LMFDB - Embedded newform 189.4.s.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57448 - 0.909026i) q^{2} +(-2.34735 - 4.06572i) q^{4} +10.3247 q^{5} +(15.1453 - 10.6593i) q^{7} +23.0796i q^{8} +O(q^{10})$	\(q+(-1.57448 - 0.909026i) q^{2} +(-2.34735 - 4.06572i) q^{4} +10.3247 q^{5} +(15.1453 - 10.6593i) q^{7} +23.0796i q^{8} +(-16.2560 - 9.38543i) q^{10} -11.7504i q^{11} +(46.7419 + 26.9865i) q^{13} +(-33.5355 + 3.01536i) q^{14} +(2.20118 - 3.81256i) q^{16} +(-31.9804 + 55.3917i) q^{17} +(87.6701 - 50.6164i) q^{19} +(-24.2357 - 41.9774i) q^{20} +(-10.6814 + 18.5008i) q^{22} -194.655i q^{23} -18.4003 q^{25} +(-49.0628 - 84.9792i) q^{26} +(-78.8889 - 36.5555i) q^{28} +(-13.4708 + 7.77735i) q^{29} +(173.244 - 100.023i) q^{31} +(152.969 - 88.3165i) q^{32} +(100.705 - 58.1420i) q^{34} +(156.371 - 110.054i) q^{35} +(-152.809 - 264.674i) q^{37} -184.046 q^{38} +238.290i q^{40} +(35.3661 - 61.2559i) q^{41} +(52.4919 + 90.9186i) q^{43} +(-47.7738 + 27.5822i) q^{44} +(-176.946 + 306.480i) q^{46} +(3.63684 - 6.29920i) q^{47} +(115.759 - 322.876i) q^{49} +(28.9709 + 16.7264i) q^{50} -253.386i q^{52} +(-460.939 - 266.123i) q^{53} -121.319i q^{55} +(246.012 + 349.547i) q^{56} +28.2792 q^{58} +(87.4084 + 151.396i) q^{59} +(261.165 + 150.784i) q^{61} -363.692 q^{62} -356.347 q^{64} +(482.597 + 278.627i) q^{65} +(-149.252 - 258.512i) q^{67} +300.276 q^{68} +(-346.244 + 31.1327i) q^{70} +709.248i q^{71} +(732.758 + 423.058i) q^{73} +555.631i q^{74} +(-411.584 - 237.628i) q^{76} +(-125.251 - 177.963i) q^{77} +(-568.486 + 984.646i) q^{79} +(22.7266 - 39.3636i) q^{80} +(-111.366 + 64.2974i) q^{82} +(164.325 + 284.620i) q^{83} +(-330.188 + 571.903i) q^{85} -190.866i q^{86} +271.194 q^{88} +(-506.312 - 876.958i) q^{89} +(995.576 - 89.5176i) q^{91} +(-791.413 + 456.922i) q^{92} +(-11.4523 + 6.61197i) q^{94} +(905.168 - 522.599i) q^{95} +(-1202.67 + 694.363i) q^{97} +(-475.763 + 403.133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.57448	−	0.909026i	−0.556662	−	0.321389i	0.195143	−	0.980775i	$-0.437483\pi$
$2$	−1.57448	−	0.909026i	−0.556662	−	0.321389i	−0.751805	+	0.659386i	$0.770816\pi$
$3$		0			0
$3$		0			0
$4$	−2.34735	−	4.06572i	−0.293418	−	0.508215i
$5$	10.3247			0.923470			0.461735	−	0.887018i	$-0.347227\pi$
$5$	10.3247			0.923470			0.461735	+	0.887018i	$0.347227\pi$
$6$		0			0
$7$	15.1453	−	10.6593i	0.817769	−	0.575547i
$7$	15.1453	−	10.6593i	0.817769	−	0.575547i
$8$			23.0796i			1.01998i
$9$		0			0
$10$	−16.2560	−	9.38543i	−0.514061	−	0.296793i
$11$		−	11.7504i		−	0.322080i	−0.986948	−	0.161040i	$-0.948515\pi$
$11$		−	11.7504i		−	0.322080i	0.986948	−	0.161040i	$-0.0514848\pi$
$12$		0			0
$13$	46.7419	+	26.9865i	0.997221	+	0.575746i	0.907425	−	0.420214i	$-0.138045\pi$
$13$	46.7419	+	26.9865i	0.997221	+	0.575746i	0.0897962	+	0.995960i	$0.471378\pi$
$14$	−33.5355	+	3.01536i	−0.640195	+	0.0575634i
$15$		0			0
$16$	2.20118	−	3.81256i	0.0343935	−	0.0595712i
$17$	−31.9804	+	55.3917i	−0.456258	+	0.790262i	−0.998760	−	0.0497928i	$-0.984144\pi$
$17$	−31.9804	+	55.3917i	−0.456258	+	0.790262i	0.542502	+	0.840055i	$0.317477\pi$
$18$		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
$23$		−	194.655i		−	1.76471i	−0.470583	−	0.882356i	$-0.655956\pi$
$23$		−	194.655i		−	1.76471i	0.470583	−	0.882356i	$-0.344044\pi$
$24$		0			0
$25$	−18.4003			−0.147203
$26$	−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	−0.542508	−	0.840051i	$-0.682525\pi$
$29$	−13.4708	+	7.77735i	−0.0862572	+	0.0498006i	0.456251	+	0.889851i	$0.349192\pi$
$30$		0			0
$31$	173.244	−	100.023i	1.00373	−	0.579502i	0.0943785	−	0.995536i	$-0.469914\pi$
$31$	173.244	−	100.023i	1.00373	−	0.579502i	0.909349	+	0.416034i	$0.136580\pi$
$32$	152.969	−	88.3165i	0.845041	−	0.487884i
$33$		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	$-0.404238\pi$
$38$	−184.046			−0.785691
$39$		0			0
$40$			238.290i			0.941925i
$41$	35.3661	−	61.2559i	0.134714	−	0.233331i	−0.790774	−	0.612108i	$-0.790322\pi$
$41$	35.3661	−	61.2559i	0.134714	−	0.233331i	0.925488	+	0.378777i	$0.123655\pi$
$42$		0			0
$43$	52.4919	+	90.9186i	0.186161	+	0.322441i	0.943967	−	0.330039i	$-0.107062\pi$
$43$	52.4919	+	90.9186i	0.186161	+	0.322441i	−0.757806	+	0.652480i	$0.773729\pi$
$44$	−47.7738	+	27.5822i	−0.163686	+	0.0945041i
$45$		0			0
$46$	−176.946	+	306.480i	−0.567159	+	0.982348i
$47$	3.63684	−	6.29920i	0.0112870	−	0.0195496i	−0.860327	−	0.509743i	$-0.829740\pi$
$47$	3.63684	−	6.29920i	0.0112870	−	0.0195496i	0.871614	+	0.490193i	$0.163074\pi$
$48$		0			0
$49$	115.759	−	322.876i	0.337491	−	0.941329i
$50$	28.9709	+	16.7264i	0.0819421	+	0.0473093i
$51$		0			0
$52$		−	253.386i		−	0.675737i
$53$	−460.939	−	266.123i	−1.19462	−	0.689714i	−0.235269	−	0.971930i	$-0.575597\pi$
$53$	−460.939	−	266.123i	−1.19462	−	0.689714i	−0.959351	+	0.282216i	$0.908931\pi$
$54$		0			0
$55$		−	121.319i		−	0.297431i
$56$	246.012	+	349.547i	0.587049	+	0.834111i
$57$		0			0
$58$	28.2792			0.0640215
$59$	87.4084	+	151.396i	0.192875	+	0.334069i	0.946202	−	0.323577i	$-0.104886\pi$
$59$	87.4084	+	151.396i	0.192875	+	0.334069i	−0.753327	+	0.657646i	$0.771552\pi$
$60$		0			0
$61$	261.165	+	150.784i	0.548176	+	0.316490i	0.748386	−	0.663263i	$-0.230829\pi$
$61$	261.165	+	150.784i	0.548176	+	0.316490i	−0.200210	+	0.979753i	$0.564162\pi$
$62$	−363.692			−0.744983
$63$		0			0
$64$	−356.347			−0.695990
$65$	482.597	+	278.627i	0.920904	+	0.531684i
$66$		0			0
$67$	−149.252	−	258.512i	−0.272150	−	0.471378i	0.697262	−	0.716816i	$-0.254401\pi$
$67$	−149.252	−	258.512i	−0.272150	−	0.471378i	−0.969412	+	0.245438i	$0.921068\pi$
$68$	300.276			0.535497
$69$		0			0
$70$	−346.244	+	31.1327i	−0.591201	+	0.0531581i
$71$			709.248i			1.18552i	0.805377	+	0.592762i	$0.201963\pi$
$71$			709.248i			1.18552i	−0.805377	+	0.592762i	$0.798037\pi$
$72$		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	$0.429388\pi$
$74$			555.631i			0.872848i
$75$		0			0
$76$	−411.584	−	237.628i	−0.621209	−	0.358655i
$77$	−125.251	−	177.963i	−0.185372	−	0.263387i
$78$		0			0
$79$	−568.486	+	984.646i	−0.809616	+	1.40230i	0.103514	+	0.994628i	$0.466991\pi$
$79$	−568.486	+	984.646i	−0.809616	+	1.40230i	−0.913130	+	0.407668i	$0.866342\pi$
$80$	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	$-0.0969372\pi$
$83$	164.325	+	284.620i	0.217314	+	0.376398i	−0.736672	+	0.676250i	$0.763604\pi$
$84$		0			0
$85$	−330.188	+	571.903i	−0.421341	+	0.729783i
$86$		−	190.866i		−	0.239321i
$87$		0			0
$88$	271.194			0.328516
$89$	−506.312	−	876.958i	−0.603022	−	1.04446i	−0.992361	−	0.123370i	$-0.960630\pi$
$89$	−506.312	−	876.958i	−0.603022	−	1.04446i	0.389339	−	0.921095i	$-0.372704\pi$
$90$		0			0
$91$	995.576	−	89.5176i	1.14687	−	0.103121i
$92$	−791.413	+	456.922i	−0.896853	+	0.517798i
$93$		0			0
$94$	−11.4523	+	6.61197i	−0.0125661	+	0.00725503i
$95$	905.168	−	522.599i	0.977561	−	0.564395i
$96$		0			0
$97$	−1202.67	+	694.363i	−1.25889	+	0.726823i	−0.972860	−	0.231396i	$-0.925671\pi$
$97$	−1202.67	+	694.363i	−1.25889	+	0.726823i	−0.286035	+	0.958219i	$0.592337\pi$
$98$	−475.763	+	403.133i	−0.490401	+	0.415536i
$99$		0			0
$100$	43.1919	+	74.8106i	0.0431919	+	0.0748106i
$101$	1558.92			1.53583			0.767914	−	0.640553i	$-0.221295\pi$
$101$	1558.92			1.53583			0.767914	+	0.640553i	$0.221295\pi$
$102$		0			0
$103$			1064.04i			1.01789i	0.860798	+	0.508946i	$0.169965\pi$
$103$			1064.04i			1.01789i	−0.860798	+	0.508946i	$0.830035\pi$
$104$	−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	−0.103530	−	0.994626i	$-0.533014\pi$
$107$	781.498	−	451.198i	0.706077	−	0.407654i	0.809607	+	0.586973i	$0.199680\pi$
$108$		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	$0.245698\pi$
$110$	−110.283	+	191.015i	−0.0955911	+	0.165569i
$111$		0			0
$112$	−7.30161	−	81.2053i	−0.00616015	−	0.0685106i
$113$	640.930	+	370.041i	0.533572	+	0.308058i	0.742470	−	0.669880i	$-0.233654\pi$
$113$	640.930	+	370.041i	0.533572	+	0.308058i	−0.208898	+	0.977937i	$0.566988\pi$
$114$		0			0
$115$		−	2009.76i		−	1.62966i
$116$	63.2411	+	36.5122i	0.0506188	+	0.0292248i
$117$		0			0
$118$		−	317.826i		−	0.247951i
$119$	106.083	+	1179.81i	0.0817195	+	0.908849i
$120$		0			0
$121$	1192.93			0.896265
$122$	−274.132	−	474.811i	−0.203433	−	0.352356i
$123$		0			0
$124$	−813.327	−	469.575i	−0.589024	−	0.340073i
$125$	−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	$0.478649\pi$
$128$	−662.689	−	382.604i	−0.457609	−	0.264201i
$129$		0			0
$130$	−506.559	−	877.386i	−0.341755	−	0.591937i
$131$	−74.3261			−0.0495718			−0.0247859	−	0.999693i	$-0.507890\pi$
$131$	−74.3261			−0.0495718			−0.0247859	+	0.999693i	$0.507890\pi$
$132$		0			0
$133$	788.255	−	1701.10i	0.513912	−	1.10905i
$134$			542.696i			0.349864i
$135$		0			0
$136$	−1278.42	−	738.095i	−0.806054	−	0.465376i
$137$		−	1039.13i		−	0.648019i	−0.946054	−	0.324010i	$-0.894969\pi$
$137$		−	1039.13i		−	0.648019i	0.946054	−	0.324010i	$-0.105031\pi$
$138$		0			0
$139$	−1698.17	−	980.437i	−1.03623	−	0.598270i	−0.117470	−	0.993076i	$-0.537478\pi$
$139$	−1698.17	−	980.437i	−1.03623	−	0.598270i	−0.918764	+	0.394806i	$0.870812\pi$
$140$	−814.505	−	377.425i	−0.491702	−	0.227845i
$141$		0			0
$142$	644.725	−	1116.70i	0.381015	−	0.659937i
$143$	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
$149$		−	2389.64i		−	1.31387i	−0.753947	−	0.656936i	$-0.771852\pi$
$149$		−	2389.64i		−	1.31387i	0.753947	−	0.656936i	$-0.228148\pi$
$150$		0			0
$151$	1639.95			0.883823			0.441912	−	0.897059i	$-0.354301\pi$
$151$	1639.95			0.883823			0.441912	+	0.897059i	$0.354301\pi$
$152$	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
$157$	1025.10	−	591.842i	0.521095	−	0.300854i	−0.216288	−	0.976330i	$-0.569395\pi$
$157$	1025.10	−	591.842i	0.521095	−	0.300854i	0.737382	+	0.675475i	$0.236062\pi$
$158$	1790.14	−	1033.54i	0.901365	−	0.520403i
$159$		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	$0.770159\pi$
$164$	−332.066			−0.158110
$165$		0			0
$166$		−	597.503i		−	0.279369i
$167$	−796.684	+	1379.90i	−0.369157	+	0.639399i	−0.989434	−	0.144984i	$-0.953687\pi$
$167$	−796.684	+	1379.90i	−0.369157	+	0.639399i	0.620277	+	0.784383i	$0.287020\pi$
$168$		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
$173$	−1130.30	+	1957.73i	−0.496733	+	0.860368i	−0.999993	−	0.00376773i	$-0.998801\pi$
$173$	−1130.30	+	1957.73i	−0.496733	+	0.860368i	0.503259	+	0.864135i	$0.332134\pi$
$174$		0			0
$175$	−278.678	+	196.134i	−0.120378	+	0.0847221i
$176$	−44.7991	−	25.8648i	−0.0191867	−	0.0110774i
$177$		0			0
$178$			1841.00i			0.775219i
$179$	1332.30	+	769.204i	0.556317	+	0.321190i	0.751666	−	0.659544i	$-0.229251\pi$
$179$	1332.30	+	769.204i	0.556317	+	0.321190i	−0.195349	+	0.980734i	$0.562584\pi$
$180$		0			0
$181$		−	249.151i		−	0.102316i	−0.998691	−	0.0511582i	$-0.983709\pi$
$181$		−	249.151i		−	0.102316i	0.998691	−	0.0511582i	$-0.0162913\pi$
$182$	−1648.89	−	764.060i	−0.671558	−	0.311186i
$183$		0			0
$184$	4492.56			1.79998
$185$	−1577.71	−	2732.68i	−0.627004	−	1.08600i
$186$		0			0
$187$	650.874	+	375.782i	0.254527	+	0.146952i
$188$	−34.1477			−0.0132472
$189$		0			0
$190$	−1900.22			−0.725562
$191$	−1862.45	−	1075.28i	−0.705560	−	0.407355i	0.103855	−	0.994592i	$-0.466882\pi$
$191$	−1862.45	−	1075.28i	−0.705560	−	0.407355i	−0.809415	+	0.587237i	$0.800216\pi$
$192$		0			0
$193$	1091.81	+	1891.07i	0.407202	+	0.705295i	0.994575	−	0.104022i	$-0.0331711\pi$
$193$	1091.81	+	1891.07i	0.407202	+	0.705295i	−0.587373	+	0.809316i	$0.699838\pi$
$194$	2524.77			0.934372
$195$		0			0
$196$	−1584.45	+	287.255i	−0.577423	+	0.104685i
$197$			4979.78i			1.80099i	0.434868	+	0.900494i	$0.356795\pi$
$197$			4979.78i			1.80099i	−0.434868	+	0.900494i	$0.643205\pi$
$198$		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	$0.516548\pi$
$200$		−	424.672i		−	0.150144i
$201$		0			0
$202$	−2454.49	−	1417.10i	−0.854937	−	0.493598i
$203$	−121.118	+	261.379i	−0.0418758	+	0.0903704i
$204$		0			0
$205$	365.145	−	632.449i	0.124404	−	0.215474i
$206$	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	0.298636	+	0.954367i	$0.403468\pi$
$211$	−2075.55	+	3594.96i	−0.677188	+	1.17292i	−0.975824	+	0.218557i	$0.929865\pi$
$212$			2498.73i			0.809499i
$213$		0			0
$214$	−1640.60			−0.524062
$215$	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
$220$	−493.251	+	284.779i	−0.151159	+	0.0872717i
$221$	−2989.65	+	1726.08i	−0.909980	+	0.525377i
$222$		0			0
$223$	−1646.73	+	950.739i	−0.494498	+	0.285499i	−0.726439	−	0.687231i	$-0.758826\pi$
$223$	−1646.73	+	950.739i	−0.494498	+	0.285499i	0.231941	+	0.972730i	$0.425493\pi$
$224$	1375.36	−	2968.12i	0.410247	−	0.885337i
$225$		0			0
$226$	−672.754	−	1165.24i	−0.198013	−	0.342968i
$227$	−78.4210			−0.0229294			−0.0114647	−	0.999934i	$-0.503649\pi$
$227$	−78.4210			−0.0229294			−0.0114647	+	0.999934i	$0.503649\pi$
$228$		0			0
$229$		−	4257.85i		−	1.22868i	−0.789043	−	0.614338i	$-0.789423\pi$
$229$		−	4257.85i		−	1.22868i	0.789043	−	0.614338i	$-0.210577\pi$
$230$	−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	−0.454846	−	0.890570i	$-0.650306\pi$
$233$	316.489	−	182.725i	0.0889868	−	0.0513765i	0.543833	+	0.839193i	$0.316972\pi$
$234$		0			0
$235$	37.5494	−	65.0374i	0.0104232	−	0.0180535i
$236$	410.356	−	710.757i	0.113186	−	0.196044i
$237$		0			0
$238$	905.453	−	1954.02i	0.246604	−	0.532186i
$239$	2801.03	+	1617.18i	0.758091	+	0.437684i	0.828610	−	0.559827i	$-0.189132\pi$
$239$	2801.03	+	1617.18i	0.758091	+	0.437684i	−0.0705190	+	0.997510i	$0.522466\pi$
$240$		0			0
$241$			2682.91i			0.717101i	0.933510	+	0.358550i	$0.116729\pi$
$241$			2682.91i			0.717101i	−0.933510	+	0.358550i	$0.883271\pi$
$242$	−1878.24	−	1084.40i	−0.498917	−	0.288050i
$243$		0			0
$244$		−	1415.76i		−	0.371455i
$245$	1195.18	−	3333.60i	0.311663	−	0.869289i
$246$		0			0
$247$	5463.82			1.40751
$248$	2308.48	+	3998.40i	0.591083	+	1.02379i
$249$		0			0
$250$	2331.12	+	1345.87i	0.589732	+	0.340482i
$251$	4725.76			1.18840			0.594198	−	0.804319i	$-0.297470\pi$
$251$	4725.76			1.18840			0.594198	+	0.804319i	$0.297470\pi$
$252$		0			0
$253$	−2287.27			−0.568378
$254$	−302.075	−	174.403i	−0.0746215	−	0.0430827i
$255$		0			0
$256$	2120.98	+	3673.65i	0.517818	+	0.896886i
$257$	−4493.81			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$257$	−4493.81			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$258$		0			0
$259$	−5135.58	−	2379.72i	−1.23208	−	0.570921i
$260$		−	2616.14i		−	0.624023i
$261$		0			0
$262$	117.025	+	67.5643i	0.0275947	+	0.0159318i
$263$			7590.93i			1.77976i	0.456195	+	0.889880i	$0.349212\pi$
$263$			7590.93i			1.77976i	−0.456195	+	0.889880i	$0.650788\pi$
$264$		0			0
$265$	−4759.06	−	2747.65i	−1.10320	−	0.636931i
$266$	−2787.43	+	1961.80i	−0.642513	+	0.452202i
$267$		0			0
$268$	−700.693	+	1213.64i	−0.159708	+	0.276622i
$269$	−2535.95	+	4392.39i	−0.574794	+	0.995572i	0.421270	+	0.906935i	$0.361584\pi$
$269$	−2535.95	+	4392.39i	−0.574794	+	0.995572i	−0.996064	+	0.0886370i	$0.971749\pi$
$270$		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
$275$			216.211i			0.0474110i
$276$		0			0
$277$	−2031.65			−0.440687			−0.220343	−	0.975422i	$-0.570718\pi$
$277$	−2031.65			−0.440687			−0.220343	+	0.975422i	$0.570718\pi$
$278$	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	−0.273704	−	0.961814i	$-0.588249\pi$
$281$	1989.68	−	1148.74i	0.422400	−	0.243873i	0.696104	+	0.717941i	$0.254915\pi$
$282$		0			0
$283$	−4911.00	+	2835.37i	−1.03155	+	0.595566i	−0.917428	−	0.397901i	$-0.869739\pi$
$283$	−4911.00	+	2835.37i	−1.03155	+	0.595566i	−0.114122	+	0.993467i	$0.536405\pi$
$284$	2883.60	−	1664.85i	0.602502	−	0.347855i
$285$		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
$290$	291.975			0.0591219
$291$		0			0
$292$		−	3972.25i		−	0.796090i
$293$	−3447.32	+	5970.93i	−0.687353	+	1.19053i	0.285339	+	0.958427i	$0.407894\pi$
$293$	−3447.32	+	5970.93i	−0.687353	+	1.19053i	−0.972691	+	0.232103i	$0.925439\pi$
$294$		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
$299$	5253.05	−	9098.54i	1.01603	−	1.75981i
$300$		0			0
$301$	1764.13	+	817.463i	0.337817	+	0.156537i
$302$	−2582.07	−	1490.76i	−0.491991	−	0.284051i
$303$		0			0
$304$		−	445.663i		−	0.0840807i
$305$	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	$-0.0234814\pi$
$308$	−429.542	+	926.976i	−0.0794656	+	0.171491i
$309$		0			0
$310$	−3755.02			−0.687970
$311$	−3884.56	−	6728.26i	−0.708275	−	1.22677i	−0.965497	−	0.260415i	$-0.916141\pi$
$311$	−3884.56	−	6728.26i	−0.708275	−	1.22677i	0.257222	−	0.966352i	$-0.417193\pi$
$312$		0			0
$313$	2994.09	+	1728.64i	0.540689	+	0.312167i	0.745358	−	0.666664i	$-0.232278\pi$
$313$	2994.09	+	1728.64i	0.540689	+	0.312167i	−0.204669	+	0.978831i	$0.565612\pi$
$314$	−2152.00			−0.386765
$315$		0			0
$316$	5337.73			0.950224
$317$	2267.37	+	1309.06i	0.401728	+	0.231938i	0.687229	−	0.726440i	$-0.258827\pi$
$317$	2267.37	+	1309.06i	0.401728	+	0.231938i	−0.285501	+	0.958378i	$0.592160\pi$
$318$		0			0
$319$	91.3870	+	158.287i	0.0160398	+	0.0277817i
$320$	−3679.18			−0.642726
$321$		0			0
$322$	586.954	+	6527.85i	0.101583	+	1.12976i
$323$			6474.92i			1.11540i
$324$		0			0
$325$	−860.067	−	496.560i	−0.146794	−	0.0847513i
$326$		−	1491.94i		−	0.253469i
$327$		0			0
$328$	1413.76	+	816.235i	0.237994	+	0.137406i
$329$	−12.0639	−	134.169i	−0.00202159	−	0.0224833i
$330$		0			0
$331$	−127.158	+	220.244i	−0.0211155	+	0.0365731i	−0.876390	−	0.481602i	$-0.840055\pi$
$331$	−127.158	+	220.244i	−0.0211155	+	0.0365731i	0.855275	+	0.518175i	$0.173388\pi$
$332$	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	−0.225537	−	0.974235i	$-0.572414\pi$
$337$	4521.98	−	7832.30i	0.730943	−	1.26603i	0.956480	−	0.291796i	$-0.0942529\pi$
$338$		−	1301.86i		−	0.209503i
$339$		0			0
$340$	3100.26			0.494516
$341$	−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
$346$	3559.26	−	2054.94i	0.553026	−	0.319289i
$347$	6246.99	−	3606.70i	0.966443	−	0.557976i	0.0682931	−	0.997665i	$-0.478245\pi$
$347$	6246.99	−	3606.70i	0.966443	−	0.557976i	0.898150	+	0.439689i	$0.144911\pi$
$348$		0			0
$349$	214.544	−	123.867i	0.0329062	−	0.0189984i	−0.483457	−	0.875368i	$-0.660619\pi$
$349$	214.544	−	123.867i	0.0329062	−	0.0189984i	0.516363	+	0.856370i	$0.327286\pi$
$350$	617.064	−	55.4835i	0.0942385	−	0.00847349i
$351$		0			0
$352$	−1037.75	−	1797.44i	−0.157138	−	0.272171i
$353$	−2398.42			−0.361630			−0.180815	−	0.983517i	$-0.557873\pi$
$353$	−2398.42			−0.361630			−0.180815	+	0.983517i	$0.557873\pi$
$354$		0			0
$355$			7322.78i			1.09480i
$356$	−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	−0.715755	−	0.698351i	$-0.753917\pi$
$359$	−3189.10	+	1841.23i	−0.468842	+	0.270686i	0.246913	+	0.969038i	$0.420584\pi$
$360$		0			0
$361$	1694.53	−	2935.01i	0.247052	−	0.427907i
$362$	−226.485	+	392.283i	−0.0328834	+	0.0569556i
$363$		0			0
$364$	−2700.91	−	3837.61i	−0.388919	−	0.552597i
$365$	7565.51	+	4367.95i	1.08492	+	0.626381i
$366$		0			0
$367$		−	11149.6i		−	1.58584i	−0.609323	−	0.792922i	$-0.708559\pi$
$367$		−	11149.6i		−	1.58584i	0.609323	−	0.792922i	$-0.291441\pi$
$368$	−742.133	−	428.471i	−0.105126	−	0.0606945i
$369$		0			0
$370$			5736.73i			0.806049i
$371$	−9817.74	+	882.766i	−1.37389	+	0.123533i
$372$		0			0
$373$	−9748.05			−1.35318			−0.676588	−	0.736362i	$-0.736542\pi$
$373$	−9748.05			−1.35318			−0.676588	+	0.736362i	$0.736542\pi$
$374$	−683.192	−	1183.32i	−0.0944572	−	0.163605i
$375$		0			0
$376$	145.383	+	83.9369i	0.0199403	+	0.0115125i
$377$	−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	$0.600084\pi$
$380$	−4249.49	−	2453.44i	−0.573668	−	0.331208i
$381$		0			0
$382$	1954.92	+	3386.02i	0.261839	+	0.453518i
$383$	3153.32			0.420698			0.210349	−	0.977626i	$-0.432540\pi$
$383$	3153.32			0.420698			0.210349	+	0.977626i	$0.432540\pi$
$384$		0			0
$385$	−1293.18	−	1837.42i	−0.171186	−	0.243230i
$386$		−	3969.92i		−	0.523481i
$387$		0			0
$388$	5646.17	+	3259.82i	0.738765	+	0.426526i
$389$			7456.02i			0.971813i	0.874011	+	0.485906i	$0.161510\pi$
$389$			7456.02i			0.971813i	−0.874011	+	0.485906i	$0.838490\pi$
$390$		0			0
$391$	10782.3	+	6225.14i	1.39458	+	0.805163i
$392$	7451.84	+	2671.68i	0.960140	+	0.344235i
$393$		0			0
$394$	4526.75	−	7840.56i	0.578818	−	1.00254i
$395$	−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
$401$		−	72.7123i		−	0.00905506i	−0.999990	−	0.00452753i	$-0.998559\pi$
$401$		−	72.7123i		−	0.00905506i	0.999990	−	0.00452753i	$-0.00144116\pi$
$402$		0			0
$403$	10797.0			1.33458
$404$	−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
$409$	−3632.66	+	2097.32i	−0.439177	+	0.253559i	−0.703248	−	0.710944i	$-0.748268\pi$
$409$	−3632.66	+	2097.32i	−0.439177	+	0.253559i	0.264072	+	0.964503i	$0.414934\pi$
$410$	−1149.83	+	663.852i	−0.138502	+	0.0799642i
$411$		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
$416$	9533.40			1.12359
$417$		0			0
$418$			2162.62i			0.253055i
$419$	7094.88	−	12288.7i	0.827226	−	1.43280i	−0.0729809	−	0.997333i	$-0.523251\pi$
$419$	7094.88	−	12288.7i	0.827226	−	1.43280i	0.900206	−	0.435463i	$-0.143415\pi$
$420$		0			0
$421$	−5387.76	−	9331.88i	−0.623714	−	1.08030i	−0.988788	−	0.149326i	$-0.952290\pi$
$421$	−5387.76	−	9331.88i	−0.623714	−	1.08030i	0.365074	−	0.930978i	$-0.381044\pi$
$422$	6535.81	−	3773.45i	0.753930	−	0.435282i
$423$		0			0
$424$	6142.02	−	10638.3i	0.703497	−	1.21849i
$425$	588.450	−	1019.23i	0.0671624	−	0.116329i
$426$		0			0
$427$	5562.66	−	500.169i	0.630436	−	0.0566859i
$428$	−3668.89	−	2118.23i	−0.414352	−	0.239226i
$429$		0			0
$430$		−	1970.64i		−	0.221006i
$431$	−9918.85	−	5726.65i	−1.10853	−	0.640007i	−0.170078	−	0.985431i	$-0.554402\pi$
$431$	−9918.85	−	5726.65i	−1.10853	−	0.640007i	−0.938447	+	0.345423i	$0.887735\pi$
$432$		0			0
$433$		−	3256.21i		−	0.361394i	−0.983539	−	0.180697i	$-0.942165\pi$
$433$		−	3256.21i		−	0.361394i	0.983539	−	0.180697i	$-0.0578353\pi$
$434$	−5508.22	+	3876.70i	−0.609224	+	0.428773i
$435$		0			0
$436$	2625.77			0.288421
$437$	−9852.72	−	17065.4i	−1.07853	−	1.86808i
$438$		0			0
$439$	4718.28	+	2724.10i	0.512964	+	0.296160i	0.734051	−	0.679094i	$-0.237627\pi$
$439$	4718.28	+	2724.10i	0.512964	+	0.296160i	−0.221087	+	0.975254i	$0.570961\pi$
$440$	2800.00			0.303375
$441$		0			0
$442$	6276.19			0.675402
$443$	7130.18	+	4116.61i	0.764707	+	0.441504i	0.830983	−	0.556297i	$-0.187778\pi$
$443$	7130.18	+	4116.61i	0.764707	+	0.441504i	−0.0662761	+	0.997801i	$0.521112\pi$
$444$		0			0
$445$	−5227.52	−	9054.34i	−0.556873	−	0.964532i
$446$	3456.98			0.367024
$447$		0			0
$448$	−5396.97	+	3798.40i	−0.569159	+	0.400575i
$449$		−	14892.7i		−	1.56532i	−0.622447	−	0.782662i	$-0.713861\pi$
$449$		−	14892.7i		−	1.56532i	0.622447	−	0.782662i	$-0.286139\pi$
$450$		0			0
$451$	−719.781	−	415.566i	−0.0751512	−	0.0433885i
$452$		−	3474.46i		−	0.361559i
$453$		0			0
$454$	123.472	+	71.2867i	0.0127640	+	0.00736927i
$455$	10279.0	−	924.243i	1.05910	−	0.0952290i
$456$		0			0
$457$	−6757.51	+	11704.3i	−0.691691	+	1.19804i	0.279592	+	0.960119i	$0.409801\pi$
$457$	−6757.51	+	11704.3i	−0.691691	+	1.19804i	−0.971283	+	0.237925i	$0.923533\pi$
$458$	−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	$-0.227501\pi$
$461$	−1880.20	−	3256.61i	−0.189956	−	0.329014i	−0.945235	+	0.326389i	$0.894168\pi$
$462$		0			0
$463$	−8271.99	+	14327.5i	−0.830307	+	1.43813i	0.0674881	+	0.997720i	$0.478502\pi$
$463$	−8271.99	+	14327.5i	−0.830307	+	1.43813i	−0.897795	+	0.440414i	$0.854832\pi$
$464$			68.4775i			0.00685126i
$465$		0			0
$466$	−664.408			−0.0660474
$467$	2187.46	+	3788.79i	0.216753	+	0.375427i	0.953813	−	0.300400i	$-0.0971200\pi$
$467$	2187.46	+	3788.79i	0.216753	+	0.375427i	−0.737060	+	0.675827i	$0.763787\pi$
$468$		0			0
$469$	−5016.03	−	2324.32i	−0.493856	−	0.228843i
$470$	−118.241	+	68.2667i	−0.0116044	+	0.00669980i
$471$		0			0
$472$	−3494.16	+	2017.35i	−0.340745	+	0.196729i
$473$	1068.33	−	616.801i	0.103852	−	0.0599588i
$474$		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
$479$	8371.26			0.798523			0.399262	−	0.916837i	$-0.369267\pi$
$479$	8371.26			0.798523			0.399262	+	0.916837i	$0.369267\pi$
$480$		0			0
$481$		−	16495.1i		−	1.56365i
$482$	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	$0.894026\pi$
$488$	−3480.03	+	6027.58i	−0.322814	+	0.559131i
$489$		0			0
$490$	−4912.12	+	4162.23i	−0.452871	+	0.383735i
$491$	−10501.0	−	6062.77i	−0.965183	−	0.557248i	−0.0674183	−	0.997725i	$-0.521476\pi$
$491$	−10501.0	−	6062.77i	−0.965183	−	0.557248i	−0.897764	+	0.440476i	$0.854810\pi$
$492$		0			0
$493$		−	994.891i		−	0.0908877i
$494$	−8602.67	−	4966.76i	−0.783507	−	0.452358i
$495$		0			0
$496$		−	880.671i		−	0.0797244i
$497$	7560.08	+	10741.8i	0.682325	+	0.969485i
$498$		0			0
$499$	3678.40			0.329996			0.164998	−	0.986294i	$-0.447238\pi$
$499$	3678.40			0.329996			0.164998	+	0.986294i	$0.447238\pi$
$500$	3475.40	+	6019.57i	0.310849	+	0.538407i
$501$		0			0
$502$	−7440.61	−	4295.84i	−0.661535	−	0.381937i
$503$	4318.33			0.382793			0.191397	−	0.981513i	$-0.438698\pi$
$503$	4318.33			0.382793			0.191397	+	0.981513i	$0.438698\pi$
$504$		0			0
$505$	16095.4			1.41829
$506$	3601.26	+	2079.19i	0.316395	+	0.182670i
$507$		0			0
$508$	−450.354	−	780.037i	−0.0393332	−	0.0681270i
$509$	−15129.0			−1.31745			−0.658725	−	0.752384i	$-0.728904\pi$
$509$	−15129.0			−1.31745			−0.658725	+	0.752384i	$0.728904\pi$
$510$		0			0
$511$	15607.3	−	1403.34i	1.35113	−	0.121487i
$512$		−	1590.44i		−	0.137282i
$513$		0			0
$514$	7075.41	+	4084.99i	0.607166	+	0.350547i
$515$			10985.9i			0.939993i
$516$		0			0
$517$	−74.0181	−	42.7344i	−0.00629654	−	0.00363531i
$518$	5922.63	+	8415.19i	0.502365	+	0.713788i
$519$		0			0
$520$	−6430.61	+	11138.1i	−0.542309	+	0.939307i
$521$	−1778.96	+	3081.24i	−0.149592	+	0.259101i	−0.931077	−	0.364823i	$-0.881129\pi$
$521$	−1778.96	+	3081.24i	−0.149592	+	0.259101i	0.781485	+	0.623924i	$0.214463\pi$
$522$		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
$527$			12795.0i			1.05761i
$528$		0			0
$529$	−25723.5			−2.11421
$530$	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
$535$	8068.74	−	4658.49i	0.652041	−	0.376456i
$536$	5966.36	−	3444.68i	0.480798	−	0.277589i
$537$		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	$0.862473\pi$
$542$	10726.1			0.850050
$543$		0			0
$544$			11297.6i			0.890405i
$545$	−2887.34	+	5001.02i	−0.226936	+	0.393064i
$546$		0			0
$547$	10075.5	+	17451.3i	0.787564	+	1.36410i	0.927455	+	0.373935i	$0.121992\pi$
$547$	10075.5	+	17451.3i	0.787564	+	1.36410i	−0.139891	+	0.990167i	$0.544675\pi$
$548$	−4224.80	+	2439.19i	−0.329333	+	0.190141i
$549$		0			0
$550$	196.542	−	340.420i	0.0152374	−	0.0263919i
$551$	−787.322	+	1363.68i	−0.0608731	+	0.105435i
$552$		0			0
$553$	1885.74	+	20972.4i	0.145009	+	1.61273i
$554$	3198.80	+	1846.83i	0.245314	+	0.141632i
$555$		0			0
$556$			9205.69i			0.702173i
$557$	−15743.2	−	9089.32i	−1.19759	−	0.691430i	−0.237575	−	0.971369i	$-0.576352\pi$
$557$	−15743.2	−	9089.32i	−1.19759	−	0.691430i	−0.960018	+	0.279939i	$0.909686\pi$
$558$		0			0
$559$			5666.28i			0.428727i
$560$	−75.3870	−	838.422i	−0.00568872	−	0.0632675i
$561$		0			0
$562$	−4176.94			−0.313512
$563$	9431.25	+	16335.4i	0.706003	+	1.22283i	0.966328	+	0.257312i	$0.0828369\pi$
$563$	9431.25	+	16335.4i	0.706003	+	1.22283i	−0.260325	+	0.965521i	$0.583830\pi$
$564$		0			0
$565$	6617.42	+	3820.57i	0.492738	+	0.284482i
$566$	10309.7			0.765633
$567$		0			0
$568$	−16369.2			−1.20922
$569$	−903.244	−	521.488i	−0.0665482	−	0.0384216i	0.466357	−	0.884597i	$-0.345566\pi$
$569$	−903.244	−	521.488i	−0.0665482	−	0.0384216i	−0.532905	+	0.846175i	$0.678900\pi$
$570$		0			0
$571$	−9025.15	−	15632.0i	−0.661455	−	1.14567i	−0.980233	−	0.197845i	$-0.936606\pi$
$571$	−9025.15	−	15632.0i	−0.661455	−	1.14567i	0.318778	−	0.947829i	$-0.396728\pi$
$572$	−2977.39			−0.217641
$573$		0			0
$574$	−1001.31	+	2160.89i	−0.0728117	+	0.157132i
$575$			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	$0.758234\pi$
$578$		−	1494.47i		−	0.107546i
$579$		0			0
$580$	652.946	+	376.978i	0.0467450	+	0.0269882i
$581$	5522.60	+	2559.06i	0.394347	+	0.182733i
$582$		0			0
$583$	−3127.06	+	5416.22i	−0.222143	+	0.384763i
$584$	−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	0.941285	+	0.337613i	$0.109619\pi$
$587$	10851.6	+	18795.6i	0.763024	+	1.32160i	−0.178261	+	0.983983i	$0.557047\pi$
$588$		0			0
$589$	10125.5	−	17538.0i	0.708346	−	1.22689i
$590$		−	3281.46i		−	0.228976i
$591$		0			0
$592$	−1345.45			−0.0934079
$593$	4093.90	+	7090.84i	0.283501	+	0.491039i	0.972245	−	0.233967i	$-0.0751706\pi$
$593$	4093.90	+	7090.84i	0.283501	+	0.491039i	−0.688743	+	0.725005i	$0.741837\pi$
$594$		0			0
$595$	1095.28	+	12181.2i	0.0754656	+	0.839295i
$596$	−9715.60	+	5609.31i	−0.667729	+	0.385514i
$597$		0			0
$598$	−16541.6	+	9550.31i	−1.13117	+	0.653079i
$599$	13181.6	−	7610.39i	0.899140	−	0.519119i	0.0222191	−	0.999753i	$-0.492927\pi$
$599$	13181.6	−	7610.39i	0.899140	−	0.519119i	0.876921	+	0.480634i	$0.159594\pi$
$600$		0			0
$601$	−4793.86	+	2767.74i	−0.325367	+	0.187851i	−0.653782	−	0.756683i	$-0.726819\pi$
$601$	−4793.86	+	2767.74i	−0.325367	+	0.187851i	0.328415	+	0.944534i	$0.393486\pi$
$602$	−2034.49	−	2890.72i	−0.137740	−	0.195709i
$603$		0			0
$604$	−3849.53	−	6667.58i	−0.259330	−	0.449172i
$605$	12316.6			0.827674
$606$		0			0
$607$		−	9085.48i		−	0.607526i	−0.952748	−	0.303763i	$-0.901757\pi$
$607$		−	9085.48i		−	0.607526i	0.952748	−	0.303763i	$-0.0982431\pi$
$608$	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	$0.136497\pi$
$614$	−720.766	+	1248.40i	−0.0473742	+	0.0820545i
$615$		0			0
$616$	4107.32	−	2890.74i	0.268650	−	0.189077i
$617$	−20061.6	−	11582.6i	−1.30900	−	0.755749i	−0.327067	−	0.945001i	$-0.606060\pi$
$617$	−20061.6	−	11582.6i	−1.30900	−	0.755749i	−0.981928	+	0.189252i	$0.939394\pi$
$618$		0			0
$619$			12541.2i			0.814335i	0.913353	+	0.407168i	$0.133483\pi$
$619$			12541.2i			0.814335i	−0.913353	+	0.407168i	$0.866517\pi$
$620$	−8397.37	−	4848.22i	−0.543946	−	0.314047i
$621$		0			0
$622$			14124.7i			0.910527i
$623$	−17016.0	−	7884.86i	−1.09427	−	0.507063i
$624$		0			0
$625$	−12986.4			−0.831129
$626$	−3142.75	−	5443.40i	−0.200654	−	0.347543i
$627$		0			0
$628$	−4812.53	−	2778.51i	−0.305797	−	0.176552i
$629$	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	$0.360302\pi$
$632$	−22725.2	−	13120.4i	−1.43032	−	0.825795i
$633$		0			0
$634$	−2379.95	−	4122.19i	−0.149085	−	0.258222i
$635$	1980.87			0.123793
$636$		0			0
$637$	14124.1	−	11967.9i	0.878519	−	0.744404i
$638$		−	332.292i		−	0.0206200i
$639$		0			0
$640$	−6842.08	−	3950.27i	−0.422589	−	0.243982i
$641$			11729.5i			0.722755i	0.932420	+	0.361377i	$0.117693\pi$
$641$			11729.5i			0.722755i	−0.932420	+	0.361377i	$0.882307\pi$
$642$		0			0
$643$	18362.0	+	10601.3i	1.12617	+	0.650193i	0.942968	−	0.332883i	$-0.108021\pi$
$643$	18362.0	+	10601.3i	1.12617	+	0.650193i	0.183199	+	0.983076i	$0.441355\pi$
$644$	−7115.71	+	15356.1i	−0.435401	+	0.939620i
$645$		0			0
$646$	5885.87	−	10194.6i	0.358478	−	0.620901i
$647$	12408.1	−	21491.4i	0.753960	−	1.30590i	−0.191929	−	0.981409i	$-0.561474\pi$
$647$	12408.1	−	21491.4i	0.753960	−	1.30590i	0.945890	−	0.324489i	$-0.105192\pi$
$648$		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
$653$			26713.1i			1.60086i	0.599425	+	0.800431i	$0.295396\pi$
$653$			26713.1i			1.60086i	−0.599425	+	0.800431i	$0.704604\pi$
$654$		0			0
$655$	−767.396			−0.0457781
$656$	−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	−0.0842889	−	0.996441i	$-0.526862\pi$
$659$	12459.7	−	7193.60i	0.736510	−	0.425224i	0.820799	+	0.571217i	$0.193529\pi$
$660$		0			0
$661$	19590.0	−	11310.3i	1.15274	−	0.665535i	0.203187	−	0.979140i	$-0.434870\pi$
$661$	19590.0	−	11310.3i	1.15274	−	0.665535i	0.949554	+	0.313605i	$0.101537\pi$
$662$	400.414	−	231.179i	0.0235084	−	0.0135726i
$663$		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
$668$	7480.37			0.433270
$669$		0			0
$670$			5603.18i			0.323089i
$671$	1771.77	−	3068.79i	0.101935	−	0.176556i
$672$		0			0
$673$	8442.83	+	14623.4i	0.483577	+	0.837580i	0.999822	−	0.0188612i	$-0.00600406\pi$
$673$	8442.83	+	14623.4i	0.483577	+	0.837580i	−0.516245	+	0.856441i	$0.672671\pi$
$674$	−14239.5	+	8221.19i	−0.813777	+	0.469834i
$675$		0			0
$676$	1680.88	−	2911.36i	0.0956347	−	0.165644i
$677$	13397.9	−	23205.8i	0.760595	−	1.31739i	−0.181950	−	0.983308i	$-0.558241\pi$
$677$	13397.9	−	23205.8i	0.760595	−	1.31739i	0.942544	−	0.334081i	$-0.108426\pi$
$678$		0			0
$679$	−10813.4	+	23335.9i	−0.611164	+	1.31893i
$680$	−13199.3	−	7620.61i	−0.744367	−	0.429761i
$681$		0			0
$682$			4273.53i			0.239944i
$683$	−12561.4	−	7252.31i	−0.703730	−	0.406299i	0.105005	−	0.994472i	$-0.466514\pi$
$683$	−12561.4	−	7252.31i	−0.703730	−	0.406299i	−0.808735	+	0.588173i	$0.799847\pi$
$684$		0			0
$685$		−	10728.7i		−	0.598427i
$686$	−2908.46	+	11176.9i	−0.161874	+	0.622061i
$687$		0			0
$688$	462.177			0.0256109
$689$	−14363.5	−	24878.2i	−0.794200	−	1.37560i
$690$		0			0
$691$	−24782.4	−	14308.2i	−1.36435	−	0.787710i	−0.374154	−	0.927367i	$-0.622067\pi$
$691$	−24782.4	−	14308.2i	−1.36435	−	0.787710i	−0.990200	+	0.139656i	$0.955400\pi$
$692$	10612.8			0.583002
$693$		0			0
$694$	−13114.3			−0.717310
$695$	−17533.1	−	10122.7i	−0.956932	−	0.552485i
$696$		0			0
$697$	2262.04	+	3917.97i	0.122928	+	0.212918i
$698$	−450.392			−0.0244235
$699$		0			0
$700$	1451.58	+	672.633i	0.0783780	+	0.0363188i
$701$		−	6936.34i		−	0.373726i	−0.982386	−	0.186863i	$-0.940168\pi$
$701$		−	6936.34i		−	0.373726i	0.982386	−	0.186863i	$-0.0598321\pi$
$702$		0			0
$703$	−26793.6	−	15469.3i	−1.43747	−	0.829924i
$704$			4187.22i			0.224164i
$705$		0			0
$706$	3776.27	+	2180.23i	0.201306	+	0.116224i
$707$	23610.3	−	16617.0i	1.25595	−	0.883941i
$708$		0			0
$709$	7731.06	−	13390.6i	0.409515	−	0.709301i	−0.585320	−	0.810802i	$-0.699031\pi$
$709$	7731.06	−	13390.6i	0.409515	−	0.709301i	0.994835	+	0.101501i	$0.0323646\pi$
$710$	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
$716$		−	7222.35i		−	0.376972i
$717$		0			0
$718$	6694.90			0.347982
$719$	4003.14	+	6933.64i	0.207638	+	0.359640i	0.950970	−	0.309283i	$-0.100089\pi$
$719$	4003.14	+	6933.64i	0.207638	+	0.359640i	−0.743332	+	0.668923i	$0.766756\pi$
$720$		0			0
$721$	11341.9	+	16115.2i	0.585845	+	0.832400i
$722$	−5336.00	+	3080.74i	−0.275049	+	0.158800i
$723$		0			0
$724$	−1012.98	+	584.844i	−0.0519987	+	0.0300215i
$725$	247.867	−	143.106i	0.0126973	−	0.00733078i
$726$		0			0
$727$	17033.8	−	9834.49i	0.868982	−	0.501707i	0.00197210	−	0.999998i	$-0.499372\pi$
$727$	17033.8	−	9834.49i	0.868982	−	0.501707i	0.867010	+	0.498291i	$0.166039\pi$
$728$	2066.03	+	22977.5i	0.105182	+	1.16978i
$729$		0			0
$730$	−7941.16	−	13754.5i	−0.402624	−	0.697365i
$731$	−6714.85			−0.339750
$732$		0			0
$733$			11221.1i			0.565433i	0.959203	+	0.282717i	$0.0912356\pi$
$733$			11221.1i			0.565433i	−0.959203	+	0.282717i	$0.908764\pi$
$734$	−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	$0.0340574\pi$
$740$	−7406.88	+	12829.1i	−0.367949	+	0.637306i
$741$		0			0
$742$	16260.3	+	7534.68i	0.804493	+	0.372786i
$743$	11556.7	+	6672.24i	0.570623	+	0.329449i	0.757398	−	0.652953i	$-0.226470\pi$
$743$	11556.7	+	6672.24i	0.570623	+	0.329449i	−0.186775	+	0.982403i	$0.559804\pi$
$744$		0			0
$745$		−	24672.3i		−	1.21332i
$746$	15348.1	+	8861.23i	0.753262	+	0.434896i
$747$		0			0
$748$		−	3528.36i		−	0.172473i
$749$	7026.56	−	15163.7i	0.342784	−	0.739747i
$750$		0			0
$751$	−8382.88			−0.407318			−0.203659	−	0.979042i	$-0.565283\pi$
$751$	−8382.88			−0.407318			−0.203659	+	0.979042i	$0.565283\pi$
$752$	−16.0107	−	27.7314i	−0.000776397	−	0.00134476i
$753$		0			0
$754$	1321.83	+	763.156i	0.0638436	+	0.0368601i
$755$	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	$0.520660\pi$
$758$	7185.59	+	4148.60i	0.344317	+	0.198791i
$759$		0			0
$760$	12061.4	+	20890.9i	0.575674	+	0.997097i
$761$	−3663.71			−0.174520			−0.0872598	−	0.996186i	$-0.527811\pi$
$761$	−3663.71			−0.174520			−0.0872598	+	0.996186i	$0.527811\pi$
$762$		0			0
$763$	927.646	+	10316.9i	0.0440145	+	0.489510i
$764$			10096.3i			0.478102i
$765$		0			0
$766$	−4964.84	−	2866.45i	−0.234186	−	0.135208i
$767$			9435.38i			0.444187i
$768$		0			0
$769$	−5627.29	−	3248.92i	−0.263882	−	0.152352i	0.362222	−	0.932092i	$-0.382018\pi$
$769$	−5627.29	−	3248.92i	−0.263882	−	0.152352i	−0.626104	+	0.779739i	$0.715352\pi$
$770$	365.821	+	4068.51i	0.0171212	+	0.190414i
$771$		0			0
$772$	5125.70	−	8877.97i	0.238961	−	0.413893i
$773$	−19412.7	+	33623.7i	−0.903266	+	1.56450i	−0.0800382	+	0.996792i	$0.525504\pi$
$773$	−19412.7	+	33623.7i	−0.903266	+	1.56450i	−0.823228	+	0.567711i	$0.807829\pi$
$774$		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
$779$		−	7160.41i		−	0.329330i
$780$		0			0
$781$	8333.95			0.381834
$782$	−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
$787$	1188.44	−	686.147i	0.0538289	−	0.0310781i	−0.472844	−	0.881146i	$-0.656773\pi$
$787$	1188.44	−	686.147i	0.0538289	−	0.0310781i	0.526673	+	0.850068i	$0.323439\pi$
$788$	20246.4	−	11689.3i	0.915289	−	0.528443i
$789$		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
$794$	7860.42			0.351330
$795$		0			0
$796$		−	11975.2i		−	0.533226i
$797$	−14473.0	+	25068.0i	−0.643239	+	1.11412i	0.341466	+	0.939894i	$0.389076\pi$
$797$	−14473.0	+	25068.0i	−0.643239	+	1.11412i	−0.984705	+	0.174228i	$0.944257\pi$
$798$		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
$803$	4971.10	−	8610.20i	0.218464	−	0.378390i
$804$		0			0
$805$	−21422.6	−	30438.3i	−0.937945	−	1.33268i
$806$	−16999.7	−	9814.76i	−0.742913	−	0.428921i
$807$		0			0
$808$			35979.3i			1.56652i
$809$	17304.5	+	9990.77i	0.752033	+	0.434186i	0.826428	−	0.563043i	$-0.190369\pi$
$809$	17304.5	+	9990.77i	0.752033	+	0.434186i	−0.0743953	+	0.997229i	$0.523703\pi$
$810$		0			0
$811$			16397.5i			0.709981i	0.934870	+	0.354990i	$0.115516\pi$
$811$			16397.5i			0.709981i	−0.934870	+	0.354990i	$0.884484\pi$
$812$	1347.00	−	121.116i	0.0582147	−	0.00523440i
$813$		0			0
$814$	6528.88			0.281127
$815$	4236.36	+	7337.59i	0.182078	+	0.315368i
$816$		0			0
$817$	9203.94	+	5313.90i	0.394131	+	0.227552i
$818$	7626.05			0.325964
$819$		0			0
$820$	−3428.48			−0.146010
$821$	3428.94	+	1979.70i	0.145762	+	0.0841559i	0.571107	−	0.820875i	$-0.306514\pi$
$821$	3428.94	+	1979.70i	0.145762	+	0.0841559i	−0.425345	+	0.905031i	$0.639847\pi$
$822$		0			0
$823$	−9626.26	−	16673.2i	−0.407716	−	0.706185i	0.586917	−	0.809647i	$-0.300341\pi$
$823$	−9626.26	−	16673.2i	−0.407716	−	0.706185i	−0.994633	+	0.103462i	$0.967008\pi$
$824$	−24557.6			−1.03823
$825$		0			0
$826$	−3387.80	−	4813.57i	−0.142708	−	0.202767i
$827$		−	21147.5i		−	0.889202i	−0.895729	−	0.444601i	$-0.853345\pi$
$827$		−	21147.5i		−	0.889202i	0.895729	−	0.444601i	$-0.146655\pi$
$828$		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	$0.450086\pi$
$830$		−	6169.05i		−	0.257989i
$831$		0			0
$832$	−16656.3	−	9616.54i	−0.694056	−	0.400713i
$833$	14182.6	+	16737.8i	0.589913	+	0.696195i
$834$		0			0
$835$	−8225.54	+	14247.0i	−0.340906	+	0.590466i
$836$	−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	$-0.269846\pi$
$839$	−7740.19	−	13406.4i	−0.318500	−	0.551658i	−0.980175	+	0.198133i	$0.936512\pi$
$840$		0			0
$841$	−12073.5	+	20912.0i	−0.495040	+	0.857434i
$842$			19590.5i			0.801819i
$843$		0			0
$844$	19488.1			0.794797
$845$	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
$850$	−1853.00	+	1069.83i	−0.0747735	+	0.0431705i
$851$	−51520.0	+	29745.1i	−2.07530	+	1.19818i
$852$		0			0
$853$	−13650.2	+	7880.96i	−0.547919	+	0.316341i	−0.748282	−	0.663381i	$-0.769121\pi$
$853$	−13650.2	+	7880.96i	−0.547919	+	0.316341i	0.200363	+	0.979722i	$0.435788\pi$
$854$	−9212.96	−	4269.10i	−0.369158	−	0.171060i
$855$		0			0
$856$	10413.5	+	18036.7i	0.415800	+	0.720187i
$857$	−31367.7			−1.25029			−0.625145	−	0.780508i	$-0.714960\pi$
$857$	−31367.7			−1.25029			−0.625145	+	0.780508i	$0.714960\pi$
$858$		0			0
$859$			14502.5i			0.576042i	0.957624	+	0.288021i	$0.0929973\pi$
$859$			14502.5i			0.576042i	−0.957624	+	0.288021i	$0.907003\pi$
$860$	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	0.307515	−	0.951543i	$-0.400503\pi$
$863$	32586.1	−	18813.6i	1.28533	−	0.742087i	0.977818	+	0.209456i	$0.0671694\pi$
$864$		0			0
$865$	−11670.0	+	20213.0i	−0.458719	+	0.794524i
$866$	−2959.98	+	5126.84i	−0.116148	+	0.201174i
$867$		0			0
$868$	−17323.4	+	1557.64i	−0.677413	+	0.0609099i
$869$	11570.0	+	6679.94i	0.451651	+	0.260761i
$870$		0			0
$871$		−	16111.2i		−	0.626757i
$872$	−11179.1	−	6454.28i	−0.434144	−	0.250653i
$873$		0			0
$874$			35825.5i			1.38652i
$875$	−22423.6	+	15781.8i	−0.866350	+	0.609739i
$876$		0			0
$877$	−9465.85			−0.364469			−0.182234	−	0.983255i	$-0.558333\pi$
$877$	−9465.85			−0.364469			−0.182234	+	0.983255i	$0.558333\pi$
$878$	−4952.55	−	8578.07i	−0.190365	−	0.329722i
$879$		0			0
$880$	−462.538	−	267.046i	−0.0177183	−	0.0102297i
$881$	15486.3			0.592221			0.296110	−	0.955154i	$-0.404310\pi$
$881$	15486.3			0.592221			0.296110	+	0.955154i	$0.404310\pi$
$882$		0			0
$883$	8390.36			0.319771			0.159886	−	0.987136i	$-0.448887\pi$
$883$	8390.36			0.319771			0.159886	+	0.987136i	$0.448887\pi$
$884$	14035.5	+	8103.39i	0.534009	+	0.308310i
$885$		0			0
$886$	−7484.21	−	12963.0i	−0.283789	−	0.491537i
$887$	19992.7			0.756807			0.378403	−	0.925641i	$-0.376473\pi$
$887$	19992.7			0.756807			0.378403	+	0.925641i	$0.376473\pi$
$888$		0			0
$889$	2905.73	−	2045.06i	0.109623	−	0.0771530i
$890$			19007.8i			0.715891i
$891$		0			0
$892$	7730.88	+	4463.42i	0.290189	+	0.167541i
$893$		−	736.335i		−	0.0275930i
$894$		0			0
$895$	13755.6	+	7941.81i	0.513743	+	0.296609i
$896$	−14114.9	+	1269.15i	−0.526279	+	0.0473205i
$897$		0			0
$898$	−13537.9	+	23448.3i	−0.503078	+	0.871357i
$899$	−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
$905$		−	2572.41i		−	0.0944861i
$906$		0			0
$907$	−34274.9			−1.25477			−0.627387	−	0.778707i	$-0.715876\pi$
$907$	−34274.9			−1.25477			−0.627387	+	0.778707i	$0.715876\pi$
$908$	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	−0.300905	−	0.953654i	$-0.597289\pi$
$911$	10298.3	−	5945.74i	0.374532	−	0.216236i	0.675437	+	0.737418i	$0.263955\pi$
$912$		0			0
$913$	3344.40	−	1930.89i	0.121230	−	0.0699924i
$914$	21279.1	−	12285.5i	0.770077	−	0.444604i
$915$		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	$0.882744\pi$
$920$	46384.4			1.66222
$921$		0			0
$922$			6836.61i			0.244199i
$923$	−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
$929$	3047.03	−	5277.62i	0.107610	−	0.186387i	−0.807191	−	0.590290i	$-0.799013\pi$
$929$	3047.03	−	5277.62i	0.107610	−	0.186387i	0.914802	+	0.403903i	$0.132347\pi$
$930$		0			0
$931$	−6194.15	−	34165.9i	−0.218051	−	1.20273i
$932$	−1485.82	−	857.839i	−0.0522207	−	0.0301496i
$933$		0			0
$934$		−	7953.83i		−	0.278648i
$935$	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	$-0.182583\pi$
$938$	5784.75	+	8219.29i	0.201363	+	0.286108i
$939$		0			0
$940$	−352.565			−0.0122334
$941$	352.121	+	609.892i	0.0121985	+	0.0211285i	0.872060	−	0.489399i	$-0.162784\pi$
$941$	352.121	+	609.892i	0.0121985	+	0.0211285i	−0.859862	+	0.510527i	$0.829450\pi$
$942$		0			0
$943$	−11923.8	−	6884.19i	−0.411761	−	0.237731i
$944$	769.608			0.0265345
$945$		0			0
$946$	−2242.75			−0.0770805
$947$	28832.8	+	16646.6i	0.989377	+	0.571217i	0.905088	−	0.425224i	$-0.139805\pi$
$947$	28832.8	+	16646.6i	0.989377	+	0.571217i	0.0842890	+	0.996441i	$0.473138\pi$
$948$		0			0
$949$	22833.7	+	39549.1i	0.781045	+	1.35281i
$950$	3386.51			0.115656
$951$		0			0
$952$	−27229.6	+	2448.36i	−0.927012	+	0.0833526i
$953$			15134.2i			0.514424i	0.966355	+	0.257212i	$0.0828039\pi$
$953$			15134.2i			0.514424i	−0.966355	+	0.257212i	$0.917196\pi$
$954$		0			0
$955$	−19229.2	−	11102.0i	−0.651564	−	0.376180i
$956$		−	15184.3i		−	0.513698i
$957$		0			0
$958$	−13180.4	−	7609.69i	−0.444508	−	0.256637i
$959$	−11076.4	−	15737.9i	−0.372966	−	0.529930i
$960$		0			0
$961$	5113.50	−	8856.85i	0.171646	−	0.297299i
$962$	−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	−0.516360	−	0.856372i	$-0.672713\pi$
$967$	14537.8	−	25180.3i	0.483460	−	0.837377i	0.999820	+	0.0189949i	$0.00604664\pi$
$968$			27532.3i			0.914175i
$969$		0			0
$970$	26067.6			0.862865
$971$	−2209.10	−	3826.28i	−0.0730108	−	0.126458i	0.827209	−	0.561895i	$-0.189927\pi$
$971$	−2209.10	−	3826.28i	−0.0730108	−	0.126458i	−0.900219	+	0.435436i	$0.856594\pi$
$972$		0			0
$973$	−36170.0	+	3252.24i	−1.19173	+	0.107155i
$974$	25570.3	−	14763.0i	0.841197	−	0.485665i
$975$		0			0
$976$	1149.74	−	663.804i	0.0377074	−	0.0217704i
$977$	4262.34	−	2460.86i	0.139574	−	0.0805834i	−0.428587	−	0.903501i	$-0.640988\pi$
$977$	4262.34	−	2460.86i	0.139574	−	0.0805834i	0.568161	+	0.822917i	$0.307655\pi$
$978$		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
$983$	−29603.1			−0.960520			−0.480260	−	0.877126i	$-0.659458\pi$
$983$	−29603.1			−0.960520			−0.480260	+	0.877126i	$0.659458\pi$
$984$		0			0
$985$			51414.8i			1.66316i
$986$	−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	$0.103832\pi$
$992$	17667.3	−	30600.6i	0.565460	−	0.979406i
$993$		0			0
$994$	−2138.64	−	23785.0i	−0.0682429	−	0.758968i
$995$	22807.8	+	13168.1i	0.726689	+	0.419554i
$996$		0			0
$997$			21115.8i			0.670756i	0.942084	+	0.335378i	$0.108864\pi$
$997$			21115.8i			0.670756i	−0.942084	+	0.335378i	$0.891136\pi$
$998$	−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.s.a.17.8		44
3.2	odd	2		63.4.s.a.59.15	yes	44
7.5	odd	6		189.4.i.a.152.15		44
9.2	odd	6		189.4.i.a.143.8		44
9.7	even	3		63.4.i.a.38.15	yes	44
21.5	even	6		63.4.i.a.5.8	✓	44
63.47	even	6	inner	189.4.s.a.89.8		44
63.61	odd	6		63.4.s.a.47.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.8	✓	44	21.5	even	6
63.4.i.a.38.15	yes	44	9.7	even	3
63.4.s.a.47.15	yes	44	63.61	odd	6
63.4.s.a.59.15	yes	44	3.2	odd	2
189.4.i.a.143.8		44	9.2	odd	6
189.4.i.a.152.15		44	7.5	odd	6
189.4.s.a.17.8		44	1.1	even	1	trivial
189.4.s.a.89.8		44	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.57448 - 0.909026i) q^{2} +(-2.34735 - 4.06572i) q^{4} +10.3247 q^{5} +(15.1453 - 10.6593i) q^{7} +23.0796i q^{8} +O(q^{10})\)	\(q+(-1.57448 - 0.909026i) q^{2} +(-2.34735 - 4.06572i) q^{4} +10.3247 q^{5} +(15.1453 - 10.6593i) q^{7} +23.0796i q^{8} +(-16.2560 - 9.38543i) q^{10} -11.7504i q^{11} +(46.7419 + 26.9865i) q^{13} +(-33.5355 + 3.01536i) q^{14} +(2.20118 - 3.81256i) q^{16} +(-31.9804 + 55.3917i) q^{17} +(87.6701 - 50.6164i) q^{19} +(-24.2357 - 41.9774i) q^{20} +(-10.6814 + 18.5008i) q^{22} -194.655i q^{23} -18.4003 q^{25} +(-49.0628 - 84.9792i) q^{26} +(-78.8889 - 36.5555i) q^{28} +(-13.4708 + 7.77735i) q^{29} +(173.244 - 100.023i) q^{31} +(152.969 - 88.3165i) q^{32} +(100.705 - 58.1420i) q^{34} +(156.371 - 110.054i) q^{35} +(-152.809 - 264.674i) q^{37} -184.046 q^{38} +238.290i q^{40} +(35.3661 - 61.2559i) q^{41} +(52.4919 + 90.9186i) q^{43} +(-47.7738 + 27.5822i) q^{44} +(-176.946 + 306.480i) q^{46} +(3.63684 - 6.29920i) q^{47} +(115.759 - 322.876i) q^{49} +(28.9709 + 16.7264i) q^{50} -253.386i q^{52} +(-460.939 - 266.123i) q^{53} -121.319i q^{55} +(246.012 + 349.547i) q^{56} +28.2792 q^{58} +(87.4084 + 151.396i) q^{59} +(261.165 + 150.784i) q^{61} -363.692 q^{62} -356.347 q^{64} +(482.597 + 278.627i) q^{65} +(-149.252 - 258.512i) q^{67} +300.276 q^{68} +(-346.244 + 31.1327i) q^{70} +709.248i q^{71} +(732.758 + 423.058i) q^{73} +555.631i q^{74} +(-411.584 - 237.628i) q^{76} +(-125.251 - 177.963i) q^{77} +(-568.486 + 984.646i) q^{79} +(22.7266 - 39.3636i) q^{80} +(-111.366 + 64.2974i) q^{82} +(164.325 + 284.620i) q^{83} +(-330.188 + 571.903i) q^{85} -190.866i q^{86} +271.194 q^{88} +(-506.312 - 876.958i) q^{89} +(995.576 - 89.5176i) q^{91} +(-791.413 + 456.922i) q^{92} +(-11.4523 + 6.61197i) q^{94} +(905.168 - 522.599i) q^{95} +(-1202.67 + 694.363i) q^{97} +(-475.763 + 403.133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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