LMFDB - Embedded newform 1500.2.i.b.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (of order $4$, degree $2$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.b.1193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66349 - 0.482501i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(2.53438 + 1.60527i) q^{9} +O(q^{10})$	$q+(-1.66349 - 0.482501i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(2.53438 + 1.60527i) q^{9} +0.311499i q^{11} +(1.37007 - 1.37007i) q^{13} +(3.17467 - 3.17467i) q^{17} +6.19476i q^{19} +(1.97935 + 3.59670i) q^{21} +(2.25967 + 2.25967i) q^{23} +(-3.44137 - 3.89319i) q^{27} +3.44417 q^{29} -3.82857 q^{31} +(0.150299 - 0.518175i) q^{33} +(-7.87537 - 7.87537i) q^{37} +(-2.94015 + 1.61803i) q^{39} -12.4547i q^{41} +(-4.00969 + 4.00969i) q^{43} +(2.99073 - 2.99073i) q^{47} -1.38197i q^{49} +(-6.81280 + 3.74924i) q^{51} +(4.61464 + 4.61464i) q^{53} +(2.98898 - 10.3049i) q^{57} +5.44983 q^{59} +3.80305 q^{61} +(-1.55721 - 6.93811i) q^{63} +(-4.34208 - 4.34208i) q^{67} +(-2.66864 - 4.84923i) q^{69} +1.51205i q^{71} +(3.58504 - 3.58504i) q^{73} +(0.522077 - 0.522077i) q^{77} -9.62560i q^{79} +(3.84621 + 8.13675i) q^{81} +(-8.28634 - 8.28634i) q^{83} +(-5.72934 - 1.66182i) q^{87} -14.2718 q^{89} -4.59251 q^{91} +(6.36879 + 1.84729i) q^{93} +(-9.91277 - 9.91277i) q^{97} +(-0.500041 + 0.789459i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) $ 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	−1.66349	−	0.482501i	−0.960415	−	0.278572i
$3$	−1.66349	−	0.482501i	−0.960415	−	0.278572i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.67601	−	1.67601i	−0.633473	−	0.633473i	0.315464	−	0.948937i	$-0.397840\pi$
$7$	−1.67601	−	1.67601i	−0.633473	−	0.633473i	−0.948937	+	0.315464i	$0.897840\pi$
$8$		0			0
$9$	2.53438	+	1.60527i	0.844795	+	0.535090i
$10$		0			0
$11$			0.311499i			0.0939206i	0.998897	+	0.0469603i	$0.0149534\pi$
$11$			0.311499i			0.0939206i	−0.998897	+	0.0469603i	$0.985047\pi$
$12$		0			0
$13$	1.37007	−	1.37007i	0.379989	−	0.379989i	−0.491109	−	0.871098i	$-0.663408\pi$
$13$	1.37007	−	1.37007i	0.379989	−	0.379989i	0.871098	+	0.491109i	$0.163408\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.17467	−	3.17467i	0.769969	−	0.769969i	−0.208131	−	0.978101i	$-0.566738\pi$
$17$	3.17467	−	3.17467i	0.769969	−	0.769969i	0.978101	+	0.208131i	$0.0667382\pi$
$18$		0			0
$19$			6.19476i			1.42118i	0.703608	+	0.710588i	$0.251571\pi$
$19$			6.19476i			1.42118i	−0.703608	+	0.710588i	$0.748429\pi$
$20$		0			0
$21$	1.97935	+	3.59670i	0.431929	+	0.784865i
$22$		0			0
$23$	2.25967	+	2.25967i	0.471174	+	0.471174i	0.902294	−	0.431121i	$-0.141882\pi$
$23$	2.25967	+	2.25967i	0.471174	+	0.471174i	−0.431121	+	0.902294i	$0.641882\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.44137	−	3.89319i	−0.662293	−	0.749245i
$28$		0			0
$29$	3.44417			0.639567			0.319783	−	0.947491i	$-0.396390\pi$
$29$	3.44417			0.639567			0.319783	+	0.947491i	$0.396390\pi$
$30$		0			0
$31$	−3.82857			−0.687632			−0.343816	−	0.939037i	$-0.611720\pi$
$31$	−3.82857			−0.687632			−0.343816	+	0.939037i	$0.611720\pi$
$32$		0			0
$33$	0.150299	−	0.518175i	0.0261637	−	0.0902028i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.87537	−	7.87537i	−1.29470	−	1.29470i	−0.931844	−	0.362859i	$-0.881800\pi$
$37$	−7.87537	−	7.87537i	−1.29470	−	1.29470i	−0.362859	−	0.931844i	$-0.618200\pi$
$38$		0			0
$39$	−2.94015	+	1.61803i	−0.470802	+	0.259093i
$40$		0			0
$41$		−	12.4547i		−	1.94510i	−0.232701	−	0.972548i	$-0.574756\pi$
$41$		−	12.4547i		−	1.94510i	0.232701	−	0.972548i	$-0.425244\pi$
$42$		0			0
$43$	−4.00969	+	4.00969i	−0.611472	+	0.611472i	−0.943330	−	0.331857i	$-0.892325\pi$
$43$	−4.00969	+	4.00969i	−0.611472	+	0.611472i	0.331857	+	0.943330i	$0.392325\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.99073	−	2.99073i	0.436242	−	0.436242i	−0.454503	−	0.890745i	$-0.650183\pi$
$47$	2.99073	−	2.99073i	0.436242	−	0.436242i	0.890745	+	0.454503i	$0.150183\pi$
$48$		0			0
$49$		−	1.38197i		−	0.197424i
$50$		0			0
$51$	−6.81280	+	3.74924i	−0.953983	+	0.524998i
$52$		0			0
$53$	4.61464	+	4.61464i	0.633870	+	0.633870i	0.949036	−	0.315167i	$-0.102060\pi$
$53$	4.61464	+	4.61464i	0.633870	+	0.633870i	−0.315167	+	0.949036i	$0.602060\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.98898	−	10.3049i	0.395900	−	1.36492i
$58$		0			0
$59$	5.44983			0.709507			0.354754	−	0.934960i	$-0.384565\pi$
$59$	5.44983			0.709507			0.354754	+	0.934960i	$0.384565\pi$
$60$		0			0
$61$	3.80305			0.486930			0.243465	−	0.969910i	$-0.421716\pi$
$61$	3.80305			0.486930			0.243465	+	0.969910i	$0.421716\pi$
$62$		0			0
$63$	−1.55721	−	6.93811i	−0.196190	−	0.874120i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.34208	−	4.34208i	−0.530469	−	0.530469i	0.390243	−	0.920712i	$-0.372391\pi$
$67$	−4.34208	−	4.34208i	−0.530469	−	0.530469i	−0.920712	+	0.390243i	$0.872391\pi$
$68$		0			0
$69$	−2.66864	−	4.84923i	−0.321266	−	0.583778i
$70$		0			0
$71$			1.51205i			0.179447i	0.995967	+	0.0897236i	$0.0285984\pi$
$71$			1.51205i			0.179447i	−0.995967	+	0.0897236i	$0.971402\pi$
$72$		0			0
$73$	3.58504	−	3.58504i	0.419597	−	0.419597i	−0.465468	−	0.885065i	$-0.654114\pi$
$73$	3.58504	−	3.58504i	0.419597	−	0.419597i	0.885065	+	0.465468i	$0.154114\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.522077	−	0.522077i	0.0594962	−	0.0594962i
$78$		0			0
$79$		−	9.62560i		−	1.08296i	−0.840712	−	0.541482i	$-0.817863\pi$
$79$		−	9.62560i		−	1.08296i	0.840712	−	0.541482i	$-0.182137\pi$
$80$		0			0
$81$	3.84621	+	8.13675i	0.427357	+	0.904083i
$82$		0			0
$83$	−8.28634	−	8.28634i	−0.909544	−	0.909544i	0.0866913	−	0.996235i	$-0.472371\pi$
$83$	−8.28634	−	8.28634i	−0.909544	−	0.909544i	−0.996235	+	0.0866913i	$0.972371\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.72934	−	1.66182i	−0.614249	−	0.178166i
$88$		0			0
$89$	−14.2718			−1.51281			−0.756404	−	0.654104i	$-0.773046\pi$
$89$	−14.2718			−1.51281			−0.756404	+	0.654104i	$0.773046\pi$
$90$		0			0
$91$	−4.59251			−0.481426
$92$		0			0
$93$	6.36879	+	1.84729i	0.660413	+	0.191555i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.91277	−	9.91277i	−1.00649	−	1.00649i	−0.999979	−	0.00651069i	$-0.997928\pi$
$97$	−9.91277	−	9.91277i	−1.00649	−	1.00649i	−0.00651069	−	0.999979i	$-0.502072\pi$
$98$		0			0
$99$	−0.500041	+	0.789459i	−0.0502560	+	0.0793436i
$100$		0			0
$101$		−	9.31805i		−	0.927180i	−0.886050	−	0.463590i	$-0.846561\pi$
$101$		−	9.31805i		−	0.927180i	0.886050	−	0.463590i	$-0.153439\pi$
$102$		0			0
$103$	−6.36015	+	6.36015i	−0.626684	+	0.626684i	−0.947232	−	0.320548i	$-0.896133\pi$
$103$	−6.36015	+	6.36015i	−0.626684	+	0.626684i	0.320548	+	0.947232i	$0.396133\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.41322	−	9.41322i	0.910010	−	0.910010i	−0.0862623	−	0.996272i	$-0.527492\pi$
$107$	9.41322	−	9.41322i	0.910010	−	0.910010i	0.996272	+	0.0862623i	$0.0274923\pi$
$108$		0			0
$109$		−	6.94292i		−	0.665011i	−0.943101	−	0.332506i	$-0.892106\pi$
$109$		−	6.94292i		−	0.665011i	0.943101	−	0.332506i	$-0.107894\pi$
$110$		0			0
$111$	9.30071	+	16.9005i	0.882784	+	1.60412i
$112$		0			0
$113$	−7.31244	−	7.31244i	−0.687897	−	0.687897i	0.273870	−	0.961767i	$-0.411696\pi$
$113$	−7.31244	−	7.31244i	−0.687897	−	0.687897i	−0.961767	+	0.273870i	$0.911696\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.67162	−	1.27295i	0.524341	−	0.117684i
$118$		0			0
$119$	−10.6416			−0.975510
$120$		0			0
$121$	10.9030			0.991179
$122$		0			0
$123$	−6.00941	+	20.7182i	−0.541850	+	1.86810i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.47062	−	5.47062i	−0.485439	−	0.485439i	0.421425	−	0.906863i	$-0.361530\pi$
$127$	−5.47062	−	5.47062i	−0.485439	−	0.485439i	−0.906863	+	0.421425i	$0.861530\pi$
$128$		0			0
$129$	8.60475	−	4.73539i	0.757606	−	0.416928i
$130$		0			0
$131$		−	17.8285i		−	1.55769i	−0.627219	−	0.778843i	$-0.715807\pi$
$131$		−	17.8285i		−	1.55769i	0.627219	−	0.778843i	$-0.284193\pi$
$132$		0			0
$133$	10.3825	−	10.3825i	0.900277	−	0.900277i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.4050	+	11.4050i	−0.974396	+	0.974396i	−0.999680	−	0.0252848i	$-0.991951\pi$
$137$	−11.4050	+	11.4050i	−0.974396	+	0.974396i	0.0252848	+	0.999680i	$0.491951\pi$
$138$		0			0
$139$		−	2.27737i		−	0.193164i	−0.995325	−	0.0965821i	$-0.969209\pi$
$139$		−	2.27737i		−	0.193164i	0.995325	−	0.0965821i	$-0.0307910\pi$
$140$		0			0
$141$	−6.41807	+	3.53201i	−0.540499	+	0.297449i
$142$		0			0
$143$	0.426776	+	0.426776i	0.0356888	+	0.0356888i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.666800	+	2.29888i	−0.0549968	+	0.189609i
$148$		0			0
$149$	0.500041			0.0409649			0.0204825	−	0.999790i	$-0.493480\pi$
$149$	0.500041			0.0409649			0.0204825	+	0.999790i	$0.493480\pi$
$150$		0			0
$151$	0.503689			0.0409896			0.0204948	−	0.999790i	$-0.493476\pi$
$151$	0.503689			0.0409896			0.0204948	+	0.999790i	$0.493476\pi$
$152$		0			0
$153$	13.1420	−	2.94963i	1.06247	−	0.238463i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	14.9606	+	14.9606i	1.19398	+	1.19398i	0.975938	+	0.218046i	$0.0699684\pi$
$157$	14.9606	+	14.9606i	1.19398	+	1.19398i	0.218046	+	0.975938i	$0.430032\pi$
$158$		0			0
$159$	−5.44983	−	9.90297i	−0.432199	−	0.785356i
$160$		0			0
$161$		−	7.57447i		−	0.596952i
$162$		0			0
$163$	1.01054	−	1.01054i	0.0791513	−	0.0791513i	−0.666423	−	0.745574i	$-0.732175\pi$
$163$	1.01054	−	1.01054i	0.0791513	−	0.0791513i	0.745574	+	0.666423i	$0.232175\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.6099	−	13.6099i	1.05317	−	1.05317i	0.0546604	−	0.998505i	$-0.482592\pi$
$167$	13.6099	−	13.6099i	1.05317	−	1.05317i	0.998505	−	0.0546604i	$-0.0174076\pi$
$168$		0			0
$169$			9.24582i			0.711217i
$170$		0			0
$171$	−9.94427	+	15.6999i	−0.760457	+	1.20060i
$172$		0			0
$173$	14.1839	+	14.1839i	1.07838	+	1.07838i	0.996655	+	0.0817232i	$0.0260423\pi$
$173$	14.1839	+	14.1839i	1.07838	+	1.07838i	0.0817232	+	0.996655i	$0.473958\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.06572	−	2.62955i	−0.681422	−	0.197649i
$178$		0			0
$179$	12.8422			0.959870			0.479935	−	0.877304i	$-0.340660\pi$
$179$	12.8422			0.959870			0.479935	+	0.877304i	$0.340660\pi$
$180$		0			0
$181$	−3.72398			−0.276801			−0.138401	−	0.990376i	$-0.544196\pi$
$181$	−3.72398			−0.276801			−0.138401	+	0.990376i	$0.544196\pi$
$182$		0			0
$183$	−6.32632	−	1.83498i	−0.467655	−	0.135645i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.988906	+	0.988906i	0.0723160	+	0.0723160i
$188$		0			0
$189$	−0.757253	+	12.2928i	−0.0550821	+	0.894171i
$190$		0			0
$191$		−	8.81801i		−	0.638049i	−0.947747	−	0.319024i	$-0.896645\pi$
$191$		−	8.81801i		−	0.638049i	0.947747	−	0.319024i	$-0.103355\pi$
$192$		0			0
$193$	3.15143	−	3.15143i	0.226845	−	0.226845i	−0.584529	−	0.811373i	$-0.698720\pi$
$193$	3.15143	−	3.15143i	0.226845	−	0.226845i	0.811373	+	0.584529i	$0.198720\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.40823	+	6.40823i	−0.456567	+	0.456567i	−0.897527	−	0.440960i	$-0.854638\pi$
$197$	−6.40823	+	6.40823i	−0.456567	+	0.456567i	0.440960	+	0.897527i	$0.354638\pi$
$198$		0			0
$199$		−	9.46239i		−	0.670771i	−0.942081	−	0.335385i	$-0.891133\pi$
$199$		−	9.46239i		−	0.670771i	0.942081	−	0.335385i	$-0.108867\pi$
$200$		0			0
$201$	5.12793	+	9.31805i	0.361697	+	0.657244i
$202$		0			0
$203$	−5.77247	−	5.77247i	−0.405148	−	0.405148i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.09949	+	9.35425i	0.145925	+	0.650166i
$208$		0			0
$209$	−1.92966			−0.133478
$210$		0			0
$211$	−17.8375			−1.22798			−0.613992	−	0.789312i	$-0.710437\pi$
$211$	−17.8375			−1.22798			−0.613992	+	0.789312i	$0.710437\pi$
$212$		0			0
$213$	0.729566	−	2.51528i	0.0499890	−	0.172344i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.41674	+	6.41674i	0.435597	+	0.435597i
$218$		0			0
$219$	−7.69345	+	4.23388i	−0.519875	+	0.286099i
$220$		0			0
$221$		−	8.69903i		−	0.585160i
$222$		0			0
$223$	−18.6487	+	18.6487i	−1.24881	+	1.24881i	−0.292563	+	0.956246i	$0.594508\pi$
$223$	−18.6487	+	18.6487i	−1.24881	+	1.24881i	−0.956246	+	0.292563i	$0.905492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.4188	+	19.4188i	−1.28887	+	1.28887i	−0.353395	+	0.935474i	$0.614973\pi$
$227$	−19.4188	+	19.4188i	−1.28887	+	1.28887i	−0.935474	+	0.353395i	$0.885027\pi$
$228$		0			0
$229$			16.3640i			1.08136i	0.841227	+	0.540682i	$0.181834\pi$
$229$			16.3640i			1.08136i	−0.841227	+	0.540682i	$0.818166\pi$
$230$		0			0
$231$	−1.12037	+	0.616566i	−0.0737150	+	0.0405670i
$232$		0			0
$233$	−7.21714	−	7.21714i	−0.472811	−	0.472811i	0.430012	−	0.902823i	$-0.358509\pi$
$233$	−7.21714	−	7.21714i	−0.472811	−	0.472811i	−0.902823	+	0.430012i	$0.858509\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.64436	+	16.0121i	−0.301684	+	1.04010i
$238$		0			0
$239$	29.3512			1.89857			0.949285	−	0.314416i	$-0.101809\pi$
$239$	29.3512			1.89857			0.949285	+	0.314416i	$0.101809\pi$
$240$		0			0
$241$	−11.6001			−0.747226			−0.373613	−	0.927585i	$-0.621881\pi$
$241$	−11.6001			−0.747226			−0.373613	+	0.927585i	$0.621881\pi$
$242$		0			0
$243$	−2.47214	−	15.3912i	−0.158588	−	0.987345i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.48726	+	8.48726i	0.540031	+	0.540031i
$248$		0			0
$249$	9.78606	+	17.7824i	0.620166	+	1.12691i
$250$		0			0
$251$		−	24.1674i		−	1.52543i	−0.646733	−	0.762717i	$-0.723865\pi$
$251$		−	24.1674i		−	1.52543i	0.646733	−	0.762717i	$-0.276135\pi$
$252$		0			0
$253$	−0.703885	+	0.703885i	−0.0442529	+	0.0442529i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	18.1222	−	18.1222i	1.13043	−	1.13043i	0.140328	−	0.990105i	$-0.455184\pi$
$257$	18.1222	−	18.1222i	1.13043	−	1.13043i	0.990105	−	0.140328i	$-0.0448156\pi$
$258$		0			0
$259$			26.3984i			1.64032i
$260$		0			0
$261$	8.72886	+	5.52883i	0.540303	+	0.342226i
$262$		0			0
$263$	−18.4740	−	18.4740i	−1.13916	−	1.13916i	−0.988601	−	0.150557i	$-0.951893\pi$
$263$	−18.4740	−	18.4740i	−1.13916	−	1.13916i	−0.150557	−	0.988601i	$-0.548107\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	23.7410	+	6.88617i	1.45292	+	0.421427i
$268$		0			0
$269$	−6.68296			−0.407467			−0.203734	−	0.979026i	$-0.565308\pi$
$269$	−6.68296			−0.407467			−0.203734	+	0.979026i	$0.565308\pi$
$270$		0			0
$271$	24.2037			1.47027			0.735134	−	0.677921i	$-0.237119\pi$
$271$	24.2037			1.47027			0.735134	+	0.677921i	$0.237119\pi$
$272$		0			0
$273$	7.63958	+	2.21589i	0.462368	+	0.134112i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.6249	+	15.6249i	0.938810	+	0.938810i	0.998233	−	0.0594226i	$-0.0189260\pi$
$277$	15.6249	+	15.6249i	0.938810	+	0.938810i	−0.0594226	+	0.998233i	$0.518926\pi$
$278$		0			0
$279$	−9.70308	−	6.14590i	−0.580908	−	0.367945i
$280$		0			0
$281$			0.938474i			0.0559846i	0.999608	+	0.0279923i	$0.00891140\pi$
$281$			0.938474i			0.0559846i	−0.999608	+	0.0279923i	$0.991089\pi$
$282$		0			0
$283$	1.51593	−	1.51593i	0.0901128	−	0.0901128i	−0.660613	−	0.750726i	$-0.729704\pi$
$283$	1.51593	−	1.51593i	0.0901128	−	0.0901128i	0.750726	+	0.660613i	$0.229704\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.8742	+	20.8742i	−1.23217	+	1.23217i
$288$		0			0
$289$		−	3.15700i		−	0.185706i
$290$		0			0
$291$	11.7069	+	21.2727i	0.686268	+	1.24703i
$292$		0			0
$293$	16.9406	+	16.9406i	0.989678	+	0.989678i	0.999947	−	0.0102695i	$-0.00326894\pi$
$293$	16.9406	+	16.9406i	0.989678	+	0.989678i	−0.0102695	+	0.999947i	$0.503269\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.21273	−	1.07199i	0.0703695	−	0.0622029i
$298$		0			0
$299$	6.19181			0.358082
$300$		0			0
$301$	13.4406			0.774702
$302$		0			0
$303$	−4.49597	+	15.5005i	−0.258287	+	0.890478i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	15.3894	+	15.3894i	0.878317	+	0.878317i	0.993360	−	0.115043i	$-0.0367007\pi$
$307$	15.3894	+	15.3894i	0.878317	+	0.878317i	−0.115043	+	0.993360i	$0.536701\pi$
$308$		0			0
$309$	13.6488	−	7.51125i	0.776454	−	0.427300i
$310$		0			0
$311$			3.52016i			0.199610i	0.995007	+	0.0998051i	$0.0318219\pi$
$311$			3.52016i			0.199610i	−0.995007	+	0.0998051i	$0.968178\pi$
$312$		0			0
$313$	18.8366	−	18.8366i	1.06471	−	1.06471i	0.0669536	−	0.997756i	$-0.478672\pi$
$313$	18.8366	−	18.8366i	1.06471	−	1.06471i	0.997756	−	0.0669536i	$-0.0213280\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.9849	+	12.9849i	−0.729306	+	0.729306i	−0.970481	−	0.241176i	$-0.922467\pi$
$317$	−12.9849	+	12.9849i	−0.729306	+	0.729306i	0.241176	+	0.970481i	$0.422467\pi$
$318$		0			0
$319$			1.07286i			0.0600685i
$320$		0			0
$321$	−20.2007	+	11.1169i	−1.12749	+	0.620484i
$322$		0			0
$323$	19.6663	+	19.6663i	1.09426	+	1.09426i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.34997	+	11.5495i	−0.185254	+	0.638687i
$328$		0			0
$329$	−10.0250			−0.552696
$330$		0			0
$331$	10.2641			0.564165			0.282082	−	0.959390i	$-0.408975\pi$
$331$	10.2641			0.564165			0.282082	+	0.959390i	$0.408975\pi$
$332$		0			0
$333$	−7.31712	−	32.6013i	−0.400976	−	1.78654i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.90454	−	8.90454i	−0.485061	−	0.485061i	0.421682	−	0.906744i	$-0.361440\pi$
$337$	−8.90454	−	8.90454i	−0.485061	−	0.485061i	−0.906744	+	0.421682i	$0.861440\pi$
$338$		0			0
$339$	8.63590	+	15.6924i	0.469038	+	0.852296i
$340$		0			0
$341$		−	1.19260i		−	0.0645828i
$342$		0			0
$343$	−14.0483	+	14.0483i	−0.758536	+	0.758536i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.5563	+	11.5563i	−0.620375	+	0.620375i	−0.945627	−	0.325252i	$-0.894551\pi$
$347$	−11.5563	+	11.5563i	−0.620375	+	0.620375i	0.325252	+	0.945627i	$0.394551\pi$
$348$		0			0
$349$		−	14.3917i		−	0.770371i	−0.922839	−	0.385185i	$-0.874137\pi$
$349$		−	14.3917i		−	0.770371i	0.922839	−	0.385185i	$-0.125863\pi$
$350$		0			0
$351$	−10.0489	−	0.619023i	−0.536369	−	0.0330410i
$352$		0			0
$353$	21.7737	+	21.7737i	1.15890	+	1.15890i	0.984713	+	0.174187i	$0.0557296\pi$
$353$	21.7737	+	21.7737i	1.15890	+	1.15890i	0.174187	+	0.984713i	$0.444270\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	17.7021	+	5.13457i	0.936895	+	0.271750i
$358$		0			0
$359$	−16.7879			−0.886032			−0.443016	−	0.896514i	$-0.646092\pi$
$359$	−16.7879			−0.886032			−0.443016	+	0.896514i	$0.646092\pi$
$360$		0			0
$361$	−19.3751			−1.01974
$362$		0			0
$363$	−18.1370	−	5.26070i	−0.951943	−	0.276115i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.7656	+	18.7656i	0.979554	+	0.979554i	0.999795	−	0.0202409i	$-0.00644332\pi$
$367$	18.7656	+	18.7656i	0.979554	+	0.979554i	−0.0202409	+	0.999795i	$0.506443\pi$
$368$		0			0
$369$	19.9932	−	31.5650i	1.04080	−	1.64321i
$370$		0			0
$371$		−	15.4684i		−	0.803079i
$372$		0			0
$373$	6.30356	−	6.30356i	0.326386	−	0.326386i	−0.524824	−	0.851210i	$-0.675869\pi$
$373$	6.30356	−	6.30356i	0.326386	−	0.326386i	0.851210	+	0.524824i	$0.175869\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.71875	−	4.71875i	0.243028	−	0.243028i
$378$		0			0
$379$			11.3564i			0.583341i	0.956519	+	0.291671i	$0.0942111\pi$
$379$			11.3564i			0.583341i	−0.956519	+	0.291671i	$0.905789\pi$
$380$		0			0
$381$	6.46072	+	11.7399i	0.330993	+	0.601452i
$382$		0			0
$383$	−4.53482	−	4.53482i	−0.231718	−	0.231718i	0.581691	−	0.813410i	$-0.302391\pi$
$383$	−4.53482	−	4.53482i	−0.231718	−	0.231718i	−0.813410	+	0.581691i	$0.802391\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−16.5987	+	3.72546i	−0.843761	+	0.189376i
$388$		0			0
$389$	−19.8796			−1.00794			−0.503969	−	0.863722i	$-0.668127\pi$
$389$	−19.8796			−1.00794			−0.503969	+	0.863722i	$0.668127\pi$
$390$		0			0
$391$	14.3474			0.725579
$392$		0			0
$393$	−8.60229	+	29.6575i	−0.433928	+	1.49603i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	21.9308	+	21.9308i	1.10067	+	1.10067i	0.994329	+	0.106344i	$0.0339146\pi$
$397$	21.9308	+	21.9308i	1.10067	+	1.10067i	0.106344	+	0.994329i	$0.466085\pi$
$398$		0			0
$399$	−22.2807	+	12.2616i	−1.11543	+	0.613848i
$400$		0			0
$401$			17.2880i			0.863319i	0.902037	+	0.431660i	$0.142072\pi$
$401$			17.2880i			0.863319i	−0.902037	+	0.431660i	$0.857928\pi$
$402$		0			0
$403$	−5.24541	+	5.24541i	−0.261293	+	0.261293i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.45317	−	2.45317i	0.121599	−	0.121599i
$408$		0			0
$409$		−	12.3956i		−	0.612921i	−0.951883	−	0.306460i	$-0.900855\pi$
$409$		−	12.3956i		−	0.612921i	0.951883	−	0.306460i	$-0.0991447\pi$
$410$		0			0
$411$	24.4750	−	13.4692i	1.20726	−	0.664385i
$412$		0			0
$413$	−9.13398	−	9.13398i	−0.449454	−	0.449454i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.09883	+	3.78838i	−0.0538102	+	0.185518i
$418$		0			0
$419$	32.9039			1.60746			0.803731	−	0.594993i	$-0.202845\pi$
$419$	32.9039			1.60746			0.803731	+	0.594993i	$0.202845\pi$
$420$		0			0
$421$	−21.7995			−1.06244			−0.531221	−	0.847233i	$-0.678267\pi$
$421$	−21.7995			−1.06244			−0.531221	+	0.847233i	$0.678267\pi$
$422$		0			0
$423$	12.3806	−	2.77873i	0.601964	−	0.135106i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.37395	−	6.37395i	−0.308457	−	0.308457i
$428$		0			0
$429$	−0.504016	−	0.915856i	−0.0243341	−	0.0442180i
$430$		0			0
$431$		−	8.44584i		−	0.406822i	−0.979093	−	0.203411i	$-0.934797\pi$
$431$		−	8.44584i		−	0.406822i	0.979093	−	0.203411i	$-0.0652027\pi$
$432$		0			0
$433$	6.85220	−	6.85220i	0.329296	−	0.329296i	−0.523023	−	0.852319i	$-0.675196\pi$
$433$	6.85220	−	6.85220i	0.329296	−	0.329296i	0.852319	+	0.523023i	$0.175196\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.9981	+	13.9981i	−0.669621	+	0.669621i
$438$		0			0
$439$		−	40.8024i		−	1.94739i	−0.227851	−	0.973696i	$-0.573170\pi$
$439$		−	40.8024i		−	1.94739i	0.227851	−	0.973696i	$-0.426830\pi$
$440$		0			0
$441$	2.21843	−	3.50243i	0.105639	−	0.166783i
$442$		0			0
$443$	−9.52690	−	9.52690i	−0.452637	−	0.452637i	0.443592	−	0.896229i	$-0.353704\pi$
$443$	−9.52690	−	9.52690i	−0.452637	−	0.452637i	−0.896229	+	0.443592i	$0.853704\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.831812	−	0.241270i	−0.0393433	−	0.0114117i
$448$		0			0
$449$	−21.6192			−1.02028			−0.510138	−	0.860093i	$-0.670406\pi$
$449$	−21.6192			−1.02028			−0.510138	+	0.860093i	$0.670406\pi$
$450$		0			0
$451$	3.87963			0.182685
$452$		0			0
$453$	−0.837881	−	0.243031i	−0.0393671	−	0.0114186i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.519177	−	0.519177i	−0.0242861	−	0.0242861i	0.694859	−	0.719146i	$-0.255467\pi$
$457$	−0.519177	−	0.519177i	−0.0242861	−	0.0242861i	−0.719146	+	0.694859i	$0.755467\pi$
$458$		0			0
$459$	−23.2848	−	1.43437i	−1.08684	−	0.0669508i
$460$		0			0
$461$		−	27.2784i		−	1.27048i	−0.772314	−	0.635242i	$-0.780901\pi$
$461$		−	27.2784i		−	1.27048i	0.772314	−	0.635242i	$-0.219099\pi$
$462$		0			0
$463$	8.03916	−	8.03916i	0.373611	−	0.373611i	−0.495179	−	0.868791i	$-0.664898\pi$
$463$	8.03916	−	8.03916i	0.373611	−	0.373611i	0.868791	+	0.495179i	$0.164898\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.0961	−	19.0961i	0.883663	−	0.883663i	−0.110242	−	0.993905i	$-0.535163\pi$
$467$	19.0961	−	19.0961i	0.883663	−	0.883663i	0.993905	+	0.110242i	$0.0351626\pi$
$468$		0			0
$469$			14.5547i			0.672076i
$470$		0			0
$471$	−17.6683	−	32.1053i	−0.814110	−	1.47933i
$472$		0			0
$473$	−1.24902	−	1.24902i	−0.0574298	−	0.0574298i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.28753	+	19.1030i	0.196312	+	0.874667i
$478$		0			0
$479$	−23.2912			−1.06420			−0.532102	−	0.846680i	$-0.678598\pi$
$479$	−23.2912			−1.06420			−0.532102	+	0.846680i	$0.678598\pi$
$480$		0			0
$481$	−21.5796			−0.983946
$482$		0			0
$483$	−3.65469	+	12.6000i	−0.166294	+	0.573321i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.155962	−	0.155962i	−0.00706730	−	0.00706730i	0.703564	−	0.710632i	$-0.251591\pi$
$487$	−0.155962	−	0.155962i	−0.00706730	−	0.00706730i	−0.710632	+	0.703564i	$0.751591\pi$
$488$		0			0
$489$	−2.16860	+	1.19343i	−0.0980674	+	0.0539687i
$490$		0			0
$491$			25.8034i			1.16449i	0.813014	+	0.582245i	$0.197825\pi$
$491$			25.8034i			1.16449i	−0.813014	+	0.582245i	$0.802175\pi$
$492$		0			0
$493$	10.9341	−	10.9341i	0.492447	−	0.492447i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.53421	−	2.53421i	0.113675	−	0.113675i
$498$		0			0
$499$		−	15.7226i		−	0.703842i	−0.936030	−	0.351921i	$-0.885529\pi$
$499$		−	15.7226i		−	0.703842i	0.936030	−	0.351921i	$-0.114471\pi$
$500$		0			0
$501$	−29.2067	+	16.0731i	−1.30486	+	0.718093i
$502$		0			0
$503$	−11.7837	−	11.7837i	−0.525408	−	0.525408i	0.393792	−	0.919200i	$-0.371163\pi$
$503$	−11.7837	−	11.7837i	−0.525408	−	0.525408i	−0.919200	+	0.393792i	$0.871163\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.46112	−	15.3803i	0.198125	−	0.683063i
$508$		0			0
$509$	18.2590			0.809317			0.404658	−	0.914468i	$-0.367390\pi$
$509$	18.2590			0.809317			0.404658	+	0.914468i	$0.367390\pi$
$510$		0			0
$511$	−12.0171			−0.531606
$512$		0			0
$513$	24.1174	−	21.3185i	1.06481	−	0.941235i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.931609	+	0.931609i	0.0409721	+	0.0409721i
$518$		0			0
$519$	−16.7509	−	30.4384i	−0.735285	−	1.33610i
$520$		0			0
$521$		−	6.89080i		−	0.301891i	−0.988542	−	0.150946i	$-0.951768\pi$
$521$		−	6.89080i		−	0.301891i	0.988542	−	0.150946i	$-0.0482319\pi$
$522$		0			0
$523$	−18.1928	+	18.1928i	−0.795514	+	0.795514i	−0.982385	−	0.186870i	$-0.940166\pi$
$523$	−18.1928	+	18.1928i	−0.795514	+	0.795514i	0.186870	+	0.982385i	$0.440166\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.1544	+	12.1544i	−0.529456	+	0.529456i
$528$		0			0
$529$		−	12.7878i		−	0.555991i
$530$		0			0
$531$	13.8120	+	8.74845i	0.599388	+	0.379650i
$532$		0			0
$533$	−17.0638	−	17.0638i	−0.739115	−	0.739115i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−21.3628	−	6.19637i	−0.921874	−	0.267393i
$538$		0			0
$539$	0.430481			0.0185421
$540$		0			0
$541$	12.6550			0.544079			0.272040	−	0.962286i	$-0.412302\pi$
$541$	12.6550			0.544079			0.272040	+	0.962286i	$0.412302\pi$
$542$		0			0
$543$	6.19480	+	1.79683i	0.265844	+	0.0771092i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.92710	−	3.92710i	−0.167911	−	0.167911i	0.618150	−	0.786060i	$-0.287883\pi$
$547$	−3.92710	−	3.92710i	−0.167911	−	0.167911i	−0.786060	+	0.618150i	$0.787883\pi$
$548$		0			0
$549$	9.63839	+	6.10492i	0.411356	+	0.260552i
$550$		0			0
$551$			21.3358i			0.908937i
$552$		0			0
$553$	−16.1326	+	16.1326i	−0.686029	+	0.686029i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.71602	−	8.71602i	0.369309	−	0.369309i	−0.497916	−	0.867225i	$-0.665901\pi$
$557$	8.71602	−	8.71602i	0.369309	−	0.369309i	0.867225	+	0.497916i	$0.165901\pi$
$558$		0			0
$559$			10.9871i			0.464705i
$560$		0			0
$561$	−1.16788	−	2.12218i	−0.0493081	−	0.0895986i
$562$		0			0
$563$	−2.02153	−	2.02153i	−0.0851972	−	0.0851972i	0.663224	−	0.748421i	$-0.269188\pi$
$563$	−2.02153	−	2.02153i	−0.0851972	−	0.0851972i	−0.748421	+	0.663224i	$0.769188\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7.19099	−	20.0836i	0.301993	−	0.843431i
$568$		0			0
$569$	15.2127			0.637751			0.318876	−	0.947797i	$-0.396695\pi$
$569$	15.2127			0.637751			0.318876	+	0.947797i	$0.396695\pi$
$570$		0			0
$571$	28.0260			1.17285			0.586427	−	0.810002i	$-0.300534\pi$
$571$	28.0260			1.17285			0.586427	+	0.810002i	$0.300534\pi$
$572$		0			0
$573$	−4.25470	+	14.6686i	−0.177743	+	0.612792i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−29.8917	−	29.8917i	−1.24441	−	1.24441i	−0.958154	−	0.286254i	$-0.907590\pi$
$577$	−29.8917	−	29.8917i	−1.24441	−	1.24441i	−0.286254	−	0.958154i	$-0.592410\pi$
$578$		0			0
$579$	−6.76293	+	3.72179i	−0.281058	+	0.154672i
$580$		0			0
$581$			27.7760i			1.15234i
$582$		0			0
$583$	−1.43746	+	1.43746i	−0.0595334	+	0.0595334i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.40096	−	4.40096i	0.181647	−	0.181647i	−0.610426	−	0.792073i	$-0.709002\pi$
$587$	4.40096	−	4.40096i	0.181647	−	0.181647i	0.792073	+	0.610426i	$0.209002\pi$
$588$		0			0
$589$		−	23.7171i		−	0.977247i
$590$		0			0
$591$	13.7520	−	7.56803i	0.565681	−	0.311307i
$592$		0			0
$593$	−1.94837	−	1.94837i	−0.0800099	−	0.0800099i	0.665969	−	0.745979i	$-0.268018\pi$
$593$	−1.94837	−	1.94837i	−0.0800099	−	0.0800099i	−0.745979	+	0.665969i	$0.768018\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.56561	+	15.7406i	−0.186858	+	0.644218i
$598$		0			0
$599$	33.8335			1.38240			0.691200	−	0.722664i	$-0.257082\pi$
$599$	33.8335			1.38240			0.691200	+	0.722664i	$0.257082\pi$
$600$		0			0
$601$	44.7999			1.82743			0.913713	−	0.406360i	$-0.133202\pi$
$601$	44.7999			1.82743			0.913713	+	0.406360i	$0.133202\pi$
$602$		0			0
$603$	−4.03429	−	17.9747i	−0.164289	−	0.731986i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.8668	−	18.8668i	−0.765778	−	0.765778i	0.211582	−	0.977360i	$-0.432138\pi$
$607$	−18.8668	−	18.8668i	−0.765778	−	0.765778i	−0.977360	+	0.211582i	$0.932138\pi$
$608$		0			0
$609$	6.81721	+	12.3877i	0.276247	+	0.501974i
$610$		0			0
$611$		−	8.19501i		−	0.331535i
$612$		0			0
$613$	−9.35448	+	9.35448i	−0.377824	+	0.377824i	−0.870317	−	0.492493i	$-0.836086\pi$
$613$	−9.35448	+	9.35448i	−0.377824	+	0.377824i	0.492493	+	0.870317i	$0.336086\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.5616	−	19.5616i	0.787521	−	0.787521i	−0.193566	−	0.981087i	$-0.562005\pi$
$617$	19.5616	−	19.5616i	0.787521	−	0.787521i	0.981087	+	0.193566i	$0.0620055\pi$
$618$		0			0
$619$			33.9956i			1.36640i	0.730232	+	0.683200i	$0.239412\pi$
$619$			33.9956i			1.36640i	−0.730232	+	0.683200i	$0.760588\pi$
$620$		0			0
$621$	1.02096	−	16.5737i	0.0409697	−	0.665079i
$622$		0			0
$623$	23.9197	+	23.9197i	0.958324	+	0.958324i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.20997	+	0.931066i	0.128194	+	0.0371832i
$628$		0			0
$629$	−50.0033			−1.99376
$630$		0			0
$631$	−34.3392			−1.36702			−0.683510	−	0.729941i	$-0.739548\pi$
$631$	−34.3392			−1.36702			−0.683510	+	0.729941i	$0.739548\pi$
$632$		0			0
$633$	29.6725	+	8.60661i	1.17937	+	0.342082i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.89339	−	1.89339i	−0.0750188	−	0.0750188i
$638$		0			0
$639$	−2.42725	+	3.83212i	−0.0960205	+	0.151596i
$640$		0			0
$641$			10.8771i			0.429618i	0.976656	+	0.214809i	$0.0689129\pi$
$641$			10.8771i			0.429618i	−0.976656	+	0.214809i	$0.931087\pi$
$642$		0			0
$643$	2.05532	−	2.05532i	0.0810540	−	0.0810540i	−0.665417	−	0.746471i	$-0.731746\pi$
$643$	2.05532	−	2.05532i	0.0810540	−	0.0810540i	0.746471	+	0.665417i	$0.231746\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.4554	−	15.4554i	0.607613	−	0.607613i	−0.334709	−	0.942322i	$-0.608638\pi$
$647$	15.4554	−	15.4554i	0.607613	−	0.607613i	0.942322	+	0.334709i	$0.108638\pi$
$648$		0			0
$649$			1.69762i			0.0666373i
$650$		0			0
$651$	−7.57808	−	13.7703i	−0.297008	−	0.539699i
$652$		0			0
$653$	12.2497	+	12.2497i	0.479370	+	0.479370i	0.904930	−	0.425560i	$-0.139923\pi$
$653$	12.2497	+	12.2497i	0.479370	+	0.479370i	−0.425560	+	0.904930i	$0.639923\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	14.8408	−	3.33091i	0.578995	−	0.129951i
$658$		0			0
$659$	−1.93458			−0.0753605			−0.0376803	−	0.999290i	$-0.511997\pi$
$659$	−1.93458			−0.0753605			−0.0376803	+	0.999290i	$0.511997\pi$
$660$		0			0
$661$	−38.0398			−1.47958			−0.739789	−	0.672839i	$-0.765075\pi$
$661$	−38.0398			−1.47958			−0.739789	+	0.672839i	$0.765075\pi$
$662$		0			0
$663$	−4.19729	+	14.4707i	−0.163009	+	0.561996i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.78269	+	7.78269i	0.301347	+	0.301347i
$668$		0			0
$669$	40.0199	−	22.0239i	1.54726	−	0.851492i
$670$		0			0
$671$			1.18465i			0.0457328i
$672$		0			0
$673$	−6.64517	+	6.64517i	−0.256152	+	0.256152i	−0.823487	−	0.567335i	$-0.807975\pi$
$673$	−6.64517	+	6.64517i	−0.256152	+	0.256152i	0.567335	+	0.823487i	$0.307975\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.04093	−	6.04093i	0.232172	−	0.232172i	−0.581427	−	0.813599i	$-0.697505\pi$
$677$	6.04093	−	6.04093i	0.232172	−	0.232172i	0.813599	+	0.581427i	$0.197505\pi$
$678$		0			0
$679$			33.2279i			1.27517i
$680$		0			0
$681$	41.6725	−	22.9333i	1.59689	−	0.878806i
$682$		0			0
$683$	−5.67427	−	5.67427i	−0.217120	−	0.217120i	0.590164	−	0.807284i	$-0.299063\pi$
$683$	−5.67427	−	5.67427i	−0.217120	−	0.217120i	−0.807284	+	0.590164i	$0.799063\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	7.89565	−	27.2213i	0.301238	−	1.03856i
$688$		0			0
$689$	12.6448			0.481727
$690$		0			0
$691$	16.1317			0.613677			0.306839	−	0.951762i	$-0.400729\pi$
$691$	16.1317			0.613677			0.306839	+	0.951762i	$0.400729\pi$
$692$		0			0
$693$	2.16122	−	0.485069i	0.0820979	−	0.0184262i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−39.5395	−	39.5395i	−1.49767	−	1.49767i
$698$		0			0
$699$	8.52335	+	15.4879i	0.322383	+	0.585807i
$700$		0			0
$701$			36.9031i			1.39381i	0.717164	+	0.696905i	$0.245440\pi$
$701$			36.9031i			1.39381i	−0.717164	+	0.696905i	$0.754560\pi$
$702$		0			0
$703$	48.7861	−	48.7861i	1.84000	−	1.84000i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.6172	+	15.6172i	−0.587344	+	0.587344i
$708$		0			0
$709$			30.7391i			1.15443i	0.816592	+	0.577216i	$0.195861\pi$
$709$			30.7391i			1.15443i	−0.816592	+	0.577216i	$0.804139\pi$
$710$		0			0
$711$	15.4517	−	24.3950i	0.579483	−	0.914883i
$712$		0			0
$713$	−8.65131	−	8.65131i	−0.323994	−	0.323994i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−48.8253	−	14.1620i	−1.82342	−	0.528889i
$718$		0			0
$719$	−2.92975			−0.109261			−0.0546305	−	0.998507i	$-0.517398\pi$
$719$	−2.92975			−0.109261			−0.0546305	+	0.998507i	$0.517398\pi$
$720$		0			0
$721$	21.3194			0.793975
$722$		0			0
$723$	19.2966	+	5.59705i	0.717647	+	0.208156i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−18.1790	−	18.1790i	−0.674221	−	0.674221i	0.284466	−	0.958686i	$-0.408184\pi$
$727$	−18.1790	−	18.1790i	−0.674221	−	0.674221i	−0.958686	+	0.284466i	$0.908184\pi$
$728$		0			0
$729$	−3.31389	+	26.7959i	−0.122737	+	0.992439i
$730$		0			0
$731$			25.4589i			0.941630i
$732$		0			0
$733$	−0.340902	+	0.340902i	−0.0125915	+	0.0125915i	−0.713375	−	0.700783i	$-0.752834\pi$
$733$	−0.340902	+	0.340902i	−0.0125915	+	0.0125915i	0.700783	+	0.713375i	$0.252834\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.35255	−	1.35255i	0.0498219	−	0.0498219i
$738$		0			0
$739$		−	19.2765i		−	0.709099i	−0.935037	−	0.354549i	$-0.884634\pi$
$739$		−	19.2765i		−	0.709099i	0.935037	−	0.354549i	$-0.115366\pi$
$740$		0			0
$741$	−10.0233	−	18.2136i	−0.368217	−	0.669092i
$742$		0			0
$743$	−7.98872	−	7.98872i	−0.293078	−	0.293078i	0.545217	−	0.838295i	$-0.316447\pi$
$743$	−7.98872	−	7.98872i	−0.293078	−	0.293078i	−0.838295	+	0.545217i	$0.816447\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.69896	−	34.3026i	−0.281690	−	1.25507i
$748$		0			0
$749$	−31.5533			−1.15293
$750$		0			0
$751$	−1.87963			−0.0685886			−0.0342943	−	0.999412i	$-0.510918\pi$
$751$	−1.87963			−0.0685886			−0.0342943	+	0.999412i	$0.510918\pi$
$752$		0			0
$753$	−11.6608	+	40.2022i	−0.424943	+	1.46505i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.98084	+	5.98084i	0.217377	+	0.217377i	0.807392	−	0.590015i	$-0.200878\pi$
$757$	5.98084	+	5.98084i	0.217377	+	0.217377i	−0.590015	+	0.807392i	$0.700878\pi$
$758$		0			0
$759$	1.51053	−	0.831279i	0.0548288	−	0.0301735i
$760$		0			0
$761$			11.2398i			0.407441i	0.979029	+	0.203721i	$0.0653034\pi$
$761$			11.2398i			0.407441i	−0.979029	+	0.203721i	$0.934697\pi$
$762$		0			0
$763$	−11.6364	+	11.6364i	−0.421267	+	0.421267i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.46664	−	7.46664i	0.269605	−	0.269605i
$768$		0			0
$769$			31.9043i			1.15050i	0.817978	+	0.575250i	$0.195095\pi$
$769$			31.9043i			1.15050i	−0.817978	+	0.575250i	$0.804905\pi$
$770$		0			0
$771$	−38.8901	+	21.4021i	−1.40059	+	0.770778i
$772$		0			0
$773$	−28.2050	−	28.2050i	−1.01446	−	1.01446i	−0.999894	−	0.0145712i	$-0.995362\pi$
$773$	−28.2050	−	28.2050i	−1.01446	−	1.01446i	−0.0145712	−	0.999894i	$-0.504638\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.7373	−	43.9135i	0.456948	−	1.57539i
$778$		0			0
$779$	77.1539			2.76433
$780$		0			0
$781$	−0.471002			−0.0168538
$782$		0			0
$783$	−11.8527	−	13.4088i	−0.423580	−	0.479192i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.68582	−	3.68582i	−0.131385	−	0.131385i	0.638356	−	0.769741i	$-0.279615\pi$
$787$	−3.68582	−	3.68582i	−0.131385	−	0.131385i	−0.769741	+	0.638356i	$0.779615\pi$
$788$		0			0
$789$	21.8176	+	39.6451i	0.776727	+	1.41140i
$790$		0			0
$791$			24.5115i			0.871528i
$792$		0			0
$793$	5.21044	−	5.21044i	0.185028	−	0.185028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.10850	−	1.10850i	0.0392651	−	0.0392651i	−0.687202	−	0.726467i	$-0.741161\pi$
$797$	1.10850	−	1.10850i	0.0392651	−	0.0392651i	0.726467	+	0.687202i	$0.241161\pi$
$798$		0			0
$799$		−	18.9891i		−	0.671787i
$800$		0			0
$801$	−36.1703	−	22.9101i	−1.27801	−	0.809489i
$802$		0			0
$803$	1.11674	+	1.11674i	0.0394088	+	0.0394088i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.1170	+	3.22454i	0.391338	+	0.113509i
$808$		0			0
$809$	−28.9167			−1.01666			−0.508329	−	0.861163i	$-0.669737\pi$
$809$	−28.9167			−1.01666			−0.508329	+	0.861163i	$0.669737\pi$
$810$		0			0
$811$	−18.5177			−0.650244			−0.325122	−	0.945672i	$-0.605405\pi$
$811$	−18.5177			−0.650244			−0.325122	+	0.945672i	$0.605405\pi$
$812$		0			0
$813$	−40.2625	−	11.6783i	−1.41207	−	0.409576i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−24.8391	−	24.8391i	−0.869010	−	0.869010i
$818$		0			0
$819$	−11.6392	−	7.37222i	−0.406706	−	0.257606i
$820$		0			0
$821$			16.1279i			0.562869i	0.959580	+	0.281435i	$0.0908102\pi$
$821$			16.1279i			0.562869i	−0.959580	+	0.281435i	$0.909190\pi$
$822$		0			0
$823$	−10.9389	+	10.9389i	−0.381308	+	0.381308i	−0.871573	−	0.490266i	$-0.836900\pi$
$823$	−10.9389	+	10.9389i	−0.381308	+	0.381308i	0.490266	+	0.871573i	$0.336900\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.21155	−	2.21155i	0.0769032	−	0.0769032i	−0.667609	−	0.744512i	$-0.732682\pi$
$827$	2.21155	−	2.21155i	0.0769032	−	0.0769032i	0.744512	+	0.667609i	$0.232682\pi$
$828$		0			0
$829$		−	1.69243i		−	0.0587804i	−0.999568	−	0.0293902i	$-0.990643\pi$
$829$		−	1.69243i		−	0.0587804i	0.999568	−	0.0293902i	$-0.00935654\pi$
$830$		0			0
$831$	−18.4528	−	33.5309i	−0.640121	−	1.16317i
$832$		0			0
$833$	−4.38728	−	4.38728i	−0.152010	−	0.152010i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.1756	+	14.9054i	0.455414	+	0.515205i
$838$		0			0
$839$	33.7354			1.16467			0.582337	−	0.812948i	$-0.302138\pi$
$839$	33.7354			1.16467			0.582337	+	0.812948i	$0.302138\pi$
$840$		0			0
$841$	−17.1377			−0.590955
$842$		0			0
$843$	0.452815	−	1.56114i	0.0155958	−	0.0537685i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−18.2735	−	18.2735i	−0.627885	−	0.627885i
$848$		0			0
$849$	−3.25317	+	1.79029i	−0.111649	+	0.0614428i
$850$		0			0
$851$		−	35.5915i		−	1.22006i
$852$		0			0
$853$	−11.6934	+	11.6934i	−0.400375	+	0.400375i	−0.878365	−	0.477990i	$-0.841365\pi$
$853$	−11.6934	+	11.6934i	−0.400375	+	0.400375i	0.477990	+	0.878365i	$0.341365\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	34.2539	−	34.2539i	1.17009	−	1.17009i	0.187902	−	0.982188i	$-0.439831\pi$
$857$	34.2539	−	34.2539i	1.17009	−	1.17009i	0.982188	−	0.187902i	$-0.0601686\pi$
$858$		0			0
$859$		−	6.19206i		−	0.211270i	−0.994405	−	0.105635i	$-0.966312\pi$
$859$		−	6.19206i		−	0.211270i	0.994405	−	0.105635i	$-0.0336876\pi$
$860$		0			0
$861$	44.7959	−	24.6522i	1.52664	−	0.840144i
$862$		0			0
$863$	24.5191	+	24.5191i	0.834639	+	0.834639i	0.988147	−	0.153508i	$-0.0490571\pi$
$863$	24.5191	+	24.5191i	0.834639	+	0.834639i	−0.153508	+	0.988147i	$0.549057\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.52326	+	5.25163i	−0.0517325	+	0.178355i
$868$		0			0
$869$	2.99837			0.101713
$870$		0			0
$871$	−11.8979			−0.403145
$872$		0			0
$873$	−9.21010	−	41.0355i	−0.311715	−	1.38884i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	27.1263	+	27.1263i	0.915990	+	0.915990i	0.996735	−	0.0807449i	$-0.0257299\pi$
$877$	27.1263	+	27.1263i	0.915990	+	0.915990i	−0.0807449	+	0.996735i	$0.525730\pi$
$878$		0			0
$879$	−20.0066	−	36.3543i	−0.674805	−	1.22620i
$880$		0			0
$881$		−	0.439372i		−	0.0148028i	−0.999973	−	0.00740140i	$-0.997644\pi$
$881$		−	0.439372i		−	0.0148028i	0.999973	−	0.00740140i	$-0.00235596\pi$
$882$		0			0
$883$	0.0107839	−	0.0107839i	0.000362907	−	0.000362907i	−0.706925	−	0.707288i	$-0.749918\pi$
$883$	0.0107839	−	0.0107839i	0.000362907	−	0.000362907i	0.707288	+	0.706925i	$0.249918\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.9142	−	13.9142i	0.467192	−	0.467192i	−0.433811	−	0.901004i	$-0.642832\pi$
$887$	13.9142	−	13.9142i	0.467192	−	0.467192i	0.901004	+	0.433811i	$0.142832\pi$
$888$		0			0
$889$			18.3376i			0.615025i
$890$		0			0
$891$	−2.53459	+	1.19809i	−0.0849120	+	0.0401376i
$892$		0			0
$893$	18.5268	+	18.5268i	0.619977	+	0.619977i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−10.3000	−	2.98756i	−0.343907	−	0.0997516i
$898$		0			0
$899$	−13.1863			−0.439787
$900$		0			0
$901$	29.2999			0.976120
$902$		0			0
$903$	−22.3582	−	6.48510i	−0.744036	−	0.215811i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−34.1899	−	34.1899i	−1.13526	−	1.13526i	−0.989289	−	0.145967i	$-0.953371\pi$
$907$	−34.1899	−	34.1899i	−1.13526	−	1.13526i	−0.145967	−	0.989289i	$-0.546629\pi$
$908$		0			0
$909$	14.9580	−	23.6155i	0.496125	−	0.783277i
$910$		0			0
$911$			51.2365i			1.69754i	0.528762	+	0.848770i	$0.322656\pi$
$911$			51.2365i			1.69754i	−0.528762	+	0.848770i	$0.677344\pi$
$912$		0			0
$913$	2.58119	−	2.58119i	0.0854249	−	0.0854249i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−29.8808	+	29.8808i	−0.986752	+	0.986752i
$918$		0			0
$919$		−	4.41287i		−	0.145567i	−0.997348	−	0.0727835i	$-0.976812\pi$
$919$		−	4.41287i		−	0.145567i	0.997348	−	0.0727835i	$-0.0231882\pi$
$920$		0			0
$921$	−18.1746	−	33.0254i	−0.598874	−	1.08822i
$922$		0			0
$923$	2.07161	+	2.07161i	0.0681880	+	0.0681880i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−26.3288	+	5.90931i	−0.864752	+	0.194087i
$928$		0			0
$929$	−11.2678			−0.369686			−0.184843	−	0.982768i	$-0.559178\pi$
$929$	−11.2678			−0.369686			−0.184843	+	0.982768i	$0.559178\pi$
$930$		0			0
$931$	8.56095			0.280574
$932$		0			0
$933$	1.69848	−	5.85575i	0.0556059	−	0.191709i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−23.1002	−	23.1002i	−0.754652	−	0.754652i	0.220692	−	0.975344i	$-0.429169\pi$
$937$	−23.1002	−	23.1002i	−0.754652	−	0.754652i	−0.975344	+	0.220692i	$0.929169\pi$
$938$		0			0
$939$	−40.4232	+	22.2458i	−1.31916	+	0.725965i
$940$		0			0
$941$		−	1.68443i		−	0.0549109i	−0.999623	−	0.0274554i	$-0.991260\pi$
$941$		−	1.68443i		−	0.0549109i	0.999623	−	0.0274554i	$-0.00874043\pi$
$942$		0			0
$943$	28.1435	−	28.1435i	0.916478	−	0.916478i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.6097	−	18.6097i	0.604733	−	0.604733i	−0.336831	−	0.941565i	$-0.609355\pi$
$947$	18.6097	−	18.6097i	0.604733	−	0.604733i	0.941565	+	0.336831i	$0.109355\pi$
$948$		0			0
$949$		−	9.82350i		−	0.318884i
$950$		0			0
$951$	27.8655	−	15.3350i	0.903601	−	0.497272i
$952$		0			0
$953$	1.88101	+	1.88101i	0.0609319	+	0.0609319i	0.736916	−	0.675984i	$-0.236281\pi$
$953$	1.88101	+	1.88101i	0.0609319	+	0.0609319i	−0.675984	+	0.736916i	$0.736281\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.517655	−	1.78468i	0.0167334	−	0.0576907i
$958$		0			0
$959$	38.2299			1.23451
$960$		0			0
$961$	−16.3420			−0.527162
$962$		0			0
$963$	38.9675	−	8.74596i	1.25571	−	0.281835i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.55730	−	1.55730i	−0.0500794	−	0.0500794i	0.681624	−	0.731703i	$-0.261274\pi$
$967$	−1.55730	−	1.55730i	−0.0500794	−	0.0500794i	−0.731703	+	0.681624i	$0.761274\pi$
$968$		0			0
$969$	−23.2256	−	42.2037i	−0.746115	−	1.35578i
$970$		0			0
$971$			30.5597i			0.980707i	0.871524	+	0.490354i	$0.163132\pi$
$971$			30.5597i			0.980707i	−0.871524	+	0.490354i	$0.836868\pi$
$972$		0			0
$973$	−3.81690	+	3.81690i	−0.122364	+	0.122364i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.8254	−	19.8254i	0.634270	−	0.634270i	−0.314866	−	0.949136i	$-0.601960\pi$
$977$	19.8254	−	19.8254i	0.634270	−	0.634270i	0.949136	+	0.314866i	$0.101960\pi$
$978$		0			0
$979$		−	4.44566i		−	0.142084i
$980$		0			0
$981$	11.1453	−	17.5960i	0.355841	−	0.561798i
$982$		0			0
$983$	38.2648	+	38.2648i	1.22046	+	1.22046i	0.967469	+	0.252988i	$0.0814134\pi$
$983$	38.2648	+	38.2648i	1.22046	+	1.22046i	0.252988	+	0.967469i	$0.418587\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	16.6765	+	4.83707i	0.530817	+	0.153966i
$988$		0			0
$989$	−18.1212			−0.576219
$990$		0			0
$991$	−34.1499			−1.08481			−0.542404	−	0.840118i	$-0.682486\pi$
$991$	−34.1499			−1.08481			−0.542404	+	0.840118i	$0.682486\pi$
$992$		0			0
$993$	−17.0742	−	4.95243i	−0.541833	−	0.157161i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.0802	+	24.0802i	0.762628	+	0.762628i	0.976797	−	0.214169i	$-0.0687043\pi$
$997$	24.0802	+	24.0802i	0.762628	+	0.762628i	−0.214169	+	0.976797i	$0.568704\pi$
$998$		0			0
$999$	−3.55824	+	57.7624i	−0.112578	+	1.82752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.b.557.1	✓	32
3.2	odd	2	inner	1500.2.i.b.557.9	yes	32
5.2	odd	4	inner	1500.2.i.b.1193.8	yes	32
5.3	odd	4	inner	1500.2.i.b.1193.9	yes	32
5.4	even	2	inner	1500.2.i.b.557.16	yes	32
15.2	even	4	inner	1500.2.i.b.1193.16	yes	32
15.8	even	4	inner	1500.2.i.b.1193.1	yes	32
15.14	odd	2	inner	1500.2.i.b.557.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.b.557.1	✓	32	1.1	even	1	trivial
1500.2.i.b.557.8	yes	32	15.14	odd	2	inner
1500.2.i.b.557.9	yes	32	3.2	odd	2	inner
1500.2.i.b.557.16	yes	32	5.4	even	2	inner
1500.2.i.b.1193.1	yes	32	15.8	even	4	inner
1500.2.i.b.1193.8	yes	32	5.2	odd	4	inner
1500.2.i.b.1193.9	yes	32	5.3	odd	4	inner
1500.2.i.b.1193.16	yes	32	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66349 - 0.482501i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(2.53438 + 1.60527i) q^{9} +O(q^{10})\)	\(q+(-1.66349 - 0.482501i) q^{3} +(-1.67601 - 1.67601i) q^{7} +(2.53438 + 1.60527i) q^{9} +0.311499i q^{11} +(1.37007 - 1.37007i) q^{13} +(3.17467 - 3.17467i) q^{17} +6.19476i q^{19} +(1.97935 + 3.59670i) q^{21} +(2.25967 + 2.25967i) q^{23} +(-3.44137 - 3.89319i) q^{27} +3.44417 q^{29} -3.82857 q^{31} +(0.150299 - 0.518175i) q^{33} +(-7.87537 - 7.87537i) q^{37} +(-2.94015 + 1.61803i) q^{39} -12.4547i q^{41} +(-4.00969 + 4.00969i) q^{43} +(2.99073 - 2.99073i) q^{47} -1.38197i q^{49} +(-6.81280 + 3.74924i) q^{51} +(4.61464 + 4.61464i) q^{53} +(2.98898 - 10.3049i) q^{57} +5.44983 q^{59} +3.80305 q^{61} +(-1.55721 - 6.93811i) q^{63} +(-4.34208 - 4.34208i) q^{67} +(-2.66864 - 4.84923i) q^{69} +1.51205i q^{71} +(3.58504 - 3.58504i) q^{73} +(0.522077 - 0.522077i) q^{77} -9.62560i q^{79} +(3.84621 + 8.13675i) q^{81} +(-8.28634 - 8.28634i) q^{83} +(-5.72934 - 1.66182i) q^{87} -14.2718 q^{89} -4.59251 q^{91} +(6.36879 + 1.84729i) q^{93} +(-9.91277 - 9.91277i) q^{97} +(-0.500041 + 0.789459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) \) 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

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