LMFDB - Embedded newform 975.2.w.h.49.3

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			49.3
Root			$2.10121 + 0.563016i$ of defining polynomial
Character	$\chi$	$=$	975.49
Dual form			975.2.w.h.199.3

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	$-0.0363320\pi$
$2$	0.563016	+	0.975173i	0.398113	+	0.689551i	−0.595380	+	0.803444i	$0.702999\pi$
$3$	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	$-0.869868\pi$
$7$	−0.303009	+	0.524827i	−0.114527	+	0.198366i	0.803064	+	0.595893i	$0.203202\pi$
$8$	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	−0.0413283	−	0.999146i	$-0.513159\pi$
$11$	2.66422	−	1.53819i	0.803293	−	0.463781i	0.844621	+	0.535364i	$0.179826\pi$
$12$		−	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	$-0.257328\pi$
$17$	1.68905	+	0.975173i	0.409654	+	0.236514i	−0.280987	+	0.959712i	$0.590662\pi$
$18$	1.12603			0.265408
$19$	4.23037	+	2.44240i	0.970513	+	0.560326i	0.899393	−	0.437142i	$-0.144009\pi$
$19$	4.23037	+	2.44240i	0.970513	+	0.560326i	0.0711202	+	0.997468i	$0.477343\pi$
$20$		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	$-0.604400\pi$
$23$	1.61457	−	0.932171i	0.336660	−	0.194371i	0.658794	+	0.752323i	$0.271067\pi$
$24$	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	0.707505	−	0.706708i	$-0.249821\pi$
$29$	−1.39085	−	2.40903i	−0.258275	−	0.447345i	−0.965780	+	0.259363i	$0.916487\pi$
$30$		0			0
$31$		−	9.15276i		−	1.64388i	−0.569572	−	0.821942i	$-0.692891\pi$
$31$		−	9.15276i		−	1.64388i	0.569572	−	0.821942i	$-0.307109\pi$
$32$	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	$-0.0669808\pi$
$37$	1.87397	+	3.24581i	0.308078	+	0.533607i	−0.669864	+	0.742484i	$0.733647\pi$
$38$			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	−0.425884	−	0.904778i	$-0.640037\pi$
$41$	0.926751	−	0.535060i	0.144734	−	0.0835623i	0.570618	+	0.821215i	$0.306704\pi$
$42$	−0.590973	+	0.341198i	−0.0911890	+	0.0526480i
$43$	4.33951	+	2.50542i	0.661770	+	0.382073i	0.792951	−	0.609285i	$-0.208544\pi$
$43$	4.33951	+	2.50542i	0.661770	+	0.382073i	−0.131181	+	0.991358i	$0.541877\pi$
$44$		−	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	$-0.767115\pi$
$47$	−10.2024			−1.48817			−0.744087	+	0.668082i	$0.767115\pi$
$48$	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	−0.323710	−	0.946156i	$-0.604930\pi$
$59$	−10.0236	−	5.78712i	−1.30496	−	0.753419i	−0.981251	+	0.192737i	$0.938264\pi$
$60$		0			0
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	−0.592614	−	0.805486i	$-0.701904\pi$
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	0.993879	+	0.110476i	$0.0352375\pi$
$62$	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	$-0.205218\pi$
$67$	−0.988929	−	1.71288i	−0.120817	−	0.209261i	−0.920090	+	0.391707i	$0.871885\pi$
$68$	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	0.164726	−	0.986339i	$-0.447326\pi$
$71$	−5.11557	−	2.95347i	−0.607106	−	0.350513i	−0.771832	+	0.635826i	$0.780659\pi$
$72$	1.53819	−	2.66422i	0.181277	−	0.313982i
$73$	4.35395			0.509592			0.254796	−	0.966995i	$-0.417992\pi$
$73$	4.35395			0.509592			0.254796	+	0.966995i	$0.417992\pi$
$74$	−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	$-0.374920\pi$
$83$	6.97707			0.765833			0.382916	+	0.923783i	$0.374920\pi$
$84$	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	−0.999991	−	0.00431721i	$-0.998626\pi$
$89$	−14.1156	+	8.14963i	−1.49625	+	0.863859i	−0.496257	+	0.868176i	$0.665292\pi$
$90$		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	0.307582	+	0.951522i	$0.400480\pi$
$97$	−6.60121	+	11.4336i	−0.670251	+	1.16091i	−0.977833	+	0.209387i	$0.932853\pi$
$98$	−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	0.601351	−	0.798985i	$-0.294629\pi$
$101$	−3.93217	−	6.81072i	−0.391266	−	0.677692i	−0.992617	+	0.121293i	$0.961296\pi$
$102$	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	$-0.796511\pi$
$107$	−7.10746	+	4.10350i	−0.687104	+	0.396700i	0.115422	+	0.993317i	$0.463178\pi$
$108$	−0.633975	−	0.366025i	−0.0610042	−	0.0352208i
$109$			10.5927i			1.01460i	0.861770	+	0.507299i	$0.169356\pi$
$109$			10.5927i			1.01460i	−0.861770	+	0.507299i	$0.830644\pi$
$110$		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	$-0.281236\pi$
$113$	3.00000	+	1.73205i	0.282216	+	0.162938i	−0.352210	+	0.935921i	$0.614570\pi$
$114$	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	$-0.962134\pi$
$127$	−15.6264	+	9.02191i	−1.38662	+	0.800565i	−0.393687	+	0.919245i	$0.628801\pi$
$128$	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	$-0.712031\pi$
$137$	4.35327	−	7.54009i	0.371925	−	0.644193i	0.989862	+	0.142035i	$0.0453645\pi$
$138$	2.09931			0.178705
$139$	4.82844	−	8.36311i	0.409543	−	0.709350i	−0.585295	−	0.810820i	$-0.699021\pi$
$139$	4.82844	−	8.36311i	0.409543	−	0.709350i	0.994839	+	0.101471i	$0.0323548\pi$
$140$		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	0.305033	−	0.952342i	$-0.401332\pi$
$149$	−4.48228	−	2.58784i	−0.367202	−	0.212004i	−0.672236	+	0.740337i	$0.734666\pi$
$150$		0			0
$151$			22.1451i			1.80215i	0.433668	+	0.901073i	$0.357219\pi$
$151$			22.1451i			1.80215i	−0.433668	+	0.901073i	$0.642781\pi$
$152$	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	$-0.962373\pi$
$163$	−5.03506	+	8.72098i	−0.394376	+	0.683080i	0.598645	+	0.801014i	$0.295706\pi$
$164$		−	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	$-0.304471\pi$
$167$	−5.42149	−	9.39030i	−0.419528	−	0.726643i	−0.995892	+	0.0905495i	$0.971138\pi$
$168$			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	−0.985883	−	0.167438i	$-0.946451\pi$
$173$	−21.3581	−	12.3311i	−1.62383	−	0.937518i	−0.637947	−	0.770081i	$-0.720216\pi$
$174$		−	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	0.877974	+	0.478709i	$0.158895\pi$
$179$	11.4199	+	19.7798i	0.853561	+	1.47841i	−0.0244128	+	0.999702i	$0.507772\pi$
$180$		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	−0.970793	−	0.239920i	$-0.922879\pi$
$191$	−3.83678	+	6.64550i	−0.277620	+	0.480851i	0.693173	+	0.720771i	$0.256212\pi$
$192$	7.26795	−	4.19615i	0.524519	−	0.302831i
$193$	−10.5054	−	18.1959i	−0.756197	−	1.30977i	−0.944777	−	0.327713i	$-0.893722\pi$
$193$	−10.5054	−	18.1959i	−0.756197	−	1.30977i	0.188581	−	0.982058i	$-0.439611\pi$
$194$	−14.8663			−1.06734
$195$		0			0
$196$	4.85550			0.346822
$197$	−10.1888	−	17.6475i	−0.725923	−	1.25734i	−0.958593	−	0.284780i	$-0.908079\pi$
$197$	−10.1888	−	17.6475i	−0.725923	−	1.25734i	0.232670	−	0.972556i	$-0.425254\pi$
$198$	3.00000	−	1.73205i	0.213201	−	0.123091i
$199$	7.40069	−	12.8184i	0.524621	−	0.908670i	−0.474968	−	0.880003i	$-0.657540\pi$
$199$	7.40069	−	12.8184i	0.524621	−	0.908670i	0.999589	−	0.0286673i	$-0.00912632\pi$
$200$		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	0.762084	−	0.647478i	$-0.224176\pi$
$211$	−2.61015	−	4.52091i	−0.179690	−	0.311232i	−0.941774	+	0.336246i	$0.890843\pi$
$212$	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	$-0.232868\pi$
$223$	−3.08342	−	5.34065i	−0.206481	−	0.357636i	−0.950604	+	0.310407i	$0.899535\pi$
$224$	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	0.428917	+	0.903344i	$0.358895\pi$
$227$	−8.55568	+	14.8189i	−0.567860	+	0.983563i	−0.996777	+	0.0802192i	$0.974438\pi$
$228$	1.78796	−	3.09684i	0.118411	−	0.205093i
$229$			28.9206i			1.91113i	0.294788	+	0.955563i	$0.404751\pi$
$229$			28.9206i			1.91113i	−0.294788	+	0.955563i	$0.595249\pi$
$230$		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	$-0.787659\pi$
$239$		−	19.1298i		−	1.23741i	0.785625	−	0.618703i	$-0.212341\pi$
$240$		0			0
$241$	4.74075	+	2.73708i	0.305379	+	0.176311i	0.644857	−	0.764303i	$-0.276917\pi$
$241$	4.74075	+	2.73708i	0.305379	+	0.176311i	−0.339478	+	0.940614i	$0.610250\pi$
$242$	−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	−0.781885	−	0.623422i	$-0.785742\pi$
$251$	2.35992	−	4.08751i	0.148957	−	0.258001i	0.930842	+	0.365421i	$0.119075\pi$
$252$	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	$-0.739565\pi$
$257$	−6.30362	+	3.63939i	−0.393209	+	0.227019i	0.290341	+	0.956923i	$0.406231\pi$
$258$	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	$-0.654036\pi$
$263$	1.11434	−	0.643362i	0.0687129	−	0.0396714i	0.533963	+	0.845508i	$0.320702\pi$
$264$	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	−0.418413	−	0.908257i	$-0.637414\pi$
$269$	9.46952	−	16.4017i	0.577367	−	1.00003i	0.995780	−	0.0917720i	$-0.0292531\pi$
$270$		0			0
$271$	9.54719	−	5.51207i	0.579950	−	0.334835i	−0.181163	−	0.983453i	$-0.557986\pi$
$271$	9.54719	−	5.51207i	0.579950	−	0.334835i	0.761114	+	0.648619i	$0.224653\pi$
$272$			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	$-0.116992\pi$
$277$	18.1185	+	10.4607i	1.08864	+	0.628525i	0.155423	+	0.987848i	$0.450326\pi$
$278$	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	$0.103051\pi$
$281$			10.6653i			0.636238i	−0.948051	+	0.318119i	$0.896949\pi$
$282$	−9.94911	−	5.74412i	−0.592461	−	0.342058i
$283$	2.41194	−	1.39254i	0.143375	−	0.0827777i	−0.426596	−	0.904442i	$-0.640288\pi$
$283$	2.41194	−	1.39254i	0.143375	−	0.0827777i	0.569972	+	0.821664i	$0.306954\pi$
$284$	−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	$-0.787066\pi$
$293$	2.47930	−	4.29428i	0.144842	−	0.250874i	0.929314	+	0.369290i	$0.120399\pi$
$294$			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	$-0.411601\pi$
$307$	9.60723			0.548314			0.274157	+	0.961685i	$0.411601\pi$
$308$	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	$-0.577880\pi$
$317$	−8.62570			−0.484467			−0.242234	+	0.970218i	$0.577880\pi$
$318$	−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	0.898138	−	0.439714i	$-0.144920\pi$
$331$	17.5822	+	10.1511i	0.966404	+	0.557953i	0.0682657	+	0.997667i	$0.478253\pi$
$332$	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	$-0.407400\pi$
$347$	−7.43996	−	4.29546i	−0.399398	−	0.230592i	−0.686224	+	0.727390i	$0.740733\pi$
$348$	−1.76353	+	1.01817i	−0.0945352	+	0.0545799i
$349$	−26.1369	+	15.0901i	−1.39908	+	0.807756i	−0.994296	−	0.106658i	$-0.965985\pi$
$349$	−26.1369	+	15.0901i	−1.39908	+	0.807756i	−0.404779	+	0.914414i	$0.632652\pi$
$350$		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	−0.941869	−	0.335981i	$-0.890932\pi$
$353$	−14.3148	−	24.7940i	−0.761903	−	1.31965i	0.179966	−	0.983673i	$-0.442401\pi$
$354$	−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	$0.152443\pi$
$359$			17.4624i			0.921632i	−0.887496	+	0.460816i	$0.847557\pi$
$360$		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	$-0.344380\pi$
$367$	28.1429	−	16.2483i	1.46905	−	0.848155i	0.999398	+	0.0346981i	$0.0110470\pi$
$368$	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	$-0.243545\pi$
$373$	9.31127	+	5.37586i	0.482119	+	0.278352i	−0.239180	+	0.970975i	$0.576879\pi$
$374$	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	−0.624268	−	0.781210i	$-0.714603\pi$
$379$	−5.05881	+	2.92071i	−0.259854	+	0.150027i	0.364414	+	0.931237i	$0.381269\pi$
$380$		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	0.388124	+	0.921607i	$0.373123\pi$
$383$	−11.8220	+	20.4762i	−0.604074	+	1.04629i	−0.992197	+	0.124679i	$0.960210\pi$
$384$	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	−0.407292	−	0.913298i	$-0.633527\pi$
$397$	11.7017	−	20.2680i	0.587293	−	1.01722i	0.994585	−	0.103923i	$-0.0331396\pi$
$398$	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	−0.497580	−	0.867418i	$-0.665778\pi$
$401$	0.0968434	−	0.0559126i	0.00483613	−	0.00279214i	0.502416	+	0.864626i	$0.332445\pi$
$402$		−	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	0.0267224	−	0.999643i	$-0.491493\pi$
$409$	−16.6974	−	9.64024i	−0.825633	−	0.476679i	−0.852355	+	0.522964i	$0.824826\pi$
$410$		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	0.998860	+	0.0477351i	$0.0152003\pi$
$419$	11.0693	+	19.1726i	0.540770	+	0.936641i	−0.458090	+	0.888906i	$0.651466\pi$
$420$		0			0
$421$		−	0.914785i		−	0.0445839i	−0.999752	−	0.0222919i	$-0.992904\pi$
$421$		−	0.914785i		−	0.0445839i	0.999752	−	0.0222919i	$-0.00709633\pi$
$422$	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	0.543817	−	0.839204i	$-0.316978\pi$
$431$	32.0231	−	18.4885i	1.54250	−	0.890561i	0.998680	−	0.0513577i	$-0.0163549\pi$
$432$	1.73205	−	1.00000i	0.0833333	−	0.0481125i
$433$	24.8461	+	14.3449i	1.19403	+	0.689371i	0.959217	−	0.282670i	$-0.0912203\pi$
$433$	24.8461	+	14.3449i	1.19403	+	0.689371i	0.234809	+	0.972042i	$0.424554\pi$
$434$			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	0.796383	−	0.604792i	$-0.206744\pi$
$439$	−2.63106	−	4.55713i	−0.125574	−	0.217500i	−0.921957	+	0.387292i	$0.873410\pi$
$440$		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	0.437265	−	0.899333i	$-0.355947\pi$
$449$	−2.60523	−	1.50413i	−0.122948	−	0.0709843i	−0.560213	+	0.828349i	$0.689281\pi$
$450$		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	$-0.100019\pi$
$457$	4.44340	+	7.69620i	0.207854	+	0.360013i	−0.743185	+	0.669087i	$0.766686\pi$
$458$	−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	0.00970733	−	0.999953i	$-0.496910\pi$
$461$	−18.2808	−	10.5544i	−0.851424	−	0.491570i	−0.861131	+	0.508383i	$0.830243\pi$
$462$	−1.04965	+	1.81805i	−0.0488343	+	0.0845836i
$463$	24.4679			1.13712			0.568560	−	0.822642i	$-0.307501\pi$
$463$	24.4679			1.13712			0.568560	+	0.822642i	$0.307501\pi$
$464$	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	−0.928068	−	0.372410i	$-0.878531\pi$
$479$	−23.4090	+	13.5152i	−1.06959	+	0.617526i	−0.141518	+	0.989936i	$0.545198\pi$
$480$		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	$-0.795616\pi$
$487$	2.60875	−	4.51849i	0.118214	−	0.204752i	0.919060	+	0.394118i	$0.128950\pi$
$488$	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	0.983204	−	0.182509i	$-0.0584219\pi$
$491$	7.39085	+	12.8013i	0.333545	+	0.577716i	−0.649660	+	0.760225i	$0.725089\pi$
$492$	−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	$-0.925823\pi$
$499$		−	10.3171i		−	0.461859i	0.972971	−	0.230929i	$-0.0741766\pi$
$500$		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	$-0.130968\pi$
$503$	23.0660	+	13.3171i	1.02846	+	0.593782i	0.111917	+	0.993718i	$0.464301\pi$
$504$	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	−0.472347	−	0.881413i	$-0.656593\pi$
$509$	1.23647	−	0.713876i	0.0548055	−	0.0316420i	0.527152	+	0.849771i	$0.323260\pi$
$510$		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	$-0.773764\pi$
$523$	−13.0772	+	7.55011i	−0.571825	+	0.330143i	0.186053	+	0.982540i	$0.440430\pi$
$524$	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	$0.344952\pi$
$541$			41.1084i			1.76739i	−0.468064	+	0.883695i	$0.655048\pi$
$542$	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	−0.999213	−	0.0396752i	$-0.987368\pi$
$557$	−12.6021	−	21.8274i	−0.533966	−	0.924856i	0.465247	−	0.885181i	$-0.345966\pi$
$558$		−	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	$-0.284900\pi$
$563$	6.22913	+	3.59639i	0.262527	+	0.151570i	−0.362960	+	0.931805i	$0.618234\pi$
$564$			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	0.607044	−	0.794668i	$-0.292355\pi$
$569$	−9.17606	−	15.8934i	−0.384681	−	0.666286i	−0.991725	+	0.128382i	$0.959022\pi$
$570$		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	$-0.369580\pi$
$577$	19.1378			0.796715			0.398358	+	0.917230i	$0.369580\pi$
$578$	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	$-0.284720\pi$
$587$	−8.78102	−	15.2092i	−0.362432	−	0.627750i	−0.988360	+	0.152130i	$0.951387\pi$
$588$	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	$-0.297587\pi$
$593$	28.9248			1.18780			0.593901	+	0.804538i	$0.297587\pi$
$594$	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	0.993468	−	0.114109i	$-0.0364012\pi$
$601$	9.75496	+	16.8961i	0.397913	+	0.689206i	−0.595555	+	0.803314i	$0.703068\pi$
$602$	−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	$-0.505909\pi$
$607$	−22.0189	−	12.7126i	−0.893721	−	0.515990i	−0.875158	+	0.483837i	$0.839243\pi$
$608$	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	−0.976277	−	0.216526i	$-0.930527\pi$
$613$	−16.7285	−	28.9745i	−0.675656	−	1.17027i	0.300621	−	0.953744i	$-0.402806\pi$
$614$	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	$-0.924003\pi$
$617$	−6.98015	+	12.0900i	−0.281010	+	0.486724i	0.690624	+	0.723214i	$0.257336\pi$
$618$	−8.50726	+	14.7350i	−0.342212	+	0.592729i
$619$			42.1677i			1.69486i	0.530904	+	0.847432i	$0.321852\pi$
$619$			42.1677i			1.69486i	−0.530904	+	0.847432i	$0.678148\pi$
$620$		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	−0.386058	−	0.922475i	$-0.626163\pi$
$631$	−34.6143	−	19.9846i	−1.37797	−	0.795573i	−0.991915	+	0.126902i	$0.959497\pi$
$632$	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	0.473384	+	0.880856i	$0.343032\pi$
$641$	−13.3211	+	23.0728i	−0.526152	+	0.911322i	−0.999536	+	0.0304659i	$0.990301\pi$
$642$	−9.24134			−0.364727
$643$	−8.30927	+	14.3921i	−0.327686	+	0.567568i	−0.982052	−	0.188609i	$-0.939602\pi$
$643$	−8.30927	+	14.3921i	−0.327686	+	0.567568i	0.654367	+	0.756177i	$0.272935\pi$
$644$	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	$-0.534830\pi$
$647$	17.7301	−	10.2365i	0.697042	−	0.402437i	0.806245	+	0.591582i	$0.201497\pi$
$648$	−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	$-0.702664\pi$
$653$	−4.99471	+	2.88370i	−0.195458	+	0.112848i	0.399077	+	0.916917i	$0.369331\pi$
$654$	−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	−0.389574	−	0.920995i	$-0.627378\pi$
$659$	15.4749	−	26.8034i	0.602818	−	1.04411i	0.992392	−	0.123116i	$-0.0392889\pi$
$660$		0			0
$661$	26.7433	−	15.4403i	1.04020	−	0.600557i	0.120307	−	0.992737i	$-0.461612\pi$
$661$	26.7433	−	15.4403i	1.04020	−	0.600557i	0.919889	+	0.392180i	$0.128279\pi$
$662$			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	$-0.516991\pi$
$673$	20.3585	−	11.7540i	0.784761	−	0.453082i	0.838115	+	0.545494i	$0.183658\pi$
$674$	−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	$-0.916316\pi$
$683$	−6.73624	+	11.6675i	−0.257755	+	0.446445i	0.707885	+	0.706328i	$0.249649\pi$
$684$		−	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	−0.994417	−	0.105518i	$-0.966350\pi$
$691$	−36.8081	+	21.2512i	−1.40025	+	0.808432i	−0.405828	+	0.913950i	$0.633017\pi$
$692$	−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	0.695979	−	0.718062i	$-0.254971\pi$
$709$	11.2395	+	6.48914i	0.422109	+	0.243705i	−0.273870	+	0.961767i	$0.588304\pi$
$710$		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	−0.577468	−	0.816413i	$-0.695959\pi$
$719$	11.2164	−	19.4273i	0.418300	−	0.724517i	0.995769	+	0.0918957i	$0.0292926\pi$
$720$		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	$-0.533722\pi$
$733$	−5.72579			−0.211487			−0.105743	+	0.994393i	$0.533722\pi$
$734$	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	−0.128743	−	0.991678i	$-0.541094\pi$
$739$	18.0968	−	10.4482i	0.665703	−	0.384344i	0.794447	+	0.607334i	$0.207761\pi$
$740$		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	−0.998777	−	0.0494487i	$-0.984254\pi$
$743$	−14.7796	−	25.5991i	−0.542212	−	0.939139i	0.456564	−	0.889690i	$-0.349080\pi$
$744$	−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	0.607627	−	0.794222i	$-0.292121\pi$
$751$	−10.5234	−	18.2270i	−0.384003	−	0.665113i	−0.991630	+	0.129110i	$0.958788\pi$
$752$	−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	$-0.584274\pi$
$757$	12.1979	−	7.04245i	0.443340	−	0.255962i	0.705013	+	0.709194i	$0.250941\pi$
$758$	−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	−0.427997	−	0.903780i	$-0.640780\pi$
$761$	−39.3019	−	22.6909i	−1.42469	−	0.822546i	−0.996695	+	0.0812342i	$0.974114\pi$
$762$	−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	0.387516	−	0.921863i	$-0.373333\pi$
$769$	38.2583	−	22.0885i	1.37963	−	0.796530i	0.992115	+	0.125333i	$0.0400000\pi$
$770$		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	−0.341952	−	0.939717i	$-0.611088\pi$
$773$	17.8729	−	30.9568i	0.642843	−	1.11344i	0.984795	−	0.173720i	$-0.0555786\pi$
$774$	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	$-0.775247\pi$
$787$	5.09097	−	8.81782i	0.181474	−	0.314321i	0.942383	+	0.334537i	$0.108580\pi$
$788$	−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	$-0.559940\pi$
$797$	−31.9438	−	18.4428i	−1.13151	−	0.653277i	−0.944314	+	0.329046i	$0.893273\pi$
$798$	−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	0.739015	−	0.673689i	$-0.235291\pi$
$809$	−6.08464	−	10.5389i	−0.213924	−	0.370528i	−0.952939	+	0.303161i	$0.901958\pi$
$810$		0			0
$811$		−	26.2312i		−	0.921104i	−0.887633	−	0.460552i	$-0.847652\pi$
$811$		−	26.2312i		−	0.921104i	0.887633	−	0.460552i	$-0.152348\pi$
$812$	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	−0.228675	−	0.973503i	$-0.573439\pi$
$821$	14.3284	−	8.27253i	0.500066	−	0.288713i	0.728741	+	0.684790i	$0.240106\pi$
$822$	8.49038	−	4.90192i	0.296136	−	0.170974i
$823$	−24.1873	−	13.9646i	−0.843117	−	0.486774i	0.0152057	−	0.999884i	$-0.495160\pi$
$823$	−24.1873	−	13.9646i	−0.843117	−	0.486774i	−0.858322	+	0.513111i	$0.828493\pi$
$824$			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	$-0.510177\pi$
$827$	−1.83852			−0.0639316			−0.0319658	+	0.999489i	$0.510177\pi$
$828$	−1.18195	−	0.682396i	−0.0410754	−	0.0237149i
$829$	17.4866	+	30.2876i	0.607333	+	1.05193i	0.991678	+	0.128743i	$0.0410941\pi$
$829$	17.4866	+	30.2876i	0.607333	+	1.05193i	−0.384345	+	0.923190i	$0.625573\pi$
$830$		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	0.297771	−	0.954637i	$-0.403757\pi$
$839$	−11.0093	−	6.35624i	−0.380085	−	0.219442i	−0.677855	+	0.735196i	$0.737090\pi$
$840$		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	$-0.612648\pi$
$853$	−20.2430			−0.693106			−0.346553	+	0.938030i	$0.612648\pi$
$854$	−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	$-0.530808\pi$
$863$	−5.67766			−0.193270			−0.0966349	+	0.995320i	$0.530808\pi$
$864$	−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	−0.454728	−	0.890630i	$-0.650264\pi$
$877$	16.1085	−	27.9007i	0.543944	−	0.942139i	0.998673	−	0.0515091i	$-0.0164031\pi$
$878$	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	0.970982	+	0.239151i	$0.0768692\pi$
$881$	20.5576	+	35.6068i	0.692602	+	1.19962i	−0.278380	+	0.960471i	$0.589797\pi$
$882$	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	$-0.617816\pi$
$887$	7.88566	−	4.55279i	0.264775	−	0.152868i	0.626511	+	0.779413i	$0.284482\pi$
$888$	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	$-0.349995\pi$
$907$	43.7482	−	25.2580i	1.45263	−	0.838679i	0.998630	+	0.0523212i	$0.0166620\pi$
$908$	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	−0.828363	−	0.560191i	$-0.810728\pi$
$919$	2.15110	−	3.72581i	0.0709582	−	0.122903i	0.899322	+	0.437288i	$0.144061\pi$
$920$		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	−0.383315	−	0.923618i	$-0.625217\pi$
$929$	−41.9047	−	24.1937i	−1.37485	−	0.793769i	−0.991534	+	0.129849i	$0.958551\pi$
$930$		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	$0.0426860\pi$
$941$			8.20272i			0.267401i	−0.991022	+	0.133701i	$0.957314\pi$
$942$	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	−0.956327	−	0.292300i	$-0.905579\pi$
$947$	−22.5046	−	38.9792i	−0.731302	−	1.26665i	0.225024	−	0.974353i	$-0.427754\pi$
$948$		−	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	$-0.662076\pi$
$953$	−45.9157	−	26.5094i	−1.48735	−	0.858724i	−0.999896	+	0.0144217i	$0.995409\pi$
$954$			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	$-0.670280\pi$
$967$	−31.7061			−1.01960			−0.509799	+	0.860293i	$0.670280\pi$
$968$	−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	−0.524406	−	0.851469i	$-0.675712\pi$
$971$	14.8074	−	25.6471i	0.475191	−	0.823054i	0.999596	+	0.0284144i	$0.00904580\pi$
$972$	−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	$-0.172937\pi$
$977$	−0.615644	−	1.06633i	−0.0196962	−	0.0341148i	−0.875706	+	0.482846i	$0.839603\pi$
$978$	−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	$-0.368562\pi$
$983$	25.1632			0.802581			0.401290	+	0.915951i	$0.368562\pi$
$984$	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	0.756974	+	0.653445i	$0.226677\pi$
$991$	29.7295	+	51.4929i	0.944387	+	1.63573i	0.187414	+	0.982281i	$0.439990\pi$
$992$	−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	$-0.538365\pi$
$997$	−32.8413	−	18.9610i	−1.04010	−	0.600499i	−0.919860	+	0.392246i	$0.871698\pi$
$998$	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.h.49.3		8
5.2	odd	4		975.2.bc.j.751.2		8
5.3	odd	4		195.2.bb.b.166.3	yes	8
5.4	even	2		975.2.w.i.49.2		8
13.4	even	6		975.2.w.i.199.2		8
15.8	even	4		585.2.bu.d.361.2		8
65.4	even	6	inner	975.2.w.h.199.3		8
65.17	odd	12		975.2.bc.j.901.2		8
65.28	even	12		2535.2.a.bk.1.3		4
65.43	odd	12		195.2.bb.b.121.3	✓	8
65.63	even	12		2535.2.a.bj.1.2		4
195.128	odd	12		7605.2.a.ci.1.3		4
195.158	odd	12		7605.2.a.ch.1.2		4
195.173	even	12		585.2.bu.d.316.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.3	✓	8	65.43	odd	12
195.2.bb.b.166.3	yes	8	5.3	odd	4
585.2.bu.d.316.2		8	195.173	even	12
585.2.bu.d.361.2		8	15.8	even	4
975.2.w.h.49.3		8	1.1	even	1	trivial
975.2.w.h.199.3		8	65.4	even	6	inner
975.2.w.i.49.2		8	5.4	even	2
975.2.w.i.199.2		8	13.4	even	6
975.2.bc.j.751.2		8	5.2	odd	4
975.2.bc.j.901.2		8	65.17	odd	12
2535.2.a.bj.1.2		4	65.63	even	12
2535.2.a.bk.1.3		4	65.28	even	12
7605.2.a.ch.1.2		4	195.158	odd	12
7605.2.a.ci.1.3		4	195.128	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

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