LMFDB - Embedded newform 3234.2.e.c.2155.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.12
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.c.2155.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +4.05345i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +4.05345i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +4.05345 q^{10} +(-1.17914 - 3.09994i) q^{11} +1.00000i q^{12} -3.91265 q^{13} +4.05345 q^{15} +1.00000 q^{16} +0.188398 q^{17} +1.00000i q^{18} +4.37877 q^{19} -4.05345i q^{20} +(-3.09994 + 1.17914i) q^{22} -3.58348 q^{23} +1.00000 q^{24} -11.4304 q^{25} +3.91265i q^{26} +1.00000i q^{27} -5.75703i q^{29} -4.05345i q^{30} -3.21035i q^{31} -1.00000i q^{32} +(-3.09994 + 1.17914i) q^{33} -0.188398i q^{34} +1.00000 q^{36} +5.09649 q^{37} -4.37877i q^{38} +3.91265i q^{39} -4.05345 q^{40} +8.14212 q^{41} -3.21078i q^{43} +(1.17914 + 3.09994i) q^{44} -4.05345i q^{45} +3.58348i q^{46} +4.37618i q^{47} -1.00000i q^{48} +11.4304i q^{50} -0.188398i q^{51} +3.91265 q^{52} +2.83716 q^{53} +1.00000 q^{54} +(12.5655 - 4.77956i) q^{55} -4.37877i q^{57} -5.75703 q^{58} +4.99905i q^{59} -4.05345 q^{60} -7.95115 q^{61} -3.21035 q^{62} -1.00000 q^{64} -15.8597i q^{65} +(1.17914 + 3.09994i) q^{66} -6.50120 q^{67} -0.188398 q^{68} +3.58348i q^{69} +16.2739 q^{71} -1.00000i q^{72} +12.3419 q^{73} -5.09649i q^{74} +11.4304i q^{75} -4.37877 q^{76} +3.91265 q^{78} +8.55410i q^{79} +4.05345i q^{80} +1.00000 q^{81} -8.14212i q^{82} +12.5690 q^{83} +0.763662i q^{85} -3.21078 q^{86} -5.75703 q^{87} +(3.09994 - 1.17914i) q^{88} -14.2616i q^{89} -4.05345 q^{90} +3.58348 q^{92} -3.21035 q^{93} +4.37618 q^{94} +17.7491i q^{95} -1.00000 q^{96} -17.4901i q^{97} +(1.17914 + 3.09994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$			4.05345i			1.81276i	0.422466	+	0.906379i	$0.361164\pi$
$5$			4.05345i			1.81276i	−0.422466	+	0.906379i	$0.638836\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	4.05345			1.28181
$11$	−1.17914	−	3.09994i	−0.355523	−	0.934668i
$11$	−1.17914	−	3.09994i	−0.355523	−	0.934668i
$12$			1.00000i			0.288675i
$13$	−3.91265			−1.08517			−0.542587	−	0.840000i	$-0.682555\pi$
$13$	−3.91265			−1.08517			−0.542587	+	0.840000i	$0.682555\pi$
$14$		0			0
$15$	4.05345			1.04660
$16$	1.00000			0.250000
$17$	0.188398			0.0456933			0.0228466	−	0.999739i	$-0.492727\pi$
$17$	0.188398			0.0456933			0.0228466	+	0.999739i	$0.492727\pi$
$18$			1.00000i			0.235702i
$19$	4.37877			1.00456			0.502279	−	0.864706i	$-0.332495\pi$
$19$	4.37877			1.00456			0.502279	+	0.864706i	$0.332495\pi$
$20$		−	4.05345i		−	0.906379i
$21$		0			0
$22$	−3.09994	+	1.17914i	−0.660910	+	0.251393i
$23$	−3.58348			−0.747208			−0.373604	−	0.927588i	$-0.621878\pi$
$23$	−3.58348			−0.747208			−0.373604	+	0.927588i	$0.621878\pi$
$24$	1.00000			0.204124
$25$	−11.4304			−2.28609
$26$			3.91265i			0.767334i
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	5.75703i		−	1.06905i	−0.845152	−	0.534527i	$-0.820490\pi$
$29$		−	5.75703i		−	1.06905i	0.845152	−	0.534527i	$-0.179510\pi$
$30$		−	4.05345i		−	0.740055i
$31$		−	3.21035i		−	0.576596i	−0.957541	−	0.288298i	$-0.906911\pi$
$31$		−	3.21035i		−	0.576596i	0.957541	−	0.288298i	$-0.0930893\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.09994	+	1.17914i	−0.539631	+	0.205261i
$34$		−	0.188398i		−	0.0323100i
$35$		0			0
$36$	1.00000			0.166667
$37$	5.09649			0.837859			0.418929	−	0.908019i	$-0.362406\pi$
$37$	5.09649			0.837859			0.418929	+	0.908019i	$0.362406\pi$
$38$		−	4.37877i		−	0.710330i
$39$			3.91265i			0.626526i
$40$	−4.05345			−0.640906
$41$	8.14212			1.27159			0.635793	−	0.771860i	$-0.280673\pi$
$41$	8.14212			1.27159			0.635793	+	0.771860i	$0.280673\pi$
$42$		0			0
$43$		−	3.21078i		−	0.489639i	−0.969569	−	0.244819i	$-0.921271\pi$
$43$		−	3.21078i		−	0.489639i	0.969569	−	0.244819i	$-0.0787287\pi$
$44$	1.17914	+	3.09994i	0.177761	+	0.467334i
$45$		−	4.05345i		−	0.604252i
$46$			3.58348i			0.528356i
$47$			4.37618i			0.638331i	0.947699	+	0.319165i	$0.103403\pi$
$47$			4.37618i			0.638331i	−0.947699	+	0.319165i	$0.896597\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$			11.4304i			1.61651i
$51$		−	0.188398i		−	0.0263810i
$52$	3.91265			0.542587
$53$	2.83716			0.389714			0.194857	−	0.980832i	$-0.437576\pi$
$53$	2.83716			0.389714			0.194857	+	0.980832i	$0.437576\pi$
$54$	1.00000			0.136083
$55$	12.5655	−	4.77956i	1.69433	−	0.644476i
$56$		0			0
$57$		−	4.37877i		−	0.579982i
$58$	−5.75703			−0.755935
$59$			4.99905i			0.650822i	0.945573	+	0.325411i	$0.105503\pi$
$59$			4.99905i			0.650822i	−0.945573	+	0.325411i	$0.894497\pi$
$60$	−4.05345			−0.523298
$61$	−7.95115			−1.01804			−0.509020	−	0.860755i	$-0.669992\pi$
$61$	−7.95115			−1.01804			−0.509020	+	0.860755i	$0.669992\pi$
$62$	−3.21035			−0.407715
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	15.8597i		−	1.96716i
$66$	1.17914	+	3.09994i	0.145142	+	0.381576i
$67$	−6.50120			−0.794248			−0.397124	−	0.917765i	$-0.629992\pi$
$67$	−6.50120			−0.794248			−0.397124	+	0.917765i	$0.629992\pi$
$68$	−0.188398			−0.0228466
$69$			3.58348i			0.431401i
$70$		0			0
$71$	16.2739			1.93136			0.965681	−	0.259732i	$-0.0836341\pi$
$71$	16.2739			1.93136			0.965681	+	0.259732i	$0.0836341\pi$
$72$		−	1.00000i		−	0.117851i
$73$	12.3419			1.44451			0.722253	−	0.691629i	$-0.243107\pi$
$73$	12.3419			1.44451			0.722253	+	0.691629i	$0.243107\pi$
$74$		−	5.09649i		−	0.592455i
$75$			11.4304i			1.31987i
$76$	−4.37877			−0.502279
$77$		0			0
$78$	3.91265			0.443021
$79$			8.55410i			0.962411i	0.876608	+	0.481206i	$0.159801\pi$
$79$			8.55410i			0.962411i	−0.876608	+	0.481206i	$0.840199\pi$
$80$			4.05345i			0.453189i
$81$	1.00000			0.111111
$82$		−	8.14212i		−	0.899147i
$83$	12.5690			1.37962			0.689811	−	0.723989i	$-0.257694\pi$
$83$	12.5690			1.37962			0.689811	+	0.723989i	$0.257694\pi$
$84$		0			0
$85$			0.763662i			0.0828308i
$86$	−3.21078			−0.346227
$87$	−5.75703			−0.617218
$88$	3.09994	−	1.17914i	0.330455	−	0.125696i
$89$		−	14.2616i		−	1.51172i	−0.654732	−	0.755861i	$-0.727219\pi$
$89$		−	14.2616i		−	1.51172i	0.654732	−	0.755861i	$-0.272781\pi$
$90$	−4.05345			−0.427271
$91$		0			0
$92$	3.58348			0.373604
$93$	−3.21035			−0.332898
$94$	4.37618			0.451368
$95$			17.7491i			1.82102i
$96$	−1.00000			−0.102062
$97$		−	17.4901i		−	1.77585i	−0.459986	−	0.887926i	$-0.652146\pi$
$97$		−	17.4901i		−	1.77585i	0.459986	−	0.887926i	$-0.347854\pi$
$98$		0			0
$99$	1.17914	+	3.09994i	0.118508	+	0.311556i
$100$	11.4304			1.14304
$101$	−2.87801			−0.286373			−0.143186	−	0.989696i	$-0.545735\pi$
$101$	−2.87801			−0.286373			−0.143186	+	0.989696i	$0.545735\pi$
$102$	−0.188398			−0.0186542
$103$		−	17.7997i		−	1.75385i	−0.480624	−	0.876927i	$-0.659590\pi$
$103$		−	17.7997i		−	1.75385i	0.480624	−	0.876927i	$-0.340410\pi$
$104$		−	3.91265i		−	0.383667i
$105$		0			0
$106$		−	2.83716i		−	0.275569i
$107$		−	6.46948i		−	0.625429i	−0.949847	−	0.312714i	$-0.898762\pi$
$107$		−	6.46948i		−	0.625429i	0.949847	−	0.312714i	$-0.101238\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	17.4531i		−	1.67171i	−0.548953	−	0.835853i	$-0.684974\pi$
$109$		−	17.4531i		−	1.67171i	0.548953	−	0.835853i	$-0.315026\pi$
$110$	−4.77956	−	12.5655i	−0.455714	−	1.19807i
$111$		−	5.09649i		−	0.483738i
$112$		0			0
$113$	0.749179			0.0704768			0.0352384	−	0.999379i	$-0.488781\pi$
$113$	0.749179			0.0704768			0.0352384	+	0.999379i	$0.488781\pi$
$114$	−4.37877			−0.410109
$115$		−	14.5255i		−	1.35451i
$116$			5.75703i			0.534527i
$117$	3.91265			0.361725
$118$	4.99905			0.460200
$119$		0			0
$120$			4.05345i			0.370028i
$121$	−8.21928	+	7.31050i	−0.747207	+	0.664591i
$122$			7.95115i			0.719863i
$123$		−	8.14212i		−	0.734150i
$124$			3.21035i			0.288298i
$125$		−	26.0655i		−	2.33137i
$126$		0			0
$127$		−	6.79955i		−	0.603363i	−0.953409	−	0.301681i	$-0.902452\pi$
$127$		−	6.79955i		−	0.603363i	0.953409	−	0.301681i	$-0.0975479\pi$
$128$			1.00000i			0.0883883i
$129$	−3.21078			−0.282693
$130$	−15.8597			−1.39099
$131$	21.7846			1.90333			0.951663	−	0.307145i	$-0.0993738\pi$
$131$	21.7846			1.90333			0.951663	+	0.307145i	$0.0993738\pi$
$132$	3.09994	−	1.17914i	0.269815	−	0.102631i
$133$		0			0
$134$			6.50120i			0.561618i
$135$	−4.05345			−0.348865
$136$			0.188398i			0.0161550i
$137$	7.02179			0.599912			0.299956	−	0.953953i	$-0.403028\pi$
$137$	7.02179			0.599912			0.299956	+	0.953953i	$0.403028\pi$
$138$	3.58348			0.305046
$139$	15.5729			1.32088			0.660438	−	0.750881i	$-0.270371\pi$
$139$	15.5729			1.32088			0.660438	+	0.750881i	$0.270371\pi$
$140$		0			0
$141$	4.37618			0.368541
$142$		−	16.2739i		−	1.36568i
$143$	4.61355	+	12.1290i	0.385804	+	1.01428i
$144$	−1.00000			−0.0833333
$145$	23.3358			1.93793
$146$		−	12.3419i		−	1.02142i
$147$		0			0
$148$	−5.09649			−0.418929
$149$		−	0.875307i		−	0.0717079i	−0.999357	−	0.0358540i	$-0.988585\pi$
$149$		−	0.875307i		−	0.0717079i	0.999357	−	0.0358540i	$-0.0114151\pi$
$150$	11.4304			0.933292
$151$			18.1267i			1.47513i	0.675275	+	0.737566i	$0.264025\pi$
$151$			18.1267i			1.47513i	−0.675275	+	0.737566i	$0.735975\pi$
$152$			4.37877i			0.355165i
$153$	−0.188398			−0.0152311
$154$		0			0
$155$	13.0130			1.04523
$156$		−	3.91265i		−	0.313263i
$157$			8.01869i			0.639961i	0.947424	+	0.319981i	$0.103676\pi$
$157$			8.01869i			0.639961i	−0.947424	+	0.319981i	$0.896324\pi$
$158$	8.55410			0.680528
$159$		−	2.83716i		−	0.225001i
$160$	4.05345			0.320453
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−3.40939			−0.267044			−0.133522	−	0.991046i	$-0.542629\pi$
$163$	−3.40939			−0.267044			−0.133522	+	0.991046i	$0.542629\pi$
$164$	−8.14212			−0.635793
$165$	−4.77956	−	12.5655i	−0.372089	−	0.978219i
$166$		−	12.5690i		−	0.975540i
$167$	−11.1360			−0.861727			−0.430863	−	0.902417i	$-0.641791\pi$
$167$	−11.1360			−0.861727			−0.430863	+	0.902417i	$0.641791\pi$
$168$		0			0
$169$	2.30884			0.177603
$170$	0.763662			0.0585702
$171$	−4.37877			−0.334853
$172$			3.21078i			0.244819i
$173$	5.89901			0.448494			0.224247	−	0.974532i	$-0.428008\pi$
$173$	5.89901			0.448494			0.224247	+	0.974532i	$0.428008\pi$
$174$			5.75703i			0.436439i
$175$		0			0
$176$	−1.17914	−	3.09994i	−0.0888807	−	0.233667i
$177$	4.99905			0.375752
$178$	−14.2616			−1.06895
$179$	−3.92282			−0.293205			−0.146603	−	0.989195i	$-0.546834\pi$
$179$	−3.92282			−0.293205			−0.146603	+	0.989195i	$0.546834\pi$
$180$			4.05345i			0.302126i
$181$			13.8033i			1.02599i	0.858392	+	0.512994i	$0.171464\pi$
$181$			13.8033i			1.02599i	−0.858392	+	0.512994i	$0.828536\pi$
$182$		0			0
$183$			7.95115i			0.587766i
$184$		−	3.58348i		−	0.264178i
$185$			20.6584i			1.51883i
$186$			3.21035i			0.235394i
$187$	−0.222147	−	0.584023i	−0.0162450	−	0.0427080i
$188$		−	4.37618i		−	0.319165i
$189$		0			0
$190$	17.7491			1.28766
$191$	−9.49736			−0.687205			−0.343602	−	0.939115i	$-0.611647\pi$
$191$	−9.49736			−0.687205			−0.343602	+	0.939115i	$0.611647\pi$
$192$			1.00000i			0.0721688i
$193$		−	13.5397i		−	0.974612i	−0.873231	−	0.487306i	$-0.837980\pi$
$193$		−	13.5397i		−	0.974612i	0.873231	−	0.487306i	$-0.162020\pi$
$194$	−17.4901			−1.25572
$195$	−15.8597			−1.13574
$196$		0			0
$197$		−	26.1952i		−	1.86633i	−0.359447	−	0.933165i	$-0.617035\pi$
$197$		−	26.1952i		−	1.86633i	0.359447	−	0.933165i	$-0.382965\pi$
$198$	3.09994	−	1.17914i	0.220303	−	0.0837975i
$199$		−	6.10803i		−	0.432987i	−0.976284	−	0.216493i	$-0.930538\pi$
$199$		−	6.10803i		−	0.432987i	0.976284	−	0.216493i	$-0.0694619\pi$
$200$		−	11.4304i		−	0.808254i
$201$			6.50120i			0.458559i
$202$			2.87801i			0.202496i
$203$		0			0
$204$			0.188398i			0.0131905i
$205$			33.0037i			2.30508i
$206$	−17.7997			−1.24016
$207$	3.58348			0.249069
$208$	−3.91265			−0.271294
$209$	−5.16316	−	13.5739i	−0.357143	−	0.938928i
$210$		0			0
$211$			19.8676i			1.36774i	0.729604	+	0.683870i	$0.239704\pi$
$211$			19.8676i			1.36774i	−0.729604	+	0.683870i	$0.760296\pi$
$212$	−2.83716			−0.194857
$213$		−	16.2739i		−	1.11507i
$214$	−6.46948			−0.442245
$215$	13.0147			0.887597
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−17.4531			−1.18207
$219$		−	12.3419i		−	0.833986i
$220$	−12.5655	+	4.77956i	−0.847163	+	0.322238i
$221$	−0.737136			−0.0495852
$222$	−5.09649			−0.342054
$223$			4.64198i			0.310850i	0.987848	+	0.155425i	$0.0496747\pi$
$223$			4.64198i			0.310850i	−0.987848	+	0.155425i	$0.950325\pi$
$224$		0			0
$225$	11.4304			0.762029
$226$		−	0.749179i		−	0.0498346i
$227$	13.0638			0.867075			0.433537	−	0.901136i	$-0.357265\pi$
$227$	13.0638			0.867075			0.433537	+	0.901136i	$0.357265\pi$
$228$			4.37877i			0.289991i
$229$		−	9.68676i		−	0.640119i	−0.947397	−	0.320060i	$-0.896297\pi$
$229$		−	9.68676i		−	0.640119i	0.947397	−	0.320060i	$-0.103703\pi$
$230$	−14.5255			−0.957781
$231$		0			0
$232$	5.75703			0.377967
$233$		−	21.6421i		−	1.41782i	−0.705298	−	0.708911i	$-0.749187\pi$
$233$		−	21.6421i		−	1.41782i	0.705298	−	0.708911i	$-0.250813\pi$
$234$		−	3.91265i		−	0.255778i
$235$	−17.7386			−1.15714
$236$		−	4.99905i		−	0.325411i
$237$	8.55410			0.555648
$238$		0			0
$239$		−	10.6397i		−	0.688225i	−0.938928	−	0.344112i	$-0.888180\pi$
$239$		−	10.6397i		−	0.688225i	0.938928	−	0.344112i	$-0.111820\pi$
$240$	4.05345			0.261649
$241$	5.68711			0.366339			0.183169	−	0.983081i	$-0.441364\pi$
$241$	5.68711			0.366339			0.183169	+	0.983081i	$0.441364\pi$
$242$	7.31050	+	8.21928i	0.469937	+	0.528355i
$243$		−	1.00000i		−	0.0641500i
$244$	7.95115			0.509020
$245$		0			0
$246$	−8.14212			−0.519123
$247$	−17.1326			−1.09012
$248$	3.21035			0.203857
$249$		−	12.5690i		−	0.796525i
$250$	−26.0655			−1.64852
$251$			0.576257i			0.0363730i	0.999835	+	0.0181865i	$0.00578927\pi$
$251$			0.576257i			0.0363730i	−0.999835	+	0.0181865i	$0.994211\pi$
$252$		0			0
$253$	4.22541	+	11.1086i	0.265649	+	0.698391i
$254$	−6.79955			−0.426642
$255$	0.763662			0.0478224
$256$	1.00000			0.0625000
$257$		−	22.2114i		−	1.38551i	−0.721174	−	0.692754i	$-0.756397\pi$
$257$		−	22.2114i		−	1.38551i	0.721174	−	0.692754i	$-0.243603\pi$
$258$			3.21078i			0.199894i
$259$		0			0
$260$			15.8597i			0.983579i
$261$			5.75703i			0.356351i
$262$		−	21.7846i		−	1.34585i
$263$			21.1657i			1.30513i	0.757731	+	0.652567i	$0.226308\pi$
$263$			21.1657i			1.30513i	−0.757731	+	0.652567i	$0.773692\pi$
$264$	−1.17914	−	3.09994i	−0.0725708	−	0.190788i
$265$			11.5003i			0.706456i
$266$		0			0
$267$	−14.2616			−0.872793
$268$	6.50120			0.397124
$269$			16.9288i			1.03217i	0.856538	+	0.516084i	$0.172611\pi$
$269$			16.9288i			1.03217i	−0.856538	+	0.516084i	$0.827389\pi$
$270$			4.05345i			0.246685i
$271$	−12.9849			−0.788777			−0.394389	−	0.918944i	$-0.629044\pi$
$271$	−12.9849			−0.788777			−0.394389	+	0.918944i	$0.629044\pi$
$272$	0.188398			0.0114233
$273$		0			0
$274$		−	7.02179i		−	0.424202i
$275$	13.4780	+	35.4337i	0.812756	+	2.13673i
$276$		−	3.58348i		−	0.215700i
$277$		−	25.5474i		−	1.53500i	−0.641051	−	0.767498i	$-0.721501\pi$
$277$		−	25.5474i		−	1.53500i	0.641051	−	0.767498i	$-0.278499\pi$
$278$		−	15.5729i		−	0.934000i
$279$			3.21035i			0.192199i
$280$		0			0
$281$			6.87709i			0.410253i	0.978735	+	0.205126i	$0.0657606\pi$
$281$			6.87709i			0.410253i	−0.978735	+	0.205126i	$0.934239\pi$
$282$		−	4.37618i		−	0.260598i
$283$	−13.6656			−0.812337			−0.406168	−	0.913798i	$-0.633135\pi$
$283$	−13.6656			−0.812337			−0.406168	+	0.913798i	$0.633135\pi$
$284$	−16.2739			−0.965681
$285$	17.7491			1.05137
$286$	12.1290	−	4.61355i	0.717202	−	0.272805i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−16.9645			−0.997912
$290$		−	23.3358i		−	1.37033i
$291$	−17.4901			−1.02529
$292$	−12.3419			−0.722253
$293$	9.49826			0.554894			0.277447	−	0.960741i	$-0.410512\pi$
$293$	9.49826			0.554894			0.277447	+	0.960741i	$0.410512\pi$
$294$		0			0
$295$	−20.2634			−1.17978
$296$			5.09649i			0.296228i
$297$	3.09994	−	1.17914i	0.179877	−	0.0684204i
$298$	−0.875307			−0.0507052
$299$	14.0209			0.810851
$300$		−	11.4304i		−	0.659937i
$301$		0			0
$302$	18.1267			1.04308
$303$			2.87801i			0.165337i
$304$	4.37877			0.251140
$305$		−	32.2296i		−	1.84546i
$306$			0.188398i			0.0107700i
$307$	−17.4551			−0.996216			−0.498108	−	0.867115i	$-0.665972\pi$
$307$	−17.4551			−0.996216			−0.498108	+	0.867115i	$0.665972\pi$
$308$		0			0
$309$	−17.7997			−1.01259
$310$		−	13.0130i		−	0.739088i
$311$		−	10.1883i		−	0.577724i	−0.957371	−	0.288862i	$-0.906723\pi$
$311$		−	10.1883i		−	0.577724i	0.957371	−	0.288862i	$-0.0932768\pi$
$312$	−3.91265			−0.221510
$313$			19.8187i			1.12022i	0.828418	+	0.560111i	$0.189241\pi$
$313$			19.8187i			1.12022i	−0.828418	+	0.560111i	$0.810759\pi$
$314$	8.01869			0.452521
$315$		0			0
$316$		−	8.55410i		−	0.481206i
$317$	−15.5000			−0.870566			−0.435283	−	0.900294i	$-0.643352\pi$
$317$	−15.5000			−0.870566			−0.435283	+	0.900294i	$0.643352\pi$
$318$	−2.83716			−0.159100
$319$	−17.8465	+	6.78832i	−0.999209	+	0.380073i
$320$		−	4.05345i		−	0.226595i
$321$	−6.46948			−0.361091
$322$		0			0
$323$	0.824952			0.0459015
$324$	−1.00000			−0.0555556
$325$	44.7233			2.48080
$326$			3.40939i			0.188828i
$327$	−17.4531			−0.965160
$328$			8.14212i			0.449573i
$329$		0			0
$330$	−12.5655	+	4.77956i	−0.691705	+	0.263106i
$331$	−22.3460			−1.22825			−0.614123	−	0.789211i	$-0.710490\pi$
$331$	−22.3460			−1.22825			−0.614123	+	0.789211i	$0.710490\pi$
$332$	−12.5690			−0.689811
$333$	−5.09649			−0.279286
$334$			11.1360i			0.609333i
$335$		−	26.3523i		−	1.43978i
$336$		0			0
$337$			21.9009i			1.19302i	0.802607	+	0.596508i	$0.203445\pi$
$337$			21.9009i			1.19302i	−0.802607	+	0.596508i	$0.796555\pi$
$338$		−	2.30884i		−	0.125584i
$339$		−	0.749179i		−	0.0406898i
$340$		−	0.763662i		−	0.0414154i
$341$	−9.95190	+	3.78544i	−0.538925	+	0.204993i
$342$			4.37877i			0.236777i
$343$		0			0
$344$	3.21078			0.173114
$345$	−14.5255			−0.782025
$346$		−	5.89901i		−	0.317133i
$347$		−	7.73409i		−	0.415188i	−0.978215	−	0.207594i	$-0.933437\pi$
$347$		−	7.73409i		−	0.415188i	0.978215	−	0.207594i	$-0.0665633\pi$
$348$	5.75703			0.308609
$349$	−20.8125			−1.11406			−0.557032	−	0.830491i	$-0.688060\pi$
$349$	−20.8125			−1.11406			−0.557032	+	0.830491i	$0.688060\pi$
$350$		0			0
$351$		−	3.91265i		−	0.208842i
$352$	−3.09994	+	1.17914i	−0.165227	+	0.0628481i
$353$		−	29.2347i		−	1.55600i	−0.628261	−	0.778002i	$-0.716233\pi$
$353$		−	29.2347i		−	1.55600i	0.628261	−	0.778002i	$-0.283767\pi$
$354$		−	4.99905i		−	0.265697i
$355$			65.9656i			3.50109i
$356$			14.2616i			0.755861i
$357$		0			0
$358$			3.92282i			0.207328i
$359$			34.8045i			1.83691i	0.395527	+	0.918454i	$0.370562\pi$
$359$			34.8045i			1.83691i	−0.395527	+	0.918454i	$0.629438\pi$
$360$	4.05345			0.213635
$361$	0.173600			0.00913684
$362$	13.8033			0.725484
$363$	7.31050	+	8.21928i	0.383702	+	0.431400i
$364$		0			0
$365$			50.0271i			2.61854i
$366$	7.95115			0.415613
$367$			28.5311i			1.48931i	0.667449	+	0.744656i	$0.267386\pi$
$367$			28.5311i			1.48931i	−0.667449	+	0.744656i	$0.732614\pi$
$368$	−3.58348			−0.186802
$369$	−8.14212			−0.423862
$370$	20.6584			1.07398
$371$		0			0
$372$	3.21035			0.166449
$373$		−	28.0262i		−	1.45114i	−0.688148	−	0.725570i	$-0.741576\pi$
$373$		−	28.0262i		−	1.45114i	0.688148	−	0.725570i	$-0.258424\pi$
$374$	−0.584023	+	0.222147i	−0.0301991	+	0.0114869i
$375$	−26.0655			−1.34601
$376$	−4.37618			−0.225684
$377$			22.5252i			1.16011i
$378$		0			0
$379$	13.1317			0.674529			0.337265	−	0.941410i	$-0.390498\pi$
$379$	13.1317			0.674529			0.337265	+	0.941410i	$0.390498\pi$
$380$		−	17.7491i		−	0.910510i
$381$	−6.79955			−0.348352
$382$			9.49736i			0.485927i
$383$		−	11.9092i		−	0.608533i	−0.952587	−	0.304266i	$-0.901589\pi$
$383$		−	11.9092i		−	0.608533i	0.952587	−	0.304266i	$-0.0984113\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−13.5397			−0.689155
$387$			3.21078i			0.163213i
$388$			17.4901i			0.887926i
$389$	36.7446			1.86303			0.931513	−	0.363709i	$-0.118490\pi$
$389$	36.7446			1.86303			0.931513	+	0.363709i	$0.118490\pi$
$390$			15.8597i			0.803089i
$391$	−0.675122			−0.0341424
$392$		0			0
$393$		−	21.7846i		−	1.09889i
$394$	−26.1952			−1.31970
$395$	−34.6736			−1.74462
$396$	−1.17914	−	3.09994i	−0.0592538	−	0.155778i
$397$			38.5547i			1.93500i	0.252865	+	0.967502i	$0.418627\pi$
$397$			38.5547i			1.93500i	−0.252865	+	0.967502i	$0.581373\pi$
$398$	−6.10803			−0.306168
$399$		0			0
$400$	−11.4304			−0.571522
$401$	13.9262			0.695441			0.347720	−	0.937598i	$-0.386956\pi$
$401$	13.9262			0.695441			0.347720	+	0.937598i	$0.386956\pi$
$402$	6.50120			0.324250
$403$			12.5610i			0.625707i
$404$	2.87801			0.143186
$405$			4.05345i			0.201417i
$406$		0			0
$407$	−6.00946	−	15.7988i	−0.297878	−	0.783119i
$408$	0.188398			0.00932710
$409$	−8.35551			−0.413153			−0.206577	−	0.978430i	$-0.566232\pi$
$409$	−8.35551			−0.413153			−0.206577	+	0.978430i	$0.566232\pi$
$410$	33.0037			1.62993
$411$		−	7.02179i		−	0.346359i
$412$			17.7997i			0.876927i
$413$		0			0
$414$		−	3.58348i		−	0.176119i
$415$			50.9476i			2.50092i
$416$			3.91265i			0.191834i
$417$		−	15.5729i		−	0.762608i
$418$	−13.5739	+	5.16316i	−0.663922	+	0.252538i
$419$			0.503760i			0.0246103i	0.999924	+	0.0123052i	$0.00391695\pi$
$419$			0.503760i			0.0246103i	−0.999924	+	0.0123052i	$0.996083\pi$
$420$		0			0
$421$	18.0435			0.879386			0.439693	−	0.898148i	$-0.355087\pi$
$421$	18.0435			0.879386			0.439693	+	0.898148i	$0.355087\pi$
$422$	19.8676			0.967138
$423$		−	4.37618i		−	0.212777i
$424$			2.83716i			0.137785i
$425$	−2.15347			−0.104459
$426$	−16.2739			−0.788475
$427$		0			0
$428$			6.46948i			0.312714i
$429$	12.1290	−	4.61355i	0.585593	−	0.222744i
$430$		−	13.0147i		−	0.627626i
$431$		−	23.7641i		−	1.14468i	−0.820017	−	0.572339i	$-0.806036\pi$
$431$		−	23.7641i		−	1.14468i	0.820017	−	0.572339i	$-0.193964\pi$
$432$			1.00000i			0.0481125i
$433$			13.2596i			0.637218i	0.947886	+	0.318609i	$0.103216\pi$
$433$			13.2596i			0.637218i	−0.947886	+	0.318609i	$0.896784\pi$
$434$		0			0
$435$		−	23.3358i		−	1.11887i
$436$			17.4531i			0.835853i
$437$	−15.6912			−0.750614
$438$	−12.3419			−0.589717
$439$	18.6515			0.890187			0.445093	−	0.895484i	$-0.353170\pi$
$439$	18.6515			0.890187			0.445093	+	0.895484i	$0.353170\pi$
$440$	4.77956	+	12.5655i	0.227857	+	0.599035i
$441$		0			0
$442$			0.737136i			0.0350620i
$443$	−12.0548			−0.572740			−0.286370	−	0.958119i	$-0.592449\pi$
$443$	−12.0548			−0.572740			−0.286370	+	0.958119i	$0.592449\pi$
$444$			5.09649i			0.241869i
$445$	57.8085			2.74038
$446$	4.64198			0.219804
$447$	−0.875307			−0.0414006
$448$		0			0
$449$	27.9760			1.32027			0.660135	−	0.751147i	$-0.270499\pi$
$449$	27.9760			1.32027			0.660135	+	0.751147i	$0.270499\pi$
$450$		−	11.4304i		−	0.538836i
$451$	−9.60066	−	25.2401i	−0.452078	−	1.18851i
$452$	−0.749179			−0.0352384
$453$	18.1267			0.851668
$454$		−	13.0638i		−	0.613114i
$455$		0			0
$456$	4.37877			0.205055
$457$		−	15.8979i		−	0.743670i	−0.928299	−	0.371835i	$-0.878729\pi$
$457$		−	15.8979i		−	0.743670i	0.928299	−	0.371835i	$-0.121271\pi$
$458$	−9.68676			−0.452633
$459$			0.188398i			0.00879367i
$460$			14.5255i			0.677254i
$461$	−37.1843			−1.73184			−0.865922	−	0.500179i	$-0.833267\pi$
$461$	−37.1843			−1.73184			−0.865922	+	0.500179i	$0.833267\pi$
$462$		0			0
$463$	−27.4293			−1.27475			−0.637374	−	0.770555i	$-0.719979\pi$
$463$	−27.4293			−1.27475			−0.637374	+	0.770555i	$0.719979\pi$
$464$		−	5.75703i		−	0.267263i
$465$		−	13.0130i		−	0.603463i
$466$	−21.6421			−1.00255
$467$		−	15.3698i		−	0.711231i	−0.934632	−	0.355616i	$-0.884271\pi$
$467$		−	15.3698i		−	0.711231i	0.934632	−	0.355616i	$-0.115729\pi$
$468$	−3.91265			−0.180862
$469$		0			0
$470$			17.7386i			0.818221i
$471$	8.01869			0.369482
$472$	−4.99905			−0.230100
$473$	−9.95322	+	3.78594i	−0.457650	+	0.174078i
$474$		−	8.55410i		−	0.392903i
$475$	−50.0512			−2.29651
$476$		0			0
$477$	−2.83716			−0.129905
$478$	−10.6397			−0.486648
$479$	36.8475			1.68360			0.841802	−	0.539786i	$-0.181495\pi$
$479$	36.8475			1.68360			0.841802	+	0.539786i	$0.181495\pi$
$480$		−	4.05345i		−	0.185014i
$481$	−19.9408			−0.909222
$482$		−	5.68711i		−	0.259041i
$483$		0			0
$484$	8.21928	−	7.31050i	0.373604	−	0.332296i
$485$	70.8953			3.21919
$486$	−1.00000			−0.0453609
$487$	12.1267			0.549511			0.274756	−	0.961514i	$-0.411403\pi$
$487$	12.1267			0.549511			0.274756	+	0.961514i	$0.411403\pi$
$488$		−	7.95115i		−	0.359932i
$489$			3.40939i			0.154178i
$490$		0			0
$491$		−	38.1431i		−	1.72138i	−0.509133	−	0.860688i	$-0.670034\pi$
$491$		−	38.1431i		−	1.72138i	0.509133	−	0.860688i	$-0.329966\pi$
$492$			8.14212i			0.367075i
$493$		−	1.08461i		−	0.0488485i
$494$			17.1326i			0.770832i
$495$	−12.5655	+	4.77956i	−0.564775	+	0.214825i
$496$		−	3.21035i		−	0.144149i
$497$		0			0
$498$	−12.5690			−0.563228
$499$	6.48858			0.290469			0.145234	−	0.989397i	$-0.453606\pi$
$499$	6.48858			0.290469			0.145234	+	0.989397i	$0.453606\pi$
$500$			26.0655i			1.16568i
$501$			11.1360i			0.497518i
$502$	0.576257			0.0257196
$503$	30.9319			1.37919			0.689593	−	0.724197i	$-0.257789\pi$
$503$	30.9319			1.37919			0.689593	+	0.724197i	$0.257789\pi$
$504$		0			0
$505$		−	11.6659i		−	0.519124i
$506$	11.1086	−	4.22541i	0.493837	−	0.187843i
$507$		−	2.30884i		−	0.102539i
$508$			6.79955i			0.301681i
$509$		−	12.3663i		−	0.548128i	−0.961711	−	0.274064i	$-0.911632\pi$
$509$		−	12.3663i		−	0.548128i	0.961711	−	0.274064i	$-0.0883680\pi$
$510$		−	0.763662i		−	0.0338155i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			4.37877i			0.193327i
$514$	−22.2114			−0.979702
$515$	72.1500			3.17931
$516$	3.21078			0.141347
$517$	13.5659	−	5.16010i	0.596627	−	0.226941i
$518$		0			0
$519$		−	5.89901i		−	0.258938i
$520$	15.8597			0.695495
$521$			32.9604i			1.44402i	0.691882	+	0.722011i	$0.256782\pi$
$521$			32.9604i			1.44402i	−0.691882	+	0.722011i	$0.743218\pi$
$522$	5.75703			0.251978
$523$	11.7372			0.513231			0.256615	−	0.966514i	$-0.417393\pi$
$523$	11.7372			0.513231			0.256615	+	0.966514i	$0.417393\pi$
$524$	−21.7846			−0.951663
$525$		0			0
$526$	21.1657			0.922869
$527$		−	0.604824i		−	0.0263465i
$528$	−3.09994	+	1.17914i	−0.134908	+	0.0513153i
$529$	−10.1586			−0.441680
$530$	11.5003			0.499540
$531$		−	4.99905i		−	0.216941i
$532$		0			0
$533$	−31.8573			−1.37989
$534$			14.2616i			0.617158i
$535$	26.2237			1.13375
$536$		−	6.50120i		−	0.280809i
$537$			3.92282i			0.169282i
$538$	16.9288			0.729853
$539$		0			0
$540$	4.05345			0.174433
$541$		−	4.32833i		−	0.186089i	−0.995662	−	0.0930447i	$-0.970340\pi$
$541$		−	4.32833i		−	0.186089i	0.995662	−	0.0930447i	$-0.0296600\pi$
$542$			12.9849i			0.557750i
$543$	13.8033			0.592355
$544$		−	0.188398i		−	0.00807750i
$545$	70.7453			3.03040
$546$		0			0
$547$		−	5.00956i		−	0.214193i	−0.994249	−	0.107097i	$-0.965845\pi$
$547$		−	5.00956i		−	0.214193i	0.994249	−	0.107097i	$-0.0341554\pi$
$548$	−7.02179			−0.299956
$549$	7.95115			0.339347
$550$	35.4337	−	13.4780i	1.51090	−	0.574706i
$551$		−	25.2087i		−	1.07393i
$552$	−3.58348			−0.152523
$553$		0			0
$554$	−25.5474			−1.08541
$555$	20.6584			0.876899
$556$	−15.5729			−0.660438
$557$			16.5353i			0.700622i	0.936633	+	0.350311i	$0.113924\pi$
$557$			16.5353i			0.700622i	−0.936633	+	0.350311i	$0.886076\pi$
$558$	3.21035			0.135905
$559$			12.5627i			0.531344i
$560$		0			0
$561$	−0.584023	+	0.222147i	−0.0246575	+	0.00937905i
$562$	6.87709			0.290093
$563$	−25.9643			−1.09427			−0.547133	−	0.837046i	$-0.684281\pi$
$563$	−25.9643			−1.09427			−0.547133	+	0.837046i	$0.684281\pi$
$564$	−4.37618			−0.184270
$565$			3.03676i			0.127757i
$566$			13.6656i			0.574409i
$567$		0			0
$568$			16.2739i			0.682839i
$569$		−	32.5397i		−	1.36414i	−0.731289	−	0.682068i	$-0.761081\pi$
$569$		−	32.5397i		−	1.36414i	0.731289	−	0.682068i	$-0.238919\pi$
$570$		−	17.7491i		−	0.743428i
$571$		−	8.55851i		−	0.358163i	−0.983834	−	0.179081i	$-0.942687\pi$
$571$		−	8.55851i		−	0.358163i	0.983834	−	0.179081i	$-0.0573125\pi$
$572$	−4.61355	−	12.1290i	−0.192902	−	0.507139i
$573$			9.49736i			0.396758i
$574$		0			0
$575$	40.9608			1.70818
$576$	1.00000			0.0416667
$577$			4.95164i			0.206139i	0.994674	+	0.103070i	$0.0328665\pi$
$577$			4.95164i			0.206139i	−0.994674	+	0.103070i	$0.967134\pi$
$578$			16.9645i			0.705630i
$579$	−13.5397			−0.562693
$580$	−23.3358			−0.968967
$581$		0			0
$582$			17.4901i			0.724989i
$583$	−3.34539	−	8.79502i	−0.138552	−	0.364253i
$584$			12.3419i			0.510710i
$585$			15.8597i			0.655719i
$586$		−	9.49826i		−	0.392370i
$587$		−	7.93396i		−	0.327469i	−0.986504	−	0.163735i	$-0.947646\pi$
$587$		−	7.93396i		−	0.327469i	0.986504	−	0.163735i	$-0.0523541\pi$
$588$		0			0
$589$		−	14.0574i		−	0.579224i
$590$			20.2634i			0.834231i
$591$	−26.1952			−1.07753
$592$	5.09649			0.209465
$593$	−21.3377			−0.876233			−0.438117	−	0.898918i	$-0.644354\pi$
$593$	−21.3377			−0.876233			−0.438117	+	0.898918i	$0.644354\pi$
$594$	−1.17914	−	3.09994i	−0.0483805	−	0.127192i
$595$		0			0
$596$			0.875307i			0.0358540i
$597$	−6.10803			−0.249985
$598$		−	14.0209i		−	0.573358i
$599$	18.6966			0.763924			0.381962	−	0.924178i	$-0.375249\pi$
$599$	18.6966			0.763924			0.381962	+	0.924178i	$0.375249\pi$
$600$	−11.4304			−0.466646
$601$	−2.99879			−0.122323			−0.0611616	−	0.998128i	$-0.519480\pi$
$601$	−2.99879			−0.122323			−0.0611616	+	0.998128i	$0.519480\pi$
$602$		0			0
$603$	6.50120			0.264749
$604$		−	18.1267i		−	0.737566i
$605$	−29.6327	−	33.3164i	−1.20474	−	1.35451i
$606$	2.87801			0.116911
$607$	−21.9575			−0.891227			−0.445613	−	0.895225i	$-0.647014\pi$
$607$	−21.9575			−0.891227			−0.445613	+	0.895225i	$0.647014\pi$
$608$		−	4.37877i		−	0.177582i
$609$		0			0
$610$	−32.2296			−1.30494
$611$		−	17.1225i		−	0.692700i
$612$	0.188398			0.00761554
$613$		−	29.8421i		−	1.20531i	−0.798002	−	0.602655i	$-0.794110\pi$
$613$		−	29.8421i		−	1.20531i	0.798002	−	0.602655i	$-0.205890\pi$
$614$			17.4551i			0.704431i
$615$	33.0037			1.33084
$616$		0			0
$617$	−24.7509			−0.996435			−0.498218	−	0.867052i	$-0.666012\pi$
$617$	−24.7509			−0.996435			−0.498218	+	0.867052i	$0.666012\pi$
$618$			17.7997i			0.716008i
$619$			19.8562i			0.798086i	0.916932	+	0.399043i	$0.130658\pi$
$619$			19.8562i			0.798086i	−0.916932	+	0.399043i	$0.869342\pi$
$620$	−13.0130			−0.522614
$621$		−	3.58348i		−	0.143800i
$622$	−10.1883			−0.408512
$623$		0			0
$624$			3.91265i			0.156631i
$625$	48.5028			1.94011
$626$	19.8187			0.792116
$627$	−13.5739	+	5.16316i	−0.542090	+	0.206197i
$628$		−	8.01869i		−	0.319981i
$629$	0.960170			0.0382845
$630$		0			0
$631$	27.2358			1.08424			0.542120	−	0.840301i	$-0.317622\pi$
$631$	27.2358			1.08424			0.542120	+	0.840301i	$0.317622\pi$
$632$	−8.55410			−0.340264
$633$	19.8676			0.789665
$634$			15.5000i			0.615583i
$635$	27.5616			1.09375
$636$			2.83716i			0.112501i
$637$		0			0
$638$	6.78832	+	17.8465i	0.268752	+	0.706548i
$639$	−16.2739			−0.643787
$640$	−4.05345			−0.160227
$641$	38.3259			1.51378			0.756892	−	0.653540i	$-0.226717\pi$
$641$	38.3259			1.51378			0.756892	+	0.653540i	$0.226717\pi$
$642$			6.46948i			0.255330i
$643$		−	48.9151i		−	1.92902i	−0.264039	−	0.964512i	$-0.585055\pi$
$643$		−	48.9151i		−	1.92902i	0.264039	−	0.964512i	$-0.414945\pi$
$644$		0			0
$645$		−	13.0147i		−	0.512454i
$646$		−	0.824952i		−	0.0324573i
$647$			38.0347i			1.49530i	0.664094	+	0.747649i	$0.268817\pi$
$647$			38.0347i			1.49530i	−0.664094	+	0.747649i	$0.731183\pi$
$648$			1.00000i			0.0392837i
$649$	15.4968	−	5.89456i	0.608302	−	0.231382i
$650$		−	44.7233i		−	1.75419i
$651$		0			0
$652$	3.40939			0.133522
$653$	−19.7568			−0.773143			−0.386572	−	0.922259i	$-0.626341\pi$
$653$	−19.7568			−0.773143			−0.386572	+	0.922259i	$0.626341\pi$
$654$			17.4531i			0.682471i
$655$			88.3026i			3.45027i
$656$	8.14212			0.317896
$657$	−12.3419			−0.481502
$658$		0			0
$659$		−	42.6746i		−	1.66237i	−0.555999	−	0.831183i	$-0.687664\pi$
$659$		−	42.6746i		−	1.66237i	0.555999	−	0.831183i	$-0.312336\pi$
$660$	4.77956	+	12.5655i	0.186044	+	0.489110i
$661$			40.6501i			1.58110i	0.612395	+	0.790552i	$0.290206\pi$
$661$			40.6501i			1.58110i	−0.612395	+	0.790552i	$0.709794\pi$
$662$			22.3460i			0.868501i
$663$			0.737136i			0.0286280i
$664$			12.5690i			0.487770i
$665$		0			0
$666$			5.09649i			0.197485i
$667$			20.6302i			0.798805i
$668$	11.1360			0.430863
$669$	4.64198			0.179469
$670$	−26.3523			−1.01808
$671$	9.37548	+	24.6481i	0.361936	+	0.951529i
$672$		0			0
$673$		−	17.6669i		−	0.681011i	−0.940243	−	0.340505i	$-0.889402\pi$
$673$		−	17.6669i		−	0.681011i	0.940243	−	0.340505i	$-0.110598\pi$
$674$	21.9009			0.843589
$675$		−	11.4304i		−	0.439958i
$676$	−2.30884			−0.0888015
$677$	−12.3507			−0.474677			−0.237338	−	0.971427i	$-0.576275\pi$
$677$	−12.3507			−0.474677			−0.237338	+	0.971427i	$0.576275\pi$
$678$	−0.749179			−0.0287720
$679$		0			0
$680$	−0.763662			−0.0292851
$681$		−	13.0638i		−	0.500606i
$682$	3.78544	+	9.95190i	0.144952	+	0.381078i
$683$	11.9147			0.455904			0.227952	−	0.973672i	$-0.426797\pi$
$683$	11.9147			0.455904			0.227952	+	0.973672i	$0.426797\pi$
$684$	4.37877			0.167426
$685$			28.4625i			1.08750i
$686$		0			0
$687$	−9.68676			−0.369573
$688$		−	3.21078i		−	0.122410i
$689$	−11.1008			−0.422907
$690$			14.5255i			0.552975i
$691$		−	40.8856i		−	1.55536i	−0.628660	−	0.777680i	$-0.716396\pi$
$691$		−	40.8856i		−	1.55536i	0.628660	−	0.777680i	$-0.283604\pi$
$692$	−5.89901			−0.224247
$693$		0			0
$694$	−7.73409			−0.293582
$695$			63.1239i			2.39443i
$696$		−	5.75703i		−	0.218220i
$697$	1.53396			0.0581029
$698$			20.8125i			0.787763i
$699$	−21.6421			−0.818580
$700$		0			0
$701$			35.4801i			1.34007i	0.742331	+	0.670033i	$0.233720\pi$
$701$			35.4801i			1.34007i	−0.742331	+	0.670033i	$0.766280\pi$
$702$	−3.91265			−0.147674
$703$	22.3164			0.841678
$704$	1.17914	+	3.09994i	0.0444403	+	0.116833i
$705$			17.7386i			0.668074i
$706$	−29.2347			−1.10026
$707$		0			0
$708$	−4.99905			−0.187876
$709$	−39.7202			−1.49172			−0.745861	−	0.666102i	$-0.767962\pi$
$709$	−39.7202			−1.49172			−0.745861	+	0.666102i	$0.767962\pi$
$710$	65.9656			2.47564
$711$		−	8.55410i		−	0.320804i
$712$	14.2616			0.534474
$713$			11.5042i			0.430837i
$714$		0			0
$715$	−49.1642	+	18.7008i	−1.83864	+	0.699369i
$716$	3.92282			0.146603
$717$	−10.6397			−0.397347
$718$	34.8045			1.29889
$719$			0.852683i			0.0317997i	0.999874	+	0.0158999i	$0.00506130\pi$
$719$			0.852683i			0.0317997i	−0.999874	+	0.0158999i	$0.994939\pi$
$720$		−	4.05345i		−	0.151063i
$721$		0			0
$722$		−	0.173600i		−	0.00646072i
$723$		−	5.68711i		−	0.211506i
$724$		−	13.8033i		−	0.512994i
$725$			65.8054i			2.44395i
$726$	8.21928	−	7.31050i	0.305046	−	0.271318i
$727$			45.9492i			1.70416i	0.523411	+	0.852080i	$0.324659\pi$
$727$			45.9492i			1.70416i	−0.523411	+	0.852080i	$0.675341\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	50.0271			1.85159
$731$		−	0.604905i		−	0.0223732i
$732$		−	7.95115i		−	0.293883i
$733$	−1.39257			−0.0514359			−0.0257179	−	0.999669i	$-0.508187\pi$
$733$	−1.39257			−0.0514359			−0.0257179	+	0.999669i	$0.508187\pi$
$734$	28.5311			1.05310
$735$		0			0
$736$			3.58348i			0.132089i
$737$	7.66579	+	20.1533i	0.282373	+	0.742358i
$738$			8.14212i			0.299716i
$739$		−	17.6182i		−	0.648096i	−0.946041	−	0.324048i	$-0.894956\pi$
$739$		−	17.6182i		−	0.648096i	0.946041	−	0.324048i	$-0.105044\pi$
$740$		−	20.6584i		−	0.759417i
$741$			17.1326i			0.629381i
$742$		0			0
$743$		−	1.42362i		−	0.0522274i	−0.999659	−	0.0261137i	$-0.991687\pi$
$743$		−	1.42362i		−	0.0522274i	0.999659	−	0.0261137i	$-0.00831320\pi$
$744$		−	3.21035i		−	0.117697i
$745$	3.54801			0.129989
$746$	−28.0262			−1.02611
$747$	−12.5690			−0.459874
$748$	0.222147	+	0.584023i	0.00812250	+	0.0213540i
$749$		0			0
$750$			26.0655i			0.951776i
$751$	33.3920			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$751$	33.3920			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$752$			4.37618i			0.159583i
$753$	0.576257			0.0210000
$754$	22.5252			0.820321
$755$	−73.4758			−2.67406
$756$		0			0
$757$	−11.9154			−0.433074			−0.216537	−	0.976274i	$-0.569476\pi$
$757$	−11.9154			−0.433074			−0.216537	+	0.976274i	$0.569476\pi$
$758$		−	13.1317i		−	0.476964i
$759$	11.1086	−	4.22541i	0.403216	−	0.153373i
$760$	−17.7491			−0.643828
$761$	17.3932			0.630504			0.315252	−	0.949008i	$-0.397911\pi$
$761$	17.3932			0.630504			0.315252	+	0.949008i	$0.397911\pi$
$762$			6.79955i			0.246322i
$763$		0			0
$764$	9.49736			0.343602
$765$		−	0.763662i		−	0.0276103i
$766$	−11.9092			−0.430298
$767$		−	19.5596i		−	0.706255i
$768$		−	1.00000i		−	0.0360844i
$769$	51.8599			1.87012			0.935059	−	0.354493i	$-0.115346\pi$
$769$	51.8599			1.87012			0.935059	+	0.354493i	$0.115346\pi$
$770$		0			0
$771$	−22.2114			−0.799923
$772$			13.5397i			0.487306i
$773$			1.68049i			0.0604430i	0.999543	+	0.0302215i	$0.00962126\pi$
$773$			1.68049i			0.0604430i	−0.999543	+	0.0302215i	$0.990379\pi$
$774$	3.21078			0.115409
$775$			36.6957i			1.31815i
$776$	17.4901			0.627859
$777$		0			0
$778$		−	36.7446i		−	1.31736i
$779$	35.6524			1.27738
$780$	15.8597			0.567869
$781$	−19.1892	−	50.4483i	−0.686643	−	1.80518i
$782$			0.675122i			0.0241423i
$783$	5.75703			0.205739
$784$		0			0
$785$	−32.5033			−1.16009
$786$	−21.7846			−0.777029
$787$	−0.926397			−0.0330225			−0.0165112	−	0.999864i	$-0.505256\pi$
$787$	−0.926397			−0.0330225			−0.0165112	+	0.999864i	$0.505256\pi$
$788$			26.1952i			0.933165i
$789$	21.1657			0.753519
$790$			34.6736i			1.23363i
$791$		0			0
$792$	−3.09994	+	1.17914i	−0.110152	+	0.0418988i
$793$	31.1101			1.10475
$794$	38.5547			1.36825
$795$	11.5003			0.407873
$796$			6.10803i			0.216493i
$797$			12.5708i			0.445280i	0.974901	+	0.222640i	$0.0714674\pi$
$797$			12.5708i			0.445280i	−0.974901	+	0.222640i	$0.928533\pi$
$798$		0			0
$799$			0.824464i			0.0291674i
$800$			11.4304i			0.404127i
$801$			14.2616i			0.503907i
$802$		−	13.9262i		−	0.491751i
$803$	−14.5527	−	38.2591i	−0.513555	−	1.35013i
$804$		−	6.50120i		−	0.229280i
$805$		0			0
$806$	12.5610			0.442442
$807$	16.9288			0.595922
$808$		−	2.87801i		−	0.101248i
$809$		−	13.3055i		−	0.467798i	−0.972261	−	0.233899i	$-0.924852\pi$
$809$		−	13.3055i		−	0.467798i	0.972261	−	0.233899i	$-0.0751484\pi$
$810$	4.05345			0.142424
$811$	−11.8888			−0.417471			−0.208735	−	0.977972i	$-0.566935\pi$
$811$	−11.8888			−0.417471			−0.208735	+	0.977972i	$0.566935\pi$
$812$		0			0
$813$			12.9849i			0.455401i
$814$	−15.7988	+	6.00946i	−0.553749	+	0.210631i
$815$		−	13.8198i		−	0.484085i
$816$		−	0.188398i		−	0.00659525i
$817$		−	14.0592i		−	0.491871i
$818$			8.35551i			0.292143i
$819$		0			0
$820$		−	33.0037i		−	1.15254i
$821$		−	29.1262i		−	1.01651i	−0.861206	−	0.508256i	$-0.830290\pi$
$821$		−	29.1262i		−	1.01651i	0.861206	−	0.508256i	$-0.169710\pi$
$822$	−7.02179			−0.244913
$823$	5.45802			0.190255			0.0951273	−	0.995465i	$-0.469674\pi$
$823$	5.45802			0.190255			0.0951273	+	0.995465i	$0.469674\pi$
$824$	17.7997			0.620081
$825$	35.4337	−	13.4780i	1.23364	−	0.469245i
$826$		0			0
$827$		−	27.0567i		−	0.940852i	−0.882439	−	0.470426i	$-0.844100\pi$
$827$		−	27.0567i		−	0.940852i	0.882439	−	0.470426i	$-0.155900\pi$
$828$	−3.58348			−0.124535
$829$		−	24.6755i		−	0.857016i	−0.903538	−	0.428508i	$-0.859039\pi$
$829$		−	24.6755i		−	0.857016i	0.903538	−	0.428508i	$-0.140961\pi$
$830$	50.9476			1.76842
$831$	−25.5474			−0.886230
$832$	3.91265			0.135647
$833$		0			0
$834$	−15.5729			−0.539245
$835$		−	45.1391i		−	1.56210i
$836$	5.16316	+	13.5739i	0.178572	+	0.469464i
$837$	3.21035			0.110966
$838$	0.503760			0.0174021
$839$			33.2478i			1.14784i	0.818911	+	0.573920i	$0.194578\pi$
$839$			33.2478i			1.14784i	−0.818911	+	0.573920i	$0.805422\pi$
$840$		0			0
$841$	−4.14337			−0.142875
$842$		−	18.0435i		−	0.621820i
$843$	6.87709			0.236860
$844$		−	19.8676i		−	0.683870i
$845$			9.35876i			0.321951i
$846$	−4.37618			−0.150456
$847$		0			0
$848$	2.83716			0.0974284
$849$			13.6656i			0.469003i
$850$			2.15347i			0.0738636i
$851$	−18.2632			−0.626055
$852$			16.2739i			0.557536i
$853$	−12.5236			−0.428802			−0.214401	−	0.976746i	$-0.568780\pi$
$853$	−12.5236			−0.428802			−0.214401	+	0.976746i	$0.568780\pi$
$854$		0			0
$855$		−	17.7491i		−	0.607007i
$856$	6.46948			0.221122
$857$	35.1338			1.20015			0.600073	−	0.799945i	$-0.295138\pi$
$857$	35.1338			1.20015			0.600073	+	0.799945i	$0.295138\pi$
$858$	−4.61355	−	12.1290i	−0.157504	−	0.414077i
$859$		−	3.08712i		−	0.105331i	−0.998612	−	0.0526656i	$-0.983228\pi$
$859$		−	3.08712i		−	0.105331i	0.998612	−	0.0526656i	$-0.0167718\pi$
$860$	−13.0147			−0.443798
$861$		0			0
$862$	−23.7641			−0.809409
$863$	16.5450			0.563200			0.281600	−	0.959532i	$-0.409135\pi$
$863$	16.5450			0.563200			0.281600	+	0.959532i	$0.409135\pi$
$864$	1.00000			0.0340207
$865$			23.9113i			0.813010i
$866$	13.2596			0.450581
$867$			16.9645i			0.576145i
$868$		0			0
$869$	26.5172	−	10.0864i	0.899535	−	0.342159i
$870$	−23.3358			−0.791158
$871$	25.4369			0.861897
$872$	17.4531			0.591037
$873$			17.4901i			0.591951i
$874$			15.6912i			0.530764i
$875$		0			0
$876$			12.3419i			0.416993i
$877$			0.198470i			0.00670185i	0.999994	+	0.00335092i	$0.00106663\pi$
$877$			0.198470i			0.00670185i	−0.999994	+	0.00335092i	$0.998933\pi$
$878$		−	18.6515i		−	0.629457i
$879$		−	9.49826i		−	0.320368i
$880$	12.5655	−	4.77956i	0.423581	−	0.161119i
$881$			35.4245i			1.19348i	0.802434	+	0.596741i	$0.203538\pi$
$881$			35.4245i			1.19348i	−0.802434	+	0.596741i	$0.796462\pi$
$882$		0			0
$883$	−7.00799			−0.235838			−0.117919	−	0.993023i	$-0.537622\pi$
$883$	−7.00799			−0.235838			−0.117919	+	0.993023i	$0.537622\pi$
$884$	0.737136			0.0247926
$885$			20.2634i			0.681147i
$886$			12.0548i			0.404989i
$887$	−5.25368			−0.176401			−0.0882007	−	0.996103i	$-0.528112\pi$
$887$	−5.25368			−0.176401			−0.0882007	+	0.996103i	$0.528112\pi$
$888$	5.09649			0.171027
$889$		0			0
$890$		−	57.8085i		−	1.93774i
$891$	−1.17914	−	3.09994i	−0.0395025	−	0.103852i
$892$		−	4.64198i		−	0.155425i
$893$			19.1623i			0.641240i
$894$			0.875307i			0.0292746i
$895$		−	15.9010i		−	0.531510i
$896$		0			0
$897$		−	14.0209i		−	0.468145i
$898$		−	27.9760i		−	0.933572i
$899$	−18.4821			−0.616412
$900$	−11.4304			−0.381015
$901$	0.534515			0.0178073
$902$	−25.2401	+	9.60066i	−0.840403	+	0.319667i
$903$		0			0
$904$			0.749179i			0.0249173i
$905$	−55.9508			−1.85987
$906$		−	18.1267i		−	0.602220i
$907$	−28.2027			−0.936455			−0.468228	−	0.883608i	$-0.655107\pi$
$907$	−28.2027			−0.936455			−0.468228	+	0.883608i	$0.655107\pi$
$908$	−13.0638			−0.433537
$909$	2.87801			0.0954576
$910$		0			0
$911$	−2.22257			−0.0736369			−0.0368184	−	0.999322i	$-0.511722\pi$
$911$	−2.22257			−0.0736369			−0.0368184	+	0.999322i	$0.511722\pi$
$912$		−	4.37877i		−	0.144995i
$913$	−14.8205	−	38.9630i	−0.490487	−	1.28949i
$914$	−15.8979			−0.525854
$915$	−32.2296			−1.06548
$916$			9.68676i			0.320060i
$917$		0			0
$918$	0.188398			0.00621807
$919$		−	43.5488i		−	1.43654i	−0.695763	−	0.718271i	$-0.744934\pi$
$919$		−	43.5488i		−	1.43654i	0.695763	−	0.718271i	$-0.255066\pi$
$920$	14.5255			0.478891
$921$			17.4551i			0.575166i
$922$			37.1843i			1.22460i
$923$	−63.6743			−2.09586
$924$		0			0
$925$	−58.2552			−1.91542
$926$			27.4293i			0.901383i
$927$			17.7997i			0.584618i
$928$	−5.75703			−0.188984
$929$			30.4460i			0.998902i	0.866342	+	0.499451i	$0.166465\pi$
$929$			30.4460i			0.998902i	−0.866342	+	0.499451i	$0.833535\pi$
$930$	−13.0130			−0.426713
$931$		0			0
$932$			21.6421i			0.708911i
$933$	−10.1883			−0.333549
$934$	−15.3698			−0.502916
$935$	2.36731	−	0.900461i	0.0774193	−	0.0294482i
$936$			3.91265i			0.127889i
$937$	−30.3254			−0.990688			−0.495344	−	0.868697i	$-0.664958\pi$
$937$	−30.3254			−0.990688			−0.495344	+	0.868697i	$0.664958\pi$
$938$		0			0
$939$	19.8187			0.646760
$940$	17.7386			0.578569
$941$	3.23897			0.105588			0.0527938	−	0.998605i	$-0.483187\pi$
$941$	3.23897			0.105588			0.0527938	+	0.998605i	$0.483187\pi$
$942$		−	8.01869i		−	0.261263i
$943$	−29.1772			−0.950139
$944$			4.99905i			0.162705i
$945$		0			0
$946$	3.78594	+	9.95322i	0.123092	+	0.323607i
$947$	−33.4714			−1.08767			−0.543837	−	0.839191i	$-0.683029\pi$
$947$	−33.4714			−1.08767			−0.543837	+	0.839191i	$0.683029\pi$
$948$	−8.55410			−0.277824
$949$	−48.2894			−1.56754
$950$			50.0512i			1.62388i
$951$			15.5000i			0.502622i
$952$		0			0
$953$			28.4159i			0.920482i	0.887794	+	0.460241i	$0.152237\pi$
$953$			28.4159i			0.920482i	−0.887794	+	0.460241i	$0.847763\pi$
$954$			2.83716i			0.0918564i
$955$		−	38.4970i		−	1.24573i
$956$			10.6397i			0.344112i
$957$	6.78832	+	17.8465i	0.219435	+	0.576894i
$958$		−	36.8475i		−	1.19049i
$959$		0			0
$960$	−4.05345			−0.130824
$961$	20.6937			0.667537
$962$			19.9408i			0.642917i
$963$			6.46948i			0.208476i
$964$	−5.68711			−0.183169
$965$	54.8827			1.76674
$966$		0			0
$967$			9.93397i			0.319455i	0.987161	+	0.159728i	$0.0510616\pi$
$967$			9.93397i			0.319455i	−0.987161	+	0.159728i	$0.948938\pi$
$968$	−7.31050	−	8.21928i	−0.234968	−	0.264178i
$969$		−	0.824952i		−	0.0265013i
$970$		−	70.8953i		−	2.27631i
$971$			61.7684i			1.98224i	0.132957	+	0.991122i	$0.457553\pi$
$971$			61.7684i			1.98224i	−0.132957	+	0.991122i	$0.542447\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$		−	12.1267i		−	0.388563i
$975$		−	44.7233i		−	1.43229i
$976$	−7.95115			−0.254510
$977$	−10.0719			−0.322228			−0.161114	−	0.986936i	$-0.551509\pi$
$977$	−10.0719			−0.322228			−0.161114	+	0.986936i	$0.551509\pi$
$978$	3.40939			0.109020
$979$	−44.2100	+	16.8163i	−1.41296	+	0.537451i
$980$		0			0
$981$			17.4531i			0.557235i
$982$	−38.1431			−1.21720
$983$			26.2075i			0.835890i	0.908472	+	0.417945i	$0.137250\pi$
$983$			26.2075i			0.835890i	−0.908472	+	0.417945i	$0.862750\pi$
$984$	8.14212			0.259561
$985$	106.181			3.38320
$986$	−1.08461			−0.0345411
$987$		0			0
$988$	17.1326			0.545060
$989$			11.5058i			0.365862i
$990$	4.77956	+	12.5655i	0.151905	+	0.399356i
$991$	7.65843			0.243278			0.121639	−	0.992574i	$-0.461185\pi$
$991$	7.65843			0.243278			0.121639	+	0.992574i	$0.461185\pi$
$992$	−3.21035			−0.101929
$993$			22.3460i			0.709128i
$994$		0			0
$995$	24.7586			0.784900
$996$			12.5690i			0.398263i
$997$	11.7961			0.373586			0.186793	−	0.982399i	$-0.440191\pi$
$997$	11.7961			0.373586			0.186793	+	0.982399i	$0.440191\pi$
$998$		−	6.48858i		−	0.205392i
$999$			5.09649i			0.161246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.c.2155.12	✓	24
7.6	odd	2		3234.2.e.d.2155.1	yes	24
11.10	odd	2		3234.2.e.d.2155.24	yes	24
77.76	even	2	inner	3234.2.e.c.2155.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.12	✓	24	1.1	even	1	trivial
3234.2.e.c.2155.13	yes	24	77.76	even	2	inner
3234.2.e.d.2155.1	yes	24	7.6	odd	2
3234.2.e.d.2155.24	yes	24	11.10	odd	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +4.05345i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +4.05345i q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +4.05345 q^{10} +(-1.17914 - 3.09994i) q^{11} +1.00000i q^{12} -3.91265 q^{13} +4.05345 q^{15} +1.00000 q^{16} +0.188398 q^{17} +1.00000i q^{18} +4.37877 q^{19} -4.05345i q^{20} +(-3.09994 + 1.17914i) q^{22} -3.58348 q^{23} +1.00000 q^{24} -11.4304 q^{25} +3.91265i q^{26} +1.00000i q^{27} -5.75703i q^{29} -4.05345i q^{30} -3.21035i q^{31} -1.00000i q^{32} +(-3.09994 + 1.17914i) q^{33} -0.188398i q^{34} +1.00000 q^{36} +5.09649 q^{37} -4.37877i q^{38} +3.91265i q^{39} -4.05345 q^{40} +8.14212 q^{41} -3.21078i q^{43} +(1.17914 + 3.09994i) q^{44} -4.05345i q^{45} +3.58348i q^{46} +4.37618i q^{47} -1.00000i q^{48} +11.4304i q^{50} -0.188398i q^{51} +3.91265 q^{52} +2.83716 q^{53} +1.00000 q^{54} +(12.5655 - 4.77956i) q^{55} -4.37877i q^{57} -5.75703 q^{58} +4.99905i q^{59} -4.05345 q^{60} -7.95115 q^{61} -3.21035 q^{62} -1.00000 q^{64} -15.8597i q^{65} +(1.17914 + 3.09994i) q^{66} -6.50120 q^{67} -0.188398 q^{68} +3.58348i q^{69} +16.2739 q^{71} -1.00000i q^{72} +12.3419 q^{73} -5.09649i q^{74} +11.4304i q^{75} -4.37877 q^{76} +3.91265 q^{78} +8.55410i q^{79} +4.05345i q^{80} +1.00000 q^{81} -8.14212i q^{82} +12.5690 q^{83} +0.763662i q^{85} -3.21078 q^{86} -5.75703 q^{87} +(3.09994 - 1.17914i) q^{88} -14.2616i q^{89} -4.05345 q^{90} +3.58348 q^{92} -3.21035 q^{93} +4.37618 q^{94} +17.7491i q^{95} -1.00000 q^{96} -17.4901i q^{97} +(1.17914 + 3.09994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Introduction

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