LMFDB - Embedded newform 189.3.k.a.10.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (of order $6$, degree $2$, not 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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.9
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.227576 - 0.394173i) q^{2} +(1.89642 + 3.28469i) q^{4} -4.37081i q^{5} +(5.22047 + 4.66334i) q^{7} +3.54692 q^{8} +O(q^{10})$	\(q+(0.227576 - 0.394173i) q^{2} +(1.89642 + 3.28469i) q^{4} -4.37081i q^{5} +(5.22047 + 4.66334i) q^{7} +3.54692 q^{8} +(-1.72285 - 0.994690i) q^{10} +0.139402 q^{11} +(-1.71085 - 0.987760i) q^{13} +(3.02621 - 0.996505i) q^{14} +(-6.77848 + 11.7407i) q^{16} +(26.7838 + 15.4636i) q^{17} +(25.2226 - 14.5623i) q^{19} +(14.3568 - 8.28888i) q^{20} +(0.0317245 - 0.0549484i) q^{22} -29.7784 q^{23} +5.89602 q^{25} +(-0.778697 + 0.449581i) q^{26} +(-5.41743 + 25.9913i) q^{28} +(-7.28707 - 12.6216i) q^{29} +(-6.82604 + 3.94101i) q^{31} +(10.1791 + 17.6307i) q^{32} +(12.1907 - 7.03829i) q^{34} +(20.3826 - 22.8177i) q^{35} +(-7.73259 - 13.3932i) q^{37} -13.2561i q^{38} -15.5029i q^{40} +(-0.747251 - 0.431426i) q^{41} +(-15.6629 - 27.1289i) q^{43} +(0.264364 + 0.457892i) q^{44} +(-6.77684 + 11.7378i) q^{46} +(-58.0205 - 33.4982i) q^{47} +(5.50659 + 48.6896i) q^{49} +(1.34179 - 2.32405i) q^{50} -7.49283i q^{52} +(-16.9285 + 29.3211i) q^{53} -0.609299i q^{55} +(18.5166 + 16.5405i) q^{56} -6.63345 q^{58} +(-57.4894 + 33.1915i) q^{59} +(-35.9279 - 20.7430i) q^{61} +3.58752i q^{62} -44.9618 q^{64} +(-4.31731 + 7.47781i) q^{65} +(-51.7774 - 89.6812i) q^{67} +117.302i q^{68} +(-4.35553 - 13.2270i) q^{70} -86.4656 q^{71} +(-28.6121 - 16.5192i) q^{73} -7.03900 q^{74} +(95.6652 + 55.2323i) q^{76} +(0.727743 + 0.650077i) q^{77} +(-24.3232 + 42.1291i) q^{79} +(51.3162 + 29.6275i) q^{80} +(-0.340113 + 0.196364i) q^{82} +(102.894 - 59.4058i) q^{83} +(67.5886 - 117.067i) q^{85} -14.2579 q^{86} +0.494447 q^{88} +(33.1431 - 19.1352i) q^{89} +(-4.32519 - 13.1348i) q^{91} +(-56.4723 - 97.8128i) q^{92} +(-26.4081 + 15.2467i) q^{94} +(-63.6489 - 110.243i) q^{95} +(70.3678 - 40.6269i) q^{97} +(20.4453 + 8.91002i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.227576	−	0.394173i	0.113788	−	0.197086i	−0.803507	−	0.595296i	$-0.797035\pi$
$2$	0.227576	−	0.394173i	0.113788	−	0.197086i	0.917295	+	0.398209i	$0.130368\pi$
$3$		0			0
$3$		0			0
$4$	1.89642	+	3.28469i	0.474105	+	0.821173i
$5$		−	4.37081i		−	0.874162i	−0.899422	−	0.437081i	$-0.856012\pi$
$5$		−	4.37081i		−	0.874162i	0.899422	−	0.437081i	$-0.143988\pi$
$6$		0			0
$7$	5.22047	+	4.66334i	0.745781	+	0.666191i
$7$	5.22047	+	4.66334i	0.745781	+	0.666191i
$8$	3.54692			0.443365
$9$		0			0
$10$	−1.72285	−	0.994690i	−0.172285	−	0.0994690i
$11$	0.139402			0.0126729			0.00633644	−	0.999980i	$-0.497983\pi$
$11$	0.139402			0.0126729			0.00633644	+	0.999980i	$0.497983\pi$
$12$		0			0
$13$	−1.71085	−	0.987760i	−0.131604	−	0.0759816i	0.432753	−	0.901513i	$-0.357542\pi$
$13$	−1.71085	−	0.987760i	−0.131604	−	0.0759816i	−0.564357	+	0.825531i	$0.690876\pi$
$14$	3.02621	−	0.996505i	0.216158	−	0.0711789i
$15$		0			0
$16$	−6.77848	+	11.7407i	−0.423655	+	0.733792i
$17$	26.7838	+	15.4636i	1.57552	+	0.909625i	0.995473	+	0.0950396i	$0.0302978\pi$
$17$	26.7838	+	15.4636i	1.57552	+	0.909625i	0.580043	+	0.814586i	$0.303036\pi$
$18$		0			0
$19$	25.2226	−	14.5623i	1.32751	−	0.766435i	0.342592	−	0.939484i	$-0.388695\pi$
$19$	25.2226	−	14.5623i	1.32751	−	0.766435i	0.984913	+	0.173049i	$0.0553619\pi$
$20$	14.3568	−	8.28888i	0.717838	−	0.414444i
$21$		0			0
$22$	0.0317245	−	0.0549484i	0.00144202	−	0.00249765i
$23$	−29.7784			−1.29471			−0.647356	−	0.762188i	$-0.724125\pi$
$23$	−29.7784			−1.29471			−0.647356	+	0.762188i	$0.724125\pi$
$24$		0			0
$25$	5.89602			0.235841
$26$	−0.778697	+	0.449581i	−0.0299499	+	0.0172916i
$27$		0			0
$28$	−5.41743	+	25.9913i	−0.193480	+	0.928260i
$29$	−7.28707	−	12.6216i	−0.251278	−	0.435227i	0.712600	−	0.701571i	$-0.247518\pi$
$29$	−7.28707	−	12.6216i	−0.251278	−	0.435227i	−0.963878	+	0.266344i	$0.914184\pi$
$30$		0			0
$31$	−6.82604	+	3.94101i	−0.220195	+	0.127129i	−0.606040	−	0.795434i	$-0.707243\pi$
$31$	−6.82604	+	3.94101i	−0.220195	+	0.127129i	0.385846	+	0.922563i	$0.373910\pi$
$32$	10.1791	+	17.6307i	0.318096	+	0.550959i
$33$		0			0
$34$	12.1907	−	7.03829i	0.358549	−	0.207009i
$35$	20.3826	−	22.8177i	0.582359	−	0.651934i
$36$		0			0
$37$	−7.73259	−	13.3932i	−0.208989	−	0.361979i	0.742407	−	0.669949i	$-0.233684\pi$
$37$	−7.73259	−	13.3932i	−0.208989	−	0.361979i	−0.951396	+	0.307969i	$0.900351\pi$
$38$		−	13.2561i		−	0.348844i
$39$		0			0
$40$		−	15.5029i		−	0.387573i
$41$	−0.747251	−	0.431426i	−0.0182256	−	0.0105226i	0.490859	−	0.871239i	$-0.336683\pi$
$41$	−0.747251	−	0.431426i	−0.0182256	−	0.0105226i	−0.509085	+	0.860716i	$0.670016\pi$
$42$		0			0
$43$	−15.6629	−	27.1289i	−0.364252	−	0.630904i	0.624403	−	0.781102i	$-0.285342\pi$
$43$	−15.6629	−	27.1289i	−0.364252	−	0.630904i	−0.988656	+	0.150198i	$0.952009\pi$
$44$	0.264364	+	0.457892i	0.00600827	+	0.0104066i
$45$		0			0
$46$	−6.77684	+	11.7378i	−0.147323	+	0.255170i
$47$	−58.0205	−	33.4982i	−1.23448	−	0.712727i	−0.266519	−	0.963830i	$-0.585873\pi$
$47$	−58.0205	−	33.4982i	−1.23448	−	0.712727i	−0.967960	+	0.251103i	$0.919207\pi$
$48$		0			0
$49$	5.50659	+	48.6896i	0.112379	+	0.993665i
$50$	1.34179	−	2.32405i	0.0268358	−	0.0464810i
$51$		0			0
$52$		−	7.49283i		−	0.144093i
$53$	−16.9285	+	29.3211i	−0.319406	+	0.553228i	−0.980364	−	0.197195i	$-0.936817\pi$
$53$	−16.9285	+	29.3211i	−0.319406	+	0.553228i	0.660958	+	0.750423i	$0.270150\pi$
$54$		0			0
$55$		−	0.609299i		−	0.0110782i
$56$	18.5166	+	16.5405i	0.330653	+	0.295366i
$57$		0			0
$58$	−6.63345			−0.114370
$59$	−57.4894	+	33.1915i	−0.974396	+	0.562568i	−0.900574	−	0.434704i	$-0.856853\pi$
$59$	−57.4894	+	33.1915i	−0.974396	+	0.562568i	−0.0738224	+	0.997271i	$0.523520\pi$
$60$		0			0
$61$	−35.9279	−	20.7430i	−0.588982	−	0.340049i	0.175713	−	0.984441i	$-0.443777\pi$
$61$	−35.9279	−	20.7430i	−0.588982	−	0.340049i	−0.764695	+	0.644393i	$0.777110\pi$
$62$			3.58752i			0.0578632i
$63$		0			0
$64$	−44.9618			−0.702528
$65$	−4.31731	+	7.47781i	−0.0664202	+	0.115043i
$66$		0			0
$67$	−51.7774	−	89.6812i	−0.772798	−	1.33852i	−0.936024	−	0.351936i	$-0.885523\pi$
$67$	−51.7774	−	89.6812i	−0.772798	−	1.33852i	0.163226	−	0.986589i	$-0.447810\pi$
$68$			117.302i			1.72503i
$69$		0			0
$70$	−4.35553	−	13.2270i	−0.0622219	−	0.188957i
$71$	−86.4656			−1.21783			−0.608913	−	0.793237i	$-0.708394\pi$
$71$	−86.4656			−1.21783			−0.608913	+	0.793237i	$0.708394\pi$
$72$		0			0
$73$	−28.6121	−	16.5192i	−0.391946	−	0.226290i	0.291057	−	0.956706i	$-0.405993\pi$
$73$	−28.6121	−	16.5192i	−0.391946	−	0.226290i	−0.683003	+	0.730416i	$0.739326\pi$
$74$	−7.03900			−0.0951216
$75$		0			0
$76$	95.6652	+	55.2323i	1.25875	+	0.726741i
$77$	0.727743	+	0.650077i	0.00945120	+	0.00844256i
$78$		0			0
$79$	−24.3232	+	42.1291i	−0.307889	+	0.533279i	−0.977900	−	0.209071i	$-0.932956\pi$
$79$	−24.3232	+	42.1291i	−0.307889	+	0.533279i	0.670011	+	0.742351i	$0.266289\pi$
$80$	51.3162	+	29.6275i	0.641453	+	0.370343i
$81$		0			0
$82$	−0.340113	+	0.196364i	−0.00414771	+	0.00239468i
$83$	102.894	−	59.4058i	1.23968	−	0.715732i	0.270655	−	0.962676i	$-0.412760\pi$
$83$	102.894	−	59.4058i	1.23968	−	0.715732i	0.969030	+	0.246944i	$0.0794264\pi$
$84$		0			0
$85$	67.5886	−	117.067i	0.795160	−	1.37726i
$86$	−14.2579			−0.165790
$87$		0			0
$88$	0.494447			0.00561872
$89$	33.1431	−	19.1352i	0.372394	−	0.215002i	−0.302110	−	0.953273i	$-0.597691\pi$
$89$	33.1431	−	19.1352i	0.372394	−	0.215002i	0.674504	+	0.738271i	$0.264358\pi$
$90$		0			0
$91$	−4.32519	−	13.1348i	−0.0475295	−	0.144339i
$92$	−56.4723	−	97.8128i	−0.613829	−	1.06318i
$93$		0			0
$94$	−26.4081	+	15.2467i	−0.280938	+	0.162199i
$95$	−63.6489	−	110.243i	−0.669989	−	1.16045i
$96$		0			0
$97$	70.3678	−	40.6269i	0.725441	−	0.418834i	−0.0913110	−	0.995822i	$-0.529106\pi$
$97$	70.3678	−	40.6269i	0.725441	−	0.418834i	0.816752	+	0.576989i	$0.195772\pi$
$98$	20.4453	+	8.91002i	0.208625	+	0.0909186i
$99$		0			0
$100$	11.1813	+	19.3666i	0.111813	+	0.193666i
$101$		−	25.4076i		−	0.251560i	−0.992058	−	0.125780i	$-0.959857\pi$
$101$		−	25.4076i		−	0.251560i	0.992058	−	0.125780i	$-0.0401434\pi$
$102$		0			0
$103$			110.223i			1.07013i	0.844811	+	0.535065i	$0.179713\pi$
$103$			110.223i			1.07013i	−0.844811	+	0.535065i	$0.820287\pi$
$104$	−6.06826	−	3.50351i	−0.0583486	−	0.0336876i
$105$		0			0
$106$	7.70504	+	13.3455i	0.0726891	+	0.125901i
$107$	78.4186	+	135.825i	0.732885	+	1.26939i	0.955645	+	0.294520i	$0.0951598\pi$
$107$	78.4186	+	135.825i	0.732885	+	1.26939i	−0.222761	+	0.974873i	$0.571507\pi$
$108$		0			0
$109$	12.4839	−	21.6227i	0.114531	−	0.198373i	−0.803061	−	0.595896i	$-0.796797\pi$
$109$	12.4839	−	21.6227i	0.114531	−	0.198373i	0.917592	+	0.397523i	$0.130130\pi$
$110$	−0.240169	−	0.138662i	−0.00218335	−	0.00126056i
$111$		0			0
$112$	−90.1376	+	29.6815i	−0.804800	+	0.265013i
$113$	50.2599	−	87.0526i	0.444777	−	0.770377i	−0.553259	−	0.833009i	$-0.686616\pi$
$113$	50.2599	−	87.0526i	0.444777	−	0.770377i	0.998037	+	0.0626320i	$0.0199494\pi$
$114$		0			0
$115$			130.156i			1.13179i
$116$	27.6387	−	47.8716i	0.238264	−	0.412686i
$117$		0			0
$118$			30.2143i			0.256054i
$119$	67.7118	+	205.629i	0.569007	+	1.72798i
$120$		0			0
$121$	−120.981			−0.999839
$122$	−16.3526	+	9.44120i	−0.134038	+	0.0773869i
$123$		0			0
$124$	−25.8900	−	14.9476i	−0.208791	−	0.120545i
$125$		−	135.041i		−	1.08033i
$126$		0			0
$127$	151.949			1.19645			0.598226	−	0.801327i	$-0.295872\pi$
$127$	151.949			1.19645			0.598226	+	0.801327i	$0.295872\pi$
$128$	−50.9485	+	88.2455i	−0.398035	+	0.689418i
$129$		0			0
$130$	1.96503	+	3.40353i	0.0151156	+	0.0261810i
$131$		−	127.978i		−	0.976931i	−0.872583	−	0.488466i	$-0.837557\pi$
$131$		−	127.978i		−	0.976931i	0.872583	−	0.488466i	$-0.162443\pi$
$132$		0			0
$133$	199.583	+	41.5995i	1.50062	+	0.312779i
$134$	−47.1332			−0.351740
$135$		0			0
$136$	95.0000	+	54.8483i	0.698529	+	0.403296i
$137$	−19.8579			−0.144949			−0.0724743	−	0.997370i	$-0.523090\pi$
$137$	−19.8579			−0.144949			−0.0724743	+	0.997370i	$0.523090\pi$
$138$		0			0
$139$	37.7617	+	21.8017i	0.271667	+	0.156847i	0.629645	−	0.776883i	$-0.283200\pi$
$139$	37.7617	+	21.8017i	0.271667	+	0.156847i	−0.357978	+	0.933730i	$0.616534\pi$
$140$	113.603	+	23.6786i	0.811449	+	0.169133i
$141$		0			0
$142$	−19.6775	+	34.0824i	−0.138574	+	0.240017i
$143$	−0.238496	−	0.137696i	−0.00166780	−	0.000962906i
$144$		0			0
$145$	−55.1665	+	31.8504i	−0.380459	+	0.219658i
$146$	−13.0228	+	7.51873i	−0.0891974	+	0.0514982i
$147$		0			0
$148$	29.3284	−	50.7984i	0.198165	−	0.343232i
$149$	201.820			1.35450			0.677248	−	0.735755i	$-0.263172\pi$
$149$	201.820			1.35450			0.677248	+	0.735755i	$0.263172\pi$
$150$		0			0
$151$	−107.429			−0.711449			−0.355725	−	0.934591i	$-0.615766\pi$
$151$	−107.429			−0.711449			−0.355725	+	0.934591i	$0.615766\pi$
$152$	89.4626	−	51.6512i	0.588570	−	0.339811i
$153$		0			0
$154$	0.421859	−	0.138915i	0.00273935	−	0.000902042i
$155$	17.2254	+	29.8353i	0.111132	+	0.192486i
$156$		0			0
$157$	86.5180	−	49.9512i	0.551070	−	0.318160i	−0.198483	−	0.980104i	$-0.563602\pi$
$157$	86.5180	−	49.9512i	0.551070	−	0.318160i	0.749553	+	0.661944i	$0.230268\pi$
$158$	11.0708	+	19.1751i	0.0700681	+	0.121361i
$159$		0			0
$160$	77.0604	−	44.4908i	0.481627	−	0.278068i
$161$	−155.457	−	138.867i	−0.965572	−	0.862525i
$162$		0			0
$163$	−62.4440	−	108.156i	−0.383092	−	0.663535i	0.608410	−	0.793623i	$-0.291808\pi$
$163$	−62.4440	−	108.156i	−0.383092	−	0.663535i	−0.991503	+	0.130087i	$0.958474\pi$
$164$		−	3.27265i		−	0.0199552i
$165$		0			0
$166$		−	54.0773i		−	0.325767i
$167$	113.210	+	65.3618i	0.677904	+	0.391388i	0.799065	−	0.601245i	$-0.205328\pi$
$167$	113.210	+	65.3618i	0.677904	+	0.391388i	−0.121161	+	0.992633i	$0.538662\pi$
$168$		0			0
$169$	−82.5487	−	142.978i	−0.488454	−	0.846026i
$170$	−30.7630	−	53.2832i	−0.180959	−	0.313430i
$171$		0			0
$172$	59.4067	−	102.895i	0.345388	−	0.598229i
$173$	72.7886	+	42.0245i	0.420743	+	0.242916i	0.695395	−	0.718628i	$-0.255229\pi$
$173$	72.7886	+	42.0245i	0.420743	+	0.242916i	−0.274652	+	0.961544i	$0.588563\pi$
$174$		0			0
$175$	30.7800	+	27.4951i	0.175886	+	0.157115i
$176$	−0.944932	+	1.63667i	−0.00536893	+	0.00929926i
$177$		0			0
$178$		−	17.4188i		−	0.0978584i
$179$	−175.212	+	303.477i	−0.978840	+	1.69540i	−0.312209	+	0.950013i	$0.601069\pi$
$179$	−175.212	+	303.477i	−0.978840	+	1.69540i	−0.666631	+	0.745388i	$0.732264\pi$
$180$		0			0
$181$			138.049i			0.762703i	0.924430	+	0.381351i	$0.124541\pi$
$181$			138.049i			0.762703i	−0.924430	+	0.381351i	$0.875459\pi$
$182$	−6.16171	−	1.28430i	−0.0338555	−	0.00705660i
$183$		0			0
$184$	−105.622			−0.574030
$185$	−58.5393	+	33.7977i	−0.316429	+	0.182690i
$186$		0			0
$187$	3.73371	+	2.15566i	0.0199663	+	0.0115276i
$188$		−	254.106i		−	1.35163i
$189$		0			0
$190$	−57.9398			−0.304946
$191$	−145.062	+	251.255i	−0.759488	+	1.31547i	0.183624	+	0.982997i	$0.441217\pi$
$191$	−145.062	+	251.255i	−0.759488	+	1.31547i	−0.943112	+	0.332476i	$0.892116\pi$
$192$		0			0
$193$	110.240	+	190.941i	0.571192	+	0.989333i	0.996444	+	0.0842581i	$0.0268520\pi$
$193$	110.240	+	190.941i	0.571192	+	0.989333i	−0.425252	+	0.905075i	$0.639815\pi$
$194$		−	36.9828i		−	0.190633i
$195$		0			0
$196$	−149.488	+	110.423i	−0.762692	+	0.563384i
$197$	−118.429			−0.601163			−0.300581	−	0.953756i	$-0.597181\pi$
$197$	−118.429			−0.601163			−0.300581	+	0.953756i	$0.597181\pi$
$198$		0			0
$199$	−152.156	−	87.8471i	−0.764601	−	0.441443i	0.0663442	−	0.997797i	$-0.478866\pi$
$199$	−152.156	−	87.8471i	−0.764601	−	0.441443i	−0.830945	+	0.556354i	$0.812200\pi$
$200$	20.9127			0.104564
$201$		0			0
$202$	−10.0150	−	5.78215i	−0.0495791	−	0.0286245i
$203$	20.8167	−	99.8726i	0.102545	−	0.491983i
$204$		0			0
$205$	−1.88568	+	3.26609i	−0.00919844	+	0.0159322i
$206$	43.4471	+	25.0842i	0.210908	+	0.121768i
$207$		0			0
$208$	23.1939	−	13.3910i	0.111509	−	0.0643800i
$209$	3.51607	−	2.03001i	0.0168233	−	0.00971295i
$210$		0			0
$211$	−9.18761	+	15.9134i	−0.0435432	+	0.0754190i	−0.886976	−	0.461816i	$-0.847198\pi$
$211$	−9.18761	+	15.9134i	−0.0435432	+	0.0754190i	0.843432	+	0.537235i	$0.180531\pi$
$212$	−128.414			−0.605728
$213$		0			0
$214$	71.3847			0.333574
$215$	−118.575	+	68.4594i	−0.551512	+	0.318416i
$216$		0			0
$217$	−54.0134	−	11.2582i	−0.248910	−	0.0518809i
$218$	−5.68205	−	9.84159i	−0.0260644	−	0.0451449i
$219$		0			0
$220$	2.00136	−	1.15549i	0.00909709	−	0.00525221i
$221$	−30.5487	−	52.9119i	−0.138229	−	0.239420i
$222$		0			0
$223$	−142.303	+	82.1586i	−0.638129	+	0.368424i	−0.783894	−	0.620895i	$-0.786769\pi$
$223$	−142.303	+	82.1586i	−0.638129	+	0.368424i	0.145764	+	0.989319i	$0.453436\pi$
$224$	−29.0782	+	139.509i	−0.129814	+	0.622808i
$225$		0			0
$226$	−22.8759	−	39.6221i	−0.101221	−	0.175319i
$227$		−	113.927i		−	0.501881i	−0.968002	−	0.250941i	$-0.919260\pi$
$227$		−	113.927i		−	0.501881i	0.968002	−	0.250941i	$-0.0807399\pi$
$228$		0			0
$229$		−	182.642i		−	0.797561i	−0.917046	−	0.398781i	$-0.869433\pi$
$229$		−	182.642i		−	0.797561i	0.917046	−	0.398781i	$-0.130567\pi$
$230$	51.3038	+	29.6203i	0.223060	+	0.128784i
$231$		0			0
$232$	−25.8467	−	44.7678i	−0.111408	−	0.192964i
$233$	−126.875	−	219.754i	−0.544527	−	0.943149i	−0.998636	−	0.0522031i	$-0.983376\pi$
$233$	−126.875	−	219.754i	−0.544527	−	0.943149i	0.454109	−	0.890946i	$-0.349958\pi$
$234$		0			0
$235$	−146.414	+	253.597i	−0.623039	+	1.07913i
$236$	−218.048	−	125.890i	−0.923931	−	0.533432i
$237$		0			0
$238$	96.4630	+	20.1061i	0.405307	+	0.0844792i
$239$	−65.6961	+	113.789i	−0.274879	+	0.476104i	−0.970105	−	0.242687i	$-0.921971\pi$
$239$	−65.6961	+	113.789i	−0.274879	+	0.476104i	0.695226	+	0.718792i	$0.255304\pi$
$240$		0			0
$241$		−	260.472i		−	1.08080i	−0.841409	−	0.540399i	$-0.818273\pi$
$241$		−	260.472i		−	1.08080i	0.841409	−	0.540399i	$-0.181727\pi$
$242$	−27.5322	+	47.6872i	−0.113770	+	0.197055i
$243$		0			0
$244$		−	157.349i		−	0.644875i
$245$	212.813	−	24.0683i	0.868624	−	0.0982379i
$246$		0			0
$247$	−57.5361			−0.232940
$248$	−24.2114	+	13.9785i	−0.0976267	+	0.0563648i
$249$		0			0
$250$	−53.2293	−	30.7320i	−0.212917	−	0.122928i
$251$			63.0463i			0.251181i	0.992082	+	0.125590i	$0.0400825\pi$
$251$			63.0463i			0.251181i	−0.992082	+	0.125590i	$0.959918\pi$
$252$		0			0
$253$	−4.15116			−0.0164077
$254$	34.5800	−	59.8944i	0.136142	−	0.235805i
$255$		0			0
$256$	−66.7343	−	115.587i	−0.260681	−	0.451512i
$257$			123.139i			0.479139i	0.970879	+	0.239570i	$0.0770063\pi$
$257$			123.139i			0.479139i	−0.970879	+	0.239570i	$0.922994\pi$
$258$		0			0
$259$	22.0894	−	105.979i	0.0852873	−	0.409184i
$260$	−32.7497			−0.125960
$261$		0			0
$262$	−50.4455	−	29.1247i	−0.192540	−	0.111163i
$263$	505.590			1.92240			0.961198	−	0.275858i	$-0.0889620\pi$
$263$	505.590			1.92240			0.961198	+	0.275858i	$0.0889620\pi$
$264$		0			0
$265$	128.157	+	73.9913i	0.483610	+	0.279213i
$266$	61.8176	−	69.2030i	0.232397	−	0.260162i
$267$		0			0
$268$	196.383	−	340.146i	0.732774	−	1.26920i
$269$	−7.68453	−	4.43667i	−0.0285670	−	0.0164932i	0.485648	−	0.874154i	$-0.338584\pi$
$269$	−7.68453	−	4.43667i	−0.0285670	−	0.0164932i	−0.514216	+	0.857661i	$0.671917\pi$
$270$		0			0
$271$	117.573	−	67.8807i	0.433848	−	0.250482i	−0.267137	−	0.963659i	$-0.586078\pi$
$271$	117.573	−	67.8807i	0.433848	−	0.250482i	0.700985	+	0.713176i	$0.252744\pi$
$272$	−363.107	+	209.640i	−1.33495	+	0.770735i
$273$		0			0
$274$	−4.51919	+	7.82746i	−0.0164934	+	0.0285674i
$275$	0.821916			0.00298878
$276$		0			0
$277$	−325.394			−1.17471			−0.587353	−	0.809331i	$-0.699830\pi$
$277$	−325.394			−1.17471			−0.587353	+	0.809331i	$0.699830\pi$
$278$	17.1873	−	9.92308i	0.0618247	−	0.0356945i
$279$		0			0
$280$	72.2953	−	80.9325i	0.258198	−	0.289045i
$281$	7.89120	+	13.6680i	0.0280826	+	0.0486404i	0.879725	−	0.475483i	$-0.157727\pi$
$281$	7.89120	+	13.6680i	0.0280826	+	0.0486404i	−0.851643	+	0.524123i	$0.824393\pi$
$282$		0			0
$283$	−273.509	+	157.910i	−0.966461	+	0.557987i	−0.898156	−	0.439678i	$-0.855093\pi$
$283$	−273.509	+	157.910i	−0.966461	+	0.557987i	−0.0683057	+	0.997664i	$0.521759\pi$
$284$	−163.975	−	284.013i	−0.577377	−	1.00005i
$285$		0			0
$286$	−0.108552	+	0.0626723i	−0.000379551	+	0.000219134i
$287$	−1.88912	−	5.73693i	−0.00658230	−	0.0199893i
$288$		0			0
$289$	333.748	+	578.068i	1.15484	+	2.00023i
$290$			28.9935i			0.0999777i
$291$		0			0
$292$		−	125.309i		−	0.429141i
$293$	344.571	+	198.938i	1.17601	+	0.678969i	0.955088	−	0.296322i	$-0.0957602\pi$
$293$	344.571	+	198.938i	1.17601	+	0.678969i	0.220922	+	0.975292i	$0.429094\pi$
$294$		0			0
$295$	145.074	+	251.275i	0.491775	+	0.851780i
$296$	−27.4269	−	47.5048i	−0.0926584	−	0.160489i
$297$		0			0
$298$	45.9293	−	79.5519i	0.154125	−	0.266953i
$299$	50.9464	+	29.4139i	0.170389	+	0.0983742i
$300$		0			0
$301$	44.7435	−	214.667i	0.148650	−	0.713178i
$302$	−24.4482	+	42.3455i	−0.0809543	+	0.140217i
$303$		0			0
$304$			394.840i			1.29882i
$305$	−90.6636	+	157.034i	−0.297258	+	0.514866i
$306$		0			0
$307$		−	266.176i		−	0.867024i	−0.901148	−	0.433512i	$-0.857274\pi$
$307$		−	266.176i		−	0.867024i	0.901148	−	0.433512i	$-0.142726\pi$
$308$	−0.755200	+	3.62323i	−0.00245195	+	0.0117637i
$309$		0			0
$310$	15.6804			0.0505818
$311$	−110.220	+	63.6356i	−0.354406	+	0.204616i	−0.666624	−	0.745394i	$-0.732261\pi$
$311$	−110.220	+	63.6356i	−0.354406	+	0.204616i	0.312218	+	0.950010i	$0.398928\pi$
$312$		0			0
$313$	432.327	+	249.604i	1.38124	+	0.797457i	0.992306	−	0.123810i	$-0.0395113\pi$
$313$	432.327	+	249.604i	1.38124	+	0.797457i	0.388930	+	0.921267i	$0.372845\pi$
$314$		−	45.4707i		−	0.144811i
$315$		0			0
$316$	−184.508			−0.583887
$317$	98.4602	−	170.538i	0.310600	−	0.537975i	−0.667892	−	0.744258i	$-0.732803\pi$
$317$	98.4602	−	170.538i	0.310600	−	0.537975i	0.978492	+	0.206283i	$0.0661367\pi$
$318$		0			0
$319$	−1.01583	−	1.75947i	−0.00318442	−	0.00551558i
$320$			196.519i			0.614123i
$321$		0			0
$322$	−90.1157	+	29.6743i	−0.279862	+	0.0921562i
$323$	900.742			2.78868
$324$		0			0
$325$	−10.0872	−	5.82386i	−0.0310376	−	0.0179196i
$326$	−56.8430			−0.174365
$327$		0			0
$328$	−2.65044	−	1.53023i	−0.00808061	−	0.00466535i
$329$	−146.681	−	445.445i	−0.445839	−	1.35394i
$330$		0			0
$331$	−96.3662	+	166.911i	−0.291137	+	0.504263i	−0.974079	−	0.226209i	$-0.927367\pi$
$331$	−96.3662	+	166.911i	−0.291137	+	0.504263i	0.682942	+	0.730472i	$0.260700\pi$
$332$	390.259	+	225.316i	1.17548	+	0.678664i
$333$		0			0
$334$	51.5277	−	29.7495i	0.154275	−	0.0890705i
$335$	−391.979	+	226.309i	−1.17009	+	0.675550i
$336$		0			0
$337$	−189.897	+	328.912i	−0.563493	+	0.975999i	0.433695	+	0.901060i	$0.357210\pi$
$337$	−189.897	+	328.912i	−0.563493	+	0.975999i	−0.997188	+	0.0749390i	$0.976124\pi$
$338$	−75.1443			−0.222320
$339$		0			0
$340$	512.705			1.50796
$341$	−0.951561	+	0.549384i	−0.00279050	+	0.00161110i
$342$		0			0
$343$	−198.309	+	279.862i	−0.578160	+	0.815923i
$344$	−55.5549	−	96.2240i	−0.161497	−	0.279721i
$345$		0			0
$346$	33.1298	−	19.1275i	0.0957509	−	0.0552818i
$347$	−96.1388	−	166.517i	−0.277057	−	0.479877i	0.693595	−	0.720365i	$-0.256026\pi$
$347$	−96.1388	−	166.517i	−0.277057	−	0.479877i	−0.970652	+	0.240488i	$0.922692\pi$
$348$		0			0
$349$	−65.3195	+	37.7122i	−0.187162	+	0.108058i	−0.590653	−	0.806926i	$-0.701130\pi$
$349$	−65.3195	+	37.7122i	−0.187162	+	0.108058i	0.403491	+	0.914983i	$0.367797\pi$
$350$	17.8426	−	5.87541i	0.0509789	−	0.0167869i
$351$		0			0
$352$	1.41898	+	2.45775i	0.00403120	+	0.00698224i
$353$		−	565.941i		−	1.60323i	−0.597840	−	0.801616i	$-0.703974\pi$
$353$		−	565.941i		−	1.60323i	0.597840	−	0.801616i	$-0.296026\pi$
$354$		0			0
$355$			377.925i			1.06458i
$356$	125.706	+	72.5766i	0.353108	+	0.203867i
$357$		0			0
$358$	79.7482	+	138.128i	0.222760	+	0.385832i
$359$	−18.3134	−	31.7198i	−0.0510123	−	0.0883559i	0.839392	−	0.543527i	$-0.182911\pi$
$359$	−18.3134	−	31.7198i	−0.0510123	−	0.0883559i	−0.890404	+	0.455171i	$0.849578\pi$
$360$		0			0
$361$	243.620	−	421.962i	0.674847	−	1.16887i
$362$	54.4152	+	31.4167i	0.150318	+	0.0867863i
$363$		0			0
$364$	34.9416	−	39.1161i	0.0959933	−	0.107462i
$365$	−72.2022	+	125.058i	−0.197814	+	0.342624i
$366$		0			0
$367$		−	337.154i		−	0.918676i	−0.888261	−	0.459338i	$-0.848087\pi$
$367$		−	337.154i		−	0.918676i	0.888261	−	0.459338i	$-0.151913\pi$
$368$	201.852	−	349.618i	0.548511	−	0.950049i
$369$		0			0
$370$			30.7661i			0.0831517i
$371$	−225.109	+	74.1263i	−0.606762	+	0.199801i
$372$		0			0
$373$	735.214			1.97108			0.985541	−	0.169437i	$-0.0541949\pi$
$373$	735.214			1.97108			0.985541	+	0.169437i	$0.0541949\pi$
$374$	1.69940	−	0.981151i	0.00454386	−	0.00262340i
$375$		0			0
$376$	−205.794	−	118.815i	−0.547325	−	0.315998i
$377$			28.7915i			0.0763701i
$378$		0			0
$379$	189.024			0.498745			0.249372	−	0.968408i	$-0.419776\pi$
$379$	189.024			0.498745			0.249372	+	0.968408i	$0.419776\pi$
$380$	241.410	−	418.134i	0.635290	−	1.10035i
$381$		0			0
$382$	66.0253	+	114.359i	0.172841	+	0.299370i
$383$			14.1663i			0.0369876i	0.999829	+	0.0184938i	$0.00588710\pi$
$383$			14.1663i			0.0369876i	−0.999829	+	0.0184938i	$0.994113\pi$
$384$		0			0
$385$	2.84136	−	3.18082i	0.00738017	−	0.00826188i
$386$	100.352			0.259979
$387$		0			0
$388$	266.894	+	154.091i	0.687870	+	0.397142i
$389$	143.994			0.370165			0.185082	−	0.982723i	$-0.440745\pi$
$389$	143.994			0.370165			0.185082	+	0.982723i	$0.440745\pi$
$390$		0			0
$391$	−797.578	−	460.482i	−2.03984	−	1.17770i
$392$	19.5315	+	172.698i	0.0498252	+	0.440557i
$393$		0			0
$394$	−26.9516	+	46.6815i	−0.0684050	+	0.118481i
$395$	184.138	+	106.312i	0.466173	+	0.269145i
$396$		0			0
$397$	−178.514	+	103.065i	−0.449657	+	0.259610i	−0.707685	−	0.706528i	$-0.750261\pi$
$397$	−178.514	+	103.065i	−0.449657	+	0.259610i	0.258028	+	0.966137i	$0.416927\pi$
$398$	−69.2539	+	39.9837i	−0.174005	+	0.100462i
$399$		0			0
$400$	−39.9661	+	69.2233i	−0.0999152	+	0.173058i
$401$	356.403			0.888786			0.444393	−	0.895832i	$-0.353419\pi$
$401$	356.403			0.888786			0.444393	+	0.895832i	$0.353419\pi$
$402$		0			0
$403$	15.5711			0.0386380
$404$	83.4561	−	48.1834i	0.206575	−	0.119266i
$405$		0			0
$406$	−34.6297	−	30.9340i	−0.0852948	−	0.0761921i
$407$	−1.07794	−	1.86704i	−0.00264849	−	0.00458732i
$408$		0			0
$409$	456.496	−	263.558i	1.11613	−	0.644396i	0.175718	−	0.984441i	$-0.443775\pi$
$409$	456.496	−	263.558i	1.11613	−	0.644396i	0.940409	+	0.340044i	$0.110442\pi$
$410$	0.858270	+	1.48657i	0.00209334	+	0.00362577i
$411$		0			0
$412$	−362.050	+	209.030i	−0.878763	+	0.507354i
$413$	−454.905	−	94.8170i	−1.10146	−	0.229581i
$414$		0			0
$415$	−259.651	−	449.729i	−0.625666	−	1.08369i
$416$		−	40.2180i		−	0.0966778i
$417$		0			0
$418$		−	1.84792i		−	0.00442086i
$419$	−274.217	−	158.319i	−0.654455	−	0.377850i	0.135706	−	0.990749i	$-0.456670\pi$
$419$	−274.217	−	158.319i	−0.654455	−	0.377850i	−0.790161	+	0.612899i	$0.790003\pi$
$420$		0			0
$421$	68.8293	+	119.216i	0.163490	+	0.283173i	0.936118	−	0.351686i	$-0.114391\pi$
$421$	68.8293	+	119.216i	0.163490	+	0.283173i	−0.772628	+	0.634859i	$0.781058\pi$
$422$	4.18175	+	7.24301i	0.00990937	+	0.0171635i
$423$		0			0
$424$	−60.0441	+	104.000i	−0.141614	+	0.245282i
$425$	157.918	+	91.1739i	0.371571	+	0.214527i
$426$		0			0
$427$	−90.8290	−	275.832i	−0.212714	−	0.645976i
$428$	−297.429	+	515.162i	−0.694928	+	1.20365i
$429$		0			0
$430$			62.3188i			0.144927i
$431$	−315.576	+	546.594i	−0.732196	+	1.26820i	0.223747	+	0.974647i	$0.428171\pi$
$431$	−315.576	+	546.594i	−0.732196	+	1.26820i	−0.955943	+	0.293553i	$0.905162\pi$
$432$		0			0
$433$			224.007i			0.517338i	0.965966	+	0.258669i	$0.0832839\pi$
$433$			224.007i			0.517338i	−0.965966	+	0.258669i	$0.916716\pi$
$434$	−16.7298	+	18.7285i	−0.0385479	+	0.0431533i
$435$		0			0
$436$	94.6984			0.217198
$437$	−751.088	+	433.641i	−1.71874	+	0.992313i
$438$		0			0
$439$	−196.906	−	113.684i	−0.448533	−	0.258961i	0.258678	−	0.965964i	$-0.416713\pi$
$439$	−196.906	−	113.684i	−0.448533	−	0.258961i	−0.707210	+	0.707003i	$0.750047\pi$
$440$		−	2.16113i		−	0.00491167i
$441$		0			0
$442$	−27.8086			−0.0629154
$443$	47.0412	−	81.4778i	0.106188	−	0.183923i	−0.808035	−	0.589134i	$-0.799469\pi$
$443$	47.0412	−	81.4778i	0.106188	−	0.183923i	0.914223	+	0.405212i	$0.132802\pi$
$444$		0			0
$445$	−83.6362	−	144.862i	−0.187946	−	0.325533i
$446$			74.7892i			0.167689i
$447$		0			0
$448$	−234.722	−	209.672i	−0.523932	−	0.468018i
$449$	293.686			0.654089			0.327044	−	0.945009i	$-0.393947\pi$
$449$	293.686			0.654089			0.327044	+	0.945009i	$0.393947\pi$
$450$		0			0
$451$	−0.104168	−	0.0601415i	−0.000230971	−	0.000133351i
$452$	381.255			0.843484
$453$		0			0
$454$	−44.9069	−	25.9270i	−0.0989140	−	0.0571080i
$455$	−57.4099	+	18.9046i	−0.126176	+	0.0415485i
$456$		0			0
$457$	142.012	−	245.972i	0.310749	−	0.538233i	−0.667776	−	0.744363i	$-0.732753\pi$
$457$	142.012	−	245.972i	0.310749	−	0.538233i	0.978525	+	0.206130i	$0.0660868\pi$
$458$	−71.9923	−	41.5648i	−0.157188	−	0.0907528i
$459$		0			0
$460$	−427.521	+	246.829i	−0.929394	+	0.536586i
$461$	−563.505	+	325.340i	−1.22235	+	0.705726i	−0.965419	−	0.260703i	$-0.916046\pi$
$461$	−563.505	+	325.340i	−1.22235	+	0.705726i	−0.256934	+	0.966429i	$0.582712\pi$
$462$		0			0
$463$	−215.001	+	372.393i	−0.464365	+	0.804304i	−0.999173	−	0.0406699i	$-0.987051\pi$
$463$	−215.001	+	372.393i	−0.464365	+	0.804304i	0.534807	+	0.844974i	$0.320384\pi$
$464$	197.581			0.425821
$465$		0			0
$466$	−115.495			−0.247842
$467$	216.900	−	125.227i	0.464454	−	0.268153i	−0.249461	−	0.968385i	$-0.580253\pi$
$467$	216.900	−	125.227i	0.464454	−	0.268153i	0.713915	+	0.700232i	$0.246920\pi$
$468$		0			0
$469$	147.911	−	709.633i	0.315375	−	1.51308i
$470$	66.6406	+	115.425i	0.141789	+	0.245585i
$471$		0			0
$472$	−203.910	+	117.728i	−0.432013	+	0.249423i
$473$	−2.18343	−	3.78181i	−0.00461613	−	0.00799537i
$474$		0			0
$475$	148.713	−	85.8595i	0.313080	−	0.180757i
$476$	−547.019	+	612.372i	−1.14920	+	1.28650i
$477$		0			0
$478$	29.9017	+	51.7912i	0.0625558	+	0.108350i
$479$		−	535.341i		−	1.11762i	−0.829295	−	0.558811i	$-0.811258\pi$
$479$		−	535.341i		−	1.11762i	0.829295	−	0.558811i	$-0.188742\pi$
$480$		0			0
$481$			30.5518i			0.0635172i
$482$	−102.671	−	59.2772i	−0.213011	−	0.122982i
$483$		0			0
$484$	−229.430	−	397.384i	−0.474028	−	0.821041i
$485$	−177.572	−	307.564i	−0.366128	−	0.634153i
$486$		0			0
$487$	−366.696	+	635.136i	−0.752969	+	1.30418i	0.193408	+	0.981118i	$0.438046\pi$
$487$	−366.696	+	635.136i	−0.752969	+	1.30418i	−0.946378	+	0.323063i	$0.895288\pi$
$488$	−127.433	−	73.5737i	−0.261134	−	0.150766i
$489$		0			0
$490$	38.9440	−	89.3625i	0.0794776	−	0.182372i
$491$	69.4113	−	120.224i	0.141367	−	0.244855i	−0.786645	−	0.617406i	$-0.788184\pi$
$491$	69.4113	−	120.224i	0.141367	−	0.244855i	0.928012	+	0.372551i	$0.121517\pi$
$492$		0			0
$493$		−	450.738i		−	0.914276i
$494$	−13.0938	+	22.6792i	−0.0265057	+	0.0459093i
$495$		0			0
$496$		−	106.856i		−	0.215436i
$497$	−451.391	−	403.218i	−0.908231	−	0.811304i
$498$		0			0
$499$	−95.8598			−0.192104			−0.0960519	−	0.995376i	$-0.530621\pi$
$499$	−95.8598			−0.192104			−0.0960519	+	0.995376i	$0.530621\pi$
$500$	443.567	−	256.094i	0.887134	−	0.512187i
$501$		0			0
$502$	24.8511	+	14.3478i	0.0495043	+	0.0285813i
$503$			41.5091i			0.0825231i	0.999148	+	0.0412615i	$0.0131377\pi$
$503$			41.5091i			0.0825231i	−0.999148	+	0.0412615i	$0.986862\pi$
$504$		0			0
$505$	−111.052			−0.219904
$506$	−0.944703	+	1.63627i	−0.00186700	+	0.00323374i
$507$		0			0
$508$	288.160	+	499.107i	0.567244	+	0.982495i
$509$			86.9188i			0.170764i	0.996348	+	0.0853819i	$0.0272110\pi$
$509$			86.9188i			0.170764i	−0.996348	+	0.0853819i	$0.972789\pi$
$510$		0			0
$511$	−72.3339	−	219.666i	−0.141554	−	0.429874i
$512$	−468.337			−0.914720
$513$		0			0
$514$	48.5380	+	28.0234i	0.0944318	+	0.0545202i
$515$	481.766			0.935468
$516$		0			0
$517$	−8.08816	−	4.66970i	−0.0156444	−	0.00903231i
$518$	−36.7469	−	32.8252i	−0.0709399	−	0.0633692i
$519$		0			0
$520$	−15.3132	+	26.5232i	−0.0294484	+	0.0510061i
$521$	156.678	+	90.4583i	0.300726	+	0.173624i	0.642769	−	0.766060i	$-0.277785\pi$
$521$	156.678	+	90.4583i	0.300726	+	0.173624i	−0.342043	+	0.939684i	$0.611119\pi$
$522$		0			0
$523$	392.571	−	226.651i	0.750614	−	0.433367i	−0.0753017	−	0.997161i	$-0.523992\pi$
$523$	392.571	−	226.651i	0.750614	−	0.433367i	0.825916	+	0.563794i	$0.190659\pi$
$524$	420.369	−	242.700i	0.802230	−	0.463168i
$525$		0			0
$526$	115.060	−	199.290i	0.218745	−	0.378878i
$527$	−243.769			−0.462561
$528$		0			0
$529$	357.751			0.676279
$530$	58.3308	−	33.6773i	0.110058	−	0.0635420i
$531$		0			0
$532$	241.850	+	734.458i	0.454606	+	1.38056i
$533$	0.852290	+	1.47621i	0.00159904	+	0.00276963i
$534$		0			0
$535$	593.666	−	342.753i	1.10966	−	0.640660i
$536$	−183.651	−	318.092i	−0.342632	−	0.593455i
$537$		0			0
$538$	−3.49763	+	2.01936i	−0.00650117	+	0.00375345i
$539$	0.767629	+	6.78742i	0.00142417	+	0.0125926i
$540$		0			0
$541$	−192.892	−	334.098i	−0.356546	−	0.617556i	0.630835	−	0.775917i	$-0.282712\pi$
$541$	−192.892	−	334.098i	−0.356546	−	0.617556i	−0.987381	+	0.158361i	$0.949379\pi$
$542$		−	61.7920i		−	0.114007i
$543$		0			0
$544$			629.622i			1.15739i
$545$	−94.5086	−	54.5646i	−0.173410	−	0.100118i
$546$		0			0
$547$	341.808	+	592.029i	0.624877	+	1.08232i	0.988565	+	0.150798i	$0.0481843\pi$
$547$	341.808	+	592.029i	0.624877	+	1.08232i	−0.363687	+	0.931521i	$0.618482\pi$
$548$	−37.6590	−	65.2273i	−0.0687208	−	0.119028i
$549$		0			0
$550$	0.187048	−	0.323977i	0.000340087	−	0.000589049i
$551$	−367.598	−	212.233i	−0.667147	−	0.385177i
$552$		0			0
$553$	−323.441	+	106.506i	−0.584884	+	0.192597i
$554$	−74.0518	+	128.261i	−0.133667	+	0.231519i
$555$		0			0
$556$			165.381i			0.297447i
$557$	80.5596	−	139.533i	0.144631	−	0.250509i	−0.784604	−	0.619997i	$-0.787134\pi$
$557$	80.5596	−	139.533i	0.144631	−	0.250509i	0.929235	+	0.369488i	$0.120467\pi$
$558$		0			0
$559$			61.8846i			0.110706i
$560$	129.732	+	393.974i	0.231665	+	0.703525i
$561$		0			0
$562$	7.18338			0.0127818
$563$	−473.617	+	273.443i	−0.841239	+	0.485689i	−0.857685	−	0.514175i	$-0.828098\pi$
$563$	−473.617	+	273.443i	−0.841239	+	0.485689i	0.0164464	+	0.999865i	$0.494765\pi$
$564$		0			0
$565$	−380.490	−	219.676i	−0.673434	−	0.388808i
$566$			143.746i			0.253969i
$567$		0			0
$568$	−306.687			−0.539941
$569$	−301.145	+	521.599i	−0.529253	+	0.916694i	0.470164	+	0.882579i	$0.344195\pi$
$569$	−301.145	+	521.599i	−0.529253	+	0.916694i	−0.999418	+	0.0341151i	$0.989139\pi$
$570$		0			0
$571$	−160.184	−	277.446i	−0.280532	−	0.485895i	0.690984	−	0.722870i	$-0.257177\pi$
$571$	−160.184	−	277.446i	−0.280532	−	0.485895i	−0.971516	+	0.236975i	$0.923844\pi$
$572$		−	1.04451i		−	0.00182607i
$573$		0			0
$574$	−2.69126	−	0.560947i	−0.00468860	−	0.000977259i
$575$	−175.574			−0.305346
$576$		0			0
$577$	−92.5287	−	53.4215i	−0.160362	−	0.0925849i	0.417672	−	0.908598i	$-0.362846\pi$
$577$	−92.5287	−	53.4215i	−0.160362	−	0.0925849i	−0.578033	+	0.816013i	$0.696180\pi$
$578$	303.811			0.525625
$579$		0			0
$580$	−209.238	−	120.803i	−0.360755	−	0.208282i
$581$	814.183	+	169.702i	1.40135	+	0.292087i
$582$		0			0
$583$	−2.35987	+	4.08741i	−0.00404780	+	0.00701099i
$584$	−101.485	−	58.5922i	−0.173775	−	0.100329i
$585$		0			0
$586$	156.832	−	90.5470i	0.267631	−	0.154517i
$587$	−269.081	+	155.354i	−0.458400	+	0.264657i	−0.711371	−	0.702816i	$-0.751926\pi$
$587$	−269.081	+	155.354i	−0.458400	+	0.264657i	0.252971	+	0.967474i	$0.418592\pi$
$588$		0			0
$589$	−114.780	+	198.805i	−0.194873	+	0.337530i
$590$	132.061			0.223832
$591$		0			0
$592$	209.661			0.354157
$593$	734.942	−	424.319i	1.23936	−	0.715546i	0.270399	−	0.962748i	$-0.412844\pi$
$593$	734.942	−	424.319i	1.23936	−	0.715546i	0.968964	+	0.247202i	$0.0795111\pi$
$594$		0			0
$595$	898.766	−	295.956i	1.51053	−	0.497404i
$596$	382.735	+	662.916i	0.642173	+	1.11228i
$597$		0			0
$598$	23.1883	−	13.3878i	0.0387764	−	0.0223876i
$599$	176.616	+	305.907i	0.294851	+	0.510697i	0.974950	−	0.222423i	$-0.0713967\pi$
$599$	176.616	+	305.907i	0.294851	+	0.510697i	−0.680099	+	0.733120i	$0.738063\pi$
$600$		0			0
$601$	−582.924	+	336.552i	−0.969924	+	0.559986i	−0.899213	−	0.437511i	$-0.855860\pi$
$601$	−582.924	+	336.552i	−0.969924	+	0.559986i	−0.0707111	+	0.997497i	$0.522527\pi$
$602$	−74.4332	−	66.4896i	−0.123643	−	0.110448i
$603$		0			0
$604$	−203.730	−	352.871i	−0.337301	−	0.584223i
$605$			528.783i			0.874022i
$606$		0			0
$607$		−	775.507i		−	1.27761i	−0.769370	−	0.638804i	$-0.779430\pi$
$607$		−	775.507i		−	1.27761i	0.769370	−	0.638804i	$-0.220570\pi$
$608$	513.486	+	296.461i	0.844549	+	0.487600i
$609$		0			0
$610$	41.2657	+	71.4743i	0.0676487	+	0.117171i
$611$	66.1763	+	114.621i	0.108308	+	0.187595i
$612$		0			0
$613$	66.6787	−	115.491i	0.108774	−	0.188403i	−0.806500	−	0.591235i	$-0.798641\pi$
$613$	66.6787	−	115.491i	0.108774	−	0.188403i	0.915274	+	0.402832i	$0.131974\pi$
$614$	−104.920	−	60.5753i	−0.170879	−	0.0986569i
$615$		0			0
$616$	2.58125	+	2.30577i	0.00419033	+	0.00374314i
$617$	496.756	−	860.406i	0.805115	−	1.39450i	−0.111099	−	0.993809i	$-0.535437\pi$
$617$	496.756	−	860.406i	0.805115	−	1.39450i	0.916214	−	0.400690i	$-0.131230\pi$
$618$		0			0
$619$			793.383i			1.28172i	0.767659	+	0.640859i	$0.221422\pi$
$619$			793.383i			1.28172i	−0.767659	+	0.640859i	$0.778578\pi$
$620$	−65.3332	+	113.160i	−0.105376	+	0.182517i
$621$		0			0
$622$			57.9277i			0.0931314i
$623$	262.256	+	54.6628i	0.420957	+	0.0877412i
$624$		0			0
$625$	−442.836			−0.708538
$626$	196.774	−	113.608i	0.314336	−	0.181482i
$627$		0			0
$628$	328.149	+	189.457i	0.522530	+	0.301683i
$629$		−	478.295i		−	0.760406i
$630$		0			0
$631$	−124.394			−0.197137			−0.0985687	−	0.995130i	$-0.531426\pi$
$631$	−124.394			−0.197137			−0.0985687	+	0.995130i	$0.531426\pi$
$632$	−86.2726	+	149.429i	−0.136507	+	0.236438i
$633$		0			0
$634$	−44.8143	−	77.6206i	−0.0706850	−	0.122430i
$635$		−	664.142i		−	1.04589i
$636$		0			0
$637$	38.6727	−	88.7399i	0.0607107	−	0.139309i
$638$	−0.924714			−0.00144939
$639$		0			0
$640$	385.704	+	222.686i	0.602663	+	0.347947i
$641$	−860.510			−1.34245			−0.671225	−	0.741254i	$-0.734231\pi$
$641$	−860.510			−1.34245			−0.671225	+	0.741254i	$0.734231\pi$
$642$		0			0
$643$	847.964	+	489.572i	1.31876	+	0.761387i	0.983529	−	0.180748i	$-0.0578519\pi$
$643$	847.964	+	489.572i	1.31876	+	0.761387i	0.335232	+	0.942135i	$0.391185\pi$
$644$	161.322	−	773.978i	0.250501	−	1.20183i
$645$		0			0
$646$	204.987	−	355.048i	0.317318	−	0.549610i
$647$	−612.039	−	353.361i	−0.945964	−	0.546153i	−0.0541391	−	0.998533i	$-0.517241\pi$
$647$	−612.039	−	353.361i	−0.945964	−	0.546153i	−0.891825	+	0.452381i	$0.850575\pi$
$648$		0			0
$649$	−8.01412	+	4.62695i	−0.0123484	+	0.00712936i
$650$	−4.59121	+	2.65074i	−0.00706340	+	0.00407806i
$651$		0			0
$652$	236.840	−	410.219i	0.363252	−	0.629170i
$653$	840.986			1.28788			0.643940	−	0.765076i	$-0.277299\pi$
$653$	840.986			1.28788			0.643940	+	0.765076i	$0.277299\pi$
$654$		0			0
$655$	−559.368			−0.853996
$656$	10.1305	−	5.84882i	0.0154428	−	0.00891589i
$657$		0			0
$658$	−208.964	−	43.5548i	−0.317574	−	0.0661928i
$659$	241.065	+	417.537i	0.365804	+	0.633591i	0.988905	−	0.148550i	$-0.0474607\pi$
$659$	241.065	+	417.537i	0.365804	+	0.633591i	−0.623101	+	0.782141i	$0.714127\pi$
$660$		0			0
$661$	−716.914	+	413.911i	−1.08459	+	0.626189i	−0.932131	−	0.362121i	$-0.882053\pi$
$661$	−716.914	+	413.911i	−1.08459	+	0.626189i	−0.152460	+	0.988310i	$0.548719\pi$
$662$	43.8612	+	75.9699i	0.0662556	+	0.114758i
$663$		0			0
$664$	364.956	−	210.708i	0.549633	−	0.317331i
$665$	181.824	−	872.337i	0.273419	−	1.31179i
$666$		0			0
$667$	216.997	+	375.850i	0.325333	+	0.563493i
$668$			495.813i			0.742236i
$669$		0			0
$670$			206.010i			0.307478i
$671$	−5.00841	−	2.89161i	−0.00746410	−	0.00430940i
$672$		0			0
$673$	325.267	+	563.379i	0.483309	+	0.837116i	0.999816	−	0.0191670i	$-0.00610143\pi$
$673$	325.267	+	563.379i	0.483309	+	0.837116i	−0.516507	+	0.856283i	$0.672768\pi$
$674$	86.4320	+	149.705i	0.128237	+	0.222114i
$675$		0			0
$676$	313.094	−	542.294i	0.463156	−	0.802210i
$677$	366.544	+	211.624i	0.541424	+	0.312591i	0.745656	−	0.666331i	$-0.232136\pi$
$677$	366.544	+	211.624i	0.541424	+	0.312591i	−0.204232	+	0.978923i	$0.565470\pi$
$678$		0			0
$679$	556.809	+	116.057i	0.820043	+	0.170924i
$680$	239.731	−	415.227i	0.352546	−	0.610628i
$681$		0			0
$682$			0.500106i			0.000733294i
$683$	219.835	−	380.766i	0.321867	−	0.557490i	−0.659006	−	0.752137i	$-0.729023\pi$
$683$	219.835	−	380.766i	0.321867	−	0.557490i	0.980873	+	0.194647i	$0.0623563\pi$
$684$		0			0
$685$			86.7953i			0.126709i
$686$	65.1835	+	141.858i	0.0950197	+	0.206790i
$687$		0			0
$688$	424.681			0.617270
$689$	57.9244	−	33.4426i	0.0840702	−	0.0485379i
$690$		0			0
$691$	700.681	+	404.539i	1.01401	+	0.585439i	0.912363	−	0.409381i	$-0.134255\pi$
$691$	700.681	+	404.539i	1.01401	+	0.585439i	0.101647	+	0.994821i	$0.467589\pi$
$692$			318.784i			0.460671i
$693$		0			0
$694$	−87.5155			−0.126103
$695$	95.2911	−	165.049i	0.137109	−	0.237481i
$696$		0			0
$697$	−13.3428	−	23.1104i	−0.0191432	−	0.0331570i
$698$			34.3296i			0.0491827i
$699$		0			0
$700$	−31.9413	+	153.245i	−0.0456304	+	0.218922i
$701$	14.5407			0.0207428			0.0103714	−	0.999946i	$-0.496699\pi$
$701$	14.5407			0.0207428			0.0103714	+	0.999946i	$0.496699\pi$
$702$		0			0
$703$	−390.072	−	225.208i	−0.554868	−	0.320353i
$704$	−6.26775			−0.00890306
$705$		0			0
$706$	−223.078	−	128.794i	−0.315975	−	0.182428i
$707$	118.484	−	132.640i	0.167587	−	0.187609i
$708$		0			0
$709$	−475.616	+	823.790i	−0.670826	+	1.16190i	0.306844	+	0.951760i	$0.400727\pi$
$709$	−475.616	+	823.790i	−0.670826	+	1.16190i	−0.977670	+	0.210145i	$0.932606\pi$
$710$	148.968	+	86.0065i	0.209814	+	0.121136i
$711$		0			0
$712$	117.556	−	67.8709i	0.165107	−	0.0953243i
$713$	203.268	−	117.357i	0.285089	−	0.164596i
$714$		0			0
$715$	−0.601841	+	1.04242i	−0.000841736	+	0.00145793i
$716$	−1329.10			−1.85629
$717$		0			0
$718$	−16.6708			−0.0232183
$719$	−915.654	+	528.653i	−1.27351	+	0.735262i	−0.975647	−	0.219346i	$-0.929608\pi$
$719$	−915.654	+	528.653i	−1.27351	+	0.735262i	−0.297864	+	0.954608i	$0.596274\pi$
$720$		0			0
$721$	−514.009	+	575.418i	−0.712911	+	0.798084i
$722$	−110.884	−	192.056i	−0.153579	−	0.266006i
$723$		0			0
$724$	−453.449	+	261.799i	−0.626311	+	0.361601i
$725$	−42.9647	−	74.4171i	−0.0592617	−	0.102644i
$726$		0			0
$727$	1105.69	−	638.372i	1.52090	−	0.878091i	0.521202	−	0.853434i	$-0.325484\pi$
$727$	1105.69	−	638.372i	1.52090	−	0.878091i	0.999696	−	0.0246570i	$-0.00784937\pi$
$728$	−15.3411	−	46.5883i	−0.0210729	−	0.0639949i
$729$		0			0
$730$	32.8629	+	56.9203i	0.0450177	+	0.0779730i
$731$		−	968.818i		−	1.32533i
$732$		0			0
$733$			86.9845i			0.118669i	0.998238	+	0.0593346i	$0.0188979\pi$
$733$			86.9845i			0.118669i	−0.998238	+	0.0593346i	$0.981102\pi$
$734$	−132.897	−	76.7281i	−0.181059	−	0.104534i
$735$		0			0
$736$	−303.116	−	525.013i	−0.411843	−	0.713333i
$737$	−7.21787	−	12.5017i	−0.00979358	−	0.0169630i
$738$		0			0
$739$	−388.913	+	673.617i	−0.526269	+	0.911525i	0.473263	+	0.880921i	$0.343076\pi$
$739$	−388.913	+	673.617i	−0.526269	+	0.911525i	−0.999532	+	0.0306034i	$0.990257\pi$
$740$	−222.030	−	128.189i	−0.300041	−	0.173228i
$741$		0			0
$742$	−22.0107	+	105.601i	−0.0296641	+	0.142320i
$743$	−162.682	+	281.774i	−0.218953	+	0.379238i	−0.954488	−	0.298249i	$-0.903597\pi$
$743$	−162.682	+	281.774i	−0.218953	+	0.379238i	0.735535	+	0.677487i	$0.236931\pi$
$744$		0			0
$745$		−	882.116i		−	1.18405i
$746$	167.317	−	289.801i	0.224285	−	0.388473i
$747$		0			0
$748$			16.3521i			0.0218611i
$749$	−224.016	+	1074.76i	−0.299087	+	1.43493i
$750$		0			0
$751$	321.596			0.428223			0.214112	−	0.976809i	$-0.431314\pi$
$751$	321.596			0.428223			0.214112	+	0.976809i	$0.431314\pi$
$752$	786.582	−	454.133i	1.04599	−	0.603901i
$753$		0			0
$754$	11.3488	+	6.55225i	0.0150515	+	0.00868999i
$755$			469.551i			0.621922i
$756$		0			0
$757$	1029.44			1.35989			0.679946	−	0.733263i	$-0.262003\pi$
$757$	1029.44			1.35989			0.679946	+	0.733263i	$0.262003\pi$
$758$	43.0174	−	74.5083i	0.0567511	−	0.0982958i
$759$		0			0
$760$	−225.758	−	391.024i	−0.297050	−	0.514505i
$761$			1081.04i			1.42056i	0.703921	+	0.710278i	$0.251431\pi$
$761$			1081.04i			1.42056i	−0.703921	+	0.710278i	$0.748569\pi$
$762$		0			0
$763$	166.005	−	54.6641i	0.217569	−	0.0716436i
$764$	−1100.40			−1.44031
$765$		0			0
$766$	5.58396	+	3.22390i	0.00728976	+	0.00420875i
$767$	131.141			0.170979
$768$		0			0
$769$	−345.681	−	199.579i	−0.449520	−	0.259531i	0.258107	−	0.966116i	$-0.416901\pi$
$769$	−345.681	−	199.579i	−0.449520	−	0.259531i	−0.707627	+	0.706586i	$0.750234\pi$
$770$	−0.607169	−	1.84387i	−0.000788531	−	0.00239463i
$771$		0			0
$772$	−418.122	+	724.209i	−0.541609	+	0.938095i
$773$	603.536	+	348.452i	0.780771	+	0.450778i	0.836703	−	0.547656i	$-0.184480\pi$
$773$	603.536	+	348.452i	0.780771	+	0.450778i	−0.0559324	+	0.998435i	$0.517813\pi$
$774$		0			0
$775$	−40.2465	+	23.2363i	−0.0519309	+	0.0299823i
$776$	249.589	−	144.100i	0.321635	−	0.185696i
$777$		0			0
$778$	32.7696	−	56.7586i	0.0421203	−	0.0729544i
$779$	−25.1302			−0.0322595
$780$		0			0
$781$	−12.0535			−0.0154334
$782$	−363.019	+	209.589i	−0.464218	+	0.268017i
$783$		0			0
$784$	−608.975	−	265.390i	−0.776754	−	0.338508i
$785$	−218.327	−	378.154i	−0.278124	−	0.481725i
$786$		0			0
$787$	−68.7086	+	39.6689i	−0.0873044	+	0.0504052i	−0.543017	−	0.839722i	$-0.682718\pi$
$787$	−68.7086	+	39.6689i	−0.0873044	+	0.0504052i	0.455712	+	0.890127i	$0.349385\pi$
$788$	−224.591	−	389.003i	−0.285014	−	0.493659i
$789$		0			0
$790$	83.8108	−	48.3882i	0.106090	−	0.0612509i
$791$	668.336	−	220.077i	0.844925	−	0.278226i
$792$		0			0
$793$	40.9782	+	70.9763i	0.0516749	+	0.0895035i
$794$			93.8204i			0.118162i
$795$		0			0
$796$		−	666.379i		−	0.837160i
$797$	−79.3190	−	45.7948i	−0.0995219	−	0.0574590i	0.449413	−	0.893324i	$-0.351633\pi$
$797$	−79.3190	−	45.7948i	−0.0995219	−	0.0574590i	−0.548935	+	0.835865i	$0.684967\pi$
$798$		0			0
$799$	−1036.01	−	1794.42i	−1.29663	−	2.24583i
$800$	60.0161	+	103.951i	0.0750201	+	0.129939i
$801$		0			0
$802$	81.1087	−	140.484i	0.101133	−	0.175168i
$803$	−3.98857	−	2.30280i	−0.00496709	−	0.00286775i
$804$		0			0
$805$	−606.959	+	679.473i	−0.753987	+	0.844066i
$806$	3.54361	−	6.13771i	0.00439654	−	0.00761502i
$807$		0			0
$808$		−	90.1187i		−	0.111533i
$809$	−639.005	+	1106.79i	−0.789871	+	1.36810i	0.136175	+	0.990685i	$0.456519\pi$
$809$	−639.005	+	1106.79i	−0.789871	+	1.36810i	−0.926046	+	0.377411i	$0.876814\pi$
$810$		0			0
$811$			176.218i			0.217285i	0.994081	+	0.108642i	$0.0346503\pi$
$811$			176.218i			0.217285i	−0.994081	+	0.108642i	$0.965350\pi$
$812$	367.528	−	121.024i	0.452621	−	0.149044i
$813$		0			0
$814$	−0.981249			−0.00120547
$815$	−472.730	+	272.931i	−0.580037	+	0.334885i
$816$		0			0
$817$	−790.116	−	456.174i	−0.967094	−	0.558352i
$818$		−	239.918i		−	0.293298i
$819$		0			0
$820$	−14.3042			−0.0174441
$821$	−195.125	+	337.966i	−0.237667	+	0.411651i	−0.960044	−	0.279848i	$-0.909716\pi$
$821$	−195.125	+	337.966i	−0.237667	+	0.411651i	0.722377	+	0.691499i	$0.243049\pi$
$822$		0			0
$823$	49.6717	+	86.0339i	0.0603544	+	0.104537i	0.894624	−	0.446820i	$-0.147444\pi$
$823$	49.6717	+	86.0339i	0.0603544	+	0.104537i	−0.834269	+	0.551357i	$0.814110\pi$
$824$			390.954i			0.474459i
$825$		0			0
$826$	−140.900	+	157.733i	−0.170581	+	0.190960i
$827$	−494.422			−0.597850			−0.298925	−	0.954277i	$-0.596628\pi$
$827$	−494.422			−0.597850			−0.298925	+	0.954277i	$0.596628\pi$
$828$		0			0
$829$	−655.567	−	378.492i	−0.790792	−	0.456564i	0.0494491	−	0.998777i	$-0.484253\pi$
$829$	−655.567	−	378.492i	−0.790792	−	0.456564i	−0.840241	+	0.542212i	$0.817587\pi$
$830$	−236.361			−0.284773
$831$		0			0
$832$	76.9229	+	44.4115i	0.0924555	+	0.0533792i
$833$	−605.430	+	1389.24i	−0.726807	+	1.66776i
$834$		0			0
$835$	285.684	−	494.819i	0.342137	−	0.592598i
$836$	13.3359	+	7.69948i	0.0159520	+	0.00920991i
$837$		0			0
$838$	−124.810	+	72.0592i	−0.148938	+	0.0859895i
$839$	1345.92	−	777.067i	1.60419	−	0.926182i	0.613559	−	0.789649i	$-0.289737\pi$
$839$	1345.92	−	777.067i	1.60419	−	0.926182i	0.990636	−	0.136533i	$-0.0435960\pi$
$840$		0			0
$841$	314.297	−	544.379i	0.373718	−	0.647299i
$842$	62.6555			0.0744128
$843$		0			0
$844$	−69.6942			−0.0825761
$845$	−624.932	+	360.804i	−0.739564	+	0.426988i
$846$		0			0
$847$	−631.575	−	564.173i	−0.745662	−	0.666084i
$848$	−229.499	−	397.504i	−0.270636	−	0.468755i
$849$		0			0
$850$	71.8765	−	41.4979i	0.0845606	−	0.0488211i
$851$	230.264	+	398.829i	0.270580	+	0.468659i
$852$		0			0
$853$	−667.098	+	385.149i	−0.782061	+	0.451523i	−0.837160	−	0.546958i	$-0.815786\pi$
$853$	−667.098	+	385.149i	−0.782061	+	0.451523i	0.0550992	+	0.998481i	$0.482452\pi$
$854$	−129.396	−	26.9704i	−0.151517	−	0.0315812i
$855$		0			0
$856$	278.145	+	481.761i	0.324936	+	0.562805i
$857$			1133.93i			1.32314i	0.749885	+	0.661568i	$0.230109\pi$
$857$			1133.93i			1.32314i	−0.749885	+	0.661568i	$0.769891\pi$
$858$		0			0
$859$		−	704.474i		−	0.820109i	−0.912061	−	0.410054i	$-0.865510\pi$
$859$		−	704.474i		−	0.820109i	0.912061	−	0.410054i	$-0.134490\pi$
$860$	−449.736	−	259.655i	−0.522949	−	0.301925i
$861$		0			0
$862$	143.635	+	248.783i	0.166630	+	0.288612i
$863$	−275.214	−	476.684i	−0.318904	−	0.552357i	0.661356	−	0.750072i	$-0.269981\pi$
$863$	−275.214	−	476.684i	−0.318904	−	0.552357i	−0.980260	+	0.197715i	$0.936648\pi$
$864$		0			0
$865$	183.681	−	318.145i	0.212348	−	0.367798i
$866$	88.2976	+	50.9786i	0.101960	+	0.0588668i
$867$		0			0
$868$	−65.4524	−	198.768i	−0.0754060	−	0.228995i
$869$	−3.39070	+	5.87287i	−0.00390184	+	0.00675819i
$870$		0			0
$871$			204.575i			0.234874i
$872$	44.2793	−	76.6939i	0.0507790	−	0.0879517i
$873$		0			0
$874$			394.745i			0.451653i
$875$	629.740	−	704.975i	0.719703	−	0.805686i
$876$		0			0
$877$	22.5206			0.0256791			0.0128396	−	0.999918i	$-0.495913\pi$
$877$	22.5206			0.0256791			0.0128396	+	0.999918i	$0.495913\pi$
$878$	−89.6220	+	51.7433i	−0.102075	+	0.0589331i
$879$		0			0
$880$	7.15358	+	4.13012i	0.00812906	+	0.00469332i
$881$		−	443.014i		−	0.502854i	−0.967876	−	0.251427i	$-0.919100\pi$
$881$		−	443.014i		−	0.502854i	0.967876	−	0.251427i	$-0.0808998\pi$
$882$		0			0
$883$	331.418			0.375332			0.187666	−	0.982233i	$-0.439908\pi$
$883$	331.418			0.375332			0.187666	+	0.982233i	$0.439908\pi$
$884$	115.866	−	200.686i	0.131070	−	0.227021i
$885$		0			0
$886$	−21.4109	−	37.0847i	−0.0241658	−	0.0418564i
$887$		−	378.842i		−	0.427105i	−0.976932	−	0.213552i	$-0.931497\pi$
$887$		−	378.842i		−	0.427105i	0.976932	−	0.213552i	$-0.0685034\pi$
$888$		0			0
$889$	793.248	+	708.591i	0.892292	+	0.797066i
$890$	−76.1343			−0.0855441
$891$		0			0
$892$	−539.731	−	311.614i	−0.605080	−	0.349343i
$893$	−1951.24			−2.18504
$894$		0			0
$895$	1326.44	+	765.820i	1.48206	+	0.855665i
$896$	−677.493	+	223.093i	−0.756131	+	0.248987i
$897$		0			0
$898$	66.8358	−	115.763i	0.0744274	−	0.128912i
$899$	99.4836	+	57.4369i	0.110660	+	0.0638898i
$900$		0			0
$901$	−906.820	+	523.553i	−1.00646	+	0.581080i
$902$	−0.0474123	+	0.0273735i	−5.25635e−5	+	3.03476e-5i
$903$		0			0
$904$	178.268	−	308.769i	0.197199	−	0.341558i
$905$	603.387			0.666726
$906$		0			0
$907$	−393.796			−0.434174			−0.217087	−	0.976152i	$-0.569656\pi$
$907$	−393.796			−0.434174			−0.217087	+	0.976152i	$0.569656\pi$
$908$	374.215	−	216.053i	0.412131	−	0.237944i
$909$		0			0
$910$	−5.61344	+	26.9317i	−0.00616861	+	0.0295952i
$911$	−571.193	−	989.335i	−0.626995	−	1.08599i	−0.988151	−	0.153482i	$-0.950951\pi$
$911$	−571.193	−	989.335i	−0.626995	−	1.08599i	0.361156	−	0.932505i	$-0.382382\pi$
$912$		0			0
$913$	14.3436	−	8.28127i	0.0157104	−	0.00907039i
$914$	−64.6371	−	111.955i	−0.0707189	−	0.122489i
$915$		0			0
$916$	599.921	−	346.365i	0.654936	−	0.378127i
$917$	596.804	−	668.105i	0.650823	−	0.728577i
$918$		0			0
$919$	187.574	+	324.889i	0.204107	+	0.353524i	0.949848	−	0.312712i	$-0.101238\pi$
$919$	187.574	+	324.889i	0.204107	+	0.353524i	−0.745741	+	0.666236i	$0.767904\pi$
$920$			461.652i			0.501795i
$921$		0			0
$922$			296.158i			0.321212i
$923$	147.930	+	85.4073i	0.160271	+	0.0925323i
$924$		0			0
$925$	−45.5915	−	78.9668i	−0.0492881	−	0.0853695i
$926$	97.8581	+	169.495i	0.105678	+	0.183040i
$927$		0			0
$928$	148.351	−	256.952i	0.159861	−	0.276888i
$929$	−56.1689	−	32.4291i	−0.0604617	−	0.0349076i	0.469464	−	0.882951i	$-0.344447\pi$
$929$	−56.1689	−	32.4291i	−0.0604617	−	0.0349076i	−0.529926	+	0.848044i	$0.677780\pi$
$930$		0			0
$931$	847.922	+	1147.89i	0.910765	+	1.23296i
$932$	481.216	−	833.490i	0.516326	−	0.894303i
$933$		0			0
$934$		−	113.995i		−	0.122050i
$935$	9.42197	−	16.3193i	0.0100770	−	0.0174538i
$936$		0			0
$937$		−	1198.08i		−	1.27863i	−0.768944	−	0.639316i	$-0.779217\pi$
$937$		−	1198.08i		−	1.27863i	0.768944	−	0.639316i	$-0.220783\pi$
$938$	−246.057	−	219.798i	−0.262321	−	0.234326i
$939$		0			0
$940$	−1110.65			−1.18154
$941$	671.665	−	387.786i	0.713778	−	0.412100i	−0.0986805	−	0.995119i	$-0.531462\pi$
$941$	671.665	−	387.786i	0.713778	−	0.412100i	0.812458	+	0.583019i	$0.198129\pi$
$942$		0			0
$943$	22.2519	+	12.8472i	0.0235969	+	0.0136237i
$944$		−	899.952i		−	0.953339i
$945$		0			0
$946$	−1.98758			−0.00210104
$947$	−424.142	+	734.636i	−0.447880	+	0.775751i	−0.998248	−	0.0591714i	$-0.981154\pi$
$947$	−424.142	+	734.636i	−0.447880	+	0.775751i	0.550368	+	0.834922i	$0.314487\pi$
$948$		0			0
$949$	32.6340	+	56.5237i	0.0343878	+	0.0595614i
$950$		−	78.1581i		−	0.0822717i
$951$		0			0
$952$	240.169	+	729.351i	0.252278	+	0.766125i
$953$	846.104			0.887832			0.443916	−	0.896068i	$-0.353589\pi$
$953$	846.104			0.887832			0.443916	+	0.896068i	$0.353589\pi$
$954$		0			0
$955$	1098.19	+	634.040i	1.14994	+	0.663916i
$956$	−498.349			−0.521286
$957$		0			0
$958$	−211.017	−	121.831i	−0.220268	−	0.127172i
$959$	−103.668	−	92.6043i	−0.108100	−	0.0965634i
$960$		0			0
$961$	−449.437	+	778.447i	−0.467676	+	0.810039i
$962$	12.0427	+	6.95285i	0.0125184	+	0.00722749i
$963$		0			0
$964$	855.572	−	493.965i	0.887523	−	0.512411i
$965$	834.568	−	481.838i	0.864837	−	0.499314i
$966$		0			0
$967$	84.2016	−	145.842i	0.0870751	−	0.150819i	−0.819198	−	0.573510i	$-0.805581\pi$
$967$	84.2016	−	145.842i	0.0870751	−	0.150819i	0.906274	+	0.422692i	$0.138915\pi$
$968$	−429.109			−0.443294
$969$		0			0
$970$	−161.645			−0.166644
$971$	891.382	−	514.639i	0.918004	−	0.530010i	0.0350061	−	0.999387i	$-0.488855\pi$
$971$	891.382	−	514.639i	0.918004	−	0.530010i	0.882998	+	0.469377i	$0.155522\pi$
$972$		0			0
$973$	95.4649	+	289.910i	0.0981140	+	0.297955i
$974$	166.902	+	289.083i	0.171358	+	0.296800i
$975$		0			0
$976$	487.073	−	281.212i	0.499050	−	0.288127i
$977$	486.819	+	843.195i	0.498279	+	0.863045i	0.999998	−	0.00198578i	$-0.000632094\pi$
$977$	486.819	+	843.195i	0.498279	+	0.863045i	−0.501719	+	0.865031i	$0.667299\pi$
$978$		0			0
$979$	4.62020	−	2.66748i	0.00471931	−	0.00272469i
$980$	482.639	+	653.382i	0.492489	+	0.666716i
$981$		0			0
$982$	−31.5926	−	54.7201i	−0.0321717	−	0.0557231i
$983$		−	612.589i		−	0.623183i	−0.950216	−	0.311591i	$-0.899138\pi$
$983$		−	612.589i		−	0.623183i	0.950216	−	0.311591i	$-0.100862\pi$
$984$		0			0
$985$			517.631i			0.525514i
$986$	−177.669	−	102.577i	−0.180191	−	0.104034i
$987$		0			0
$988$	−109.113	−	188.989i	−0.110438	−	0.191284i
$989$	466.414	+	807.853i	0.471602	+	0.816839i
$990$		0			0
$991$	102.781	−	178.022i	0.103714	−	0.179639i	−0.809498	−	0.587123i	$-0.800261\pi$
$991$	102.781	−	178.022i	0.103714	−	0.179639i	0.913212	+	0.407484i	$0.133594\pi$
$992$	−138.966	−	80.2318i	−0.140086	−	0.0808788i
$993$		0			0
$994$	−261.663	+	86.1634i	−0.263243	+	0.0866835i
$995$	−383.963	+	665.043i	−0.385892	+	0.668385i
$996$		0			0
$997$			227.691i			0.228376i	0.993459	+	0.114188i	$0.0364266\pi$
$997$			227.691i			0.228376i	−0.993459	+	0.114188i	$0.963573\pi$
$998$	−21.8154	+	37.7853i	−0.0218591	+	0.0378610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.9		28
3.2	odd	2		63.3.k.a.31.6	✓	28
7.5	odd	6		189.3.t.a.145.6		28
9.2	odd	6		63.3.t.a.52.9	yes	28
9.7	even	3		189.3.t.a.73.6		28
21.2	odd	6		441.3.t.a.166.9		28
21.5	even	6		63.3.t.a.40.9	yes	28
21.11	odd	6		441.3.l.a.391.6		28
21.17	even	6		441.3.l.b.391.6		28
21.20	even	2		441.3.k.b.31.6		28
63.2	odd	6		441.3.k.b.313.6		28
63.11	odd	6		441.3.l.b.97.6		28
63.20	even	6		441.3.t.a.178.9		28
63.38	even	6		441.3.l.a.97.6		28
63.47	even	6		63.3.k.a.61.6	yes	28
63.61	odd	6	inner	189.3.k.a.19.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.6	✓	28	3.2	odd	2
63.3.k.a.61.6	yes	28	63.47	even	6
63.3.t.a.40.9	yes	28	21.5	even	6
63.3.t.a.52.9	yes	28	9.2	odd	6
189.3.k.a.10.9		28	1.1	even	1	trivial
189.3.k.a.19.9		28	63.61	odd	6	inner
189.3.t.a.73.6		28	9.7	even	3
189.3.t.a.145.6		28	7.5	odd	6
441.3.k.b.31.6		28	21.20	even	2
441.3.k.b.313.6		28	63.2	odd	6
441.3.l.a.97.6		28	63.38	even	6
441.3.l.a.391.6		28	21.11	odd	6
441.3.l.b.97.6		28	63.11	odd	6
441.3.l.b.391.6		28	21.17	even	6
441.3.t.a.166.9		28	21.2	odd	6
441.3.t.a.178.9		28	63.20	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.227576 - 0.394173i) q^{2} +(1.89642 + 3.28469i) q^{4} -4.37081i q^{5} +(5.22047 + 4.66334i) q^{7} +3.54692 q^{8} +O(q^{10})\)	\(q+(0.227576 - 0.394173i) q^{2} +(1.89642 + 3.28469i) q^{4} -4.37081i q^{5} +(5.22047 + 4.66334i) q^{7} +3.54692 q^{8} +(-1.72285 - 0.994690i) q^{10} +0.139402 q^{11} +(-1.71085 - 0.987760i) q^{13} +(3.02621 - 0.996505i) q^{14} +(-6.77848 + 11.7407i) q^{16} +(26.7838 + 15.4636i) q^{17} +(25.2226 - 14.5623i) q^{19} +(14.3568 - 8.28888i) q^{20} +(0.0317245 - 0.0549484i) q^{22} -29.7784 q^{23} +5.89602 q^{25} +(-0.778697 + 0.449581i) q^{26} +(-5.41743 + 25.9913i) q^{28} +(-7.28707 - 12.6216i) q^{29} +(-6.82604 + 3.94101i) q^{31} +(10.1791 + 17.6307i) q^{32} +(12.1907 - 7.03829i) q^{34} +(20.3826 - 22.8177i) q^{35} +(-7.73259 - 13.3932i) q^{37} -13.2561i q^{38} -15.5029i q^{40} +(-0.747251 - 0.431426i) q^{41} +(-15.6629 - 27.1289i) q^{43} +(0.264364 + 0.457892i) q^{44} +(-6.77684 + 11.7378i) q^{46} +(-58.0205 - 33.4982i) q^{47} +(5.50659 + 48.6896i) q^{49} +(1.34179 - 2.32405i) q^{50} -7.49283i q^{52} +(-16.9285 + 29.3211i) q^{53} -0.609299i q^{55} +(18.5166 + 16.5405i) q^{56} -6.63345 q^{58} +(-57.4894 + 33.1915i) q^{59} +(-35.9279 - 20.7430i) q^{61} +3.58752i q^{62} -44.9618 q^{64} +(-4.31731 + 7.47781i) q^{65} +(-51.7774 - 89.6812i) q^{67} +117.302i q^{68} +(-4.35553 - 13.2270i) q^{70} -86.4656 q^{71} +(-28.6121 - 16.5192i) q^{73} -7.03900 q^{74} +(95.6652 + 55.2323i) q^{76} +(0.727743 + 0.650077i) q^{77} +(-24.3232 + 42.1291i) q^{79} +(51.3162 + 29.6275i) q^{80} +(-0.340113 + 0.196364i) q^{82} +(102.894 - 59.4058i) q^{83} +(67.5886 - 117.067i) q^{85} -14.2579 q^{86} +0.494447 q^{88} +(33.1431 - 19.1352i) q^{89} +(-4.32519 - 13.1348i) q^{91} +(-56.4723 - 97.8128i) q^{92} +(-26.4081 + 15.2467i) q^{94} +(-63.6489 - 110.243i) q^{95} +(70.3678 - 40.6269i) q^{97} +(20.4453 + 8.91002i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Introduction

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