LMFDB - Embedded newform 975.2.bc.j.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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, 0, 5]))

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

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
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:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-2.10121 - 0.563016i$ of defining polynomial
Character	$\chi$	$=$	975.901
Dual form			975.2.bc.j.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.975173 - 0.563016i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.366025 - 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(-0.524827 + 0.303009i) q^{7} +3.07638i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.975173 - 0.563016i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.366025 - 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(-0.524827 + 0.303009i) q^{7} +3.07638i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.66422 + 1.53819i) q^{11} +0.732051 q^{12} +(0.176977 - 3.60121i) q^{13} +0.682396 q^{14} +(1.00000 - 1.73205i) q^{16} +(-0.975173 - 1.68905i) q^{17} +1.12603i q^{18} +(-4.23037 + 2.44240i) q^{19} -0.606018i q^{21} +(-1.73205 - 3.00000i) q^{22} +(-0.932171 + 1.61457i) q^{23} +(-2.66422 - 1.53819i) q^{24} +(-2.20012 + 3.41216i) q^{26} +1.00000 q^{27} +(0.384200 + 0.221818i) q^{28} +(1.39085 - 2.40903i) q^{29} +9.15276i q^{31} +(3.37810 - 1.95035i) q^{32} +(-2.66422 + 1.53819i) q^{33} +2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(-3.24581 - 1.87397i) q^{37} +5.50045 q^{38} +(3.03025 + 1.95387i) q^{39} +(0.926751 + 0.535060i) q^{41} +(-0.341198 + 0.590973i) q^{42} +(2.50542 + 4.33951i) q^{43} -2.25207i q^{44} +(1.81805 - 1.04965i) q^{46} +10.2024i q^{47} +(1.00000 + 1.73205i) q^{48} +(-3.31637 + 5.74412i) q^{49} +1.95035 q^{51} +(-2.34785 + 1.20593i) q^{52} +10.6569 q^{53} +(-0.975173 - 0.563016i) q^{54} +(-0.932171 - 1.61457i) q^{56} -4.88481i q^{57} +(-2.71264 + 1.56615i) q^{58} +(10.0236 - 5.78712i) q^{59} +(3.13397 + 5.42820i) q^{61} +(5.15315 - 8.92552i) q^{62} +(0.524827 + 0.303009i) q^{63} -8.39230 q^{64} +3.46410 q^{66} +(1.71288 + 0.988929i) q^{67} +(-0.713876 + 1.23647i) q^{68} +(-0.932171 - 1.61457i) q^{69} +(-5.11557 + 2.95347i) q^{71} +(2.66422 - 1.53819i) q^{72} +4.35395i q^{73} +(2.11015 + 3.65488i) q^{74} +(3.09684 + 1.78796i) q^{76} -1.86434 q^{77} +(-1.85495 - 3.61144i) q^{78} -3.29546 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.602495 - 1.04355i) q^{82} +6.97707i q^{83} +(-0.384200 + 0.221818i) q^{84} -5.64237i q^{86} +(1.39085 + 2.40903i) q^{87} +(-4.73205 + 8.19615i) q^{88} +(14.1156 + 8.14963i) q^{89} +(0.998316 + 1.94364i) q^{91} +1.36479 q^{92} +(-7.92652 - 4.57638i) q^{93} +(5.74412 - 9.94911i) q^{94} +3.90069i q^{96} +(-11.4336 + 6.60121i) q^{97} +(6.46807 - 3.73434i) q^{98} -3.07638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 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} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 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 - 48 * q^92 + 12 * q^94 + 72 * 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 $

$2$	−0.975173	−	0.563016i	−0.689551	−	0.398113i	0.113893	−	0.993493i	$-0.463668\pi$
$2$	−0.975173	−	0.563016i	−0.689551	−	0.398113i	−0.803444	+	0.595380i	$0.797001\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.366025	−	0.633975i	−0.183013	−	0.316987i
$5$		0			0
$5$		0			0
$6$	0.975173	−	0.563016i	0.398113	−	0.229850i
$7$	−0.524827	+	0.303009i	−0.198366	+	0.114527i	−0.595893	−	0.803064i	$-0.703202\pi$
$7$	−0.524827	+	0.303009i	−0.198366	+	0.114527i	0.397527	+	0.917590i	$0.369868\pi$
$8$			3.07638i			1.08766i
$9$	−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	$0.513159\pi$
$12$	0.732051			0.211325
$13$	0.176977	−	3.60121i	0.0490845	−	0.998795i
$13$	0.176977	−	3.60121i	0.0490845	−	0.998795i
$14$	0.682396			0.182378
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	−0.975173	−	1.68905i	−0.236514	−	0.409654i	0.723198	−	0.690641i	$-0.242672\pi$
$17$	−0.975173	−	1.68905i	−0.236514	−	0.409654i	−0.959712	+	0.280987i	$0.909338\pi$
$18$			1.12603i			0.265408i
$19$	−4.23037	+	2.44240i	−0.970513	+	0.560326i	−0.899393	−	0.437142i	$-0.855991\pi$
$19$	−4.23037	+	2.44240i	−0.970513	+	0.560326i	−0.0711202	+	0.997468i	$0.522657\pi$
$20$		0			0
$21$		−	0.606018i		−	0.132244i
$22$	−1.73205	−	3.00000i	−0.369274	−	0.639602i
$23$	−0.932171	+	1.61457i	−0.194371	+	0.336660i	−0.946694	−	0.322134i	$-0.895600\pi$
$23$	−0.932171	+	1.61457i	−0.194371	+	0.336660i	0.752323	+	0.658794i	$0.228933\pi$
$24$	−2.66422	−	1.53819i	−0.543832	−	0.313982i
$25$		0			0
$26$	−2.20012	+	3.41216i	−0.431479	+	0.669179i
$27$	1.00000			0.192450
$28$	0.384200	+	0.221818i	0.0726070	+	0.0419197i
$29$	1.39085	−	2.40903i	0.258275	−	0.447345i	−0.707505	−	0.706708i	$-0.750179\pi$
$29$	1.39085	−	2.40903i	0.258275	−	0.447345i	0.965780	+	0.259363i	$0.0835127\pi$
$30$		0			0
$31$			9.15276i			1.64388i	0.569572	+	0.821942i	$0.307109\pi$
$31$			9.15276i			1.64388i	−0.569572	+	0.821942i	$0.692891\pi$
$32$	3.37810	−	1.95035i	0.597169	−	0.344776i
$33$	−2.66422	+	1.53819i	−0.463781	+	0.267764i
$34$			2.19615i			0.376637i
$35$		0			0
$36$	−0.366025	+	0.633975i	−0.0610042	+	0.105662i
$37$	−3.24581	−	1.87397i	−0.533607	−	0.308078i	0.208877	−	0.977942i	$-0.433019\pi$
$37$	−3.24581	−	1.87397i	−0.533607	−	0.308078i	−0.742484	+	0.669864i	$0.766353\pi$
$38$	5.50045			0.892291
$39$	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	$0.640037\pi$
$42$	−0.341198	+	0.590973i	−0.0526480	+	0.0911890i
$43$	2.50542	+	4.33951i	0.382073	+	0.661770i	0.991358	−	0.131181i	$-0.0418770\pi$
$43$	2.50542	+	4.33951i	0.382073	+	0.661770i	−0.609285	+	0.792951i	$0.708544\pi$
$44$		−	2.25207i		−	0.339512i
$45$		0			0
$46$	1.81805	−	1.04965i	0.268058	−	0.154763i
$47$			10.2024i			1.48817i	0.668082	+	0.744087i	$0.267115\pi$
$47$			10.2024i			1.48817i	−0.668082	+	0.744087i	$0.732885\pi$
$48$	1.00000	+	1.73205i	0.144338	+	0.250000i
$49$	−3.31637	+	5.74412i	−0.473767	+	0.820589i
$50$		0			0
$51$	1.95035			0.273103
$52$	−2.34785	+	1.20593i	−0.325588	+	0.167233i
$53$	10.6569			1.46384			0.731918	−	0.681393i	$-0.238625\pi$
$53$	10.6569			1.46384			0.731918	+	0.681393i	$0.238625\pi$
$54$	−0.975173	−	0.563016i	−0.132704	−	0.0766168i
$55$		0			0
$56$	−0.932171	−	1.61457i	−0.124567	−	0.215756i
$57$		−	4.88481i		−	0.647008i
$58$	−2.71264	+	1.56615i	−0.356188	+	0.205645i
$59$	10.0236	−	5.78712i	1.30496	−	0.753419i	0.323710	−	0.946156i	$-0.395070\pi$
$59$	10.0236	−	5.78712i	1.30496	−	0.753419i	0.981251	+	0.192737i	$0.0617363\pi$
$60$		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	$0.701904\pi$
$62$	5.15315	−	8.92552i	0.654451	−	1.13354i
$63$	0.524827	+	0.303009i	0.0661220	+	0.0381756i
$64$	−8.39230			−1.04904
$65$		0			0
$66$	3.46410			0.426401
$67$	1.71288	+	0.988929i	0.209261	+	0.120817i	0.600968	−	0.799273i	$-0.294782\pi$
$67$	1.71288	+	0.988929i	0.209261	+	0.120817i	−0.391707	+	0.920090i	$0.628115\pi$
$68$	−0.713876	+	1.23647i	−0.0865702	+	0.149944i
$69$	−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	$0.447326\pi$
$72$	2.66422	−	1.53819i	0.313982	−	0.181277i
$73$			4.35395i			0.509592i	0.966995	+	0.254796i	$0.0820083\pi$
$73$			4.35395i			0.509592i	−0.966995	+	0.254796i	$0.917992\pi$
$74$	2.11015	+	3.65488i	0.245300	+	0.424872i
$75$		0			0
$76$	3.09684	+	1.78796i	0.355232	+	0.205093i
$77$	−1.86434			−0.212461
$78$	−1.85495	−	3.61144i	−0.210032	−	0.408915i
$79$	−3.29546			−0.370768			−0.185384	−	0.982666i	$-0.559353\pi$
$79$	−3.29546			−0.370768			−0.185384	+	0.982666i	$0.559353\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.602495	−	1.04355i	−0.0665344	−	0.115241i
$83$			6.97707i			0.765833i	0.923783	+	0.382916i	$0.125080\pi$
$83$			6.97707i			0.765833i	−0.923783	+	0.382916i	$0.874920\pi$
$84$	−0.384200	+	0.221818i	−0.0419197	+	0.0242023i
$85$		0			0
$86$		−	5.64237i		−	0.608432i
$87$	1.39085	+	2.40903i	0.149115	+	0.258275i
$88$	−4.73205	+	8.19615i	−0.504438	+	0.873713i
$89$	14.1156	+	8.14963i	1.49625	+	0.863859i	0.999991	−	0.00431721i	$-0.00137421\pi$
$89$	14.1156	+	8.14963i	1.49625	+	0.863859i	0.496257	+	0.868176i	$0.334708\pi$
$90$		0			0
$91$	0.998316	+	1.94364i	0.104652	+	0.203748i
$92$	1.36479			0.142289
$93$	−7.92652	−	4.57638i	−0.821942	−	0.474548i
$94$	5.74412	−	9.94911i	0.592461	−	1.02617i
$95$		0			0
$96$			3.90069i			0.398113i
$97$	−11.4336	+	6.60121i	−1.16091	+	0.670251i	−0.951522	−	0.307582i	$-0.900480\pi$
$97$	−11.4336	+	6.60121i	−1.16091	+	0.670251i	−0.209387	+	0.977833i	$0.567147\pi$
$98$	6.46807	−	3.73434i	0.653374	−	0.377225i
$99$		−	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	$0.294629\pi$
$102$	−1.90192	−	1.09808i	−0.188319	−	0.108726i
$103$	15.1101			1.48885			0.744424	−	0.667708i	$-0.232724\pi$
$103$	15.1101			1.48885			0.744424	+	0.667708i	$0.232724\pi$
$104$	11.0787	+	0.544447i	1.08635	+	0.0533874i
$105$		0			0
$106$	−10.3923	−	6.00000i	−1.00939	−	0.582772i
$107$	−4.10350	+	7.10746i	−0.396700	+	0.687104i	−0.993317	−	0.115422i	$-0.963178\pi$
$107$	−4.10350	+	7.10746i	−0.396700	+	0.687104i	0.596617	+	0.802526i	$0.296511\pi$
$108$	−0.366025	−	0.633975i	−0.0352208	−	0.0610042i
$109$			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
$112$			1.21204i			0.114527i
$113$	1.73205	+	3.00000i	0.162938	+	0.282216i	0.935921	−	0.352210i	$-0.114570\pi$
$113$	1.73205	+	3.00000i	0.162938	+	0.282216i	−0.772983	+	0.634426i	$0.781236\pi$
$114$	−2.75023	+	4.76353i	−0.257582	+	0.446146i
$115$		0			0
$116$	−2.03635			−0.189070
$117$	−3.20722	+	1.64734i	−0.296508	+	0.152296i
$118$	−13.0330			−1.19978
$119$	1.02359	+	0.590973i	0.0938328	+	0.0541744i
$120$		0			0
$121$	−0.767949	−	1.33013i	−0.0698136	−	0.120921i
$122$		−	7.05791i		−	0.638994i
$123$	−0.926751	+	0.535060i	−0.0835623	+	0.0482447i
$124$	5.80261	−	3.35014i	0.521090	−	0.300852i
$125$		0			0
$126$	−0.341198	−	0.590973i	−0.0303963	−	0.0526480i
$127$	−9.02191	+	15.6264i	−0.800565	+	1.38662i	0.118680	+	0.992933i	$0.462134\pi$
$127$	−9.02191	+	15.6264i	−0.800565	+	1.38662i	−0.919245	+	0.393687i	$0.871199\pi$
$128$	1.42775	+	0.824313i	0.126197	+	0.0728597i
$129$	−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	$0.484434\pi$
$132$	1.95035	+	1.12603i	0.169756	+	0.0980085i
$133$	1.48014	−	2.56368i	0.128345	−	0.222299i
$134$	−1.11357	−	1.92875i	−0.0961975	−	0.166619i
$135$		0			0
$136$	5.19615	−	3.00000i	0.445566	−	0.257248i
$137$	7.54009	−	4.35327i	0.644193	−	0.371925i	−0.142035	−	0.989862i	$-0.545365\pi$
$137$	7.54009	−	4.35327i	0.644193	−	0.371925i	0.786228	+	0.617937i	$0.212031\pi$
$138$			2.09931i			0.178705i
$139$	−4.82844	−	8.36311i	−0.409543	−	0.709350i	0.585295	−	0.810820i	$-0.300979\pi$
$139$	−4.82844	−	8.36311i	−0.409543	−	0.709350i	−0.994839	+	0.101471i	$0.967645\pi$
$140$		0			0
$141$	−8.83555	−	5.10121i	−0.744087	−	0.429599i
$142$	6.65142			0.558174
$143$	6.01084	−	9.32218i	0.502652	−	0.779560i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	2.45135	−	4.24586i	0.202875	−	0.351390i
$147$	−3.31637	−	5.74412i	−0.273530	−	0.473767i
$148$			2.74368i			0.225529i
$149$	4.48228	−	2.58784i	0.367202	−	0.212004i	−0.305033	−	0.952342i	$-0.598668\pi$
$149$	4.48228	−	2.58784i	0.367202	−	0.212004i	0.672236	+	0.740337i	$0.265334\pi$
$150$		0			0
$151$		−	22.1451i		−	1.80215i	−0.433668	−	0.901073i	$-0.642781\pi$
$151$		−	22.1451i		−	1.80215i	0.433668	−	0.901073i	$-0.357219\pi$
$152$	−7.51376	−	13.0142i	−0.609446	−	1.05559i
$153$	−0.975173	+	1.68905i	−0.0788380	+	0.136551i
$154$	1.81805	+	1.04965i	0.146503	+	0.0845836i
$155$		0			0
$156$	0.129556	−	2.63627i	0.0103728	−	0.211070i
$157$	14.3756			1.14730			0.573650	−	0.819100i	$-0.305527\pi$
$157$	14.3756			1.14730			0.573650	+	0.819100i	$0.305527\pi$
$158$	3.21364	+	1.85540i	0.255664	+	0.147608i
$159$	−5.32844	+	9.22913i	−0.422573	+	0.731918i
$160$		0			0
$161$		−	1.12983i		−	0.0890427i
$162$	0.975173	−	0.563016i	0.0766168	−	0.0442347i
$163$	8.72098	−	5.03506i	0.683080	−	0.394376i	−0.117935	−	0.993021i	$-0.537627\pi$
$163$	8.72098	−	5.03506i	0.683080	−	0.394376i	0.801014	+	0.598645i	$0.204294\pi$
$164$		−	0.783382i		−	0.0611719i
$165$		0			0
$166$	3.92820	−	6.80385i	0.304888	−	0.528081i
$167$	9.39030	+	5.42149i	0.726643	+	0.419528i	0.817193	−	0.576364i	$-0.195529\pi$
$167$	9.39030	+	5.42149i	0.726643	+	0.419528i	−0.0905495	+	0.995892i	$0.528862\pi$
$168$	1.86434			0.143837
$169$	−12.9374	−	1.27466i	−0.995181	−	0.0980507i
$170$		0			0
$171$	4.23037	+	2.44240i	0.323504	+	0.186775i
$172$	1.83409	−	3.17674i	0.139848	−	0.242225i
$173$	−12.3311	−	21.3581i	−0.937518	−	1.62383i	−0.770081	−	0.637947i	$-0.779784\pi$
$173$	−12.3311	−	21.3581i	−0.937518	−	1.62383i	−0.167438	−	0.985883i	$-0.553549\pi$
$174$		−	3.13229i		−	0.237458i
$175$		0			0
$176$	5.32844	−	3.07638i	0.401647	−	0.231891i
$177$			11.5742i			0.869974i
$178$	−9.17674	−	15.8946i	−0.687826	−	1.19135i
$179$	−11.4199	+	19.7798i	−0.853561	+	1.47841i	0.0244128	+	0.999702i	$0.492228\pi$
$179$	−11.4199	+	19.7798i	−0.853561	+	1.47841i	−0.877974	+	0.478709i	$0.841105\pi$
$180$		0			0
$181$	−17.4616			−1.29791			−0.648957	−	0.760825i	$-0.724794\pi$
$181$	−17.4616			−1.29791			−0.648957	+	0.760825i	$0.724794\pi$
$182$	0.120768	−	2.45745i	0.00895194	−	0.182158i
$183$	−6.26795			−0.463340
$184$	−4.96702	−	2.86771i	−0.366173	−	0.211410i
$185$		0			0
$186$	5.15315	+	8.92552i	0.377847	+	0.654451i
$187$		−	6.00000i		−	0.438763i
$188$	6.46807	−	3.73434i	0.471732	−	0.272355i
$189$	−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	$0.922879\pi$
$192$	4.19615	−	7.26795i	0.302831	−	0.524519i
$193$	−18.1959	−	10.5054i	−1.30977	−	0.756197i	−0.327713	−	0.944777i	$-0.606278\pi$
$193$	−18.1959	−	10.5054i	−1.30977	−	0.756197i	−0.982058	+	0.188581i	$0.939611\pi$
$194$	14.8663			1.06734
$195$		0			0
$196$	4.85550			0.346822
$197$	17.6475	+	10.1888i	1.25734	+	0.725923i	0.972556	−	0.232670i	$-0.0747461\pi$
$197$	17.6475	+	10.1888i	1.25734	+	0.725923i	0.284780	+	0.958593i	$0.408079\pi$
$198$	−1.73205	+	3.00000i	−0.123091	+	0.213201i
$199$	−7.40069	−	12.8184i	−0.524621	−	0.908670i	−0.999589	−	0.0286673i	$-0.990874\pi$
$199$	−7.40069	−	12.8184i	−0.524621	−	0.908670i	0.474968	−	0.880003i	$-0.342460\pi$
$200$		0			0
$201$	−1.71288	+	0.988929i	−0.120817	+	0.0697537i
$202$	7.66909	−	4.42775i	0.539595	−	0.311536i
$203$			1.68576i			0.118317i
$204$	−0.713876	−	1.23647i	−0.0499813	−	0.0865702i
$205$		0			0
$206$	−14.7350	−	8.50726i	−1.02664	−	0.592729i
$207$	1.86434			0.129581
$208$	−6.06049	−	3.90774i	−0.420220	−	0.270953i
$209$	−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	$0.224176\pi$
$212$	−3.90069	−	6.75620i	−0.267901	−	0.464017i
$213$		−	5.90695i		−	0.404737i
$214$	8.00323	−	4.62067i	0.547090	−	0.315862i
$215$		0			0
$216$			3.07638i			0.209321i
$217$	−2.77337	−	4.80362i	−0.188269	−	0.326091i
$218$	5.96387	−	10.3297i	0.403924	−	0.699617i
$219$	−3.77063	−	2.17698i	−0.254796	−	0.147106i
$220$		0			0
$221$	−6.25519	+	3.21288i	−0.420770	+	0.216121i
$222$	−4.22030			−0.283248
$223$	−5.34065	−	3.08342i	−0.357636	−	0.206481i	0.310407	−	0.950604i	$-0.399535\pi$
$223$	−5.34065	−	3.08342i	−0.357636	−	0.206481i	−0.668043	+	0.744122i	$0.732868\pi$
$224$	−1.18195	+	2.04719i	−0.0789720	+	0.136784i
$225$		0			0
$226$		−	3.90069i		−	0.259470i
$227$	−14.8189	+	8.55568i	−0.983563	+	0.567860i	−0.903344	−	0.428917i	$-0.858895\pi$
$227$	−14.8189	+	8.55568i	−0.983563	+	0.567860i	−0.0802192	+	0.996777i	$0.525562\pi$
$228$	−3.09684	+	1.78796i	−0.205093	+	0.118411i
$229$			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
$232$	7.41108	+	4.27879i	0.486561	+	0.280916i
$233$	11.3284			0.742151			0.371075	−	0.928603i	$-0.378989\pi$
$233$	11.3284			0.742151			0.371075	+	0.928603i	$0.378989\pi$
$234$	4.05507	+	0.199281i	0.265088	+	0.0130274i
$235$		0			0
$236$	−7.33778	−	4.23647i	−0.477649	−	0.275771i
$237$	1.64773	−	2.85395i	0.107032	−	0.185384i
$238$	−0.665454	−	1.15260i	−0.0431350	−	0.0747120i
$239$		−	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	−0.339478	−	0.940614i	$-0.610250\pi$
$241$	4.74075	−	2.73708i	0.305379	−	0.176311i	0.644857	+	0.764303i	$0.276917\pi$
$242$			1.72947i			0.111175i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.29423	−	3.97372i	0.146873	−	0.254391i
$245$		0			0
$246$	1.20499			0.0768273
$247$	8.04692	+	15.6667i	0.512013	+	0.996846i
$248$	−28.1573			−1.78799
$249$	−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	$0.785742\pi$
$252$		−	0.443636i		−	0.0279465i
$253$	−4.96702	+	2.86771i	−0.312274	+	0.180291i
$254$	17.5958	−	10.1590i	1.10406	−	0.637430i
$255$		0			0
$256$	7.46410	+	12.9282i	0.466506	+	0.808013i
$257$	−3.63939	+	6.30362i	−0.227019	+	0.393209i	−0.956923	−	0.290341i	$-0.906231\pi$
$257$	−3.63939	+	6.30362i	−0.227019	+	0.393209i	0.729904	+	0.683550i	$0.239565\pi$
$258$	4.88643	+	2.82118i	0.304216	+	0.175639i
$259$	2.27132			0.141133
$260$		0			0
$261$	−2.78171			−0.172183
$262$	−1.09120	−	0.630007i	−0.0674148	−	0.0389220i
$263$	−0.643362	+	1.11434i	−0.0396714	+	0.0687129i	−0.885179	−	0.465250i	$-0.845964\pi$
$263$	−0.643362	+	1.11434i	−0.0396714	+	0.0687129i	0.845508	+	0.533963i	$0.179298\pi$
$264$	−4.73205	−	8.19615i	−0.291238	−	0.504438i
$265$		0			0
$266$	−2.88679	+	1.66669i	−0.177000	+	0.102191i
$267$	−14.1156	+	8.14963i	−0.863859	+	0.498749i
$268$		−	1.44789i		−	0.0884441i
$269$	−9.46952	−	16.4017i	−0.577367	−	1.00003i	−0.995780	−	0.0917720i	$-0.970747\pi$
$269$	−9.46952	−	16.4017i	−0.577367	−	1.00003i	0.418413	−	0.908257i	$-0.362586\pi$
$270$		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	$0.557986\pi$
$272$	−3.90069			−0.236514
$273$	−2.18240	−	0.107251i	−0.132085	−	0.00649113i
$274$	−9.80385			−0.592272
$275$		0			0
$276$	−0.682396	+	1.18195i	−0.0410754	+	0.0711447i
$277$	−10.4607	−	18.1185i	−0.628525	−	1.08864i	−0.987848	−	0.155423i	$-0.950326\pi$
$277$	−10.4607	−	18.1185i	−0.628525	−	1.08864i	0.359323	−	0.933213i	$-0.383008\pi$
$278$			10.8740i			0.652177i
$279$	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	$-0.103051\pi$
$282$	5.74412	+	9.94911i	0.342058	+	0.592461i
$283$	−1.39254	+	2.41194i	−0.0827777	+	0.143375i	−0.904442	−	0.426596i	$-0.859712\pi$
$283$	−1.39254	+	2.41194i	−0.0827777	+	0.143375i	0.821664	+	0.569972i	$0.193046\pi$
$284$	3.74486	+	2.16209i	0.222216	+	0.128297i
$285$		0			0
$286$	−11.1101	+	5.70654i	−0.656957	+	0.337435i
$287$	−0.648512			−0.0382805
$288$	−3.37810	−	1.95035i	−0.199056	−	0.114925i
$289$	6.59808	−	11.4282i	0.388122	−	0.672247i
$290$		0			0
$291$		−	13.2024i		−	0.773939i
$292$	2.76030	−	1.59366i	0.161534	−	0.0932618i
$293$	−4.29428	+	2.47930i	−0.250874	+	0.144842i	−0.620165	−	0.784472i	$-0.712934\pi$
$293$	−4.29428	+	2.47930i	−0.250874	+	0.144842i	0.369290	+	0.929314i	$0.379601\pi$
$294$			7.46868i			0.435582i
$295$		0			0
$296$	5.76503	−	9.98533i	0.335086	−	0.580385i
$297$	2.66422	+	1.53819i	0.154594	+	0.0892548i
$298$	−5.82799			−0.337606
$299$	5.64941	+	3.64268i	0.326714	+	0.210662i
$300$		0			0
$301$	−2.62983	−	1.51833i	−0.151581	−	0.0875151i
$302$	−12.4681	+	21.5953i	−0.717457	+	1.24267i
$303$	−3.93217	−	6.81072i	−0.225897	−	0.391266i
$304$			9.76961i			0.560326i
$305$		0			0
$306$	1.90192	−	1.09808i	0.108726	−	0.0627728i
$307$		−	9.60723i		−	0.548314i	−0.961685	−	0.274157i	$-0.911601\pi$
$307$		−	9.60723i		−	0.548314i	0.961685	−	0.274157i	$-0.0883987\pi$
$308$	0.682396	+	1.18195i	0.0388831	+	0.0673476i
$309$	−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	$0.235641\pi$
$312$	−6.01084	+	9.32218i	−0.340297	+	0.527765i
$313$	−29.2311			−1.65224			−0.826121	−	0.563493i	$-0.809457\pi$
$313$	−29.2311			−1.65224			−0.826121	+	0.563493i	$0.809457\pi$
$314$	−14.0187	−	8.09371i	−0.791122	−	0.456755i
$315$		0			0
$316$	1.20622	+	2.08924i	0.0678553	+	0.117529i
$317$			8.62570i			0.484467i	0.970218	+	0.242234i	$0.0778801\pi$
$317$			8.62570i			0.484467i	−0.970218	+	0.242234i	$0.922120\pi$
$318$	10.3923	−	6.00000i	0.582772	−	0.336463i
$319$	7.41108	−	4.27879i	0.414941	−	0.239566i
$320$		0			0
$321$	−4.10350	−	7.10746i	−0.229035	−	0.396700i
$322$	−0.636110	+	1.10177i	−0.0354490	+	0.0613995i
$323$	8.25068	+	4.76353i	0.459080	+	0.265050i
$324$	0.732051			0.0406695
$325$		0			0
$326$	−11.3393			−0.628025
$327$	−9.17356	−	5.29636i	−0.507299	−	0.292889i
$328$	−1.64605	+	2.85104i	−0.0908877	+	0.157422i
$329$	−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	$0.144920\pi$
$332$	4.42328	−	2.55378i	0.242759	−	0.140157i
$333$			3.74793i			0.205386i
$334$	−6.10478	−	10.5738i	−0.334039	−	0.578572i
$335$		0			0
$336$	−1.04965	−	0.606018i	−0.0572633	−	0.0330610i
$337$	−17.7847			−0.968795			−0.484397	−	0.874848i	$-0.660961\pi$
$337$	−17.7847			−0.968795			−0.484397	+	0.874848i	$0.660961\pi$
$338$	11.8985	+	8.52696i	0.647193	+	0.463805i
$339$	−3.46410			−0.188144
$340$		0			0
$341$	−14.0787	+	24.3850i	−0.762403	+	1.32052i
$342$	−2.75023	−	4.76353i	−0.148715	−	0.257582i
$343$		−	8.26169i		−	0.446089i
$344$	−13.3500	+	7.70762i	−0.719783	+	0.415567i
$345$		0			0
$346$			27.7705i			1.49295i
$347$	4.29546	+	7.43996i	0.230592	+	0.399398i	0.957983	−	0.286826i	$-0.0926003\pi$
$347$	4.29546	+	7.43996i	0.230592	+	0.399398i	−0.727390	+	0.686224i	$0.759267\pi$
$348$	1.01817	−	1.76353i	0.0545799	−	0.0945352i
$349$	26.1369	+	15.0901i	1.39908	+	0.807756i	0.994296	−	0.106658i	$-0.0340150\pi$
$349$	26.1369	+	15.0901i	1.39908	+	0.807756i	0.404779	+	0.914414i	$0.367348\pi$
$350$		0			0
$351$	0.176977	−	3.60121i	0.00944631	−	0.192218i
$352$	12.0000			0.639602
$353$	−24.7940	−	14.3148i	−1.31965	−	0.761903i	−0.335981	−	0.941869i	$-0.609068\pi$
$353$	−24.7940	−	14.3148i	−1.31965	−	0.761903i	−0.983673	+	0.179966i	$0.942401\pi$
$354$	6.51649	−	11.2869i	0.346348	−	0.599892i
$355$		0			0
$356$		−	11.9319i		−	0.632388i
$357$	−1.02359	+	0.590973i	−0.0541744	+	0.0312776i
$358$	22.2727	−	12.8591i	1.17715	−	0.679627i
$359$			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
$362$	17.0281	+	9.83118i	0.894978	+	0.516716i
$363$	1.53590			0.0806138
$364$	0.866807	−	1.34433i	0.0454330	−	0.0704619i
$365$		0			0
$366$	6.11233	+	3.52896i	0.319497	+	0.184462i
$367$	16.2483	−	28.1429i	0.848155	−	1.46905i	−0.0346981	−	0.999398i	$-0.511047\pi$
$367$	16.2483	−	28.1429i	0.848155	−	1.46905i	0.882853	−	0.469649i	$-0.155620\pi$
$368$	1.86434	+	3.22913i	0.0971855	+	0.168330i
$369$		−	1.07012i		−	0.0557082i
$370$		0			0
$371$	−5.59302	+	3.22913i	−0.290375	+	0.167648i
$372$			6.70028i			0.347393i
$373$	5.37586	+	9.31127i	0.278352	+	0.482119i	0.970975	−	0.239180i	$-0.0768786\pi$
$373$	5.37586	+	9.31127i	0.278352	+	0.482119i	−0.692624	+	0.721299i	$0.743545\pi$
$374$	−3.37810	+	5.85104i	−0.174677	+	0.302550i
$375$		0			0
$376$	−31.3865			−1.61863
$377$	−8.42925	−	5.43509i	−0.434129	−	0.279921i
$378$	0.682396			0.0350987
$379$	5.05881	+	2.92071i	0.259854	+	0.150027i	0.624268	−	0.781210i	$-0.285397\pi$
$379$	5.05881	+	2.92071i	0.259854	+	0.150027i	−0.364414	+	0.931237i	$0.618731\pi$
$380$		0			0
$381$	−9.02191	−	15.6264i	−0.462206	−	0.800565i
$382$			8.64068i			0.442095i
$383$	20.4762	−	11.8220i	1.04629	−	0.604074i	0.124679	−	0.992197i	$-0.460210\pi$
$383$	20.4762	−	11.8220i	1.04629	−	0.604074i	0.921607	+	0.388124i	$0.126877\pi$
$384$	−1.42775	+	0.824313i	−0.0728597	+	0.0420655i
$385$		0			0
$386$	11.8294	+	20.4892i	0.602103	+	1.04287i
$387$	2.50542	−	4.33951i	0.127358	−	0.220590i
$388$	8.36999	+	4.83242i	0.424922	+	0.245329i
$389$	−16.5939			−0.841345			−0.420673	−	0.907212i	$-0.638206\pi$
$389$	−16.5939			−0.841345			−0.420673	+	0.907212i	$0.638206\pi$
$390$		0			0
$391$	3.63611			0.183886
$392$	−17.6711	−	10.2024i	−0.892525	−	0.515300i
$393$	−0.559493	+	0.969070i	−0.0282227	+	0.0488831i
$394$	−11.4729	−	19.8717i	−0.577998	−	1.00112i
$395$		0			0
$396$	−1.95035	+	1.12603i	−0.0980085	+	0.0565853i
$397$	20.2680	−	11.7017i	1.01722	−	0.587293i	0.103923	−	0.994585i	$-0.466860\pi$
$397$	20.2680	−	11.7017i	1.01722	−	0.587293i	0.913298	+	0.407292i	$0.133527\pi$
$398$			16.6668i			0.835433i
$399$	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	$0.665778\pi$
$402$	2.22713			0.111079
$403$	32.9610	+	1.61982i	1.64190	+	0.0806892i
$404$	5.75710			0.286426
$405$		0			0
$406$	0.949113	−	1.64391i	0.0471037	−	0.0815860i
$407$	−5.76503	−	9.98533i	−0.285762	−	0.494954i
$408$			6.00000i			0.297044i
$409$	16.6974	−	9.64024i	0.825633	−	0.476679i	−0.0267224	−	0.999643i	$-0.508507\pi$
$409$	16.6974	−	9.64024i	0.825633	−	0.476679i	0.852355	+	0.522964i	$0.175174\pi$
$410$		0			0
$411$			8.70654i			0.429462i
$412$	−5.53070	−	9.57945i	−0.272478	−	0.471946i
$413$	−3.50710	+	6.07448i	−0.172573	+	0.298906i
$414$	−1.81805	−	1.04965i	−0.0893525	−	0.0515877i
$415$		0			0
$416$	−6.42575	−	12.5104i	−0.315048	−	0.613372i
$417$	9.65689			0.472900
$418$	14.6544	+	8.46073i	0.716771	+	0.413828i
$419$	−11.0693	+	19.1726i	−0.540770	+	0.936641i	0.458090	+	0.888906i	$0.348534\pi$
$419$	−11.0693	+	19.1726i	−0.540770	+	0.936641i	−0.998860	+	0.0477351i	$0.984800\pi$
$420$		0			0
$421$			0.914785i			0.0445839i	0.999752	+	0.0222919i	$0.00709633\pi$
$421$			0.914785i			0.0445839i	−0.999752	+	0.0222919i	$0.992904\pi$
$422$	5.09069	−	2.93911i	0.247811	−	0.143074i
$423$	8.83555	−	5.10121i	0.429599	−	0.248029i
$424$			32.7846i			1.59216i
$425$		0			0
$426$	−3.32571	+	5.76030i	−0.161131	+	0.279087i
$427$	−3.28959	−	1.89925i	−0.159194	−	0.0919110i
$428$	6.00793			0.290404
$429$	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	$0.316978\pi$
$432$	1.00000	−	1.73205i	0.0481125	−	0.0833333i
$433$	14.3449	+	24.8461i	0.689371	+	1.19403i	0.972042	+	0.234809i	$0.0754464\pi$
$433$	14.3449	+	24.8461i	0.689371	+	1.19403i	−0.282670	+	0.959217i	$0.591220\pi$
$434$			6.24581i			0.299808i
$435$		0			0
$436$	6.71551	−	3.87720i	0.321615	−	0.185684i
$437$		−	9.10695i		−	0.435644i
$438$	2.45135	+	4.24586i	0.117130	+	0.202875i
$439$	2.63106	−	4.55713i	0.125574	−	0.217500i	−0.796383	−	0.604792i	$-0.793256\pi$
$439$	2.63106	−	4.55713i	0.125574	−	0.217500i	0.921957	+	0.387292i	$0.126590\pi$
$440$		0			0
$441$	6.63274			0.315845
$442$	7.90880	+	0.388668i	0.376183	+	0.0184870i
$443$	−28.8275			−1.36964			−0.684819	−	0.728714i	$-0.740119\pi$
$443$	−28.8275			−1.36964			−0.684819	+	0.728714i	$0.740119\pi$
$444$	−2.37610	−	1.37184i	−0.112765	−	0.0651046i
$445$		0			0
$446$	3.47204	+	6.01374i	0.164406	+	0.284759i
$447$			5.17569i			0.244802i
$448$	4.40451	−	2.54295i	0.208094	−	0.120143i
$449$	2.60523	−	1.50413i	0.122948	−	0.0709843i	−0.437265	−	0.899333i	$-0.644053\pi$
$449$	2.60523	−	1.50413i	0.122948	−	0.0709843i	0.560213	+	0.828349i	$0.310719\pi$
$450$		0			0
$451$	1.64605	+	2.85104i	0.0775093	+	0.134250i
$452$	1.26795	−	2.19615i	0.0596393	−	0.103298i
$453$	19.1782	+	11.0726i	0.901073	+	0.520235i
$454$	19.2679			0.904290
$455$		0			0
$456$	15.0275			0.703728
$457$	−7.69620	−	4.44340i	−0.360013	−	0.207854i	0.309073	−	0.951038i	$-0.399981\pi$
$457$	−7.69620	−	4.44340i	−0.360013	−	0.207854i	−0.669087	+	0.743185i	$0.733314\pi$
$458$	16.2828	−	28.2026i	0.760843	−	1.31782i
$459$	−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	$0.496910\pi$
$462$	−1.81805	+	1.04965i	−0.0845836	+	0.0488343i
$463$			24.4679i			1.13712i	0.822642	+	0.568560i	$0.192499\pi$
$463$			24.4679i			1.13712i	−0.822642	+	0.568560i	$0.807501\pi$
$464$	−2.78171	−	4.81805i	−0.129137	−	0.223673i
$465$		0			0
$466$	−11.0472	−	6.37810i	−0.511751	−	0.295460i
$467$	−19.5058			−0.902622			−0.451311	−	0.892367i	$-0.649043\pi$
$467$	−19.5058			−0.902622			−0.451311	+	0.892367i	$0.649043\pi$
$468$	2.21829	+	1.43033i	0.102541	+	0.0661171i
$469$	−1.19862			−0.0553470
$470$		0			0
$471$	−7.18782	+	12.4497i	−0.331197	+	0.573650i
$472$	17.8034	+	30.8364i	0.819467	+	1.41936i
$473$			15.4152i			0.708793i
$474$	−3.21364	+	1.85540i	−0.147608	+	0.0852213i
$475$		0			0
$476$		−	0.865244i		−	0.0396584i
$477$	−5.32844	−	9.22913i	−0.243973	−	0.422573i
$478$	−10.7704	+	18.6549i	−0.492627	+	0.853255i
$479$	23.4090	+	13.5152i	1.06959	+	0.617526i	0.928068	−	0.372410i	$-0.121469\pi$
$479$	23.4090	+	13.5152i	1.06959	+	0.617526i	0.141518	+	0.989936i	$0.454802\pi$
$480$		0			0
$481$	−7.32297	+	11.3572i	−0.333899	+	0.517842i
$482$	−6.16407			−0.280766
$483$	0.978457	+	0.564913i	0.0445213	+	0.0257044i
$484$	−0.562178	+	0.973721i	−0.0255535	+	0.0442600i
$485$		0			0
$486$			1.12603i			0.0510779i
$487$	4.51849	−	2.60875i	0.204752	−	0.118214i	−0.394118	−	0.919060i	$-0.628950\pi$
$487$	4.51849	−	2.60875i	0.204752	−	0.118214i	0.598870	+	0.800846i	$0.295616\pi$
$488$	−16.6992	+	9.64129i	−0.755937	+	0.436441i
$489$			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	$0.0584219\pi$
$492$	0.678429	+	0.391691i	0.0305859	+	0.0176588i
$493$	−5.42529			−0.244343
$494$	0.973451	−	19.8083i	0.0437977	−	0.891215i
$495$		0			0
$496$	15.8530	+	9.15276i	0.711822	+	0.410971i
$497$	1.78986	−	3.10013i	0.0802862	−	0.139060i
$498$	3.92820	+	6.80385i	0.176027	+	0.304888i
$499$		−	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
$502$		−	5.31470i		−	0.237207i
$503$	13.3171	+	23.0660i	0.593782	+	1.02846i	0.993718	+	0.111917i	$0.0356992\pi$
$503$	13.3171	+	23.0660i	0.593782	+	1.02846i	−0.399936	+	0.916543i	$0.630968\pi$
$504$	−0.932171	+	1.61457i	−0.0415222	+	0.0719185i
$505$		0			0
$506$	6.45827			0.287105
$507$	7.57257	−	10.5668i	0.336309	−	0.469286i
$508$	13.2090			0.586054
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	0.472347	−	0.881413i	$-0.343407\pi$
$509$	−1.23647	−	0.713876i	−0.0548055	−	0.0316420i	−0.527152	+	0.849771i	$0.676740\pi$
$510$		0			0
$511$	−1.31929	−	2.28507i	−0.0583619	−	0.101086i
$512$		−	20.1069i		−	0.888608i
$513$	−4.23037	+	2.44240i	−0.186775	+	0.107835i
$514$	7.09808	−	4.09808i	0.313083	−	0.180758i
$515$		0			0
$516$	1.83409	+	3.17674i	0.0807415	+	0.139848i
$517$	−15.6932	+	27.1815i	−0.690188	+	1.19544i
$518$	−2.21493	−	1.27879i	−0.0973183	−	0.0561867i
$519$	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	$0.409084\pi$
$522$	2.71264	+	1.56615i	0.118729	+	0.0685483i
$523$	7.55011	−	13.0772i	0.330143	−	0.571825i	−0.652397	−	0.757878i	$-0.726236\pi$
$523$	7.55011	−	13.0772i	0.330143	−	0.571825i	0.982540	+	0.186053i	$0.0595697\pi$
$524$	−0.409577	−	0.709409i	−0.0178925	−	0.0309907i
$525$		0			0
$526$	1.25478	−	0.724446i	0.0547109	−	0.0315874i
$527$	15.4595	−	8.92552i	0.673424	−	0.388802i
$528$			6.15276i			0.267764i
$529$	9.76212	+	16.9085i	0.424440	+	0.735151i
$530$		0			0
$531$	−10.0236	−	5.78712i	−0.434987	−	0.251140i
$532$	−2.16708			−0.0939547
$533$	2.09087	−	3.24273i	0.0905658	−	0.140458i
$534$	18.3535			0.794233
$535$		0			0
$536$	−3.04232	+	5.26945i	−0.131408	+	0.227606i
$537$	−11.4199	−	19.7798i	−0.492804	−	0.853561i
$538$			21.3260i			0.919428i
$539$	−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	$-0.344952\pi$
$542$	−6.20677	−	10.7504i	−0.266604	−	0.461771i
$543$	8.73082	−	15.1222i	0.374675	−	0.648957i
$544$	−6.58846	−	3.80385i	−0.282478	−	0.163089i
$545$		0			0
$546$	2.06783	+	1.33331i	0.0884949	+	0.0570605i
$547$	−30.1327			−1.28838			−0.644191	−	0.764864i	$-0.722806\pi$
$547$	−30.1327			−1.28838			−0.644191	+	0.764864i	$0.722806\pi$
$548$	−5.51973	−	3.18682i	−0.235791	−	0.136134i
$549$	3.13397	−	5.42820i	0.133755	−	0.231670i
$550$		0			0
$551$			13.5881i			0.578872i
$552$	4.96702	−	2.86771i	0.211410	−	0.122058i
$553$	1.72955	−	0.998555i	0.0735479	−	0.0424629i
$554$			23.5583i			1.00089i
$555$		0			0
$556$	−3.53467	+	6.12222i	−0.149903	+	0.259640i
$557$	21.8274	+	12.6021i	0.924856	+	0.533966i	0.885181	−	0.465247i	$-0.154034\pi$
$557$	21.8274	+	12.6021i	0.924856	+	0.533966i	0.0396752	+	0.999213i	$0.487368\pi$
$558$	−10.3063			−0.436301
$559$	16.0709	−	8.25454i	0.679726	−	0.349130i
$560$		0			0
$561$	5.19615	+	3.00000i	0.219382	+	0.126660i
$562$	−6.00474	+	10.4005i	−0.253295	+	0.438719i
$563$	3.59639	+	6.22913i	0.151570	+	0.262527i	0.931805	−	0.362960i	$-0.118234\pi$
$563$	3.59639	+	6.22913i	0.151570	+	0.262527i	−0.780235	+	0.625487i	$0.784900\pi$
$564$			7.46868i			0.314488i
$565$		0			0
$566$	2.71593	−	1.56804i	0.114159	−	0.0659097i
$567$		−	0.606018i		−	0.0254504i
$568$	−9.08600	−	15.7374i	−0.381240	−	0.660328i
$569$	9.17606	−	15.8934i	0.384681	−	0.666286i	−0.607044	−	0.794668i	$-0.707645\pi$
$569$	9.17606	−	15.8934i	0.384681	−	0.666286i	0.991725	+	0.128382i	$0.0409783\pi$
$570$		0			0
$571$	27.5433			1.15265			0.576325	−	0.817221i	$-0.304486\pi$
$571$	27.5433			1.15265			0.576325	+	0.817221i	$0.304486\pi$
$572$	−8.11015	−	0.398563i	−0.339102	−	0.0166648i
$573$	7.67356			0.320568
$574$	0.632411	+	0.365123i	0.0263963	+	0.0152399i
$575$		0			0
$576$	4.19615	+	7.26795i	0.174840	+	0.302831i
$577$		−	19.1378i		−	0.796715i	−0.917230	−	0.398358i	$-0.869580\pi$
$577$		−	19.1378i		−	0.796715i	0.917230	−	0.398358i	$-0.130420\pi$
$578$	−12.8685	+	7.42965i	−0.535260	+	0.309033i
$579$	18.1959	−	10.5054i	0.756197	−	0.436590i
$580$		0			0
$581$	−2.11412	−	3.66176i	−0.0877083	−	0.151915i
$582$	−7.43317	+	12.8746i	−0.308115	+	0.533671i
$583$	28.3923	+	16.3923i	1.17589	+	0.678900i
$584$	−13.3944			−0.554264
$585$		0			0
$586$	5.58355			0.230654
$587$	15.2092	+	8.78102i	0.627750	+	0.362432i	0.779880	−	0.625929i	$-0.215280\pi$
$587$	15.2092	+	8.78102i	0.627750	+	0.362432i	−0.152130	+	0.988360i	$0.548613\pi$
$588$	−2.42775	+	4.20499i	−0.100119	+	0.173411i
$589$	−22.3547	−	38.7195i	−0.921110	−	1.59541i
$590$		0			0
$591$	−17.6475	+	10.1888i	−0.725923	+	0.419112i
$592$	−6.49161	+	3.74793i	−0.266804	+	0.154039i
$593$			28.9248i			1.18780i	0.804538	+	0.593901i	$0.202413\pi$
$593$			28.9248i			1.18780i	−0.804538	+	0.593901i	$0.797587\pi$
$594$	−1.73205	−	3.00000i	−0.0710669	−	0.123091i
$595$		0			0
$596$	−3.28125	−	1.89443i	−0.134405	−	0.0775990i
$597$	14.8014			0.605780
$598$	−3.45827	−	6.73295i	−0.141419	−	0.275331i
$599$	−46.1052			−1.88381			−0.941904	−	0.335882i	$-0.890966\pi$
$599$	−46.1052			−1.88381			−0.941904	+	0.335882i	$0.890966\pi$
$600$		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	$0.0364012\pi$
$602$	1.70969	+	2.96127i	0.0696817	+	0.120692i
$603$		−	1.97786i		−	0.0805446i
$604$	−14.0395	+	8.10568i	−0.571257	+	0.329815i
$605$		0			0
$606$			8.85550i			0.359730i
$607$	12.7126	+	22.0189i	0.515990	+	0.893721i	0.999828	+	0.0185635i	$0.00590927\pi$
$607$	12.7126	+	22.0189i	0.515990	+	0.893721i	−0.483837	+	0.875158i	$0.660757\pi$
$608$	−9.52706	+	16.5014i	−0.386373	+	0.669218i
$609$	−1.45991	−	0.842882i	−0.0591587	−	0.0341553i
$610$		0			0
$611$	36.7410	+	1.80559i	1.48638	+	0.0730463i
$612$	1.42775			0.0577135
$613$	−28.9745	−	16.7285i	−1.17027	−	0.675656i	−0.216526	−	0.976277i	$-0.569473\pi$
$613$	−28.9745	−	16.7285i	−1.17027	−	0.675656i	−0.953744	+	0.300621i	$0.902806\pi$
$614$	−5.40903	+	9.36871i	−0.218291	+	0.378090i
$615$		0			0
$616$		−	5.73542i		−	0.231087i
$617$	−12.0900	+	6.98015i	−0.486724	+	0.281010i	−0.723214	−	0.690624i	$-0.757336\pi$
$617$	−12.0900	+	6.98015i	−0.486724	+	0.281010i	0.236490	+	0.971634i	$0.424003\pi$
$618$	14.7350	−	8.50726i	0.592729	−	0.342212i
$619$			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
$622$	−25.3928	−	14.6605i	−1.01816	−	0.587833i
$623$	−9.87765			−0.395740
$624$	6.41445	−	3.29467i	0.256783	−	0.131892i
$625$		0			0
$626$	28.5054	+	16.4576i	1.13931	+	0.657778i
$627$	7.51376	−	13.0142i	0.300071	−	0.519737i
$628$	−5.26185	−	9.11379i	−0.209971	−	0.363680i
$629$			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	$0.626163\pi$
$632$		−	10.1381i		−	0.403271i
$633$	−2.61015	−	4.52091i	−0.103744	−	0.179690i
$634$	4.85641	−	8.41154i	0.192873	−	0.334065i
$635$		0			0
$636$	7.80138			0.309345
$637$	20.0988	+	12.9595i	0.796345	+	0.513474i
$638$	−9.63611			−0.381497
$639$	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	$-0.343032\pi$
$642$			9.24134i			0.364727i
$643$	14.3921	−	8.30927i	0.567568	−	0.327686i	−0.188609	−	0.982052i	$-0.560398\pi$
$643$	14.3921	−	8.30927i	0.567568	−	0.327686i	0.756177	+	0.654367i	$0.227065\pi$
$644$	−0.716280	+	0.413545i	−0.0282254	+	0.0162959i
$645$		0			0
$646$	−5.36389	−	9.29053i	−0.211039	−	0.365531i
$647$	10.2365	−	17.7301i	0.402437	−	0.697042i	−0.591582	−	0.806245i	$-0.701497\pi$
$647$	10.2365	−	17.7301i	0.402437	−	0.697042i	0.994019	+	0.109203i	$0.0348299\pi$
$648$	−2.66422	−	1.53819i	−0.104661	−	0.0604258i
$649$	35.6068			1.39769
$650$		0			0
$651$	5.54674			0.217394
$652$	−6.38420	−	3.68592i	−0.250025	−	0.144352i
$653$	2.88370	−	4.99471i	0.112848	−	0.195458i	−0.804070	−	0.594535i	$-0.797336\pi$
$653$	2.88370	−	4.99471i	0.112848	−	0.195458i	0.916917	+	0.399077i	$0.130669\pi$
$654$	5.96387	+	10.3297i	0.233206	+	0.403924i
$655$		0			0
$656$	1.85350	−	1.07012i	0.0723671	−	0.0417812i
$657$	3.77063	−	2.17698i	0.147106	−	0.0849319i
$658$			6.96209i			0.271410i
$659$	−15.4749	−	26.8034i	−0.602818	−	1.04411i	−0.992392	−	0.123116i	$-0.960711\pi$
$659$	−15.4749	−	26.8034i	−0.602818	−	1.04411i	0.389574	−	0.920995i	$-0.372622\pi$
$660$		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	$0.461612\pi$
$662$	−22.8609			−0.888513
$663$	0.345166	−	7.02359i	0.0134051	−	0.272774i
$664$	−21.4641			−0.832969
$665$		0			0
$666$	2.11015	−	3.65488i	0.0817666	−	0.141624i
$667$	2.59302	+	4.49125i	0.100402	+	0.173902i
$668$		−	7.93762i		−	0.307116i
$669$	5.34065	−	3.08342i	0.206481	−	0.119212i
$670$		0			0
$671$			19.2826i			0.744396i
$672$	−1.18195	−	2.04719i	−0.0455945	−	0.0789720i
$673$	−11.7540	+	20.3585i	−0.453082	+	0.784761i	−0.998576	−	0.0533540i	$-0.983009\pi$
$673$	−11.7540	+	20.3585i	−0.453082	+	0.784761i	0.545494	+	0.838115i	$0.316342\pi$
$674$	17.3432	+	10.0131i	0.668034	+	0.385689i
$675$		0			0
$676$	3.92730	+	8.66851i	0.151050	+	0.333404i
$677$	5.52213			0.212233			0.106116	−	0.994354i	$-0.466158\pi$
$677$	5.52213			0.212233			0.106116	+	0.994354i	$0.466158\pi$
$678$	3.37810	+	1.95035i	0.129735	+	0.0749026i
$679$	4.00045	−	6.92898i	0.153523	−	0.265910i
$680$		0			0
$681$		−	17.1114i		−	0.655709i
$682$	27.4583	−	15.8530i	1.05143	−	0.607044i
$683$	11.6675	−	6.73624i	0.446445	−	0.257755i	−0.259883	−	0.965640i	$-0.583684\pi$
$683$	11.6675	−	6.73624i	0.446445	−	0.257755i	0.706328	+	0.707885i	$0.250351\pi$
$684$		−	3.57593i		−	0.136729i
$685$		0			0
$686$	−4.65147	+	8.05658i	−0.177594	+	0.307602i
$687$	−25.0460	−	14.4603i	−0.955563	−	0.551694i
$688$	10.0217			0.382073
$689$	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	$0.966350\pi$
$692$	−9.02701	+	15.6352i	−0.343156	+	0.594363i
$693$	0.932171	+	1.61457i	0.0354102	+	0.0613323i
$694$		−	9.67366i		−	0.367207i
$695$		0			0
$696$	−7.41108	+	4.27879i	−0.280916	+	0.162187i
$697$		−	2.08710i		−	0.0790547i
$698$	−16.9920	−	29.4310i	−0.643156	−	1.11398i
$699$	−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	$0.496672\pi$
$702$	−2.20012	+	3.41216i	−0.0830382	+	0.128784i
$703$	18.3079			0.690497
$704$	−22.3590	−	12.9090i	−0.842685	−	0.486524i
$705$		0			0
$706$	16.1190	+	27.9189i	0.606646	+	1.05074i
$707$		−	4.76593i		−	0.179241i
$708$	7.33778	−	4.23647i	0.275771	−	0.159216i
$709$	−11.2395	+	6.48914i	−0.422109	+	0.243705i	−0.695979	−	0.718062i	$-0.745029\pi$
$709$	−11.2395	+	6.48914i	−0.422109	+	0.243705i	0.273870	+	0.961767i	$0.411696\pi$
$710$		0			0
$711$	1.64773	+	2.85395i	0.0617947	+	0.107032i
$712$	−25.0713	+	43.4248i	−0.939588	+	1.62741i
$713$	−14.7777	−	8.53193i	−0.553431	−	0.319523i
$714$	1.33091			0.0498080
$715$		0			0
$716$	16.7198			0.624850
$717$	16.5669	+	9.56491i	0.618703	+	0.357208i
$718$	9.83163	−	17.0289i	0.366913	−	0.635512i
$719$	−11.2164	−	19.4273i	−0.418300	−	0.724517i	0.577468	−	0.816413i	$-0.304041\pi$
$719$	−11.2164	−	19.4273i	−0.418300	−	0.724517i	−0.995769	+	0.0918957i	$0.970707\pi$
$720$		0			0
$721$	−7.93022	+	4.57851i	−0.295337	+	0.170513i
$722$	−4.74064	+	2.73701i	−0.176428	+	0.101861i
$723$			5.47415i			0.203586i
$724$	6.39140	+	11.0702i	0.237535	+	0.411422i
$725$		0			0
$726$	−1.49777	−	0.864736i	−0.0555873	−	0.0320934i
$727$	−48.3530			−1.79331			−0.896657	−	0.442725i	$-0.854012\pi$
$727$	−48.3530			−1.79331			−0.896657	+	0.442725i	$0.854012\pi$
$728$	−5.97936	+	3.07120i	−0.221610	+	0.113826i
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.88643	−	8.46355i	0.180731	−	0.313036i
$732$	2.29423	+	3.97372i	0.0847971	+	0.146873i
$733$		−	5.72579i		−	0.211487i	−0.994393	−	0.105743i	$-0.966278\pi$
$733$		−	5.72579i		−	0.211487i	0.994393	−	0.105743i	$-0.0337222\pi$
$734$	−31.6898	+	18.2961i	−1.16969	+	0.675322i
$735$		0			0
$736$			7.27222i			0.268058i
$737$	3.04232	+	5.26945i	0.112065	+	0.194103i
$738$	−0.602495	+	1.04355i	−0.0221781	+	0.0384137i
$739$	−18.0968	−	10.4482i	−0.665703	−	0.384344i	0.128743	−	0.991678i	$-0.458906\pi$
$739$	−18.0968	−	10.4482i	−0.665703	−	0.384344i	−0.794447	+	0.607334i	$0.792239\pi$
$740$		0			0
$741$	−17.5912	−	0.864497i	−0.646229	−	0.0317581i
$742$	7.27222			0.266972
$743$	−25.5991	−	14.7796i	−0.939139	−	0.542212i	−0.0494487	−	0.998777i	$-0.515746\pi$
$743$	−25.5991	−	14.7796i	−0.939139	−	0.542212i	−0.889690	+	0.456564i	$0.849080\pi$
$744$	14.0787	−	24.3850i	0.516149	−	0.893996i
$745$		0			0
$746$		−	12.1068i		−	0.443261i
$747$	6.04232	−	3.48853i	0.221077	−	0.127639i
$748$	−3.80385	+	2.19615i	−0.139082	+	0.0802993i
$749$		−	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	$0.292121\pi$
$752$	17.6711	+	10.2024i	0.644398	+	0.372044i
$753$	−4.71985			−0.172001
$754$	5.15994	+	10.0460i	0.187914	+	0.365852i
$755$		0			0
$756$	0.384200	+	0.221818i	0.0139732	+	0.00806745i
$757$	7.04245	−	12.1979i	0.255962	−	0.443340i	−0.709194	−	0.705013i	$-0.750941\pi$
$757$	7.04245	−	12.1979i	0.255962	−	0.443340i	0.965156	+	0.261674i	$0.0842744\pi$
$758$	−3.28881	−	5.69638i	−0.119455	−	0.206902i
$759$		−	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	$0.640780\pi$
$762$			20.3179i			0.736041i
$763$	−3.20969	−	5.55934i	−0.116199	−	0.201262i
$764$	−2.80872	+	4.86484i	−0.101616	+	0.176004i
$765$		0			0
$766$	−26.6238			−0.961957
$767$	−19.0667	−	37.1212i	−0.688458	−	1.34037i
$768$	−14.9282			−0.538675
$769$	−38.2583	−	22.0885i	−1.37963	−	0.796530i	−0.387516	−	0.921863i	$-0.626667\pi$
$769$	−38.2583	−	22.0885i	−1.37963	−	0.796530i	−0.992115	+	0.125333i	$0.960000\pi$
$770$		0			0
$771$	−3.63939	−	6.30362i	−0.131070	−	0.227019i
$772$			15.3810i			0.553574i
$773$	−30.9568	+	17.8729i	−1.11344	+	0.642843i	−0.939717	−	0.341952i	$-0.888912\pi$
$773$	−30.9568	+	17.8729i	−1.11344	+	0.642843i	−0.173720	+	0.984795i	$0.555579\pi$
$774$	−4.88643	+	2.82118i	−0.175639	+	0.101405i
$775$		0			0
$776$	−20.3078	−	35.1741i	−0.729008	−	1.26268i
$777$	−1.13566	+	1.96702i	−0.0407415	+	0.0705664i
$778$	16.1819	+	9.34265i	0.580151	+	0.334950i
$779$	−5.22733			−0.187289
$780$		0			0
$781$	−18.1720			−0.650246
$782$	−3.54584	−	2.04719i	−0.126799	−	0.0732073i
$783$	1.39085	−	2.40903i	0.0497050	−	0.0860916i
$784$	6.63274	+	11.4882i	0.236884	+	0.410294i
$785$		0			0
$786$	1.09120	−	0.630007i	0.0389220	−	0.0224716i
$787$	8.81782	−	5.09097i	0.314321	−	0.181474i	−0.334537	−	0.942383i	$-0.608580\pi$
$787$	8.81782	−	5.09097i	0.314321	−	0.181474i	0.648859	+	0.760909i	$0.275247\pi$
$788$		−	14.9175i		−	0.531413i
$789$	−0.643362	−	1.11434i	−0.0229043	−	0.0396714i
$790$		0			0
$791$	−1.81805	−	1.04965i	−0.0646426	−	0.0373214i
$792$	9.46410			0.336292
$793$	20.1027	−	10.3254i	0.713868	−	0.366666i
$794$	−26.3531			−0.935235
$795$		0			0
$796$	−5.41768	+	9.38370i	−0.192025	+	0.332596i
$797$	18.4428	+	31.9438i	0.653277	+	1.13151i	0.982323	+	0.187195i	$0.0599395\pi$
$797$	18.4428	+	31.9438i	0.653277	+	1.13151i	−0.329046	+	0.944314i	$0.606727\pi$
$798$		−	3.33337i		−	0.118000i
$799$	17.2324	−	9.94911i	0.609637	−	0.351974i
$800$		0			0
$801$		−	16.2993i		−	0.575906i
$802$	−0.0629594	−	0.109049i	−0.00222317	−	0.00385065i
$803$	−6.69720	+	11.5999i	−0.236339	+	0.409351i
$804$	1.25391	+	0.723946i	0.0442221	+	0.0255316i
$805$		0			0
$806$	−31.2306	−	20.1372i	−1.10005	−	0.709301i
$807$	18.9390			0.666686
$808$	−20.9523	−	12.0968i	−0.737101	−	0.425565i
$809$	6.08464	−	10.5389i	0.213924	−	0.370528i	−0.739015	−	0.673689i	$-0.764709\pi$
$809$	6.08464	−	10.5389i	0.213924	−	0.370528i	0.952939	+	0.303161i	$0.0980420\pi$
$810$		0			0
$811$			26.2312i			0.921104i	0.887633	+	0.460552i	$0.152348\pi$
$811$			26.2312i			0.921104i	−0.887633	+	0.460552i	$0.847652\pi$
$812$	1.06873	−	0.617033i	0.0375051	−	0.0216536i
$813$	−9.54719	+	5.51207i	−0.334835	+	0.193317i
$814$			12.9832i			0.455062i
$815$		0			0
$816$	1.95035	−	3.37810i	0.0682757	−	0.118257i
$817$	−21.1977	−	12.2385i	−0.741613	−	0.428171i
$818$	−21.7104			−0.759088
$819$	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	$0.573439\pi$
$822$	4.90192	−	8.49038i	0.170974	−	0.296136i
$823$	−13.9646	−	24.1873i	−0.486774	−	0.843117i	0.513111	−	0.858322i	$-0.328493\pi$
$823$	−13.9646	−	24.1873i	−0.486774	−	0.843117i	−0.999884	+	0.0152057i	$0.995160\pi$
$824$			46.4845i			1.61937i
$825$		0			0
$826$	6.84006	−	3.94911i	0.237996	−	0.137407i
$827$			1.83852i			0.0639316i	0.999489	+	0.0319658i	$0.0101768\pi$
$827$			1.83852i			0.0639316i	−0.999489	+	0.0319658i	$0.989823\pi$
$828$	−0.682396	−	1.18195i	−0.0237149	−	0.0410754i
$829$	−17.4866	+	30.2876i	−0.607333	+	1.05193i	0.384345	+	0.923190i	$0.374427\pi$
$829$	−17.4866	+	30.2876i	−0.607333	+	1.05193i	−0.991678	+	0.128743i	$0.958906\pi$
$830$		0			0
$831$	20.9215			0.725758
$832$	−1.48524	+	30.2224i	−0.0514915	+	1.04777i
$833$	12.9361			0.448211
$834$	−9.41713	−	5.43698i	−0.326089	−	0.188267i
$835$		0			0
$836$	5.50045	+	9.52706i	0.190237	+	0.329500i
$837$			9.15276i			0.316366i
$838$	21.5889	−	12.4644i	0.745777	−	0.430575i
$839$	11.0093	−	6.35624i	0.380085	−	0.219442i	−0.297771	−	0.954637i	$-0.596243\pi$
$839$	11.0093	−	6.35624i	0.380085	−	0.219442i	0.677855	+	0.735196i	$0.262910\pi$
$840$		0			0
$841$	10.6311	+	18.4135i	0.366588	+	0.634949i
$842$	0.515039	−	0.892073i	0.0177494	−	0.0307429i
$843$	9.23642	+	5.33265i	0.318119	+	0.183666i
$844$	3.82152			0.131542
$845$		0			0
$846$	−11.4882			−0.394974
$847$	0.806081	+	0.465391i	0.0276973	+	0.0159910i
$848$	10.6569	−	18.4583i	0.365959	−	0.633860i
$849$	−1.39254	−	2.41194i	−0.0477917	−	0.0827777i
$850$		0			0
$851$	6.05129	−	3.49372i	0.207436	−	0.119763i
$852$	−3.74486	+	2.16209i	−0.128297	+	0.0740721i
$853$		−	20.2430i		−	0.693106i	−0.938030	−	0.346553i	$-0.887352\pi$
$853$		−	20.2430i		−	0.693106i	0.938030	−	0.346553i	$-0.112648\pi$
$854$	2.13861	+	3.70419i	0.0731818	+	0.126755i
$855$		0			0
$856$	−21.8652	−	12.6239i	−0.747339	−	0.431476i
$857$	53.5208			1.82823			0.914117	−	0.405450i	$-0.132885\pi$
$857$	53.5208			1.82823			0.914117	+	0.405450i	$0.132885\pi$
$858$	0.613065	−	12.4749i	0.0209297	−	0.425887i
$859$	−0.969120			−0.0330659			−0.0165330	−	0.999863i	$-0.505263\pi$
$859$	−0.969120			−0.0330659			−0.0165330	+	0.999863i	$0.505263\pi$
$860$		0			0
$861$	0.324256	−	0.561628i	0.0110506	−	0.0191402i
$862$	−20.8187	−	36.0590i	−0.709087	−	1.22818i
$863$		−	5.67766i		−	0.193270i	−0.995320	−	0.0966349i	$-0.969192\pi$
$863$		−	5.67766i		−	0.193270i	0.995320	−	0.0966349i	$-0.0308079\pi$
$864$	3.37810	−	1.95035i	0.114925	−	0.0663521i
$865$		0			0
$866$		−	32.3056i		−	1.09779i
$867$	6.59808	+	11.4282i	0.224082	+	0.388122i
$868$	−2.03025	+	3.51649i	−0.0689111	+	0.119357i
$869$	−8.77984	−	5.06904i	−0.297836	−	0.171955i
$870$		0			0
$871$	3.86447	−	5.99340i	0.130943	−	0.203079i
$872$	−32.5872			−1.10354
$873$	11.4336	+	6.60121i	0.386970	+	0.223417i
$874$	−5.12736	+	8.88085i	−0.173436	+	0.300399i
$875$		0			0
$876$			3.18732i			0.107689i
$877$	27.9007	−	16.1085i	0.942139	−	0.543944i	0.0515091	−	0.998673i	$-0.483597\pi$
$877$	27.9007	−	16.1085i	0.942139	−	0.543944i	0.890630	+	0.454728i	$0.150264\pi$
$878$	−5.13147	+	2.96266i	−0.173179	+	0.0999848i
$879$		−	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	$-0.0768692\pi$
$882$	−6.46807	−	3.73434i	−0.217791	−	0.125742i
$883$	−14.6027			−0.491419			−0.245709	−	0.969344i	$-0.579021\pi$
$883$	−14.6027			−0.491419			−0.245709	+	0.969344i	$0.579021\pi$
$884$	4.32644	+	2.78964i	0.145514	+	0.0938258i
$885$		0			0
$886$	28.1118	+	16.2304i	0.944435	+	0.545270i
$887$	4.55279	−	7.88566i	0.152868	−	0.264775i	−0.779413	−	0.626511i	$-0.784482\pi$
$887$	4.55279	−	7.88566i	0.152868	−	0.264775i	0.932281	+	0.361736i	$0.117816\pi$
$888$	5.76503	+	9.98533i	0.193462	+	0.335086i
$889$		−	10.9349i		−	0.366744i
$890$		0			0
$891$	−2.66422	+	1.53819i	−0.0892548	+	0.0515313i
$892$			4.51445i			0.151155i
$893$	−24.9184	−	43.1599i	−0.833863	−	1.44429i
$894$	2.91400	−	5.04719i	0.0974586	−	0.168803i
$895$		0			0
$896$	−0.999098			−0.0333775
$897$	−5.97936	+	3.07120i	−0.199645	+	0.102544i
$898$	−3.38740			−0.113039
$899$	22.0492	+	12.7301i	0.735383	+	0.424574i
$900$		0			0
$901$	−10.3923	−	18.0000i	−0.346218	−	0.599667i
$902$		−	3.70700i		−	0.123430i
$903$	2.62983	−	1.51833i	0.0875151	−	0.0505269i
$904$	−9.22913	+	5.32844i	−0.306956	+	0.177221i
$905$		0			0
$906$	−12.4681	−	21.5953i	−0.414224	−	0.717457i
$907$	25.2580	−	43.7482i	0.838679	−	1.45263i	−0.0523212	−	0.998630i	$-0.516662\pi$
$907$	25.2580	−	43.7482i	0.838679	−	1.45263i	0.891000	−	0.454004i	$-0.150005\pi$
$908$	10.8482	+	6.26319i	0.360009	+	0.207851i
$909$	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	$0.229391\pi$
$912$	−8.46073	−	4.88481i	−0.280163	−	0.161752i
$913$	−10.7321	+	18.5885i	−0.355179	+	0.615188i
$914$	5.00342	+	8.66617i	0.165498	+	0.286652i
$915$		0			0
$916$	18.3349	−	10.5857i	0.605803	−	0.349760i
$917$	−0.587274	+	0.339063i	−0.0193935	+	0.0111968i
$918$			2.19615i			0.0724838i
$919$	−2.15110	−	3.72581i	−0.0709582	−	0.122903i	0.828363	−	0.560191i	$-0.189272\pi$
$919$	−2.15110	−	3.72581i	−0.0709582	−	0.122903i	−0.899322	+	0.437288i	$0.855939\pi$
$920$		0			0
$921$	8.32011	+	4.80362i	0.274157	+	0.158285i
$922$	23.7693			0.782800
$923$	9.73073	+	18.9449i	0.320291	+	0.623579i
$924$	−1.36479			−0.0448984
$925$		0			0
$926$	13.7758	−	23.8604i	0.452702	−	0.784102i
$927$	−7.55507	−	13.0858i	−0.248141	−	0.429793i
$928$		−	10.8506i		−	0.356188i
$929$	41.9047	−	24.1937i	1.37485	−	0.793769i	0.383315	−	0.923618i	$-0.374783\pi$
$929$	41.9047	−	24.1937i	1.37485	−	0.793769i	0.991534	+	0.129849i	$0.0414492\pi$
$930$		0			0
$931$		−	32.3997i		−	1.06186i
$932$	−4.14650	−	7.18195i	−0.135823	−	0.235252i
$933$	−13.0196	+	22.5507i	−0.426243	+	0.738275i
$934$	19.0215	+	10.9821i	0.622404	+	0.359345i
$935$		0			0
$936$	−5.06783	−	9.86663i	−0.165647	−	0.322501i
$937$	−33.9291			−1.10842			−0.554208	−	0.832378i	$-0.686979\pi$
$937$	−33.9291			−1.10842			−0.554208	+	0.832378i	$0.686979\pi$
$938$	1.16886	+	0.674841i	0.0381646	+	0.0220344i
$939$	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	$-0.0426860\pi$
$942$	14.0187	−	8.09371i	0.456755	−	0.263707i
$943$	−1.72778	+	0.997534i	−0.0562643	+	0.0324842i
$944$		−	23.1485i		−	0.753419i
$945$		0			0
$946$	8.67903	−	15.0325i	0.282180	−	0.488749i
$947$	38.9792	+	22.5046i	1.26665	+	0.731302i	0.974353	−	0.225024i	$-0.0722461\pi$
$947$	38.9792	+	22.5046i	1.26665	+	0.731302i	0.292300	+	0.956327i	$0.405579\pi$
$948$	−2.41245			−0.0783526
$949$	15.6795	+	0.770548i	0.508977	+	0.0250130i
$950$		0			0
$951$	−7.47007	−	4.31285i	−0.242234	−	0.139854i
$952$	−1.81805	+	3.14896i	−0.0589235	+	0.102058i
$953$	−26.5094	−	45.9157i	−0.858724	−	1.48735i	−0.873146	−	0.487458i	$-0.837924\pi$
$953$	−26.5094	−	45.9157i	−0.858724	−	1.48735i	0.0144217	−	0.999896i	$-0.495409\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$	−12.1278	+	7.00200i	−0.392242	+	0.226461i
$957$			8.55758i			0.276627i
$958$	−15.2186	−	26.3593i	−0.491689	−	0.851631i
$959$	−2.63816	+	4.56943i	−0.0851907	+	0.147555i
$960$		0			0
$961$	−52.7729			−1.70235
$962$	13.5354	−	6.95225i	0.436400	−	0.224149i
$963$	8.20699			0.264467
$964$	−3.47047	−	2.00368i	−0.111776	−	0.0645341i
$965$		0			0
$966$	−0.636110	−	1.10177i	−0.0204665	−	0.0354490i
$967$			31.7061i			1.01960i	0.860293	+	0.509799i	$0.170280\pi$
$967$			31.7061i			1.01960i	−0.860293	+	0.509799i	$0.829720\pi$
$968$	4.09197	−	2.36250i	0.131521	−	0.0759337i
$969$	−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	$0.675712\pi$
$972$	−0.366025	+	0.633975i	−0.0117403	+	0.0203347i
$973$	5.06820	+	2.92612i	0.162479	+	0.0938073i
$974$	−5.87508			−0.188250
$975$		0			0
$976$	12.5359			0.401264
$977$	1.06633	+	0.615644i	0.0341148	+	0.0196962i	0.516960	−	0.856009i	$-0.327063\pi$
$977$	1.06633	+	0.615644i	0.0341148	+	0.0196962i	−0.482846	+	0.875706i	$0.660397\pi$
$978$	5.66964	−	9.82011i	0.181295	−	0.314012i
$979$	25.0713	+	43.4248i	0.801283	+	1.38786i
$980$		0			0
$981$	9.17356	−	5.29636i	0.292889	−	0.169100i
$982$	−14.4147	+	8.32234i	−0.459992	+	0.265577i
$983$			25.1632i			0.802581i	0.915951	+	0.401290i	$0.131438\pi$
$983$			25.1632i			0.802581i	−0.915951	+	0.401290i	$0.868562\pi$
$984$	−1.64605	−	2.85104i	−0.0524741	−	0.0908877i
$985$		0			0
$986$	5.29059	+	3.05452i	0.168487	+	0.0972759i
$987$	6.18285			0.196802
$988$	6.98689	−	10.8359i	0.222283	−	0.344737i
$989$	−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	$-0.226677\pi$
$992$	17.8510	+	30.9189i	0.566771	+	0.981676i
$993$			20.3021i			0.644269i
$994$	−3.49084	+	2.01544i	−0.110723	+	0.0639259i
$995$		0			0
$996$			5.10757i			0.161840i
$997$	18.9610	+	32.8413i	0.600499	+	1.04010i	0.992745	+	0.120235i	$0.0383649\pi$
$997$	18.9610	+	32.8413i	0.600499	+	1.04010i	−0.392246	+	0.919860i	$0.628302\pi$
$998$	−5.80872	+	10.0610i	−0.183872	+	0.318475i
$999$	−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.bc.j.901.2		8
5.2	odd	4		975.2.w.h.199.3		8
5.3	odd	4		975.2.w.i.199.2		8
5.4	even	2		195.2.bb.b.121.3	✓	8
13.10	even	6	inner	975.2.bc.j.751.2		8
15.14	odd	2		585.2.bu.d.316.2		8
65.19	odd	12		2535.2.a.bj.1.2		4
65.23	odd	12		975.2.w.h.49.3		8
65.49	even	6		195.2.bb.b.166.3	yes	8
65.59	odd	12		2535.2.a.bk.1.3		4
65.62	odd	12		975.2.w.i.49.2		8
195.59	even	12		7605.2.a.ch.1.2		4
195.149	even	12		7605.2.a.ci.1.3		4
195.179	odd	6		585.2.bu.d.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.3	✓	8	5.4	even	2
195.2.bb.b.166.3	yes	8	65.49	even	6
585.2.bu.d.316.2		8	15.14	odd	2
585.2.bu.d.361.2		8	195.179	odd	6
975.2.w.h.49.3		8	65.23	odd	12
975.2.w.h.199.3		8	5.2	odd	4
975.2.w.i.49.2		8	65.62	odd	12
975.2.w.i.199.2		8	5.3	odd	4
975.2.bc.j.751.2		8	13.10	even	6	inner
975.2.bc.j.901.2		8	1.1	even	1	trivial
2535.2.a.bj.1.2		4	65.19	odd	12
2535.2.a.bk.1.3		4	65.59	odd	12
7605.2.a.ch.1.2		4	195.59	even	12
7605.2.a.ci.1.3		4	195.149	even	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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.975173 - 0.563016i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.366025 - 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(-0.524827 + 0.303009i) q^{7} +3.07638i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.975173 - 0.563016i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.366025 - 0.633975i) q^{4} +(0.975173 - 0.563016i) q^{6} +(-0.524827 + 0.303009i) q^{7} +3.07638i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.66422 + 1.53819i) q^{11} +0.732051 q^{12} +(0.176977 - 3.60121i) q^{13} +0.682396 q^{14} +(1.00000 - 1.73205i) q^{16} +(-0.975173 - 1.68905i) q^{17} +1.12603i q^{18} +(-4.23037 + 2.44240i) q^{19} -0.606018i q^{21} +(-1.73205 - 3.00000i) q^{22} +(-0.932171 + 1.61457i) q^{23} +(-2.66422 - 1.53819i) q^{24} +(-2.20012 + 3.41216i) q^{26} +1.00000 q^{27} +(0.384200 + 0.221818i) q^{28} +(1.39085 - 2.40903i) q^{29} +9.15276i q^{31} +(3.37810 - 1.95035i) q^{32} +(-2.66422 + 1.53819i) q^{33} +2.19615i q^{34} +(-0.366025 + 0.633975i) q^{36} +(-3.24581 - 1.87397i) q^{37} +5.50045 q^{38} +(3.03025 + 1.95387i) q^{39} +(0.926751 + 0.535060i) q^{41} +(-0.341198 + 0.590973i) q^{42} +(2.50542 + 4.33951i) q^{43} -2.25207i q^{44} +(1.81805 - 1.04965i) q^{46} +10.2024i q^{47} +(1.00000 + 1.73205i) q^{48} +(-3.31637 + 5.74412i) q^{49} +1.95035 q^{51} +(-2.34785 + 1.20593i) q^{52} +10.6569 q^{53} +(-0.975173 - 0.563016i) q^{54} +(-0.932171 - 1.61457i) q^{56} -4.88481i q^{57} +(-2.71264 + 1.56615i) q^{58} +(10.0236 - 5.78712i) q^{59} +(3.13397 + 5.42820i) q^{61} +(5.15315 - 8.92552i) q^{62} +(0.524827 + 0.303009i) q^{63} -8.39230 q^{64} +3.46410 q^{66} +(1.71288 + 0.988929i) q^{67} +(-0.713876 + 1.23647i) q^{68} +(-0.932171 - 1.61457i) q^{69} +(-5.11557 + 2.95347i) q^{71} +(2.66422 - 1.53819i) q^{72} +4.35395i q^{73} +(2.11015 + 3.65488i) q^{74} +(3.09684 + 1.78796i) q^{76} -1.86434 q^{77} +(-1.85495 - 3.61144i) q^{78} -3.29546 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.602495 - 1.04355i) q^{82} +6.97707i q^{83} +(-0.384200 + 0.221818i) q^{84} -5.64237i q^{86} +(1.39085 + 2.40903i) q^{87} +(-4.73205 + 8.19615i) q^{88} +(14.1156 + 8.14963i) q^{89} +(0.998316 + 1.94364i) q^{91} +1.36479 q^{92} +(-7.92652 - 4.57638i) q^{93} +(5.74412 - 9.94911i) q^{94} +3.90069i q^{96} +(-11.4336 + 6.60121i) q^{97} +(6.46807 - 3.73434i) q^{98} -3.07638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 24 q^{74} - 48 q^{76} + 12 q^{78} - 16 q^{79} - 4 q^{81} + 12 q^{82} + 12 q^{84} + 12 q^{87} - 24 q^{88} + 36 q^{89} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 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 - 48 * q^92 + 12 * q^94 + 72 * q^98

Introduction

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