−8.55029	−	0.822238i	−0.277554	−	0.0266910i
$950$	5.74002	+	9.94200i	0.186231	+	0.322561i
$951$	−0.672363	−	9.51741i	−0.0218029	−	0.308623i
$952$	−21.1083	+	36.5607i	−0.684125	+	1.18494i
$953$	41.0587			1.33002			0.665011	−	0.746834i	$-0.268427\pi$
$953$	41.0587			1.33002			0.665011	+	0.746834i	$0.268427\pi$
$954$	−33.4939	+	26.2456i	−1.08441	+	0.849732i
$955$		−	10.4692i		−	0.338776i
$956$	139.363	+	80.4613i	4.50732	+	2.60230i
$957$	−18.7276	−	9.11748i	−0.605377	−	0.294726i
$958$	−35.3121	−	61.1624i	−1.14088	−	1.97607i
$959$	5.13875	+	8.90058i	0.165939	+	0.287415i
$960$	58.3805	+	28.4224i	1.88422	+	0.917329i
$961$	10.1752	−	17.6240i	0.328232	−	0.568515i
$962$	41.5339	+	29.6182i	1.33911	+	0.954928i
$963$	−2.10209	+	5.22436i	−0.0677390	+	0.168353i
$964$			51.1701i			1.64808i
$965$	13.8075	−	23.9152i	0.444478	−	0.769858i
$966$	−35.1881	+	2.48588i	−1.13216	+	0.0799820i
$967$	−18.9432	+	10.9369i	−0.609174	+	0.351707i	−0.772642	−	0.634842i	$-0.781065\pi$
$967$	−18.9432	+	10.9369i	−0.609174	+	0.351707i	0.163468	+	0.986549i	$0.447732\pi$
$968$	−78.6198	+	45.3912i	−2.52694	+	1.45893i
$969$	−26.6322	+	17.9914i	−0.855549	+	0.577966i
$970$	5.88827	+	3.39960i	0.189061	+	0.109154i
$971$	4.60745			0.147860			0.0739301	−	0.997263i	$-0.476446\pi$
$971$	4.60745			0.147860			0.0739301	+	0.997263i	$0.476446\pi$
$972$	−82.4709	+	30.3514i	−2.64526	+	0.973521i
$973$		−	2.86874i		−	0.0919675i
$974$	−1.41381	+	2.44878i	−0.0453013	+	0.0784641i
$975$	0.158243	−	6.24299i	0.00506782	−	0.199936i
$976$	59.8104	+	103.595i	1.91448	+	3.31598i
$977$	−5.38906	+	3.11137i	−0.172411	+	0.0995417i	−0.583722	−	0.811953i	$-0.698404\pi$
$977$	−5.38906	+	3.11137i	−0.172411	+	0.0995417i	0.411311	+	0.911495i	$0.365071\pi$
$978$	73.2328	−	5.17357i	2.34173	−	0.165433i
$979$	−3.76611	+	6.52309i	−0.120365	+	0.208479i
$980$		−	34.4789i		−	1.10139i
$981$	11.1406	+	4.48256i	0.355691	+	0.143117i
$982$		−	98.5472i		−	3.14477i
$983$	−5.86536	−	3.38637i	−0.187076	−	0.108008i	0.403537	−	0.914963i	$-0.367781\pi$
$983$	−5.86536	−	3.38637i	−0.187076	−	0.108008i	−0.590613	+	0.806955i	$0.701114\pi$
$984$	45.2147	−	92.8724i	1.44139	−	2.96066i
$985$	1.58949	+	2.75308i	0.0506455	+	0.0877206i
$986$	−91.6220	+	52.8980i	−2.91784	+	1.68461i
$987$	2.49932	−	5.13368i	0.0795543	−	0.163407i
$988$	35.0240	+	76.8282i	1.11426	+	2.44423i
$989$	−5.74974			−0.182831
$990$	9.15727	−	7.17556i	0.291037	−	0.228054i
$991$	−15.8577			−0.503738			−0.251869	−	0.967761i	$-0.581045\pi$
$991$	−15.8577			−0.503738			−0.251869	+	0.967761i	$0.581045\pi$
$992$	91.4019	−	158.313i	2.90201	−	5.02643i
$993$	0.351701	+	4.97839i	0.0111609	+	0.157985i
$994$	−5.87292	+	3.39073i	−0.186278	+	0.107547i
$995$	7.16667	−	4.13768i	0.227199	−	0.131173i
$996$	−122.471	+	82.7354i	−3.88065	+	2.62157i
$997$	−13.9238	+	24.1168i	−0.440973	+	0.763787i	−0.997762	−	0.0668667i	$-0.978700\pi$
$997$	−13.9238	+	24.1168i	−0.440973	+	0.763787i	0.556789	+	0.830654i	$0.312033\pi$
$998$	54.0450			1.71077
$999$	5.58671	+	26.0089i	0.176756	+	0.822884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.1	✓	108
9.4	even	3	inner	585.2.bt.b.571.54	yes	108
13.12	even	2	inner	585.2.bt.b.376.54	yes	108
117.103	even	6	inner	585.2.bt.b.571.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.1	✓	108	1.1	even	1	trivial
585.2.bt.b.376.54	yes	108	13.12	even	2	inner
585.2.bt.b.571.1	yes	108	117.103	even	6	inner
585.2.bt.b.571.54	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
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

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