LMFDB - Embedded newform 189.4.i.a.143.8

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			143.8
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81805i q^{2} +4.69469 q^{4} +(5.16236 - 8.94146i) q^{5} +(-16.8039 - 7.78656i) q^{7} -23.0796i q^{8} +O(q^{10})$	\(q-1.81805i q^{2} +4.69469 q^{4} +(5.16236 - 8.94146i) q^{5} +(-16.8039 - 7.78656i) q^{7} -23.0796i q^{8} +(-16.2560 - 9.38543i) q^{10} +(10.1761 - 5.87520i) q^{11} +(-46.7419 + 26.9865i) q^{13} +(-14.1564 + 30.5503i) q^{14} -4.40236 q^{16} +(31.9804 - 55.3917i) q^{17} +(87.6701 - 50.6164i) q^{19} +(24.2357 - 41.9774i) q^{20} +(-10.6814 - 18.5008i) q^{22} +(-168.576 - 97.3275i) q^{23} +(9.20017 + 15.9352i) q^{25} +(49.0628 + 84.9792i) q^{26} +(-78.8889 - 36.5555i) q^{28} +(-13.4708 - 7.77735i) q^{29} +200.045i q^{31} -176.633i q^{32} +(-100.705 - 58.1420i) q^{34} +(-156.371 + 110.054i) q^{35} +(-152.809 - 264.674i) q^{37} +(-92.0231 - 159.389i) q^{38} +(-206.365 - 119.145i) q^{40} +(-35.3661 - 61.2559i) q^{41} +(52.4919 - 90.9186i) q^{43} +(47.7738 - 27.5822i) q^{44} +(-176.946 + 306.480i) q^{46} +7.27369 q^{47} +(221.739 + 261.688i) q^{49} +(28.9709 - 16.7264i) q^{50} +(-219.439 + 126.693i) q^{52} +(460.939 + 266.123i) q^{53} -121.319i q^{55} +(-179.711 + 387.826i) q^{56} +(-14.1396 + 24.4905i) q^{58} +174.817 q^{59} -301.567i q^{61} +363.692 q^{62} -356.347 q^{64} +557.255i q^{65} +298.504 q^{67} +(150.138 - 260.047i) q^{68} +(200.084 + 284.290i) q^{70} -709.248i q^{71} +(732.758 + 423.058i) q^{73} +(-481.190 + 277.815i) q^{74} +(411.584 - 237.628i) q^{76} +(-216.746 + 19.4888i) q^{77} +1136.97 q^{79} +(-22.7266 + 39.3636i) q^{80} +(-111.366 + 64.2974i) q^{82} +(-164.325 + 284.620i) q^{83} +(-330.188 - 571.903i) q^{85} +(-165.295 - 95.4330i) q^{86} +(-135.597 - 234.861i) q^{88} +(506.312 + 876.958i) q^{89} +(995.576 - 89.5176i) q^{91} +(-791.413 - 456.922i) q^{92} -13.2239i q^{94} -1045.20i q^{95} +(1202.67 + 694.363i) q^{97} +(475.763 - 403.133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.81805i		−	0.642778i	−0.946947	−	0.321389i	$-0.895850\pi$
$2$		−	1.81805i		−	0.642778i	0.946947	−	0.321389i	$-0.104150\pi$
$3$		0			0
$3$		0			0
$4$	4.69469			0.586836
$5$	5.16236	−	8.94146i	0.461735	−	0.799749i	−0.537312	−	0.843383i	$-0.680560\pi$
$5$	5.16236	−	8.94146i	0.461735	−	0.799749i	0.999048	+	0.0436346i	$0.0138937\pi$
$6$		0			0
$7$	−16.8039	−	7.78656i	−0.907323	−	0.420435i
$7$	−16.8039	−	7.78656i	−0.907323	−	0.420435i
$8$		−	23.0796i		−	1.01998i
$9$		0			0
$10$	−16.2560	−	9.38543i	−0.514061	−	0.296793i
$11$	10.1761	−	5.87520i	0.278929	−	0.161040i	−0.354009	−	0.935242i	$-0.615182\pi$
$11$	10.1761	−	5.87520i	0.278929	−	0.161040i	0.632939	+	0.774202i	$0.281849\pi$
$12$		0			0
$13$	−46.7419	+	26.9865i	−0.997221	+	0.575746i	−0.907425	−	0.420214i	$-0.861955\pi$
$13$	−46.7419	+	26.9865i	−0.997221	+	0.575746i	−0.0897962	+	0.995960i	$0.528622\pi$
$14$	−14.1564	+	30.5503i	−0.270246	+	0.583207i
$15$		0			0
$16$	−4.40236			−0.0687869
$17$	31.9804	−	55.3917i	0.456258	−	0.790262i	−0.542502	−	0.840055i	$-0.682523\pi$
$17$	31.9804	−	55.3917i	0.456258	−	0.790262i	0.998760	+	0.0497928i	$0.0158561\pi$
$18$		0			0
$19$	87.6701	−	50.6164i	1.05857	−	0.611168i	0.133536	−	0.991044i	$-0.457367\pi$
$19$	87.6701	−	50.6164i	1.05857	−	0.611168i	0.925037	+	0.379876i	$0.124033\pi$
$20$	24.2357	−	41.9774i	0.270963	−	0.469322i
$21$		0			0
$22$	−10.6814	−	18.5008i	−0.103513	−	0.179290i
$23$	−168.576	−	97.3275i	−1.52828	−	0.882356i	−0.999434	−	0.0336407i	$-0.989290\pi$
$23$	−168.576	−	97.3275i	−1.52828	−	0.882356i	−0.528851	−	0.848715i	$-0.677377\pi$
$24$		0			0
$25$	9.20017	+	15.9352i	0.0736013	+	0.127481i
$26$	49.0628	+	84.9792i	0.370077	+	0.640992i
$27$		0			0
$28$	−78.8889	−	36.5555i	−0.532450	−	0.246726i
$29$	−13.4708	−	7.77735i	−0.0862572	−	0.0498006i	0.456251	−	0.889851i	$-0.349192\pi$
$29$	−13.4708	−	7.77735i	−0.0862572	−	0.0498006i	−0.542508	+	0.840051i	$0.682525\pi$
$30$		0			0
$31$			200.045i			1.15900i	0.814971	+	0.579502i	$0.196753\pi$
$31$			200.045i			1.15900i	−0.814971	+	0.579502i	$0.803247\pi$
$32$		−	176.633i		−	0.975769i
$33$		0			0
$34$	−100.705	−	58.1420i	−0.507963	−	0.293273i
$35$	−156.371	+	110.054i	−0.755185	+	0.531501i
$36$		0			0
$37$	−152.809	−	264.674i	−0.678965	−	1.17600i	−0.975293	−	0.220916i	$-0.929095\pi$
$37$	−152.809	−	264.674i	−0.678965	−	1.17600i	0.296327	−	0.955086i	$-0.404238\pi$
$38$	−92.0231	−	159.389i	−0.392845	−	0.680428i
$39$		0			0
$40$	−206.365	−	119.145i	−0.815731	−	0.470962i
$41$	−35.3661	−	61.2559i	−0.134714	−	0.233331i	0.790774	−	0.612108i	$-0.209678\pi$
$41$	−35.3661	−	61.2559i	−0.134714	−	0.233331i	−0.925488	+	0.378777i	$0.876345\pi$
$42$		0			0
$43$	52.4919	−	90.9186i	0.186161	−	0.322441i	−0.757806	−	0.652480i	$-0.773729\pi$
$43$	52.4919	−	90.9186i	0.186161	−	0.322441i	0.943967	+	0.330039i	$0.107062\pi$
$44$	47.7738	−	27.5822i	0.163686	−	0.0945041i
$45$		0			0
$46$	−176.946	+	306.480i	−0.567159	+	0.982348i
$47$	7.27369			0.0225740			0.0112870	−	0.999936i	$-0.496407\pi$
$47$	7.27369			0.0225740			0.0112870	+	0.999936i	$0.496407\pi$
$48$		0			0
$49$	221.739	+	261.688i	0.646469	+	0.762940i
$50$	28.9709	−	16.7264i	0.0819421	−	0.0473093i
$51$		0			0
$52$	−219.439	+	126.693i	−0.585206	+	0.337869i
$53$	460.939	+	266.123i	1.19462	+	0.689714i	0.959351	−	0.282216i	$-0.0910695\pi$
$53$	460.939	+	266.123i	1.19462	+	0.689714i	0.235269	+	0.971930i	$0.424403\pi$
$54$		0			0
$55$		−	121.319i		−	0.297431i
$56$	−179.711	+	387.826i	−0.428837	+	0.925454i
$57$		0			0
$58$	−14.1396	+	24.4905i	−0.0320107	+	0.0554442i
$59$	174.817			0.385750			0.192875	−	0.981223i	$-0.438219\pi$
$59$	174.817			0.385750			0.192875	+	0.981223i	$0.438219\pi$
$60$		0			0
$61$		−	301.567i		−	0.632979i	−0.948596	−	0.316490i	$-0.897496\pi$
$61$		−	301.567i		−	0.632979i	0.948596	−	0.316490i	$-0.102504\pi$
$62$	363.692			0.744983
$63$		0			0
$64$	−356.347			−0.695990
$65$			557.255i			1.06337i
$66$		0			0
$67$	298.504			0.544300			0.272150	−	0.962255i	$-0.412265\pi$
$67$	298.504			0.544300			0.272150	+	0.962255i	$0.412265\pi$
$68$	150.138	−	260.047i	0.267749	−	0.463754i
$69$		0			0
$70$	200.084	+	284.290i	0.341637	+	0.485416i
$71$		−	709.248i		−	1.18552i	−0.805377	−	0.592762i	$-0.798037\pi$
$71$		−	709.248i		−	1.18552i	0.805377	−	0.592762i	$-0.201963\pi$
$72$		0			0
$73$	732.758	+	423.058i	1.17483	+	0.678290i	0.954814	−	0.297205i	$-0.0960546\pi$
$73$	732.758	+	423.058i	1.17483	+	0.678290i	0.220019	+	0.975496i	$0.429388\pi$
$74$	−481.190	+	277.815i	−0.755909	+	0.436424i
$75$		0			0
$76$	411.584	−	237.628i	0.621209	−	0.358655i
$77$	−216.746	+	19.4888i	−0.320786	+	0.0288436i
$78$		0			0
$79$	1136.97			1.61923			0.809616	−	0.586960i	$-0.199675\pi$
$79$	1136.97			1.61923			0.809616	+	0.586960i	$0.199675\pi$
$80$	−22.7266	+	39.3636i	−0.0317613	+	0.0550123i
$81$		0			0
$82$	−111.366	+	64.2974i	−0.149980	+	0.0865910i
$83$	−164.325	+	284.620i	−0.217314	+	0.376398i	−0.953986	−	0.299852i	$-0.903063\pi$
$83$	−164.325	+	284.620i	−0.217314	+	0.376398i	0.736672	+	0.676250i	$0.236396\pi$
$84$		0			0
$85$	−330.188	−	571.903i	−0.421341	−	0.729783i
$86$	−165.295	−	95.4330i	−0.207258	−	0.119660i
$87$		0			0
$88$	−135.597	−	234.861i	−0.164258	−	0.284503i
$89$	506.312	+	876.958i	0.603022	+	1.04446i	0.992361	+	0.123370i	$0.0393702\pi$
$89$	506.312	+	876.958i	0.603022	+	1.04446i	−0.389339	+	0.921095i	$0.627296\pi$
$90$		0			0
$91$	995.576	−	89.5176i	1.14687	−	0.103121i
$92$	−791.413	−	456.922i	−0.896853	−	0.517798i
$93$		0			0
$94$		−	13.2239i		−	0.0145101i
$95$		−	1045.20i		−	1.12879i
$96$		0			0
$97$	1202.67	+	694.363i	1.25889	+	0.726823i	0.972860	−	0.231396i	$-0.0743293\pi$
$97$	1202.67	+	694.363i	1.25889	+	0.726823i	0.286035	+	0.958219i	$0.407663\pi$
$98$	475.763	−	403.133i	0.490401	−	0.415536i
$99$		0			0
$100$	43.1919	+	74.8106i	0.0431919	+	0.0748106i
$101$	779.461	+	1350.07i	0.767914	+	1.33007i	0.938692	+	0.344757i	$0.112039\pi$
$101$	779.461	+	1350.07i	0.767914	+	1.33007i	−0.170778	+	0.985310i	$0.554628\pi$
$102$		0			0
$103$	−921.485	−	532.020i	−0.881520	−	0.508946i	−0.0103610	−	0.999946i	$-0.503298\pi$
$103$	−921.485	−	532.020i	−0.881520	−	0.508946i	−0.871159	+	0.491000i	$0.836631\pi$
$104$	622.837	+	1078.78i	0.587251	+	1.01715i
$105$		0			0
$106$	483.826	−	838.011i	0.443333	−	0.767876i
$107$	−781.498	+	451.198i	−0.706077	+	0.407654i	−0.809607	−	0.586973i	$-0.800320\pi$
$107$	−781.498	+	451.198i	−0.706077	+	0.407654i	0.103530	+	0.994626i	$0.466986\pi$
$108$		0			0
$109$	−279.653	+	484.374i	−0.245742	+	0.425638i	−0.962340	−	0.271848i	$-0.912365\pi$
$109$	−279.653	+	484.374i	−0.245742	+	0.425638i	0.716598	+	0.697487i	$0.245698\pi$
$110$	−220.565			−0.191182
$111$		0			0
$112$	73.9767	+	34.2793i	0.0624120	+	0.0289204i
$113$	640.930	−	370.041i	0.533572	−	0.308058i	−0.208898	−	0.977937i	$-0.566988\pi$
$113$	640.930	−	370.041i	0.533572	−	0.308058i	0.742470	+	0.669880i	$0.233654\pi$
$114$		0			0
$115$	−1740.50	+	1004.88i	−1.41133	+	0.814829i
$116$	−63.2411	−	36.5122i	−0.0506188	−	0.0292248i
$117$		0			0
$118$		−	317.826i		−	0.247951i
$119$	−968.705	+	681.776i	−0.746227	+	0.525196i
$120$		0			0
$121$	−596.464	+	1033.11i	−0.448132	+	0.776188i
$122$	−548.265			−0.406865
$123$		0			0
$124$			939.149i			0.680146i
$125$	1480.57			1.05941
$126$		0			0
$127$	191.857			0.134052			0.0670258	−	0.997751i	$-0.478649\pi$
$127$	191.857			0.134052			0.0670258	+	0.997751i	$0.478649\pi$
$128$		−	765.208i		−	0.528402i
$129$		0			0
$130$	1013.12			0.683510
$131$	−37.1631	+	64.3683i	−0.0247859	+	0.0429304i	−0.878152	−	0.478381i	$-0.841224\pi$
$131$	−37.1631	+	64.3683i	−0.0247859	+	0.0429304i	0.853366	+	0.521312i	$0.174557\pi$
$132$		0			0
$133$	−1867.32	+	167.901i	−1.21742	+	0.109465i
$134$		−	542.696i		−	0.349864i
$135$		0			0
$136$	−1278.42	−	738.095i	−0.806054	−	0.465376i
$137$	899.911	−	519.564i	0.561201	−	0.324010i	−0.192426	−	0.981311i	$-0.561636\pi$
$137$	899.911	−	519.564i	0.561201	−	0.324010i	0.753627	+	0.657302i	$0.228302\pi$
$138$		0			0
$139$	1698.17	−	980.437i	1.03623	−	0.598270i	0.117470	−	0.993076i	$-0.462522\pi$
$139$	1698.17	−	980.437i	1.03623	−	0.598270i	0.918764	+	0.394806i	$0.129188\pi$
$140$	−734.112	+	516.669i	−0.443170	+	0.311904i
$141$		0			0
$142$	−1289.45			−0.762029
$143$	−317.102	+	549.236i	−0.185436	+	0.321185i
$144$		0			0
$145$	−139.082	+	80.2989i	−0.0796559	+	0.0459894i
$146$	769.141	−	1332.19i	0.435990	−	0.755157i
$147$		0			0
$148$	−717.393	−	1242.56i	−0.398442	−	0.690121i
$149$	−2069.49	−	1194.82i	−1.13785	−	0.656936i	−0.191950	−	0.981405i	$-0.561481\pi$
$149$	−2069.49	−	1194.82i	−1.13785	−	0.656936i	−0.945896	+	0.324469i	$0.894814\pi$
$150$		0			0
$151$	−819.975	−	1420.24i	−0.441912	−	0.765413i	0.555920	−	0.831236i	$-0.312366\pi$
$151$	−819.975	−	1420.24i	−0.441912	−	0.765413i	−0.997831	+	0.0658227i	$0.979033\pi$
$152$	−1168.20	−	2023.39i	−0.623381	−	1.07973i
$153$		0			0
$154$	35.4316	+	394.055i	0.0185400	+	0.206194i
$155$	1788.70	+	1032.70i	0.926913	+	0.535153i
$156$		0			0
$157$			1183.68i			0.601708i	0.953670	+	0.300854i	$0.0972717\pi$
$157$			1183.68i			0.601708i	−0.953670	+	0.300854i	$0.902728\pi$
$158$		−	2067.07i		−	1.04081i
$159$		0			0
$160$	−1579.36	−	911.843i	−0.780370	−	0.450547i
$161$	2074.88	+	2948.10i	1.01567	+	1.44313i
$162$		0			0
$163$	410.313	+	710.683i	0.197167	+	0.341503i	0.947609	−	0.319434i	$-0.103493\pi$
$163$	410.313	+	710.683i	0.197167	+	0.341503i	−0.750442	+	0.660936i	$0.770159\pi$
$164$	−166.033	−	287.577i	−0.0790548	−	0.136927i
$165$		0			0
$166$	517.453	+	298.752i	0.241941	+	0.139685i
$167$	796.684	+	1379.90i	0.369157	+	0.639399i	0.989434	−	0.144984i	$-0.0463130\pi$
$167$	796.684	+	1379.90i	0.369157	+	0.639399i	−0.620277	+	0.784383i	$0.712980\pi$
$168$		0			0
$169$	358.038	−	620.139i	0.162967	−	0.282266i
$170$	−1039.75	+	600.299i	−0.469089	+	0.270829i
$171$		0			0
$172$	246.433	−	426.835i	0.109246	−	0.189220i
$173$	−2260.59			−0.993467			−0.496733	−	0.867903i	$-0.665467\pi$
$173$	−2260.59			−0.993467			−0.496733	+	0.867903i	$0.665467\pi$
$174$		0			0
$175$	−30.5181	−	339.410i	−0.0131826	−	0.146611i
$176$	−44.7991	+	25.8648i	−0.0191867	+	0.0110774i
$177$		0			0
$178$	1594.35	−	920.501i	0.671359	−	0.387609i
$179$	−1332.30	−	769.204i	−0.556317	−	0.321190i	0.195349	−	0.980734i	$-0.437416\pi$
$179$	−1332.30	−	769.204i	−0.556317	−	0.321190i	−0.751666	+	0.659544i	$0.770749\pi$
$180$		0			0
$181$		−	249.151i		−	0.102316i	−0.998691	−	0.0511582i	$-0.983709\pi$
$181$		−	249.151i		−	0.102316i	0.998691	−	0.0511582i	$-0.0162913\pi$
$182$	−162.748	−	1810.01i	−0.0662838	−	0.737180i
$183$		0			0
$184$	−2246.28	+	3890.67i	−0.899988	+	1.55883i
$185$	−3155.43			−1.25401
$186$		0			0
$187$		−	751.565i		−	0.293903i
$188$	34.1477			0.0132472
$189$		0			0
$190$	−1900.22			−0.725562
$191$		−	2150.57i		−	0.814710i	−0.913270	−	0.407355i	$-0.866451\pi$
$191$		−	2150.57i		−	0.814710i	0.913270	−	0.407355i	$-0.133549\pi$
$192$		0			0
$193$	−2183.61			−0.814404			−0.407202	−	0.913338i	$-0.633496\pi$
$193$	−2183.61			−0.814404			−0.407202	+	0.913338i	$0.633496\pi$
$194$	1262.39	−	2186.52i	0.467186	−	0.809190i
$195$		0			0
$196$	1041.00	+	1228.55i	0.379371	+	0.447721i
$197$		−	4979.78i		−	1.80099i	−0.434868	−	0.900494i	$-0.643205\pi$
$197$		−	4979.78i		−	1.80099i	0.434868	−	0.900494i	$-0.356795\pi$
$198$		0			0
$199$	2209.05	+	1275.39i	0.786911	+	0.454323i	0.838874	−	0.544326i	$-0.183215\pi$
$199$	2209.05	+	1275.39i	0.786911	+	0.454323i	−0.0519632	+	0.998649i	$0.516548\pi$
$200$	367.777	−	212.336i	0.130029	−	0.0750721i
$201$		0			0
$202$	2454.49	−	1417.10i	0.854937	−	0.493598i
$203$	165.802	+	235.580i	0.0573252	+	0.0814507i
$204$		0			0
$205$	−730.290			−0.248808
$206$	−967.239	+	1675.31i	−0.327139	+	0.566622i
$207$		0			0
$208$	205.775	−	118.804i	0.0685958	−	0.0396038i
$209$	594.762	−	1030.16i	0.196845	−	0.340945i
$210$		0			0
$211$	−2075.55	−	3594.96i	−0.677188	−	1.17292i	−0.975824	−	0.218557i	$-0.929865\pi$
$211$	−2075.55	−	3594.96i	−0.677188	−	1.17292i	0.298636	−	0.954367i	$-0.403468\pi$
$212$	2163.97	+	1249.37i	0.701046	+	0.404749i
$213$		0			0
$214$	820.301	+	1420.80i	0.262031	+	0.453851i
$215$	−541.964	−	938.709i	−0.171915	−	0.297765i
$216$		0			0
$217$	1557.66	−	3361.53i	0.487286	−	1.05159i
$218$	880.616	+	508.424i	0.273591	+	0.157958i
$219$		0			0
$220$		−	569.557i		−	0.174543i
$221$			3452.15i			1.05075i
$222$		0			0
$223$	1646.73	+	950.739i	0.494498	+	0.285499i	0.726439	−	0.687231i	$-0.241174\pi$
$223$	1646.73	+	950.739i	0.494498	+	0.285499i	−0.231941	+	0.972730i	$0.574507\pi$
$224$	−1375.36	+	2968.12i	−0.410247	+	0.885337i
$225$		0			0
$226$	−672.754	−	1165.24i	−0.198013	−	0.342968i
$227$	−39.2105	−	67.9146i	−0.0114647	−	0.0198575i	0.860236	−	0.509896i	$-0.170316\pi$
$227$	−39.2105	−	67.9146i	−0.0114647	−	0.0198575i	−0.871701	+	0.490038i	$0.836983\pi$
$228$		0			0
$229$	3687.41	+	2128.93i	1.06406	+	0.614338i	0.926554	−	0.376162i	$-0.122756\pi$
$229$	3687.41	+	2128.93i	1.06406	+	0.614338i	0.137511	+	0.990500i	$0.456090\pi$
$230$	1826.92	+	3164.32i	0.523754	+	0.907169i
$231$		0			0
$232$	−179.498	+	310.900i	−0.0507958	+	0.0879809i
$233$	−316.489	+	182.725i	−0.0889868	+	0.0513765i	−0.543833	−	0.839193i	$-0.683028\pi$
$233$	−316.489	+	182.725i	−0.0889868	+	0.0513765i	0.454846	+	0.890570i	$0.349694\pi$
$234$		0			0
$235$	37.5494	−	65.0374i	0.0104232	−	0.0180535i
$236$	820.711			0.226372
$237$		0			0
$238$	1239.50	+	1761.15i	0.337584	+	0.479658i
$239$	2801.03	−	1617.18i	0.758091	−	0.437684i	−0.0705190	−	0.997510i	$-0.522466\pi$
$239$	2801.03	−	1617.18i	0.758091	−	0.437684i	0.828610	+	0.559827i	$0.189132\pi$
$240$		0			0
$241$	2323.47	−	1341.45i	0.621028	−	0.358550i	−0.156241	−	0.987719i	$-0.549938\pi$
$241$	2323.47	−	1341.45i	0.621028	−	0.358550i	0.777269	+	0.629168i	$0.216604\pi$
$242$	1878.24	+	1084.40i	0.498917	+	0.288050i
$243$		0			0
$244$		−	1415.76i		−	0.371455i
$245$	3484.57	−	631.741i	0.908658	−	0.164737i
$246$		0			0
$247$	−2731.91	+	4731.81i	−0.703755	+	1.21894i
$248$	4616.96			1.18217
$249$		0			0
$250$		−	2691.75i		−	0.680964i
$251$	−4725.76			−1.18840			−0.594198	−	0.804319i	$-0.702530\pi$
$251$	−4725.76			−1.18840			−0.594198	+	0.804319i	$0.702530\pi$
$252$		0			0
$253$	−2287.27			−0.568378
$254$		−	348.806i		−	0.0861654i
$255$		0			0
$256$	−4241.96			−1.03564
$257$	−2246.91	+	3891.76i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$257$	−2246.91	+	3891.76i	−0.545363	+	0.944596i	−0.998584	+	0.0531980i	$0.983059\pi$
$258$		0			0
$259$	506.889	+	5637.40i	0.121608	+	1.35247i
$260$			2616.14i			0.624023i
$261$		0			0
$262$	117.025	+	67.5643i	0.0275947	+	0.0159318i
$263$	−6573.94	+	3795.47i	−1.54132	+	0.889880i	−0.542561	+	0.840016i	$0.682545\pi$
$263$	−6573.94	+	3795.47i	−1.54132	+	0.889880i	−0.998756	+	0.0498640i	$0.984121\pi$
$264$		0			0
$265$	4759.06	−	2747.65i	1.10320	−	0.636931i
$266$	305.253	+	3394.89i	0.0703618	+	0.782534i
$267$		0			0
$268$	1401.39			0.319415
$269$	2535.95	−	4392.39i	0.574794	−	0.995572i	−0.421270	−	0.906935i	$-0.638416\pi$
$269$	2535.95	−	4392.39i	0.574794	−	0.995572i	0.996064	−	0.0886370i	$-0.0282511\pi$
$270$		0			0
$271$	−5109.38	+	2949.90i	−1.14529	+	0.661232i	−0.947734	−	0.319061i	$-0.896633\pi$
$271$	−5109.38	+	2949.90i	−1.14529	+	0.661232i	−0.197552	+	0.980292i	$0.563299\pi$
$272$	−140.789	+	243.854i	−0.0313846	+	0.0543597i
$273$		0			0
$274$	−944.593	−	1636.08i	−0.208266	−	0.360728i
$275$	187.244	+	108.106i	0.0410591	+	0.0237055i
$276$		0			0
$277$	1015.83	+	1759.46i	0.220343	+	0.381646i	0.954912	−	0.296888i	$-0.0959489\pi$
$277$	1015.83	+	1759.46i	0.220343	+	0.381646i	−0.734569	+	0.678534i	$0.762616\pi$
$278$	−1782.48	−	3087.35i	−0.384555	−	0.666069i
$279$		0			0
$280$	2540.00	+	3608.97i	0.542122	+	0.770276i
$281$	1989.68	+	1148.74i	0.422400	+	0.243873i	0.696104	−	0.717941i	$-0.254915\pi$
$281$	1989.68	+	1148.74i	0.422400	+	0.243873i	−0.273704	+	0.961814i	$0.588249\pi$
$282$		0			0
$283$		−	5670.73i		−	1.19113i	−0.803307	−	0.595566i	$-0.796928\pi$
$283$		−	5670.73i		−	1.19113i	0.803307	−	0.595566i	$-0.203072\pi$
$284$		−	3329.70i		−	0.695709i
$285$		0			0
$286$	998.539	+	576.507i	0.206451	+	0.119194i
$287$	117.314	+	1304.72i	0.0241283	+	0.268345i
$288$		0			0
$289$	411.009	+	711.888i	0.0836574	+	0.144899i
$290$	145.987	+	252.858i	0.0295610	+	0.0512011i
$291$		0			0
$292$	3440.07	+	1986.13i	0.689435	+	0.398045i
$293$	3447.32	+	5970.93i	0.687353	+	1.19053i	0.972691	+	0.232103i	$0.0745606\pi$
$293$	3447.32	+	5970.93i	0.687353	+	1.19053i	−0.285339	+	0.958427i	$0.592106\pi$
$294$		0			0
$295$	902.467	−	1563.12i	0.178114	−	0.308503i
$296$	−6108.56	+	3526.78i	−1.19950	+	0.692534i
$297$		0			0
$298$	−2172.24	+	3762.43i	−0.422264	+	0.731382i
$299$	10506.1			2.03205
$300$		0			0
$301$	−1590.01	+	1119.05i	−0.304474	+	0.214289i
$302$	−2582.07	+	1490.76i	−0.491991	+	0.284051i
$303$		0			0
$304$	−385.956	+	222.832i	−0.0728160	+	0.0420404i
$305$	−2696.45	−	1556.80i	−0.506224	−	0.292269i
$306$		0			0
$307$		−	792.899i		−	0.147404i	−0.997280	−	0.0737022i	$-0.976519\pi$
$307$		−	792.899i		−	0.147404i	0.997280	−	0.0737022i	$-0.0234814\pi$
$308$	−1017.56	+	91.4939i	−0.188249	+	0.0169265i
$309$		0			0
$310$	1877.51	−	3251.94i	0.343985	−	0.595799i
$311$	−7769.13			−1.41655			−0.708275	−	0.705937i	$-0.750526\pi$
$311$	−7769.13			−1.41655			−0.708275	+	0.705937i	$0.750526\pi$
$312$		0			0
$313$		−	3457.27i		−	0.624334i	−0.950027	−	0.312167i	$-0.898945\pi$
$313$		−	3457.27i		−	0.624334i	0.950027	−	0.312167i	$-0.101055\pi$
$314$	2152.00			0.386765
$315$		0			0
$316$	5337.73			0.950224
$317$			2618.13i			0.463876i	0.972731	+	0.231938i	$0.0745067\pi$
$317$			2618.13i			0.463876i	−0.972731	+	0.231938i	$0.925493\pi$
$318$		0			0
$319$	−182.774			−0.0320795
$320$	−1839.59	+	3186.26i	−0.321363	+	0.556617i
$321$		0			0
$322$	5359.80	−	3772.24i	0.927609	−	0.652853i
$323$		−	6474.92i		−	1.11540i
$324$		0			0
$325$	−860.067	−	496.560i	−0.146794	−	0.0847513i
$326$	1292.06	−	745.970i	0.219511	−	0.126734i
$327$		0			0
$328$	−1413.76	+	816.235i	−0.237994	+	0.137406i
$329$	−122.226	−	56.6370i	−0.0204819	−	0.00949088i
$330$		0			0
$331$	254.315			0.0422309			0.0211155	−	0.999777i	$-0.493278\pi$
$331$	254.315			0.0422309			0.0211155	+	0.999777i	$0.493278\pi$
$332$	−771.456	+	1336.20i	−0.127528	+	0.220884i
$333$		0			0
$334$	2508.72	−	1448.41i	0.410992	−	0.237286i
$335$	1540.99	−	2669.07i	0.251323	−	0.435304i
$336$		0			0
$337$	4521.98	+	7832.30i	0.730943	+	1.26603i	0.956480	+	0.291796i	$0.0942529\pi$
$337$	4521.98	+	7832.30i	0.730943	+	1.26603i	−0.225537	+	0.974235i	$0.572414\pi$
$338$	−1127.45	−	650.931i	−0.181435	−	0.104751i
$339$		0			0
$340$	−1550.13	−	2684.91i	−0.247258	−	0.428263i
$341$	1175.30	+	2035.69i	0.186646	+	0.323280i
$342$		0			0
$343$	−1688.41	−	6123.96i	−0.265789	−	0.964031i
$344$	−2098.37	−	1211.49i	−0.328885	−	0.189882i
$345$		0			0
$346$			4109.88i			0.638579i
$347$		−	7213.40i		−	1.11595i	−0.829857	−	0.557976i	$-0.811578\pi$
$347$		−	7213.40i		−	1.11595i	0.829857	−	0.557976i	$-0.188422\pi$
$348$		0			0
$349$	−214.544	−	123.867i	−0.0329062	−	0.0189984i	0.483457	−	0.875368i	$-0.339381\pi$
$349$	−214.544	−	123.867i	−0.0329062	−	0.0189984i	−0.516363	+	0.856370i	$0.672714\pi$
$350$	−617.064	+	55.4835i	−0.0942385	+	0.00847349i
$351$		0			0
$352$	−1037.75	−	1797.44i	−0.157138	−	0.272171i
$353$	−1199.21	−	2077.10i	−0.180815	−	0.313180i	0.761343	−	0.648349i	$-0.224540\pi$
$353$	−1199.21	−	2077.10i	−0.180815	−	0.313180i	−0.942158	+	0.335168i	$0.891207\pi$
$354$		0			0
$355$	−6341.72	−	3661.39i	−0.948122	−	0.547399i
$356$	2376.98	+	4117.05i	0.353875	+	0.612930i
$357$		0			0
$358$	−1398.45	+	2422.19i	−0.206454	+	0.357589i
$359$	3189.10	−	1841.23i	0.468842	−	0.270686i	−0.246913	−	0.969038i	$-0.579416\pi$
$359$	3189.10	−	1841.23i	0.468842	−	0.270686i	0.715755	+	0.698351i	$0.246083\pi$
$360$		0			0
$361$	1694.53	−	2935.01i	0.247052	−	0.427907i
$362$	−452.970			−0.0657667
$363$		0			0
$364$	4673.92	−	420.257i	0.673022	−	0.0605150i
$365$	7565.51	−	4367.95i	1.08492	−	0.626381i
$366$		0			0
$367$	−9655.84	+	5574.80i	−1.37338	+	0.792922i	−0.991352	−	0.131228i	$-0.958108\pi$
$367$	−9655.84	+	5574.80i	−1.37338	+	0.792922i	−0.382029	+	0.924150i	$0.624775\pi$
$368$	742.133	+	428.471i	0.105126	+	0.0606945i
$369$		0			0
$370$			5736.73i			0.806049i
$371$	−5673.37	−	8061.03i	−0.793926	−	1.12805i
$372$		0			0
$373$	4874.02	−	8442.06i	0.676588	−	1.17189i	−0.299414	−	0.954123i	$-0.596791\pi$
$373$	4874.02	−	8442.06i	0.676588	−	1.17189i	0.976002	−	0.217762i	$-0.0698756\pi$
$374$	−1366.38			−0.188914
$375$		0			0
$376$		−	167.874i		−	0.0230251i
$377$	839.532			0.114690
$378$		0			0
$379$	−4563.79			−0.618538			−0.309269	−	0.950975i	$-0.600084\pi$
$379$	−4563.79			−0.618538			−0.309269	+	0.950975i	$0.600084\pi$
$380$		−	4906.88i		−	0.662415i
$381$		0			0
$382$	−3909.84			−0.523678
$383$	1576.66	−	2730.86i	0.210349	−	0.364335i	−0.741475	−	0.670981i	$-0.765873\pi$
$383$	1576.66	−	2730.86i	0.210349	−	0.364335i	0.951824	+	0.306646i	$0.0992067\pi$
$384$		0			0
$385$	−944.662	+	2038.63i	−0.125050	+	0.269866i
$386$			3969.92i			0.523481i
$387$		0			0
$388$	5646.17	+	3259.82i	0.738765	+	0.426526i
$389$	−6457.10	+	3728.01i	−0.841614	+	0.485906i	−0.857813	−	0.513963i	$-0.828177\pi$
$389$	−6457.10	+	3728.01i	−0.841614	+	0.485906i	0.0161983	+	0.999869i	$0.494844\pi$
$390$		0			0
$391$	−10782.3	+	6225.14i	−1.39458	+	0.805163i
$392$	6039.66	−	5117.64i	0.778187	−	0.659388i
$393$		0			0
$394$	−9053.50			−1.15764
$395$	5869.45	−	10166.2i	0.747656	−	1.29498i
$396$		0			0
$397$	−3744.30	+	2161.77i	−0.473353	+	0.273290i	−0.717642	−	0.696412i	$-0.754779\pi$
$397$	−3744.30	+	2161.77i	−0.473353	+	0.273290i	0.244290	+	0.969702i	$0.421445\pi$
$398$	2318.73	−	4016.16i	0.292029	−	0.505809i
$399$		0			0
$400$	−40.5025	−	70.1524i	−0.00506281	−	0.00876904i
$401$	−62.9707	−	36.3561i	−0.00784191	−	0.00452753i	0.496074	−	0.868280i	$-0.334774\pi$
$401$	−62.9707	−	36.3561i	−0.00784191	−	0.00452753i	−0.503916	+	0.863753i	$0.668108\pi$
$402$		0			0
$403$	−5398.51	−	9350.49i	−0.667292	−	1.15578i
$404$	3659.33	+	6338.15i	0.450640	+	0.780531i
$405$		0			0
$406$	428.297	−	301.436i	0.0523548	−	0.0368474i
$407$	−3110.02	−	1795.57i	−0.378767	−	0.218681i
$408$		0			0
$409$		−	4194.63i		−	0.507118i	−0.967320	−	0.253559i	$-0.918399\pi$
$409$		−	4194.63i		−	0.507118i	0.967320	−	0.253559i	$-0.0816012\pi$
$410$			1327.70i			0.159928i
$411$		0			0
$412$	−4326.09	−	2497.67i	−0.517308	−	0.298668i
$413$	−2937.60	−	1361.22i	−0.349999	−	0.162183i
$414$		0			0
$415$	1696.61	+	2938.62i	0.200683	+	0.347593i
$416$	4766.70	+	8256.17i	0.561795	+	0.973057i
$417$		0			0
$418$	−1872.88	−	1081.31i	−0.219152	−	0.126528i
$419$	−7094.88	−	12288.7i	−0.827226	−	1.43280i	−0.900206	−	0.435463i	$-0.856585\pi$
$419$	−7094.88	−	12288.7i	−0.827226	−	1.43280i	0.0729809	−	0.997333i	$-0.476749\pi$
$420$		0			0
$421$	−5387.76	+	9331.88i	−0.623714	+	1.08030i	0.365074	+	0.930978i	$0.381044\pi$
$421$	−5387.76	+	9331.88i	−0.623714	+	1.08030i	−0.988788	+	0.149326i	$0.952290\pi$
$422$	−6535.81	+	3773.45i	−0.753930	+	0.435282i
$423$		0			0
$424$	6142.02	−	10638.3i	0.703497	−	1.21849i
$425$	1176.90			0.134325
$426$		0			0
$427$	−2348.17	+	5067.49i	−0.266127	+	0.574316i
$428$	−3668.89	+	2118.23i	−0.414352	+	0.239226i
$429$		0			0
$430$	−1706.62	+	985.318i	−0.191397	+	0.110503i
$431$	9918.85	+	5726.65i	1.10853	+	0.640007i	0.938447	−	0.345423i	$-0.112265\pi$
$431$	9918.85	+	5726.65i	1.10853	+	0.640007i	0.170078	+	0.985431i	$0.445598\pi$
$432$		0			0
$433$		−	3256.21i		−	0.361394i	−0.983539	−	0.180697i	$-0.942165\pi$
$433$		−	3256.21i		−	0.361394i	0.983539	−	0.180697i	$-0.0578353\pi$
$434$	−6111.43	−	2831.91i	−0.675940	−	0.313217i
$435$		0			0
$436$	−1312.89	+	2273.98i	−0.144211	+	0.249780i
$437$	−19705.4			−2.15707
$438$		0			0
$439$		−	5448.19i		−	0.592319i	−0.955138	−	0.296160i	$-0.904294\pi$
$439$		−	5448.19i		−	0.592319i	0.955138	−	0.296160i	$-0.0957060\pi$
$440$	−2800.00			−0.303375
$441$		0			0
$442$	6276.19			0.675402
$443$			8233.23i			0.883008i	0.897259	+	0.441504i	$0.145555\pi$
$443$			8233.23i			0.883008i	−0.897259	+	0.441504i	$0.854445\pi$
$444$		0			0
$445$	10455.0			1.11375
$446$	1728.49	−	2993.84i	0.183512	−	0.317853i
$447$		0			0
$448$	5988.00	+	2774.72i	0.631487	+	0.292618i
$449$			14892.7i			1.56532i	0.622447	+	0.782662i	$0.286139\pi$
$449$			14892.7i			1.56532i	−0.622447	+	0.782662i	$0.713861\pi$
$450$		0			0
$451$	−719.781	−	415.566i	−0.0751512	−	0.0433885i
$452$	3008.97	−	1737.23i	0.313119	−	0.180780i
$453$		0			0
$454$	−123.472	+	71.2867i	−0.0127640	+	0.00736927i
$455$	4339.10	−	9364.03i	0.447077	−	0.964818i
$456$		0			0
$457$	13515.0			1.38338			0.691691	−	0.722193i	$-0.256866\pi$
$457$	13515.0			1.38338			0.691691	+	0.722193i	$0.256866\pi$
$458$	3870.50	−	6703.90i	0.394883	−	0.683957i
$459$		0			0
$460$	−8171.11	+	4717.59i	−0.828217	+	0.478171i
$461$	1880.20	−	3256.61i	0.189956	−	0.329014i	−0.755279	−	0.655403i	$-0.772499\pi$
$461$	1880.20	−	3256.61i	0.189956	−	0.329014i	0.945235	+	0.326389i	$0.105832\pi$
$462$		0			0
$463$	−8271.99	−	14327.5i	−0.830307	−	1.43813i	−0.897795	−	0.440414i	$-0.854832\pi$
$463$	−8271.99	−	14327.5i	−0.830307	−	1.43813i	0.0674881	−	0.997720i	$-0.478502\pi$
$464$	59.3032	+	34.2387i	0.00593337	+	0.00342563i
$465$		0			0
$466$	332.204	+	575.394i	0.0330237	+	0.0571987i
$467$	−2187.46	−	3788.79i	−0.216753	−	0.375427i	0.737060	−	0.675827i	$-0.236213\pi$
$467$	−2187.46	−	3788.79i	−0.216753	−	0.375427i	−0.953813	+	0.300400i	$0.902880\pi$
$468$		0			0
$469$	−5016.03	−	2324.32i	−0.493856	−	0.228843i
$470$	−118.241	−	68.2667i	−0.0116044	−	0.00669980i
$471$		0			0
$472$		−	4034.70i		−	0.393458i
$473$		−	1233.60i		−	0.119918i
$474$		0			0
$475$	1613.16	+	931.358i	0.155825	+	0.0899655i
$476$	−4547.77	+	3200.73i	−0.437913	+	0.308204i
$477$		0			0
$478$	−2940.11	−	5092.42i	−0.281334	−	0.487284i
$479$	4185.63	+	7249.72i	0.399262	+	0.691541i	0.993635	−	0.112648i	$-0.0359332\pi$
$479$	4185.63	+	7249.72i	0.399262	+	0.691541i	−0.594373	+	0.804189i	$0.702600\pi$
$480$		0			0
$481$	14285.2	+	8247.57i	1.35416	+	0.781823i
$482$	−2438.83	−	4224.18i	−0.230468	−	0.399183i
$483$		0			0
$484$	−2800.21	+	4850.11i	−0.262980	+	0.455495i
$485$	12417.2	−	7169.09i	1.16255	−	0.671200i
$486$		0			0
$487$	−8120.25	+	14064.7i	−0.755572	+	1.30869i	0.189517	+	0.981877i	$0.439308\pi$
$487$	−8120.25	+	14064.7i	−0.755572	+	1.30869i	−0.945089	+	0.326812i	$0.894026\pi$
$488$	−6960.05			−0.645628
$489$		0			0
$490$	−1148.54	−	6335.13i	−0.105889	−	0.584065i
$491$	−10501.0	+	6062.77i	−0.965183	+	0.557248i	−0.897764	−	0.440476i	$-0.854810\pi$
$491$	−10501.0	+	6062.77i	−0.965183	+	0.557248i	−0.0674183	+	0.997725i	$0.521476\pi$
$492$		0			0
$493$	−861.601	+	497.445i	−0.0787110	+	0.0454438i
$494$	8602.67	+	4966.76i	0.783507	+	0.452358i
$495$		0			0
$496$		−	880.671i		−	0.0797244i
$497$	−5522.61	+	11918.1i	−0.498436	+	1.07565i
$498$		0			0
$499$	−1839.20	+	3185.59i	−0.164998	+	0.285785i	−0.936655	−	0.350254i	$-0.886095\pi$
$499$	−1839.20	+	3185.59i	−0.164998	+	0.285785i	0.771657	+	0.636039i	$0.219428\pi$
$500$	6950.80			0.621699
$501$		0			0
$502$			8591.67i			0.763875i
$503$	−4318.33			−0.382793			−0.191397	−	0.981513i	$-0.561302\pi$
$503$	−4318.33			−0.382793			−0.191397	+	0.981513i	$0.561302\pi$
$504$		0			0
$505$	16095.4			1.41829
$506$			4158.38i			0.365341i
$507$		0			0
$508$	900.709			0.0786663
$509$	−7564.51	+	13102.1i	−0.658725	+	1.14094i	0.322221	+	0.946664i	$0.395571\pi$
$509$	−7564.51	+	13102.1i	−0.658725	+	1.14094i	−0.980946	+	0.194281i	$0.937763\pi$
$510$		0			0
$511$	−9018.99	−	12814.7i	−0.780776	−	1.10937i
$512$			1590.44i			0.137282i
$513$		0			0
$514$	7075.41	+	4084.99i	0.607166	+	0.350547i
$515$	−9514.07	+	5492.95i	−0.814058	+	0.469997i
$516$		0			0
$517$	74.0181	−	42.7344i	0.00629654	−	0.00363531i
$518$	10249.1	−	921.550i	0.869341	−	0.0781671i
$519$		0			0
$520$	12861.2			1.08462
$521$	1778.96	−	3081.24i	0.149592	−	0.259101i	−0.781485	−	0.623924i	$-0.785537\pi$
$521$	1778.96	−	3081.24i	0.149592	−	0.259101i	0.931077	+	0.364823i	$0.118871\pi$
$522$		0			0
$523$	5150.60	−	2973.70i	0.430631	−	0.248625i	−0.268984	−	0.963145i	$-0.586688\pi$
$523$	5150.60	−	2973.70i	0.430631	−	0.248625i	0.699616	+	0.714519i	$0.253355\pi$
$524$	−174.469	+	302.189i	−0.0145453	+	0.0251931i
$525$		0			0
$526$	6900.35	+	11951.8i	0.571995	+	0.990725i
$527$	11080.8	+	6397.52i	0.915917	+	0.528805i
$528$		0			0
$529$	12861.8	+	22277.2i	1.05710	+	1.83096i
$530$	−4995.36	−	8652.22i	−0.409405	−	0.709110i
$531$		0			0
$532$	−8766.50	+	788.243i	−0.714429	+	0.0642381i
$533$	3306.16	+	1908.81i	0.268678	+	0.155122i
$534$		0			0
$535$			9316.98i			0.752912i
$536$		−	6889.36i		−	0.555178i
$537$		0			0
$538$	−7985.60	−	4610.49i	−0.639932	−	0.369465i
$539$	3793.92	+	1360.22i	0.303183	+	0.108699i
$540$		0			0
$541$	−1150.34	−	1992.45i	−0.0914179	−	0.158340i	0.816690	−	0.577077i	$-0.195807\pi$
$541$	−1150.34	−	1992.45i	−0.0914179	−	0.158340i	−0.908108	+	0.418736i	$0.862473\pi$
$542$	5363.07	+	9289.11i	0.425025	+	0.736165i
$543$		0			0
$544$	−9784.00	−	5648.79i	−0.771113	−	0.445202i
$545$	2887.34	+	5001.02i	0.226936	+	0.393064i
$546$		0			0
$547$	10075.5	−	17451.3i	0.787564	−	1.36410i	−0.139891	−	0.990167i	$-0.544675\pi$
$547$	10075.5	−	17451.3i	0.787564	−	1.36410i	0.927455	−	0.373935i	$-0.121992\pi$
$548$	4224.80	−	2439.19i	0.329333	−	0.190141i
$549$		0			0
$550$	196.542	−	340.420i	0.0152374	−	0.0263919i
$551$	−1574.64			−0.121746
$552$		0			0
$553$	−19105.5	−	8853.10i	−1.46917	−	0.680781i
$554$	3198.80	−	1846.83i	0.245314	−	0.141632i
$555$		0			0
$556$	7972.36	−	4602.85i	0.608100	−	0.351087i
$557$	15743.2	+	9089.32i	1.19759	+	0.691430i	0.960018	−	0.279939i	$-0.0903143\pi$
$557$	15743.2	+	9089.32i	1.19759	+	0.691430i	0.237575	+	0.971369i	$0.423648\pi$
$558$		0			0
$559$			5666.28i			0.428727i
$560$	688.401	−	484.498i	0.0519469	−	0.0365603i
$561$		0			0
$562$	2088.47	−	3617.34i	0.156756	−	0.271509i
$563$	18862.5			1.41201			0.706003	−	0.708209i	$-0.250496\pi$
$563$	18862.5			1.41201			0.706003	+	0.708209i	$0.250496\pi$
$564$		0			0
$565$		−	7641.14i		−	0.568965i
$566$	−10309.7			−0.765633
$567$		0			0
$568$	−16369.2			−1.20922
$569$		−	1042.98i		−	0.0768433i	−0.999262	−	0.0384216i	$-0.987767\pi$
$569$		−	1042.98i		−	0.0768433i	0.999262	−	0.0384216i	$-0.0122330\pi$
$570$		0			0
$571$	18050.3			1.32291			0.661455	−	0.749985i	$-0.269939\pi$
$571$	18050.3			1.32291			0.661455	+	0.749985i	$0.269939\pi$
$572$	−1488.69	+	2578.49i	−0.108821	+	0.188483i
$573$		0			0
$574$	2372.04	−	213.283i	0.172486	−	0.0155091i
$575$		−	3581.71i		−	0.259770i
$576$		0			0
$577$	−6810.96	−	3932.31i	−0.491411	−	0.283716i	0.233749	−	0.972297i	$-0.424901\pi$
$577$	−6810.96	−	3932.31i	−0.491411	−	0.283716i	−0.725160	+	0.688581i	$0.758234\pi$
$578$	1294.25	−	747.235i	0.0931378	−	0.0537731i
$579$		0			0
$580$	−652.946	+	376.978i	−0.0467450	+	0.0269882i
$581$	4977.51	−	3503.18i	0.355425	−	0.250149i
$582$		0			0
$583$	6254.11			0.444286
$584$	9764.00	−	16911.8i	0.691845	−	1.19831i
$585$		0			0
$586$	10855.4	−	6267.40i	0.765246	−	0.441815i
$587$	−10851.6	+	18795.6i	−0.763024	+	1.32160i	0.178261	+	0.983983i	$0.442953\pi$
$587$	−10851.6	+	18795.6i	−0.763024	+	1.32160i	−0.941285	+	0.337613i	$0.890381\pi$
$588$		0			0
$589$	10125.5	+	17538.0i	0.708346	+	1.22689i
$590$	−2841.83	−	1640.73i	−0.198299	−	0.114488i
$591$		0			0
$592$	672.723	+	1165.19i	0.0467040	+	0.0808936i
$593$	−4093.90	−	7090.84i	−0.283501	−	0.491039i	0.688743	−	0.725005i	$-0.258163\pi$
$593$	−4093.90	−	7090.84i	−0.283501	−	0.491039i	−0.972245	+	0.233967i	$0.924829\pi$
$594$		0			0
$595$	1095.28	+	12181.2i	0.0754656	+	0.839295i
$596$	−9715.60	−	5609.31i	−0.667729	−	0.385514i
$597$		0			0
$598$		−	19100.6i		−	1.30616i
$599$		−	15220.8i		−	1.03824i	−0.854702	−	0.519119i	$-0.826260\pi$
$599$		−	15220.8i		−	1.03824i	0.854702	−	0.519119i	$-0.173740\pi$
$600$		0			0
$601$	4793.86	+	2767.74i	0.325367	+	0.187851i	0.653782	−	0.756683i	$-0.273181\pi$
$601$	4793.86	+	2767.74i	0.325367	+	0.187851i	−0.328415	+	0.944534i	$0.606514\pi$
$602$	2034.49	+	2890.72i	0.137740	+	0.195709i
$603$		0			0
$604$	−3849.53	−	6667.58i	−0.259330	−	0.449172i
$605$	6158.32	+	10666.5i	0.413837	+	0.716786i
$606$		0			0
$607$	7868.26	+	4542.74i	0.526133	+	0.303763i	0.739440	−	0.673222i	$-0.235090\pi$
$607$	7868.26	+	4542.74i	0.526133	+	0.303763i	−0.213307	+	0.976985i	$0.568424\pi$
$608$	−8940.52	−	15485.4i	−0.596359	−	1.03292i
$609$		0			0
$610$	−2830.34	+	4902.29i	−0.187864	+	0.325390i
$611$	−339.986	+	196.291i	−0.0225112	+	0.0129969i
$612$		0			0
$613$	1436.35	−	2487.83i	0.0946389	−	0.163919i	−0.814819	−	0.579716i	$-0.803164\pi$
$613$	1436.35	−	2487.83i	0.0946389	−	0.163919i	0.909458	+	0.415796i	$0.136497\pi$
$614$	−1441.53			−0.0947483
$615$		0			0
$616$	449.794	+	5002.41i	0.0294200	+	0.327196i
$617$	−20061.6	+	11582.6i	−1.30900	+	0.755749i	−0.981928	−	0.189252i	$-0.939394\pi$
$617$	−20061.6	+	11582.6i	−1.30900	+	0.755749i	−0.327067	+	0.945001i	$0.606060\pi$
$618$		0			0
$619$	10861.0	−	6270.60i	0.705235	−	0.407168i	−0.104059	−	0.994571i	$-0.533183\pi$
$619$	10861.0	−	6270.60i	0.705235	−	0.407168i	0.809294	+	0.587404i	$0.199850\pi$
$620$	8397.37	+	4848.22i	0.543946	+	0.314047i
$621$		0			0
$622$			14124.7i			0.910527i
$623$	−1679.50	−	18678.7i	−0.108006	−	1.20120i
$624$		0			0
$625$	6493.19	−	11246.5i	0.415564	−	0.719779i
$626$	−6285.50			−0.401308
$627$		0			0
$628$			5557.03i			0.353104i
$629$	−19547.6			−1.23913
$630$		0			0
$631$	13470.4			0.849839			0.424919	−	0.905231i	$-0.360302\pi$
$631$	13470.4			0.849839			0.424919	+	0.905231i	$0.360302\pi$
$632$		−	26240.8i		−	1.65159i
$633$		0			0
$634$	4759.89			0.298169
$635$	990.434	−	1715.48i	0.0618963	−	0.107208i
$636$		0			0
$637$	−17426.5	−	6247.87i	−1.08393	−	0.388618i
$638$			332.292i			0.0206200i
$639$		0			0
$640$	−6842.08	−	3950.27i	−0.422589	−	0.243982i
$641$	−10158.0	+	5864.73i	−0.625924	+	0.361377i	−0.779172	−	0.626810i	$-0.784360\pi$
$641$	−10158.0	+	5864.73i	−0.625924	+	0.361377i	0.153248	+	0.988188i	$0.451027\pi$
$642$		0			0
$643$	−18362.0	+	10601.3i	−1.12617	+	0.650193i	−0.942968	−	0.332883i	$-0.891979\pi$
$643$	−18362.0	+	10601.3i	−1.12617	+	0.650193i	−0.183199	+	0.983076i	$0.558645\pi$
$644$	9740.93	+	13840.4i	0.596035	+	0.846878i
$645$		0			0
$646$	−11771.7			−0.716955
$647$	−12408.1	+	21491.4i	−0.753960	+	1.30590i	0.191929	+	0.981409i	$0.438526\pi$
$647$	−12408.1	+	21491.4i	−0.753960	+	1.30590i	−0.945890	+	0.324489i	$0.894808\pi$
$648$		0			0
$649$	1778.96	−	1027.08i	0.107597	−	0.0621211i
$650$	−902.771	+	1563.65i	−0.0544763	+	0.0943557i
$651$		0			0
$652$	1926.29	+	3336.43i	0.115705	+	0.200406i
$653$	23134.2	+	13356.5i	1.38639	+	0.800431i	0.992906	−	0.118902i	$-0.0379373\pi$
$653$	23134.2	+	13356.5i	1.38639	+	0.800431i	0.393481	+	0.919333i	$0.371271\pi$
$654$		0			0
$655$	383.698	+	664.584i	0.0228890	+	0.0396450i
$656$	155.694	+	269.671i	0.00926654	+	0.0160501i
$657$		0			0
$658$	−102.969	+	222.213i	−0.00610053	+	0.0131653i
$659$	12459.7	+	7193.60i	0.736510	+	0.425224i	0.820799	−	0.571217i	$-0.193529\pi$
$659$	12459.7	+	7193.60i	0.736510	+	0.425224i	−0.0842889	+	0.996441i	$0.526862\pi$
$660$		0			0
$661$			22620.5i			1.33107i	0.746367	+	0.665535i	$0.231797\pi$
$661$			22620.5i			1.33107i	−0.746367	+	0.665535i	$0.768203\pi$
$662$		−	462.358i		−	0.0271451i
$663$		0			0
$664$	6568.91	+	3792.56i	0.383920	+	0.221656i
$665$	−8138.50	+	17563.4i	−0.474583	+	1.02418i
$666$		0			0
$667$	1513.90	+	2622.15i	0.0878837	+	0.152219i
$668$	3740.19	+	6478.19i	0.216635	+	0.375223i
$669$		0			0
$670$	−4852.50	−	2801.59i	−0.279804	−	0.161545i
$671$	−1771.77	−	3068.79i	−0.101935	−	0.176556i
$672$		0			0
$673$	8442.83	−	14623.4i	0.483577	−	0.837580i	−0.516245	−	0.856441i	$-0.672671\pi$
$673$	8442.83	−	14623.4i	0.483577	−	0.837580i	0.999822	+	0.0188612i	$0.00600406\pi$
$674$	14239.5	−	8221.19i	0.813777	−	0.469834i
$675$		0			0
$676$	1680.88	−	2911.36i	0.0956347	−	0.165644i
$677$	26795.8			1.52119			0.760595	−	0.649227i	$-0.224907\pi$
$677$	26795.8			1.52119			0.760595	+	0.649227i	$0.224907\pi$
$678$		0			0
$679$	−14802.8	−	21032.6i	−0.836642	−	1.18875i
$680$	−13199.3	+	7620.61i	−0.744367	+	0.429761i
$681$		0			0
$682$	3700.98	−	2136.76i	0.207798	−	0.119972i
$683$	12561.4	+	7252.31i	0.703730	+	0.406299i	0.808735	−	0.588173i	$-0.200153\pi$
$683$	12561.4	+	7252.31i	0.703730	+	0.406299i	−0.105005	+	0.994472i	$0.533486\pi$
$684$		0			0
$685$		−	10728.7i		−	0.598427i
$686$	−11133.7	+	3069.62i	−0.619658	+	0.170844i
$687$		0			0
$688$	−231.088	+	400.257i	−0.0128055	+	0.0221797i
$689$	−28726.9			−1.58840
$690$		0			0
$691$			28616.3i			1.57542i	0.616046	+	0.787710i	$0.288734\pi$
$691$			28616.3i			1.57542i	−0.616046	+	0.787710i	$0.711266\pi$
$692$	−10612.8			−0.583002
$693$		0			0
$694$	−13114.3			−0.717310
$695$		−	20245.5i		−	1.10497i
$696$		0			0
$697$	−4524.09			−0.245857
$698$	−225.196	+	390.051i	−0.0122118	+	0.0211514i
$699$		0			0
$700$	−143.273	−	1593.42i	−0.00773603	−	0.0860368i
$701$			6936.34i			0.373726i	0.982386	+	0.186863i	$0.0598321\pi$
$701$			6936.34i			0.373726i	−0.982386	+	0.186863i	$0.940168\pi$
$702$		0			0
$703$	−26793.6	−	15469.3i	−1.43747	−	0.829924i
$704$	−3626.24	+	2093.61i	−0.194132	+	0.112082i
$705$		0			0
$706$	−3776.27	+	2180.23i	−0.201306	+	0.116224i
$707$	−2585.58	−	28755.6i	−0.137540	−	1.52966i
$708$		0			0
$709$	−15462.1			−0.819030			−0.409515	−	0.912303i	$-0.634302\pi$
$709$	−15462.1			−0.819030			−0.409515	+	0.912303i	$0.634302\pi$
$710$	−6656.60	+	11529.6i	−0.351856	+	0.609432i
$711$		0			0
$712$	20239.8	−	11685.5i	1.06534	−	0.615072i
$713$	19469.9	−	33722.8i	1.02265	−	1.77129i
$714$		0			0
$715$	3273.98	+	5670.71i	0.171245	+	0.296605i
$716$	−6254.74	−	3611.17i	−0.326467	−	0.188486i
$717$		0			0
$718$	−3347.45	−	5797.95i	−0.173991	−	0.301362i
$719$	−4003.14	−	6933.64i	−0.207638	−	0.359640i	0.743332	−	0.668923i	$-0.233244\pi$
$719$	−4003.14	−	6933.64i	−0.207638	−	0.359640i	−0.950970	+	0.309283i	$0.899911\pi$
$720$		0			0
$721$	11341.9	+	16115.2i	0.585845	+	0.832400i
$722$	−5336.00	−	3080.74i	−0.275049	−	0.158800i
$723$		0			0
$724$		−	1169.69i		−	0.0600429i
$725$		−	286.212i		−	0.0146616i
$726$		0			0
$727$	−17033.8	−	9834.49i	−0.868982	−	0.501707i	−0.00197210	−	0.999998i	$-0.500628\pi$
$727$	−17033.8	−	9834.49i	−0.868982	−	0.501707i	−0.867010	+	0.498291i	$0.833961\pi$
$728$	−2066.03	−	22977.5i	−0.105182	−	1.16978i
$729$		0			0
$730$	−7941.16	−	13754.5i	−0.402624	−	0.697365i
$731$	−3357.42	−	5815.23i	−0.169875	−	0.294233i
$732$		0			0
$733$	−9717.80	−	5610.57i	−0.489680	−	0.282717i	0.234762	−	0.972053i	$-0.424569\pi$
$733$	−9717.80	−	5610.57i	−0.489680	−	0.282717i	−0.724442	+	0.689336i	$0.757902\pi$
$734$	10135.3	+	17554.8i	0.509673	+	0.882779i
$735$		0			0
$736$	−17191.2	+	29776.1i	−0.860975	+	1.49125i
$737$	3037.62	−	1753.77i	0.151821	−	0.0876541i
$738$		0			0
$739$	8129.32	−	14080.4i	0.404657	−	0.700887i	−0.589624	−	0.807678i	$-0.700724\pi$
$739$	8129.32	−	14080.4i	0.404657	−	0.700887i	0.994282	+	0.106791i	$0.0340574\pi$
$740$	−14813.8			−0.735898
$741$		0			0
$742$	−14655.4	+	10314.5i	−0.725088	+	0.510318i
$743$	11556.7	−	6672.24i	0.570623	−	0.329449i	−0.186775	−	0.982403i	$-0.559804\pi$
$743$	11556.7	−	6672.24i	0.570623	−	0.329449i	0.757398	+	0.652953i	$0.226470\pi$
$744$		0			0
$745$	−21366.9	+	12336.2i	−1.05077	+	0.606660i
$746$	−15348.1	−	8861.23i	−0.753262	−	0.434896i
$747$		0			0
$748$		−	3528.36i		−	0.172473i
$749$	16645.5	−	1496.68i	0.812032	−	0.0730141i
$750$		0			0
$751$	4191.44	−	7259.79i	0.203659	−	0.352748i	−0.746046	−	0.665895i	$-0.768050\pi$
$751$	4191.44	−	7259.79i	0.203659	−	0.352748i	0.949705	+	0.313147i	$0.101383\pi$
$752$	−32.0214			−0.00155279
$753$		0			0
$754$		−	1526.31i		−	0.0737202i
$755$	−16932.0			−0.816184
$756$		0			0
$757$	−2701.73			−0.129717			−0.0648586	−	0.997894i	$-0.520660\pi$
$757$	−2701.73			−0.129717			−0.0648586	+	0.997894i	$0.520660\pi$
$758$			8297.20i			0.397583i
$759$		0			0
$760$	−24122.8			−1.15135
$761$	−1831.85	+	3172.87i	−0.0872598	+	0.151138i	−0.906352	−	0.422524i	$-0.861144\pi$
$761$	−1831.85	+	3172.87i	−0.0872598	+	0.151138i	0.819092	+	0.573662i	$0.194478\pi$
$762$		0			0
$763$	8470.86	−	5961.81i	0.401921	−	0.282873i
$764$		−	10096.3i		−	0.478102i
$765$		0			0
$766$	−4964.84	−	2866.45i	−0.234186	−	0.135208i
$767$	−8171.28	+	4717.69i	−0.384678	+	0.222094i
$768$		0			0
$769$	5627.29	−	3248.92i	0.263882	−	0.152352i	−0.362222	−	0.932092i	$-0.617982\pi$
$769$	5627.29	−	3248.92i	0.263882	−	0.152352i	0.626104	+	0.779739i	$0.284648\pi$
$770$	3706.34	+	1717.44i	0.173464	+	0.0803797i
$771$		0			0
$772$	−10251.4			−0.477922
$773$	19412.7	−	33623.7i	0.903266	−	1.56450i	0.0800382	−	0.996792i	$-0.474496\pi$
$773$	19412.7	−	33623.7i	0.903266	−	1.56450i	0.823228	−	0.567711i	$-0.192171\pi$
$774$		0			0
$775$	−3187.75	+	1840.45i	−0.147751	+	0.0853043i
$776$	16025.6	−	27757.2i	0.741348	−	1.28405i
$777$		0			0
$778$	6777.71	+	11739.3i	0.312330	+	0.540971i
$779$	−6201.10	−	3580.21i	−0.285209	−	0.164665i
$780$		0			0
$781$	−4166.97	−	7217.41i	−0.190917	−	0.330678i
$782$	11317.6	+	19602.7i	0.517541	+	0.896408i
$783$		0			0
$784$	−976.175	−	1152.05i	−0.0444686	−	0.0524803i
$785$	10583.9	+	6110.59i	0.481216	+	0.277830i
$786$		0			0
$787$			1372.29i			0.0621563i	0.999517	+	0.0310781i	$0.00989407\pi$
$787$			1372.29i			0.0621563i	−0.999517	+	0.0310781i	$0.990106\pi$
$788$		−	23378.5i		−	1.05689i
$789$		0			0
$790$	−18482.7	−	10671.0i	−0.832384	−	0.480577i
$791$	−13651.4	+	1227.47i	−0.613640	+	0.0551757i
$792$		0			0
$793$	8138.23	+	14095.8i	0.364435	+	0.631220i
$794$	3930.21	+	6807.33i	0.175665	+	0.304261i
$795$		0			0
$796$	10370.8	+	5987.58i	0.461788	+	0.266613i
$797$	14473.0	+	25068.0i	0.643239	+	1.11412i	0.984705	+	0.174228i	$0.0557431\pi$
$797$	14473.0	+	25068.0i	0.643239	+	1.11412i	−0.341466	+	0.939894i	$0.610924\pi$
$798$		0			0
$799$	232.615	−	402.902i	0.0102996	−	0.0178393i
$800$	2814.67	−	1625.05i	0.124392	−	0.0718179i
$801$		0			0
$802$	−66.0973	+	114.484i	−0.00291020	+	0.00504061i
$803$	9942.20			0.436927
$804$		0			0
$805$	37071.6	−	3333.31i	1.62311	−	0.145943i
$806$	−16999.7	+	9814.76i	−0.742913	+	0.428921i
$807$		0			0
$808$	31159.0	−	17989.7i	1.35665	−	0.783260i
$809$	−17304.5	−	9990.77i	−0.752033	−	0.434186i	0.0743953	−	0.997229i	$-0.476297\pi$
$809$	−17304.5	−	9990.77i	−0.752033	−	0.434186i	−0.826428	+	0.563043i	$0.809631\pi$
$810$		0			0
$811$			16397.5i			0.709981i	0.934870	+	0.354990i	$0.115516\pi$
$811$			16397.5i			0.709981i	−0.934870	+	0.354990i	$0.884484\pi$
$812$	778.389	+	1105.98i	0.0336405	+	0.0477983i
$813$		0			0
$814$	−3264.44	+	5654.18i	−0.140563	+	0.243463i
$815$	8472.72			0.364155
$816$		0			0
$817$		−	10627.8i		−	0.455103i
$818$	−7626.05			−0.325964
$819$		0			0
$820$	−3428.48			−0.146010
$821$			3959.40i			0.168312i	0.996453	+	0.0841559i	$0.0268194\pi$
$821$			3959.40i			0.168312i	−0.996453	+	0.0841559i	$0.973181\pi$
$822$		0			0
$823$	19252.5			0.815432			0.407716	−	0.913109i	$-0.366325\pi$
$823$	19252.5			0.815432			0.407716	+	0.913109i	$0.366325\pi$
$824$	−12278.8	+	21267.5i	−0.519117	+	0.899136i
$825$		0			0
$826$	−2474.77	+	5340.70i	−0.104247	+	0.224972i
$827$			21147.5i			0.889202i	0.895729	+	0.444601i	$0.146655\pi$
$827$			21147.5i			0.889202i	−0.895729	+	0.444601i	$0.853345\pi$
$828$		0			0
$829$	26008.8	+	15016.2i	1.08965	+	0.629111i	0.933484	−	0.358619i	$-0.116752\pi$
$829$	26008.8	+	15016.2i	1.08965	+	0.629111i	0.156169	+	0.987730i	$0.450086\pi$
$830$	5342.56	−	3084.53i	0.223425	−	0.128995i
$831$		0			0
$832$	16656.3	−	9616.54i	0.694056	−	0.400713i
$833$	21586.7	−	3913.59i	0.897879	−	0.162782i
$834$		0			0
$835$	16451.1			0.681812
$836$	2792.23	−	4836.28i	0.115516	−	0.200079i
$837$		0			0
$838$	−22341.5	+	12898.9i	−0.920970	+	0.531722i
$839$	7740.19	−	13406.4i	0.318500	−	0.551658i	−0.661676	−	0.749790i	$-0.730154\pi$
$839$	7740.19	−	13406.4i	0.318500	−	0.551658i	0.980175	+	0.198133i	$0.0634877\pi$
$840$		0			0
$841$	−12073.5	−	20912.0i	−0.495040	−	0.857434i
$842$	16965.8	+	9795.23i	0.694396	+	0.400910i
$843$		0			0
$844$	−9744.06	−	16877.2i	−0.397398	−	0.688314i
$845$	−3696.64	−	6402.76i	−0.150495	−	0.260665i
$846$		0			0
$847$	18067.2	−	12715.8i	0.732937	−	0.515842i
$848$	−2029.22	−	1171.57i	−0.0821743	−	0.0474433i
$849$		0			0
$850$		−	2139.66i		−	0.0863410i
$851$			59490.2i			2.39636i
$852$		0			0
$853$	13650.2	+	7880.96i	0.547919	+	0.316341i	0.748282	−	0.663381i	$-0.230879\pi$
$853$	13650.2	+	7880.96i	0.547919	+	0.316341i	−0.200363	+	0.979722i	$0.564212\pi$
$854$	9212.96	+	4269.10i	0.369158	+	0.171060i
$855$		0			0
$856$	10413.5	+	18036.7i	0.415800	+	0.720187i
$857$	−15683.8	−	27165.2i	−0.625145	−	1.08278i	−0.988513	−	0.151137i	$-0.951706\pi$
$857$	−15683.8	−	27165.2i	−0.625145	−	1.08278i	0.363367	−	0.931646i	$-0.381627\pi$
$858$		0			0
$859$	−12559.6	−	7251.26i	−0.498867	−	0.288021i	0.229379	−	0.973337i	$-0.426331\pi$
$859$	−12559.6	−	7251.26i	−0.498867	−	0.288021i	−0.728245	+	0.685316i	$0.759664\pi$
$860$	−2544.35	−	4406.95i	−0.100886	−	0.174739i
$861$		0			0
$862$	10411.3	−	18033.0i	0.411383	−	0.712536i
$863$	−32586.1	+	18813.6i	−1.28533	+	0.742087i	−0.977818	−	0.209456i	$-0.932831\pi$
$863$	−32586.1	+	18813.6i	−1.28533	+	0.742087i	−0.307515	+	0.951543i	$0.599497\pi$
$864$		0			0
$865$	−11670.0	+	20213.0i	−0.458719	+	0.794524i
$866$	−5919.96			−0.232296
$867$		0			0
$868$	7312.75	−	15781.3i	0.285957	−	0.617112i
$869$	11570.0	−	6679.94i	0.451651	−	0.260761i
$870$		0			0
$871$	−13952.7	+	8055.58i	−0.542788	+	0.313379i
$872$	11179.1	+	6454.28i	0.434144	+	0.250653i
$873$		0			0
$874$			35825.5i			1.38652i
$875$	−24879.2	−	11528.5i	−0.961225	−	0.445412i
$876$		0			0
$877$	4732.93	−	8197.67i	0.182234	−	0.315639i	−0.760407	−	0.649447i	$-0.775000\pi$
$877$	4732.93	−	8197.67i	0.182234	−	0.315639i	0.942641	+	0.333808i	$0.108334\pi$
$878$	−9905.10			−0.380730
$879$		0			0
$880$			534.093i			0.0204594i
$881$	−15486.3			−0.592221			−0.296110	−	0.955154i	$-0.595690\pi$
$881$	−15486.3			−0.592221			−0.296110	+	0.955154i	$0.595690\pi$
$882$		0			0
$883$	8390.36			0.319771			0.159886	−	0.987136i	$-0.448887\pi$
$883$	8390.36			0.319771			0.159886	+	0.987136i	$0.448887\pi$
$884$			16206.8i			0.616621i
$885$		0			0
$886$	14968.4			0.567578
$887$	9996.33	−	17314.1i	0.378403	−	0.655414i	−0.612427	−	0.790527i	$-0.709807\pi$
$887$	9996.33	−	17314.1i	0.378403	−	0.655414i	0.990830	+	0.135113i	$0.0431399\pi$
$888$		0			0
$889$	−3223.94	−	1493.91i	−0.121628	−	0.0563600i
$890$		−	19007.8i		−	0.715891i
$891$		0			0
$892$	7730.88	+	4463.42i	0.290189	+	0.167541i
$893$	637.685	−	368.168i	0.0238962	−	0.0137965i
$894$		0			0
$895$	−13755.6	+	7941.81i	−0.513743	+	0.296609i
$896$	−5958.34	+	12858.4i	−0.222159	+	0.479431i
$897$		0			0
$898$	27075.7			1.00616
$899$	1555.82	−	2694.76i	0.0577191	−	0.0999725i
$900$		0			0
$901$	29482.0	−	17021.5i	1.09011	−	0.629375i
$902$	−755.520	+	1308.60i	−0.0278892	+	0.0483055i
$903$		0			0
$904$	−8540.40	−	14792.4i	−0.314214	−	0.544235i
$905$	−2227.78	−	1286.21i	−0.0818274	−	0.0472431i
$906$		0			0
$907$	17137.5	+	29683.0i	0.627387	+	1.08667i	0.988074	+	0.153979i	$0.0492090\pi$
$907$	17137.5	+	29683.0i	0.627387	+	1.08667i	−0.360687	+	0.932687i	$0.617458\pi$
$908$	−184.081	−	318.838i	−0.00672791	−	0.0116531i
$909$		0			0
$910$	−17024.3	−	7888.70i	−0.620164	−	0.287371i
$911$	10298.3	+	5945.74i	0.374532	+	0.216236i	0.675437	−	0.737418i	$-0.263955\pi$
$911$	10298.3	+	5945.74i	0.374532	+	0.216236i	−0.300905	+	0.953654i	$0.597289\pi$
$912$		0			0
$913$			3861.78i			0.139985i
$914$		−	24571.0i		−	0.889208i
$915$		0			0
$916$	17311.2	+	9994.65i	0.624432	+	0.360516i
$917$	1125.69	−	792.263i	0.0405382	−	0.0285309i
$918$		0			0
$919$	−4307.26	−	7460.39i	−0.154607	−	0.267786i	0.778309	−	0.627881i	$-0.216078\pi$
$919$	−4307.26	−	7460.39i	−0.154607	−	0.267786i	−0.932916	+	0.360095i	$0.882744\pi$
$920$	23192.2	+	40170.0i	0.831112	+	1.43953i
$921$		0			0
$922$	−5920.68	−	3418.30i	−0.211483	−	0.122100i
$923$	19140.1	+	33151.6i	0.682561	+	1.18223i
$924$		0			0
$925$	2811.74	−	4870.08i	0.0999455	−	0.173111i
$926$	−26048.1	+	15038.9i	−0.924401	+	0.533703i
$927$		0			0
$928$	−1373.74	+	2379.38i	−0.0485939	+	0.0841671i
$929$	6094.07			0.215221			0.107610	−	0.994193i	$-0.465680\pi$
$929$	6094.07			0.215221			0.107610	+	0.994193i	$0.465680\pi$
$930$		0			0
$931$	32685.6	+	11718.6i	1.15062	+	0.412527i
$932$	−1485.82	+	857.839i	−0.0522207	+	0.0301496i
$933$		0			0
$934$	−6888.22	+	3976.92i	−0.241316	+	0.139324i
$935$	−6720.09	−	3879.85i	−0.235049	−	0.135705i
$936$		0			0
$937$		−	31129.2i		−	1.08532i	−0.839952	−	0.542660i	$-0.817417\pi$
$937$		−	31129.2i		−	1.08532i	0.839952	−	0.542660i	$-0.182583\pi$
$938$	−4225.74	+	9119.39i	−0.147095	+	0.317440i
$939$		0			0
$940$	176.283	−	305.330i	0.00611671	−	0.0105944i
$941$	704.243			0.0243971			0.0121985	−	0.999926i	$-0.496117\pi$
$941$	704.243			0.0243971			0.0121985	+	0.999926i	$0.496117\pi$
$942$		0			0
$943$			13768.4i			0.475461i
$944$	−769.608			−0.0265345
$945$		0			0
$946$	−2242.75			−0.0770805
$947$			33293.2i			1.14243i	0.820799	+	0.571217i	$0.193529\pi$
$947$			33293.2i			1.14243i	−0.820799	+	0.571217i	$0.806471\pi$
$948$		0			0
$949$	−45667.3			−1.56209
$950$	1693.26	−	2932.81i	0.0578279	−	0.100161i
$951$		0			0
$952$	15735.1	+	22357.3i	0.535691	+	0.761139i
$953$		−	15134.2i		−	0.514424i	−0.966355	−	0.257212i	$-0.917196\pi$
$953$		−	15134.2i		−	0.514424i	0.966355	−	0.257212i	$-0.0828039\pi$
$954$		0			0
$955$	−19229.2	−	11102.0i	−0.651564	−	0.376180i
$956$	13150.0	−	7592.14i	0.444875	−	0.256849i
$957$		0			0
$958$	13180.4	−	7609.69i	0.444508	−	0.256637i
$959$	−19167.6	+	1723.46i	−0.645416	+	0.0580328i
$960$		0			0
$961$	−10227.0			−0.343292
$962$	14994.5	−	25971.2i	0.502539	−	0.870423i
$963$		0			0
$964$	10908.0	−	6297.71i	0.364441	−	0.210410i
$965$	−11272.6	+	19524.7i	−0.376039	+	0.651319i
$966$		0			0
$967$	14537.8	+	25180.3i	0.483460	+	0.837377i	0.999820	−	0.0189949i	$-0.00604664\pi$
$967$	14537.8	+	25180.3i	0.483460	+	0.837377i	−0.516360	+	0.856372i	$0.672713\pi$
$968$	23843.7	+	13766.1i	0.791699	+	0.457088i
$969$		0			0
$970$	−13033.8	−	22575.2i	−0.431432	−	0.747263i
$971$	2209.10	+	3826.28i	0.0730108	+	0.126458i	0.900219	−	0.435436i	$-0.143406\pi$
$971$	2209.10	+	3826.28i	0.0730108	+	0.126458i	−0.827209	+	0.561895i	$0.810073\pi$
$972$		0			0
$973$	−36170.0	+	3252.24i	−1.19173	+	0.107155i
$974$	25570.3	+	14763.0i	0.841197	+	0.485665i
$975$		0			0
$976$			1327.61i			0.0435407i
$977$		−	4921.72i		−	0.161167i	−0.996748	−	0.0805834i	$-0.974322\pi$
$977$		−	4921.72i		−	0.161167i	0.996748	−	0.0805834i	$-0.0256783\pi$
$978$		0			0
$979$	10304.6	+	5949.37i	0.336401	+	0.194221i
$980$	16359.0	−	2965.83i	0.533233	−	0.0966734i
$981$		0			0
$982$	11022.4	+	19091.4i	0.358187	+	0.620398i
$983$	−14801.5	−	25637.0i	−0.480260	−	0.831835i	0.519483	−	0.854481i	$-0.326124\pi$
$983$	−14801.5	−	25637.0i	−0.480260	−	0.831835i	−0.999744	+	0.0226455i	$0.992791\pi$
$984$		0			0
$985$	−44526.5	−	25707.4i	−1.44034	−	0.831580i
$986$	904.381	+	1566.43i	0.0292103	+	0.0505937i
$987$		0			0
$988$	−12825.5	+	22214.4i	−0.412989	+	0.715318i
$989$	−17697.8	+	10217.8i	−0.569015	+	0.328521i
$990$		0			0
$991$	6118.36	−	10597.3i	0.196121	−	0.339692i	−0.751146	−	0.660136i	$-0.770499\pi$
$991$	6118.36	−	10597.3i	0.196121	−	0.339692i	0.947267	+	0.320444i	$0.103832\pi$
$992$	35334.6			1.13092
$993$		0			0
$994$	21667.7	+	10040.4i	0.691407	+	0.320384i
$995$	22807.8	−	13168.1i	0.726689	−	0.419554i
$996$		0			0
$997$	18286.8	−	10557.9i	0.580892	−	0.335378i	−0.180596	−	0.983557i	$-0.557803\pi$
$997$	18286.8	−	10557.9i	0.580892	−	0.335378i	0.761488	+	0.648179i	$0.224469\pi$
$998$	5791.57	+	3343.76i	0.183696	+	0.106057i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.8		44
3.2	odd	2		63.4.i.a.38.15	yes	44
7.5	odd	6		189.4.s.a.89.8		44
9.4	even	3		63.4.s.a.59.15	yes	44
9.5	odd	6		189.4.s.a.17.8		44
21.5	even	6		63.4.s.a.47.15	yes	44
63.5	even	6	inner	189.4.i.a.152.15		44
63.40	odd	6		63.4.i.a.5.8	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.8	✓	44	63.40	odd	6
63.4.i.a.38.15	yes	44	3.2	odd	2
63.4.s.a.47.15	yes	44	21.5	even	6
63.4.s.a.59.15	yes	44	9.4	even	3
189.4.i.a.143.8		44	1.1	even	1	trivial
189.4.i.a.152.15		44	63.5	even	6	inner
189.4.s.a.17.8		44	9.5	odd	6
189.4.s.a.89.8		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)

\(f(q)\)	\(=\)	\(q-1.81805i q^{2} +4.69469 q^{4} +(5.16236 - 8.94146i) q^{5} +(-16.8039 - 7.78656i) q^{7} -23.0796i q^{8} +O(q^{10})\)	\(q-1.81805i q^{2} +4.69469 q^{4} +(5.16236 - 8.94146i) q^{5} +(-16.8039 - 7.78656i) q^{7} -23.0796i q^{8} +(-16.2560 - 9.38543i) q^{10} +(10.1761 - 5.87520i) q^{11} +(-46.7419 + 26.9865i) q^{13} +(-14.1564 + 30.5503i) q^{14} -4.40236 q^{16} +(31.9804 - 55.3917i) q^{17} +(87.6701 - 50.6164i) q^{19} +(24.2357 - 41.9774i) q^{20} +(-10.6814 - 18.5008i) q^{22} +(-168.576 - 97.3275i) q^{23} +(9.20017 + 15.9352i) q^{25} +(49.0628 + 84.9792i) q^{26} +(-78.8889 - 36.5555i) q^{28} +(-13.4708 - 7.77735i) q^{29} +200.045i q^{31} -176.633i q^{32} +(-100.705 - 58.1420i) q^{34} +(-156.371 + 110.054i) q^{35} +(-152.809 - 264.674i) q^{37} +(-92.0231 - 159.389i) q^{38} +(-206.365 - 119.145i) q^{40} +(-35.3661 - 61.2559i) q^{41} +(52.4919 - 90.9186i) q^{43} +(47.7738 - 27.5822i) q^{44} +(-176.946 + 306.480i) q^{46} +7.27369 q^{47} +(221.739 + 261.688i) q^{49} +(28.9709 - 16.7264i) q^{50} +(-219.439 + 126.693i) q^{52} +(460.939 + 266.123i) q^{53} -121.319i q^{55} +(-179.711 + 387.826i) q^{56} +(-14.1396 + 24.4905i) q^{58} +174.817 q^{59} -301.567i q^{61} +363.692 q^{62} -356.347 q^{64} +557.255i q^{65} +298.504 q^{67} +(150.138 - 260.047i) q^{68} +(200.084 + 284.290i) q^{70} -709.248i q^{71} +(732.758 + 423.058i) q^{73} +(-481.190 + 277.815i) q^{74} +(411.584 - 237.628i) q^{76} +(-216.746 + 19.4888i) q^{77} +1136.97 q^{79} +(-22.7266 + 39.3636i) q^{80} +(-111.366 + 64.2974i) q^{82} +(-164.325 + 284.620i) q^{83} +(-330.188 - 571.903i) q^{85} +(-165.295 - 95.4330i) q^{86} +(-135.597 - 234.861i) q^{88} +(506.312 + 876.958i) q^{89} +(995.576 - 89.5176i) q^{91} +(-791.413 - 456.922i) q^{92} -13.2239i q^{94} -1045.20i q^{95} +(1202.67 + 694.363i) q^{97} +(475.763 - 403.133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 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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