LMFDB - Embedded newform 1600.2.l.h.1201.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.8
Root			$0.238945 - 1.39388i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.h.401.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99154 - 1.99154i) q^{3} +1.09033i q^{7} -4.93244i q^{9} +O(q^{10})$	$q+(1.99154 - 1.99154i) q^{3} +1.09033i q^{7} -4.93244i q^{9} +(2.33225 + 2.33225i) q^{11} +(1.80775 - 1.80775i) q^{13} +4.93886 q^{17} +(2.03957 - 2.03957i) q^{19} +(2.17142 + 2.17142i) q^{21} +1.45791i q^{23} +(-3.84853 - 3.84853i) q^{27} +(0.707323 - 0.707323i) q^{29} -10.1286 q^{31} +9.28951 q^{33} +(4.35066 + 4.35066i) q^{37} -7.20039i q^{39} -10.2753i q^{41} +(-2.22457 - 2.22457i) q^{43} +2.09458 q^{47} +5.81119 q^{49} +(9.83592 - 9.83592i) q^{51} +(-0.215297 - 0.215297i) q^{53} -8.12376i q^{57} +(-1.16082 - 1.16082i) q^{59} +(-3.46410 + 3.46410i) q^{61} +5.37797 q^{63} +(-5.04189 + 5.04189i) q^{67} +(2.90348 + 2.90348i) q^{69} -6.40078i q^{71} -5.24343i q^{73} +(-2.54291 + 2.54291i) q^{77} +2.61504 q^{79} -0.531659 q^{81} +(-5.67856 + 5.67856i) q^{83} -2.81732i q^{87} -6.87875i q^{89} +(1.97103 + 1.97103i) q^{91} +(-20.1715 + 20.1715i) q^{93} -3.77310 q^{97} +(11.5037 - 11.5037i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.99154	−	1.99154i	1.14981	−	1.14981i	0.163226	−	0.986589i	$-0.447810\pi$
$3$	1.99154	−	1.99154i	1.14981	−	1.14981i	0.986589	−	0.163226i	$-0.0521899\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.09033i			0.412104i	0.978541	+	0.206052i	$0.0660617\pi$
$7$			1.09033i			0.412104i	−0.978541	+	0.206052i	$0.933938\pi$
$8$		0			0
$9$		−	4.93244i		−	1.64415i
$10$		0			0
$11$	2.33225	+	2.33225i	0.703199	+	0.703199i	0.965096	−	0.261897i	$-0.0843481\pi$
$11$	2.33225	+	2.33225i	0.703199	+	0.703199i	−0.261897	+	0.965096i	$0.584348\pi$
$12$		0			0
$13$	1.80775	−	1.80775i	0.501379	−	0.501379i	−0.410487	−	0.911866i	$-0.634641\pi$
$13$	1.80775	−	1.80775i	0.501379	−	0.501379i	0.911866	+	0.410487i	$0.134641\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.93886			1.19785			0.598924	−	0.800806i	$-0.295595\pi$
$17$	4.93886			1.19785			0.598924	+	0.800806i	$0.295595\pi$
$18$		0			0
$19$	2.03957	−	2.03957i	0.467909	−	0.467909i	−0.433327	−	0.901237i	$-0.642661\pi$
$19$	2.03957	−	2.03957i	0.467909	−	0.467909i	0.901237	+	0.433327i	$0.142661\pi$
$20$		0			0
$21$	2.17142	+	2.17142i	0.473844	+	0.473844i
$22$		0			0
$23$			1.45791i			0.303995i	0.988381	+	0.151997i	$0.0485705\pi$
$23$			1.45791i			0.303995i	−0.988381	+	0.151997i	$0.951430\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.84853	−	3.84853i	−0.740650	−	0.740650i
$28$		0			0
$29$	0.707323	−	0.707323i	0.131347	−	0.131347i	−0.638377	−	0.769724i	$-0.720394\pi$
$29$	0.707323	−	0.707323i	0.131347	−	0.131347i	0.769724	+	0.638377i	$0.220394\pi$
$30$		0			0
$31$	−10.1286			−1.81915			−0.909575	−	0.415541i	$-0.863592\pi$
$31$	−10.1286			−1.81915			−0.909575	+	0.415541i	$0.863592\pi$
$32$		0			0
$33$	9.28951			1.61710
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.35066	+	4.35066i	0.715243	+	0.715243i	0.967627	−	0.252384i	$-0.0812146\pi$
$37$	4.35066	+	4.35066i	0.715243	+	0.715243i	−0.252384	+	0.967627i	$0.581215\pi$
$38$		0			0
$39$		−	7.20039i		−	1.15299i
$40$		0			0
$41$		−	10.2753i		−	1.60473i	−0.596833	−	0.802365i	$-0.703575\pi$
$41$		−	10.2753i		−	1.60473i	0.596833	−	0.802365i	$-0.296425\pi$
$42$		0			0
$43$	−2.22457	−	2.22457i	−0.339244	−	0.339244i	0.516839	−	0.856083i	$-0.327109\pi$
$43$	−2.22457	−	2.22457i	−0.339244	−	0.339244i	−0.856083	+	0.516839i	$0.827109\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.09458			0.305525			0.152763	−	0.988263i	$-0.451183\pi$
$47$	2.09458			0.305525			0.152763	+	0.988263i	$0.451183\pi$
$48$		0			0
$49$	5.81119			0.830170
$50$		0			0
$51$	9.83592	−	9.83592i	1.37730	−	1.37730i
$52$		0			0
$53$	−0.215297	−	0.215297i	−0.0295733	−	0.0295733i	0.692166	−	0.721739i	$-0.256657\pi$
$53$	−0.215297	−	0.215297i	−0.0295733	−	0.0295733i	−0.721739	+	0.692166i	$0.756657\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	8.12376i		−	1.07602i
$58$		0			0
$59$	−1.16082	−	1.16082i	−0.151126	−	0.151126i	0.627495	−	0.778621i	$-0.284080\pi$
$59$	−1.16082	−	1.16082i	−0.151126	−	0.151126i	−0.778621	+	0.627495i	$0.784080\pi$
$60$		0			0
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$		0			0
$63$	5.37797			0.677560
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.04189	+	5.04189i	−0.615965	+	0.615965i	−0.944494	−	0.328529i	$-0.893447\pi$
$67$	−5.04189	+	5.04189i	−0.615965	+	0.615965i	0.328529	+	0.944494i	$0.393447\pi$
$68$		0			0
$69$	2.90348	+	2.90348i	0.349537	+	0.349537i
$70$		0			0
$71$		−	6.40078i		−	0.759633i	−0.925062	−	0.379817i	$-0.875987\pi$
$71$		−	6.40078i		−	0.759633i	0.925062	−	0.379817i	$-0.124013\pi$
$72$		0			0
$73$		−	5.24343i		−	0.613696i	−0.951758	−	0.306848i	$-0.900726\pi$
$73$		−	5.24343i		−	0.613696i	0.951758	−	0.306848i	$-0.0992744\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.54291	+	2.54291i	−0.289791	+	0.289791i
$78$		0			0
$79$	2.61504			0.294215			0.147107	−	0.989121i	$-0.453004\pi$
$79$	2.61504			0.294215			0.147107	+	0.989121i	$0.453004\pi$
$80$		0			0
$81$	−0.531659			−0.0590733
$82$		0			0
$83$	−5.67856	+	5.67856i	−0.623303	+	0.623303i	−0.946375	−	0.323071i	$-0.895285\pi$
$83$	−5.67856	+	5.67856i	−0.623303	+	0.623303i	0.323071	+	0.946375i	$0.395285\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	2.81732i		−	0.302048i
$88$		0			0
$89$		−	6.87875i		−	0.729146i	−0.931175	−	0.364573i	$-0.881215\pi$
$89$		−	6.87875i		−	0.729146i	0.931175	−	0.364573i	$-0.118785\pi$
$90$		0			0
$91$	1.97103	+	1.97103i	0.206620	+	0.206620i
$92$		0			0
$93$	−20.1715	+	20.1715i	−2.09168	+	2.09168i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.77310			−0.383100			−0.191550	−	0.981483i	$-0.561351\pi$
$97$	−3.77310			−0.383100			−0.191550	+	0.981483i	$0.561351\pi$
$98$		0			0
$99$	11.5037	−	11.5037i	1.15616	−	1.15616i
$100$		0			0
$101$	−0.707323	−	0.707323i	−0.0703813	−	0.0703813i	0.671040	−	0.741421i	$-0.265848\pi$
$101$	−0.707323	−	0.707323i	−0.0703813	−	0.0703813i	−0.741421	+	0.671040i	$0.765848\pi$
$102$		0			0
$103$			12.9320i			1.27422i	0.770771	+	0.637112i	$0.219871\pi$
$103$			12.9320i			1.27422i	−0.770771	+	0.637112i	$0.780129\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.56094	−	1.56094i	−0.150902	−	0.150902i	0.627619	−	0.778521i	$-0.284030\pi$
$107$	−1.56094	−	1.56094i	−0.150902	−	0.150902i	−0.778521	+	0.627619i	$0.784030\pi$
$108$		0			0
$109$	7.13283	−	7.13283i	0.683202	−	0.683202i	−0.277519	−	0.960720i	$-0.589512\pi$
$109$	7.13283	−	7.13283i	0.683202	−	0.683202i	0.960720	+	0.277519i	$0.0895120\pi$
$110$		0			0
$111$	17.3290			1.64479
$112$		0			0
$113$	−9.23949			−0.869178			−0.434589	−	0.900629i	$-0.643106\pi$
$113$	−9.23949			−0.869178			−0.434589	+	0.900629i	$0.643106\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.91661	−	8.91661i	−0.824341	−	0.824341i
$118$		0			0
$119$			5.38496i			0.493639i
$120$		0			0
$121$		−	0.121253i		−	0.0110230i
$122$		0			0
$123$	−20.4636	−	20.4636i	−1.84514	−	1.84514i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.99608			−0.177124			−0.0885618	−	0.996071i	$-0.528227\pi$
$127$	−1.99608			−0.177124			−0.0885618	+	0.996071i	$0.528227\pi$
$128$		0			0
$129$	−8.86065			−0.780136
$130$		0			0
$131$	−11.2894	+	11.2894i	−0.986361	+	0.986361i	−0.999908	−	0.0135473i	$-0.995688\pi$
$131$	−11.2894	+	11.2894i	−0.986361	+	0.986361i	0.0135473	+	0.999908i	$0.495688\pi$
$132$		0			0
$133$	2.22380	+	2.22380i	0.192827	+	0.192827i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			15.9429i			1.36210i	0.732238	+	0.681049i	$0.238476\pi$
$137$			15.9429i			1.36210i	−0.732238	+	0.681049i	$0.761524\pi$
$138$		0			0
$139$	3.79635	+	3.79635i	0.322002	+	0.322002i	0.849535	−	0.527533i	$-0.176883\pi$
$139$	3.79635	+	3.79635i	0.322002	+	0.322002i	−0.527533	+	0.849535i	$0.676883\pi$
$140$		0			0
$141$	4.17142	−	4.17142i	0.351297	−	0.351297i
$142$		0			0
$143$	8.43222			0.705138
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11.5732	−	11.5732i	0.954542	−	0.954542i
$148$		0			0
$149$	−13.3290	−	13.3290i	−1.09195	−	1.09195i	−0.995320	−	0.0966330i	$-0.969193\pi$
$149$	−13.3290	−	13.3290i	−1.09195	−	1.09195i	−0.0966330	−	0.995320i	$-0.530807\pi$
$150$		0			0
$151$			5.60117i			0.455817i	0.973683	+	0.227909i	$0.0731887\pi$
$151$			5.60117i			0.455817i	−0.973683	+	0.227909i	$0.926811\pi$
$152$		0			0
$153$		−	24.3606i		−	1.96944i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.11951	+	7.11951i	−0.568199	+	0.568199i	−0.931624	−	0.363425i	$-0.881607\pi$
$157$	−7.11951	+	7.11951i	−0.568199	+	0.568199i	0.363425	+	0.931624i	$0.381607\pi$
$158$		0			0
$159$	−0.857542			−0.0680075
$160$		0			0
$161$	−1.58959			−0.125277
$162$		0			0
$163$	−0.546047	+	0.546047i	−0.0427697	+	0.0427697i	−0.728168	−	0.685398i	$-0.759628\pi$
$163$	−0.546047	+	0.546047i	−0.0427697	+	0.0427697i	0.685398	+	0.728168i	$0.259628\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			21.3103i			1.64904i	0.565834	+	0.824519i	$0.308554\pi$
$167$			21.3103i			1.64904i	−0.565834	+	0.824519i	$0.691446\pi$
$168$		0			0
$169$			6.46410i			0.497239i
$170$		0			0
$171$	−10.0601	−	10.0601i	−0.769312	−	0.769312i
$172$		0			0
$173$	−2.64673	+	2.64673i	−0.201227	+	0.201227i	−0.800525	−	0.599299i	$-0.795446\pi$
$173$	−2.64673	+	2.64673i	−0.201227	+	0.201227i	0.599299	+	0.800525i	$0.295446\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.62364			−0.347534
$178$		0			0
$179$	−13.4747	+	13.4747i	−1.00715	+	1.00715i	−0.00717240	+	0.999974i	$0.502283\pi$
$179$	−13.4747	+	13.4747i	−1.00715	+	1.00715i	−0.999974	+	0.00717240i	$0.997717\pi$
$180$		0			0
$181$	−1.63553	−	1.63553i	−0.121568	−	0.121568i	0.643706	−	0.765273i	$-0.277396\pi$
$181$	−1.63553	−	1.63553i	−0.121568	−	0.121568i	−0.765273	+	0.643706i	$0.777396\pi$
$182$		0			0
$183$			13.7978i			1.01996i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	11.5186	+	11.5186i	0.842326	+	0.842326i
$188$		0			0
$189$	4.19615	−	4.19615i	0.305225	−	0.305225i
$190$		0			0
$191$	−5.07180			−0.366982			−0.183491	−	0.983021i	$-0.558740\pi$
$191$	−5.07180			−0.366982			−0.183491	+	0.983021i	$0.558740\pi$
$192$		0			0
$193$	22.0369			1.58625			0.793126	−	0.609058i	$-0.208452\pi$
$193$	22.0369			1.58625			0.793126	+	0.609058i	$0.208452\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.06997	−	8.06997i	−0.574961	−	0.574961i	0.358549	−	0.933511i	$-0.383271\pi$
$197$	−8.06997	−	8.06997i	−0.574961	−	0.574961i	−0.933511	+	0.358549i	$0.883271\pi$
$198$		0			0
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$		0			0
$201$			20.0822i			1.41649i
$202$		0			0
$203$	0.771212	+	0.771212i	0.0541285	+	0.0541285i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.19104			0.499812
$208$		0			0
$209$	9.51356			0.658067
$210$		0			0
$211$	−5.18203	+	5.18203i	−0.356745	+	0.356745i	−0.862612	−	0.505866i	$-0.831173\pi$
$211$	−5.18203	+	5.18203i	−0.356745	+	0.356745i	0.505866	+	0.862612i	$0.331173\pi$
$212$		0			0
$213$	−12.7474	−	12.7474i	−0.873437	−	0.873437i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	11.0435i		−	0.749679i
$218$		0			0
$219$	−10.4425	−	10.4425i	−0.705637	−	0.705637i
$220$		0			0
$221$	8.92820	−	8.92820i	0.600576	−	0.600576i
$222$		0			0
$223$	18.7097			1.25289			0.626446	−	0.779465i	$-0.284509\pi$
$223$	18.7097			1.25289			0.626446	+	0.779465i	$0.284509\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.68435	−	8.68435i	0.576401	−	0.576401i	−0.357509	−	0.933910i	$-0.616374\pi$
$227$	8.68435	−	8.68435i	0.576401	−	0.576401i	0.933910	+	0.357509i	$0.116374\pi$
$228$		0			0
$229$	4.22936	+	4.22936i	0.279484	+	0.279484i	0.832903	−	0.553419i	$-0.186677\pi$
$229$	4.22936	+	4.22936i	0.279484	+	0.279484i	−0.553419	+	0.832903i	$0.686677\pi$
$230$		0			0
$231$			10.1286i			0.666413i
$232$		0			0
$233$			19.7054i			1.29094i	0.763784	+	0.645472i	$0.223339\pi$
$233$			19.7054i			1.29094i	−0.763784	+	0.645472i	$0.776661\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.20794	−	5.20794i	0.338292	−	0.338292i
$238$		0			0
$239$	−0.957886			−0.0619605			−0.0309803	−	0.999520i	$-0.509863\pi$
$239$	−0.957886			−0.0619605			−0.0309803	+	0.999520i	$0.509863\pi$
$240$		0			0
$241$	10.4599			0.673779			0.336889	−	0.941544i	$-0.390625\pi$
$241$	10.4599			0.673779			0.336889	+	0.941544i	$0.390625\pi$
$242$		0			0
$243$	10.4868	−	10.4868i	0.672727	−	0.672727i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	7.37405i		−	0.469200i
$248$		0			0
$249$			22.6181i			1.43337i
$250$		0			0
$251$	−7.29013	−	7.29013i	−0.460149	−	0.460149i	0.438555	−	0.898704i	$-0.355490\pi$
$251$	−7.29013	−	7.29013i	−0.460149	−	0.460149i	−0.898704	+	0.438555i	$0.855490\pi$
$252$		0			0
$253$	−3.40020	+	3.40020i	−0.213769	+	0.213769i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.2830			1.26522			0.632608	−	0.774472i	$-0.281984\pi$
$257$	20.2830			1.26522			0.632608	+	0.774472i	$0.281984\pi$
$258$		0			0
$259$	−4.74363	+	4.74363i	−0.294755	+	0.294755i
$260$		0			0
$261$	−3.48883	−	3.48883i	−0.215953	−	0.215953i
$262$		0			0
$263$		−	20.2075i		−	1.24605i	−0.782202	−	0.623025i	$-0.785904\pi$
$263$		−	20.2075i		−	1.24605i	0.782202	−	0.623025i	$-0.214096\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−13.6993	−	13.6993i	−0.838382	−	0.838382i
$268$		0			0
$269$	−16.2657	+	16.2657i	−0.991735	+	0.991735i	−0.999966	−	0.00823090i	$-0.997380\pi$
$269$	−16.2657	+	16.2657i	−0.991735	+	0.991735i	0.00823090	+	0.999966i	$0.497380\pi$
$270$		0			0
$271$	24.4714			1.48653			0.743267	−	0.668995i	$-0.233275\pi$
$271$	24.4714			1.48653			0.743267	+	0.668995i	$0.233275\pi$
$272$		0			0
$273$	7.85077			0.475150
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.7978	+	13.7978i	0.829028	+	0.829028i	0.987382	−	0.158354i	$-0.0506188\pi$
$277$	13.7978	+	13.7978i	0.829028	+	0.829028i	−0.158354	+	0.987382i	$0.550619\pi$
$278$		0			0
$279$			49.9587i			2.99095i
$280$		0			0
$281$			16.5673i			0.988319i	0.869371	+	0.494160i	$0.164524\pi$
$281$			16.5673i			0.988319i	−0.869371	+	0.494160i	$0.835476\pi$
$282$		0			0
$283$	13.6823	+	13.6823i	0.813330	+	0.813330i	0.985132	−	0.171802i	$-0.0549589\pi$
$283$	13.6823	+	13.6823i	0.813330	+	0.813330i	−0.171802	+	0.985132i	$0.554959\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.2034			0.661317
$288$		0			0
$289$	7.39230			0.434841
$290$		0			0
$291$	−7.51427	+	7.51427i	−0.440495	+	0.440495i
$292$		0			0
$293$	23.0518	+	23.0518i	1.34670	+	1.34670i	0.889219	+	0.457482i	$0.151249\pi$
$293$	23.0518	+	23.0518i	1.34670	+	1.34670i	0.457482	+	0.889219i	$0.348751\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	17.9514i		−	1.04165i
$298$		0			0
$299$	2.63553	+	2.63553i	0.152416	+	0.152416i
$300$		0			0
$301$	2.42551	−	2.42551i	0.139804	−	0.139804i
$302$		0			0
$303$	−2.81732			−0.161851
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−23.3518	+	23.3518i	−1.33276	+	1.33276i	−0.429867	+	0.902892i	$0.641440\pi$
$307$	−23.3518	+	23.3518i	−1.33276	+	1.33276i	−0.902892	+	0.429867i	$0.858560\pi$
$308$		0			0
$309$	25.7545	+	25.7545i	1.46512	+	1.46512i
$310$		0			0
$311$		−	17.8004i		−	1.00937i	−0.863304	−	0.504685i	$-0.831609\pi$
$311$		−	17.8004i		−	1.00937i	0.863304	−	0.504685i	$-0.168391\pi$
$312$		0			0
$313$		−	23.7909i		−	1.34474i	−0.740216	−	0.672370i	$-0.765277\pi$
$313$		−	23.7909i		−	1.34474i	0.740216	−	0.672370i	$-0.234723\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.6940	+	13.6940i	−0.769129	+	0.769129i	−0.977953	−	0.208824i	$-0.933036\pi$
$317$	−13.6940	+	13.6940i	−0.769129	+	0.769129i	0.208824	+	0.977953i	$0.433036\pi$
$318$		0			0
$319$	3.29930			0.184725
$320$		0			0
$321$	−6.21736			−0.347019
$322$		0			0
$323$	10.0731	−	10.0731i	0.560485	−	0.560485i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	28.4106i		−	1.57111i
$328$		0			0
$329$			2.28377i			0.125908i
$330$		0			0
$331$	−1.96043	−	1.96043i	−0.107755	−	0.107755i	0.651174	−	0.758929i	$-0.274277\pi$
$331$	−1.96043	−	1.96043i	−0.107755	−	0.107755i	−0.758929	+	0.651174i	$0.774277\pi$
$332$		0			0
$333$	21.4594	−	21.4594i	1.17597	−	1.17597i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−18.5606			−1.01106			−0.505530	−	0.862809i	$-0.668703\pi$
$337$	−18.5606			−1.01106			−0.505530	+	0.862809i	$0.668703\pi$
$338$		0			0
$339$	−18.4008	+	18.4008i	−0.999393	+	0.999393i
$340$		0			0
$341$	−23.6224	−	23.6224i	−1.27922	−	1.27922i
$342$		0			0
$343$			13.9684i			0.754221i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.01007	−	8.01007i	−0.430003	−	0.430003i	0.458626	−	0.888629i	$-0.348342\pi$
$347$	−8.01007	−	8.01007i	−0.430003	−	0.430003i	−0.888629	+	0.458626i	$0.848342\pi$
$348$		0			0
$349$	−19.2579	+	19.2579i	−1.03085	+	1.03085i	−0.0313434	+	0.999509i	$0.509979\pi$
$349$	−19.2579	+	19.2579i	−1.03085	+	1.03085i	−0.999509	+	0.0313434i	$0.990021\pi$
$350$		0			0
$351$	−13.9143			−0.742693
$352$		0			0
$353$	6.05459			0.322253			0.161127	−	0.986934i	$-0.448487\pi$
$353$	6.05459			0.322253			0.161127	+	0.986934i	$0.448487\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.7244	+	10.7244i	0.567593	+	0.567593i
$358$		0			0
$359$		−	8.74167i		−	0.461368i	−0.973029	−	0.230684i	$-0.925904\pi$
$359$		−	8.74167i		−	0.461368i	0.973029	−	0.230684i	$-0.0740964\pi$
$360$		0			0
$361$			10.6803i			0.562122i
$362$		0			0
$363$	−0.241479	−	0.241479i	−0.0126744	−	0.0126744i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	22.7558			1.18784			0.593920	−	0.804524i	$-0.297579\pi$
$367$	22.7558			1.18784			0.593920	+	0.804524i	$0.297579\pi$
$368$		0			0
$369$	−50.6823			−2.63841
$370$		0			0
$371$	0.234743	−	0.234743i	0.0121873	−	0.0121873i
$372$		0			0
$373$	−19.1172	−	19.1172i	−0.989851	−	0.989851i	0.0100979	−	0.999949i	$-0.496786\pi$
$373$	−19.1172	−	19.1172i	−0.989851	−	0.989851i	−0.999949	+	0.0100979i	$0.996786\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.55732i		−	0.131709i
$378$		0			0
$379$	19.2110	+	19.2110i	0.986802	+	0.986802i	0.999914	−	0.0131116i	$-0.00417366\pi$
$379$	19.2110	+	19.2110i	0.986802	+	0.986802i	−0.0131116	+	0.999914i	$0.504174\pi$
$380$		0			0
$381$	−3.97527	+	3.97527i	−0.203659	+	0.203659i
$382$		0			0
$383$	−20.7721			−1.06140			−0.530702	−	0.847558i	$-0.678072\pi$
$383$	−20.7721			−1.06140			−0.530702	+	0.847558i	$0.678072\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.9726	+	10.9726i	−0.557768	+	0.557768i
$388$		0			0
$389$	−22.9514	−	22.9514i	−1.16368	−	1.16368i	−0.983664	−	0.180017i	$-0.942385\pi$
$389$	−22.9514	−	22.9514i	−1.16368	−	1.16368i	−0.180017	−	0.983664i	$-0.557615\pi$
$390$		0			0
$391$			7.20039i			0.364139i
$392$		0			0
$393$			44.9666i			2.26826i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.9562	−	19.9562i	1.00157	−	1.00157i	0.00157311	−	0.999999i	$-0.499499\pi$
$397$	19.9562	−	19.9562i	1.00157	−	1.00157i	0.999999	−	0.00157311i	$-0.000500736\pi$
$398$		0			0
$399$	8.85754			0.443432
$400$		0			0
$401$	−35.5367			−1.77462			−0.887310	−	0.461174i	$-0.847428\pi$
$401$	−35.5367			−1.77462			−0.887310	+	0.461174i	$0.847428\pi$
$402$		0			0
$403$	−18.3099	+	18.3099i	−0.912083	+	0.912083i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			20.2936i			1.00592i
$408$		0			0
$409$		−	6.50932i		−	0.321865i	−0.986965	−	0.160933i	$-0.948550\pi$
$409$		−	6.50932i		−	0.321865i	0.986965	−	0.160933i	$-0.0514502\pi$
$410$		0			0
$411$	31.7510	+	31.7510i	1.56616	+	1.56616i
$412$		0			0
$413$	1.26567	−	1.26567i	0.0622798	−	0.0622798i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.1211			0.740485
$418$		0			0
$419$	10.8597	−	10.8597i	0.530529	−	0.530529i	−0.390200	−	0.920730i	$-0.627594\pi$
$419$	10.8597	−	10.8597i	0.530529	−	0.530529i	0.920730	+	0.390200i	$0.127594\pi$
$420$		0			0
$421$	17.0865	+	17.0865i	0.832744	+	0.832744i	0.987891	−	0.155147i	$-0.0495852\pi$
$421$	17.0865	+	17.0865i	0.832744	+	0.832744i	−0.155147	+	0.987891i	$0.549585\pi$
$422$		0			0
$423$		−	10.3314i		−	0.502328i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.77700	−	3.77700i	−0.182782	−	0.182782i
$428$		0			0
$429$	16.7931	−	16.7931i	0.810778	−	0.810778i
$430$		0			0
$431$	−24.6877			−1.18916			−0.594581	−	0.804036i	$-0.702682\pi$
$431$	−24.6877			−1.18916			−0.594581	+	0.804036i	$0.702682\pi$
$432$		0			0
$433$	−34.7872			−1.67176			−0.835882	−	0.548909i	$-0.815043\pi$
$433$	−34.7872			−1.67176			−0.835882	+	0.548909i	$0.815043\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.97350	+	2.97350i	0.142242	+	0.142242i
$438$		0			0
$439$			1.12777i			0.0538257i	0.999638	+	0.0269128i	$0.00856766\pi$
$439$			1.12777i			0.0538257i	−0.999638	+	0.0269128i	$0.991432\pi$
$440$		0			0
$441$		−	28.6634i		−	1.36492i
$442$		0			0
$443$	−1.20401	−	1.20401i	−0.0572043	−	0.0572043i	0.677926	−	0.735130i	$-0.262879\pi$
$443$	−1.20401	−	1.20401i	−0.0572043	−	0.0572043i	−0.735130	+	0.677926i	$0.762879\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−53.0903			−2.51109
$448$		0			0
$449$	18.1896			0.858422			0.429211	−	0.903204i	$-0.358792\pi$
$449$	18.1896			0.858422			0.429211	+	0.903204i	$0.358792\pi$
$450$		0			0
$451$	23.9645	−	23.9645i	1.12844	−	1.12844i
$452$		0			0
$453$	11.1549	+	11.1549i	0.524105	+	0.524105i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			4.25060i			0.198835i	0.995046	+	0.0994174i	$0.0316979\pi$
$457$			4.25060i			0.198835i	−0.995046	+	0.0994174i	$0.968302\pi$
$458$		0			0
$459$	−19.0073	−	19.0073i	−0.887187	−	0.887187i
$460$		0			0
$461$	−25.7081	+	25.7081i	−1.19735	+	1.19735i	−0.222390	+	0.974958i	$0.571386\pi$
$461$	−25.7081	+	25.7081i	−1.19735	+	1.19735i	−0.974958	+	0.222390i	$0.928614\pi$
$462$		0			0
$463$	−32.8289			−1.52569			−0.762844	−	0.646582i	$-0.776198\pi$
$463$	−32.8289			−1.52569			−0.762844	+	0.646582i	$0.776198\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.1611	−	17.1611i	0.794123	−	0.794123i	−0.188039	−	0.982162i	$-0.560213\pi$
$467$	17.1611	−	17.1611i	0.794123	−	0.794123i	0.982162	+	0.188039i	$0.0602130\pi$
$468$		0			0
$469$	−5.49731	−	5.49731i	−0.253842	−	0.253842i
$470$		0			0
$471$			28.3575i			1.30665i
$472$		0			0
$473$		−	10.3765i		−	0.477112i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.06194	+	1.06194i	−0.0486228	+	0.0486228i
$478$		0			0
$479$	−25.2711			−1.15466			−0.577332	−	0.816510i	$-0.695906\pi$
$479$	−25.2711			−1.15466			−0.577332	+	0.816510i	$0.695906\pi$
$480$		0			0
$481$	15.7298			0.717216
$482$		0			0
$483$	−3.16573	+	3.16573i	−0.144046	+	0.144046i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			12.9056i			0.584807i	0.956295	+	0.292404i	$0.0944551\pi$
$487$			12.9056i			0.584807i	−0.956295	+	0.292404i	$0.905545\pi$
$488$		0			0
$489$			2.17495i			0.0983545i
$490$		0			0
$491$	−10.3909	−	10.3909i	−0.468935	−	0.468935i	0.432635	−	0.901569i	$-0.357584\pi$
$491$	−10.3909	−	10.3909i	−0.468935	−	0.468935i	−0.901569	+	0.432635i	$0.857584\pi$
$492$		0			0
$493$	3.49337	−	3.49337i	0.157333	−	0.157333i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.97894			0.313048
$498$		0			0
$499$	−19.8755	+	19.8755i	−0.889749	+	0.889749i	−0.994499	−	0.104750i	$-0.966596\pi$
$499$	−19.8755	+	19.8755i	−0.889749	+	0.889749i	0.104750	+	0.994499i	$0.466596\pi$
$500$		0			0
$501$	42.4402	+	42.4402i	1.89609	+	1.89609i
$502$		0			0
$503$		−	12.8059i		−	0.570989i	−0.958380	−	0.285494i	$-0.907842\pi$
$503$		−	12.8059i		−	0.570989i	0.958380	−	0.285494i	$-0.0921578\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.8735	+	12.8735i	0.571732	+	0.571732i
$508$		0			0
$509$	−5.77064	+	5.77064i	−0.255779	+	0.255779i	−0.823335	−	0.567556i	$-0.807889\pi$
$509$	−5.77064	+	5.77064i	−0.255779	+	0.255779i	0.567556	+	0.823335i	$0.307889\pi$
$510$		0			0
$511$	5.71704			0.252907
$512$		0			0
$513$	−15.6987			−0.693114
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.88507	+	4.88507i	0.214845	+	0.214845i
$518$		0			0
$519$			10.5421i			0.462747i
$520$		0			0
$521$		−	18.9514i		−	0.830274i	−0.909759	−	0.415137i	$-0.863734\pi$
$521$		−	18.9514i		−	0.830274i	0.909759	−	0.415137i	$-0.136266\pi$
$522$		0			0
$523$	−7.32161	−	7.32161i	−0.320152	−	0.320152i	0.528674	−	0.848825i	$-0.322690\pi$
$523$	−7.32161	−	7.32161i	−0.320152	−	0.320152i	−0.848825	+	0.528674i	$0.822690\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−50.0237			−2.17907
$528$		0			0
$529$	20.8745			0.907587
$530$		0			0
$531$	−5.72569	+	5.72569i	−0.248474	+	0.248474i
$532$		0			0
$533$	−18.5751	−	18.5751i	−0.804578	−	0.804578i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			53.6708i			2.31606i
$538$		0			0
$539$	13.5531	+	13.5531i	0.583774	+	0.583774i
$540$		0			0
$541$	−6.08576	+	6.08576i	−0.261647	+	0.261647i	−0.825723	−	0.564076i	$-0.809233\pi$
$541$	−6.08576	+	6.08576i	−0.261647	+	0.261647i	0.564076	+	0.825723i	$0.309233\pi$
$542$		0			0
$543$	−6.51442			−0.279561
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.68638	+	3.68638i	−0.157618	+	0.157618i	−0.781510	−	0.623892i	$-0.785550\pi$
$547$	−3.68638	+	3.68638i	−0.157618	+	0.157618i	0.623892	+	0.781510i	$0.285550\pi$
$548$		0			0
$549$	17.0865	+	17.0865i	0.729233	+	0.729233i
$550$		0			0
$551$		−	2.88527i		−	0.122917i
$552$		0			0
$553$			2.85124i			0.121247i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	−0.619071	−	0.785335i	$-0.712491\pi$
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	0.785335	+	0.619071i	$0.212491\pi$
$558$		0			0
$559$	−8.04293			−0.340180
$560$		0			0
$561$	45.8796			1.93704
$562$		0			0
$563$	−2.42213	+	2.42213i	−0.102081	+	0.102081i	−0.756303	−	0.654222i	$-0.772996\pi$
$563$	−2.42213	+	2.42213i	−0.102081	+	0.102081i	0.654222	+	0.756303i	$0.272996\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	0.579682i		−	0.0243444i
$568$		0			0
$569$		−	0.577163i		−	0.0241959i	−0.999927	−	0.0120980i	$-0.996149\pi$
$569$		−	0.577163i		−	0.0241959i	0.999927	−	0.0120980i	$-0.00385099\pi$
$570$		0			0
$571$	18.5485	+	18.5485i	0.776229	+	0.776229i	0.979187	−	0.202959i	$-0.0650557\pi$
$571$	18.5485	+	18.5485i	0.776229	+	0.776229i	−0.202959	+	0.979187i	$0.565056\pi$
$572$		0			0
$573$	−10.1007	+	10.1007i	−0.421962	+	0.421962i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−9.63346			−0.401046			−0.200523	−	0.979689i	$-0.564264\pi$
$577$	−9.63346			−0.401046			−0.200523	+	0.979689i	$0.564264\pi$
$578$		0			0
$579$	43.8873	−	43.8873i	1.82390	−	1.82390i
$580$		0			0
$581$	−6.19148	−	6.19148i	−0.256866	−	0.256866i
$582$		0			0
$583$		−	1.00425i		−	0.0415918i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.5202	+	17.5202i	0.723136	+	0.723136i	0.969243	−	0.246107i	$-0.0791513\pi$
$587$	17.5202	+	17.5202i	0.723136	+	0.723136i	−0.246107	+	0.969243i	$0.579151\pi$
$588$		0			0
$589$	−20.6580	+	20.6580i	−0.851197	+	0.851197i
$590$		0			0
$591$	−32.1433			−1.32220
$592$		0			0
$593$	−15.7065			−0.644988			−0.322494	−	0.946571i	$-0.604521\pi$
$593$	−15.7065			−0.644988			−0.322494	+	0.946571i	$0.604521\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−43.5279	−	43.5279i	−1.78148	−	1.78148i
$598$		0			0
$599$		−	29.6865i		−	1.21296i	−0.795099	−	0.606479i	$-0.792581\pi$
$599$		−	29.6865i		−	1.21296i	0.795099	−	0.606479i	$-0.207419\pi$
$600$		0			0
$601$		−	13.3688i		−	0.545325i	−0.962110	−	0.272663i	$-0.912096\pi$
$601$		−	13.3688i		−	0.545325i	0.962110	−	0.272663i	$-0.0879043\pi$
$602$		0			0
$603$	24.8689	+	24.8689i	1.01274	+	1.01274i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	39.5508			1.60532			0.802659	−	0.596439i	$-0.203418\pi$
$607$	39.5508			1.60532			0.802659	+	0.596439i	$0.203418\pi$
$608$		0			0
$609$	3.07180			0.124475
$610$		0			0
$611$	3.78646	−	3.78646i	0.153184	−	0.153184i
$612$		0			0
$613$	15.1788	+	15.1788i	0.613067	+	0.613067i	0.943744	−	0.330677i	$-0.107277\pi$
$613$	15.1788	+	15.1788i	0.613067	+	0.613067i	−0.330677	+	0.943744i	$0.607277\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			18.6184i			0.749549i	0.927116	+	0.374774i	$0.122280\pi$
$617$			18.6184i			0.749549i	−0.927116	+	0.374774i	$0.877720\pi$
$618$		0			0
$619$	−15.6388	−	15.6388i	−0.628576	−	0.628576i	0.319134	−	0.947710i	$-0.396608\pi$
$619$	−15.6388	−	15.6388i	−0.628576	−	0.628576i	−0.947710	+	0.319134i	$0.896608\pi$
$620$		0			0
$621$	5.61080	−	5.61080i	0.225154	−	0.225154i
$622$		0			0
$623$	7.50008			0.300484
$624$		0			0
$625$		0			0
$626$		0			0
$627$	18.9466	−	18.9466i	0.756655	−	0.756655i
$628$		0			0
$629$	21.4873	+	21.4873i	0.856753	+	0.856753i
$630$		0			0
$631$		−	32.2591i		−	1.28422i	−0.766614	−	0.642108i	$-0.778060\pi$
$631$		−	32.2591i		−	1.28422i	0.766614	−	0.642108i	$-0.221940\pi$
$632$		0			0
$633$			20.6404i			0.820382i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	10.5052	−	10.5052i	0.416230	−	0.416230i
$638$		0			0
$639$	−31.5715			−1.24895
$640$		0			0
$641$	−8.87760			−0.350644			−0.175322	−	0.984511i	$-0.556097\pi$
$641$	−8.87760			−0.350644			−0.175322	+	0.984511i	$0.556097\pi$
$642$		0			0
$643$	−19.5500	+	19.5500i	−0.770977	+	0.770977i	−0.978277	−	0.207301i	$-0.933532\pi$
$643$	−19.5500	+	19.5500i	−0.770977	+	0.770977i	0.207301	+	0.978277i	$0.433532\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	33.1992i		−	1.30519i	−0.757705	−	0.652597i	$-0.773679\pi$
$647$		−	33.1992i		−	1.30519i	0.757705	−	0.652597i	$-0.226321\pi$
$648$		0			0
$649$		−	5.41465i		−	0.212543i
$650$		0			0
$651$	−21.9935	−	21.9935i	−0.861992	−	0.861992i
$652$		0			0
$653$	10.3869	−	10.3869i	0.406472	−	0.406472i	−0.474034	−	0.880506i	$-0.657203\pi$
$653$	10.3869	−	10.3869i	0.406472	−	0.406472i	0.880506	+	0.474034i	$0.157203\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−25.8629			−1.00901
$658$		0			0
$659$	3.29013	−	3.29013i	0.128165	−	0.128165i	−0.640114	−	0.768280i	$-0.721113\pi$
$659$	3.29013	−	3.29013i	0.128165	−	0.128165i	0.768280	+	0.640114i	$0.221113\pi$
$660$		0			0
$661$	−8.43866	−	8.43866i	−0.328226	−	0.328226i	0.523686	−	0.851912i	$-0.324557\pi$
$661$	−8.43866	−	8.43866i	−0.328226	−	0.328226i	−0.851912	+	0.523686i	$0.824557\pi$
$662$		0			0
$663$		−	35.5617i		−	1.38110i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.03121	+	1.03121i	0.0399286	+	0.0399286i
$668$		0			0
$669$	37.2610	−	37.2610i	1.44059	−	1.44059i
$670$		0			0
$671$	−16.1583			−0.623783
$672$		0			0
$673$	7.49618			0.288956			0.144478	−	0.989508i	$-0.453850\pi$
$673$	7.49618			0.288956			0.144478	+	0.989508i	$0.453850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.2336	−	11.2336i	−0.431741	−	0.431741i	0.457479	−	0.889220i	$-0.348752\pi$
$677$	−11.2336	−	11.2336i	−0.431741	−	0.431741i	−0.889220	+	0.457479i	$0.848752\pi$
$678$		0			0
$679$		−	4.11391i		−	0.157877i
$680$		0			0
$681$		−	34.5904i		−	1.32551i
$682$		0			0
$683$	24.1607	+	24.1607i	0.924482	+	0.924482i	0.997342	−	0.0728605i	$-0.0232128\pi$
$683$	24.1607	+	24.1607i	0.924482	+	0.924482i	−0.0728605	+	0.997342i	$0.523213\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	16.8458			0.642709
$688$		0			0
$689$	−0.778403			−0.0296548
$690$		0			0
$691$	−20.6744	+	20.6744i	−0.786490	+	0.786490i	−0.980917	−	0.194427i	$-0.937715\pi$
$691$	−20.6744	+	20.6744i	−0.786490	+	0.786490i	0.194427	+	0.980917i	$0.437715\pi$
$692$		0			0
$693$	12.5427	+	12.5427i	0.476460	+	0.476460i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	50.7482i		−	1.92222i
$698$		0			0
$699$	39.2440	+	39.2440i	1.48435	+	1.48435i
$700$		0			0
$701$	−5.10967	+	5.10967i	−0.192990	+	0.192990i	−0.796987	−	0.603997i	$-0.793574\pi$
$701$	−5.10967	+	5.10967i	−0.192990	+	0.192990i	0.603997	+	0.796987i	$0.293574\pi$
$702$		0			0
$703$	17.7469			0.669338
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.771212	−	0.771212i	0.0290044	−	0.0290044i
$708$		0			0
$709$	−13.7429	−	13.7429i	−0.516126	−	0.516126i	0.400271	−	0.916397i	$-0.368916\pi$
$709$	−13.7429	−	13.7429i	−0.516126	−	0.516126i	−0.916397	+	0.400271i	$0.868916\pi$
$710$		0			0
$711$		−	12.8985i		−	0.483732i
$712$		0			0
$713$		−	14.7665i		−	0.553011i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.90767	+	1.90767i	−0.0712431	+	0.0712431i
$718$		0			0
$719$	23.0266			0.858747			0.429373	−	0.903127i	$-0.358734\pi$
$719$	23.0266			0.858747			0.429373	+	0.903127i	$0.358734\pi$
$720$		0			0
$721$	−14.1001			−0.525114
$722$		0			0
$723$	20.8312	−	20.8312i	0.774721	−	0.774721i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	43.6601i		−	1.61926i	−0.586939	−	0.809631i	$-0.699667\pi$
$727$		−	43.6601i		−	1.61926i	0.586939	−	0.809631i	$-0.300333\pi$
$728$		0			0
$729$		−	43.3646i		−	1.60610i
$730$		0			0
$731$	−10.9869	−	10.9869i	−0.406363	−	0.406363i
$732$		0			0
$733$	20.4799	−	20.4799i	0.756444	−	0.756444i	−0.219229	−	0.975673i	$-0.570354\pi$
$733$	20.4799	−	20.4799i	0.756444	−	0.756444i	0.975673	+	0.219229i	$0.0703543\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.5179			−0.866292
$738$		0			0
$739$	−5.57362	+	5.57362i	−0.205029	+	0.205029i	−0.802151	−	0.597122i	$-0.796311\pi$
$739$	−5.57362	+	5.57362i	−0.205029	+	0.205029i	0.597122	+	0.802151i	$0.296311\pi$
$740$		0			0
$741$	−14.6857	−	14.6857i	−0.539493	−	0.539493i
$742$		0			0
$743$			13.1917i			0.483957i	0.970282	+	0.241978i	$0.0777963\pi$
$743$			13.1917i			0.483957i	−0.970282	+	0.241978i	$0.922204\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	28.0092	+	28.0092i	1.02480	+	1.02480i
$748$		0			0
$749$	1.70194	−	1.70194i	0.0621875	−	0.0621875i
$750$		0			0
$751$	16.1003			0.587510			0.293755	−	0.955881i	$-0.405095\pi$
$751$	16.1003			0.587510			0.293755	+	0.955881i	$0.405095\pi$
$752$		0			0
$753$	−29.0371			−1.05817
$754$		0			0
$755$		0			0
$756$		0			0
$757$	23.2342	+	23.2342i	0.844463	+	0.844463i	0.989436	−	0.144973i	$-0.0463094\pi$
$757$	23.2342	+	23.2342i	0.844463	+	0.844463i	−0.144973	+	0.989436i	$0.546309\pi$
$758$		0			0
$759$			13.5432i			0.491588i
$760$		0			0
$761$		−	15.4641i		−	0.560573i	−0.959916	−	0.280287i	$-0.909570\pi$
$761$		−	15.4641i		−	0.560573i	0.959916	−	0.280287i	$-0.0904295\pi$
$762$		0			0
$763$	7.77711	+	7.77711i	0.281550	+	0.281550i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.19694			−0.151543
$768$		0			0
$769$	−20.7352			−0.747729			−0.373864	−	0.927483i	$-0.621967\pi$
$769$	−20.7352			−0.747729			−0.373864	+	0.927483i	$0.621967\pi$
$770$		0			0
$771$	40.3943	−	40.3943i	1.45476	−	1.45476i
$772$		0			0
$773$	−9.64112	−	9.64112i	−0.346767	−	0.346767i	0.512137	−	0.858904i	$-0.328854\pi$
$773$	−9.64112	−	9.64112i	−0.346767	−	0.346767i	−0.858904	+	0.512137i	$0.828854\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			18.8942i			0.677827i
$778$		0			0
$779$	−20.9572	−	20.9572i	−0.750869	−	0.750869i
$780$		0			0
$781$	14.9282	−	14.9282i	0.534173	−	0.534173i
$782$		0			0
$783$	−5.44431			−0.194564
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−20.1485	+	20.1485i	−0.718216	+	0.718216i	−0.968240	−	0.250024i	$-0.919562\pi$
$787$	−20.1485	+	20.1485i	−0.718216	+	0.718216i	0.250024	+	0.968240i	$0.419562\pi$
$788$		0			0
$789$	−40.2440	−	40.2440i	−1.43273	−	1.43273i
$790$		0			0
$791$		−	10.0741i		−	0.358192i
$792$		0			0
$793$			12.5244i			0.444756i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.9707	−	19.9707i	0.707399	−	0.707399i	−0.258588	−	0.965988i	$-0.583257\pi$
$797$	19.9707	−	19.9707i	0.707399	−	0.707399i	0.965988	+	0.258588i	$0.0832573\pi$
$798$		0			0
$799$	10.3448			0.365973
$800$		0			0
$801$	−33.9290			−1.19882
$802$		0			0
$803$	12.2290	−	12.2290i	0.431551	−	0.431551i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			64.7874i			2.28062i
$808$		0			0
$809$			16.2764i			0.572249i	0.958192	+	0.286125i	$0.0923671\pi$
$809$			16.2764i			0.572249i	−0.958192	+	0.286125i	$0.907633\pi$
$810$		0			0
$811$	27.7616	+	27.7616i	0.974841	+	0.974841i	0.999691	−	0.0248504i	$-0.00791094\pi$
$811$	27.7616	+	27.7616i	0.974841	+	0.974841i	−0.0248504	+	0.999691i	$0.507911\pi$
$812$		0			0
$813$	48.7358	−	48.7358i	1.70924	−	1.70924i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−9.07435			−0.317471
$818$		0			0
$819$	9.72201	−	9.72201i	0.339714	−	0.339714i
$820$		0			0
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	0.822467	−	0.568813i	$-0.192597\pi$
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	−0.568813	+	0.822467i	$0.692597\pi$
$822$		0			0
$823$		−	44.1075i		−	1.53749i	−0.639554	−	0.768746i	$-0.720881\pi$
$823$		−	44.1075i		−	1.53749i	0.639554	−	0.768746i	$-0.279119\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.9202	−	12.9202i	−0.449279	−	0.449279i	0.445836	−	0.895115i	$-0.352907\pi$
$827$	−12.9202	−	12.9202i	−0.449279	−	0.449279i	−0.895115	+	0.445836i	$0.852907\pi$
$828$		0			0
$829$	16.1583	−	16.1583i	0.561200	−	0.561200i	−0.368448	−	0.929648i	$-0.620111\pi$
$829$	16.1583	−	16.1583i	0.561200	−	0.561200i	0.929648	+	0.368448i	$0.120111\pi$
$830$		0			0
$831$	54.9576			1.90646
$832$		0			0
$833$	28.7006			0.994418
$834$		0			0
$835$		0			0
$836$		0			0
$837$	38.9802	+	38.9802i	1.34735	+	1.34735i
$838$		0			0
$839$		−	50.4452i		−	1.74156i	−0.491673	−	0.870780i	$-0.663614\pi$
$839$		−	50.4452i		−	1.74156i	0.491673	−	0.870780i	$-0.336386\pi$
$840$		0			0
$841$			27.9994i			0.965496i
$842$		0			0
$843$	32.9943	+	32.9943i	1.13638	+	1.13638i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.132205			0.00454261
$848$		0			0
$849$	54.4977			1.87036
$850$		0			0
$851$	−6.34285	+	6.34285i	−0.217430	+	0.217430i
$852$		0			0
$853$	26.2184	+	26.2184i	0.897701	+	0.897701i	0.995232	−	0.0975316i	$-0.0310947\pi$
$853$	26.2184	+	26.2184i	0.897701	+	0.897701i	−0.0975316	+	0.995232i	$0.531095\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	31.6388i		−	1.08076i	−0.841421	−	0.540380i	$-0.818280\pi$
$857$		−	31.6388i		−	1.08076i	0.841421	−	0.540380i	$-0.181720\pi$
$858$		0			0
$859$	14.1168	+	14.1168i	0.481657	+	0.481657i	0.905661	−	0.424003i	$-0.139376\pi$
$859$	14.1168	+	14.1168i	0.481657	+	0.481657i	−0.424003	+	0.905661i	$0.639376\pi$
$860$		0			0
$861$	22.3120	−	22.3120i	0.760392	−	0.760392i
$862$		0			0
$863$	−1.50248			−0.0511449			−0.0255724	−	0.999673i	$-0.508141\pi$
$863$	−1.50248			−0.0511449			−0.0255724	+	0.999673i	$0.508141\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	14.7221	−	14.7221i	0.499987	−	0.499987i
$868$		0			0
$869$	6.09891	+	6.09891i	0.206891	+	0.206891i
$870$		0			0
$871$			18.2289i			0.617664i
$872$		0			0
$873$			18.6106i			0.629874i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.9903	+	26.9903i	−0.911398	+	0.911398i	−0.996382	−	0.0849842i	$-0.972916\pi$
$877$	−26.9903	+	26.9903i	−0.911398	+	0.911398i	0.0849842	+	0.996382i	$0.472916\pi$
$878$		0			0
$879$	91.8171			3.09691
$880$		0			0
$881$	−0.184858			−0.00622802			−0.00311401	−	0.999995i	$-0.500991\pi$
$881$	−0.184858			−0.00622802			−0.00311401	+	0.999995i	$0.500991\pi$
$882$		0			0
$883$	17.9054	−	17.9054i	0.602564	−	0.602564i	−0.338428	−	0.940992i	$-0.609895\pi$
$883$	17.9054	−	17.9054i	0.602564	−	0.602564i	0.940992	+	0.338428i	$0.109895\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	12.7152i		−	0.426936i	−0.976950	−	0.213468i	$-0.931524\pi$
$887$		−	12.7152i		−	0.426936i	0.976950	−	0.213468i	$-0.0684759\pi$
$888$		0			0
$889$		−	2.17638i		−	0.0729934i
$890$		0			0
$891$	−1.23996	−	1.23996i	−0.0415403	−	0.0415403i
$892$		0			0
$893$	4.27203	−	4.27203i	0.142958	−	0.142958i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	10.4975			0.350501
$898$		0			0
$899$	−7.16419	+	7.16419i	−0.238939	+	0.238939i
$900$		0			0
$901$	−1.06332	−	1.06332i	−0.0354243	−	0.0354243i
$902$		0			0
$903$		−	9.66099i		−	0.321498i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.807340	+	0.807340i	0.0268073	+	0.0268073i	0.720383	−	0.693576i	$-0.243966\pi$
$907$	0.807340	+	0.807340i	0.0268073	+	0.0268073i	−0.693576	+	0.720383i	$0.743966\pi$
$908$		0			0
$909$	−3.48883	+	3.48883i	−0.115717	+	0.115717i
$910$		0			0
$911$	9.38640			0.310985			0.155493	−	0.987837i	$-0.450304\pi$
$911$	9.38640			0.310985			0.155493	+	0.987837i	$0.450304\pi$
$912$		0			0
$913$	−26.4876			−0.876612
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.3091	−	12.3091i	−0.406484	−	0.406484i
$918$		0			0
$919$			13.6402i			0.449949i	0.974365	+	0.224974i	$0.0722298\pi$
$919$			13.6402i			0.449949i	−0.974365	+	0.224974i	$0.927770\pi$
$920$		0			0
$921$			93.0121i			3.06485i
$922$		0			0
$923$	−11.5710	−	11.5710i	−0.380864	−	0.380864i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	63.7862			2.09501
$928$		0			0
$929$	−18.0314			−0.591590			−0.295795	−	0.955252i	$-0.595584\pi$
$929$	−18.0314			−0.591590			−0.295795	+	0.955252i	$0.595584\pi$
$930$		0			0
$931$	11.8523	−	11.8523i	0.388444	−	0.388444i
$932$		0			0
$933$	−35.4502	−	35.4502i	−1.16059	−	1.16059i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	15.1318i		−	0.494334i	−0.968973	−	0.247167i	$-0.920500\pi$
$937$		−	15.1318i		−	0.494334i	0.968973	−	0.247167i	$-0.0794996\pi$
$938$		0			0
$939$	−47.3804	−	47.3804i	−1.54620	−	1.54620i
$940$		0			0
$941$	−5.08494	+	5.08494i	−0.165764	+	0.165764i	−0.785115	−	0.619350i	$-0.787396\pi$
$941$	−5.08494	+	5.08494i	−0.165764	+	0.165764i	0.619350	+	0.785115i	$0.287396\pi$
$942$		0			0
$943$	14.9804			0.487829
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.36920	−	2.36920i	0.0769885	−	0.0769885i	−0.667564	−	0.744552i	$-0.732663\pi$
$947$	2.36920	−	2.36920i	0.0769885	−	0.0769885i	0.744552	+	0.667564i	$0.232663\pi$
$948$		0			0
$949$	−9.47879	−	9.47879i	−0.307694	−	0.307694i
$950$		0			0
$951$			54.5441i			1.76871i
$952$		0			0
$953$			35.0311i			1.13477i	0.823454	+	0.567384i	$0.192044\pi$
$953$			35.0311i			1.13477i	−0.823454	+	0.567384i	$0.807956\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.57068	−	6.57068i	0.212400	−	0.212400i
$958$		0			0
$959$	−17.3830			−0.561327
$960$		0			0
$961$	71.5884			2.30930
$962$		0			0
$963$	−7.69927	+	7.69927i	−0.248105	+	0.248105i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	54.2039i		−	1.74308i	−0.490323	−	0.871541i	$-0.663121\pi$
$967$		−	54.2039i		−	1.74308i	0.490323	−	0.871541i	$-0.336879\pi$
$968$		0			0
$969$		−	40.1221i		−	1.28891i
$970$		0			0
$971$	−20.8327	−	20.8327i	−0.668552	−	0.668552i	0.288829	−	0.957381i	$-0.406734\pi$
$971$	−20.8327	−	20.8327i	−0.668552	−	0.668552i	−0.957381	+	0.288829i	$0.906734\pi$
$972$		0			0
$973$	−4.13926	+	4.13926i	−0.132698	+	0.132698i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.03891			0.161209			0.0806045	−	0.996746i	$-0.474315\pi$
$977$	5.03891			0.161209			0.0806045	+	0.996746i	$0.474315\pi$
$978$		0			0
$979$	16.0429	−	16.0429i	0.512734	−	0.512734i
$980$		0			0
$981$	−35.1823	−	35.1823i	−1.12328	−	1.12328i
$982$		0			0
$983$			40.6047i			1.29509i	0.762027	+	0.647545i	$0.224204\pi$
$983$			40.6047i			1.29509i	−0.762027	+	0.647545i	$0.775796\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.54821	+	4.54821i	0.144771	+	0.144771i
$988$		0			0
$989$	3.24322	−	3.24322i	0.103128	−	0.103128i
$990$		0			0
$991$	18.5421			0.589009			0.294505	−	0.955650i	$-0.404845\pi$
$991$	18.5421			0.589009			0.294505	+	0.955650i	$0.404845\pi$
$992$		0			0
$993$	−7.80854			−0.247797
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−11.0618	−	11.0618i	−0.350330	−	0.350330i	0.509902	−	0.860232i	$-0.329682\pi$
$997$	−11.0618	−	11.0618i	−0.350330	−	0.350330i	−0.860232	+	0.509902i	$0.829682\pi$
$998$		0			0
$999$		−	33.4873i		−	1.05949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.h.1201.8		16
4.3	odd	2		400.2.l.i.101.2		16
5.2	odd	4		320.2.q.c.49.1		16
5.3	odd	4		320.2.q.c.49.8		16
5.4	even	2	inner	1600.2.l.h.1201.1		16
16.3	odd	4		400.2.l.i.301.2		16
16.13	even	4	inner	1600.2.l.h.401.8		16
20.3	even	4		80.2.q.c.69.3	yes	16
20.7	even	4		80.2.q.c.69.6	yes	16
20.19	odd	2		400.2.l.i.101.7		16
40.3	even	4		640.2.q.e.609.8		16
40.13	odd	4		640.2.q.f.609.1		16
40.27	even	4		640.2.q.e.609.1		16
40.37	odd	4		640.2.q.f.609.8		16
60.23	odd	4		720.2.bm.f.469.6		16
60.47	odd	4		720.2.bm.f.469.3		16
80.3	even	4		80.2.q.c.29.6	yes	16
80.13	odd	4		320.2.q.c.209.1		16
80.19	odd	4		400.2.l.i.301.7		16
80.27	even	4		640.2.q.e.289.8		16
80.29	even	4	inner	1600.2.l.h.401.1		16
80.37	odd	4		640.2.q.f.289.1		16
80.43	even	4		640.2.q.e.289.1		16
80.53	odd	4		640.2.q.f.289.8		16
80.67	even	4		80.2.q.c.29.3	✓	16
80.77	odd	4		320.2.q.c.209.8		16
240.83	odd	4		720.2.bm.f.109.3		16
240.227	odd	4		720.2.bm.f.109.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.3	✓	16	80.67	even	4
80.2.q.c.29.6	yes	16	80.3	even	4
80.2.q.c.69.3	yes	16	20.3	even	4
80.2.q.c.69.6	yes	16	20.7	even	4
320.2.q.c.49.1		16	5.2	odd	4
320.2.q.c.49.8		16	5.3	odd	4
320.2.q.c.209.1		16	80.13	odd	4
320.2.q.c.209.8		16	80.77	odd	4
400.2.l.i.101.2		16	4.3	odd	2
400.2.l.i.101.7		16	20.19	odd	2
400.2.l.i.301.2		16	16.3	odd	4
400.2.l.i.301.7		16	80.19	odd	4
640.2.q.e.289.1		16	80.43	even	4
640.2.q.e.289.8		16	80.27	even	4
640.2.q.e.609.1		16	40.27	even	4
640.2.q.e.609.8		16	40.3	even	4
640.2.q.f.289.1		16	80.37	odd	4
640.2.q.f.289.8		16	80.53	odd	4
640.2.q.f.609.1		16	40.13	odd	4
640.2.q.f.609.8		16	40.37	odd	4
720.2.bm.f.109.3		16	240.83	odd	4
720.2.bm.f.109.6		16	240.227	odd	4
720.2.bm.f.469.3		16	60.47	odd	4
720.2.bm.f.469.6		16	60.23	odd	4
1600.2.l.h.401.1		16	80.29	even	4	inner
1600.2.l.h.401.8		16	16.13	even	4	inner
1600.2.l.h.1201.1		16	5.4	even	2	inner
1600.2.l.h.1201.8		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.99154 - 1.99154i) q^{3} +1.09033i q^{7} -4.93244i q^{9} +O(q^{10})\)	\(q+(1.99154 - 1.99154i) q^{3} +1.09033i q^{7} -4.93244i q^{9} +(2.33225 + 2.33225i) q^{11} +(1.80775 - 1.80775i) q^{13} +4.93886 q^{17} +(2.03957 - 2.03957i) q^{19} +(2.17142 + 2.17142i) q^{21} +1.45791i q^{23} +(-3.84853 - 3.84853i) q^{27} +(0.707323 - 0.707323i) q^{29} -10.1286 q^{31} +9.28951 q^{33} +(4.35066 + 4.35066i) q^{37} -7.20039i q^{39} -10.2753i q^{41} +(-2.22457 - 2.22457i) q^{43} +2.09458 q^{47} +5.81119 q^{49} +(9.83592 - 9.83592i) q^{51} +(-0.215297 - 0.215297i) q^{53} -8.12376i q^{57} +(-1.16082 - 1.16082i) q^{59} +(-3.46410 + 3.46410i) q^{61} +5.37797 q^{63} +(-5.04189 + 5.04189i) q^{67} +(2.90348 + 2.90348i) q^{69} -6.40078i q^{71} -5.24343i q^{73} +(-2.54291 + 2.54291i) q^{77} +2.61504 q^{79} -0.531659 q^{81} +(-5.67856 + 5.67856i) q^{83} -2.81732i q^{87} -6.87875i q^{89} +(1.97103 + 1.97103i) q^{91} +(-20.1715 + 20.1715i) q^{93} -3.77310 q^{97} +(11.5037 - 11.5037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

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