LMFDB - Embedded newform 189.3.j.b.116.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.j (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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.8
Character	$\chi$	$=$	189.116
Dual form			189.3.j.b.44.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.46555i q^{2} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(-4.05935 + 5.70277i) q^{7} +8.57663i q^{8} +O(q^{10})$	\(q+1.46555i q^{2} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(-4.05935 + 5.70277i) q^{7} +8.57663i q^{8} +(0.844669 - 1.46301i) q^{10} +(-0.209014 + 0.120674i) q^{11} +(7.70332 + 13.3426i) q^{13} +(-8.35769 - 5.94918i) q^{14} -5.16078 q^{16} +(10.9102 + 6.29901i) q^{17} +(13.7090 + 23.7446i) q^{19} +(-1.84896 - 1.06750i) q^{20} +(-0.176854 - 0.306320i) q^{22} +(-17.6566 - 10.1940i) q^{23} +(-11.8356 - 20.4999i) q^{25} +(-19.5541 + 11.2896i) q^{26} +(-7.51862 + 10.5625i) q^{28} +(-16.9161 - 9.76653i) q^{29} -2.72674 q^{31} +26.7432i q^{32} +(-9.23150 + 15.9894i) q^{34} +(7.33912 - 3.35329i) q^{35} +(-11.4455 - 19.8242i) q^{37} +(-34.7989 + 20.0911i) q^{38} +(4.94315 - 8.56178i) q^{40} +(61.9933 - 35.7918i) q^{41} +(14.8972 - 25.8028i) q^{43} +(-0.387130 + 0.223510i) q^{44} +(14.9398 - 25.8766i) q^{46} +29.9915i q^{47} +(-16.0433 - 46.2992i) q^{49} +(30.0436 - 17.3457i) q^{50} +(14.2679 + 24.7127i) q^{52} +(90.5906 + 52.3025i) q^{53} +0.278203 q^{55} +(-48.9106 - 34.8156i) q^{56} +(14.3133 - 24.7914i) q^{58} -86.7123i q^{59} +17.8845 q^{61} -3.99616i q^{62} -59.8365 q^{64} -17.7593i q^{65} -18.0439 q^{67} +(20.2076 + 11.6669i) q^{68} +(4.91440 + 10.7558i) q^{70} -74.2118i q^{71} +(13.0598 - 22.6203i) q^{73} +(29.0533 - 16.7739i) q^{74} +(25.3914 + 43.9791i) q^{76} +(0.160284 - 1.68182i) q^{77} +22.5123 q^{79} +(5.15184 + 2.97442i) q^{80} +(52.4546 + 90.8541i) q^{82} +(77.0996 + 44.5135i) q^{83} +(-7.26088 - 12.5762i) q^{85} +(37.8152 + 21.8326i) q^{86} +(-1.03498 - 1.79264i) q^{88} +(-49.7459 + 28.7208i) q^{89} +(-107.360 - 10.2318i) q^{91} +(-32.7030 - 18.8811i) q^{92} -43.9540 q^{94} -31.6047i q^{95} +(73.9883 - 128.152i) q^{97} +(67.8536 - 23.5122i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) $ 22 * q - 24 * q^4 - 12 * q^5	$ 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) $ 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.46555i			0.732774i	0.930463	+	0.366387i	$0.119405\pi$
$2$			1.46555i			0.732774i	−0.930463	+	0.366387i	$0.880595\pi$
$3$		0			0
$3$		0			0
$4$	1.85217			0.463043
$5$	−0.998268	−	0.576350i	−0.199654	−	0.115270i	0.396840	−	0.917888i	$-0.370107\pi$
$5$	−0.998268	−	0.576350i	−0.199654	−	0.115270i	−0.596494	+	0.802618i	$0.703440\pi$
$6$		0			0
$7$	−4.05935	+	5.70277i	−0.579908	+	0.814682i
$7$	−4.05935	+	5.70277i	−0.579908	+	0.814682i
$8$			8.57663i			1.07208i
$9$		0			0
$10$	0.844669	−	1.46301i	0.0844669	−	0.146301i
$11$	−0.209014	+	0.120674i	−0.0190013	+	0.0109704i	−0.509471	−	0.860488i	$-0.670159\pi$
$11$	−0.209014	+	0.120674i	−0.0190013	+	0.0109704i	0.490469	+	0.871458i	$0.336825\pi$
$12$		0			0
$13$	7.70332	+	13.3426i	0.592563	+	1.02635i	0.993886	+	0.110413i	$0.0352174\pi$
$13$	7.70332	+	13.3426i	0.592563	+	1.02635i	−0.401322	+	0.915937i	$0.631449\pi$
$14$	−8.35769	−	5.94918i	−0.596978	−	0.424941i
$15$		0			0
$16$	−5.16078			−0.322549
$17$	10.9102	+	6.29901i	0.641777	+	0.370530i	0.785299	−	0.619117i	$-0.212509\pi$
$17$	10.9102	+	6.29901i	0.641777	+	0.370530i	−0.143522	+	0.989647i	$0.545843\pi$
$18$		0			0
$19$	13.7090	+	23.7446i	0.721525	+	1.24972i	0.960389	+	0.278664i	$0.0898917\pi$
$19$	13.7090	+	23.7446i	0.721525	+	1.24972i	−0.238864	+	0.971053i	$0.576775\pi$
$20$	−1.84896	−	1.06750i	−0.0924482	−	0.0533750i
$21$		0			0
$22$	−0.176854	−	0.306320i	−0.00803882	−	0.0139236i
$23$	−17.6566	−	10.1940i	−0.767678	−	0.443219i	0.0643676	−	0.997926i	$-0.479497\pi$
$23$	−17.6566	−	10.1940i	−0.767678	−	0.443219i	−0.832046	+	0.554707i	$0.812830\pi$
$24$		0			0
$25$	−11.8356	−	20.4999i	−0.473426	−	0.819997i
$26$	−19.5541	+	11.2896i	−0.752082	+	0.434215i
$27$		0			0
$28$	−7.51862	+	10.5625i	−0.268522	+	0.377233i
$29$	−16.9161	−	9.76653i	−0.583315	−	0.336777i	0.179135	−	0.983825i	$-0.442670\pi$
$29$	−16.9161	−	9.76653i	−0.583315	−	0.336777i	−0.762450	+	0.647048i	$0.776003\pi$
$30$		0			0
$31$	−2.72674			−0.0879592			−0.0439796	−	0.999032i	$-0.514004\pi$
$31$	−2.72674			−0.0879592			−0.0439796	+	0.999032i	$0.514004\pi$
$32$			26.7432i			0.835724i
$33$		0			0
$34$	−9.23150	+	15.9894i	−0.271515	+	0.470277i
$35$	7.33912	−	3.35329i	0.209689	−	0.0958082i
$36$		0			0
$37$	−11.4455	−	19.8242i	−0.309338	−	0.535789i	0.668880	−	0.743371i	$-0.266774\pi$
$37$	−11.4455	−	19.8242i	−0.309338	−	0.535789i	−0.978218	+	0.207582i	$0.933441\pi$
$38$	−34.7989	+	20.0911i	−0.915760	+	0.528714i
$39$		0			0
$40$	4.94315	−	8.56178i	0.123579	−	0.214045i
$41$	61.9933	−	35.7918i	1.51203	−	0.872972i	0.512130	−	0.858908i	$-0.328856\pi$
$41$	61.9933	−	35.7918i	1.51203	−	0.872972i	0.999901	−	0.0140641i	$-0.00447689\pi$
$42$		0			0
$43$	14.8972	−	25.8028i	0.346447	−	0.600064i	−0.639168	−	0.769067i	$-0.720721\pi$
$43$	14.8972	−	25.8028i	0.346447	−	0.600064i	0.985616	+	0.169003i	$0.0540546\pi$
$44$	−0.387130	+	0.223510i	−0.00879841	+	0.00507977i
$45$		0			0
$46$	14.9398	−	25.8766i	0.324779	−	0.562534i
$47$			29.9915i			0.638117i	0.947735	+	0.319059i	$0.103367\pi$
$47$			29.9915i			0.638117i	−0.947735	+	0.319059i	$0.896633\pi$
$48$		0			0
$49$	−16.0433	−	46.2992i	−0.327414	−	0.944881i
$50$	30.0436	−	17.3457i	0.600872	−	0.346914i
$51$		0			0
$52$	14.2679	+	24.7127i	0.274382	+	0.475244i
$53$	90.5906	+	52.3025i	1.70926	+	0.986840i	0.935479	+	0.353383i	$0.114969\pi$
$53$	90.5906	+	52.3025i	1.70926	+	0.986840i	0.773778	+	0.633457i	$0.218365\pi$
$54$		0			0
$55$	0.278203			0.00505824
$56$	−48.9106	−	34.8156i	−0.873404	−	0.621707i
$57$		0			0
$58$	14.3133	−	24.7914i	0.246781	−	0.427438i
$59$		−	86.7123i		−	1.46970i	−0.678230	−	0.734850i	$-0.737253\pi$
$59$		−	86.7123i		−	1.46970i	0.678230	−	0.734850i	$-0.262747\pi$
$60$		0			0
$61$	17.8845			0.293188			0.146594	−	0.989197i	$-0.453169\pi$
$61$	17.8845			0.293188			0.146594	+	0.989197i	$0.453169\pi$
$62$		−	3.99616i		−	0.0644542i
$63$		0			0
$64$	−59.8365			−0.934945
$65$		−	17.7593i		−	0.273219i
$66$		0			0
$67$	−18.0439			−0.269312			−0.134656	−	0.990892i	$-0.542993\pi$
$67$	−18.0439			−0.269312			−0.134656	+	0.990892i	$0.542993\pi$
$68$	20.2076	+	11.6669i	0.297170	+	0.171571i
$69$		0			0
$70$	4.91440	+	10.7558i	0.0702058	+	0.153655i
$71$		−	74.2118i		−	1.04524i	−0.852567	−	0.522618i	$-0.824955\pi$
$71$		−	74.2118i		−	1.04524i	0.852567	−	0.522618i	$-0.175045\pi$
$72$		0			0
$73$	13.0598	−	22.6203i	0.178902	−	0.309867i	−0.762603	−	0.646867i	$-0.776079\pi$
$73$	13.0598	−	22.6203i	0.178902	−	0.309867i	0.941505	+	0.337000i	$0.109412\pi$
$74$	29.0533	−	16.7739i	0.392612	−	0.226675i
$75$		0			0
$76$	25.3914	+	43.9791i	0.334097	+	0.578673i
$77$	0.160284	−	1.68182i	0.00208161	−	0.0218418i
$78$		0			0
$79$	22.5123			0.284966			0.142483	−	0.989797i	$-0.454491\pi$
$79$	22.5123			0.284966			0.142483	+	0.989797i	$0.454491\pi$
$80$	5.15184	+	2.97442i	0.0643980	+	0.0371802i
$81$		0			0
$82$	52.4546	+	90.8541i	0.639691	+	1.10798i
$83$	77.0996	+	44.5135i	0.928911	+	0.536307i	0.886467	−	0.462792i	$-0.153152\pi$
$83$	77.0996	+	44.5135i	0.928911	+	0.536307i	0.0424438	+	0.999099i	$0.486486\pi$
$84$		0			0
$85$	−7.26088	−	12.5762i	−0.0854221	−	0.147955i
$86$	37.8152	+	21.8326i	0.439711	+	0.253867i
$87$		0			0
$88$	−1.03498	−	1.79264i	−0.0117611	−	0.0203709i
$89$	−49.7459	+	28.7208i	−0.558942	+	0.322706i	−0.752721	−	0.658340i	$-0.771259\pi$
$89$	−49.7459	+	28.7208i	−0.558942	+	0.322706i	0.193779	+	0.981045i	$0.437926\pi$
$90$		0			0
$91$	−107.360	−	10.2318i	−1.17978	−	0.112438i
$92$	−32.7030	−	18.8811i	−0.355468	−	0.205229i
$93$		0			0
$94$	−43.9540			−0.467596
$95$		−	31.6047i		−	0.332681i
$96$		0			0
$97$	73.9883	−	128.152i	0.762766	−	1.32115i	−0.178653	−	0.983912i	$-0.557174\pi$
$97$	73.9883	−	128.152i	0.762766	−	1.32115i	0.941419	−	0.337238i	$-0.109493\pi$
$98$	67.8536	−	23.5122i	0.692384	−	0.239920i
$99$		0			0
$100$	−21.9216	−	37.9694i	−0.219216	−	0.379694i
$101$	−72.8647	+	42.0685i	−0.721433	+	0.416519i	−0.815280	−	0.579067i	$-0.803417\pi$
$101$	−72.8647	+	42.0685i	−0.721433	+	0.416519i	0.0938471	+	0.995587i	$0.470084\pi$
$102$		0			0
$103$	−29.4838	+	51.0674i	−0.286250	+	0.495800i	−0.972912	−	0.231178i	$-0.925742\pi$
$103$	−29.4838	+	51.0674i	−0.286250	+	0.495800i	0.686661	+	0.726977i	$0.259076\pi$
$104$	−114.434	+	66.0686i	−1.10033	+	0.635275i
$105$		0			0
$106$	−76.6518	+	132.765i	−0.723130	+	1.25250i
$107$	−76.9320	+	44.4167i	−0.718990	+	0.415109i	−0.814381	−	0.580331i	$-0.802923\pi$
$107$	−76.9320	+	44.4167i	−0.718990	+	0.415109i	0.0953906	+	0.995440i	$0.469590\pi$
$108$		0			0
$109$	94.4610	−	163.611i	0.866615	−	1.50102i	0.00117990	−	0.999999i	$-0.499624\pi$
$109$	94.4610	−	163.611i	0.866615	−	1.50102i	0.865435	−	0.501021i	$-0.167042\pi$
$110$			0.407720i			0.00370654i
$111$		0			0
$112$	20.9494	−	29.4308i	0.187048	−	0.262775i
$113$	−101.115	+	58.3790i	−0.894827	+	0.516629i	−0.875518	−	0.483185i	$-0.839480\pi$
$113$	−101.115	+	58.3790i	−0.894827	+	0.516629i	−0.0193087	+	0.999814i	$0.506147\pi$
$114$		0			0
$115$	11.7507	+	20.3528i	0.102180	+	0.176981i
$116$	−31.3316	−	18.0893i	−0.270100	−	0.155942i
$117$		0			0
$118$	127.081			1.07696
$119$	−80.2103	+	36.6485i	−0.674036	+	0.307971i
$120$		0			0
$121$	−60.4709	+	104.739i	−0.499759	+	0.865609i
$122$			26.2106i			0.214841i
$123$		0			0
$124$	−5.05038			−0.0407289
$125$			56.1034i			0.448827i
$126$		0			0
$127$	−33.5427			−0.264116			−0.132058	−	0.991242i	$-0.542159\pi$
$127$	−33.5427			−0.264116			−0.132058	+	0.991242i	$0.542159\pi$
$128$			19.2795i			0.150621i
$129$		0			0
$130$	26.0270			0.200208
$131$	61.9195	+	35.7493i	0.472668	+	0.272895i	0.717356	−	0.696707i	$-0.245352\pi$
$131$	61.9195	+	35.7493i	0.472668	+	0.272895i	−0.244688	+	0.969602i	$0.578685\pi$
$132$		0			0
$133$	−191.060	−	18.2087i	−1.43654	−	0.136908i
$134$		−	26.4442i		−	0.197345i
$135$		0			0
$136$	−54.0243	+	93.5729i	−0.397238	+	0.688036i
$137$	187.723	−	108.382i	1.37024	−	0.791108i	0.379281	−	0.925281i	$-0.376171\pi$
$137$	187.723	−	108.382i	1.37024	−	0.791108i	0.990958	+	0.134173i	$0.0428379\pi$
$138$		0			0
$139$	53.7032	+	93.0167i	0.386354	+	0.669185i	0.991956	−	0.126583i	$-0.0404009\pi$
$139$	53.7032	+	93.0167i	0.386354	+	0.669185i	−0.605602	+	0.795768i	$0.707068\pi$
$140$	13.5933	−	6.21086i	0.0970951	−	0.0443633i
$141$		0			0
$142$	108.761			0.765921
$143$	−3.22021	−	1.85919i	−0.0225189	−	0.0130013i
$144$		0			0
$145$	11.2579	+	19.4992i	0.0776406	+	0.134477i
$146$	33.1511	+	19.1398i	0.227062	+	0.131094i
$147$		0			0
$148$	−21.1990	−	36.7178i	−0.143237	−	0.248093i
$149$	−136.043	−	78.5443i	−0.913038	−	0.527143i	−0.0316309	−	0.999500i	$-0.510070\pi$
$149$	−136.043	−	78.5443i	−0.913038	−	0.527143i	−0.881408	+	0.472357i	$0.843403\pi$
$150$		0			0
$151$	60.2412	+	104.341i	0.398948	+	0.690999i	0.993596	−	0.112987i	$-0.0360419\pi$
$151$	60.2412	+	104.341i	0.398948	+	0.690999i	−0.594648	+	0.803986i	$0.702709\pi$
$152$	−203.649	+	117.577i	−1.33980	+	0.773532i
$153$		0			0
$154$	2.46479	+	0.234904i	0.0160051	+	0.00152535i
$155$	2.72201	+	1.57156i	0.0175614	+	0.0101391i
$156$		0			0
$157$	7.75554			0.0493984			0.0246992	−	0.999695i	$-0.492137\pi$
$157$	7.75554			0.0493984			0.0246992	+	0.999695i	$0.492137\pi$
$158$			32.9928i			0.208815i
$159$		0			0
$160$	15.4134	−	26.6969i	0.0963340	−	0.166855i
$161$	129.809	−	59.3104i	0.806265	−	0.368387i
$162$		0			0
$163$	129.964	+	225.104i	0.797323	+	1.38100i	0.921354	+	0.388725i	$0.127084\pi$
$163$	129.964	+	225.104i	0.797323	+	1.38100i	−0.124031	+	0.992278i	$0.539582\pi$
$164$	114.822	−	66.2926i	0.700135	−	0.404223i
$165$		0			0
$166$	−65.2366	+	112.993i	−0.392992	+	0.680681i
$167$	−97.3809	+	56.2229i	−0.583119	+	0.336664i	−0.762372	−	0.647139i	$-0.775965\pi$
$167$	−97.3809	+	56.2229i	−0.583119	+	0.336664i	0.179253	+	0.983803i	$0.442632\pi$
$168$		0			0
$169$	−34.1824	+	59.2057i	−0.202263	+	0.350330i
$170$	18.4310	−	10.6412i	0.108418	−	0.0625951i
$171$		0			0
$172$	27.5922	−	47.7911i	0.160420	−	0.277855i
$173$		−	13.9867i		−	0.0808478i	−0.999183	−	0.0404239i	$-0.987129\pi$
$173$		−	13.9867i		−	0.0808478i	0.999183	−	0.0404239i	$-0.0128708\pi$
$174$		0			0
$175$	164.952	+	15.7205i	0.942580	+	0.0898314i
$176$	1.07868	−	0.622774i	0.00612884	−	0.00353849i
$177$		0			0
$178$	−42.0917	−	72.9049i	−0.236470	−	0.409578i
$179$	−44.1214	−	25.4735i	−0.246488	−	0.142310i	0.371667	−	0.928366i	$-0.378786\pi$
$179$	−44.1214	−	25.4735i	−0.246488	−	0.142310i	−0.618155	+	0.786056i	$0.712120\pi$
$180$		0			0
$181$	−239.784			−1.32477			−0.662387	−	0.749161i	$-0.730457\pi$
$181$	−239.784			−1.32477			−0.662387	+	0.749161i	$0.730457\pi$
$182$	14.9952	−	157.341i	0.0823913	−	0.864513i
$183$		0			0
$184$	87.4305	−	151.434i	0.475166	−	0.823012i
$185$			26.3865i			0.142630i
$186$		0			0
$187$	−3.04052			−0.0162595
$188$			55.5494i			0.295476i
$189$		0			0
$190$	46.3182			0.243780
$191$			183.841i			0.962519i	0.876578	+	0.481259i	$0.159820\pi$
$191$			183.841i			0.962519i	−0.876578	+	0.481259i	$0.840180\pi$
$192$		0			0
$193$	152.797			0.791695			0.395847	−	0.918316i	$-0.370451\pi$
$193$	152.797			0.791695			0.395847	+	0.918316i	$0.370451\pi$
$194$	187.812	+	108.433i	0.968104	+	0.558935i
$195$		0			0
$196$	−29.7149	−	85.7540i	−0.151607	−	0.437520i
$197$		−	386.007i		−	1.95943i	−0.200402	−	0.979714i	$-0.564225\pi$
$197$		−	386.007i		−	1.95943i	0.200402	−	0.979714i	$-0.435775\pi$
$198$		0			0
$199$	−22.8387	+	39.5577i	−0.114767	+	0.198782i	−0.917687	−	0.397305i	$-0.869946\pi$
$199$	−22.8387	+	39.5577i	−0.114767	+	0.198782i	0.802920	+	0.596087i	$0.203279\pi$
$200$	175.820	−	101.510i	0.879102	−	0.507550i
$201$		0			0
$202$	−61.6533	−	106.787i	−0.305214	−	0.528647i
$203$	124.365	−	56.8231i	0.612635	−	0.279917i
$204$		0			0
$205$	−82.5146			−0.402510
$206$	−74.8417	−	43.2099i	−0.363309	−	0.209757i
$207$		0			0
$208$	−39.7552	−	68.8579i	−0.191131	−	0.331048i
$209$	−5.73074	−	3.30864i	−0.0274198	−	0.0158308i
$210$		0			0
$211$	−169.338	−	293.302i	−0.802550	−	1.39006i	−0.917933	−	0.396736i	$-0.870143\pi$
$211$	−169.338	−	293.302i	−0.802550	−	1.39006i	0.115383	−	0.993321i	$-0.463190\pi$
$212$	167.789	+	96.8732i	0.791459	+	0.456949i
$213$		0			0
$214$	−65.0948	−	112.747i	−0.304181	−	0.526857i
$215$	−29.7429	+	17.1721i	−0.138339	+	0.0798700i
$216$		0			0
$217$	11.0688	−	15.5500i	0.0510082	−	0.0716588i
$218$	239.780	+	138.437i	1.09991	+	0.635032i
$219$		0			0
$220$	0.515280			0.00234218
$221$			194.093i			0.878251i
$222$		0			0
$223$	43.8681	−	75.9817i	0.196718	−	0.340725i	−0.750745	−	0.660593i	$-0.770305\pi$
$223$	43.8681	−	75.9817i	0.196718	−	0.340725i	0.947462	+	0.319868i	$0.103638\pi$
$224$	−152.510	−	108.560i	−0.680849	−	0.484643i
$225$		0			0
$226$	−85.5572	−	148.189i	−0.378572	−	0.655706i
$227$	−305.444	+	176.348i	−1.34557	+	0.776864i	−0.987618	−	0.156876i	$-0.949858\pi$
$227$	−305.444	+	176.348i	−1.34557	+	0.776864i	−0.357950	+	0.933741i	$0.616524\pi$
$228$		0			0
$229$	190.395	−	329.774i	0.831421	−	1.44006i	−0.0654913	−	0.997853i	$-0.520861\pi$
$229$	190.395	−	329.774i	0.831421	−	1.44006i	0.896912	−	0.442209i	$-0.145805\pi$
$230$	−29.8280	+	17.2212i	−0.129687	+	0.0748747i
$231$		0			0
$232$	83.7640	−	145.083i	0.361052	−	0.625360i
$233$	271.555	−	156.782i	1.16547	−	0.672885i	0.212862	−	0.977082i	$-0.431722\pi$
$233$	271.555	−	156.782i	1.16547	−	0.672885i	0.952609	+	0.304197i	$0.0983882\pi$
$234$		0			0
$235$	17.2856	−	29.9396i	0.0735558	−	0.127402i
$236$		−	160.606i		−	0.680534i
$237$		0			0
$238$	−53.7102	−	117.552i	−0.225673	−	0.493916i
$239$	−199.851	+	115.384i	−0.836195	+	0.482777i	−0.855969	−	0.517027i	$-0.827039\pi$
$239$	−199.851	+	115.384i	−0.836195	+	0.482777i	0.0197741	+	0.999804i	$0.493705\pi$
$240$		0			0
$241$	90.4282	+	156.626i	0.375221	+	0.649902i	0.990360	−	0.138517i	$-0.0442335\pi$
$241$	90.4282	+	156.626i	0.375221	+	0.649902i	−0.615139	+	0.788419i	$0.710900\pi$
$242$	−153.499	−	88.6229i	−0.634295	−	0.366210i
$243$		0			0
$244$	33.1251			0.135759
$245$	−10.6691	+	55.4655i	−0.0435471	+	0.226390i
$246$		0			0
$247$	−211.209	+	365.825i	−0.855098	+	1.48107i
$248$		−	23.3862i		−	0.0942992i
$249$		0			0
$250$	−82.2222			−0.328889
$251$		−	161.864i		−	0.644878i	−0.946590	−	0.322439i	$-0.895497\pi$
$251$		−	161.864i		−	0.644878i	0.946590	−	0.322439i	$-0.104503\pi$
$252$		0			0
$253$	4.92064			0.0194492
$254$		−	49.1585i		−	0.193537i
$255$		0			0
$256$	−267.601			−1.04532
$257$	−65.5360	−	37.8372i	−0.255004	−	0.147227i	0.367049	−	0.930201i	$-0.380368\pi$
$257$	−65.5360	−	37.8372i	−0.255004	−	0.147227i	−0.622053	+	0.782975i	$0.713701\pi$
$258$		0			0
$259$	159.514	+	15.2023i	0.615885	+	0.0586962i
$260$		−	32.8932i		−	0.126512i
$261$		0			0
$262$	−52.3922	+	90.7460i	−0.199970	+	0.346359i
$263$	−10.0862	+	5.82326i	−0.0383505	+	0.0221417i	−0.519053	−	0.854742i	$-0.673715\pi$
$263$	−10.0862	+	5.82326i	−0.0383505	+	0.0221417i	0.480702	+	0.876884i	$0.340382\pi$
$264$		0			0
$265$	−60.2892	−	104.424i	−0.227506	−	0.394052i
$266$	26.6857	−	280.007i	0.100322	−	1.05266i
$267$		0			0
$268$	−33.4204			−0.124703
$269$	265.976	+	153.562i	0.988760	+	0.570861i	0.904903	−	0.425617i	$-0.139943\pi$
$269$	265.976	+	153.562i	0.988760	+	0.570861i	0.0838565	+	0.996478i	$0.473276\pi$
$270$		0			0
$271$	169.039	+	292.784i	0.623759	+	1.08038i	0.988779	+	0.149383i	$0.0477287\pi$
$271$	169.039	+	292.784i	0.623759	+	1.08038i	−0.365020	+	0.931000i	$0.618938\pi$
$272$	−56.3052	−	32.5078i	−0.207004	−	0.119514i
$273$		0			0
$274$	158.839	+	275.117i	0.579703	+	1.00408i
$275$	4.94763	+	2.85652i	0.0179914	+	0.0103873i
$276$		0			0
$277$	66.0110	+	114.334i	0.238307	+	0.412760i	0.960229	−	0.279215i	$-0.0900743\pi$
$277$	66.0110	+	114.334i	0.238307	+	0.412760i	−0.721922	+	0.691975i	$0.756741\pi$
$278$	−136.320	+	78.7046i	−0.490361	+	0.283110i
$279$		0			0
$280$	28.7599	+	62.9450i	0.102714	+	0.224803i
$281$	64.2832	+	37.1139i	0.228766	+	0.132078i	0.610003	−	0.792399i	$-0.291168\pi$
$281$	64.2832	+	37.1139i	0.228766	+	0.132078i	−0.381237	+	0.924477i	$0.624502\pi$
$282$		0			0
$283$	−11.3030			−0.0399401			−0.0199701	−	0.999801i	$-0.506357\pi$
$283$	−11.3030			−0.0399401			−0.0199701	+	0.999801i	$0.506357\pi$
$284$		−	137.453i		−	0.483989i
$285$		0			0
$286$	2.72473	−	4.71937i	0.00952702	−	0.0165013i
$287$	−47.5399	+	498.826i	−0.165644	+	1.73807i
$288$		0			0
$289$	−65.1449	−	112.834i	−0.225415	−	0.390430i
$290$	−28.5771	+	16.4990i	−0.0985416	+	0.0568930i
$291$		0			0
$292$	24.1890	−	41.8966i	0.0828391	−	0.143482i
$293$	144.131	−	83.2139i	0.491913	−	0.284006i	−0.233454	−	0.972368i	$-0.575003\pi$
$293$	144.131	−	83.2139i	0.491913	−	0.284006i	0.725368	+	0.688361i	$0.241670\pi$
$294$		0			0
$295$	−49.9767	+	86.5621i	−0.169412	+	0.293431i
$296$	170.025	−	98.1639i	0.574408	−	0.331635i
$297$		0			0
$298$	115.110	−	199.377i	0.386276	−	0.669050i
$299$		−	314.112i		−	1.05054i
$300$		0			0
$301$	86.6742	+	189.698i	0.287954	+	0.630226i
$302$	−152.916	+	88.2864i	−0.506346	+	0.292339i
$303$		0			0
$304$	−70.7490	−	122.541i	−0.232727	−	0.403095i
$305$	−17.8535	−	10.3077i	−0.0585361	−	0.0337958i
$306$		0			0
$307$	−382.982			−1.24750			−0.623749	−	0.781625i	$-0.714391\pi$
$307$	−382.982			−1.24750			−0.623749	+	0.781625i	$0.714391\pi$
$308$	0.296873	−	3.11502i	0.000963874	−	0.0101137i
$309$		0			0
$310$	−2.30319	+	3.98924i	−0.00742964	+	0.0128685i
$311$		−	156.011i		−	0.501642i	−0.968033	−	0.250821i	$-0.919299\pi$
$311$		−	156.011i		−	0.501642i	0.968033	−	0.250821i	$-0.0807006\pi$
$312$		0			0
$313$	116.530			0.372301			0.186150	−	0.982521i	$-0.440399\pi$
$313$	116.530			0.372301			0.186150	+	0.982521i	$0.440399\pi$
$314$			11.3661i			0.0361978i
$315$		0			0
$316$	41.6966			0.131951
$317$			187.863i			0.592626i	0.955091	+	0.296313i	$0.0957572\pi$
$317$			187.863i			0.592626i	−0.955091	+	0.296313i	$0.904243\pi$
$318$		0			0
$319$	4.71428			0.0147783
$320$	59.7329	+	34.4868i	0.186665	+	0.107771i
$321$		0			0
$322$	86.9221	+	190.241i	0.269945	+	0.590810i
$323$			345.412i			1.06939i
$324$		0			0
$325$	182.348	−	315.835i	0.561069	−	0.971801i
$326$	−329.900	+	190.468i	−1.01196	+	0.584257i
$327$		0			0
$328$	306.974	+	531.694i	0.935895	+	1.62102i
$329$	−171.035	−	121.746i	−0.519863	−	0.370049i
$330$		0			0
$331$	−63.4321			−0.191638			−0.0958189	−	0.995399i	$-0.530547\pi$
$331$	−63.4321			−0.191638			−0.0958189	+	0.995399i	$0.530547\pi$
$332$	142.802	+	82.4466i	0.430125	+	0.248333i
$333$		0			0
$334$	−82.3973	−	142.716i	−0.246698	−	0.427294i
$335$	18.0127	+	10.3996i	0.0537692	+	0.0310437i
$336$		0			0
$337$	88.4049	+	153.122i	0.262329	+	0.454367i	0.966860	−	0.255306i	$-0.0821761\pi$
$337$	88.4049	+	153.122i	0.262329	+	0.454367i	−0.704531	+	0.709673i	$0.748843\pi$
$338$	−86.7688	−	50.0960i	−0.256712	−	0.148213i
$339$		0			0
$340$	−13.4484	−	23.2933i	−0.0395541	−	0.0685097i
$341$	0.569926	−	0.329047i	0.00167134	−	0.000964948i
$342$		0			0
$343$	329.159	+	96.4535i	0.959648	+	0.281206i
$344$	221.301	+	127.768i	0.643316	+	0.371419i
$345$		0			0
$346$	20.4981			0.0592431
$347$			243.303i			0.701161i	0.936533	+	0.350580i	$0.114016\pi$
$347$			243.303i			0.701161i	−0.936533	+	0.350580i	$0.885984\pi$
$348$		0			0
$349$	−209.668	+	363.156i	−0.600768	+	1.04056i	0.391937	+	0.919992i	$0.371805\pi$
$349$	−209.668	+	363.156i	−0.600768	+	1.04056i	−0.992705	+	0.120568i	$0.961528\pi$
$350$	−23.0391	+	241.744i	−0.0658261	+	0.690698i
$351$		0			0
$352$	−3.22722	−	5.58970i	−0.00916823	−	0.0158798i
$353$	301.257	−	173.931i	0.853419	−	0.492722i	−0.00838407	−	0.999965i	$-0.502669\pi$
$353$	301.257	−	173.931i	0.853419	−	0.492722i	0.861803	+	0.507243i	$0.169335\pi$
$354$		0			0
$355$	−42.7720	+	74.0833i	−0.120484	+	0.208685i
$356$	−92.1379	+	53.1958i	−0.258814	+	0.149426i
$357$		0			0
$358$	37.3326	−	64.6620i	0.104281	−	0.180620i
$359$	−392.233	+	226.456i	−1.09257	+	0.630796i	−0.934260	−	0.356593i	$-0.883938\pi$
$359$	−392.233	+	226.456i	−1.09257	+	0.630796i	−0.158311	+	0.987389i	$0.550605\pi$
$360$		0			0
$361$	−195.372	+	338.394i	−0.541196	+	0.937379i
$362$		−	351.415i		−	0.970760i
$363$		0			0
$364$	−198.849	−	18.9511i	−0.546289	−	0.0520634i
$365$	−26.0744	+	15.0541i	−0.0714368	+	0.0412440i
$366$		0			0
$367$	1.59980	+	2.77094i	0.00435913	+	0.00755024i	0.868197	−	0.496220i	$-0.165279\pi$
$367$	1.59980	+	2.77094i	0.00435913	+	0.00755024i	−0.863838	+	0.503770i	$0.831946\pi$
$368$	91.1218	+	52.6092i	0.247613	+	0.142960i
$369$		0			0
$370$	−38.6706			−0.104515
$371$	−666.009	+	304.303i	−1.79517	+	0.820225i
$372$		0			0
$373$	74.7215	−	129.421i	0.200326	−	0.346974i	−0.748308	−	0.663352i	$-0.769133\pi$
$373$	74.7215	−	129.421i	0.200326	−	0.346974i	0.948633	+	0.316377i	$0.102467\pi$
$374$		−	4.45602i		−	0.0119145i
$375$		0			0
$376$	−257.226			−0.684112
$377$		−	300.939i		−	0.798247i
$378$		0			0
$379$	431.217			1.13778			0.568888	−	0.822415i	$-0.307374\pi$
$379$	431.217			1.13778			0.568888	+	0.822415i	$0.307374\pi$
$380$		−	58.5373i		−	0.154045i
$381$		0			0
$382$	−269.428			−0.705308
$383$	155.685	+	89.8850i	0.406489	+	0.234687i	0.689280	−	0.724495i	$-0.257927\pi$
$383$	155.685	+	89.8850i	0.406489	+	0.234687i	−0.282791	+	0.959182i	$0.591260\pi$
$384$		0			0
$385$	−1.12932	+	1.58653i	−0.00293331	+	0.00412086i
$386$			223.931i			0.580133i
$387$		0			0
$388$	137.039	−	237.359i	0.353193	−	0.611749i
$389$	−291.978	+	168.574i	−0.750587	+	0.433352i	−0.825906	−	0.563808i	$-0.809336\pi$
$389$	−291.978	+	168.574i	−0.750587	+	0.433352i	0.0753189	+	0.997159i	$0.476003\pi$
$390$		0			0
$391$	−128.425	−	222.438i	−0.328452	−	0.568896i
$392$	397.091	−	137.597i	1.01299	−	0.351014i
$393$		0			0
$394$	565.712			1.43582
$395$	−22.4733	−	12.9750i	−0.0568945	−	0.0328480i
$396$		0			0
$397$	−266.853	−	462.203i	−0.672174	−	1.16424i	−0.977286	−	0.211923i	$-0.932027\pi$
$397$	−266.853	−	462.203i	−0.672174	−	1.16424i	0.305113	−	0.952316i	$-0.401306\pi$
$398$	−57.9737	−	33.4711i	−0.145663	−	0.0840983i
$399$		0			0
$400$	61.0811	+	105.796i	0.152703	+	0.264489i
$401$	−525.012	−	303.116i	−1.30926	−	0.755900i	−0.327286	−	0.944925i	$-0.606134\pi$
$401$	−525.012	−	303.116i	−1.30926	−	0.755900i	−0.981972	+	0.189025i	$0.939467\pi$
$402$		0			0
$403$	−21.0049	−	36.3816i	−0.0521214	−	0.0902769i
$404$	−134.958	+	77.9180i	−0.334054	+	0.192866i
$405$		0			0
$406$	83.2769	+	182.263i	0.205115	+	0.448923i
$407$	4.78455	+	2.76236i	0.0117556	+	0.00678712i
$408$		0			0
$409$	−392.113			−0.958711			−0.479355	−	0.877621i	$-0.659130\pi$
$409$	−392.113			−0.958711			−0.479355	+	0.877621i	$0.659130\pi$
$410$		−	120.929i		−	0.294949i
$411$		0			0
$412$	−54.6090	+	94.5855i	−0.132546	+	0.229577i
$413$	494.501	+	351.996i	1.19734	+	0.852291i
$414$		0			0
$415$	−51.3107	−	88.8728i	−0.123640	−	0.214151i
$416$	−356.822	+	206.011i	−0.857745	+	0.495220i
$417$		0			0
$418$	4.84897	−	8.39867i	0.0116004	−	0.0200925i
$419$	577.328	−	333.321i	1.37787	−	0.795515i	0.385969	−	0.922512i	$-0.373867\pi$
$419$	577.328	−	333.321i	1.37787	−	0.795515i	0.991903	+	0.126997i	$0.0405338\pi$
$420$		0			0
$421$	235.637	−	408.136i	0.559708	−	0.969443i	−0.437812	−	0.899067i	$-0.644246\pi$
$421$	235.637	−	408.136i	0.559708	−	0.969443i	0.997520	−	0.0703769i	$-0.0224202\pi$
$422$	429.848	−	248.173i	1.01860	−	0.588087i
$423$		0			0
$424$	−448.579	+	776.962i	−1.05797	+	1.83246i
$425$		−	298.211i		−	0.701674i
$426$		0			0
$427$	−72.5995	+	101.991i	−0.170022	+	0.238855i
$428$	−142.491	+	82.2673i	−0.332923	+	0.192213i
$429$		0			0
$430$	−25.1665	−	43.5896i	−0.0585266	−	0.101371i
$431$	−204.379	−	117.998i	−0.474197	−	0.273778i	0.243798	−	0.969826i	$-0.421607\pi$
$431$	−204.379	−	117.998i	−0.474197	−	0.273778i	−0.717995	+	0.696048i	$0.754940\pi$
$432$		0			0
$433$	388.304			0.896776			0.448388	−	0.893839i	$-0.351998\pi$
$433$	388.304			0.896776			0.448388	+	0.893839i	$0.351998\pi$
$434$	22.7892	+	16.2218i	0.0525097	+	0.0373775i
$435$		0			0
$436$	174.958	−	303.036i	0.401280	−	0.695037i
$437$		−	558.999i		−	1.27917i
$438$		0			0
$439$	−351.316			−0.800264			−0.400132	−	0.916458i	$-0.631036\pi$
$439$	−351.316			−0.800264			−0.400132	+	0.916458i	$0.631036\pi$
$440$			2.38605i			0.00542283i
$441$		0			0
$442$	−284.453			−0.643559
$443$		−	53.1399i		−	0.119955i	−0.998200	−	0.0599773i	$-0.980897\pi$
$443$		−	53.1399i		−	0.119955i	0.998200	−	0.0599773i	$-0.0191028\pi$
$444$		0			0
$445$	66.2130			0.148793
$446$	111.355	+	64.2907i	0.249674	+	0.144150i
$447$		0			0
$448$	242.898	−	341.234i	0.542182	−	0.761683i
$449$		−	526.389i		−	1.17236i	−0.810181	−	0.586179i	$-0.800631\pi$
$449$		−	526.389i		−	1.17236i	0.810181	−	0.586179i	$-0.199369\pi$
$450$		0			0
$451$	−8.63832	+	14.9620i	−0.0191537	+	0.0331752i
$452$	−187.283	+	108.128i	−0.414343	+	0.239221i
$453$		0			0
$454$	−258.447	−	447.643i	−0.569266	−	0.985997i
$455$	101.277	+	72.0911i	0.222587	+	0.158442i
$456$		0			0
$457$	−739.761			−1.61873			−0.809367	−	0.587303i	$-0.800190\pi$
$457$	−739.761			−1.61873			−0.809367	+	0.587303i	$0.800190\pi$
$458$	483.300	+	279.033i	1.05524	+	0.609243i
$459$		0			0
$460$	21.7643	+	37.6968i	0.0473136	+	0.0819496i
$461$	−284.624	−	164.328i	−0.617406	−	0.356460i	0.158452	−	0.987367i	$-0.449350\pi$
$461$	−284.624	−	164.328i	−0.617406	−	0.356460i	−0.775858	+	0.630907i	$0.782683\pi$
$462$		0			0
$463$	3.64605	+	6.31515i	0.00787484	+	0.0136396i	0.869936	−	0.493165i	$-0.164160\pi$
$463$	3.64605	+	6.31515i	0.00787484	+	0.0136396i	−0.862061	+	0.506804i	$0.830827\pi$
$464$	87.3004	+	50.4029i	0.188147	+	0.108627i
$465$		0			0
$466$	229.772	+	397.976i	0.493072	+	0.854026i
$467$	446.593	−	257.841i	0.956303	−	0.552122i	0.0612697	−	0.998121i	$-0.480485\pi$
$467$	446.593	−	257.841i	0.956303	−	0.552122i	0.895033	+	0.445999i	$0.147152\pi$
$468$		0			0
$469$	73.2467	−	102.900i	0.156176	−	0.219404i
$470$	43.8779	+	25.3329i	0.0933572	+	0.0538998i
$471$		0			0
$472$	743.700			1.57563
$473$			7.19086i			0.0152027i
$474$		0			0
$475$	324.509	−	562.066i	0.683177	−	1.18330i
$476$	−148.563	+	67.8794i	−0.312107	+	0.142604i
$477$		0			0
$478$	−169.100	−	292.890i	−0.353767	−	0.612742i
$479$	250.854	−	144.830i	0.523703	−	0.302360i	−0.214746	−	0.976670i	$-0.568892\pi$
$479$	250.854	−	144.830i	0.523703	−	0.302360i	0.738448	+	0.674310i	$0.235559\pi$
$480$		0			0
$481$	176.337	−	305.424i	0.366605	−	0.634978i
$482$	−229.543	+	132.527i	−0.476231	+	0.274952i
$483$		0			0
$484$	−112.002	+	193.994i	−0.231410	+	0.400814i
$485$	−147.720	+	85.2864i	−0.304578	+	0.175848i
$486$		0			0
$487$	−252.275	+	436.953i	−0.518018	+	0.897234i	0.481763	+	0.876302i	$0.339997\pi$
$487$	−252.275	+	436.953i	−0.518018	+	0.897234i	−0.999781	+	0.0209323i	$0.993337\pi$
$488$			153.389i			0.314321i
$489$		0			0
$490$	−81.2874	−	15.6360i	−0.165893	−	0.0319102i
$491$	311.614	−	179.910i	0.634651	−	0.366416i	−0.147900	−	0.989002i	$-0.547251\pi$
$491$	311.614	−	179.910i	0.634651	−	0.366416i	0.782551	+	0.622586i	$0.213918\pi$
$492$		0			0
$493$	−123.039	−	213.110i	−0.249572	−	0.432271i
$494$	−536.134	−	309.537i	−1.08529	−	0.626594i
$495$		0			0
$496$	14.0721			0.0283711
$497$	423.213	+	301.252i	0.851535	+	0.606141i
$498$		0			0
$499$	323.521	−	560.354i	0.648338	−	1.12295i	−0.335181	−	0.942154i	$-0.608798\pi$
$499$	323.521	−	560.354i	0.648338	−	1.12295i	0.983520	−	0.180801i	$-0.0578691\pi$
$500$			103.913i			0.207826i
$501$		0			0
$502$	237.220			0.472549
$503$			183.191i			0.364198i	0.983280	+	0.182099i	$0.0582891\pi$
$503$			183.191i			0.364198i	−0.983280	+	0.182099i	$0.941711\pi$
$504$		0			0
$505$	96.9847			0.192049
$506$			7.21143i			0.0142518i
$507$		0			0
$508$	−62.1269			−0.122297
$509$	751.000	+	433.590i	1.47544	+	0.851846i	0.999616	−	0.0276937i	$-0.00881632\pi$
$509$	751.000	+	433.590i	1.47544	+	0.851846i	0.475825	+	0.879540i	$0.342150\pi$
$510$		0			0
$511$	75.9839	+	166.301i	0.148696	+	0.325442i
$512$		−	315.064i		−	0.615359i
$513$		0			0
$514$	55.4523	−	96.0462i	0.107884	−	0.186860i
$515$	58.8654	−	33.9860i	0.114302	−	0.0659922i
$516$		0			0
$517$	−3.61921	−	6.26865i	−0.00700040	−	0.0121251i
$518$	−22.2797	+	233.776i	−0.0430110	+	0.451304i
$519$		0			0
$520$	152.315			0.292913
$521$	−60.2047	−	34.7592i	−0.115556	−	0.0667163i	0.441108	−	0.897454i	$-0.354586\pi$
$521$	−60.2047	−	34.7592i	−0.115556	−	0.0667163i	−0.556664	+	0.830738i	$0.687919\pi$
$522$		0			0
$523$	−356.425	−	617.347i	−0.681502	−	1.18040i	−0.974523	−	0.224290i	$-0.927994\pi$
$523$	−356.425	−	617.347i	−0.681502	−	1.18040i	0.293021	−	0.956106i	$-0.405339\pi$
$524$	114.686	+	66.2137i	0.218866	+	0.126362i
$525$		0			0
$526$	−8.53426	−	14.7818i	−0.0162248	−	0.0281022i
$527$	−29.7493	−	17.1757i	−0.0564502	−	0.0325915i
$528$		0			0
$529$	−56.6631	−	98.1434i	−0.107114	−	0.185526i
$530$	153.038	−	88.3566i	0.288751	−	0.166711i
$531$		0			0
$532$	−353.876	−	33.7257i	−0.665180	−	0.0633941i
$533$	955.109	+	551.432i	1.79195	+	1.03458i
$534$		0			0
$535$	102.398			0.191399
$536$		−	154.756i		−	0.288724i
$537$		0			0
$538$	−225.052	+	389.801i	−0.418312	+	0.724537i
$539$	8.94040	+	7.74117i	0.0165870	+	0.0143621i
$540$		0			0
$541$	180.101	+	311.944i	0.332904	+	0.576607i	0.983080	−	0.183177i	$-0.0586381\pi$
$541$	180.101	+	311.944i	0.332904	+	0.576607i	−0.650176	+	0.759784i	$0.725305\pi$
$542$	−429.088	+	247.734i	−0.791676	+	0.457074i
$543$		0			0
$544$	−168.456	+	291.774i	−0.309661	+	0.536349i
$545$	−188.595	+	108.885i	−0.346046	+	0.199790i
$546$		0			0
$547$	−47.0212	+	81.4432i	−0.0859620	+	0.148891i	−0.905801	−	0.423704i	$-0.860730\pi$
$547$	−47.0212	+	81.4432i	−0.0859620	+	0.148891i	0.819839	+	0.572595i	$0.194063\pi$
$548$	347.695	−	200.742i	0.634479	−	0.366317i
$549$		0			0
$550$	−4.18636	+	7.25099i	−0.00761157	+	0.0131836i
$551$		−	535.556i		−	0.971972i
$552$		0			0
$553$	−91.3854	+	128.383i	−0.165254	+	0.232157i
$554$	−167.562	+	96.7422i	−0.302459	+	0.174625i
$555$		0			0
$556$	99.4676	+	172.283i	0.178899	+	0.309861i
$557$	−516.609	−	298.264i	−0.927484	−	0.535483i	−0.0414691	−	0.999140i	$-0.513204\pi$
$557$	−516.609	−	298.264i	−0.927484	−	0.535483i	−0.886015	+	0.463657i	$0.846537\pi$
$558$		0			0
$559$	459.033			0.821168
$560$	−37.8756	+	17.3056i	−0.0676350	+	0.0309028i
$561$		0			0
$562$	−54.3922	+	94.2101i	−0.0967833	+	0.167634i
$563$		−	724.219i		−	1.28636i	−0.765716	−	0.643179i	$-0.777615\pi$
$563$		−	724.219i		−	1.28636i	0.765716	−	0.643179i	$-0.222385\pi$
$564$		0			0
$565$	134.587			0.238207
$566$		−	16.5652i		−	0.0292671i
$567$		0			0
$568$	636.487			1.12058
$569$		−	328.919i		−	0.578065i	−0.957319	−	0.289032i	$-0.906666\pi$
$569$		−	328.919i		−	0.578065i	0.957319	−	0.289032i	$-0.0933335\pi$
$570$		0			0
$571$	7.51403			0.0131594			0.00657971	−	0.999978i	$-0.497906\pi$
$571$	7.51403			0.0131594			0.00657971	+	0.999978i	$0.497906\pi$
$572$	−5.96438	−	3.44354i	−0.0104272	−	0.00602017i
$573$		0			0
$574$	−731.052	−	69.6720i	−1.27361	−	0.121380i
$575$			482.612i			0.839325i
$576$		0			0
$577$	−367.284	+	636.154i	−0.636540	+	1.10252i	0.349647	+	0.936882i	$0.386302\pi$
$577$	−367.284	+	636.154i	−0.636540	+	1.10252i	−0.986187	+	0.165638i	$0.947032\pi$
$578$	165.364	−	95.4729i	0.286097	−	0.165178i
$579$		0			0
$580$	20.8515	+	36.1159i	0.0359509	+	0.0622688i
$581$	−566.825	+	258.986i	−0.975602	+	0.445758i
$582$		0			0
$583$	−25.2463			−0.0433041
$584$	194.006	+	112.009i	0.332202	+	0.191797i
$585$		0			0
$586$	121.954	+	211.230i	0.208112	+	0.360461i
$587$	−125.855	−	72.6624i	−0.214404	−	0.123786i	0.388953	−	0.921258i	$-0.372837\pi$
$587$	−125.855	−	72.6624i	−0.214404	−	0.123786i	−0.603356	+	0.797472i	$0.706170\pi$
$588$		0			0
$589$	−37.3807	−	64.7453i	−0.0634647	−	0.109924i
$590$	−126.861	−	73.2432i	−0.215019	−	0.124141i
$591$		0			0
$592$	59.0677	+	102.308i	0.0997765	+	0.172818i
$593$	−248.428	+	143.430i	−0.418934	+	0.241872i	−0.694621	−	0.719376i	$-0.744428\pi$
$593$	−248.428	+	143.430i	−0.418934	+	0.241872i	0.275687	+	0.961247i	$0.411095\pi$
$594$		0			0
$595$	101.194	+	9.64414i	0.170074	+	0.0162086i
$596$	−251.974	−	145.477i	−0.422776	−	0.244090i
$597$		0			0
$598$	460.346			0.769809
$599$			699.608i			1.16796i	0.811768	+	0.583980i	$0.198505\pi$
$599$			699.608i			1.16796i	−0.811768	+	0.583980i	$0.801495\pi$
$600$		0			0
$601$	58.2075	−	100.818i	0.0968511	−	0.167751i	−0.813529	−	0.581525i	$-0.802456\pi$
$601$	58.2075	−	100.818i	0.0968511	−	0.167751i	0.910380	+	0.413774i	$0.135790\pi$
$602$	−278.012	+	127.025i	−0.461813	+	0.211005i
$603$		0			0
$604$	111.577	+	193.257i	0.184730	+	0.319962i
$605$	120.732	−	69.7048i	0.199558	−	0.115215i
$606$		0			0
$607$	−321.155	+	556.257i	−0.529086	+	0.916404i	0.470339	+	0.882486i	$0.344132\pi$
$607$	−321.155	+	556.257i	−0.529086	+	0.916404i	−0.999425	+	0.0339178i	$0.989202\pi$
$608$	−635.007	+	366.621i	−1.04442	+	0.602996i
$609$		0			0
$610$	15.1065	−	26.1652i	0.0247647	−	0.0428937i
$611$	−400.163	+	231.034i	−0.654932	+	0.378125i
$612$		0			0
$613$	257.842	−	446.595i	0.420623	−	0.728540i	−0.575378	−	0.817888i	$-0.695145\pi$
$613$	257.842	−	446.595i	0.420623	−	0.728540i	0.996000	+	0.0893481i	$0.0284783\pi$
$614$		−	561.278i		−	0.914133i
$615$		0			0
$616$	14.4244	+	1.37470i	0.0234162	+	0.00223165i
$617$	−352.937	+	203.768i	−0.572021	+	0.330257i	−0.757956	−	0.652305i	$-0.773802\pi$
$617$	−352.937	+	203.768i	−0.572021	+	0.330257i	0.185935	+	0.982562i	$0.440469\pi$
$618$		0			0
$619$	21.1760	+	36.6779i	0.0342100	+	0.0592535i	0.882624	−	0.470081i	$-0.155775\pi$
$619$	21.1760	+	36.6779i	0.0342100	+	0.0592535i	−0.848413	+	0.529334i	$0.822442\pi$
$620$	5.04163	+	2.91079i	0.00813167	+	0.00469482i
$621$		0			0
$622$	228.641			0.367590
$623$	38.1479	−	400.277i	0.0612326	−	0.642500i
$624$		0			0
$625$	−263.556	+	456.492i	−0.421689	+	0.730387i
$626$			170.780i			0.272812i
$627$		0			0
$628$	14.3646			0.0228736
$629$		−	288.382i		−	0.458476i
$630$		0			0
$631$	−534.410			−0.846926			−0.423463	−	0.905914i	$-0.639186\pi$
$631$	−534.410			−0.846926			−0.423463	+	0.905914i	$0.639186\pi$
$632$			193.080i			0.305506i
$633$		0			0
$634$	−275.321			−0.434261
$635$	33.4847	+	19.3324i	0.0527318	+	0.0304447i
$636$		0			0
$637$	494.162	−	570.716i	0.775765	−	0.895943i
$638$			6.90900i			0.0108292i
$639$		0			0
$640$	11.1117	−	19.2461i	0.0173621	−	0.0300720i
$641$	303.746	−	175.368i	0.473862	−	0.273584i	−0.243993	−	0.969777i	$-0.578457\pi$
$641$	303.746	−	175.368i	0.473862	−	0.273584i	0.717855	+	0.696193i	$0.245124\pi$
$642$		0			0
$643$	−329.068	−	569.963i	−0.511770	−	0.886412i	−0.999907	−	0.0136450i	$-0.995657\pi$
$643$	−329.068	−	569.963i	−0.511770	−	0.886412i	0.488137	−	0.872767i	$-0.337677\pi$
$644$	240.428	−	109.853i	0.373335	−	0.170579i
$645$		0			0
$646$	−506.218			−0.783619
$647$	−482.718	−	278.697i	−0.746087	−	0.430753i	0.0781915	−	0.996938i	$-0.475085\pi$
$647$	−482.718	−	278.697i	−0.746087	−	0.430753i	−0.824278	+	0.566185i	$0.808419\pi$
$648$		0			0
$649$	10.4640	+	18.1241i	0.0161232	+	0.0279262i
$650$	462.871	+	267.239i	0.712110	+	0.411137i
$651$		0			0
$652$	240.715	+	416.930i	0.369194	+	0.639464i
$653$	−158.002	−	91.2224i	−0.241963	−	0.139697i	0.374116	−	0.927382i	$-0.377946\pi$
$653$	−158.002	−	91.2224i	−0.241963	−	0.139697i	−0.616079	+	0.787685i	$0.711280\pi$
$654$		0			0
$655$	−41.2082	−	71.3747i	−0.0629133	−	0.108969i
$656$	−319.934	+	184.714i	−0.487704	+	0.281576i
$657$		0			0
$658$	178.425	−	250.660i	0.271162	−	0.380942i
$659$	10.7149	+	6.18625i	0.0162593	+	0.00938733i	0.508108	−	0.861294i	$-0.330345\pi$
$659$	10.7149	+	6.18625i	0.0162593	+	0.00938733i	−0.491848	+	0.870681i	$0.663679\pi$
$660$		0			0
$661$	−531.258			−0.803719			−0.401860	−	0.915701i	$-0.631636\pi$
$661$	−531.258			−0.803719			−0.401860	+	0.915701i	$0.631636\pi$
$662$		−	92.9628i		−	0.140427i
$663$		0			0
$664$	−381.776	+	661.255i	−0.574963	+	0.995866i
$665$	180.234	+	128.295i	0.271029	+	0.192924i
$666$		0			0
$667$	199.121	+	344.887i	0.298532	+	0.517072i
$668$	−180.366	+	104.134i	−0.270009	+	0.155890i
$669$		0			0
$670$	−15.2411	+	26.3984i	−0.0227480	+	0.0394006i
$671$	−3.73811	+	2.15820i	−0.00557096	+	0.00321639i
$672$		0			0
$673$	−29.8818	+	51.7568i	−0.0444009	+	0.0769046i	−0.887372	−	0.461055i	$-0.847471\pi$
$673$	−29.8818	+	51.7568i	−0.0444009	+	0.0769046i	0.842971	+	0.537959i	$0.180805\pi$
$674$	−224.407	+	129.561i	−0.332948	+	0.192228i
$675$		0			0
$676$	−63.3117	+	109.659i	−0.0936564	+	0.162218i
$677$			920.447i			1.35960i	0.733399	+	0.679799i	$0.237933\pi$
$677$			920.447i			1.35960i	−0.733399	+	0.679799i	$0.762067\pi$
$678$		0			0
$679$	430.475	+	942.151i	0.633983	+	1.38756i
$680$	107.862	−	62.2739i	0.158620	−	0.0915793i
$681$		0			0
$682$	0.482234	+	0.835254i	0.000707088	+	0.00122471i
$683$	487.711	+	281.580i	0.714071	+	0.412269i	0.812567	−	0.582868i	$-0.198070\pi$
$683$	487.711	+	281.580i	0.714071	+	0.412269i	−0.0984954	+	0.995138i	$0.531403\pi$
$684$		0			0
$685$	−249.864			−0.364764
$686$	−141.357	+	482.398i	−0.206060	+	0.703204i
$687$		0			0
$688$	−76.8813	+	133.162i	−0.111746	+	0.193550i
$689$			1611.61i			2.33906i
$690$		0			0
$691$	421.308			0.609708			0.304854	−	0.952399i	$-0.401392\pi$
$691$	421.308			0.609708			0.304854	+	0.952399i	$0.401392\pi$
$692$		−	25.9057i		−	0.0374360i
$693$		0			0
$694$	−356.572			−0.513792
$695$		−	123.808i		−	0.178140i
$696$		0			0
$697$	901.813			1.29385
$698$	−532.222	−	307.278i	−0.762495	−	0.440227i
$699$		0			0
$700$	305.518	+	29.1170i	0.436455	+	0.0415958i
$701$		−	523.850i		−	0.747289i	−0.927572	−	0.373645i	$-0.878108\pi$
$701$		−	523.850i		−	0.747289i	0.927572	−	0.373645i	$-0.121892\pi$
$702$		0			0
$703$	313.812	−	543.539i	0.446390	−	0.773170i
$704$	12.5067	−	7.22073i	0.0177652	−	0.0102567i
$705$		0			0
$706$	254.904	+	441.506i	0.361053	+	0.625363i
$707$	55.8767	−	586.302i	0.0790336	−	0.829281i
$708$		0			0
$709$	67.9357			0.0958190			0.0479095	−	0.998852i	$-0.484744\pi$
$709$	67.9357			0.0958190			0.0479095	+	0.998852i	$0.484744\pi$
$710$	−108.573	−	62.6844i	−0.152919	−	0.0882878i
$711$		0			0
$712$	−246.328	−	426.652i	−0.345966	−	0.599230i
$713$	48.1449	+	27.7964i	0.0675243	+	0.0389852i
$714$		0			0
$715$	2.14309	+	3.71194i	0.00299733	+	0.00519152i
$716$	−81.7204	−	47.1813i	−0.114135	−	0.0658957i
$717$		0			0
$718$	−331.882	−	574.836i	−0.462231	−	0.800607i
$719$	−766.286	+	442.415i	−1.06577	+	0.615321i	−0.927022	−	0.375008i	$-0.877640\pi$
$719$	−766.286	+	442.415i	−1.06577	+	0.615321i	−0.138745	+	0.990328i	$0.544307\pi$
$720$		0			0
$721$	−171.541	−	375.440i	−0.237921	−	0.520721i
$722$	−495.932	−	286.327i	−0.686887	−	0.396574i
$723$		0			0
$724$	−444.121			−0.613427
$725$			462.373i			0.637755i
$726$		0			0
$727$	−228.413	+	395.623i	−0.314186	+	0.544186i	−0.979264	−	0.202588i	$-0.935065\pi$
$727$	−228.413	+	395.623i	−0.314186	+	0.544186i	0.665078	+	0.746774i	$0.268398\pi$
$728$	87.7545	−	920.788i	0.120542	−	1.26482i
$729$		0			0
$730$	−22.0625	−	38.2133i	−0.0302225	−	0.0523470i
$731$	325.064	−	187.676i	0.444684	−	0.256738i
$732$		0			0
$733$	52.6692	−	91.2258i	0.0718543	−	0.124455i	−0.827860	−	0.560935i	$-0.810442\pi$
$733$	52.6692	−	91.2258i	0.0718543	−	0.124455i	0.899714	+	0.436480i	$0.143775\pi$
$734$	−4.06094	+	2.34458i	−0.00553261	+	0.00319426i
$735$		0			0
$736$	272.621	−	472.193i	0.370409	−	0.641567i
$737$	3.77144	−	2.17744i	0.00511728	−	0.00295446i
$738$		0			0
$739$	169.442	−	293.482i	0.229285	−	0.397133i	−0.728311	−	0.685246i	$-0.759695\pi$
$739$	169.442	−	293.482i	0.229285	−	0.397133i	0.957596	+	0.288113i	$0.0930279\pi$
$740$			48.8723i			0.0660436i
$741$		0			0
$742$	−445.971	−	976.068i	−0.601039	−	1.31545i
$743$	−200.529	+	115.776i	−0.269891	+	0.155822i	−0.628838	−	0.777536i	$-0.716469\pi$
$743$	−200.529	+	115.776i	−0.269891	+	0.155822i	0.358947	+	0.933358i	$0.383136\pi$
$744$		0			0
$745$	90.5381	+	156.817i	0.121528	+	0.210492i
$746$	189.673	+	109.508i	0.254254	+	0.146793i
$747$		0			0
$748$	−5.63156			−0.00752883
$749$	58.9957	−	619.029i	0.0787660	−	0.826474i
$750$		0			0
$751$	61.2911	−	106.159i	0.0816127	−	0.141357i	−0.822330	−	0.569011i	$-0.807326\pi$
$751$	61.2911	−	106.159i	0.0816127	−	0.141357i	0.903943	+	0.427653i	$0.140660\pi$
$752$		−	154.780i		−	0.205824i
$753$		0			0
$754$	441.040			0.584934
$755$		−	138.880i		−	0.183947i
$756$		0			0
$757$	162.273			0.214363			0.107181	−	0.994239i	$-0.465817\pi$
$757$	162.273			0.214363			0.107181	+	0.994239i	$0.465817\pi$
$758$			631.969i			0.833732i
$759$		0			0
$760$	271.062			0.356660
$761$	−301.090	−	173.834i	−0.395650	−	0.228429i	0.288955	−	0.957343i	$-0.406692\pi$
$761$	−301.090	−	173.834i	−0.395650	−	0.228429i	−0.684605	+	0.728914i	$0.740025\pi$
$762$		0			0
$763$	549.587	+	1202.85i	0.720298	+	1.57647i
$764$			340.505i			0.445687i
$765$		0			0
$766$	−131.731	+	228.164i	−0.171972	+	0.297865i
$767$	1156.96	−	667.973i	1.50843	−	0.870891i
$768$		0			0
$769$	21.9448	+	38.0094i	0.0285367	+	0.0494271i	0.879941	−	0.475083i	$-0.157582\pi$
$769$	21.9448	+	38.0094i	0.0285367	+	0.0494271i	−0.851404	+	0.524510i	$0.824249\pi$
$770$	−2.32513	−	1.65508i	−0.00301965	−	0.00214945i
$771$		0			0
$772$	283.006			0.366588
$773$	31.3486	+	18.0991i	0.0405545	+	0.0234141i	0.520140	−	0.854081i	$-0.325880\pi$
$773$	31.3486	+	18.0991i	0.0405545	+	0.0234141i	−0.479586	+	0.877495i	$0.659213\pi$
$774$		0			0
$775$	32.2727	+	55.8979i	0.0416421	+	0.0721263i
$776$	1099.11	+	634.571i	1.41638	+	0.817746i
$777$		0			0
$778$	−247.053	−	427.908i	−0.317549	−	0.550010i
$779$	1699.73	+	981.339i	2.18194	+	1.25974i
$780$		0			0
$781$	8.95546	+	15.5113i	0.0114667	+	0.0198608i
$782$	325.994	−	188.213i	0.416872	−	0.240681i
$783$		0			0
$784$	82.7958	+	238.940i	0.105607	+	0.304770i
$785$	−7.74211	−	4.46991i	−0.00986256	−	0.00569415i
$786$		0			0
$787$	−669.648			−0.850887			−0.425443	−	0.904985i	$-0.639882\pi$
$787$	−669.648			−0.850887			−0.425443	+	0.904985i	$0.639882\pi$
$788$		−	714.951i		−	0.907299i
$789$		0			0
$790$	19.0154	−	32.9357i	0.0240702	−	0.0416908i
$791$	77.5410	−	813.620i	0.0980291	−	1.02860i
$792$		0			0
$793$	137.770	+	238.625i	0.173733	+	0.300914i
$794$	677.380	−	391.086i	0.853124	−	0.492551i
$795$		0			0
$796$	−42.3011	+	73.2677i	−0.0531421	+	0.0920448i
$797$	−12.4445	+	7.18485i	−0.0156142	+	0.00901487i	−0.507787	−	0.861483i	$-0.669536\pi$
$797$	−12.4445	+	7.18485i	−0.0156142	+	0.00901487i	0.492173	+	0.870498i	$0.336203\pi$
$798$		0			0
$799$	−188.917	+	327.214i	−0.236442	+	0.409529i
$800$	548.233	−	316.523i	0.685291	−	0.395653i
$801$		0			0
$802$	444.231	−	769.431i	0.553904	−	0.959390i
$803$			6.30395i			0.00785049i
$804$		0			0
$805$	−163.767	−	15.6076i	−0.203438	−	0.0193884i
$806$	53.3190	−	30.7837i	0.0661526	−	0.0381932i
$807$		0			0
$808$	−360.806	−	624.934i	−0.446542	−	0.773433i
$809$	−134.305	−	77.5408i	−0.166013	−	0.0958478i	0.414691	−	0.909962i	$-0.363890\pi$
$809$	−134.305	−	77.5408i	−0.166013	−	0.0958478i	−0.580705	+	0.814114i	$0.697223\pi$
$810$		0			0
$811$	−758.588			−0.935374			−0.467687	−	0.883894i	$-0.654913\pi$
$811$	−758.588			−0.935374			−0.467687	+	0.883894i	$0.654913\pi$
$812$	230.345	−	105.246i	0.283676	−	0.129613i
$813$		0			0
$814$	−4.04837	+	7.01198i	−0.00497343	+	0.00861422i
$815$		−	299.618i		−	0.367630i
$816$		0			0
$817$	816.903			0.999881
$818$		−	574.660i		−	0.702518i
$819$		0			0
$820$	−152.831			−0.186379
$821$		−	225.364i		−	0.274500i	−0.990536	−	0.137250i	$-0.956174\pi$
$821$		−	225.364i		−	0.274500i	0.990536	−	0.137250i	$-0.0438263\pi$
$822$		0			0
$823$	599.694			0.728668			0.364334	−	0.931268i	$-0.381297\pi$
$823$	599.694			0.728668			0.364334	+	0.931268i	$0.381297\pi$
$824$	−437.986	−	252.871i	−0.531537	−	0.306883i
$825$		0			0
$826$	−515.867	+	724.714i	−0.624536	+	0.877378i
$827$		−	634.083i		−	0.766727i	−0.923598	−	0.383363i	$-0.874766\pi$
$827$		−	634.083i		−	0.766727i	0.923598	−	0.383363i	$-0.125234\pi$
$828$		0			0
$829$	−376.723	+	652.503i	−0.454431	+	0.787097i	−0.998655	−	0.0518425i	$-0.983491\pi$
$829$	−376.723	+	652.503i	−0.454431	+	0.787097i	0.544225	+	0.838940i	$0.316824\pi$
$830$	130.247	−	75.1983i	0.156924	−	0.0906003i
$831$		0			0
$832$	−460.940	−	798.371i	−0.554014	−	0.959581i
$833$	116.604	−	606.191i	0.139980	−	0.727720i
$834$		0			0
$835$	129.616			0.155229
$836$	−10.6143	−	6.12817i	−0.0126965	−	0.00733035i
$837$		0			0
$838$	488.497	+	846.102i	0.582932	+	1.00967i
$839$	−953.473	−	550.488i	−1.13644	−	0.656124i	−0.190893	−	0.981611i	$-0.561138\pi$
$839$	−953.473	−	550.488i	−1.13644	−	0.656124i	−0.945547	+	0.325487i	$0.894472\pi$
$840$		0			0
$841$	−229.730	−	397.904i	−0.273163	−	0.473132i
$842$	598.142	+	345.338i	0.710383	+	0.410140i
$843$		0			0
$844$	−313.643	−	543.246i	−0.371615	−	0.643656i
$845$	68.2465	−	39.4021i	0.0807651	−	0.0466297i
$846$		0			0
$847$	−351.828	−	770.023i	−0.415381	−	0.909118i
$848$	−467.518	−	269.922i	−0.551318	−	0.318304i
$849$		0			0
$850$	437.043			0.514168
$851$			466.704i			0.548418i
$852$		0			0
$853$	161.623	−	279.939i	0.189476	−	0.328181i	−0.755600	−	0.655033i	$-0.772655\pi$
$853$	161.623	−	279.939i	0.189476	−	0.328181i	0.945076	+	0.326852i	$0.105988\pi$
$854$	−149.473	−	106.398i	−0.175027	−	0.124588i
$855$		0			0
$856$	−380.946	−	659.817i	−0.445030	−	0.770815i
$857$	−1128.73	+	651.675i	−1.31708	+	0.760414i	−0.983257	−	0.182224i	$-0.941671\pi$
$857$	−1128.73	+	651.675i	−1.31708	+	0.760414i	−0.333818	+	0.942637i	$0.608337\pi$
$858$		0			0
$859$	87.8268	−	152.121i	0.102243	−	0.177090i	−0.810365	−	0.585925i	$-0.800731\pi$
$859$	87.8268	−	152.121i	0.102243	−	0.177090i	0.912609	+	0.408835i	$0.134065\pi$
$860$	−55.0889	+	31.8056i	−0.0640568	+	0.0369832i
$861$		0			0
$862$	172.932	−	299.527i	0.200617	−	0.347479i
$863$	−289.608	+	167.205i	−0.335582	+	0.193749i	−0.658317	−	0.752741i	$-0.728731\pi$
$863$	−289.608	+	167.205i	−0.335582	+	0.193749i	0.322734	+	0.946490i	$0.395398\pi$
$864$		0			0
$865$	−8.06122	+	13.9624i	−0.00931933	+	0.0161416i
$866$			569.078i			0.657134i
$867$		0			0
$868$	20.5013	−	28.8012i	0.0236190	−	0.0331811i
$869$	−4.70539	+	2.71666i	−0.00541472	+	0.00312619i
$870$		0			0
$871$	−138.998	−	240.752i	−0.159585	−	0.276409i
$872$	1403.23	+	810.157i	1.60921	+	0.929080i
$873$		0			0
$874$	819.240			0.937345
$875$	−319.945	−	227.744i	−0.365652	−	0.260279i
$876$		0			0
$877$	−395.615	+	685.225i	−0.451100	+	0.781328i	−0.998455	−	0.0555725i	$-0.982302\pi$
$877$	−395.615	+	685.225i	−0.451100	+	0.781328i	0.547355	+	0.836901i	$0.315635\pi$
$878$		−	514.870i		−	0.586412i
$879$		0			0
$880$	−1.43574			−0.00163153
$881$			307.622i			0.349174i	0.984642	+	0.174587i	$0.0558591\pi$
$881$			307.622i			0.349174i	−0.984642	+	0.174587i	$0.944141\pi$
$882$		0			0
$883$	−1744.35			−1.97548			−0.987742	−	0.156094i	$-0.950110\pi$
$883$	−1744.35			−1.97548			−0.987742	+	0.156094i	$0.950110\pi$
$884$			359.494i			0.406668i
$885$		0			0
$886$	77.8791			0.0878996
$887$	−152.854	−	88.2501i	−0.172327	−	0.0994928i	0.411356	−	0.911475i	$-0.365055\pi$
$887$	−152.854	−	88.2501i	−0.172327	−	0.0994928i	−0.583682	+	0.811982i	$0.698389\pi$
$888$		0			0
$889$	136.162	−	191.287i	0.153163	−	0.215171i
$890$			97.0382i			0.109032i
$891$		0			0
$892$	81.2511	−	140.731i	0.0910887	−	0.157770i
$893$	−712.138	+	411.153i	−0.797466	+	0.460417i
$894$		0			0
$895$	29.3634	+	50.8588i	0.0328082	+	0.0568255i
$896$	−109.946	−	78.2622i	−0.122708	−	0.0873462i
$897$		0			0
$898$	771.448			0.859074
$899$	46.1258	+	26.6307i	0.0513079	+	0.0296226i
$900$		0			0
$901$	658.908	+	1141.26i	0.731308	+	1.26666i
$902$	−21.9275	−	12.6599i	−0.0243099	−	0.0140353i
$903$		0			0
$904$	−500.696	−	867.230i	−0.553867	−	0.959325i
$905$	239.369	+	138.200i	0.264496	+	0.152707i
$906$		0			0
$907$	−847.482	−	1467.88i	−0.934379	−	1.61839i	−0.775737	−	0.631056i	$-0.782622\pi$
$907$	−847.482	−	1467.88i	−0.934379	−	1.61839i	−0.158642	−	0.987336i	$-0.550711\pi$
$908$	−565.735	+	326.627i	−0.623056	+	0.359721i
$909$		0			0
$910$	−105.653	+	148.426i	−0.116102	+	0.163106i
$911$	−893.443	−	515.830i	−0.980728	−	0.566224i	−0.0782381	−	0.996935i	$-0.524929\pi$
$911$	−893.443	−	515.830i	−0.980728	−	0.566224i	−0.902490	+	0.430711i	$0.858263\pi$
$912$		0			0
$913$	−21.4865			−0.0235340
$914$		−	1084.16i		−	1.18617i
$915$		0			0
$916$	352.645	−	610.798i	0.384983	−	0.666811i
$917$	−455.223	+	207.994i	−0.496427	+	0.226820i
$918$		0			0
$919$	362.145	+	627.254i	0.394064	+	0.682539i	0.992981	−	0.118272i	$-0.0377354\pi$
$919$	362.145	+	627.254i	0.394064	+	0.682539i	−0.598917	+	0.800811i	$0.704402\pi$
$920$	−174.558	+	100.781i	−0.189737	+	0.109545i
$921$		0			0
$922$	240.830	−	417.130i	0.261204	−	0.452419i
$923$	990.174	−	571.677i	1.07278	−	0.619369i
$924$		0			0
$925$	−270.930	+	469.264i	−0.292897	+	0.507312i
$926$	−9.25515	+	5.34346i	−0.00999476	+	0.00577048i
$927$		0			0
$928$	261.188	−	452.391i	0.281453	−	0.487490i
$929$			1463.68i			1.57555i	0.615966	+	0.787773i	$0.288766\pi$
$929$			1463.68i			1.57555i	−0.615966	+	0.787773i	$0.711234\pi$
$930$		0			0
$931$	879.420	−	1015.66i	0.944597	−	1.09093i
$932$	502.966	−	290.387i	0.539663	−	0.311575i
$933$		0			0
$934$	377.878	+	654.504i	0.404580	+	0.700754i
$935$	3.03525	+	1.75240i	0.00324626	+	0.00187423i
$936$		0			0
$937$	282.325			0.301308			0.150654	−	0.988587i	$-0.451862\pi$
$937$	282.325			0.301308			0.150654	+	0.988587i	$0.451862\pi$
$938$	150.805	+	107.346i	0.160773	+	0.114442i
$939$		0			0
$940$	32.0159	−	55.4532i	0.0340595	−	0.0589928i
$941$			294.458i			0.312921i	0.987684	+	0.156460i	$0.0500083\pi$
$941$			294.458i			0.312921i	−0.987684	+	0.156460i	$0.949992\pi$
$942$		0			0
$943$	−1459.45			−1.54767
$944$			447.503i			0.474050i
$945$		0			0
$946$	−10.5385			−0.0111401
$947$		−	882.114i		−	0.931482i	−0.884921	−	0.465741i	$-0.845788\pi$
$947$		−	882.114i		−	0.931482i	0.884921	−	0.465741i	$-0.154212\pi$
$948$		0			0
$949$	402.416			0.424042
$950$	823.734	+	475.583i	0.867089	+	0.500614i
$951$		0			0
$952$	−314.321	−	687.934i	−0.330169	−	0.722620i
$953$			347.203i			0.364326i	0.983268	+	0.182163i	$0.0583099\pi$
$953$			347.203i			0.364326i	−0.983268	+	0.182163i	$0.941690\pi$
$954$		0			0
$955$	105.957	−	183.523i	0.110950	−	0.192170i
$956$	−370.157	+	213.711i	−0.387194	+	0.223547i
$957$		0			0
$958$	212.256	+	367.638i	0.221561	+	0.383756i
$959$	−143.956	+	1510.50i	−0.150111	+	1.57508i
$960$		0			0
$961$	−953.565			−0.992263
$962$	447.614	+	258.430i	0.465295	+	0.268638i
$963$		0			0
$964$	167.489	+	290.099i	0.173743	+	0.300932i
$965$	−152.532	−	88.0647i	−0.158065	−	0.0912587i
$966$		0			0
$967$	774.207	+	1340.97i	0.800627	+	1.38673i	0.919204	+	0.393782i	$0.128834\pi$
$967$	774.207	+	1340.97i	0.800627	+	1.38673i	−0.118577	+	0.992945i	$0.537833\pi$
$968$	−898.305	−	518.637i	−0.928001	−	0.535782i
$969$		0			0
$970$	−124.991	−	216.491i	−0.128857	−	0.223187i
$971$	859.844	−	496.431i	0.885525	−	0.511258i	0.0130486	−	0.999915i	$-0.495846\pi$
$971$	859.844	−	496.431i	0.885525	−	0.511258i	0.872476	+	0.488657i	$0.162513\pi$
$972$		0			0
$973$	−748.454	−	71.3304i	−0.769223	−	0.0733098i
$974$	−640.375	−	369.721i	−0.657470	−	0.379590i
$975$		0			0
$976$	−92.2978			−0.0945675
$977$		−	238.021i		−	0.243625i	−0.992553	−	0.121812i	$-0.961129\pi$
$977$		−	238.021i		−	0.243625i	0.992553	−	0.121812i	$-0.0388706\pi$
$978$		0			0
$979$	6.93173	−	12.0061i	0.00708042	−	0.0122636i
$980$	−19.7609	+	102.732i	−0.0201642	+	0.104828i
$981$		0			0
$982$	263.667	+	456.685i	0.268500	+	0.465056i
$983$	−548.070	+	316.428i	−0.557548	+	0.321901i	−0.752161	−	0.658980i	$-0.770988\pi$
$983$	−548.070	+	316.428i	−0.557548	+	0.321901i	0.194613	+	0.980880i	$0.437655\pi$
$984$		0			0
$985$	−222.475	+	385.339i	−0.225863	+	0.391207i
$986$	312.323	−	180.320i	0.316757	−	0.182880i
$987$		0			0
$988$	−391.196	+	677.571i	−0.395947	+	0.685801i
$989$	−526.069	+	303.726i	−0.531920	+	0.307104i
$990$		0			0
$991$	589.789	−	1021.54i	0.595145	−	1.03082i	−0.398381	−	0.917220i	$-0.630428\pi$
$991$	589.789	−	1021.54i	0.595145	−	1.03082i	0.993526	−	0.113602i	$-0.0362389\pi$
$992$		−	72.9215i		−	0.0735096i
$993$		0			0
$994$	−441.499	+	620.239i	−0.444164	+	0.623983i
$995$	45.5982	−	26.3261i	0.0458274	−	0.0264584i
$996$		0			0
$997$	746.149	+	1292.37i	0.748394	+	1.29626i	0.948592	+	0.316501i	$0.102508\pi$
$997$	746.149	+	1292.37i	0.748394	+	1.29626i	−0.200198	+	0.979755i	$0.564159\pi$
$998$	821.226	+	474.135i	0.822872	+	0.475085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.b.116.8		22
3.2	odd	2		63.3.j.b.11.4	✓	22
7.2	even	3		189.3.n.b.170.8		22
9.4	even	3		63.3.n.b.32.4	yes	22
9.5	odd	6		189.3.n.b.179.8		22
21.2	odd	6		63.3.n.b.2.4	yes	22
21.5	even	6		441.3.n.f.128.4		22
21.11	odd	6		441.3.r.g.344.8		22
21.17	even	6		441.3.r.f.344.8		22
21.20	even	2		441.3.j.f.263.4		22
63.4	even	3		441.3.r.g.50.8		22
63.13	odd	6		441.3.n.f.410.4		22
63.23	odd	6	inner	189.3.j.b.44.4		22
63.31	odd	6		441.3.r.f.50.8		22
63.40	odd	6		441.3.j.f.275.8		22
63.58	even	3		63.3.j.b.23.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.4	✓	22	3.2	odd	2
63.3.j.b.23.8	yes	22	63.58	even	3
63.3.n.b.2.4	yes	22	21.2	odd	6
63.3.n.b.32.4	yes	22	9.4	even	3
189.3.j.b.44.4		22	63.23	odd	6	inner
189.3.j.b.116.8		22	1.1	even	1	trivial
189.3.n.b.170.8		22	7.2	even	3
189.3.n.b.179.8		22	9.5	odd	6
441.3.j.f.263.4		22	21.20	even	2
441.3.j.f.275.8		22	63.40	odd	6
441.3.n.f.128.4		22	21.5	even	6
441.3.n.f.410.4		22	63.13	odd	6
441.3.r.f.50.8		22	63.31	odd	6
441.3.r.f.344.8		22	21.17	even	6
441.3.r.g.50.8		22	63.4	even	3
441.3.r.g.344.8		22	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.46555i q^{2} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(-4.05935 + 5.70277i) q^{7} +8.57663i q^{8} +O(q^{10})\)	\(q+1.46555i q^{2} +1.85217 q^{4} +(-0.998268 - 0.576350i) q^{5} +(-4.05935 + 5.70277i) q^{7} +8.57663i q^{8} +(0.844669 - 1.46301i) q^{10} +(-0.209014 + 0.120674i) q^{11} +(7.70332 + 13.3426i) q^{13} +(-8.35769 - 5.94918i) q^{14} -5.16078 q^{16} +(10.9102 + 6.29901i) q^{17} +(13.7090 + 23.7446i) q^{19} +(-1.84896 - 1.06750i) q^{20} +(-0.176854 - 0.306320i) q^{22} +(-17.6566 - 10.1940i) q^{23} +(-11.8356 - 20.4999i) q^{25} +(-19.5541 + 11.2896i) q^{26} +(-7.51862 + 10.5625i) q^{28} +(-16.9161 - 9.76653i) q^{29} -2.72674 q^{31} +26.7432i q^{32} +(-9.23150 + 15.9894i) q^{34} +(7.33912 - 3.35329i) q^{35} +(-11.4455 - 19.8242i) q^{37} +(-34.7989 + 20.0911i) q^{38} +(4.94315 - 8.56178i) q^{40} +(61.9933 - 35.7918i) q^{41} +(14.8972 - 25.8028i) q^{43} +(-0.387130 + 0.223510i) q^{44} +(14.9398 - 25.8766i) q^{46} +29.9915i q^{47} +(-16.0433 - 46.2992i) q^{49} +(30.0436 - 17.3457i) q^{50} +(14.2679 + 24.7127i) q^{52} +(90.5906 + 52.3025i) q^{53} +0.278203 q^{55} +(-48.9106 - 34.8156i) q^{56} +(14.3133 - 24.7914i) q^{58} -86.7123i q^{59} +17.8845 q^{61} -3.99616i q^{62} -59.8365 q^{64} -17.7593i q^{65} -18.0439 q^{67} +(20.2076 + 11.6669i) q^{68} +(4.91440 + 10.7558i) q^{70} -74.2118i q^{71} +(13.0598 - 22.6203i) q^{73} +(29.0533 - 16.7739i) q^{74} +(25.3914 + 43.9791i) q^{76} +(0.160284 - 1.68182i) q^{77} +22.5123 q^{79} +(5.15184 + 2.97442i) q^{80} +(52.4546 + 90.8541i) q^{82} +(77.0996 + 44.5135i) q^{83} +(-7.26088 - 12.5762i) q^{85} +(37.8152 + 21.8326i) q^{86} +(-1.03498 - 1.79264i) q^{88} +(-49.7459 + 28.7208i) q^{89} +(-107.360 - 10.2318i) q^{91} +(-32.7030 - 18.8811i) q^{92} -43.9540 q^{94} -31.6047i q^{95} +(73.9883 - 128.152i) q^{97} +(67.8536 - 23.5122i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) 22 * q - 24 * q^4 - 12 * q^5	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Introduction

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