LMFDB - Embedded newform 495.2.bj.c.73.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.11
Character	$\chi$	$=$	495.73
Dual form			495.2.bj.c.217.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.338930 + 2.13992i) q^{2} +(-2.56227 + 0.832532i) q^{4} +(1.49161 + 1.66586i) q^{5} +(-0.392386 + 0.770101i) q^{7} +(-0.682757 - 1.33999i) q^{8} +O(q^{10})$	\(q+(0.338930 + 2.13992i) q^{2} +(-2.56227 + 0.832532i) q^{4} +(1.49161 + 1.66586i) q^{5} +(-0.392386 + 0.770101i) q^{7} +(-0.682757 - 1.33999i) q^{8} +(-3.05926 + 3.75654i) q^{10} +(2.59884 + 2.06059i) q^{11} +(3.81380 - 0.604046i) q^{13} +(-1.78095 - 0.578664i) q^{14} +(-1.72314 + 1.25193i) q^{16} +(-4.74922 - 0.752203i) q^{17} +(0.838408 - 2.58036i) q^{19} +(-5.20879 - 3.02658i) q^{20} +(-3.52868 + 6.25970i) q^{22} +(-4.79338 - 4.79338i) q^{23} +(-0.550202 + 4.96964i) q^{25} +(2.58522 + 7.95649i) q^{26} +(0.364266 - 2.29988i) q^{28} +(1.50081 + 4.61903i) q^{29} +(0.834544 + 0.606332i) q^{31} +(-5.38990 - 5.38990i) q^{32} -10.4179i q^{34} +(-1.86817 + 0.495028i) q^{35} +(-3.87086 - 1.97230i) q^{37} +(5.80592 + 0.919567i) q^{38} +(1.21383 - 3.13612i) q^{40} +(-3.96986 - 1.28989i) q^{41} +(7.22637 - 7.22637i) q^{43} +(-8.37444 - 3.11618i) q^{44} +(8.63283 - 11.8821i) q^{46} +(3.41765 + 6.70751i) q^{47} +(3.67541 + 5.05877i) q^{49} +(-10.8211 + 0.506971i) q^{50} +(-9.26910 + 4.72284i) q^{52} +(-1.02442 - 6.46794i) q^{53} +(0.443785 + 7.40291i) q^{55} +1.29983 q^{56} +(-9.37568 + 4.77715i) q^{58} +(7.48114 - 2.43077i) q^{59} +(0.304083 + 0.418534i) q^{61} +(-1.01465 + 1.99136i) q^{62} +(7.20329 - 9.91448i) q^{64} +(6.69495 + 5.45226i) q^{65} +(-4.30527 + 4.30527i) q^{67} +(12.7950 - 2.02653i) q^{68} +(-1.69250 - 3.82995i) q^{70} +(13.0228 - 9.46160i) q^{71} +(1.91331 + 0.974881i) q^{73} +(2.90862 - 8.95180i) q^{74} +7.30957i q^{76} +(-2.60661 + 1.19282i) q^{77} +(3.33797 + 2.42518i) q^{79} +(-4.65580 - 1.00312i) q^{80} +(1.41475 - 8.93237i) q^{82} +(2.13082 - 13.4534i) q^{83} +(-5.83092 - 9.03355i) q^{85} +(17.9131 + 13.0146i) q^{86} +(0.986791 - 4.88929i) q^{88} +4.64987i q^{89} +(-1.03130 + 3.17403i) q^{91} +(16.2726 + 8.29130i) q^{92} +(-13.1952 + 9.58687i) q^{94} +(5.54910 - 2.45221i) q^{95} +(9.04989 - 1.43336i) q^{97} +(-9.57965 + 9.57965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) $ 96 * q + 8 * q^5 - 20 * q^7	$ 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.338930	+	2.13992i	0.239660	+	1.51315i	0.754748	+	0.656015i	$0.227759\pi$
$2$	0.338930	+	2.13992i	0.239660	+	1.51315i	−0.515088	+	0.857137i	$0.672241\pi$
$3$		0			0
$3$		0			0
$4$	−2.56227	+	0.832532i	−1.28114	+	0.416266i
$5$	1.49161	+	1.66586i	0.667068	+	0.744997i
$5$	1.49161	+	1.66586i	0.667068	+	0.744997i
$6$		0			0
$7$	−0.392386	+	0.770101i	−0.148308	+	0.291071i	−0.953194	−	0.302358i	$-0.902226\pi$
$7$	−0.392386	+	0.770101i	−0.148308	+	0.291071i	0.804886	+	0.593429i	$0.202226\pi$
$8$	−0.682757	−	1.33999i	−0.241391	−	0.473757i
$9$		0			0
$10$	−3.05926	+	3.75654i	−0.967424	+	1.18792i
$11$	2.59884	+	2.06059i	0.783579	+	0.621292i
$11$	2.59884	+	2.06059i	0.783579	+	0.621292i
$12$		0			0
$13$	3.81380	−	0.604046i	1.05776	−	0.167532i	0.396761	−	0.917922i	$-0.370134\pi$
$13$	3.81380	−	0.604046i	1.05776	−	0.167532i	0.660996	+	0.750390i	$0.270134\pi$
$14$	−1.78095	−	0.578664i	−0.475978	−	0.154655i
$15$		0			0
$16$	−1.72314	+	1.25193i	−0.430785	+	0.312984i
$17$	−4.74922	−	0.752203i	−1.15186	−	0.182436i	−0.448841	−	0.893612i	$-0.648163\pi$
$17$	−4.74922	−	0.752203i	−1.15186	−	0.182436i	−0.703014	+	0.711176i	$0.748163\pi$
$18$		0			0
$19$	0.838408	−	2.58036i	0.192344	−	0.591974i	−0.807653	−	0.589658i	$-0.799263\pi$
$19$	0.838408	−	2.58036i	0.192344	−	0.591974i	0.999997	−	0.00231648i	$-0.000737359\pi$
$20$	−5.20879	−	3.02658i	−1.16472	−	0.676764i
$21$		0			0
$22$	−3.52868	+	6.25970i	−0.752317	+	1.33457i
$23$	−4.79338	−	4.79338i	−0.999489	−	0.999489i	0.000510925	−	1.00000i	$-0.499837\pi$
$23$	−4.79338	−	4.79338i	−0.999489	−	0.999489i	−1.00000		0.000510925i	$0.999837\pi$
$24$		0			0
$25$	−0.550202	+	4.96964i	−0.110040	+	0.993927i
$26$	2.58522	+	7.95649i	0.507004	+	1.56040i
$27$		0			0
$28$	0.364266	−	2.29988i	0.0688397	−	0.434637i
$29$	1.50081	+	4.61903i	0.278694	+	0.857732i	0.988218	+	0.153051i	$0.0489100\pi$
$29$	1.50081	+	4.61903i	0.278694	+	0.857732i	−0.709524	+	0.704681i	$0.751090\pi$
$30$		0			0
$31$	0.834544	+	0.606332i	0.149889	+	0.108900i	0.660202	−	0.751088i	$-0.270471\pi$
$31$	0.834544	+	0.606332i	0.149889	+	0.108900i	−0.510314	+	0.859988i	$0.670471\pi$
$32$	−5.38990	−	5.38990i	−0.952809	−	0.952809i
$33$		0			0
$34$		−	10.4179i		−	1.78665i
$35$	−1.86817	+	0.495028i	−0.315778	+	0.0836751i
$36$		0			0
$37$	−3.87086	−	1.97230i	−0.636365	−	0.324244i	0.105874	−	0.994380i	$-0.466236\pi$
$37$	−3.87086	−	1.97230i	−0.636365	−	0.324244i	−0.742239	+	0.670135i	$0.766236\pi$
$38$	5.80592	+	0.919567i	0.941844	+	0.149173i
$39$		0			0
$40$	1.21383	−	3.13612i	0.191923	−	0.495863i
$41$	−3.96986	−	1.28989i	−0.619988	−	0.201446i	−0.0178531	−	0.999841i	$-0.505683\pi$
$41$	−3.96986	−	1.28989i	−0.619988	−	0.201446i	−0.602135	+	0.798394i	$0.705683\pi$
$42$		0			0
$43$	7.22637	−	7.22637i	1.10201	−	1.10201i	0.107843	−	0.994168i	$-0.465606\pi$
$43$	7.22637	−	7.22637i	1.10201	−	1.10201i	0.994168	−	0.107843i	$-0.0343945\pi$
$44$	−8.37444	−	3.11618i	−1.26249	−	0.469782i
$45$		0			0
$46$	8.63283	−	11.8821i	1.27284	−	1.75192i
$47$	3.41765	+	6.70751i	0.498515	+	0.978391i	0.993959	+	0.109751i	$0.0350054\pi$
$47$	3.41765	+	6.70751i	0.498515	+	0.978391i	−0.495444	+	0.868640i	$0.664995\pi$
$48$		0			0
$49$	3.67541	+	5.05877i	0.525058	+	0.722681i
$50$	−10.8211	+	0.506971i	−1.53034	+	0.0716966i
$51$		0			0
$52$	−9.26910	+	4.72284i	−1.28539	+	0.654940i
$53$	−1.02442	−	6.46794i	−0.140715	−	0.888440i	−0.952512	−	0.304501i	$-0.901510\pi$
$53$	−1.02442	−	6.46794i	−0.140715	−	0.888440i	0.811797	−	0.583940i	$-0.198490\pi$
$54$		0			0
$55$	0.443785	+	7.40291i	0.0598400	+	0.998208i
$56$	1.29983			0.173697
$57$		0			0
$58$	−9.37568	+	4.77715i	−1.23109	+	0.627271i
$59$	7.48114	−	2.43077i	0.973962	−	0.316459i	0.221548	−	0.975150i	$-0.428889\pi$
$59$	7.48114	−	2.43077i	0.973962	−	0.316459i	0.752414	+	0.658690i	$0.228889\pi$
$60$		0			0
$61$	0.304083	+	0.418534i	0.0389338	+	0.0535878i	0.828040	−	0.560669i	$-0.189456\pi$
$61$	0.304083	+	0.418534i	0.0389338	+	0.0535878i	−0.789106	+	0.614257i	$0.789456\pi$
$62$	−1.01465	+	1.99136i	−0.128861	+	0.252903i
$63$		0			0
$64$	7.20329	−	9.91448i	0.900411	−	1.23931i
$65$	6.69495	+	5.45226i	0.830407	+	0.676270i
$66$		0			0
$67$	−4.30527	+	4.30527i	−0.525972	+	0.525972i	−0.919369	−	0.393397i	$-0.871300\pi$
$67$	−4.30527	+	4.30527i	−0.525972	+	0.525972i	0.393397	+	0.919369i	$0.371300\pi$
$68$	12.7950	−	2.02653i	1.55162	−	0.245753i
$69$		0			0
$70$	−1.69250	−	3.82995i	−0.202292	−	0.457767i
$71$	13.0228	−	9.46160i	1.54552	−	1.12289i	0.598766	−	0.800924i	$-0.295658\pi$
$71$	13.0228	−	9.46160i	1.54552	−	1.12289i	0.946753	−	0.321961i	$-0.104342\pi$
$72$		0			0
$73$	1.91331	+	0.974881i	0.223936	+	0.114101i	0.562360	−	0.826893i	$-0.309894\pi$
$73$	1.91331	+	0.974881i	0.223936	+	0.114101i	−0.338424	+	0.940994i	$0.609894\pi$
$74$	2.90862	−	8.95180i	0.338120	−	1.04063i
$75$		0			0
$76$			7.30957i			0.838466i
$77$	−2.60661	+	1.19282i	−0.297051	+	0.135934i
$78$		0			0
$79$	3.33797	+	2.42518i	0.375551	+	0.272854i	0.759509	−	0.650497i	$-0.225439\pi$
$79$	3.33797	+	2.42518i	0.375551	+	0.272854i	−0.383958	+	0.923351i	$0.625439\pi$
$80$	−4.65580	−	1.00312i	−0.520535	−	0.112152i
$81$		0			0
$82$	1.41475	−	8.93237i	0.156233	−	0.986415i
$83$	2.13082	−	13.4534i	0.233887	−	1.47671i	−0.539076	−	0.842257i	$-0.681227\pi$
$83$	2.13082	−	13.4534i	0.233887	−	1.47671i	0.772964	−	0.634450i	$-0.218773\pi$
$84$		0			0
$85$	−5.83092	−	9.03355i	−0.632452	−	0.979826i
$86$	17.9131	+	13.0146i	1.93162	+	1.40340i
$87$		0			0
$88$	0.986791	−	4.88929i	0.105192	−	0.521200i
$89$			4.64987i			0.492885i	0.969157	+	0.246443i	$0.0792617\pi$
$89$			4.64987i			0.492885i	−0.969157	+	0.246443i	$0.920738\pi$
$90$		0			0
$91$	−1.03130	+	3.17403i	−0.108110	+	0.332729i
$92$	16.2726	+	8.29130i	1.69653	+	0.864427i
$93$		0			0
$94$	−13.1952	+	9.58687i	−1.36098	+	0.988810i
$95$	5.54910	−	2.45221i	0.569325	−	0.251591i
$96$		0			0
$97$	9.04989	−	1.43336i	0.918877	−	0.145536i	0.320959	−	0.947093i	$-0.395995\pi$
$97$	9.04989	−	1.43336i	0.918877	−	0.145536i	0.597918	+	0.801557i	$0.295995\pi$
$98$	−9.57965	+	9.57965i	−0.967690	+	0.967690i
$99$		0			0
$100$	−2.72762	−	13.1916i	−0.272762	−	1.31916i
$101$	6.69495	−	9.21481i	0.666172	−	0.916908i	−0.333494	−	0.942752i	$-0.608228\pi$
$101$	6.69495	−	9.21481i	0.666172	−	0.916908i	0.999666	+	0.0258448i	$0.00822757\pi$
$102$		0			0
$103$	−7.01893	+	13.7754i	−0.691596	+	1.35733i	0.231527	+	0.972829i	$0.425628\pi$
$103$	−7.01893	+	13.7754i	−0.691596	+	1.35733i	−0.923123	+	0.384505i	$0.874372\pi$
$104$	−3.41331	−	4.69802i	−0.334703	−	0.460679i
$105$		0			0
$106$	13.4937	−	4.38436i	1.31062	−	0.425847i
$107$	4.18366	−	2.13168i	0.404450	−	0.206078i	−0.239918	−	0.970793i	$-0.577121\pi$
$107$	4.18366	−	2.13168i	0.404450	−	0.206078i	0.644368	+	0.764716i	$0.277121\pi$
$108$		0			0
$109$	7.54711			0.722882			0.361441	−	0.932395i	$-0.382285\pi$
$109$	7.54711			0.722882			0.361441	+	0.932395i	$0.382285\pi$
$110$	−15.6912	+	3.45873i	−1.49610	+	0.329777i
$111$		0			0
$112$	−0.287980	−	1.81823i	−0.0272115	−	0.171807i
$113$	−14.8881	+	7.58585i	−1.40055	+	0.713617i	−0.980981	−	0.194105i	$-0.937820\pi$
$113$	−14.8881	+	7.58585i	−1.40055	+	0.713617i	−0.419572	+	0.907722i	$0.637820\pi$
$114$		0			0
$115$	0.835265	−	15.1350i	0.0778888	−	1.41134i
$116$	−7.69099	−	10.5857i	−0.714090	−	0.982861i
$117$		0			0
$118$	7.73724	+	15.1852i	0.712271	+	1.39791i
$119$	2.44280	−	3.36223i	0.223931	−	0.308215i
$120$		0			0
$121$	2.50792	+	10.7103i	0.227992	+	0.973663i
$122$	−0.792567	+	0.792567i	−0.0717556	+	0.0717556i
$123$		0			0
$124$	−2.64312	−	0.858802i	−0.237359	−	0.0771227i
$125$	−9.09942	+	6.49620i	−0.813877	+	0.581037i
$126$		0			0
$127$	−1.54847	−	0.245254i	−0.137404	−	0.0217627i	0.0873533	−	0.996177i	$-0.472159\pi$
$127$	−1.54847	−	0.245254i	−0.137404	−	0.0217627i	−0.224758	+	0.974415i	$0.572159\pi$
$128$	10.0743	+	5.13309i	0.890447	+	0.453705i
$129$		0			0
$130$	−9.39829	+	16.1746i	−0.824284	+	1.41861i
$131$			7.80413i			0.681850i	0.940090	+	0.340925i	$0.110740\pi$
$131$			7.80413i			0.681850i	−0.940090	+	0.340925i	$0.889260\pi$
$132$		0			0
$133$	1.65815	+	1.65815i	0.143780	+	0.143780i
$134$	−10.6721	−	7.75374i	−0.921930	−	0.669821i
$135$		0			0
$136$	2.23462	+	6.87746i	0.191617	+	0.589737i
$137$	−3.35231	+	21.1656i	−0.286407	+	1.80830i	0.254336	+	0.967116i	$0.418143\pi$
$137$	−3.35231	+	21.1656i	−0.286407	+	1.80830i	−0.540743	+	0.841188i	$0.681857\pi$
$138$		0			0
$139$	−3.78913	−	11.6617i	−0.321390	−	0.989136i	−0.973044	−	0.230620i	$-0.925925\pi$
$139$	−3.78913	−	11.6617i	−0.321390	−	0.989136i	0.651654	−	0.758516i	$-0.274075\pi$
$140$	4.37463	−	2.82371i	0.369724	−	0.238647i
$141$		0			0
$142$	24.6609	+	24.6609i	2.06949	+	2.06949i
$143$	11.1561	+	6.28886i	0.932923	+	0.525901i
$144$		0			0
$145$	−5.45605	+	9.38994i	−0.453100	+	0.779792i
$146$	−1.43769	+	4.42475i	−0.118984	+	0.366195i
$147$		0			0
$148$	11.5602	+	1.83095i	0.950242	+	0.150504i
$149$	7.63358	−	5.54612i	0.625367	−	0.454356i	−0.229425	−	0.973326i	$-0.573685\pi$
$149$	7.63358	−	5.54612i	0.625367	−	0.454356i	0.854792	+	0.518971i	$0.173685\pi$
$150$		0			0
$151$	−12.3035	−	3.99764i	−1.00124	−	0.325323i	−0.237880	−	0.971295i	$-0.576452\pi$
$151$	−12.3035	−	3.99764i	−1.00124	−	0.325323i	−0.763361	+	0.645972i	$0.776452\pi$
$152$	−4.03007	+	0.638300i	−0.326882	+	0.0517730i
$153$		0			0
$154$	−3.43600	−	5.17366i	−0.276881	−	0.416905i
$155$	0.234748	+	2.29465i	0.0188554	+	0.184310i
$156$		0			0
$157$	0.606051	+	1.18944i	0.0483682	+	0.0949278i	0.913925	−	0.405882i	$-0.133036\pi$
$157$	0.606051	+	1.18944i	0.0483682	+	0.0949278i	−0.865557	+	0.500810i	$0.833036\pi$
$158$	−4.05835	+	7.96495i	−0.322865	+	0.633657i
$159$		0			0
$160$	0.939211	−	17.0185i	0.0742511	−	1.34543i
$161$	5.57224	−	1.81053i	0.439154	−	0.142690i
$162$		0			0
$163$	−0.814729	−	5.14399i	−0.0638145	−	0.402909i	−0.998832	−	0.0483085i	$-0.984617\pi$
$163$	−0.814729	−	5.14399i	−0.0638145	−	0.402909i	0.935018	−	0.354600i	$-0.115383\pi$
$164$	11.2457			0.878144
$165$		0			0
$166$	29.5115			2.29054
$167$	−3.80285	−	24.0103i	−0.294274	−	1.85797i	−0.482570	−	0.875858i	$-0.660296\pi$
$167$	−3.80285	−	24.0103i	−0.294274	−	1.85797i	0.188296	−	0.982112i	$-0.439704\pi$
$168$		0			0
$169$	1.81644	−	0.590198i	0.139726	−	0.0453998i
$170$	17.3548	−	15.5394i	1.33105	−	1.19182i
$171$		0			0
$172$	−12.4997	+	24.5321i	−0.953096	+	1.87056i
$173$	9.61191	+	18.8644i	0.730780	+	1.43424i	0.894195	+	0.447679i	$0.147749\pi$
$173$	9.61191	+	18.8644i	0.730780	+	1.43424i	−0.163415	+	0.986557i	$0.552251\pi$
$174$		0			0
$175$	−3.61123	−	2.37373i	−0.272983	−	0.179437i
$176$	−7.05789	−	0.297115i	−0.532008	−	0.0223959i
$177$		0			0
$178$	−9.95035	+	1.57598i	−0.745811	+	0.118125i
$179$	−1.88959	−	0.613966i	−0.141235	−	0.0458900i	0.237547	−	0.971376i	$-0.423657\pi$
$179$	−1.88959	−	0.613966i	−0.141235	−	0.0458900i	−0.378781	+	0.925486i	$0.623657\pi$
$180$		0			0
$181$	0.514109	−	0.373522i	0.0382134	−	0.0277637i	−0.568515	−	0.822673i	$-0.692482\pi$
$181$	0.514109	−	0.373522i	0.0382134	−	0.0277637i	0.606728	+	0.794910i	$0.292482\pi$
$182$	−7.14171	−	1.13114i	−0.529379	−	0.0838453i
$183$		0			0
$184$	−3.15035	+	9.69578i	−0.232247	+	0.714782i
$185$	−2.48823	−	9.39022i	−0.182938	−	0.690383i
$186$		0			0
$187$	−10.7925	−	11.7411i	−0.789224	−	0.858592i
$188$	−14.3412	−	14.3412i	−1.04594	−	1.04594i
$189$		0			0
$190$	7.12829	+	11.0435i	0.517140	+	0.801180i
$191$	−5.29545	−	16.2977i	−0.383165	−	1.17926i	−0.937802	−	0.347169i	$-0.887143\pi$
$191$	−5.29545	−	16.2977i	−0.383165	−	1.17926i	0.554637	−	0.832092i	$-0.312857\pi$
$192$		0			0
$193$	3.24026	−	20.4582i	0.233239	−	1.47261i	−0.541697	−	0.840574i	$-0.682218\pi$
$193$	3.24026	−	20.4582i	0.233239	−	1.47261i	0.774936	−	0.632040i	$-0.217782\pi$
$194$	6.13456	+	18.8802i	0.440436	+	1.35552i
$195$		0			0
$196$	−13.6290	−	9.90203i	−0.973498	−	0.707288i
$197$	−15.1802	−	15.1802i	−1.08154	−	1.08154i	−0.996366	−	0.0851750i	$-0.972855\pi$
$197$	−15.1802	−	15.1802i	−1.08154	−	1.08154i	−0.0851750	−	0.996366i	$-0.527145\pi$
$198$		0			0
$199$		−	6.97596i		−	0.494513i	−0.968950	−	0.247256i	$-0.920471\pi$
$199$		−	6.97596i		−	0.494513i	0.968950	−	0.247256i	$-0.0795290\pi$
$200$	7.03490	−	2.65579i	0.497442	−	0.187793i
$201$		0			0
$202$	21.9881	+	11.2035i	1.54708	+	0.788274i
$203$	−4.14602	−	0.656665i	−0.290993	−	0.0460888i
$204$		0			0
$205$	−3.77271	−	8.53725i	−0.263497	−	0.596268i
$206$	−31.8573	−	10.3510i	−2.21960	−	0.721192i
$207$		0			0
$208$	−5.81548	+	5.81548i	−0.403231	+	0.403231i
$209$	7.49595	−	4.97831i	0.518506	−	0.344357i
$210$		0			0
$211$	12.2002	−	16.7921i	0.839896	−	1.15602i	−0.146103	−	0.989269i	$-0.546673\pi$
$211$	12.2002	−	16.7921i	0.839896	−	1.15602i	0.985999	−	0.166749i	$-0.0533269\pi$
$212$	8.00962	+	15.7198i	0.550103	+	1.07964i
$213$		0			0
$214$	5.97960	+	8.23021i	0.408757	+	0.562606i
$215$	22.8171	+	1.25922i	1.55611	+	0.0858783i
$216$		0			0
$217$	−0.794400	+	0.404767i	−0.0539274	+	0.0274774i
$218$	2.55794	+	16.1502i	0.173246	+	1.09383i
$219$		0			0
$220$	−7.30026	−	18.5988i	−0.492183	−	1.25393i
$221$	−18.5669			−1.24895
$222$		0			0
$223$	3.53336	−	1.80034i	0.236611	−	0.120559i	−0.331665	−	0.943397i	$-0.607610\pi$
$223$	3.53336	−	1.80034i	0.236611	−	0.120559i	0.568276	+	0.822838i	$0.307610\pi$
$224$	6.26569	−	2.03585i	0.418644	−	0.136026i
$225$		0			0
$226$	−21.2791	−	29.2882i	−1.41547	−	1.94822i
$227$	3.23205	−	6.34326i	0.214519	−	0.421017i	−0.758523	−	0.651647i	$-0.774079\pi$
$227$	3.23205	−	6.34326i	0.214519	−	0.421017i	0.973042	+	0.230630i	$0.0740786\pi$
$228$		0			0
$229$	−15.4505	+	21.2658i	−1.02100	+	1.40529i	−0.109500	+	0.993987i	$0.534925\pi$
$229$	−15.4505	+	21.2658i	−1.02100	+	1.40529i	−0.911500	+	0.411300i	$0.865075\pi$
$230$	32.6707	−	3.34230i	2.15424	−	0.220384i
$231$		0			0
$232$	5.16474	−	5.16474i	0.339082	−	0.339082i
$233$	0.412834	−	0.0653864i	0.0270456	−	0.00428361i	−0.142897	−	0.989738i	$-0.545642\pi$
$233$	0.412834	−	0.0653864i	0.0270456	−	0.00428361i	0.169943	+	0.985454i	$0.445642\pi$
$234$		0			0
$235$	−6.07600	+	15.6983i	−0.396355	+	1.02405i
$236$	−17.1450	+	12.4566i	−1.11605	+	0.810855i
$237$		0			0
$238$	8.02283	+	4.08784i	0.520043	+	0.264975i
$239$	−2.76541	+	8.51105i	−0.178879	+	0.550534i	−0.999789	−	0.0205236i	$-0.993467\pi$
$239$	−2.76541	+	8.51105i	−0.178879	+	0.550534i	0.820910	+	0.571058i	$0.193467\pi$
$240$		0			0
$241$		−	5.14635i		−	0.331506i	−0.986167	−	0.165753i	$-0.946995\pi$
$241$		−	5.14635i		−	0.331506i	0.986167	−	0.165753i	$-0.0530054\pi$
$242$	−22.0692	+	8.99678i	−1.41866	+	0.578335i
$243$		0			0
$244$	−1.12759	−	0.819239i	−0.0721863	−	0.0524464i
$245$	−2.94494	+	13.6684i	−0.188145	+	0.873244i
$246$		0			0
$247$	1.63887	−	10.3474i	0.104279	−	0.658389i
$248$	0.242685	−	1.53225i	0.0154105	−	0.0972983i
$249$		0			0
$250$	−16.9854	−	17.2703i	−1.07425	−	1.09227i
$251$	10.2950	+	7.47972i	0.649812	+	0.472116i	0.863207	−	0.504850i	$-0.168452\pi$
$251$	10.2950	+	7.47972i	0.649812	+	0.472116i	−0.213395	+	0.976966i	$0.568452\pi$
$252$		0			0
$253$	−2.58001	−	22.3344i	−0.162204	−	1.40415i
$254$		−	3.39673i		−	0.213130i
$255$		0			0
$256$	0.00405212	−	0.0124712i	0.000253258	−	0.000779447i
$257$	−2.96165	−	1.50904i	−0.184743	−	0.0941312i	0.359173	−	0.933271i	$-0.383059\pi$
$257$	−2.96165	−	1.50904i	−0.184743	−	0.0941312i	−0.543916	+	0.839140i	$0.683059\pi$
$258$		0			0
$259$	3.03774	−	2.20705i	0.188756	−	0.137139i
$260$	−21.6935	−	8.39641i	−1.34537	−	0.520723i
$261$		0			0
$262$	−16.7002	+	2.64506i	−1.03174	+	0.163412i
$263$	−1.88137	+	1.88137i	−0.116010	+	0.116010i	−0.762729	−	0.646719i	$-0.776141\pi$
$263$	−1.88137	+	1.88137i	−0.116010	+	0.116010i	0.646719	+	0.762729i	$0.276141\pi$
$264$		0			0
$265$	9.24667	−	11.3542i	0.568019	−	0.697482i
$266$	−2.98632	+	4.11032i	−0.183103	+	0.252020i
$267$		0			0
$268$	7.44699	−	14.6155i	0.454897	−	0.892786i
$269$	5.92437	+	8.15420i	0.361215	+	0.497170i	0.950487	−	0.310765i	$-0.100585\pi$
$269$	5.92437	+	8.15420i	0.361215	+	0.497170i	−0.589272	+	0.807935i	$0.700585\pi$
$270$		0			0
$271$	−18.8796	+	6.13437i	−1.14686	+	0.372636i	−0.819958	−	0.572423i	$-0.806004\pi$
$271$	−18.8796	+	6.13437i	−1.14686	+	0.372636i	−0.326899	+	0.945059i	$0.606004\pi$
$272$	9.12528	−	4.64956i	0.553302	−	0.281921i
$273$		0			0
$274$	−46.4290			−2.80488
$275$	−11.6703	+	11.7815i	−0.703744	+	0.710453i
$276$		0			0
$277$	−2.90964	−	18.3708i	−0.174823	−	1.10379i	−0.906520	−	0.422162i	$-0.861271\pi$
$277$	−2.90964	−	18.3708i	−0.174823	−	1.10379i	0.731697	−	0.681630i	$-0.238729\pi$
$278$	23.6710	−	12.0610i	1.41969	−	0.723368i
$279$		0			0
$280$	1.93884	+	2.16534i	0.115868	+	0.129404i
$281$	−12.9374	−	17.8068i	−0.771779	−	1.06226i	−0.996142	−	0.0877573i	$-0.972030\pi$
$281$	−12.9374	−	17.8068i	−0.771779	−	1.06226i	0.224363	−	0.974506i	$-0.427970\pi$
$282$		0			0
$283$	6.97507	+	13.6893i	0.414625	+	0.813747i	0.999996	+	0.00298147i	$0.000949032\pi$
$283$	6.97507	+	13.6893i	0.414625	+	0.813747i	−0.585371	+	0.810766i	$0.699051\pi$
$284$	−25.4908	+	35.0851i	−1.51260	+	2.08192i
$285$		0			0
$286$	−9.67652	+	26.0047i	−0.572185	+	1.53769i
$287$	2.55106	−	2.55106i	0.150584	−	0.150584i
$288$		0			0
$289$	5.82133	+	1.89147i	0.342431	+	0.111263i
$290$	−21.9429	−	8.49297i	−1.28853	−	0.498724i
$291$		0			0
$292$	−5.71404	−	0.905015i	−0.334389	−	0.0529620i
$293$	−19.4936	−	9.93247i	−1.13883	−	0.580261i	−0.220226	−	0.975449i	$-0.570680\pi$
$293$	−19.4936	−	9.93247i	−1.13883	−	0.580261i	−0.918600	+	0.395188i	$0.870680\pi$
$294$		0			0
$295$	15.2083	+	8.83680i	0.885460	+	0.514499i
$296$			6.53350i			0.379752i
$297$		0			0
$298$	14.4555	+	14.4555i	0.837385	+	0.837385i
$299$	−21.1764	−	15.3856i	−1.22466	−	0.889770i
$300$		0			0
$301$	2.72951	+	8.40056i	0.157326	+	0.484200i
$302$	4.38461	−	27.6833i	0.252306	−	1.59300i
$303$		0			0
$304$	1.78574	+	5.49595i	0.102419	+	0.315214i
$305$	−0.243648	+	1.13085i	−0.0139512	+	0.0647523i
$306$		0			0
$307$	1.44060	+	1.44060i	0.0822191	+	0.0822191i	0.747020	−	0.664801i	$-0.231484\pi$
$307$	1.44060	+	1.44060i	0.0822191	+	0.0822191i	−0.664801	+	0.747020i	$0.731484\pi$
$308$	5.68579	−	5.22642i	0.323978	−	0.297803i
$309$		0			0
$310$	−4.83080	+	1.28007i	−0.274371	+	0.0727029i
$311$	4.96363	−	15.2765i	0.281462	−	0.866250i	−0.705975	−	0.708236i	$-0.749491\pi$
$311$	4.96363	−	15.2765i	0.281462	−	0.866250i	0.987437	−	0.158013i	$-0.0505089\pi$
$312$		0			0
$313$	−8.01675	−	1.26973i	−0.453134	−	0.0717693i	−0.0743038	−	0.997236i	$-0.523673\pi$
$313$	−8.01675	−	1.26973i	−0.453134	−	0.0717693i	−0.378830	+	0.925466i	$0.623673\pi$
$314$	−2.33990	+	1.70004i	−0.132048	+	0.0959387i
$315$		0			0
$316$	−10.5718	−	3.43499i	−0.594711	−	0.193233i
$317$	6.20421	−	0.982650i	0.348463	−	0.0551911i	0.0202502	−	0.999795i	$-0.493554\pi$
$317$	6.20421	−	0.982650i	0.348463	−	0.0551911i	0.328213	+	0.944604i	$0.393554\pi$
$318$		0			0
$319$	−5.61757	+	15.0967i	−0.314523	+	0.845252i
$320$	27.2607	−	2.78883i	1.52392	−	0.155901i
$321$		0			0
$322$	5.76299	+	11.3105i	0.321159	+	0.630310i
$323$	−5.92274	+	11.6240i	−0.329550	+	0.646778i
$324$		0			0
$325$	0.903532	+	19.2855i	0.0501189	+	1.06977i
$326$	10.7316	−	3.48691i	0.594368	−	0.193122i
$327$		0			0
$328$	0.982021	+	6.20024i	0.0542230	+	0.342351i
$329$	−6.50650			−0.358715
$330$		0			0
$331$	12.6157			0.693420			0.346710	−	0.937972i	$-0.387299\pi$
$331$	12.6157			0.693420			0.346710	+	0.937972i	$0.387299\pi$
$332$	5.74070	+	36.2453i	0.315062	+	1.98922i
$333$		0			0
$334$	50.0911	−	16.2756i	2.74087	−	0.890561i
$335$	−13.5938	−	0.750209i	−0.742707	−	0.0409883i
$336$		0			0
$337$	−4.41119	+	8.65746i	−0.240293	+	0.471602i	−0.979385	−	0.202003i	$-0.935255\pi$
$337$	−4.41119	+	8.65746i	−0.240293	+	0.471602i	0.739092	+	0.673605i	$0.235255\pi$
$338$	1.87862	+	3.68701i	0.102184	+	0.200547i
$339$		0			0
$340$	22.4611	+	18.2920i	1.21812	+	0.992021i
$341$	0.919442	+	3.29541i	0.0497906	+	0.178457i
$342$		0			0
$343$	−11.3136	+	1.79190i	−0.610876	+	0.0967533i
$344$	−14.6171	−	4.74938i	−0.788101	−	0.256069i
$345$		0			0
$346$	−37.1106	+	26.9624i	−1.99508	+	1.44951i
$347$	7.98922	+	1.26537i	0.428884	+	0.0679285i	0.367145	−	0.930164i	$-0.380335\pi$
$347$	7.98922	+	1.26537i	0.428884	+	0.0679285i	0.0617391	+	0.998092i	$0.480335\pi$
$348$		0			0
$349$	−6.69962	+	20.6193i	−0.358622	+	1.10373i	0.595257	+	0.803535i	$0.297050\pi$
$349$	−6.69962	+	20.6193i	−0.358622	+	1.10373i	−0.953879	+	0.300191i	$0.902950\pi$
$350$	3.85563	−	8.53227i	0.206092	−	0.456069i
$351$		0			0
$352$	−2.90109	−	25.1139i	−0.154628	−	1.33857i
$353$	3.46607	+	3.46607i	0.184480	+	0.184480i	0.793305	−	0.608825i	$-0.208359\pi$
$353$	3.46607	+	3.46607i	0.184480	+	0.184480i	−0.608825	+	0.793305i	$0.708359\pi$
$354$		0			0
$355$	35.1866	+	7.58115i	1.86751	+	0.402366i
$356$	−3.87117	−	11.9142i	−0.205172	−	0.631453i
$357$		0			0
$358$	0.673398	−	4.25167i	0.0355902	−	0.224708i
$359$	7.66946	+	23.6042i	0.404778	+	1.24578i	0.921080	+	0.389373i	$0.127308\pi$
$359$	7.66946	+	23.6042i	0.404778	+	1.24578i	−0.516302	+	0.856407i	$0.672692\pi$
$360$		0			0
$361$	9.41602	+	6.84114i	0.495580	+	0.360060i
$362$	0.973554	+	0.973554i	0.0511689	+	0.0511689i
$363$		0			0
$364$		−	8.99132i		−	0.471273i
$365$	1.22990	+	4.64146i	0.0643757	+	0.242945i
$366$		0			0
$367$	−15.8364	−	8.06905i	−0.826653	−	0.421201i	−0.0111390	−	0.999938i	$-0.503546\pi$
$367$	−15.8364	−	8.06905i	−0.826653	−	0.421201i	−0.815514	+	0.578737i	$0.803546\pi$
$368$	14.2607	+	2.25867i	0.743389	+	0.117741i
$369$		0			0
$370$	19.2510	−	8.50723i	1.00081	−	0.442270i
$371$	5.38294	+	1.74902i	0.279468	+	0.0908047i
$372$		0			0
$373$	−2.68094	+	2.68094i	−0.138814	+	0.138814i	−0.773099	−	0.634285i	$-0.781294\pi$
$373$	−2.68094	+	2.68094i	−0.138814	+	0.138814i	0.634285	+	0.773099i	$0.281294\pi$
$374$	21.4670	−	27.0744i	1.11003	−	1.39999i
$375$		0			0
$376$	6.65455	−	9.15920i	0.343182	−	0.472350i
$377$	8.51391	+	16.7095i	0.438489	+	0.860582i
$378$		0			0
$379$	16.4337	+	22.6190i	0.844142	+	1.16186i	0.985123	+	0.171849i	$0.0549741\pi$
$379$	16.4337	+	22.6190i	0.844142	+	1.16186i	−0.140982	+	0.990012i	$0.545026\pi$
$380$	−12.1768	+	10.9030i	−0.624654	+	0.559314i
$381$		0			0
$382$	33.0810	−	16.8556i	1.69257	−	0.862409i
$383$	−0.844178	−	5.32993i	−0.0431355	−	0.272347i	0.956688	−	0.291114i	$-0.0940259\pi$
$383$	−0.844178	−	5.32993i	−0.0431355	−	0.272347i	−0.999824	+	0.0187671i	$0.994026\pi$
$384$		0			0
$385$	−5.87512	−	2.56304i	−0.299424	−	0.130625i
$386$	44.8771			2.28419
$387$		0			0
$388$	−21.9950	+	11.2070i	−1.11662	+	0.568949i
$389$	−23.4661	+	7.62459i	−1.18978	+	0.386582i	−0.835991	−	0.548744i	$-0.815106\pi$
$389$	−23.4661	+	7.62459i	−1.18978	+	0.386582i	−0.353787	+	0.935326i	$0.615106\pi$
$390$		0			0
$391$	19.1592	+	26.3704i	0.968924	+	1.33361i
$392$	4.26926	−	8.37890i	0.215630	−	0.423198i
$393$		0			0
$394$	27.3393	−	37.6293i	1.37733	−	1.89574i
$395$	0.938934	+	9.17802i	0.0472429	+	0.461796i
$396$		0			0
$397$	−19.9092	+	19.9092i	−0.999213	+	0.999213i	−1.00000		0.000786386i	$-0.999750\pi$
$397$	−19.9092	+	19.9092i	−0.999213	+	0.999213i	0.000786386		1.00000i	$0.499750\pi$
$398$	14.9280	−	2.36436i	0.748273	−	0.118515i
$399$		0			0
$400$	−5.27358	−	9.25220i	−0.263679	−	0.462610i
$401$	−29.8989	+	21.7228i	−1.49308	+	1.08479i	−0.520041	+	0.854141i	$0.674083\pi$
$401$	−29.8989	+	21.7228i	−1.49308	+	1.08479i	−0.973038	+	0.230644i	$0.925917\pi$
$402$		0			0
$403$	3.54903	+	1.80832i	0.176790	+	0.0900790i
$404$	−9.48265	+	29.1846i	−0.471779	+	1.45199i
$405$		0			0
$406$		−	9.09471i		−	0.451363i
$407$	−5.99562	−	13.1020i	−0.297192	−	0.649440i
$408$		0			0
$409$	−23.5917	−	17.1404i	−1.16653	−	0.847536i	−0.175943	−	0.984400i	$-0.556298\pi$
$409$	−23.5917	−	17.1404i	−1.16653	−	0.847536i	−0.990590	+	0.136864i	$0.956298\pi$
$410$	16.9904	−	10.9668i	0.839094	−	0.541613i
$411$		0			0
$412$	6.51592	−	41.1399i	0.321016	−	2.02682i
$413$	−1.06356	+	6.71504i	−0.0523342	+	0.330425i
$414$		0			0
$415$	25.5899	−	16.5176i	1.25616	−	0.810819i
$416$	−23.8117	−	17.3002i	−1.16747	−	0.848214i
$417$		0			0
$418$	13.1938	+	14.3534i	0.645329	+	0.702049i
$419$			3.99414i			0.195126i	0.995229	+	0.0975632i	$0.0311048\pi$
$419$			3.99414i			0.195126i	−0.995229	+	0.0975632i	$0.968895\pi$
$420$		0			0
$421$	3.84749	−	11.8414i	0.187515	−	0.577113i	−0.812467	−	0.583007i	$-0.801876\pi$
$421$	3.84749	−	11.8414i	0.187515	−	0.577113i	0.999983	+	0.00589398i	$0.00187612\pi$
$422$	40.0688	+	20.4161i	1.95052	+	0.993840i
$423$		0			0
$424$	−7.96752	+	5.78874i	−0.386937	+	0.281126i
$425$	6.35120	−	23.1880i	0.308079	−	1.12478i
$426$		0			0
$427$	−0.441631	+	0.0699475i	−0.0213720	+	0.00338500i
$428$	−8.94499	+	8.94499i	−0.432372	+	0.432372i
$429$		0			0
$430$	5.03875	+	49.2535i	0.242990	+	2.37521i
$431$	−1.02475	+	1.41044i	−0.0493603	+	0.0679386i	−0.832984	−	0.553298i	$-0.813369\pi$
$431$	−1.02475	+	1.41044i	−0.0493603	+	0.0679386i	0.783623	+	0.621236i	$0.213369\pi$
$432$		0			0
$433$	−6.43267	+	12.6248i	−0.309135	+	0.606711i	−0.992343	−	0.123513i	$-0.960584\pi$
$433$	−6.43267	+	12.6248i	−0.309135	+	0.606711i	0.683208	+	0.730223i	$0.260584\pi$
$434$	−1.13542	−	1.56277i	−0.0545017	−	0.0750151i
$435$		0			0
$436$	−19.3378	+	6.28322i	−0.926111	+	0.300912i
$437$	−16.3874	+	8.34982i	−0.783917	+	0.399426i
$438$		0			0
$439$	−3.06567			−0.146316			−0.0731582	−	0.997320i	$-0.523308\pi$
$439$	−3.06567			−0.146316			−0.0731582	+	0.997320i	$0.523308\pi$
$440$	9.61680	−	5.64905i	0.458463	−	0.269308i
$441$		0			0
$442$	−6.29289	−	39.7317i	−0.299322	−	1.88985i
$443$	1.82512	−	0.929947i	0.0867143	−	0.0441831i	−0.410096	−	0.912043i	$-0.634505\pi$
$443$	1.82512	−	0.929947i	0.0867143	−	0.0441831i	0.496810	+	0.867859i	$0.334505\pi$
$444$		0			0
$445$	−7.74605	+	6.93579i	−0.367198	+	0.328788i
$446$	5.05014	+	6.95092i	0.239131	+	0.329136i
$447$		0			0
$448$	4.80868	+	9.43756i	0.227189	+	0.445883i
$449$	17.9978	−	24.7719i	0.849370	−	1.16906i	−0.134631	−	0.990896i	$-0.542985\pi$
$449$	17.9978	−	24.7719i	0.849370	−	1.16906i	0.984001	−	0.178162i	$-0.0570152\pi$
$450$		0			0
$451$	−7.65909	−	11.5325i	−0.360653	−	0.543043i
$452$	31.8318	−	31.8318i	1.49724	−	1.49724i
$453$		0			0
$454$	14.6695	+	4.76641i	0.688474	+	0.223699i
$455$	−6.82580	+	3.01640i	−0.319998	+	0.141411i
$456$		0			0
$457$	12.4392	+	1.97017i	0.581880	+	0.0921607i	0.440433	−	0.897785i	$-0.354825\pi$
$457$	12.4392	+	1.97017i	0.581880	+	0.0921607i	0.141446	+	0.989946i	$0.454825\pi$
$458$	−50.7439	−	25.8553i	−2.37110	−	1.20814i
$459$		0			0
$460$	10.4602	+	39.4753i	0.487708	+	1.84054i
$461$			34.8146i			1.62148i	0.585409	+	0.810738i	$0.300934\pi$
$461$			34.8146i			1.62148i	−0.585409	+	0.810738i	$0.699066\pi$
$462$		0			0
$463$	−26.7521	−	26.7521i	−1.24327	−	1.24327i	−0.958635	−	0.284639i	$-0.908126\pi$
$463$	−26.7521	−	26.7521i	−1.24327	−	1.24327i	−0.284639	−	0.958635i	$-0.591874\pi$
$464$	−8.36884	−	6.08032i	−0.388513	−	0.282272i
$465$		0			0
$466$	0.279843	+	0.861269i	0.0129635	+	0.0398975i
$467$	5.10776	−	32.2491i	0.236359	−	1.49231i	−0.528952	−	0.848652i	$-0.677415\pi$
$467$	5.10776	−	32.2491i	0.236359	−	1.49231i	0.765311	−	0.643661i	$-0.222585\pi$
$468$		0			0
$469$	−1.62616	−	5.00482i	−0.0750893	−	0.231101i
$470$	−35.6525	−	7.68152i	−1.64453	−	0.354322i
$471$		0			0
$472$	−8.36500	−	8.36500i	−0.385030	−	0.385030i
$473$	33.6708	−	3.88956i	1.54818	−	0.178842i
$474$		0			0
$475$	12.3621	+	5.58630i	0.567214	+	0.256317i
$476$	−3.45995	+	10.6486i	−0.158587	+	0.488080i
$477$		0			0
$478$	−19.1502	−	3.03310i	−0.875912	−	0.138731i
$479$	−17.2715	+	12.5485i	−0.789155	+	0.573355i	−0.907713	−	0.419592i	$-0.862173\pi$
$479$	−17.2715	+	12.5485i	−0.789155	+	0.573355i	0.118557	+	0.992947i	$0.462173\pi$
$480$		0			0
$481$	−15.9540	−	5.18378i	−0.727441	−	0.236360i
$482$	11.0128	−	1.74425i	0.501618	−	0.0794485i
$483$		0			0
$484$	−15.3426	−	25.3548i	−0.697392	−	1.15249i
$485$	15.8867	+	12.9379i	0.721377	+	0.587478i
$486$		0			0
$487$	−3.61173	−	7.08841i	−0.163663	−	0.321207i	0.794581	−	0.607158i	$-0.207690\pi$
$487$	−3.61173	−	7.08841i	−0.163663	−	0.321207i	−0.958244	+	0.285951i	$0.907690\pi$
$488$	0.353215	−	0.693224i	0.0159893	−	0.0313808i
$489$		0			0
$490$	−30.2475	−	1.66929i	−1.36644	−	0.0754108i
$491$	14.1432	−	4.59541i	0.638275	−	0.207388i	0.0280376	−	0.999607i	$-0.491074\pi$
$491$	14.1432	−	4.59541i	0.638275	−	0.207388i	0.610237	+	0.792219i	$0.291074\pi$
$492$		0			0
$493$	−3.65325	−	23.0657i	−0.164534	−	1.03883i
$494$	22.6981			1.02123
$495$		0			0
$496$	−2.19712			−0.0986538
$497$	2.17643	+	13.7415i	0.0976263	+	0.616388i
$498$		0			0
$499$	3.20365	−	1.04093i	0.143415	−	0.0465985i	−0.236430	−	0.971649i	$-0.575977\pi$
$499$	3.20365	−	1.04093i	0.143415	−	0.0465985i	0.379845	+	0.925050i	$0.375977\pi$
$500$	17.9069	−	24.2206i	0.800820	−	1.08318i
$501$		0			0
$502$	−12.5167	+	24.5655i	−0.558649	+	1.09641i
$503$	4.13606	+	8.11747i	0.184418	+	0.361940i	0.964644	−	0.263558i	$-0.0848959\pi$
$503$	4.13606	+	8.11747i	0.184418	+	0.361940i	−0.780226	+	0.625498i	$0.784896\pi$
$504$		0			0
$505$	25.3369	−	2.59202i	1.12748	−	0.115344i
$506$	46.9194	−	13.0908i	2.08582	−	0.581958i
$507$		0			0
$508$	4.17178	−	0.660745i	0.185093	−	0.0293158i
$509$	0.588312	+	0.191154i	0.0260765	+	0.00847276i	0.322026	−	0.946731i	$-0.395636\pi$
$509$	0.588312	+	0.191154i	0.0260765	+	0.00847276i	−0.295950	+	0.955204i	$0.595636\pi$
$510$		0			0
$511$	−1.50151	+	1.09091i	−0.0664230	+	0.0482592i
$512$	22.3629	+	3.54193i	0.988308	+	0.156533i
$513$		0			0
$514$	2.22543	−	6.84916i	0.0981594	−	0.302104i
$515$	−33.4175	+	8.85498i	−1.47255	+	0.390197i
$516$		0			0
$517$	−4.93954	+	24.4741i	−0.217241	+	1.07637i
$518$	5.75249	+	5.75249i	0.252750	+	0.252750i
$519$		0			0
$520$	2.73493	−	12.6937i	0.119935	−	0.556656i
$521$	1.47759	+	4.54754i	0.0647342	+	0.199231i	0.978192	−	0.207702i	$-0.0665983\pi$
$521$	1.47759	+	4.54754i	0.0647342	+	0.199231i	−0.913458	+	0.406933i	$0.866598\pi$
$522$		0			0
$523$	−1.09596	+	6.91964i	−0.0479231	+	0.302575i	−0.999995	−	0.00330118i	$-0.998949\pi$
$523$	−1.09596	+	6.91964i	−0.0479231	+	0.302575i	0.952071	+	0.305876i	$0.0989492\pi$
$524$	−6.49719	−	19.9963i	−0.283831	−	0.873543i
$525$		0			0
$526$	−4.66363	−	3.38833i	−0.203344	−	0.147738i
$527$	−3.50735	−	3.50735i	−0.152783	−	0.152783i
$528$		0			0
$529$			22.9530i			0.997956i
$530$	27.4310	+	15.9389i	1.19153	+	0.692340i
$531$		0			0
$532$	−5.62911	−	2.86817i	−0.244053	−	0.124351i
$533$	−15.9194	−	2.52138i	−0.689545	−	0.109213i
$534$		0			0
$535$	9.79149	+	3.78977i	0.423323	+	0.163846i
$536$	8.70845	+	2.82955i	0.376148	+	0.122218i
$537$		0			0
$538$	−15.4414	+	15.4414i	−0.665725	+	0.665725i
$539$	−0.872266	+	20.7204i	−0.0375711	+	0.892492i
$540$		0			0
$541$	10.5952	−	14.5831i	0.455524	−	0.626975i	−0.518049	−	0.855351i	$-0.673342\pi$
$541$	10.5952	−	14.5831i	0.455524	−	0.626975i	0.973573	+	0.228376i	$0.0733415\pi$
$542$	−19.5259	−	38.3218i	−0.838711	−	1.64606i
$543$		0			0
$544$	21.5435	+	29.6521i	0.923672	+	1.27132i
$545$	11.2573	+	12.5725i	0.482212	+	0.538545i
$546$		0			0
$547$	−11.1521	+	5.68228i	−0.476830	+	0.242957i	−0.675851	−	0.737038i	$-0.736224\pi$
$547$	−11.1521	+	5.68228i	−0.476830	+	0.242957i	0.199021	+	0.979995i	$0.436224\pi$
$548$	−9.03156	−	57.0230i	−0.385809	−	2.43590i
$549$		0			0
$550$	−29.1670	−	20.9803i	−1.24368	−	0.894605i
$551$	13.1770			0.561361
$552$		0			0
$553$	−3.17740	+	1.61897i	−0.135117	+	0.0688455i
$554$	38.3258	−	12.4528i	1.62831	−	0.529069i
$555$		0			0
$556$	19.4176	+	26.7260i	0.823488	+	1.13343i
$557$	−8.96222	+	17.5893i	−0.379741	+	0.745285i	−0.999210	−	0.0397367i	$-0.987348\pi$
$557$	−8.96222	+	17.5893i	−0.379741	+	0.745285i	0.619469	+	0.785021i	$0.287348\pi$
$558$		0			0
$559$	23.1948	−	31.9250i	0.981038	−	1.35028i
$560$	2.59938	−	3.19183i	0.109844	−	0.134879i
$561$		0			0
$562$	33.7202	−	33.7202i	1.42240	−	1.42240i
$563$	−21.9349	+	3.47414i	−0.924445	+	0.146418i	−0.600469	−	0.799648i	$-0.705020\pi$
$563$	−21.9349	+	3.47414i	−0.924445	+	0.146418i	−0.323976	+	0.946065i	$0.605020\pi$
$564$		0			0
$565$	−34.8442	−	13.4864i	−1.46591	−	0.567376i
$566$	−26.9301	+	19.5658i	−1.13195	+	0.822413i
$567$		0			0
$568$	−21.5698	−	10.9904i	−0.905049	−	0.461145i
$569$	12.9364	−	39.8142i	0.542323	−	1.66910i	−0.184947	−	0.982748i	$-0.559211\pi$
$569$	12.9364	−	39.8142i	0.542323	−	1.66910i	0.727271	−	0.686351i	$-0.240789\pi$
$570$		0			0
$571$		−	17.1045i		−	0.715801i	−0.933760	−	0.357901i	$-0.883493\pi$
$571$		−	17.1045i		−	0.715801i	0.933760	−	0.357901i	$-0.116507\pi$
$572$	−33.8207	−	6.82594i	−1.41412	−	0.285407i
$573$		0			0
$574$	6.32370	+	4.59443i	0.263946	+	0.191768i
$575$	26.4587	−	21.1840i	1.10340	−	0.883435i
$576$		0			0
$577$	0.193873	−	1.22406i	0.00807102	−	0.0509584i	−0.983324	−	0.181862i	$-0.941788\pi$
$577$	0.193873	−	1.22406i	0.00807102	−	0.0509584i	0.991395	+	0.130903i	$0.0417877\pi$
$578$	−2.07456	+	13.0983i	−0.0862903	+	0.544816i
$579$		0			0
$580$	6.16244	−	28.6019i	0.255881	−	1.18763i
$581$	9.52441	+	6.91989i	0.395139	+	0.287085i
$582$		0			0
$583$	10.6655	−	18.9200i	0.441719	−	0.783588i
$584$		−	3.22942i		−	0.133634i
$585$		0			0
$586$	14.6477	−	45.0811i	0.605092	−	1.86228i
$587$	−33.2912	−	16.9627i	−1.37407	−	0.700126i	−0.397964	−	0.917401i	$-0.630283\pi$
$587$	−33.2912	−	16.9627i	−1.37407	−	0.700126i	−0.976110	+	0.217275i	$0.930283\pi$
$588$		0			0
$589$	2.26424	−	1.64507i	0.0932964	−	0.0677838i
$590$	−13.7555	+	35.5396i	−0.566305	+	1.46314i
$591$		0			0
$592$	9.13922	−	1.44751i	0.375620	−	0.0594923i
$593$	19.7192	−	19.7192i	0.809770	−	0.809770i	−0.174829	−	0.984599i	$-0.555937\pi$
$593$	19.7192	−	19.7192i	0.809770	−	0.809770i	0.984599	+	0.174829i	$0.0559371\pi$
$594$		0			0
$595$	9.24471	−	0.945757i	0.378996	−	0.0387723i
$596$	−14.9420	+	20.5659i	−0.612047	+	0.842410i
$597$		0			0
$598$	25.7465	−	50.5304i	1.05285	−	2.06634i
$599$	11.2303	+	15.4572i	0.458859	+	0.631566i	0.974272	−	0.225377i	$-0.0723613\pi$
$599$	11.2303	+	15.4572i	0.458859	+	0.631566i	−0.515412	+	0.856942i	$0.672361\pi$
$600$		0			0
$601$	−20.1867	+	6.55907i	−0.823434	+	0.267550i	−0.690277	−	0.723545i	$-0.742511\pi$
$601$	−20.1867	+	6.55907i	−0.823434	+	0.267550i	−0.133157	+	0.991095i	$0.542511\pi$
$602$	−17.0514	+	8.68813i	−0.694964	+	0.354102i
$603$		0			0
$604$	34.8530			1.41815
$605$	−14.1011	+	20.1534i	−0.573289	+	0.819353i
$606$		0			0
$607$	3.40302	+	21.4858i	0.138124	+	0.872082i	0.955288	+	0.295677i	$0.0955451\pi$
$607$	3.40302	+	21.4858i	0.138124	+	0.872082i	−0.817164	+	0.576405i	$0.804455\pi$
$608$	−18.4268	+	9.38893i	−0.747306	+	0.380771i
$609$		0			0
$610$	−2.50251	−	0.138108i	−0.101324	−	0.00559182i
$611$	17.0859	+	23.5167i	0.691220	+	0.951383i
$612$		0			0
$613$	12.9919	+	25.4981i	0.524740	+	1.02986i	0.989515	+	0.144431i	$0.0461352\pi$
$613$	12.9919	+	25.4981i	0.524740	+	1.02986i	−0.464775	+	0.885429i	$0.653865\pi$
$614$	−2.59450	+	3.57102i	−0.104705	+	0.144115i
$615$		0			0
$616$	3.37804	+	2.67842i	0.136105	+	0.107917i
$617$	−3.05678	+	3.05678i	−0.123061	+	0.123061i	−0.765955	−	0.642894i	$-0.777734\pi$
$617$	−3.05678	+	3.05678i	−0.123061	+	0.123061i	0.642894	+	0.765955i	$0.277734\pi$
$618$		0			0
$619$	−32.8210	−	10.6642i	−1.31919	−	0.428629i	−0.436971	−	0.899476i	$-0.643949\pi$
$619$	−32.8210	−	10.6642i	−1.31919	−	0.428629i	−0.882215	+	0.470846i	$0.843949\pi$
$620$	−2.51186	−	5.68407i	−0.100879	−	0.228278i
$621$		0			0
$622$	34.3728	+	5.44411i	1.37822	+	0.218289i
$623$	−3.58087	−	1.82454i	−0.143465	−	0.0730988i
$624$		0			0
$625$	−24.3946	−	5.46860i	−0.975782	−	0.218744i
$626$		−	17.5856i		−	0.702860i
$627$		0			0
$628$	−2.54312	−	2.54312i	−0.101481	−	0.101481i
$629$	16.9000	+	12.2786i	0.673847	+	0.489578i
$630$		0			0
$631$	7.36128	+	22.6557i	0.293048	+	0.901908i	0.983870	+	0.178884i	$0.0572487\pi$
$631$	7.36128	+	22.6557i	0.293048	+	0.901908i	−0.690822	+	0.723025i	$0.742751\pi$
$632$	0.970681	−	6.12864i	0.0386116	−	0.243784i
$633$		0			0
$634$	4.20558	+	12.9435i	0.167025	+	0.514050i
$635$	−1.90115	−	2.94536i	−0.0754450	−	0.116883i
$636$		0			0
$637$	17.0730	+	17.0730i	0.676456	+	0.676456i
$638$	−34.2096	−	6.90443i	−1.35437	−	0.273349i
$639$		0			0
$640$	6.47583	+	24.4389i	0.255980	+	0.966033i
$641$	7.69272	−	23.6758i	0.303844	−	0.935137i	−0.676262	−	0.736662i	$-0.736401\pi$
$641$	7.69272	−	23.6758i	0.303844	−	0.935137i	0.980106	−	0.198475i	$-0.0635989\pi$
$642$		0			0
$643$	−0.103141	−	0.0163360i	−0.00406749	−	0.000644228i	0.154400	−	0.988008i	$-0.450655\pi$
$643$	−0.103141	−	0.0163360i	−0.00406749	−	0.000644228i	−0.158468	+	0.987364i	$0.550655\pi$
$644$	−12.7703	+	9.27815i	−0.503219	+	0.365610i
$645$		0			0
$646$	−26.8819	−	8.73445i	−1.05765	−	0.343652i
$647$	19.6094	−	3.10582i	0.770924	−	0.122102i	0.241433	−	0.970418i	$-0.422383\pi$
$647$	19.6094	−	3.10582i	0.770924	−	0.122102i	0.529492	+	0.848315i	$0.322383\pi$
$648$		0			0
$649$	24.4511	+	9.09841i	0.959790	+	0.357144i
$650$	−40.9633	+	8.46993i	−1.60671	+	0.332218i
$651$		0			0
$652$	6.37010	+	12.5020i	0.249472	+	0.489617i
$653$	10.3834	−	20.3785i	0.406333	−	0.797474i	−0.593641	−	0.804730i	$-0.702310\pi$
$653$	10.3834	−	20.3785i	0.406333	−	0.797474i	0.999974	+	0.00725675i	$0.00230992\pi$
$654$		0			0
$655$	−13.0006	+	11.6407i	−0.507976	+	0.454841i
$656$	8.45548	−	2.74735i	0.330131	−	0.107266i
$657$		0			0
$658$	−2.20525	−	13.9234i	−0.0859695	−	0.542790i
$659$	15.2005			0.592126			0.296063	−	0.955168i	$-0.404326\pi$
$659$	15.2005			0.592126			0.296063	+	0.955168i	$0.404326\pi$
$660$		0			0
$661$	9.56894			0.372189			0.186094	−	0.982532i	$-0.440417\pi$
$661$	9.56894			0.372189			0.186094	+	0.982532i	$0.440417\pi$
$662$	4.27583	+	26.9965i	0.166185	+	1.04925i
$663$		0			0
$664$	−19.4823	+	6.33017i	−0.756058	+	0.245658i
$665$	−0.288940	+	5.23558i	−0.0112046	+	0.203027i
$666$		0			0
$667$	14.9468	−	29.3347i	0.578742	−	1.13585i
$668$	29.7333	+	58.3548i	1.15041	+	2.25782i
$669$		0			0
$670$	−3.00195	−	29.3438i	−0.115975	−	1.13365i
$671$	−0.0721664	+	1.71429i	−0.00278595	+	0.0661796i
$672$		0			0
$673$	3.19857	−	0.506604i	0.123296	−	0.0195282i	−0.0944815	−	0.995527i	$-0.530119\pi$
$673$	3.19857	−	0.506604i	0.123296	−	0.0195282i	0.217777	+	0.975998i	$0.430119\pi$
$674$	−20.0214	−	6.50533i	−0.771194	−	0.250576i
$675$		0			0
$676$	−4.16286	+	3.02449i	−0.160110	+	0.116327i
$677$	5.66156	+	0.896704i	0.217592	+	0.0344631i	0.264278	−	0.964446i	$-0.414866\pi$
$677$	5.66156	+	0.896704i	0.217592	+	0.0344631i	−0.0466867	+	0.998910i	$0.514866\pi$
$678$		0			0
$679$	−2.44722	+	7.53176i	−0.0939156	+	0.289042i
$680$	−8.12373	+	13.9811i	−0.311531	+	0.536149i
$681$		0			0
$682$	−6.74030	+	3.08445i	−0.258099	+	0.118110i
$683$	−5.04567	−	5.04567i	−0.193067	−	0.193067i	0.603953	−	0.797020i	$-0.293592\pi$
$683$	−5.04567	−	5.04567i	−0.193067	−	0.193067i	−0.797020	+	0.603953i	$0.793592\pi$
$684$		0			0
$685$	−40.2594	+	25.9864i	−1.53823	+	0.992889i
$686$	−7.66903	−	23.6028i	−0.292805	−	0.901161i
$687$		0			0
$688$	−3.40511	+	21.4990i	−0.129818	+	0.819641i
$689$	−7.81387	−	24.0486i	−0.297685	−	0.916180i
$690$		0			0
$691$	14.3602	+	10.4333i	0.546289	+	0.396903i	0.826416	−	0.563061i	$-0.190376\pi$
$691$	14.3602	+	10.4333i	0.546289	+	0.396903i	−0.280126	+	0.959963i	$0.590376\pi$
$692$	−40.3336	−	40.3336i	−1.53325	−	1.53325i
$693$		0			0
$694$			17.5252i			0.665246i
$695$	13.7750	−	23.7069i	0.522514	−	0.899256i
$696$		0			0
$697$	17.8835	+	9.11209i	0.677385	+	0.345145i
$698$	−46.3944	−	7.34815i	−1.75605	−	0.278131i
$699$		0			0
$700$	11.2292	+	3.07567i	0.424422	+	0.116249i
$701$	7.00098	+	2.27476i	0.264423	+	0.0859164i	0.438228	−	0.898864i	$-0.355606\pi$
$701$	7.00098	+	2.27476i	0.264423	+	0.0859164i	−0.173805	+	0.984780i	$0.555606\pi$
$702$		0			0
$703$	−8.33460	+	8.33460i	−0.314345	+	0.314345i
$704$	39.1499	−	10.9231i	1.47552	−	0.411679i
$705$		0			0
$706$	−6.24235	+	8.59186i	−0.234934	+	0.323359i
$707$	4.46933	+	8.77155i	0.168086	+	0.329888i
$708$		0			0
$709$	5.88349	+	8.09792i	0.220959	+	0.304124i	0.905077	−	0.425247i	$-0.139813\pi$
$709$	5.88349	+	8.09792i	0.220959	+	0.304124i	−0.684118	+	0.729371i	$0.739813\pi$
$710$	−4.29725	+	77.8660i	−0.161273	+	2.92226i
$711$		0			0
$712$	6.23076	−	3.17473i	0.233508	−	0.118978i
$713$	−1.09391	−	6.90667i	−0.0409672	−	0.258657i
$714$		0			0
$715$	6.16421	+	27.9651i	0.230528	+	1.04584i
$716$	5.35280			0.200043
$717$		0			0
$718$	−47.9116	+	24.4122i	−1.78805	+	0.911054i
$719$	−19.0499	+	6.18968i	−0.710440	+	0.230836i	−0.641873	−	0.766811i	$-0.721843\pi$
$719$	−19.0499	+	6.18968i	−0.710440	+	0.230836i	−0.0685666	+	0.997647i	$0.521843\pi$
$720$		0			0
$721$	−7.85434	−	10.8106i	−0.292511	−	0.402607i
$722$	−11.4481	+	22.4682i	−0.426055	+	0.836179i
$723$		0			0
$724$	−1.00632	+	1.38508i	−0.0373995	+	0.0514760i
$725$	−23.7806	+	4.91710i	−0.883191	+	0.182617i
$726$		0			0
$727$	0.469364	−	0.469364i	0.0174077	−	0.0174077i	−0.698349	−	0.715757i	$-0.746082\pi$
$727$	0.469364	−	0.469364i	0.0174077	−	0.0174077i	0.715757	+	0.698349i	$0.246082\pi$
$728$	4.95728	−	0.785157i	0.183729	−	0.0290998i
$729$		0			0
$730$	−9.51550	+	4.20501i	−0.352184	+	0.155634i
$731$	−39.7553	+	28.8839i	−1.47040	+	1.06831i
$732$		0			0
$733$	−9.79023	−	4.98837i	−0.361610	−	0.184250i	0.263740	−	0.964594i	$-0.415044\pi$
$733$	−9.79023	−	4.98837i	−0.361610	−	0.184250i	−0.625350	+	0.780344i	$0.715044\pi$
$734$	11.8997	−	36.6235i	0.439225	−	1.35180i
$735$		0			0
$736$			51.6717i			1.90464i
$737$	−20.0601	+	2.31729i	−0.738923	+	0.0853584i
$738$		0			0
$739$	6.41880	+	4.66353i	0.236119	+	0.171551i	0.699553	−	0.714581i	$-0.253383\pi$
$739$	6.41880	+	4.66353i	0.236119	+	0.171551i	−0.463433	+	0.886132i	$0.653383\pi$
$740$	14.1932	+	21.9888i	0.521751	+	0.808323i
$741$		0			0
$742$	−1.91833	+	12.1119i	−0.0704241	+	0.444640i
$743$	2.54941	−	16.0963i	0.0935288	−	0.590518i	−0.895759	−	0.444540i	$-0.853367\pi$
$743$	2.54941	−	16.0963i	0.0935288	−	0.590518i	0.989288	−	0.145978i	$-0.0466328\pi$
$744$		0			0
$745$	20.6254	+	4.44385i	0.755656	+	0.162810i
$746$	−6.64564	−	4.82834i	−0.243314	−	0.176778i
$747$		0			0
$748$	37.4281	+	21.0987i	1.36851	+	0.771445i
$749$			4.05829i			0.148287i
$750$		0			0
$751$	−5.73752	+	17.6583i	−0.209365	+	0.644360i	0.790141	+	0.612926i	$0.210007\pi$
$751$	−5.73752	+	17.6583i	−0.209365	+	0.644360i	−0.999506	+	0.0314342i	$0.989993\pi$
$752$	−14.2864	−	7.27931i	−0.520973	−	0.265449i
$753$		0			0
$754$	−32.8713	+	23.8824i	−1.19710	+	0.869747i
$755$	−11.6924	−	26.4588i	−0.425531	−	0.962934i
$756$		0			0
$757$	−42.6364	+	6.75295i	−1.54965	+	0.245440i	−0.871837	−	0.489796i	$-0.837071\pi$
$757$	−42.6364	+	6.75295i	−1.54965	+	0.245440i	−0.677811	+	0.735237i	$0.737071\pi$
$758$	−42.8330	+	42.8330i	−1.55577	+	1.55577i
$759$		0			0
$760$	−7.07461	−	5.76145i	−0.256623	−	0.208990i
$761$	1.53149	−	2.10792i	0.0555166	−	0.0764120i	−0.780356	−	0.625335i	$-0.784962\pi$
$761$	1.53149	−	2.10792i	0.0555166	−	0.0764120i	0.835873	+	0.548923i	$0.184962\pi$
$762$		0			0
$763$	−2.96138	+	5.81204i	−0.107209	+	0.210410i
$764$	27.1368	+	37.3505i	0.981773	+	1.35130i
$765$		0			0
$766$	11.1195	−	3.61295i	0.401764	−	0.130541i
$767$	27.0633	−	13.7894i	0.977198	−	0.497907i
$768$		0			0
$769$	−53.6748			−1.93556			−0.967781	−	0.251793i	$-0.918980\pi$
$769$	−53.6748			−1.93556			−0.967781	+	0.251793i	$0.918980\pi$
$770$	3.49344	−	13.4410i	0.125895	−	0.484379i
$771$		0			0
$772$	8.72969	+	55.1171i	0.314188	+	1.98371i
$773$	−2.38902	+	1.21726i	−0.0859269	+	0.0437820i	−0.496426	−	0.868079i	$-0.665355\pi$
$773$	−2.38902	+	1.21726i	−0.0859269	+	0.0437820i	0.410499	+	0.911861i	$0.365355\pi$
$774$		0			0
$775$	−3.47242	+	3.81378i	−0.124733	+	0.136995i
$776$	−8.09956	−	11.1481i	−0.290757	−	0.400193i
$777$		0			0
$778$	−24.2694	−	47.6313i	−0.870099	−	1.70767i
$779$	−6.65673	+	9.16220i	−0.238502	+	0.328270i
$780$		0			0
$781$	53.3406	+	2.24547i	1.90868	+	0.0803493i
$782$	−49.9369	+	49.9369i	−1.78574	+	1.78574i
$783$		0			0
$784$	−12.6665	−	4.11559i	−0.452375	−	0.146985i
$785$	−1.07746	+	2.78378i	−0.0384561	+	0.0993574i
$786$		0			0
$787$	−3.22644	−	0.511018i	−0.115010	−	0.0182158i	0.0986640	−	0.995121i	$-0.468543\pi$
$787$	−3.22644	−	0.511018i	−0.115010	−	0.0182158i	−0.213674	+	0.976905i	$0.568543\pi$
$788$	51.5336	+	26.2577i	1.83581	+	0.935392i
$789$		0			0
$790$	−19.3220	+	5.11995i	−0.687445	+	0.182160i
$791$		−	14.4419i		−	0.513495i
$792$		0			0
$793$	1.41252	+	1.41252i	0.0501602	+	0.0501602i
$794$	−49.3519	−	35.8562i	−1.75143	−	1.27249i
$795$		0			0
$796$	5.80771	+	17.8743i	0.205849	+	0.633538i
$797$	−0.692661	+	4.37329i	−0.0245353	+	0.154910i	−0.996914	−	0.0784978i	$-0.974988\pi$
$797$	−0.692661	+	4.37329i	−0.0245353	+	0.154910i	0.972379	+	0.233408i	$0.0749877\pi$
$798$		0			0
$799$	−11.1858	−	34.4262i	−0.395724	−	1.21791i
$800$	29.7514	−	23.8203i	1.05187	−	0.842175i
$801$		0			0
$802$	−56.6187	−	56.6187i	−1.99928	−	1.99928i
$803$	2.96355	+	6.47611i	0.104582	+	0.228537i
$804$		0			0
$805$	11.3277	+	6.58199i	0.399249	+	0.231985i
$806$	−2.66679	+	8.20755i	−0.0939338	+	0.289098i
$807$		0			0
$808$	−16.9187	−	2.67966i	−0.595199	−	0.0942703i
$809$	−0.650906	+	0.472911i	−0.0228846	+	0.0166267i	−0.599169	−	0.800623i	$-0.704502\pi$
$809$	−0.650906	+	0.472911i	−0.0228846	+	0.0166267i	0.576284	+	0.817249i	$0.304502\pi$
$810$		0			0
$811$	−26.9792	−	8.76606i	−0.947367	−	0.307818i	−0.205722	−	0.978611i	$-0.565954\pi$
$811$	−26.9792	−	8.76606i	−0.947367	−	0.307818i	−0.741645	+	0.670792i	$0.765954\pi$
$812$	11.1699	−	1.76914i	0.391987	−	0.0620847i
$813$		0			0
$814$	26.0050	−	17.2708i	0.911476	−	0.605341i
$815$	7.35393	−	9.03006i	0.257597	−	0.316309i
$816$		0			0
$817$	−12.5880	−	24.7053i	−0.440397	−	0.864328i
$818$	28.6831	−	56.2937i	1.00288	−	1.96826i
$819$		0			0
$820$	16.7742	+	18.7339i	0.585782	+	0.654215i
$821$	−17.9704	+	5.83895i	−0.627173	+	0.203781i	−0.605322	−	0.795980i	$-0.706956\pi$
$821$	−17.9704	+	5.83895i	−0.627173	+	0.203781i	−0.0218505	+	0.999761i	$0.506956\pi$
$822$		0			0
$823$	−3.50190	−	22.1101i	−0.122068	−	0.770710i	−0.970446	−	0.241318i	$-0.922420\pi$
$823$	−3.50190	−	22.1101i	−0.122068	−	0.770710i	0.848378	−	0.529392i	$-0.177580\pi$
$824$	23.2511			0.809991
$825$		0			0
$826$	−14.7301			−0.512526
$827$	−2.19213	−	13.8406i	−0.0762280	−	0.481284i	−0.996039	−	0.0889219i	$-0.971658\pi$
$827$	−2.19213	−	13.8406i	−0.0762280	−	0.481284i	0.919811	−	0.392363i	$-0.128342\pi$
$828$		0			0
$829$	−30.3401	+	9.85809i	−1.05375	+	0.342385i	−0.784141	−	0.620583i	$-0.786896\pi$
$829$	−30.3401	+	9.85809i	−1.05375	+	0.342385i	−0.269613	+	0.962969i	$0.586896\pi$
$830$	44.0196	+	49.1621i	1.52794	+	1.70644i
$831$		0			0
$832$	21.4831	−	42.1629i	0.744792	−	1.46174i
$833$	−13.6501	−	26.7898i	−0.472948	−	0.928213i
$834$		0			0
$835$	34.3254	−	42.1490i	1.18788	−	1.45863i
$836$	−15.0621	+	18.9964i	−0.520932	+	0.657004i
$837$		0			0
$838$	−8.54713	+	1.35373i	−0.295256	+	0.0467639i
$839$	14.8731	+	4.83255i	0.513475	+	0.166838i	0.554282	−	0.832329i	$-0.312993\pi$
$839$	14.8731	+	4.83255i	0.513475	+	0.166838i	−0.0408068	+	0.999167i	$0.512993\pi$
$840$		0			0
$841$	4.37849	−	3.18116i	0.150983	−	0.109695i
$842$	26.6436	+	4.21993i	0.918199	+	0.145428i
$843$		0			0
$844$	−17.2802	+	53.1831i	−0.594810	+	1.83064i
$845$	3.69261	+	2.14560i	0.127030	+	0.0738109i
$846$		0			0
$847$	−9.23208	−	2.27122i	−0.317218	−	0.0780401i
$848$	9.86266	+	9.86266i	0.338685	+	0.338685i
$849$		0			0
$850$	51.7732	+	5.73194i	1.77580	+	0.196604i
$851$	9.10051	+	28.0085i	0.311961	+	0.960118i
$852$		0			0
$853$	1.58977	−	10.0374i	0.0544328	−	0.343675i	−0.945409	−	0.325886i	$-0.894337\pi$
$853$	1.58977	−	10.0374i	0.0544328	−	0.343675i	0.999842	−	0.0177890i	$-0.00566271\pi$
$854$	−0.299364	−	0.921349i	−0.0102440	−	0.0315279i
$855$		0			0
$856$	−5.71285	−	4.15063i	−0.195261	−	0.141866i
$857$	22.7332	+	22.7332i	0.776550	+	0.776550i	0.979243	−	0.202692i	$-0.0649691\pi$
$857$	22.7332	+	22.7332i	0.776550	+	0.776550i	−0.202692	+	0.979243i	$0.564969\pi$
$858$		0			0
$859$		−	45.0738i		−	1.53790i	−0.639310	−	0.768949i	$-0.720780\pi$
$859$		−	45.0738i		−	1.53790i	0.639310	−	0.768949i	$-0.279220\pi$
$860$	−59.5119	+	15.7695i	−2.02934	+	0.537735i
$861$		0			0
$862$	−3.36555	−	1.71483i	−0.114631	−	0.0584075i
$863$	−24.7343	−	3.91752i	−0.841964	−	0.133354i	−0.279469	−	0.960155i	$-0.590158\pi$
$863$	−24.7343	−	3.91752i	−0.841964	−	0.133354i	−0.562495	+	0.826801i	$0.690158\pi$
$864$		0			0
$865$	−17.0884	+	44.1505i	−0.581021	+	1.50116i
$866$	−29.1964	−	9.48647i	−0.992133	−	0.322363i
$867$		0			0
$868$	1.69849	−	1.69849i	0.0576504	−	0.0576504i
$869$	3.67754	+	13.1808i	0.124752	+	0.447129i
$870$		0			0
$871$	−13.8188	+	19.0200i	−0.468233	+	0.644468i
$872$	−5.15285	−	10.1130i	−0.174497	−	0.342470i
$873$		0			0
$874$	−23.4221	−	32.2378i	−0.792266	−	1.09046i
$875$	−1.43224	−	9.55649i	−0.0484186	−	0.323068i
$876$		0			0
$877$	50.7034	−	25.8347i	1.71213	−	0.872374i	0.730176	−	0.683259i	$-0.239438\pi$
$877$	50.7034	−	25.8347i	1.71213	−	0.872374i	0.981955	−	0.189116i	$-0.0605621\pi$
$878$	−1.03905	−	6.56029i	−0.0350662	−	0.221399i
$879$		0			0
$880$	−10.0327	−	12.2007i	−0.338201	−	0.411284i
$881$	2.85135			0.0960644			0.0480322	−	0.998846i	$-0.484705\pi$
$881$	2.85135			0.0960644			0.0480322	+	0.998846i	$0.484705\pi$
$882$		0			0
$883$	21.0450	−	10.7230i	0.708221	−	0.360857i	−0.0624865	−	0.998046i	$-0.519903\pi$
$883$	21.0450	−	10.7230i	0.708221	−	0.360857i	0.770707	+	0.637189i	$0.219903\pi$
$884$	47.5735	−	15.4576i	1.60007	−	0.519894i
$885$		0			0
$886$	2.60860	+	3.59043i	0.0876377	+	0.120623i
$887$	−23.4721	+	46.0666i	−0.788116	+	1.54676i	0.0484036	+	0.998828i	$0.484587\pi$
$887$	−23.4721	+	46.0666i	−0.788116	+	1.54676i	−0.836520	+	0.547937i	$0.815413\pi$
$888$		0			0
$889$	0.796468	−	1.09624i	0.0267127	−	0.0367668i
$890$	−17.4674	−	14.2252i	−0.585509	−	0.476829i
$891$		0			0
$892$	−7.55459	+	7.55459i	−0.252946	+	0.252946i
$893$	20.1731	−	3.19511i	0.675069	−	0.106920i
$894$		0			0
$895$	−1.79575	−	4.06360i	−0.0600254	−	0.135831i
$896$	−7.90600	+	5.74404i	−0.264121	+	0.191895i
$897$		0			0
$898$	59.1099	+	30.1180i	1.97252	+	1.00505i
$899$	−1.54817	+	4.76478i	−0.0516343	+	0.158914i
$900$		0			0
$901$			31.4883i			1.04903i
$902$	22.0827	−	20.2985i	0.735272	−	0.675868i
$903$		0			0
$904$	20.3299	+	14.7705i	0.676162	+	0.491260i
$905$	1.38909	+	0.299286i	0.0461748	+	0.00994861i
$906$		0			0
$907$	6.42481	−	40.5647i	0.213332	−	1.34693i	−0.615812	−	0.787893i	$-0.711172\pi$
$907$	6.42481	−	40.5647i	0.213332	−	1.34693i	0.829144	−	0.559035i	$-0.188828\pi$
$908$	−3.00043	+	18.9439i	−0.0995726	+	0.628677i
$909$		0			0
$910$	−8.76832	−	13.5843i	−0.290667	−	0.450316i
$911$	10.8571	+	7.88817i	0.359713	+	0.261347i	0.752932	−	0.658098i	$-0.228639\pi$
$911$	10.8571	+	7.88817i	0.359713	+	0.261347i	−0.393220	+	0.919445i	$0.628639\pi$
$912$		0			0
$913$	33.2597	−	30.5726i	1.10074	−	1.01180i
$914$			27.2866i			0.902559i
$915$		0			0
$916$	21.8840	−	67.3519i	0.723067	−	2.22537i
$917$	−6.00997	−	3.06223i	−0.198467	−	0.101124i
$918$		0			0
$919$	6.41832	−	4.66318i	0.211721	−	0.153824i	−0.476871	−	0.878973i	$-0.658229\pi$
$919$	6.41832	−	4.66318i	0.211721	−	0.153824i	0.688592	+	0.725149i	$0.258229\pi$
$920$	−20.8509	+	9.21426i	−0.687435	+	0.303785i
$921$		0			0
$922$	−74.5004	+	11.7997i	−2.45354	+	0.388603i
$923$	43.9510	−	43.9510i	1.44666	−	1.44666i
$924$		0			0
$925$	11.9314	−	18.1516i	0.392301	−	0.596821i
$926$	48.1802	−	66.3144i	1.58330	−	2.17923i
$927$		0			0
$928$	16.8069	−	32.9854i	0.551713	−	1.08280i
$929$	−2.16567	−	2.98079i	−0.0710533	−	0.0977965i	0.772011	−	0.635609i	$-0.219251\pi$
$929$	−2.16567	−	2.98079i	−0.0710533	−	0.0977965i	−0.843065	+	0.537812i	$0.819251\pi$
$930$		0			0
$931$	16.1349	−	5.24255i	0.528800	−	0.171818i
$932$	−1.00336	+	0.511235i	−0.0328660	+	0.0167461i
$933$		0			0
$934$	70.7418			2.31474
$935$	3.46085	−	35.4919i	0.113182	−	1.16071i
$936$		0			0
$937$	5.01336	+	31.6531i	0.163779	+	1.03406i	0.923440	+	0.383742i	$0.125365\pi$
$937$	5.01336	+	31.6531i	0.163779	+	1.03406i	−0.759661	+	0.650319i	$0.774635\pi$
$938$	10.1588	−	5.17614i	0.331695	−	0.169007i
$939$		0			0
$940$	2.49900	−	45.2818i	0.0815084	−	1.47693i
$941$	−14.1350	−	19.4552i	−0.460788	−	0.634221i	0.513884	−	0.857860i	$-0.328206\pi$
$941$	−14.1350	−	19.4552i	−0.460788	−	0.634221i	−0.974672	+	0.223639i	$0.928206\pi$
$942$		0			0
$943$	12.8461	+	25.2120i	0.418328	+	0.821015i
$944$	−9.84789	+	13.5545i	−0.320522	+	0.441160i
$945$		0			0
$946$	19.7354	+	70.7345i	0.641652	+	2.29978i
$947$	−14.0245	+	14.0245i	−0.455736	+	0.455736i	−0.897253	−	0.441517i	$-0.854441\pi$
$947$	−14.0245	+	14.0245i	−0.455736	+	0.455736i	0.441517	+	0.897253i	$0.354441\pi$
$948$		0			0
$949$	7.88585	+	2.56227i	0.255986	+	0.0831748i
$950$	−7.76434	+	28.3473i	−0.251908	+	0.919709i
$951$		0			0
$952$	−6.17318	−	0.977735i	−0.200074	−	0.0316886i
$953$	8.37310	+	4.26631i	0.271231	+	0.138199i	0.584317	−	0.811526i	$-0.301363\pi$
$953$	8.37310	+	4.26631i	0.271231	+	0.138199i	−0.313085	+	0.949725i	$0.601363\pi$
$954$		0			0
$955$	19.2510	−	33.1313i	0.622949	−	1.07210i
$956$		−	24.1099i		−	0.779770i
$957$		0			0
$958$	−32.7066	−	32.7066i	−1.05670	−	1.05670i
$959$	−14.9843	−	10.8867i	−0.483868	−	0.351551i
$960$		0			0
$961$	−9.25070	−	28.4707i	−0.298410	−	0.918411i
$962$	5.68557	−	35.8973i	0.183310	−	1.15737i
$963$		0			0
$964$	4.28450	+	13.1863i	0.137995	+	0.424704i
$965$	38.9138	−	25.1178i	1.25268	−	0.808571i
$966$		0			0
$967$	−25.7543	−	25.7543i	−0.828201	−	0.828201i	0.159067	−	0.987268i	$-0.449151\pi$
$967$	−25.7543	−	25.7543i	−0.828201	−	0.828201i	−0.987268	+	0.159067i	$0.949151\pi$
$968$	12.6393	−	10.6731i	0.406244	−	0.343046i
$969$		0			0
$970$	−22.3015	+	38.3813i	−0.716059	+	1.23235i
$971$	2.81437	−	8.66173i	0.0903173	−	0.277968i	−0.895688	−	0.444684i	$-0.853316\pi$
$971$	2.81437	−	8.66173i	0.0903173	−	0.277968i	0.986005	+	0.166715i	$0.0533161\pi$
$972$		0			0
$973$	10.4675	+	1.65789i	0.335573	+	0.0531496i
$974$	13.9445	−	10.1313i	0.446811	−	0.324627i
$975$		0			0
$976$	−1.04795	−	0.340501i	−0.0335442	−	0.0108992i
$977$	40.5932	−	6.42933i	1.29869	−	0.205693i	0.531471	−	0.847076i	$-0.321639\pi$
$977$	40.5932	−	6.42933i	1.29869	−	0.205693i	0.767220	+	0.641384i	$0.221639\pi$
$978$		0			0
$979$	−9.58149	+	12.0843i	−0.306226	+	0.386215i
$980$	−3.83368	−	37.4740i	−0.122462	−	1.19706i
$981$		0			0
$982$	14.6274	+	28.7078i	0.466778	+	0.916104i
$983$	−0.862341	+	1.69244i	−0.0275044	+	0.0539804i	−0.904350	−	0.426792i	$-0.859644\pi$
$983$	−0.862341	+	1.69244i	−0.0275044	+	0.0539804i	0.876845	+	0.480772i	$0.159644\pi$
$984$		0			0
$985$	2.64520	−	47.9309i	0.0842830	−	1.52721i
$986$	48.1206	−	15.6353i	1.53247	−	0.497930i
$987$		0			0
$988$	4.41532	+	27.8772i	0.140470	+	0.886893i
$989$	−69.2775			−2.20290
$990$		0			0
$991$	−47.5039			−1.50901			−0.754506	−	0.656294i	$-0.772123\pi$
$991$	−47.5039			−1.50901			−0.754506	+	0.656294i	$0.772123\pi$
$992$	−1.23004	−	7.76618i	−0.0390539	−	0.246576i
$993$		0			0
$994$	−28.6679	+	9.31478i	−0.909292	+	0.295447i
$995$	11.6210	−	10.4054i	0.368410	−	0.329874i
$996$		0			0
$997$	−2.88231	+	5.65684i	−0.0912835	+	0.179154i	−0.932134	−	0.362113i	$-0.882055\pi$
$997$	−2.88231	+	5.65684i	−0.0912835	+	0.179154i	0.840851	+	0.541267i	$0.182055\pi$
$998$	3.31332	+	6.50276i	0.104881	+	0.205841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.c.73.11		96
3.2	odd	2		165.2.w.a.73.2	yes	96
5.2	odd	4	inner	495.2.bj.c.172.2		96
11.8	odd	10	inner	495.2.bj.c.118.2		96
15.2	even	4		165.2.w.a.7.11	✓	96
15.8	even	4		825.2.cw.b.7.2		96
15.14	odd	2		825.2.cw.b.568.11		96
33.8	even	10		165.2.w.a.118.11	yes	96
55.52	even	20	inner	495.2.bj.c.217.11		96
165.8	odd	20		825.2.cw.b.382.11		96
165.74	even	10		825.2.cw.b.118.2		96
165.107	odd	20		165.2.w.a.52.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.w.a.7.11	✓	96	15.2	even	4
165.2.w.a.52.2	yes	96	165.107	odd	20
165.2.w.a.73.2	yes	96	3.2	odd	2
165.2.w.a.118.11	yes	96	33.8	even	10
495.2.bj.c.73.11		96	1.1	even	1	trivial
495.2.bj.c.118.2		96	11.8	odd	10	inner
495.2.bj.c.172.2		96	5.2	odd	4	inner
495.2.bj.c.217.11		96	55.52	even	20	inner
825.2.cw.b.7.2		96	15.8	even	4
825.2.cw.b.118.2		96	165.74	even	10
825.2.cw.b.382.11		96	165.8	odd	20
825.2.cw.b.568.11		96	15.14	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.338930 + 2.13992i) q^{2} +(-2.56227 + 0.832532i) q^{4} +(1.49161 + 1.66586i) q^{5} +(-0.392386 + 0.770101i) q^{7} +(-0.682757 - 1.33999i) q^{8} +O(q^{10})\)	\(q+(0.338930 + 2.13992i) q^{2} +(-2.56227 + 0.832532i) q^{4} +(1.49161 + 1.66586i) q^{5} +(-0.392386 + 0.770101i) q^{7} +(-0.682757 - 1.33999i) q^{8} +(-3.05926 + 3.75654i) q^{10} +(2.59884 + 2.06059i) q^{11} +(3.81380 - 0.604046i) q^{13} +(-1.78095 - 0.578664i) q^{14} +(-1.72314 + 1.25193i) q^{16} +(-4.74922 - 0.752203i) q^{17} +(0.838408 - 2.58036i) q^{19} +(-5.20879 - 3.02658i) q^{20} +(-3.52868 + 6.25970i) q^{22} +(-4.79338 - 4.79338i) q^{23} +(-0.550202 + 4.96964i) q^{25} +(2.58522 + 7.95649i) q^{26} +(0.364266 - 2.29988i) q^{28} +(1.50081 + 4.61903i) q^{29} +(0.834544 + 0.606332i) q^{31} +(-5.38990 - 5.38990i) q^{32} -10.4179i q^{34} +(-1.86817 + 0.495028i) q^{35} +(-3.87086 - 1.97230i) q^{37} +(5.80592 + 0.919567i) q^{38} +(1.21383 - 3.13612i) q^{40} +(-3.96986 - 1.28989i) q^{41} +(7.22637 - 7.22637i) q^{43} +(-8.37444 - 3.11618i) q^{44} +(8.63283 - 11.8821i) q^{46} +(3.41765 + 6.70751i) q^{47} +(3.67541 + 5.05877i) q^{49} +(-10.8211 + 0.506971i) q^{50} +(-9.26910 + 4.72284i) q^{52} +(-1.02442 - 6.46794i) q^{53} +(0.443785 + 7.40291i) q^{55} +1.29983 q^{56} +(-9.37568 + 4.77715i) q^{58} +(7.48114 - 2.43077i) q^{59} +(0.304083 + 0.418534i) q^{61} +(-1.01465 + 1.99136i) q^{62} +(7.20329 - 9.91448i) q^{64} +(6.69495 + 5.45226i) q^{65} +(-4.30527 + 4.30527i) q^{67} +(12.7950 - 2.02653i) q^{68} +(-1.69250 - 3.82995i) q^{70} +(13.0228 - 9.46160i) q^{71} +(1.91331 + 0.974881i) q^{73} +(2.90862 - 8.95180i) q^{74} +7.30957i q^{76} +(-2.60661 + 1.19282i) q^{77} +(3.33797 + 2.42518i) q^{79} +(-4.65580 - 1.00312i) q^{80} +(1.41475 - 8.93237i) q^{82} +(2.13082 - 13.4534i) q^{83} +(-5.83092 - 9.03355i) q^{85} +(17.9131 + 13.0146i) q^{86} +(0.986791 - 4.88929i) q^{88} +4.64987i q^{89} +(-1.03130 + 3.17403i) q^{91} +(16.2726 + 8.29130i) q^{92} +(-13.1952 + 9.58687i) q^{94} +(5.54910 - 2.45221i) q^{95} +(9.04989 - 1.43336i) q^{97} +(-9.57965 + 9.57965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) \) 96 * q + 8 * q^5 - 20 * q^7	\( 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more