LMFDB - Embedded newform 78.2.g.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(5,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, 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("78.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.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:	$0.622833135766$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.1
Root			$1.54662 + 0.779723i$ of defining polynomial
Character	$\chi$	$=$	78.5
Dual form			78.2.g.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} +1.00000i q^{4} +(-2.32634 - 2.32634i) q^{5} +(0.779723 + 1.54662i) q^{6} +(-1.76690 - 1.76690i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} +1.00000i q^{4} +(-2.32634 - 2.32634i) q^{5} +(0.779723 + 1.54662i) 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} +(0.766897 - 3.52305i) q^{13} +2.49877i q^{14} +(2.56525 + 5.08829i) q^{15} -1.00000 q^{16} +5.73724 q^{17} +(-0.443925 - 2.96697i) q^{18} +(2.28995 - 2.28995i) q^{19} +(2.32634 - 2.32634i) q^{20} +(1.94835 + 3.86465i) q^{21} +1.53379 q^{22} -4.65268 q^{23} +(-1.54662 + 0.779723i) q^{24} +5.82374i q^{25} +(-3.03345 + 1.94889i) q^{26} +(-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} +(2.37220 - 1.19593i) 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} +(-3.17200 + 5.37945i) q^{39} -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} +(-1.46049 - 9.76118i) 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} +(3.52305 + 0.766897i) q^{52} +10.9689i q^{53} +(-0.878680 + 5.12132i) q^{54} +5.04610 q^{55} -2.49877 q^{56} +(-5.00868 + 2.52511i) q^{57} +(-3.28995 + 3.28995i) q^{58} +(4.65268 - 4.65268i) q^{59} +(-5.08829 + 2.56525i) q^{60} +3.06759 q^{61} +5.40758 q^{62} +(-1.10927 - 7.41378i) q^{63} -1.00000i q^{64} +(-9.97988 + 6.41175i) q^{65} +(-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} +(2.96697 - 0.443925i) 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} +(6.04678 - 1.56090i) q^{78} +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} +(-3.86465 + 1.94835i) 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} +(-7.57989 + 4.86984i) q^{91} -4.65268i q^{92} +(8.36347 - 4.21642i) q^{93} -10.8237 q^{94} -10.6544 q^{95} +(-0.779723 - 1.54662i) q^{96} +(-11.5799 + 11.5799i) q^{97} +(-0.534680 + 0.534680i) q^{98} +(-4.55072 + 0.680889i) 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} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 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 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	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	−0.999150	−	0.0412220i	$-0.986875\pi$
$5$	−2.32634	−	2.32634i	−1.04037	−	1.04037i	−0.0412220	−	0.999150i	$-0.513125\pi$
$6$	0.779723	+	1.54662i	0.318321	+	0.631405i
$7$	−1.76690	−	1.76690i	−0.667824	−	0.667824i	0.289388	−	0.957212i	$-0.406548\pi$
$7$	−1.76690	−	1.76690i	−0.667824	−	0.667824i	−0.957212	+	0.289388i	$0.906548\pi$
$8$	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	−0.851447	−	0.524441i	$-0.824274\pi$
$11$	−1.08456	+	1.08456i	−0.327006	+	0.327006i	0.524441	+	0.851447i	$0.324274\pi$
$12$	0.542278	−	1.64497i	0.156542	−	0.474863i
$13$	0.766897	−	3.52305i	0.212699	−	0.977118i
$13$	0.766897	−	3.52305i	0.212699	−	0.977118i
$14$			2.49877i			0.667824i
$15$	2.56525	+	5.08829i	0.662344	+	1.31379i
$16$	−1.00000			−0.250000
$17$	5.73724			1.39149			0.695743	−	0.718291i	$-0.255075\pi$
$17$	5.73724			1.39149			0.695743	+	0.718291i	$0.255075\pi$
$18$	−0.443925	−	2.96697i	−0.104634	−	0.699322i
$19$	2.28995	−	2.28995i	0.525349	−	0.525349i	−0.393833	−	0.919182i	$-0.628851\pi$
$19$	2.28995	−	2.28995i	0.525349	−	0.525349i	0.919182	+	0.393833i	$0.128851\pi$
$20$	2.32634	−	2.32634i	0.520186	−	0.520186i
$21$	1.94835	+	3.86465i	0.425164	+	0.843335i
$22$	1.53379			0.327006
$23$	−4.65268			−0.970152			−0.485076	−	0.874472i	$-0.661208\pi$
$23$	−4.65268			−0.970152			−0.485076	+	0.874472i	$0.661208\pi$
$24$	−1.54662	+	0.779723i	−0.315702	+	0.159160i
$25$			5.82374i			1.16475i
$26$	−3.03345	+	1.94889i	−0.594908	+	0.382209i
$27$	−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	$-0.911404\pi$
$31$	−3.82374	+	3.82374i	−0.686764	+	0.686764i	0.274752	+	0.961515i	$0.411404\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.37220	−	1.19593i	0.412946	−	0.208185i
$34$	−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	$-0.365639\pi$
$37$	−3.05684	−	3.05684i	−0.502542	−	0.502542i	−0.912227	+	0.409685i	$0.865639\pi$
$38$	−3.23847			−0.525349
$39$	−3.17200	+	5.37945i	−0.507926	+	0.861401i
$40$	−3.28995			−0.520186
$41$	0.410044	+	0.410044i	0.0640382	+	0.0640382i	0.738401	−	0.674362i	$-0.235581\pi$
$41$	0.410044	+	0.410044i	0.0640382	+	0.0640382i	−0.674362	+	0.738401i	$0.735581\pi$
$42$	1.35503	−	4.11041i	0.209085	−	0.634250i
$43$			0.222358i			0.0339093i	0.999856	+	0.0169546i	$0.00539709\pi$
$43$			0.222358i			0.0339093i	−0.999856	+	0.0169546i	$0.994603\pi$
$44$	−1.08456	−	1.08456i	−0.163503	−	0.163503i
$45$	−1.46049	−	9.76118i	−0.217717	−	1.45511i
$46$	3.28995	+	3.28995i	0.485076	+	0.485076i
$47$	7.65354	−	7.65354i	1.11638	−	1.11638i	0.124116	−	0.992268i	$-0.460391\pi$
$47$	7.65354	−	7.65354i	1.11638	−	1.11638i	0.992268	−	0.124116i	$-0.0396094\pi$
$48$	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
$52$	3.52305	+	0.766897i	0.488559	+	0.106349i
$53$			10.9689i			1.50669i	0.657627	+	0.753344i	$0.271560\pi$
$53$			10.9689i			1.50669i	−0.657627	+	0.753344i	$0.728440\pi$
$54$	−0.878680	+	5.12132i	−0.119573	+	0.696923i
$55$	5.04610			0.680416
$56$	−2.49877			−0.333912
$57$	−5.00868	+	2.52511i	−0.663416	+	0.334459i
$58$	−3.28995	+	3.28995i	−0.431991	+	0.431991i
$59$	4.65268	−	4.65268i	0.605728	−	0.605728i	−0.336099	−	0.941827i	$-0.609108\pi$
$59$	4.65268	−	4.65268i	0.605728	−	0.605728i	0.941827	+	0.336099i	$0.109108\pi$
$60$	−5.08829	+	2.56525i	−0.656896	+	0.331172i
$61$	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
$63$	−1.10927	−	7.41378i	−0.139754	−	0.934049i
$64$		−	1.00000i		−	0.125000i
$65$	−9.97988	+	6.41175i	−1.23785	+	0.795280i
$66$	−2.52305	−	0.831742i	−0.310566	−	0.102380i
$67$	0.533794	−	0.533794i	0.0652133	−	0.0652133i	−0.673748	−	0.738961i	$-0.735317\pi$
$67$	0.533794	−	0.533794i	0.0652133	−	0.0652133i	0.738961	+	0.673748i	$0.235317\pi$
$68$			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	0.953205	−	0.302324i	$-0.0977623\pi$
$71$	5.48443	+	5.48443i	0.650882	+	0.650882i	−0.302324	+	0.953205i	$0.597762\pi$
$72$	2.96697	−	0.443925i	0.349661	−	0.0523171i
$73$	2.28995	+	2.28995i	0.268018	+	0.268018i	0.828301	−	0.560283i	$-0.189308\pi$
$73$	2.28995	+	2.28995i	0.268018	+	0.268018i	−0.560283	+	0.828301i	$0.689308\pi$
$74$			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
$78$	6.04678	−	1.56090i	0.684663	−	0.176738i
$79$	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	0.626145	−	0.779707i	$-0.284632\pi$
$83$	−1.39902	−	1.39902i	−0.153562	−	0.153562i	−0.779707	+	0.626145i	$0.784632\pi$
$84$	−3.86465	+	1.94835i	−0.421667	+	0.212582i
$85$	−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	−0.280275	−	0.959920i	$-0.590426\pi$
$89$	6.41175	−	6.41175i	0.679644	−	0.679644i	0.959920	+	0.280275i	$0.0904257\pi$
$90$	−5.86947	+	7.93492i	−0.618697	+	0.836414i
$91$	−7.57989	+	4.86984i	−0.794588	+	0.510497i
$92$		−	4.65268i		−	0.485076i
$93$	8.36347	−	4.21642i	0.867252	−	0.437222i
$94$	−10.8237			−1.11638
$95$	−10.6544			−1.09312
$96$	−0.779723	−	1.54662i	−0.0795801	−	0.157851i
$97$	−11.5799	+	11.5799i	−1.17576	+	1.17576i	−0.194946	+	0.980814i	$0.562453\pi$
$97$	−11.5799	+	11.5799i	−1.17576	+	1.17576i	−0.980814	+	0.194946i	$0.937547\pi$
$98$	−0.534680	+	0.534680i	−0.0540108	+	0.0540108i
$99$	−4.55072	+	0.680889i	−0.457365	+	0.0684320i
$100$	−5.82374			−0.582374
$101$	−12.8235			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$101$	−12.8235			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$102$	4.47346	+	8.87333i	0.442938	+	0.878591i
$103$		−	2.11368i		−	0.208267i	−0.994563	−	0.104134i	$-0.966793\pi$
$103$		−	2.11368i		−	0.208267i	0.994563	−	0.104134i	$-0.0332070\pi$
$104$	−1.94889	−	3.03345i	−0.191105	−	0.297454i
$105$	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	$-0.696347\pi$
$109$	2.47695	−	2.47695i	0.237249	−	0.237249i	0.815710	+	0.578461i	$0.196347\pi$
$110$	−3.56813	−	3.56813i	−0.340208	−	0.340208i
$111$	3.37076	+	6.68608i	0.319939	+	0.634615i
$112$	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
$117$	8.13500	−	7.12894i	0.752081	−	0.659071i
$118$	−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
$123$	−0.452154	−	0.896870i	−0.0407693	−	0.0808680i
$124$	−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	$-0.842647\pi$
$127$		−	10.6936i		−	0.948901i	0.880282	−	0.474451i	$-0.157353\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.120580	−	0.365773i	0.0106165	−	0.0322045i
$130$	11.5906	+	2.52305i	1.01657	+	0.221286i
$131$			0.264467i			0.0231066i	0.999933	+	0.0115533i	$0.00367761\pi$
$131$			0.264467i			0.0231066i	−0.999933	+	0.0115533i	$0.996322\pi$
$132$	1.19593	+	2.37220i	0.104093	+	0.206473i
$133$	−8.09219			−0.701682
$134$	−0.754898			−0.0652133
$135$	−2.89081	+	16.8489i	−0.248801	+	1.45012i
$136$	4.05684	−	4.05684i	0.347871	−	0.347871i
$137$	−3.66371	+	3.66371i	−0.313012	+	0.313012i	−0.846075	−	0.533063i	$-0.821041\pi$
$137$	−3.66371	+	3.66371i	−0.313012	+	0.313012i	0.533063	+	0.846075i	$0.321041\pi$
$138$	−3.62780	−	7.19593i	−0.308819	−	0.612559i
$139$	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
$141$	−16.7402	+	8.43952i	−1.40978	+	0.710735i
$142$		−	7.75615i		−	0.650882i
$143$	2.98920	+	4.65268i	0.249969	+	0.389077i
$144$	−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	0.919159	−	0.393887i	$-0.128870\pi$
$149$	6.41175	+	6.41175i	0.525271	+	0.525271i	−0.393887	+	0.919159i	$0.628870\pi$
$150$	−9.00711	+	4.54090i	−0.735427	+	0.370763i
$151$	0.812993	+	0.812993i	0.0661605	+	0.0661605i	0.739413	−	0.673252i	$-0.235103\pi$
$151$	0.812993	+	0.812993i	0.0661605	+	0.0661605i	−0.673252	+	0.739413i	$0.735103\pi$
$152$		−	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
$156$	−5.37945	−	3.17200i	−0.430700	−	0.253963i
$157$	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
$162$	4.22258	−	7.94794i	0.331757	−	0.624449i
$163$	17.2274	+	17.2274i	1.34935	+	1.34935i	0.886366	+	0.462986i	$0.153222\pi$
$163$	17.2274	+	17.2274i	1.34935	+	1.34935i	0.462986	+	0.886366i	$0.346778\pi$
$164$	−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	−0.919942	−	0.392055i	$-0.871764\pi$
$167$	−6.82180	+	6.82180i	−0.527886	+	0.527886i	0.392055	+	0.919942i	$0.371764\pi$
$168$	4.11041	+	1.35503i	0.317125	+	0.104543i
$169$	−11.8237	−	5.40363i	−0.909518	−	0.415664i
$170$			18.8752i			1.44766i
$171$	9.60846	−	1.43764i	0.734777	−	0.109939i
$172$	−0.222358			−0.0169546
$173$	1.85465			0.141006			0.0705032	−	0.997512i	$-0.477539\pi$
$173$	1.85465			0.141006			0.0705032	+	0.997512i	$0.477539\pi$
$174$	7.19593	−	3.62780i	0.545522	−	0.275023i
$175$	10.2899	−	10.2899i	0.777847	−	0.777847i
$176$	1.08456	−	1.08456i	0.0817515	−	0.0817515i
$177$	−10.1766	+	5.13049i	−0.764919	+	0.385631i
$178$	−9.06759			−0.679644
$179$	−0.264467			−0.0197672			−0.00988361	−	0.999951i	$-0.503146\pi$
$179$	−0.264467			−0.0197672			−0.00988361	+	0.999951i	$0.503146\pi$
$180$	9.76118	−	1.46049i	0.727555	−	0.108858i
$181$		−	8.11368i		−	0.603085i	−0.953453	−	0.301543i	$-0.902498\pi$
$181$		−	8.11368i		−	0.603085i	0.953453	−	0.301543i	$-0.0975016\pi$
$182$	8.80329	+	1.91630i	0.652543	+	0.142045i
$183$	−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
$189$	−2.19562	+	12.7970i	−0.159708	+	0.930845i
$190$	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	$-0.291166\pi$
$193$	−2.53379	−	2.53379i	−0.182386	−	0.182386i	−0.792395	+	0.610008i	$0.791166\pi$
$194$	16.3764			1.17576
$195$	19.8936	−	5.13529i	1.42461	−	0.367746i
$196$	0.756152			0.0540108
$197$	−4.49545	−	4.49545i	−0.320288	−	0.320288i	0.528590	−	0.848877i	$-0.322721\pi$
$197$	−4.49545	−	4.49545i	−0.320288	−	0.320288i	−0.848877	+	0.528590i	$0.822721\pi$
$198$	3.69931	+	2.73639i	0.262898	+	0.194467i
$199$		−	23.1383i		−	1.64023i	−0.572199	−	0.820115i	$-0.693909\pi$
$199$		−	23.1383i		−	1.64023i	0.572199	−	0.820115i	$-0.306091\pi$
$200$	4.11801	+	4.11801i	0.291187	+	0.291187i
$201$	−1.16754	+	0.588611i	−0.0823519	+	0.0415174i
$202$	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
$208$	−0.766897	+	3.52305i	−0.0531747	+	0.244279i
$209$			4.96715i			0.343585i
$210$	−12.7145	+	6.40996i	−0.877382	+	0.442329i
$211$	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
$213$	−6.04765	−	11.9958i	−0.414378	−	0.821940i
$214$	−1.53379	+	1.53379i	−0.104848	+	0.104848i
$215$	0.517281	−	0.517281i	0.0352783	−	0.0352783i
$216$	−5.12132	−	0.878680i	−0.348462	−	0.0597866i
$217$	13.5123			0.917275
$218$	−3.50294			−0.237249
$219$	−2.52511	−	5.00868i	−0.170631	−	0.338455i
$220$			5.04610i			0.340208i
$221$	4.39987	−	20.2126i	0.295967	−	1.35965i
$222$	2.34428	−	7.11126i	0.157338	−	0.477277i
$223$	−3.30069	+	3.30069i	−0.221031	+	0.221031i	−0.808932	−	0.587902i	$-0.799954\pi$
$223$	−3.30069	+	3.30069i	−0.221031	+	0.221031i	0.587902	+	0.808932i	$0.299954\pi$
$224$		−	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	0.548326	−	0.836264i	$-0.315265\pi$
$227$	−4.33822	−	4.33822i	−0.287938	−	0.287938i	−0.836264	+	0.548326i	$0.815265\pi$
$228$	−2.52511	−	5.00868i	−0.167230	−	0.331708i
$229$	2.47695	+	2.47695i	0.163682	+	0.163682i	0.784195	−	0.620514i	$-0.213076\pi$
$229$	2.47695	+	2.47695i	0.163682	+	0.163682i	−0.620514	+	0.784195i	$0.713076\pi$
$230$		−	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	$-0.629194\pi$
$233$	−12.0534			−0.789645			−0.394823	+	0.918757i	$0.629194\pi$
$234$	−10.7932	−	0.711393i	−0.705576	−	0.0465052i
$235$	−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	0.999100	−	0.0424271i	$-0.0135090\pi$
$239$	14.7898	+	14.7898i	0.956672	+	0.956672i	−0.0424271	+	0.999100i	$0.513509\pi$
$240$	−2.56525	−	5.08829i	−0.165586	−	0.328448i
$241$	−12.3821	−	12.3821i	−0.797604	−	0.797604i	0.185114	−	0.982717i	$-0.440735\pi$
$241$	−12.3821	−	12.3821i	−0.797604	−	0.797604i	−0.982717	+	0.185114i	$0.940735\pi$
$242$	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
$247$	−6.31144	−	9.82374i	−0.401587	−	0.625070i
$248$			5.40758i			0.343382i
$249$	1.54269	+	3.06000i	0.0977639	+	0.193920i
$250$	−2.71005			−0.171399
$251$	−12.2946			−0.776026			−0.388013	−	0.921654i	$-0.626839\pi$
$251$	−12.2946			−0.776026			−0.388013	+	0.921654i	$0.626839\pi$
$252$	7.41378	−	1.10927i	0.467024	−	0.0698772i
$253$	5.04610	−	5.04610i	0.317245	−	0.317245i
$254$	−7.56150	+	7.56150i	−0.474451	+	0.474451i
$255$	14.7174	+	29.1928i	0.921641	+	1.82812i
$256$	1.00000			0.0625000
$257$	30.0352			1.87355			0.936773	−	0.349938i	$-0.113797\pi$
$257$	30.0352			1.87355			0.936773	+	0.349938i	$0.113797\pi$
$258$	−0.343903	+	0.173378i	−0.0214105	+	0.0107940i
$259$			10.8022i			0.671219i
$260$	−6.41175	−	9.97988i	−0.397640	−	0.618926i
$261$	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
$267$	−14.0241	+	7.07020i	−0.858261	+	0.432690i
$268$	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	$-0.389193\pi$
$271$	−9.85909	−	9.85909i	−0.598897	−	0.598897i	−0.940019	+	0.341122i	$0.889193\pi$
$272$	−5.73724			−0.347871
$273$	15.1095	−	3.90034i	0.914469	−	0.236059i
$274$	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	$0.174943\pi$
$277$			17.3871i			1.04469i	−0.852733	+	0.522346i	$0.825057\pi$
$278$	−1.57144	−	1.57144i	−0.0942490	−	0.0942490i
$279$	−16.0442	+	2.40056i	−0.960538	+	0.143718i
$280$	5.81299	+	5.81299i	0.347393	+	0.347393i
$281$	13.5480	−	13.5480i	0.808207	−	0.808207i	−0.176156	−	0.984362i	$-0.556366\pi$
$281$	13.5480	−	13.5480i	0.808207	−	0.808207i	0.984362	+	0.176156i	$0.0563662\pi$
$282$	17.8048	+	5.86947i	1.06026	+	0.349522i
$283$			17.6475i			1.04903i	0.851400	+	0.524517i	$0.175754\pi$
$283$			17.6475i			1.04903i	−0.851400	+	0.524517i	$0.824246\pi$
$284$	−5.48443	+	5.48443i	−0.325441	+	0.325441i
$285$	17.5262	+	5.77764i	1.03816	+	0.342238i
$286$	1.17626	−	5.40363i	0.0695538	−	0.319523i
$287$		−	1.44901i		−	0.0855325i
$288$	0.443925	+	2.96697i	0.0261585	+	0.174831i
$289$	15.9159			0.936231
$290$	15.3071			0.898863
$291$	25.3281	−	12.7691i	1.48476	−	0.748537i
$292$	−2.28995	+	2.28995i	−0.134009	+	0.134009i
$293$	−15.4643	+	15.4643i	−0.903435	+	0.903435i	−0.995732	−	0.0922970i	$-0.970579\pi$
$293$	−15.4643	+	15.4643i	−0.903435	+	0.903435i	0.0922970	+	0.995732i	$0.470579\pi$
$294$	1.16948	−	0.589589i	0.0682054	−	0.0343855i
$295$	−21.6475			−1.26036
$296$	−4.32303			−0.251271
$297$	7.85505	+	1.34771i	0.455796	+	0.0782023i
$298$		−	9.06759i		−	0.525271i
$299$	−3.56813	+	16.3916i	−0.206350	+	0.947953i
$300$	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
$306$	−2.54690	−	17.0222i	−0.145597	−	0.973097i
$307$	−20.8698	−	20.8698i	−1.19110	−	1.19110i	−0.976758	−	0.214347i	$-0.931238\pi$
$307$	−20.8698	−	20.8698i	−1.19110	−	1.19110i	−0.214347	−	0.976758i	$-0.568762\pi$
$308$			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	$-0.353947\pi$
$311$	15.6215			0.885816			0.442908	+	0.896567i	$0.353947\pi$
$312$	1.56090	+	6.04678i	0.0883688	+	0.342332i
$313$	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	0.783683	−	0.621161i	$-0.213339\pi$
$317$	2.89362	+	2.89362i	0.162522	+	0.162522i	−0.621161	+	0.783683i	$0.713339\pi$
$318$	−16.9646	+	8.55267i	−0.951330	+	0.479610i
$319$	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
$325$	20.5173	+	4.46621i	1.13810	+	0.247741i
$326$		−	24.3632i		−	1.34935i
$327$	−5.41771	+	2.73132i	−0.299600	+	0.151042i
$328$	0.579890			0.0320191
$329$	−27.0460			−1.49110
$330$	3.93456	+	7.80439i	0.216590	+	0.429618i
$331$	2.06759	−	2.06759i	0.113645	−	0.113645i	−0.647998	−	0.761642i	$-0.724393\pi$
$331$	2.06759	−	2.06759i	0.113645	−	0.113645i	0.761642	+	0.647998i	$0.224393\pi$
$332$	1.39902	−	1.39902i	0.0767811	−	0.0767811i
$333$	−1.91910	−	12.8263i	−0.105166	−	0.702877i
$334$	9.64748			0.527886
$335$	−2.48357			−0.135692
$336$	−1.94835	−	3.86465i	−0.106291	−	0.210834i
$337$			20.5634i			1.12016i	0.828438	+	0.560080i	$0.189230\pi$
$337$			20.5634i			1.12016i	−0.828438	+	0.560080i	$0.810770\pi$
$338$	4.53970	+	12.1816i	0.246927	+	0.662591i
$339$	−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
$345$	−11.9353	−	23.6742i	−0.642574	−	1.27458i
$346$	−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	0.984865	+	0.173323i	$0.0554503\pi$
$349$	21.6367	+	21.6367i	1.15819	+	1.15819i	0.173323	+	0.984865i	$0.444550\pi$
$350$	−14.5522			−0.777847
$351$	−17.2477	+	7.31548i	−0.920615	+	0.390471i
$352$	−1.53379			−0.0817515
$353$	−1.49460	−	1.49460i	−0.0795495	−	0.0795495i	0.666212	−	0.745762i	$-0.267914\pi$
$353$	−1.49460	−	1.49460i	−0.0795495	−	0.0795495i	−0.745762	+	0.666212i	$0.767914\pi$
$354$	10.8237	+	3.56813i	0.575275	+	0.189644i
$355$		−	25.5173i		−	1.35432i
$356$	6.41175	+	6.41175i	0.339822	+	0.339822i
$357$	11.1781	+	22.1724i	0.591610	+	1.17349i
$358$	0.187007	+	0.187007i	0.00988361	+	0.00988361i
$359$	0.314462	−	0.314462i	0.0165967	−	0.0165967i	−0.698760	−	0.715356i	$-0.746264\pi$
$359$	0.314462	−	0.314462i	0.0165967	−	0.0165967i	0.715356	+	0.698760i	$0.246264\pi$
$360$	−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
$364$	−4.86984	−	7.57989i	−0.255249	−	0.397294i
$365$		−	10.6544i		−	0.557676i
$366$	2.39187	+	4.74439i	0.125025	+	0.247993i
$367$	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
$369$	0.257428	+	1.72052i	0.0134012	+	0.0895666i
$370$	10.0568	−	10.0568i	0.522830	−	0.522830i
$371$	19.3808	−	19.3808i	1.00620	−	1.00620i
$372$	4.21642	+	8.36347i	0.218611	+	0.433626i
$373$	−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
$375$	−4.19142	+	2.11309i	−0.216444	+	0.109120i
$376$		−	10.8237i		−	0.558192i
$377$	−16.3916	−	3.56813i	−0.844212	−	0.183768i
$378$	10.6014	−	7.49631i	0.545276	−	0.385568i
$379$	−18.1598	+	18.1598i	−0.932805	+	0.932805i	−0.997880	−	0.0650751i	$-0.979271\pi$
$379$	−18.1598	+	18.1598i	−0.932805	+	0.932805i	0.0650751	+	0.997880i	$0.479271\pi$
$380$		−	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	0.00651435	−	0.999979i	$-0.497926\pi$
$383$	−19.4425	−	19.4425i	−0.993464	−	0.993464i	−0.999979	+	0.00651435i	$0.997926\pi$
$384$	1.54662	−	0.779723i	0.0789256	−	0.0397901i
$385$	−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	$-0.482488\pi$
$389$	2.16911			0.109978			0.0549892	+	0.998487i	$0.482488\pi$
$390$	−17.6981	−	10.4357i	−0.896177	−	0.528432i
$391$	−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
$396$	−0.680889	−	4.55072i	−0.0342160	−	0.228683i
$397$	10.2685	+	10.2685i	0.515359	+	0.515359i	0.916164	−	0.400805i	$-0.131269\pi$
$397$	10.2685	+	10.2685i	0.515359	+	0.515359i	−0.400805	+	0.916164i	$0.631269\pi$
$398$	−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	−0.546307	−	0.837585i	$-0.683967\pi$
$401$	5.83282	−	5.83282i	0.291277	−	0.291277i	0.837585	+	0.546307i	$0.183967\pi$
$402$	1.24179	+	0.409365i	0.0619347	+	0.0204172i
$403$	10.5388	+	16.4036i	0.524975	+	0.817123i
$404$		−	12.8235i		−	0.637993i
$405$	13.8921	−	26.1483i	0.690302	−	1.29932i
$406$	11.6260			0.576988
$407$	6.63063			0.328668
$408$	−8.87333	+	4.47346i	−0.439295	+	0.221469i
$409$	−6.62599	+	6.62599i	−0.327634	+	0.327634i	−0.851686	−	0.524052i	$-0.824420\pi$
$409$	−6.62599	+	6.62599i	−0.327634	+	0.327634i	0.524052	+	0.851686i	$0.324420\pi$
$410$	−1.34902	+	1.34902i	−0.0666235	+	0.0666235i
$411$	8.01346	−	4.03996i	0.395275	−	0.199276i
$412$	2.11368			0.104134
$413$	−16.4416			−0.809040
$414$	2.06544	+	13.8044i	0.101511	+	0.678449i
$415$			6.50919i			0.319523i
$416$	3.03345	−	1.94889i	0.148727	−	0.0955524i
$417$	−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	$-0.760584\pi$
$421$	−0.964649	+	0.964649i	−0.0470141	+	0.0470141i	0.683209	+	0.730223i	$0.260584\pi$
$422$	−10.8116	−	10.8116i	−0.526302	−	0.526302i
$423$	32.1137	−	4.80493i	1.56142	−	0.233624i
$424$	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
$429$	−2.39410	−	9.27452i	−0.115588	−	0.447778i
$430$	−0.731545			−0.0352783
$431$	25.4442	+	25.4442i	1.22560	+	1.22560i	0.965610	+	0.259993i	$0.0837203\pi$
$431$	25.4442	+	25.4442i	1.22560	+	1.22560i	0.259993	+	0.965610i	$0.416280\pi$
$432$	3.00000	+	4.24264i	0.144338	+	0.204124i
$433$		−	39.6740i		−	1.90661i	−0.302010	−	0.953305i	$-0.597658\pi$
$433$		−	39.6740i		−	1.90661i	0.302010	−	0.953305i	$-0.402342\pi$
$434$	−9.55464	−	9.55464i	−0.458637	−	0.458637i
$435$	23.6742	−	11.9353i	1.13509	−	0.572253i
$436$	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	$-0.858673\pi$
$439$		−	18.0000i		−	0.859093i	0.903045	−	0.429547i	$-0.141327\pi$
$440$	3.56813	−	3.56813i	0.170104	−	0.170104i
$441$	1.34902	−	1.82374i	0.0642392	−	0.0868447i
$442$	−17.4036	+	11.1813i	−0.827806	+	0.531839i
$443$			31.9899i			1.51988i	0.649991	+	0.759942i	$0.274773\pi$
$443$			31.9899i			1.51988i	−0.649991	+	0.759942i	$0.725227\pi$
$444$	−6.68608	+	3.37076i	−0.317307	+	0.159969i
$445$	−29.8319			−1.41417
$446$	4.66788			0.221031
$447$	−7.07020	−	14.0241i	−0.334409	−	0.663318i
$448$	−1.76690	+	1.76690i	−0.0834780	+	0.0834780i
$449$	5.95612	−	5.95612i	0.281087	−	0.281087i	−0.552456	−	0.833542i	$-0.686309\pi$
$449$	5.95612	−	5.95612i	0.281087	−	0.281087i	0.833542	+	0.552456i	$0.186309\pi$
$450$	17.2789	−	2.58530i	0.814534	−	0.121872i
$451$	−0.889432			−0.0418817
$452$	15.6215			0.734775
$453$	−0.896483	−	1.77822i	−0.0421205	−	0.0835481i
$454$			6.13517i			0.287938i
$455$	28.9623	+	6.30452i	1.35777	+	0.295560i
$456$	−1.75615	+	5.32720i	−0.0822393	+	0.249469i
$457$	10.4251	−	10.4251i	0.487667	−	0.487667i	−0.419903	−	0.907569i	$-0.637936\pi$
$457$	10.4251	−	10.4251i	0.487667	−	0.487667i	0.907569	+	0.419903i	$0.137936\pi$
$458$		−	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	0.941667	+	0.336547i	$0.109259\pi$
$461$	27.4444	+	27.4444i	1.27821	+	1.27821i	0.336547	+	0.941667i	$0.390741\pi$
$462$	2.98836	+	5.92757i	0.139031	+	0.275775i
$463$	8.89133	+	8.89133i	0.413215	+	0.413215i	0.882857	−	0.469642i	$-0.155617\pi$
$463$	8.89133	+	8.89133i	0.413215	+	0.413215i	−0.469642	+	0.882857i	$0.655617\pi$
$464$			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	$-0.826115\pi$
$467$	−36.9303			−1.70893			−0.854466	+	0.519508i	$0.826115\pi$
$468$	7.12894	+	8.13500i	0.329535	+	0.376041i
$469$	−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
$474$	11.0048	+	21.8285i	0.505465	+	1.00262i
$475$	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	−0.785152	−	0.619303i	$-0.787415\pi$
$479$	−3.62978	+	3.62978i	−0.165849	+	0.165849i	0.619303	+	0.785152i	$0.287415\pi$
$480$	−1.78406	+	5.41187i	−0.0814310	+	0.247017i
$481$	−13.1137	+	8.42512i	−0.597933	+	0.384152i
$482$			17.5110i			0.797604i
$483$	−9.06505	−	17.9810i	−0.412474	−	0.818163i
$484$	−8.64748			−0.393067
$485$	53.8776			2.44645
$486$	−11.2560	+	10.7843i	−0.510584	+	0.489187i
$487$	9.33604	−	9.33604i	0.423056	−	0.423056i	−0.463198	−	0.886255i	$-0.653298\pi$
$487$	9.33604	−	9.33604i	0.423056	−	0.423056i	0.886255	+	0.463198i	$0.153298\pi$
$488$	2.16911	−	2.16911i	0.0981911	−	0.0981911i
$489$	−18.9965	−	37.6806i	−0.859053	−	1.70397i
$490$	2.48770			0.112383
$491$	9.37867			0.423254			0.211627	−	0.977351i	$-0.432124\pi$
$491$	9.37867			0.423254			0.211627	+	0.977351i	$0.432124\pi$
$492$	0.896870	−	0.452154i	0.0404340	−	0.0203847i
$493$		−	26.6936i		−	1.20222i
$494$	−2.48357	+	11.4093i	−0.111741	+	0.513328i
$495$	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	$-0.751776\pi$
$499$	−0.176261	+	0.176261i	−0.00789054	+	0.00789054i	0.703151	+	0.711041i	$0.251776\pi$
$500$	1.91630	+	1.91630i	0.0856995	+	0.0856995i
$501$	14.9210	−	7.52236i	0.666620	−	0.336074i
$502$	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
$507$	16.5195	+	15.3006i	0.733655	+	0.679522i
$508$	10.6936			0.474451
$509$	0.724506	+	0.724506i	0.0321132	+	0.0321132i	0.722981	−	0.690868i	$-0.242771\pi$
$509$	0.724506	+	0.724506i	0.0321132	+	0.0321132i	−0.690868	+	0.722981i	$0.742771\pi$
$510$	10.2356	−	31.0492i	0.453240	−	1.37488i
$511$		−	8.09219i		−	0.357978i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−16.5852	−	2.84558i	−0.732257	−	0.125635i
$514$	−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
$520$	−2.52305	+	11.5906i	−0.110643	+	0.508283i
$521$		−	23.5279i		−	1.03078i	−0.856957	−	0.515388i	$-0.827648\pi$
$521$		−	23.5279i		−	1.03078i	0.856957	−	0.515388i	$-0.172352\pi$
$522$	−13.8044	+	2.06544i	−0.604202	+	0.0904020i
$523$	−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
$525$	−22.5067	+	11.3467i	−0.982272	+	0.495209i
$526$	13.1598	−	13.1598i	0.573794	−	0.573794i
$527$	−21.9377	+	21.9377i	−0.955622	+	0.955622i
$528$	−2.37220	+	1.19593i	−0.103237	+	0.0520463i
$529$	−1.35252			−0.0588053
$530$	−36.0869			−1.56752
$531$	19.5224	−	2.92098i	0.847198	−	0.126760i
$532$		−	8.09219i		−	0.350841i
$533$	1.75907	−	1.13014i	0.0761937	−	0.0489520i
$534$	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
$540$	−16.8489	−	2.89081i	−0.725060	−	0.124401i
$541$	14.5477	+	14.5477i	0.625453	+	0.625453i	0.946920	−	0.321468i	$-0.104176\pi$
$541$	14.5477	+	14.5477i	0.625453	+	0.625453i	−0.321468	+	0.946920i	$0.604176\pi$
$542$			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
$546$	−13.4420	−	7.92609i	−0.575264	−	0.339205i
$547$	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
$552$	7.19593	−	3.62780i	0.306279	−	0.154410i
$553$	−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	−0.834060	−	0.551673i	$-0.813989\pi$
$557$	−6.66457	+	6.66457i	−0.282387	+	0.282387i	0.551673	+	0.834060i	$0.313989\pi$
$558$	13.0424	+	9.64748i	0.552128	+	0.408410i
$559$	0.783378	+	0.170526i	0.0331334	+	0.00721246i
$560$		−	8.22081i		−	0.347393i
$561$	13.6099	−	6.86136i	0.574609	−	0.289687i
$562$	−19.1598			−0.808207
$563$	41.2952			1.74039			0.870193	−	0.492710i	$-0.163994\pi$
$563$	41.2952			1.74039			0.870193	+	0.492710i	$0.163994\pi$
$564$	−8.43952	−	16.7402i	−0.355368	−	0.704890i
$565$	−36.3411	+	36.3411i	−1.52888	+	1.52888i
$566$	12.4787	−	12.4787i	0.524517	−	0.524517i
$567$	10.5513	−	19.8601i	0.443111	−	0.834045i
$568$	7.75615			0.325441
$569$	−9.35536			−0.392197			−0.196099	−	0.980584i	$-0.562827\pi$
$569$	−9.35536			−0.392197			−0.196099	+	0.980584i	$0.562827\pi$
$570$	−8.30747	−	16.4783i	−0.347962	−	0.690200i
$571$		−	9.96203i		−	0.416898i	−0.978033	−	0.208449i	$-0.933158\pi$
$571$		−	9.96203i		−	0.416898i	0.978033	−	0.208449i	$-0.0668415\pi$
$572$	−4.65268	+	2.98920i	−0.194539	+	0.124985i
$573$	−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	0.0771415	−	0.997020i	$-0.475421\pi$
$577$	25.8022	−	25.8022i	1.07416	−	1.07416i	0.997020	−	0.0771415i	$-0.0245793\pi$
$578$	−11.2543	−	11.2543i	−0.468116	−	0.468116i
$579$	2.79400	+	5.54204i	0.116115	+	0.230319i
$580$	−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
$585$	−35.5092	−	2.34044i	−1.46812	−	0.0967655i
$586$	21.8698			0.903435
$587$	20.5387	+	20.5387i	0.847723	+	0.847723i	0.989849	−	0.142126i	$-0.0453938\pi$
$587$	20.5387	+	20.5387i	0.847723	+	0.847723i	−0.142126	+	0.989849i	$0.545394\pi$
$588$	−1.24385	−	0.410044i	−0.0512954	−	0.0169099i
$589$			17.5123i			0.721582i
$590$	15.3071	+	15.3071i	0.630182	+	0.630182i
$591$	4.95711	+	9.83268i	0.203908	+	0.404463i
$592$	3.05684	+	3.05684i	0.125635	+	0.125635i
$593$	−23.9379	+	23.9379i	−0.983013	+	0.983013i	−0.999858	−	0.0168449i	$-0.994638\pi$
$593$	−23.9379	+	23.9379i	−0.983013	+	0.983013i	0.0168449	+	0.999858i	$0.494638\pi$
$594$	−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
$598$	14.1137	−	9.06759i	0.577151	−	0.370801i
$599$		−	41.0774i		−	1.67838i	−0.543841	−	0.839188i	$-0.683031\pi$
$599$		−	41.0774i		−	1.67838i	0.543841	−	0.839188i	$-0.316969\pi$
$600$	−4.54090	−	9.00711i	−0.185382	−	0.367714i
$601$	−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
$603$	2.23976	−	0.335118i	0.0912102	−	0.0136471i
$604$	−0.812993	+	0.812993i	−0.0330802	+	0.0330802i
$605$	20.1170	−	20.1170i	0.817872	−	0.817872i
$606$	−9.99878	−	19.8331i	−0.406173	−	0.805664i
$607$	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
$609$	17.9810	−	9.06505i	0.728626	−	0.367334i
$610$			10.0922i			0.408621i
$611$	−21.0943	−	32.8333i	−0.853385	−	1.32829i
$612$	−10.2356	+	13.8375i	−0.413750	+	0.559347i
$613$	18.0296	−	18.0296i	0.728209	−	0.728209i	−0.242054	−	0.970263i	$-0.577821\pi$
$613$	18.0296	−	18.0296i	0.728209	−	0.728209i	0.970263	+	0.242054i	$0.0778210\pi$
$614$			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	0.641770	−	0.766897i	$-0.278200\pi$
$617$	−3.10809	−	3.10809i	−0.125127	−	0.125127i	−0.766897	+	0.641770i	$0.778200\pi$
$618$	3.26906	−	1.64809i	0.131501	−	0.0662958i
$619$	−14.3114	−	14.3114i	−0.575225	−	0.575225i	0.358359	−	0.933584i	$-0.383336\pi$
$619$	−14.3114	−	14.3114i	−0.575225	−	0.575225i	−0.933584	+	0.358359i	$0.883336\pi$
$620$			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
$624$	3.17200	−	5.37945i	0.126981	−	0.215350i
$625$	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
$630$	24.3909	−	3.64942i	0.971758	−	0.145397i
$631$	−12.8130	−	12.8130i	−0.510077	−	0.510077i	0.404473	−	0.914550i	$-0.367455\pi$
$631$	−12.8130	−	12.8130i	−0.510077	−	0.510077i	−0.914550	+	0.404473i	$0.867455\pi$
$632$	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
$637$	−2.66396	−	0.579890i	−0.105550	−	0.0229761i
$638$		−	7.13626i		−	0.282527i
$639$	3.44315	+	23.0123i	0.136209	+	0.910352i
$640$	3.28995			0.130046
$641$	−13.1147			−0.517998			−0.258999	−	0.965878i	$-0.583393\pi$
$641$	−13.1147			−0.517998			−0.258999	+	0.965878i	$0.583393\pi$
$642$	3.35479	−	1.69131i	0.132403	−	0.0667505i
$643$	−5.60138	+	5.60138i	−0.220897	+	0.220897i	−0.808876	−	0.587979i	$-0.799924\pi$
$643$	−5.60138	+	5.60138i	−0.220897	+	0.220897i	0.587979	+	0.808876i	$0.299924\pi$
$644$	−8.22081	+	8.22081i	−0.323945	+	0.323945i
$645$	−1.13142	+	0.570403i	−0.0445497	+	0.0224596i
$646$	−18.5799			−0.731016
$647$	11.4745			0.451108			0.225554	−	0.974231i	$-0.427581\pi$
$647$	11.4745			0.451108			0.225554	+	0.974231i	$0.427581\pi$
$648$	7.94794	+	4.22258i	0.312225	+	0.165879i
$649$			10.0922i			0.396153i
$650$	−11.3498	−	17.6660i	−0.445178	−	0.692918i
$651$	−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
$657$	1.43764	+	9.60846i	0.0560876	+	0.374862i
$658$	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	$-0.359355\pi$
$661$	−12.2470	−	12.2470i	−0.476352	−	0.476352i	−0.903963	+	0.427611i	$0.859355\pi$
$662$	−2.92401			−0.113645
$663$	−18.1985	+	30.8632i	−0.706771	+	1.19863i
$664$	−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
$669$	7.21944	−	3.63965i	0.279120	−	0.140717i
$670$	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	$-0.701323\pi$
$673$		−	41.8483i		−	1.61314i	0.591142	−	0.806568i	$-0.298677\pi$
$674$	14.5405	−	14.5405i	0.560080	−	0.560080i
$675$	24.7080	−	17.4712i	0.951013	−	0.672467i
$676$	5.40363	−	11.8237i	0.207832	−	0.454759i
$677$		−	15.9360i		−	0.612470i	−0.951956	−	0.306235i	$-0.900931\pi$
$677$		−	15.9360i		−	0.612470i	0.951956	−	0.306235i	$-0.0990694\pi$
$678$	24.1606	−	12.1805i	0.927881	−	0.467788i
$679$	40.9209			1.57040
$680$	−18.8752			−0.723831
$681$	4.78374	+	9.48878i	0.183313	+	0.363611i
$682$	−5.86483	+	5.86483i	−0.224576	+	0.224576i
$683$	23.5279	−	23.5279i	0.900270	−	0.900270i	−0.0951894	−	0.995459i	$-0.530346\pi$
$683$	23.5279	−	23.5279i	0.900270	−	0.900270i	0.995459	+	0.0951894i	$0.0303457\pi$
$684$	1.43764	+	9.60846i	0.0549695	+	0.367389i
$685$	17.0461			0.651298
$686$	19.3808			0.739964
$687$	−2.73132	−	5.41771i	−0.104206	−	0.206699i
$688$		−	0.222358i		−	0.00847732i
$689$	38.6438	+	8.41198i	1.47221	+	0.320471i
$690$	−8.30069	+	25.1797i	−0.316002	+	0.958576i
$691$	14.1763	−	14.1763i	0.539290	−	0.539290i	−0.384030	−	0.923321i	$-0.625464\pi$
$691$	14.1763	−	14.1763i	0.539290	−	0.539290i	0.923321	+	0.384030i	$0.125464\pi$
$692$			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
$696$	3.62780	+	7.19593i	0.137512	+	0.272761i
$697$	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	$-0.642837\pi$
$701$	−22.9723			−0.867651			−0.433825	+	0.900997i	$0.642837\pi$
$702$	17.3688	+	7.02315i	0.655543	+	0.265072i
$703$	−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
$708$	−5.13049	−	10.1766i	−0.192816	−	0.382460i
$709$	−3.10867	−	3.10867i	−0.116749	−	0.116749i	0.646319	−	0.763068i	$-0.276308\pi$
$709$	−3.10867	−	3.10867i	−0.116749	−	0.116749i	−0.763068	+	0.646319i	$0.776308\pi$
$710$	−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
$715$	3.86984	−	17.7776i	0.144724	−	0.664846i
$716$		−	0.264467i		−	0.00988361i
$717$	−16.3086	−	32.3490i	−0.609057	−	1.20810i
$718$	−0.444716			−0.0165967
$719$	−8.46197			−0.315578			−0.157789	−	0.987473i	$-0.550437\pi$
$719$	−8.46197			−0.315578			−0.157789	+	0.987473i	$0.550437\pi$
$720$	1.46049	+	9.76118i	0.0544292	+	0.363778i
$721$	−3.73466	+	3.73466i	−0.139086	+	0.139086i
$722$	6.01911	−	6.01911i	0.224008	−	0.224008i
$723$	13.6537	+	27.0828i	0.507787	+	1.00722i
$724$	8.11368			0.301543
$725$	27.0960			1.00632
$726$	−13.3744	+	6.74264i	−0.496369	+	0.250243i
$727$			13.0461i			0.483853i	0.970295	+	0.241926i	$0.0777793\pi$
$727$			13.0461i			0.483853i	−0.970295	+	0.241926i	$0.922221\pi$
$728$	−1.91630	+	8.80329i	−0.0710227	+	0.326271i
$729$	−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	$-0.876492\pi$
$733$	−14.8180	+	14.8180i	−0.547315	+	0.547315i	0.378348	+	0.925663i	$0.376492\pi$
$734$	−14.8818	−	14.8818i	−0.549299	−	0.549299i
$735$	3.84752	−	1.93971i	0.141918	−	0.0715474i
$736$	−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	$-0.385867\pi$
$739$	−15.9159	−	15.9159i	−0.585477	−	0.585477i	−0.936403	+	0.350926i	$0.885867\pi$
$740$	−14.2225			−0.522830
$741$	5.05494	+	19.5823i	0.185698	+	0.719375i
$742$	−27.4086			−1.00620
$743$	−12.3062	−	12.3062i	−0.451472	−	0.451472i	0.444371	−	0.895843i	$-0.353427\pi$
$743$	−12.3062	−	12.3062i	−0.451472	−	0.451472i	−0.895843	+	0.444371i	$0.853427\pi$
$744$	2.93241	−	8.89533i	0.107507	−	0.326118i
$745$		−	29.8319i		−	1.09295i
$746$	2.98920	+	2.98920i	0.109442	+	0.109442i
$747$	−0.878310	−	5.87018i	−0.0321357	−	0.214779i
$748$	−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	$-0.960903\pi$
$751$		−	6.71506i		−	0.245036i	0.992466	−	0.122518i	$-0.0390970\pi$
$752$	−7.65354	+	7.65354i	−0.279096	+	0.279096i
$753$	20.2242	+	6.66707i	0.737012	+	0.242962i
$754$	9.06759	+	14.1137i	0.330222	+	0.513990i
$755$		−	3.78260i		−	0.137663i
$756$	−12.7970	−	2.19562i	−0.465422	−	0.0798538i
$757$	−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
$759$	−11.0371	+	5.56430i	−0.400621	+	0.201971i
$760$	−7.53379	+	7.53379i	−0.273279	+	0.273279i
$761$	−25.5514	+	25.5514i	−0.926238	+	0.926238i	−0.997460	−	0.0712220i	$-0.977310\pi$
$761$	−25.5514	+	25.5514i	−0.926238	+	0.926238i	0.0712220	+	0.997460i	$0.477310\pi$
$762$	16.5389	−	8.33802i	0.599141	−	0.302055i
$763$	−8.75304			−0.316881
$764$	16.1272			0.583460
$765$	−8.37918	−	56.0022i	−0.302950	−	2.02477i
$766$			27.4958i			0.993464i
$767$	−12.8235	−	19.9598i	−0.463030	−	0.720705i
$768$	−1.64497	−	0.542278i	−0.0593578	−	0.0195678i
$769$	−36.1433	+	36.1433i	−1.30336	+	1.30336i	−0.377249	+	0.926112i	$0.623130\pi$
$769$	−36.1433	+	36.1433i	−1.30336	+	1.30336i	−0.926112	+	0.377249i	$0.876870\pi$
$770$			12.6090i			0.454398i
$771$	−49.4071	−	16.2874i	−1.77935	−	0.586578i
$772$	2.53379	−	2.53379i	0.0911932	−	0.0911932i

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} +1.00000i q^{4} +(-2.32634 - 2.32634i) q^{5} +(0.779723 + 1.54662i) q^{6} +(-1.76690 - 1.76690i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} +1.00000i q^{4} +(-2.32634 - 2.32634i) q^{5} +(0.779723 + 1.54662i) 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} +(0.766897 - 3.52305i) q^{13} +2.49877i q^{14} +(2.56525 + 5.08829i) q^{15} -1.00000 q^{16} +5.73724 q^{17} +(-0.443925 - 2.96697i) q^{18} +(2.28995 - 2.28995i) q^{19} +(2.32634 - 2.32634i) q^{20} +(1.94835 + 3.86465i) q^{21} +1.53379 q^{22} -4.65268 q^{23} +(-1.54662 + 0.779723i) q^{24} +5.82374i q^{25} +(-3.03345 + 1.94889i) q^{26} +(-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} +(2.37220 - 1.19593i) 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} +(-3.17200 + 5.37945i) q^{39} -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} +(-1.46049 - 9.76118i) 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} +(3.52305 + 0.766897i) q^{52} +10.9689i q^{53} +(-0.878680 + 5.12132i) q^{54} +5.04610 q^{55} -2.49877 q^{56} +(-5.00868 + 2.52511i) q^{57} +(-3.28995 + 3.28995i) q^{58} +(4.65268 - 4.65268i) q^{59} +(-5.08829 + 2.56525i) q^{60} +3.06759 q^{61} +5.40758 q^{62} +(-1.10927 - 7.41378i) q^{63} -1.00000i q^{64} +(-9.97988 + 6.41175i) q^{65} +(-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} +(2.96697 - 0.443925i) 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} +(6.04678 - 1.56090i) q^{78} +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} +(-3.86465 + 1.94835i) 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} +(-7.57989 + 4.86984i) q^{91} -4.65268i q^{92} +(8.36347 - 4.21642i) q^{93} -10.8237 q^{94} -10.6544 q^{95} +(-0.779723 - 1.54662i) q^{96} +(-11.5799 + 11.5799i) q^{97} +(-0.534680 + 0.534680i) q^{98} +(-4.55072 + 0.680889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) 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 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 36 * q^93 - 72 * q^94 - 60 * q^97 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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