LMFDB - Embedded newform 1512.2.bu.a.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(881,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))

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

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

chi := DirichletCharacter("1512.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.bu (of order $6$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.1
Character	$\chi$	$=$	1512.881
Dual form			1512.2.bu.a.1385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91834 + 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +O(q^{10})$	$q+(-1.91834 + 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-0.585698 + 0.338153i) q^{11} +(4.22006 + 2.43645i) q^{13} +5.79523 q^{17} +4.22456i q^{19} +(-4.76574 - 2.75150i) q^{23} +(-4.86003 - 8.41782i) q^{25} +(6.85239 - 3.95623i) q^{29} +(-1.78257 - 1.02917i) q^{31} +(-8.19684 + 5.98768i) q^{35} -8.71513 q^{37} +(-4.84009 + 8.38328i) q^{41} +(3.57545 + 6.19287i) q^{43} +(0.666092 + 1.15370i) q^{47} +(4.71066 + 5.17781i) q^{49} +5.18304i q^{53} -2.59476i q^{55} +(-2.09619 + 3.63071i) q^{59} +(2.38178 - 1.37512i) q^{61} +(-16.1910 + 9.34787i) q^{65} +(-3.27636 + 5.67483i) q^{67} -11.1515i q^{71} +3.65100i q^{73} +(-1.77905 + 0.191621i) q^{77} +(-5.61720 - 9.72928i) q^{79} +(-4.61279 - 7.98959i) q^{83} +(-11.1172 + 19.2556i) q^{85} -1.79702 q^{89} +(7.60487 + 10.4107i) q^{91} +(-14.0368 - 8.10413i) q^{95} +(-2.60513 + 1.50407i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{23} - 24 q^{25} + 36 q^{29} + 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} - 12 q^{79} - 12 q^{91} + 108 q^{95}+O(q^{100}) $ 48 * q - 12 * q^23 - 24 * q^25 + 36 * q^29 + 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 - 12 * q^79 - 12 * q^91 + 108 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.91834	+	3.32266i	−0.857906	+	1.48594i	0.0160164	+	0.999872i	$0.494902\pi$
$5$	−1.91834	+	3.32266i	−0.857906	+	1.48594i	−0.873923	+	0.486065i	$0.838432\pi$
$6$		0			0
$7$	2.41978	+	1.06989i	0.914590	+	0.404382i
$7$	2.41978	+	1.06989i	0.914590	+	0.404382i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.585698	+	0.338153i	−0.176595	+	0.101957i	−0.585692	−	0.810534i	$-0.699177\pi$
$11$	−0.585698	+	0.338153i	−0.176595	+	0.101957i	0.409097	+	0.912491i	$0.365844\pi$
$12$		0			0
$13$	4.22006	+	2.43645i	1.17043	+	0.675751i	0.953782	−	0.300498i	$-0.0971530\pi$
$13$	4.22006	+	2.43645i	1.17043	+	0.675751i	0.216652	+	0.976249i	$0.430486\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.79523			1.40555			0.702775	−	0.711412i	$-0.251944\pi$
$17$	5.79523			1.40555			0.702775	+	0.711412i	$0.251944\pi$
$18$		0			0
$19$			4.22456i			0.969181i	0.874741	+	0.484590i	$0.161031\pi$
$19$			4.22456i			0.969181i	−0.874741	+	0.484590i	$0.838969\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.76574	−	2.75150i	−0.993725	−	0.573727i	−0.0873394	−	0.996179i	$-0.527836\pi$
$23$	−4.76574	−	2.75150i	−0.993725	−	0.573727i	−0.906386	+	0.422451i	$0.861170\pi$
$24$		0			0
$25$	−4.86003	−	8.41782i	−0.972006	−	1.68356i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.85239	−	3.95623i	1.27246	−	0.734653i	0.297007	−	0.954875i	$-0.404012\pi$
$29$	6.85239	−	3.95623i	1.27246	−	0.734653i	0.975450	+	0.220222i	$0.0706782\pi$
$30$		0			0
$31$	−1.78257	−	1.02917i	−0.320159	−	0.184844i	0.331305	−	0.943524i	$-0.392511\pi$
$31$	−1.78257	−	1.02917i	−0.320159	−	0.184844i	−0.651463	+	0.758680i	$0.725845\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.19684	+	5.98768i	−1.38552	+	1.01210i
$36$		0			0
$37$	−8.71513			−1.43276			−0.716380	−	0.697711i	$-0.754202\pi$
$37$	−8.71513			−1.43276			−0.716380	+	0.697711i	$0.754202\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.84009	+	8.38328i	−0.755895	+	1.30925i	0.189033	+	0.981971i	$0.439465\pi$
$41$	−4.84009	+	8.38328i	−0.755895	+	1.30925i	−0.944928	+	0.327278i	$0.893869\pi$
$42$		0			0
$43$	3.57545	+	6.19287i	0.545251	+	0.944403i	0.998591	+	0.0530654i	$0.0168992\pi$
$43$	3.57545	+	6.19287i	0.545251	+	0.944403i	−0.453340	+	0.891338i	$0.649767\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.666092	+	1.15370i	0.0971594	+	0.168285i	0.910508	−	0.413492i	$-0.135691\pi$
$47$	0.666092	+	1.15370i	0.0971594	+	0.168285i	−0.813348	+	0.581777i	$0.802358\pi$
$48$		0			0
$49$	4.71066	+	5.17781i	0.672951	+	0.739687i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			5.18304i			0.711945i	0.934496	+	0.355972i	$0.115850\pi$
$53$			5.18304i			0.711945i	−0.934496	+	0.355972i	$0.884150\pi$
$54$		0			0
$55$		−	2.59476i		−	0.349878i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.09619	+	3.63071i	−0.272901	+	0.472678i	−0.969603	−	0.244682i	$-0.921316\pi$
$59$	−2.09619	+	3.63071i	−0.272901	+	0.472678i	0.696703	+	0.717360i	$0.254650\pi$
$60$		0			0
$61$	2.38178	−	1.37512i	0.304956	−	0.176066i	−0.339711	−	0.940530i	$-0.610329\pi$
$61$	2.38178	−	1.37512i	0.304956	−	0.176066i	0.644667	+	0.764463i	$0.276996\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−16.1910	+	9.34787i	−2.00825	+	1.15946i
$66$		0			0
$67$	−3.27636	+	5.67483i	−0.400271	+	0.693290i	−0.993758	−	0.111553i	$-0.964417\pi$
$67$	−3.27636	+	5.67483i	−0.400271	+	0.693290i	0.593487	+	0.804844i	$0.297751\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.1515i		−	1.32344i	−0.749751	−	0.661721i	$-0.769827\pi$
$71$		−	11.1515i		−	1.32344i	0.749751	−	0.661721i	$-0.230173\pi$
$72$		0			0
$73$			3.65100i			0.427318i	0.976908	+	0.213659i	$0.0685381\pi$
$73$			3.65100i			0.427318i	−0.976908	+	0.213659i	$0.931462\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.77905	+	0.191621i	−0.202741	+	0.0218372i
$78$		0			0
$79$	−5.61720	−	9.72928i	−0.631985	−	1.09463i	−0.987145	−	0.159825i	$-0.948907\pi$
$79$	−5.61720	−	9.72928i	−0.631985	−	1.09463i	0.355161	−	0.934805i	$-0.384426\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.61279	−	7.98959i	−0.506320	−	0.876971i	−0.999973	−	0.00731261i	$-0.997672\pi$
$83$	−4.61279	−	7.98959i	−0.506320	−	0.876971i	0.493654	−	0.869659i	$-0.335661\pi$
$84$		0			0
$85$	−11.1172	+	19.2556i	−1.20583	+	2.08856i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.79702			−0.190484			−0.0952419	−	0.995454i	$-0.530362\pi$
$89$	−1.79702			−0.190484			−0.0952419	+	0.995454i	$0.530362\pi$
$90$		0			0
$91$	7.60487	+	10.4107i	0.797207	+	1.09134i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−14.0368	−	8.10413i	−1.44014	−	0.831466i
$96$		0			0
$97$	−2.60513	+	1.50407i	−0.264511	+	0.152715i	−0.626390	−	0.779509i	$-0.715468\pi$
$97$	−2.60513	+	1.50407i	−0.264511	+	0.152715i	0.361880	+	0.932225i	$0.382135\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.15494	+	7.19657i	0.413432	+	0.716085i	0.995262	−	0.0972249i	$-0.0309966\pi$
$101$	4.15494	+	7.19657i	0.413432	+	0.716085i	−0.581830	+	0.813310i	$0.697663\pi$
$102$		0			0
$103$	−6.74606	−	3.89484i	−0.664709	−	0.383770i	0.129360	−	0.991598i	$-0.458708\pi$
$103$	−6.74606	−	3.89484i	−0.664709	−	0.383770i	−0.794069	+	0.607828i	$0.792041\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	5.50520i		−	0.532207i	−0.963944	−	0.266104i	$-0.914264\pi$
$107$		−	5.50520i		−	0.532207i	0.963944	−	0.266104i	$-0.0857364\pi$
$108$		0			0
$109$	14.2890			1.36864			0.684320	−	0.729182i	$-0.260099\pi$
$109$	14.2890			1.36864			0.684320	+	0.729182i	$0.260099\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.58249	+	2.64570i	0.431085	+	0.248887i	0.699809	−	0.714330i	$-0.253269\pi$
$113$	4.58249	+	2.64570i	0.431085	+	0.248887i	−0.268724	+	0.963217i	$0.586602\pi$
$114$		0			0
$115$	18.2846	−	10.5566i	1.70505	−	0.984409i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.0232	+	6.20028i	1.28550	+	0.568379i
$120$		0			0
$121$	−5.27131	+	9.13017i	−0.479210	+	0.830015i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	18.1093			1.61975
$126$		0			0
$127$	−2.23048			−0.197923			−0.0989615	−	0.995091i	$-0.531552\pi$
$127$	−2.23048			−0.197923			−0.0989615	+	0.995091i	$0.531552\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.474634	−	0.822091i	0.0414690	−	0.0718264i	−0.844546	−	0.535483i	$-0.820130\pi$
$131$	0.474634	−	0.822091i	0.0414690	−	0.0718264i	0.886015	+	0.463657i	$0.153463\pi$
$132$		0			0
$133$	−4.51983	+	10.2225i	−0.391919	+	0.886403i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.4037	+	6.00658i	−0.888848	+	0.513177i	−0.873565	−	0.486707i	$-0.838198\pi$
$137$	−10.4037	+	6.00658i	−0.888848	+	0.513177i	−0.0152823	+	0.999883i	$0.504865\pi$
$138$		0			0
$139$	1.92937	+	1.11392i	0.163647	+	0.0944816i	0.579587	−	0.814911i	$-0.303214\pi$
$139$	1.92937	+	1.11392i	0.163647	+	0.0944816i	−0.415940	+	0.909392i	$0.636547\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.29557			−0.275590
$144$		0			0
$145$			30.3575i			2.52105i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.64079	−	3.25671i	−0.462111	−	0.266800i	0.250820	−	0.968034i	$-0.419300\pi$
$149$	−5.64079	−	3.25671i	−0.462111	−	0.266800i	−0.712932	+	0.701234i	$0.752633\pi$
$150$		0			0
$151$	−1.17106	−	2.02834i	−0.0952997	−	0.165064i	0.814434	−	0.580256i	$-0.197048\pi$
$151$	−1.17106	−	2.02834i	−0.0952997	−	0.165064i	−0.909734	+	0.415192i	$0.863714\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.83913	−	3.94857i	0.549332	−	0.317157i
$156$		0			0
$157$	−2.03731	−	1.17624i	−0.162595	−	0.0938742i	0.416495	−	0.909138i	$-0.363258\pi$
$157$	−2.03731	−	1.17624i	−0.162595	−	0.0938742i	−0.579089	+	0.815264i	$0.696592\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.58822	−	11.7569i	−0.676846	−	0.926570i
$162$		0			0
$163$	17.0419			1.33482			0.667412	−	0.744689i	$-0.267402\pi$
$163$	17.0419			1.33482			0.667412	+	0.744689i	$0.267402\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.89906	+	5.02133i	−0.224336	+	0.388562i	−0.956120	−	0.292975i	$-0.905355\pi$
$167$	−2.89906	+	5.02133i	−0.224336	+	0.388562i	0.731784	+	0.681537i	$0.238688\pi$
$168$		0			0
$169$	5.37261	+	9.30563i	0.413278	+	0.715818i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.97021	+	3.41251i	0.149792	+	0.259448i	0.931151	−	0.364635i	$-0.118806\pi$
$173$	1.97021	+	3.41251i	0.149792	+	0.259448i	−0.781358	+	0.624083i	$0.785473\pi$
$174$		0			0
$175$	−2.75403	−	25.5690i	−0.208185	−	1.93283i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			6.52749i			0.487888i	0.969789	+	0.243944i	$0.0784412\pi$
$179$			6.52749i			0.487888i	−0.969789	+	0.243944i	$0.921559\pi$
$180$		0			0
$181$			6.39901i			0.475635i	0.971310	+	0.237817i	$0.0764320\pi$
$181$			6.39901i			0.475635i	−0.971310	+	0.237817i	$0.923568\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	16.7186	−	28.9574i	1.22917	−	2.12899i
$186$		0			0
$187$	−3.39426	+	1.95967i	−0.248213	+	0.143306i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	15.5755	−	8.99253i	1.12701	−	0.650677i	0.183825	−	0.982959i	$-0.441152\pi$
$191$	15.5755	−	8.99253i	1.12701	−	0.650677i	0.943180	+	0.332282i	$0.107819\pi$
$192$		0			0
$193$	7.67270	−	13.2895i	0.552293	−	0.956599i	−0.445816	−	0.895125i	$-0.647086\pi$
$193$	7.67270	−	13.2895i	0.552293	−	0.956599i	0.998109	−	0.0614746i	$-0.0195803\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	11.3420i		−	0.808086i	−0.914740	−	0.404043i	$-0.867605\pi$
$197$		−	11.3420i		−	0.808086i	0.914740	−	0.404043i	$-0.132395\pi$
$198$		0			0
$199$		−	11.2568i		−	0.797971i	−0.916957	−	0.398986i	$-0.869362\pi$
$199$		−	11.2568i		−	0.797971i	0.916957	−	0.398986i	$-0.130638\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	20.8140	−	2.24187i	1.46086	−	0.157348i
$204$		0			0
$205$	−18.5698	−	32.1639i	−1.29697	−	2.24643i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.42855	−	2.47432i	−0.0988147	−	0.171152i
$210$		0			0
$211$	−3.79773	+	6.57785i	−0.261446	+	0.452838i	−0.966626	−	0.256190i	$-0.917533\pi$
$211$	−3.79773	+	6.57785i	−0.261446	+	0.452838i	0.705180	+	0.709028i	$0.250866\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−27.4357			−1.87110
$216$		0			0
$217$	−3.21232	−	4.39751i	−0.218067	−	0.298522i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	24.4562	+	14.1198i	1.64510	+	0.949801i
$222$		0			0
$223$	20.2215	−	11.6749i	1.35413	−	0.781807i	0.365304	−	0.930888i	$-0.380965\pi$
$223$	20.2215	−	11.6749i	1.35413	−	0.781807i	0.988825	+	0.149081i	$0.0476316\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.81056	+	13.5283i	0.518405	+	0.897904i	0.999771	+	0.0213844i	$0.00680739\pi$
$227$	7.81056	+	13.5283i	0.518405	+	0.897904i	−0.481366	+	0.876520i	$0.659859\pi$
$228$		0			0
$229$	−9.15650	−	5.28651i	−0.605078	−	0.349342i	0.165959	−	0.986133i	$-0.446928\pi$
$229$	−9.15650	−	5.28651i	−0.605078	−	0.349342i	−0.771037	+	0.636791i	$0.780262\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			5.08862i			0.333367i	0.986010	+	0.166683i	$0.0533057\pi$
$233$			5.08862i			0.333367i	−0.986010	+	0.166683i	$0.946694\pi$
$234$		0			0
$235$	−5.11115			−0.333415
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.73315	+	3.88739i	0.435531	+	0.251454i	0.701700	−	0.712472i	$-0.252425\pi$
$239$	6.73315	+	3.88739i	0.435531	+	0.251454i	−0.266169	+	0.963926i	$0.585758\pi$
$240$		0			0
$241$	21.5690	−	12.4529i	1.38938	−	0.802161i	0.396137	−	0.918191i	$-0.370350\pi$
$241$	21.5690	−	12.4529i	1.38938	−	0.802161i	0.993246	+	0.116030i	$0.0370170\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−26.2407	+	5.71911i	−1.67646	+	0.365380i
$246$		0			0
$247$	−10.2929	+	17.8279i	−0.654924	+	1.13436i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.76999			0.616676			0.308338	−	0.951277i	$-0.400227\pi$
$251$	9.76999			0.616676			0.308338	+	0.951277i	$0.400227\pi$
$252$		0			0
$253$	3.72171			0.233982
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.49085	+	12.9745i	−0.467267	+	0.809329i	−0.999301	−	0.0373936i	$-0.988094\pi$
$257$	−7.49085	+	12.9745i	−0.467267	+	0.809329i	0.532034	+	0.846723i	$0.321428\pi$
$258$		0			0
$259$	−21.0887	−	9.32427i	−1.31039	−	0.579382i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.3343	+	8.27590i	−0.883889	+	0.510314i	−0.871939	−	0.489615i	$-0.837137\pi$
$263$	−14.3343	+	8.27590i	−0.883889	+	0.510314i	−0.0119504	+	0.999929i	$0.503804\pi$
$264$		0			0
$265$	−17.2214	−	9.94281i	−1.05791	−	0.610782i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.269785			−0.0164491			−0.00822455	−	0.999966i	$-0.502618\pi$
$269$	−0.269785			−0.0164491			−0.00822455	+	0.999966i	$0.502618\pi$
$270$		0			0
$271$		−	13.3371i		−	0.810172i	−0.914279	−	0.405086i	$-0.867242\pi$
$271$		−	13.3371i		−	0.810172i	0.914279	−	0.405086i	$-0.132758\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.69302	+	3.28687i	0.343302	+	0.198205i
$276$		0			0
$277$	−1.03411	−	1.79113i	−0.0621336	−	0.107619i	0.833285	−	0.552843i	$-0.186457\pi$
$277$	−1.03411	−	1.79113i	−0.0621336	−	0.107619i	−0.895419	+	0.445225i	$0.853124\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.06406	−	2.92374i	0.302096	−	0.174415i	−0.341288	−	0.939959i	$-0.610863\pi$
$281$	5.06406	−	2.92374i	0.302096	−	0.174415i	0.643384	+	0.765543i	$0.277530\pi$
$282$		0			0
$283$	−20.5862	−	11.8854i	−1.22372	−	0.706515i	−0.258011	−	0.966142i	$-0.583067\pi$
$283$	−20.5862	−	11.8854i	−1.22372	−	0.706515i	−0.965709	+	0.259626i	$0.916401\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.6812	+	15.1073i	−1.22077	+	0.891756i
$288$		0			0
$289$	16.5847			0.975572
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.47112	+	2.54805i	−0.0859437	+	0.148859i	−0.905793	−	0.423721i	$-0.860724\pi$
$293$	−1.47112	+	2.54805i	−0.0859437	+	0.148859i	0.819849	+	0.572579i	$0.194057\pi$
$294$		0			0
$295$	−8.04239	−	13.9298i	−0.468246	−	0.811026i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.4078	−	23.2230i	−0.775393	−	1.34302i
$300$		0			0
$301$	2.02610	+	18.8107i	0.116782	+	1.08423i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			10.5518i			0.604194i
$306$		0			0
$307$		−	22.8040i		−	1.30149i	−0.759296	−	0.650745i	$-0.774457\pi$
$307$		−	22.8040i		−	1.30149i	0.759296	−	0.650745i	$-0.225543\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.2514	−	26.4163i	0.864830	−	1.49793i	−0.00238601	−	0.999997i	$-0.500759\pi$
$311$	15.2514	−	26.4163i	0.864830	−	1.49793i	0.867216	−	0.497932i	$-0.165907\pi$
$312$		0			0
$313$	7.08223	−	4.08892i	0.400311	−	0.231120i	−0.286307	−	0.958138i	$-0.592428\pi$
$313$	7.08223	−	4.08892i	0.400311	−	0.231120i	0.686618	+	0.727018i	$0.259094\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.3445	−	7.12707i	0.693334	−	0.400296i	−0.111526	−	0.993762i	$-0.535574\pi$
$317$	12.3445	−	7.12707i	0.693334	−	0.400296i	0.804860	+	0.593465i	$0.202241\pi$
$318$		0			0
$319$	−2.67562	+	4.63431i	−0.149806	+	0.259472i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			24.4823i			1.36223i
$324$		0			0
$325$		−	47.3649i		−	2.62733i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.377453	+	3.50436i	0.0208097	+	0.193201i
$330$		0			0
$331$	10.0254	+	17.3646i	0.551048	+	0.954444i	0.998199	+	0.0599851i	$0.0191053\pi$
$331$	10.0254	+	17.3646i	0.551048	+	0.954444i	−0.447151	+	0.894458i	$0.647561\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.5703	−	21.7725i	−0.686791	−	1.18956i
$336$		0			0
$337$	14.6930	−	25.4490i	0.800378	−	1.38629i	−0.118990	−	0.992895i	$-0.537966\pi$
$337$	14.6930	−	25.4490i	0.800378	−	1.38629i	0.919368	−	0.393399i	$-0.128701\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.39206			0.0753844
$342$		0			0
$343$	5.85904	+	17.5691i	0.316358	+	0.948640i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.57973	−	0.912059i	−0.0848045	−	0.0489619i	0.456998	−	0.889468i	$-0.348925\pi$
$347$	−1.57973	−	0.912059i	−0.0848045	−	0.0489619i	−0.541803	+	0.840506i	$0.682258\pi$
$348$		0			0
$349$	−21.9455	+	12.6703i	−1.17472	+	0.678224i	−0.954787	−	0.297292i	$-0.903917\pi$
$349$	−21.9455	+	12.6703i	−1.17472	+	0.678224i	−0.219931	+	0.975515i	$0.570583\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.86705	+	11.8941i	0.365496	+	0.633058i	0.988856	−	0.148878i	$-0.0475661\pi$
$353$	6.86705	+	11.8941i	0.365496	+	0.633058i	−0.623360	+	0.781935i	$0.714233\pi$
$354$		0			0
$355$	37.0526	+	21.3924i	1.96655	+	1.13539i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			5.77932i			0.305021i	0.988302	+	0.152510i	$0.0487357\pi$
$359$			5.77932i			0.305021i	−0.988302	+	0.152510i	$0.951264\pi$
$360$		0			0
$361$	1.15309			0.0606891
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.1310	−	7.00385i	−0.634967	−	0.366598i
$366$		0			0
$367$	−29.9207	+	17.2747i	−1.56185	+	0.901734i	−0.564780	+	0.825242i	$0.691039\pi$
$367$	−29.9207	+	17.2747i	−1.56185	+	0.901734i	−0.997070	+	0.0764926i	$0.975628\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.54530	+	12.5418i	−0.287897	+	0.651138i
$372$		0			0
$373$	0.720369	−	1.24772i	0.0372993	−	0.0646043i	−0.846773	−	0.531954i	$-0.821458\pi$
$373$	0.720369	−	1.24772i	0.0372993	−	0.0646043i	0.884072	+	0.467350i	$0.154791\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	38.5567			1.98577
$378$		0			0
$379$	−4.53029			−0.232705			−0.116353	−	0.993208i	$-0.537120\pi$
$379$	−4.53029			−0.232705			−0.116353	+	0.993208i	$0.537120\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.49154	+	12.9757i	−0.382800	+	0.663029i	−0.991461	−	0.130401i	$-0.958373\pi$
$383$	−7.49154	+	12.9757i	−0.382800	+	0.663029i	0.608662	+	0.793430i	$0.291707\pi$
$384$		0			0
$385$	2.77612	−	6.27875i	0.141484	−	0.319995i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	32.3559	−	18.6807i	1.64051	−	0.947148i	0.659855	−	0.751393i	$-0.270617\pi$
$389$	32.3559	−	18.6807i	1.64051	−	0.947148i	0.980653	−	0.195755i	$-0.0627158\pi$
$390$		0			0
$391$	−27.6186	−	15.9456i	−1.39673	−	0.806403i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	43.1027			2.16873
$396$		0			0
$397$			18.4269i			0.924820i	0.886666	+	0.462410i	$0.153015\pi$
$397$			18.4269i			0.924820i	−0.886666	+	0.462410i	$0.846985\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	27.6794	+	15.9807i	1.38224	+	0.798038i	0.992425	−	0.122854i	$-0.0392046\pi$
$401$	27.6794	+	15.9807i	1.38224	+	0.798038i	0.389818	+	0.920892i	$0.372538\pi$
$402$		0			0
$403$	−5.01503	−	8.68628i	−0.249816	−	0.432695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.10444	−	2.94705i	0.253018	−	0.146080i
$408$		0			0
$409$	−1.67567	−	0.967449i	−0.0828566	−	0.0478373i	0.457999	−	0.888953i	$-0.348566\pi$
$409$	−1.67567	−	0.967449i	−0.0828566	−	0.0478373i	−0.540856	+	0.841115i	$0.681900\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.95678	+	6.54281i	−0.440734	+	0.321950i
$414$		0			0
$415$	35.3955			1.73750
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.0386	−	26.0476i	0.734684	−	1.27251i	−0.220178	−	0.975460i	$-0.570664\pi$
$419$	15.0386	−	26.0476i	0.734684	−	1.27251i	0.954862	−	0.297050i	$-0.0960029\pi$
$420$		0			0
$421$	1.17975	+	2.04338i	0.0574974	+	0.0995885i	0.893341	−	0.449379i	$-0.148355\pi$
$421$	1.17975	+	2.04338i	0.0574974	+	0.0995885i	−0.835844	+	0.548967i	$0.815021\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−28.1650	−	48.7832i	−1.36620	−	2.36633i
$426$		0			0
$427$	7.23462	−	0.779239i	0.350108	−	0.0377100i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	33.3518i		−	1.60650i	−0.595643	−	0.803249i	$-0.703103\pi$
$431$		−	33.3518i		−	1.60650i	0.595643	−	0.803249i	$-0.296897\pi$
$432$		0			0
$433$			11.9121i			0.572459i	0.958161	+	0.286229i	$0.0924019\pi$
$433$			11.9121i			0.572459i	−0.958161	+	0.286229i	$0.907598\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.6239	−	20.1331i	0.556045	−	0.963099i
$438$		0			0
$439$	−34.1958	+	19.7429i	−1.63207	+	0.942279i	−0.648622	+	0.761110i	$0.724655\pi$
$439$	−34.1958	+	19.7429i	−1.63207	+	0.942279i	−0.983452	+	0.181168i	$0.942012\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.7023	−	14.8392i	1.22115	−	0.705034i	0.255990	−	0.966679i	$-0.417598\pi$
$443$	25.7023	−	14.8392i	1.22115	−	0.705034i	0.965164	+	0.261645i	$0.0842651\pi$
$444$		0			0
$445$	3.44729	−	5.97088i	0.163417	−	0.283047i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	27.9245i		−	1.31784i	−0.752213	−	0.658920i	$-0.771014\pi$
$449$		−	27.9245i		−	1.31784i	0.752213	−	0.658920i	$-0.228986\pi$
$450$		0			0
$451$		−	6.54676i		−	0.308275i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−49.1798	+	5.29715i	−2.30559	+	0.248334i
$456$		0			0
$457$	18.0390	+	31.2444i	0.843828	+	1.46155i	0.886635	+	0.462469i	$0.153036\pi$
$457$	18.0390	+	31.2444i	0.843828	+	1.46155i	−0.0428078	+	0.999083i	$0.513630\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.34942	+	2.33727i	0.0628488	+	0.108857i	0.895738	−	0.444583i	$-0.146648\pi$
$461$	1.34942	+	2.33727i	0.0628488	+	0.108857i	−0.832889	+	0.553440i	$0.813315\pi$
$462$		0			0
$463$	14.9993	−	25.9796i	0.697077	−	1.20737i	−0.272399	−	0.962184i	$-0.587817\pi$
$463$	14.9993	−	25.9796i	0.697077	−	1.20737i	0.969476	−	0.245188i	$-0.0788497\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.1160			0.653211			0.326605	−	0.945161i	$-0.394095\pi$
$467$	14.1160			0.653211			0.326605	+	0.945161i	$0.394095\pi$
$468$		0			0
$469$	−13.9995	+	10.2265i	−0.646438	+	0.472214i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.18827	−	2.41810i	−0.192577	−	0.111184i
$474$		0			0
$475$	35.5616	−	20.5315i	1.63168	−	0.942049i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.3516	+	30.0538i	0.792815	+	1.37320i	0.924218	+	0.381866i	$0.124719\pi$
$479$	17.3516	+	30.0538i	0.792815	+	1.37320i	−0.131403	+	0.991329i	$0.541948\pi$
$480$		0			0
$481$	−36.7784	−	21.2340i	−1.67695	−	0.968188i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	11.5413i		−	0.524062i
$486$		0			0
$487$	36.2125			1.64094			0.820472	−	0.571686i	$-0.193711\pi$
$487$	36.2125			1.64094			0.820472	+	0.571686i	$0.193711\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−29.3233	−	16.9298i	−1.32334	−	0.764032i	−0.339082	−	0.940757i	$-0.610117\pi$
$491$	−29.3233	−	16.9298i	−1.32334	−	0.764032i	−0.984260	+	0.176724i	$0.943450\pi$
$492$		0			0
$493$	39.7112	−	22.9273i	1.78850	−	1.03259i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.9309	−	26.9842i	0.535175	−	1.21041i
$498$		0			0
$499$	−13.8586	+	24.0038i	−0.620395	+	1.07456i	0.369017	+	0.929423i	$0.379694\pi$
$499$	−13.8586	+	24.0038i	−0.620395	+	1.07456i	−0.989412	+	0.145133i	$0.953639\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.08643			0.405144			0.202572	−	0.979267i	$-0.435070\pi$
$503$	9.08643			0.405144			0.202572	+	0.979267i	$0.435070\pi$
$504$		0			0
$505$	−31.8823			−1.41874
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.7675	+	23.8461i	−0.610236	+	1.05696i	0.380965	+	0.924590i	$0.375592\pi$
$509$	−13.7675	+	23.8461i	−0.610236	+	1.05696i	−0.991200	+	0.132370i	$0.957741\pi$
$510$		0			0
$511$	−3.90619	+	8.83462i	−0.172799	+	0.390821i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	25.8824	−	14.9432i	1.14052	−	0.658478i
$516$		0			0
$517$	−0.780257	−	0.450482i	−0.0343157	−	0.0198122i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.47559			0.152268			0.0761341	−	0.997098i	$-0.475742\pi$
$521$	3.47559			0.152268			0.0761341	+	0.997098i	$0.475742\pi$
$522$		0			0
$523$			0.315295i			0.0137869i	0.999976	+	0.00689344i	$0.00219427\pi$
$523$			0.315295i			0.0137869i	−0.999976	+	0.00689344i	$0.997806\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.3304	−	5.96425i	−0.449999	−	0.259807i
$528$		0			0
$529$	3.64150	+	6.30727i	0.158326	+	0.274229i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−40.8509	+	23.5853i	−1.76945	+	1.02159i
$534$		0			0
$535$	18.2919	+	10.5608i	0.790827	+	0.456584i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.50991	−	1.43971i	−0.194256	−	0.0620128i
$540$		0			0
$541$	39.0741			1.67993			0.839964	−	0.542643i	$-0.182576\pi$
$541$	39.0741			1.67993			0.839964	+	0.542643i	$0.182576\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−27.4111	+	47.4775i	−1.17416	+	2.03371i
$546$		0			0
$547$	−0.609894	−	1.05637i	−0.0260772	−	0.0451670i	0.852692	−	0.522413i	$-0.174968\pi$
$547$	−0.609894	−	1.05637i	−0.0260772	−	0.0451670i	−0.878769	+	0.477246i	$0.841635\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	16.7133	+	28.9483i	0.712012	+	1.23324i
$552$		0			0
$553$	−3.18309	−	29.5525i	−0.135359	−	1.25670i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	0.456650i		−	0.0193489i	−0.999953	−	0.00967444i	$-0.996920\pi$
$557$		−	0.456650i		−	0.0193489i	0.999953	−	0.00967444i	$-0.00307952\pi$
$558$		0			0
$559$			34.8457i			1.47382i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.7680	−	27.3110i	0.664541	−	1.15102i	−0.314868	−	0.949135i	$-0.601960\pi$
$563$	15.7680	−	27.3110i	0.664541	−	1.15102i	0.979409	−	0.201884i	$-0.0647064\pi$
$564$		0			0
$565$	−17.5815	+	10.1507i	−0.739660	+	0.427043i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−24.1376	+	13.9359i	−1.01190	+	0.584221i	−0.911748	−	0.410751i	$-0.865267\pi$
$569$	−24.1376	+	13.9359i	−1.01190	+	0.584221i	−0.100153	+	0.994972i	$0.531933\pi$
$570$		0			0
$571$	−13.2588	+	22.9649i	−0.554864	+	0.961052i	0.443050	+	0.896497i	$0.353896\pi$
$571$	−13.2588	+	22.9649i	−0.554864	+	0.961052i	−0.997914	+	0.0645555i	$0.979437\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			53.4895i			2.23067i
$576$		0			0
$577$		−	6.69146i		−	0.278569i	−0.990252	−	0.139285i	$-0.955520\pi$
$577$		−	6.69146i		−	0.278569i	0.990252	−	0.139285i	$-0.0444803\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.61392	−	24.2682i	−0.108444	−	1.00682i
$582$		0			0
$583$	−1.75266	−	3.03569i	−0.0725877	−	0.125726i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.49388	−	6.05157i	−0.144208	−	0.249775i	0.784869	−	0.619661i	$-0.212730\pi$
$587$	−3.49388	−	6.05157i	−0.144208	−	0.249775i	−0.929077	+	0.369886i	$0.879397\pi$
$588$		0			0
$589$	4.34777	−	7.53056i	0.179147	−	0.310291i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	8.96766			0.368258			0.184129	−	0.982902i	$-0.441054\pi$
$593$	8.96766			0.368258			0.184129	+	0.982902i	$0.441054\pi$
$594$		0			0
$595$	−47.5026	+	34.7000i	−1.94742	+	1.42256i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	24.5323	+	14.1637i	1.00236	+	0.578714i	0.908946	−	0.416914i	$-0.136888\pi$
$599$	24.5323	+	14.1637i	1.00236	+	0.578714i	0.0934151	+	0.995627i	$0.470222\pi$
$600$		0			0
$601$	8.23991	−	4.75731i	0.336113	−	0.194055i	−0.322439	−	0.946590i	$-0.604503\pi$
$601$	8.23991	−	4.75731i	0.336113	−	0.194055i	0.658552	+	0.752535i	$0.271169\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20.2243	−	35.0295i	−0.822234	−	1.42415i
$606$		0			0
$607$	12.7545	+	7.36381i	0.517689	+	0.298888i	0.735988	−	0.676994i	$-0.236718\pi$
$607$	12.7545	+	7.36381i	0.517689	+	0.298888i	−0.218300	+	0.975882i	$0.570051\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			6.49160i			0.262622i
$612$		0			0
$613$	−8.63782			−0.348878			−0.174439	−	0.984668i	$-0.555811\pi$
$613$	−8.63782			−0.348878			−0.174439	+	0.984668i	$0.555811\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.8009	+	8.54533i	0.595864	+	0.344022i	0.767413	−	0.641154i	$-0.221544\pi$
$617$	14.8009	+	8.54533i	0.595864	+	0.344022i	−0.171549	+	0.985176i	$0.554877\pi$
$618$		0			0
$619$	9.66939	−	5.58263i	0.388646	−	0.224385i	−0.292928	−	0.956135i	$-0.594629\pi$
$619$	9.66939	−	5.58263i	0.388646	−	0.224385i	0.681573	+	0.731750i	$0.261296\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.34839	−	1.92262i	−0.174215	−	0.0770282i
$624$		0			0
$625$	−10.4396	+	18.0820i	−0.417585	+	0.723278i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−50.5062			−2.01382
$630$		0			0
$631$	−37.1187			−1.47767			−0.738835	−	0.673886i	$-0.764624\pi$
$631$	−37.1187			−1.47767			−0.738835	+	0.673886i	$0.764624\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.27881	−	7.41112i	0.169799	−	0.294101i
$636$		0			0
$637$	7.26376	+	33.3280i	0.287801	+	1.32050i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.1548	+	9.32700i	−0.638078	+	0.368395i	−0.783874	−	0.620920i	$-0.786759\pi$
$641$	−16.1548	+	9.32700i	−0.638078	+	0.368395i	0.145796	+	0.989315i	$0.453426\pi$
$642$		0			0
$643$	33.1356	+	19.1309i	1.30674	+	0.754448i	0.981551	−	0.191201i	$-0.0612381\pi$
$643$	33.1356	+	19.1309i	1.30674	+	0.754448i	0.325191	+	0.945648i	$0.394571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.28252			−0.0897350			−0.0448675	−	0.998993i	$-0.514287\pi$
$647$	−2.28252			−0.0897350			−0.0448675	+	0.998993i	$0.514287\pi$
$648$		0			0
$649$		−	2.83533i		−	0.111296i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	34.7684	+	20.0735i	1.36059	+	0.785538i	0.989703	−	0.143139i	$-0.0457197\pi$
$653$	34.7684	+	20.0735i	1.36059	+	0.785538i	0.370889	+	0.928677i	$0.379053\pi$
$654$		0			0
$655$	1.82102	+	3.15409i	0.0711530	+	0.123241i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−33.7362	+	19.4776i	−1.31418	+	0.758740i	−0.982785	−	0.184753i	$-0.940851\pi$
$659$	−33.7362	+	19.4776i	−1.31418	+	0.758740i	−0.331391	+	0.943493i	$0.607518\pi$
$660$		0			0
$661$	−7.33192	−	4.23309i	−0.285179	−	0.164648i	0.350587	−	0.936530i	$-0.385982\pi$
$661$	−7.33192	−	4.23309i	−0.285179	−	0.164648i	−0.635766	+	0.771882i	$0.719315\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−25.2953	−	34.6280i	−0.980910	−	1.34282i
$666$		0			0
$667$	−43.5423			−1.68596
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.930003	+	1.61081i	−0.0359024	+	0.0621848i
$672$		0			0
$673$	−8.72960	−	15.1201i	−0.336501	−	0.582837i	0.647271	−	0.762260i	$-0.275910\pi$
$673$	−8.72960	−	15.1201i	−0.336501	−	0.582837i	−0.983772	+	0.179423i	$0.942577\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24.5011	+	42.4372i	0.941654	+	1.63099i	0.762315	+	0.647206i	$0.224063\pi$
$677$	24.5011	+	42.4372i	0.941654	+	1.63099i	0.179339	+	0.983787i	$0.442604\pi$
$678$		0			0
$679$	−7.91303	+	0.852310i	−0.303674	+	0.0327087i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			22.1852i			0.848893i	0.905453	+	0.424446i	$0.139531\pi$
$683$			22.1852i			0.848893i	−0.905453	+	0.424446i	$0.860469\pi$
$684$		0			0
$685$		−	46.0905i		−	1.76103i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12.6282	+	21.8727i	−0.481097	+	0.833285i
$690$		0			0
$691$	−26.7708	+	15.4561i	−1.01841	+	0.587978i	−0.913642	−	0.406519i	$-0.866742\pi$
$691$	−26.7708	+	15.4561i	−1.01841	+	0.587978i	−0.104765	+	0.994497i	$0.533409\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.40236	+	4.27375i	−0.280788	+	0.162113i
$696$		0			0
$697$	−28.0495	+	48.5831i	−1.06245	+	1.84022i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			32.4719i			1.22645i	0.789910	+	0.613223i	$0.210127\pi$
$701$			32.4719i			1.22645i	−0.789910	+	0.613223i	$0.789873\pi$
$702$		0			0
$703$		−	36.8176i		−	1.38860i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.35447	+	21.8594i	0.0885491	+	0.822109i
$708$		0			0
$709$	−25.6834	−	44.4849i	−0.964560	−	1.67067i	−0.710792	−	0.703402i	$-0.751663\pi$
$709$	−25.6834	−	44.4849i	−0.964560	−	1.67067i	−0.253768	−	0.967265i	$-0.581670\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.66350	+	9.80947i	0.212100	+	0.367367i
$714$		0			0
$715$	6.32202	−	10.9501i	0.236430	−	0.409509i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−37.9805			−1.41643			−0.708216	−	0.705996i	$-0.750500\pi$
$719$	−37.9805			−1.41643			−0.708216	+	0.705996i	$0.750500\pi$
$720$		0			0
$721$	−12.1569	−	16.6422i	−0.452747	−	0.619789i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−66.6056	−	38.4548i	−2.47367	−	1.42817i
$726$		0			0
$727$	14.6498	−	8.45808i	0.543332	−	0.313693i	−0.203096	−	0.979159i	$-0.565101\pi$
$727$	14.6498	−	8.45808i	0.543332	−	0.313693i	0.746428	+	0.665466i	$0.231767\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.7206	+	35.8891i	0.766378	+	1.32741i
$732$		0			0
$733$	26.4599	+	15.2766i	0.977320	+	0.564256i	0.901460	−	0.432863i	$-0.142496\pi$
$733$	26.4599	+	15.2766i	0.977320	+	0.564256i	0.0758600	+	0.997118i	$0.475830\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	4.43165i		−	0.163242i
$738$		0			0
$739$	−23.0562			−0.848138			−0.424069	−	0.905630i	$-0.639399\pi$
$739$	−23.0562			−0.848138			−0.424069	+	0.905630i	$0.639399\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.88934	+	1.09081i	0.0693130	+	0.0400179i	0.534256	−	0.845323i	$-0.320592\pi$
$743$	1.88934	+	1.09081i	0.0693130	+	0.0400179i	−0.464943	+	0.885341i	$0.653925\pi$
$744$		0			0
$745$	21.6419	−	12.4949i	0.792897	−	0.457779i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.88997	−	13.3214i	0.215215	−	0.486752i
$750$		0			0
$751$	9.46865	−	16.4002i	0.345516	−	0.598451i	−0.639931	−	0.768432i	$-0.721037\pi$
$751$	9.46865	−	16.4002i	0.345516	−	0.598451i	0.985447	+	0.169981i	$0.0543706\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.98597			0.327033
$756$		0			0
$757$	11.6383			0.423002			0.211501	−	0.977378i	$-0.432165\pi$
$757$	11.6383			0.423002			0.211501	+	0.977378i	$0.432165\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.13819	+	7.16755i	−0.150009	+	0.259824i	−0.931231	−	0.364430i	$-0.881264\pi$
$761$	−4.13819	+	7.16755i	−0.150009	+	0.259824i	0.781221	+	0.624254i	$0.214597\pi$
$762$		0			0
$763$	34.5763	+	15.2877i	1.25174	+	0.553453i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.6921	+	10.2145i	−0.638824	+	0.368825i
$768$		0			0
$769$	45.8329	+	26.4616i	1.65277	+	0.954230i	0.975924	+	0.218110i	$0.0699890\pi$
$769$	45.8329	+	26.4616i	1.65277	+	0.954230i	0.676851	+	0.736120i	$0.263344\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.1905			0.402494			0.201247	−	0.979540i	$-0.435501\pi$
$773$	11.1905			0.402494			0.201247	+	0.979540i	$0.435501\pi$
$774$		0			0
$775$			20.0071i			0.718676i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−35.4157	−	20.4473i	−1.26890	−	0.732599i
$780$		0			0
$781$	3.77092	+	6.53142i	0.134934	+	0.233713i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.81648	−	4.51285i	0.278982	−	0.161070i
$786$		0			0
$787$	24.5820	+	14.1924i	0.876254	+	0.505905i	0.869421	−	0.494071i	$-0.164492\pi$
$787$	24.5820	+	14.1924i	0.876254	+	0.505905i	0.00683237	+	0.999977i	$0.497825\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	8.25800	+	11.3048i	0.293621	+	0.401952i
$792$		0			0
$793$	13.4017			0.475908
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.351421	+	0.608679i	−0.0124480	+	0.0215605i	−0.872182	−	0.489181i	$-0.837296\pi$
$797$	−0.351421	+	0.608679i	−0.0124480	+	0.0215605i	0.859734	+	0.510742i	$0.170629\pi$
$798$		0			0
$799$	3.86016	+	6.68599i	0.136562	+	0.236533i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.23460	−	2.13839i	−0.0435680	−	0.0754620i
$804$		0			0
$805$	55.5391	−	5.98210i	1.95749	−	0.210841i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	40.0190i		−	1.40699i	−0.710699	−	0.703496i	$-0.751621\pi$
$809$		−	40.0190i		−	1.40699i	0.710699	−	0.703496i	$-0.248379\pi$
$810$		0			0
$811$			16.5473i			0.581055i	0.956867	+	0.290528i	$0.0938309\pi$
$811$			16.5473i			0.581055i	−0.956867	+	0.290528i	$0.906169\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−32.6921	+	56.6243i	−1.14515	+	1.98346i
$816$		0			0
$817$	−26.1621	+	15.1047i	−0.915297	+	0.528447i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.7148	−	10.2277i	0.618251	−	0.356948i	−0.157937	−	0.987449i	$-0.550484\pi$
$821$	17.7148	−	10.2277i	0.618251	−	0.356948i	0.776188	+	0.630502i	$0.217151\pi$
$822$		0			0
$823$	1.49600	−	2.59115i	0.0521474	−	0.0903220i	−0.838773	−	0.544481i	$-0.816727\pi$
$823$	1.49600	−	2.59115i	0.0521474	−	0.0903220i	0.890921	+	0.454159i	$0.150060\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	37.3399i		−	1.29843i	−0.760603	−	0.649217i	$-0.775097\pi$
$827$		−	37.3399i		−	1.29843i	0.760603	−	0.649217i	$-0.224903\pi$
$828$		0			0
$829$		−	12.7334i		−	0.442250i	−0.975246	−	0.221125i	$-0.929027\pi$
$829$		−	12.7334i		−	0.442250i	0.975246	−	0.221125i	$-0.0709728\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	27.2993	+	30.0066i	0.945866	+	1.03967i
$834$		0			0
$835$	−11.1228	−	19.2652i	−0.384919	−	0.666699i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.35897	+	2.35381i	0.0469169	+	0.0812625i	0.888530	−	0.458818i	$-0.151727\pi$
$839$	1.35897	+	2.35381i	0.0469169	+	0.0812625i	−0.841613	+	0.540081i	$0.818394\pi$
$840$		0			0
$841$	16.8035	−	29.1045i	0.579431	−	1.00360i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−41.2259			−1.41821
$846$		0			0
$847$	−22.5237	+	16.4532i	−0.773923	+	0.565340i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	41.5340	+	23.9797i	1.42377	+	0.822013i
$852$		0			0
$853$	−43.6414	+	25.1964i	−1.49425	+	0.862707i	−0.999978	−	0.00659961i	$-0.997899\pi$
$853$	−43.6414	+	25.1964i	−1.49425	+	0.862707i	−0.494274	+	0.869306i	$0.664566\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.97633	−	15.5475i	−0.306626	−	0.531091i	0.670996	−	0.741461i	$-0.265867\pi$
$857$	−8.97633	−	15.5475i	−0.306626	−	0.531091i	−0.977622	+	0.210370i	$0.932533\pi$
$858$		0			0
$859$	11.0055	+	6.35400i	0.375501	+	0.216796i	0.675859	−	0.737031i	$-0.263773\pi$
$859$	11.0055	+	6.35400i	0.375501	+	0.216796i	−0.300358	+	0.953827i	$0.597106\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	2.05813i		−	0.0700595i	−0.999386	−	0.0350298i	$-0.988847\pi$
$863$		−	2.05813i		−	0.0700595i	0.999386	−	0.0350298i	$-0.0111526\pi$
$864$		0			0
$865$	−15.1181			−0.514031
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.57997	+	3.79895i	0.223210	+	0.128870i
$870$		0			0
$871$	−27.6529	+	15.9654i	−0.936983	+	0.540967i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	43.8205	+	19.3750i	1.48140	+	0.654996i
$876$		0			0
$877$	13.8077	−	23.9156i	0.466253	−	0.807574i	−0.533004	−	0.846113i	$-0.678937\pi$
$877$	13.8077	−	23.9156i	0.466253	−	0.807574i	0.999257	+	0.0385389i	$0.0122704\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	10.2629			0.345765			0.172882	−	0.984942i	$-0.444692\pi$
$881$	10.2629			0.345765			0.172882	+	0.984942i	$0.444692\pi$
$882$		0			0
$883$	49.8978			1.67919			0.839597	−	0.543210i	$-0.182791\pi$
$883$	49.8978			1.67919			0.839597	+	0.543210i	$0.182791\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.5367	−	21.7141i	0.420940	−	0.729089i	−0.575092	−	0.818089i	$-0.695034\pi$
$887$	12.5367	−	21.7141i	0.420940	−	0.729089i	0.996032	+	0.0889997i	$0.0283670\pi$
$888$		0			0
$889$	−5.39727	−	2.38638i	−0.181018	−	0.0800365i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.87389	+	2.81394i	−0.163099	+	0.0941650i
$894$		0			0
$895$	−21.6886	−	12.5219i	−0.724970	−	0.418562i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.2865			−0.543184
$900$		0			0
$901$			30.0369i			1.00067i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.2617	−	12.2755i	−0.706763	−	0.408050i
$906$		0			0
$907$	9.84739	+	17.0562i	0.326977	+	0.566341i	0.981911	−	0.189346i	$-0.0606366\pi$
$907$	9.84739	+	17.0562i	0.326977	+	0.566341i	−0.654933	+	0.755687i	$0.727303\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.9666	+	6.33157i	−0.363340	+	0.209774i	−0.670545	−	0.741869i	$-0.733940\pi$
$911$	−10.9666	+	6.33157i	−0.363340	+	0.209774i	0.307205	+	0.951643i	$0.400606\pi$
$912$		0			0
$913$	5.40340	+	3.11966i	0.178827	+	0.103246i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.02806	−	1.48147i	0.0669724	−	0.0489224i
$918$		0			0
$919$	−34.9422			−1.15264			−0.576318	−	0.817226i	$-0.695511\pi$
$919$	−34.9422			−1.15264			−0.576318	+	0.817226i	$0.695511\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	27.1701	−	47.0601i	0.894316	−	1.54900i
$924$		0			0
$925$	42.3558	+	73.3624i	1.39265	+	2.41214i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.9097	+	20.6283i	0.390746	+	0.676792i	0.992548	−	0.121853i	$-0.0388837\pi$
$929$	11.9097	+	20.6283i	0.390746	+	0.676792i	−0.601802	+	0.798645i	$0.705550\pi$
$930$		0			0
$931$	−21.8740	+	19.9004i	−0.716890	+	0.652211i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	15.0373i		−	0.491771i
$936$		0			0
$937$		−	30.0910i		−	0.983029i	−0.870869	−	0.491514i	$-0.836444\pi$
$937$		−	30.0910i		−	0.983029i	0.870869	−	0.491514i	$-0.163556\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.1672	−	19.3422i	0.364042	−	0.630539i	−0.624580	−	0.780961i	$-0.714730\pi$
$941$	11.1672	−	19.3422i	0.364042	−	0.630539i	0.988622	+	0.150422i	$0.0480632\pi$
$942$		0			0
$943$	46.1332	−	26.6350i	1.50230	−	0.867355i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.7683	+	18.3414i	−1.03233	+	0.596016i	−0.917651	−	0.397386i	$-0.869917\pi$
$947$	−31.7683	+	18.3414i	−1.03233	+	0.596016i	−0.114679	+	0.993403i	$0.536584\pi$
$948$		0			0
$949$	−8.89550	+	15.4075i	−0.288760	+	0.500147i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	23.4461i		−	0.759495i	−0.925090	−	0.379747i	$-0.876011\pi$
$953$		−	23.4461i		−	0.759495i	0.925090	−	0.379747i	$-0.123989\pi$
$954$		0			0
$955$			69.0028i			2.23288i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−31.6010	+	3.40374i	−1.02045	+	0.109912i
$960$		0			0
$961$	−13.3816	−	23.1777i	−0.431666	−	0.747667i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	29.4376	+	50.9875i	0.947631	+	1.64134i
$966$		0			0
$967$	21.2372	−	36.7839i	0.682941	−	1.18289i	−0.291138	−	0.956681i	$-0.594034\pi$
$967$	21.2372	−	36.7839i	0.682941	−	1.18289i	0.974079	−	0.226208i	$-0.0726329\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.9007			−0.414002			−0.207001	−	0.978341i	$-0.566370\pi$
$971$	−12.9007			−0.414002			−0.207001	+	0.978341i	$0.566370\pi$
$972$		0			0
$973$	3.47687	+	4.75966i	0.111463	+	0.152588i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.22775	−	2.44089i	−0.135258	−	0.0780911i	0.430844	−	0.902426i	$-0.358216\pi$
$977$	−4.22775	−	2.44089i	−0.135258	−	0.0780911i	−0.566102	+	0.824335i	$0.691549\pi$
$978$		0			0
$979$	1.05251	−	0.607668i	0.0336384	−	0.0194211i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.48312	+	16.4252i	0.302464	+	0.523884i	0.976694	−	0.214638i	$-0.0688573\pi$
$983$	9.48312	+	16.4252i	0.302464	+	0.523884i	−0.674229	+	0.738522i	$0.735524\pi$
$984$		0			0
$985$	37.6857	+	21.7578i	1.20077	+	0.693262i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	39.3514i		−	1.25130i
$990$		0			0
$991$	−34.1369			−1.08439			−0.542197	−	0.840251i	$-0.682407\pi$
$991$	−34.1369			−1.08439			−0.542197	+	0.840251i	$0.682407\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	37.4024	+	21.5943i	1.18573	+	0.684584i
$996$		0			0
$997$	9.92534	−	5.73040i	0.314339	−	0.181484i	−0.334528	−	0.942386i	$-0.608577\pi$
$997$	9.92534	−	5.73040i	0.314339	−	0.181484i	0.648866	+	0.760902i	$0.275243\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.bu.a.881.1		48
3.2	odd	2		504.2.bu.a.41.15	yes	48
4.3	odd	2		3024.2.cc.d.881.1		48
7.6	odd	2	inner	1512.2.bu.a.881.24		48
9.2	odd	6	inner	1512.2.bu.a.1385.24		48
9.4	even	3		4536.2.k.a.3401.48		48
9.5	odd	6		4536.2.k.a.3401.1		48
9.7	even	3		504.2.bu.a.209.10	yes	48
12.11	even	2		1008.2.cc.d.545.10		48
21.20	even	2		504.2.bu.a.41.10	✓	48
28.27	even	2		3024.2.cc.d.881.24		48
36.7	odd	6		1008.2.cc.d.209.15		48
36.11	even	6		3024.2.cc.d.2897.24		48
63.13	odd	6		4536.2.k.a.3401.2		48
63.20	even	6	inner	1512.2.bu.a.1385.1		48
63.34	odd	6		504.2.bu.a.209.15	yes	48
63.41	even	6		4536.2.k.a.3401.47		48
84.83	odd	2		1008.2.cc.d.545.15		48
252.83	odd	6		3024.2.cc.d.2897.1		48
252.223	even	6		1008.2.cc.d.209.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.10	✓	48	21.20	even	2
504.2.bu.a.41.15	yes	48	3.2	odd	2
504.2.bu.a.209.10	yes	48	9.7	even	3
504.2.bu.a.209.15	yes	48	63.34	odd	6
1008.2.cc.d.209.10		48	252.223	even	6
1008.2.cc.d.209.15		48	36.7	odd	6
1008.2.cc.d.545.10		48	12.11	even	2
1008.2.cc.d.545.15		48	84.83	odd	2
1512.2.bu.a.881.1		48	1.1	even	1	trivial
1512.2.bu.a.881.24		48	7.6	odd	2	inner
1512.2.bu.a.1385.1		48	63.20	even	6	inner
1512.2.bu.a.1385.24		48	9.2	odd	6	inner
3024.2.cc.d.881.1		48	4.3	odd	2
3024.2.cc.d.881.24		48	28.27	even	2
3024.2.cc.d.2897.1		48	252.83	odd	6
3024.2.cc.d.2897.24		48	36.11	even	6
4536.2.k.a.3401.1		48	9.5	odd	6
4536.2.k.a.3401.2		48	63.13	odd	6
4536.2.k.a.3401.47		48	63.41	even	6
4536.2.k.a.3401.48		48	9.4	even	3

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.bu (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91834 + 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +O(q^{10})\)	\(q+(-1.91834 + 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-0.585698 + 0.338153i) q^{11} +(4.22006 + 2.43645i) q^{13} +5.79523 q^{17} +4.22456i q^{19} +(-4.76574 - 2.75150i) q^{23} +(-4.86003 - 8.41782i) q^{25} +(6.85239 - 3.95623i) q^{29} +(-1.78257 - 1.02917i) q^{31} +(-8.19684 + 5.98768i) q^{35} -8.71513 q^{37} +(-4.84009 + 8.38328i) q^{41} +(3.57545 + 6.19287i) q^{43} +(0.666092 + 1.15370i) q^{47} +(4.71066 + 5.17781i) q^{49} +5.18304i q^{53} -2.59476i q^{55} +(-2.09619 + 3.63071i) q^{59} +(2.38178 - 1.37512i) q^{61} +(-16.1910 + 9.34787i) q^{65} +(-3.27636 + 5.67483i) q^{67} -11.1515i q^{71} +3.65100i q^{73} +(-1.77905 + 0.191621i) q^{77} +(-5.61720 - 9.72928i) q^{79} +(-4.61279 - 7.98959i) q^{83} +(-11.1172 + 19.2556i) q^{85} -1.79702 q^{89} +(7.60487 + 10.4107i) q^{91} +(-14.0368 - 8.10413i) q^{95} +(-2.60513 + 1.50407i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{23} - 24 q^{25} + 36 q^{29} + 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} - 12 q^{79} - 12 q^{91} + 108 q^{95}+O(q^{100}) \) 48 * q - 12 * q^23 - 24 * q^25 + 36 * q^29 + 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 - 12 * q^79 - 12 * q^91 + 108 * q^95

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