LMFDB - Embedded newform 1274.2.m.g.589.9

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			589.9
Root			$-2.35757i$ of defining polynomial
Character	$\chi$	$=$	1274.589
Dual form			1274.2.m.g.491.9

$q$-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 $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

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

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	−0.294234	−	0.955733i	$-0.595065\pi$
$3$	1.17879	−	2.04172i	0.680572	−	1.17879i	0.974807	−	0.223052i	$-0.0716020\pi$
$4$	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	−0.332182	−	0.943215i	$-0.607785\pi$
$11$	−4.36176	−	2.51826i	−1.31512	−	0.759285i	−0.982939	+	0.183930i	$0.941118\pi$
$12$	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	$-0.316190\pi$
$17$	−1.86635	−	3.23261i	−0.452657	−	0.784024i	−0.998550	+	0.0538304i	$0.982857\pi$
$18$		−	2.55814i		−	0.602959i
$19$	5.08703	−	2.93700i	1.16705	−	0.673794i	0.214063	−	0.976820i	$-0.431330\pi$
$19$	5.08703	−	2.93700i	1.16705	−	0.673794i	0.952982	+	0.303026i	$0.0979969\pi$
$20$	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	−0.993034	−	0.117824i	$-0.962408\pi$
$23$	−1.89185	+	3.27678i	−0.394478	+	0.683257i	0.598556	+	0.801081i	$0.295741\pi$
$24$	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	−0.364494	−	0.931206i	$-0.618758\pi$
$29$	3.36143	−	5.82216i	0.624201	−	1.08115i	0.988695	−	0.149942i	$-0.0479088\pi$
$30$	−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	0.530174	−	0.847889i	$-0.322127\pi$
$37$	0.370851	+	0.214111i	0.0609676	+	0.0351997i	−0.469206	+	0.883089i	$0.655460\pi$
$38$	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	$-0.306957\pi$
$41$	0.917963	+	0.529986i	0.143362	+	0.0827699i	−0.426603	+	0.904439i	$0.640290\pi$
$42$		0			0
$43$	1.65120	+	2.85996i	0.251805	+	0.436140i	0.964023	−	0.265819i	$-0.0856423\pi$
$43$	1.65120	+	2.85996i	0.251805	+	0.436140i	−0.712217	+	0.701959i	$0.752309\pi$
$44$		−	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	$-0.843124\pi$
$59$	−7.00324	+	4.04332i	−0.911745	+	0.526396i	−0.0307526	+	0.999527i	$0.509790\pi$
$60$		−	7.88408i		−	1.01783i
$61$	5.05050	+	8.74773i	0.646651	+	1.12003i	0.983918	+	0.178623i	$0.0571643\pi$
$61$	5.05050	+	8.74773i	0.646651	+	1.12003i	−0.337267	+	0.941409i	$0.609502\pi$
$62$	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	0.995095	−	0.0989215i	$-0.0315393\pi$
$67$	11.5166	+	6.64910i	1.40697	+	0.812317i	0.411879	+	0.911239i	$0.364873\pi$
$68$	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	−0.353539	−	0.935420i	$-0.615022\pi$
$71$	2.35754	−	1.36113i	0.279788	−	0.161536i	0.633328	+	0.773884i	$0.281689\pi$
$72$	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	$-0.425953\pi$
$89$	−4.68772	−	2.70646i	−0.496897	−	0.286884i	−0.727431	+	0.686181i	$0.759286\pi$
$90$	−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	0.510318	−	0.859986i	$-0.329528\pi$
$97$	14.8742	−	8.58763i	1.51025	−	0.871941i	0.999929	−	0.0119557i	$-0.00380571\pi$
$98$		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	$-0.872202\pi$
$101$	−1.22413	+	2.12026i	−0.121806	+	0.210973i	0.798674	+	0.601764i	$0.205535\pi$
$102$	−7.62112	−	4.40005i	−0.754603	−	0.435670i
$103$	17.9286			1.76655			0.883277	−	0.468852i	$-0.155332\pi$
$103$	17.9286			1.76655			0.883277	+	0.468852i	$0.155332\pi$
$104$	−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	−0.521050	−	0.853526i	$-0.674460\pi$
$107$	4.95119	−	8.57572i	0.478650	−	0.829046i	0.999700	+	0.0244799i	$0.00779297\pi$
$108$	0.520858	+	0.902152i	0.0501196	+	0.0868096i
$109$			3.55788i			0.340783i	0.985376	+	0.170391i	$0.0545032\pi$
$109$			3.55788i			0.340783i	−0.985376	+	0.170391i	$0.945497\pi$
$110$	−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	0.957798	−	0.287442i	$-0.0928049\pi$
$113$	2.44458	+	4.23414i	0.229967	+	0.398314i	−0.727831	+	0.685756i	$0.759472\pi$
$114$	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	−0.989242	−	0.146285i	$-0.953268\pi$
$127$	−4.14641	+	7.18180i	−0.367935	+	0.637281i	0.621308	+	0.783567i	$0.286602\pi$
$128$	−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	$-0.413249\pi$
$131$	6.16169			0.538349			0.269174	+	0.963091i	$0.413249\pi$
$132$	−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	−0.749261	−	0.662274i	$-0.769591\pi$
$137$	−6.44163	+	3.71908i	−0.550346	+	0.317742i	0.198916	+	0.980017i	$0.436258\pi$
$138$			8.92035i			0.759351i
$139$	2.44199	+	4.22965i	0.207127	+	0.358754i	0.950808	−	0.309780i	$-0.100255\pi$
$139$	2.44199	+	4.22965i	0.207127	+	0.358754i	−0.743682	+	0.668534i	$0.766922\pi$
$140$		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	−0.287262	−	0.957852i	$-0.592745\pi$
$149$	4.86592	−	2.80934i	0.398632	−	0.230150i	0.685894	+	0.727702i	$0.259412\pi$
$150$	−12.6247	+	7.28885i	−1.03080	+	0.595132i
$151$			8.30978i			0.676240i	0.941103	+	0.338120i	$0.109791\pi$
$151$			8.30978i			0.676240i	−0.941103	+	0.338120i	$0.890209\pi$
$152$	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	$-0.433271\pi$
$157$	5.21503			0.416204			0.208102	+	0.978107i	$0.433271\pi$
$158$	−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	−0.0129528	−	0.999916i	$-0.504123\pi$
$163$	10.8077	−	6.23982i	0.846524	−	0.488741i	0.859476	+	0.511176i	$0.170790\pi$
$164$			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	$-0.339164\pi$
$167$	−0.409946	−	0.236682i	−0.0317226	−	0.0183150i	−0.515777	+	0.856723i	$0.672497\pi$
$168$		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	$-0.292521\pi$
$173$	−5.06601	−	8.77459i	−0.385162	−	0.667120i	−0.991792	+	0.127865i	$0.959188\pi$
$174$		−	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	−0.993775	−	0.111405i	$-0.964465\pi$
$179$	−5.35710	+	9.27876i	−0.400408	+	0.693527i	0.593367	+	0.804932i	$0.297798\pi$
$180$	−7.40868	−	4.27741i	−0.552211	−	0.318819i
$181$	1.56347			0.116212			0.0581058	−	0.998310i	$-0.481494\pi$
$181$	1.56347			0.116212			0.0581058	+	0.998310i	$0.481494\pi$
$182$		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	0.984401	−	0.175939i	$-0.0562961\pi$
$191$	4.69659	+	8.13473i	0.339833	+	0.588608i	−0.644568	+	0.764547i	$0.722963\pi$
$192$	−1.17879	+	2.04172i	−0.0850715	+	0.147348i
$193$	−7.93269	−	4.57994i	−0.571008	−	0.329672i	0.186544	−	0.982447i	$-0.440271\pi$
$193$	−7.93269	−	4.57994i	−0.571008	−	0.329672i	−0.757552	+	0.652775i	$0.773605\pi$
$194$	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	0.894876	−	0.446316i	$-0.147264\pi$
$197$	13.4152	+	7.74526i	0.955793	+	0.551827i	0.0609170	+	0.998143i	$0.480598\pi$
$198$	−6.44208	+	11.1580i	−0.457818	+	0.792965i
$199$	2.74194	+	4.74917i	0.194371	+	0.336660i	0.946694	−	0.322134i	$-0.104400\pi$
$199$	2.74194	+	4.74917i	0.194371	+	0.336660i	−0.752323	+	0.658794i	$0.771067\pi$
$200$		−	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	−0.940288	−	0.340381i	$-0.889444\pi$
$211$	−2.54733	+	4.41210i	−0.175365	+	0.303741i	0.764922	+	0.644122i	$0.222777\pi$
$212$	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	$-0.441924\pi$
$223$	−8.65366	−	4.99619i	−0.579492	−	0.334570i	−0.760931	+	0.648832i	$0.775258\pi$
$224$		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	$-0.811171\pi$
$227$	−11.4442	+	6.60729i	−0.759575	+	0.438541i	0.0695679	+	0.997577i	$0.477838\pi$
$228$	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	$0.0120787\pi$
$239$			1.17300i			0.0758748i	−0.999280	+	0.0379374i	$0.987921\pi$
$240$	6.82781	−	3.94204i	0.440733	−	0.254457i
$241$	21.1208	−	12.1941i	1.36051	−	0.785490i	0.370817	−	0.928706i	$-0.379078\pi$
$241$	21.1208	−	12.1941i	1.36051	−	0.785490i	0.989691	+	0.143216i	$0.0457443\pi$
$242$			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	−0.977002	−	0.213228i	$-0.931602\pi$
$251$	−10.6649	−	18.4721i	−0.673162	−	1.16595i	0.303840	−	0.952723i	$-0.401731\pi$
$252$		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	$-0.964693\pi$
$257$	−6.42956	+	11.1363i	−0.401065	+	0.694664i	0.592790	+	0.805357i	$0.298026\pi$
$258$	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	0.172997	+	0.984922i	$0.444655\pi$
$263$	−12.4300	+	21.5295i	−0.766470	+	1.32756i	−0.939466	+	0.342642i	$0.888678\pi$
$264$	−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	0.987938	+	0.154851i	$0.0494897\pi$
$269$	10.3012	+	17.8422i	0.628074	+	1.08786i	−0.359864	+	0.933005i	$0.617177\pi$
$270$	1.74183	−	3.01693i	0.106004	−	0.183605i
$271$	4.57387	+	2.64072i	0.277843	+	0.160413i	0.632446	−	0.774604i	$-0.282051\pi$
$271$	4.57387	+	2.64072i	0.277843	+	0.160413i	−0.354604	+	0.935017i	$0.615384\pi$
$272$	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	0.776323	−	0.630335i	$-0.217083\pi$
$277$	−2.62506	−	4.54674i	−0.157725	−	0.273187i	−0.934048	+	0.357148i	$0.883749\pi$
$278$			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	$0.383752\pi$
$281$			31.3151i			1.86810i	−0.357141	+	0.934051i	$0.616248\pi$
$282$	−6.26339	−	10.8485i	−0.372980	−	0.646020i
$283$	−3.86020	+	6.68606i	−0.229465	+	0.397445i	−0.957650	−	0.287936i	$-0.907031\pi$
$283$	−3.86020	+	6.68606i	−0.229465	+	0.397445i	0.728185	+	0.685381i	$0.240364\pi$
$284$	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	$-0.453745\pi$
$293$	18.3856	−	10.6150i	1.07410	−	0.620133i	0.929299	+	0.369328i	$0.120412\pi$
$294$		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	$-0.493395\pi$
$311$	0.731766			0.0414946			0.0207473	+	0.999785i	$0.493395\pi$
$312$	−7.52797	+	3.94784i	−0.426188	+	0.223502i
$313$	−7.36717			−0.416417			−0.208209	−	0.978084i	$-0.566763\pi$
$313$	−7.36717			−0.416417			−0.208209	+	0.978084i	$0.566763\pi$
$314$	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	$-0.706024\pi$
$317$		−	28.4070i		−	1.59550i	0.602991	−	0.797748i	$-0.293976\pi$
$318$	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	−0.898073	−	0.439846i	$-0.855033\pi$
$331$	−17.5783	+	10.1489i	−0.966193	+	0.557832i	−0.0681192	+	0.997677i	$0.521700\pi$
$332$	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	0.758490	−	0.651685i	$-0.225938\pi$
$347$	−3.44861	−	5.97316i	−0.185131	−	0.320656i	−0.943621	+	0.331029i	$0.892604\pi$
$348$	7.92480	−	13.7262i	0.424814	−	0.735799i
$349$	−3.63303	−	2.09753i	−0.194472	−	0.112278i	0.399602	−	0.916689i	$-0.369148\pi$
$349$	−3.63303	−	2.09753i	−0.194472	−	0.112278i	−0.594074	+	0.804410i	$0.702482\pi$
$350$		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	$-0.565812\pi$
$353$	−21.7100	−	12.5343i	−1.15551	−	0.667132i	−0.950223	+	0.311570i	$0.899145\pi$
$354$	−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	$0.175734\pi$
$359$			19.8743i			1.04893i	−0.851433	+	0.524463i	$0.824266\pi$
$360$	−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	$-0.954300\pi$
$367$	−7.10630	+	12.3085i	−0.370946	+	0.642497i	0.618765	+	0.785576i	$0.287633\pi$
$368$	−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	0.913358	+	0.407157i	$0.133480\pi$
$373$	15.6299	+	27.0718i	0.809288	+	1.40173i	−0.104070	+	0.994570i	$0.533187\pi$
$374$	−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	0.901623	−	0.432523i	$-0.142377\pi$
$379$	19.0369	+	10.9909i	0.977858	+	0.564567i	0.0762355	+	0.997090i	$0.475710\pi$
$380$	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	$-0.626997\pi$
$383$	4.21349	−	2.43266i	0.215299	−	0.124303i	0.603772	+	0.797157i	$0.293664\pi$
$384$	−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	$-0.935583\pi$
$397$	−25.8091	+	14.9009i	−1.29532	+	0.747855i	−0.315731	+	0.948849i	$0.602250\pi$
$398$			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	0.697739	−	0.716352i	$-0.254190\pi$
$401$	8.53523	+	4.92782i	0.426229	+	0.246084i	−0.271510	+	0.962436i	$0.587523\pi$
$402$	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	$-0.450376\pi$
$409$	22.0121	−	12.7087i	1.08843	−	0.628403i	0.933157	+	0.359469i	$0.117042\pi$
$410$	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	0.182712	+	0.983167i	$0.441512\pi$
$419$	−15.5587	+	26.9484i	−0.760091	+	1.31652i	−0.942803	+	0.333350i	$0.891821\pi$
$420$		0			0
$421$			13.8090i			0.673009i	0.941682	+	0.336505i	$0.109245\pi$
$421$			13.8090i			0.673009i	−0.941682	+	0.336505i	$0.890755\pi$
$422$	−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	0.983965	−	0.178362i	$-0.0570798\pi$
$431$	27.4347	+	15.8394i	1.32148	+	0.762958i	0.337516	+	0.941320i	$0.390413\pi$
$432$	−0.520858	+	0.902152i	−0.0250598	+	0.0434048i
$433$	−13.7233	−	23.7695i	−0.659500	−	1.14229i	−0.980745	−	0.195292i	$-0.937435\pi$
$433$	−13.7233	−	23.7695i	−0.659500	−	1.14229i	0.321245	−	0.946996i	$-0.395899\pi$
$434$		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	$-0.927227\pi$
$439$	−6.09116	+	10.5502i	−0.290715	+	0.503534i	0.683264	+	0.730172i	$0.260560\pi$
$440$	−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	0.449121	−	0.893471i	$-0.351737\pi$
$449$	30.6709	−	17.7079i	1.44745	−	0.835685i	0.998329	+	0.0577858i	$0.0184040\pi$
$450$			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	0.0232325	−	0.999730i	$-0.492604\pi$
$457$	−17.7635	−	10.2558i	−0.830943	−	0.479745i	−0.854175	+	0.519985i	$0.825938\pi$
$458$	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	$-0.691875\pi$
$461$	−2.94204	+	1.69858i	−0.137024	+	0.0791110i	0.429921	+	0.902867i	$0.358541\pi$
$462$		0			0
$463$		−	39.3586i		−	1.82915i	−0.404417	−	0.914575i	$-0.632526\pi$
$463$		−	39.3586i		−	1.82915i	0.404417	−	0.914575i	$-0.367474\pi$
$464$	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	$-0.544249\pi$
$467$	−5.98885			−0.277131			−0.138565	+	0.990353i	$0.544249\pi$
$468$	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	$-0.434512\pi$
$479$	−11.8476	−	6.84021i	−0.541330	−	0.312537i	−0.745618	+	0.666374i	$0.767846\pi$
$480$	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	−0.520476	−	0.853876i	$-0.674246\pi$
$487$	−0.910007	+	0.525393i	−0.0412364	+	0.0238078i	0.479240	+	0.877684i	$0.340912\pi$
$488$	−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	0.367484	+	0.930030i	$0.380219\pi$
$491$	−13.7757	+	23.8602i	−0.621688	+	1.07679i	−0.989171	+	0.146765i	$0.953114\pi$
$492$	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	$-0.985002\pi$
$499$		−	2.10425i		−	0.0941991i	0.998890	−	0.0470995i	$-0.0149978\pi$
$500$	−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	0.870106	+	0.492864i	$0.164050\pi$
$503$	19.3301	+	33.4807i	0.861886	+	1.49283i	−0.00822020	+	0.999966i	$0.502617\pi$
$504$		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	$-0.142662\pi$
$509$	22.0326	+	12.7205i	0.976578	+	0.563828i	0.0753428	+	0.997158i	$0.475995\pi$
$510$	−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	$-0.613893\pi$
$521$	−15.9879			−0.700441			−0.350221	+	0.936667i	$0.613893\pi$
$522$	−14.8939	−	8.59900i	−0.651889	−	0.376368i
$523$	−9.11459	+	15.7869i	−0.398553	+	0.690315i	−0.993548	−	0.113415i	$-0.963821\pi$
$523$	−9.11459	+	15.7869i	−0.398553	+	0.690315i	0.594994	+	0.803730i	$0.297154\pi$
$524$	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	$0.135477\pi$
$541$			19.2066i			0.825758i	−0.910786	+	0.412879i	$0.864523\pi$
$542$	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	0.932023	−	0.362399i	$-0.118042\pi$
$557$	25.5877	+	14.7731i	1.08419	+	0.625956i	0.152165	+	0.988355i	$0.451376\pi$
$558$	−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	$-0.149735\pi$
$563$	1.26155	+	2.18506i	0.0531678	+	0.0920894i	−0.838217	+	0.545337i	$0.816402\pi$
$564$		−	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	−0.954403	−	0.298520i	$-0.903507\pi$
$569$	−5.21623	+	9.03478i	−0.218676	+	0.378758i	0.735728	+	0.677278i	$0.236840\pi$
$570$	−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	$-0.476820\pi$
$587$	−18.2824	−	10.5554i	−0.754596	−	0.435666i	−0.827352	+	0.561684i	$0.810154\pi$
$588$		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	−0.161785	−	0.986826i	$-0.551725\pi$
$601$	18.9681	−	32.8537i	0.773724	−	1.34013i	0.935509	−	0.353303i	$-0.114942\pi$
$602$		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	−0.957769	−	0.287538i	$-0.907163\pi$
$607$	−17.9335	−	31.0618i	−0.727900	−	1.26076i	0.229870	−	0.973221i	$-0.426170\pi$
$608$	−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	0.262146	−	0.965028i	$-0.415570\pi$
$613$	−10.9563	−	6.32562i	−0.442521	−	0.255489i	−0.704666	+	0.709539i	$0.748903\pi$
$614$	−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	0.400131	−	0.916458i	$-0.368965\pi$
$617$	34.6231	−	19.9896i	1.39387	−	0.804753i	0.993741	+	0.111705i	$0.0356312\pi$
$618$	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	−0.00129129	−	0.999999i	$-0.500411\pi$
$631$	21.7056	−	12.5318i	0.864088	−	0.498881i	0.865379	+	0.501118i	$0.167078\pi$
$632$		−	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	0.934359	−	0.356334i	$-0.115973\pi$
$641$	4.01506	+	6.95429i	0.158585	+	0.274678i	−0.775773	+	0.631012i	$0.782640\pi$
$642$		−	23.3456i		−	0.921377i
$643$	−13.3951	+	7.73367i	−0.528251	+	0.304986i	−0.740304	−	0.672272i	$-0.765318\pi$
$643$	−13.3951	+	7.73367i	−0.528251	+	0.304986i	0.212053	+	0.977258i	$0.431985\pi$
$644$		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	$-0.875329\pi$
$647$	−3.34618	+	5.79575i	−0.131552	+	0.227854i	0.792723	+	0.609582i	$0.208663\pi$
$648$	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	−0.526772	−	0.850006i	$-0.676598\pi$
$653$	12.0804	−	20.9238i	0.472741	−	0.818811i	0.999513	+	0.0311950i	$0.00993128\pi$
$654$	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	0.711833	−	0.702349i	$-0.247865\pi$
$659$	−6.47769	−	11.2197i	−0.252335	−	0.437057i	−0.964168	+	0.265291i	$0.914532\pi$
$660$	−19.8542	+	34.3885i	−0.772823	+	1.33857i
$661$	−16.7049	−	9.64460i	−0.649747	−	0.375132i	0.138612	−	0.990347i	$-0.455736\pi$
$661$	−16.7049	−	9.64460i	−0.649747	−	0.375132i	−0.788359	+	0.615215i	$0.789069\pi$
$662$	−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	0.426258	+	0.904602i	$0.359832\pi$
$673$	−14.7943	+	25.6245i	−0.570279	+	0.987752i	−0.996537	+	0.0831505i	$0.973502\pi$
$674$	−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	$-0.585702\pi$
$677$	−13.8422			−0.531998			−0.265999	+	0.963973i	$0.585702\pi$
$678$	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	0.226749	−	0.973953i	$-0.427190\pi$
$683$	30.9323	−	17.8588i	1.18359	−	0.683347i	0.956843	+	0.290607i	$0.0938571\pi$
$684$		−	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	$-0.498042\pi$
$691$	−22.5221	−	13.0031i	−0.856782	−	0.494663i	−0.862933	+	0.505318i	$0.831375\pi$
$692$	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	−0.0894476	−	0.995992i	$-0.528510\pi$
$709$	19.3947	−	11.1975i	0.728383	−	0.420532i	0.817830	+	0.575460i	$0.195177\pi$
$710$		−	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	$-0.0103896\pi$
$719$	12.6421	+	21.8968i	0.471472	+	0.816613i	−0.527996	+	0.849247i	$0.677056\pi$
$720$		−	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	$-0.765699\pi$
$727$	−39.9649			−1.48221			−0.741107	+	0.671386i	$0.765699\pi$
$728$		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	−0.0290890	−	0.999577i	$-0.509261\pi$
$739$	−24.7187	−	14.2714i	−0.909292	−	0.524980i	−0.880203	+	0.474597i	$0.842594\pi$
$740$	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	−0.398104	−	0.917340i	$-0.630332\pi$
$743$	−37.9322	−	21.9001i	−1.39160	−	0.803438i	−0.993492	+	0.113902i	$0.963665\pi$
$744$	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	−0.214906	−	0.976635i	$-0.568944\pi$
$751$	20.2337	−	35.0458i	0.738338	−	1.27884i	0.953243	−	0.302204i	$-0.0977223\pi$
$752$	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	−0.958160	−	0.286232i	$-0.907597\pi$
$757$	−6.36103	+	11.0176i	−0.231196	+	0.400442i	0.726965	+	0.686675i	$0.240930\pi$
$758$	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	$-0.478577\pi$
$761$	26.6191	−	15.3686i	0.964943	−	0.557110i	0.897691	+	0.440626i	$0.145244\pi$
$762$			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	$-0.400694\pi$
$769$	−10.0887	−	5.82469i	−0.363806	−	0.210044i	−0.670749	+	0.741684i	$0.734027\pi$
$770$		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	$-0.836981\pi$
$773$	−24.5544	+	14.1765i	−0.883159	+	0.509892i	−0.0114603	+	0.999934i	$0.503648\pi$
$774$	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	$-0.654538\pi$
$787$	1.85099	−	1.06867i	0.0659808	−	0.0380940i	0.532627	+	0.846350i	$0.321205\pi$
$788$			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	$-0.331593\pi$
$797$	−13.9817	−	24.2170i	−0.495257	−	0.857810i	−0.999985	+	0.00546806i	$0.998259\pi$
$798$		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	−0.0186933	−	0.999825i	$-0.505951\pi$
$809$	24.3621	−	42.1965i	0.856527	−	1.48355i	0.875221	−	0.483724i	$-0.160716\pi$
$810$	−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	0.299500	−	0.954096i	$-0.403180\pi$
$821$	−10.8028	−	6.23701i	−0.377021	−	0.217673i	−0.676521	+	0.736423i	$0.736513\pi$
$822$	−8.76799	+	15.1866i	−0.305819	+	0.529694i
$823$	8.01300	+	13.8789i	0.279316	+	0.483789i	0.971215	−	0.238205i	$-0.0765591\pi$
$823$	8.01300	+	13.8789i	0.279316	+	0.483789i	−0.691899	+	0.721994i	$0.743226\pi$
$824$			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	$0.0385148\pi$
$827$			6.94225i			0.241406i	−0.992689	+	0.120703i	$0.961485\pi$
$828$	4.83962	+	8.38247i	0.168189	+	0.291311i
$829$	4.54445	−	7.87122i	0.157835	−	0.273379i	−0.776252	−	0.630422i	$-0.782882\pi$
$829$	4.54445	−	7.87122i	0.157835	−	0.273379i	0.934088	+	0.357043i	$0.116215\pi$
$830$	−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	$-0.769210\pi$
$839$	−15.8840	+	9.17062i	−0.548376	+	0.316605i	0.200091	+	0.979777i	$0.435876\pi$
$840$		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	$-0.273328\pi$
$857$	38.2580			1.30687			0.653434	+	0.756984i	$0.273328\pi$
$858$	22.8935	−	36.1770i	0.781572	−	1.23506i
$859$	−15.7899			−0.538744			−0.269372	−	0.963036i	$-0.586816\pi$
$859$	−15.7899			−0.538744			−0.269372	+	0.963036i	$0.586816\pi$
$860$	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	$0.274184\pi$
$863$			44.5788i			1.51748i	−0.651394	+	0.758739i	$0.725816\pi$
$864$	−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	−0.502046	−	0.864841i	$-0.667419\pi$
$877$	−0.121237	+	0.0699963i	−0.00409389	+	0.00236361i	0.497952	+	0.867205i	$0.334086\pi$
$878$	−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	0.178036	+	0.984024i	$0.443026\pi$
$881$	−22.6522	+	39.2347i	−0.763172	+	1.32185i	−0.941208	+	0.337828i	$0.890308\pi$
$882$		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	0.0831471	+	0.996537i	$0.473503\pi$
$887$	−24.4650	+	42.3746i	−0.821453	+	1.42280i	−0.904600	+	0.426261i	$0.859830\pi$
$888$	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	0.0682950	+	0.997665i	$0.478244\pi$
$907$	−24.9923	+	43.2879i	−0.829856	+	1.43735i	−0.898151	+	0.439687i	$0.855089\pi$
$908$	−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	0.704474	−	0.709729i	$-0.251183\pi$
$919$	−7.95486	−	13.7782i	−0.262407	−	0.454502i	−0.966881	+	0.255228i	$0.917849\pi$
$920$	−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	$-0.545423\pi$
$929$	19.6257	−	11.3309i	0.643900	−	0.371756i	0.786115	+	0.618080i	$0.212089\pi$
$930$	−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	$-0.619012\pi$
$937$	−22.3601			−0.730473			−0.365237	+	0.930915i	$0.619012\pi$
$938$		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	0.407730	−	0.913102i	$-0.366320\pi$
$947$	−5.51380	−	3.18339i	−0.179174	−	0.103446i	−0.586905	+	0.809656i	$0.699654\pi$
$948$	−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	0.884241	−	0.467031i	$-0.154676\pi$
$953$	1.16258	+	2.01365i	0.0376597	+	0.0652285i	−0.846581	+	0.532260i	$0.821343\pi$
$954$		−	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	$0.393215\pi$
$967$			58.7262i			1.88851i	−0.329219	+	0.944254i	$0.606785\pi$
$968$	−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	$-0.115008\pi$
$971$	5.03497	+	8.72083i	0.161580	+	0.279865i	−0.773855	+	0.633362i	$0.781674\pi$
$972$	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	−0.364118	−	0.931353i	$-0.618629\pi$
$977$	−42.2830	−	24.4121i	−1.35275	−	0.781012i	−0.988634	+	0.150341i	$0.951963\pi$
$978$	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	−0.993303	−	0.115543i	$-0.963139\pi$
$991$	−12.4847	+	21.6241i	−0.396589	+	0.686911i	0.596714	+	0.802454i	$0.296473\pi$
$992$	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	0.988394	+	0.151909i	$0.0485421\pi$
$997$	19.7584	+	34.2225i	0.625754	+	1.08384i	−0.362640	+	0.931929i	$0.618125\pi$
$998$	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.g.589.9		20
7.2	even	3		182.2.o.a.95.4	yes	20
7.3	odd	6		1274.2.v.h.667.4		20
7.4	even	3		182.2.v.a.121.2	yes	20
7.5	odd	6		1274.2.o.h.459.2		20
7.6	odd	2		1274.2.m.f.589.7		20
13.10	even	6	inner	1274.2.m.g.491.9		20
21.2	odd	6		1638.2.dt.c.1369.10		20
21.11	odd	6		1638.2.cr.c.667.6		20
91.10	odd	6		1274.2.o.h.569.7		20
91.23	even	6		182.2.v.a.179.2	yes	20
91.62	odd	6		1274.2.m.f.491.7		20
91.75	odd	6		1274.2.v.h.361.4		20
91.88	even	6		182.2.o.a.23.9	✓	20
273.23	odd	6		1638.2.cr.c.361.6		20
273.179	odd	6		1638.2.dt.c.1297.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.9	✓	20	91.88	even	6
182.2.o.a.95.4	yes	20	7.2	even	3
182.2.v.a.121.2	yes	20	7.4	even	3
182.2.v.a.179.2	yes	20	91.23	even	6
1274.2.m.f.491.7		20	91.62	odd	6
1274.2.m.f.589.7		20	7.6	odd	2
1274.2.m.g.491.9		20	13.10	even	6	inner
1274.2.m.g.589.9		20	1.1	even	1	trivial
1274.2.o.h.459.2		20	7.5	odd	6
1274.2.o.h.569.7		20	91.10	odd	6
1274.2.v.h.361.4		20	91.75	odd	6
1274.2.v.h.667.4		20	7.3	odd	6
1638.2.cr.c.361.6		20	273.23	odd	6
1638.2.cr.c.667.6		20	21.11	odd	6
1638.2.dt.c.1297.5		20	273.179	odd	6
1638.2.dt.c.1369.10		20	21.2	odd	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

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Representations

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Database

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