LMFDB - Embedded newform 441.3.k.a.31.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(31,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.12
Character	$\chi$	$=$	441.31
Dual form			441.3.k.a.313.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30753 - 2.26471i) q^{2} +(2.30352 + 1.92193i) q^{3} +(-1.41927 - 2.45825i) q^{4} -3.68512i q^{5} +(7.36452 - 2.70382i) q^{6} +3.03728 q^{8} +(1.61239 + 8.85439i) q^{9} +O(q^{10})$	\(q+(1.30753 - 2.26471i) q^{2} +(2.30352 + 1.92193i) q^{3} +(-1.41927 - 2.45825i) q^{4} -3.68512i q^{5} +(7.36452 - 2.70382i) q^{6} +3.03728 q^{8} +(1.61239 + 8.85439i) q^{9} +(-8.34571 - 4.81840i) q^{10} +13.2613 q^{11} +(1.45526 - 8.39036i) q^{12} +(-16.2463 - 9.37981i) q^{13} +(7.08252 - 8.48873i) q^{15} +(9.64842 - 16.7116i) q^{16} +(7.13083 + 4.11699i) q^{17} +(22.1609 + 7.92578i) q^{18} +(19.6096 - 11.3216i) q^{19} +(-9.05893 + 5.23018i) q^{20} +(17.3396 - 30.0330i) q^{22} -0.738115 q^{23} +(6.99644 + 5.83744i) q^{24} +11.4199 q^{25} +(-42.4851 + 24.5288i) q^{26} +(-13.3033 + 23.4952i) q^{27} +(-6.13829 - 10.6318i) q^{29} +(-9.96389 - 27.1391i) q^{30} +(-28.6323 + 16.5308i) q^{31} +(-19.1566 - 33.1803i) q^{32} +(30.5477 + 25.4873i) q^{33} +(18.6476 - 10.7662i) q^{34} +(19.4779 - 16.5304i) q^{36} +(4.98430 + 8.63306i) q^{37} -59.2132i q^{38} +(-19.3964 - 52.8308i) q^{39} -11.1927i q^{40} +(23.3769 + 13.4966i) q^{41} +(10.1549 + 17.5888i) q^{43} +(-18.8214 - 32.5996i) q^{44} +(32.6294 - 5.94186i) q^{45} +(-0.965107 + 1.67161i) q^{46} +(-69.3523 - 40.0406i) q^{47} +(54.3437 - 19.9518i) q^{48} +(14.9319 - 25.8628i) q^{50} +(8.51346 + 23.1885i) q^{51} +53.2499i q^{52} +(-19.5210 + 33.8113i) q^{53} +(35.8152 + 60.8487i) q^{54} -48.8695i q^{55} +(66.9302 + 11.6087i) q^{57} -32.1040 q^{58} +(-40.3543 + 23.2986i) q^{59} +(-30.9194 - 5.36279i) q^{60} +(34.7549 + 20.0658i) q^{61} +86.4583i q^{62} -23.0042 q^{64} +(-34.5657 + 59.8695i) q^{65} +(97.6633 - 35.8562i) q^{66} +(-54.5167 - 94.4257i) q^{67} -23.3725i q^{68} +(-1.70026 - 1.41860i) q^{69} +83.8258 q^{71} +(4.89730 + 26.8933i) q^{72} +(32.3201 + 18.6600i) q^{73} +26.0685 q^{74} +(26.3060 + 21.9483i) q^{75} +(-55.6625 - 32.1368i) q^{76} +(-145.008 - 25.1507i) q^{78} +(-49.4165 + 85.5918i) q^{79} +(-61.5840 - 35.5556i) q^{80} +(-75.8004 + 28.5535i) q^{81} +(61.1319 - 35.2945i) q^{82} +(-124.459 + 71.8564i) q^{83} +(15.1716 - 26.2779i) q^{85} +53.1113 q^{86} +(6.29393 - 36.2879i) q^{87} +40.2784 q^{88} +(-115.280 + 66.5571i) q^{89} +(29.2074 - 81.6653i) q^{90} +(1.04758 + 1.81447i) q^{92} +(-97.7260 - 16.9500i) q^{93} +(-181.360 + 104.708i) q^{94} +(-41.7213 - 72.2635i) q^{95} +(19.6424 - 113.249i) q^{96} +(58.0415 - 33.5103i) q^{97} +(21.3825 + 117.421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30753	−	2.26471i	0.653765	−	1.13235i	−0.328437	−	0.944526i	$-0.606522\pi$
$2$	1.30753	−	2.26471i	0.653765	−	1.13235i	0.982202	−	0.187828i	$-0.0601449\pi$
$3$	2.30352	+	1.92193i	0.767839	+	0.640642i
$3$	2.30352	+	1.92193i	0.767839	+	0.640642i
$4$	−1.41927	−	2.45825i	−0.354818	−	0.614562i
$5$		−	3.68512i		−	0.737023i	−0.929623	−	0.368512i	$-0.879868\pi$
$5$		−	3.68512i		−	0.737023i	0.929623	−	0.368512i	$-0.120132\pi$
$6$	7.36452	−	2.70382i	1.22742	−	0.450637i
$7$		0			0
$7$		0			0
$8$	3.03728			0.379661
$9$	1.61239	+	8.85439i	0.179155	+	0.983821i
$10$	−8.34571	−	4.81840i	−0.834571	−	0.481840i
$11$	13.2613			1.20557			0.602787	−	0.797902i	$-0.294057\pi$
$11$	13.2613			1.20557			0.602787	+	0.797902i	$0.294057\pi$
$12$	1.45526	−	8.39036i	0.121272	−	0.699196i
$13$	−16.2463	−	9.37981i	−1.24972	−	0.721524i	−0.278663	−	0.960389i	$-0.589891\pi$
$13$	−16.2463	−	9.37981i	−1.24972	−	0.721524i	−0.971053	+	0.238865i	$0.923225\pi$
$14$		0			0
$15$	7.08252	−	8.48873i	0.472168	−	0.565915i
$16$	9.64842	−	16.7116i	0.603027	−	1.04447i
$17$	7.13083	+	4.11699i	0.419461	+	0.242176i	0.694847	−	0.719158i	$-0.255472\pi$
$17$	7.13083	+	4.11699i	0.419461	+	0.242176i	−0.275386	+	0.961334i	$0.588806\pi$
$18$	22.1609	+	7.92578i	1.23116	+	0.440321i
$19$	19.6096	−	11.3216i	1.03208	−	0.595873i	0.114501	−	0.993423i	$-0.463473\pi$
$19$	19.6096	−	11.3216i	1.03208	−	0.595873i	0.917580	+	0.397550i	$0.130140\pi$
$20$	−9.05893	+	5.23018i	−0.452947	+	0.261509i
$21$		0			0
$22$	17.3396	−	30.0330i	0.788162	−	1.36514i
$23$	−0.738115			−0.0320919			−0.0160460	−	0.999871i	$-0.505108\pi$
$23$	−0.738115			−0.0320919			−0.0160460	+	0.999871i	$0.505108\pi$
$24$	6.99644	+	5.83744i	0.291518	+	0.243227i
$25$	11.4199			0.456797
$26$	−42.4851	+	24.5288i	−1.63404	+	0.943414i
$27$	−13.3033	+	23.4952i	−0.492715	+	0.870191i
$28$		0			0
$29$	−6.13829	−	10.6318i	−0.211665	−	0.366615i	0.740571	−	0.671978i	$-0.234555\pi$
$29$	−6.13829	−	10.6318i	−0.211665	−	0.366615i	−0.952236	+	0.305364i	$0.901222\pi$
$30$	−9.96389	−	27.1391i	−0.332130	−	0.904637i
$31$	−28.6323	+	16.5308i	−0.923621	+	0.533253i	−0.884788	−	0.465993i	$-0.845697\pi$
$31$	−28.6323	+	16.5308i	−0.923621	+	0.533253i	−0.0388326	+	0.999246i	$0.512364\pi$
$32$	−19.1566	−	33.1803i	−0.598645	−	1.03688i
$33$	30.5477	+	25.4873i	0.925687	+	0.772342i
$34$	18.6476	−	10.7662i	0.548458	−	0.316652i
$35$		0			0
$36$	19.4779	−	16.5304i	0.541052	−	0.459179i
$37$	4.98430	+	8.63306i	0.134711	+	0.233326i	0.925487	−	0.378780i	$-0.123656\pi$
$37$	4.98430	+	8.63306i	0.134711	+	0.233326i	−0.790776	+	0.612105i	$0.790323\pi$
$38$		−	59.2132i		−	1.55824i
$39$	−19.3964	−	52.8308i	−0.497342	−	1.35463i
$40$		−	11.1927i		−	0.279819i
$41$	23.3769	+	13.4966i	0.570167	+	0.329186i	0.757216	−	0.653164i	$-0.226559\pi$
$41$	23.3769	+	13.4966i	0.570167	+	0.329186i	−0.187049	+	0.982351i	$0.559892\pi$
$42$		0			0
$43$	10.1549	+	17.5888i	0.236160	+	0.409042i	0.959609	−	0.281336i	$-0.0907776\pi$
$43$	10.1549	+	17.5888i	0.236160	+	0.409042i	−0.723449	+	0.690378i	$0.757444\pi$
$44$	−18.8214	−	32.5996i	−0.427759	−	0.740900i
$45$	32.6294	−	5.94186i	0.725099	−	0.132041i
$46$	−0.965107	+	1.67161i	−0.0209806	+	0.0363395i
$47$	−69.3523	−	40.0406i	−1.47558	−	0.851927i	−0.475959	−	0.879467i	$-0.657899\pi$
$47$	−69.3523	−	40.0406i	−1.47558	−	0.851927i	−0.999621	+	0.0275406i	$0.991232\pi$
$48$	54.3437	−	19.9518i	1.13216	−	0.415663i
$49$		0			0
$50$	14.9319	−	25.8628i	0.298638	−	0.517256i
$51$	8.51346	+	23.1885i	0.166931	+	0.454676i
$52$			53.2499i			1.02404i
$53$	−19.5210	+	33.8113i	−0.368320	+	0.637950i	−0.989303	−	0.145875i	$-0.953400\pi$
$53$	−19.5210	+	33.8113i	−0.368320	+	0.637950i	0.620983	+	0.783824i	$0.286734\pi$
$54$	35.8152	+	60.8487i	0.663245	+	1.12683i
$55$		−	48.8695i		−	0.888536i
$56$		0			0
$57$	66.9302	+	11.6087i	1.17421	+	0.203661i
$58$	−32.1040			−0.553517
$59$	−40.3543	+	23.2986i	−0.683971	+	0.394891i	−0.801350	−	0.598196i	$-0.795884\pi$
$59$	−40.3543	+	23.2986i	−0.683971	+	0.394891i	0.117378	+	0.993087i	$0.462551\pi$
$60$	−30.9194	−	5.36279i	−0.515324	−	0.0893799i
$61$	34.7549	+	20.0658i	0.569753	+	0.328947i	0.757051	−	0.653356i	$-0.226640\pi$
$61$	34.7549	+	20.0658i	0.569753	+	0.328947i	−0.187298	+	0.982303i	$0.559973\pi$
$62$			86.4583i			1.39449i
$63$		0			0
$64$	−23.0042			−0.359440
$65$	−34.5657	+	59.8695i	−0.531779	+	0.921069i
$66$	97.6633	−	35.8562i	1.47975	−	0.543276i
$67$	−54.5167	−	94.4257i	−0.813682	−	1.40934i	−0.910270	−	0.414014i	$-0.864126\pi$
$67$	−54.5167	−	94.4257i	−0.813682	−	1.40934i	0.0965884	−	0.995324i	$-0.469207\pi$
$68$		−	23.3725i		−	0.343713i
$69$	−1.70026	−	1.41860i	−0.0246415	−	0.0205595i
$70$		0			0
$71$	83.8258			1.18064			0.590322	−	0.807168i	$-0.299001\pi$
$71$	83.8258			1.18064			0.590322	+	0.807168i	$0.299001\pi$
$72$	4.89730	+	26.8933i	0.0680181	+	0.373518i
$73$	32.3201	+	18.6600i	0.442741	+	0.255617i	0.704760	−	0.709446i	$-0.251055\pi$
$73$	32.3201	+	18.6600i	0.442741	+	0.255617i	−0.262019	+	0.965063i	$0.584388\pi$
$74$	26.0685			0.352277
$75$	26.3060	+	21.9483i	0.350747	+	0.292643i
$76$	−55.6625	−	32.1368i	−0.732402	−	0.422852i
$77$		0			0
$78$	−145.008	−	25.1507i	−1.85907	−	0.322445i
$79$	−49.4165	+	85.5918i	−0.625525	+	1.08344i	0.362914	+	0.931823i	$0.381782\pi$
$79$	−49.4165	+	85.5918i	−0.625525	+	1.08344i	−0.988439	+	0.151618i	$0.951552\pi$
$80$	−61.5840	−	35.5556i	−0.769800	−	0.444444i
$81$	−75.8004	+	28.5535i	−0.935807	+	0.352513i
$82$	61.1319	−	35.2945i	0.745511	−	0.430421i
$83$	−124.459	+	71.8564i	−1.49951	+	0.865740i	−1.00000		0.000570370i	$-0.999818\pi$
$83$	−124.459	+	71.8564i	−1.49951	+	0.865740i	−0.499506	+	0.866310i	$0.666485\pi$
$84$		0			0
$85$	15.1716	−	26.2779i	0.178489	−	0.309152i
$86$	53.1113			0.617574
$87$	6.29393	−	36.2879i	0.0723440	−	0.417103i
$88$	40.2784			0.457709
$89$	−115.280	+	66.5571i	−1.29528	+	0.747832i	−0.979586	−	0.201027i	$-0.935572\pi$
$89$	−115.280	+	66.5571i	−1.29528	+	0.747832i	−0.315698	+	0.948860i	$0.602239\pi$
$90$	29.2074	−	81.6653i	0.324527	−	0.907393i
$91$		0			0
$92$	1.04758	+	1.81447i	0.0113868	+	0.0197225i
$93$	−97.7260	−	16.9500i	−1.05082	−	0.182258i
$94$	−181.360	+	104.708i	−1.92937	+	1.11392i
$95$	−41.7213	−	72.2635i	−0.439172	−	0.760668i
$96$	19.6424	−	113.249i	0.204608	−	1.17968i
$97$	58.0415	−	33.5103i	0.598366	−	0.345467i	−0.170032	−	0.985438i	$-0.554387\pi$
$97$	58.0415	−	33.5103i	0.598366	−	0.345467i	0.768399	+	0.639972i	$0.221054\pi$
$98$		0			0
$99$	21.3825	+	117.421i	0.215985	+	1.18607i
$100$	−16.2080	−	28.0730i	−0.162080	−	0.280730i
$101$		−	21.4783i		−	0.212657i	−0.994331	−	0.106328i	$-0.966091\pi$
$101$		−	21.4783i		−	0.212657i	0.994331	−	0.106328i	$-0.0339095\pi$
$102$	63.6468	+	11.0392i	0.623988	+	0.108227i
$103$		−	15.0014i		−	0.145644i	−0.997345	−	0.0728222i	$-0.976799\pi$
$103$		−	15.0014i		−	0.145644i	0.997345	−	0.0728222i	$-0.0232006\pi$
$104$	−49.3446	−	28.4891i	−0.474468	−	0.273934i
$105$		0			0
$106$	51.0485	+	88.4187i	0.481590	+	0.834138i
$107$	25.8939	+	44.8496i	0.241999	+	0.419155i	0.961284	−	0.275561i	$-0.0888636\pi$
$107$	25.8939	+	44.8496i	0.241999	+	0.419155i	−0.719285	+	0.694716i	$0.755530\pi$
$108$	76.6379	−	0.643146i	0.709610	−	0.00595506i
$109$	−70.7366	+	122.519i	−0.648960	+	1.12403i	0.334412	+	0.942427i	$0.391462\pi$
$109$	−70.7366	+	122.519i	−0.648960	+	1.12403i	−0.983372	+	0.181604i	$0.941871\pi$
$110$	−110.675	−	63.8983i	−1.00614	−	0.580894i
$111$	−5.11068	+	29.4659i	−0.0460422	+	0.265458i
$112$		0			0
$113$	−53.4919	+	92.6507i	−0.473380	+	0.819918i	−0.999536	−	0.0304701i	$-0.990300\pi$
$113$	−53.4919	+	92.6507i	−0.473380	+	0.819918i	0.526156	+	0.850388i	$0.323633\pi$
$114$	113.804	−	136.399i	0.998276	−	1.19648i
$115$			2.72004i			0.0236525i
$116$	−17.4238	+	30.1789i	−0.150205	+	0.260163i
$117$	56.8570	−	158.975i	0.485957	−	1.35876i
$118$			121.854i			1.03266i
$119$		0			0
$120$	21.5116	−	25.7827i	0.179264	−	0.214856i
$121$	54.8625			0.453409
$122$	90.8862	−	52.4732i	0.744969	−	0.430108i
$123$	27.9095	+	76.0183i	0.226906	+	0.618035i
$124$	81.2738	+	46.9235i	0.655434	+	0.378415i
$125$		−	134.212i		−	1.07369i
$126$		0			0
$127$	−179.059			−1.40991			−0.704956	−	0.709251i	$-0.749033\pi$
$127$	−179.059			−1.40991			−0.704956	+	0.709251i	$0.749033\pi$
$128$	46.5479	−	80.6234i	0.363656	−	0.629870i
$129$	−10.4124	+	60.0331i	−0.0807162	+	0.465373i
$130$	90.3913	+	156.562i	0.695318	+	1.20433i
$131$			116.644i			0.890411i	0.895428	+	0.445206i	$0.146869\pi$
$131$			116.644i			0.890411i	−0.895428	+	0.445206i	$0.853131\pi$
$132$	19.2986	−	111.267i	0.146202	−	0.842933i
$133$		0			0
$134$	−285.129			−2.12783
$135$	86.5823	+	49.0242i	0.641351	+	0.363142i
$136$	21.6584	+	12.5045i	0.159253	+	0.0919446i
$137$	71.6320			0.522861			0.261430	−	0.965222i	$-0.415806\pi$
$137$	71.6320			0.522861			0.261430	+	0.965222i	$0.415806\pi$
$138$	−5.43586	+	1.99573i	−0.0393903	+	0.0144618i
$139$	188.775	+	108.989i	1.35809	+	0.784094i	0.989366	−	0.145445i	$-0.0464612\pi$
$139$	188.775	+	108.989i	1.35809	+	0.784094i	0.368724	+	0.929539i	$0.379795\pi$
$140$		0			0
$141$	−82.7992	−	225.524i	−0.587229	−	1.59946i
$142$	109.605	−	189.841i	0.771864	−	1.33691i
$143$	−215.447	−	124.389i	−1.50662	−	0.869850i
$144$	163.528	+	58.4853i	1.13561	+	0.406148i
$145$	−39.1795	+	22.6203i	−0.270203	+	0.156002i
$146$	84.5190	−	48.7971i	0.578897	−	0.334226i
$147$		0			0
$148$	14.1481	−	24.5053i	0.0955955	−	0.165576i
$149$	26.4183			0.177304			0.0886520	−	0.996063i	$-0.471744\pi$
$149$	26.4183			0.177304			0.0886520	+	0.996063i	$0.471744\pi$
$150$	84.1023	−	30.8774i	0.560682	−	0.205850i
$151$	83.3032			0.551677			0.275838	−	0.961204i	$-0.411045\pi$
$151$	83.3032			0.551677			0.275838	+	0.961204i	$0.411045\pi$
$152$	59.5598	−	34.3869i	0.391841	−	0.226229i
$153$	−24.9557	+	69.7774i	−0.163109	+	0.456061i
$154$		0			0
$155$	60.9180	+	105.513i	0.393020	+	0.680730i
$156$	−102.342	+	122.662i	−0.656042	+	0.786296i
$157$	128.067	−	73.9397i	0.815715	−	0.470953i	−0.0332215	−	0.999448i	$-0.510577\pi$
$157$	128.067	−	73.9397i	0.815715	−	0.470953i	0.848937	+	0.528495i	$0.177243\pi$
$158$	129.227	+	223.828i	0.817893	+	1.41663i
$159$	−109.950	+	40.3671i	−0.691508	+	0.253881i
$160$	−122.273	+	70.5944i	−0.764207	+	0.441215i
$161$		0			0
$162$	−34.4458	+	209.000i	−0.212629	+	1.29013i
$163$	40.4807	+	70.1147i	0.248348	+	0.430151i	0.963068	−	0.269260i	$-0.0867790\pi$
$163$	40.4807	+	70.1147i	0.248348	+	0.430151i	−0.714720	+	0.699411i	$0.753446\pi$
$164$		−	76.6215i		−	0.467204i
$165$	93.9235	−	112.572i	0.569234	−	0.682253i
$166$			375.818i			2.26396i
$167$	1.93139	+	1.11509i	0.0115652	+	0.00667716i	0.505771	−	0.862668i	$-0.331208\pi$
$167$	1.93139	+	1.11509i	0.0115652	+	0.00667716i	−0.494206	+	0.869345i	$0.664541\pi$
$168$		0			0
$169$	91.4615	+	158.416i	0.541192	+	0.937373i
$170$	−39.6746	−	68.7184i	−0.233380	−	0.404226i
$171$	131.864	+	155.376i	0.771135	+	0.908630i
$172$	28.8251	−	49.9265i	0.167588	−	0.290270i
$173$	146.304	+	84.4688i	0.845690	+	0.488259i	0.859194	−	0.511650i	$-0.170965\pi$
$173$	146.304	+	84.4688i	0.845690	+	0.488259i	−0.0135045	+	0.999909i	$0.504299\pi$
$174$	−73.9521	−	61.7015i	−0.425012	−	0.354606i
$175$		0			0
$176$	127.951	−	221.617i	0.726993	−	1.25919i
$177$	−137.735	−	23.8893i	−0.778164	−	0.134968i
$178$			348.102i			1.95563i
$179$	−37.4472	+	64.8605i	−0.209202	+	0.362349i	−0.951463	−	0.307762i	$-0.900420\pi$
$179$	−37.4472	+	64.8605i	−0.209202	+	0.362349i	0.742261	+	0.670111i	$0.233753\pi$
$180$	−60.9166	−	71.7782i	−0.338425	−	0.398768i
$181$		−	1.66857i		−	0.00921864i	−0.999989	−	0.00460932i	$-0.998533\pi$
$181$		−	1.66857i		−	0.00921864i	0.999989	−	0.00460932i	$-0.00146720\pi$
$182$		0			0
$183$	41.4937	+	113.018i	0.226741	+	0.617586i
$184$	−2.24186			−0.0121840
$185$	31.8138	−	18.3677i	0.171967	−	0.0992849i
$186$	−166.167	+	199.158i	−0.893368	+	1.07074i
$187$	94.5642	+	54.5967i	0.505691	+	0.291961i
$188$			227.314i			1.20911i
$189$		0			0
$190$	−218.208			−1.14846
$191$	−60.4724	+	104.741i	−0.316609	+	0.548383i	−0.979778	−	0.200086i	$-0.935878\pi$
$191$	−60.4724	+	104.741i	−0.316609	+	0.548383i	0.663169	+	0.748470i	$0.269211\pi$
$192$	−52.9905	−	44.2123i	−0.275992	−	0.230273i
$193$	−101.401	−	175.631i	−0.525393	−	0.910007i	−0.999563	−	0.0295736i	$-0.990585\pi$
$193$	−101.401	−	175.631i	−0.525393	−	0.910007i	0.474170	−	0.880433i	$-0.342748\pi$
$194$		−	175.263i		−	0.903417i
$195$	−194.687	+	71.4778i	−0.998397	+	0.366553i
$196$		0			0
$197$	−213.013			−1.08129			−0.540643	−	0.841252i	$-0.681819\pi$
$197$	−213.013			−1.08129			−0.540643	+	0.841252i	$0.681819\pi$
$198$	293.882	+	105.106i	1.48425	+	0.530839i
$199$	−173.472	−	100.154i	−0.871718	−	0.503287i	−0.00379954	−	0.999993i	$-0.501209\pi$
$199$	−173.472	−	100.154i	−0.871718	−	0.503287i	−0.867919	+	0.496706i	$0.834543\pi$
$200$	34.6856			0.173428
$201$	55.8990	−	322.288i	0.278105	−	1.60342i
$202$	−48.6422	−	28.0836i	−0.240803	−	0.139028i
$203$		0			0
$204$	44.9202	−	53.8390i	0.220197	−	0.263916i
$205$	49.7366	−	86.1464i	0.242618	−	0.420226i
$206$	−33.9737	−	19.6147i	−0.164921	−	0.0952172i
$207$	−1.19013	−	6.53555i	−0.00574943	−	0.0315727i
$208$	−313.502	+	181.001i	−1.50722	+	0.870196i
$209$	260.048	−	150.139i	1.24425	−	0.718369i
$210$		0			0
$211$	142.883	−	247.481i	0.677173	−	1.17290i	−0.298656	−	0.954361i	$-0.596538\pi$
$211$	142.883	−	247.481i	0.677173	−	1.17290i	0.975829	−	0.218537i	$-0.0701284\pi$
$212$	110.822			0.522746
$213$	193.094	+	161.107i	0.906546	+	0.756371i
$214$	135.428			0.632842
$215$	64.8167	−	37.4220i	0.301473	−	0.174056i
$216$	−40.4059	+	71.3615i	−0.187064	+	0.330377i
$217$		0			0
$218$	184.981	+	320.396i	0.848535	+	1.46970i
$219$	38.5867	+	105.101i	0.176195	+	0.479911i
$220$	−120.133	+	69.3590i	−0.546061	+	0.315268i
$221$	−77.2331	−	133.772i	−0.349471	−	0.605302i
$222$	60.0492	+	50.1017i	0.270492	+	0.225683i
$223$	326.190	−	188.326i	1.46273	−	0.844510i	0.463597	−	0.886046i	$-0.346559\pi$
$223$	326.190	−	188.326i	1.46273	−	0.844510i	0.999137	+	0.0415367i	$0.0132254\pi$
$224$		0			0
$225$	18.4134	+	101.116i	0.0818375	+	0.449406i
$226$	139.885	+	242.287i	0.618959	+	1.07207i
$227$		−	220.964i		−	0.973409i	−0.873567	−	0.486704i	$-0.838199\pi$
$227$		−	220.964i		−	0.973409i	0.873567	−	0.486704i	$-0.161801\pi$
$228$	−66.4551	−	181.007i	−0.291470	−	0.793890i
$229$			28.7647i			0.125610i	0.998026	+	0.0628049i	$0.0200046\pi$
$229$			28.7647i			0.125610i	−0.998026	+	0.0628049i	$0.979995\pi$
$230$	6.16009	+	3.55653i	0.0267830	+	0.0154632i
$231$		0			0
$232$	−18.6437	−	32.2919i	−0.0803609	−	0.139189i
$233$	−202.832	−	351.315i	−0.870524	−	1.50779i	−0.861456	−	0.507832i	$-0.830447\pi$
$233$	−202.832	−	351.315i	−0.870524	−	1.50779i	−0.00906787	−	0.999959i	$-0.502886\pi$
$234$	−285.690	−	336.629i	−1.22090	−	1.43859i
$235$	−147.554	+	255.571i	−0.627890	+	1.08754i
$236$	114.547	+	66.1340i	0.485370	+	0.280229i
$237$	−278.333	+	102.188i	−1.17440	+	0.431171i
$238$		0			0
$239$	66.2069	−	114.674i	0.277016	−	0.479807i	−0.693625	−	0.720336i	$-0.743988\pi$
$239$	66.2069	−	114.674i	0.277016	−	0.479807i	0.970642	+	0.240529i	$0.0773210\pi$
$240$	−73.5248	−	200.263i	−0.306353	−	0.834429i
$241$		−	82.8584i		−	0.343811i	−0.985113	−	0.171905i	$-0.945008\pi$
$241$		−	82.8584i		−	0.343811i	0.985113	−	0.171905i	$-0.0549923\pi$
$242$	71.7343	−	124.247i	0.296423	−	0.513419i
$243$	−229.485	−	79.9092i	−0.944384	−	0.328844i
$244$		−	113.915i		−	0.466865i
$245$		0			0
$246$	208.652	+	36.1895i	0.848178	+	0.147112i
$247$	−424.777			−1.71974
$248$	−86.9643	+	50.2089i	−0.350662	+	0.202455i
$249$	−424.796	−	73.6784i	−1.70601	−	0.295897i
$250$	−303.950	−	175.486i	−1.21580	−	0.701943i
$251$		−	182.888i		−	0.728636i	−0.931275	−	0.364318i	$-0.881302\pi$
$251$		−	182.888i		−	0.728636i	0.931275	−	0.364318i	$-0.118698\pi$
$252$		0			0
$253$	−9.78837			−0.0386892
$254$	−234.125	+	405.516i	−0.921752	+	1.59652i
$255$	85.4523	−	31.3731i	0.335107	−	0.123032i
$256$	−167.734	−	290.524i	−0.655211	−	1.13486i
$257$			47.5369i			0.184968i	0.995714	+	0.0924842i	$0.0294808\pi$
$257$			47.5369i			0.184968i	−0.995714	+	0.0924842i	$0.970519\pi$
$258$	122.343	+	102.076i	0.474197	+	0.395644i
$259$		0			0
$260$	196.232			0.754739
$261$	84.2410	−	71.4935i	0.322762	−	0.273921i
$262$	264.164	+	152.515i	1.00826	+	0.582120i
$263$	−409.592			−1.55739			−0.778693	−	0.627406i	$-0.784117\pi$
$263$	−409.592			−1.55739			−0.778693	+	0.627406i	$0.784117\pi$
$264$	92.7820	+	77.4121i	0.351447	+	0.293228i
$265$	124.599	+	71.9371i	0.470184	+	0.271461i
$266$		0			0
$267$	−393.468	−	68.2447i	−1.47366	−	0.255598i
$268$	−154.748	+	268.031i	−0.577418	+	1.00012i
$269$	133.745	+	77.2175i	0.497192	+	0.287054i	0.727553	−	0.686051i	$-0.240657\pi$
$269$	133.745	+	77.2175i	0.497192	+	0.287054i	−0.230361	+	0.973105i	$0.573991\pi$
$270$	224.235	−	131.983i	0.830498	−	0.488826i
$271$	53.8667	−	31.1000i	0.198770	−	0.114760i	−0.397312	−	0.917684i	$-0.630057\pi$
$271$	53.8667	−	31.1000i	0.198770	−	0.114760i	0.596082	+	0.802924i	$0.296723\pi$
$272$	137.603	−	79.4449i	0.505892	−	0.292077i
$273$		0			0
$274$	93.6609	−	162.226i	0.341828	−	0.592064i
$275$	151.443			0.550703
$276$	−1.07415	+	6.19304i	−0.00389184	+	0.0224386i
$277$	−5.75274			−0.0207680			−0.0103840	−	0.999946i	$-0.503305\pi$
$277$	−5.75274			−0.0207680			−0.0103840	+	0.999946i	$0.503305\pi$
$278$	493.657	−	285.013i	1.77574	−	1.02523i
$279$	−192.537	−	226.867i	−0.690097	−	0.813143i
$280$		0			0
$281$	−126.093	−	218.400i	−0.448731	−	0.777225i	0.549573	−	0.835446i	$-0.314791\pi$
$281$	−126.093	−	218.400i	−0.448731	−	0.777225i	−0.998304	+	0.0582207i	$0.981457\pi$
$282$	−619.009	−	107.363i	−2.19507	−	0.380722i
$283$	117.523	−	67.8520i	0.415276	−	0.239760i	−0.277778	−	0.960645i	$-0.589598\pi$
$283$	117.523	−	67.8520i	0.415276	−	0.239760i	0.693054	+	0.720886i	$0.256265\pi$
$284$	−118.971	−	206.065i	−0.418914	−	0.725580i
$285$	42.7792	−	246.646i	0.150103	−	0.865423i
$286$	−563.408	+	325.284i	−1.96996	+	1.13736i
$287$		0			0
$288$	262.903	−	223.120i	0.912858	−	0.774722i
$289$	−110.601	−	191.566i	−0.382702	−	0.662859i
$290$			118.307i			0.407955i
$291$	198.104	+	34.3600i	0.680770	+	0.118076i
$292$		−	105.934i		−	0.362789i
$293$	−72.9007	−	42.0892i	−0.248808	−	0.143649i	0.370410	−	0.928868i	$-0.379217\pi$
$293$	−72.9007	−	42.0892i	−0.248808	−	0.143649i	−0.619218	+	0.785219i	$0.712550\pi$
$294$		0			0
$295$	85.8579	+	148.710i	0.291044	+	0.504103i
$296$	15.1387	+	26.2211i	0.0511444	+	0.0885846i
$297$	−176.419	+	311.577i	−0.594004	+	1.04908i
$298$	34.5427	−	59.8297i	0.115915	−	0.200771i
$299$	11.9916	+	6.92337i	0.0401058	+	0.0231551i
$300$	16.6189	−	95.8172i	0.0553965	−	0.319391i
$301$		0			0
$302$	108.921	−	188.658i	0.360667	−	0.624694i
$303$	41.2798	−	49.4757i	0.136237	−	0.163286i
$304$		−	436.942i		−	1.43731i
$305$	73.9447	−	128.076i	0.242441	−	0.419921i
$306$	125.395	+	147.753i	0.409788	+	0.482854i
$307$			155.490i			0.506483i	0.967403	+	0.253242i	$0.0814968\pi$
$307$			155.490i			0.506483i	−0.967403	+	0.253242i	$0.918503\pi$
$308$		0			0
$309$	28.8315	−	34.5559i	0.0933059	−	0.111831i
$310$	318.609			1.02777
$311$	−168.154	+	97.0835i	−0.540687	+	0.312166i	−0.745357	−	0.666665i	$-0.767721\pi$
$311$	−168.154	+	97.0835i	−0.540687	+	0.312166i	0.204670	+	0.978831i	$0.434388\pi$
$312$	−58.9122	−	160.462i	−0.188821	−	0.514301i
$313$	300.308	+	173.383i	0.959450	+	0.553939i	0.896004	−	0.444047i	$-0.146458\pi$
$313$	300.308	+	173.383i	0.959450	+	0.553939i	0.0634463	+	0.997985i	$0.479791\pi$
$314$		−	386.713i		−	1.23157i
$315$		0			0
$316$	280.541			0.887789
$317$	−34.5304	+	59.8083i	−0.108929	+	0.188670i	−0.915336	−	0.402690i	$-0.868075\pi$
$317$	−34.5304	+	59.8083i	−0.108929	+	0.188670i	0.806408	+	0.591360i	$0.201409\pi$
$318$	−52.3429	+	301.786i	−0.164600	+	0.949011i
$319$	−81.4018	−	140.992i	−0.255178	−	0.441981i
$320$			84.7730i			0.264916i
$321$	−26.5505	+	153.078i	−0.0827118	+	0.476878i
$322$		0			0
$323$	186.443			0.577224
$324$	177.773	+	145.811i	0.548682	+	0.450034i
$325$	−185.532	−	107.117i	−0.570866	−	0.329590i
$326$	211.719			0.649445
$327$	−398.416	+	146.275i	−1.21840	+	0.447325i
$328$	71.0022	+	40.9931i	0.216470	+	0.124979i
$329$		0			0
$330$	−132.134	−	359.900i	−0.400407	−	1.09061i
$331$	125.821	−	217.928i	0.380123	−	0.658393i	−0.610956	−	0.791664i	$-0.709215\pi$
$331$	125.821	−	217.928i	0.380123	−	0.658393i	0.991080	+	0.133272i	$0.0425483\pi$
$332$	353.282	+	203.967i	1.06410	+	0.614360i
$333$	−68.4038	+	58.0528i	−0.205417	+	0.174333i
$334$	5.05069	−	2.91602i	0.0151218	−	0.00873059i
$335$	−347.970	+	200.900i	−1.03872	+	0.599702i
$336$		0			0
$337$	−140.785	+	243.846i	−0.417759	+	0.723580i	−0.995714	−	0.0924890i	$-0.970518\pi$
$337$	−140.785	+	243.846i	−0.417759	+	0.723580i	0.577955	+	0.816069i	$0.303851\pi$
$338$	478.355			1.41525
$339$	−301.288	+	110.615i	−0.888754	+	0.326298i
$340$	−86.1303			−0.253324
$341$	−379.701	+	219.221i	−1.11349	+	0.642876i
$342$	524.297	−	95.4751i	1.53303	−	0.279167i
$343$		0			0
$344$	30.8433	+	53.4222i	0.0896608	+	0.155297i
$345$	−5.22771	+	6.26566i	−0.0151528	+	0.0181613i
$346$	382.595	−	220.891i	1.10576	−	0.638414i
$347$	105.071	+	181.988i	0.302798	+	0.524462i	0.976769	−	0.214296i	$-0.0687459\pi$
$347$	105.071	+	181.988i	0.302798	+	0.524462i	−0.673971	+	0.738758i	$0.735413\pi$
$348$	−98.1376	+	36.0304i	−0.282005	+	0.103536i
$349$	64.0467	−	36.9774i	0.183515	−	0.105952i	−0.405428	−	0.914127i	$-0.632878\pi$
$349$	64.0467	−	36.9774i	0.183515	−	0.105952i	0.588943	+	0.808175i	$0.299544\pi$
$350$		0			0
$351$	436.509	−	256.927i	1.24362	−	0.731985i
$352$	−254.042	−	440.014i	−0.721711	−	1.25004i
$353$			324.482i			0.919212i	0.888123	+	0.459606i	$0.152009\pi$
$353$			324.482i			0.919212i	−0.888123	+	0.459606i	$0.847991\pi$
$354$	−234.195	+	280.694i	−0.661568	+	0.792920i
$355$		−	308.908i		−	0.870163i
$356$	327.228	+	188.925i	0.919179	+	0.530688i
$357$		0			0
$358$	97.9267	+	169.614i	0.273538	+	0.473782i
$359$	−130.585	−	226.180i	−0.363748	−	0.630029i	0.624827	−	0.780763i	$-0.285170\pi$
$359$	−130.585	−	226.180i	−0.363748	−	0.630029i	−0.988574	+	0.150734i	$0.951836\pi$
$360$	99.1049	−	18.0471i	0.275291	−	0.0501309i
$361$	75.8564	−	131.387i	0.210129	−	0.363953i
$362$	−3.77883	−	2.18171i	−0.0104388	−	0.00602683i
$363$	126.377	+	105.442i	0.348145	+	0.290473i
$364$		0			0
$365$	68.7643	−	119.103i	0.188395	−	0.326310i
$366$	310.208	+	53.8037i	0.847562	+	0.147005i
$367$		−	112.180i		−	0.305668i	−0.988252	−	0.152834i	$-0.951160\pi$
$367$		−	112.180i		−	0.305668i	0.988252	−	0.152834i	$-0.0488399\pi$
$368$	−7.12164	+	12.3350i	−0.0193523	+	0.0335192i
$369$	−81.8117	+	228.750i	−0.221712	+	0.619918i
$370$		−	96.0654i		−	0.259636i
$371$		0			0
$372$	97.0323	+	264.291i	0.260840	+	0.710461i
$373$	−15.6936			−0.0420740			−0.0210370	−	0.999779i	$-0.506697\pi$
$373$	−15.6936			−0.0420740			−0.0210370	+	0.999779i	$0.506697\pi$
$374$	247.291	−	142.774i	0.661206	−	0.381748i
$375$	257.945	−	309.159i	0.687853	−	0.824424i
$376$	−210.643	−	121.615i	−0.560220	−	0.323443i
$377$			230.304i			0.610885i
$378$		0			0
$379$	197.268			0.520496			0.260248	−	0.965542i	$-0.416196\pi$
$379$	197.268			0.520496			0.260248	+	0.965542i	$0.416196\pi$
$380$	−118.428	+	205.123i	−0.311652	+	0.539797i
$381$	−412.465	−	344.138i	−1.08259	−	0.903249i
$382$	158.139	+	273.905i	0.413976	+	0.717028i
$383$			548.135i			1.43116i	0.698530	+	0.715580i	$0.253838\pi$
$383$			548.135i			1.43116i	−0.698530	+	0.715580i	$0.746162\pi$
$384$	262.176	−	96.2557i	0.682751	−	0.250666i
$385$		0			0
$386$	−530.339			−1.37393
$387$	−139.364	+	118.275i	−0.360115	+	0.305621i
$388$	−164.753	−	95.1204i	−0.424622	−	0.245156i
$389$	305.510			0.785372			0.392686	−	0.919673i	$-0.371546\pi$
$389$	305.510			0.785372			0.392686	+	0.919673i	$0.371546\pi$
$390$	−92.6833	+	534.370i	−0.237649	+	1.37018i
$391$	−5.26337	−	3.03881i	−0.0134613	−	0.00777189i
$392$		0			0
$393$	−224.181	+	268.691i	−0.570435	+	0.683693i
$394$	−278.522	+	482.413i	−0.706907	+	1.22440i
$395$	315.416	+	182.105i	0.798521	+	0.461026i
$396$	258.302	−	219.215i	0.652278	−	0.553574i
$397$	408.861	−	236.056i	1.02988	−	0.594599i	0.112927	−	0.993603i	$-0.463977\pi$
$397$	408.861	−	236.056i	1.02988	−	0.594599i	0.916949	+	0.399004i	$0.130644\pi$
$398$	−453.640	+	261.909i	−1.13980	+	0.658063i
$399$		0			0
$400$	110.184	−	190.845i	0.275461	−	0.477112i
$401$	694.513			1.73195			0.865976	−	0.500085i	$-0.166698\pi$
$401$	694.513			1.73195			0.865976	+	0.500085i	$0.166698\pi$
$402$	−656.800	−	547.997i	−1.63383	−	1.36318i
$403$	620.224			1.53902
$404$	−52.7991	+	30.4836i	−0.130691	+	0.0754544i
$405$	105.223	+	279.333i	0.259810	+	0.689711i
$406$		0			0
$407$	66.0983	+	114.486i	0.162404	+	0.281292i
$408$	25.8578	+	70.4301i	0.0633769	+	0.172623i
$409$	256.107	−	147.864i	0.626180	−	0.361525i	−0.153091	−	0.988212i	$-0.548923\pi$
$409$	256.107	−	147.864i	0.626180	−	0.361525i	0.779271	+	0.626687i	$0.215590\pi$
$410$	−130.064	−	225.278i	−0.317230	−	0.549459i
$411$	165.006	+	137.671i	0.401473	+	0.334967i
$412$	−36.8771	+	21.2910i	−0.0895075	+	0.0516772i
$413$		0			0
$414$	−16.3573	−	5.85013i	−0.0395103	−	0.0141308i
$415$	264.799	+	458.646i	0.638070	+	1.10517i
$416$			718.742i			1.72775i
$417$	225.377	+	613.869i	0.540472	+	1.47211i
$418$		−	785.245i		−	1.87858i
$419$	−191.051	−	110.304i	−0.455970	−	0.263254i	0.254378	−	0.967105i	$-0.418129\pi$
$419$	−191.051	−	110.304i	−0.455970	−	0.263254i	−0.710348	+	0.703850i	$0.751463\pi$
$420$		0			0
$421$	−355.146	−	615.130i	−0.843576	−	1.46112i	−0.886852	−	0.462054i	$-0.847113\pi$
$421$	−355.146	−	615.130i	−0.843576	−	1.46112i	0.0432759	−	0.999063i	$-0.486221\pi$
$422$	−373.649	−	647.179i	−0.885424	−	1.53360i
$423$	242.711	−	678.633i	0.573786	−	1.60433i
$424$	−59.2908	+	102.695i	−0.139837	+	0.242204i
$425$	81.4336	+	47.0157i	0.191608	+	0.110625i
$426$	617.337	−	226.650i	1.44915	−	0.532042i
$427$		0			0
$428$	73.5009	−	127.307i	0.171731	−	0.297447i
$429$	−257.221	−	700.605i	−0.599583	−	1.63311i
$430$		−	195.721i		−	0.455166i
$431$	−36.3099	+	62.8905i	−0.0842456	+	0.145918i	−0.905070	−	0.425264i	$-0.860181\pi$
$431$	−36.3099	+	62.8905i	−0.0842456	+	0.145918i	0.820824	+	0.571181i	$0.193515\pi$
$432$	264.285	+	449.010i	0.611770	+	1.03938i
$433$		−	572.654i		−	1.32253i	−0.750154	−	0.661264i	$-0.770020\pi$
$433$		−	572.654i		−	1.32253i	0.750154	−	0.661264i	$-0.229980\pi$
$434$		0			0
$435$	−133.725	−	23.1939i	−0.307414	−	0.0533192i
$436$	401.578			0.921050
$437$	−14.4741	+	8.35663i	−0.0331215	+	0.0191227i
$438$	288.475	+	50.0344i	0.658620	+	0.114234i
$439$	−386.765	−	223.299i	−0.881013	−	0.508653i	−0.0100205	−	0.999950i	$-0.503190\pi$
$439$	−386.765	−	223.299i	−0.881013	−	0.508653i	−0.870992	+	0.491297i	$0.836523\pi$
$440$		−	148.430i		−	0.337342i
$441$		0			0
$442$	−403.939			−0.913888
$443$	−301.249	+	521.778i	−0.680020	+	1.17783i	0.294955	+	0.955511i	$0.404695\pi$
$443$	−301.249	+	521.778i	−0.680020	+	1.17783i	−0.974974	+	0.222317i	$0.928638\pi$
$444$	79.6879	−	29.2567i	0.179477	−	0.0658935i
$445$	245.271	+	424.821i	0.551170	+	0.954654i
$446$		−	984.966i		−	2.20844i
$447$	60.8550	+	50.7740i	0.136141	+	0.113588i
$448$		0			0
$449$	−59.7471			−0.133067			−0.0665335	−	0.997784i	$-0.521194\pi$
$449$	−59.7471			−0.133067			−0.0665335	+	0.997784i	$0.521194\pi$
$450$	253.075	+	90.5118i	0.562390	+	0.201137i
$451$	310.008	+	178.983i	0.687379	+	0.396858i
$452$	303.678			0.671854
$453$	191.891	+	160.103i	0.423599	+	0.353428i
$454$	−500.419	−	288.917i	−1.10224	−	0.636381i
$455$		0			0
$456$	203.286	+	35.2588i	0.445803	+	0.0773219i
$457$	355.662	−	616.024i	0.778253	−	1.34797i	−0.154695	−	0.987962i	$-0.549439\pi$
$457$	355.662	−	616.024i	0.778253	−	1.34797i	0.932948	−	0.360012i	$-0.117227\pi$
$458$	65.1436	+	37.6107i	0.142235	+	0.0821193i
$459$	−191.593	+	112.770i	−0.417414	+	0.245687i
$460$	6.68653	−	3.86047i	0.0145359	−	0.00839233i
$461$	1.39410	−	0.804886i	0.00302409	−	0.00174596i	−0.498487	−	0.866897i	$-0.666111\pi$
$461$	1.39410	−	0.804886i	0.00302409	−	0.00174596i	0.501511	+	0.865151i	$0.332778\pi$
$462$		0			0
$463$	21.4251	−	37.1094i	0.0462745	−	0.0801499i	−0.841960	−	0.539539i	$-0.818598\pi$
$463$	21.4251	−	37.1094i	0.0462745	−	0.0801499i	0.888235	+	0.459389i	$0.151932\pi$
$464$	−236.899			−0.510559
$465$	−62.4627	+	360.132i	−0.134328	+	0.774476i
$466$	−1060.84			−2.27647
$467$	−200.182	+	115.575i	−0.428656	+	0.247485i	−0.698774	−	0.715343i	$-0.746271\pi$
$467$	−200.182	+	115.575i	−0.428656	+	0.247485i	0.270118	+	0.962827i	$0.412937\pi$
$468$	−471.496	+	85.8599i	−1.00747	+	0.183461i
$469$		0			0
$470$	385.863	+	668.334i	0.820985	+	1.42199i
$471$	437.112	+	75.8145i	0.928051	+	0.160965i
$472$	−122.568	+	70.7644i	−0.259677	+	0.149925i
$473$	134.667	+	233.251i	0.284709	+	0.493130i
$474$	−132.504	+	763.956i	−0.279544	+	1.61172i
$475$	223.940	−	129.292i	0.471452	−	0.272193i
$476$		0			0
$477$	−330.854	−	118.329i	−0.693615	−	0.248069i
$478$	−173.135	−	299.879i	−0.362207	−	0.627362i
$479$			246.810i			0.515261i	0.966243	+	0.257631i	$0.0829418\pi$
$479$			246.810i			0.515261i	−0.966243	+	0.257631i	$0.917058\pi$
$480$	−417.336	−	72.3845i	−0.869450	−	0.150801i
$481$		−	187.007i		−	0.388788i
$482$	−187.650	−	108.340i	−0.389316	−	0.224771i
$483$		0			0
$484$	−77.8647	−	134.866i	−0.160877	−	0.278648i
$485$	−123.489	−	213.890i	−0.254617	−	0.441010i
$486$	−481.030	+	415.234i	−0.989774	+	0.854391i
$487$	309.236	−	535.613i	0.634982	−	1.09982i	−0.351537	−	0.936174i	$-0.614341\pi$
$487$	309.236	−	535.613i	0.634982	−	1.09982i	0.986519	−	0.163647i	$-0.0523259\pi$
$488$	105.561	+	60.9454i	0.216313	+	0.124888i
$489$	−41.5072	+	239.311i	−0.0848818	+	0.489390i
$490$		0			0
$491$	−160.661	+	278.274i	−0.327212	+	0.566749i	−0.981958	−	0.189101i	$-0.939443\pi$
$491$	−160.661	+	278.274i	−0.327212	+	0.566749i	0.654745	+	0.755850i	$0.272776\pi$
$492$	147.261	−	176.499i	0.299311	−	0.358738i
$493$		−	101.085i		−	0.205041i
$494$	−555.409	+	961.996i	−1.12431	+	1.94736i
$495$	432.709	−	78.7969i	0.874160	−	0.159186i
$496$			637.986i			1.28626i
$497$		0			0
$498$	−722.294	+	865.703i	−1.45039	+	1.73836i
$499$	160.971			0.322587			0.161293	−	0.986906i	$-0.448433\pi$
$499$	160.971			0.322587			0.161293	+	0.986906i	$0.448433\pi$
$500$	−329.926	+	190.483i	−0.659851	+	0.380965i
$501$	2.30587	+	6.28060i	0.00460253	+	0.0125361i
$502$	−414.187	−	239.131i	−0.825074	−	0.476357i
$503$			941.248i			1.87127i	0.352971	+	0.935634i	$0.385171\pi$
$503$			941.248i			1.87127i	−0.352971	+	0.935634i	$0.614829\pi$
$504$		0			0
$505$	−79.1501			−0.156733
$506$	−12.7986	+	22.1678i	−0.0252937	+	0.0438099i
$507$	−93.7807	+	540.697i	−0.184972	+	1.06646i
$508$	254.133	+	440.171i	0.500262	+	0.866479i
$509$		−	474.049i		−	0.931335i	−0.884960	−	0.465667i	$-0.845814\pi$
$509$		−	474.049i		−	0.931335i	0.884960	−	0.465667i	$-0.154186\pi$
$510$	40.6806	−	234.546i	0.0797659	−	0.459894i
$511$		0			0
$512$	−504.886			−0.986105
$513$	5.13040	+	611.344i	0.0100008	+	1.19170i
$514$	107.657	+	62.1559i	0.209450	+	0.120926i
$515$	−55.2818			−0.107343
$516$	162.354	−	59.6070i	0.314640	−	0.115517i
$517$	−919.702	−	530.990i	−1.77892	−	1.02706i
$518$		0			0
$519$	174.672	+	475.762i	0.336554	+	0.916689i
$520$	−104.986	+	181.841i	−0.201896	+	0.349694i
$521$	155.090	+	89.5412i	0.297677	+	0.171864i	0.641399	−	0.767207i	$-0.278354\pi$
$521$	155.090	+	89.5412i	0.297677	+	0.171864i	−0.343722	+	0.939072i	$0.611688\pi$
$522$	−51.7643	−	284.261i	−0.0991653	−	0.544562i
$523$	642.856	−	371.153i	1.22917	−	0.709662i	0.262314	−	0.964982i	$-0.415514\pi$
$523$	642.856	−	371.153i	1.22917	−	0.709662i	0.966857	+	0.255320i	$0.0821809\pi$
$524$	286.740	−	165.549i	0.547213	−	0.315934i
$525$		0			0
$526$	−535.554	+	927.607i	−1.01816	+	1.76351i
$527$	−272.229			−0.516564
$528$	720.669	−	264.587i	1.36490	−	0.501113i
$529$	−528.455			−0.998970
$530$	325.833	−	188.120i	0.614779	−	0.354943i
$531$	−271.362	−	319.746i	−0.511039	−	0.602159i
$532$		0			0
$533$	−253.192	−	438.541i	−0.475031	−	0.822778i
$534$	−669.026	+	801.859i	−1.25286	+	1.50161i
$535$	165.276	−	95.4220i	0.308927	−	0.178359i
$536$	−165.583	−	286.798i	−0.308923	−	0.535070i
$537$	−210.917	+	77.4365i	−0.392770	+	0.144202i
$538$	349.751	−	201.929i	0.650094	−	0.375332i
$539$		0			0
$540$	−2.37007	−	282.420i	−0.00438902	−	0.522999i
$541$	273.249	+	473.282i	0.505082	+	0.874828i	0.999983	+	0.00587807i	$0.00187106\pi$
$541$	273.249	+	473.282i	0.505082	+	0.874828i	−0.494901	+	0.868949i	$0.664796\pi$
$542$		−	162.657i		−	0.300104i
$543$	3.20688	−	3.84359i	0.00590585	−	0.00707844i
$544$		−	315.471i		−	0.579909i
$545$	451.498	+	260.673i	0.828437	+	0.478298i
$546$		0			0
$547$	192.148	+	332.810i	0.351276	+	0.608429i	0.986473	−	0.163922i	$-0.0524144\pi$
$547$	192.148	+	332.810i	0.351276	+	0.608429i	−0.635197	+	0.772350i	$0.719081\pi$
$548$	−101.665	−	176.089i	−0.185520	−	0.321331i
$549$	−121.631	+	340.088i	−0.221551	+	0.619467i
$550$	198.017	−	342.975i	0.360030	−	0.623591i
$551$	−240.738	−	138.990i	−0.436911	−	0.252251i
$552$	−5.16418	−	4.30870i	−0.00935539	−	0.00780561i
$553$		0			0
$554$	−7.52189	+	13.0283i	−0.0135774	+	0.0235168i
$555$	108.585	+	18.8335i	0.195649	+	0.0339341i
$556$		−	618.740i		−	1.11284i
$557$	157.125	−	272.148i	0.282091	−	0.488596i	−0.689809	−	0.723992i	$-0.742305\pi$
$557$	157.125	−	272.148i	0.282091	−	0.488596i	0.971900	+	0.235396i	$0.0756386\pi$
$558$	−765.535	+	139.405i	−1.37193	+	0.249830i
$559$		−	381.004i		−	0.681581i
$560$		0			0
$561$	112.900	+	307.510i	0.201247	+	0.548146i
$562$	−659.484			−1.17346
$563$	−98.8474	+	57.0696i	−0.175573	+	0.101367i	−0.585211	−	0.810881i	$-0.698988\pi$
$563$	−98.8474	+	57.0696i	−0.175573	+	0.101367i	0.409638	+	0.912248i	$0.365655\pi$
$564$	−436.880	+	523.621i	−0.774610	+	0.928406i
$565$	341.429	+	197.124i	0.604299	+	0.348892i
$566$		−	354.874i		−	0.626986i
$567$		0			0
$568$	254.603			0.448244
$569$	178.041	−	308.376i	0.312901	−	0.541961i	−0.666088	−	0.745873i	$-0.732032\pi$
$569$	178.041	−	308.376i	0.312901	−	0.541961i	0.978989	+	0.203912i	$0.0653657\pi$
$570$	−502.645	−	419.379i	−0.881834	−	0.735753i
$571$	−170.256	−	294.892i	−0.298171	−	0.516448i	0.677546	−	0.735480i	$-0.263043\pi$
$571$	−170.256	−	294.892i	−0.298171	−	0.516448i	−0.975718	+	0.219032i	$0.929710\pi$
$572$			706.164i			1.23455i
$573$	−340.604	+	125.050i	−0.594423	+	0.218237i
$574$		0			0
$575$	−8.42921			−0.0146595
$576$	−37.0918	−	203.688i	−0.0643955	−	0.353625i
$577$	−338.473	−	195.417i	−0.586608	−	0.338678i	0.177147	−	0.984184i	$-0.443313\pi$
$577$	−338.473	−	195.417i	−0.586608	−	0.338678i	−0.763755	+	0.645506i	$0.776646\pi$
$578$	−578.456			−1.00079
$579$	103.972	−	599.455i	0.179572	−	1.03533i
$580$	111.213	+	64.2086i	0.191746	+	0.110705i
$581$		0			0
$582$	336.842	−	403.721i	0.578767	−	0.693679i
$583$	−258.874	+	448.383i	−0.444037	+	0.769095i
$584$	98.1653	+	56.6758i	0.168091	+	0.0970475i
$585$	−585.841	−	209.525i	−1.00144	−	0.358162i
$586$	−190.640	+	110.066i	−0.325324	+	0.187826i
$587$	878.394	−	507.141i	1.49641	−	0.863954i	0.496421	−	0.868082i	$-0.334647\pi$
$587$	878.394	−	507.141i	1.49641	−	0.863954i	0.999991	+	0.00412823i	$0.00131406\pi$
$588$		0			0
$589$	−374.311	+	648.325i	−0.635502	+	1.10072i
$590$	449.047			0.761097
$591$	−490.680	−	409.396i	−0.830254	−	0.692718i
$592$	192.362			0.324937
$593$	−666.105	+	384.576i	−1.12328	+	0.648526i	−0.942236	−	0.334949i	$-0.891281\pi$
$593$	−666.105	+	384.576i	−1.12328	+	0.648526i	−0.181044	+	0.983475i	$0.557947\pi$
$594$	474.957	+	806.934i	0.799590	+	1.35847i
$595$		0			0
$596$	−37.4947	−	64.9427i	−0.0629106	−	0.108964i
$597$	−207.107	−	564.107i	−0.346913	−	0.944903i
$598$	31.3588	−	18.1050i	0.0524395	−	0.0302760i
$599$	263.413	+	456.244i	0.439754	+	0.761677i	0.997670	−	0.0682206i	$-0.0217322\pi$
$599$	263.413	+	456.244i	0.439754	+	0.761677i	−0.557916	+	0.829897i	$0.688399\pi$
$600$	79.8988	+	66.6631i	0.133165	+	0.111105i
$601$	−35.7573	+	20.6445i	−0.0594963	+	0.0343502i	−0.529453	−	0.848339i	$-0.677603\pi$
$601$	−35.7573	+	20.6445i	−0.0594963	+	0.0343502i	0.469957	+	0.882689i	$0.344269\pi$
$602$		0			0
$603$	748.179	−	634.963i	1.24076	−	1.05301i
$604$	−118.230	−	204.780i	−0.195745	−	0.339040i
$605$		−	202.174i		−	0.334173i
$606$	−58.0736	−	158.178i	−0.0958310	−	0.261019i
$607$			448.326i			0.738592i	0.929312	+	0.369296i	$0.120401\pi$
$607$			448.326i			0.738592i	−0.929312	+	0.369296i	$0.879599\pi$
$608$	−751.307	−	433.767i	−1.23570	−	0.713433i
$609$		0			0
$610$	−193.370	−	334.926i	−0.317000	−	0.549059i
$611$	751.145	+	1301.02i	1.22937	+	2.12933i
$612$	206.949	−	37.6857i	0.338152	−	0.0615779i
$613$	−500.398	+	866.714i	−0.816309	+	1.41389i	0.0920744	+	0.995752i	$0.470650\pi$
$613$	−500.398	+	866.714i	−0.816309	+	1.41389i	−0.908384	+	0.418137i	$0.862683\pi$
$614$	352.140	+	203.308i	0.573518	+	0.331121i
$615$	280.136	−	102.850i	0.455506	−	0.167235i
$616$		0			0
$617$	−88.6179	+	153.491i	−0.143627	+	0.248769i	−0.928860	−	0.370431i	$-0.879210\pi$
$617$	−88.6179	+	153.491i	−0.143627	+	0.248769i	0.785233	+	0.619201i	$0.212543\pi$
$618$	−40.5610	−	110.478i	−0.0656327	−	0.178767i
$619$		−	335.171i		−	0.541472i	−0.962654	−	0.270736i	$-0.912733\pi$
$619$		−	335.171i		−	0.541472i	0.962654	−	0.270736i	$-0.0872670\pi$
$620$	172.918	−	299.503i	0.278901	−	0.483070i
$621$	9.81936	−	17.3421i	0.0158122	−	0.0279261i
$622$			507.759i			0.816332i
$623$		0			0
$624$	−1070.03	−	185.590i	−1.71479	−	0.297420i
$625$	−209.087			−0.334539
$626$	785.323	−	453.407i	1.25451	−	0.724292i
$627$	887.583	+	153.946i	1.41560	+	0.245528i
$628$	−363.524	−	209.881i	−0.578860	−	0.334205i
$629$			82.0812i			0.130495i
$630$		0			0
$631$	1077.15			1.70705			0.853524	−	0.521053i	$-0.174461\pi$
$631$	1077.15			1.70705			0.853524	+	0.521053i	$0.174461\pi$
$632$	−150.092	+	259.967i	−0.237487	+	0.411340i
$633$	804.776	−	295.466i	1.27137	−	0.466772i
$634$	90.2990	+	156.402i	0.142427	+	0.246691i
$635$			659.853i			1.03914i
$636$	255.281	+	212.992i	0.401385	+	0.334893i
$637$		0			0
$638$	−425.741			−0.667306
$639$	135.160	+	742.226i	0.211518	+	1.16154i
$640$	−297.106	−	171.534i	−0.464229	−	0.268023i
$641$	205.531			0.320641			0.160320	−	0.987065i	$-0.448747\pi$
$641$	205.531			0.320641			0.160320	+	0.987065i	$0.448747\pi$
$642$	311.961	+	260.283i	0.485921	+	0.405426i
$643$	413.913	+	238.973i	0.643721	+	0.371653i	0.786047	−	0.618167i	$-0.212125\pi$
$643$	413.913	+	238.973i	0.643721	+	0.371653i	−0.142325	+	0.989820i	$0.545458\pi$
$644$		0			0
$645$	221.229	+	38.3708i	0.342990	+	0.0594897i
$646$	243.780	−	422.240i	0.377369	−	0.653622i
$647$	266.892	+	154.090i	0.412507	+	0.238161i	0.691866	−	0.722026i	$-0.256789\pi$
$647$	266.892	+	154.090i	0.412507	+	0.238161i	−0.279359	+	0.960187i	$0.590122\pi$
$648$	−230.227	+	86.7252i	−0.355289	+	0.133835i
$649$	−535.151	+	308.970i	−0.824578	+	0.476070i
$650$	−485.176	+	280.117i	−0.746425	+	0.430949i
$651$		0			0
$652$	114.906	−	199.023i	0.176237	−	0.305251i
$653$	−701.549			−1.07435			−0.537174	−	0.843471i	$-0.680508\pi$
$653$	−701.549			−1.07435			−0.537174	+	0.843471i	$0.680508\pi$
$654$	−189.671	+	1093.56i	−0.290017	+	1.67210i
$655$	429.846			0.656253
$656$	451.100	−	260.442i	0.687652	−	0.397016i
$657$	−113.110	+	316.262i	−0.172162	+	0.481373i
$658$		0			0
$659$	362.623	+	628.082i	0.550263	+	0.953084i	0.998255	+	0.0590463i	$0.0188060\pi$
$659$	362.623	+	628.082i	0.550263	+	0.953084i	−0.447992	+	0.894038i	$0.647861\pi$
$660$	−410.032	−	71.1177i	−0.621261	−	0.107754i
$661$	−716.938	+	413.924i	−1.08463	+	0.626210i	−0.932141	−	0.362096i	$-0.882061\pi$
$661$	−716.938	+	413.924i	−1.08463	+	0.626210i	−0.152486	+	0.988306i	$0.548728\pi$
$662$	−329.029	−	569.895i	−0.497023	−	0.860868i
$663$	79.1915	−	456.582i	0.119444	−	0.688661i
$664$	−378.017	+	218.248i	−0.569303	+	0.328687i
$665$		0			0
$666$	42.0327	+	230.820i	0.0631121	+	0.346577i
$667$	4.53076	+	7.84751i	0.00679274	+	0.0117654i
$668$		−	6.33043i		−	0.00947670i
$669$	1113.33	+	193.101i	1.66417	+	0.288641i
$670$			1050.73i			1.56826i
$671$	460.896	+	266.098i	0.686879	+	0.396570i
$672$		0			0
$673$	−582.601	−	1009.10i	−0.865678	−	1.49940i	−0.866372	−	0.499399i	$-0.833554\pi$
$673$	−582.601	−	1009.10i	−0.865678	−	1.49940i	0.000694329	−	1.00000i	$-0.499779\pi$
$674$	368.161	+	637.673i	0.546233	+	0.946102i
$675$	−151.923	+	268.313i	−0.225071	+	0.397501i
$676$	259.617	−	449.670i	0.384049	−	0.665193i
$677$	−255.760	−	147.663i	−0.377785	−	0.218114i	0.299069	−	0.954231i	$-0.403324\pi$
$677$	−255.760	−	147.663i	−0.377785	−	0.218114i	−0.676854	+	0.736117i	$0.736657\pi$
$678$	−143.432	+	826.961i	−0.211551	+	1.21971i
$679$		0			0
$680$	46.0804	−	79.8136i	0.0677653	−	0.117373i
$681$	424.676	−	508.994i	0.623607	−	0.747422i
$682$			1146.55i			1.68116i
$683$	318.779	−	552.142i	0.466734	−	0.808406i	−0.532544	−	0.846402i	$-0.678764\pi$
$683$	318.779	−	552.142i	0.466734	−	0.808406i	0.999278	+	0.0379957i	$0.0120973\pi$
$684$	194.802	−	544.675i	0.284798	−	0.796308i
$685$		−	263.972i		−	0.385361i
$686$		0			0
$687$	−55.2836	+	66.2599i	−0.0804710	+	0.0964482i
$688$	391.915			0.569644
$689$	634.287	−	366.206i	0.920591	−	0.531504i
$690$	7.35450	+	20.0318i	0.0106587	+	0.0290316i
$691$	635.956	+	367.169i	0.920342	+	0.531360i	0.883744	−	0.467971i	$-0.155015\pi$
$691$	635.956	+	367.169i	0.920342	+	0.531360i	0.0365976	+	0.999330i	$0.488348\pi$
$692$		−	479.537i		−	0.692972i
$693$		0			0
$694$	549.534			0.791835
$695$	401.637	−	695.656i	0.577895	−	1.00094i
$696$	19.1165	−	110.217i	0.0274662	−	0.158357i
$697$	111.131	+	192.484i	0.159442	+	0.276161i
$698$		−	193.396i		−	0.277072i
$699$	207.975	−	1199.09i	0.297532	−	1.71544i
$700$		0			0
$701$	1045.20			1.49101			0.745507	−	0.666498i	$-0.232208\pi$
$701$	1045.20			1.49101			0.745507	+	0.666498i	$0.232208\pi$
$702$	−11.1153	−	1324.51i	−0.0158337	−	1.88676i
$703$	195.480	+	112.860i	0.278065	+	0.160541i
$704$	−305.066			−0.433332
$705$	−831.082	+	305.125i	−1.17884	+	0.432801i
$706$	734.857	+	424.270i	1.04087	+	0.600949i
$707$		0			0
$708$	136.757	+	372.493i	0.193160	+	0.526119i
$709$	−25.0780	+	43.4364i	−0.0353710	+	0.0612644i	−0.883169	−	0.469055i	$-0.844595\pi$
$709$	−25.0780	+	43.4364i	−0.0353710	+	0.0612644i	0.847798	+	0.530319i	$0.177928\pi$
$710$	−699.586	−	403.906i	−0.985332	−	0.568882i
$711$	−837.542	−	299.545i	−1.17798	−	0.421301i
$712$	−350.139	+	202.153i	−0.491768	+	0.283922i
$713$	21.1339	−	12.2017i	0.0296408	−	0.0171131i
$714$		0			0
$715$	−458.386	+	793.948i	−0.641100	+	1.11042i
$716$	212.591			0.296915
$717$	372.904	−	136.908i	0.520089	−	0.190946i
$718$	−682.977			−0.951222
$719$	1138.84	−	657.512i	1.58393	−	0.914481i	0.589649	−	0.807660i	$-0.299266\pi$
$719$	1138.84	−	657.512i	1.58393	−	0.914481i	0.994278	−	0.106821i	$-0.0340672\pi$
$720$	215.525	−	602.618i	0.299340	−	0.836970i
$721$		0			0
$722$	−198.369	−	343.585i	−0.274750	−	0.475880i
$723$	159.248	−	190.866i	0.220260	−	0.263991i
$724$	−4.10177	+	2.36816i	−0.00566543	+	0.00327094i
$725$	−70.0988	−	121.415i	−0.0966880	−	0.167468i
$726$	404.036	−	148.338i	0.556523	−	0.204323i
$727$	−701.577	+	405.056i	−0.965030	+	0.557160i	−0.897717	−	0.440572i	$-0.854776\pi$
$727$	−701.577	+	405.056i	−0.965030	+	0.557160i	−0.0673125	+	0.997732i	$0.521442\pi$
$728$		0			0
$729$	−375.044	−	625.126i	−0.514464	−	0.857512i
$730$	−179.823	−	311.462i	−0.246333	−	0.426661i
$731$			167.230i			0.228769i
$732$	218.936	−	262.405i	0.299093	−	0.358477i
$733$		−	100.659i		−	0.137324i	−0.997640	−	0.0686622i	$-0.978127\pi$
$733$		−	100.659i		−	0.137324i	0.997640	−	0.0686622i	$-0.0218731\pi$
$734$	−254.055	−	146.679i	−0.346124	−	0.199835i
$735$		0			0
$736$	14.1398	+	24.4909i	0.0192117	+	0.0332756i
$737$	−722.963	−	1252.21i	−0.980954	−	1.69906i
$738$	411.080	+	484.377i	0.557019	+	0.656337i
$739$	−211.146	+	365.716i	−0.285719	+	0.494879i	−0.972783	−	0.231717i	$-0.925566\pi$
$739$	−211.146	+	365.716i	−0.285719	+	0.494879i	0.687065	+	0.726596i	$0.258899\pi$
$740$	−90.3048	−	52.1375i	−0.122034	−	0.0704561i
$741$	−978.482	−	816.390i	−1.32049	−	1.10174i
$742$		0			0
$743$	405.350	−	702.087i	0.545559	−	0.944936i	−0.453013	−	0.891504i	$-0.649651\pi$
$743$	405.350	−	702.087i	0.545559	−	0.944936i	0.998572	−	0.0534316i	$-0.0170159\pi$
$744$	−296.822	−	51.4820i	−0.398954	−	0.0691962i
$745$		−	97.3544i		−	0.130677i
$746$	−20.5199	+	35.5414i	−0.0275065	+	0.0476427i
$747$	−836.922	−	986.147i	−1.12038	−	1.32014i
$748$		−	309.950i		−	0.414372i
$749$		0			0
$750$	−362.884	−	988.405i	−0.483846	−	1.31787i
$751$	398.375			0.530459			0.265230	−	0.964185i	$-0.414552\pi$
$751$	398.375			0.530459			0.265230	+	0.964185i	$0.414552\pi$
$752$	−1338.28	+	772.656i	−1.77963	+	1.02747i
$753$	351.497	−	421.285i	0.466795	−	0.559476i
$754$	521.571	+	301.129i	0.691739	+	0.399376i
$755$		−	306.982i		−	0.406599i
$756$		0			0
$757$	730.998			0.965652			0.482826	−	0.875716i	$-0.339610\pi$
$757$	730.998			0.965652			0.482826	+	0.875716i	$0.339610\pi$
$758$	257.934	−	446.754i	0.340282	−	0.589385i
$759$	−22.5477	−	18.8125i	−0.0297071	−	0.0247859i
$760$	−126.720	−	219.485i	−0.166736	−	0.288796i
$761$			91.5060i			0.120244i	0.998191	+	0.0601222i	$0.0191491\pi$
$761$			91.5060i			0.120244i	−0.998191	+	0.0601222i	$0.980851\pi$
$762$	−1318.68	+	484.143i	−1.73056	+	0.635358i
$763$		0			0
$764$	343.307			0.449354
$765$	257.138	+	91.9646i	0.336128	+	0.120215i
$766$	1241.37	+	716.702i	1.62058	+	0.935643i
$767$	874.144			1.13969
$768$	171.987	−	991.599i	0.223942	−	1.29114i
$769$	391.783	+	226.196i	0.509470	+	0.294143i	0.732616	−	0.680642i	$-0.238299\pi$
$769$	391.783	+	226.196i	0.509470	+	0.294143i	−0.223146	+	0.974785i	$0.571633\pi$
$770$		0			0
$771$	−91.3624	+	109.502i	−0.118499	+	0.142026i
$772$	−287.830	+	498.537i	−0.372837	+	0.645773i
$773$	−986.225	−	569.397i	−1.27584	−	0.736607i	−0.299760	−	0.954015i	$-0.596907\pi$
$773$	−986.225	−	569.397i	−1.27584	−	0.736607i	−0.976081	+	0.217407i	$0.930240\pi$
$774$	85.6364	+	470.268i	0.110641	+	0.607582i
$775$	−326.978	+	188.781i	−0.421907	+	0.243588i
$776$	176.289	−	101.780i	0.227176	−	0.131160i
$777$		0			0
$778$	399.463	−	691.890i	0.513449	−	0.889319i
$779$	611.213			0.784612
$780$	452.024	+	377.144i	0.579518	+	0.483518i
$781$	1111.64			1.42335
$782$	−13.7640	+	7.94667i	−0.0176011	+	0.0101620i
$783$	331.456	−	2.78158i	0.423315	−	0.00355247i
$784$		0			0
$785$	−272.476	−	471.943i	−0.347103	−	0.601201i
$786$	315.384	+	859.026i	0.401252	+	1.09291i
$787$	252.358	−	145.699i	0.320659	−	0.185132i	−0.331028	−	0.943621i	$-0.607395\pi$
$787$	252.358	−	145.699i	0.320659	−	0.185132i	0.651686	+	0.758489i	$0.274062\pi$
$788$	302.324	+	523.640i	0.383660	+	0.664518i
$789$	−943.503	−	787.206i	−1.19582	−	0.997727i
$790$	824.831	−	476.217i	1.04409	−	0.602806i
$791$		0			0
$792$	64.9447	+	356.640i	0.0820008	+	0.450304i
$793$	−376.426	−	651.989i	−0.474686	−	0.822180i
$794$		−	1234.60i		−	1.55491i
$795$	148.758	+	405.178i	0.187116	+	0.509658i
$796$			568.583i			0.714300i
$797$	833.171	+	481.032i	1.04538	+	0.603553i	0.921354	−	0.388725i	$-0.127085\pi$
$797$	833.171	+	481.032i	1.04538	+	0.603553i	0.124031	+	0.992278i	$0.460418\pi$
$798$		0			0
$799$	−329.693	−	571.045i	−0.412632	−	0.714700i
$800$	−218.767	−	378.916i	−0.273459	−	0.473645i
$801$	−775.200	−	913.420i	−0.967790	−	1.14035i
$802$	908.097	−	1572.87i	1.13229	−	1.96118i
$803$	428.607	+	247.456i	0.533757	+	0.308165i
$804$	−871.601	+	320.001i	−1.08408	+	0.398011i
$805$		0			0
$806$	810.962	−	1404.63i	1.00616	−	1.74271i
$807$	159.677	+	434.920i	0.197865	+	0.538934i
$808$		−	65.2358i		−	0.0807374i
$809$	−340.874	+	590.412i	−0.421353	+	0.729804i	−0.996072	−	0.0885462i	$-0.971778\pi$
$809$	−340.874	+	590.412i	−0.421353	+	0.729804i	0.574719	+	0.818351i	$0.305111\pi$
$810$	770.190	+	126.937i	0.950852	+	0.156712i
$811$			1531.25i			1.88810i	0.329801	+	0.944050i	$0.393018\pi$
$811$			1531.25i			1.88810i	−0.329801	+	0.944050i	$0.606982\pi$
$812$		0			0
$813$	183.855	+	31.8886i	0.226144	+	0.0392233i
$814$	345.702			0.424696
$815$	258.381	−	149.176i	0.317032	−	0.183038i
$816$	469.657	+	81.4593i	0.575561	+	0.0998276i
$817$	398.266	+	229.939i	0.487474	+	0.281443i
$818$		−	773.345i		−	0.945410i
$819$		0			0
$820$	−282.359			−0.344340
$821$	−46.3290	+	80.2441i	−0.0564299	+	0.0977395i	−0.892860	−	0.450334i	$-0.851305\pi$
$821$	−46.3290	+	80.2441i	−0.0564299	+	0.0977395i	0.836430	+	0.548073i	$0.184638\pi$
$822$	527.535	−	193.680i	0.641770	−	0.235620i
$823$	−253.184	−	438.528i	−0.307636	−	0.532841i	0.670209	−	0.742172i	$-0.266204\pi$
$823$	−253.184	−	438.528i	−0.307636	−	0.532841i	−0.977845	+	0.209332i	$0.932871\pi$
$824$		−	45.5634i		−	0.0552954i
$825$	348.852	+	291.063i	0.422851	+	0.352803i
$826$		0			0
$827$	−909.882			−1.10022			−0.550110	−	0.835092i	$-0.685414\pi$
$827$	−909.882			−1.10022			−0.550110	+	0.835092i	$0.685414\pi$
$828$	−14.3769	+	12.2014i	−0.0173634	+	0.0147359i
$829$	−140.408	−	81.0647i	−0.169371	−	0.0977862i	0.412918	−	0.910768i	$-0.364509\pi$
$829$	−140.408	−	81.0647i	−0.169371	−	0.0977862i	−0.582289	+	0.812982i	$0.697843\pi$
$830$	1384.93			1.66859
$831$	−13.2516	−	11.0564i	−0.0159465	−	0.0133049i
$832$	373.733	+	215.775i	0.449198	+	0.259345i
$833$		0			0
$834$	1684.92	+	292.240i	2.02029	+	0.350408i
$835$	4.10922	−	7.11738i	0.00492122	−	0.00852380i
$836$	−738.158	−	426.176i	−0.882965	−	0.509780i
$837$	−7.49099	−	892.634i	−0.00894981	−	1.06647i
$838$	−499.611	+	288.451i	−0.596195	+	0.344213i
$839$	−640.732	+	369.927i	−0.763686	+	0.440914i	−0.830617	−	0.556843i	$-0.812012\pi$
$839$	−640.732	+	369.927i	−0.763686	+	0.440914i	0.0669319	+	0.997758i	$0.478679\pi$
$840$		0			0
$841$	345.143	−	597.805i	0.410396	−	0.710826i
$842$	−1857.45			−2.20600
$843$	129.291	−	745.432i	0.153370	−	0.884260i
$844$	−811.161			−0.961092
$845$	583.781	−	337.046i	0.690865	−	0.398871i
$846$	−1219.55	−	1437.00i	−1.44155	−	1.69859i
$847$		0			0
$848$	376.693	+	652.452i	0.444214	+	0.769401i
$849$	401.123	+	69.5724i	0.472465	+	0.0819463i
$850$	212.954	−	122.949i	0.250534	−	0.144646i
$851$	−3.67898	−	6.37219i	−0.00432313	−	0.00748788i
$852$	121.988	−	703.328i	0.143179	−	0.825503i
$853$	824.037	−	475.758i	0.966045	−	0.557747i	0.0680170	−	0.997684i	$-0.478333\pi$
$853$	824.037	−	475.758i	0.966045	−	0.557747i	0.898028	+	0.439938i	$0.144999\pi$
$854$		0			0
$855$	572.578	−	485.934i	0.669681	−	0.568344i
$856$	78.6472	+	136.221i	0.0918775	+	0.159137i
$857$		−	1280.77i		−	1.49449i	−0.664551	−	0.747243i	$-0.731377\pi$
$857$		−	1280.77i		−	1.49449i	0.664551	−	0.747243i	$-0.268623\pi$
$858$	−1922.99	−	333.532i	−2.24125	−	0.388731i
$859$			757.762i			0.882144i	0.897472	+	0.441072i	$0.145402\pi$
$859$			757.762i			0.882144i	−0.897472	+	0.441072i	$0.854598\pi$
$860$	−183.985	−	106.224i	−0.213936	−	0.123516i
$861$		0			0
$862$	94.9525	+	164.462i	0.110154	+	0.190792i
$863$	660.877	+	1144.67i	0.765790	+	1.32639i	0.939828	+	0.341648i	$0.110985\pi$
$863$	660.877	+	1144.67i	0.765790	+	1.32639i	−0.174038	+	0.984739i	$0.555682\pi$
$864$	1034.42	−	8.68088i	1.19725	−	0.0100473i
$865$	311.277	−	539.148i	0.359858	−	0.623293i
$866$	−1296.90	−	748.763i	−1.49757	−	0.864622i
$867$	113.405	−	653.843i	0.130802	−	0.754144i
$868$		0			0
$869$	−655.327	+	1135.06i	−0.754117	+	1.30617i
$870$	−227.377	+	272.522i	−0.261353	+	0.313244i
$871$			2045.42i			2.34836i
$872$	−214.847	+	372.126i	−0.246384	+	0.426750i
$873$	390.299	+	459.890i	0.447078	+	0.526793i
$874$			43.7062i			0.0500071i
$875$		0			0
$876$	203.598	−	244.022i	0.232418	−	0.278564i
$877$	−483.486			−0.551295			−0.275648	−	0.961259i	$-0.588892\pi$
$877$	−483.486			−0.551295			−0.275648	+	0.961259i	$0.588892\pi$
$878$	−1011.41	+	583.939i	−1.15195	+	0.665079i
$879$	−87.0357	−	237.063i	−0.0990167	−	0.269696i
$880$	−816.685	−	471.513i	−0.928051	−	0.535811i
$881$			379.667i			0.430950i	0.976509	+	0.215475i	$0.0691299\pi$
$881$			379.667i			0.430950i	−0.976509	+	0.215475i	$0.930870\pi$
$882$		0			0
$883$	−754.801			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$883$	−754.801			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$884$	−219.229	+	379.716i	−0.247997	+	0.429543i
$885$	−88.0350	+	507.570i	−0.0994745	+	0.573525i
$886$	787.784	+	1364.48i	0.889146	+	1.54005i
$887$			209.469i			0.236154i	0.993004	+	0.118077i	$0.0376730\pi$
$887$			209.469i			0.236154i	−0.993004	+	0.118077i	$0.962327\pi$
$888$	−15.5226	+	89.4962i	−0.0174804	+	0.100784i
$889$		0			0
$890$	1282.79			1.44134
$891$	−1005.21	+	378.657i	−1.12818	+	0.424980i
$892$	−925.903	−	534.570i	−1.03801	−	0.599294i
$893$	−1813.29			−2.03056
$894$	194.558	−	71.4303i	0.217627	−	0.0798997i
$895$	239.018	+	137.997i	0.267060	+	0.154187i
$896$		0			0
$897$	14.3167	+	38.9952i	0.0159607	+	0.0434729i
$898$	−78.1211	+	135.310i	−0.0869945	+	0.150679i
$899$	351.506	+	202.942i	0.390997	+	0.225742i
$900$	222.436	−	188.776i	0.247151	−	0.209752i
$901$	−278.402	+	160.735i	−0.308992	+	0.178397i
$902$	810.689	−	468.052i	0.898768	−	0.518904i
$903$		0			0
$904$	−162.470	+	281.407i	−0.179724	+	0.311291i
$905$	−6.14889			−0.00679435
$906$	613.489	−	225.237i	0.677140	−	0.248606i
$907$	−928.747			−1.02398			−0.511988	−	0.858992i	$-0.671091\pi$
$907$	−928.747			−1.02398			−0.511988	+	0.858992i	$0.671091\pi$
$908$	−543.184	+	313.607i	−0.598220	+	0.345383i
$909$	190.177	−	34.6315i	0.209216	−	0.0380985i
$910$		0			0
$911$	−157.855	−	273.414i	−0.173277	−	0.300125i	0.766287	−	0.642499i	$-0.222102\pi$
$911$	−157.855	−	273.414i	−0.173277	−	0.300125i	−0.939564	+	0.342374i	$0.888769\pi$
$912$	839.770	−	1006.50i	0.920800	−	1.10362i
$913$	−1650.49	+	952.911i	−1.80777	+	1.04371i
$914$	−930.077	−	1610.94i	−1.01759	−	1.76252i
$915$	416.485	−	152.909i	0.455175	−	0.167114i
$916$	70.7107	−	40.8248i	0.0771951	−	0.0445686i
$917$		0			0
$918$	4.87872	+	581.353i	0.00531451	+	0.633282i
$919$	187.419	+	324.619i	0.203938	+	0.353231i	0.949794	−	0.312877i	$-0.101293\pi$
$919$	187.419	+	324.619i	0.203938	+	0.353231i	−0.745856	+	0.666107i	$0.767959\pi$
$920$			8.26153i			0.00897992i
$921$	−298.841	+	358.175i	−0.324475	+	0.388898i
$922$		−	4.20965i		−	0.00456578i
$923$	−1361.86	−	786.270i	−1.47547	−	0.851863i
$924$		0			0
$925$	56.9203	+	98.5889i	0.0615355	+	0.106583i
$926$	−56.0280	−	97.0433i	−0.0605054	−	0.104798i
$927$	132.828	−	24.1881i	0.143288	−	0.0260929i
$928$	−235.178	+	407.340i	−0.253425	+	0.438944i
$929$	838.196	+	483.932i	0.902256	+	0.520918i	0.877931	−	0.478787i	$-0.158923\pi$
$929$	838.196	+	483.932i	0.902256	+	0.520918i	0.0243244	+	0.999704i	$0.492257\pi$
$930$	733.921	+	612.343i	0.789163	+	0.658433i
$931$		0			0
$932$	−575.747	+	997.223i	−0.617754	+	1.06998i
$933$	−573.932	−	99.5452i	−0.615147	−	0.106694i
$934$			604.473i			0.647187i
$935$	201.195	−	348.480i	0.215182	−	0.372706i
$936$	172.691	−	482.852i	0.184499	−	0.515868i
$937$		−	184.891i		−	0.197322i	−0.995121	−	0.0986610i	$-0.968544\pi$
$937$		−	184.891i		−	0.197322i	0.995121	−	0.0986610i	$-0.0314559\pi$
$938$		0			0
$939$	358.536	+	976.560i	0.381827	+	1.04000i
$940$	837.677			0.891145
$941$	1091.52	−	630.188i	1.15995	−	0.669700i	0.208661	−	0.977988i	$-0.433089\pi$
$941$	1091.52	−	630.188i	1.15995	−	0.669700i	0.951293	+	0.308288i	$0.0997561\pi$
$942$	743.235	−	890.802i	0.788997	−	0.945649i
$943$	−17.2548	−	9.96206i	−0.0182978	−	0.0105642i
$944$			899.178i			0.952519i
$945$		0			0
$946$	704.326			0.744531
$947$	229.847	−	398.107i	0.242711	−	0.420387i	−0.718775	−	0.695243i	$-0.755297\pi$
$947$	229.847	−	398.107i	0.242711	−	0.420387i	0.961485	+	0.274856i	$0.0886301\pi$
$948$	646.232	+	539.180i	0.681680	+	0.568755i
$949$	−350.055	−	606.312i	−0.368867	−	0.638896i
$950$		−	676.211i		−	0.711801i
$951$	−194.489	+	71.4048i	−0.204510	+	0.0750839i
$952$		0			0
$953$	−278.059			−0.291772			−0.145886	−	0.989301i	$-0.546603\pi$
$953$	−278.059			−0.291772			−0.145886	+	0.989301i	$0.546603\pi$
$954$	−700.583	+	594.569i	−0.734363	+	0.623238i
$955$	385.983	+	222.848i	0.404171	+	0.233348i
$956$	−375.862			−0.393161
$957$	83.4658	−	481.226i	0.0872161	−	0.502848i
$958$	558.953	+	322.712i	0.583459	+	0.336860i
$959$		0			0
$960$	−162.928	+	195.276i	−0.169716	+	0.203413i
$961$	66.0373	−	114.380i	0.0687173	−	0.119022i
$962$	−423.516	−	244.517i	−0.440246	−	0.254176i
$963$	−355.364	+	301.590i	−0.369018	+	0.313177i
$964$	−203.687	+	117.598i	−0.211293	+	0.121990i
$965$	−647.222	+	373.674i	−0.670696	+	0.387227i
$966$		0			0
$967$	239.574	−	414.955i	0.247750	−	0.429116i	−0.715151	−	0.698970i	$-0.753642\pi$
$967$	239.574	−	414.955i	0.247750	−	0.429116i	0.962901	+	0.269854i	$0.0869755\pi$
$968$	166.633			0.172141
$969$	429.476	+	358.330i	0.443215	+	0.369794i
$970$	−645.864			−0.665839
$971$	−1404.28	+	810.759i	−1.44622	+	0.834973i	−0.998253	−	0.0590795i	$-0.981183\pi$
$971$	−1404.28	+	810.759i	−1.44622	+	0.834973i	−0.447962	+	0.894052i	$0.647850\pi$
$972$	129.265	+	677.545i	0.132989	+	0.697063i
$973$		0			0
$974$	−808.672	−	1400.66i	−0.830258	−	1.43805i
$975$	−221.505	−	603.323i	−0.227185	−	0.618793i
$976$	670.660	−	387.206i	0.687152	−	0.396727i
$977$	211.767	+	366.791i	0.216752	+	0.375425i	0.953813	−	0.300401i	$-0.0971204\pi$
$977$	211.767	+	366.791i	0.216752	+	0.375425i	−0.737061	+	0.675826i	$0.763787\pi$
$978$	487.699	+	406.909i	0.498670	+	0.416062i
$979$	−1528.77	+	882.634i	−1.56156	+	0.901567i
$980$		0			0
$981$	−1198.89	−	428.780i	−1.22211	−	0.437084i
$982$	420.139	+	727.702i	0.427840	+	0.741041i
$983$			1574.91i			1.60215i	0.598566	+	0.801073i	$0.295737\pi$
$983$			1574.91i			1.60215i	−0.598566	+	0.801073i	$0.704263\pi$
$984$	84.7690	+	230.889i	0.0861474	+	0.234644i
$985$			784.979i			0.796933i
$986$	−228.928	−	132.172i	−0.232179	−	0.134048i
$987$		0			0
$988$	602.874	+	1044.21i	0.610196	+	1.05689i
$989$	−7.49548	−	12.9825i	−0.00757884	−	0.0131269i
$990$	387.328	−	1082.99i	0.391241	−	1.09393i
$991$	−320.315	+	554.802i	−0.323224	+	0.559840i	−0.981151	−	0.193241i	$-0.938100\pi$
$991$	−320.315	+	554.802i	−0.323224	+	0.559840i	0.657927	+	0.753081i	$0.271433\pi$
$992$	1097.00	+	633.351i	1.10584	+	0.638458i
$993$	708.672	−	260.183i	0.713668	−	0.262017i
$994$		0			0
$995$	−369.079	+	639.264i	−0.370934	+	0.642477i
$996$	421.781	+	1148.82i	0.423475	+	1.15344i
$997$			305.870i			0.306790i	0.988165	+	0.153395i	$0.0490207\pi$
$997$			305.870i			0.306790i	−0.988165	+	0.153395i	$0.950979\pi$
$998$	210.474	−	364.552i	0.210896	−	0.365283i
$999$	−269.143	+	2.25865i	−0.269412	+	0.00226091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.k.a.31.12		28
7.2	even	3		441.3.t.b.166.3		28
7.3	odd	6		63.3.l.a.13.11	✓	28
7.4	even	3		63.3.l.a.13.12	yes	28
7.5	odd	6		441.3.t.b.166.4		28
7.6	odd	2	inner	441.3.k.a.31.11		28
9.7	even	3		441.3.t.b.178.4		28
21.11	odd	6		189.3.l.a.118.3		28
21.17	even	6		189.3.l.a.118.4		28
63.4	even	3		567.3.d.h.244.3		14
63.11	odd	6		189.3.l.a.181.4		28
63.16	even	3	inner	441.3.k.a.313.11		28
63.25	even	3		63.3.l.a.34.11	yes	28
63.31	odd	6		567.3.d.h.244.4		14
63.32	odd	6		567.3.d.g.244.12		14
63.34	odd	6		441.3.t.b.178.3		28
63.38	even	6		189.3.l.a.181.3		28
63.52	odd	6		63.3.l.a.34.12	yes	28
63.59	even	6		567.3.d.g.244.11		14
63.61	odd	6	inner	441.3.k.a.313.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.11	✓	28	7.3	odd	6
63.3.l.a.13.12	yes	28	7.4	even	3
63.3.l.a.34.11	yes	28	63.25	even	3
63.3.l.a.34.12	yes	28	63.52	odd	6
189.3.l.a.118.3		28	21.11	odd	6
189.3.l.a.118.4		28	21.17	even	6
189.3.l.a.181.3		28	63.38	even	6
189.3.l.a.181.4		28	63.11	odd	6
441.3.k.a.31.11		28	7.6	odd	2	inner
441.3.k.a.31.12		28	1.1	even	1	trivial
441.3.k.a.313.11		28	63.16	even	3	inner
441.3.k.a.313.12		28	63.61	odd	6	inner
441.3.t.b.166.3		28	7.2	even	3
441.3.t.b.166.4		28	7.5	odd	6
441.3.t.b.178.3		28	63.34	odd	6
441.3.t.b.178.4		28	9.7	even	3
567.3.d.g.244.11		14	63.59	even	6
567.3.d.g.244.12		14	63.32	odd	6
567.3.d.h.244.3		14	63.4	even	3
567.3.d.h.244.4		14	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30753 - 2.26471i) q^{2} +(2.30352 + 1.92193i) q^{3} +(-1.41927 - 2.45825i) q^{4} -3.68512i q^{5} +(7.36452 - 2.70382i) q^{6} +3.03728 q^{8} +(1.61239 + 8.85439i) q^{9} +O(q^{10})\)	\(q+(1.30753 - 2.26471i) q^{2} +(2.30352 + 1.92193i) q^{3} +(-1.41927 - 2.45825i) q^{4} -3.68512i q^{5} +(7.36452 - 2.70382i) q^{6} +3.03728 q^{8} +(1.61239 + 8.85439i) q^{9} +(-8.34571 - 4.81840i) q^{10} +13.2613 q^{11} +(1.45526 - 8.39036i) q^{12} +(-16.2463 - 9.37981i) q^{13} +(7.08252 - 8.48873i) q^{15} +(9.64842 - 16.7116i) q^{16} +(7.13083 + 4.11699i) q^{17} +(22.1609 + 7.92578i) q^{18} +(19.6096 - 11.3216i) q^{19} +(-9.05893 + 5.23018i) q^{20} +(17.3396 - 30.0330i) q^{22} -0.738115 q^{23} +(6.99644 + 5.83744i) q^{24} +11.4199 q^{25} +(-42.4851 + 24.5288i) q^{26} +(-13.3033 + 23.4952i) q^{27} +(-6.13829 - 10.6318i) q^{29} +(-9.96389 - 27.1391i) q^{30} +(-28.6323 + 16.5308i) q^{31} +(-19.1566 - 33.1803i) q^{32} +(30.5477 + 25.4873i) q^{33} +(18.6476 - 10.7662i) q^{34} +(19.4779 - 16.5304i) q^{36} +(4.98430 + 8.63306i) q^{37} -59.2132i q^{38} +(-19.3964 - 52.8308i) q^{39} -11.1927i q^{40} +(23.3769 + 13.4966i) q^{41} +(10.1549 + 17.5888i) q^{43} +(-18.8214 - 32.5996i) q^{44} +(32.6294 - 5.94186i) q^{45} +(-0.965107 + 1.67161i) q^{46} +(-69.3523 - 40.0406i) q^{47} +(54.3437 - 19.9518i) q^{48} +(14.9319 - 25.8628i) q^{50} +(8.51346 + 23.1885i) q^{51} +53.2499i q^{52} +(-19.5210 + 33.8113i) q^{53} +(35.8152 + 60.8487i) q^{54} -48.8695i q^{55} +(66.9302 + 11.6087i) q^{57} -32.1040 q^{58} +(-40.3543 + 23.2986i) q^{59} +(-30.9194 - 5.36279i) q^{60} +(34.7549 + 20.0658i) q^{61} +86.4583i q^{62} -23.0042 q^{64} +(-34.5657 + 59.8695i) q^{65} +(97.6633 - 35.8562i) q^{66} +(-54.5167 - 94.4257i) q^{67} -23.3725i q^{68} +(-1.70026 - 1.41860i) q^{69} +83.8258 q^{71} +(4.89730 + 26.8933i) q^{72} +(32.3201 + 18.6600i) q^{73} +26.0685 q^{74} +(26.3060 + 21.9483i) q^{75} +(-55.6625 - 32.1368i) q^{76} +(-145.008 - 25.1507i) q^{78} +(-49.4165 + 85.5918i) q^{79} +(-61.5840 - 35.5556i) q^{80} +(-75.8004 + 28.5535i) q^{81} +(61.1319 - 35.2945i) q^{82} +(-124.459 + 71.8564i) q^{83} +(15.1716 - 26.2779i) q^{85} +53.1113 q^{86} +(6.29393 - 36.2879i) q^{87} +40.2784 q^{88} +(-115.280 + 66.5571i) q^{89} +(29.2074 - 81.6653i) q^{90} +(1.04758 + 1.81447i) q^{92} +(-97.7260 - 16.9500i) q^{93} +(-181.360 + 104.708i) q^{94} +(-41.7213 - 72.2635i) q^{95} +(19.6424 - 113.249i) q^{96} +(58.0415 - 33.5103i) q^{97} +(21.3825 + 117.421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Introduction

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