LMFDB - Embedded newform 975.2.i.n.601.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 10x^{10} - 4x^{9} + 79x^{8} - 24x^{7} + 210x^{6} - 38x^{5} + 429x^{4} - 76x^{3} + 58x^{2} + 8x + 4 $ x^12 + 10x^10 - 4x^9 + 79x^8 - 24x^7 + 210x^6 - 38x^5 + 429x^4 - 76x^3 + 58x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.4
Root			$0.215564 - 0.373368i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.n.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.215564 + 0.373368i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.907064 - 1.57108i) q^{4} +(0.215564 - 0.373368i) q^{6} +(2.03980 - 3.53303i) q^{7} +1.64438 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.18676 + 3.78758i) q^{11} -1.81413 q^{12} +(3.39041 + 1.22684i) q^{13} +1.75883 q^{14} +(-1.45966 - 2.52820i) q^{16} +(2.88837 - 5.00280i) q^{17} -0.431128 q^{18} +(-1.16512 + 2.01805i) q^{19} -4.07959 q^{21} +(-0.942775 + 1.63293i) q^{22} +(3.98461 + 6.90155i) q^{23} +(-0.822190 - 1.42407i) q^{24} +(0.272789 + 1.53033i) q^{26} +1.00000 q^{27} +(-3.70045 - 6.40937i) q^{28} +(-1.29122 - 2.23645i) q^{29} -7.52862 q^{31} +(2.27368 - 3.93813i) q^{32} +(2.18676 - 3.78758i) q^{33} +2.49051 q^{34} +(0.907064 + 1.57108i) q^{36} +(-3.08460 - 5.34269i) q^{37} -1.00463 q^{38} +(-0.632732 - 3.54960i) q^{39} +(2.88837 + 5.00280i) q^{41} +(-0.879414 - 1.52319i) q^{42} +(3.42280 - 5.92846i) q^{43} +7.93414 q^{44} +(-1.71788 + 2.97546i) q^{46} -6.00254 q^{47} +(-1.45966 + 2.52820i) q^{48} +(-4.82154 - 8.35115i) q^{49} -5.77673 q^{51} +(5.00278 - 4.21379i) q^{52} -10.2347 q^{53} +(0.215564 + 0.373368i) q^{54} +(3.35420 - 5.80964i) q^{56} +2.33024 q^{57} +(0.556680 - 0.964198i) q^{58} +(2.28174 - 3.95209i) q^{59} +(-5.95928 + 10.3218i) q^{61} +(-1.62290 - 2.81095i) q^{62} +(2.03980 + 3.53303i) q^{63} -3.87814 q^{64} +1.88555 q^{66} +(1.96429 + 3.40225i) q^{67} +(-5.23987 - 9.07572i) q^{68} +(3.98461 - 6.90155i) q^{69} +(4.18676 - 7.25169i) q^{71} +(-0.822190 + 1.42407i) q^{72} -4.01327 q^{73} +(1.32986 - 2.30339i) q^{74} +(2.11368 + 3.66099i) q^{76} +17.8422 q^{77} +(1.18891 - 1.00141i) q^{78} +9.17355 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.24526 + 2.15685i) q^{82} -12.6272 q^{83} +(-3.70045 + 6.40937i) q^{84} +2.95133 q^{86} +(-1.29122 + 2.23645i) q^{87} +(3.59587 + 6.22822i) q^{88} +(6.99498 + 12.1157i) q^{89} +(11.2502 - 9.47592i) q^{91} +14.4572 q^{92} +(3.76431 + 6.51998i) q^{93} +(-1.29393 - 2.24116i) q^{94} -4.54736 q^{96} +(-1.74194 + 3.01714i) q^{97} +(2.07870 - 3.60042i) q^{98} -4.37352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 8 q^{4} + q^{7} + 12 q^{8} - 6 q^{9} - q^{11} + 16 q^{12} - 3 q^{13} + 30 q^{14} - 20 q^{16} + 8 q^{17} + 3 q^{19} - 2 q^{21} - 3 q^{22} - q^{23} - 6 q^{24} + 9 q^{26} + 12 q^{27} + 3 q^{28}+ \cdots + 2 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 8 * q^4 + q^7 + 12 * q^8 - 6 * q^9 - q^11 + 16 * q^12 - 3 * q^13 + 30 * q^14 - 20 * q^16 + 8 * q^17 + 3 * q^19 - 2 * q^21 - 3 * q^22 - q^23 - 6 * q^24 + 9 * q^26 + 12 * q^27 + 3 * q^28 - 12 * q^29 + 24 * q^31 - 32 * q^32 - q^33 - 56 * q^34 - 8 * q^36 - 5 * q^37 + 14 * q^38 - 3 * q^39 + 8 * q^41 - 15 * q^42 - 15 * q^43 + 78 * q^44 - 5 * q^46 - 24 * q^47 - 20 * q^48 - 9 * q^49 - 16 * q^51 + 62 * q^52 - 16 * q^53 - 17 * q^56 - 6 * q^57 - 6 * q^58 + 2 * q^59 - 33 * q^61 - 2 * q^62 + q^63 + 72 * q^64 + 6 * q^66 + 13 * q^67 + 36 * q^68 - q^69 + 23 * q^71 - 6 * q^72 - 12 * q^73 - 59 * q^74 + 35 * q^76 - 36 * q^77 - 6 * q^78 + 22 * q^79 - 6 * q^81 + 28 * q^82 - 34 * q^83 + 3 * q^84 - 26 * q^86 - 12 * q^87 - 7 * q^88 - 8 * q^89 + 5 * q^91 + 38 * q^92 - 12 * q^93 - 8 * q^94 + 64 * q^96 - 19 * q^97 + 43 * q^98 + 2 * q^99

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.215564	+	0.373368i	0.152427	+	0.264011i	0.932119	−	0.362152i	$-0.117958\pi$
$2$	0.215564	+	0.373368i	0.152427	+	0.264011i	−0.779692	+	0.626163i	$0.784624\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.907064	−	1.57108i	0.453532	−	0.785541i
$5$		0			0
$5$		0			0
$6$	0.215564	−	0.373368i	0.0880037	−	0.152427i
$7$	2.03980	−	3.53303i	0.770970	−	1.33536i	−0.166061	−	0.986115i	$-0.553105\pi$
$7$	2.03980	−	3.53303i	0.770970	−	1.33536i	0.937032	−	0.349245i	$-0.113562\pi$
$8$	1.64438			0.581376
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.18676	+	3.78758i	0.659334	+	1.14200i	0.980788	+	0.195075i	$0.0624949\pi$
$11$	2.18676	+	3.78758i	0.659334	+	1.14200i	−0.321455	+	0.946925i	$0.604172\pi$
$12$	−1.81413			−0.523694
$13$	3.39041	+	1.22684i	0.940330	+	0.340263i
$13$	3.39041	+	1.22684i	0.940330	+	0.340263i
$14$	1.75883			0.470067
$15$		0			0
$16$	−1.45966	−	2.52820i	−0.364915	−	0.632051i
$17$	2.88837	−	5.00280i	0.700532	−	1.21336i	−0.267748	−	0.963489i	$-0.586280\pi$
$17$	2.88837	−	5.00280i	0.700532	−	1.21336i	0.968280	−	0.249868i	$-0.0803871\pi$
$18$	−0.431128			−0.101618
$19$	−1.16512	+	2.01805i	−0.267297	+	0.462972i	−0.968163	−	0.250321i	$-0.919464\pi$
$19$	−1.16512	+	2.01805i	−0.267297	+	0.462972i	0.700866	+	0.713293i	$0.252797\pi$
$20$		0			0
$21$	−4.07959			−0.890240
$22$	−0.942775	+	1.63293i	−0.201000	+	0.348143i
$23$	3.98461	+	6.90155i	0.830849	+	1.43907i	0.897365	+	0.441288i	$0.145478\pi$
$23$	3.98461	+	6.90155i	0.830849	+	1.43907i	−0.0665160	+	0.997785i	$0.521188\pi$
$24$	−0.822190	−	1.42407i	−0.167829	−	0.290688i
$25$		0			0
$26$	0.272789	+	1.53033i	0.0534983	+	0.300123i
$27$	1.00000			0.192450
$28$	−3.70045	−	6.40937i	−0.699320	−	1.21126i
$29$	−1.29122	−	2.23645i	−0.239773	−	0.415299i	0.720876	−	0.693064i	$-0.243740\pi$
$29$	−1.29122	−	2.23645i	−0.239773	−	0.415299i	−0.960649	+	0.277765i	$0.910406\pi$
$30$		0			0
$31$	−7.52862			−1.35218			−0.676090	−	0.736819i	$-0.736327\pi$
$31$	−7.52862			−1.35218			−0.676090	+	0.736819i	$0.736327\pi$
$32$	2.27368	−	3.93813i	0.401934	−	0.696169i
$33$	2.18676	−	3.78758i	0.380666	−	0.659334i
$34$	2.49051			0.427120
$35$		0			0
$36$	0.907064	+	1.57108i	0.151177	+	0.261847i
$37$	−3.08460	−	5.34269i	−0.507106	−	0.878333i	−0.999966	−	0.00822447i	$-0.997382\pi$
$37$	−3.08460	−	5.34269i	−0.507106	−	0.878333i	0.492860	−	0.870108i	$-0.335951\pi$
$38$	−1.00463			−0.162973
$39$	−0.632732	−	3.54960i	−0.101318	−	0.568391i
$40$		0			0
$41$	2.88837	+	5.00280i	0.451087	+	0.781306i	0.998454	−	0.0555872i	$-0.0177031\pi$
$41$	2.88837	+	5.00280i	0.451087	+	0.781306i	−0.547367	+	0.836893i	$0.684370\pi$
$42$	−0.879414	−	1.52319i	−0.135697	−	0.235033i
$43$	3.42280	−	5.92846i	0.521972	−	0.904081i	−0.477702	−	0.878522i	$-0.658530\pi$
$43$	3.42280	−	5.92846i	0.521972	−	0.904081i	0.999673	−	0.0255591i	$-0.00813661\pi$
$44$	7.93414			1.19612
$45$		0			0
$46$	−1.71788	+	2.97546i	−0.253288	+	0.438707i
$47$	−6.00254			−0.875560			−0.437780	−	0.899082i	$-0.644235\pi$
$47$	−6.00254			−0.875560			−0.437780	+	0.899082i	$0.644235\pi$
$48$	−1.45966	+	2.52820i	−0.210684	+	0.364915i
$49$	−4.82154	−	8.35115i	−0.688791	−	1.19302i
$50$		0			0
$51$	−5.77673			−0.808904
$52$	5.00278	−	4.21379i	0.693761	−	0.584347i
$53$	−10.2347			−1.40584			−0.702922	−	0.711267i	$-0.748122\pi$
$53$	−10.2347			−1.40584			−0.702922	+	0.711267i	$0.748122\pi$
$54$	0.215564	+	0.373368i	0.0293346	+	0.0508090i
$55$		0			0
$56$	3.35420	−	5.80964i	0.448224	−	0.776346i
$57$	2.33024			0.308648
$58$	0.556680	−	0.964198i	0.0730956	−	0.126605i
$59$	2.28174	−	3.95209i	0.297057	−	0.514518i	−0.678404	−	0.734689i	$-0.737328\pi$
$59$	2.28174	−	3.95209i	0.297057	−	0.514518i	0.975461	+	0.220171i	$0.0706614\pi$
$60$		0			0
$61$	−5.95928	+	10.3218i	−0.763008	+	1.32157i	0.178286	+	0.983979i	$0.442945\pi$
$61$	−5.95928	+	10.3218i	−0.763008	+	1.32157i	−0.941294	+	0.337589i	$0.890389\pi$
$62$	−1.62290	−	2.81095i	−0.206109	−	0.356991i
$63$	2.03980	+	3.53303i	0.256990	+	0.445120i
$64$	−3.87814			−0.484768
$65$		0			0
$66$	1.88555			0.232095
$67$	1.96429	+	3.40225i	0.239976	+	0.415651i	0.960707	−	0.277564i	$-0.0895271\pi$
$67$	1.96429	+	3.40225i	0.239976	+	0.415651i	−0.720731	+	0.693215i	$0.756194\pi$
$68$	−5.23987	−	9.07572i	−0.635427	−	1.10059i
$69$	3.98461	−	6.90155i	0.479691	−	0.830849i
$70$		0			0
$71$	4.18676	−	7.25169i	0.496877	−	0.860617i	−0.503116	−	0.864219i	$-0.667813\pi$
$71$	4.18676	−	7.25169i	0.496877	−	0.860617i	0.999994	+	0.00360204i	$0.00114657\pi$
$72$	−0.822190	+	1.42407i	−0.0968960	+	0.167829i
$73$	−4.01327			−0.469718			−0.234859	−	0.972029i	$-0.575463\pi$
$73$	−4.01327			−0.469718			−0.234859	+	0.972029i	$0.575463\pi$
$74$	1.32986	−	2.30339i	0.154593	−	0.267763i
$75$		0			0
$76$	2.11368	+	3.66099i	0.242455	+	0.419945i
$77$	17.8422			2.03331
$78$	1.18891	−	1.00141i	0.134618	−	0.113387i
$79$	9.17355			1.03210			0.516052	−	0.856557i	$-0.327401\pi$
$79$	9.17355			1.03210			0.516052	+	0.856557i	$0.327401\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.24526	+	2.15685i	−0.137516	+	0.238184i
$83$	−12.6272			−1.38601			−0.693006	−	0.720932i	$-0.743714\pi$
$83$	−12.6272			−1.38601			−0.693006	+	0.720932i	$0.743714\pi$
$84$	−3.70045	+	6.40937i	−0.403752	+	0.699320i
$85$		0			0
$86$	2.95133			0.318250
$87$	−1.29122	+	2.23645i	−0.138433	+	0.239773i
$88$	3.59587	+	6.22822i	0.383321	+	0.663931i
$89$	6.99498	+	12.1157i	0.741466	+	1.28426i	0.951828	+	0.306634i	$0.0992027\pi$
$89$	6.99498	+	12.1157i	0.741466	+	1.28426i	−0.210361	+	0.977624i	$0.567464\pi$
$90$		0			0
$91$	11.2502	−	9.47592i	1.17934	−	0.993346i
$92$	14.4572			1.50727
$93$	3.76431	+	6.51998i	0.390341	+	0.676090i
$94$	−1.29393	−	2.24116i	−0.133459	−	0.231158i
$95$		0			0
$96$	−4.54736			−0.464113
$97$	−1.74194	+	3.01714i	−0.176868	+	0.306344i	−0.940806	−	0.338945i	$-0.889930\pi$
$97$	−1.74194	+	3.01714i	−0.176868	+	0.306344i	0.763938	+	0.645289i	$0.223263\pi$
$98$	2.07870	−	3.60042i	0.209981	−	0.363697i
$99$	−4.37352			−0.439556
$100$		0			0
$101$	5.12143	+	8.87058i	0.509601	+	0.882656i	0.999938	+	0.0111225i	$0.00354047\pi$
$101$	5.12143	+	8.87058i	0.509601	+	0.882656i	−0.490337	+	0.871533i	$0.663126\pi$
$102$	−1.24526	−	2.15685i	−0.123299	−	0.213560i
$103$	15.8100			1.55781			0.778903	−	0.627145i	$-0.215777\pi$
$103$	15.8100			1.55781			0.778903	+	0.627145i	$0.215777\pi$
$104$	5.57512	+	2.01739i	0.546685	+	0.197821i
$105$		0			0
$106$	−2.20623	−	3.82131i	−0.214288	−	0.371158i
$107$	−1.12791	−	1.95360i	−0.109039	−	0.188861i	0.806342	−	0.591449i	$-0.201444\pi$
$107$	−1.12791	−	1.95360i	−0.109039	−	0.188861i	−0.915381	+	0.402588i	$0.868111\pi$
$108$	0.907064	−	1.57108i	0.0872823	−	0.151177i
$109$	−13.6978			−1.31201			−0.656007	−	0.754755i	$-0.727756\pi$
$109$	−13.6978			−1.31201			−0.656007	+	0.754755i	$0.727756\pi$
$110$		0			0
$111$	−3.08460	+	5.34269i	−0.292778	+	0.507106i
$112$	−11.9096			−1.12535
$113$	5.86353	−	10.1559i	0.551594	−	0.955389i	−0.446566	−	0.894751i	$-0.647353\pi$
$113$	5.86353	−	10.1559i	0.551594	−	0.955389i	0.998160	−	0.0606383i	$-0.0193136\pi$
$114$	0.502316	+	0.870037i	0.0470462	+	0.0814864i
$115$		0			0
$116$	−4.68486			−0.434978
$117$	−2.75768	+	2.32276i	−0.254947	+	0.214739i
$118$	1.96745			0.181118
$119$	−11.7834	−	20.4094i	−1.08018	−	1.87092i
$120$		0			0
$121$	−4.06386	+	7.03881i	−0.369442	+	0.639892i
$122$	−5.13843			−0.465212
$123$	2.88837	−	5.00280i	0.260435	−	0.451087i
$124$	−6.82895	+	11.8281i	−0.613257	+	1.06219i
$125$		0			0
$126$	−0.879414	+	1.52319i	−0.0783444	+	0.135697i
$127$	0.862259	+	1.49348i	0.0765132	+	0.132525i	0.901743	−	0.432272i	$-0.142288\pi$
$127$	0.862259	+	1.49348i	0.0765132	+	0.132525i	−0.825230	+	0.564797i	$0.808955\pi$
$128$	−5.38335	−	9.32423i	−0.475825	−	0.824153i
$129$	−6.84559			−0.602721
$130$		0			0
$131$	−3.81897			−0.333665			−0.166833	−	0.985985i	$-0.553354\pi$
$131$	−3.81897			−0.333665			−0.166833	+	0.985985i	$0.553354\pi$
$132$	−3.96707	−	6.87116i	−0.345289	−	0.598058i
$133$	4.75321	+	8.23281i	0.412156	+	0.713875i
$134$	−0.846861	+	1.46681i	−0.0731576	+	0.126713i
$135$		0			0
$136$	4.74957	−	8.22649i	0.407272	−	0.705416i
$137$	−4.66601	+	8.08177i	−0.398644	+	0.690472i	−0.993559	−	0.113317i	$-0.963852\pi$
$137$	−4.66601	+	8.08177i	−0.398644	+	0.690472i	0.594915	+	0.803789i	$0.297186\pi$
$138$	3.43576			0.292471
$139$	0.976709	−	1.69171i	0.0828433	−	0.143489i	−0.821627	−	0.570026i	$-0.806933\pi$
$139$	0.976709	−	1.69171i	0.0828433	−	0.143489i	0.904470	+	0.426537i	$0.140267\pi$
$140$		0			0
$141$	3.00127	+	5.19835i	0.252753	+	0.437780i
$142$	3.61006			0.302950
$143$	2.76727	+	15.5243i	0.231411	+	1.29820i
$144$	2.91932			0.243277
$145$		0			0
$146$	−0.865118	−	1.49843i	−0.0715977	−	0.124011i
$147$	−4.82154	+	8.35115i	−0.397674	+	0.688791i
$148$	−11.1917			−0.919955
$149$	−8.74433	+	15.1456i	−0.716364	+	1.24078i	0.246068	+	0.969253i	$0.420861\pi$
$149$	−8.74433	+	15.1456i	−0.716364	+	1.24078i	−0.962431	+	0.271526i	$0.912472\pi$
$150$		0			0
$151$	−8.03580			−0.653944			−0.326972	−	0.945034i	$-0.606028\pi$
$151$	−8.03580			−0.653944			−0.326972	+	0.945034i	$0.606028\pi$
$152$	−1.91590	+	3.31843i	−0.155400	+	0.269160i
$153$	2.88837	+	5.00280i	0.233511	+	0.404452i
$154$	3.84614	+	6.66171i	0.309931	+	0.536816i
$155$		0			0
$156$	−6.15064	−	2.22564i	−0.492445	−	0.178194i
$157$	−15.4942			−1.23657			−0.618287	−	0.785953i	$-0.712173\pi$
$157$	−15.4942			−1.23657			−0.618287	+	0.785953i	$0.712173\pi$
$158$	1.97749	+	3.42511i	0.157321	+	0.272487i
$159$	5.11735	+	8.86350i	0.405832	+	0.702922i
$160$		0			0
$161$	32.5112			2.56224
$162$	0.215564	−	0.373368i	0.0169363	−	0.0293346i
$163$	1.86394	−	3.22845i	0.145995	−	0.252871i	−0.783748	−	0.621078i	$-0.786695\pi$
$163$	1.86394	−	3.22845i	0.145995	−	0.252871i	0.929744	+	0.368207i	$0.120028\pi$
$164$	10.4797			0.818330
$165$		0			0
$166$	−2.72197	−	4.71458i	−0.211265	−	0.365923i
$167$	4.17457	+	7.23057i	0.323038	+	0.559518i	0.981113	−	0.193434i	$-0.0619625\pi$
$167$	4.17457	+	7.23057i	0.323038	+	0.559518i	−0.658075	+	0.752952i	$0.728629\pi$
$168$	−6.70840			−0.517564
$169$	9.98974	+	8.31896i	0.768442	+	0.639920i
$170$		0			0
$171$	−1.16512	−	2.01805i	−0.0890989	−	0.154324i
$172$	−6.20939	−	10.7550i	−0.473462	−	0.820060i
$173$	−7.68083	+	13.3036i	−0.583963	+	1.01145i	0.411041	+	0.911617i	$0.365165\pi$
$173$	−7.68083	+	13.3036i	−0.583963	+	1.01145i	−0.995004	+	0.0998361i	$0.968168\pi$
$174$	−1.11336			−0.0844036
$175$		0			0
$176$	6.38386	−	11.0572i	0.481201	−	0.833465i
$177$	−4.56348			−0.343012
$178$	−3.01573	+	5.22341i	−0.226039	+	0.391511i
$179$	−0.347795	−	0.602398i	−0.0259954	−	0.0450253i	0.852735	−	0.522344i	$-0.174942\pi$
$179$	−0.347795	−	0.602398i	−0.0259954	−	0.0450253i	−0.878730	+	0.477318i	$0.841609\pi$
$180$		0			0
$181$	8.76032			0.651150			0.325575	−	0.945516i	$-0.394442\pi$
$181$	8.76032			0.651150			0.325575	+	0.945516i	$0.394442\pi$
$182$	5.96315	+	2.15780i	0.442018	+	0.159946i
$183$	11.9186			0.881045
$184$	6.55222	+	11.3488i	0.483036	+	0.836643i
$185$		0			0
$186$	−1.62290	+	2.81095i	−0.118997	+	0.206109i
$187$	25.2647			1.84754
$188$	−5.44469	+	9.43048i	−0.397095	+	0.687788i
$189$	2.03980	−	3.53303i	0.148373	−	0.256990i
$190$		0			0
$191$	6.34059	−	10.9822i	0.458789	−	0.794646i	−0.540108	−	0.841596i	$-0.681617\pi$
$191$	6.34059	−	10.9822i	0.458789	−	0.794646i	0.998897	+	0.0469495i	$0.0149500\pi$
$192$	1.93907	+	3.35857i	0.139940	+	0.242384i
$193$	−0.863956	−	1.49642i	−0.0621889	−	0.107714i	0.833255	−	0.552889i	$-0.186475\pi$
$193$	−0.863956	−	1.49642i	−0.0621889	−	0.107714i	−0.895444	+	0.445175i	$0.853141\pi$
$194$	−1.50200			−0.107838
$195$		0			0
$196$	−17.4938			−1.24956
$197$	8.96796	+	15.5330i	0.638941	+	1.10668i	0.985666	+	0.168711i	$0.0539604\pi$
$197$	8.96796	+	15.5330i	0.638941	+	1.10668i	−0.346725	+	0.937967i	$0.612706\pi$
$198$	−0.942775	−	1.63293i	−0.0670001	−	0.116048i
$199$	6.94299	−	12.0256i	0.492176	−	0.852473i	−0.507784	−	0.861485i	$-0.669535\pi$
$199$	6.94299	−	12.0256i	0.492176	−	0.852473i	0.999959	+	0.00901136i	$0.00286844\pi$
$200$		0			0
$201$	1.96429	−	3.40225i	0.138550	−	0.239976i
$202$	−2.20799	+	3.82436i	−0.155354	+	0.269081i
$203$	−10.5353			−0.739431
$204$	−5.23987	+	9.07572i	−0.366864	+	0.635427i
$205$		0			0
$206$	3.40807	+	5.90295i	0.237451	+	0.411278i
$207$	−7.96923			−0.553900
$208$	−1.84715	−	10.3624i	−0.128077	−	0.718504i
$209$	−10.1914			−0.704951
$210$		0			0
$211$	−7.49885	−	12.9884i	−0.516242	−	0.894157i	−0.999822	−	0.0188573i	$-0.993997\pi$
$211$	−7.49885	−	12.9884i	−0.516242	−	0.894157i	0.483580	−	0.875300i	$-0.339336\pi$
$212$	−9.28352	+	16.0795i	−0.637595	+	1.10435i
$213$	−8.37352			−0.573744
$214$	0.486274	−	0.842252i	0.0332410	−	0.0575751i
$215$		0			0
$216$	1.64438			0.111886
$217$	−15.3569	+	26.5989i	−1.04249	+	1.80565i
$218$	−2.95276	−	5.11433i	−0.199986	−	0.346386i
$219$	2.00664	+	3.47560i	0.135596	+	0.234859i
$220$		0			0
$221$	15.9304	−	13.4180i	1.07159	−	0.902590i
$222$	−2.65972			−0.178509
$223$	3.14128	+	5.44086i	0.210356	+	0.364347i	0.951826	−	0.306639i	$-0.0992044\pi$
$223$	3.14128	+	5.44086i	0.210356	+	0.364347i	−0.741470	+	0.670986i	$0.765871\pi$
$224$	−9.27569	−	16.0660i	−0.619758	−	1.07345i
$225$		0			0
$226$	5.05587			0.336311
$227$	2.18586	−	3.78603i	0.145081	−	0.251287i	−0.784322	−	0.620354i	$-0.786989\pi$
$227$	2.18586	−	3.78603i	0.145081	−	0.251287i	0.929403	+	0.369066i	$0.120322\pi$
$228$	2.11368	−	3.66099i	0.139982	−	0.242455i
$229$	−10.0497			−0.664100			−0.332050	−	0.943262i	$-0.607740\pi$
$229$	−10.0497			−0.664100			−0.332050	+	0.943262i	$0.607740\pi$
$230$		0			0
$231$	−8.92110	−	15.4518i	−0.586965	−	1.01665i
$232$	−2.12325	−	3.67757i	−0.139398	−	0.241445i
$233$	2.90450			0.190280			0.0951399	−	0.995464i	$-0.469670\pi$
$233$	2.90450			0.190280			0.0951399	+	0.995464i	$0.469670\pi$
$234$	−1.46170	−	0.528924i	−0.0955544	−	0.0345769i
$235$		0			0
$236$	−4.13937	−	7.16960i	−0.269450	−	0.466701i
$237$	−4.58677	−	7.94452i	−0.297943	−	0.516052i
$238$	5.08014	−	8.79906i	0.329297	−	0.570358i
$239$	19.3460			1.25139			0.625694	−	0.780068i	$-0.284816\pi$
$239$	19.3460			1.25139			0.625694	+	0.780068i	$0.284816\pi$
$240$		0			0
$241$	−4.55976	+	7.89774i	−0.293720	+	0.508738i	−0.974686	−	0.223577i	$-0.928227\pi$
$241$	−4.55976	+	7.89774i	−0.293720	+	0.508738i	0.680966	+	0.732315i	$0.261560\pi$
$242$	−3.50409			−0.225252
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	10.8109	+	18.7250i	0.692097	+	1.19875i
$245$		0			0
$246$	2.49051			0.158789
$247$	−6.42605	+	5.41259i	−0.408879	+	0.344395i
$248$	−12.3799			−0.786125
$249$	6.31358	+	10.9354i	0.400107	+	0.693006i
$250$		0			0
$251$	−11.1047	+	19.2339i	−0.700921	+	1.21403i	0.267223	+	0.963635i	$0.413894\pi$
$251$	−11.1047	+	19.2339i	−0.700921	+	1.21403i	−0.968144	+	0.250396i	$0.919439\pi$
$252$	7.40090			0.466213
$253$	−17.4268	+	30.1841i	−1.09561	+	1.89766i
$254$	−0.371745	+	0.643880i	−0.0233253	+	0.0404007i
$255$		0			0
$256$	−1.55723	+	2.69720i	−0.0973266	+	0.168575i
$257$	−10.0381	−	17.3865i	−0.626159	−	1.08454i	−0.988316	−	0.152422i	$-0.951293\pi$
$257$	−10.0381	−	17.3865i	−0.626159	−	1.08454i	0.362157	−	0.932117i	$-0.382040\pi$
$258$	−1.47566	−	2.55593i	−0.0918709	−	0.159125i
$259$	−25.1678			−1.56385
$260$		0			0
$261$	2.58243			0.159848
$262$	−0.823233	−	1.42588i	−0.0508595	−	0.0880913i
$263$	11.0037	+	19.0590i	0.678518	+	1.17523i	0.975427	+	0.220321i	$0.0707106\pi$
$263$	11.0037	+	19.0590i	0.678518	+	1.17523i	−0.296910	+	0.954906i	$0.595956\pi$
$264$	3.59587	−	6.22822i	0.221310	−	0.383321i
$265$		0			0
$266$	−2.04925	+	3.54940i	−0.125647	+	0.217627i
$267$	6.99498	−	12.1157i	0.428086	−	0.741466i
$268$	7.12694			0.435347
$269$	−5.53737	+	9.59101i	−0.337620	+	0.584774i	−0.983984	−	0.178254i	$-0.942955\pi$
$269$	−5.53737	+	9.59101i	−0.337620	+	0.584774i	0.646365	+	0.763028i	$0.276288\pi$
$270$		0			0
$271$	11.9216	+	20.6489i	0.724188	+	1.25433i	0.959307	+	0.282364i	$0.0911187\pi$
$271$	11.9216	+	20.6489i	0.724188	+	1.25433i	−0.235119	+	0.971967i	$0.575548\pi$
$272$	−16.8641			−1.02254
$273$	−13.8315	−	5.00500i	−0.837120	−	0.302916i
$274$	−4.02330			−0.243056
$275$		0			0
$276$	−7.22860	−	12.5203i	−0.435111	−	0.753634i
$277$	−4.28621	+	7.42393i	−0.257533	+	0.446061i	−0.965580	−	0.260104i	$-0.916243\pi$
$277$	−4.28621	+	7.42393i	−0.257533	+	0.446061i	0.708047	+	0.706165i	$0.249576\pi$
$278$	0.842174			0.0505102
$279$	3.76431	−	6.51998i	0.225363	−	0.390341i
$280$		0			0
$281$	3.48613			0.207965			0.103982	−	0.994579i	$-0.466841\pi$
$281$	3.48613			0.207965			0.103982	+	0.994579i	$0.466841\pi$
$282$	−1.29393	+	2.24116i	−0.0770526	+	0.133459i
$283$	−4.22976	−	7.32615i	−0.251433	−	0.435494i	0.712488	−	0.701685i	$-0.247568\pi$
$283$	−4.22976	−	7.32615i	−0.251433	−	0.435494i	−0.963921	+	0.266190i	$0.914235\pi$
$284$	−7.59532	−	13.1555i	−0.450700	−	0.780635i
$285$		0			0
$286$	−5.19974	+	4.37968i	−0.307467	+	0.258976i
$287$	23.5667			1.39110
$288$	2.27368	+	3.93813i	0.133978	+	0.232056i
$289$	−8.18532	−	14.1774i	−0.481489	−	0.833964i
$290$		0			0
$291$	3.48389			0.204229
$292$	−3.64029	+	6.30518i	−0.213032	+	0.368983i
$293$	0.722056	−	1.25064i	0.0421830	−	0.0730630i	−0.844163	−	0.536086i	$-0.819902\pi$
$293$	0.722056	−	1.25064i	0.0421830	−	0.0730630i	0.886346	+	0.463023i	$0.153235\pi$
$294$	−4.15740			−0.242465
$295$		0			0
$296$	−5.07226	−	8.78541i	−0.294819	−	0.510641i
$297$	2.18676	+	3.78758i	0.126889	+	0.219778i
$298$	−7.53986			−0.436772
$299$	5.04239	+	28.2876i	0.291609	+	1.63591i
$300$		0			0
$301$	−13.9636	−	24.1857i	−0.804849	−	1.39404i
$302$	−1.73223	−	3.00031i	−0.0996787	−	0.172649i
$303$	5.12143	−	8.87058i	0.294219	−	0.509601i
$304$	6.80271			0.390162
$305$		0			0
$306$	−1.24526	+	2.15685i	−0.0711866	+	0.123299i
$307$	−3.55726			−0.203024			−0.101512	−	0.994834i	$-0.532368\pi$
$307$	−3.55726			−0.203024			−0.101512	+	0.994834i	$0.532368\pi$
$308$	16.1840	−	28.0315i	0.922170	−	1.59725i
$309$	−7.90500	−	13.6919i	−0.449700	−	0.778903i
$310$		0			0
$311$	−18.7527			−1.06337			−0.531683	−	0.846943i	$-0.678440\pi$
$311$	−18.7527			−1.06337			−0.531683	+	0.846943i	$0.678440\pi$
$312$	−1.04045	−	5.83689i	−0.0589040	−	0.330449i
$313$	13.8732			0.784161			0.392081	−	0.919931i	$-0.371755\pi$
$313$	13.8732			0.784161			0.392081	+	0.919931i	$0.371755\pi$
$314$	−3.34000	−	5.78505i	−0.188487	−	0.326469i
$315$		0			0
$316$	8.32099	−	14.4124i	0.468093	−	0.810760i
$317$	7.36281			0.413537			0.206768	−	0.978390i	$-0.433705\pi$
$317$	7.36281			0.413537			0.206768	+	0.978390i	$0.433705\pi$
$318$	−2.20623	+	3.82131i	−0.123719	+	0.214288i
$319$	5.64716	−	9.78118i	0.316180	−	0.547641i
$320$		0			0
$321$	−1.12791	+	1.95360i	−0.0629538	+	0.109039i
$322$	7.00825	+	12.1386i	0.390555	+	0.676460i
$323$	6.73058	+	11.6577i	0.374500	+	0.648652i
$324$	−1.81413			−0.100785
$325$		0			0
$326$	1.60720			0.0890145
$327$	6.84892	+	11.8627i	0.378746	+	0.656007i
$328$	4.74957	+	8.22649i	0.262251	+	0.454232i
$329$	−12.2440	+	21.2072i	−0.675031	+	1.16919i
$330$		0			0
$331$	2.62472	−	4.54614i	0.144267	−	0.249879i	−0.784832	−	0.619709i	$-0.787251\pi$
$331$	2.62472	−	4.54614i	0.144267	−	0.249879i	0.929099	+	0.369830i	$0.120584\pi$
$332$	−11.4537	+	19.8383i	−0.628601	+	1.08877i
$333$	6.16921			0.338070
$334$	−1.79978	+	3.11730i	−0.0984794	+	0.170571i
$335$		0			0
$336$	5.95481	+	10.3140i	0.324862	+	0.562677i
$337$	−16.3450			−0.890371			−0.445185	−	0.895438i	$-0.646862\pi$
$337$	−16.3450			−0.890371			−0.445185	+	0.895438i	$0.646862\pi$
$338$	−0.952604	+	5.52312i	−0.0518148	+	0.300418i
$339$	−11.7271			−0.636926
$340$		0			0
$341$	−16.4633	−	28.5153i	−0.891538	−	1.54419i
$342$	0.502316	−	0.870037i	0.0271621	−	0.0470462i
$343$	−10.7827			−0.582209
$344$	5.62837	−	9.74863i	0.303462	−	0.525611i
$345$		0			0
$346$	−6.62285			−0.356046
$347$	6.31091	−	10.9308i	0.338787	−	0.586797i	−0.645417	−	0.763830i	$-0.723317\pi$
$347$	6.31091	−	10.9308i	0.338787	−	0.586797i	0.984205	+	0.177033i	$0.0566499\pi$
$348$	2.34243	+	4.05721i	0.125567	+	0.217489i
$349$	−5.18018	−	8.97234i	−0.277289	−	0.480278i	0.693421	−	0.720532i	$-0.256103\pi$
$349$	−5.18018	−	8.97234i	−0.277289	−	0.480278i	−0.970710	+	0.240254i	$0.922769\pi$
$350$		0			0
$351$	3.39041	+	1.22684i	0.180967	+	0.0654837i
$352$	19.8880			1.06003
$353$	−0.711780	−	1.23284i	−0.0378842	−	0.0656174i	0.846462	−	0.532450i	$-0.178728\pi$
$353$	−0.711780	−	1.23284i	−0.0378842	−	0.0656174i	−0.884346	+	0.466832i	$0.845395\pi$
$354$	−0.983723	−	1.70386i	−0.0522843	−	0.0905591i
$355$		0			0
$356$	25.3796			1.34512
$357$	−11.7834	+	20.4094i	−0.623641	+	1.08018i
$358$	0.149944	−	0.259711i	0.00792479	−	0.0137261i
$359$	7.01038			0.369994			0.184997	−	0.982739i	$-0.440773\pi$
$359$	7.01038			0.369994			0.184997	+	0.982739i	$0.440773\pi$
$360$		0			0
$361$	6.78499	+	11.7520i	0.357105	+	0.618524i
$362$	1.88841	+	3.27083i	0.0992527	+	0.171911i
$363$	8.12772			0.426595
$364$	−4.68279	−	26.2702i	−0.245445	−	1.37693i
$365$		0			0
$366$	2.56921	+	4.45001i	0.134295	+	0.232606i
$367$	−11.8017	−	20.4412i	−0.616044	−	1.06702i	−0.990200	−	0.139654i	$-0.955401\pi$
$367$	−11.8017	−	20.4412i	−0.616044	−	1.06702i	0.374156	−	0.927366i	$-0.377932\pi$
$368$	11.6324	−	20.1478i	0.606378	−	1.05028i
$369$	−5.77673			−0.300725
$370$		0			0
$371$	−20.8767	+	36.1595i	−1.08386	+	1.87731i
$372$	13.6579			0.708129
$373$	13.9540	−	24.1690i	0.722509	−	1.25142i	−0.237482	−	0.971392i	$-0.576322\pi$
$373$	13.9540	−	24.1690i	0.722509	−	1.25142i	0.959991	−	0.280031i	$-0.0903446\pi$
$374$	5.44616	+	9.43303i	0.281614	+	0.487770i
$375$		0			0
$376$	−9.87045			−0.509030
$377$	−1.63399	−	9.16659i	−0.0841546	−	0.472104i
$378$	1.75883			0.0904644
$379$	6.45018	+	11.1720i	0.331323	+	0.573869i	0.982772	−	0.184824i	$-0.0591716\pi$
$379$	6.45018	+	11.1720i	0.331323	+	0.573869i	−0.651448	+	0.758693i	$0.725838\pi$
$380$		0			0
$381$	0.862259	−	1.49348i	0.0441749	−	0.0765132i
$382$	5.46722			0.279727
$383$	−0.141703	+	0.245438i	−0.00724071	+	0.0125413i	−0.869623	−	0.493716i	$-0.835638\pi$
$383$	−0.141703	+	0.245438i	−0.00724071	+	0.0125413i	0.862382	+	0.506258i	$0.168971\pi$
$384$	−5.38335	+	9.32423i	−0.274718	+	0.475825i
$385$		0			0
$386$	0.372476	−	0.645147i	0.0189585	−	0.0328371i
$387$	3.42280	+	5.92846i	0.173991	+	0.301360i
$388$	3.16011	+	5.47347i	0.160430	+	0.277873i
$389$	31.3460			1.58930			0.794652	−	0.607065i	$-0.207653\pi$
$389$	31.3460			1.58930			0.794652	+	0.607065i	$0.207653\pi$
$390$		0			0
$391$	46.0361			2.32815
$392$	−7.92843	−	13.7325i	−0.400446	−	0.693594i
$393$	1.90949	+	3.30733i	0.0963208	+	0.166833i
$394$	−3.86634	+	6.69670i	−0.194783	+	0.337375i
$395$		0			0
$396$	−3.96707	+	6.87116i	−0.199353	+	0.345289i
$397$	12.7611	−	22.1028i	0.640459	−	1.10931i	−0.344872	−	0.938650i	$-0.612078\pi$
$397$	12.7611	−	22.1028i	0.640459	−	1.10931i	0.985330	−	0.170657i	$-0.0545891\pi$
$398$	5.98664			0.300083
$399$	4.75321	−	8.23281i	0.237958	−	0.412156i
$400$		0			0
$401$	1.36383	+	2.36222i	0.0681062	+	0.117963i	0.898068	−	0.439857i	$-0.144971\pi$
$401$	1.36383	+	2.36222i	0.0681062	+	0.117963i	−0.829961	+	0.557821i	$0.811638\pi$
$402$	1.69372			0.0844751
$403$	−25.5251	−	9.23640i	−1.27150	−	0.460098i
$404$	18.5819			0.924482
$405$		0			0
$406$	−2.27103	−	3.93353i	−0.112709	−	0.195218i
$407$	13.4906	−	23.3664i	0.668704	−	1.15823i
$408$	−9.49914			−0.470277
$409$	13.9097	−	24.0923i	0.687790	−	1.19129i	−0.284762	−	0.958598i	$-0.591915\pi$
$409$	13.9097	−	24.0923i	0.687790	−	1.19129i	0.972551	−	0.232688i	$-0.0747522\pi$
$410$		0			0
$411$	9.33202			0.460315
$412$	14.3407	−	24.8388i	0.706515	−	1.22372i
$413$	−9.30857	−	16.1229i	−0.458045	−	0.793357i
$414$	−1.71788	−	2.97546i	−0.0844292	−	0.146236i
$415$		0			0
$416$	12.5401	−	10.5624i	0.614831	−	0.517866i
$417$	−1.95342			−0.0956592
$418$	−2.19689	−	3.80513i	−0.107454	−	0.186115i
$419$	−12.4959	−	21.6435i	−0.610464	−	1.05735i	−0.991162	−	0.132655i	$-0.957650\pi$
$419$	−12.4959	−	21.6435i	−0.610464	−	1.05735i	0.380698	−	0.924699i	$-0.375684\pi$
$420$		0			0
$421$	29.7327			1.44908			0.724541	−	0.689232i	$-0.242052\pi$
$421$	29.7327			1.44908			0.724541	+	0.689232i	$0.242052\pi$
$422$	3.23297	−	5.59966i	0.157378	−	0.272587i
$423$	3.00127	−	5.19835i	0.145927	−	0.252753i
$424$	−16.8297			−0.817323
$425$		0			0
$426$	−1.80503	−	3.12641i	−0.0874541	−	0.151475i
$427$	24.3114	+	42.1086i	1.17651	+	2.03778i
$428$	−4.09235			−0.197811
$429$	12.0608	−	10.1587i	0.582299	−	0.490464i
$430$		0			0
$431$	12.5345	+	21.7105i	0.603768	+	1.04576i	0.992245	+	0.124298i	$0.0396680\pi$
$431$	12.5345	+	21.7105i	0.603768	+	1.04576i	−0.388477	+	0.921458i	$0.626999\pi$
$432$	−1.45966	−	2.52820i	−0.0702279	−	0.121638i
$433$	−10.8722	+	18.8312i	−0.522485	+	0.904970i	0.477173	+	0.878809i	$0.341662\pi$
$433$	−10.8722	+	18.8312i	−0.522485	+	0.904970i	−0.999658	+	0.0261608i	$0.991672\pi$
$434$	−13.2416			−0.635615
$435$		0			0
$436$	−12.4248	+	21.5204i	−0.595041	+	1.03064i
$437$	−18.5702			−0.888333
$438$	−0.865118	+	1.49843i	−0.0413369	+	0.0715977i
$439$	−3.50887	−	6.07754i	−0.167469	−	0.290065i	0.770060	−	0.637971i	$-0.220226\pi$
$439$	−3.50887	−	6.07754i	−0.167469	−	0.290065i	−0.937529	+	0.347906i	$0.886893\pi$
$440$		0			0
$441$	9.64307			0.459194
$442$	8.44386	+	3.05545i	0.401633	+	0.145333i
$443$	−4.44015			−0.210958			−0.105479	−	0.994422i	$-0.533638\pi$
$443$	−4.44015			−0.210958			−0.105479	+	0.994422i	$0.533638\pi$
$444$	5.59587	+	9.69233i	0.265568	+	0.459977i
$445$		0			0
$446$	−1.35430	+	2.34571i	−0.0641278	+	0.111073i
$447$	17.4887			0.827186
$448$	−7.91062	+	13.7016i	−0.373741	+	0.647339i
$449$	−13.6990	+	23.7274i	−0.646497	+	1.11977i	0.337457	+	0.941341i	$0.390433\pi$
$449$	−13.6990	+	23.7274i	−0.646497	+	1.11977i	−0.983954	+	0.178424i	$0.942900\pi$
$450$		0			0
$451$	−12.6323	+	21.8799i	−0.594834	+	1.03028i
$452$	−10.6372	−	18.4242i	−0.500331	−	0.866599i
$453$	4.01790	+	6.95921i	0.188777	+	0.326972i
$454$	1.88477			0.0884569
$455$		0			0
$456$	3.83180			0.179440
$457$	−6.10188	−	10.5688i	−0.285434	−	0.494386i	0.687280	−	0.726392i	$-0.258804\pi$
$457$	−6.10188	−	10.5688i	−0.285434	−	0.494386i	−0.972714	+	0.232006i	$0.925471\pi$
$458$	−2.16635	−	3.75222i	−0.101227	−	0.175330i
$459$	2.88837	−	5.00280i	0.134817	−	0.233511i
$460$		0			0
$461$	−12.6371	+	21.8882i	−0.588570	+	1.01943i	0.405850	+	0.913940i	$0.366976\pi$
$461$	−12.6371	+	21.8882i	−0.588570	+	1.01943i	−0.994420	+	0.105494i	$0.966358\pi$
$462$	3.84614	−	6.66171i	0.178939	−	0.309931i
$463$	21.2503			0.987587			0.493794	−	0.869579i	$-0.335610\pi$
$463$	21.2503			0.987587			0.493794	+	0.869579i	$0.335610\pi$
$464$	−3.76947	+	6.52891i	−0.174993	+	0.303097i
$465$		0			0
$466$	0.626105	+	1.08445i	0.0290038	+	0.0502360i
$467$	11.7763			0.544944			0.272472	−	0.962164i	$-0.412159\pi$
$467$	11.7763			0.544944			0.272472	+	0.962164i	$0.412159\pi$
$468$	1.14786	+	6.43943i	0.0530597	+	0.297663i
$469$	16.0270			0.740058
$470$		0			0
$471$	7.74711	+	13.4184i	0.356968	+	0.618287i
$472$	3.75205	−	6.49874i	0.172702	−	0.299129i
$473$	29.9394			1.37661
$474$	1.97749	−	3.42511i	0.0908290	−	0.157321i
$475$		0			0
$476$	−42.7530			−1.95958
$477$	5.11735	−	8.86350i	0.234307	−	0.405832i
$478$	4.17031	+	7.22318i	0.190745	+	0.330381i
$479$	13.4407	+	23.2801i	0.614123	+	1.06369i	0.990538	+	0.137241i	$0.0438236\pi$
$479$	13.4407	+	23.2801i	0.614123	+	1.06369i	−0.376414	+	0.926451i	$0.622843\pi$
$480$		0			0
$481$	−3.90345	−	21.8982i	−0.177982	−	0.998472i
$482$	−3.93169			−0.179083
$483$	−16.2556	−	28.1555i	−0.739655	−	1.28112i
$484$	7.37236	+	12.7693i	0.335107	+	0.580423i
$485$		0			0
$486$	−0.431128			−0.0195564
$487$	10.8520	−	18.7963i	0.491752	−	0.851740i	−0.508203	−	0.861238i	$-0.669690\pi$
$487$	10.8520	−	18.7963i	0.491752	−	0.851740i	0.999955	+	0.00949761i	$0.00302323\pi$
$488$	−9.79932	+	16.9729i	−0.443594	+	0.768328i
$489$	−3.72789			−0.168581
$490$		0			0
$491$	−12.9622	−	22.4512i	−0.584977	−	1.01321i	−0.994878	−	0.101080i	$-0.967770\pi$
$491$	−12.9622	−	22.4512i	−0.584977	−	1.01321i	0.409901	−	0.912130i	$-0.365563\pi$
$492$	−5.23987	−	9.07572i	−0.236231	−	0.409165i
$493$	−14.9180			−0.671874
$494$	−3.40611	−	1.23252i	−0.153248	−	0.0554537i
$495$		0			0
$496$	10.9892	+	19.0339i	0.493431	+	0.854647i
$497$	−17.0803	−	29.5839i	−0.766155	−	1.32702i
$498$	−2.72197	+	4.71458i	−0.121974	+	0.211265i
$499$	39.5723			1.77150			0.885749	−	0.464164i	$-0.153645\pi$
$499$	39.5723			1.77150			0.885749	+	0.464164i	$0.153645\pi$
$500$		0			0
$501$	4.17457	−	7.23057i	0.186506	−	0.323038i
$502$	−9.57508			−0.427357
$503$	18.3907	−	31.8536i	0.820000	−	1.42028i	−0.0856806	−	0.996323i	$-0.527306\pi$
$503$	18.3907	−	31.8536i	0.820000	−	1.42028i	0.905681	−	0.423960i	$-0.139360\pi$
$504$	3.35420	+	5.80964i	0.149408	+	0.258782i
$505$		0			0
$506$	−15.0264			−0.668004
$507$	2.20956	−	12.8108i	0.0981300	−	0.568950i
$508$	3.12850			0.138805
$509$	−5.64492	−	9.77729i	−0.250207	−	0.433371i	0.713376	−	0.700782i	$-0.247165\pi$
$509$	−5.64492	−	9.77729i	−0.250207	−	0.433371i	−0.963583	+	0.267411i	$0.913832\pi$
$510$		0			0
$511$	−8.18626	+	14.1790i	−0.362139	+	0.627243i
$512$	−22.8761			−1.01099
$513$	−1.16512	+	2.01805i	−0.0514413	+	0.0890989i
$514$	4.32770	−	7.49580i	0.190887	−	0.330626i
$515$		0			0
$516$	−6.20939	+	10.7550i	−0.273353	+	0.473462i
$517$	−13.1261	−	22.7351i	−0.577286	−	0.999889i
$518$	−5.42529	−	9.39687i	−0.238373	−	0.412875i
$519$	15.3617			0.674302
$520$		0			0
$521$	−23.9842			−1.05077			−0.525384	−	0.850865i	$-0.676078\pi$
$521$	−23.9842			−1.05077			−0.525384	+	0.850865i	$0.676078\pi$
$522$	0.556680	+	0.964198i	0.0243652	+	0.0422018i
$523$	8.04348	+	13.9317i	0.351717	+	0.609191i	0.986550	−	0.163458i	$-0.0522647\pi$
$523$	8.04348	+	13.9317i	0.351717	+	0.609191i	−0.634834	+	0.772649i	$0.718931\pi$
$524$	−3.46405	+	5.99991i	−0.151328	+	0.262107i
$525$		0			0
$526$	−4.74401	+	8.21687i	−0.206849	+	0.358272i
$527$	−21.7454	+	37.6642i	−0.947246	+	1.64068i
$528$	−12.7677			−0.555643
$529$	−20.2543	+	35.0815i	−0.880622	+	1.52528i
$530$		0			0
$531$	2.28174	+	3.95209i	0.0990191	+	0.171506i
$532$	17.2459			0.747704
$533$	3.65512	+	20.5051i	0.158321	+	0.888174i
$534$	6.03147			0.261007
$535$		0			0
$536$	3.23004	+	5.59459i	0.139516	+	0.241649i
$537$	−0.347795	+	0.602398i	−0.0150084	+	0.0259954i
$538$	−4.77464			−0.205849
$539$	21.0871	−	36.5240i	0.908286	−	1.57320i
$540$		0			0
$541$	−21.7133			−0.933526			−0.466763	−	0.884382i	$-0.654580\pi$
$541$	−21.7133			−0.933526			−0.466763	+	0.884382i	$0.654580\pi$
$542$	−5.13976	+	8.90232i	−0.220772	+	0.382388i
$543$	−4.38016	−	7.58666i	−0.187971	−	0.325575i
$544$	−13.1344	−	22.7495i	−0.563134	−	0.975377i
$545$		0			0
$546$	−1.11287	−	6.24313i	−0.0476263	−	0.267181i
$547$	19.3261			0.826326			0.413163	−	0.910657i	$-0.364424\pi$
$547$	19.3261			0.826326			0.413163	+	0.910657i	$0.364424\pi$
$548$	8.46474	+	14.6614i	0.361596	+	0.626302i
$549$	−5.95928	−	10.3218i	−0.254336	−	0.440523i
$550$		0			0
$551$	6.01768			0.256362
$552$	6.55222	−	11.3488i	0.278881	−	0.483036i
$553$	18.7122	−	32.4104i	0.795722	−	1.37823i
$554$	−3.69581			−0.157020
$555$		0			0
$556$	−1.77187	−	3.06898i	−0.0751442	−	0.130154i
$557$	4.07013	+	7.04967i	0.172457	+	0.298704i	0.939278	−	0.343156i	$-0.111496\pi$
$557$	4.07013	+	7.04967i	0.172457	+	0.298704i	−0.766821	+	0.641861i	$0.778163\pi$
$558$	3.24580			0.137406
$559$	18.8779	−	15.9007i	0.798451	−	0.672527i
$560$		0			0
$561$	−12.6323	−	21.8799i	−0.533338	−	0.923768i
$562$	0.751484	+	1.30161i	0.0316994	+	0.0549051i
$563$	−2.65348	+	4.59595i	−0.111831	+	0.193696i	−0.916508	−	0.400015i	$-0.869005\pi$
$563$	−2.65348	+	4.59595i	−0.111831	+	0.193696i	0.804678	+	0.593712i	$0.202338\pi$
$564$	10.8894			0.458525
$565$		0			0
$566$	1.82357	−	3.15851i	0.0766503	−	0.132762i
$567$	−4.07959			−0.171327
$568$	6.88462	−	11.9245i	0.288872	−	0.500342i
$569$	−19.6823	−	34.0907i	−0.825124	−	1.42916i	−0.901824	−	0.432103i	$-0.857772\pi$
$569$	−19.6823	−	34.0907i	−0.825124	−	1.42916i	0.0767005	−	0.997054i	$-0.475561\pi$
$570$		0			0
$571$	−13.7188			−0.574115			−0.287057	−	0.957913i	$-0.592677\pi$
$571$	−13.7188			−0.574115			−0.287057	+	0.957913i	$0.592677\pi$
$572$	26.9000	+	9.73389i	1.12474	+	0.406995i
$573$	−12.6812			−0.529764
$574$	5.08014	+	8.79906i	0.212041	+	0.367266i
$575$		0			0
$576$	1.93907	−	3.35857i	0.0807946	−	0.139940i
$577$	2.55146			0.106219			0.0531093	−	0.998589i	$-0.483087\pi$
$577$	2.55146			0.106219			0.0531093	+	0.998589i	$0.483087\pi$
$578$	3.52892	−	6.11227i	0.146784	−	0.254237i
$579$	−0.863956	+	1.49642i	−0.0359048	+	0.0621889i
$580$		0			0
$581$	−25.7568	+	44.6122i	−1.06857	+	1.85082i
$582$	0.751002	+	1.30077i	0.0311300	+	0.0539188i
$583$	−22.3808	−	38.7648i	−0.926920	−	1.60547i
$584$	−6.59934			−0.273083
$585$		0			0
$586$	0.622598			0.0257193
$587$	−3.66291	−	6.34435i	−0.151185	−	0.261860i	0.780479	−	0.625183i	$-0.214975\pi$
$587$	−3.66291	−	6.34435i	−0.151185	−	0.261860i	−0.931663	+	0.363323i	$0.881642\pi$
$588$	8.74689	+	15.1501i	0.360716	+	0.624778i
$589$	8.77175	−	15.1931i	0.361434	−	0.626021i
$590$		0			0
$591$	8.96796	−	15.5330i	0.368893	−	0.638941i
$592$	−9.00494	+	15.5970i	−0.370101	+	0.641033i
$593$	−25.1001			−1.03074			−0.515368	−	0.856969i	$-0.672345\pi$
$593$	−25.1001			−1.03074			−0.515368	+	0.856969i	$0.672345\pi$
$594$	−0.942775	+	1.63293i	−0.0386825	+	0.0670001i
$595$		0			0
$596$	15.8633	+	27.4761i	0.649788	+	1.12547i
$597$	−13.8860			−0.568315
$598$	−9.47472	+	7.98045i	−0.387450	+	0.326345i
$599$	−3.86368			−0.157866			−0.0789329	−	0.996880i	$-0.525151\pi$
$599$	−3.86368			−0.157866			−0.0789329	+	0.996880i	$0.525151\pi$
$600$		0			0
$601$	−7.78766	−	13.4886i	−0.317665	−	0.550213i	0.662335	−	0.749208i	$-0.269566\pi$
$601$	−7.78766	−	13.4886i	−0.317665	−	0.550213i	−0.980000	+	0.198995i	$0.936232\pi$
$602$	6.02011	−	10.4271i	0.245361	−	0.424978i
$603$	−3.92858			−0.159984
$604$	−7.28899	+	12.6249i	−0.296585	+	0.513700i
$605$		0			0
$606$	4.41599			0.179387
$607$	−11.8159	+	20.4658i	−0.479594	+	0.830681i	−0.999726	−	0.0234047i	$-0.992549\pi$
$607$	−11.8159	+	20.4658i	−0.479594	+	0.830681i	0.520132	+	0.854086i	$0.325883\pi$
$608$	5.29822	+	9.17678i	0.214871	+	0.372168i
$609$	5.26763	+	9.12381i	0.213455	+	0.369715i
$610$		0			0
$611$	−20.3511	−	7.36414i	−0.823316	−	0.297921i
$612$	10.4797			0.423618
$613$	−6.37334	−	11.0390i	−0.257417	−	0.445859i	0.708132	−	0.706080i	$-0.249538\pi$
$613$	−6.37334	−	11.0390i	−0.257417	−	0.445859i	−0.965549	+	0.260221i	$0.916205\pi$
$614$	−0.766818	−	1.32817i	−0.0309463	−	0.0536005i
$615$		0			0
$616$	29.3393			1.18212
$617$	7.08690	−	12.2749i	0.285308	−	0.494168i	−0.687376	−	0.726302i	$-0.741238\pi$
$617$	7.08690	−	12.2749i	0.285308	−	0.494168i	0.972684	+	0.232134i	$0.0745709\pi$
$618$	3.40807	−	5.90295i	0.137093	−	0.237451i
$619$	14.0510			0.564756			0.282378	−	0.959303i	$-0.408877\pi$
$619$	14.0510			0.564756			0.282378	+	0.959303i	$0.408877\pi$
$620$		0			0
$621$	3.98461	+	6.90155i	0.159897	+	0.276950i
$622$	−4.04240	−	7.00165i	−0.162086	−	0.280740i
$623$	57.0733			2.28659
$624$	−8.05053	+	6.78088i	−0.322279	+	0.271452i
$625$		0			0
$626$	2.99057	+	5.17982i	0.119527	+	0.207027i
$627$	5.09568	+	8.82598i	0.203502	+	0.352476i
$628$	−14.0543	+	24.3427i	−0.560826	+	0.971379i
$629$	−35.6379			−1.42097
$630$		0			0
$631$	0.816528	−	1.41427i	0.0325055	−	0.0563012i	−0.849315	−	0.527886i	$-0.822985\pi$
$631$	0.816528	−	1.41427i	0.0325055	−	0.0563012i	0.881821	+	0.471585i	$0.156318\pi$
$632$	15.0848			0.600041
$633$	−7.49885	+	12.9884i	−0.298052	+	0.516242i
$634$	1.58716	+	2.74904i	0.0630341	+	0.109178i
$635$		0			0
$636$	18.5670			0.736231
$637$	−6.10148	−	34.2290i	−0.241750	−	1.35620i
$638$	4.86931			0.192778
$639$	4.18676	+	7.25169i	0.165626	+	0.286872i
$640$		0			0
$641$	15.1744	−	26.2829i	0.599353	−	1.03811i	−0.393563	−	0.919298i	$-0.628758\pi$
$641$	15.1744	−	26.2829i	0.599353	−	1.03811i	0.992917	−	0.118813i	$-0.0379089\pi$
$642$	−0.972549			−0.0383834
$643$	24.2513	−	42.0045i	0.956378	−	1.65649i	0.225194	−	0.974314i	$-0.427698\pi$
$643$	24.2513	−	42.0045i	0.956378	−	1.65649i	0.731184	−	0.682181i	$-0.238968\pi$
$644$	29.4897	−	51.0777i	1.16206	−	2.01274i
$645$		0			0
$646$	−2.90175	+	5.02597i	−0.114168	+	0.197744i
$647$	−7.71712	−	13.3664i	−0.303391	−	0.525489i	0.673510	−	0.739178i	$-0.264786\pi$
$647$	−7.71712	−	13.3664i	−0.303391	−	0.525489i	−0.976902	+	0.213688i	$0.931452\pi$
$648$	−0.822190	−	1.42407i	−0.0322987	−	0.0559429i
$649$	19.9585			0.783440
$650$		0			0
$651$	30.7137			1.20377
$652$	−3.38143	−	5.85682i	−0.132427	−	0.229371i
$653$	9.60342	+	16.6336i	0.375811	+	0.650923i	0.990448	−	0.137887i	$-0.0440309\pi$
$653$	9.60342	+	16.6336i	0.375811	+	0.650923i	−0.614637	+	0.788810i	$0.710698\pi$
$654$	−2.95276	+	5.11433i	−0.115462	+	0.199986i
$655$		0			0
$656$	8.43206	−	14.6048i	0.329217	−	0.570220i
$657$	2.00664	−	3.47560i	0.0782863	−	0.135596i
$658$	−10.5574			−0.411572
$659$	−12.1660	+	21.0722i	−0.473921	+	0.820855i	−0.999554	−	0.0298565i	$-0.990495\pi$
$659$	−12.1660	+	21.0722i	−0.473921	+	0.820855i	0.525634	+	0.850711i	$0.323828\pi$
$660$		0			0
$661$	7.56031	+	13.0948i	0.294062	+	0.509330i	0.974766	−	0.223228i	$-0.0716594\pi$
$661$	7.56031	+	13.0948i	0.294062	+	0.509330i	−0.680704	+	0.732558i	$0.738326\pi$
$662$	2.26318			0.0879610
$663$	−19.5855	−	7.08711i	−0.760637	−	0.275241i
$664$	−20.7638			−0.805794
$665$		0			0
$666$	1.32986	+	2.30339i	0.0515310	+	0.0892544i
$667$	10.2900	−	17.8228i	0.398430	−	0.690101i
$668$	15.1464			0.586032
$669$	3.14128	−	5.44086i	0.121449	−	0.210356i
$670$		0			0
$671$	−52.1261			−2.01231
$672$	−9.27569	+	16.0660i	−0.357817	+	0.619758i
$673$	11.4920	+	19.9047i	0.442983	+	0.767269i	0.997909	−	0.0646304i	$-0.0205868\pi$
$673$	11.4920	+	19.9047i	0.442983	+	0.767269i	−0.554926	+	0.831900i	$0.687254\pi$
$674$	−3.52341	−	6.10272i	−0.135716	−	0.235068i
$675$		0			0
$676$	22.1311	−	8.14886i	0.851196	−	0.313418i
$677$	−49.6667			−1.90885			−0.954424	−	0.298454i	$-0.903529\pi$
$677$	−49.6667			−1.90885			−0.954424	+	0.298454i	$0.903529\pi$
$678$	−2.52793	−	4.37851i	−0.0970847	−	0.168156i
$679$	7.10642	+	12.3087i	0.272720	+	0.472364i
$680$		0			0
$681$	−4.37173			−0.167525
$682$	7.09780	−	12.2938i	0.271789	−	0.470752i
$683$	−15.4972	+	26.8419i	−0.592982	+	1.02708i	0.400846	+	0.916145i	$0.368716\pi$
$683$	−15.4972	+	26.8419i	−0.592982	+	1.02708i	−0.993828	+	0.110930i	$0.964617\pi$
$684$	−4.22735			−0.161637
$685$		0			0
$686$	−2.32436	−	4.02590i	−0.0887443	−	0.153710i
$687$	5.02483	+	8.70326i	0.191709	+	0.332050i
$688$	−19.9845			−0.761900
$689$	−34.6998	−	12.5563i	−1.32196	−	0.478357i
$690$		0			0
$691$	12.1961	+	21.1242i	0.463961	+	0.803604i	0.999154	−	0.0411261i	$-0.0130945\pi$
$691$	12.1961	+	21.1242i	0.463961	+	0.803604i	−0.535193	+	0.844730i	$0.679761\pi$
$692$	13.9340	+	24.1344i	0.529691	+	0.917453i
$693$	−8.92110	+	15.4518i	−0.338885	+	0.586965i
$694$	5.44163			0.206561
$695$		0			0
$696$	−2.12325	+	3.67757i	−0.0804815	+	0.139398i
$697$	33.3706			1.26400
$698$	2.23332	−	3.86823i	0.0845325	−	0.146415i
$699$	−1.45225	−	2.51537i	−0.0549291	−	0.0951399i
$700$		0			0
$701$	16.8858			0.637769			0.318885	−	0.947794i	$-0.396692\pi$
$701$	16.8858			0.637769			0.318885	+	0.947794i	$0.396692\pi$
$702$	0.272789	+	1.53033i	0.0102957	+	0.0577587i
$703$	14.3757			0.542191
$704$	−8.48057	−	14.6888i	−0.319624	−	0.553604i
$705$		0			0
$706$	0.306868	−	0.531512i	0.0115491	−	0.0200037i
$707$	41.7867			1.57155
$708$	−4.13937	+	7.16960i	−0.155567	+	0.269450i
$709$	−25.7740	+	44.6419i	−0.967962	+	1.67656i	−0.266526	+	0.963828i	$0.585876\pi$
$709$	−25.7740	+	44.6419i	−0.967962	+	1.67656i	−0.701436	+	0.712732i	$0.747457\pi$
$710$		0			0
$711$	−4.58677	+	7.94452i	−0.172017	+	0.297943i
$712$	11.5024	+	19.9227i	0.431071	+	0.746636i
$713$	−29.9987	−	51.9592i	−1.12346	−	1.94589i
$714$	−10.1603			−0.380239
$715$		0			0
$716$	−1.26189			−0.0471590
$717$	−9.67300	−	16.7541i	−0.361245	−	0.625694i
$718$	1.51119	+	2.61745i	0.0563970	+	0.0976824i
$719$	−8.30694	+	14.3880i	−0.309796	+	0.536583i	−0.978318	−	0.207110i	$-0.933594\pi$
$719$	−8.30694	+	14.3880i	−0.309796	+	0.536583i	0.668521	+	0.743693i	$0.266928\pi$
$720$		0			0
$721$	32.2492	−	55.8572i	1.20102	−	2.08023i
$722$	−2.92520	+	5.06660i	−0.108865	+	0.188559i
$723$	9.11953			0.339159
$724$	7.94617	−	13.7632i	0.295317	−	0.511504i
$725$		0			0
$726$	1.75205	+	3.03463i	0.0650245	+	0.112626i
$727$	−27.8553			−1.03310			−0.516549	−	0.856258i	$-0.672783\pi$
$727$	−27.8553			−1.03310			−0.516549	+	0.856258i	$0.672783\pi$
$728$	18.4996	−	15.5820i	0.685640	−	0.577507i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−19.7726	−	34.2471i	−0.731315	−	1.26668i
$732$	10.8109	−	18.7250i	0.399582	−	0.692097i
$733$	−21.6887			−0.801090			−0.400545	−	0.916277i	$-0.631179\pi$
$733$	−21.6887			−0.801090			−0.400545	+	0.916277i	$0.631179\pi$
$734$	5.08805	−	8.81277i	0.187803	−	0.325285i
$735$		0			0
$736$	36.2389			1.33579
$737$	−8.59087	+	14.8798i	−0.316449	+	0.548105i
$738$	−1.24526	−	2.15685i	−0.0458385	−	0.0793947i
$739$	−3.94439	−	6.83188i	−0.145097	−	0.251315i	0.784312	−	0.620366i	$-0.213016\pi$
$739$	−3.94439	−	6.83188i	−0.145097	−	0.251315i	−0.929409	+	0.369051i	$0.879683\pi$
$740$		0			0
$741$	7.90046	+	2.85882i	0.290231	+	0.105022i
$742$	−18.0011			−0.660840
$743$	18.3130	+	31.7190i	0.671839	+	1.16366i	0.977382	+	0.211480i	$0.0678284\pi$
$743$	18.3130	+	31.7190i	0.671839	+	1.16366i	−0.305544	+	0.952178i	$0.598838\pi$
$744$	6.18996	+	10.7213i	0.226935	+	0.393063i
$745$		0			0
$746$	12.0319			0.440519
$747$	6.31358	−	10.9354i	0.231002	−	0.400107i
$748$	22.9167	−	39.6929i	0.837917	−	1.45131i
$749$	−9.20283			−0.336264
$750$		0			0
$751$	−21.8207	−	37.7945i	−0.796247	−	1.37914i	−0.922044	−	0.387085i	$-0.873482\pi$
$751$	−21.8207	−	37.7945i	−0.796247	−	1.37914i	0.125797	−	0.992056i	$-0.459851\pi$
$752$	8.76166	+	15.1756i	0.319505	+	0.553399i
$753$	22.2094			0.809354
$754$	3.07029	−	2.58607i	0.111813	−	0.0941791i
$755$		0			0
$756$	−3.70045	−	6.40937i	−0.134584	−	0.233107i
$757$	7.51652	+	13.0190i	0.273193	+	0.473184i	0.969678	−	0.244388i	$-0.0785870\pi$
$757$	7.51652	+	13.0190i	0.273193	+	0.473184i	−0.696485	+	0.717571i	$0.745254\pi$
$758$	−2.78085	+	4.81658i	−0.101005	+	0.174946i
$759$	34.8536			1.26511
$760$		0			0
$761$	−23.1894	+	40.1652i	−0.840614	+	1.45599i	0.0487618	+	0.998810i	$0.484472\pi$
$761$	−23.1894	+	40.1652i	−0.840614	+	1.45599i	−0.889376	+	0.457176i	$0.848861\pi$
$762$	0.743489			0.0269338
$763$	−27.9408	+	48.3949i	−1.01152	+	1.75201i
$764$	−11.5026	−	19.9232i	−0.416151	−	0.720795i
$765$		0			0
$766$	−0.122185			−0.00441471
$767$	12.5846	−	10.5999i	0.454404	−	0.382739i
$768$	3.11445			0.112383
$769$	−19.2871	−	33.4062i	−0.695510	−	1.20466i	−0.970008	−	0.243071i	$-0.921845\pi$
$769$	−19.2871	−	33.4062i	−0.695510	−	1.20466i	0.274498	−	0.961588i	$-0.411488\pi$
$770$		0			0
$771$	−10.0381	+	17.3865i	−0.361513	+	0.626159i
$772$	−3.13465			−0.112819
$773$	6.42419	−	11.1270i	0.231062	−	0.400211i	−0.727059	−	0.686575i	$-0.759113\pi$
$773$	6.42419	−	11.1270i	0.231062	−	0.400211i	0.958121	+	0.286364i	$0.0924466\pi$
$774$	−1.47566	+	2.55593i	−0.0530417	+	0.0918709i
$775$		0			0
$776$	−2.86442	+	4.96132i	−0.102827	+	0.178101i
$777$	12.5839	+	21.7960i	0.451446	+	0.781927i
$778$	6.75707	+	11.7036i	0.242253	+	0.419594i
$779$	−13.4612			−0.482296
$780$		0			0
$781$	36.6218			1.31043
$782$	9.92373	+	17.1884i	0.354872	+	0.614656i
$783$	−1.29122	−	2.23645i	−0.0461443	−	0.0799242i
$784$	−14.0756	+	24.3797i	−0.502700	+	0.870702i
$785$		0			0
$786$	−0.823233	+	1.42588i	−0.0293638	+	0.0508595i
$787$	−1.53008	+	2.65017i	−0.0545413	+	0.0944683i	−0.892007	−	0.452022i	$-0.850703\pi$
$787$	−1.53008	+	2.65017i	−0.0545413	+	0.0944683i	0.837466	+	0.546490i	$0.184036\pi$
$788$	32.5381			1.15912
$789$	11.0037	−	19.0590i	0.391742	−	0.678518i
$790$		0			0
$791$	−23.9208	−	41.4320i	−0.850526	−	1.47315i
$792$	−7.19173			−0.255547
$793$	−32.8675	+	27.6840i	−1.16716	+	0.983087i
$794$	11.0033			0.390493
$795$		0			0
$796$	−12.5955	−	21.8160i	−0.446435	−	0.773248i
$797$	−15.5423	+	26.9201i	−0.550537	+	0.953559i	0.447698	+	0.894185i	$0.352244\pi$
$797$	−15.5423	+	26.9201i	−0.550537	+	0.953559i	−0.998236	+	0.0593742i	$0.981089\pi$
$798$	4.09849			0.145085
$799$	−17.3375	+	30.0295i	−0.613358	+	1.06237i
$800$		0			0
$801$	−13.9900			−0.494311
$802$	−0.587984	+	1.01842i	−0.0207624	+	0.0359616i
$803$	−8.77607	−	15.2006i	−0.309701	−	0.536418i
$804$	−3.56347	−	6.17211i	−0.125674	−	0.217674i
$805$		0			0
$806$	−2.05372	−	11.5213i	−0.0723394	−	0.405821i
$807$	11.0747			0.389849
$808$	8.42157	+	14.5866i	0.296270	+	0.513155i
$809$	14.5887	+	25.2683i	0.512910	+	0.888386i	0.999888	+	0.0149717i	$0.00476581\pi$
$809$	14.5887	+	25.2683i	0.512910	+	0.888386i	−0.486978	+	0.873414i	$0.661901\pi$
$810$		0			0
$811$	−38.1464			−1.33950			−0.669751	−	0.742586i	$-0.733599\pi$
$811$	−38.1464			−1.33950			−0.669751	+	0.742586i	$0.733599\pi$
$812$	−9.55616	+	16.5518i	−0.335356	+	0.580853i
$813$	11.9216	−	20.6489i	0.418110	−	0.724188i
$814$	11.6324			0.407714
$815$		0			0
$816$	8.43206	+	14.6048i	0.295181	+	0.511269i
$817$	7.97593	+	13.8147i	0.279043	+	0.483316i
$818$	11.9937			0.419351
$819$	2.58129	+	14.4809i	0.0901975	+	0.506004i
$820$		0			0
$821$	8.38745	+	14.5275i	0.292724	+	0.507013i	0.974453	−	0.224592i	$-0.0721049\pi$
$821$	8.38745	+	14.5275i	0.292724	+	0.507013i	−0.681729	+	0.731605i	$0.738772\pi$
$822$	2.01165	+	3.48428i	0.0701643	+	0.121528i
$823$	5.48404	−	9.49863i	0.191161	−	0.331101i	−0.754474	−	0.656330i	$-0.772108\pi$
$823$	5.48404	−	9.49863i	0.191161	−	0.331101i	0.945635	+	0.325229i	$0.105441\pi$
$824$	25.9976			0.905670
$825$		0			0
$826$	4.01319	−	6.95105i	0.139637	−	0.241858i
$827$	−44.1457			−1.53509			−0.767547	−	0.640992i	$-0.778523\pi$
$827$	−44.1457			−1.53509			−0.767547	+	0.640992i	$0.778523\pi$
$828$	−7.22860	+	12.5203i	−0.251211	+	0.435111i
$829$	5.30857	+	9.19472i	0.184374	+	0.319346i	0.943366	−	0.331755i	$-0.107641\pi$
$829$	5.30857	+	9.19472i	0.184374	+	0.319346i	−0.758991	+	0.651101i	$0.774307\pi$
$830$		0			0
$831$	8.57241			0.297374
$832$	−13.1485	−	4.75785i	−0.455842	−	0.164949i
$833$	−55.7055			−1.93008
$834$	−0.421087	−	0.729344i	−0.0145810	−	0.0252551i
$835$		0			0
$836$	−9.24422	+	16.0115i	−0.319718	+	0.553768i
$837$	−7.52862			−0.260227
$838$	5.38733	−	9.33113i	0.186102	−	0.322339i
$839$	−26.2026	+	45.3843i	−0.904616	+	1.56684i	−0.0831833	+	0.996534i	$0.526509\pi$
$839$	−26.2026	+	45.3843i	−0.904616	+	1.56684i	−0.821432	+	0.570306i	$0.806825\pi$
$840$		0			0
$841$	11.1655	−	19.3393i	0.385018	−	0.666871i
$842$	6.40930	+	11.1012i	0.220879	+	0.382574i
$843$	−1.74306	−	3.01907i	−0.0600343	−	0.103982i
$844$	−27.2077			−0.936529
$845$		0			0
$846$	2.58787			0.0889726
$847$	16.5789	+	28.7155i	0.569658	+	0.986676i
$848$	14.9392	+	25.8754i	0.513013	+	0.888564i
$849$	−4.22976	+	7.32615i	−0.145165	+	0.251433i
$850$		0			0
$851$	24.5819	−	42.5771i	0.842657	−	1.45952i
$852$	−7.59532	+	13.1555i	−0.260212	+	0.450700i
$853$	30.1487			1.03227			0.516136	−	0.856507i	$-0.327370\pi$
$853$	30.1487			1.03227			0.516136	+	0.856507i	$0.327370\pi$
$854$	−10.4813	+	18.1542i	−0.358664	+	0.621225i
$855$		0			0
$856$	−1.85471	−	3.21246i	−0.0633928	−	0.109799i
$857$	−45.3756			−1.55000			−0.775001	−	0.631960i	$-0.782251\pi$
$857$	−45.3756			−1.55000			−0.775001	+	0.631960i	$0.782251\pi$
$858$	6.39279	+	2.31326i	0.218246	+	0.0789735i
$859$	8.14892			0.278038			0.139019	−	0.990290i	$-0.455605\pi$
$859$	8.14892			0.278038			0.139019	+	0.990290i	$0.455605\pi$
$860$		0			0
$861$	−11.7834	−	20.4094i	−0.401576	−	0.695550i
$862$	−5.40400	+	9.36000i	−0.184061	+	0.318803i
$863$	−54.6860			−1.86153			−0.930767	−	0.365613i	$-0.880859\pi$
$863$	−54.6860			−1.86153			−0.930767	+	0.365613i	$0.880859\pi$
$864$	2.27368	−	3.93813i	0.0773521	−	0.133978i
$865$		0			0
$866$	−9.37463			−0.318563
$867$	−8.18532	+	14.1774i	−0.277988	+	0.481489i
$868$	27.8593	+	48.2537i	0.945607	+	1.63784i
$869$	20.0604	+	34.7456i	0.680501	+	1.17866i
$870$		0			0
$871$	2.48574	+	13.9449i	0.0842260	+	0.472504i
$872$	−22.5244			−0.762773
$873$	−1.74194	−	3.01714i	−0.0589559	−	0.102115i
$874$	−4.00307	−	6.93352i	−0.135406	−	0.234530i
$875$		0			0
$876$	7.28059			0.245988
$877$	−15.9743	+	27.6684i	−0.539415	+	0.934295i	0.459520	+	0.888167i	$0.348021\pi$
$877$	−15.9743	+	27.6684i	−0.539415	+	0.934295i	−0.998936	+	0.0461276i	$0.985312\pi$
$878$	1.51277	−	2.62020i	0.0510536	−	0.0884274i
$879$	−1.44411			−0.0487087
$880$		0			0
$881$	5.03344	+	8.71818i	0.169581	+	0.293723i	0.938273	−	0.345897i	$-0.112425\pi$
$881$	5.03344	+	8.71818i	0.169581	+	0.293723i	−0.768692	+	0.639620i	$0.779092\pi$
$882$	2.07870	+	3.60042i	0.0699935	+	0.121232i
$883$	31.1293			1.04758			0.523791	−	0.851847i	$-0.324517\pi$
$883$	31.1293			1.04758			0.523791	+	0.851847i	$0.324517\pi$
$884$	−6.63086	−	37.1988i	−0.223020	−	1.25113i
$885$		0			0
$886$	−0.957137	−	1.65781i	−0.0321556	−	0.0556952i
$887$	−14.7924	−	25.6212i	−0.496681	−	0.860277i	0.503311	−	0.864105i	$-0.332115\pi$
$887$	−14.7924	−	25.6212i	−0.496681	−	0.860277i	−0.999993	+	0.00382795i	$0.998782\pi$
$888$	−5.07226	+	8.78541i	−0.170214	+	0.294819i
$889$	7.03533			0.235958
$890$		0			0
$891$	2.18676	−	3.78758i	0.0732593	−	0.126889i
$892$	11.3974			0.381613
$893$	6.99368	−	12.1134i	0.234034	−	0.405360i
$894$	3.76993	+	6.52971i	0.126085	+	0.218386i
$895$		0			0
$896$	−43.9237			−1.46739
$897$	21.9766	−	18.5106i	0.733776	−	0.618051i
$898$	−11.8121			−0.394174
$899$	9.72108	+	16.8374i	0.324216	+	0.561559i
$900$		0			0
$901$	−29.5615	+	51.2021i	−0.984838	+	1.70579i
$902$	−10.8923			−0.362675
$903$	−13.9636	+	24.1857i	−0.464680	+	0.804849i
$904$	9.64186	−	16.7002i	0.320684	−	0.555440i
$905$		0			0
$906$	−1.73223	+	3.00031i	−0.0575495	+	0.0996787i
$907$	−10.8827	−	18.8494i	−0.361354	−	0.625883i	0.626830	−	0.779156i	$-0.284352\pi$
$907$	−10.8827	−	18.8494i	−0.361354	−	0.625883i	−0.988184	+	0.153273i	$0.951019\pi$
$908$	−3.96544	−	6.86834i	−0.131598	−	0.227934i
$909$	−10.2429			−0.339734
$910$		0			0
$911$	−45.7577			−1.51602			−0.758010	−	0.652243i	$-0.773828\pi$
$911$	−45.7577			−1.51602			−0.758010	+	0.652243i	$0.773828\pi$
$912$	−3.40135	−	5.89132i	−0.112630	−	0.195081i
$913$	−27.6126	−	47.8265i	−0.913844	−	1.58282i
$914$	2.63069	−	4.55650i	0.0870156	−	0.150715i
$915$		0			0
$916$	−9.11568	+	15.7888i	−0.301191	+	0.521677i
$917$	−7.78992	+	13.4925i	−0.257246	+	0.445563i
$918$	2.49051			0.0821992
$919$	20.2578	−	35.0875i	0.668242	−	1.15743i	−0.310153	−	0.950687i	$-0.600380\pi$
$919$	20.2578	−	35.0875i	0.668242	−	1.15743i	0.978395	−	0.206743i	$-0.0662863\pi$
$920$		0			0
$921$	1.77863	+	3.08068i	0.0586078	+	0.101512i
$922$	−10.8965			−0.358856
$923$	23.0915	−	19.4497i	0.760065	−	0.640195i
$924$	−32.3680			−1.06483
$925$		0			0
$926$	4.58081	+	7.93420i	0.150535	+	0.260734i
$927$	−7.90500	+	13.6919i	−0.259634	+	0.449700i
$928$	−11.7432			−0.385491
$929$	−15.0862	+	26.1300i	−0.494961	+	0.857298i	−0.999983	−	0.00580842i	$-0.998151\pi$
$929$	−15.0862	+	26.1300i	−0.494961	+	0.857298i	0.505022	+	0.863107i	$0.331484\pi$
$930$		0			0
$931$	22.4707			0.736446
$932$	2.63456	−	4.56320i	0.0862980	−	0.149473i
$933$	9.37633	+	16.2403i	0.306967	+	0.531683i
$934$	2.53856	+	4.39691i	0.0830641	+	0.143871i
$935$		0			0
$936$	−4.53467	+	3.81950i	−0.148220	+	0.124844i
$937$	−15.6637			−0.511709			−0.255855	−	0.966715i	$-0.582357\pi$
$937$	−15.6637			−0.511709			−0.255855	+	0.966715i	$0.582357\pi$
$938$	3.45485	+	5.98397i	0.112805	+	0.195384i
$939$	−6.93661	−	12.0146i	−0.226368	−	0.392081i
$940$		0			0
$941$	24.8149			0.808942			0.404471	−	0.914551i	$-0.367456\pi$
$941$	24.8149			0.808942			0.404471	+	0.914551i	$0.367456\pi$
$942$	−3.34000	+	5.78505i	−0.108823	+	0.188487i
$943$	−23.0180	+	39.8684i	−0.749571	+	1.29829i
$944$	−13.3223			−0.433602
$945$		0			0
$946$	6.45386	+	11.1784i	0.209833	+	0.363441i
$947$	1.02809	+	1.78070i	0.0334084	+	0.0578651i	0.882246	−	0.470788i	$-0.156030\pi$
$947$	1.02809	+	1.78070i	0.0334084	+	0.0578651i	−0.848838	+	0.528653i	$0.822697\pi$
$948$	−16.6420			−0.540507
$949$	−13.6066	−	4.92363i	−0.441690	−	0.159828i
$950$		0			0
$951$	−3.68141	−	6.37638i	−0.119378	−	0.206768i
$952$	−19.3763	−	33.5607i	−0.627990	−	1.08771i
$953$	18.4121	−	31.8908i	0.596428	−	1.03304i	−0.396916	−	0.917855i	$-0.629920\pi$
$953$	18.4121	−	31.8908i	0.596428	−	1.03304i	0.993344	−	0.115188i	$-0.0367471\pi$
$954$	4.41247			0.142859
$955$		0			0
$956$	17.5481	−	30.3941i	0.567545	−	0.983017i
$957$	−11.2943			−0.365094
$958$	−5.79469	+	10.0367i	−0.187218	+	0.324271i
$959$	19.0354	+	32.9703i	0.614686	+	1.06467i
$960$		0			0
$961$	25.6802			0.828393
$962$	7.33465	−	6.17790i	0.236479	−	0.199183i
$963$	2.25582			0.0726928
$964$	8.27200	+	14.3275i	0.266423	+	0.461458i
$965$		0			0
$966$	7.00825	−	12.1386i	0.225487	−	0.390555i
$967$	15.3768			0.494486			0.247243	−	0.968954i	$-0.420475\pi$
$967$	15.3768			0.494486			0.247243	+	0.968954i	$0.420475\pi$
$968$	−6.68253	+	11.5745i	−0.214785	+	0.372018i
$969$	6.73058	−	11.6577i	0.216217	−	0.374500i
$970$		0			0
$971$	3.72881	−	6.45849i	0.119663	−	0.207263i	−0.799971	−	0.600039i	$-0.795152\pi$
$971$	3.72881	−	6.45849i	0.119663	−	0.207263i	0.919634	+	0.392776i	$0.128485\pi$
$972$	0.907064	+	1.57108i	0.0290941	+	0.0503925i
$973$	−3.98457	−	6.90148i	−0.127740	−	0.221251i
$974$	9.35723			0.299825
$975$		0			0
$976$	34.7941			1.11373
$977$	−21.5217	−	37.2766i	−0.688539	−	1.19259i	−0.972310	−	0.233693i	$-0.924919\pi$
$977$	−21.5217	−	37.2766i	−0.688539	−	1.19259i	0.283771	−	0.958892i	$-0.408414\pi$
$978$	−0.803599	−	1.39187i	−0.0256963	−	0.0445072i
$979$	−30.5927	+	52.9881i	−0.977748	+	1.69351i
$980$		0			0
$981$	6.84892	−	11.8627i	0.218669	−	0.378746i
$982$	5.58838	−	9.67936i	0.178332	−	0.308881i
$983$	−45.7988			−1.46076			−0.730378	−	0.683044i	$-0.760656\pi$
$983$	−45.7988			−1.46076			−0.730378	+	0.683044i	$0.760656\pi$
$984$	4.74957	−	8.22649i	0.151411	−	0.262251i
$985$		0			0
$986$	−3.21579	−	5.56991i	−0.102412	−	0.177382i
$987$	24.4879			0.779459
$988$	2.67478	+	15.0054i	0.0850961	+	0.477386i
$989$	54.5541			1.73472
$990$		0			0
$991$	−28.8574	−	49.9824i	−0.916684	−	1.58774i	−0.804417	−	0.594065i	$-0.797522\pi$
$991$	−28.8574	−	49.9824i	−0.916684	−	1.58774i	−0.112267	−	0.993678i	$-0.535811\pi$
$992$	−17.1177	+	29.6487i	−0.543487	+	0.941347i
$993$	−5.24943			−0.166586
$994$	7.36380	−	12.7545i	0.233565	−	0.404547i
$995$		0			0
$996$	22.9073			0.725846
$997$	−18.8132	+	32.5854i	−0.595820	+	1.03199i	0.397611	+	0.917554i	$0.369839\pi$
$997$	−18.8132	+	32.5854i	−0.595820	+	1.03199i	−0.993431	+	0.114436i	$0.963494\pi$
$998$	8.53037	+	14.7750i	0.270024	+	0.467695i
$999$	−3.08460	−	5.34269i	−0.0975925	−	0.169035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.n.601.4	yes	12
5.2	odd	4		975.2.bb.l.874.5		24
5.3	odd	4		975.2.bb.l.874.8		24
5.4	even	2		975.2.i.p.601.3	yes	12
13.9	even	3	inner	975.2.i.n.451.4	✓	12
65.9	even	6		975.2.i.p.451.3	yes	12
65.22	odd	12		975.2.bb.l.724.8		24
65.48	odd	12		975.2.bb.l.724.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.i.n.451.4	✓	12	13.9	even	3	inner
975.2.i.n.601.4	yes	12	1.1	even	1	trivial
975.2.i.p.451.3	yes	12	65.9	even	6
975.2.i.p.601.3	yes	12	5.4	even	2
975.2.bb.l.724.5		24	65.48	odd	12
975.2.bb.l.724.8		24	65.22	odd	12
975.2.bb.l.874.5		24	5.2	odd	4
975.2.bb.l.874.8		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.215564 + 0.373368i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.907064 - 1.57108i) q^{4} +(0.215564 - 0.373368i) q^{6} +(2.03980 - 3.53303i) q^{7} +1.64438 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.18676 + 3.78758i) q^{11} -1.81413 q^{12} +(3.39041 + 1.22684i) q^{13} +1.75883 q^{14} +(-1.45966 - 2.52820i) q^{16} +(2.88837 - 5.00280i) q^{17} -0.431128 q^{18} +(-1.16512 + 2.01805i) q^{19} -4.07959 q^{21} +(-0.942775 + 1.63293i) q^{22} +(3.98461 + 6.90155i) q^{23} +(-0.822190 - 1.42407i) q^{24} +(0.272789 + 1.53033i) q^{26} +1.00000 q^{27} +(-3.70045 - 6.40937i) q^{28} +(-1.29122 - 2.23645i) q^{29} -7.52862 q^{31} +(2.27368 - 3.93813i) q^{32} +(2.18676 - 3.78758i) q^{33} +2.49051 q^{34} +(0.907064 + 1.57108i) q^{36} +(-3.08460 - 5.34269i) q^{37} -1.00463 q^{38} +(-0.632732 - 3.54960i) q^{39} +(2.88837 + 5.00280i) q^{41} +(-0.879414 - 1.52319i) q^{42} +(3.42280 - 5.92846i) q^{43} +7.93414 q^{44} +(-1.71788 + 2.97546i) q^{46} -6.00254 q^{47} +(-1.45966 + 2.52820i) q^{48} +(-4.82154 - 8.35115i) q^{49} -5.77673 q^{51} +(5.00278 - 4.21379i) q^{52} -10.2347 q^{53} +(0.215564 + 0.373368i) q^{54} +(3.35420 - 5.80964i) q^{56} +2.33024 q^{57} +(0.556680 - 0.964198i) q^{58} +(2.28174 - 3.95209i) q^{59} +(-5.95928 + 10.3218i) q^{61} +(-1.62290 - 2.81095i) q^{62} +(2.03980 + 3.53303i) q^{63} -3.87814 q^{64} +1.88555 q^{66} +(1.96429 + 3.40225i) q^{67} +(-5.23987 - 9.07572i) q^{68} +(3.98461 - 6.90155i) q^{69} +(4.18676 - 7.25169i) q^{71} +(-0.822190 + 1.42407i) q^{72} -4.01327 q^{73} +(1.32986 - 2.30339i) q^{74} +(2.11368 + 3.66099i) q^{76} +17.8422 q^{77} +(1.18891 - 1.00141i) q^{78} +9.17355 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.24526 + 2.15685i) q^{82} -12.6272 q^{83} +(-3.70045 + 6.40937i) q^{84} +2.95133 q^{86} +(-1.29122 + 2.23645i) q^{87} +(3.59587 + 6.22822i) q^{88} +(6.99498 + 12.1157i) q^{89} +(11.2502 - 9.47592i) q^{91} +14.4572 q^{92} +(3.76431 + 6.51998i) q^{93} +(-1.29393 - 2.24116i) q^{94} -4.54736 q^{96} +(-1.74194 + 3.01714i) q^{97} +(2.07870 - 3.60042i) q^{98} -4.37352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 8 q^{4} + q^{7} + 12 q^{8} - 6 q^{9} - q^{11} + 16 q^{12} - 3 q^{13} + 30 q^{14} - 20 q^{16} + 8 q^{17} + 3 q^{19} - 2 q^{21} - 3 q^{22} - q^{23} - 6 q^{24} + 9 q^{26} + 12 q^{27} + 3 q^{28}+ \cdots + 2 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 8 * q^4 + q^7 + 12 * q^8 - 6 * q^9 - q^11 + 16 * q^12 - 3 * q^13 + 30 * q^14 - 20 * q^16 + 8 * q^17 + 3 * q^19 - 2 * q^21 - 3 * q^22 - q^23 - 6 * q^24 + 9 * q^26 + 12 * q^27 + 3 * q^28 - 12 * q^29 + 24 * q^31 - 32 * q^32 - q^33 - 56 * q^34 - 8 * q^36 - 5 * q^37 + 14 * q^38 - 3 * q^39 + 8 * q^41 - 15 * q^42 - 15 * q^43 + 78 * q^44 - 5 * q^46 - 24 * q^47 - 20 * q^48 - 9 * q^49 - 16 * q^51 + 62 * q^52 - 16 * q^53 - 17 * q^56 - 6 * q^57 - 6 * q^58 + 2 * q^59 - 33 * q^61 - 2 * q^62 + q^63 + 72 * q^64 + 6 * q^66 + 13 * q^67 + 36 * q^68 - q^69 + 23 * q^71 - 6 * q^72 - 12 * q^73 - 59 * q^74 + 35 * q^76 - 36 * q^77 - 6 * q^78 + 22 * q^79 - 6 * q^81 + 28 * q^82 - 34 * q^83 + 3 * q^84 - 26 * q^86 - 12 * q^87 - 7 * q^88 - 8 * q^89 + 5 * q^91 + 38 * q^92 - 12 * q^93 - 8 * q^94 + 64 * q^96 - 19 * q^97 + 43 * q^98 + 2 * q^99

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