LMFDB - Embedded newform 78.2.g.a.5.4

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			5.4
Root			$-0.779723 - 1.54662i$ of defining polynomial
Character	$\chi$	$=$	78.5
Dual form			78.2.g.a.47.4

$q$-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} +(0.766897 - 3.52305i) q^{13} -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} +(3.03345 - 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} +(-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} +(0.648947 + 6.21119i) 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} +(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} +(3.52305 + 0.766897i) q^{52} -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} +(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} +(-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} +(-3.93310 + 4.85085i) 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} +(-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} +(-7.57989 + 4.86984i) q^{91} +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} + 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	$0.0131251\pi$
$5$	2.32634	+	2.32634i	1.04037	+	1.04037i	0.0412220	+	0.999150i	$0.486875\pi$
$6$	−1.54662	−	0.779723i	−0.631405	−	0.318321i
$7$	−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	−0.524441	−	0.851447i	$-0.675726\pi$
$11$	1.08456	−	1.08456i	0.327006	−	0.327006i	0.851447	+	0.524441i	$0.175726\pi$
$12$	−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
$15$	−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	$-0.628851\pi$
$19$	2.28995	−	2.28995i	0.525349	−	0.525349i	0.919182	+	0.393833i	$0.128851\pi$
$20$	−2.32634	+	2.32634i	−0.520186	+	0.520186i
$21$	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
$26$	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	$0.142189\pi$
$29$			4.65268i			0.863982i	−0.901878	+	0.431991i	$0.857811\pi$
$30$	−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
$33$	−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	$-0.365639\pi$
$37$	−3.05684	−	3.05684i	−0.502542	−	0.502542i	−0.912227	+	0.409685i	$0.865639\pi$
$38$	3.23847			0.525349
$39$	0.648947	+	6.21119i	0.103915	+	0.994586i
$40$	−3.28995			−0.520186
$41$	−0.410044	−	0.410044i	−0.0640382	−	0.0640382i	0.674362	−	0.738401i	$-0.264419\pi$
$41$	−0.410044	−	0.410044i	−0.0640382	−	0.0640382i	−0.738401	+	0.674362i	$0.764419\pi$
$42$	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
$45$	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	−0.124116	+	0.992268i	$0.539609\pi$
$47$	−7.65354	+	7.65354i	−1.11638	+	1.11638i	−0.992268	+	0.124116i	$0.960391\pi$
$48$	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	$-0.728440\pi$
$53$		−	10.9689i		−	1.50669i	0.657627	−	0.753344i	$-0.271560\pi$
$54$	−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	$-0.890892\pi$
$59$	−4.65268	+	4.65268i	−0.605728	+	0.605728i	0.336099	+	0.941827i	$0.390892\pi$
$60$	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
$65$	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	0.302324	−	0.953205i	$-0.402238\pi$
$71$	−5.48443	−	5.48443i	−0.650882	−	0.650882i	−0.953205	+	0.302324i	$0.902238\pi$
$72$	−0.443925	+	2.96697i	−0.0523171	+	0.349661i
$73$	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
$78$	−3.93310	+	4.85085i	−0.445336	+	0.549250i
$79$	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	$-0.215368\pi$
$83$	1.39902	+	1.39902i	0.153562	+	0.153562i	−0.626145	+	0.779707i	$0.715368\pi$
$84$	−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	$-0.909574\pi$
$89$	−6.41175	+	6.41175i	−0.679644	+	0.679644i	0.280275	+	0.959920i	$0.409574\pi$
$90$	5.86947	+	7.93492i	0.618697	+	0.836414i
$91$	−7.57989	+	4.86984i	−0.794588	+	0.510497i
$92$			4.65268i			0.485076i
$93$	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	−0.194946	+	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
$99$	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	$-0.966793\pi$
$103$		−	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	$0.0334356\pi$
$107$			2.16911i			0.209696i	−0.994488	+	0.104848i	$0.966564\pi$
$108$	−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
$111$	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	$0.262712\pi$
$113$			15.6215i			1.46955i	−0.678310	+	0.734775i	$0.737288\pi$
$114$	−5.32720	+	1.75615i	−0.498938	+	0.164479i
$115$	10.8237	+	10.8237i	1.00932	+	1.00932i
$116$	−4.65268			−0.431991
$117$	−4.43569	−	9.86533i	−0.410080	−	0.912050i
$118$	−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	$-0.842647\pi$
$127$		−	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	$-0.996322\pi$
$131$		−	0.264467i		−	0.0231066i	0.999933	−	0.0115533i	$-0.00367761\pi$
$132$	−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	$-0.678959\pi$
$137$	3.66371	−	3.66371i	0.313012	−	0.313012i	0.846075	+	0.533063i	$0.178959\pi$
$138$	−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
$143$	−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	0.393887	−	0.919159i	$-0.371130\pi$
$149$	−6.41175	−	6.41175i	−0.525271	−	0.525271i	−0.919159	+	0.393887i	$0.871130\pi$
$150$	4.54090	−	9.00711i	0.370763	−	0.735427i
$151$	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
$156$	−6.21119	+	0.648947i	−0.497293	+	0.0519574i
$157$	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	0.886366	+	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	−0.392055	−	0.919942i	$-0.628236\pi$
$167$	6.82180	−	6.82180i	0.527886	−	0.527886i	0.919942	+	0.392055i	$0.128236\pi$
$168$	−4.11041	+	1.35503i	−0.317125	+	0.104543i
$169$	−11.8237	−	5.40363i	−0.909518	−	0.415664i
$170$		−	18.8752i		−	1.44766i
$171$	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	$-0.902498\pi$
$181$		−	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
$189$	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	$0.198302\pi$
$191$			16.1272i			1.16692i	−0.812142	+	0.583460i	$0.801698\pi$
$192$	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
$195$	−12.9397	+	15.9590i	−0.926630	+	1.14285i
$196$	0.756152			0.0540108
$197$	4.49545	+	4.49545i	0.320288	+	0.320288i	0.848877	−	0.528590i	$-0.177279\pi$
$197$	4.49545	+	4.49545i	0.320288	+	0.320288i	−0.528590	+	0.848877i	$0.677279\pi$
$198$	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
$201$	−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
$208$	−0.766897	+	3.52305i	−0.0531747	+	0.244279i
$209$		−	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
$221$	−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	0.836264	−	0.548326i	$-0.184735\pi$
$227$	4.33822	+	4.33822i	0.287938	+	0.287938i	−0.548326	+	0.836264i	$0.684735\pi$
$228$	−5.00868	−	2.52511i	−0.331708	−	0.167230i
$229$	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	$-0.370806\pi$
$233$	12.0534			0.789645			0.394823	+	0.918757i	$0.370806\pi$
$234$	3.83933	−	10.1123i	0.250985	−	0.661065i
$235$	−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	$-0.486491\pi$
$239$	−14.7898	−	14.7898i	−0.956672	−	0.956672i	−0.999100	+	0.0424271i	$0.986491\pi$
$240$	5.08829	+	2.56525i	0.328448	+	0.165586i
$241$	−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
$249$	−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
$260$	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	$-0.805471\pi$
$263$		−	18.6107i		−	1.14759i	0.819000	−	0.573794i	$-0.194529\pi$
$264$	−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	$0.00795884\pi$
$269$			0.820089i			0.0500017i	−0.999687	+	0.0250008i	$0.992041\pi$
$270$	−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
$273$	9.82791	−	12.1212i	0.594812	−	0.733606i
$274$	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
$279$	−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	$-0.943634\pi$
$281$	−13.5480	+	13.5480i	−0.808207	+	0.808207i	0.176156	+	0.984362i	$0.443634\pi$
$282$	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
$288$	−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	$-0.529421\pi$
$293$	15.4643	−	15.4643i	0.903435	−	0.903435i	0.995732	+	0.0922970i	$0.0294209\pi$
$294$	−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
$299$	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
$306$	−17.0222	−	2.54690i	−0.973097	−	0.145597i
$307$	−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	$-0.646053\pi$
$311$	−15.6215			−0.885816			−0.442908	+	0.896567i	$0.646053\pi$
$312$	−4.85085	−	3.93310i	−0.274625	−	0.222668i
$313$	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	$-0.286661\pi$
$317$	−2.89362	−	2.89362i	−0.162522	−	0.162522i	−0.783683	+	0.621161i	$0.786661\pi$
$318$	−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
$325$	20.5173	+	4.46621i	1.13810	+	0.247741i
$326$			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	$-0.724393\pi$
$331$	2.06759	−	2.06759i	0.113645	−	0.113645i	0.761642	+	0.647998i	$0.224393\pi$
$332$	−1.39902	+	1.39902i	−0.0767811	+	0.0767811i
$333$	−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	$0.189230\pi$
$337$			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
$345$	−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	$-0.976699\pi$
$347$		−	2.72473i		−	0.146271i	0.997322	−	0.0731357i	$-0.0233006\pi$
$348$	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
$351$	12.6463	+	13.8228i	0.675012	+	0.737807i
$352$	−1.53379			−0.0817515
$353$	1.49460	+	1.49460i	0.0795495	+	0.0795495i	0.745762	−	0.666212i	$-0.232086\pi$
$353$	1.49460	+	1.49460i	0.0795495	+	0.0795495i	−0.666212	+	0.745762i	$0.732086\pi$
$354$	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	$-0.753736\pi$
$359$	−0.314462	+	0.314462i	−0.0165967	+	0.0165967i	0.698760	+	0.715356i	$0.253736\pi$
$360$	−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
$366$	−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
$377$	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	0.999979	−	0.00651435i	$-0.00207360\pi$
$383$	19.4425	+	19.4425i	0.993464	+	0.993464i	−0.00651435	+	0.999979i	$0.502074\pi$
$384$	−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	$0.517512\pi$
$390$	−20.4345	+	2.13500i	−1.03474	+	0.108110i
$391$	−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	$-0.131269\pi$
$397$	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	−0.837585	−	0.546307i	$-0.816033\pi$
$401$	−5.83282	+	5.83282i	−0.291277	+	0.291277i	0.546307	+	0.837585i	$0.316033\pi$
$402$	−1.24179	+	0.409365i	−0.0619347	+	0.0204172i
$403$	10.5388	+	16.4036i	0.524975	+	0.817123i
$404$			12.8235i			0.637993i
$405$	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	$-0.824420\pi$
$409$	−6.62599	+	6.62599i	−0.327634	+	0.327634i	0.524052	+	0.851686i	$0.324420\pi$
$410$	1.34902	−	1.34902i	0.0666235	−	0.0666235i
$411$	−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
$416$	−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	$0.0658743\pi$
$419$			8.41198i			0.410952i	−0.978662	+	0.205476i	$0.934126\pi$
$420$	−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
$423$	−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
$429$	7.44020	+	6.03256i	0.359216	+	0.291255i
$430$	−0.731545			−0.0352783
$431$	−25.4442	−	25.4442i	−1.22560	−	1.22560i	−0.965610	−	0.259993i	$-0.916280\pi$
$431$	−25.4442	−	25.4442i	−1.22560	−	1.22560i	−0.259993	−	0.965610i	$-0.583720\pi$
$432$	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
$435$	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	$-0.858673\pi$
$439$		−	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	$-0.725227\pi$
$443$		−	31.9899i		−	1.51988i	0.649991	−	0.759942i	$-0.274773\pi$
$444$	−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	$-0.813691\pi$
$449$	−5.95612	+	5.95612i	−0.281087	+	0.281087i	0.552456	+	0.833542i	$0.313691\pi$
$450$	−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
$455$	−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	$-0.890741\pi$
$461$	−27.4444	−	27.4444i	−1.27821	−	1.27821i	−0.336547	−	0.941667i	$-0.609259\pi$
$462$	5.92757	+	2.98836i	0.275775	+	0.139031i
$463$	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	$-0.173885\pi$
$467$	36.9303			1.70893			0.854466	+	0.519508i	$0.173885\pi$
$468$	9.86533	−	4.43569i	0.456025	−	0.205040i
$469$	−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	$-0.712585\pi$
$479$	3.62978	−	3.62978i	0.165849	−	0.165849i	0.785152	+	0.619303i	$0.212585\pi$
$480$	1.78406	+	5.41187i	0.0814310	+	0.247017i
$481$	−13.1137	+	8.42512i	−0.597933	+	0.384152i
$482$		−	17.5110i		−	0.797604i
$483$	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	$-0.653298\pi$
$487$	9.33604	−	9.33604i	0.423056	−	0.423056i	0.886255	+	0.463198i	$0.153298\pi$
$488$	−2.16911	+	2.16911i	−0.0981911	+	0.0981911i
$489$	−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
$494$	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
$501$	−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	$-0.897673\pi$
$503$		−	14.1725i		−	0.631922i	0.948772	−	0.315961i	$-0.102327\pi$
$504$	6.02671	−	4.45797i	0.268451	−	0.198574i
$505$	29.8319	+	29.8319i	1.32750	+	1.32750i
$506$	7.13626			0.317245
$507$	22.3800	+	2.47707i	0.993930	+	0.110010i
$508$	10.6936			0.474451
$509$	−0.724506	−	0.724506i	−0.0321132	−	0.0321132i	0.690868	−	0.722981i	$-0.257229\pi$
$509$	−0.724506	−	0.724506i	−0.0321132	−	0.0321132i	−0.722981	+	0.690868i	$0.757229\pi$
$510$	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
$520$	−2.52305	+	11.5906i	−0.110643	+	0.508283i
$521$			23.5279i			1.03078i	0.856957	+	0.515388i	$0.172352\pi$
$521$			23.5279i			1.03078i	−0.856957	+	0.515388i	$0.827648\pi$
$522$	−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
$533$	−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
$540$	−2.89081	−	16.8489i	−0.124401	−	0.725060i
$541$	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
$546$	15.5203	−	1.62157i	0.664209	−	0.0693968i
$547$	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	$-0.686011\pi$
$557$	6.66457	−	6.66457i	0.282387	−	0.282387i	0.834060	+	0.551673i	$0.186011\pi$
$558$	−13.0424	+	9.64748i	−0.552128	+	0.408410i
$559$	0.783378	+	0.170526i	0.0331334	+	0.00721246i
$560$			8.22081i			0.347393i
$561$	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	$-0.933158\pi$
$571$		−	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
$579$	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
$585$	12.6312	−	33.2691i	0.522235	−	1.37551i
$586$	21.8698			0.903435
$587$	−20.5387	−	20.5387i	−0.847723	−	0.847723i	0.142126	−	0.989849i	$-0.454606\pi$
$587$	−20.5387	−	20.5387i	−0.847723	−	0.847723i	−0.989849	+	0.142126i	$0.954606\pi$
$588$	−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	$-0.505362\pi$
$593$	23.9379	−	23.9379i	0.983013	−	0.983013i	0.999858	+	0.0168449i	$0.00536215\pi$
$594$	−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	$0.316969\pi$
$599$			41.0774i			1.67838i	−0.543841	+	0.839188i	$0.683031\pi$
$600$	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
$611$	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	0.766897	−	0.641770i	$-0.221800\pi$
$617$	3.10809	+	3.10809i	0.125127	+	0.125127i	−0.641770	+	0.766897i	$0.721800\pi$
$618$	−1.64809	+	3.26906i	−0.0662958	+	0.131501i
$619$	−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
$624$	−0.648947	−	6.21119i	−0.0259787	−	0.248647i
$625$	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	$-0.367455\pi$
$631$	−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
$639$	−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	$-0.799924\pi$
$643$	−5.60138	+	5.60138i	−0.220897	+	0.220897i	0.587979	+	0.808876i	$0.299924\pi$
$644$	8.22081	−	8.22081i	0.323945	−	0.323945i
$645$	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
$650$	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	$-0.923310\pi$
$653$		−	12.1946i		−	0.477211i	0.971117	−	0.238605i	$-0.0766903\pi$
$654$	−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	$-0.786095\pi$
$659$		−	31.9632i		−	1.24511i	0.782577	−	0.622554i	$-0.213905\pi$
$660$	−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
$663$	−3.72317	−	35.6351i	−0.144596	−	1.38395i
$664$	−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	$-0.701323\pi$
$673$		−	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	$0.0990694\pi$
$677$			15.9360i			0.612470i	−0.951956	+	0.306235i	$0.900931\pi$
$678$	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	$-0.969654\pi$
$683$	−23.5279	+	23.5279i	−0.900270	+	0.900270i	0.0951894	+	0.995459i	$0.469654\pi$
$684$	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
$689$	−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
$696$	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	$0.357163\pi$
$702$	−0.831893	+	18.7165i	−0.0313978	+	0.706409i
$703$	−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	$-0.276308\pi$
$709$	−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
$717$	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	$0.0777793\pi$
$727$			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
$735$	−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	$-0.385867\pi$
$739$	−15.9159	−	15.9159i	−0.585477	−	0.585477i	−0.936403	+	0.350926i	$0.885867\pi$
$740$	14.2225			0.522830
$741$	15.7093	+	12.7372i	0.577097	+	0.467914i
$742$	−27.4086			−1.00620
$743$	12.3062	+	12.3062i	0.451472	+	0.451472i	0.895843	−	0.444371i	$-0.146573\pi$
$743$	12.3062	+	12.3062i	0.451472	+	0.451472i	−0.444371	+	0.895843i	$0.646573\pi$
$744$	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	$-0.960903\pi$
$751$		−	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
$756$	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	$-0.522690\pi$
$761$	25.5514	−	25.5514i	0.926238	−	0.926238i	0.997460	+	0.0712220i	$0.0226899\pi$
$762$	−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
$767$	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
$773$	32.0971	+	32.0971i	1.15445	+	1.15445i	0.985650	+	0.168803i	$0.0539901\pi$
$773$	32.0971	+	32.0971i	1.15445	+	1.15445i	0.168803	+	0.985650i	$0.446010\pi$
$774$	−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
$780$	−15.9590	−	12.9397i	−0.571425	−	0.463315i
$781$	−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	$-0.128693\pi$
$787$	14.7562	+	14.7562i	0.526000	+	0.526000i	−0.393377	+	0.919377i	$0.628693\pi$
$788$	−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
$793$	2.35252	−	10.8073i	0.0835405	−	0.383777i
$794$			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
$806$	−4.14706	+	19.0512i	−0.146074	+	0.671049i
$807$	−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	$-0.886728\pi$
$809$		−	19.8186i		−	0.696785i	0.937349	−	0.348392i	$-0.113272\pi$
$810$	28.3128	+	8.66646i	0.994811	+	0.304508i
$811$	25.0265	−	25.0265i	0.878799	−	0.878799i	−0.114611	−	0.993410i	$-0.536562\pi$
$811$	25.0265	−	25.0265i	0.878799	−	0.878799i	0.993410	+	0.114611i	$0.0365622\pi$
$812$	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
$819$	−9.59360	+	25.2684i	−0.335228	+	0.882950i
$820$	1.90781			0.0666235
$821$	5.31554	+	5.31554i	0.185514	+	0.185514i	0.793753	−	0.608240i	$-0.208124\pi$
$821$	5.31554	+	5.31554i	0.185514	+	0.185514i	−0.608240	+	0.793753i	$0.708124\pi$
$822$	−8.52305	+	2.80969i	−0.297275	+	0.0979991i
$823$			54.4118i			1.89667i	0.317264	+	0.948337i	$0.397236\pi$
$823$			54.4118i			1.89667i	−0.317264	+	0.948337i	$0.602764\pi$
$824$	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	$-0.910471\pi$
$827$	−19.6453	+	19.6453i	−0.683134	+	0.683134i	0.277571	+	0.960705i	$0.410471\pi$
$828$	8.30069	+	11.2217i	0.288469	+	0.389980i
$829$		−	0.248858i		−	0.00864320i	−0.999991	−	0.00432160i	$-0.998624\pi$
$829$		−	0.248858i		−	0.00864320i	0.999991	−	0.00432160i	$-0.00137561\pi$
$830$	−4.60269	+	4.60269i	−0.159762	+	0.159762i
$831$	−9.42867	−	28.6014i	−0.327077	−	0.992171i
$832$	−3.52305	−	0.766897i	−0.122140	−	0.0265874i
$833$			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	$-0.700906\pi$
$839$	6.29286	−	6.29286i	0.217254	−	0.217254i	0.807340	+	0.590086i	$0.200906\pi$
$840$	−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
$845$	−14.9354	−	40.0768i	−0.513792	−	1.37868i
$846$	−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	$-0.0306835\pi$
$853$	26.2596	+	26.2596i	0.899112	+	0.899112i	−0.0962459	+	0.995358i	$0.530684\pi$
$854$		−	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	$0.814519\pi$
$858$	0.995351	+	9.52668i	0.0339807	+	0.325236i
$859$	−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	−0.808221	−	0.588879i	$-0.799569\pi$
$863$	−41.0424	−	41.0424i	−1.39710	−	1.39710i	−0.588879	−	0.808221i	$-0.700431\pi$
$864$	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
$871$	−1.47122	−	2.28995i	−0.0498503	−	0.0775918i
$872$			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	$-0.654704\pi$
$877$	12.3518	−	12.3518i	0.417091	−	0.417091i	0.884200	+	0.467109i	$0.154704\pi$
$878$	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	$0.232201\pi$
$883$			39.6095i			1.33297i	−0.745520	+	0.666483i	$0.767799\pi$
$884$	−20.2126	−	4.39987i	−0.679823	−	0.147984i
$885$	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	$-0.951103\pi$
$887$		−	9.11420i		−	0.306025i	0.988224	−	0.153013i	$-0.0488975\pi$
$888$	−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
$897$	3.01935	+	28.8987i	0.100813	+	0.964900i
$898$	−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	$-0.939254\pi$
$907$		−	11.4251i		−	0.379365i	0.981845	−	0.189682i	$-0.0607458\pi$
$908$	−4.33822	+	4.33822i	−0.143969	+	0.143969i
$909$	30.9286	−	22.8780i	1.02584	−	0.758814i
$910$	−16.0215	−	24.9374i	−0.531107	−	0.826668i
$911$		−	19.4541i		−	0.644544i	−0.946647	−	0.322272i	$-0.895553\pi$
$911$		−	19.4541i		−	0.644544i	0.946647	−	0.322272i	$-0.104447\pi$
$912$	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
$923$	−23.5279	+	15.1159i	−0.774430	+	0.497546i
$924$	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	$-0.232357\pi$
$929$	2.38799	+	2.38799i	0.0783474	+	0.0783474i	−0.666847	+	0.745195i	$0.732357\pi$
$930$	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
$936$	10.1123	+	3.83933i	0.330532	+	0.125492i
$937$	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	−0.974536	−	0.224233i	$-0.928012\pi$
$941$	−36.7731	−	36.7731i	−1.19877	−	1.19877i	−0.224233	−	0.974536i	$-0.571988\pi$
$942$	−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	−0.160628	+	0.987015i	$0.551352\pi$
$947$	−35.3168	+	35.3168i	−1.14764	+	1.14764i	−0.987015	+	0.160628i	$0.948648\pi$
$948$	−7.65354	−	23.2166i	−0.248575	−	0.754041i
$949$	9.82374	−	6.31144i	0.318892	−	0.204878i
$950$			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
$962$	−15.2302	−	3.31532i	−0.491042	−	0.106890i
$963$	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	−0.232042	+	0.972706i	$0.574541\pi$
$967$	−37.4636	+	37.4636i	−1.20475	+	1.20475i	−0.972706	+	0.232042i	$0.925459\pi$
$968$	−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	$-0.684932\pi$
$971$		−	52.0962i		−	1.67185i	0.548845	−	0.835924i	$-0.315068\pi$
$972$	−15.5849	+	0.333537i	−0.499886	+	0.0106982i
$973$	−3.92668	−	3.92668i	−0.125883	−	0.125883i
$974$	13.2032			0.423056
$975$	−36.1723	+	3.77930i	−1.15844	+	0.121034i
$976$	−3.06759			−0.0981911
$977$	14.4414	+	14.4414i	0.462021	+	0.462021i	0.899318	−	0.437296i	$-0.144064\pi$
$977$	14.4414	+	14.4414i	0.462021	+	0.462021i	−0.437296	+	0.899318i	$0.644064\pi$
$978$	−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	$-0.543674\pi$
$983$	26.7699	−	26.7699i	0.853827	−	0.853827i	0.990602	+	0.136775i	$0.0436737\pi$
$984$	−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
$988$	9.82374	−	6.31144i	0.312535	−	0.200794i
$989$			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	78.2.g.a.5.4	yes	12
3.2	odd	2	inner	78.2.g.a.5.1	✓	12
4.3	odd	2		624.2.bf.f.161.5		12
12.11	even	2		624.2.bf.f.161.6		12
13.5	odd	4		1014.2.g.b.437.4		12
13.8	odd	4	inner	78.2.g.a.47.1	yes	12
13.12	even	2		1014.2.g.b.239.1		12
39.5	even	4		1014.2.g.b.437.1		12
39.8	even	4	inner	78.2.g.a.47.4	yes	12
39.38	odd	2		1014.2.g.b.239.4		12
52.47	even	4		624.2.bf.f.593.5		12
156.47	odd	4		624.2.bf.f.593.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.g.a.5.1	✓	12	3.2	odd	2	inner
78.2.g.a.5.4	yes	12	1.1	even	1	trivial
78.2.g.a.47.1	yes	12	13.8	odd	4	inner
78.2.g.a.47.4	yes	12	39.8	even	4	inner
624.2.bf.f.161.5		12	4.3	odd	2
624.2.bf.f.161.6		12	12.11	even	2
624.2.bf.f.593.5		12	52.47	even	4
624.2.bf.f.593.6		12	156.47	odd	4
1014.2.g.b.239.1		12	13.12	even	2
1014.2.g.b.239.4		12	39.38	odd	2
1014.2.g.b.437.1		12	39.5	even	4
1014.2.g.b.437.4		12	13.5	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.64497 + 0.542278i) q^{3} +1.00000i q^{4} +(2.32634 + 2.32634i) q^{5} +(-1.54662 - 0.779723i) q^{6} +(-1.76690 - 1.76690i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.41187 - 1.78406i) q^{9} +O(q^{10})\)	\(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} +(0.766897 - 3.52305i) q^{13} -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} +(3.03345 - 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} +(-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} +(0.648947 + 6.21119i) 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} +(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} +(3.52305 + 0.766897i) q^{52} -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} +(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} +(-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} +(-3.93310 + 4.85085i) 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} +(-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} +(-7.57989 + 4.86984i) q^{91} +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	\( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more