LMFDB - Embedded newform 3456.2.i.k.1153.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3456,2,Mod(1153,3456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("3456.1153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3456 = 2^{7} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3456.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.5962989386$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 1152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.1
Root			$-0.433633 + 1.67689i$ of defining polynomial
Character	$\chi$	$=$	3456.1153
Dual form			3456.2.i.k.2305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22043 - 3.84590i) q^{5} +(-1.45488 + 2.51992i) q^{7} +O(q^{10})$	$q+(-2.22043 - 3.84590i) q^{5} +(-1.45488 + 2.51992i) q^{7} +(1.08263 - 1.87517i) q^{11} +(1.96377 + 3.40135i) q^{13} -1.79720 q^{17} +1.76882 q^{19} +(-3.44197 - 5.96166i) q^{23} +(-7.36062 + 12.7490i) q^{25} +(-2.87353 + 4.97710i) q^{29} +(-3.27671 - 5.67542i) q^{31} +12.9218 q^{35} +2.51332 q^{37} +(3.68420 + 6.38122i) q^{41} +(2.53640 - 4.39317i) q^{43} +(-4.98598 + 8.63597i) q^{47} +(-0.733339 - 1.27018i) q^{49} -3.30620 q^{53} -9.61562 q^{55} +(2.30090 + 3.98528i) q^{59} +(-1.87353 + 3.24505i) q^{61} +(8.72084 - 15.1049i) q^{65} +(2.36045 + 4.08841i) q^{67} +0.907539 q^{71} -1.87740 q^{73} +(3.15019 + 5.45629i) q^{77} +(-1.23661 + 2.14187i) q^{79} +(1.09251 - 1.89227i) q^{83} +(3.99056 + 6.91185i) q^{85} +5.30620 q^{89} -11.4282 q^{91} +(-3.92754 - 6.80271i) q^{95} +(4.45302 - 7.71286i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{5} - 6 q^{7}+O(q^{10}) $ 12 * q + 2 * q^5 - 6 * q^7	$ 12 q + 2 q^{5} - 6 q^{7} + 4 q^{11} + 10 q^{13} - 4 q^{17} - 4 q^{19} + 8 q^{23} - 14 q^{25} + 2 q^{29} - 8 q^{31} + 8 q^{35} + 2 q^{41} + 2 q^{43} - 14 q^{47} - 18 q^{49} - 24 q^{53} + 16 q^{55} + 6 q^{59} + 14 q^{61} + 8 q^{65} - 4 q^{67} - 28 q^{71} + 60 q^{73} - 2 q^{77} - 16 q^{79} + 24 q^{83} + 16 q^{85} + 48 q^{89} + 52 q^{91} - 20 q^{95} - 14 q^{97}+O(q^{100}) $ 12 * q + 2 * q^5 - 6 * q^7 + 4 * q^11 + 10 * q^13 - 4 * q^17 - 4 * q^19 + 8 * q^23 - 14 * q^25 + 2 * q^29 - 8 * q^31 + 8 * q^35 + 2 * q^41 + 2 * q^43 - 14 * q^47 - 18 * q^49 - 24 * q^53 + 16 * q^55 + 6 * q^59 + 14 * q^61 + 8 * q^65 - 4 * q^67 - 28 * q^71 + 60 * q^73 - 2 * q^77 - 16 * q^79 + 24 * q^83 + 16 * q^85 + 48 * q^89 + 52 * q^91 - 20 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times$.

$n$	$2053$	$2431$	$2945$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.22043	−	3.84590i	−0.993006	−	1.71994i	−0.598746	−	0.800939i	$-0.704334\pi$
$5$	−2.22043	−	3.84590i	−0.993006	−	1.71994i	−0.394260	−	0.918999i	$-0.628999\pi$
$6$		0			0
$7$	−1.45488	+	2.51992i	−0.549892	+	0.952441i	0.448389	+	0.893838i	$0.351998\pi$
$7$	−1.45488	+	2.51992i	−0.549892	+	0.952441i	−0.998281	+	0.0586028i	$0.981335\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.08263	−	1.87517i	0.326425	−	0.565385i	−0.655374	−	0.755304i	$-0.727489\pi$
$11$	1.08263	−	1.87517i	0.326425	−	0.565385i	0.981800	+	0.189919i	$0.0608225\pi$
$12$		0			0
$13$	1.96377	+	3.40135i	0.544652	+	0.943366i	0.998629	+	0.0523518i	$0.0166717\pi$
$13$	1.96377	+	3.40135i	0.544652	+	0.943366i	−0.453976	+	0.891014i	$0.649995\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.79720			−0.435885			−0.217943	−	0.975962i	$-0.569935\pi$
$17$	−1.79720			−0.435885			−0.217943	+	0.975962i	$0.569935\pi$
$18$		0			0
$19$	1.76882			0.405795			0.202898	−	0.979200i	$-0.434964\pi$
$19$	1.76882			0.405795			0.202898	+	0.979200i	$0.434964\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.44197	−	5.96166i	−0.717700	−	1.24309i	−0.961909	−	0.273370i	$-0.911862\pi$
$23$	−3.44197	−	5.96166i	−0.717700	−	1.24309i	0.244209	−	0.969723i	$-0.421472\pi$
$24$		0			0
$25$	−7.36062	+	12.7490i	−1.47212	+	2.54979i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.87353	+	4.97710i	−0.533601	+	0.924224i	0.465629	+	0.884980i	$0.345828\pi$
$29$	−2.87353	+	4.97710i	−0.533601	+	0.924224i	−0.999230	+	0.0392435i	$0.987505\pi$
$30$		0			0
$31$	−3.27671	−	5.67542i	−0.588514	−	1.01934i	−0.994427	−	0.105425i	$-0.966380\pi$
$31$	−3.27671	−	5.67542i	−0.588514	−	1.01934i	0.405913	−	0.913912i	$-0.366953\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	12.9218			2.18419
$36$		0			0
$37$	2.51332			0.413187			0.206593	−	0.978427i	$-0.433762\pi$
$37$	2.51332			0.413187			0.206593	+	0.978427i	$0.433762\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.68420	+	6.38122i	0.575376	+	0.996580i	0.996001	+	0.0893453i	$0.0284775\pi$
$41$	3.68420	+	6.38122i	0.575376	+	0.996580i	−0.420625	+	0.907235i	$0.638189\pi$
$42$		0			0
$43$	2.53640	−	4.39317i	0.386797	−	0.669953i	−0.605219	−	0.796059i	$-0.706915\pi$
$43$	2.53640	−	4.39317i	0.386797	−	0.669953i	0.992017	+	0.126106i	$0.0402479\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.98598	+	8.63597i	−0.727280	+	1.25969i	0.230748	+	0.973013i	$0.425883\pi$
$47$	−4.98598	+	8.63597i	−0.727280	+	1.25969i	−0.958029	+	0.286673i	$0.907451\pi$
$48$		0			0
$49$	−0.733339	−	1.27018i	−0.104763	−	0.181454i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.30620			−0.454141			−0.227070	−	0.973878i	$-0.572915\pi$
$53$	−3.30620			−0.454141			−0.227070	+	0.973878i	$0.572915\pi$
$54$		0			0
$55$	−9.61562			−1.29657
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.30090	+	3.98528i	0.299552	+	0.518839i	0.976033	−	0.217621i	$-0.0698296\pi$
$59$	2.30090	+	3.98528i	0.299552	+	0.518839i	−0.676482	+	0.736459i	$0.736496\pi$
$60$		0			0
$61$	−1.87353	+	3.24505i	−0.239881	+	0.415485i	−0.960680	−	0.277658i	$-0.910442\pi$
$61$	−1.87353	+	3.24505i	−0.239881	+	0.415485i	0.720799	+	0.693144i	$0.243775\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.72084	−	15.1049i	1.08169	−	1.87354i
$66$		0			0
$67$	2.36045	+	4.08841i	0.288374	+	0.499479i	0.973422	−	0.229019i	$-0.0735519\pi$
$67$	2.36045	+	4.08841i	0.288374	+	0.499479i	−0.685047	+	0.728498i	$0.740219\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.907539			0.107705			0.0538525	−	0.998549i	$-0.482850\pi$
$71$	0.907539			0.107705			0.0538525	+	0.998549i	$0.482850\pi$
$72$		0			0
$73$	−1.87740			−0.219733			−0.109866	−	0.993946i	$-0.535042\pi$
$73$	−1.87740			−0.219733			−0.109866	+	0.993946i	$0.535042\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.15019	+	5.45629i	0.358998	+	0.621802i
$78$		0			0
$79$	−1.23661	+	2.14187i	−0.139129	+	0.240979i	−0.927167	−	0.374648i	$-0.877764\pi$
$79$	−1.23661	+	2.14187i	−0.139129	+	0.240979i	0.788038	+	0.615627i	$0.211097\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.09251	−	1.89227i	0.119918	−	0.207704i	−0.799817	−	0.600244i	$-0.795070\pi$
$83$	1.09251	−	1.89227i	0.119918	−	0.207704i	0.919735	+	0.392540i	$0.128403\pi$
$84$		0			0
$85$	3.99056	+	6.91185i	0.432837	+	0.749696i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.30620			0.562456			0.281228	−	0.959641i	$-0.409258\pi$
$89$	5.30620			0.562456			0.281228	+	0.959641i	$0.409258\pi$
$90$		0			0
$91$	−11.4282			−1.19800
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.92754	−	6.80271i	−0.402958	−	0.697943i
$96$		0			0
$97$	4.45302	−	7.71286i	0.452136	−	0.783123i	−0.546382	−	0.837536i	$-0.683995\pi$
$97$	4.45302	−	7.71286i	0.452136	−	0.783123i	0.998519	+	0.0544132i	$0.0173288\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.689326	−	1.19395i	0.0685905	−	0.118802i	−0.829691	−	0.558224i	$-0.811483\pi$
$101$	0.689326	−	1.19395i	0.0685905	−	0.118802i	0.898281	+	0.439421i	$0.144816\pi$
$102$		0			0
$103$	−2.54512	−	4.40828i	−0.250778	−	0.434361i	0.712962	−	0.701203i	$-0.247353\pi$
$103$	−2.54512	−	4.40828i	−0.250778	−	0.434361i	−0.963740	+	0.266842i	$0.914020\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	17.2062			1.66338			0.831692	−	0.555238i	$-0.187373\pi$
$107$	17.2062			1.66338			0.831692	+	0.555238i	$0.187373\pi$
$108$		0			0
$109$	6.59351			0.631544			0.315772	−	0.948835i	$-0.397737\pi$
$109$	6.59351			0.631544			0.315772	+	0.948835i	$0.397737\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.90072	+	15.4165i	0.837309	+	1.45026i	0.892137	+	0.451766i	$0.149206\pi$
$113$	8.90072	+	15.4165i	0.837309	+	1.45026i	−0.0548276	+	0.998496i	$0.517461\pi$
$114$		0			0
$115$	−15.2853	+	26.4749i	−1.42536	+	2.46880i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.61471	−	4.52881i	0.239690	−	0.415155i
$120$		0			0
$121$	3.15582	+	5.46604i	0.286893	+	0.496913i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	43.1706			3.86130
$126$		0			0
$127$	18.2258			1.61728			0.808639	−	0.588305i	$-0.200205\pi$
$127$	18.2258			1.61728			0.808639	+	0.588305i	$0.200205\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.33057	−	7.50076i	−0.378363	−	0.655345i	0.612461	−	0.790501i	$-0.290180\pi$
$131$	−4.33057	−	7.50076i	−0.378363	−	0.655345i	−0.990824	+	0.135156i	$0.956846\pi$
$132$		0			0
$133$	−2.57342	+	4.45729i	−0.223144	+	0.386496i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.774446	−	1.34138i	0.0661654	−	0.114602i	−0.831045	−	0.556205i	$-0.812257\pi$
$137$	0.774446	−	1.34138i	0.0661654	−	0.114602i	0.897210	+	0.441603i	$0.145590\pi$
$138$		0			0
$139$	9.78618	+	16.9502i	0.830053	+	1.43769i	0.897996	+	0.440005i	$0.145023\pi$
$139$	9.78618	+	16.9502i	0.830053	+	1.43769i	−0.0679426	+	0.997689i	$0.521643\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.50416			0.711154
$144$		0			0
$145$	25.5219			2.11948
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.945984	+	1.63849i	0.0774980	+	0.134230i	0.902170	−	0.431381i	$-0.141974\pi$
$149$	0.945984	+	1.63849i	0.0774980	+	0.134230i	−0.824672	+	0.565612i	$0.808640\pi$
$150$		0			0
$151$	4.27927	−	7.41191i	0.348242	−	0.603173i	−0.637695	−	0.770289i	$-0.720112\pi$
$151$	4.27927	−	7.41191i	0.348242	−	0.603173i	0.985937	+	0.167116i	$0.0534454\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.5514	+	25.2038i	−1.16880	+	2.02441i
$156$		0			0
$157$	2.22265	+	3.84974i	0.177387	+	0.307242i	0.940985	−	0.338449i	$-0.109902\pi$
$157$	2.22265	+	3.84974i	0.177387	+	0.307242i	−0.763598	+	0.645692i	$0.776569\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	20.0306			1.57863
$162$		0			0
$163$	18.8817			1.47893			0.739465	−	0.673195i	$-0.235078\pi$
$163$	18.8817			1.47893			0.739465	+	0.673195i	$0.235078\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.31394	+	7.47197i	0.333823	+	0.578198i	0.983258	−	0.182219i	$-0.0583279\pi$
$167$	4.31394	+	7.47197i	0.333823	+	0.578198i	−0.649435	+	0.760417i	$0.724995\pi$
$168$		0			0
$169$	−1.21280	+	2.10063i	−0.0932924	+	0.161587i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.91423	−	6.77965i	0.297594	−	0.515447i	−0.677991	−	0.735070i	$-0.737149\pi$
$173$	3.91423	−	6.77965i	0.297594	−	0.515447i	0.975585	+	0.219623i	$0.0704826\pi$
$174$		0			0
$175$	−21.4176	−	37.0964i	−1.61902	−	2.80422i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.6390			−1.01943			−0.509714	−	0.860344i	$-0.670249\pi$
$179$	−13.6390			−1.01943			−0.509714	+	0.860344i	$0.670249\pi$
$180$		0			0
$181$	−0.504672			−0.0375120			−0.0187560	−	0.999824i	$-0.505971\pi$
$181$	−0.504672			−0.0375120			−0.0187560	+	0.999824i	$0.505971\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.58064	−	9.66596i	−0.410297	−	0.710655i
$186$		0			0
$187$	−1.94571	+	3.37006i	−0.142284	+	0.246443i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.0083	+	17.3349i	−0.724175	+	1.25431i	0.235138	+	0.971962i	$0.424446\pi$
$191$	−10.0083	+	17.3349i	−0.724175	+	1.25431i	−0.959313	+	0.282345i	$0.908888\pi$
$192$		0			0
$193$	−1.08462	−	1.87862i	−0.0780726	−	0.135226i	0.824346	−	0.566087i	$-0.191543\pi$
$193$	−1.08462	−	1.87862i	−0.0780726	−	0.135226i	−0.902418	+	0.430861i	$0.858210\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.67460			0.404298			0.202149	−	0.979355i	$-0.435207\pi$
$197$	5.67460			0.404298			0.202149	+	0.979355i	$0.435207\pi$
$198$		0			0
$199$	11.5032			0.815439			0.407719	−	0.913107i	$-0.366324\pi$
$199$	11.5032			0.815439			0.407719	+	0.913107i	$0.366324\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.36126	−	14.4821i	−0.586846	−	1.01645i
$204$		0			0
$205$	16.3610	−	28.3381i	1.14270	−	1.97922i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.91498	−	3.31684i	0.132462	−	0.229431i
$210$		0			0
$211$	−10.3177	−	17.8707i	−0.710297	−	1.23027i	−0.964746	−	0.263184i	$-0.915227\pi$
$211$	−10.3177	−	17.8707i	−0.710297	−	1.23027i	0.254449	−	0.967086i	$-0.418106\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−22.5276			−1.53637
$216$		0			0
$217$	19.0688			1.29448
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.52929	−	6.11292i	−0.237406	−	0.411199i
$222$		0			0
$223$	−2.54291	+	4.40444i	−0.170286	+	0.294943i	−0.938520	−	0.345226i	$-0.887802\pi$
$223$	−2.54291	+	4.40444i	−0.170286	+	0.294943i	0.768234	+	0.640169i	$0.221136\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.14484	−	15.8393i	0.606964	−	1.05129i	−0.384773	−	0.923011i	$-0.625720\pi$
$227$	9.14484	−	15.8393i	0.606964	−	1.05129i	0.991738	−	0.128282i	$-0.0409462\pi$
$228$		0			0
$229$	9.62341	+	16.6682i	0.635933	+	1.10147i	0.986317	+	0.164862i	$0.0527178\pi$
$229$	9.62341	+	16.6682i	0.635933	+	1.10147i	−0.350384	+	0.936606i	$0.613949\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.4263			−1.07612			−0.538061	−	0.842906i	$-0.680843\pi$
$233$	−16.4263			−1.07612			−0.538061	+	0.842906i	$0.680843\pi$
$234$		0			0
$235$	44.2841			2.88878
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.08563	−	15.7368i	−0.587700	−	1.01793i	−0.994533	−	0.104424i	$-0.966700\pi$
$239$	−9.08563	−	15.7368i	−0.587700	−	1.01793i	0.406833	−	0.913503i	$-0.366633\pi$
$240$		0			0
$241$	−11.4344	+	19.8050i	−0.736556	+	1.27575i	0.217481	+	0.976065i	$0.430216\pi$
$241$	−11.4344	+	19.8050i	−0.736556	+	1.27575i	−0.954037	+	0.299688i	$0.903117\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.25666	+	5.64070i	−0.208060	+	0.360371i
$246$		0			0
$247$	3.47356	+	6.01639i	0.221017	+	0.382813i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.139530			−0.00880707			−0.00440353	−	0.999990i	$-0.501402\pi$
$251$	−0.139530			−0.00880707			−0.00440353	+	0.999990i	$0.501402\pi$
$252$		0			0
$253$	−14.9055			−0.937102
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.17682	+	12.4306i	0.447678	+	0.775400i	0.998234	−	0.0593974i	$-0.0189179\pi$
$257$	7.17682	+	12.4306i	0.447678	+	0.775400i	−0.550557	+	0.834798i	$0.685585\pi$
$258$		0			0
$259$	−3.65657	+	6.33336i	−0.227208	+	0.393536i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.968751	+	1.67793i	−0.0597357	+	0.103465i	−0.894347	−	0.447374i	$-0.852359\pi$
$263$	−0.968751	+	1.67793i	−0.0597357	+	0.103465i	0.834611	+	0.550840i	$0.185692\pi$
$264$		0			0
$265$	7.34118	+	12.7153i	0.450965	+	0.781094i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.91415			−0.604477			−0.302238	−	0.953232i	$-0.597734\pi$
$269$	−9.91415			−0.604477			−0.302238	+	0.953232i	$0.597734\pi$
$270$		0			0
$271$	4.56777			0.277472			0.138736	−	0.990329i	$-0.455696\pi$
$271$	4.56777			0.277472			0.138736	+	0.990329i	$0.455696\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.9377	+	27.6048i	0.961077	+	1.66463i
$276$		0			0
$277$	−14.4728	+	25.0676i	−0.869585	+	1.50616i	−0.00716263	+	0.999974i	$0.502280\pi$
$277$	−14.4728	+	25.0676i	−0.869585	+	1.50616i	−0.862422	+	0.506190i	$0.831053\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.1351	+	19.2865i	−0.664262	+	1.15054i	0.315223	+	0.949018i	$0.397921\pi$
$281$	−11.1351	+	19.2865i	−0.664262	+	1.15054i	−0.979485	+	0.201518i	$0.935412\pi$
$282$		0			0
$283$	−6.79946	−	11.7770i	−0.404186	−	0.700071i	0.590040	−	0.807374i	$-0.299112\pi$
$283$	−6.79946	−	11.7770i	−0.404186	−	0.700071i	−0.994226	+	0.107303i	$0.965779\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−21.4403			−1.26558
$288$		0			0
$289$	−13.7701			−0.810004
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.21821	+	12.5023i	0.421693	+	0.730393i	0.996105	−	0.0881730i	$-0.0281028\pi$
$293$	7.21821	+	12.5023i	0.421693	+	0.730393i	−0.574413	+	0.818566i	$0.694770\pi$
$294$		0			0
$295$	10.2180	−	17.6980i	0.594913	−	1.03042i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.5185	−	23.4147i	0.781794	−	1.35411i
$300$		0			0
$301$	7.38030	+	12.7831i	0.425394	+	0.736804i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	16.6401			0.952812
$306$		0			0
$307$	16.5451			0.944280			0.472140	−	0.881524i	$-0.343482\pi$
$307$	16.5451			0.944280			0.472140	+	0.881524i	$0.343482\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.19366	−	8.99568i	−0.294505	−	0.510098i	0.680364	−	0.732874i	$-0.261822\pi$
$311$	−5.19366	−	8.99568i	−0.294505	−	0.510098i	−0.974870	+	0.222776i	$0.928488\pi$
$312$		0			0
$313$	−6.76501	+	11.7173i	−0.382381	+	0.662303i	−0.991402	−	0.130851i	$-0.958229\pi$
$313$	−6.76501	+	11.7173i	−0.382381	+	0.662303i	0.609021	+	0.793154i	$0.291562\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.9869	−	20.7619i	0.673251	−	1.16611i	−0.303726	−	0.952760i	$-0.598231\pi$
$317$	11.9869	−	20.7619i	0.673251	−	1.16611i	0.976977	−	0.213346i	$-0.0684360\pi$
$318$		0			0
$319$	6.22194	+	10.7767i	0.348362	+	0.603380i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.17893			−0.176880
$324$		0			0
$325$	−57.8183			−3.20718
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.5080	−	25.1286i	−0.799851	−	1.38538i
$330$		0			0
$331$	1.29103	−	2.23612i	0.0709612	−	0.122908i	−0.828362	−	0.560194i	$-0.810727\pi$
$331$	1.29103	−	2.23612i	0.0709612	−	0.122908i	0.899323	+	0.437285i	$0.144060\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.4824	−	18.1561i	0.572715	−	0.991972i
$336$		0			0
$337$	−1.79736	−	3.11313i	−0.0979087	−	0.169583i	0.812910	−	0.582389i	$-0.197882\pi$
$337$	−1.79736	−	3.11313i	−0.0979087	−	0.169583i	−0.910819	+	0.412806i	$0.864549\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.1899			−0.768424
$342$		0			0
$343$	−16.1006			−0.869351
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.85180	+	10.1356i	0.314141	+	0.544108i	0.979255	−	0.202634i	$-0.0649502\pi$
$347$	5.85180	+	10.1356i	0.314141	+	0.544108i	−0.665114	+	0.746742i	$0.731617\pi$
$348$		0			0
$349$	9.34856	−	16.1922i	0.500417	−	0.866747i	−0.499583	−	0.866266i	$-0.666513\pi$
$349$	9.34856	−	16.1922i	0.500417	−	0.866747i	1.00000		0.000481224i	$-0.000153178\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.3410	+	24.8394i	−0.763295	+	1.32207i	0.177848	+	0.984058i	$0.443086\pi$
$353$	−14.3410	+	24.8394i	−0.763295	+	1.32207i	−0.941143	+	0.338008i	$0.890247\pi$
$354$		0			0
$355$	−2.01513	−	3.49030i	−0.106952	−	0.185246i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.8202			−0.834958			−0.417479	−	0.908687i	$-0.637086\pi$
$359$	−15.8202			−0.834958			−0.417479	+	0.908687i	$0.637086\pi$
$360$		0			0
$361$	−15.8713			−0.835330
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.16863	+	7.22028i	0.218196	+	0.377927i
$366$		0			0
$367$	−13.1383	+	22.7563i	−0.685815	+	1.18787i	0.287364	+	0.957821i	$0.407221\pi$
$367$	−13.1383	+	22.7563i	−0.685815	+	1.18787i	−0.973180	+	0.230046i	$0.926112\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.81011	−	8.33136i	0.249729	−	0.432543i
$372$		0			0
$373$	10.8735	+	18.8335i	0.563010	+	0.975162i	0.997232	+	0.0743558i	$0.0236901\pi$
$373$	10.8735	+	18.8335i	0.563010	+	0.975162i	−0.434222	+	0.900806i	$0.642977\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.5718			−1.16251
$378$		0			0
$379$	−32.8861			−1.68925			−0.844623	−	0.535362i	$-0.820175\pi$
$379$	−32.8861			−1.68925			−0.844623	+	0.535362i	$0.820175\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.81269	+	10.0679i	0.297015	+	0.514444i	0.975452	−	0.220214i	$-0.0706757\pi$
$383$	5.81269	+	10.0679i	0.297015	+	0.514444i	−0.678437	+	0.734659i	$0.737342\pi$
$384$		0			0
$385$	13.9896	−	24.2306i	0.712974	−	1.23491i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.61687	−	6.26460i	0.183383	−	0.317628i	−0.759648	−	0.650335i	$-0.774629\pi$
$389$	3.61687	−	6.26460i	0.183383	−	0.317628i	0.943030	+	0.332707i	$0.107962\pi$
$390$		0			0
$391$	6.18591	+	10.7143i	0.312835	+	0.541846i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.9832			0.552625
$396$		0			0
$397$	29.8911			1.50019			0.750095	−	0.661330i	$-0.230008\pi$
$397$	29.8911			1.50019			0.750095	+	0.661330i	$0.230008\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.03226	−	5.25202i	−0.151424	−	0.262273i	0.780327	−	0.625371i	$-0.215052\pi$
$401$	−3.03226	−	5.25202i	−0.151424	−	0.262273i	−0.931751	+	0.363098i	$0.881719\pi$
$402$		0			0
$403$	12.8694	−	22.2905i	0.641071	−	1.11037i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.72099	−	4.71290i	0.134875	−	0.233610i
$408$		0			0
$409$	−14.4396	−	25.0101i	−0.713993	−	1.23667i	−0.963347	−	0.268259i	$-0.913552\pi$
$409$	−14.4396	−	25.0101i	−0.713993	−	1.23667i	0.249354	−	0.968412i	$-0.419782\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.3901			−0.658884
$414$		0			0
$415$	−9.70332			−0.476317
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.63281	+	9.75631i	0.275181	+	0.476627i	0.970181	−	0.242383i	$-0.0779290\pi$
$419$	5.63281	+	9.75631i	0.275181	+	0.476627i	−0.695000	+	0.719010i	$0.744596\pi$
$420$		0			0
$421$	−6.03050	+	10.4451i	−0.293909	+	0.509065i	−0.974730	−	0.223384i	$-0.928289\pi$
$421$	−6.03050	+	10.4451i	−0.293909	+	0.509065i	0.680822	+	0.732449i	$0.261623\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.2285	−	22.9125i	0.641677	−	1.11142i
$426$		0			0
$427$	−5.45151	−	9.44229i	−0.263817	−	0.456944i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−25.5079			−1.22867			−0.614336	−	0.789045i	$-0.710576\pi$
$431$	−25.5079			−1.22867			−0.614336	+	0.789045i	$0.710576\pi$
$432$		0			0
$433$	29.4513			1.41534			0.707670	−	0.706543i	$-0.249746\pi$
$433$	29.4513			1.41534			0.707670	+	0.706543i	$0.249746\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.08823	−	10.5451i	−0.291239	−	0.504441i
$438$		0			0
$439$	−17.8086	+	30.8454i	−0.849959	+	1.47217i	0.0312845	+	0.999511i	$0.490040\pi$
$439$	−17.8086	+	30.8454i	−0.849959	+	1.47217i	−0.881244	+	0.472662i	$0.843293\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.60886	+	11.4469i	−0.313996	+	0.543857i	−0.979224	−	0.202783i	$-0.935001\pi$
$443$	−6.60886	+	11.4469i	−0.313996	+	0.543857i	0.665227	+	0.746641i	$0.268335\pi$
$444$		0			0
$445$	−11.7820	−	20.4071i	−0.558522	−	0.967389i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5.83739			0.275483			0.137742	−	0.990468i	$-0.456016\pi$
$449$	5.83739			0.275483			0.137742	+	0.990468i	$0.456016\pi$
$450$		0			0
$451$	15.9545			0.751269
$452$		0			0
$453$		0			0
$454$		0			0
$455$	25.3755	+	43.9517i	1.18962	+	2.06049i
$456$		0			0
$457$	−13.5037	+	23.3891i	−0.631677	+	1.09410i	0.355532	+	0.934664i	$0.384300\pi$
$457$	−13.5037	+	23.3891i	−0.631677	+	1.09410i	−0.987209	+	0.159433i	$0.949034\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.78550	+	3.09258i	−0.0831591	+	0.144036i	−0.904605	−	0.426250i	$-0.859834\pi$
$461$	−1.78550	+	3.09258i	−0.0831591	+	0.144036i	0.821446	+	0.570286i	$0.193168\pi$
$462$		0			0
$463$	19.8396	+	34.3631i	0.922023	+	1.59699i	0.796281	+	0.604927i	$0.206798\pi$
$463$	19.8396	+	34.3631i	0.922023	+	1.59699i	0.125742	+	0.992063i	$0.459869\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.8522			−0.872376			−0.436188	−	0.899855i	$-0.643672\pi$
$467$	−18.8522			−0.872376			−0.436188	+	0.899855i	$0.643672\pi$
$468$		0			0
$469$	−13.7366			−0.634299
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.49197	−	9.51237i	−0.252521	−	0.437379i
$474$		0			0
$475$	−13.0196	+	22.5506i	−0.597381	+	1.03469i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.0879	−	19.2049i	0.506621	−	0.877492i	−0.493350	−	0.869831i	$-0.664228\pi$
$479$	11.0879	−	19.2049i	0.506621	−	0.877492i	0.999971	−	0.00766167i	$-0.00243881\pi$
$480$		0			0
$481$	4.93558	+	8.54867i	0.225043	+	0.389786i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−39.5505			−1.79590
$486$		0			0
$487$	17.9432			0.813086			0.406543	−	0.913632i	$-0.366734\pi$
$487$	17.9432			0.813086			0.406543	+	0.913632i	$0.366734\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.71919	+	2.97773i	0.0775861	+	0.134383i	0.902208	−	0.431301i	$-0.141945\pi$
$491$	1.71919	+	2.97773i	0.0775861	+	0.134383i	−0.824622	+	0.565684i	$0.808612\pi$
$492$		0			0
$493$	5.16431	−	8.94485i	0.232589	−	0.402856i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.32036	+	2.28693i	−0.0592262	+	0.102583i
$498$		0			0
$499$	−5.41124	−	9.37254i	−0.242240	−	0.419572i	0.719112	−	0.694894i	$-0.244549\pi$
$499$	−5.41124	−	9.37254i	−0.242240	−	0.419572i	−0.961352	+	0.275322i	$0.911216\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.71510			0.433175			0.216587	−	0.976263i	$-0.430507\pi$
$503$	9.71510			0.433175			0.216587	+	0.976263i	$0.430507\pi$
$504$		0			0
$505$	−6.12240			−0.272443
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.5991	+	30.4825i	0.780066	+	1.35111i	0.931903	+	0.362708i	$0.118148\pi$
$509$	17.5991	+	30.4825i	0.780066	+	1.35111i	−0.151837	+	0.988406i	$0.548519\pi$
$510$		0			0
$511$	2.73138	−	4.73090i	0.120829	−	0.209283i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.3025	+	19.5766i	−0.498049	+	0.862646i
$516$		0			0
$517$	10.7960	+	18.6991i	0.474806	+	0.822387i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.57440			0.331840			0.165920	−	0.986139i	$-0.446941\pi$
$521$	7.57440			0.331840			0.165920	+	0.986139i	$0.446941\pi$
$522$		0			0
$523$	−10.0630			−0.440025			−0.220013	−	0.975497i	$-0.570610\pi$
$523$	−10.0630			−0.440025			−0.220013	+	0.975497i	$0.570610\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.88890	+	10.1999i	0.256525	+	0.444314i
$528$		0			0
$529$	−12.1943	+	21.1211i	−0.530187	+	0.918310i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−14.4699	+	25.0625i	−0.626759	+	1.08558i
$534$		0			0
$535$	−38.2051	−	66.1732i	−1.65175	−	2.86092i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.17574			−0.136789
$540$		0			0
$541$	−26.2133			−1.12700			−0.563498	−	0.826117i	$-0.690545\pi$
$541$	−26.2133			−1.12700			−0.563498	+	0.826117i	$0.690545\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.6404	−	25.3580i	−0.627127	−	1.08622i
$546$		0			0
$547$	−9.57620	+	16.5865i	−0.409449	+	0.709186i	−0.994828	−	0.101574i	$-0.967612\pi$
$547$	−9.57620	+	16.5865i	−0.409449	+	0.709186i	0.585379	+	0.810760i	$0.300946\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.08276	+	8.80359i	−0.216533	+	0.375046i
$552$		0			0
$553$	−3.59823	−	6.23232i	−0.153012	−	0.265025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.5019			−0.953435			−0.476717	−	0.879057i	$-0.658173\pi$
$557$	−22.5019			−0.953435			−0.476717	+	0.879057i	$0.658173\pi$
$558$		0			0
$559$	19.9236			0.842680
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.7085	+	22.0118i	0.535599	+	0.927685i	0.999134	+	0.0416066i	$0.0132476\pi$
$563$	12.7085	+	22.0118i	0.535599	+	0.927685i	−0.463535	+	0.886079i	$0.653419\pi$
$564$		0			0
$565$	39.5268	−	68.4625i	1.66291	−	2.88024i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.14798	+	15.8448i	−0.383503	+	0.664247i	−0.991560	−	0.129646i	$-0.958616\pi$
$569$	−9.14798	+	15.8448i	−0.383503	+	0.664247i	0.608057	+	0.793893i	$0.291949\pi$
$570$		0			0
$571$	−1.27484	−	2.20808i	−0.0533503	−	0.0924054i	0.838117	−	0.545491i	$-0.183657\pi$
$571$	−1.27484	−	2.20808i	−0.0533503	−	0.0924054i	−0.891467	+	0.453085i	$0.850323\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	101.340			4.22617
$576$		0			0
$577$	2.22842			0.0927702			0.0463851	−	0.998924i	$-0.485230\pi$
$577$	2.22842			0.0927702			0.0463851	+	0.998924i	$0.485230\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.17892	+	5.50606i	0.131884	+	0.228430i
$582$		0			0
$583$	−3.57939	+	6.19968i	−0.148243	+	0.256765i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.2694	−	26.4473i	0.630234	−	1.09160i	−0.357270	−	0.934001i	$-0.616292\pi$
$587$	15.2694	−	26.4473i	0.630234	−	1.09160i	0.987504	−	0.157596i	$-0.0503743\pi$
$588$		0			0
$589$	−5.79591	−	10.0388i	−0.238816	−	0.413642i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.96281			0.244863			0.122432	−	0.992477i	$-0.460931\pi$
$593$	5.96281			0.244863			0.122432	+	0.992477i	$0.460931\pi$
$594$		0			0
$595$	−23.2231			−0.952055
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.29265	−	7.43508i	−0.175393	−	0.303789i	0.764904	−	0.644144i	$-0.222786\pi$
$599$	−4.29265	−	7.43508i	−0.175393	−	0.303789i	−0.940297	+	0.340355i	$0.889453\pi$
$600$		0			0
$601$	1.44648	−	2.50538i	0.0590033	−	0.102197i	−0.835015	−	0.550227i	$-0.814541\pi$
$601$	1.44648	−	2.50538i	0.0590033	−	0.102197i	0.894018	+	0.448031i	$0.147874\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.0146	−	24.2739i	0.569773	−	0.986876i
$606$		0			0
$607$	−9.96773	−	17.2646i	−0.404577	−	0.700749i	0.589695	−	0.807626i	$-0.299248\pi$
$607$	−9.96773	−	17.2646i	−0.404577	−	0.700749i	−0.994272	+	0.106877i	$0.965915\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.1653			−1.58446
$612$		0			0
$613$	35.4941			1.43359			0.716797	−	0.697282i	$-0.245607\pi$
$613$	35.4941			1.43359			0.716797	+	0.697282i	$0.245607\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.6891	+	27.1743i	0.631618	+	1.09399i	0.987221	+	0.159357i	$0.0509422\pi$
$617$	15.6891	+	27.1743i	0.631618	+	1.09399i	−0.355603	+	0.934637i	$0.615724\pi$
$618$		0			0
$619$	−16.7289	+	28.9752i	−0.672389	+	1.16461i	0.304835	+	0.952405i	$0.401399\pi$
$619$	−16.7289	+	28.9752i	−0.672389	+	1.16461i	−0.977225	+	0.212207i	$0.931935\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.71987	+	13.3712i	−0.309290	+	0.535706i
$624$		0			0
$625$	−59.0543	−	102.285i	−2.36217	−	4.09140i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.51694			−0.180102
$630$		0			0
$631$	8.12216			0.323338			0.161669	−	0.986845i	$-0.448312\pi$
$631$	8.12216			0.323338			0.161669	+	0.986845i	$0.448312\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−40.4691	−	70.0945i	−1.60597	−	2.78162i
$636$		0			0
$637$	2.88022	−	4.98869i	0.114119	−	0.197659i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.4782	−	18.1488i	0.413865	−	0.716836i	−0.581443	−	0.813587i	$-0.697512\pi$
$641$	10.4782	−	18.1488i	0.413865	−	0.716836i	0.995309	+	0.0967511i	$0.0308451\pi$
$642$		0			0
$643$	−16.3547	−	28.3272i	−0.644967	−	1.11712i	−0.984309	−	0.176453i	$-0.943538\pi$
$643$	−16.3547	−	28.3272i	−0.644967	−	1.11712i	0.339342	−	0.940663i	$-0.389796\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.7820			0.738395			0.369198	−	0.929351i	$-0.379633\pi$
$647$	18.7820			0.738395			0.369198	+	0.929351i	$0.379633\pi$
$648$		0			0
$649$	9.96410			0.391125
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.85977	−	8.41736i	−0.190177	−	0.329397i	0.755132	−	0.655573i	$-0.227573\pi$
$653$	−4.85977	−	8.41736i	−0.190177	−	0.329397i	−0.945309	+	0.326176i	$0.894240\pi$
$654$		0			0
$655$	−19.2314	+	33.3098i	−0.751435	+	1.30152i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.1773	−	28.0198i	0.630177	−	1.09150i	−0.357338	−	0.933975i	$-0.616316\pi$
$659$	16.1773	−	28.0198i	0.630177	−	1.09150i	0.987515	−	0.157523i	$-0.0503510\pi$
$660$		0			0
$661$	−13.0319	−	22.5719i	−0.506883	−	0.877946i	−0.999968	−	0.00796563i	$-0.997464\pi$
$661$	−13.0319	−	22.5719i	−0.506883	−	0.877946i	0.493086	−	0.869981i	$-0.335869\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	22.8564			0.886333
$666$		0			0
$667$	39.5624			1.53186
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.05668	+	7.02637i	0.156606	+	0.271250i
$672$		0			0
$673$	16.6951	−	28.9167i	0.643549	−	1.11466i	−0.341086	−	0.940032i	$-0.610795\pi$
$673$	16.6951	−	28.9167i	0.643549	−	1.11466i	0.984635	−	0.174627i	$-0.0558719\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.6991	−	21.9955i	0.488065	−	0.845354i	−0.511840	−	0.859081i	$-0.671036\pi$
$677$	12.6991	−	21.9955i	0.488065	−	0.845354i	0.999906	+	0.0137265i	$0.00436941\pi$
$678$		0			0
$679$	12.9572	+	22.4425i	0.497252	+	0.861266i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−37.2800			−1.42648			−0.713241	−	0.700919i	$-0.752773\pi$
$683$	−37.2800			−1.42648			−0.713241	+	0.700919i	$0.752773\pi$
$684$		0			0
$685$	−6.87841			−0.262811
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.49261	−	11.2455i	−0.247349	−	0.428421i
$690$		0			0
$691$	6.41730	−	11.1151i	0.244126	−	0.422838i	−0.717760	−	0.696291i	$-0.754832\pi$
$691$	6.41730	−	11.1151i	0.244126	−	0.422838i	0.961885	+	0.273453i	$0.0881657\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	43.4591	−	75.2733i	1.64850	−	2.85528i
$696$		0			0
$697$	−6.62125	−	11.4683i	−0.250798	−	0.434395i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.89156			0.260290			0.130145	−	0.991495i	$-0.458456\pi$
$701$	6.89156			0.260290			0.130145	+	0.991495i	$0.458456\pi$
$702$		0			0
$703$	4.44561			0.167669
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.00577	+	3.47410i	0.0754347	+	0.130657i
$708$		0			0
$709$	10.1178	−	17.5246i	0.379983	−	0.658150i	−0.611076	−	0.791572i	$-0.709263\pi$
$709$	10.1178	−	17.5246i	0.379983	−	0.658150i	0.991059	+	0.133422i	$0.0425964\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−22.5566	+	39.0693i	−0.844753	+	1.46316i
$714$		0			0
$715$	−18.8829	−	32.7061i	−0.706180	−	1.22314i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	44.1706			1.64729			0.823643	−	0.567108i	$-0.191938\pi$
$719$	44.1706			1.64729			0.823643	+	0.567108i	$0.191938\pi$
$720$		0			0
$721$	14.8114			0.551604
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−42.3019	−	73.2690i	−1.57105	−	2.72114i
$726$		0			0
$727$	−7.29193	+	12.6300i	−0.270443	+	0.468421i	−0.968975	−	0.247158i	$-0.920503\pi$
$727$	−7.29193	+	12.6300i	−0.270443	+	0.468421i	0.698532	+	0.715578i	$0.253837\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.55842	+	7.89542i	−0.168599	+	0.292023i
$732$		0			0
$733$	16.4444	+	28.4826i	0.607388	+	1.05203i	0.991669	+	0.128811i	$0.0411161\pi$
$733$	16.4444	+	28.4826i	0.607388	+	1.05203i	−0.384281	+	0.923216i	$0.625551\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.2220			0.376531
$738$		0			0
$739$	−35.3966			−1.30208			−0.651042	−	0.759041i	$-0.725668\pi$
$739$	−35.3966			−1.30208			−0.651042	+	0.759041i	$0.725668\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.8177	+	32.5932i	0.690353	+	1.19573i	0.971722	+	0.236127i	$0.0758782\pi$
$743$	18.8177	+	32.5932i	0.690353	+	1.19573i	−0.281369	+	0.959600i	$0.590788\pi$
$744$		0			0
$745$	4.20098	−	7.27631i	0.153912	−	0.266584i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−25.0329	+	43.3582i	−0.914682	+	1.58427i
$750$		0			0
$751$	−8.38950	−	14.5310i	−0.306137	−	0.530245i	0.671377	−	0.741116i	$-0.265703\pi$
$751$	−8.38950	−	14.5310i	−0.306137	−	0.530245i	−0.977514	+	0.210871i	$0.932370\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−38.0073			−1.38323
$756$		0			0
$757$	19.4825			0.708103			0.354051	−	0.935226i	$-0.384804\pi$
$757$	19.4825			0.708103			0.354051	+	0.935226i	$0.384804\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.49573	+	16.4471i	0.344220	+	0.596206i	0.985212	−	0.171341i	$-0.0548101\pi$
$761$	9.49573	+	16.4471i	0.344220	+	0.596206i	−0.640992	+	0.767548i	$0.721477\pi$
$762$		0			0
$763$	−9.59276	+	16.6151i	−0.347281	+	0.601508i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.03688	+	15.6523i	−0.326303	+	0.565173i
$768$		0			0
$769$	21.2098	+	36.7365i	0.764846	+	1.32475i	0.940328	+	0.340270i	$0.110518\pi$
$769$	21.2098	+	36.7365i	0.764846	+	1.32475i	−0.175482	+	0.984483i	$0.556148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.55333			−0.0918368			−0.0459184	−	0.998945i	$-0.514621\pi$
$773$	−2.55333			−0.0918368			−0.0459184	+	0.998945i	$0.514621\pi$
$774$		0			0
$775$	96.4744			3.46546
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.51670	+	11.2872i	0.233485	+	0.404408i
$780$		0			0
$781$	0.982529	−	1.70179i	0.0351577	−	0.0608949i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.87046	−	17.0961i	0.352292	−	0.610188i
$786$		0			0
$787$	6.70128	+	11.6069i	0.238875	+	0.413743i	0.960392	−	0.278654i	$-0.0898882\pi$
$787$	6.70128	+	11.6069i	0.238875	+	0.413743i	−0.721517	+	0.692397i	$0.756555\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−51.7978			−1.84172
$792$		0			0
$793$	−14.7167			−0.522606
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.0873	+	27.8640i	0.569840	+	0.986992i	0.996581	+	0.0826182i	$0.0263282\pi$
$797$	16.0873	+	27.8640i	0.569840	+	0.986992i	−0.426741	+	0.904374i	$0.640338\pi$
$798$		0			0
$799$	8.96082	−	15.5206i	0.317011	−	0.549079i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.03253	+	3.52044i	−0.0717264	+	0.124234i
$804$		0			0
$805$	−44.4765	−	77.0355i	−1.56759	−	2.71515i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−34.7417			−1.22145			−0.610727	−	0.791841i	$-0.709123\pi$
$809$	−34.7417			−1.22145			−0.610727	+	0.791841i	$0.709123\pi$
$810$		0			0
$811$	−40.7570			−1.43117			−0.715587	−	0.698524i	$-0.753841\pi$
$811$	−40.7570			−1.43117			−0.715587	+	0.698524i	$0.753841\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−41.9255	−	72.6172i	−1.46859	−	2.54367i
$816$		0			0
$817$	4.48644	−	7.77074i	0.156961	−	0.271864i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.25420	+	14.2967i	−0.288073	+	0.498958i	−0.973350	−	0.229325i	$-0.926348\pi$
$821$	−8.25420	+	14.2967i	−0.288073	+	0.498958i	0.685276	+	0.728283i	$0.259681\pi$
$822$		0			0
$823$	2.28675	+	3.96078i	0.0797113	+	0.138064i	0.903125	−	0.429377i	$-0.141267\pi$
$823$	2.28675	+	3.96078i	0.0797113	+	0.138064i	−0.823414	+	0.567441i	$0.807934\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	47.2992			1.64475			0.822377	−	0.568943i	$-0.192648\pi$
$827$	47.2992			1.64475			0.822377	+	0.568943i	$0.192648\pi$
$828$		0			0
$829$	2.10329			0.0730501			0.0365251	−	0.999333i	$-0.488371\pi$
$829$	2.10329			0.0730501			0.0365251	+	0.999333i	$0.488371\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.31796	+	2.28277i	0.0456646	+	0.0790934i
$834$		0			0
$835$	19.1576	−	33.1820i	0.662977	−	1.14831i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.60255	−	7.97185i	0.158898	−	0.275219i	−0.775574	−	0.631257i	$-0.782539\pi$
$839$	4.60255	−	7.97185i	0.158898	−	0.275219i	0.934471	+	0.356038i	$0.115873\pi$
$840$		0			0
$841$	−2.01432	−	3.48891i	−0.0694595	−	0.120307i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.7718			0.370560
$846$		0			0
$847$	−18.3653			−0.631041
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−8.65075	−	14.9835i	−0.296544	−	0.513629i
$852$		0			0
$853$	−7.43348	+	12.8752i	−0.254518	+	0.440837i	−0.964764	−	0.263115i	$-0.915250\pi$
$853$	−7.43348	+	12.8752i	−0.254518	+	0.440837i	0.710247	+	0.703953i	$0.248583\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.9611	−	39.7698i	0.784337	−	1.35851i	−0.145058	−	0.989423i	$-0.546337\pi$
$857$	22.9611	−	39.7698i	0.784337	−	1.35851i	0.929394	−	0.369088i	$-0.120330\pi$
$858$		0			0
$859$	−14.6542	−	25.3818i	−0.499994	−	0.866015i	0.500006	−	0.866022i	$-0.333331\pi$
$859$	−14.6542	−	25.3818i	−0.499994	−	0.866015i	−1.00000		6.84699e-6i	$0.999998\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.5606			−0.802012			−0.401006	−	0.916075i	$-0.631339\pi$
$863$	−23.5606			−0.802012			−0.401006	+	0.916075i	$0.631339\pi$
$864$		0			0
$865$	−34.7651			−1.18205
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.67758	+	4.63771i	0.0908307	+	0.157323i
$870$		0			0
$871$	−9.27076	+	16.0574i	−0.314128	+	0.544085i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−62.8080	+	108.787i	−2.12330	+	3.67766i
$876$		0			0
$877$	−9.29438	−	16.0983i	−0.313849	−	0.543602i	0.665343	−	0.746538i	$-0.268285\pi$
$877$	−9.29438	−	16.0983i	−0.313849	−	0.543602i	−0.979192	+	0.202935i	$0.934952\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−24.6693			−0.831129			−0.415564	−	0.909564i	$-0.636416\pi$
$881$	−24.6693			−0.831129			−0.415564	+	0.909564i	$0.636416\pi$
$882$		0			0
$883$	−4.42122			−0.148786			−0.0743930	−	0.997229i	$-0.523702\pi$
$883$	−4.42122			−0.148786			−0.0743930	+	0.997229i	$0.523702\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.1558	+	38.3750i	0.743919	+	1.28851i	0.950698	+	0.310118i	$0.100369\pi$
$887$	22.1558	+	38.3750i	0.743919	+	1.28851i	−0.206779	+	0.978388i	$0.566298\pi$
$888$		0			0
$889$	−26.5163	+	45.9276i	−0.889328	+	1.54036i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.81931	+	15.2755i	−0.295127	+	0.511175i
$894$		0			0
$895$	30.2845	+	52.4543i	1.01230	+	1.75335i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	37.6628			1.25613
$900$		0			0
$901$	5.94190			0.197953
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.12059	+	1.94092i	0.0372497	+	0.0645183i
$906$		0			0
$907$	23.2939	−	40.3462i	0.773461	−	1.33967i	−0.162195	−	0.986759i	$-0.551857\pi$
$907$	23.2939	−	40.3462i	0.773461	−	1.33967i	0.935656	−	0.352914i	$-0.114809\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.29458	+	7.43844i	−0.142286	+	0.246446i	−0.928357	−	0.371690i	$-0.878779\pi$
$911$	−4.29458	+	7.43844i	−0.142286	+	0.246446i	0.786071	+	0.618136i	$0.212112\pi$
$912$		0			0
$913$	−2.36556	−	4.09727i	−0.0782886	−	0.135600i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.2018			0.832236
$918$		0			0
$919$	−41.7394			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$919$	−41.7394			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.78220	+	3.08686i	0.0586618	+	0.101605i
$924$		0			0
$925$	−18.4996	+	32.0422i	−0.608262	+	1.05354i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.5014	+	35.5094i	−0.672628	+	1.16503i	0.304528	+	0.952503i	$0.401501\pi$
$929$	−20.5014	+	35.5094i	−0.672628	+	1.16503i	−0.977156	+	0.212523i	$0.931832\pi$
$930$		0			0
$931$	−1.29715	−	2.24672i	−0.0425123	−	0.0736334i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	17.2812			0.565156
$936$		0			0
$937$	−10.1921			−0.332962			−0.166481	−	0.986045i	$-0.553240\pi$
$937$	−10.1921			−0.332962			−0.166481	+	0.986045i	$0.553240\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−20.7130	−	35.8761i	−0.675226	−	1.16953i	−0.976403	−	0.215958i	$-0.930713\pi$
$941$	−20.7130	−	35.8761i	−0.675226	−	1.16953i	0.301177	−	0.953568i	$-0.402621\pi$
$942$		0			0
$943$	25.3618	−	43.9279i	0.825894	−	1.43049i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.04880	−	1.81658i	0.0340815	−	0.0590309i	−0.848482	−	0.529225i	$-0.822483\pi$
$947$	1.04880	−	1.81658i	0.0340815	−	0.0590309i	0.882563	+	0.470194i	$0.155816\pi$
$948$		0			0
$949$	−3.68678	−	6.38569i	−0.119678	−	0.207288i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−31.7663			−1.02901			−0.514506	−	0.857487i	$-0.672025\pi$
$953$	−31.7663			−1.02901			−0.514506	+	0.857487i	$0.672025\pi$
$954$		0			0
$955$	88.8908			2.87644
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.25345	+	3.90309i	0.0727677	+	0.126037i
$960$		0			0
$961$	−5.97362	+	10.3466i	−0.192697	+	0.333762i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.81664	+	8.34267i	−0.155053	+	0.268560i
$966$		0			0
$967$	1.76817	+	3.06256i	0.0568605	+	0.0984853i	0.893055	−	0.449948i	$-0.148558\pi$
$967$	1.76817	+	3.06256i	0.0568605	+	0.0984853i	−0.836194	+	0.548434i	$0.815224\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.4727			0.689093			0.344546	−	0.938769i	$-0.388033\pi$
$971$	21.4727			0.689093			0.344546	+	0.938769i	$0.388033\pi$
$972$		0			0
$973$	−56.9508			−1.82576
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.6237	−	40.9174i	−0.755788	−	1.30906i	−0.944982	−	0.327124i	$-0.893921\pi$
$977$	−23.6237	−	40.9174i	−0.755788	−	1.30906i	0.189193	−	0.981940i	$-0.439413\pi$
$978$		0			0
$979$	5.74465	−	9.95003i	0.183600	−	0.318004i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.4576	+	37.1656i	−0.684390	+	1.18540i	0.289238	+	0.957257i	$0.406598\pi$
$983$	−21.4576	+	37.1656i	−0.684390	+	1.18540i	−0.973628	+	0.228141i	$0.926735\pi$
$984$		0			0
$985$	−12.6001	−	21.8239i	−0.401471	−	0.695368i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−34.9208			−1.11042
$990$		0			0
$991$	11.5080			0.365563			0.182782	−	0.983154i	$-0.441490\pi$
$991$	11.5080			0.365563			0.182782	+	0.983154i	$0.441490\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.5420	−	44.2401i	−0.809736	−	1.40250i
$996$		0			0
$997$	−8.46934	+	14.6693i	−0.268227	+	0.464582i	−0.968404	−	0.249387i	$-0.919771\pi$
$997$	−8.46934	+	14.6693i	−0.268227	+	0.464582i	0.700177	+	0.713969i	$0.253104\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3456.2.i.k.1153.1		12
3.2	odd	2		1152.2.i.i.385.2	✓	12
4.3	odd	2		3456.2.i.l.1153.1		12
8.3	odd	2		3456.2.i.j.1153.6		12
8.5	even	2		3456.2.i.i.1153.6		12
9.4	even	3	inner	3456.2.i.k.2305.1		12
9.5	odd	6		1152.2.i.i.769.2	yes	12
12.11	even	2		1152.2.i.k.385.5	yes	12
24.5	odd	2		1152.2.i.l.385.5	yes	12
24.11	even	2		1152.2.i.j.385.2	yes	12
36.23	even	6		1152.2.i.k.769.5	yes	12
36.31	odd	6		3456.2.i.l.2305.1		12
72.5	odd	6		1152.2.i.l.769.5	yes	12
72.13	even	6		3456.2.i.i.2305.6		12
72.59	even	6		1152.2.i.j.769.2	yes	12
72.67	odd	6		3456.2.i.j.2305.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.2	✓	12	3.2	odd	2
1152.2.i.i.769.2	yes	12	9.5	odd	6
1152.2.i.j.385.2	yes	12	24.11	even	2
1152.2.i.j.769.2	yes	12	72.59	even	6
1152.2.i.k.385.5	yes	12	12.11	even	2
1152.2.i.k.769.5	yes	12	36.23	even	6
1152.2.i.l.385.5	yes	12	24.5	odd	2
1152.2.i.l.769.5	yes	12	72.5	odd	6
3456.2.i.i.1153.6		12	8.5	even	2
3456.2.i.i.2305.6		12	72.13	even	6
3456.2.i.j.1153.6		12	8.3	odd	2
3456.2.i.j.2305.6		12	72.67	odd	6
3456.2.i.k.1153.1		12	1.1	even	1	trivial
3456.2.i.k.2305.1		12	9.4	even	3	inner
3456.2.i.l.1153.1		12	4.3	odd	2
3456.2.i.l.2305.1		12	36.31	odd	6

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:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22043 - 3.84590i) q^{5} +(-1.45488 + 2.51992i) q^{7} +O(q^{10})\)	\(q+(-2.22043 - 3.84590i) q^{5} +(-1.45488 + 2.51992i) q^{7} +(1.08263 - 1.87517i) q^{11} +(1.96377 + 3.40135i) q^{13} -1.79720 q^{17} +1.76882 q^{19} +(-3.44197 - 5.96166i) q^{23} +(-7.36062 + 12.7490i) q^{25} +(-2.87353 + 4.97710i) q^{29} +(-3.27671 - 5.67542i) q^{31} +12.9218 q^{35} +2.51332 q^{37} +(3.68420 + 6.38122i) q^{41} +(2.53640 - 4.39317i) q^{43} +(-4.98598 + 8.63597i) q^{47} +(-0.733339 - 1.27018i) q^{49} -3.30620 q^{53} -9.61562 q^{55} +(2.30090 + 3.98528i) q^{59} +(-1.87353 + 3.24505i) q^{61} +(8.72084 - 15.1049i) q^{65} +(2.36045 + 4.08841i) q^{67} +0.907539 q^{71} -1.87740 q^{73} +(3.15019 + 5.45629i) q^{77} +(-1.23661 + 2.14187i) q^{79} +(1.09251 - 1.89227i) q^{83} +(3.99056 + 6.91185i) q^{85} +5.30620 q^{89} -11.4282 q^{91} +(-3.92754 - 6.80271i) q^{95} +(4.45302 - 7.71286i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{5} - 6 q^{7}+O(q^{10}) \) 12 * q + 2 * q^5 - 6 * q^7	\( 12 q + 2 q^{5} - 6 q^{7} + 4 q^{11} + 10 q^{13} - 4 q^{17} - 4 q^{19} + 8 q^{23} - 14 q^{25} + 2 q^{29} - 8 q^{31} + 8 q^{35} + 2 q^{41} + 2 q^{43} - 14 q^{47} - 18 q^{49} - 24 q^{53} + 16 q^{55} + 6 q^{59} + 14 q^{61} + 8 q^{65} - 4 q^{67} - 28 q^{71} + 60 q^{73} - 2 q^{77} - 16 q^{79} + 24 q^{83} + 16 q^{85} + 48 q^{89} + 52 q^{91} - 20 q^{95} - 14 q^{97}+O(q^{100}) \) 12 * q + 2 * q^5 - 6 * q^7 + 4 * q^11 + 10 * q^13 - 4 * q^17 - 4 * q^19 + 8 * q^23 - 14 * q^25 + 2 * q^29 - 8 * q^31 + 8 * q^35 + 2 * q^41 + 2 * q^43 - 14 * q^47 - 18 * q^49 - 24 * q^53 + 16 * q^55 + 6 * q^59 + 14 * q^61 + 8 * q^65 - 4 * q^67 - 28 * q^71 + 60 * q^73 - 2 * q^77 - 16 * q^79 + 24 * q^83 + 16 * q^85 + 48 * q^89 + 52 * q^91 - 20 * q^95 - 14 * q^97

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