LMFDB - Embedded newform 1014.2.g.b.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.58498535041007616.52
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 $ x^12 - 12x^9 + 72x^6 - 324*x^3 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.1
Root			$-0.779723 - 1.54662i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.b.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(1.54662 - 0.779723i) q^{6} +(1.76690 - 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(1.54662 - 0.779723i) q^{6} +(1.76690 - 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} -3.28995i q^{10} +(-1.08456 - 1.08456i) q^{11} +(-0.542278 + 1.64497i) q^{12} +2.49877i q^{14} +(5.08829 - 2.56525i) q^{15} -1.00000 q^{16} -5.73724 q^{17} +(-2.96697 + 0.443925i) q^{18} +(-2.28995 - 2.28995i) q^{19} +(2.32634 + 2.32634i) q^{20} +(-3.86465 + 1.94835i) q^{21} +1.53379 q^{22} +4.65268 q^{23} +(-0.779723 - 1.54662i) q^{24} -5.82374i q^{25} +(-3.00000 - 4.24264i) q^{27} +(-1.76690 - 1.76690i) q^{28} -4.65268i q^{29} +(-1.78406 + 5.41187i) q^{30} +(3.82374 + 3.82374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.19593 + 2.37220i) q^{33} +(4.05684 - 4.05684i) q^{34} +8.22081i q^{35} +(1.78406 - 2.41187i) q^{36} +(3.05684 - 3.05684i) q^{37} +3.23847 q^{38} -3.28995 q^{40} +(0.410044 - 0.410044i) q^{41} +(1.35503 - 4.11041i) q^{42} -0.222358i q^{43} +(-1.08456 + 1.08456i) q^{44} +(-9.76118 + 1.46049i) q^{45} +(-3.28995 + 3.28995i) q^{46} +(7.65354 + 7.65354i) q^{47} +(1.64497 + 0.542278i) q^{48} +0.756152i q^{49} +(4.11801 + 4.11801i) q^{50} +(9.43760 + 3.11118i) q^{51} +10.9689i q^{53} +(5.12132 + 0.878680i) q^{54} +5.04610 q^{55} +2.49877 q^{56} +(2.52511 + 5.00868i) q^{57} +(3.28995 + 3.28995i) q^{58} +(4.65268 + 4.65268i) q^{59} +(-2.56525 - 5.08829i) q^{60} +3.06759 q^{61} -5.40758 q^{62} +(7.41378 - 1.10927i) q^{63} +1.00000i q^{64} +(-2.52305 - 0.831742i) q^{66} +(-0.533794 - 0.533794i) q^{67} +5.73724i q^{68} +(-7.65354 - 2.52305i) q^{69} +(-5.81299 - 5.81299i) q^{70} +(5.48443 - 5.48443i) q^{71} +(0.443925 + 2.96697i) q^{72} +(-2.28995 + 2.28995i) q^{73} +4.32303i q^{74} +(-3.15808 + 9.57989i) q^{75} +(-2.28995 + 2.28995i) q^{76} -3.83260 q^{77} +14.1137 q^{79} +(2.32634 - 2.32634i) q^{80} +(2.63423 + 8.60586i) q^{81} +0.579890i q^{82} +(-1.39902 + 1.39902i) q^{83} +(1.94835 + 3.86465i) q^{84} +(13.3468 - 13.3468i) q^{85} +(0.157231 + 0.157231i) q^{86} +(-2.52305 + 7.65354i) q^{87} -1.53379i q^{88} +(6.41175 + 6.41175i) q^{89} +(5.86947 - 7.93492i) q^{90} -4.65268i q^{92} +(-4.21642 - 8.36347i) q^{93} -10.8237 q^{94} +10.6544 q^{95} +(-1.54662 + 0.779723i) q^{96} +(11.5799 + 11.5799i) q^{97} +(-0.534680 - 0.534680i) q^{98} +(-0.680889 - 4.55072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{7}+O(q^{10}) $ 12 * q + 12 * q^7	$ 12 q + 12 q^{7} - 12 q^{16} + 12 q^{19} - 36 q^{27} - 12 q^{28} - 12 q^{31} - 36 q^{33} - 12 q^{37} + 36 q^{42} - 36 q^{45} + 36 q^{54} + 36 q^{57} + 36 q^{63} + 12 q^{67} + 12 q^{73} + 12 q^{76} + 72 q^{79} + 72 q^{85} - 36 q^{93} - 72 q^{94} + 60 q^{97} - 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^7 - 12 * q^16 + 12 * q^19 - 36 * q^27 - 12 * q^28 - 12 * q^31 - 36 * q^33 - 12 * q^37 + 36 * q^42 - 36 * q^45 + 36 * q^54 + 36 * q^57 + 36 * q^63 + 12 * q^67 + 12 * q^73 + 12 * q^76 + 72 * q^79 + 72 * q^85 - 36 * q^93 - 72 * q^94 + 60 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.64497	−	0.542278i	−0.949725	−	0.313084i
$3$	−1.64497	−	0.542278i	−0.949725	−	0.313084i
$4$		−	1.00000i		−	0.500000i
$5$	−2.32634	+	2.32634i	−1.04037	+	1.04037i	−0.0412220	+	0.999150i	$0.513125\pi$
$5$	−2.32634	+	2.32634i	−1.04037	+	1.04037i	−0.999150	+	0.0412220i	$0.986875\pi$
$6$	1.54662	−	0.779723i	0.631405	−	0.318321i
$7$	1.76690	−	1.76690i	0.667824	−	0.667824i	−0.289388	−	0.957212i	$-0.593452\pi$
$7$	1.76690	−	1.76690i	0.667824	−	0.667824i	0.957212	+	0.289388i	$0.0934517\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.41187	+	1.78406i	0.803956	+	0.594688i
$10$		−	3.28995i		−	1.04037i
$11$	−1.08456	−	1.08456i	−0.327006	−	0.327006i	0.524441	−	0.851447i	$-0.324274\pi$
$11$	−1.08456	−	1.08456i	−0.327006	−	0.327006i	−0.851447	+	0.524441i	$0.824274\pi$
$12$	−0.542278	+	1.64497i	−0.156542	+	0.474863i
$13$		0			0
$13$		0			0
$14$			2.49877i			0.667824i
$15$	5.08829	−	2.56525i	1.31379	−	0.662344i
$16$	−1.00000			−0.250000
$17$	−5.73724			−1.39149			−0.695743	−	0.718291i	$-0.744925\pi$
$17$	−5.73724			−1.39149			−0.695743	+	0.718291i	$0.744925\pi$
$18$	−2.96697	+	0.443925i	−0.699322	+	0.104634i
$19$	−2.28995	−	2.28995i	−0.525349	−	0.525349i	0.393833	−	0.919182i	$-0.371149\pi$
$19$	−2.28995	−	2.28995i	−0.525349	−	0.525349i	−0.919182	+	0.393833i	$0.871149\pi$
$20$	2.32634	+	2.32634i	0.520186	+	0.520186i
$21$	−3.86465	+	1.94835i	−0.843335	+	0.425164i
$22$	1.53379			0.327006
$23$	4.65268			0.970152			0.485076	−	0.874472i	$-0.338792\pi$
$23$	4.65268			0.970152			0.485076	+	0.874472i	$0.338792\pi$
$24$	−0.779723	−	1.54662i	−0.159160	−	0.315702i
$25$		−	5.82374i		−	1.16475i
$26$		0			0
$27$	−3.00000	−	4.24264i	−0.577350	−	0.816497i
$28$	−1.76690	−	1.76690i	−0.333912	−	0.333912i
$29$		−	4.65268i		−	0.863982i	−0.901878	−	0.431991i	$-0.857811\pi$
$29$		−	4.65268i		−	0.863982i	0.901878	−	0.431991i	$-0.142189\pi$
$30$	−1.78406	+	5.41187i	−0.325724	+	0.988068i
$31$	3.82374	+	3.82374i	0.686764	+	0.686764i	0.961515	−	0.274752i	$-0.0885956\pi$
$31$	3.82374	+	3.82374i	0.686764	+	0.686764i	−0.274752	+	0.961515i	$0.588596\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.19593	+	2.37220i	0.208185	+	0.412946i
$34$	4.05684	−	4.05684i	0.695743	−	0.695743i
$35$			8.22081i			1.38957i
$36$	1.78406	−	2.41187i	0.297344	−	0.401978i
$37$	3.05684	−	3.05684i	0.502542	−	0.502542i	−0.409685	−	0.912227i	$-0.634361\pi$
$37$	3.05684	−	3.05684i	0.502542	−	0.502542i	0.912227	+	0.409685i	$0.134361\pi$
$38$	3.23847			0.525349
$39$		0			0
$40$	−3.28995			−0.520186
$41$	0.410044	−	0.410044i	0.0640382	−	0.0640382i	−0.674362	−	0.738401i	$-0.735581\pi$
$41$	0.410044	−	0.410044i	0.0640382	−	0.0640382i	0.738401	+	0.674362i	$0.235581\pi$
$42$	1.35503	−	4.11041i	0.209085	−	0.634250i
$43$		−	0.222358i		−	0.0339093i	−0.999856	−	0.0169546i	$-0.994603\pi$
$43$		−	0.222358i		−	0.0339093i	0.999856	−	0.0169546i	$-0.00539709\pi$
$44$	−1.08456	+	1.08456i	−0.163503	+	0.163503i
$45$	−9.76118	+	1.46049i	−1.45511	+	0.217717i
$46$	−3.28995	+	3.28995i	−0.485076	+	0.485076i
$47$	7.65354	+	7.65354i	1.11638	+	1.11638i	0.992268	+	0.124116i	$0.0396094\pi$
$47$	7.65354	+	7.65354i	1.11638	+	1.11638i	0.124116	+	0.992268i	$0.460391\pi$
$48$	1.64497	+	0.542278i	0.237431	+	0.0782711i
$49$			0.756152i			0.108022i
$50$	4.11801	+	4.11801i	0.582374	+	0.582374i
$51$	9.43760	+	3.11118i	1.32153	+	0.435652i
$52$		0			0
$53$			10.9689i			1.50669i	0.657627	+	0.753344i	$0.271560\pi$
$53$			10.9689i			1.50669i	−0.657627	+	0.753344i	$0.728440\pi$
$54$	5.12132	+	0.878680i	0.696923	+	0.119573i
$55$	5.04610			0.680416
$56$	2.49877			0.333912
$57$	2.52511	+	5.00868i	0.334459	+	0.663416i
$58$	3.28995	+	3.28995i	0.431991	+	0.431991i
$59$	4.65268	+	4.65268i	0.605728	+	0.605728i	0.941827	−	0.336099i	$-0.109108\pi$
$59$	4.65268	+	4.65268i	0.605728	+	0.605728i	−0.336099	+	0.941827i	$0.609108\pi$
$60$	−2.56525	−	5.08829i	−0.331172	−	0.656896i
$61$	3.06759			0.392764			0.196382	−	0.980527i	$-0.437081\pi$
$61$	3.06759			0.392764			0.196382	+	0.980527i	$0.437081\pi$
$62$	−5.40758			−0.686764
$63$	7.41378	−	1.10927i	0.934049	−	0.139754i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.52305	−	0.831742i	−0.310566	−	0.102380i
$67$	−0.533794	−	0.533794i	−0.0652133	−	0.0652133i	0.673748	−	0.738961i	$-0.264683\pi$
$67$	−0.533794	−	0.533794i	−0.0652133	−	0.0652133i	−0.738961	+	0.673748i	$0.764683\pi$
$68$			5.73724i			0.695743i
$69$	−7.65354	−	2.52305i	−0.921378	−	0.303739i
$70$	−5.81299	−	5.81299i	−0.694786	−	0.694786i
$71$	5.48443	−	5.48443i	0.650882	−	0.650882i	−0.302324	−	0.953205i	$-0.597762\pi$
$71$	5.48443	−	5.48443i	0.650882	−	0.650882i	0.953205	+	0.302324i	$0.0977623\pi$
$72$	0.443925	+	2.96697i	0.0523171	+	0.349661i
$73$	−2.28995	+	2.28995i	−0.268018	+	0.268018i	−0.828301	−	0.560283i	$-0.810692\pi$
$73$	−2.28995	+	2.28995i	−0.268018	+	0.268018i	0.560283	+	0.828301i	$0.310692\pi$
$74$			4.32303i			0.502542i
$75$	−3.15808	+	9.57989i	−0.364664	+	1.10619i
$76$	−2.28995	+	2.28995i	−0.262675	+	0.262675i
$77$	−3.83260			−0.436765
$78$		0			0
$79$	14.1137			1.58791			0.793957	−	0.607974i	$-0.208018\pi$
$79$	14.1137			1.58791			0.793957	+	0.607974i	$0.208018\pi$
$80$	2.32634	−	2.32634i	0.260093	−	0.260093i
$81$	2.63423	+	8.60586i	0.292692	+	0.956207i
$82$			0.579890i			0.0640382i
$83$	−1.39902	+	1.39902i	−0.153562	+	0.153562i	−0.779707	−	0.626145i	$-0.784632\pi$
$83$	−1.39902	+	1.39902i	−0.153562	+	0.153562i	0.626145	+	0.779707i	$0.284632\pi$
$84$	1.94835	+	3.86465i	0.212582	+	0.421667i
$85$	13.3468	−	13.3468i	1.44766	−	1.44766i
$86$	0.157231	+	0.157231i	0.0169546	+	0.0169546i
$87$	−2.52305	+	7.65354i	−0.270499	+	0.820546i
$88$		−	1.53379i		−	0.163503i
$89$	6.41175	+	6.41175i	0.679644	+	0.679644i	0.959920	−	0.280275i	$-0.0904257\pi$
$89$	6.41175	+	6.41175i	0.679644	+	0.679644i	−0.280275	+	0.959920i	$0.590426\pi$
$90$	5.86947	−	7.93492i	0.618697	−	0.836414i
$91$		0			0
$92$		−	4.65268i		−	0.485076i
$93$	−4.21642	−	8.36347i	−0.437222	−	0.867252i
$94$	−10.8237			−1.11638
$95$	10.6544			1.09312
$96$	−1.54662	+	0.779723i	−0.157851	+	0.0795801i
$97$	11.5799	+	11.5799i	1.17576	+	1.17576i	0.980814	+	0.194946i	$0.0624531\pi$
$97$	11.5799	+	11.5799i	1.17576	+	1.17576i	0.194946	+	0.980814i	$0.437547\pi$
$98$	−0.534680	−	0.534680i	−0.0540108	−	0.0540108i
$99$	−0.680889	−	4.55072i	−0.0684320	−	0.457365i
$100$	−5.82374			−0.582374
$101$	12.8235			1.27599			0.637993	−	0.770042i	$-0.279765\pi$
$101$	12.8235			1.27599			0.637993	+	0.770042i	$0.279765\pi$
$102$	−8.87333	+	4.47346i	−0.878591	+	0.442938i
$103$			2.11368i			0.208267i	0.994563	+	0.104134i	$0.0332070\pi$
$103$			2.11368i			0.208267i	−0.994563	+	0.104134i	$0.966793\pi$
$104$		0			0
$105$	4.45797	−	13.5230i	0.435053	−	1.31971i
$106$	−7.75615	−	7.75615i	−0.753344	−	0.753344i
$107$		−	2.16911i		−	0.209696i	−0.994488	−	0.104848i	$-0.966564\pi$
$107$		−	2.16911i		−	0.209696i	0.994488	−	0.104848i	$-0.0334356\pi$
$108$	−4.24264	+	3.00000i	−0.408248	+	0.288675i
$109$	−2.47695	−	2.47695i	−0.237249	−	0.237249i	0.578461	−	0.815710i	$-0.303653\pi$
$109$	−2.47695	−	2.47695i	−0.237249	−	0.237249i	−0.815710	+	0.578461i	$0.803653\pi$
$110$	−3.56813	+	3.56813i	−0.340208	+	0.340208i
$111$	−6.68608	+	3.37076i	−0.634615	+	0.319939i
$112$	−1.76690	+	1.76690i	−0.166956	+	0.166956i
$113$		−	15.6215i		−	1.46955i	−0.678310	−	0.734775i	$-0.737288\pi$
$113$		−	15.6215i		−	1.46955i	0.678310	−	0.734775i	$-0.262712\pi$
$114$	−5.32720	−	1.75615i	−0.498938	−	0.164479i
$115$	−10.8237	+	10.8237i	−1.00932	+	1.00932i
$116$	−4.65268			−0.431991
$117$		0			0
$118$	−6.57989			−0.605728
$119$	−10.1371	+	10.1371i	−0.929268	+	0.929268i
$120$	5.41187	+	1.78406i	0.494034	+	0.162862i
$121$		−	8.64748i		−	0.786134i
$122$	−2.16911	+	2.16911i	−0.196382	+	0.196382i
$123$	−0.896870	+	0.452154i	−0.0808680	+	0.0407693i
$124$	3.82374	−	3.82374i	0.343382	−	0.343382i
$125$	1.91630	+	1.91630i	0.171399	+	0.171399i
$126$	−4.45797	+	6.02671i	−0.397147	+	0.536902i
$127$			10.6936i			0.948901i	0.880282	+	0.474451i	$0.157353\pi$
$127$			10.6936i			0.948901i	−0.880282	+	0.474451i	$0.842647\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.120580	+	0.365773i	−0.0106165	+	0.0322045i
$130$		0			0
$131$			0.264467i			0.0231066i	0.999933	+	0.0115533i	$0.00367761\pi$
$131$			0.264467i			0.0231066i	−0.999933	+	0.0115533i	$0.996322\pi$
$132$	2.37220	−	1.19593i	0.206473	−	0.104093i
$133$	−8.09219			−0.701682
$134$	0.754898			0.0652133
$135$	16.8489	+	2.89081i	1.45012	+	0.248801i
$136$	−4.05684	−	4.05684i	−0.347871	−	0.347871i
$137$	−3.66371	−	3.66371i	−0.313012	−	0.313012i	0.533063	−	0.846075i	$-0.321041\pi$
$137$	−3.66371	−	3.66371i	−0.313012	−	0.313012i	−0.846075	+	0.533063i	$0.821041\pi$
$138$	7.19593	−	3.62780i	0.612559	−	0.308819i
$139$	2.22236			0.188498			0.0942490	−	0.995549i	$-0.469955\pi$
$139$	2.22236			0.188498			0.0942490	+	0.995549i	$0.469955\pi$
$140$	8.22081			0.694786
$141$	−8.43952	−	16.7402i	−0.710735	−	1.40978i
$142$			7.75615i			0.650882i
$143$		0			0
$144$	−2.41187	−	1.78406i	−0.200989	−	0.148672i
$145$	10.8237	+	10.8237i	0.898863	+	0.898863i
$146$		−	3.23847i		−	0.268018i
$147$	0.410044	−	1.24385i	0.0338199	−	0.102591i
$148$	−3.05684	−	3.05684i	−0.251271	−	0.251271i
$149$	6.41175	−	6.41175i	0.525271	−	0.525271i	−0.393887	−	0.919159i	$-0.628870\pi$
$149$	6.41175	−	6.41175i	0.525271	−	0.525271i	0.919159	+	0.393887i	$0.128870\pi$
$150$	−4.54090	−	9.00711i	−0.370763	−	0.735427i
$151$	−0.812993	+	0.812993i	−0.0661605	+	0.0661605i	−0.739413	−	0.673252i	$-0.764897\pi$
$151$	−0.812993	+	0.812993i	−0.0661605	+	0.0661605i	0.673252	+	0.739413i	$0.264897\pi$
$152$		−	3.23847i		−	0.262675i
$153$	−13.8375	−	10.2356i	−1.11869	−	0.827500i
$154$	2.71005	−	2.71005i	0.218382	−	0.218382i
$155$	−17.7907			−1.42898
$156$		0			0
$157$	8.09219			0.645827			0.322914	−	0.946428i	$-0.395338\pi$
$157$	8.09219			0.645827			0.322914	+	0.946428i	$0.395338\pi$
$158$	−9.97988	+	9.97988i	−0.793957	+	0.793957i
$159$	5.94817	−	18.0435i	0.471720	−	1.43094i
$160$			3.28995i			0.260093i
$161$	8.22081	−	8.22081i	0.647891	−	0.647891i
$162$	−7.94794	−	4.22258i	−0.624449	−	0.331757i
$163$	−17.2274	+	17.2274i	−1.34935	+	1.34935i	−0.462986	+	0.886366i	$0.653222\pi$
$163$	−17.2274	+	17.2274i	−1.34935	+	1.34935i	−0.886366	+	0.462986i	$0.846778\pi$
$164$	−0.410044	−	0.410044i	−0.0320191	−	0.0320191i
$165$	−8.30069	−	2.73639i	−0.646208	−	0.213027i
$166$		−	1.97851i		−	0.153562i
$167$	−6.82180	−	6.82180i	−0.527886	−	0.527886i	0.392055	−	0.919942i	$-0.371764\pi$
$167$	−6.82180	−	6.82180i	−0.527886	−	0.527886i	−0.919942	+	0.392055i	$0.871764\pi$
$168$	−4.11041	−	1.35503i	−0.317125	−	0.104543i
$169$		0			0
$170$			18.8752i			1.44766i
$171$	−1.43764	−	9.60846i	−0.109939	−	0.734777i
$172$	−0.222358			−0.0169546
$173$	−1.85465			−0.141006			−0.0705032	−	0.997512i	$-0.522461\pi$
$173$	−1.85465			−0.141006			−0.0705032	+	0.997512i	$0.522461\pi$
$174$	−3.62780	−	7.19593i	−0.275023	−	0.545522i
$175$	−10.2899	−	10.2899i	−0.777847	−	0.777847i
$176$	1.08456	+	1.08456i	0.0817515	+	0.0817515i
$177$	−5.13049	−	10.1766i	−0.385631	−	0.764919i
$178$	−9.06759			−0.679644
$179$	0.264467			0.0197672			0.00988361	−	0.999951i	$-0.496854\pi$
$179$	0.264467			0.0197672			0.00988361	+	0.999951i	$0.496854\pi$
$180$	1.46049	+	9.76118i	0.108858	+	0.727555i
$181$			8.11368i			0.603085i	0.953453	+	0.301543i	$0.0975016\pi$
$181$			8.11368i			0.603085i	−0.953453	+	0.301543i	$0.902498\pi$
$182$		0			0
$183$	−5.04610	−	1.66348i	−0.373018	−	0.122968i
$184$	3.28995	+	3.28995i	0.242538	+	0.242538i
$185$			14.2225i			1.04566i
$186$	8.89533	+	2.93241i	0.652237	+	0.215015i
$187$	6.22236	+	6.22236i	0.455024	+	0.455024i
$188$	7.65354	−	7.65354i	0.558192	−	0.558192i
$189$	−12.7970	−	2.19562i	−0.930845	−	0.159708i
$190$	−7.53379	+	7.53379i	−0.546559	+	0.546559i
$191$		−	16.1272i		−	1.16692i	−0.812142	−	0.583460i	$-0.801698\pi$
$191$		−	16.1272i		−	1.16692i	0.812142	−	0.583460i	$-0.198302\pi$
$192$	0.542278	−	1.64497i	0.0391355	−	0.118716i
$193$	2.53379	−	2.53379i	0.182386	−	0.182386i	−0.610008	−	0.792395i	$-0.708834\pi$
$193$	2.53379	−	2.53379i	0.182386	−	0.182386i	0.792395	+	0.610008i	$0.208834\pi$
$194$	−16.3764			−1.17576
$195$		0			0
$196$	0.756152			0.0540108
$197$	−4.49545	+	4.49545i	−0.320288	+	0.320288i	−0.848877	−	0.528590i	$-0.822721\pi$
$197$	−4.49545	+	4.49545i	−0.320288	+	0.320288i	0.528590	+	0.848877i	$0.322721\pi$
$198$	3.69931	+	2.73639i	0.262898	+	0.194467i
$199$			23.1383i			1.64023i	0.572199	+	0.820115i	$0.306091\pi$
$199$			23.1383i			1.64023i	−0.572199	+	0.820115i	$0.693909\pi$
$200$	4.11801	−	4.11801i	0.291187	−	0.291187i
$201$	0.588611	+	1.16754i	0.0415174	+	0.0823519i
$202$	−9.06759	+	9.06759i	−0.637993	+	0.637993i
$203$	−8.22081	−	8.22081i	−0.576988	−	0.576988i
$204$	3.11118	−	9.43760i	0.217826	−	0.660764i
$205$			1.90781i			0.133247i
$206$	−1.49460	−	1.49460i	−0.104134	−	0.104134i
$207$	11.2217	+	8.30069i	0.779960	+	0.576938i
$208$		0			0
$209$			4.96715i			0.343585i
$210$	6.40996	+	12.7145i	0.442329	+	0.877382i
$211$	15.2899			1.05260			0.526302	−	0.850298i	$-0.323578\pi$
$211$	15.2899			1.05260			0.526302	+	0.850298i	$0.323578\pi$
$212$	10.9689			0.753344
$213$	−11.9958	+	6.04765i	−0.821940	+	0.414378i
$214$	1.53379	+	1.53379i	0.104848	+	0.104848i
$215$	0.517281	+	0.517281i	0.0352783	+	0.0352783i
$216$	0.878680	−	5.12132i	0.0597866	−	0.348462i
$217$	13.5123			0.917275
$218$	3.50294			0.237249
$219$	5.00868	−	2.52511i	0.338455	−	0.170631i
$220$		−	5.04610i		−	0.340208i
$221$		0			0
$222$	2.34428	−	7.11126i	0.157338	−	0.477277i
$223$	3.30069	+	3.30069i	0.221031	+	0.221031i	0.808932	−	0.587902i	$-0.200046\pi$
$223$	3.30069	+	3.30069i	0.221031	+	0.221031i	−0.587902	+	0.808932i	$0.700046\pi$
$224$		−	2.49877i		−	0.166956i
$225$	10.3899	−	14.0461i	0.692662	−	0.936406i
$226$	11.0461	+	11.0461i	0.734775	+	0.734775i
$227$	−4.33822	+	4.33822i	−0.287938	+	0.287938i	−0.836264	−	0.548326i	$-0.815265\pi$
$227$	−4.33822	+	4.33822i	−0.287938	+	0.287938i	0.548326	+	0.836264i	$0.315265\pi$
$228$	5.00868	−	2.52511i	0.331708	−	0.167230i
$229$	−2.47695	+	2.47695i	−0.163682	+	0.163682i	−0.784195	−	0.620514i	$-0.786924\pi$
$229$	−2.47695	+	2.47695i	−0.163682	+	0.163682i	0.620514	+	0.784195i	$0.286924\pi$
$230$		−	15.3071i		−	1.00932i
$231$	6.30452	+	2.07833i	0.414807	+	0.136744i
$232$	3.28995	−	3.28995i	0.215995	−	0.215995i
$233$	12.0534			0.789645			0.394823	−	0.918757i	$-0.370806\pi$
$233$	12.0534			0.789645			0.394823	+	0.918757i	$0.370806\pi$
$234$		0			0
$235$	−35.6095			−2.32291
$236$	4.65268	−	4.65268i	0.302864	−	0.302864i
$237$	−23.2166	−	7.65354i	−1.50808	−	0.497151i
$238$		−	14.3360i		−	0.929268i
$239$	14.7898	−	14.7898i	0.956672	−	0.956672i	−0.0424271	−	0.999100i	$-0.513509\pi$
$239$	14.7898	−	14.7898i	0.956672	−	0.956672i	0.999100	+	0.0424271i	$0.0135090\pi$
$240$	−5.08829	+	2.56525i	−0.328448	+	0.165586i
$241$	12.3821	−	12.3821i	0.797604	−	0.797604i	−0.185114	−	0.982717i	$-0.559265\pi$
$241$	12.3821	−	12.3821i	0.797604	−	0.797604i	0.982717	+	0.185114i	$0.0592653\pi$
$242$	6.11469	+	6.11469i	0.393067	+	0.393067i
$243$	0.333537	−	15.5849i	0.0213964	−	0.999771i
$244$		−	3.06759i		−	0.196382i
$245$	−1.75907	−	1.75907i	−0.112383	−	0.112383i
$246$	0.314462	−	0.953903i	0.0200493	−	0.0608187i
$247$		0			0
$248$			5.40758i			0.343382i
$249$	3.06000	−	1.54269i	0.193920	−	0.0977639i
$250$	−2.71005			−0.171399
$251$	12.2946			0.776026			0.388013	−	0.921654i	$-0.373161\pi$
$251$	12.2946			0.776026			0.388013	+	0.921654i	$0.373161\pi$
$252$	−1.10927	−	7.41378i	−0.0698772	−	0.467024i
$253$	−5.04610	−	5.04610i	−0.317245	−	0.317245i
$254$	−7.56150	−	7.56150i	−0.474451	−	0.474451i
$255$	−29.1928	+	14.7174i	−1.82812	+	0.921641i
$256$	1.00000			0.0625000
$257$	−30.0352			−1.87355			−0.936773	−	0.349938i	$-0.886203\pi$
$257$	−30.0352			−1.87355			−0.936773	+	0.349938i	$0.886203\pi$
$258$	−0.173378	−	0.343903i	−0.0107940	−	0.0214105i
$259$		−	10.8022i		−	0.671219i
$260$		0			0
$261$	8.30069	−	11.2217i	0.513800	−	0.694604i
$262$	−0.187007	−	0.187007i	−0.0115533	−	0.0115533i
$263$			18.6107i			1.14759i	0.819000	+	0.573794i	$0.194529\pi$
$263$			18.6107i			1.14759i	−0.819000	+	0.573794i	$0.805471\pi$
$264$	−0.831742	+	2.52305i	−0.0511902	+	0.155283i
$265$	−25.5173	−	25.5173i	−1.56752	−	1.56752i
$266$	5.72204	−	5.72204i	0.350841	−	0.350841i
$267$	−7.07020	−	14.0241i	−0.432690	−	0.858261i
$268$	−0.533794	+	0.533794i	−0.0326066	+	0.0326066i
$269$		−	0.820089i		−	0.0500017i	−0.999687	−	0.0250008i	$-0.992041\pi$
$269$		−	0.820089i		−	0.0500017i	0.999687	−	0.0250008i	$-0.00795884\pi$
$270$	−13.9581	+	9.86984i	−0.849460	+	0.600659i
$271$	9.85909	−	9.85909i	0.598897	−	0.598897i	−0.341122	−	0.940019i	$-0.610807\pi$
$271$	9.85909	−	9.85909i	0.598897	−	0.598897i	0.940019	+	0.341122i	$0.110807\pi$
$272$	5.73724			0.347871
$273$		0			0
$274$	5.18127			0.313012
$275$	−6.31617	+	6.31617i	−0.380879	+	0.380879i
$276$	−2.52305	+	7.65354i	−0.151870	+	0.460689i
$277$		−	17.3871i		−	1.04469i	−0.852733	−	0.522346i	$-0.825057\pi$
$277$		−	17.3871i		−	1.04469i	0.852733	−	0.522346i	$-0.174943\pi$
$278$	−1.57144	+	1.57144i	−0.0942490	+	0.0942490i
$279$	2.40056	+	16.0442i	0.143718	+	0.960538i
$280$	−5.81299	+	5.81299i	−0.347393	+	0.347393i
$281$	13.5480	+	13.5480i	0.808207	+	0.808207i	0.984362	−	0.176156i	$-0.0563662\pi$
$281$	13.5480	+	13.5480i	0.808207	+	0.808207i	−0.176156	+	0.984362i	$0.556366\pi$
$282$	17.8048	+	5.86947i	1.06026	+	0.349522i
$283$		−	17.6475i		−	1.04903i	−0.851400	−	0.524517i	$-0.824246\pi$
$283$		−	17.6475i		−	1.04903i	0.851400	−	0.524517i	$-0.175754\pi$
$284$	−5.48443	−	5.48443i	−0.325441	−	0.325441i
$285$	−17.5262	−	5.77764i	−1.03816	−	0.342238i
$286$		0			0
$287$		−	1.44901i		−	0.0855325i
$288$	2.96697	−	0.443925i	0.174831	−	0.0261585i
$289$	15.9159			0.936231
$290$	−15.3071			−0.898863
$291$	−12.7691	−	25.3281i	−0.748537	−	1.48476i
$292$	2.28995	+	2.28995i	0.134009	+	0.134009i
$293$	−15.4643	−	15.4643i	−0.903435	−	0.903435i	0.0922970	−	0.995732i	$-0.470579\pi$
$293$	−15.4643	−	15.4643i	−0.903435	−	0.903435i	−0.995732	+	0.0922970i	$0.970579\pi$
$294$	0.589589	+	1.16948i	0.0343855	+	0.0682054i
$295$	−21.6475			−1.26036
$296$	4.32303			0.251271
$297$	−1.34771	+	7.85505i	−0.0782023	+	0.455796i
$298$			9.06759i			0.525271i
$299$		0			0
$300$	9.57989	+	3.15808i	0.553095	+	0.182332i
$301$	−0.392884	−	0.392884i	−0.0226454	−	0.0226454i
$302$		−	1.14975i		−	0.0661605i
$303$	−21.0943	−	6.95390i	−1.21184	−	0.399491i
$304$	2.28995	+	2.28995i	0.131337	+	0.131337i
$305$	−7.13626	+	7.13626i	−0.408621	+	0.408621i
$306$	17.0222	−	2.54690i	0.973097	−	0.145597i
$307$	20.8698	−	20.8698i	1.19110	−	1.19110i	0.214347	−	0.976758i	$-0.431238\pi$
$307$	20.8698	−	20.8698i	1.19110	−	1.19110i	0.976758	−	0.214347i	$-0.0687623\pi$
$308$			3.83260i			0.218382i
$309$	1.14620	−	3.47695i	0.0652053	−	0.197797i
$310$	12.5799	−	12.5799i	0.714490	−	0.714490i
$311$	−15.6215			−0.885816			−0.442908	−	0.896567i	$-0.646053\pi$
$311$	−15.6215			−0.885816			−0.442908	+	0.896567i	$0.646053\pi$
$312$		0			0
$313$	17.4036			0.983711			0.491856	−	0.870677i	$-0.336319\pi$
$313$	17.4036			0.983711			0.491856	+	0.870677i	$0.336319\pi$
$314$	−5.72204	+	5.72204i	−0.322914	+	0.322914i
$315$	−14.6665	+	19.8275i	−0.826362	+	1.11715i
$316$		−	14.1137i		−	0.793957i
$317$	2.89362	−	2.89362i	0.162522	−	0.162522i	−0.621161	−	0.783683i	$-0.713339\pi$
$317$	2.89362	−	2.89362i	0.162522	−	0.162522i	0.783683	+	0.621161i	$0.213339\pi$
$318$	8.55267	+	16.9646i	0.479610	+	0.951330i
$319$	−5.04610	+	5.04610i	−0.282527	+	0.282527i
$320$	−2.32634	−	2.32634i	−0.130046	−	0.130046i
$321$	−1.17626	+	3.56813i	−0.0656525	+	0.199154i
$322$			11.6260i			0.647891i
$323$	13.1380	+	13.1380i	0.731016	+	0.731016i
$324$	8.60586	−	2.63423i	0.478103	−	0.146346i
$325$		0			0
$326$		−	24.3632i		−	1.34935i
$327$	2.73132	+	5.41771i	0.151042	+	0.299600i
$328$	0.579890			0.0320191
$329$	27.0460			1.49110
$330$	7.80439	−	3.93456i	0.429618	−	0.216590i
$331$	−2.06759	−	2.06759i	−0.113645	−	0.113645i	0.647998	−	0.761642i	$-0.275607\pi$
$331$	−2.06759	−	2.06759i	−0.113645	−	0.113645i	−0.761642	+	0.647998i	$0.775607\pi$
$332$	1.39902	+	1.39902i	0.0767811	+	0.0767811i
$333$	12.8263	−	1.91910i	0.702877	−	0.105166i
$334$	9.64748			0.527886
$335$	2.48357			0.135692
$336$	3.86465	−	1.94835i	0.210834	−	0.106291i
$337$		−	20.5634i		−	1.12016i	−0.828438	−	0.560080i	$-0.810770\pi$
$337$		−	20.5634i		−	1.12016i	0.828438	−	0.560080i	$-0.189230\pi$
$338$		0			0
$339$	−8.47122	+	25.6970i	−0.460093	+	1.39567i
$340$	−13.3468	−	13.3468i	−0.723831	−	0.723831i
$341$		−	8.29412i		−	0.449152i
$342$	7.81077	+	5.77764i	0.422358	+	0.312419i
$343$	13.7043	+	13.7043i	0.739964	+	0.739964i
$344$	0.157231	−	0.157231i	0.00847732	−	0.00847732i
$345$	23.6742	−	11.9353i	1.27458	−	0.642574i
$346$	1.31144	−	1.31144i	0.0705032	−	0.0705032i
$347$			2.72473i			0.146271i	0.997322	+	0.0731357i	$0.0233006\pi$
$347$			2.72473i			0.146271i	−0.997322	+	0.0731357i	$0.976699\pi$
$348$	7.65354	+	2.52305i	0.410273	+	0.135250i
$349$	−21.6367	+	21.6367i	−1.15819	+	1.15819i	−0.173323	+	0.984865i	$0.555450\pi$
$349$	−21.6367	+	21.6367i	−1.15819	+	1.15819i	−0.984865	+	0.173323i	$0.944550\pi$
$350$	14.5522			0.777847
$351$		0			0
$352$	−1.53379			−0.0817515
$353$	−1.49460	+	1.49460i	−0.0795495	+	0.0795495i	−0.745762	−	0.666212i	$-0.767914\pi$
$353$	−1.49460	+	1.49460i	−0.0795495	+	0.0795495i	0.666212	+	0.745762i	$0.267914\pi$
$354$	10.8237	+	3.56813i	0.575275	+	0.189644i
$355$			25.5173i			1.35432i
$356$	6.41175	−	6.41175i	0.339822	−	0.339822i
$357$	22.1724	−	11.1781i	1.17349	−	0.591610i
$358$	−0.187007	+	0.187007i	−0.00988361	+	0.00988361i
$359$	0.314462	+	0.314462i	0.0165967	+	0.0165967i	0.715356	−	0.698760i	$-0.246264\pi$
$359$	0.314462	+	0.314462i	0.0165967	+	0.0165967i	−0.698760	+	0.715356i	$0.746264\pi$
$360$	−7.93492	−	5.86947i	−0.418207	−	0.309348i
$361$		−	8.51230i		−	0.448016i
$362$	−5.73724	−	5.73724i	−0.301543	−	0.301543i
$363$	−4.68934	+	14.2249i	−0.246126	+	0.746612i
$364$		0			0
$365$		−	10.6544i		−	0.557676i
$366$	4.74439	−	2.39187i	0.247993	−	0.125025i
$367$	21.0461			1.09860			0.549299	−	0.835626i	$-0.314895\pi$
$367$	21.0461			1.09860			0.549299	+	0.835626i	$0.314895\pi$
$368$	−4.65268			−0.242538
$369$	1.72052	−	0.257428i	0.0895666	−	0.0134012i
$370$	−10.0568	−	10.0568i	−0.522830	−	0.522830i
$371$	19.3808	+	19.3808i	1.00620	+	1.00620i
$372$	−8.36347	+	4.21642i	−0.433626	+	0.218611i
$373$	−4.22737			−0.218885			−0.109442	−	0.993993i	$-0.534907\pi$
$373$	−4.22737			−0.218885			−0.109442	+	0.993993i	$0.534907\pi$
$374$	−8.79974			−0.455024
$375$	−2.11309	−	4.19142i	−0.109120	−	0.216444i
$376$			10.8237i			0.558192i
$377$		0			0
$378$	10.6014	−	7.49631i	0.545276	−	0.385568i
$379$	18.1598	+	18.1598i	0.932805	+	0.932805i	0.997880	−	0.0650751i	$-0.0207287\pi$
$379$	18.1598	+	18.1598i	0.932805	+	0.932805i	−0.0650751	+	0.997880i	$0.520729\pi$
$380$		−	10.6544i		−	0.546559i
$381$	5.79889	−	17.5906i	0.297086	−	0.901196i
$382$	11.4036	+	11.4036i	0.583460	+	0.583460i
$383$	−19.4425	+	19.4425i	−0.993464	+	0.993464i	−0.999979	−	0.00651435i	$-0.997926\pi$
$383$	−19.4425	+	19.4425i	−0.993464	+	0.993464i	0.00651435	+	0.999979i	$0.497926\pi$
$384$	0.779723	+	1.54662i	0.0397901	+	0.0789256i
$385$	8.91593	−	8.91593i	0.454398	−	0.454398i
$386$			3.58333i			0.182386i
$387$	0.396701	−	0.536298i	0.0201654	−	0.0272616i
$388$	11.5799	−	11.5799i	0.587880	−	0.587880i
$389$	−2.16911			−0.109978			−0.0549892	−	0.998487i	$-0.517512\pi$
$389$	−2.16911			−0.109978			−0.0549892	+	0.998487i	$0.517512\pi$
$390$		0			0
$391$	−26.6936			−1.34995
$392$	−0.534680	+	0.534680i	−0.0270054	+	0.0270054i
$393$	0.143415	−	0.435041i	0.00723432	−	0.0219449i
$394$		−	6.35753i		−	0.320288i
$395$	−32.8333	+	32.8333i	−1.65202	+	1.65202i
$396$	−4.55072	+	0.680889i	−0.228683	+	0.0342160i
$397$	−10.2685	+	10.2685i	−0.515359	+	0.515359i	−0.916164	−	0.400805i	$-0.868731\pi$
$397$	−10.2685	+	10.2685i	−0.515359	+	0.515359i	0.400805	+	0.916164i	$0.368731\pi$
$398$	−16.3612	−	16.3612i	−0.820115	−	0.820115i
$399$	13.3114	+	4.38822i	0.666405	+	0.219686i
$400$			5.82374i			0.291187i
$401$	5.83282	+	5.83282i	0.291277	+	0.291277i	0.837585	−	0.546307i	$-0.183967\pi$
$401$	5.83282	+	5.83282i	0.291277	+	0.291277i	−0.546307	+	0.837585i	$0.683967\pi$
$402$	−1.24179	−	0.409365i	−0.0619347	−	0.0204172i
$403$		0			0
$404$		−	12.8235i		−	0.637993i
$405$	−26.1483	−	13.8921i	−1.29932	−	0.690302i
$406$	11.6260			0.576988
$407$	−6.63063			−0.328668
$408$	4.47346	+	8.87333i	0.221469	+	0.439295i
$409$	6.62599	+	6.62599i	0.327634	+	0.327634i	0.851686	−	0.524052i	$-0.175580\pi$
$409$	6.62599	+	6.62599i	0.327634	+	0.327634i	−0.524052	+	0.851686i	$0.675580\pi$
$410$	−1.34902	−	1.34902i	−0.0666235	−	0.0666235i
$411$	4.03996	+	8.01346i	0.199276	+	0.395275i
$412$	2.11368			0.104134
$413$	16.4416			0.809040
$414$	−13.8044	+	2.06544i	−0.678449	+	0.101511i
$415$		−	6.50919i		−	0.319523i
$416$		0			0
$417$	−3.65572	−	1.20514i	−0.179021	−	0.0590157i
$418$	−3.51230	−	3.51230i	−0.171792	−	0.171792i
$419$		−	8.41198i		−	0.410952i	−0.978662	−	0.205476i	$-0.934126\pi$
$419$		−	8.41198i		−	0.410952i	0.978662	−	0.205476i	$-0.0658743\pi$
$420$	−13.5230	−	4.45797i	−0.659855	−	0.217526i
$421$	0.964649	+	0.964649i	0.0470141	+	0.0470141i	0.730223	−	0.683209i	$-0.239416\pi$
$421$	0.964649	+	0.964649i	0.0470141	+	0.0470141i	−0.683209	+	0.730223i	$0.739416\pi$
$422$	−10.8116	+	10.8116i	−0.526302	+	0.526302i
$423$	4.80493	+	32.1137i	0.233624	+	1.56142i
$424$	−7.75615	+	7.75615i	−0.376672	+	0.376672i
$425$			33.4122i			1.62073i
$426$	4.20599	−	12.7587i	0.203781	−	0.618159i
$427$	5.42011	−	5.42011i	0.262297	−	0.262297i
$428$	−2.16911			−0.104848
$429$		0			0
$430$	−0.731545			−0.0352783
$431$	25.4442	−	25.4442i	1.22560	−	1.22560i	0.259993	−	0.965610i	$-0.416280\pi$
$431$	25.4442	−	25.4442i	1.22560	−	1.22560i	0.965610	−	0.259993i	$-0.0837203\pi$
$432$	3.00000	+	4.24264i	0.144338	+	0.204124i
$433$			39.6740i			1.90661i	0.302010	+	0.953305i	$0.402342\pi$
$433$			39.6740i			1.90661i	−0.302010	+	0.953305i	$0.597658\pi$
$434$	−9.55464	+	9.55464i	−0.458637	+	0.458637i
$435$	−11.9353	−	23.6742i	−0.572253	−	1.13509i
$436$	−2.47695	+	2.47695i	−0.118624	+	0.118624i
$437$	−10.6544	−	10.6544i	−0.509669	−	0.509669i
$438$	−1.75615	+	5.32720i	−0.0839122	+	0.254543i
$439$			18.0000i			0.859093i	0.903045	+	0.429547i	$0.141327\pi$
$439$			18.0000i			0.859093i	−0.903045	+	0.429547i	$0.858673\pi$
$440$	3.56813	+	3.56813i	0.170104	+	0.170104i
$441$	−1.34902	+	1.82374i	−0.0642392	+	0.0868447i
$442$		0			0
$443$			31.9899i			1.51988i	0.649991	+	0.759942i	$0.274773\pi$
$443$			31.9899i			1.51988i	−0.649991	+	0.759942i	$0.725227\pi$
$444$	3.37076	+	6.68608i	0.159969	+	0.317307i
$445$	−29.8319			−1.41417
$446$	−4.66788			−0.221031
$447$	−14.0241	+	7.07020i	−0.663318	+	0.334409i
$448$	1.76690	+	1.76690i	0.0834780	+	0.0834780i
$449$	5.95612	+	5.95612i	0.281087	+	0.281087i	0.833542	−	0.552456i	$-0.186309\pi$
$449$	5.95612	+	5.95612i	0.281087	+	0.281087i	−0.552456	+	0.833542i	$0.686309\pi$
$450$	2.58530	+	17.2789i	0.121872	+	0.814534i
$451$	−0.889432			−0.0418817
$452$	−15.6215			−0.734775
$453$	1.77822	−	0.896483i	0.0835481	−	0.0421205i
$454$		−	6.13517i		−	0.287938i
$455$		0			0
$456$	−1.75615	+	5.32720i	−0.0822393	+	0.249469i
$457$	−10.4251	−	10.4251i	−0.487667	−	0.487667i	0.419903	−	0.907569i	$-0.362064\pi$
$457$	−10.4251	−	10.4251i	−0.487667	−	0.487667i	−0.907569	+	0.419903i	$0.862064\pi$
$458$		−	3.50294i		−	0.163682i
$459$	17.2117	+	24.3411i	0.803374	+	1.13614i
$460$	10.8237	+	10.8237i	0.504659	+	0.504659i
$461$	27.4444	−	27.4444i	1.27821	−	1.27821i	0.336547	−	0.941667i	$-0.390741\pi$
$461$	27.4444	−	27.4444i	1.27821	−	1.27821i	0.941667	−	0.336547i	$-0.109259\pi$
$462$	−5.92757	+	2.98836i	−0.275775	+	0.139031i
$463$	−8.89133	+	8.89133i	−0.413215	+	0.413215i	−0.882857	−	0.469642i	$-0.844383\pi$
$463$	−8.89133	+	8.89133i	−0.413215	+	0.413215i	0.469642	+	0.882857i	$0.344383\pi$
$464$			4.65268i			0.215995i
$465$	29.2651	+	9.64748i	1.35714	+	0.447391i
$466$	−8.52305	+	8.52305i	−0.394823	+	0.394823i
$467$	36.9303			1.70893			0.854466	−	0.519508i	$-0.173885\pi$
$467$	36.9303			1.70893			0.854466	+	0.519508i	$0.173885\pi$
$468$		0			0
$469$	−1.88632			−0.0871020
$470$	25.1797	−	25.1797i	1.16145	−	1.16145i
$471$	−13.3114	−	4.38822i	−0.613359	−	0.202198i
$472$			6.57989i			0.302864i
$473$	−0.241160	+	0.241160i	−0.0110885	+	0.0110885i
$474$	21.8285	−	11.0048i	1.00262	−	0.505465i
$475$	−13.3360	+	13.3360i	−0.611900	+	0.611900i
$476$	10.1371	+	10.1371i	0.464634	+	0.464634i
$477$	−19.5691	+	26.4554i	−0.896010	+	1.21131i
$478$			20.9159i			0.956672i
$479$	−3.62978	−	3.62978i	−0.165849	−	0.165849i	0.619303	−	0.785152i	$-0.287415\pi$
$479$	−3.62978	−	3.62978i	−0.165849	−	0.165849i	−0.785152	+	0.619303i	$0.787415\pi$
$480$	1.78406	−	5.41187i	0.0814310	−	0.247017i
$481$		0			0
$482$			17.5110i			0.797604i
$483$	−17.9810	+	9.06505i	−0.818163	+	0.412474i
$484$	−8.64748			−0.393067
$485$	−53.8776			−2.44645
$486$	10.7843	+	11.2560i	0.489187	+	0.510584i
$487$	−9.33604	−	9.33604i	−0.423056	−	0.423056i	0.463198	−	0.886255i	$-0.346702\pi$
$487$	−9.33604	−	9.33604i	−0.423056	−	0.423056i	−0.886255	+	0.463198i	$0.846702\pi$
$488$	2.16911	+	2.16911i	0.0981911	+	0.0981911i
$489$	37.6806	−	18.9965i	1.70397	−	0.859053i
$490$	2.48770			0.112383
$491$	−9.37867			−0.423254			−0.211627	−	0.977351i	$-0.567876\pi$
$491$	−9.37867			−0.423254			−0.211627	+	0.977351i	$0.567876\pi$
$492$	0.452154	+	0.896870i	0.0203847	+	0.0404340i
$493$			26.6936i			1.20222i
$494$		0			0
$495$	12.1705	+	9.00256i	0.547024	+	0.404635i
$496$	−3.82374	−	3.82374i	−0.171691	−	0.171691i
$497$		−	19.3808i		−	0.869349i
$498$	−1.07290	+	3.25459i	−0.0480779	+	0.145842i
$499$	0.176261	+	0.176261i	0.00789054	+	0.00789054i	0.711041	−	0.703151i	$-0.248224\pi$
$499$	0.176261	+	0.176261i	0.00789054	+	0.00789054i	−0.703151	+	0.711041i	$0.748224\pi$
$500$	1.91630	−	1.91630i	0.0856995	−	0.0856995i
$501$	7.52236	+	14.9210i	0.336074	+	0.666620i
$502$	−8.69357	+	8.69357i	−0.388013	+	0.388013i
$503$			14.1725i			0.631922i	0.948772	+	0.315961i	$0.102327\pi$
$503$			14.1725i			0.631922i	−0.948772	+	0.315961i	$0.897673\pi$
$504$	6.02671	+	4.45797i	0.268451	+	0.198574i
$505$	−29.8319	+	29.8319i	−1.32750	+	1.32750i
$506$	7.13626			0.317245
$507$		0			0
$508$	10.6936			0.474451
$509$	0.724506	−	0.724506i	0.0321132	−	0.0321132i	−0.690868	−	0.722981i	$-0.742771\pi$
$509$	0.724506	−	0.724506i	0.0321132	−	0.0321132i	0.722981	+	0.690868i	$0.242771\pi$
$510$	10.2356	−	31.0492i	0.453240	−	1.37488i
$511$			8.09219i			0.357978i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.84558	+	16.5852i	−0.125635	+	0.732257i
$514$	21.2381	−	21.2381i	0.936773	−	0.936773i
$515$	−4.91715	−	4.91715i	−0.216676	−	0.216676i
$516$	0.365773	+	0.120580i	0.0161022	+	0.00530823i
$517$		−	16.6014i		−	0.730128i
$518$	7.63834	+	7.63834i	0.335610	+	0.335610i
$519$	3.05085	+	1.00574i	0.133917	+	0.0441469i
$520$		0			0
$521$		−	23.5279i		−	1.03078i	−0.856957	−	0.515388i	$-0.827648\pi$
$521$		−	23.5279i		−	1.03078i	0.856957	−	0.515388i	$-0.172352\pi$
$522$	2.06544	+	13.8044i	0.0904020	+	0.604202i
$523$	−6.09219			−0.266393			−0.133197	−	0.991090i	$-0.542524\pi$
$523$	−6.09219			−0.266393			−0.133197	+	0.991090i	$0.542524\pi$
$524$	0.264467			0.0115533
$525$	11.3467	+	22.5067i	0.495209	+	0.982272i
$526$	−13.1598	−	13.1598i	−0.573794	−	0.573794i
$527$	−21.9377	−	21.9377i	−0.955622	−	0.955622i
$528$	−1.19593	−	2.37220i	−0.0520463	−	0.103237i
$529$	−1.35252			−0.0588053
$530$	36.0869			1.56752
$531$	2.92098	+	19.5224i	0.126760	+	0.847198i
$532$			8.09219i			0.350841i
$533$		0			0
$534$	14.9159	+	4.91715i	0.645475	+	0.212786i
$535$	5.04610	+	5.04610i	0.218162	+	0.218162i
$536$		−	0.754898i		−	0.0326066i
$537$	−0.435041	−	0.143415i	−0.0187734	−	0.00618880i
$538$	0.579890	+	0.579890i	0.0250008	+	0.0250008i
$539$	0.820089	−	0.820089i	0.0353237	−	0.0353237i
$540$	2.89081	−	16.8489i	0.124401	−	0.725060i
$541$	−14.5477	+	14.5477i	−0.625453	+	0.625453i	−0.946920	−	0.321468i	$-0.895824\pi$
$541$	−14.5477	+	14.5477i	−0.625453	+	0.625453i	0.321468	+	0.946920i	$0.395824\pi$
$542$			13.9429i			0.598897i
$543$	4.39987	−	13.3468i	0.188817	−	0.572765i
$544$	−4.05684	+	4.05684i	−0.173936	+	0.173936i
$545$	11.5245			0.493654
$546$		0			0
$547$	16.1302			0.689676			0.344838	−	0.938662i	$-0.387934\pi$
$547$	16.1302			0.689676			0.344838	+	0.938662i	$0.387934\pi$
$548$	−3.66371	+	3.66371i	−0.156506	+	0.156506i
$549$	7.39862	+	5.47277i	0.315765	+	0.233572i
$550$		−	8.93241i		−	0.380879i
$551$	−10.6544	+	10.6544i	−0.453892	+	0.453892i
$552$	−3.62780	−	7.19593i	−0.154410	−	0.306279i
$553$	24.9374	−	24.9374i	1.06045	−	1.06045i
$554$	12.2946	+	12.2946i	0.522346	+	0.522346i
$555$	7.71256	−	23.3957i	0.327380	−	0.993090i
$556$		−	2.22236i		−	0.0942490i
$557$	−6.66457	−	6.66457i	−0.282387	−	0.282387i	0.551673	−	0.834060i	$-0.313989\pi$
$557$	−6.66457	−	6.66457i	−0.282387	−	0.282387i	−0.834060	+	0.551673i	$0.813989\pi$
$558$	−13.0424	−	9.64748i	−0.552128	−	0.408410i
$559$		0			0
$560$		−	8.22081i		−	0.347393i
$561$	−6.86136	−	13.6099i	−0.289687	−	0.574609i
$562$	−19.1598			−0.808207
$563$	−41.2952			−1.74039			−0.870193	−	0.492710i	$-0.836006\pi$
$563$	−41.2952			−1.74039			−0.870193	+	0.492710i	$0.836006\pi$
$564$	−16.7402	+	8.43952i	−0.704890	+	0.355368i
$565$	36.3411	+	36.3411i	1.52888	+	1.52888i
$566$	12.4787	+	12.4787i	0.524517	+	0.524517i
$567$	19.8601	+	10.5513i	0.834045	+	0.443111i
$568$	7.75615			0.325441
$569$	9.35536			0.392197			0.196099	−	0.980584i	$-0.437173\pi$
$569$	9.35536			0.392197			0.196099	+	0.980584i	$0.437173\pi$
$570$	16.4783	−	8.30747i	0.690200	−	0.347962i
$571$			9.96203i			0.416898i	0.978033	+	0.208449i	$0.0668415\pi$
$571$			9.96203i			0.416898i	−0.978033	+	0.208449i	$0.933158\pi$
$572$		0			0
$573$	−8.74541	+	26.5287i	−0.365345	+	1.10825i
$574$	1.02461	+	1.02461i	0.0427662	+	0.0427662i
$575$		−	27.0960i		−	1.12998i
$576$	−1.78406	+	2.41187i	−0.0743360	+	0.100495i
$577$	−25.8022	−	25.8022i	−1.07416	−	1.07416i	−0.997020	−	0.0771415i	$-0.975421\pi$
$577$	−25.8022	−	25.8022i	−1.07416	−	1.07416i	−0.0771415	−	0.997020i	$-0.524579\pi$
$578$	−11.2543	+	11.2543i	−0.468116	+	0.468116i
$579$	−5.54204	+	2.79400i	−0.230319	+	0.116115i
$580$	10.8237	−	10.8237i	0.449431	−	0.449431i
$581$			4.94384i			0.205105i
$582$	26.9388	+	8.88058i	1.11665	+	0.368112i
$583$	11.8963	−	11.8963i	0.492696	−	0.492696i
$584$	−3.23847			−0.134009
$585$		0			0
$586$	21.8698			0.903435
$587$	20.5387	−	20.5387i	0.847723	−	0.847723i	−0.142126	−	0.989849i	$-0.545394\pi$
$587$	20.5387	−	20.5387i	0.847723	−	0.847723i	0.989849	+	0.142126i	$0.0453938\pi$
$588$	−1.24385	−	0.410044i	−0.0512954	−	0.0169099i
$589$		−	17.5123i		−	0.721582i
$590$	15.3071	−	15.3071i	0.630182	−	0.630182i
$591$	9.83268	−	4.95711i	0.404463	−	0.203908i
$592$	−3.05684	+	3.05684i	−0.125635	+	0.125635i
$593$	−23.9379	−	23.9379i	−0.983013	−	0.983013i	0.0168449	−	0.999858i	$-0.494638\pi$
$593$	−23.9379	−	23.9379i	−0.983013	−	0.983013i	−0.999858	+	0.0168449i	$0.994638\pi$
$594$	−4.60138	−	6.50733i	−0.188797	−	0.266999i
$595$		−	47.1648i		−	1.93357i
$596$	−6.41175	−	6.41175i	−0.262636	−	0.262636i
$597$	12.5474	−	38.0619i	0.513530	−	1.55777i
$598$		0			0
$599$		−	41.0774i		−	1.67838i	−0.543841	−	0.839188i	$-0.683031\pi$
$599$		−	41.0774i		−	1.67838i	0.543841	−	0.839188i	$-0.316969\pi$
$600$	−9.00711	+	4.54090i	−0.367714	+	0.185382i
$601$	−32.0265			−1.30639			−0.653194	−	0.757191i	$-0.726571\pi$
$601$	−32.0265			−1.30639			−0.653194	+	0.757191i	$0.726571\pi$
$602$	0.555621			0.0226454
$603$	−0.335118	−	2.23976i	−0.0136471	−	0.0912102i
$604$	0.812993	+	0.812993i	0.0330802	+	0.0330802i
$605$	20.1170	+	20.1170i	0.817872	+	0.817872i
$606$	19.8331	−	9.99878i	0.805664	−	0.406173i
$607$	32.9424			1.33709			0.668546	−	0.743671i	$-0.266917\pi$
$607$	32.9424			1.33709			0.668546	+	0.743671i	$0.266917\pi$
$608$	−3.23847			−0.131337
$609$	9.06505	+	17.9810i	0.367334	+	0.728626i
$610$		−	10.0922i		−	0.408621i
$611$		0			0
$612$	−10.2356	+	13.8375i	−0.413750	+	0.559347i
$613$	−18.0296	−	18.0296i	−0.728209	−	0.728209i	0.242054	−	0.970263i	$-0.422179\pi$
$613$	−18.0296	−	18.0296i	−0.728209	−	0.728209i	−0.970263	+	0.242054i	$0.922179\pi$
$614$			29.5144i			1.19110i
$615$	1.03456	−	3.13829i	0.0417175	−	0.126548i
$616$	−2.71005	−	2.71005i	−0.109191	−	0.109191i
$617$	−3.10809	+	3.10809i	−0.125127	+	0.125127i	−0.766897	−	0.641770i	$-0.778200\pi$
$617$	−3.10809	+	3.10809i	−0.125127	+	0.125127i	0.641770	+	0.766897i	$0.278200\pi$
$618$	1.64809	+	3.26906i	0.0662958	+	0.131501i
$619$	14.3114	−	14.3114i	0.575225	−	0.575225i	−0.358359	−	0.933584i	$-0.616664\pi$
$619$	14.3114	−	14.3114i	0.575225	−	0.575225i	0.933584	+	0.358359i	$0.116664\pi$
$620$			17.7907i			0.714490i
$621$	−13.9581	−	19.7397i	−0.560117	−	0.792126i
$622$	11.0461	−	11.0461i	0.442908	−	0.442908i
$623$	22.6578			0.907766
$624$		0			0
$625$	20.2028			0.808110
$626$	−12.3062	+	12.3062i	−0.491856	+	0.491856i
$627$	2.69357	−	8.17082i	0.107571	−	0.326311i
$628$		−	8.09219i		−	0.322914i
$629$	−17.5378	+	17.5378i	−0.699279	+	0.699279i
$630$	−3.64942	−	24.3909i	−0.145397	−	0.971758i
$631$	12.8130	−	12.8130i	0.510077	−	0.510077i	−0.404473	−	0.914550i	$-0.632545\pi$
$631$	12.8130	−	12.8130i	0.510077	−	0.510077i	0.914550	+	0.404473i	$0.132545\pi$
$632$	9.97988	+	9.97988i	0.396978	+	0.396978i
$633$	−25.1515	−	8.29140i	−0.999684	−	0.329554i
$634$			4.09219i			0.162522i
$635$	−24.8769	−	24.8769i	−0.987210	−	0.987210i
$636$	−18.0435	−	5.94817i	−0.715470	−	0.235860i
$637$		0			0
$638$		−	7.13626i		−	0.282527i
$639$	23.0123	−	3.44315i	0.910352	−	0.136209i
$640$	3.28995			0.130046
$641$	13.1147			0.517998			0.258999	−	0.965878i	$-0.416607\pi$
$641$	13.1147			0.517998			0.258999	+	0.965878i	$0.416607\pi$
$642$	−1.69131	−	3.35479i	−0.0667505	−	0.132403i
$643$	5.60138	+	5.60138i	0.220897	+	0.220897i	0.808876	−	0.587979i	$-0.200076\pi$
$643$	5.60138	+	5.60138i	0.220897	+	0.220897i	−0.587979	+	0.808876i	$0.700076\pi$
$644$	−8.22081	−	8.22081i	−0.323945	−	0.323945i
$645$	−0.570403	−	1.13142i	−0.0224596	−	0.0445497i
$646$	−18.5799			−0.731016
$647$	−11.4745			−0.451108			−0.225554	−	0.974231i	$-0.572419\pi$
$647$	−11.4745			−0.451108			−0.225554	+	0.974231i	$0.572419\pi$
$648$	−4.22258	+	7.94794i	−0.165879	+	0.312225i
$649$		−	10.0922i		−	0.396153i
$650$		0			0
$651$	−22.2274	−	7.32742i	−0.871159	−	0.287184i
$652$	17.2274	+	17.2274i	0.674676	+	0.674676i
$653$			12.1946i			0.477211i	0.971117	+	0.238605i	$0.0766903\pi$
$653$			12.1946i			0.477211i	−0.971117	+	0.238605i	$0.923310\pi$
$654$	−5.76224	−	1.89957i	−0.225321	−	0.0742789i
$655$	−0.615242	−	0.615242i	−0.0240395	−	0.0240395i
$656$	−0.410044	+	0.410044i	−0.0160095	+	0.0160095i
$657$	−9.60846	+	1.43764i	−0.374862	+	0.0560876i
$658$	−19.1244	+	19.1244i	−0.745548	+	0.745548i
$659$			31.9632i			1.24511i	0.782577	+	0.622554i	$0.213905\pi$
$659$			31.9632i			1.24511i	−0.782577	+	0.622554i	$0.786095\pi$
$660$	−2.73639	+	8.30069i	−0.106514	+	0.323104i
$661$	12.2470	−	12.2470i	0.476352	−	0.476352i	−0.427611	−	0.903963i	$-0.640645\pi$
$661$	12.2470	−	12.2470i	0.476352	−	0.476352i	0.903963	+	0.427611i	$0.140645\pi$
$662$	2.92401			0.113645
$663$		0			0
$664$	−1.97851			−0.0767811
$665$	18.8252	−	18.8252i	0.730010	−	0.730010i
$666$	−7.71256	+	10.4266i	−0.298856	+	0.404022i
$667$		−	21.6475i		−	0.838194i
$668$	−6.82180	+	6.82180i	−0.263943	+	0.263943i
$669$	−3.63965	−	7.21944i	−0.140717	−	0.279120i
$670$	−1.75615	+	1.75615i	−0.0678461	+	0.0678461i
$671$	−3.32697	−	3.32697i	−0.128436	−	0.128436i
$672$	−1.35503	+	4.11041i	−0.0522713	+	0.158562i
$673$			41.8483i			1.61314i	0.591142	+	0.806568i	$0.298677\pi$
$673$			41.8483i			1.61314i	−0.591142	+	0.806568i	$0.701323\pi$
$674$	14.5405	+	14.5405i	0.560080	+	0.560080i
$675$	−24.7080	+	17.4712i	−0.951013	+	0.672467i
$676$		0			0
$677$		−	15.9360i		−	0.612470i	−0.951956	−	0.306235i	$-0.900931\pi$
$677$		−	15.9360i		−	0.612470i	0.951956	−	0.306235i	$-0.0990694\pi$
$678$	−12.1805	−	24.1606i	−0.467788	−	0.927881i
$679$	40.9209			1.57040
$680$	18.8752			0.723831
$681$	9.48878	−	4.78374i	0.363611	−	0.183313i
$682$	5.86483	+	5.86483i	0.224576	+	0.224576i
$683$	23.5279	+	23.5279i	0.900270	+	0.900270i	0.995459	−	0.0951894i	$-0.0303457\pi$
$683$	23.5279	+	23.5279i	0.900270	+	0.900270i	−0.0951894	+	0.995459i	$0.530346\pi$
$684$	−9.60846	+	1.43764i	−0.367389	+	0.0549695i
$685$	17.0461			0.651298
$686$	−19.3808			−0.739964
$687$	5.41771	−	2.73132i	0.206699	−	0.104206i
$688$			0.222358i			0.00847732i
$689$		0			0
$690$	−8.30069	+	25.1797i	−0.316002	+	0.958576i
$691$	−14.1763	−	14.1763i	−0.539290	−	0.539290i	0.384030	−	0.923321i	$-0.374536\pi$
$691$	−14.1763	−	14.1763i	−0.539290	−	0.539290i	−0.923321	+	0.384030i	$0.874536\pi$
$692$			1.85465i			0.0705032i
$693$	−9.24372	−	6.83760i	−0.351140	−	0.259739i
$694$	−1.92668	−	1.92668i	−0.0731357	−	0.0731357i
$695$	−5.16997	+	5.16997i	−0.196108	+	0.196108i
$696$	−7.19593	+	3.62780i	−0.272761	+	0.137512i
$697$	−2.35252	+	2.35252i	−0.0891082	+	0.0891082i
$698$		−	30.5990i		−	1.15819i
$699$	−19.8275	−	6.53630i	−0.749946	−	0.247226i
$700$	−10.2899	+	10.2899i	−0.388923	+	0.388923i
$701$	22.9723			0.867651			0.433825	−	0.900997i	$-0.357163\pi$
$701$	22.9723			0.867651			0.433825	+	0.900997i	$0.357163\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	1.08456	−	1.08456i	0.0408757	−	0.0408757i
$705$	58.5767	+	19.3102i	2.20612	+	0.727266i
$706$		−	2.11368i		−	0.0795495i
$707$	22.6578	−	22.6578i	0.852135	−	0.852135i
$708$	−10.1766	+	5.13049i	−0.382460	+	0.192816i
$709$	3.10867	−	3.10867i	0.116749	−	0.116749i	−0.646319	−	0.763068i	$-0.723692\pi$
$709$	3.10867	−	3.10867i	0.116749	−	0.116749i	0.763068	+	0.646319i	$0.223692\pi$
$710$	−18.0435	−	18.0435i	−0.677159	−	0.677159i
$711$	34.0404	+	25.1797i	1.27661	+	0.944313i
$712$			9.06759i			0.339822i
$713$	17.7907	+	17.7907i	0.666265	+	0.666265i
$714$	−7.77412	+	23.5824i	−0.290939	+	0.882549i
$715$		0			0
$716$		−	0.264467i		−	0.00988361i
$717$	−32.3490	+	16.3086i	−1.20810	+	0.609057i
$718$	−0.444716			−0.0165967
$719$	8.46197			0.315578			0.157789	−	0.987473i	$-0.449563\pi$
$719$	8.46197			0.315578			0.157789	+	0.987473i	$0.449563\pi$
$720$	9.76118	−	1.46049i	0.363778	−	0.0544292i
$721$	3.73466	+	3.73466i	0.139086	+	0.139086i
$722$	6.01911	+	6.01911i	0.224008	+	0.224008i
$723$	−27.0828	+	13.6537i	−1.00722	+	0.507787i
$724$	8.11368			0.301543
$725$	−27.0960			−1.00632
$726$	−6.74264	−	13.3744i	−0.250243	−	0.496369i
$727$		−	13.0461i		−	0.483853i	−0.970295	−	0.241926i	$-0.922221\pi$
$727$		−	13.0461i		−	0.483853i	0.970295	−	0.241926i	$-0.0777793\pi$
$728$		0			0
$729$	−9.00000	+	25.4558i	−0.333333	+	0.942809i
$730$	7.53379	+	7.53379i	0.278838	+	0.278838i
$731$			1.27572i			0.0471842i
$732$	−1.66348	+	5.04610i	−0.0614842	+	0.186509i
$733$	14.8180	+	14.8180i	0.547315	+	0.547315i	0.925663	−	0.378348i	$-0.123508\pi$
$733$	14.8180	+	14.8180i	0.547315	+	0.547315i	−0.378348	+	0.925663i	$0.623508\pi$
$734$	−14.8818	+	14.8818i	−0.549299	+	0.549299i
$735$	1.93971	+	3.84752i	0.0715474	+	0.141918i
$736$	3.28995	−	3.28995i	0.121269	−	0.121269i
$737$			1.15786i			0.0426502i
$738$	−1.03456	+	1.39862i	−0.0380827	+	0.0514839i
$739$	15.9159	−	15.9159i	0.585477	−	0.585477i	−0.350926	−	0.936403i	$-0.614133\pi$
$739$	15.9159	−	15.9159i	0.585477	−	0.585477i	0.936403	+	0.350926i	$0.114133\pi$
$740$	14.2225			0.522830
$741$		0			0
$742$	−27.4086			−1.00620
$743$	−12.3062	+	12.3062i	−0.451472	+	0.451472i	−0.895843	−	0.444371i	$-0.853427\pi$
$743$	−12.3062	+	12.3062i	−0.451472	+	0.451472i	0.444371	+	0.895843i	$0.353427\pi$
$744$	2.93241	−	8.89533i	0.107507	−	0.326118i
$745$			29.8319i			1.09295i
$746$	2.98920	−	2.98920i	0.109442	−	0.109442i
$747$	−5.87018	+	0.878310i	−0.214779	+	0.0321357i
$748$	6.22236	−	6.22236i	0.227512	−	0.227512i
$749$	−3.83260	−	3.83260i	−0.140040	−	0.140040i
$750$	4.45797	+	1.46960i	0.162782	+	0.0536623i
$751$			6.71506i			0.245036i	0.992466	+	0.122518i	$0.0390970\pi$
$751$			6.71506i			0.245036i	−0.992466	+	0.122518i	$0.960903\pi$
$752$	−7.65354	−	7.65354i	−0.279096	−	0.279096i
$753$	−20.2242	−	6.66707i	−0.737012	−	0.242962i
$754$		0			0
$755$		−	3.78260i		−	0.137663i
$756$	−2.19562	+	12.7970i	−0.0798538	+	0.465422i
$757$	−35.1813			−1.27869			−0.639343	−	0.768922i	$-0.720793\pi$
$757$	−35.1813			−1.27869			−0.639343	+	0.768922i	$0.720793\pi$
$758$	−25.6818			−0.932805
$759$	5.56430	+	11.0371i	0.201971	+	0.400621i
$760$	7.53379	+	7.53379i	0.273279	+	0.273279i
$761$	−25.5514	−	25.5514i	−0.926238	−	0.926238i	0.0712220	−	0.997460i	$-0.477310\pi$
$761$	−25.5514	−	25.5514i	−0.926238	−	0.926238i	−0.997460	+	0.0712220i	$0.977310\pi$
$762$	8.33802	+	16.5389i	0.302055	+	0.599141i
$763$	−8.75304			−0.316881
$764$	−16.1272			−0.583460
$765$	56.0022	−	8.37918i	2.02477	−	0.302950i
$766$		−	27.4958i		−	0.993464i
$767$		0			0
$768$	−1.64497	−	0.542278i	−0.0593578	−	0.0195678i
$769$	36.1433	+	36.1433i	1.30336	+	1.30336i	0.926112	+	0.377249i	$0.123130\pi$
$769$	36.1433	+	36.1433i	1.30336	+	1.30336i	0.377249	+	0.926112i	$0.376870\pi$
$770$			12.6090i			0.454398i
$771$	49.4071	+	16.2874i	1.77935	+	0.586578i
$772$	−2.53379	−	2.53379i	−0.0911932	−	0.0911932i
$773$	−32.0971	+	32.0971i	−1.15445	+	1.15445i	−0.168803	+	0.985650i	$0.553990\pi$
$773$	−32.0971	+	32.0971i	−1.15445	+	1.15445i	−0.985650	+	0.168803i	$0.946010\pi$
$774$	0.0987103	+	0.659730i	0.00354807	+	0.0237135i
$775$	22.2685	−	22.2685i	0.799907	−	0.799907i
$776$			16.3764i			0.587880i
$777$	−5.85782	+	17.7694i	−0.210148	+	0.637474i
$778$	1.53379	−	1.53379i	0.0549892	−	0.0549892i
$779$	−1.87796			−0.0672848
$780$		0			0
$781$	−11.8963			−0.425684
$782$	18.8752	−	18.8752i	0.674976	−	0.674976i
$783$	−19.7397	+	13.9581i	−0.705438	+	0.498820i
$784$		−	0.756152i		−	0.0270054i
$785$	−18.8252	+	18.8252i	−0.671901	+	0.671901i
$786$	0.206211	+	0.409030i	0.00735531	+	0.0145896i
$787$	−14.7562	+	14.7562i	−0.526000	+	0.526000i	−0.919377	−	0.393377i	$-0.871307\pi$
$787$	−14.7562	+	14.7562i	−0.526000	+	0.526000i	0.393377	+	0.919377i	$0.371307\pi$
$788$	4.49545	+	4.49545i	0.160144	+	0.160144i
$789$	10.0922	−	30.6142i	0.359292	−	1.08989i
$790$		−	46.4332i		−	1.65202i
$791$	−27.6016	−	27.6016i	−0.981402	−	0.981402i
$792$	2.73639	−	3.69931i	0.0972333	−	0.131449i
$793$		0			0
$794$		−	14.5218i		−	0.515359i
$795$	28.1378	+	55.8128i	0.997945	+	1.97947i
$796$	23.1383			0.820115
$797$	34.0411			1.20580			0.602899	−	0.797817i	$-0.294012\pi$
$797$	34.0411			1.20580			0.602899	+	0.797817i	$0.294012\pi$
$798$	−12.5155	+	6.30967i	−0.443045	+	0.223360i
$799$	−43.9102	−	43.9102i	−1.55343	−	1.55343i
$800$	−4.11801	−	4.11801i	−0.145593	−	0.145593i
$801$	4.02533	+	26.9033i	0.142228	+	0.950581i
$802$	−8.24886			−0.291277
$803$	4.96715			0.175287
$804$	1.16754	−	0.588611i	0.0411760	−	0.0207587i
$805$			38.2489i			1.34810i
$806$		0			0
$807$	−0.444716	+	1.34902i	−0.0156547	+	0.0474879i
$808$	9.06759	+	9.06759i	0.318997	+	0.318997i
$809$			19.8186i			0.696785i	0.937349	+	0.348392i	$0.113272\pi$
$809$			19.8186i			0.696785i	−0.937349	+	0.348392i	$0.886728\pi$
$810$	28.3128	−	8.66646i	0.994811	−	0.304508i
$811$	−25.0265	−	25.0265i	−0.878799	−	0.878799i	0.114611	−	0.993410i	$-0.463438\pi$
$811$	−25.0265	−	25.0265i	−0.878799	−	0.878799i	−0.993410	+	0.114611i	$0.963438\pi$
$812$	−8.22081	+	8.22081i	−0.288494	+	0.288494i
$813$	−21.5643	+	10.8716i	−0.756293	+	0.381282i
$814$	4.68856	−	4.68856i	0.164334	−	0.164334i
$815$		−	80.1535i		−	2.80766i
$816$	−9.43760	−	3.11118i	−0.330382	−	0.108913i
$817$	−0.509187	+	0.509187i	−0.0178142	+	0.0178142i
$818$	−9.37056			−0.327634
$819$		0			0
$820$	1.90781			0.0666235
$821$	−5.31554	+	5.31554i	−0.185514	+	0.185514i	−0.793753	−	0.608240i	$-0.791876\pi$
$821$	−5.31554	+	5.31554i	−0.185514	+	0.185514i	0.608240	+	0.793753i	$0.291876\pi$
$822$	−8.52305	−	2.80969i	−0.297275	−	0.0979991i
$823$		−	54.4118i		−	1.89667i	−0.317264	−	0.948337i	$-0.602764\pi$
$823$		−	54.4118i		−	1.89667i	0.317264	−	0.948337i	$-0.397236\pi$
$824$	−1.49460	+	1.49460i	−0.0520669	+	0.0520669i
$825$	13.8150	−	6.96481i	0.480978	−	0.242483i
$826$	−11.6260	+	11.6260i	−0.404520	+	0.404520i
$827$	19.6453	+	19.6453i	0.683134	+	0.683134i	0.960705	−	0.277571i	$-0.0895294\pi$
$827$	19.6453	+	19.6453i	0.683134	+	0.683134i	−0.277571	+	0.960705i	$0.589529\pi$
$828$	8.30069	−	11.2217i	0.288469	−	0.389980i
$829$			0.248858i			0.00864320i	0.999991	+	0.00432160i	$0.00137561\pi$
$829$			0.248858i			0.00864320i	−0.999991	+	0.00432160i	$0.998624\pi$
$830$	4.60269	+	4.60269i	0.159762	+	0.159762i
$831$	−9.42867	+	28.6014i	−0.327077	+	0.992171i
$832$		0			0
$833$		−	4.33822i		−	0.150311i
$834$	3.43714	−	1.73282i	0.119019	−	0.0600028i
$835$	31.7397			1.09840
$836$	4.96715			0.171792
$837$	4.75153	−	27.6940i	0.164237	−	0.957243i
$838$	5.94817	+	5.94817i	0.205476	+	0.205476i
$839$	−6.29286	−	6.29286i	−0.217254	−	0.217254i	0.590086	−	0.807340i	$-0.299094\pi$
$839$	−6.29286	−	6.29286i	−0.217254	−	0.217254i	−0.807340	+	0.590086i	$0.799094\pi$
$840$	12.7145	−	6.40996i	0.438691	−	0.221165i
$841$	7.35252			0.253535
$842$	−1.36422			−0.0470141
$843$	−14.9393	−	29.6329i	−0.514537	−	1.02061i
$844$		−	15.2899i		−	0.526302i
$845$		0			0
$846$	−26.1054	−	19.3102i	−0.897524	−	0.663900i
$847$	−15.2792	−	15.2792i	−0.525000	−	0.525000i
$848$		−	10.9689i		−	0.376672i
$849$	−9.56984	+	29.0296i	−0.328436	+	0.996294i
$850$	−23.6260	−	23.6260i	−0.810365	−	0.810365i
$851$	14.2225	−	14.2225i	0.487542	−	0.487542i
$852$	6.04765	+	11.9958i	0.207189	+	0.410970i
$853$	−26.2596	+	26.2596i	−0.899112	+	0.899112i	−0.995358	−	0.0962459i	$-0.969316\pi$
$853$	−26.2596	+	26.2596i	−0.899112	+	0.899112i	0.0962459	+	0.995358i	$0.469316\pi$
$854$			7.66519i			0.262297i
$855$	25.6970	+	19.0081i	0.878819	+	0.650064i
$856$	1.53379	−	1.53379i	0.0524240	−	0.0524240i
$857$	−48.8871			−1.66995			−0.834976	−	0.550286i	$-0.814519\pi$
$857$	−48.8871			−1.66995			−0.834976	+	0.550286i	$0.814519\pi$
$858$		0			0
$859$	−11.6905			−0.398873			−0.199437	−	0.979911i	$-0.563911\pi$
$859$	−11.6905			−0.398873			−0.199437	+	0.979911i	$0.563911\pi$
$860$	0.517281	−	0.517281i	0.0176391	−	0.0176391i
$861$	−0.785767	+	2.38358i	−0.0267789	+	0.0812323i
$862$			35.9835i			1.22560i
$863$	41.0424	−	41.0424i	1.39710	−	1.39710i	0.588879	−	0.808221i	$-0.299569\pi$
$863$	41.0424	−	41.0424i	1.39710	−	1.39710i	0.808221	−	0.588879i	$-0.200431\pi$
$864$	−5.12132	−	0.878680i	−0.174231	−	0.0298933i
$865$	4.31455	−	4.31455i	0.146699	−	0.146699i
$866$	−28.0537	−	28.0537i	−0.953305	−	0.953305i
$867$	−26.1813	−	8.63086i	−0.889163	−	0.293119i
$868$		−	13.5123i		−	0.458637i
$869$	−15.3071	−	15.3071i	−0.519257	−	0.519257i
$870$	25.1797	+	8.30069i	0.853673	+	0.281420i
$871$		0			0
$872$		−	3.50294i		−	0.118624i
$873$	7.26991	+	48.5885i	0.246049	+	1.64447i
$874$	15.0676			0.509669
$875$	6.77180			0.228929
$876$	−2.52511	−	5.00868i	−0.0853156	−	0.169228i
$877$	−12.3518	−	12.3518i	−0.417091	−	0.417091i	0.467109	−	0.884200i	$-0.345296\pi$
$877$	−12.3518	−	12.3518i	−0.417091	−	0.417091i	−0.884200	+	0.467109i	$0.845296\pi$
$878$	−12.7279	−	12.7279i	−0.429547	−	0.429547i
$879$	17.0524	+	33.8243i	0.575164	+	1.14087i
$880$	−5.04610			−0.170104
$881$	26.2259			0.883574			0.441787	−	0.897120i	$-0.354345\pi$
$881$	26.2259			0.883574			0.441787	+	0.897120i	$0.354345\pi$
$882$	−0.335675	−	2.24348i	−0.0113028	−	0.0755419i
$883$		−	39.6095i		−	1.33297i	−0.745520	−	0.666483i	$-0.767799\pi$
$883$		−	39.6095i		−	1.33297i	0.745520	−	0.666483i	$-0.232201\pi$
$884$		0			0
$885$	35.6095	+	11.7389i	1.19700	+	0.394600i
$886$	−22.6203	−	22.6203i	−0.759942	−	0.759942i
$887$			9.11420i			0.306025i	0.988224	+	0.153013i	$0.0488975\pi$
$887$			9.11420i			0.306025i	−0.988224	+	0.153013i	$0.951103\pi$
$888$	−7.11126	−	2.34428i	−0.238638	−	0.0786690i
$889$	18.8944	+	18.8944i	0.633699	+	0.633699i
$890$	21.0943	−	21.0943i	0.707083	−	0.707083i
$891$	6.47657	−	12.1905i	0.216973	−	0.408397i
$892$	3.30069	−	3.30069i	0.110515	−	0.110515i
$893$		−	35.0524i		−	1.17298i
$894$	4.91715	−	14.9159i	0.164454	−	0.498863i
$895$	−0.615242	+	0.615242i	−0.0205653	+	0.0205653i
$896$	−2.49877			−0.0834780
$897$		0			0
$898$	−8.42323			−0.281087
$899$	17.7907	−	17.7907i	0.593351	−	0.593351i
$900$	−14.0461	−	10.3899i	−0.468203	−	0.346331i
$901$		−	62.9310i		−	2.09653i
$902$	0.628923	−	0.628923i	0.0209409	−	0.0209409i
$903$	0.433231	+	0.859335i	0.0144170	+	0.0285969i
$904$	11.0461	−	11.0461i	0.367388	−	0.367388i
$905$	−18.8752	−	18.8752i	−0.627433	−	0.627433i
$906$	−0.623482	+	1.89130i	−0.0207138	+	0.0628343i
$907$			11.4251i			0.379365i	0.981845	+	0.189682i	$0.0607458\pi$
$907$			11.4251i			0.379365i	−0.981845	+	0.189682i	$0.939254\pi$
$908$	4.33822	+	4.33822i	0.143969	+	0.143969i
$909$	30.9286	+	22.8780i	1.02584	+	0.758814i
$910$		0			0
$911$			19.4541i			0.644544i	0.946647	+	0.322272i	$0.104447\pi$
$911$			19.4541i			0.644544i	−0.946647	+	0.322272i	$0.895553\pi$
$912$	−2.52511	−	5.00868i	−0.0836148	−	0.165854i
$913$	3.03463			0.100431
$914$	14.7433			0.487667
$915$	15.6088	−	7.86911i	0.516010	−	0.260145i
$916$	2.47695	+	2.47695i	0.0818408	+	0.0818408i
$917$	0.467286	+	0.467286i	0.0154312	+	0.0154312i
$918$	−29.3822	−	5.04120i	−0.969759	−	0.166384i
$919$	−48.8502			−1.61142			−0.805710	−	0.592310i	$-0.798216\pi$
$919$	−48.8502			−1.61142			−0.805710	+	0.592310i	$0.798216\pi$
$920$	−15.3071			−0.504659
$921$	−45.6476	+	23.0131i	−1.50414	+	0.758306i
$922$			38.8123i			1.27821i
$923$		0			0
$924$	2.07833	−	6.30452i	0.0683721	−	0.207403i
$925$	−17.8022	−	17.8022i	−0.585334	−	0.585334i
$926$		−	12.5742i		−	0.413215i
$927$	−3.77095	+	5.09793i	−0.123854	+	0.167438i
$928$	−3.28995	−	3.28995i	−0.107998	−	0.107998i
$929$	−2.38799	+	2.38799i	−0.0783474	+	0.0783474i	−0.745195	−	0.666847i	$-0.767643\pi$
$929$	−2.38799	+	2.38799i	−0.0783474	+	0.0783474i	0.666847	+	0.745195i	$0.267643\pi$
$930$	−27.5154	+	13.8718i	−0.902265	+	0.454873i
$931$	1.73155	−	1.73155i	0.0567491	−	0.0567491i
$932$		−	12.0534i		−	0.394823i
$933$	25.6970	+	8.47122i	0.841282	+	0.277335i
$934$	−26.1137	+	26.1137i	−0.854466	+	0.854466i
$935$	−28.9507			−0.946788
$936$		0			0
$937$	43.7067			1.42784			0.713918	−	0.700229i	$-0.246919\pi$
$937$	43.7067			1.42784			0.713918	+	0.700229i	$0.246919\pi$
$938$	1.33383	−	1.33383i	0.0435510	−	0.0435510i
$939$	−28.6285	−	9.43760i	−0.934256	−	0.307985i
$940$			35.6095i			1.16145i
$941$	36.7731	−	36.7731i	1.19877	−	1.19877i	0.224233	−	0.974536i	$-0.428012\pi$
$941$	36.7731	−	36.7731i	1.19877	−	1.19877i	0.974536	−	0.224233i	$-0.0719877\pi$
$942$	12.5155	−	6.30967i	0.407778	−	0.205580i
$943$	1.90781	−	1.90781i	0.0621267	−	0.0621267i
$944$	−4.65268	−	4.65268i	−0.151432	−	0.151432i
$945$	34.8780	−	24.6624i	1.13458	−	0.802269i
$946$		−	0.341051i		−	0.0110885i
$947$	35.3168	+	35.3168i	1.14764	+	1.14764i	0.987015	+	0.160628i	$0.0513519\pi$
$947$	35.3168	+	35.3168i	1.14764	+	1.14764i	0.160628	+	0.987015i	$0.448648\pi$
$948$	−7.65354	+	23.2166i	−0.248575	+	0.754041i
$949$		0			0
$950$		−	18.8600i		−	0.611900i
$951$	−6.32907	+	3.19078i	−0.205234	+	0.103468i
$952$	−14.3360			−0.464634
$953$	−52.6019			−1.70394			−0.851971	−	0.523589i	$-0.824593\pi$
$953$	−52.6019			−1.70394			−0.851971	+	0.523589i	$0.824593\pi$
$954$	−4.86935	−	32.5443i	−0.157651	−	1.05366i
$955$	37.5173	+	37.5173i	1.21403	+	1.21403i
$956$	−14.7898	−	14.7898i	−0.478336	−	0.478336i
$957$	11.0371	−	5.56430i	0.356778	−	0.179868i
$958$	5.13328			0.165849
$959$	−12.9468			−0.418074
$960$	2.56525	+	5.08829i	0.0827929	+	0.164224i
$961$		−	1.75805i		−	0.0567111i
$962$		0			0
$963$	3.86984	−	5.23161i	0.124704	−	0.168586i
$964$	−12.3821	−	12.3821i	−0.398802	−	0.398802i
$965$			11.7889i			0.379500i
$966$	6.30452	−	19.1244i	0.202844	−	0.615318i
$967$	37.4636	+	37.4636i	1.20475	+	1.20475i	0.972706	+	0.232042i	$0.0745407\pi$
$967$	37.4636	+	37.4636i	1.20475	+	1.20475i	0.232042	+	0.972706i	$0.425459\pi$
$968$	6.11469	−	6.11469i	0.196534	−	0.196534i
$969$	−14.4872	−	28.7360i	−0.465395	−	0.923134i
$970$	38.0972	−	38.0972i	1.22323	−	1.22323i
$971$			52.0962i			1.67185i	0.548845	+	0.835924i	$0.315068\pi$
$971$			52.0962i			1.67185i	−0.548845	+	0.835924i	$0.684932\pi$
$972$	−15.5849	−	0.333537i	−0.499886	−	0.0106982i
$973$	3.92668	−	3.92668i	0.125883	−	0.125883i
$974$	13.2032			0.423056
$975$		0			0
$976$	−3.06759			−0.0981911
$977$	−14.4414	+	14.4414i	−0.462021	+	0.462021i	−0.899318	−	0.437296i	$-0.855936\pi$
$977$	−14.4414	+	14.4414i	−0.462021	+	0.462021i	0.437296	+	0.899318i	$0.355936\pi$
$978$	−13.2116	+	40.0768i	−0.422461	+	1.28151i
$979$		−	13.9078i		−	0.444495i
$980$	−1.75907	+	1.75907i	−0.0561913	+	0.0561913i
$981$	−1.55504	−	10.3931i	−0.0496487	−	0.331827i
$982$	6.63172	−	6.63172i	0.211627	−	0.211627i
$983$	−26.7699	−	26.7699i	−0.853827	−	0.853827i	0.136775	−	0.990602i	$-0.456326\pi$
$983$	−26.7699	−	26.7699i	−0.853827	−	0.853827i	−0.990602	+	0.136775i	$0.956326\pi$
$984$	−0.953903	−	0.314462i	−0.0304093	−	0.0100247i
$985$		−	20.9159i		−	0.666437i
$986$	−18.8752	−	18.8752i	−0.601109	−	0.601109i
$987$	−44.4900	−	14.6665i	−1.41613	−	0.466839i
$988$		0			0
$989$		−	1.03456i		−	0.0328971i
$990$	−14.9716	+	2.24009i	−0.475830	+	0.0711947i
$991$	−43.9241			−1.39529			−0.697647	−	0.716442i	$-0.745770\pi$
$991$	−43.9241			−1.39529			−0.697647	+	0.716442i	$0.745770\pi$
$992$	5.40758			0.171691
$993$	2.27992	+	4.52233i	0.0723510	+	0.143512i
$994$	13.7043	+	13.7043i	0.434675	+	0.434675i
$995$	−53.8276	−	53.8276i	−1.70645	−	1.70645i
$996$	−1.54269	−	3.06000i	−0.0488820	−	0.0969599i
$997$	−34.5254			−1.09343			−0.546716	−	0.837318i	$-0.684122\pi$
$997$	−34.5254			−1.09343			−0.546716	+	0.837318i	$0.684122\pi$
$998$	−0.249271			−0.00789054
$999$	−22.1396	−	3.79856i	−0.700466	−	0.120181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.b.437.1		12
3.2	odd	2	inner	1014.2.g.b.437.4		12
13.5	odd	4	inner	1014.2.g.b.239.4		12
13.8	odd	4		78.2.g.a.5.1	✓	12
13.12	even	2		78.2.g.a.47.4	yes	12
39.5	even	4	inner	1014.2.g.b.239.1		12
39.8	even	4		78.2.g.a.5.4	yes	12
39.38	odd	2		78.2.g.a.47.1	yes	12
52.47	even	4		624.2.bf.f.161.6		12
52.51	odd	2		624.2.bf.f.593.6		12
156.47	odd	4		624.2.bf.f.161.5		12
156.155	even	2		624.2.bf.f.593.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.g.a.5.1	✓	12	13.8	odd	4
78.2.g.a.5.4	yes	12	39.8	even	4
78.2.g.a.47.1	yes	12	39.38	odd	2
78.2.g.a.47.4	yes	12	13.12	even	2
624.2.bf.f.161.5		12	156.47	odd	4
624.2.bf.f.161.6		12	52.47	even	4
624.2.bf.f.593.5		12	156.155	even	2
624.2.bf.f.593.6		12	52.51	odd	2
1014.2.g.b.239.1		12	39.5	even	4	inner
1014.2.g.b.239.4		12	13.5	odd	4	inner
1014.2.g.b.437.1		12	1.1	even	1	trivial
1014.2.g.b.437.4		12	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(1.54662 - 0.779723i) q^{6} +(1.76690 - 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(1.54662 - 0.779723i) q^{6} +(1.76690 - 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} -3.28995i q^{10} +(-1.08456 - 1.08456i) q^{11} +(-0.542278 + 1.64497i) q^{12} +2.49877i q^{14} +(5.08829 - 2.56525i) q^{15} -1.00000 q^{16} -5.73724 q^{17} +(-2.96697 + 0.443925i) q^{18} +(-2.28995 - 2.28995i) q^{19} +(2.32634 + 2.32634i) q^{20} +(-3.86465 + 1.94835i) q^{21} +1.53379 q^{22} +4.65268 q^{23} +(-0.779723 - 1.54662i) q^{24} -5.82374i q^{25} +(-3.00000 - 4.24264i) q^{27} +(-1.76690 - 1.76690i) q^{28} -4.65268i q^{29} +(-1.78406 + 5.41187i) q^{30} +(3.82374 + 3.82374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.19593 + 2.37220i) q^{33} +(4.05684 - 4.05684i) q^{34} +8.22081i q^{35} +(1.78406 - 2.41187i) q^{36} +(3.05684 - 3.05684i) q^{37} +3.23847 q^{38} -3.28995 q^{40} +(0.410044 - 0.410044i) q^{41} +(1.35503 - 4.11041i) q^{42} -0.222358i q^{43} +(-1.08456 + 1.08456i) q^{44} +(-9.76118 + 1.46049i) q^{45} +(-3.28995 + 3.28995i) q^{46} +(7.65354 + 7.65354i) q^{47} +(1.64497 + 0.542278i) q^{48} +0.756152i q^{49} +(4.11801 + 4.11801i) q^{50} +(9.43760 + 3.11118i) q^{51} +10.9689i q^{53} +(5.12132 + 0.878680i) q^{54} +5.04610 q^{55} +2.49877 q^{56} +(2.52511 + 5.00868i) q^{57} +(3.28995 + 3.28995i) q^{58} +(4.65268 + 4.65268i) q^{59} +(-2.56525 - 5.08829i) q^{60} +3.06759 q^{61} -5.40758 q^{62} +(7.41378 - 1.10927i) q^{63} +1.00000i q^{64} +(-2.52305 - 0.831742i) q^{66} +(-0.533794 - 0.533794i) q^{67} +5.73724i q^{68} +(-7.65354 - 2.52305i) q^{69} +(-5.81299 - 5.81299i) q^{70} +(5.48443 - 5.48443i) q^{71} +(0.443925 + 2.96697i) q^{72} +(-2.28995 + 2.28995i) q^{73} +4.32303i q^{74} +(-3.15808 + 9.57989i) q^{75} +(-2.28995 + 2.28995i) q^{76} -3.83260 q^{77} +14.1137 q^{79} +(2.32634 - 2.32634i) q^{80} +(2.63423 + 8.60586i) q^{81} +0.579890i q^{82} +(-1.39902 + 1.39902i) q^{83} +(1.94835 + 3.86465i) q^{84} +(13.3468 - 13.3468i) q^{85} +(0.157231 + 0.157231i) q^{86} +(-2.52305 + 7.65354i) q^{87} -1.53379i q^{88} +(6.41175 + 6.41175i) q^{89} +(5.86947 - 7.93492i) q^{90} -4.65268i q^{92} +(-4.21642 - 8.36347i) q^{93} -10.8237 q^{94} +10.6544 q^{95} +(-1.54662 + 0.779723i) q^{96} +(11.5799 + 11.5799i) q^{97} +(-0.534680 - 0.534680i) q^{98} +(-0.680889 - 4.55072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{7}+O(q^{10}) \) 12 * q + 12 * q^7	\( 12 q + 12 q^{7} - 12 q^{16} + 12 q^{19} - 36 q^{27} - 12 q^{28} - 12 q^{31} - 36 q^{33} - 12 q^{37} + 36 q^{42} - 36 q^{45} + 36 q^{54} + 36 q^{57} + 36 q^{63} + 12 q^{67} + 12 q^{73} + 12 q^{76} + 72 q^{79} + 72 q^{85} - 36 q^{93} - 72 q^{94} + 60 q^{97} - 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^7 - 12 * q^16 + 12 * q^19 - 36 * q^27 - 12 * q^28 - 12 * q^31 - 36 * q^33 - 12 * q^37 + 36 * q^42 - 36 * q^45 + 36 * q^54 + 36 * q^57 + 36 * q^63 + 12 * q^67 + 12 * q^73 + 12 * q^76 + 72 * q^79 + 72 * q^85 - 36 * q^93 - 72 * q^94 + 60 * q^97 - 36 * q^99

Introduction

L-functions

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