LMFDB - Embedded newform 75.3.k.a.22.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,3,Mod(13,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.13"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 19])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			22.10
Character	$\chi$	$=$	75.22
Dual form			75.3.k.a.58.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.93190 - 1.49388i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(4.01322 - 5.52372i) q^{4} +(-0.890939 - 4.91998i) q^{5} +(-4.61091 + 3.35002i) q^{6} +(4.34391 + 4.34391i) q^{7} +(1.45557 - 9.19012i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-9.96199 - 13.0939i) q^{10} +(-4.51369 + 13.8917i) q^{11} +(-5.36886 + 10.5370i) q^{12} +(6.86423 + 3.49750i) q^{13} +(19.2252 + 6.24664i) q^{14} +(2.85723 + 8.17534i) q^{15} +(-1.02182 - 3.14483i) q^{16} +(-25.6357 - 4.06030i) q^{17} +(6.98030 - 6.98030i) q^{18} +(-1.24222 - 1.70977i) q^{19} +(-30.7522 - 14.8237i) q^{20} +(-8.60824 - 6.25425i) q^{21} +(7.51883 + 47.4720i) q^{22} +(-2.15443 - 4.22830i) q^{23} +16.1162i q^{24} +(-23.4125 + 8.76681i) q^{25} +25.3501 q^{26} +(-4.62981 + 2.35900i) q^{27} +(41.4277 - 6.56150i) q^{28} +(32.6254 - 44.9050i) q^{29} +(20.5901 + 19.7009i) q^{30} +(27.1558 - 19.7298i) q^{31} +(18.6237 + 18.6237i) q^{32} +(3.95770 - 24.9879i) q^{33} +(-81.2269 + 26.3922i) q^{34} +(17.5018 - 25.2421i) q^{35} +(6.32962 - 19.4806i) q^{36} +(-18.7363 + 36.7721i) q^{37} +(-6.19627 - 3.15716i) q^{38} +(-12.6905 - 4.12339i) q^{39} +(-46.5120 + 1.02645i) q^{40} +(-1.20677 - 3.71404i) q^{41} +(-34.5816 - 5.47718i) q^{42} +(-32.8976 + 32.8976i) q^{43} +(58.6196 + 80.6829i) q^{44} +(-7.10308 - 13.2116i) q^{45} +(-12.6331 - 9.17851i) q^{46} +(-12.8776 - 81.3060i) q^{47} +(2.60015 + 5.10308i) q^{48} -11.2608i q^{49} +(-55.5464 + 60.6787i) q^{50} +44.9558 q^{51} +(46.8669 - 23.8799i) q^{52} +(-81.1884 + 12.8590i) q^{53} +(-10.0501 + 13.8327i) q^{54} +(72.3684 + 9.83061i) q^{55} +(46.2440 - 33.5982i) q^{56} +(2.58837 + 2.58837i) q^{57} +(28.5718 - 180.395i) q^{58} +(-10.7101 + 3.47991i) q^{59} +(56.6250 + 17.0269i) q^{60} +(-9.84864 + 30.3110i) q^{61} +(50.1440 - 98.4132i) q^{62} +(16.4210 + 8.36689i) q^{63} +(95.0038 + 30.8686i) q^{64} +(11.0920 - 36.8880i) q^{65} +(-25.7253 - 79.1744i) q^{66} +(-0.351533 - 0.0556774i) q^{67} +(-125.310 + 125.310i) q^{68} +(4.83131 + 6.64972i) q^{69} +(13.6049 - 100.153i) q^{70} +(88.5525 + 64.3371i) q^{71} +(-4.36672 - 27.5704i) q^{72} +(-20.1163 - 39.4805i) q^{73} +135.802i q^{74} +(37.6769 - 21.3413i) q^{75} -14.4296 q^{76} +(-79.9515 + 40.7373i) q^{77} +(-43.3670 + 6.86866i) q^{78} +(33.1447 - 45.6197i) q^{79} +(-14.5621 + 7.82918i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-9.08644 - 9.08644i) q^{82} +(-2.71085 + 17.1156i) q^{83} +(-69.0935 + 22.4499i) q^{84} +(2.86327 + 129.745i) q^{85} +(-47.3074 + 145.597i) q^{86} +(-43.6460 + 85.6602i) q^{87} +(121.097 + 61.7018i) q^{88} +(-85.2857 - 27.7110i) q^{89} +(-40.5620 - 28.1239i) q^{90} +(14.6248 + 45.0105i) q^{91} +(-32.0022 - 5.06865i) q^{92} +(-41.1102 + 41.1102i) q^{93} +(-159.217 - 219.143i) q^{94} +(-7.30531 + 7.63503i) q^{95} +(-36.9063 - 26.8140i) q^{96} +(1.37908 + 8.70714i) q^{97} +(-16.8223 - 33.0156i) q^{98} +43.8198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26}+ \cdots - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	2.93190	−	1.49388i	1.46595	−	0.746939i	0.474850	−	0.880066i	$-0.342502\pi$
$2$	2.93190	−	1.49388i	1.46595	−	0.746939i	0.991099	+	0.133128i	$0.0425021\pi$
$3$	−1.71073	+	0.270952i	−0.570242	+	0.0903175i
$3$	−1.71073	+	0.270952i	−0.570242	+	0.0903175i
$4$	4.01322	−	5.52372i	1.00331	−	1.38093i
$5$	−0.890939	−	4.91998i	−0.178188	−	0.983996i
$5$	−0.890939	−	4.91998i	−0.178188	−	0.983996i
$6$	−4.61091	+	3.35002i	−0.768484	+	0.558337i
$7$	4.34391	+	4.34391i	0.620559	+	0.620559i	0.945674	−	0.325115i	$-0.105403\pi$
$7$	4.34391	+	4.34391i	0.620559	+	0.620559i	−0.325115	+	0.945674i	$0.605403\pi$
$8$	1.45557	−	9.19012i	0.181946	−	1.14876i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$	−9.96199	−	13.0939i	−0.996199	−	1.30939i
$11$	−4.51369	+	13.8917i	−0.410336	+	1.26288i	0.506021	+	0.862521i	$0.331116\pi$
$11$	−4.51369	+	13.8917i	−0.410336	+	1.26288i	−0.916357	+	0.400362i	$0.868884\pi$
$12$	−5.36886	+	10.5370i	−0.447405	+	0.878081i
$13$	6.86423	+	3.49750i	0.528018	+	0.269039i	0.697612	−	0.716475i	$-0.254246\pi$
$13$	6.86423	+	3.49750i	0.528018	+	0.269039i	−0.169595	+	0.985514i	$0.554246\pi$
$14$	19.2252	+	6.24664i	1.37323	+	0.446189i
$15$	2.85723	+	8.17534i	0.190482	+	0.545023i
$16$	−1.02182	−	3.14483i	−0.0638636	−	0.196552i
$17$	−25.6357	−	4.06030i	−1.50798	−	0.238841i	−0.652945	−	0.757405i	$-0.726467\pi$
$17$	−25.6357	−	4.06030i	−1.50798	−	0.238841i	−0.855039	+	0.518564i	$0.826467\pi$
$18$	6.98030	−	6.98030i	0.387795	−	0.387795i
$19$	−1.24222	−	1.70977i	−0.0653802	−	0.0899881i	0.775075	−	0.631870i	$-0.217712\pi$
$19$	−1.24222	−	1.70977i	−0.0653802	−	0.0899881i	−0.840455	+	0.541881i	$0.817712\pi$
$20$	−30.7522	−	14.8237i	−1.53761	−	0.741184i
$21$	−8.60824	−	6.25425i	−0.409916	−	0.297822i
$22$	7.51883	+	47.4720i	0.341765	+	2.15782i
$23$	−2.15443	−	4.22830i	−0.0936708	−	0.183839i	0.839417	−	0.543488i	$-0.182897\pi$
$23$	−2.15443	−	4.22830i	−0.0936708	−	0.183839i	−0.933088	+	0.359649i	$0.882897\pi$
$24$			16.1162i			0.671507i
$25$	−23.4125	+	8.76681i	−0.936498	+	0.350672i
$26$	25.3501			0.975003
$27$	−4.62981	+	2.35900i	−0.171474	+	0.0873705i
$28$	41.4277	−	6.56150i	1.47956	−	0.234339i
$29$	32.6254	−	44.9050i	1.12501	−	1.54845i	0.327806	−	0.944745i	$-0.393691\pi$
$29$	32.6254	−	44.9050i	1.12501	−	1.54845i	0.797208	−	0.603704i	$-0.206309\pi$
$30$	20.5901	+	19.7009i	0.686336	+	0.656697i
$31$	27.1558	−	19.7298i	0.875993	−	0.636446i	−0.0561957	−	0.998420i	$-0.517897\pi$
$31$	27.1558	−	19.7298i	0.875993	−	0.636446i	0.932188	+	0.361974i	$0.117897\pi$
$32$	18.6237	+	18.6237i	0.581992	+	0.581992i
$33$	3.95770	−	24.9879i	0.119930	−	0.757210i
$34$	−81.2269	+	26.3922i	−2.38903	+	0.776242i
$35$	17.5018	−	25.2421i	0.500052	−	0.721204i
$36$	6.32962	−	19.4806i	0.175823	−	0.541127i
$37$	−18.7363	+	36.7721i	−0.506388	+	0.993842i	0.486375	+	0.873750i	$0.338319\pi$
$37$	−18.7363	+	36.7721i	−0.506388	+	0.993842i	−0.992763	+	0.120092i	$0.961681\pi$
$38$	−6.19627	−	3.15716i	−0.163060	−	0.0830831i
$39$	−12.6905	−	4.12339i	−0.325397	−	0.105728i
$40$	−46.5120	+	1.02645i	−1.16280	+	0.0256613i
$41$	−1.20677	−	3.71404i	−0.0294333	−	0.0905864i	0.935261	−	0.353960i	$-0.115165\pi$
$41$	−1.20677	−	3.71404i	−0.0294333	−	0.0905864i	−0.964694	+	0.263373i	$0.915165\pi$
$42$	−34.5816	−	5.47718i	−0.823371	−	0.130409i
$43$	−32.8976	+	32.8976i	−0.765060	+	0.765060i	−0.977232	−	0.212172i	$-0.931946\pi$
$43$	−32.8976	+	32.8976i	−0.765060	+	0.765060i	0.212172	+	0.977232i	$0.431946\pi$
$44$	58.6196	+	80.6829i	1.33226	+	1.83370i
$45$	−7.10308	−	13.2116i	−0.157846	−	0.293591i
$46$	−12.6331	−	9.17851i	−0.274633	−	0.199533i
$47$	−12.8776	−	81.3060i	−0.273991	−	1.72991i	−0.613837	−	0.789433i	$-0.710375\pi$
$47$	−12.8776	−	81.3060i	−0.273991	−	1.72991i	0.339846	−	0.940481i	$-0.389625\pi$
$48$	2.60015	+	5.10308i	0.0541698	+	0.106314i
$49$		−	11.2608i		−	0.229813i
$50$	−55.5464	+	60.6787i	−1.11093	+	1.21357i
$51$	44.9558			0.881487
$52$	46.8669	−	23.8799i	0.901287	−	0.459229i
$53$	−81.1884	+	12.8590i	−1.53186	+	0.242622i	−0.864697	−	0.502293i	$-0.832490\pi$
$53$	−81.1884	+	12.8590i	−1.53186	+	0.242622i	−0.667159	+	0.744916i	$0.732490\pi$
$54$	−10.0501	+	13.8327i	−0.186112	+	0.256161i
$55$	72.3684	+	9.83061i	1.31579	+	0.178738i
$56$	46.2440	−	33.5982i	0.825785	−	0.599968i
$57$	2.58837	+	2.58837i	0.0454101	+	0.0454101i
$58$	28.5718	−	180.395i	0.492618	−	3.11026i
$59$	−10.7101	+	3.47991i	−0.181526	+	0.0589815i	−0.398370	−	0.917225i	$-0.630424\pi$
$59$	−10.7101	+	3.47991i	−0.181526	+	0.0589815i	0.216843	+	0.976206i	$0.430424\pi$
$60$	56.6250	+	17.0269i	0.943751	+	0.283781i
$61$	−9.84864	+	30.3110i	−0.161453	+	0.496902i	−0.998757	−	0.0498356i	$-0.984130\pi$
$61$	−9.84864	+	30.3110i	−0.161453	+	0.496902i	0.837304	+	0.546737i	$0.184130\pi$
$62$	50.1440	−	98.4132i	0.808775	−	1.58731i
$63$	16.4210	+	8.36689i	0.260650	+	0.132808i
$64$	95.0038	+	30.8686i	1.48443	+	0.482322i
$65$	11.0920	−	36.8880i	0.170647	−	0.567507i
$66$	−25.7253	−	79.1744i	−0.389777	−	1.19961i
$67$	−0.351533	−	0.0556774i	−0.00524677	−	0.000831006i	0.153811	−	0.988100i	$-0.450845\pi$
$67$	−0.351533	−	0.0556774i	−0.00524677	−	0.000831006i	−0.159057	+	0.987269i	$0.550845\pi$
$68$	−125.310	+	125.310i	−1.84279	+	1.84279i
$69$	4.83131	+	6.64972i	0.0700189	+	0.0963728i
$70$	13.6049	−	100.153i	0.194356	−	1.43076i
$71$	88.5525	+	64.3371i	1.24722	+	0.906157i	0.998057	−	0.0623051i	$-0.0198452\pi$
$71$	88.5525	+	64.3371i	1.24722	+	0.906157i	0.249161	+	0.968462i	$0.419845\pi$
$72$	−4.36672	−	27.5704i	−0.0606488	−	0.382922i
$73$	−20.1163	−	39.4805i	−0.275566	−	0.540828i	0.711198	−	0.702992i	$-0.248153\pi$
$73$	−20.1163	−	39.4805i	−0.275566	−	0.540828i	−0.986764	+	0.162163i	$0.948153\pi$
$74$			135.802i			1.83516i
$75$	37.6769	−	21.3413i	0.502359	−	0.284550i
$76$	−14.4296			−0.189864
$77$	−79.9515	+	40.7373i	−1.03833	+	0.529056i
$78$	−43.3670	+	6.86866i	−0.555988	+	0.0880598i
$79$	33.1447	−	45.6197i	0.419553	−	0.577465i	−0.545963	−	0.837809i	$-0.683836\pi$
$79$	33.1447	−	45.6197i	0.419553	−	0.577465i	0.965516	+	0.260344i	$0.0838361\pi$
$80$	−14.5621	+	7.82918i	−0.182027	+	0.0978648i
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	−9.08644	−	9.08644i	−0.110810	−	0.110810i
$83$	−2.71085	+	17.1156i	−0.0326608	+	0.206212i	−0.998622	−	0.0524736i	$-0.983289\pi$
$83$	−2.71085	+	17.1156i	−0.0326608	+	0.206212i	0.965961	+	0.258686i	$0.0832895\pi$
$84$	−69.0935	+	22.4499i	−0.822542	+	0.267260i
$85$	2.86327	+	129.745i	0.0336855	+	1.52641i
$86$	−47.3074	+	145.597i	−0.550087	+	1.69299i
$87$	−43.6460	+	85.6602i	−0.501679	+	0.984600i
$88$	121.097	+	61.7018i	1.37610	+	0.701156i
$89$	−85.2857	−	27.7110i	−0.958267	−	0.311360i	−0.212196	−	0.977227i	$-0.568062\pi$
$89$	−85.2857	−	27.7110i	−0.958267	−	0.311360i	−0.746070	+	0.665867i	$0.768062\pi$
$90$	−40.5620	−	28.1239i	−0.450689	−	0.312488i
$91$	14.6248	+	45.0105i	0.160712	+	0.494621i
$92$	−32.0022	−	5.06865i	−0.347850	−	0.0550940i
$93$	−41.1102	+	41.1102i	−0.442046	+	0.442046i
$94$	−159.217	−	219.143i	−1.69380	−	2.33131i
$95$	−7.30531	+	7.63503i	−0.0768981	+	0.0803687i
$96$	−36.9063	−	26.8140i	−0.384440	−	0.279312i
$97$	1.37908	+	8.70714i	0.0142173	+	0.0897643i	0.993777	−	0.111391i	$-0.0355305\pi$
$97$	1.37908	+	8.70714i	0.0142173	+	0.0897643i	−0.979559	+	0.201155i	$0.935531\pi$
$98$	−16.8223	−	33.0156i	−0.171656	−	0.336894i
$99$			43.8198i			0.442625i
$100$	−45.5339	+	164.507i	−0.455339	+	1.64507i
$101$	4.54639			0.0450138			0.0225069	−	0.999747i	$-0.492835\pi$
$101$	4.54639			0.0450138			0.0225069	+	0.999747i	$0.492835\pi$
$102$	131.806	−	67.1585i	1.29222	−	0.658417i
$103$	98.1209	−	15.5408i	0.952630	−	0.150882i	0.339273	−	0.940688i	$-0.389819\pi$
$103$	98.1209	−	15.5408i	0.952630	−	0.150882i	0.613357	+	0.789806i	$0.289819\pi$
$104$	42.1338	−	57.9922i	0.405133	−	0.557618i
$105$	−23.1014	+	47.9246i	−0.220013	+	0.456424i
$106$	−218.826	+	158.987i	−2.06440	+	1.49987i
$107$	58.0204	+	58.0204i	0.542247	+	0.542247i	0.924187	−	0.381940i	$-0.124744\pi$
$107$	58.0204	+	58.0204i	0.542247	+	0.542247i	−0.381940	+	0.924187i	$0.624744\pi$
$108$	−5.54994	+	35.0410i	−0.0513884	+	0.324453i
$109$	77.8317	−	25.2890i	0.714052	−	0.232010i	0.0706096	−	0.997504i	$-0.477506\pi$
$109$	77.8317	−	25.2890i	0.714052	−	0.232010i	0.643442	+	0.765494i	$0.277506\pi$
$110$	226.863	−	79.2872i	2.06239	−	0.720793i
$111$	22.0893	−	67.9837i	0.199002	−	0.612466i
$112$	9.22219	−	18.0996i	0.0823410	−	0.161603i
$113$	168.661	+	85.9369i	1.49257	+	0.760504i	0.994310	−	0.106523i	$-0.0339718\pi$
$113$	168.661	+	85.9369i	1.49257	+	0.760504i	0.498262	+	0.867027i	$0.333972\pi$
$114$	11.4556	+	3.72214i	0.100487	+	0.0326503i
$115$	−18.8837	+	14.3669i	−0.164206	+	0.124930i
$116$	−117.110	−	360.428i	−1.00957	−	3.10713i
$117$	22.8272	+	3.61547i	0.195104	+	0.0309015i
$118$	−26.2022	+	26.2022i	−0.222053	+	0.222053i
$119$	−93.7218	−	128.997i	−0.787578	−	1.08401i
$120$	79.2913	−	14.3585i	0.660761	−	0.119654i
$121$	−74.7153	−	54.2839i	−0.617482	−	0.448627i
$122$	16.4057	+	103.581i	0.134473	+	0.849028i
$123$	3.07077	+	6.02673i	0.0249656	+	0.0489978i
$124$		−	229.181i		−	1.84823i
$125$	63.9916	+	107.378i	0.511933	+	0.859025i
$126$	60.6437			0.481299
$127$	−99.6529	+	50.7757i	−0.784668	+	0.399808i	−0.799944	−	0.600075i	$-0.795137\pi$
$127$	−99.6529	+	50.7757i	−0.784668	+	0.399808i	0.0152756	+	0.999883i	$0.495137\pi$
$128$	220.601	−	34.9397i	1.72344	−	0.272967i
$129$	47.3651	−	65.1924i	0.367171	−	0.505368i
$130$	−22.5854	−	124.722i	−0.173734	−	0.959399i
$131$	−84.3598	+	61.2910i	−0.643968	+	0.467870i	−0.861211	−	0.508247i	$-0.830294\pi$
$131$	−84.3598	+	61.2910i	−0.643968	+	0.467870i	0.217243	+	0.976118i	$0.430294\pi$
$132$	−122.143	−	122.143i	−0.925328	−	0.925328i
$133$	2.03100	−	12.8232i	0.0152707	−	0.0964152i
$134$	−1.11384	+	0.361907i	−0.00831221	+	0.00270080i
$135$	15.7311	+	20.6768i	0.116527	+	0.153162i
$136$	−74.6293	+	229.685i	−0.548745	+	1.68886i
$137$	69.3960	−	136.197i	0.506540	−	0.994141i	−0.486198	−	0.873849i	$-0.661617\pi$
$137$	69.3960	−	136.197i	0.506540	−	0.994141i	0.992738	−	0.120293i	$-0.0383833\pi$
$138$	24.0988	+	12.2789i	0.174629	+	0.0889778i
$139$	149.736	+	48.6523i	1.07724	+	0.350016i	0.793303	−	0.608827i	$-0.208359\pi$
$139$	149.736	+	48.6523i	1.07724	+	0.350016i	0.283937	+	0.958843i	$0.408359\pi$
$140$	−69.1920	−	197.977i	−0.494228	−	1.41412i
$141$	44.0601	+	135.603i	0.312483	+	0.961724i
$142$	355.739	+	56.3435i	2.50520	+	0.396785i
$143$	−79.5693	+	79.5693i	−0.556429	+	0.556429i
$144$	−5.83084	−	8.02546i	−0.0404920	−	0.0557324i
$145$	−249.999	−	120.509i	−1.72413	−	0.831095i
$146$	−117.958	−	85.7015i	−0.807931	−	0.586996i
$147$	3.05115	+	19.2642i	0.0207561	+	0.131049i
$148$	127.926	+	251.069i	0.864365	+	1.69641i
$149$		−	80.4685i		−	0.540057i	−0.962852	−	0.270028i	$-0.912967\pi$
$149$		−	80.4685i		−	0.540057i	0.962852	−	0.270028i	$-0.0870331\pi$
$150$	78.5837	−	118.855i	0.523891	−	0.792368i
$151$	187.435			1.24129			0.620647	−	0.784090i	$-0.286870\pi$
$151$	187.435			1.24129			0.620647	+	0.784090i	$0.286870\pi$
$152$	−17.5212	+	8.92749i	−0.115271	+	0.0587335i
$153$	−76.9072	+	12.1809i	−0.502661	+	0.0796137i
$154$	−173.553	+	238.875i	−1.12697	+	1.55114i
$155$	−121.265	−	116.028i	−0.782352	−	0.748567i
$156$	−73.7061	+	53.5506i	−0.472475	+	0.343273i
$157$	−90.0864	−	90.0864i	−0.573798	−	0.573798i	0.359389	−	0.933188i	$-0.382985\pi$
$157$	−90.0864	−	90.0864i	−0.573798	−	0.573798i	−0.933188	+	0.359389i	$0.882985\pi$
$158$	29.0266	−	183.267i	0.183712	−	1.15991i
$159$	135.407	−	43.9964i	0.851616	−	0.276707i
$160$	75.0358	−	108.221i	0.468974	−	0.676382i
$161$	9.00873	−	27.7260i	0.0559549	−	0.172211i
$162$	13.4449	−	26.3871i	0.0829932	−	0.162883i
$163$	−30.5160	−	15.5487i	−0.187215	−	0.0953908i	0.357871	−	0.933771i	$-0.383503\pi$
$163$	−30.5160	−	15.5487i	−0.187215	−	0.0953908i	−0.545086	+	0.838380i	$0.683503\pi$
$164$	−25.3584	−	8.23943i	−0.154624	−	0.0502404i
$165$	−126.466	+	2.79092i	−0.766462	+	0.0169147i
$166$	17.6207	+	54.2310i	0.106149	+	0.326693i
$167$	−58.2426	−	9.22473i	−0.348758	−	0.0552379i	−0.0204021	−	0.999792i	$-0.506495\pi$
$167$	−58.2426	−	9.22473i	−0.348758	−	0.0552379i	−0.328356	+	0.944554i	$0.606495\pi$
$168$	−70.0072	+	70.0072i	−0.416710	+	0.416710i
$169$	−64.4505	−	88.7086i	−0.381364	−	0.524903i
$170$	202.218	+	376.121i	1.18951	+	2.21248i
$171$	−5.12932	−	3.72667i	−0.0299960	−	0.0217934i
$172$	49.6919	+	313.742i	0.288907	+	1.82408i
$173$	35.3231	+	69.3255i	0.204180	+	0.400726i	0.970276	−	0.242000i	$-0.0778035\pi$
$173$	35.3231	+	69.3255i	0.204180	+	0.400726i	−0.766096	+	0.642726i	$0.777803\pi$
$174$			316.349i			1.81810i
$175$	−139.784	−	63.6194i	−0.798765	−	0.363539i
$176$	48.2993			0.274428
$177$	17.3791	−	8.85509i	0.0981869	−	0.0500287i
$178$	−291.446	+	46.1605i	−1.63734	+	0.259329i
$179$	−89.6932	+	123.452i	−0.501080	+	0.689677i	−0.982383	−	0.186877i	$-0.940163\pi$
$179$	−89.6932	+	123.452i	−0.501080	+	0.689677i	0.481304	+	0.876554i	$0.340163\pi$
$180$	−101.483	−	13.7856i	−0.563797	−	0.0765868i
$181$	−26.4190	+	19.1945i	−0.145961	+	0.106047i	−0.658369	−	0.752695i	$-0.728753\pi$
$181$	−26.4190	+	19.1945i	−0.145961	+	0.106047i	0.512408	+	0.858742i	$0.328753\pi$
$182$	110.119	+	110.119i	0.605047	+	0.605047i
$183$	8.63549	−	54.5223i	0.0471885	−	0.297936i
$184$	−41.9945	+	13.6449i	−0.228231	+	0.0741568i
$185$	197.611	+	59.4207i	1.06817	+	0.321193i
$186$	−59.1174	+	181.945i	−0.317836	+	0.978198i
$187$	172.116	−	337.797i	0.920408	−	1.80640i
$188$	−500.792	−	255.166i	−2.66379	−	1.35727i
$189$	−30.3588	−	9.86417i	−0.160628	−	0.0521914i
$190$	−10.0127	+	33.2984i	−0.0526982	+	0.175255i
$191$	15.5033	+	47.7143i	0.0811692	+	0.249813i	0.983403	−	0.181434i	$-0.0580738\pi$
$191$	15.5033	+	47.7143i	0.0811692	+	0.249813i	−0.902234	+	0.431247i	$0.858074\pi$
$192$	−170.889	−	27.0662i	−0.890049	−	0.140970i
$193$	49.2763	−	49.2763i	0.255318	−	0.255318i	−0.567829	−	0.823147i	$-0.692216\pi$
$193$	49.2763	−	49.2763i	0.255318	−	0.255318i	0.823147	+	0.567829i	$0.192216\pi$
$194$	17.0507	+	23.4683i	0.0878902	+	0.120971i
$195$	−8.98054	+	66.1106i	−0.0460541	+	0.339029i
$196$	−62.2017	−	45.1922i	−0.317356	−	0.230572i
$197$	−54.5847	−	344.634i	−0.277080	−	1.74941i	−0.597253	−	0.802053i	$-0.703741\pi$
$197$	−54.5847	−	344.634i	−0.277080	−	1.74941i	0.320174	−	0.947359i	$-0.396259\pi$
$198$	65.4615	+	128.475i	0.330613	+	0.648865i
$199$			39.9002i			0.200504i	0.994962	+	0.100252i	$0.0319648\pi$
$199$			39.9002i			0.200504i	−0.994962	+	0.100252i	$0.968035\pi$
$200$	46.4895	+	227.924i	0.232448	+	1.13962i
$201$	0.616463			0.00306698
$202$	13.3296	−	6.79175i	0.0659879	−	0.0336225i
$203$	336.786	−	53.3416i	1.65904	−	0.262766i
$204$	180.418	−	248.324i	0.884401	−	1.21727i
$205$	−17.1979	+	9.24625i	−0.0838920	+	0.0451037i
$206$	264.464	−	192.145i	1.28381	−	0.932741i
$207$	−10.0668	−	10.0668i	−0.0486319	−	0.0486319i
$208$	3.98506	−	25.1607i	0.0191589	−	0.120965i
$209$	29.3587	−	9.53923i	0.140472	−	0.0456422i
$210$	3.86244	+	175.021i	0.0183926	+	0.833431i
$211$	59.1092	−	181.919i	0.280138	−	0.862177i	−0.707676	−	0.706538i	$-0.750256\pi$
$211$	59.1092	−	181.919i	0.280138	−	0.862177i	0.987814	−	0.155640i	$-0.0497439\pi$
$212$	−254.797	+	500.068i	−1.20187	+	2.35881i
$213$	−168.921	−	86.0697i	−0.793058	−	0.404083i
$214$	256.785	+	83.4346i	1.19993	+	0.389882i
$215$	191.165	+	132.546i	0.889141	+	0.616492i
$216$	14.9405	+	45.9822i	0.0691690	+	0.212880i
$217$	203.667	+	32.2577i	0.938557	+	0.148653i
$218$	190.416	−	190.416i	0.873467	−	0.873467i
$219$	45.1108	+	62.0897i	0.205985	+	0.283515i
$220$	344.732	−	360.291i	1.56696	−	1.63769i
$221$	−161.769	−	117.532i	−0.731985	−	0.531818i
$222$	−36.7959	−	232.320i	−0.165747	−	1.04649i
$223$	82.3253	+	161.572i	0.369172	+	0.724540i	0.998621	−	0.0525014i	$-0.0167194\pi$
$223$	82.3253	+	161.572i	0.369172	+	0.724540i	−0.629449	+	0.777042i	$0.716719\pi$
$224$			161.800i			0.722320i
$225$	−58.6724	+	46.7177i	−0.260766	+	0.207634i
$226$	622.875			2.75608
$227$	−266.514	+	135.796i	−1.17407	+	0.598220i	−0.928563	−	0.371174i	$-0.878955\pi$
$227$	−266.514	+	135.796i	−1.17407	+	0.598220i	−0.245509	+	0.969394i	$0.578955\pi$
$228$	24.6852	−	3.90975i	0.108268	−	0.0171480i
$229$	−128.483	+	176.841i	−0.561060	+	0.772232i	−0.991461	−	0.130405i	$-0.958372\pi$
$229$	−128.483	+	176.841i	−0.561060	+	0.772232i	0.430401	+	0.902638i	$0.358372\pi$
$230$	−33.9027	+	70.3323i	−0.147403	+	0.305792i
$231$	125.737	−	91.3535i	0.544317	−	0.395470i
$232$	−365.194	−	365.194i	−1.57411	−	1.57411i
$233$	−28.5917	+	180.521i	−0.122711	+	0.774767i	0.847194	+	0.531284i	$0.178290\pi$
$233$	−28.5917	+	180.521i	−0.122711	+	0.774767i	−0.969905	+	0.243484i	$0.921710\pi$
$234$	72.3280	−	23.5008i	0.309094	−	0.100431i
$235$	−388.551	+	135.796i	−1.65341	+	0.577856i
$236$	−23.7598	+	73.1250i	−0.100677	+	0.309852i
$237$	−44.3407	+	87.0235i	−0.187092	+	0.367188i
$238$	−467.488	−	238.197i	−1.96424	−	1.00083i
$239$	−434.275	−	141.105i	−1.81705	−	0.590396i	−0.999902	−	0.0139688i	$-0.995553\pi$
$239$	−434.275	−	141.105i	−1.81705	−	0.590396i	−0.817149	−	0.576427i	$-0.804447\pi$
$240$	22.7905	−	17.3392i	0.0949605	−	0.0722468i
$241$	−123.592	−	380.378i	−0.512831	−	1.57833i	−0.787194	−	0.616706i	$-0.788467\pi$
$241$	−123.592	−	380.378i	−0.512831	−	1.57833i	0.274363	−	0.961626i	$-0.411533\pi$
$242$	−300.151	−	47.5393i	−1.24029	−	0.196443i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$	127.905	+	176.046i	0.524200	+	0.721499i
$245$	−55.4031	+	10.0327i	−0.226135	+	0.0409499i
$246$	18.0064	+	13.0824i	0.0731967	+	0.0531805i
$247$	−2.54698	−	16.0810i	−0.0103116	−	0.0651051i
$248$	−141.792	−	278.283i	−0.571743	−	1.12211i
$249$		−	30.0147i		−	0.120541i
$250$	348.027	+	219.226i	1.39211	+	0.876905i
$251$	153.360			0.610995			0.305497	−	0.952193i	$-0.401177\pi$
$251$	153.360			0.610995			0.305497	+	0.952193i	$0.401177\pi$
$252$	112.117	−	57.1266i	0.444910	−	0.226693i
$253$	68.4628	−	10.8434i	0.270604	−	0.0428595i
$254$	−216.319	+	297.738i	−0.851652	+	1.17220i
$255$	−40.0529	−	221.182i	−0.157070	−	0.867380i
$256$	271.323	−	197.128i	1.05986	−	0.770030i
$257$	208.413	+	208.413i	0.810947	+	0.810947i	0.984776	−	0.173829i	$-0.0556139\pi$
$257$	208.413	+	208.413i	0.810947	+	0.810947i	−0.173829	+	0.984776i	$0.555614\pi$
$258$	41.4801	−	261.895i	0.160776	−	1.01510i
$259$	−241.124	+	78.3459i	−0.930981	+	0.302494i
$260$	−159.244	−	209.309i	−0.612478	−	0.805034i
$261$	51.4566	−	158.367i	0.197152	−	0.606770i
$262$	−155.773	+	305.722i	−0.594554	+	1.16688i
$263$	−9.36797	−	4.77322i	−0.0356197	−	0.0181491i	0.436090	−	0.899903i	$-0.356363\pi$
$263$	−9.36797	−	4.77322i	−0.0356197	−	0.0181491i	−0.471710	+	0.881754i	$0.656363\pi$
$264$	−223.881	−	72.7434i	−0.848035	−	0.275543i
$265$	135.600	+	387.989i	0.511698	+	1.46411i
$266$	−13.2016	−	40.6305i	−0.0496302	−	0.152746i
$267$	153.409	+	24.2976i	0.574565	+	0.0910022i
$268$	−1.71833	+	1.71833i	−0.00641167	+	0.00641167i
$269$	270.816	+	372.747i	1.00675	+	1.38568i	0.921089	+	0.389351i	$0.127301\pi$
$269$	270.816	+	372.747i	1.00675	+	1.38568i	0.0856627	+	0.996324i	$0.472699\pi$
$270$	77.0107	+	37.1220i	0.285225	+	0.137489i
$271$	120.422	+	87.4918i	0.444362	+	0.322848i	0.787366	−	0.616486i	$-0.211444\pi$
$271$	120.422	+	87.4918i	0.444362	+	0.322848i	−0.343004	+	0.939334i	$0.611444\pi$
$272$	13.4261	+	84.7689i	0.0493606	+	0.311651i
$273$	−37.2147	−	73.0380i	−0.136318	−	0.267538i
$274$		−	502.986i		−	1.83572i
$275$	−16.1095	−	364.810i	−0.0585798	−	1.32658i
$276$	56.1203			0.203335
$277$	−229.696	+	117.036i	−0.829229	+	0.422513i	−0.816458	−	0.577405i	$-0.804065\pi$
$277$	−229.696	+	117.036i	−0.829229	+	0.422513i	−0.0127710	+	0.999918i	$0.504065\pi$
$278$	511.692	−	81.0441i	1.84062	−	0.291526i
$279$	59.1895	−	81.4673i	0.212149	−	0.291998i
$280$	−206.503	−	197.586i	−0.737511	−	0.705663i
$281$	−64.5890	+	46.9267i	−0.229854	+	0.166999i	−0.696751	−	0.717313i	$-0.745372\pi$
$281$	−64.5890	+	46.9267i	−0.229854	+	0.166999i	0.466897	+	0.884312i	$0.345372\pi$
$282$	331.754	+	331.754i	1.17643	+	1.17643i
$283$	5.52224	−	34.8661i	0.0195132	−	0.123202i	−0.976009	−	0.217731i	$-0.930135\pi$
$283$	5.52224	−	34.8661i	0.0195132	−	0.123202i	0.995522	+	0.0945291i	$0.0301345\pi$
$284$	710.761	−	230.940i	2.50268	−	0.813170i
$285$	10.4287	−	15.0408i	0.0365918	−	0.0527749i
$286$	−114.422	+	352.156i	−0.400078	+	1.23131i
$287$	10.8914	−	21.3756i	0.0379491	−	0.0744793i
$288$	70.4018	+	35.8715i	0.244451	+	0.124554i
$289$	365.849	+	118.871i	1.26591	+	0.411320i
$290$	−912.998	+	20.1485i	−3.14827	+	0.0694775i
$291$	−4.71844	−	14.5219i	−0.0162146	−	0.0499033i
$292$	−298.810	−	47.3269i	−1.02332	−	0.162078i
$293$	−16.7371	+	16.7371i	−0.0571231	+	0.0571231i	−0.735091	−	0.677968i	$-0.762861\pi$
$293$	−16.7371	+	16.7371i	−0.0571231	+	0.0571231i	0.677968	+	0.735091i	$0.262861\pi$
$294$	37.7240	+	51.9226i	0.128313	+	0.176608i
$295$	26.6631	+	49.5929i	0.0903834	+	0.168112i
$296$	310.668	+	225.714i	1.04955	+	0.762546i
$297$	−11.8731	−	74.9638i	−0.0399768	−	0.252403i
$298$	−120.210	−	235.925i	−0.403389	−	0.791696i
$299$		−	36.5592i		−	0.122271i
$300$	33.3224	−	293.764i	0.111075	−	0.979214i
$301$	−285.809			−0.949530
$302$	549.541	−	280.005i	1.81967	−	0.927170i
$303$	−7.77763	+	1.23186i	−0.0256688	+	0.00406553i
$304$	−4.10763	+	5.65367i	−0.0135119	+	0.0185976i
$305$	157.904	+	21.4499i	0.517718	+	0.0703275i
$306$	−207.287	+	150.603i	−0.677409	+	0.492167i
$307$	14.0410	+	14.0410i	0.0457363	+	0.0457363i	0.729605	−	0.683869i	$-0.239704\pi$
$307$	14.0410	+	14.0410i	0.0457363	+	0.0457363i	−0.683869	+	0.729605i	$0.739704\pi$
$308$	−95.8413	+	605.118i	−0.311173	+	1.96467i
$309$	−163.647	+	53.1722i	−0.529603	+	0.172078i
$310$	−528.867	−	159.028i	−1.70602	−	0.512992i
$311$	−59.5063	+	183.142i	−0.191339	+	0.588880i	0.808661	+	0.588275i	$0.200193\pi$
$311$	−59.5063	+	183.142i	−0.191339	+	0.588880i	−1.00000		0.000605266i	$0.999807\pi$
$312$	−56.3663	+	110.625i	−0.180661	+	0.354568i
$313$	141.673	+	72.1860i	0.452629	+	0.230626i	0.665416	−	0.746473i	$-0.268254\pi$
$313$	141.673	+	72.1860i	0.452629	+	0.230626i	−0.212787	+	0.977099i	$0.568254\pi$
$314$	−398.702	−	129.546i	−1.26975	−	0.412567i
$315$	26.5349	−	88.2452i	0.0842378	−	0.280143i
$316$	−118.974	−	366.164i	−0.376500	−	1.15875i
$317$	378.338	+	59.9228i	1.19349	+	0.189031i	0.721401	−	0.692518i	$-0.243499\pi$
$317$	378.338	+	59.9228i	1.19349	+	0.189031i	0.472093	+	0.881549i	$0.343499\pi$
$318$	331.274	−	331.274i	1.04174	−	1.04174i
$319$	476.547	+	655.911i	1.49388	+	2.05615i
$320$	67.2304	−	494.919i	0.210095	−	1.54662i
$321$	−114.978	−	83.5363i	−0.358187	−	0.260238i
$322$	−15.0066	−	94.7479i	−0.0466043	−	0.294248i
$323$	24.9031	+	48.8751i	0.0770994	+	0.151316i
$324$		−	61.4493i		−	0.189658i
$325$	−191.370	−	21.7076i	−0.588832	−	0.0667928i
$326$	−112.698			−0.345699
$327$	−126.297	+	64.3513i	−0.386228	+	0.196793i
$328$	−35.8890	+	5.68426i	−0.109418	+	0.0173301i
$329$	297.247	−	409.125i	0.903486	−	1.24354i
$330$	−366.617	+	197.108i	−1.11096	+	0.597296i
$331$	−450.680	+	327.439i	−1.36157	+	0.989240i	−0.363229	+	0.931700i	$0.618326\pi$
$331$	−450.680	+	327.439i	−1.36157	+	0.989240i	−0.998343	+	0.0575405i	$0.981674\pi$
$332$	83.6628	+	83.6628i	0.251996	+	0.251996i
$333$	−19.3683	+	122.287i	−0.0581631	+	0.367227i
$334$	−184.542	+	59.9614i	−0.552521	+	0.179525i
$335$	0.0392630	+	1.77914i	0.000117203	+	0.00531088i
$336$	−10.8725	+	33.4622i	−0.0323587	+	0.0995899i
$337$	86.1758	−	169.130i	0.255715	−	0.501868i	−0.727084	−	0.686548i	$-0.759125\pi$
$337$	86.1758	−	169.130i	0.255715	−	0.501868i	0.982799	+	0.184680i	$0.0591250\pi$
$338$	−321.482	−	163.803i	−0.951131	−	0.484625i
$339$	−311.817	−	101.316i	−0.919814	−	0.298866i
$340$	728.165	+	504.878i	2.14166	+	1.48494i
$341$	151.508	+	466.295i	0.444306	+	1.36743i
$342$	−20.6058	−	3.26365i	−0.0602510	−	0.00954282i
$343$	261.768	−	261.768i	0.763172	−	0.763172i
$344$	254.448	+	350.217i	0.739674	+	1.01807i
$345$	28.4121	−	29.6944i	0.0823540	−	0.0860708i
$346$	207.128	+	150.487i	0.598635	+	0.434934i
$347$	23.6780	+	149.497i	0.0682362	+	0.430827i	0.998030	+	0.0627447i	$0.0199854\pi$
$347$	23.6780	+	149.497i	0.0682362	+	0.430827i	−0.929793	+	0.368082i	$0.880015\pi$
$348$	298.002	+	584.862i	0.856327	+	1.68064i
$349$		−	124.533i		−	0.356829i	−0.983955	−	0.178415i	$-0.942903\pi$
$349$		−	124.533i		−	0.356829i	0.983955	−	0.178415i	$-0.0570968\pi$
$350$	−504.872	+	22.2944i	−1.44249	+	0.0636982i
$351$	−40.0307			−0.114048
$352$	−342.777	+	174.654i	−0.973800	+	0.496176i
$353$	−367.421	+	58.1938i	−1.04085	+	0.164855i	−0.653383	−	0.757027i	$-0.726651\pi$
$353$	−367.421	+	58.1938i	−1.04085	+	0.164855i	−0.387470	+	0.921882i	$0.626651\pi$
$354$	37.7253	−	51.9244i	0.106569	−	0.146679i
$355$	237.643	−	492.997i	0.669416	−	1.38872i
$356$	−495.338	+	359.884i	−1.39140	+	1.01091i
$357$	195.284	+	195.284i	0.547015	+	0.547015i
$358$	−78.5492	+	495.940i	−0.219411	+	1.38531i
$359$	−232.340	+	75.4918i	−0.647186	+	0.210283i	−0.614173	−	0.789171i	$-0.710510\pi$
$359$	−232.340	+	75.4918i	−0.647186	+	0.210283i	−0.0330130	+	0.999455i	$0.510510\pi$
$360$	−131.755	+	46.0477i	−0.365987	+	0.127910i
$361$	110.175	−	339.084i	0.305194	−	0.939290i
$362$	−48.7835	+	95.7430i	−0.134761	+	0.264483i
$363$	142.526	+	72.6206i	0.392633	+	0.200057i
$364$	307.318	+	99.8537i	0.844280	+	0.274323i
$365$	−176.321	+	134.147i	−0.483071	+	0.367525i
$366$	−56.1313	−	172.754i	−0.153364	−	0.472006i
$367$	−170.553	−	27.0130i	−0.464723	−	0.0736049i	−0.0803176	−	0.996769i	$-0.525593\pi$
$367$	−170.553	−	27.0130i	−0.464723	−	0.0736049i	−0.384405	+	0.923164i	$0.625593\pi$
$368$	−11.0959	+	11.0959i	−0.0301518	+	0.0301518i
$369$	−6.88621	−	9.47806i	−0.0186618	−	0.0256858i
$370$	668.143	−	120.991i	1.80579	−	0.327004i
$371$	−408.534	−	296.817i	−1.10117	−	0.800046i
$372$	62.0972	+	392.066i	0.166928	+	1.05394i
$373$	−17.9357	−	35.2007i	−0.0480849	−	0.0943718i	0.865714	−	0.500539i	$-0.166865\pi$
$373$	−17.9357	−	35.2007i	−0.0480849	−	0.0943718i	−0.913799	+	0.406168i	$0.866865\pi$
$374$		−	1247.51i		−	3.33558i
$375$	−138.567	−	166.356i	−0.369511	−	0.443616i
$376$	−765.956			−2.03712
$377$	381.004	−	194.131i	1.01062	−	0.514937i
$378$	−103.745	+	16.4316i	−0.274457	+	0.0434697i
$379$	−52.2973	+	71.9811i	−0.137988	+	0.189924i	−0.872418	−	0.488760i	$-0.837449\pi$
$379$	−52.2973	+	71.9811i	−0.137988	+	0.189924i	0.734431	+	0.678684i	$0.237449\pi$
$380$	12.8559	+	70.9936i	0.0338314	+	0.186825i
$381$	156.721	−	113.864i	0.411341	−	0.298857i
$382$	116.734	+	116.734i	0.305585	+	0.305585i
$383$	−50.0372	+	315.922i	−0.130645	+	0.824863i	0.832134	+	0.554575i	$0.187119\pi$
$383$	−50.0372	+	315.922i	−0.130645	+	0.824863i	−0.962779	+	0.270288i	$0.912881\pi$
$384$	−367.920	+	119.545i	−0.958126	+	0.311314i
$385$	271.659	+	357.066i	0.705608	+	0.927443i
$386$	70.8604	−	218.086i	0.183576	−	0.564989i
$387$	−63.3646	+	124.360i	−0.163733	+	0.321344i
$388$	53.6304	+	27.3260i	0.138223	+	0.0704279i
$389$	−77.7419	−	25.2599i	−0.199851	−	0.0649354i	0.207381	−	0.978260i	$-0.433506\pi$
$389$	−77.7419	−	25.2599i	−0.199851	−	0.0649354i	−0.407232	+	0.913325i	$0.633506\pi$
$390$	72.4311	+	207.245i	0.185721	+	0.531399i
$391$	38.0621	+	117.143i	0.0973456	+	0.299599i
$392$	−103.488	−	16.3909i	−0.264001	−	0.0418136i
$393$	127.710	−	127.710i	0.324961	−	0.324961i
$394$	−674.878	−	928.889i	−1.71289	−	2.35759i
$395$	−253.978	−	122.427i	−0.642983	−	0.309941i
$396$	242.049	+	175.859i	0.611234	+	0.444088i
$397$	8.70402	+	54.9550i	0.0219245	+	0.138426i	0.996223	−	0.0868371i	$-0.0276760\pi$
$397$	8.70402	+	54.9550i	0.0219245	+	0.138426i	−0.974298	+	0.225263i	$0.927676\pi$
$398$	59.6060	+	116.983i	0.149764	+	0.293928i
$399$			22.4873i			0.0563592i
$400$	51.4934	+	64.6702i	0.128734	+	0.161675i
$401$	706.598			1.76209			0.881045	−	0.473032i	$-0.156840\pi$
$401$	706.598			1.76209			0.881045	+	0.473032i	$0.156840\pi$
$402$	1.80741	−	0.920921i	0.00449604	−	0.00229085i
$403$	255.409	−	40.4527i	0.633768	−	0.100379i
$404$	18.2457	−	25.1130i	0.0451626	−	0.0621609i
$405$	−32.5141	−	31.1100i	−0.0802817	−	0.0768149i
$406$	907.735	−	659.508i	2.23580	−	1.62440i
$407$	−426.258	−	426.258i	−1.04732	−	1.04732i
$408$	65.4365	−	413.150i	0.160383	−	1.01262i
$409$	225.857	−	73.3853i	0.552217	−	0.179426i	−0.0195993	−	0.999808i	$-0.506239\pi$
$409$	225.857	−	73.3853i	0.552217	−	0.179426i	0.571816	+	0.820382i	$0.306239\pi$
$410$	−36.6096	+	52.8006i	−0.0892918	+	0.128782i
$411$	−81.8146	+	251.799i	−0.199062	+	0.612651i
$412$	307.938	−	604.362i	0.747421	−	1.46690i
$413$	−61.6400	−	31.4071i	−0.149249	−	0.0760463i
$414$	−44.5534	−	14.4763i	−0.107617	−	0.0349669i
$415$	86.6238	−	1.91166i	0.208732	−	0.00460640i
$416$	62.7011	+	192.974i	0.150724	+	0.463880i
$417$	−269.340	−	42.6593i	−0.645900	−	0.102301i
$418$	71.8264	−	71.8264i	0.171833	−	0.171833i
$419$	140.550	+	193.451i	0.335443	+	0.461697i	0.943103	−	0.332500i	$-0.107892\pi$
$419$	140.550	+	193.451i	0.335443	+	0.461697i	−0.607661	+	0.794197i	$0.707892\pi$
$420$	172.011	+	319.938i	0.409550	+	0.761756i
$421$	−392.951	−	285.496i	−0.933375	−	0.678137i	0.0134415	−	0.999910i	$-0.495721\pi$
$421$	−392.951	−	285.496i	−0.933375	−	0.678137i	−0.946817	+	0.321773i	$0.895721\pi$
$422$	−98.4630	−	621.671i	−0.233325	−	1.47315i
$423$	−112.117	−	220.041i	−0.265051	−	0.520193i
$424$			764.848i			1.80389i
$425$	635.791	−	129.682i	1.49598	−	0.305134i
$426$	−623.838			−1.46441
$427$	−174.450	+	88.8867i	−0.408548	+	0.208166i
$428$	553.338	−	87.6401i	1.29285	−	0.204767i
$429$	114.562	−	157.681i	0.267044	−	0.367554i
$430$	758.484	+	103.033i	1.76392	+	0.239613i
$431$	−224.130	+	162.840i	−0.520023	+	0.377819i	−0.816613	−	0.577186i	$-0.804151\pi$
$431$	−224.130	+	162.840i	−0.520023	+	0.377819i	0.296589	+	0.955005i	$0.404151\pi$
$432$	12.1495	+	12.1495i	0.0281238	+	0.0281238i
$433$	78.8616	−	497.912i	0.182128	−	1.14991i	−0.712026	−	0.702154i	$-0.752222\pi$
$433$	78.8616	−	497.912i	0.182128	−	1.14991i	0.894154	−	0.447760i	$-0.147778\pi$
$434$	645.320	−	209.677i	1.48691	−	0.483127i
$435$	460.332	+	138.420i	1.05824	+	0.318206i
$436$	172.666	−	531.411i	0.396023	−	1.21883i
$437$	−4.55316	+	8.93609i	−0.0104191	+	0.0204487i
$438$	225.015	+	114.651i	0.513732	+	0.261760i
$439$	−644.964	−	209.562i	−1.46917	−	0.477361i	−0.538310	−	0.842747i	$-0.680937\pi$
$439$	−644.964	−	209.562i	−1.46917	−	0.477361i	−0.930856	+	0.365385i	$0.880937\pi$
$440$	195.682	−	650.765i	0.444732	−	1.47901i
$441$	−10.4394	−	32.1291i	−0.0236720	−	0.0728550i
$442$	−649.867	−	102.929i	−1.47029	−	0.232871i
$443$	229.580	−	229.580i	0.518238	−	0.518238i	−0.398800	−	0.917038i	$-0.630573\pi$
$443$	229.580	−	229.580i	0.518238	−	0.518238i	0.917038	+	0.398800i	$0.130573\pi$
$444$	−286.874	−	394.849i	−0.646113	−	0.889299i
$445$	−60.3533	+	444.293i	−0.135625	+	0.998412i
$446$	482.739	+	350.730i	1.08237	+	0.786391i
$447$	21.8031	+	137.660i	0.0487766	+	0.307963i
$448$	278.598	+	546.779i	0.621870	+	1.22049i
$449$			72.7747i			0.162082i	0.996711	+	0.0810409i	$0.0258244\pi$
$449$			72.7747i			0.162082i	−0.996711	+	0.0810409i	$0.974176\pi$
$450$	−102.231	+	224.621i	−0.227180	+	0.499158i
$451$	57.0414			0.126478
$452$	1151.56	−	586.751i	2.54771	−	1.29812i
$453$	−320.650	+	50.7860i	−0.707838	+	0.112110i
$454$	−578.531	+	796.280i	−1.27430	+	1.75392i
$455$	208.421	−	112.055i	0.458068	−	0.246275i
$456$	27.5550	−	20.0199i	0.0604277	−	0.0439033i
$457$	209.874	+	209.874i	0.459243	+	0.459243i	0.898407	−	0.439164i	$-0.144725\pi$
$457$	209.874	+	209.874i	0.459243	+	0.459243i	−0.439164	+	0.898407i	$0.644725\pi$
$458$	−112.519	+	710.418i	−0.245675	+	1.55113i
$459$	128.267	−	41.6764i	0.279448	−	0.0907982i
$460$	3.57435	+	161.966i	0.00777032	+	0.352100i
$461$	41.7392	−	128.460i	0.0905406	−	0.278655i	−0.895525	−	0.445011i	$-0.853200\pi$
$461$	41.7392	−	128.460i	0.0905406	−	0.278655i	0.986066	+	0.166355i	$0.0531999\pi$
$462$	232.178	−	455.675i	0.502550	−	0.986310i
$463$	−657.694	−	335.112i	−1.42051	−	0.723784i	−0.436133	−	0.899882i	$-0.643652\pi$
$463$	−657.694	−	335.112i	−1.42051	−	0.723784i	−0.984373	+	0.176099i	$0.943652\pi$
$464$	−174.556	−	56.7167i	−0.376198	−	0.122234i
$465$	238.888	+	165.635i	0.513739	+	0.356204i
$466$	185.848	+	571.981i	0.398815	+	1.22743i
$467$	−193.470	−	30.6426i	−0.414282	−	0.0656158i	−0.0541855	−	0.998531i	$-0.517256\pi$
$467$	−193.470	−	30.6426i	−0.414282	−	0.0656158i	−0.360096	+	0.932915i	$0.617256\pi$
$468$	111.581	−	111.581i	0.238422	−	0.238422i
$469$	−1.28517	−	1.76889i	−0.00274024	−	0.00377162i
$470$	−936.328	+	978.588i	−1.99219	+	2.08210i
$471$	178.522	+	129.704i	0.379028	+	0.275380i
$472$	16.3915	+	103.492i	0.0347278	+	0.219263i
$473$	−308.514	−	605.494i	−0.652250	−	1.28011i
$474$			321.384i			0.678025i
$475$	44.0728	+	29.1397i	0.0927848	+	0.0613467i
$476$	−1088.67			−2.28712
$477$	−219.723	+	111.955i	−0.460636	+	0.234706i
$478$	−1484.04	+	235.049i	−3.10469	+	0.491735i
$479$	−84.2910	+	116.017i	−0.175973	+	0.242206i	−0.887888	−	0.460060i	$-0.847828\pi$
$479$	−84.2910	+	116.017i	−0.175973	+	0.242206i	0.711915	+	0.702265i	$0.247828\pi$
$480$	−99.0430	+	205.468i	−0.206340	+	0.428058i
$481$	−257.221	+	186.882i	−0.534763	+	0.388528i
$482$	−930.598	−	930.598i	−1.93070	−	1.93070i
$483$	−7.89904	+	49.8726i	−0.0163541	+	0.103256i
$484$	−599.698	+	194.854i	−1.23905	+	0.402590i
$485$	41.6103	−	14.5426i	0.0857944	−	0.0299847i
$486$	−15.8509	+	48.7840i	−0.0326150	+	0.100379i
$487$	152.898	−	300.080i	0.313959	−	0.616180i	−0.679067	−	0.734077i	$-0.737615\pi$
$487$	152.898	−	300.080i	0.313959	−	0.616180i	0.993026	+	0.117897i	$0.0376152\pi$
$488$	264.226	+	134.630i	0.541447	+	0.275881i
$489$	56.4176	+	18.3312i	0.115373	+	0.0374871i
$490$	−147.449	+	112.180i	−0.300916	+	0.228939i
$491$	196.552	+	604.925i	0.400310	+	1.23203i	0.924748	+	0.380579i	$0.124275\pi$
$491$	196.552	+	604.925i	0.400310	+	1.23203i	−0.524439	+	0.851448i	$0.675725\pi$
$492$	45.6137	+	7.22450i	0.0927108	+	0.0146839i
$493$	−1018.70	+	1018.70i	−2.06634	+	2.06634i
$494$	−31.4905	−	43.3429i	−0.0637459	−	0.0877387i
$495$	215.593	−	39.0408i	0.435541	−	0.0788704i
$496$	−89.7953	−	65.2401i	−0.181039	−	0.131532i
$497$	105.189	+	664.139i	0.211649	+	1.33630i
$498$	−44.8382	−	88.0000i	−0.0900366	−	0.176707i
$499$			220.616i			0.442116i	0.975261	+	0.221058i	$0.0709511\pi$
$499$			220.616i			0.442116i	−0.975261	+	0.221058i	$0.929049\pi$
$500$	849.940	+	77.4601i	1.69988	+	0.154920i
$501$	102.137			0.203866
$502$	449.635	−	229.100i	0.895687	−	0.456375i
$503$	−377.227	+	59.7469i	−0.749954	+	0.118781i	−0.519699	−	0.854349i	$-0.673956\pi$
$503$	−377.227	+	59.7469i	−0.749954	+	0.118781i	−0.230255	+	0.973130i	$0.573956\pi$
$504$	100.795	−	138.732i	0.199989	−	0.275262i
$505$	−4.05056	−	22.3682i	−0.00802091	−	0.0442934i
$506$	184.527	−	134.067i	0.364678	−	0.264954i
$507$	134.293	+	134.293i	0.264878	+	0.264878i
$508$	−119.458	+	754.229i	−0.235154	+	1.48470i
$509$	−54.3299	+	17.6528i	−0.106738	+	0.0346814i	−0.361899	−	0.932217i	$-0.617872\pi$
$509$	−54.3299	+	17.6528i	−0.106738	+	0.0346814i	0.255161	+	0.966899i	$0.417872\pi$
$510$	−447.850	−	588.649i	−0.878137	−	1.15421i
$511$	84.1163	−	258.883i	0.164611	−	0.506621i
$512$	95.4111	−	187.255i	0.186350	−	0.365732i
$513$	9.78462	+	4.98551i	0.0190733	+	0.00971835i
$514$	922.391	+	299.703i	1.79454	+	0.583080i
$515$	−163.880	−	468.907i	−0.318214	−	0.910499i
$516$	−170.019	−	523.263i	−0.329493	−	1.01408i
$517$	1187.60	+	188.098i	2.29711	+	0.363826i
$518$	−589.912	+	589.912i	−1.13883	+	1.13883i
$519$	−79.2121	−	109.026i	−0.152624	−	0.210070i
$520$	−322.860	−	155.630i	−0.620884	−	0.299289i
$521$	37.2208	+	27.0425i	0.0714410	+	0.0519050i	0.622933	−	0.782276i	$-0.285941\pi$
$521$	37.2208	+	27.0425i	0.0714410	+	0.0519050i	−0.551492	+	0.834181i	$0.685941\pi$
$522$	−85.7155	−	541.186i	−0.164206	−	1.03675i
$523$	138.623	+	272.063i	0.265053	+	0.520197i	0.984725	−	0.174118i	$-0.0557075\pi$
$523$	138.623	+	272.063i	0.265053	+	0.520197i	−0.719671	+	0.694315i	$0.755707\pi$
$524$			711.954i			1.35869i
$525$	256.370	+	70.9606i	0.488324	+	0.135163i
$526$	−34.5965			−0.0657729
$527$	−776.267	+	395.528i	−1.47299	+	0.750527i
$528$	−82.6269	+	13.0868i	−0.156490	+	0.0247856i
$529$	297.701	−	409.751i	0.562763	−	0.774576i
$530$	977.173	+	934.974i	1.84372	+	1.76410i
$531$	−27.3316	+	19.8575i	−0.0514719	+	0.0373965i
$532$	−62.6811	−	62.6811i	−0.117822	−	0.117822i
$533$	4.70635	−	29.7147i	0.00882992	−	0.0557499i
$534$	486.077	−	157.936i	0.910257	−	0.295760i
$535$	233.767	−	337.152i	0.436947	−	0.630191i
$536$	−1.02336	+	3.14959i	−0.00190926	+	0.00587610i
$537$	119.991	−	235.495i	0.223447	−	0.438539i
$538$	1350.84	+	688.289i	2.51086	+	1.27935i
$539$	156.432	+	50.8279i	0.290227	+	0.0943004i
$540$	177.346	−	3.91375i	0.328418	−	0.00724769i
$541$	−72.3805	−	222.764i	−0.133790	−	0.411764i	0.861610	−	0.507571i	$-0.169457\pi$
$541$	−72.3805	−	222.764i	−0.133790	−	0.411764i	−0.995400	+	0.0958075i	$0.969457\pi$
$542$	483.768	+	76.6213i	0.892560	+	0.141368i
$543$	39.9948	−	39.9948i	0.0736553	−	0.0736553i
$544$	−401.815	−	553.051i	−0.738630	−	1.01664i
$545$	−193.765	−	360.399i	−0.355532	−	0.661283i
$546$	−218.220	−	158.546i	−0.399669	−	0.290377i
$547$	−126.813	−	800.663i	−0.231833	−	1.46374i	−0.779164	−	0.626819i	$-0.784356\pi$
$547$	−126.813	−	800.663i	−0.231833	−	1.46374i	0.547332	−	0.836916i	$-0.315644\pi$
$548$	−473.815	−	929.914i	−0.864626	−	1.69692i
$549$			95.6126i			0.174158i
$550$	−592.212	−	1045.52i	−1.07675	−	1.90095i
$551$	−117.306			−0.212896
$552$	68.1440	−	34.7211i	0.123449	−	0.0629006i
$553$	342.146	−	54.1906i	0.618708	−	0.0979938i
$554$	−498.609	+	686.276i	−0.900016	+	1.23877i
$555$	−354.159	−	48.1094i	−0.638124	−	0.0866835i
$556$	869.667	−	631.850i	1.56415	−	1.13642i
$557$	581.702	+	581.702i	1.04435	+	1.04435i	0.998970	+	0.0453787i	$0.0144494\pi$
$557$	581.702	+	581.702i	1.04435	+	1.04435i	0.0453787	+	0.998970i	$0.485551\pi$
$558$	51.8354	−	327.276i	0.0928949	−	0.586516i
$559$	−340.876	+	110.757i	−0.609796	+	0.198135i
$560$	−97.2660	−	29.2474i	−0.173689	−	0.0522275i
$561$	−202.917	+	624.514i	−0.361706	+	1.11322i
$562$	−119.266	+	234.072i	−0.212217	+	0.416499i
$563$	−376.119	−	191.642i	−0.668062	−	0.340395i	0.0868492	−	0.996221i	$-0.472320\pi$
$563$	−376.119	−	191.642i	−0.668062	−	0.340395i	−0.754911	+	0.655827i	$0.772320\pi$
$564$	925.857	+	300.829i	1.64159	+	0.533385i
$565$	272.542	−	906.372i	0.482375	−	1.60420i
$566$	−35.8950	−	110.473i	−0.0634187	−	0.195183i
$567$	54.6083	+	8.64910i	0.0963109	+	0.0152542i
$568$	720.161	−	720.161i	1.26789	−	1.26789i
$569$	−470.636	−	647.774i	−0.827128	−	1.13844i	−0.988451	−	0.151542i	$-0.951576\pi$
$569$	−470.636	−	647.774i	−0.827128	−	1.13844i	0.161323	−	0.986902i	$-0.448424\pi$
$570$	8.10664	−	59.6773i	0.0142222	−	0.104697i
$571$	545.948	+	396.655i	0.956127	+	0.694667i	0.952248	−	0.305326i	$-0.0987653\pi$
$571$	545.948	+	396.655i	0.956127	+	0.694667i	0.00387883	+	0.999992i	$0.498765\pi$
$572$	120.190	+	758.848i	0.210122	+	1.32666i
$573$	−39.4503	−	77.4255i	−0.0688486	−	0.135123i
$574$		−	78.9414i		−	0.137529i
$575$	87.5092	+	80.1075i	0.152190	+	0.139317i
$576$	299.679			0.520276
$577$	−809.001	+	412.206i	−1.40208	+	0.714396i	−0.981249	−	0.192743i	$-0.938262\pi$
$577$	−809.001	+	412.206i	−1.40208	+	0.714396i	−0.420831	+	0.907139i	$0.638262\pi$
$578$	1250.21	−	198.014i	2.16299	−	0.342585i
$579$	−70.9468	+	97.6498i	−0.122533	+	0.168653i
$580$	−1668.96	+	897.298i	−2.87752	+	1.54707i
$581$	−86.1245	+	62.5731i	−0.148235	+	0.107699i
$582$	−35.5279	−	35.5279i	−0.0610445	−	0.0610445i
$583$	187.826	−	1185.89i	0.322172	−	2.03411i
$584$	−392.111	+	127.405i	−0.671423	+	0.218159i
$585$	−2.54958	−	115.530i	−0.00435826	−	0.197488i
$586$	−24.0682	+	74.0745i	−0.0410721	+	0.126407i
$587$	54.6357	−	107.229i	0.0930761	−	0.182672i	−0.839775	−	0.542935i	$-0.817313\pi$
$587$	54.6357	−	107.229i	0.0930761	−	0.182672i	0.932851	+	0.360263i	$0.117313\pi$
$588$	118.655	+	60.4578i	0.201794	+	0.102819i
$589$	−67.4671	−	21.9214i	−0.114545	−	0.0372180i
$590$	152.259	+	105.570i	0.258066	+	0.178932i
$591$	186.759	+	574.785i	0.316005	+	0.972563i
$592$	134.787	+	21.3482i	0.227681	+	0.0360612i
$593$	255.390	−	255.390i	0.430674	−	0.430674i	−0.458183	−	0.888858i	$-0.651500\pi$
$593$	255.390	−	255.390i	0.430674	−	0.430674i	0.888858	+	0.458183i	$0.151500\pi$
$594$	−146.797	−	202.049i	−0.247134	−	0.340150i
$595$	−551.162	+	576.038i	−0.926323	+	0.968131i
$596$	−444.486	−	322.938i	−0.745781	−	0.541842i
$597$	−10.8111	−	68.2584i	−0.0181090	−	0.114336i
$598$	−54.6149	−	107.188i	−0.0913293	−	0.179244i
$599$			546.766i			0.912799i	0.889775	+	0.456399i	$0.150861\pi$
$599$			546.766i			0.912799i	−0.889775	+	0.456399i	$0.849139\pi$
$600$	−141.287	−	377.319i	−0.235479	−	0.628865i
$601$	−768.536			−1.27876			−0.639381	−	0.768890i	$-0.720809\pi$
$601$	−768.536			−1.27876			−0.639381	+	0.768890i	$0.720809\pi$
$602$	−837.962	+	426.963i	−1.39196	+	0.709241i
$603$	−1.05460	+	0.167032i	−0.00174892	+	0.000277002i
$604$	752.219	−	1035.34i	1.24540	−	1.71414i
$605$	−200.509	+	415.962i	−0.331420	+	0.687540i
$606$	−20.9630	+	15.2305i	−0.0345924	+	0.0251328i
$607$	−163.485	−	163.485i	−0.269333	−	0.269333i	0.559498	−	0.828832i	$-0.310994\pi$
$607$	−163.485	−	163.485i	−0.269333	−	0.269333i	−0.828832	+	0.559498i	$0.810994\pi$
$608$	8.70754	−	54.9772i	0.0143216	−	0.0904231i
$609$	−561.695	+	182.506i	−0.922323	+	0.299681i
$610$	495.002	−	173.000i	0.811479	−	0.283607i
$611$	195.973	−	603.142i	0.320741	−	0.987140i
$612$	−241.361	+	473.699i	−0.394381	+	0.774017i
$613$	530.506	+	270.306i	0.865426	+	0.440957i	0.829572	−	0.558400i	$-0.188585\pi$
$613$	530.506	+	270.306i	0.865426	+	0.440957i	0.0358546	+	0.999357i	$0.488585\pi$
$614$	62.1425	+	20.1913i	0.101209	+	0.0328849i
$615$	26.9155	−	20.4776i	0.0437651	−	0.0332969i
$616$	258.006	+	794.060i	0.418840	+	1.28906i
$617$	319.636	+	50.6254i	0.518049	+	0.0820509i	0.409984	−	0.912093i	$-0.365534\pi$
$617$	319.636	+	50.6254i	0.518049	+	0.0820509i	0.108065	+	0.994144i	$0.465534\pi$
$618$	−400.364	+	400.364i	−0.647839	+	0.647839i
$619$	6.19820	+	8.53110i	0.0100133	+	0.0137821i	0.813994	−	0.580873i	$-0.197289\pi$
$619$	6.19820	+	8.53110i	0.0100133	+	0.0137821i	−0.803981	+	0.594655i	$0.797289\pi$
$620$	−1127.57	+	204.186i	−1.81866	+	0.329333i
$621$	19.9492	+	14.4939i	0.0321243	+	0.0233396i
$622$	99.1246	+	625.848i	0.159364	+	1.00619i
$623$	−250.100	−	490.848i	−0.401444	−	0.787878i
$624$			44.1228i			0.0707096i
$625$	471.286	−	410.505i	0.754058	−	0.656808i
$626$	523.208			0.835795
$627$	−47.6401	+	24.2738i	−0.0759810	+	0.0387142i
$628$	−859.149	+	136.076i	−1.36807	+	0.216681i
$629$	629.625	−	866.605i	1.00099	−	1.37775i
$630$	−54.0298	−	298.366i	−0.0857616	−	0.473597i
$631$	−25.4826	+	18.5142i	−0.0403844	+	0.0293410i	−0.607794	−	0.794094i	$-0.707946\pi$
$631$	−25.4826	+	18.5142i	−0.0403844	+	0.0293410i	0.567410	+	0.823435i	$0.307946\pi$
$632$	−371.006	−	371.006i	−0.587035	−	0.587035i
$633$	−51.8282	+	327.230i	−0.0818770	+	0.516951i
$634$	1198.77	−	389.502i	1.89080	−	0.614357i
$635$	338.600	+	445.052i	0.533228	+	0.700870i
$636$	300.394	−	924.518i	0.472318	−	1.45364i
$637$	39.3848	−	77.2970i	0.0618285	−	0.121345i
$638$	2377.04	+	1211.16i	3.72576	+	1.89837i
$639$	312.299	+	101.472i	0.488731	+	0.158798i
$640$	−368.445	−	1054.22i	−0.575695	−	1.64722i
$641$	−347.695	−	1070.09i	−0.542425	−	1.66941i	−0.727034	−	0.686601i	$-0.759102\pi$
$641$	−347.695	−	1070.09i	−0.542425	−	1.66941i	0.184609	−	0.982812i	$-0.440898\pi$
$642$	−461.896	−	73.1572i	−0.719465	−	0.113952i
$643$	737.920	−	737.920i	1.14762	−	1.14762i	0.160602	−	0.987019i	$-0.448656\pi$
$643$	737.920	−	737.920i	1.14762	−	1.14762i	0.987019	−	0.160602i	$-0.0513436\pi$
$644$	−116.997	−	161.032i	−0.181672	−	0.250050i
$645$	−362.945	−	174.953i	−0.562706	−	0.271245i
$646$	146.027	+	106.095i	0.226048	+	0.164233i
$647$	167.580	+	1058.06i	0.259011	+	1.63533i	0.683536	+	0.729916i	$0.260441\pi$
$647$	167.580	+	1058.06i	0.259011	+	1.63533i	−0.424525	+	0.905416i	$0.639559\pi$
$648$	−38.0181	−	74.6147i	−0.0586699	−	0.115146i
$649$		−	164.488i		−	0.253449i
$650$	−593.507	+	222.239i	−0.913088	+	0.341907i
$651$	−357.159			−0.548631
$652$	−208.354	+	106.162i	−0.319562	+	0.162825i
$653$	−375.029	+	59.3987i	−0.574317	+	0.0909628i	−0.436835	−	0.899542i	$-0.643901\pi$
$653$	−375.029	+	59.3987i	−0.574317	+	0.0909628i	−0.137481	+	0.990504i	$0.543901\pi$
$654$	−274.156	+	377.343i	−0.419198	+	0.576977i
$655$	376.710	+	360.442i	0.575130	+	0.550293i
$656$	−10.4469	+	7.59015i	−0.0159252	+	0.0115704i
$657$	−93.9956	−	93.9956i	−0.143068	−	0.143068i
$658$	260.315	−	1643.56i	0.395615	−	2.49782i
$659$	329.556	−	107.079i	0.500085	−	0.162487i	−0.0481033	−	0.998842i	$-0.515318\pi$
$659$	329.556	−	107.079i	0.500085	−	0.162487i	0.548188	+	0.836355i	$0.315318\pi$
$660$	−492.121	+	709.765i	−0.745637	+	1.07540i
$661$	−246.800	+	759.573i	−0.373374	+	1.14913i	0.571195	+	0.820814i	$0.306480\pi$
$661$	−246.800	+	759.573i	−0.373374	+	1.14913i	−0.944569	+	0.328312i	$0.893520\pi$
$662$	−832.197	+	1633.28i	−1.25709	+	2.46719i
$663$	308.587	+	157.233i	0.465441	+	0.237154i
$664$	153.349	+	49.8260i	0.230947	+	0.0750392i
$665$	−64.8995	+	1.43224i	−0.0975933	+	0.00215374i
$666$	125.895	+	387.466i	0.189032	+	0.581781i
$667$	−260.161	−	41.2055i	−0.390047	−	0.0617773i
$668$	−284.695	+	284.695i	−0.426191	+	0.426191i
$669$	−184.615	−	254.100i	−0.275956	−	0.379821i
$670$	2.77294	+	5.15761i	0.00413871	+	0.00769793i
$671$	−376.618	−	273.629i	−0.561279	−	0.407793i
$672$	−43.8400	−	276.795i	−0.0652382	−	0.411898i
$673$	32.9059	+	64.5815i	0.0488944	+	0.0959606i	0.914161	−	0.405352i	$-0.132851\pi$
$673$	32.9059	+	64.5815i	0.0488944	+	0.0959606i	−0.865267	+	0.501312i	$0.832851\pi$
$674$		−	624.607i		−	0.926716i
$675$	87.7142	−	95.8187i	0.129947	−	0.141954i
$676$	−748.656			−1.10748
$677$	−529.170	+	269.626i	−0.781640	+	0.398265i	−0.798807	−	0.601587i	$-0.794535\pi$
$677$	−529.170	+	269.626i	−0.781640	+	0.398265i	0.0171675	+	0.999853i	$0.494535\pi$
$678$	−1065.57	+	168.770i	−1.57164	+	0.248923i
$679$	−31.8325	+	43.8136i	−0.0468814	+	0.0645267i
$680$	1196.54	+	162.539i	1.75961	+	0.239028i
$681$	419.139	−	304.522i	0.615476	−	0.447169i
$682$	1140.79	+	1140.79i	1.67272	+	1.67272i
$683$	114.459	−	722.664i	0.167582	−	1.05807i	−0.750264	−	0.661138i	$-0.770074\pi$
$683$	114.459	−	722.664i	0.167582	−	1.05807i	0.917847	−	0.396935i	$-0.129926\pi$
$684$	−41.1702	+	13.3770i	−0.0601904	+	0.0195570i
$685$	−731.916	−	220.084i	−1.06849	−	0.321290i
$686$	376.428	−	1158.53i	0.548729	−	1.68881i
$687$	171.883	−	337.340i	0.250194	−	0.491033i
$688$	137.073	+	69.8421i	0.199234	+	0.101515i
$689$	−602.270	−	195.689i	−0.874122	−	0.284019i
$690$	38.9416	−	129.505i	0.0564371	−	0.187689i
$691$	161.872	+	498.191i	0.234257	+	0.720970i	0.997219	+	0.0745265i	$0.0237445\pi$
$691$	161.872	+	498.191i	0.234257	+	0.720970i	−0.762962	+	0.646444i	$0.776255\pi$
$692$	524.694	+	83.1034i	0.758229	+	0.120092i
$693$	−190.350	+	190.350i	−0.274675	+	0.274675i
$694$	292.751	+	402.938i	0.421832	+	0.580602i
$695$	105.962	−	780.046i	0.152464	−	1.12237i
$696$	723.697	+	525.797i	1.03979	+	0.755455i
$697$	15.8562	+	100.112i	0.0227492	+	0.143633i
$698$	−186.038	−	365.119i	−0.266530	−	0.523094i
$699$		−	316.569i		−	0.452888i
$700$	−912.400	+	516.809i	−1.30343	+	0.738299i
$701$	−699.523			−0.997893			−0.498947	−	0.866633i	$-0.666280\pi$
$701$	−699.523			−0.997893			−0.498947	+	0.866633i	$0.666280\pi$
$702$	−117.366	+	59.8009i	−0.167188	+	0.0851865i
$703$	86.1468	−	13.6443i	0.122542	−	0.0194087i
$704$	−857.636	+	1180.43i	−1.21823	+	1.67675i
$705$	627.910	−	337.589i	0.890652	−	0.478850i
$706$	−990.308	+	719.501i	−1.40270	+	1.01912i
$707$	19.7491	+	19.7491i	0.0279337	+	0.0279337i
$708$	20.8330	−	131.535i	0.0294252	−	0.185783i
$709$	145.144	−	47.1600i	0.204716	−	0.0665162i	−0.204864	−	0.978790i	$-0.565675\pi$
$709$	145.144	−	47.1600i	0.204716	−	0.0665162i	0.409580	+	0.912274i	$0.365675\pi$
$710$	−39.7327	−	1800.43i	−0.0559616	−	2.53581i
$711$	52.2756	−	160.888i	0.0735240	−	0.226284i
$712$	−378.807	+	743.451i	−0.532032	+	1.04417i
$713$	−141.929	−	72.3163i	−0.199059	−	0.101425i
$714$	864.285	+	280.823i	1.21048	+	0.393310i
$715$	462.371	+	320.588i	0.646673	+	0.448375i
$716$	321.957	+	990.882i	0.449661	+	1.38391i
$717$	781.159	+	123.723i	1.08948	+	0.172557i
$718$	−568.421	+	568.421i	−0.791673	+	0.791673i
$719$	431.478	+	593.879i	0.600109	+	0.825979i	0.995718	−	0.0924401i	$-0.0294667\pi$
$719$	431.478	+	593.879i	0.600109	+	0.825979i	−0.395610	+	0.918419i	$0.629467\pi$
$720$	−34.2902	+	35.8378i	−0.0476253	+	0.0497748i
$721$	493.737	+	358.721i	0.684794	+	0.497532i
$722$	−183.527	−	1158.75i	−0.254193	−	1.60491i
$723$	314.497	+	617.235i	0.434989	+	0.853714i
$724$			222.963i			0.307960i
$725$	−370.167	+	1337.36i	−0.510575	+	1.84463i
$726$	526.358			0.725010
$727$	1179.77	−	601.120i	1.62279	−	0.826851i	0.623811	−	0.781575i	$-0.285583\pi$
$727$	1179.77	−	601.120i	1.62279	−	0.826851i	0.998975	−	0.0452756i	$-0.0144166\pi$
$728$	434.939	−	68.8876i	0.597444	−	0.0946258i
$729$	15.8702	−	21.8435i	0.0217698	−	0.0299636i
$730$	−316.556	+	656.706i	−0.433639	+	0.899597i
$731$	976.927	−	709.779i	1.33643	−	0.970970i
$732$	−266.510	−	266.510i	−0.364085	−	0.364085i
$733$	−133.600	+	843.514i	−0.182264	+	1.15077i	0.711651	+	0.702533i	$0.247948\pi$
$733$	−133.600	+	843.514i	−0.182264	+	1.15077i	−0.893915	+	0.448237i	$0.852052\pi$
$734$	−540.399	+	175.586i	−0.736238	+	0.239218i
$735$	92.0611	−	32.1748i	0.125253	−	0.0437753i
$736$	38.6233	−	118.870i	0.0524773	−	0.161509i
$737$	2.36017	−	4.63209i	0.00320240	−	0.00628506i
$738$	−34.3487	−	17.5016i	−0.0465430	−	0.0237148i
$739$	32.3337	+	10.5059i	0.0437534	+	0.0142163i	0.330812	−	0.943697i	$-0.392677\pi$
$739$	32.3337	+	10.5059i	0.0437534	+	0.0142163i	−0.287059	+	0.957913i	$0.592677\pi$
$740$	1121.28	−	853.081i	1.51524	−	1.15281i
$741$	8.71436	+	26.8200i	0.0117603	+	0.0361944i
$742$	−1641.19	−	259.938i	−2.21184	−	0.350321i
$743$	−327.809	+	327.809i	−0.441197	+	0.441197i	−0.892414	−	0.451217i	$-0.850990\pi$
$743$	−327.809	+	327.809i	−0.441197	+	0.441197i	0.451217	+	0.892414i	$0.350990\pi$
$744$	317.969	+	437.647i	0.427378	+	0.588235i
$745$	−395.904	+	71.6925i	−0.531414	+	0.0962316i
$746$	−105.171	−	76.4112i	−0.140980	−	0.102428i
$747$	8.13255	+	51.3469i	0.0108869	+	0.0687375i
$748$	−1175.16	−	2306.38i	−1.57107	−	3.08339i
$749$			504.071i			0.672993i
$750$	−654.778	−	280.737i	−0.873038	−	0.374317i
$751$	436.259			0.580905			0.290452	−	0.956889i	$-0.406194\pi$
$751$	436.259			0.580905			0.290452	+	0.956889i	$0.406194\pi$
$752$	−242.535	+	123.578i	−0.322520	+	0.164332i
$753$	−262.356	+	41.5532i	−0.348415	+	0.0551835i
$754$	827.057	−	1138.35i	1.09689	−	1.50974i
$755$	−166.993	−	922.178i	−0.221183	−	1.22143i
$756$	−176.323	+	128.106i	−0.233232	+	0.169453i
$757$	−667.784	−	667.784i	−0.882145	−	0.882145i	0.111607	−	0.993752i	$-0.464400\pi$
$757$	−667.784	−	667.784i	−0.882145	−	0.882145i	−0.993752	+	0.111607i	$0.964400\pi$
$758$	−45.7996	+	289.167i	−0.0604216	+	0.381487i
$759$	−114.183	+	37.1003i	−0.150439	+	0.0488805i
$760$	59.5334	+	78.2500i	0.0783334	+	0.102961i
$761$	265.924	−	818.431i	0.349440	−	1.07547i	−0.609723	−	0.792615i	$-0.708719\pi$
$761$	265.924	−	818.431i	0.349440	−	1.07547i	0.959163	−	0.282853i	$-0.0912807\pi$
$762$	289.391	−	567.961i	0.379778	−	0.745356i
$763$	447.947	+	228.241i	0.587087	+	0.299136i
$764$	325.779	+	105.852i	0.426412	+	0.138550i
$765$	128.449	+	367.529i	0.167908	+	0.480431i
$766$	325.245	+	1001.00i	0.424602	+	1.30679i
$767$	−85.6873	−	13.5715i	−0.111717	−	0.0176943i
$768$	−410.747	+	410.747i	−0.534827	+	0.534827i
$769$	534.634	+	735.861i	0.695233	+	0.956907i	0.999990	+	0.00447640i	$0.00142489\pi$
$769$	534.634	+	735.861i	0.695233	+	0.956907i	−0.304757	+	0.952430i	$0.598575\pi$
$770$	1329.89	+	641.055i	1.72713	+	0.832539i
$771$	−413.009	−	300.068i	−0.535679	−	0.389194i
$772$	−74.4320	−	469.945i	−0.0964146	−	0.608738i
$773$	−330.014	−	647.689i	−0.426926	−	0.837889i	−0.999833	−	0.0182691i	$-0.994184\pi$
$773$	−330.014	−	647.689i	−0.426926	−	0.837889i	0.572907	−	0.819620i	$-0.305816\pi$
$774$			459.270i			0.593372i
$775$	−462.816	+	699.993i	−0.597181	+	0.903217i
$776$	82.0270			0.105705
$777$	391.269	−	199.362i	0.503564	−	0.256579i
$778$	−265.666	+	42.0774i	−0.341474	+	0.0540841i
$779$	−4.85110	+	6.67697i	−0.00622734	+	0.00857120i
$780$	329.136	+	314.923i	0.421969	+	0.403747i
$781$	−1293.45	+	939.748i	−1.65615	+	1.20326i
$782$	286.592	+	286.592i	0.366486	+	0.366486i
$783$	−45.1182	+	284.865i	−0.0576222	+	0.363812i
$784$	−35.4134	+	11.5065i	−0.0451702	+	0.0146767i
$785$	−362.962	+	523.485i	−0.462372	+	0.666860i
$786$	183.649	−	565.214i	0.233650	−	0.719102i
$787$	−665.324	+	1305.77i	−0.845393	+	1.65918i	−0.0976189	+	0.995224i	$0.531123\pi$
$787$	−665.324	+	1305.77i	−0.845393	+	1.65918i	−0.747774	+	0.663953i	$0.768877\pi$
$788$	−2122.72	−	1081.58i	−2.69381	−	1.37257i
$789$	17.3194	+	5.62740i	0.0219510	+	0.00713232i
$790$	−927.529	+	20.4692i	−1.17409	+	0.0259103i
$791$	359.345	+	1105.95i	0.454292	+	1.39817i
$792$	402.710	+	63.7829i	0.508472	+	0.0805340i
$793$	−173.616	+	173.616i	−0.218936	+	0.218936i
$794$	107.615	+	148.120i	0.135536	+	0.186549i
$795$	−337.101	−	627.002i	−0.424026	−	0.788681i
$796$	220.398	+	160.128i	0.276882	+	0.201166i
$797$	−118.617	−	748.917i	−0.148829	−	0.939669i	−0.943197	−	0.332233i	$-0.892198\pi$
$797$	−118.617	−	748.917i	−0.148829	−	0.939669i	0.794368	−	0.607436i	$-0.207802\pi$
$798$	33.5933	+	65.9306i	0.0420969	+	0.0826198i
$799$			2136.62i			2.67412i
$800$	−599.298	−	272.757i	−0.749123	−	0.340946i
$801$	−269.024			−0.335860
$802$	2071.68	−	1055.57i	2.58314	−	1.31617i
$803$	639.250	−	101.247i	0.796078	−	0.126086i
$804$	2.47400	−	3.40517i	0.00307712	−	0.00423529i
$805$	−144.438	−	19.6206i	−0.179426	−	0.0243734i
$806$	688.401	−	500.152i	0.854095	−	0.620536i
$807$	−564.289	−	564.289i	−0.699243	−	0.699243i
$808$	6.61760	−	41.7819i	0.00819010	−	0.0517102i
$809$	−684.508	+	222.410i	−0.846116	+	0.274920i	−0.699818	−	0.714321i	$-0.746736\pi$
$809$	−684.508	+	222.410i	−0.846116	+	0.274920i	−0.146298	+	0.989241i	$0.546736\pi$
$810$	−141.803	−	42.6393i	−0.175065	−	0.0526412i
$811$	−27.5305	+	84.7302i	−0.0339464	+	0.104476i	−0.966594	−	0.256312i	$-0.917492\pi$
$811$	−27.5305	+	84.7302i	−0.0339464	+	0.104476i	0.932648	+	0.360789i	$0.117492\pi$
$812$	1056.95	−	2074.38i	1.30166	−	2.55466i
$813$	−229.715	−	117.046i	−0.282553	−	0.143968i
$814$	−1886.52	−	612.968i	−2.31760	−	0.753032i
$815$	−49.3114	+	163.991i	−0.0605048	+	0.201216i
$816$	−45.9367	−	141.379i	−0.0562950	−	0.173258i
$817$	97.1136	+	15.3813i	0.118866	+	0.0188265i
$818$	552.560	−	552.560i	0.675502	−	0.675502i
$819$	83.4540	+	114.865i	0.101897	+	0.140250i
$820$	−17.9451	+	132.104i	−0.0218843	+	0.161102i
$821$	543.123	+	394.602i	0.661538	+	0.480635i	0.867182	−	0.497991i	$-0.165929\pi$
$821$	543.123	+	394.602i	0.661538	+	0.480635i	−0.205644	+	0.978627i	$0.565929\pi$
$822$	136.285	+	860.471i	0.165797	+	1.04680i
$823$	558.523	+	1096.16i	0.678643	+	1.33191i	0.931263	+	0.364347i	$0.118708\pi$
$823$	558.523	+	1096.16i	0.678643	+	1.33191i	−0.252620	+	0.967566i	$0.581292\pi$
$824$		−	924.364i		−	1.12180i
$825$	126.405	+	619.725i	0.153218	+	0.751182i
$826$	−227.641			−0.275594
$827$	150.479	−	76.6727i	0.181957	−	0.0927119i	−0.360639	−	0.932705i	$-0.617441\pi$
$827$	150.479	−	76.6727i	0.181957	−	0.0927119i	0.542596	+	0.839994i	$0.317441\pi$
$828$	−96.0065	+	15.2059i	−0.115950	+	0.0183647i
$829$	637.618	−	877.605i	0.769141	−	1.05863i	−0.227258	−	0.973835i	$-0.572976\pi$
$829$	637.618	−	877.605i	0.769141	−	1.05863i	0.996398	−	0.0847965i	$-0.0270240\pi$
$830$	251.116	−	135.010i	0.302550	−	0.162663i
$831$	361.236	−	262.454i	0.434701	−	0.315829i
$832$	544.165	+	544.165i	0.654045	+	0.654045i
$833$	−45.7223	+	288.679i	−0.0548888	+	0.346554i
$834$	−853.406	+	277.289i	−1.02327	+	0.332480i
$835$	6.50516	+	294.771i	0.00779061	+	0.353020i
$836$	65.1310	−	200.453i	0.0779079	−	0.239776i
$837$	−79.1832	+	155.406i	−0.0946036	+	0.185670i
$838$	701.072	+	357.214i	0.836601	+	0.426270i
$839$	1156.94	+	375.911i	1.37895	+	0.448047i	0.902323	−	0.431061i	$-0.141861\pi$
$839$	1156.94	+	375.911i	1.37895	+	0.448047i	0.476623	+	0.879108i	$0.341861\pi$
$840$	406.807	+	282.062i	0.484294	+	0.335788i
$841$	−692.161	−	2130.25i	−0.823021	−	2.53300i
$842$	−1578.59	−	250.024i	−1.87481	−	0.296940i
$843$	97.7792	−	97.7792i	0.115990	−	0.115990i
$844$	−767.654	−	1056.59i	−0.909543	−	1.25188i
$845$	−379.023	+	396.129i	−0.448548	+	0.468792i
$846$	−657.430	−	477.651i	−0.777104	−	0.564599i
$847$	−88.7525	−	560.361i	−0.104785	−	0.661584i
$848$	123.399	+	242.184i	0.145518	+	0.285595i
$849$			61.1426i			0.0720172i
$850$	1670.35	−	1330.01i	1.96511	−	1.56472i
$851$	195.850			0.230141
$852$	−1153.34	+	587.658i	−1.35369	+	0.689740i
$853$	−182.560	+	28.9147i	−0.214021	+	0.0338977i	−0.262524	−	0.964925i	$-0.584555\pi$
$853$	−182.560	+	28.9147i	−0.214021	+	0.0338977i	0.0485029	+	0.998823i	$0.484555\pi$
$854$	−378.684	+	521.214i	−0.443424	+	0.610320i
$855$	−13.7652	+	28.5564i	−0.0160997	+	0.0333993i
$856$	617.668	−	448.762i	0.721574	−	0.524254i
$857$	203.015	+	203.015i	0.236890	+	0.236890i	0.815561	−	0.578671i	$-0.196428\pi$
$857$	203.015	+	203.015i	0.236890	+	0.236890i	−0.578671	+	0.815561i	$0.696428\pi$
$858$	100.328	−	633.446i	0.116932	−	0.738282i
$859$	−1263.62	+	410.575i	−1.47103	+	0.477968i	−0.931421	−	0.363944i	$-0.881430\pi$
$859$	−1263.62	+	410.575i	−1.47103	+	0.477968i	−0.539614	+	0.841913i	$0.681430\pi$
$860$	1499.33	−	524.009i	1.74341	−	0.609313i
$861$	−12.8404	+	39.5188i	−0.0149134	+	0.0458987i
$862$	−413.864	+	812.253i	−0.480120	+	0.942289i
$863$	1200.75	+	611.814i	1.39137	+	0.708938i	0.979338	−	0.202231i	$-0.0648192\pi$
$863$	1200.75	+	611.814i	1.39137	+	0.708938i	0.412032	+	0.911169i	$0.364819\pi$
$864$	−130.158	−	42.2908i	−0.150646	−	0.0489477i
$865$	309.610	−	235.554i	0.357930	−	0.272317i
$866$	−512.606	−	1577.64i	−0.591924	−	1.82175i
$867$	−658.076	−	104.229i	−0.759026	−	0.120218i
$868$	995.543	−	995.543i	1.14694	−	1.14694i
$869$	484.132	+	666.350i	0.557113	+	0.766801i
$870$	1556.43	−	281.848i	1.78900	−	0.323963i
$871$	−2.21828	−	1.61167i	−0.00254681	−	0.00185037i
$872$	−119.120	−	752.092i	−0.136605	−	0.862491i
$873$	12.0067	+	23.5645i	0.0137534	+	0.0269925i
$874$			33.0016i			0.0377592i
$875$	−188.467	+	744.416i	−0.215391	+	0.850761i
$876$	524.006			0.598181
$877$	892.419	−	454.710i	1.01758	−	0.518484i	0.136096	−	0.990696i	$-0.456544\pi$
$877$	892.419	−	454.710i	1.01758	−	0.518484i	0.881485	+	0.472212i	$0.156544\pi$
$878$	−2204.03	+	349.084i	−2.51028	+	0.397590i
$879$	24.0976	−	33.1675i	0.0274148	−	0.0377332i
$880$	−43.0318	−	237.632i	−0.0488997	−	0.270036i
$881$	610.778	−	443.756i	0.693278	−	0.503696i	−0.184458	−	0.982840i	$-0.559053\pi$
$881$	610.778	−	443.756i	0.693278	−	0.503696i	0.877736	+	0.479145i	$0.159053\pi$
$882$	−78.6040	−	78.6040i	−0.0891202	−	0.0891202i
$883$	−143.134	+	903.715i	−0.162100	+	1.02346i	0.763735	+	0.645530i	$0.223364\pi$
$883$	−143.134	+	903.715i	−0.162100	+	1.02346i	−0.925835	+	0.377929i	$0.876636\pi$
$884$	−1298.43	+	421.884i	−1.46881	+	0.477245i
$885$	−59.0506	−	77.6155i	−0.0667238	−	0.0877011i
$886$	330.140	−	1016.07i	0.372619	−	1.14680i
$887$	668.313	−	1311.64i	0.753453	−	1.47874i	−0.120494	−	0.992714i	$-0.538448\pi$
$887$	668.313	−	1311.64i	0.753453	−	1.47874i	0.873947	−	0.486021i	$-0.161552\pi$
$888$	−592.626	−	301.958i	−0.667372	−	0.340043i
$889$	−653.449	−	212.318i	−0.735038	−	0.238828i
$890$	486.770	+	1392.78i	0.546932	+	1.56492i
$891$	40.6232	+	125.025i	0.0455929	+	0.140320i
$892$	1222.87	+	193.684i	1.37093	+	0.217134i
$893$	−123.018	+	123.018i	−0.137758	+	0.137758i
$894$	269.571	+	371.033i	0.301534	+	0.415025i
$895$	687.294	+	331.301i	0.767926	+	0.370169i
$896$	1110.05	+	806.495i	1.23889	+	0.900106i
$897$	9.90580	+	62.5427i	0.0110433	+	0.0697243i
$898$	108.716	+	213.368i	0.121065	+	0.237604i
$899$		−	1863.12i		−	2.07244i
$900$	22.5905	+	511.579i	0.0251006	+	0.568421i
$901$	2133.53			2.36796
$902$	167.240	−	85.2128i	0.185410	−	0.0944710i
$903$	488.940	−	77.4405i	0.541462	−	0.0857592i
$904$	1035.27	−	1424.92i	1.14521	−	1.57624i
$905$	117.974	+	112.880i	0.130358	+	0.124729i
$906$	−864.247	+	627.912i	−0.953914	+	0.693059i
$907$	−511.441	−	511.441i	−0.563882	−	0.563882i	0.366526	−	0.930408i	$-0.380547\pi$
$907$	−511.441	−	511.441i	−0.563882	−	0.563882i	−0.930408	+	0.366526i	$0.880547\pi$
$908$	−319.482	+	2017.13i	−0.351853	+	2.22151i
$909$	12.9716	−	4.21474i	0.0142702	−	0.00463667i
$910$	443.672	−	639.890i	0.487552	−	0.703176i
$911$	−196.843	+	605.821i	−0.216074	+	0.665007i	0.783002	+	0.622019i	$0.213688\pi$
$911$	−196.843	+	605.821i	−0.216074	+	0.665007i	−0.999076	+	0.0429874i	$0.986312\pi$
$912$	5.49515	−	10.7848i	0.00602539	−	0.0118255i
$913$	−225.530	−	114.913i	−0.247020	−	0.125863i
$914$	928.856	+	301.803i	1.01625	+	0.330201i
$915$	−275.943	+	6.08964i	−0.301577	+	0.00665534i
$916$	461.193	+	1419.41i	0.503486	+	1.54957i
$917$	−632.694	−	100.209i	−0.689961	−	0.109279i
$918$	313.805	−	313.805i	0.341836	−	0.341836i
$919$	−576.765	−	793.848i	−0.627600	−	0.863818i	0.370278	−	0.928921i	$-0.379262\pi$
$919$	−576.765	−	793.848i	−0.627600	−	0.863818i	−0.997879	+	0.0651032i	$0.979262\pi$
$920$	104.547	+	194.456i	0.113638	+	0.211365i
$921$	−27.8248	−	20.2159i	−0.0302115	−	0.0219500i
$922$	−69.5284	−	438.985i	−0.0754105	−	0.476123i
$923$	382.826	+	751.338i	0.414762	+	0.814017i
$924$		−	1061.16i		−	1.14844i
$925$	116.289	−	1025.18i	0.125718	−	1.10831i
$926$	−2428.91			−2.62301
$927$	265.548	−	135.304i	0.286460	−	0.145959i
$928$	1443.91	−	228.692i	1.55593	−	0.246436i
$929$	−503.341	+	692.790i	−0.541810	+	0.745737i	−0.988873	−	0.148765i	$-0.952470\pi$
$929$	−503.341	+	692.790i	−0.541810	+	0.745737i	0.447063	+	0.894503i	$0.352470\pi$
$930$	947.835	+	128.755i	1.01918	+	0.138446i
$931$	−19.2535	+	13.9885i	−0.0206804	+	0.0150252i
$932$	882.402	+	882.402i	0.946784	+	0.946784i
$933$	52.1764	−	329.429i	0.0559232	−	0.353085i
$934$	−613.010	+	199.179i	−0.656327	+	0.213254i
$935$	−1815.30	−	545.852i	−1.94150	−	0.583799i
$936$	66.4532	−	204.522i	0.0709970	−	0.218506i
$937$	−80.6308	+	158.247i	−0.0860521	+	0.168887i	−0.930022	−	0.367504i	$-0.880213\pi$
$937$	−80.6308	+	158.247i	−0.0860521	+	0.168887i	0.843970	+	0.536390i	$0.180213\pi$
$938$	−6.41050	−	3.26631i	−0.00683422	−	0.00348221i
$939$	−261.923	−	85.1038i	−0.278938	−	0.0906324i
$940$	−809.239	+	2691.23i	−0.860892	+	2.86301i
$941$	−254.617	−	783.630i	−0.270581	−	0.832763i	−0.990355	−	0.138554i	$-0.955755\pi$
$941$	−254.617	−	783.630i	−0.270581	−	0.832763i	0.719774	−	0.694209i	$-0.244245\pi$
$942$	717.171	+	113.589i	0.761328	+	0.120583i
$943$	−13.1042	+	13.1042i	−0.0138963	+	0.0138963i
$944$	21.8875	+	30.1255i	0.0231859	+	0.0319126i
$945$	−21.4837	+	158.153i	−0.0227341	+	0.167358i
$946$	−1809.07	−	1314.36i	−1.91233	−	1.38939i
$947$	34.8644	+	220.125i	0.0368156	+	0.232444i	0.999234	−	0.0391254i	$-0.0124572\pi$
$947$	34.8644	+	220.125i	0.0368156	+	0.232444i	−0.962419	+	0.271570i	$0.912457\pi$
$948$	302.745	+	594.170i	0.319351	+	0.626762i
$949$		−	341.360i		−	0.359705i
$950$	172.748	+	19.5953i	0.181840	+	0.0206266i
$951$	−663.469			−0.697654
$952$	−1321.92	+	673.550i	−1.38857	+	0.707510i
$953$	−794.568	+	125.847i	−0.833754	+	0.132054i	−0.558694	−	0.829374i	$-0.688698\pi$
$953$	−794.568	+	125.847i	−0.833754	+	0.132054i	−0.275060	+	0.961427i	$0.588698\pi$
$954$	−476.960	+	656.479i	−0.499958	+	0.688133i
$955$	220.941	−	118.787i	0.231352	−	0.124384i
$956$	−2522.26	+	1832.53i	−2.63835	+	1.91688i
$957$	−992.962	−	992.962i	−1.03758	−	1.03758i
$958$	−73.8181	+	466.069i	−0.0770544	+	0.486502i
$959$	893.080	−	290.179i	0.931261	−	0.302585i
$960$	19.0868	+	864.887i	0.0198820	+	0.900924i
$961$	51.2046	−	157.592i	0.0532826	−	0.163987i
$962$	−474.968	+	932.176i	−0.493729	+	0.968998i
$963$	219.330	+	111.754i	0.227757	+	0.116048i
$964$	−2597.11	−	843.851i	−2.69409	−	0.875364i
$965$	−286.341	−	198.536i	−0.296726	−	0.205737i
$966$	51.3443	+	158.022i	0.0531515	+	0.163583i
$967$	193.991	+	30.7251i	0.200611	+	0.0317736i	0.255931	−	0.966695i	$-0.417618\pi$
$967$	193.991	+	30.7251i	0.200611	+	0.0317736i	−0.0553203	+	0.998469i	$0.517618\pi$
$968$	−607.629	+	607.629i	−0.627716	+	0.627716i
$969$	−55.8452	−	76.8644i	−0.0576318	−	0.0793234i
$970$	100.272	−	104.798i	0.103374	−	0.108039i
$971$	−465.952	−	338.534i	−0.479868	−	0.348645i	0.321406	−	0.946941i	$-0.395844\pi$
$971$	−465.952	−	338.534i	−0.479868	−	0.348645i	−0.801275	+	0.598297i	$0.795844\pi$
$972$	16.6498	+	105.123i	0.0171295	+	0.108151i
$973$	439.100	+	861.783i	0.451285	+	0.885697i
$974$		−	1108.21i		−	1.13780i
$975$	333.264	−	14.7164i	0.341809	−	0.0150938i
$976$	105.387			0.107978
$977$	−478.563	+	243.840i	−0.489829	+	0.249581i	−0.681418	−	0.731895i	$-0.738636\pi$
$977$	−478.563	+	243.840i	−0.489829	+	0.249581i	0.191588	+	0.981475i	$0.438636\pi$
$978$	192.795	−	30.5357i	0.197132	−	0.0312226i
$979$	769.907	−	1059.69i	0.786422	−	1.08242i
$980$	−166.927	+	346.295i	−0.170334	+	0.353362i
$981$	198.623	−	144.308i	0.202470	−	0.147103i
$982$	1479.96	+	1479.96i	1.50708	+	1.50708i
$983$	−81.0532	+	511.749i	−0.0824549	+	0.520600i	0.911543	+	0.411204i	$0.134892\pi$
$983$	−81.0532	+	511.749i	−0.0824549	+	0.520600i	−0.993998	+	0.109396i	$0.965108\pi$
$984$	59.8561	−	19.4484i	0.0608294	−	0.0197647i
$985$	−1646.96	+	575.604i	−1.67204	+	0.584369i
$986$	−1464.92	+	4508.55i	−1.48572	+	4.57257i
$987$	−397.655	+	780.441i	−0.402892	+	0.790720i
$988$	−99.0484	−	50.4677i	−0.100251	−	0.0510807i
$989$	209.976	+	68.2255i	0.212312	+	0.0689843i
$990$	573.774	−	436.533i	0.579570	−	0.440942i
$991$	−372.803	−	1147.37i	−0.376189	−	1.15779i	−0.942673	−	0.333717i	$-0.891697\pi$
$991$	−372.803	−	1147.37i	−0.376189	−	1.15779i	0.566485	−	0.824072i	$-0.308303\pi$
$992$	873.185	+	138.299i	0.880226	+	0.139414i
$993$	682.271	−	682.271i	0.687080	−	0.687080i
$994$	1300.55	+	1790.05i	1.30840	+	1.80085i
$995$	196.308	−	35.5487i	0.197295	−	0.0357273i
$996$	−165.793	−	120.455i	−0.166459	−	0.120939i
$997$	24.0632	+	151.929i	0.0241356	+	0.152386i	0.996813	−	0.0797753i	$-0.0254203\pi$
$997$	24.0632	+	151.929i	0.0241356	+	0.152386i	−0.972677	+	0.232161i	$0.925420\pi$
$998$	329.573	+	646.824i	0.330234	+	0.648120i
$999$		−	214.447i		−	0.214662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.22.10	✓	80
3.2	odd	2		225.3.r.b.172.1		80
5.2	odd	4		375.3.k.b.118.10		80
5.3	odd	4		375.3.k.c.118.1		80
5.4	even	2		375.3.k.a.7.1		80
25.6	even	5		375.3.k.c.232.1		80
25.8	odd	20	inner	75.3.k.a.58.10	yes	80
25.17	odd	20		375.3.k.a.268.1		80
25.19	even	10		375.3.k.b.232.10		80
75.8	even	20		225.3.r.b.208.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.10	✓	80	1.1	even	1	trivial
75.3.k.a.58.10	yes	80	25.8	odd	20	inner
225.3.r.b.172.1		80	3.2	odd	2
225.3.r.b.208.1		80	75.8	even	20
375.3.k.a.7.1		80	5.4	even	2
375.3.k.a.268.1		80	25.17	odd	20
375.3.k.b.118.10		80	5.2	odd	4
375.3.k.b.232.10		80	25.19	even	10
375.3.k.c.118.1		80	5.3	odd	4
375.3.k.c.232.1		80	25.6	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.93190 - 1.49388i) q^{2} +(-1.71073 + 0.270952i) q^{3} +(4.01322 - 5.52372i) q^{4} +(-0.890939 - 4.91998i) q^{5} +(-4.61091 + 3.35002i) q^{6} +(4.34391 + 4.34391i) q^{7} +(1.45557 - 9.19012i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-9.96199 - 13.0939i) q^{10} +(-4.51369 + 13.8917i) q^{11} +(-5.36886 + 10.5370i) q^{12} +(6.86423 + 3.49750i) q^{13} +(19.2252 + 6.24664i) q^{14} +(2.85723 + 8.17534i) q^{15} +(-1.02182 - 3.14483i) q^{16} +(-25.6357 - 4.06030i) q^{17} +(6.98030 - 6.98030i) q^{18} +(-1.24222 - 1.70977i) q^{19} +(-30.7522 - 14.8237i) q^{20} +(-8.60824 - 6.25425i) q^{21} +(7.51883 + 47.4720i) q^{22} +(-2.15443 - 4.22830i) q^{23} +16.1162i q^{24} +(-23.4125 + 8.76681i) q^{25} +25.3501 q^{26} +(-4.62981 + 2.35900i) q^{27} +(41.4277 - 6.56150i) q^{28} +(32.6254 - 44.9050i) q^{29} +(20.5901 + 19.7009i) q^{30} +(27.1558 - 19.7298i) q^{31} +(18.6237 + 18.6237i) q^{32} +(3.95770 - 24.9879i) q^{33} +(-81.2269 + 26.3922i) q^{34} +(17.5018 - 25.2421i) q^{35} +(6.32962 - 19.4806i) q^{36} +(-18.7363 + 36.7721i) q^{37} +(-6.19627 - 3.15716i) q^{38} +(-12.6905 - 4.12339i) q^{39} +(-46.5120 + 1.02645i) q^{40} +(-1.20677 - 3.71404i) q^{41} +(-34.5816 - 5.47718i) q^{42} +(-32.8976 + 32.8976i) q^{43} +(58.6196 + 80.6829i) q^{44} +(-7.10308 - 13.2116i) q^{45} +(-12.6331 - 9.17851i) q^{46} +(-12.8776 - 81.3060i) q^{47} +(2.60015 + 5.10308i) q^{48} -11.2608i q^{49} +(-55.5464 + 60.6787i) q^{50} +44.9558 q^{51} +(46.8669 - 23.8799i) q^{52} +(-81.1884 + 12.8590i) q^{53} +(-10.0501 + 13.8327i) q^{54} +(72.3684 + 9.83061i) q^{55} +(46.2440 - 33.5982i) q^{56} +(2.58837 + 2.58837i) q^{57} +(28.5718 - 180.395i) q^{58} +(-10.7101 + 3.47991i) q^{59} +(56.6250 + 17.0269i) q^{60} +(-9.84864 + 30.3110i) q^{61} +(50.1440 - 98.4132i) q^{62} +(16.4210 + 8.36689i) q^{63} +(95.0038 + 30.8686i) q^{64} +(11.0920 - 36.8880i) q^{65} +(-25.7253 - 79.1744i) q^{66} +(-0.351533 - 0.0556774i) q^{67} +(-125.310 + 125.310i) q^{68} +(4.83131 + 6.64972i) q^{69} +(13.6049 - 100.153i) q^{70} +(88.5525 + 64.3371i) q^{71} +(-4.36672 - 27.5704i) q^{72} +(-20.1163 - 39.4805i) q^{73} +135.802i q^{74} +(37.6769 - 21.3413i) q^{75} -14.4296 q^{76} +(-79.9515 + 40.7373i) q^{77} +(-43.3670 + 6.86866i) q^{78} +(33.1447 - 45.6197i) q^{79} +(-14.5621 + 7.82918i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-9.08644 - 9.08644i) q^{82} +(-2.71085 + 17.1156i) q^{83} +(-69.0935 + 22.4499i) q^{84} +(2.86327 + 129.745i) q^{85} +(-47.3074 + 145.597i) q^{86} +(-43.6460 + 85.6602i) q^{87} +(121.097 + 61.7018i) q^{88} +(-85.2857 - 27.7110i) q^{89} +(-40.5620 - 28.1239i) q^{90} +(14.6248 + 45.0105i) q^{91} +(-32.0022 - 5.06865i) q^{92} +(-41.1102 + 41.1102i) q^{93} +(-159.217 - 219.143i) q^{94} +(-7.30531 + 7.63503i) q^{95} +(-36.9063 - 26.8140i) q^{96} +(1.37908 + 8.70714i) q^{97} +(-16.8223 - 33.0156i) q^{98} +43.8198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26}+ \cdots - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

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