LMFDB - Embedded newform 220.3.w.a.7.4

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			7.4
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96643 + 0.364900i) q^{2} +(1.14015 - 0.580936i) q^{3} +(3.73370 - 1.43510i) q^{4} +(1.56915 - 4.74740i) q^{5} +(-2.03004 + 1.55841i) q^{6} +(-5.70983 + 11.2062i) q^{7} +(-6.81838 + 4.18445i) q^{8} +(-4.32761 + 5.95644i) q^{9} +(-1.35329 + 9.90801i) q^{10} +(10.9222 + 1.30573i) q^{11} +(3.42328 - 3.80527i) q^{12} +(2.16315 + 13.6576i) q^{13} +(7.13885 - 24.1197i) q^{14} +(-0.968868 - 6.32433i) q^{15} +(11.8810 - 10.7165i) q^{16} +(2.20685 - 13.9335i) q^{17} +(6.33643 - 13.2921i) q^{18} +(8.78672 + 2.85498i) q^{19} +(-0.954276 - 19.9772i) q^{20} +16.0938i q^{21} +(-21.9543 + 1.41790i) q^{22} +(29.9456 + 29.9456i) q^{23} +(-5.34309 + 8.73196i) q^{24} +(-20.0755 - 14.8987i) q^{25} +(-9.23734 - 26.0674i) q^{26} +(-3.27541 + 20.6801i) q^{27} +(-5.23677 + 50.0347i) q^{28} +(7.25970 + 22.3431i) q^{29} +(4.21296 + 12.0828i) q^{30} +(11.6482 - 16.0323i) q^{31} +(-19.4526 + 25.4086i) q^{32} +(13.2115 - 4.85639i) q^{33} +(0.744723 + 28.2045i) q^{34} +(44.2406 + 44.6910i) q^{35} +(-7.60987 + 28.4501i) q^{36} +(12.5830 - 24.6955i) q^{37} +(-18.3203 - 2.40784i) q^{38} +(10.4005 + 14.3151i) q^{39} +(9.16621 + 38.9356i) q^{40} +(-12.0228 - 3.90645i) q^{41} +(-5.87263 - 31.6473i) q^{42} +(-25.4909 + 25.4909i) q^{43} +(42.6541 - 10.7993i) q^{44} +(21.4869 + 29.8914i) q^{45} +(-69.8130 - 47.9587i) q^{46} +(11.5996 + 22.7655i) q^{47} +(7.32052 - 19.1205i) q^{48} +(-64.1748 - 88.3290i) q^{49} +(44.9137 + 21.9718i) q^{50} +(-5.57833 - 17.1683i) q^{51} +(27.6766 + 47.8889i) q^{52} +(-7.11181 + 1.12640i) q^{53} +(-1.10532 - 41.8612i) q^{54} +(23.3374 - 49.8033i) q^{55} +(-7.95992 - 100.301i) q^{56} +(11.6768 - 1.84942i) q^{57} +(-22.4287 - 41.2870i) q^{58} +(15.9174 + 48.9888i) q^{59} +(-12.6935 - 22.2227i) q^{60} +(7.37946 + 10.1570i) q^{61} +(-17.0551 + 35.7769i) q^{62} +(-42.0390 - 82.5063i) q^{63} +(28.9807 - 57.0624i) q^{64} +(68.2323 + 11.1615i) q^{65} +(-24.2075 + 14.3706i) q^{66} +(-57.2536 + 57.2536i) q^{67} +(-11.7563 - 55.1905i) q^{68} +(51.5390 + 16.7460i) q^{69} +(-103.304 - 71.7383i) q^{70} +(-18.6543 - 25.6754i) q^{71} +(4.58283 - 58.7220i) q^{72} +(-25.0092 + 49.0833i) q^{73} +(-15.7321 + 53.1534i) q^{74} +(-31.5444 - 5.32421i) q^{75} +(36.9041 - 1.95022i) q^{76} +(-76.9963 + 114.941i) q^{77} +(-25.6754 - 24.3544i) q^{78} +(36.7254 - 50.5482i) q^{79} +(-32.2323 - 73.2194i) q^{80} +(-12.1971 - 37.5387i) q^{81} +(25.0675 + 3.29463i) q^{82} +(17.1464 - 108.258i) q^{83} +(23.0962 + 60.0893i) q^{84} +(-62.6849 - 32.3405i) q^{85} +(40.8244 - 59.4277i) q^{86} +(21.2570 + 21.2570i) q^{87} +(-79.9357 + 36.8006i) q^{88} +42.5205i q^{89} +(-53.1599 - 50.9388i) q^{90} +(-165.401 - 53.7419i) q^{91} +(154.783 + 68.8327i) q^{92} +(3.96692 - 25.0461i) q^{93} +(-31.1169 - 40.5340i) q^{94} +(27.3414 - 37.2342i) q^{95} +(-7.41821 + 40.2704i) q^{96} +(-2.69477 - 17.0141i) q^{97} +(158.427 + 150.275i) q^{98} +(-55.0446 + 59.4069i) 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 $

$2$	−1.96643	+	0.364900i	−0.983215	+	0.182450i
$2$	−1.96643	+	0.364900i	−0.983215	+	0.182450i
$3$	1.14015	−	0.580936i	0.380051	−	0.193645i	−0.253520	−	0.967330i	$-0.581588\pi$
$3$	1.14015	−	0.580936i	0.380051	−	0.193645i	0.633571	+	0.773685i	$0.281588\pi$
$4$	3.73370	−	1.43510i	0.933424	−	0.358776i
$5$	1.56915	−	4.74740i	0.313830	−	0.949479i
$5$	1.56915	−	4.74740i	0.313830	−	0.949479i
$6$	−2.03004	+	1.55841i	−0.338341	+	0.259735i
$7$	−5.70983	+	11.2062i	−0.815691	+	1.60088i	−0.0164553	+	0.999865i	$0.505238\pi$
$7$	−5.70983	+	11.2062i	−0.815691	+	1.60088i	−0.799235	+	0.601018i	$0.794762\pi$
$8$	−6.81838	+	4.18445i	−0.852298	+	0.523057i
$9$	−4.32761	+	5.95644i	−0.480845	+	0.661827i
$10$	−1.35329	+	9.90801i	−0.135329	+	0.990801i
$11$	10.9222	+	1.30573i	0.992930	+	0.118703i
$11$	10.9222	+	1.30573i	0.992930	+	0.118703i
$12$	3.42328	−	3.80527i	0.285273	−	0.317106i
$13$	2.16315	+	13.6576i	0.166396	+	1.05058i	0.919617	+	0.392816i	$0.128499\pi$
$13$	2.16315	+	13.6576i	0.166396	+	1.05058i	−0.753221	+	0.657768i	$0.771501\pi$
$14$	7.13885	−	24.1197i	0.509918	−	1.72284i
$15$	−0.968868	−	6.32433i	−0.0645912	−	0.421622i
$16$	11.8810	−	10.7165i	0.742560	−	0.669779i
$17$	2.20685	−	13.9335i	0.129815	−	0.819617i	−0.833750	−	0.552142i	$-0.813811\pi$
$17$	2.20685	−	13.9335i	0.129815	−	0.819617i	0.963565	−	0.267475i	$-0.0861893\pi$
$18$	6.33643	−	13.2921i	0.352024	−	0.738449i
$19$	8.78672	+	2.85498i	0.462459	+	0.150262i	0.530974	−	0.847388i	$-0.321826\pi$
$19$	8.78672	+	2.85498i	0.462459	+	0.150262i	−0.0685150	+	0.997650i	$0.521826\pi$
$20$	−0.954276	−	19.9772i	−0.0477138	−	0.998861i
$21$			16.0938i			0.766371i
$22$	−21.9543	+	1.41790i	−0.997921	+	0.0644500i
$23$	29.9456	+	29.9456i	1.30198	+	1.30198i	0.927054	+	0.374927i	$0.122332\pi$
$23$	29.9456	+	29.9456i	1.30198	+	1.30198i	0.374927	+	0.927054i	$0.377668\pi$
$24$	−5.34309	+	8.73196i	−0.222629	+	0.363832i
$25$	−20.0755	−	14.8987i	−0.803022	−	0.595950i
$26$	−9.23734	−	26.0674i	−0.355282	−	1.00259i
$27$	−3.27541	+	20.6801i	−0.121311	+	0.765930i
$28$	−5.23677	+	50.0347i	−0.187027	+	1.78695i
$29$	7.25970	+	22.3431i	0.250334	+	0.770450i	0.994713	+	0.102692i	$0.0327458\pi$
$29$	7.25970	+	22.3431i	0.250334	+	0.770450i	−0.744379	+	0.667758i	$0.767254\pi$
$30$	4.21296	+	12.0828i	0.140432	+	0.402760i
$31$	11.6482	−	16.0323i	0.375747	−	0.517172i	−0.578704	−	0.815537i	$-0.696442\pi$
$31$	11.6482	−	16.0323i	0.375747	−	0.517172i	0.954452	+	0.298366i	$0.0964415\pi$
$32$	−19.4526	+	25.4086i	−0.607895	+	0.794017i
$33$	13.2115	−	4.85639i	0.400350	−	0.147163i
$34$	0.744723	+	28.2045i	0.0219036	+	0.829545i
$35$	44.2406	+	44.6910i	1.26402	+	1.27689i
$36$	−7.60987	+	28.4501i	−0.211385	+	0.790281i
$37$	12.5830	−	24.6955i	0.340080	−	0.667445i	−0.656109	−	0.754666i	$-0.727799\pi$
$37$	12.5830	−	24.6955i	0.340080	−	0.667445i	0.996189	+	0.0872213i	$0.0277987\pi$
$38$	−18.3203	−	2.40784i	−0.482112	−	0.0633642i
$39$	10.4005	+	14.3151i	0.266680	+	0.367053i
$40$	9.16621	+	38.9356i	0.229155	+	0.973390i
$41$	−12.0228	−	3.90645i	−0.293239	−	0.0952792i	0.158703	−	0.987326i	$-0.449269\pi$
$41$	−12.0228	−	3.90645i	−0.293239	−	0.0952792i	−0.451942	+	0.892047i	$0.649269\pi$
$42$	−5.87263	−	31.6473i	−0.139825	−	0.753508i
$43$	−25.4909	+	25.4909i	−0.592811	+	0.592811i	−0.938390	−	0.345579i	$-0.887683\pi$
$43$	−25.4909	+	25.4909i	−0.592811	+	0.592811i	0.345579	+	0.938390i	$0.387683\pi$
$44$	42.6541	−	10.7993i	0.969412	−	0.245439i
$45$	21.4869	+	29.8914i	0.477487	+	0.664254i
$46$	−69.8130	−	47.9587i	−1.51767	−	1.04258i
$47$	11.5996	+	22.7655i	0.246800	+	0.484371i	0.980860	−	0.194712i	$-0.0623773\pi$
$47$	11.5996	+	22.7655i	0.246800	+	0.484371i	−0.734061	+	0.679084i	$0.762377\pi$
$48$	7.32052	−	19.1205i	0.152511	−	0.398343i
$49$	−64.1748	−	88.3290i	−1.30969	−	1.80263i
$50$	44.9137	+	21.9718i	0.898274	+	0.439435i
$51$	−5.57833	−	17.1683i	−0.109379	−	0.336634i
$52$	27.6766	+	47.8889i	0.532242	+	0.920941i
$53$	−7.11181	+	1.12640i	−0.134185	+	0.0212528i	−0.223166	−	0.974781i	$-0.571639\pi$
$53$	−7.11181	+	1.12640i	−0.134185	+	0.0212528i	0.0889806	+	0.996033i	$0.471639\pi$
$54$	−1.10532	−	41.8612i	−0.0204689	−	0.775208i
$55$	23.3374	−	49.8033i	0.424317	−	0.905514i
$56$	−7.95992	−	100.301i	−0.142141	−	1.79108i
$57$	11.6768	−	1.84942i	0.204855	−	0.0324459i
$58$	−22.4287	−	41.2870i	−0.386701	−	0.711845i
$59$	15.9174	+	48.9888i	0.269787	+	0.830318i	0.990552	+	0.137139i	$0.0437906\pi$
$59$	15.9174	+	48.9888i	0.269787	+	0.830318i	−0.720765	+	0.693179i	$0.756209\pi$
$60$	−12.6935	−	22.2227i	−0.211559	−	0.370378i
$61$	7.37946	+	10.1570i	0.120975	+	0.166507i	0.865209	−	0.501411i	$-0.167186\pi$
$61$	7.37946	+	10.1570i	0.120975	+	0.166507i	−0.744235	+	0.667918i	$0.767186\pi$
$62$	−17.0551	+	35.7769i	−0.275082	+	0.577046i
$63$	−42.0390	−	82.5063i	−0.667286	−	1.30962i
$64$	28.9807	−	57.0624i	0.452823	−	0.891600i
$65$	68.2323	+	11.1615i	1.04973	+	0.171715i
$66$	−24.2075	+	14.3706i	−0.366780	+	0.217737i
$67$	−57.2536	+	57.2536i	−0.854532	+	0.854532i	−0.990687	−	0.136156i	$-0.956525\pi$
$67$	−57.2536	+	57.2536i	−0.854532	+	0.854532i	0.136156	+	0.990687i	$0.456525\pi$
$68$	−11.7563	−	55.1905i	−0.172887	−	0.811624i
$69$	51.5390	+	16.7460i	0.746942	+	0.242696i
$70$	−103.304	−	71.7383i	−1.47577	−	1.02483i
$71$	−18.6543	−	25.6754i	−0.262736	−	0.361625i	0.657185	−	0.753730i	$-0.271747\pi$
$71$	−18.6543	−	25.6754i	−0.262736	−	0.361625i	−0.919921	+	0.392104i	$0.871747\pi$
$72$	4.58283	−	58.7220i	0.0636504	−	0.815583i
$73$	−25.0092	+	49.0833i	−0.342592	+	0.672374i	−0.996445	−	0.0842474i	$-0.973151\pi$
$73$	−25.0092	+	49.0833i	−0.342592	+	0.672374i	0.653853	+	0.756621i	$0.273151\pi$
$74$	−15.7321	+	53.1534i	−0.212597	+	0.718290i
$75$	−31.5444	−	5.32421i	−0.420592	−	0.0709894i
$76$	36.9041	−	1.95022i	0.485581	−	0.0256608i
$77$	−76.9963	+	114.941i	−0.999953	+	1.49274i
$78$	−25.6754	−	24.3544i	−0.329172	−	0.312236i
$79$	36.7254	−	50.5482i	0.464878	−	0.639850i	−0.510633	−	0.859799i	$-0.670589\pi$
$79$	36.7254	−	50.5482i	0.464878	−	0.639850i	0.975511	+	0.219948i	$0.0705889\pi$
$80$	−32.2323	−	73.2194i	−0.402904	−	0.915242i
$81$	−12.1971	−	37.5387i	−0.150581	−	0.463440i
$82$	25.0675	+	3.29463i	0.305701	+	0.0401784i
$83$	17.1464	−	108.258i	0.206583	−	1.30432i	−0.638475	−	0.769642i	$-0.720434\pi$
$83$	17.1464	−	108.258i	0.206583	−	1.30432i	0.845059	−	0.534674i	$-0.179566\pi$
$84$	23.0962	+	60.0893i	0.274955	+	0.715349i
$85$	−62.6849	−	32.3405i	−0.737470	−	0.380476i
$86$	40.8244	−	59.4277i	0.474702	−	0.691020i
$87$	21.2570	+	21.2570i	0.244334	+	0.244334i
$88$	−79.9357	+	36.8006i	−0.908360	+	0.418189i
$89$			42.5205i			0.477758i	0.971049	+	0.238879i	$0.0767799\pi$
$89$			42.5205i			0.477758i	−0.971049	+	0.238879i	$0.923220\pi$
$90$	−53.1599	−	50.9388i	−0.590666	−	0.565987i
$91$	−165.401	−	53.7419i	−1.81759	−	0.590571i
$92$	154.783	+	68.8327i	1.68242	+	0.748182i
$93$	3.96692	−	25.0461i	0.0426550	−	0.269313i
$94$	−31.1169	−	40.5340i	−0.331031	−	0.431213i
$95$	27.3414	−	37.2342i	0.287804	−	0.391939i
$96$	−7.41821	+	40.2704i	−0.0772730	+	0.419483i
$97$	−2.69477	−	17.0141i	−0.0277811	−	0.175403i	0.969896	−	0.243518i	$-0.0783015\pi$
$97$	−2.69477	−	17.0141i	−0.0277811	−	0.175403i	−0.997677	+	0.0681150i	$0.978302\pi$
$98$	158.427	+	150.275i	1.61660	+	1.53342i
$99$	−55.0446	+	59.4069i	−0.556006	+	0.600070i
$100$	−96.3372	−	26.8169i	−0.963372	−	0.268169i
$101$	85.4230	−	117.575i	0.845772	−	1.16411i	−0.139007	−	0.990291i	$-0.544391\pi$
$101$	85.4230	−	117.575i	0.845772	−	1.16411i	0.984779	−	0.173814i	$-0.0556090\pi$
$102$	17.2341	+	31.7248i	0.168962	+	0.311027i
$103$	−14.9480	+	29.3370i	−0.145126	+	0.284825i	−0.952115	−	0.305741i	$-0.901096\pi$
$103$	−14.9480	+	29.3370i	−0.145126	+	0.284825i	0.806989	+	0.590567i	$0.201096\pi$
$104$	−71.8988	−	84.0711i	−0.691334	−	0.808376i
$105$	76.4036	+	25.2536i	0.727654	+	0.240510i
$106$	13.5738	−	4.81009i	0.128055	−	0.0453782i
$107$	85.0458	−	43.3330i	0.794821	−	0.404981i	−0.00892073	−	0.999960i	$-0.502840\pi$
$107$	85.0458	−	43.3330i	0.794821	−	0.404981i	0.803741	+	0.594979i	$0.202840\pi$
$108$	17.4487	+	81.9138i	0.161562	+	0.758461i
$109$	70.5708			0.647438			0.323719	−	0.946153i	$-0.395067\pi$
$109$	70.5708			0.647438			0.323719	+	0.946153i	$0.395067\pi$
$110$	−27.7182	+	106.450i	−0.251983	+	0.967732i
$111$		−	35.4665i		−	0.319518i
$112$	52.2523	+	194.329i	0.466539	+	1.73508i
$113$	−50.8538	−	99.8062i	−0.450033	−	0.883240i	−0.998880	−	0.0473172i	$-0.984933\pi$
$113$	−50.8538	−	99.8062i	−0.450033	−	0.883240i	0.548846	−	0.835923i	$-0.315067\pi$
$114$	−22.2867	+	7.89760i	−0.195497	+	0.0692772i
$115$	189.153	−	95.1745i	1.64481	−	0.827604i
$116$	59.1701	+	73.0038i	0.510087	+	0.629343i
$117$	−90.7119	−	46.2200i	−0.775315	−	0.395043i
$118$	−49.1765	−	90.5247i	−0.416750	−	0.767159i
$119$	143.540	+	104.288i	1.20622	+	0.876372i
$120$	33.0700	+	39.0675i	0.275583	+	0.325562i
$121$	117.590	+	28.5229i	0.971819	+	0.235727i
$122$	−18.2175	−	17.2802i	−0.149323	−	0.141641i
$123$	−15.9772	+	2.53054i	−0.129896	+	0.0205735i
$124$	20.4827	−	76.5761i	0.165183	−	0.617549i
$125$	−102.232	+	71.9282i	−0.817854	+	0.575426i
$126$	112.773	+	146.903i	0.895027	+	1.16589i
$127$	−189.532	−	30.0190i	−1.49238	−	0.236370i	−0.643702	−	0.765277i	$-0.722602\pi$
$127$	−189.532	−	30.0190i	−1.49238	−	0.236370i	−0.848680	+	0.528907i	$0.822602\pi$
$128$	−36.1664	+	122.784i	−0.282550	+	0.959253i
$129$	−14.2549	+	43.8721i	−0.110503	+	0.340093i
$130$	−138.247	+	2.94976i	−1.06344	+	0.0226905i
$131$	−203.551			−1.55383			−0.776913	−	0.629608i	$-0.783216\pi$
$131$	−203.551			−1.55383			−0.776913	+	0.629608i	$0.783216\pi$
$132$	42.3585	−	37.0922i	0.320897	−	0.281001i
$133$	−82.1642	+	82.1642i	−0.617776	+	0.617776i
$134$	91.6934	−	133.477i	0.684279	−	0.996098i
$135$	93.0371	+	47.9998i	0.689164	+	0.355554i
$136$	43.2569	+	104.238i	0.318066	+	0.766458i
$137$	40.3614	+	6.39261i	0.294609	+	0.0466614i	0.301989	−	0.953311i	$-0.402349\pi$
$137$	40.3614	+	6.39261i	0.294609	+	0.0466614i	−0.00738061	+	0.999973i	$0.502349\pi$
$138$	−107.458	−	14.1233i	−0.778684	−	0.102343i
$139$	−14.2923	+	4.64385i	−0.102822	+	0.0334090i	−0.359976	−	0.932961i	$-0.617215\pi$
$139$	−14.2923	+	4.64385i	−0.102822	+	0.0334090i	0.257154	+	0.966370i	$0.417215\pi$
$140$	229.317	+	103.373i	1.63798	+	0.738377i
$141$	26.4506	+	19.2175i	0.187593	+	0.136294i
$142$	46.0513	+	43.6819i	0.324305	+	0.307619i
$143$	5.79331	+	151.996i	0.0405126	+	1.06291i
$144$	12.4159	+	117.145i	0.0862213	+	0.813507i
$145$	117.463	+	0.594900i	0.810089	+	0.00410276i
$146$	31.2683	−	105.645i	0.214167	−	0.723594i
$147$	−124.483	−	63.4270i	−0.846820	−	0.431476i
$148$	11.5405	−	110.263i	0.0779761	−	0.745022i
$149$	48.3138	−	35.1020i	0.324254	−	0.235584i	−0.413735	−	0.910397i	$-0.635776\pi$
$149$	48.3138	−	35.1020i	0.324254	−	0.235584i	0.737988	+	0.674813i	$0.235776\pi$
$150$	63.9726	−	1.04087i	0.426484	−	0.00693915i
$151$	−74.0712	+	227.968i	−0.490538	+	1.50972i	0.333259	+	0.942835i	$0.391852\pi$
$151$	−74.0712	+	227.968i	−0.490538	+	1.50972i	−0.823797	+	0.566885i	$0.808148\pi$
$152$	−71.8578	+	17.3013i	−0.472749	+	0.113824i
$153$	73.4437	+	73.4437i	0.480024	+	0.480024i
$154$	109.466	−	254.119i	0.710818	−	1.65013i
$155$	−57.8341	−	80.4555i	−0.373123	−	0.519068i
$156$	59.3759	+	38.5223i	0.380615	+	0.246938i
$157$	−26.0580	+	13.2772i	−0.165974	+	0.0845681i	−0.535004	−	0.844849i	$-0.679690\pi$
$157$	−26.0580	+	13.2772i	−0.165974	+	0.0845681i	0.369030	+	0.929418i	$0.379690\pi$
$158$	−53.7729	+	112.801i	−0.340335	+	0.713928i
$159$	−7.45417	+	5.41577i	−0.0468816	+	0.0340615i
$160$	90.1004	+	132.219i	0.563127	+	0.826370i
$161$	−506.560	+	164.591i	−3.14633	+	1.02231i
$162$	37.6825	+	69.3665i	0.232608	+	0.428188i
$163$	−13.9140	−	87.8497i	−0.0853621	−	0.538955i	−0.992897	−	0.118978i	$-0.962038\pi$
$163$	−13.9140	−	87.8497i	−0.0853621	−	0.538955i	0.907535	−	0.419977i	$-0.137962\pi$
$164$	−50.4956	+	2.66847i	−0.307900	+	0.0162712i
$165$	−2.32434	−	70.3408i	−0.0140869	−	0.426308i
$166$	5.78623	+	219.139i	0.0348568	+	1.32011i
$167$	−9.33352	−	58.9295i	−0.0558893	−	0.352871i	−0.999746	−	0.0225173i	$-0.992832\pi$
$167$	−9.33352	−	58.9295i	−0.0558893	−	0.352871i	0.943857	−	0.330354i	$-0.107168\pi$
$168$	−67.3438	−	109.734i	−0.400856	−	0.653176i
$169$	−21.1220	+	6.86296i	−0.124982	+	0.0406092i
$170$	135.067	+	40.7216i	0.794509	+	0.239539i
$171$	−55.0310	+	39.9824i	−0.321819	+	0.233815i
$172$	−58.5932	+	131.757i	−0.340658	+	0.766030i
$173$	254.328	−	129.587i	1.47010	−	0.749056i	0.478466	−	0.878106i	$-0.341193\pi$
$173$	254.328	−	129.587i	1.47010	−	0.749056i	0.991638	+	0.129050i	$0.0411928\pi$
$174$	−49.5572	−	34.0438i	−0.284812	−	0.195654i
$175$	281.586	−	139.901i	1.60906	−	0.799434i
$176$	143.759	−	101.534i	0.816815	−	0.576900i
$177$	46.6076	+	46.6076i	0.263320	+	0.263320i
$178$	−15.5157	−	83.6135i	−0.0871670	−	0.469739i
$179$	−30.4193	+	93.6208i	−0.169940	+	0.523021i	−0.999366	−	0.0355947i	$-0.988667\pi$
$179$	−30.4193	+	93.6208i	−0.169940	+	0.523021i	0.829426	+	0.558616i	$0.188667\pi$
$180$	123.123	+	80.7695i	0.684016	+	0.448719i
$181$	170.356	−	123.771i	0.941195	−	0.683819i	−0.00751269	−	0.999972i	$-0.502391\pi$
$181$	170.356	−	123.771i	0.941195	−	0.683819i	0.948708	+	0.316153i	$0.102391\pi$
$182$	344.859	+	45.3250i	1.89483	+	0.249038i
$183$	14.3142	+	7.29347i	0.0782199	+	0.0398550i
$184$	−329.486	−	78.8745i	−1.79069	−	0.428666i
$185$	−97.4946	−	98.4872i	−0.526998	−	0.532363i
$186$	1.33867	+	50.6990i	0.00719717	+	0.272575i
$187$	42.2971	−	149.303i	0.226187	−	0.798413i
$188$	75.9800	+	68.3527i	0.404149	+	0.363578i
$189$	−213.043	−	154.785i	−1.12721	−	0.818968i
$190$	−40.1782	+	83.1953i	−0.211464	+	0.437870i
$191$	171.039	−	55.5739i	0.895491	−	0.290963i	0.175116	−	0.984548i	$-0.443970\pi$
$191$	171.039	−	55.5739i	0.895491	−	0.290963i	0.720375	+	0.693585i	$0.243970\pi$
$192$	−0.107267	−	81.8957i	−0.000558682	−	0.426540i
$193$	−121.790	−	19.2896i	−0.631034	−	0.0999459i	−0.167279	−	0.985910i	$-0.553498\pi$
$193$	−121.790	−	19.2896i	−0.631034	−	0.0999459i	−0.463755	+	0.885964i	$0.653498\pi$
$194$	11.5075	+	32.4737i	0.0593171	+	0.167390i
$195$	84.2793	−	26.9129i	0.432201	−	0.138015i
$196$	−366.370	−	237.696i	−1.86924	−	1.21274i
$197$	207.848	−	207.848i	1.05506	−	1.05506i	0.0566714	−	0.998393i	$-0.481951\pi$
$197$	207.848	−	207.848i	1.05506	−	1.05506i	0.998393	−	0.0566714i	$-0.0180487\pi$
$198$	86.5638	−	136.905i	0.437191	−	0.691441i
$199$	20.9279			0.105166			0.0525828	−	0.998617i	$-0.483255\pi$
$199$	20.9279			0.105166			0.0525828	+	0.998617i	$0.483255\pi$
$200$	199.226	+	17.5801i	0.996129	+	0.0879004i
$201$	−32.0171	+	98.5385i	−0.159289	+	0.490241i
$202$	−125.075	+	262.373i	−0.619185	+	1.29888i
$203$	−291.832	−	46.2216i	−1.43760	−	0.227693i
$204$	−45.4661	−	56.0958i	−0.222873	−	0.274980i
$205$	−37.4110	+	50.9472i	−0.182493	+	0.248523i
$206$	18.6890	−	63.1437i	0.0907234	−	0.306523i
$207$	−307.962	+	48.7764i	−1.48774	+	0.235635i
$208$	172.061	+	139.084i	0.827218	+	0.668673i
$209$	92.2428	+	42.6558i	0.441353	+	0.204095i
$210$	−159.457	−	21.7796i	−0.759321	−	0.103713i
$211$	−234.256	−	170.197i	−1.11022	−	0.806621i	−0.127520	−	0.991836i	$-0.540702\pi$
$211$	−234.256	−	170.197i	−1.11022	−	0.806621i	−0.982698	+	0.185215i	$0.940702\pi$
$212$	−24.9368	+	14.4118i	−0.117627	+	0.0679802i
$213$	−36.1845	−	18.4369i	−0.169880	−	0.0865582i
$214$	−151.424	+	116.245i	−0.707591	+	0.543199i
$215$	81.0164	+	161.014i	0.376820	+	0.748904i
$216$	−64.2020	−	154.711i	−0.297232	−	0.716254i
$217$	113.152	+	222.073i	0.521438	+	1.02338i
$218$	−138.772	+	25.7513i	−0.636571	+	0.118125i
$219$			70.4912i			0.321877i
$220$	15.6620	−	219.442i	0.0711910	−	0.997463i
$221$	195.072			0.882677
$222$	12.9417	+	69.7424i	0.0582961	+	0.314155i
$223$	320.680	−	163.395i	1.43803	−	0.732712i	0.450890	−	0.892580i	$-0.351107\pi$
$223$	320.680	−	163.395i	1.43803	−	0.732712i	0.987138	+	0.159867i	$0.0511067\pi$
$224$	−173.661	−	363.068i	−0.775274	−	1.62084i
$225$	175.623	−	55.1029i	0.780545	−	0.244902i
$226$	136.420	+	177.705i	0.603627	+	0.786307i
$227$	131.133	−	257.362i	0.577676	−	1.13375i	−0.398580	−	0.917134i	$-0.630497\pi$
$227$	131.133	−	257.362i	0.577676	−	1.13375i	0.976256	−	0.216620i	$-0.0695032\pi$
$228$	40.9434	−	23.6625i	0.179576	−	0.103783i
$229$	−96.6116	+	132.974i	−0.421885	+	0.580675i	−0.966067	−	0.258293i	$-0.916840\pi$
$229$	−96.6116	+	132.974i	−0.421885	+	0.580675i	0.544182	+	0.838967i	$0.316840\pi$
$230$	−337.226	+	256.176i	−1.46620	+	1.11381i
$231$	−21.0141	+	175.780i	−0.0909703	+	0.760953i
$232$	−142.993	−	121.966i	−0.616349	−	0.525714i
$233$	−33.7105	−	212.840i	−0.144680	−	0.913476i	−0.948079	−	0.318035i	$-0.896977\pi$
$233$	−33.7105	−	212.840i	−0.144680	−	0.913476i	0.803399	−	0.595442i	$-0.203023\pi$
$234$	195.244	+	57.7877i	0.834378	+	0.246956i
$235$	126.278	−	19.3454i	0.537354	−	0.0823209i
$236$	129.735	+	160.066i	0.549723	+	0.678246i
$237$	12.5073	−	78.9677i	0.0527732	−	0.333197i
$238$	−320.317	−	152.698i	−1.34587	−	0.641587i
$239$	−219.393	−	71.2851i	−0.917962	−	0.298264i	−0.188332	−	0.982106i	$-0.560308\pi$
$239$	−219.393	−	71.2851i	−0.917962	−	0.298264i	−0.729631	+	0.683842i	$0.760308\pi$
$240$	−79.2855	−	64.7563i	−0.330356	−	0.269818i
$241$			134.969i			0.560038i	0.959995	+	0.280019i	$0.0903407\pi$
$241$			134.969i			0.560038i	−0.959995	+	0.280019i	$0.909659\pi$
$242$	−241.641	−	13.1797i	−0.998516	−	0.0544615i
$243$	−168.962	−	168.962i	−0.695317	−	0.695317i
$244$	42.1289	+	27.3327i	0.172659	+	0.112019i
$245$	−520.033	+	166.062i	−2.12258	+	0.677803i
$246$	30.4947	−	10.8062i	0.123962	−	0.0439278i
$247$	−19.9851	+	126.181i	−0.0809115	+	0.510855i
$248$	−12.3351	+	158.056i	−0.0497383	+	0.637321i
$249$	−43.3416	−	133.392i	−0.174063	−	0.535710i
$250$	174.785	−	178.746i	0.699140	−	0.714985i
$251$	99.4209	−	136.841i	0.396099	−	0.545184i	−0.563660	−	0.826007i	$-0.690607\pi$
$251$	99.4209	−	136.841i	0.396099	−	0.545184i	0.959760	+	0.280823i	$0.0906073\pi$
$252$	−275.366	−	247.723i	−1.09272	−	0.983027i
$253$	287.972	+	366.173i	1.13823	+	1.44733i
$254$	383.656	−	10.1302i	1.51046	−	0.0398827i
$255$	−90.2581	−	0.457120i	−0.353953	−	0.00179263i
$256$	26.3146	−	254.644i	0.102791	−	0.994703i
$257$	218.027	−	427.902i	0.848354	−	1.66499i	0.106614	−	0.994301i	$-0.465999\pi$
$257$	218.027	−	427.902i	0.848354	−	1.66499i	0.741740	−	0.670688i	$-0.234001\pi$
$258$	12.0223	−	91.4729i	0.0465982	−	0.354546i
$259$	204.895	+	282.014i	0.791101	+	1.08886i
$260$	270.776	−	56.2468i	1.04145	−	0.216334i
$261$	−164.502	−	53.4500i	−0.630277	−	0.204789i
$262$	400.269	−	74.2759i	1.52775	−	0.283496i
$263$	136.497	−	136.497i	0.519002	−	0.519002i	−0.398268	−	0.917269i	$-0.630388\pi$
$263$	136.497	−	136.497i	0.519002	−	0.519002i	0.917269	+	0.398268i	$0.130388\pi$
$264$	−69.7600	+	88.3958i	−0.264242	+	0.334833i
$265$	−5.81201	+	35.5300i	−0.0219321	+	0.134076i
$266$	131.588	−	191.552i	0.494693	−	0.720120i
$267$	24.7017	+	48.4798i	0.0925157	+	0.181572i
$268$	−131.603	+	295.932i	−0.491055	+	1.10423i
$269$	203.979	+	280.753i	0.758287	+	1.04369i	0.997355	+	0.0726892i	$0.0231581\pi$
$269$	203.979	+	280.753i	0.758287	+	1.04369i	−0.239068	+	0.971003i	$0.576842\pi$
$270$	−200.466	−	60.4391i	−0.742467	−	0.223848i
$271$	105.639	+	325.122i	0.389811	+	1.19971i	0.932930	+	0.360058i	$0.117243\pi$
$271$	105.639	+	325.122i	0.389811	+	1.19971i	−0.543119	+	0.839656i	$0.682757\pi$
$272$	−123.098	−	189.193i	−0.452567	−	0.695562i
$273$	−219.802	+	34.8133i	−0.805137	+	0.127521i
$274$	−81.7005	+	2.15725i	−0.298177	+	0.00787318i
$275$	−199.816	−	188.941i	−0.726604	−	0.687057i
$276$	216.463	−	11.4391i	0.784286	−	0.0414461i
$277$	−271.666	+	43.0277i	−0.980744	+	0.155335i	−0.626164	−	0.779691i	$-0.715376\pi$
$277$	−271.666	+	43.0277i	−0.980744	+	0.155335i	−0.354580	+	0.935026i	$0.615376\pi$
$278$	26.4103	−	14.3471i	0.0950010	−	0.0516082i
$279$	45.0869	+	138.763i	0.161602	+	0.497359i
$280$	−488.657	−	119.598i	−1.74520	−	0.427134i
$281$	217.880	+	299.886i	0.775374	+	1.06721i	0.995777	+	0.0918017i	$0.0292626\pi$
$281$	217.880	+	299.886i	0.775374	+	1.06721i	−0.220404	+	0.975409i	$0.570737\pi$
$282$	−59.0256	−	28.1380i	−0.209311	−	0.0997800i
$283$	157.212	+	308.545i	0.555518	+	1.09026i	0.982545	+	0.186026i	$0.0595609\pi$
$283$	157.212	+	308.545i	0.555518	+	1.09026i	−0.427027	+	0.904239i	$0.640439\pi$
$284$	−106.496	−	69.0933i	−0.374987	−	0.243286i
$285$	9.54265	−	58.3362i	0.0334830	−	0.204688i
$286$	−66.8555	−	296.775i	−0.233760	−	1.03768i
$287$	112.425	−	112.425i	0.391723	−	0.391723i
$288$	−67.1612	−	225.827i	−0.233198	−	0.784121i
$289$	85.5834	+	27.8077i	0.296136	+	0.0962205i
$290$	−231.200	+	41.6924i	−0.797240	+	0.143767i
$291$	−12.9566	−	17.8332i	−0.0445242	−	0.0612824i
$292$	−22.9372	+	219.153i	−0.0785519	+	0.750523i
$293$	−130.463	+	256.047i	−0.445265	+	0.873882i	0.553882	+	0.832595i	$0.313146\pi$
$293$	−130.463	+	256.047i	−0.445265	+	0.873882i	−0.999147	+	0.0412870i	$0.986854\pi$
$294$	267.931	+	79.3011i	0.911329	+	0.269732i
$295$	257.546	+	1.30436i	0.873037	+	0.00442157i
$296$	17.5416	+	221.036i	0.0592621	+	0.746743i
$297$	−62.7774	+	221.596i	−0.211372	+	0.746115i
$298$	−82.1970	+	86.6554i	−0.275829	+	0.290790i
$299$	−344.208	+	473.761i	−1.15120	+	1.58449i
$300$	−125.418	+	25.3904i	−0.418060	+	0.0846348i
$301$	−140.107	−	431.204i	−0.465471	−	1.43257i
$302$	62.4704	−	475.311i	0.206855	−	1.57388i
$303$	29.0918	−	183.678i	0.0960124	−	0.606199i
$304$	134.990	−	60.2427i	0.444046	−	0.198167i
$305$	59.7985	−	19.0954i	0.196061	−	0.0626080i
$306$	−171.221	−	117.622i	−0.559547	−	0.384386i
$307$	250.280	+	250.280i	0.815245	+	0.815245i	0.985415	−	0.170170i	$-0.0544315\pi$
$307$	250.280	+	250.280i	0.815245	+	0.815245i	−0.170170	+	0.985415i	$0.554432\pi$
$308$	−122.529	+	539.652i	−0.397821	+	1.75212i
$309$			42.1324i			0.136351i
$310$	143.085	+	137.107i	0.461564	+	0.442279i
$311$	257.788	+	83.7604i	0.828901	+	0.269326i	0.692582	−	0.721339i	$-0.256473\pi$
$311$	257.788	+	83.7604i	0.828901	+	0.269326i	0.136318	+	0.990665i	$0.456473\pi$
$312$	−130.815	−	54.0852i	−0.419280	−	0.173350i
$313$	59.7559	−	377.284i	0.190913	−	1.20538i	−0.687035	−	0.726624i	$-0.741088\pi$
$313$	59.7559	−	377.284i	0.190913	−	1.20538i	0.877949	−	0.478755i	$-0.158912\pi$
$314$	46.3963	−	35.6172i	0.147759	−	0.113431i
$315$	−457.655	+	70.1114i	−1.45287	+	0.222576i
$316$	64.5797	−	241.436i	0.204366	−	0.764039i
$317$	64.8925	+	409.715i	0.204708	+	1.29248i	0.849284	+	0.527937i	$0.177034\pi$
$317$	64.8925	+	409.715i	0.204708	+	1.29248i	−0.644575	+	0.764541i	$0.722966\pi$
$318$	12.6819	−	13.3698i	0.0398802	−	0.0420433i
$319$	50.1181	+	253.515i	0.157110	+	0.794718i
$320$	−225.423	−	227.122i	−0.704447	−	0.709757i
$321$	71.7914	−	98.8124i	0.223649	−	0.307827i
$322$	936.055	−	508.501i	2.90700	−	1.57920i
$323$	59.1708	−	116.129i	0.183191	−	0.359533i
$324$	−99.4119	−	122.654i	−0.306827	−	0.378562i
$325$	160.054	−	306.412i	0.492475	−	0.942806i
$326$	59.4173	+	167.673i	0.182262	+	0.514335i
$327$	80.4614	−	40.9971i	0.246059	−	0.125373i
$328$	98.3224	−	23.6732i	0.299763	−	0.0721745i
$329$	−321.345			−0.976734
$330$	30.2380	+	137.472i	0.0916304	+	0.416582i
$331$			214.985i			0.649500i	0.945800	+	0.324750i	$0.105280\pi$
$331$			214.985i			0.649500i	−0.945800	+	0.324750i	$0.894720\pi$
$332$	−91.3421	−	428.810i	−0.275127	−	1.29160i
$333$	92.6430	+	181.822i	0.278207	+	0.546012i
$334$	39.8571	+	112.475i	0.119333	+	0.336751i
$335$	181.966	+	361.645i	0.543183	+	1.07954i
$336$	172.469	+	191.210i	0.513299	+	0.569077i
$337$	−350.857	−	178.771i	−1.04112	−	0.530477i	−0.152109	−	0.988364i	$-0.548606\pi$
$337$	−350.857	−	178.771i	−1.04112	−	0.530477i	−0.889010	+	0.457887i	$0.848606\pi$
$338$	39.0307	−	21.2030i	0.115475	−	0.0627306i
$339$	−115.962	−	84.2514i	−0.342071	−	0.248529i
$340$	−280.458	−	30.7903i	−0.824878	−	0.0905597i
$341$	148.158	−	159.899i	0.434480	−	0.468913i
$342$	93.6251	−	98.7034i	0.273758	−	0.288606i
$343$	747.573	−	118.404i	2.17951	−	0.345201i
$344$	67.1411	−	280.472i	0.195178	−	0.815326i
$345$	160.372	−	218.399i	0.464847	−	0.633040i
$346$	−452.832	+	347.627i	−1.30876	+	1.00470i
$347$	−461.418	−	73.0815i	−1.32974	−	0.210609i	−0.549184	−	0.835701i	$-0.685062\pi$
$347$	−461.418	−	73.0815i	−1.32974	−	0.210609i	−0.780551	+	0.625092i	$0.785062\pi$
$348$	109.873	+	48.8613i	0.315728	+	0.140406i
$349$	11.3458	−	34.9188i	0.0325095	−	0.100054i	−0.933485	−	0.358616i	$-0.883249\pi$
$349$	11.3458	−	34.9188i	0.0325095	−	0.100054i	0.965995	+	0.258562i	$0.0832487\pi$
$350$	−502.669	+	377.856i	−1.43620	+	1.07959i
$351$	−289.526			−0.824860
$352$	−245.643	+	252.118i	−0.697849	+	0.716245i
$353$	459.925	−	459.925i	1.30290	−	1.30290i	0.376479	−	0.926425i	$-0.377135\pi$
$353$	459.925	−	459.925i	1.30290	−	1.30290i	0.926425	−	0.376479i	$-0.122865\pi$
$354$	−108.658	−	74.6435i	−0.306943	−	0.210857i
$355$	−151.163	+	48.2707i	−0.425810	+	0.135974i
$356$	61.0212	+	158.758i	0.171408	+	0.445951i
$357$	224.243	+	35.5166i	0.628131	+	0.0994862i
$358$	25.6551	−	195.199i	0.0716622	−	0.545248i
$359$	76.3153	−	24.7963i	0.212577	−	0.0690706i	−0.200792	−	0.979634i	$-0.564352\pi$
$359$	76.3153	−	24.7963i	0.212577	−	0.0690706i	0.413370	+	0.910563i	$0.364352\pi$
$360$	−271.585	−	113.900i	−0.754404	−	0.316389i
$361$	−223.000	−	162.019i	−0.617727	−	0.448805i
$362$	−289.830	+	305.550i	−0.800635	+	0.844062i
$363$	150.641	−	35.7919i	0.414988	−	0.0986003i
$364$	−694.681	+	36.7108i	−1.90846	+	0.100854i
$365$	193.775	+	195.748i	0.530890	+	0.536295i
$366$	−30.8093	−	9.11883i	−0.0841785	−	0.0249148i
$367$	−127.184	−	64.8033i	−0.346550	−	0.176576i	0.272048	−	0.962284i	$-0.412299\pi$
$367$	−127.184	−	64.8033i	−0.346550	−	0.176576i	−0.618598	+	0.785708i	$0.712299\pi$
$368$	676.693	+	34.8715i	1.83884	+	0.0947595i
$369$	75.2985	−	54.7076i	0.204061	−	0.148259i
$370$	227.654	+	158.092i	0.615282	+	0.427277i
$371$	27.9846	−	86.1277i	0.0754302	−	0.232150i
$372$	−21.1325	−	99.2075i	−0.0568077	−	0.266687i
$373$	−278.179	−	278.179i	−0.745788	−	0.745788i	0.227897	−	0.973685i	$-0.426815\pi$
$373$	−278.179	−	278.179i	−0.745788	−	0.745788i	−0.973685	+	0.227897i	$0.926815\pi$
$374$	−28.6934	+	309.029i	−0.0767204	+	0.826280i
$375$	−74.7739	+	141.399i	−0.199397	+	0.377065i
$376$	−174.351	−	106.686i	−0.463700	−	0.283738i
$377$	−289.448	+	147.481i	−0.767768	+	0.391197i
$378$	475.415	+	226.634i	1.25771	+	0.599561i
$379$	495.949	−	360.328i	1.30857	−	0.950734i	0.308574	−	0.951200i	$-0.400148\pi$
$379$	495.949	−	360.328i	1.30857	−	0.950734i	1.00000		0.000466071i	$0.000148355\pi$
$380$	48.6496	−	178.259i	0.128025	−	0.469102i
$381$	−233.535	+	75.8801i	−0.612952	+	0.199160i
$382$	−316.057	+	171.694i	−0.827374	+	0.449461i
$383$	44.8932	+	283.445i	0.117215	+	0.740064i	0.974361	+	0.224991i	$0.0722353\pi$
$383$	44.8932	+	283.445i	0.117215	+	0.740064i	−0.857146	+	0.515073i	$0.827765\pi$
$384$	30.0947	+	161.003i	0.0783717	+	0.419279i
$385$	424.852	+	545.892i	1.10351	+	1.41790i
$386$	246.529	−	6.50945i	0.638677	−	0.0168639i
$387$	−41.5204	−	262.150i	−0.107288	−	0.677389i
$388$	−34.4784	−	59.6582i	−0.0888619	−	0.153758i
$389$	443.797	−	144.198i	1.14087	−	0.370690i	0.323170	−	0.946341i	$-0.395251\pi$
$389$	443.797	−	144.198i	1.14087	−	0.370690i	0.817695	+	0.575651i	$0.195251\pi$
$390$	−155.909	+	83.6758i	−0.399766	+	0.214553i
$391$	483.332	−	351.161i	1.23614	−	0.898110i
$392$	807.177	+	333.725i	2.05913	+	0.851338i
$393$	−232.079	+	118.250i	−0.590533	+	0.300891i
$394$	−332.874	+	484.562i	−0.844858	+	1.22985i
$395$	−182.345	−	253.668i	−0.461632	−	0.642196i
$396$	−120.265	+	300.802i	−0.303699	+	0.759601i
$397$	−250.793	−	250.793i	−0.631720	−	0.631720i	0.316779	−	0.948499i	$-0.397399\pi$
$397$	−250.793	−	250.793i	−0.631720	−	0.631720i	−0.948499	+	0.316779i	$0.897399\pi$
$398$	−41.1533	+	7.63661i	−0.103400	+	0.0191875i
$399$	−45.9475	+	141.412i	−0.115157	+	0.354415i
$400$	−398.179	+	38.1276i	−0.995447	+	0.0953189i
$401$	−243.162	+	176.668i	−0.606390	+	0.440568i	−0.848141	−	0.529770i	$-0.822278\pi$
$401$	−243.162	+	176.668i	−0.606390	+	0.440568i	0.241751	+	0.970338i	$0.422278\pi$
$402$	27.0027	−	205.452i	0.0671708	−	0.511075i
$403$	244.160	+	124.406i	0.605855	+	0.308699i
$404$	150.212	−	561.578i	0.371811	−	1.39005i
$405$	−197.350	−	0.999495i	−0.487284	−	0.00246789i
$406$	590.733	−	15.5979i	1.45501	−	0.0384186i
$407$	169.680	−	253.300i	0.416903	−	0.622358i
$408$	109.875	+	93.7180i	0.269302	+	0.229701i
$409$	19.9686	+	14.5081i	0.0488230	+	0.0354720i	0.611929	−	0.790913i	$-0.290394\pi$
$409$	19.9686	+	14.5081i	0.0488230	+	0.0354720i	−0.563106	+	0.826385i	$0.690394\pi$
$410$	54.9755	−	113.835i	0.134087	−	0.277647i
$411$	49.7318	−	16.1588i	0.121002	−	0.0393159i
$412$	−13.7095	+	130.987i	−0.0332755	+	0.317930i
$413$	−639.863	−	101.344i	−1.54930	−	0.245386i
$414$	587.787	−	208.291i	1.41978	−	0.503118i
$415$	−487.040	−	251.274i	−1.17359	−	0.605480i
$416$	−389.099	−	210.714i	−0.935333	−	0.506523i
$417$	−13.5976	+	13.5976i	−0.0326082	+	0.0326082i
$418$	−196.954	−	50.2203i	−0.471182	−	0.120144i
$419$	18.9614			0.0452539			0.0226269	−	0.999744i	$-0.492797\pi$
$419$	18.9614			0.0452539			0.0226269	+	0.999744i	$0.492797\pi$
$420$	321.509	−	15.3579i	0.765498	−	0.0365665i
$421$	−132.572	+	408.015i	−0.314898	+	0.969157i	0.660898	+	0.750475i	$0.270175\pi$
$421$	−132.572	+	408.015i	−0.314898	+	0.969157i	−0.975796	+	0.218681i	$0.929825\pi$
$422$	522.753	+	249.200i	1.23875	+	0.590522i
$423$	−185.800	−	29.4278i	−0.439242	−	0.0695692i
$424$	43.7776	−	37.4393i	0.103249	−	0.0883001i
$425$	−251.895	+	246.843i	−0.592694	+	0.580808i
$426$	77.8819	+	23.0512i	0.182821	+	0.0541107i
$427$	−155.956	+	24.7010i	−0.365237	+	0.0578478i
$428$	255.348	−	283.842i	0.596607	−	0.663181i
$429$	94.9051	+	169.933i	0.221224	+	0.396114i
$430$	−218.067	−	287.061i	−0.507133	−	0.667583i
$431$	513.594	+	373.148i	1.19163	+	0.865772i	0.993436	−	0.114391i	$-0.0364915\pi$
$431$	513.594	+	373.148i	1.19163	+	0.865772i	0.198197	+	0.980162i	$0.436492\pi$
$432$	182.703	+	280.801i	0.422923	+	0.650001i
$433$	344.698	+	175.633i	0.796070	+	0.405618i	0.804207	−	0.594349i	$-0.202590\pi$
$433$	344.698	+	175.633i	0.796070	+	0.405618i	−0.00813710	+	0.999967i	$0.502590\pi$
$434$	−303.540	−	395.402i	−0.699401	−	0.911066i
$435$	134.271	−	67.5602i	0.308669	−	0.155311i
$436$	263.490	−	101.276i	0.604334	−	0.232285i
$437$	177.630	+	348.618i	0.406475	+	0.797752i
$438$	−25.7222	−	138.616i	−0.0587266	−	0.316475i
$439$			23.8521i			0.0543328i	0.999631	+	0.0271664i	$0.00864840\pi$
$439$			23.8521i			0.0543328i	−0.999631	+	0.0271664i	$0.991352\pi$
$440$	49.2761	+	437.232i	0.111991	+	0.993709i
$441$	803.850			1.82279
$442$	−383.595	+	71.1817i	−0.867862	+	0.161045i
$443$	−605.407	+	308.470i	−1.36661	+	0.696322i	−0.974665	−	0.223668i	$-0.928197\pi$
$443$	−605.407	+	308.470i	−1.36661	+	0.696322i	−0.391943	+	0.919990i	$0.628197\pi$
$444$	−50.8980	−	132.421i	−0.114635	−	0.298246i
$445$	201.862	+	66.7209i	0.453621	+	0.149935i
$446$	−570.973	+	438.321i	−1.28021	+	0.982782i
$447$	34.6930	−	68.0889i	0.0776130	−	0.152324i
$448$	473.977	+	650.580i	1.05798	+	1.45219i
$449$	−37.5024	+	51.6176i	−0.0835243	+	0.114961i	−0.848735	−	0.528819i	$-0.822635\pi$
$449$	−37.5024	+	51.6176i	−0.0835243	+	0.114961i	0.765210	+	0.643780i	$0.222635\pi$
$450$	−325.242	+	172.441i	−0.722761	+	0.383202i
$451$	−126.215	−	58.3656i	−0.279856	−	0.129414i
$452$	−333.105	−	299.665i	−0.736957	−	0.662977i
$453$	47.9823	+	302.948i	0.105921	+	0.668760i
$454$	−163.951	+	553.935i	−0.361127	+	1.22012i
$455$	−514.672	+	700.893i	−1.13115	+	1.54043i
$456$	−71.8778	+	61.4709i	−0.157627	+	0.134805i
$457$	45.1170	−	284.857i	0.0987242	−	0.623320i	−0.887866	−	0.460102i	$-0.847813\pi$
$457$	45.1170	−	284.857i	0.0987242	−	0.623320i	0.986590	−	0.163218i	$-0.0521873\pi$
$458$	141.458	−	296.739i	0.308859	−	0.647901i
$459$	280.918	+	91.2758i	0.612022	+	0.198858i
$460$	569.653	−	626.806i	1.23838	−	1.36262i
$461$		−	210.778i		−	0.457219i	−0.973518	−	0.228610i	$-0.926582\pi$
$461$		−	210.778i		−	0.457219i	0.973518	−	0.228610i	$-0.0734179\pi$
$462$	−22.8194	−	353.327i	−0.0493926	−	0.764778i
$463$	425.161	+	425.161i	0.918275	+	0.918275i	0.996904	−	0.0786294i	$-0.0250544\pi$
$463$	425.161	+	425.161i	0.918275	+	0.918275i	−0.0786294	+	0.996904i	$0.525054\pi$
$464$	325.691	+	187.659i	0.701920	+	0.404437i
$465$	−112.679	−	58.1336i	−0.242321	−	0.125018i
$466$	143.955	+	406.234i	0.308916	+	0.871747i
$467$	−71.3695	+	450.609i	−0.152826	+	0.964902i	0.785428	+	0.618953i	$0.212443\pi$
$467$	−71.3695	+	450.609i	−0.152826	+	0.964902i	−0.938253	+	0.345949i	$0.887557\pi$
$468$	−405.021	−	42.3907i	−0.865430	−	0.0905783i
$469$	−314.686	−	968.503i	−0.670972	−	2.06504i
$470$	−241.258	+	84.1203i	−0.513315	+	0.178979i
$471$	−21.9968	+	30.2760i	−0.0467024	+	0.0642803i
$472$	−313.522	−	267.418i	−0.664242	−	0.566564i
$473$	−311.701	+	245.133i	−0.658988	+	0.518252i
$474$	4.22070	+	159.848i	0.00890442	+	0.337233i
$475$	−133.863	−	188.226i	−0.281816	−	0.396266i
$476$	685.601	+	183.385i	1.44034	+	0.385263i
$477$	24.0678	−	47.2357i	0.0504566	−	0.0990266i
$478$	457.433	+	60.1206i	0.956973	+	0.125775i
$479$	−67.9061	−	93.4647i	−0.141766	−	0.195125i	0.732230	−	0.681058i	$-0.238480\pi$
$479$	−67.9061	−	93.4647i	−0.141766	−	0.195125i	−0.873996	+	0.485933i	$0.838480\pi$
$480$	179.539	+	98.4074i	0.374040	+	0.205015i
$481$	364.499	+	118.433i	0.757795	+	0.246223i
$482$	−49.2502	−	265.407i	−0.102179	−	0.550637i
$483$	−481.938	+	481.938i	−0.997801	+	0.997801i
$484$	479.979	−	62.2579i	0.991692	−	0.128632i
$485$	−85.0012	−	13.9045i	−0.175260	−	0.0286691i
$486$	393.906	+	270.598i	0.810507	+	0.556786i
$487$	−310.925	−	610.224i	−0.638449	−	1.25303i	−0.952765	−	0.303708i	$-0.901775\pi$
$487$	−310.925	−	610.224i	−0.638449	−	1.25303i	0.314316	−	0.949318i	$-0.398225\pi$
$488$	−92.8173	−	38.3750i	−0.190199	−	0.0786372i
$489$	−66.8992	−	92.0788i	−0.136808	−	0.188300i
$490$	962.012	−	516.309i	1.96329	−	1.05369i
$491$	−101.745	−	313.138i	−0.207220	−	0.637756i	−0.999615	−	0.0277483i	$-0.991166\pi$
$491$	−101.745	−	313.138i	−0.207220	−	0.637756i	0.792395	−	0.610008i	$-0.208834\pi$
$492$	−56.0225	+	32.3772i	−0.113867	+	0.0658073i
$493$	327.338	−	51.8452i	0.663971	−	0.105163i
$494$	−6.74418	−	255.419i	−0.0136522	−	0.517043i
$495$	195.655	+	354.537i	0.395263	+	0.716236i
$496$	−33.4185	−	315.307i	−0.0673759	−	0.635699i
$497$	394.236	−	62.4408i	0.793231	−	0.125635i
$498$	133.903	+	246.490i	0.268882	+	0.494960i
$499$	−119.220	−	366.921i	−0.238918	−	0.735313i	−0.996578	−	0.0826633i	$-0.973657\pi$
$499$	−119.220	−	366.921i	−0.238918	−	0.735313i	0.757660	−	0.652650i	$-0.226343\pi$
$500$	−278.478	+	415.271i	−0.556956	+	0.830542i
$501$	−44.8759	−	61.7664i	−0.0895727	−	0.123286i
$502$	−145.571	+	305.367i	−0.289982	+	0.608301i
$503$	−181.255	−	355.732i	−0.360347	−	0.707221i	0.637660	−	0.770318i	$-0.279902\pi$
$503$	−181.255	−	355.732i	−0.360347	−	0.707221i	−0.998007	+	0.0630966i	$0.979902\pi$
$504$	631.882	+	386.649i	1.25373	+	0.767160i
$505$	−424.132	−	590.029i	−0.839865	−	1.16837i
$506$	−699.893	−	614.973i	−1.38319	−	1.21536i
$507$	−20.0954	+	20.0954i	−0.0396358	+	0.0396358i
$508$	−750.737	+	159.917i	−1.47783	+	0.314797i
$509$	−245.184	−	79.6652i	−0.481698	−	0.156513i	0.0580947	−	0.998311i	$-0.481497\pi$
$509$	−245.184	−	79.6652i	−0.481698	−	0.156513i	−0.539793	+	0.841798i	$0.681497\pi$
$510$	177.653	−	32.0363i	0.348339	−	0.0628163i
$511$	−407.238	−	560.515i	−0.796943	−	1.09690i
$512$	41.1738	+	510.342i	0.0804176	+	0.996761i
$513$	−87.8215	+	172.359i	−0.171192	+	0.335983i
$514$	−272.593	+	920.997i	−0.530337	+	1.79182i
$515$	115.819	+	116.998i	0.224891	+	0.227181i
$516$	9.73744	+	184.262i	0.0188710	+	0.357097i
$517$	96.9677	+	263.795i	0.187558	+	0.510242i
$518$	−505.819	−	479.795i	−0.976485	−	0.926244i
$519$	214.691	−	295.497i	0.413663	−	0.569358i
$520$	−511.939	+	209.412i	−0.984497	+	0.402715i
$521$	−253.411	−	779.918i	−0.486393	−	1.49696i	−0.829953	−	0.557833i	$-0.811633\pi$
$521$	−253.411	−	779.918i	−0.486393	−	1.49696i	0.343561	−	0.939131i	$-0.388367\pi$
$522$	342.986	+	45.0788i	0.657061	+	0.0863579i
$523$	−11.9863	+	75.6784i	−0.0229183	+	0.144701i	−0.996494	−	0.0836639i	$-0.973338\pi$
$523$	−11.9863	+	75.6784i	−0.0229183	+	0.144701i	0.973576	+	0.228364i	$0.0733378\pi$
$524$	−759.998	+	292.117i	−1.45038	+	0.557475i
$525$	239.777	−	323.092i	0.456719	−	0.615413i
$526$	−218.605	+	318.221i	−0.415598	+	0.604982i
$527$	−197.680	−	197.680i	−0.375105	−	0.375105i
$528$	104.923	−	199.280i	0.198717	−	0.377424i
$529$			1264.48i			2.39031i
$530$	−1.53601	−	71.9882i	−0.00289813	−	0.135827i
$531$	−360.683	−	117.193i	−0.679252	−	0.220703i
$532$	−188.862	+	424.690i	−0.355004	+	0.798289i
$533$	27.3455	−	172.653i	0.0513049	−	0.323926i
$534$	−66.2644	−	86.3185i	−0.124091	−	0.161645i
$535$	−72.2695	−	471.742i	−0.135083	−	0.881761i
$536$	150.802	−	629.952i	0.281347	−	1.17528i
$537$	19.7052	+	124.414i	0.0366949	+	0.231683i
$538$	−503.558	−	477.649i	−0.935981	−	0.887824i
$539$	−585.598	−	1048.54i	−1.08645	−	1.94535i
$540$	416.257	+	45.6990i	0.770846	+	0.0846278i
$541$	−92.3756	+	127.144i	−0.170750	+	0.235017i	−0.885812	−	0.464044i	$-0.846398\pi$
$541$	−92.3756	+	127.144i	−0.170750	+	0.235017i	0.715063	+	0.699060i	$0.246398\pi$
$542$	−326.368	−	600.783i	−0.602156	−	1.10846i
$543$	122.329	−	240.084i	0.225284	−	0.442144i
$544$	311.101	+	327.116i	0.571877	+	0.601316i
$545$	110.736	−	335.027i	0.203185	−	0.614729i
$546$	419.523	−	148.664i	0.768357	−	0.272278i
$547$	681.405	−	347.193i	1.24571	−	0.634723i	0.298220	−	0.954497i	$-0.403607\pi$
$547$	681.405	−	347.193i	1.24571	−	0.634723i	0.947494	+	0.319775i	$0.103607\pi$
$548$	159.871	−	34.0546i	0.291736	−	0.0621435i
$549$	−92.4347			−0.168369
$550$	461.869	+	298.626i	0.839761	+	0.542956i
$551$			217.049i			0.393918i
$552$	−421.485	+	101.482i	−0.763560	+	0.183844i
$553$	356.756	+	700.173i	0.645128	+	1.26614i
$554$	518.511	−	183.742i	0.935941	−	0.331664i
$555$	−168.373	−	55.6522i	−0.303376	−	0.100274i
$556$	−46.6987	+	37.8496i	−0.0839905	+	0.0680749i
$557$	−170.997	−	87.1273i	−0.306996	−	0.156422i	0.293705	−	0.955896i	$-0.405112\pi$
$557$	−170.997	−	87.1273i	−0.306996	−	0.156422i	−0.600701	+	0.799474i	$0.705112\pi$
$558$	−139.295	−	256.416i	−0.249633	−	0.459527i
$559$	−403.285	−	293.003i	−0.721439	−	0.524156i
$560$	1004.55	+	56.8692i	1.79384	+	0.101552i
$561$	−38.5106	−	194.800i	−0.0686463	−	0.347237i
$562$	−537.874	−	510.201i	−0.957072	−	0.907830i
$563$	−853.232	+	135.139i	−1.51551	+	0.240033i	−0.858093	−	0.513495i	$-0.828351\pi$
$563$	−853.232	+	135.139i	−1.51551	+	0.240033i	−0.657416	+	0.753528i	$0.728351\pi$
$564$	126.337	+	33.7929i	0.224002	+	0.0599164i
$565$	−553.617	+	84.8124i	−0.979852	+	0.150110i
$566$	−421.734	−	549.366i	−0.745112	−	0.970611i
$567$	490.308	+	77.6572i	0.864741	+	0.136962i
$568$	234.629	+	97.0067i	0.413080	+	0.170787i
$569$	202.545	−	623.371i	0.355967	−	1.09556i	−0.599479	−	0.800391i	$-0.704625\pi$
$569$	202.545	−	623.371i	0.355967	−	1.09556i	0.955446	−	0.295165i	$-0.0953745\pi$
$570$	2.52195	+	118.196i	0.00442447	+	0.207362i
$571$	135.907			0.238016			0.119008	−	0.992893i	$-0.462029\pi$
$571$	135.907			0.238016			0.119008	+	0.992893i	$0.462029\pi$
$572$	239.760	+	559.192i	0.419161	+	0.977609i
$573$	162.725	−	162.725i	0.283988	−	0.283988i
$574$	−180.051	+	262.099i	−0.313678	+	0.456618i
$575$	−155.022	−	1047.33i	−0.269604	−	1.82144i
$576$	214.472	+	419.566i	0.372347	+	0.728412i
$577$	142.991	+	22.6475i	0.247818	+	0.0392505i	0.279108	−	0.960260i	$-0.409961\pi$
$577$	142.991	+	22.6475i	0.247818	+	0.0392505i	−0.0312896	+	0.999510i	$0.509961\pi$
$578$	−178.441	−	23.4525i	−0.308721	−	0.0405753i
$579$	−150.065	+	48.7589i	−0.259179	+	0.0842123i
$580$	439.424	−	166.350i	0.757628	−	0.286810i
$581$	1115.26	+	810.283i	1.91955	+	1.39463i
$582$	31.9855	+	30.3398i	0.0549579	+	0.0521303i
$583$	−79.1475	+	3.01670i	−0.135759	+	0.00517444i
$584$	−34.8646	−	439.319i	−0.0596997	−	0.752258i
$585$	−361.765	+	358.119i	−0.618402	+	0.612170i
$586$	163.114	−	551.105i	0.278351	−	0.940453i
$587$	27.7181	+	14.1231i	0.0472199	+	0.0240597i	0.477441	−	0.878664i	$-0.341564\pi$
$587$	27.7181	+	14.1231i	0.0472199	+	0.0240597i	−0.430221	+	0.902724i	$0.641564\pi$
$588$	−555.804	−	58.1720i	−0.945245	−	0.0989320i
$589$	148.121	−	107.616i	0.251479	−	0.182710i
$590$	−506.922	+	91.4136i	−0.859190	+	0.154938i
$591$	116.232	−	357.724i	0.196669	−	0.605286i
$592$	−115.150	−	428.251i	−0.194511	−	0.723397i
$593$	407.789	+	407.789i	0.687671	+	0.687671i	0.961717	−	0.274046i	$-0.0883621\pi$
$593$	407.789	+	407.789i	0.687671	+	0.687671i	−0.274046	+	0.961717i	$0.588362\pi$
$594$	42.5868	−	458.661i	0.0716950	−	0.772157i
$595$	720.334	−	517.800i	1.21065	−	0.870252i
$596$	130.014	−	200.396i	0.218144	−	0.336234i
$597$	23.8610	−	12.1578i	0.0399682	−	0.0203648i
$598$	503.985	−	1057.22i	0.842784	−	1.76793i
$599$	−411.162	+	298.727i	−0.686414	+	0.498709i	−0.875479	−	0.483256i	$-0.839454\pi$
$599$	−411.162	+	298.727i	−0.686414	+	0.498709i	0.189065	+	0.981964i	$0.439454\pi$
$600$	237.361	−	95.6936i	0.395601	−	0.159489i
$601$	−521.114	+	169.320i	−0.867078	+	0.281731i	−0.708582	−	0.705629i	$-0.750665\pi$
$601$	−521.114	+	169.320i	−0.867078	+	0.281731i	−0.158496	+	0.987360i	$0.550665\pi$
$602$	432.857	+	796.808i	0.719031	+	1.32360i
$603$	−93.2566	−	588.799i	−0.154654	−	0.976450i
$604$	50.5976	+	957.462i	0.0837709	+	1.58520i
$605$	319.926	−	513.490i	0.528803	−	0.848744i
$606$	9.81730	+	371.806i	0.0162002	+	0.613541i
$607$	62.2856	+	393.256i	0.102612	+	0.647868i	0.984363	+	0.176152i	$0.0563651\pi$
$607$	62.2856	+	393.256i	0.102612	+	0.647868i	−0.881751	+	0.471716i	$0.843635\pi$
$608$	−243.466	+	167.721i	−0.400437	+	0.275857i
$609$	−359.584	+	116.836i	−0.590451	+	0.191849i
$610$	−110.622	+	59.3704i	−0.181347	+	0.0973285i
$611$	−285.830	+	207.667i	−0.467806	+	0.339881i
$612$	379.615	+	168.817i	0.620287	+	0.275845i
$613$	−391.518	+	199.488i	−0.638692	+	0.325430i	−0.743175	−	0.669097i	$-0.766681\pi$
$613$	−391.518	+	199.488i	−0.638692	+	0.325430i	0.104483	+	0.994527i	$0.466681\pi$
$614$	−583.486	−	400.831i	−0.950303	−	0.652820i
$615$	−13.0571	+	79.8210i	−0.0212311	+	0.129790i
$616$	44.0253	−	1105.90i	0.0714696	−	1.79529i
$617$	−597.836	−	597.836i	−0.968941	−	0.968941i	0.0305913	−	0.999532i	$-0.490261\pi$
$617$	−597.836	−	597.836i	−0.968941	−	0.968941i	−0.999532	+	0.0305913i	$0.990261\pi$
$618$	−15.3741	−	82.8505i	−0.0248773	−	0.134062i
$619$	30.6391	−	94.2974i	0.0494977	−	0.152338i	−0.923253	−	0.384193i	$-0.874480\pi$
$619$	30.6391	−	94.2974i	0.0494977	−	0.152338i	0.972750	+	0.231855i	$0.0744796\pi$
$620$	−331.397	−	217.399i	−0.534511	−	0.350643i
$621$	−717.362	+	521.194i	−1.15517	+	0.839282i
$622$	−537.487	−	70.6421i	−0.864126	−	0.113572i
$623$	−476.492	−	242.785i	−0.764835	−	0.389703i
$624$	276.975	+	58.6201i	0.443870	+	0.0939425i
$625$	181.055	+	598.201i	0.289688	+	0.957121i
$626$	20.1652	+	763.707i	0.0322128	+	1.21998i
$627$	129.951	−	4.95307i	0.207258	−	0.00789964i
$628$	−78.2384	+	86.9689i	−0.124583	+	0.138485i
$629$	−316.325	−	229.824i	−0.502902	−	0.365380i
$630$	874.364	−	304.868i	1.38788	−	0.483917i
$631$	−136.339	+	44.2994i	−0.216069	+	0.0702050i	−0.415051	−	0.909798i	$-0.636236\pi$
$631$	−136.339	+	44.2994i	−0.216069	+	0.0702050i	0.198982	+	0.980003i	$0.436236\pi$
$632$	−38.8913	+	498.333i	−0.0615368	+	0.788501i
$633$	−365.961	−	57.9625i	−0.578137	−	0.0915680i
$634$	−277.112	−	781.997i	−0.437085	−	1.23343i
$635$	−439.917	+	852.681i	−0.692782	+	1.34281i
$636$	−20.0594	+	30.9183i	−0.0315400	+	0.0486137i
$637$	1067.54	−	1067.54i	1.67589	−	1.67589i
$638$	−191.062	−	480.232i	−0.299469	−	0.752714i
$639$	233.662			0.365669
$640$	526.156	+	364.363i	0.822118	+	0.569317i
$641$	−124.564	+	383.368i	−0.194327	+	0.598078i	0.805656	+	0.592383i	$0.201813\pi$
$641$	−124.564	+	383.368i	−0.194327	+	0.598078i	−0.999984	+	0.00569511i	$0.998187\pi$
$642$	−105.116	+	220.504i	−0.163732	+	0.343465i
$643$	311.199	+	49.2891i	0.483980	+	0.0766548i	0.393656	−	0.919258i	$-0.371210\pi$
$643$	311.199	+	49.2891i	0.483980	+	0.0766548i	0.0903232	+	0.995913i	$0.471210\pi$
$644$	−1655.13	+	1341.50i	−2.57009	+	2.08307i
$645$	185.910	+	136.515i	0.288233	+	0.211652i
$646$	−73.9797	+	249.951i	−0.114520	+	0.386922i
$647$	935.119	−	148.108i	1.44532	−	0.228915i	0.616022	−	0.787729i	$-0.288743\pi$
$647$	935.119	−	148.108i	1.44532	−	0.228915i	0.829293	+	0.558814i	$0.188743\pi$
$648$	240.243	+	204.915i	0.370746	+	0.316227i
$649$	109.888	+	555.850i	0.169318	+	0.856472i
$650$	−202.926	+	660.941i	−0.312194	+	1.01683i
$651$	258.021	+	187.463i	0.396345	+	0.287962i
$652$	−178.024	−	308.036i	−0.273043	−	0.472448i
$653$	27.7207	+	14.1244i	0.0424513	+	0.0216300i	0.475087	−	0.879939i	$-0.342416\pi$
$653$	27.7207	+	14.1244i	0.0424513	+	0.0216300i	−0.432636	+	0.901569i	$0.642416\pi$
$654$	−143.262	+	109.978i	−0.219055	+	0.168163i
$655$	−319.402	+	966.339i	−0.487637	+	1.47533i
$656$	−184.706	+	82.4297i	−0.281564	+	0.125655i
$657$	−184.132	−	361.379i	−0.280262	−	0.550044i
$658$	631.903	−	117.259i	0.960339	−	0.178205i
$659$		−	495.499i		−	0.751895i	−0.926641	−	0.375948i	$-0.877317\pi$
$659$		−	495.499i		−	0.751895i	0.926641	−	0.375948i	$-0.122683\pi$
$660$	−109.625	−	259.296i	−0.166098	−	0.392872i
$661$	278.241			0.420940			0.210470	−	0.977600i	$-0.432501\pi$
$661$	278.241			0.420940			0.210470	+	0.977600i	$0.432501\pi$
$662$	−78.4479	−	422.752i	−0.118501	−	0.638598i
$663$	222.411	−	113.324i	0.335462	−	0.170926i
$664$	336.091	+	809.895i	0.506161	+	1.21972i
$665$	261.138	+	518.994i	0.392689	+	0.780441i
$666$	−248.523	−	323.735i	−0.373157	−	0.486089i
$667$	−451.680	+	886.471i	−0.677181	+	1.32904i
$668$	−119.418	−	206.630i	−0.178770	−	0.309327i
$669$	270.702	−	372.590i	0.404637	−	0.556935i
$670$	−489.788	−	644.750i	−0.731027	−	0.962314i
$671$	67.3379	+	120.572i	0.100355	+	0.179690i
$672$	−408.920	−	313.067i	−0.608512	−	0.465873i
$673$	−104.338	−	658.765i	−0.155034	−	0.978849i	−0.935417	−	0.353547i	$-0.884976\pi$
$673$	−104.338	−	658.765i	−0.155034	−	0.978849i	0.780383	−	0.625302i	$-0.215024\pi$
$674$	755.169	+	223.512i	1.12043	+	0.331620i
$675$	373.863	−	366.365i	0.553872	−	0.542763i
$676$	−69.0141	+	55.9364i	−0.102092	+	0.0827462i
$677$	−59.2079	+	373.824i	−0.0874563	+	0.552178i	0.904588	+	0.426287i	$0.140179\pi$
$677$	−59.2079	+	373.824i	−0.0874563	+	0.552178i	−0.992044	+	0.125890i	$0.959821\pi$
$678$	258.775	+	123.360i	0.381673	+	0.181947i
$679$	206.050	+	66.9496i	0.303461	+	0.0986003i
$680$	562.737	−	41.7924i	0.827555	−	0.0614594i
$681$		−	369.611i		−	0.542748i
$682$	−232.995	+	368.494i	−0.341634	+	0.540313i
$683$	−271.543	−	271.543i	−0.397573	−	0.397573i	0.479803	−	0.877376i	$-0.340708\pi$
$683$	−271.543	−	271.543i	−0.397573	−	0.397573i	−0.877376	+	0.479803i	$0.840708\pi$
$684$	−148.090	+	228.257i	−0.216506	+	0.333709i
$685$	93.6813	−	181.580i	0.136761	−	0.265081i
$686$	−1426.84	+	505.623i	−2.07995	+	0.737059i
$687$	−32.9022	+	207.736i	−0.0478926	+	0.302382i
$688$	−29.6840	+	576.029i	−0.0431454	+	0.837251i
$689$	−30.7678	−	94.6936i	−0.0446557	−	0.137436i
$690$	−235.667	+	487.986i	−0.341547	+	0.707226i
$691$	−295.402	+	406.585i	−0.427499	+	0.588402i	−0.967377	−	0.253342i	$-0.918470\pi$
$691$	−295.402	+	406.585i	−0.427499	+	0.588402i	0.539878	+	0.841743i	$0.318470\pi$
$692$	763.614	−	848.824i	1.10349	−	1.22662i
$693$	−351.429	−	956.044i	−0.507113	−	1.37957i
$694$	934.014	−	24.6621i	1.34584	−	0.0355361i
$695$	−0.380543	+	75.1381i	−0.000547544	+	0.108112i
$696$	−233.888	−	55.9895i	−0.336046	−	0.0804447i
$697$	−80.9629	+	158.899i	−0.116159	+	0.227975i
$698$	−9.56885	+	72.8055i	−0.0137090	+	0.104306i
$699$	−162.082	−	223.086i	−0.231876	−	0.319150i
$700$	850.584	−	926.452i	1.21512	−	1.32350i
$701$	−812.067	−	263.857i	−1.15844	−	0.376400i	−0.334124	−	0.942529i	$-0.608441\pi$
$701$	−812.067	−	263.857i	−1.15844	−	0.376400i	−0.824317	+	0.566129i	$0.808441\pi$
$702$	569.332	−	105.648i	0.811015	−	0.150496i
$703$	181.068	−	181.068i	0.257565	−	0.257565i
$704$	391.042	−	585.408i	0.555457	−	0.831545i
$705$	132.738	−	95.4162i	0.188280	−	0.135342i
$706$	−736.584	+	1072.24i	−1.04332	+	1.51875i
$707$	829.811	+	1628.60i	1.17371	+	2.30353i
$708$	240.905	+	107.132i	0.340262	+	0.151316i
$709$	−93.5263	−	128.728i	−0.131913	−	0.181563i	0.737951	−	0.674854i	$-0.235794\pi$
$709$	−93.5263	−	128.728i	−0.131913	−	0.181563i	−0.869864	+	0.493292i	$0.835794\pi$
$710$	279.637	−	150.080i	0.393855	−	0.211381i
$711$	142.154	+	437.505i	0.199935	+	0.615338i
$712$	−177.925	−	289.921i	−0.249895	−	0.407192i
$713$	828.908	−	131.286i	1.16256	−	0.184132i
$714$	−453.918	+	11.9854i	−0.635739	+	0.0167863i
$715$	730.675	+	211.001i	1.02192	+	0.295106i
$716$	20.7792	+	393.206i	0.0290213	+	0.549171i
$717$	−291.553	+	46.1775i	−0.406629	+	0.0644038i
$718$	−141.020	+	76.6077i	−0.196407	+	0.106696i
$719$	−215.325	−	662.701i	−0.299478	−	0.921698i	−0.981680	−	0.190535i	$-0.938978\pi$
$719$	−215.325	−	662.701i	−0.299478	−	0.921698i	0.682203	−	0.731163i	$-0.261022\pi$
$720$	575.616	+	124.875i	0.799466	+	0.173437i
$721$	−243.405	−	335.019i	−0.337594	−	0.464659i
$722$	497.634	+	237.226i	0.689243	+	0.328567i
$723$	78.4084	+	153.885i	0.108449	+	0.212843i
$724$	458.435	−	706.603i	0.633197	−	0.975970i
$725$	187.141	−	556.709i	0.258125	−	0.767875i
$726$	−283.164	+	125.351i	−0.390033	+	0.172660i
$727$	−200.970	+	200.970i	−0.276437	+	0.276437i	−0.831685	−	0.555248i	$-0.812623\pi$
$727$	−200.970	+	200.970i	−0.276437	+	0.276437i	0.555248	+	0.831685i	$0.312623\pi$
$728$	1352.65	−	325.679i	1.85803	−	0.447361i
$729$	47.0496	+	15.2873i	0.0645399	+	0.0209703i
$730$	−452.473	−	314.215i	−0.619826	−	0.430432i
$731$	298.922	+	411.432i	0.408923	+	0.562834i
$732$	63.9119	+	6.68920i	0.0873113	+	0.00913825i
$733$	327.790	−	643.323i	0.447189	−	0.877658i	−0.551855	−	0.833940i	$-0.686080\pi$
$733$	327.790	−	643.323i	0.447189	−	0.877658i	0.999044	−	0.0437176i	$-0.0139202\pi$
$734$	273.745	+	81.0219i	0.372949	+	0.110384i
$735$	−496.445	+	491.442i	−0.675435	+	0.668628i
$736$	−1343.39	+	178.353i	−1.82526	+	0.242328i
$737$	−700.095	+	550.580i	−0.949925	+	0.747055i
$738$	−128.106	+	135.055i	−0.173586	+	0.183001i
$739$	191.895	−	264.121i	0.259669	−	0.357403i	−0.659199	−	0.751968i	$-0.729105\pi$
$739$	191.895	−	264.121i	0.259669	−	0.357403i	0.918868	+	0.394565i	$0.129105\pi$
$740$	−505.354	−	227.806i	−0.682911	−	0.307847i
$741$	50.5172	+	155.476i	0.0681743	+	0.209819i
$742$	−23.6017	+	179.576i	−0.0318082	+	0.242016i
$743$	−20.0681	+	126.705i	−0.0270096	+	0.170532i	−0.997506	−	0.0705845i	$-0.977514\pi$
$743$	−20.0681	+	126.705i	−0.0270096	+	0.170532i	0.970496	+	0.241116i	$0.0775135\pi$
$744$	77.7564	+	187.373i	0.104511	+	0.251846i
$745$	−90.8317	−	284.445i	−0.121922	−	0.381805i
$746$	648.527	+	445.512i	0.869339	+	0.597201i
$747$	570.631	+	570.631i	0.763897	+	0.763897i
$748$	−56.3410	−	618.153i	−0.0753222	−	0.826408i
$749$			1200.46i			1.60275i
$750$	95.4411	−	305.337i	0.127255	−	0.407116i
$751$	946.021	+	307.381i	1.25968	+	0.409295i	0.861381	−	0.507960i	$-0.169600\pi$
$751$	946.021	+	307.381i	1.25968	+	0.409295i	0.398300	+	0.917255i	$0.369600\pi$
$752$	381.779	+	146.169i	0.507685	+	0.194374i
$753$	33.8589	−	213.777i	0.0449654	−	0.283900i
$754$	515.364	−	395.632i	0.683507	−	0.524710i
$755$	966.024	+	709.361i	1.27950	+	0.939550i
$756$	−1017.57	−	272.181i	−1.34599	−	0.360028i
$757$	229.595	+	1449.61i	0.303296	+	1.91494i	0.394102	+	0.919067i	$0.371056\pi$
$757$	229.595	+	1449.61i	0.303296	+	1.91494i	−0.0908056	+	0.995869i	$0.528944\pi$
$758$	−843.766	+	889.533i	−1.11315	+	1.17353i
$759$	541.055	+	250.200i	0.712852	+	0.329644i
$760$	−30.6194	+	368.286i	−0.0402886	+	0.484586i
$761$	401.804	−	553.035i	0.527994	−	0.726722i	−0.458829	−	0.888525i	$-0.651731\pi$
$761$	401.804	−	553.035i	0.527994	−	0.726722i	0.986823	+	0.161803i	$0.0517309\pi$
$762$	431.541	−	234.430i	0.566327	−	0.307651i
$763$	−402.947	+	790.829i	−0.528109	+	1.03647i
$764$	558.852	−	452.954i	0.731482	−	0.592872i
$765$	463.910	−	233.422i	0.606418	−	0.305127i
$766$	−191.708	−	540.993i	−0.250272	−	0.706257i
$767$	−634.637	+	323.364i	−0.827427	+	0.421595i
$768$	−117.929	−	305.620i	−0.153554	−	0.397942i
$769$	951.979			1.23794			0.618972	−	0.785413i	$-0.287549\pi$
$769$	951.979			1.23794

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+(-1.96643 + 0.364900i) q^{2} +(1.14015 - 0.580936i) q^{3} +(3.73370 - 1.43510i) q^{4} +(1.56915 - 4.74740i) q^{5} +(-2.03004 + 1.55841i) q^{6} +(-5.70983 + 11.2062i) q^{7} +(-6.81838 + 4.18445i) q^{8} +(-4.32761 + 5.95644i) q^{9} +(-1.35329 + 9.90801i) q^{10} +(10.9222 + 1.30573i) q^{11} +(3.42328 - 3.80527i) q^{12} +(2.16315 + 13.6576i) q^{13} +(7.13885 - 24.1197i) q^{14} +(-0.968868 - 6.32433i) q^{15} +(11.8810 - 10.7165i) q^{16} +(2.20685 - 13.9335i) q^{17} +(6.33643 - 13.2921i) q^{18} +(8.78672 + 2.85498i) q^{19} +(-0.954276 - 19.9772i) q^{20} +16.0938i q^{21} +(-21.9543 + 1.41790i) q^{22} +(29.9456 + 29.9456i) q^{23} +(-5.34309 + 8.73196i) q^{24} +(-20.0755 - 14.8987i) q^{25} +(-9.23734 - 26.0674i) q^{26} +(-3.27541 + 20.6801i) q^{27} +(-5.23677 + 50.0347i) q^{28} +(7.25970 + 22.3431i) q^{29} +(4.21296 + 12.0828i) q^{30} +(11.6482 - 16.0323i) q^{31} +(-19.4526 + 25.4086i) q^{32} +(13.2115 - 4.85639i) q^{33} +(0.744723 + 28.2045i) q^{34} +(44.2406 + 44.6910i) q^{35} +(-7.60987 + 28.4501i) q^{36} +(12.5830 - 24.6955i) q^{37} +(-18.3203 - 2.40784i) q^{38} +(10.4005 + 14.3151i) q^{39} +(9.16621 + 38.9356i) q^{40} +(-12.0228 - 3.90645i) q^{41} +(-5.87263 - 31.6473i) q^{42} +(-25.4909 + 25.4909i) q^{43} +(42.6541 - 10.7993i) q^{44} +(21.4869 + 29.8914i) q^{45} +(-69.8130 - 47.9587i) q^{46} +(11.5996 + 22.7655i) q^{47} +(7.32052 - 19.1205i) q^{48} +(-64.1748 - 88.3290i) q^{49} +(44.9137 + 21.9718i) q^{50} +(-5.57833 - 17.1683i) q^{51} +(27.6766 + 47.8889i) q^{52} +(-7.11181 + 1.12640i) q^{53} +(-1.10532 - 41.8612i) q^{54} +(23.3374 - 49.8033i) q^{55} +(-7.95992 - 100.301i) q^{56} +(11.6768 - 1.84942i) q^{57} +(-22.4287 - 41.2870i) q^{58} +(15.9174 + 48.9888i) q^{59} +(-12.6935 - 22.2227i) q^{60} +(7.37946 + 10.1570i) q^{61} +(-17.0551 + 35.7769i) q^{62} +(-42.0390 - 82.5063i) q^{63} +(28.9807 - 57.0624i) q^{64} +(68.2323 + 11.1615i) q^{65} +(-24.2075 + 14.3706i) q^{66} +(-57.2536 + 57.2536i) q^{67} +(-11.7563 - 55.1905i) q^{68} +(51.5390 + 16.7460i) q^{69} +(-103.304 - 71.7383i) q^{70} +(-18.6543 - 25.6754i) q^{71} +(4.58283 - 58.7220i) q^{72} +(-25.0092 + 49.0833i) q^{73} +(-15.7321 + 53.1534i) q^{74} +(-31.5444 - 5.32421i) q^{75} +(36.9041 - 1.95022i) q^{76} +(-76.9963 + 114.941i) q^{77} +(-25.6754 - 24.3544i) q^{78} +(36.7254 - 50.5482i) q^{79} +(-32.2323 - 73.2194i) q^{80} +(-12.1971 - 37.5387i) q^{81} +(25.0675 + 3.29463i) q^{82} +(17.1464 - 108.258i) q^{83} +(23.0962 + 60.0893i) q^{84} +(-62.6849 - 32.3405i) q^{85} +(40.8244 - 59.4277i) q^{86} +(21.2570 + 21.2570i) q^{87} +(-79.9357 + 36.8006i) q^{88} +42.5205i q^{89} +(-53.1599 - 50.9388i) q^{90} +(-165.401 - 53.7419i) q^{91} +(154.783 + 68.8327i) q^{92} +(3.96692 - 25.0461i) q^{93} +(-31.1169 - 40.5340i) q^{94} +(27.3414 - 37.2342i) q^{95} +(-7.41821 + 40.2704i) q^{96} +(-2.69477 - 17.0141i) q^{97} +(158.427 + 150.275i) q^{98} +(-55.0446 + 59.4069i) 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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