LMFDB - Embedded newform 220.3.w.a.7.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.16
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56459 - 1.24582i) q^{2} +(3.70393 - 1.88724i) q^{3} +(0.895857 + 3.89839i) q^{4} +(-4.57559 + 2.01593i) q^{5} +(-8.14628 - 1.66168i) q^{6} +(-4.38944 + 8.61475i) q^{7} +(3.45505 - 7.21544i) q^{8} +(4.86731 - 6.69928i) q^{9} +(9.67039 + 2.54628i) q^{10} +(5.58926 + 9.47419i) q^{11} +(10.6754 + 12.7486i) q^{12} +(2.35735 + 14.8837i) q^{13} +(17.6001 - 8.01007i) q^{14} +(-13.1431 + 16.1021i) q^{15} +(-14.3949 + 6.98480i) q^{16} +(-0.213950 + 1.35083i) q^{17} +(-15.9614 + 4.41780i) q^{18} +(16.2148 + 5.26850i) q^{19} +(-11.9579 - 16.0315i) q^{20} +40.1924i q^{21} +(3.05827 - 21.7864i) q^{22} +(-28.5180 - 28.5180i) q^{23} +(-0.820048 - 33.2460i) q^{24} +(16.8721 - 18.4481i) q^{25} +(14.8542 - 26.2237i) q^{26} +(-0.467718 + 2.95306i) q^{27} +(-37.5160 - 9.39414i) q^{28} +(5.39617 + 16.6077i) q^{29} +(40.6239 - 8.81916i) q^{30} +(-18.6680 + 25.6943i) q^{31} +(31.2238 + 7.00513i) q^{32} +(38.5823 + 24.5434i) q^{33} +(2.01764 - 1.84694i) q^{34} +(2.71755 - 48.2664i) q^{35} +(30.4768 + 12.9731i) q^{36} +(6.68530 - 13.1206i) q^{37} +(-18.8058 - 28.4437i) q^{38} +(36.8207 + 50.6793i) q^{39} +(-1.26310 + 39.9801i) q^{40} +(55.3081 + 17.9707i) q^{41} +(50.0725 - 62.8844i) q^{42} +(-8.50943 + 8.50943i) q^{43} +(-31.9269 + 30.2766i) q^{44} +(-8.76557 + 40.4653i) q^{45} +(9.09050 + 80.1471i) q^{46} +(-17.2467 - 33.8485i) q^{47} +(-40.1355 + 53.0379i) q^{48} +(-26.1454 - 35.9860i) q^{49} +(-49.3809 + 7.84407i) q^{50} +(1.75689 + 5.40715i) q^{51} +(-55.9107 + 22.5235i) q^{52} +(68.0547 - 10.7788i) q^{53} +(4.41077 - 4.03762i) q^{54} +(-44.6734 - 32.0825i) q^{55} +(46.9935 + 61.4362i) q^{56} +(70.0013 - 11.0871i) q^{57} +(12.2475 - 32.7068i) q^{58} +(-8.95586 - 27.5633i) q^{59} +(-74.5466 - 36.8118i) q^{60} +(-39.1807 - 53.9276i) q^{61} +(61.2183 - 16.9440i) q^{62} +(36.3479 + 71.3368i) q^{63} +(-40.1252 - 49.8595i) q^{64} +(-40.7908 - 63.3496i) q^{65} +(-29.7886 - 86.4669i) q^{66} +(-47.5763 + 47.5763i) q^{67} +(-5.45773 + 0.376088i) q^{68} +(-159.449 - 51.8081i) q^{69} +(-64.3831 + 72.1313i) q^{70} +(43.5437 + 59.9328i) q^{71} +(-31.5215 - 58.2662i) q^{72} +(7.89363 - 15.4921i) q^{73} +(-26.8057 + 12.1997i) q^{74} +(27.6768 - 100.172i) q^{75} +(-6.01254 + 67.9313i) q^{76} +(-106.151 + 6.56373i) q^{77} +(5.52827 - 125.164i) q^{78} +(-81.3459 + 111.963i) q^{79} +(51.7842 - 60.9786i) q^{80} +(26.8708 + 82.6999i) q^{81} +(-64.1459 - 97.0206i) q^{82} +(7.68527 - 48.5229i) q^{83} +(-156.685 + 36.0066i) q^{84} +(-1.74422 - 6.61215i) q^{85} +(23.9150 - 2.71250i) q^{86} +(51.3298 + 51.3298i) q^{87} +(87.6716 - 7.59515i) q^{88} -52.5737i q^{89} +(64.1271 - 52.3911i) q^{90} +(-138.567 - 45.0231i) q^{91} +(85.6261 - 136.722i) q^{92} +(-20.6535 + 130.401i) q^{93} +(-15.1853 + 74.4452i) q^{94} +(-84.8131 + 8.58130i) q^{95} +(128.871 - 32.9805i) q^{96} +(6.75594 + 42.6553i) q^{97} +(-3.92548 + 88.8757i) q^{98} +(90.6749 + 8.66983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.56459	−	1.24582i	−0.782293	−	0.622911i
$2$	−1.56459	−	1.24582i	−0.782293	−	0.622911i
$3$	3.70393	−	1.88724i	1.23464	−	0.629082i	0.289951	−	0.957042i	$-0.406361\pi$
$3$	3.70393	−	1.88724i	1.23464	−	0.629082i	0.944692	+	0.327960i	$0.106361\pi$
$4$	0.895857	+	3.89839i	0.223964	+	0.974597i
$5$	−4.57559	+	2.01593i	−0.915118	+	0.403185i
$5$	−4.57559	+	2.01593i	−0.915118	+	0.403185i
$6$	−8.14628	−	1.66168i	−1.35771	−	0.276946i
$7$	−4.38944	+	8.61475i	−0.627062	+	1.23068i	0.330868	+	0.943677i	$0.392659\pi$
$7$	−4.38944	+	8.61475i	−0.627062	+	1.23068i	−0.957930	+	0.287002i	$0.907341\pi$
$8$	3.45505	−	7.21544i	0.431882	−	0.901930i
$9$	4.86731	−	6.69928i	0.540812	−	0.744364i
$10$	9.67039	+	2.54628i	0.967039	+	0.254628i
$11$	5.58926	+	9.47419i	0.508114	+	0.861290i
$11$	5.58926	+	9.47419i	0.508114	+	0.861290i
$12$	10.6754	+	12.7486i	0.889617	+	1.06239i
$13$	2.35735	+	14.8837i	0.181335	+	1.14490i	0.895545	+	0.444970i	$0.146786\pi$
$13$	2.35735	+	14.8837i	0.181335	+	1.14490i	−0.714211	+	0.699931i	$0.753214\pi$
$14$	17.6001	−	8.01007i	1.25715	−	0.572148i
$15$	−13.1431	+	16.1021i	−0.876207	+	1.07347i
$16$	−14.3949	+	6.98480i	−0.899680	+	0.436550i
$17$	−0.213950	+	1.35083i	−0.0125853	+	0.0794605i	−0.993182	−	0.116578i	$-0.962808\pi$
$17$	−0.213950	+	1.35083i	−0.0125853	+	0.0794605i	0.980596	+	0.196038i	$0.0628076\pi$
$18$	−15.9614	+	4.41780i	−0.886746	+	0.245433i
$19$	16.2148	+	5.26850i	0.853409	+	0.277289i	0.702873	−	0.711315i	$-0.251900\pi$
$19$	16.2148	+	5.26850i	0.853409	+	0.277289i	0.150536	+	0.988605i	$0.451900\pi$
$20$	−11.9579	−	16.0315i	−0.597897	−	0.801573i
$21$			40.1924i			1.91392i
$22$	3.05827	−	21.7864i	0.139012	−	0.990291i
$23$	−28.5180	−	28.5180i	−1.23991	−	1.23991i	−0.960037	−	0.279875i	$-0.909707\pi$
$23$	−28.5180	−	28.5180i	−1.23991	−	1.23991i	−0.279875	−	0.960037i	$-0.590293\pi$
$24$	−0.820048	−	33.2460i	−0.0341687	−	1.38525i
$25$	16.8721	−	18.4481i	0.674883	−	0.737925i
$26$	14.8542	−	26.2237i	0.571315	−	1.00860i
$27$	−0.467718	+	2.95306i	−0.0173229	+	0.109372i
$28$	−37.5160	−	9.39414i	−1.33986	−	0.335505i
$29$	5.39617	+	16.6077i	0.186075	+	0.572679i	0.999965	−	0.00833928i	$-0.00265451\pi$
$29$	5.39617	+	16.6077i	0.186075	+	0.572679i	−0.813891	+	0.581018i	$0.802655\pi$
$30$	40.6239	−	8.81916i	1.35413	−	0.293972i
$31$	−18.6680	+	25.6943i	−0.602195	+	0.828850i	−0.995907	−	0.0903840i	$-0.971191\pi$
$31$	−18.6680	+	25.6943i	−0.602195	+	0.828850i	0.393712	+	0.919234i	$0.371191\pi$
$32$	31.2238	+	7.00513i	0.975745	+	0.218910i
$33$	38.5823	+	24.5434i	1.16916	+	0.743739i
$34$	2.01764	−	1.84694i	0.0593422	−	0.0543219i
$35$	2.71755	−	48.2664i	0.0776443	−	1.37904i
$36$	30.4768	+	12.9731i	0.846578	+	0.360363i
$37$	6.68530	−	13.1206i	0.180684	−	0.354612i	−0.782845	−	0.622217i	$-0.786232\pi$
$37$	6.68530	−	13.1206i	0.180684	−	0.354612i	0.963529	+	0.267605i	$0.0862322\pi$
$38$	−18.8058	−	28.4437i	−0.494889	−	0.748519i
$39$	36.8207	+	50.6793i	0.944120	+	1.29947i
$40$	−1.26310	+	39.9801i	−0.0315775	+	0.999501i
$41$	55.3081	+	17.9707i	1.34898	+	0.438309i	0.892348	−	0.451348i	$-0.149057\pi$
$41$	55.3081	+	17.9707i	1.34898	+	0.438309i	0.456629	+	0.889657i	$0.349057\pi$
$42$	50.0725	−	62.8844i	1.19220	−	1.49725i
$43$	−8.50943	+	8.50943i	−0.197894	+	0.197894i	−0.799096	−	0.601203i	$-0.794688\pi$
$43$	−8.50943	+	8.50943i	−0.197894	+	0.197894i	0.601203	+	0.799096i	$0.294688\pi$
$44$	−31.9269	+	30.2766i	−0.725611	+	0.688105i
$45$	−8.76557	+	40.4653i	−0.194790	+	0.899229i
$46$	9.09050	+	80.1471i	0.197620	+	1.74233i
$47$	−17.2467	−	33.8485i	−0.366951	−	0.720181i	0.631526	−	0.775355i	$-0.282429\pi$
$47$	−17.2467	−	33.8485i	−0.366951	−	0.720181i	−0.998477	+	0.0551733i	$0.982429\pi$
$48$	−40.1355	+	53.0379i	−0.836157	+	1.10496i
$49$	−26.1454	−	35.9860i	−0.533579	−	0.734408i
$50$	−49.3809	+	7.84407i	−0.987617	+	0.156881i
$51$	1.75689	+	5.40715i	0.0344488	+	0.106023i
$52$	−55.9107	+	22.5235i	−1.07521	+	0.433145i
$53$	68.0547	−	10.7788i	1.28405	−	0.203374i	0.523149	−	0.852241i	$-0.324757\pi$
$53$	68.0547	−	10.7788i	1.28405	−	0.203374i	0.760902	+	0.648867i	$0.224757\pi$
$54$	4.41077	−	4.03762i	0.0816809	−	0.0747707i
$55$	−44.6734	−	32.0825i	−0.812244	−	0.583318i
$56$	46.9935	+	61.4362i	0.839170	+	1.09707i
$57$	70.0013	−	11.0871i	1.22809	−	0.194511i
$58$	12.2475	−	32.7068i	0.211163	−	0.563911i
$59$	−8.95586	−	27.5633i	−0.151794	−	0.467175i	0.846028	−	0.533139i	$-0.178988\pi$
$59$	−8.95586	−	27.5633i	−0.151794	−	0.467175i	−0.997822	+	0.0659641i	$0.978988\pi$
$60$	−74.5466	−	36.8118i	−1.24244	−	0.613529i
$61$	−39.1807	−	53.9276i	−0.642306	−	0.884058i	0.356430	−	0.934322i	$-0.383994\pi$
$61$	−39.1807	−	53.9276i	−0.642306	−	0.884058i	−0.998736	+	0.0502636i	$0.983994\pi$
$62$	61.2183	−	16.9440i	0.987392	−	0.273290i
$63$	36.3479	+	71.3368i	0.576951	+	1.13233i
$64$	−40.1252	−	49.8595i	−0.626957	−	0.779054i
$65$	−40.7908	−	63.3496i	−0.627550	−	0.974609i
$66$	−29.7886	−	86.4669i	−0.451343	−	1.31010i
$67$	−47.5763	+	47.5763i	−0.710094	+	0.710094i	−0.966555	−	0.256461i	$-0.917444\pi$
$67$	−47.5763	+	47.5763i	−0.710094	+	0.710094i	0.256461	+	0.966555i	$0.417444\pi$
$68$	−5.45773	+	0.376088i	−0.0802607	+	0.00553071i
$69$	−159.449	−	51.8081i	−2.31085	−	0.750841i
$70$	−64.3831	+	72.1313i	−0.919759	+	1.03045i
$71$	43.5437	+	59.9328i	0.613292	+	0.844124i	0.996843	−	0.0793955i	$-0.0252990\pi$
$71$	43.5437	+	59.9328i	0.613292	+	0.844124i	−0.383551	+	0.923520i	$0.625299\pi$
$72$	−31.5215	−	58.2662i	−0.437798	−	0.809252i
$73$	7.89363	−	15.4921i	0.108132	−	0.212221i	−0.830600	−	0.556870i	$-0.812002\pi$
$73$	7.89363	−	15.4921i	0.108132	−	0.212221i	0.938732	+	0.344649i	$0.112002\pi$
$74$	−26.8057	+	12.1997i	−0.362239	+	0.164861i
$75$	27.6768	−	100.172i	0.369024	−	1.33563i
$76$	−6.01254	+	67.9313i	−0.0791124	+	0.893833i
$77$	−106.151	+	6.56373i	−1.37859	+	0.0852433i
$78$	5.52827	−	125.164i	0.0708753	−	1.60467i
$79$	−81.3459	+	111.963i	−1.02970	+	1.41725i	−0.124519	+	0.992217i	$0.539739\pi$
$79$	−81.3459	+	111.963i	−1.02970	+	1.41725i	−0.905176	+	0.425037i	$0.860261\pi$
$80$	51.7842	−	60.9786i	0.647303	−	0.762233i
$81$	26.8708	+	82.6999i	0.331739	+	1.02099i
$82$	−64.1459	−	97.0206i	−0.782268	−	1.18318i
$83$	7.68527	−	48.5229i	0.0925937	−	0.584613i	−0.897146	−	0.441733i	$-0.854364\pi$
$83$	7.68527	−	48.5229i	0.0925937	−	0.584613i	0.989740	−	0.142880i	$-0.0456363\pi$
$84$	−156.685	+	36.0066i	−1.86530	+	0.428650i
$85$	−1.74422	−	6.61215i	−0.0205203	−	0.0777900i
$86$	23.9150	−	2.71250i	0.278081	−	0.0315407i
$87$	51.3298	+	51.3298i	0.589997	+	0.589997i
$88$	87.6716	−	7.59515i	0.996268	−	0.0863085i
$89$		−	52.5737i		−	0.590715i	−0.955387	−	0.295358i	$-0.904561\pi$
$89$		−	52.5737i		−	0.590715i	0.955387	−	0.295358i	$-0.0954388\pi$
$90$	64.1271	−	52.3911i	0.712523	−	0.582124i
$91$	−138.567	−	45.0231i	−1.52271	−	0.494760i
$92$	85.6261	−	136.722i	0.930718	−	1.48611i
$93$	−20.6535	+	130.401i	−0.222081	+	1.40216i
$94$	−15.1853	+	74.4452i	−0.161546	+	0.791970i
$95$	−84.8131	+	8.58130i	−0.892769	+	0.0903295i
$96$	128.871	−	32.9805i	1.34241	−	0.343547i
$97$	6.75594	+	42.6553i	0.0696488	+	0.439746i	0.997728	+	0.0673637i	$0.0214588\pi$
$97$	6.75594	+	42.6553i	0.0696488	+	0.439746i	−0.928080	+	0.372382i	$0.878541\pi$
$98$	−3.92548	+	88.8757i	−0.0400559	+	0.906895i
$99$	90.6749	+	8.66983i	0.915908	+	0.0875740i
$100$	87.0329	+	49.2470i	0.870329	+	0.492470i
$101$	−15.5309	+	21.3764i	−0.153771	+	0.211648i	−0.878952	−	0.476911i	$-0.841756\pi$
$101$	−15.5309	+	21.3764i	−0.153771	+	0.211648i	0.725180	+	0.688559i	$0.241756\pi$
$102$	3.98754	−	10.6487i	0.0390935	−	0.104399i
$103$	61.0453	−	119.808i	0.592672	−	1.16319i	−0.378677	−	0.925529i	$-0.623621\pi$
$103$	61.0453	−	119.808i	0.592672	−	1.16319i	0.971349	−	0.237656i	$-0.0763792\pi$
$104$	115.537	+	34.4147i	1.11094	+	0.330911i
$105$	−81.0249	−	183.904i	−0.771665	−	1.75147i
$106$	−119.906	−	67.9197i	−1.13119	−	0.640751i
$107$	−12.2464	+	6.23984i	−0.114452	+	0.0583162i	−0.510279	−	0.860009i	$-0.670458\pi$
$107$	−12.2464	+	6.23984i	−0.114452	+	0.0583162i	0.395827	+	0.918325i	$0.370458\pi$
$108$	−11.9312	+	0.822169i	−0.110474	+	0.00761268i
$109$	165.504			1.51839			0.759193	−	0.650865i	$-0.225594\pi$
$109$	165.504			1.51839			0.759193	+	0.650865i	$0.225594\pi$
$110$	29.9264	+	105.851i	0.272058	+	0.962281i
$111$		−	61.2147i		−	0.551484i
$112$	3.01307	−	154.668i	0.0269024	−	1.38096i
$113$	−61.5970	−	120.891i	−0.545106	−	1.06983i	−0.985124	−	0.171842i	$-0.945028\pi$
$113$	−61.5970	−	120.891i	−0.545106	−	1.06983i	0.440018	−	0.897989i	$-0.354972\pi$
$114$	−123.336	−	69.8624i	−1.08189	−	0.612828i
$115$	187.977	+	72.9964i	1.63458	+	0.634751i
$116$	−59.9090	+	35.9145i	−0.516457	+	0.309608i
$117$	111.184	+	56.6511i	0.950292	+	0.484198i
$118$	−20.3268	+	54.2826i	−0.172261	+	0.460022i
$119$	−10.6979	−	7.77251i	−0.0898987	−	0.0653152i
$120$	70.7737	+	150.467i	0.589781	+	1.25389i
$121$	−58.5204	+	105.907i	−0.483640	+	0.875267i
$122$	−5.88261	+	133.186i	−0.0482181	+	1.09169i
$123$	238.772	−	37.8178i	1.94124	−	0.307462i
$124$	−116.890	−	49.7568i	−0.942665	−	0.401264i
$125$	−40.0097	+	118.424i	−0.320077	+	0.947391i
$126$	32.0035	−	156.895i	0.253996	−	1.24520i
$127$	156.354	+	24.7640i	1.23113	+	0.194992i	0.737903	−	0.674907i	$-0.235816\pi$
$127$	156.354	+	24.7640i	1.23113	+	0.194992i	0.493230	+	0.869899i	$0.335816\pi$
$128$	0.663367	+	127.998i	0.00518256	+	0.999987i
$129$	−15.4589	+	47.5777i	−0.119837	+	0.368819i
$130$	−15.1016	+	149.934i	−0.116166	+	1.15334i
$131$	−5.86097			−0.0447402			−0.0223701	−	0.999750i	$-0.507121\pi$
$131$	−5.86097			−0.0447402			−0.0223701	+	0.999750i	$0.507121\pi$
$132$	−61.1155	+	172.396i	−0.462996	+	1.30603i
$133$	−116.561	+	116.561i	−0.876395	+	0.876395i
$134$	133.709	−	15.1656i	0.997826	−	0.113176i
$135$	−3.81306	−	14.4549i	−0.0282449	−	0.107073i
$136$	9.00762	+	6.21093i	0.0662325	+	0.0456686i
$137$	96.3927	+	15.2671i	0.703596	+	0.111439i	0.497973	−	0.867193i	$-0.334078\pi$
$137$	96.3927	+	15.2671i	0.703596	+	0.111439i	0.205623	+	0.978631i	$0.434078\pi$
$138$	184.928	+	279.703i	1.34006	+	2.02683i
$139$	−173.825	+	56.4793i	−1.25054	+	0.406326i	−0.858115	−	0.513457i	$-0.828364\pi$
$139$	−173.825	+	56.4793i	−1.25054	+	0.406326i	−0.392427	+	0.919783i	$0.628364\pi$
$140$	190.596	−	32.6457i	1.36140	−	0.233184i
$141$	−127.761	−	92.8237i	−0.906106	−	0.658324i
$142$	6.53768	−	148.018i	0.0460400	−	1.04238i
$143$	−127.835	+	105.523i	−0.893953	+	0.737922i
$144$	−23.2712	+	130.433i	−0.161606	+	0.905782i
$145$	−58.1705	−	65.1117i	−0.401176	−	0.449046i
$146$	−31.6507	+	14.4047i	−0.216786	+	0.0986624i
$147$	−164.755	−	83.9468i	−1.12078	−	0.571067i
$148$	57.1385	+	14.3077i	0.386071	+	0.0966736i
$149$	155.193	−	112.754i	1.04156	−	0.756740i	0.0709727	−	0.997478i	$-0.477390\pi$
$149$	155.193	−	112.754i	1.04156	−	0.756740i	0.970590	+	0.240739i	$0.0773897\pi$
$150$	−168.099	+	122.248i	−1.12066	+	0.814984i
$151$	−15.1857	+	46.7368i	−0.100568	+	0.309515i	−0.988665	−	0.150141i	$-0.952027\pi$
$151$	−15.1857	+	46.7368i	−0.100568	+	0.309515i	0.888097	+	0.459656i	$0.152027\pi$
$152$	94.0375	−	98.7938i	0.618667	−	0.649959i
$153$	8.00822	+	8.00822i	0.0523413	+	0.0523413i
$154$	174.260	+	121.976i	1.13156	+	0.792054i
$155$	33.6194	−	155.200i	0.216899	−	1.00129i
$156$	−164.582	+	188.943i	−1.05501	+	1.21117i
$157$	76.8684	−	39.1664i	0.489608	−	0.249468i	−0.191715	−	0.981451i	$-0.561405\pi$
$157$	76.8684	−	39.1664i	0.489608	−	0.249468i	0.681323	+	0.731983i	$0.261405\pi$
$158$	266.759	−	73.8333i	1.68835	−	0.467299i
$159$	231.727	−	168.360i	1.45741	−	1.05887i
$160$	−156.989	+	30.8924i	−0.981184	+	0.193077i
$161$	370.853	−	120.497i	2.30343	−	0.748431i
$162$	60.9876	−	162.867i	0.376467	−	1.00535i
$163$	−24.3448	−	153.707i	−0.149355	−	0.942988i	−0.942561	−	0.334035i	$-0.891590\pi$
$163$	−24.3448	−	153.707i	−0.149355	−	0.942988i	0.793206	−	0.608953i	$-0.208410\pi$
$164$	−20.5086	+	231.712i	−0.125052	+	1.41288i
$165$	−226.015	−	34.5214i	−1.36979	−	0.209221i
$166$	−72.4752	+	66.3438i	−0.436597	+	0.399661i
$167$	−17.2192	−	108.718i	−0.103109	−	0.651003i	−0.984065	−	0.177806i	$-0.943100\pi$
$167$	−17.2192	−	108.718i	−0.103109	−	0.651003i	0.880957	−	0.473197i	$-0.156900\pi$
$168$	290.006	+	138.867i	1.72622	+	0.826588i
$169$	−55.2393	+	17.9483i	−0.326860	+	0.106203i
$170$	−5.50857	+	12.5183i	−0.0324034	+	0.0736369i
$171$	114.218	−	82.9839i	0.667939	−	0.485286i
$172$	−40.7963	−	25.5498i	−0.237188	−	0.148546i
$173$	−226.175	+	115.242i	−1.30737	+	0.666139i	−0.962185	−	0.272395i	$-0.912184\pi$
$173$	−226.175	+	115.242i	−1.30737	+	0.666139i	−0.345186	+	0.938534i	$0.612184\pi$
$174$	−16.3621	−	144.258i	−0.0940350	−	0.829067i
$175$	84.8671	+	226.326i	0.484955	+	1.29329i
$176$	−146.632	−	97.3399i	−0.833136	−	0.553068i
$177$	−85.1906	−	85.1906i	−0.481303	−	0.481303i
$178$	−65.4974	+	82.2560i	−0.367963	+	0.462112i
$179$	11.0187	−	33.9120i	0.0615568	−	0.189452i	−0.915549	−	0.402207i	$-0.868243\pi$
$179$	11.0187	−	33.9120i	0.0615568	−	0.189452i	0.977106	+	0.212754i	$0.0682434\pi$
$180$	−165.602	+	2.07954i	−0.920013	+	0.0115530i
$181$	242.639	−	176.288i	1.34055	−	0.973965i	0.341124	−	0.940018i	$-0.389192\pi$
$181$	242.639	−	176.288i	1.34055	−	0.973965i	0.999424	−	0.0339465i	$-0.0108076\pi$
$182$	160.709	+	243.072i	0.883017	+	1.33556i
$183$	−246.897	−	125.800i	−1.34916	−	0.687433i
$184$	−304.301	+	107.239i	−1.65381	+	0.582819i
$185$	−4.13895	+	73.5118i	−0.0223727	+	0.397361i
$186$	194.771	−	178.293i	1.04715	−	0.958565i
$187$	−13.9938	+	5.52313i	−0.0748333	+	0.0295354i
$188$	116.504	−	97.5577i	0.619703	−	0.518924i
$189$	−23.3868	−	16.9915i	−0.123740	−	0.0899023i
$190$	143.388	+	92.2358i	0.754674	+	0.485452i
$191$	142.490	−	46.2978i	0.746021	−	0.242397i	0.0887529	−	0.996054i	$-0.471712\pi$
$191$	142.490	−	46.2978i	0.746021	−	0.242397i	0.657268	+	0.753657i	$0.271712\pi$
$192$	−242.718	−	108.950i	−1.26416	−	0.567446i
$193$	50.0238	+	7.92300i	0.259191	+	0.0410518i	0.284677	−	0.958623i	$-0.408113\pi$
$193$	50.0238	+	7.92300i	0.259191	+	0.0410518i	−0.0254865	+	0.999675i	$0.508113\pi$
$194$	42.5707	−	75.1546i	0.219436	−	0.387395i
$195$	−270.642	−	157.660i	−1.38791	−	0.808513i
$196$	116.865	−	134.163i	0.596250	−	0.684506i
$197$	152.828	−	152.828i	0.775779	−	0.775779i	−0.203331	−	0.979110i	$-0.565177\pi$
$197$	152.828	−	152.828i	0.775779	−	0.775779i	0.979110	+	0.203331i	$0.0651767\pi$
$198$	−131.068	−	126.529i	−0.661957	−	0.639037i
$199$	310.012			1.55785			0.778923	−	0.627119i	$-0.215766\pi$
$199$	310.012			1.55785			0.778923	+	0.627119i	$0.215766\pi$
$200$	−74.8174	−	185.479i	−0.374087	−	0.927394i
$201$	−86.4310	+	266.007i	−0.430005	+	1.32342i
$202$	50.9306	−	14.0965i	0.252132	−	0.0697849i
$203$	−166.757	−	26.4118i	−0.821464	−	0.130107i
$204$	−19.5053	+	11.6931i	−0.0956140	+	0.0573190i
$205$	−289.295	+	29.2705i	−1.41119	+	0.142783i
$206$	−244.770	+	111.399i	−1.18820	+	0.540769i
$207$	−329.856	+	52.2440i	−1.59351	+	0.252386i
$208$	−137.894	−	197.784i	−0.662950	−	0.950883i
$209$	40.7138	+	183.069i	0.194803	+	0.875927i
$210$	−102.341	+	388.676i	−0.487338	+	1.85084i
$211$	162.649	+	118.171i	0.770848	+	0.560054i	0.902218	−	0.431279i	$-0.141938\pi$
$211$	162.649	+	118.171i	0.770848	+	0.560054i	−0.131370	+	0.991333i	$0.541938\pi$
$212$	102.987	+	255.647i	0.485789	+	1.20588i
$213$	274.391	+	139.809i	1.28822	+	0.656381i
$214$	26.9342	+	5.49403i	0.125861	+	0.0256730i
$215$	21.7813	−	56.0901i	0.101308	−	0.260884i
$216$	19.6916	+	13.5778i	0.0911649	+	0.0628600i
$217$	−139.408	−	273.604i	−0.642435	−	1.26085i
$218$	−258.945	−	206.189i	−1.18782	−	0.945819i
$219$		−	72.2789i		−	0.330041i
$220$	85.0490	−	202.896i	0.386586	−	0.922253i
$221$	−20.6097			−0.0932566
$222$	−76.2626	+	95.7757i	−0.343525	+	0.431422i
$223$	−59.4794	+	30.3063i	−0.266724	+	0.135902i	−0.582238	−	0.813018i	$-0.697823\pi$
$223$	−59.4794	+	30.3063i	−0.266724	+	0.135902i	0.315515	+	0.948921i	$0.397823\pi$
$224$	−197.403	+	238.237i	−0.881261	+	1.06356i
$225$	−41.4675	−	202.824i	−0.184300	−	0.901438i
$226$	−54.2347	+	265.883i	−0.239977	+	1.17647i
$227$	0.435011	−	0.853757i	0.00191635	−	0.00376105i	−0.890046	−	0.455870i	$-0.849328\pi$
$227$	0.435011	−	0.853757i	0.00191635	−	0.00376105i	0.891963	+	0.452109i	$0.149328\pi$
$228$	105.933	+	262.960i	0.464619	+	1.15333i
$229$	141.556	−	194.835i	0.618147	−	0.850807i	−0.379069	−	0.925368i	$-0.623756\pi$
$229$	141.556	−	194.835i	0.618147	−	0.850807i	0.997216	+	0.0745614i	$0.0237557\pi$
$230$	−203.165	−	348.395i	−0.883327	−	1.51476i
$231$	−380.790	+	224.645i	−1.64844	+	0.972491i
$232$	138.476	+	18.4447i	0.596879	+	0.0795031i
$233$	−52.2463	−	329.870i	−0.224233	−	1.41575i	−0.800913	−	0.598781i	$-0.795652\pi$
$233$	−52.2463	−	329.870i	−0.224233	−	1.41575i	0.576680	−	0.816970i	$-0.304348\pi$
$234$	−103.380	−	227.151i	−0.441794	−	0.970731i
$235$	147.150	+	120.109i	0.626170	+	0.511102i
$236$	99.4294	−	59.6062i	0.421311	−	0.252569i
$237$	−89.9976	+	568.223i	−0.379737	+	2.39756i
$238$	7.05469	+	25.4885i	0.0296415	+	0.107094i
$239$	253.929	+	82.5064i	1.06246	+	0.345215i	0.787548	−	0.616254i	$-0.211350\pi$
$239$	253.929	+	82.5064i	1.06246	+	0.345215i	0.274915	+	0.961469i	$0.411350\pi$
$240$	76.7234	−	323.590i	0.319681	−	1.34829i
$241$			331.121i			1.37395i	0.726682	+	0.686974i	$0.241061\pi$
$241$			331.121i			1.37395i	−0.726682	+	0.686974i	$0.758939\pi$
$242$	223.502	−	92.7951i	0.923561	−	0.383451i
$243$	236.575	+	236.575i	0.973560	+	0.973560i
$244$	175.130	−	201.053i	0.717747	−	0.823987i
$245$	192.176	+	111.950i	0.784391	+	0.456939i
$246$	−420.694	−	238.298i	−1.71014	−	0.968692i
$247$	−40.1910	+	253.756i	−0.162716	+	1.02735i
$248$	120.897	+	223.473i	0.487488	+	0.901102i
$249$	−63.1089	−	194.229i	−0.253449	−	0.780037i
$250$	210.134	−	135.439i	0.840535	−	0.541758i
$251$	−147.258	+	202.683i	−0.586686	+	0.807503i	−0.994408	−	0.105602i	$-0.966323\pi$
$251$	−147.258	+	202.683i	−0.586686	+	0.807503i	0.407723	+	0.913106i	$0.366323\pi$
$252$	−245.536	+	205.606i	−0.974349	+	0.815896i
$253$	110.790	−	429.579i	0.437906	−	1.69794i
$254$	−213.778	−	233.534i	−0.841644	−	0.919427i
$255$	−18.9392	−	21.1991i	−0.0742715	−	0.0831339i
$256$	158.425	−	201.091i	0.618848	−	0.785511i
$257$	−78.0036	+	153.091i	−0.303516	+	0.595683i	−0.991510	−	0.130033i	$-0.958492\pi$
$257$	−78.0036	+	153.091i	−0.303516	+	0.595683i	0.687994	+	0.725717i	$0.258492\pi$
$258$	83.4601	−	55.1803i	0.323489	−	0.213877i
$259$	83.6864	+	115.184i	0.323114	+	0.444728i
$260$	210.419	−	215.770i	0.809302	−	0.829886i
$261$	137.524	+	44.6844i	0.526913	+	0.171205i
$262$	9.16999	+	7.30173i	0.0350000	+	0.0278692i
$263$	−108.429	+	108.429i	−0.412277	+	0.412277i	−0.882531	−	0.470254i	$-0.844162\pi$
$263$	−108.429	+	108.429i	−0.412277	+	0.412277i	0.470254	+	0.882531i	$0.344162\pi$
$264$	310.395	−	193.590i	1.17574	−	0.733294i
$265$	−289.661	+	186.513i	−1.09306	+	0.703822i
$266$	327.583	−	37.1553i	1.23151	−	0.139682i
$267$	−99.2194	−	194.729i	−0.371608	−	0.729322i
$268$	−228.092	−	142.849i	−0.851091	−	0.533020i
$269$	−6.26232	−	8.61934i	−0.0232800	−	0.0320422i	0.797218	−	0.603691i	$-0.206304\pi$
$269$	−6.26232	−	8.61934i	−0.0232800	−	0.0320422i	−0.820498	+	0.571649i	$0.806304\pi$
$270$	−12.0423	+	27.3663i	−0.0446012	+	0.101357i
$271$	−22.7928	−	70.1491i	−0.0841063	−	0.258853i	0.900156	−	0.435569i	$-0.143453\pi$
$271$	−22.7928	−	70.1491i	−0.0841063	−	0.258853i	−0.984262	+	0.176716i	$0.943453\pi$
$272$	−6.35548	−	20.9394i	−0.0233657	−	0.0769832i
$273$	−598.212	+	94.7474i	−2.19125	+	0.347060i
$274$	−131.795	−	143.975i	−0.481002	−	0.525455i
$275$	269.083	+	56.7379i	0.978485	+	0.206320i
$276$	59.1246	−	668.006i	0.214220	−	2.42031i
$277$	56.2013	−	8.90142i	0.202893	−	0.0321351i	−0.0541607	−	0.998532i	$-0.517248\pi$
$277$	56.2013	−	8.90142i	0.202893	−	0.0321351i	0.257054	+	0.966397i	$0.417248\pi$
$278$	342.328	+	128.189i	1.23139	+	0.461110i
$279$	81.2705	+	250.125i	0.291292	+	0.896504i
$280$	−338.874	−	186.371i	−1.21026	−	0.665611i
$281$	−56.4746	−	77.7306i	−0.200977	−	0.276621i	0.696618	−	0.717442i	$-0.254687\pi$
$281$	−56.4746	−	77.7306i	−0.200977	−	0.276621i	−0.897595	+	0.440821i	$0.854687\pi$
$282$	84.2511	+	304.398i	0.298763	+	1.07943i
$283$	−86.9801	−	170.708i	−0.307350	−	0.603209i	0.684733	−	0.728794i	$-0.259919\pi$
$283$	−86.9801	−	170.708i	−0.307350	−	0.603209i	−0.992083	+	0.125586i	$0.959919\pi$
$284$	−194.632	+	223.442i	−0.685326	+	0.786767i
$285$	−297.946	+	191.848i	−1.04543	+	0.673149i
$286$	331.472	−	5.83964i	1.15899	−	0.0204183i
$287$	−397.584	+	397.584i	−1.38531	+	1.38531i
$288$	198.906	−	175.081i	0.690644	−	0.607920i
$289$	273.076	+	88.7279i	0.944901	+	0.307017i
$290$	9.89521	+	174.343i	0.0341214	+	0.601183i
$291$	105.525	+	145.242i	0.362627	+	0.499114i
$292$	67.4659	+	16.8937i	0.231048	+	0.0578552i
$293$	116.615	−	228.870i	0.398004	−	0.781127i	−0.601843	−	0.798614i	$-0.705567\pi$
$293$	116.615	−	228.870i	0.398004	−	0.781127i	0.999847	+	0.0174874i	$0.00556670\pi$
$294$	153.190	+	336.597i	0.521056	+	1.14489i
$295$	96.5440	+	108.064i	0.327268	+	0.366319i
$296$	−71.5732	−	93.5699i	−0.241801	−	0.316115i
$297$	−30.5920	+	12.0741i	−0.103003	+	0.0406537i
$298$	−383.284	−	16.9290i	−1.28619	−	0.0568086i
$299$	357.226	−	491.680i	1.19474	−	1.64441i
$300$	415.305	+	18.1550i	1.38435	+	0.0605166i
$301$	−35.9550	−	110.658i	−0.119452	−	0.367635i
$302$	81.9851	−	54.2051i	0.271474	−	0.179487i
$303$	−17.1827	+	108.487i	−0.0567086	+	0.358044i
$304$	−270.209	+	37.4175i	−0.888846	+	0.123084i
$305$	287.989	+	167.765i	0.944226	+	0.550050i
$306$	−2.55273	−	22.5064i	−0.00834227	−	0.0735502i
$307$	45.8431	+	45.8431i	0.149326	+	0.149326i	0.777817	−	0.628491i	$-0.216327\pi$
$307$	45.8431	+	45.8431i	0.149326	+	0.149326i	−0.628491	+	0.777817i	$0.716327\pi$
$308$	−120.685	−	407.940i	−0.391833	−	1.32448i
$309$		−	558.968i		−	1.80896i
$310$	−245.952	+	200.940i	−0.793394	+	0.648194i
$311$	56.4604	+	18.3451i	0.181545	+	0.0589874i	0.398379	−	0.917221i	$-0.369573\pi$
$311$	56.4604	+	18.3451i	0.181545	+	0.0589874i	−0.216834	+	0.976208i	$0.569573\pi$
$312$	492.891	−	90.5778i	1.57978	−	0.290313i
$313$	−45.5433	+	287.549i	−0.145506	+	0.918687i	0.801622	+	0.597831i	$0.203971\pi$
$313$	−45.5433	+	287.549i	−0.145506	+	0.918687i	−0.947128	+	0.320856i	$0.896029\pi$
$314$	−169.062	−	34.4851i	−0.538413	−	0.109825i
$315$	−310.123	−	253.133i	−0.984517	−	0.803597i
$316$	−509.350	−	216.815i	−1.61187	−	0.686124i
$317$	62.4007	+	393.983i	0.196848	+	1.24285i	0.866122	+	0.499832i	$0.166605\pi$
$317$	62.4007	+	393.983i	0.196848	+	1.24285i	−0.669275	+	0.743015i	$0.733395\pi$
$318$	−572.304	−	25.2776i	−1.79970	−	0.0794894i
$319$	−127.184	+	143.949i	−0.398695	+	0.451250i
$320$	284.110	+	147.247i	0.887843	+	0.460147i
$321$	−33.5836	+	46.2238i	−0.104622	+	0.143999i
$322$	−730.350	−	273.488i	−2.26817	−	0.849342i
$323$	−10.5860	+	20.7762i	−0.0327740	+	0.0643226i
$324$	−298.324	+	178.840i	−0.920753	+	0.551976i
$325$	314.350	+	207.631i	0.967231	+	0.638863i
$326$	−153.402	+	270.817i	−0.470558	+	0.830727i
$327$	613.015	−	312.347i	1.87466	−	0.955189i
$328$	320.759	−	336.983i	0.977923	−	1.02739i
$329$	367.300			1.11641
$330$	310.612	+	335.586i	0.941247	+	1.01693i
$331$		−	470.924i		−	1.42273i	−0.702822	−	0.711366i	$-0.748077\pi$
$331$		−	470.924i		−	1.42273i	0.702822	−	0.711366i	$-0.251923\pi$
$332$	196.046	−	13.5094i	0.590500	−	0.0406910i
$333$	−55.3594	−	108.649i	−0.166244	−	0.326273i
$334$	−108.502	+	191.550i	−0.324856	+	0.573503i
$335$	121.779	−	313.600i	0.363520	−	0.936119i
$336$	−280.736	−	578.564i	−0.835523	−	1.72192i
$337$	263.378	+	134.198i	0.781536	+	0.398213i	0.798768	−	0.601639i	$-0.205485\pi$
$337$	263.378	+	134.198i	0.781536	+	0.398213i	−0.0172318	+	0.999852i	$0.505485\pi$
$338$	108.787	+	40.7366i	0.321855	+	0.120523i
$339$	−456.301	−	331.522i	−1.34602	−	0.977942i
$340$	24.2142	−	12.7232i	0.0712181	−	0.0374212i
$341$	−347.773	−	33.2522i	−1.01986	−	0.0975136i
$342$	−282.086	−	12.4592i	−0.824814	−	0.0364305i
$343$	−43.1528	+	6.83474i	−0.125810	+	0.0199263i
$344$	31.9988	+	90.7998i	0.0930197	+	0.263953i
$345$	834.014	−	84.3847i	2.41743	−	0.244593i
$346$	497.442	+	101.468i	1.43769	+	0.293260i
$347$	−106.604	−	16.8844i	−0.307215	−	0.0486581i	0.000923451	−	1.00000i	$-0.499706\pi$
$347$	−106.604	−	16.8844i	−0.307215	−	0.0486581i	−0.308139	+	0.951341i	$0.599706\pi$
$348$	−154.119	+	246.088i	−0.442872	+	0.707148i
$349$	33.9663	−	104.538i	0.0973248	−	0.299535i	−0.890528	−	0.454929i	$-0.849665\pi$
$349$	33.9663	−	104.538i	0.0973248	−	0.299535i	0.987853	+	0.155394i	$0.0496647\pi$
$350$	149.179	−	459.835i	0.426227	−	1.31381i
$351$	−45.0550			−0.128362
$352$	108.150	+	334.974i	0.307245	+	0.951631i
$353$	−78.2550	+	78.2550i	−0.221685	+	0.221685i	−0.809208	−	0.587522i	$-0.800103\pi$
$353$	−78.2550	+	78.2550i	−0.221685	+	0.221685i	0.587522	+	0.809208i	$0.300103\pi$
$354$	27.1557	+	239.420i	0.0767110	+	0.676328i
$355$	−320.059	−	186.447i	−0.901573	−	0.525203i
$356$	204.953	−	47.0985i	0.575710	−	0.132299i
$357$	−54.2930	−	8.59917i	−0.152081	−	0.0240873i
$358$	−59.4879	+	39.3309i	−0.166167	+	0.109863i
$359$	−287.561	+	93.4341i	−0.801004	+	0.260262i	−0.680783	−	0.732485i	$-0.738360\pi$
$359$	−287.561	+	93.4341i	−0.801004	+	0.260262i	−0.120221	+	0.992747i	$0.538360\pi$
$360$	261.690	+	203.057i	0.726916	+	0.564048i
$361$	−56.8933	−	41.3354i	−0.157599	−	0.114502i
$362$	−599.253	−	26.4679i	−1.65539	−	0.0731158i
$363$	−16.8823	+	502.715i	−0.0465077	+	1.38489i
$364$	51.3815	−	580.522i	0.141158	−	1.59484i
$365$	−4.88704	+	86.7986i	−0.0133892	+	0.237804i
$366$	229.567	+	504.415i	0.627231	+	1.37818i
$367$	−440.526	−	224.459i	−1.20034	−	0.611606i	−0.264624	−	0.964352i	$-0.585248\pi$
$367$	−440.526	−	224.459i	−1.20034	−	0.611606i	−0.935719	+	0.352746i	$0.885248\pi$
$368$	609.705	+	211.320i	1.65681	+	0.574240i
$369$	389.592	−	283.055i	1.05581	−	0.767088i
$370$	98.0583	−	109.859i	0.265022	−	0.296916i
$371$	−205.865	+	633.588i	−0.554892	+	1.70778i
$372$	−526.857	+	36.3054i	−1.41628	+	0.0975951i
$373$	−31.8614	−	31.8614i	−0.0854194	−	0.0854194i	0.663106	−	0.748525i	$-0.269238\pi$
$373$	−31.8614	−	31.8614i	−0.0854194	−	0.0854194i	−0.748525	+	0.663106i	$0.769238\pi$
$374$	28.7754	+	8.79241i	0.0769395	+	0.0235091i
$375$	75.3021	+	514.142i	0.200806	+	1.37104i
$376$	−303.820	+	7.49405i	−0.808033	+	0.0199310i
$377$	−234.463	+	119.465i	−0.621919	+	0.316884i
$378$	15.4223	+	55.7205i	0.0407997	+	0.147409i
$379$	−73.7409	+	53.5759i	−0.194567	+	0.141361i	−0.680804	−	0.732466i	$-0.738369\pi$
$379$	−73.7409	+	53.5759i	−0.194567	+	0.141361i	0.486237	+	0.873827i	$0.338369\pi$
$380$	−109.434	−	322.947i	−0.287983	−	0.849860i
$381$	625.859	−	203.354i	1.64267	−	0.533737i
$382$	−280.617	−	105.080i	−0.734599	−	0.275079i
$383$	54.1330	+	341.782i	0.141339	+	0.892382i	0.951829	+	0.306629i	$0.0992011\pi$
$383$	54.1330	+	341.782i	0.141339	+	0.892382i	−0.810490	+	0.585753i	$0.800799\pi$
$384$	244.021	+	472.844i	0.635472	+	1.23137i
$385$	472.474	−	244.027i	1.22720	−	0.633835i
$386$	−68.3960	−	74.7170i	−0.177192	−	0.193567i
$387$	15.5890	+	98.4251i	0.0402817	+	0.254328i
$388$	−160.235	+	64.5503i	−0.412976	+	0.166367i
$389$	−657.590	+	213.664i	−1.69046	+	0.549265i	−0.986895	−	0.161364i	$-0.948411\pi$
$389$	−657.590	+	213.664i	−1.69046	+	0.549265i	−0.703568	+	0.710628i	$0.748411\pi$
$390$	227.027	+	583.844i	0.582119	+	1.49704i
$391$	44.6243	−	32.4215i	0.114129	−	0.0829194i
$392$	−349.989	+	64.3169i	−0.892828	+	0.164074i
$393$	−21.7086	+	11.0611i	−0.0552382	+	0.0281453i
$394$	−429.510	+	48.7162i	−1.09013	+	0.123645i
$395$	146.496	−	676.285i	0.370877	−	1.71211i
$396$	47.4334	+	361.253i	0.119781	+	0.912255i
$397$	390.071	+	390.071i	0.982548	+	0.982548i	0.999850	−	0.0173026i	$-0.00550788\pi$
$397$	390.071	+	390.071i	0.982548	+	0.982548i	−0.0173026	+	0.999850i	$0.505508\pi$
$398$	−485.040	−	386.219i	−1.21869	−	0.970400i
$399$	−211.753	+	651.710i	−0.530710	+	1.63336i
$400$	−114.015	+	383.407i	−0.285038	+	0.958516i
$401$	−461.219	+	335.095i	−1.15017	+	0.835649i	−0.988504	−	0.151197i	$-0.951687\pi$
$401$	−461.219	+	335.095i	−1.15017	+	0.835649i	−0.161668	+	0.986845i	$0.551687\pi$
$402$	466.626	−	308.513i	1.16076	−	0.767446i
$403$	−426.434	−	217.279i	−1.05815	−	0.539154i
$404$	−97.2471	−	41.3952i	−0.240711	−	0.102463i
$405$	−289.667	−	324.231i	−0.715227	−	0.800571i
$406$	228.002	+	249.073i	0.561581	+	0.613481i
$407$	161.673	−	9.99685i	0.397232	−	0.0245623i
$408$	45.0851	+	6.00525i	0.110503	+	0.0147187i
$409$	629.299	+	457.212i	1.53863	+	1.11788i	0.951188	+	0.308611i	$0.0998642\pi$
$409$	629.299	+	457.212i	1.53863	+	1.11788i	0.587440	+	0.809268i	$0.300136\pi$
$410$	489.092	+	314.613i	1.19291	+	0.767349i
$411$	385.844	−	125.368i	0.938793	−	0.305032i
$412$	521.746	+	130.647i	1.26637	+	0.317105i
$413$	276.762	+	43.8349i	0.670127	+	0.106138i
$414$	581.174	+	329.201i	1.40380	+	0.795172i
$415$	62.6540	+	237.514i	0.150973	+	0.572323i
$416$	−30.6569	+	481.240i	−0.0736945	+	1.15683i
$417$	−537.246	+	537.246i	−1.28836	+	1.28836i
$418$	164.371	−	337.149i	0.393232	−	0.806576i
$419$	−75.2997			−0.179713			−0.0898564	−	0.995955i	$-0.528641\pi$
$419$	−75.2997			−0.179713			−0.0898564	+	0.995955i	$0.528641\pi$
$420$	644.342	−	480.618i	1.53415	−	1.14433i
$421$	220.448	−	678.468i	0.523628	−	1.61156i	−0.243384	−	0.969930i	$-0.578257\pi$
$421$	220.448	−	678.468i	0.523628	−	1.61156i	0.767012	−	0.641632i	$-0.221743\pi$
$422$	−107.258	−	387.521i	−0.254165	−	0.918296i
$423$	−310.706	−	49.2110i	−0.734529	−	0.116338i
$424$	157.359	−	528.286i	0.371129	−	1.24596i
$425$	21.3105	+	26.7383i	0.0501423	+	0.0629136i
$426$	−255.131	−	560.585i	−0.598898	−	1.31593i
$427$	636.554	−	100.820i	1.49076	−	0.236113i
$428$	−35.2963	−	42.1511i	−0.0824680	−	0.0984839i
$429$	−274.345	+	632.105i	−0.639499	+	1.47344i
$430$	−103.957	+	60.6221i	−0.241760	+	0.140982i
$431$	−362.923	−	263.679i	−0.842050	−	0.611785i	0.0808928	−	0.996723i	$-0.474223\pi$
$431$	−362.923	−	263.679i	−0.842050	−	0.611785i	−0.922942	+	0.384938i	$0.874223\pi$
$432$	−13.8938	−	45.7758i	−0.0321615	−	0.105963i
$433$	130.247	+	66.3642i	0.300801	+	0.153266i	0.597877	−	0.801588i	$-0.296011\pi$
$433$	130.247	+	66.3642i	0.300801	+	0.153266i	−0.297075	+	0.954854i	$0.596011\pi$
$434$	−122.746	+	601.755i	−0.282824	+	1.38653i
$435$	−338.341	−	131.387i	−0.777796	−	0.302039i
$436$	148.268	+	645.199i	0.340064	+	1.47982i
$437$	−312.165	−	612.659i	−0.714337	−	1.40197i
$438$	−90.0466	+	113.087i	−0.205586	+	0.258189i
$439$			167.234i			0.380944i	0.981693	+	0.190472i	$0.0610018\pi$
$439$			167.234i			0.380944i	−0.981693	+	0.190472i	$0.938998\pi$
$440$	−385.838	+	211.492i	−0.876905	+	0.480663i
$441$	−368.338			−0.835234
$442$	32.2457	+	25.6760i	0.0729540	+	0.0580906i
$443$	433.230	−	220.742i	0.977947	−	0.498289i	0.109455	−	0.993992i	$-0.465090\pi$
$443$	433.230	−	220.742i	0.977947	−	0.498289i	0.868492	+	0.495703i	$0.165090\pi$
$444$	238.639	−	54.8396i	0.537475	−	0.123513i
$445$	105.985	+	240.556i	0.238168	+	0.540574i
$446$	130.817	+	26.6840i	0.293311	+	0.0598295i
$447$	362.028	−	710.520i	0.809906	−	1.58953i
$448$	605.654	−	126.814i	1.35191	−	0.283067i
$449$	−228.830	+	314.958i	−0.509644	+	0.701465i	−0.983859	−	0.178944i	$-0.942732\pi$
$449$	−228.830	+	314.958i	−0.509644	+	0.701465i	0.474215	+	0.880409i	$0.342732\pi$
$450$	−187.802	+	368.996i	−0.417339	+	0.819991i
$451$	138.873	+	624.442i	0.307923	+	1.38457i
$452$	416.098	−	348.430i	0.920570	−	0.770863i
$453$	31.9571	+	201.769i	0.0705454	+	0.445406i
$454$	−1.74424	+	0.793830i	−0.00384194	+	0.00174852i
$455$	724.789	−	73.3334i	1.59294	−	0.161172i
$456$	161.860	−	543.397i	0.354955	−	1.19166i
$457$	−17.6947	+	111.720i	−0.0387191	+	0.244463i	−0.999455	−	0.0330004i	$-0.989494\pi$
$457$	−17.6947	+	111.720i	−0.0387191	+	0.244463i	0.960736	+	0.277463i	$0.0894937\pi$
$458$	−464.206	+	128.483i	−1.01355	+	0.280530i
$459$	−3.88901	−	1.26361i	−0.00847278	−	0.00275297i
$460$	−116.168	+	798.201i	−0.252539	+	1.73522i
$461$			154.413i			0.334952i	0.985876	+	0.167476i	$0.0535616\pi$
$461$			154.413i			0.334952i	−0.985876	+	0.167476i	$0.946438\pi$
$462$	875.647	+	122.919i	1.89534	+	0.266059i
$463$	177.865	+	177.865i	0.384157	+	0.384157i	0.872597	−	0.488440i	$-0.162434\pi$
$463$	177.865	+	177.865i	0.384157	+	0.384157i	−0.488440	+	0.872597i	$0.662434\pi$
$464$	−193.679	−	201.375i	−0.417411	−	0.433997i
$465$	−168.377	−	638.298i	−0.362101	−	1.37268i
$466$	−329.216	+	581.200i	−0.706471	+	1.24721i
$467$	13.3565	−	84.3293i	0.0286005	−	0.180577i	−0.969253	−	0.246068i	$-0.920861\pi$
$467$	13.3565	−	84.3293i	0.0286005	−	0.180577i	0.997853	+	0.0654911i	$0.0208614\pi$
$468$	−121.243	+	484.190i	−0.259066	+	1.03459i
$469$	−201.025	−	618.691i	−0.428625	−	1.31917i
$470$	−80.5944	−	371.243i	−0.171477	−	0.789879i
$471$	210.798	−	290.139i	0.447555	−	0.616007i
$472$	−229.824	−	30.6122i	−0.486916	−	0.0648563i
$473$	−128.181	−	33.0585i	−0.270996	−	0.0698912i
$474$	848.713	−	776.912i	1.79053	−	1.63905i
$475$	370.771	−	210.242i	0.780570	−	0.442614i
$476$	20.7164	−	48.6678i	0.0435219	−	0.102243i
$477$	259.033	−	508.381i	0.543047	−	1.06579i
$478$	−294.505	−	445.438i	−0.616119	−	0.931879i
$479$	35.5151	+	48.8823i	0.0741442	+	0.102051i	0.844478	−	0.535590i	$-0.179911\pi$
$479$	35.5151	+	48.8823i	0.0741442	+	0.102051i	−0.770334	+	0.637640i	$0.779911\pi$
$480$	−523.176	+	410.700i	−1.08995	+	0.855626i
$481$	211.044	+	68.5722i	0.438760	+	0.142562i
$482$	412.518	−	518.068i	0.855846	−	1.07483i
$483$	1146.20	−	1146.20i	2.37309	−	2.37309i
$484$	−465.294	−	133.258i	−0.961351	−	0.275326i
$485$	−116.902	−	181.554i	−0.241036	−	0.374338i
$486$	−75.4117	−	664.872i	−0.155168	−	1.36805i
$487$	359.000	+	704.576i	0.737165	+	1.44677i	0.888783	+	0.458329i	$0.151552\pi$
$487$	359.000	+	704.576i	0.737165	+	1.44677i	−0.151617	+	0.988439i	$0.548448\pi$
$488$	−524.483	+	96.3833i	−1.07476	+	0.197507i
$489$	−380.254	−	523.375i	−0.777616	−	1.07030i
$490$	−161.205	−	414.572i	−0.328991	−	0.846066i
$491$	−185.086	−	569.636i	−0.376957	−	1.16015i	−0.942149	−	0.335195i	$-0.891198\pi$
$491$	−185.086	−	569.636i	−0.376957	−	1.16015i	0.565192	−	0.824960i	$-0.308802\pi$
$492$	361.334	+	896.947i	0.734419	+	1.82306i
$493$	−23.5887	+	3.73608i	−0.0478472	+	0.00757825i
$494$	379.017	−	346.952i	0.767240	−	0.702332i
$495$	−432.369	+	143.124i	−0.873473	+	0.289140i
$496$	89.2542	−	500.259i	0.179948	−	1.00859i
$497$	−707.439	+	112.047i	−1.42342	+	0.225447i
$498$	−143.236	+	382.511i	−0.287622	+	0.768094i
$499$	−132.275	−	407.100i	−0.265080	−	0.815831i	−0.991675	−	0.128765i	$-0.958899\pi$
$499$	−132.275	−	407.100i	−0.265080	−	0.815831i	0.726596	−	0.687065i	$-0.241101\pi$
$500$	−497.506	−	49.8823i	−0.995011	−	0.0997646i
$501$	−268.955	−	370.185i	−0.536837	−	0.738893i
$502$	482.905	−	133.658i	0.961963	−	0.266251i
$503$	−213.577	−	419.169i	−0.424606	−	0.833337i	−0.999882	−	0.0153773i	$-0.995105\pi$
$503$	−213.577	−	419.169i	−0.424606	−	0.833337i	0.575275	−	0.817960i	$-0.304895\pi$
$504$	640.310	−	15.7939i	1.27046	−	0.0313372i
$505$	27.9697	−	129.119i	0.0553855	−	0.255681i
$506$	−708.519	+	534.088i	−1.40024	+	1.05551i
$507$	−170.730	+	170.730i	−0.336745	+	0.336745i
$508$	43.5310	+	631.713i	0.0856908	+	1.24353i
$509$	−267.827	−	87.0222i	−0.526183	−	0.170967i	0.0338668	−	0.999426i	$-0.489218\pi$
$509$	−267.827	−	87.0222i	−0.526183	−	0.170967i	−0.560049	+	0.828459i	$0.689218\pi$
$510$	3.22169	+	56.7628i	0.00631704	+	0.111300i
$511$	98.8123	+	136.003i	0.193370	+	0.266152i
$512$	−498.393	+	117.254i	−0.973424	+	0.229012i
$513$	−23.1421	+	45.4190i	−0.0451114	+	0.0885360i
$514$	312.767	−	142.345i	0.608496	−	0.276936i
$515$	−37.7938	+	671.256i	−0.0733861	+	1.30341i
$516$	−199.325	−	17.6421i	−0.386289	−	0.0341901i
$517$	224.291	−	352.586i	0.433832	−	0.681985i
$518$	12.5647	−	284.474i	0.0242562	−	0.549178i
$519$	−620.247	+	853.696i	−1.19508	+	1.64489i
$520$	−598.029	+	75.4473i	−1.15006	+	0.145091i
$521$	−221.985	−	683.199i	−0.426075	−	1.31132i	−0.901961	−	0.431817i	$-0.857873\pi$
$521$	−221.985	−	683.199i	−0.426075	−	1.31132i	0.475887	−	0.879507i	$-0.342127\pi$
$522$	−159.500	−	241.243i	−0.305555	−	0.462152i
$523$	−24.7307	+	156.143i	−0.0472862	+	0.298553i	−0.999986	−	0.00536075i	$-0.998294\pi$
$523$	−24.7307	+	156.143i	−0.0472862	+	0.298553i	0.952699	+	0.303914i	$0.0982936\pi$
$524$	−5.25059	−	22.8483i	−0.0100202	−	0.0436037i
$525$	741.473	+	678.129i	1.41233	+	1.29167i
$526$	304.730	−	34.5633i	0.579334	−	0.0657096i
$527$	−30.7146	−	30.7146i	−0.0582820	−	0.0582820i
$528$	−726.818	−	83.8095i	−1.37655	−	0.158730i
$529$			1097.55i			2.07476i
$530$	685.562	+	69.0510i	1.29351	+	0.130285i
$531$	−228.245	−	74.1614i	−0.429841	−	0.139664i
$532$	−558.820	−	349.977i	−1.05041	−	0.657851i
$533$	−137.090	+	865.553i	−0.257205	+	1.62393i
$534$	−87.3603	+	428.280i	−0.163596	+	0.802022i
$535$	43.4553	−	53.2387i	0.0812249	−	0.0995117i
$536$	178.905	+	507.662i	0.333779	+	0.947131i
$537$	−23.1879	−	146.402i	−0.0431804	−	0.272630i
$538$	−0.940228	+	21.2874i	−0.00174763	+	0.0395677i
$539$	194.805	−	448.841i	0.361419	−	0.832729i
$540$	52.9347	−	27.8143i	0.0980273	−	0.0515079i
$541$	53.3300	−	73.4025i	0.0985767	−	0.135679i	−0.756879	−	0.653555i	$-0.773277\pi$
$541$	53.3300	−	73.4025i	0.0985767	−	0.135679i	0.855456	+	0.517875i	$0.173277\pi$
$542$	−51.7319	+	138.150i	−0.0954463	+	0.254889i
$543$	566.020	−	1110.88i	1.04239	−	2.04581i
$544$	−16.1431	+	40.6793i	−0.0296748	+	0.0747782i
$545$	−757.279	+	333.644i	−1.38950	+	0.612191i
$546$	1053.99	+	597.025i	1.93039	+	1.09345i
$547$	3.19096	−	1.62587i	0.00583356	−	0.00297235i	−0.451071	−	0.892488i	$-0.648958\pi$
$547$	3.19096	−	1.62587i	0.00583356	−	0.00297235i	0.456905	+	0.889516i	$0.348958\pi$
$548$	26.8370	+	389.453i	0.0489726	+	0.710681i
$549$	−551.980			−1.00543
$550$	−350.319	−	424.001i	−0.636943	−	0.770911i
$551$			297.720i			0.540326i
$552$	−924.722	+	971.494i	−1.67522	+	1.75995i
$553$	−607.471	−	1192.23i	−1.09850	−	2.15593i
$554$	−99.0214	−	56.0898i	−0.178739	−	0.101245i
$555$	123.404	+	280.093i	0.222350	+	0.504673i
$556$	−375.901	−	627.042i	−0.676081	−	1.12777i
$557$	−863.464	−	439.957i	−1.55020	−	0.789869i	−0.551196	−	0.834376i	$-0.685828\pi$
$557$	−863.464	−	439.957i	−1.55020	−	0.789869i	−0.999009	+	0.0445073i	$0.985828\pi$
$558$	184.456	−	492.590i	0.330567	−	0.882778i
$559$	−146.712	−	106.592i	−0.262454	−	0.190684i
$560$	298.012	+	713.770i	0.532165	+	1.27459i
$561$	−41.4086	+	46.8670i	−0.0738122	+	0.0835420i
$562$	−8.47912	+	191.973i	−0.0150874	+	0.341590i
$563$	−649.340	+	102.845i	−1.15336	+	0.182674i	−0.703680	−	0.710517i	$-0.748461\pi$
$563$	−649.340	+	102.845i	−1.15336	+	0.182674i	−0.449677	+	0.893191i	$0.648461\pi$
$564$	247.408	−	581.219i	0.438666	−	1.03053i
$565$	525.550	+	428.972i	0.930177	+	0.759243i
$566$	−76.5840	+	375.449i	−0.135307	+	0.663338i
$567$	−830.387	−	131.520i	−1.46453	−	0.231958i
$568$	582.888	−	107.116i	1.02621	−	0.188585i
$569$	173.147	−	532.890i	0.304300	−	0.936539i	−0.675638	−	0.737234i	$-0.736132\pi$
$569$	173.147	−	532.890i	0.304300	−	0.936539i	0.979938	−	0.199305i	$-0.0638684\pi$
$570$	705.171	+	71.0261i	1.23714	+	0.124607i
$571$	83.8993			0.146934			0.0734670	−	0.997298i	$-0.476594\pi$
$571$	83.8993			0.146934			0.0734670	+	0.997298i	$0.476594\pi$
$572$	−525.891	−	403.818i	−0.919391	−	0.705976i
$573$	440.397	−	440.397i	0.768582	−	0.768582i
$574$	1117.37	−	126.736i	1.94664	−	0.220794i
$575$	−1007.26	+	44.9456i	−1.75176	+	0.0781662i
$576$	−529.325	+	26.1286i	−0.918966	+	0.0453621i
$577$	−265.805	−	42.0995i	−0.460668	−	0.0729627i	−0.0782129	−	0.996937i	$-0.524921\pi$
$577$	−265.805	−	42.0995i	−0.460668	−	0.0729627i	−0.382455	+	0.923974i	$0.624921\pi$
$578$	−316.712	−	479.027i	−0.547945	−	0.828766i
$579$	200.237	−	65.0610i	0.345833	−	0.112368i
$580$	201.718	−	285.102i	0.347790	−	0.491556i
$581$	384.279	+	279.195i	0.661410	+	0.480542i
$582$	15.8435	−	358.708i	0.0272225	−	0.616337i
$583$	482.496	+	584.518i	0.827608	+	1.00260i
$584$	−84.5096	−	110.482i	−0.144708	−	0.189182i
$585$	−622.938	−	35.0734i	−1.06485	−	0.0599545i
$586$	−467.586	+	212.805i	−0.797928	+	0.363149i
$587$	640.299	+	326.249i	1.09080	+	0.555790i	0.904401	−	0.426685i	$-0.140319\pi$
$587$	640.299	+	326.249i	1.09080	+	0.555790i	0.186398	+	0.982474i	$0.440319\pi$
$588$	179.661	−	717.483i	0.305545	−	1.22021i
$589$	−438.069	+	318.275i	−0.743750	+	0.540366i
$590$	−16.4228	−	289.352i	−0.0278352	−	0.490427i
$591$	277.641	−	854.490i	0.469781	−	1.44584i
$592$	−4.58904	+	235.566i	−0.00775175	+	0.397915i
$593$	342.294	+	342.294i	0.577224	+	0.577224i	0.934137	−	0.356914i	$-0.116171\pi$
$593$	342.294	+	342.294i	0.577224	+	0.577224i	−0.356914	+	0.934137i	$0.616171\pi$
$594$	62.9060	+	19.2212i	0.105902	+	0.0323588i
$595$	64.6182	+	13.9976i	0.108602	+	0.0235253i
$596$	578.590	+	503.990i	0.970789	+	0.845622i
$597$	1148.26	−	585.068i	1.92338	−	0.980013i
$598$	−1171.46	+	324.235i	−1.95896	+	0.542199i
$599$	581.303	−	422.341i	0.970456	−	0.705078i	0.0149005	−	0.999889i	$-0.495257\pi$
$599$	581.303	−	422.341i	0.970456	−	0.705078i	0.955555	+	0.294811i	$0.0952568\pi$
$600$	−627.162	−	545.801i	−1.04527	−	0.909668i
$601$	−444.741	+	144.505i	−0.740002	+	0.240441i	−0.654674	−	0.755912i	$-0.727194\pi$
$601$	−444.741	+	144.505i	−0.740002	+	0.240441i	−0.0853284	+	0.996353i	$0.527194\pi$
$602$	−81.6057	+	217.928i	−0.135558	+	0.362006i
$603$	87.1582	+	550.295i	0.144541	+	0.912596i
$604$	−195.803	−	17.3303i	−0.324176	−	0.0286926i
$605$	54.2641	−	602.562i	0.0896927	−	0.995969i
$606$	162.040	−	148.331i	0.267392	−	0.244771i
$607$	146.358	+	924.067i	0.241117	+	1.52235i	0.749955	+	0.661489i	$0.230075\pi$
$607$	146.358	+	924.067i	0.241117	+	1.52235i	−0.508838	+	0.860862i	$0.669925\pi$
$608$	469.381	+	278.089i	0.772008	+	0.457384i
$609$	−667.502	+	216.885i	−1.09606	+	0.356132i
$610$	−241.578	−	621.266i	−0.396029	−	1.01847i
$611$	463.135	−	336.488i	0.757996	−	0.550716i
$612$	−24.0449	+	38.3934i	−0.0392891	+	0.0627343i
$613$	−225.808	+	115.055i	−0.368366	+	0.187692i	−0.628368	−	0.777916i	$-0.716277\pi$
$613$	−225.808	+	115.055i	−0.368366	+	0.187692i	0.260002	+	0.965608i	$0.416277\pi$
$614$	−14.6131	−	128.838i	−0.0237999	−	0.209833i
$615$	−1016.29	+	654.386i	−1.65250	+	1.06404i
$616$	−319.399	+	788.608i	−0.518504	+	1.28021i
$617$	210.613	+	210.613i	0.341350	+	0.341350i	0.856875	−	0.515525i	$-0.172403\pi$
$617$	210.613	+	210.613i	0.341350	+	0.341350i	−0.515525	+	0.856875i	$0.672403\pi$
$618$	−696.374	+	874.553i	−1.12682	+	1.41513i
$619$	110.087	−	338.811i	0.177846	−	0.547353i	−0.821906	−	0.569623i	$-0.807089\pi$
$619$	110.087	−	338.811i	0.177846	−	0.547353i	0.999752	+	0.0222698i	$0.00708930\pi$
$620$	635.149	−	7.97584i	1.02443	−	0.0128643i
$621$	97.5535	−	70.8768i	0.157091	−	0.114133i
$622$	−65.4824	−	99.0420i	−0.105277	−	0.159232i
$623$	452.909	+	230.769i	0.726981	+	0.370415i
$624$	−884.014	−	472.337i	−1.41669	−	0.756951i
$625$	−55.6662	−	622.516i	−0.0890659	−	0.996026i
$626$	429.491	−	393.156i	0.686088	−	0.628045i
$627$	496.297	+	601.237i	0.791542	+	0.958910i
$628$	221.549	+	264.576i	0.352785	+	0.421299i
$629$	16.2934	+	11.8379i	0.0259037	+	0.0188201i
$630$	169.855	+	782.406i	0.269611	+	1.24191i
$631$	65.4122	−	21.2537i	0.103664	−	0.0336826i	−0.256726	−	0.966484i	$-0.582644\pi$
$631$	65.4122	−	21.2537i	0.103664	−	0.0336826i	0.360390	+	0.932802i	$0.382644\pi$
$632$	526.809	+	973.785i	0.833558	+	1.54080i
$633$	825.458	+	130.740i	1.30404	+	0.206540i
$634$	393.201	−	694.160i	0.620190	−	1.09489i
$635$	−765.334	+	201.888i	−1.20525	+	0.317934i
$636$	863.927	+	752.537i	1.35838	+	1.18323i
$637$	473.972	−	473.972i	0.744069	−	0.744069i
$638$	378.325	−	66.7721i	0.592985	−	0.104658i
$639$	613.448			0.960012
$640$	−261.071	−	584.331i	−0.407923	−	0.913016i
$641$	168.173	−	517.584i	0.262361	−	0.807464i	−0.729929	−	0.683523i	$-0.760447\pi$
$641$	168.173	−	517.584i	0.262361	−	0.807464i	0.992290	−	0.123941i	$-0.0395532\pi$
$642$	110.131	−	30.4820i	0.171544	−	0.0474797i
$643$	−593.398	−	93.9850i	−0.922859	−	0.146166i	−0.323116	−	0.946359i	$-0.604730\pi$
$643$	−593.398	−	93.9850i	−0.922859	−	0.146166i	−0.599743	+	0.800193i	$0.704730\pi$
$644$	801.977	+	1337.78i	1.24531	+	2.07730i
$645$	−25.1794	−	248.860i	−0.0390378	−	0.385830i
$646$	42.4461	−	19.3179i	0.0657061	−	0.0299038i
$647$	−1038.31	+	164.452i	−1.60481	+	0.254177i	−0.893620	−	0.448823i	$-0.851843\pi$
$647$	−1038.31	+	164.452i	−1.60481	+	0.254177i	−0.711190	+	0.703000i	$0.751843\pi$
$648$	689.556	+	91.8475i	1.06413	+	0.141740i
$649$	211.083	−	238.908i	0.325244	−	0.368117i
$650$	−233.157	−	716.480i	−0.358703	−	1.10228i
$651$	−1032.72	−	750.312i	−1.58635	−	1.15255i
$652$	577.400	−	232.605i	0.885583	−	0.356756i
$653$	586.213	+	298.690i	0.897722	+	0.457412i	0.841036	−	0.540980i	$-0.181946\pi$
$653$	586.213	+	298.690i	0.897722	+	0.457412i	0.0566867	+	0.998392i	$0.481946\pi$
$654$	−1348.24	−	275.014i	−2.06153	−	0.420511i
$655$	26.8174	−	11.8153i	0.0409426	−	0.0180386i
$656$	−921.674	+	127.630i	−1.40499	+	0.194558i
$657$	−65.3653	−	128.287i	−0.0994906	−	0.195261i
$658$	−574.672	−	457.590i	−0.873362	−	0.695426i
$659$			728.015i			1.10473i	0.833603	+	0.552364i	$0.186274\pi$
$659$			728.015i			1.10473i	−0.833603	+	0.552364i	$0.813726\pi$
$660$	−67.8988	−	912.019i	−0.102877	−	1.38185i
$661$	−239.938			−0.362992			−0.181496	−	0.983392i	$-0.558094\pi$
$661$	−239.938			−0.362992			−0.181496	+	0.983392i	$0.558094\pi$
$662$	−586.687	+	736.801i	−0.886235	+	1.11299i
$663$	−76.3369	+	38.8956i	−0.115139	+	0.0586660i
$664$	−323.561	−	223.102i	−0.487291	−	0.335997i
$665$	298.356	−	768.311i	0.448656	−	1.15536i
$666$	−48.7427	+	238.959i	−0.0731872	+	0.358797i
$667$	319.730	−	627.505i	0.479355	−	0.940787i
$668$	408.398	−	164.522i	0.611374	−	0.246291i
$669$	−163.112	+	224.504i	−0.243815	+	0.335582i
$670$	−581.224	+	338.939i	−0.867498	+	0.505879i
$671$	291.929	−	672.620i	0.435066	−	1.00241i
$672$	−281.553	+	1254.96i	−0.418977	+	1.86750i
$673$	−70.5884	−	445.677i	−0.104886	−	0.662225i	−0.982977	−	0.183730i	$-0.941183\pi$
$673$	−70.5884	−	445.677i	−0.104886	−	0.662225i	0.878091	−	0.478494i	$-0.158817\pi$
$674$	−244.891	−	538.086i	−0.363339	−	0.798346i
$675$	46.5870	+	58.4527i	0.0690177	+	0.0865966i
$676$	−119.456	−	199.265i	−0.176710	−	0.294771i
$677$	−142.010	+	896.614i	−0.209763	+	1.32439i	0.627938	+	0.778263i	$0.283899\pi$
$677$	−142.010	+	896.614i	−0.209763	+	1.32439i	−0.837701	+	0.546129i	$0.816101\pi$
$678$	300.905	+	1087.17i	0.443813	+	1.60349i
$679$	−397.120	−	129.032i	−0.584860	−	0.190032i
$680$	−53.7360	−	10.2600i	−0.0790235	−	0.0150882i
$681$		−	3.98323i		−	0.00584908i
$682$	502.695	+	485.289i	0.737090	+	0.711568i
$683$	−486.122	−	486.122i	−0.711746	−	0.711746i	0.255155	−	0.966900i	$-0.417874\pi$
$683$	−486.122	−	486.122i	−0.711746	−	0.711746i	−0.966900	+	0.255155i	$0.917874\pi$
$684$	425.826	+	370.923i	0.622553	+	0.542285i
$685$	−471.831	+	124.465i	−0.688804	+	0.181700i
$686$	76.0312	+	43.0672i	0.110833	+	0.0627802i
$687$	156.611	−	988.804i	0.227964	−	1.43931i
$688$	63.0555	−	181.929i	0.0916505	−	0.264431i
$689$	320.857	+	987.498i	0.465686	+	1.43323i
$690$	−1410.01	−	907.005i	−2.04350	−	1.31450i
$691$	119.989	−	165.151i	0.173646	−	0.239003i	−0.713320	−	0.700839i	$-0.752809\pi$
$691$	119.989	−	165.151i	0.173646	−	0.239003i	0.886965	+	0.461836i	$0.152809\pi$
$692$	−651.879	−	778.479i	−0.942022	−	1.12497i
$693$	−472.700	+	743.086i	−0.682107	+	1.07227i
$694$	145.756	+	159.226i	0.210023	+	0.229433i
$695$	681.496	−	608.845i	0.980569	−	0.876036i
$696$	547.714	−	193.020i	0.786946	−	0.277328i
$697$	−36.1085	+	70.8669i	−0.0518056	+	0.101674i
$698$	−183.379	+	121.242i	−0.262720	+	0.173699i
$699$	−816.062	−	1123.21i	−1.16747	−	1.60689i
$700$	−806.277	+	533.601i	−1.15182	+	0.762286i
$701$	−866.890	−	281.670i	−1.23665	−	0.401811i	−0.383530	−	0.923529i	$-0.625292\pi$
$701$	−866.890	−	281.670i	−1.23665	−	0.401811i	−0.853119	+	0.521717i	$0.825292\pi$
$702$	70.4925	+	56.1305i	0.100417	+	0.0799580i
$703$	177.527	−	177.527i	0.252527	−	0.252527i
$704$	248.108	−	658.831i	0.352426	−	0.935840i
$705$	771.708	+	167.167i	1.09462	+	0.237116i
$706$	219.928	−	24.9449i	0.311513	−	0.0353327i
$707$	−115.981	−	227.625i	−0.164046	−	0.321959i
$708$	255.787	−	408.425i	0.361282	−	0.576871i
$709$	344.974	+	474.816i	0.486565	+	0.669699i	0.979750	−	0.200226i	$-0.0641675\pi$
$709$	344.974	+	474.816i	0.486565	+	0.669699i	−0.493185	+	0.869924i	$0.664167\pi$
$710$	268.479	+	690.448i	0.378140	+	0.972462i
$711$	354.136	+	1089.92i	0.498081	+	1.53294i
$712$	−379.342	−	181.645i	−0.532784	−	0.255119i
$713$	1265.12	−	200.376i	1.77437	−	0.281032i
$714$	74.2331	+	81.0936i	0.103968	+	0.113576i
$715$	372.196	−	740.536i	0.520553	−	1.03571i
$716$	142.073	+	12.5748i	0.198426	+	0.0175625i
$717$	1096.24	−	173.628i	1.52893	−	0.242159i
$718$	566.315	+	212.064i	0.788740	+	0.295353i
$719$	−121.316	−	373.373i	−0.168729	−	0.519294i	0.830563	−	0.556925i	$-0.188019\pi$
$719$	−121.316	−	373.373i	−0.168729	−	0.519294i	−0.999292	+	0.0376306i	$0.988019\pi$
$720$	−156.463	−	643.719i	−0.217309	−	0.894054i
$721$	764.163	+	1051.78i	1.05987	+	1.45878i
$722$	37.5179	+	135.552i	0.0519639	+	0.187745i
$723$	624.907	+	1226.45i	0.864325	+	1.69633i
$724$	904.608	+	787.973i	1.24946	+	1.08836i
$725$	397.425	+	180.657i	0.548173	+	0.249182i
$726$	652.707	−	765.509i	0.899046	−	1.05442i
$727$	−351.028	+	351.028i	−0.482844	+	0.482844i	−0.906039	−	0.423195i	$-0.860909\pi$
$727$	−351.028	+	351.028i	−0.482844	+	0.482844i	0.423195	+	0.906039i	$0.360909\pi$
$728$	−803.618	+	844.265i	−1.10387	+	1.15970i
$729$	578.433	+	187.944i	0.793461	+	0.257811i
$730$	115.782	−	129.716i	0.158605	−	0.177693i
$731$	−9.67419	−	13.3154i	−0.0132342	−	0.0182153i
$732$	269.234	−	1075.20i	0.367806	−	1.46885i
$733$	−52.9819	+	103.983i	−0.0722809	+	0.141859i	−0.924319	−	0.381620i	$-0.875366\pi$
$733$	−52.9819	+	103.983i	−0.0722809	+	0.141859i	0.852038	+	0.523479i	$0.175366\pi$
$734$	409.605	+	900.003i	0.558044	+	1.22616i
$735$	923.082	+	51.9725i	1.25589	+	0.0707108i
$736$	−690.668	−	1090.21i	−0.938408	−	1.48127i
$737$	−716.663	−	184.831i	−0.972405	−	0.250788i
$738$	−962.187	−	42.4981i	−1.30378	−	0.0575855i
$739$	−363.644	+	500.513i	−0.492075	+	0.677284i	−0.980769	−	0.195172i	$-0.937474\pi$
$739$	−363.644	+	500.513i	−0.492075	+	0.677284i	0.488694	+	0.872455i	$0.337474\pi$
$740$	−290.285	+	49.7208i	−0.392278	+	0.0671903i
$741$	330.035	+	1015.74i	0.445391	+	1.37077i
$742$	1111.43	−	734.831i	1.49788	−	0.990338i
$743$	−116.075	+	732.872i	−0.156225	+	0.986368i	0.777631	+	0.628721i	$0.216421\pi$
$743$	−116.075	+	732.872i	−0.156225	+	0.986368i	−0.933857	+	0.357648i	$0.883579\pi$
$744$	869.543	+	599.567i	1.16874	+	0.805869i
$745$	−482.795	+	828.775i	−0.648047	+	1.11245i
$746$	10.1563	+	89.5436i	0.0136143	+	0.120032i
$747$	−287.662	−	287.662i	−0.385090	−	0.385090i
$748$	−34.0678	−	49.6055i	−0.0455451	−	0.0663175i
$749$		−	132.889i		−	0.177422i
$750$	522.712	−	898.232i	0.696949	−	1.19764i
$751$	−664.913	−	216.043i	−0.885370	−	0.287674i	−0.169185	−	0.985584i	$-0.554114\pi$
$751$	−664.913	−	216.043i	−0.885370	−	0.287674i	−0.716185	+	0.697910i	$0.754114\pi$
$752$	484.689	+	366.781i	0.644533	+	0.487740i
$753$	−162.920	+	1028.64i	−0.216361	+	1.36605i
$754$	515.670	+	105.186i	0.683913	+	0.139504i
$755$	−24.7344	−	244.462i	−0.0327608	−	0.323791i
$756$	45.2883	−	106.393i	0.0599052	−	0.140731i
$757$	−212.115	−	1339.24i	−0.280205	−	1.76914i	−0.579490	−	0.814980i	$-0.696748\pi$
$757$	−212.115	−	1339.24i	−0.280205	−	1.76914i	0.299285	−	0.954164i	$-0.403252\pi$
$758$	182.120	+	8.04392i	0.240264	+	0.0106120i
$759$	−400.361	−	1800.22i	−0.527485	−	2.37183i
$760$	−231.116	+	641.613i	−0.304100	+	0.844228i
$761$	155.640	−	214.221i	0.204521	−	0.281499i	−0.694419	−	0.719571i	$-0.744339\pi$
$761$	155.640	−	214.221i	0.204521	−	0.281499i	0.898940	+	0.438072i	$0.144339\pi$
$762$	−1232.55	−	461.544i	−1.61752	−	0.605701i
$763$	−726.470	+	1425.78i	−0.952123	+	1.86865i
$764$	308.138	+	514.005i	0.403322	+	0.672782i
$765$	−52.7863	−	20.4984i	−0.0690018	−	0.0267952i
$766$	341.104	−	602.188i	0.445305	−	0.786146i
$767$	389.132	−	198.273i	0.507343	−	0.258504i
$768$	207.288	−	1043.81i	0.269906	−	1.35913i
$769$	682.852			0.887974			0.443987	−	0.896033i	$-0.353564\pi$
$769$	682.852			0.887974			0.443987

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56459 - 1.24582i) q^{2} +(3.70393 - 1.88724i) q^{3} +(0.895857 + 3.89839i) q^{4} +(-4.57559 + 2.01593i) q^{5} +(-8.14628 - 1.66168i) q^{6} +(-4.38944 + 8.61475i) q^{7} +(3.45505 - 7.21544i) q^{8} +(4.86731 - 6.69928i) q^{9} +(9.67039 + 2.54628i) q^{10} +(5.58926 + 9.47419i) q^{11} +(10.6754 + 12.7486i) q^{12} +(2.35735 + 14.8837i) q^{13} +(17.6001 - 8.01007i) q^{14} +(-13.1431 + 16.1021i) q^{15} +(-14.3949 + 6.98480i) q^{16} +(-0.213950 + 1.35083i) q^{17} +(-15.9614 + 4.41780i) q^{18} +(16.2148 + 5.26850i) q^{19} +(-11.9579 - 16.0315i) q^{20} +40.1924i q^{21} +(3.05827 - 21.7864i) q^{22} +(-28.5180 - 28.5180i) q^{23} +(-0.820048 - 33.2460i) q^{24} +(16.8721 - 18.4481i) q^{25} +(14.8542 - 26.2237i) q^{26} +(-0.467718 + 2.95306i) q^{27} +(-37.5160 - 9.39414i) q^{28} +(5.39617 + 16.6077i) q^{29} +(40.6239 - 8.81916i) q^{30} +(-18.6680 + 25.6943i) q^{31} +(31.2238 + 7.00513i) q^{32} +(38.5823 + 24.5434i) q^{33} +(2.01764 - 1.84694i) q^{34} +(2.71755 - 48.2664i) q^{35} +(30.4768 + 12.9731i) q^{36} +(6.68530 - 13.1206i) q^{37} +(-18.8058 - 28.4437i) q^{38} +(36.8207 + 50.6793i) q^{39} +(-1.26310 + 39.9801i) q^{40} +(55.3081 + 17.9707i) q^{41} +(50.0725 - 62.8844i) q^{42} +(-8.50943 + 8.50943i) q^{43} +(-31.9269 + 30.2766i) q^{44} +(-8.76557 + 40.4653i) q^{45} +(9.09050 + 80.1471i) q^{46} +(-17.2467 - 33.8485i) q^{47} +(-40.1355 + 53.0379i) q^{48} +(-26.1454 - 35.9860i) q^{49} +(-49.3809 + 7.84407i) q^{50} +(1.75689 + 5.40715i) q^{51} +(-55.9107 + 22.5235i) q^{52} +(68.0547 - 10.7788i) q^{53} +(4.41077 - 4.03762i) q^{54} +(-44.6734 - 32.0825i) q^{55} +(46.9935 + 61.4362i) q^{56} +(70.0013 - 11.0871i) q^{57} +(12.2475 - 32.7068i) q^{58} +(-8.95586 - 27.5633i) q^{59} +(-74.5466 - 36.8118i) q^{60} +(-39.1807 - 53.9276i) q^{61} +(61.2183 - 16.9440i) q^{62} +(36.3479 + 71.3368i) q^{63} +(-40.1252 - 49.8595i) q^{64} +(-40.7908 - 63.3496i) q^{65} +(-29.7886 - 86.4669i) q^{66} +(-47.5763 + 47.5763i) q^{67} +(-5.45773 + 0.376088i) q^{68} +(-159.449 - 51.8081i) q^{69} +(-64.3831 + 72.1313i) q^{70} +(43.5437 + 59.9328i) q^{71} +(-31.5215 - 58.2662i) q^{72} +(7.89363 - 15.4921i) q^{73} +(-26.8057 + 12.1997i) q^{74} +(27.6768 - 100.172i) q^{75} +(-6.01254 + 67.9313i) q^{76} +(-106.151 + 6.56373i) q^{77} +(5.52827 - 125.164i) q^{78} +(-81.3459 + 111.963i) q^{79} +(51.7842 - 60.9786i) q^{80} +(26.8708 + 82.6999i) q^{81} +(-64.1459 - 97.0206i) q^{82} +(7.68527 - 48.5229i) q^{83} +(-156.685 + 36.0066i) q^{84} +(-1.74422 - 6.61215i) q^{85} +(23.9150 - 2.71250i) q^{86} +(51.3298 + 51.3298i) q^{87} +(87.6716 - 7.59515i) q^{88} -52.5737i q^{89} +(64.1271 - 52.3911i) q^{90} +(-138.567 - 45.0231i) q^{91} +(85.6261 - 136.722i) q^{92} +(-20.6535 + 130.401i) q^{93} +(-15.1853 + 74.4452i) q^{94} +(-84.8131 + 8.58130i) q^{95} +(128.871 - 32.9805i) q^{96} +(6.75594 + 42.6553i) q^{97} +(-3.92548 + 88.8757i) q^{98} +(90.6749 + 8.66983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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