LMFDB - Embedded newform 189.4.i.a.143.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(143,189)]

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([1, 1]))

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.i (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			143.10
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.837567i q^{2} +7.29848 q^{4} +(10.9584 - 18.9806i) q^{5} +(14.8276 - 11.0969i) q^{7} -12.8135i q^{8} +O(q^{10})$	\(q-0.837567i q^{2} +7.29848 q^{4} +(10.9584 - 18.9806i) q^{5} +(14.8276 - 11.0969i) q^{7} -12.8135i q^{8} +(-15.8975 - 9.17842i) q^{10} +(-13.3893 + 7.73030i) q^{11} +(-33.3594 + 19.2600i) q^{13} +(-9.29440 - 12.4191i) q^{14} +47.6557 q^{16} +(-34.8682 + 60.3936i) q^{17} +(-55.4679 + 32.0244i) q^{19} +(79.9799 - 138.529i) q^{20} +(6.47465 + 11.2144i) q^{22} +(60.4685 + 34.9115i) q^{23} +(-177.674 - 307.741i) q^{25} +(16.1316 + 27.9407i) q^{26} +(108.219 - 80.9905i) q^{28} +(168.609 + 97.3466i) q^{29} +78.6078i q^{31} -142.423i q^{32} +(50.5837 + 29.2045i) q^{34} +(-48.1376 - 403.041i) q^{35} +(3.34533 + 5.79428i) q^{37} +(26.8226 + 46.4581i) q^{38} +(-243.208 - 140.416i) q^{40} +(9.21172 + 15.9552i) q^{41} +(-12.2255 + 21.1752i) q^{43} +(-97.7214 + 56.4195i) q^{44} +(29.2407 - 50.6465i) q^{46} +276.541 q^{47} +(96.7179 - 329.082i) q^{49} +(-257.754 + 148.814i) q^{50} +(-243.473 + 140.569i) q^{52} +(-95.3706 - 55.0622i) q^{53} +338.848i q^{55} +(-142.190 - 189.994i) q^{56} +(81.5343 - 141.222i) q^{58} -353.564 q^{59} +531.967i q^{61} +65.8393 q^{62} +261.957 q^{64} +844.239i q^{65} +524.043 q^{67} +(-254.485 + 440.781i) q^{68} +(-337.574 + 40.3185i) q^{70} -43.3150i q^{71} +(54.9811 + 31.7433i) q^{73} +(4.85310 - 2.80194i) q^{74} +(-404.831 + 233.729i) q^{76} +(-112.749 + 263.202i) q^{77} +1212.35 q^{79} +(522.231 - 904.531i) q^{80} +(13.3635 - 7.71543i) q^{82} +(111.327 - 192.824i) q^{83} +(764.202 + 1323.64i) q^{85} +(17.7356 + 10.2397i) q^{86} +(99.0523 + 171.564i) q^{88} +(-35.2649 - 61.0806i) q^{89} +(-280.914 + 655.766i) q^{91} +(441.328 + 254.801i) q^{92} -231.622i q^{94} +1403.75i q^{95} +(-483.359 - 279.067i) q^{97} +(-275.628 - 81.0077i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	0.837567i		−	0.296125i	−0.988978	−	0.148062i	$-0.952696\pi$
$2$		−	0.837567i		−	0.296125i	0.988978	−	0.148062i	$-0.0473036\pi$
$3$		0			0
$3$		0			0
$4$	7.29848			0.912310
$5$	10.9584	−	18.9806i	0.980152	−	1.69767i	0.318387	−	0.947961i	$-0.396859\pi$
$5$	10.9584	−	18.9806i	0.980152	−	1.69767i	0.661764	−	0.749712i	$-0.269808\pi$
$6$		0			0
$7$	14.8276	−	11.0969i	0.800617	−	0.599176i
$7$	14.8276	−	11.0969i	0.800617	−	0.599176i
$8$		−	12.8135i		−	0.566282i
$9$		0			0
$10$	−15.8975	−	9.17842i	−0.502723	−	0.290247i
$11$	−13.3893	+	7.73030i	−0.367002	+	0.211889i	−0.672148	−	0.740417i	$-0.734628\pi$
$11$	−13.3893	+	7.73030i	−0.367002	+	0.211889i	0.305146	+	0.952306i	$0.401295\pi$
$12$		0			0
$13$	−33.3594	+	19.2600i	−0.711709	+	0.410906i	−0.811694	−	0.584083i	$-0.801454\pi$
$13$	−33.3594	+	19.2600i	−0.711709	+	0.410906i	0.0999842	+	0.994989i	$0.468121\pi$
$14$	−9.29440	−	12.4191i	−0.177431	−	0.237083i
$15$		0			0
$16$	47.6557			0.744620
$17$	−34.8682	+	60.3936i	−0.497458	+	0.861623i	−0.999996	−	0.00293248i	$-0.999067\pi$
$17$	−34.8682	+	60.3936i	−0.497458	+	0.861623i	0.502537	+	0.864555i	$0.332400\pi$
$18$		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
$23$	60.4685	+	34.9115i	0.548198	+	0.316502i	0.748395	−	0.663253i	$-0.230825\pi$
$23$	60.4685	+	34.9115i	0.548198	+	0.316502i	−0.200197	+	0.979756i	$0.564158\pi$
$24$		0			0
$25$	−177.674	−	307.741i	−1.42139	−	2.46193i
$26$	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	0.930803	−	0.365521i	$-0.119109\pi$
$29$	168.609	+	97.3466i	1.07965	+	0.623338i	0.148851	+	0.988860i	$0.452443\pi$
$30$		0			0
$31$			78.6078i			0.455432i	0.973728	+	0.227716i	$0.0731257\pi$
$31$			78.6078i			0.455432i	−0.973728	+	0.227716i	$0.926874\pi$
$32$		−	142.423i		−	0.786783i
$33$		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	$0.828602\pi$
$38$	26.8226	+	46.4581i	0.114505	+	0.198329i
$39$		0			0
$40$	−243.208	−	140.416i	−0.961362	−	0.555043i
$41$	9.21172	+	15.9552i	0.0350885	+	0.0607751i	0.883036	−	0.469305i	$-0.155495\pi$
$41$	9.21172	+	15.9552i	0.0350885	+	0.0607751i	−0.847948	+	0.530080i	$0.822162\pi$
$42$		0			0
$43$	−12.2255	+	21.1752i	−0.0433574	+	0.0750973i	−0.886890	−	0.461981i	$-0.847139\pi$
$43$	−12.2255	+	21.1752i	−0.0433574	+	0.0750973i	0.843532	+	0.537078i	$0.180472\pi$
$44$	−97.7214	+	56.4195i	−0.334819	+	0.193308i
$45$		0			0
$46$	29.2407	−	50.6465i	0.0937242	−	0.162335i
$47$	276.541			0.858247			0.429124	−	0.903246i	$-0.358822\pi$
$47$	276.541			0.858247			0.429124	+	0.903246i	$0.358822\pi$
$48$		0			0
$49$	96.7179	−	329.082i	0.281976	−	0.959421i
$50$	−257.754	+	148.814i	−0.729038	+	0.420910i
$51$		0			0
$52$	−243.473	+	140.569i	−0.649300	+	0.374873i
$53$	−95.3706	−	55.0622i	−0.247173	−	0.142705i	0.371296	−	0.928514i	$-0.378913\pi$
$53$	−95.3706	−	55.0622i	−0.247173	−	0.142705i	−0.618469	+	0.785809i	$0.712247\pi$
$54$		0			0
$55$			338.848i			0.830732i
$56$	−142.190	−	189.994i	−0.339303	−	0.453376i
$57$		0			0
$58$	81.5343	−	141.222i	0.184586	−	0.319712i
$59$	−353.564			−0.780172			−0.390086	−	0.920778i	$-0.627555\pi$
$59$	−353.564			−0.780172			−0.390086	+	0.920778i	$0.627555\pi$
$60$		0			0
$61$			531.967i			1.11658i	0.829646	+	0.558290i	$0.188542\pi$
$61$			531.967i			1.11658i	−0.829646	+	0.558290i	$0.811458\pi$
$62$	65.8393			0.134865
$63$		0			0
$64$	261.957			0.511634
$65$			844.239i			1.61100i
$66$		0			0
$67$	524.043			0.955552			0.477776	−	0.878482i	$-0.341443\pi$
$67$	524.043			0.955552			0.477776	+	0.878482i	$0.341443\pi$
$68$	−254.485	+	440.781i	−0.453836	+	0.786067i
$69$		0			0
$70$	−337.574	+	40.3185i	−0.576398	+	0.0688425i
$71$		−	43.3150i		−	0.0724020i	−0.999345	−	0.0362010i	$-0.988474\pi$
$71$		−	43.3150i		−	0.0724020i	0.999345	−	0.0362010i	$-0.0115256\pi$
$72$		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	$0.650460\pi$
$74$	4.85310	−	2.80194i	0.00762381	−	0.00440161i
$75$		0			0
$76$	−404.831	+	233.729i	−0.611018	+	0.352771i
$77$	−112.749	+	263.202i	−0.166869	+	0.389540i
$78$		0			0
$79$	1212.35			1.72658			0.863289	−	0.504710i	$-0.168401\pi$
$79$	1212.35			1.72658			0.863289	+	0.504710i	$0.168401\pi$
$80$	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	$-0.786299\pi$
$83$	111.327	−	192.824i	0.147226	−	0.255003i	0.930201	+	0.367050i	$0.119632\pi$
$84$		0			0
$85$	764.202	+	1323.64i	0.975169	+	1.68904i
$86$	17.7356	+	10.2397i	0.0222382	+	0.0128392i
$87$		0			0
$88$	99.0523	+	171.564i	0.119989	+	0.207827i
$89$	−35.2649	−	61.0806i	−0.0420008	−	0.0727475i	0.844261	−	0.535933i	$-0.180040\pi$
$89$	−35.2649	−	61.0806i	−0.0420008	−	0.0727475i	−0.886262	+	0.463185i	$0.846707\pi$
$90$		0			0
$91$	−280.914	+	655.766i	−0.323602	+	0.755417i
$92$	441.328	+	254.801i	0.500127	+	0.288748i
$93$		0			0
$94$		−	231.622i		−	0.254148i
$95$			1403.75i			1.51602i
$96$		0			0
$97$	−483.359	−	279.067i	−0.505955	−	0.292114i	0.225214	−	0.974309i	$-0.427692\pi$
$97$	−483.359	−	279.067i	−0.505955	−	0.292114i	−0.731170	+	0.682196i	$0.761025\pi$
$98$	−275.628	−	81.0077i	−0.284108	−	0.0835002i
$99$		0			0
$100$	−1296.75	−	2246.04i	−1.29675	−	2.24604i
$101$	−367.079	−	635.799i	−0.361641	−	0.626380i	0.626590	−	0.779349i	$-0.284450\pi$
$101$	−367.079	−	635.799i	−0.361641	−	0.626380i	−0.988231	+	0.152969i	$0.951117\pi$
$102$		0			0
$103$	−648.400	−	374.354i	−0.620279	−	0.358119i	0.156698	−	0.987647i	$-0.449915\pi$
$103$	−648.400	−	374.354i	−0.620279	−	0.358119i	−0.776978	+	0.629528i	$0.783248\pi$
$104$	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	−0.159142	−	0.987256i	$-0.550873\pi$
$107$	682.104	−	393.813i	0.616276	−	0.355807i	0.775418	+	0.631449i	$0.217539\pi$
$108$		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	$0.919110\pi$
$110$	283.808			0.246000
$111$		0			0
$112$	706.621	−	528.830i	0.596156	−	0.446158i
$113$	−1648.59	+	951.814i	−1.37245	+	0.792382i	−0.991235	−	0.132107i	$-0.957826\pi$
$113$	−1648.59	+	951.814i	−1.37245	+	0.792382i	−0.381210	+	0.924489i	$0.624492\pi$
$114$		0			0
$115$	1325.28	−	765.151i	1.07463	−	0.620441i
$116$	1230.59	+	710.482i	0.984979	+	0.568678i
$117$		0			0
$118$			296.134i			0.231028i
$119$	153.167	+	1282.42i	0.117990	+	0.987895i
$120$		0			0
$121$	−545.985	+	945.673i	−0.410206	+	0.710498i
$122$	445.558			0.330647
$123$		0			0
$124$			573.718i			0.415495i
$125$	−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	$0.484254\pi$
$128$		−	1358.79i		−	0.938290i
$129$		0			0
$130$	707.107			0.477057
$131$	568.461	−	984.603i	0.379135	−	0.656681i	−0.611802	−	0.791011i	$-0.709555\pi$
$131$	568.461	−	984.603i	0.379135	−	0.656681i	0.990937	+	0.134330i	$0.0428883\pi$
$132$		0			0
$133$	−467.087	+	1090.37i	−0.304523	+	0.710879i
$134$		−	438.921i		−	0.282963i
$135$		0			0
$136$	773.853	+	446.785i	0.487922	+	0.281702i
$137$	755.791	−	436.356i	0.471325	−	0.272120i	−0.245469	−	0.969404i	$-0.578942\pi$
$137$	755.791	−	436.356i	0.471325	−	0.272120i	0.716794	+	0.697285i	$0.245609\pi$
$138$		0			0
$139$	−920.123	+	531.233i	−0.561466	+	0.324163i	−0.753734	−	0.657180i	$-0.771749\pi$
$139$	−920.123	+	531.233i	−0.561466	+	0.324163i	0.192268	+	0.981343i	$0.438416\pi$
$140$	−351.331	−	2941.59i	−0.212092	−	1.77578i
$141$		0			0
$142$	−36.2792			−0.0214400
$143$	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
$149$	2101.78	+	1213.46i	1.15560	+	0.667187i	0.950246	−	0.311500i	$-0.100831\pi$
$149$	2101.78	+	1213.46i	1.15560	+	0.667187i	0.205356	+	0.978687i	$0.434165\pi$
$150$		0			0
$151$	−333.824	−	578.200i	−0.179909	−	0.311611i	0.761940	−	0.647647i	$-0.224247\pi$
$151$	−333.824	−	578.200i	−0.179909	−	0.311611i	−0.941849	+	0.336036i	$0.890914\pi$
$152$	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
$157$		−	2237.05i		−	1.13717i	−0.822625	−	0.568585i	$-0.807491\pi$
$157$		−	2237.05i		−	1.13717i	0.822625	−	0.568585i	$-0.192509\pi$
$158$		−	1015.42i		−	0.511283i
$159$		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	$0.895795\pi$
$164$	67.2315	+	116.448i	0.0320116	+	0.0554457i
$165$		0			0
$166$	−161.503	−	93.2440i	−0.0755126	−	0.0435972i
$167$	−927.945	−	1607.25i	−0.429979	−	0.744746i	0.566892	−	0.823792i	$-0.308146\pi$
$167$	−927.945	−	1607.25i	−0.429979	−	0.744746i	−0.996871	+	0.0790465i	$0.974812\pi$
$168$		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
$173$	−580.302			−0.255026			−0.127513	−	0.991837i	$-0.540700\pi$
$173$	−580.302			−0.255026			−0.127513	+	0.991837i	$0.540700\pi$
$174$		0			0
$175$	−6049.46	−	2591.44i	−2.61312	−	1.11940i
$176$	−638.075	+	368.393i	−0.273277	+	0.157776i
$177$		0			0
$178$	−51.1591	+	29.5367i	−0.0215424	+	0.0124375i
$179$	−23.5912	−	13.6204i	−0.00985077	−	0.00568735i	0.495067	−	0.868855i	$-0.335144\pi$
$179$	−23.5912	−	13.6204i	−0.00985077	−	0.00568735i	−0.504917	+	0.863168i	$0.668477\pi$
$180$		0			0
$181$			2680.82i			1.10090i	0.834867	+	0.550452i	$0.185545\pi$
$181$			2680.82i			1.10090i	−0.834867	+	0.550452i	$0.814455\pi$
$182$	549.248	+	235.284i	0.223698	+	0.0958266i
$183$		0			0
$184$	447.339	−	774.814i	0.179230	−	0.310435i
$185$	146.638			0.0582760
$186$		0			0
$187$		−	1078.17i		−	0.421623i
$188$	2018.33			0.782988
$189$		0			0
$190$	1175.73			0.448930
$191$		−	3717.75i		−	1.40841i	−0.709995	−	0.704206i	$-0.751303\pi$
$191$		−	3717.75i		−	1.40841i	0.709995	−	0.704206i	$-0.248697\pi$
$192$		0			0
$193$	1716.99			0.640370			0.320185	−	0.947355i	$-0.396255\pi$
$193$	1716.99			0.640370			0.320185	+	0.947355i	$0.396255\pi$
$194$	−233.738	+	404.846i	−0.0865021	+	0.149826i
$195$		0			0
$196$	705.894	−	2401.80i	0.257250	−	0.875290i
$197$			2991.54i			1.08192i	0.841048	+	0.540961i	$0.181939\pi$
$197$			2991.54i			1.08192i	−0.841048	+	0.540961i	$0.818061\pi$
$198$		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	$-0.688836\pi$
$200$	−3943.24	+	2276.63i	−1.39415	+	0.804911i
$201$		0			0
$202$	−532.524	+	307.453i	−0.185487	+	0.107091i
$203$	3580.32	−	427.619i	1.23788	−	0.147847i
$204$		0			0
$205$	403.784			0.137568
$206$	−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	0.981505	+	0.191438i	$0.0613151\pi$
$211$	2012.27	+	3485.36i	0.656543	+	1.13717i	−0.324962	+	0.945727i	$0.605352\pi$
$212$	−696.060	−	401.871i	−0.225498	−	0.130191i
$213$		0			0
$214$	−329.845	−	571.308i	−0.105363	−	0.182494i
$215$	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
$220$			2473.08i			0.757885i
$221$		−	2686.25i		−	0.817634i
$222$		0			0
$223$	3886.54	+	2243.90i	1.16709	+	0.673822i	0.952994	−	0.302989i	$-0.0979846\pi$
$223$	3886.54	+	2243.90i	1.16709	+	0.673822i	0.214101	+	0.976812i	$0.431318\pi$
$224$	−1580.45	−	2111.80i	−0.471421	−	0.629912i
$225$		0			0
$226$	797.208	+	1380.81i	0.234644	+	0.406415i
$227$	2725.77	+	4721.17i	0.796984	+	1.38042i	0.921571	+	0.388209i	$0.126906\pi$
$227$	2725.77	+	4721.17i	0.796984	+	1.38042i	−0.124587	+	0.992209i	$0.539761\pi$
$228$		0			0
$229$	5209.59	+	3007.76i	1.50332	+	0.867940i	0.999993	+	0.00384139i	$0.00122276\pi$
$229$	5209.59	+	3007.76i	1.50332	+	0.867940i	0.503323	+	0.864098i	$0.332111\pi$
$230$	−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	−0.165739	−	0.986170i	$-0.553001\pi$
$233$	2153.30	−	1243.21i	0.605440	−	0.349551i	0.771179	+	0.636619i	$0.219667\pi$
$234$		0			0
$235$	3030.45	−	5248.90i	0.841213	−	1.45702i
$236$	−2580.48			−0.711759
$237$		0			0
$238$	1074.12	−	128.288i	0.292540	−	0.0349398i
$239$	−1860.18	+	1073.98i	−0.503453	+	0.290669i	−0.730138	−	0.683299i	$-0.760544\pi$
$239$	−1860.18	+	1073.98i	−0.503453	+	0.290669i	0.226685	+	0.973968i	$0.427211\pi$
$240$		0			0
$241$	−2614.62	+	1509.55i	−0.698849	+	0.403481i	−0.806919	−	0.590663i	$-0.798866\pi$
$241$	−2614.62	+	1509.55i	−0.698849	+	0.403481i	0.108069	+	0.994143i	$0.465533\pi$
$242$	792.065	+	457.299i	0.210396	+	0.121472i
$243$		0			0
$244$			3882.55i			1.01867i
$245$	−5186.27	−	5441.98i	−1.35240	−	1.41908i
$246$		0			0
$247$	1233.58	−	2136.63i	0.317777	−	0.550406i
$248$	1007.24			0.257903
$249$		0			0
$250$			4228.48i			1.06973i
$251$	−4007.26			−1.00771			−0.503856	−	0.863788i	$-0.668086\pi$
$251$	−4007.26			−1.00771			−0.503856	+	0.863788i	$0.668086\pi$
$252$		0			0
$253$	−1079.51			−0.268253
$254$		−	118.545i		−	0.0292843i
$255$		0			0
$256$	957.575			0.233783
$257$	−1428.38	+	2474.02i	−0.346692	+	0.600487i	−0.985660	−	0.168746i	$-0.946028\pi$
$257$	−1428.38	+	2474.02i	−0.346692	+	0.600487i	0.638968	+	0.769233i	$0.279362\pi$
$258$		0			0
$259$	113.902	+	48.7928i	0.0273263	+	0.0117059i
$260$			6161.66i			1.46973i
$261$		0			0
$262$	−824.672	−	476.124i	−0.194460	−	0.112271i
$263$	−1822.93	+	1052.47i	−0.427401	+	0.246760i	−0.698239	−	0.715865i	$-0.746033\pi$
$263$	−1822.93	+	1052.47i	−0.427401	+	0.246760i	0.270838	+	0.962625i	$0.412699\pi$
$264$		0			0
$265$	−2090.22	+	1206.79i	−0.484534	+	0.279746i
$266$	913.256	+	391.216i	0.210509	+	0.0901768i
$267$		0			0
$268$	3824.71			0.871760
$269$	−1624.71	+	2814.07i	−0.368253	+	0.637833i	−0.989293	−	0.145946i	$-0.953377\pi$
$269$	−1624.71	+	2814.07i	−0.368253	+	0.637833i	0.621039	+	0.783779i	$0.286711\pi$
$270$		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
$275$	4757.86	+	2746.95i	1.04331	+	0.602355i
$276$		0			0
$277$	265.671	+	460.155i	0.0576267	+	0.0998124i	0.893400	−	0.449263i	$-0.148313\pi$
$277$	265.671	+	460.155i	0.0576267	+	0.0998124i	−0.835773	+	0.549075i	$0.814980\pi$
$278$	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	−0.0221380	−	0.999755i	$-0.507047\pi$
$281$	−4234.76	−	2444.94i	−0.899020	−	0.519049i	−0.876882	+	0.480705i	$0.840381\pi$
$282$		0			0
$283$		−	4558.86i		−	0.957583i	−0.877929	−	0.478792i	$-0.841075\pi$
$283$		−	4558.86i		−	0.957583i	0.877929	−	0.478792i	$-0.158925\pi$
$284$		−	316.133i		−	0.0660530i
$285$		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
$290$	−1786.98	−	3095.13i	−0.361844	−	0.626733i
$291$		0			0
$292$	401.278	+	231.678i	0.0804214	+	0.0464313i
$293$	2199.14	+	3809.02i	0.438482	+	0.759473i	0.997573	−	0.0696337i	$-0.0221830\pi$
$293$	2199.14	+	3809.02i	0.438482	+	0.759473i	−0.559091	+	0.829106i	$0.688850\pi$
$294$		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
$299$	−2689.59			−0.520210
$300$		0			0
$301$	53.7035	+	449.643i	0.0102838	+	0.0861029i
$302$	−484.282	+	279.600i	−0.0922757	+	0.0532754i
$303$		0			0
$304$	−2643.36	+	1526.14i	−0.498707	+	0.287929i
$305$	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	$-0.155418\pi$
$308$	−822.897	+	1920.97i	−0.152237	+	0.355382i
$309$		0			0
$310$	721.496	−	1249.67i	0.132188	−	0.228956i
$311$	−2032.39			−0.370567			−0.185283	−	0.982685i	$-0.559320\pi$
$311$	−2032.39			−0.370567			−0.185283	+	0.982685i	$0.559320\pi$
$312$		0			0
$313$		−	8987.72i		−	1.62305i	−0.584315	−	0.811527i	$-0.698637\pi$
$313$		−	8987.72i		−	1.62305i	0.584315	−	0.811527i	$-0.301363\pi$
$314$	−1873.68			−0.336744
$315$		0			0
$316$	8848.29			1.57517
$317$			2859.71i			0.506679i	0.967377	+	0.253339i	$0.0815289\pi$
$317$			2859.71i			0.506679i	−0.967377	+	0.253339i	$0.918471\pi$
$318$		0			0
$319$	−3010.08			−0.528313
$320$	2870.63	−	4972.08i	0.501479	−	0.868587i
$321$		0			0
$322$	−128.447	−	1075.45i	−0.0222301	−	0.186126i
$323$		−	4466.54i		−	0.769427i
$324$		0			0
$325$	11854.2	+	6844.03i	2.02324	+	1.16812i
$326$	−588.618	+	339.839i	−0.100002	+	0.0577360i
$327$		0			0
$328$	204.442	−	118.034i	0.0344158	−	0.0198700i
$329$	4100.45	−	3068.74i	0.687128	−	0.514241i
$330$		0			0
$331$	−5877.15			−0.975944			−0.487972	−	0.872859i	$-0.662263\pi$
$331$	−5877.15			−0.975944			−0.487972	+	0.872859i	$0.662263\pi$
$332$	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	0.927069	−	0.374891i	$-0.122320\pi$
$337$	859.112	+	1488.03i	0.138869	+	0.240528i	−0.788200	+	0.615419i	$0.788987\pi$
$338$	517.326	+	298.678i	0.0832509	+	0.0480649i
$339$		0			0
$340$	5577.52	+	9660.54i	0.889657	+	1.54093i
$341$	−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
$346$			486.042i			0.0755196i
$347$		−	5943.55i		−	0.919500i	−0.888048	−	0.459750i	$-0.847939\pi$
$347$		−	5943.55i		−	0.919500i	0.888048	−	0.459750i	$-0.152061\pi$
$348$		0			0
$349$	−5172.94	−	2986.60i	−0.793414	−	0.458078i	0.0477492	−	0.998859i	$-0.484795\pi$
$349$	−5172.94	−	2986.60i	−0.793414	−	0.458078i	−0.841163	+	0.540782i	$0.818128\pi$
$350$	−2170.51	+	5066.83i	−0.331481	+	0.773810i
$351$		0			0
$352$	1100.97	+	1906.94i	0.166710	+	0.288751i
$353$	231.537	+	401.033i	0.0349106	+	0.0604670i	0.882953	−	0.469462i	$-0.155552\pi$
$353$	231.537	+	401.033i	0.0349106	+	0.0604670i	−0.848042	+	0.529929i	$0.822219\pi$
$354$		0			0
$355$	−822.142	−	474.664i	−0.122915	−	0.0709649i
$356$	−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	−0.914923	−	0.403628i	$-0.867749\pi$
$359$	−6957.39	+	4016.85i	−1.02283	+	0.590532i	−0.107909	+	0.994161i	$0.534416\pi$
$360$		0			0
$361$	−1378.38	+	2387.42i	−0.200959	+	0.348071i
$362$	2245.37			0.326005
$363$		0			0
$364$	−2050.25	+	4786.10i	−0.295226	+	0.689175i
$365$	1205.01	−	695.714i	0.172803	−	0.0997681i
$366$		0			0
$367$	6617.44	−	3820.58i	0.941219	−	0.543413i	0.0508770	−	0.998705i	$-0.483798\pi$
$367$	6617.44	−	3820.58i	0.941219	−	0.543413i	0.890342	+	0.455292i	$0.150465\pi$
$368$	2881.67	+	1663.73i	0.408199	+	0.235674i
$369$		0			0
$370$		−	122.819i		−	0.0172570i
$371$	−2025.14	+	241.874i	−0.283396	+	0.0338477i
$372$		0			0
$373$	4990.92	−	8644.54i	0.692816	−	1.19999i	−0.278096	−	0.960553i	$-0.589703\pi$
$373$	4990.92	−	8644.54i	0.692816	−	1.19999i	0.970911	−	0.239439i	$-0.0769634\pi$
$374$	−903.039			−0.124853
$375$		0			0
$376$		−	3543.46i		−	0.486010i
$377$	−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	$0.470281\pi$
$380$			10245.2i			1.38308i
$381$		0			0
$382$	−3113.86			−0.417066
$383$	−4585.91	+	7943.02i	−0.611825	+	1.05971i	0.379108	+	0.925352i	$0.376231\pi$
$383$	−4585.91	+	7943.02i	−0.611825	+	1.05971i	−0.990933	+	0.134359i	$0.957103\pi$
$384$		0			0
$385$	3760.16	+	5024.32i	0.497755	+	0.665098i
$386$		−	1438.09i		−	0.189629i
$387$		0			0
$388$	−3527.79	−	2036.77i	−0.461588	−	0.266498i
$389$	10549.2	−	6090.60i	1.37498	−	0.793845i	0.383430	−	0.923570i	$-0.374743\pi$
$389$	10549.2	−	6090.60i	1.37498	−	0.793845i	0.991550	+	0.129725i	$0.0414093\pi$
$390$		0			0
$391$	−4216.86	+	2434.61i	−0.545411	+	0.314893i
$392$	−4216.69	−	1239.30i	−0.543303	−	0.159678i
$393$		0			0
$394$	2505.62			0.320384
$395$	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
$401$	−9947.52	−	5743.20i	−1.23879	−	0.715217i	−0.269944	−	0.962876i	$-0.587005\pi$
$401$	−9947.52	−	5743.20i	−1.23879	−	0.715217i	−0.968847	+	0.247659i	$0.920339\pi$
$402$		0			0
$403$	−1513.99	−	2622.31i	−0.187139	−	0.324135i
$404$	−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
$409$			6002.93i			0.725735i	0.931841	+	0.362868i	$0.118202\pi$
$409$			6002.93i			0.725735i	−0.931841	+	0.362868i	$0.881798\pi$
$410$		−	338.196i		−	0.0407374i
$411$		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
$416$	2743.07	+	4751.14i	0.323294	+	0.559961i
$417$		0			0
$418$	−718.270	−	414.694i	−0.0840473	−	0.0485247i
$419$	−2054.99	−	3559.35i	−0.239601	−	0.415001i	0.720999	−	0.692936i	$-0.243683\pi$
$419$	−2054.99	−	3559.35i	−0.239601	−	0.415001i	−0.960600	+	0.277935i	$0.910350\pi$
$420$		0			0
$421$	4576.65	−	7926.99i	0.529816	−	0.917668i	−0.469579	−	0.882890i	$-0.655594\pi$
$421$	4576.65	−	7926.99i	0.529816	−	0.917668i	0.999395	−	0.0347773i	$-0.0110722\pi$
$422$	2919.22	−	1685.41i	0.336743	−	0.194419i
$423$		0			0
$424$	−705.540	+	1222.03i	−0.0808115	+	0.139970i
$425$	24780.8			2.82834
$426$		0			0
$427$	5903.18	+	7887.81i	0.669028	+	0.893953i
$428$	4978.32	−	2874.24i	0.562234	−	0.324606i
$429$		0			0
$430$	388.709	−	224.421i	0.0435936	−	0.0251688i
$431$	−4959.23	−	2863.21i	−0.554241	−	0.319991i	0.196590	−	0.980486i	$-0.437013\pi$
$431$	−4959.23	−	2863.21i	−0.554241	−	0.319991i	−0.750831	+	0.660495i	$0.770347\pi$
$432$		0			0
$433$		−	7458.28i		−	0.827764i	−0.910331	−	0.413882i	$-0.864173\pi$
$433$		−	7458.28i		−	0.827764i	0.910331	−	0.413882i	$-0.135827\pi$
$434$	976.242	−	730.612i	0.107975	−	0.0808076i
$435$		0			0
$436$	−5827.70	+	10093.9i	−0.640129	+	1.10874i
$437$	−4472.08			−0.489539
$438$		0			0
$439$		−	13900.9i		−	1.51128i	−0.654986	−	0.755641i	$-0.727326\pi$
$439$		−	13900.9i		−	1.51128i	0.654986	−	0.755641i	$-0.272674\pi$
$440$	4341.83			0.470429
$441$		0			0
$442$	−2249.92			−0.242122
$443$		−	14506.2i		−	1.55578i	−0.628398	−	0.777892i	$-0.716289\pi$
$443$		−	14506.2i		−	1.55578i	0.628398	−	0.777892i	$-0.283711\pi$
$444$		0			0
$445$	−1545.79			−0.164669
$446$	1879.41	−	3255.24i	0.199536	−	0.345606i
$447$		0			0
$448$	3884.20	−	2906.90i	0.409623	−	0.306559i
$449$			2949.31i			0.309993i	0.987915	+	0.154996i	$0.0495366\pi$
$449$			2949.31i			0.309993i	−0.987915	+	0.154996i	$0.950463\pi$
$450$		0			0
$451$	−246.676	−	142.419i	−0.0257551	−	0.0148697i
$452$	−12032.2	+	6946.80i	−1.25210	+	0.722898i
$453$		0			0
$454$	3954.29	−	2283.01i	0.408776	−	0.236007i
$455$	9368.43	+	12518.1i	0.965272	+	1.28979i
$456$		0			0
$457$	−15906.3			−1.62815			−0.814074	−	0.580761i	$-0.802755\pi$
$457$	−15906.3			−1.62815			−0.814074	+	0.580761i	$0.802755\pi$
$458$	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	$-0.878456\pi$
$461$	−1398.44	+	2422.16i	−0.141283	+	0.244710i	0.786697	+	0.617340i	$0.211790\pi$
$462$		0			0
$463$	2736.29	+	4739.39i	0.274657	+	0.475719i	0.970048	−	0.242911i	$-0.0781024\pi$
$463$	2736.29	+	4739.39i	0.274657	+	0.475719i	−0.695392	+	0.718631i	$0.744769\pi$
$464$	8035.19	+	4639.12i	0.803932	+	0.464150i
$465$		0			0
$466$	−1041.27	−	1803.54i	−0.103511	−	0.179286i
$467$	−5003.44	−	8666.21i	−0.495785	−	0.858724i	0.504203	−	0.863585i	$-0.331786\pi$
$467$	−5003.44	−	8666.21i	−0.495785	−	0.858724i	−0.999988	+	0.00486046i	$0.998453\pi$
$468$		0			0
$469$	7770.31	−	5815.24i	0.765032	−	0.572544i
$470$	−4396.31	−	2538.21i	−0.431461	−	0.249104i
$471$		0			0
$472$			4530.40i			0.441798i
$473$		−	378.027i		−	0.0367478i
$474$		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
$479$	5993.83	+	10381.6i	0.571744	+	0.990289i	0.996387	+	0.0849284i	$0.0270662\pi$
$479$	5993.83	+	10381.6i	0.571744	+	0.990289i	−0.424643	+	0.905361i	$0.639601\pi$
$480$		0			0
$481$	−223.196	−	128.862i	−0.0211577	−	0.0122154i
$482$	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	$0.293767\pi$
$488$	6816.36			0.632299
$489$		0			0
$490$	−4558.02	+	4343.85i	−0.420225	+	0.400480i
$491$	5884.50	−	3397.42i	0.540863	−	0.312268i	−0.204565	−	0.978853i	$-0.565578\pi$
$491$	5884.50	−	3397.42i	0.540863	−	0.312268i	0.745429	+	0.666585i	$0.232245\pi$
$492$		0			0
$493$	−11758.2	+	6788.61i	−1.07417	+	0.620170i
$494$	−1789.57	−	1033.21i	−0.162989	−	0.0941017i
$495$		0			0
$496$			3746.11i			0.339123i
$497$	−480.662	−	642.259i	−0.0433815	−	0.0579663i
$498$		0			0
$499$	5478.11	−	9488.37i	0.491451	−	0.851218i	−0.508501	−	0.861061i	$-0.669800\pi$
$499$	5478.11	−	9488.37i	0.491451	−	0.851218i	0.999952	+	0.00984392i	$0.00313347\pi$
$500$	−36846.5			−3.29565
$501$		0			0
$502$			3356.35i			0.298409i
$503$	20300.4			1.79950			0.899752	−	0.436402i	$-0.143747\pi$
$503$	20300.4			1.79950			0.899752	+	0.436402i	$0.143747\pi$
$504$		0			0
$505$	−16090.4			−1.41785
$506$			904.159i			0.0794363i
$507$		0			0
$508$	1032.99			0.0902198
$509$	−11169.4	+	19345.9i	−0.972641	+	1.68466i	−0.285132	+	0.958488i	$0.592037\pi$
$509$	−11169.4	+	19345.9i	−0.972641	+	1.68466i	−0.687509	+	0.726175i	$0.741296\pi$
$510$		0			0
$511$	1167.49	−	139.440i	0.101070	−	0.0120714i
$512$		−	11672.3i		−	1.00752i
$513$		0			0
$514$	2072.16	+	1196.36i	0.177819	+	0.102664i
$515$	−14210.9	+	8204.67i	−1.21594	+	0.702021i
$516$		0			0
$517$	−3702.68	+	2137.74i	−0.314978	+	0.181853i
$518$	40.8672	−	95.4006i	0.00346642	−	0.00809201i
$519$		0			0
$520$	10817.7			0.912281
$521$	−8830.18	+	15294.3i	−0.742528	+	1.28610i	0.208812	+	0.977956i	$0.433040\pi$
$521$	−8830.18	+	15294.3i	−0.742528	+	1.28610i	−0.951341	+	0.308141i	$0.900293\pi$
$522$		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
$527$	−4747.41	−	2740.92i	−0.392410	−	0.226558i
$528$		0			0
$529$	−3645.87	−	6314.84i	−0.299653	−	0.519013i
$530$	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
$535$		−	17262.3i		−	1.39498i
$536$		−	6714.82i		−	0.541112i
$537$		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	$0.663842\pi$
$542$	2889.62	+	5004.97i	0.229003	+	0.396646i
$543$		0			0
$544$	8601.43	+	4966.04i	0.677910	+	0.391392i
$545$	17500.2	+	30311.3i	1.37546	+	2.38237i
$546$		0			0
$547$	−2018.12	+	3495.49i	−0.157749	+	0.273229i	−0.934057	−	0.357125i	$-0.883757\pi$
$547$	−2018.12	+	3495.49i	−0.157749	+	0.273229i	0.776308	+	0.630354i	$0.217090\pi$
$548$	5516.13	−	3184.74i	0.429995	−	0.248258i
$549$		0			0
$550$	2300.76	−	3985.03i	0.178372	−	0.308950i
$551$	−12469.9			−0.964127
$552$		0			0
$553$	17976.2	−	13453.3i	1.38233	−	1.03452i
$554$	385.411	−	222.517i	0.0295569	−	0.0170647i
$555$		0			0
$556$	−6715.50	+	3877.19i	−0.512231	+	0.295737i
$557$	−16380.5	−	9457.30i	−1.24608	−	0.719423i	−0.275752	−	0.961229i	$-0.588927\pi$
$557$	−16380.5	−	9457.30i	−1.24608	−	0.719423i	−0.970325	+	0.241806i	$0.922260\pi$
$558$		0			0
$559$		−	941.854i		−	0.0712633i
$560$	−2294.03	−	19207.2i	−0.173108	−	1.44938i
$561$		0			0
$562$	−2047.80	+	3546.90i	−0.153703	+	0.266222i
$563$	9450.27			0.707427			0.353713	−	0.935354i	$-0.384919\pi$
$563$	9450.27			0.707427			0.353713	+	0.935354i	$0.384919\pi$
$564$		0			0
$565$			41721.5i			3.10662i
$566$	−3818.35			−0.283564
$567$		0			0
$568$	−555.017			−0.0410000
$569$		−	1012.87i		−	0.0746252i	−0.999304	−	0.0373126i	$-0.988120\pi$
$569$		−	1012.87i		−	0.0746252i	0.999304	−	0.0373126i	$-0.0118797\pi$
$570$		0			0
$571$	−9635.93			−0.706219			−0.353109	−	0.935582i	$-0.614876\pi$
$571$	−9635.93			−0.706219			−0.353109	+	0.935582i	$0.614876\pi$
$572$	2173.28	−	3764.24i	0.158863	−	0.275158i
$573$		0			0
$574$	112.532	−	262.695i	0.00818293	−	0.0191022i
$575$		−	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	$0.576399\pi$
$578$	36.1397	−	20.8653i	0.00260072	−	0.00150152i
$579$		0			0
$580$	26970.7	−	15571.5i	1.93086	−	1.11478i
$581$	−489.031	−	4094.51i	−0.0349199	−	0.292374i
$582$		0			0
$583$	1702.59			0.120950
$584$	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	$-0.738024\pi$
$587$	4195.04	−	7266.02i	0.294970	−	0.510904i	0.974978	+	0.222301i	$0.0713568\pi$
$588$		0			0
$589$	−2517.37	−	4360.21i	−0.176106	−	0.305024i
$590$	5620.79	+	3245.16i	0.392210	+	0.226443i
$591$		0			0
$592$	159.424	+	276.131i	0.0110681	+	0.0191704i
$593$	−3762.06	−	6516.09i	−0.260522	−	0.451237i	0.705859	−	0.708353i	$-0.250561\pi$
$593$	−3762.06	−	6516.09i	−0.260522	−	0.451237i	−0.966381	+	0.257115i	$0.917228\pi$
$594$		0			0
$595$	26019.6	+	11146.1i	1.79277	+	0.767979i
$596$	15339.8	+	8856.45i	1.05427	+	0.608682i
$597$		0			0
$598$			2252.71i			0.154047i
$599$		−	3235.23i		−	0.220681i	−0.993894	−	0.110341i	$-0.964806\pi$
$599$		−	3235.23i		−	0.220681i	0.993894	−	0.110341i	$-0.0351942\pi$
$600$		0			0
$601$	−4501.29	−	2598.82i	−0.305510	−	0.176386i	0.339405	−	0.940640i	$-0.389774\pi$
$601$	−4501.29	−	2598.82i	−0.305510	−	0.176386i	−0.644916	+	0.764254i	$0.723107\pi$
$602$	376.606	−	44.9803i	0.0254972	−	0.00304528i
$603$		0			0
$604$	−2436.41	−	4219.98i	−0.164133	−	0.284286i
$605$	11966.3	+	20726.2i	0.804129	+	1.39279i
$606$		0			0
$607$	−10453.6	−	6035.41i	−0.699012	−	0.403575i	0.107968	−	0.994154i	$-0.465566\pi$
$607$	−10453.6	−	6035.41i	−0.699012	−	0.403575i	−0.806979	+	0.590580i	$0.798899\pi$
$608$	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	$0.116891\pi$
$614$	−4226.81			−0.277818
$615$		0			0
$616$	3372.54	+	1444.71i	0.220590	+	0.0944952i
$617$	−21673.5	+	12513.2i	−1.41417	+	0.816473i	−0.995778	−	0.0917932i	$-0.970740\pi$
$617$	−21673.5	+	12513.2i	−1.41417	+	0.816473i	−0.418394	+	0.908266i	$0.637407\pi$
$618$		0			0
$619$	9442.26	−	5451.49i	0.613112	−	0.353980i	−0.161070	−	0.986943i	$-0.551495\pi$
$619$	9442.26	−	5451.49i	0.613112	−	0.353980i	0.774182	+	0.632962i	$0.218161\pi$
$620$	10889.5	+	6287.04i	0.705374	+	0.407248i
$621$		0			0
$622$			1702.26i			0.109734i
$623$	−1200.70	−	514.350i	−0.0772152	−	0.0330771i
$624$		0			0
$625$	−33114.5	+	57356.1i	−2.11933	+	3.67079i
$626$	−7527.82			−0.480626
$627$		0			0
$628$		−	16327.0i		−	1.03745i
$629$	−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	$0.696162\pi$
$632$		−	15534.4i		−	0.977731i
$633$		0			0
$634$	2395.20			0.150040
$635$	1551.01	−	2686.42i	0.0969288	−	0.167886i
$636$		0			0
$637$	3111.68	+	12840.7i	0.193546	+	0.798695i
$638$			2521.14i			0.156447i
$639$		0			0
$640$	−25790.6	−	14890.2i	−1.59291	−	0.919667i
$641$	−13648.6	+	7879.99i	−0.841007	+	0.485555i	−0.857606	−	0.514307i	$-0.828049\pi$
$641$	−13648.6	+	7879.99i	−0.841007	+	0.485555i	0.0165996	+	0.999862i	$0.494716\pi$
$642$		0			0
$643$	22823.4	−	13177.1i	1.39979	−	0.808170i	0.405421	−	0.914130i	$-0.367125\pi$
$643$	22823.4	−	13177.1i	1.39979	−	0.808170i	0.994370	+	0.105961i	$0.0337917\pi$
$644$	9371.36	−	1119.28i	0.573421	−	0.0684870i
$645$		0			0
$646$	−3741.03			−0.227846
$647$	1173.51	−	2032.57i	0.0713065	−	0.123507i	−0.828168	−	0.560480i	$-0.810616\pi$
$647$	1173.51	−	2032.57i	0.0713065	−	0.123507i	0.899474	+	0.436974i	$0.143950\pi$
$648$		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
$653$	−14647.9	−	8456.96i	−0.877819	−	0.506809i	−0.00788024	−	0.999969i	$-0.502508\pi$
$653$	−14647.9	−	8456.96i	−0.877819	−	0.506809i	−0.869939	+	0.493160i	$0.835842\pi$
$654$		0			0
$655$	−12458.9	−	21579.4i	−0.743219	−	1.28729i
$656$	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	0.813582	−	0.581450i	$-0.197514\pi$
$659$	12126.6	+	7001.31i	0.716822	+	0.413858i	−0.0967597	+	0.995308i	$0.530848\pi$
$660$		0			0
$661$			3373.68i			0.198519i	0.995062	+	0.0992593i	$0.0316473\pi$
$661$			3373.68i			0.198519i	−0.995062	+	0.0992593i	$0.968353\pi$
$662$			4922.51i			0.289001i
$663$		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
$668$	−6772.59	−	11730.5i	−0.392274	−	0.679439i
$669$		0			0
$670$	−8330.96	−	4809.88i	−0.480378	−	0.277346i
$671$	−4112.26	−	7122.65i	−0.236590	−	0.409787i
$672$		0			0
$673$	10197.9	−	17663.3i	0.584102	−	1.01169i	−0.410884	−	0.911687i	$-0.634780\pi$
$673$	10197.9	−	17663.3i	0.584102	−	1.01169i	0.994987	−	0.100007i	$-0.0318866\pi$
$674$	1246.32	−	719.564i	0.0712263	−	0.0411225i
$675$		0			0
$676$	−2602.65	+	4507.92i	−0.148080	+	0.256482i
$677$	−4336.88			−0.246204			−0.123102	−	0.992394i	$-0.539284\pi$
$677$	−4336.88			−0.246204			−0.123102	+	0.992394i	$0.539284\pi$
$678$		0			0
$679$	−10263.9	+	1225.87i	−0.580104	+	0.0692852i
$680$	16960.4	−	9792.11i	0.956475	−	0.552221i
$681$		0			0
$682$	−881.541	+	508.958i	−0.0494955	+	0.0285763i
$683$	25968.2	+	14992.7i	1.45483	+	0.839944i	0.998749	−	0.0499974i	$-0.0159213\pi$
$683$	25968.2	+	14992.7i	1.45483	+	0.839944i	0.456076	+	0.889941i	$0.349255\pi$
$684$		0			0
$685$		−	19127.1i		−	1.06687i
$686$	−4985.85	+	1857.46i	−0.277493	+	0.103379i
$687$		0			0
$688$	−582.614	+	1009.12i	−0.0322848	+	0.0559189i
$689$	4242.00			0.234554
$690$		0			0
$691$			1609.92i			0.0886314i	0.999018	+	0.0443157i	$0.0141107\pi$
$691$			1609.92i			0.0886314i	−0.999018	+	0.0443157i	$0.985889\pi$
$692$	−4235.33			−0.232663
$693$		0			0
$694$	−4978.13			−0.272287
$695$			23285.9i			1.27091i
$696$		0			0
$697$	−1284.79			−0.0698202
$698$	−2501.48	+	4332.69i	−0.135648	+	0.234949i
$699$		0			0
$700$	−44151.9	−	18913.6i	−2.38398	−	1.02124i
$701$			9944.60i			0.535809i	0.963445	+	0.267905i	$0.0863312\pi$
$701$			9944.60i			0.535809i	−0.963445	+	0.267905i	$0.913669\pi$
$702$		0			0
$703$	−371.117	−	214.264i	−0.0199103	−	0.0114952i
$704$	−3507.41	+	2025.00i	−0.187771	+	0.108409i
$705$		0			0
$706$	335.892	−	193.927i	0.0179058	−	0.0103379i
$707$	−12498.3	−	5353.96i	−0.664847	−	0.284804i
$708$		0			0
$709$	19070.4			1.01016			0.505079	−	0.863073i	$-0.331463\pi$
$709$	19070.4			1.01016			0.505079	+	0.863073i	$0.331463\pi$
$710$	−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
$716$	−172.180	−	99.4081i	−0.00898696	−	0.00518862i
$717$		0			0
$718$	3364.38	+	5827.28i	0.174871	+	0.302886i
$719$	−15050.6	−	26068.3i	−0.780655	−	1.35213i	−0.931561	−	0.363586i	$-0.881552\pi$
$719$	−15050.6	−	26068.3i	−0.780655	−	1.35213i	0.150906	−	0.988548i	$-0.451781\pi$
$720$		0			0
$721$	−13768.4	+	1644.44i	−0.711183	+	0.0849406i
$722$	1999.62	+	1154.48i	0.103072	+	0.0595089i
$723$		0			0
$724$			19565.9i			1.00437i
$725$		−	69184.0i		−	3.54404i
$726$		0			0
$727$	−11506.5	−	6643.29i	−0.587005	−	0.338908i	0.176907	−	0.984228i	$-0.443391\pi$
$727$	−11506.5	−	6643.29i	−0.587005	−	0.338908i	−0.763912	+	0.645320i	$0.776724\pi$
$728$	8402.67	+	3599.50i	0.427780	+	0.183250i
$729$		0			0
$730$	−582.708	−	1009.28i	−0.0295438	−	0.0511714i
$731$	−852.563	−	1476.68i	−0.0431370	−	0.0747155i
$732$		0			0
$733$	6449.91	+	3723.86i	0.325011	+	0.187645i	0.653624	−	0.756820i	$-0.273248\pi$
$733$	6449.91	+	3723.86i	0.325011	+	0.187645i	−0.328613	+	0.944465i	$0.606581\pi$
$734$	−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	$0.328153\pi$
$740$	1070.24			0.0531658
$741$		0			0
$742$	202.586	+	1696.19i	0.0100231	+	0.0839207i
$743$	30522.1	−	17621.9i	1.50706	−	0.870103i	0.507097	−	0.861889i	$-0.330719\pi$
$743$	30522.1	−	17621.9i	1.50706	−	0.870103i	0.999966	−	0.00821382i	$-0.00261457\pi$
$744$		0			0
$745$	46064.5	−	26595.3i	2.26533	−	1.30789i
$746$	−7240.38	−	4180.24i	−0.355347	−	0.205160i
$747$		0			0
$748$		−	7868.99i		−	0.384651i
$749$	5743.89	−	13408.6i	0.280210	−	0.654123i
$750$		0			0
$751$	9702.99	−	16806.1i	0.471461	−	0.816594i	−0.528006	−	0.849241i	$-0.677060\pi$
$751$	9702.99	−	16806.1i	0.471461	−	0.816594i	0.999467	+	0.0326465i	$0.0103935\pi$
$752$	13178.7			0.639068
$753$		0			0
$754$			6281.42i			0.303390i
$755$	−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	$0.293618\pi$
$758$		−	1152.29i		−	0.0552150i
$759$		0			0
$760$	17986.9			0.858493
$761$	12992.9	−	22504.3i	0.618912	−	1.07199i	−0.370773	−	0.928724i	$-0.620907\pi$
$761$	12992.9	−	22504.3i	0.618912	−	1.07199i	0.989685	−	0.143263i	$-0.0457595\pi$
$762$		0			0
$763$	3507.53	+	29367.5i	0.166423	+	1.39341i
$764$		−	27133.9i		−	1.28491i
$765$		0			0
$766$	6652.82	+	3841.00i	0.313807	+	0.181176i
$767$	11794.7	−	6809.66i	0.555256	−	0.320577i
$768$		0			0
$769$	−21774.7	+	12571.6i	−1.02109	+	0.589525i	−0.914419	−	0.404770i	$-0.867352\pi$
$769$	−21774.7	+	12571.6i	−1.02109	+	0.589525i	−0.106668	+	0.994295i	$0.534018\pi$
$770$	4208.20	−	3149.39i	0.196952	−	0.147397i
$771$		0			0
$772$	12531.4			0.584216
$773$	12751.7	−	22086.6i	0.593335	−	1.02769i	−0.400445	−	0.916321i	$-0.631144\pi$
$773$	12751.7	−	22086.6i	0.593335	−	1.02769i	0.993780	−	0.111365i	$-0.0355223\pi$
$774$		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
$779$	−1021.91	−	589.999i	−0.0470009	−	0.0271360i
$780$		0			0
$781$	334.838	+	579.956i	0.0153412	+	0.0265717i
$782$	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
$787$			15322.9i			0.694030i	0.937860	+	0.347015i	$0.112805\pi$
$787$			15322.9i			0.694030i	−0.937860	+	0.347015i	$0.887195\pi$
$788$			21833.7i			0.987048i
$789$		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
$794$	3411.83	+	5909.46i	0.152495	+	0.264130i
$795$		0			0
$796$	−31893.2	−	18413.5i	−1.42013	−	0.819912i
$797$	15911.5	+	27559.5i	0.707169	+	1.22485i	0.965903	+	0.258904i	$0.0833614\pi$
$797$	15911.5	+	27559.5i	0.707169	+	1.22485i	−0.258734	+	0.965949i	$0.583305\pi$
$798$		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
$803$	−981.543			−0.0431356
$804$		0			0
$805$	11160.0	−	26051.9i	0.488618	−	1.14063i
$806$	−2196.36	+	1268.07i	−0.0959844	+	0.0554166i
$807$		0			0
$808$	−8146.82	+	4703.57i	−0.354708	+	0.204791i
$809$	33531.7	+	19359.5i	1.45724	+	0.841341i	0.998875	−	0.0474209i	$-0.0151002\pi$
$809$	33531.7	+	19359.5i	1.45724	+	0.841341i	0.458370	+	0.888762i	$0.348434\pi$
$810$		0			0
$811$			10326.3i			0.447108i	0.974692	+	0.223554i	$0.0717658\pi$
$811$			10326.3i			0.447108i	−0.974692	+	0.223554i	$0.928234\pi$
$812$	26130.9	−	3120.97i	1.12933	−	0.134882i
$813$		0			0
$814$	−43.3197	+	75.0319i	−0.00186530	+	0.00323080i
$815$	−17785.3			−0.764408
$816$		0			0
$817$		−	1566.06i		−	0.0670617i
$818$	5027.86			0.214908
$819$		0			0
$820$	2947.01			0.125505
$821$		−	1940.96i		−	0.0825092i	−0.999149	−	0.0412546i	$-0.986865\pi$
$821$		−	1940.96i		−	0.0825092i	0.999149	−	0.0412546i	$-0.0131355\pi$
$822$		0			0
$823$	9115.42			0.386080			0.193040	−	0.981191i	$-0.438165\pi$
$823$	9115.42			0.386080			0.193040	+	0.981191i	$0.438165\pi$
$824$	−4796.79	+	8308.28i	−0.202796	+	0.351253i
$825$		0			0
$826$	3286.17	+	4390.97i	0.138427	+	0.184965i
$827$			33576.1i			1.41180i	0.708314	+	0.705898i	$0.249456\pi$
$827$			33576.1i			1.41180i	−0.708314	+	0.705898i	$0.750544\pi$
$828$		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	$0.527778\pi$
$830$	−3539.64	+	2043.61i	−0.148028	+	0.0854637i
$831$		0			0
$832$	−8738.70	+	5045.29i	−0.364135	+	0.210233i
$833$	16502.0	+	17315.6i	0.686388	+	0.720229i
$834$		0			0
$835$	−40675.3			−1.68578
$836$	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	−0.322022	−	0.946732i	$-0.604362\pi$
$839$	16012.2	−	27734.0i	0.658883	−	1.14122i	0.980905	−	0.194487i	$-0.0623043\pi$
$840$		0			0
$841$	6758.22	+	11705.6i	0.277101	+	0.479954i
$842$	−6639.39	−	3833.25i	−0.271744	−	0.156892i
$843$		0			0
$844$	14686.5	+	25437.8i	0.598970	+	1.03745i
$845$	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
$850$		−	20755.6i		−	0.837541i
$851$			467.162i			0.0188180i
$852$		0			0
$853$	13435.9	+	7757.24i	0.539317	+	0.311375i	0.744802	−	0.667285i	$-0.232544\pi$
$853$	13435.9	+	7757.24i	0.539317	+	0.311375i	−0.205485	+	0.978660i	$0.565877\pi$
$854$	6606.57	−	4944.31i	0.264722	−	0.198116i
$855$		0			0
$856$	−5046.13	−	8740.15i	−0.201487	−	0.348986i
$857$	−9345.66	−	16187.2i	−0.372511	−	0.645208i	0.617440	−	0.786618i	$-0.288170\pi$
$857$	−9345.66	−	16187.2i	−0.372511	−	0.645208i	−0.989951	+	0.141410i	$0.954836\pi$
$858$		0			0
$859$	−14050.4	−	8112.03i	−0.558085	−	0.322211i	0.194291	−	0.980944i	$-0.437759\pi$
$859$	−14050.4	−	8112.03i	−0.558085	−	0.322211i	−0.752377	+	0.658733i	$0.771093\pi$
$860$	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	0.402390	−	0.915468i	$-0.368180\pi$
$863$	35402.0	−	20439.3i	1.39640	−	0.806214i	0.994014	+	0.109254i	$0.0348463\pi$
$864$		0			0
$865$	−6359.20	+	11014.5i	−0.249965	+	0.432951i
$866$	−6246.81			−0.245121
$867$		0			0
$868$	6366.48	+	8506.88i	0.248955	+	0.332652i
$869$	−16232.4	+	9371.81i	−0.633657	+	0.365842i
$870$		0			0
$871$	−17481.7	+	10093.1i	−0.680075	+	0.392642i
$872$	17721.2	+	10231.4i	0.688207	+	0.397336i
$873$		0			0
$874$			3745.67i			0.144965i
$875$	−74857.6	+	56022.9i	−2.89217	+	2.16448i
$876$		0			0
$877$	3748.55	−	6492.68i	0.144332	−	0.249991i	−0.784791	−	0.619760i	$-0.787230\pi$
$877$	3748.55	−	6492.68i	0.144332	−	0.249991i	0.929124	+	0.369769i	$0.120563\pi$
$878$	−11642.9			−0.447528
$879$		0			0
$880$			16148.0i			0.618579i
$881$	−25989.7			−0.993887			−0.496944	−	0.867783i	$-0.665544\pi$
$881$	−25989.7			−0.993887			−0.496944	+	0.867783i	$0.665544\pi$
$882$		0			0
$883$	−20005.7			−0.762454			−0.381227	−	0.924481i	$-0.624498\pi$
$883$	−20005.7			−0.762454			−0.381227	+	0.924481i	$0.624498\pi$
$884$		−	19605.6i		−	0.745935i
$885$		0			0
$886$	−12150.0			−0.460706
$887$	675.344	−	1169.73i	0.0255646	−	0.0442792i	−0.852960	−	0.521976i	$-0.825195\pi$
$887$	675.344	−	1169.73i	0.0255646	−	0.0442792i	0.878525	+	0.477697i	$0.158528\pi$
$888$		0			0
$889$	2098.64	−	1570.60i	0.0791744	−	0.0592535i
$890$			1294.70i			0.0487625i
$891$		0			0
$892$	28365.9	+	16377.0i	1.06475	+	0.614735i
$893$	−15339.1	+	8856.05i	−0.574809	+	0.331866i
$894$		0			0
$895$	−517.045	+	298.516i	−0.0193105	+	0.0111489i
$896$	−15078.3	−	20147.6i	−0.562201	−	0.751212i
$897$		0			0
$898$	2470.25			0.0917966
$899$	−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
$905$	50883.4	+	29377.6i	1.86898	+	1.07905i
$906$		0			0
$907$	−11625.2	−	20135.4i	−0.425588	−	0.737140i	0.570887	−	0.821029i	$-0.306599\pi$
$907$	−11625.2	−	20135.4i	−0.425588	−	0.737140i	−0.996475	+	0.0838885i	$0.973266\pi$
$908$	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	0.941663	−	0.336558i	$-0.109263\pi$
$911$	30824.3	+	17796.4i	1.12103	+	0.647225i	0.179364	+	0.983783i	$0.442596\pi$
$912$		0			0
$913$			3442.37i			0.124782i
$914$			13322.6i			0.482135i
$915$		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	$0.759577\pi$
$920$	−9804.27	−	16981.5i	−0.351345	−	0.608547i
$921$		0			0
$922$	2028.73	+	1171.29i	0.0724648	+	0.0418375i
$923$	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
$929$	−29899.9			−1.05596			−0.527979	−	0.849258i	$-0.677050\pi$
$929$	−29899.9			−1.05596			−0.527979	+	0.849258i	$0.677050\pi$
$930$		0			0
$931$	5173.90	+	21350.8i	0.182135	+	0.751605i
$932$	15715.8	−	9073.54i	0.552349	−	0.318899i
$933$		0			0
$934$	−7258.53	+	4190.72i	−0.254290	+	0.146814i
$935$	−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	$-0.121021\pi$
$938$	−4870.66	−	6508.16i	−0.169544	−	0.226545i
$939$		0			0
$940$	22117.7	−	38309.0i	0.767447	−	1.32926i
$941$	26505.7			0.918238			0.459119	−	0.888375i	$-0.348165\pi$
$941$	26505.7			0.918238			0.459119	+	0.888375i	$0.348165\pi$
$942$		0			0
$943$			1286.38i			0.0444224i
$944$	−16849.3			−0.580932
$945$		0			0
$946$	−316.623			−0.0108819
$947$		−	9088.41i		−	0.311862i	−0.987768	−	0.155931i	$-0.950162\pi$
$947$		−	9088.41i		−	0.311862i	0.987768	−	0.155931i	$-0.0498378\pi$
$948$		0			0
$949$	−2445.51			−0.0836509
$950$	9531.37	−	16508.8i	0.325514	−	0.563807i
$951$		0			0
$952$	16432.3	−	1962.61i	0.559428	−	0.0668157i
$953$		−	21333.9i		−	0.725156i	−0.931953	−	0.362578i	$-0.881897\pi$
$953$		−	21333.9i		−	0.725156i	0.931953	−	0.362578i	$-0.118103\pi$
$954$		0			0
$955$	−70564.9	−	40740.7i	−2.39102	−	1.38046i
$956$	−13576.5	+	7838.40i	−0.459305	+	0.265180i
$957$		0			0
$958$	8695.31	−	5020.24i	0.293249	−	0.169307i
$959$	6364.40	−	14857.1i	0.214304	−	0.500271i
$960$		0			0
$961$	23611.8			0.792582
$962$	−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	0.987544	−	0.157342i	$-0.0502926\pi$
$967$	10750.5	+	18620.4i	0.357510	+	0.619225i	−0.630035	+	0.776567i	$0.716959\pi$
$968$	12117.4	+	6995.98i	0.402343	+	0.232293i
$969$		0			0
$970$	5122.80	+	8872.95i	0.169570	+	0.293704i
$971$	25147.4	+	43556.5i	0.831120	+	1.43954i	0.897151	+	0.441725i	$0.145633\pi$
$971$	25147.4	+	43556.5i	0.831120	+	1.43954i	−0.0660306	+	0.997818i	$0.521033\pi$
$972$		0			0
$973$	−7748.21	+	18087.4i	−0.255289	+	0.595947i
$974$	6061.33	+	3499.51i	0.199402	+	0.115125i
$975$		0			0
$976$			25351.2i			0.831427i
$977$		−	30754.0i		−	1.00707i	−0.863975	−	0.503535i	$-0.832033\pi$
$977$		−	30754.0i		−	1.00707i	0.863975	−	0.503535i	$-0.167967\pi$
$978$		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
$983$	26601.0	+	46074.4i	0.863115	+	1.49496i	0.868907	+	0.494975i	$0.164823\pi$
$983$	26601.0	+	46074.4i	0.863115	+	1.49496i	−0.00579243	+	0.999983i	$0.501844\pi$
$984$		0			0
$985$	56781.1	+	32782.6i	1.83675	+	1.06045i
$986$	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	$0.0197877\pi$
$992$	11195.6			0.358326
$993$		0			0
$994$	−537.935	+	402.586i	−0.0171653	+	0.0128463i
$995$	−95773.0	+	55294.6i	−3.05147	+	1.76177i
$996$		0			0
$997$	−40854.1	+	23587.1i	−1.29776	+	0.749260i	−0.980016	−	0.198918i	$-0.936257\pi$
$997$	−40854.1	+	23587.1i	−1.29776	+	0.749260i	−0.317740	+	0.948178i	$0.602924\pi$
$998$	−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.i.a.143.10		44
3.2	odd	2		63.4.i.a.38.13	yes	44
7.5	odd	6		189.4.s.a.89.10		44
9.4	even	3		63.4.s.a.59.13	yes	44
9.5	odd	6		189.4.s.a.17.10		44
21.5	even	6		63.4.s.a.47.13	yes	44
63.5	even	6	inner	189.4.i.a.152.13		44
63.40	odd	6		63.4.i.a.5.10	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.10	✓	44	63.40	odd	6
63.4.i.a.38.13	yes	44	3.2	odd	2
63.4.s.a.47.13	yes	44	21.5	even	6
63.4.s.a.59.13	yes	44	9.4	even	3
189.4.i.a.143.10		44	1.1	even	1	trivial
189.4.i.a.152.13		44	63.5	even	6	inner
189.4.s.a.17.10		44	9.5	odd	6
189.4.s.a.89.10		44	7.5	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.837567i q^{2} +7.29848 q^{4} +(10.9584 - 18.9806i) q^{5} +(14.8276 - 11.0969i) q^{7} -12.8135i q^{8} +O(q^{10})\)	\(q-0.837567i q^{2} +7.29848 q^{4} +(10.9584 - 18.9806i) q^{5} +(14.8276 - 11.0969i) q^{7} -12.8135i q^{8} +(-15.8975 - 9.17842i) q^{10} +(-13.3893 + 7.73030i) q^{11} +(-33.3594 + 19.2600i) q^{13} +(-9.29440 - 12.4191i) q^{14} +47.6557 q^{16} +(-34.8682 + 60.3936i) q^{17} +(-55.4679 + 32.0244i) q^{19} +(79.9799 - 138.529i) q^{20} +(6.47465 + 11.2144i) q^{22} +(60.4685 + 34.9115i) q^{23} +(-177.674 - 307.741i) q^{25} +(16.1316 + 27.9407i) q^{26} +(108.219 - 80.9905i) q^{28} +(168.609 + 97.3466i) q^{29} +78.6078i q^{31} -142.423i q^{32} +(50.5837 + 29.2045i) q^{34} +(-48.1376 - 403.041i) q^{35} +(3.34533 + 5.79428i) q^{37} +(26.8226 + 46.4581i) q^{38} +(-243.208 - 140.416i) q^{40} +(9.21172 + 15.9552i) q^{41} +(-12.2255 + 21.1752i) q^{43} +(-97.7214 + 56.4195i) q^{44} +(29.2407 - 50.6465i) q^{46} +276.541 q^{47} +(96.7179 - 329.082i) q^{49} +(-257.754 + 148.814i) q^{50} +(-243.473 + 140.569i) q^{52} +(-95.3706 - 55.0622i) q^{53} +338.848i q^{55} +(-142.190 - 189.994i) q^{56} +(81.5343 - 141.222i) q^{58} -353.564 q^{59} +531.967i q^{61} +65.8393 q^{62} +261.957 q^{64} +844.239i q^{65} +524.043 q^{67} +(-254.485 + 440.781i) q^{68} +(-337.574 + 40.3185i) q^{70} -43.3150i q^{71} +(54.9811 + 31.7433i) q^{73} +(4.85310 - 2.80194i) q^{74} +(-404.831 + 233.729i) q^{76} +(-112.749 + 263.202i) q^{77} +1212.35 q^{79} +(522.231 - 904.531i) q^{80} +(13.3635 - 7.71543i) q^{82} +(111.327 - 192.824i) q^{83} +(764.202 + 1323.64i) q^{85} +(17.7356 + 10.2397i) q^{86} +(99.0523 + 171.564i) q^{88} +(-35.2649 - 61.0806i) q^{89} +(-280.914 + 655.766i) q^{91} +(441.328 + 254.801i) q^{92} -231.622i q^{94} +1403.75i q^{95} +(-483.359 - 279.067i) q^{97} +(-275.628 - 81.0077i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

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