LMFDB - Embedded newform 243.3.f.a.188.1

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,-21] 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			188.1
Character	$\chi$	$=$	243.188
Dual form			243.3.f.a.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13691 - 3.12364i) q^{2} +(-5.40039 + 4.53146i) q^{4} +(-6.77366 + 1.19438i) q^{5} +(4.88842 + 4.10187i) q^{7} +(8.77937 + 5.06877i) q^{8} +(11.4319 + 19.8006i) q^{10} +(1.22557 + 0.216101i) q^{11} +(5.01761 + 1.82626i) q^{13} +(7.25506 - 19.9331i) q^{14} +(0.954979 - 5.41596i) q^{16} +(13.7418 - 7.93385i) q^{17} +(6.78917 - 11.7592i) q^{19} +(31.1681 - 37.1447i) q^{20} +(-0.718343 - 4.07393i) q^{22} +(15.9486 + 19.0069i) q^{23} +(20.9636 - 7.63012i) q^{25} -17.7495i q^{26} -44.9868 q^{28} +(10.5985 + 29.1191i) q^{29} +(-12.1638 + 10.2066i) q^{31} +(21.9309 - 3.86701i) q^{32} +(-40.4057 - 33.9044i) q^{34} +(-38.0116 - 21.9460i) q^{35} +(26.0365 + 45.0965i) q^{37} +(-44.4502 - 7.83777i) q^{38} +(-65.5225 - 23.8482i) q^{40} +(0.369522 - 1.01525i) q^{41} +(8.38780 - 47.5696i) q^{43} +(-7.59780 + 4.38659i) q^{44} +(41.2384 - 71.4270i) q^{46} +(-37.0273 + 44.1274i) q^{47} +(-1.43747 - 8.15231i) q^{49} +(-47.6675 - 56.8079i) q^{50} +(-35.3727 + 12.8746i) q^{52} +13.8414i q^{53} -8.55969 q^{55} +(22.1258 + 60.7901i) q^{56} +(78.9079 - 66.2116i) q^{58} +(59.3860 - 10.4714i) q^{59} +(77.3581 + 64.9112i) q^{61} +(45.7111 + 26.3913i) q^{62} +(-48.0117 - 83.1587i) q^{64} +(-36.1688 - 6.37754i) q^{65} +(73.8833 + 26.8913i) q^{67} +(-38.2592 + 105.116i) q^{68} +(-25.3356 + 143.685i) q^{70} +(-39.7545 + 22.9523i) q^{71} +(-34.4926 + 59.7430i) q^{73} +(111.264 - 132.599i) q^{74} +(16.6222 + 94.2690i) q^{76} +(5.10467 + 6.08351i) q^{77} +(-37.1596 + 13.5250i) q^{79} +37.8265i q^{80} -3.59141 q^{82} +(14.4344 + 39.6581i) q^{83} +(-83.6064 + 70.1541i) q^{85} +(-158.126 + 27.8820i) q^{86} +(9.66436 + 8.10936i) q^{88} +(61.8262 + 35.6954i) q^{89} +(17.0371 + 29.5091i) q^{91} +(-172.258 - 30.3737i) q^{92} +(179.935 + 65.4909i) q^{94} +(-31.9426 + 87.7616i) q^{95} +(0.196567 - 1.11479i) q^{97} +(-23.8306 + 13.7586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} - 57 q^{11} + 3 q^{13} + 114 q^{14} + 27 q^{16} + 9 q^{17} - 3 q^{19} + 183 q^{20} + 75 q^{22} - 48 q^{23} + 21 q^{25} - 12 q^{28} + 78 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 - 57 * q^11 + 3 * q^13 + 114 * q^14 + 27 * q^16 + 9 * q^17 - 3 * q^19 + 183 * q^20 + 75 * q^22 - 48 * q^23 + 21 * q^25 - 12 * q^28 + 78 * q^29 - 87 * q^31 - 243 * q^32 - 153 * q^34 + 252 * q^35 - 3 * q^37 - 321 * q^38 - 168 * q^40 + 357 * q^41 - 87 * q^43 - 639 * q^44 - 3 * q^46 + 51 * q^47 - 69 * q^49 - 168 * q^50 - 36 * q^52 - 12 * q^55 + 177 * q^56 + 138 * q^58 - 48 * q^59 + 147 * q^61 + 900 * q^62 - 51 * q^64 - 624 * q^65 + 12 * q^67 + 477 * q^68 - 6 * q^70 - 315 * q^71 - 66 * q^73 + 480 * q^74 - 57 * q^76 - 453 * q^77 - 15 * q^79 - 12 * q^82 + 591 * q^83 + 243 * q^85 - 669 * q^86 + 591 * q^88 - 72 * q^89 + 96 * q^91 - 564 * q^92 + 957 * q^94 + 606 * q^95 + 696 * q^97 - 882 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.13691	−	3.12364i	−0.568456	−	1.56182i	−0.806915	−	0.590668i	$-0.798864\pi$
$2$	−1.13691	−	3.12364i	−0.568456	−	1.56182i	0.238459	−	0.971153i	$-0.423358\pi$
$3$		0			0
$3$		0			0
$4$	−5.40039	+	4.53146i	−1.35010	+	1.13287i
$5$	−6.77366	+	1.19438i	−1.35473	+	0.238876i	−0.803415	−	0.595420i	$-0.796986\pi$
$5$	−6.77366	+	1.19438i	−1.35473	+	0.238876i	−0.551317	+	0.834296i	$0.685875\pi$
$6$		0			0
$7$	4.88842	+	4.10187i	0.698345	+	0.585981i	0.921302	−	0.388847i	$-0.127127\pi$
$7$	4.88842	+	4.10187i	0.698345	+	0.585981i	−0.222957	+	0.974828i	$0.571571\pi$
$8$	8.77937	+	5.06877i	1.09742	+	0.633597i
$9$		0			0
$10$	11.4319	+	19.8006i	1.14319	+	1.98006i
$11$	1.22557	+	0.216101i	0.111415	+	0.0196455i	0.229078	−	0.973408i	$-0.426429\pi$
$11$	1.22557	+	0.216101i	0.111415	+	0.0196455i	−0.117662	+	0.993054i	$0.537540\pi$
$12$		0			0
$13$	5.01761	+	1.82626i	0.385970	+	0.140482i	0.527715	−	0.849422i	$-0.323049\pi$
$13$	5.01761	+	1.82626i	0.385970	+	0.140482i	−0.141745	+	0.989903i	$0.545271\pi$
$14$	7.25506	−	19.9331i	0.518219	−	1.42379i
$15$		0			0
$16$	0.954979	−	5.41596i	0.0596862	−	0.338497i
$17$	13.7418	−	7.93385i	0.808343	−	0.466697i	−0.0380373	−	0.999276i	$-0.512111\pi$
$17$	13.7418	−	7.93385i	0.808343	−	0.466697i	0.846380	+	0.532579i	$0.178777\pi$
$18$		0			0
$19$	6.78917	−	11.7592i	0.357325	−	0.618905i	−0.630188	−	0.776442i	$-0.717022\pi$
$19$	6.78917	−	11.7592i	0.357325	−	0.618905i	0.987513	+	0.157538i	$0.0503556\pi$
$20$	31.1681	−	37.1447i	1.55840	−	1.85723i
$21$		0			0
$22$	−0.718343	−	4.07393i	−0.0326520	−	0.185178i
$23$	15.9486	+	19.0069i	0.693419	+	0.826385i	0.991765	−	0.128073i	$-0.0408792\pi$
$23$	15.9486	+	19.0069i	0.693419	+	0.826385i	−0.298345	+	0.954458i	$0.596435\pi$
$24$		0			0
$25$	20.9636	−	7.63012i	0.838543	−	0.305205i
$26$		−	17.7495i		−	0.682674i
$27$		0			0
$28$	−44.9868			−1.60667
$29$	10.5985	+	29.1191i	0.365464	+	1.00411i	0.977065	+	0.212939i	$0.0683036\pi$
$29$	10.5985	+	29.1191i	0.365464	+	1.00411i	−0.611601	+	0.791166i	$0.709474\pi$
$30$		0			0
$31$	−12.1638	+	10.2066i	−0.392381	+	0.329247i	−0.817540	−	0.575872i	$-0.804663\pi$
$31$	−12.1638	+	10.2066i	−0.392381	+	0.329247i	0.425159	+	0.905119i	$0.360218\pi$
$32$	21.9309	−	3.86701i	0.685341	−	0.120844i
$33$		0			0
$34$	−40.4057	−	33.9044i	−1.18840	−	0.997189i
$35$	−38.0116	−	21.9460i	−1.08605	−	0.627029i
$36$		0			0
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	0.967163	+	0.254158i	$0.0817982\pi$
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	−0.263474	+	0.964666i	$0.584868\pi$
$38$	−44.4502	−	7.83777i	−1.16974	−	0.206257i
$39$		0			0
$40$	−65.5225	−	23.8482i	−1.63806	−	0.596206i
$41$	0.369522	−	1.01525i	0.00901274	−	0.0247623i	−0.935105	−	0.354372i	$-0.884695\pi$
$41$	0.369522	−	1.01525i	0.00901274	−	0.0247623i	0.944117	+	0.329609i	$0.106917\pi$
$42$		0			0
$43$	8.38780	−	47.5696i	0.195065	−	1.10627i	−0.717261	−	0.696805i	$-0.754604\pi$
$43$	8.38780	−	47.5696i	0.195065	−	1.10627i	0.912326	−	0.409465i	$-0.134284\pi$
$44$	−7.59780	+	4.38659i	−0.172677	+	0.0996953i
$45$		0			0
$46$	41.2384	−	71.4270i	0.896487	−	1.55276i
$47$	−37.0273	+	44.1274i	−0.787814	+	0.938881i	−0.999258	−	0.0385095i	$-0.987739\pi$
$47$	−37.0273	+	44.1274i	−0.787814	+	0.938881i	0.211444	+	0.977390i	$0.432183\pi$
$48$		0			0
$49$	−1.43747	−	8.15231i	−0.0293362	−	0.166374i
$50$	−47.6675	−	56.8079i	−0.953350	−	1.13616i
$51$		0			0
$52$	−35.3727	+	12.8746i	−0.680244	+	0.247588i
$53$			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
$56$	22.1258	+	60.7901i	0.395103	+	1.08554i
$57$		0			0
$58$	78.9079	−	66.2116i	1.36048	−	1.14158i
$59$	59.3860	−	10.4714i	1.00654	−	0.177481i	0.354011	−	0.935241i	$-0.384818\pi$
$59$	59.3860	−	10.4714i	1.00654	−	0.177481i	0.652533	+	0.757761i	$0.273707\pi$
$60$		0			0
$61$	77.3581	+	64.9112i	1.26817	+	1.06412i	0.994762	+	0.102218i	$0.0325941\pi$
$61$	77.3581	+	64.9112i	1.26817	+	1.06412i	0.273404	+	0.961899i	$0.411850\pi$
$62$	45.7111	+	26.3913i	0.737276	+	0.425666i
$63$		0			0
$64$	−48.0117	−	83.1587i	−0.750183	−	1.29935i
$65$	−36.1688	−	6.37754i	−0.556443	−	0.0981160i
$66$		0			0
$67$	73.8833	+	26.8913i	1.10274	+	0.401363i	0.828324	−	0.560250i	$-0.189295\pi$
$67$	73.8833	+	26.8913i	1.10274	+	0.401363i	0.274411	+	0.961612i	$0.411517\pi$
$68$	−38.2592	+	105.116i	−0.562636	+	1.54583i
$69$		0			0
$70$	−25.3356	+	143.685i	−0.361937	+	2.05265i
$71$	−39.7545	+	22.9523i	−0.559922	+	0.323271i	−0.753114	−	0.657890i	$-0.771449\pi$
$71$	−39.7545	+	22.9523i	−0.559922	+	0.323271i	0.193192	+	0.981161i	$0.438116\pi$
$72$		0			0
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	−0.999505	−	0.0314663i	$-0.989982\pi$
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	0.527003	+	0.849863i	$0.323316\pi$
$74$	111.264	−	132.599i	1.50357	−	1.79188i
$75$		0			0
$76$	16.6222	+	94.2690i	0.218713	+	1.24038i
$77$	5.10467	+	6.08351i	0.0662945	+	0.0790067i
$78$		0			0
$79$	−37.1596	+	13.5250i	−0.470375	+	0.171203i	−0.566322	−	0.824184i	$-0.691634\pi$
$79$	−37.1596	+	13.5250i	−0.470375	+	0.171203i	0.0959471	+	0.995386i	$0.469412\pi$
$80$			37.8265i			0.472831i
$81$		0			0
$82$	−3.59141			−0.0437976
$83$	14.4344	+	39.6581i	0.173908	+	0.477809i	0.995770	−	0.0918778i	$-0.0292869\pi$
$83$	14.4344	+	39.6581i	0.173908	+	0.477809i	−0.821862	+	0.569686i	$0.807065\pi$
$84$		0			0
$85$	−83.6064	+	70.1541i	−0.983605	+	0.825342i
$86$	−158.126	+	27.8820i	−1.83868	+	0.324209i
$87$		0			0
$88$	9.66436	+	8.10936i	0.109822	+	0.0921519i
$89$	61.8262	+	35.6954i	0.694676	+	0.401072i	0.805361	−	0.592784i	$-0.201971\pi$
$89$	61.8262	+	35.6954i	0.694676	+	0.401072i	−0.110685	+	0.993856i	$0.535305\pi$
$90$		0			0
$91$	17.0371	+	29.5091i	0.187221	+	0.324276i
$92$	−172.258	−	30.3737i	−1.87237	−	0.330149i
$93$		0			0
$94$	179.935	+	65.4909i	1.91420	+	0.696712i
$95$	−31.9426	+	87.7616i	−0.336238	+	0.923806i
$96$		0			0
$97$	0.196567	−	1.11479i	0.00202646	−	0.0114926i	−0.983778	−	0.179392i	$-0.942587\pi$
$97$	0.196567	−	1.11479i	0.00202646	−	0.0114926i	0.985804	+	0.167899i	$0.0536982\pi$
$98$	−23.8306	+	13.7586i	−0.243169	+	0.140394i
$99$		0			0
$100$	−78.6359	+	136.201i	−0.786359	+	1.36201i
$101$	7.29847	−	8.69798i	0.0722621	−	0.0861186i	−0.728702	−	0.684831i	$-0.759876\pi$
$101$	7.29847	−	8.69798i	0.0722621	−	0.0861186i	0.800964	+	0.598712i	$0.204321\pi$
$102$		0			0
$103$	−28.5782	−	162.075i	−0.277458	−	1.57354i	−0.731043	−	0.682331i	$-0.760966\pi$
$103$	−28.5782	−	162.075i	−0.277458	−	1.57354i	0.453585	−	0.891213i	$-0.350145\pi$
$104$	34.7946	+	41.4666i	0.334563	+	0.398717i
$105$		0			0
$106$	43.2356	−	15.7365i	0.407883	−	0.148457i
$107$			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	$0.200134\pi$
$110$	9.73162	+	26.7374i	0.0884693	+	0.243067i
$111$		0			0
$112$	26.8839	−	22.5583i	0.240035	−	0.201413i
$113$	−123.332	+	21.7467i	−1.09143	+	0.192449i	−0.690265	−	0.723557i	$-0.742506\pi$
$113$	−123.332	+	21.7467i	−1.09143	+	0.192449i	−0.401166	+	0.916005i	$0.631395\pi$
$114$		0			0
$115$	−130.732	−	109.697i	−1.13680	−	0.953889i
$116$	−189.188	−	109.228i	−1.63093	−	0.941617i
$117$		0			0
$118$	−100.226	−	173.596i	−0.849369	−	1.47115i
$119$	99.7194	+	17.5832i	0.837978	+	0.147758i
$120$		0			0
$121$	−112.247	−	40.8547i	−0.927665	−	0.337643i
$122$	114.810	−	315.437i	0.941064	−	2.58555i
$123$		0			0
$124$	19.4382	−	110.240i	0.156760	−	0.889030i
$125$	16.0295	−	9.25462i	0.128236	−	0.0740369i
$126$		0			0
$127$	−0.644295	+	1.11595i	−0.00507319	+	0.00878702i	−0.868551	−	0.495600i	$-0.834948\pi$
$127$	−0.644295	+	1.11595i	−0.00507319	+	0.00878702i	0.863478	+	0.504387i	$0.168282\pi$
$128$	−147.915	+	176.279i	−1.15559	+	1.37718i
$129$		0			0
$130$	21.1996	+	120.229i	0.163074	+	0.924840i
$131$	59.0713	+	70.3984i	0.450926	+	0.537392i	0.942838	−	0.333253i	$-0.108146\pi$
$131$	59.0713	+	70.3984i	0.450926	+	0.537392i	−0.491912	+	0.870645i	$0.663702\pi$
$132$		0			0
$133$	81.4229	−	29.6355i	0.612202	−	0.222823i
$134$		−	261.358i		−	1.95043i
$135$		0			0
$136$	160.860			1.18279
$137$	−20.2017	−	55.5038i	−0.147458	−	0.405137i	0.843870	−	0.536547i	$-0.180272\pi$
$137$	−20.2017	−	55.5038i	−0.147458	−	0.405137i	−0.991328	+	0.131410i	$0.958050\pi$
$138$		0			0
$139$	−38.6814	+	32.4575i	−0.278283	+	0.233508i	−0.771237	−	0.636548i	$-0.780362\pi$
$139$	−38.6814	+	32.4575i	−0.278283	+	0.233508i	0.492954	+	0.870056i	$0.335917\pi$
$140$	304.725	−	53.7313i	2.17661	−	0.383795i
$141$		0			0
$142$	116.892	+	98.0840i	0.823183	+	0.690732i
$143$	5.75477	+	3.32252i	0.0402432	+	0.0232344i
$144$		0			0
$145$	−106.570	−	184.584i	−0.734963	−	1.27299i
$146$	225.831	+	39.8201i	1.54679	+	0.272740i
$147$		0			0
$148$	−344.960	−	125.555i	−2.33081	−	0.848346i
$149$	24.8604	−	68.3034i	0.166848	−	0.458412i	−0.827886	−	0.560896i	$-0.810457\pi$
$149$	24.8604	−	68.3034i	0.166848	−	0.458412i	0.994735	+	0.102484i	$0.0326789\pi$
$150$		0			0
$151$	−0.589241	+	3.34175i	−0.00390226	+	0.0221308i	−0.986697	−	0.162572i	$-0.948021\pi$
$151$	−0.589241	+	3.34175i	−0.00390226	+	0.0221308i	0.982794	+	0.184703i	$0.0591322\pi$
$152$	119.209	−	68.8255i	0.784272	−	0.452800i
$153$		0			0
$154$	13.1991	−	22.8616i	0.0857087	−	0.148452i
$155$	70.2029	−	83.6645i	0.452922	−	0.539771i
$156$		0			0
$157$	−44.5612	−	252.719i	−0.283830	−	1.60968i	−0.709436	−	0.704769i	$-0.751050\pi$
$157$	−44.5612	−	252.719i	−0.283830	−	1.60968i	0.425607	−	0.904908i	$-0.360061\pi$
$158$	84.4945	+	100.697i	0.534775	+	0.637321i
$159$		0			0
$160$	−143.934	+	52.3876i	−0.899586	+	0.327423i
$161$			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	$0.802457\pi$
$164$	2.60502	+	7.15724i	0.0158843	+	0.0436417i
$165$		0			0
$166$	107.467	−	90.1756i	0.647392	−	0.543226i
$167$	−3.18840	+	0.562201i	−0.0190922	+	0.00336647i	−0.183186	−	0.983078i	$-0.558641\pi$
$167$	−3.18840	+	0.562201i	−0.0190922	+	0.00336647i	0.164094	+	0.986445i	$0.447530\pi$
$168$		0			0
$169$	−107.620	−	90.3042i	−0.636807	−	0.534344i
$170$	314.189	+	181.397i	1.84817	+	1.06704i
$171$		0			0
$172$	170.262	+	294.903i	0.989898	+	1.71455i
$173$	−189.550	−	33.4228i	−1.09567	−	0.193195i	−0.403532	−	0.914965i	$-0.632218\pi$
$173$	−189.550	−	33.4228i	−1.09567	−	0.193195i	−0.692133	+	0.721770i	$0.743329\pi$
$174$		0			0
$175$	133.776	+	48.6907i	0.764437	+	0.278232i
$176$	2.34079	−	6.43126i	0.0132999	−	0.0365412i
$177$		0			0
$178$	41.2086	−	233.705i	0.231509	−	1.31295i
$179$	191.363	−	110.484i	1.06907	−	0.617228i	0.141142	−	0.989989i	$-0.454922\pi$
$179$	191.363	−	110.484i	1.06907	−	0.617228i	0.927927	+	0.372762i	$0.121589\pi$
$180$		0			0
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	−0.993983	−	0.109534i	$-0.965064\pi$
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	0.591851	+	0.806048i	$0.298398\pi$
$182$	72.8062	−	86.7670i	0.400034	−	0.476742i
$183$		0			0
$184$	43.6777	+	247.708i	0.237379	+	1.34624i
$185$	−230.224	−	274.371i	−1.24446	−	1.48309i
$186$		0			0
$187$	18.5561	−	6.75386i	0.0992303	−	0.0361169i
$188$		−	406.093i		−	2.16007i
$189$		0			0
$190$	310.452			1.63396
$191$	−26.7275	−	73.4332i	−0.139935	−	0.384467i	0.849853	−	0.527021i	$-0.176691\pi$
$191$	−26.7275	−	73.4332i	−0.139935	−	0.384467i	−0.989787	+	0.142554i	$0.954469\pi$
$192$		0			0
$193$	−171.527	+	143.929i	−0.888743	+	0.745744i	−0.967958	−	0.251114i	$-0.919203\pi$
$193$	−171.527	+	143.929i	−0.888743	+	0.745744i	0.0792145	+	0.996858i	$0.474759\pi$
$194$	−3.70567	+	0.653410i	−0.0191014	+	0.00336809i
$195$		0			0
$196$	44.7048	+	37.5118i	0.228086	+	0.191386i
$197$	−299.369	−	172.841i	−1.51964	−	0.877364i	−0.999732	−	0.0231411i	$-0.992633\pi$
$197$	−299.369	−	172.841i	−1.51964	−	0.877364i	−0.519907	−	0.854223i	$-0.674033\pi$
$198$		0			0
$199$	78.7794	+	136.450i	0.395876	+	0.685678i	0.993213	−	0.116313i	$-0.0371075\pi$
$199$	78.7794	+	136.450i	0.395876	+	0.685678i	−0.597336	+	0.801991i	$0.703774\pi$
$200$	222.723	+	39.2720i	1.11361	+	0.196360i
$201$		0			0
$202$	−35.4671	−	12.9090i	−0.175580	−	0.0639058i
$203$	−67.6328	+	185.820i	−0.333166	+	0.915367i
$204$		0			0
$205$	−1.29042	+	7.31834i	−0.00629473	+	0.0356992i
$206$	−473.773	+	273.533i	−2.29987	+	1.32783i
$207$		0			0
$208$	14.6827	−	25.4311i	0.0705897	−	0.122265i
$209$	10.8618	−	12.9446i	0.0519702	−	0.0619356i
$210$		0			0
$211$	64.6540	+	366.671i	0.306417	+	1.73778i	0.616758	+	0.787153i	$0.288446\pi$
$211$	64.6540	+	366.671i	0.306417	+	1.73778i	−0.310341	+	0.950625i	$0.600443\pi$
$212$	−62.7218	−	74.7489i	−0.295858	−	0.352589i
$213$		0			0
$214$	336.925	−	122.631i	1.57442	−	0.573041i
$215$			332.238i			1.54529i
$216$		0			0
$217$	−101.328			−0.466950
$218$	−200.451	−	550.735i	−0.919501	−	2.52631i
$219$		0			0
$220$	46.2256	−	38.7879i	0.210117	−	0.176309i
$221$	83.4404	−	14.7128i	0.377558	−	0.0665737i
$222$		0			0
$223$	71.5494	+	60.0371i	0.320849	+	0.269225i	0.788959	−	0.614446i	$-0.210620\pi$
$223$	71.5494	+	60.0371i	0.320849	+	0.269225i	−0.468110	+	0.883670i	$0.655065\pi$
$224$	123.069	+	71.0541i	0.549417	+	0.317206i
$225$		0			0
$226$	208.146	+	360.520i	0.921001	+	1.59522i
$227$	359.629	+	63.4124i	1.58427	+	0.279350i	0.895308	−	0.445447i	$-0.146955\pi$
$227$	359.629	+	63.4124i	1.58427	+	0.279350i	0.688963	+	0.724797i	$0.258066\pi$
$228$		0			0
$229$	100.106	+	36.4355i	0.437143	+	0.159107i	0.551211	−	0.834366i	$-0.314166\pi$
$229$	100.106	+	36.4355i	0.437143	+	0.159107i	−0.114068	+	0.993473i	$0.536388\pi$
$230$	−194.024	+	533.076i	−0.843582	+	2.31772i
$231$		0			0
$232$	−54.5500	+	309.368i	−0.235129	+	1.33348i
$233$	206.035	−	118.954i	0.884270	−	0.510533i	0.0122058	−	0.999926i	$-0.496115\pi$
$233$	206.035	−	118.954i	0.884270	−	0.510533i	0.872064	+	0.489392i	$0.162781\pi$
$234$		0			0
$235$	198.105	−	343.128i	0.843001	−	1.46012i
$236$	−273.257	+	325.655i	−1.15787	+	1.37989i
$237$		0			0
$238$	−58.4485	−	331.478i	−0.245582	−	1.39276i
$239$	55.2369	+	65.8287i	0.231117	+	0.275434i	0.869122	−	0.494598i	$-0.164685\pi$
$239$	55.2369	+	65.8287i	0.231117	+	0.275434i	−0.638005	+	0.770032i	$0.720240\pi$
$240$		0			0
$241$	27.5917	−	10.0426i	0.114489	−	0.0416704i	−0.284141	−	0.958783i	$-0.591708\pi$
$241$	27.5917	−	10.0426i	0.114489	−	0.0416704i	0.398629	+	0.917112i	$0.369486\pi$
$242$			397.069i			1.64078i
$243$		0			0
$244$	−711.906			−2.91765
$245$	19.4739	+	53.5040i	0.0794852	+	0.218384i
$246$		0			0
$247$	55.5408	−	46.6042i	0.224861	−	0.188681i
$248$	−158.526	+	27.9524i	−0.639217	+	0.112711i
$249$		0			0
$250$	−47.1322	−	39.5486i	−0.188529	−	0.158194i
$251$	108.333	+	62.5458i	0.431604	+	0.249186i	0.700030	−	0.714114i	$-0.253170\pi$
$251$	108.333	+	62.5458i	0.431604	+	0.249186i	−0.268426	+	0.963300i	$0.586503\pi$
$252$		0			0
$253$	15.4388	+	26.7407i	0.0610228	+	0.105695i
$254$	4.21834	+	0.743807i	0.0166076	+	0.00292837i
$255$		0			0
$256$	357.868	+	130.253i	1.39792	+	0.508802i
$257$	79.8744	−	219.453i	0.310795	−	0.853903i	−0.681701	−	0.731631i	$-0.738760\pi$
$257$	79.8744	−	219.453i	0.310795	−	0.853903i	0.992497	−	0.122272i	$-0.0390182\pi$
$258$		0			0
$259$	−57.7028	+	327.249i	−0.222791	+	1.26351i
$260$	224.225	−	129.456i	0.862405	−	0.497910i
$261$		0			0
$262$	152.740	−	264.554i	0.582979	−	1.00975i
$263$	−79.3706	+	94.5901i	−0.301789	+	0.359658i	−0.895532	−	0.444996i	$-0.853205\pi$
$263$	−79.3706	+	94.5901i	−0.301789	+	0.359658i	0.593743	+	0.804655i	$0.297649\pi$
$264$		0			0
$265$	−16.5319	−	93.7569i	−0.0623844	−	0.353800i
$266$	−185.141	−	220.643i	−0.696021	−	0.829485i
$267$		0			0
$268$	−520.855	+	189.576i	−1.94349	+	0.707372i
$269$		−	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	$0.470787\pi$
$272$	−29.8462	−	82.0018i	−0.109729	−	0.301477i
$273$		0			0
$274$	−150.406	+	126.206i	−0.548929	+	0.460606i
$275$	27.3412	−	4.82099i	0.0994225	−	0.0175309i
$276$		0			0
$277$	87.4101	+	73.3458i	0.315560	+	0.264786i	0.786785	−	0.617227i	$-0.211744\pi$
$277$	87.4101	+	73.3458i	0.315560	+	0.264786i	−0.471226	+	0.882013i	$0.656188\pi$
$278$	145.363	+	83.9254i	0.522889	+	0.301890i
$279$		0			0
$280$	−222.479	−	385.345i	−0.794568	−	1.37623i
$281$	−25.5124	−	4.49853i	−0.0907915	−	0.0160090i	0.128068	−	0.991765i	$-0.459122\pi$
$281$	−25.5124	−	4.49853i	−0.0907915	−	0.0160090i	−0.218859	+	0.975756i	$0.570234\pi$
$282$		0			0
$283$	148.018	+	53.8742i	0.523032	+	0.190368i	0.590025	−	0.807385i	$-0.299118\pi$
$283$	148.018	+	53.8742i	0.523032	+	0.190368i	−0.0669923	+	0.997753i	$0.521340\pi$
$284$	110.682	−	304.097i	0.389726	−	1.07076i
$285$		0			0
$286$	3.83569	−	21.7533i	0.0134115	−	0.0760603i
$287$	5.97082	−	3.44725i	0.0208042	−	0.0120113i
$288$		0			0
$289$	−18.6082	+	32.2303i	−0.0643881	+	0.111523i
$290$	−455.414	+	542.741i	−1.57039	+	1.87152i
$291$		0			0
$292$	−84.4496	−	478.937i	−0.289211	−	1.64020i
$293$	269.929	+	321.689i	0.921259	+	1.09791i	0.994924	+	0.100631i	$0.0320860\pi$
$293$	269.929	+	321.689i	0.921259	+	1.09791i	−0.0736650	+	0.997283i	$0.523470\pi$
$294$		0			0
$295$	−389.754	+	141.859i	−1.32120	+	0.480877i
$296$			527.892i			1.78342i
$297$		0			0
$298$	−241.620			−0.810804
$299$	45.3126	+	124.495i	0.151547	+	0.416373i
$300$		0			0
$301$	236.127	−	198.134i	0.784476	−	0.658253i
$302$	11.1084	−	1.95870i	0.0367826	−	0.00648577i
$303$		0			0
$304$	−57.2037	−	47.9996i	−0.188170	−	0.157894i
$305$	−601.526	−	347.291i	−1.97222	−	1.13866i
$306$		0			0
$307$	−101.037	−	175.001i	−0.329110	−	0.570035i	0.653225	−	0.757163i	$-0.273415\pi$
$307$	−101.037	−	175.001i	−0.329110	−	0.570035i	−0.982336	+	0.187128i	$0.940082\pi$
$308$	−55.1344	−	9.72169i	−0.179008	−	0.0315639i
$309$		0			0
$310$	−341.153	−	124.169i	−1.10049	−	0.400546i
$311$	90.7146	−	249.236i	0.291687	−	0.801403i	−0.704133	−	0.710068i	$-0.748664\pi$
$311$	90.7146	−	249.236i	0.291687	−	0.801403i	0.995820	−	0.0913353i	$-0.0291135\pi$
$312$		0			0
$313$	47.8820	−	271.553i	0.152978	−	0.867580i	−0.807634	−	0.589685i	$-0.799252\pi$
$313$	47.8820	−	271.553i	0.152978	−	0.867580i	0.960611	−	0.277895i	$-0.0896369\pi$
$314$	−738.742	+	426.513i	−2.35268	+	1.35832i
$315$		0			0
$316$	139.388	−	241.428i	0.441102	−	0.764012i
$317$	22.5014	−	26.8161i	0.0709824	−	0.0845935i	−0.729385	−	0.684104i	$-0.760194\pi$
$317$	22.5014	−	26.8161i	0.0709824	−	0.0845935i	0.800367	+	0.599510i	$0.204638\pi$
$318$		0			0
$319$	6.69650	+	37.9777i	0.0209922	+	0.119053i
$320$	424.538	+	505.944i	1.32668	+	1.58108i
$321$		0			0
$322$	494.574	−	180.010i	1.53595	−	0.559038i
$323$		−	215.457i		−	0.667049i
$324$		0			0
$325$	119.122			0.366528
$326$	301.522	+	828.424i	0.924913	+	2.54118i
$327$		0			0
$328$	8.39027	−	7.04027i	0.0255801	−	0.0214643i
$329$	−362.009	+	63.8320i	−1.10033	+	0.194018i
$330$		0			0
$331$	161.531	+	135.541i	0.488010	+	0.409489i	0.853312	−	0.521400i	$-0.174590\pi$
$331$	161.531	+	135.541i	0.488010	+	0.409489i	−0.365303	+	0.930889i	$0.619035\pi$
$332$	−257.660	−	148.760i	−0.776086	−	0.448073i
$333$		0			0
$334$	5.38105	+	9.32025i	0.0161109	+	0.0279049i
$335$	−532.578	−	93.9079i	−1.58979	−	0.280322i
$336$		0			0
$337$	−144.965	−	52.7629i	−0.430163	−	0.156566i	0.117859	−	0.993030i	$-0.462397\pi$
$337$	−144.965	−	52.7629i	−0.430163	−	0.156566i	−0.548022	+	0.836464i	$0.684619\pi$
$338$	−159.723	+	438.835i	−0.472553	+	1.29833i
$339$		0			0
$340$	133.606	−	757.719i	0.392959	−	2.22858i
$341$	−17.1133	+	9.88034i	−0.0501855	+	0.0289746i
$342$		0			0
$343$	182.756	−	316.543i	0.532817	−	0.922867i
$344$	314.759	−	375.115i	0.914997	−	1.09045i
$345$		0			0
$346$	111.101	+	630.085i	0.321101	+	1.82106i
$347$	−188.521	−	224.671i	−0.543289	−	0.647467i	0.422632	−	0.906301i	$-0.361106\pi$
$347$	−188.521	−	224.671i	−0.543289	−	0.647467i	−0.965922	+	0.258834i	$0.916662\pi$
$348$		0			0
$349$	384.360	−	139.896i	1.10132	−	0.400847i	0.273516	−	0.961867i	$-0.411813\pi$
$349$	384.360	−	139.896i	1.10132	−	0.400847i	0.827802	+	0.561020i	$0.189591\pi$
$350$		−	473.227i		−	1.35208i
$351$		0			0
$352$	27.7135			0.0787316
$353$	−171.031	−	469.905i	−0.484508	−	1.33117i	−0.905591	−	0.424152i	$-0.860572\pi$
$353$	−171.031	−	469.905i	−0.484508	−	1.33117i	0.421083	−	0.907022i	$-0.361650\pi$
$354$		0			0
$355$	241.870	−	202.953i	0.681323	−	0.571698i
$356$	−495.637	+	87.3943i	−1.39224	+	0.245489i
$357$		0			0
$358$	−562.675	−	472.140i	−1.57172	−	1.31883i
$359$	216.295	+	124.878i	0.602492	+	0.347849i	0.770021	−	0.638018i	$-0.220246\pi$
$359$	216.295	+	124.878i	0.602492	+	0.347849i	−0.167529	+	0.985867i	$0.553579\pi$
$360$		0			0
$361$	88.3143	+	152.965i	0.244638	+	0.423725i
$362$	476.546	+	84.0279i	1.31642	+	0.232121i
$363$		0			0
$364$	−225.726	−	82.1576i	−0.620127	−	0.225708i
$365$	162.286	−	445.876i	0.444618	−	1.22158i
$366$		0			0
$367$	−55.5902	+	315.268i	−0.151472	+	0.859040i	0.810469	+	0.585782i	$0.199212\pi$
$367$	−55.5902	+	315.268i	−0.151472	+	0.859040i	−0.961941	+	0.273258i	$0.911899\pi$
$368$	118.171	−	68.2260i	0.321117	−	0.185397i
$369$		0			0
$370$	−595.291	+	1031.07i	−1.60889	+	2.78669i
$371$	−56.7756	+	67.6625i	−0.153034	+	0.182379i
$372$		0			0
$373$	34.3314	+	194.703i	0.0920414	+	0.521993i	0.995614	+	0.0935574i	$0.0298239\pi$
$373$	34.3314	+	194.703i	0.0920414	+	0.521993i	−0.903573	+	0.428435i	$0.859065\pi$
$374$	−42.1932	−	50.2839i	−0.112816	−	0.134449i
$375$		0			0
$376$	−548.748	+	199.728i	−1.45944	+	0.531191i
$377$			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	$0.340127\pi$
$380$	−225.186	−	618.693i	−0.592594	−	1.62814i
$381$		0			0
$382$	−198.992	+	166.974i	−0.520922	+	0.437105i
$383$	637.422	−	112.395i	1.66429	−	0.293459i	0.739278	−	0.673400i	$-0.235167\pi$
$383$	637.422	−	112.395i	1.66429	−	0.293459i	0.925011	+	0.379941i	$0.124056\pi$
$384$		0			0
$385$	−41.8433	−	35.1107i	−0.108684	−	0.0911967i
$386$	644.593	+	372.156i	1.66993	+	0.964134i
$387$		0			0
$388$	3.99007	+	6.91101i	0.0102837	+	0.0178119i
$389$	55.7208	+	9.82508i	0.143241	+	0.0252573i	0.244809	−	0.969571i	$-0.421275\pi$
$389$	55.7208	+	9.82508i	0.143241	+	0.0252573i	−0.101568	+	0.994829i	$0.532386\pi$
$390$		0			0
$391$	369.961	+	134.655i	0.946192	+	0.344386i
$392$	28.7021	−	78.8584i	0.0732196	−	0.201169i
$393$		0			0
$394$	−199.536	+	1131.63i	−0.506437	+	2.87215i
$395$	235.553	−	135.996i	0.596336	−	0.344295i
$396$		0			0
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	0.0770876	+	0.997024i	$0.475438\pi$
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	−0.901992	+	0.431752i	$0.857895\pi$
$398$	336.655	−	401.210i	0.845868	−	1.00807i
$399$		0			0
$400$	−21.3046	−	120.824i	−0.0532615	−	0.302061i
$401$	81.4322	+	97.0471i	0.203073	+	0.242013i	0.857963	−	0.513711i	$-0.171730\pi$
$401$	81.4322	+	97.0471i	0.203073	+	0.242013i	−0.654890	+	0.755724i	$0.727285\pi$
$402$		0			0
$403$	−79.6733	+	28.9987i	−0.197700	+	0.0719571i
$404$			80.0452i			0.198132i
$405$		0			0
$406$	657.326			1.61903
$407$	22.1641	+	60.8954i	0.0544572	+	0.149620i
$408$		0			0
$409$	417.238	−	350.105i	1.02014	−	0.856001i	0.0304973	−	0.999535i	$-0.490291\pi$
$409$	417.238	−	350.105i	1.02014	−	0.856001i	0.989645	+	0.143533i	$0.0458464\pi$
$410$	24.3270	−	4.28950i	0.0593340	−	0.0104622i
$411$		0			0
$412$	888.770	+	745.767i	2.15721	+	1.81011i
$413$	333.256	+	192.405i	0.806915	+	0.465873i
$414$		0			0
$415$	−145.140	−	251.390i	−0.349736	−	0.605760i
$416$	117.103	+	20.6484i	0.281497	+	0.0496356i
$417$		0			0
$418$	−52.7830	−	19.2114i	−0.126275	−	0.0459604i
$419$	−228.512	+	627.831i	−0.545374	+	1.49840i	0.294516	+	0.955647i	$0.404842\pi$
$419$	−228.512	+	627.831i	−0.545374	+	1.49840i	−0.839890	+	0.542757i	$0.817381\pi$
$420$		0			0
$421$	39.4928	−	223.975i	0.0938071	−	0.532006i	−0.901299	−	0.433197i	$-0.857385\pi$
$421$	39.4928	−	223.975i	0.0938071	−	0.532006i	0.995106	−	0.0988094i	$-0.0315034\pi$
$422$	1071.84	−	618.829i	2.53991	−	1.46642i
$423$		0			0
$424$	−70.1589	+	121.519i	−0.165469	+	0.286601i
$425$	227.542	−	271.174i	0.535392	−	0.638056i
$426$		0			0
$427$	111.902	+	634.626i	0.262065	+	1.48624i
$428$	−488.777	−	582.502i	−1.14200	−	1.36099i
$429$		0			0
$430$	1037.79	−	377.726i	2.41347	−	0.878432i
$431$			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	$0.504410\pi$
$434$	115.201	+	316.513i	0.265440	+	0.729292i
$435$		0			0
$436$	−952.153	+	798.951i	−2.18384	+	1.83246i
$437$	331.783	−	58.5023i	0.759229	−	0.133873i
$438$		0			0
$439$	−57.7349	−	48.4453i	−0.131515	−	0.110354i	0.574658	−	0.818394i	$-0.305135\pi$
$439$	−57.7349	−	48.4453i	−0.131515	−	0.110354i	−0.706172	+	0.708040i	$0.749580\pi$
$440$	−75.1487	−	43.3871i	−0.170793	−	0.0986071i
$441$		0			0
$442$	−140.822	−	243.911i	−0.318602	−	0.551834i
$443$	244.217	+	43.0620i	0.551279	+	0.0972054i	0.442347	−	0.896844i	$-0.354146\pi$
$443$	244.217	+	43.0620i	0.551279	+	0.0972054i	0.108932	+	0.994049i	$0.465257\pi$
$444$		0			0
$445$	−461.423	−	167.944i	−1.03691	−	0.377403i
$446$	106.189	−	291.752i	0.238092	−	0.654151i
$447$		0			0
$448$	106.405	−	603.452i	0.237511	−	1.34699i
$449$	−178.012	+	102.775i	−0.396462	+	0.228898i	−0.684956	−	0.728584i	$-0.740179\pi$
$449$	−178.012	+	102.775i	−0.396462	+	0.228898i	0.288494	+	0.957482i	$0.406845\pi$
$450$		0			0
$451$	0.672273	−	1.16441i	0.00149063	−	0.00258184i
$452$	567.495	−	676.314i	1.25552	−	1.49627i
$453$		0			0
$454$	−210.790	−	1195.45i	−0.464294	−	2.63314i
$455$	−150.648	−	179.536i	−0.331095	−	0.394584i
$456$		0			0
$457$	−600.521	+	218.572i	−1.31405	+	0.478276i	−0.901547	−	0.432680i	$-0.857568\pi$
$457$	−600.521	+	218.572i	−1.31405	+	0.478276i	−0.412504	+	0.910956i	$0.635346\pi$
$458$		−	354.118i		−	0.773184i
$459$		0			0
$460$	1203.09			2.61542
$461$	−48.4455	−	133.103i	−0.105088	−	0.288727i	0.875993	−	0.482323i	$-0.160207\pi$
$461$	−48.4455	−	133.103i	−0.105088	−	0.288727i	−0.981081	+	0.193597i	$0.937985\pi$
$462$		0			0
$463$	−215.833	+	181.106i	−0.466163	+	0.391157i	−0.845393	−	0.534146i	$-0.820633\pi$
$463$	−215.833	+	181.106i	−0.466163	+	0.391157i	0.379230	+	0.925303i	$0.376189\pi$
$464$	167.829	−	29.5928i	0.361700	−	0.0637775i
$465$		0			0
$466$	−605.814	−	508.338i	−1.30003	−	1.09085i
$467$	−462.423	−	266.980i	−0.990199	−	0.571692i	−0.0848656	−	0.996392i	$-0.527046\pi$
$467$	−462.423	−	266.980i	−0.990199	−	0.571692i	−0.905334	+	0.424700i	$0.860379\pi$
$468$		0			0
$469$	250.868	+	434.515i	0.534899	+	0.926472i
$470$	−1297.04	−	228.703i	−2.75966	−	0.486602i
$471$		0			0
$472$	574.449	+	209.082i	1.21705	+	0.442971i
$473$	20.5597	−	56.4872i	0.0434665	−	0.119423i
$474$		0			0
$475$	52.6013	−	298.317i	0.110740	−	0.628036i
$476$	−618.201	+	356.918i	−1.29874	+	0.749828i
$477$		0			0
$478$	142.826	−	247.382i	0.298799	−	0.517535i
$479$	−109.060	+	129.973i	−0.227683	+	0.271343i	−0.867776	−	0.496955i	$-0.834451\pi$
$479$	−109.060	+	129.973i	−0.227683	+	0.271343i	0.640093	+	0.768298i	$0.278896\pi$
$480$		0			0
$481$	48.2829	+	273.826i	0.100380	+	0.569285i
$482$	−62.7388	−	74.7692i	−0.130163	−	0.155123i
$483$		0			0
$484$	791.312	−	288.014i	1.63494	−	0.595070i
$485$			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	$0.493200\pi$
$488$	350.136	+	961.990i	0.717492	+	1.97129i
$489$		0			0
$490$	144.987	−	121.659i	0.295893	−	0.248283i
$491$	148.829	−	26.2425i	0.303113	−	0.0534471i	−0.0200228	−	0.999800i	$-0.506374\pi$
$491$	148.829	−	26.2425i	0.303113	−	0.0534471i	0.323136	+	0.946352i	$0.395263\pi$
$492$		0			0
$493$	376.668	+	316.062i	0.764033	+	0.641100i
$494$	−208.720	−	120.504i	−0.422510	−	0.243936i
$495$		0			0
$496$	43.6626	+	75.6258i	0.0880294	+	0.152471i
$497$	−288.484	−	50.8674i	−0.580450	−	0.102349i
$498$		0			0
$499$	−768.271	−	279.628i	−1.53962	−	0.560376i	−0.573666	−	0.819089i	$-0.694479\pi$
$499$	−768.271	−	279.628i	−1.53962	−	0.560376i	−0.965954	+	0.258713i	$0.916702\pi$
$500$	−44.6284	+	122.615i	−0.0892568	+	0.245231i
$501$		0			0
$502$	72.2061	−	409.501i	0.143837	−	0.815739i
$503$	201.176	−	116.149i	0.399953	−	0.230913i	−0.286511	−	0.958077i	$-0.592495\pi$
$503$	201.176	−	116.149i	0.399953	−	0.230913i	0.686464	+	0.727164i	$0.259162\pi$
$504$		0			0
$505$	−39.0487	+	67.6343i	−0.0773241	+	0.133929i
$506$	65.9759	−	78.6270i	0.130387	−	0.155389i
$507$		0			0
$508$	−1.57745	−	8.94617i	−0.00310522	−	0.0176106i
$509$	−208.104	−	248.008i	−0.408848	−	0.487246i	0.521849	−	0.853038i	$-0.325243\pi$
$509$	−208.104	−	248.008i	−0.408848	−	0.487246i	−0.930697	+	0.365792i	$0.880798\pi$
$510$		0			0
$511$	−413.672	+	150.564i	−0.809535	+	0.294647i
$512$		−	345.476i		−	0.674758i
$513$		0			0
$514$	−776.303			−1.51032
$515$	387.158	+	1063.71i	0.751763	+	2.06545i
$516$		0			0
$517$	−54.9154	+	46.0795i	−0.106219	+	0.0891287i
$518$	1087.81	−	191.810i	2.10002	−	0.370290i
$519$		0			0
$520$	−285.213	−	239.322i	−0.548487	−	0.460235i
$521$	−480.156	−	277.218i	−0.921604	−	0.532088i	−0.0374577	−	0.999298i	$-0.511926\pi$
$521$	−480.156	−	277.218i	−0.921604	−	0.532088i	−0.884146	+	0.467210i	$0.845259\pi$
$522$		0			0
$523$	−472.881	−	819.053i	−0.904170	−	1.56607i	−0.822028	−	0.569447i	$-0.807157\pi$
$523$	−472.881	−	819.053i	−0.904170	−	1.56607i	−0.0821414	−	0.996621i	$-0.526176\pi$
$524$	−638.015	−	112.499i	−1.21759	−	0.214693i
$525$		0			0
$526$	385.703	+	140.384i	0.733276	+	0.266891i
$527$	−86.1750	+	236.764i	−0.163520	+	0.449267i
$528$		0			0
$529$	−15.0414	+	85.3039i	−0.0284336	+	0.161255i
$530$	−274.068	+	158.233i	−0.517109	+	0.298553i
$531$		0			0
$532$	−305.423	+	529.008i	−0.574103	+	0.994376i
$533$	3.70824	−	4.41931i	0.00695730	−	0.00829138i
$534$		0			0
$535$	−128.829	−	730.627i	−0.240802	−	1.36566i
$536$	512.343	+	610.586i	0.955864	+	1.13915i
$537$		0			0
$538$	−1591.66	+	579.317i	−2.95848	+	1.07680i
$539$		−	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	$0.617425\pi$
$542$	−56.4729	−	155.158i	−0.104194	−	0.286270i
$543$		0			0
$544$	270.690	−	227.136i	0.497593	−	0.417530i
$545$	−1194.28	+	210.583i	−2.19133	+	0.386391i
$546$		0			0
$547$	−355.618	−	298.399i	−0.650124	−	0.545519i	0.256984	−	0.966416i	$-0.417271\pi$
$547$	−355.618	−	298.399i	−0.650124	−	0.545519i	−0.907109	+	0.420897i	$0.861716\pi$
$548$	360.611	+	208.199i	0.658049	+	0.379925i
$549$		0			0
$550$	−46.1436	−	79.9230i	−0.0838974	−	0.145315i
$551$	414.371	+	73.0648i	0.752035	+	0.132604i
$552$		0			0
$553$	−237.130	−	86.3081i	−0.428806	−	0.156073i
$554$	129.728	−	356.425i	0.234167	−	0.643367i
$555$		0			0
$556$	61.8144	−	350.567i	0.111177	−	0.630515i
$557$	203.531	−	117.509i	0.365406	−	0.210967i	−0.306043	−	0.952018i	$-0.599005\pi$
$557$	203.531	−	117.509i	0.365406	−	0.210967i	0.671450	+	0.741050i	$0.265672\pi$
$558$		0			0
$559$	128.961	−	223.367i	0.230700	−	0.399584i
$560$	−155.159	+	184.911i	−0.277070	+	0.330199i
$561$		0			0
$562$	14.9536	+	84.8061i	0.0266078	+	0.150901i
$563$	−53.7352	−	64.0391i	−0.0954443	−	0.113746i	0.716208	−	0.697887i	$-0.245876\pi$
$563$	−53.7352	−	64.0391i	−0.0954443	−	0.113746i	−0.811652	+	0.584141i	$0.801432\pi$
$564$		0			0
$565$	809.433	−	294.610i	1.43263	−	0.521433i
$566$		−	523.606i		−	0.925099i
$567$		0			0
$568$	−465.359			−0.819295
$569$	−315.330	−	866.363i	−0.554183	−	1.52261i	−0.827945	−	0.560809i	$-0.810490\pi$
$569$	−315.330	−	866.363i	−0.554183	−	1.52261i	0.273762	−	0.961798i	$-0.411732\pi$
$570$		0			0
$571$	305.347	−	256.216i	0.534758	−	0.448715i	−0.334983	−	0.942224i	$-0.608731\pi$
$571$	305.347	−	256.216i	0.534758	−	0.448715i	0.869741	+	0.493509i	$0.164286\pi$
$572$	−46.1339	+	8.13464i	−0.0806536	+	0.0142214i
$573$		0			0
$574$	−17.5563	−	14.7315i	−0.0305859	−	0.0256646i
$575$	479.365	+	276.762i	0.833679	+	0.481325i
$576$		0			0
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	0.873155	−	0.487442i	$-0.162070\pi$
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	−0.858715	+	0.512454i	$0.828737\pi$
$578$	121.832	+	21.4822i	0.210781	+	0.0371664i
$579$		0			0
$580$	1411.95	+	513.909i	2.43440	+	0.886049i
$581$	−92.1111	+	253.073i	−0.158539	+	0.435582i
$582$		0			0
$583$	−2.99114	+	16.9636i	−0.00513060	+	0.0290971i
$584$	−605.648	+	349.671i	−1.03707	+	0.598751i
$585$		0			0
$586$	697.955	−	1208.89i	1.19105	−	2.06296i
$587$	119.848	−	142.830i	0.204171	−	0.243321i	−0.654236	−	0.756290i	$-0.727010\pi$
$587$	119.848	−	142.830i	0.204171	−	0.243321i	0.858407	+	0.512969i	$0.171454\pi$
$588$		0			0
$589$	37.4397	+	212.331i	0.0635649	+	0.360494i
$590$	886.232	+	1056.17i	1.50209	+	1.79012i
$591$		0			0
$592$	269.105	−	97.9462i	0.454569	−	0.165450i
$593$			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
$596$	175.259	+	481.519i	0.294058	+	0.807918i
$597$		0			0
$598$	337.362	−	283.081i	0.564151	−	0.473379i
$599$	14.5762	−	2.57018i	0.0243343	−	0.00429079i	−0.161468	−	0.986878i	$-0.551623\pi$
$599$	14.5762	−	2.57018i	0.0243343	−	0.00429079i	0.185802	+	0.982587i	$0.440512\pi$
$600$		0			0
$601$	−148.863	−	124.911i	−0.247692	−	0.207838i	0.510486	−	0.859886i	$-0.329466\pi$
$601$	−148.863	−	124.911i	−0.247692	−	0.207838i	−0.758178	+	0.652048i	$0.773910\pi$
$602$	−887.356	−	512.315i	−1.47401	−	0.851022i
$603$		0			0
$604$	−11.9609	−	20.7169i	−0.0198028	−	0.0342995i
$605$	809.122	+	142.670i	1.33739	+	0.235818i
$606$		0			0
$607$	−545.203	−	198.438i	−0.898192	−	0.326915i	−0.148664	−	0.988888i	$-0.547497\pi$
$607$	−545.203	−	198.438i	−0.898192	−	0.326915i	−0.749528	+	0.661973i	$0.769720\pi$
$608$	103.420	−	284.144i	0.170098	−	0.467341i
$609$		0			0
$610$	−400.931	+	2273.79i	−0.657263	+	3.72753i
$611$	−266.377	+	153.793i	−0.435968	+	0.251706i
$612$		0			0
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	−0.793185	−	0.608980i	$-0.791579\pi$
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	0.923985	+	0.382428i	$0.124912\pi$
$614$	−431.770	+	514.563i	−0.703208	+	0.838051i
$615$		0			0
$616$	13.9799	+	79.2839i	0.0226946	+	0.128708i
$617$	267.304	+	318.561i	0.433232	+	0.516306i	0.937852	−	0.347036i	$-0.112812\pi$
$617$	267.304	+	318.561i	0.433232	+	0.516306i	−0.504620	+	0.863342i	$0.668367\pi$
$618$		0			0
$619$	616.164	−	224.265i	0.995418	−	0.362303i	0.207602	−	0.978213i	$-0.433434\pi$
$619$	616.164	−	224.265i	0.995418	−	0.362303i	0.787816	+	0.615911i	$0.211212\pi$
$620$			769.943i			1.24184i
$621$		0			0
$622$	−881.659			−1.41746
$623$	155.814	+	428.097i	0.250103	+	0.687154i
$624$		0			0
$625$	−524.766	+	440.331i	−0.839626	+	0.704530i
$626$	−902.671	+	159.165i	−1.44197	+	0.254257i
$627$		0			0
$628$	1385.84	+	1162.85i	2.20675	+	1.85168i
$629$	715.577	+	413.139i	1.13764	+	0.656818i
$630$		0			0
$631$	321.500	+	556.855i	0.509509	+	0.882496i	0.999939	+	0.0110155i	$0.00350642\pi$
$631$	321.500	+	556.855i	0.509509	+	0.882496i	−0.490430	+	0.871481i	$0.663160\pi$
$632$	−394.794	−	69.6128i	−0.624673	−	0.110147i
$633$		0			0
$634$	−109.346	−	39.7987i	−0.172470	−	0.0627740i
$635$	3.03137	−	8.32861i	0.00477380	−	0.0131159i
$636$		0			0
$637$	7.67557	−	43.5303i	0.0120496	−	0.0683364i
$638$	111.016	−	64.0948i	0.174006	−	0.100462i
$639$		0			0
$640$	791.384	−	1370.72i	1.23654	−	2.14175i
$641$	−75.6202	+	90.1206i	−0.117972	+	0.140594i	−0.821798	−	0.569779i	$-0.807029\pi$
$641$	−75.6202	+	90.1206i	−0.117972	+	0.140594i	0.703826	+	0.710372i	$0.251473\pi$
$642$		0			0
$643$	75.3782	+	427.491i	0.117229	+	0.664839i	0.985622	+	0.168963i	$0.0540418\pi$
$643$	75.3782	+	427.491i	0.117229	+	0.664839i	−0.868393	+	0.495876i	$0.834847\pi$
$644$	−717.478	−	855.057i	−1.11410	−	1.32773i
$645$		0			0
$646$	−673.010	+	244.956i	−1.04181	+	0.379188i
$647$			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
$650$	−135.431	−	372.093i	−0.208355	−	0.572451i
$651$		0			0
$652$	1432.24	−	1201.79i	2.19669	−	1.84324i
$653$	−881.502	+	155.433i	−1.34993	+	0.238028i	−0.801412	−	0.598113i	$-0.795917\pi$
$653$	−881.502	+	155.433i	−1.34993	+	0.238028i	−0.548514	+	0.836141i	$0.684806\pi$
$654$		0			0
$655$	−484.211	−	406.301i	−0.739253	−	0.620307i
$656$	−5.14569	−	2.97087i	−0.00784404	−	0.00452876i
$657$		0			0
$658$	610.961	+	1058.22i	0.928513	+	1.60823i
$659$	−829.023	−	146.179i	−1.25800	−	0.221820i	−0.495387	−	0.868673i	$-0.664974\pi$
$659$	−829.023	−	146.179i	−1.25800	−	0.221820i	−0.762615	+	0.646853i	$0.776085\pi$
$660$		0			0
$661$	−212.344	−	77.2868i	−0.321246	−	0.116924i	0.176363	−	0.984325i	$-0.443567\pi$
$661$	−212.344	−	77.2868i	−0.321246	−	0.116924i	−0.497610	+	0.867401i	$0.665789\pi$
$662$	239.734	−	658.664i	0.362136	−	0.994960i
$663$		0			0
$664$	−74.2933	+	421.338i	−0.111887	+	0.634545i
$665$	−516.135	+	297.991i	−0.776143	+	0.448106i
$666$		0			0
$667$	−384.430	+	665.853i	−0.576357	+	0.998280i
$668$	14.6710	−	17.4842i	0.0219626	−	0.0261740i
$669$		0			0
$670$	312.160	+	1770.35i	0.465911	+	2.64231i
$671$	80.7804	+	96.2703i	0.120388	+	0.143473i
$672$		0			0
$673$	103.888	−	37.8120i	0.154365	−	0.0561843i	−0.263682	−	0.964610i	$-0.584937\pi$
$673$	103.888	−	37.8120i	0.154365	−	0.0561843i	0.418047	+	0.908425i	$0.362715\pi$
$674$			512.805i			0.760838i
$675$		0			0
$676$	990.401			1.46509
$677$	−0.977873	−	2.68668i	−0.00144442	−	0.00396851i	0.938968	−	0.344004i	$-0.111783\pi$
$677$	−0.977873	−	2.68668i	−0.00144442	−	0.00396851i	−0.940413	+	0.340035i	$0.889561\pi$
$678$		0			0
$679$	5.53361	−	4.64325i	0.00814964	−	0.00683836i
$680$	−1089.61	+	192.127i	−1.60236	+	0.282540i
$681$		0			0
$682$	50.3189	+	42.2226i	0.0737814	+	0.0619099i
$683$	843.279	+	486.868i	1.23467	+	0.712837i	0.968000	−	0.250951i	$-0.0807434\pi$
$683$	843.279	+	486.868i	1.23467	+	0.712837i	0.266670	+	0.963788i	$0.414077\pi$
$684$		0			0
$685$	203.132	+	351.835i	0.296543	+	0.513628i
$686$	−1196.55	−	210.983i	−1.74424	−	0.307556i
$687$		0			0
$688$	−249.625	−	90.8559i	−0.362827	−	0.132058i
$689$	−25.2780	+	69.4508i	−0.0366880	+	0.100799i
$690$		0			0
$691$	113.572	−	644.097i	0.164358	−	0.932123i	−0.785365	−	0.619033i	$-0.787525\pi$
$691$	113.572	−	644.097i	0.164358	−	0.932123i	0.949723	−	0.313090i	$-0.101364\pi$
$692$	1175.10	−	678.443i	1.69812	−	0.980409i
$693$		0			0
$694$	−487.460	+	844.305i	−0.702391	+	1.21658i
$695$	223.248	−	266.057i	0.321220	−	0.382815i
$696$		0			0
$697$	−2.97696	−	16.8832i	−0.00427111	−	0.0242226i
$698$	−873.967	−	1041.55i	−1.25210	−	1.49220i
$699$		0			0
$700$	−943.084	+	343.255i	−1.34726	+	0.490364i
$701$		−	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
$704$	−40.8710	−	112.292i	−0.0580554	−	0.159506i
$705$		0			0
$706$	−1273.37	+	1068.48i	−1.80363	+	1.51343i
$707$	71.3559	−	12.5820i	0.100928	−	0.0177963i
$708$		0			0
$709$	−379.570	−	318.497i	−0.535360	−	0.449220i	0.334587	−	0.942365i	$-0.391403\pi$
$709$	−379.570	−	318.497i	−0.535360	−	0.449220i	−0.869948	+	0.493144i	$0.835847\pi$
$710$	−908.936	−	524.774i	−1.28019	−	0.739119i
$711$		0			0
$712$	361.863	+	626.766i	0.508235	+	0.880289i
$713$	−387.993	−	68.4136i	−0.544169	−	0.0959517i
$714$		0			0
$715$	−42.9492	−	15.6322i	−0.0600688	−	0.0218633i
$716$	−532.784	+	1463.81i	−0.744111	+	2.04443i
$717$		0			0
$718$	144.165	−	817.602i	0.200787	−	1.13872i
$719$	−124.160	+	71.6839i	−0.172684	+	0.0996994i	−0.583851	−	0.811861i	$-0.698455\pi$
$719$	−124.160	+	71.6839i	−0.172684	+	0.0996994i	0.411167	+	0.911560i	$0.365121\pi$
$720$		0			0
$721$	525.108	−	909.514i	0.728305	−	1.26146i
$722$	377.402	−	449.770i	0.522717	−	0.622950i
$723$		0			0
$724$	−178.205	−	1010.65i	−0.246139	−	1.39592i
$725$	444.364	+	529.572i	0.612916	+	0.730444i
$726$		0			0
$727$	310.011	−	112.835i	0.426425	−	0.155206i	−0.119888	−	0.992787i	$-0.538253\pi$
$727$	310.011	−	112.835i	0.426425	−	0.155206i	0.546312	+	0.837582i	$0.316031\pi$
$728$			345.429i			0.474490i
$729$		0			0
$730$	−1577.26			−2.16063
$731$	−262.146	−	720.240i	−0.358613	−	0.985281i
$732$		0			0
$733$	141.211	−	118.490i	0.192647	−	0.161650i	−0.541362	−	0.840790i	$-0.682091\pi$
$733$	141.211	−	118.490i	0.192647	−	0.161650i	0.734010	+	0.679139i	$0.237647\pi$
$734$	1047.98	−	184.788i	1.42777	−	0.251755i
$735$		0			0
$736$	423.268	+	355.164i	0.575092	+	0.482560i
$737$	84.7378	+	48.9234i	0.114977	+	0.0663818i
$738$		0			0
$739$	225.818	+	391.128i	0.305572	+	0.529267i	0.977389	−	0.211451i	$-0.0678189\pi$
$739$	225.818	+	391.128i	0.305572	+	0.529267i	−0.671816	+	0.740718i	$0.734486\pi$
$740$	2486.60	+	438.455i	3.36027	+	0.592507i
$741$		0			0
$742$	275.902	+	100.420i	0.371836	+	0.135337i
$743$	−204.452	+	561.728i	−0.275171	+	0.756027i	0.722721	+	0.691140i	$0.242891\pi$
$743$	−204.452	+	561.728i	−0.275171	+	0.756027i	−0.997893	+	0.0648876i	$0.979331\pi$
$744$		0			0
$745$	−86.8158	+	492.357i	−0.116531	+	0.660882i
$746$	569.151	−	328.600i	0.762937	−	0.440482i
$747$		0			0
$748$	−69.6051	+	120.560i	−0.0930549	+	0.161176i
$749$	−442.440	+	527.279i	−0.590707	+	0.703977i
$750$		0			0
$751$	−108.200	−	613.635i	−0.144075	−	0.817091i	−0.968105	−	0.250545i	$-0.919390\pi$
$751$	−108.200	−	613.635i	−0.144075	−	0.817091i	0.824030	−	0.566546i	$-0.191721\pi$
$752$	203.632	+	242.679i	0.270787	+	0.322711i
$753$		0			0
$754$	516.849	−	188.118i	0.685476	−	0.249493i
$755$		−	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	$0.737933\pi$
$758$	−414.865	−	1139.83i	−0.547316	−	1.50374i
$759$		0			0
$760$	−725.280	+	608.582i	−0.954315	+	0.800766i
$761$	613.431	−	108.164i	0.806086	−	0.142135i	0.244603	−	0.969623i	$-0.421342\pi$
$761$	613.431	−	108.164i	0.806086	−	0.142135i	0.561483	+	0.827489i	$0.310231\pi$
$762$		0			0
$763$	861.886	+	723.208i	1.12960	+	0.947848i
$764$	477.099	+	275.453i	0.624475	+	0.360541i
$765$		0			0
$766$	−1075.77	−	1863.30i	−1.40441	−	2.43250i
$767$	317.100	+	55.9132i	0.413428	+	0.0728986i
$768$		0			0
$769$	985.221	+	358.591i	1.28117	+	0.466308i	0.890820	−	0.454357i	$-0.150131\pi$
$769$	985.221	+	358.591i	1.28117	+	0.466308i	0.390352	+	0.920666i	$0.372353\pi$
$770$	−62.1011	+	170.621i	−0.0806508	+	0.221586i
$771$		0			0
$772$	274.107	−	1554.54i	0.355061	−	2.01365i
$773$	−719.632	+	415.480i	−0.930960	+	0.537490i	−0.887115	−	0.461549i	$-0.847294\pi$
$773$	−719.632	+	415.480i	−0.930960	+	0.537490i	−0.0438447	+	0.999038i	$0.513961\pi$
$774$		0			0
$775$	−177.119	+	306.779i	−0.228541	+	0.395844i
$776$	7.37633	−	8.79077i	0.00950559	−	0.0113283i
$777$		0			0
$778$	−32.6596	−	185.222i	−0.0419790	−	0.238075i
$779$	−9.42982	−	11.2380i	−0.0121050	−	0.0144262i
$780$		0			0
$781$	−53.6819	+	19.5386i	−0.0687348	+	0.0250174i
$782$		−	1308.72i		−	1.67355i
$783$		0			0
$784$	−45.5253			−0.0580680
$785$	603.685	+	1658.61i	0.769026	+	2.11288i
$786$		0			0
$787$	142.235	−	119.349i	0.180730	−	0.151650i	−0.547935	−	0.836521i	$-0.684586\pi$
$787$	142.235	−	119.349i	0.180730	−	0.151650i	0.728665	+	0.684871i	$0.240141\pi$
$788$	2399.93	−	423.172i	3.04560	−	0.537021i
$789$		0			0
$790$	−692.607	−	581.166i	−0.876718	−	0.735653i
$791$	−692.099	−	399.584i	−0.874967	−	0.505162i
$792$		0			0
$793$	269.608	+	466.975i	0.339985	+	0.588872i
$794$	2144.13	+	378.068i	2.70041	+	0.476156i
$795$		0			0
$796$	−1043.76	−	379.896i	−1.31125	−	0.477257i
$797$	505.124	−	1387.82i	0.633782	−	1.74130i	−0.0366483	−	0.999328i	$-0.511668\pi$
$797$	505.124	−	1387.82i	0.633782	−	1.74130i	0.670430	−	0.741973i	$-0.266110\pi$
$798$		0			0
$799$	−158.722	+	900.160i	−0.198651	+	1.12661i
$800$	430.245	−	248.402i	0.537806	−	0.310502i
$801$		0			0
$802$	210.559	−	364.699i	0.262542	−	0.454737i
$803$	−55.1836	+	65.7653i	−0.0687218	+	0.0818995i
$804$		0			0
$805$	−189.109	−	1072.49i	−0.234918	−	1.33229i
$806$	181.163	+	215.902i	0.224768	+	0.267868i
$807$		0			0
$808$	108.164	−	39.3685i	0.133866	−	0.0487234i
$809$		−	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	$0.422361\pi$
$812$	−476.791	−	1309.97i	−0.587181	−	1.61327i
$813$		0			0
$814$	165.017	−	138.465i	0.202723	−	0.170105i
$815$	1796.45	−	316.762i	2.20423	−	0.388665i
$816$		0			0
$817$	−502.433	−	421.592i	−0.614974	−	0.516024i
$818$	−1567.96	−	905.265i	−1.91683	−	1.10668i
$819$		0			0
$820$	−26.1940	−	45.3693i	−0.0319439	−	0.0553285i
$821$	2.96508	+	0.522823i	0.00361155	+	0.000636813i	0.175454	−	0.984488i	$-0.443861\pi$
$821$	2.96508	+	0.522823i	0.00361155	+	0.000636813i	−0.171842	+	0.985125i	$0.554972\pi$
$822$		0			0
$823$	1272.53	+	463.162i	1.54621	+	0.562773i	0.967524	−	0.252781i	$-0.0813451\pi$
$823$	1272.53	+	463.162i	1.54621	+	0.562773i	0.578682	+	0.815553i	$0.303567\pi$
$824$	570.623	−	1567.77i	0.692504	−	1.90264i
$825$		0			0
$826$	222.123	−	1259.72i	0.268914	−	1.52508i
$827$	−1186.03	+	684.755i	−1.43414	+	0.827999i	−0.997433	−	0.0716069i	$-0.977187\pi$
$827$	−1186.03	+	684.755i	−1.43414	+	0.827999i	−0.436703	+	0.899606i	$0.643854\pi$
$828$		0			0
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	−0.889033	−	0.457842i	$-0.848622\pi$
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	0.841020	+	0.541005i	$0.181956\pi$
$830$	−620.242	+	739.175i	−0.747279	+	0.890572i
$831$		0			0
$832$	−89.0345	−	504.940i	−0.107013	−	0.606899i
$833$	−84.4326	−	100.623i	−0.101360	−	0.120796i
$834$		0			0
$835$	20.9257	−	7.61631i	0.0250607	−	0.00912134i
$836$			119.125i			0.142494i
$837$		0			0
$838$	2220.92			2.65026
$839$	−343.904	−	944.868i	−0.409898	−	1.12618i	−0.957245	−	0.289279i	$-0.906585\pi$
$839$	−343.904	−	944.868i	−0.409898	−	1.12618i	0.547347	−	0.836905i	$-0.315638\pi$
$840$		0			0
$841$	−91.3485	+	76.6505i	−0.108619	+	0.0911421i
$842$	−744.516	+	131.278i	−0.884224	+	0.155912i
$843$		0			0
$844$	−2010.71	−	1687.19i	−2.38236	−	1.99904i
$845$	836.841	+	483.150i	0.990344	+	0.571775i
$846$		0			0
$847$	−381.132	−	660.139i	−0.449978	−	0.779385i
$848$	74.9644	+	13.2183i	0.0884015	+	0.0155876i
$849$		0			0
$850$	−1105.74	−	402.458i	−1.30088	−	0.473480i
$851$	−441.896	+	1214.10i	−0.519267	+	1.42667i
$852$		0			0
$853$	61.2131	−	347.157i	0.0717621	−	0.406983i	−0.927674	−	0.373392i	$-0.878195\pi$
$853$	61.2131	−	347.157i	0.0717621	−	0.406983i	0.999436	−	0.0335909i	$-0.0106943\pi$
$854$	1855.12	−	1071.05i	2.17227	−	1.25416i
$855$		0			0
$856$	−546.733	+	946.969i	−0.638707	+	1.10627i
$857$	−774.755	+	923.318i	−0.904032	+	1.07738i	0.0926264	+	0.995701i	$0.470474\pi$
$857$	−774.755	+	923.318i	−0.904032	+	1.07738i	−0.996658	+	0.0816825i	$0.973971\pi$
$858$		0			0
$859$	109.839	+	622.927i	0.127868	+	0.725177i	0.979563	+	0.201139i	$0.0644642\pi$
$859$	109.839	+	622.927i	0.127868	+	0.725177i	−0.851694	+	0.524039i	$0.824425\pi$
$860$	−1505.53	−	1794.22i	−1.75061	−	2.08630i
$861$		0			0
$862$	1341.94	−	488.426i	1.55678	−	0.566620i
$863$		−	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
$866$	13.6414	+	37.4795i	0.0157522	+	0.0432789i
$867$		0			0
$868$	547.211	−	459.164i	0.630427	−	0.528991i
$869$	−48.4645	+	8.54559i	−0.0557704	+	0.00983383i
$870$		0			0
$871$	321.607	+	269.860i	0.369239	+	0.309828i
$872$	1547.91	+	893.685i	1.77512	+	1.02487i
$873$		0			0
$874$	−559.949	−	969.860i	−0.640674	−	1.10968i
$875$	116.320	+	20.5103i	0.132937	+	0.0234404i
$876$		0			0
$877$	−1203.97	−	438.208i	−1.37282	−	0.499667i	−0.452829	−	0.891597i	$-0.649585\pi$
$877$	−1203.97	−	438.208i	−1.37282	−	0.499667i	−0.919995	+	0.391930i	$0.871807\pi$
$878$	−85.6863	+	235.421i	−0.0975926	+	0.268133i
$879$		0			0
$880$	−8.17433	+	46.3589i	−0.00928901	+	0.0526806i
$881$	787.917	−	454.904i	0.894344	−	0.516350i	0.0189831	−	0.999820i	$-0.493957\pi$
$881$	787.917	−	454.904i	0.894344	−	0.516350i	0.875361	+	0.483470i	$0.160624\pi$
$882$		0			0
$883$	−817.068	+	1415.20i	−0.925332	+	1.60272i	−0.134305	+	0.990940i	$0.542880\pi$
$883$	−817.068	+	1415.20i	−0.925332	+	1.60272i	−0.791027	+	0.611782i	$0.790453\pi$
$884$	−383.940	+	457.562i	−0.434321	+	0.517604i
$885$		0			0
$886$	−143.143	−	811.803i	−0.161561	−	0.916256i
$887$	−382.256	−	455.555i	−0.430954	−	0.513591i	0.506243	−	0.862391i	$-0.331034\pi$
$887$	−382.256	−	455.555i	−0.430954	−	0.513591i	−0.937197	+	0.348800i	$0.886589\pi$
$888$		0			0
$889$	−7.72707	+	2.81242i	−0.00869187	+	0.00316358i
$890$			1632.26i			1.83400i
$891$		0			0
$892$	−658.450			−0.738173
$893$	267.518	+	734.999i	0.299572	+	0.823067i
$894$		0			0
$895$	−1164.27	+	976.939i	−1.30086	+	1.09155i
$896$	−1446.14	+	254.994i	−1.61400	+	0.284592i
$897$		0			0
$898$	523.416	+	439.198i	0.582869	+	0.489085i
$899$	−426.126	−	246.024i	−0.474000	−	0.273664i
$900$		0			0
$901$	109.816	+	190.206i	0.121882	+	0.211106i
$902$	−4.40152	−	0.776106i	−0.00487973	−	0.000860428i
$903$		0			0
$904$	−1193.00	−	434.218i	−1.31970	−	0.480330i
$905$	342.453	−	940.883i	0.378401	−	1.03965i
$906$		0			0
$907$	51.1786	−	290.248i	0.0564263	−	0.320009i	−0.943509	−	0.331346i	$-0.892497\pi$
$907$	51.1786	−	290.248i	0.0564263	−	0.320009i	0.999936	+	0.0113363i	$0.00360853\pi$
$908$	−2229.49	+	1287.20i	−2.45538	+	1.41762i
$909$		0			0
$910$	−389.531	+	674.688i	−0.428056	+	0.741416i
$911$	−535.738	+	638.468i	−0.588077	+	0.700843i	−0.975235	−	0.221170i	$-0.929012\pi$
$911$	−535.738	+	638.468i	−0.588077	+	0.700843i	0.387158	+	0.922013i	$0.373457\pi$
$912$		0			0
$913$	9.12017	+	51.7230i	0.00998923	+	0.0566517i
$914$	1365.48	+	1627.32i	1.49396	+	1.78043i
$915$		0			0
$916$	−705.716	+	256.860i	−0.770432	+	0.280414i
$917$			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	$0.129711\pi$
$920$	−591.715	−	1625.72i	−0.643169	−	1.76709i
$921$		0			0
$922$	−360.688	+	302.653i	−0.391201	+	0.328257i
$923$	−241.389	+	42.5634i	−0.261527	+	0.0461142i
$924$		0			0
$925$	889.909	+	746.723i	0.962064	+	0.807268i
$926$	811.093	+	468.285i	0.875910	+	0.505707i
$927$		0			0
$928$	345.038	+	597.623i	0.371808	+	0.643990i
$929$	−1019.87	−	179.830i	−1.09781	−	0.193574i	−0.404733	−	0.914435i	$-0.632636\pi$
$929$	−1019.87	−	179.830i	−1.09781	−	0.193574i	−0.693080	+	0.720861i	$0.743747\pi$
$930$		0			0
$931$	−105.624	−	38.4439i	−0.113452	−	0.0412931i
$932$	−573.631	+	1576.04i	−0.615484	+	1.69103i
$933$		0			0
$934$	−308.216	+	1747.98i	−0.329995	+	1.87150i
$935$	−117.626	+	67.9113i	−0.125803	+	0.0726324i
$936$		0			0
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	−0.221071	−	0.975258i	$-0.570955\pi$
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	0.955133	−	0.296176i	$-0.0957115\pi$
$938$	1072.06	−	1277.63i	1.14292	−	1.36207i
$939$		0			0
$940$	485.028	+	2750.73i	0.515988	+	2.92631i
$941$	1095.50	+	1305.57i	1.16419	+	1.38743i	0.907032	+	0.421061i	$0.138342\pi$
$941$	1095.50	+	1305.57i	1.16419	+	1.38743i	0.257160	+	0.966369i	$0.417213\pi$
$942$		0			0
$943$	25.1902	−	9.16848i	0.0267128	−	0.00972267i
$944$		−	331.632i		−	0.351305i
$945$		0			0
$946$	−199.820			−0.211226
$947$	7.72529	+	21.2251i	0.00815765	+	0.0224130i	0.943705	−	0.330789i	$-0.107315\pi$
$947$	7.72529	+	21.2251i	0.00815765	+	0.0224130i	−0.935547	+	0.353202i	$0.885093\pi$
$948$		0			0
$949$	−282.177	+	236.775i	−0.297341	+	0.249499i
$950$	−991.638	+	174.853i	−1.04383	+	0.184055i
$951$		0			0
$952$	786.348	+	659.825i	0.825996	+	0.693093i
$953$	−877.360	−	506.544i	−0.920630	−	0.531526i	−0.0367941	−	0.999323i	$-0.511715\pi$
$953$	−877.360	−	506.544i	−0.920630	−	0.531526i	−0.883836	+	0.467797i	$0.845048\pi$
$954$		0			0
$955$	268.750	+	465.489i	0.281414	+	0.487423i
$956$	−596.601	−	105.197i	−0.624059	−	0.110038i
$957$		0			0
$958$	529.981	+	192.897i	0.553216	+	0.201354i
$959$	128.915	−	354.191i	0.134426	−	0.369333i
$960$		0			0
$961$	−123.093	+	698.097i	−0.128089	+	0.726427i
$962$	800.441	−	462.135i	0.832059	−	0.480390i
$963$		0			0
$964$	−103.499	+	179.265i	−0.107364	+	0.185959i
$965$	989.963	−	1179.79i	1.02587	−	1.22258i
$966$		0			0
$967$	17.1645	+	97.3447i	0.0177503	+	0.100667i	0.992396	−	0.123088i	$-0.0392797\pi$
$967$	17.1645	+	97.3447i	0.0177503	+	0.100667i	−0.974646	+	0.223755i	$0.928169\pi$
$968$	−778.379	−	927.636i	−0.804111	−	0.958302i
$969$		0			0
$970$	24.3205	−	8.85195i	0.0250727	−	0.00912572i
$971$		−	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
$974$	−23.6544	−	64.9898i	−0.0242858	−	0.0667246i
$975$		0			0
$976$	425.432	−	356.980i	0.435893	−	0.365758i
$977$	−310.619	+	54.7705i	−0.317931	+	0.0560599i	−0.330337	−	0.943863i	$-0.607162\pi$
$977$	−310.619	+	54.7705i	−0.317931	+	0.0560599i	0.0124054	+	0.999923i	$0.496051\pi$
$978$		0			0
$979$	68.0585	+	57.1078i	0.0695183	+	0.0583328i
$980$	−347.618	−	200.697i	−0.354712	−	0.204793i
$981$		0			0
$982$	−251.177	−	435.052i	−0.255781	−	0.443027i
$983$	631.264	+	111.309i	0.642181	+	0.113234i	0.485249	−	0.874376i	$-0.338729\pi$
$983$	631.264	+	111.309i	0.642181	+	0.113234i	0.156931	+	0.987610i	$0.449840\pi$
$984$		0			0
$985$	2234.26	+	813.204i	2.26828	+	0.825588i
$986$	559.026	−	1535.91i	0.566964	−	1.55772i
$987$		0			0
$988$	−88.7563	+	503.362i	−0.0898343	+	0.509475i
$989$	1037.92	−	599.245i	1.04947	−	0.605910i
$990$		0			0
$991$	−464.001	+	803.674i	−0.468215	+	0.810973i	−0.999340	−	0.0363209i	$-0.988436\pi$
$991$	−464.001	+	803.674i	−0.468215	+	0.810973i	0.531125	+	0.847294i	$0.321769\pi$
$992$	−227.294	+	270.879i	−0.229127	+	0.273063i
$993$		0			0
$994$	169.089	+	958.951i	0.170110	+	0.964739i
$995$	−696.598	−	830.173i	−0.700098	−	0.834344i
$996$		0			0
$997$	−1070.66	+	389.689i	−1.07388	+	0.390862i	−0.817628	−	0.575747i	$-0.804711\pi$
$997$	−1070.66	+	389.689i	−1.07388	+	0.390862i	−0.256256	+	0.966609i	$0.582489\pi$
$998$			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.a.188.1		30
3.2	odd	2		243.3.f.d.188.5		30
9.2	odd	6		27.3.f.a.11.5	yes	30
9.4	even	3		243.3.f.b.26.5		30
9.5	odd	6		243.3.f.c.26.1		30
9.7	even	3		81.3.f.a.35.1		30
27.2	odd	18		729.3.b.a.728.4		30
27.4	even	9		243.3.f.d.53.5		30
27.5	odd	18		243.3.f.b.215.5		30
27.13	even	9		27.3.f.a.5.5	✓	30
27.14	odd	18		81.3.f.a.44.1		30
27.22	even	9		243.3.f.c.215.1		30
27.23	odd	18	inner	243.3.f.a.53.1		30
27.25	even	9		729.3.b.a.728.27		30
36.11	even	6		432.3.bc.a.65.4		30
108.67	odd	18		432.3.bc.a.113.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.5	✓	30	27.13	even	9
27.3.f.a.11.5	yes	30	9.2	odd	6
81.3.f.a.35.1		30	9.7	even	3
81.3.f.a.44.1		30	27.14	odd	18
243.3.f.a.53.1		30	27.23	odd	18	inner
243.3.f.a.188.1		30	1.1	even	1	trivial
243.3.f.b.26.5		30	9.4	even	3
243.3.f.b.215.5		30	27.5	odd	18
243.3.f.c.26.1		30	9.5	odd	6
243.3.f.c.215.1		30	27.22	even	9
243.3.f.d.53.5		30	27.4	even	9
243.3.f.d.188.5		30	3.2	odd	2
432.3.bc.a.65.4		30	36.11	even	6
432.3.bc.a.113.4		30	108.67	odd	18
729.3.b.a.728.4		30	27.2	odd	18
729.3.b.a.728.27		30	27.25	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)

\(f(q)\)	\(=\)	\(q+(-1.13691 - 3.12364i) q^{2} +(-5.40039 + 4.53146i) q^{4} +(-6.77366 + 1.19438i) q^{5} +(4.88842 + 4.10187i) q^{7} +(8.77937 + 5.06877i) q^{8} +(11.4319 + 19.8006i) q^{10} +(1.22557 + 0.216101i) q^{11} +(5.01761 + 1.82626i) q^{13} +(7.25506 - 19.9331i) q^{14} +(0.954979 - 5.41596i) q^{16} +(13.7418 - 7.93385i) q^{17} +(6.78917 - 11.7592i) q^{19} +(31.1681 - 37.1447i) q^{20} +(-0.718343 - 4.07393i) q^{22} +(15.9486 + 19.0069i) q^{23} +(20.9636 - 7.63012i) q^{25} -17.7495i q^{26} -44.9868 q^{28} +(10.5985 + 29.1191i) q^{29} +(-12.1638 + 10.2066i) q^{31} +(21.9309 - 3.86701i) q^{32} +(-40.4057 - 33.9044i) q^{34} +(-38.0116 - 21.9460i) q^{35} +(26.0365 + 45.0965i) q^{37} +(-44.4502 - 7.83777i) q^{38} +(-65.5225 - 23.8482i) q^{40} +(0.369522 - 1.01525i) q^{41} +(8.38780 - 47.5696i) q^{43} +(-7.59780 + 4.38659i) q^{44} +(41.2384 - 71.4270i) q^{46} +(-37.0273 + 44.1274i) q^{47} +(-1.43747 - 8.15231i) q^{49} +(-47.6675 - 56.8079i) q^{50} +(-35.3727 + 12.8746i) q^{52} +13.8414i q^{53} -8.55969 q^{55} +(22.1258 + 60.7901i) q^{56} +(78.9079 - 66.2116i) q^{58} +(59.3860 - 10.4714i) q^{59} +(77.3581 + 64.9112i) q^{61} +(45.7111 + 26.3913i) q^{62} +(-48.0117 - 83.1587i) q^{64} +(-36.1688 - 6.37754i) q^{65} +(73.8833 + 26.8913i) q^{67} +(-38.2592 + 105.116i) q^{68} +(-25.3356 + 143.685i) q^{70} +(-39.7545 + 22.9523i) q^{71} +(-34.4926 + 59.7430i) q^{73} +(111.264 - 132.599i) q^{74} +(16.6222 + 94.2690i) q^{76} +(5.10467 + 6.08351i) q^{77} +(-37.1596 + 13.5250i) q^{79} +37.8265i q^{80} -3.59141 q^{82} +(14.4344 + 39.6581i) q^{83} +(-83.6064 + 70.1541i) q^{85} +(-158.126 + 27.8820i) q^{86} +(9.66436 + 8.10936i) q^{88} +(61.8262 + 35.6954i) q^{89} +(17.0371 + 29.5091i) q^{91} +(-172.258 - 30.3737i) q^{92} +(179.935 + 65.4909i) q^{94} +(-31.9426 + 87.7616i) q^{95} +(0.196567 - 1.11479i) q^{97} +(-23.8306 + 13.7586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} - 57 q^{11} + 3 q^{13} + 114 q^{14} + 27 q^{16} + 9 q^{17} - 3 q^{19} + 183 q^{20} + 75 q^{22} - 48 q^{23} + 21 q^{25} - 12 q^{28} + 78 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 - 57 * q^11 + 3 * q^13 + 114 * q^14 + 27 * q^16 + 9 * q^17 - 3 * q^19 + 183 * q^20 + 75 * q^22 - 48 * q^23 + 21 * q^25 - 12 * q^28 + 78 * q^29 - 87 * q^31 - 243 * q^32 - 153 * q^34 + 252 * q^35 - 3 * q^37 - 321 * q^38 - 168 * q^40 + 357 * q^41 - 87 * q^43 - 639 * q^44 - 3 * q^46 + 51 * q^47 - 69 * q^49 - 168 * q^50 - 36 * q^52 - 12 * q^55 + 177 * q^56 + 138 * q^58 - 48 * q^59 + 147 * q^61 + 900 * q^62 - 51 * q^64 - 624 * q^65 + 12 * q^67 + 477 * q^68 - 6 * q^70 - 315 * q^71 - 66 * q^73 + 480 * q^74 - 57 * q^76 - 453 * q^77 - 15 * q^79 - 12 * q^82 + 591 * q^83 + 243 * q^85 - 669 * q^86 + 591 * q^88 - 72 * q^89 + 96 * q^91 - 564 * q^92 + 957 * q^94 + 606 * q^95 + 696 * q^97 - 882 * q^98

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