LMFDB - Embedded newform 1274.2.m.f.491.7

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			491.7
Root			$-2.35757i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.f.589.7

$q$-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} +(-1.17879 - 2.04172i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.34415i q^{5} +(-2.04172 - 1.17879i) q^{6} -1.00000i q^{8} +(-1.27907 + 2.21541i) q^{9} +(-1.67208 - 2.89612i) q^{10} +(-4.36176 + 2.51826i) q^{11} -2.35757 q^{12} +(1.92804 + 3.04674i) q^{13} +(-6.82781 + 3.94204i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86635 - 3.23261i) q^{17} +2.55814i q^{18} +(-5.08703 - 2.93700i) q^{19} +(-2.89612 - 1.67208i) q^{20} +(-2.51826 + 4.36176i) q^{22} +(-1.89185 - 3.27678i) q^{23} +(-2.04172 + 1.17879i) q^{24} -6.18336 q^{25} +(3.19311 + 1.67454i) q^{26} -1.04172 q^{27} +(3.36143 + 5.82216i) q^{29} +(-3.94204 + 6.82781i) q^{30} -1.02180i q^{31} +(-0.866025 - 0.500000i) q^{32} +(10.2832 + 5.93699i) q^{33} -3.73270i q^{34} +(1.27907 + 2.21541i) q^{36} +(0.370851 - 0.214111i) q^{37} -5.87400 q^{38} +(3.94784 - 7.52797i) q^{39} -3.34415 q^{40} +(-0.917963 + 0.529986i) q^{41} +(1.65120 - 2.85996i) q^{43} +5.03653i q^{44} +(7.40868 + 4.27741i) q^{45} +(-3.27678 - 1.89185i) q^{46} -5.31343i q^{47} +(-1.17879 + 2.04172i) q^{48} +(-5.35494 + 3.09168i) q^{50} -8.80011 q^{51} +(3.60258 - 0.146362i) q^{52} +2.31672 q^{53} +(-0.902152 + 0.520858i) q^{54} +(8.42146 + 14.5864i) q^{55} +13.8484i q^{57} +(5.82216 + 3.36143i) q^{58} +(7.00324 + 4.04332i) q^{59} +7.88408i q^{60} +(-5.05050 + 8.74773i) q^{61} +(-0.510901 - 0.884906i) q^{62} -1.00000 q^{64} +(10.1888 - 6.44767i) q^{65} +11.8740 q^{66} +(11.5166 - 6.64910i) q^{67} +(-1.86635 - 3.23261i) q^{68} +(-4.46017 + 7.72525i) q^{69} +(2.35754 + 1.36113i) q^{71} +(2.21541 + 1.27907i) q^{72} -7.95457i q^{73} +(0.214111 - 0.370851i) q^{74} +(7.28885 + 12.6247i) q^{75} +(-5.08703 + 2.93700i) q^{76} +(-0.345059 - 8.49334i) q^{78} -14.1422 q^{79} +(-2.89612 + 1.67208i) q^{80} +(5.06517 + 8.77313i) q^{81} +(-0.529986 + 0.917963i) q^{82} -9.17859i q^{83} +(-10.8104 - 6.24136i) q^{85} -3.30240i q^{86} +(7.92480 - 13.7262i) q^{87} +(2.51826 + 4.36176i) q^{88} +(4.68772 - 2.70646i) q^{89} +8.55481 q^{90} -3.78370 q^{92} +(-2.08623 + 1.20449i) q^{93} +(-2.65672 - 4.60157i) q^{94} +(-9.82177 + 17.0118i) q^{95} +2.35757i q^{96} +(-14.8742 - 8.58763i) q^{97} -12.8842i 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
$3$	−1.17879	−	2.04172i	−0.680572	−	1.17879i	−0.974807	−	0.223052i	$-0.928398\pi$
$3$	−1.17879	−	2.04172i	−0.680572	−	1.17879i	0.294234	−	0.955733i	$-0.404935\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.34415i		−	1.49555i	−0.663952	−	0.747775i	$-0.731122\pi$
$5$		−	3.34415i		−	1.49555i	0.663952	−	0.747775i	$-0.268878\pi$
$6$	−2.04172	−	1.17879i	−0.833527	−	0.481237i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.27907	+	2.21541i	−0.426357	+	0.738472i
$10$	−1.67208	−	2.89612i	−0.528757	−	0.915834i
$11$	−4.36176	+	2.51826i	−1.31512	+	0.759285i	−0.982939	−	0.183930i	$-0.941118\pi$
$11$	−4.36176	+	2.51826i	−1.31512	+	0.759285i	−0.332182	+	0.943215i	$0.607785\pi$
$12$	−2.35757			−0.680572
$13$	1.92804	+	3.04674i	0.534743	+	0.845015i
$13$	1.92804	+	3.04674i	0.534743	+	0.845015i
$14$		0			0
$15$	−6.82781	+	3.94204i	−1.76293	+	1.01783i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.86635	−	3.23261i	0.452657	−	0.784024i	−0.545894	−	0.837855i	$-0.683810\pi$
$17$	1.86635	−	3.23261i	0.452657	−	0.784024i	0.998550	+	0.0538304i	$0.0171430\pi$
$18$			2.55814i			0.602959i
$19$	−5.08703	−	2.93700i	−1.16705	−	0.673794i	−0.214063	−	0.976820i	$-0.568670\pi$
$19$	−5.08703	−	2.93700i	−1.16705	−	0.673794i	−0.952982	+	0.303026i	$0.902003\pi$
$20$	−2.89612	−	1.67208i	−0.647592	−	0.373888i
$21$		0			0
$22$	−2.51826	+	4.36176i	−0.536896	+	0.929931i
$23$	−1.89185	−	3.27678i	−0.394478	−	0.683257i	0.598556	−	0.801081i	$-0.295741\pi$
$23$	−1.89185	−	3.27678i	−0.394478	−	0.683257i	−0.993034	+	0.117824i	$0.962408\pi$
$24$	−2.04172	+	1.17879i	−0.416764	+	0.240619i
$25$	−6.18336			−1.23667
$26$	3.19311	+	1.67454i	0.626220	+	0.328404i
$27$	−1.04172			−0.200478
$28$		0			0
$29$	3.36143	+	5.82216i	0.624201	+	1.08115i	0.988695	+	0.149942i	$0.0479088\pi$
$29$	3.36143	+	5.82216i	0.624201	+	1.08115i	−0.364494	+	0.931206i	$0.618758\pi$
$30$	−3.94204	+	6.82781i	−0.719714	+	1.24658i
$31$		−	1.02180i		−	0.183521i	−0.995781	−	0.0917605i	$-0.970751\pi$
$31$		−	1.02180i		−	0.183521i	0.995781	−	0.0917605i	$-0.0292494\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	10.2832	+	5.93699i	1.79007	+	1.03350i
$34$		−	3.73270i		−	0.640153i
$35$		0			0
$36$	1.27907	+	2.21541i	0.213178	+	0.369236i
$37$	0.370851	−	0.214111i	0.0609676	−	0.0351997i	−0.469206	−	0.883089i	$-0.655460\pi$
$37$	0.370851	−	0.214111i	0.0609676	−	0.0351997i	0.530174	+	0.847889i	$0.322127\pi$
$38$	−5.87400			−0.952888
$39$	3.94784	−	7.52797i	0.632160	−	1.20544i
$40$	−3.34415			−0.528757
$41$	−0.917963	+	0.529986i	−0.143362	+	0.0827699i	−0.569965	−	0.821669i	$-0.693043\pi$
$41$	−0.917963	+	0.529986i	−0.143362	+	0.0827699i	0.426603	+	0.904439i	$0.359710\pi$
$42$		0			0
$43$	1.65120	−	2.85996i	0.251805	−	0.436140i	−0.712217	−	0.701959i	$-0.752309\pi$
$43$	1.65120	−	2.85996i	0.251805	−	0.436140i	0.964023	+	0.265819i	$0.0856423\pi$
$44$			5.03653i			0.759285i
$45$	7.40868	+	4.27741i	1.10442	+	0.637638i
$46$	−3.27678	−	1.89185i	−0.483135	−	0.278938i
$47$		−	5.31343i		−	0.775044i	−0.921861	−	0.387522i	$-0.873331\pi$
$47$		−	5.31343i		−	0.775044i	0.921861	−	0.387522i	$-0.126669\pi$
$48$	−1.17879	+	2.04172i	−0.170143	+	0.294696i
$49$		0			0
$50$	−5.35494	+	3.09168i	−0.757303	+	0.437229i
$51$	−8.80011			−1.23226
$52$	3.60258	−	0.146362i	0.499588	−	0.0202968i
$53$	2.31672			0.318227			0.159113	−	0.987260i	$-0.449136\pi$
$53$	2.31672			0.318227			0.159113	+	0.987260i	$0.449136\pi$
$54$	−0.902152	+	0.520858i	−0.122767	+	0.0708798i
$55$	8.42146	+	14.5864i	1.13555	+	1.96683i
$56$		0			0
$57$			13.8484i			1.83426i
$58$	5.82216	+	3.36143i	0.764487	+	0.441377i
$59$	7.00324	+	4.04332i	0.911745	+	0.526396i	0.880992	−	0.473131i	$-0.156876\pi$
$59$	7.00324	+	4.04332i	0.911745	+	0.526396i	0.0307526	+	0.999527i	$0.490210\pi$
$60$			7.88408i			1.01783i
$61$	−5.05050	+	8.74773i	−0.646651	+	1.12003i	0.337267	+	0.941409i	$0.390498\pi$
$61$	−5.05050	+	8.74773i	−0.646651	+	1.12003i	−0.983918	+	0.178623i	$0.942836\pi$
$62$	−0.510901	−	0.884906i	−0.0648845	−	0.112383i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	10.1888	−	6.44767i	1.26376	−	0.799735i
$66$	11.8740			1.46159
$67$	11.5166	−	6.64910i	1.40697	−	0.812317i	0.411879	−	0.911239i	$-0.364873\pi$
$67$	11.5166	−	6.64910i	1.40697	−	0.812317i	0.995095	+	0.0989215i	$0.0315393\pi$
$68$	−1.86635	−	3.23261i	−0.226328	−	0.392012i
$69$	−4.46017	+	7.72525i	−0.536942	+	0.930011i
$70$		0			0
$71$	2.35754	+	1.36113i	0.279788	+	0.161536i	0.633328	−	0.773884i	$-0.281689\pi$
$71$	2.35754	+	1.36113i	0.279788	+	0.161536i	−0.353539	+	0.935420i	$0.615022\pi$
$72$	2.21541	+	1.27907i	0.261089	+	0.150740i
$73$		−	7.95457i		−	0.931012i	−0.885045	−	0.465506i	$-0.845872\pi$
$73$		−	7.95457i		−	0.931012i	0.885045	−	0.465506i	$-0.154128\pi$
$74$	0.214111	−	0.370851i	0.0248899	−	0.0431106i
$75$	7.28885	+	12.6247i	0.841644	+	1.45777i
$76$	−5.08703	+	2.93700i	−0.583523	+	0.336897i
$77$		0			0
$78$	−0.345059	−	8.49334i	−0.0390702	−	0.961681i
$79$	−14.1422			−1.59113			−0.795563	−	0.605871i	$-0.792825\pi$
$79$	−14.1422			−1.59113			−0.795563	+	0.605871i	$0.792825\pi$
$80$	−2.89612	+	1.67208i	−0.323796	+	0.186944i
$81$	5.06517	+	8.77313i	0.562797	+	0.974792i
$82$	−0.529986	+	0.917963i	−0.0585272	+	0.101372i
$83$		−	9.17859i		−	1.00748i	−0.863855	−	0.503741i	$-0.831957\pi$
$83$		−	9.17859i		−	1.00748i	0.863855	−	0.503741i	$-0.168043\pi$
$84$		0			0
$85$	−10.8104	−	6.24136i	−1.17255	−	0.676971i
$86$		−	3.30240i		−	0.356107i
$87$	7.92480	−	13.7262i	0.849628	−	1.47160i
$88$	2.51826	+	4.36176i	0.268448	+	0.464965i
$89$	4.68772	−	2.70646i	0.496897	−	0.286884i	−0.230534	−	0.973064i	$-0.574047\pi$
$89$	4.68772	−	2.70646i	0.496897	−	0.286884i	0.727431	+	0.686181i	$0.240714\pi$
$90$	8.55481			0.901756
$91$		0			0
$92$	−3.78370			−0.394478
$93$	−2.08623	+	1.20449i	−0.216332	+	0.124899i
$94$	−2.65672	−	4.60157i	−0.274019	−	0.474615i
$95$	−9.82177	+	17.0118i	−1.00769	+	1.74537i
$96$			2.35757i			0.240619i
$97$	−14.8742	−	8.58763i	−1.51025	−	0.871941i	−0.999929	−	0.0119557i	$-0.996194\pi$
$97$	−14.8742	−	8.58763i	−1.51025	−	0.871941i	−0.510318	−	0.859986i	$-0.670472\pi$
$98$		0			0
$99$		−	12.8842i		−	1.29491i
$100$	−3.09168	+	5.35494i	−0.309168	+	0.535494i
$101$	1.22413	+	2.12026i	0.121806	+	0.210973i	0.920480	−	0.390790i	$-0.127798\pi$
$101$	1.22413	+	2.12026i	0.121806	+	0.210973i	−0.798674	+	0.601764i	$0.794465\pi$
$102$	−7.62112	+	4.40005i	−0.754603	+	0.435670i
$103$	−17.9286			−1.76655			−0.883277	−	0.468852i	$-0.844668\pi$
$103$	−17.9286			−1.76655			−0.883277	+	0.468852i	$0.844668\pi$
$104$	3.04674	−	1.92804i	0.298758	−	0.189060i
$105$		0			0
$106$	2.00634	−	1.15836i	0.194873	−	0.112510i
$107$	4.95119	+	8.57572i	0.478650	+	0.829046i	0.999700	−	0.0244799i	$-0.00779297\pi$
$107$	4.95119	+	8.57572i	0.478650	+	0.829046i	−0.521050	+	0.853526i	$0.674460\pi$
$108$	−0.520858	+	0.902152i	−0.0501196	+	0.0868096i
$109$		−	3.55788i		−	0.340783i	−0.985376	−	0.170391i	$-0.945497\pi$
$109$		−	3.55788i		−	0.340783i	0.985376	−	0.170391i	$-0.0545032\pi$
$110$	14.5864	+	8.42146i	1.39076	+	0.802955i
$111$	−0.874309	−	0.504782i	−0.0829857	−	0.0479118i
$112$		0			0
$113$	2.44458	−	4.23414i	0.229967	−	0.398314i	−0.727831	−	0.685756i	$-0.759472\pi$
$113$	2.44458	−	4.23414i	0.229967	−	0.398314i	0.957798	+	0.287442i	$0.0928049\pi$
$114$	6.92418	+	11.9930i	0.648509	+	1.12325i
$115$	−10.9581	+	6.32664i	−1.02184	+	0.589962i
$116$	6.72285			0.624201
$117$	−9.21590	+	0.374414i	−0.852011	+	0.0346146i
$118$	8.08665			0.744436
$119$		0			0
$120$	3.94204	+	6.82781i	0.359857	+	0.623291i
$121$	7.18332	−	12.4419i	0.653029	−	1.13108i
$122$			10.1010i			0.914502i
$123$	2.16416	+	1.24948i	0.195136	+	0.112662i
$124$	−0.884906	−	0.510901i	−0.0794669	−	0.0458803i
$125$			3.95733i			0.353954i
$126$		0			0
$127$	−4.14641	−	7.18180i	−0.367935	−	0.637281i	0.621308	−	0.783567i	$-0.286602\pi$
$127$	−4.14641	−	7.18180i	−0.367935	−	0.637281i	−0.989242	+	0.146285i	$0.953268\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−7.78564			−0.685487
$130$	5.59991	−	10.6782i	0.491144	−	0.936543i
$131$	−6.16169			−0.538349			−0.269174	−	0.963091i	$-0.586751\pi$
$131$	−6.16169			−0.538349			−0.269174	+	0.963091i	$0.586751\pi$
$132$	10.2832	−	5.93699i	0.895035	−	0.516748i
$133$		0			0
$134$	6.64910	−	11.5166i	0.574395	−	0.994881i
$135$			3.48366i			0.299825i
$136$	−3.23261	−	1.86635i	−0.277194	−	0.160038i
$137$	−6.44163	−	3.71908i	−0.550346	−	0.317742i	0.198916	−	0.980017i	$-0.436258\pi$
$137$	−6.44163	−	3.71908i	−0.550346	−	0.317742i	−0.749261	+	0.662274i	$0.769591\pi$
$138$			8.92035i			0.759351i
$139$	−2.44199	+	4.22965i	−0.207127	+	0.358754i	−0.950808	−	0.309780i	$-0.899745\pi$
$139$	−2.44199	+	4.22965i	−0.207127	+	0.358754i	0.743682	+	0.668534i	$0.233078\pi$
$140$		0			0
$141$	−10.8485	+	6.26339i	−0.913610	+	0.527473i
$142$	2.72225			0.228446
$143$	−16.0822	−	8.43385i	−1.34486	−	0.705274i
$144$	2.55814			0.213178
$145$	19.4702	−	11.2411i	1.61691	−	0.933524i
$146$	−3.97728	−	6.88886i	−0.329162	−	0.570126i
$147$		0			0
$148$		−	0.428222i		−	0.0351997i
$149$	4.86592	+	2.80934i	0.398632	+	0.230150i	0.685894	−	0.727702i	$-0.259412\pi$
$149$	4.86592	+	2.80934i	0.398632	+	0.230150i	−0.287262	+	0.957852i	$0.592745\pi$
$150$	12.6247	+	7.28885i	1.03080	+	0.595132i
$151$		−	8.30978i		−	0.676240i	−0.941103	−	0.338120i	$-0.890209\pi$
$151$		−	8.30978i		−	0.676240i	0.941103	−	0.338120i	$-0.109791\pi$
$152$	−2.93700	+	5.08703i	−0.238222	+	0.412613i
$153$	4.77439	+	8.26948i	0.385986	+	0.668548i
$154$		0			0
$155$	−3.41706			−0.274465
$156$	−4.54550	−	7.18292i	−0.363931	−	0.575094i
$157$	−5.21503			−0.416204			−0.208102	−	0.978107i	$-0.566729\pi$
$157$	−5.21503			−0.416204			−0.208102	+	0.978107i	$0.566729\pi$
$158$	−12.2475	+	7.07112i	−0.974362	+	0.562548i
$159$	−2.73092	−	4.73009i	−0.216576	−	0.375121i
$160$	−1.67208	+	2.89612i	−0.132189	+	0.228958i
$161$		0			0
$162$	8.77313	+	5.06517i	0.689282	+	0.397957i
$163$	10.8077	+	6.23982i	0.846524	+	0.488741i	0.859476	−	0.511176i	$-0.170790\pi$
$163$	10.8077	+	6.23982i	0.846524	+	0.488741i	−0.0129528	+	0.999916i	$0.504123\pi$
$164$			1.05997i			0.0827699i
$165$	19.8542	−	34.3885i	1.54565	−	2.67714i
$166$	−4.58930	−	7.94889i	−0.356198	−	0.616954i
$167$	0.409946	−	0.236682i	0.0317226	−	0.0183150i	−0.484055	−	0.875038i	$-0.660836\pi$
$167$	0.409946	−	0.236682i	0.0317226	−	0.0183150i	0.515777	+	0.856723i	$0.327503\pi$
$168$		0			0
$169$	−5.56530	+	11.7485i	−0.428100	+	0.903731i
$170$	−12.4827			−0.957381
$171$	13.0133	−	7.51326i	0.995155	−	0.574553i
$172$	−1.65120	−	2.85996i	−0.125903	−	0.218070i
$173$	5.06601	−	8.77459i	0.385162	−	0.667120i	−0.606630	−	0.794984i	$-0.707479\pi$
$173$	5.06601	−	8.77459i	0.385162	−	0.667120i	0.991792	+	0.127865i	$0.0408123\pi$
$174$		−	15.8496i		−	1.20156i
$175$		0			0
$176$	4.36176	+	2.51826i	0.328780	+	0.189821i
$177$		−	19.0648i		−	1.43300i
$178$	2.70646	−	4.68772i	0.202857	−	0.351359i
$179$	−5.35710	−	9.27876i	−0.400408	−	0.693527i	0.593367	−	0.804932i	$-0.297798\pi$
$179$	−5.35710	−	9.27876i	−0.400408	−	0.693527i	−0.993775	+	0.111405i	$0.964465\pi$
$180$	7.40868	−	4.27741i	0.552211	−	0.318819i
$181$	−1.56347			−0.116212			−0.0581058	−	0.998310i	$-0.518506\pi$
$181$	−1.56347			−0.116212			−0.0581058	+	0.998310i	$0.518506\pi$
$182$		0			0
$183$	23.8138			1.76037
$184$	−3.27678	+	1.89185i	−0.241568	+	0.139469i
$185$	−0.716021	−	1.24018i	−0.0526429	−	0.0911801i
$186$	−1.20449	+	2.08623i	−0.0883171	+	0.152970i
$187$			18.7999i			1.37478i
$188$	−4.60157	−	2.65672i	−0.335604	−	0.193761i
$189$		0			0
$190$			19.6435i			1.42509i
$191$	4.69659	−	8.13473i	0.339833	−	0.588608i	−0.644568	−	0.764547i	$-0.722963\pi$
$191$	4.69659	−	8.13473i	0.339833	−	0.588608i	0.984401	+	0.175939i	$0.0562961\pi$
$192$	1.17879	+	2.04172i	0.0850715	+	0.147348i
$193$	−7.93269	+	4.57994i	−0.571008	+	0.329672i	−0.757552	−	0.652775i	$-0.773605\pi$
$193$	−7.93269	+	4.57994i	−0.571008	+	0.329672i	0.186544	+	0.982447i	$0.440271\pi$
$194$	−17.1753			−1.23311
$195$	−25.1747	−	13.2022i	−1.80280	−	0.945427i
$196$		0			0
$197$	13.4152	−	7.74526i	0.955793	−	0.551827i	0.0609170	−	0.998143i	$-0.480598\pi$
$197$	13.4152	−	7.74526i	0.955793	−	0.551827i	0.894876	+	0.446316i	$0.147264\pi$
$198$	−6.44208	−	11.1580i	−0.457818	−	0.792965i
$199$	−2.74194	+	4.74917i	−0.194371	+	0.336660i	−0.946694	−	0.322134i	$-0.895600\pi$
$199$	−2.74194	+	4.74917i	−0.194371	+	0.336660i	0.752323	+	0.658794i	$0.228933\pi$
$200$			6.18336i			0.437229i
$201$	−27.1512	−	15.6757i	−1.91509	−	1.10568i
$202$	2.12026	+	1.22413i	0.149181	+	0.0861295i
$203$		0			0
$204$	−4.40005	+	7.62112i	−0.308065	+	0.533585i
$205$	1.77235	+	3.06981i	0.123787	+	0.214405i
$206$	−15.5266	+	8.96428i	−1.08179	+	0.624571i
$207$	9.67924			0.672754
$208$	1.67454	−	3.19311i	0.116108	−	0.221402i
$209$	29.5846			2.04641
$210$		0			0
$211$	−2.54733	−	4.41210i	−0.175365	−	0.303741i	0.764922	−	0.644122i	$-0.222777\pi$
$211$	−2.54733	−	4.41210i	−0.175365	−	0.303741i	−0.940288	+	0.340381i	$0.889444\pi$
$212$	1.15836	−	2.00634i	0.0795567	−	0.137796i
$213$		−	6.41790i		−	0.439747i
$214$	8.57572	+	4.95119i	0.586224	+	0.338457i
$215$	−9.56414	−	5.52186i	−0.652269	−	0.376588i
$216$			1.04172i			0.0708798i
$217$		0			0
$218$	−1.77894	−	3.08121i	−0.120485	−	0.208686i
$219$	−16.2410	+	9.37673i	−1.09746	+	0.633621i
$220$	16.8429			1.13555
$221$	13.4474	−	0.546325i	0.904567	−	0.0367498i
$222$	−1.00956			−0.0677575
$223$	8.65366	−	4.99619i	0.579492	−	0.334570i	−0.181440	−	0.983402i	$-0.558076\pi$
$223$	8.65366	−	4.99619i	0.579492	−	0.334570i	0.760931	+	0.648832i	$0.224742\pi$
$224$		0			0
$225$	7.90895	−	13.6987i	0.527263	−	0.913247i
$226$		−	4.88916i		−	0.325222i
$227$	11.4442	+	6.60729i	0.759575	+	0.438541i	0.829143	−	0.559036i	$-0.188829\pi$
$227$	11.4442	+	6.60729i	0.759575	+	0.438541i	−0.0695679	+	0.997577i	$0.522162\pi$
$228$	11.9930	+	6.92418i	0.794258	+	0.458565i
$229$		−	9.95986i		−	0.658166i	−0.944301	−	0.329083i	$-0.893260\pi$
$229$		−	9.95986i		−	0.658166i	0.944301	−	0.329083i	$-0.106740\pi$
$230$	−6.32664	+	10.9581i	−0.417166	+	0.722553i
$231$		0			0
$232$	5.82216	−	3.36143i	0.382244	−	0.220688i
$233$	8.58467			0.562400			0.281200	−	0.959649i	$-0.409267\pi$
$233$	8.58467			0.562400			0.281200	+	0.959649i	$0.409267\pi$
$234$	−7.79400	+	4.93220i	−0.509510	+	0.322428i
$235$	−17.7689			−1.15912
$236$	7.00324	−	4.04332i	0.455872	−	0.263198i
$237$	16.6707	+	28.8744i	1.08288	+	1.87560i
$238$		0			0
$239$		−	1.17300i		−	0.0758748i	−0.999280	−	0.0379374i	$-0.987921\pi$
$239$		−	1.17300i		−	0.0758748i	0.999280	−	0.0379374i	$-0.0120787\pi$
$240$	6.82781	+	3.94204i	0.440733	+	0.254457i
$241$	−21.1208	−	12.1941i	−1.36051	−	0.785490i	−0.370817	−	0.928706i	$-0.620922\pi$
$241$	−21.1208	−	12.1941i	−1.36051	−	0.785490i	−0.989691	+	0.143216i	$0.954256\pi$
$242$		−	14.3666i		−	0.923522i
$243$	10.3789	−	17.9768i	0.665808	−	1.15321i
$244$	5.05050	+	8.74773i	0.323325	+	0.560016i
$245$		0			0
$246$	2.49896			0.159328
$247$	−0.859730	−	21.1615i	−0.0547033	−	1.34648i
$248$	−1.02180			−0.0648845
$249$	−18.7401	+	10.8196i	−1.18760	+	0.685664i
$250$	1.97866	+	3.42714i	0.125142	+	0.216752i
$251$	10.6649	−	18.4721i	0.673162	−	1.16595i	−0.303840	−	0.952723i	$-0.598269\pi$
$251$	10.6649	−	18.4721i	0.673162	−	1.16595i	0.977002	−	0.213228i	$-0.0683978\pi$
$252$		0			0
$253$	16.5036	+	9.52837i	1.03757	+	0.599043i
$254$	−7.18180	−	4.14641i	−0.450626	−	0.260169i
$255$			29.4289i			1.84291i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.42956	+	11.1363i	0.401065	+	0.694664i	0.993855	−	0.110693i	$-0.0353069\pi$
$257$	6.42956	+	11.1363i	0.401065	+	0.694664i	−0.592790	+	0.805357i	$0.701974\pi$
$258$	−6.74256	+	3.89282i	−0.419773	+	0.242356i
$259$		0			0
$260$	−0.489457	−	12.0476i	−0.0303548	−	0.747159i
$261$	−17.1980			−1.06453
$262$	−5.33618	+	3.08084i	−0.329670	+	0.190335i
$263$	−12.4300	−	21.5295i	−0.766470	−	1.32756i	−0.939466	−	0.342642i	$-0.888678\pi$
$263$	−12.4300	−	21.5295i	−0.766470	−	1.32756i	0.172997	−	0.984922i	$-0.444655\pi$
$264$	5.93699	−	10.2832i	0.365396	−	0.632885i
$265$		−	7.74748i		−	0.475924i
$266$		0			0
$267$	−11.0516	−	6.38066i	−0.676349	−	0.390490i
$268$		−	13.2982i		−	0.812317i
$269$	−10.3012	+	17.8422i	−0.628074	+	1.08786i	0.359864	+	0.933005i	$0.382823\pi$
$269$	−10.3012	+	17.8422i	−0.628074	+	1.08786i	−0.987938	+	0.154851i	$0.950510\pi$
$270$	1.74183	+	3.01693i	0.106004	+	0.183605i
$271$	−4.57387	+	2.64072i	−0.277843	+	0.160413i	−0.632446	−	0.774604i	$-0.717949\pi$
$271$	−4.57387	+	2.64072i	−0.277843	+	0.160413i	0.354604	+	0.935017i	$0.384616\pi$
$272$	−3.73270			−0.226328
$273$		0			0
$274$	−7.43816			−0.449355
$275$	26.9703	−	15.5713i	1.62637	−	0.938987i
$276$	4.46017	+	7.72525i	0.268471	+	0.465005i
$277$	−2.62506	+	4.54674i	−0.157725	+	0.273187i	−0.934048	−	0.357148i	$-0.883749\pi$
$277$	−2.62506	+	4.54674i	−0.157725	+	0.273187i	0.776323	+	0.630335i	$0.217083\pi$
$278$			4.88398i			0.292921i
$279$	2.26371	+	1.30696i	0.135525	+	0.0782454i
$280$		0			0
$281$		−	31.3151i		−	1.86810i	−0.357141	−	0.934051i	$-0.616248\pi$
$281$		−	31.3151i		−	1.86810i	0.357141	−	0.934051i	$-0.383752\pi$
$282$	−6.26339	+	10.8485i	−0.372980	+	0.646020i
$283$	3.86020	+	6.68606i	0.229465	+	0.397445i	0.957650	−	0.287936i	$-0.0929690\pi$
$283$	3.86020	+	6.68606i	0.229465	+	0.397445i	−0.728185	+	0.685381i	$0.759636\pi$
$284$	2.35754	−	1.36113i	0.139894	−	0.0807679i
$285$	46.3111			2.74323
$286$	−18.1445	+	0.737156i	−1.07291	+	0.0435890i
$287$		0			0
$288$	2.21541	−	1.27907i	0.130545	−	0.0753699i
$289$	1.53347	+	2.65605i	0.0902041	+	0.156238i
$290$	11.2411	−	19.4702i	0.660101	−	1.14333i
$291$			40.4919i			2.37368i
$292$	−6.88886	−	3.97728i	−0.403140	−	0.232753i
$293$	−18.3856	−	10.6150i	−1.07410	−	0.620133i	−0.144802	−	0.989461i	$-0.546255\pi$
$293$	−18.3856	−	10.6150i	−1.07410	−	0.620133i	−0.929299	+	0.369328i	$0.879588\pi$
$294$		0			0
$295$	13.5215	−	23.4199i	0.787252	−	1.36356i
$296$	−0.214111	−	0.370851i	−0.0124450	−	0.0215553i
$297$	4.54372	−	2.62332i	0.263653	−	0.152220i
$298$	5.61868			0.325482
$299$	6.33595	−	12.0818i	0.366417	−	0.698707i
$300$	14.5777			0.841644
$301$		0			0
$302$	−4.15489	−	7.19648i	−0.239087	−	0.414111i
$303$	2.88597	−	4.99865i	0.165795	−	0.287165i
$304$			5.87400i			0.336897i
$305$	29.2537	+	16.8897i	1.67506	+	0.967099i
$306$	8.26948	+	4.77439i	0.472735	+	0.272934i
$307$			33.9938i			1.94013i	0.242850	+	0.970064i	$0.421918\pi$
$307$			33.9938i			1.94013i	−0.242850	+	0.970064i	$0.578082\pi$
$308$		0			0
$309$	21.1339	+	36.6050i	1.20227	+	2.08239i
$310$	−2.95926	+	1.70853i	−0.168075	+	0.0970380i
$311$	−0.731766			−0.0414946			−0.0207473	−	0.999785i	$-0.506605\pi$
$311$	−0.731766			−0.0414946			−0.0207473	+	0.999785i	$0.506605\pi$
$312$	−7.52797	−	3.94784i	−0.426188	−	0.223502i
$313$	7.36717			0.416417			0.208209	−	0.978084i	$-0.433237\pi$
$313$	7.36717			0.416417			0.208209	+	0.978084i	$0.433237\pi$
$314$	−4.51635	+	2.60751i	−0.254872	+	0.147150i
$315$		0			0
$316$	−7.07112	+	12.2475i	−0.397782	+	0.688978i
$317$			28.4070i			1.59550i	0.602991	+	0.797748i	$0.293976\pi$
$317$			28.4070i			1.59550i	−0.602991	+	0.797748i	$0.706024\pi$
$318$	−4.73009	−	2.73092i	−0.265251	−	0.153142i
$319$	−29.3235	−	16.9299i	−1.64180	−	0.947894i
$320$			3.34415i			0.186944i
$321$	11.6728	−	20.2179i	0.651512	−	1.12845i
$322$		0			0
$323$	−18.9884	+	10.9629i	−1.05654	+	0.609994i
$324$	10.1303			0.562797
$325$	−11.9218	−	18.8391i	−0.661301	−	1.04501i
$326$	12.4796			0.691184
$327$	−7.26418	+	4.19398i	−0.401710	+	0.231927i
$328$	0.529986	+	0.917963i	0.0292636	+	0.0506860i
$329$		0			0
$330$		−	39.7084i		−	2.18587i
$331$	−17.5783	−	10.1489i	−0.966193	−	0.557832i	−0.0681192	−	0.997677i	$-0.521700\pi$
$331$	−17.5783	−	10.1489i	−0.966193	−	0.557832i	−0.898073	+	0.439846i	$0.855033\pi$
$332$	−7.94889	−	4.58930i	−0.436252	−	0.251870i
$333$			1.09545i			0.0600305i
$334$	0.236682	−	0.409946i	0.0129507	−	0.0224312i
$335$	−22.2356	−	38.5132i	−1.21486	−	2.10420i
$336$		0			0
$337$	−8.85616			−0.482426			−0.241213	−	0.970472i	$-0.577545\pi$
$337$	−8.85616			−0.482426			−0.241213	+	0.970472i	$0.577545\pi$
$338$	1.05456	+	12.9572i	0.0573606	+	0.704776i
$339$	−11.5265			−0.626036
$340$	−10.8104	+	6.24136i	−0.586274	+	0.338485i
$341$	2.57317	+	4.45686i	0.139345	+	0.241352i
$342$	7.51326	−	13.0133i	0.406270	−	0.703681i
$343$		0			0
$344$	−2.85996	−	1.65120i	−0.154199	−	0.0890267i
$345$	25.8344	+	14.9155i	1.39088	+	0.803024i
$346$		−	10.1320i		−	0.544701i
$347$	−3.44861	+	5.97316i	−0.185131	+	0.320656i	−0.943621	−	0.331029i	$-0.892604\pi$
$347$	−3.44861	+	5.97316i	−0.185131	+	0.320656i	0.758490	+	0.651685i	$0.225938\pi$
$348$	−7.92480	−	13.7262i	−0.424814	−	0.735799i
$349$	3.63303	−	2.09753i	0.194472	−	0.112278i	−0.399602	−	0.916689i	$-0.630852\pi$
$349$	3.63303	−	2.09753i	0.194472	−	0.112278i	0.594074	+	0.804410i	$0.297518\pi$
$350$		0			0
$351$	−2.00847	−	3.17384i	−0.107204	−	0.169407i
$352$	5.03653			0.268448
$353$	21.7100	−	12.5343i	1.15551	−	0.667132i	0.205284	−	0.978702i	$-0.434188\pi$
$353$	21.7100	−	12.5343i	1.15551	−	0.667132i	0.950223	+	0.311570i	$0.100855\pi$
$354$	−9.53242	−	16.5106i	−0.506643	−	0.877531i
$355$	4.55181	−	7.88397i	0.241585	−	0.418438i
$356$		−	5.41291i		−	0.286884i
$357$		0			0
$358$	−9.27876	−	5.35710i	−0.490398	−	0.283131i
$359$		−	19.8743i		−	1.04893i	−0.851433	−	0.524463i	$-0.824266\pi$
$359$		−	19.8743i		−	1.04893i	0.851433	−	0.524463i	$-0.175734\pi$
$360$	4.27741	−	7.40868i	0.225439	−	0.390472i
$361$	7.75193	+	13.4267i	0.407996	+	0.706670i
$362$	−1.35400	+	0.781733i	−0.0711648	+	0.0410870i
$363$	−33.8704			−1.77773
$364$		0			0
$365$	−26.6013			−1.39238
$366$	20.6234	−	11.9069i	1.07800	−	0.622385i
$367$	7.10630	+	12.3085i	0.370946	+	0.642497i	0.989711	−	0.143079i	$-0.0457002\pi$
$367$	7.10630	+	12.3085i	0.370946	+	0.642497i	−0.618765	+	0.785576i	$0.712367\pi$
$368$	−1.89185	+	3.27678i	−0.0986196	+	0.170814i
$369$		−	2.71156i		−	0.141158i
$370$	−1.24018	−	0.716021i	−0.0644741	−	0.0372241i
$371$		0			0
$372$			2.40897i			0.124899i
$373$	15.6299	−	27.0718i	0.809288	−	1.40173i	−0.104070	−	0.994570i	$-0.533187\pi$
$373$	15.6299	−	27.0718i	0.809288	−	1.40173i	0.913358	−	0.407157i	$-0.133480\pi$
$374$	9.39993	+	16.2812i	0.486059	+	0.841879i
$375$	8.07974	−	4.66484i	0.417236	−	0.240891i
$376$	−5.31343			−0.274019
$377$	−11.2577	+	21.4668i	−0.579799	+	1.10560i
$378$		0			0
$379$	19.0369	−	10.9909i	0.977858	−	0.564567i	0.0762355	−	0.997090i	$-0.475710\pi$
$379$	19.0369	−	10.9909i	0.977858	−	0.564567i	0.901623	+	0.432523i	$0.142377\pi$
$380$	9.82177	+	17.0118i	0.503846	+	0.872687i
$381$	−9.77546	+	16.9316i	−0.500812	+	0.867432i
$382$		−	9.39317i		−	0.480597i
$383$	−4.21349	−	2.43266i	−0.215299	−	0.124303i	0.388472	−	0.921460i	$-0.373003\pi$
$383$	−4.21349	−	2.43266i	−0.215299	−	0.124303i	−0.603772	+	0.797157i	$0.706336\pi$
$384$	2.04172	+	1.17879i	0.104191	+	0.0601546i
$385$		0			0
$386$	−4.57994	+	7.93269i	−0.233113	+	0.403764i
$387$	4.22400	+	7.31618i	0.214718	+	0.371902i
$388$	−14.8742	+	8.58763i	−0.755123	+	0.435971i
$389$	−12.8779			−0.652938			−0.326469	−	0.945208i	$-0.605859\pi$
$389$	−12.8779			−0.652938			−0.326469	+	0.945208i	$0.605859\pi$
$390$	−28.4030	+	1.15393i	−1.43824	+	0.0584315i
$391$	−14.1234			−0.714253
$392$		0			0
$393$	7.26330	+	12.5804i	0.366385	+	0.634598i
$394$	7.74526	−	13.4152i	0.390201	−	0.675847i
$395$			47.2938i			2.37961i
$396$	−11.1580	−	6.44208i	−0.560711	−	0.323726i
$397$	25.8091	+	14.9009i	1.29532	+	0.747855i	0.979593	−	0.200993i	$-0.0644170\pi$
$397$	25.8091	+	14.9009i	1.29532	+	0.747855i	0.315731	+	0.948849i	$0.397750\pi$
$398$			5.48387i			0.274882i
$399$		0			0
$400$	3.09168	+	5.35494i	0.154584	+	0.267747i
$401$	8.53523	−	4.92782i	0.426229	−	0.246084i	−0.271510	−	0.962436i	$-0.587523\pi$
$401$	8.53523	−	4.92782i	0.426229	−	0.246084i	0.697739	+	0.716352i	$0.254190\pi$
$402$	−31.3515			−1.56367
$403$	3.11317	−	1.97008i	0.155078	−	0.0981366i
$404$	2.44826			0.121806
$405$	29.3387	−	16.9387i	1.45785	−	0.841691i
$406$		0			0
$407$	−1.07838	+	1.86780i	−0.0534532	+	0.0925836i
$408$			8.80011i			0.435670i
$409$	−22.0121	−	12.7087i	−1.08843	−	0.628403i	−0.155269	−	0.987872i	$-0.549624\pi$
$409$	−22.0121	−	12.7087i	−1.08843	−	0.628403i	−0.933157	+	0.359469i	$0.882958\pi$
$410$	3.06981	+	1.77235i	0.151607	+	0.0875304i
$411$			17.5360i			0.864986i
$412$	−8.96428	+	15.5266i	−0.441638	+	0.764940i
$413$		0			0
$414$	8.38247	−	4.83962i	0.411976	−	0.237854i
$415$	−30.6946			−1.50674
$416$	−0.146362	−	3.60258i	−0.00717598	−	0.176631i
$417$	11.5143			0.563859
$418$	25.6210	−	14.7923i	1.25316	−	0.723514i
$419$	15.5587	+	26.9484i	0.760091	+	1.31652i	0.942803	+	0.333350i	$0.108179\pi$
$419$	15.5587	+	26.9484i	0.760091	+	1.31652i	−0.182712	+	0.983167i	$0.558488\pi$
$420$		0			0
$421$		−	13.8090i		−	0.673009i	−0.941682	−	0.336505i	$-0.890755\pi$
$421$		−	13.8090i		−	0.673009i	0.941682	−	0.336505i	$-0.109245\pi$
$422$	−4.41210	−	2.54733i	−0.214778	−	0.124002i
$423$	11.7715	+	6.79625i	0.572348	+	0.330445i
$424$		−	2.31672i		−	0.112510i
$425$	−11.5403	+	19.9884i	−0.559787	+	0.969580i
$426$	−3.20895	−	5.55806i	−0.155474	−	0.269289i
$427$		0			0
$428$	9.90239			0.478650
$429$	1.73790	+	42.7769i	0.0839065	+	2.06529i
$430$	−11.0437			−0.532576
$431$	27.4347	−	15.8394i	1.32148	−	0.762958i	0.337516	−	0.941320i	$-0.390413\pi$
$431$	27.4347	−	15.8394i	1.32148	−	0.762958i	0.983965	+	0.178362i	$0.0570798\pi$
$432$	0.520858	+	0.902152i	0.0250598	+	0.0434048i
$433$	13.7233	−	23.7695i	0.659500	−	1.14229i	−0.321245	−	0.946996i	$-0.604101\pi$
$433$	13.7233	−	23.7695i	0.659500	−	1.14229i	0.980745	−	0.195292i	$-0.0625655\pi$
$434$		0			0
$435$	−45.9024	−	26.5017i	−2.20085	−	1.27066i
$436$	−3.08121	−	1.77894i	−0.147563	−	0.0851957i
$437$			22.2255i			1.06319i
$438$	−9.37673	+	16.2410i	−0.448037	+	0.776024i
$439$	6.09116	+	10.5502i	0.290715	+	0.503534i	0.973979	−	0.226638i	$-0.0727734\pi$
$439$	6.09116	+	10.5502i	0.290715	+	0.503534i	−0.683264	+	0.730172i	$0.739440\pi$
$440$	14.5864	−	8.42146i	0.695379	−	0.401477i
$441$		0			0
$442$	11.3726	−	7.19681i	0.540939	−	0.342317i
$443$	−29.9063			−1.42089			−0.710445	−	0.703753i	$-0.751506\pi$
$443$	−29.9063			−1.42089			−0.710445	+	0.703753i	$0.751506\pi$
$444$	−0.874309	+	0.504782i	−0.0414928	+	0.0239559i
$445$	−9.05080	−	15.6764i	−0.429049	−	0.743135i
$446$	4.99619	−	8.65366i	0.236577	−	0.409763i
$447$		−	13.2464i		−	0.626535i
$448$		0			0
$449$	30.6709	+	17.7079i	1.44745	+	0.835685i	0.998329	−	0.0577858i	$-0.0184040\pi$
$449$	30.6709	+	17.7079i	1.44745	+	0.835685i	0.449121	+	0.893471i	$0.351737\pi$
$450$		−	15.8179i		−	0.745663i
$451$	2.66929	−	4.62335i	0.125692	−	0.217705i
$452$	−2.44458	−	4.23414i	−0.114983	−	0.199157i
$453$	−16.9662	+	9.79545i	−0.797142	+	0.460230i
$454$	13.2146			0.620191
$455$		0			0
$456$	13.8484			0.648509
$457$	−17.7635	+	10.2558i	−0.830943	+	0.479745i	−0.854175	−	0.519985i	$-0.825938\pi$
$457$	−17.7635	+	10.2558i	−0.830943	+	0.479745i	0.0232325	+	0.999730i	$0.492604\pi$
$458$	−4.97993	−	8.62549i	−0.232697	−	0.403043i
$459$	−1.94421	+	3.36746i	−0.0907478	+	0.157180i
$460$			12.6533i			0.589962i
$461$	2.94204	+	1.69858i	0.137024	+	0.0791110i	0.566945	−	0.823756i	$-0.308125\pi$
$461$	2.94204	+	1.69858i	0.137024	+	0.0791110i	−0.429921	+	0.902867i	$0.641459\pi$
$462$		0			0
$463$			39.3586i			1.82915i	0.404417	+	0.914575i	$0.367474\pi$
$463$			39.3586i			1.82915i	−0.404417	+	0.914575i	$0.632526\pi$
$464$	3.36143	−	5.82216i	0.156050	−	0.270287i
$465$	4.02798	+	6.97667i	0.186793	+	0.323535i
$466$	7.43454	−	4.29233i	0.344399	−	0.198839i
$467$	5.98885			0.277131			0.138565	−	0.990353i	$-0.455751\pi$
$467$	5.98885			0.277131			0.138565	+	0.990353i	$0.455751\pi$
$468$	−4.28370	+	8.16841i	−0.198014	+	0.377585i
$469$		0			0
$470$	−15.3883	+	8.88446i	−0.709811	+	0.409810i
$471$	6.14740	+	10.6476i	0.283257	+	0.490616i
$472$	4.04332	−	7.00324i	0.186109	−	0.322350i
$473$			16.6326i			0.764769i
$474$	28.8744	+	16.6707i	1.32625	+	0.765709i
$475$	31.4549	+	18.1605i	1.44325	+	0.833262i
$476$		0			0
$477$	−2.96325	+	5.13251i	−0.135678	+	0.235001i
$478$	−0.586498	−	1.01584i	−0.0268258	−	0.0464636i
$479$	11.8476	−	6.84021i	0.541330	−	0.312537i	−0.204288	−	0.978911i	$-0.565488\pi$
$479$	11.8476	−	6.84021i	0.541330	−	0.312537i	0.745618	+	0.666374i	$0.232154\pi$
$480$	7.88408			0.359857
$481$	1.36736	+	0.717074i	0.0623462	+	0.0326958i
$482$	−24.3882			−1.11085
$483$		0			0
$484$	−7.18332	−	12.4419i	−0.326514	−	0.565539i
$485$	−28.7183	+	49.7416i	−1.30403	+	2.25865i
$486$		−	20.7578i		−	0.941595i
$487$	−0.910007	−	0.525393i	−0.0412364	−	0.0238078i	0.479240	−	0.877684i	$-0.340912\pi$
$487$	−0.910007	−	0.525393i	−0.0412364	−	0.0238078i	−0.520476	+	0.853876i	$0.674246\pi$
$488$	8.74773	+	5.05050i	0.395991	+	0.228626i
$489$		−	29.4216i		−	1.33049i
$490$		0			0
$491$	−13.7757	−	23.8602i	−0.621688	−	1.07679i	−0.989171	−	0.146765i	$-0.953114\pi$
$491$	−13.7757	−	23.8602i	−0.621688	−	1.07679i	0.367484	−	0.930030i	$-0.380219\pi$
$492$	2.16416	−	1.24948i	0.0975680	−	0.0563309i
$493$	25.0944			1.13019
$494$	−11.3253	−	17.8966i	−0.509550	−	0.805205i
$495$	−43.0866			−1.93660
$496$	−0.884906	+	0.510901i	−0.0397335	+	0.0229401i
$497$		0			0
$498$	−10.8196	+	18.7401i	−0.484837	+	0.839763i
$499$			2.10425i			0.0941991i	0.998890	+	0.0470995i	$0.0149978\pi$
$499$			2.10425i			0.0941991i	−0.998890	+	0.0470995i	$0.985002\pi$
$500$	3.42714	+	1.97866i	0.153267	+	0.0884885i
$501$	−0.966477	−	0.557996i	−0.0431790	−	0.0249294i
$502$		−	21.3298i		−	0.951995i
$503$	−19.3301	+	33.4807i	−0.861886	+	1.49283i	0.00822020	+	0.999966i	$0.497383\pi$
$503$	−19.3301	+	33.4807i	−0.861886	+	1.49283i	−0.870106	+	0.492864i	$0.835950\pi$
$504$		0			0
$505$	7.09046	−	4.09368i	0.315521	−	0.182166i
$506$	19.0567			0.847175
$507$	30.5474	−	2.48620i	1.35666	−	0.110416i
$508$	−8.29282			−0.367935
$509$	−22.0326	+	12.7205i	−0.976578	+	0.563828i	−0.901235	−	0.433330i	$-0.857338\pi$
$509$	−22.0326	+	12.7205i	−0.976578	+	0.563828i	−0.0753428	+	0.997158i	$0.524005\pi$
$510$	14.7145	+	25.4862i	0.651567	+	1.12855i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	5.29924	+	3.05952i	0.233967	+	0.135081i
$514$	11.1363	+	6.42956i	0.491202	+	0.283596i
$515$			59.9559i			2.64197i
$516$	−3.89282	+	6.74256i	−0.171372	+	0.296825i
$517$	13.3806	+	23.1759i	0.588479	+	1.01928i
$518$		0			0
$519$	−23.8870			−1.04852
$520$	−6.44767	−	10.1888i	−0.282749	−	0.446807i
$521$	15.9879			0.700441			0.350221	−	0.936667i	$-0.386107\pi$
$521$	15.9879			0.700441			0.350221	+	0.936667i	$0.386107\pi$
$522$	−14.8939	+	8.59900i	−0.651889	+	0.376368i
$523$	9.11459	+	15.7869i	0.398553	+	0.690315i	0.993548	−	0.113415i	$-0.0361790\pi$
$523$	9.11459	+	15.7869i	0.398553	+	0.690315i	−0.594994	+	0.803730i	$0.702846\pi$
$524$	−3.08084	+	5.33618i	−0.134587	+	0.233112i
$525$		0			0
$526$	−21.5295	−	12.4300i	−0.938730	−	0.541976i
$527$	−3.30309	−	1.90704i	−0.143885	−	0.0830720i
$528$		−	11.8740i		−	0.516748i
$529$	4.34179	−	7.52021i	0.188774	−	0.326966i
$530$	−3.87374	−	6.70952i	−0.168265	−	0.291443i
$531$	−17.9153	+	10.3434i	−0.777457	+	0.448865i
$532$		0			0
$533$	−3.38460	−	1.77496i	−0.146603	−	0.0768822i
$534$	−12.7613			−0.552236
$535$	28.6785	−	16.5575i	1.23988	−	0.715845i
$536$	−6.64910	−	11.5166i	−0.287197	−	0.497441i
$537$	−12.6297	+	21.8753i	−0.545013	+	0.943991i
$538$			20.6024i			0.888231i
$539$		0			0
$540$	3.01693	+	1.74183i	0.129828	+	0.0749563i
$541$		−	19.2066i		−	0.825758i	−0.910786	−	0.412879i	$-0.864523\pi$
$541$		−	19.2066i		−	0.825758i	0.910786	−	0.412879i	$-0.135477\pi$
$542$	−2.64072	+	4.57387i	−0.113429	+	0.196464i
$543$	1.84299	+	3.19216i	0.0790903	+	0.136988i
$544$	−3.23261	+	1.86635i	−0.138597	+	0.0800191i
$545$	−11.8981			−0.509658
$546$		0			0
$547$	−12.3643			−0.528659			−0.264329	−	0.964432i	$-0.585151\pi$
$547$	−12.3643			−0.528659			−0.264329	+	0.964432i	$0.585151\pi$
$548$	−6.44163	+	3.71908i	−0.275173	+	0.158871i
$549$	−12.9199	−	22.3779i	−0.551408	−	0.955067i
$550$	15.5713	−	26.9703i	0.663964	−	1.15002i
$551$		−	39.4900i		−	1.68233i
$552$	7.72525	+	4.46017i	0.328808	+	0.189838i
$553$		0			0
$554$			5.25013i			0.223057i
$555$	−1.68807	+	2.92382i	−0.0716545	+	0.124109i
$556$	2.44199	+	4.22965i	0.103563	+	0.179377i
$557$	25.5877	−	14.7731i	1.08419	−	0.625956i	0.152165	−	0.988355i	$-0.451376\pi$
$557$	25.5877	−	14.7731i	1.08419	−	0.625956i	0.932023	+	0.362399i	$0.118042\pi$
$558$	2.61391			0.110656
$559$	11.8972	−	0.483345i	0.503196	−	0.0204433i
$560$		0			0
$561$	38.3840	−	22.1610i	1.62057	−	0.935638i
$562$	−15.6575	−	27.1197i	−0.660474	−	1.14397i
$563$	−1.26155	+	2.18506i	−0.0531678	+	0.0920894i	−0.891384	−	0.453248i	$-0.850265\pi$
$563$	−1.26155	+	2.18506i	−0.0531678	+	0.0920894i	0.838217	+	0.545337i	$0.183598\pi$
$564$			12.5268i			0.527473i
$565$	−14.1596	−	8.17505i	−0.595699	−	0.343927i
$566$	6.68606	+	3.86020i	0.281036	+	0.162256i
$567$		0			0
$568$	1.36113	−	2.35754i	0.0571115	−	0.0989201i
$569$	−5.21623	−	9.03478i	−0.218676	−	0.378758i	0.735728	−	0.677278i	$-0.236840\pi$
$569$	−5.21623	−	9.03478i	−0.218676	−	0.378758i	−0.954403	+	0.298520i	$0.903507\pi$
$570$	40.1065	−	23.1555i	1.67988	−	0.969878i
$571$	−0.145787			−0.00610099			−0.00305049	−	0.999995i	$-0.500971\pi$
$571$	−0.145787			−0.00610099			−0.00305049	+	0.999995i	$0.500971\pi$
$572$	−15.3450	+	9.71065i	−0.641607	+	0.406022i
$573$	−22.1451			−0.925124
$574$		0			0
$575$	11.6980	+	20.2615i	0.487840	+	0.844964i
$576$	1.27907	−	2.21541i	0.0532946	−	0.0923089i
$577$		−	22.4447i		−	0.934385i	−0.884156	−	0.467192i	$-0.845266\pi$
$577$		−	22.4447i		−	0.934385i	0.884156	−	0.467192i	$-0.154734\pi$
$578$	2.65605	+	1.53347i	0.110477	+	0.0637840i
$579$	18.7019	+	10.7975i	0.777224	+	0.448731i
$580$		−	22.4822i		−	0.933524i
$581$		0			0
$582$	20.2459	+	35.0670i	0.839221	+	1.45357i
$583$	−10.1050	+	5.83413i	−0.418507	+	0.241625i
$584$	−7.95457			−0.329162
$585$	1.25210	+	30.8194i	0.0517679	+	1.27422i
$586$	−21.2299			−0.877000
$587$	18.2824	−	10.5554i	0.754596	−	0.435666i	−0.0727563	−	0.997350i	$-0.523180\pi$
$587$	18.2824	−	10.5554i	0.754596	−	0.435666i	0.827352	+	0.561684i	$0.189846\pi$
$588$		0			0
$589$	−3.00103	+	5.19794i	−0.123655	+	0.214177i
$590$		−	27.0430i		−	1.11334i
$591$	−31.6273	−	18.2600i	−1.30097	−	0.751116i
$592$	−0.370851	−	0.214111i	−0.0152419	−	0.00879992i
$593$		−	29.8304i		−	1.22499i	−0.790475	−	0.612494i	$-0.790166\pi$
$593$		−	29.8304i		−	1.22499i	0.790475	−	0.612494i	$-0.209834\pi$
$594$	2.62332	−	4.54372i	0.107636	−	0.186431i
$595$		0			0
$596$	4.86592	−	2.80934i	0.199316	−	0.115075i
$597$	12.9286			0.529133
$598$	−0.553790	−	13.6311i	−0.0226462	−	0.557417i
$599$	33.5040			1.36894			0.684469	−	0.729042i	$-0.260034\pi$
$599$	33.5040			1.36894			0.684469	+	0.729042i	$0.260034\pi$
$600$	12.6247	−	7.28885i	0.515400	−	0.297566i
$601$	−18.9681	−	32.8537i	−0.773724	−	1.34013i	−0.935509	−	0.353303i	$-0.885058\pi$
$601$	−18.9681	−	32.8537i	−0.773724	−	1.34013i	0.161785	−	0.986826i	$-0.448275\pi$
$602$		0			0
$603$			34.0187i			1.38535i
$604$	−7.19648	−	4.15489i	−0.292821	−	0.169060i
$605$	−41.6075	−	24.0221i	−1.69159	−	0.976637i
$606$		−	5.77195i		−	0.234469i
$607$	17.9335	−	31.0618i	0.727900	−	1.26076i	−0.229870	−	0.973221i	$-0.573830\pi$
$607$	17.9335	−	31.0618i	0.727900	−	1.26076i	0.957769	−	0.287538i	$-0.0928366\pi$
$608$	2.93700	+	5.08703i	0.119111	+	0.206306i
$609$		0			0
$610$	33.7793			1.36768
$611$	16.1887	−	10.2445i	0.654923	−	0.414449i
$612$	9.54877			0.385986
$613$	−10.9563	+	6.32562i	−0.442521	+	0.255489i	−0.704666	−	0.709539i	$-0.748903\pi$
$613$	−10.9563	+	6.32562i	−0.442521	+	0.255489i	0.262146	+	0.965028i	$0.415570\pi$
$614$	16.9969	+	29.4395i	0.685939	+	1.18808i
$615$	4.17845	−	7.23729i	0.168491	−	0.291836i
$616$		0			0
$617$	34.6231	+	19.9896i	1.39387	+	0.804753i	0.993741	−	0.111705i	$-0.0356312\pi$
$617$	34.6231	+	19.9896i	1.39387	+	0.804753i	0.400131	+	0.916458i	$0.368965\pi$
$618$	36.6050	+	21.1339i	1.47247	+	0.850131i
$619$			9.91384i			0.398471i	0.979952	+	0.199235i	$0.0638459\pi$
$619$			9.91384i			0.398471i	−0.979952	+	0.199235i	$0.936154\pi$
$620$	−1.70853	+	2.95926i	−0.0686162	+	0.118847i
$621$	1.97077	+	3.41348i	0.0790843	+	0.136978i
$622$	−0.633728	+	0.365883i	−0.0254102	+	0.0146706i
$623$		0			0
$624$	−8.49334	+	0.345059i	−0.340006	+	0.0138134i
$625$	−17.6829			−0.707315
$626$	6.38016	−	3.68359i	0.255002	−	0.147226i
$627$	−34.8739	−	60.4033i	−1.39273	−	2.41228i
$628$	−2.60751	+	4.51635i	−0.104051	+	0.180222i
$629$		−	1.59843i		−	0.0637334i
$630$		0			0
$631$	21.7056	+	12.5318i	0.864088	+	0.498881i	0.865379	−	0.501118i	$-0.167078\pi$
$631$	21.7056	+	12.5318i	0.864088	+	0.498881i	−0.00129129	+	0.999999i	$0.500411\pi$
$632$			14.1422i			0.562548i
$633$	−6.00550	+	10.4018i	−0.238697	+	0.413436i
$634$	14.2035	+	24.6012i	0.564093	+	0.977038i
$635$	−24.0170	+	13.8662i	−0.953087	+	0.550265i
$636$	−5.46184			−0.216576
$637$		0			0
$638$	−33.8598			−1.34052
$639$	−6.03091	+	3.48195i	−0.238579	+	0.137744i
$640$	1.67208	+	2.89612i	0.0660946	+	0.114479i
$641$	4.01506	−	6.95429i	0.158585	−	0.274678i	−0.775773	−	0.631012i	$-0.782640\pi$
$641$	4.01506	−	6.95429i	0.158585	−	0.274678i	0.934359	+	0.356334i	$0.115973\pi$
$642$		−	23.3456i		−	0.921377i
$643$	13.3951	+	7.73367i	0.528251	+	0.304986i	0.740304	−	0.672272i	$-0.234682\pi$
$643$	13.3951	+	7.73367i	0.528251	+	0.304986i	−0.212053	+	0.977258i	$0.568015\pi$
$644$		0			0
$645$			26.0364i			1.02518i
$646$	−10.9629	+	18.9884i	−0.431331	+	0.747087i
$647$	3.34618	+	5.79575i	0.131552	+	0.227854i	0.924275	−	0.381727i	$-0.124671\pi$
$647$	3.34618	+	5.79575i	0.131552	+	0.227854i	−0.792723	+	0.609582i	$0.791337\pi$
$648$	8.77313	−	5.06517i	0.344641	−	0.198979i
$649$	−40.7286			−1.59874
$650$	−19.7441	−	10.3543i	−0.774428	−	0.406127i
$651$		0			0
$652$	10.8077	−	6.23982i	0.423262	−	0.244370i
$653$	12.0804	+	20.9238i	0.472741	+	0.818811i	0.999513	−	0.0311950i	$-0.00993128\pi$
$653$	12.0804	+	20.9238i	0.472741	+	0.818811i	−0.526772	+	0.850006i	$0.676598\pi$
$654$	−4.19398	+	7.26418i	−0.163997	+	0.284052i
$655$			20.6056i			0.805128i
$656$	0.917963	+	0.529986i	0.0358404	+	0.0206925i
$657$	17.6227	+	10.1745i	0.687526	+	0.396943i
$658$		0			0
$659$	−6.47769	+	11.2197i	−0.252335	+	0.437057i	−0.964168	−	0.265291i	$-0.914532\pi$
$659$	−6.47769	+	11.2197i	−0.252335	+	0.437057i	0.711833	+	0.702349i	$0.247865\pi$
$660$	−19.8542	−	34.3885i	−0.772823	−	1.33857i
$661$	16.7049	−	9.64460i	0.649747	−	0.375132i	−0.138612	−	0.990347i	$-0.544264\pi$
$661$	16.7049	−	9.64460i	0.649747	−	0.375132i	0.788359	+	0.615215i	$0.210931\pi$
$662$	−20.2977			−0.788893
$663$	−16.9670	−	26.8117i	−0.658943	−	1.04128i
$664$	−9.17859			−0.356198
$665$		0			0
$666$	0.547726	+	0.948690i	0.0212240	+	0.0367610i
$667$	12.7186	−	22.0293i	0.492468	−	0.852979i
$668$		−	0.473365i		−	0.0183150i
$669$	−20.4016	−	11.7789i	−0.788772	−	0.455398i
$670$	−38.5132	−	22.2356i	−1.48789	−	0.859037i
$671$		−	50.8740i		−	1.96397i
$672$		0			0
$673$	−14.7943	−	25.6245i	−0.570279	−	0.987752i	−0.996537	−	0.0831505i	$-0.973502\pi$
$673$	−14.7943	−	25.6245i	−0.570279	−	0.987752i	0.426258	−	0.904602i	$-0.359832\pi$
$674$	−7.66966	+	4.42808i	−0.295424	+	0.170563i
$675$	6.44130			0.247926
$676$	7.39185	+	10.6939i	0.284302	+	0.411306i
$677$	13.8422			0.531998			0.265999	−	0.963973i	$-0.414298\pi$
$677$	13.8422			0.531998			0.265999	+	0.963973i	$0.414298\pi$
$678$	−9.98228	+	5.76327i	−0.383367	+	0.221337i
$679$		0			0
$680$	−6.24136	+	10.8104i	−0.239345	+	0.414558i
$681$		−	31.1543i		−	1.19384i
$682$	4.45686	+	2.57317i	0.170662	+	0.0985317i
$683$	30.9323	+	17.8588i	1.18359	+	0.683347i	0.956843	−	0.290607i	$-0.0938571\pi$
$683$	30.9323	+	17.8588i	1.18359	+	0.683347i	0.226749	+	0.973953i	$0.427190\pi$
$684$		−	15.0265i		−	0.574553i
$685$	−12.4372	+	21.5418i	−0.475200	+	0.823070i
$686$		0			0
$687$	−20.3352	+	11.7405i	−0.775837	+	0.447929i
$688$	−3.30240			−0.125903
$689$	4.46674	+	7.05847i	0.170169	+	0.268906i
$690$	29.8310			1.13565
$691$	22.5221	−	13.0031i	0.856782	−	0.494663i	−0.00615160	−	0.999981i	$-0.501958\pi$
$691$	22.5221	−	13.0031i	0.856782	−	0.494663i	0.862933	+	0.505318i	$0.168625\pi$
$692$	−5.06601	−	8.77459i	−0.192581	−	0.333560i
$693$		0			0
$694$			6.89722i			0.261815i
$695$	14.1446	+	8.16638i	0.536535	+	0.309768i
$696$	−13.7262	−	7.92480i	−0.520289	−	0.300389i
$697$			3.95656i			0.149865i
$698$	2.09753	−	3.63303i	0.0793928	−	0.137512i
$699$	−10.1195	−	17.5275i	−0.382754	−	0.662949i
$700$		0			0
$701$	24.7068			0.933164			0.466582	−	0.884478i	$-0.345485\pi$
$701$	24.7068			0.933164			0.466582	+	0.884478i	$0.345485\pi$
$702$	−3.32631	−	1.74439i	−0.125543	−	0.0658378i
$703$	−2.51538			−0.0948693
$704$	4.36176	−	2.51826i	0.164390	−	0.0949107i
$705$	20.9457	+	36.2791i	0.788863	+	1.36635i
$706$	12.5343	−	21.7100i	0.471734	−	0.817067i
$707$		0			0
$708$	−16.5106	−	9.53242i	−0.620508	−	0.358250i
$709$	19.3947	+	11.1975i	0.728383	+	0.420532i	0.817830	−	0.575460i	$-0.195177\pi$
$709$	19.3947	+	11.1975i	0.728383	+	0.420532i	−0.0894476	+	0.995992i	$0.528510\pi$
$710$		−	9.10362i		−	0.341653i
$711$	18.0889	−	31.3309i	0.678387	−	1.17500i
$712$	−2.70646	−	4.68772i	−0.101429	−	0.175680i
$713$	−3.34822	+	1.93310i	−0.125392	+	0.0723951i
$714$		0			0
$715$	−28.2041	+	53.7812i	−1.05477	+	2.01130i
$716$	−10.7142			−0.400408
$717$	−2.39492	+	1.38271i	−0.0894401	+	0.0516383i
$718$	−9.93716	−	17.2117i	−0.370852	−	0.642334i
$719$	−12.6421	+	21.8968i	−0.471472	+	0.816613i	−0.999467	−	0.0326342i	$-0.989610\pi$
$719$	−12.6421	+	21.8968i	−0.471472	+	0.816613i	0.527996	+	0.849247i	$0.322944\pi$
$720$		−	8.55481i		−	0.318819i
$721$		0			0
$722$	13.4267	+	7.75193i	0.499691	+	0.288497i
$723$			57.4968i			2.13833i
$724$	−0.781733	+	1.35400i	−0.0290529	+	0.0503211i
$725$	−20.7849	−	36.0005i	−0.771932	−	1.33702i
$726$	−29.3326	+	16.9352i	−1.08863	+	0.628523i
$727$	39.9649			1.48221			0.741107	−	0.671386i	$-0.234301\pi$
$727$	39.9649			1.48221			0.741107	+	0.671386i	$0.234301\pi$
$728$		0			0
$729$	−18.5471			−0.686929
$730$	−23.0374	+	13.3006i	−0.852652	+	0.492279i
$731$	−6.16343	−	10.6754i	−0.227963	−	0.394843i
$732$	11.9069	−	20.6234i	0.440093	−	0.762263i
$733$		−	24.1168i		−	0.890774i	−0.895338	−	0.445387i	$-0.853066\pi$
$733$		−	24.1168i		−	0.890774i	0.895338	−	0.445387i	$-0.146934\pi$
$734$	12.3085	+	7.10630i	0.454314	+	0.262298i
$735$		0			0
$736$			3.78370i			0.139469i
$737$	−33.4884	+	58.0036i	−1.23356	+	2.13659i
$738$	−1.35578	−	2.34828i	−0.0499069	−	0.0864413i
$739$	−24.7187	+	14.2714i	−0.909292	+	0.524980i	−0.880203	−	0.474597i	$-0.842594\pi$
$739$	−24.7187	+	14.2714i	−0.909292	+	0.524980i	−0.0290890	+	0.999577i	$0.509261\pi$
$740$	−1.43204			−0.0526429
$741$	−42.1924	+	26.7002i	−1.54998	+	0.980858i
$742$		0			0
$743$	−37.9322	+	21.9001i	−1.39160	+	0.803438i	−0.993492	−	0.113902i	$-0.963665\pi$
$743$	−37.9322	+	21.9001i	−1.39160	+	0.803438i	−0.398104	+	0.917340i	$0.630332\pi$
$744$	1.20449	+	2.08623i	0.0441586	+	0.0764849i
$745$	9.39487	−	16.2724i	0.344201	−	0.596174i
$746$		−	31.2599i		−	1.14451i
$747$	20.3344	+	11.7401i	0.743996	+	0.429546i
$748$	16.2812	+	9.39993i	0.595298	+	0.343696i
$749$		0			0
$750$	4.66484	−	8.07974i	0.170336	−	0.295030i
$751$	20.2337	+	35.0458i	0.738338	+	1.27884i	0.953243	+	0.302204i	$0.0977223\pi$
$751$	20.2337	+	35.0458i	0.738338	+	1.27884i	−0.214906	+	0.976635i	$0.568944\pi$
$752$	−4.60157	+	2.65672i	−0.167802	+	0.0968804i
$753$	−50.2865			−1.83254
$754$	0.983970	+	24.2196i	0.0358341	+	0.882026i
$755$	−27.7892			−1.01135
$756$		0			0
$757$	−6.36103	−	11.0176i	−0.231196	−	0.400442i	0.726965	−	0.686675i	$-0.240930\pi$
$757$	−6.36103	−	11.0176i	−0.231196	−	0.400442i	−0.958160	+	0.286232i	$0.907597\pi$
$758$	10.9909	−	19.0369i	0.399209	−	0.691450i
$759$		−	44.9276i		−	1.63077i
$760$	17.0118	+	9.82177i	0.617083	+	0.356273i
$761$	−26.6191	−	15.3686i	−0.964943	−	0.557110i	−0.0672521	−	0.997736i	$-0.521423\pi$
$761$	−26.6191	−	15.3686i	−0.964943	−	0.557110i	−0.897691	+	0.440626i	$0.854756\pi$
$762$			19.5509i			0.708255i
$763$		0			0
$764$	−4.69659	−	8.13473i	−0.169917	−	0.294304i
$765$	27.6544	−	15.9663i	0.999847	−	0.577262i
$766$	−4.86532			−0.175791
$767$	1.18358	+	29.1328i	0.0427365	+	1.05192i
$768$	2.35757			0.0850715
$769$	10.0887	−	5.82469i	0.363806	−	0.210044i	−0.306943	−	0.951728i	$-0.599306\pi$
$769$	10.0887	−	5.82469i	0.363806	−	0.210044i	0.670749	+	0.741684i	$0.265973\pi$
$770$		0			0
$771$	15.1581	−	26.2547i	0.545907	−	0.945538i
$772$			9.15989i			0.329672i
$773$	24.5544	+	14.1765i	0.883159	+	0.509892i	0.871699	−	0.490042i	$-0.163019\pi$
$773$	24.5544	+	14.1765i	0.883159	+	0.509892i	0.0114603	+	0.999934i	$0.496352\pi$
$774$	7.31618	+	4.22400i	0.262975	+	0.151829i
$775$			6.31817i			0.226955i
$776$	−8.58763	+	14.8742i	−0.308278	+	0.533953i
$777$		0			0
$778$	−11.1526	+	6.43897i	−0.399841	+	0.230848i
$779$	6.22628			0.223079
$780$	−24.0208	+	15.2008i	−0.860081	+	0.544277i
$781$	−13.7107			−0.490607
$782$	−12.2313	+	7.06172i	−0.437389	+	0.252527i
$783$	−3.50165	−	6.06503i	−0.125139	−	0.216747i
$784$		0			0
$785$			17.4398i			0.622455i
$786$	12.5804	+	7.26330i	0.448728	+	0.259074i
$787$	−1.85099	−	1.06867i	−0.0659808	−	0.0380940i	0.466647	−	0.884444i	$-0.345462\pi$
$787$	−1.85099	−	1.06867i	−0.0659808	−	0.0380940i	−0.532627	+	0.846350i	$0.678795\pi$
$788$		−	15.4905i		−	0.551827i
$789$	−29.3047	+	50.7573i	−1.04328	+	1.80701i
$790$	23.6469	+	40.9576i	0.841319	+	1.45721i
$791$		0			0
$792$	−12.8842			−0.457818
$793$	−36.3897	+	1.47840i	−1.29224	+	0.0524996i
$794$	29.8018			1.05763
$795$	−15.8182	+	9.13262i	−0.561012	+	0.323901i
$796$	2.74194	+	4.74917i	0.0971853	+	0.168330i
$797$	13.9817	−	24.2170i	0.495257	−	0.857810i	−0.504728	−	0.863278i	$-0.668407\pi$
$797$	13.9817	−	24.2170i	0.495257	−	0.857810i	0.999985	+	0.00546806i	$0.00174055\pi$
$798$		0			0
$799$	−17.1763	−	9.91672i	−0.607653	−	0.350829i
$800$	5.35494	+	3.09168i	0.189326	+	0.109307i
$801$			13.8470i			0.489259i
$802$	4.92782	−	8.53523i	0.174007	−	0.301390i
$803$	20.0317	+	34.6959i	0.706904	+	1.22439i
$804$	−27.1512	+	15.6757i	−0.957547	+	0.552840i
$805$		0			0
$806$	1.71104	−	3.26272i	0.0602690	−	0.114924i
$807$	48.5715			1.70980
$808$	2.12026	−	1.22413i	0.0745903	−	0.0430648i
$809$	24.3621	+	42.1965i	0.856527	+	1.48355i	0.875221	+	0.483724i	$0.160716\pi$
$809$	24.3621	+	42.1965i	0.856527	+	1.48355i	−0.0186933	+	0.999825i	$0.505951\pi$
$810$	16.9387	−	29.3387i	0.595165	−	1.03086i
$811$		−	31.9965i		−	1.12355i	−0.827290	−	0.561774i	$-0.810119\pi$
$811$		−	31.9965i		−	1.12355i	0.827290	−	0.561774i	$-0.189881\pi$
$812$		0			0
$813$	10.7832	+	6.22569i	0.378184	+	0.218345i
$814$			2.15675i			0.0755942i
$815$	20.8669	−	36.1426i	0.730936	−	1.26602i
$816$	4.40005	+	7.62112i	0.154033	+	0.266792i
$817$	−16.7994	+	9.69914i	−0.587737	+	0.339330i
$818$	−25.4173			−0.888696
$819$		0			0
$820$	3.54471			0.123787
$821$	−10.8028	+	6.23701i	−0.377021	+	0.217673i	−0.676521	−	0.736423i	$-0.736513\pi$
$821$	−10.8028	+	6.23701i	−0.377021	+	0.217673i	0.299500	+	0.954096i	$0.403180\pi$
$822$	8.76799	+	15.1866i	0.305819	+	0.529694i
$823$	8.01300	−	13.8789i	0.279316	−	0.483789i	−0.691899	−	0.721994i	$-0.743226\pi$
$823$	8.01300	−	13.8789i	0.279316	−	0.483789i	0.971215	+	0.238205i	$0.0765591\pi$
$824$			17.9286i			0.624571i
$825$	−63.5845	−	36.7105i	−2.21373	−	1.27810i
$826$		0			0
$827$		−	6.94225i		−	0.241406i	−0.992689	−	0.120703i	$-0.961485\pi$
$827$		−	6.94225i		−	0.241406i	0.992689	−	0.120703i	$-0.0385148\pi$
$828$	4.83962	−	8.38247i	0.168189	−	0.291311i
$829$	−4.54445	−	7.87122i	−0.157835	−	0.273379i	0.776252	−	0.630422i	$-0.217118\pi$
$829$	−4.54445	−	7.87122i	−0.157835	−	0.273379i	−0.934088	+	0.357043i	$0.883785\pi$
$830$	−26.5823	+	15.3473i	−0.922686	+	0.532713i
$831$	12.3775			0.429372
$832$	−1.92804	−	3.04674i	−0.0668429	−	0.105627i
$833$		0			0
$834$	9.97169	−	5.75716i	0.345291	−	0.199354i
$835$	−0.791502	−	1.37092i	−0.0273911	−	0.0474427i
$836$	14.7923	−	25.6210i	0.511602	−	0.886120i
$837$			1.06443i			0.0367920i
$838$	26.9484	+	15.5587i	0.930918	+	0.537466i
$839$	15.8840	+	9.17062i	0.548376	+	0.316605i	0.748467	−	0.663173i	$-0.230790\pi$
$839$	15.8840	+	9.17062i	0.548376	+	0.316605i	−0.200091	+	0.979777i	$0.564124\pi$
$840$		0			0
$841$	−8.09837	+	14.0268i	−0.279254	+	0.483683i
$842$	−6.90450	−	11.9589i	−0.237945	−	0.412132i
$843$	−63.9365	+	36.9138i	−2.20209	+	1.27138i
$844$	−5.09465			−0.175365
$845$	39.2888	+	18.6112i	1.35158	+	0.640245i
$846$	13.5925			0.467320
$847$		0			0
$848$	−1.15836	−	2.00634i	−0.0397783	−	0.0688981i
$849$	9.10069	−	15.7629i	0.312335	−	0.540980i
$850$			23.0806i			0.791659i
$851$	−1.40319	−	0.810133i	−0.0481008	−	0.0277710i
$852$	−5.55806	−	3.20895i	−0.190416	−	0.109937i
$853$			53.7617i			1.84077i	0.391018	+	0.920383i	$0.372123\pi$
$853$			53.7617i			1.84077i	−0.391018	+	0.920383i	$0.627877\pi$
$854$		0			0
$855$	−25.1255	−	43.5186i	−0.859273	−	1.48830i
$856$	8.57572	−	4.95119i	0.293112	−	0.169228i
$857$	−38.2580			−1.30687			−0.653434	−	0.756984i	$-0.726672\pi$
$857$	−38.2580			−1.30687			−0.653434	+	0.756984i	$0.726672\pi$
$858$	22.8935	+	36.1770i	0.781572	+	1.23506i
$859$	15.7899			0.538744			0.269372	−	0.963036i	$-0.413184\pi$
$859$	15.7899			0.538744			0.269372	+	0.963036i	$0.413184\pi$
$860$	−9.56414	+	5.52186i	−0.326135	+	0.188294i
$861$		0			0
$862$	15.8394	−	27.4347i	0.539492	−	0.934428i
$863$		−	44.5788i		−	1.51748i	−0.651394	−	0.758739i	$-0.725816\pi$
$863$		−	44.5788i		−	1.51748i	0.651394	−	0.758739i	$-0.274184\pi$
$864$	0.902152	+	0.520858i	0.0306918	+	0.0177199i
$865$	−29.3436	−	16.9415i	−0.997711	−	0.576029i
$866$		−	27.4466i		−	0.932674i
$867$	3.61527	−	6.26182i	0.122781	−	0.212663i
$868$		0			0
$869$	61.6851	−	35.6139i	2.09252	−	1.20812i
$870$	−53.0035			−1.79699
$871$	42.4626	+	22.2683i	1.43879	+	0.754533i
$872$	−3.55788			−0.120485
$873$	38.0503	−	21.9684i	1.28781	−	0.743516i
$874$	11.1127	+	19.2478i	0.375894	+	0.651067i
$875$		0			0
$876$			18.7535i			0.633621i
$877$	−0.121237	−	0.0699963i	−0.00409389	−	0.00236361i	0.497952	−	0.867205i	$-0.334086\pi$
$877$	−0.121237	−	0.0699963i	−0.00409389	−	0.00236361i	−0.502046	+	0.864841i	$0.667419\pi$
$878$	10.5502	+	6.09116i	0.356052	+	0.205567i
$879$			50.0510i			1.68818i
$880$	8.42146	−	14.5864i	0.283887	−	0.491707i
$881$	22.6522	+	39.2347i	0.763172	+	1.32185i	0.941208	+	0.337828i	$0.109692\pi$
$881$	22.6522	+	39.2347i	0.763172	+	1.32185i	−0.178036	+	0.984024i	$0.556974\pi$
$882$		0			0
$883$	−46.5419			−1.56626			−0.783130	−	0.621858i	$-0.786378\pi$
$883$	−46.5419			−1.56626			−0.783130	+	0.621858i	$0.786378\pi$
$884$	6.25054	−	11.9189i	0.210229	−	0.400876i
$885$	−63.7558			−2.14313
$886$	−25.8996	+	14.9531i	−0.870114	+	0.502360i
$887$	24.4650	+	42.3746i	0.821453	+	1.42280i	0.904600	+	0.426261i	$0.140170\pi$
$887$	24.4650	+	42.3746i	0.821453	+	1.42280i	−0.0831471	+	0.996537i	$0.526497\pi$
$888$	−0.504782	+	0.874309i	−0.0169394	+	0.0293399i
$889$		0			0
$890$	−15.6764	−	9.05080i	−0.525476	−	0.303383i
$891$	−44.1861	−	25.5109i	−1.48029	−	0.854647i
$892$		−	9.99239i		−	0.334570i
$893$	−15.6055	+	27.0296i	−0.522220	+	0.904511i
$894$	−6.62322	−	11.4718i	−0.221514	−	0.383673i
$895$	−31.0296	+	17.9149i	−1.03721	+	0.598831i
$896$		0			0
$897$	−32.1363	+	1.30560i	−1.07300	+	0.0435927i
$898$	35.4157			1.18184
$899$	5.94910	−	3.43471i	0.198413	−	0.114554i
$900$	−7.90895	−	13.6987i	−0.263632	−	0.456623i
$901$	4.32382	−	7.48908i	0.144047	−	0.249497i
$902$		−	5.33858i		−	0.177755i
$903$		0			0
$904$	−4.23414	−	2.44458i	−0.140825	−	0.0813056i
$905$			5.22847i			0.173800i
$906$	−9.79545	+	16.9662i	−0.325432	+	0.563665i
$907$	−24.9923	−	43.2879i	−0.829856	−	1.43735i	−0.898151	−	0.439687i	$-0.855089\pi$
$907$	−24.9923	−	43.2879i	−0.829856	−	1.43735i	0.0682950	−	0.997665i	$-0.478244\pi$
$908$	11.4442	−	6.60729i	0.379788	−	0.219271i
$909$	−6.26299			−0.207730
$910$		0			0
$911$	17.2655			0.572033			0.286016	−	0.958225i	$-0.407669\pi$
$911$	17.2655			0.572033			0.286016	+	0.958225i	$0.407669\pi$
$912$	11.9930	−	6.92418i	0.397129	−	0.229283i
$913$	23.1141	+	40.0348i	0.764966	+	1.32496i
$914$	−10.2558	+	17.7635i	−0.339231	+	0.587565i
$915$		−	79.6371i		−	2.63272i
$916$	−8.62549	−	4.97993i	−0.284994	−	0.164542i
$917$		0			0
$918$			3.88841i			0.128337i
$919$	−7.95486	+	13.7782i	−0.262407	+	0.454502i	−0.966881	−	0.255228i	$-0.917849\pi$
$919$	−7.95486	+	13.7782i	−0.262407	+	0.454502i	0.704474	+	0.709729i	$0.251183\pi$
$920$	6.32664	+	10.9581i	0.208583	+	0.361277i
$921$	69.4057	−	40.0714i	2.28699	−	1.32040i
$922$	3.39717			0.111880
$923$	0.398434	+	9.80712i	0.0131146	+	0.322805i
$924$		0			0
$925$	−2.29311	+	1.32393i	−0.0753969	+	0.0435304i
$926$	19.6793	+	34.0856i	0.646702	+	1.12012i
$927$	22.9319	−	39.7192i	0.753182	−	1.30455i
$928$		−	6.72285i		−	0.220688i
$929$	−19.6257	−	11.3309i	−0.643900	−	0.371756i	0.142215	−	0.989836i	$-0.454577\pi$
$929$	−19.6257	−	11.3309i	−0.643900	−	0.371756i	−0.786115	+	0.618080i	$0.787911\pi$
$930$	6.97667	+	4.02798i	0.228774	+	0.132083i
$931$		0			0
$932$	4.29233	−	7.43454i	0.140600	−	0.243527i
$933$	0.862595	+	1.49406i	0.0282401	+	0.0489133i
$934$	5.18650	−	2.99442i	0.169707	−	0.0979806i
$935$	62.8696			2.05606
$936$	0.374414	+	9.21590i	0.0122381	+	0.301231i
$937$	22.3601			0.730473			0.365237	−	0.930915i	$-0.380988\pi$
$937$	22.3601			0.730473			0.365237	+	0.930915i	$0.380988\pi$
$938$		0			0
$939$	−8.68432	−	15.0417i	−0.283402	−	0.490867i
$940$	−8.88446	+	15.3883i	−0.289779	+	0.501912i
$941$		−	28.2183i		−	0.919892i	−0.887947	−	0.459946i	$-0.847869\pi$
$941$		−	28.2183i		−	0.919892i	0.887947	−	0.459946i	$-0.152131\pi$
$942$	10.6476	+	6.14740i	0.346918	+	0.200293i
$943$	3.47330	+	2.00531i	0.113106	+	0.0653019i
$944$		−	8.08665i		−	0.263198i
$945$		0			0
$946$	8.31631	+	14.4043i	0.270387	+	0.468323i
$947$	−5.51380	+	3.18339i	−0.179174	+	0.103446i	−0.586905	−	0.809656i	$-0.699654\pi$
$947$	−5.51380	+	3.18339i	−0.179174	+	0.103446i	0.407730	+	0.913102i	$0.366320\pi$
$948$	33.3413			1.08288
$949$	24.2355	−	15.3367i	0.786719	−	0.497852i
$950$	36.3210			1.17841
$951$	57.9990	−	33.4858i	1.88075	−	1.08585i
$952$		0			0
$953$	1.16258	−	2.01365i	0.0376597	−	0.0652285i	−0.846581	−	0.532260i	$-0.821343\pi$
$953$	1.16258	−	2.01365i	0.0376597	−	0.0652285i	0.884241	+	0.467031i	$0.154676\pi$
$954$			5.92651i			0.191878i
$955$	−27.2038	−	15.7061i	−0.880293	−	0.508238i
$956$	−1.01584	−	0.586498i	−0.0328547	−	0.0189687i
$957$			79.8270i			2.58044i
$958$	6.84021	−	11.8476i	0.220997	−	0.382778i
$959$		0			0
$960$	6.82781	−	3.94204i	0.220367	−	0.127229i
$961$	29.9559			0.966320
$962$	1.54271	−	0.0626755i	0.0497388	−	0.00202074i
$963$	−25.3317			−0.816302
$964$	−21.1208	+	12.1941i	−0.680254	+	0.392745i
$965$	15.3160	+	26.5281i	0.493040	+	0.853971i
$966$		0			0
$967$		−	58.7262i		−	1.88851i	−0.329219	−	0.944254i	$-0.606785\pi$
$967$		−	58.7262i		−	1.88851i	0.329219	−	0.944254i	$-0.393215\pi$
$968$	−12.4419	−	7.18332i	−0.399897	−	0.230881i
$969$	44.7664	+	25.8459i	1.43810	+	0.830290i
$970$			57.4367i			1.84418i
$971$	−5.03497	+	8.72083i	−0.161580	+	0.279865i	−0.935436	−	0.353497i	$-0.884992\pi$
$971$	−5.03497	+	8.72083i	−0.161580	+	0.279865i	0.773855	+	0.633362i	$0.218326\pi$
$972$	−10.3789	−	17.9768i	−0.332904	−	0.576607i
$973$		0			0
$974$	−1.05079			−0.0336693
$975$	−24.4109	+	46.5482i	−0.781774	+	1.49073i
$976$	10.1010			0.323325
$977$	−42.2830	+	24.4121i	−1.35275	+	0.781012i	−0.988634	−	0.150341i	$-0.951963\pi$
$977$	−42.2830	+	24.4121i	−1.35275	+	0.781012i	−0.364118	+	0.931353i	$0.618629\pi$
$978$	−14.7108	−	25.4799i	−0.470400	−	0.814757i
$979$	−13.6311	+	23.6098i	−0.435653	+	0.754573i
$980$		0			0
$981$	7.88218	+	4.55078i	0.251658	+	0.145295i
$982$	−23.8602	−	13.7757i	−0.761409	−	0.439600i
$983$			6.62899i			0.211432i	0.994396	+	0.105716i	$0.0337134\pi$
$983$			6.62899i			0.211432i	−0.994396	+	0.105716i	$0.966287\pi$
$984$	1.24948	−	2.16416i	0.0398320	−	0.0689910i
$985$	−25.9013	−	44.8624i	−0.825285	−	1.42944i
$986$	21.7324	−	12.5472i	0.692100	−	0.399584i
$987$		0			0
$988$	−18.7563	−	9.83622i	−0.596717	−	0.312932i
$989$	−12.4953			−0.397327
$990$	−37.3141	+	21.5433i	−1.18592	+	0.684690i
$991$	−12.4847	−	21.6241i	−0.396589	−	0.686911i	0.596714	−	0.802454i	$-0.296473\pi$
$991$	−12.4847	−	21.6241i	−0.396589	−	0.686911i	−0.993303	+	0.115543i	$0.963139\pi$
$992$	−0.510901	+	0.884906i	−0.0162211	+	0.0280958i
$993$			47.8533i			1.51858i
$994$		0			0
$995$	15.8820	+	9.16945i	0.503492	+	0.290691i
$996$			21.6392i			0.685664i
$997$	−19.7584	+	34.2225i	−0.625754	+	1.08384i	0.362640	+	0.931929i	$0.381875\pi$
$997$	−19.7584	+	34.2225i	−0.625754	+	1.08384i	−0.988394	+	0.151909i	$0.951458\pi$
$998$	1.05212	+	1.82233i	0.0333044	+	0.0576849i
$999$	−0.386322	+	0.223043i	−0.0122227	+	0.00705677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.f.491.7		20
7.2	even	3		1274.2.v.h.361.4		20
7.3	odd	6		182.2.o.a.23.9	✓	20
7.4	even	3		1274.2.o.h.569.7		20
7.5	odd	6		182.2.v.a.179.2	yes	20
7.6	odd	2		1274.2.m.g.491.9		20
13.4	even	6	inner	1274.2.m.f.589.7		20
21.5	even	6		1638.2.cr.c.361.6		20
21.17	even	6		1638.2.dt.c.1297.5		20
91.4	even	6		1274.2.v.h.667.4		20
91.17	odd	6		182.2.v.a.121.2	yes	20
91.30	even	6		1274.2.o.h.459.2		20
91.69	odd	6		1274.2.m.g.589.9		20
91.82	odd	6		182.2.o.a.95.4	yes	20
273.17	even	6		1638.2.cr.c.667.6		20
273.173	even	6		1638.2.dt.c.1369.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.9	✓	20	7.3	odd	6
182.2.o.a.95.4	yes	20	91.82	odd	6
182.2.v.a.121.2	yes	20	91.17	odd	6
182.2.v.a.179.2	yes	20	7.5	odd	6
1274.2.m.f.491.7		20	1.1	even	1	trivial
1274.2.m.f.589.7		20	13.4	even	6	inner
1274.2.m.g.491.9		20	7.6	odd	2
1274.2.m.g.589.9		20	91.69	odd	6
1274.2.o.h.459.2		20	91.30	even	6
1274.2.o.h.569.7		20	7.4	even	3
1274.2.v.h.361.4		20	7.2	even	3
1274.2.v.h.667.4		20	91.4	even	6
1638.2.cr.c.361.6		20	21.5	even	6
1638.2.cr.c.667.6		20	273.17	even	6
1638.2.dt.c.1297.5		20	21.17	even	6
1638.2.dt.c.1369.10		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} +(-1.17879 - 2.04172i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.34415i q^{5} +(-2.04172 - 1.17879i) q^{6} -1.00000i q^{8} +(-1.27907 + 2.21541i) q^{9} +(-1.67208 - 2.89612i) q^{10} +(-4.36176 + 2.51826i) q^{11} -2.35757 q^{12} +(1.92804 + 3.04674i) q^{13} +(-6.82781 + 3.94204i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86635 - 3.23261i) q^{17} +2.55814i q^{18} +(-5.08703 - 2.93700i) q^{19} +(-2.89612 - 1.67208i) q^{20} +(-2.51826 + 4.36176i) q^{22} +(-1.89185 - 3.27678i) q^{23} +(-2.04172 + 1.17879i) q^{24} -6.18336 q^{25} +(3.19311 + 1.67454i) q^{26} -1.04172 q^{27} +(3.36143 + 5.82216i) q^{29} +(-3.94204 + 6.82781i) q^{30} -1.02180i q^{31} +(-0.866025 - 0.500000i) q^{32} +(10.2832 + 5.93699i) q^{33} -3.73270i q^{34} +(1.27907 + 2.21541i) q^{36} +(0.370851 - 0.214111i) q^{37} -5.87400 q^{38} +(3.94784 - 7.52797i) q^{39} -3.34415 q^{40} +(-0.917963 + 0.529986i) q^{41} +(1.65120 - 2.85996i) q^{43} +5.03653i q^{44} +(7.40868 + 4.27741i) q^{45} +(-3.27678 - 1.89185i) q^{46} -5.31343i q^{47} +(-1.17879 + 2.04172i) q^{48} +(-5.35494 + 3.09168i) q^{50} -8.80011 q^{51} +(3.60258 - 0.146362i) q^{52} +2.31672 q^{53} +(-0.902152 + 0.520858i) q^{54} +(8.42146 + 14.5864i) q^{55} +13.8484i q^{57} +(5.82216 + 3.36143i) q^{58} +(7.00324 + 4.04332i) q^{59} +7.88408i q^{60} +(-5.05050 + 8.74773i) q^{61} +(-0.510901 - 0.884906i) q^{62} -1.00000 q^{64} +(10.1888 - 6.44767i) q^{65} +11.8740 q^{66} +(11.5166 - 6.64910i) q^{67} +(-1.86635 - 3.23261i) q^{68} +(-4.46017 + 7.72525i) q^{69} +(2.35754 + 1.36113i) q^{71} +(2.21541 + 1.27907i) q^{72} -7.95457i q^{73} +(0.214111 - 0.370851i) q^{74} +(7.28885 + 12.6247i) q^{75} +(-5.08703 + 2.93700i) q^{76} +(-0.345059 - 8.49334i) q^{78} -14.1422 q^{79} +(-2.89612 + 1.67208i) q^{80} +(5.06517 + 8.77313i) q^{81} +(-0.529986 + 0.917963i) q^{82} -9.17859i q^{83} +(-10.8104 - 6.24136i) q^{85} -3.30240i q^{86} +(7.92480 - 13.7262i) q^{87} +(2.51826 + 4.36176i) q^{88} +(4.68772 - 2.70646i) q^{89} +8.55481 q^{90} -3.78370 q^{92} +(-2.08623 + 1.20449i) q^{93} +(-2.65672 - 4.60157i) q^{94} +(-9.82177 + 17.0118i) q^{95} +2.35757i q^{96} +(-14.8742 - 8.58763i) q^{97} -12.8842i 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

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