LMFDB - Embedded newform 243.3.f.c.215.1

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			215.1
Character	$\chi$	$=$	243.215
Dual form			243.3.f.c.26.1

$q$-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	−0.914991	−	0.403475i	$-0.867802\pi$
$2$	−3.27361	+	0.577226i	−1.63680	+	0.288613i	−0.721814	+	0.692088i	$0.756691\pi$
$3$		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	$0.463652\pi$
$5$	−4.42119	+	5.26897i	−0.884238	+	1.05379i	−0.998180	+	0.0603067i	$0.980792\pi$
$6$		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	0.801178	−	0.598425i	$-0.204207\pi$
$11$	0.799933	+	0.953323i	0.0727212	+	0.0866658i	−0.728457	+	0.685091i	$0.759762\pi$
$12$		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	0.0380373	−	0.999276i	$-0.487889\pi$
$17$	−13.7418	−	7.93385i	−0.808343	−	0.466697i	−0.846380	+	0.532579i	$0.821223\pi$
$18$		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	$-0.929768\pi$
$23$	−8.48610	−	23.3154i	−0.368961	−	1.01371i	0.606797	−	0.794857i	$-0.292454\pi$
$24$		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	0.379370	−	0.925245i	$-0.376141\pi$
$29$	30.5171	−	5.38098i	1.05231	−	0.185551i	0.672943	+	0.739694i	$0.265030\pi$
$30$		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	0.186609	−	0.982434i	$-0.440250\pi$
$41$	1.06400	+	0.187611i	0.0259512	+	0.00457589i	−0.160658	+	0.987010i	$0.551361\pi$
$42$		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	$-0.678928\pi$
$47$	19.7018	−	54.1303i	0.419187	−	1.15171i	0.952167	−	0.305579i	$-0.0988501\pi$
$48$		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	$0.0416837\pi$
$53$			13.8414i			0.261159i	−0.991438	+	0.130579i	$0.958316\pi$
$54$		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	−0.329974	−	0.943990i	$-0.607040\pi$
$59$	38.7615	−	46.1941i	0.656974	−	0.782952i	0.986948	+	0.161039i	$0.0514843\pi$
$60$		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	0.753114	−	0.657890i	$-0.228551\pi$
$71$	39.7545	+	22.9523i	0.559922	+	0.323271i	−0.193192	+	0.981161i	$0.561884\pi$
$72$		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	0.0824318	−	0.996597i	$-0.473731\pi$
$83$	41.5621	−	7.32852i	0.500748	−	0.0882955i	0.418317	+	0.908301i	$0.362620\pi$
$84$		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	−0.805361	−	0.592784i	$-0.798029\pi$
$89$	−61.8262	+	35.6954i	−0.694676	+	0.401072i	0.110685	+	0.993856i	$0.464695\pi$
$90$		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	−0.957432	−	0.288659i	$-0.906791\pi$
$101$	−3.88344	+	10.6697i	−0.0384499	+	0.105640i	0.918982	+	0.394299i	$0.129013\pi$
$102$		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	$0.168151\pi$
$107$			107.863i			1.00807i	−0.863685	+	0.504033i	$0.831849\pi$
$108$		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	−0.993867	−	0.110583i	$-0.964728\pi$
$113$	−80.4991	+	95.9351i	−0.712381	+	0.848983i	0.281486	+	0.959565i	$0.409173\pi$
$114$		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	$-0.997035\pi$
$131$	−31.4312	−	86.3564i	−0.239933	−	0.659209i	0.760024	−	0.649895i	$-0.225187\pi$
$132$		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	−0.381860	−	0.924220i	$-0.624716\pi$
$137$	−58.1686	+	10.2567i	−0.424588	+	0.0748664i	−0.0427287	+	0.999087i	$0.513605\pi$
$138$		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	0.408614	−	0.912707i	$-0.366012\pi$
$149$	71.5827	+	12.6220i	0.480421	+	0.0847112i	0.0718072	+	0.997419i	$0.477123\pi$
$150$		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	−0.772239	−	0.635332i	$-0.780863\pi$
$167$	−2.08108	+	2.48014i	−0.0124616	+	0.0148511i	0.759778	+	0.650183i	$0.225308\pi$
$168$		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	0.279005	−	0.960290i	$-0.409995\pi$
$173$	−123.720	−	147.444i	−0.715145	−	0.852276i	−0.994149	+	0.108013i	$0.965551\pi$
$174$		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	−0.141142	−	0.989989i	$-0.545078\pi$
$179$	−191.363	−	110.484i	−1.06907	−	0.617228i	−0.927927	+	0.372762i	$0.878411\pi$
$180$		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	−0.371439	−	0.928458i	$-0.621135\pi$
$191$	−76.9588	+	13.5699i	−0.402926	+	0.0710466i	−0.0314869	+	0.999504i	$0.510024\pi$
$192$		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	$-0.325967\pi$
$197$	299.369	−	172.841i	1.51964	−	0.877364i	0.999732	−	0.0231411i	$-0.00736671\pi$
$198$		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	$0.0752669\pi$
$227$	234.731	+	279.742i	1.03406	+	1.23234i	0.0618854	+	0.998083i	$0.480289\pi$
$228$		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	−0.0122058	−	0.999926i	$-0.503885\pi$
$233$	−206.035	−	118.954i	−0.884270	−	0.510533i	−0.872064	+	0.489392i	$0.837219\pi$
$234$		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	0.862895	−	0.505383i	$-0.168649\pi$
$239$	−29.3909	−	80.7509i	−0.122975	−	0.337870i	−0.985870	+	0.167513i	$0.946426\pi$
$240$		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	−0.700030	−	0.714114i	$-0.746830\pi$
$251$	−108.333	+	62.5458i	−0.431604	+	0.249186i	0.268426	+	0.963300i	$0.413497\pi$
$252$		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	0.602139	−	0.798391i	$-0.294315\pi$
$257$	229.989	+	40.5533i	0.894899	+	0.157795i	0.292760	+	0.956186i	$0.405426\pi$
$258$		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	−0.833144	−	0.553056i	$-0.813462\pi$
$263$	42.2322	−	116.032i	0.160579	−	0.441186i	0.993723	+	0.111869i	$0.0356839\pi$
$264$		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	$-0.603974\pi$
$269$		−	509.553i		−	1.89425i	0.320867	−	0.947124i	$-0.396026\pi$
$270$		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	0.735600	−	0.677416i	$-0.236900\pi$
$281$	−16.6521	−	19.8451i	−0.0592600	−	0.0706233i	−0.794860	+	0.606793i	$0.792456\pi$
$282$		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	$-0.856803\pi$
$293$	−143.626	−	394.610i	−0.490192	−	1.34679i	0.410313	−	0.911945i	$-0.365419\pi$
$294$		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	0.577009	−	0.816738i	$-0.304220\pi$
$311$	261.202	+	46.0570i	0.839879	+	0.148093i	0.262870	+	0.964831i	$0.415331\pi$
$312$		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	−0.957144	−	0.289614i	$-0.906473\pi$
$317$	−11.9728	+	32.8949i	−0.0377689	+	0.103769i	0.919375	+	0.393383i	$0.128695\pi$
$318$		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	$0.0277728\pi$
$347$	100.310	+	275.600i	0.289078	+	0.794236i	−0.707118	+	0.707096i	$0.750005\pi$
$348$		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	−0.820122	−	0.572188i	$-0.806095\pi$
$353$	−492.465	+	86.8349i	−1.39508	+	0.245991i	−0.574963	+	0.818180i	$0.694983\pi$
$354$		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	−0.770021	−	0.638018i	$-0.779754\pi$
$359$	−216.295	+	124.878i	−0.602492	+	0.347849i	0.167529	+	0.985867i	$0.446421\pi$
$360$		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	$-0.457389\pi$
$383$	416.048	−	495.827i	1.08629	−	1.29459i	0.952821	−	0.303533i	$-0.0981663\pi$
$384$		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	0.810763	−	0.585375i	$-0.199053\pi$
$389$	36.3692	+	43.3431i	0.0934940	+	0.111422i	−0.717269	+	0.696796i	$0.754608\pi$
$390$		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	0.873869	−	0.486162i	$-0.161604\pi$
$401$	−43.3291	−	119.046i	−0.108053	−	0.296872i	−0.981921	+	0.189290i	$0.939381\pi$
$402$		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	−0.680356	−	0.732881i	$-0.738175\pi$
$419$	−657.974	−	116.018i	−1.57034	−	0.276894i	−0.889986	+	0.455988i	$0.849286\pi$
$420$		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	$0.166073\pi$
$431$			429.608i			0.996769i	−0.866956	+	0.498385i	$0.833927\pi$
$432$		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	0.915338	−	0.402687i	$-0.131924\pi$
$443$	159.401	+	189.967i	0.359822	+	0.428819i	−0.555516	+	0.831506i	$0.687479\pi$
$444$		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	0.684956	−	0.728584i	$-0.259821\pi$
$449$	178.012	+	102.775i	0.396462	+	0.228898i	−0.288494	+	0.957482i	$0.593155\pi$
$450$		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	−0.322881	−	0.946440i	$-0.604651\pi$
$461$	−139.493	+	24.5964i	−0.302588	+	0.0533545i	0.0202925	+	0.999794i	$0.493540\pi$
$462$		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	0.0848656	−	0.996392i	$-0.472954\pi$
$467$	462.423	−	266.980i	0.990199	−	0.571692i	0.905334	+	0.424700i	$0.139621\pi$
$468$		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	−0.864264	−	0.503039i	$-0.832215\pi$
$479$	58.0298	−	159.436i	0.121148	−	0.332851i	0.985412	+	0.170188i	$0.0544375\pi$
$480$		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	−0.657997	−	0.753020i	$-0.728596\pi$
$491$	97.1410	−	115.768i	0.197843	−	0.235780i	0.855840	+	0.517240i	$0.173041\pi$
$492$		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	0.286511	−	0.958077i	$-0.407505\pi$
$503$	−201.176	−	116.149i	−0.399953	−	0.230913i	−0.686464	+	0.727164i	$0.740838\pi$
$504$		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	0.999677	−	0.0254151i	$-0.00809074\pi$
$509$	110.730	+	304.227i	0.217543	+	0.597696i	−0.782133	+	0.623111i	$0.785869\pi$
$510$		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	0.0374577	−	0.999298i	$-0.488074\pi$
$521$	480.156	−	277.218i	0.921604	−	0.532088i	0.884146	+	0.467210i	$0.154741\pi$
$522$		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	0.306043	−	0.952018i	$-0.400995\pi$
$557$	−203.531	−	117.509i	−0.365406	−	0.210967i	−0.671450	+	0.741050i	$0.734328\pi$
$558$		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	0.962492	−	0.271311i	$-0.0874572\pi$
$563$	28.5919	+	78.5555i	0.0507849	+	0.139530i	−0.911707	+	0.410841i	$0.865235\pi$
$564$		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	−0.899647	−	0.436617i	$-0.856176\pi$
$569$	−907.958	+	160.097i	−1.59571	+	0.281366i	−0.696060	+	0.717983i	$0.745065\pi$
$570$		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	−0.982085	−	0.188440i	$-0.939657\pi$
$587$	−63.7700	+	175.207i	−0.108637	+	0.298478i	0.873448	+	0.486918i	$0.161879\pi$
$588$		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	$0.102043\pi$
$593$			373.725i			0.630228i	−0.949054	+	0.315114i	$0.897957\pi$
$594$		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	−0.758044	−	0.652203i	$-0.773845\pi$
$599$	9.51395	−	11.3383i	0.0158831	−	0.0189287i	0.773928	+	0.633274i	$0.218289\pi$
$600$		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	0.769468	−	0.638685i	$-0.220521\pi$
$617$	−142.229	−	390.772i	−0.230518	−	0.633343i	−0.999986	+	0.00534297i	$0.998299\pi$
$618$		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	−0.904342	−	0.426809i	$-0.859638\pi$
$641$	40.2366	−	110.549i	0.0627717	−	0.172464i	0.967114	+	0.254345i	$0.0818599\pi$
$642$		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	$0.0500924\pi$
$647$			202.797i			0.313443i	−0.987643	+	0.156721i	$0.949908\pi$
$648$		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	$0.462584\pi$
$653$	−575.359	+	685.687i	−0.881102	+	1.05006i	−0.998377	+	0.0569567i	$0.981860\pi$
$654$		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	0.178884	−	0.983870i	$-0.442751\pi$
$659$	−541.106	−	644.865i	−0.821102	−	0.978551i	−0.999986	+	0.00531879i	$0.998307\pi$
$660$		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	−0.175727	−	0.984439i	$-0.556228\pi$
$677$	−2.81567	+	0.496479i	−0.00415904	+	0.000733352i	0.171568	+	0.985172i	$0.445117\pi$
$678$		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	−0.968000	−	0.250951i	$-0.919257\pi$
$683$	−843.279	+	486.868i	−1.23467	+	0.712837i	−0.266670	+	0.963788i	$0.585923\pi$
$684$		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	$-0.990529\pi$
$701$		−	41.7083i		−	0.0594983i	0.999557	−	0.0297492i	$-0.00947085\pi$
$702$		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	0.583851	−	0.811861i	$-0.301545\pi$
$719$	124.160	+	71.6839i	0.172684	+	0.0996994i	−0.411167	+	0.911560i	$0.634879\pi$
$720$		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	−0.237184	−	0.971465i	$-0.576224\pi$
$743$	−588.697	−	103.803i	−0.792325	−	0.139708i	−0.555141	+	0.831757i	$0.687336\pi$
$744$		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	−0.435885	−	0.900002i	$-0.643565\pi$
$761$	400.389	−	477.165i	0.526135	−	0.627023i	0.962020	+	0.272979i	$0.0880090\pi$
$762$		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	0.887115	−	0.461549i	$-0.152706\pi$
$773$	719.632	+	415.480i	0.930960	+	0.537490i	0.0438447	+	0.999038i	$0.486039\pi$
$774$		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	0.977782	−	0.209623i	$-0.0672237\pi$
$797$	1454.45	+	256.458i	1.82490	+	0.321779i	0.847119	+	0.531402i	$0.178335\pi$
$798$		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	$-0.628582\pi$
$809$		−	1487.78i		−	1.83903i	0.393055	−	0.919515i	$-0.371418\pi$
$810$		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	0.767222	−	0.641382i	$-0.221639\pi$
$821$	1.93532	+	2.30642i	0.00235727	+	0.00280928i	−0.764865	+	0.644191i	$0.777194\pi$
$822$		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	0.997433	−	0.0716069i	$-0.0228127\pi$
$827$	1186.03	+	684.755i	1.43414	+	0.827999i	0.436703	+	0.899606i	$0.356146\pi$
$828$		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	−0.729145	−	0.684359i	$-0.760082\pi$
$839$	−990.232	+	174.605i	−1.18025	+	0.208110i	−0.451108	+	0.892470i	$0.648971\pi$
$840$		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	$-0.640637\pi$
$857$	412.239	−	1132.62i	0.481025	−	1.32161i	0.908615	−	0.417634i	$-0.137140\pi$
$858$		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	$-0.785631\pi$
$863$		−	1076.50i		−	1.24739i	0.781668	−	0.623695i	$-0.214369\pi$
$864$		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	−0.0189831	−	0.999820i	$-0.506043\pi$
$881$	−787.917	−	454.904i	−0.894344	−	0.516350i	−0.875361	+	0.483470i	$0.839376\pi$
$882$		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	0.999974	−	0.00722414i	$-0.00229954\pi$
$887$	203.394	+	558.821i	0.229306	+	0.630013i	−0.770668	+	0.637237i	$0.780077\pi$
$888$		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	$-0.737654\pi$
$911$	285.060	−	783.197i	0.312909	−	0.859711i	0.992066	−	0.125718i	$-0.0401234\pi$
$912$		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	0.277744	−	0.960655i	$-0.410413\pi$
$929$	−665.672	−	793.316i	−0.716546	−	0.853947i	−0.994290	+	0.106708i	$0.965969\pi$
$930$		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	$-0.750547\pi$
$941$	−582.906	−	1601.52i	−0.619454	−	1.70193i	0.0888666	−	0.996044i	$-0.471676\pi$
$942$		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	−0.161891	−	0.986809i	$-0.551759\pi$
$947$	22.2441	−	3.92223i	0.0234890	−	0.00414175i	0.185380	+	0.982667i	$0.440648\pi$
$948$		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	0.0367941	−	0.999323i	$-0.488285\pi$
$953$	877.360	−	506.544i	0.920630	−	0.531526i	0.883836	+	0.467797i	$0.154952\pi$
$954$		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	$-0.931406\pi$
$971$		−	415.261i		−	0.427664i	0.976871	−	0.213832i	$-0.0685944\pi$
$972$		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	−0.859756	−	0.510705i	$-0.829384\pi$
$977$	−202.742	+	241.619i	−0.207515	+	0.247307i	0.652241	+	0.758011i	$0.273829\pi$
$978$		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	0.933761	−	0.357898i	$-0.116507\pi$
$983$	412.028	+	491.036i	0.419154	+	0.499528i	−0.514607	+	0.857426i	$0.672062\pi$
$984$		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.c.215.1		30
3.2	odd	2		243.3.f.b.215.5		30
9.2	odd	6		81.3.f.a.44.1		30
9.4	even	3		243.3.f.d.53.5		30
9.5	odd	6		243.3.f.a.53.1		30
9.7	even	3		27.3.f.a.5.5	✓	30
27.2	odd	18	inner	243.3.f.c.26.1		30
27.5	odd	18		729.3.b.a.728.4		30
27.7	even	9		81.3.f.a.35.1		30
27.11	odd	18		243.3.f.d.188.5		30
27.16	even	9		243.3.f.a.188.1		30
27.20	odd	18		27.3.f.a.11.5	yes	30
27.22	even	9		729.3.b.a.728.27		30
27.25	even	9		243.3.f.b.26.5		30
36.7	odd	6		432.3.bc.a.113.4		30
108.47	even	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	9.7	even	3
27.3.f.a.11.5	yes	30	27.20	odd	18
81.3.f.a.35.1		30	27.7	even	9
81.3.f.a.44.1		30	9.2	odd	6
243.3.f.a.53.1		30	9.5	odd	6
243.3.f.a.188.1		30	27.16	even	9
243.3.f.b.26.5		30	27.25	even	9
243.3.f.b.215.5		30	3.2	odd	2
243.3.f.c.26.1		30	27.2	odd	18	inner
243.3.f.c.215.1		30	1.1	even	1	trivial
243.3.f.d.53.5		30	9.4	even	3
243.3.f.d.188.5		30	27.11	odd	18
432.3.bc.a.65.4		30	108.47	even	18
432.3.bc.a.113.4		30	36.7	odd	6
729.3.b.a.728.4		30	27.5	odd	18
729.3.b.a.728.27		30	27.22	even	9

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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