LMFDB - Embedded newform 1500.2.i.b.557.8

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			557.8
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.b.1193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.482501 - 1.66349i) q^{3} +(1.67601 + 1.67601i) q^{7} +(-2.53438 + 1.60527i) q^{9} +O(q^{10})$	$q+(-0.482501 - 1.66349i) q^{3} +(1.67601 + 1.67601i) q^{7} +(-2.53438 + 1.60527i) q^{9} -0.311499i q^{11} +(-1.37007 + 1.37007i) q^{13} +(3.17467 - 3.17467i) q^{17} +6.19476i q^{19} +(1.97935 - 3.59670i) q^{21} +(2.25967 + 2.25967i) q^{23} +(3.89319 + 3.44137i) q^{27} -3.44417 q^{29} -3.82857 q^{31} +(-0.518175 + 0.150299i) q^{33} +(7.87537 + 7.87537i) q^{37} +(2.94015 + 1.61803i) q^{39} +12.4547i q^{41} +(4.00969 - 4.00969i) q^{43} +(2.99073 - 2.99073i) q^{47} -1.38197i q^{49} +(-6.81280 - 3.74924i) q^{51} +(4.61464 + 4.61464i) q^{53} +(10.3049 - 2.98898i) q^{57} -5.44983 q^{59} +3.80305 q^{61} +(-6.93811 - 1.55721i) q^{63} +(4.34208 + 4.34208i) q^{67} +(2.66864 - 4.84923i) q^{69} -1.51205i q^{71} +(-3.58504 + 3.58504i) q^{73} +(0.522077 - 0.522077i) q^{77} -9.62560i q^{79} +(3.84621 - 8.13675i) q^{81} +(-8.28634 - 8.28634i) q^{83} +(1.66182 + 5.72934i) q^{87} +14.2718 q^{89} -4.59251 q^{91} +(1.84729 + 6.36879i) q^{93} +(9.91277 + 9.91277i) q^{97} +(0.500041 + 0.789459i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.482501	−	1.66349i	−0.278572	−	0.960415i
$3$	−0.482501	−	1.66349i	−0.278572	−	0.960415i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.67601	+	1.67601i	0.633473	+	0.633473i	0.948937	−	0.315464i	$-0.102160\pi$
$7$	1.67601	+	1.67601i	0.633473	+	0.633473i	−0.315464	+	0.948937i	$0.602160\pi$
$8$		0			0
$9$	−2.53438	+	1.60527i	−0.844795	+	0.535090i
$10$		0			0
$11$		−	0.311499i		−	0.0939206i	−0.998897	−	0.0469603i	$-0.985047\pi$
$11$		−	0.311499i		−	0.0939206i	0.998897	−	0.0469603i	$-0.0149534\pi$
$12$		0			0
$13$	−1.37007	+	1.37007i	−0.379989	+	0.379989i	−0.871098	−	0.491109i	$-0.836592\pi$
$13$	−1.37007	+	1.37007i	−0.379989	+	0.379989i	0.491109	+	0.871098i	$0.336592\pi$
$14$		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
$27$	3.89319	+	3.44137i	0.749245	+	0.662293i
$28$		0			0
$29$	−3.44417			−0.639567			−0.319783	−	0.947491i	$-0.603610\pi$
$29$	−3.44417			−0.639567			−0.319783	+	0.947491i	$0.603610\pi$
$30$		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
$33$	−0.518175	+	0.150299i	−0.0902028	+	0.0261637i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.87537	+	7.87537i	1.29470	+	1.29470i	0.931844	+	0.362859i	$0.118200\pi$
$37$	7.87537	+	7.87537i	1.29470	+	1.29470i	0.362859	+	0.931844i	$0.381800\pi$
$38$		0			0
$39$	2.94015	+	1.61803i	0.470802	+	0.259093i
$40$		0			0
$41$			12.4547i			1.94510i	0.232701	+	0.972548i	$0.425244\pi$
$41$			12.4547i			1.94510i	−0.232701	+	0.972548i	$0.574756\pi$
$42$		0			0
$43$	4.00969	−	4.00969i	0.611472	−	0.611472i	−0.331857	−	0.943330i	$-0.607675\pi$
$43$	4.00969	−	4.00969i	0.611472	−	0.611472i	0.943330	+	0.331857i	$0.107675\pi$
$44$		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
$57$	10.3049	−	2.98898i	1.36492	−	0.395900i
$58$		0			0
$59$	−5.44983			−0.709507			−0.354754	−	0.934960i	$-0.615435\pi$
$59$	−5.44983			−0.709507			−0.354754	+	0.934960i	$0.615435\pi$
$60$		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
$63$	−6.93811	−	1.55721i	−0.874120	−	0.196190i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.34208	+	4.34208i	0.530469	+	0.530469i	0.920712	−	0.390243i	$-0.127609\pi$
$67$	4.34208	+	4.34208i	0.530469	+	0.530469i	−0.390243	+	0.920712i	$0.627609\pi$
$68$		0			0
$69$	2.66864	−	4.84923i	0.321266	−	0.583778i
$70$		0			0
$71$		−	1.51205i		−	0.179447i	−0.995967	−	0.0897236i	$-0.971402\pi$
$71$		−	1.51205i		−	0.179447i	0.995967	−	0.0897236i	$-0.0285984\pi$
$72$		0			0
$73$	−3.58504	+	3.58504i	−0.419597	+	0.419597i	−0.885065	−	0.465468i	$-0.845886\pi$
$73$	−3.58504	+	3.58504i	−0.419597	+	0.419597i	0.465468	+	0.885065i	$0.345886\pi$
$74$		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
$87$	1.66182	+	5.72934i	0.178166	+	0.614249i
$88$		0			0
$89$	14.2718			1.51281			0.756404	−	0.654104i	$-0.226954\pi$
$89$	14.2718			1.51281			0.756404	+	0.654104i	$0.226954\pi$
$90$		0			0
$91$	−4.59251			−0.481426
$92$		0			0
$93$	1.84729	+	6.36879i	0.191555	+	0.660413i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.91277	+	9.91277i	1.00649	+	1.00649i	0.999979	+	0.00651069i	$0.00207243\pi$
$97$	9.91277	+	9.91277i	1.00649	+	1.00649i	0.00651069	+	0.999979i	$0.497928\pi$
$98$		0			0
$99$	0.500041	+	0.789459i	0.0502560	+	0.0793436i
$100$		0			0
$101$			9.31805i			0.927180i	0.886050	+	0.463590i	$0.153439\pi$
$101$			9.31805i			0.927180i	−0.886050	+	0.463590i	$0.846561\pi$
$102$		0			0
$103$	6.36015	−	6.36015i	0.626684	−	0.626684i	−0.320548	−	0.947232i	$-0.603867\pi$
$103$	6.36015	−	6.36015i	0.626684	−	0.626684i	0.947232	+	0.320548i	$0.103867\pi$
$104$		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
$117$	1.27295	−	5.67162i	0.117684	−	0.524341i
$118$		0			0
$119$	10.6416			0.975510
$120$		0			0
$121$	10.9030			0.991179
$122$		0			0
$123$	20.7182	−	6.00941i	1.86810	−	0.541850i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.47062	+	5.47062i	0.485439	+	0.485439i	0.906863	−	0.421425i	$-0.138470\pi$
$127$	5.47062	+	5.47062i	0.485439	+	0.485439i	−0.421425	+	0.906863i	$0.638470\pi$
$128$		0			0
$129$	−8.60475	−	4.73539i	−0.757606	−	0.416928i
$130$		0			0
$131$			17.8285i			1.55769i	0.627219	+	0.778843i	$0.284193\pi$
$131$			17.8285i			1.55769i	−0.627219	+	0.778843i	$0.715807\pi$
$132$		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
$147$	−2.29888	+	0.666800i	−0.189609	+	0.0549968i
$148$		0			0
$149$	−0.500041			−0.0409649			−0.0204825	−	0.999790i	$-0.506520\pi$
$149$	−0.500041			−0.0409649			−0.0204825	+	0.999790i	$0.506520\pi$
$150$		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
$153$	−2.94963	+	13.1420i	−0.238463	+	1.06247i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.9606	−	14.9606i	−1.19398	−	1.19398i	−0.975938	−	0.218046i	$-0.930032\pi$
$157$	−14.9606	−	14.9606i	−1.19398	−	1.19398i	−0.218046	−	0.975938i	$-0.569968\pi$
$158$		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	−0.745574	−	0.666423i	$-0.767825\pi$
$163$	−1.01054	+	1.01054i	−0.0791513	+	0.0791513i	0.666423	+	0.745574i	$0.267825\pi$
$164$		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
$177$	2.62955	+	9.06572i	0.197649	+	0.681422i
$178$		0			0
$179$	−12.8422			−0.959870			−0.479935	−	0.877304i	$-0.659340\pi$
$179$	−12.8422			−0.959870			−0.479935	+	0.877304i	$0.659340\pi$
$180$		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
$183$	−1.83498	−	6.32632i	−0.135645	−	0.467655i
$184$		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	$0.103355\pi$
$191$			8.81801i			0.638049i	−0.947747	+	0.319024i	$0.896645\pi$
$192$		0			0
$193$	−3.15143	+	3.15143i	−0.226845	+	0.226845i	−0.811373	−	0.584529i	$-0.801280\pi$
$193$	−3.15143	+	3.15143i	−0.226845	+	0.226845i	0.584529	+	0.811373i	$0.301280\pi$
$194$		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
$207$	−9.35425	−	2.09949i	−0.650166	−	0.145925i
$208$		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
$213$	−2.51528	+	0.729566i	−0.172344	+	0.0499890i
$214$		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	$-0.405492\pi$
$223$	18.6487	−	18.6487i	1.24881	−	1.24881i	0.956246	−	0.292563i	$-0.0945081\pi$
$224$		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
$237$	−16.0121	+	4.64436i	−1.04010	+	0.301684i
$238$		0			0
$239$	−29.3512			−1.89857			−0.949285	−	0.314416i	$-0.898191\pi$
$239$	−29.3512			−1.89857			−0.949285	+	0.314416i	$0.898191\pi$
$240$		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
$243$	−15.3912	−	2.47214i	−0.987345	−	0.158588i
$244$		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	$0.276135\pi$
$251$			24.1674i			1.52543i	−0.646733	+	0.762717i	$0.723865\pi$
$252$		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
$267$	−6.88617	−	23.7410i	−0.421427	−	1.45292i
$268$		0			0
$269$	6.68296			0.407467			0.203734	−	0.979026i	$-0.434692\pi$
$269$	6.68296			0.407467			0.203734	+	0.979026i	$0.434692\pi$
$270$		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
$273$	2.21589	+	7.63958i	0.134112	+	0.462368i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.6249	−	15.6249i	−0.938810	−	0.938810i	0.0594226	−	0.998233i	$-0.481074\pi$
$277$	−15.6249	−	15.6249i	−0.938810	−	0.938810i	−0.998233	+	0.0594226i	$0.981074\pi$
$278$		0			0
$279$	9.70308	−	6.14590i	0.580908	−	0.367945i
$280$		0			0
$281$		−	0.938474i		−	0.0559846i	−0.999608	−	0.0279923i	$-0.991089\pi$
$281$		−	0.938474i		−	0.0559846i	0.999608	−	0.0279923i	$-0.00891140\pi$
$282$		0			0
$283$	−1.51593	+	1.51593i	−0.0901128	+	0.0901128i	−0.750726	−	0.660613i	$-0.770296\pi$
$283$	−1.51593	+	1.51593i	−0.0901128	+	0.0901128i	0.660613	+	0.750726i	$0.270296\pi$
$284$		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
$297$	1.07199	−	1.21273i	0.0622029	−	0.0703695i
$298$		0			0
$299$	−6.19181			−0.358082
$300$		0			0
$301$	13.4406			0.774702
$302$		0			0
$303$	15.5005	−	4.49597i	0.890478	−	0.258287i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−15.3894	−	15.3894i	−0.878317	−	0.878317i	0.115043	−	0.993360i	$-0.463299\pi$
$307$	−15.3894	−	15.3894i	−0.878317	−	0.878317i	−0.993360	+	0.115043i	$0.963299\pi$
$308$		0			0
$309$	−13.6488	−	7.51125i	−0.776454	−	0.427300i
$310$		0			0
$311$		−	3.52016i		−	0.199610i	−0.995007	−	0.0998051i	$-0.968178\pi$
$311$		−	3.52016i		−	0.199610i	0.995007	−	0.0998051i	$-0.0318219\pi$
$312$		0			0
$313$	−18.8366	+	18.8366i	−1.06471	+	1.06471i	−0.0669536	+	0.997756i	$0.521328\pi$
$313$	−18.8366	+	18.8366i	−1.06471	+	1.06471i	−0.997756	+	0.0669536i	$0.978672\pi$
$314$		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
$327$	−11.5495	+	3.34997i	−0.638687	+	0.185254i
$328$		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
$333$	−32.6013	−	7.31712i	−1.78654	−	0.400976i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.90454	+	8.90454i	0.485061	+	0.485061i	0.906744	−	0.421682i	$-0.138560\pi$
$337$	8.90454	+	8.90454i	0.485061	+	0.485061i	−0.421682	+	0.906744i	$0.638560\pi$
$338$		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
$357$	−5.13457	−	17.7021i	−0.271750	−	0.936895i
$358$		0			0
$359$	16.7879			0.886032			0.443016	−	0.896514i	$-0.353908\pi$
$359$	16.7879			0.886032			0.443016	+	0.896514i	$0.353908\pi$
$360$		0			0
$361$	−19.3751			−1.01974
$362$		0			0
$363$	−5.26070	−	18.1370i	−0.276115	−	0.951943i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−18.7656	−	18.7656i	−0.979554	−	0.979554i	0.0202409	−	0.999795i	$-0.493557\pi$
$367$	−18.7656	−	18.7656i	−0.979554	−	0.979554i	−0.999795	+	0.0202409i	$0.993557\pi$
$368$		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	−0.851210	−	0.524824i	$-0.824131\pi$
$373$	−6.30356	+	6.30356i	−0.326386	+	0.326386i	0.524824	+	0.851210i	$0.324131\pi$
$374$		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
$387$	−3.72546	+	16.5987i	−0.189376	+	0.843761i
$388$		0			0
$389$	19.8796			1.00794			0.503969	−	0.863722i	$-0.331873\pi$
$389$	19.8796			1.00794			0.503969	+	0.863722i	$0.331873\pi$
$390$		0			0
$391$	14.3474			0.725579
$392$		0			0
$393$	29.6575	−	8.60229i	1.49603	−	0.433928i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.9308	−	21.9308i	−1.10067	−	1.10067i	−0.994329	−	0.106344i	$-0.966085\pi$
$397$	−21.9308	−	21.9308i	−1.10067	−	1.10067i	−0.106344	−	0.994329i	$-0.533915\pi$
$398$		0			0
$399$	22.2807	+	12.2616i	1.11543	+	0.613848i
$400$		0			0
$401$		−	17.2880i		−	0.863319i	−0.902037	−	0.431660i	$-0.857928\pi$
$401$		−	17.2880i		−	0.863319i	0.902037	−	0.431660i	$-0.142072\pi$
$402$		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
$417$	−3.78838	+	1.09883i	−0.185518	+	0.0538102i
$418$		0			0
$419$	−32.9039			−1.60746			−0.803731	−	0.594993i	$-0.797155\pi$
$419$	−32.9039			−1.60746			−0.803731	+	0.594993i	$0.797155\pi$
$420$		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
$423$	−2.77873	+	12.3806i	−0.135106	+	0.601964i
$424$		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	$0.0652027\pi$
$431$			8.44584i			0.406822i	−0.979093	+	0.203411i	$0.934797\pi$
$432$		0			0
$433$	−6.85220	+	6.85220i	−0.329296	+	0.329296i	−0.852319	−	0.523023i	$-0.824804\pi$
$433$	−6.85220	+	6.85220i	−0.329296	+	0.329296i	0.523023	+	0.852319i	$0.324804\pi$
$434$		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
$447$	0.241270	+	0.831812i	0.0114117	+	0.0393433i
$448$		0			0
$449$	21.6192			1.02028			0.510138	−	0.860093i	$-0.329594\pi$
$449$	21.6192			1.02028			0.510138	+	0.860093i	$0.329594\pi$
$450$		0			0
$451$	3.87963			0.182685
$452$		0			0
$453$	−0.243031	−	0.837881i	−0.0114186	−	0.0393671i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.519177	+	0.519177i	0.0242861	+	0.0242861i	0.719146	−	0.694859i	$-0.244533\pi$
$457$	0.519177	+	0.519177i	0.0242861	+	0.0242861i	−0.694859	+	0.719146i	$0.744533\pi$
$458$		0			0
$459$	23.2848	−	1.43437i	1.08684	−	0.0669508i
$460$		0			0
$461$			27.2784i			1.27048i	0.772314	+	0.635242i	$0.219099\pi$
$461$			27.2784i			1.27048i	−0.772314	+	0.635242i	$0.780901\pi$
$462$		0			0
$463$	−8.03916	+	8.03916i	−0.373611	+	0.373611i	−0.868791	−	0.495179i	$-0.835102\pi$
$463$	−8.03916	+	8.03916i	−0.373611	+	0.373611i	0.495179	+	0.868791i	$0.335102\pi$
$464$		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
$477$	−19.1030	−	4.28753i	−0.874667	−	0.196312i
$478$		0			0
$479$	23.2912			1.06420			0.532102	−	0.846680i	$-0.321402\pi$
$479$	23.2912			1.06420			0.532102	+	0.846680i	$0.321402\pi$
$480$		0			0
$481$	−21.5796			−0.983946
$482$		0			0
$483$	12.6000	−	3.65469i	0.573321	−	0.166294i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.155962	+	0.155962i	0.00706730	+	0.00706730i	0.710632	−	0.703564i	$-0.248409\pi$
$487$	0.155962	+	0.155962i	0.00706730	+	0.00706730i	−0.703564	+	0.710632i	$0.748409\pi$
$488$		0			0
$489$	2.16860	+	1.19343i	0.0980674	+	0.0539687i
$490$		0			0
$491$		−	25.8034i		−	1.16449i	−0.813014	−	0.582245i	$-0.802175\pi$
$491$		−	25.8034i		−	1.16449i	0.813014	−	0.582245i	$-0.197825\pi$
$492$		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
$507$	15.3803	−	4.46112i	0.683063	−	0.198125i
$508$		0			0
$509$	−18.2590			−0.809317			−0.404658	−	0.914468i	$-0.632610\pi$
$509$	−18.2590			−0.809317			−0.404658	+	0.914468i	$0.632610\pi$
$510$		0			0
$511$	−12.0171			−0.531606
$512$		0			0
$513$	−21.3185	+	24.1174i	−0.941235	+	1.06481i
$514$		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	$0.0482319\pi$
$521$			6.89080i			0.301891i	−0.988542	+	0.150946i	$0.951768\pi$
$522$		0			0
$523$	18.1928	−	18.1928i	0.795514	−	0.795514i	−0.186870	−	0.982385i	$-0.559834\pi$
$523$	18.1928	−	18.1928i	0.795514	−	0.795514i	0.982385	+	0.186870i	$0.0598344\pi$
$524$		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
$537$	6.19637	+	21.3628i	0.267393	+	0.921874i
$538$		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
$543$	1.79683	+	6.19480i	0.0771092	+	0.265844i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.92710	+	3.92710i	0.167911	+	0.167911i	0.786060	−	0.618150i	$-0.212117\pi$
$547$	3.92710	+	3.92710i	0.167911	+	0.167911i	−0.618150	+	0.786060i	$0.712117\pi$
$548$		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
$567$	20.0836	−	7.19099i	0.843431	−	0.301993i
$568$		0			0
$569$	−15.2127			−0.637751			−0.318876	−	0.947797i	$-0.603305\pi$
$569$	−15.2127			−0.637751			−0.318876	+	0.947797i	$0.603305\pi$
$570$		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
$573$	14.6686	−	4.25470i	0.612792	−	0.177743i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	29.8917	+	29.8917i	1.24441	+	1.24441i	0.958154	+	0.286254i	$0.0924103\pi$
$577$	29.8917	+	29.8917i	1.24441	+	1.24441i	0.286254	+	0.958154i	$0.407590\pi$
$578$		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
$597$	−15.7406	+	4.56561i	−0.644218	+	0.186858i
$598$		0			0
$599$	−33.8335			−1.38240			−0.691200	−	0.722664i	$-0.742918\pi$
$599$	−33.8335			−1.38240			−0.691200	+	0.722664i	$0.742918\pi$
$600$		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
$603$	−17.9747	−	4.03429i	−0.731986	−	0.164289i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.8668	+	18.8668i	0.765778	+	0.765778i	0.977360	−	0.211582i	$-0.0678616\pi$
$607$	18.8668	+	18.8668i	0.765778	+	0.765778i	−0.211582	+	0.977360i	$0.567862\pi$
$608$		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	−0.492493	−	0.870317i	$-0.663914\pi$
$613$	9.35448	−	9.35448i	0.377824	−	0.377824i	0.870317	+	0.492493i	$0.163914\pi$
$614$		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
$627$	−0.931066	−	3.20997i	−0.0371832	−	0.128194i
$628$		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
$633$	8.60661	+	29.6725i	0.342082	+	1.17937i
$634$		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	$-0.931087\pi$
$641$		−	10.8771i		−	0.429618i	0.976656	−	0.214809i	$-0.0689129\pi$
$642$		0			0
$643$	−2.05532	+	2.05532i	−0.0810540	+	0.0810540i	−0.746471	−	0.665417i	$-0.768254\pi$
$643$	−2.05532	+	2.05532i	−0.0810540	+	0.0810540i	0.665417	+	0.746471i	$0.268254\pi$
$644$		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
$657$	3.33091	−	14.8408i	0.129951	−	0.578995i
$658$		0			0
$659$	1.93458			0.0753605			0.0376803	−	0.999290i	$-0.488003\pi$
$659$	1.93458			0.0753605			0.0376803	+	0.999290i	$0.488003\pi$
$660$		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
$663$	14.4707	−	4.19729i	0.561996	−	0.163009i
$664$		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	−0.567335	−	0.823487i	$-0.692025\pi$
$673$	6.64517	−	6.64517i	0.256152	−	0.256152i	0.823487	+	0.567335i	$0.192025\pi$
$674$		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
$687$	27.2213	−	7.89565i	1.03856	−	0.301238i
$688$		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
$693$	−0.485069	+	2.16122i	−0.0184262	+	0.0820979i
$694$		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	$-0.754560\pi$
$701$		−	36.9031i		−	1.39381i	0.717164	−	0.696905i	$-0.245440\pi$
$702$		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
$717$	14.1620	+	48.8253i	0.528889	+	1.82342i
$718$		0			0
$719$	2.92975			0.109261			0.0546305	−	0.998507i	$-0.482602\pi$
$719$	2.92975			0.109261			0.0546305	+	0.998507i	$0.482602\pi$
$720$		0			0
$721$	21.3194			0.793975
$722$		0			0
$723$	5.59705	+	19.2966i	0.208156	+	0.717647i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	18.1790	+	18.1790i	0.674221	+	0.674221i	0.958686	−	0.284466i	$-0.0918161\pi$
$727$	18.1790	+	18.1790i	0.674221	+	0.674221i	−0.284466	+	0.958686i	$0.591816\pi$
$728$		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	−0.700783	−	0.713375i	$-0.747166\pi$
$733$	0.340902	−	0.340902i	0.0125915	−	0.0125915i	0.713375	+	0.700783i	$0.247166\pi$
$734$		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
$747$	34.3026	+	7.69896i	1.25507	+	0.281690i
$748$		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
$753$	40.2022	−	11.6608i	1.46505	−	0.424943i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.98084	−	5.98084i	−0.217377	−	0.217377i	0.590015	−	0.807392i	$-0.299122\pi$
$757$	−5.98084	−	5.98084i	−0.217377	−	0.217377i	−0.807392	+	0.590015i	$0.799122\pi$
$758$		0			0
$759$	−1.51053	−	0.831279i	−0.0548288	−	0.0301735i
$760$		0			0
$761$		−	11.2398i		−	0.407441i	−0.979029	−	0.203721i	$-0.934697\pi$
$761$		−	11.2398i		−	0.407441i	0.979029	−	0.203721i	$-0.0653034\pi$
$762$		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
$777$	43.9135	−	12.7373i	1.57539	−	0.456948i
$778$		0			0
$779$	−77.1539			−2.76433
$780$		0			0
$781$	−0.471002			−0.0168538
$782$		0			0
$783$	−13.4088	−	11.8527i	−0.479192	−	0.423580i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.68582	+	3.68582i	0.131385	+	0.131385i	0.769741	−	0.638356i	$-0.220385\pi$
$787$	3.68582	+	3.68582i	0.131385	+	0.131385i	−0.638356	+	0.769741i	$0.720385\pi$
$788$		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
$807$	−3.22454	−	11.1170i	−0.113509	−	0.391338i
$808$		0			0
$809$	28.9167			1.01666			0.508329	−	0.861163i	$-0.330263\pi$
$809$	28.9167			1.01666			0.508329	+	0.861163i	$0.330263\pi$
$810$		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
$813$	−11.6783	−	40.2625i	−0.409576	−	1.41207i
$814$		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	$-0.909190\pi$
$821$		−	16.1279i		−	0.562869i	0.959580	−	0.281435i	$-0.0908102\pi$
$822$		0			0
$823$	10.9389	−	10.9389i	0.381308	−	0.381308i	−0.490266	−	0.871573i	$-0.663100\pi$
$823$	10.9389	−	10.9389i	0.381308	−	0.381308i	0.871573	+	0.490266i	$0.163100\pi$
$824$		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
$837$	−14.9054	−	13.1756i	−0.515205	−	0.455414i
$838$		0			0
$839$	−33.7354			−1.16467			−0.582337	−	0.812948i	$-0.697862\pi$
$839$	−33.7354			−1.16467			−0.582337	+	0.812948i	$0.697862\pi$
$840$		0			0
$841$	−17.1377			−0.590955
$842$		0			0
$843$	−1.56114	+	0.452815i	−0.0537685	+	0.0155958i
$844$		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	−0.477990	−	0.878365i	$-0.658635\pi$
$853$	11.6934	−	11.6934i	0.400375	−	0.400375i	0.878365	+	0.477990i	$0.158635\pi$
$854$		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
$867$	−5.25163	+	1.52326i	−0.178355	+	0.0517325i
$868$		0			0
$869$	−2.99837			−0.101713
$870$		0			0
$871$	−11.8979			−0.403145
$872$		0			0
$873$	−41.0355	−	9.21010i	−1.38884	−	0.311715i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−27.1263	−	27.1263i	−0.915990	−	0.915990i	0.0807449	−	0.996735i	$-0.474270\pi$
$877$	−27.1263	−	27.1263i	−0.915990	−	0.915990i	−0.996735	+	0.0807449i	$0.974270\pi$
$878$		0			0
$879$	20.0066	−	36.3543i	0.674805	−	1.22620i
$880$		0			0
$881$			0.439372i			0.0148028i	0.999973	+	0.00740140i	$0.00235596\pi$
$881$			0.439372i			0.0148028i	−0.999973	+	0.00740140i	$0.997644\pi$
$882$		0			0
$883$	−0.0107839	+	0.0107839i	−0.000362907	+	0.000362907i	−0.707288	−	0.706925i	$-0.750082\pi$
$883$	−0.0107839	+	0.0107839i	−0.000362907	+	0.000362907i	0.706925	+	0.707288i	$0.250082\pi$
$884$		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
$897$	2.98756	+	10.3000i	0.0997516	+	0.343907i
$898$		0			0
$899$	13.1863			0.439787
$900$		0			0
$901$	29.2999			0.976120
$902$		0			0
$903$	−6.48510	−	22.3582i	−0.215811	−	0.744036i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	34.1899	+	34.1899i	1.13526	+	1.13526i	0.989289	+	0.145967i	$0.0466293\pi$
$907$	34.1899	+	34.1899i	1.13526	+	1.13526i	0.145967	+	0.989289i	$0.453371\pi$
$908$		0			0
$909$	−14.9580	−	23.6155i	−0.496125	−	0.783277i
$910$		0			0
$911$		−	51.2365i		−	1.69754i	−0.528762	−	0.848770i	$-0.677344\pi$
$911$		−	51.2365i		−	1.69754i	0.528762	−	0.848770i	$-0.322656\pi$
$912$		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
$927$	−5.90931	+	26.3288i	−0.194087	+	0.864752i
$928$		0			0
$929$	11.2678			0.369686			0.184843	−	0.982768i	$-0.440822\pi$
$929$	11.2678			0.369686			0.184843	+	0.982768i	$0.440822\pi$
$930$		0			0
$931$	8.56095			0.280574
$932$		0			0
$933$	−5.85575	+	1.69848i	−0.191709	+	0.0556059i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.1002	+	23.1002i	0.754652	+	0.754652i	0.975344	−	0.220692i	$-0.0708315\pi$
$937$	23.1002	+	23.1002i	0.754652	+	0.754652i	−0.220692	+	0.975344i	$0.570831\pi$
$938$		0			0
$939$	40.4232	+	22.2458i	1.31916	+	0.725965i
$940$		0			0
$941$			1.68443i			0.0549109i	0.999623	+	0.0274554i	$0.00874043\pi$
$941$			1.68443i			0.0549109i	−0.999623	+	0.0274554i	$0.991260\pi$
$942$		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
$957$	1.78468	−	0.517655i	0.0576907	−	0.0167334i
$958$		0			0
$959$	−38.2299			−1.23451
$960$		0			0
$961$	−16.3420			−0.527162
$962$		0			0
$963$	−8.74596	+	38.9675i	−0.281835	+	1.25571i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.55730	+	1.55730i	0.0500794	+	0.0500794i	0.731703	−	0.681624i	$-0.238726\pi$
$967$	1.55730	+	1.55730i	0.0500794	+	0.0500794i	−0.681624	+	0.731703i	$0.738726\pi$
$968$		0			0
$969$	23.2256	−	42.2037i	0.746115	−	1.35578i
$970$		0			0
$971$		−	30.5597i		−	0.980707i	−0.871524	−	0.490354i	$-0.836868\pi$
$971$		−	30.5597i		−	0.980707i	0.871524	−	0.490354i	$-0.163132\pi$
$972$		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
$987$	−4.83707	−	16.6765i	−0.153966	−	0.530817i
$988$		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
$993$	−4.95243	−	17.0742i	−0.157161	−	0.541833i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−24.0802	−	24.0802i	−0.762628	−	0.762628i	0.214169	−	0.976797i	$-0.431296\pi$
$997$	−24.0802	−	24.0802i	−0.762628	−	0.762628i	−0.976797	+	0.214169i	$0.931296\pi$
$998$		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.557.8	yes	32
3.2	odd	2	inner	1500.2.i.b.557.16	yes	32
5.2	odd	4	inner	1500.2.i.b.1193.1	yes	32
5.3	odd	4	inner	1500.2.i.b.1193.16	yes	32
5.4	even	2	inner	1500.2.i.b.557.9	yes	32
15.2	even	4	inner	1500.2.i.b.1193.9	yes	32
15.8	even	4	inner	1500.2.i.b.1193.8	yes	32
15.14	odd	2	inner	1500.2.i.b.557.1	✓	32

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

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