LMFDB - Embedded newform 135.3.l.a.127.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(37,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.37"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	135.127
Dual form			135.3.l.a.118.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.38711 - 0.639624i) q^{2} +(1.82507 - 1.05371i) q^{4} +(1.83989 + 4.64917i) q^{5} +(10.3622 - 2.77655i) q^{7} +(-3.30727 + 3.30727i) q^{8} +(7.36573 + 9.92126i) q^{10} +(5.66397 - 9.81028i) q^{11} +(-9.44533 - 2.53087i) q^{13} +(22.9598 - 13.2559i) q^{14} +(-9.99423 + 17.3105i) q^{16} +(-8.05728 - 8.05728i) q^{17} +3.73565i q^{19} +(8.25680 + 6.54639i) q^{20} +(7.24562 - 27.0410i) q^{22} +(-13.4504 - 3.60402i) q^{23} +(-18.2296 + 17.1079i) q^{25} -24.1658 q^{26} +(15.9862 - 15.9862i) q^{28} +(-28.7625 - 16.6061i) q^{29} +(7.67855 + 13.2996i) q^{31} +(-7.94293 + 29.6434i) q^{32} +(-24.3873 - 14.0800i) q^{34} +(31.9740 + 43.0673i) q^{35} +(13.7991 + 13.7991i) q^{37} +(2.38941 + 8.91741i) q^{38} +(-21.4611 - 9.29107i) q^{40} +(-4.87477 - 8.44335i) q^{41} +(-10.2845 - 38.3822i) q^{43} -23.8727i q^{44} -34.4127 q^{46} +(-1.68543 + 0.451608i) q^{47} +(57.2314 - 33.0426i) q^{49} +(-32.5735 + 52.4986i) q^{50} +(-19.9052 + 5.33359i) q^{52} +(45.3574 - 45.3574i) q^{53} +(56.0308 + 8.28298i) q^{55} +(-25.0879 + 43.4535i) q^{56} +(-79.2810 - 21.2433i) q^{58} +(10.2473 - 5.91626i) q^{59} +(-28.0510 + 48.5858i) q^{61} +(26.8363 + 26.8363i) q^{62} -4.11124i q^{64} +(-5.61188 - 48.5695i) q^{65} +(-12.7011 + 47.4011i) q^{67} +(-23.1952 - 6.21513i) q^{68} +(103.872 + 82.3550i) q^{70} -22.2795 q^{71} +(37.2225 - 37.2225i) q^{73} +(41.7661 + 24.1137i) q^{74} +(3.93628 + 6.81784i) q^{76} +(31.4526 - 117.383i) q^{77} +(-105.323 - 60.8084i) q^{79} +(-98.8678 - 14.6155i) q^{80} +(-17.0372 - 17.0372i) q^{82} +(28.1424 + 105.029i) q^{83} +(22.6352 - 52.2842i) q^{85} +(-49.1003 - 85.0443i) q^{86} +(13.7130 + 51.1775i) q^{88} +16.0767i q^{89} -104.902 q^{91} +(-28.3455 + 7.59516i) q^{92} +(-3.73444 + 2.15608i) q^{94} +(-17.3677 + 6.87317i) q^{95} +(172.402 - 46.1951i) q^{97} +(115.483 - 115.483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.38711	−	0.639624i	1.19356	−	0.319812i	0.393265	−	0.919425i	$-0.371345\pi$
$2$	2.38711	−	0.639624i	1.19356	−	0.319812i	0.800290	+	0.599613i	$0.204679\pi$
$3$		0			0
$3$		0			0
$4$	1.82507	−	1.05371i	0.456269	−	0.263427i
$5$	1.83989	+	4.64917i	0.367977	+	0.929835i
$5$	1.83989	+	4.64917i	0.367977	+	0.929835i
$6$		0			0
$7$	10.3622	−	2.77655i	1.48032	−	0.396650i	0.573863	−	0.818951i	$-0.305444\pi$
$7$	10.3622	−	2.77655i	1.48032	−	0.396650i	0.906456	+	0.422301i	$0.138777\pi$
$8$	−3.30727	+	3.30727i	−0.413408	+	0.413408i
$9$		0			0
$10$	7.36573	+	9.92126i	0.736573	+	0.992126i
$11$	5.66397	−	9.81028i	0.514906	−	0.891844i	−0.484944	−	0.874545i	$-0.661160\pi$
$11$	5.66397	−	9.81028i	0.514906	−	0.891844i	0.999850	−	0.0172985i	$-0.00550657\pi$
$12$		0			0
$13$	−9.44533	−	2.53087i	−0.726564	−	0.194682i	−0.123465	−	0.992349i	$-0.539401\pi$
$13$	−9.44533	−	2.53087i	−0.726564	−	0.194682i	−0.603098	+	0.797667i	$0.706067\pi$
$14$	22.9598	−	13.2559i	1.63999	−	0.946848i
$15$		0			0
$16$	−9.99423	+	17.3105i	−0.624639	+	1.08191i
$17$	−8.05728	−	8.05728i	−0.473958	−	0.473958i	0.429235	−	0.903193i	$-0.358783\pi$
$17$	−8.05728	−	8.05728i	−0.473958	−	0.473958i	−0.903193	+	0.429235i	$0.858783\pi$
$18$		0			0
$19$			3.73565i			0.196613i	0.995156	+	0.0983066i	$0.0313426\pi$
$19$			3.73565i			0.196613i	−0.995156	+	0.0983066i	$0.968657\pi$
$20$	8.25680	+	6.54639i	0.412840	+	0.327319i
$21$		0			0
$22$	7.24562	−	27.0410i	0.329346	−	1.22914i
$23$	−13.4504	−	3.60402i	−0.584799	−	0.156696i	−0.0457238	−	0.998954i	$-0.514559\pi$
$23$	−13.4504	−	3.60402i	−0.584799	−	0.156696i	−0.539075	+	0.842258i	$0.681226\pi$
$24$		0			0
$25$	−18.2296	+	17.1079i	−0.729186	+	0.684316i
$26$	−24.1658			−0.929456
$27$		0			0
$28$	15.9862	−	15.9862i	0.570935	−	0.570935i
$29$	−28.7625	−	16.6061i	−0.991812	−	0.572623i	−0.0859964	−	0.996295i	$-0.527407\pi$
$29$	−28.7625	−	16.6061i	−0.991812	−	0.572623i	−0.905815	+	0.423673i	$0.860741\pi$
$30$		0			0
$31$	7.67855	+	13.2996i	0.247695	+	0.429021i	0.962886	−	0.269909i	$-0.0869935\pi$
$31$	7.67855	+	13.2996i	0.247695	+	0.429021i	−0.715191	+	0.698929i	$0.753660\pi$
$32$	−7.94293	+	29.6434i	−0.248217	+	0.926357i
$33$		0			0
$34$	−24.3873	−	14.0800i	−0.717272	−	0.414117i
$35$	31.9740	+	43.0673i	0.913543	+	1.23049i
$36$		0			0
$37$	13.7991	+	13.7991i	0.372947	+	0.372947i	0.868550	−	0.495602i	$-0.165053\pi$
$37$	13.7991	+	13.7991i	0.372947	+	0.372947i	−0.495602	+	0.868550i	$0.665053\pi$
$38$	2.38941	+	8.91741i	0.0628793	+	0.234669i
$39$		0			0
$40$	−21.4611	−	9.29107i	−0.536526	−	0.232277i
$41$	−4.87477	−	8.44335i	−0.118897	−	0.205935i	0.800434	−	0.599421i	$-0.204602\pi$
$41$	−4.87477	−	8.44335i	−0.118897	−	0.205935i	−0.919331	+	0.393486i	$0.871269\pi$
$42$		0			0
$43$	−10.2845	−	38.3822i	−0.239174	−	0.892609i	−0.976223	−	0.216769i	$-0.930448\pi$
$43$	−10.2845	−	38.3822i	−0.239174	−	0.892609i	0.737049	−	0.675839i	$-0.236219\pi$
$44$		−	23.8727i		−	0.542560i
$45$		0			0
$46$	−34.4127			−0.748103
$47$	−1.68543	+	0.451608i	−0.0358601	+	0.00960869i	−0.276705	−	0.960955i	$-0.589242\pi$
$47$	−1.68543	+	0.451608i	−0.0358601	+	0.00960869i	0.240844	+	0.970564i	$0.422576\pi$
$48$		0			0
$49$	57.2314	−	33.0426i	1.16799	−	0.674338i
$50$	−32.5735	+	52.4986i	−0.651471	+	1.04997i
$51$		0			0
$52$	−19.9052	+	5.33359i	−0.382793	+	0.102569i
$53$	45.3574	−	45.3574i	0.855801	−	0.855801i	−0.135040	−	0.990840i	$-0.543116\pi$
$53$	45.3574	−	45.3574i	0.855801	−	0.855801i	0.990840	+	0.135040i	$0.0431161\pi$
$54$		0			0
$55$	56.0308	+	8.28298i	1.01874	+	0.150600i
$56$	−25.0879	+	43.4535i	−0.447998	+	0.775955i
$57$		0			0
$58$	−79.2810	−	21.2433i	−1.36691	−	0.366263i
$59$	10.2473	−	5.91626i	0.173683	−	0.100276i	−0.410639	−	0.911798i	$-0.634694\pi$
$59$	10.2473	−	5.91626i	0.173683	−	0.100276i	0.584321	+	0.811523i	$0.301361\pi$
$60$		0			0
$61$	−28.0510	+	48.5858i	−0.459852	+	0.796488i	−0.998953	−	0.0457538i	$-0.985431\pi$
$61$	−28.0510	+	48.5858i	−0.459852	+	0.796488i	0.539100	+	0.842242i	$0.318764\pi$
$62$	26.8363	+	26.8363i	0.432844	+	0.432844i
$63$		0			0
$64$		−	4.11124i		−	0.0642381i
$65$	−5.61188	−	48.5695i	−0.0863366	−	0.747223i
$66$		0			0
$67$	−12.7011	+	47.4011i	−0.189569	+	0.707480i	0.804038	+	0.594578i	$0.202681\pi$
$67$	−12.7011	+	47.4011i	−0.189569	+	0.707480i	−0.993606	+	0.112901i	$0.963986\pi$
$68$	−23.1952	−	6.21513i	−0.341105	−	0.0913989i
$69$		0			0
$70$	103.872	+	82.3550i	1.48389	+	1.17650i
$71$	−22.2795			−0.313795			−0.156898	−	0.987615i	$-0.550149\pi$
$71$	−22.2795			−0.313795			−0.156898	+	0.987615i	$0.550149\pi$
$72$		0			0
$73$	37.2225	−	37.2225i	0.509898	−	0.509898i	−0.404597	−	0.914495i	$-0.632588\pi$
$73$	37.2225	−	37.2225i	0.509898	−	0.509898i	0.914495	+	0.404597i	$0.132588\pi$
$74$	41.7661	+	24.1137i	0.564407	+	0.325860i
$75$		0			0
$76$	3.93628	+	6.81784i	0.0517932	+	0.0897084i
$77$	31.4526	−	117.383i	0.408475	−	1.52445i
$78$		0			0
$79$	−105.323	−	60.8084i	−1.33321	−	0.769726i	−0.347416	−	0.937711i	$-0.612941\pi$
$79$	−105.323	−	60.8084i	−1.33321	−	0.769726i	−0.985790	+	0.167985i	$0.946274\pi$
$80$	−98.8678	−	14.6155i	−1.23585	−	0.182694i
$81$		0			0
$82$	−17.0372	−	17.0372i	−0.207771	−	0.207771i
$83$	28.1424	+	105.029i	0.339065	+	1.26541i	0.899394	+	0.437139i	$0.144008\pi$
$83$	28.1424	+	105.029i	0.339065	+	1.26541i	−0.560329	+	0.828270i	$0.689325\pi$
$84$		0			0
$85$	22.6352	−	52.2842i	0.266297	−	0.615108i
$86$	−49.1003	−	85.0443i	−0.570934	−	0.988887i
$87$		0			0
$88$	13.7130	+	51.1775i	0.155829	+	0.581562i
$89$			16.0767i			0.180637i	0.995913	+	0.0903186i	$0.0287885\pi$
$89$			16.0767i			0.180637i	−0.995913	+	0.0903186i	$0.971211\pi$
$90$		0			0
$91$	−104.902			−1.15277
$92$	−28.3455	+	7.59516i	−0.308103	+	0.0825560i
$93$		0			0
$94$	−3.73444	+	2.15608i	−0.0397281	+	0.0229370i
$95$	−17.3677	+	6.87317i	−0.182818	+	0.0723492i
$96$		0			0
$97$	172.402	−	46.1951i	1.77734	−	0.476238i	0.787248	−	0.616636i	$-0.211505\pi$
$97$	172.402	−	46.1951i	1.77734	−	0.476238i	0.990095	+	0.140398i	$0.0448383\pi$
$98$	115.483	−	115.483i	1.17840	−	1.17840i
$99$		0			0
$100$	−15.2437	+	50.4319i	−0.152437	+	0.504319i
$101$	13.8448	−	23.9798i	0.137077	−	0.237424i	−0.789312	−	0.613992i	$-0.789563\pi$
$101$	13.8448	−	23.9798i	0.137077	−	0.237424i	0.926389	+	0.376568i	$0.122896\pi$
$102$		0			0
$103$	147.434	+	39.5049i	1.43140	+	0.383543i	0.889514	−	0.456908i	$-0.151043\pi$
$103$	147.434	+	39.5049i	1.43140	+	0.383543i	0.541888	+	0.840451i	$0.317710\pi$
$104$	39.6085	−	22.8680i	0.380851	−	0.219884i
$105$		0			0
$106$	79.2615	−	137.285i	0.747750	−	1.29514i
$107$	108.283	+	108.283i	1.01199	+	1.01199i	0.999927	+	0.0120628i	$0.00383979\pi$
$107$	108.283	+	108.283i	1.01199	+	1.01199i	0.0120628	+	0.999927i	$0.496160\pi$
$108$		0			0
$109$			184.036i			1.68841i	0.536024	+	0.844203i	$0.319926\pi$
$109$			184.036i			1.68841i	−0.536024	+	0.844203i	$0.680074\pi$
$110$	139.050	−	16.0662i	1.26409	−	0.146057i
$111$		0			0
$112$	−55.4990	+	207.125i	−0.495527	+	1.84933i
$113$	162.637	+	43.5785i	1.43927	+	0.385650i	0.892277	−	0.451489i	$-0.149107\pi$
$113$	162.637	+	43.5785i	1.43927	+	0.385650i	0.546990	+	0.837139i	$0.315774\pi$
$114$		0			0
$115$	−7.99145	−	69.1641i	−0.0694909	−	0.601427i
$116$	−69.9917			−0.603377
$117$		0			0
$118$	20.6772	−	20.6772i	0.175230	−	0.175230i
$119$	−105.863	−	61.1200i	−0.889604	−	0.513613i
$120$		0			0
$121$	−3.66106	−	6.34114i	−0.0302567	−	0.0524061i
$122$	−35.8842	+	133.922i	−0.294133	+	1.09772i
$123$		0			0
$124$	28.0279	+	16.1819i	0.226031	+	0.130499i
$125$	−113.078	−	53.2762i	−0.904624	−	0.426210i
$126$		0			0
$127$	−94.7770	−	94.7770i	−0.746275	−	0.746275i	0.227502	−	0.973778i	$-0.426944\pi$
$127$	−94.7770	−	94.7770i	−0.746275	−	0.746275i	−0.973778	+	0.227502i	$0.926944\pi$
$128$	−34.4014	−	128.388i	−0.268761	−	1.00303i
$129$		0			0
$130$	−44.4624	−	112.351i	−0.342018	−	0.864240i
$131$	56.6078	+	98.0476i	0.432121	+	0.748455i	0.997056	−	0.0766803i	$-0.0244321\pi$
$131$	56.6078	+	98.0476i	0.432121	+	0.748455i	−0.564935	+	0.825135i	$0.691099\pi$
$132$		0			0
$133$	10.3722	+	38.7097i	0.0779867	+	0.291050i
$134$			121.276i			0.905042i
$135$		0			0
$136$	53.2952			0.391876
$137$	−23.3586	+	6.25891i	−0.170501	+	0.0456855i	−0.343059	−	0.939314i	$-0.611463\pi$
$137$	−23.3586	+	6.25891i	−0.170501	+	0.0456855i	0.172559	+	0.984999i	$0.444797\pi$
$138$		0			0
$139$	−98.1741	+	56.6809i	−0.706289	+	0.407776i	−0.809685	−	0.586864i	$-0.800362\pi$
$139$	−98.1741	+	56.6809i	−0.706289	+	0.407776i	0.103397	+	0.994640i	$0.467029\pi$
$140$	103.735	+	44.9098i	0.740966	+	0.320784i
$141$		0			0
$142$	−53.1835	+	14.2505i	−0.374532	+	0.100355i
$143$	−78.3266	+	78.3266i	−0.547738	+	0.547738i
$144$		0			0
$145$	24.2847	−	164.275i	0.167481	−	1.13293i
$146$	65.0459	−	112.663i	0.445520	−	0.771663i
$147$		0			0
$148$	39.7245	+	10.6441i	0.268409	+	0.0719199i
$149$	−136.216	+	78.6442i	−0.914199	+	0.527813i	−0.881780	−	0.471661i	$-0.843655\pi$
$149$	−136.216	+	78.6442i	−0.914199	+	0.527813i	−0.0324193	+	0.999474i	$0.510321\pi$
$150$		0			0
$151$	9.10366	−	15.7680i	0.0602891	−	0.104424i	−0.834306	−	0.551302i	$-0.814131\pi$
$151$	9.10366	−	15.7680i	0.0602891	−	0.104424i	0.894595	+	0.446879i	$0.147464\pi$
$152$	−12.3548	−	12.3548i	−0.0812815	−	0.0812815i
$153$		0			0
$154$		−	300.323i		−	1.95015i
$155$	−47.7047	+	60.1688i	−0.307772	+	0.388186i
$156$		0			0
$157$	43.8009	−	163.467i	0.278987	−	1.04119i	−0.674136	−	0.738607i	$-0.735484\pi$
$157$	43.8009	−	163.467i	0.278987	−	1.04119i	0.953122	−	0.302585i	$-0.0978496\pi$
$158$	−290.313	−	77.7890i	−1.83742	−	0.492336i
$159$		0			0
$160$	−152.432	+	17.6124i	−0.952697	+	0.110078i
$161$	−149.383			−0.927842
$162$		0			0
$163$	−152.193	+	152.193i	−0.933698	+	0.933698i	−0.997935	−	0.0642365i	$-0.979539\pi$
$163$	−152.193	+	152.193i	−0.933698	+	0.933698i	0.0642365	+	0.997935i	$0.479539\pi$
$164$	−17.7936	−	10.2732i	−0.108498	−	0.0626412i
$165$		0			0
$166$	134.358	+	232.715i	0.809387	+	1.40190i
$167$	29.2359	−	109.110i	0.175065	−	0.653353i	−0.821475	−	0.570245i	$-0.806848\pi$
$167$	29.2359	−	109.110i	0.175065	−	0.653353i	0.996540	−	0.0831087i	$-0.0264849\pi$
$168$		0			0
$169$	−63.5494	−	36.6902i	−0.376032	−	0.217102i
$170$	20.5906	−	139.286i	0.121121	−	0.819331i
$171$		0			0
$172$	−59.2135	−	59.2135i	−0.344264	−	0.344264i
$173$	18.4527	+	68.8666i	0.106663	+	0.398073i	0.998529	−	0.0542285i	$-0.0172699\pi$
$173$	18.4527	+	68.8666i	0.106663	+	0.398073i	−0.891865	+	0.452301i	$0.850603\pi$
$174$		0			0
$175$	−141.399	+	227.892i	−0.807993	+	1.30224i
$176$	113.214	+	196.092i	0.643261	+	1.11416i
$177$		0			0
$178$	10.2831	+	38.3769i	0.0577700	+	0.215600i
$179$			46.2183i			0.258203i	0.991631	+	0.129101i	$0.0412092\pi$
$179$			46.2183i			0.258203i	−0.991631	+	0.129101i	$0.958791\pi$
$180$		0			0
$181$	−166.274			−0.918640			−0.459320	−	0.888271i	$-0.651907\pi$
$181$	−166.274			−0.918640			−0.459320	+	0.888271i	$0.651907\pi$
$182$	−250.412	+	67.0977i	−1.37589	+	0.368669i
$183$		0			0
$184$	56.4034	−	32.5645i	0.306540	−	0.176981i
$185$	−38.7655	+	89.5429i	−0.209543	+	0.484016i
$186$		0			0
$187$	−124.680	+	33.4080i	−0.666740	+	0.178652i
$188$	−2.60016	+	2.60016i	−0.0138307	+	0.0138307i
$189$		0			0
$190$	−37.0623	+	27.5158i	−0.195065	+	0.144820i
$191$	58.2778	−	100.940i	0.305119	−	0.528482i	−0.672169	−	0.740398i	$-0.734637\pi$
$191$	58.2778	−	100.940i	0.305119	−	0.528482i	0.977288	+	0.211916i	$0.0679704\pi$
$192$		0			0
$193$	−120.711	−	32.3443i	−0.625443	−	0.167587i	−0.0678422	−	0.997696i	$-0.521611\pi$
$193$	−120.711	−	32.3443i	−0.625443	−	0.167587i	−0.557601	+	0.830109i	$0.688278\pi$
$194$	381.996	−	220.545i	1.96905	−	1.13683i
$195$		0			0
$196$	69.6344	−	120.610i	0.355277	−	0.615358i
$197$	−83.4305	−	83.4305i	−0.423505	−	0.423505i	0.462903	−	0.886409i	$-0.346808\pi$
$197$	−83.4305	−	83.4305i	−0.423505	−	0.423505i	−0.886409	+	0.462903i	$0.846808\pi$
$198$		0			0
$199$			271.461i			1.36412i	0.731294	+	0.682062i	$0.238917\pi$
$199$			271.461i			1.36412i	−0.731294	+	0.682062i	$0.761083\pi$
$200$	3.70990	−	116.871i	0.0185495	−	0.584353i
$201$		0			0
$202$	17.7109	−	66.0980i	0.0876777	−	0.327218i
$203$	−344.152	−	92.2152i	−1.69533	−	0.454262i
$204$		0			0
$205$	30.2856	−	38.1985i	0.147735	−	0.186334i
$206$	377.210			1.83112
$207$		0			0
$208$	138.209	−	138.209i	0.664468	−	0.664468i
$209$	36.6478	+	21.1586i	0.175348	+	0.101237i
$210$		0			0
$211$	−65.7689	−	113.915i	−0.311701	−	0.539882i	0.667030	−	0.745031i	$-0.267565\pi$
$211$	−65.7689	−	113.915i	−0.311701	−	0.539882i	−0.978731	+	0.205149i	$0.934232\pi$
$212$	34.9872	−	130.574i	0.165034	−	0.615916i
$213$		0			0
$214$	327.744	+	189.223i	1.53151	+	0.884219i
$215$	159.523	−	118.433i	0.741968	−	0.550852i
$216$		0			0
$217$	116.494	+	116.494i	0.536839	+	0.536839i
$218$	117.714	+	439.315i	0.539972	+	2.01520i
$219$		0			0
$220$	110.988	−	43.9230i	0.504492	−	0.199650i
$221$	55.7118	+	96.4956i	0.252089	+	0.436632i
$222$		0			0
$223$	−8.00949	−	29.8918i	−0.0359170	−	0.134044i	0.945639	−	0.325217i	$-0.105437\pi$
$223$	−8.00949	−	29.8918i	−0.0359170	−	0.134044i	−0.981556	+	0.191173i	$0.938771\pi$
$224$			329.226i			1.46976i
$225$		0			0
$226$	416.107			1.84118
$227$	63.1736	−	16.9273i	0.278298	−	0.0745697i	−0.116970	−	0.993135i	$-0.537318\pi$
$227$	63.1736	−	16.9273i	0.278298	−	0.0745697i	0.395268	+	0.918566i	$0.370652\pi$
$228$		0			0
$229$	240.813	−	139.033i	1.05158	−	0.607132i	0.128491	−	0.991711i	$-0.458987\pi$
$229$	240.813	−	139.033i	1.05158	−	0.607132i	0.923092	+	0.384579i	$0.125653\pi$
$230$	−63.3155	−	159.991i	−0.275285	−	0.695612i
$231$		0			0
$232$	150.046	−	40.2047i	0.646750	−	0.173296i
$233$	106.791	−	106.791i	0.458329	−	0.458329i	−0.439778	−	0.898107i	$-0.644943\pi$
$233$	106.791	−	106.791i	0.458329	−	0.458329i	0.898107	+	0.439778i	$0.144943\pi$
$234$		0			0
$235$	−5.20060	−	7.00493i	−0.0221302	−	0.0298082i
$236$	12.4680	−	21.5952i	0.0528306	−	0.0915053i
$237$		0			0
$238$	−291.800	−	78.1876i	−1.22605	−	0.328520i
$239$	−136.295	+	78.6901i	−0.570273	+	0.329247i	−0.757258	−	0.653115i	$-0.773462\pi$
$239$	−136.295	+	78.6901i	−0.570273	+	0.329247i	0.186985	+	0.982363i	$0.440128\pi$
$240$		0			0
$241$	−10.1579	+	17.5940i	−0.0421489	+	0.0730040i	−0.886330	−	0.463054i	$-0.846754\pi$
$241$	−10.1579	+	17.5940i	−0.0421489	+	0.0730040i	0.844181	+	0.536058i	$0.180087\pi$
$242$	−12.7953	−	12.7953i	−0.0528731	−	0.0528731i
$243$		0			0
$244$			118.230i			0.484550i
$245$	258.920	+	205.284i	1.05682	+	0.837894i
$246$		0			0
$247$	9.45444	−	35.2844i	0.0382771	−	0.142852i
$248$	−69.3805	−	18.5905i	−0.279760	−	0.0749615i
$249$		0			0
$250$	−304.007	−	54.8487i	−1.21603	−	0.219395i
$251$	92.7758			0.369625			0.184812	−	0.982774i	$-0.440832\pi$
$251$	92.7758			0.369625			0.184812	+	0.982774i	$0.440832\pi$
$252$		0			0
$253$	−111.539	+	111.539i	−0.440865	+	0.440865i
$254$	−286.865	−	165.621i	−1.12939	−	0.652053i
$255$		0			0
$256$	−156.017	−	270.230i	−0.609442	−	1.05559i
$257$	110.663	−	413.001i	0.430596	−	1.60701i	−0.320794	−	0.947149i	$-0.603950\pi$
$257$	110.663	−	413.001i	0.430596	−	1.60701i	0.751390	−	0.659858i	$-0.229383\pi$
$258$		0			0
$259$	181.303	+	104.675i	0.700011	+	0.404152i
$260$	−61.4201	−	82.7297i	−0.236231	−	0.318191i
$261$		0			0
$262$	197.843	+	197.843i	0.755125	+	0.755125i
$263$	46.0569	+	171.887i	0.175121	+	0.653562i	0.996531	+	0.0832230i	$0.0265214\pi$
$263$	46.0569	+	171.887i	0.175121	+	0.653562i	−0.821410	+	0.570339i	$0.806812\pi$
$264$		0			0
$265$	294.327	+	127.422i	1.11067	+	0.480838i
$266$	49.5193	+	85.7699i	0.186163	+	0.322443i
$267$		0			0
$268$	26.7665	+	99.8939i	0.0998749	+	0.372738i
$269$		−	175.152i		−	0.651123i	−0.945521	−	0.325562i	$-0.894447\pi$
$269$		−	175.152i		−	0.651123i	0.945521	−	0.325562i	$-0.105553\pi$
$270$		0			0
$271$	463.337			1.70973			0.854865	−	0.518850i	$-0.173640\pi$
$271$	463.337			1.70973			0.854865	+	0.518850i	$0.173640\pi$
$272$	220.002	−	58.9494i	0.808831	−	0.216726i
$273$		0			0
$274$	−51.7562	+	29.8814i	−0.188891	+	0.109056i
$275$	64.5812	+	275.736i	0.234841	+	1.00268i
$276$		0			0
$277$	−372.528	+	99.8186i	−1.34487	+	0.360356i	−0.858238	−	0.513252i	$-0.828441\pi$
$277$	−372.528	+	99.8186i	−1.34487	+	0.360356i	−0.486630	+	0.873608i	$0.661774\pi$
$278$	−198.098	+	198.098i	−0.712583	+	0.712583i
$279$		0			0
$280$	−248.182	−	36.6885i	−0.886363	−	0.131030i
$281$	−39.8147	+	68.9610i	−0.141689	+	0.245413i	−0.928133	−	0.372249i	$-0.878587\pi$
$281$	−39.8147	+	68.9610i	−0.141689	+	0.245413i	0.786444	+	0.617662i	$0.211920\pi$
$282$		0			0
$283$	231.373	+	61.9962i	0.817573	+	0.219068i	0.643285	−	0.765627i	$-0.277571\pi$
$283$	231.373	+	61.9962i	0.817573	+	0.219068i	0.174288	+	0.984695i	$0.444238\pi$
$284$	−40.6617	+	23.4760i	−0.143175	+	0.0826621i
$285$		0			0
$286$	−136.875	+	237.074i	−0.478582	+	0.828929i
$287$	−73.9569	−	73.9569i	−0.257690	−	0.257690i
$288$		0			0
$289$		−	159.160i		−	0.550728i
$290$	−47.1043	−	407.676i	−0.162429	−	1.40578i
$291$		0			0
$292$	28.7122	−	107.156i	0.0983296	−	0.366971i
$293$	83.9027	+	22.4817i	0.286357	+	0.0767292i	0.399139	−	0.916891i	$-0.369309\pi$
$293$	83.9027	+	22.4817i	0.286357	+	0.0767292i	−0.112781	+	0.993620i	$0.535976\pi$
$294$		0			0
$295$	46.3596	+	36.7561i	0.157151	+	0.124597i
$296$	−91.2743			−0.308359
$297$		0			0
$298$	−274.859	+	274.859i	−0.922346	+	0.922346i
$299$	117.922	+	68.0822i	0.394388	+	0.227700i
$300$		0			0
$301$	−213.140	−	369.170i	−0.708107	−	1.22648i
$302$	11.6458	−	43.4629i	0.0385624	−	0.143917i
$303$		0			0
$304$	−64.6660	−	37.3350i	−0.212717	−	0.122812i
$305$	−277.494	−	41.0217i	−0.909817	−	0.134497i
$306$		0			0
$307$	−220.805	−	220.805i	−0.719234	−	0.719234i	0.249215	−	0.968448i	$-0.419828\pi$
$307$	−220.805	−	220.805i	−0.719234	−	0.719234i	−0.968448	+	0.249215i	$0.919828\pi$
$308$	−66.2837	−	247.374i	−0.215207	−	0.803162i
$309$		0			0
$310$	−75.3910	+	174.143i	−0.243197	+	0.561750i
$311$	−50.9290	−	88.2115i	−0.163759	−	0.283638i	0.772455	−	0.635069i	$-0.219029\pi$
$311$	−50.9290	−	88.2115i	−0.163759	−	0.283638i	−0.936214	+	0.351431i	$0.885695\pi$
$312$		0			0
$313$	−69.7840	−	260.438i	−0.222952	−	0.832069i	−0.983215	−	0.182453i	$-0.941596\pi$
$313$	−69.7840	−	260.438i	−0.222952	−	0.832069i	0.760262	−	0.649616i	$-0.225070\pi$
$314$		−	418.230i		−	1.33194i
$315$		0			0
$316$	−256.297			−0.811066
$317$	−73.6824	+	19.7431i	−0.232437	+	0.0622812i	−0.373157	−	0.927768i	$-0.621725\pi$
$317$	−73.6824	+	19.7431i	−0.232437	+	0.0622812i	0.140721	+	0.990049i	$0.455058\pi$
$318$		0			0
$319$	−325.820	+	188.112i	−1.02138	+	0.589694i
$320$	19.1139	−	7.56421i	0.0597308	−	0.0236382i
$321$		0			0
$322$	−356.593	+	95.5488i	−1.10743	+	0.296735i
$323$	30.0992	−	30.0992i	0.0931864	−	0.0931864i
$324$		0			0
$325$	215.483	−	115.453i	0.663024	−	0.355240i
$326$	−265.955	+	460.647i	−0.815812	+	1.41303i
$327$		0			0
$328$	44.0466	+	11.8022i	0.134288	+	0.0359825i
$329$	−16.2109	+	9.35934i	−0.0492731	+	0.0284479i
$330$		0			0
$331$	−39.1180	+	67.7543i	−0.118181	+	0.204696i	−0.919047	−	0.394148i	$-0.871040\pi$
$331$	−39.1180	+	67.7543i	−0.118181	+	0.204696i	0.800866	+	0.598844i	$0.204373\pi$
$332$	162.032	+	162.032i	0.488048	+	0.488048i
$333$		0			0
$334$		−	279.158i		−	0.835801i
$335$	−243.745	+	28.1631i	−0.727596	+	0.0840689i
$336$		0			0
$337$	44.4872	−	166.029i	0.132010	−	0.492667i	−0.867983	−	0.496595i	$-0.834584\pi$
$337$	44.4872	−	166.029i	0.132010	−	0.492667i	0.999992	+	0.00392788i	$0.00125029\pi$
$338$	−175.167	−	46.9359i	−0.518246	−	0.138864i
$339$		0			0
$340$	−13.7813	−	119.273i	−0.0405331	−	0.350804i
$341$	173.964			0.510159
$342$		0			0
$343$	129.602	−	129.602i	0.377849	−	0.377849i
$344$	160.954	+	92.9266i	0.467888	+	0.270135i
$345$		0			0
$346$	88.0974	+	152.589i	0.254617	+	0.441009i
$347$	−167.536	+	625.254i	−0.482813	+	1.80188i	0.106899	+	0.994270i	$0.465908\pi$
$347$	−167.536	+	625.254i	−0.482813	+	1.80188i	−0.589712	+	0.807614i	$0.700759\pi$
$348$		0			0
$349$	−74.5409	−	43.0362i	−0.213584	−	0.123313i	0.389392	−	0.921072i	$-0.372685\pi$
$349$	−74.5409	−	43.0362i	−0.213584	−	0.123313i	−0.602976	+	0.797759i	$0.706019\pi$
$350$	−191.770	+	634.444i	−0.547913	+	1.81270i
$351$		0			0
$352$	245.822	+	245.822i	0.698357	+	0.698357i
$353$	−164.703	−	614.682i	−0.466582	−	1.74131i	−0.651590	−	0.758571i	$-0.725898\pi$
$353$	−164.703	−	614.682i	−0.466582	−	1.74131i	0.185008	−	0.982737i	$-0.440769\pi$
$354$		0			0
$355$	−40.9917	−	103.581i	−0.115469	−	0.291778i
$356$	16.9401	+	29.3412i	0.0475847	+	0.0824191i
$357$		0			0
$358$	29.5623	+	110.328i	0.0825763	+	0.308179i
$359$			651.608i			1.81506i	0.419983	+	0.907532i	$0.362036\pi$
$359$			651.608i			1.81506i	−0.419983	+	0.907532i	$0.637964\pi$
$360$		0			0
$361$	347.045			0.961343
$362$	−396.914	+	106.353i	−1.09645	+	0.293792i
$363$		0			0
$364$	−191.454	+	110.536i	−0.525971	+	0.303670i
$365$	241.539	+	104.569i	0.661751	+	0.286490i
$366$		0			0
$367$	93.6571	−	25.0954i	0.255197	−	0.0683797i	−0.128953	−	0.991651i	$-0.541162\pi$
$367$	93.6571	−	25.0954i	0.255197	−	0.0683797i	0.384149	+	0.923271i	$0.374495\pi$
$368$	196.814	−	196.814i	0.534819	−	0.534819i
$369$		0			0
$370$	−35.2638	+	238.544i	−0.0953075	+	0.644714i
$371$	344.067	−	595.942i	0.927404	−	1.60631i
$372$		0			0
$373$	459.385	+	123.092i	1.23160	+	0.330005i	0.815200	−	0.579179i	$-0.196627\pi$
$373$	459.385	+	123.092i	1.23160	+	0.330005i	0.416395	+	0.909184i	$0.363293\pi$
$374$	−276.257	+	159.497i	−0.738656	+	0.426463i
$375$		0			0
$376$	4.08056	−	7.06774i	0.0108526	−	0.0187972i
$377$	229.644	+	229.644i	0.609135	+	0.609135i
$378$		0			0
$379$		−	556.768i		−	1.46905i	−0.678584	−	0.734523i	$-0.737406\pi$
$379$		−	556.768i		−	1.46905i	0.678584	−	0.734523i	$-0.262594\pi$
$380$	−24.4550	+	30.8445i	−0.0643553	+	0.0811698i
$381$		0			0
$382$	74.5517	−	278.231i	0.195162	−	0.728353i
$383$	707.233	+	189.503i	1.84656	+	0.494785i	0.999336	−	0.0364479i	$-0.0116043\pi$
$383$	707.233	+	189.503i	1.84656	+	0.494785i	0.847226	+	0.531233i	$0.178271\pi$
$384$		0			0
$385$	603.602	−	69.7422i	1.56780	−	0.181148i
$386$	−308.838			−0.800097
$387$		0			0
$388$	265.971	−	265.971i	0.685492	−	0.685492i
$389$	−180.704	−	104.330i	−0.464535	−	0.268200i	0.249414	−	0.968397i	$-0.419762\pi$
$389$	−180.704	−	104.330i	−0.464535	−	0.268200i	−0.713949	+	0.700197i	$0.753095\pi$
$390$		0			0
$391$	79.3349	+	137.412i	0.202903	+	0.351437i
$392$	−79.9989	+	298.560i	−0.204079	+	0.761633i
$393$		0			0
$394$	−252.522	−	145.794i	−0.640919	−	0.370035i
$395$	88.9261	−	601.546i	0.225129	−	1.52290i
$396$		0			0
$397$	109.933	+	109.933i	0.276910	+	0.276910i	0.831874	−	0.554964i	$-0.187268\pi$
$397$	109.933	+	109.933i	0.276910	+	0.276910i	−0.554964	+	0.831874i	$0.687268\pi$
$398$	173.633	+	648.007i	0.436264	+	1.62816i
$399$		0			0
$400$	−113.955	−	486.545i	−0.284888	−	1.21636i
$401$	−311.573	−	539.660i	−0.776989	−	1.34578i	−0.933670	−	0.358135i	$-0.883413\pi$
$401$	−311.573	−	539.660i	−0.776989	−	1.34578i	0.156680	−	0.987649i	$-0.449921\pi$
$402$		0			0
$403$	−38.8668	−	145.053i	−0.0964437	−	0.359933i
$404$		−	58.3533i		−	0.144439i
$405$		0			0
$406$	−880.511			−2.16875
$407$	213.530	−	57.2152i	0.524644	−	0.140578i
$408$		0			0
$409$	−446.525	+	257.801i	−1.09175	+	0.630321i	−0.934041	−	0.357165i	$-0.883743\pi$
$409$	−446.525	+	257.801i	−1.09175	+	0.630321i	−0.157707	+	0.987486i	$0.550410\pi$
$410$	47.8624	−	110.555i	0.116738	−	0.269647i
$411$		0			0
$412$	310.705	−	83.2532i	0.754139	−	0.202071i
$413$	89.7578	−	89.7578i	0.217331	−	0.217331i
$414$		0			0
$415$	−436.519	+	324.080i	−1.05185	+	0.780917i
$416$	150.047	−	259.889i	0.360690	−	0.624734i
$417$		0			0
$418$	101.016	+	27.0671i	0.241665	+	0.0647539i
$419$	127.314	−	73.5049i	0.303852	−	0.175429i	−0.340320	−	0.940310i	$-0.610535\pi$
$419$	127.314	−	73.5049i	0.303852	−	0.175429i	0.644172	+	0.764880i	$0.277202\pi$
$420$		0			0
$421$	−317.026	+	549.106i	−0.753032	+	1.30429i	0.193315	+	0.981137i	$0.438076\pi$
$421$	−317.026	+	549.106i	−0.753032	+	1.30429i	−0.946347	+	0.323152i	$0.895257\pi$
$422$	−229.860	−	229.860i	−0.544693	−	0.544693i
$423$		0			0
$424$			300.018i			0.707590i
$425$	284.725	+	9.03819i	0.669940	+	0.0212663i
$426$		0			0
$427$	−155.770	+	581.342i	−0.364801	+	1.36146i
$428$	311.723	+	83.5259i	0.728325	+	0.195154i
$429$		0			0
$430$	305.047	−	384.748i	0.709411	−	0.894762i
$431$	−735.767			−1.70712			−0.853559	−	0.520997i	$-0.825560\pi$
$431$	−735.767			−1.70712			−0.853559	+	0.520997i	$0.825560\pi$
$432$		0			0
$433$	69.9073	−	69.9073i	0.161449	−	0.161449i	−0.621760	−	0.783208i	$-0.713582\pi$
$433$	69.9073	−	69.9073i	0.161449	−	0.161449i	0.783208	+	0.621760i	$0.213582\pi$
$434$	352.597	+	203.572i	0.812435	+	0.469060i
$435$		0			0
$436$	193.920	+	335.880i	0.444771	+	0.770366i
$437$	13.4633	−	50.2459i	0.0308086	−	0.114979i
$438$		0			0
$439$	290.918	+	167.962i	0.662683	+	0.382600i	0.793299	−	0.608833i	$-0.208362\pi$
$439$	290.918	+	167.962i	0.662683	+	0.382600i	−0.130615	+	0.991433i	$0.541695\pi$
$440$	−212.703	+	157.915i	−0.483415	+	0.358897i
$441$		0			0
$442$	194.711	+	194.711i	0.440523	+	0.440523i
$443$	−79.9082	−	298.222i	−0.180380	−	0.673187i	−0.995573	−	0.0939967i	$-0.970036\pi$
$443$	−79.9082	−	298.222i	−0.180380	−	0.673187i	0.815193	−	0.579190i	$-0.196631\pi$
$444$		0			0
$445$	−74.7434	+	29.5793i	−0.167963	+	0.0664704i
$446$	−38.2391	−	66.2320i	−0.0857379	−	0.148502i
$447$		0			0
$448$	−11.4151	−	42.6016i	−0.0254801	−	0.0950929i
$449$		−	391.868i		−	0.872757i	−0.899763	−	0.436378i	$-0.856261\pi$
$449$		−	391.868i		−	0.872757i	0.899763	−	0.436378i	$-0.143739\pi$
$450$		0			0
$451$	−110.442			−0.244883
$452$	342.744	−	91.8379i	0.758283	−	0.203181i
$453$		0			0
$454$	139.975	−	80.8148i	0.308316	−	0.178006i
$455$	−193.007	−	487.707i	−0.424192	−	1.07188i
$456$		0			0
$457$	164.664	−	44.1215i	0.360314	−	0.0965459i	−0.0741204	−	0.997249i	$-0.523615\pi$
$457$	164.664	−	44.1215i	0.360314	−	0.0965459i	0.434434	+	0.900703i	$0.356948\pi$
$458$	485.917	−	485.917i	1.06095	−	1.06095i
$459$		0			0
$460$	−87.4637	−	117.809i	−0.190138	−	0.256107i
$461$	−378.908	+	656.288i	−0.821926	+	1.42362i	0.0823197	+	0.996606i	$0.473767\pi$
$461$	−378.908	+	656.288i	−0.821926	+	1.42362i	−0.904246	+	0.427012i	$0.859566\pi$
$462$		0			0
$463$	168.336	+	45.1054i	0.363576	+	0.0974199i	0.435982	−	0.899955i	$-0.356401\pi$
$463$	168.336	+	45.1054i	0.363576	+	0.0974199i	−0.0724060	+	0.997375i	$0.523068\pi$
$464$	574.919	−	331.930i	1.23905	−	0.715366i
$465$		0			0
$466$	186.615	−	323.227i	0.400462	−	0.693620i
$467$	191.561	+	191.561i	0.410194	+	0.410194i	0.881806	−	0.471612i	$-0.156328\pi$
$467$	191.561	+	191.561i	0.410194	+	0.410194i	−0.471612	+	0.881806i	$0.656328\pi$
$468$		0			0
$469$			526.447i			1.12249i
$470$	−16.8949	−	13.3951i	−0.0359466	−	0.0285002i
$471$		0			0
$472$	−14.3238	+	53.4571i	−0.0303470	+	0.113257i
$473$	−434.791	−	116.502i	−0.919219	−	0.246304i
$474$		0			0
$475$	−63.9091	−	68.0996i	−0.134546	−	0.143368i
$476$	−257.610			−0.541198
$477$		0			0
$478$	−275.020	+	275.020i	−0.575355	+	0.575355i
$479$	−135.340	−	78.1383i	−0.282546	−	0.163128i	0.352029	−	0.935989i	$-0.385492\pi$
$479$	−135.340	−	78.1383i	−0.282546	−	0.163128i	−0.634575	+	0.772861i	$0.718825\pi$
$480$		0			0
$481$	−95.4130	−	165.260i	−0.198364	−	0.343576i
$482$	−12.9945	+	48.4960i	−0.0269595	+	0.100614i
$483$		0			0
$484$	−13.3634	−	7.71537i	−0.0276104	−	0.0159408i
$485$	531.969	+	716.535i	1.09684	+	1.47739i
$486$		0			0
$487$	−451.121	−	451.121i	−0.926326	−	0.926326i	0.0711400	−	0.997466i	$-0.477336\pi$
$487$	−451.121	−	451.121i	−0.926326	−	0.926326i	−0.997466	+	0.0711400i	$0.977336\pi$
$488$	−67.9139	−	253.458i	−0.139168	−	0.519381i
$489$		0			0
$490$	749.375	+	324.424i	1.52934	+	0.662091i
$491$	−200.071	−	346.533i	−0.407476	−	0.705769i	0.587130	−	0.809493i	$-0.300258\pi$
$491$	−200.071	−	346.533i	−0.407476	−	0.705769i	−0.994606	+	0.103723i	$0.966924\pi$
$492$		0			0
$493$	97.9482	+	365.548i	0.198678	+	0.741476i
$494$		−	90.2752i		−	0.182743i
$495$		0			0
$496$	−306.965			−0.618881
$497$	−230.865	+	61.8601i	−0.464517	+	0.124467i
$498$		0			0
$499$	236.699	−	136.658i	0.474347	−	0.273864i	−0.243711	−	0.969848i	$-0.578365\pi$
$499$	236.699	−	136.658i	0.474347	−	0.273864i	0.718058	+	0.695984i	$0.245031\pi$
$500$	−262.513	+	21.9182i	−0.525027	+	0.0438363i
$501$		0			0
$502$	221.466	−	59.3417i	0.441168	−	0.118211i
$503$	−297.206	+	297.206i	−0.590867	+	0.590867i	−0.937866	−	0.346999i	$-0.887201\pi$
$503$	−297.206	+	297.206i	−0.590867	+	0.590867i	0.346999	+	0.937866i	$0.387201\pi$
$504$		0			0
$505$	136.959	+	20.2466i	0.271206	+	0.0400922i
$506$	−194.913	+	337.599i	−0.385203	+	0.667191i
$507$		0			0
$508$	−272.842	−	73.1079i	−0.537091	−	0.143913i
$509$	60.1552	−	34.7306i	0.118183	−	0.0682330i	−0.439743	−	0.898124i	$-0.644931\pi$
$509$	60.1552	−	34.7306i	0.118183	−	0.0682330i	0.557926	+	0.829891i	$0.311597\pi$
$510$		0			0
$511$	282.358	−	489.059i	0.552560	−	0.957062i
$512$	−169.331	−	169.331i	−0.330724	−	0.330724i
$513$		0			0
$514$		−	1056.66i		−	2.05576i
$515$	87.5972	+	758.133i	0.170092	+	1.47210i
$516$		0			0
$517$	−5.11579	+	19.0924i	−0.00989515	+	0.0369292i
$518$	499.743	+	133.906i	0.964754	+	0.258505i
$519$		0			0
$520$	179.192	+	142.072i	0.344600	+	0.273216i
$521$	532.558			1.02218			0.511092	−	0.859526i	$-0.329241\pi$
$521$	532.558			1.02218			0.511092	+	0.859526i	$0.329241\pi$
$522$		0			0
$523$	322.137	−	322.137i	0.615941	−	0.615941i	−0.328547	−	0.944488i	$-0.606559\pi$
$523$	322.137	−	322.137i	0.615941	−	0.615941i	0.944488	+	0.328547i	$0.106559\pi$
$524$	206.627	+	119.296i	0.394326	+	0.227664i
$525$		0			0
$526$	219.886	+	380.853i	0.418034	+	0.724056i
$527$	45.2907	−	169.027i	0.0859407	−	0.320735i
$528$		0			0
$529$	−290.204	−	167.549i	−0.548590	−	0.316728i
$530$	784.094	+	115.912i	1.47942	+	0.218702i
$531$		0			0
$532$	59.7188	+	59.7188i	0.112253	+	0.112253i
$533$	24.6748	+	92.0876i	0.0462942	+	0.172772i
$534$		0			0
$535$	−304.198	+	702.654i	−0.568594	+	1.31337i
$536$	−114.762	−	198.774i	−0.214109	−	0.370847i
$537$		0			0
$538$	−112.032	−	418.108i	−0.208237	−	0.777152i
$539$		−	748.608i		−	1.38888i
$540$		0			0
$541$	201.002			0.371538			0.185769	−	0.982593i	$-0.440522\pi$
$541$	201.002			0.371538			0.185769	+	0.982593i	$0.440522\pi$
$542$	1106.04	−	296.362i	2.04066	−	0.546792i
$543$		0			0
$544$	302.844	−	174.847i	0.556698	−	0.321410i
$545$	−855.616	+	338.606i	−1.56994	+	0.621295i
$546$		0			0
$547$	603.281	−	161.649i	1.10289	−	0.295519i	0.338950	−	0.940804i	$-0.389928\pi$
$547$	603.281	−	161.649i	1.10289	−	0.295519i	0.763941	+	0.645286i	$0.223262\pi$
$548$	−36.0361	+	36.0361i	−0.0657593	+	0.0657593i
$549$		0			0
$550$	330.530	+	616.906i	0.600964	+	1.12165i
$551$	62.0344	−	107.447i	0.112585	−	0.195003i
$552$		0			0
$553$	−1260.22	−	337.675i	−2.27888	−	0.610624i
$554$	−825.420	+	476.556i	−1.48993	+	0.860210i
$555$		0			0
$556$	−119.450	+	206.894i	−0.214838	+	0.372111i
$557$	227.470	+	227.470i	0.408384	+	0.408384i	0.881175	−	0.472791i	$-0.156753\pi$
$557$	227.470	+	227.470i	0.408384	+	0.408384i	−0.472791	+	0.881175i	$0.656753\pi$
$558$		0			0
$559$			388.561i			0.695100i
$560$	−1065.07	+	123.062i	−1.90192	+	0.219754i
$561$		0			0
$562$	−50.9328	+	190.084i	−0.0906278	+	0.338228i
$563$	−52.8921	−	14.1724i	−0.0939469	−	0.0251730i	0.211539	−	0.977369i	$-0.432152\pi$
$563$	−52.8921	−	14.1724i	−0.0939469	−	0.0251730i	−0.305486	+	0.952196i	$0.598819\pi$
$564$		0			0
$565$	96.6297	+	836.308i	0.171026	+	1.48019i
$566$	591.967			1.04588
$567$		0			0
$568$	73.6841	−	73.6841i	0.129726	−	0.129726i
$569$	−211.299	−	121.993i	−0.371351	−	0.214399i	0.302698	−	0.953087i	$-0.402113\pi$
$569$	−211.299	−	121.993i	−0.371351	−	0.214399i	−0.674048	+	0.738687i	$0.735446\pi$
$570$		0			0
$571$	−284.750	−	493.202i	−0.498687	−	0.863751i	0.501312	−	0.865267i	$-0.332851\pi$
$571$	−284.750	−	493.202i	−0.498687	−	0.863751i	−0.999999	+	0.00151580i	$0.999518\pi$
$572$	−60.4185	+	225.485i	−0.105627	+	0.394205i
$573$		0			0
$574$	−223.848	−	129.239i	−0.389979	−	0.225155i
$575$	306.853	−	164.408i	0.533657	−	0.285926i
$576$		0			0
$577$	−258.911	−	258.911i	−0.448719	−	0.448719i	0.446209	−	0.894929i	$-0.352774\pi$
$577$	−258.911	−	258.911i	−0.448719	−	0.448719i	−0.894929	+	0.446209i	$0.852774\pi$
$578$	−101.803	−	379.933i	−0.176129	−	0.657324i
$579$		0			0
$580$	−128.777	−	325.404i	−0.222029	−	0.561041i
$581$	583.237	+	1010.20i	1.00385	+	1.73872i
$582$		0			0
$583$	−188.066	−	701.872i	−0.322583	−	1.20390i
$584$			246.210i			0.421592i
$585$		0			0
$586$	214.665			0.366322
$587$	−855.160	+	229.139i	−1.45683	+	0.390357i	−0.898394	−	0.439190i	$-0.855266\pi$
$587$	−855.160	+	229.139i	−1.45683	+	0.390357i	−0.558437	+	0.829547i	$0.688599\pi$
$588$		0			0
$589$	−49.6828	+	28.6844i	−0.0843512	+	0.0487002i
$590$	134.175	+	58.0882i	0.227416	+	0.0984545i
$591$		0			0
$592$	−376.780	+	100.958i	−0.636452	+	0.170537i
$593$	−638.841	+	638.841i	−1.07730	+	1.07730i	−0.0805534	+	0.996750i	$0.525669\pi$
$593$	−638.841	+	638.841i	−1.07730	+	1.07730i	−0.996750	+	0.0805534i	$0.974331\pi$
$594$		0			0
$595$	89.3818	−	604.629i	0.150221	−	1.01618i
$596$	−165.736	+	287.063i	−0.278080	+	0.481649i
$597$		0			0
$598$	325.040	+	87.0941i	0.543544	+	0.145642i
$599$	350.554	−	202.393i	0.585233	−	0.337884i	−0.177977	−	0.984035i	$-0.556955\pi$
$599$	350.554	−	202.393i	0.585233	−	0.337884i	0.763210	+	0.646150i	$0.223622\pi$
$600$		0			0
$601$	−419.760	+	727.046i	−0.698437	+	1.20973i	0.270572	+	0.962700i	$0.412787\pi$
$601$	−419.760	+	727.046i	−0.698437	+	1.20973i	−0.969008	+	0.247028i	$0.920546\pi$
$602$	−744.919	−	744.919i	−1.23741	−	1.23741i
$603$		0			0
$604$		−	38.3704i		−	0.0635271i
$605$	22.7451	−	28.6879i	0.0375953	−	0.0474180i
$606$		0			0
$607$	83.8870	−	313.071i	0.138199	−	0.515767i	−0.861765	−	0.507308i	$-0.830641\pi$
$607$	83.8870	−	313.071i	0.138199	−	0.515767i	0.999964	−	0.00845910i	$-0.00269265\pi$
$608$	−110.737	−	29.6720i	−0.182134	−	0.0488027i
$609$		0			0
$610$	−688.648	+	79.5687i	−1.12893	+	0.130440i
$611$	17.0624			0.0279253
$612$		0			0
$613$	−164.098	+	164.098i	−0.267697	+	0.267697i	−0.828171	−	0.560475i	$-0.810619\pi$
$613$	−164.098	+	164.098i	−0.267697	+	0.267697i	0.560475	+	0.828171i	$0.310619\pi$
$614$	−668.317	−	385.853i	−1.08846	−	0.628425i
$615$		0			0
$616$	284.194	+	492.238i	0.461353	+	0.799088i
$617$	39.3191	−	146.741i	0.0637263	−	0.237830i	−0.926715	−	0.375765i	$-0.877380\pi$
$617$	39.3191	−	146.741i	0.0637263	−	0.237830i	0.990441	+	0.137935i	$0.0440466\pi$
$618$		0			0
$619$	371.036	+	214.218i	0.599412	+	0.346071i	0.768810	−	0.639477i	$-0.220849\pi$
$619$	371.036	+	214.218i	0.599412	+	0.346071i	−0.169398	+	0.985548i	$0.554182\pi$
$620$	−23.6644	+	160.079i	−0.0381684	+	0.258192i
$621$		0			0
$622$	−177.995	−	177.995i	−0.286166	−	0.286166i
$623$	44.6378	+	166.591i	0.0716498	+	0.267401i
$624$		0			0
$625$	39.6396	−	623.742i	0.0634233	−	0.997987i
$626$	−333.164	−	577.058i	−0.532211	−	0.921817i
$627$		0			0
$628$	−92.3067	−	344.493i	−0.146985	−	0.548556i
$629$		−	222.366i		−	0.353523i
$630$		0			0
$631$	−1077.98			−1.70837			−0.854185	−	0.519969i	$-0.825943\pi$
$631$	−1077.98			−1.70837			−0.854185	+	0.519969i	$0.825943\pi$
$632$	549.441	−	147.222i	0.869369	−	0.232947i
$633$		0			0
$634$	−163.260	+	94.2581i	−0.257508	+	0.148672i
$635$	266.256	−	615.013i	0.419301	−	0.968525i
$636$		0			0
$637$	−624.196	+	167.253i	−0.979899	+	0.262563i
$638$	−657.447	+	657.447i	−1.03048	+	1.03048i
$639$		0			0
$640$	533.602	−	396.157i	0.833753	−	0.618995i
$641$	434.510	−	752.593i	0.677862	−	1.17409i	−0.297761	−	0.954640i	$-0.596240\pi$
$641$	434.510	−	752.593i	0.677862	−	1.17409i	0.975623	−	0.219451i	$-0.0704267\pi$
$642$		0			0
$643$	119.275	+	31.9596i	0.185497	+	0.0497039i	0.350372	−	0.936611i	$-0.386055\pi$
$643$	119.275	+	31.9596i	0.185497	+	0.0497039i	−0.164874	+	0.986315i	$0.552722\pi$
$644$	−272.634	+	157.406i	−0.423345	+	0.244419i
$645$		0			0
$646$	52.5979	−	91.1023i	0.0814209	−	0.141025i
$647$	−303.440	−	303.440i	−0.468996	−	0.468996i	0.432593	−	0.901589i	$-0.357599\pi$
$647$	−303.440	−	303.440i	−0.468996	−	0.468996i	−0.901589	+	0.432593i	$0.857599\pi$
$648$		0			0
$649$		−	134.038i		−	0.206530i
$650$	440.535	−	413.427i	0.677746	−	0.636041i
$651$		0			0
$652$	−117.397	+	438.130i	−0.180056	+	0.671978i
$653$	728.322	+	195.153i	1.11535	+	0.298856i	0.768999	−	0.639250i	$-0.220755\pi$
$653$	728.322	+	195.153i	1.11535	+	0.298856i	0.346348	+	0.938106i	$0.387422\pi$
$654$		0			0
$655$	−351.689	+	443.576i	−0.536929	+	0.677215i
$656$	194.878			0.297071
$657$		0			0
$658$	−32.7106	+	32.7106i	−0.0497122	+	0.0497122i
$659$	1030.08	+	594.718i	1.56310	+	0.902456i	0.996941	+	0.0781594i	$0.0249043\pi$
$659$	1030.08	+	594.718i	1.56310	+	0.902456i	0.566158	+	0.824296i	$0.308429\pi$
$660$		0			0
$661$	384.281	+	665.595i	0.581364	+	1.00695i	0.995318	+	0.0966537i	$0.0308139\pi$
$661$	384.281	+	665.595i	0.581364	+	1.00695i	−0.413954	+	0.910298i	$0.635853\pi$
$662$	−50.0416	+	186.758i	−0.0755916	+	0.282112i
$663$		0			0
$664$	−440.433	−	254.284i	−0.663303	−	0.382958i
$665$	−160.884	+	119.444i	−0.241931	+	0.179615i
$666$		0			0
$667$	327.018	+	327.018i	0.490282	+	0.490282i
$668$	−61.6122	−	229.940i	−0.0922339	−	0.344222i
$669$		0			0
$670$	−563.832	+	223.133i	−0.841540	+	0.333035i
$671$	317.760	+	550.376i	0.473562	+	0.820233i
$672$		0			0
$673$	−75.2762	−	280.935i	−0.111852	−	0.417436i	0.887180	−	0.461423i	$-0.152661\pi$
$673$	−75.2762	−	280.935i	−0.111852	−	0.417436i	−0.999032	+	0.0439863i	$0.985994\pi$
$674$		−	424.784i		−	0.630243i
$675$		0			0
$676$	−154.643			−0.228762
$677$	−874.273	+	234.261i	−1.29139	+	0.346028i	−0.838190	−	0.545379i	$-0.816386\pi$
$677$	−874.273	+	234.261i	−1.29139	+	0.346028i	−0.453204	+	0.891407i	$0.649719\pi$
$678$		0			0
$679$	1658.21	−	957.368i	2.44214	−	1.40997i
$680$	98.0570	+	247.779i	0.144202	+	0.364380i
$681$		0			0
$682$	415.272	−	111.272i	0.608903	−	0.163155i
$683$	−579.270	+	579.270i	−0.848125	+	0.848125i	−0.989899	−	0.141774i	$-0.954719\pi$
$683$	−579.270	+	579.270i	−0.848125	+	0.848125i	0.141774	+	0.989899i	$0.454719\pi$
$684$		0			0
$685$	−72.0759	−	97.0824i	−0.105220	−	0.141726i
$686$	226.478	−	392.271i	0.330143	−	0.571824i
$687$		0			0
$688$	767.200	+	205.571i	1.11512	+	0.298795i
$689$	−543.210	+	313.622i	−0.788403	+	0.455185i
$690$		0			0
$691$	479.893	−	831.199i	0.694491	−	1.20289i	−0.275861	−	0.961197i	$-0.588963\pi$
$691$	479.893	−	831.199i	0.694491	−	1.20289i	0.970352	−	0.241696i	$-0.0777036\pi$
$692$	106.243	+	106.243i	0.153530	+	0.153530i
$693$		0			0
$694$			1599.71i			2.30506i
$695$	−444.148	−	352.142i	−0.639062	−	0.506680i
$696$		0			0
$697$	−28.7531	+	107.308i	−0.0412526	+	0.153957i
$698$	−205.464	−	55.0540i	−0.294361	−	0.0788739i
$699$		0			0
$700$	−17.9324	+	564.912i	−0.0256176	+	0.807017i
$701$	−1285.91			−1.83439			−0.917197	−	0.398434i	$-0.869554\pi$
$701$	−1285.91			−1.83439			−0.917197	+	0.398434i	$0.869554\pi$
$702$		0			0
$703$	−51.5485	+	51.5485i	−0.0733264	+	0.0733264i
$704$	−40.3324	−	23.2859i	−0.0572903	−	0.0330766i
$705$		0			0
$706$	−786.331	−	1361.96i	−1.11378	−	1.92913i
$707$	76.8814	−	286.925i	0.108743	−	0.405835i
$708$		0			0
$709$	−433.296	−	250.163i	−0.611137	−	0.352840i	0.162274	−	0.986746i	$-0.448117\pi$
$709$	−433.296	−	250.163i	−0.611137	−	0.352840i	−0.773410	+	0.633906i	$0.781451\pi$
$710$	−164.105	−	221.040i	−0.231133	−	0.311324i
$711$		0			0
$712$	−53.1700	−	53.1700i	−0.0746769	−	0.0746769i
$713$	−55.3473	−	206.559i	−0.0776259	−	0.289704i
$714$		0			0
$715$	−508.266	−	220.042i	−0.710861	−	0.307751i
$716$	48.7005	+	84.3518i	0.0680175	+	0.117810i
$717$		0			0
$718$	416.784	+	1555.46i	0.580479	+	2.16638i
$719$			111.332i			0.154843i	0.996998	+	0.0774217i	$0.0246688\pi$
$719$			111.332i			0.154843i	−0.996998	+	0.0774217i	$0.975331\pi$
$720$		0			0
$721$	1637.44			2.27106
$722$	828.434	−	221.978i	1.14742	−	0.307449i
$723$		0			0
$724$	−303.462	+	175.204i	−0.419147	+	0.241994i
$725$	808.426	−	189.344i	1.11507	−	0.261164i
$726$		0			0
$727$	594.341	−	159.253i	0.817526	−	0.219055i	0.174261	−	0.984699i	$-0.444246\pi$
$727$	594.341	−	159.253i	0.817526	−	0.219055i	0.643264	+	0.765644i	$0.277580\pi$
$728$	346.938	−	346.938i	0.476563	−	0.476563i
$729$		0			0
$730$	643.466	+	95.1230i	0.881460	+	0.130305i
$731$	−226.391	+	392.121i	−0.309701	+	0.536417i
$732$		0			0
$733$	−1126.11	−	301.741i	−1.53631	−	0.411652i	−0.611237	−	0.791447i	$-0.709328\pi$
$733$	−1126.11	−	301.741i	−1.53631	−	0.411652i	−0.925071	+	0.379795i	$0.875995\pi$
$734$	207.518	−	119.811i	0.282723	−	0.163230i
$735$		0			0
$736$	213.671	−	370.089i	0.290314	−	0.502838i
$737$	393.080	+	393.080i	0.533351	+	0.533351i
$738$		0			0
$739$			318.962i			0.431612i	0.976436	+	0.215806i	$0.0692379\pi$
$739$			318.962i			0.431612i	−0.976436	+	0.215806i	$0.930762\pi$
$740$	23.6020	+	204.270i	0.0318946	+	0.276041i
$741$		0			0
$742$	440.147	−	1642.65i	0.593190	−	2.21382i
$743$	453.316	+	121.466i	0.610116	+	0.163480i	0.550631	−	0.834749i	$-0.314387\pi$
$743$	453.316	+	121.466i	0.610116	+	0.163480i	0.0594856	+	0.998229i	$0.481054\pi$
$744$		0			0
$745$	−616.252	−	488.594i	−0.827183	−	0.655831i
$746$	1175.34			1.57552
$747$		0			0
$748$	−192.349	+	192.349i	−0.257151	+	0.257151i
$749$	1422.71	+	821.400i	1.89947	+	1.09666i
$750$		0			0
$751$	76.0823	+	131.778i	0.101308	+	0.175471i	0.912224	−	0.409692i	$-0.134364\pi$
$751$	76.0823	+	131.778i	0.101308	+	0.175471i	−0.810916	+	0.585163i	$0.801031\pi$
$752$	9.02696	−	33.6891i	0.0120039	−	0.0447993i
$753$		0			0
$754$	695.071	+	401.299i	0.921845	+	0.532227i
$755$	90.0579	+	13.3132i	0.119282	+	0.0176333i
$756$		0			0
$757$	488.444	+	488.444i	0.645236	+	0.645236i	0.951838	−	0.306602i	$-0.0991919\pi$
$757$	488.444	+	488.444i	0.645236	+	0.645236i	−0.306602	+	0.951838i	$0.599192\pi$
$758$	−356.123	−	1329.07i	−0.469819	−	1.75339i
$759$		0			0
$760$	34.7082	−	80.1710i	0.0456686	−	0.105488i
$761$	−88.9996	−	154.152i	−0.116951	−	0.202565i	0.801607	−	0.597851i	$-0.203979\pi$
$761$	−88.9996	−	154.152i	−0.116951	−	0.202565i	−0.918558	+	0.395286i	$0.870645\pi$
$762$		0			0
$763$	510.986	+	1907.03i	0.669706	+	2.49938i
$764$		−	245.631i		−	0.321506i
$765$		0			0
$766$	1809.45			2.36221
$767$	−111.762	+	29.9466i	−0.145713	+	0.0390438i
$768$		0			0
$769$	−179.757	+	103.783i	−0.233754	+	0.134958i	−0.612303	−	0.790623i	$-0.709757\pi$
$769$	−179.757	+	103.783i	−0.233754	+	0.134958i	0.378548	+	0.925581i	$0.376423\pi$
$770$	1396.26	−	552.561i	1.81332	−	0.717611i
$771$		0			0
$772$	−254.387	+	68.1628i	−0.329517	+	0.0882938i
$773$	199.628	−	199.628i	0.258251	−	0.258251i	−0.566091	−	0.824342i	$-0.691545\pi$
$773$	199.628	−	199.628i	0.258251	−	0.258251i	0.824342	+	0.566091i	$0.191545\pi$
$774$		0			0
$775$	−367.506	−	111.084i	−0.474202	−	0.143334i
$776$	−417.401	+	722.960i	−0.537888	+	0.931649i
$777$		0			0
$778$	−498.093	−	133.464i	−0.640222	−	0.171547i
$779$	31.5414	−	18.2104i	0.0404896	−	0.0233767i
$780$		0			0
$781$	−126.190	+	218.568i	−0.161575	+	0.279856i
$782$	277.273	+	277.273i	0.354569	+	0.354569i
$783$		0			0
$784$			1320.94i			1.68487i
$785$	840.576	−	97.1229i	1.07080	−	0.123723i
$786$		0			0
$787$	−335.169	+	1250.87i	−0.425882	+	1.58941i	0.336108	+	0.941823i	$0.390889\pi$
$787$	−335.169	+	1250.87i	−0.425882	+	1.58941i	−0.761990	+	0.647589i	$0.775777\pi$
$788$	−240.178	−	64.3556i	−0.304795	−	0.0816695i
$789$		0			0
$790$	−172.487	−	1492.84i	−0.218338	−	1.88967i
$791$	1806.28			2.28354
$792$		0			0
$793$	387.915	−	387.915i	0.489174	−	0.489174i
$794$	332.739	+	192.107i	0.419067	+	0.241948i
$795$		0			0
$796$	286.040	+	495.436i	0.359347	+	0.622407i
$797$	130.147	−	485.714i	0.163296	−	0.609428i	−0.834956	−	0.550317i	$-0.814507\pi$
$797$	130.147	−	485.714i	0.163296	−	0.609428i	0.998251	−	0.0591106i	$-0.0188265\pi$
$798$		0			0
$799$	17.2187	+	9.94121i	0.0215503	+	0.0124421i
$800$	−362.340	−	676.276i	−0.452925	−	0.845345i
$801$		0			0
$802$	−1088.94	−	1088.94i	−1.35778	−	1.35778i
$803$	−154.336	−	575.991i	−0.192200	−	0.717299i
$804$		0			0
$805$	−274.847	−	694.506i	−0.341425	−	0.862740i
$806$	−185.559	−	321.397i	−0.230222	−	0.398756i
$807$		0			0
$808$	33.5194	+	125.096i	0.0414844	+	0.154822i
$809$			329.434i			0.407212i	0.979053	+	0.203606i	$0.0652661\pi$
$809$			329.434i			0.407212i	−0.979053	+	0.203606i	$0.934734\pi$
$810$		0			0
$811$	−736.236			−0.907812			−0.453906	−	0.891049i	$-0.649970\pi$
$811$	−736.236			−0.907812			−0.453906	+	0.891049i	$0.649970\pi$
$812$	−725.270	+	194.336i	−0.893190	+	0.239330i
$813$		0			0
$814$	473.123	−	273.158i	0.581233	−	0.335575i
$815$	−987.588	−	427.553i	−1.21176	−	0.524606i
$816$		0			0
$817$	143.382	−	38.4192i	0.175499	−	0.0470247i
$818$	−901.008	+	901.008i	−1.10148	+	1.10148i
$819$		0			0
$820$	15.0235	−	101.627i	0.0183213	−	0.123936i
$821$	−235.531	+	407.952i	−0.286883	+	0.496896i	−0.973064	−	0.230535i	$-0.925953\pi$
$821$	−235.531	+	407.952i	−0.286883	+	0.496896i	0.686181	+	0.727431i	$0.259286\pi$
$822$		0			0
$823$	842.487	+	225.744i	1.02368	+	0.274294i	0.731334	−	0.682019i	$-0.238898\pi$
$823$	842.487	+	225.744i	1.02368	+	0.274294i	0.292344	+	0.956313i	$0.405565\pi$
$824$	−618.258	+	356.951i	−0.750313	+	0.433194i
$825$		0			0
$826$	156.850	−	271.673i	0.189892	−	0.328902i
$827$	−796.631	−	796.631i	−0.963278	−	0.963278i	0.0360709	−	0.999349i	$-0.488516\pi$
$827$	−796.631	−	796.631i	−0.963278	−	0.963278i	−0.999349	+	0.0360709i	$0.988516\pi$
$828$		0			0
$829$		−	860.599i		−	1.03812i	−0.854739	−	0.519059i	$-0.826283\pi$
$829$		−	860.599i		−	1.03812i	0.854739	−	0.519059i	$-0.173717\pi$
$830$	−834.730	+	1052.82i	−1.00570	+	1.26846i
$831$		0			0
$832$	−10.4050	+	38.8320i	−0.0125060	+	0.0466731i
$833$	−727.363	−	194.896i	−0.873185	−	0.233969i
$834$		0			0
$835$	561.062	−	64.8270i	0.671931	−	0.0776371i
$836$	89.1799			0.106675
$837$		0			0
$838$	256.897	−	256.897i	0.306560	−	0.306560i
$839$	−878.746	−	507.344i	−1.04737	−	0.604701i	−0.125460	−	0.992099i	$-0.540041\pi$
$839$	−878.746	−	507.344i	−1.04737	−	0.604701i	−0.921913	+	0.387398i	$0.873374\pi$
$840$		0			0
$841$	131.022	+	226.938i	0.155794	+	0.269842i
$842$	−405.555	+	1513.55i	−0.481657	+	1.79757i
$843$		0			0
$844$	−240.066	−	138.602i	−0.284439	−	0.164221i
$845$	53.6558	−	362.958i	0.0634979	−	0.429536i
$846$		0			0
$847$	−55.5433	−	55.5433i	−0.0655765	−	0.0655765i
$848$	331.848	+	1238.47i	0.391330	+	1.46046i
$849$		0			0
$850$	685.450	−	160.542i	0.806412	−	0.188872i
$851$	−135.870	−	235.334i	−0.159660	−	0.276539i
$852$		0			0
$853$	90.6761	+	338.408i	0.106303	+	0.396726i	0.998490	−	0.0549394i	$-0.0174966\pi$
$853$	90.6761	+	338.408i	0.106303	+	0.396726i	−0.892187	+	0.451666i	$0.850830\pi$
$854$			1487.36i			1.74164i
$855$		0			0
$856$	−716.241			−0.836730
$857$	1041.37	−	279.033i	1.21513	−	0.325593i	0.406358	−	0.913714i	$-0.366799\pi$
$857$	1041.37	−	279.033i	1.21513	−	0.325593i	0.808773	+	0.588121i	$0.200132\pi$
$858$		0			0
$859$	−508.578	+	293.627i	−0.592058	+	0.341825i	−0.765911	−	0.642947i	$-0.777712\pi$
$859$	−508.578	+	293.627i	−0.592058	+	0.341825i	0.173853	+	0.984772i	$0.444378\pi$
$860$	166.348	−	384.240i	0.193428	−	0.446791i
$861$		0			0
$862$	−1756.36	+	470.615i	−2.03754	+	0.545957i
$863$	659.791	−	659.791i	0.764532	−	0.764532i	−0.212606	−	0.977138i	$-0.568195\pi$
$863$	659.791	−	659.791i	0.764532	−	0.764532i	0.977138	+	0.212606i	$0.0681951\pi$
$864$		0			0
$865$	−286.222	+	212.497i	−0.330892	+	0.245661i
$866$	122.162	−	211.591i	0.141065	−	0.244331i
$867$		0			0
$868$	335.361	+	89.8598i	0.386361	+	0.103525i
$869$	−1193.09	+	688.833i	−1.37295	+	0.792674i
$870$		0			0
$871$	239.932	−	415.575i	0.275467	−	0.477123i
$872$	−608.657	−	608.657i	−0.698001	−	0.698001i
$873$		0			0
$874$		−	128.554i		−	0.147087i
$875$	−1319.67	−	238.093i	−1.50819	−	0.272107i
$876$		0			0
$877$	−3.29344	+	12.2913i	−0.00375535	+	0.0140152i	−0.967778	−	0.251805i	$-0.918976\pi$
$877$	−3.29344	+	12.2913i	−0.00375535	+	0.0140152i	0.964023	+	0.265820i	$0.0856426\pi$
$878$	801.886	+	214.865i	0.913309	+	0.244721i
$879$		0			0
$880$	−703.367	+	887.139i	−0.799281	+	1.00811i
$881$	−933.779			−1.05991			−0.529954	−	0.848026i	$-0.677791\pi$
$881$	−933.779			−1.05991			−0.529954	+	0.848026i	$0.677791\pi$
$882$		0			0
$883$	−463.817	+	463.817i	−0.525274	+	0.525274i	−0.919159	−	0.393886i	$-0.871131\pi$
$883$	−463.817	+	463.817i	−0.525274	+	0.525274i	0.393886	+	0.919159i	$0.371131\pi$
$884$	203.356	+	117.408i	0.230041	+	0.132814i
$885$		0			0
$886$	−381.500	−	660.777i	−0.430586	−	0.745798i
$887$	−69.4192	+	259.076i	−0.0782630	+	0.292081i	−0.993953	−	0.109803i	$-0.964978\pi$
$887$	−69.4192	+	259.076i	−0.0782630	+	0.292081i	0.915690	+	0.401884i	$0.131645\pi$
$888$		0			0
$889$	−1245.25	−	718.948i	−1.40074	−	0.808715i
$890$	−159.501	+	118.417i	−0.179215	+	0.133053i
$891$		0			0
$892$	−46.1152	−	46.1152i	−0.0516986	−	0.0516986i
$893$	−1.68705	−	6.29616i	−0.00188920	−	0.00705057i
$894$		0			0
$895$	−214.877	+	85.0363i	−0.240086	+	0.0950127i
$896$	−712.950	−	1234.87i	−0.795703	−	1.37820i
$897$		0			0
$898$	−250.648	−	935.432i	−0.279118	−	1.04168i
$899$		−	510.042i		−	0.567344i
$900$		0			0
$901$	−730.915			−0.811227
$902$	−263.638	+	70.6415i	−0.292281	+	0.0783165i
$903$		0			0
$904$	−682.010	+	393.759i	−0.754436	+	0.435574i
$905$	−305.925	−	773.036i	−0.338038	−	0.854183i
$906$		0			0
$907$	−182.473	+	48.8935i	−0.201183	+	0.0539069i	−0.358003	−	0.933720i	$-0.616542\pi$
$907$	−182.473	+	48.8935i	−0.201183	+	0.0539069i	0.156820	+	0.987627i	$0.449876\pi$
$908$	97.4601	−	97.4601i	0.107335	−	0.107335i
$909$		0			0
$910$	−772.679	−	1040.76i	−0.849097	−	1.14369i
$911$	432.982	−	749.947i	0.475282	−	0.823213i	−0.524317	−	0.851523i	$-0.675679\pi$
$911$	432.982	−	749.947i	0.475282	−	0.823213i	0.999599	+	0.0283104i	$0.00901269\pi$
$912$		0			0
$913$	1189.76	+	318.796i	1.30313	+	0.349174i
$914$	364.849	−	210.646i	0.399178	−	0.230466i
$915$		0			0
$916$	293.001	−	507.492i	0.319870	−	0.554031i
$917$	858.818	+	858.818i	0.936551	+	0.936551i
$918$		0			0
$919$		−	864.507i		−	0.940704i	−0.882479	−	0.470352i	$-0.844127\pi$
$919$		−	864.507i		−	0.940704i	0.882479	−	0.470352i	$-0.155873\pi$
$920$	255.174	+	202.314i	0.277363	+	0.219907i
$921$		0			0
$922$	−484.717	+	1808.99i	−0.525724	+	1.96203i
$923$	210.437	+	56.3864i	0.227992	+	0.0610903i
$924$		0			0
$925$	−487.625	−	15.4790i	−0.527162	−	0.0167340i
$926$	430.687			0.465104
$927$		0			0
$928$	720.719	−	720.719i	0.776637	−	0.776637i
$929$	−884.539	−	510.689i	−0.952142	−	0.549719i	−0.0583960	−	0.998293i	$-0.518599\pi$
$929$	−884.539	−	510.689i	−0.952142	−	0.549719i	−0.893746	+	0.448574i	$0.851932\pi$
$930$		0			0
$931$	123.435	+	213.796i	0.132584	+	0.229642i
$932$	82.3748	−	307.427i	0.0883850	−	0.329857i
$933$		0			0
$934$	579.804	+	334.750i	0.620775	+	0.358404i
$935$	−384.717	−	518.194i	−0.411462	−	0.554218i
$936$		0			0
$937$	776.808	+	776.808i	0.829037	+	0.829037i	0.987384	−	0.158347i	$-0.0506163\pi$
$937$	776.808	+	776.808i	0.829037	+	0.829037i	−0.158347	+	0.987384i	$0.550616\pi$
$938$	336.728	+	1256.69i	0.358985	+	1.33975i
$939$		0			0
$940$	−16.8726	−	7.30461i	−0.0179496	−	0.00777086i
$941$	851.116	+	1474.18i	0.904480	+	1.56661i	0.821614	+	0.570044i	$0.193074\pi$
$941$	851.116	+	1474.18i	0.904480	+	1.56661i	0.0828659	+	0.996561i	$0.473593\pi$
$942$		0			0
$943$	35.1375	+	131.135i	0.0372614	+	0.139061i
$944$			236.514i			0.250545i
$945$		0			0
$946$	−1112.41			−1.17591
$947$	703.326	−	188.456i	0.742688	−	0.199003i	0.132416	−	0.991194i	$-0.457727\pi$
$947$	703.326	−	188.456i	0.742688	−	0.199003i	0.610273	+	0.792192i	$0.291060\pi$
$948$		0			0
$949$	−445.784	+	257.374i	−0.469741	+	0.271205i
$950$	−196.116	−	121.683i	−0.206438	−	0.128088i
$951$		0			0
$952$	552.257	−	147.977i	0.580102	−	0.155438i
$953$	783.686	−	783.686i	0.822336	−	0.822336i	−0.164106	−	0.986443i	$-0.552474\pi$
$953$	783.686	−	783.686i	0.822336	−	0.822336i	0.986443	+	0.164106i	$0.0524741\pi$
$954$		0			0
$955$	576.512	+	85.2253i	0.603678	+	0.0892412i
$956$	−165.833	+	287.231i	−0.173465	+	0.300450i
$957$		0			0
$958$	−373.050	−	99.9583i	−0.389405	−	0.104341i
$959$	−224.669	+	129.713i	−0.234274	+	0.135258i
$960$		0			0
$961$	362.580	−	628.006i	0.377294	−	0.653492i
$962$	−333.466	−	333.466i	−0.346638	−	0.346638i
$963$		0			0
$964$			42.8137i			0.0444126i
$965$	−71.7194	−	620.714i	−0.0743206	−	0.643227i
$966$		0			0
$967$	316.923	−	1182.77i	0.327738	−	1.22314i	−0.583792	−	0.811903i	$-0.698432\pi$
$967$	316.923	−	1182.77i	0.327738	−	1.22314i	0.911530	−	0.411233i	$-0.134902\pi$
$968$	33.0799	+	8.86374i	0.0341735	+	0.00915676i
$969$		0			0
$970$	1728.18	+	1370.19i	1.78163	+	1.41256i
$971$	313.188			0.322542			0.161271	−	0.986910i	$-0.448441\pi$
$971$	313.188			0.322542			0.161271	+	0.986910i	$0.448441\pi$
$972$		0			0
$973$	−859.926	+	859.926i	−0.883788	+	0.883788i
$974$	−1365.42	−	788.327i	−1.40187	−	0.809371i
$975$		0			0
$976$	−560.696	−	971.155i	−0.574484	−	0.995035i
$977$	−399.627	+	1491.43i	−0.409035	+	1.52654i	0.387455	+	0.921889i	$0.373354\pi$
$977$	−399.627	+	1491.43i	−0.409035	+	1.52654i	−0.796490	+	0.604652i	$0.793312\pi$
$978$		0			0
$979$	157.717	+	91.0580i	0.161100	+	0.0930112i
$980$	688.857	+	101.833i	0.702916	+	0.103911i
$981$		0			0
$982$	−699.242	−	699.242i	−0.712059	−	0.712059i
$983$	177.336	+	661.825i	0.180402	+	0.673271i	0.995568	+	0.0940430i	$0.0299791\pi$
$983$	177.336	+	661.825i	0.180402	+	0.673271i	−0.815166	+	0.579228i	$0.803354\pi$
$984$		0			0
$985$	234.380	−	541.386i	0.237950	−	0.549630i
$986$	467.626	+	809.953i	0.474266	+	0.821453i
$987$		0			0
$988$	−19.9244	−	74.3590i	−0.0201664	−	0.0752621i
$989$			553.320i			0.559474i
$990$		0			0
$991$	888.305			0.896373			0.448186	−	0.893940i	$-0.352070\pi$
$991$	888.305			0.896373			0.448186	+	0.893940i	$0.352070\pi$
$992$	−455.237	+	121.980i	−0.458909	+	0.122964i
$993$		0			0
$994$	−511.533	+	295.334i	−0.514620	+	0.297116i
$995$	−1262.07	+	499.457i	−1.26841	+	0.501967i
$996$		0			0
$997$	197.259	−	52.8555i	0.197853	−	0.0530146i	−0.158532	−	0.987354i	$-0.550676\pi$
$997$	197.259	−	52.8555i	0.197853	−	0.0530146i	0.356385	+	0.934339i	$0.384009\pi$
$998$	477.617	−	477.617i	0.478574	−	0.478574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.l.a.127.8		40
3.2	odd	2		45.3.k.a.7.3	✓	40
5.3	odd	4	inner	135.3.l.a.73.3		40
9.2	odd	6		405.3.g.h.82.8		20
9.4	even	3	inner	135.3.l.a.37.3		40
9.5	odd	6		45.3.k.a.22.8	yes	40
9.7	even	3		405.3.g.g.82.3		20
15.2	even	4		225.3.o.b.43.3		40
15.8	even	4		45.3.k.a.43.8	yes	40
15.14	odd	2		225.3.o.b.7.8		40
45.13	odd	12	inner	135.3.l.a.118.8		40
45.14	odd	6		225.3.o.b.157.3		40
45.23	even	12		45.3.k.a.13.3	yes	40
45.32	even	12		225.3.o.b.193.8		40
45.38	even	12		405.3.g.h.163.8		20
45.43	odd	12		405.3.g.g.163.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.3	✓	40	3.2	odd	2
45.3.k.a.13.3	yes	40	45.23	even	12
45.3.k.a.22.8	yes	40	9.5	odd	6
45.3.k.a.43.8	yes	40	15.8	even	4
135.3.l.a.37.3		40	9.4	even	3	inner
135.3.l.a.73.3		40	5.3	odd	4	inner
135.3.l.a.118.8		40	45.13	odd	12	inner
135.3.l.a.127.8		40	1.1	even	1	trivial
225.3.o.b.7.8		40	15.14	odd	2
225.3.o.b.43.3		40	15.2	even	4
225.3.o.b.157.3		40	45.14	odd	6
225.3.o.b.193.8		40	45.32	even	12
405.3.g.g.82.3		20	9.7	even	3
405.3.g.g.163.3		20	45.43	odd	12
405.3.g.h.82.8		20	9.2	odd	6
405.3.g.h.163.8		20	45.38	even	12

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.38711 - 0.639624i) q^{2} +(1.82507 - 1.05371i) q^{4} +(1.83989 + 4.64917i) q^{5} +(10.3622 - 2.77655i) q^{7} +(-3.30727 + 3.30727i) q^{8} +(7.36573 + 9.92126i) q^{10} +(5.66397 - 9.81028i) q^{11} +(-9.44533 - 2.53087i) q^{13} +(22.9598 - 13.2559i) q^{14} +(-9.99423 + 17.3105i) q^{16} +(-8.05728 - 8.05728i) q^{17} +3.73565i q^{19} +(8.25680 + 6.54639i) q^{20} +(7.24562 - 27.0410i) q^{22} +(-13.4504 - 3.60402i) q^{23} +(-18.2296 + 17.1079i) q^{25} -24.1658 q^{26} +(15.9862 - 15.9862i) q^{28} +(-28.7625 - 16.6061i) q^{29} +(7.67855 + 13.2996i) q^{31} +(-7.94293 + 29.6434i) q^{32} +(-24.3873 - 14.0800i) q^{34} +(31.9740 + 43.0673i) q^{35} +(13.7991 + 13.7991i) q^{37} +(2.38941 + 8.91741i) q^{38} +(-21.4611 - 9.29107i) q^{40} +(-4.87477 - 8.44335i) q^{41} +(-10.2845 - 38.3822i) q^{43} -23.8727i q^{44} -34.4127 q^{46} +(-1.68543 + 0.451608i) q^{47} +(57.2314 - 33.0426i) q^{49} +(-32.5735 + 52.4986i) q^{50} +(-19.9052 + 5.33359i) q^{52} +(45.3574 - 45.3574i) q^{53} +(56.0308 + 8.28298i) q^{55} +(-25.0879 + 43.4535i) q^{56} +(-79.2810 - 21.2433i) q^{58} +(10.2473 - 5.91626i) q^{59} +(-28.0510 + 48.5858i) q^{61} +(26.8363 + 26.8363i) q^{62} -4.11124i q^{64} +(-5.61188 - 48.5695i) q^{65} +(-12.7011 + 47.4011i) q^{67} +(-23.1952 - 6.21513i) q^{68} +(103.872 + 82.3550i) q^{70} -22.2795 q^{71} +(37.2225 - 37.2225i) q^{73} +(41.7661 + 24.1137i) q^{74} +(3.93628 + 6.81784i) q^{76} +(31.4526 - 117.383i) q^{77} +(-105.323 - 60.8084i) q^{79} +(-98.8678 - 14.6155i) q^{80} +(-17.0372 - 17.0372i) q^{82} +(28.1424 + 105.029i) q^{83} +(22.6352 - 52.2842i) q^{85} +(-49.1003 - 85.0443i) q^{86} +(13.7130 + 51.1775i) q^{88} +16.0767i q^{89} -104.902 q^{91} +(-28.3455 + 7.59516i) q^{92} +(-3.73444 + 2.15608i) q^{94} +(-17.3677 + 6.87317i) q^{95} +(172.402 - 46.1951i) q^{97} +(115.483 - 115.483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

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