LMFDB - Embedded newform 189.3.j.b.44.4

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			44.4
Character	$\chi$	$=$	189.44
Dual form			189.3.j.b.116.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46555i q^{2} +1.85217 q^{4} +(-0.998268 + 0.576350i) q^{5} +(-4.05935 - 5.70277i) q^{7} -8.57663i q^{8} +O(q^{10})$	\(q-1.46555i q^{2} +1.85217 q^{4} +(-0.998268 + 0.576350i) q^{5} +(-4.05935 - 5.70277i) q^{7} -8.57663i q^{8} +(0.844669 + 1.46301i) q^{10} +(-0.209014 - 0.120674i) q^{11} +(7.70332 - 13.3426i) q^{13} +(-8.35769 + 5.94918i) q^{14} -5.16078 q^{16} +(10.9102 - 6.29901i) q^{17} +(13.7090 - 23.7446i) q^{19} +(-1.84896 + 1.06750i) q^{20} +(-0.176854 + 0.306320i) q^{22} +(-17.6566 + 10.1940i) q^{23} +(-11.8356 + 20.4999i) q^{25} +(-19.5541 - 11.2896i) q^{26} +(-7.51862 - 10.5625i) q^{28} +(-16.9161 + 9.76653i) q^{29} -2.72674 q^{31} -26.7432i q^{32} +(-9.23150 - 15.9894i) q^{34} +(7.33912 + 3.35329i) q^{35} +(-11.4455 + 19.8242i) q^{37} +(-34.7989 - 20.0911i) q^{38} +(4.94315 + 8.56178i) q^{40} +(61.9933 + 35.7918i) q^{41} +(14.8972 + 25.8028i) q^{43} +(-0.387130 - 0.223510i) q^{44} +(14.9398 + 25.8766i) q^{46} -29.9915i q^{47} +(-16.0433 + 46.2992i) q^{49} +(30.0436 + 17.3457i) q^{50} +(14.2679 - 24.7127i) q^{52} +(90.5906 - 52.3025i) q^{53} +0.278203 q^{55} +(-48.9106 + 34.8156i) q^{56} +(14.3133 + 24.7914i) q^{58} +86.7123i q^{59} +17.8845 q^{61} +3.99616i q^{62} -59.8365 q^{64} +17.7593i q^{65} -18.0439 q^{67} +(20.2076 - 11.6669i) q^{68} +(4.91440 - 10.7558i) q^{70} +74.2118i q^{71} +(13.0598 + 22.6203i) q^{73} +(29.0533 + 16.7739i) q^{74} +(25.3914 - 43.9791i) q^{76} +(0.160284 + 1.68182i) q^{77} +22.5123 q^{79} +(5.15184 - 2.97442i) q^{80} +(52.4546 - 90.8541i) q^{82} +(77.0996 - 44.5135i) q^{83} +(-7.26088 + 12.5762i) q^{85} +(37.8152 - 21.8326i) q^{86} +(-1.03498 + 1.79264i) q^{88} +(-49.7459 - 28.7208i) q^{89} +(-107.360 + 10.2318i) q^{91} +(-32.7030 + 18.8811i) q^{92} -43.9540 q^{94} +31.6047i q^{95} +(73.9883 + 128.152i) q^{97} +(67.8536 + 23.5122i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.880595\pi$
$2$		−	1.46555i		−	0.732774i	0.930463	−	0.366387i	$-0.119405\pi$
$3$		0			0
$3$		0			0
$4$	1.85217			0.463043
$5$	−0.998268	+	0.576350i	−0.199654	+	0.115270i	−0.596494	−	0.802618i	$-0.703440\pi$
$5$	−0.998268	+	0.576350i	−0.199654	+	0.115270i	0.396840	+	0.917888i	$0.370107\pi$
$6$		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	0.490469	−	0.871458i	$-0.336825\pi$
$11$	−0.209014	−	0.120674i	−0.0190013	−	0.0109704i	−0.509471	+	0.860488i	$0.670159\pi$
$12$		0			0
$13$	7.70332	−	13.3426i	0.592563	−	1.02635i	−0.401322	−	0.915937i	$-0.631449\pi$
$13$	7.70332	−	13.3426i	0.592563	−	1.02635i	0.993886	−	0.110413i	$-0.0352174\pi$
$14$	−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	−0.143522	−	0.989647i	$-0.545843\pi$
$17$	10.9102	−	6.29901i	0.641777	−	0.370530i	0.785299	+	0.619117i	$0.212509\pi$
$18$		0			0
$19$	13.7090	−	23.7446i	0.721525	−	1.24972i	−0.238864	−	0.971053i	$-0.576775\pi$
$19$	13.7090	−	23.7446i	0.721525	−	1.24972i	0.960389	−	0.278664i	$-0.0898917\pi$
$20$	−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	−0.832046	−	0.554707i	$-0.812830\pi$
$23$	−17.6566	+	10.1940i	−0.767678	+	0.443219i	0.0643676	+	0.997926i	$0.479497\pi$
$24$		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	−0.762450	−	0.647048i	$-0.776003\pi$
$29$	−16.9161	+	9.76653i	−0.583315	+	0.336777i	0.179135	+	0.983825i	$0.442670\pi$
$30$		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	−0.978218	−	0.207582i	$-0.933441\pi$
$37$	−11.4455	+	19.8242i	−0.309338	+	0.535789i	0.668880	+	0.743371i	$0.266774\pi$
$38$	−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	0.999901	+	0.0140641i	$0.00447689\pi$
$41$	61.9933	+	35.7918i	1.51203	+	0.872972i	0.512130	+	0.858908i	$0.328856\pi$
$42$		0			0
$43$	14.8972	+	25.8028i	0.346447	+	0.600064i	0.985616	−	0.169003i	$-0.0540546\pi$
$43$	14.8972	+	25.8028i	0.346447	+	0.600064i	−0.639168	+	0.769067i	$0.720721\pi$
$44$	−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	$-0.896633\pi$
$47$		−	29.9915i		−	0.638117i	0.947735	−	0.319059i	$-0.103367\pi$
$48$		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	0.773778	−	0.633457i	$-0.218365\pi$
$53$	90.5906	−	52.3025i	1.70926	−	0.986840i	0.935479	−	0.353383i	$-0.114969\pi$
$54$		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	$0.262747\pi$
$59$			86.7123i			1.46970i	−0.678230	+	0.734850i	$0.737253\pi$
$60$		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	$0.175045\pi$
$71$			74.2118i			1.04524i	−0.852567	+	0.522618i	$0.824955\pi$
$72$		0			0
$73$	13.0598	+	22.6203i	0.178902	+	0.309867i	0.941505	−	0.337000i	$-0.109412\pi$
$73$	13.0598	+	22.6203i	0.178902	+	0.309867i	−0.762603	+	0.646867i	$0.776079\pi$
$74$	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	0.0424438	−	0.999099i	$-0.486486\pi$
$83$	77.0996	−	44.5135i	0.928911	−	0.536307i	0.886467	+	0.462792i	$0.153152\pi$
$84$		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	0.193779	−	0.981045i	$-0.437926\pi$
$89$	−49.7459	−	28.7208i	−0.558942	−	0.322706i	−0.752721	+	0.658340i	$0.771259\pi$
$90$		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	0.941419	+	0.337238i	$0.109493\pi$
$97$	73.9883	+	128.152i	0.762766	+	1.32115i	−0.178653	+	0.983912i	$0.557174\pi$
$98$	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	0.0938471	−	0.995587i	$-0.470084\pi$
$101$	−72.8647	−	42.0685i	−0.721433	−	0.416519i	−0.815280	+	0.579067i	$0.803417\pi$
$102$		0			0
$103$	−29.4838	−	51.0674i	−0.286250	−	0.495800i	0.686661	−	0.726977i	$-0.259076\pi$
$103$	−29.4838	−	51.0674i	−0.286250	−	0.495800i	−0.972912	+	0.231178i	$0.925742\pi$
$104$	−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	0.0953906	−	0.995440i	$-0.469590\pi$
$107$	−76.9320	−	44.4167i	−0.718990	−	0.415109i	−0.814381	+	0.580331i	$0.802923\pi$
$108$		0			0
$109$	94.4610	+	163.611i	0.866615	+	1.50102i	0.865435	+	0.501021i	$0.167042\pi$
$109$	94.4610	+	163.611i	0.866615	+	1.50102i	0.00117990	+	0.999999i	$0.499624\pi$
$110$		−	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	−0.0193087	−	0.999814i	$-0.506147\pi$
$113$	−101.115	−	58.3790i	−0.894827	−	0.516629i	−0.875518	+	0.483185i	$0.839480\pi$
$114$		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	−0.244688	−	0.969602i	$-0.578685\pi$
$131$	61.9195	−	35.7493i	0.472668	−	0.272895i	0.717356	+	0.696707i	$0.245352\pi$
$132$		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	0.990958	−	0.134173i	$-0.0428379\pi$
$137$	187.723	+	108.382i	1.37024	+	0.791108i	0.379281	+	0.925281i	$0.376171\pi$
$138$		0			0
$139$	53.7032	−	93.0167i	0.386354	−	0.669185i	−0.605602	−	0.795768i	$-0.707068\pi$
$139$	53.7032	−	93.0167i	0.386354	−	0.669185i	0.991956	+	0.126583i	$0.0404009\pi$
$140$	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	−0.881408	−	0.472357i	$-0.843403\pi$
$149$	−136.043	+	78.5443i	−0.913038	+	0.527143i	−0.0316309	+	0.999500i	$0.510070\pi$
$150$		0			0
$151$	60.2412	−	104.341i	0.398948	−	0.690999i	−0.594648	−	0.803986i	$-0.702709\pi$
$151$	60.2412	−	104.341i	0.398948	−	0.690999i	0.993596	+	0.112987i	$0.0360419\pi$
$152$	−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	−0.124031	−	0.992278i	$-0.539582\pi$
$163$	129.964	−	225.104i	0.797323	−	1.38100i	0.921354	−	0.388725i	$-0.127084\pi$
$164$	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	0.179253	−	0.983803i	$-0.442632\pi$
$167$	−97.3809	−	56.2229i	−0.583119	−	0.336664i	−0.762372	+	0.647139i	$0.775965\pi$
$168$		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	$0.0128708\pi$
$173$			13.9867i			0.0808478i	−0.999183	+	0.0404239i	$0.987129\pi$
$174$		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	−0.618155	−	0.786056i	$-0.712120\pi$
$179$	−44.1214	+	25.4735i	−0.246488	+	0.142310i	0.371667	+	0.928366i	$0.378786\pi$
$180$		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	$-0.840180\pi$
$191$		−	183.841i		−	0.962519i	0.876578	−	0.481259i	$-0.159820\pi$
$192$		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	$0.435775\pi$
$197$			386.007i			1.95943i	−0.200402	+	0.979714i	$0.564225\pi$
$198$		0			0
$199$	−22.8387	−	39.5577i	−0.114767	−	0.198782i	0.802920	−	0.596087i	$-0.203279\pi$
$199$	−22.8387	−	39.5577i	−0.114767	−	0.198782i	−0.917687	+	0.397305i	$0.869946\pi$
$200$	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	0.115383	+	0.993321i	$0.463190\pi$
$211$	−169.338	+	293.302i	−0.802550	+	1.39006i	−0.917933	+	0.396736i	$0.870143\pi$
$212$	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	0.947462	−	0.319868i	$-0.103638\pi$
$223$	43.8681	+	75.9817i	0.196718	+	0.340725i	−0.750745	+	0.660593i	$0.770305\pi$
$224$	−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	−0.357950	−	0.933741i	$-0.616524\pi$
$227$	−305.444	−	176.348i	−1.34557	−	0.776864i	−0.987618	+	0.156876i	$0.949858\pi$
$228$		0			0
$229$	190.395	+	329.774i	0.831421	+	1.44006i	0.896912	+	0.442209i	$0.145805\pi$
$229$	190.395	+	329.774i	0.831421	+	1.44006i	−0.0654913	+	0.997853i	$0.520861\pi$
$230$	−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	0.952609	−	0.304197i	$-0.0983882\pi$
$233$	271.555	+	156.782i	1.16547	+	0.672885i	0.212862	+	0.977082i	$0.431722\pi$
$234$		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	0.0197741	−	0.999804i	$-0.493705\pi$
$239$	−199.851	−	115.384i	−0.836195	−	0.482777i	−0.855969	+	0.517027i	$0.827039\pi$
$240$		0			0
$241$	90.4282	−	156.626i	0.375221	−	0.649902i	−0.615139	−	0.788419i	$-0.710900\pi$
$241$	90.4282	−	156.626i	0.375221	−	0.649902i	0.990360	+	0.138517i	$0.0442335\pi$
$242$	−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	$0.104503\pi$
$251$			161.864i			0.644878i	−0.946590	+	0.322439i	$0.895497\pi$
$252$		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	−0.622053	−	0.782975i	$-0.713701\pi$
$257$	−65.5360	+	37.8372i	−0.255004	+	0.147227i	0.367049	+	0.930201i	$0.380368\pi$
$258$		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	0.480702	−	0.876884i	$-0.340382\pi$
$263$	−10.0862	−	5.82326i	−0.0383505	−	0.0221417i	−0.519053	+	0.854742i	$0.673715\pi$
$264$		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	0.0838565	−	0.996478i	$-0.473276\pi$
$269$	265.976	−	153.562i	0.988760	−	0.570861i	0.904903	+	0.425617i	$0.139943\pi$
$270$		0			0
$271$	169.039	−	292.784i	0.623759	−	1.08038i	−0.365020	−	0.931000i	$-0.618938\pi$
$271$	169.039	−	292.784i	0.623759	−	1.08038i	0.988779	−	0.149383i	$-0.0477287\pi$
$272$	−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	−0.721922	−	0.691975i	$-0.756741\pi$
$277$	66.0110	−	114.334i	0.238307	−	0.412760i	0.960229	+	0.279215i	$0.0900743\pi$
$278$	−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	−0.381237	−	0.924477i	$-0.624502\pi$
$281$	64.2832	−	37.1139i	0.228766	−	0.132078i	0.610003	+	0.792399i	$0.291168\pi$
$282$		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	0.725368	−	0.688361i	$-0.241670\pi$
$293$	144.131	+	83.2139i	0.491913	+	0.284006i	−0.233454	+	0.972368i	$0.575003\pi$
$294$		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	$0.0807006\pi$
$311$			156.011i			0.501642i	−0.968033	+	0.250821i	$0.919299\pi$
$312$		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	$-0.904243\pi$
$317$		−	187.863i		−	0.592626i	0.955091	−	0.296313i	$-0.0957572\pi$
$318$		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	−0.704531	−	0.709673i	$-0.748843\pi$
$337$	88.4049	−	153.122i	0.262329	−	0.454367i	0.966860	+	0.255306i	$0.0821761\pi$
$338$	−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	$-0.885984\pi$
$347$		−	243.303i		−	0.701161i	0.936533	−	0.350580i	$-0.114016\pi$
$348$		0			0
$349$	−209.668	−	363.156i	−0.600768	−	1.04056i	−0.992705	−	0.120568i	$-0.961528\pi$
$349$	−209.668	−	363.156i	−0.600768	−	1.04056i	0.391937	−	0.919992i	$-0.371805\pi$
$350$	−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	0.861803	−	0.507243i	$-0.169335\pi$
$353$	301.257	+	173.931i	0.853419	+	0.492722i	−0.00838407	+	0.999965i	$0.502669\pi$
$354$		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	−0.158311	−	0.987389i	$-0.550605\pi$
$359$	−392.233	−	226.456i	−1.09257	−	0.630796i	−0.934260	+	0.356593i	$0.883938\pi$
$360$		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	−0.863838	−	0.503770i	$-0.831946\pi$
$367$	1.59980	−	2.77094i	0.00435913	−	0.00755024i	0.868197	+	0.496220i	$0.165279\pi$
$368$	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	0.948633	−	0.316377i	$-0.102467\pi$
$373$	74.7215	+	129.421i	0.200326	+	0.346974i	−0.748308	+	0.663352i	$0.769133\pi$
$374$			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	−0.282791	−	0.959182i	$-0.591260\pi$
$383$	155.685	−	89.8850i	0.406489	−	0.234687i	0.689280	+	0.724495i	$0.257927\pi$
$384$		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	0.0753189	−	0.997159i	$-0.476003\pi$
$389$	−291.978	−	168.574i	−0.750587	−	0.433352i	−0.825906	+	0.563808i	$0.809336\pi$
$390$		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	0.305113	+	0.952316i	$0.401306\pi$
$397$	−266.853	+	462.203i	−0.672174	+	1.16424i	−0.977286	+	0.211923i	$0.932027\pi$
$398$	−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	−0.981972	−	0.189025i	$-0.939467\pi$
$401$	−525.012	+	303.116i	−1.30926	+	0.755900i	−0.327286	+	0.944925i	$0.606134\pi$
$402$		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	0.991903	−	0.126997i	$-0.0405338\pi$
$419$	577.328	+	333.321i	1.37787	+	0.795515i	0.385969	+	0.922512i	$0.373867\pi$
$420$		0			0
$421$	235.637	+	408.136i	0.559708	+	0.969443i	0.997520	+	0.0703769i	$0.0224202\pi$
$421$	235.637	+	408.136i	0.559708	+	0.969443i	−0.437812	+	0.899067i	$0.644246\pi$
$422$	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	−0.717995	−	0.696048i	$-0.754940\pi$
$431$	−204.379	+	117.998i	−0.474197	+	0.273778i	0.243798	+	0.969826i	$0.421607\pi$
$432$		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	$0.0191028\pi$
$443$			53.1399i			0.119955i	−0.998200	+	0.0599773i	$0.980897\pi$
$444$		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	$0.199369\pi$
$449$			526.389i			1.17236i	−0.810181	+	0.586179i	$0.800631\pi$
$450$		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	−0.775858	−	0.630907i	$-0.782683\pi$
$461$	−284.624	+	164.328i	−0.617406	+	0.356460i	0.158452	+	0.987367i	$0.449350\pi$
$462$		0			0
$463$	3.64605	−	6.31515i	0.00787484	−	0.0136396i	−0.862061	−	0.506804i	$-0.830827\pi$
$463$	3.64605	−	6.31515i	0.00787484	−	0.0136396i	0.869936	+	0.493165i	$0.164160\pi$
$464$	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	0.895033	−	0.445999i	$-0.147152\pi$
$467$	446.593	+	257.841i	0.956303	+	0.552122i	0.0612697	+	0.998121i	$0.480485\pi$
$468$		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	0.738448	−	0.674310i	$-0.235559\pi$
$479$	250.854	+	144.830i	0.523703	+	0.302360i	−0.214746	+	0.976670i	$0.568892\pi$
$480$		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	−0.999781	−	0.0209323i	$-0.993337\pi$
$487$	−252.275	−	436.953i	−0.518018	−	0.897234i	0.481763	−	0.876302i	$-0.339997\pi$
$488$		−	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	0.782551	−	0.622586i	$-0.213918\pi$
$491$	311.614	+	179.910i	0.634651	+	0.366416i	−0.147900	+	0.989002i	$0.547251\pi$
$492$		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	0.983520	+	0.180801i	$0.0578691\pi$
$499$	323.521	+	560.354i	0.648338	+	1.12295i	−0.335181	+	0.942154i	$0.608798\pi$
$500$		−	103.913i		−	0.207826i
$501$		0			0
$502$	237.220			0.472549
$503$		−	183.191i		−	0.364198i	−0.983280	−	0.182099i	$-0.941711\pi$
$503$		−	183.191i		−	0.364198i	0.983280	−	0.182099i	$-0.0582891\pi$
$504$		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	0.475825	−	0.879540i	$-0.342150\pi$
$509$	751.000	−	433.590i	1.47544	−	0.851846i	0.999616	+	0.0276937i	$0.00881632\pi$
$510$		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	−0.556664	−	0.830738i	$-0.687919\pi$
$521$	−60.2047	+	34.7592i	−0.115556	+	0.0667163i	0.441108	+	0.897454i	$0.354586\pi$
$522$		0			0
$523$	−356.425	+	617.347i	−0.681502	+	1.18040i	0.293021	+	0.956106i	$0.405339\pi$
$523$	−356.425	+	617.347i	−0.681502	+	1.18040i	−0.974523	+	0.224290i	$0.927994\pi$
$524$	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	−0.650176	−	0.759784i	$-0.725305\pi$
$541$	180.101	−	311.944i	0.332904	−	0.576607i	0.983080	+	0.183177i	$0.0586381\pi$
$542$	−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	0.819839	−	0.572595i	$-0.194063\pi$
$547$	−47.0212	−	81.4432i	−0.0859620	−	0.148891i	−0.905801	+	0.423704i	$0.860730\pi$
$548$	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	−0.886015	−	0.463657i	$-0.846537\pi$
$557$	−516.609	+	298.264i	−0.927484	+	0.535483i	−0.0414691	+	0.999140i	$0.513204\pi$
$558$		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	$0.222385\pi$
$563$			724.219i			1.28636i	−0.765716	+	0.643179i	$0.777615\pi$
$564$		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	$0.0933335\pi$
$569$			328.919i			0.578065i	−0.957319	+	0.289032i	$0.906666\pi$
$570$		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	−0.986187	−	0.165638i	$-0.947032\pi$
$577$	−367.284	−	636.154i	−0.636540	−	1.10252i	0.349647	−	0.936882i	$-0.386302\pi$
$578$	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	−0.603356	−	0.797472i	$-0.706170\pi$
$587$	−125.855	+	72.6624i	−0.214404	+	0.123786i	0.388953	+	0.921258i	$0.372837\pi$
$588$		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	0.275687	−	0.961247i	$-0.411095\pi$
$593$	−248.428	−	143.430i	−0.418934	−	0.241872i	−0.694621	+	0.719376i	$0.744428\pi$
$594$		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	$-0.801495\pi$
$599$		−	699.608i		−	1.16796i	0.811768	−	0.583980i	$-0.198505\pi$
$600$		0			0
$601$	58.2075	+	100.818i	0.0968511	+	0.167751i	0.910380	−	0.413774i	$-0.135790\pi$
$601$	58.2075	+	100.818i	0.0968511	+	0.167751i	−0.813529	+	0.581525i	$0.802456\pi$
$602$	−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	−0.999425	−	0.0339178i	$-0.989202\pi$
$607$	−321.155	−	556.257i	−0.529086	−	0.916404i	0.470339	−	0.882486i	$-0.344132\pi$
$608$	−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	0.996000	−	0.0893481i	$-0.0284783\pi$
$613$	257.842	+	446.595i	0.420623	+	0.728540i	−0.575378	+	0.817888i	$0.695145\pi$
$614$			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	0.185935	−	0.982562i	$-0.440469\pi$
$617$	−352.937	−	203.768i	−0.572021	−	0.330257i	−0.757956	+	0.652305i	$0.773802\pi$
$618$		0			0
$619$	21.1760	−	36.6779i	0.0342100	−	0.0592535i	−0.848413	−	0.529334i	$-0.822442\pi$
$619$	21.1760	−	36.6779i	0.0342100	−	0.0592535i	0.882624	+	0.470081i	$0.155775\pi$
$620$	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	0.717855	−	0.696193i	$-0.245124\pi$
$641$	303.746	+	175.368i	0.473862	+	0.273584i	−0.243993	+	0.969777i	$0.578457\pi$
$642$		0			0
$643$	−329.068	+	569.963i	−0.511770	+	0.886412i	0.488137	+	0.872767i	$0.337677\pi$
$643$	−329.068	+	569.963i	−0.511770	+	0.886412i	−0.999907	+	0.0136450i	$0.995657\pi$
$644$	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	−0.824278	−	0.566185i	$-0.808419\pi$
$647$	−482.718	+	278.697i	−0.746087	+	0.430753i	0.0781915	+	0.996938i	$0.475085\pi$
$648$		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	−0.616079	−	0.787685i	$-0.711280\pi$
$653$	−158.002	+	91.2224i	−0.241963	+	0.139697i	0.374116	+	0.927382i	$0.377946\pi$
$654$		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	−0.491848	−	0.870681i	$-0.663679\pi$
$659$	10.7149	−	6.18625i	0.0162593	−	0.00938733i	0.508108	+	0.861294i	$0.330345\pi$
$660$		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	0.842971	−	0.537959i	$-0.180805\pi$
$673$	−29.8818	−	51.7568i	−0.0444009	−	0.0769046i	−0.887372	+	0.461055i	$0.847471\pi$
$674$	−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	$-0.762067\pi$
$677$		−	920.447i		−	1.35960i	0.733399	−	0.679799i	$-0.237933\pi$
$678$		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	−0.0984954	−	0.995138i	$-0.531403\pi$
$683$	487.711	−	281.580i	0.714071	−	0.412269i	0.812567	+	0.582868i	$0.198070\pi$
$684$		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	$0.121892\pi$
$701$			523.850i			0.747289i	−0.927572	+	0.373645i	$0.878108\pi$
$702$		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	−0.138745	−	0.990328i	$-0.544307\pi$
$719$	−766.286	−	442.415i	−1.06577	−	0.615321i	−0.927022	+	0.375008i	$0.877640\pi$
$720$		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	0.665078	−	0.746774i	$-0.268398\pi$
$727$	−228.413	−	395.623i	−0.314186	−	0.544186i	−0.979264	+	0.202588i	$0.935065\pi$
$728$	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	0.899714	−	0.436480i	$-0.143775\pi$
$733$	52.6692	+	91.2258i	0.0718543	+	0.124455i	−0.827860	+	0.560935i	$0.810442\pi$
$734$	−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	0.957596	−	0.288113i	$-0.0930279\pi$
$739$	169.442	+	293.482i	0.229285	+	0.397133i	−0.728311	+	0.685246i	$0.759695\pi$
$740$		−	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	0.358947	−	0.933358i	$-0.383136\pi$
$743$	−200.529	−	115.776i	−0.269891	−	0.155822i	−0.628838	+	0.777536i	$0.716469\pi$
$744$		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	0.903943	−	0.427653i	$-0.140660\pi$
$751$	61.2911	+	106.159i	0.0816127	+	0.141357i	−0.822330	+	0.569011i	$0.807326\pi$
$752$			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	−0.684605	−	0.728914i	$-0.740025\pi$
$761$	−301.090	+	173.834i	−0.395650	+	0.228429i	0.288955	+	0.957343i	$0.406692\pi$
$762$		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	−0.851404	−	0.524510i	$-0.824249\pi$
$769$	21.9448	−	38.0094i	0.0285367	−	0.0494271i	0.879941	+	0.475083i	$0.157582\pi$
$770$	−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	−0.479586	−	0.877495i	$-0.659213\pi$
$773$	31.3486	−	18.0991i	0.0405545	−	0.0234141i	0.520140	+	0.854081i	$0.325880\pi$
$774$		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	0.492173	−	0.870498i	$-0.336203\pi$
$797$	−12.4445	−	7.18485i	−0.0156142	−	0.00901487i	−0.507787	+	0.861483i	$0.669536\pi$
$798$		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	−0.580705	−	0.814114i	$-0.697223\pi$
$809$	−134.305	+	77.5408i	−0.166013	+	0.0958478i	0.414691	+	0.909962i	$0.363890\pi$
$810$		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	$0.0438263\pi$
$821$			225.364i			0.274500i	−0.990536	+	0.137250i	$0.956174\pi$
$822$		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	$0.125234\pi$
$827$			634.083i			0.766727i	−0.923598	+	0.383363i	$0.874766\pi$
$828$		0			0
$829$	−376.723	−	652.503i	−0.454431	−	0.787097i	0.544225	−	0.838940i	$-0.316824\pi$
$829$	−376.723	−	652.503i	−0.454431	−	0.787097i	−0.998655	+	0.0518425i	$0.983491\pi$
$830$	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	−0.945547	−	0.325487i	$-0.894472\pi$
$839$	−953.473	+	550.488i	−1.13644	+	0.656124i	−0.190893	+	0.981611i	$0.561138\pi$
$840$		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	0.945076	−	0.326852i	$-0.105988\pi$
$853$	161.623	+	279.939i	0.189476	+	0.328181i	−0.755600	+	0.655033i	$0.772655\pi$
$854$	−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	−0.333818	−	0.942637i	$-0.608337\pi$
$857$	−1128.73	−	651.675i	−1.31708	−	0.760414i	−0.983257	+	0.182224i	$0.941671\pi$
$858$		0			0
$859$	87.8268	+	152.121i	0.102243	+	0.177090i	0.912609	−	0.408835i	$-0.134065\pi$
$859$	87.8268	+	152.121i	0.102243	+	0.177090i	−0.810365	+	0.585925i	$0.800731\pi$
$860$	−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	0.322734	−	0.946490i	$-0.395398\pi$
$863$	−289.608	−	167.205i	−0.335582	−	0.193749i	−0.658317	+	0.752741i	$0.728731\pi$
$864$		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	0.547355	−	0.836901i	$-0.315635\pi$
$877$	−395.615	−	685.225i	−0.451100	−	0.781328i	−0.998455	+	0.0555725i	$0.982302\pi$
$878$			514.870i			0.586412i
$879$		0			0
$880$	−1.43574			−0.00163153
$881$		−	307.622i		−	0.349174i	−0.984642	−	0.174587i	$-0.944141\pi$
$881$		−	307.622i		−	0.349174i	0.984642	−	0.174587i	$-0.0558591\pi$
$882$		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	−0.583682	−	0.811982i	$-0.698389\pi$
$887$	−152.854	+	88.2501i	−0.172327	+	0.0994928i	0.411356	+	0.911475i	$0.365055\pi$
$888$		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	−0.158642	+	0.987336i	$0.550711\pi$
$907$	−847.482	+	1467.88i	−0.934379	+	1.61839i	−0.775737	+	0.631056i	$0.782622\pi$
$908$	−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	−0.902490	−	0.430711i	$-0.858263\pi$
$911$	−893.443	+	515.830i	−0.980728	+	0.566224i	−0.0782381	+	0.996935i	$0.524929\pi$
$912$		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	−0.598917	−	0.800811i	$-0.704402\pi$
$919$	362.145	−	627.254i	0.394064	−	0.682539i	0.992981	+	0.118272i	$0.0377354\pi$
$920$	−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	$-0.711234\pi$
$929$		−	1463.68i		−	1.57555i	0.615966	−	0.787773i	$-0.288766\pi$
$930$		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	$-0.949992\pi$
$941$		−	294.458i		−	0.312921i	0.987684	−	0.156460i	$-0.0500083\pi$
$942$		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	$0.154212\pi$
$947$			882.114i			0.931482i	−0.884921	+	0.465741i	$0.845788\pi$
$948$		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	$-0.941690\pi$
$953$		−	347.203i		−	0.364326i	0.983268	−	0.182163i	$-0.0583099\pi$
$954$		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	−0.118577	−	0.992945i	$-0.537833\pi$
$967$	774.207	−	1340.97i	0.800627	−	1.38673i	0.919204	−	0.393782i	$-0.128834\pi$
$968$	−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	0.872476	−	0.488657i	$-0.162513\pi$
$971$	859.844	+	496.431i	0.885525	+	0.511258i	0.0130486	+	0.999915i	$0.495846\pi$
$972$		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	$0.0388706\pi$
$977$			238.021i			0.243625i	−0.992553	+	0.121812i	$0.961129\pi$
$978$		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	0.194613	−	0.980880i	$-0.437655\pi$
$983$	−548.070	−	316.428i	−0.557548	−	0.321901i	−0.752161	+	0.658980i	$0.770988\pi$
$984$		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	0.993526	+	0.113602i	$0.0362389\pi$
$991$	589.789	+	1021.54i	0.595145	+	1.03082i	−0.398381	+	0.917220i	$0.630428\pi$
$992$			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	−0.200198	−	0.979755i	$-0.564159\pi$
$997$	746.149	−	1292.37i	0.748394	−	1.29626i	0.948592	−	0.316501i	$-0.102508\pi$
$998$	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.44.4		22
3.2	odd	2		63.3.j.b.23.8	yes	22
7.4	even	3		189.3.n.b.179.8		22
9.2	odd	6		189.3.n.b.170.8		22
9.7	even	3		63.3.n.b.2.4	yes	22
21.2	odd	6		441.3.r.g.50.8		22
21.5	even	6		441.3.r.f.50.8		22
21.11	odd	6		63.3.n.b.32.4	yes	22
21.17	even	6		441.3.n.f.410.4		22
21.20	even	2		441.3.j.f.275.8		22
63.11	odd	6	inner	189.3.j.b.116.8		22
63.16	even	3		441.3.r.g.344.8		22
63.25	even	3		63.3.j.b.11.4	✓	22
63.34	odd	6		441.3.n.f.128.4		22
63.52	odd	6		441.3.j.f.263.4		22
63.61	odd	6		441.3.r.f.344.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.4	✓	22	63.25	even	3
63.3.j.b.23.8	yes	22	3.2	odd	2
63.3.n.b.2.4	yes	22	9.7	even	3
63.3.n.b.32.4	yes	22	21.11	odd	6
189.3.j.b.44.4		22	1.1	even	1	trivial
189.3.j.b.116.8		22	63.11	odd	6	inner
189.3.n.b.170.8		22	9.2	odd	6
189.3.n.b.179.8		22	7.4	even	3
441.3.j.f.263.4		22	63.52	odd	6
441.3.j.f.275.8		22	21.20	even	2
441.3.n.f.128.4		22	63.34	odd	6
441.3.n.f.410.4		22	21.17	even	6
441.3.r.f.50.8		22	21.5	even	6
441.3.r.f.344.8		22	63.61	odd	6
441.3.r.g.50.8		22	21.2	odd	6
441.3.r.g.344.8		22	63.16	even	3

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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