LMFDB - Embedded newform 975.2.w.i.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-2.10121 + 0.563016i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.i.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563016 + 0.975173i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(0.303009 + 0.524827i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.563016 + 0.975173i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(0.303009 + 0.524827i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.66422 + 1.53819i) q^{11} -0.732051i q^{12} +(3.60121 + 0.176977i) q^{13} -0.682396 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.68905 + 0.975173i) q^{17} -1.12603 q^{18} +(4.23037 - 2.44240i) q^{19} -0.606018i q^{21} +(-3.00000 + 1.73205i) q^{22} +(-1.61457 - 0.932171i) q^{23} +(2.66422 + 1.53819i) q^{24} +(-2.20012 + 3.41216i) q^{26} -1.00000i q^{27} +(-0.221818 + 0.384200i) q^{28} +(-1.39085 + 2.40903i) q^{29} +9.15276i q^{31} +(-1.95035 - 3.37810i) q^{32} +(-1.53819 - 2.66422i) q^{33} -2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(-1.87397 + 3.24581i) q^{37} +5.50045i q^{38} +(-3.03025 - 1.95387i) q^{39} +(0.926751 + 0.535060i) q^{41} +(0.590973 + 0.341198i) q^{42} +(-4.33951 + 2.50542i) q^{43} +2.25207i q^{44} +(1.81805 - 1.04965i) q^{46} +10.2024 q^{47} +(-1.73205 + 1.00000i) q^{48} +(3.31637 - 5.74412i) q^{49} +1.95035 q^{51} +(1.20593 + 2.34785i) q^{52} +10.6569i q^{53} +(0.975173 + 0.563016i) q^{54} +(-0.932171 - 1.61457i) q^{56} -4.88481 q^{57} +(-1.56615 - 2.71264i) q^{58} +(-10.0236 + 5.78712i) q^{59} +(3.13397 + 5.42820i) q^{61} +(-8.92552 - 5.15315i) q^{62} +(-0.303009 + 0.524827i) q^{63} +8.39230 q^{64} +3.46410 q^{66} +(0.988929 - 1.71288i) q^{67} +(-1.23647 - 0.713876i) q^{68} +(0.932171 + 1.61457i) q^{69} +(-5.11557 + 2.95347i) q^{71} +(-1.53819 - 2.66422i) q^{72} -4.35395 q^{73} +(-2.11015 - 3.65488i) q^{74} +(3.09684 + 1.78796i) q^{76} +1.86434i q^{77} +(3.61144 - 1.85495i) q^{78} +3.29546 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.04355 + 0.602495i) q^{82} -6.97707 q^{83} +(0.384200 - 0.221818i) q^{84} -5.64237i q^{86} +(2.40903 - 1.39085i) q^{87} +(-8.19615 - 4.73205i) q^{88} +(-14.1156 - 8.14963i) q^{89} +(0.998316 + 1.94364i) q^{91} -1.36479i q^{92} +(4.57638 - 7.92652i) q^{93} +(-5.74412 + 9.94911i) q^{94} +3.90069i q^{96} +(6.60121 + 11.4336i) q^{97} +(3.73434 + 6.46807i) q^{98} +3.07638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 4 * q^9	$ 8 q - 4 q^{4} + 4 q^{9} + 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{28} - 12 q^{29} + 4 q^{36} - 24 q^{37} + 4 q^{39} + 36 q^{41} + 12 q^{42} - 12 q^{43} + 48 q^{47} + 4 q^{49} - 12 q^{52} + 24 q^{57} - 12 q^{58} - 36 q^{59} + 32 q^{61} - 48 q^{62} - 16 q^{64} - 12 q^{67} + 36 q^{71} - 48 q^{73} + 24 q^{74} - 48 q^{76} - 12 q^{78} + 16 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{87} - 24 q^{88} - 36 q^{89} + 12 q^{93} - 12 q^{94} + 36 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 4 * q^9 + 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 - 24 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^28 - 12 * q^29 + 4 * q^36 - 24 * q^37 + 4 * q^39 + 36 * q^41 + 12 * q^42 - 12 * q^43 + 48 * q^47 + 4 * q^49 - 12 * q^52 + 24 * q^57 - 12 * q^58 - 36 * q^59 + 32 * q^61 - 48 * q^62 - 16 * q^64 - 12 * q^67 + 36 * q^71 - 48 * q^73 + 24 * q^74 - 48 * q^76 - 12 * q^78 + 16 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^87 - 24 * q^88 - 36 * q^89 + 12 * q^93 - 12 * q^94 + 36 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.563016	+	0.975173i	−0.398113	+	0.689551i	−0.993493	−	0.113893i	$-0.963668\pi$
$2$	−0.563016	+	0.975173i	−0.398113	+	0.689551i	0.595380	+	0.803444i	$0.297001\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.366025	+	0.633975i	0.183013	+	0.316987i
$5$		0			0
$5$		0			0
$6$	0.975173	−	0.563016i	0.398113	−	0.229850i
$7$	0.303009	+	0.524827i	0.114527	+	0.198366i	0.917590	−	0.397527i	$-0.130132\pi$
$7$	0.303009	+	0.524827i	0.114527	+	0.198366i	−0.803064	+	0.595893i	$0.796798\pi$
$8$	−3.07638			−1.08766
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.66422	+	1.53819i	0.803293	+	0.463781i	0.844621	−	0.535364i	$-0.179826\pi$
$11$	2.66422	+	1.53819i	0.803293	+	0.463781i	−0.0413283	+	0.999146i	$0.513159\pi$
$12$		−	0.732051i		−	0.211325i
$13$	3.60121	+	0.176977i	0.998795	+	0.0490845i
$13$	3.60121	+	0.176977i	0.998795	+	0.0490845i
$14$	−0.682396			−0.182378
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	−1.68905	+	0.975173i	−0.409654	+	0.236514i	−0.690641	−	0.723198i	$-0.742672\pi$
$17$	−1.68905	+	0.975173i	−0.409654	+	0.236514i	0.280987	+	0.959712i	$0.409338\pi$
$18$	−1.12603			−0.265408
$19$	4.23037	−	2.44240i	0.970513	−	0.560326i	0.0711202	−	0.997468i	$-0.477343\pi$
$19$	4.23037	−	2.44240i	0.970513	−	0.560326i	0.899393	+	0.437142i	$0.144009\pi$
$20$		0			0
$21$		−	0.606018i		−	0.132244i
$22$	−3.00000	+	1.73205i	−0.639602	+	0.369274i
$23$	−1.61457	−	0.932171i	−0.336660	−	0.194371i	0.322134	−	0.946694i	$-0.395600\pi$
$23$	−1.61457	−	0.932171i	−0.336660	−	0.194371i	−0.658794	+	0.752323i	$0.728933\pi$
$24$	2.66422	+	1.53819i	0.543832	+	0.313982i
$25$		0			0
$26$	−2.20012	+	3.41216i	−0.431479	+	0.669179i
$27$		−	1.00000i		−	0.192450i
$28$	−0.221818	+	0.384200i	−0.0419197	+	0.0726070i
$29$	−1.39085	+	2.40903i	−0.258275	+	0.447345i	−0.965780	−	0.259363i	$-0.916487\pi$
$29$	−1.39085	+	2.40903i	−0.258275	+	0.447345i	0.707505	+	0.706708i	$0.249821\pi$
$30$		0			0
$31$			9.15276i			1.64388i	0.569572	+	0.821942i	$0.307109\pi$
$31$			9.15276i			1.64388i	−0.569572	+	0.821942i	$0.692891\pi$
$32$	−1.95035	−	3.37810i	−0.344776	−	0.597169i
$33$	−1.53819	−	2.66422i	−0.267764	−	0.463781i
$34$		−	2.19615i		−	0.376637i
$35$		0			0
$36$	−0.366025	+	0.633975i	−0.0610042	+	0.105662i
$37$	−1.87397	+	3.24581i	−0.308078	+	0.533607i	−0.977942	−	0.208877i	$-0.933019\pi$
$37$	−1.87397	+	3.24581i	−0.308078	+	0.533607i	0.669864	+	0.742484i	$0.266353\pi$
$38$			5.50045i			0.892291i
$39$	−3.03025	−	1.95387i	−0.485228	−	0.312869i
$40$		0			0
$41$	0.926751	+	0.535060i	0.144734	+	0.0835623i	0.570618	−	0.821215i	$-0.306704\pi$
$41$	0.926751	+	0.535060i	0.144734	+	0.0835623i	−0.425884	+	0.904778i	$0.640037\pi$
$42$	0.590973	+	0.341198i	0.0911890	+	0.0526480i
$43$	−4.33951	+	2.50542i	−0.661770	+	0.382073i	−0.792951	−	0.609285i	$-0.791456\pi$
$43$	−4.33951	+	2.50542i	−0.661770	+	0.382073i	0.131181	+	0.991358i	$0.458123\pi$
$44$			2.25207i			0.339512i
$45$		0			0
$46$	1.81805	−	1.04965i	0.268058	−	0.154763i
$47$	10.2024			1.48817			0.744087	−	0.668082i	$-0.232885\pi$
$47$	10.2024			1.48817			0.744087	+	0.668082i	$0.232885\pi$
$48$	−1.73205	+	1.00000i	−0.250000	+	0.144338i
$49$	3.31637	−	5.74412i	0.473767	−	0.820589i
$50$		0			0
$51$	1.95035			0.273103
$52$	1.20593	+	2.34785i	0.167233	+	0.325588i
$53$			10.6569i			1.46384i	0.681393	+	0.731918i	$0.261375\pi$
$53$			10.6569i			1.46384i	−0.681393	+	0.731918i	$0.738625\pi$
$54$	0.975173	+	0.563016i	0.132704	+	0.0766168i
$55$		0			0
$56$	−0.932171	−	1.61457i	−0.124567	−	0.215756i
$57$	−4.88481			−0.647008
$58$	−1.56615	−	2.71264i	−0.205645	−	0.356188i
$59$	−10.0236	+	5.78712i	−1.30496	+	0.753419i	−0.981251	−	0.192737i	$-0.938264\pi$
$59$	−10.0236	+	5.78712i	−1.30496	+	0.753419i	−0.323710	+	0.946156i	$0.604930\pi$
$60$		0			0
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	0.993879	−	0.110476i	$-0.0352375\pi$
$61$	3.13397	+	5.42820i	0.401264	+	0.695010i	−0.592614	+	0.805486i	$0.701904\pi$
$62$	−8.92552	−	5.15315i	−1.13354	−	0.654451i
$63$	−0.303009	+	0.524827i	−0.0381756	+	0.0661220i
$64$	8.39230			1.04904
$65$		0			0
$66$	3.46410			0.426401
$67$	0.988929	−	1.71288i	0.120817	−	0.209261i	−0.799273	−	0.600968i	$-0.794782\pi$
$67$	0.988929	−	1.71288i	0.120817	−	0.209261i	0.920090	+	0.391707i	$0.128115\pi$
$68$	−1.23647	−	0.713876i	−0.149944	−	0.0865702i
$69$	0.932171	+	1.61457i	0.112220	+	0.194371i
$70$		0			0
$71$	−5.11557	+	2.95347i	−0.607106	+	0.350513i	−0.771832	−	0.635826i	$-0.780659\pi$
$71$	−5.11557	+	2.95347i	−0.607106	+	0.350513i	0.164726	+	0.986339i	$0.447326\pi$
$72$	−1.53819	−	2.66422i	−0.181277	−	0.313982i
$73$	−4.35395			−0.509592			−0.254796	−	0.966995i	$-0.582008\pi$
$73$	−4.35395			−0.509592			−0.254796	+	0.966995i	$0.582008\pi$
$74$	−2.11015	−	3.65488i	−0.245300	−	0.424872i
$75$		0			0
$76$	3.09684	+	1.78796i	0.355232	+	0.205093i
$77$			1.86434i			0.212461i
$78$	3.61144	−	1.85495i	0.408915	−	0.210032i
$79$	3.29546			0.370768			0.185384	−	0.982666i	$-0.440647\pi$
$79$	3.29546			0.370768			0.185384	+	0.982666i	$0.440647\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.04355	+	0.602495i	−0.115241	+	0.0665344i
$83$	−6.97707			−0.765833			−0.382916	−	0.923783i	$-0.625080\pi$
$83$	−6.97707			−0.765833			−0.382916	+	0.923783i	$0.625080\pi$
$84$	0.384200	−	0.221818i	0.0419197	−	0.0242023i
$85$		0			0
$86$		−	5.64237i		−	0.608432i
$87$	2.40903	−	1.39085i	0.258275	−	0.149115i
$88$	−8.19615	−	4.73205i	−0.873713	−	0.504438i
$89$	−14.1156	−	8.14963i	−1.49625	−	0.863859i	−0.496257	−	0.868176i	$-0.665292\pi$
$89$	−14.1156	−	8.14963i	−1.49625	−	0.863859i	−0.999991	+	0.00431721i	$0.998626\pi$
$90$		0			0
$91$	0.998316	+	1.94364i	0.104652	+	0.203748i
$92$		−	1.36479i		−	0.142289i
$93$	4.57638	−	7.92652i	0.474548	−	0.821942i
$94$	−5.74412	+	9.94911i	−0.592461	+	1.02617i
$95$		0			0
$96$			3.90069i			0.398113i
$97$	6.60121	+	11.4336i	0.670251	+	1.16091i	0.977833	+	0.209387i	$0.0671468\pi$
$97$	6.60121	+	11.4336i	0.670251	+	1.16091i	−0.307582	+	0.951522i	$0.599520\pi$
$98$	3.73434	+	6.46807i	0.377225	+	0.653374i
$99$			3.07638i			0.309188i
$100$		0			0
$101$	−3.93217	+	6.81072i	−0.391266	+	0.677692i	−0.992617	−	0.121293i	$-0.961296\pi$
$101$	−3.93217	+	6.81072i	−0.391266	+	0.677692i	0.601351	+	0.798985i	$0.294629\pi$
$102$	−1.09808	+	1.90192i	−0.108726	+	0.188319i
$103$			15.1101i			1.48885i	0.667708	+	0.744424i	$0.267276\pi$
$103$			15.1101i			1.48885i	−0.667708	+	0.744424i	$0.732724\pi$
$104$	−11.0787	−	0.544447i	−1.08635	−	0.0533874i
$105$		0			0
$106$	−10.3923	−	6.00000i	−1.00939	−	0.582772i
$107$	7.10746	+	4.10350i	0.687104	+	0.396700i	0.802526	−	0.596617i	$-0.203489\pi$
$107$	7.10746	+	4.10350i	0.687104	+	0.396700i	−0.115422	+	0.993317i	$0.536822\pi$
$108$	0.633975	−	0.366025i	0.0610042	−	0.0352208i
$109$		−	10.5927i		−	1.01460i	−0.861770	−	0.507299i	$-0.830644\pi$
$109$		−	10.5927i		−	1.01460i	0.861770	−	0.507299i	$-0.169356\pi$
$110$		0			0
$111$	3.24581	−	1.87397i	0.308078	−	0.177869i
$112$	1.21204			0.114527
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	−0.634426	−	0.772983i	$-0.718764\pi$
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	0.352210	+	0.935921i	$0.385430\pi$
$114$	2.75023	−	4.76353i	0.257582	−	0.446146i
$115$		0			0
$116$	−2.03635			−0.189070
$117$	1.64734	+	3.20722i	0.152296	+	0.296508i
$118$		−	13.0330i		−	1.19978i
$119$	−1.02359	−	0.590973i	−0.0938328	−	0.0541744i
$120$		0			0
$121$	−0.767949	−	1.33013i	−0.0698136	−	0.120921i
$122$	−7.05791			−0.638994
$123$	−0.535060	−	0.926751i	−0.0482447	−	0.0835623i
$124$	−5.80261	+	3.35014i	−0.521090	+	0.300852i
$125$		0			0
$126$	−0.341198	−	0.590973i	−0.0303963	−	0.0526480i
$127$	15.6264	+	9.02191i	1.38662	+	0.800565i	0.992933	−	0.118680i	$-0.0378661\pi$
$127$	15.6264	+	9.02191i	1.38662	+	0.800565i	0.393687	+	0.919245i	$0.371199\pi$
$128$	−0.824313	+	1.42775i	−0.0728597	+	0.126197i
$129$	5.01084			0.441180
$130$		0			0
$131$	1.11899			0.0977662			0.0488831	−	0.998805i	$-0.484434\pi$
$131$	1.11899			0.0977662			0.0488831	+	0.998805i	$0.484434\pi$
$132$	1.12603	−	1.95035i	0.0980085	−	0.169756i
$133$	2.56368	+	1.48014i	0.222299	+	0.128345i
$134$	1.11357	+	1.92875i	0.0961975	+	0.166619i
$135$		0			0
$136$	5.19615	−	3.00000i	0.445566	−	0.257248i
$137$	−4.35327	−	7.54009i	−0.371925	−	0.644193i	0.617937	−	0.786228i	$-0.287969\pi$
$137$	−4.35327	−	7.54009i	−0.371925	−	0.644193i	−0.989862	+	0.142035i	$0.954635\pi$
$138$	−2.09931			−0.178705
$139$	4.82844	+	8.36311i	0.409543	+	0.709350i	0.994839	−	0.101471i	$-0.0323548\pi$
$139$	4.82844	+	8.36311i	0.409543	+	0.709350i	−0.585295	+	0.810820i	$0.699021\pi$
$140$		0			0
$141$	−8.83555	−	5.10121i	−0.744087	−	0.429599i
$142$		−	6.65142i		−	0.558174i
$143$	9.32218	+	6.01084i	0.779560	+	0.502652i
$144$	2.00000			0.166667
$145$		0			0
$146$	2.45135	−	4.24586i	0.202875	−	0.351390i
$147$	−5.74412	+	3.31637i	−0.473767	+	0.273530i
$148$	−2.74368			−0.225529
$149$	−4.48228	+	2.58784i	−0.367202	+	0.212004i	−0.672236	−	0.740337i	$-0.734666\pi$
$149$	−4.48228	+	2.58784i	−0.367202	+	0.212004i	0.305033	+	0.952342i	$0.401332\pi$
$150$		0			0
$151$		−	22.1451i		−	1.80215i	−0.433668	−	0.901073i	$-0.642781\pi$
$151$		−	22.1451i		−	1.80215i	0.433668	−	0.901073i	$-0.357219\pi$
$152$	−13.0142	+	7.51376i	−1.05559	+	0.609446i
$153$	−1.68905	−	0.975173i	−0.136551	−	0.0788380i
$154$	−1.81805	−	1.04965i	−0.146503	−	0.0845836i
$155$		0			0
$156$	0.129556	−	2.63627i	0.0103728	−	0.211070i
$157$		−	14.3756i		−	1.14730i	−0.819100	−	0.573650i	$-0.805527\pi$
$157$		−	14.3756i		−	1.14730i	0.819100	−	0.573650i	$-0.194473\pi$
$158$	−1.85540	+	3.21364i	−0.147608	+	0.255664i
$159$	5.32844	−	9.22913i	0.422573	−	0.731918i
$160$		0			0
$161$		−	1.12983i		−	0.0890427i
$162$	−0.563016	−	0.975173i	−0.0442347	−	0.0766168i
$163$	5.03506	+	8.72098i	0.394376	+	0.683080i	0.993021	−	0.117935i	$-0.0376273\pi$
$163$	5.03506	+	8.72098i	0.394376	+	0.683080i	−0.598645	+	0.801014i	$0.704294\pi$
$164$			0.783382i			0.0611719i
$165$		0			0
$166$	3.92820	−	6.80385i	0.304888	−	0.528081i
$167$	5.42149	−	9.39030i	0.419528	−	0.726643i	−0.576364	−	0.817193i	$-0.695529\pi$
$167$	5.42149	−	9.39030i	0.419528	−	0.726643i	0.995892	+	0.0905495i	$0.0288623\pi$
$168$			1.86434i			0.143837i
$169$	12.9374	+	1.27466i	0.995181	+	0.0980507i
$170$		0			0
$171$	4.23037	+	2.44240i	0.323504	+	0.186775i
$172$	−3.17674	−	1.83409i	−0.242225	−	0.139848i
$173$	21.3581	−	12.3311i	1.62383	−	0.937518i	0.637947	−	0.770081i	$-0.279784\pi$
$173$	21.3581	−	12.3311i	1.62383	−	0.937518i	0.985883	−	0.167438i	$-0.0535493\pi$
$174$			3.13229i			0.237458i
$175$		0			0
$176$	5.32844	−	3.07638i	0.401647	−	0.231891i
$177$	11.5742			0.869974
$178$	15.8946	−	9.17674i	1.19135	−	0.687826i
$179$	11.4199	−	19.7798i	0.853561	−	1.47841i	−0.0244128	−	0.999702i	$-0.507772\pi$
$179$	11.4199	−	19.7798i	0.853561	−	1.47841i	0.877974	−	0.478709i	$-0.158895\pi$
$180$		0			0
$181$	−17.4616			−1.29791			−0.648957	−	0.760825i	$-0.724794\pi$
$181$	−17.4616			−1.29791			−0.648957	+	0.760825i	$0.724794\pi$
$182$	−2.45745	−	0.120768i	−0.182158	−	0.00895194i
$183$		−	6.26795i		−	0.463340i
$184$	4.96702	+	2.86771i	0.366173	+	0.211410i
$185$		0			0
$186$	5.15315	+	8.92552i	0.377847	+	0.654451i
$187$	−6.00000			−0.438763
$188$	3.73434	+	6.46807i	0.272355	+	0.471732i
$189$	0.524827	−	0.303009i	0.0381756	−	0.0220407i
$190$		0			0
$191$	−3.83678	−	6.64550i	−0.277620	−	0.480851i	0.693173	−	0.720771i	$-0.256212\pi$
$191$	−3.83678	−	6.64550i	−0.277620	−	0.480851i	−0.970793	+	0.239920i	$0.922879\pi$
$192$	−7.26795	−	4.19615i	−0.524519	−	0.302831i
$193$	10.5054	−	18.1959i	0.756197	−	1.30977i	−0.188581	−	0.982058i	$-0.560389\pi$
$193$	10.5054	−	18.1959i	0.756197	−	1.30977i	0.944777	−	0.327713i	$-0.106278\pi$
$194$	−14.8663			−1.06734
$195$		0			0
$196$	4.85550			0.346822
$197$	10.1888	−	17.6475i	0.725923	−	1.25734i	−0.232670	−	0.972556i	$-0.574746\pi$
$197$	10.1888	−	17.6475i	0.725923	−	1.25734i	0.958593	−	0.284780i	$-0.0919205\pi$
$198$	−3.00000	−	1.73205i	−0.213201	−	0.123091i
$199$	7.40069	+	12.8184i	0.524621	+	0.908670i	0.999589	+	0.0286673i	$0.00912632\pi$
$199$	7.40069	+	12.8184i	0.524621	+	0.908670i	−0.474968	+	0.880003i	$0.657540\pi$
$200$		0			0
$201$	−1.71288	+	0.988929i	−0.120817	+	0.0697537i
$202$	−4.42775	−	7.66909i	−0.311536	−	0.539595i
$203$	−1.68576			−0.118317
$204$	0.713876	+	1.23647i	0.0499813	+	0.0865702i
$205$		0			0
$206$	−14.7350	−	8.50726i	−1.02664	−	0.592729i
$207$		−	1.86434i		−	0.129581i
$208$	3.90774	−	6.06049i	0.270953	−	0.420220i
$209$	15.0275			1.03947
$210$		0			0
$211$	−2.61015	+	4.52091i	−0.179690	+	0.311232i	−0.941774	−	0.336246i	$-0.890843\pi$
$211$	−2.61015	+	4.52091i	−0.179690	+	0.311232i	0.762084	+	0.647478i	$0.224176\pi$
$212$	−6.75620	+	3.90069i	−0.464017	+	0.267901i
$213$	5.90695			0.404737
$214$	−8.00323	+	4.62067i	−0.547090	+	0.315862i
$215$		0			0
$216$			3.07638i			0.209321i
$217$	−4.80362	+	2.77337i	−0.326091	+	0.188269i
$218$	10.3297	+	5.96387i	0.699617	+	0.403924i
$219$	3.77063	+	2.17698i	0.254796	+	0.147106i
$220$		0			0
$221$	−6.25519	+	3.21288i	−0.420770	+	0.216121i
$222$			4.22030i			0.283248i
$223$	3.08342	−	5.34065i	0.206481	−	0.357636i	−0.744122	−	0.668043i	$-0.767132\pi$
$223$	3.08342	−	5.34065i	0.206481	−	0.357636i	0.950604	+	0.310407i	$0.100465\pi$
$224$	1.18195	−	2.04719i	0.0789720	−	0.136784i
$225$		0			0
$226$		−	3.90069i		−	0.259470i
$227$	8.55568	+	14.8189i	0.567860	+	0.983563i	0.996777	+	0.0802192i	$0.0255620\pi$
$227$	8.55568	+	14.8189i	0.567860	+	0.983563i	−0.428917	+	0.903344i	$0.641105\pi$
$228$	−1.78796	−	3.09684i	−0.118411	−	0.205093i
$229$		−	28.9206i		−	1.91113i	−0.294788	−	0.955563i	$-0.595249\pi$
$229$		−	28.9206i		−	1.91113i	0.294788	−	0.955563i	$-0.404751\pi$
$230$		0			0
$231$	0.932171	−	1.61457i	0.0613323	−	0.106231i
$232$	4.27879	−	7.41108i	0.280916	−	0.486561i
$233$			11.3284i			0.742151i	0.928603	+	0.371075i	$0.121011\pi$
$233$			11.3284i			0.742151i	−0.928603	+	0.371075i	$0.878989\pi$
$234$	−4.05507	−	0.199281i	−0.265088	−	0.0130274i
$235$		0			0
$236$	−7.33778	−	4.23647i	−0.477649	−	0.275771i
$237$	−2.85395	−	1.64773i	−0.185384	−	0.107032i
$238$	1.15260	−	0.665454i	0.0747120	−	0.0431350i
$239$			19.1298i			1.23741i	0.785625	+	0.618703i	$0.212341\pi$
$239$			19.1298i			1.23741i	−0.785625	+	0.618703i	$0.787659\pi$
$240$		0			0
$241$	4.74075	−	2.73708i	0.305379	−	0.176311i	−0.339478	−	0.940614i	$-0.610250\pi$
$241$	4.74075	−	2.73708i	0.305379	−	0.176311i	0.644857	+	0.764303i	$0.276917\pi$
$242$	1.72947			0.111175
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−2.29423	+	3.97372i	−0.146873	+	0.254391i
$245$		0			0
$246$	1.20499			0.0768273
$247$	15.6667	−	8.04692i	0.996846	−	0.512013i
$248$		−	28.1573i		−	1.78799i
$249$	6.04232	+	3.48853i	0.382916	+	0.221077i
$250$		0			0
$251$	2.35992	+	4.08751i	0.148957	+	0.258001i	0.930842	−	0.365421i	$-0.119075\pi$
$251$	2.35992	+	4.08751i	0.148957	+	0.258001i	−0.781885	+	0.623422i	$0.785742\pi$
$252$	−0.443636			−0.0279465
$253$	−2.86771	−	4.96702i	−0.180291	−	0.312274i
$254$	−17.5958	+	10.1590i	−1.10406	+	0.637430i
$255$		0			0
$256$	7.46410	+	12.9282i	0.466506	+	0.808013i
$257$	6.30362	+	3.63939i	0.393209	+	0.227019i	0.683550	−	0.729904i	$-0.260435\pi$
$257$	6.30362	+	3.63939i	0.393209	+	0.227019i	−0.290341	+	0.956923i	$0.593769\pi$
$258$	−2.82118	+	4.88643i	−0.175639	+	0.304216i
$259$	−2.27132			−0.141133
$260$		0			0
$261$	−2.78171			−0.172183
$262$	−0.630007	+	1.09120i	−0.0389220	+	0.0674148i
$263$	−1.11434	−	0.643362i	−0.0687129	−	0.0396714i	0.465250	−	0.885179i	$-0.345964\pi$
$263$	−1.11434	−	0.643362i	−0.0687129	−	0.0396714i	−0.533963	+	0.845508i	$0.679298\pi$
$264$	4.73205	+	8.19615i	0.291238	+	0.504438i
$265$		0			0
$266$	−2.88679	+	1.66669i	−0.177000	+	0.102191i
$267$	8.14963	+	14.1156i	0.498749	+	0.863859i
$268$	1.44789			0.0884441
$269$	9.46952	+	16.4017i	0.577367	+	1.00003i	0.995780	+	0.0917720i	$0.0292531\pi$
$269$	9.46952	+	16.4017i	0.577367	+	1.00003i	−0.418413	+	0.908257i	$0.637414\pi$
$270$		0			0
$271$	9.54719	+	5.51207i	0.579950	+	0.334835i	0.761114	−	0.648619i	$-0.224653\pi$
$271$	9.54719	+	5.51207i	0.579950	+	0.334835i	−0.181163	+	0.983453i	$0.557986\pi$
$272$			3.90069i			0.236514i
$273$	0.107251	−	2.18240i	0.00649113	−	0.132085i
$274$	9.80385			0.592272
$275$		0			0
$276$	−0.682396	+	1.18195i	−0.0410754	+	0.0711447i
$277$	−18.1185	+	10.4607i	−1.08864	+	0.628525i	−0.933213	−	0.359323i	$-0.883008\pi$
$277$	−18.1185	+	10.4607i	−1.08864	+	0.628525i	−0.155423	+	0.987848i	$0.549674\pi$
$278$	−10.8740			−0.652177
$279$	−7.92652	+	4.57638i	−0.474548	+	0.273981i
$280$		0			0
$281$		−	10.6653i		−	0.636238i	−0.948051	−	0.318119i	$-0.896949\pi$
$281$		−	10.6653i		−	0.636238i	0.948051	−	0.318119i	$-0.103051\pi$
$282$	9.94911	−	5.74412i	0.592461	−	0.342058i
$283$	−2.41194	−	1.39254i	−0.143375	−	0.0827777i	0.426596	−	0.904442i	$-0.359712\pi$
$283$	−2.41194	−	1.39254i	−0.143375	−	0.0827777i	−0.569972	+	0.821664i	$0.693046\pi$
$284$	−3.74486	−	2.16209i	−0.222216	−	0.128297i
$285$		0			0
$286$	−11.1101	+	5.70654i	−0.656957	+	0.337435i
$287$			0.648512i			0.0382805i
$288$	1.95035	−	3.37810i	0.114925	−	0.199056i
$289$	−6.59808	+	11.4282i	−0.388122	+	0.672247i
$290$		0			0
$291$		−	13.2024i		−	0.773939i
$292$	−1.59366	−	2.76030i	−0.0932618	−	0.161534i
$293$	−2.47930	−	4.29428i	−0.144842	−	0.250874i	0.784472	−	0.620165i	$-0.212934\pi$
$293$	−2.47930	−	4.29428i	−0.144842	−	0.250874i	−0.929314	+	0.369290i	$0.879601\pi$
$294$		−	7.46868i		−	0.435582i
$295$		0			0
$296$	5.76503	−	9.98533i	0.335086	−	0.580385i
$297$	1.53819	−	2.66422i	0.0892548	−	0.154594i
$298$		−	5.82799i		−	0.337606i
$299$	−5.64941	−	3.64268i	−0.326714	−	0.210662i
$300$		0			0
$301$	−2.62983	−	1.51833i	−0.151581	−	0.0875151i
$302$	21.5953	+	12.4681i	1.24267	+	0.717457i
$303$	6.81072	−	3.93217i	0.391266	−	0.225897i
$304$		−	9.76961i		−	0.560326i
$305$		0			0
$306$	1.90192	−	1.09808i	0.108726	−	0.0627728i
$307$	−9.60723			−0.548314			−0.274157	−	0.961685i	$-0.588399\pi$
$307$	−9.60723			−0.548314			−0.274157	+	0.961685i	$0.588399\pi$
$308$	−1.18195	+	0.682396i	−0.0673476	+	0.0388831i
$309$	7.55507	−	13.0858i	0.429793	−	0.744424i
$310$		0			0
$311$	26.0393			1.47655			0.738275	−	0.674499i	$-0.235641\pi$
$311$	26.0393			1.47655			0.738275	+	0.674499i	$0.235641\pi$
$312$	9.32218	+	6.01084i	0.527765	+	0.340297i
$313$		−	29.2311i		−	1.65224i	−0.563493	−	0.826121i	$-0.690543\pi$
$313$		−	29.2311i		−	1.65224i	0.563493	−	0.826121i	$-0.309457\pi$
$314$	14.0187	+	8.09371i	0.791122	+	0.456755i
$315$		0			0
$316$	1.20622	+	2.08924i	0.0678553	+	0.117529i
$317$	8.62570			0.484467			0.242234	−	0.970218i	$-0.422120\pi$
$317$	8.62570			0.484467			0.242234	+	0.970218i	$0.422120\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$	−7.41108	+	4.27879i	−0.414941	+	0.239566i
$320$		0			0
$321$	−4.10350	−	7.10746i	−0.229035	−	0.396700i
$322$	1.10177	+	0.636110i	0.0613995	+	0.0354490i
$323$	−4.76353	+	8.25068i	−0.265050	+	0.459080i
$324$	−0.732051			−0.0406695
$325$		0			0
$326$	−11.3393			−0.628025
$327$	−5.29636	+	9.17356i	−0.292889	+	0.507299i
$328$	−2.85104	−	1.64605i	−0.157422	−	0.0908877i
$329$	3.09142	+	5.35450i	0.170436	+	0.295203i
$330$		0			0
$331$	17.5822	−	10.1511i	0.966404	−	0.557953i	0.0682657	−	0.997667i	$-0.478253\pi$
$331$	17.5822	−	10.1511i	0.966404	−	0.557953i	0.898138	+	0.439714i	$0.144920\pi$
$332$	−2.55378	−	4.42328i	−0.140157	−	0.242759i
$333$	−3.74793			−0.205386
$334$	6.10478	+	10.5738i	0.334039	+	0.578572i
$335$		0			0
$336$	−1.04965	−	0.606018i	−0.0572633	−	0.0330610i
$337$			17.7847i			0.968795i	0.874848	+	0.484397i	$0.160961\pi$
$337$			17.7847i			0.968795i	−0.874848	+	0.484397i	$0.839039\pi$
$338$	−8.52696	+	11.8985i	−0.463805	+	0.647193i
$339$	3.46410			0.188144
$340$		0			0
$341$	−14.0787	+	24.3850i	−0.762403	+	1.32052i
$342$	−4.76353	+	2.75023i	−0.257582	+	0.148715i
$343$	8.26169			0.446089
$344$	13.3500	−	7.70762i	0.719783	−	0.415567i
$345$		0			0
$346$			27.7705i			1.49295i
$347$	7.43996	−	4.29546i	0.399398	−	0.230592i	−0.286826	−	0.957983i	$-0.592600\pi$
$347$	7.43996	−	4.29546i	0.399398	−	0.230592i	0.686224	+	0.727390i	$0.259267\pi$
$348$	1.76353	+	1.01817i	0.0945352	+	0.0545799i
$349$	−26.1369	−	15.0901i	−1.39908	−	0.807756i	−0.404779	−	0.914414i	$-0.632652\pi$
$349$	−26.1369	−	15.0901i	−1.39908	−	0.807756i	−0.994296	+	0.106658i	$0.965985\pi$
$350$		0			0
$351$	0.176977	−	3.60121i	0.00944631	−	0.192218i
$352$		−	12.0000i		−	0.639602i
$353$	14.3148	−	24.7940i	0.761903	−	1.31965i	−0.179966	−	0.983673i	$-0.557599\pi$
$353$	14.3148	−	24.7940i	0.761903	−	1.31965i	0.941869	−	0.335981i	$-0.109068\pi$
$354$	−6.51649	+	11.2869i	−0.346348	+	0.599892i
$355$		0			0
$356$		−	11.9319i		−	0.632388i
$357$	0.590973	+	1.02359i	0.0312776	+	0.0541744i
$358$	12.8591	+	22.2727i	0.679627	+	1.17715i
$359$		−	17.4624i		−	0.921632i	−0.887496	−	0.460816i	$-0.847557\pi$
$359$		−	17.4624i		−	0.921632i	0.887496	−	0.460816i	$-0.152443\pi$
$360$		0			0
$361$	2.43067	−	4.21004i	0.127930	−	0.221581i
$362$	9.83118	−	17.0281i	0.516716	−	0.894978i
$363$			1.53590i			0.0806138i
$364$	−0.866807	+	1.34433i	−0.0454330	+	0.0704619i
$365$		0			0
$366$	6.11233	+	3.52896i	0.319497	+	0.184462i
$367$	−28.1429	−	16.2483i	−1.46905	−	0.848155i	−0.469649	−	0.882853i	$-0.655620\pi$
$367$	−28.1429	−	16.2483i	−1.46905	−	0.848155i	−0.999398	+	0.0346981i	$0.988953\pi$
$368$	−3.22913	+	1.86434i	−0.168330	+	0.0971855i
$369$			1.07012i			0.0557082i
$370$		0			0
$371$	−5.59302	+	3.22913i	−0.290375	+	0.167648i
$372$	6.70028			0.347393
$373$	−9.31127	+	5.37586i	−0.482119	+	0.278352i	−0.721299	−	0.692624i	$-0.756455\pi$
$373$	−9.31127	+	5.37586i	−0.482119	+	0.278352i	0.239180	+	0.970975i	$0.423121\pi$
$374$	3.37810	−	5.85104i	0.174677	−	0.302550i
$375$		0			0
$376$	−31.3865			−1.61863
$377$	−5.43509	+	8.42925i	−0.279921	+	0.434129i
$378$			0.682396i			0.0350987i
$379$	−5.05881	−	2.92071i	−0.259854	−	0.150027i	0.364414	−	0.931237i	$-0.381269\pi$
$379$	−5.05881	−	2.92071i	−0.259854	−	0.150027i	−0.624268	+	0.781210i	$0.714603\pi$
$380$		0			0
$381$	−9.02191	−	15.6264i	−0.462206	−	0.800565i
$382$	8.64068			0.442095
$383$	11.8220	+	20.4762i	0.604074	+	1.04629i	0.992197	+	0.124679i	$0.0397900\pi$
$383$	11.8220	+	20.4762i	0.604074	+	1.04629i	−0.388124	+	0.921607i	$0.626877\pi$
$384$	1.42775	−	0.824313i	0.0728597	−	0.0420655i
$385$		0			0
$386$	11.8294	+	20.4892i	0.602103	+	1.04287i
$387$	−4.33951	−	2.50542i	−0.220590	−	0.127358i
$388$	−4.83242	+	8.36999i	−0.245329	+	0.424922i
$389$	16.5939			0.841345			0.420673	−	0.907212i	$-0.361794\pi$
$389$	16.5939			0.841345			0.420673	+	0.907212i	$0.361794\pi$
$390$		0			0
$391$	3.63611			0.183886
$392$	−10.2024	+	17.6711i	−0.515300	+	0.892525i
$393$	−0.969070	−	0.559493i	−0.0488831	−	0.0282227i
$394$	11.4729	+	19.8717i	0.577998	+	1.00112i
$395$		0			0
$396$	−1.95035	+	1.12603i	−0.0980085	+	0.0565853i
$397$	−11.7017	−	20.2680i	−0.587293	−	1.01722i	−0.994585	−	0.103923i	$-0.966860\pi$
$397$	−11.7017	−	20.2680i	−0.587293	−	1.01722i	0.407292	−	0.913298i	$-0.366473\pi$
$398$	−16.6668			−0.835433
$399$	−1.48014	−	2.56368i	−0.0740997	−	0.128345i
$400$		0			0
$401$	0.0968434	+	0.0559126i	0.00483613	+	0.00279214i	0.502416	−	0.864626i	$-0.332445\pi$
$401$	0.0968434	+	0.0559126i	0.00483613	+	0.00279214i	−0.497580	+	0.867418i	$0.665778\pi$
$402$		−	2.22713i		−	0.111079i
$403$	−1.61982	+	32.9610i	−0.0806892	+	1.64190i
$404$	−5.75710			−0.286426
$405$		0			0
$406$	0.949113	−	1.64391i	0.0471037	−	0.0815860i
$407$	−9.98533	+	5.76503i	−0.494954	+	0.285762i
$408$	−6.00000			−0.297044
$409$	−16.6974	+	9.64024i	−0.825633	+	0.476679i	−0.852355	−	0.522964i	$-0.824826\pi$
$409$	−16.6974	+	9.64024i	−0.825633	+	0.476679i	0.0267224	+	0.999643i	$0.491493\pi$
$410$		0			0
$411$			8.70654i			0.429462i
$412$	−9.57945	+	5.53070i	−0.471946	+	0.272478i
$413$	−6.07448	−	3.50710i	−0.298906	−	0.172573i
$414$	1.81805	+	1.04965i	0.0893525	+	0.0515877i
$415$		0			0
$416$	−6.42575	−	12.5104i	−0.315048	−	0.613372i
$417$		−	9.65689i		−	0.472900i
$418$	−8.46073	+	14.6544i	−0.413828	+	0.716771i
$419$	11.0693	−	19.1726i	0.540770	−	0.936641i	−0.458090	−	0.888906i	$-0.651466\pi$
$419$	11.0693	−	19.1726i	0.540770	−	0.936641i	0.998860	−	0.0477351i	$-0.0152003\pi$
$420$		0			0
$421$			0.914785i			0.0445839i	0.999752	+	0.0222919i	$0.00709633\pi$
$421$			0.914785i			0.0445839i	−0.999752	+	0.0222919i	$0.992904\pi$
$422$	−2.93911	−	5.09069i	−0.143074	−	0.247811i
$423$	5.10121	+	8.83555i	0.248029	+	0.429599i
$424$		−	32.7846i		−	1.59216i
$425$		0			0
$426$	−3.32571	+	5.76030i	−0.161131	+	0.279087i
$427$	−1.89925	+	3.28959i	−0.0919110	+	0.159194i
$428$			6.00793i			0.290404i
$429$	−5.06783	−	9.86663i	−0.244677	−	0.476365i
$430$		0			0
$431$	32.0231	+	18.4885i	1.54250	+	0.890561i	0.998680	+	0.0513577i	$0.0163549\pi$
$431$	32.0231	+	18.4885i	1.54250	+	0.890561i	0.543817	+	0.839204i	$0.316978\pi$
$432$	−1.73205	−	1.00000i	−0.0833333	−	0.0481125i
$433$	−24.8461	+	14.3449i	−1.19403	+	0.689371i	−0.959217	−	0.282670i	$-0.908780\pi$
$433$	−24.8461	+	14.3449i	−1.19403	+	0.689371i	−0.234809	+	0.972042i	$0.575446\pi$
$434$		−	6.24581i		−	0.299808i
$435$		0			0
$436$	6.71551	−	3.87720i	0.321615	−	0.185684i
$437$	−9.10695			−0.435644
$438$	−4.24586	+	2.45135i	−0.202875	+	0.117130i
$439$	−2.63106	+	4.55713i	−0.125574	+	0.217500i	−0.921957	−	0.387292i	$-0.873410\pi$
$439$	−2.63106	+	4.55713i	−0.125574	+	0.217500i	0.796383	+	0.604792i	$0.206744\pi$
$440$		0			0
$441$	6.63274			0.315845
$442$	0.388668	−	7.90880i	0.0184870	−	0.376183i
$443$		−	28.8275i		−	1.36964i	−0.728714	−	0.684819i	$-0.759881\pi$
$443$		−	28.8275i		−	1.36964i	0.728714	−	0.684819i	$-0.240119\pi$
$444$	2.37610	+	1.37184i	0.112765	+	0.0651046i
$445$		0			0
$446$	3.47204	+	6.01374i	0.164406	+	0.284759i
$447$	5.17569			0.244802
$448$	2.54295	+	4.40451i	0.120143	+	0.208094i
$449$	−2.60523	+	1.50413i	−0.122948	+	0.0709843i	−0.560213	−	0.828349i	$-0.689281\pi$
$449$	−2.60523	+	1.50413i	−0.122948	+	0.0709843i	0.437265	+	0.899333i	$0.355947\pi$
$450$		0			0
$451$	1.64605	+	2.85104i	0.0775093	+	0.134250i
$452$	−2.19615	−	1.26795i	−0.103298	−	0.0596393i
$453$	−11.0726	+	19.1782i	−0.520235	+	0.901073i
$454$	−19.2679			−0.904290
$455$		0			0
$456$	15.0275			0.703728
$457$	−4.44340	+	7.69620i	−0.207854	+	0.360013i	−0.951038	−	0.309073i	$-0.899981\pi$
$457$	−4.44340	+	7.69620i	−0.207854	+	0.360013i	0.743185	+	0.669087i	$0.233314\pi$
$458$	28.2026	+	16.2828i	1.31782	+	0.760843i
$459$	0.975173	+	1.68905i	0.0455172	+	0.0788380i
$460$		0			0
$461$	−18.2808	+	10.5544i	−0.851424	+	0.491570i	−0.861131	−	0.508383i	$-0.830243\pi$
$461$	−18.2808	+	10.5544i	−0.851424	+	0.491570i	0.00970733	+	0.999953i	$0.496910\pi$
$462$	1.04965	+	1.81805i	0.0488343	+	0.0845836i
$463$	−24.4679			−1.13712			−0.568560	−	0.822642i	$-0.692499\pi$
$463$	−24.4679			−1.13712			−0.568560	+	0.822642i	$0.692499\pi$
$464$	2.78171	+	4.81805i	0.129137	+	0.223673i
$465$		0			0
$466$	−11.0472	−	6.37810i	−0.511751	−	0.295460i
$467$			19.5058i			0.902622i	0.892367	+	0.451311i	$0.149043\pi$
$467$			19.5058i			0.902622i	−0.892367	+	0.451311i	$0.850957\pi$
$468$	−1.43033	+	2.21829i	−0.0661171	+	0.102541i
$469$	1.19862			0.0553470
$470$		0			0
$471$	−7.18782	+	12.4497i	−0.331197	+	0.573650i
$472$	30.8364	−	17.8034i	1.41936	−	0.819467i
$473$	−15.4152			−0.708793
$474$	3.21364	−	1.85540i	0.147608	−	0.0852213i
$475$		0			0
$476$		−	0.865244i		−	0.0396584i
$477$	−9.22913	+	5.32844i	−0.422573	+	0.243973i
$478$	−18.6549	−	10.7704i	−0.853255	−	0.492627i
$479$	−23.4090	−	13.5152i	−1.06959	−	0.617526i	−0.141518	−	0.989936i	$-0.545198\pi$
$479$	−23.4090	−	13.5152i	−1.06959	−	0.617526i	−0.928068	+	0.372410i	$0.878531\pi$
$480$		0			0
$481$	−7.32297	+	11.3572i	−0.333899	+	0.517842i
$482$			6.16407i			0.280766i
$483$	−0.564913	+	0.978457i	−0.0257044	+	0.0445213i
$484$	0.562178	−	0.973721i	0.0255535	−	0.0442600i
$485$		0			0
$486$			1.12603i			0.0510779i
$487$	−2.60875	−	4.51849i	−0.118214	−	0.204752i	0.800846	−	0.598870i	$-0.204384\pi$
$487$	−2.60875	−	4.51849i	−0.118214	−	0.204752i	−0.919060	+	0.394118i	$0.871050\pi$
$488$	−9.64129	−	16.6992i	−0.436441	−	0.755937i
$489$		−	10.0701i		−	0.455387i
$490$		0			0
$491$	7.39085	−	12.8013i	0.333545	−	0.577716i	−0.649660	−	0.760225i	$-0.725089\pi$
$491$	7.39085	−	12.8013i	0.333545	−	0.577716i	0.983204	+	0.182509i	$0.0584219\pi$
$492$	0.391691	−	0.678429i	0.0176588	−	0.0305859i
$493$		−	5.42529i		−	0.244343i
$494$	−0.973451	+	19.8083i	−0.0437977	+	0.891215i
$495$		0			0
$496$	15.8530	+	9.15276i	0.711822	+	0.410971i
$497$	−3.10013	−	1.78986i	−0.139060	−	0.0802862i
$498$	−6.80385	+	3.92820i	−0.304888	+	0.176027i
$499$			10.3171i			0.461859i	0.972971	+	0.230929i	$0.0741766\pi$
$499$			10.3171i			0.461859i	−0.972971	+	0.230929i	$0.925823\pi$
$500$		0			0
$501$	−9.39030	+	5.42149i	−0.419528	+	0.242214i
$502$	−5.31470			−0.237207
$503$	−23.0660	+	13.3171i	−1.02846	+	0.593782i	−0.916543	−	0.399936i	$-0.869032\pi$
$503$	−23.0660	+	13.3171i	−1.02846	+	0.593782i	−0.111917	+	0.993718i	$0.535699\pi$
$504$	0.932171	−	1.61457i	0.0415222	−	0.0719185i
$505$		0			0
$506$	6.45827			0.287105
$507$	−10.5668	−	7.57257i	−0.469286	−	0.336309i
$508$			13.2090i			0.586054i
$509$	1.23647	+	0.713876i	0.0548055	+	0.0316420i	0.527152	−	0.849771i	$-0.323260\pi$
$509$	1.23647	+	0.713876i	0.0548055	+	0.0316420i	−0.472347	+	0.881413i	$0.656593\pi$
$510$		0			0
$511$	−1.31929	−	2.28507i	−0.0583619	−	0.101086i
$512$	−20.1069			−0.888608
$513$	−2.44240	−	4.23037i	−0.107835	−	0.186775i
$514$	−7.09808	+	4.09808i	−0.313083	+	0.180758i
$515$		0			0
$516$	1.83409	+	3.17674i	0.0807415	+	0.139848i
$517$	27.1815	+	15.6932i	1.19544	+	0.690188i
$518$	1.27879	−	2.21493i	0.0561867	−	0.0973183i
$519$	−24.6623			−1.08255
$520$		0			0
$521$	12.8623			0.563509			0.281755	−	0.959486i	$-0.409084\pi$
$521$	12.8623			0.563509			0.281755	+	0.959486i	$0.409084\pi$
$522$	1.56615	−	2.71264i	0.0685483	−	0.118729i
$523$	13.0772	+	7.55011i	0.571825	+	0.330143i	0.757878	−	0.652397i	$-0.226236\pi$
$523$	13.0772	+	7.55011i	0.571825	+	0.330143i	−0.186053	+	0.982540i	$0.559570\pi$
$524$	0.409577	+	0.709409i	0.0178925	+	0.0309907i
$525$		0			0
$526$	1.25478	−	0.724446i	0.0547109	−	0.0315874i
$527$	−8.92552	−	15.4595i	−0.388802	−	0.673424i
$528$	−6.15276			−0.267764
$529$	−9.76212	−	16.9085i	−0.424440	−	0.735151i
$530$		0			0
$531$	−10.0236	−	5.78712i	−0.434987	−	0.251140i
$532$			2.16708i			0.0939547i
$533$	3.24273	+	2.09087i	0.140458	+	0.0905658i
$534$	−18.3535			−0.794233
$535$		0			0
$536$	−3.04232	+	5.26945i	−0.131408	+	0.227606i
$537$	−19.7798	+	11.4199i	−0.853561	+	0.492804i
$538$	−21.3260			−0.919428
$539$	17.6711	−	10.2024i	0.761148	−	0.439449i
$540$		0			0
$541$		−	41.1084i		−	1.76739i	−0.468064	−	0.883695i	$-0.655048\pi$
$541$		−	41.1084i		−	1.76739i	0.468064	−	0.883695i	$-0.344952\pi$
$542$	−10.7504	+	6.20677i	−0.461771	+	0.266604i
$543$	15.1222	+	8.73082i	0.648957	+	0.374675i
$544$	6.58846	+	3.80385i	0.282478	+	0.163089i
$545$		0			0
$546$	2.06783	+	1.33331i	0.0884949	+	0.0570605i
$547$			30.1327i			1.28838i	0.764864	+	0.644191i	$0.222806\pi$
$547$			30.1327i			1.28838i	−0.764864	+	0.644191i	$0.777194\pi$
$548$	3.18682	−	5.51973i	0.136134	−	0.235791i
$549$	−3.13397	+	5.42820i	−0.133755	+	0.231670i
$550$		0			0
$551$			13.5881i			0.578872i
$552$	−2.86771	−	4.96702i	−0.122058	−	0.211410i
$553$	0.998555	+	1.72955i	0.0424629	+	0.0735479i
$554$		−	23.5583i		−	1.00089i
$555$		0			0
$556$	−3.53467	+	6.12222i	−0.149903	+	0.259640i
$557$	12.6021	−	21.8274i	0.533966	−	0.924856i	−0.465247	−	0.885181i	$-0.654034\pi$
$557$	12.6021	−	21.8274i	0.533966	−	0.924856i	0.999213	−	0.0396752i	$-0.0126323\pi$
$558$		−	10.3063i		−	0.436301i
$559$	−16.0709	+	8.25454i	−0.679726	+	0.349130i
$560$		0			0
$561$	5.19615	+	3.00000i	0.219382	+	0.126660i
$562$	10.4005	+	6.00474i	0.438719	+	0.253295i
$563$	−6.22913	+	3.59639i	−0.262527	+	0.151570i	−0.625487	−	0.780235i	$-0.715100\pi$
$563$	−6.22913	+	3.59639i	−0.262527	+	0.151570i	0.362960	+	0.931805i	$0.381766\pi$
$564$		−	7.46868i		−	0.314488i
$565$		0			0
$566$	2.71593	−	1.56804i	0.114159	−	0.0659097i
$567$	−0.606018			−0.0254504
$568$	15.7374	−	9.08600i	0.660328	−	0.381240i
$569$	−9.17606	+	15.8934i	−0.384681	+	0.666286i	−0.991725	−	0.128382i	$-0.959022\pi$
$569$	−9.17606	+	15.8934i	−0.384681	+	0.666286i	0.607044	+	0.794668i	$0.292355\pi$
$570$		0			0
$571$	27.5433			1.15265			0.576325	−	0.817221i	$-0.304486\pi$
$571$	27.5433			1.15265			0.576325	+	0.817221i	$0.304486\pi$
$572$	−0.398563	+	8.11015i	−0.0166648	+	0.339102i
$573$			7.67356i			0.320568i
$574$	−0.632411	−	0.365123i	−0.0263963	−	0.0152399i
$575$		0			0
$576$	4.19615	+	7.26795i	0.174840	+	0.302831i
$577$	−19.1378			−0.796715			−0.398358	−	0.917230i	$-0.630420\pi$
$577$	−19.1378			−0.796715			−0.398358	+	0.917230i	$0.630420\pi$
$578$	−7.42965	−	12.8685i	−0.309033	−	0.535260i
$579$	−18.1959	+	10.5054i	−0.756197	+	0.436590i
$580$		0			0
$581$	−2.11412	−	3.66176i	−0.0877083	−	0.151915i
$582$	12.8746	+	7.43317i	0.533671	+	0.308115i
$583$	−16.3923	+	28.3923i	−0.678900	+	1.17589i
$584$	13.3944			0.554264
$585$		0			0
$586$	5.58355			0.230654
$587$	8.78102	−	15.2092i	0.362432	−	0.627750i	−0.625929	−	0.779880i	$-0.715280\pi$
$587$	8.78102	−	15.2092i	0.362432	−	0.627750i	0.988360	+	0.152130i	$0.0486133\pi$
$588$	−4.20499	−	2.42775i	−0.173411	−	0.100119i
$589$	22.3547	+	38.7195i	0.921110	+	1.59541i
$590$		0			0
$591$	−17.6475	+	10.1888i	−0.725923	+	0.419112i
$592$	3.74793	+	6.49161i	0.154039	+	0.266804i
$593$	−28.9248			−1.18780			−0.593901	−	0.804538i	$-0.702413\pi$
$593$	−28.9248			−1.18780			−0.593901	+	0.804538i	$0.702413\pi$
$594$	1.73205	+	3.00000i	0.0710669	+	0.123091i
$595$		0			0
$596$	−3.28125	−	1.89443i	−0.134405	−	0.0775990i
$597$		−	14.8014i		−	0.605780i
$598$	6.73295	−	3.45827i	0.275331	−	0.141419i
$599$	46.1052			1.88381			0.941904	−	0.335882i	$-0.109034\pi$
$599$	46.1052			1.88381			0.941904	+	0.335882i	$0.109034\pi$
$600$		0			0
$601$	9.75496	−	16.8961i	0.397913	−	0.689206i	−0.595555	−	0.803314i	$-0.703068\pi$
$601$	9.75496	−	16.8961i	0.397913	−	0.689206i	0.993468	+	0.114109i	$0.0364012\pi$
$602$	2.96127	−	1.70969i	0.120692	−	0.0696817i
$603$	1.97786			0.0805446
$604$	14.0395	−	8.10568i	0.571257	−	0.329815i
$605$		0			0
$606$			8.85550i			0.359730i
$607$	22.0189	−	12.7126i	0.893721	−	0.515990i	0.0185635	−	0.999828i	$-0.494091\pi$
$607$	22.0189	−	12.7126i	0.893721	−	0.515990i	0.875158	+	0.483837i	$0.160757\pi$
$608$	−16.5014	−	9.52706i	−0.669218	−	0.386373i
$609$	1.45991	+	0.842882i	0.0591587	+	0.0341553i
$610$		0			0
$611$	36.7410	+	1.80559i	1.48638	+	0.0730463i
$612$		−	1.42775i		−	0.0577135i
$613$	16.7285	−	28.9745i	0.675656	−	1.17027i	−0.300621	−	0.953744i	$-0.597194\pi$
$613$	16.7285	−	28.9745i	0.675656	−	1.17027i	0.976277	−	0.216526i	$-0.0694728\pi$
$614$	5.40903	−	9.36871i	0.218291	−	0.378090i
$615$		0			0
$616$		−	5.73542i		−	0.231087i
$617$	6.98015	+	12.0900i	0.281010	+	0.486724i	0.971634	−	0.236490i	$-0.0759972\pi$
$617$	6.98015	+	12.0900i	0.281010	+	0.486724i	−0.690624	+	0.723214i	$0.742664\pi$
$618$	8.50726	+	14.7350i	0.342212	+	0.592729i
$619$		−	42.1677i		−	1.69486i	−0.530904	−	0.847432i	$-0.678148\pi$
$619$		−	42.1677i		−	1.69486i	0.530904	−	0.847432i	$-0.321852\pi$
$620$		0			0
$621$	−0.932171	+	1.61457i	−0.0374067	+	0.0647903i
$622$	−14.6605	+	25.3928i	−0.587833	+	1.01816i
$623$		−	9.87765i		−	0.395740i
$624$	−6.41445	+	3.29467i	−0.256783	+	0.131892i
$625$		0			0
$626$	28.5054	+	16.4576i	1.13931	+	0.657778i
$627$	−13.0142	−	7.51376i	−0.519737	−	0.300071i
$628$	9.11379	−	5.26185i	0.363680	−	0.209971i
$629$		−	7.30977i		−	0.291460i
$630$		0			0
$631$	−34.6143	+	19.9846i	−1.37797	+	0.795573i	−0.991915	−	0.126902i	$-0.959497\pi$
$631$	−34.6143	+	19.9846i	−1.37797	+	0.795573i	−0.386058	+	0.922475i	$0.626163\pi$
$632$	−10.1381			−0.403271
$633$	4.52091	−	2.61015i	0.179690	−	0.103744i
$634$	−4.85641	+	8.41154i	−0.192873	+	0.334065i
$635$		0			0
$636$	7.80138			0.309345
$637$	12.9595	−	20.0988i	0.513474	−	0.796345i
$638$		−	9.63611i		−	0.381497i
$639$	−5.11557	−	2.95347i	−0.202369	−	0.116838i
$640$		0			0
$641$	−13.3211	−	23.0728i	−0.526152	−	0.911322i	−0.999536	−	0.0304659i	$-0.990301\pi$
$641$	−13.3211	−	23.0728i	−0.526152	−	0.911322i	0.473384	−	0.880856i	$-0.343032\pi$
$642$	9.24134			0.364727
$643$	8.30927	+	14.3921i	0.327686	+	0.567568i	0.982052	−	0.188609i	$-0.0603980\pi$
$643$	8.30927	+	14.3921i	0.327686	+	0.567568i	−0.654367	+	0.756177i	$0.727065\pi$
$644$	0.716280	−	0.413545i	0.0282254	−	0.0162959i
$645$		0			0
$646$	−5.36389	−	9.29053i	−0.211039	−	0.365531i
$647$	−17.7301	−	10.2365i	−0.697042	−	0.402437i	0.109203	−	0.994019i	$-0.465170\pi$
$647$	−17.7301	−	10.2365i	−0.697042	−	0.402437i	−0.806245	+	0.591582i	$0.798503\pi$
$648$	1.53819	−	2.66422i	0.0604258	−	0.104661i
$649$	−35.6068			−1.39769
$650$		0			0
$651$	5.54674			0.217394
$652$	−3.68592	+	6.38420i	−0.144352	+	0.250025i
$653$	4.99471	+	2.88370i	0.195458	+	0.112848i	0.594535	−	0.804070i	$-0.297336\pi$
$653$	4.99471	+	2.88370i	0.195458	+	0.112848i	−0.399077	+	0.916917i	$0.630669\pi$
$654$	−5.96387	−	10.3297i	−0.233206	−	0.403924i
$655$		0			0
$656$	1.85350	−	1.07012i	0.0723671	−	0.0417812i
$657$	−2.17698	−	3.77063i	−0.0849319	−	0.147106i
$658$	−6.96209			−0.271410
$659$	15.4749	+	26.8034i	0.602818	+	1.04411i	0.992392	+	0.123116i	$0.0392889\pi$
$659$	15.4749	+	26.8034i	0.602818	+	1.04411i	−0.389574	+	0.920995i	$0.627378\pi$
$660$		0			0
$661$	26.7433	+	15.4403i	1.04020	+	0.600557i	0.919889	−	0.392180i	$-0.128279\pi$
$661$	26.7433	+	15.4403i	1.04020	+	0.600557i	0.120307	+	0.992737i	$0.461612\pi$
$662$			22.8609i			0.888513i
$663$	7.02359	+	0.345166i	0.272774	+	0.0134051i
$664$	21.4641			0.832969
$665$		0			0
$666$	2.11015	−	3.65488i	0.0817666	−	0.141624i
$667$	4.49125	−	2.59302i	0.173902	−	0.100402i
$668$	7.93762			0.307116
$669$	−5.34065	+	3.08342i	−0.206481	+	0.119212i
$670$		0			0
$671$			19.2826i			0.744396i
$672$	−2.04719	+	1.18195i	−0.0789720	+	0.0455945i
$673$	−20.3585	−	11.7540i	−0.784761	−	0.453082i	0.0533540	−	0.998576i	$-0.483009\pi$
$673$	−20.3585	−	11.7540i	−0.784761	−	0.453082i	−0.838115	+	0.545494i	$0.816342\pi$
$674$	−17.3432	−	10.0131i	−0.668034	−	0.385689i
$675$		0			0
$676$	3.92730	+	8.66851i	0.151050	+	0.333404i
$677$		−	5.52213i		−	0.212233i	−0.994354	−	0.106116i	$-0.966158\pi$
$677$		−	5.52213i		−	0.212233i	0.994354	−	0.106116i	$-0.0338416\pi$
$678$	−1.95035	+	3.37810i	−0.0749026	+	0.129735i
$679$	−4.00045	+	6.92898i	−0.153523	+	0.265910i
$680$		0			0
$681$		−	17.1114i		−	0.655709i
$682$	−15.8530	−	27.4583i	−0.607044	−	1.05143i
$683$	6.73624	+	11.6675i	0.257755	+	0.446445i	0.965640	−	0.259883i	$-0.0836839\pi$
$683$	6.73624	+	11.6675i	0.257755	+	0.446445i	−0.707885	+	0.706328i	$0.750351\pi$
$684$			3.57593i			0.136729i
$685$		0			0
$686$	−4.65147	+	8.05658i	−0.177594	+	0.307602i
$687$	−14.4603	+	25.0460i	−0.551694	+	0.955563i
$688$			10.0217i			0.382073i
$689$	−1.88602	+	38.3776i	−0.0718516	+	1.46207i
$690$		0			0
$691$	−36.8081	−	21.2512i	−1.40025	−	0.808432i	−0.405828	−	0.913950i	$-0.633017\pi$
$691$	−36.8081	−	21.2512i	−1.40025	−	0.808432i	−0.994417	+	0.105518i	$0.966350\pi$
$692$	15.6352	+	9.02701i	0.594363	+	0.343156i
$693$	−1.61457	+	0.932171i	−0.0613323	+	0.0354102i
$694$			9.67366i			0.367207i
$695$		0			0
$696$	−7.41108	+	4.27879i	−0.280916	+	0.162187i
$697$	−2.08710			−0.0790547
$698$	29.4310	−	16.9920i	1.11398	−	0.643156i
$699$	5.66422	−	9.81072i	0.214241	−	0.371075i
$700$		0			0
$701$	0.553573			0.0209082			0.0104541	−	0.999945i	$-0.496672\pi$
$701$	0.553573			0.0209082			0.0104541	+	0.999945i	$0.496672\pi$
$702$	3.41216	+	2.20012i	0.128784	+	0.0830382i
$703$			18.3079i			0.690497i
$704$	22.3590	+	12.9090i	0.842685	+	0.486524i
$705$		0			0
$706$	16.1190	+	27.9189i	0.606646	+	1.05074i
$707$	−4.76593			−0.179241
$708$	4.23647	+	7.33778i	0.159216	+	0.275771i
$709$	11.2395	−	6.48914i	0.422109	−	0.243705i	−0.273870	−	0.961767i	$-0.588304\pi$
$709$	11.2395	−	6.48914i	0.422109	−	0.243705i	0.695979	+	0.718062i	$0.254971\pi$
$710$		0			0
$711$	1.64773	+	2.85395i	0.0617947	+	0.107032i
$712$	43.4248	+	25.0713i	1.62741	+	0.939588i
$713$	8.53193	−	14.7777i	0.319523	−	0.553431i
$714$	−1.33091			−0.0498080
$715$		0			0
$716$	16.7198			0.624850
$717$	9.56491	−	16.5669i	0.357208	−	0.618703i
$718$	17.0289	+	9.83163i	0.635512	+	0.366913i
$719$	11.2164	+	19.4273i	0.418300	+	0.724517i	0.995769	−	0.0918957i	$-0.0292926\pi$
$719$	11.2164	+	19.4273i	0.418300	+	0.724517i	−0.577468	+	0.816413i	$0.695959\pi$
$720$		0			0
$721$	−7.93022	+	4.57851i	−0.295337	+	0.170513i
$722$	2.73701	+	4.74064i	0.101861	+	0.176428i
$723$	−5.47415			−0.203586
$724$	−6.39140	−	11.0702i	−0.237535	−	0.411422i
$725$		0			0
$726$	−1.49777	−	0.864736i	−0.0555873	−	0.0320934i
$727$			48.3530i			1.79331i	0.442725	+	0.896657i	$0.354012\pi$
$727$			48.3530i			1.79331i	−0.442725	+	0.896657i	$0.645988\pi$
$728$	−3.07120	−	5.97936i	−0.113826	−	0.221610i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.88643	−	8.46355i	0.180731	−	0.313036i
$732$	3.97372	−	2.29423i	0.146873	−	0.0847971i
$733$	5.72579			0.211487			0.105743	−	0.994393i	$-0.466278\pi$
$733$	5.72579			0.211487			0.105743	+	0.994393i	$0.466278\pi$
$734$	31.6898	−	18.2961i	1.16969	−	0.675322i
$735$		0			0
$736$			7.27222i			0.268058i
$737$	5.26945	−	3.04232i	0.194103	−	0.112065i
$738$	−1.04355	−	0.602495i	−0.0384137	−	0.0221781i
$739$	18.0968	+	10.4482i	0.665703	+	0.384344i	0.794447	−	0.607334i	$-0.207761\pi$
$739$	18.0968	+	10.4482i	0.665703	+	0.384344i	−0.128743	+	0.991678i	$0.541094\pi$
$740$		0			0
$741$	−17.5912	−	0.864497i	−0.646229	−	0.0317581i
$742$		−	7.27222i		−	0.266972i
$743$	14.7796	−	25.5991i	0.542212	−	0.939139i	−0.456564	−	0.889690i	$-0.650920\pi$
$743$	14.7796	−	25.5991i	0.542212	−	0.939139i	0.998777	−	0.0494487i	$-0.0157464\pi$
$744$	−14.0787	+	24.3850i	−0.516149	+	0.893996i
$745$		0			0
$746$		−	12.1068i		−	0.443261i
$747$	−3.48853	−	6.04232i	−0.127639	−	0.221077i
$748$	−2.19615	−	3.80385i	−0.0802993	−	0.139082i
$749$			4.97359i			0.181731i
$750$		0			0
$751$	−10.5234	+	18.2270i	−0.384003	+	0.665113i	−0.991630	−	0.129110i	$-0.958788\pi$
$751$	−10.5234	+	18.2270i	−0.384003	+	0.665113i	0.607627	+	0.794222i	$0.292121\pi$
$752$	10.2024	−	17.6711i	0.372044	−	0.644398i
$753$		−	4.71985i		−	0.172001i
$754$	−5.15994	−	10.0460i	−0.187914	−	0.365852i
$755$		0			0
$756$	0.384200	+	0.221818i	0.0139732	+	0.00806745i
$757$	−12.1979	−	7.04245i	−0.443340	−	0.255962i	0.261674	−	0.965156i	$-0.415726\pi$
$757$	−12.1979	−	7.04245i	−0.443340	−	0.255962i	−0.705013	+	0.709194i	$0.749059\pi$
$758$	5.69638	−	3.28881i	0.206902	−	0.119455i
$759$			5.73542i			0.208183i
$760$		0			0
$761$	−39.3019	+	22.6909i	−1.42469	+	0.822546i	−0.996695	−	0.0812342i	$-0.974114\pi$
$761$	−39.3019	+	22.6909i	−1.42469	+	0.822546i	−0.427997	+	0.903780i	$0.640780\pi$
$762$	20.3179			0.736041
$763$	5.55934	−	3.20969i	0.201262	−	0.116199i
$764$	2.80872	−	4.86484i	0.101616	−	0.176004i
$765$		0			0
$766$	−26.6238			−0.961957
$767$	−37.1212	+	19.0667i	−1.34037	+	0.688458i
$768$		−	14.9282i		−	0.538675i
$769$	38.2583	+	22.0885i	1.37963	+	0.796530i	0.992115	−	0.125333i	$-0.0400000\pi$
$769$	38.2583	+	22.0885i	1.37963	+	0.796530i	0.387516	+	0.921863i	$0.373333\pi$
$770$		0			0
$771$	−3.63939	−	6.30362i	−0.131070	−	0.227019i
$772$	15.3810			0.553574
$773$	−17.8729	−	30.9568i	−0.642843	−	1.11344i	−0.984795	−	0.173720i	$-0.944421\pi$
$773$	−17.8729	−	30.9568i	−0.642843	−	1.11344i	0.341952	−	0.939717i	$-0.388912\pi$
$774$	4.88643	−	2.82118i	0.175639	−	0.101405i
$775$		0			0
$776$	−20.3078	−	35.1741i	−0.729008	−	1.26268i
$777$	1.96702	+	1.13566i	0.0705664	+	0.0407415i
$778$	−9.34265	+	16.1819i	−0.334950	+	0.580151i
$779$	5.22733			0.187289
$780$		0			0
$781$	−18.1720			−0.650246
$782$	−2.04719	+	3.54584i	−0.0732073	+	0.126799i
$783$	2.40903	+	1.39085i	0.0860916	+	0.0497050i
$784$	−6.63274	−	11.4882i	−0.236884	−	0.410294i
$785$		0			0
$786$	1.09120	−	0.630007i	0.0389220	−	0.0224716i
$787$	−5.09097	−	8.81782i	−0.181474	−	0.314321i	0.760909	−	0.648859i	$-0.224753\pi$
$787$	−5.09097	−	8.81782i	−0.181474	−	0.314321i	−0.942383	+	0.334537i	$0.891420\pi$
$788$	14.9175			0.531413
$789$	0.643362	+	1.11434i	0.0229043	+	0.0396714i
$790$		0			0
$791$	−1.81805	−	1.04965i	−0.0646426	−	0.0373214i
$792$		−	9.46410i		−	0.336292i
$793$	10.3254	+	20.1027i	0.366666	+	0.713868i
$794$	26.3531			0.935235
$795$		0			0
$796$	−5.41768	+	9.38370i	−0.192025	+	0.332596i
$797$	31.9438	−	18.4428i	1.13151	−	0.653277i	0.187195	−	0.982323i	$-0.440060\pi$
$797$	31.9438	−	18.4428i	1.13151	−	0.653277i	0.944314	+	0.329046i	$0.106727\pi$
$798$	3.33337			0.118000
$799$	−17.2324	+	9.94911i	−0.609637	+	0.351974i
$800$		0			0
$801$		−	16.2993i		−	0.575906i
$802$	−0.109049	+	0.0629594i	−0.00385065	+	0.00222317i
$803$	−11.5999	−	6.69720i	−0.409351	−	0.236339i
$804$	−1.25391	−	0.723946i	−0.0442221	−	0.0255316i
$805$		0			0
$806$	−31.2306	−	20.1372i	−1.10005	−	0.709301i
$807$		−	18.9390i		−	0.666686i
$808$	12.0968	−	20.9523i	0.425565	−	0.737101i
$809$	−6.08464	+	10.5389i	−0.213924	+	0.370528i	−0.952939	−	0.303161i	$-0.901958\pi$
$809$	−6.08464	+	10.5389i	−0.213924	+	0.370528i	0.739015	+	0.673689i	$0.235291\pi$
$810$		0			0
$811$			26.2312i			0.921104i	0.887633	+	0.460552i	$0.152348\pi$
$811$			26.2312i			0.921104i	−0.887633	+	0.460552i	$0.847652\pi$
$812$	−0.617033	−	1.06873i	−0.0216536	−	0.0375051i
$813$	−5.51207	−	9.54719i	−0.193317	−	0.334835i
$814$		−	12.9832i		−	0.455062i
$815$		0			0
$816$	1.95035	−	3.37810i	0.0682757	−	0.118257i
$817$	−12.2385	+	21.1977i	−0.428171	+	0.741613i
$818$		−	21.7104i		−	0.759088i
$819$	−1.18408	+	1.83639i	−0.0413751	+	0.0641685i
$820$		0			0
$821$	14.3284	+	8.27253i	0.500066	+	0.288713i	0.728741	−	0.684790i	$-0.240106\pi$
$821$	14.3284	+	8.27253i	0.500066	+	0.288713i	−0.228675	+	0.973503i	$0.573439\pi$
$822$	−8.49038	−	4.90192i	−0.296136	−	0.170974i
$823$	24.1873	−	13.9646i	0.843117	−	0.486774i	−0.0152057	−	0.999884i	$-0.504840\pi$
$823$	24.1873	−	13.9646i	0.843117	−	0.486774i	0.858322	+	0.513111i	$0.171507\pi$
$824$		−	46.4845i		−	1.61937i
$825$		0			0
$826$	6.84006	−	3.94911i	0.237996	−	0.137407i
$827$	1.83852			0.0639316			0.0319658	−	0.999489i	$-0.489823\pi$
$827$	1.83852			0.0639316			0.0319658	+	0.999489i	$0.489823\pi$
$828$	1.18195	−	0.682396i	0.0410754	−	0.0237149i
$829$	17.4866	−	30.2876i	0.607333	−	1.05193i	−0.384345	−	0.923190i	$-0.625573\pi$
$829$	17.4866	−	30.2876i	0.607333	−	1.05193i	0.991678	−	0.128743i	$-0.0410941\pi$
$830$		0			0
$831$	20.9215			0.725758
$832$	30.2224	+	1.48524i	1.04777	+	0.0514915i
$833$			12.9361i			0.448211i
$834$	9.41713	+	5.43698i	0.326089	+	0.188267i
$835$		0			0
$836$	5.50045	+	9.52706i	0.190237	+	0.329500i
$837$	9.15276			0.316366
$838$	12.4644	+	21.5889i	0.430575	+	0.745777i
$839$	−11.0093	+	6.35624i	−0.380085	+	0.219442i	−0.677855	−	0.735196i	$-0.737090\pi$
$839$	−11.0093	+	6.35624i	−0.380085	+	0.219442i	0.297771	+	0.954637i	$0.403757\pi$
$840$		0			0
$841$	10.6311	+	18.4135i	0.366588	+	0.634949i
$842$	−0.892073	−	0.515039i	−0.0307429	−	0.0177494i
$843$	−5.33265	+	9.23642i	−0.183666	+	0.318119i
$844$	−3.82152			−0.131542
$845$		0			0
$846$	−11.4882			−0.394974
$847$	0.465391	−	0.806081i	0.0159910	−	0.0276973i
$848$	18.4583	+	10.6569i	0.633860	+	0.365959i
$849$	1.39254	+	2.41194i	0.0477917	+	0.0827777i
$850$		0			0
$851$	6.05129	−	3.49372i	0.207436	−	0.119763i
$852$	2.16209	+	3.74486i	0.0740721	+	0.128297i
$853$	20.2430			0.693106			0.346553	−	0.938030i	$-0.387352\pi$
$853$	20.2430			0.693106			0.346553	+	0.938030i	$0.387352\pi$
$854$	−2.13861	−	3.70419i	−0.0731818	−	0.126755i
$855$		0			0
$856$	−21.8652	−	12.6239i	−0.747339	−	0.431476i
$857$		−	53.5208i		−	1.82823i	−0.405450	−	0.914117i	$-0.632885\pi$
$857$		−	53.5208i		−	1.82823i	0.405450	−	0.914117i	$-0.367115\pi$
$858$	12.4749	+	0.613065i	0.425887	+	0.0209297i
$859$	0.969120			0.0330659			0.0165330	−	0.999863i	$-0.494737\pi$
$859$	0.969120			0.0330659			0.0165330	+	0.999863i	$0.494737\pi$
$860$		0			0
$861$	0.324256	−	0.561628i	0.0110506	−	0.0191402i
$862$	−36.0590	+	20.8187i	−1.22818	+	0.709087i
$863$	5.67766			0.193270			0.0966349	−	0.995320i	$-0.469192\pi$
$863$	5.67766			0.193270			0.0966349	+	0.995320i	$0.469192\pi$
$864$	−3.37810	+	1.95035i	−0.114925	+	0.0663521i
$865$		0			0
$866$		−	32.3056i		−	1.09779i
$867$	11.4282	−	6.59808i	0.388122	−	0.224082i
$868$	−3.51649	−	2.03025i	−0.119357	−	0.0689111i
$869$	8.77984	+	5.06904i	0.297836	+	0.171955i
$870$		0			0
$871$	3.86447	−	5.99340i	0.130943	−	0.203079i
$872$			32.5872i			1.10354i
$873$	−6.60121	+	11.4336i	−0.223417	+	0.386970i
$874$	5.12736	−	8.88085i	0.173436	−	0.300399i
$875$		0			0
$876$			3.18732i			0.107689i
$877$	−16.1085	−	27.9007i	−0.543944	−	0.942139i	−0.998673	−	0.0515091i	$-0.983597\pi$
$877$	−16.1085	−	27.9007i	−0.543944	−	0.942139i	0.454728	−	0.890630i	$-0.349736\pi$
$878$	−2.96266	−	5.13147i	−0.0999848	−	0.173179i
$879$			4.95861i			0.167250i
$880$		0			0
$881$	20.5576	−	35.6068i	0.692602	−	1.19962i	−0.278380	−	0.960471i	$-0.589797\pi$
$881$	20.5576	−	35.6068i	0.692602	−	1.19962i	0.970982	−	0.239151i	$-0.0768692\pi$
$882$	−3.73434	+	6.46807i	−0.125742	+	0.217791i
$883$		−	14.6027i		−	0.491419i	−0.969344	−	0.245709i	$-0.920979\pi$
$883$		−	14.6027i		−	0.491419i	0.969344	−	0.245709i	$-0.0790209\pi$
$884$	−4.32644	−	2.78964i	−0.145514	−	0.0938258i
$885$		0			0
$886$	28.1118	+	16.2304i	0.944435	+	0.545270i
$887$	−7.88566	−	4.55279i	−0.264775	−	0.152868i	0.361736	−	0.932281i	$-0.382184\pi$
$887$	−7.88566	−	4.55279i	−0.264775	−	0.152868i	−0.626511	+	0.779413i	$0.715518\pi$
$888$	−9.98533	+	5.76503i	−0.335086	+	0.193462i
$889$			10.9349i			0.366744i
$890$		0			0
$891$	−2.66422	+	1.53819i	−0.0892548	+	0.0515313i
$892$	4.51445			0.151155
$893$	43.1599	−	24.9184i	1.44429	−	0.833863i
$894$	−2.91400	+	5.04719i	−0.0974586	+	0.168803i
$895$		0			0
$896$	−0.999098			−0.0333775
$897$	3.07120	+	5.97936i	0.102544	+	0.199645i
$898$		−	3.38740i		−	0.113039i
$899$	−22.0492	−	12.7301i	−0.735383	−	0.424574i
$900$		0			0
$901$	−10.3923	−	18.0000i	−0.346218	−	0.599667i
$902$	−3.70700			−0.123430
$903$	1.51833	+	2.62983i	0.0505269	+	0.0875151i
$904$	9.22913	−	5.32844i	0.306956	−	0.177221i
$905$		0			0
$906$	−12.4681	−	21.5953i	−0.414224	−	0.717457i
$907$	−43.7482	−	25.2580i	−1.45263	−	0.838679i	−0.454004	−	0.891000i	$-0.650005\pi$
$907$	−43.7482	−	25.2580i	−1.45263	−	0.838679i	−0.998630	+	0.0523212i	$0.983338\pi$
$908$	−6.26319	+	10.8482i	−0.207851	+	0.360009i
$909$	−7.86434			−0.260844
$910$		0			0
$911$	45.3571			1.50275			0.751374	−	0.659876i	$-0.229391\pi$
$911$	45.3571			1.50275			0.751374	+	0.659876i	$0.229391\pi$
$912$	−4.88481	+	8.46073i	−0.161752	+	0.280163i
$913$	−18.5885	−	10.7321i	−0.615188	−	0.355179i
$914$	−5.00342	−	8.66617i	−0.165498	−	0.286652i
$915$		0			0
$916$	18.3349	−	10.5857i	0.605803	−	0.349760i
$917$	0.339063	+	0.587274i	0.0111968	+	0.0193935i
$918$	−2.19615			−0.0724838
$919$	2.15110	+	3.72581i	0.0709582	+	0.122903i	0.899322	−	0.437288i	$-0.144061\pi$
$919$	2.15110	+	3.72581i	0.0709582	+	0.122903i	−0.828363	+	0.560191i	$0.810728\pi$
$920$		0			0
$921$	8.32011	+	4.80362i	0.274157	+	0.158285i
$922$		−	23.7693i		−	0.782800i
$923$	−18.9449	+	9.73073i	−0.623579	+	0.320291i
$924$	1.36479			0.0448984
$925$		0			0
$926$	13.7758	−	23.8604i	0.452702	−	0.784102i
$927$	−13.0858	+	7.55507i	−0.429793	+	0.248141i
$928$	10.8506			0.356188
$929$	−41.9047	+	24.1937i	−1.37485	+	0.793769i	−0.991534	−	0.129849i	$-0.958551\pi$
$929$	−41.9047	+	24.1937i	−1.37485	+	0.793769i	−0.383315	+	0.923618i	$0.625217\pi$
$930$		0			0
$931$		−	32.3997i		−	1.06186i
$932$	−7.18195	+	4.14650i	−0.235252	+	0.135823i
$933$	−22.5507	−	13.0196i	−0.738275	−	0.426243i
$934$	−19.0215	−	10.9821i	−0.622404	−	0.359345i
$935$		0			0
$936$	−5.06783	−	9.86663i	−0.165647	−	0.322501i
$937$			33.9291i			1.10842i	0.832378	+	0.554208i	$0.186979\pi$
$937$			33.9291i			1.10842i	−0.832378	+	0.554208i	$0.813021\pi$
$938$	−0.674841	+	1.16886i	−0.0220344	+	0.0381646i
$939$	−14.6156	+	25.3149i	−0.476961	+	0.826121i
$940$		0			0
$941$		−	8.20272i		−	0.267401i	−0.991022	−	0.133701i	$-0.957314\pi$
$941$		−	8.20272i		−	0.267401i	0.991022	−	0.133701i	$-0.0426860\pi$
$942$	−8.09371	−	14.0187i	−0.263707	−	0.456755i
$943$	−0.997534	−	1.72778i	−0.0324842	−	0.0562643i
$944$			23.1485i			0.753419i
$945$		0			0
$946$	8.67903	−	15.0325i	0.282180	−	0.488749i
$947$	22.5046	−	38.9792i	0.731302	−	1.26665i	−0.225024	−	0.974353i	$-0.572246\pi$
$947$	22.5046	−	38.9792i	0.731302	−	1.26665i	0.956327	−	0.292300i	$-0.0944205\pi$
$948$		−	2.41245i		−	0.0783526i
$949$	−15.6795	−	0.770548i	−0.508977	−	0.0250130i
$950$		0			0
$951$	−7.47007	−	4.31285i	−0.242234	−	0.139854i
$952$	3.14896	+	1.81805i	0.102058	+	0.0589235i
$953$	45.9157	−	26.5094i	1.48735	−	0.858724i	0.487458	−	0.873146i	$-0.337924\pi$
$953$	45.9157	−	26.5094i	1.48735	−	0.858724i	0.999896	+	0.0144217i	$0.00459073\pi$
$954$		−	12.0000i		−	0.388514i
$955$		0			0
$956$	−12.1278	+	7.00200i	−0.392242	+	0.226461i
$957$	8.55758			0.276627
$958$	26.3593	−	15.2186i	0.851631	−	0.491689i
$959$	2.63816	−	4.56943i	0.0851907	−	0.147555i
$960$		0			0
$961$	−52.7729			−1.70235
$962$	−6.95225	−	13.5354i	−0.224149	−	0.436400i
$963$			8.20699i			0.264467i
$964$	3.47047	+	2.00368i	0.111776	+	0.0645341i
$965$		0			0
$966$	−0.636110	−	1.10177i	−0.0204665	−	0.0354490i
$967$	31.7061			1.01960			0.509799	−	0.860293i	$-0.329720\pi$
$967$	31.7061			1.01960			0.509799	+	0.860293i	$0.329720\pi$
$968$	2.36250	+	4.09197i	0.0759337	+	0.131521i
$969$	8.25068	−	4.76353i	0.265050	−	0.153027i
$970$		0			0
$971$	14.8074	+	25.6471i	0.475191	+	0.823054i	0.999596	−	0.0284144i	$-0.00904580\pi$
$971$	14.8074	+	25.6471i	0.475191	+	0.823054i	−0.524406	+	0.851469i	$0.675712\pi$
$972$	0.633975	+	0.366025i	0.0203347	+	0.0117403i
$973$	−2.92612	+	5.06820i	−0.0938073	+	0.162479i
$974$	5.87508			0.188250
$975$		0			0
$976$	12.5359			0.401264
$977$	0.615644	−	1.06633i	0.0196962	−	0.0341148i	−0.856009	−	0.516960i	$-0.827063\pi$
$977$	0.615644	−	1.06633i	0.0196962	−	0.0341148i	0.875706	+	0.482846i	$0.160397\pi$
$978$	9.82011	+	5.66964i	0.314012	+	0.181295i
$979$	−25.0713	−	43.4248i	−0.801283	−	1.38786i
$980$		0			0
$981$	9.17356	−	5.29636i	0.292889	−	0.169100i
$982$	8.32234	+	14.4147i	0.265577	+	0.459992i
$983$	−25.1632			−0.802581			−0.401290	−	0.915951i	$-0.631438\pi$
$983$	−25.1632			−0.802581			−0.401290	+	0.915951i	$0.631438\pi$
$984$	1.64605	+	2.85104i	0.0524741	+	0.0908877i
$985$		0			0
$986$	5.29059	+	3.05452i	0.168487	+	0.0972759i
$987$		−	6.18285i		−	0.196802i
$988$	10.8359	+	6.98689i	0.344737	+	0.222283i
$989$	9.34192			0.297056
$990$		0			0
$991$	29.7295	−	51.4929i	0.944387	−	1.63573i	0.187414	−	0.982281i	$-0.439990\pi$
$991$	29.7295	−	51.4929i	0.944387	−	1.63573i	0.756974	−	0.653445i	$-0.226677\pi$
$992$	30.9189	−	17.8510i	0.981676	−	0.566771i
$993$	−20.3021			−0.644269
$994$	3.49084	−	2.01544i	0.110723	−	0.0639259i
$995$		0			0
$996$			5.10757i			0.161840i
$997$	32.8413	−	18.9610i	1.04010	−	0.600499i	0.120235	−	0.992745i	$-0.461635\pi$
$997$	32.8413	−	18.9610i	1.04010	−	0.600499i	0.919860	+	0.392246i	$0.128302\pi$
$998$	−10.0610	−	5.80872i	−0.318475	−	0.183872i
$999$	3.24581	+	1.87397i	0.102693	+	0.0592897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.i.199.2		8
5.2	odd	4		975.2.bc.j.901.2		8
5.3	odd	4		195.2.bb.b.121.3	✓	8
5.4	even	2		975.2.w.h.199.3		8
13.10	even	6		975.2.w.h.49.3		8
15.8	even	4		585.2.bu.d.316.2		8
65.23	odd	12		195.2.bb.b.166.3	yes	8
65.33	even	12		2535.2.a.bk.1.3		4
65.49	even	6	inner	975.2.w.i.49.2		8
65.58	even	12		2535.2.a.bj.1.2		4
65.62	odd	12		975.2.bc.j.751.2		8
195.23	even	12		585.2.bu.d.361.2		8
195.98	odd	12		7605.2.a.ch.1.2		4
195.188	odd	12		7605.2.a.ci.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.3	✓	8	5.3	odd	4
195.2.bb.b.166.3	yes	8	65.23	odd	12
585.2.bu.d.316.2		8	15.8	even	4
585.2.bu.d.361.2		8	195.23	even	12
975.2.w.h.49.3		8	13.10	even	6
975.2.w.h.199.3		8	5.4	even	2
975.2.w.i.49.2		8	65.49	even	6	inner
975.2.w.i.199.2		8	1.1	even	1	trivial
975.2.bc.j.751.2		8	65.62	odd	12
975.2.bc.j.901.2		8	5.2	odd	4
2535.2.a.bj.1.2		4	65.58	even	12
2535.2.a.bk.1.3		4	65.33	even	12
7605.2.a.ch.1.2		4	195.98	odd	12
7605.2.a.ci.1.3		4	195.188	odd	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.563016 + 0.975173i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(0.303009 + 0.524827i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.563016 + 0.975173i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.366025 + 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(0.303009 + 0.524827i) q^{7} -3.07638 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.66422 + 1.53819i) q^{11} -0.732051i q^{12} +(3.60121 + 0.176977i) q^{13} -0.682396 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.68905 + 0.975173i) q^{17} -1.12603 q^{18} +(4.23037 - 2.44240i) q^{19} -0.606018i q^{21} +(-3.00000 + 1.73205i) q^{22} +(-1.61457 - 0.932171i) q^{23} +(2.66422 + 1.53819i) q^{24} +(-2.20012 + 3.41216i) q^{26} -1.00000i q^{27} +(-0.221818 + 0.384200i) q^{28} +(-1.39085 + 2.40903i) q^{29} +9.15276i q^{31} +(-1.95035 - 3.37810i) q^{32} +(-1.53819 - 2.66422i) q^{33} -2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(-1.87397 + 3.24581i) q^{37} +5.50045i q^{38} +(-3.03025 - 1.95387i) q^{39} +(0.926751 + 0.535060i) q^{41} +(0.590973 + 0.341198i) q^{42} +(-4.33951 + 2.50542i) q^{43} +2.25207i q^{44} +(1.81805 - 1.04965i) q^{46} +10.2024 q^{47} +(-1.73205 + 1.00000i) q^{48} +(3.31637 - 5.74412i) q^{49} +1.95035 q^{51} +(1.20593 + 2.34785i) q^{52} +10.6569i q^{53} +(0.975173 + 0.563016i) q^{54} +(-0.932171 - 1.61457i) q^{56} -4.88481 q^{57} +(-1.56615 - 2.71264i) q^{58} +(-10.0236 + 5.78712i) q^{59} +(3.13397 + 5.42820i) q^{61} +(-8.92552 - 5.15315i) q^{62} +(-0.303009 + 0.524827i) q^{63} +8.39230 q^{64} +3.46410 q^{66} +(0.988929 - 1.71288i) q^{67} +(-1.23647 - 0.713876i) q^{68} +(0.932171 + 1.61457i) q^{69} +(-5.11557 + 2.95347i) q^{71} +(-1.53819 - 2.66422i) q^{72} -4.35395 q^{73} +(-2.11015 - 3.65488i) q^{74} +(3.09684 + 1.78796i) q^{76} +1.86434i q^{77} +(3.61144 - 1.85495i) q^{78} +3.29546 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.04355 + 0.602495i) q^{82} -6.97707 q^{83} +(0.384200 - 0.221818i) q^{84} -5.64237i q^{86} +(2.40903 - 1.39085i) q^{87} +(-8.19615 - 4.73205i) q^{88} +(-14.1156 - 8.14963i) q^{89} +(0.998316 + 1.94364i) q^{91} -1.36479i q^{92} +(4.57638 - 7.92652i) q^{93} +(-5.74412 + 9.94911i) q^{94} +3.90069i q^{96} +(6.60121 + 11.4336i) q^{97} +(3.73434 + 6.46807i) q^{98} +3.07638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 4 * q^9	\( 8 q - 4 q^{4} + 4 q^{9} + 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{28} - 12 q^{29} + 4 q^{36} - 24 q^{37} + 4 q^{39} + 36 q^{41} + 12 q^{42} - 12 q^{43} + 48 q^{47} + 4 q^{49} - 12 q^{52} + 24 q^{57} - 12 q^{58} - 36 q^{59} + 32 q^{61} - 48 q^{62} - 16 q^{64} - 12 q^{67} + 36 q^{71} - 48 q^{73} + 24 q^{74} - 48 q^{76} - 12 q^{78} + 16 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{87} - 24 q^{88} - 36 q^{89} + 12 q^{93} - 12 q^{94} + 36 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 4 * q^9 + 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 - 24 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^28 - 12 * q^29 + 4 * q^36 - 24 * q^37 + 4 * q^39 + 36 * q^41 + 12 * q^42 - 12 * q^43 + 48 * q^47 + 4 * q^49 - 12 * q^52 + 24 * q^57 - 12 * q^58 - 36 * q^59 + 32 * q^61 - 48 * q^62 - 16 * q^64 - 12 * q^67 + 36 * q^71 - 48 * q^73 + 24 * q^74 - 48 * q^76 - 12 * q^78 + 16 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^87 - 24 * q^88 - 36 * q^89 + 12 * q^93 - 12 * q^94 + 36 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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