LMFDB - Embedded newform 966.2.g.a.643.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(643,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("966.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.g (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			643.1
Root			$-1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	966.643
Dual form			966.2.g.a.643.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +(-1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +(-1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} -3.74166i q^{11} -1.00000i q^{12} +2.00000i q^{13} +(1.87083 + 1.87083i) q^{14} +1.00000 q^{16} +3.74166 q^{17} +1.00000 q^{18} +(-1.87083 + 1.87083i) q^{21} +3.74166i q^{22} +(-3.00000 - 3.74166i) q^{23} +1.00000i q^{24} -5.00000 q^{25} -2.00000i q^{26} +1.00000i q^{27} +(-1.87083 - 1.87083i) q^{28} -8.00000 q^{29} +4.00000i q^{31} -1.00000 q^{32} -3.74166 q^{33} -3.74166 q^{34} -1.00000 q^{36} +3.74166i q^{37} +2.00000 q^{39} +2.00000i q^{41} +(1.87083 - 1.87083i) q^{42} -3.74166i q^{44} +(3.00000 + 3.74166i) q^{46} -8.00000i q^{47} -1.00000i q^{48} +7.00000i q^{49} +5.00000 q^{50} -3.74166i q^{51} +2.00000i q^{52} -7.48331i q^{53} -1.00000i q^{54} +(1.87083 + 1.87083i) q^{56} +8.00000 q^{58} -11.2250 q^{61} -4.00000i q^{62} +(1.87083 + 1.87083i) q^{63} +1.00000 q^{64} +3.74166 q^{66} +3.74166 q^{68} +(-3.74166 + 3.00000i) q^{69} -8.00000 q^{71} +1.00000 q^{72} +10.0000i q^{73} -3.74166i q^{74} +5.00000i q^{75} +(-7.00000 + 7.00000i) q^{77} -2.00000 q^{78} -3.74166i q^{79} +1.00000 q^{81} -2.00000i q^{82} -3.74166 q^{83} +(-1.87083 + 1.87083i) q^{84} +8.00000i q^{87} +3.74166i q^{88} -11.2250 q^{89} +(3.74166 - 3.74166i) q^{91} +(-3.00000 - 3.74166i) q^{92} +4.00000 q^{93} +8.00000i q^{94} +1.00000i q^{96} -7.00000i q^{98} +3.74166i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} - 12 q^{23} - 20 q^{25} - 32 q^{29} - 4 q^{32} - 4 q^{36} + 8 q^{39} + 12 q^{46} + 20 q^{50} + 32 q^{58} + 4 q^{64} - 32 q^{71} + 4 q^{72} - 28 q^{77} - 8 q^{78} + 4 q^{81} - 12 q^{92} + 16 q^{93}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 + 4 * q^16 + 4 * q^18 - 12 * q^23 - 20 * q^25 - 32 * q^29 - 4 * q^32 - 4 * q^36 + 8 * q^39 + 12 * q^46 + 20 * q^50 + 32 * q^58 + 4 * q^64 - 32 * q^71 + 4 * q^72 - 28 * q^77 - 8 * q^78 + 4 * q^81 - 12 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$			1.00000i			0.408248i
$7$	−1.87083	−	1.87083i	−0.707107	−	0.707107i
$7$	−1.87083	−	1.87083i	−0.707107	−	0.707107i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$		0			0
$11$		−	3.74166i		−	1.12815i	−0.825723	−	0.564076i	$-0.809232\pi$
$11$		−	3.74166i		−	1.12815i	0.825723	−	0.564076i	$-0.190768\pi$
$12$		−	1.00000i		−	0.288675i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	1.87083	+	1.87083i	0.500000	+	0.500000i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.74166			0.907485			0.453743	−	0.891133i	$-0.350089\pi$
$17$	3.74166			0.907485			0.453743	+	0.891133i	$0.350089\pi$
$18$	1.00000			0.235702
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$	−1.87083	+	1.87083i	−0.408248	+	0.408248i
$22$			3.74166i			0.797724i
$23$	−3.00000	−	3.74166i	−0.625543	−	0.780189i
$23$	−3.00000	−	3.74166i	−0.625543	−	0.780189i
$24$			1.00000i			0.204124i
$25$	−5.00000			−1.00000
$26$		−	2.00000i		−	0.392232i
$27$			1.00000i			0.192450i
$28$	−1.87083	−	1.87083i	−0.353553	−	0.353553i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	−1.00000			−0.176777
$33$	−3.74166			−0.651339
$34$	−3.74166			−0.641689
$35$		0			0
$36$	−1.00000			−0.166667
$37$			3.74166i			0.615125i	0.951528	+	0.307562i	$0.0995133\pi$
$37$			3.74166i			0.615125i	−0.951528	+	0.307562i	$0.900487\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$	1.87083	−	1.87083i	0.288675	−	0.288675i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		−	3.74166i		−	0.564076i
$45$		0			0
$46$	3.00000	+	3.74166i	0.442326	+	0.551677i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		−	1.00000i		−	0.144338i
$49$			7.00000i			1.00000i
$50$	5.00000			0.707107
$51$		−	3.74166i		−	0.523937i
$52$			2.00000i			0.277350i
$53$		−	7.48331i		−	1.02791i	−0.857816	−	0.513956i	$-0.828179\pi$
$53$		−	7.48331i		−	1.02791i	0.857816	−	0.513956i	$-0.171821\pi$
$54$		−	1.00000i		−	0.136083i
$55$		0			0
$56$	1.87083	+	1.87083i	0.250000	+	0.250000i
$57$		0			0
$58$	8.00000			1.05045
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	−11.2250			−1.43721			−0.718605	−	0.695418i	$-0.755219\pi$
$61$	−11.2250			−1.43721			−0.718605	+	0.695418i	$0.755219\pi$
$62$		−	4.00000i		−	0.508001i
$63$	1.87083	+	1.87083i	0.235702	+	0.235702i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.74166			0.460566
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	3.74166			0.453743
$69$	−3.74166	+	3.00000i	−0.450443	+	0.361158i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	1.00000			0.117851
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$		−	3.74166i		−	0.434959i
$75$			5.00000i			0.577350i
$76$		0			0
$77$	−7.00000	+	7.00000i	−0.797724	+	0.797724i
$78$	−2.00000			−0.226455
$79$		−	3.74166i		−	0.420969i	−0.977597	−	0.210485i	$-0.932496\pi$
$79$		−	3.74166i		−	0.420969i	0.977597	−	0.210485i	$-0.0675042\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		−	2.00000i		−	0.220863i
$83$	−3.74166			−0.410700			−0.205350	−	0.978689i	$-0.565833\pi$
$83$	−3.74166			−0.410700			−0.205350	+	0.978689i	$0.565833\pi$
$84$	−1.87083	+	1.87083i	−0.204124	+	0.204124i
$85$		0			0
$86$		0			0
$87$			8.00000i			0.857690i
$88$			3.74166i			0.398862i
$89$	−11.2250			−1.18984			−0.594922	−	0.803783i	$-0.702817\pi$
$89$	−11.2250			−1.18984			−0.594922	+	0.803783i	$0.702817\pi$
$90$		0			0
$91$	3.74166	−	3.74166i	0.392232	−	0.392232i
$92$	−3.00000	−	3.74166i	−0.312772	−	0.390095i
$93$	4.00000			0.414781
$94$			8.00000i			0.825137i
$95$		0			0
$96$			1.00000i			0.102062i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		−	7.00000i		−	0.707107i
$99$			3.74166i			0.376051i
$100$	−5.00000			−0.500000
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$			3.74166i			0.370479i
$103$	−11.2250			−1.10603			−0.553015	−	0.833172i	$-0.686523\pi$
$103$	−11.2250			−1.10603			−0.553015	+	0.833172i	$0.686523\pi$
$104$		−	2.00000i		−	0.196116i
$105$		0			0
$106$			7.48331i			0.726844i
$107$			3.74166i			0.361720i	0.983509	+	0.180860i	$0.0578880\pi$
$107$			3.74166i			0.361720i	−0.983509	+	0.180860i	$0.942112\pi$
$108$			1.00000i			0.0962250i
$109$		−	3.74166i		−	0.358386i	−0.983814	−	0.179193i	$-0.942651\pi$
$109$		−	3.74166i		−	0.358386i	0.983814	−	0.179193i	$-0.0573486\pi$
$110$		0			0
$111$	3.74166			0.355142
$112$	−1.87083	−	1.87083i	−0.176777	−	0.176777i
$113$		−	11.2250i		−	1.05596i	−0.849258	−	0.527978i	$-0.822950\pi$
$113$		−	11.2250i		−	1.05596i	0.849258	−	0.527978i	$-0.177050\pi$
$114$		0			0
$115$		0			0
$116$	−8.00000			−0.742781
$117$		−	2.00000i		−	0.184900i
$118$		0			0
$119$	−7.00000	−	7.00000i	−0.641689	−	0.641689i
$120$		0			0
$121$	−3.00000			−0.272727
$122$	11.2250			1.01626
$123$	2.00000			0.180334
$124$			4.00000i			0.359211i
$125$		0			0
$126$	−1.87083	−	1.87083i	−0.166667	−	0.166667i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$		0			0
$131$			8.00000i			0.698963i	0.936943	+	0.349482i	$0.113642\pi$
$131$			8.00000i			0.698963i	−0.936943	+	0.349482i	$0.886358\pi$
$132$	−3.74166			−0.325669
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−3.74166			−0.320844
$137$			3.74166i			0.319671i	0.987144	+	0.159836i	$0.0510964\pi$
$137$			3.74166i			0.319671i	−0.987144	+	0.159836i	$0.948904\pi$
$138$	3.74166	−	3.00000i	0.318511	−	0.255377i
$139$		−	2.00000i		−	0.169638i	−0.996396	−	0.0848189i	$-0.972969\pi$
$139$		−	2.00000i		−	0.169638i	0.996396	−	0.0848189i	$-0.0270312\pi$
$140$		0			0
$141$	−8.00000			−0.673722
$142$	8.00000			0.671345
$143$	7.48331			0.625786
$144$	−1.00000			−0.0833333
$145$		0			0
$146$		−	10.0000i		−	0.827606i
$147$	7.00000			0.577350
$148$			3.74166i			0.307562i
$149$		−	14.9666i		−	1.22611i	−0.790039	−	0.613057i	$-0.789940\pi$
$149$		−	14.9666i		−	1.22611i	0.790039	−	0.613057i	$-0.210060\pi$
$150$		−	5.00000i		−	0.408248i
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$		0			0
$153$	−3.74166			−0.302495
$154$	7.00000	−	7.00000i	0.564076	−	0.564076i
$155$		0			0
$156$	2.00000			0.160128
$157$	18.7083			1.49308			0.746542	−	0.665338i	$-0.231713\pi$
$157$	18.7083			1.49308			0.746542	+	0.665338i	$0.231713\pi$
$158$			3.74166i			0.297670i
$159$	−7.48331			−0.593465
$160$		0			0
$161$	−1.38751	+	12.6125i	−0.109351	+	0.994003i
$162$	−1.00000			−0.0785674
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	3.74166			0.290409
$167$		−	14.0000i		−	1.08335i	−0.840587	−	0.541676i	$-0.817790\pi$
$167$		−	14.0000i		−	1.08335i	0.840587	−	0.541676i	$-0.182210\pi$
$168$	1.87083	−	1.87083i	0.144338	−	0.144338i
$169$	9.00000			0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	14.0000i		−	1.06440i	−0.846619	−	0.532200i	$-0.821365\pi$
$173$		−	14.0000i		−	1.06440i	0.846619	−	0.532200i	$-0.178635\pi$
$174$		−	8.00000i		−	0.606478i
$175$	9.35414	+	9.35414i	0.707107	+	0.707107i
$176$		−	3.74166i		−	0.282038i
$177$		0			0
$178$	11.2250			0.841347
$179$	16.0000			1.19590			0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000			1.19590			0.597948	+	0.801535i	$0.295983\pi$
$180$		0			0
$181$	−18.7083			−1.39058			−0.695288	−	0.718731i	$-0.744723\pi$
$181$	−18.7083			−1.39058			−0.695288	+	0.718731i	$0.744723\pi$
$182$	−3.74166	+	3.74166i	−0.277350	+	0.277350i
$183$			11.2250i			0.829774i
$184$	3.00000	+	3.74166i	0.221163	+	0.275839i
$185$		0			0
$186$	−4.00000			−0.293294
$187$		−	14.0000i		−	1.02378i
$188$		−	8.00000i		−	0.583460i
$189$	1.87083	−	1.87083i	0.136083	−	0.136083i
$190$		0			0
$191$			7.48331i			0.541474i	0.962653	+	0.270737i	$0.0872673\pi$
$191$			7.48331i			0.541474i	−0.962653	+	0.270737i	$0.912733\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	12.0000			0.863779			0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000			0.863779			0.431889	+	0.901927i	$0.357847\pi$
$194$		0			0
$195$		0			0
$196$			7.00000i			0.500000i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		−	3.74166i		−	0.265908i
$199$	18.7083			1.32620			0.663098	−	0.748533i	$-0.269241\pi$
$199$	18.7083			1.32620			0.663098	+	0.748533i	$0.269241\pi$
$200$	5.00000			0.353553
$201$		0			0
$202$		0			0
$203$	14.9666	+	14.9666i	1.05045	+	1.05045i
$204$		−	3.74166i		−	0.261968i
$205$		0			0
$206$	11.2250			0.782081
$207$	3.00000	+	3.74166i	0.208514	+	0.260063i
$208$			2.00000i			0.138675i
$209$		0			0
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$		−	7.48331i		−	0.513956i
$213$			8.00000i			0.548151i
$214$		−	3.74166i		−	0.255774i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	7.48331	−	7.48331i	0.508001	−	0.508001i
$218$			3.74166i			0.253417i
$219$	10.0000			0.675737
$220$		0			0
$221$			7.48331i			0.503382i
$222$	−3.74166			−0.251124
$223$		−	28.0000i		−	1.87502i	−0.347960	−	0.937509i	$-0.613126\pi$
$223$		−	28.0000i		−	1.87502i	0.347960	−	0.937509i	$-0.386874\pi$
$224$	1.87083	+	1.87083i	0.125000	+	0.125000i
$225$	5.00000			0.333333
$226$			11.2250i			0.746674i
$227$	18.7083			1.24171			0.620856	−	0.783924i	$-0.286785\pi$
$227$	18.7083			1.24171			0.620856	+	0.783924i	$0.286785\pi$
$228$		0			0
$229$	−3.74166			−0.247256			−0.123628	−	0.992329i	$-0.539453\pi$
$229$	−3.74166			−0.247256			−0.123628	+	0.992329i	$0.539453\pi$
$230$		0			0
$231$	7.00000	+	7.00000i	0.460566	+	0.460566i
$232$	8.00000			0.525226
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$			2.00000i			0.130744i
$235$		0			0
$236$		0			0
$237$	−3.74166			−0.243047
$238$	7.00000	+	7.00000i	0.453743	+	0.453743i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$		0			0
$241$	−14.9666			−0.964085			−0.482043	−	0.876148i	$-0.660105\pi$
$241$	−14.9666			−0.964085			−0.482043	+	0.876148i	$0.660105\pi$
$242$	3.00000			0.192847
$243$		−	1.00000i		−	0.0641500i
$244$	−11.2250			−0.718605
$245$		0			0
$246$	−2.00000			−0.127515
$247$		0			0
$248$		−	4.00000i		−	0.254000i
$249$			3.74166i			0.237118i
$250$		0			0
$251$	3.74166			0.236171			0.118086	−	0.993003i	$-0.462324\pi$
$251$	3.74166			0.236171			0.118086	+	0.993003i	$0.462324\pi$
$252$	1.87083	+	1.87083i	0.117851	+	0.117851i
$253$	−14.0000	+	11.2250i	−0.880172	+	0.705708i
$254$	−8.00000			−0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	22.0000i		−	1.37232i	−0.727450	−	0.686161i	$-0.759294\pi$
$257$		−	22.0000i		−	1.37232i	0.727450	−	0.686161i	$-0.240706\pi$
$258$		0			0
$259$	7.00000	−	7.00000i	0.434959	−	0.434959i
$260$		0			0
$261$	8.00000			0.495188
$262$		−	8.00000i		−	0.494242i
$263$		−	14.9666i		−	0.922882i	−0.887171	−	0.461441i	$-0.847333\pi$
$263$		−	14.9666i		−	0.922882i	0.887171	−	0.461441i	$-0.152667\pi$
$264$	3.74166			0.230283
$265$		0			0
$266$		0			0
$267$			11.2250i			0.686957i
$268$		0			0
$269$			24.0000i			1.46331i	0.681677	+	0.731653i	$0.261251\pi$
$269$			24.0000i			1.46331i	−0.681677	+	0.731653i	$0.738749\pi$
$270$		0			0
$271$		−	28.0000i		−	1.70088i	−0.526073	−	0.850439i	$-0.676336\pi$
$271$		−	28.0000i		−	1.70088i	0.526073	−	0.850439i	$-0.323664\pi$
$272$	3.74166			0.226871
$273$	−3.74166	−	3.74166i	−0.226455	−	0.226455i
$274$		−	3.74166i		−	0.226042i
$275$			18.7083i			1.12815i
$276$	−3.74166	+	3.00000i	−0.225221	+	0.180579i
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$			2.00000i			0.119952i
$279$		−	4.00000i		−	0.239474i
$280$		0			0
$281$		−	3.74166i		−	0.223209i	−0.993753	−	0.111604i	$-0.964401\pi$
$281$		−	3.74166i		−	0.223209i	0.993753	−	0.111604i	$-0.0355989\pi$
$282$	8.00000			0.476393
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	−7.48331			−0.442498
$287$	3.74166	−	3.74166i	0.220863	−	0.220863i
$288$	1.00000			0.0589256
$289$	−3.00000			−0.176471
$290$		0			0
$291$		0			0
$292$			10.0000i			0.585206i
$293$	−7.48331			−0.437180			−0.218590	−	0.975817i	$-0.570146\pi$
$293$	−7.48331			−0.437180			−0.218590	+	0.975817i	$0.570146\pi$
$294$	−7.00000			−0.408248
$295$		0			0
$296$		−	3.74166i		−	0.217479i
$297$	3.74166			0.217113
$298$			14.9666i			0.866994i
$299$	7.48331	−	6.00000i	0.432771	−	0.346989i
$300$			5.00000i			0.288675i
$301$		0			0
$302$	12.0000			0.690522
$303$		0			0
$304$		0			0
$305$		0			0
$306$	3.74166			0.213896
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$	−7.00000	+	7.00000i	−0.398862	+	0.398862i
$309$			11.2250i			0.638566i
$310$		0			0
$311$			18.0000i			1.02069i	0.859971	+	0.510343i	$0.170482\pi$
$311$			18.0000i			1.02069i	−0.859971	+	0.510343i	$0.829518\pi$
$312$	−2.00000			−0.113228
$313$	22.4499			1.26895			0.634473	−	0.772945i	$-0.281217\pi$
$313$	22.4499			1.26895			0.634473	+	0.772945i	$0.281217\pi$
$314$	−18.7083			−1.05577
$315$		0			0
$316$		−	3.74166i		−	0.210485i
$317$	−8.00000			−0.449325			−0.224662	−	0.974437i	$-0.572128\pi$
$317$	−8.00000			−0.449325			−0.224662	+	0.974437i	$0.572128\pi$
$318$	7.48331			0.419643
$319$			29.9333i			1.67594i
$320$		0			0
$321$	3.74166			0.208839
$322$	1.38751	−	12.6125i	0.0773231	−	0.702866i
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	10.0000i		−	0.554700i
$326$	4.00000			0.221540
$327$	−3.74166			−0.206914
$328$		−	2.00000i		−	0.110432i
$329$	−14.9666	+	14.9666i	−0.825137	+	0.825137i
$330$		0			0
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$	−3.74166			−0.205350
$333$		−	3.74166i		−	0.205042i
$334$			14.0000i			0.766046i
$335$		0			0
$336$	−1.87083	+	1.87083i	−0.102062	+	0.102062i
$337$		−	7.48331i		−	0.407642i	−0.979008	−	0.203821i	$-0.934664\pi$
$337$		−	7.48331i		−	0.407642i	0.979008	−	0.203821i	$-0.0653361\pi$
$338$	−9.00000			−0.489535
$339$	−11.2250			−0.609657
$340$		0			0
$341$	14.9666			0.810488
$342$		0			0
$343$	13.0958	−	13.0958i	0.707107	−	0.707107i
$344$		0			0
$345$		0			0
$346$			14.0000i			0.752645i
$347$	24.0000			1.28839			0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000			1.28839			0.644194	+	0.764862i	$0.277193\pi$
$348$			8.00000i			0.428845i
$349$			30.0000i			1.60586i	0.596071	+	0.802932i	$0.296728\pi$
$349$			30.0000i			1.60586i	−0.596071	+	0.802932i	$0.703272\pi$
$350$	−9.35414	−	9.35414i	−0.500000	−	0.500000i
$351$	−2.00000			−0.106752
$352$			3.74166i			0.199431i
$353$		−	10.0000i		−	0.532246i	−0.963939	−	0.266123i	$-0.914257\pi$
$353$		−	10.0000i		−	0.532246i	0.963939	−	0.266123i	$-0.0857428\pi$
$354$		0			0
$355$		0			0
$356$	−11.2250			−0.594922
$357$	−7.00000	+	7.00000i	−0.370479	+	0.370479i
$358$	−16.0000			−0.845626
$359$			37.4166i			1.97477i	0.158334	+	0.987386i	$0.449388\pi$
$359$			37.4166i			1.97477i	−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	18.7083			0.983286
$363$			3.00000i			0.157459i
$364$	3.74166	−	3.74166i	0.196116	−	0.196116i
$365$		0			0
$366$		−	11.2250i		−	0.586739i
$367$	33.6749			1.75782			0.878908	−	0.476991i	$-0.158273\pi$
$367$	33.6749			1.75782			0.878908	+	0.476991i	$0.158273\pi$
$368$	−3.00000	−	3.74166i	−0.156386	−	0.195047i
$369$		−	2.00000i		−	0.104116i
$370$		0			0
$371$	−14.0000	+	14.0000i	−0.726844	+	0.726844i
$372$	4.00000			0.207390
$373$		−	11.2250i		−	0.581207i	−0.956844	−	0.290604i	$-0.906144\pi$
$373$		−	11.2250i		−	0.581207i	0.956844	−	0.290604i	$-0.0938561\pi$
$374$			14.0000i			0.723923i
$375$		0			0
$376$			8.00000i			0.412568i
$377$		−	16.0000i		−	0.824042i
$378$	−1.87083	+	1.87083i	−0.0962250	+	0.0962250i
$379$		−	37.4166i		−	1.92196i	−0.276617	−	0.960980i	$-0.589213\pi$
$379$		−	37.4166i		−	1.92196i	0.276617	−	0.960980i	$-0.410787\pi$
$380$		0			0
$381$		−	8.00000i		−	0.409852i
$382$		−	7.48331i		−	0.382880i
$383$	−37.4166			−1.91190			−0.955949	−	0.293533i	$-0.905169\pi$
$383$	−37.4166			−1.91190			−0.955949	+	0.293533i	$0.905169\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	−12.0000			−0.610784
$387$		0			0
$388$		0			0
$389$		−	29.9333i		−	1.51768i	−0.651279	−	0.758838i	$-0.725767\pi$
$389$		−	29.9333i		−	1.51768i	0.651279	−	0.758838i	$-0.274233\pi$
$390$		0			0
$391$	−11.2250	−	14.0000i	−0.567671	−	0.708010i
$392$		−	7.00000i		−	0.353553i
$393$	8.00000			0.403547
$394$	−6.00000			−0.302276
$395$		0			0
$396$			3.74166i			0.188025i
$397$			6.00000i			0.301131i	0.988600	+	0.150566i	$0.0481095\pi$
$397$			6.00000i			0.301131i	−0.988600	+	0.150566i	$0.951890\pi$
$398$	−18.7083			−0.937762
$399$		0			0
$400$	−5.00000			−0.250000
$401$		−	3.74166i		−	0.186849i	−0.995626	−	0.0934247i	$-0.970219\pi$
$401$		−	3.74166i		−	0.186849i	0.995626	−	0.0934247i	$-0.0297814\pi$
$402$		0			0
$403$	−8.00000			−0.398508
$404$		0			0
$405$		0			0
$406$	−14.9666	−	14.9666i	−0.742781	−	0.742781i
$407$	14.0000			0.693954
$408$			3.74166i			0.185240i
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$	3.74166			0.184562
$412$	−11.2250			−0.553015
$413$		0			0
$414$	−3.00000	−	3.74166i	−0.147442	−	0.183892i
$415$		0			0
$416$		−	2.00000i		−	0.0980581i
$417$	−2.00000			−0.0979404
$418$		0			0
$419$	−33.6749			−1.64513			−0.822564	−	0.568673i	$-0.807457\pi$
$419$	−33.6749			−1.64513			−0.822564	+	0.568673i	$0.807457\pi$
$420$		0			0
$421$		−	33.6749i		−	1.64122i	−0.571492	−	0.820608i	$-0.693635\pi$
$421$		−	33.6749i		−	1.64122i	0.571492	−	0.820608i	$-0.306365\pi$
$422$	2.00000			0.0973585
$423$			8.00000i			0.388973i
$424$			7.48331i			0.363422i
$425$	−18.7083			−0.907485
$426$		−	8.00000i		−	0.387601i
$427$	21.0000	+	21.0000i	1.01626	+	1.01626i
$428$			3.74166i			0.180860i
$429$		−	7.48331i		−	0.361298i
$430$		0			0
$431$		−	29.9333i		−	1.44183i	−0.693021	−	0.720917i	$-0.743721\pi$
$431$		−	29.9333i		−	1.44183i	0.693021	−	0.720917i	$-0.256279\pi$
$432$			1.00000i			0.0481125i
$433$	37.4166			1.79813			0.899063	−	0.437819i	$-0.144249\pi$
$433$	37.4166			1.79813			0.899063	+	0.437819i	$0.144249\pi$
$434$	−7.48331	+	7.48331i	−0.359211	+	0.359211i
$435$		0			0
$436$		−	3.74166i		−	0.179193i
$437$		0			0
$438$	−10.0000			−0.477818
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$		0			0
$441$		−	7.00000i		−	0.333333i
$442$		−	7.48331i		−	0.355945i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	3.74166			0.177571
$445$		0			0
$446$			28.0000i			1.32584i
$447$	−14.9666			−0.707897
$448$	−1.87083	−	1.87083i	−0.0883883	−	0.0883883i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−5.00000			−0.235702
$451$	7.48331			0.352376
$452$		−	11.2250i		−	0.527978i
$453$			12.0000i			0.563809i
$454$	−18.7083			−0.878023
$455$		0			0
$456$		0			0
$457$			14.9666i			0.700109i	0.936729	+	0.350055i	$0.113837\pi$
$457$			14.9666i			0.700109i	−0.936729	+	0.350055i	$0.886163\pi$
$458$	3.74166			0.174836
$459$			3.74166i			0.174646i
$460$		0			0
$461$			12.0000i			0.558896i	0.960161	+	0.279448i	$0.0901514\pi$
$461$			12.0000i			0.558896i	−0.960161	+	0.279448i	$0.909849\pi$
$462$	−7.00000	−	7.00000i	−0.325669	−	0.325669i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−8.00000			−0.371391
$465$		0			0
$466$	−10.0000			−0.463241
$467$	−26.1916			−1.21200			−0.606001	−	0.795464i	$-0.707227\pi$
$467$	−26.1916			−1.21200			−0.606001	+	0.795464i	$0.707227\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$		0			0
$471$		−	18.7083i		−	0.862032i
$472$		0			0
$473$		0			0
$474$	3.74166			0.171860
$475$		0			0
$476$	−7.00000	−	7.00000i	−0.320844	−	0.320844i
$477$			7.48331i			0.342637i
$478$	−22.0000			−1.00626
$479$	29.9333			1.36769			0.683843	−	0.729629i	$-0.260307\pi$
$479$	29.9333			1.36769			0.683843	+	0.729629i	$0.260307\pi$
$480$		0			0
$481$	−7.48331			−0.341210
$482$	14.9666			0.681711
$483$	12.6125	+	1.38751i	0.573888	+	0.0631341i
$484$	−3.00000			−0.136364
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	11.2250			0.508131
$489$			4.00000i			0.180886i
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	2.00000			0.0901670
$493$	−29.9333			−1.34813
$494$		0			0
$495$		0			0
$496$			4.00000i			0.179605i
$497$	14.9666	+	14.9666i	0.671345	+	0.671345i
$498$		−	3.74166i		−	0.167668i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	−14.0000			−0.625474
$502$	−3.74166			−0.166998
$503$	7.48331			0.333665			0.166832	−	0.985985i	$-0.446646\pi$
$503$	7.48331			0.333665			0.166832	+	0.985985i	$0.446646\pi$
$504$	−1.87083	−	1.87083i	−0.0833333	−	0.0833333i
$505$		0			0
$506$	14.0000	−	11.2250i	0.622376	−	0.499011i
$507$		−	9.00000i		−	0.399704i
$508$	8.00000			0.354943
$509$			34.0000i			1.50702i	0.657434	+	0.753512i	$0.271642\pi$
$509$			34.0000i			1.50702i	−0.657434	+	0.753512i	$0.728358\pi$
$510$		0			0
$511$	18.7083	−	18.7083i	0.827606	−	0.827606i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			22.0000i			0.970378i
$515$		0			0
$516$		0			0
$517$	−29.9333			−1.31646
$518$	−7.00000	+	7.00000i	−0.307562	+	0.307562i
$519$	−14.0000			−0.614532
$520$		0			0
$521$	−26.1916			−1.14747			−0.573737	−	0.819039i	$-0.694507\pi$
$521$	−26.1916			−1.14747			−0.573737	+	0.819039i	$0.694507\pi$
$522$	−8.00000			−0.350150
$523$	−7.48331			−0.327223			−0.163611	−	0.986525i	$-0.552314\pi$
$523$	−7.48331			−0.327223			−0.163611	+	0.986525i	$0.552314\pi$
$524$			8.00000i			0.349482i
$525$	9.35414	−	9.35414i	0.408248	−	0.408248i
$526$			14.9666i			0.652576i
$527$			14.9666i			0.651957i
$528$	−3.74166			−0.162835
$529$	−5.00000	+	22.4499i	−0.217391	+	0.976085i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.00000			−0.173259
$534$		−	11.2250i		−	0.485752i
$535$		0			0
$536$		0			0
$537$		−	16.0000i		−	0.690451i
$538$		−	24.0000i		−	1.03471i
$539$	26.1916			1.12815
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$			28.0000i			1.20270i
$543$			18.7083i			0.802849i
$544$	−3.74166			−0.160422
$545$		0			0
$546$	3.74166	+	3.74166i	0.160128	+	0.160128i
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$			3.74166i			0.159836i
$549$	11.2250			0.479070
$550$		−	18.7083i		−	0.797724i
$551$		0			0
$552$	3.74166	−	3.00000i	0.159256	−	0.127688i
$553$	−7.00000	+	7.00000i	−0.297670	+	0.297670i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$		−	2.00000i		−	0.0848189i
$557$			14.9666i			0.634156i	0.948399	+	0.317078i	$0.102702\pi$
$557$			14.9666i			0.634156i	−0.948399	+	0.317078i	$0.897298\pi$
$558$			4.00000i			0.169334i
$559$		0			0
$560$		0			0
$561$	−14.0000			−0.591080
$562$			3.74166i			0.157832i
$563$	−41.1582			−1.73461			−0.867306	−	0.497775i	$-0.834151\pi$
$563$	−41.1582			−1.73461			−0.867306	+	0.497775i	$0.834151\pi$
$564$	−8.00000			−0.336861
$565$		0			0
$566$		0			0
$567$	−1.87083	−	1.87083i	−0.0785674	−	0.0785674i
$568$	8.00000			0.335673
$569$		−	3.74166i		−	0.156858i	−0.996920	−	0.0784292i	$-0.975010\pi$
$569$		−	3.74166i		−	0.156858i	0.996920	−	0.0784292i	$-0.0249905\pi$
$570$		0			0
$571$			29.9333i			1.25267i	0.779555	+	0.626334i	$0.215445\pi$
$571$			29.9333i			1.25267i	−0.779555	+	0.626334i	$0.784555\pi$
$572$	7.48331			0.312893
$573$	7.48331			0.312620
$574$	−3.74166	+	3.74166i	−0.156174	+	0.156174i
$575$	15.0000	+	18.7083i	0.625543	+	0.780189i
$576$	−1.00000			−0.0416667
$577$		−	24.0000i		−	0.999133i	−0.866276	−	0.499567i	$-0.833493\pi$
$577$		−	24.0000i		−	0.999133i	0.866276	−	0.499567i	$-0.166507\pi$
$578$	3.00000			0.124784
$579$		−	12.0000i		−	0.498703i
$580$		0			0
$581$	7.00000	+	7.00000i	0.290409	+	0.290409i
$582$		0			0
$583$	−28.0000			−1.15964
$584$		−	10.0000i		−	0.413803i
$585$		0			0
$586$	7.48331			0.309133
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	7.00000			0.288675
$589$		0			0
$590$		0			0
$591$		−	6.00000i		−	0.246807i
$592$			3.74166i			0.153781i
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	−3.74166			−0.153522
$595$		0			0
$596$		−	14.9666i		−	0.613057i
$597$		−	18.7083i		−	0.765679i
$598$	−7.48331	+	6.00000i	−0.306015	+	0.245358i
$599$	10.0000			0.408589			0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000			0.408589			0.204294	+	0.978909i	$0.434510\pi$
$600$		−	5.00000i		−	0.204124i
$601$		−	16.0000i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$601$		−	16.0000i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$602$		0			0
$603$		0			0
$604$	−12.0000			−0.488273
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$	14.9666	−	14.9666i	0.606478	−	0.606478i
$610$		0			0
$611$	16.0000			0.647291
$612$	−3.74166			−0.151248
$613$		−	41.1582i		−	1.66237i	−0.555999	−	0.831183i	$-0.687664\pi$
$613$		−	41.1582i		−	1.66237i	0.555999	−	0.831183i	$-0.312336\pi$
$614$			14.0000i			0.564994i
$615$		0			0
$616$	7.00000	−	7.00000i	0.282038	−	0.282038i
$617$			41.1582i			1.65697i	0.560013	+	0.828484i	$0.310796\pi$
$617$			41.1582i			1.65697i	−0.560013	+	0.828484i	$0.689204\pi$
$618$		−	11.2250i		−	0.451535i
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	3.74166	−	3.00000i	0.150148	−	0.120386i
$622$		−	18.0000i		−	0.721734i
$623$	21.0000	+	21.0000i	0.841347	+	0.841347i
$624$	2.00000			0.0800641
$625$	25.0000			1.00000
$626$	−22.4499			−0.897280
$627$		0			0
$628$	18.7083			0.746542
$629$			14.0000i			0.558217i
$630$		0			0
$631$		−	18.7083i		−	0.744765i	−0.928079	−	0.372383i	$-0.878541\pi$
$631$		−	18.7083i		−	0.744765i	0.928079	−	0.372383i	$-0.121459\pi$
$632$			3.74166i			0.148835i
$633$			2.00000i			0.0794929i
$634$	8.00000			0.317721
$635$		0			0
$636$	−7.48331			−0.296733
$637$	−14.0000			−0.554700
$638$		−	29.9333i		−	1.18507i
$639$	8.00000			0.316475
$640$		0			0
$641$		−	18.7083i		−	0.738933i	−0.929244	−	0.369466i	$-0.879540\pi$
$641$		−	18.7083i		−	0.738933i	0.929244	−	0.369466i	$-0.120460\pi$
$642$	−3.74166			−0.147671
$643$	7.48331			0.295113			0.147557	−	0.989054i	$-0.452859\pi$
$643$	7.48331			0.295113			0.147557	+	0.989054i	$0.452859\pi$
$644$	−1.38751	+	12.6125i	−0.0546757	+	0.497002i
$645$		0			0
$646$		0			0
$647$		−	10.0000i		−	0.393141i	−0.980490	−	0.196570i	$-0.937020\pi$
$647$		−	10.0000i		−	0.393141i	0.980490	−	0.196570i	$-0.0629804\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$			10.0000i			0.392232i
$651$	−7.48331	−	7.48331i	−0.293294	−	0.293294i
$652$	−4.00000			−0.156652
$653$	−38.0000			−1.48705			−0.743527	−	0.668705i	$-0.766849\pi$
$653$	−38.0000			−1.48705			−0.743527	+	0.668705i	$0.766849\pi$
$654$	3.74166			0.146310
$655$		0			0
$656$			2.00000i			0.0780869i
$657$		−	10.0000i		−	0.390137i
$658$	14.9666	−	14.9666i	0.583460	−	0.583460i
$659$		−	3.74166i		−	0.145754i	−0.997341	−	0.0728771i	$-0.976782\pi$
$659$		−	3.74166i		−	0.145754i	0.997341	−	0.0728771i	$-0.0232181\pi$
$660$		0			0
$661$	−33.6749			−1.30980			−0.654901	−	0.755714i	$-0.727290\pi$
$661$	−33.6749			−1.30980			−0.654901	+	0.755714i	$0.727290\pi$
$662$	10.0000			0.388661
$663$	7.48331			0.290628
$664$	3.74166			0.145204
$665$		0			0
$666$			3.74166i			0.144986i
$667$	24.0000	+	29.9333i	0.929284	+	1.15902i
$668$		−	14.0000i		−	0.541676i
$669$	−28.0000			−1.08254
$670$		0			0
$671$			42.0000i			1.62139i
$672$	1.87083	−	1.87083i	0.0721688	−	0.0721688i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$			7.48331i			0.288247i
$675$		−	5.00000i		−	0.192450i
$676$	9.00000			0.346154
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	11.2250			0.431092
$679$		0			0
$680$		0			0
$681$		−	18.7083i		−	0.716903i
$682$	−14.9666			−0.573102
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$		0			0
$686$	−13.0958	+	13.0958i	−0.500000	+	0.500000i
$687$			3.74166i			0.142753i
$688$		0			0
$689$	14.9666			0.570183
$690$		0			0
$691$			28.0000i			1.06517i	0.846376	+	0.532585i	$0.178779\pi$
$691$			28.0000i			1.06517i	−0.846376	+	0.532585i	$0.821221\pi$
$692$		−	14.0000i		−	0.532200i
$693$	7.00000	−	7.00000i	0.265908	−	0.265908i
$694$	−24.0000			−0.911028
$695$		0			0
$696$		−	8.00000i		−	0.303239i
$697$			7.48331i			0.283451i
$698$		−	30.0000i		−	1.13552i
$699$		−	10.0000i		−	0.378235i
$700$	9.35414	+	9.35414i	0.353553	+	0.353553i
$701$		−	22.4499i		−	0.847923i	−0.905680	−	0.423961i	$-0.860639\pi$
$701$		−	22.4499i		−	0.847923i	0.905680	−	0.423961i	$-0.139361\pi$
$702$	2.00000			0.0754851
$703$		0			0
$704$		−	3.74166i		−	0.141019i
$705$		0			0
$706$			10.0000i			0.376355i
$707$		0			0
$708$		0			0
$709$			33.6749i			1.26469i	0.774688	+	0.632344i	$0.217907\pi$
$709$			33.6749i			1.26469i	−0.774688	+	0.632344i	$0.782093\pi$
$710$		0			0
$711$			3.74166i			0.140323i
$712$	11.2250			0.420674
$713$	14.9666	−	12.0000i	0.560505	−	0.449404i
$714$	7.00000	−	7.00000i	0.261968	−	0.261968i
$715$		0			0
$716$	16.0000			0.597948
$717$		−	22.0000i		−	0.821605i
$718$		−	37.4166i		−	1.39637i
$719$			14.0000i			0.522112i	0.965324	+	0.261056i	$0.0840707\pi$
$719$			14.0000i			0.522112i	−0.965324	+	0.261056i	$0.915929\pi$
$720$		0			0
$721$	21.0000	+	21.0000i	0.782081	+	0.782081i
$722$	19.0000			0.707107
$723$			14.9666i			0.556615i
$724$	−18.7083			−0.695288
$725$	40.0000			1.48556
$726$		−	3.00000i		−	0.111340i
$727$	33.6749			1.24893			0.624467	−	0.781051i	$-0.285316\pi$
$727$	33.6749			1.24893			0.624467	+	0.781051i	$0.285316\pi$
$728$	−3.74166	+	3.74166i	−0.138675	+	0.138675i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$			11.2250i			0.414887i
$733$	−33.6749			−1.24381			−0.621906	−	0.783092i	$-0.713641\pi$
$733$	−33.6749			−1.24381			−0.621906	+	0.783092i	$0.713641\pi$
$734$	−33.6749			−1.24296
$735$		0			0
$736$	3.00000	+	3.74166i	0.110581	+	0.137919i
$737$		0			0
$738$			2.00000i			0.0736210i
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$		0			0
$741$		0			0
$742$	14.0000	−	14.0000i	0.513956	−	0.513956i
$743$			29.9333i			1.09814i	0.835775	+	0.549072i	$0.185019\pi$
$743$			29.9333i			1.09814i	−0.835775	+	0.549072i	$0.814981\pi$
$744$	−4.00000			−0.146647
$745$		0			0
$746$			11.2250i			0.410975i
$747$	3.74166			0.136900
$748$		−	14.0000i		−	0.511891i
$749$	7.00000	−	7.00000i	0.255774	−	0.255774i
$750$		0			0
$751$		−	18.7083i		−	0.682675i	−0.939941	−	0.341338i	$-0.889120\pi$
$751$		−	18.7083i		−	0.682675i	0.939941	−	0.341338i	$-0.110880\pi$
$752$		−	8.00000i		−	0.291730i
$753$		−	3.74166i		−	0.136354i
$754$			16.0000i			0.582686i
$755$		0			0
$756$	1.87083	−	1.87083i	0.0680414	−	0.0680414i
$757$			33.6749i			1.22394i	0.790883	+	0.611968i	$0.209622\pi$
$757$			33.6749i			1.22394i	−0.790883	+	0.611968i	$0.790378\pi$
$758$			37.4166i			1.35903i
$759$	11.2250	+	14.0000i	0.407441	+	0.508168i
$760$		0			0
$761$			6.00000i			0.217500i	0.994069	+	0.108750i	$0.0346848\pi$
$761$			6.00000i			0.217500i	−0.994069	+	0.108750i	$0.965315\pi$
$762$			8.00000i			0.289809i
$763$	−7.00000	+	7.00000i	−0.253417	+	0.253417i
$764$			7.48331i			0.270737i
$765$		0			0
$766$	37.4166			1.35192
$767$		0			0
$768$		−	1.00000i		−	0.0360844i
$769$	7.48331			0.269855			0.134928	−	0.990855i	$-0.456920\pi$
$769$	7.48331			0.269855			0.134928	+	0.990855i	$0.456920\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$	12.0000			0.431889
$773$	−37.4166			−1.34578			−0.672890	−	0.739742i	$-0.734947\pi$
$773$	−37.4166			−1.34578			−0.672890	+	0.739742i	$0.734947\pi$
$774$		0			0
$775$		−	20.0000i		−	0.718421i
$776$		0			0
$777$	−7.00000	−	7.00000i	−0.251124	−	0.251124i
$778$			29.9333i			1.07316i
$779$		0			0
$780$		0			0
$781$			29.9333i			1.07110i
$782$	11.2250	+	14.0000i	0.401404	+	0.500639i
$783$		−	8.00000i		−	0.285897i
$784$			7.00000i			0.250000i
$785$		0			0
$786$	−8.00000			−0.285351
$787$	−7.48331			−0.266751			−0.133376	−	0.991066i	$-0.542582\pi$
$787$	−7.48331			−0.266751			−0.133376	+	0.991066i	$0.542582\pi$
$788$	6.00000			0.213741
$789$	−14.9666			−0.532826
$790$		0			0
$791$	−21.0000	+	21.0000i	−0.746674	+	0.746674i
$792$		−	3.74166i		−	0.132954i
$793$		−	22.4499i		−	0.797221i
$794$		−	6.00000i		−	0.212932i
$795$		0			0
$796$	18.7083			0.663098
$797$	14.9666			0.530145			0.265073	−	0.964228i	$-0.414604\pi$
$797$	14.9666			0.530145			0.265073	+	0.964228i	$0.414604\pi$
$798$		0			0
$799$		−	29.9333i		−	1.05896i
$800$	5.00000			0.176777
$801$	11.2250			0.396615
$802$			3.74166i			0.132123i
$803$	37.4166			1.32040
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$	24.0000			0.844840
$808$		0			0
$809$	46.0000			1.61727			0.808637	−	0.588308i	$-0.200206\pi$
$809$	46.0000			1.61727			0.808637	+	0.588308i	$0.200206\pi$
$810$		0			0
$811$		−	12.0000i		−	0.421377i	−0.977553	−	0.210688i	$-0.932429\pi$
$811$		−	12.0000i		−	0.421377i	0.977553	−	0.210688i	$-0.0675706\pi$
$812$	14.9666	+	14.9666i	0.525226	+	0.525226i
$813$	−28.0000			−0.982003
$814$	−14.0000			−0.490700
$815$		0			0
$816$		−	3.74166i		−	0.130984i
$817$		0			0
$818$		−	10.0000i		−	0.349642i
$819$	−3.74166	+	3.74166i	−0.130744	+	0.130744i
$820$		0			0
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$	−3.74166			−0.130505
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	11.2250			0.391040
$825$	18.7083			0.651339
$826$		0			0
$827$		−	3.74166i		−	0.130110i	−0.997882	−	0.0650551i	$-0.979278\pi$
$827$		−	3.74166i		−	0.130110i	0.997882	−	0.0650551i	$-0.0207223\pi$
$828$	3.00000	+	3.74166i	0.104257	+	0.130032i
$829$		−	42.0000i		−	1.45872i	−0.684130	−	0.729360i	$-0.739818\pi$
$829$		−	42.0000i		−	1.45872i	0.684130	−	0.729360i	$-0.260182\pi$
$830$		0			0
$831$		−	2.00000i		−	0.0693792i
$832$			2.00000i			0.0693375i
$833$			26.1916i			0.907485i
$834$	2.00000			0.0692543
$835$		0			0
$836$		0			0
$837$	−4.00000			−0.138260
$838$	33.6749			1.16328
$839$	−37.4166			−1.29176			−0.645882	−	0.763437i	$-0.723510\pi$
$839$	−37.4166			−1.29176			−0.645882	+	0.763437i	$0.723510\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$			33.6749i			1.16051i
$843$	−3.74166			−0.128870
$844$	−2.00000			−0.0688428
$845$		0			0
$846$		−	8.00000i		−	0.275046i
$847$	5.61249	+	5.61249i	0.192847	+	0.192847i
$848$		−	7.48331i		−	0.256978i
$849$		0			0
$850$	18.7083			0.641689
$851$	14.0000	−	11.2250i	0.479914	−	0.384787i
$852$			8.00000i			0.274075i
$853$			42.0000i			1.43805i	0.694983	+	0.719026i	$0.255412\pi$
$853$			42.0000i			1.43805i	−0.694983	+	0.719026i	$0.744588\pi$
$854$	−21.0000	−	21.0000i	−0.718605	−	0.718605i
$855$		0			0
$856$		−	3.74166i		−	0.127887i
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$			7.48331i			0.255476i
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$		0			0
$861$	−3.74166	−	3.74166i	−0.127515	−	0.127515i
$862$			29.9333i			1.01953i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		0			0
$866$	−37.4166			−1.27147
$867$			3.00000i			0.101885i
$868$	7.48331	−	7.48331i	0.254000	−	0.254000i
$869$	−14.0000			−0.474917
$870$		0			0
$871$		0			0
$872$			3.74166i			0.126709i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	10.0000			0.337869
$877$	50.0000			1.68838			0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000			1.68838			0.844190	+	0.536044i	$0.180082\pi$
$878$			8.00000i			0.269987i
$879$			7.48331i			0.252406i
$880$		0			0
$881$	18.7083			0.630298			0.315149	−	0.949042i	$-0.397945\pi$
$881$	18.7083			0.630298			0.315149	+	0.949042i	$0.397945\pi$
$882$			7.00000i			0.235702i
$883$	−30.0000			−1.00958			−0.504790	−	0.863242i	$-0.668430\pi$
$883$	−30.0000			−1.00958			−0.504790	+	0.863242i	$0.668430\pi$
$884$			7.48331i			0.251691i
$885$		0			0
$886$	4.00000			0.134383
$887$		−	48.0000i		−	1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$		−	48.0000i		−	1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$	−3.74166			−0.125562
$889$	−14.9666	−	14.9666i	−0.501965	−	0.501965i
$890$		0			0
$891$		−	3.74166i		−	0.125350i
$892$		−	28.0000i		−	0.937509i
$893$		0			0
$894$	14.9666			0.500559
$895$		0			0
$896$	1.87083	+	1.87083i	0.0625000	+	0.0625000i
$897$	−6.00000	−	7.48331i	−0.200334	−	0.249861i
$898$	30.0000			1.00111
$899$		−	32.0000i		−	1.06726i
$900$	5.00000			0.166667
$901$		−	28.0000i		−	0.932815i
$902$	−7.48331			−0.249167
$903$		0			0
$904$			11.2250i			0.373337i
$905$		0			0
$906$		−	12.0000i		−	0.398673i
$907$			37.4166i			1.24240i	0.783653	+	0.621198i	$0.213354\pi$
$907$			37.4166i			1.24240i	−0.783653	+	0.621198i	$0.786646\pi$
$908$	18.7083			0.620856
$909$		0			0
$910$		0			0
$911$			14.9666i			0.495867i	0.968777	+	0.247933i	$0.0797514\pi$
$911$			14.9666i			0.495867i	−0.968777	+	0.247933i	$0.920249\pi$
$912$		0			0
$913$			14.0000i			0.463332i
$914$		−	14.9666i		−	0.495052i
$915$		0			0
$916$	−3.74166			−0.123628
$917$	14.9666	−	14.9666i	0.494242	−	0.494242i
$918$		−	3.74166i		−	0.123493i
$919$		−	41.1582i		−	1.35768i	−0.734284	−	0.678842i	$-0.762482\pi$
$919$		−	41.1582i		−	1.35768i	0.734284	−	0.678842i	$-0.237518\pi$
$920$		0			0
$921$	−14.0000			−0.461316
$922$		−	12.0000i		−	0.395199i
$923$		−	16.0000i		−	0.526646i
$924$	7.00000	+	7.00000i	0.230283	+	0.230283i
$925$		−	18.7083i		−	0.615125i
$926$	16.0000			0.525793
$927$	11.2250			0.368676
$928$	8.00000			0.262613
$929$		−	34.0000i		−	1.11550i	−0.830008	−	0.557752i	$-0.811664\pi$
$929$		−	34.0000i		−	1.11550i	0.830008	−	0.557752i	$-0.188336\pi$
$930$		0			0
$931$		0			0
$932$	10.0000			0.327561
$933$	18.0000			0.589294
$934$	26.1916			0.857015
$935$		0			0
$936$			2.00000i			0.0653720i
$937$	14.9666			0.488938			0.244469	−	0.969657i	$-0.421386\pi$
$937$	14.9666			0.488938			0.244469	+	0.969657i	$0.421386\pi$
$938$		0			0
$939$		−	22.4499i		−	0.732626i
$940$		0			0
$941$	29.9333			0.975796			0.487898	−	0.872901i	$-0.337764\pi$
$941$	29.9333			0.975796			0.487898	+	0.872901i	$0.337764\pi$
$942$			18.7083i			0.609549i
$943$	7.48331	−	6.00000i	0.243690	−	0.195387i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−52.0000			−1.68977			−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000			−1.68977			−0.844886	+	0.534946i	$0.820332\pi$
$948$	−3.74166			−0.121523
$949$	−20.0000			−0.649227
$950$		0			0
$951$			8.00000i			0.259418i
$952$	7.00000	+	7.00000i	0.226871	+	0.226871i
$953$		−	3.74166i		−	0.121204i	−0.998162	−	0.0606021i	$-0.980698\pi$
$953$		−	3.74166i		−	0.121204i	0.998162	−	0.0606021i	$-0.0193021\pi$
$954$		−	7.48331i		−	0.242281i
$955$		0			0
$956$	22.0000			0.711531
$957$	29.9333			0.967605
$958$	−29.9333			−0.967100
$959$	7.00000	−	7.00000i	0.226042	−	0.226042i
$960$		0			0
$961$	15.0000			0.483871
$962$	7.48331			0.241272
$963$		−	3.74166i		−	0.120573i
$964$	−14.9666			−0.482043
$965$		0			0
$966$	−12.6125	−	1.38751i	−0.405800	−	0.0446425i
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$	3.00000			0.0964237
$969$		0			0
$970$		0			0
$971$	−18.7083			−0.600377			−0.300189	−	0.953880i	$-0.597050\pi$
$971$	−18.7083			−0.600377			−0.300189	+	0.953880i	$0.597050\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−3.74166	+	3.74166i	−0.119952	+	0.119952i
$974$	16.0000			0.512673
$975$	−10.0000			−0.320256
$976$	−11.2250			−0.359303
$977$		−	48.6415i		−	1.55618i	−0.628152	−	0.778090i	$-0.716188\pi$
$977$		−	48.6415i		−	1.55618i	0.628152	−	0.778090i	$-0.283812\pi$
$978$		−	4.00000i		−	0.127906i
$979$			42.0000i			1.34233i
$980$		0			0
$981$			3.74166i			0.119462i
$982$	−20.0000			−0.638226
$983$	−52.3832			−1.67076			−0.835382	−	0.549669i	$-0.814754\pi$
$983$	−52.3832			−1.67076			−0.835382	+	0.549669i	$0.814754\pi$
$984$	−2.00000			−0.0637577
$985$		0			0
$986$	29.9333			0.953269
$987$	14.9666	+	14.9666i	0.476393	+	0.476393i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$		−	4.00000i		−	0.127000i
$993$			10.0000i			0.317340i
$994$	−14.9666	−	14.9666i	−0.474713	−	0.474713i
$995$		0			0
$996$			3.74166i			0.118559i
$997$			14.0000i			0.443384i	0.975117	+	0.221692i	$0.0711580\pi$
$997$			14.0000i			0.443384i	−0.975117	+	0.221692i	$0.928842\pi$
$998$	−4.00000			−0.126618
$999$	−3.74166			−0.118381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.g.a.643.1	✓	4
3.2	odd	2		2898.2.g.g.2575.1		4
7.6	odd	2	inner	966.2.g.a.643.4	yes	4
21.20	even	2		2898.2.g.g.2575.3		4
23.22	odd	2	inner	966.2.g.a.643.2	yes	4
69.68	even	2		2898.2.g.g.2575.4		4
161.160	even	2	inner	966.2.g.a.643.3	yes	4
483.482	odd	2		2898.2.g.g.2575.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.g.a.643.1	✓	4	1.1	even	1	trivial
966.2.g.a.643.2	yes	4	23.22	odd	2	inner
966.2.g.a.643.3	yes	4	161.160	even	2	inner
966.2.g.a.643.4	yes	4	7.6	odd	2	inner
2898.2.g.g.2575.1		4	3.2	odd	2
2898.2.g.g.2575.2		4	483.482	odd	2
2898.2.g.g.2575.3		4	21.20	even	2
2898.2.g.g.2575.4		4	69.68	even	2

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +(-1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} +(-1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} -3.74166i q^{11} -1.00000i q^{12} +2.00000i q^{13} +(1.87083 + 1.87083i) q^{14} +1.00000 q^{16} +3.74166 q^{17} +1.00000 q^{18} +(-1.87083 + 1.87083i) q^{21} +3.74166i q^{22} +(-3.00000 - 3.74166i) q^{23} +1.00000i q^{24} -5.00000 q^{25} -2.00000i q^{26} +1.00000i q^{27} +(-1.87083 - 1.87083i) q^{28} -8.00000 q^{29} +4.00000i q^{31} -1.00000 q^{32} -3.74166 q^{33} -3.74166 q^{34} -1.00000 q^{36} +3.74166i q^{37} +2.00000 q^{39} +2.00000i q^{41} +(1.87083 - 1.87083i) q^{42} -3.74166i q^{44} +(3.00000 + 3.74166i) q^{46} -8.00000i q^{47} -1.00000i q^{48} +7.00000i q^{49} +5.00000 q^{50} -3.74166i q^{51} +2.00000i q^{52} -7.48331i q^{53} -1.00000i q^{54} +(1.87083 + 1.87083i) q^{56} +8.00000 q^{58} -11.2250 q^{61} -4.00000i q^{62} +(1.87083 + 1.87083i) q^{63} +1.00000 q^{64} +3.74166 q^{66} +3.74166 q^{68} +(-3.74166 + 3.00000i) q^{69} -8.00000 q^{71} +1.00000 q^{72} +10.0000i q^{73} -3.74166i q^{74} +5.00000i q^{75} +(-7.00000 + 7.00000i) q^{77} -2.00000 q^{78} -3.74166i q^{79} +1.00000 q^{81} -2.00000i q^{82} -3.74166 q^{83} +(-1.87083 + 1.87083i) q^{84} +8.00000i q^{87} +3.74166i q^{88} -11.2250 q^{89} +(3.74166 - 3.74166i) q^{91} +(-3.00000 - 3.74166i) q^{92} +4.00000 q^{93} +8.00000i q^{94} +1.00000i q^{96} -7.00000i q^{98} +3.74166i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} - 12 q^{23} - 20 q^{25} - 32 q^{29} - 4 q^{32} - 4 q^{36} + 8 q^{39} + 12 q^{46} + 20 q^{50} + 32 q^{58} + 4 q^{64} - 32 q^{71} + 4 q^{72} - 28 q^{77} - 8 q^{78} + 4 q^{81} - 12 q^{92} + 16 q^{93}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 + 4 * q^16 + 4 * q^18 - 12 * q^23 - 20 * q^25 - 32 * q^29 - 4 * q^32 - 4 * q^36 + 8 * q^39 + 12 * q^46 + 20 * q^50 + 32 * q^58 + 4 * q^64 - 32 * q^71 + 4 * q^72 - 28 * q^77 - 8 * q^78 + 4 * q^81 - 12 * q^92 + 16 * q^93

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