LMFDB - Embedded newform 189.4.s.a.17.15

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			17.15
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59189 + 0.919076i) q^{2} +(-2.31060 - 4.00207i) q^{4} -0.414554 q^{5} +(12.7471 + 13.4355i) q^{7} -23.1997i q^{8} +O(q^{10})$	\(q+(1.59189 + 0.919076i) q^{2} +(-2.31060 - 4.00207i) q^{4} -0.414554 q^{5} +(12.7471 + 13.4355i) q^{7} -23.1997i q^{8} +(-0.659923 - 0.381007i) q^{10} -49.6101i q^{11} +(1.43477 + 0.828367i) q^{13} +(7.94365 + 33.1033i) q^{14} +(2.83751 - 4.91471i) q^{16} +(20.6496 - 35.7662i) q^{17} +(130.814 - 75.5256i) q^{19} +(0.957866 + 1.65907i) q^{20} +(45.5955 - 78.9737i) q^{22} -131.651i q^{23} -124.828 q^{25} +(1.52267 + 2.63733i) q^{26} +(24.3164 - 82.0587i) q^{28} +(136.539 - 78.8310i) q^{29} +(-15.9411 + 9.20357i) q^{31} +(-151.698 + 87.5830i) q^{32} +(65.7437 - 37.9571i) q^{34} +(-5.28434 - 5.56973i) q^{35} +(173.836 + 301.092i) q^{37} +277.655 q^{38} +9.61751i q^{40} +(16.9818 - 29.4134i) q^{41} +(29.5623 + 51.2034i) q^{43} +(-198.543 + 114.629i) q^{44} +(120.997 - 209.573i) q^{46} +(-108.266 + 187.523i) q^{47} +(-18.0246 + 342.526i) q^{49} +(-198.712 - 114.727i) q^{50} -7.65609i q^{52} +(-174.040 - 100.482i) q^{53} +20.5661i q^{55} +(311.699 - 295.728i) q^{56} +289.807 q^{58} +(-149.819 - 259.493i) q^{59} +(-69.6527 - 40.2140i) q^{61} -33.8351 q^{62} -367.382 q^{64} +(-0.594791 - 0.343403i) q^{65} +(128.788 + 223.067i) q^{67} -190.852 q^{68} +(-3.29307 - 13.7231i) q^{70} +1032.80i q^{71} +(-711.100 - 410.554i) q^{73} +639.073i q^{74} +(-604.518 - 349.019i) q^{76} +(666.536 - 632.384i) q^{77} +(-52.6589 + 91.2079i) q^{79} +(-1.17630 + 2.03741i) q^{80} +(54.0663 - 31.2152i) q^{82} +(-245.110 - 424.542i) q^{83} +(-8.56037 + 14.8270i) q^{85} +108.680i q^{86} -1150.94 q^{88} +(754.828 + 1307.40i) q^{89} +(7.15964 + 29.8361i) q^{91} +(-526.875 + 304.191i) q^{92} +(-344.695 + 199.010i) q^{94} +(-54.2295 + 31.3094i) q^{95} +(1087.14 - 627.661i) q^{97} +(-343.501 + 528.697i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.59189	+	0.919076i	0.562817	+	0.324943i	0.754275	−	0.656558i	$-0.227988\pi$
$2$	1.59189	+	0.919076i	0.562817	+	0.324943i	−0.191458	+	0.981501i	$0.561322\pi$
$3$		0			0
$3$		0			0
$4$	−2.31060	−	4.00207i	−0.288825	−	0.500259i
$5$	−0.414554			−0.0370788			−0.0185394	−	0.999828i	$-0.505902\pi$
$5$	−0.414554			−0.0370788			−0.0185394	+	0.999828i	$0.505902\pi$
$6$		0			0
$7$	12.7471	+	13.4355i	0.688277	+	0.725448i
$7$	12.7471	+	13.4355i	0.688277	+	0.725448i
$8$		−	23.1997i		−	1.02529i
$9$		0			0
$10$	−0.659923	−	0.381007i	−0.0208686	−	0.0120485i
$11$		−	49.6101i		−	1.35982i	−0.733296	−	0.679910i	$-0.762019\pi$
$11$		−	49.6101i		−	1.35982i	0.733296	−	0.679910i	$-0.237981\pi$
$12$		0			0
$13$	1.43477	+	0.828367i	0.0306104	+	0.0176729i	0.515227	−	0.857054i	$-0.327708\pi$
$13$	1.43477	+	0.828367i	0.0306104	+	0.0176729i	−0.484617	+	0.874727i	$0.661041\pi$
$14$	7.94365	+	33.1033i	0.151645	+	0.631945i
$15$		0			0
$16$	2.83751	−	4.91471i	0.0443360	−	0.0767923i
$17$	20.6496	−	35.7662i	0.294604	−	0.510269i	−0.680289	−	0.732944i	$-0.738146\pi$
$17$	20.6496	−	35.7662i	0.294604	−	0.510269i	0.974893	+	0.222675i	$0.0714790\pi$
$18$		0			0
$19$	130.814	−	75.5256i	1.57952	−	0.911935i	0.584592	−	0.811327i	$-0.301255\pi$
$19$	130.814	−	75.5256i	1.57952	−	0.911935i	0.994926	−	0.100608i	$-0.0320787\pi$
$20$	0.957866	+	1.65907i	0.0107093	+	0.0185490i
$21$		0			0
$22$	45.5955	−	78.9737i	0.441863	−	0.765330i
$23$		−	131.651i		−	1.19352i	−0.802418	−	0.596762i	$-0.796454\pi$
$23$		−	131.651i		−	1.19352i	0.802418	−	0.596762i	$-0.203546\pi$
$24$		0			0
$25$	−124.828			−0.998625
$26$	1.52267	+	2.63733i	0.0114854	+	0.0198932i
$27$		0			0
$28$	24.3164	−	82.0587i	0.164121	−	0.553844i
$29$	136.539	−	78.8310i	0.874300	−	0.504777i	0.00552512	−	0.999985i	$-0.498241\pi$
$29$	136.539	−	78.8310i	0.874300	−	0.504777i	0.868775	+	0.495207i	$0.164908\pi$
$30$		0			0
$31$	−15.9411	+	9.20357i	−0.0923580	+	0.0533229i	−0.545468	−	0.838132i	$-0.683648\pi$
$31$	−15.9411	+	9.20357i	−0.0923580	+	0.0533229i	0.453110	+	0.891455i	$0.350315\pi$
$32$	−151.698	+	87.5830i	−0.838022	+	0.483832i
$33$		0			0
$34$	65.7437	−	37.9571i	0.331616	−	0.191459i
$35$	−5.28434	−	5.56973i	−0.0255205	−	0.0268988i
$36$		0			0
$37$	173.836	+	301.092i	0.772390	+	1.33782i	0.936250	+	0.351335i	$0.114272\pi$
$37$	173.836	+	301.092i	0.772390	+	1.33782i	−0.163860	+	0.986484i	$0.552395\pi$
$38$	277.655			1.18531
$39$		0			0
$40$			9.61751i			0.0380166i
$41$	16.9818	−	29.4134i	0.0646857	−	0.112039i	−0.831869	−	0.554972i	$-0.812729\pi$
$41$	16.9818	−	29.4134i	0.0646857	−	0.112039i	0.896555	+	0.442933i	$0.146062\pi$
$42$		0			0
$43$	29.5623	+	51.2034i	0.104842	+	0.181592i	0.913674	−	0.406449i	$-0.133233\pi$
$43$	29.5623	+	51.2034i	0.104842	+	0.181592i	−0.808832	+	0.588040i	$0.799900\pi$
$44$	−198.543	+	114.629i	−0.680262	+	0.392749i
$45$		0			0
$46$	120.997	−	209.573i	0.387827	−	0.671736i
$47$	−108.266	+	187.523i	−0.336005	+	0.581978i	−0.983677	−	0.179941i	$-0.942409\pi$
$47$	−108.266	+	187.523i	−0.336005	+	0.581978i	0.647672	+	0.761919i	$0.275743\pi$
$48$		0			0
$49$	−18.0246	+	342.526i	−0.0525500	+	0.998618i
$50$	−198.712	−	114.727i	−0.562043	−	0.324496i
$51$		0			0
$52$		−	7.65609i		−	0.0204175i
$53$	−174.040	−	100.482i	−0.451062	−	0.260421i	0.257217	−	0.966354i	$-0.417195\pi$
$53$	−174.040	−	100.482i	−0.451062	−	0.260421i	−0.708278	+	0.705933i	$0.750528\pi$
$54$		0			0
$55$			20.5661i			0.0504205i
$56$	311.699	−	295.728i	0.743795	−	0.705684i
$57$		0			0
$58$	289.807			0.656095
$59$	−149.819	−	259.493i	−0.330588	−	0.572596i	0.652039	−	0.758185i	$-0.273914\pi$
$59$	−149.819	−	259.493i	−0.330588	−	0.572596i	−0.982627	+	0.185590i	$0.940581\pi$
$60$		0			0
$61$	−69.6527	−	40.2140i	−0.146199	−	0.0844078i	0.425116	−	0.905139i	$-0.360233\pi$
$61$	−69.6527	−	40.2140i	−0.146199	−	0.0844078i	−0.571315	+	0.820731i	$0.693567\pi$
$62$	−33.8351			−0.0693075
$63$		0			0
$64$	−367.382			−0.717543
$65$	−0.594791	−	0.343403i	−0.00113500	−	0.000655290i
$66$		0			0
$67$	128.788	+	223.067i	0.234835	+	0.406746i	0.959225	−	0.282645i	$-0.0912117\pi$
$67$	128.788	+	223.067i	0.234835	+	0.406746i	−0.724390	+	0.689391i	$0.757878\pi$
$68$	−190.852			−0.340355
$69$		0			0
$70$	−3.29307	−	13.7231i	−0.00562281	−	0.0234318i
$71$			1032.80i			1.72635i	0.504902	+	0.863177i	$0.331529\pi$
$71$			1032.80i			1.72635i	−0.504902	+	0.863177i	$0.668471\pi$
$72$		0			0
$73$	−711.100	−	410.554i	−1.14011	−	0.658243i	−0.193652	−	0.981070i	$-0.562033\pi$
$73$	−711.100	−	410.554i	−1.14011	−	0.658243i	−0.946458	+	0.322828i	$0.895367\pi$
$74$			639.073i			1.00393i
$75$		0			0
$76$	−604.518	−	349.019i	−0.912407	−	0.526779i
$77$	666.536	−	632.384i	0.986479	−	0.935933i
$78$		0			0
$79$	−52.6589	+	91.2079i	−0.0749948	+	0.129895i	−0.901084	−	0.433645i	$-0.857227\pi$
$79$	−52.6589	+	91.2079i	−0.0749948	+	0.129895i	0.826089	+	0.563539i	$0.190561\pi$
$80$	−1.17630	+	2.03741i	−0.00164393	+	0.00284737i
$81$		0			0
$82$	54.0663	−	31.2152i	0.0728125	−	0.0420383i
$83$	−245.110	−	424.542i	−0.324148	−	0.561441i	0.657192	−	0.753724i	$-0.271744\pi$
$83$	−245.110	−	424.542i	−0.324148	−	0.561441i	−0.981340	+	0.192283i	$0.938411\pi$
$84$		0			0
$85$	−8.56037	+	14.8270i	−0.0109236	+	0.0189202i
$86$			108.680i			0.136270i
$87$		0			0
$88$	−1150.94			−1.39421
$89$	754.828	+	1307.40i	0.899007	+	1.55713i	0.828766	+	0.559596i	$0.189044\pi$
$89$	754.828	+	1307.40i	0.899007	+	1.55713i	0.0702410	+	0.997530i	$0.477623\pi$
$90$		0			0
$91$	7.15964	+	29.8361i	0.00824763	+	0.0343701i
$92$	−526.875	+	304.191i	−0.597071	+	0.344719i
$93$		0			0
$94$	−344.695	+	199.010i	−0.378219	+	0.218365i
$95$	−54.2295	+	31.3094i	−0.0585666	+	0.0338135i
$96$		0			0
$97$	1087.14	−	627.661i	1.13796	−	0.657003i	0.192037	−	0.981388i	$-0.438490\pi$
$97$	1087.14	−	627.661i	1.13796	−	0.657003i	0.945925	+	0.324384i	$0.105157\pi$
$98$	−343.501	+	528.697i	−0.354070	+	0.544964i
$99$		0			0
$100$	288.428	+	499.571i	0.288428	+	0.499571i
$101$	1201.49			1.18369			0.591846	−	0.806051i	$-0.298399\pi$
$101$	1201.49			1.18369			0.591846	+	0.806051i	$0.298399\pi$
$102$		0			0
$103$		−	219.409i		−	0.209893i	−0.994478	−	0.104946i	$-0.966533\pi$
$103$		−	219.409i		−	0.209893i	0.994478	−	0.104946i	$-0.0334671\pi$
$104$	19.2179	−	33.2863i	0.0181199	−	0.0313845i
$105$		0			0
$106$	−184.702	−	319.913i	−0.169243	−	0.293138i
$107$	−165.493	+	95.5472i	−0.149521	+	0.0863261i	−0.572894	−	0.819629i	$-0.694179\pi$
$107$	−165.493	+	95.5472i	−0.149521	+	0.0863261i	0.423373	+	0.905956i	$0.360846\pi$
$108$		0			0
$109$	−761.102	+	1318.27i	−0.668810	+	1.15841i	0.309427	+	0.950923i	$0.399863\pi$
$109$	−761.102	+	1318.27i	−0.668810	+	1.15841i	−0.978237	+	0.207490i	$0.933470\pi$
$110$	−18.9018	+	32.7389i	−0.0163838	+	0.0283775i
$111$		0			0
$112$	102.201	−	24.5248i	0.0862243	−	0.0206908i
$113$	−1363.73	−	787.351i	−1.13530	−	0.655467i	−0.190039	−	0.981777i	$-0.560861\pi$
$113$	−1363.73	−	787.351i	−1.13530	−	0.655467i	−0.945263	+	0.326310i	$0.894195\pi$
$114$		0			0
$115$			54.5762i			0.0442544i
$116$	−630.974	−	364.293i	−0.505039	−	0.291584i
$117$		0			0
$118$		−	550.779i		−	0.429689i
$119$	743.758	−	178.476i	0.572943	−	0.137486i
$120$		0			0
$121$	−1130.17			−0.849110
$122$	−73.9195	−	128.032i	−0.0548554	−	0.0950123i
$123$		0			0
$124$	73.6667	+	42.5315i	0.0533505	+	0.0308019i
$125$	103.567			0.0741066
$126$		0			0
$127$	84.3766			0.0589544			0.0294772	−	0.999565i	$-0.490616\pi$
$127$	84.3766			0.0589544			0.0294772	+	0.999565i	$0.490616\pi$
$128$	628.755	+	363.012i	0.434177	+	0.250672i
$129$		0			0
$130$	−0.631227	−	1.09332i	−0.000425863	−	0.000737617i
$131$	−792.466			−0.528535			−0.264267	−	0.964449i	$-0.585130\pi$
$131$	−792.466			−0.528535			−0.264267	+	0.964449i	$0.585130\pi$
$132$		0			0
$133$	2682.22	+	794.823i	1.74871	+	0.518195i
$134$			473.464i			0.305232i
$135$		0			0
$136$	−829.764	−	479.064i	−0.523174	−	0.302055i
$137$		−	678.899i		−	0.423374i	−0.977337	−	0.211687i	$-0.932104\pi$
$137$		−	678.899i		−	0.423374i	0.977337	−	0.211687i	$-0.0678958\pi$
$138$		0			0
$139$	2217.73	+	1280.41i	1.35328	+	0.781314i	0.988707	−	0.149863i	$-0.0478832\pi$
$139$	2217.73	+	1280.41i	1.35328	+	0.781314i	0.364568	+	0.931177i	$0.381217\pi$
$140$	−10.0805	+	34.0177i	−0.00608540	+	0.0205359i
$141$		0			0
$142$	−949.225	+	1644.11i	−0.560966	+	0.971621i
$143$	41.0954	−	71.1794i	0.0240320	−	0.0416246i
$144$		0			0
$145$	−56.6028	+	32.6797i	−0.0324180	+	0.0187165i
$146$	−754.661	−	1307.11i	−0.427782	−	0.740940i
$147$		0			0
$148$	803.329	−	1391.41i	0.446170	−	0.772790i
$149$			2357.74i			1.29633i	0.761498	+	0.648167i	$0.224464\pi$
$149$			2357.74i			1.29633i	−0.761498	+	0.648167i	$0.775536\pi$
$150$		0			0
$151$	592.855			0.319509			0.159754	−	0.987157i	$-0.448930\pi$
$151$	592.855			0.319509			0.159754	+	0.987157i	$0.448930\pi$
$152$	−1752.17	−	3034.85i	−0.934999	−	1.61947i
$153$		0			0
$154$	1642.26	−	394.086i	0.859331	−	0.206210i
$155$	6.60842	−	3.81537i	0.00342452	−	0.00197715i
$156$		0			0
$157$	1613.35	−	931.467i	0.820122	−	0.473498i	−0.0303366	−	0.999540i	$-0.509658\pi$
$157$	1613.35	−	931.467i	0.820122	−	0.473498i	0.850459	+	0.526042i	$0.176325\pi$
$158$	−167.654	+	96.7951i	−0.0844167	+	0.0487380i
$159$		0			0
$160$	62.8870	−	36.3078i	0.0310728	−	0.0179399i
$161$	1768.79	−	1678.16i	0.865840	−	0.821475i
$162$		0			0
$163$	1052.23	+	1822.52i	0.505627	+	0.875771i	0.999979	+	0.00650957i	$0.00207207\pi$
$163$	1052.23	+	1822.52i	0.505627	+	0.875771i	−0.494352	+	0.869262i	$0.664595\pi$
$164$	−156.953			−0.0747313
$165$		0			0
$166$		−	901.098i		−	0.421318i
$167$	970.922	−	1681.69i	0.449893	−	0.779238i	−0.548485	−	0.836160i	$-0.684795\pi$
$167$	970.922	−	1681.69i	0.449893	−	0.779238i	0.998379	+	0.0569221i	$0.0181287\pi$
$168$		0			0
$169$	−1097.13	−	1900.28i	−0.499375	−	0.864943i
$170$	−27.2543	+	15.7353i	−0.0122959	+	0.00709906i
$171$		0			0
$172$	136.613	−	236.621i	0.0605619	−	0.104896i
$173$	215.024	−	372.433i	0.0944971	−	0.163674i	−0.814901	−	0.579599i	$-0.803209\pi$
$173$	215.024	−	372.433i	0.0944971	−	0.163674i	0.909399	+	0.415926i	$0.136542\pi$
$174$		0			0
$175$	−1591.19	−	1677.13i	−0.687331	−	0.724451i
$176$	−243.819	−	140.769i	−0.104424	−	0.0602890i
$177$		0			0
$178$			2774.98i			1.16850i
$179$	316.818	+	182.915i	0.132291	+	0.0763783i	0.564685	−	0.825307i	$-0.308998\pi$
$179$	316.818	+	182.915i	0.132291	+	0.0763783i	−0.432394	+	0.901685i	$0.642331\pi$
$180$		0			0
$181$		−	3311.27i		−	1.35980i	−0.733303	−	0.679902i	$-0.762022\pi$
$181$		−	3311.27i		−	1.35980i	0.733303	−	0.679902i	$-0.237978\pi$
$182$	−16.0244	+	54.0760i	−0.00652640	+	0.0220241i
$183$		0			0
$184$	−3054.25			−1.22371
$185$	−72.0642	−	124.819i	−0.0286393	−	0.0496047i
$186$		0			0
$187$	−1774.37	−	1024.43i	−0.693874	−	0.400608i
$188$	1000.64			0.388187
$189$		0			0
$190$	−115.103			−0.0439497
$191$	3470.27	+	2003.56i	1.31466	+	0.759019i	0.982864	−	0.184333i	$-0.0590124\pi$
$191$	3470.27	+	2003.56i	1.31466	+	0.759019i	0.331795	+	0.943351i	$0.392346\pi$
$192$		0			0
$193$	−1168.46	−	2023.83i	−0.435791	−	0.754812i	0.561569	−	0.827430i	$-0.310198\pi$
$193$	−1168.46	−	2023.83i	−0.435791	−	0.754812i	−0.997360	+	0.0726178i	$0.976865\pi$
$194$	2307.47			0.853953
$195$		0			0
$196$	1412.46	−	719.304i	0.514745	−	0.262137i
$197$			337.074i			0.121906i	0.998141	+	0.0609531i	$0.0194140\pi$
$197$			337.074i			0.121906i	−0.998141	+	0.0609531i	$0.980586\pi$
$198$		0			0
$199$	4282.30	+	2472.39i	1.52545	+	0.880719i	0.999545	+	0.0301752i	$0.00960652\pi$
$199$	4282.30	+	2472.39i	1.52545	+	0.880719i	0.525905	+	0.850543i	$0.323727\pi$
$200$			2895.97i			1.02388i
$201$		0			0
$202$	1912.64	+	1104.26i	0.666203	+	0.384632i
$203$	2799.61	+	829.608i	0.967950	+	0.286833i
$204$		0			0
$205$	−7.03988	+	12.1934i	−0.00239847	+	0.00415427i
$206$	201.653	−	349.274i	0.0682032	−	0.118131i
$207$		0			0
$208$	8.14236	−	4.70100i	0.00271429	−	0.00156709i
$209$	−3746.84	−	6489.71i	−1.24007	−	2.14786i
$210$		0			0
$211$	−600.104	+	1039.41i	−0.195795	+	0.339128i	−0.947161	−	0.320758i	$-0.896062\pi$
$211$	−600.104	+	1039.41i	−0.195795	+	0.339128i	0.751366	+	0.659886i	$0.229396\pi$
$212$			928.695i			0.300863i
$213$		0			0
$214$	−351.261			−0.112204
$215$	−12.2551	−	21.2265i	−0.00388741	−	0.00673320i
$216$		0			0
$217$	−326.856	−	96.8573i	−0.102251	−	0.0303000i
$218$	−2423.18	+	1399.02i	−0.752836	+	0.434650i
$219$		0			0
$220$	82.3069	−	47.5199i	0.0252233	−	0.0145627i
$221$	59.2551	−	34.2109i	0.0180359	−	0.0104130i
$222$		0			0
$223$	1065.22	−	615.003i	0.319875	−	0.184680i	−0.331462	−	0.943469i	$-0.607542\pi$
$223$	1065.22	−	615.003i	0.319875	−	0.184680i	0.651337	+	0.758789i	$0.274208\pi$
$224$	−3110.43	−	921.713i	−0.927786	−	0.274931i
$225$		0			0
$226$	−1447.27	−	2506.75i	−0.425978	−	0.737816i
$227$	−1823.86			−0.533276			−0.266638	−	0.963797i	$-0.585913\pi$
$227$	−1823.86			−0.533276			−0.266638	+	0.963797i	$0.585913\pi$
$228$		0			0
$229$			5127.88i			1.47974i	0.672751	+	0.739869i	$0.265112\pi$
$229$			5127.88i			1.47974i	−0.672751	+	0.739869i	$0.734888\pi$
$230$	−50.1597	+	86.8792i	−0.0143802	+	0.0249072i
$231$		0			0
$232$	−1828.85	−	3167.67i	−0.517544	−	0.896412i
$233$	3036.86	−	1753.33i	0.853869	−	0.492981i	−0.00808557	−	0.999967i	$-0.502574\pi$
$233$	3036.86	−	1753.33i	0.853869	−	0.492981i	0.861954	+	0.506986i	$0.169240\pi$
$234$		0			0
$235$	44.8822	−	77.7382i	0.0124587	−	0.0215791i
$236$	−692.341	+	1199.17i	−0.190964	+	0.330760i
$237$		0			0
$238$	1348.01	+	399.456i	0.367137	+	0.108794i
$239$	−3414.05	−	1971.10i	−0.924002	−	0.533473i	−0.0390925	−	0.999236i	$-0.512447\pi$
$239$	−3414.05	−	1971.10i	−0.924002	−	0.533473i	−0.884910	+	0.465763i	$0.845780\pi$
$240$		0			0
$241$		−	1022.27i		−	0.273238i	−0.990624	−	0.136619i	$-0.956376\pi$
$241$		−	1022.27i		−	0.273238i	0.990624	−	0.136619i	$-0.0436236\pi$
$242$	−1799.10	−	1038.71i	−0.477894	−	0.275912i
$243$		0			0
$244$			371.673i			0.0975162i
$245$	7.47218	−	141.995i	0.00194849	−	0.0370276i
$246$		0			0
$247$	250.252			0.0644662
$248$	213.520	+	369.827i	0.0546715	+	0.0946938i
$249$		0			0
$250$	164.867	+	95.1861i	0.0417085	+	0.0240804i
$251$	646.886			0.162674			0.0813369	−	0.996687i	$-0.474081\pi$
$251$	646.886			0.162674			0.0813369	+	0.996687i	$0.474081\pi$
$252$		0			0
$253$	−6531.20			−1.62298
$254$	134.318	+	77.5485i	0.0331806	+	0.0191568i
$255$		0			0
$256$	2136.80	+	3701.04i	0.521679	+	0.903575i
$257$	−1189.28			−0.288660			−0.144330	−	0.989530i	$-0.546103\pi$
$257$	−1189.28			−0.288660			−0.144330	+	0.989530i	$0.546103\pi$
$258$		0			0
$259$	−1829.43	+	6173.61i	−0.438900	+	1.48112i
$260$			3.17386i			0.000757056i
$261$		0			0
$262$	−1261.52	−	728.336i	−0.297468	−	0.171743i
$263$			4767.82i			1.11786i	0.829216	+	0.558928i	$0.188787\pi$
$263$			4767.82i			1.11786i	−0.829216	+	0.558928i	$0.811213\pi$
$264$		0			0
$265$	72.1490	+	41.6553i	0.0167248	+	0.00965608i
$266$	3539.29	+	3730.43i	0.815819	+	0.859878i
$267$		0			0
$268$	595.154	−	1030.84i	0.135652	−	0.234957i
$269$	−2176.22	+	3769.33i	−0.493259	+	0.854350i	−0.999970	−	0.00776629i	$-0.997528\pi$
$269$	−2176.22	+	3769.33i	−0.493259	+	0.854350i	0.506711	+	0.862116i	$0.330861\pi$
$270$		0			0
$271$	−476.614	+	275.173i	−0.106835	+	0.0616811i	−0.552465	−	0.833536i	$-0.686313\pi$
$271$	−476.614	+	275.173i	−0.106835	+	0.0616811i	0.445631	+	0.895217i	$0.352979\pi$
$272$	−117.187	−	202.974i	−0.0261231	−	0.0452466i
$273$		0			0
$274$	623.960	−	1080.73i	0.137572	−	0.238282i
$275$			6192.74i			1.35795i
$276$		0			0
$277$	−1456.16			−0.315855			−0.157928	−	0.987451i	$-0.550481\pi$
$277$	−1456.16			−0.315855			−0.157928	+	0.987451i	$0.550481\pi$
$278$	2353.58	+	4076.52i	0.507764	+	0.879473i
$279$		0			0
$280$	−129.216	+	122.595i	−0.0275790	+	0.0261659i
$281$	−6158.20	+	3555.44i	−1.30736	+	0.754803i	−0.981654	−	0.190670i	$-0.938934\pi$
$281$	−6158.20	+	3555.44i	−1.30736	+	0.754803i	−0.325702	+	0.945472i	$0.605601\pi$
$282$		0			0
$283$	−2355.21	+	1359.78i	−0.494710	+	0.285621i	−0.726526	−	0.687139i	$-0.758866\pi$
$283$	−2355.21	+	1359.78i	−0.494710	+	0.285621i	0.231816	+	0.972760i	$0.425533\pi$
$284$	4133.35	−	2386.39i	0.863624	−	0.498614i
$285$		0			0
$286$	130.839	−	75.5397i	0.0270512	−	0.0156180i
$287$	611.651	−	146.775i	0.125800	−	0.0301877i
$288$		0			0
$289$	1603.69	+	2777.67i	0.326417	+	0.565371i
$290$	−120.140			−0.0243272
$291$		0			0
$292$			3794.50i			0.760467i
$293$	−2004.64	+	3472.14i	−0.399701	+	0.692302i	−0.993689	−	0.112172i	$-0.964219\pi$
$293$	−2004.64	+	3472.14i	−0.399701	+	0.692302i	0.593988	+	0.804474i	$0.297553\pi$
$294$		0			0
$295$	62.1078	+	107.574i	0.0122578	+	0.0212312i
$296$	6985.25	−	4032.93i	1.37165	−	0.791924i
$297$		0			0
$298$	−2166.94	+	3753.26i	−0.421234	+	0.729599i
$299$	109.055	−	188.889i	0.0210930	−	0.0365342i
$300$		0			0
$301$	−311.110	+	1049.88i	−0.0595750	+	0.201043i
$302$	943.758	+	544.879i	0.179825	+	0.103822i
$303$		0			0
$304$		−	857.218i		−	0.161726i
$305$	28.8748	+	16.6709i	0.00542087	+	0.00312974i
$306$		0			0
$307$		−	3968.59i		−	0.737783i	−0.929473	−	0.368891i	$-0.879737\pi$
$307$		−	3968.59i		−	0.737783i	0.929473	−	0.368891i	$-0.120263\pi$
$308$	−4070.94	−	1206.34i	−0.753128	−	0.223174i
$309$		0			0
$310$	14.0265			0.00256984
$311$	2387.59	+	4135.43i	0.435331	+	0.754016i	0.997323	−	0.0731274i	$-0.0232980\pi$
$311$	2387.59	+	4135.43i	0.435331	+	0.754016i	−0.561991	+	0.827143i	$0.689965\pi$
$312$		0			0
$313$	−8330.83	−	4809.81i	−1.50443	−	0.868583i	−0.999987	−	0.00513795i	$-0.998365\pi$
$313$	−8330.83	−	4809.81i	−1.50443	−	0.868583i	−0.504443	−	0.863445i	$-0.668302\pi$
$314$	3424.36			0.615438
$315$		0			0
$316$	486.694			0.0866414
$317$	−7775.68	−	4489.29i	−1.37768	−	0.795406i	−0.385803	−	0.922581i	$-0.626076\pi$
$317$	−7775.68	−	4489.29i	−1.37768	−	0.795406i	−0.991880	+	0.127175i	$0.959409\pi$
$318$		0			0
$319$	−3910.81	−	6773.73i	−0.686406	−	1.18889i
$320$	152.299			0.0266056
$321$		0			0
$322$	4358.07	−	1045.79i	0.754241	−	0.180992i
$323$		−	6238.30i		−	1.07464i
$324$		0			0
$325$	−179.100	−	103.404i	−0.0305683	−	0.0176486i
$326$			3868.33i			0.657199i
$327$		0			0
$328$	−682.381	−	393.973i	−0.114873	−	0.0663217i
$329$	−3899.54	+	935.754i	−0.653460	+	0.156808i
$330$		0			0
$331$	571.533	−	989.924i	0.0949072	−	0.164384i	−0.814663	−	0.579935i	$-0.803078\pi$
$331$	571.533	−	989.924i	0.0949072	−	0.164384i	0.909570	+	0.415551i	$0.136411\pi$
$332$	−1132.70	+	1961.89i	−0.187244	+	0.324316i
$333$		0			0
$334$	3091.20	−	1784.70i	0.506415	−	0.292379i
$335$	−53.3895	−	92.4733i	−0.00870740	−	0.0150817i
$336$		0			0
$337$	2865.89	−	4963.87i	0.463250	−	0.802372i	−0.535871	−	0.844300i	$-0.680017\pi$
$337$	2865.89	−	4963.87i	0.463250	−	0.802372i	0.999121	+	0.0419278i	$0.0133499\pi$
$338$		−	4033.38i		−	0.649073i
$339$		0			0
$340$	79.1183			0.0126200
$341$	456.591	+	790.838i	0.0725096	+	0.125590i
$342$		0			0
$343$	−4831.77	+	4124.03i	−0.760615	+	0.649204i
$344$	1187.90	−	685.835i	0.186184	−	0.107493i
$345$		0			0
$346$	684.589	−	395.248i	0.106369	−	0.0614123i
$347$	2758.89	−	1592.85i	0.426816	−	0.246422i	−0.271173	−	0.962530i	$-0.587412\pi$
$347$	2758.89	−	1592.85i	0.426816	−	0.246422i	0.697989	+	0.716108i	$0.254078\pi$
$348$		0			0
$349$	6403.54	−	3697.08i	0.982159	−	0.567050i	0.0792376	−	0.996856i	$-0.474751\pi$
$349$	6403.54	−	3697.08i	0.982159	−	0.567050i	0.902921	+	0.429806i	$0.141418\pi$
$350$	−991.591	−	4132.22i	−0.151436	−	0.631076i
$351$		0			0
$352$	4345.00	+	7525.77i	0.657925	+	1.13956i
$353$	11089.9			1.67211			0.836055	−	0.548646i	$-0.184857\pi$
$353$	11089.9			1.67211			0.836055	+	0.548646i	$0.184857\pi$
$354$		0			0
$355$		−	428.152i		−	0.0640111i
$356$	3488.21	−	6041.75i	0.519311	−	0.899472i
$357$		0			0
$358$	336.226	+	582.360i	0.0496371	+	0.0859740i
$359$	−8302.65	+	4793.54i	−1.22060	+	0.704716i	−0.965047	−	0.262077i	$-0.915592\pi$
$359$	−8302.65	+	4793.54i	−1.22060	+	0.704716i	−0.255558	+	0.966794i	$0.582259\pi$
$360$		0			0
$361$	7978.74	−	13819.6i	1.16325	−	2.01481i
$362$	3043.31	−	5271.16i	0.441858	−	0.765321i
$363$		0			0
$364$	102.863	−	97.5927i	0.0148118	−	0.0140529i
$365$	294.789	+	170.197i	0.0422739	+	0.0244068i
$366$		0			0
$367$			11623.3i			1.65322i	0.562772	+	0.826612i	$0.309735\pi$
$367$			11623.3i			1.65322i	−0.562772	+	0.826612i	$0.690265\pi$
$368$	−647.024	−	373.559i	−0.0916534	−	0.0529161i
$369$		0			0
$370$		−	264.930i		−	0.0372245i
$371$	−868.475	−	3619.17i	−0.121534	−	0.506463i
$372$		0			0
$373$	−3902.56			−0.541734			−0.270867	−	0.962617i	$-0.587310\pi$
$373$	−3902.56			−0.541734			−0.270867	+	0.962617i	$0.587310\pi$
$374$	−1883.06	−	3261.55i	−0.260349	−	0.450938i
$375$		0			0
$376$	4350.47	+	2511.74i	0.596697	+	0.344503i
$377$	261.204			0.0356835
$378$		0			0
$379$	−699.252			−0.0947709			−0.0473855	−	0.998877i	$-0.515089\pi$
$379$	−699.252			−0.0947709			−0.0473855	+	0.998877i	$0.515089\pi$
$380$	250.605	+	144.687i	0.0338310	+	0.0195323i
$381$		0			0
$382$	3682.85	+	6378.89i	0.493275	+	0.854378i
$383$	−10158.5			−1.35528			−0.677641	−	0.735393i	$-0.736998\pi$
$383$	−10158.5			−1.35528			−0.677641	+	0.735393i	$0.736998\pi$
$384$		0			0
$385$	−276.315	+	262.157i	−0.0365775	+	0.0347033i
$386$		−	4295.62i		−	0.566428i
$387$		0			0
$388$	−5023.89	−	2900.54i	−0.657343	−	0.379517i
$389$		−	4758.61i		−	0.620234i	−0.950698	−	0.310117i	$-0.899632\pi$
$389$		−	4758.61i		−	0.620234i	0.950698	−	0.310117i	$-0.100368\pi$
$390$		0			0
$391$	−4708.64	−	2718.53i	−0.609018	−	0.351617i
$392$	7946.50	+	418.166i	1.02387	+	0.0538790i
$393$		0			0
$394$	−309.797	+	536.584i	−0.0396125	+	0.0686109i
$395$	21.8299	−	37.8106i	0.00278072	−	0.00481635i
$396$		0			0
$397$	6232.29	−	3598.21i	0.787883	−	0.454885i	−0.0513336	−	0.998682i	$-0.516347\pi$
$397$	6232.29	−	3598.21i	0.787883	−	0.454885i	0.839217	+	0.543797i	$0.183014\pi$
$398$	4544.63	+	7871.53i	0.572366	+	0.991367i
$399$		0			0
$400$	−354.201	+	613.494i	−0.0442751	+	0.0766867i
$401$		−	6733.30i		−	0.838517i	−0.907867	−	0.419258i	$-0.862290\pi$
$401$		−	6733.30i		−	0.838517i	0.907867	−	0.419258i	$-0.137710\pi$
$402$		0			0
$403$	−30.4958			−0.00376948
$404$	−2776.17	−	4808.46i	−0.341880	−	0.592153i
$405$		0			0
$406$	3694.18	+	3893.69i	0.451575	+	0.475963i
$407$	14937.2	−	8624.01i	1.81919	−	1.05031i
$408$		0			0
$409$	9440.71	−	5450.60i	1.14135	−	0.658960i	0.194587	−	0.980885i	$-0.437663\pi$
$409$	9440.71	−	5450.60i	1.14135	−	0.658960i	0.946765	+	0.321925i	$0.104330\pi$
$410$	−22.4134	+	12.9404i	−0.00269980	+	0.00155873i
$411$		0			0
$412$	−878.089	+	506.965i	−0.105001	+	0.0606223i
$413$	1576.67	−	5320.66i	0.187852	−	0.633929i
$414$		0			0
$415$	101.611	+	175.996i	0.0120190	+	0.0208175i
$416$	−290.204			−0.0342029
$417$		0			0
$418$		−	13774.5i		−	1.61180i
$419$	−8088.59	+	14009.8i	−0.943087	+	1.63347i	−0.183549	+	0.983011i	$0.558759\pi$
$419$	−8088.59	+	14009.8i	−0.943087	+	1.63347i	−0.759538	+	0.650463i	$0.774575\pi$
$420$		0			0
$421$	2966.25	+	5137.69i	0.343387	+	0.594764i	0.985059	−	0.172215i	$-0.0550924\pi$
$421$	2966.25	+	5137.69i	0.343387	+	0.594764i	−0.641672	+	0.766979i	$0.721759\pi$
$422$	−1910.60	+	1103.08i	−0.220394	+	0.127245i
$423$		0			0
$424$	−2331.15	+	4037.68i	−0.267007	+	0.462469i
$425$	−2577.65	+	4464.63i	−0.294199	+	0.509567i
$426$		0			0
$427$	−347.573	−	1448.43i	−0.0393916	−	0.164155i
$428$	764.773	+	441.542i	0.0863708	+	0.0498662i
$429$		0			0
$430$		−	45.0537i		−	0.00505275i
$431$	−5735.59	−	3311.44i	−0.641006	−	0.370085i	0.143996	−	0.989578i	$-0.454005\pi$
$431$	−5735.59	−	3311.44i	−0.641006	−	0.370085i	−0.785002	+	0.619493i	$0.787338\pi$
$432$		0			0
$433$			9664.86i			1.07266i	0.844007	+	0.536332i	$0.180191\pi$
$433$			9664.86i			1.07266i	−0.844007	+	0.536332i	$0.819809\pi$
$434$	−431.299	−	454.592i	−0.0477028	−	0.0502790i
$435$		0			0
$436$	7034.40			0.772676
$437$	−9942.99	−	17221.8i	−1.08842	−	1.88519i
$438$		0			0
$439$	4883.74	+	2819.63i	0.530953	+	0.306546i	0.741404	−	0.671058i	$-0.234160\pi$
$439$	4883.74	+	2819.63i	0.530953	+	0.306546i	−0.210451	+	0.977604i	$0.567493\pi$
$440$	477.126			0.0516957
$441$		0			0
$442$	125.770			0.0135345
$443$	7383.09	+	4262.63i	0.791832	+	0.457164i	0.840607	−	0.541646i	$-0.182199\pi$
$443$	7383.09	+	4262.63i	0.791832	+	0.457164i	−0.0487754	+	0.998810i	$0.515532\pi$
$444$		0			0
$445$	−312.917	−	541.988i	−0.0333341	−	0.0577364i
$446$	2260.94			0.240042
$447$		0			0
$448$	−4683.04	−	4935.95i	−0.493868	−	0.520540i
$449$			12740.7i			1.33914i	0.742751	+	0.669568i	$0.233521\pi$
$449$			12740.7i			1.33914i	−0.742751	+	0.669568i	$0.766479\pi$
$450$		0			0
$451$	−1459.20	−	842.470i	−0.152353	−	0.0879609i
$452$			7277.00i			0.757260i
$453$		0			0
$454$	−2903.37	−	1676.26i	−0.300137	−	0.173284i
$455$	−2.96806	−	12.3687i	−0.000305812	−	0.00127440i
$456$		0			0
$457$	6550.30	−	11345.4i	0.670481	−	1.16131i	−0.307287	−	0.951617i	$-0.599421\pi$
$457$	6550.30	−	11345.4i	0.670481	−	1.16131i	0.977768	−	0.209691i	$-0.0672457\pi$
$458$	−4712.91	+	8163.01i	−0.480830	+	0.832821i
$459$		0			0
$460$	218.418	−	126.104i	0.0221387	−	0.0127818i
$461$	−5864.00	−	10156.8i	−0.592438	−	1.02613i	−0.993903	−	0.110258i	$-0.964832\pi$
$461$	−5864.00	−	10156.8i	−0.592438	−	1.02613i	0.401465	−	0.915874i	$-0.368501\pi$
$462$		0			0
$463$	−3831.27	+	6635.96i	−0.384567	+	0.666089i	−0.991709	−	0.128504i	$-0.958982\pi$
$463$	−3831.27	+	6635.96i	−0.384567	+	0.666089i	0.607142	+	0.794593i	$0.292316\pi$
$464$		−	894.733i		−	0.0895193i
$465$		0			0
$466$	6445.79			0.640763
$467$	7179.19	+	12434.7i	0.711378	+	1.23214i	0.964340	+	0.264666i	$0.0852619\pi$
$467$	7179.19	+	12434.7i	0.711378	+	1.23214i	−0.252962	+	0.967476i	$0.581405\pi$
$468$		0			0
$469$	−1355.35	+	4573.78i	−0.133442	+	0.450315i
$470$	142.895	−	82.5003i	0.0140239	−	0.00809671i
$471$		0			0
$472$	−6020.16	+	3475.74i	−0.587077	+	0.338949i
$473$	2540.21	−	1466.59i	0.246932	−	0.142566i
$474$		0			0
$475$	−16329.3	+	9427.73i	−1.57735	+	0.910681i
$476$	−2432.80	−	2564.19i	−0.234259	−	0.246910i
$477$		0			0
$478$	−3623.19	−	6275.54i	−0.346696	−	0.600495i
$479$	17463.5			1.66582			0.832908	−	0.553412i	$-0.186675\pi$
$479$	17463.5			1.66582			0.832908	+	0.553412i	$0.186675\pi$
$480$		0			0
$481$			575.999i			0.0546015i
$482$	939.547	−	1627.34i	0.0887867	−	0.153783i
$483$		0			0
$484$	2611.36	+	4523.00i	0.245244	+	0.424775i
$485$	−450.678	+	260.199i	−0.0421943	+	0.0243609i
$486$		0			0
$487$	−1345.48	+	2330.44i	−0.125194	+	0.216842i	−0.921809	−	0.387645i	$-0.873289\pi$
$487$	−1345.48	+	2330.44i	−0.125194	+	0.216842i	0.796615	+	0.604487i	$0.206622\pi$
$488$	−932.952	+	1615.92i	−0.0865425	+	0.149896i
$489$		0			0
$490$	142.400	−	219.173i	0.0131285	−	0.0202066i
$491$	5823.37	+	3362.13i	0.535245	+	0.309024i	0.743149	−	0.669125i	$-0.233331\pi$
$491$	5823.37	+	3362.13i	0.535245	+	0.309024i	−0.207905	+	0.978149i	$0.566664\pi$
$492$		0			0
$493$		−	6511.31i		−	0.594837i
$494$	398.373	+	230.001i	0.0362827	+	0.0209478i
$495$		0			0
$496$			104.461i			0.00945651i
$497$	−13876.2	+	13165.2i	−1.25238	+	1.18821i
$498$		0			0
$499$	202.746			0.0181887			0.00909435	−	0.999959i	$-0.497105\pi$
$499$	202.746			0.0181887			0.00909435	+	0.999959i	$0.497105\pi$
$500$	−239.302	−	414.483i	−0.0214038	−	0.0370725i
$501$		0			0
$502$	1029.77	+	594.538i	0.0915556	+	0.0528596i
$503$	7820.60			0.693247			0.346624	−	0.938004i	$-0.387328\pi$
$503$	7820.60			0.693247			0.346624	+	0.938004i	$0.387328\pi$
$504$		0			0
$505$	−498.083			−0.0438899
$506$	−10396.9	−	6002.68i	−0.913439	−	0.527374i
$507$		0			0
$508$	−194.960	−	337.681i	−0.0170275	−	0.0294925i
$509$	−9845.24			−0.857333			−0.428667	−	0.903463i	$-0.641016\pi$
$509$	−9845.24			−0.857333			−0.428667	+	0.903463i	$0.641016\pi$
$510$		0			0
$511$	−3548.45	−	14787.3i	−0.307190	−	1.28014i
$512$			2047.34i			0.176719i
$513$		0			0
$514$	−1893.21	−	1093.04i	−0.162463	−	0.0937978i
$515$			90.9567i			0.00778258i
$516$		0			0
$517$	9303.02	+	5371.10i	0.791386	+	0.456907i
$518$	−8586.26	+	8146.31i	−0.728298	+	0.690981i
$519$		0			0
$520$	−7.96684	+	13.7990i	−0.000671863	+	0.00116370i
$521$	−3985.06	+	6902.32i	−0.335103	+	0.580415i	−0.983505	−	0.180883i	$-0.942104\pi$
$521$	−3985.06	+	6902.32i	−0.335103	+	0.580415i	0.648402	+	0.761298i	$0.275438\pi$
$522$		0			0
$523$	−4651.74	+	2685.68i	−0.388922	+	0.224544i	−0.681693	−	0.731638i	$-0.738756\pi$
$523$	−4651.74	+	2685.68i	−0.388922	+	0.224544i	0.292771	+	0.956183i	$0.405423\pi$
$524$	1831.07	+	3171.50i	0.152654	+	0.264404i
$525$		0			0
$526$	−4381.99	+	7589.83i	−0.363239	+	0.629149i
$527$			760.201i			0.0628366i
$528$		0			0
$529$	−5164.88			−0.424499
$530$	76.5687	+	132.621i	0.00627535	+	0.0108692i
$531$		0			0
$532$	−3016.60	−	12571.0i	−0.245838	−	1.02447i
$533$	48.7302	−	28.1344i	0.00396011	−	0.00228637i
$534$		0			0
$535$	68.6056	−	39.6094i	0.00554407	−	0.00320087i
$536$	5175.09	−	2987.84i	0.417033	−	0.240774i
$537$		0			0
$538$	−6928.60	+	4000.23i	−0.555229	+	0.320562i
$539$	16992.8	+	894.205i	1.35794	+	0.0714585i
$540$		0			0
$541$	−2172.50	−	3762.88i	−0.172649	−	0.299037i	0.766696	−	0.642010i	$-0.221899\pi$
$541$	−2172.50	−	3762.88i	−0.172649	−	0.299037i	−0.939345	+	0.342973i	$0.888566\pi$
$542$	−1011.62			−0.0801712
$543$		0			0
$544$			7234.22i			0.570155i
$545$	315.518	−	546.493i	0.0247987	−	0.0429526i
$546$		0			0
$547$	4859.25	+	8416.46i	0.379829	+	0.657883i	0.991037	−	0.133587i	$-0.0426495\pi$
$547$	4859.25	+	8416.46i	0.379829	+	0.657883i	−0.611208	+	0.791470i	$0.709316\pi$
$548$	−2717.00	+	1568.66i	−0.211797	+	0.122281i
$549$		0			0
$550$	−5691.60	+	9858.15i	−0.441256	+	0.764278i
$551$	11907.5	−	20624.4i	0.920648	−	1.59461i
$552$		0			0
$553$	−1896.67	+	455.135i	−0.145849	+	0.0349988i
$554$	−2318.04	−	1338.32i	−0.177769	−	0.102635i
$555$		0			0
$556$		−	11834.0i		−	0.902651i
$557$	−13997.2	−	8081.28i	−1.06478	−	0.614749i	−0.138026	−	0.990429i	$-0.544076\pi$
$557$	−13997.2	−	8081.28i	−1.06478	−	0.614749i	−0.926749	+	0.375680i	$0.877409\pi$
$558$		0			0
$559$			97.9537i			0.00741145i
$560$	−42.3679	+	10.1668i	−0.00319709	+	0.000767192i
$561$		0			0
$562$	−13070.9			−0.981070
$563$	−7136.84	−	12361.4i	−0.534249	−	0.925346i	−0.999199	−	0.0400092i	$-0.987261\pi$
$563$	−7136.84	−	12361.4i	−0.534249	−	0.925346i	0.464951	−	0.885337i	$-0.346072\pi$
$564$		0			0
$565$	565.340	+	326.399i	0.0420956	+	0.0243039i
$566$	−4998.98			−0.371242
$567$		0			0
$568$	23960.7			1.77001
$569$	−10570.7	−	6103.00i	−0.778817	−	0.449650i	0.0571938	−	0.998363i	$-0.481785\pi$
$569$	−10570.7	−	6103.00i	−0.778817	−	0.449650i	−0.836011	+	0.548713i	$0.815118\pi$
$570$		0			0
$571$	9366.03	+	16222.4i	0.686438	+	1.18895i	0.972982	+	0.230879i	$0.0741602\pi$
$571$	9366.03	+	16222.4i	0.686438	+	1.18895i	−0.286544	+	0.958067i	$0.592506\pi$
$572$	−379.820			−0.0277641
$573$		0			0
$574$	1108.58	+	328.505i	0.0806117	+	0.0238877i
$575$			16433.7i			1.19188i
$576$		0			0
$577$	−14902.3	−	8603.86i	−1.07520	−	0.620768i	−0.145604	−	0.989343i	$-0.546513\pi$
$577$	−14902.3	−	8603.86i	−1.07520	−	0.620768i	−0.929598	+	0.368574i	$0.879846\pi$
$578$			5895.64i			0.424267i
$579$		0			0
$580$	261.573	+	151.019i	0.0187262	+	0.0108116i
$581$	2579.50	−	8704.84i	0.184193	−	0.621579i
$582$		0			0
$583$	−4984.94	+	8634.16i	−0.354125	+	0.613363i
$584$	−9524.72	+	16497.3i	−0.674890	+	1.16894i
$585$		0			0
$586$	−6382.32	+	3684.83i	−0.449917	+	0.259759i
$587$	8021.17	+	13893.1i	0.564002	+	0.976880i	0.997142	+	0.0755529i	$0.0240722\pi$
$587$	8021.17	+	13893.1i	0.564002	+	0.976880i	−0.433140	+	0.901327i	$0.642594\pi$
$588$		0			0
$589$	−1390.21	+	2407.92i	−0.0972541	+	0.168449i
$590$			228.327i			0.0159324i
$591$		0			0
$592$	1973.04			0.136979
$593$	7608.23	+	13177.8i	0.526868	+	0.912562i	0.999510	+	0.0313075i	$0.00996713\pi$
$593$	7608.23	+	13177.8i	0.526868	+	0.912562i	−0.472642	+	0.881255i	$0.656700\pi$
$594$		0			0
$595$	−308.328	+	73.9880i	−0.0212440	+	0.00509783i
$596$	9435.85	−	5447.79i	0.648502	−	0.374413i
$597$		0			0
$598$	347.207	−	200.460i	0.0237430	−	0.0137080i
$599$	21676.6	−	12515.0i	1.47860	−	0.853670i	0.478892	−	0.877874i	$-0.341039\pi$
$599$	21676.6	−	12515.0i	1.47860	−	0.853670i	0.999707	+	0.0242042i	$0.00770519\pi$
$600$		0			0
$601$	−4104.86	+	2369.94i	−0.278604	+	0.160852i	−0.632791	−	0.774323i	$-0.718091\pi$
$601$	−4104.86	+	2369.94i	−0.278604	+	0.160852i	0.354187	+	0.935174i	$0.384757\pi$
$602$	−1460.17	+	1385.35i	−0.0988571	+	0.0937918i
$603$		0			0
$604$	−1369.85	−	2372.65i	−0.0922820	−	0.159837i
$605$	468.514			0.0314840
$606$		0			0
$607$			10613.6i			0.709711i	0.934921	+	0.354855i	$0.115470\pi$
$607$			10613.6i			0.709711i	−0.934921	+	0.354855i	$0.884530\pi$
$608$	−13229.5	+	22914.2i	−0.882447	+	1.52844i
$609$		0			0
$610$	30.6436	+	53.0763i	0.00203397	+	0.00352294i
$611$	−310.675	+	179.368i	−0.0205705	+	0.0118764i
$612$		0			0
$613$	6179.57	−	10703.3i	0.407163	−	0.705226i	−0.587408	−	0.809291i	$-0.699852\pi$
$613$	6179.57	−	10703.3i	0.407163	−	0.705226i	0.994571	+	0.104065i	$0.0331849\pi$
$614$	3647.44	−	6317.54i	0.239737	−	0.415237i
$615$		0			0
$616$	−14671.1	−	15463.4i	−0.959603	−	1.01143i
$617$	13982.2	+	8072.63i	0.912322	+	0.526729i	0.881177	−	0.472786i	$-0.156752\pi$
$617$	13982.2	+	8072.63i	0.912322	+	0.526729i	0.0311444	+	0.999515i	$0.490085\pi$
$618$		0			0
$619$		−	6724.76i		−	0.436657i	−0.975875	−	0.218329i	$-0.929940\pi$
$619$		−	6724.76i		−	0.436657i	0.975875	−	0.218329i	$-0.0700605\pi$
$620$	−30.5388	−	17.6316i	−0.00197817	−	0.00114210i
$621$		0			0
$622$			8777.52i			0.565830i
$623$	−7943.72	+	26807.0i	−0.510848	+	1.72392i
$624$		0			0
$625$	15560.6			0.995877
$626$	−8841.16	−	15313.3i	−0.564479	−	0.977707i
$627$		0			0
$628$	−7455.59	−	4304.49i	−0.473743	−	0.273516i
$629$	14358.6			0.910196
$630$		0			0
$631$	15753.1			0.993855			0.496928	−	0.867792i	$-0.334461\pi$
$631$	15753.1			0.993855			0.496928	+	0.867792i	$0.334461\pi$
$632$	2115.99	+	1221.67i	0.133180	+	0.0768915i
$633$		0			0
$634$	−8252.00	−	14292.9i	−0.516922	−	0.895336i
$635$	−34.9786			−0.00218596
$636$		0			0
$637$	−309.599	+	476.517i	−0.0192571	+	0.0296394i
$638$		−	14377.3i		−	0.892170i
$639$		0			0
$640$	−260.653	−	150.488i	−0.0160987	−	0.00929462i
$641$		−	13811.5i		−	0.851049i	−0.904947	−	0.425525i	$-0.860090\pi$
$641$		−	13811.5i		−	0.851049i	0.904947	−	0.425525i	$-0.139910\pi$
$642$		0			0
$643$	−12084.2	−	6976.82i	−0.741142	−	0.427899i	0.0813422	−	0.996686i	$-0.474079\pi$
$643$	−12084.2	−	6976.82i	−0.741142	−	0.427899i	−0.822484	+	0.568788i	$0.807413\pi$
$644$	−10803.1	−	3201.27i	−0.661026	−	0.195882i
$645$		0			0
$646$	5733.47	−	9930.67i	0.349196	−	0.604825i
$647$	7274.72	−	12600.2i	0.442038	−	0.765633i	−0.555802	−	0.831314i	$-0.687589\pi$
$647$	7274.72	−	12600.2i	0.442038	−	0.765633i	0.997841	+	0.0656817i	$0.0209222\pi$
$648$		0			0
$649$	−12873.5	+	7432.52i	−0.778627	+	0.449541i
$650$	−190.072	−	329.214i	−0.0114696	−	0.0198659i
$651$		0			0
$652$	4862.57	−	8422.22i	0.292075	−	0.505889i
$653$			1830.45i			0.109695i	0.998495	+	0.0548475i	$0.0174673\pi$
$653$			1830.45i			0.109695i	−0.998495	+	0.0548475i	$0.982533\pi$
$654$		0			0
$655$	328.520			0.0195974
$656$	−96.3720	−	166.921i	−0.00573582	−	0.00993473i
$657$		0			0
$658$	−7067.65	−	2094.36i	−0.418732	−	0.124083i
$659$	−8381.93	+	4839.31i	−0.495468	+	0.286059i	−0.726840	−	0.686807i	$-0.759012\pi$
$659$	−8381.93	+	4839.31i	−0.495468	+	0.286059i	0.231372	+	0.972865i	$0.425679\pi$
$660$		0			0
$661$	10341.4	−	5970.60i	0.608522	−	0.351330i	−0.163865	−	0.986483i	$-0.552396\pi$
$661$	10341.4	−	5970.60i	0.608522	−	0.351330i	0.772387	+	0.635153i	$0.219063\pi$
$662$	1819.63	−	1050.56i	0.106831	−	0.0616788i
$663$		0			0
$664$	−9849.25	+	5686.47i	−0.575640	+	0.332346i
$665$	−1111.92	−	329.497i	−0.0648400	−	0.0192140i
$666$		0			0
$667$	−10378.1	−	17975.5i	−0.602464	−	1.04350i
$668$	−8973.64			−0.519761
$669$		0			0
$670$		−	196.276i		−	0.0113176i
$671$	−1995.02	+	3455.48i	−0.114779	+	0.198804i
$672$		0			0
$673$	215.515	+	373.284i	0.0123440	+	0.0213804i	0.872131	−	0.489272i	$-0.162737\pi$
$673$	215.515	+	373.284i	0.0123440	+	0.0213804i	−0.859787	+	0.510652i	$0.829404\pi$
$674$	9124.36	−	5267.95i	0.521450	−	0.301059i
$675$		0			0
$676$	−5070.04	+	8781.57i	−0.288464	+	0.499634i
$677$	7902.98	−	13688.4i	0.448650	−	0.777085i	−0.549648	−	0.835396i	$-0.685238\pi$
$677$	7902.98	−	13688.4i	0.448650	−	0.777085i	0.998298	+	0.0583110i	$0.0185715\pi$
$678$		0			0
$679$	22290.8	+	6605.43i	1.25986	+	0.373333i
$680$	343.982	+	198.598i	0.0193987	+	0.0111998i
$681$		0			0
$682$			1678.57i			0.0942458i
$683$	−27402.6	−	15820.9i	−1.53518	−	0.886338i	−0.999111	−	0.0421653i	$-0.986574\pi$
$683$	−27402.6	−	15820.9i	−1.53518	−	0.886338i	−0.536072	−	0.844173i	$-0.680092\pi$
$684$		0			0
$685$			281.440i			0.0156982i
$686$	−11481.9	+	2124.23i	−0.639041	+	0.118227i
$687$		0			0
$688$	335.533			0.0185931
$689$	−166.472	−	288.339i	−0.00920478	−	0.0159431i
$690$		0			0
$691$	13298.8	+	7678.08i	0.732144	+	0.422703i	0.819206	−	0.573499i	$-0.194415\pi$
$691$	13298.8	+	7678.08i	0.732144	+	0.422703i	−0.0870621	+	0.996203i	$0.527748\pi$
$692$	−1987.34			−0.109172
$693$		0			0
$694$	5855.79			0.320292
$695$	−919.367	−	530.797i	−0.0501778	−	0.0289702i
$696$		0			0
$697$	−701.336	−	1214.75i	−0.0381133	−	0.0660142i
$698$	13591.6			0.737034
$699$		0			0
$700$	−3035.38	+	10243.2i	−0.163895	+	0.553082i
$701$		−	7678.12i		−	0.413693i	−0.978373	−	0.206846i	$-0.933680\pi$
$701$		−	7678.12i		−	0.413693i	0.978373	−	0.206846i	$-0.0663200\pi$
$702$		0			0
$703$	45480.4	+	26258.1i	2.44001	+	1.40874i
$704$			18225.9i			0.975729i
$705$		0			0
$706$	17653.8	+	10192.4i	0.941092	+	0.543339i
$707$	15315.5	+	16142.6i	0.814708	+	0.858708i
$708$		0			0
$709$	8017.46	−	13886.7i	0.424686	−	0.735577i	−0.571705	−	0.820459i	$-0.693718\pi$
$709$	8017.46	−	13886.7i	0.424686	−	0.735577i	0.996391	+	0.0848818i	$0.0270513\pi$
$710$	393.505	−	681.570i	0.0207999	−	0.0360266i
$711$		0			0
$712$	30331.3	−	17511.8i	1.59651	−	0.921744i
$713$	1211.66	+	2098.65i	0.0636422	+	0.110231i
$714$		0			0
$715$	−17.0363	+	29.5077i	−0.000891077	+	0.00154339i
$716$		−	1690.57i		−	0.0882398i
$717$		0			0
$718$	−17622.5			−0.915969
$719$	−9585.35	−	16602.3i	−0.497181	−	0.861143i	0.502814	−	0.864395i	$-0.332298\pi$
$719$	−9585.35	−	16602.3i	−0.497181	−	0.861143i	−0.999995	+	0.00325214i	$0.998965\pi$
$720$		0			0
$721$	2947.86	−	2796.82i	0.152266	−	0.144464i
$722$	25402.5	−	14666.2i	1.30940	−	0.755980i
$723$		0			0
$724$	−13251.9	+	7651.01i	−0.680254	+	0.392745i
$725$	−17043.9	+	9840.32i	−0.873098	+	0.504083i
$726$		0			0
$727$	13432.8	−	7755.44i	0.685276	−	0.395644i	−0.116564	−	0.993183i	$-0.537188\pi$
$727$	13432.8	−	7755.44i	0.685276	−	0.395644i	0.801840	+	0.597539i	$0.203855\pi$
$728$	692.189	−	166.101i	0.0352393	−	0.00845622i
$729$		0			0
$730$	312.847	+	541.868i	0.0158616	+	0.0274732i
$731$	2441.80			0.123547
$732$		0			0
$733$			20363.2i			1.02610i	0.858359	+	0.513050i	$0.171485\pi$
$733$			20363.2i			1.02610i	−0.858359	+	0.513050i	$0.828515\pi$
$734$	−10682.7	+	18503.0i	−0.537203	+	0.930463i
$735$		0			0
$736$	11530.3	+	19971.1i	0.577465	+	1.00020i
$737$	11066.4	−	6389.18i	0.553101	−	0.319333i
$738$		0			0
$739$	1493.90	−	2587.52i	0.0743629	−	0.128800i	−0.826446	−	0.563016i	$-0.809641\pi$
$739$	1493.90	−	2587.52i	0.0743629	−	0.128800i	0.900809	+	0.434215i	$0.142974\pi$
$740$	−333.023	+	576.812i	−0.0165435	+	0.0286541i
$741$		0			0
$742$	1943.78	−	6559.50i	0.0961703	−	0.324538i
$743$	−4165.48	−	2404.94i	−0.205675	−	0.118747i	0.393625	−	0.919271i	$-0.371221\pi$
$743$	−4165.48	−	2404.94i	−0.205675	−	0.118747i	−0.599300	+	0.800525i	$0.704554\pi$
$744$		0			0
$745$		−	977.410i		−	0.0480665i
$746$	−6212.43	−	3586.75i	−0.304897	−	0.176033i
$747$		0			0
$748$			9468.18i			0.462822i
$749$	−3393.27	−	1005.53i	−0.165537	−	0.0490536i
$750$		0			0
$751$	−2250.12			−0.109331			−0.0546657	−	0.998505i	$-0.517409\pi$
$751$	−2250.12			−0.109331			−0.0546657	+	0.998505i	$0.517409\pi$
$752$	614.412	+	1064.19i	0.0297943	+	0.0516052i
$753$		0			0
$754$	415.807	+	240.066i	0.0200833	+	0.0115951i
$755$	−245.770			−0.0118470
$756$		0			0
$757$	−16948.7			−0.813754			−0.406877	−	0.913483i	$-0.633382\pi$
$757$	−16948.7			−0.813754			−0.406877	+	0.913483i	$0.633382\pi$
$758$	−1113.13	−	642.666i	−0.0533387	−	0.0307951i
$759$		0			0
$760$	726.369	+	1258.11i	0.0346686	+	0.0600478i
$761$	24129.2			1.14938			0.574692	−	0.818369i	$-0.305122\pi$
$761$	24129.2			1.14938			0.574692	+	0.818369i	$0.305122\pi$
$762$		0			0
$763$	−27413.4	+	6578.26i	−1.30070	+	0.312122i
$764$		−	18517.7i		−	0.876893i
$765$		0			0
$766$	−16171.1	−	9336.40i	−0.762776	−	0.440389i
$767$		−	496.419i		−	0.0233698i
$768$		0			0
$769$	−33734.0	−	19476.3i	−1.58190	−	0.913308i	−0.994583	−	0.103949i	$-0.966852\pi$
$769$	−33734.0	−	19476.3i	−1.58190	−	0.913308i	−0.587314	−	0.809359i	$-0.699815\pi$
$770$	−680.805	+	163.370i	−0.0318630	+	0.00764602i
$771$		0			0
$772$	−5399.69	+	9352.53i	−0.251734	+	0.436017i
$773$	9505.37	−	16463.8i	0.442283	−	0.766056i	−0.555576	−	0.831466i	$-0.687502\pi$
$773$	9505.37	−	16463.8i	0.442283	−	0.766056i	0.997858	+	0.0654098i	$0.0208355\pi$
$774$		0			0
$775$	1989.89	−	1148.86i	0.0922310	−	0.0532496i
$776$	−14561.5	−	25221.3i	−0.673619	−	1.16674i
$777$		0			0
$778$	4373.53	−	7575.17i	0.201540	−	0.349078i
$779$		−	5130.25i		−	0.235957i
$780$		0			0
$781$	51237.5			2.34753
$782$	−4997.08	−	8655.20i	−0.228511	−	0.395792i
$783$		0			0
$784$	1632.27	+	1060.51i	0.0743563	+	0.0483102i
$785$	−668.819	+	386.143i	−0.0304091	+	0.0175567i
$786$		0			0
$787$	−1717.77	+	991.754i	−0.0778041	+	0.0449202i	−0.538397	−	0.842691i	$-0.680970\pi$
$787$	−1717.77	+	991.754i	−0.0778041	+	0.0449202i	0.460593	+	0.887611i	$0.347637\pi$
$788$	1348.99	−	778.842i	0.0609847	−	0.0352095i
$789$		0			0
$790$	69.5016	−	40.1268i	0.00313007	−	0.00180715i
$791$	−6805.13	−	28358.8i	−0.305895	−	1.27474i
$792$		0			0
$793$	−66.6239	−	115.396i	−0.00298346	−	0.00516751i
$794$	13228.1			0.591245
$795$		0			0
$796$		−	22850.8i		−	1.01749i
$797$	−1555.18	+	2693.65i	−0.0691182	+	0.119716i	−0.898513	−	0.438946i	$-0.855352\pi$
$797$	−1555.18	+	2693.65i	−0.0691182	+	0.119716i	0.829395	+	0.558662i	$0.188685\pi$
$798$		0			0
$799$	4471.31	+	7744.54i	0.197977	+	0.342906i
$800$	18936.2	−	10932.8i	0.836870	−	0.483167i
$801$		0			0
$802$	6188.42	−	10718.7i	0.272470	−	0.471932i
$803$	−20367.6	+	35277.8i	−0.895091	+	1.55034i
$804$		0			0
$805$	−733.258	+	695.687i	−0.0321043	+	0.0304593i
$806$	−48.5458	−	28.0279i	−0.00212153	−	0.00122487i
$807$		0			0
$808$		−	27874.2i		−	1.21363i
$809$	1302.95	+	752.256i	0.0566244	+	0.0326921i	0.528045	−	0.849216i	$-0.322925\pi$
$809$	1302.95	+	752.256i	0.0566244	+	0.0326921i	−0.471421	+	0.881909i	$0.656259\pi$
$810$		0			0
$811$			28460.1i			1.23227i	0.787642	+	0.616133i	$0.211302\pi$
$811$			28460.1i			1.23227i	−0.787642	+	0.616133i	$0.788698\pi$
$812$	−3148.61	−	13121.1i	−0.136077	−	0.567070i
$813$		0			0
$814$	31704.5			1.36516
$815$	−436.207	−	755.532i	−0.0187480	−	0.0324726i
$816$		0			0
$817$	7734.33	+	4465.42i	0.331200	+	0.191218i
$818$	20038.1			0.856497
$819$		0			0
$820$	65.0653			0.00277095
$821$	−19584.5	−	11307.1i	−0.832527	−	0.480660i	0.0221902	−	0.999754i	$-0.492936\pi$
$821$	−19584.5	−	11307.1i	−0.832527	−	0.480660i	−0.854717	+	0.519094i	$0.826269\pi$
$822$		0			0
$823$	−13034.6	−	22576.6i	−0.552076	−	0.956224i	−0.998125	−	0.0612152i	$-0.980502\pi$
$823$	−13034.6	−	22576.6i	−0.552076	−	0.956224i	0.446048	−	0.895009i	$-0.352831\pi$
$824$	−5090.21			−0.215201
$825$		0			0
$826$	7399.98	−	7020.81i	0.311717	−	0.295745i
$827$			37100.7i			1.56000i	0.625782	+	0.779998i	$0.284780\pi$
$827$			37100.7i			1.56000i	−0.625782	+	0.779998i	$0.715220\pi$
$828$		0			0
$829$	6606.87	+	3814.48i	0.276799	+	0.159810i	0.631973	−	0.774990i	$-0.282245\pi$
$829$	6606.87	+	3814.48i	0.276799	+	0.159810i	−0.355175	+	0.934800i	$0.615579\pi$
$830$			373.553i			0.0156220i
$831$		0			0
$832$	−527.110	−	304.327i	−0.0219642	−	0.0126811i
$833$	11878.6	+	7717.70i	0.494082	+	0.321011i
$834$		0			0
$835$	−402.499	+	697.149i	−0.0166815	+	0.0288932i
$836$	−17314.9	+	29990.2i	−0.716324	+	1.24071i
$837$		0			0
$838$	−25752.2	+	14868.1i	−1.06157	+	0.612898i
$839$	−10297.8	−	17836.3i	−0.423741	−	0.733942i	0.572561	−	0.819862i	$-0.305950\pi$
$839$	−10297.8	−	17836.3i	−0.423741	−	0.733942i	−0.996302	+	0.0859208i	$0.972617\pi$
$840$		0			0
$841$	234.138	−	405.540i	0.00960017	−	0.0166280i
$842$			10904.8i			0.446324i
$843$		0			0
$844$	5546.39			0.226202
$845$	454.818	+	787.768i	0.0185162	+	0.0320711i
$846$		0			0
$847$	−14406.3	−	15184.3i	−0.584423	−	0.615985i
$848$	−987.681	+	570.238i	−0.0399966	+	0.0230920i
$849$		0			0
$850$	−8206.66	+	4738.12i	−0.331160	+	0.191195i
$851$	39639.0	−	22885.6i	1.59672	−	0.921865i
$852$		0			0
$853$	−25770.4	+	14878.6i	−1.03442	+	0.597224i	−0.918248	−	0.396005i	$-0.870396\pi$
$853$	−25770.4	+	14878.6i	−1.03442	+	0.597224i	−0.116174	+	0.993229i	$0.537063\pi$
$854$	777.920	−	2625.18i	0.0311708	−	0.105189i
$855$		0			0
$856$	2216.66	+	3839.38i	0.0885094	+	0.153303i
$857$	−11724.5			−0.467330			−0.233665	−	0.972317i	$-0.575072\pi$
$857$	−11724.5			−0.467330			−0.233665	+	0.972317i	$0.575072\pi$
$858$		0			0
$859$		−	28577.9i		−	1.13512i	−0.823333	−	0.567558i	$-0.807888\pi$
$859$		−	28577.9i		−	1.13512i	0.823333	−	0.567558i	$-0.192112\pi$
$860$	−56.6334	+	98.0920i	−0.00224556	+	0.00388943i
$861$		0			0
$862$	−6086.94	−	10542.9i	−0.240513	−	0.416580i
$863$	−20733.1	+	11970.2i	−0.817800	+	0.472157i	−0.849657	−	0.527335i	$-0.823191\pi$
$863$	−20733.1	+	11970.2i	−0.817800	+	0.472157i	0.0318572	+	0.999492i	$0.489858\pi$
$864$		0			0
$865$	−89.1391	+	154.394i	−0.00350384	+	0.00606883i
$866$	−8882.75	+	15385.4i	−0.348554	+	0.603714i
$867$		0			0
$868$	367.603	+	1531.90i	0.0143747	+	0.0599033i
$869$	4524.84	+	2612.42i	0.176634	+	0.101979i
$870$		0			0
$871$			426.735i			0.0166009i
$872$	30583.4	+	17657.3i	1.18771	+	0.685725i
$873$		0			0
$874$		−	36553.5i		−	1.41469i
$875$	1320.18	+	1391.48i	0.0510059	+	0.0537605i
$876$		0			0
$877$	−948.432			−0.0365180			−0.0182590	−	0.999833i	$-0.505812\pi$
$877$	−948.432			−0.0365180			−0.0182590	+	0.999833i	$0.505812\pi$
$878$	5182.91	+	8977.07i	0.199220	+	0.345058i
$879$		0			0
$880$	101.076	+	58.3563i	0.00387190	+	0.00223545i
$881$	39460.9			1.50905			0.754524	−	0.656273i	$-0.227868\pi$
$881$	39460.9			1.50905			0.754524	+	0.656273i	$0.227868\pi$
$882$		0			0
$883$	−34371.8			−1.30997			−0.654984	−	0.755643i	$-0.727325\pi$
$883$	−34371.8			−1.30997			−0.654984	+	0.755643i	$0.727325\pi$
$884$	−273.829	−	158.095i	−0.0104184	−	0.00601507i
$885$		0			0
$886$	7835.37	+	13571.3i	0.297104	+	0.514600i
$887$	−26214.7			−0.992336			−0.496168	−	0.868226i	$-0.665260\pi$
$887$	−26214.7			−0.992336			−0.496168	+	0.868226i	$0.665260\pi$
$888$		0			0
$889$	1075.55	+	1133.64i	0.0405770	+	0.0427684i
$890$		−	1150.38i		−	0.0433267i
$891$		0			0
$892$	−4922.58	−	2842.05i	−0.184776	−	0.106680i
$893$			32707.5i			1.22566i
$894$		0			0
$895$	−131.338	−	75.8281i	−0.00490520	−	0.00283202i
$896$	3137.54	+	13075.0i	0.116984	+	0.487504i
$897$		0			0
$898$	−11709.7	+	20281.8i	−0.435142	+	0.753688i
$899$	−1451.05	+	2513.30i	−0.0538324	+	0.0932404i
$900$		0			0
$901$	−7187.73	+	4149.84i	−0.265769	+	0.153442i
$902$	−1548.59	−	2682.24i	−0.0571645	−	0.0990118i
$903$		0			0
$904$	−18266.3	+	31638.1i	−0.672044	+	1.16401i
$905$			1372.70i			0.0504199i
$906$		0			0
$907$	−25864.7			−0.946885			−0.473443	−	0.880825i	$-0.656989\pi$
$907$	−25864.7			−0.946885			−0.473443	+	0.880825i	$0.656989\pi$
$908$	4214.20	+	7299.20i	0.154023	+	0.266776i
$909$		0			0
$910$	6.64296	−	22.4174i	0.000241991	−	0.000816627i
$911$	−21902.9	+	12645.6i	−0.796570	+	0.459900i	−0.842270	−	0.539055i	$-0.818781\pi$
$911$	−21902.9	+	12645.6i	−0.796570	+	0.459900i	0.0457002	+	0.998955i	$0.485448\pi$
$912$		0			0
$913$	−21061.6	+	12159.9i	−0.763458	+	0.440783i
$914$	20854.7	−	12040.4i	0.754717	−	0.435736i
$915$		0			0
$916$	20522.1	−	11848.5i	0.740252	−	0.427385i
$917$	−10101.6	−	10647.2i	−0.363778	−	0.383424i
$918$		0			0
$919$	−2197.32	−	3805.87i	−0.0788715	−	0.136609i	0.823892	−	0.566747i	$-0.191798\pi$
$919$	−2197.32	−	3805.87i	−0.0788715	−	0.136609i	−0.902763	+	0.430138i	$0.858465\pi$
$920$	1266.15			0.0453737
$921$		0			0
$922$		−	21557.9i		−	0.770033i
$923$	−855.540	+	1481.84i	−0.0305097	+	0.0528443i
$924$		0			0
$925$	−21699.6	−	37584.8i	−0.771328	−	1.33598i
$926$	−12197.9	+	7042.46i	−0.432881	+	0.249924i
$927$		0			0
$928$	−13808.5	+	23917.0i	−0.488455	+	0.846029i
$929$	2801.35	−	4852.09i	0.0989338	−	0.171358i	−0.812310	−	0.583226i	$-0.801790\pi$
$929$	2801.35	−	4852.09i	0.0989338	−	0.171358i	0.911244	+	0.411868i	$0.135123\pi$
$930$		0			0
$931$	23511.6	+	46168.6i	0.827672	+	1.62526i
$932$	−14033.9	−	8102.49i	−0.493237	−	0.284770i
$933$		0			0
$934$			26392.9i			0.924628i
$935$	735.570	+	424.681i	0.0257280	+	0.0148541i
$936$		0			0
$937$			1117.11i			0.0389481i	0.999810	+	0.0194740i	$0.00619917\pi$
$937$			1117.11i			0.0389481i	−0.999810	+	0.0194740i	$0.993801\pi$
$938$	−6361.21	+	6035.27i	−0.221430	+	0.210084i
$939$		0			0
$940$	−414.818			−0.0143935
$941$	26616.3	+	46100.9i	0.922070	+	1.59707i	0.796207	+	0.605024i	$0.206837\pi$
$941$	26616.3	+	46100.9i	0.922070	+	1.59707i	0.125863	+	0.992048i	$0.459830\pi$
$942$		0			0
$943$	−3872.29	−	2235.67i	−0.133721	−	0.0772039i
$944$	−1700.44			−0.0586279
$945$		0			0
$946$	5391.63			0.185303
$947$	−18693.0	−	10792.4i	−0.641436	−	0.370333i	0.143731	−	0.989617i	$-0.454090\pi$
$947$	−18693.0	−	10792.4i	−0.641436	−	0.370333i	−0.785168	+	0.619283i	$0.787423\pi$
$948$		0			0
$949$	−680.179	−	1178.10i	−0.0232661	−	0.0402981i
$950$	−34659.2			−1.18368
$951$		0			0
$952$	−4140.59	−	17255.0i	−0.140964	−	0.587433i
$953$		−	27626.3i		−	0.939040i	−0.882922	−	0.469520i	$-0.844427\pi$
$953$		−	27626.3i		−	0.939040i	0.882922	−	0.469520i	$-0.155573\pi$
$954$		0			0
$955$	−1438.61	−	830.584i	−0.0487460	−	0.0281435i
$956$			18217.7i			0.616320i
$957$		0			0
$958$	27799.8	+	16050.2i	0.937549	+	0.541294i
$959$	9121.34	−	8653.97i	0.307136	−	0.291399i
$960$		0			0
$961$	−14726.1	+	25506.3i	−0.494313	+	0.856176i
$962$	−529.387	+	916.926i	−0.0177423	+	0.0307306i
$963$		0			0
$964$	−4091.21	+	2362.06i	−0.136690	+	0.0789179i
$965$	484.390	+	838.988i	0.0161586	+	0.0279875i
$966$		0			0
$967$	1972.99	−	3417.31i	0.0656122	−	0.113644i	−0.831353	−	0.555744i	$-0.812433\pi$
$967$	1972.99	−	3417.31i	0.0656122	−	0.113644i	0.896965	+	0.442101i	$0.145767\pi$
$968$			26219.5i			0.870585i
$969$		0			0
$970$	−956.571			−0.0316636
$971$	1848.32	+	3201.38i	0.0610869	+	0.105806i	0.894951	−	0.446163i	$-0.147210\pi$
$971$	1848.32	+	3201.38i	0.0610869	+	0.105806i	−0.833865	+	0.551969i	$0.813877\pi$
$972$		0			0
$973$	11066.6	+	46117.7i	0.364625	+	1.51949i
$974$	−4283.70	+	2473.19i	−0.140923	+	0.0813617i
$975$		0			0
$976$	−395.280	+	228.215i	−0.0129637	+	0.00748461i
$977$	−29474.2	+	17016.9i	−0.965162	+	0.557237i	−0.897758	−	0.440489i	$-0.854805\pi$
$977$	−29474.2	+	17016.9i	−0.965162	+	0.557237i	−0.0674042	+	0.997726i	$0.521472\pi$
$978$		0			0
$979$	64860.3	−	37447.1i	2.11741	−	1.22249i
$980$	−585.541	+	298.190i	−0.0190861	+	0.00971973i
$981$		0			0
$982$	6180.10	+	10704.2i	0.200830	+	0.347848i
$983$	19621.0			0.636635			0.318317	−	0.947984i	$-0.396882\pi$
$983$	19621.0			0.636635			0.318317	+	0.947984i	$0.396882\pi$
$984$		0			0
$985$		−	139.735i		−	0.00452014i
$986$	5984.40	−	10365.3i	0.193288	−	0.334785i
$987$		0			0
$988$	−578.231	−	1001.53i	−0.0186194	−	0.0322498i
$989$	6740.95	−	3891.89i	0.216734	−	0.125131i
$990$		0			0
$991$	10727.8	−	18581.1i	0.343874	−	0.595607i	−0.641275	−	0.767311i	$-0.721594\pi$
$991$	10727.8	−	18581.1i	0.343874	−	0.595607i	0.985149	+	0.171704i	$0.0549274\pi$
$992$	1612.15	−	2792.33i	0.0515987	−	0.0893715i
$993$		0			0
$994$	−34189.2	+	8204.22i	−1.09096	+	0.261793i
$995$	−1775.24	−	1024.94i	−0.0565618	−	0.0326560i
$996$		0			0
$997$			34686.1i			1.10183i	0.834563	+	0.550913i	$0.185720\pi$
$997$			34686.1i			1.10183i	−0.834563	+	0.550913i	$0.814280\pi$
$998$	322.749	+	186.339i	0.0102369	+	0.00591028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.15		44
3.2	odd	2		63.4.s.a.59.8	yes	44
7.5	odd	6		189.4.i.a.152.8		44
9.2	odd	6		189.4.i.a.143.15		44
9.7	even	3		63.4.i.a.38.8	yes	44
21.5	even	6		63.4.i.a.5.15	✓	44
63.47	even	6	inner	189.4.s.a.89.15		44
63.61	odd	6		63.4.s.a.47.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.15	✓	44	21.5	even	6
63.4.i.a.38.8	yes	44	9.7	even	3
63.4.s.a.47.8	yes	44	63.61	odd	6
63.4.s.a.59.8	yes	44	3.2	odd	2
189.4.i.a.143.15		44	9.2	odd	6
189.4.i.a.152.8		44	7.5	odd	6
189.4.s.a.17.15		44	1.1	even	1	trivial
189.4.s.a.89.15		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)

\(f(q)\)	\(=\)	\(q+(1.59189 + 0.919076i) q^{2} +(-2.31060 - 4.00207i) q^{4} -0.414554 q^{5} +(12.7471 + 13.4355i) q^{7} -23.1997i q^{8} +O(q^{10})\)	\(q+(1.59189 + 0.919076i) q^{2} +(-2.31060 - 4.00207i) q^{4} -0.414554 q^{5} +(12.7471 + 13.4355i) q^{7} -23.1997i q^{8} +(-0.659923 - 0.381007i) q^{10} -49.6101i q^{11} +(1.43477 + 0.828367i) q^{13} +(7.94365 + 33.1033i) q^{14} +(2.83751 - 4.91471i) q^{16} +(20.6496 - 35.7662i) q^{17} +(130.814 - 75.5256i) q^{19} +(0.957866 + 1.65907i) q^{20} +(45.5955 - 78.9737i) q^{22} -131.651i q^{23} -124.828 q^{25} +(1.52267 + 2.63733i) q^{26} +(24.3164 - 82.0587i) q^{28} +(136.539 - 78.8310i) q^{29} +(-15.9411 + 9.20357i) q^{31} +(-151.698 + 87.5830i) q^{32} +(65.7437 - 37.9571i) q^{34} +(-5.28434 - 5.56973i) q^{35} +(173.836 + 301.092i) q^{37} +277.655 q^{38} +9.61751i q^{40} +(16.9818 - 29.4134i) q^{41} +(29.5623 + 51.2034i) q^{43} +(-198.543 + 114.629i) q^{44} +(120.997 - 209.573i) q^{46} +(-108.266 + 187.523i) q^{47} +(-18.0246 + 342.526i) q^{49} +(-198.712 - 114.727i) q^{50} -7.65609i q^{52} +(-174.040 - 100.482i) q^{53} +20.5661i q^{55} +(311.699 - 295.728i) q^{56} +289.807 q^{58} +(-149.819 - 259.493i) q^{59} +(-69.6527 - 40.2140i) q^{61} -33.8351 q^{62} -367.382 q^{64} +(-0.594791 - 0.343403i) q^{65} +(128.788 + 223.067i) q^{67} -190.852 q^{68} +(-3.29307 - 13.7231i) q^{70} +1032.80i q^{71} +(-711.100 - 410.554i) q^{73} +639.073i q^{74} +(-604.518 - 349.019i) q^{76} +(666.536 - 632.384i) q^{77} +(-52.6589 + 91.2079i) q^{79} +(-1.17630 + 2.03741i) q^{80} +(54.0663 - 31.2152i) q^{82} +(-245.110 - 424.542i) q^{83} +(-8.56037 + 14.8270i) q^{85} +108.680i q^{86} -1150.94 q^{88} +(754.828 + 1307.40i) q^{89} +(7.15964 + 29.8361i) q^{91} +(-526.875 + 304.191i) q^{92} +(-344.695 + 199.010i) q^{94} +(-54.2295 + 31.3094i) q^{95} +(1087.14 - 627.661i) q^{97} +(-343.501 + 528.697i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 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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