LMFDB - Embedded newform 1274.2.m.f.491.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-2,10,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.10
Root			$3.16760i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.f.589.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(1.58380 + 2.74322i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.36560i q^{5} +(2.74322 + 1.58380i) q^{6} -1.00000i q^{8} +(-3.51684 + 6.09135i) q^{9} +(1.68280 + 2.91470i) q^{10} +(1.85380 - 1.07029i) q^{11} +3.16760 q^{12} +(1.39219 + 3.32593i) q^{13} +(-9.23259 + 5.33044i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.38022 - 4.12266i) q^{17} +7.03369i q^{18} +(-0.852891 - 0.492417i) q^{19} +(2.91470 + 1.68280i) q^{20} +(1.07029 - 1.85380i) q^{22} +(-1.59384 - 2.76062i) q^{23} +(2.74322 - 1.58380i) q^{24} -6.32727 q^{25} +(2.86864 + 2.18424i) q^{26} -12.7771 q^{27} +(-2.13687 - 3.70117i) q^{29} +(-5.33044 + 9.23259i) q^{30} -0.825595i q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.87211 + 3.39026i) q^{33} -4.76044i q^{34} +(3.51684 + 6.09135i) q^{36} +(7.47646 - 4.31654i) q^{37} -0.984833 q^{38} +(-6.91880 + 9.08670i) q^{39} +3.36560 q^{40} +(-2.86076 + 1.65166i) q^{41} +(-2.74451 + 4.75362i) q^{43} -2.14059i q^{44} +(-20.5011 - 11.8363i) q^{45} +(-2.76062 - 1.59384i) q^{46} -4.02219i q^{47} +(1.58380 - 2.74322i) q^{48} +(-5.47958 + 3.16364i) q^{50} +15.0792 q^{51} +(3.57644 + 0.457288i) q^{52} +13.0781 q^{53} +(-11.0653 + 6.38856i) q^{54} +(3.60218 + 6.23916i) q^{55} -3.11956i q^{57} +(-3.70117 - 2.13687i) q^{58} +(3.09394 + 1.78629i) q^{59} +10.6609i q^{60} +(-2.03816 + 3.53019i) q^{61} +(-0.412798 - 0.714987i) q^{62} -1.00000 q^{64} +(-11.1937 + 4.68557i) q^{65} +6.78052 q^{66} +(0.319284 - 0.184338i) q^{67} +(-2.38022 - 4.12266i) q^{68} +(5.04865 - 8.74453i) q^{69} +(-0.525851 - 0.303600i) q^{71} +(6.09135 + 3.51684i) q^{72} -6.45285i q^{73} +(4.31654 - 7.47646i) q^{74} +(-10.0211 - 17.3571i) q^{75} +(-0.852891 + 0.492417i) q^{76} +(-1.44850 + 11.3287i) q^{78} -9.83378 q^{79} +(2.91470 - 1.68280i) q^{80} +(-9.68586 - 16.7764i) q^{81} +(-1.65166 + 2.86076i) q^{82} +10.7180i q^{83} +(13.8752 + 8.01087i) q^{85} +5.48901i q^{86} +(6.76875 - 11.7238i) q^{87} +(-1.07029 - 1.85380i) q^{88} +(-4.30275 + 2.48419i) q^{89} -23.6726 q^{90} -3.18768 q^{92} +(2.26479 - 1.30758i) q^{93} +(-2.01109 - 3.48332i) q^{94} +(1.65728 - 2.87049i) q^{95} -3.16760i q^{96} +(-10.0273 - 5.78928i) q^{97} +15.0562i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 10 q^{4} - 16 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{19} + 2 q^{22} - 36 q^{25} + 28 q^{27} + 2 q^{29} - 2 q^{30} + 12 q^{33} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) $ 20 * q - 2 * q^3 + 10 * q^4 - 16 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^19 + 2 * q^22 - 36 * q^25 + 28 * q^27 + 2 * q^29 - 2 * q^30 + 12 * q^33 + 16 * q^36 + 36 * q^37 - 28 * q^38 + 4 * q^39 + 8 * q^40 - 18 * q^41 + 8 * q^43 - 60 * q^45 - 12 * q^46 - 2 * q^48 - 12 * q^50 + 44 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 2 * q^55 + 24 * q^58 + 4 * q^61 + 24 * q^62 - 20 * q^64 + 24 * q^65 + 64 * q^66 + 60 * q^67 - 10 * q^68 + 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 + 16 * q^82 - 12 * q^85 + 64 * q^87 - 2 * q^88 - 18 * q^89 - 52 * q^90 - 60 * q^93 - 16 * q^94 - 12 * q^95 - 78 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.58380	+	2.74322i	0.914407	+	1.58380i	0.807767	+	0.589502i	$0.200676\pi$
$3$	1.58380	+	2.74322i	0.914407	+	1.58380i	0.106641	+	0.994298i	$0.465991\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			3.36560i			1.50514i	0.658511	+	0.752571i	$0.271187\pi$
$5$			3.36560i			1.50514i	−0.658511	+	0.752571i	$0.728813\pi$
$6$	2.74322	+	1.58380i	1.11992	+	0.646584i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−3.51684	+	6.09135i	−1.17228	+	2.03045i
$10$	1.68280	+	2.91470i	0.532148	+	0.921708i
$11$	1.85380	−	1.07029i	0.558943	−	0.322706i	−0.193778	−	0.981045i	$-0.562074\pi$
$11$	1.85380	−	1.07029i	0.558943	−	0.322706i	0.752721	+	0.658340i	$0.228741\pi$
$12$	3.16760			0.914407
$13$	1.39219	+	3.32593i	0.386125	+	0.922446i
$13$	1.39219	+	3.32593i	0.386125	+	0.922446i
$14$		0			0
$15$	−9.23259	+	5.33044i	−2.38385	+	1.37631i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.38022	−	4.12266i	0.577288	−	0.999892i	−0.418501	−	0.908216i	$-0.637444\pi$
$17$	2.38022	−	4.12266i	0.577288	−	0.999892i	0.995789	−	0.0916759i	$-0.0292224\pi$
$18$			7.03369i			1.65786i
$19$	−0.852891	−	0.492417i	−0.195667	−	0.112968i	0.398966	−	0.916966i	$-0.369369\pi$
$19$	−0.852891	−	0.492417i	−0.195667	−	0.112968i	−0.594633	+	0.803998i	$0.702702\pi$
$20$	2.91470	+	1.68280i	0.651746	+	0.376286i
$21$		0			0
$22$	1.07029	−	1.85380i	0.228187	−	0.395232i
$23$	−1.59384	−	2.76062i	−0.332339	−	0.575628i	0.650631	−	0.759394i	$-0.274505\pi$
$23$	−1.59384	−	2.76062i	−0.332339	−	0.575628i	−0.982970	+	0.183766i	$0.941171\pi$
$24$	2.74322	−	1.58380i	0.559958	−	0.323292i
$25$	−6.32727			−1.26545
$26$	2.86864	+	2.18424i	0.562587	+	0.428365i
$27$	−12.7771			−2.45896
$28$		0			0
$29$	−2.13687	−	3.70117i	−0.396807	−	0.687290i	0.596523	−	0.802596i	$-0.296548\pi$
$29$	−2.13687	−	3.70117i	−0.396807	−	0.687290i	−0.993330	+	0.115306i	$0.963215\pi$
$30$	−5.33044	+	9.23259i	−0.973201	+	1.68563i
$31$		−	0.825595i		−	0.148281i	−0.997248	−	0.0741407i	$-0.976379\pi$
$31$		−	0.825595i		−	0.148281i	0.997248	−	0.0741407i	$-0.0236214\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.87211	+	3.39026i	1.02220	+	0.590169i
$34$		−	4.76044i		−	0.816409i
$35$		0			0
$36$	3.51684	+	6.09135i	0.586141	+	1.01523i
$37$	7.47646	−	4.31654i	1.22912	−	0.709635i	0.262277	−	0.964993i	$-0.415527\pi$
$37$	7.47646	−	4.31654i	1.22912	−	0.709635i	0.966847	+	0.255358i	$0.0821934\pi$
$38$	−0.984833			−0.159761
$39$	−6.91880	+	9.08670i	−1.10789	+	1.45504i
$40$	3.36560			0.532148
$41$	−2.86076	+	1.65166i	−0.446776	+	0.257946i	−0.706468	−	0.707745i	$-0.749712\pi$
$41$	−2.86076	+	1.65166i	−0.446776	+	0.257946i	0.259692	+	0.965692i	$0.416379\pi$
$42$		0			0
$43$	−2.74451	+	4.75362i	−0.418533	+	0.724921i	−0.995792	−	0.0916402i	$-0.970789\pi$
$43$	−2.74451	+	4.75362i	−0.418533	+	0.724921i	0.577259	+	0.816561i	$0.304122\pi$
$44$		−	2.14059i		−	0.322706i
$45$	−20.5011	−	11.8363i	−3.05612	−	1.76445i
$46$	−2.76062	−	1.59384i	−0.407031	−	0.234999i
$47$		−	4.02219i		−	0.586696i	−0.956006	−	0.293348i	$-0.905231\pi$
$47$		−	4.02219i		−	0.586696i	0.956006	−	0.293348i	$-0.0947695\pi$
$48$	1.58380	−	2.74322i	0.228602	−	0.395950i
$49$		0			0
$50$	−5.47958	+	3.16364i	−0.774930	+	0.447406i
$51$	15.0792			2.11151
$52$	3.57644	+	0.457288i	0.495962	+	0.0634144i
$53$	13.0781			1.79642			0.898210	−	0.439567i	$-0.144868\pi$
$53$	13.0781			1.79642			0.898210	+	0.439567i	$0.144868\pi$
$54$	−11.0653	+	6.38856i	−1.50580	+	0.869372i
$55$	3.60218	+	6.23916i	0.485718	+	0.841289i
$56$		0			0
$57$		−	3.11956i		−	0.413196i
$58$	−3.70117	−	2.13687i	−0.485987	−	0.280585i
$59$	3.09394	+	1.78629i	0.402796	+	0.232555i	0.687690	−	0.726005i	$-0.258625\pi$
$59$	3.09394	+	1.78629i	0.402796	+	0.232555i	−0.284893	+	0.958559i	$0.591958\pi$
$60$			10.6609i			1.37631i
$61$	−2.03816	+	3.53019i	−0.260959	+	0.451995i	−0.966497	−	0.256678i	$-0.917372\pi$
$61$	−2.03816	+	3.53019i	−0.260959	+	0.451995i	0.705538	+	0.708672i	$0.250705\pi$
$62$	−0.412798	−	0.714987i	−0.0524254	−	0.0908034i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−11.1937	+	4.68557i	−1.38841	+	0.581174i
$66$	6.78052			0.834625
$67$	0.319284	−	0.184338i	0.0390067	−	0.0225205i	−0.480370	−	0.877066i	$-0.659498\pi$
$67$	0.319284	−	0.184338i	0.0390067	−	0.0225205i	0.519377	+	0.854545i	$0.326164\pi$
$68$	−2.38022	−	4.12266i	−0.288644	−	0.499946i
$69$	5.04865	−	8.74453i	0.607787	−	1.05272i
$70$		0			0
$71$	−0.525851	−	0.303600i	−0.0624070	−	0.0360307i	0.468472	−	0.883478i	$-0.344805\pi$
$71$	−0.525851	−	0.303600i	−0.0624070	−	0.0360307i	−0.530879	+	0.847448i	$0.678138\pi$
$72$	6.09135	+	3.51684i	0.717873	+	0.414464i
$73$		−	6.45285i		−	0.755248i	−0.925959	−	0.377624i	$-0.876741\pi$
$73$		−	6.45285i		−	0.755248i	0.925959	−	0.377624i	$-0.123259\pi$
$74$	4.31654	−	7.47646i	0.501787	−	0.869121i
$75$	−10.0211	−	17.3571i	−1.15714	−	2.00423i
$76$	−0.852891	+	0.492417i	−0.0978333	+	0.0564841i
$77$		0			0
$78$	−1.44850	+	11.3287i	−0.164011	+	1.28272i
$79$	−9.83378			−1.10639			−0.553193	−	0.833053i	$-0.686591\pi$
$79$	−9.83378			−1.10639			−0.553193	+	0.833053i	$0.686591\pi$
$80$	2.91470	−	1.68280i	0.325873	−	0.188143i
$81$	−9.68586	−	16.7764i	−1.07621	−	1.86404i
$82$	−1.65166	+	2.86076i	−0.182396	+	0.315918i
$83$			10.7180i			1.17646i	0.808694	+	0.588229i	$0.200175\pi$
$83$			10.7180i			1.17646i	−0.808694	+	0.588229i	$0.799825\pi$
$84$		0			0
$85$	13.8752	+	8.01087i	1.50498	+	0.868901i
$86$			5.48901i			0.591895i
$87$	6.76875	−	11.7238i	0.725686	−	1.25693i
$88$	−1.07029	−	1.85380i	−0.114094	−	0.197616i
$89$	−4.30275	+	2.48419i	−0.456090	+	0.263324i	−0.710399	−	0.703799i	$-0.751485\pi$
$89$	−4.30275	+	2.48419i	−0.456090	+	0.263324i	0.254309	+	0.967123i	$0.418152\pi$
$90$	−23.6726			−2.49531
$91$		0			0
$92$	−3.18768			−0.332339
$93$	2.26479	−	1.30758i	0.234848	−	0.135590i
$94$	−2.01109	−	3.48332i	−0.207428	−	0.359277i
$95$	1.65728	−	2.87049i	0.170033	−	0.294506i
$96$		−	3.16760i		−	0.323292i
$97$	−10.0273	−	5.78928i	−1.01812	−	0.587812i	−0.104562	−	0.994518i	$-0.533344\pi$
$97$	−10.0273	−	5.78928i	−1.01812	−	0.587812i	−0.913559	+	0.406706i	$0.866677\pi$
$98$		0			0
$99$			15.0562i			1.51321i
$100$	−3.16364	+	5.47958i	−0.316364	+	0.547958i
$101$	3.09598	+	5.36239i	0.308061	+	0.533578i	0.977938	−	0.208894i	$-0.0669865\pi$
$101$	3.09598	+	5.36239i	0.308061	+	0.533578i	−0.669877	+	0.742472i	$0.733653\pi$
$102$	13.0589	−	7.53958i	1.29303	−	0.746530i
$103$	3.30691			0.325839			0.162920	−	0.986639i	$-0.447909\pi$
$103$	3.30691			0.325839			0.162920	+	0.986639i	$0.447909\pi$
$104$	3.32593	−	1.39219i	0.326134	−	0.136516i
$105$		0			0
$106$	11.3260	−	6.53907i	1.10008	−	0.635130i
$107$	5.09798	+	8.82996i	0.492840	+	0.853625i	0.999966	−	0.00824751i	$-0.00262529\pi$
$107$	5.09798	+	8.82996i	0.492840	+	0.853625i	−0.507126	+	0.861872i	$0.669292\pi$
$108$	−6.38856	+	11.0653i	−0.614739	+	1.06476i
$109$		−	7.46908i		−	0.715408i	−0.933835	−	0.357704i	$-0.883560\pi$
$109$		−	7.46908i		−	0.715408i	0.933835	−	0.357704i	$-0.116440\pi$
$110$	6.23916	+	3.60218i	0.594881	+	0.343455i
$111$	23.6824	+	13.6731i	2.24784	+	1.29779i
$112$		0			0
$113$	1.05003	−	1.81870i	0.0987784	−	0.171089i	−0.812401	−	0.583099i	$-0.801840\pi$
$113$	1.05003	−	1.81870i	0.0987784	−	0.171089i	0.911179	+	0.412010i	$0.135173\pi$
$114$	−1.55978	−	2.70162i	−0.146087	−	0.253030i
$115$	9.29113	−	5.36424i	0.866403	−	0.500218i
$116$	−4.27374			−0.396807
$117$	−25.1555	−	3.21642i	−2.32563	−	0.297358i
$118$	3.57257			0.328882
$119$		0			0
$120$	5.33044	+	9.23259i	0.486600	+	0.842817i
$121$	−3.20894	+	5.55805i	−0.291722	+	0.505277i
$122$			4.07631i			0.369052i
$123$	−9.06175	−	5.23181i	−0.817071	−	0.471736i
$124$	−0.714987	−	0.412798i	−0.0642077	−	0.0370703i
$125$		−	4.46708i		−	0.399548i
$126$		0			0
$127$	−2.09804	−	3.63391i	−0.186171	−	0.322458i	0.757800	−	0.652487i	$-0.226275\pi$
$127$	−2.09804	−	3.63391i	−0.186171	−	0.322458i	−0.943970	+	0.330030i	$0.892941\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−17.3870			−1.53084
$130$	−7.35128	+	9.65470i	−0.644750	+	0.846773i
$131$	10.3960			0.908303			0.454152	−	0.890924i	$-0.349942\pi$
$131$	10.3960			0.908303			0.454152	+	0.890924i	$0.349942\pi$
$132$	5.87211	−	3.39026i	0.511101	−	0.295084i
$133$		0			0
$134$	0.184338	−	0.319284i	0.0159244	−	0.0275819i
$135$		−	43.0027i		−	3.70108i
$136$	−4.12266	−	2.38022i	−0.353515	−	0.204102i
$137$	8.90891	+	5.14356i	0.761140	+	0.439444i	0.829705	−	0.558202i	$-0.188509\pi$
$137$	8.90891	+	5.14356i	0.761140	+	0.439444i	−0.0685651	+	0.997647i	$0.521842\pi$
$138$		−	10.0973i		−	0.859540i
$139$	5.72470	−	9.91547i	0.485563	−	0.841019i	−0.514300	−	0.857611i	$-0.671948\pi$
$139$	5.72470	−	9.91547i	0.485563	−	0.841019i	0.999862	+	0.0165912i	$0.00528138\pi$
$140$		0			0
$141$	11.0337	−	6.37034i	0.929209	−	0.536479i
$142$	−0.607200			−0.0509551
$143$	6.14057	+	4.67556i	0.513501	+	0.390990i
$144$	7.03369			0.586141
$145$	12.4567	−	7.19186i	1.03447	−	0.597251i
$146$	−3.22642	−	5.58833i	−0.267021	−	0.462493i
$147$		0			0
$148$		−	8.63308i		−	0.709635i
$149$	−15.0887	−	8.71148i	−1.23612	−	0.713672i	−0.267818	−	0.963470i	$-0.586303\pi$
$149$	−15.0887	−	8.71148i	−1.23612	−	0.713672i	−0.968298	+	0.249798i	$0.919636\pi$
$150$	−17.3571	−	10.0211i	−1.41720	−	0.818222i
$151$		−	12.9755i		−	1.05593i	−0.849267	−	0.527964i	$-0.822956\pi$
$151$		−	12.9755i		−	1.05593i	0.849267	−	0.527964i	$-0.177044\pi$
$152$	−0.492417	+	0.852891i	−0.0399403	+	0.0691786i
$153$	16.7417	+	28.9975i	1.35349	+	2.34431i
$154$		0			0
$155$	2.77863			0.223185
$156$	4.40992	+	10.5352i	0.353076	+	0.843492i
$157$	24.3865			1.94625			0.973127	−	0.230267i	$-0.0739601\pi$
$157$	24.3865			1.94625			0.973127	+	0.230267i	$0.0739601\pi$
$158$	−8.51630	+	4.91689i	−0.677521	+	0.391167i
$159$	20.7131	+	35.8762i	1.64266	+	2.84517i
$160$	1.68280	−	2.91470i	0.133037	−	0.230427i
$161$		0			0
$162$	−16.7764	−	9.68586i	−1.31808	−	0.760993i
$163$	−11.5032	−	6.64137i	−0.900999	−	0.520192i	−0.0234749	−	0.999724i	$-0.507473\pi$
$163$	−11.5032	−	6.64137i	−0.900999	−	0.520192i	−0.877524	+	0.479532i	$0.840806\pi$
$164$			3.30333i			0.257946i
$165$	−11.4103	+	19.7632i	−0.888288	+	1.53856i
$166$	5.35902	+	9.28210i	0.415941	+	0.720430i
$167$	−15.4031	+	8.89300i	−1.19193	+	0.688161i	−0.958744	−	0.284271i	$-0.908248\pi$
$167$	−15.4031	+	8.89300i	−1.19193	+	0.688161i	−0.233186	+	0.972432i	$0.574915\pi$
$168$		0			0
$169$	−9.12359	+	9.26068i	−0.701814	+	0.712360i
$170$	16.0217			1.22881
$171$	5.99897	−	3.46351i	0.458753	−	0.264861i
$172$	2.74451	+	4.75362i	0.209267	+	0.362460i
$173$	−2.94124	+	5.09437i	−0.223618	+	0.387318i	−0.955904	−	0.293680i	$-0.905120\pi$
$173$	−2.94124	+	5.09437i	−0.223618	+	0.387318i	0.732286	+	0.680997i	$0.238453\pi$
$174$		−	13.5375i		−	1.02628i
$175$		0			0
$176$	−1.85380	−	1.07029i	−0.139736	−	0.0806764i
$177$			11.3165i			0.850598i
$178$	−2.48419	+	4.30275i	−0.186198	+	0.322505i
$179$	4.94561	+	8.56604i	0.369652	+	0.640256i	0.989511	−	0.144457i	$-0.0461435\pi$
$179$	4.94561	+	8.56604i	0.369652	+	0.640256i	−0.619859	+	0.784713i	$0.712810\pi$
$180$	−20.5011	+	11.8363i	−1.52806	+	0.882226i
$181$	19.7017			1.46442			0.732209	−	0.681080i	$-0.238489\pi$
$181$	19.7017			1.46442			0.732209	+	0.681080i	$0.238489\pi$
$182$		0			0
$183$	−12.9121			−0.954492
$184$	−2.76062	+	1.59384i	−0.203515	+	0.117500i
$185$	14.5278	+	25.1628i	1.06810	+	1.85001i
$186$	1.30758	−	2.26479i	0.0958763	−	0.166063i
$187$		−	10.1901i		−	0.745177i
$188$	−3.48332	−	2.01109i	−0.254047	−	0.146674i
$189$		0			0
$190$		−	3.31456i		−	0.240463i
$191$	−8.08740	+	14.0078i	−0.585184	+	1.01357i	0.409669	+	0.912234i	$0.365644\pi$
$191$	−8.08740	+	14.0078i	−0.585184	+	1.01357i	−0.994852	+	0.101334i	$0.967689\pi$
$192$	−1.58380	−	2.74322i	−0.114301	−	0.197975i
$193$	12.5167	−	7.22652i	0.900972	−	0.520176i	0.0234565	−	0.999725i	$-0.492533\pi$
$193$	12.5167	−	7.22652i	0.900972	−	0.520176i	0.877515	+	0.479549i	$0.159200\pi$
$194$	−11.5786			−0.831292
$195$	−30.5822	−	23.2859i	−2.19004	−	1.66754i
$196$		0			0
$197$	16.4684	−	9.50802i	1.17332	−	0.677419i	0.218863	−	0.975756i	$-0.429765\pi$
$197$	16.4684	−	9.50802i	1.17332	−	0.677419i	0.954461	+	0.298337i	$0.0964319\pi$
$198$	7.52811	+	13.0391i	0.535000	+	0.926647i
$199$	0.812870	−	1.40793i	0.0576228	−	0.0998056i	−0.835775	−	0.549072i	$-0.814981\pi$
$199$	0.812870	−	1.40793i	0.0576228	−	0.0998056i	0.893398	+	0.449266i	$0.148315\pi$
$200$			6.32727i			0.447406i
$201$	1.01136	+	0.583911i	0.0713360	+	0.0411859i
$202$	5.36239	+	3.09598i	0.377296	+	0.217832i
$203$		0			0
$204$	7.53958	−	13.0589i	0.527876	−	0.914309i
$205$	−5.55884	−	9.62819i	−0.388246	−	0.672462i
$206$	2.86387	−	1.65345i	0.199535	−	0.115202i
$207$	22.4212			1.55838
$208$	2.18424	−	2.86864i	0.151450	−	0.198904i
$209$	−2.10812			−0.145822
$210$		0			0
$211$	−9.03133	−	15.6427i	−0.621742	−	1.07689i	−0.989161	−	0.146834i	$-0.953092\pi$
$211$	−9.03133	−	15.6427i	−0.621742	−	1.07689i	0.367419	−	0.930056i	$-0.380242\pi$
$212$	6.53907	−	11.3260i	0.449105	−	0.777872i
$213$		−	1.92337i		−	0.131787i
$214$	8.82996	+	5.09798i	0.603604	+	0.348491i
$215$	−15.9988	−	9.23692i	−1.09111	−	0.629952i
$216$			12.7771i			0.869372i
$217$		0			0
$218$	−3.73454	−	6.46841i	−0.252935	−	0.438096i
$219$	17.7016	−	10.2200i	1.19616	−	0.690605i
$220$	7.20436			0.485718
$221$	17.0254	+	2.17689i	1.14525	+	0.146434i
$222$	27.3461			1.83535
$223$	20.8994	−	12.0663i	1.39953	−	0.808017i	0.405184	−	0.914235i	$-0.367207\pi$
$223$	20.8994	−	12.0663i	1.39953	−	0.808017i	0.994343	+	0.106218i	$0.0338740\pi$
$224$		0			0
$225$	22.2520	−	38.5417i	1.48347	−	2.56944i
$226$		−	2.10006i		−	0.139694i
$227$	−7.87201	−	4.54491i	−0.522484	−	0.301656i	0.215467	−	0.976511i	$-0.430873\pi$
$227$	−7.87201	−	4.54491i	−0.522484	−	0.301656i	−0.737950	+	0.674855i	$0.764206\pi$
$228$	−2.70162	−	1.55978i	−0.178919	−	0.103299i
$229$			6.33642i			0.418722i	0.977838	+	0.209361i	$0.0671384\pi$
$229$			6.33642i			0.418722i	−0.977838	+	0.209361i	$0.932862\pi$
$230$	5.36424	−	9.29113i	0.353707	−	0.612639i
$231$		0			0
$232$	−3.70117	+	2.13687i	−0.242994	+	0.140292i
$233$	17.1230			1.12177			0.560883	−	0.827895i	$-0.310462\pi$
$233$	17.1230			1.12177			0.560883	+	0.827895i	$0.310462\pi$
$234$	−23.3935	+	9.79226i	−1.52928	+	0.640140i
$235$	13.5371			0.883062
$236$	3.09394	−	1.78629i	0.201398	−	0.116277i
$237$	−15.5747	−	26.9762i	−1.01169	−	1.75229i
$238$		0			0
$239$		−	18.3950i		−	1.18987i	−0.803772	−	0.594937i	$-0.797177\pi$
$239$		−	18.3950i		−	1.18987i	0.803772	−	0.594937i	$-0.202823\pi$
$240$	9.23259	+	5.33044i	0.595961	+	0.344078i
$241$	−14.2664	−	8.23670i	−0.918979	−	0.530573i	−0.0356697	−	0.999364i	$-0.511356\pi$
$241$	−14.2664	−	8.23670i	−0.918979	−	0.530573i	−0.883309	+	0.468791i	$0.844690\pi$
$242$			6.41789i			0.412557i
$243$	11.5153	−	19.9450i	0.738704	−	1.27947i
$244$	2.03816	+	3.53019i	0.130480	+	0.225997i
$245$		0			0
$246$	−10.4636			−0.667136
$247$	0.450352	−	3.52219i	0.0286552	−	0.224112i
$248$	−0.825595			−0.0524254
$249$	−29.4020	+	16.9752i	−1.86327	+	1.07576i
$250$	−2.23354	−	3.86860i	−0.141261	−	0.244672i
$251$	11.3118	−	19.5926i	0.713993	−	1.23667i	−0.249354	−	0.968412i	$-0.580218\pi$
$251$	11.3118	−	19.5926i	0.713993	−	1.23667i	0.963347	−	0.268259i	$-0.0864484\pi$
$252$		0			0
$253$	−5.90934	−	3.41176i	−0.371517	−	0.214495i
$254$	−3.63391	−	2.09804i	−0.228012	−	0.131643i
$255$			50.7505i			3.17812i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.10320	+	8.83901i	0.318329	+	0.551362i	0.980140	−	0.198309i	$-0.0635450\pi$
$257$	5.10320	+	8.83901i	0.318329	+	0.551362i	−0.661811	+	0.749671i	$0.730212\pi$
$258$	−15.0576	+	8.69350i	−0.937444	+	0.541234i
$259$		0			0
$260$	−1.53905	+	12.0369i	−0.0954478	+	0.746494i
$261$	30.0602			1.86068
$262$	9.00321	−	5.19800i	0.556220	−	0.321134i
$263$	−8.96671	−	15.5308i	−0.552911	−	0.957670i	−0.998063	−	0.0622150i	$-0.980184\pi$
$263$	−8.96671	−	15.5308i	−0.552911	−	0.957670i	0.445152	−	0.895455i	$-0.353150\pi$
$264$	3.39026	−	5.87211i	0.208656	−	0.361403i
$265$			44.0158i			2.70387i
$266$		0			0
$267$	−13.6294	−	7.86893i	−0.834105	−	0.481571i
$268$		−	0.368677i		−	0.0225205i
$269$	−14.5400	+	25.1841i	−0.886522	+	1.53550i	−0.0425633	+	0.999094i	$0.513552\pi$
$269$	−14.5400	+	25.1841i	−0.886522	+	1.53550i	−0.843959	+	0.536408i	$0.819781\pi$
$270$	−21.5013	−	37.2414i	−1.30853	−	2.26644i
$271$	−4.79671	+	2.76938i	−0.291379	+	0.168228i	−0.638564	−	0.769569i	$-0.720471\pi$
$271$	−4.79671	+	2.76938i	−0.291379	+	0.168228i	0.347184	+	0.937797i	$0.387138\pi$
$272$	−4.76044			−0.288644
$273$		0			0
$274$	10.2871			0.621468
$275$	−11.7295	+	6.77204i	−0.707317	+	0.408370i
$276$	−5.04865	−	8.74453i	−0.303893	−	0.526359i
$277$	−1.53567	+	2.65986i	−0.0922696	+	0.159816i	−0.908466	−	0.417959i	$-0.862745\pi$
$277$	−1.53567	+	2.65986i	−0.0922696	+	0.159816i	0.816196	+	0.577775i	$0.196079\pi$
$278$		−	11.4494i		−	0.686689i
$279$	5.02899	+	2.90349i	0.301078	+	0.173827i
$280$		0			0
$281$			28.7901i			1.71747i	0.512419	+	0.858735i	$0.328749\pi$
$281$			28.7901i			1.71747i	−0.512419	+	0.858735i	$0.671251\pi$
$282$	6.37034	−	11.0337i	0.379348	−	0.657050i
$283$	0.146547	+	0.253827i	0.00871132	+	0.0150885i	0.870348	−	0.492437i	$-0.163894\pi$
$283$	0.146547	+	0.253827i	0.00871132	+	0.0150885i	−0.861637	+	0.507525i	$0.830560\pi$
$284$	−0.525851	+	0.303600i	−0.0312035	+	0.0180154i
$285$	10.4992			0.621918
$286$	7.65567	+	0.978865i	0.452689	+	0.0578815i
$287$		0			0
$288$	6.09135	−	3.51684i	0.358936	−	0.207232i
$289$	−2.83089	−	4.90325i	−0.166523	−	0.288427i
$290$	7.19186	−	12.4567i	0.422320	−	0.731480i
$291$		−	36.6762i		−	2.15000i
$292$	−5.58833	−	3.22642i	−0.327032	−	0.188812i
$293$	−20.3451	−	11.7463i	−1.18857	−	0.686223i	−0.230591	−	0.973051i	$-0.574066\pi$
$293$	−20.3451	−	11.7463i	−1.18857	−	0.686223i	−0.957982	+	0.286827i	$0.907399\pi$
$294$		0			0
$295$	−6.01193	+	10.4130i	−0.350028	+	0.606266i
$296$	−4.31654	−	7.47646i	−0.250894	−	0.434561i
$297$	−23.6863	+	13.6753i	−1.37442	+	0.793519i
$298$	−17.4230			−1.00928
$299$	6.96267	−	9.14432i	0.402662	−	0.528830i
$300$	−20.0423			−1.15714
$301$		0			0
$302$	−6.48773	−	11.2371i	−0.373327	−	0.646621i
$303$	−9.80681	+	16.9859i	−0.563387	+	0.975815i
$304$			0.984833i			0.0564841i
$305$	−11.8812	−	6.85962i	−0.680316	−	0.392781i
$306$	28.9975	+	16.7417i	1.65768	+	0.957061i
$307$			9.44232i			0.538902i	0.963014	+	0.269451i	$0.0868422\pi$
$307$			9.44232i			0.538902i	−0.963014	+	0.269451i	$0.913158\pi$
$308$		0			0
$309$	5.23748	+	9.07158i	0.297950	+	0.516064i
$310$	2.40636	−	1.38931i	0.136672	−	0.0789077i
$311$	5.49342			0.311503			0.155752	−	0.987796i	$-0.450220\pi$
$311$	5.49342			0.311503			0.155752	+	0.987796i	$0.450220\pi$
$312$	9.08670	+	6.91880i	0.514433	+	0.391700i
$313$	−11.1616			−0.630889			−0.315445	−	0.948944i	$-0.602154\pi$
$313$	−11.1616			−0.630889			−0.315445	+	0.948944i	$0.602154\pi$
$314$	21.1193	−	12.1933i	1.19183	−	0.688105i
$315$		0			0
$316$	−4.91689	+	8.51630i	−0.276597	+	0.479079i
$317$			2.47705i			0.139125i	0.997578	+	0.0695624i	$0.0221603\pi$
$317$			2.47705i			0.139125i	−0.997578	+	0.0695624i	$0.977840\pi$
$318$	35.8762	+	20.7131i	2.01184	+	1.16154i
$319$	−7.92268	−	4.57416i	−0.443585	−	0.256104i
$320$		−	3.36560i		−	0.188143i
$321$	−16.1484	+	27.9698i	−0.901314	+	1.56112i
$322$		0			0
$323$	−4.06013	+	2.34412i	−0.225912	+	0.130430i
$324$	−19.3717			−1.07621
$325$	−8.80880	−	21.0441i	−0.488624	−	1.16731i
$326$	−13.2827			−0.735663
$327$	20.4893	−	11.8295i	1.13306	−	0.654174i
$328$	1.65166	+	2.86076i	0.0911978	+	0.157959i
$329$		0			0
$330$			22.8205i			1.25623i
$331$	−15.9990	−	9.23702i	−0.879384	−	0.507713i	−0.00892890	−	0.999960i	$-0.502842\pi$
$331$	−15.9990	−	9.23702i	−0.879384	−	0.507713i	−0.870455	+	0.492247i	$0.836176\pi$
$332$	9.28210	+	5.35902i	0.509421	+	0.294114i
$333$			60.7224i			3.32757i
$334$	−8.89300	+	15.4031i	−0.486603	+	0.842822i
$335$	0.620410	+	1.07458i	0.0338966	+	0.0587107i
$336$		0			0
$337$	20.2662			1.10397			0.551984	−	0.833855i	$-0.313871\pi$
$337$	20.2662			1.10397			0.551984	+	0.833855i	$0.313871\pi$
$338$	−3.27092	+	12.5818i	−0.177915	+	0.684358i
$339$	6.65214			0.361295
$340$	13.8752	−	8.01087i	0.752490	−	0.434451i
$341$	−0.883630	−	1.53049i	−0.0478512	−	0.0828808i
$342$	3.46351	−	5.99897i	0.187285	−	0.324387i
$343$		0			0
$344$	4.75362	+	2.74451i	0.256298	+	0.147974i
$345$	29.4306	+	16.9918i	1.58449	+	0.914806i
$346$			5.88247i			0.316244i
$347$	−3.47239	+	6.01435i	−0.186408	+	0.322867i	−0.944050	−	0.329803i	$-0.893018\pi$
$347$	−3.47239	+	6.01435i	−0.186408	+	0.322867i	0.757642	+	0.652670i	$0.226351\pi$
$348$	−6.76875	−	11.7238i	−0.362843	−	0.628463i
$349$	−1.83312	+	1.05835i	−0.0981249	+	0.0566524i	−0.548259	−	0.836308i	$-0.684709\pi$
$349$	−1.83312	+	1.05835i	−0.0981249	+	0.0566524i	0.450135	+	0.892961i	$0.351376\pi$
$350$		0			0
$351$	−17.7882	−	42.4958i	−0.949465	−	2.26826i
$352$	−2.14059			−0.114094
$353$	−6.65507	+	3.84230i	−0.354213	+	0.204505i	−0.666539	−	0.745470i	$-0.732225\pi$
$353$	−6.65507	+	3.84230i	−0.354213	+	0.204505i	0.312326	+	0.949975i	$0.398892\pi$
$354$	5.65824	+	9.80036i	0.300732	+	0.520883i
$355$	1.02180	−	1.76980i	0.0542313	−	0.0939315i
$356$			4.96839i			0.263324i
$357$		0			0
$358$	8.56604	+	4.94561i	0.452730	+	0.261384i
$359$		−	9.39300i		−	0.495744i	−0.968793	−	0.247872i	$-0.920269\pi$
$359$		−	9.39300i		−	0.495744i	0.968793	−	0.247872i	$-0.0797312\pi$
$360$	−11.8363	+	20.5011i	−0.623828	+	1.08050i
$361$	−9.01505	−	15.6145i	−0.474476	−	0.821817i
$362$	17.0622	−	9.85087i	0.896769	−	0.517750i
$363$	−20.3293			−1.06701
$364$		0			0
$365$	21.7177			1.13676
$366$	−11.1822	+	6.45606i	−0.584505	+	0.337464i
$367$	−14.4340	−	25.0005i	−0.753450	−	1.30501i	−0.946141	−	0.323755i	$-0.895055\pi$
$367$	−14.4340	−	25.0005i	−0.753450	−	1.30501i	0.192691	−	0.981260i	$-0.438279\pi$
$368$	−1.59384	+	2.76062i	−0.0830848	+	0.143907i
$369$		−	23.2346i		−	1.20954i
$370$	25.1628	+	14.5278i	1.30815	+	0.755262i
$371$		0			0
$372$		−	2.61516i		−	0.135590i
$373$	10.8721	−	18.8310i	0.562934	−	0.975030i	−0.434305	−	0.900766i	$-0.643006\pi$
$373$	10.8721	−	18.8310i	0.562934	−	0.975030i	0.997239	−	0.0742642i	$-0.0236608\pi$
$374$	−5.09507	−	8.82492i	−0.263460	−	0.456326i
$375$	12.2542	−	7.07496i	0.632803	−	0.365349i
$376$	−4.02219			−0.207428
$377$	9.33488	−	12.2598i	0.480771	−	0.631413i
$378$		0			0
$379$	−30.6531	+	17.6976i	−1.57455	+	0.909065i	−0.578946	+	0.815366i	$0.696536\pi$
$379$	−30.6531	+	17.6976i	−1.57455	+	0.909065i	−0.995601	+	0.0936990i	$0.970131\pi$
$380$	−1.65728	−	2.87049i	−0.0850166	−	0.147253i
$381$	6.64575	−	11.5108i	0.340472	−	0.589715i
$382$			16.1748i			0.827575i
$383$	−6.73904	−	3.89078i	−0.344349	−	0.198810i	0.317845	−	0.948143i	$-0.397041\pi$
$383$	−6.73904	−	3.89078i	−0.344349	−	0.198810i	−0.662193	+	0.749333i	$0.730374\pi$
$384$	−2.74322	−	1.58380i	−0.139989	−	0.0808230i
$385$		0			0
$386$	7.22652	−	12.5167i	0.367820	−	0.637083i
$387$	−19.3040	−	33.4355i	−0.981278	−	1.69962i
$388$	−10.0273	+	5.78928i	−0.509060	+	0.293906i
$389$	8.74901			0.443592			0.221796	−	0.975093i	$-0.428808\pi$
$389$	8.74901			0.443592			0.221796	+	0.975093i	$0.428808\pi$
$390$	−38.1279	−	4.87509i	−1.93068	−	0.246860i
$391$	−15.1748			−0.767422
$392$		0			0
$393$	16.4652	+	28.5186i	0.830559	+	1.43857i
$394$	9.50802	−	16.4684i	0.479007	−	0.829665i
$395$		−	33.0966i		−	1.66527i
$396$	13.0391	+	7.52811i	0.655238	+	0.378302i
$397$	−24.9631	−	14.4124i	−1.25286	−	0.723340i	−0.281185	−	0.959654i	$-0.590727\pi$
$397$	−24.9631	−	14.4124i	−1.25286	−	0.723340i	−0.971677	+	0.236313i	$0.924061\pi$
$398$		−	1.62574i		−	0.0814909i
$399$		0			0
$400$	3.16364	+	5.47958i	0.158182	+	0.273979i
$401$	0.884338	−	0.510573i	0.0441618	−	0.0254968i	−0.477757	−	0.878492i	$-0.658550\pi$
$401$	0.884338	−	0.510573i	0.0441618	−	0.0254968i	0.521918	+	0.852995i	$0.325217\pi$
$402$	1.16782			0.0582456
$403$	2.74587	−	1.14939i	0.136782	−	0.0572552i
$404$	6.19195			0.308061
$405$	56.4627	−	32.5987i	2.80565	−	1.61984i
$406$		0			0
$407$	9.23993	−	16.0040i	0.458006	−	0.793290i
$408$		−	15.0792i		−	0.746530i
$409$	−10.8725	−	6.27726i	−0.537612	−	0.310391i	0.206498	−	0.978447i	$-0.433793\pi$
$409$	−10.8725	−	6.27726i	−0.537612	−	0.310391i	−0.744111	+	0.668056i	$0.767126\pi$
$410$	−9.62819	−	5.55884i	−0.475502	−	0.274531i
$411$			32.5855i			1.60732i
$412$	1.65345	−	2.86387i	0.0814598	−	0.141093i
$413$		0			0
$414$	19.4173	−	11.2106i	0.954309	−	0.550971i
$415$	−36.0727			−1.77074
$416$	0.457288	−	3.57644i	0.0224204	−	0.175349i
$417$	36.2671			1.77601
$418$	−1.82569	+	1.05406i	−0.0892973	+	0.0515558i
$419$	7.27959	+	12.6086i	0.355631	+	0.615971i	0.987226	−	0.159328i	$-0.0509326\pi$
$419$	7.27959	+	12.6086i	0.355631	+	0.615971i	−0.631595	+	0.775299i	$0.717599\pi$
$420$		0			0
$421$		−	15.5200i		−	0.756401i	−0.925724	−	0.378200i	$-0.876543\pi$
$421$		−	15.5200i		−	0.756401i	0.925724	−	0.378200i	$-0.123457\pi$
$422$	−15.6427	−	9.03133i	−0.761476	−	0.439638i
$423$	24.5006	+	14.1454i	1.19126	+	0.687773i
$424$		−	13.0781i		−	0.635130i
$425$	−15.0603	+	26.0852i	−0.730532	+	1.26532i
$426$	−0.961684	−	1.66568i	−0.0465937	−	0.0807027i
$427$		0			0
$428$	10.1960			0.492840
$429$	−3.10065	+	24.2501i	−0.149701	+	1.17081i
$430$	−18.4738			−0.890887
$431$	−3.70768	+	2.14063i	−0.178593	+	0.103111i	−0.586631	−	0.809854i	$-0.699546\pi$
$431$	−3.70768	+	2.14063i	−0.178593	+	0.103111i	0.408039	+	0.912965i	$0.366213\pi$
$432$	6.38856	+	11.0653i	0.307370	+	0.532380i
$433$	−11.9795	+	20.7491i	−0.575697	+	0.997137i	0.420268	+	0.907400i	$0.361936\pi$
$433$	−11.9795	+	20.7491i	−0.575697	+	0.997137i	−0.995966	+	0.0897368i	$0.971397\pi$
$434$		0			0
$435$	39.4577	+	22.7809i	1.89185	+	1.09226i
$436$	−6.46841	−	3.73454i	−0.309781	−	0.178852i
$437$			3.13934i			0.150175i
$438$	10.2200	−	17.7016i	0.488331	−	0.845815i
$439$	−13.3486	−	23.1204i	−0.637092	−	1.10348i	−0.986068	−	0.166344i	$-0.946804\pi$
$439$	−13.3486	−	23.1204i	−0.637092	−	1.10348i	0.348975	−	0.937132i	$-0.386530\pi$
$440$	6.23916	−	3.60218i	0.297440	−	0.171727i
$441$		0			0
$442$	15.8329	−	6.62746i	0.753093	−	0.315236i
$443$	17.1779			0.816145			0.408073	−	0.912950i	$-0.366201\pi$
$443$	17.1779			0.816145			0.408073	+	0.912950i	$0.366201\pi$
$444$	23.6824	−	13.6731i	1.12392	−	0.648895i
$445$	−8.36080	−	14.4813i	−0.396340	−	0.686481i
$446$	12.0663	−	20.8994i	0.571355	−	0.989615i
$447$		−	55.1889i		−	2.61035i
$448$		0			0
$449$	−9.05342	−	5.22699i	−0.427257	−	0.246677i	0.270920	−	0.962602i	$-0.412672\pi$
$449$	−9.05342	−	5.22699i	−0.427257	−	0.246677i	−0.698177	+	0.715925i	$0.746005\pi$
$450$		−	44.5041i		−	2.09794i
$451$	−3.53553	+	6.12371i	−0.166482	+	0.288354i
$452$	−1.05003	−	1.81870i	−0.0493892	−	0.0855446i
$453$	35.5946	−	20.5505i	1.67238	−	0.965548i
$454$	−9.08981			−0.426606
$455$		0			0
$456$	−3.11956			−0.146087
$457$	−8.99602	+	5.19386i	−0.420816	+	0.242958i	−0.695426	−	0.718597i	$-0.744784\pi$
$457$	−8.99602	+	5.19386i	−0.420816	+	0.242958i	0.274610	+	0.961556i	$0.411451\pi$
$458$	3.16821	+	5.48750i	0.148041	+	0.256414i
$459$	−30.4123	+	52.6757i	−1.41953	+	2.45869i
$460$		−	10.7285i		−	0.500218i
$461$	−6.01121	−	3.47058i	−0.279970	−	0.161641i	0.353440	−	0.935457i	$-0.385012\pi$
$461$	−6.01121	−	3.47058i	−0.279970	−	0.161641i	−0.633410	+	0.773816i	$0.718345\pi$
$462$		0			0
$463$		−	29.5056i		−	1.37124i	−0.727960	−	0.685620i	$-0.759531\pi$
$463$		−	29.5056i		−	1.37124i	0.727960	−	0.685620i	$-0.240469\pi$
$464$	−2.13687	+	3.70117i	−0.0992018	+	0.171822i
$465$	4.40079	+	7.62239i	0.204082	+	0.353480i
$466$	14.8290	−	8.56151i	0.686939	−	0.396604i
$467$	−32.5194			−1.50482			−0.752410	−	0.658695i	$-0.771109\pi$
$467$	−32.5194			−1.50482			−0.752410	+	0.658695i	$0.771109\pi$
$468$	−15.3633	+	20.1771i	−0.710167	+	0.932688i
$469$		0			0
$470$	11.7235	−	6.76854i	0.540763	−	0.312209i
$471$	38.6233	+	66.8976i	1.77967	+	3.08248i
$472$	1.78629	−	3.09394i	0.0822205	−	0.142410i
$473$			11.7497i			0.540252i
$474$	−26.9762	−	15.5747i	−1.23906	−	0.715371i
$475$	5.39647	+	3.11566i	0.247607	+	0.142956i
$476$		0			0
$477$	−45.9938	+	79.6635i	−2.10591	+	3.64754i
$478$	−9.19751	−	15.9306i	−0.420684	−	0.728647i
$479$	35.0245	−	20.2214i	1.60031	−	0.923938i	0.608884	−	0.793260i	$-0.291618\pi$
$479$	35.0245	−	20.2214i	1.60031	−	0.923938i	0.991425	−	0.130679i	$-0.0417157\pi$
$480$	10.6609			0.486600
$481$	24.7652	+	18.8567i	1.12920	+	0.859792i
$482$	−16.4734			−0.750343
$483$		0			0
$484$	3.20894	+	5.55805i	0.145861	+	0.252639i
$485$	19.4844	−	33.7480i	0.884741	−	1.53242i
$486$		−	23.0305i		−	1.04469i
$487$	−30.0331	−	17.3396i	−1.36093	−	0.785733i	−0.371182	−	0.928560i	$-0.621047\pi$
$487$	−30.0331	−	17.3396i	−1.36093	−	0.785733i	−0.989748	+	0.142827i	$0.954381\pi$
$488$	3.53019	+	2.03816i	0.159804	+	0.0922630i
$489$		−	42.0744i		−	1.90267i
$490$		0			0
$491$	1.67954	+	2.90904i	0.0757964	+	0.131283i	0.901432	−	0.432920i	$-0.142517\pi$
$491$	1.67954	+	2.90904i	0.0757964	+	0.131283i	−0.825636	+	0.564203i	$0.809183\pi$
$492$	−9.06175	+	5.23181i	−0.408535	+	0.235868i
$493$	−20.3449			−0.916288
$494$	−1.37108	−	3.27548i	−0.0616878	−	0.147371i
$495$	−50.6733			−2.27759
$496$	−0.714987	+	0.412798i	−0.0321038	+	0.0185352i
$497$		0			0
$498$	−16.9752	+	29.4020i	−0.760678	+	1.31753i
$499$			24.5977i			1.10114i	0.834788	+	0.550572i	$0.185590\pi$
$499$			24.5977i			1.10114i	−0.834788	+	0.550572i	$0.814410\pi$
$500$	−3.86860	−	2.23354i	−0.173009	−	0.0998869i
$501$	−48.7909	−	28.1695i	−2.17982	−	1.25852i
$502$		−	22.6235i		−	1.00974i
$503$	0.0232016	−	0.0401863i	0.00103451	−	0.00179182i	−0.865508	−	0.500896i	$-0.833004\pi$
$503$	0.0232016	−	0.0401863i	0.00103451	−	0.00179182i	0.866542	+	0.499104i	$0.166337\pi$
$504$		0			0
$505$	−18.0477	+	10.4198i	−0.803110	+	0.463676i
$506$	−6.82352			−0.303342
$507$	−39.8540	−	10.3610i	−1.76998	−	0.460147i
$508$	−4.19608			−0.186171
$509$	36.9879	−	21.3550i	1.63946	−	0.946542i	0.658439	−	0.752634i	$-0.271217\pi$
$509$	36.9879	−	21.3550i	1.63946	−	0.946542i	0.981020	−	0.193908i	$-0.0621165\pi$
$510$	25.3752	+	43.9512i	1.12363	+	1.94619i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	10.8975	+	6.29166i	0.481136	+	0.277784i
$514$	8.83901	+	5.10320i	0.389872	+	0.225093i
$515$			11.1297i			0.490435i
$516$	−8.69350	+	15.0576i	−0.382710	+	0.662873i
$517$	−4.30492	−	7.45634i	−0.189330	−	0.327930i
$518$		0			0
$519$	−18.6333			−0.817912
$520$	4.68557	+	11.1937i	0.205476	+	0.490878i
$521$	18.3425			0.803602			0.401801	−	0.915727i	$-0.368384\pi$
$521$	18.3425			0.803602			0.401801	+	0.915727i	$0.368384\pi$
$522$	26.0329	−	15.0301i	1.13943	−	0.657849i
$523$	−6.16294	−	10.6745i	−0.269487	−	0.466765i	0.699243	−	0.714884i	$-0.253521\pi$
$523$	−6.16294	−	10.6745i	−0.269487	−	0.466765i	−0.968729	+	0.248120i	$0.920187\pi$
$524$	5.19800	−	9.00321i	0.227076	−	0.393307i
$525$		0			0
$526$	−15.5308	−	8.96671i	−0.677175	−	0.390967i
$527$	−3.40365	−	1.96510i	−0.148265	−	0.0856010i
$528$		−	6.78052i		−	0.295084i
$529$	6.41933	−	11.1186i	0.279101	−	0.483418i
$530$	22.0079	+	38.1188i	0.955962	+	1.65577i
$531$	−21.7618	+	12.5642i	−0.944381	+	0.545239i
$532$		0			0
$533$	−9.47605	−	7.21526i	−0.410453	−	0.312527i
$534$	−15.7379			−0.681044
$535$	−29.7181	+	17.1578i	−1.28483	+	0.741795i
$536$	−0.184338	−	0.319284i	−0.00796221	−	0.0137910i
$537$	−15.6657	+	27.1338i	−0.676025	+	1.17091i
$538$			29.0801i			1.25373i
$539$		0			0
$540$	−37.2414	−	21.5013i	−1.60262	−	0.925270i
$541$		−	19.1727i		−	0.824297i	−0.911117	−	0.412148i	$-0.864778\pi$
$541$		−	19.1727i		−	0.824297i	0.911117	−	0.412148i	$-0.135222\pi$
$542$	−2.76938	+	4.79671i	−0.118955	+	0.206036i
$543$	31.2036	+	54.0462i	1.33907	+	2.31935i
$544$	−4.12266	+	2.38022i	−0.176758	+	0.102051i
$545$	25.1380			1.07679
$546$		0			0
$547$	−1.25358			−0.0535993			−0.0267997	−	0.999641i	$-0.508532\pi$
$547$	−1.25358			−0.0535993			−0.0267997	+	0.999641i	$0.508532\pi$
$548$	8.90891	−	5.14356i	0.380570	−	0.219722i
$549$	−14.3358	−	24.8303i	−0.611835	−	1.05973i
$550$	−6.77204	+	11.7295i	−0.288761	+	0.500148i
$551$			4.20892i			0.179306i
$552$	−8.74453	−	5.04865i	−0.372192	−	0.214885i
$553$		0			0
$554$			3.07134i			0.130489i
$555$	−46.0181	+	79.7057i	−1.95336	+	3.38332i
$556$	−5.72470	−	9.91547i	−0.242781	−	0.420510i
$557$	−25.1832	+	14.5395i	−1.06704	+	0.616058i	−0.927372	−	0.374139i	$-0.877938\pi$
$557$	−25.1832	+	14.5395i	−1.06704	+	0.616058i	−0.139672	+	0.990198i	$0.544605\pi$
$558$	5.80698			0.245829
$559$	−19.6311	−	2.51006i	−0.830307	−	0.106164i
$560$		0			0
$561$	27.9538	−	16.1391i	1.18021	−	0.681395i
$562$	14.3950	+	24.9329i	0.607218	+	1.05173i
$563$	−21.6177	+	37.4430i	−0.911078	+	1.57803i	−0.0985342	+	0.995134i	$0.531415\pi$
$563$	−21.6177	+	37.4430i	−0.911078	+	1.57803i	−0.812544	+	0.582900i	$0.801918\pi$
$564$		−	12.7407i		−	0.536479i
$565$	6.12103	+	3.53398i	0.257514	+	0.148676i
$566$	0.253827	+	0.146547i	0.0106692	+	0.00615984i
$567$		0			0
$568$	−0.303600	+	0.525851i	−0.0127388	+	0.0220642i
$569$	19.6059	+	33.9584i	0.821921	+	1.42361i	0.904250	+	0.427004i	$0.140431\pi$
$569$	19.6059	+	33.9584i	0.821921	+	1.42361i	−0.0823283	+	0.996605i	$0.526236\pi$
$570$	9.09257	−	5.24959i	0.380846	−	0.219881i
$571$	−9.73232			−0.407285			−0.203642	−	0.979045i	$-0.565278\pi$
$571$	−9.73232			−0.407285			−0.203642	+	0.979045i	$0.565278\pi$
$572$	7.11944	−	2.98011i	0.297679	−	0.124605i
$573$	−51.2353			−2.14039
$574$		0			0
$575$	10.0847	+	17.4672i	0.420560	+	0.728432i
$576$	3.51684	−	6.09135i	0.146535	−	0.253806i
$577$			32.9589i			1.37210i	0.727555	+	0.686049i	$0.240657\pi$
$577$			32.9589i			1.37210i	−0.727555	+	0.686049i	$0.759343\pi$
$578$	−4.90325	−	2.83089i	−0.203948	−	0.117750i
$579$	39.6479	+	22.8907i	1.64771	+	0.951306i
$580$		−	14.3837i		−	0.597251i
$581$		0			0
$582$	−18.3381	−	31.7626i	−0.760139	−	1.31660i
$583$	24.2443	−	13.9974i	1.00410	−	0.579715i
$584$	−6.45285			−0.267021
$585$	10.8252	−	84.6635i	0.447567	−	3.50041i
$586$	−23.4925			−0.970466
$587$	−17.6862	+	10.2112i	−0.729989	+	0.421460i	−0.818418	−	0.574623i	$-0.805149\pi$
$587$	−17.6862	+	10.2112i	−0.729989	+	0.421460i	0.0884289	+	0.996082i	$0.471815\pi$
$588$		0			0
$589$	−0.406537	+	0.704143i	−0.0167511	+	0.0290137i
$590$			12.0239i			0.495014i
$591$	52.1652	+	30.1176i	2.14579	+	1.23887i
$592$	−7.47646	−	4.31654i	−0.307281	−	0.177409i
$593$			2.94734i			0.121033i	0.998167	+	0.0605165i	$0.0192748\pi$
$593$			2.94734i			0.121033i	−0.998167	+	0.0605165i	$0.980725\pi$
$594$	−13.6753	+	23.6863i	−0.561103	+	0.971859i
$595$		0			0
$596$	−15.0887	+	8.71148i	−0.618058	+	0.356836i
$597$	5.14969			0.210763
$598$	1.45769	−	11.4005i	0.0596094	−	0.466203i
$599$	22.1745			0.906025			0.453012	−	0.891504i	$-0.350349\pi$
$599$	22.1745			0.906025			0.453012	+	0.891504i	$0.350349\pi$
$600$	−17.3571	+	10.0211i	−0.708601	+	0.409111i
$601$	21.9356	+	37.9936i	0.894772	+	1.54979i	0.834086	+	0.551634i	$0.185996\pi$
$601$	21.9356	+	37.9936i	0.894772	+	1.54979i	0.0606864	+	0.998157i	$0.480671\pi$
$602$		0			0
$603$			2.59316i			0.105602i
$604$	−11.2371	−	6.48773i	−0.457230	−	0.263982i
$605$	−18.7062	−	10.8000i	−0.760515	−	0.439083i
$606$			19.6136i			0.796749i
$607$	−11.7640	+	20.3758i	−0.477485	+	0.827028i	−0.999667	−	0.0258057i	$-0.991785\pi$
$607$	−11.7640	+	20.3758i	−0.477485	+	0.827028i	0.522182	+	0.852834i	$0.325118\pi$
$608$	0.492417	+	0.852891i	0.0199701	+	0.0345893i
$609$		0			0
$610$	−13.7192			−0.555476
$611$	13.3775	−	5.59967i	0.541196	−	0.226538i
$612$	33.4835			1.35349
$613$	−4.94319	+	2.85395i	−0.199654	+	0.115270i	−0.596494	−	0.802618i	$-0.703440\pi$
$613$	−4.94319	+	2.85395i	−0.199654	+	0.115270i	0.396840	+	0.917888i	$0.370107\pi$
$614$	4.72116	+	8.17729i	0.190531	+	0.330009i
$615$	17.6082	−	30.4983i	0.710030	−	1.22981i
$616$		0			0
$617$	−9.94900	−	5.74406i	−0.400531	−	0.231247i	0.286182	−	0.958175i	$-0.407614\pi$
$617$	−9.94900	−	5.74406i	−0.400531	−	0.231247i	−0.686713	+	0.726928i	$0.740947\pi$
$618$	9.07158	+	5.23748i	0.364912	+	0.210682i
$619$		−	11.6996i		−	0.470246i	−0.971966	−	0.235123i	$-0.924451\pi$
$619$		−	11.6996i		−	0.470246i	0.971966	−	0.235123i	$-0.0755493\pi$
$620$	1.38931	−	2.40636i	0.0557961	−	0.0966418i
$621$	20.3647	+	35.2727i	0.817207	+	1.41544i
$622$	4.75744	−	2.74671i	0.190756	−	0.110133i
$623$		0			0
$624$	11.3287	+	1.44850i	0.453512	+	0.0579866i
$625$	−16.6020			−0.664079
$626$	−9.66620	+	5.58079i	−0.386339	+	0.223053i
$627$	−3.33884	−	5.78305i	−0.133341	−	0.230953i
$628$	12.1933	−	21.1193i	0.486564	−	0.842753i
$629$		−	41.0972i		−	1.63865i
$630$		0			0
$631$	32.2871	+	18.6410i	1.28533	+	0.742085i	0.977817	−	0.209459i	$-0.0671703\pi$
$631$	32.2871	+	18.6410i	1.28533	+	0.742085i	0.307512	+	0.951544i	$0.400504\pi$
$632$			9.83378i			0.391167i
$633$	28.6076	−	49.5499i	1.13705	−	1.96943i
$634$	1.23852	+	2.14518i	0.0491880	+	0.0851961i
$635$	12.2303	−	7.06117i	0.485345	−	0.280214i
$636$	41.4263			1.64266
$637$		0			0
$638$	−9.14832			−0.362185
$639$	3.69867	−	2.13543i	0.146317	−	0.0844763i
$640$	−1.68280	−	2.91470i	−0.0665185	−	0.115213i
$641$	15.2287	−	26.3769i	0.601499	−	1.04183i	−0.391095	−	0.920350i	$-0.627904\pi$
$641$	15.2287	−	26.3769i	0.601499	−	1.04183i	0.992594	−	0.121477i	$-0.0387629\pi$
$642$			32.2967i			1.27465i
$643$	4.04254	+	2.33396i	0.159422	+	0.0920426i	0.577589	−	0.816328i	$-0.303994\pi$
$643$	4.04254	+	2.33396i	0.159422	+	0.0920426i	−0.418166	+	0.908370i	$0.637327\pi$
$644$		0			0
$645$		−	58.5177i		−	2.30413i
$646$	−2.34412	+	4.06013i	−0.0922282	+	0.159744i
$647$	−11.2208	−	19.4350i	−0.441136	−	0.764070i	0.556638	−	0.830755i	$-0.312091\pi$
$647$	−11.2208	−	19.4350i	−0.441136	−	0.764070i	−0.997774	+	0.0666848i	$0.978758\pi$
$648$	−16.7764	+	9.68586i	−0.659039	+	0.380496i
$649$	7.64740			0.300187
$650$	−18.1507	−	13.8203i	−0.711928	−	0.542076i
$651$		0			0
$652$	−11.5032	+	6.64137i	−0.450500	+	0.260096i
$653$	−2.22584	−	3.85527i	−0.0871039	−	0.150868i	0.819182	−	0.573534i	$-0.194428\pi$
$653$	−2.22584	−	3.85527i	−0.0871039	−	0.150868i	−0.906286	+	0.422665i	$0.861095\pi$
$654$	11.8295	−	20.4893i	0.462571	−	0.801197i
$655$			34.9888i			1.36713i
$656$	2.86076	+	1.65166i	0.111694	+	0.0644866i
$657$	39.3066	+	22.6937i	1.53350	+	0.885364i
$658$		0			0
$659$	13.8502	−	23.9893i	0.539529	−	0.934491i	−0.459400	−	0.888229i	$-0.651936\pi$
$659$	13.8502	−	23.9893i	0.539529	−	0.934491i	0.998929	−	0.0462621i	$-0.0147309\pi$
$660$	11.4103	+	19.7632i	0.444144	+	0.769280i
$661$	−26.6584	+	15.3912i	−1.03689	+	0.598649i	−0.918951	−	0.394372i	$-0.870962\pi$
$661$	−26.6584	+	15.3912i	−1.03689	+	0.598649i	−0.117940	+	0.993021i	$0.537629\pi$
$662$	−18.4740			−0.718014
$663$	20.9931	+	50.1522i	0.815306	+	1.94775i
$664$	10.7180			0.415941
$665$		0			0
$666$	30.3612	+	52.5871i	1.17647	+	2.03771i
$667$	−6.81167	+	11.7982i	−0.263749	+	0.456827i
$668$			17.7860i			0.688161i
$669$	66.2009	+	38.2211i	2.55948	+	1.47771i
$670$	1.07458	+	0.620410i	0.0415147	+	0.0239685i
$671$			8.72570i			0.336852i
$672$		0			0
$673$	7.54026	+	13.0601i	0.290656	+	0.503430i	0.973965	−	0.226699i	$-0.0727933\pi$
$673$	7.54026	+	13.0601i	0.290656	+	0.503430i	−0.683309	+	0.730129i	$0.739460\pi$
$674$	17.5510	−	10.1331i	0.676039	−	0.390312i
$675$	80.8443			3.11170
$676$	3.45819	+	12.5316i	0.133007	+	0.481985i
$677$	−7.45886			−0.286667			−0.143334	−	0.989674i	$-0.545782\pi$
$677$	−7.45886			−0.286667			−0.143334	+	0.989674i	$0.545782\pi$
$678$	5.76092	−	3.32607i	0.221247	−	0.127737i
$679$		0			0
$680$	8.01087	−	13.8752i	0.307203	−	0.532091i
$681$		−	28.7929i		−	1.10335i
$682$	−1.53049	−	0.883630i	−0.0586055	−	0.0338359i
$683$	27.0516	+	15.6183i	1.03510	+	0.597616i	0.918442	−	0.395556i	$-0.129448\pi$
$683$	27.0516	+	15.6183i	1.03510	+	0.597616i	0.116659	+	0.993172i	$0.462782\pi$
$684$		−	6.92701i		−	0.264861i
$685$	−17.3112	+	29.9838i	−0.661426	+	1.14562i
$686$		0			0
$687$	−17.3822	+	10.0356i	−0.663172	+	0.382883i
$688$	5.48901			0.209267
$689$	18.2073	+	43.4969i	0.693643	+	1.65710i
$690$	33.9835			1.29373
$691$	−16.4111	+	9.47494i	−0.624307	+	0.360444i	−0.778544	−	0.627590i	$-0.784041\pi$
$691$	−16.4111	+	9.47494i	−0.624307	+	0.360444i	0.154237	+	0.988034i	$0.450708\pi$
$692$	2.94124	+	5.09437i	0.111809	+	0.193659i
$693$		0			0
$694$			6.94477i			0.263620i
$695$	33.3715	+	19.2671i	1.26585	+	0.730841i
$696$	−11.7238	−	6.76875i	−0.444390	−	0.256569i
$697$			15.7253i			0.595637i
$698$	−1.05835	+	1.83312i	−0.0400593	+	0.0693848i
$699$	27.1195	+	46.9723i	1.02575	+	1.77665i
$700$		0			0
$701$	−31.8599			−1.20333			−0.601665	−	0.798748i	$-0.705496\pi$
$701$	−31.8599			−1.20333			−0.601665	+	0.798748i	$0.705496\pi$
$702$	−36.6529	−	27.9083i	−1.38338	−	1.05333i
$703$	−8.50214			−0.320664
$704$	−1.85380	+	1.07029i	−0.0698678	+	0.0403382i
$705$	21.4400	+	37.1352i	0.807478	+	1.39859i
$706$	−3.84230	+	6.65507i	−0.144607	+	0.250467i
$707$		0			0
$708$	9.80036	+	5.65824i	0.368320	+	0.212650i
$709$	10.5513	+	6.09179i	0.396262	+	0.228782i	0.684870	−	0.728665i	$-0.259859\pi$
$709$	10.5513	+	6.09179i	0.396262	+	0.228782i	−0.288608	+	0.957447i	$0.593192\pi$
$710$		−	2.04359i		−	0.0766947i
$711$	34.5839	−	59.9010i	1.29700	−	2.24646i
$712$	2.48419	+	4.30275i	0.0930991	+	0.161252i
$713$	−2.27915	+	1.31587i	−0.0853549	+	0.0492797i
$714$		0			0
$715$	−15.7361	+	20.6667i	−0.588495	+	0.772892i
$716$	9.89122			0.369652
$717$	50.4616	−	29.1340i	1.88452	−	1.08803i
$718$	−4.69650	−	8.13458i	−0.175272	−	0.303580i
$719$	−19.1614	+	33.1885i	−0.714599	+	1.23772i	0.248515	+	0.968628i	$0.420058\pi$
$719$	−19.1614	+	33.1885i	−0.714599	+	1.23772i	−0.963114	+	0.269094i	$0.913276\pi$
$720$			23.6726i			0.882226i
$721$		0			0
$722$	−15.6145	−	9.01505i	−0.581113	−	0.335505i
$723$		−	52.1812i		−	1.94064i
$724$	9.85087	−	17.0622i	0.366105	−	0.634112i
$725$	13.5206	+	23.4183i	0.502141	+	0.869734i
$726$	−17.6057	+	10.1646i	−0.653408	+	0.377245i
$727$	−32.7827			−1.21584			−0.607921	−	0.793997i	$-0.707996\pi$
$727$	−32.7827			−1.21584			−0.607921	+	0.793997i	$0.707996\pi$
$728$		0			0
$729$	14.8363			0.549492
$730$	18.8081	−	10.8589i	0.696119	−	0.401904i
$731$	13.0651	+	22.6293i	0.483229	+	0.836977i
$732$	−6.45606	+	11.1822i	−0.238623	+	0.413307i
$733$			30.9479i			1.14309i	0.820572	+	0.571543i	$0.193655\pi$
$733$			30.9479i			1.14309i	−0.820572	+	0.571543i	$0.806345\pi$
$734$	−25.0005	−	14.4340i	−0.922784	−	0.532770i
$735$		0			0
$736$			3.18768i			0.117500i
$737$	0.394593	−	0.683454i	0.0145350	−	0.0251754i
$738$	−11.6173	−	20.1217i	−0.427638	−	0.740691i
$739$	2.54693	−	1.47047i	0.0936904	−	0.0540922i	−0.452423	−	0.891804i	$-0.649440\pi$
$739$	2.54693	−	1.47047i	0.0936904	−	0.0540922i	0.546113	+	0.837711i	$0.316107\pi$
$740$	29.0555			1.06810
$741$	10.3754	−	4.34303i	0.381151	−	0.159545i
$742$		0			0
$743$	10.9357	−	6.31376i	0.401194	−	0.231629i	−0.285805	−	0.958288i	$-0.592261\pi$
$743$	10.9357	−	6.31376i	0.401194	−	0.231629i	0.686999	+	0.726658i	$0.258928\pi$
$744$	−1.30758	−	2.26479i	−0.0479381	−	0.0830313i
$745$	29.3194	−	50.7826i	1.07418	−	1.86053i
$746$		−	21.7441i		−	0.796109i
$747$	−65.2874	−	37.6937i	−2.38874	−	1.37914i
$748$	−8.82492	−	5.09507i	−0.322671	−	0.186294i
$749$		0			0
$750$	7.07496	−	12.2542i	0.258341	−	0.447460i
$751$	12.7063	+	22.0080i	0.463660	+	0.803082i	0.999140	−	0.0414655i	$-0.0132027\pi$
$751$	12.7063	+	22.0080i	0.463660	+	0.803082i	−0.535480	+	0.844548i	$0.679869\pi$
$752$	−3.48332	+	2.01109i	−0.127023	+	0.0733370i
$753$	71.6623			2.61152
$754$	1.95433	−	15.2848i	0.0711725	−	0.556638i
$755$	43.6702			1.58932
$756$		0			0
$757$	−3.88828	−	6.73469i	−0.141322	−	0.244777i	0.786673	−	0.617370i	$-0.211802\pi$
$757$	−3.88828	−	6.73469i	−0.141322	−	0.244777i	−0.927995	+	0.372594i	$0.878469\pi$
$758$	−17.6976	+	30.6531i	−0.642806	+	1.11337i
$759$		−	21.6142i		−	0.784545i
$760$	−2.87049	−	1.65728i	−0.104124	−	0.0601158i
$761$	−33.3076	−	19.2301i	−1.20740	−	0.697092i	−0.245209	−	0.969470i	$-0.578857\pi$
$761$	−33.3076	−	19.2301i	−1.20740	−	0.697092i	−0.962190	+	0.272378i	$0.912190\pi$
$762$		−	13.2915i		−	0.481500i
$763$		0			0
$764$	8.08740	+	14.0078i	0.292592	+	0.506784i
$765$	−97.5941	+	56.3460i	−3.52852	+	2.03719i
$766$	−7.78157			−0.281160
$767$	−1.63369	+	12.7771i	−0.0589893	+	0.461353i
$768$	−3.16760			−0.114301
$769$	−15.1551	+	8.74980i	−0.546507	+	0.315526i	−0.747712	−	0.664023i	$-0.768848\pi$
$769$	−15.1551	+	8.74980i	−0.546507	+	0.315526i	0.201205	+	0.979549i	$0.435514\pi$
$770$		0			0
$771$	−16.1649	+	27.9984i	−0.582165	+	1.00834i
$772$		−	14.4530i		−	0.520176i
$773$	−6.17873	−	3.56729i	−0.222233	−	0.128306i	0.384751	−	0.923021i	$-0.374287\pi$
$773$	−6.17873	−	3.56729i	−0.222233	−	0.128306i	−0.606984	+	0.794714i	$0.707621\pi$
$774$	−33.4355	−	19.3040i	−1.20181	−	0.693868i
$775$			5.22377i			0.187643i
$776$	−5.78928	+	10.0273i	−0.207823	+	0.359960i
$777$		0			0
$778$	7.57687	−	4.37451i	0.271644	−	0.156834i
$779$	3.25322			0.116559
$780$	−35.4573	+	14.8420i	−1.26958	+	0.531430i
$781$	−1.29976			−0.0465092
$782$	−13.1417	+	7.58739i	−0.469948	+	0.271325i
$783$	27.3030	+	47.2903i	0.975731	+	1.69002i
$784$		0			0
$785$			82.0753i			2.92939i
$786$	28.5186	+	16.4652i	1.01722	+	0.587294i
$787$	28.2009	+	16.2818i	1.00525	+	0.580383i	0.909798	−	0.415050i	$-0.136236\pi$
$787$	28.2009	+	16.2818i	1.00525	+	0.580383i	0.0954550	+	0.995434i	$0.469569\pi$
$788$		−	19.0160i		−	0.677419i
$789$	28.4030	−	49.1954i	1.01117	−	1.75140i
$790$	−16.5483	−	28.6625i	−0.588762	−	1.01977i
$791$		0			0
$792$	15.0562			0.535000
$793$	−14.5787	−	1.86405i	−0.517704	−	0.0661943i
$794$	−28.8249			−1.02296
$795$	−120.745	+	69.7122i	−4.28239	+	2.47244i
$796$	−0.812870	−	1.40793i	−0.0288114	−	0.0499028i
$797$	5.18869	−	8.98708i	0.183793	−	0.318339i	−0.759376	−	0.650652i	$-0.774496\pi$
$797$	5.18869	−	8.98708i	0.183793	−	0.318339i	0.943169	+	0.332313i	$0.107829\pi$
$798$		0			0
$799$	−16.5821	−	9.57369i	−0.586633	−	0.338693i
$800$	5.47958	+	3.16364i	0.193732	+	0.111851i
$801$		−	34.9461i		−	1.23476i
$802$	0.510573	−	0.884338i	0.0180290	−	0.0312271i
$803$	−6.90644	−	11.9623i	−0.243723	−	0.422141i
$804$	1.01136	−	0.583911i	0.0356680	−	0.0205929i
$805$		0			0
$806$	1.80330	−	2.36834i	0.0635185	−	0.0834211i
$807$	−92.1141			−3.24257
$808$	5.36239	−	3.09598i	0.188648	−	0.108916i
$809$	16.3533	+	28.3248i	0.574953	+	0.995847i	0.996047	+	0.0888304i	$0.0283129\pi$
$809$	16.3533	+	28.3248i	0.574953	+	0.995847i	−0.421094	+	0.907017i	$0.638354\pi$
$810$	32.5987	−	56.4627i	1.14540	−	1.98390i
$811$		−	51.4793i		−	1.80768i	−0.427869	−	0.903841i	$-0.640736\pi$
$811$		−	51.4793i		−	1.80768i	0.427869	−	0.903841i	$-0.359264\pi$
$812$		0			0
$813$	−15.1941	−	8.77229i	−0.532879	−	0.307658i
$814$		−	18.4799i		−	0.647719i
$815$	22.3522	−	38.7151i	0.782963	−	1.35613i
$816$	−7.53958	−	13.0589i	−0.263938	−	0.457154i
$817$	4.68153	−	2.70288i	0.163786	−	0.0945619i
$818$	−12.5545			−0.438959
$819$		0			0
$820$	−11.1177			−0.388246
$821$	22.9971	−	13.2774i	0.802603	−	0.463383i	−0.0417774	−	0.999127i	$-0.513302\pi$
$821$	22.9971	−	13.2774i	0.802603	−	0.463383i	0.844381	+	0.535744i	$0.179969\pi$
$822$	16.2927	+	28.2199i	0.568275	+	0.984281i
$823$	−17.1965	+	29.7851i	−0.599431	+	1.03824i	0.393474	+	0.919336i	$0.371273\pi$
$823$	−17.1965	+	29.7851i	−0.599431	+	1.03824i	−0.992905	+	0.118909i	$0.962060\pi$
$824$		−	3.30691i		−	0.115202i
$825$	−37.1544	−	21.4511i	−1.29355	−	0.746832i
$826$		0			0
$827$			5.99914i			0.208610i	0.994545	+	0.104305i	$0.0332619\pi$
$827$			5.99914i			0.208610i	−0.994545	+	0.104305i	$0.966738\pi$
$828$	11.2106	−	19.4173i	0.389595	−	0.674798i
$829$	26.3198	+	45.5873i	0.914125	+	1.58331i	0.808178	+	0.588939i	$0.200454\pi$
$829$	26.3198	+	45.5873i	0.914125	+	1.58331i	0.105947	+	0.994372i	$0.466213\pi$
$830$	−31.2398	+	18.0363i	−1.08435	+	0.626050i
$831$	−9.72879			−0.337488
$832$	−1.39219	−	3.32593i	−0.0482657	−	0.115306i
$833$		0			0
$834$	31.4083	−	18.1336i	1.08758	−	0.627914i
$835$	−29.9303	−	51.8408i	−1.03578	−	1.79402i
$836$	−1.05406	+	1.82569i	−0.0364555	+	0.0631427i
$837$			10.5487i			0.364617i
$838$	12.6086	+	7.27959i	0.435558	+	0.251469i
$839$	−29.2128	−	16.8660i	−1.00854	−	0.582279i	−0.0977743	−	0.995209i	$-0.531172\pi$
$839$	−29.2128	−	16.8660i	−1.00854	−	0.582279i	−0.910763	+	0.412929i	$0.864506\pi$
$840$		0			0
$841$	5.36756	−	9.29689i	0.185088	−	0.320583i
$842$	−7.76002	−	13.4408i	−0.267428	−	0.463199i
$843$	−78.9775	+	45.5977i	−2.72013	+	1.57047i
$844$	−18.0627			−0.621742
$845$	−31.1678	−	30.7064i	−1.07220	−	1.05633i
$846$	28.2908			0.972658
$847$		0			0
$848$	−6.53907	−	11.3260i	−0.224552	−	0.388936i
$849$	−0.464203	+	0.804023i	−0.0159314	+	0.0275940i
$850$			30.1206i			1.03313i
$851$	−23.8326	−	13.7598i	−0.816971	−	0.471679i
$852$	−1.66568	−	0.961684i	−0.0570654	−	0.0329467i
$853$		−	23.9213i		−	0.819049i	−0.912299	−	0.409525i	$-0.865695\pi$
$853$		−	23.9213i		−	0.819049i	0.912299	−	0.409525i	$-0.134305\pi$
$854$		0			0
$855$	11.6568	+	20.1901i	0.398654	+	0.690488i
$856$	8.82996	−	5.09798i	0.301802	−	0.174245i
$857$	−36.9629			−1.26263			−0.631314	−	0.775527i	$-0.717484\pi$
$857$	−36.9629			−1.26263			−0.631314	+	0.775527i	$0.717484\pi$
$858$	9.43981	+	22.5515i	0.322270	+	0.769897i
$859$	−2.09326			−0.0714211			−0.0357105	−	0.999362i	$-0.511369\pi$
$859$	−2.09326			−0.0714211			−0.0357105	+	0.999362i	$0.511369\pi$
$860$	−15.9988	+	9.23692i	−0.545555	+	0.314976i
$861$		0			0
$862$	−2.14063	+	3.70768i	−0.0729102	+	0.126284i
$863$			25.7306i			0.875881i	0.899004	+	0.437941i	$0.144292\pi$
$863$			25.7306i			0.875881i	−0.899004	+	0.437941i	$0.855708\pi$
$864$	11.0653	+	6.38856i	0.376449	+	0.217343i
$865$	−17.1456	−	9.89903i	−0.582969	−	0.336577i
$866$			23.9590i			0.814159i
$867$	8.96714	−	15.5315i	0.304540	−	0.527479i
$868$		0			0
$869$	−18.2299	+	10.5250i	−0.618407	+	0.357037i
$870$	45.5619			1.54469
$871$	1.05760	+	0.805279i	0.0358355	+	0.0272858i
$872$	−7.46908			−0.252935
$873$	70.5291	−	40.7200i	2.38705	−	1.37816i
$874$	1.56967	+	2.71875i	0.0530948	+	0.0919630i
$875$		0			0
$876$		−	20.4400i		−	0.690605i
$877$	−0.540703	−	0.312175i	−0.0182582	−	0.0105414i	0.490843	−	0.871248i	$-0.336689\pi$
$877$	−0.540703	−	0.312175i	−0.0182582	−	0.0105414i	−0.509101	+	0.860707i	$0.670022\pi$
$878$	−23.1204	−	13.3486i	−0.780276	−	0.450492i
$879$		−	74.4148i		−	2.50995i
$880$	3.60218	−	6.23916i	0.121430	−	0.210322i
$881$	11.7941	+	20.4280i	0.397355	+	0.688238i	0.993399	−	0.114713i	$-0.0365950\pi$
$881$	11.7941	+	20.4280i	0.397355	+	0.688238i	−0.596044	+	0.802952i	$0.703262\pi$
$882$		0			0
$883$	−3.01641			−0.101510			−0.0507551	−	0.998711i	$-0.516163\pi$
$883$	−3.01641			−0.101510			−0.0507551	+	0.998711i	$0.516163\pi$
$884$	10.3979	−	13.6560i	0.349721	−	0.459301i
$885$	−38.0868			−1.28027
$886$	14.8765	−	8.58893i	0.499785	−	0.288551i
$887$	4.57839	+	7.93000i	0.153727	+	0.266263i	0.932595	−	0.360925i	$-0.117539\pi$
$887$	4.57839	+	7.93000i	0.153727	+	0.266263i	−0.778868	+	0.627188i	$0.784206\pi$
$888$	13.6731	−	23.6824i	0.458838	−	0.794731i
$889$		0			0
$890$	−14.4813	−	8.36080i	−0.485416	−	0.280255i
$891$	−35.9113	−	20.7334i	−1.20308	−	0.694596i
$892$		−	24.1325i		−	0.808017i
$893$	−1.98059	+	3.43049i	−0.0662780	+	0.114797i
$894$	−27.5945	−	47.7950i	−0.922897	−	1.59850i
$895$	−28.8299	+	16.6449i	−0.963677	+	0.556379i
$896$		0			0
$897$	36.1124	+	4.61738i	1.20576	+	0.154170i
$898$	−10.4540			−0.348854
$899$	−3.05567	+	1.76419i	−0.101912	+	0.0588391i
$900$	−22.2520	−	38.5417i	−0.741735	−	1.28472i
$901$	31.1288	−	53.9167i	1.03705	−	1.79623i
$902$			7.07106i			0.235440i
$903$		0			0
$904$	−1.81870	−	1.05003i	−0.0604892	−	0.0349234i
$905$			66.3082i			2.20416i
$906$	20.5505	−	35.5946i	0.682746	−	1.18255i
$907$	−23.3637	−	40.4672i	−0.775780	−	1.34369i	−0.934355	−	0.356344i	$-0.884023\pi$
$907$	−23.3637	−	40.4672i	−0.775780	−	1.34369i	0.158574	−	0.987347i	$-0.449310\pi$
$908$	−7.87201	+	4.54491i	−0.261242	+	0.150828i
$909$	−43.5523			−1.44454
$910$		0			0
$911$	41.7044			1.38173			0.690864	−	0.722985i	$-0.257230\pi$
$911$	41.7044			1.38173			0.690864	+	0.722985i	$0.257230\pi$
$912$	−2.70162	+	1.55978i	−0.0894595	+	0.0516494i
$913$	11.4715	+	19.8691i	0.379650	+	0.657572i
$914$	−5.19386	+	8.99602i	−0.171797	+	0.297562i
$915$		−	43.4571i		−	1.43665i
$916$	5.48750	+	3.16821i	0.181312	+	0.104681i
$917$		0			0
$918$			60.8247i			2.00751i
$919$	3.95481	−	6.84994i	0.130457	−	0.225959i	−0.793396	−	0.608706i	$-0.791689\pi$
$919$	3.95481	−	6.84994i	0.130457	−	0.225959i	0.923853	+	0.382748i	$0.125022\pi$
$920$	−5.36424	−	9.29113i	−0.176854	−	0.306320i
$921$	−25.9024	+	14.9547i	−0.853513	+	0.492776i
$922$	−6.94115			−0.228595
$923$	0.277665	−	2.17161i	0.00913946	−	0.0714795i
$924$		0			0
$925$	−47.3056	+	27.3119i	−1.55540	+	0.898011i
$926$	−14.7528	−	25.5526i	−0.484806	−	0.839709i
$927$	−11.6299	+	20.1435i	−0.381975	+	0.661601i
$928$			4.27374i			0.140292i
$929$	−5.51012	−	3.18127i	−0.180781	−	0.104374i	0.406878	−	0.913482i	$-0.366617\pi$
$929$	−5.51012	−	3.18127i	−0.180781	−	0.104374i	−0.587660	+	0.809108i	$0.699951\pi$
$930$	7.62239	+	4.40079i	0.249948	+	0.144307i
$931$		0			0
$932$	8.56151	−	14.8290i	0.280442	−	0.485739i
$933$	8.70048	+	15.0697i	0.284841	+	0.493359i
$934$	−28.1626	+	16.2597i	−0.921510	+	0.532034i
$935$	34.2959			1.12160
$936$	−3.21642	+	25.1555i	−0.105132	+	0.822234i
$937$	41.7048			1.36244			0.681219	−	0.732080i	$-0.261450\pi$
$937$	41.7048			1.36244			0.681219	+	0.732080i	$0.261450\pi$
$938$		0			0
$939$	−17.6777	−	30.6187i	−0.576890	−	0.999202i
$940$	6.76854	−	11.7235i	0.220765	−	0.382377i
$941$		−	20.6192i		−	0.672167i	−0.941832	−	0.336083i	$-0.890898\pi$
$941$		−	20.6192i		−	0.672167i	0.941832	−	0.336083i	$-0.109102\pi$
$942$	66.8976	+	38.6233i	2.17964	+	1.25842i
$943$	9.11921	+	5.26498i	0.296962	+	0.171451i
$944$		−	3.57257i		−	0.116277i
$945$		0			0
$946$	5.87486	+	10.1755i	0.191008	+	0.330836i
$947$	4.43704	−	2.56172i	0.144184	−	0.0832449i	−0.426172	−	0.904642i	$-0.640138\pi$
$947$	4.43704	−	2.56172i	0.144184	−	0.0832449i	0.570357	+	0.821397i	$0.306805\pi$
$948$	−31.1495			−1.01169
$949$	21.4617	−	8.98362i	0.696676	−	0.291621i
$950$	6.23131			0.202170
$951$	−6.79508	+	3.92314i	−0.220346	+	0.127217i
$952$		0			0
$953$	−15.2986	+	26.4979i	−0.495570	+	0.858352i	−0.999987	−	0.00510792i	$-0.998374\pi$
$953$	−15.2986	+	26.4979i	−0.495570	+	0.858352i	0.504417	+	0.863460i	$0.331707\pi$
$954$			91.9875i			2.97821i
$955$	−47.1446	−	27.2190i	−1.52556	−	0.880785i
$956$	−15.9306	−	9.19751i	−0.515231	−	0.297469i
$957$		−	28.9782i		−	0.936733i
$958$	20.2214	−	35.0245i	0.653323	−	1.13159i
$959$		0			0
$960$	9.23259	−	5.33044i	0.297981	−	0.172039i
$961$	30.3184			0.978013
$962$	30.8756	+	3.94780i	0.995471	+	0.127282i
$963$	−71.7152			−2.31099
$964$	−14.2664	+	8.23670i	−0.459489	+	0.265286i
$965$	24.3216	+	42.1262i	0.782940	+	1.35609i
$966$		0			0
$967$		−	48.2365i		−	1.55118i	−0.631236	−	0.775591i	$-0.717452\pi$
$967$		−	48.2365i		−	1.55118i	0.631236	−	0.775591i	$-0.282548\pi$
$968$	5.55805	+	3.20894i	0.178643	+	0.103139i
$969$	−12.8609	−	7.42523i	−0.413151	−	0.238533i
$970$		−	38.9688i		−	1.25121i
$971$	−16.3486	+	28.3166i	−0.524651	+	0.908721i	0.474937	+	0.880020i	$0.342471\pi$
$971$	−16.3486	+	28.3166i	−0.524651	+	0.908721i	−0.999588	+	0.0287019i	$0.990863\pi$
$972$	−11.5153	−	19.9450i	−0.369352	−	0.639736i
$973$		0			0
$974$	−34.6792			−1.11119
$975$	43.7771	−	57.4941i	1.40199	−	1.84128i
$976$	4.07631			0.130480
$977$	22.0714	−	12.7429i	0.706125	−	0.407682i	−0.103499	−	0.994630i	$-0.533004\pi$
$977$	22.0714	−	12.7429i	0.706125	−	0.407682i	0.809625	+	0.586948i	$0.199671\pi$
$978$	−21.0372	−	36.4375i	−0.672695	−	1.16514i
$979$	−5.31763	+	9.21041i	−0.169952	+	0.294366i
$980$		0			0
$981$	45.4968	+	26.2676i	1.45260	+	0.838660i
$982$	2.90904	+	1.67954i	0.0928313	+	0.0535962i
$983$		−	27.7551i		−	0.885249i	−0.896707	−	0.442625i	$-0.854047\pi$
$983$		−	27.7551i		−	0.885249i	0.896707	−	0.442625i	$-0.145953\pi$
$984$	−5.23181	+	9.06175i	−0.166784	+	0.288878i
$985$	32.0002	+	55.4260i	1.01961	+	1.76602i
$986$	−17.6192	+	10.1724i	−0.561109	+	0.323957i
$987$		0			0
$988$	−2.82513	−	2.15111i	−0.0898794	−	0.0684360i
$989$	17.4972			0.556380
$990$	−43.8843	+	25.3366i	−1.39474	+	0.805251i
$991$	9.79291	+	16.9618i	0.311082	+	0.538810i	0.978597	−	0.205786i	$-0.0659752\pi$
$991$	9.79291	+	16.9618i	0.311082	+	0.538810i	−0.667515	+	0.744597i	$0.732642\pi$
$992$	−0.412798	+	0.714987i	−0.0131063	+	0.0227008i
$993$		−	58.5184i		−	1.85702i
$994$		0			0
$995$	4.73854	+	2.73580i	0.150222	+	0.0867305i
$996$			33.9505i			1.07576i
$997$	−2.38826	+	4.13659i	−0.0756370	+	0.131007i	−0.901363	−	0.433064i	$-0.857432\pi$
$997$	−2.38826	+	4.13659i	−0.0756370	+	0.131007i	0.825726	+	0.564071i	$0.190766\pi$
$998$	12.2988	+	21.3022i	0.389313	+	0.674310i
$999$	−95.5276	+	55.1529i	−3.02236	+	1.74496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.f.491.10		20
7.2	even	3		1274.2.v.h.361.1		20
7.3	odd	6		182.2.o.a.23.6	✓	20
7.4	even	3		1274.2.o.h.569.10		20
7.5	odd	6		182.2.v.a.179.5	yes	20
7.6	odd	2		1274.2.m.g.491.6		20
13.4	even	6	inner	1274.2.m.f.589.10		20
21.5	even	6		1638.2.cr.c.361.10		20
21.17	even	6		1638.2.dt.c.1297.1		20
91.4	even	6		1274.2.v.h.667.1		20
91.17	odd	6		182.2.v.a.121.5	yes	20
91.30	even	6		1274.2.o.h.459.5		20
91.69	odd	6		1274.2.m.g.589.6		20
91.82	odd	6		182.2.o.a.95.1	yes	20
273.17	even	6		1638.2.cr.c.667.10		20
273.173	even	6		1638.2.dt.c.1369.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.6	✓	20	7.3	odd	6
182.2.o.a.95.1	yes	20	91.82	odd	6
182.2.v.a.121.5	yes	20	91.17	odd	6
182.2.v.a.179.5	yes	20	7.5	odd	6
1274.2.m.f.491.10		20	1.1	even	1	trivial
1274.2.m.f.589.10		20	13.4	even	6	inner
1274.2.m.g.491.6		20	7.6	odd	2
1274.2.m.g.589.6		20	91.69	odd	6
1274.2.o.h.459.5		20	91.30	even	6
1274.2.o.h.569.10		20	7.4	even	3
1274.2.v.h.361.1		20	7.2	even	3
1274.2.v.h.667.1		20	91.4	even	6
1638.2.cr.c.361.10		20	21.5	even	6
1638.2.cr.c.667.10		20	273.17	even	6
1638.2.dt.c.1297.1		20	21.17	even	6
1638.2.dt.c.1369.6		20	273.173	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.58380 + 2.74322i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.36560i q^{5} +(2.74322 + 1.58380i) q^{6} -1.00000i q^{8} +(-3.51684 + 6.09135i) q^{9} +(1.68280 + 2.91470i) q^{10} +(1.85380 - 1.07029i) q^{11} +3.16760 q^{12} +(1.39219 + 3.32593i) q^{13} +(-9.23259 + 5.33044i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.38022 - 4.12266i) q^{17} +7.03369i q^{18} +(-0.852891 - 0.492417i) q^{19} +(2.91470 + 1.68280i) q^{20} +(1.07029 - 1.85380i) q^{22} +(-1.59384 - 2.76062i) q^{23} +(2.74322 - 1.58380i) q^{24} -6.32727 q^{25} +(2.86864 + 2.18424i) q^{26} -12.7771 q^{27} +(-2.13687 - 3.70117i) q^{29} +(-5.33044 + 9.23259i) q^{30} -0.825595i q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.87211 + 3.39026i) q^{33} -4.76044i q^{34} +(3.51684 + 6.09135i) q^{36} +(7.47646 - 4.31654i) q^{37} -0.984833 q^{38} +(-6.91880 + 9.08670i) q^{39} +3.36560 q^{40} +(-2.86076 + 1.65166i) q^{41} +(-2.74451 + 4.75362i) q^{43} -2.14059i q^{44} +(-20.5011 - 11.8363i) q^{45} +(-2.76062 - 1.59384i) q^{46} -4.02219i q^{47} +(1.58380 - 2.74322i) q^{48} +(-5.47958 + 3.16364i) q^{50} +15.0792 q^{51} +(3.57644 + 0.457288i) q^{52} +13.0781 q^{53} +(-11.0653 + 6.38856i) q^{54} +(3.60218 + 6.23916i) q^{55} -3.11956i q^{57} +(-3.70117 - 2.13687i) q^{58} +(3.09394 + 1.78629i) q^{59} +10.6609i q^{60} +(-2.03816 + 3.53019i) q^{61} +(-0.412798 - 0.714987i) q^{62} -1.00000 q^{64} +(-11.1937 + 4.68557i) q^{65} +6.78052 q^{66} +(0.319284 - 0.184338i) q^{67} +(-2.38022 - 4.12266i) q^{68} +(5.04865 - 8.74453i) q^{69} +(-0.525851 - 0.303600i) q^{71} +(6.09135 + 3.51684i) q^{72} -6.45285i q^{73} +(4.31654 - 7.47646i) q^{74} +(-10.0211 - 17.3571i) q^{75} +(-0.852891 + 0.492417i) q^{76} +(-1.44850 + 11.3287i) q^{78} -9.83378 q^{79} +(2.91470 - 1.68280i) q^{80} +(-9.68586 - 16.7764i) q^{81} +(-1.65166 + 2.86076i) q^{82} +10.7180i q^{83} +(13.8752 + 8.01087i) q^{85} +5.48901i q^{86} +(6.76875 - 11.7238i) q^{87} +(-1.07029 - 1.85380i) q^{88} +(-4.30275 + 2.48419i) q^{89} -23.6726 q^{90} -3.18768 q^{92} +(2.26479 - 1.30758i) q^{93} +(-2.01109 - 3.48332i) q^{94} +(1.65728 - 2.87049i) q^{95} -3.16760i q^{96} +(-10.0273 - 5.78928i) q^{97} +15.0562i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 10 q^{4} - 16 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{19} + 2 q^{22} - 36 q^{25} + 28 q^{27} + 2 q^{29} - 2 q^{30} + 12 q^{33} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) \) 20 * q - 2 * q^3 + 10 * q^4 - 16 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^19 + 2 * q^22 - 36 * q^25 + 28 * q^27 + 2 * q^29 - 2 * q^30 + 12 * q^33 + 16 * q^36 + 36 * q^37 - 28 * q^38 + 4 * q^39 + 8 * q^40 - 18 * q^41 + 8 * q^43 - 60 * q^45 - 12 * q^46 - 2 * q^48 - 12 * q^50 + 44 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 2 * q^55 + 24 * q^58 + 4 * q^61 + 24 * q^62 - 20 * q^64 + 24 * q^65 + 64 * q^66 + 60 * q^67 - 10 * q^68 + 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 + 16 * q^82 - 12 * q^85 + 64 * q^87 - 2 * q^88 - 18 * q^89 - 52 * q^90 - 60 * q^93 - 16 * q^94 - 12 * q^95 - 78 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more