LMFDB - Embedded newform 189.4.s.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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([5, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725355 - 0.418784i) q^{2} +(-3.64924 - 6.32067i) q^{4} +21.9169 q^{5} +(2.19637 + 18.3896i) q^{7} +12.8135i q^{8} +O(q^{10})$	\(q+(-0.725355 - 0.418784i) q^{2} +(-3.64924 - 6.32067i) q^{4} +21.9169 q^{5} +(2.19637 + 18.3896i) q^{7} +12.8135i q^{8} +(-15.8975 - 9.17842i) q^{10} +15.4606i q^{11} +(33.3594 + 19.2600i) q^{13} +(6.10810 - 14.2588i) q^{14} +(-23.8278 + 41.2710i) q^{16} +(34.8682 - 60.3936i) q^{17} +(-55.4679 + 32.0244i) q^{19} +(-79.9799 - 138.529i) q^{20} +(6.47465 - 11.2144i) q^{22} +69.8230i q^{23} +355.349 q^{25} +(-16.1316 - 27.9407i) q^{26} +(108.219 - 80.9905i) q^{28} +(168.609 - 97.3466i) q^{29} +(68.0764 - 39.3039i) q^{31} +(123.342 - 71.2115i) q^{32} +(-50.5837 + 29.2045i) q^{34} +(48.1376 + 403.041i) q^{35} +(3.34533 + 5.79428i) q^{37} +53.6452 q^{38} +280.832i q^{40} +(-9.21172 + 15.9552i) q^{41} +(-12.2255 - 21.1752i) q^{43} +(97.7214 - 56.4195i) q^{44} +(29.2407 - 50.6465i) q^{46} +(138.270 - 239.491i) q^{47} +(-333.352 + 80.7806i) q^{49} +(-257.754 - 148.814i) q^{50} -281.138i q^{52} +(95.3706 + 55.0622i) q^{53} +338.848i q^{55} +(-235.635 + 28.1432i) q^{56} -163.069 q^{58} +(-176.782 - 306.196i) q^{59} +(-460.697 - 265.983i) q^{61} -65.8393 q^{62} +261.957 q^{64} +(731.132 + 422.120i) q^{65} +(-262.021 - 453.834i) q^{67} -508.970 q^{68} +(133.870 - 312.507i) q^{70} +43.3150i q^{71} +(54.9811 + 31.7433i) q^{73} -5.60388i q^{74} +(404.831 + 233.729i) q^{76} +(-284.314 + 33.9572i) q^{77} +(-606.173 + 1049.92i) q^{79} +(-522.231 + 904.531i) q^{80} +(13.3635 - 7.71543i) q^{82} +(-111.327 - 192.824i) q^{83} +(764.202 - 1323.64i) q^{85} +20.4793i q^{86} -198.105 q^{88} +(35.2649 + 61.0806i) q^{89} +(-280.914 + 655.766i) q^{91} +(441.328 - 254.801i) q^{92} +(-200.590 + 115.811i) q^{94} +(-1215.68 + 701.874i) q^{95} +(483.359 - 279.067i) q^{97} +(275.628 + 81.0077i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.725355	−	0.418784i	−0.256452	−	0.148062i	0.366263	−	0.930511i	$-0.380637\pi$
$2$	−0.725355	−	0.418784i	−0.256452	−	0.148062i	−0.622715	+	0.782449i	$0.713970\pi$
$3$		0			0
$3$		0			0
$4$	−3.64924	−	6.32067i	−0.456155	−	0.790084i
$5$	21.9169			1.96030			0.980152	−	0.198249i	$-0.0635254\pi$
$5$	21.9169			1.96030			0.980152	+	0.198249i	$0.0635254\pi$
$6$		0			0
$7$	2.19637	+	18.3896i	0.118593	+	0.992943i
$7$	2.19637	+	18.3896i	0.118593	+	0.992943i
$8$			12.8135i			0.566282i
$9$		0			0
$10$	−15.8975	−	9.17842i	−0.502723	−	0.290247i
$11$			15.4606i			0.423777i	0.977294	+	0.211889i	$0.0679614\pi$
$11$			15.4606i			0.423777i	−0.977294	+	0.211889i	$0.932039\pi$
$12$		0			0
$13$	33.3594	+	19.2600i	0.711709	+	0.410906i	0.811694	−	0.584083i	$-0.198546\pi$
$13$	33.3594	+	19.2600i	0.711709	+	0.410906i	−0.0999842	+	0.994989i	$0.531879\pi$
$14$	6.10810	−	14.2588i	0.116604	−	0.272201i
$15$		0			0
$16$	−23.8278	+	41.2710i	−0.372310	+	0.644860i
$17$	34.8682	−	60.3936i	0.497458	−	0.861623i	−0.502537	−	0.864555i	$-0.667600\pi$
$17$	34.8682	−	60.3936i	0.497458	−	0.861623i	0.999996	+	0.00293248i	$0.000933438\pi$
$18$		0			0
$19$	−55.4679	+	32.0244i	−0.669748	+	0.386679i	−0.795981	−	0.605322i	$-0.793045\pi$
$19$	−55.4679	+	32.0244i	−0.669748	+	0.386679i	0.126233	+	0.992001i	$0.459711\pi$
$20$	−79.9799	−	138.529i	−0.894202	−	1.54880i
$21$		0			0
$22$	6.47465	−	11.2144i	0.0627455	−	0.108678i
$23$			69.8230i			0.633005i	0.948592	+	0.316502i	$0.102509\pi$
$23$			69.8230i			0.633005i	−0.948592	+	0.316502i	$0.897491\pi$
$24$		0			0
$25$	355.349			2.84279
$26$	−16.1316	−	27.9407i	−0.121679	−	0.210755i
$27$		0			0
$28$	108.219	−	80.9905i	0.730411	−	0.546634i
$29$	168.609	−	97.3466i	1.07965	−	0.623338i	0.148851	−	0.988860i	$-0.452443\pi$
$29$	168.609	−	97.3466i	1.07965	−	0.623338i	0.930803	+	0.365521i	$0.119109\pi$
$30$		0			0
$31$	68.0764	−	39.3039i	0.394415	−	0.227716i	−0.289656	−	0.957131i	$-0.593541\pi$
$31$	68.0764	−	39.3039i	0.394415	−	0.227716i	0.684071	+	0.729415i	$0.260208\pi$
$32$	123.342	−	71.2115i	0.681374	−	0.393391i
$33$		0			0
$34$	−50.5837	+	29.2045i	−0.255148	+	0.147310i
$35$	48.1376	+	403.041i	0.232478	+	1.94647i
$36$		0			0
$37$	3.34533	+	5.79428i	0.0148640	+	0.0257453i	0.873362	−	0.487072i	$-0.161935\pi$
$37$	3.34533	+	5.79428i	0.0148640	+	0.0257453i	−0.858498	+	0.512817i	$0.828602\pi$
$38$	53.6452			0.229010
$39$		0			0
$40$			280.832i			1.11009i
$41$	−9.21172	+	15.9552i	−0.0350885	+	0.0607751i	−0.883036	−	0.469305i	$-0.844505\pi$
$41$	−9.21172	+	15.9552i	−0.0350885	+	0.0607751i	0.847948	+	0.530080i	$0.177838\pi$
$42$		0			0
$43$	−12.2255	−	21.1752i	−0.0433574	−	0.0750973i	0.843532	−	0.537078i	$-0.180472\pi$
$43$	−12.2255	−	21.1752i	−0.0433574	−	0.0750973i	−0.886890	+	0.461981i	$0.847139\pi$
$44$	97.7214	−	56.4195i	0.334819	−	0.193308i
$45$		0			0
$46$	29.2407	−	50.6465i	0.0937242	−	0.162335i
$47$	138.270	−	239.491i	0.429124	−	0.743264i	−0.567672	−	0.823255i	$-0.692156\pi$
$47$	138.270	−	239.491i	0.429124	−	0.743264i	0.996796	+	0.0799909i	$0.0254891\pi$
$48$		0			0
$49$	−333.352	+	80.7806i	−0.971871	+	0.235512i
$50$	−257.754	−	148.814i	−0.729038	−	0.420910i
$51$		0			0
$52$		−	281.138i		−	0.749747i
$53$	95.3706	+	55.0622i	0.247173	+	0.142705i	0.618469	−	0.785809i	$-0.287753\pi$
$53$	95.3706	+	55.0622i	0.247173	+	0.142705i	−0.371296	+	0.928514i	$0.621087\pi$
$54$		0			0
$55$			338.848i			0.830732i
$56$	−235.635	+	28.1432i	−0.562286	+	0.0671571i
$57$		0			0
$58$	−163.069			−0.369172
$59$	−176.782	−	306.196i	−0.390086	−	0.675649i	0.602374	−	0.798214i	$-0.294221\pi$
$59$	−176.782	−	306.196i	−0.390086	−	0.675649i	−0.992461	+	0.122565i	$0.960888\pi$
$60$		0			0
$61$	−460.697	−	265.983i	−0.966986	−	0.558290i	−0.0686701	−	0.997639i	$-0.521876\pi$
$61$	−460.697	−	265.983i	−0.966986	−	0.558290i	−0.898316	+	0.439350i	$0.855209\pi$
$62$	−65.8393			−0.134865
$63$		0			0
$64$	261.957			0.511634
$65$	731.132	+	422.120i	1.39517	+	0.805500i
$66$		0			0
$67$	−262.021	−	453.834i	−0.477776	−	0.827532i	0.521899	−	0.853007i	$-0.325224\pi$
$67$	−262.021	−	453.834i	−0.477776	−	0.827532i	−0.999675	+	0.0254747i	$0.991890\pi$
$68$	−508.970			−0.907672
$69$		0			0
$70$	133.870	−	312.507i	0.228580	−	0.533596i
$71$			43.3150i			0.0724020i	0.999345	+	0.0362010i	$0.0115256\pi$
$71$			43.3150i			0.0724020i	−0.999345	+	0.0362010i	$0.988474\pi$
$72$		0			0
$73$	54.9811	+	31.7433i	0.0881513	+	0.0508942i	0.543428	−	0.839456i	$-0.317126\pi$
$73$	54.9811	+	31.7433i	0.0881513	+	0.0508942i	−0.455276	+	0.890350i	$0.650460\pi$
$74$		−	5.60388i		−	0.00880322i
$75$		0			0
$76$	404.831	+	233.729i	0.611018	+	0.352771i
$77$	−284.314	+	33.9572i	−0.420787	+	0.0502570i
$78$		0			0
$79$	−606.173	+	1049.92i	−0.863289	+	1.49526i	0.00544698	+	0.999985i	$0.498266\pi$
$79$	−606.173	+	1049.92i	−0.863289	+	1.49526i	−0.868736	+	0.495275i	$0.835067\pi$
$80$	−522.231	+	904.531i	−0.729840	+	1.26412i
$81$		0			0
$82$	13.3635	−	7.71543i	0.0179970	−	0.0103906i
$83$	−111.327	−	192.824i	−0.147226	−	0.255003i	0.782975	−	0.622053i	$-0.213701\pi$
$83$	−111.327	−	192.824i	−0.147226	−	0.255003i	−0.930201	+	0.367050i	$0.880368\pi$
$84$		0			0
$85$	764.202	−	1323.64i	0.975169	−	1.68904i
$86$			20.4793i			0.0256784i
$87$		0			0
$88$	−198.105			−0.239978
$89$	35.2649	+	61.0806i	0.0420008	+	0.0727475i	0.886262	−	0.463185i	$-0.153293\pi$
$89$	35.2649	+	61.0806i	0.0420008	+	0.0727475i	−0.844261	+	0.535933i	$0.819960\pi$
$90$		0			0
$91$	−280.914	+	655.766i	−0.323602	+	0.755417i
$92$	441.328	−	254.801i	0.500127	−	0.288748i
$93$		0			0
$94$	−200.590	+	115.811i	−0.220099	+	0.127074i
$95$	−1215.68	+	701.874i	−1.31291	+	0.758008i
$96$		0			0
$97$	483.359	−	279.067i	0.505955	−	0.292114i	−0.225214	−	0.974309i	$-0.572308\pi$
$97$	483.359	−	279.067i	0.505955	−	0.292114i	0.731170	+	0.682196i	$0.238975\pi$
$98$	275.628	+	81.0077i	0.284108	+	0.0835002i
$99$		0			0
$100$	−1296.75	−	2246.04i	−1.29675	−	2.24604i
$101$	−734.157			−0.723281			−0.361641	−	0.932318i	$-0.617783\pi$
$101$	−734.157			−0.723281			−0.361641	+	0.932318i	$0.617783\pi$
$102$		0			0
$103$			748.708i			0.716237i	0.933676	+	0.358119i	$0.116582\pi$
$103$			748.708i			0.716237i	−0.933676	+	0.358119i	$0.883418\pi$
$104$	−246.789	+	427.451i	−0.232689	+	0.403029i
$105$		0			0
$106$	−46.1183	−	79.8793i	−0.0422586	−	0.0731940i
$107$	−682.104	+	393.813i	−0.616276	+	0.355807i	−0.775418	−	0.631449i	$-0.782461\pi$
$107$	−682.104	+	393.813i	−0.616276	+	0.355807i	0.159142	+	0.987256i	$0.449127\pi$
$108$		0			0
$109$	−798.482	+	1383.01i	−0.701658	+	1.21531i	0.266227	+	0.963910i	$0.414223\pi$
$109$	−798.482	+	1383.01i	−0.701658	+	1.21531i	−0.967884	+	0.251396i	$0.919110\pi$
$110$	141.904	−	245.785i	0.123000	−	0.213042i
$111$		0			0
$112$	−811.291	−	347.537i	−0.684462	−	0.293207i
$113$	−1648.59	−	951.814i	−1.37245	−	0.792382i	−0.381210	−	0.924489i	$-0.624492\pi$
$113$	−1648.59	−	951.814i	−1.37245	−	0.792382i	−0.991235	+	0.132107i	$0.957826\pi$
$114$		0			0
$115$			1530.30i			1.24088i
$116$	−1230.59	−	710.482i	−0.984979	−	0.568678i
$117$		0			0
$118$			296.134i			0.231028i
$119$	1187.19	+	508.565i	0.914537	+	0.391765i
$120$		0			0
$121$	1091.97			0.820413
$122$	222.779	+	385.864i	0.165323	+	0.286349i
$123$		0			0
$124$	−496.854	−	286.859i	−0.359829	−	0.207747i
$125$	5048.52			3.61243
$126$		0			0
$127$	141.535			0.0988916			0.0494458	−	0.998777i	$-0.484254\pi$
$127$	141.535			0.0988916			0.0494458	+	0.998777i	$0.484254\pi$
$128$	−1176.75	−	679.395i	−0.812583	−	0.469145i
$129$		0			0
$130$	−353.554	−	612.373i	−0.238528	−	0.413143i
$131$	1136.92			0.758270			0.379135	−	0.925341i	$-0.376222\pi$
$131$	1136.92			0.758270			0.379135	+	0.925341i	$0.376222\pi$
$132$		0			0
$133$	−710.743	−	949.693i	−0.463378	−	0.619164i
$134$			438.921i			0.282963i
$135$		0			0
$136$	773.853	+	446.785i	0.487922	+	0.281702i
$137$		−	872.712i		−	0.544240i	−0.962263	−	0.272120i	$-0.912275\pi$
$137$		−	872.712i		−	0.544240i	0.962263	−	0.272120i	$-0.0877247\pi$
$138$		0			0
$139$	920.123	+	531.233i	0.561466	+	0.324163i	0.753734	−	0.657180i	$-0.228251\pi$
$139$	920.123	+	531.233i	0.561466	+	0.324163i	−0.192268	+	0.981343i	$0.561584\pi$
$140$	2371.83	−	1775.06i	1.43183	−	1.07157i
$141$		0			0
$142$	18.1396	−	31.4187i	0.0107200	−	0.0185676i
$143$	−297.772	+	515.756i	−0.174132	+	0.301606i
$144$		0			0
$145$	3695.39	−	2133.53i	2.11645	−	1.22193i
$146$	−26.5872	−	46.0504i	−0.0150710	−	0.0261038i
$147$		0			0
$148$	24.4158	−	42.2895i	0.0135606	−	0.0234877i
$149$			2426.93i			1.33437i	0.744890	+	0.667187i	$0.232502\pi$
$149$			2426.93i			1.33437i	−0.744890	+	0.667187i	$0.767498\pi$
$150$		0			0
$151$	667.648			0.359817			0.179909	−	0.983683i	$-0.442420\pi$
$151$	667.648			0.359817			0.179909	+	0.983683i	$0.442420\pi$
$152$	−410.345	−	710.738i	−0.218970	−	0.379266i
$153$		0			0
$154$	220.449	+	94.4349i	0.115353	+	0.0494142i
$155$	1492.02	−	861.418i	0.773174	−	0.446392i
$156$		0			0
$157$	−1937.34	+	1118.52i	−0.984818	+	0.568585i	−0.903721	−	0.428121i	$-0.859176\pi$
$157$	−1937.34	+	1118.52i	−0.984818	+	0.568585i	−0.0810967	+	0.996706i	$0.525842\pi$
$158$	879.381	−	507.711i	0.442784	−	0.255641i
$159$		0			0
$160$	2703.27	−	1560.73i	1.33570	−	0.771167i
$161$	−1284.01	+	153.357i	−0.628538	+	0.0750699i
$162$		0			0
$163$	−405.745	−	702.771i	−0.194972	−	0.337701i	0.751919	−	0.659255i	$-0.229128\pi$
$163$	−405.745	−	702.771i	−0.194972	−	0.337701i	−0.946891	+	0.321554i	$0.895795\pi$
$164$	134.463			0.0640232
$165$		0			0
$166$			186.488i			0.0871944i
$167$	927.945	−	1607.25i	0.429979	−	0.744746i	−0.566892	−	0.823792i	$-0.691854\pi$
$167$	927.945	−	1607.25i	0.429979	−	0.744746i	0.996871	+	0.0790465i	$0.0251876\pi$
$168$		0			0
$169$	−356.602	−	617.652i	−0.162313	−	0.281134i
$170$	−1108.64	+	640.071i	−0.500167	+	0.288772i
$171$		0			0
$172$	−89.2275	+	154.547i	−0.0395554	+	0.0685120i
$173$	−290.151	+	502.557i	−0.127513	+	0.220859i	−0.922713	−	0.385489i	$-0.874033\pi$
$173$	−290.151	+	502.557i	−0.127513	+	0.220859i	0.795199	+	0.606348i	$0.207366\pi$
$174$		0			0
$175$	780.478	+	6534.71i	0.337135	+	2.82273i
$176$	−638.075	−	368.393i	−0.273277	−	0.157776i
$177$		0			0
$178$		−	59.0735i		−	0.0248750i
$179$	23.5912	+	13.6204i	0.00985077	+	0.00568735i	0.504917	−	0.863168i	$-0.331523\pi$
$179$	23.5912	+	13.6204i	0.00985077	+	0.00568735i	−0.495067	+	0.868855i	$0.664856\pi$
$180$		0			0
$181$			2680.82i			1.10090i	0.834867	+	0.550452i	$0.185545\pi$
$181$			2680.82i			1.10090i	−0.834867	+	0.550452i	$0.814455\pi$
$182$	478.387	−	358.021i	0.194837	−	0.145815i
$183$		0			0
$184$	−894.678			−0.358459
$185$	73.3192	+	126.993i	0.0291380	+	0.0504685i
$186$		0			0
$187$	933.721	+	539.084i	0.365136	+	0.210811i
$188$	−2018.33			−0.782988
$189$		0			0
$190$	1175.73			0.448930
$191$	−3219.66	−	1858.87i	−1.21972	−	0.704206i	−0.254863	−	0.966977i	$-0.582030\pi$
$191$	−3219.66	−	1858.87i	−1.21972	−	0.704206i	−0.964858	+	0.262771i	$0.915364\pi$
$192$		0			0
$193$	−858.493	−	1486.95i	−0.320185	−	0.554577i	0.660341	−	0.750966i	$-0.270412\pi$
$193$	−858.493	−	1486.95i	−0.320185	−	0.554577i	−0.980526	+	0.196389i	$0.937078\pi$
$194$	−467.476			−0.173004
$195$		0			0
$196$	1727.07	+	1812.22i	0.629398	+	0.660430i
$197$		−	2991.54i		−	1.08192i	−0.841048	−	0.540961i	$-0.818061\pi$
$197$		−	2991.54i		−	1.08192i	0.841048	−	0.540961i	$-0.181939\pi$
$198$		0			0
$199$	−4369.83	−	2522.93i	−1.55663	−	0.898721i	−0.997576	−	0.0695896i	$-0.977831\pi$
$199$	−4369.83	−	2522.93i	−1.55663	−	0.898721i	−0.559054	−	0.829131i	$-0.688836\pi$
$200$			4553.26i			1.60982i
$201$		0			0
$202$	532.524	+	307.453i	0.185487	+	0.107091i
$203$	2160.49	+	2886.84i	0.746979	+	0.998111i
$204$		0			0
$205$	−201.892	+	349.687i	−0.0687841	+	0.119138i
$206$	313.547	−	543.079i	0.106048	−	0.183680i
$207$		0			0
$208$	−1589.76	+	917.850i	−0.529953	+	0.305968i
$209$	−495.117	−	857.567i	−0.163866	−	0.283824i
$210$		0			0
$211$	2012.27	−	3485.36i	0.656543	−	1.13717i	−0.324962	−	0.945727i	$-0.605352\pi$
$211$	2012.27	−	3485.36i	0.656543	−	1.13717i	0.981505	−	0.191438i	$-0.0613151\pi$
$212$		−	803.741i		−	0.260383i
$213$		0			0
$214$	659.690			0.210726
$215$	−267.944	−	464.093i	−0.0849937	−	0.147213i
$216$		0			0
$217$	872.303	+	1165.57i	0.272884	+	0.364626i
$218$	1158.36	−	668.782i	0.359882	−	0.207778i
$219$		0			0
$220$	2141.75	−	1236.54i	0.656348	−	0.378943i
$221$	2326.36	−	1343.13i	0.708092	−	0.408817i
$222$		0			0
$223$	−3886.54	+	2243.90i	−1.16709	+	0.673822i	−0.952994	−	0.302989i	$-0.902015\pi$
$223$	−3886.54	+	2243.90i	−1.16709	+	0.673822i	−0.214101	+	0.976812i	$0.568682\pi$
$224$	1580.45	+	2111.80i	0.471421	+	0.629912i
$225$		0			0
$226$	797.208	+	1380.81i	0.234644	+	0.406415i
$227$	5451.53			1.59397			0.796984	−	0.604000i	$-0.206427\pi$
$227$	5451.53			1.59397			0.796984	+	0.604000i	$0.206427\pi$
$228$		0			0
$229$		−	6015.51i		−	1.73588i	−0.496670	−	0.867940i	$-0.665444\pi$
$229$		−	6015.51i		−	1.73588i	0.496670	−	0.867940i	$-0.334556\pi$
$230$	640.865	−	1110.01i	0.183728	−	0.318226i
$231$		0			0
$232$	1247.35	+	2160.48i	0.352986	+	0.611389i
$233$	−2153.30	+	1243.21i	−0.605440	+	0.349551i	−0.771179	−	0.636619i	$-0.780333\pi$
$233$	−2153.30	+	1243.21i	−0.605440	+	0.349551i	0.165739	+	0.986170i	$0.446999\pi$
$234$		0			0
$235$	3030.45	−	5248.90i	0.841213	−	1.45702i
$236$	−1290.24	+	2234.76i	−0.355879	+	0.616401i
$237$		0			0
$238$	−648.159	−	866.068i	−0.176529	−	0.235877i
$239$	−1860.18	−	1073.98i	−0.503453	−	0.290669i	0.226685	−	0.973968i	$-0.427211\pi$
$239$	−1860.18	−	1073.98i	−0.503453	−	0.290669i	−0.730138	+	0.683299i	$0.760544\pi$
$240$		0			0
$241$		−	3019.11i		−	0.806961i	−0.914988	−	0.403481i	$-0.867800\pi$
$241$		−	3019.11i		−	0.806961i	0.914988	−	0.403481i	$-0.132200\pi$
$242$	−792.065	−	457.299i	−0.210396	−	0.121472i
$243$		0			0
$244$			3882.55i			1.01867i
$245$	−7306.03	+	1770.46i	−1.90516	+	0.461675i
$246$		0			0
$247$	−2467.16			−0.635554
$248$	503.621	+	872.297i	0.128951	+	0.223350i
$249$		0			0
$250$	−3661.97	−	2114.24i	−0.926413	−	0.534865i
$251$	4007.26			1.00771			0.503856	−	0.863788i	$-0.331914\pi$
$251$	4007.26			1.00771			0.503856	+	0.863788i	$0.331914\pi$
$252$		0			0
$253$	−1079.51			−0.268253
$254$	−102.663	−	59.2727i	−0.0253609	−	0.0146421i
$255$		0			0
$256$	−478.787	−	829.284i	−0.116891	−	0.202462i
$257$	−2856.75			−0.693383			−0.346692	−	0.937979i	$-0.612695\pi$
$257$	−2856.75			−0.693383			−0.346692	+	0.937979i	$0.612695\pi$
$258$		0			0
$259$	−99.2068	+	74.2456i	−0.0238008	+	0.0178123i
$260$		−	6161.66i		−	1.46973i
$261$		0			0
$262$	−824.672	−	476.124i	−0.194460	−	0.112271i
$263$			2104.93i			0.493520i	0.969077	+	0.246760i	$0.0793659\pi$
$263$			2104.93i			0.493520i	−0.969077	+	0.246760i	$0.920634\pi$
$264$		0			0
$265$	2090.22	+	1206.79i	0.484534	+	0.279746i
$266$	117.825	+	986.511i	0.0271590	+	0.227394i
$267$		0			0
$268$	−1912.36	+	3312.30i	−0.435880	+	0.754966i
$269$	1624.71	−	2814.07i	0.368253	−	0.637833i	−0.621039	−	0.783779i	$-0.713289\pi$
$269$	1624.71	−	2814.07i	0.368253	−	0.637833i	0.989293	+	0.145946i	$0.0466227\pi$
$270$		0			0
$271$	−5975.60	+	3450.02i	−1.33945	+	0.773334i	−0.986726	−	0.162392i	$-0.948079\pi$
$271$	−5975.60	+	3450.02i	−1.33945	+	0.773334i	−0.352728	+	0.935726i	$0.614746\pi$
$272$	1661.67	+	2878.10i	0.370417	+	0.641582i
$273$		0			0
$274$	−365.478	+	633.026i	−0.0805814	+	0.139571i
$275$			5493.91i			1.20471i
$276$		0			0
$277$	−531.341			−0.115253			−0.0576267	−	0.998338i	$-0.518353\pi$
$277$	−531.341			−0.115253			−0.0576267	+	0.998338i	$0.518353\pi$
$278$	−444.944	−	770.665i	−0.0959926	−	0.166264i
$279$		0			0
$280$	−5164.37	+	616.811i	−1.10225	+	0.131648i
$281$	−4234.76	+	2444.94i	−0.899020	+	0.519049i	−0.876882	−	0.480705i	$-0.840381\pi$
$281$	−4234.76	+	2444.94i	−0.899020	+	0.519049i	−0.0221380	+	0.999755i	$0.507047\pi$
$282$		0			0
$283$	−3948.09	+	2279.43i	−0.829291	+	0.478792i	−0.853610	−	0.520913i	$-0.825592\pi$
$283$	−3948.09	+	2279.43i	−0.829291	+	0.478792i	0.0243187	+	0.999704i	$0.492258\pi$
$284$	273.780	−	158.067i	0.0572036	−	0.0330265i
$285$		0			0
$286$	431.980	−	249.404i	0.0893131	−	0.0515649i
$287$	−313.641	−	134.356i	−0.0645074	−	0.0276334i
$288$		0			0
$289$	24.9118	+	43.1484i	0.00507058	+	0.00878250i
$290$	−3573.95			−0.723689
$291$		0			0
$292$		−	463.356i		−	0.0928626i
$293$	−2199.14	+	3809.02i	−0.438482	+	0.759473i	−0.997573	−	0.0696337i	$-0.977817\pi$
$293$	−2199.14	+	3809.02i	−0.438482	+	0.759473i	0.559091	+	0.829106i	$0.311150\pi$
$294$		0			0
$295$	−3874.51	−	6710.85i	−0.764687	−	1.32448i
$296$	−74.2451	+	42.8654i	−0.0145791	+	0.00841724i
$297$		0			0
$298$	1016.36	−	1760.38i	0.197571	−	0.342203i
$299$	−1344.79	+	2329.25i	−0.260105	+	0.450515i
$300$		0			0
$301$	362.550	−	271.330i	0.0694254	−	0.0519575i
$302$	−484.282	−	279.600i	−0.0922757	−	0.0532754i
$303$		0			0
$304$		−	3052.29i		−	0.575858i
$305$	−10097.0	−	5829.52i	−1.89559	−	1.09442i
$306$		0			0
$307$		−	5046.53i		−	0.938179i	−0.883151	−	0.469089i	$-0.844582\pi$
$307$		−	5046.53i		−	0.938179i	0.883151	−	0.469089i	$-0.155418\pi$
$308$	1252.16	+	1673.14i	0.231651	+	0.309532i
$309$		0			0
$310$	−1442.99			−0.264376
$311$	−1016.19	−	1760.10i	−0.185283	−	0.320920i	0.758389	−	0.651803i	$-0.225987\pi$
$311$	−1016.19	−	1760.10i	−0.185283	−	0.320920i	−0.943672	+	0.330883i	$0.892654\pi$
$312$		0			0
$313$	7783.59	+	4493.86i	1.40561	+	0.811527i	0.994960	−	0.100269i	$-0.0319702\pi$
$313$	7783.59	+	4493.86i	1.40561	+	0.811527i	0.410645	+	0.911795i	$0.365304\pi$
$314$	1873.68			0.336744
$315$		0			0
$316$	8848.29			1.57517
$317$	2476.58	+	1429.85i	0.438797	+	0.253339i	0.703087	−	0.711104i	$-0.251804\pi$
$317$	2476.58	+	1429.85i	0.438797	+	0.253339i	−0.264290	+	0.964443i	$0.585138\pi$
$318$		0			0
$319$	1505.04	+	2606.80i	0.264157	+	0.457533i
$320$	5741.26			1.00296
$321$		0			0
$322$	995.590	+	426.486i	0.172304	+	0.0738110i
$323$			4466.54i			0.769427i
$324$		0			0
$325$	11854.2	+	6844.03i	2.02324	+	1.16812i
$326$			679.678i			0.115472i
$327$		0			0
$328$	−204.442	−	118.034i	−0.0344158	−	0.0198700i
$329$	4707.83	+	2016.72i	0.788910	+	0.337949i
$330$		0			0
$331$	2938.58	−	5089.76i	0.487972	−	0.845193i	−0.511932	−	0.859026i	$-0.671070\pi$
$331$	2938.58	−	5089.76i	0.487972	−	0.845193i	0.999904	+	0.0138333i	$0.00440343\pi$
$332$	−812.519	+	1407.32i	−0.134316	+	0.232641i
$333$		0			0
$334$	−1346.18	+	777.216i	−0.220538	+	0.127328i
$335$	−5742.68	−	9946.62i	−0.936586	−	1.62221i
$336$		0			0
$337$	859.112	−	1488.03i	0.138869	−	0.240528i	−0.788200	−	0.615419i	$-0.788987\pi$
$337$	859.112	−	1488.03i	0.138869	−	0.240528i	0.927069	+	0.374891i	$0.122320\pi$
$338$			597.356i			0.0961299i
$339$		0			0
$340$	−11155.0			−1.77931
$341$	607.662	+	1052.50i	0.0965007	+	0.167144i
$342$		0			0
$343$	−2217.68	−	5952.77i	−0.349107	−	0.937083i
$344$	271.328	−	156.651i	0.0425263	−	0.0245526i
$345$		0			0
$346$	420.925	−	243.021i	0.0654019	−	0.0377598i
$347$	5147.27	−	2971.78i	0.796311	−	0.459750i	−0.0458688	−	0.998947i	$-0.514606\pi$
$347$	5147.27	−	2971.78i	0.796311	−	0.459750i	0.842179	+	0.539197i	$0.181272\pi$
$348$		0			0
$349$	5172.94	−	2986.60i	0.793414	−	0.458078i	−0.0477492	−	0.998859i	$-0.515205\pi$
$349$	5172.94	−	2986.60i	0.793414	−	0.458078i	0.841163	+	0.540782i	$0.181872\pi$
$350$	2170.51	−	5066.83i	0.331481	−	0.773810i
$351$		0			0
$352$	1100.97	+	1906.94i	0.166710	+	0.288751i
$353$	463.073			0.0698212			0.0349106	−	0.999390i	$-0.488885\pi$
$353$	463.073			0.0698212			0.0349106	+	0.999390i	$0.488885\pi$
$354$		0			0
$355$			949.328i			0.141930i
$356$	257.380	−	445.796i	0.0383178	−	0.0663683i
$357$		0			0
$358$	−11.4080	−	19.7592i	−0.00168416	−	0.00291706i
$359$	6957.39	−	4016.85i	1.02283	−	0.590532i	0.107909	−	0.994161i	$-0.465584\pi$
$359$	6957.39	−	4016.85i	1.02283	−	0.590532i	0.914923	+	0.403628i	$0.132251\pi$
$360$		0			0
$361$	−1378.38	+	2387.42i	−0.200959	+	0.348071i
$362$	1122.68	−	1944.54i	0.163003	−	0.282329i
$363$		0			0
$364$	5170.01	−	617.484i	0.744456	−	0.0889147i
$365$	1205.01	+	695.714i	0.172803	+	0.0997681i
$366$		0			0
$367$			7641.16i			1.08683i	0.839465	+	0.543413i	$0.182868\pi$
$367$			7641.16i			1.08683i	−0.839465	+	0.543413i	$0.817132\pi$
$368$	−2881.67	−	1663.73i	−0.408199	−	0.235674i
$369$		0			0
$370$		−	122.819i		−	0.0172570i
$371$	−803.101	+	1874.76i	−0.112385	+	0.262352i
$372$		0			0
$373$	−9981.85			−1.38563			−0.692816	−	0.721115i	$-0.743630\pi$
$373$	−9981.85			−1.38563			−0.692816	+	0.721115i	$0.743630\pi$
$374$	−451.519	−	782.054i	−0.0624265	−	0.108126i
$375$		0			0
$376$	3068.73	+	1771.73i	0.420897	+	0.243005i
$377$	7499.60			1.02453
$378$		0			0
$379$	1375.75			0.186458			0.0932292	−	0.995645i	$-0.470281\pi$
$379$	1375.75			0.186458			0.0932292	+	0.995645i	$0.470281\pi$
$380$	8872.63	+	5122.62i	1.19778	+	0.691538i
$381$		0			0
$382$	1556.93	+	2696.69i	0.208533	+	0.361190i
$383$	−9171.81			−1.22365			−0.611825	−	0.790993i	$-0.709564\pi$
$383$	−9171.81			−1.22365			−0.611825	+	0.790993i	$0.709564\pi$
$384$		0			0
$385$	−6231.27	+	744.236i	−0.824869	+	0.0985189i
$386$			1438.09i			0.189629i
$387$		0			0
$388$	−3527.79	−	2036.77i	−0.461588	−	0.266498i
$389$		−	12181.2i		−	1.58769i	−0.608120	−	0.793845i	$-0.708076\pi$
$389$		−	12181.2i		−	1.58769i	0.608120	−	0.793845i	$-0.291924\pi$
$390$		0			0
$391$	4216.86	+	2434.61i	0.545411	+	0.314893i
$392$	−1035.08	−	4271.41i	−0.133366	−	0.550354i
$393$		0			0
$394$	−1252.81	+	2169.93i	−0.160192	+	0.277460i
$395$	−13285.4	+	23011.0i	−1.69231	+	2.93116i
$396$		0			0
$397$	−7055.50	+	4073.50i	−0.891953	+	0.514970i	−0.874581	−	0.484880i	$-0.838863\pi$
$397$	−7055.50	+	4073.50i	−0.891953	+	0.514970i	−0.0173725	+	0.999849i	$0.505530\pi$
$398$	2113.12	+	3660.03i	0.266133	+	0.460957i
$399$		0			0
$400$	−8467.19	+	14665.6i	−1.05840	+	1.83320i
$401$		−	11486.4i		−	1.43043i	−0.698903	−	0.715217i	$-0.746328\pi$
$401$		−	11486.4i		−	1.43043i	0.698903	−	0.715217i	$-0.253672\pi$
$402$		0			0
$403$	3027.98			0.374279
$404$	2679.12	+	4640.37i	0.329928	+	0.571453i
$405$		0			0
$406$	−358.159	−	2998.76i	−0.0437812	−	0.366567i
$407$	−89.5832	+	51.7209i	−0.0109103	+	0.00629904i
$408$		0			0
$409$	5198.69	−	3001.46i	0.628505	−	0.362868i	−0.151668	−	0.988432i	$-0.548464\pi$
$409$	5198.69	−	3001.46i	0.628505	−	0.362868i	0.780173	+	0.625564i	$0.215131\pi$
$410$	292.886	−	169.098i	0.0352796	−	0.0203687i
$411$		0			0
$412$	4732.34	−	2732.22i	0.565887	−	0.326715i
$413$	5242.53	−	3923.47i	0.624619	−	0.467460i
$414$		0			0
$415$	−2439.94	−	4226.10i	−0.288607	−	0.499882i
$416$	5486.14			0.646587
$417$		0			0
$418$			829.387i			0.0970494i
$419$	2054.99	−	3559.35i	0.239601	−	0.415001i	−0.720999	−	0.692936i	$-0.756317\pi$
$419$	2054.99	−	3559.35i	0.239601	−	0.415001i	0.960600	+	0.277935i	$0.0896500\pi$
$420$		0			0
$421$	4576.65	+	7926.99i	0.529816	+	0.917668i	0.999395	+	0.0347773i	$0.0110722\pi$
$421$	4576.65	+	7926.99i	0.529816	+	0.917668i	−0.469579	+	0.882890i	$0.655594\pi$
$422$	−2919.22	+	1685.41i	−0.336743	+	0.194419i
$423$		0			0
$424$	−705.540	+	1222.03i	−0.0808115	+	0.139970i
$425$	12390.4	−	21460.8i	1.41417	−	2.44941i
$426$		0			0
$427$	3879.46	−	9056.21i	0.439672	−	1.02637i
$428$	4978.32	+	2874.24i	0.562234	+	0.324606i
$429$		0			0
$430$			448.843i			0.0503375i
$431$	4959.23	+	2863.21i	0.554241	+	0.319991i	0.750831	−	0.660495i	$-0.229653\pi$
$431$	4959.23	+	2863.21i	0.554241	+	0.319991i	−0.196590	+	0.980486i	$0.562987\pi$
$432$		0			0
$433$		−	7458.28i		−	0.827764i	−0.910331	−	0.413882i	$-0.864173\pi$
$433$		−	7458.28i		−	0.827764i	0.910331	−	0.413882i	$-0.135827\pi$
$434$	−144.608	−	1210.76i	−0.0159940	−	0.133913i
$435$		0			0
$436$	11655.4			1.28026
$437$	−2236.04	−	3872.94i	−0.244770	−	0.423953i
$438$		0			0
$439$	12038.5	+	6950.44i	1.30881	+	0.755641i	0.981897	−	0.189415i	$-0.0606590\pi$
$439$	12038.5	+	6950.44i	1.30881	+	0.755641i	0.326911	+	0.945055i	$0.393992\pi$
$440$	−4341.83			−0.470429
$441$		0			0
$442$	−2249.92			−0.242122
$443$	−12562.8	−	7253.12i	−1.34735	−	0.777892i	−0.359476	−	0.933154i	$-0.617044\pi$
$443$	−12562.8	−	7253.12i	−1.34735	−	0.777892i	−0.987873	+	0.155262i	$0.950378\pi$
$444$		0			0
$445$	772.896	+	1338.69i	0.0823343	+	0.142607i
$446$	3758.83			0.399071
$447$		0			0
$448$	575.354	+	4817.27i	0.0606762	+	0.508023i
$449$		−	2949.31i		−	0.309993i	−0.987915	−	0.154996i	$-0.950463\pi$
$449$		−	2949.31i		−	0.309993i	0.987915	−	0.154996i	$-0.0495366\pi$
$450$		0			0
$451$	−246.676	−	142.419i	−0.0257551	−	0.0148697i
$452$			13893.6i			1.44580i
$453$		0			0
$454$	−3954.29	−	2283.01i	−0.408776	−	0.236007i
$455$	−6156.75	+	14372.3i	−0.634358	+	1.48085i
$456$		0			0
$457$	7953.13	−	13775.2i	0.814074	−	1.41002i	−0.0959168	−	0.995389i	$-0.530578\pi$
$457$	7953.13	−	13775.2i	0.814074	−	1.41002i	0.909991	−	0.414628i	$-0.136088\pi$
$458$	−2519.20	+	4363.38i	−0.257018	+	0.445169i
$459$		0			0
$460$	9672.53	−	5584.44i	0.980400	−	0.566034i
$461$	1398.44	+	2422.16i	0.141283	+	0.244710i	0.927980	−	0.372629i	$-0.121544\pi$
$461$	1398.44	+	2422.16i	0.141283	+	0.244710i	−0.786697	+	0.617340i	$0.788210\pi$
$462$		0			0
$463$	2736.29	−	4739.39i	0.274657	−	0.475719i	−0.695392	−	0.718631i	$-0.744769\pi$
$463$	2736.29	−	4739.39i	0.274657	−	0.475719i	0.970048	+	0.242911i	$0.0781024\pi$
$464$			9278.24i			0.928300i
$465$		0			0
$466$	2082.54			0.207021
$467$	5003.44	+	8666.21i	0.495785	+	0.858724i	0.999988	−	0.00486046i	$-0.00154714\pi$
$467$	5003.44	+	8666.21i	0.495785	+	0.858724i	−0.504203	+	0.863585i	$0.668214\pi$
$468$		0			0
$469$	7770.31	−	5815.24i	0.765032	−	0.572544i
$470$	−4396.31	+	2538.21i	−0.431461	+	0.249104i
$471$		0			0
$472$	3923.44	−	2265.20i	0.382608	−	0.220899i
$473$	327.381	−	189.014i	0.0318245	−	0.0183739i
$474$		0			0
$475$	−19710.4	+	11379.8i	−1.90395	+	1.09925i
$476$	−1117.89	−	9359.74i	−0.107644	−	0.901267i
$477$		0			0
$478$	899.528	+	1558.03i	0.0860742	+	0.149085i
$479$	11987.7			1.14349			0.571744	−	0.820432i	$-0.306267\pi$
$479$	11987.7			1.14349			0.571744	+	0.820432i	$0.306267\pi$
$480$		0			0
$481$			257.725i			0.0244309i
$482$	−1264.35	+	2189.92i	−0.119481	+	0.206947i
$483$		0			0
$484$	−3984.86	−	6901.98i	−0.374235	−	0.648195i
$485$	10593.7	−	6116.28i	0.991826	−	0.572631i
$486$		0			0
$487$	−4178.18	+	7236.82i	−0.388771	+	0.673371i	−0.992285	−	0.123982i	$-0.960434\pi$
$487$	−4178.18	+	7236.82i	−0.388771	+	0.673371i	0.603513	+	0.797353i	$0.293767\pi$
$488$	3408.18	−	5903.14i	0.316150	−	0.547587i
$489$		0			0
$490$	6040.90	+	1775.44i	0.556939	+	0.163686i
$491$	5884.50	+	3397.42i	0.540863	+	0.312268i	0.745429	−	0.666585i	$-0.232245\pi$
$491$	5884.50	+	3397.42i	0.540863	+	0.312268i	−0.204565	+	0.978853i	$0.565578\pi$
$492$		0			0
$493$		−	13577.2i		−	1.24034i
$494$	1789.57	+	1033.21i	0.162989	+	0.0941017i
$495$		0			0
$496$			3746.11i			0.339123i
$497$	−796.543	+	95.1358i	−0.0718910	+	0.00858636i
$498$		0			0
$499$	−10956.2			−0.982901			−0.491451	−	0.870905i	$-0.663533\pi$
$499$	−10956.2			−0.982901			−0.491451	+	0.870905i	$0.663533\pi$
$500$	−18423.3	−	31910.0i	−1.64783	−	2.85412i
$501$		0			0
$502$	−2906.68	−	1678.17i	−0.258429	−	0.149204i
$503$	−20300.4			−1.79950			−0.899752	−	0.436402i	$-0.856253\pi$
$503$	−20300.4			−1.79950			−0.899752	+	0.436402i	$0.856253\pi$
$504$		0			0
$505$	−16090.4			−1.41785
$506$	783.025	+	452.080i	0.0687939	+	0.0397182i
$507$		0			0
$508$	−516.497	−	894.599i	−0.0451099	−	0.0781327i
$509$	−22338.8			−1.94528			−0.972641	−	0.232313i	$-0.925371\pi$
$509$	−22338.8			−1.94528			−0.972641	+	0.232313i	$0.925371\pi$
$510$		0			0
$511$	−462.987	+	1080.80i	−0.0400809	+	0.0935650i
$512$			11672.3i			1.00752i
$513$		0			0
$514$	2072.16	+	1196.36i	0.177819	+	0.102664i
$515$			16409.3i			1.40404i
$516$		0			0
$517$	3702.68	+	2137.74i	0.314978	+	0.181853i
$518$	103.053	−	12.3082i	0.00874109	−	0.00104400i
$519$		0			0
$520$	−5408.83	+	9368.37i	−0.456140	+	0.790058i
$521$	8830.18	−	15294.3i	0.742528	−	1.28610i	−0.208812	−	0.977956i	$-0.566960\pi$
$521$	8830.18	−	15294.3i	0.742528	−	1.28610i	0.951341	−	0.308141i	$-0.0997069\pi$
$522$		0			0
$523$	−2859.14	+	1650.72i	−0.239046	+	0.138014i	−0.614738	−	0.788731i	$-0.710738\pi$
$523$	−2859.14	+	1650.72i	−0.239046	+	0.138014i	0.375692	+	0.926745i	$0.377405\pi$
$524$	−4148.90	−	7186.11i	−0.345889	−	0.599097i
$525$		0			0
$526$	881.511	−	1526.82i	0.0730717	−	0.126564i
$527$		−	5481.83i		−	0.453116i
$528$		0			0
$529$	7291.74			0.599305
$530$	−1010.77	−	1750.70i	−0.0828396	−	0.143482i
$531$		0			0
$532$	−3409.02	+	7958.03i	−0.277819	+	0.648542i
$533$	−614.594	+	354.836i	−0.0499456	+	0.0288361i
$534$		0			0
$535$	−14949.6	+	8631.14i	−1.20809	+	0.697489i
$536$	5815.21	−	3357.41i	0.468617	−	0.270556i
$537$		0			0
$538$	−2356.98	+	1360.80i	−0.188878	+	0.109049i
$539$	−1248.92	−	5153.82i	−0.0998046	−	0.411857i
$540$		0			0
$541$	6388.13	+	11064.6i	0.507666	+	0.879303i	0.999961	+	0.00887458i	$0.00282490\pi$
$541$	6388.13	+	11064.6i	0.507666	+	0.879303i	−0.492295	+	0.870429i	$0.663842\pi$
$542$	5779.24			0.458007
$543$		0			0
$544$		−	9932.07i		−	0.782783i
$545$	−17500.2	+	30311.3i	−1.37546	+	2.38237i
$546$		0			0
$547$	−2018.12	−	3495.49i	−0.157749	−	0.273229i	0.776308	−	0.630354i	$-0.217090\pi$
$547$	−2018.12	−	3495.49i	−0.157749	−	0.273229i	−0.934057	+	0.357125i	$0.883757\pi$
$548$	−5516.13	+	3184.74i	−0.429995	+	0.248258i
$549$		0			0
$550$	2300.76	−	3985.03i	0.178372	−	0.308950i
$551$	−6234.93	+	10799.2i	−0.482064	+	0.834959i
$552$		0			0
$553$	−20639.0	−	8841.24i	−1.58709	−	0.679869i
$554$	385.411	+	222.517i	0.0295569	+	0.0170647i
$555$		0			0
$556$		−	7754.39i		−	0.591474i
$557$	16380.5	+	9457.30i	1.24608	+	0.719423i	0.970325	−	0.241806i	$-0.0777398\pi$
$557$	16380.5	+	9457.30i	1.24608	+	0.719423i	0.275752	+	0.961229i	$0.411073\pi$
$558$		0			0
$559$		−	941.854i		−	0.0712633i
$560$	−17780.9	−	7616.92i	−1.34175	−	0.574774i
$561$		0			0
$562$	4095.60			0.307407
$563$	4725.13	+	8184.17i	0.353713	+	0.612650i	0.986897	−	0.161352i	$-0.0515855\pi$
$563$	4725.13	+	8184.17i	0.353713	+	0.612650i	−0.633183	+	0.774002i	$0.718252\pi$
$564$		0			0
$565$	−36131.9	−	20860.8i	−2.69041	−	1.55331i
$566$	3818.35			0.283564
$567$		0			0
$568$	−555.017			−0.0410000
$569$	−877.171	−	506.435i	−0.0646273	−	0.0373126i	0.467338	−	0.884079i	$-0.345213\pi$
$569$	−877.171	−	506.435i	−0.0646273	−	0.0373126i	−0.531965	+	0.846766i	$0.678546\pi$
$570$		0			0
$571$	4817.96	+	8344.96i	0.353109	+	0.611603i	0.986793	−	0.161989i	$-0.0517910\pi$
$571$	4817.96	+	8344.96i	0.353109	+	0.611603i	−0.633683	+	0.773593i	$0.718458\pi$
$572$	4346.57			0.317726
$573$		0			0
$574$	171.235	+	228.803i	0.0124516	+	0.0166377i
$575$			24811.5i			1.79950i
$576$		0			0
$577$	6716.95	+	3878.03i	0.484628	+	0.279800i	0.722343	−	0.691535i	$-0.243065\pi$
$577$	6716.95	+	3878.03i	0.484628	+	0.279800i	−0.237715	+	0.971335i	$0.576399\pi$
$578$		−	41.7305i		−	0.00300305i
$579$		0			0
$580$	−26970.7	−	15571.5i	−1.93086	−	1.11478i
$581$	3301.44	−	2470.77i	0.235743	−	0.176428i
$582$		0			0
$583$	−851.296	+	1474.49i	−0.0604752	+	0.104746i
$584$	−406.744	+	704.501i	−0.0288205	+	0.0499186i
$585$		0			0
$586$	3190.31	−	1841.93i	0.224899	−	0.129845i
$587$	−4195.04	−	7266.02i	−0.294970	−	0.510904i	0.680008	−	0.733205i	$-0.261976\pi$
$587$	−4195.04	−	7266.02i	−0.294970	−	0.510904i	−0.974978	+	0.222301i	$0.928643\pi$
$588$		0			0
$589$	−2517.37	+	4360.21i	−0.176106	+	0.305024i
$590$			6490.33i			0.452886i
$591$		0			0
$592$	−318.848			−0.0221361
$593$	3762.06	+	6516.09i	0.260522	+	0.451237i	0.966381	−	0.257115i	$-0.0827721\pi$
$593$	3762.06	+	6516.09i	0.260522	+	0.451237i	−0.705859	+	0.708353i	$0.749439\pi$
$594$		0			0
$595$	26019.6	+	11146.1i	1.79277	+	0.767979i
$596$	15339.8	−	8856.45i	1.05427	−	0.608682i
$597$		0			0
$598$	1950.91	−	1126.36i	0.133409	−	0.0770236i
$599$	2801.79	−	1617.62i	0.191116	−	0.110341i	−0.401389	−	0.915908i	$-0.631472\pi$
$599$	2801.79	−	1617.62i	0.191116	−	0.110341i	0.592505	+	0.805567i	$0.298139\pi$
$600$		0			0
$601$	4501.29	−	2598.82i	0.305510	−	0.176386i	−0.339405	−	0.940640i	$-0.610226\pi$
$601$	4501.29	−	2598.82i	0.305510	−	0.176386i	0.644916	+	0.764254i	$0.276893\pi$
$602$	−376.606	+	44.9803i	−0.0254972	+	0.00304528i
$603$		0			0
$604$	−2436.41	−	4219.98i	−0.164133	−	0.284286i
$605$	23932.5			1.60826
$606$		0			0
$607$			12070.8i			0.807149i	0.914947	+	0.403575i	$0.132232\pi$
$607$			12070.8i			0.807149i	−0.914947	+	0.403575i	$0.867768\pi$
$608$	−4561.01	+	7899.90i	−0.304232	+	0.526946i
$609$		0			0
$610$	4882.62	+	8456.94i	0.324084	+	0.561330i
$611$	9225.23	−	5326.19i	0.610823	−	0.352659i
$612$		0			0
$613$	2363.66	−	4093.98i	0.155738	−	0.269746i	−0.777590	−	0.628772i	$-0.783558\pi$
$613$	2363.66	−	4093.98i	0.155738	−	0.269746i	0.933327	+	0.359026i	$0.116891\pi$
$614$	−2113.41	+	3660.53i	−0.138909	+	0.240597i
$615$		0			0
$616$	−435.111	−	3643.06i	−0.0284596	−	0.238284i
$617$	−21673.5	−	12513.2i	−1.41417	−	0.816473i	−0.418394	−	0.908266i	$-0.637407\pi$
$617$	−21673.5	−	12513.2i	−1.41417	−	0.816473i	−0.995778	+	0.0917932i	$0.970740\pi$
$618$		0			0
$619$			10903.0i			0.707961i	0.935253	+	0.353980i	$0.115172\pi$
$619$			10903.0i			0.707961i	−0.935253	+	0.353980i	$0.884828\pi$
$620$	−10889.5	−	6287.04i	−0.705374	−	0.407248i
$621$		0			0
$622$			1702.26i			0.109734i
$623$	−1045.79	+	782.662i	−0.0672532	+	0.0503318i
$624$		0			0
$625$	66229.1			4.23866
$626$	−3763.91	−	6519.28i	−0.240313	−	0.416235i
$627$		0			0
$628$	14139.6	+	8163.52i	0.898459	+	0.518726i
$629$	466.583			0.0295769
$630$		0			0
$631$	−18322.8			−1.15598			−0.577988	−	0.816046i	$-0.696162\pi$
$631$	−18322.8			−1.15598			−0.577988	+	0.816046i	$0.696162\pi$
$632$	−13453.2	−	7767.21i	−0.846740	−	0.488865i
$633$		0			0
$634$	−1197.60	−	2074.30i	−0.0750201	−	0.129939i
$635$	3102.01			0.193858
$636$		0			0
$637$	−12676.2	−	3725.58i	−0.788463	−	0.231731i
$638$		−	2521.14i		−	0.156447i
$639$		0			0
$640$	−25790.6	−	14890.2i	−1.59291	−	0.919667i
$641$			15760.0i			0.971111i	0.874206	+	0.485555i	$0.161383\pi$
$641$			15760.0i			0.971111i	−0.874206	+	0.485555i	$0.838617\pi$
$642$		0			0
$643$	−22823.4	−	13177.1i	−1.39979	−	0.808170i	−0.405421	−	0.914130i	$-0.632875\pi$
$643$	−22823.4	−	13177.1i	−1.39979	−	0.808170i	−0.994370	+	0.105961i	$0.966208\pi$
$644$	5655.00	+	7556.20i	0.346022	+	0.462354i
$645$		0			0
$646$	1870.51	−	3239.82i	0.113923	−	0.197321i
$647$	−1173.51	+	2032.57i	−0.0713065	+	0.123507i	−0.899474	−	0.436974i	$-0.856050\pi$
$647$	−1173.51	+	2032.57i	−0.0713065	+	0.123507i	0.828168	+	0.560480i	$0.189384\pi$
$648$		0			0
$649$	4733.97	−	2733.16i	0.286325	−	0.165310i
$650$	−5732.34	−	9928.70i	−0.345909	−	0.599132i
$651$		0			0
$652$	−2961.32	+	5129.16i	−0.177875	+	0.308088i
$653$		−	16913.9i		−	1.01362i	−0.862058	−	0.506809i	$-0.830825\pi$
$653$		−	16913.9i		−	1.01362i	0.862058	−	0.506809i	$-0.169175\pi$
$654$		0			0
$655$	24917.8			1.48644
$656$	−438.990	−	760.354i	−0.0261276	−	0.0452543i
$657$		0			0
$658$	−2570.28	−	3434.40i	−0.152280	−	0.203476i
$659$	12126.6	−	7001.31i	0.716822	−	0.413858i	−0.0967597	−	0.995308i	$-0.530848\pi$
$659$	12126.6	−	7001.31i	0.716822	−	0.413858i	0.813582	+	0.581450i	$0.197514\pi$
$660$		0			0
$661$	2921.69	−	1686.84i	0.171922	−	0.0992593i	−0.411570	−	0.911378i	$-0.635019\pi$
$661$	2921.69	−	1686.84i	0.171922	−	0.0992593i	0.583492	+	0.812119i	$0.301686\pi$
$662$	−4263.02	+	2461.26i	−0.250282	+	0.144501i
$663$		0			0
$664$	2470.75	−	1426.49i	0.144403	−	0.0833714i
$665$	−15577.2	−	20814.3i	−0.908361	−	1.21375i
$666$		0			0
$667$	6797.04	+	11772.8i	0.394576	+	0.683426i
$668$	−13545.2			−0.784549
$669$		0			0
$670$			9619.77i			0.554693i
$671$	4112.26	−	7122.65i	0.236590	−	0.409787i
$672$		0			0
$673$	10197.9	+	17663.3i	0.584102	+	1.01169i	0.994987	+	0.100007i	$0.0318866\pi$
$673$	10197.9	+	17663.3i	0.584102	+	1.01169i	−0.410884	+	0.911687i	$0.634780\pi$
$674$	−1246.32	+	719.564i	−0.0712263	+	0.0411225i
$675$		0			0
$676$	−2602.65	+	4507.92i	−0.148080	+	0.256482i
$677$	−2168.44	+	3755.85i	−0.123102	+	0.213219i	−0.920989	−	0.389588i	$-0.872618\pi$
$677$	−2168.44	+	3755.85i	−0.123102	+	0.213219i	0.797888	+	0.602806i	$0.205951\pi$
$678$		0			0
$679$	6193.56	+	8275.83i	0.350055	+	0.467742i
$680$	16960.4	+	9792.11i	0.956475	+	0.552221i
$681$		0			0
$682$		−	1017.92i		−	0.0571525i
$683$	−25968.2	−	14992.7i	−1.45483	−	0.839944i	−0.456076	−	0.889941i	$-0.650745\pi$
$683$	−25968.2	−	14992.7i	−1.45483	−	0.839944i	−0.998749	+	0.0499974i	$0.984079\pi$
$684$		0			0
$685$		−	19127.1i		−	1.06687i
$686$	−884.315	+	5246.60i	−0.0492177	+	0.292006i
$687$		0			0
$688$	1165.23			0.0645696
$689$	2121.00	+	3673.68i	0.117277	+	0.203129i
$690$		0			0
$691$	−1394.23	−	804.961i	−0.0767570	−	0.0443157i	0.461130	−	0.887332i	$-0.347444\pi$
$691$	−1394.23	−	804.961i	−0.0767570	−	0.0443157i	−0.537887	+	0.843017i	$0.680777\pi$
$692$	4235.33			0.232663
$693$		0			0
$694$	−4978.13			−0.272287
$695$	20166.2	+	11643.0i	1.10064	+	0.635457i
$696$		0			0
$697$	642.393	+	1112.66i	0.0349101	+	0.0604661i
$698$	−5002.96			−0.271296
$699$		0			0
$700$	38455.6	−	28779.9i	2.07641	−	1.55397i
$701$		−	9944.60i		−	0.535809i	−0.963445	−	0.267905i	$-0.913669\pi$
$701$		−	9944.60i		−	0.535809i	0.963445	−	0.267905i	$-0.0863312\pi$
$702$		0			0
$703$	−371.117	−	214.264i	−0.0199103	−	0.0114952i
$704$			4050.01i			0.216819i
$705$		0			0
$706$	−335.892	−	193.927i	−0.0179058	−	0.0103379i
$707$	−1612.48	−	13500.8i	−0.0857760	−	0.718177i
$708$		0			0
$709$	−9535.18	+	16515.4i	−0.505079	+	0.874823i	0.494904	+	0.868948i	$0.335203\pi$
$709$	−9535.18	+	16515.4i	−0.505079	+	0.874823i	−0.999983	+	0.00587486i	$0.998130\pi$
$710$	397.563	−	688.599i	0.0210145	−	0.0363981i
$711$		0			0
$712$	−782.657	+	451.867i	−0.0411957	+	0.0237843i
$713$	2744.32	+	4753.30i	0.144145	+	0.249667i
$714$		0			0
$715$	−6526.22	+	11303.8i	−0.341352	+	0.591240i
$716$		−	198.816i		−	0.0103772i
$717$		0			0
$718$	−6728.76			−0.349743
$719$	15050.6	+	26068.3i	0.780655	+	1.35213i	0.931561	+	0.363586i	$0.118448\pi$
$719$	15050.6	+	26068.3i	0.780655	+	1.35213i	−0.150906	+	0.988548i	$0.548219\pi$
$720$		0			0
$721$	−13768.4	+	1644.44i	−0.711183	+	0.0849406i
$722$	1999.62	−	1154.48i	0.103072	−	0.0595089i
$723$		0			0
$724$	16944.6	−	9782.95i	0.869807	−	0.502183i
$725$	59915.1	−	34592.0i	3.06923	−	1.77202i
$726$		0			0
$727$	11506.5	−	6643.29i	0.587005	−	0.338908i	−0.176907	−	0.984228i	$-0.556609\pi$
$727$	11506.5	−	6643.29i	0.587005	−	0.338908i	0.763912	+	0.645320i	$0.223276\pi$
$728$	−8402.67	−	3599.50i	−0.427780	−	0.183250i
$729$		0			0
$730$	−582.708	−	1009.28i	−0.0295438	−	0.0511714i
$731$	−1705.13			−0.0862741
$732$		0			0
$733$		−	7447.71i		−	0.375290i	−0.982237	−	0.187645i	$-0.939915\pi$
$733$		−	7447.71i		−	0.375290i	0.982237	−	0.187645i	$-0.0600855\pi$
$734$	3199.99	−	5542.55i	0.160918	−	0.278718i
$735$		0			0
$736$	4972.20	+	8612.10i	0.249019	+	0.431313i
$737$	7016.55	−	4051.01i	0.350689	−	0.202471i
$738$		0			0
$739$	−9760.23	+	16905.2i	−0.485840	+	0.841500i	−0.999868	−	0.0162741i	$-0.994820\pi$
$739$	−9760.23	+	16905.2i	−0.485840	+	0.841500i	0.514028	+	0.857774i	$0.328153\pi$
$740$	535.119	−	926.852i	0.0265829	−	0.0460429i
$741$		0			0
$742$	1367.65	−	1023.54i	0.0676659	−	0.0506406i
$743$	30522.1	+	17621.9i	1.50706	+	0.870103i	0.999966	+	0.00821382i	$0.00261457\pi$
$743$	30522.1	+	17621.9i	1.50706	+	0.870103i	0.507097	+	0.861889i	$0.330719\pi$
$744$		0			0
$745$			53190.7i			2.61578i
$746$	7240.38	+	4180.24i	0.355347	+	0.205160i
$747$		0			0
$748$		−	7868.99i		−	0.384651i
$749$	−8740.20	−	11678.6i	−0.426382	−	0.569730i
$750$		0			0
$751$	−19406.0			−0.942922			−0.471461	−	0.881887i	$-0.656273\pi$
$751$	−19406.0			−0.942922			−0.471461	+	0.881887i	$0.656273\pi$
$752$	6589.37	+	11413.1i	0.319534	+	0.553449i
$753$		0			0
$754$	−5439.87	−	3140.71i	−0.262743	−	0.151695i
$755$	14632.7			0.705351
$756$		0			0
$757$	25155.3			1.20777			0.603886	−	0.797071i	$-0.293618\pi$
$757$	25155.3			1.20777			0.603886	+	0.797071i	$0.293618\pi$
$758$	−997.909	−	576.143i	−0.0478175	−	0.0276075i
$759$		0			0
$760$	−8993.47	−	15577.1i	−0.429247	−	0.743477i
$761$	25985.8			1.23782			0.618912	−	0.785461i	$-0.287574\pi$
$761$	25985.8			1.23782			0.618912	+	0.785461i	$0.287574\pi$
$762$		0			0
$763$	−27186.7	−	11646.1i	−1.28994	−	0.552579i
$764$			27133.9i			1.28491i
$765$		0			0
$766$	6652.82	+	3841.00i	0.313807	+	0.181176i
$767$		−	13619.3i		−	0.641154i
$768$		0			0
$769$	21774.7	+	12571.6i	1.02109	+	0.589525i	0.914419	−	0.404770i	$-0.132648\pi$
$769$	21774.7	+	12571.6i	1.02109	+	0.589525i	0.106668	+	0.994295i	$0.465982\pi$
$770$	4831.55	+	2069.72i	0.226126	+	0.0968668i
$771$		0			0
$772$	−6265.70	+	10852.5i	−0.292108	+	0.505946i
$773$	−12751.7	+	22086.6i	−0.593335	+	1.02769i	0.400445	+	0.916321i	$0.368856\pi$
$773$	−12751.7	+	22086.6i	−0.593335	+	1.02769i	−0.993780	+	0.111365i	$0.964478\pi$
$774$		0			0
$775$	24190.8	−	13966.6i	1.12124	−	0.647348i
$776$	3575.83	+	6193.53i	0.165419	+	0.286514i
$777$		0			0
$778$	−5101.29	+	8835.69i	−0.235077	+	0.407166i
$779$		−	1180.00i		−	0.0542719i
$780$		0			0
$781$	−669.676			−0.0306823
$782$	−2039.15	−	3531.91i	−0.0932478	−	0.161510i
$783$		0			0
$784$	4609.16	−	15682.6i	0.209965	−	0.714404i
$785$	−42460.4	+	24514.5i	−1.93054	+	1.11460i
$786$		0			0
$787$	13270.0	−	7661.44i	0.601048	−	0.347015i	−0.168406	−	0.985718i	$-0.553862\pi$
$787$	13270.0	−	7661.44i	0.601048	−	0.347015i	0.769454	+	0.638703i	$0.220529\pi$
$788$	−18908.5	+	10916.9i	−0.854808	+	0.493524i
$789$		0			0
$790$	19273.3	−	11127.4i	0.867990	−	0.501135i
$791$	13882.5	−	32407.4i	0.624027	−	1.45673i
$792$		0			0
$793$	−10245.7	−	17746.1i	−0.458809	−	0.794680i
$794$	6823.66			0.304991
$795$		0			0
$796$			36827.0i			1.63982i
$797$	−15911.5	+	27559.5i	−0.707169	+	1.22485i	0.258734	+	0.965949i	$0.416695\pi$
$797$	−15911.5	+	27559.5i	−0.707169	+	1.22485i	−0.965903	+	0.258904i	$0.916639\pi$
$798$		0			0
$799$	−9642.49	−	16701.3i	−0.426942	−	0.739486i
$800$	43829.4	−	25304.9i	1.93700	−	1.11833i
$801$		0			0
$802$	−4810.32	+	8331.72i	−0.211793	+	0.366837i
$803$	−490.771	+	850.041i	−0.0215678	+	0.0373565i
$804$		0			0
$805$	−28141.6	+	3361.11i	−1.23212	+	0.147160i
$806$	−2196.36	−	1268.07i	−0.0959844	−	0.0554166i
$807$		0			0
$808$		−	9407.13i		−	0.409581i
$809$	−33531.7	−	19359.5i	−1.45724	−	0.841341i	−0.458370	−	0.888762i	$-0.651566\pi$
$809$	−33531.7	−	19359.5i	−1.45724	−	0.841341i	−0.998875	+	0.0474209i	$0.984900\pi$
$810$		0			0
$811$			10326.3i			0.447108i	0.974692	+	0.223554i	$0.0717658\pi$
$811$			10326.3i			0.447108i	−0.974692	+	0.223554i	$0.928234\pi$
$812$	10362.6	−	24190.5i	0.447853	−	1.04547i
$813$		0			0
$814$	86.6394			0.00373060
$815$	−8892.66	−	15402.5i	−0.382204	−	0.661997i
$816$		0			0
$817$	1356.24	+	783.028i	0.0580771	+	0.0335308i
$818$	−5027.86			−0.214908
$819$		0			0
$820$	2947.01			0.125505
$821$	−1680.92	−	970.482i	−0.0714551	−	0.0412546i	0.463847	−	0.885915i	$-0.346469\pi$
$821$	−1680.92	−	970.482i	−0.0714551	−	0.0412546i	−0.535302	+	0.844661i	$0.679802\pi$
$822$		0			0
$823$	−4557.71	−	7894.19i	−0.193040	−	0.334355i	0.753216	−	0.657773i	$-0.228501\pi$
$823$	−4557.71	−	7894.19i	−0.193040	−	0.334355i	−0.946256	+	0.323418i	$0.895168\pi$
$824$	−9593.58			−0.405592
$825$		0			0
$826$	−5445.77	+	650.420i	−0.229398	+	0.0273983i
$827$		−	33576.1i		−	1.41180i	−0.708314	−	0.705898i	$-0.750544\pi$
$827$		−	33576.1i		−	1.41180i	0.708314	−	0.705898i	$-0.249456\pi$
$828$		0			0
$829$	17471.9	+	10087.4i	0.731996	+	0.422618i	0.819152	−	0.573577i	$-0.194445\pi$
$829$	17471.9	+	10087.4i	0.731996	+	0.422618i	−0.0871560	+	0.996195i	$0.527778\pi$
$830$			4087.23i			0.170927i
$831$		0			0
$832$	8738.70	+	5045.29i	0.364135	+	0.210233i
$833$	−6744.76	+	22949.0i	−0.280543	+	0.954544i
$834$		0			0
$835$	20337.6	−	35225.8i	0.842890	−	1.45993i
$836$	−3613.60	+	6258.94i	−0.149496	+	0.258935i
$837$		0			0
$838$	−2981.19	+	1721.19i	−0.122892	+	0.0709518i
$839$	−16012.2	−	27734.0i	−0.658883	−	1.14122i	−0.980905	−	0.194487i	$-0.937696\pi$
$839$	−16012.2	−	27734.0i	−0.658883	−	1.14122i	0.322022	−	0.946732i	$-0.395638\pi$
$840$		0			0
$841$	6758.22	−	11705.6i	0.277101	−	0.479954i
$842$		−	7666.51i		−	0.313783i
$843$		0			0
$844$	−29373.0			−1.19794
$845$	−7815.59	−	13537.0i	−0.318183	−	0.551109i
$846$		0			0
$847$	2398.37	+	20080.8i	0.0972952	+	0.814623i
$848$	−4544.95	+	2624.03i	−0.184050	+	0.106261i
$849$		0			0
$850$	−17974.8	+	10377.8i	−0.725332	+	0.418771i
$851$	−404.575	+	233.581i	−0.0162969	+	0.00940900i
$852$		0			0
$853$	−13435.9	+	7757.24i	−0.539317	+	0.311375i	−0.744802	−	0.667285i	$-0.767456\pi$
$853$	−13435.9	+	7757.24i	−0.539317	+	0.311375i	0.205485	+	0.978660i	$0.434123\pi$
$854$	−6606.57	+	4944.31i	−0.264722	+	0.198116i
$855$		0			0
$856$	−5046.13	−	8740.15i	−0.201487	−	0.348986i
$857$	−18691.3			−0.745022			−0.372511	−	0.928028i	$-0.621503\pi$
$857$	−18691.3			−0.745022			−0.372511	+	0.928028i	$0.621503\pi$
$858$		0			0
$859$			16224.1i			0.644421i	0.946668	+	0.322211i	$0.104426\pi$
$859$			16224.1i			0.644421i	−0.946668	+	0.322211i	$0.895574\pi$
$860$	−1955.59	+	3387.18i	−0.0775407	+	0.134304i
$861$		0			0
$862$	−2398.13	−	4153.69i	−0.0947573	−	0.164124i
$863$	−35402.0	+	20439.3i	−1.39640	+	0.806214i	−0.994014	−	0.109254i	$-0.965154\pi$
$863$	−35402.0	+	20439.3i	−1.39640	+	0.806214i	−0.402390	+	0.915468i	$0.631820\pi$
$864$		0			0
$865$	−6359.20	+	11014.5i	−0.249965	+	0.432951i
$866$	−3123.40	+	5409.90i	−0.122561	+	0.212281i
$867$		0			0
$868$	4183.93	−	9766.98i	0.163608	−	0.381927i
$869$	−16232.4	−	9371.81i	−0.633657	−	0.365842i
$870$		0			0
$871$		−	20186.2i		−	0.785283i
$872$	−17721.2	−	10231.4i	−0.688207	−	0.397336i
$873$		0			0
$874$			3745.67i			0.144965i
$875$	11088.4	+	92840.1i	0.428408	+	3.58693i
$876$		0			0
$877$	−7497.10			−0.288665			−0.144332	−	0.989529i	$-0.546103\pi$
$877$	−7497.10			−0.288665			−0.144332	+	0.989529i	$0.546103\pi$
$878$	−5821.46	−	10083.1i	−0.223764	−	0.387571i
$879$		0			0
$880$	−13984.6	−	8074.01i	−0.535705	−	0.309290i
$881$	25989.7			0.993887			0.496944	−	0.867783i	$-0.334456\pi$
$881$	25989.7			0.993887			0.496944	+	0.867783i	$0.334456\pi$
$882$		0			0
$883$	−20005.7			−0.762454			−0.381227	−	0.924481i	$-0.624498\pi$
$883$	−20005.7			−0.762454			−0.381227	+	0.924481i	$0.624498\pi$
$884$	−16978.9	−	9802.79i	−0.645999	−	0.372968i
$885$		0			0
$886$	6074.98	+	10522.2i	0.230353	+	0.398983i
$887$	1350.69			0.0511292			0.0255646	−	0.999673i	$-0.491862\pi$
$887$	1350.69			0.0511292			0.0255646	+	0.999673i	$0.491862\pi$
$888$		0			0
$889$	310.864	+	2602.77i	0.0117278	+	0.0981937i
$890$		−	1294.70i		−	0.0487625i
$891$		0			0
$892$	28365.9	+	16377.0i	1.06475	+	0.614735i
$893$			17712.1i			0.663732i
$894$		0			0
$895$	517.045	+	298.516i	0.0193105	+	0.0111489i
$896$	9909.20	−	23132.1i	0.369468	−	0.862486i
$897$		0			0
$898$	−1235.13	+	2139.30i	−0.0458983	+	0.0794982i
$899$	7652.20	−	13254.0i	0.283888	−	0.491708i
$900$		0			0
$901$	6650.81	−	3839.85i	0.245916	−	0.141980i
$902$	119.285	+	206.608i	0.00440329	+	0.00762672i
$903$		0			0
$904$	12196.1	−	21124.2i	0.448712	−	0.777192i
$905$			58755.1i			2.15811i
$906$		0			0
$907$	23250.4			0.851176			0.425588	−	0.904917i	$-0.360067\pi$
$907$	23250.4			0.851176			0.425588	+	0.904917i	$0.360067\pi$
$908$	−19894.0	−	34457.3i	−0.727097	−	1.25937i
$909$		0			0
$910$	10484.7	−	7846.69i	0.381940	−	0.285841i
$911$	30824.3	−	17796.4i	1.12103	−	0.647225i	0.179364	−	0.983783i	$-0.442596\pi$
$911$	30824.3	−	17796.4i	1.12103	−	0.647225i	0.941663	+	0.336558i	$0.109263\pi$
$912$		0			0
$913$	2981.18	−	1721.18i	0.108064	−	0.0623909i
$914$	−11537.7	+	6661.28i	−0.417541	+	0.241068i
$915$		0			0
$916$	−38022.1	+	21952.1i	−1.37149	+	0.791830i
$917$	2497.10	+	20907.5i	0.0899254	+	0.752919i
$918$		0			0
$919$	6397.75	+	11081.2i	0.229643	+	0.397754i	0.957702	−	0.287761i	$-0.0929107\pi$
$919$	6397.75	+	11081.2i	0.229643	+	0.397754i	−0.728059	+	0.685514i	$0.759577\pi$
$920$	−19608.5			−0.702689
$921$		0			0
$922$		−	2342.57i		−	0.0836751i
$923$	−834.248	+	1444.96i	−0.0297504	+	0.0515292i
$924$		0			0
$925$	1188.76	+	2058.99i	0.0422553	+	0.0731883i
$926$	−3969.56	+	2291.83i	−0.140872	+	0.0813327i
$927$		0			0
$928$	13864.4	−	24013.8i	0.490432	−	0.849453i
$929$	−14950.0	+	25894.1i	−0.527979	+	0.914486i	0.471489	+	0.881872i	$0.343717\pi$
$929$	−14950.0	+	25894.1i	−0.527979	+	0.914486i	−0.999468	+	0.0326142i	$0.989617\pi$
$930$		0			0
$931$	15903.4	−	15156.1i	0.559841	−	0.533536i
$932$	15715.8	+	9073.54i	0.552349	+	0.318899i
$933$		0			0
$934$		−	8381.43i		−	0.293628i
$935$	20464.2	+	11815.0i	0.715778	+	0.413254i
$936$		0			0
$937$		−	21288.1i		−	0.742211i	−0.928591	−	0.371106i	$-0.878979\pi$
$937$		−	21288.1i		−	0.742211i	0.928591	−	0.371106i	$-0.121021\pi$
$938$	−8071.56	+	964.034i	−0.280966	+	0.0335574i
$939$		0			0
$940$	−44235.4			−1.53489
$941$	13252.9	+	22954.6i	0.459119	+	0.795218i	0.998915	−	0.0465785i	$-0.0148318\pi$
$941$	13252.9	+	22954.6i	0.459119	+	0.795218i	−0.539795	+	0.841796i	$0.681498\pi$
$942$		0			0
$943$	−1114.04	−	643.190i	−0.0384709	−	0.0222112i
$944$	16849.3			0.580932
$945$		0			0
$946$	−316.623			−0.0108819
$947$	−7870.79	−	4544.20i	−0.270081	−	0.155931i	0.358844	−	0.933398i	$-0.383171\pi$
$947$	−7870.79	−	4544.20i	−0.270081	−	0.155931i	−0.628924	+	0.777467i	$0.716504\pi$
$948$		0			0
$949$	1222.76	+	2117.88i	0.0418254	+	0.0724438i
$950$	19062.7			0.651029
$951$		0			0
$952$	−6516.50	+	15212.1i	−0.221850	+	0.517887i
$953$			21333.9i			0.725156i	0.931953	+	0.362578i	$0.118103\pi$
$953$			21333.9i			0.725156i	−0.931953	+	0.362578i	$0.881897\pi$
$954$		0			0
$955$	−70564.9	−	40740.7i	−2.39102	−	1.38046i
$956$			15676.8i			0.530360i
$957$		0			0
$958$	−8695.31	−	5020.24i	−0.293249	−	0.169307i
$959$	16048.8	−	1916.80i	0.540399	−	0.0645430i
$960$		0			0
$961$	−11805.9	+	20448.4i	−0.396291	+	0.686396i
$962$	107.931	−	186.942i	0.00361729	−	0.00626533i
$963$		0			0
$964$	−19082.8	+	11017.4i	−0.637567	+	0.368100i
$965$	−18815.5	−	32589.4i	−0.627660	−	1.08714i
$966$		0			0
$967$	10750.5	−	18620.4i	0.357510	−	0.619225i	−0.630035	−	0.776567i	$-0.716959\pi$
$967$	10750.5	−	18620.4i	0.357510	−	0.619225i	0.987544	+	0.157342i	$0.0502926\pi$
$968$			13992.0i			0.464585i
$969$		0			0
$970$	−10245.6			−0.339141
$971$	−25147.4	−	43556.5i	−0.831120	−	1.43954i	−0.897151	−	0.441725i	$-0.854367\pi$
$971$	−25147.4	−	43556.5i	−0.831120	−	1.43954i	0.0660306	−	0.997818i	$-0.478967\pi$
$972$		0			0
$973$	−7748.21	+	18087.4i	−0.255289	+	0.595947i
$974$	6061.33	−	3499.51i	0.199402	−	0.115125i
$975$		0			0
$976$	21954.8	−	12675.6i	0.720037	−	0.415714i
$977$	26633.7	−	15377.0i	0.872148	−	0.503535i	0.00408625	−	0.999992i	$-0.498699\pi$
$977$	26633.7	−	15377.0i	0.872148	−	0.503535i	0.868061	+	0.496457i	$0.165366\pi$
$978$		0			0
$979$	−944.343	+	545.217i	−0.0308287	+	0.0177990i
$980$	37851.9	+	39718.2i	1.23381	+	1.29464i
$981$		0			0
$982$	−2845.57	−	4928.67i	−0.0924702	−	0.160163i
$983$	53202.1			1.72623			0.863115	−	0.505008i	$-0.168510\pi$
$983$	53202.1			1.72623			0.863115	+	0.505008i	$0.168510\pi$
$984$		0			0
$985$		−	65565.2i		−	2.12089i
$986$	−5685.92	+	9848.30i	−0.183648	+	0.318087i
$987$		0			0
$988$	9003.28	+	15594.1i	0.289911	+	0.502141i
$989$	1478.51	−	853.621i	0.0475369	−	0.0274455i
$990$		0			0
$991$	13889.8	−	24057.9i	0.445232	−	0.771165i	−0.552836	−	0.833290i	$-0.686454\pi$
$991$	13889.8	−	24057.9i	0.445232	−	0.771165i	0.998068	+	0.0621249i	$0.0197877\pi$
$992$	5597.78	−	9695.63i	0.179163	−	0.310319i
$993$		0			0
$994$	617.618	+	264.572i	0.0197079	+	0.00844237i
$995$	−95773.0	−	55294.6i	−3.05147	−	1.76177i
$996$		0			0
$997$		−	47174.3i		−	1.49852i	−0.662276	−	0.749260i	$-0.730410\pi$
$997$		−	47174.3i		−	1.49852i	0.662276	−	0.749260i	$-0.269590\pi$
$998$	7947.15	+	4588.29i	0.252067	+	0.145531i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.10		44
3.2	odd	2		63.4.s.a.59.13	yes	44
7.5	odd	6		189.4.i.a.152.13		44
9.2	odd	6		189.4.i.a.143.10		44
9.7	even	3		63.4.i.a.38.13	yes	44
21.5	even	6		63.4.i.a.5.10	✓	44
63.47	even	6	inner	189.4.s.a.89.10		44
63.61	odd	6		63.4.s.a.47.13	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.10	✓	44	21.5	even	6
63.4.i.a.38.13	yes	44	9.7	even	3
63.4.s.a.47.13	yes	44	63.61	odd	6
63.4.s.a.59.13	yes	44	3.2	odd	2
189.4.i.a.143.10		44	9.2	odd	6
189.4.i.a.152.13		44	7.5	odd	6
189.4.s.a.17.10		44	1.1	even	1	trivial
189.4.s.a.89.10		44	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.725355 - 0.418784i) q^{2} +(-3.64924 - 6.32067i) q^{4} +21.9169 q^{5} +(2.19637 + 18.3896i) q^{7} +12.8135i q^{8} +O(q^{10})\)	\(q+(-0.725355 - 0.418784i) q^{2} +(-3.64924 - 6.32067i) q^{4} +21.9169 q^{5} +(2.19637 + 18.3896i) q^{7} +12.8135i q^{8} +(-15.8975 - 9.17842i) q^{10} +15.4606i q^{11} +(33.3594 + 19.2600i) q^{13} +(6.10810 - 14.2588i) q^{14} +(-23.8278 + 41.2710i) q^{16} +(34.8682 - 60.3936i) q^{17} +(-55.4679 + 32.0244i) q^{19} +(-79.9799 - 138.529i) q^{20} +(6.47465 - 11.2144i) q^{22} +69.8230i q^{23} +355.349 q^{25} +(-16.1316 - 27.9407i) q^{26} +(108.219 - 80.9905i) q^{28} +(168.609 - 97.3466i) q^{29} +(68.0764 - 39.3039i) q^{31} +(123.342 - 71.2115i) q^{32} +(-50.5837 + 29.2045i) q^{34} +(48.1376 + 403.041i) q^{35} +(3.34533 + 5.79428i) q^{37} +53.6452 q^{38} +280.832i q^{40} +(-9.21172 + 15.9552i) q^{41} +(-12.2255 - 21.1752i) q^{43} +(97.7214 - 56.4195i) q^{44} +(29.2407 - 50.6465i) q^{46} +(138.270 - 239.491i) q^{47} +(-333.352 + 80.7806i) q^{49} +(-257.754 - 148.814i) q^{50} -281.138i q^{52} +(95.3706 + 55.0622i) q^{53} +338.848i q^{55} +(-235.635 + 28.1432i) q^{56} -163.069 q^{58} +(-176.782 - 306.196i) q^{59} +(-460.697 - 265.983i) q^{61} -65.8393 q^{62} +261.957 q^{64} +(731.132 + 422.120i) q^{65} +(-262.021 - 453.834i) q^{67} -508.970 q^{68} +(133.870 - 312.507i) q^{70} +43.3150i q^{71} +(54.9811 + 31.7433i) q^{73} -5.60388i q^{74} +(404.831 + 233.729i) q^{76} +(-284.314 + 33.9572i) q^{77} +(-606.173 + 1049.92i) q^{79} +(-522.231 + 904.531i) q^{80} +(13.3635 - 7.71543i) q^{82} +(-111.327 - 192.824i) q^{83} +(764.202 - 1323.64i) q^{85} +20.4793i q^{86} -198.105 q^{88} +(35.2649 + 61.0806i) q^{89} +(-280.914 + 655.766i) q^{91} +(441.328 - 254.801i) q^{92} +(-200.590 + 115.811i) q^{94} +(-1215.68 + 701.874i) q^{95} +(483.359 - 279.067i) q^{97} +(275.628 + 81.0077i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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