LMFDB - Embedded newform 1380.2.p.a.91.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (of order $2$, degree $1$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.7
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.a.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25058 - 0.660333i) q^{2} -1.00000i q^{3} +(1.12792 + 1.65160i) q^{4} -1.00000i q^{5} +(-0.660333 + 1.25058i) q^{6} -3.91467 q^{7} +(-0.319949 - 2.81027i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.25058 - 0.660333i) q^{2} -1.00000i q^{3} +(1.12792 + 1.65160i) q^{4} -1.00000i q^{5} +(-0.660333 + 1.25058i) q^{6} -3.91467 q^{7} +(-0.319949 - 2.81027i) q^{8} -1.00000 q^{9} +(-0.660333 + 1.25058i) q^{10} -3.56454 q^{11} +(1.65160 - 1.12792i) q^{12} -6.21448 q^{13} +(4.89562 + 2.58498i) q^{14} -1.00000 q^{15} +(-1.45559 + 3.72575i) q^{16} +6.87185i q^{17} +(1.25058 + 0.660333i) q^{18} +5.29017 q^{19} +(1.65160 - 1.12792i) q^{20} +3.91467i q^{21} +(4.45776 + 2.35379i) q^{22} +(3.05366 - 3.69800i) q^{23} +(-2.81027 + 0.319949i) q^{24} -1.00000 q^{25} +(7.77173 + 4.10363i) q^{26} +1.00000i q^{27} +(-4.41543 - 6.46548i) q^{28} +7.14975 q^{29} +(1.25058 + 0.660333i) q^{30} -5.49174i q^{31} +(4.28058 - 3.69819i) q^{32} +3.56454i q^{33} +(4.53771 - 8.59383i) q^{34} +3.91467i q^{35} +(-1.12792 - 1.65160i) q^{36} -1.30997i q^{37} +(-6.61580 - 3.49327i) q^{38} +6.21448i q^{39} +(-2.81027 + 0.319949i) q^{40} +10.4481 q^{41} +(2.58498 - 4.89562i) q^{42} +3.43010 q^{43} +(-4.02052 - 5.88721i) q^{44} +1.00000i q^{45} +(-6.26076 + 2.60822i) q^{46} -2.84469i q^{47} +(3.72575 + 1.45559i) q^{48} +8.32462 q^{49} +(1.25058 + 0.660333i) q^{50} +6.87185 q^{51} +(-7.00944 - 10.2639i) q^{52} +11.0291i q^{53} +(0.660333 - 1.25058i) q^{54} +3.56454i q^{55} +(1.25250 + 11.0013i) q^{56} -5.29017i q^{57} +(-8.94137 - 4.72122i) q^{58} -5.12833i q^{59} +(-1.12792 - 1.65160i) q^{60} +5.14642i q^{61} +(-3.62638 + 6.86788i) q^{62} +3.91467 q^{63} +(-7.79526 + 1.79829i) q^{64} +6.21448i q^{65} +(2.35379 - 4.45776i) q^{66} -14.0791 q^{67} +(-11.3496 + 7.75090i) q^{68} +(-3.69800 - 3.05366i) q^{69} +(2.58498 - 4.89562i) q^{70} +11.6817i q^{71} +(0.319949 + 2.81027i) q^{72} +11.4110 q^{73} +(-0.865019 + 1.63823i) q^{74} +1.00000i q^{75} +(5.96689 + 8.73726i) q^{76} +13.9540 q^{77} +(4.10363 - 7.77173i) q^{78} -0.545018 q^{79} +(3.72575 + 1.45559i) q^{80} +1.00000 q^{81} +(-13.0662 - 6.89923i) q^{82} +3.08427 q^{83} +(-6.46548 + 4.41543i) q^{84} +6.87185 q^{85} +(-4.28963 - 2.26501i) q^{86} -7.14975i q^{87} +(1.14047 + 10.0173i) q^{88} +7.41651i q^{89} +(0.660333 - 1.25058i) q^{90} +24.3276 q^{91} +(9.55191 + 0.872391i) q^{92} -5.49174 q^{93} +(-1.87844 + 3.55752i) q^{94} -5.29017i q^{95} +(-3.69819 - 4.28058i) q^{96} -7.95043i q^{97} +(-10.4106 - 5.49702i) q^{98} +3.56454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.25058	−	0.660333i	−0.884296	−	0.466926i
$2$	−1.25058	−	0.660333i	−0.884296	−	0.466926i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.12792	+	1.65160i	0.563960	+	0.825802i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.660333	+	1.25058i	−0.269580	+	0.510549i
$7$	−3.91467			−1.47961			−0.739803	−	0.672824i	$-0.765081\pi$
$7$	−3.91467			−1.47961			−0.739803	+	0.672824i	$0.765081\pi$
$8$	−0.319949	−	2.81027i	−0.113119	−	0.993581i
$9$	−1.00000			−0.333333
$10$	−0.660333	+	1.25058i	−0.208816	+	0.395469i
$11$	−3.56454			−1.07475			−0.537375	−	0.843344i	$-0.680584\pi$
$11$	−3.56454			−1.07475			−0.537375	+	0.843344i	$0.680584\pi$
$12$	1.65160	−	1.12792i	0.476777	−	0.325602i
$13$	−6.21448			−1.72359			−0.861793	−	0.507259i	$-0.830659\pi$
$13$	−6.21448			−1.72359			−0.861793	+	0.507259i	$0.830659\pi$
$14$	4.89562	+	2.58498i	1.30841	+	0.690866i
$15$	−1.00000			−0.258199
$16$	−1.45559	+	3.72575i	−0.363898	+	0.931439i
$17$			6.87185i			1.66667i	0.552769	+	0.833335i	$0.313571\pi$
$17$			6.87185i			1.66667i	−0.552769	+	0.833335i	$0.686429\pi$
$18$	1.25058	+	0.660333i	0.294765	+	0.155642i
$19$	5.29017			1.21365			0.606824	−	0.794836i	$-0.292443\pi$
$19$	5.29017			1.21365			0.606824	+	0.794836i	$0.292443\pi$
$20$	1.65160	−	1.12792i	0.369310	−	0.252211i
$21$			3.91467i			0.854250i
$22$	4.45776	+	2.35379i	0.950397	+	0.501829i
$23$	3.05366	−	3.69800i	0.636732	−	0.771085i
$23$	3.05366	−	3.69800i	0.636732	−	0.771085i
$24$	−2.81027	+	0.319949i	−0.573645	+	0.0653094i
$25$	−1.00000			−0.200000
$26$	7.77173	+	4.10363i	1.52416	+	0.804788i
$27$			1.00000i			0.192450i
$28$	−4.41543	−	6.46548i	−0.834438	−	1.22186i
$29$	7.14975			1.32768			0.663838	−	0.747876i	$-0.268926\pi$
$29$	7.14975			1.32768			0.663838	+	0.747876i	$0.268926\pi$
$30$	1.25058	+	0.660333i	0.228324	+	0.120560i
$31$		−	5.49174i		−	0.986346i	−0.869931	−	0.493173i	$-0.835837\pi$
$31$		−	5.49174i		−	0.986346i	0.869931	−	0.493173i	$-0.164163\pi$
$32$	4.28058	−	3.69819i	0.756707	−	0.653754i
$33$			3.56454i			0.620507i
$34$	4.53771	−	8.59383i	0.778212	−	1.47383i
$35$			3.91467i			0.661699i
$36$	−1.12792	−	1.65160i	−0.187987	−	0.275267i
$37$		−	1.30997i		−	0.215358i	−0.994186	−	0.107679i	$-0.965658\pi$
$37$		−	1.30997i		−	0.215358i	0.994186	−	0.107679i	$-0.0343419\pi$
$38$	−6.61580	−	3.49327i	−1.07322	−	0.566684i
$39$			6.21448i			0.995113i
$40$	−2.81027	+	0.319949i	−0.444343	+	0.0505884i
$41$	10.4481			1.63172			0.815860	−	0.578250i	$-0.196264\pi$
$41$	10.4481			1.63172			0.815860	+	0.578250i	$0.196264\pi$
$42$	2.58498	−	4.89562i	0.398872	−	0.755410i
$43$	3.43010			0.523086			0.261543	−	0.965192i	$-0.415769\pi$
$43$	3.43010			0.523086			0.261543	+	0.965192i	$0.415769\pi$
$44$	−4.02052	−	5.88721i	−0.606116	−	0.887530i
$45$			1.00000i			0.149071i
$46$	−6.26076	+	2.60822i	−0.923099	+	0.384561i
$47$		−	2.84469i		−	0.414940i	−0.978241	−	0.207470i	$-0.933477\pi$
$47$		−	2.84469i		−	0.414940i	0.978241	−	0.207470i	$-0.0665230\pi$
$48$	3.72575	+	1.45559i	0.537766	+	0.210097i
$49$	8.32462			1.18923
$50$	1.25058	+	0.660333i	0.176859	+	0.0933852i
$51$	6.87185			0.962252
$52$	−7.00944	−	10.2639i	−0.972034	−	1.42334i
$53$			11.0291i			1.51497i	0.652855	+	0.757483i	$0.273571\pi$
$53$			11.0291i			1.51497i	−0.652855	+	0.757483i	$0.726429\pi$
$54$	0.660333	−	1.25058i	0.0898600	−	0.170183i
$55$			3.56454i			0.480643i
$56$	1.25250	+	11.0013i	0.167372	+	1.47011i
$57$		−	5.29017i		−	0.700700i
$58$	−8.94137	−	4.72122i	−1.17406	−	0.619927i
$59$		−	5.12833i		−	0.667652i	−0.942635	−	0.333826i	$-0.891660\pi$
$59$		−	5.12833i		−	0.667652i	0.942635	−	0.333826i	$-0.108340\pi$
$60$	−1.12792	−	1.65160i	−0.145614	−	0.213221i
$61$			5.14642i			0.658932i	0.944168	+	0.329466i	$0.106869\pi$
$61$			5.14642i			0.658932i	−0.944168	+	0.329466i	$0.893131\pi$
$62$	−3.62638	+	6.86788i	−0.460551	+	0.872222i
$63$	3.91467			0.493202
$64$	−7.79526	+	1.79829i	−0.974408	+	0.224786i
$65$			6.21448i			0.770811i
$66$	2.35379	−	4.45776i	0.289731	−	0.548712i
$67$	−14.0791			−1.72004			−0.860019	−	0.510262i	$-0.829549\pi$
$67$	−14.0791			−1.72004			−0.860019	+	0.510262i	$0.829549\pi$
$68$	−11.3496	+	7.75090i	−1.37634	+	0.939935i
$69$	−3.69800	−	3.05366i	−0.445186	−	0.367617i
$70$	2.58498	−	4.89562i	0.308965	−	0.585138i
$71$			11.6817i			1.38636i	0.720764	+	0.693181i	$0.243791\pi$
$71$			11.6817i			1.38636i	−0.720764	+	0.693181i	$0.756209\pi$
$72$	0.319949	+	2.81027i	0.0377064	+	0.331194i
$73$	11.4110			1.33556			0.667780	−	0.744359i	$-0.267245\pi$
$73$	11.4110			1.33556			0.667780	+	0.744359i	$0.267245\pi$
$74$	−0.865019	+	1.63823i	−0.100556	+	0.190441i
$75$			1.00000i			0.115470i
$76$	5.96689	+	8.73726i	0.684449	+	1.00223i
$77$	13.9540			1.59020
$78$	4.10363	−	7.77173i	0.464644	−	0.879975i
$79$	−0.545018			−0.0613194			−0.0306597	−	0.999530i	$-0.509761\pi$
$79$	−0.545018			−0.0613194			−0.0306597	+	0.999530i	$0.509761\pi$
$80$	3.72575	+	1.45559i	0.416552	+	0.162740i
$81$	1.00000			0.111111
$82$	−13.0662	−	6.89923i	−1.44292	−	0.761892i
$83$	3.08427			0.338543			0.169272	−	0.985569i	$-0.445859\pi$
$83$	3.08427			0.338543			0.169272	+	0.985569i	$0.445859\pi$
$84$	−6.46548	+	4.41543i	−0.705442	+	0.481763i
$85$	6.87185			0.745357
$86$	−4.28963	−	2.26501i	−0.462563	−	0.244243i
$87$		−	7.14975i		−	0.766534i
$88$	1.14047	+	10.0173i	0.121575	+	1.06785i
$89$			7.41651i			0.786149i	0.919507	+	0.393074i	$0.128589\pi$
$89$			7.41651i			0.786149i	−0.919507	+	0.393074i	$0.871411\pi$
$90$	0.660333	−	1.25058i	0.0696052	−	0.131823i
$91$	24.3276			2.55023
$92$	9.55191	+	0.872391i	0.995855	+	0.0909530i
$93$	−5.49174			−0.569467
$94$	−1.87844	+	3.55752i	−0.193746	+	0.366930i
$95$		−	5.29017i		−	0.542760i
$96$	−3.69819	−	4.28058i	−0.377445	−	0.436885i
$97$		−	7.95043i		−	0.807244i	−0.914926	−	0.403622i	$-0.867751\pi$
$97$		−	7.95043i		−	0.807244i	0.914926	−	0.403622i	$-0.132249\pi$
$98$	−10.4106	−	5.49702i	−1.05163	−	0.555283i
$99$	3.56454			0.358250
$100$	−1.12792	−	1.65160i	−0.112792	−	0.165160i
$101$	−14.5657			−1.44934			−0.724670	−	0.689096i	$-0.758008\pi$
$101$	−14.5657			−1.44934			−0.724670	+	0.689096i	$0.758008\pi$
$102$	−8.59383	−	4.53771i	−0.850916	−	0.449301i
$103$	−5.43923			−0.535943			−0.267971	−	0.963427i	$-0.586353\pi$
$103$	−5.43923			−0.535943			−0.267971	+	0.963427i	$0.586353\pi$
$104$	1.98832	+	17.4644i	0.194971	+	1.71252i
$105$	3.91467			0.382032
$106$	7.28289	−	13.7928i	0.707377	−	1.33968i
$107$	3.07805			0.297567			0.148783	−	0.988870i	$-0.452464\pi$
$107$	3.07805			0.297567			0.148783	+	0.988870i	$0.452464\pi$
$108$	−1.65160	+	1.12792i	−0.158926	+	0.108534i
$109$		−	5.62701i		−	0.538970i	−0.963005	−	0.269485i	$-0.913147\pi$
$109$		−	5.62701i		−	0.538970i	0.963005	−	0.269485i	$-0.0868534\pi$
$110$	2.35379	−	4.45776i	0.224425	−	0.425031i
$111$	−1.30997			−0.124337
$112$	5.69816	−	14.5851i	0.538426	−	1.37816i
$113$			9.92254i			0.933434i	0.884407	+	0.466717i	$0.154563\pi$
$113$			9.92254i			0.933434i	−0.884407	+	0.466717i	$0.845437\pi$
$114$	−3.49327	+	6.61580i	−0.327175	+	0.619626i
$115$	−3.69800	−	3.05366i	−0.344840	−	0.284755i
$116$	8.06435	+	11.8086i	0.748756	+	1.09640i
$117$	6.21448			0.574529
$118$	−3.38641	+	6.41341i	−0.311744	+	0.590402i
$119$		−	26.9010i		−	2.46601i
$120$	0.319949	+	2.81027i	0.0292072	+	0.256542i
$121$	1.70595			0.155087
$122$	3.39835	−	6.43603i	0.307672	−	0.582691i
$123$		−	10.4481i		−	0.942073i
$124$	9.07018	−	6.19425i	0.814527	−	0.556260i
$125$			1.00000i			0.0894427i
$126$	−4.89562	−	2.58498i	−0.436136	−	0.230289i
$127$		−	4.13193i		−	0.366650i	−0.983052	−	0.183325i	$-0.941314\pi$
$127$		−	4.13193i		−	0.366650i	0.983052	−	0.183325i	$-0.0586860\pi$
$128$	10.9361	+	2.89856i	0.966624	+	0.256199i
$129$		−	3.43010i		−	0.302004i
$130$	4.10363	−	7.77173i	0.359912	−	0.681626i
$131$			13.3832i			1.16930i	0.811287	+	0.584649i	$0.198768\pi$
$131$			13.3832i			1.16930i	−0.811287	+	0.584649i	$0.801232\pi$
$132$	−5.88721	+	4.02052i	−0.512416	+	0.349941i
$133$	−20.7092			−1.79572
$134$	17.6071	+	9.29691i	1.52102	+	0.803131i
$135$	1.00000			0.0860663
$136$	19.3118	−	2.19865i	1.65597	−	0.188532i
$137$			3.37576i			0.288411i	0.989548	+	0.144205i	$0.0460626\pi$
$137$			3.37576i			0.288411i	−0.989548	+	0.144205i	$0.953937\pi$
$138$	2.60822	+	6.26076i	0.222027	+	0.532952i
$139$			6.81463i			0.578010i	0.957328	+	0.289005i	$0.0933243\pi$
$139$			6.81463i			0.578010i	−0.957328	+	0.289005i	$0.906676\pi$
$140$	−6.46548	+	4.41543i	−0.546433	+	0.373172i
$141$	−2.84469			−0.239566
$142$	7.71381	−	14.6089i	0.647328	−	1.22595i
$143$	22.1518			1.85242
$144$	1.45559	−	3.72575i	0.121299	−	0.310480i
$145$		−	7.14975i		−	0.593755i
$146$	−14.2704	−	7.53508i	−1.18103	−	0.623608i
$147$		−	8.32462i		−	0.686603i
$148$	2.16356	−	1.47755i	0.177843	−	0.121454i
$149$			0.569849i			0.0466839i	0.999728	+	0.0233419i	$0.00743065\pi$
$149$			0.569849i			0.0466839i	−0.999728	+	0.0233419i	$0.992569\pi$
$150$	0.660333	−	1.25058i	0.0539160	−	0.102110i
$151$		−	12.8309i		−	1.04416i	−0.852896	−	0.522080i	$-0.825156\pi$
$151$		−	12.8309i		−	1.04416i	0.852896	−	0.522080i	$-0.174844\pi$
$152$	−1.69259	−	14.8668i	−0.137287	−	1.20586i
$153$		−	6.87185i		−	0.555557i
$154$	−17.4506	−	9.21428i	−1.40621	−	0.742508i
$155$	−5.49174			−0.441107
$156$	−10.2639	+	7.00944i	−0.821767	+	0.561204i
$157$			13.7090i			1.09409i	0.837102	+	0.547047i	$0.184248\pi$
$157$			13.7090i			1.09409i	−0.837102	+	0.547047i	$0.815752\pi$
$158$	0.681591	+	0.359894i	0.0542245	+	0.0286316i
$159$	11.0291			0.874666
$160$	−3.69819	−	4.28058i	−0.292368	−	0.338410i
$161$	−11.9541	+	14.4764i	−0.942111	+	1.14090i
$162$	−1.25058	−	0.660333i	−0.0982551	−	0.0518807i
$163$			19.9288i			1.56095i	0.625189	+	0.780474i	$0.285022\pi$
$163$			19.9288i			1.56095i	−0.625189	+	0.780474i	$0.714978\pi$
$164$	11.7846	+	17.2561i	0.920224	+	1.34748i
$165$	3.56454			0.277499
$166$	−3.85714	−	2.03665i	−0.299372	−	0.158075i
$167$		−	5.97291i		−	0.462198i	−0.972930	−	0.231099i	$-0.925768\pi$
$167$		−	5.97291i		−	0.462198i	0.972930	−	0.231099i	$-0.0742321\pi$
$168$	11.0013	−	1.25250i	0.848767	−	0.0966321i
$169$	25.6198			1.97075
$170$	−8.59383	−	4.53771i	−0.659117	−	0.348027i
$171$	−5.29017			−0.404549
$172$	3.86888	+	5.66518i	0.295000	+	0.431966i
$173$	−0.447042			−0.0339879			−0.0169940	−	0.999856i	$-0.505410\pi$
$173$	−0.447042			−0.0339879			−0.0169940	+	0.999856i	$0.505410\pi$
$174$	−4.72122	+	8.94137i	−0.357915	+	0.677843i
$175$	3.91467			0.295921
$176$	5.18852	−	13.2806i	0.391100	−	1.00106i
$177$	−5.12833			−0.385469
$178$	4.89737	−	9.27497i	0.367073	−	0.695188i
$179$		−	2.54930i		−	0.190544i	−0.995451	−	0.0952719i	$-0.969628\pi$
$179$		−	2.54930i		−	0.190544i	0.995451	−	0.0952719i	$-0.0303720\pi$
$180$	−1.65160	+	1.12792i	−0.123103	+	0.0840702i
$181$			4.27974i			0.318111i	0.987270	+	0.159055i	$0.0508448\pi$
$181$			4.27974i			0.318111i	−0.987270	+	0.159055i	$0.949155\pi$
$182$	−30.4237	−	16.0643i	−2.25516	−	1.19077i
$183$	5.14642			0.380434
$184$	−11.3694	−	7.39844i	−0.838163	−	0.545420i
$185$	−1.30997			−0.0963112
$186$	6.86788	+	3.62638i	0.503578	+	0.265899i
$187$		−	24.4950i		−	1.79125i
$188$	4.69830	−	3.20858i	0.342658	−	0.234010i
$189$		−	3.91467i		−	0.284750i
$190$	−3.49327	+	6.61580i	−0.253429	+	0.479960i
$191$	18.0629			1.30698			0.653491	−	0.756934i	$-0.273304\pi$
$191$	18.0629			1.30698			0.653491	+	0.756934i	$0.273304\pi$
$192$	1.79829	+	7.79526i	0.129780	+	0.562575i
$193$	6.37298			0.458737			0.229369	−	0.973340i	$-0.426334\pi$
$193$	6.37298			0.458737			0.229369	+	0.973340i	$0.426334\pi$
$194$	−5.24993	+	9.94268i	−0.376923	+	0.713843i
$195$	6.21448			0.445028
$196$	9.38950	+	13.7490i	0.670679	+	0.982070i
$197$	20.0921			1.43150			0.715750	−	0.698357i	$-0.246085\pi$
$197$	20.0921			1.43150			0.715750	+	0.698357i	$0.246085\pi$
$198$	−4.45776	−	2.35379i	−0.316799	−	0.167276i
$199$	5.03970			0.357255			0.178628	−	0.983917i	$-0.442834\pi$
$199$	5.03970			0.357255			0.178628	+	0.983917i	$0.442834\pi$
$200$	0.319949	+	2.81027i	0.0226238	+	0.198716i
$201$			14.0791i			0.993065i
$202$	18.2156	+	9.61821i	1.28165	+	0.676735i
$203$	−27.9889			−1.96444
$204$	7.75090	+	11.3496i	0.542672	+	0.794630i
$205$		−	10.4481i		−	0.729727i
$206$	6.80221	+	3.59170i	0.473932	+	0.250246i
$207$	−3.05366	+	3.69800i	−0.212244	+	0.257028i
$208$	9.04575	−	23.1536i	0.627210	−	1.60542i
$209$	−18.8570			−1.30437
$210$	−4.89562	−	2.58498i	−0.337830	−	0.178381i
$211$			17.2717i			1.18903i	0.804084	+	0.594515i	$0.202656\pi$
$211$			17.2717i			1.18903i	−0.804084	+	0.594515i	$0.797344\pi$
$212$	−18.2157	+	12.4400i	−1.25106	+	0.854380i
$213$	11.6817			0.800416
$214$	−3.84936	−	2.03254i	−0.263137	−	0.138942i
$215$		−	3.43010i		−	0.233931i
$216$	2.81027	−	0.319949i	0.191215	−	0.0217698i
$217$			21.4983i			1.45940i
$218$	−3.71570	+	7.03705i	−0.251659	+	0.476609i
$219$		−	11.4110i		−	0.771086i
$220$	−5.88721	+	4.02052i	−0.396916	+	0.271063i
$221$		−	42.7050i		−	2.87265i
$222$	1.63823	+	0.865019i	0.109951	+	0.0580563i
$223$			1.00859i			0.0675402i	0.999430	+	0.0337701i	$0.0107514\pi$
$223$			1.00859i			0.0675402i	−0.999430	+	0.0337701i	$0.989249\pi$
$224$	−16.7570	+	14.4772i	−1.11963	+	0.967298i
$225$	1.00000			0.0666667
$226$	6.55219	−	12.4090i	0.435845	−	0.825433i
$227$	27.6273			1.83369			0.916844	−	0.399246i	$-0.130728\pi$
$227$	27.6273			1.83369			0.916844	+	0.399246i	$0.130728\pi$
$228$	8.73726	−	5.96689i	0.578639	−	0.395167i
$229$			4.72289i			0.312097i	0.987749	+	0.156049i	$0.0498756\pi$
$229$			4.72289i			0.312097i	−0.987749	+	0.156049i	$0.950124\pi$
$230$	2.60822	+	6.26076i	0.171981	+	0.412823i
$231$		−	13.9540i		−	0.918105i
$232$	−2.28756	−	20.0928i	−0.150186	−	1.31915i
$233$	8.77953			0.575166			0.287583	−	0.957756i	$-0.407148\pi$
$233$	8.77953			0.575166			0.287583	+	0.957756i	$0.407148\pi$
$234$	−7.77173	−	4.10363i	−0.508054	−	0.268263i
$235$	−2.84469			−0.185567
$236$	8.46997	−	5.78435i	0.551348	−	0.376529i
$237$			0.545018i			0.0354028i
$238$	−17.7636	+	33.6420i	−1.15145	+	2.18069i
$239$			10.3755i			0.671138i	0.942016	+	0.335569i	$0.108929\pi$
$239$			10.3755i			0.671138i	−0.942016	+	0.335569i	$0.891071\pi$
$240$	1.45559	−	3.72575i	0.0939581	−	0.240496i
$241$			26.7704i			1.72443i	0.506541	+	0.862216i	$0.330924\pi$
$241$			26.7704i			1.72443i	−0.506541	+	0.862216i	$0.669076\pi$
$242$	−2.13344	−	1.12650i	−0.137143	−	0.0724140i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.49985	+	5.80475i	−0.544147	+	0.371611i
$245$		−	8.32462i		−	0.531840i
$246$	−6.89923	+	13.0662i	−0.439879	+	0.833072i
$247$	−32.8756			−2.09183
$248$	−15.4333	+	1.75708i	−0.980015	+	0.111575i
$249$		−	3.08427i		−	0.195458i
$250$	0.660333	−	1.25058i	0.0417631	−	0.0790939i
$251$	−28.6509			−1.80843			−0.904215	−	0.427077i	$-0.859543\pi$
$251$	−28.6509			−1.80843			−0.904215	+	0.427077i	$0.859543\pi$
$252$	4.41543	+	6.46548i	0.278146	+	0.407287i
$253$	−10.8849	+	13.1817i	−0.684327	+	0.828724i
$254$	−2.72845	+	5.16733i	−0.171198	+	0.324227i
$255$		−	6.87185i		−	0.430332i
$256$	−11.7625	−	10.8464i	−0.735156	−	0.677898i
$257$	17.7379			1.10646			0.553230	−	0.833029i	$-0.313395\pi$
$257$	17.7379			1.10646			0.553230	+	0.833029i	$0.313395\pi$
$258$	−2.26501	+	4.28963i	−0.141013	+	0.267061i
$259$			5.12811i			0.318645i
$260$	−10.2639	+	7.00944i	−0.636538	+	0.434707i
$261$	−7.14975			−0.442559
$262$	8.83739	−	16.7368i	0.545975	−	1.03401i
$263$	22.3989			1.38118			0.690588	−	0.723248i	$-0.257352\pi$
$263$	22.3989			1.38118			0.690588	+	0.723248i	$0.257352\pi$
$264$	10.0173	−	1.14047i	0.616524	−	0.0701912i
$265$	11.0291			0.677513
$266$	25.8986	+	13.6750i	1.58795	+	0.838468i
$267$	7.41651			0.453883
$268$	−15.8801	−	23.2531i	−0.970033	−	1.42041i
$269$	9.69449			0.591084			0.295542	−	0.955330i	$-0.404500\pi$
$269$	9.69449			0.591084			0.295542	+	0.955330i	$0.404500\pi$
$270$	−1.25058	−	0.660333i	−0.0761081	−	0.0401866i
$271$			2.94386i			0.178827i	0.995995	+	0.0894134i	$0.0284992\pi$
$271$			2.94386i			0.178827i	−0.995995	+	0.0894134i	$0.971501\pi$
$272$	−25.6028	−	10.0026i	−1.55240	−	0.606498i
$273$		−	24.3276i		−	1.47237i
$274$	2.22913	−	4.22167i	0.134666	−	0.255040i
$275$	3.56454			0.214950
$276$	0.872391	−	9.55191i	0.0525118	−	0.574957i
$277$	−29.7292			−1.78625			−0.893126	−	0.449806i	$-0.851493\pi$
$277$	−29.7292			−1.78625			−0.893126	+	0.449806i	$0.851493\pi$
$278$	4.49993	−	8.52227i	0.269888	−	0.511132i
$279$			5.49174i			0.328782i
$280$	11.0013	−	1.25250i	0.657452	−	0.0748509i
$281$			1.33749i			0.0797881i	0.999204	+	0.0398941i	$0.0127020\pi$
$281$			1.33749i			0.0797881i	−0.999204	+	0.0398941i	$0.987298\pi$
$282$	3.55752	+	1.87844i	0.211847	+	0.111860i
$283$	2.40320			0.142856			0.0714278	−	0.997446i	$-0.477244\pi$
$283$	2.40320			0.142856			0.0714278	+	0.997446i	$0.477244\pi$
$284$	−19.2935	+	13.1760i	−1.14486	+	0.781852i
$285$	−5.29017			−0.313362
$286$	−27.7026	−	14.6276i	−1.63809	−	0.864945i
$287$	−40.9008			−2.41430
$288$	−4.28058	+	3.69819i	−0.252236	+	0.217918i
$289$	−30.2224			−1.77779
$290$	−4.72122	+	8.94137i	−0.277240	+	0.525055i
$291$	−7.95043			−0.466062
$292$	12.8707	+	18.8465i	0.753202	+	1.10291i
$293$		−	1.76785i		−	0.103279i	−0.998666	−	0.0516395i	$-0.983555\pi$
$293$		−	1.76785i		−	0.103279i	0.998666	−	0.0516395i	$-0.0164447\pi$
$294$	−5.49702	+	10.4106i	−0.320593	+	0.607160i
$295$	−5.12833			−0.298583
$296$	−3.68138	+	0.419125i	−0.213976	+	0.0243612i
$297$		−	3.56454i		−	0.206836i
$298$	0.376291	−	0.712644i	0.0217979	−	0.0412824i
$299$	−18.9769	+	22.9811i	−1.09746	+	1.32903i
$300$	−1.65160	+	1.12792i	−0.0953554	+	0.0651205i
$301$	−13.4277			−0.773961
$302$	−8.47264	+	16.0461i	−0.487546	+	0.923347i
$303$			14.5657i			0.836777i
$304$	−7.70033	+	19.7099i	−0.441644	+	1.13044i
$305$	5.14642			0.294683
$306$	−4.53771	+	8.59383i	−0.259404	+	0.491277i
$307$			15.2035i			0.867709i	0.900983	+	0.433854i	$0.142847\pi$
$307$			15.2035i			0.867709i	−0.900983	+	0.433854i	$0.857153\pi$
$308$	15.7390	+	23.0465i	0.896812	+	1.31319i
$309$			5.43923i			0.309427i
$310$	6.86788	+	3.62638i	0.390070	+	0.205965i
$311$		−	1.53631i		−	0.0871160i	−0.999051	−	0.0435580i	$-0.986131\pi$
$311$		−	1.53631i		−	0.0871160i	0.999051	−	0.0435580i	$-0.0138693\pi$
$312$	17.4644	−	1.98832i	0.988726	−	0.112566i
$313$		−	3.50866i		−	0.198321i	−0.995071	−	0.0991605i	$-0.968384\pi$
$313$		−	3.50866i		−	0.198321i	0.995071	−	0.0991605i	$-0.0316157\pi$
$314$	9.05248	−	17.1442i	0.510861	−	0.967503i
$315$		−	3.91467i		−	0.220566i
$316$	−0.614737	−	0.900155i	−0.0345817	−	0.0506377i
$317$	18.8734			1.06004			0.530018	−	0.847986i	$-0.322185\pi$
$317$	18.8734			1.06004			0.530018	+	0.847986i	$0.322185\pi$
$318$	−13.7928	−	7.28289i	−0.773464	−	0.408404i
$319$	−25.4856			−1.42692
$320$	1.79829	+	7.79526i	0.100527	+	0.435769i
$321$		−	3.07805i		−	0.171800i
$322$	24.5088	−	10.2103i	1.36582	−	0.568999i
$323$			36.3533i			2.02275i
$324$	1.12792	+	1.65160i	0.0626622	+	0.0917558i
$325$	6.21448			0.344717
$326$	13.1597	−	24.9227i	0.728847	−	1.38034i
$327$	−5.62701			−0.311174
$328$	−3.34286	−	29.3620i	−0.184579	−	1.62125i
$329$			11.1360i			0.613948i
$330$	−4.45776	−	2.35379i	−0.245391	−	0.129572i
$331$			30.4098i			1.67147i	0.549130	+	0.835737i	$0.314959\pi$
$331$			30.4098i			1.67147i	−0.549130	+	0.835737i	$0.685041\pi$
$332$	3.47881	+	5.09400i	0.190925	+	0.279570i
$333$			1.30997i			0.0717861i
$334$	−3.94411	+	7.46963i	−0.215812	+	0.408720i
$335$			14.0791i			0.769225i
$336$	−14.5851	−	5.69816i	−0.795682	−	0.310860i
$337$		−	33.9686i		−	1.85039i	−0.379494	−	0.925194i	$-0.623902\pi$
$337$		−	33.9686i		−	1.85039i	0.379494	−	0.925194i	$-0.376098\pi$
$338$	−32.0397	−	16.9176i	−1.74273	−	0.920195i
$339$	9.92254			0.538919
$340$	7.75090	+	11.3496i	0.420352	+	0.615518i
$341$			19.5755i			1.06008i
$342$	6.61580	+	3.49327i	0.357741	+	0.188895i
$343$	−5.18544			−0.279987
$344$	−1.09746	−	9.63953i	−0.0591711	−	0.519729i
$345$	−3.05366	+	3.69800i	−0.164403	+	0.199093i
$346$	0.559063	+	0.295196i	0.0300554	+	0.0158699i
$347$		−	12.0233i		−	0.645444i	−0.946494	−	0.322722i	$-0.895402\pi$
$347$		−	12.0233i		−	0.645444i	0.946494	−	0.322722i	$-0.104598\pi$
$348$	11.8086	−	8.06435i	0.633005	−	0.432295i
$349$	−14.6968			−0.786700			−0.393350	−	0.919389i	$-0.628684\pi$
$349$	−14.6968			−0.786700			−0.393350	+	0.919389i	$0.628684\pi$
$350$	−4.89562	−	2.58498i	−0.261682	−	0.138173i
$351$		−	6.21448i		−	0.331704i
$352$	−15.2583	+	13.1824i	−0.813270	+	0.702622i
$353$	−18.3628			−0.977353			−0.488676	−	0.872465i	$-0.662520\pi$
$353$	−18.3628			−0.977353			−0.488676	+	0.872465i	$0.662520\pi$
$354$	6.41341	+	3.38641i	0.340869	+	0.179986i
$355$	11.6817			0.620000
$356$	−12.2491	+	8.36523i	−0.649203	+	0.443356i
$357$	−26.9010			−1.42375
$358$	−1.68339	+	3.18811i	−0.0889698	+	0.168497i
$359$	7.33490			0.387121			0.193561	−	0.981088i	$-0.437996\pi$
$359$	7.33490			0.387121			0.193561	+	0.981088i	$0.437996\pi$
$360$	2.81027	−	0.319949i	0.148114	−	0.0168628i
$361$	8.98588			0.472941
$362$	2.82606	−	5.35218i	0.148534	−	0.281304i
$363$		−	1.70595i		−	0.0895393i
$364$	27.4396	+	40.1796i	1.43823	+	2.10598i
$365$		−	11.4110i		−	0.597280i
$366$	−6.43603	−	3.39835i	−0.336417	−	0.177635i
$367$	−8.66677			−0.452402			−0.226201	−	0.974081i	$-0.572631\pi$
$367$	−8.66677			−0.452402			−0.226201	+	0.974081i	$0.572631\pi$
$368$	9.33294	+	16.7600i	0.486513	+	0.873673i
$369$	−10.4481			−0.543906
$370$	1.63823	+	0.865019i	0.0851676	+	0.0449702i
$371$		−	43.1753i		−	2.24155i
$372$	−6.19425	−	9.07018i	−0.321157	−	0.470267i
$373$			5.74203i			0.297311i	0.988889	+	0.148656i	$0.0474946\pi$
$373$			5.74203i			0.297311i	−0.988889	+	0.148656i	$0.952505\pi$
$374$	−16.1749	+	30.6331i	−0.836383	+	1.58400i
$375$	1.00000			0.0516398
$376$	−7.99434	+	0.910156i	−0.412277	+	0.0469377i
$377$	−44.4320			−2.28836
$378$	−2.58498	+	4.89562i	−0.132957	+	0.251803i
$379$	−4.59883			−0.236226			−0.118113	−	0.993000i	$-0.537684\pi$
$379$	−4.59883			−0.236226			−0.118113	+	0.993000i	$0.537684\pi$
$380$	8.73726	−	5.96689i	0.448212	−	0.306095i
$381$	−4.13193			−0.211685
$382$	−22.5891	−	11.9275i	−1.15576	−	0.610264i
$383$	−9.34111			−0.477308			−0.238654	−	0.971105i	$-0.576706\pi$
$383$	−9.34111			−0.477308			−0.238654	+	0.971105i	$0.576706\pi$
$384$	2.89856	−	10.9361i	0.147917	−	0.558081i
$385$		−	13.9540i		−	0.711161i
$386$	−7.96995	−	4.20829i	−0.405660	−	0.214196i
$387$	−3.43010			−0.174362
$388$	13.1310	−	8.96745i	0.666624	−	0.455253i
$389$		−	24.9069i		−	1.26283i	−0.775445	−	0.631416i	$-0.782474\pi$
$389$		−	24.9069i		−	1.26283i	0.775445	−	0.631416i	$-0.217526\pi$
$390$	−7.77173	−	4.10363i	−0.393537	−	0.207795i
$391$	25.4121	+	20.9843i	1.28514	+	1.06122i
$392$	−2.66346	−	23.3944i	−0.134525	−	1.18160i
$393$	13.3832			0.675094
$394$	−25.1268	−	13.2675i	−1.26587	−	0.668405i
$395$			0.545018i			0.0274229i
$396$	4.02052	+	5.88721i	0.202039	+	0.295843i
$397$	15.9626			0.801139			0.400570	−	0.916266i	$-0.368812\pi$
$397$	15.9626			0.801139			0.400570	+	0.916266i	$0.368812\pi$
$398$	−6.30257	−	3.32788i	−0.315919	−	0.166812i
$399$			20.7092i			1.03676i
$400$	1.45559	−	3.72575i	0.0727797	−	0.186288i
$401$		−	26.0520i		−	1.30098i	−0.759517	−	0.650488i	$-0.774565\pi$
$401$		−	26.0520i		−	1.30098i	0.759517	−	0.650488i	$-0.225435\pi$
$402$	9.29691	−	17.6071i	0.463688	−	0.878163i
$403$			34.1283i			1.70005i
$404$	−16.4289	−	24.0567i	−0.817370	−	1.19687i
$405$		−	1.00000i		−	0.0496904i
$406$	35.0025	+	18.4820i	1.73714	+	0.917246i
$407$			4.66946i			0.231456i
$408$	−2.19865	−	19.3118i	−0.108849	−	0.956076i
$409$	9.84257			0.486684			0.243342	−	0.969941i	$-0.421756\pi$
$409$	9.84257			0.486684			0.243342	+	0.969941i	$0.421756\pi$
$410$	−6.89923	+	13.0662i	−0.340729	+	0.645295i
$411$	3.37576			0.166514
$412$	−6.13501	−	8.98345i	−0.302250	−	0.442583i
$413$			20.0757i			0.987861i
$414$	6.26076	−	2.60822i	0.307700	−	0.128187i
$415$		−	3.08427i		−	0.151401i
$416$	−26.6016	+	22.9823i	−1.30425	+	1.12680i
$417$	6.81463			0.333714
$418$	23.5823	+	12.4519i	1.15345	+	0.609043i
$419$	−7.38704			−0.360881			−0.180440	−	0.983586i	$-0.557752\pi$
$419$	−7.38704			−0.360881			−0.180440	+	0.983586i	$0.557752\pi$
$420$	4.41543	+	6.46548i	0.215451	+	0.315483i
$421$		−	6.93017i		−	0.337756i	−0.985637	−	0.168878i	$-0.945986\pi$
$421$		−	6.93017i		−	0.337756i	0.985637	−	0.168878i	$-0.0540143\pi$
$422$	11.4051	−	21.5997i	0.555189	−	1.05145i
$423$			2.84469i			0.138313i
$424$	30.9948	−	3.52876i	1.50524	−	0.171372i
$425$		−	6.87185i		−	0.333334i
$426$	−14.6089	−	7.71381i	−0.707805	−	0.373735i
$427$		−	20.1465i		−	0.974959i
$428$	3.47180	+	5.08373i	0.167816	+	0.245731i
$429$		−	22.1518i		−	1.06950i
$430$	−2.26501	+	4.28963i	−0.109229	+	0.206864i
$431$	−9.62172			−0.463462			−0.231731	−	0.972780i	$-0.574439\pi$
$431$	−9.62172			−0.463462			−0.231731	+	0.972780i	$0.574439\pi$
$432$	−3.72575	−	1.45559i	−0.179255	−	0.0700323i
$433$			19.3827i			0.931472i	0.884924	+	0.465736i	$0.154210\pi$
$433$			19.3827i			0.931472i	−0.884924	+	0.465736i	$0.845790\pi$
$434$	14.1961	−	26.8855i	0.681433	−	1.29054i
$435$	−7.14975			−0.342804
$436$	9.29359	−	6.34682i	0.445082	−	0.303957i
$437$	16.1544	−	19.5630i	0.772768	−	0.935826i
$438$	−7.53508	+	14.2704i	−0.360040	+	0.681868i
$439$		−	4.99409i		−	0.238355i	−0.992873	−	0.119177i	$-0.961974\pi$
$439$		−	4.99409i		−	0.238355i	0.992873	−	0.119177i	$-0.0380257\pi$
$440$	10.0173	−	1.14047i	0.477558	−	0.0543699i
$441$	−8.32462			−0.396410
$442$	−28.1995	+	53.4062i	−1.34132	+	2.54027i
$443$			15.0814i			0.716541i	0.933618	+	0.358271i	$0.116633\pi$
$443$			15.0814i			0.716541i	−0.933618	+	0.358271i	$0.883367\pi$
$444$	−1.47755	−	2.16356i	−0.0701212	−	0.102678i
$445$	7.41651			0.351576
$446$	0.666006	−	1.26133i	0.0315363	−	0.0597256i
$447$	0.569849			0.0269530
$448$	30.5159	−	7.03971i	1.44174	−	0.332595i
$449$	34.9465			1.64923			0.824614	−	0.565696i	$-0.191392\pi$
$449$	34.9465			1.64923			0.824614	+	0.565696i	$0.191392\pi$
$450$	−1.25058	−	0.660333i	−0.0589531	−	0.0311284i
$451$	−37.2427			−1.75369
$452$	−16.3881	+	11.1918i	−0.770832	+	0.526420i
$453$	−12.8309			−0.602846
$454$	−34.5502	−	18.2432i	−1.62152	−	0.856197i
$455$		−	24.3276i		−	1.14050i
$456$	−14.8668	+	1.69259i	−0.696202	+	0.0792626i
$457$		−	16.3188i		−	0.763361i	−0.924294	−	0.381681i	$-0.875345\pi$
$457$		−	16.3188i		−	0.763361i	0.924294	−	0.381681i	$-0.124655\pi$
$458$	3.11868	−	5.90637i	0.145726	−	0.275986i
$459$	−6.87185			−0.320751
$460$	0.872391	−	9.55191i	0.0406754	−	0.445360i
$461$	−0.112877			−0.00525721			−0.00262861	−	0.999997i	$-0.500837\pi$
$461$	−0.112877			−0.00525721			−0.00262861	+	0.999997i	$0.500837\pi$
$462$	−9.21428	+	17.4506i	−0.428687	+	0.811877i
$463$			27.4755i			1.27690i	0.769665	+	0.638448i	$0.220423\pi$
$463$			27.4755i			1.27690i	−0.769665	+	0.638448i	$0.779577\pi$
$464$	−10.4071	+	26.6382i	−0.483139	+	1.23665i
$465$			5.49174i			0.254673i
$466$	−10.9795	−	5.79741i	−0.508617	−	0.268560i
$467$	10.1856			0.471335			0.235667	−	0.971834i	$-0.424272\pi$
$467$	10.1856			0.471335			0.235667	+	0.971834i	$0.424272\pi$
$468$	7.00944	+	10.2639i	0.324011	+	0.474447i
$469$	55.1151			2.54498
$470$	3.55752	+	1.87844i	0.164096	+	0.0866460i
$471$	13.7090			0.631675
$472$	−14.4120	+	1.64081i	−0.663367	+	0.0755242i
$473$	−12.2267			−0.562187
$474$	0.359894	−	0.681591i	0.0165305	−	0.0313065i
$475$	−5.29017			−0.242730
$476$	44.4298	−	30.3422i	2.03644	−	1.39073i
$477$		−	11.0291i		−	0.504989i
$478$	6.85131	−	12.9755i	0.313372	−	0.593485i
$479$	9.55762			0.436699			0.218349	−	0.975871i	$-0.429933\pi$
$479$	9.55762			0.436699			0.218349	+	0.975871i	$0.429933\pi$
$480$	−4.28058	+	3.69819i	−0.195381	+	0.168799i
$481$			8.14081i			0.371189i
$482$	17.6774	−	33.4786i	0.805182	−	1.52491i
$483$	14.4764	+	11.9541i	0.658700	+	0.543928i
$484$	1.92418	+	2.81756i	0.0874627	+	0.128071i
$485$	−7.95043			−0.361010
$486$	−0.660333	+	1.25058i	−0.0299533	+	0.0567276i
$487$			32.5478i			1.47488i	0.675412	+	0.737441i	$0.263966\pi$
$487$			32.5478i			1.47488i	−0.675412	+	0.737441i	$0.736034\pi$
$488$	14.4628	−	1.64659i	0.654702	−	0.0745378i
$489$	19.9288			0.901213
$490$	−5.49702	+	10.4106i	−0.248330	+	0.470304i
$491$		−	5.56517i		−	0.251153i	−0.992084	−	0.125576i	$-0.959922\pi$
$491$		−	5.56517i		−	0.251153i	0.992084	−	0.125576i	$-0.0400780\pi$
$492$	17.2561	−	11.7846i	0.777966	−	0.531292i
$493$			49.1321i			2.21280i
$494$	41.1138	+	21.7089i	1.84980	+	0.976729i
$495$		−	3.56454i		−	0.160214i
$496$	20.4609	+	7.99374i	0.918721	+	0.358930i
$497$		−	45.7299i		−	2.05127i
$498$	−2.03665	+	3.85714i	−0.0912644	+	0.172843i
$499$		−	32.9843i		−	1.47658i	−0.674484	−	0.738289i	$-0.735634\pi$
$499$		−	32.9843i		−	1.47658i	0.674484	−	0.738289i	$-0.264366\pi$
$500$	−1.65160	+	1.12792i	−0.0738620	+	0.0504421i
$501$	−5.97291			−0.266850
$502$	35.8304	+	18.9192i	1.59919	+	0.844404i
$503$	16.7209			0.745549			0.372775	−	0.927922i	$-0.378406\pi$
$503$	16.7209			0.745549			0.372775	+	0.927922i	$0.378406\pi$
$504$	−1.25250	−	11.0013i	−0.0557906	−	0.490036i
$505$			14.5657i			0.648164i
$506$	22.3168	−	9.29711i	0.992101	−	0.413307i
$507$		−	25.6198i		−	1.13781i
$508$	6.82432	−	4.66049i	0.302780	−	0.206776i
$509$	−8.57338			−0.380008			−0.190004	−	0.981783i	$-0.560850\pi$
$509$	−8.57338			−0.380008			−0.190004	+	0.981783i	$0.560850\pi$
$510$	−4.53771	+	8.59383i	−0.200933	+	0.380541i
$511$	−44.6704			−1.97610
$512$	7.54777	+	21.3315i	0.333568	+	0.942726i
$513$			5.29017i			0.233567i
$514$	−22.1827	−	11.7129i	−0.978438	−	0.516635i
$515$			5.43923i			0.239681i
$516$	5.66518	−	3.86888i	0.249395	−	0.170318i
$517$			10.1400i			0.445957i
$518$	3.38626	−	6.41313i	0.148784	−	0.281777i
$519$			0.447042i			0.0196229i
$520$	17.4644	−	1.98832i	0.765864	−	0.0871936i
$521$			9.81425i			0.429970i	0.976617	+	0.214985i	$0.0689703\pi$
$521$			9.81425i			0.429970i	−0.976617	+	0.214985i	$0.931030\pi$
$522$	8.94137	+	4.72122i	0.391353	+	0.206642i
$523$	39.4912			1.72683			0.863416	−	0.504493i	$-0.168321\pi$
$523$	39.4912			1.72683			0.863416	+	0.504493i	$0.168321\pi$
$524$	−22.1038	+	15.0952i	−0.965608	+	0.659437i
$525$		−	3.91467i		−	0.170850i
$526$	−28.0117	−	14.7908i	−1.22137	−	0.644908i
$527$	37.7385			1.64391
$528$	−13.2806	−	5.18852i	−0.577964	−	0.225801i
$529$	−4.35035	−	22.5848i	−0.189146	−	0.981949i
$530$	−13.7928	−	7.28289i	−0.599123	−	0.316349i
$531$			5.12833i			0.222551i
$532$	−23.3584	−	34.2035i	−1.01271	−	1.48291i
$533$	−64.9295			−2.81241
$534$	−9.27497	−	4.89737i	−0.401367	−	0.211930i
$535$		−	3.07805i		−	0.133076i
$536$	4.50461	+	39.5662i	0.194569	+	1.70900i
$537$	−2.54930			−0.110010
$538$	−12.1238	−	6.40160i	−0.522693	−	0.275992i
$539$	−29.6734			−1.27813
$540$	1.12792	+	1.65160i	0.0485379	+	0.0710737i
$541$	11.5680			0.497347			0.248673	−	0.968587i	$-0.420005\pi$
$541$	11.5680			0.497347			0.248673	+	0.968587i	$0.420005\pi$
$542$	1.94393	−	3.68154i	0.0834989	−	0.158136i
$543$	4.27974			0.183661
$544$	25.4134	+	29.4155i	1.08959	+	1.26118i
$545$	−5.62701			−0.241035
$546$	−16.0643	+	30.4237i	−0.687490	+	1.30202i
$547$		−	21.6493i		−	0.925658i	−0.886448	−	0.462829i	$-0.846834\pi$
$547$		−	21.6493i		−	0.925658i	0.886448	−	0.462829i	$-0.153166\pi$
$548$	−5.57542	+	3.80759i	−0.238170	+	0.162652i
$549$		−	5.14642i		−	0.219644i
$550$	−4.45776	−	2.35379i	−0.190079	−	0.100366i
$551$	37.8234			1.61133
$552$	−7.39844	+	11.3694i	−0.314899	+	0.483913i
$553$	2.13357			0.0907284
$554$	37.1788	+	19.6312i	1.57958	+	0.834048i
$555$			1.30997i			0.0556053i
$556$	−11.2551	+	7.68636i	−0.477322	+	0.325974i
$557$		−	25.5493i		−	1.08256i	−0.840843	−	0.541279i	$-0.817940\pi$
$557$		−	25.5493i		−	1.08256i	0.840843	−	0.541279i	$-0.182060\pi$
$558$	3.62638	−	6.86788i	0.153517	−	0.290741i
$559$	−21.3163			−0.901584
$560$	−14.5851	−	5.69816i	−0.616333	−	0.240791i
$561$	−24.4950			−1.03418
$562$	0.883191	−	1.67265i	0.0372552	−	0.0705564i
$563$	−9.74851			−0.410851			−0.205425	−	0.978673i	$-0.565858\pi$
$563$	−9.74851			−0.410851			−0.205425	+	0.978673i	$0.565858\pi$
$564$	−3.20858	−	4.69830i	−0.135106	−	0.197834i
$565$	9.92254			0.417445
$566$	−3.00541	−	1.58691i	−0.126327	−	0.0667030i
$567$	−3.91467			−0.164401
$568$	32.8287	−	3.73755i	1.37746	−	0.156824i
$569$			33.0556i			1.38576i	0.721051	+	0.692882i	$0.243660\pi$
$569$			33.0556i			1.38576i	−0.721051	+	0.692882i	$0.756340\pi$
$570$	6.61580	+	3.49327i	0.277105	+	0.146317i
$571$	−33.0864			−1.38462			−0.692311	−	0.721599i	$-0.743407\pi$
$571$	−33.0864			−1.38462			−0.692311	+	0.721599i	$0.743407\pi$
$572$	24.9854	+	36.5860i	1.04469	+	1.52974i
$573$		−	18.0629i		−	0.754587i
$574$	51.1499	+	27.0082i	2.13496	+	1.12730i
$575$	−3.05366	+	3.69800i	−0.127346	+	0.154217i
$576$	7.79526	−	1.79829i	0.324803	−	0.0749287i
$577$	−13.4401			−0.559517			−0.279759	−	0.960070i	$-0.590254\pi$
$577$	−13.4401			−0.559517			−0.279759	+	0.960070i	$0.590254\pi$
$578$	37.7956	+	19.9568i	1.57209	+	0.830095i
$579$		−	6.37298i		−	0.264852i
$580$	11.8086	−	8.06435i	0.490324	−	0.334854i
$581$	−12.0739			−0.500910
$582$	9.94268	+	5.24993i	0.412137	+	0.217617i
$583$		−	39.3137i		−	1.62821i
$584$	−3.65095	−	32.0681i	−0.151077	−	1.32699i
$585$		−	6.21448i		−	0.256937i
$586$	−1.16737	+	2.21084i	−0.0482236	+	0.0913292i
$587$		−	3.66303i		−	0.151189i	−0.997139	−	0.0755947i	$-0.975914\pi$
$587$		−	3.66303i		−	0.151189i	0.997139	−	0.0755947i	$-0.0240855\pi$
$588$	13.7490	−	9.38950i	0.566998	−	0.387217i
$589$		−	29.0522i		−	1.19708i
$590$	6.41341	+	3.38641i	0.264036	+	0.139416i
$591$		−	20.0921i		−	0.826477i
$592$	4.88064	+	1.90679i	0.200593	+	0.0783685i
$593$	−17.5134			−0.719190			−0.359595	−	0.933109i	$-0.617085\pi$
$593$	−17.5134			−0.719190			−0.359595	+	0.933109i	$0.617085\pi$
$594$	−2.35379	+	4.45776i	−0.0965770	+	0.182904i
$595$	−26.9010			−1.10283
$596$	−0.941166	+	0.642745i	−0.0385516	+	0.0263278i
$597$		−	5.03970i		−	0.206261i
$598$	38.9074	−	16.2087i	1.59104	−	0.662825i
$599$			8.21639i			0.335713i	0.985811	+	0.167856i	$0.0536845\pi$
$599$			8.21639i			0.335713i	−0.985811	+	0.167856i	$0.946316\pi$
$600$	2.81027	−	0.319949i	0.114729	−	0.0130619i
$601$	21.7813			0.888477			0.444238	−	0.895909i	$-0.353474\pi$
$601$	21.7813			0.888477			0.444238	+	0.895909i	$0.353474\pi$
$602$	16.7925	+	8.86677i	0.684411	+	0.361382i
$603$	14.0791			0.573346
$604$	21.1915	−	14.4722i	0.862270	−	0.588865i
$605$		−	1.70595i		−	0.0693569i
$606$	9.61821	−	18.2156i	0.390713	−	0.739959i
$607$		−	16.8882i		−	0.685472i	−0.939432	−	0.342736i	$-0.888646\pi$
$607$		−	16.8882i		−	0.685472i	0.939432	−	0.342736i	$-0.111354\pi$
$608$	22.6450	−	19.5641i	0.918376	−	0.793427i
$609$			27.9889i			1.13417i
$610$	−6.43603	−	3.39835i	−0.260587	−	0.137595i
$611$			17.6782i			0.715185i
$612$	11.3496	−	7.75090i	0.458780	−	0.313312i
$613$		−	17.5741i		−	0.709813i	−0.934902	−	0.354906i	$-0.884513\pi$
$613$		−	17.5741i		−	0.709813i	0.934902	−	0.354906i	$-0.115487\pi$
$614$	10.0394	−	19.0132i	0.405156	−	0.767312i
$615$	−10.4481			−0.421308
$616$	−4.46457	−	39.2145i	−0.179883	−	1.58000i
$617$			47.2184i			1.90094i	0.310814	+	0.950471i	$0.399398\pi$
$617$			47.2184i			1.90094i	−0.310814	+	0.950471i	$0.600602\pi$
$618$	3.59170	−	6.80221i	0.144479	−	0.273625i
$619$	−31.9904			−1.28580			−0.642902	−	0.765949i	$-0.722270\pi$
$619$	−31.9904			−1.28580			−0.642902	+	0.765949i	$0.722270\pi$
$620$	−6.19425	−	9.07018i	−0.248767	−	0.364267i
$621$	3.69800	+	3.05366i	0.148395	+	0.122539i
$622$	−1.01447	+	1.92128i	−0.0406767	+	0.0770363i
$623$		−	29.0332i		−	1.16319i
$624$	−23.1536	−	9.04575i	−0.926887	−	0.362120i
$625$	1.00000			0.0400000
$626$	−2.31688	+	4.38787i	−0.0926012	+	0.175374i
$627$			18.8570i			0.753077i
$628$	−22.6418	+	15.4626i	−0.903505	+	0.617025i
$629$	9.00195			0.358931
$630$	−2.58498	+	4.89562i	−0.102988	+	0.195046i
$631$	−0.295167			−0.0117504			−0.00587521	−	0.999983i	$-0.501870\pi$
$631$	−0.295167			−0.0117504			−0.00587521	+	0.999983i	$0.501870\pi$
$632$	0.174378	+	1.53165i	0.00693640	+	0.0609258i
$633$	17.2717			0.686487
$634$	−23.6028	−	12.4627i	−0.937386	−	0.494959i
$635$	−4.13193			−0.163971
$636$	12.4400	+	18.2157i	0.493277	+	0.722301i
$637$	−51.7332			−2.04974
$638$	31.8719	+	16.8290i	1.26182	+	0.666266i
$639$		−	11.6817i		−	0.462120i
$640$	2.89856	−	10.9361i	0.114576	−	0.432287i
$641$			42.3493i			1.67270i	0.548197	+	0.836349i	$0.315314\pi$
$641$			42.3493i			1.67270i	−0.548197	+	0.836349i	$0.684686\pi$
$642$	−2.03254	+	3.84936i	−0.0802180	+	0.151922i
$643$	−10.9530			−0.431945			−0.215972	−	0.976399i	$-0.569292\pi$
$643$	−10.9530			−0.431945			−0.215972	+	0.976399i	$0.569292\pi$
$644$	−37.3925	−	3.41512i	−1.47347	−	0.134575i
$645$	−3.43010			−0.135060
$646$	24.0053	−	45.4628i	0.944475	−	1.78871i
$647$			9.57379i			0.376384i	0.982132	+	0.188192i	$0.0602628\pi$
$647$			9.57379i			0.376384i	−0.982132	+	0.188192i	$0.939737\pi$
$648$	−0.319949	−	2.81027i	−0.0125688	−	0.110398i
$649$			18.2802i			0.717559i
$650$	−7.77173	−	4.10363i	−0.304832	−	0.160958i
$651$	21.4983			0.842586
$652$	−32.9146	+	22.4781i	−1.28903	+	0.880312i
$653$	−32.7339			−1.28098			−0.640488	−	0.767968i	$-0.721268\pi$
$653$	−32.7339			−1.28098			−0.640488	+	0.767968i	$0.721268\pi$
$654$	7.03705	+	3.71570i	0.275170	+	0.145295i
$655$	13.3832			0.522926
$656$	−15.2082	+	38.9271i	−0.593780	+	1.51985i
$657$	−11.4110			−0.445186
$658$	7.35347	−	13.9265i	0.286668	−	0.542912i
$659$	30.6434			1.19370			0.596848	−	0.802354i	$-0.296420\pi$
$659$	30.6434			1.19370			0.596848	+	0.802354i	$0.296420\pi$
$660$	4.02052	+	5.88721i	0.156498	+	0.229159i
$661$		−	33.9119i		−	1.31902i	−0.751695	−	0.659511i	$-0.770764\pi$
$661$		−	33.9119i		−	1.31902i	0.751695	−	0.659511i	$-0.229236\pi$
$662$	20.0806	−	38.0300i	0.780455	−	1.47808i
$663$	−42.7050			−1.65853
$664$	−0.986811	−	8.66765i	−0.0382957	−	0.336370i
$665$			20.7092i			0.803070i
$666$	0.865019	−	1.63823i	0.0335188	−	0.0634802i
$667$	21.8329	−	26.4398i	0.845373	−	1.02375i
$668$	9.86489	−	6.73697i	0.381684	−	0.260661i
$669$	1.00859			0.0389944
$670$	9.29691	−	17.6071i	0.359171	−	0.680223i
$671$		−	18.3446i		−	0.708186i
$672$	14.4772	+	16.7570i	0.558470	+	0.646417i
$673$	28.1079			1.08348			0.541740	−	0.840546i	$-0.317766\pi$
$673$	28.1079			1.08348			0.541740	+	0.840546i	$0.317766\pi$
$674$	−22.4306	+	42.4806i	−0.863995	+	1.63629i
$675$		−	1.00000i		−	0.0384900i
$676$	28.8971	+	42.3137i	1.11143	+	1.62745i
$677$		−	27.8099i		−	1.06882i	−0.845225	−	0.534410i	$-0.820534\pi$
$677$		−	27.8099i		−	1.06882i	0.845225	−	0.534410i	$-0.179466\pi$
$678$	−12.4090	−	6.55219i	−0.476564	−	0.251635i
$679$			31.1233i			1.19440i
$680$	−2.19865	−	19.3118i	−0.0843142	−	0.740573i
$681$		−	27.6273i		−	1.05868i
$682$	12.9264	−	24.4809i	0.494977	−	0.937420i
$683$		−	19.3710i		−	0.741212i	−0.928790	−	0.370606i	$-0.879150\pi$
$683$		−	19.3710i		−	0.741212i	0.928790	−	0.370606i	$-0.120850\pi$
$684$	−5.96689	−	8.73726i	−0.228150	−	0.334078i
$685$	3.37576			0.128981
$686$	6.48482	+	3.42412i	0.247592	+	0.130733i
$687$	4.72289			0.180189
$688$	−4.99284	+	12.7797i	−0.190350	+	0.487223i
$689$		−	68.5402i		−	2.61118i
$690$	6.26076	−	2.60822i	0.238343	−	0.0992933i
$691$			26.2417i			0.998283i	0.866521	+	0.499141i	$0.166351\pi$
$691$			26.2417i			0.998283i	−0.866521	+	0.499141i	$0.833649\pi$
$692$	−0.504227	−	0.738336i	−0.0191678	−	0.0280673i
$693$	−13.9540			−0.530068
$694$	−7.93938	+	15.0361i	−0.301375	+	0.570764i
$695$	6.81463			0.258494
$696$	−20.0928	+	2.28756i	−0.761614	+	0.0867097i
$697$			71.7978i			2.71954i
$698$	18.3796	+	9.70477i	0.695676	+	0.367331i
$699$		−	8.77953i		−	0.332072i
$700$	4.41543	+	6.46548i	0.166888	+	0.244372i
$701$		−	11.6964i		−	0.441767i	−0.975300	−	0.220884i	$-0.929106\pi$
$701$		−	11.6964i		−	0.441767i	0.975300	−	0.220884i	$-0.0708941\pi$
$702$	−4.10363	+	7.77173i	−0.154881	+	0.293325i
$703$		−	6.92998i		−	0.261369i
$704$	27.7865	−	6.41008i	1.04724	−	0.241589i
$705$			2.84469i			0.107137i
$706$	22.9642	+	12.1256i	0.864269	+	0.456352i
$707$	57.0198			2.14445
$708$	−5.78435	−	8.46997i	−0.217389	−	0.318321i
$709$			4.90911i			0.184365i	0.995742	+	0.0921827i	$0.0293844\pi$
$709$			4.90911i			0.184365i	−0.995742	+	0.0921827i	$0.970616\pi$
$710$	−14.6089	−	7.71381i	−0.548263	−	0.289494i
$711$	0.545018			0.0204398
$712$	20.8424	−	2.37291i	0.781103	−	0.0889285i
$713$	−20.3084	−	16.7699i	−0.760557	−	0.628038i
$714$	33.6420	+	17.7636i	1.25902	+	0.664788i
$715$		−	22.1518i		−	0.828429i
$716$	4.21044	−	2.87541i	0.157351	−	0.107459i
$717$	10.3755			0.387482
$718$	−9.17291	−	4.84348i	−0.342330	−	0.180757i
$719$		−	36.1521i		−	1.34824i	−0.738620	−	0.674122i	$-0.764522\pi$
$719$		−	36.1521i		−	1.34824i	0.738620	−	0.674122i	$-0.235478\pi$
$720$	−3.72575	−	1.45559i	−0.138851	−	0.0542467i
$721$	21.2928			0.792984
$722$	−11.2376	−	5.93367i	−0.418220	−	0.220828i
$723$	26.7704			0.995601
$724$	−7.06844	+	4.82721i	−0.262696	+	0.179402i
$725$	−7.14975			−0.265535
$726$	−1.12650	+	2.13344i	−0.0418083	+	0.0791793i
$727$	31.1631			1.15578			0.577888	−	0.816116i	$-0.303877\pi$
$727$	31.1631			1.15578			0.577888	+	0.816116i	$0.303877\pi$
$728$	−7.78361	−	68.3673i	−0.288480	−	2.53386i
$729$	−1.00000			−0.0370370
$730$	−7.53508	+	14.2704i	−0.278886	+	0.528173i
$731$			23.5712i			0.871812i
$732$	5.80475	+	8.49985i	0.214550	+	0.314163i
$733$		−	39.2366i		−	1.44924i	−0.689151	−	0.724618i	$-0.742016\pi$
$733$		−	39.2366i		−	1.44924i	0.689151	−	0.724618i	$-0.257984\pi$
$734$	10.8385	+	5.72296i	0.400057	+	0.211238i
$735$	−8.32462			−0.307058
$736$	−0.604470	−	27.1226i	−0.0222811	−	0.999752i
$737$	50.1856			1.84861
$738$	13.0662	+	6.89923i	0.480974	+	0.253964i
$739$			42.3677i			1.55852i	0.626699	+	0.779261i	$0.284405\pi$
$739$			42.3677i			1.55852i	−0.626699	+	0.779261i	$0.715595\pi$
$740$	−1.47755	−	2.16356i	−0.0543157	−	0.0795340i
$741$			32.8756i			1.20772i
$742$	−28.5101	+	53.9944i	−1.04664	+	1.98220i
$743$	−0.526357			−0.0193102			−0.00965508	−	0.999953i	$-0.503073\pi$
$743$	−0.526357			−0.0193102			−0.00965508	+	0.999953i	$0.503073\pi$
$744$	1.75708	+	15.4333i	0.0644177	+	0.565812i
$745$	0.569849			0.0208777
$746$	3.79165	−	7.18089i	0.138822	−	0.262911i
$747$	−3.08427			−0.112848
$748$	40.4561	−	27.6284i	1.47922	−	1.01019i
$749$	−12.0496			−0.440281
$750$	−1.25058	−	0.660333i	−0.0456649	−	0.0241120i
$751$	−11.1318			−0.406205			−0.203102	−	0.979158i	$-0.565102\pi$
$751$	−11.1318			−0.406205			−0.203102	+	0.979158i	$0.565102\pi$
$752$	10.5986	+	4.14071i	0.386491	+	0.150996i
$753$			28.6509i			1.04410i
$754$	55.5659	+	29.3399i	2.02359	+	1.06850i
$755$	−12.8309			−0.466963
$756$	6.46548	−	4.41543i	0.235147	−	0.160588i
$757$		−	4.84281i		−	0.176015i	−0.996120	−	0.0880074i	$-0.971950\pi$
$757$		−	4.84281i		−	0.176015i	0.996120	−	0.0880074i	$-0.0280499\pi$
$758$	5.75122	+	3.03676i	0.208894	+	0.110300i
$759$	13.1817	+	10.8849i	0.478464	+	0.395096i
$760$	−14.8668	+	1.69259i	−0.539276	+	0.0613965i
$761$	47.1174			1.70801			0.854003	−	0.520268i	$-0.174168\pi$
$761$	47.1174			1.70801			0.854003	+	0.520268i	$0.174168\pi$
$762$	5.16733	+	2.72845i	0.187192	+	0.0988414i
$763$			22.0279i			0.797462i
$764$	20.3735	+	29.8327i	0.737086	+	1.07931i
$765$	−6.87185			−0.248452
$766$	11.6818	+	6.16825i	0.422082	+	0.222868i
$767$			31.8699i			1.15076i
$768$	−10.8464	+	11.7625i	−0.391385	+	0.424443i
$769$			14.7753i			0.532810i	0.963861	+	0.266405i	$0.0858358\pi$
$769$			14.7753i			0.532810i	−0.963861	+	0.266405i	$0.914164\pi$
$770$	−9.21428	+	17.4506i	−0.332060	+	0.628877i
$771$		−	17.7379i		−	0.638814i
$772$	7.18821	+	10.5256i	0.258709	+	0.378826i
$773$		−	8.69778i		−	0.312837i	−0.987691	−	0.156419i	$-0.950005\pi$
$773$		−	8.69778i		−	0.312837i	0.987691	−	0.156419i	$-0.0499949\pi$
$774$	4.28963	+	2.26501i	0.154188	+	0.0814142i
$775$			5.49174i			0.197269i
$776$	−22.3429	+	2.54373i	−0.802063	+	0.0913148i
$777$	5.12811			0.183970
$778$	−16.4469	+	31.1482i	−0.589649	+	1.11672i
$779$	55.2722			1.98033
$780$	7.00944	+	10.2639i	0.250978	+	0.367505i
$781$		−	41.6399i		−	1.48999i
$782$	−17.9233	−	43.0231i	−0.640937	−	1.53850i
$783$			7.14975i			0.255511i
$784$	−12.1173	+	31.0155i	−0.432759	+	1.10770i
$785$	13.7090			0.489294
$786$	−16.7368	−	8.83739i	−0.596983	−	0.315219i
$787$	−15.4238			−0.549798			−0.274899	−	0.961473i	$-0.588644\pi$
$787$	−15.4238			−0.549798			−0.274899	+	0.961473i	$0.588644\pi$
$788$	22.6622	+	33.1841i	0.807309	+	1.18214i
$789$		−	22.3989i		−	0.797423i
$790$	0.359894	−	0.681591i	0.0128044	−	0.0242499i
$791$		−	38.8435i		−	1.38111i
$792$	−1.14047	−	10.0173i	−0.0405249	−	0.355950i
$793$		−	31.9823i		−	1.13573i
$794$	−19.9626	−	10.5406i	−0.708445	−	0.374073i
$795$		−	11.0291i		−	0.391163i
$796$	5.68438	+	8.32359i	0.201478	+	0.295022i
$797$			36.7662i			1.30233i	0.758938	+	0.651163i	$0.225718\pi$
$797$			36.7662i			1.30233i	−0.758938	+	0.651163i	$0.774282\pi$
$798$	13.6750	−	25.8986i	0.484090	−	0.916802i
$799$	19.5483			0.691568
$800$	−4.28058	+	3.69819i	−0.151341	+	0.130751i
$801$		−	7.41651i		−	0.262050i
$802$	−17.2030	+	32.5802i	−0.607459	+	1.15045i
$803$	−40.6751			−1.43539
$804$	−23.2531	+	15.8801i	−0.820075	+	0.560049i
$805$	14.4764	+	11.9541i	0.510227	+	0.421325i
$806$	22.5361	−	42.6803i	0.793799	−	1.50335i
$807$		−	9.69449i		−	0.341262i
$808$	4.66028	+	40.9335i	0.163948	+	1.44004i
$809$	−10.4329			−0.366800			−0.183400	−	0.983038i	$-0.558710\pi$
$809$	−10.4329			−0.366800			−0.183400	+	0.983038i	$0.558710\pi$
$810$	−0.660333	+	1.25058i	−0.0232017	+	0.0439410i
$811$		−	10.9645i		−	0.385017i	−0.981295	−	0.192509i	$-0.938338\pi$
$811$		−	10.9645i		−	0.385017i	0.981295	−	0.192509i	$-0.0616623\pi$
$812$	−31.5692	−	46.2266i	−1.10786	−	1.62224i
$813$	2.94386			0.103246
$814$	3.08340	−	5.83955i	0.108073	−	0.204676i
$815$	19.9288			0.698077
$816$	−10.0026	+	25.6028i	−0.350162	+	0.896279i
$817$	18.1458			0.634842
$818$	−12.3090	−	6.49938i	−0.430373	−	0.227245i
$819$	−24.3276			−0.850076
$820$	17.2561	−	11.7846i	0.602610	−	0.411537i
$821$	−35.1027			−1.22509			−0.612545	−	0.790435i	$-0.709854\pi$
$821$	−35.1027			−1.22509			−0.612545	+	0.790435i	$0.709854\pi$
$822$	−4.22167	−	2.22913i	−0.147248	−	0.0777497i
$823$			46.1419i			1.60841i	0.594355	+	0.804203i	$0.297407\pi$
$823$			46.1419i			1.60841i	−0.594355	+	0.804203i	$0.702593\pi$
$824$	1.74028	+	15.2857i	0.0606254	+	0.532503i
$825$		−	3.56454i		−	0.124101i
$826$	13.2567	−	25.1064i	0.461258	−	0.873562i
$827$	−23.8671			−0.829942			−0.414971	−	0.909835i	$-0.636208\pi$
$827$	−23.8671			−0.829942			−0.414971	+	0.909835i	$0.636208\pi$
$828$	−9.55191	−	0.872391i	−0.331952	−	0.0303177i
$829$	−5.61865			−0.195144			−0.0975719	−	0.995228i	$-0.531108\pi$
$829$	−5.61865			−0.195144			−0.0975719	+	0.995228i	$0.531108\pi$
$830$	−2.03665	+	3.85714i	−0.0706931	+	0.133883i
$831$			29.7292i			1.03129i
$832$	48.4435	−	11.1754i	1.67948	−	0.387439i
$833$			57.2056i			1.98206i
$834$	−8.52227	−	4.49993i	−0.295102	−	0.155820i
$835$	−5.97291			−0.206701
$836$	−21.2692	−	31.1443i	−0.735611	−	1.07715i
$837$	5.49174			0.189822
$838$	9.23811	+	4.87791i	0.319125	+	0.168505i
$839$	−7.47060			−0.257914			−0.128957	−	0.991650i	$-0.541163\pi$
$839$	−7.47060			−0.257914			−0.128957	+	0.991650i	$0.541163\pi$
$840$	−1.25250	−	11.0013i	−0.0432152	−	0.379580i
$841$	22.1190			0.762723
$842$	−4.57622	+	8.66675i	−0.157707	+	0.298676i
$843$	1.33749			0.0460657
$844$	−28.5259	+	19.4811i	−0.981904	+	0.670565i
$845$		−	25.6198i		−	0.881347i
$846$	1.87844	−	3.55752i	0.0645821	−	0.122310i
$847$	−6.67824			−0.229467
$848$	−41.0918	−	16.0539i	−1.41110	−	0.551293i
$849$		−	2.40320i		−	0.0824777i
$850$	−4.53771	+	8.59383i	−0.155642	+	0.294766i
$851$	−4.84428	−	4.00021i	−0.166060	−	0.137126i
$852$	13.1760	+	19.2935i	0.451403	+	0.660985i
$853$	−3.94418			−0.135046			−0.0675231	−	0.997718i	$-0.521510\pi$
$853$	−3.94418			−0.135046			−0.0675231	+	0.997718i	$0.521510\pi$
$854$	−13.3034	+	25.1949i	−0.455234	+	0.862152i
$855$			5.29017i			0.180920i
$856$	−0.984821	−	8.65017i	−0.0336605	−	0.295657i
$857$	−7.36707			−0.251654			−0.125827	−	0.992052i	$-0.540158\pi$
$857$	−7.36707			−0.251654			−0.125827	+	0.992052i	$0.540158\pi$
$858$	−14.6276	+	27.7026i	−0.499376	+	0.945753i
$859$			22.4648i			0.766488i	0.923647	+	0.383244i	$0.125193\pi$
$859$			22.4648i			0.766488i	−0.923647	+	0.383244i	$0.874807\pi$
$860$	5.66518	−	3.86888i	0.193181	−	0.131928i
$861$			40.9008i			1.39390i
$862$	12.0328	+	6.35354i	0.409838	+	0.216402i
$863$		−	14.9997i		−	0.510597i	−0.966862	−	0.255298i	$-0.917826\pi$
$863$		−	14.9997i		−	0.510597i	0.966862	−	0.255298i	$-0.0821737\pi$
$864$	3.69819	+	4.28058i	0.125815	+	0.145628i
$865$			0.447042i			0.0151999i
$866$	12.7990	−	24.2397i	0.434929	−	0.823697i
$867$			30.2224i			1.02641i
$868$	−35.5068	+	24.2484i	−1.20518	+	0.823045i
$869$	1.94274			0.0659030
$870$	8.94137	+	4.72122i	0.303141	+	0.160064i
$871$	87.4944			2.96464
$872$	−15.8134	+	1.80036i	−0.535510	+	0.0609678i
$873$			7.95043i			0.269081i
$874$	−33.1205	+	13.7979i	−1.12032	+	0.466722i
$875$		−	3.91467i		−	0.132340i
$876$	18.8465	−	12.8707i	0.636764	−	0.434861i
$877$	−5.85851			−0.197828			−0.0989138	−	0.995096i	$-0.531537\pi$
$877$	−5.85851			−0.197828			−0.0989138	+	0.995096i	$0.531537\pi$
$878$	−3.29776	+	6.24552i	−0.111294	+	0.210776i
$879$	−1.76785			−0.0596281
$880$	−13.2806	−	5.18852i	−0.447689	−	0.174905i
$881$		−	37.0664i		−	1.24880i	−0.781105	−	0.624399i	$-0.785344\pi$
$881$		−	37.0664i		−	1.24880i	0.781105	−	0.624399i	$-0.214656\pi$
$882$	10.4106	+	5.49702i	0.350544	+	0.185094i
$883$		−	26.2767i		−	0.884282i	−0.896946	−	0.442141i	$-0.854219\pi$
$883$		−	26.2767i		−	0.884282i	0.896946	−	0.442141i	$-0.145781\pi$
$884$	70.5318	−	48.1678i	2.37224	−	1.62006i
$885$			5.12833i			0.172387i
$886$	9.95878	−	18.8606i	0.334572	−	0.633635i
$887$			43.4303i			1.45825i	0.684382	+	0.729124i	$0.260072\pi$
$887$			43.4303i			1.45825i	−0.684382	+	0.729124i	$0.739928\pi$
$888$	0.419125	+	3.68138i	0.0140649	+	0.123539i
$889$			16.1751i			0.542497i
$890$	−9.27497	−	4.89737i	−0.310898	−	0.164160i
$891$	−3.56454			−0.119417
$892$	−1.66579	+	1.13761i	−0.0557748	+	0.0380900i
$893$		−	15.0489i		−	0.503591i
$894$	−0.712644	−	0.376291i	−0.0238344	−	0.0125850i
$895$	−2.54930			−0.0852137
$896$	−42.8112	−	11.3469i	−1.43022	−	0.379073i
$897$	22.9811	+	18.9769i	0.767317	+	0.633620i
$898$	−43.7036	−	23.0764i	−1.45841	−	0.770068i
$899$		−	39.2646i		−	1.30955i
$900$	1.12792	+	1.65160i	0.0375973	+	0.0550535i
$901$	−75.7905			−2.52495
$902$	46.5751	+	24.5926i	1.55078	+	0.818843i
$903$			13.4277i			0.446846i
$904$	27.8851	−	3.17471i	0.927443	−	0.105589i
$905$	4.27974			0.142263
$906$	16.0461	+	8.47264i	0.533095	+	0.281485i
$907$	−53.8160			−1.78693			−0.893465	−	0.449132i	$-0.851733\pi$
$907$	−53.8160			−1.78693			−0.893465	+	0.449132i	$0.851733\pi$
$908$	31.1614	+	45.6294i	1.03413	+	1.51426i
$909$	14.5657			0.483113
$910$	−16.0643	+	30.4237i	−0.532528	+	1.00854i
$911$	−21.1665			−0.701277			−0.350639	−	0.936511i	$-0.614035\pi$
$911$	−21.1665			−0.701277			−0.350639	+	0.936511i	$0.614035\pi$
$912$	19.7099	+	7.70033i	0.652659	+	0.254983i
$913$	−10.9940			−0.363849
$914$	−10.7758	+	20.4080i	−0.356433	+	0.675038i
$915$		−	5.14642i		−	0.170135i
$916$	−7.80034	+	5.32704i	−0.257731	+	0.176010i
$917$		−	52.3908i		−	1.73010i
$918$	8.59383	+	4.53771i	0.283639	+	0.149767i
$919$	18.8274			0.621060			0.310530	−	0.950564i	$-0.399494\pi$
$919$	18.8274			0.621060			0.310530	+	0.950564i	$0.399494\pi$
$920$	−7.39844	+	11.3694i	−0.243919	+	0.374838i
$921$	15.2035			0.500972
$922$	0.141162	+	0.0745365i	0.00464893	+	0.00245473i
$923$		−	72.5956i		−	2.38951i
$924$	23.0465	−	15.7390i	0.758173	−	0.517775i
$925$			1.30997i			0.0430717i
$926$	18.1430	−	34.3605i	0.596216	−	1.12916i
$927$	5.43923			0.178648
$928$	30.6051	−	26.4412i	1.00466	−	0.867974i
$929$	21.0228			0.689734			0.344867	−	0.938651i	$-0.387924\pi$
$929$	21.0228			0.689734			0.344867	+	0.938651i	$0.387924\pi$
$930$	3.62638	−	6.86788i	0.118914	−	0.225207i
$931$	44.0386			1.44331
$932$	9.90260	+	14.5003i	0.324371	+	0.474973i
$933$	−1.53631			−0.0502964
$934$	−12.7380	−	6.72591i	−0.416800	−	0.220079i
$935$	−24.4950			−0.801072
$936$	−1.98832	−	17.4644i	−0.0649902	−	0.570841i
$937$			57.7881i			1.88786i	0.330151	+	0.943928i	$0.392900\pi$
$937$			57.7881i			1.88786i	−0.330151	+	0.943928i	$0.607100\pi$
$938$	−68.9260	−	36.3943i	−2.25051	−	1.18832i
$939$	−3.50866			−0.114501
$940$	−3.20858	−	4.69830i	−0.104652	−	0.153242i
$941$			29.4007i			0.958435i	0.877696	+	0.479217i	$0.159079\pi$
$941$			29.4007i			0.958435i	−0.877696	+	0.479217i	$0.840921\pi$
$942$	−17.1442	−	9.05248i	−0.558588	−	0.294946i
$943$	31.9049	−	38.6370i	1.03897	−	1.25819i
$944$	19.1069	+	7.46476i	0.621877	+	0.242957i
$945$	−3.91467			−0.127344
$946$	15.2906	+	8.07373i	0.497139	+	0.262500i
$947$			50.6199i			1.64493i	0.568819	+	0.822463i	$0.307401\pi$
$947$			50.6199i			1.64493i	−0.568819	+	0.822463i	$0.692599\pi$
$948$	−0.900155	+	0.614737i	−0.0292357	+	0.0199657i
$949$	−70.9136			−2.30195
$950$	6.61580	+	3.49327i	0.214645	+	0.113337i
$951$		−	18.8734i		−	0.612012i
$952$	−75.5992	+	8.60696i	−2.45018	+	0.278953i
$953$			53.7967i			1.74265i	0.490711	+	0.871323i	$0.336737\pi$
$953$			53.7967i			1.74265i	−0.490711	+	0.871323i	$0.663263\pi$
$954$	−7.28289	+	13.7928i	−0.235792	+	0.446560i
$955$		−	18.0629i		−	0.584500i
$956$	−17.1363	+	11.7028i	−0.554227	+	0.378495i
$957$			25.4856i			0.823832i
$958$	−11.9526	−	6.31121i	−0.386171	−	0.203906i
$959$		−	13.2150i		−	0.426734i
$960$	7.79526	−	1.79829i	0.251591	−	0.0580396i
$961$	0.840766			0.0271215
$962$	5.37565	−	10.1808i	0.173318	−	0.328241i
$963$	−3.07805			−0.0991889
$964$	−44.2141	+	30.1948i	−1.42404	+	0.972510i
$965$		−	6.37298i		−	0.205154i
$966$	−10.2103	−	24.5088i	−0.328512	−	0.788558i
$967$			37.8789i			1.21810i	0.793131	+	0.609051i	$0.208450\pi$
$967$			37.8789i			1.21810i	−0.793131	+	0.609051i	$0.791550\pi$
$968$	−0.545819	−	4.79419i	−0.0175433	−	0.154091i
$969$	36.3533			1.16784
$970$	9.94268	+	5.24993i	0.319240	+	0.168565i
$971$	34.0734			1.09347			0.546734	−	0.837306i	$-0.315871\pi$
$971$	34.0734			1.09347			0.546734	+	0.837306i	$0.315871\pi$
$972$	1.65160	−	1.12792i	0.0529752	−	0.0361781i
$973$		−	26.6770i		−	0.855226i
$974$	21.4924	−	40.7038i	0.688661	−	1.30423i
$975$		−	6.21448i		−	0.199023i
$976$	−19.1743	−	7.49109i	−0.613754	−	0.239784i
$977$		−	45.1720i		−	1.44518i	−0.691277	−	0.722590i	$-0.742951\pi$
$977$		−	45.1720i		−	1.44518i	0.691277	−	0.722590i	$-0.257049\pi$
$978$	−24.9227	−	13.1597i	−0.796940	−	0.420800i
$979$		−	26.4365i		−	0.844913i
$980$	13.7490	−	9.38950i	0.439195	−	0.299937i
$981$			5.62701i			0.179657i
$982$	−3.67487	+	6.95972i	−0.117270	+	0.222093i
$983$	18.5440			0.591462			0.295731	−	0.955271i	$-0.404437\pi$
$983$	18.5440			0.591462			0.295731	+	0.955271i	$0.404437\pi$
$984$	−29.3620	+	3.34286i	−0.936027	+	0.106567i
$985$		−	20.0921i		−	0.640186i
$986$	32.4435	−	61.4438i	1.03321	−	1.95677i
$987$	11.1360			0.354463
$988$	−37.0811	−	54.2976i	−1.17971	−	1.72744i
$989$	10.4744	−	12.6845i	0.333065	−	0.403344i
$990$	−2.35379	+	4.45776i	−0.0748082	+	0.141677i
$991$			24.2053i			0.768906i	0.923145	+	0.384453i	$0.125610\pi$
$991$			24.2053i			0.768906i	−0.923145	+	0.384453i	$0.874390\pi$
$992$	−20.3095	−	23.5078i	−0.644828	−	0.746375i
$993$	30.4098			0.965026
$994$	−30.1970	+	57.1891i	−0.957790	+	1.81393i
$995$		−	5.03970i		−	0.159769i
$996$	5.09400	−	3.47881i	0.161410	−	0.110230i
$997$	20.5579			0.651074			0.325537	−	0.945529i	$-0.394455\pi$
$997$	20.5579			0.651074			0.325537	+	0.945529i	$0.394455\pi$
$998$	−21.7806	+	41.2496i	−0.689453	+	1.30573i
$999$	1.30997			0.0414457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.a.91.7	✓	48
4.3	odd	2		1380.2.p.b.91.8	yes	48
23.22	odd	2		1380.2.p.b.91.7	yes	48
92.91	even	2	inner	1380.2.p.a.91.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.7	✓	48	1.1	even	1	trivial
1380.2.p.a.91.8	yes	48	92.91	even	2	inner
1380.2.p.b.91.7	yes	48	23.22	odd	2
1380.2.p.b.91.8	yes	48	4.3	odd	2

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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25058 - 0.660333i) q^{2} -1.00000i q^{3} +(1.12792 + 1.65160i) q^{4} -1.00000i q^{5} +(-0.660333 + 1.25058i) q^{6} -3.91467 q^{7} +(-0.319949 - 2.81027i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.25058 - 0.660333i) q^{2} -1.00000i q^{3} +(1.12792 + 1.65160i) q^{4} -1.00000i q^{5} +(-0.660333 + 1.25058i) q^{6} -3.91467 q^{7} +(-0.319949 - 2.81027i) q^{8} -1.00000 q^{9} +(-0.660333 + 1.25058i) q^{10} -3.56454 q^{11} +(1.65160 - 1.12792i) q^{12} -6.21448 q^{13} +(4.89562 + 2.58498i) q^{14} -1.00000 q^{15} +(-1.45559 + 3.72575i) q^{16} +6.87185i q^{17} +(1.25058 + 0.660333i) q^{18} +5.29017 q^{19} +(1.65160 - 1.12792i) q^{20} +3.91467i q^{21} +(4.45776 + 2.35379i) q^{22} +(3.05366 - 3.69800i) q^{23} +(-2.81027 + 0.319949i) q^{24} -1.00000 q^{25} +(7.77173 + 4.10363i) q^{26} +1.00000i q^{27} +(-4.41543 - 6.46548i) q^{28} +7.14975 q^{29} +(1.25058 + 0.660333i) q^{30} -5.49174i q^{31} +(4.28058 - 3.69819i) q^{32} +3.56454i q^{33} +(4.53771 - 8.59383i) q^{34} +3.91467i q^{35} +(-1.12792 - 1.65160i) q^{36} -1.30997i q^{37} +(-6.61580 - 3.49327i) q^{38} +6.21448i q^{39} +(-2.81027 + 0.319949i) q^{40} +10.4481 q^{41} +(2.58498 - 4.89562i) q^{42} +3.43010 q^{43} +(-4.02052 - 5.88721i) q^{44} +1.00000i q^{45} +(-6.26076 + 2.60822i) q^{46} -2.84469i q^{47} +(3.72575 + 1.45559i) q^{48} +8.32462 q^{49} +(1.25058 + 0.660333i) q^{50} +6.87185 q^{51} +(-7.00944 - 10.2639i) q^{52} +11.0291i q^{53} +(0.660333 - 1.25058i) q^{54} +3.56454i q^{55} +(1.25250 + 11.0013i) q^{56} -5.29017i q^{57} +(-8.94137 - 4.72122i) q^{58} -5.12833i q^{59} +(-1.12792 - 1.65160i) q^{60} +5.14642i q^{61} +(-3.62638 + 6.86788i) q^{62} +3.91467 q^{63} +(-7.79526 + 1.79829i) q^{64} +6.21448i q^{65} +(2.35379 - 4.45776i) q^{66} -14.0791 q^{67} +(-11.3496 + 7.75090i) q^{68} +(-3.69800 - 3.05366i) q^{69} +(2.58498 - 4.89562i) q^{70} +11.6817i q^{71} +(0.319949 + 2.81027i) q^{72} +11.4110 q^{73} +(-0.865019 + 1.63823i) q^{74} +1.00000i q^{75} +(5.96689 + 8.73726i) q^{76} +13.9540 q^{77} +(4.10363 - 7.77173i) q^{78} -0.545018 q^{79} +(3.72575 + 1.45559i) q^{80} +1.00000 q^{81} +(-13.0662 - 6.89923i) q^{82} +3.08427 q^{83} +(-6.46548 + 4.41543i) q^{84} +6.87185 q^{85} +(-4.28963 - 2.26501i) q^{86} -7.14975i q^{87} +(1.14047 + 10.0173i) q^{88} +7.41651i q^{89} +(0.660333 - 1.25058i) q^{90} +24.3276 q^{91} +(9.55191 + 0.872391i) q^{92} -5.49174 q^{93} +(-1.87844 + 3.55752i) q^{94} -5.29017i q^{95} +(-3.69819 - 4.28058i) q^{96} -7.95043i q^{97} +(-10.4106 - 5.49702i) q^{98} +3.56454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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