LMFDB - Embedded newform 570.2.bh.b.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.b.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.19781 + 1.88819i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.291238 - 1.08692i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.19781 + 1.88819i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.291238 - 1.08692i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-1.02868 - 1.98540i) q^{10} +(-2.64257 - 4.57707i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.21242 - 4.74454i) q^{13} +(0.195399 + 1.10816i) q^{14} +(1.88357 + 1.20506i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.159405 + 1.82200i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(2.92739 - 3.22962i) q^{19} +(0.851731 + 2.06750i) q^{20} +(-0.723302 - 0.861997i) q^{21} +(2.23360 + 4.78997i) q^{22} +(3.67454 - 2.57294i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(-2.13051 + 4.52338i) q^{25} +(-2.61751 + 4.53366i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-0.0980727 - 1.12098i) q^{28} +(7.21644 + 6.05531i) q^{29} +(-1.77137 - 1.36464i) q^{30} +(7.31997 + 4.22619i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-4.32934 - 3.03143i) q^{33} +(0.317596 - 1.80118i) q^{34} +(1.70345 - 1.85183i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-7.00656 - 7.00656i) q^{37} +(-3.19773 + 2.96219i) q^{38} -5.23502i q^{39} +(-0.668296 - 2.13387i) q^{40} +(-4.11745 + 11.3126i) q^{41} +(0.645421 + 0.921757i) q^{42} +(0.282325 - 0.403202i) q^{43} +(-1.80763 - 4.96641i) q^{44} +(2.21637 + 0.296129i) q^{45} +(-3.88480 + 2.24289i) q^{46} +(1.52548 - 0.133462i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(4.96561 - 2.86690i) q^{49} +(2.51664 - 4.32048i) q^{50} +(0.625543 + 1.71866i) q^{51} +(3.00269 - 4.28828i) q^{52} +(-2.22801 - 3.18193i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(5.47707 - 10.4721i) q^{55} +1.12526i q^{56} +(1.28822 - 4.16419i) q^{57} +(-6.66122 - 6.66122i) q^{58} +(-4.79701 + 4.02517i) q^{59} +(1.64569 + 1.51383i) q^{60} +(0.823289 - 4.66911i) q^{61} +(-6.92378 - 4.84809i) q^{62} +(-1.01983 - 0.475554i) q^{63} +(0.866025 + 0.500000i) q^{64} +(11.6086 - 1.50560i) q^{65} +(4.04866 + 3.39723i) q^{66} +(-0.735927 - 8.41169i) q^{67} +(-0.473371 + 1.76664i) q^{68} +(2.24289 - 3.88480i) q^{69} +(-1.85837 + 1.69632i) q^{70} +(-12.5064 + 2.20522i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(5.77779 + 12.3905i) q^{73} +(6.36924 + 7.59056i) q^{74} +(-0.0192329 + 4.99996i) q^{75} +(3.44373 - 2.67221i) q^{76} +(-4.20527 + 4.20527i) q^{77} +(-0.456262 + 5.21510i) q^{78} +(2.12465 + 0.773309i) q^{79} +(0.479774 + 2.18399i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(5.08775 - 10.9107i) q^{82} +(5.55490 - 1.48843i) q^{83} +(-0.562629 - 0.974502i) q^{84} +(-3.63122 + 1.88143i) q^{85} +(-0.316392 + 0.377061i) q^{86} +(9.09940 + 2.43818i) q^{87} +(1.36790 + 5.10506i) q^{88} +(0.0291272 - 0.0106014i) q^{89} +(-2.18213 - 0.488171i) q^{90} +(-5.80125 - 1.02292i) q^{91} +(4.06550 - 1.89577i) q^{92} +(8.42021 + 0.736673i) q^{93} -1.53131 q^{94} +(9.60457 + 1.65899i) q^{95} -1.00000 q^{96} +(-10.6317 - 0.930156i) q^{97} +(-5.19658 + 2.42321i) q^{98} +(-5.20485 - 0.917756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	1.19781	+	1.88819i	0.535677	+	0.844423i
$5$	1.19781	+	1.88819i	0.535677	+	0.844423i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−0.291238	−	1.08692i	−0.110078	−	0.410815i	0.888794	−	0.458307i	$-0.151544\pi$
$7$	−0.291238	−	1.08692i	−0.110078	−	0.410815i	−0.998872	+	0.0474915i	$0.984877\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	−1.02868	−	1.98540i	−0.325299	−	0.627838i
$11$	−2.64257	−	4.57707i	−0.796765	−	1.38004i	−0.921712	−	0.387875i	$-0.873209\pi$
$11$	−2.64257	−	4.57707i	−0.796765	−	1.38004i	0.124947	−	0.992163i	$-0.460124\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	2.21242	−	4.74454i	0.613614	−	1.31590i	−0.316488	−	0.948597i	$-0.602504\pi$
$13$	2.21242	−	4.74454i	0.613614	−	1.31590i	0.930102	−	0.367302i	$-0.119719\pi$
$14$	0.195399	+	1.10816i	0.0522226	+	0.296169i
$15$	1.88357	+	1.20506i	0.486335	+	0.311146i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.159405	+	1.82200i	−0.0386613	+	0.441901i	0.952052	+	0.305936i	$0.0989692\pi$
$17$	−0.159405	+	1.82200i	−0.0386613	+	0.441901i	−0.990714	+	0.135966i	$0.956586\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	2.92739	−	3.22962i	0.671588	−	0.740925i
$19$	2.92739	−	3.22962i	0.671588	−	0.740925i
$20$	0.851731	+	2.06750i	0.190453	+	0.462307i
$21$	−0.723302	−	0.861997i	−0.157837	−	0.188103i
$22$	2.23360	+	4.78997i	0.476205	+	1.02122i
$23$	3.67454	−	2.57294i	0.766194	−	0.536495i	−0.123887	−	0.992296i	$-0.539536\pi$
$23$	3.67454	−	2.57294i	0.766194	−	0.536495i	0.890081	+	0.455801i	$0.150647\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	−2.13051	+	4.52338i	−0.426101	+	0.904675i
$26$	−2.61751	+	4.53366i	−0.513336	+	0.889124i
$27$	0.258819	−	0.965926i	0.0498097	−	0.185893i
$28$	−0.0980727	−	1.12098i	−0.0185340	−	0.211844i
$29$	7.21644	+	6.05531i	1.34006	+	1.12444i	0.981611	+	0.190894i	$0.0611385\pi$
$29$	7.21644	+	6.05531i	1.34006	+	1.12444i	0.358448	+	0.933550i	$0.383306\pi$
$30$	−1.77137	−	1.36464i	−0.323407	−	0.249148i
$31$	7.31997	+	4.22619i	1.31471	+	0.759046i	0.982872	−	0.184292i	$-0.0589991\pi$
$31$	7.31997	+	4.22619i	1.31471	+	0.759046i	0.331835	+	0.943338i	$0.392332\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	−4.32934	−	3.03143i	−0.753641	−	0.527705i
$34$	0.317596	−	1.80118i	0.0544673	−	0.308900i
$35$	1.70345	−	1.85183i	0.287936	−	0.313016i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−7.00656	−	7.00656i	−1.15187	−	1.15187i	−0.986177	−	0.165695i	$-0.947013\pi$
$37$	−7.00656	−	7.00656i	−1.15187	−	1.15187i	−0.165695	−	0.986177i	$-0.552987\pi$
$38$	−3.19773	+	2.96219i	−0.518740	+	0.480530i
$39$		−	5.23502i		−	0.838274i
$40$	−0.668296	−	2.13387i	−0.105667	−	0.337394i
$41$	−4.11745	+	11.3126i	−0.643038	+	1.76673i	−0.00107330	+	0.999999i	$0.500342\pi$
$41$	−4.11745	+	11.3126i	−0.643038	+	1.76673i	−0.641965	+	0.766734i	$0.721881\pi$
$42$	0.645421	+	0.921757i	0.0995907	+	0.142230i
$43$	0.282325	−	0.403202i	0.0430542	−	0.0614877i	−0.797048	−	0.603916i	$-0.793606\pi$
$43$	0.282325	−	0.403202i	0.0430542	−	0.0614877i	0.840102	+	0.542428i	$0.182495\pi$
$44$	−1.80763	−	4.96641i	−0.272510	−	0.748715i
$45$	2.21637	+	0.296129i	0.330397	+	0.0441443i
$46$	−3.88480	+	2.24289i	−0.572783	+	0.330696i
$47$	1.52548	−	0.133462i	0.222514	−	0.0194675i	0.0246467	−	0.999696i	$-0.492154\pi$
$47$	1.52548	−	0.133462i	0.222514	−	0.0194675i	0.197868	+	0.980229i	$0.436598\pi$
$48$	0.996195	−	0.0871557i	0.143788	−	0.0125798i
$49$	4.96561	−	2.86690i	0.709373	−	0.409557i
$50$	2.51664	−	4.32048i	0.355906	−	0.611008i
$51$	0.625543	+	1.71866i	0.0875935	+	0.240661i
$52$	3.00269	−	4.28828i	0.416397	−	0.594677i
$53$	−2.22801	−	3.18193i	−0.306041	−	0.437072i	0.636443	−	0.771324i	$-0.280405\pi$
$53$	−2.22801	−	3.18193i	−0.306041	−	0.437072i	−0.942484	+	0.334252i	$0.891516\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	5.47707	−	10.4721i	0.738528	−	1.41206i
$56$			1.12526i			0.150369i
$57$	1.28822	−	4.16419i	0.170629	−	0.551561i
$58$	−6.66122	−	6.66122i	−0.874661	−	0.874661i
$59$	−4.79701	+	4.02517i	−0.624518	+	0.524033i	−0.899220	−	0.437497i	$-0.855865\pi$
$59$	−4.79701	+	4.02517i	−0.624518	+	0.524033i	0.274702	+	0.961529i	$0.411421\pi$
$60$	1.64569	+	1.51383i	0.212458	+	0.195435i
$61$	0.823289	−	4.66911i	0.105411	−	0.597818i	−0.885644	−	0.464365i	$-0.846283\pi$
$61$	0.823289	−	4.66911i	0.105411	−	0.597818i	0.991055	−	0.133453i	$-0.0426064\pi$
$62$	−6.92378	−	4.84809i	−0.879321	−	0.615707i
$63$	−1.01983	−	0.475554i	−0.128486	−	0.0599142i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	11.6086	−	1.50560i	1.43987	−	0.186746i
$66$	4.04866	+	3.39723i	0.498355	+	0.418170i
$67$	−0.735927	−	8.41169i	−0.0899078	−	1.02765i	−0.898410	−	0.439158i	$-0.855277\pi$
$67$	−0.735927	−	8.41169i	−0.0899078	−	1.02765i	0.808502	−	0.588493i	$-0.200279\pi$
$68$	−0.473371	+	1.76664i	−0.0574047	+	0.214237i
$69$	2.24289	−	3.88480i	0.270012	−	0.467675i
$70$	−1.85837	+	1.69632i	−0.222117	+	0.202749i
$71$	−12.5064	+	2.20522i	−1.48424	+	0.261712i	−0.856271	−	0.516526i	$-0.827225\pi$
$71$	−12.5064	+	2.20522i	−1.48424	+	0.261712i	−0.627969	+	0.778238i	$0.716114\pi$
$72$	−0.819152	+	0.573576i	−0.0965380	+	0.0675966i
$73$	5.77779	+	12.3905i	0.676239	+	1.45020i	0.881833	+	0.471561i	$0.156309\pi$
$73$	5.77779	+	12.3905i	0.676239	+	1.45020i	−0.205594	+	0.978637i	$0.565913\pi$
$74$	6.36924	+	7.59056i	0.740409	+	0.882385i
$75$	−0.0192329	+	4.99996i	−0.00222082	+	0.577346i
$76$	3.44373	−	2.67221i	0.395023	−	0.306524i
$77$	−4.20527	+	4.20527i	−0.479235	+	0.479235i
$78$	−0.456262	+	5.21510i	−0.0516615	+	0.590494i
$79$	2.12465	+	0.773309i	0.239042	+	0.0870040i	0.458763	−	0.888559i	$-0.348293\pi$
$79$	2.12465	+	0.773309i	0.239042	+	0.0870040i	−0.219722	+	0.975563i	$0.570515\pi$
$80$	0.479774	+	2.18399i	0.0536404	+	0.244178i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	5.08775	−	10.9107i	0.561847	−	1.20489i
$83$	5.55490	−	1.48843i	0.609729	−	0.163376i	0.0592749	−	0.998242i	$-0.481121\pi$
$83$	5.55490	−	1.48843i	0.609729	−	0.163376i	0.550454	+	0.834865i	$0.314454\pi$
$84$	−0.562629	−	0.974502i	−0.0613878	−	0.106327i
$85$	−3.63122	+	1.88143i	−0.393862	+	0.204070i
$86$	−0.316392	+	0.377061i	−0.0341174	+	0.0406596i
$87$	9.09940	+	2.43818i	0.975558	+	0.261400i
$88$	1.36790	+	5.10506i	0.145818	+	0.544201i
$89$	0.0291272	−	0.0106014i	0.00308748	−	0.00112375i	−0.340476	−	0.940253i	$-0.610588\pi$
$89$	0.0291272	−	0.0106014i	0.00308748	−	0.00112375i	0.343563	+	0.939129i	$0.388366\pi$
$90$	−2.18213	−	0.488171i	−0.230017	−	0.0514578i
$91$	−5.80125	−	1.02292i	−0.608137	−	0.107231i
$92$	4.06550	−	1.89577i	0.423858	−	0.197648i
$93$	8.42021	+	0.736673i	0.873136	+	0.0763895i
$94$	−1.53131			−0.157943
$95$	9.60457	+	1.65899i	0.985408	+	0.170209i
$96$	−1.00000			−0.102062
$97$	−10.6317	−	0.930156i	−1.07949	−	0.0944430i	−0.466489	−	0.884527i	$-0.654481\pi$
$97$	−10.6317	−	0.930156i	−1.07949	−	0.0944430i	−0.612999	+	0.790084i	$0.710037\pi$
$98$	−5.19658	+	2.42321i	−0.524934	+	0.244781i
$99$	−5.20485	−	0.917756i	−0.523107	−	0.0922379i
$100$	−2.88362	+	4.08470i	−0.288362	+	0.408470i
$101$	−6.97186	+	2.53755i	−0.693726	+	0.252496i	−0.664730	−	0.747084i	$-0.731453\pi$
$101$	−6.97186	+	2.53755i	−0.693726	+	0.252496i	−0.0289961	+	0.999580i	$0.509231\pi$
$102$	−0.473371	−	1.76664i	−0.0468707	−	0.174924i
$103$	−15.5804	−	4.17476i	−1.53518	−	0.411351i	−0.610478	−	0.792033i	$-0.709023\pi$
$103$	−15.5804	−	4.17476i	−1.53518	−	0.411351i	−0.924706	+	0.380682i	$0.875689\pi$
$104$	−3.36501	+	4.01026i	−0.329966	+	0.393238i
$105$	0.761236	−	2.39824i	0.0742890	−	0.234044i
$106$	1.94221	+	3.36401i	0.188644	+	0.326741i
$107$	−2.21721	+	0.594101i	−0.214346	+	0.0574339i	−0.364394	−	0.931245i	$-0.618724\pi$
$107$	−2.21721	+	0.594101i	−0.214346	+	0.0574339i	0.150048	+	0.988679i	$0.452057\pi$
$108$	0.422618	−	0.906308i	0.0406665	−	0.0872095i
$109$	0.194694	+	1.10416i	0.0186483	+	0.105760i	0.992711	−	0.120518i	$-0.0384555\pi$
$109$	0.194694	+	1.10416i	0.0186483	+	0.105760i	−0.974063	+	0.226277i	$0.927344\pi$
$110$	−6.36893	+	9.95492i	−0.607254	+	0.949164i
$111$	−9.31121	−	3.38900i	−0.883781	−	0.321670i
$112$	0.0980727	−	1.12098i	0.00926700	−	0.105922i
$113$	5.50304	−	5.50304i	0.517683	−	0.517683i	−0.399187	−	0.916870i	$-0.630708\pi$
$113$	5.50304	−	5.50304i	0.517683	−	0.517683i	0.916870	+	0.399187i	$0.130708\pi$
$114$	−1.64625	+	4.03607i	−0.154185	+	0.378013i
$115$	9.25959	+	3.85633i	0.863461	+	0.359604i
$116$	6.05531	+	7.21644i	0.562222	+	0.670030i
$117$	−2.21242	−	4.74454i	−0.204538	−	0.438633i
$118$	5.12958	−	3.59177i	0.472216	−	0.330649i
$119$	2.02679	−	0.357378i	0.185796	−	0.0327608i
$120$	−1.50749	−	1.65150i	−0.137615	−	0.150761i
$121$	−8.46637	+	14.6642i	−0.769670	+	1.33311i
$122$	−1.22710	+	4.57958i	−0.111096	+	0.414616i
$123$	1.04924	+	11.9928i	0.0946064	+	1.08136i
$124$	6.47490	+	5.43308i	0.581463	+	0.487905i
$125$	−11.0929	+	1.39535i	−0.992181	+	0.124804i
$126$	0.974502	+	0.562629i	0.0868155	+	0.0501230i
$127$	−1.98049	−	0.923517i	−0.175740	−	0.0819489i	0.332757	−	0.943013i	$-0.392021\pi$
$127$	−1.98049	−	0.923517i	−0.175740	−	0.0819489i	−0.508497	+	0.861064i	$0.669799\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	0.0854729	−	0.484741i	0.00752547	−	0.0426791i
$130$	−11.6957	+	0.488109i	−1.02578	+	0.0428100i
$131$	13.8693	−	11.6377i	1.21177	−	1.01679i	0.212554	−	0.977149i	$-0.431822\pi$
$131$	13.8693	−	11.6377i	1.21177	−	1.01679i	0.999214	−	0.0396451i	$-0.0126227\pi$
$132$	−3.73716	−	3.73716i	−0.325278	−	0.325278i
$133$	−4.36288	−	2.24123i	−0.378310	−	0.194340i
$134$			8.44382i			0.729435i
$135$	2.13387	−	0.668296i	0.183654	−	0.0575177i
$136$	0.625543	−	1.71866i	0.0536398	−	0.147374i
$137$	−5.38439	−	7.68971i	−0.460020	−	0.656976i	0.520394	−	0.853926i	$-0.325785\pi$
$137$	−5.38439	−	7.68971i	−0.460020	−	0.656976i	−0.980413	+	0.196950i	$0.936896\pi$
$138$	−2.57294	+	3.67454i	−0.219023	+	0.312797i
$139$	6.19285	+	17.0147i	0.525271	+	1.44317i	0.864580	+	0.502495i	$0.167584\pi$
$139$	6.19285	+	17.0147i	0.525271	+	1.44317i	−0.339310	+	0.940675i	$0.610193\pi$
$140$	1.99914	−	1.52789i	0.168958	−	0.129131i
$141$	1.32615	−	0.765655i	0.111682	−	0.0644798i
$142$	12.6510	−	1.10682i	1.06165	−	0.0928825i
$143$	−27.5626	+	2.41141i	−2.30490	+	0.201652i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−2.78965	+	20.8791i	−0.231668	+	1.73391i
$146$	−4.67590	−	12.8469i	−0.386980	−	1.06322i
$147$	3.28877	−	4.69685i	0.271253	−	0.387390i
$148$	−5.68344	−	8.11680i	−0.467176	−	0.667197i
$149$	−3.92463	+	10.7828i	−0.321518	+	0.883365i	0.668662	+	0.743567i	$0.266867\pi$
$149$	−3.92463	+	10.7828i	−0.321518	+	0.883365i	−0.990180	+	0.139798i	$0.955355\pi$
$150$	0.454935	−	4.97926i	0.0371453	−	0.406555i
$151$			15.4174i			1.25465i	0.778757	+	0.627326i	$0.215851\pi$
$151$			15.4174i			1.25465i	−0.778757	+	0.627326i	$0.784149\pi$
$152$	−3.66352	+	2.36191i	−0.297151	+	0.191576i
$153$	1.29327	+	1.29327i	0.104555	+	0.104555i
$154$	4.55578	−	3.82275i	0.367115	−	0.308046i
$155$	0.788093	+	18.8837i	0.0633012	+	1.51677i
$156$	0.909052	−	5.15549i	0.0727824	−	0.412770i
$157$	2.21719	+	1.55249i	0.176951	+	0.123902i	0.658696	−	0.752409i	$-0.271108\pi$
$157$	2.21719	+	1.55249i	0.176951	+	0.123902i	−0.481746	+	0.876311i	$0.659997\pi$
$158$	−2.04916	−	0.955541i	−0.163023	−	0.0760188i
$159$	−3.36401	−	1.94221i	−0.266783	−	0.154027i
$160$	−0.287601	−	2.21750i	−0.0227369	−	0.175308i
$161$	−3.86673	−	3.24457i	−0.304741	−	0.255708i
$162$	0.0871557	+	0.996195i	0.00684760	+	0.0782684i
$163$	−3.38401	+	12.6293i	−0.265056	+	0.989203i	0.697160	+	0.716916i	$0.254447\pi$
$163$	−3.38401	+	12.6293i	−0.265056	+	0.989203i	−0.962216	+	0.272288i	$0.912220\pi$
$164$	−6.01932	+	10.4258i	−0.470030	+	0.814115i
$165$	0.538198	−	11.8057i	0.0418987	−	0.919071i
$166$	−5.66348	+	0.998625i	−0.439572	+	0.0775083i
$167$	−8.46580	+	5.92781i	−0.655103	+	0.458708i	−0.853276	−	0.521459i	$-0.825388\pi$
$167$	−8.46580	+	5.92781i	−0.655103	+	0.458708i	0.198173	+	0.980167i	$0.436499\pi$
$168$	0.475554	+	1.01983i	0.0366898	+	0.0786816i
$169$	−9.25965	−	11.0352i	−0.712280	−	0.848863i
$170$	3.78138	−	1.55779i	0.290019	−	0.119477i
$171$	−0.592342	−	4.31846i	−0.0452975	−	0.330241i
$172$	0.348051	−	0.348051i	0.0265387	−	0.0265387i
$173$	−0.847627	+	9.68842i	−0.0644439	+	0.736597i	0.893391	+	0.449279i	$0.148319\pi$
$173$	−0.847627	+	9.68842i	−0.0644439	+	0.736597i	−0.957835	+	0.287318i	$0.907236\pi$
$174$	−8.85227	−	3.22196i	−0.671089	−	0.244256i
$175$	5.53701	+	0.998301i	0.418559	+	0.0754644i
$176$	−0.917756	−	5.20485i	−0.0691784	−	0.392330i
$177$	−2.64646	+	5.67535i	−0.198920	+	0.426585i
$178$	−0.0299403	+	0.00802248i	−0.00224412	+	0.000601311i
$179$	−11.1888	−	19.3796i	−0.836291	−	1.44850i	−0.892975	−	0.450106i	$-0.851386\pi$
$179$	−11.1888	−	19.3796i	−0.836291	−	1.44850i	0.0566841	−	0.998392i	$-0.481947\pi$
$180$	2.13128	+	0.676499i	0.158856	+	0.0504233i
$181$	−14.7726	+	17.6053i	−1.09804	+	1.30859i	−0.150621	+	0.988592i	$0.548127\pi$
$181$	−14.7726	+	17.6053i	−1.09804	+	1.30859i	−0.947417	+	0.320000i	$0.896317\pi$
$182$	5.69003	+	1.52464i	0.421773	+	0.113014i
$183$	−1.22710	−	4.57958i	−0.0907095	−	0.338533i
$184$	−4.21526	+	1.53423i	−0.310753	+	0.113105i
$185$	4.83718	−	21.6222i	0.355637	−	1.58970i
$186$	−8.32397	−	1.46774i	−0.610343	−	0.107620i
$187$	8.76068	−	4.08517i	0.640644	−	0.298737i
$188$	1.52548	+	0.133462i	0.111257	+	0.00973375i
$189$	−1.12526			−0.0818504
$190$	−9.42343	−	2.48977i	−0.683647	−	0.180627i
$191$	14.2081			1.02806			0.514032	−	0.857771i	$-0.328151\pi$
$191$	14.2081			1.02806			0.514032	+	0.857771i	$0.328151\pi$
$192$	0.996195	+	0.0871557i	0.0718942	+	0.00628992i
$193$	16.1695	−	7.53994i	1.16390	−	0.542737i	0.257968	−	0.966154i	$-0.416947\pi$
$193$	16.1695	−	7.53994i	1.16390	−	0.542737i	0.905935	+	0.423417i	$0.139169\pi$
$194$	10.5102	+	1.85323i	0.754588	+	0.133054i
$195$	9.88470	−	6.27056i	0.707858	−	0.449044i
$196$	5.38801	−	1.96107i	0.384858	−	0.140077i
$197$	−3.04908	−	11.3793i	−0.217238	−	0.810742i	−0.985367	−	0.170447i	$-0.945479\pi$
$197$	−3.04908	−	11.3793i	−0.217238	−	0.810742i	0.768129	−	0.640295i	$-0.221188\pi$
$198$	5.10506	+	1.36790i	0.362801	+	0.0972121i
$199$	6.09705	−	7.26618i	0.432208	−	0.515086i	−0.505350	−	0.862915i	$-0.668637\pi$
$199$	6.09705	−	7.26618i	0.432208	−	0.515086i	0.937558	+	0.347829i	$0.113081\pi$
$200$	3.22865	−	3.81783i	0.228300	−	0.269961i
$201$	−4.22191	−	7.31256i	−0.297790	−	0.515788i
$202$	7.16649	−	1.92025i	0.504232	−	0.135109i
$203$	4.47991	−	9.60720i	0.314428	−	0.674293i
$204$	0.317596	+	1.80118i	0.0222362	+	0.126108i
$205$	−26.2923	+	5.77582i	−1.83633	+	0.403401i
$206$	15.1573	+	5.51680i	1.05606	+	0.384374i
$207$	0.390962	−	4.46871i	0.0271737	−	0.310597i
$208$	3.70172	−	3.70172i	0.256668	−	0.256668i
$209$	−22.5180	−	4.86436i	−1.55760	−	0.336474i
$210$	−0.967359	+	2.32277i	−0.0667541	+	0.160286i
$211$	4.71836	+	5.62312i	0.324825	+	0.387111i	0.903601	−	0.428375i	$-0.140914\pi$
$211$	4.71836	+	5.62312i	0.324825	+	0.387111i	−0.578776	+	0.815487i	$0.696469\pi$
$212$	−1.64163	−	3.52048i	−0.112747	−	0.241788i
$213$	−10.4027	+	7.28406i	−0.712782	+	0.499095i
$214$	2.26056	−	0.398597i	0.154528	−	0.0272475i
$215$	1.09949	+	0.0501237i	0.0749848	+	0.00341841i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	2.46165	−	9.18702i	0.167108	−	0.623656i
$218$	−0.0977187	−	1.11693i	−0.00661834	−	0.0756480i
$219$	10.4729	+	8.78781i	0.707693	+	0.593825i
$220$	7.21233	−	9.36195i	0.486255	−	0.631183i
$221$	8.29191	+	4.78733i	0.557774	+	0.322031i
$222$	8.98040	+	4.18763i	0.602725	+	0.281055i
$223$	15.2918	+	10.7074i	1.02401	+	0.717021i	0.959734	−	0.280911i	$-0.0906367\pi$
$223$	15.2918	+	10.7074i	1.02401	+	0.717021i	0.0642779	+	0.997932i	$0.479526\pi$
$224$	−0.195399	+	1.10816i	−0.0130556	+	0.0740422i
$225$	2.09564	+	4.53963i	0.139710	+	0.302642i
$226$	−5.96172	+	5.00248i	−0.396568	+	0.332760i
$227$	15.5057	+	15.5057i	1.02915	+	1.02915i	0.999562	+	0.0295900i	$0.00942016\pi$
$227$	15.5057	+	15.5057i	1.02915	+	1.02915i	0.0295900	+	0.999562i	$0.490580\pi$
$228$	1.99175	−	3.87723i	0.131907	−	0.256776i
$229$			9.35047i			0.617897i	0.951079	+	0.308948i	$0.0999770\pi$
$229$			9.35047i			0.617897i	−0.951079	+	0.308948i	$0.900023\pi$
$230$	−8.88825	−	4.64868i	−0.586074	−	0.306525i
$231$	−2.03404	+	5.58849i	−0.133830	+	0.367696i
$232$	−5.40332	−	7.71673i	−0.354745	−	0.506628i
$233$	0.821062	−	1.17260i	0.0537895	−	0.0768194i	−0.791356	−	0.611355i	$-0.790625\pi$
$233$	0.821062	−	1.17260i	0.0537895	−	0.0768194i	0.845146	+	0.534536i	$0.179514\pi$
$234$	1.79048	+	4.91931i	0.117048	+	0.321585i
$235$	2.07924	+	2.72053i	0.135635	+	0.177468i
$236$	−5.42310	+	3.13103i	−0.353014	+	0.203813i
$237$	2.25240	−	0.197059i	0.146309	−	0.0128004i
$238$	−2.05022	+	0.179371i	−0.132896	+	0.0116269i
$239$	9.53554	−	5.50535i	0.616803	−	0.356111i	−0.158820	−	0.987308i	$-0.550769\pi$
$239$	9.53554	−	5.50535i	0.616803	−	0.356111i	0.775623	+	0.631196i	$0.217436\pi$
$240$	1.35782	+	1.77661i	0.0876467	+	0.114679i
$241$	5.29035	+	14.5351i	0.340781	+	0.936289i	0.985169	+	0.171589i	$0.0548903\pi$
$241$	5.29035	+	14.5351i	0.340781	+	0.936289i	−0.644387	+	0.764699i	$0.722888\pi$
$242$	9.71223	−	13.8705i	0.624326	−	0.891629i
$243$	−0.573576	−	0.819152i	−0.0367949	−	0.0525486i
$244$	1.62156	−	4.45521i	0.103810	−	0.285216i
$245$	11.3611	+	5.94201i	0.725834	+	0.379621i
$246$		−	12.0386i		−	0.767555i
$247$	−8.84645	−	21.0344i	−0.562886	−	1.33838i
$248$	−5.97673	−	5.97673i	−0.379523	−	0.379523i
$249$	4.40541	−	3.69658i	0.279181	−	0.234261i
$250$	11.1723	−	0.423224i	0.706600	−	0.0267670i
$251$	0.723094	−	4.10087i	0.0456413	−	0.258844i	−0.953446	−	0.301564i	$-0.902491\pi$
$251$	0.723094	−	4.10087i	0.0456413	−	0.258844i	0.999087	+	0.0427199i	$0.0136023\pi$
$252$	−0.921757	−	0.645421i	−0.0580652	−	0.0406577i
$253$	−21.4867	−	10.0194i	−1.35086	−	0.629916i
$254$	1.89246	+	1.09261i	0.118744	+	0.0685567i
$255$	−2.49588	+	3.23977i	−0.156298	+	0.202883i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.08030	+	12.3479i	0.0673871	+	0.770238i	0.952436	+	0.304739i	$0.0985694\pi$
$257$	1.08030	+	12.3479i	0.0673871	+	0.770238i	−0.885049	+	0.465498i	$0.845875\pi$
$258$	−0.127396	+	0.475447i	−0.00793130	+	0.0296000i
$259$	−5.57496	+	9.65612i	−0.346411	+	0.600002i
$260$	11.6937	+	0.533094i	0.725214	+	0.0330611i
$261$	9.27728	−	1.63583i	0.574249	−	0.101256i
$262$	−14.8308	+	10.3847i	−0.916252	+	0.641567i
$263$	0.954008	+	2.04588i	0.0588267	+	0.126154i	0.933523	−	0.358516i	$-0.116717\pi$
$263$	0.954008	+	2.04588i	0.0588267	+	0.126154i	−0.874697	+	0.484671i	$0.838939\pi$
$264$	3.39723	+	4.04866i	0.209085	+	0.249178i
$265$	3.33935	−	8.01825i	0.205135	−	0.492557i
$266$	4.15095	+	2.61296i	0.254511	+	0.160211i
$267$	0.0219178	−	0.0219178i	0.00134135	−	0.00134135i
$268$	0.735927	−	8.41169i	0.0449539	−	0.513826i
$269$	22.0089	+	8.01058i	1.34190	+	0.488413i	0.910412	−	0.413703i	$-0.135765\pi$
$269$	22.0089	+	8.01058i	1.34190	+	0.488413i	0.431493	+	0.902116i	$0.357987\pi$
$270$	−2.18399	+	0.479774i	−0.132913	+	0.0291981i
$271$	−3.89677	−	22.0997i	−0.236712	−	1.34246i	−0.838979	−	0.544164i	$-0.816847\pi$
$271$	−3.89677	−	22.0997i	−0.236712	−	1.34246i	0.602267	−	0.798295i	$-0.294264\pi$
$272$	−0.772954	+	1.65760i	−0.0468672	+	0.100507i
$273$	−5.69003	+	1.52464i	−0.344376	+	0.0922753i
$274$	4.69370	+	8.12973i	0.283557	+	0.491135i
$275$	26.3338	−	2.20187i	1.58799	−	0.132778i
$276$	2.88340	−	3.43631i	0.173561	−	0.206841i
$277$	5.63878	+	1.51091i	0.338801	+	0.0907815i	0.424208	−	0.905565i	$-0.360552\pi$
$277$	5.63878	+	1.51091i	0.338801	+	0.0907815i	−0.0854071	+	0.996346i	$0.527219\pi$
$278$	−4.68635	−	17.4897i	−0.281069	−	1.04896i
$279$	7.94264	−	2.89088i	0.475513	−	0.173073i
$280$	−2.12470	+	1.34784i	−0.126975	+	0.0805491i
$281$	−20.4704	−	3.60948i	−1.22116	−	0.215323i	−0.474335	−	0.880344i	$-0.657312\pi$
$281$	−20.4704	−	3.60948i	−1.22116	−	0.215323i	−0.746825	+	0.665021i	$0.768423\pi$
$282$	−1.38784	+	0.647159i	−0.0826445	+	0.0385378i
$283$	1.84611	+	0.161513i	0.109740	+	0.00960097i	0.141893	−	0.989882i	$-0.454681\pi$
$283$	1.84611	+	0.161513i	0.109740	+	0.00960097i	−0.0321536	+	0.999483i	$0.510237\pi$
$284$	−12.6994			−0.753569
$285$	9.40582	−	2.55551i	0.557152	−	0.151375i
$286$	27.6678			1.63603
$287$	13.4950	+	1.18066i	0.796585	+	0.0696922i
$288$	−0.906308	+	0.422618i	−0.0534047	+	0.0249030i
$289$	13.4474	+	2.37115i	0.791026	+	0.139479i
$290$	4.59877	−	20.5565i	0.270049	−	1.20712i
$291$	−10.0287	+	3.65015i	−0.587894	+	0.213976i
$292$	3.53842	+	13.2056i	0.207070	+	0.772797i
$293$	−7.69243	−	2.06118i	−0.449397	−	0.120415i	0.0270204	−	0.999635i	$-0.491398\pi$
$293$	−7.69243	−	2.06118i	−0.449397	−	0.120415i	−0.476417	+	0.879219i	$0.658065\pi$
$294$	−3.68561	+	4.39234i	−0.214949	+	0.256167i
$295$	−13.3462	−	4.23627i	−0.777045	−	0.246645i
$296$	4.95439	+	8.58125i	0.287968	+	0.498775i
$297$	−5.10506	+	1.36790i	−0.296225	+	0.0793734i
$298$	4.84948	−	10.3998i	0.280923	−	0.602442i
$299$	−4.07781	−	23.1264i	−0.235826	−	1.33743i
$300$	−0.887175	+	4.92066i	−0.0512211	+	0.284095i
$301$	−0.520470	−	0.189436i	−0.0299994	−	0.0109189i
$302$	1.34372	−	15.3587i	0.0773222	−	0.883797i
$303$	−5.24623	+	5.24623i	−0.301388	+	0.301388i
$304$	3.85544	−	2.03362i	0.221124	−	0.116636i
$305$	9.80229	−	4.03817i	0.561278	−	0.231225i
$306$	−1.17564	−	1.40107i	−0.0672066	−	0.0800937i
$307$	3.57956	+	7.67640i	0.204296	+	0.438115i	0.981584	−	0.191030i	$-0.0611828\pi$
$307$	3.57956	+	7.67640i	0.204296	+	0.438115i	−0.777288	+	0.629145i	$0.783405\pi$
$308$	−4.87162	+	3.41114i	−0.277586	+	0.194368i
$309$	−15.8850	+	2.80095i	−0.903665	+	0.159341i
$310$	0.860725	−	18.8805i	0.0488859	−	1.07234i
$311$	0.890071	−	1.54165i	0.0504713	−	0.0874188i	−0.839686	−	0.543072i	$-0.817261\pi$
$311$	0.890071	−	1.54165i	0.0504713	−	0.0874188i	0.890157	+	0.455653i	$0.150594\pi$
$312$	−1.35492	+	5.05664i	−0.0767074	+	0.286276i
$313$	1.66382	+	19.0176i	0.0940447	+	1.07494i	0.885790	+	0.464085i	$0.153617\pi$
$313$	1.66382	+	19.0176i	0.0940447	+	1.07494i	−0.791746	+	0.610851i	$0.790827\pi$
$314$	−2.07344	−	1.73982i	−0.117011	−	0.0981839i
$315$	−0.323625	−	2.49525i	−0.0182342	−	0.140592i
$316$	1.95809	+	1.13050i	0.110151	+	0.0635957i
$317$	−13.5978	−	6.34076i	−0.763729	−	0.356133i	0.00140900	−	0.999999i	$-0.499552\pi$
$317$	−13.5978	−	6.34076i	−0.763729	−	0.356133i	−0.765138	+	0.643866i	$0.777329\pi$
$318$	3.18193	+	2.22801i	0.178434	+	0.124941i
$319$	8.64562	−	49.0317i	0.484062	−	2.74525i
$320$	0.0932392	+	2.23412i	0.00521223	+	0.124891i
$321$	−1.75840	+	1.47547i	−0.0981443	+	0.0823529i
$322$	3.56923	+	3.56923i	0.198906	+	0.198906i
$323$	5.41774	+	5.84853i	0.301451	+	0.325421i
$324$		−	1.00000i		−	0.0555556i
$325$	16.7478	+	20.1159i	0.929000	+	1.11583i
$326$	4.47185	−	12.2863i	0.247673	−	0.680476i
$327$	0.643092	+	0.918430i	0.0355630	+	0.0507893i
$328$	6.90508	−	9.86147i	0.381269	−	0.544509i
$329$	−0.589341	−	1.61920i	−0.0324914	−	0.0892694i
$330$	−1.56508	+	11.7138i	−0.0861550	+	0.644826i
$331$	1.25785	−	0.726221i	0.0691378	−	0.0399167i	−0.465033	−	0.885294i	$-0.653957\pi$
$331$	1.25785	−	0.726221i	0.0691378	−	0.0399167i	0.534170	+	0.845377i	$0.320624\pi$
$332$	5.72897	−	0.501220i	0.314418	−	0.0275080i
$333$	−9.87107	+	0.863607i	−0.540931	+	0.0473254i
$334$	8.95023	−	5.16741i	0.489735	−	0.282748i
$335$	15.0013	−	11.4652i	0.819611	−	0.626409i
$336$	−0.384861	−	1.05740i	−0.0209959	−	0.0576857i
$337$	−17.2110	+	24.5798i	−0.937540	+	1.33895i	0.00326325	+	0.999995i	$0.498961\pi$
$337$	−17.2110	+	24.5798i	−0.937540	+	1.33895i	−0.940804	+	0.338952i	$0.889928\pi$
$338$	8.26263	+	11.8003i	0.449428	+	0.641849i
$339$	2.66176	−	7.31313i	0.144567	−	0.397195i
$340$	−3.90276	+	1.22229i	−0.211657	+	0.0662880i
$341$		−	44.6720i		−	2.41913i
$342$	0.213709	+	4.35366i	0.0115560	+	0.235419i
$343$	−10.1320	−	10.1320i	−0.547076	−	0.547076i
$344$	−0.377061	+	0.316392i	−0.0203298	+	0.0170587i
$345$	10.0218	−	0.418251i	0.539555	−	0.0225179i
$346$	1.68880	−	9.57768i	0.0907906	−	0.514899i
$347$	1.82075	+	1.27490i	0.0977429	+	0.0684403i	0.621426	−	0.783473i	$-0.286554\pi$
$347$	1.82075	+	1.27490i	0.0977429	+	0.0684403i	−0.523683	+	0.851913i	$0.675442\pi$
$348$	8.53778	+	3.98123i	0.457673	+	0.213416i
$349$	5.06520	+	2.92440i	0.271134	+	0.156539i	0.629403	−	0.777079i	$-0.283300\pi$
$349$	5.06520	+	2.92440i	0.271134	+	0.156539i	−0.358269	+	0.933618i	$0.616633\pi$
$350$	−5.42894	−	1.47708i	−0.290189	−	0.0789535i
$351$	−4.01026	−	3.36501i	−0.214052	−	0.179611i
$352$	0.460631	+	5.26503i	0.0245517	+	0.280627i
$353$	1.44066	−	5.37660i	0.0766783	−	0.286167i	−0.916930	−	0.399047i	$-0.869341\pi$
$353$	1.44066	−	5.37660i	0.0766783	−	0.286167i	0.993609	+	0.112880i	$0.0360076\pi$
$354$	3.13103	−	5.42310i	0.166412	−	0.288235i
$355$	−19.1442	−	20.9731i	−1.01607	−	1.11313i
$356$	0.0305256	−	0.00538249i	0.00161785	−	0.000285271i
$357$	1.68586	−	1.18045i	0.0892252	−	0.0624762i
$358$	9.45719	+	20.2810i	0.499828	+	1.07188i
$359$	0.486978	+	0.580358i	0.0257017	+	0.0306301i	0.778742	−	0.627344i	$-0.215858\pi$
$359$	0.486978	+	0.580358i	0.0257017	+	0.0306301i	−0.753040	+	0.657974i	$0.771414\pi$
$360$	−2.06421	−	0.859678i	−0.108793	−	0.0453090i
$361$	−1.86083	−	18.9087i	−0.0979383	−	0.995192i
$362$	16.2508	−	16.2508i	0.854123	−	0.854123i
$363$	−1.47579	+	16.8683i	−0.0774587	+	0.885357i
$364$	−5.53549	−	2.01475i	−0.290139	−	0.105602i
$365$	−16.4749	+	25.7510i	−0.862336	+	1.34787i
$366$	0.823289	+	4.66911i	0.0430340	+	0.244058i
$367$	−11.7021	+	25.0952i	−0.610843	+	1.30996i	0.320994	+	0.947081i	$0.395983\pi$
$367$	−11.7021	+	25.0952i	−0.610843	+	1.30996i	−0.931837	+	0.362877i	$0.881795\pi$
$368$	4.33293	−	1.16101i	0.225870	−	0.0605216i
$369$	6.01932	+	10.4258i	0.313353	+	0.542743i
$370$	−6.70328	+	21.1184i	−0.348487	+	1.09789i
$371$	−2.80961	+	3.34836i	−0.145868	+	0.173838i
$372$	8.16437	+	2.18764i	0.423303	+	0.113424i
$373$	−7.96475	−	29.7249i	−0.412399	−	1.53909i	−0.789989	−	0.613121i	$-0.789914\pi$
$373$	−7.96475	−	29.7249i	−0.412399	−	1.53909i	0.377590	−	0.925973i	$-0.376753\pi$
$374$	−9.08339	+	3.30608i	−0.469691	+	0.170954i
$375$	−9.46391	+	5.95269i	−0.488714	+	0.307395i
$376$	−1.50805	−	0.265909i	−0.0777715	−	0.0137132i
$377$	44.6954	−	20.8418i	2.30193	−	1.07341i
$378$	1.12098	+	0.0980727i	0.0576568	+	0.00504431i
$379$	−9.74065			−0.500344			−0.250172	−	0.968201i	$-0.580487\pi$
$379$	−9.74065			−0.500344			−0.250172	+	0.968201i	$0.580487\pi$
$380$	9.17057	+	3.30160i	0.470440	+	0.169369i
$381$	−2.18523			−0.111953
$382$	−14.1541	−	1.23832i	−0.724185	−	0.0633580i
$383$	−18.3395	+	8.55185i	−0.937105	+	0.436979i	−0.830310	−	0.557302i	$-0.811837\pi$
$383$	−18.3395	+	8.55185i	−0.937105	+	0.436979i	−0.106795	+	0.994281i	$0.534059\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	−12.9774	−	2.90323i	−0.661392	−	0.147962i
$386$	−16.7651	+	6.10199i	−0.853320	+	0.310583i
$387$	−0.127396	−	0.475447i	−0.00647588	−	0.0241683i
$388$	−10.3087	−	2.76220i	−0.523344	−	0.140230i
$389$	−0.971152	+	1.15737i	−0.0492393	+	0.0586812i	−0.790102	−	0.612975i	$-0.789972\pi$
$389$	−0.971152	+	1.15737i	−0.0492393	+	0.0586812i	0.740863	+	0.671657i	$0.234417\pi$
$390$	−10.3936	+	5.38519i	−0.526301	+	0.272690i
$391$	4.10217	+	7.10516i	0.207456	+	0.359324i
$392$	−5.53842	+	1.48402i	−0.279733	+	0.0749541i
$393$	7.65155	−	16.4088i	0.385970	−	0.827715i
$394$	2.04570	+	11.6018i	0.103061	+	0.584488i
$395$	1.08477	+	4.93801i	0.0545807	+	0.248458i
$396$	−4.96641	−	1.80763i	−0.249572	−	0.0908366i
$397$	−0.961260	+	10.9873i	−0.0482443	+	0.551435i	0.933157	+	0.359468i	$0.117042\pi$
$397$	−0.961260	+	10.9873i	−0.0482443	+	0.551435i	−0.981402	+	0.191966i	$0.938514\pi$
$398$	−6.70713	+	6.70713i	−0.336198	+	0.336198i
$399$	−4.90130	−	0.187413i	−0.245372	−	0.00938236i
$400$	−3.54911	+	3.52191i	−0.177455	+	0.176095i
$401$	−16.0213	−	19.0934i	−0.800063	−	0.953478i	0.199588	−	0.979880i	$-0.436040\pi$
$401$	−16.0213	−	19.0934i	−0.800063	−	0.953478i	−0.999651	+	0.0264017i	$0.991595\pi$
$402$	3.56851	+	7.65270i	0.177981	+	0.381682i
$403$	36.2462	−	25.3798i	1.80555	−	1.26426i
$404$	−7.30658	+	1.28835i	−0.363516	+	0.0640977i
$405$	1.65150	−	1.50749i	0.0820639	−	0.0749079i
$406$	−5.30018	+	9.18019i	−0.263044	+	0.455605i
$407$	−13.5542	+	50.5849i	−0.671856	+	2.50740i
$408$	−0.159405	−	1.82200i	−0.00789171	−	0.0902027i
$409$	−8.96120	−	7.51934i	−0.443103	−	0.371807i	0.393766	−	0.919211i	$-0.371172\pi$
$409$	−8.96120	−	7.51934i	−0.443103	−	0.371807i	−0.836869	+	0.547403i	$0.815616\pi$
$410$	26.6956	−	3.46232i	1.31840	−	0.170992i
$411$	−8.12973	−	4.69370i	−0.401010	−	0.231523i
$412$	−14.6188	−	6.81685i	−0.720216	−	0.335842i
$413$	5.77209	+	4.04166i	0.284026	+	0.198877i
$414$	−0.778948	+	4.41763i	−0.0382832	+	0.217115i
$415$	9.46414	+	8.70583i	0.464577	+	0.427353i
$416$	−4.01026	+	3.36501i	−0.196619	+	0.164983i
$417$	12.8034	+	12.8034i	0.626983	+	0.626983i
$418$	22.0084	+	6.80842i	1.07646	+	0.333011i
$419$			11.7754i			0.575265i	0.957741	+	0.287632i	$0.0928682\pi$
$419$			11.7754i			0.575265i	−0.957741	+	0.287632i	$0.907132\pi$
$420$	1.16612	−	2.22962i	0.0569008	−	0.108794i
$421$	−10.2319	+	28.1118i	−0.498671	+	1.37009i	0.393889	+	0.919158i	$0.371129\pi$
$421$	−10.2319	+	28.1118i	−0.498671	+	1.37009i	−0.892560	+	0.450929i	$0.851093\pi$
$422$	−4.21031	−	6.01295i	−0.204955	−	0.292706i
$423$	0.878323	−	1.25438i	0.0427055	−	0.0609898i
$424$	1.32855	+	3.65016i	0.0645201	+	0.177268i
$425$	−7.90200	−	4.60284i	−0.383303	−	0.223271i
$426$	10.9980	−	6.34968i	0.532854	−	0.307643i
$427$	−5.31470	+	0.464976i	−0.257196	+	0.0225018i
$428$	−2.28669	+	0.200060i	−0.110532	+	0.00967025i
$429$	−23.9611	+	13.8339i	−1.15685	+	0.667908i
$430$	−1.09094	−	0.145760i	−0.0526098	−	0.00702918i
$431$	−4.77478	−	13.1186i	−0.229993	−	0.631900i	0.769988	−	0.638058i	$-0.220262\pi$
$431$	−4.77478	−	13.1186i	−0.229993	−	0.631900i	−0.999981	+	0.00615791i	$0.998040\pi$
$432$	0.573576	−	0.819152i	0.0275962	−	0.0394115i
$433$	13.1567	+	18.7898i	0.632272	+	0.902978i	0.999633	−	0.0271006i	$-0.00862744\pi$
$433$	13.1567	+	18.7898i	0.632272	+	0.902978i	−0.367361	+	0.930079i	$0.619739\pi$
$434$	−3.25299	+	8.93751i	−0.156148	+	0.429014i
$435$	6.29561	+	20.1018i	0.301851	+	0.963810i
$436$			1.12120i			0.0536956i
$437$	2.44719	−	19.3993i	0.117065	−	0.927996i
$438$	−9.66715	−	9.66715i	−0.461914	−	0.461914i
$439$	−1.13632	+	0.953484i	−0.0542335	+	0.0455073i	−0.669502	−	0.742811i	$-0.733492\pi$
$439$	−1.13632	+	0.953484i	−0.0542335	+	0.0455073i	0.615268	+	0.788318i	$0.289048\pi$
$440$	−8.00083	+	8.69773i	−0.381425	+	0.414648i
$441$	0.995663	−	5.64669i	0.0474125	−	0.268890i
$442$	−7.84311	−	5.49180i	−0.373059	−	0.261219i
$443$	3.80680	+	1.77514i	0.180867	+	0.0843395i	0.510942	−	0.859615i	$-0.329297\pi$
$443$	3.80680	+	1.77514i	0.180867	+	0.0843395i	−0.330076	+	0.943954i	$0.607074\pi$
$444$	−8.58125	−	4.95439i	−0.407248	−	0.235125i
$445$	0.0549063	+	0.0422991i	0.00260281	+	0.00200517i
$446$	−14.3004	−	11.9994i	−0.677141	−	0.568189i
$447$	1.00010	+	11.4312i	0.0473031	+	0.540677i
$448$	0.291238	−	1.08692i	0.0137597	−	0.0513519i
$449$	−4.65583	+	8.06414i	−0.219722	+	0.380570i	−0.954723	−	0.297496i	$-0.903848\pi$
$449$	−4.65583	+	8.06414i	−0.219722	+	0.380570i	0.735001	+	0.678066i	$0.237182\pi$
$450$	−1.69202	−	4.70501i	−0.0797624	−	0.221796i
$451$	62.6593	−	11.0485i	2.95051	−	0.520255i
$452$	6.37503	−	4.46384i	0.299856	−	0.209962i
$453$	6.51568	+	13.9729i	0.306133	+	0.656505i
$454$	−14.0953	−	16.7982i	−0.661526	−	0.788376i
$455$	−5.01733	−	12.1791i	−0.235216	−	0.570966i
$456$	−2.32210	+	3.68889i	−0.108742	+	0.172748i
$457$	1.87187	−	1.87187i	0.0875625	−	0.0875625i	−0.661969	−	0.749531i	$-0.730279\pi$
$457$	1.87187	−	1.87187i	0.0875625	−	0.0875625i	0.749531	+	0.661969i	$0.230279\pi$
$458$	0.814947	−	9.31489i	0.0380800	−	0.435256i
$459$	1.71866	+	0.625543i	0.0802204	+	0.0291978i
$460$	8.44927	+	5.40565i	0.393949	+	0.252040i
$461$	2.24838	+	12.7512i	0.104718	+	0.593883i	0.991333	+	0.131375i	$0.0419392\pi$
$461$	2.24838	+	12.7512i	0.104718	+	0.593883i	−0.886615	+	0.462508i	$0.846950\pi$
$462$	2.51337	−	5.38995i	0.116933	−	0.250763i
$463$	−1.57880	+	0.423039i	−0.0733733	+	0.0196603i	−0.295319	−	0.955399i	$-0.595426\pi$
$463$	−1.57880	+	0.423039i	−0.0733733	+	0.0196603i	0.221946	+	0.975059i	$0.428759\pi$
$464$	4.71020	+	8.15830i	0.218665	+	0.378740i
$465$	8.69483	+	16.7813i	0.403213	+	0.778216i
$466$	−0.920136	+	1.09658i	−0.0426245	+	0.0507979i
$467$	−19.6219	−	5.25767i	−0.907992	−	0.243296i	−0.225547	−	0.974232i	$-0.572417\pi$
$467$	−19.6219	−	5.25767i	−0.907992	−	0.243296i	−0.682446	+	0.730936i	$0.739084\pi$
$468$	−1.35492	−	5.05664i	−0.0626314	−	0.233743i
$469$	−8.92846	+	3.24969i	−0.412278	+	0.150057i
$470$	−1.83422	−	2.89140i	−0.0846061	−	0.133370i
$471$	2.66556	+	0.470011i	0.122823	+	0.0216569i
$472$	5.67535	−	2.64646i	0.261229	−	0.121813i
$473$	−2.59155	−	0.226731i	−0.119159	−	0.0104251i
$474$	−2.26100			−0.103851
$475$	8.37195	+	20.1224i	0.384132	+	0.923278i
$476$	2.05806			0.0943309
$477$	−3.86964	−	0.338550i	−0.177179	−	0.0155011i
$478$	−9.97908	+	4.65332i	−0.456432	+	0.212838i
$479$	−20.0438	−	3.53426i	−0.915823	−	0.161484i	−0.304177	−	0.952616i	$-0.598381\pi$
$479$	−20.0438	−	3.53426i	−0.915823	−	0.161484i	−0.611646	+	0.791131i	$0.709492\pi$
$480$	−1.19781	−	1.88819i	−0.0546723	−	0.0861836i
$481$	−48.7444	+	17.7415i	−2.22255	+	0.808943i
$482$	−4.00340	−	14.9409i	−0.182350	−	0.680539i
$483$	−4.87566	−	1.30643i	−0.221850	−	0.0594446i
$484$	−10.8842	+	12.9712i	−0.494735	+	0.589602i
$485$	−10.9785	−	21.1888i	−0.498507	−	0.962136i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−17.9524	+	4.81034i	−0.813503	+	0.217977i	−0.641504	−	0.767120i	$-0.721689\pi$
$487$	−17.9524	+	4.81034i	−0.813503	+	0.217977i	−0.171999	+	0.985097i	$0.555023\pi$
$488$	−2.00369	+	4.29693i	−0.0907028	+	0.194513i
$489$	2.27042	+	12.8762i	0.102672	+	0.582281i
$490$	−10.8000	−	6.90959i	−0.487894	−	0.312143i
$491$	17.9401	+	6.52966i	0.809625	+	0.294679i	0.713469	−	0.700687i	$-0.247123\pi$
$491$	17.9401	+	6.52966i	0.809625	+	0.294679i	0.0961559	+	0.995366i	$0.469345\pi$
$492$	−1.04924	+	11.9928i	−0.0473032	+	0.540678i
$493$	−12.1831	+	12.1831i	−0.548701	+	0.548701i
$494$	6.97952	+	21.7253i	0.314023	+	0.977469i
$495$	−4.50152	−	10.9270i	−0.202328	−	0.491134i
$496$	5.43308	+	6.47490i	0.243953	+	0.290731i
$497$	6.03924	+	12.9512i	0.270897	+	0.580940i
$498$	−4.71082	+	3.29855i	−0.211097	+	0.147812i
$499$	6.35493	−	1.12055i	0.284486	−	0.0501625i	−0.0295844	−	0.999562i	$-0.509418\pi$
$499$	6.35493	−	1.12055i	0.284486	−	0.0501625i	0.314070	+	0.949400i	$0.398307\pi$
$500$	−11.1667	−	0.552119i	−0.499390	−	0.0246915i
$501$	−5.16741	+	8.95023i	−0.230863	+	0.399867i
$502$	−1.07776	+	4.02224i	−0.0481026	+	0.179521i
$503$	0.0676830	+	0.773620i	0.00301784	+	0.0344940i	0.997554	−	0.0698957i	$-0.0222666\pi$
$503$	0.0676830	+	0.773620i	0.00301784	+	0.0344940i	−0.994536	+	0.104390i	$0.966711\pi$
$504$	0.861997	+	0.723302i	0.0383964	+	0.0322184i
$505$	−13.1423	−	10.1247i	−0.584826	−	0.450542i
$506$	20.5317	+	11.8540i	0.912747	+	0.526975i
$507$	−13.0558	−	6.08801i	−0.579827	−	0.270378i
$508$	−1.79003	−	1.25339i	−0.0794199	−	0.0556104i
$509$	4.17685	−	23.6881i	0.185136	−	1.04996i	−0.740645	−	0.671896i	$-0.765480\pi$
$509$	4.17685	−	23.6881i	0.185136	−	1.04996i	0.925781	−	0.378060i	$-0.123409\pi$
$510$	2.76875	−	3.00992i	0.122602	−	0.133281i
$511$	11.7847	−	9.88855i	0.521325	−	0.437444i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.36191	−	3.66352i	−0.104281	−	0.161749i
$514$		−	12.3950i		−	0.546721i
$515$	−10.7796	−	34.4193i	−0.475008	−	1.51670i
$516$	0.168349	−	0.462534i	0.00741114	−	0.0203619i
$517$	−4.64206	−	6.62955i	−0.204158	−	0.291567i
$518$	6.39534	−	9.13349i	0.280995	−	0.401302i
$519$	3.32629	+	9.13891i	0.146008	+	0.401154i
$520$	−11.6028	−	1.55024i	−0.508815	−	0.0679825i
$521$	11.8989	−	6.86983i	0.521300	−	0.300973i	−0.216166	−	0.976357i	$-0.569355\pi$
$521$	11.8989	−	6.86983i	0.521300	−	0.300973i	0.737466	+	0.675384i	$0.236022\pi$
$522$	−9.38454	+	0.821041i	−0.410750	+	0.0359360i
$523$	31.1069	−	2.72150i	1.36021	−	0.119003i	0.616421	−	0.787417i	$-0.288582\pi$
$523$	31.1069	−	2.72150i	1.36021	−	0.119003i	0.743790	+	0.668414i	$0.233026\pi$
$524$	15.6795	−	9.05256i	0.684962	−	0.395463i
$525$	5.44014	−	1.43528i	0.237427	−	0.0626405i
$526$	−0.772068	−	2.12124i	−0.0336638	−	0.0924904i
$527$	−8.86698	+	12.6634i	−0.386252	+	0.551624i
$528$	−3.03143	−	4.32934i	−0.131926	−	0.188410i
$529$	−0.984253	+	2.70421i	−0.0427936	+	0.117574i
$530$	−4.02548	+	7.69670i	−0.174856	+	0.334323i
$531$			6.26206i			0.271750i
$532$	−3.90742	−	2.96479i	−0.169408	−	0.128540i
$533$	44.5636	+	44.5636i	1.93027	+	1.93027i
$534$	−0.0237447	+	0.0199242i	−0.00102753	+	0.000862203i
$535$	−3.77757	−	3.47490i	−0.163319	−	0.150233i
$536$	−1.46625	+	8.31554i	−0.0633325	+	0.359176i
$537$	−18.3307	−	12.8353i	−0.791027	−	0.553883i
$538$	−21.2270	−	9.89829i	−0.915159	−	0.426746i
$539$	−26.2440	−	15.1520i	−1.13041	−	0.652641i
$540$	2.21750	−	0.287601i	0.0954258	−	0.0123764i
$541$	−2.04836	−	1.71878i	−0.0880661	−	0.0738962i	0.597692	−	0.801726i	$-0.296085\pi$
$541$	−2.04836	−	1.71878i	−0.0880661	−	0.0738962i	−0.685758	+	0.727830i	$0.740529\pi$
$542$	1.95583	+	22.3552i	0.0840099	+	0.960238i
$543$	−5.94820	+	22.1990i	−0.255262	+	0.952650i
$544$	0.914482	−	1.58393i	0.0392081	−	0.0679104i
$545$	−1.85166	+	1.69019i	−0.0793164	+	0.0724000i
$546$	5.80125	−	1.02292i	0.248271	−	0.0437768i
$547$	8.94776	−	6.26529i	0.382579	−	0.267885i	−0.366429	−	0.930446i	$-0.619420\pi$
$547$	8.94776	−	6.26529i	0.382579	−	0.267885i	0.749007	+	0.662562i	$0.230531\pi$
$548$	−3.96729	−	8.50787i	−0.169474	−	0.363438i
$549$	−3.04754	−	3.63192i	−0.130066	−	0.155007i
$550$	−26.4255	−	0.101648i	−1.12679	−	0.00433430i
$551$	40.6816	−	5.58009i	1.73310	−	0.237720i
$552$	−3.17193	+	3.17193i	−0.135006	+	0.135006i
$553$	0.221743	−	2.53453i	0.00942945	−	0.107779i
$554$	−5.48564	−	1.99661i	−0.233062	−	0.0848277i
$555$	−4.75398	−	21.6407i	−0.201795	−	0.918596i
$556$	3.14419	+	17.8316i	0.133343	+	0.756228i
$557$	−14.9451	+	32.0500i	−0.633246	+	1.35800i	0.283671	+	0.958922i	$0.408448\pi$
$557$	−14.9451	+	32.0500i	−0.633246	+	1.35800i	−0.916917	+	0.399078i	$0.869330\pi$
$558$	−8.16437	+	2.18764i	−0.345625	+	0.0926100i
$559$	−1.28839	−	2.23155i	−0.0544930	−	0.0943846i
$560$	2.23408	−	1.15754i	0.0944073	−	0.0489148i
$561$	6.21340	−	7.40485i	0.262330	−	0.312633i
$562$	20.0779	+	5.37985i	0.846935	+	0.226935i
$563$	2.81787	+	10.5164i	0.118759	+	0.443215i	0.999541	−	0.0303080i	$-0.00964880\pi$
$563$	2.81787	+	10.5164i	0.118759	+	0.443215i	−0.880782	+	0.473523i	$0.842982\pi$
$564$	1.43896	−	0.523739i	0.0605912	−	0.0220534i
$565$	16.9824	+	3.79918i	0.714454	+	0.159833i
$566$	−1.82500	−	0.321798i	−0.0767107	−	0.0135262i
$567$	−1.01983	+	0.475554i	−0.0428288	+	0.0199714i
$568$	12.6510	+	1.10682i	0.530826	+	0.0464412i
$569$	20.0136			0.839013			0.419507	−	0.907752i	$-0.362203\pi$
$569$	20.0136			0.839013			0.419507	+	0.907752i	$0.362203\pi$
$570$	−9.59275	+	1.72601i	−0.401796	+	0.0722948i
$571$	−15.1690			−0.634801			−0.317401	−	0.948292i	$-0.602810\pi$
$571$	−15.1690			−0.634801			−0.317401	+	0.948292i	$0.602810\pi$
$572$	−27.5626	−	2.41141i	−1.15245	−	0.100826i
$573$	12.8769	−	6.00462i	0.537942	−	0.250846i
$574$	−13.3408	−	2.35234i	−0.556833	−	0.0981846i
$575$	3.80975	+	22.1030i	0.158877	+	0.921758i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	5.08734	+	18.9862i	0.211789	+	0.790406i	0.987272	+	0.159039i	$0.0508394\pi$
$577$	5.08734	+	18.9862i	0.211789	+	0.790406i	−0.775484	+	0.631368i	$0.782494\pi$
$578$	−13.1896	−	3.53415i	−0.548615	−	0.147001i
$579$	11.4680	−	13.6670i	0.476593	−	0.567982i
$580$	−6.37289	+	20.0775i	−0.264620	+	0.833672i
$581$	−3.23560	−	5.60422i	−0.134235	−	0.232502i
$582$	10.3087	−	2.76220i	0.427309	−	0.114497i
$583$	−8.67624	+	18.6063i	−0.359333	+	0.770592i
$584$	−2.37402	−	13.4637i	−0.0982374	−	0.557132i
$585$	6.30853	−	9.86051i	0.260826	−	0.407682i
$586$	7.48352	+	2.72378i	0.309141	+	0.112518i
$587$	0.701414	−	8.01720i	0.0289504	−	0.330905i	−0.967884	−	0.251398i	$-0.919110\pi$
$587$	0.701414	−	8.01720i	0.0289504	−	0.330905i	0.996834	−	0.0795073i	$-0.0253347\pi$
$588$	4.05441	−	4.05441i	0.167201	−	0.167201i
$589$	35.0774	−	11.2690i	1.44534	−	0.464332i
$590$	12.9262	+	5.38335i	0.532163	+	0.221629i
$591$	−7.57251	−	9.02456i	−0.311491	−	0.371221i
$592$	−4.18763	−	8.98040i	−0.172111	−	0.369092i
$593$	−17.9149	+	12.5441i	−0.735676	+	0.515126i	−0.880333	−	0.474356i	$-0.842681\pi$
$593$	−17.9149	+	12.5441i	−0.735676	+	0.515126i	0.144657	+	0.989482i	$0.453792\pi$
$594$	5.20485	−	0.917756i	0.213558	−	0.0376560i
$595$	3.10250	+	3.39889i	0.127190	+	0.139341i
$596$	−5.73743	+	9.93752i	−0.235014	+	0.407057i
$597$	2.45498	−	9.16212i	0.100476	−	0.374980i
$598$	2.04669	+	23.3938i	0.0836955	+	0.956644i
$599$	−18.4824	−	15.5085i	−0.755169	−	0.633662i	0.181696	−	0.983355i	$-0.441841\pi$
$599$	−18.4824	−	15.5085i	−0.755169	−	0.633662i	−0.936864	+	0.349693i	$0.886286\pi$
$600$	1.31266	−	4.82462i	0.0535892	−	0.196964i
$601$	4.60284	+	2.65745i	0.187754	+	0.108400i	0.590931	−	0.806722i	$-0.298761\pi$
$601$	4.60284	+	2.65745i	0.187754	+	0.108400i	−0.403177	+	0.915122i	$0.632094\pi$
$602$	0.501979	+	0.234077i	0.0204591	+	0.00954026i
$603$	−6.91677	−	4.84317i	−0.281673	−	0.197229i
$604$	−2.67721	+	15.1832i	−0.108934	+	0.617795i
$605$	−37.8298	+	1.57880i	−1.53800	+	0.0641872i
$606$	5.68351	−	4.76903i	0.230877	−	0.193729i
$607$	−5.96676	−	5.96676i	−0.242183	−	0.242183i	0.575570	−	0.817753i	$-0.304780\pi$
$607$	−5.96676	−	5.96676i	−0.242183	−	0.242183i	−0.817753	+	0.575570i	$0.804780\pi$
$608$	−4.01801	+	1.68986i	−0.162952	+	0.0685328i
$609$		−	10.6004i		−	0.429549i
$610$	−10.1169	+	3.16848i	−0.409623	+	0.128288i
$611$	2.74178	−	7.53299i	0.110921	−	0.304752i
$612$	1.04905	+	1.49820i	0.0424054	+	0.0605612i
$613$	26.7209	−	38.1614i	1.07925	−	1.54133i	0.261975	−	0.965075i	$-0.415626\pi$
$613$	26.7209	−	38.1614i	1.07925	−	1.54133i	0.817273	−	0.576251i	$-0.195485\pi$
$614$	−2.89690	−	7.95917i	−0.116909	−	0.321206i
$615$	−21.3879	+	16.3463i	−0.862444	+	0.659145i
$616$	5.15038	−	2.97357i	0.207515	−	0.119809i
$617$	29.9048	−	2.61633i	1.20392	−	0.105330i	0.532517	−	0.846419i	$-0.321246\pi$
$617$	29.9048	−	2.61633i	1.20392	−	0.105330i	0.671406	+	0.741090i	$0.265691\pi$
$618$	16.0687	−	1.40583i	0.646376	−	0.0565506i
$619$	23.8036	−	13.7430i	0.956747	−	0.552378i	0.0615763	−	0.998102i	$-0.480387\pi$
$619$	23.8036	−	13.7430i	0.956747	−	0.552378i	0.895170	+	0.445725i	$0.147054\pi$
$620$	−2.50299	+	18.7336i	−0.100523	+	0.752360i
$621$	−1.53423	−	4.21526i	−0.0615664	−	0.169152i
$622$	−1.02105	+	1.45821i	−0.0409403	+	0.0584688i
$623$	−0.0200058	−	0.0285712i	−0.000801515	−	0.00114468i
$624$	1.79048	−	4.91931i	0.0716767	−	0.196930i
$625$	−15.9219	−	19.2742i	−0.636875	−	0.770967i
$626$		−	19.0902i		−	0.762998i
$627$	−22.4640	+	5.10791i	−0.897126	+	0.203990i
$628$	1.91391	+	1.91391i	0.0763735	+	0.0763735i
$629$	13.8829	−	11.6491i	0.553546	−	0.464481i
$630$	0.104918	+	2.51396i	0.00418004	+	0.100159i
$631$	−0.963302	+	5.46316i	−0.0383485	+	0.217485i	−0.997960	−	0.0638439i	$-0.979664\pi$
$631$	−0.963302	+	5.46316i	−0.0383485	+	0.217485i	0.959611	+	0.281329i	$0.0907751\pi$
$632$	−1.85211	−	1.29686i	−0.0736728	−	0.0515862i
$633$	6.65271	+	3.10221i	0.264422	+	0.123302i
$634$	12.9934	+	7.50176i	0.516035	+	0.297933i
$635$	−0.628474	−	4.84573i	−0.0249402	−	0.192297i
$636$	−2.97564	−	2.49686i	−0.117992	−	0.0990069i
$637$	−2.61611	−	29.9023i	−0.103654	−	1.18477i
$638$	−12.8861	+	48.0916i	−0.510166	+	1.90397i
$639$	−6.34968	+	10.9980i	−0.251190	+	0.435073i
$640$	0.101832	−	2.23375i	0.00402527	−	0.0882966i
$641$	21.8945	−	3.86060i	0.864782	−	0.152484i	0.276376	−	0.961050i	$-0.410867\pi$
$641$	21.8945	−	3.86060i	0.864782	−	0.152484i	0.588407	+	0.808565i	$0.299755\pi$
$642$	1.88030	−	1.31660i	0.0742097	−	0.0519622i
$643$	−8.08637	−	17.3413i	−0.318895	−	0.683873i	0.679881	−	0.733322i	$-0.262031\pi$
$643$	−8.08637	−	17.3413i	−0.318895	−	0.683873i	−0.998777	+	0.0494491i	$0.984253\pi$
$644$	−3.24457	−	3.86673i	−0.127854	−	0.152371i
$645$	1.01766	−	0.419238i	0.0400704	−	0.0165075i
$646$	−4.88739	−	6.29846i	−0.192292	−	0.247810i
$647$	11.4019	−	11.4019i	0.448257	−	0.448257i	−0.446518	−	0.894775i	$-0.647336\pi$
$647$	11.4019	−	11.4019i	0.448257	−	0.448257i	0.894775	+	0.446518i	$0.147336\pi$
$648$	−0.0871557	+	0.996195i	−0.00342380	+	0.0391342i
$649$	31.0999	+	11.3195i	1.22078	+	0.444327i
$650$	−14.9308	−	21.4990i	−0.585636	−	0.843260i
$651$	−1.65159	−	9.36661i	−0.0647307	−	0.367106i
$652$	−5.52566	+	11.8498i	−0.216401	+	0.464074i
$653$	12.1522	−	3.25617i	0.475553	−	0.127424i	−0.0130784	−	0.999914i	$-0.504163\pi$
$653$	12.1522	−	3.25617i	0.475553	−	0.127424i	0.488631	+	0.872491i	$0.337496\pi$
$654$	−0.560598	−	0.970984i	−0.0219211	−	0.0379685i
$655$	38.5870	+	12.2481i	1.50772	+	0.478572i
$656$	−7.73828	+	9.22213i	−0.302129	+	0.360064i
$657$	13.2056	+	3.53842i	0.515198	+	0.138047i
$658$	0.445976	+	1.66440i	0.0173859	+	0.0648852i
$659$	−17.8984	+	6.51447i	−0.697221	+	0.253768i	−0.666224	−	0.745752i	$-0.732091\pi$
$659$	−17.8984	+	6.51447i	−0.697221	+	0.253768i	−0.0309972	+	0.999519i	$0.509868\pi$
$660$	2.58006	−	11.5329i	0.100429	−	0.448916i
$661$	−10.0644	−	1.77463i	−0.391460	−	0.0690250i	−0.0255460	−	0.999674i	$-0.508132\pi$
$661$	−10.0644	−	1.77463i	−0.391460	−	0.0690250i	−0.365914	+	0.930649i	$0.619244\pi$
$662$	−1.31636	+	0.613828i	−0.0511617	+	0.0238571i
$663$	9.53824	+	0.834487i	0.370434	+	0.0324088i
$664$	−5.75085			−0.223176
$665$	−0.994033	−	10.9225i	−0.0385470	−	0.423557i
$666$	9.90878			0.383957
$667$	42.0970	+	3.68301i	1.63000	+	0.142607i
$668$	−9.36654	+	4.36769i	−0.362402	+	0.168991i
$669$	18.3842	+	3.24163i	0.710773	+	0.125329i
$670$	−15.9435	+	10.1141i	−0.615952	+	0.390741i
$671$	−23.5464	+	8.57020i	−0.909000	+	0.330849i
$672$	0.291238	+	1.08692i	0.0112348	+	0.0419287i
$673$	9.16286	+	2.45518i	0.353202	+	0.0946403i	0.431058	−	0.902324i	$-0.358141\pi$
$673$	9.16286	+	2.45518i	0.353202	+	0.0946403i	−0.0778554	+	0.996965i	$0.524807\pi$
$674$	19.2877	−	22.9862i	0.742936	−	0.885396i
$675$	3.81783	+	3.22865i	0.146948	+	0.124271i
$676$	−7.20273	−	12.4755i	−0.277028	−	0.479826i
$677$	−18.3727	+	4.92294i	−0.706119	+	0.189204i	−0.593970	−	0.804487i	$-0.702440\pi$
$677$	−18.3727	+	4.92294i	−0.706119	+	0.189204i	−0.112149	+	0.993691i	$0.535773\pi$
$678$	−3.28902	+	7.05332i	−0.126314	+	0.270881i
$679$	2.08536	+	11.8267i	0.0800289	+	0.453866i
$680$	3.99444	−	0.877490i	0.153180	−	0.0336502i
$681$	20.6060	+	7.49996i	0.789623	+	0.287399i
$682$	−3.89342	+	44.5020i	−0.149087	+	1.70407i
$683$	23.7284	−	23.7284i	0.907944	−	0.907944i	−0.0881624	−	0.996106i	$-0.528099\pi$
$683$	23.7284	−	23.7284i	0.907944	−	0.907944i	0.996106	+	0.0881624i	$0.0280995\pi$
$684$	0.166551	−	4.35572i	0.00636823	−	0.166545i
$685$	8.07014	−	19.3775i	0.308344	−	0.740378i
$686$	9.21038	+	10.9765i	0.351654	+	0.419085i
$687$	3.95168	+	8.47441i	0.150766	+	0.323319i
$688$	0.403202	−	0.282325i	0.0153719	−	0.0107635i
$689$	−20.0261	+	3.53114i	−0.762934	+	0.134526i
$690$	−10.0201	−	0.456797i	−0.381459	−	0.0173900i
$691$	16.7305	−	28.9780i	0.636457	−	1.10238i	−0.349748	−	0.936844i	$-0.613733\pi$
$691$	16.7305	−	28.9780i	0.636457	−	1.10238i	0.986204	−	0.165532i	$-0.0529340\pi$
$692$	−2.51713	+	9.39404i	−0.0956868	+	0.357108i
$693$	0.518328	+	5.92452i	0.0196897	+	0.225054i
$694$	−1.70270	−	1.42874i	−0.0646338	−	0.0542342i
$695$	−24.7091	+	32.0736i	−0.937271	+	1.21662i
$696$	−8.15830	−	4.71020i	−0.309240	−	0.178540i
$697$	−19.9553	−	9.30531i	−0.755861	−	0.352464i
$698$	−4.79105	−	3.35473i	−0.181344	−	0.126978i
$699$	0.248573	−	1.40973i	0.00940191	−	0.0533209i
$700$	5.27954	+	1.94463i	0.199548	+	0.0735000i
$701$	−3.43721	+	2.88416i	−0.129822	+	0.108933i	−0.705387	−	0.708823i	$-0.749227\pi$
$701$	−3.43721	+	2.88416i	−0.129822	+	0.108933i	0.575565	+	0.817756i	$0.304782\pi$
$702$	3.70172	+	3.70172i	0.139712	+	0.139712i
$703$	−43.1394	+	2.11759i	−1.62703	+	0.0798665i
$704$		−	5.28514i		−	0.199191i
$705$	3.03418	+	1.58692i	0.114274	+	0.0597668i
$706$	−1.90377	+	5.23058i	−0.0716495	+	0.196855i
$707$	4.78857	+	6.83879i	0.180093	+	0.257199i
$708$	−3.59177	+	5.12958i	−0.134987	+	0.192781i
$709$	−5.67131	−	15.5818i	−0.212990	−	0.585186i	0.786484	−	0.617611i	$-0.211899\pi$
$709$	−5.67131	−	15.5818i	−0.212990	−	0.585186i	−0.999474	+	0.0324247i	$0.989677\pi$
$710$	17.2434	+	22.5618i	0.647134	+	0.846729i
$711$	1.95809	−	1.13050i	0.0734340	−	0.0423971i
$712$	−0.0308785	+	0.00270152i	−0.00115722	+	0.000101244i
$713$	37.7712	−	3.30456i	1.41454	−	0.123757i
$714$	−1.78233	+	1.02903i	−0.0667020	+	0.0385104i
$715$	−37.5679	−	49.1549i	−1.40496	−	1.83829i
$716$	−7.65360	−	21.0281i	−0.286028	−	0.785856i
$717$	6.31547	−	9.01943i	0.235856	−	0.336837i
$718$	−0.434543	−	0.620592i	−0.0162170	−	0.0231603i
$719$	−8.60985	+	23.6554i	−0.321093	+	0.882197i	0.669185	+	0.743096i	$0.266643\pi$
$719$	−8.60985	+	23.6554i	−0.321093	+	0.882197i	−0.990278	+	0.139101i	$0.955579\pi$
$720$	1.98143	+	1.03631i	0.0738434	+	0.0386211i
$721$			18.1504i			0.675958i
$722$	0.205749	+	18.9989i	0.00765718	+	0.707065i
$723$	10.9375	+	10.9375i	0.406769	+	0.406769i
$724$	−17.6053	+	14.7726i	−0.654296	+	0.549019i
$725$	−42.7651	+	19.7418i	−1.58826	+	0.733192i
$726$	2.94034	−	16.6755i	0.109126	−	0.618886i
$727$	−17.0177	−	11.9159i	−0.631150	−	0.441936i	0.213729	−	0.976893i	$-0.431439\pi$
$727$	−17.0177	−	11.9159i	−0.631150	−	0.441936i	−0.844879	+	0.534957i	$0.820328\pi$
$728$	5.33883	+	2.48954i	0.197870	+	0.0922684i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	18.6566	−	24.2171i	0.690511	−	0.896316i
$731$	0.689632	+	0.578670i	0.0255070	+	0.0214029i
$732$	−0.413217	−	4.72309i	−0.0152729	−	0.174571i
$733$	8.54470	−	31.8893i	0.315606	−	1.17786i	−0.607819	−	0.794076i	$-0.707955\pi$
$733$	8.54470	−	31.8893i	0.315606	−	1.17786i	0.923424	−	0.383781i	$-0.125378\pi$
$734$	13.8447	−	23.9798i	0.511019	−	0.885110i
$735$	12.8079	+	0.583885i	0.472425	+	0.0215369i
$736$	−4.41763	+	0.778948i	−0.162836	+	0.0287124i
$737$	−36.5561	+	25.5969i	−1.34656	+	0.942873i
$738$	−5.08775	−	10.9107i	−0.187282	−	0.401629i
$739$	−14.5104	−	17.2928i	−0.533772	−	0.636125i	0.430007	−	0.902825i	$-0.358511\pi$
$739$	−14.5104	−	17.2928i	−0.533772	−	0.636125i	−0.963779	+	0.266701i	$0.914066\pi$
$740$	8.51836	−	20.4538i	0.313141	−	0.751896i
$741$	−16.9071	−	15.3249i	−0.621098	−	0.562975i
$742$	3.09075	−	3.09075i	0.113465	−	0.113465i
$743$	−1.67293	+	19.1216i	−0.0613737	+	0.701504i	0.901717	+	0.432327i	$0.142307\pi$
$743$	−1.67293	+	19.1216i	−0.0613737	+	0.701504i	−0.963091	+	0.269177i	$0.913248\pi$
$744$	−7.94264	−	2.89088i	−0.291191	−	0.105985i
$745$	−25.0610	+	5.50534i	−0.918164	+	0.201700i
$746$	5.34375	+	30.3059i	0.195649	+	1.10958i
$747$	2.43042	−	5.21204i	0.0889243	−	0.190699i
$748$	9.33697	−	2.50183i	0.341393	−	0.0914761i
$749$	1.29147	+	2.23690i	0.0471894	+	0.0817345i
$750$	9.94670	−	5.10520i	0.363202	−	0.186416i
$751$	11.2551	−	13.4133i	0.410704	−	0.489458i	−0.520548	−	0.853832i	$-0.674272\pi$
$751$	11.2551	−	13.4133i	0.410704	−	0.489458i	0.931253	+	0.364374i	$0.118717\pi$
$752$	1.47913	+	0.396332i	0.0539384	+	0.0144527i
$753$	−1.07776	−	4.02224i	−0.0392756	−	0.146579i
$754$	−46.3418	+	16.8671i	−1.68767	+	0.614262i
$755$	−29.1110	+	18.4671i	−1.05946	+	0.672087i
$756$	−1.10816	−	0.195399i	−0.0403035	−	0.00710659i
$757$	−0.492687	+	0.229744i	−0.0179070	+	0.00835018i	−0.431551	−	0.902088i	$-0.642034\pi$
$757$	−0.492687	+	0.229744i	−0.0179070	+	0.00835018i	0.413644	+	0.910439i	$0.364256\pi$
$758$	9.70358	+	0.848954i	0.352450	+	0.0308354i
$759$	−23.7080			−0.860546
$760$	−8.84792	−	4.08831i	−0.320948	−	0.148299i
$761$	28.7792			1.04324			0.521622	−	0.853177i	$-0.325327\pi$
$761$	28.7792			1.04324			0.521622	+	0.853177i	$0.325327\pi$
$762$	2.17691	+	0.190455i	0.0788612	+	0.00689946i
$763$	1.14343	−	0.533190i	0.0413949	−	0.0193028i
$764$	13.9923	+	2.46722i	0.506223	+	0.0892608i
$765$	−0.892848	+	3.99104i	−0.0322810	+	0.144296i
$766$	19.0151	−	6.92091i	0.687042	−	0.250063i
$767$	8.48461	+	31.6650i	0.306361	+	1.14336i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	−0.00765185	+	0.00911912i	−0.000275933	+	0.000328844i	−0.766182	−	0.642623i	$-0.777846\pi$
$769$	−0.00765185	+	0.00911912i	−0.000275933	+	0.000328844i	0.765906	+	0.642952i	$0.222291\pi$
$770$	12.6750	+	4.02324i	0.456776	+	0.144987i
$771$	6.19751	+	10.7344i	0.223198	+	0.386590i
$772$	17.2331	−	4.61759i	0.620233	−	0.166191i
$773$	19.2212	−	41.2199i	0.691337	−	1.48258i	−0.175758	−	0.984433i	$-0.556238\pi$
$773$	19.2212	−	41.2199i	0.691337	−	1.48258i	0.867095	−	0.498143i	$-0.165985\pi$
$774$	0.0854729	+	0.484741i	0.00307226	+	0.0174236i
$775$	−34.7119	+	24.1071i	−1.24689	+	0.865952i
$776$	10.0287	+	3.65015i	0.360010	+	0.131033i
$777$	−0.971780	+	11.1075i	−0.0348624	+	0.398479i
$778$	1.06833	−	1.06833i	0.0383014	−	0.0383014i
$779$	24.4820	+	46.4142i	0.877159	+	1.66296i
$780$	10.8234	−	4.45883i	0.387540	−	0.159652i
$781$	43.1426	+	51.4154i	1.54376	+	1.83979i
$782$	−3.46730	−	7.43565i	−0.123990	−	0.265898i
$783$	7.71673	−	5.40332i	0.275774	−	0.193099i
$784$	5.64669	−	0.995663i	0.201667	−	0.0355594i
$785$	−0.275628	+	6.04605i	−0.00983757	+	0.215793i
$786$	−9.05256	+	15.6795i	−0.322894	+	0.559269i
$787$	−5.31545	+	19.8375i	−0.189475	+	0.707131i	0.804153	+	0.594423i	$0.202619\pi$
$787$	−5.31545	+	19.8375i	−0.189475	+	0.707131i	−0.993628	+	0.112709i	$0.964047\pi$
$788$	−1.02676	−	11.7359i	−0.0365767	−	0.418074i
$789$	1.72925	+	1.45101i	0.0615629	+	0.0516574i
$790$	−0.650267	−	5.01376i	−0.0231355	−	0.178382i
$791$	−7.58403	−	4.37864i	−0.269657	−	0.155687i
$792$	4.78997	+	2.23360i	0.170204	+	0.0793675i
$793$	−20.3313	−	14.2361i	−0.721986	−	0.505540i
$794$	1.91520	−	10.8617i	0.0679681	−	0.385466i
$795$	−0.362181	−	8.67828i	−0.0128452	−	0.307787i
$796$	7.26618	−	6.09705i	0.257543	−	0.216104i
$797$	23.7378	+	23.7378i	0.840834	+	0.840834i	0.988967	−	0.148133i	$-0.0473264\pi$
$797$	23.7378	+	23.7378i	0.840834	+	0.840834i	−0.148133	+	0.988967i	$0.547326\pi$
$798$	4.86632	+	0.613876i	0.172266	+	0.0217310i
$799$			2.80071i			0.0990820i
$800$	3.84256	−	3.19918i	0.135855	−	0.113108i
$801$	0.0106014	−	0.0291272i	0.000374583	−	0.00102916i
$802$	14.2962	+	20.4171i	0.504816	+	0.720952i
$803$	41.4440	−	59.1881i	1.46253	−	2.08870i
$804$	−2.88796	−	7.93459i	−0.101850	−	0.279832i
$805$	1.49476	−	11.1875i	0.0526833	−	0.394307i
$806$	−38.3202	+	22.1242i	−1.34977	+	0.779291i
$807$	23.3322	−	2.04131i	0.821334	−	0.0718574i
$808$	7.39106	−	0.646634i	0.260017	−	0.0227485i
$809$	39.0660	−	22.5547i	1.37349	−	0.792982i	0.382121	−	0.924112i	$-0.375194\pi$
$809$	39.0660	−	22.5547i	1.37349	−	0.792982i	0.991365	+	0.131130i	$0.0418605\pi$
$810$	−1.77661	+	1.35782i	−0.0624236	+	0.0477088i
$811$	−6.89397	−	18.9410i	−0.242080	−	0.665109i	−0.999920	−	0.0126686i	$-0.995967\pi$
$811$	−6.89397	−	18.9410i	−0.242080	−	0.665109i	0.757840	−	0.652441i	$-0.226255\pi$
$812$	6.08012	−	8.68331i	0.213370	−	0.304725i
$813$	−12.8714	−	18.3823i	−0.451419	−	0.644694i
$814$	17.9114	−	49.2111i	0.627793	−	1.72485i
$815$	−27.8999	+	8.73785i	−0.977291	+	0.306073i
$816$			1.82896i			0.0640266i
$817$	−0.475713	−	2.09213i	−0.0166431	−	0.0731943i
$818$	8.27174	+	8.27174i	0.289215	+	0.289215i
$819$	−4.51257	+	3.78650i	−0.157682	+	0.132311i
$820$	−26.8958	+	1.12247i	−0.939242	+	0.0391984i
$821$	−0.0958951	+	0.543848i	−0.00334676	+	0.0189804i	−0.986435	−	0.164150i	$-0.947512\pi$
$821$	−0.0958951	+	0.543848i	−0.00334676	+	0.0189804i	0.983089	+	0.183130i	$0.0586230\pi$
$822$	7.68971	+	5.38439i	0.268209	+	0.187802i
$823$	−7.66915	−	3.57618i	−0.267330	−	0.124658i	0.284332	−	0.958726i	$-0.408228\pi$
$823$	−7.66915	−	3.57618i	−0.267330	−	0.124658i	−0.551662	+	0.834068i	$0.686006\pi$
$824$	13.9690	+	8.06502i	0.486634	+	0.280958i
$825$	22.9360	−	13.1247i	0.798529	−	0.456945i
$826$	−5.39788	−	4.52936i	−0.187816	−	0.157596i
$827$	−1.64897	−	18.8479i	−0.0573404	−	0.655404i	−0.969423	−	0.245397i	$-0.921082\pi$
$827$	−1.64897	−	18.8479i	−0.0573404	−	0.655404i	0.912082	−	0.410007i	$-0.134474\pi$
$828$	1.16101	−	4.33293i	0.0403477	−	0.150580i
$829$	3.97934	−	6.89241i	0.138208	−	0.239383i	−0.788610	−	0.614893i	$-0.789199\pi$
$829$	3.97934	−	6.89241i	0.138208	−	0.239383i	0.926818	+	0.375510i	$0.122532\pi$
$830$	−8.66937	−	9.49756i	−0.300918	−	0.329665i
$831$	5.74900	−	1.01370i	0.199431	−	0.0351650i
$832$	4.28828	−	3.00269i	0.148669	−	0.104099i
$833$	4.43196	+	9.50437i	0.153558	+	0.329307i
$834$	−11.6388	−	13.8705i	−0.403017	−	0.480297i
$835$	−21.3332	−	8.88462i	−0.738267	−	0.307465i
$836$	−21.3312	−	8.70066i	−0.737755	−	0.300919i
$837$	5.97673	−	5.97673i	0.206586	−	0.206586i
$838$	1.02629	−	11.7306i	0.0354527	−	0.405226i
$839$	−35.9365	−	13.0798i	−1.24067	−	0.451566i	−0.363429	−	0.931622i	$-0.618394\pi$
$839$	−35.9365	−	13.0798i	−1.24067	−	0.451566i	−0.877238	+	0.480056i	$0.840616\pi$
$840$	−1.35601	+	2.11950i	−0.0467867	+	0.0731296i
$841$	10.3744	+	58.8362i	0.357738	+	2.02883i
$842$	12.6430	−	27.1131i	0.435708	−	0.934379i
$843$	−20.0779	+	5.37985i	−0.691519	+	0.185292i
$844$	3.67023	+	6.35702i	0.126334	+	0.218818i
$845$	9.74527	−	30.7020i	0.335248	−	1.05618i
$846$	−0.984307	+	1.17305i	−0.0338412	+	0.0403303i
$847$	18.4045	+	4.93146i	0.632385	+	0.169447i
$848$	−1.00536	−	3.75206i	−0.0345243	−	0.128846i
$849$	1.74140	−	0.633817i	0.0597647	−	0.0217526i
$850$	7.47077	+	5.27403i	0.256245	+	0.180898i
$851$	−43.7733	−	7.71842i	−1.50053	−	0.264584i
$852$	−11.5095	+	5.36698i	−0.394310	+	0.183870i
$853$	26.9726	+	2.35980i	0.923524	+	0.0807979i	0.538989	−	0.842313i	$-0.318806\pi$
$853$	26.9726	+	2.35980i	0.923524	+	0.0807979i	0.384535	+	0.923111i	$0.374362\pi$
$854$	5.33500			0.182560
$855$	7.44456	−	6.29115i	0.254599	−	0.215153i
$856$	2.29543			0.0784561
$857$	36.4200	+	3.18634i	1.24408	+	0.108843i	0.690119	−	0.723696i	$-0.257558\pi$
$857$	36.4200	+	3.18634i	1.24408	+	0.108843i	0.553966	+	0.832539i	$0.313114\pi$
$858$	25.0756	−	11.6929i	0.856066	−	0.399190i
$859$	3.53326	+	0.623010i	0.120553	+	0.0212568i	0.233599	−	0.972333i	$-0.424950\pi$
$859$	3.53326	+	0.623010i	0.120553	+	0.0212568i	−0.113046	+	0.993590i	$0.536061\pi$
$860$	1.07408	+	0.240287i	0.0366260	+	0.00819372i
$861$	12.7296	−	4.63320i	0.433824	−	0.157899i
$862$	3.61325	+	13.4848i	0.123068	+	0.459295i
$863$	−24.1435	−	6.46923i	−0.821854	−	0.220215i	−0.176697	−	0.984265i	$-0.556541\pi$
$863$	−24.1435	−	6.46923i	−0.821854	−	0.220215i	−0.645157	+	0.764050i	$0.723208\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−19.3088	+	10.0044i	−0.656521	+	0.340160i
$866$	−11.4690	−	19.8649i	−0.389733	−	0.675038i
$867$	13.1896	−	3.53415i	0.447943	−	0.120026i
$868$	4.01957	−	8.61999i	0.136433	−	0.292581i
$869$	−2.07505	−	11.7682i	−0.0703912	−	0.399208i
$870$	−4.51966	−	20.5741i	−0.153231	−	0.697526i
$871$	−41.5378	−	15.1185i	−1.40745	−	0.512271i
$872$	0.0977187	−	1.11693i	0.00330917	−	0.0378240i
$873$	−7.54648	+	7.54648i	−0.255410	+	0.255410i
$874$	−4.12864	+	19.1122i	−0.139653	+	0.646480i
$875$	4.74731	+	11.6507i	0.160488	+	0.393865i
$876$	8.78781	+	10.4729i	0.296913	+	0.353847i
$877$	−0.171632	−	0.368065i	−0.00579559	−	0.0124287i	0.903389	−	0.428823i	$-0.141071\pi$
$877$	−0.171632	−	0.368065i	−0.00579559	−	0.0124287i	−0.909184	+	0.416394i	$0.863294\pi$
$878$	1.21510	−	0.850819i	0.0410075	−	0.0287138i
$879$	−7.84280	+	1.38290i	−0.264531	+	0.0466440i
$880$	8.72844	−	7.96731i	0.294236	−	0.268578i
$881$	24.6773	−	42.7423i	0.831400	−	1.44003i	−0.0655290	−	0.997851i	$-0.520873\pi$
$881$	24.6773	−	42.7423i	0.831400	−	1.44003i	0.896929	−	0.442176i	$-0.145793\pi$
$882$	−1.48402	+	5.53842i	−0.0499694	+	0.186488i
$883$	1.34700	+	15.3962i	0.0453301	+	0.518125i	0.984585	+	0.174905i	$0.0559619\pi$
$883$	1.34700	+	15.3962i	0.0453301	+	0.518125i	−0.939255	+	0.343220i	$0.888482\pi$
$884$	7.33462	+	6.15448i	0.246690	+	0.206998i
$885$	−13.8861	+	1.80097i	−0.466775	+	0.0605391i
$886$	−3.63760	−	2.10017i	−0.122208	−	0.0705567i
$887$	24.9171	+	11.6190i	0.836634	+	0.390129i	0.793225	−	0.608929i	$-0.208400\pi$
$887$	24.9171	+	11.6190i	0.836634	+	0.390129i	0.0434088	+	0.999057i	$0.486178\pi$
$888$	8.11680	+	5.68344i	0.272382	+	0.190724i
$889$	−0.426991	+	2.42159i	−0.0143208	+	0.0812174i
$890$	−0.0510107	−	0.0469235i	−0.00170988	−	0.00157288i
$891$	−4.04866	+	3.39723i	−0.135635	+	0.113811i
$892$	13.2001	+	13.2001i	0.441973	+	0.441973i
$893$	4.03464	−	5.31742i	0.135014	−	0.177941i
$894$		−	11.4749i		−	0.383777i
$895$	23.1902	−	44.3396i	0.775164	−	1.48211i
$896$	−0.384861	+	1.05740i	−0.0128573	+	0.0353251i
$897$	−13.4694	−	19.2363i	−0.449730	−	0.642281i
$898$	5.34095	−	7.62767i	0.178230	−	0.254539i
$899$	27.2333	+	74.8228i	0.908280	+	2.49548i
$900$	1.27551	+	4.83457i	0.0425169	+	0.161152i
$901$	6.15265	−	3.55224i	0.204975	−	0.118342i
$902$	−63.3838	+	5.54536i	−2.11045	+	0.184640i
$903$	−0.551765	+	0.0482732i	−0.0183616	+	0.00160643i
$904$	−6.73982	+	3.89124i	−0.224163	+	0.129421i
$905$	−50.9369	−	6.80566i	−1.69320	−	0.226228i
$906$	−5.27307	−	14.4876i	−0.175186	−	0.481319i
$907$	−2.57662	+	3.67979i	−0.0855552	+	0.122186i	−0.859648	−	0.510886i	$-0.829317\pi$
$907$	−2.57662	+	3.67979i	−0.0855552	+	0.122186i	0.774093	+	0.633072i	$0.218206\pi$
$908$	12.5776	+	17.9627i	0.417403	+	0.596114i
$909$	−2.53755	+	6.97186i	−0.0841652	+	0.231242i
$910$	3.93676	+	12.5701i	0.130502	+	0.416693i
$911$			7.28237i			0.241276i	0.992697	+	0.120638i	$0.0384940\pi$
$911$			7.28237i			0.241276i	−0.992697	+	0.120638i	$0.961506\pi$
$912$	2.63477	−	3.47246i	0.0872458	−	0.114985i
$913$	−21.4919	−	21.4919i	−0.711277	−	0.711277i
$914$	−2.02789	+	1.70161i	−0.0670768	+	0.0562841i
$915$	7.17729	−	7.80246i	0.237274	−	0.257941i
$916$	−1.62369	+	9.20842i	−0.0536483	+	0.304255i
$917$	−16.6885	−	11.6854i	−0.551103	−	0.385887i
$918$	−1.65760	−	0.772954i	−0.0547091	−	0.0255113i
$919$	−3.53732	−	2.04227i	−0.116685	−	0.0673684i	0.440521	−	0.897742i	$-0.354794\pi$
$919$	−3.53732	−	2.04227i	−0.116685	−	0.0673684i	−0.557207	+	0.830374i	$0.688127\pi$
$920$	−7.94598	−	6.12148i	−0.261971	−	0.201819i
$921$	6.48837	+	5.44439i	0.213799	+	0.179399i
$922$	−1.12848	−	12.8986i	−0.0371647	−	0.424794i
$923$	−17.2067	+	64.2162i	−0.566364	+	2.11370i
$924$	−2.97357	+	5.15038i	−0.0978234	+	0.169435i
$925$	46.6209	−	16.7658i	1.53288	−	0.551256i
$926$	1.60967	−	0.283828i	0.0528969	−	0.00932716i
$927$	−13.2130	+	9.25181i	−0.433970	+	0.303869i
$928$	−3.98123	−	8.53778i	−0.130690	−	0.280266i
$929$	−19.5321	−	23.2775i	−0.640828	−	0.763709i	0.343673	−	0.939089i	$-0.388329\pi$
$929$	−19.5321	−	23.2775i	−0.640828	−	0.763709i	−0.984501	+	0.175381i	$0.943884\pi$
$930$	−7.19916	−	17.4753i	−0.236070	−	0.573037i
$931$	5.27729	−	24.4295i	0.172956	−	0.800646i
$932$	1.01221	−	1.01221i	0.0331560	−	0.0331560i
$933$	0.155150	−	1.77337i	0.00507937	−	0.0580574i
$934$	19.0890	+	6.94782i	0.624610	+	0.227340i
$935$	18.2072	+	11.6486i	0.595439	+	0.380948i
$936$	0.909052	+	5.15549i	0.0297133	+	0.168512i
$937$	−3.41533	+	7.32420i	−0.111574	+	0.239271i	−0.954164	−	0.299285i	$-0.903252\pi$
$937$	−3.41533	+	7.32420i	−0.111574	+	0.239271i	0.842590	+	0.538556i	$0.181030\pi$
$938$	9.17771	−	2.45916i	0.299663	−	0.0802945i
$939$	9.54510	+	16.5326i	0.311493	+	0.539521i
$940$	1.57523	+	3.04026i	0.0513785	+	0.0991623i
$941$	−18.4230	+	21.9557i	−0.600573	+	0.715735i	−0.977601	−	0.210467i	$-0.932502\pi$
$941$	−18.4230	+	21.9557i	−0.600573	+	0.715735i	0.377028	+	0.926202i	$0.376946\pi$
$942$	−2.61446	−	0.700541i	−0.0851836	−	0.0228249i
$943$	13.9769	+	52.1626i	0.455151	+	1.69865i
$944$	−5.88441	+	2.14175i	−0.191521	+	0.0697080i
$945$	−1.34784	−	2.12470i	−0.0438454	−	0.0691164i
$946$	2.56193	+	0.451737i	0.0832954	+	0.0146872i
$947$	−24.9115	+	11.6164i	−0.809515	+	0.377483i	−0.782888	−	0.622162i	$-0.786254\pi$
$947$	−24.9115	+	11.6164i	−0.809515	+	0.377483i	−0.0266267	+	0.999645i	$0.508477\pi$
$948$	2.25240	+	0.197059i	0.0731545	+	0.00640019i
$949$	71.5701			2.32326
$950$	−6.58631	−	20.7755i	−0.213688	−	0.674045i
$951$	−15.0035			−0.486523
$952$	−2.05022	−	0.179371i	−0.0664482	−	0.00581346i
$953$	−27.9384	+	13.0279i	−0.905014	+	0.422015i	−0.818679	−	0.574251i	$-0.805293\pi$
$953$	−27.9384	+	13.0279i	−0.905014	+	0.422015i	−0.0863350	+	0.996266i	$0.527516\pi$
$954$	3.82541	+	0.674523i	0.123852	+	0.0218385i
$955$	17.0186	+	26.8276i	0.550710	+	0.868122i
$956$	10.3467	−	3.76588i	0.334635	−	0.121797i
$957$	−12.8861	−	48.0916i	−0.416549	−	1.55458i
$958$	19.6595	+	5.26774i	0.635168	+	0.170193i
$959$	−6.78992	+	8.09191i	−0.219258	+	0.261302i
$960$	1.02868	+	1.98540i	0.0332007	+	0.0640785i
$961$	20.2213	+	35.0244i	0.652302	+	1.12982i
$962$	50.1052	−	13.4256i	1.61545	−	0.432860i
$963$	−0.970090	+	2.08036i	−0.0312607	+	0.0670388i
$964$	2.68598	+	15.2329i	0.0865096	+	0.490620i
$965$	33.6047	+	21.4996i	1.08177	+	0.692095i
$966$	4.74325	+	1.72640i	0.152612	+	0.0555461i
$967$	−0.0904735	+	1.03412i	−0.00290943	+	0.0332550i	−0.997511	−	0.0705161i	$-0.977535\pi$
$967$	−0.0904735	+	1.03412i	−0.00290943	+	0.0332550i	0.994601	+	0.103771i	$0.0330909\pi$
$968$	11.9733	−	11.9733i	0.384835	−	0.384835i
$969$	7.38183	+	3.01093i	0.237139	+	0.0967251i
$970$	9.08996	+	22.0651i	0.291861	+	0.708466i
$971$	−12.0896	−	14.4078i	−0.387974	−	0.462369i	0.536340	−	0.844002i	$-0.319806\pi$
$971$	−12.0896	−	14.4078i	−0.387974	−	0.462369i	−0.924314	+	0.381633i	$0.875362\pi$
$972$	−0.422618	−	0.906308i	−0.0135555	−	0.0290698i
$973$	16.6900	−	11.6864i	0.535056	−	0.374650i
$974$	18.3034	−	3.22738i	0.586478	−	0.103412i
$975$	23.6800	+	11.1532i	0.758366	+	0.357190i
$976$	2.37057	−	4.10594i	0.0758800	−	0.131428i
$977$	8.34005	−	31.1255i	0.266822	−	0.995793i	−0.694304	−	0.719682i	$-0.744288\pi$
$977$	8.34005	−	31.1255i	0.266822	−	0.995793i	0.961126	−	0.276111i	$-0.0890458\pi$
$978$	−1.13955	−	13.0251i	−0.0364386	−	0.416496i
$979$	−0.125494	−	0.105302i	−0.00401081	−	0.00336547i
$980$	10.1567	+	7.82457i	0.324443	+	0.249947i
$981$	0.970984	+	0.560598i	0.0310011	+	0.0178985i
$982$	−17.3027	−	8.06839i	−0.552152	−	0.257473i
$983$	−32.3456	−	22.6486i	−1.03166	−	0.722378i	−0.0702617	−	0.997529i	$-0.522383\pi$
$983$	−32.3456	−	22.6486i	−1.03166	−	0.722378i	−0.961401	+	0.275150i	$0.911272\pi$
$984$	2.09049	−	11.8557i	0.0666423	−	0.377947i
$985$	17.8341	−	19.3875i	0.568241	−	0.617736i
$986$	13.1986	−	11.0750i	0.420329	−	0.352698i
$987$	−1.21843	−	1.21843i	−0.0387830	−	0.0387830i
$988$	−5.05947	−	22.2510i	−0.160963	−	0.707897i
$989$		−	2.20799i		−	0.0702099i
$990$	3.53204	+	11.2778i	0.112256	+	0.358432i
$991$	−7.86734	+	21.6154i	−0.249914	+	0.686634i	0.749775	+	0.661693i	$0.230162\pi$
$991$	−7.86734	+	21.6154i	−0.249914	+	0.686634i	−0.999689	+	0.0249408i	$0.992060\pi$
$992$	−4.84809	−	6.92378i	−0.153927	−	0.219830i
$993$	0.833086	−	1.18977i	0.0264372	−	0.0377562i
$994$	−4.88749	−	13.4283i	−0.155022	−	0.425919i
$995$	21.0230	+	2.80888i	0.666474	+	0.0890473i
$996$	4.98039	−	2.87543i	0.157810	−	0.0911114i
$997$	−6.90351	+	0.603979i	−0.218636	+	0.0191282i	−0.195948	−	0.980614i	$-0.562778\pi$
$997$	−6.90351	+	0.603979i	−0.218636	+	0.0191282i	−0.0226888	+	0.999743i	$0.507223\pi$
$998$	−6.42841	+	0.562413i	−0.203488	+	0.0178029i
$999$	−8.58125	+	4.95439i	−0.271499	+	0.156750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.13.4	✓	120
5.2	odd	4	inner	570.2.bh.b.127.7	yes	120
19.3	odd	18	inner	570.2.bh.b.193.7	yes	120
95.22	even	36	inner	570.2.bh.b.307.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.13.4	✓	120	1.1	even	1	trivial
570.2.bh.b.127.7	yes	120	5.2	odd	4	inner
570.2.bh.b.193.7	yes	120	19.3	odd	18	inner
570.2.bh.b.307.4	yes	120	95.22	even	36	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.19781 + 1.88819i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.291238 - 1.08692i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.19781 + 1.88819i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.291238 - 1.08692i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-1.02868 - 1.98540i) q^{10} +(-2.64257 - 4.57707i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.21242 - 4.74454i) q^{13} +(0.195399 + 1.10816i) q^{14} +(1.88357 + 1.20506i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.159405 + 1.82200i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(2.92739 - 3.22962i) q^{19} +(0.851731 + 2.06750i) q^{20} +(-0.723302 - 0.861997i) q^{21} +(2.23360 + 4.78997i) q^{22} +(3.67454 - 2.57294i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(-2.13051 + 4.52338i) q^{25} +(-2.61751 + 4.53366i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-0.0980727 - 1.12098i) q^{28} +(7.21644 + 6.05531i) q^{29} +(-1.77137 - 1.36464i) q^{30} +(7.31997 + 4.22619i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-4.32934 - 3.03143i) q^{33} +(0.317596 - 1.80118i) q^{34} +(1.70345 - 1.85183i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-7.00656 - 7.00656i) q^{37} +(-3.19773 + 2.96219i) q^{38} -5.23502i q^{39} +(-0.668296 - 2.13387i) q^{40} +(-4.11745 + 11.3126i) q^{41} +(0.645421 + 0.921757i) q^{42} +(0.282325 - 0.403202i) q^{43} +(-1.80763 - 4.96641i) q^{44} +(2.21637 + 0.296129i) q^{45} +(-3.88480 + 2.24289i) q^{46} +(1.52548 - 0.133462i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(4.96561 - 2.86690i) q^{49} +(2.51664 - 4.32048i) q^{50} +(0.625543 + 1.71866i) q^{51} +(3.00269 - 4.28828i) q^{52} +(-2.22801 - 3.18193i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(5.47707 - 10.4721i) q^{55} +1.12526i q^{56} +(1.28822 - 4.16419i) q^{57} +(-6.66122 - 6.66122i) q^{58} +(-4.79701 + 4.02517i) q^{59} +(1.64569 + 1.51383i) q^{60} +(0.823289 - 4.66911i) q^{61} +(-6.92378 - 4.84809i) q^{62} +(-1.01983 - 0.475554i) q^{63} +(0.866025 + 0.500000i) q^{64} +(11.6086 - 1.50560i) q^{65} +(4.04866 + 3.39723i) q^{66} +(-0.735927 - 8.41169i) q^{67} +(-0.473371 + 1.76664i) q^{68} +(2.24289 - 3.88480i) q^{69} +(-1.85837 + 1.69632i) q^{70} +(-12.5064 + 2.20522i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(5.77779 + 12.3905i) q^{73} +(6.36924 + 7.59056i) q^{74} +(-0.0192329 + 4.99996i) q^{75} +(3.44373 - 2.67221i) q^{76} +(-4.20527 + 4.20527i) q^{77} +(-0.456262 + 5.21510i) q^{78} +(2.12465 + 0.773309i) q^{79} +(0.479774 + 2.18399i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(5.08775 - 10.9107i) q^{82} +(5.55490 - 1.48843i) q^{83} +(-0.562629 - 0.974502i) q^{84} +(-3.63122 + 1.88143i) q^{85} +(-0.316392 + 0.377061i) q^{86} +(9.09940 + 2.43818i) q^{87} +(1.36790 + 5.10506i) q^{88} +(0.0291272 - 0.0106014i) q^{89} +(-2.18213 - 0.488171i) q^{90} +(-5.80125 - 1.02292i) q^{91} +(4.06550 - 1.89577i) q^{92} +(8.42021 + 0.736673i) q^{93} -1.53131 q^{94} +(9.60457 + 1.65899i) q^{95} -1.00000 q^{96} +(-10.6317 - 0.930156i) q^{97} +(-5.19658 + 2.42321i) q^{98} +(-5.20485 - 0.917756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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