LMFDB - Embedded newform 3024.2.bf.i.2287.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1711,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 1]))

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

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

chi := DirichletCharacter("3024.1711");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bf (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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2287.3
Character	$\chi$	$=$	3024.2287
Dual form			3024.2.bf.i.1711.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +O(q^{10})$	$q-2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} -0.442942i q^{11} +(-1.96099 + 1.13218i) q^{13} +(-4.01950 + 2.32066i) q^{17} +(-3.30879 + 5.73100i) q^{19} +1.13645i q^{23} -0.514760 q^{25} +(-4.37712 + 7.58140i) q^{29} +(-2.32034 + 4.01894i) q^{31} +(0.877649 - 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-4.55283 + 2.62858i) q^{41} +(-3.81500 - 2.20259i) q^{43} +(2.67363 + 4.63087i) q^{47} +(6.72065 + 1.95776i) q^{49} +(1.54428 + 2.67478i) q^{53} -1.04018 q^{55} +(0.689570 - 1.19437i) q^{59} +(-8.88607 + 5.13038i) q^{61} +(2.65875 + 4.60510i) q^{65} +(2.10780 + 1.21694i) q^{67} -7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(0.165541 - 1.16016i) q^{77} +(7.26542 - 4.19469i) q^{79} +(7.87941 - 13.6475i) q^{83} +(5.44973 + 9.43920i) q^{85} +(-5.32537 - 3.07461i) q^{89} +(-5.55940 + 2.23255i) q^{91} +(13.4584 + 7.77021i) q^{95} +(14.9489 + 8.63074i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) $ 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$		−	2.34835i		−	1.05022i	−0.851036	−	0.525108i	$-0.824025\pi$
$5$		−	2.34835i		−	1.05022i	0.851036	−	0.525108i	$-0.175975\pi$
$6$		0			0
$7$	2.61922	+	0.373730i	0.989973	+	0.141257i
$7$	2.61922	+	0.373730i	0.989973	+	0.141257i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.442942i		−	0.133552i	−0.997768	−	0.0667761i	$-0.978729\pi$
$11$		−	0.442942i		−	0.133552i	0.997768	−	0.0667761i	$-0.0212713\pi$
$12$		0			0
$13$	−1.96099	+	1.13218i	−0.543881	+	0.314010i	−0.746650	−	0.665217i	$-0.768339\pi$
$13$	−1.96099	+	1.13218i	−0.543881	+	0.314010i	0.202769	+	0.979226i	$0.435006\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.01950	+	2.32066i	−0.974872	+	0.562843i	−0.900718	−	0.434404i	$-0.856959\pi$
$17$	−4.01950	+	2.32066i	−0.974872	+	0.562843i	−0.0741541	+	0.997247i	$0.523626\pi$
$18$		0			0
$19$	−3.30879	+	5.73100i	−0.759089	+	1.31478i	0.184227	+	0.982884i	$0.441022\pi$
$19$	−3.30879	+	5.73100i	−0.759089	+	1.31478i	−0.943316	+	0.331897i	$0.892311\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			1.13645i			0.236965i	0.992956	+	0.118483i	$0.0378030\pi$
$23$			1.13645i			0.236965i	−0.992956	+	0.118483i	$0.962197\pi$
$24$		0			0
$25$	−0.514760			−0.102952
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.37712	+	7.58140i	−0.812811	+	1.40783i	0.0980775	+	0.995179i	$0.468731\pi$
$29$	−4.37712	+	7.58140i	−0.812811	+	1.40783i	−0.910889	+	0.412652i	$0.864603\pi$
$30$		0			0
$31$	−2.32034	+	4.01894i	−0.416745	+	0.721824i	−0.995610	−	0.0935998i	$-0.970163\pi$
$31$	−2.32034	+	4.01894i	−0.416745	+	0.721824i	0.578865	+	0.815424i	$0.303496\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.877649	−	6.15086i	0.148350	−	1.03968i
$36$		0			0
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	−0.958491	−	0.285122i	$-0.907966\pi$
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	0.726169	+	0.687517i	$0.241299\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.55283	+	2.62858i	−0.711032	+	0.410515i	−0.811443	−	0.584431i	$-0.801318\pi$
$41$	−4.55283	+	2.62858i	−0.711032	+	0.410515i	0.100411	+	0.994946i	$0.467984\pi$
$42$		0			0
$43$	−3.81500	−	2.20259i	−0.581782	−	0.335892i	0.180059	−	0.983656i	$-0.442371\pi$
$43$	−3.81500	−	2.20259i	−0.581782	−	0.335892i	−0.761841	+	0.647764i	$0.775704\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.67363	+	4.63087i	0.389989	+	0.675481i	0.992448	−	0.122669i	$-0.0391453\pi$
$47$	2.67363	+	4.63087i	0.389989	+	0.675481i	−0.602458	+	0.798150i	$0.705812\pi$
$48$		0			0
$49$	6.72065	+	1.95776i	0.960093	+	0.279680i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.54428	+	2.67478i	0.212124	+	0.367409i	0.952379	−	0.304917i	$-0.0986287\pi$
$53$	1.54428	+	2.67478i	0.212124	+	0.367409i	−0.740255	+	0.672326i	$0.765295\pi$
$54$		0			0
$55$	−1.04018			−0.140259
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.689570	−	1.19437i	0.0897743	−	0.155494i	−0.817641	−	0.575728i	$-0.804719\pi$
$59$	0.689570	−	1.19437i	0.0897743	−	0.155494i	0.907416	+	0.420234i	$0.138052\pi$
$60$		0			0
$61$	−8.88607	+	5.13038i	−1.13775	+	0.656877i	−0.945871	−	0.324542i	$-0.894790\pi$
$61$	−8.88607	+	5.13038i	−1.13775	+	0.656877i	−0.191874	+	0.981420i	$0.561456\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.65875	+	4.60510i	0.329778	+	0.571192i
$66$		0			0
$67$	2.10780	+	1.21694i	0.257509	+	0.148673i	0.623198	−	0.782064i	$-0.285833\pi$
$67$	2.10780	+	1.21694i	0.257509	+	0.148673i	−0.365689	+	0.930737i	$0.619167\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.20644i		−	0.855247i	−0.903957	−	0.427623i	$-0.859351\pi$
$71$		−	7.20644i		−	0.855247i	0.903957	−	0.427623i	$-0.140649\pi$
$72$		0			0
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	−0.302341	−	0.953200i	$-0.597768\pi$
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	0.674325	+	0.738435i	$0.264435\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.165541	−	1.16016i	0.0188651	−	0.132213i
$78$		0			0
$79$	7.26542	−	4.19469i	0.817423	−	0.471939i	−0.0321039	−	0.999485i	$-0.510221\pi$
$79$	7.26542	−	4.19469i	0.817423	−	0.471939i	0.849527	+	0.527545i	$0.176887\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.87941	−	13.6475i	0.864878	−	1.49801i	−0.00229000	−	0.999997i	$-0.500729\pi$
$83$	7.87941	−	13.6475i	0.864878	−	1.49801i	0.867168	−	0.498015i	$-0.165938\pi$
$84$		0			0
$85$	5.44973	+	9.43920i	0.591106	+	1.02383i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.32537	−	3.07461i	−0.564488	−	0.325908i	0.190457	−	0.981696i	$-0.439003\pi$
$89$	−5.32537	−	3.07461i	−0.564488	−	0.325908i	−0.754945	+	0.655788i	$0.772336\pi$
$90$		0			0
$91$	−5.55940	+	2.23255i	−0.582783	+	0.234034i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	13.4584	+	7.77021i	1.38080	+	0.797207i
$96$		0			0
$97$	14.9489	+	8.63074i	1.51783	+	0.876319i	0.999780	+	0.0209677i	$0.00667473\pi$
$97$	14.9489	+	8.63074i	1.51783	+	0.876319i	0.518049	+	0.855351i	$0.326659\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			17.3667i			1.72806i	0.503444	+	0.864028i	$0.332066\pi$
$101$			17.3667i			1.72806i	−0.503444	+	0.864028i	$0.667934\pi$
$102$		0			0
$103$	−9.23888			−0.910334			−0.455167	−	0.890406i	$-0.650420\pi$
$103$	−9.23888			−0.910334			−0.455167	+	0.890406i	$0.650420\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.76296	−	4.48195i	−0.750474	−	0.433286i	0.0753911	−	0.997154i	$-0.475979\pi$
$107$	−7.76296	−	4.48195i	−0.750474	−	0.433286i	−0.825865	+	0.563868i	$0.809313\pi$
$108$		0			0
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	−0.989677	−	0.143315i	$-0.954224\pi$
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	0.370724	−	0.928743i	$-0.379110\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.12502	+	3.68064i	0.199905	+	0.346246i	0.948497	−	0.316785i	$-0.102603\pi$
$113$	2.12502	+	3.68064i	0.199905	+	0.346246i	−0.748592	+	0.663031i	$0.769270\pi$
$114$		0			0
$115$	2.66877			0.248864
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.3953	+	4.57612i	−1.04460	+	0.419492i
$120$		0			0
$121$	10.8038			0.982164
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	10.5329i		−	0.942094i
$126$		0			0
$127$		−	19.6660i		−	1.74507i	−0.488549	−	0.872536i	$-0.662474\pi$
$127$		−	19.6660i		−	1.74507i	0.488549	−	0.872536i	$-0.337526\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−17.0737			−1.49173			−0.745867	−	0.666095i	$-0.767965\pi$
$131$	−17.0737			−1.49173			−0.745867	+	0.666095i	$0.767965\pi$
$132$		0			0
$133$	−10.8083	+	13.7742i	−0.937199	+	1.19437i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.51361			0.300188			0.150094	−	0.988672i	$-0.452042\pi$
$137$	3.51361			0.300188			0.150094	+	0.988672i	$0.452042\pi$
$138$		0			0
$139$	8.66086	+	15.0011i	0.734605	+	1.27237i	0.954896	+	0.296939i	$0.0959658\pi$
$139$	8.66086	+	15.0011i	0.734605	+	1.27237i	−0.220292	+	0.975434i	$0.570701\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.501490	+	0.868606i	0.0419367	+	0.0726365i
$144$		0			0
$145$	17.8038	+	10.2790i	1.47853	+	0.853627i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.08533			0.498529			0.249265	−	0.968435i	$-0.419811\pi$
$149$	6.08533			0.498529			0.249265	+	0.968435i	$0.419811\pi$
$150$		0			0
$151$		−	2.61258i		−	0.212609i	−0.994334	−	0.106304i	$-0.966098\pi$
$151$		−	2.61258i		−	0.212609i	0.994334	−	0.106304i	$-0.0339018\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.43790	+	5.44897i	0.758070	+	0.437672i
$156$		0			0
$157$	16.2746	+	9.39612i	1.29885	+	0.749892i	0.980206	−	0.197982i	$-0.0634386\pi$
$157$	16.2746	+	9.39612i	1.29885	+	0.749892i	0.318646	+	0.947874i	$0.396772\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.424723	+	2.97660i	−0.0334729	+	0.234589i
$162$		0			0
$163$	−2.90466	−	1.67700i	−0.227510	−	0.131353i	0.381913	−	0.924198i	$-0.375266\pi$
$163$	−2.90466	−	1.67700i	−0.227510	−	0.131353i	−0.609423	+	0.792845i	$0.708599\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.58344	+	7.93876i	0.354678	+	0.614320i	0.987063	−	0.160335i	$-0.0512573\pi$
$167$	4.58344	+	7.93876i	0.354678	+	0.614320i	−0.632385	+	0.774654i	$0.717924\pi$
$168$		0			0
$169$	−3.93635	+	6.81795i	−0.302796	+	0.524458i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−19.6171	+	11.3260i	−1.49146	+	0.861097i	−0.999952	−	0.00977454i	$-0.996889\pi$
$173$	−19.6171	+	11.3260i	−1.49146	+	0.861097i	−0.491511	+	0.870871i	$0.663555\pi$
$174$		0			0
$175$	−1.34827	−	0.192381i	−0.101920	−	0.0145426i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−19.2752	+	11.1285i	−1.44069	+	0.831785i	−0.997896	−	0.0648357i	$-0.979348\pi$
$179$	−19.2752	+	11.1285i	−1.44069	+	0.831785i	−0.442799	+	0.896621i	$0.646014\pi$
$180$		0			0
$181$		−	4.33319i		−	0.322084i	−0.986948	−	0.161042i	$-0.948515\pi$
$181$		−	4.33319i		−	0.322084i	0.986948	−	0.161042i	$-0.0514854\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.74799	+	3.31861i	0.422601	+	0.243989i
$186$		0			0
$187$	1.02792	+	1.78041i	0.0751689	+	0.130196i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	21.5649	−	12.4505i	1.56038	−	0.900885i	0.563160	−	0.826348i	$-0.309585\pi$
$191$	21.5649	−	12.4505i	1.56038	−	0.900885i	0.997218	−	0.0745371i	$-0.0237479\pi$
$192$		0			0
$193$	−10.6627	+	18.4683i	−0.767517	+	1.32938i	0.171389	+	0.985204i	$0.445175\pi$
$193$	−10.6627	+	18.4683i	−0.767517	+	1.32938i	−0.938906	+	0.344175i	$0.888159\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.5315			−1.32032			−0.660158	−	0.751127i	$-0.729511\pi$
$197$	−18.5315			−1.32032			−0.660158	+	0.751127i	$0.729511\pi$
$198$		0			0
$199$	0.918721	+	1.59127i	0.0651264	+	0.112802i	0.896750	−	0.442537i	$-0.145922\pi$
$199$	0.918721	+	1.59127i	0.0651264	+	0.112802i	−0.831624	+	0.555340i	$0.812588\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−14.2981	+	18.2215i	−1.00353	+	1.27890i
$204$		0			0
$205$	6.17283	+	10.6916i	0.431129	+	0.746737i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.53850	+	1.46560i	0.175592	+	0.101378i
$210$		0			0
$211$	17.5295	−	10.1207i	1.20678	−	0.696735i	0.244725	−	0.969592i	$-0.421302\pi$
$211$	17.5295	−	10.1207i	1.20678	−	0.696735i	0.962054	+	0.272858i	$0.0879689\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.17246	+	8.95897i	−0.352759	+	0.610997i
$216$		0			0
$217$	−7.57948	+	9.65933i	−0.514529	+	0.655718i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.25480	−	9.10158i	0.353476	−	0.612239i
$222$		0			0
$223$	0.492098	−	0.852339i	0.0329533	−	0.0570768i	−0.849078	−	0.528267i	$-0.822842\pi$
$223$	0.492098	−	0.852339i	0.0329533	−	0.0570768i	0.882032	+	0.471190i	$0.156175\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.1928			0.875639			0.437820	−	0.899063i	$-0.355751\pi$
$227$	13.1928			0.875639			0.437820	+	0.899063i	$0.355751\pi$
$228$		0			0
$229$		−	5.67964i		−	0.375321i	−0.982234	−	0.187660i	$-0.939910\pi$
$229$		−	5.67964i		−	0.375321i	0.982234	−	0.187660i	$-0.0600905\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.42995	+	12.8691i	−0.486752	+	0.843080i	−0.999884	−	0.0152301i	$-0.995152\pi$
$233$	−7.42995	+	12.8691i	−0.486752	+	0.843080i	0.513132	+	0.858310i	$0.328485\pi$
$234$		0			0
$235$	10.8749	−	6.27863i	0.709401	−	0.409573i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−15.6484	+	9.03459i	−1.01221	+	0.584399i	−0.911837	−	0.410551i	$-0.865336\pi$
$239$	−15.6484	+	9.03459i	−1.01221	+	0.584399i	−0.100371	+	0.994950i	$0.532003\pi$
$240$		0			0
$241$		−	20.7503i		−	1.33664i	−0.743872	−	0.668322i	$-0.767013\pi$
$241$		−	20.7503i		−	1.33664i	0.743872	−	0.668322i	$-0.232987\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.59752	−	15.7825i	0.293725	−	1.00830i
$246$		0			0
$247$		−	14.9846i		−	0.953445i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.53037			0.601552			0.300776	−	0.953695i	$-0.402754\pi$
$251$	9.53037			0.601552			0.300776	+	0.953695i	$0.402754\pi$
$252$		0			0
$253$	0.503380			0.0316472
$254$		0			0
$255$		0			0
$256$		0			0
$257$			11.3949i			0.710796i	0.934715	+	0.355398i	$0.115655\pi$
$257$			11.3949i			0.710796i	−0.934715	+	0.355398i	$0.884345\pi$
$258$		0			0
$259$	−4.61616	+	5.88285i	−0.286834	+	0.365543i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			6.23768i			0.384632i	0.981333	+	0.192316i	$0.0615998\pi$
$263$			6.23768i			0.384632i	−0.981333	+	0.192316i	$0.938400\pi$
$264$		0			0
$265$	6.28132	−	3.62652i	0.385859	−	0.222776i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−22.5563	+	13.0229i	−1.37528	+	0.794018i	−0.991587	−	0.129443i	$-0.958681\pi$
$269$	−22.5563	+	13.0229i	−1.37528	+	0.794018i	−0.383693	+	0.923461i	$0.625348\pi$
$270$		0			0
$271$	−10.3180	+	17.8713i	−0.626775	+	1.08561i	0.361420	+	0.932403i	$0.382292\pi$
$271$	−10.3180	+	17.8713i	−0.626775	+	1.08561i	−0.988195	+	0.153203i	$0.951041\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			0.228009i			0.0137494i
$276$		0			0
$277$	−12.0722			−0.725350			−0.362675	−	0.931916i	$-0.618136\pi$
$277$	−12.0722			−0.725350			−0.362675	+	0.931916i	$0.618136\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.67299	−	6.36180i	0.219112	−	0.379513i	−0.735425	−	0.677606i	$-0.763017\pi$
$281$	3.67299	−	6.36180i	0.219112	−	0.379513i	0.954537	+	0.298093i	$0.0963507\pi$
$282$		0			0
$283$	8.65315	−	14.9877i	0.514376	−	0.890926i	−0.485484	−	0.874245i	$-0.661357\pi$
$283$	8.65315	−	14.9877i	0.514376	−	0.890926i	0.999861	−	0.0166808i	$-0.00530990\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.9072	+	5.18330i	−0.761891	+	0.305961i
$288$		0			0
$289$	2.27092	−	3.93336i	0.133584	−	0.231374i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.965862	+	0.557641i	−0.0564263	+	0.0325777i	−0.527948	−	0.849277i	$-0.677038\pi$
$293$	−0.965862	+	0.557641i	−0.0564263	+	0.0325777i	0.471521	+	0.881855i	$0.343705\pi$
$294$		0			0
$295$	−2.80480	−	1.61935i	−0.163302	−	0.0942823i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.28666	−	2.22856i	−0.0744094	−	0.128881i
$300$		0			0
$301$	−9.16916	−	7.19486i	−0.528502	−	0.414705i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.0479	+	20.8676i	0.689863	+	1.19488i
$306$		0			0
$307$	30.5465			1.74338			0.871690	−	0.490058i	$-0.163025\pi$
$307$	30.5465			1.74338			0.871690	+	0.490058i	$0.163025\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.44800	+	5.97210i	−0.195518	+	0.338647i	−0.947070	−	0.321027i	$-0.895972\pi$
$311$	−3.44800	+	5.97210i	−0.195518	+	0.338647i	0.751552	+	0.659674i	$0.229305\pi$
$312$		0			0
$313$	12.1393	−	7.00865i	0.686156	−	0.396153i	−0.116014	−	0.993248i	$-0.537012\pi$
$313$	12.1393	−	7.00865i	0.686156	−	0.396153i	0.802171	+	0.597095i	$0.203678\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.0887	−	17.4742i	−0.566638	−	0.981446i	−0.996895	−	0.0787397i	$-0.974910\pi$
$317$	−10.0887	−	17.4742i	−0.566638	−	0.981446i	0.430257	−	0.902706i	$-0.358423\pi$
$318$		0			0
$319$	3.35812	+	1.93881i	0.188019	+	0.108553i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	30.7143i		−	1.70899i
$324$		0			0
$325$	1.00944	−	0.582800i	0.0559936	−	0.0323279i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.27214	+	13.1285i	0.290663	+	0.723797i
$330$		0			0
$331$	−27.9703	+	16.1486i	−1.53738	+	0.887609i	−0.538394	+	0.842693i	$0.680969\pi$
$331$	−27.9703	+	16.1486i	−1.53738	+	0.887609i	−0.998991	+	0.0449159i	$0.985698\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.85780	−	4.94986i	0.156138	−	0.270440i
$336$		0			0
$337$	−10.1378	−	17.5591i	−0.552239	−	0.956506i	−0.998113	−	0.0614102i	$-0.980440\pi$
$337$	−10.1378	−	17.5591i	−0.552239	−	0.956506i	0.445873	−	0.895096i	$-0.352893\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.78016	+	1.02778i	0.0964011	+	0.0556572i
$342$		0			0
$343$	16.8712	+	7.63953i	0.910960	+	0.412496i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.63139	+	2.09658i	0.194943	+	0.112550i	0.594295	−	0.804247i	$-0.297431\pi$
$347$	3.63139	+	2.09658i	0.194943	+	0.112550i	−0.399352	+	0.916798i	$0.630765\pi$
$348$		0			0
$349$	−6.54079	−	3.77632i	−0.350120	−	0.202142i	0.314618	−	0.949218i	$-0.398124\pi$
$349$	−6.54079	−	3.77632i	−0.350120	−	0.202142i	−0.664738	+	0.747076i	$0.731457\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			17.5410i			0.933613i	0.884359	+	0.466807i	$0.154596\pi$
$353$			17.5410i			0.933613i	−0.884359	+	0.466807i	$0.845404\pi$
$354$		0			0
$355$	−16.9233			−0.898193
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.3430	−	10.5904i	−0.968108	−	0.558937i	−0.0694490	−	0.997586i	$-0.522124\pi$
$359$	−18.3430	−	10.5904i	−0.968108	−	0.558937i	−0.898659	+	0.438648i	$0.855457\pi$
$360$		0			0
$361$	−12.3962	−	21.4709i	−0.652432	−	1.13005i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.30912	−	7.46362i	−0.225550	−	0.390664i
$366$		0			0
$367$	−2.22135			−0.115954			−0.0579768	−	0.998318i	$-0.518465\pi$
$367$	−2.22135			−0.115954			−0.0579768	+	0.998318i	$0.518465\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.04518	+	7.58298i	0.158098	+	0.393689i
$372$		0			0
$373$	−7.61418			−0.394248			−0.197124	−	0.980379i	$-0.563160\pi$
$373$	−7.61418			−0.394248			−0.197124	+	0.980379i	$0.563160\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	19.8227i		−	1.02092i
$378$		0			0
$379$		−	4.06894i		−	0.209007i	−0.994525	−	0.104504i	$-0.966675\pi$
$379$		−	4.06894i		−	0.209007i	0.994525	−	0.104504i	$-0.0333254\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.04253			−0.104368			−0.0521842	−	0.998637i	$-0.516618\pi$
$383$	−2.04253			−0.104368			−0.0521842	+	0.998637i	$0.516618\pi$
$384$		0			0
$385$	−2.72448	−	0.388748i	−0.138852	−	0.0198124i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	24.3587			1.23503			0.617517	−	0.786558i	$-0.288139\pi$
$389$	24.3587			1.23503			0.617517	+	0.786558i	$0.288139\pi$
$390$		0			0
$391$	−2.63730	−	4.56794i	−0.133374	−	0.231011i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.85061	−	17.0618i	−0.495638	−	0.858470i
$396$		0			0
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	0.146227	−	0.989251i	$-0.453287\pi$
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	−0.783603	+	0.621262i	$0.786620\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.5778			−0.678045			−0.339022	−	0.940778i	$-0.610096\pi$
$401$	−13.5778			−0.678045			−0.339022	+	0.940778i	$0.610096\pi$
$402$		0			0
$403$		−	10.5081i		−	0.523448i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.08418	+	0.625950i	0.0537407	+	0.0310272i
$408$		0			0
$409$	−5.70365	−	3.29300i	−0.282027	−	0.162828i	0.352314	−	0.935882i	$-0.385395\pi$
$409$	−5.70365	−	3.29300i	−0.282027	−	0.162828i	−0.634341	+	0.773054i	$0.718728\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.25251	−	2.87061i	0.110839	−	0.141253i
$414$		0			0
$415$	−32.0493	−	18.5036i	−1.57324	−	0.908308i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.4919	+	19.9046i	0.561416	+	0.972401i	0.997373	+	0.0724336i	$0.0230765\pi$
$419$	11.4919	+	19.9046i	0.561416	+	0.972401i	−0.435957	+	0.899967i	$0.643590\pi$
$420$		0			0
$421$	−1.00338	+	1.73790i	−0.0489017	+	0.0847003i	−0.889440	−	0.457052i	$-0.848905\pi$
$421$	−1.00338	+	1.73790i	−0.0489017	+	0.0847003i	0.840538	+	0.541752i	$0.182239\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.06908	−	1.19458i	0.100365	−	0.0579457i
$426$		0			0
$427$	−25.1920	+	10.1166i	−1.21913	+	0.489577i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	28.7684	−	16.6095i	1.38573	−	0.800049i	0.392896	−	0.919583i	$-0.371473\pi$
$431$	28.7684	−	16.6095i	1.38573	−	0.800049i	0.992830	+	0.119534i	$0.0381399\pi$
$432$		0			0
$433$			35.6573i			1.71358i	0.515663	+	0.856791i	$0.327546\pi$
$433$			35.6573i			1.71358i	−0.515663	+	0.856791i	$0.672454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.51296	−	3.76026i	−0.311557	−	0.179878i
$438$		0			0
$439$	4.29613	+	7.44111i	0.205043	+	0.355145i	0.950146	−	0.311804i	$-0.100933\pi$
$439$	4.29613	+	7.44111i	0.205043	+	0.355145i	−0.745103	+	0.666949i	$0.767600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	31.5462	−	18.2132i	1.49880	−	0.865335i	0.498805	−	0.866714i	$-0.333772\pi$
$443$	31.5462	−	18.2132i	1.49880	−	0.865335i	0.999999	+	0.00137907i	$0.000438973\pi$
$444$		0			0
$445$	−7.22026	+	12.5059i	−0.342273	+	0.592834i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.2858			0.579801			0.289900	−	0.957057i	$-0.406378\pi$
$449$	12.2858			0.579801			0.289900	+	0.957057i	$0.406378\pi$
$450$		0			0
$451$	1.16431	+	2.01664i	0.0548251	+	0.0949599i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.24280	+	13.0554i	0.245786	+	0.612048i
$456$		0			0
$457$	3.64674	+	6.31634i	0.170587	+	0.295466i	0.938625	−	0.344938i	$-0.112100\pi$
$457$	3.64674	+	6.31634i	0.170587	+	0.295466i	−0.768038	+	0.640404i	$0.778767\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.33329	−	4.23388i	−0.341545	−	0.197191i	0.319410	−	0.947617i	$-0.396515\pi$
$461$	−7.33329	−	4.23388i	−0.341545	−	0.197191i	−0.660955	+	0.750425i	$0.729849\pi$
$462$		0			0
$463$	−4.53400	+	2.61771i	−0.210713	+	0.121655i	−0.601643	−	0.798765i	$-0.705487\pi$
$463$	−4.53400	+	2.61771i	−0.210713	+	0.121655i	0.390930	+	0.920421i	$0.372154\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.96542	−	17.2606i	0.461145	−	0.798726i	−0.537874	−	0.843025i	$-0.680772\pi$
$467$	9.96542	−	17.2606i	0.461145	−	0.798726i	0.999018	+	0.0442995i	$0.0141056\pi$
$468$		0			0
$469$	5.06599	+	3.97518i	0.233926	+	0.183557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.975621	+	1.68983i	−0.0448591	+	0.0776983i
$474$		0			0
$475$	1.70323	−	2.95008i	0.0781497	−	0.135359i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	29.0246			1.32617			0.663083	−	0.748545i	$-0.269247\pi$
$479$	29.0246			1.32617			0.663083	+	0.748545i	$0.269247\pi$
$480$		0			0
$481$		−	6.39981i		−	0.291806i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.2680	−	35.1052i	0.920323	−	1.59405i
$486$		0			0
$487$	11.9472	−	6.89770i	0.541378	−	0.312565i	−0.204259	−	0.978917i	$-0.565479\pi$
$487$	11.9472	−	6.89770i	0.541378	−	0.312565i	0.745637	+	0.666352i	$0.232145\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.6069	−	8.43329i	0.659200	−	0.380589i	−0.132772	−	0.991147i	$-0.542388\pi$
$491$	14.6069	−	8.43329i	0.659200	−	0.380589i	0.791972	+	0.610557i	$0.209055\pi$
$492$		0			0
$493$		−	40.6313i		−	1.82994i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.69326	−	18.8753i	0.120809	−	0.846671i
$498$		0			0
$499$		−	16.7654i		−	0.750523i	−0.926919	−	0.375262i	$-0.877553\pi$
$499$		−	16.7654i		−	0.750523i	0.926919	−	0.375262i	$-0.122447\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−36.2366			−1.61571			−0.807856	−	0.589380i	$-0.799372\pi$
$503$	−36.2366			−1.61571			−0.807856	+	0.589380i	$0.799372\pi$
$504$		0			0
$505$	40.7832			1.81483
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	29.0797i		−	1.28894i	−0.764631	−	0.644468i	$-0.777079\pi$
$509$		−	29.0797i		−	1.28894i	0.764631	−	0.644468i	$-0.222921\pi$
$510$		0			0
$511$	9.01028	−	3.61835i	0.398591	−	0.160067i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			21.6962i			0.956047i
$516$		0			0
$517$	2.05121	−	1.18427i	0.0902120	−	0.0520839i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	31.1742	−	17.9984i	1.36576	−	0.788524i	0.375381	−	0.926871i	$-0.377512\pi$
$521$	31.1742	−	17.9984i	1.36576	−	0.788524i	0.990384	+	0.138346i	$0.0441787\pi$
$522$		0			0
$523$	−17.0333	+	29.5026i	−0.744816	+	1.29006i	0.205465	+	0.978664i	$0.434129\pi$
$523$	−17.0333	+	29.5026i	−0.744816	+	1.29006i	−0.950281	+	0.311394i	$0.899204\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	21.5389i		−	0.938248i
$528$		0			0
$529$	21.7085			0.943848
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.95203	−	10.3092i	0.257811	−	0.446542i
$534$		0			0
$535$	−10.5252	+	18.2302i	−0.455044	+	0.788159i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.867176	−	2.97686i	0.0373519	−	0.128223i
$540$		0			0
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	−0.939737	−	0.341898i	$-0.888930\pi$
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	0.765961	+	0.642887i	$0.222264\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−26.2842	+	15.1752i	−1.12589	+	0.650034i
$546$		0			0
$547$	22.5917	+	13.0433i	0.965950	+	0.557691i	0.897999	−	0.439997i	$-0.145021\pi$
$547$	22.5917	+	13.0433i	0.965950	+	0.557691i	0.0679508	+	0.997689i	$0.478354\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−28.9660	−	50.1705i	−1.23399	−	2.13734i
$552$		0			0
$553$	20.5974	−	8.27152i	0.875891	−	0.351741i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.12408	−	10.6072i	−0.259486	−	0.449442i	0.706619	−	0.707595i	$-0.250220\pi$
$557$	−6.12408	−	10.6072i	−0.259486	−	0.449442i	−0.966104	+	0.258152i	$0.916886\pi$
$558$		0			0
$559$	9.97491			0.421894
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.4252	+	19.7890i	−0.481515	+	0.834008i	−0.999775	−	0.0212152i	$-0.993246\pi$
$563$	−11.4252	+	19.7890i	−0.481515	+	0.834008i	0.518260	+	0.855223i	$0.326580\pi$
$564$		0			0
$565$	8.64345	−	4.99030i	0.363633	−	0.209943i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.86898	−	4.96922i	−0.120274	−	0.208321i	0.799602	−	0.600531i	$-0.205044\pi$
$569$	−2.86898	−	4.96922i	−0.120274	−	0.208321i	−0.919876	+	0.392210i	$0.871711\pi$
$570$		0			0
$571$	21.6157	+	12.4798i	0.904588	+	0.522264i	0.878686	−	0.477401i	$-0.158421\pi$
$571$	21.6157	+	12.4798i	0.904588	+	0.522264i	0.0259018	+	0.999664i	$0.491754\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.584996i		−	0.0243960i
$576$		0			0
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	−0.836858	−	0.547421i	$-0.815610\pi$
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	0.0556514	+	0.998450i	$0.482276\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	25.7384	−	32.8012i	1.06781	−	1.36082i
$582$		0			0
$583$	1.18477	−	0.684029i	0.0490683	−	0.0283296i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.7121	+	25.4821i	−0.607233	+	1.05176i	0.384461	+	0.923141i	$0.374387\pi$
$587$	−14.7121	+	25.4821i	−0.607233	+	1.05176i	−0.991694	+	0.128617i	$0.958946\pi$
$588$		0			0
$589$	−15.3550	−	26.5957i	−0.632693	−	1.09586i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	25.5917	+	14.7754i	1.05092	+	0.606752i	0.922908	−	0.385020i	$-0.125806\pi$
$593$	25.5917	+	14.7754i	1.05092	+	0.606752i	0.128017	+	0.991772i	$0.459139\pi$
$594$		0			0
$595$	10.7463	+	26.7601i	0.440557	+	1.09706i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	34.4099	+	19.8666i	1.40595	+	0.811727i	0.994995	−	0.0999281i	$-0.0318613\pi$
$599$	34.4099	+	19.8666i	1.40595	+	0.811727i	0.410957	+	0.911655i	$0.365195\pi$
$600$		0			0
$601$	9.64604	+	5.56915i	0.393470	+	0.227170i	0.683663	−	0.729798i	$-0.260386\pi$
$601$	9.64604	+	5.56915i	0.393470	+	0.227170i	−0.290192	+	0.956968i	$0.593719\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	25.3711i		−	1.03148i
$606$		0			0
$607$	−34.6629			−1.40692			−0.703461	−	0.710734i	$-0.748363\pi$
$607$	−34.6629			−1.40692			−0.703461	+	0.710734i	$0.748363\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.4859	−	6.05406i	−0.424215	−	0.244921i
$612$		0			0
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	−0.982583	−	0.185823i	$-0.940505\pi$
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	0.330365	−	0.943853i	$-0.392828\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.0343	+	38.1645i	0.887067	+	1.53644i	0.843327	+	0.537401i	$0.180594\pi$
$617$	22.0343	+	38.1645i	0.887067	+	1.53644i	0.0437400	+	0.999043i	$0.486073\pi$
$618$		0			0
$619$	−9.30313			−0.373924			−0.186962	−	0.982367i	$-0.559864\pi$
$619$	−9.30313			−0.373924			−0.186962	+	0.982367i	$0.559864\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.7993	−	10.0433i	−0.512792	−	0.402377i
$624$		0			0
$625$	−27.3088			−1.09235
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	13.1179i		−	0.523044i
$630$		0			0
$631$			28.6463i			1.14039i	0.821509	+	0.570196i	$0.193133\pi$
$631$			28.6463i			1.14039i	−0.821509	+	0.570196i	$0.806867\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−46.1826			−1.83270
$636$		0			0
$637$	−15.3957	+	3.76982i	−0.609999	+	0.149366i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.03251			−0.0802795			−0.0401397	−	0.999194i	$-0.512780\pi$
$641$	−2.03251			−0.0802795			−0.0401397	+	0.999194i	$0.512780\pi$
$642$		0			0
$643$	−14.7575	−	25.5608i	−0.581980	−	1.00802i	−0.995245	−	0.0974077i	$-0.968945\pi$
$643$	−14.7575	−	25.5608i	−0.581980	−	1.00802i	0.413265	−	0.910611i	$-0.364388\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.18434	−	14.1757i	−0.321759	−	0.557304i	0.659092	−	0.752063i	$-0.270941\pi$
$647$	−8.18434	−	14.1757i	−0.321759	−	0.557304i	−0.980851	+	0.194759i	$0.937608\pi$
$648$		0			0
$649$	−0.529037	−	0.305440i	−0.0207665	−	0.0119896i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.178525			−0.00698623			−0.00349312	−	0.999994i	$-0.501112\pi$
$653$	−0.178525			−0.00698623			−0.00349312	+	0.999994i	$0.501112\pi$
$654$		0			0
$655$			40.0950i			1.56664i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.4428	+	10.0706i	0.679474	+	0.392294i	0.799657	−	0.600457i	$-0.205015\pi$
$659$	17.4428	+	10.0706i	0.679474	+	0.392294i	−0.120183	+	0.992752i	$0.538348\pi$
$660$		0			0
$661$	−7.59315	−	4.38391i	−0.295339	−	0.170514i	0.345008	−	0.938600i	$-0.387876\pi$
$661$	−7.59315	−	4.38391i	−0.295339	−	0.170514i	−0.640347	+	0.768086i	$0.721210\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	32.3466	+	25.3817i	1.25435	+	0.984261i
$666$		0			0
$667$	−8.61584	−	4.97436i	−0.333607	−	0.192608i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.27246	+	3.93602i	0.0877274	+	0.151948i
$672$		0			0
$673$	−1.04120	+	1.80341i	−0.0401353	+	0.0695164i	−0.885395	−	0.464839i	$-0.846112\pi$
$673$	−1.04120	+	1.80341i	−0.0401353	+	0.0695164i	0.845260	+	0.534355i	$0.179446\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.0742	−	6.97106i	0.464050	−	0.267919i	−0.249696	−	0.968324i	$-0.580331\pi$
$677$	12.0742	−	6.97106i	0.464050	−	0.267919i	0.713746	+	0.700405i	$0.246997\pi$
$678$		0			0
$679$	35.9289	+	28.1927i	1.37882	+	1.08194i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.5049	−	7.79708i	0.516752	−	0.298347i	−0.218853	−	0.975758i	$-0.570231\pi$
$683$	13.5049	−	7.79708i	0.516752	−	0.298347i	0.735605	+	0.677411i	$0.236898\pi$
$684$		0			0
$685$		−	8.25120i		−	0.315262i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.05665	−	3.49681i	−0.230740	−	0.133218i
$690$		0			0
$691$	0.986734	+	1.70907i	0.0375371	+	0.0650162i	0.884184	−	0.467139i	$-0.154715\pi$
$691$	0.986734	+	1.70907i	0.0375371	+	0.0650162i	−0.846646	+	0.532156i	$0.821382\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	35.2278	−	20.3388i	1.33627	−	0.771493i
$696$		0			0
$697$	12.2001	−	21.1311i	0.462110	−	0.800399i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.57171			0.134902			0.0674508	−	0.997723i	$-0.478513\pi$
$701$	3.57171			0.134902			0.0674508	+	0.997723i	$0.478513\pi$
$702$		0			0
$703$	−9.35173	−	16.1977i	−0.352707	−	0.610907i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.49047	+	45.4874i	−0.244099	+	1.71073i
$708$		0			0
$709$	−12.6279	−	21.8721i	−0.474250	−	0.821425i	0.525316	−	0.850907i	$-0.323947\pi$
$709$	−12.6279	−	21.8721i	−0.474250	−	0.821425i	−0.999565	+	0.0294829i	$0.990614\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.56731	−	2.63694i	−0.171047	−	0.0987541i
$714$		0			0
$715$	2.03979	−	1.17767i	0.0762839	−	0.0440425i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.0045	+	32.9168i	−0.708749	+	1.22759i	0.256572	+	0.966525i	$0.417407\pi$
$719$	−19.0045	+	32.9168i	−0.708749	+	1.22759i	−0.965321	+	0.261065i	$0.915926\pi$
$720$		0			0
$721$	−24.1987	−	3.45285i	−0.901206	−	0.128591i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.25317	−	3.90260i	0.0836805	−	0.144939i
$726$		0			0
$727$	8.14853	−	14.1137i	0.302212	−	0.523447i	−0.674424	−	0.738344i	$-0.735608\pi$
$727$	8.14853	−	14.1137i	0.302212	−	0.523447i	0.976637	+	0.214897i	$0.0689415\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.4459			0.756218
$732$		0			0
$733$		−	12.7119i		−	0.469525i	−0.972053	−	0.234763i	$-0.924569\pi$
$733$		−	12.7119i		−	0.469525i	0.972053	−	0.234763i	$-0.0754313\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.539034	−	0.933634i	0.0198556	−	0.0343909i
$738$		0			0
$739$	21.2467	−	12.2668i	0.781574	−	0.451242i	−0.0554141	−	0.998463i	$-0.517648\pi$
$739$	21.2467	−	12.2668i	0.781574	−	0.451242i	0.836988	+	0.547222i	$0.184315\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.5305	−	14.7400i	0.936624	−	0.540760i	0.0477233	−	0.998861i	$-0.484803\pi$
$743$	25.5305	−	14.7400i	0.936624	−	0.540760i	0.888900	+	0.458101i	$0.151470\pi$
$744$		0			0
$745$		−	14.2905i		−	0.523563i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.6579	−	14.6405i	−0.681745	−	0.534951i
$750$		0			0
$751$		−	39.7434i		−	1.45026i	−0.688613	−	0.725129i	$-0.741780\pi$
$751$		−	39.7434i		−	1.45026i	0.688613	−	0.725129i	$-0.258220\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.13526			−0.223285
$756$		0			0
$757$	−3.23130			−0.117444			−0.0587218	−	0.998274i	$-0.518702\pi$
$757$	−3.23130			−0.117444			−0.0587218	+	0.998274i	$0.518702\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	36.8650i		−	1.33636i	−0.744001	−	0.668178i	$-0.767074\pi$
$761$		−	36.8650i		−	1.33636i	0.744001	−	0.668178i	$-0.232926\pi$
$762$		0			0
$763$	−12.7426	−	31.7310i	−0.461312	−	1.14874i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			3.12286i			0.112760i
$768$		0			0
$769$	−21.3838	+	12.3460i	−0.771120	+	0.445206i	−0.833274	−	0.552860i	$-0.813536\pi$
$769$	−21.3838	+	12.3460i	−0.771120	+	0.445206i	0.0621539	+	0.998067i	$0.480203\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.1598	−	10.4846i	0.653164	−	0.377104i	−0.136503	−	0.990640i	$-0.543586\pi$
$773$	18.1598	−	10.4846i	0.653164	−	0.377104i	0.789667	+	0.613535i	$0.210253\pi$
$774$		0			0
$775$	1.19442	−	2.06879i	0.0429047	−	0.0743131i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	34.7897i		−	1.24647i
$780$		0			0
$781$	−3.19204			−0.114220
$782$		0			0
$783$		0			0
$784$		0			0
$785$	22.0654	−	38.2184i	0.787548	−	1.36407i
$786$		0			0
$787$	7.44418	−	12.8937i	0.265356	−	0.459611i	−0.702300	−	0.711881i	$-0.747844\pi$
$787$	7.44418	−	12.8937i	0.265356	−	0.459611i	0.967657	+	0.252270i	$0.0811770\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.19033	+	10.4346i	0.148991	+	0.371012i
$792$		0			0
$793$	11.6170	−	20.1212i	0.412532	−	0.714526i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.5335	+	10.1230i	−0.621068	+	0.358574i	−0.777285	−	0.629149i	$-0.783404\pi$
$797$	−17.5335	+	10.1230i	−0.621068	+	0.358574i	0.156216	+	0.987723i	$0.450070\pi$
$798$		0			0
$799$	−21.4933	−	12.4092i	−0.760380	−	0.439005i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.812779	−	1.40778i	−0.0286824	−	0.0496793i
$804$		0			0
$805$	6.99011	+	0.997400i	0.246369	+	0.0351537i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17.2300	+	29.8433i	0.605775	+	1.04923i	0.991928	+	0.126799i	$0.0404703\pi$
$809$	17.2300	+	29.8433i	0.605775	+	1.04923i	−0.386153	+	0.922435i	$0.626196\pi$
$810$		0			0
$811$	−49.5905			−1.74136			−0.870679	−	0.491852i	$-0.836320\pi$
$811$	−49.5905			−1.74136			−0.870679	+	0.491852i	$0.836320\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.93820	+	6.82116i	−0.137949	+	0.238935i
$816$		0			0
$817$	25.2461	−	14.5758i	0.883249	−	0.509944i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.5801	+	33.9137i	0.683349	+	1.18360i	0.973953	+	0.226752i	$0.0728106\pi$
$821$	19.5801	+	33.9137i	0.683349	+	1.18360i	−0.290604	+	0.956844i	$0.593856\pi$
$822$		0			0
$823$	33.6699	+	19.4393i	1.17366	+	0.677612i	0.954539	−	0.298087i	$-0.0963484\pi$
$823$	33.6699	+	19.4393i	1.17366	+	0.677612i	0.219119	+	0.975698i	$0.429682\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			41.0227i			1.42650i	0.700909	+	0.713250i	$0.252778\pi$
$827$			41.0227i			1.42650i	−0.700909	+	0.713250i	$0.747222\pi$
$828$		0			0
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	−0.686157	−	0.727453i	$-0.740704\pi$
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	0.286915	+	0.957956i	$0.407370\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−31.5570	+	7.72712i	−1.09338	+	0.267729i
$834$		0			0
$835$	18.6430	−	10.7635i	0.645168	−	0.372488i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.9028	+	27.5445i	−0.549025	+	0.950940i	0.449316	+	0.893373i	$0.351668\pi$
$839$	−15.9028	+	27.5445i	−0.549025	+	0.950940i	−0.998342	+	0.0575672i	$0.981666\pi$
$840$		0			0
$841$	−23.8184	−	41.2547i	−0.821325	−	1.42258i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	16.0110	+	9.24393i	0.550793	+	0.318001i
$846$		0			0
$847$	28.2976	+	4.03770i	0.972316	+	0.138737i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.78164	−	1.60598i	−0.0953535	−	0.0550524i
$852$		0			0
$853$	−0.551551	−	0.318438i	−0.0188847	−	0.0109031i	0.490528	−	0.871425i	$-0.336804\pi$
$853$	−0.551551	−	0.318438i	−0.0188847	−	0.0109031i	−0.509413	+	0.860522i	$0.670137\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	4.54984i		−	0.155420i	−0.996976	−	0.0777098i	$-0.975239\pi$
$857$		−	4.54984i		−	0.155420i	0.996976	−	0.0777098i	$-0.0247608\pi$
$858$		0			0
$859$	13.5634			0.462776			0.231388	−	0.972862i	$-0.425673\pi$
$859$	13.5634			0.462776			0.231388	+	0.972862i	$0.425673\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.1996	+	8.19817i	0.483361	+	0.279069i	0.721816	−	0.692085i	$-0.243308\pi$
$863$	14.1996	+	8.19817i	0.483361	+	0.279069i	−0.238455	+	0.971154i	$0.576641\pi$
$864$		0			0
$865$	26.5973	+	46.0680i	0.904337	+	1.56636i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.85801	−	3.21816i	−0.0630285	−	0.109169i
$870$		0			0
$871$	−5.51117			−0.186739
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.93647	−	27.5881i	0.133077	−	0.932647i
$876$		0			0
$877$	−49.5189			−1.67214			−0.836068	−	0.548626i	$-0.815151\pi$
$877$	−49.5189			−1.67214			−0.836068	+	0.548626i	$0.815151\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	16.2659i		−	0.548012i	−0.961728	−	0.274006i	$-0.911651\pi$
$881$		−	16.2659i		−	0.548012i	0.961728	−	0.274006i	$-0.0883488\pi$
$882$		0			0
$883$		−	26.6667i		−	0.897404i	−0.893681	−	0.448702i	$-0.851886\pi$
$883$		−	26.6667i		−	0.897404i	0.893681	−	0.448702i	$-0.148114\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−53.9957			−1.81300			−0.906499	−	0.422208i	$-0.861255\pi$
$887$	−53.9957			−1.81300			−0.906499	+	0.422208i	$0.861255\pi$
$888$		0			0
$889$	7.34976	−	51.5096i	0.246503	−	1.72758i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−35.3860			−1.18415
$894$		0			0
$895$	26.1337	+	45.2649i	0.873554	+	1.51304i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−20.3128	−	35.1828i	−0.677470	−	1.17341i
$900$		0			0
$901$	−12.4145	−	7.16752i	−0.413587	−	0.238785i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.1759			−0.338257
$906$		0			0
$907$		−	45.5452i		−	1.51230i	−0.654397	−	0.756151i	$-0.727077\pi$
$907$		−	45.5452i		−	1.51230i	0.654397	−	0.756151i	$-0.272923\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10.7265	+	6.19296i	0.355385	+	0.205182i	0.667055	−	0.745009i	$-0.267555\pi$
$911$	10.7265	+	6.19296i	0.355385	+	0.205182i	−0.311669	+	0.950191i	$0.600888\pi$
$912$		0			0
$913$	−6.04508	−	3.49013i	−0.200063	−	0.115506i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−44.7198	−	6.38094i	−1.47678	−	0.210717i
$918$		0			0
$919$	−38.9097	−	22.4645i	−1.28351	−	0.741037i	−0.306024	−	0.952024i	$-0.598999\pi$
$919$	−38.9097	−	22.4645i	−1.28351	−	0.741037i	−0.977489	+	0.210987i	$0.932332\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.15897	+	14.1318i	0.268556	+	0.465152i
$924$		0			0
$925$	0.727439	−	1.25996i	0.0239181	−	0.0414273i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.1152	+	12.7682i	−0.725578	+	0.418912i	−0.816802	−	0.576918i	$-0.804255\pi$
$929$	−22.1152	+	12.7682i	−0.725578	+	0.418912i	0.0912245	+	0.995830i	$0.470922\pi$
$930$		0			0
$931$	−33.4572	+	32.0382i	−1.09651	+	1.05001i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.18102	−	2.41392i	0.136734	−	0.0789435i
$936$		0			0
$937$		−	29.7933i		−	0.973304i	−0.873596	−	0.486652i	$-0.838218\pi$
$937$		−	29.7933i		−	0.973304i	0.873596	−	0.486652i	$-0.161782\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−32.9292	−	19.0117i	−1.07346	−	0.619763i	−0.144336	−	0.989529i	$-0.546105\pi$
$941$	−32.9292	−	19.0117i	−1.07346	−	0.619763i	−0.929125	+	0.369766i	$0.879438\pi$
$942$		0			0
$943$	−2.98723	−	5.17404i	−0.0972777	−	0.168490i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.9431	+	13.8235i	−0.778045	+	0.449205i	−0.835737	−	0.549130i	$-0.814959\pi$
$947$	−23.9431	+	13.8235i	−0.778045	+	0.449205i	0.0576920	+	0.998334i	$0.481626\pi$
$948$		0			0
$949$	−4.15499	+	7.19666i	−0.134877	+	0.233613i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−38.4588			−1.24580			−0.622901	−	0.782301i	$-0.714046\pi$
$953$	−38.4588			−1.24580			−0.622901	+	0.782301i	$0.714046\pi$
$954$		0			0
$955$	−29.2381	−	50.6419i	−0.946123	−	1.63873i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.20294	+	1.31314i	0.297178	+	0.0424036i
$960$		0			0
$961$	4.73206	+	8.19616i	0.152647	+	0.264392i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	43.3701	+	25.0397i	1.39613	+	0.806058i
$966$		0			0
$967$	1.40644	−	0.812009i	0.0452281	−	0.0261125i	−0.477215	−	0.878786i	$-0.658354\pi$
$967$	1.40644	−	0.812009i	0.0452281	−	0.0261125i	0.522444	+	0.852674i	$0.325021\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.2966	−	33.4227i	0.619257	−	1.07258i	−0.370365	−	0.928886i	$-0.620767\pi$
$971$	19.2966	−	33.4227i	0.619257	−	1.07258i	0.989622	−	0.143698i	$-0.0458994\pi$
$972$		0			0
$973$	17.0784	+	42.5279i	0.547508	+	1.36338i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.20038	−	10.7394i	0.198368	−	0.343583i	−0.749632	−	0.661855i	$-0.769769\pi$
$977$	6.20038	−	10.7394i	0.198368	−	0.343583i	0.947999	+	0.318272i	$0.103103\pi$
$978$		0			0
$979$	−1.36187	+	2.35883i	−0.0435257	+	0.0753886i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.9967			−0.542112			−0.271056	−	0.962564i	$-0.587373\pi$
$983$	−16.9967			−0.542112			−0.271056	+	0.962564i	$0.587373\pi$
$984$		0			0
$985$			43.5185i			1.38662i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.50313	−	4.33554i	0.0795947	−	0.137862i
$990$		0			0
$991$	39.0008	−	22.5171i	1.23890	−	0.715280i	0.270032	−	0.962851i	$-0.412966\pi$
$991$	39.0008	−	22.5171i	1.23890	−	0.715280i	0.968870	+	0.247571i	$0.0796324\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.73687	−	2.15748i	0.118467	−	0.0683967i
$996$		0			0
$997$			8.00101i			0.253395i	0.991941	+	0.126697i	$0.0404377\pi$
$997$			8.00101i			0.253395i	−0.991941	+	0.126697i	$0.959562\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bf.i.2287.3		32
3.2	odd	2		1008.2.bf.i.943.11	yes	32
4.3	odd	2	inner	3024.2.bf.i.2287.4		32
7.3	odd	6		3024.2.cz.i.2719.4		32
9.4	even	3		3024.2.cz.i.1279.3		32
9.5	odd	6		1008.2.cz.i.607.11	yes	32
12.11	even	2		1008.2.bf.i.943.6	yes	32
21.17	even	6		1008.2.cz.i.367.6	yes	32
28.3	even	6		3024.2.cz.i.2719.3		32
36.23	even	6		1008.2.cz.i.607.6	yes	32
36.31	odd	6		3024.2.cz.i.1279.4		32
63.31	odd	6	inner	3024.2.bf.i.1711.13		32
63.59	even	6		1008.2.bf.i.31.6	✓	32
84.59	odd	6		1008.2.cz.i.367.11	yes	32
252.31	even	6	inner	3024.2.bf.i.1711.14		32
252.59	odd	6		1008.2.bf.i.31.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.6	✓	32	63.59	even	6
1008.2.bf.i.31.11	yes	32	252.59	odd	6
1008.2.bf.i.943.6	yes	32	12.11	even	2
1008.2.bf.i.943.11	yes	32	3.2	odd	2
1008.2.cz.i.367.6	yes	32	21.17	even	6
1008.2.cz.i.367.11	yes	32	84.59	odd	6
1008.2.cz.i.607.6	yes	32	36.23	even	6
1008.2.cz.i.607.11	yes	32	9.5	odd	6
3024.2.bf.i.1711.13		32	63.31	odd	6	inner
3024.2.bf.i.1711.14		32	252.31	even	6	inner
3024.2.bf.i.2287.3		32	1.1	even	1	trivial
3024.2.bf.i.2287.4		32	4.3	odd	2	inner
3024.2.cz.i.1279.3		32	9.4	even	3
3024.2.cz.i.1279.4		32	36.31	odd	6
3024.2.cz.i.2719.3		32	28.3	even	6
3024.2.cz.i.2719.4		32	7.3	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +O(q^{10})\)	\(q-2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} -0.442942i q^{11} +(-1.96099 + 1.13218i) q^{13} +(-4.01950 + 2.32066i) q^{17} +(-3.30879 + 5.73100i) q^{19} +1.13645i q^{23} -0.514760 q^{25} +(-4.37712 + 7.58140i) q^{29} +(-2.32034 + 4.01894i) q^{31} +(0.877649 - 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-4.55283 + 2.62858i) q^{41} +(-3.81500 - 2.20259i) q^{43} +(2.67363 + 4.63087i) q^{47} +(6.72065 + 1.95776i) q^{49} +(1.54428 + 2.67478i) q^{53} -1.04018 q^{55} +(0.689570 - 1.19437i) q^{59} +(-8.88607 + 5.13038i) q^{61} +(2.65875 + 4.60510i) q^{65} +(2.10780 + 1.21694i) q^{67} -7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(0.165541 - 1.16016i) q^{77} +(7.26542 - 4.19469i) q^{79} +(7.87941 - 13.6475i) q^{83} +(5.44973 + 9.43920i) q^{85} +(-5.32537 - 3.07461i) q^{89} +(-5.55940 + 2.23255i) q^{91} +(13.4584 + 7.77021i) q^{95} +(14.9489 + 8.63074i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) \) 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

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