LMFDB - Embedded newform 243.3.f.b.215.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,3,Mod(26,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.26"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,-3,0,3,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.5
Character	$\chi$	$=$	243.215
Dual form			243.3.f.b.26.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.27361 - 0.577226i) q^{2} +(6.62455 - 2.41114i) q^{4} +(4.42119 - 5.26897i) q^{5} +(-5.99653 - 2.18256i) q^{7} +(8.77937 - 5.06877i) q^{8} +(11.4319 - 19.8006i) q^{10} +(-0.799933 - 0.953323i) q^{11} +(-0.927217 + 5.25851i) q^{13} +(-20.8901 - 3.68349i) q^{14} +(4.21287 - 3.53502i) q^{16} +(13.7418 + 7.93385i) q^{17} +(6.78917 + 11.7592i) q^{19} +(16.5842 - 45.5647i) q^{20} +(-3.16895 - 2.65907i) q^{22} +(8.48610 + 23.3154i) q^{23} +(-3.87391 - 21.9701i) q^{25} +17.7495i q^{26} -44.9868 q^{28} +(-30.5171 + 5.38098i) q^{29} +(14.9211 - 5.43084i) q^{31} +(-14.3144 + 17.0592i) q^{32} +(49.5650 + 18.0402i) q^{34} +(-38.0116 + 21.9460i) q^{35} +(26.0365 - 45.0965i) q^{37} +(29.0128 + 34.5761i) q^{38} +(12.1081 - 68.6683i) q^{40} +(-1.06400 - 0.187611i) q^{41} +(37.0026 - 31.0488i) q^{43} +(-7.59780 - 4.38659i) q^{44} +(41.2384 + 71.4270i) q^{46} +(-19.7018 + 54.1303i) q^{47} +(-6.34137 - 5.32104i) q^{49} +(-25.3634 - 69.6853i) q^{50} +(6.53661 + 37.0709i) q^{52} -13.8414i q^{53} -8.55969 q^{55} +(-63.7087 + 11.2336i) q^{56} +(-96.7949 + 35.2305i) q^{58} +(-38.7615 + 46.1941i) q^{59} +(-94.8938 - 34.5385i) q^{61} +(45.7111 - 26.3913i) q^{62} +(-48.0117 + 83.1587i) q^{64} +(23.6075 + 28.1344i) q^{65} +(-13.6531 + 77.4304i) q^{67} +(110.163 + 19.4247i) q^{68} +(-111.767 + 93.7840i) q^{70} +(-39.7545 - 22.9523i) q^{71} +(-34.4926 - 59.7430i) q^{73} +(59.2024 - 162.657i) q^{74} +(73.3283 + 61.5297i) q^{76} +(2.71614 + 7.46253i) q^{77} +(6.86682 + 38.9437i) q^{79} -37.8265i q^{80} -3.59141 q^{82} +(-41.5621 + 7.32852i) q^{83} +(102.558 - 37.3282i) q^{85} +(103.210 - 123.001i) q^{86} +(-11.8551 - 4.31490i) q^{88} +(61.8262 - 35.6954i) q^{89} +(17.0371 - 29.5091i) q^{91} +(112.433 + 133.993i) q^{92} +(-33.2506 + 188.574i) q^{94} +(91.9750 + 16.2177i) q^{95} +(0.867150 - 0.727625i) q^{97} +(-23.8306 - 13.7586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	3.27361	−	0.577226i	1.63680	−	0.288613i	0.721814	−	0.692088i	$-0.243309\pi$
$2$	3.27361	−	0.577226i	1.63680	−	0.288613i	0.914991	+	0.403475i	$0.132198\pi$
$3$		0			0
$3$		0			0
$4$	6.62455	−	2.41114i	1.65614	−	0.602785i
$5$	4.42119	−	5.26897i	0.884238	−	1.05379i	−0.113942	−	0.993487i	$-0.536348\pi$
$5$	4.42119	−	5.26897i	0.884238	−	1.05379i	0.998180	−	0.0603067i	$-0.0192079\pi$
$6$		0			0
$7$	−5.99653	−	2.18256i	−0.856647	−	0.311794i	−0.123900	−	0.992295i	$-0.539540\pi$
$7$	−5.99653	−	2.18256i	−0.856647	−	0.311794i	−0.732747	+	0.680501i	$0.761762\pi$
$8$	8.77937	−	5.06877i	1.09742	−	0.633597i
$9$		0			0
$10$	11.4319	−	19.8006i	1.14319	−	1.98006i
$11$	−0.799933	−	0.953323i	−0.0727212	−	0.0866658i	0.728457	−	0.685091i	$-0.240238\pi$
$11$	−0.799933	−	0.953323i	−0.0727212	−	0.0866658i	−0.801178	+	0.598425i	$0.795793\pi$
$12$		0			0
$13$	−0.927217	+	5.25851i	−0.0713244	+	0.404501i	0.928154	+	0.372197i	$0.121395\pi$
$13$	−0.927217	+	5.25851i	−0.0713244	+	0.404501i	−0.999478	+	0.0323036i	$0.989716\pi$
$14$	−20.8901	−	3.68349i	−1.49215	−	0.263107i
$15$		0			0
$16$	4.21287	−	3.53502i	0.263304	−	0.220938i
$17$	13.7418	+	7.93385i	0.808343	+	0.466697i	0.846380	−	0.532579i	$-0.178777\pi$
$17$	13.7418	+	7.93385i	0.808343	+	0.466697i	−0.0380373	+	0.999276i	$0.512111\pi$
$18$		0			0
$19$	6.78917	+	11.7592i	0.357325	+	0.618905i	0.987513	−	0.157538i	$-0.0503556\pi$
$19$	6.78917	+	11.7592i	0.357325	+	0.618905i	−0.630188	+	0.776442i	$0.717022\pi$
$20$	16.5842	−	45.5647i	0.829210	−	2.27823i
$21$		0			0
$22$	−3.16895	−	2.65907i	−0.144043	−	0.120867i
$23$	8.48610	+	23.3154i	0.368961	+	1.01371i	0.975758	+	0.218854i	$0.0702319\pi$
$23$	8.48610	+	23.3154i	0.368961	+	1.01371i	−0.606797	+	0.794857i	$0.707546\pi$
$24$		0			0
$25$	−3.87391	−	21.9701i	−0.154957	−	0.878802i
$26$			17.7495i			0.682674i
$27$		0			0
$28$	−44.9868			−1.60667
$29$	−30.5171	+	5.38098i	−1.05231	+	0.185551i	−0.672943	−	0.739694i	$-0.734970\pi$
$29$	−30.5171	+	5.38098i	−1.05231	+	0.185551i	−0.379370	+	0.925245i	$0.623859\pi$
$30$		0			0
$31$	14.9211	−	5.43084i	0.481327	−	0.175189i	−0.0899498	−	0.995946i	$-0.528671\pi$
$31$	14.9211	−	5.43084i	0.481327	−	0.175189i	0.571276	+	0.820758i	$0.306448\pi$
$32$	−14.3144	+	17.0592i	−0.447325	+	0.533101i
$33$		0			0
$34$	49.5650	+	18.0402i	1.45779	+	0.530593i
$35$	−38.0116	+	21.9460i	−1.08605	+	0.627029i
$36$		0			0
$37$	26.0365	−	45.0965i	0.703688	−	1.21882i	−0.263474	−	0.964666i	$-0.584868\pi$
$37$	26.0365	−	45.0965i	0.703688	−	1.21882i	0.967163	−	0.254158i	$-0.0817982\pi$
$38$	29.0128	+	34.5761i	0.763495	+	0.909897i
$39$		0			0
$40$	12.1081	−	68.6683i	0.302702	−	1.71671i
$41$	−1.06400	−	0.187611i	−0.0259512	−	0.00457589i	0.160658	−	0.987010i	$-0.448639\pi$
$41$	−1.06400	−	0.187611i	−0.0259512	−	0.00457589i	−0.186609	+	0.982434i	$0.559750\pi$
$42$		0			0
$43$	37.0026	−	31.0488i	0.860525	−	0.722066i	−0.101556	−	0.994830i	$-0.532382\pi$
$43$	37.0026	−	31.0488i	0.860525	−	0.722066i	0.962081	+	0.272764i	$0.0879377\pi$
$44$	−7.59780	−	4.38659i	−0.172677	−	0.0996953i
$45$		0			0
$46$	41.2384	+	71.4270i	0.896487	+	1.55276i
$47$	−19.7018	+	54.1303i	−0.419187	+	1.15171i	0.532979	+	0.846128i	$0.321072\pi$
$47$	−19.7018	+	54.1303i	−0.419187	+	1.15171i	−0.952167	+	0.305579i	$0.901150\pi$
$48$		0			0
$49$	−6.34137	−	5.32104i	−0.129416	−	0.108593i
$50$	−25.3634	−	69.6853i	−0.507267	−	1.39371i
$51$		0			0
$52$	6.53661	+	37.0709i	0.125704	+	0.712903i
$53$		−	13.8414i		−	0.261159i	−0.991438	−	0.130579i	$-0.958316\pi$
$53$		−	13.8414i		−	0.261159i	0.991438	−	0.130579i	$-0.0416837\pi$
$54$		0			0
$55$	−8.55969			−0.155631
$56$	−63.7087	+	11.2336i	−1.13766	+	0.200599i
$57$		0			0
$58$	−96.7949	+	35.2305i	−1.66888	+	0.607422i
$59$	−38.7615	+	46.1941i	−0.656974	+	0.782952i	−0.986948	−	0.161039i	$-0.948516\pi$
$59$	−38.7615	+	46.1941i	−0.656974	+	0.782952i	0.329974	+	0.943990i	$0.392960\pi$
$60$		0			0
$61$	−94.8938	−	34.5385i	−1.55564	−	0.566205i	−0.585905	−	0.810380i	$-0.699261\pi$
$61$	−94.8938	−	34.5385i	−1.55564	−	0.566205i	−0.969731	+	0.244175i	$0.921483\pi$
$62$	45.7111	−	26.3913i	0.737276	−	0.425666i
$63$		0			0
$64$	−48.0117	+	83.1587i	−0.750183	+	1.29935i
$65$	23.6075	+	28.1344i	0.363193	+	0.432836i
$66$		0			0
$67$	−13.6531	+	77.4304i	−0.203777	+	1.15568i	0.695575	+	0.718453i	$0.255150\pi$
$67$	−13.6531	+	77.4304i	−0.203777	+	1.15568i	−0.899352	+	0.437225i	$0.855961\pi$
$68$	110.163	+	19.4247i	1.62005	+	0.285658i
$69$		0			0
$70$	−111.767	+	93.7840i	−1.59668	+	1.33977i
$71$	−39.7545	−	22.9523i	−0.559922	−	0.323271i	0.193192	−	0.981161i	$-0.438116\pi$
$71$	−39.7545	−	22.9523i	−0.559922	−	0.323271i	−0.753114	+	0.657890i	$0.771449\pi$
$72$		0			0
$73$	−34.4926	−	59.7430i	−0.472502	−	0.818397i	0.527003	−	0.849863i	$-0.323316\pi$
$73$	−34.4926	−	59.7430i	−0.472502	−	0.818397i	−0.999505	+	0.0314663i	$0.989982\pi$
$74$	59.2024	−	162.657i	0.800032	−	2.19807i
$75$		0			0
$76$	73.3283	+	61.5297i	0.964846	+	0.809602i
$77$	2.71614	+	7.46253i	0.0352745	+	0.0969160i
$78$		0			0
$79$	6.86682	+	38.9437i	0.0869218	+	0.492958i	0.996925	+	0.0783576i	$0.0249676\pi$
$79$	6.86682	+	38.9437i	0.0869218	+	0.492958i	−0.910003	+	0.414601i	$0.863921\pi$
$80$		−	37.8265i		−	0.472831i
$81$		0			0
$82$	−3.59141			−0.0437976
$83$	−41.5621	+	7.32852i	−0.500748	+	0.0882955i	−0.418317	−	0.908301i	$-0.637380\pi$
$83$	−41.5621	+	7.32852i	−0.500748	+	0.0882955i	−0.0824318	+	0.996597i	$0.526269\pi$
$84$		0			0
$85$	102.558	−	37.3282i	1.20657	−	0.439156i
$86$	103.210	−	123.001i	1.20011	−	1.43024i
$87$		0			0
$88$	−11.8551	−	4.31490i	−0.134717	−	0.0490330i
$89$	61.8262	−	35.6954i	0.694676	−	0.401072i	−0.110685	−	0.993856i	$-0.535305\pi$
$89$	61.8262	−	35.6954i	0.694676	−	0.401072i	0.805361	+	0.592784i	$0.201971\pi$
$90$		0			0
$91$	17.0371	−	29.5091i	0.187221	−	0.324276i
$92$	112.433	+	133.993i	1.22210	+	1.45644i
$93$		0			0
$94$	−33.2506	+	188.574i	−0.353730	+	2.00610i
$95$	91.9750	+	16.2177i	0.968158	+	0.170712i
$96$		0			0
$97$	0.867150	−	0.727625i	0.00893969	−	0.00750129i	−0.638307	−	0.769782i	$-0.720365\pi$
$97$	0.867150	−	0.727625i	0.00893969	−	0.00750129i	0.647247	+	0.762281i	$0.275920\pi$
$98$	−23.8306	−	13.7586i	−0.243169	−	0.140394i
$99$		0			0
$100$	−78.6359	−	136.201i	−0.786359	−	1.36201i
$101$	3.88344	−	10.6697i	0.0384499	−	0.105640i	−0.918982	−	0.394299i	$-0.870987\pi$
$101$	3.88344	−	10.6697i	0.0384499	−	0.105640i	0.957432	+	0.288659i	$0.0932095\pi$
$102$		0			0
$103$	−126.072	−	105.787i	−1.22400	−	1.02706i	−0.998606	−	0.0527901i	$-0.983189\pi$
$103$	−126.072	−	105.787i	−1.22400	−	1.02706i	−0.225394	−	0.974268i	$-0.572367\pi$
$104$	18.5138	+	50.8663i	0.178017	+	0.489099i
$105$		0			0
$106$	−7.98961	−	45.3113i	−0.0753737	−	0.427465i
$107$		−	107.863i		−	1.00807i	−0.863685	−	0.504033i	$-0.831849\pi$
$107$		−	107.863i		−	1.00807i	0.863685	−	0.504033i	$-0.168151\pi$
$108$		0			0
$109$	176.312			1.61754			0.808770	−	0.588125i	$-0.200134\pi$
$109$	176.312			1.61754			0.808770	+	0.588125i	$0.200134\pi$
$110$	−28.0211	+	4.94087i	−0.254737	+	0.0449170i
$111$		0			0
$112$	−32.9780	+	12.0030i	−0.294446	+	0.107170i
$113$	80.4991	−	95.9351i	0.712381	−	0.848983i	−0.281486	−	0.959565i	$-0.590827\pi$
$113$	80.4991	−	95.9351i	0.712381	−	0.848983i	0.993867	+	0.110583i	$0.0352717\pi$
$114$		0			0
$115$	160.367	+	58.3687i	1.39449	+	0.507554i
$116$	−189.188	+	109.228i	−1.63093	+	0.941617i
$117$		0			0
$118$	−100.226	+	173.596i	−0.849369	+	1.47115i
$119$	−65.0872	−	77.5679i	−0.546951	−	0.651831i
$120$		0			0
$121$	20.7425	−	117.637i	0.171426	−	0.972203i
$122$	−330.582	−	58.2905i	−2.70969	−	0.477791i
$123$		0			0
$124$	85.7513	−	71.9539i	0.691542	−	0.580273i
$125$	16.0295	+	9.25462i	0.128236	+	0.0740369i
$126$		0			0
$127$	−0.644295	−	1.11595i	−0.00507319	−	0.00878702i	0.863478	−	0.504387i	$-0.168282\pi$
$127$	−0.644295	−	1.11595i	−0.00507319	−	0.00878702i	−0.868551	+	0.495600i	$0.834948\pi$
$128$	−78.7041	+	216.238i	−0.614876	+	1.68936i
$129$		0			0
$130$	93.5217	+	78.4740i	0.719397	+	0.603646i
$131$	31.4312	+	86.3564i	0.239933	+	0.659209i	0.999957	+	0.00931439i	$0.00296490\pi$
$131$	31.4312	+	86.3564i	0.239933	+	0.659209i	−0.760024	+	0.649895i	$0.774813\pi$
$132$		0			0
$133$	−15.0463	−	85.3321i	−0.113130	−	0.641595i
$134$			261.358i			1.95043i
$135$		0			0
$136$	160.860			1.18279
$137$	58.1686	−	10.2567i	0.424588	−	0.0748664i	0.0427287	−	0.999087i	$-0.486395\pi$
$137$	58.1686	−	10.2567i	0.424588	−	0.0748664i	0.381860	+	0.924220i	$0.375284\pi$
$138$		0			0
$139$	47.4498	−	17.2703i	0.341365	−	0.124247i	−0.165648	−	0.986185i	$-0.552972\pi$
$139$	47.4498	−	17.2703i	0.341365	−	0.124247i	0.507013	+	0.861938i	$0.330749\pi$
$140$	−198.895	+	237.034i	−1.42068	+	1.69310i
$141$		0			0
$142$	−143.389	−	52.1894i	−1.00978	−	0.367531i
$143$	5.75477	−	3.32252i	0.0402432	−	0.0232344i
$144$		0			0
$145$	−106.570	+	184.584i	−0.734963	+	1.27299i
$146$	−147.401	−	175.665i	−1.00959	−	1.20319i
$147$		0			0
$148$	63.7460	−	361.522i	0.430717	−	2.44271i
$149$	−71.5827	−	12.6220i	−0.480421	−	0.0847112i	−0.0718072	−	0.997419i	$-0.522877\pi$
$149$	−71.5827	−	12.6220i	−0.480421	−	0.0847112i	−0.408614	+	0.912707i	$0.633988\pi$
$150$		0			0
$151$	−2.59942	+	2.18117i	−0.0172147	+	0.0144449i	−0.651354	−	0.758774i	$-0.725799\pi$
$151$	−2.59942	+	2.18117i	−0.0172147	+	0.0144449i	0.634140	+	0.773219i	$0.281354\pi$
$152$	119.209	+	68.8255i	0.784272	+	0.452800i
$153$		0			0
$154$	13.1991	+	22.8616i	0.0857087	+	0.148452i
$155$	37.3542	−	102.630i	0.240995	−	0.662127i
$156$		0			0
$157$	−196.581	−	164.951i	−1.25211	−	1.05064i	−0.996477	−	0.0838678i	$-0.973273\pi$
$157$	−196.581	−	164.951i	−1.25211	−	1.05064i	−0.255630	−	0.966775i	$-0.582283\pi$
$158$	44.9586	+	123.523i	0.284548	+	0.781789i
$159$		0			0
$160$	26.5979	+	150.844i	0.166237	+	0.942776i
$161$		−	158.333i		−	0.983433i
$162$		0			0
$163$	−265.211			−1.62706			−0.813530	−	0.581523i	$-0.802457\pi$
$163$	−265.211			−1.62706			−0.813530	+	0.581523i	$0.802457\pi$
$164$	−7.50087	+	1.32261i	−0.0457370	+	0.00806467i
$165$		0			0
$166$	−131.828	+	47.9814i	−0.794144	+	0.289045i
$167$	2.08108	−	2.48014i	0.0124616	−	0.0148511i	−0.759778	−	0.650183i	$-0.774692\pi$
$167$	2.08108	−	2.48014i	0.0124616	−	0.0148511i	0.772239	+	0.635332i	$0.219137\pi$
$168$		0			0
$169$	132.016	+	48.0498i	0.781159	+	0.284319i
$170$	314.189	−	181.397i	1.84817	−	1.06704i
$171$		0			0
$172$	170.262	−	294.903i	0.989898	−	1.71455i
$173$	123.720	+	147.444i	0.715145	+	0.852276i	0.994149	−	0.108013i	$-0.0344490\pi$
$173$	123.720	+	147.444i	0.715145	+	0.852276i	−0.279005	+	0.960290i	$0.590005\pi$
$174$		0			0
$175$	−24.7209	+	140.199i	−0.141262	+	0.801138i
$176$	−6.74003	−	1.18845i	−0.0382956	−	0.00675255i
$177$		0			0
$178$	181.790	−	152.540i	1.02129	−	0.856968i
$179$	191.363	+	110.484i	1.06907	+	0.617228i	0.927927	−	0.372762i	$-0.121589\pi$
$179$	191.363	+	110.484i	1.06907	+	0.617228i	0.141142	+	0.989989i	$0.454922\pi$
$180$		0			0
$181$	−72.7860	−	126.069i	−0.402133	−	0.696514i	0.591851	−	0.806048i	$-0.298398\pi$
$181$	−72.7860	−	126.069i	−0.402133	−	0.696514i	−0.993983	+	0.109534i	$0.965064\pi$
$182$	38.7394	−	106.435i	0.212854	−	0.584810i
$183$		0			0
$184$	192.683	+	161.680i	1.04719	+	0.878697i
$185$	−122.500	−	336.566i	−0.662161	−	1.81927i
$186$		0			0
$187$	−3.42902	−	19.4470i	−0.0183370	−	0.103994i
$188$			406.093i			2.16007i
$189$		0			0
$190$	310.452			1.63396
$191$	76.9588	−	13.5699i	0.402926	−	0.0710466i	0.0314869	−	0.999504i	$-0.489976\pi$
$191$	76.9588	−	13.5699i	0.402926	−	0.0710466i	0.371439	+	0.928458i	$0.378865\pi$
$192$		0			0
$193$	210.410	−	76.5828i	1.09020	−	0.396802i	0.266508	−	0.963833i	$-0.414130\pi$
$193$	210.410	−	76.5828i	1.09020	−	0.396802i	0.823697	+	0.567031i	$0.191908\pi$
$194$	2.41871	−	2.88250i	0.0124676	−	0.0148583i
$195$		0			0
$196$	−54.8385	−	19.9596i	−0.279788	−	0.101835i
$197$	−299.369	+	172.841i	−1.51964	+	0.877364i	−0.519907	+	0.854223i	$0.674033\pi$
$197$	−299.369	+	172.841i	−1.51964	+	0.877364i	−0.999732	+	0.0231411i	$0.992633\pi$
$198$		0			0
$199$	78.7794	−	136.450i	0.395876	−	0.685678i	−0.597336	−	0.801991i	$-0.703774\pi$
$199$	78.7794	−	136.450i	0.395876	−	0.685678i	0.993213	+	0.116313i	$0.0371075\pi$
$200$	−145.372	−	173.247i	−0.726859	−	0.866237i
$201$		0			0
$202$	6.55405	−	37.1699i	0.0324458	−	0.184009i
$203$	194.741	+	34.3381i	0.959315	+	0.169153i
$204$		0			0
$205$	−5.69266	+	4.77671i	−0.0277691	+	0.0233010i
$206$	−473.773	−	273.533i	−2.29987	−	1.32783i
$207$		0			0
$208$	14.6827	+	25.4311i	0.0705897	+	0.122265i
$209$	5.77943	−	15.8788i	0.0276528	−	0.0759753i
$210$		0			0
$211$	285.220	+	239.328i	1.35175	+	1.13425i	0.978436	+	0.206549i	$0.0662234\pi$
$211$	285.220	+	239.328i	1.35175	+	1.13425i	0.373315	+	0.927705i	$0.378221\pi$
$212$	−33.3736	−	91.6931i	−0.157422	−	0.432515i
$213$		0			0
$214$	−62.2613	−	353.101i	−0.290940	−	1.65001i
$215$		−	332.238i		−	1.54529i
$216$		0			0
$217$	−101.328			−0.466950
$218$	577.176	−	101.772i	2.64760	−	0.466843i
$219$		0			0
$220$	−56.7041	+	20.6386i	−0.257746	+	0.0938119i
$221$	−54.4619	+	64.9051i	−0.246434	+	0.293688i
$222$		0			0
$223$	−87.7683	−	31.9451i	−0.393580	−	0.143251i	0.137646	−	0.990481i	$-0.456046\pi$
$223$	−87.7683	−	31.9451i	−0.393580	−	0.143251i	−0.531226	+	0.847230i	$0.678269\pi$
$224$	123.069	−	71.0541i	0.549417	−	0.317206i
$225$		0			0
$226$	208.146	−	360.520i	0.921001	−	1.59522i
$227$	−234.731	−	279.742i	−1.03406	−	1.23234i	−0.972174	−	0.234261i	$-0.924733\pi$
$227$	−234.731	−	279.742i	−1.03406	−	1.23234i	−0.0618854	−	0.998083i	$-0.519711\pi$
$228$		0			0
$229$	−18.4988	+	104.912i	−0.0807808	+	0.458131i	0.917407	+	0.397951i	$0.130279\pi$
$229$	−18.4988	+	104.912i	−0.0807808	+	0.458131i	−0.998188	+	0.0601798i	$0.980833\pi$
$230$	558.669	+	98.5085i	2.42900	+	0.428298i
$231$		0			0
$232$	−240.646	+	201.926i	−1.03727	+	0.870370i
$233$	206.035	+	118.954i	0.884270	+	0.510533i	0.872064	−	0.489392i	$-0.162781\pi$
$233$	206.035	+	118.954i	0.884270	+	0.510533i	0.0122058	+	0.999926i	$0.496115\pi$
$234$		0			0
$235$	198.105	+	343.128i	0.843001	+	1.46012i
$236$	−145.397	+	399.475i	−0.616089	+	1.69269i
$237$		0			0
$238$	−257.844	−	216.357i	−1.08338	−	0.909063i
$239$	29.3909	+	80.7509i	0.122975	+	0.337870i	0.985870	−	0.167513i	$-0.0535736\pi$
$239$	29.3909	+	80.7509i	0.122975	+	0.337870i	−0.862895	+	0.505383i	$0.831351\pi$
$240$		0			0
$241$	−5.09875	−	28.9164i	−0.0211566	−	0.119985i	0.972400	−	0.233318i	$-0.0749584\pi$
$241$	−5.09875	−	28.9164i	−0.0211566	−	0.119985i	−0.993557	+	0.113333i	$0.963847\pi$
$242$		−	397.069i		−	1.64078i
$243$		0			0
$244$	−711.906			−2.91765
$245$	−56.0728	+	9.88715i	−0.228869	+	0.0403557i
$246$		0			0
$247$	−68.1308	+	24.7976i	−0.275833	+	0.100395i
$248$	103.470	−	123.311i	0.417219	−	0.497223i
$249$		0			0
$250$	57.8162	+	21.0434i	0.231265	+	0.0841735i
$251$	108.333	−	62.5458i	0.431604	−	0.249186i	−0.268426	−	0.963300i	$-0.586503\pi$
$251$	108.333	−	62.5458i	0.431604	−	0.249186i	0.700030	+	0.714114i	$0.253170\pi$
$252$		0			0
$253$	15.4388	−	26.7407i	0.0610228	−	0.105695i
$254$	−2.75333	−	3.28129i	−0.0108399	−	0.0129184i
$255$		0			0
$256$	−66.1313	+	375.049i	−0.258325	+	1.46504i
$257$	−229.989	−	40.5533i	−0.894899	−	0.157795i	−0.292760	−	0.956186i	$-0.594574\pi$
$257$	−229.989	−	40.5533i	−0.894899	−	0.157795i	−0.602139	+	0.798391i	$0.705685\pi$
$258$		0			0
$259$	−254.554	+	213.596i	−0.982835	+	0.824696i
$260$	224.225	+	129.456i	0.862405	+	0.497910i
$261$		0			0
$262$	152.740	+	264.554i	0.582979	+	1.00975i
$263$	−42.2322	+	116.032i	−0.160579	+	0.441186i	−0.993723	−	0.111869i	$-0.964316\pi$
$263$	−42.2322	+	116.032i	−0.160579	+	0.441186i	0.833144	+	0.553056i	$0.186538\pi$
$264$		0			0
$265$	−72.9299	−	61.1955i	−0.275207	−	0.230926i
$266$	−98.5117	−	270.659i	−0.370345	−	1.01751i
$267$		0			0
$268$	96.2501	+	545.862i	0.359142	+	2.03680i
$269$			509.553i			1.89425i	0.320867	+	0.947124i	$0.396026\pi$
$269$			509.553i			1.89425i	−0.320867	+	0.947124i	$0.603974\pi$
$270$		0			0
$271$	49.6722			0.183292			0.0916461	−	0.995792i	$-0.470787\pi$
$271$	49.6722			0.183292			0.0916461	+	0.995792i	$0.470787\pi$
$272$	85.9388	−	15.1533i	0.315951	−	0.0557107i
$273$		0			0
$274$	184.501	−	67.1528i	0.673361	−	0.245083i
$275$	−17.8457	+	21.2677i	−0.0648934	+	0.0773370i
$276$		0			0
$277$	−107.224	−	39.0265i	−0.387092	−	0.140890i	0.141141	−	0.989989i	$-0.454923\pi$
$277$	−107.224	−	39.0265i	−0.387092	−	0.140890i	−0.528233	+	0.849100i	$0.677145\pi$
$278$	145.363	−	83.9254i	0.522889	−	0.301890i
$279$		0			0
$280$	−222.479	+	385.345i	−0.794568	+	1.37623i
$281$	16.6521	+	19.8451i	0.0592600	+	0.0706233i	0.794860	−	0.606793i	$-0.207544\pi$
$281$	16.6521	+	19.8451i	0.0592600	+	0.0706233i	−0.735600	+	0.677416i	$0.763100\pi$
$282$		0			0
$283$	−27.3526	+	155.125i	−0.0966525	+	0.548143i	0.897576	+	0.440860i	$0.145326\pi$
$283$	−27.3526	+	155.125i	−0.0966525	+	0.548143i	−0.994228	+	0.107284i	$0.965785\pi$
$284$	−318.697	−	56.1948i	−1.12217	−	0.197869i
$285$		0			0
$286$	16.9210	−	14.1984i	0.0591644	−	0.0496449i
$287$	5.97082	+	3.44725i	0.0208042	+	0.0120113i
$288$		0			0
$289$	−18.6082	−	32.2303i	−0.0643881	−	0.111523i
$290$	−242.321	+	665.770i	−0.835588	+	2.29576i
$291$		0			0
$292$	−372.547	−	312.604i	−1.27585	−	1.07056i
$293$	143.626	+	394.610i	0.490192	+	1.34679i	0.900505	+	0.434846i	$0.143197\pi$
$293$	143.626	+	394.610i	0.490192	+	1.34679i	−0.410313	+	0.911945i	$0.634581\pi$
$294$		0			0
$295$	72.0236	+	408.466i	0.244148	+	1.38463i
$296$		−	527.892i		−	1.78342i
$297$		0			0
$298$	−241.620			−0.810804
$299$	−130.472	+	23.0058i	−0.436363	+	0.0769425i
$300$		0			0
$301$	−289.653	+	105.425i	−0.962302	+	0.350249i
$302$	−7.25046	+	8.64076i	−0.0240082	+	0.0286118i
$303$		0			0
$304$	70.1708	+	25.5401i	0.230825	+	0.0840134i
$305$	−601.526	+	347.291i	−1.97222	+	1.13866i
$306$		0			0
$307$	−101.037	+	175.001i	−0.329110	+	0.570035i	−0.982336	−	0.187128i	$-0.940082\pi$
$307$	−101.037	+	175.001i	−0.329110	+	0.570035i	0.653225	+	0.757163i	$0.273415\pi$
$308$	35.9864	+	42.8870i	0.116839	+	0.139243i
$309$		0			0
$310$	63.0424	−	357.531i	0.203363	−	1.15333i
$311$	−261.202	−	46.0570i	−0.839879	−	0.148093i	−0.262870	−	0.964831i	$-0.584669\pi$
$311$	−261.202	−	46.0570i	−0.839879	−	0.148093i	−0.577009	+	0.816738i	$0.695780\pi$
$312$		0			0
$313$	211.230	−	177.243i	0.674858	−	0.566273i	−0.239641	−	0.970862i	$-0.577030\pi$
$313$	211.230	−	177.243i	0.674858	−	0.566273i	0.914499	+	0.404589i	$0.132585\pi$
$314$	−738.742	−	426.513i	−2.35268	−	1.35832i
$315$		0			0
$316$	139.388	+	241.428i	0.441102	+	0.764012i
$317$	11.9728	−	32.8949i	0.0377689	−	0.103769i	−0.919375	−	0.393383i	$-0.871305\pi$
$317$	11.9728	−	32.8949i	0.0377689	−	0.103769i	0.957144	+	0.289614i	$0.0935269\pi$
$318$		0			0
$319$	29.5414	+	24.7882i	0.0926064	+	0.0777060i
$320$	225.892	+	620.633i	0.705912	+	1.93948i
$321$		0			0
$322$	−91.3937	−	518.319i	−0.283831	−	1.60969i
$323$			215.457i			0.667049i
$324$		0			0
$325$	119.122			0.366528
$326$	−868.197	+	153.086i	−2.66318	+	0.469590i
$327$		0			0
$328$	−10.2922	+	3.74605i	−0.0313786	+	0.0114209i
$329$	236.285	−	281.593i	0.718191	−	0.855907i
$330$		0			0
$331$	−198.147	−	72.1197i	−0.598633	−	0.217884i	0.0248895	−	0.999690i	$-0.492077\pi$
$331$	−198.147	−	72.1197i	−0.598633	−	0.217884i	−0.623522	+	0.781806i	$0.714299\pi$
$332$	−257.660	+	148.760i	−0.776086	+	0.448073i
$333$		0			0
$334$	5.38105	−	9.32025i	0.0161109	−	0.0279049i
$335$	347.616	+	414.272i	1.03766	+	1.23663i
$336$		0			0
$337$	26.7884	−	151.925i	0.0794908	−	0.450815i	−0.918919	−	0.394446i	$-0.870937\pi$
$337$	26.7884	−	151.925i	0.0794908	−	0.450815i	0.998410	−	0.0563691i	$-0.0179523\pi$
$338$	459.904	+	81.0935i	1.36066	+	0.239921i
$339$		0			0
$340$	589.400	−	494.566i	1.73353	−	1.45460i
$341$	−17.1133	−	9.88034i	−0.0501855	−	0.0289746i
$342$		0			0
$343$	182.756	+	316.543i	0.532817	+	0.922867i
$344$	167.480	−	460.147i	0.486860	−	1.33764i
$345$		0			0
$346$	490.119	+	411.259i	1.41653	+	1.18861i
$347$	−100.310	−	275.600i	−0.289078	−	0.794236i	−0.996196	−	0.0871403i	$-0.972227\pi$
$347$	−100.310	−	275.600i	−0.289078	−	0.794236i	0.707118	−	0.707096i	$-0.249995\pi$
$348$		0			0
$349$	−71.0269	−	402.813i	−0.203515	−	1.15419i	−0.899759	−	0.436387i	$-0.856258\pi$
$349$	−71.0269	−	402.813i	−0.203515	−	1.15419i	0.696244	−	0.717806i	$-0.254853\pi$
$350$			473.227i			1.35208i
$351$		0			0
$352$	27.7135			0.0787316
$353$	492.465	−	86.8349i	1.39508	−	0.245991i	0.574963	−	0.818180i	$-0.305017\pi$
$353$	492.465	−	86.8349i	1.39508	−	0.245991i	0.820122	+	0.572188i	$0.193905\pi$
$354$		0			0
$355$	−296.697	+	107.989i	−0.835766	+	0.304194i
$356$	323.504	−	385.538i	0.908720	−	1.08297i
$357$		0			0
$358$	690.223	+	251.221i	1.92800	+	0.701734i
$359$	216.295	−	124.878i	0.602492	−	0.347849i	−0.167529	−	0.985867i	$-0.553579\pi$
$359$	216.295	−	124.878i	0.602492	−	0.347849i	0.770021	+	0.638018i	$0.220246\pi$
$360$		0			0
$361$	88.3143	−	152.965i	0.244638	−	0.423725i
$362$	−311.043	−	370.687i	−0.859235	−	1.02400i
$363$		0			0
$364$	41.7125	−	236.563i	0.114595	−	0.649900i
$365$	−467.283	−	82.3945i	−1.28023	−	0.225738i
$366$		0			0
$367$	−245.235	+	205.776i	−0.668215	+	0.560699i	−0.912536	−	0.408996i	$-0.865879\pi$
$367$	−245.235	+	205.776i	−0.668215	+	0.560699i	0.244322	+	0.969694i	$0.421435\pi$
$368$	118.171	+	68.2260i	0.321117	+	0.185397i
$369$		0			0
$370$	−595.291	−	1031.07i	−1.60889	−	2.78669i
$371$	−30.2097	+	83.0004i	−0.0814277	+	0.223721i
$372$		0			0
$373$	151.452	+	127.083i	0.406038	+	0.340706i	0.822822	−	0.568299i	$-0.192398\pi$
$373$	151.452	+	127.083i	0.406038	+	0.340706i	−0.416784	+	0.909006i	$0.636843\pi$
$374$	−22.4506	−	61.6824i	−0.0600282	−	0.164926i
$375$		0			0
$376$	101.405	+	575.094i	0.269693	+	1.52950i
$377$		−	165.464i		−	0.438896i
$378$		0			0
$379$	364.905			0.962811			0.481405	−	0.876498i	$-0.340127\pi$
$379$	364.905			0.962811			0.481405	+	0.876498i	$0.340127\pi$
$380$	648.397	−	114.330i	1.70631	−	0.300868i
$381$		0			0
$382$	244.100	−	88.8451i	0.639005	−	0.232579i
$383$	−416.048	+	495.827i	−1.08629	+	1.29459i	−0.133466	+	0.991053i	$0.542611\pi$
$383$	−416.048	+	495.827i	−1.08629	+	1.29459i	−0.952821	+	0.303533i	$0.901834\pi$
$384$		0			0
$385$	51.3284	+	18.6820i	0.133321	+	0.0485247i
$386$	644.593	−	372.156i	1.66993	−	0.964134i
$387$		0			0
$388$	3.99007	−	6.91101i	0.0102837	−	0.0178119i
$389$	−36.3692	−	43.3431i	−0.0934940	−	0.111422i	0.717269	−	0.696796i	$-0.245392\pi$
$389$	−36.3692	−	43.3431i	−0.0934940	−	0.111422i	−0.810763	+	0.585375i	$0.800947\pi$
$390$		0			0
$391$	−68.3660	+	387.723i	−0.174849	+	0.991619i
$392$	−82.6444	−	14.5724i	−0.210828	−	0.0371746i
$393$		0			0
$394$	−880.249	+	738.616i	−2.23413	+	1.87466i
$395$	235.553	+	135.996i	0.596336	+	0.344295i
$396$		0			0
$397$	−327.487	−	567.224i	−0.824905	−	1.42878i	−0.901992	−	0.431752i	$-0.857895\pi$
$397$	−327.487	−	567.224i	−0.824905	−	1.42878i	0.0770876	−	0.997024i	$-0.475438\pi$
$398$	179.131	−	492.157i	0.450077	−	1.23658i
$399$		0			0
$400$	−93.9848	−	78.8626i	−0.234962	−	0.197156i
$401$	43.3291	+	119.046i	0.108053	+	0.296872i	0.981921	−	0.189290i	$-0.0606186\pi$
$401$	43.3291	+	119.046i	0.108053	+	0.296872i	−0.873869	+	0.486162i	$0.838396\pi$
$402$		0			0
$403$	14.7230	+	83.4984i	0.0365336	+	0.207192i
$404$		−	80.0452i		−	0.198132i
$405$		0			0
$406$	657.326			1.61903
$407$	−63.8190	+	11.2530i	−0.156803	+	0.0276487i
$408$		0			0
$409$	−511.819	+	186.287i	−1.25139	+	0.455469i	−0.880871	−	0.473356i	$-0.843042\pi$
$409$	−511.819	+	186.287i	−1.25139	+	0.455469i	−0.370519	+	0.928825i	$0.620820\pi$
$410$	−15.8783	+	18.9230i	−0.0387275	+	0.0461537i
$411$		0			0
$412$	−1090.24	−	396.814i	−2.64621	−	0.963141i
$413$	333.256	−	192.405i	0.806915	−	0.465873i
$414$		0			0
$415$	−145.140	+	251.390i	−0.349736	+	0.605760i
$416$	−76.4335	−	91.0899i	−0.183734	−	0.218966i
$417$		0			0
$418$	9.75391	−	55.3171i	0.0233347	−	0.132338i
$419$	657.974	+	116.018i	1.57034	+	0.276894i	0.889986	−	0.455988i	$-0.150714\pi$
$419$	657.974	+	116.018i	1.57034	+	0.276894i	0.680356	+	0.732881i	$0.261825\pi$
$420$		0			0
$421$	174.221	−	146.189i	0.413827	−	0.347242i	−0.411982	−	0.911192i	$-0.635163\pi$
$421$	174.221	−	146.189i	0.413827	−	0.347242i	0.825809	+	0.563950i	$0.190719\pi$
$422$	1071.84	+	618.829i	2.53991	+	1.46642i
$423$		0			0
$424$	−70.1589	−	121.519i	−0.165469	−	0.286601i
$425$	121.072	−	332.644i	0.284876	−	0.782691i
$426$		0			0
$427$	493.651	+	414.222i	1.15609	+	0.970076i
$428$	−260.073	−	714.544i	−0.607647	−	1.66950i
$429$		0			0
$430$	−191.776	−	1087.62i	−0.445992	−	2.52934i
$431$		−	429.608i		−	0.996769i	−0.866956	−	0.498385i	$-0.833927\pi$
$431$		−	429.608i		−	0.996769i	0.866956	−	0.498385i	$-0.166073\pi$
$432$		0			0
$433$	−11.9987			−0.0277106			−0.0138553	−	0.999904i	$-0.504410\pi$
$433$	−11.9987			−0.0277106			−0.0138553	+	0.999904i	$0.504410\pi$
$434$	−331.709	+	58.4892i	−0.764305	+	0.134768i
$435$		0			0
$436$	1167.99	−	425.113i	2.67887	−	0.975029i
$437$	−216.556	+	258.082i	−0.495552	+	0.590576i
$438$		0			0
$439$	70.8223	+	25.7772i	0.161327	+	0.0587180i	0.421421	−	0.906865i	$-0.361531\pi$
$439$	70.8223	+	25.7772i	0.161327	+	0.0587180i	−0.260094	+	0.965583i	$0.583754\pi$
$440$	−75.1487	+	43.3871i	−0.170793	+	0.0986071i
$441$		0			0
$442$	−140.822	+	243.911i	−0.318602	+	0.551834i
$443$	−159.401	−	189.967i	−0.359822	−	0.428819i	0.555516	−	0.831506i	$-0.312521\pi$
$443$	−159.401	−	189.967i	−0.359822	−	0.428819i	−0.915338	+	0.402687i	$0.868076\pi$
$444$		0			0
$445$	85.2676	−	483.576i	0.191612	−	1.08669i
$446$	−305.759	−	53.9135i	−0.685558	−	0.120882i
$447$		0			0
$448$	469.402	−	393.875i	1.04777	−	0.879186i
$449$	−178.012	−	102.775i	−0.396462	−	0.228898i	0.288494	−	0.957482i	$-0.406845\pi$
$449$	−178.012	−	102.775i	−0.396462	−	0.228898i	−0.684956	+	0.728584i	$0.740179\pi$
$450$		0			0
$451$	0.672273	+	1.16441i	0.00149063	+	0.00258184i
$452$	301.958	−	829.622i	0.668048	−	1.83545i
$453$		0			0
$454$	−929.893	−	780.273i	−2.04822	−	1.71866i
$455$	−80.1584	−	220.233i	−0.176172	−	0.484029i
$456$		0			0
$457$	110.972	+	629.353i	0.242827	+	1.37714i	0.825486	+	0.564423i	$0.190901\pi$
$457$	110.972	+	629.353i	0.242827	+	1.37714i	−0.582659	+	0.812717i	$0.697988\pi$
$458$			354.118i			0.773184i
$459$		0			0
$460$	1203.09			2.61542
$461$	139.493	−	24.5964i	0.302588	−	0.0533545i	−0.0202925	−	0.999794i	$-0.506460\pi$
$461$	139.493	−	24.5964i	0.302588	−	0.0533545i	0.322881	+	0.946440i	$0.395349\pi$
$462$		0			0
$463$	264.759	−	96.3643i	0.571833	−	0.208130i	−0.0398874	−	0.999204i	$-0.512700\pi$
$463$	264.759	−	96.3643i	0.571833	−	0.208130i	0.611721	+	0.791074i	$0.290478\pi$
$464$	−109.543	+	130.548i	−0.236083	+	0.281353i
$465$		0			0
$466$	743.141	+	270.481i	1.59472	+	0.580432i
$467$	−462.423	+	266.980i	−0.990199	+	0.571692i	−0.905334	−	0.424700i	$-0.860379\pi$
$467$	−462.423	+	266.980i	−0.990199	+	0.571692i	−0.0848656	+	0.996392i	$0.527046\pi$
$468$		0			0
$469$	250.868	−	434.515i	0.534899	−	0.926472i
$470$	846.582	+	1008.92i	1.80124	+	2.14663i
$471$		0			0
$472$	−106.154	+	602.029i	−0.224902	+	1.27549i
$473$	−59.1992	−	10.4384i	−0.125157	−	0.0220685i
$474$		0			0
$475$	232.049	−	194.713i	0.488525	−	0.409921i
$476$	−618.201	−	356.918i	−1.29874	−	0.749828i
$477$		0			0
$478$	142.826	+	247.382i	0.298799	+	0.517535i
$479$	−58.0298	+	159.436i	−0.121148	+	0.332851i	−0.985412	−	0.170188i	$-0.945563\pi$
$479$	−58.0298	+	159.436i	−0.121148	+	0.332851i	0.864264	+	0.503039i	$0.167785\pi$
$480$		0			0
$481$	212.999	+	178.727i	0.442825	+	0.371574i
$482$	−33.3826	−	91.7180i	−0.0692585	−	0.190286i
$483$		0			0
$484$	−146.228	−	829.303i	−0.302125	−	1.71344i
$485$		−	7.78596i		−	0.0160535i
$486$		0			0
$487$	20.8058			0.0427223			0.0213612	−	0.999772i	$-0.493200\pi$
$487$	20.8058			0.0427223			0.0213612	+	0.999772i	$0.493200\pi$
$488$	−1008.18	+	177.769i	−2.06593	+	0.364280i
$489$		0			0
$490$	−177.853	+	64.7333i	−0.362966	+	0.132109i
$491$	−97.1410	+	115.768i	−0.197843	+	0.235780i	−0.855840	−	0.517240i	$-0.826959\pi$
$491$	−97.1410	+	115.768i	−0.197843	+	0.235780i	0.657997	+	0.753020i	$0.271404\pi$
$492$		0			0
$493$	−462.052	−	168.173i	−0.937226	−	0.341122i
$494$	−208.720	+	120.504i	−0.422510	+	0.243936i
$495$		0			0
$496$	43.6626	−	75.6258i	0.0880294	−	0.152471i
$497$	188.294	+	224.400i	0.378862	+	0.451510i
$498$		0			0
$499$	141.971	−	805.156i	0.284510	−	1.61354i	−0.422519	−	0.906354i	$-0.638854\pi$
$499$	141.971	−	805.156i	0.284510	−	1.61354i	0.707029	−	0.707184i	$-0.250035\pi$
$500$	128.502	+	22.6584i	0.257005	+	0.0453168i
$501$		0			0
$502$	318.535	−	267.283i	0.634532	−	0.532436i
$503$	201.176	+	116.149i	0.399953	+	0.230913i	0.686464	−	0.727164i	$-0.259162\pi$
$503$	201.176	+	116.149i	0.399953	+	0.230913i	−0.286511	+	0.958077i	$0.592495\pi$
$504$		0			0
$505$	−39.0487	−	67.6343i	−0.0773241	−	0.133929i
$506$	35.1050	−	96.4503i	0.0693776	−	0.190613i
$507$		0			0
$508$	−6.95888	−	5.83920i	−0.0136986	−	0.0114945i
$509$	−110.730	−	304.227i	−0.217543	−	0.597696i	0.782133	−	0.623111i	$-0.214131\pi$
$509$	−110.730	−	304.227i	−0.217543	−	0.597696i	−0.999677	+	0.0254151i	$0.991909\pi$
$510$		0			0
$511$	76.4435	+	433.533i	0.149596	+	0.848401i
$512$			345.476i			0.674758i
$513$		0			0
$514$	−776.303			−1.51032
$515$	−1114.78	+	196.565i	−2.16461	+	0.381680i
$516$		0			0
$517$	67.3638	−	24.5184i	0.130297	−	0.0474244i
$518$	−710.018	+	846.166i	−1.37069	+	1.63353i
$519$		0			0
$520$	349.866	+	127.341i	0.672819	+	0.244886i
$521$	−480.156	+	277.218i	−0.921604	+	0.532088i	−0.884146	−	0.467210i	$-0.845259\pi$
$521$	−480.156	+	277.218i	−0.921604	+	0.532088i	−0.0374577	+	0.999298i	$0.511926\pi$
$522$		0			0
$523$	−472.881	+	819.053i	−0.904170	+	1.56607i	−0.0821414	+	0.996621i	$0.526176\pi$
$523$	−472.881	+	819.053i	−0.904170	+	1.56607i	−0.822028	+	0.569447i	$0.807157\pi$
$524$	416.435	+	496.288i	0.794723	+	0.947114i
$525$		0			0
$526$	−71.2750	+	404.221i	−0.135504	+	0.768481i
$527$	248.131	+	43.7522i	0.470837	+	0.0830212i
$528$		0			0
$529$	−66.3546	+	55.6782i	−0.125434	+	0.105252i
$530$	−274.068	−	158.233i	−0.517109	−	0.298553i
$531$		0			0
$532$	−305.423	−	529.008i	−0.574103	−	0.994376i
$533$	1.97311	−	5.42108i	0.00370190	−	0.0101709i
$534$		0			0
$535$	−568.327	−	476.883i	−1.06229	−	0.891370i
$536$	272.612	+	748.995i	0.508604	+	1.39738i
$537$		0			0
$538$	294.127	+	1668.08i	0.546704	+	3.10051i
$539$			10.3019i			0.0191129i
$540$		0			0
$541$	−390.158			−0.721179			−0.360590	−	0.932725i	$-0.617425\pi$
$541$	−390.158			−0.721179			−0.360590	+	0.932725i	$0.617425\pi$
$542$	162.607	−	28.6721i	0.300013	−	0.0529005i
$543$		0			0
$544$	−332.051	+	120.857i	−0.610388	+	0.222163i
$545$	779.509	−	928.982i	1.43029	−	1.70455i
$546$		0			0
$547$	436.230	+	158.775i	0.797495	+	0.290265i	0.708448	−	0.705763i	$-0.249396\pi$
$547$	436.230	+	158.775i	0.797495	+	0.290265i	0.0890472	+	0.996027i	$0.471618\pi$
$548$	360.611	−	208.199i	0.658049	−	0.379925i
$549$		0			0
$550$	−46.1436	+	79.9230i	−0.0838974	+	0.145315i
$551$	−270.462	−	322.324i	−0.490856	−	0.584979i
$552$		0			0
$553$	43.8198	−	248.514i	0.0792401	−	0.449393i
$554$	−373.538	−	65.8648i	−0.674256	−	0.118889i
$555$		0			0
$556$	272.692	−	228.816i	0.490454	−	0.411540i
$557$	203.531	+	117.509i	0.365406	+	0.210967i	0.671450	−	0.741050i	$-0.265672\pi$
$557$	203.531	+	117.509i	0.365406	+	0.210967i	−0.306043	+	0.952018i	$0.599005\pi$
$558$		0			0
$559$	128.961	+	223.367i	0.230700	+	0.399584i
$560$	−82.5584	+	226.827i	−0.147426	+	0.405049i
$561$		0			0
$562$	65.9674	+	55.3532i	0.117380	+	0.0984933i
$563$	−28.5919	−	78.5555i	−0.0507849	−	0.139530i	0.911707	−	0.410841i	$-0.134765\pi$
$563$	−28.5919	−	78.5555i	−0.0507849	−	0.139530i	−0.962492	+	0.271311i	$0.912543\pi$
$564$		0			0
$565$	−149.577	−	848.294i	−0.264738	−	1.50141i
$566$			523.606i			0.925099i
$567$		0			0
$568$	−465.359			−0.819295
$569$	907.958	−	160.097i	1.59571	−	0.281366i	0.696060	−	0.717983i	$-0.254935\pi$
$569$	907.958	−	160.097i	1.59571	−	0.281366i	0.899647	+	0.436617i	$0.143824\pi$
$570$		0			0
$571$	−374.563	+	136.330i	−0.655977	+	0.238756i	−0.648499	−	0.761216i	$-0.724603\pi$
$571$	−374.563	+	136.330i	−0.655977	+	0.238756i	−0.00747873	+	0.999972i	$0.502381\pi$
$572$	30.1117	−	35.8858i	0.0526429	−	0.0627374i
$573$		0			0
$574$	21.5360	+	7.83845i	0.0375191	+	0.0136558i
$575$	479.365	−	276.762i	0.833679	−	0.481325i
$576$		0			0
$577$	8.33213	−	14.4317i	0.0144404	−	0.0250116i	−0.858715	−	0.512454i	$-0.828737\pi$
$577$	8.33213	−	14.4317i	0.0144404	−	0.0250116i	0.873155	+	0.487442i	$0.162070\pi$
$578$	−79.5200	−	94.7682i	−0.137578	−	0.163959i
$579$		0			0
$580$	−260.918	+	1479.74i	−0.449859	+	2.55128i
$581$	265.223	+	46.7660i	0.456495	+	0.0804923i
$582$		0			0
$583$	−13.1953	+	11.0722i	−0.0226335	+	0.0189918i
$584$	−605.648	−	349.671i	−1.03707	−	0.598751i
$585$		0			0
$586$	697.955	+	1208.89i	1.19105	+	2.06296i
$587$	63.7700	−	175.207i	0.108637	−	0.298478i	−0.873448	−	0.486918i	$-0.838121\pi$
$587$	63.7700	−	175.207i	0.108637	−	0.298478i	0.982085	+	0.188440i	$0.0603432\pi$
$588$		0			0
$589$	165.164	+	138.589i	0.280415	+	0.235296i
$590$	471.554	+	1295.58i	0.799245	+	2.19591i
$591$		0			0
$592$	−49.7286	−	282.025i	−0.0840010	−	0.476393i
$593$		−	373.725i		−	0.630228i	−0.949054	−	0.315114i	$-0.897957\pi$
$593$		−	373.725i		−	0.630228i	0.949054	−	0.315114i	$-0.102043\pi$
$594$		0			0
$595$	−696.466			−1.17053
$596$	−504.637	+	88.9811i	−0.846706	+	0.149297i
$597$		0			0
$598$	−413.836	+	150.624i	−0.692034	+	0.251880i
$599$	−9.51395	+	11.3383i	−0.0158831	+	0.0189287i	−0.773928	−	0.633274i	$-0.781711\pi$
$599$	−9.51395	+	11.3383i	−0.0158831	+	0.0189287i	0.758044	+	0.652203i	$0.226155\pi$
$600$		0			0
$601$	182.608	+	66.4637i	0.303839	+	0.110589i	0.489441	−	0.872037i	$-0.337201\pi$
$601$	182.608	+	66.4637i	0.303839	+	0.110589i	−0.185601	+	0.982625i	$0.559423\pi$
$602$	−887.356	+	512.315i	−1.47401	+	0.851022i
$603$		0			0
$604$	−11.9609	+	20.7169i	−0.0198028	+	0.0342995i
$605$	−528.117	−	629.385i	−0.872921	−	1.04031i
$606$		0			0
$607$	100.749	−	571.378i	0.165979	−	0.941315i	−0.782070	−	0.623191i	$-0.785836\pi$
$607$	100.749	−	571.378i	0.165979	−	0.941315i	0.948049	−	0.318124i	$-0.103053\pi$
$608$	−297.785	−	52.5076i	−0.489779	−	0.0863612i
$609$		0			0
$610$	−1768.70	+	1484.11i	−2.89950	+	2.43297i
$611$	−266.377	−	153.793i	−0.435968	−	0.251706i
$612$		0			0
$613$	80.1803	+	138.876i	0.130800	+	0.226552i	0.923985	−	0.382428i	$-0.124912\pi$
$613$	80.1803	+	138.876i	0.130800	+	0.226552i	−0.793185	+	0.608980i	$0.791579\pi$
$614$	−229.740	+	631.205i	−0.374169	+	1.02802i
$615$		0			0
$616$	61.6719	+	51.7489i	0.100117	+	0.0840079i
$617$	142.229	+	390.772i	0.230518	+	0.633343i	0.999986	−	0.00534297i	$-0.00170073\pi$
$617$	142.229	+	390.772i	0.230518	+	0.633343i	−0.769468	+	0.638685i	$0.779479\pi$
$618$		0			0
$619$	−113.862	−	645.746i	−0.183946	−	1.04321i	−0.927302	−	0.374313i	$-0.877878\pi$
$619$	−113.862	−	645.746i	−0.183946	−	1.04321i	0.743356	−	0.668895i	$-0.233233\pi$
$620$		−	769.943i		−	1.24184i
$621$		0			0
$622$	−881.659			−1.41746
$623$	−448.650	+	79.1091i	−0.720144	+	0.126981i
$624$		0			0
$625$	643.721	−	234.295i	1.02995	−	0.374873i
$626$	589.176	−	702.153i	0.941176	−	1.12165i
$627$		0			0
$628$	−1699.98	−	618.742i	−2.70697	−	0.985258i
$629$	715.577	−	413.139i	1.13764	−	0.656818i
$630$		0			0
$631$	321.500	−	556.855i	0.509509	−	0.882496i	−0.490430	−	0.871481i	$-0.663160\pi$
$631$	321.500	−	556.855i	0.509509	−	0.882496i	0.999939	−	0.0110155i	$-0.00350642\pi$
$632$	257.683	+	307.095i	0.407727	+	0.485910i
$633$		0			0
$634$	20.2063	−	114.596i	0.0318712	−	0.180751i
$635$	−8.72847	−	1.53906i	−0.0137456	−	0.00242372i
$636$		0			0
$637$	33.8606	−	28.4124i	0.0531563	−	0.0446034i
$638$	111.016	+	64.0948i	0.174006	+	0.100462i
$639$		0			0
$640$	791.384	+	1370.72i	1.23654	+	2.14175i
$641$	−40.2366	+	110.549i	−0.0627717	+	0.172464i	−0.967114	−	0.254345i	$-0.918140\pi$
$641$	−40.2366	+	110.549i	−0.0627717	+	0.172464i	0.904342	+	0.426809i	$0.140362\pi$
$642$		0			0
$643$	332.529	+	279.025i	0.517153	+	0.433943i	0.863638	−	0.504113i	$-0.168180\pi$
$643$	332.529	+	279.025i	0.517153	+	0.433943i	−0.346485	+	0.938055i	$0.612625\pi$
$644$	−381.762	−	1048.88i	−0.592799	−	1.62870i
$645$		0			0
$646$	124.367	+	705.322i	0.192519	+	1.09183i
$647$		−	202.797i		−	0.313443i	−0.987643	−	0.156721i	$-0.949908\pi$
$647$		−	202.797i		−	0.313443i	0.987643	−	0.156721i	$-0.0500924\pi$
$648$		0			0
$649$	75.0446			0.115631
$650$	389.958	−	68.7601i	0.599935	−	0.105785i
$651$		0			0
$652$	−1756.90	+	639.461i	−2.69464	+	0.980768i
$653$	575.359	−	685.687i	0.881102	−	1.05006i	−0.117275	−	0.993099i	$-0.537416\pi$
$653$	575.359	−	685.687i	0.881102	−	1.05006i	0.998377	−	0.0569567i	$-0.0181397\pi$
$654$		0			0
$655$	593.973	+	216.188i	0.906828	+	0.330059i
$656$	−5.14569	+	2.97087i	−0.00784404	+	0.00452876i
$657$		0			0
$658$	610.961	−	1058.22i	0.928513	−	1.60823i
$659$	541.106	+	644.865i	0.821102	+	0.978551i	0.999986	−	0.00531879i	$-0.00169303\pi$
$659$	541.106	+	644.865i	0.821102	+	0.978551i	−0.178884	+	0.983870i	$0.557249\pi$
$660$		0			0
$661$	39.2395	−	222.538i	0.0593639	−	0.336669i	−0.940632	−	0.339427i	$-0.889767\pi$
$661$	39.2395	−	222.538i	0.0593639	−	0.336669i	0.999996	+	0.00275788i	$0.000877862\pi$
$662$	−690.286	−	121.716i	−1.04273	−	0.183861i
$663$		0			0
$664$	−327.743	+	275.009i	−0.493589	+	0.414170i
$665$	−516.135	−	297.991i	−0.776143	−	0.448106i
$666$		0			0
$667$	−384.430	−	665.853i	−0.576357	−	0.998280i
$668$	7.80628	−	21.4476i	0.0116860	−	0.0321071i
$669$		0			0
$670$	1377.09	+	1155.51i	2.05535	+	1.72465i
$671$	42.9823	+	118.093i	0.0640571	+	0.175996i
$672$		0			0
$673$	−19.1977	−	108.875i	−0.0285255	−	0.161776i	0.967217	−	0.253950i	$-0.0817297\pi$
$673$	−19.1977	−	108.875i	−0.0285255	−	0.161776i	−0.995743	+	0.0921733i	$0.970619\pi$
$674$		−	512.805i		−	0.760838i
$675$		0			0
$676$	990.401			1.46509
$677$	2.81567	−	0.496479i	0.00415904	−	0.000733352i	−0.171568	−	0.985172i	$-0.554883\pi$
$677$	2.81567	−	0.496479i	0.00415904	−	0.000733352i	0.175727	+	0.984439i	$0.443772\pi$
$678$		0			0
$679$	−6.78797	+	2.47062i	−0.00999702	+	0.00363862i
$680$	711.191	−	847.564i	1.04587	−	1.24642i
$681$		0			0
$682$	−61.7253	−	22.4662i	−0.0905063	−	0.0329416i
$683$	843.279	−	486.868i	1.23467	−	0.712837i	0.266670	−	0.963788i	$-0.414077\pi$
$683$	843.279	−	486.868i	1.23467	−	0.712837i	0.968000	+	0.250951i	$0.0807434\pi$
$684$		0			0
$685$	203.132	−	351.835i	0.296543	−	0.513628i
$686$	780.990	+	930.747i	1.13847	+	1.35677i
$687$		0			0
$688$	46.1288	−	261.609i	0.0670476	−	0.380246i
$689$	72.7851	+	12.8340i	0.105639	+	0.0186270i
$690$		0			0
$691$	501.018	−	420.404i	0.725063	−	0.608400i	−0.203718	−	0.979030i	$-0.565303\pi$
$691$	501.018	−	420.404i	0.725063	−	0.608400i	0.928781	+	0.370630i	$0.120858\pi$
$692$	1175.10	+	678.443i	1.69812	+	0.980409i
$693$		0			0
$694$	−487.460	−	844.305i	−0.702391	−	1.21658i
$695$	118.788	−	326.367i	0.170918	−	0.469592i
$696$		0			0
$697$	−13.1328	−	11.0197i	−0.0188419	−	0.0158102i
$698$	−465.028	−	1277.65i	−0.666230	−	1.83045i
$699$		0			0
$700$	174.275	+	988.362i	0.248964	+	1.41195i
$701$			41.7083i			0.0594983i	0.999557	+	0.0297492i	$0.00947085\pi$
$701$			41.7083i			0.0594983i	−0.999557	+	0.0297492i	$0.990529\pi$
$702$		0			0
$703$	707.064			1.00578
$704$	117.683	−	20.7507i	0.167164	−	0.0294755i
$705$		0			0
$706$	1562.01	−	568.527i	2.21249	−	0.805279i
$707$	−46.5743	+	55.5051i	−0.0658759	+	0.0785079i
$708$		0			0
$709$	465.612	+	169.469i	0.656716	+	0.239025i	0.648818	−	0.760944i	$-0.275264\pi$
$709$	465.612	+	169.469i	0.656716	+	0.239025i	0.00789831	+	0.999969i	$0.497486\pi$
$710$	−908.936	+	524.774i	−1.28019	+	0.739119i
$711$		0			0
$712$	361.863	−	626.766i	0.508235	−	0.880289i
$713$	253.244	+	301.805i	0.355181	+	0.423288i
$714$		0			0
$715$	7.93669	−	45.0112i	0.0111003	−	0.0629527i
$716$	1534.09	+	270.501i	2.14258	+	0.377795i
$717$		0			0
$718$	635.981	−	533.652i	0.885768	−	0.743248i
$719$	−124.160	−	71.6839i	−0.172684	−	0.0996994i	0.411167	−	0.911560i	$-0.365121\pi$
$719$	−124.160	−	71.6839i	−0.172684	−	0.0996994i	−0.583851	+	0.811861i	$0.698455\pi$
$720$		0			0
$721$	525.108	+	909.514i	0.728305	+	1.26146i
$722$	200.811	−	551.725i	0.278132	−	0.764161i
$723$		0			0
$724$	−786.145	−	659.654i	−1.08584	−	0.911124i
$725$	236.441	+	649.616i	0.326126	+	0.896023i
$726$		0			0
$727$	−57.2876	−	324.894i	−0.0788001	−	0.446897i	−0.998523	−	0.0543294i	$-0.982698\pi$
$727$	−57.2876	−	324.894i	−0.0788001	−	0.446897i	0.919723	−	0.392568i	$-0.128413\pi$
$728$		−	345.429i		−	0.474490i
$729$		0			0
$730$	−1577.26			−2.16063
$731$	754.820	−	133.095i	1.03258	−	0.182073i
$732$		0			0
$733$	−173.220	+	63.0471i	−0.236317	+	0.0860124i	−0.457464	−	0.889228i	$-0.651242\pi$
$733$	−173.220	+	63.0471i	−0.236317	+	0.0860124i	0.221147	+	0.975240i	$0.429020\pi$
$734$	−684.023	+	815.187i	−0.931912	+	1.11061i
$735$		0			0
$736$	−519.215	−	188.979i	−0.705455	−	0.256765i
$737$	84.7378	−	48.9234i	0.114977	−	0.0663818i
$738$		0			0
$739$	225.818	−	391.128i	0.305572	−	0.529267i	−0.671816	−	0.740718i	$-0.734486\pi$
$739$	225.818	−	391.128i	0.305572	−	0.529267i	0.977389	+	0.211451i	$0.0678189\pi$
$740$	−1623.01	−	1934.23i	−2.19326	−	2.61383i
$741$		0			0
$742$	−50.9847	+	289.149i	−0.0687125	+	0.389688i
$743$	588.697	+	103.803i	0.792325	+	0.139708i	0.555141	−	0.831757i	$-0.312664\pi$
$743$	588.697	+	103.803i	0.792325	+	0.139708i	0.237184	+	0.971465i	$0.423776\pi$
$744$		0			0
$745$	−382.986	+	321.363i	−0.514075	+	0.431360i
$746$	569.151	+	328.600i	0.762937	+	0.440482i
$747$		0			0
$748$	−69.6051	−	120.560i	−0.0930549	−	0.161176i
$749$	−235.417	+	646.804i	−0.314309	+	0.863556i
$750$		0			0
$751$	−477.323	−	400.522i	−0.635584	−	0.533318i	0.267075	−	0.963676i	$-0.413943\pi$
$751$	−477.323	−	400.522i	−0.635584	−	0.533318i	−0.902658	+	0.430358i	$0.858387\pi$
$752$	108.350	+	297.690i	0.144083	+	0.395864i
$753$		0			0
$754$	−95.5099	−	541.663i	−0.126671	−	0.718386i
$755$			23.3397i			0.0309135i
$756$		0			0
$757$	−1029.21			−1.35960			−0.679798	−	0.733399i	$-0.737933\pi$
$757$	−1029.21			−1.35960			−0.679798	+	0.733399i	$0.737933\pi$
$758$	1194.56	−	210.633i	1.57593	−	0.277879i
$759$		0			0
$760$	889.687	−	323.820i	1.17064	−	0.426078i
$761$	−400.389	+	477.165i	−0.526135	+	0.627023i	−0.962020	−	0.272979i	$-0.911991\pi$
$761$	−400.389	+	477.165i	−0.526135	+	0.627023i	0.435885	+	0.900002i	$0.356435\pi$
$762$		0			0
$763$	−1057.26	−	384.811i	−1.38566	−	0.504340i
$764$	477.099	−	275.453i	0.624475	−	0.360541i
$765$		0			0
$766$	−1075.77	+	1863.30i	−1.40441	+	2.43250i
$767$	−206.972	−	246.660i	−0.269846	−	0.321590i
$768$		0			0
$769$	−182.061	+	1032.52i	−0.236751	+	1.34268i	0.602144	+	0.798388i	$0.294313\pi$
$769$	−182.061	+	1032.52i	−0.236751	+	1.34268i	−0.838895	+	0.544294i	$0.816798\pi$
$770$	178.813	+	31.5296i	0.232225	+	0.0409475i
$771$		0			0
$772$	1209.22	−	1014.65i	1.56634	−	1.31432i
$773$	−719.632	−	415.480i	−0.930960	−	0.537490i	−0.0438447	−	0.999038i	$-0.513961\pi$
$773$	−719.632	−	415.480i	−0.930960	−	0.537490i	−0.887115	+	0.461549i	$0.847294\pi$
$774$		0			0
$775$	−177.119	−	306.779i	−0.228541	−	0.395844i
$776$	3.92487	−	10.7835i	0.00505782	−	0.0138962i
$777$		0			0
$778$	−144.077	−	120.895i	−0.185189	−	0.155392i
$779$	−5.01750	−	13.7855i	−0.00644095	−	0.0176964i
$780$		0			0
$781$	9.92001	+	56.2592i	0.0127017	+	0.0720348i
$782$			1308.72i			1.67355i
$783$		0			0
$784$	−45.5253			−0.0580680
$785$	−1738.24	+	306.499i	−2.21432	+	0.390445i
$786$		0			0
$787$	−174.476	+	63.5042i	−0.221698	+	0.0806915i	−0.450481	−	0.892786i	$-0.648748\pi$
$787$	−174.476	+	63.5042i	−0.221698	+	0.0806915i	0.228783	+	0.973477i	$0.426525\pi$
$788$	−1566.44	+	1866.81i	−1.98787	+	2.36905i
$789$		0			0
$790$	849.608	+	309.232i	1.07545	+	0.391433i
$791$	−692.099	+	399.584i	−0.874967	+	0.505162i
$792$		0			0
$793$	269.608	−	466.975i	0.339985	−	0.588872i
$794$	−1399.48	−	1667.84i	−1.76257	−	2.10055i
$795$		0			0
$796$	192.878	−	1093.87i	0.242310	−	1.37421i
$797$	−1454.45	−	256.458i	−1.82490	−	0.321779i	−0.847119	−	0.531402i	$-0.821665\pi$
$797$	−1454.45	−	256.458i	−1.82490	−	0.321779i	−0.977782	+	0.209623i	$0.932776\pi$
$798$		0			0
$799$	−700.200	+	587.537i	−0.876345	+	0.735341i
$800$	430.245	+	248.402i	0.537806	+	0.310502i
$801$		0			0
$802$	210.559	+	364.699i	0.262542	+	0.454737i
$803$	−29.3626	+	80.6730i	−0.0365661	+	0.100465i
$804$		0			0
$805$	−834.250	−	700.019i	−1.03634	−	0.869589i
$806$	96.3949	+	264.843i	0.119597	+	0.328589i
$807$		0			0
$808$	−19.9879	−	113.357i	−0.0247375	−	0.140293i
$809$			1487.78i			1.83903i	0.393055	+	0.919515i	$0.371418\pi$
$809$			1487.78i			1.83903i	−0.393055	+	0.919515i	$0.628582\pi$
$810$		0			0
$811$	391.709			0.482995			0.241497	−	0.970401i	$-0.422361\pi$
$811$	391.709			0.482995			0.241497	+	0.970401i	$0.422361\pi$
$812$	1372.87	−	242.073i	1.69072	−	0.298120i
$813$		0			0
$814$	−202.423	+	73.6759i	−0.248677	+	0.0905109i
$815$	−1172.55	+	1397.39i	−1.43871	+	1.71459i
$816$		0			0
$817$	616.326	+	224.324i	0.754377	+	0.274571i
$818$	−1567.96	+	905.265i	−1.91683	+	1.10668i
$819$		0			0
$820$	−26.1940	+	45.3693i	−0.0319439	+	0.0553285i
$821$	−1.93532	−	2.30642i	−0.00235727	−	0.00280928i	0.764865	−	0.644191i	$-0.222806\pi$
$821$	−1.93532	−	2.30642i	−0.00235727	−	0.00280928i	−0.767222	+	0.641382i	$0.778361\pi$
$822$		0			0
$823$	−235.153	+	1333.62i	−0.285727	+	1.62044i	0.416949	+	0.908930i	$0.363099\pi$
$823$	−235.153	+	1333.62i	−0.285727	+	1.62044i	−0.702676	+	0.711510i	$0.748012\pi$
$824$	−1643.04	−	289.713i	−1.99398	−	0.351593i
$825$		0			0
$826$	979.888	−	822.224i	1.18631	−	0.995428i
$827$	−1186.03	−	684.755i	−1.43414	−	0.827999i	−0.436703	−	0.899606i	$-0.643854\pi$
$827$	−1186.03	−	684.755i	−1.43414	−	0.827999i	−0.997433	+	0.0716069i	$0.977187\pi$
$828$		0			0
$829$	−39.8034	−	68.9416i	−0.0480138	−	0.0831623i	0.841020	−	0.541005i	$-0.181956\pi$
$829$	−39.8034	−	68.9416i	−0.0480138	−	0.0831623i	−0.889033	+	0.457842i	$0.848622\pi$
$830$	−330.024	+	906.732i	−0.397619	+	1.09245i
$831$		0			0
$832$	−392.773	−	329.576i	−0.472084	−	0.396125i
$833$	−44.9257	−	123.432i	−0.0539324	−	0.148178i
$834$		0			0
$835$	−3.86690	−	21.9303i	−0.00463102	−	0.0262638i
$836$		−	119.125i		−	0.142494i
$837$		0			0
$838$	2220.92			2.65026
$839$	990.232	−	174.605i	1.18025	−	0.208110i	0.451108	−	0.892470i	$-0.351029\pi$
$839$	990.232	−	174.605i	1.18025	−	0.208110i	0.729145	+	0.684359i	$0.239918\pi$
$840$		0			0
$841$	112.055	−	40.7849i	0.133241	−	0.0484957i
$842$	485.949	−	579.131i	0.577136	−	0.687804i
$843$		0			0
$844$	2466.50	+	897.734i	2.92240	+	1.06367i
$845$	836.841	−	483.150i	0.990344	−	0.571775i
$846$		0			0
$847$	−381.132	+	660.139i	−0.449978	+	0.779385i
$848$	−48.9296	−	58.3120i	−0.0577000	−	0.0687641i
$849$		0			0
$850$	204.333	−	1158.83i	0.240392	−	1.36333i
$851$	1272.39	+	224.357i	1.49517	+	0.263639i
$852$		0			0
$853$	270.040	−	226.590i	0.316577	−	0.265639i	−0.470627	−	0.882332i	$-0.655972\pi$
$853$	270.040	−	226.590i	0.316577	−	0.265639i	0.787204	+	0.616693i	$0.211528\pi$
$854$	1855.12	+	1071.05i	2.17227	+	1.25416i
$855$		0			0
$856$	−546.733	−	946.969i	−0.638707	−	1.10627i
$857$	−412.239	+	1132.62i	−0.481025	+	1.32161i	0.427590	+	0.903973i	$0.359363\pi$
$857$	−412.239	+	1132.62i	−0.481025	+	1.32161i	−0.908615	+	0.417634i	$0.862860\pi$
$858$		0			0
$859$	484.551	+	406.587i	0.564088	+	0.473326i	0.879678	−	0.475570i	$-0.157758\pi$
$859$	484.551	+	406.587i	0.564088	+	0.473326i	−0.315590	+	0.948896i	$0.602202\pi$
$860$	−801.073	−	2200.93i	−0.931480	−	2.55922i
$861$		0			0
$862$	−247.980	−	1406.37i	−0.287680	−	1.63152i
$863$			1076.50i			1.24739i	0.781668	+	0.623695i	$0.214369\pi$
$863$			1076.50i			1.24739i	−0.781668	+	0.623695i	$0.785631\pi$
$864$		0			0
$865$	1323.87			1.53048
$866$	−39.2789	+	6.92594i	−0.0453568	+	0.00799762i
$867$		0			0
$868$	−671.253	+	244.316i	−0.773334	+	0.281470i
$869$	31.6329	−	37.6987i	0.0364015	−	0.0433817i
$870$		0			0
$871$	−394.509	−	143.590i	−0.452938	−	0.164856i
$872$	1547.91	−	893.685i	1.77512	−	1.02487i
$873$		0			0
$874$	−559.949	+	969.860i	−0.640674	+	1.10968i
$875$	−75.9224	−	90.4809i	−0.0867685	−	0.103407i
$876$		0			0
$877$	222.484	−	1261.77i	0.253688	−	1.43873i	−0.545732	−	0.837960i	$-0.683748\pi$
$877$	222.484	−	1261.77i	0.253688	−	1.43873i	0.799419	−	0.600774i	$-0.205141\pi$
$878$	246.724	+	43.5041i	0.281007	+	0.0495491i
$879$		0			0
$880$	−36.0608	+	30.2586i	−0.0409782	+	0.0343848i
$881$	787.917	+	454.904i	0.894344	+	0.516350i	0.875361	−	0.483470i	$-0.160624\pi$
$881$	787.917	+	454.904i	0.894344	+	0.516350i	0.0189831	+	0.999820i	$0.493957\pi$
$882$		0			0
$883$	−817.068	−	1415.20i	−0.925332	−	1.60272i	−0.791027	−	0.611782i	$-0.790453\pi$
$883$	−817.068	−	1415.20i	−0.925332	−	1.60272i	−0.134305	−	0.990940i	$-0.542880\pi$
$884$	−204.290	+	561.283i	−0.231098	+	0.634935i
$885$		0			0
$886$	−631.471	−	529.867i	−0.712721	−	0.598044i
$887$	−203.394	−	558.821i	−0.229306	−	0.630013i	0.770668	−	0.637237i	$-0.219923\pi$
$887$	−203.394	−	558.821i	−0.229306	−	0.630013i	−0.999974	+	0.00722414i	$0.997700\pi$
$888$		0			0
$889$	1.42790	+	8.09805i	0.00160619	+	0.00910917i
$890$		−	1632.26i		−	1.83400i
$891$		0			0
$892$	−658.450			−0.738173
$893$	−770.287	+	135.822i	−0.862583	+	0.152097i
$894$		0			0
$895$	1428.19	−	519.819i	1.59574	−	0.580803i
$896$	943.903	−	1124.90i	1.05346	−	1.25547i
$897$		0			0
$898$	−642.065	−	233.692i	−0.714994	−	0.260237i
$899$	−426.126	+	246.024i	−0.474000	+	0.273664i
$900$		0			0
$901$	109.816	−	190.206i	0.121882	−	0.211106i
$902$	2.87289	+	3.42377i	0.00318502	+	0.00379576i
$903$		0			0
$904$	220.458	−	1250.28i	0.243870	−	1.38305i
$905$	−986.055	−	173.868i	−1.08956	−	0.192119i
$906$		0			0
$907$	225.773	−	189.446i	0.248923	−	0.208871i	−0.509785	−	0.860302i	$-0.670275\pi$
$907$	225.773	−	189.446i	0.248923	−	0.208871i	0.758708	+	0.651430i	$0.225831\pi$
$908$	−2229.49	−	1287.20i	−2.45538	−	1.41762i
$909$		0			0
$910$	−389.531	−	674.688i	−0.428056	−	0.741416i
$911$	−285.060	+	783.197i	−0.312909	+	0.859711i	0.679157	+	0.733993i	$0.262346\pi$
$911$	−285.060	+	783.197i	−0.312909	+	0.859711i	−0.992066	+	0.125718i	$0.959877\pi$
$912$		0			0
$913$	40.2334	+	33.7598i	0.0440672	+	0.0369768i
$914$	726.557	+	1996.20i	0.794920	+	2.18403i
$915$		0			0
$916$	130.411	+	739.598i	0.142370	+	0.807421i
$917$		−	586.439i		−	0.639519i
$918$		0			0
$919$	1687.49			1.83623			0.918114	−	0.396315i	$-0.129711\pi$
$919$	1687.49			1.83623			0.918114	+	0.396315i	$0.129711\pi$
$920$	1703.78	−	300.422i	1.85193	−	0.326545i
$921$		0			0
$922$	442.449	−	161.038i	0.479879	−	0.174662i
$923$	157.556	−	187.768i	0.170700	−	0.203432i
$924$		0			0
$925$	−1091.64	−	397.323i	−1.18015	−	0.429538i
$926$	811.093	−	468.285i	0.875910	−	0.505707i
$927$		0			0
$928$	345.038	−	597.623i	0.371808	−	0.643990i
$929$	665.672	+	793.316i	0.716546	+	0.853947i	0.994290	−	0.106708i	$-0.0340311\pi$
$929$	665.672	+	793.316i	0.716546	+	0.853947i	−0.277744	+	0.960655i	$0.589587\pi$
$930$		0			0
$931$	19.5185	−	110.695i	0.0209651	−	0.118899i
$932$	1651.70	+	291.240i	1.77222	+	0.312489i
$933$		0			0
$934$	−1359.68	+	1140.91i	−1.45577	+	1.22153i
$935$	−117.626	−	67.9113i	−0.125803	−	0.0726324i
$936$		0			0
$937$	687.817	+	1191.33i	0.734063	+	1.27143i	0.955133	+	0.296176i	$0.0957115\pi$
$937$	687.817	+	1191.33i	0.734063	+	1.27143i	−0.221071	+	0.975258i	$0.570955\pi$
$938$	570.429	−	1567.24i	0.608133	−	1.67083i
$939$		0			0
$940$	2139.69	+	1795.41i	2.27627	+	1.91001i
$941$	582.906	+	1601.52i	0.619454	+	1.70193i	0.708320	+	0.705891i	$0.249453\pi$
$941$	582.906	+	1601.52i	0.619454	+	1.70193i	−0.0888666	+	0.996044i	$0.528324\pi$
$942$		0			0
$943$	−4.65496	−	26.3996i	−0.00493633	−	0.0279953i
$944$			331.632i			0.351305i
$945$		0			0
$946$	−199.820			−0.211226
$947$	−22.2441	+	3.92223i	−0.0234890	+	0.00414175i	−0.185380	−	0.982667i	$-0.559352\pi$
$947$	−22.2441	+	3.92223i	−0.0234890	+	0.00414175i	0.161891	+	0.986809i	$0.448241\pi$
$948$		0			0
$949$	346.141	−	125.985i	0.364743	−	0.132756i
$950$	647.246	−	771.358i	0.681311	−	0.811955i
$951$		0			0
$952$	−964.599	−	351.085i	−1.01323	−	0.368787i
$953$	−877.360	+	506.544i	−0.920630	+	0.531526i	−0.883836	−	0.467797i	$-0.845048\pi$
$953$	−877.360	+	506.544i	−0.920630	+	0.531526i	−0.0367941	+	0.999323i	$0.511715\pi$
$954$		0			0
$955$	268.750	−	465.489i	0.281414	−	0.487423i
$956$	389.403	+	464.073i	0.407326	+	0.485432i
$957$		0			0
$958$	−97.9366	+	555.426i	−0.102230	+	0.579777i
$959$	−371.196	−	65.4518i	−0.387065	−	0.0682500i
$960$		0			0
$961$	−543.023	+	455.650i	−0.565060	+	0.474142i
$962$	800.441	+	462.135i	0.832059	+	0.480390i
$963$		0			0
$964$	−103.499	−	179.265i	−0.107364	−	0.185959i
$965$	526.748	−	1447.23i	0.545853	−	1.49972i
$966$		0			0
$967$	75.7208	+	63.5373i	0.0783048	+	0.0657055i	0.681100	−	0.732190i	$-0.261502\pi$
$967$	75.7208	+	63.5373i	0.0783048	+	0.0657055i	−0.602795	+	0.797896i	$0.705946\pi$
$968$	−414.167	−	1137.91i	−0.427858	−	1.17553i
$969$		0			0
$970$	−4.49425	−	25.4882i	−0.00463325	−	0.0262765i
$971$			415.261i			0.427664i	0.976871	+	0.213832i	$0.0685944\pi$
$971$			415.261i			0.427664i	−0.976871	+	0.213832i	$0.931406\pi$
$972$		0			0
$973$	−322.227			−0.331169
$974$	68.1100	−	12.0096i	0.0699281	−	0.0123302i
$975$		0			0
$976$	−521.869	+	189.945i	−0.534702	+	0.194616i
$977$	202.742	−	241.619i	0.207515	−	0.247307i	−0.652241	−	0.758011i	$-0.726171\pi$
$977$	202.742	−	241.619i	0.207515	−	0.247307i	0.859756	+	0.510705i	$0.170616\pi$
$978$		0			0
$979$	−83.4861	−	30.3864i	−0.0852769	−	0.0310382i
$980$	−347.618	+	200.697i	−0.354712	+	0.204793i
$981$		0			0
$982$	−251.177	+	435.052i	−0.255781	+	0.443027i
$983$	−412.028	−	491.036i	−0.419154	−	0.499528i	0.514607	−	0.857426i	$-0.327938\pi$
$983$	−412.028	−	491.036i	−0.419154	−	0.499528i	−0.933761	+	0.357898i	$0.883493\pi$
$984$		0			0
$985$	−412.875	+	2341.53i	−0.419162	+	2.37719i
$986$	−1609.65	−	283.825i	−1.63251	−	0.287855i
$987$		0			0
$988$	−391.546	+	328.546i	−0.396302	+	0.332536i
$989$	1037.92	+	599.245i	1.04947	+	0.605910i
$990$		0			0
$991$	−464.001	−	803.674i	−0.468215	−	0.810973i	0.531125	−	0.847294i	$-0.321769\pi$
$991$	−464.001	−	803.674i	−0.468215	−	0.810973i	−0.999340	+	0.0363209i	$0.988436\pi$
$992$	−120.941	+	332.282i	−0.121916	+	0.334962i
$993$		0			0
$994$	745.931	+	625.911i	0.750434	+	0.629689i
$995$	−370.652	−	1018.36i	−0.372514	−	1.02348i
$996$		0			0
$997$	197.850	+	1122.06i	0.198446	+	1.12544i	0.907426	+	0.420212i	$0.138044\pi$
$997$	197.850	+	1122.06i	0.198446	+	1.12544i	−0.708980	+	0.705228i	$0.750844\pi$
$998$		−	2717.71i		−	2.72316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.b.215.5		30
3.2	odd	2		243.3.f.c.215.1		30
9.2	odd	6		27.3.f.a.5.5	✓	30
9.4	even	3		243.3.f.a.53.1		30
9.5	odd	6		243.3.f.d.53.5		30
9.7	even	3		81.3.f.a.44.1		30
27.2	odd	18	inner	243.3.f.b.26.5		30
27.5	odd	18		729.3.b.a.728.27		30
27.7	even	9		27.3.f.a.11.5	yes	30
27.11	odd	18		243.3.f.a.188.1		30
27.16	even	9		243.3.f.d.188.5		30
27.20	odd	18		81.3.f.a.35.1		30
27.22	even	9		729.3.b.a.728.4		30
27.25	even	9		243.3.f.c.26.1		30
36.11	even	6		432.3.bc.a.113.4		30
108.7	odd	18		432.3.bc.a.65.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.5	✓	30	9.2	odd	6
27.3.f.a.11.5	yes	30	27.7	even	9
81.3.f.a.35.1		30	27.20	odd	18
81.3.f.a.44.1		30	9.7	even	3
243.3.f.a.53.1		30	9.4	even	3
243.3.f.a.188.1		30	27.11	odd	18
243.3.f.b.26.5		30	27.2	odd	18	inner
243.3.f.b.215.5		30	1.1	even	1	trivial
243.3.f.c.26.1		30	27.25	even	9
243.3.f.c.215.1		30	3.2	odd	2
243.3.f.d.53.5		30	9.5	odd	6
243.3.f.d.188.5		30	27.16	even	9
432.3.bc.a.65.4		30	108.7	odd	18
432.3.bc.a.113.4		30	36.11	even	6
729.3.b.a.728.4		30	27.22	even	9
729.3.b.a.728.27		30	27.5	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.27361 - 0.577226i) q^{2} +(6.62455 - 2.41114i) q^{4} +(4.42119 - 5.26897i) q^{5} +(-5.99653 - 2.18256i) q^{7} +(8.77937 - 5.06877i) q^{8} +(11.4319 - 19.8006i) q^{10} +(-0.799933 - 0.953323i) q^{11} +(-0.927217 + 5.25851i) q^{13} +(-20.8901 - 3.68349i) q^{14} +(4.21287 - 3.53502i) q^{16} +(13.7418 + 7.93385i) q^{17} +(6.78917 + 11.7592i) q^{19} +(16.5842 - 45.5647i) q^{20} +(-3.16895 - 2.65907i) q^{22} +(8.48610 + 23.3154i) q^{23} +(-3.87391 - 21.9701i) q^{25} +17.7495i q^{26} -44.9868 q^{28} +(-30.5171 + 5.38098i) q^{29} +(14.9211 - 5.43084i) q^{31} +(-14.3144 + 17.0592i) q^{32} +(49.5650 + 18.0402i) q^{34} +(-38.0116 + 21.9460i) q^{35} +(26.0365 - 45.0965i) q^{37} +(29.0128 + 34.5761i) q^{38} +(12.1081 - 68.6683i) q^{40} +(-1.06400 - 0.187611i) q^{41} +(37.0026 - 31.0488i) q^{43} +(-7.59780 - 4.38659i) q^{44} +(41.2384 + 71.4270i) q^{46} +(-19.7018 + 54.1303i) q^{47} +(-6.34137 - 5.32104i) q^{49} +(-25.3634 - 69.6853i) q^{50} +(6.53661 + 37.0709i) q^{52} -13.8414i q^{53} -8.55969 q^{55} +(-63.7087 + 11.2336i) q^{56} +(-96.7949 + 35.2305i) q^{58} +(-38.7615 + 46.1941i) q^{59} +(-94.8938 - 34.5385i) q^{61} +(45.7111 - 26.3913i) q^{62} +(-48.0117 + 83.1587i) q^{64} +(23.6075 + 28.1344i) q^{65} +(-13.6531 + 77.4304i) q^{67} +(110.163 + 19.4247i) q^{68} +(-111.767 + 93.7840i) q^{70} +(-39.7545 - 22.9523i) q^{71} +(-34.4926 - 59.7430i) q^{73} +(59.2024 - 162.657i) q^{74} +(73.3283 + 61.5297i) q^{76} +(2.71614 + 7.46253i) q^{77} +(6.86682 + 38.9437i) q^{79} -37.8265i q^{80} -3.59141 q^{82} +(-41.5621 + 7.32852i) q^{83} +(102.558 - 37.3282i) q^{85} +(103.210 - 123.001i) q^{86} +(-11.8551 - 4.31490i) q^{88} +(61.8262 - 35.6954i) q^{89} +(17.0371 - 29.5091i) q^{91} +(112.433 + 133.993i) q^{92} +(-33.2506 + 188.574i) q^{94} +(91.9750 + 16.2177i) q^{95} +(0.867150 - 0.727625i) q^{97} +(-23.8306 - 13.7586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

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