LMFDB - Embedded newform 1600.2.l.f.1201.4

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.4
Root			$-0.507829 - 1.31989i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.f.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0623209 + 0.0623209i) q^{3} +0.375877i q^{7} +2.99223i q^{9} +O(q^{10})$	$q+(-0.0623209 + 0.0623209i) q^{3} +0.375877i q^{7} +2.99223i q^{9} +(-2.36756 - 2.36756i) q^{11} +(1.76442 - 1.76442i) q^{13} +4.64955 q^{17} +(2.34965 - 2.34965i) q^{19} +(-0.0234250 - 0.0234250i) q^{21} +2.07779i q^{23} +(-0.373441 - 0.373441i) q^{27} +(2.55422 - 2.55422i) q^{29} -8.51714 q^{31} +0.295096 q^{33} +(7.62613 + 7.62613i) q^{37} +0.219921i q^{39} +3.77709i q^{41} +(6.21191 + 6.21191i) q^{43} +9.71696 q^{47} +6.85872 q^{49} +(-0.289764 + 0.289764i) q^{51} +(-3.03609 - 3.03609i) q^{53} +0.292864i q^{57} +(8.11663 + 8.11663i) q^{59} +(0.728329 - 0.728329i) q^{61} -1.12471 q^{63} +(-0.969239 + 0.969239i) q^{67} +(-0.129490 - 0.129490i) q^{69} -9.14230i q^{71} +7.56793i q^{73} +(0.889909 - 0.889909i) q^{77} -11.8065 q^{79} -8.93015 q^{81} +(10.6393 - 10.6393i) q^{83} +0.318363i q^{87} +15.7111i q^{89} +(0.663205 + 0.663205i) q^{91} +(0.530796 - 0.530796i) q^{93} +3.86020 q^{97} +(7.08428 - 7.08428i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3}+O(q^{10}) $ 12 * q - 2 * q^3	$ 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * 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
$3$	−0.0623209	+	0.0623209i	−0.0359810	+	0.0359810i	−0.724868	−	0.688887i	$-0.758099\pi$
$3$	−0.0623209	+	0.0623209i	−0.0359810	+	0.0359810i	0.688887	+	0.724868i	$0.258099\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.375877i			0.142068i	0.997474	+	0.0710340i	$0.0226299\pi$
$7$			0.375877i			0.142068i	−0.997474	+	0.0710340i	$0.977370\pi$
$8$		0			0
$9$			2.99223i			0.997411i
$10$		0			0
$11$	−2.36756	−	2.36756i	−0.713845	−	0.713845i	0.253492	−	0.967337i	$-0.418421\pi$
$11$	−2.36756	−	2.36756i	−0.713845	−	0.713845i	−0.967337	+	0.253492i	$0.918421\pi$
$12$		0			0
$13$	1.76442	−	1.76442i	0.489363	−	0.489363i	−0.418742	−	0.908105i	$-0.637529\pi$
$13$	1.76442	−	1.76442i	0.489363	−	0.489363i	0.908105	+	0.418742i	$0.137529\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.64955			1.12768			0.563841	−	0.825883i	$-0.309323\pi$
$17$	4.64955			1.12768			0.563841	+	0.825883i	$0.309323\pi$
$18$		0			0
$19$	2.34965	−	2.34965i	0.539047	−	0.539047i	−0.384202	−	0.923249i	$-0.625524\pi$
$19$	2.34965	−	2.34965i	0.539047	−	0.539047i	0.923249	+	0.384202i	$0.125524\pi$
$20$		0			0
$21$	−0.0234250	−	0.0234250i	−0.00511175	−	0.00511175i
$22$		0			0
$23$			2.07779i			0.433250i	0.976255	+	0.216625i	$0.0695048\pi$
$23$			2.07779i			0.433250i	−0.976255	+	0.216625i	$0.930495\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.373441	−	0.373441i	−0.0718688	−	0.0718688i
$28$		0			0
$29$	2.55422	−	2.55422i	0.474307	−	0.474307i	−0.428998	−	0.903305i	$-0.641133\pi$
$29$	2.55422	−	2.55422i	0.474307	−	0.474307i	0.903305	+	0.428998i	$0.141133\pi$
$30$		0			0
$31$	−8.51714			−1.52972			−0.764862	−	0.644194i	$-0.777193\pi$
$31$	−8.51714			−1.52972			−0.764862	+	0.644194i	$0.777193\pi$
$32$		0			0
$33$	0.295096			0.0513697
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.62613	+	7.62613i	1.25373	+	1.25373i	0.954036	+	0.299691i	$0.0968837\pi$
$37$	7.62613	+	7.62613i	1.25373	+	1.25373i	0.299691	+	0.954036i	$0.403116\pi$
$38$		0			0
$39$			0.219921i			0.0352155i
$40$		0			0
$41$			3.77709i			0.589882i	0.955515	+	0.294941i	$0.0953001\pi$
$41$			3.77709i			0.589882i	−0.955515	+	0.294941i	$0.904700\pi$
$42$		0			0
$43$	6.21191	+	6.21191i	0.947307	+	0.947307i	0.998680	−	0.0513725i	$-0.0163596\pi$
$43$	6.21191	+	6.21191i	0.947307	+	0.947307i	−0.0513725	+	0.998680i	$0.516360\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.71696			1.41736			0.708682	−	0.705528i	$-0.249290\pi$
$47$	9.71696			1.41736			0.708682	+	0.705528i	$0.249290\pi$
$48$		0			0
$49$	6.85872			0.979817
$50$		0			0
$51$	−0.289764	+	0.289764i	−0.0405751	+	0.0405751i
$52$		0			0
$53$	−3.03609	−	3.03609i	−0.417040	−	0.417040i	0.467143	−	0.884182i	$-0.345283\pi$
$53$	−3.03609	−	3.03609i	−0.417040	−	0.417040i	−0.884182	+	0.467143i	$0.845283\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.292864i			0.0387908i
$58$		0			0
$59$	8.11663	+	8.11663i	1.05670	+	1.05670i	0.998293	+	0.0584019i	$0.0186005\pi$
$59$	8.11663	+	8.11663i	1.05670	+	1.05670i	0.0584019	+	0.998293i	$0.481400\pi$
$60$		0			0
$61$	0.728329	−	0.728329i	0.0932529	−	0.0932529i	−0.658941	−	0.752194i	$-0.728995\pi$
$61$	0.728329	−	0.728329i	0.0932529	−	0.0932529i	0.752194	+	0.658941i	$0.228995\pi$
$62$		0			0
$63$	−1.12471			−0.141700
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.969239	+	0.969239i	−0.118411	+	0.118411i	−0.763829	−	0.645418i	$-0.776683\pi$
$67$	−0.969239	+	0.969239i	−0.118411	+	0.118411i	0.645418	+	0.763829i	$0.276683\pi$
$68$		0			0
$69$	−0.129490	−	0.129490i	−0.0155887	−	0.0155887i
$70$		0			0
$71$		−	9.14230i		−	1.08499i	−0.840058	−	0.542496i	$-0.817479\pi$
$71$		−	9.14230i		−	1.08499i	0.840058	−	0.542496i	$-0.182521\pi$
$72$		0			0
$73$			7.56793i			0.885759i	0.896581	+	0.442879i	$0.146043\pi$
$73$			7.56793i			0.885759i	−0.896581	+	0.442879i	$0.853957\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.889909	−	0.889909i	0.101415	−	0.101415i
$78$		0			0
$79$	−11.8065			−1.32834			−0.664169	−	0.747583i	$-0.731214\pi$
$79$	−11.8065			−1.32834			−0.664169	+	0.747583i	$0.731214\pi$
$80$		0			0
$81$	−8.93015			−0.992239
$82$		0			0
$83$	10.6393	−	10.6393i	1.16782	−	1.16782i	0.185101	−	0.982720i	$-0.440739\pi$
$83$	10.6393	−	10.6393i	1.16782	−	1.16782i	0.982720	−	0.185101i	$-0.0592611\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			0.318363i			0.0341320i
$88$		0			0
$89$			15.7111i			1.66538i	0.553741	+	0.832689i	$0.313200\pi$
$89$			15.7111i			1.66538i	−0.553741	+	0.832689i	$0.686800\pi$
$90$		0			0
$91$	0.663205	+	0.663205i	0.0695228	+	0.0695228i
$92$		0			0
$93$	0.530796	−	0.530796i	0.0550410	−	0.0550410i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.86020			0.391943			0.195972	−	0.980610i	$-0.437214\pi$
$97$	3.86020			0.391943			0.195972	+	0.980610i	$0.437214\pi$
$98$		0			0
$99$	7.08428	−	7.08428i	0.711997	−	0.711997i
$100$		0			0
$101$	−6.87437	−	6.87437i	−0.684026	−	0.684026i	0.276879	−	0.960905i	$-0.410700\pi$
$101$	−6.87437	−	6.87437i	−0.684026	−	0.684026i	−0.960905	+	0.276879i	$0.910700\pi$
$102$		0			0
$103$		−	1.15407i		−	0.113714i	−0.998382	−	0.0568571i	$-0.981892\pi$
$103$		−	1.15407i		−	0.113714i	0.998382	−	0.0568571i	$-0.0181079\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.70435	+	5.70435i	0.551460	+	0.551460i	0.926862	−	0.375402i	$-0.122495\pi$
$107$	5.70435	+	5.70435i	0.551460	+	0.551460i	−0.375402	+	0.926862i	$0.622495\pi$
$108$		0			0
$109$	11.1863	−	11.1863i	1.07145	−	1.07145i	0.0742092	−	0.997243i	$-0.476357\pi$
$109$	11.1863	−	11.1863i	1.07145	−	1.07145i	0.997243	−	0.0742092i	$-0.0236433\pi$
$110$		0			0
$111$	−0.950534			−0.0902207
$112$		0			0
$113$	4.08163			0.383967			0.191984	−	0.981398i	$-0.438508\pi$
$113$	4.08163			0.383967			0.191984	+	0.981398i	$0.438508\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.27956	+	5.27956i	0.488096	+	0.488096i
$118$		0			0
$119$			1.74766i			0.160208i
$120$		0			0
$121$			0.210643i			0.0191493i
$122$		0			0
$123$	−0.235392	−	0.235392i	−0.0212245	−	0.0212245i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	17.0918			1.51665			0.758326	−	0.651876i	$-0.226018\pi$
$127$	17.0918			1.51665			0.758326	+	0.651876i	$0.226018\pi$
$128$		0			0
$129$	−0.774263			−0.0681701
$130$		0			0
$131$	3.56424	−	3.56424i	0.311409	−	0.311409i	−0.534046	−	0.845455i	$-0.679329\pi$
$131$	3.56424	−	3.56424i	0.311409	−	0.311409i	0.845455	+	0.534046i	$0.179329\pi$
$132$		0			0
$133$	0.883179	+	0.883179i	0.0765813	+	0.0765813i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	16.6995i		−	1.42673i	−0.700792	−	0.713366i	$-0.747170\pi$
$137$		−	16.6995i		−	1.42673i	0.700792	−	0.713366i	$-0.252830\pi$
$138$		0			0
$139$	7.56455	+	7.56455i	0.641616	+	0.641616i	0.950953	−	0.309336i	$-0.100107\pi$
$139$	7.56455	+	7.56455i	0.641616	+	0.641616i	−0.309336	+	0.950953i	$0.600107\pi$
$140$		0			0
$141$	−0.605569	+	0.605569i	−0.0509982	+	0.0509982i
$142$		0			0
$143$	−8.35474			−0.698658
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.427441	+	0.427441i	−0.0352548	+	0.0352548i
$148$		0			0
$149$	−10.2542	−	10.2542i	−0.840056	−	0.840056i	0.148810	−	0.988866i	$-0.452456\pi$
$149$	−10.2542	−	10.2542i	−0.840056	−	0.840056i	−0.988866	+	0.148810i	$0.952456\pi$
$150$		0			0
$151$			19.0430i			1.54970i	0.632147	+	0.774849i	$0.282174\pi$
$151$			19.0430i			1.54970i	−0.632147	+	0.774849i	$0.717826\pi$
$152$		0			0
$153$			13.9125i			1.12476i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.1335	+	10.1335i	−0.808741	+	0.808741i	−0.984443	−	0.175702i	$-0.943780\pi$
$157$	−10.1335	+	10.1335i	−0.808741	+	0.808741i	0.175702	+	0.984443i	$0.443780\pi$
$158$		0			0
$159$	0.378424			0.0300110
$160$		0			0
$161$	−0.780994			−0.0615509
$162$		0			0
$163$	−7.35501	+	7.35501i	−0.576089	+	0.576089i	−0.933823	−	0.357735i	$-0.883549\pi$
$163$	−7.35501	+	7.35501i	−0.576089	+	0.576089i	0.357735	+	0.933823i	$0.383549\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			8.02936i			0.621331i	0.950519	+	0.310665i	$0.100552\pi$
$167$			8.02936i			0.621331i	−0.950519	+	0.310665i	$0.899448\pi$
$168$		0			0
$169$			6.77363i			0.521048i
$170$		0			0
$171$	7.03070	+	7.03070i	0.537651	+	0.537651i
$172$		0			0
$173$	10.4326	−	10.4326i	0.793177	−	0.793177i	−0.188832	−	0.982009i	$-0.560470\pi$
$173$	10.4326	−	10.4326i	0.793177	−	0.793177i	0.982009	+	0.188832i	$0.0604702\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.01167			−0.0760418
$178$		0			0
$179$	8.30280	−	8.30280i	0.620580	−	0.620580i	−0.325099	−	0.945680i	$-0.605398\pi$
$179$	8.30280	−	8.30280i	0.620580	−	0.620580i	0.945680	+	0.325099i	$0.105398\pi$
$180$		0			0
$181$	−10.4772	−	10.4772i	−0.778765	−	0.778765i	0.200856	−	0.979621i	$-0.435628\pi$
$181$	−10.4772	−	10.4772i	−0.778765	−	0.778765i	−0.979621	+	0.200856i	$0.935628\pi$
$182$		0			0
$183$			0.0907802i			0.00671066i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−11.0081	−	11.0081i	−0.804990	−	0.804990i
$188$		0			0
$189$	0.140368	−	0.140368i	0.0102103	−	0.0102103i
$190$		0			0
$191$	−1.68079			−0.121618			−0.0608089	−	0.998149i	$-0.519368\pi$
$191$	−1.68079			−0.121618			−0.0608089	+	0.998149i	$0.519368\pi$
$192$		0			0
$193$	1.61403			0.116181			0.0580903	−	0.998311i	$-0.481499\pi$
$193$	1.61403			0.116181			0.0580903	+	0.998311i	$0.481499\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.10322	−	5.10322i	−0.363589	−	0.363589i	0.501543	−	0.865133i	$-0.332766\pi$
$197$	−5.10322	−	5.10322i	−0.363589	−	0.363589i	−0.865133	+	0.501543i	$0.832766\pi$
$198$		0			0
$199$			11.1545i			0.790725i	0.918525	+	0.395362i	$0.129381\pi$
$199$			11.1545i			0.790725i	−0.918525	+	0.395362i	$0.870619\pi$
$200$		0			0
$201$		−	0.120808i		−	0.00852111i
$202$		0			0
$203$	0.960072	+	0.960072i	0.0673839	+	0.0673839i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.21724			−0.432128
$208$		0			0
$209$	−11.1259			−0.769591
$210$		0			0
$211$	2.48377	−	2.48377i	0.170989	−	0.170989i	−0.616425	−	0.787414i	$-0.711419\pi$
$211$	2.48377	−	2.48377i	0.170989	−	0.170989i	0.787414	+	0.616425i	$0.211419\pi$
$212$		0			0
$213$	0.569756	+	0.569756i	0.0390391	+	0.0390391i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	3.20140i		−	0.217325i
$218$		0			0
$219$	−0.471640	−	0.471640i	−0.0318705	−	0.0318705i
$220$		0			0
$221$	8.20377	−	8.20377i	0.551846	−	0.551846i
$222$		0			0
$223$	−21.1384			−1.41553			−0.707765	−	0.706448i	$-0.750297\pi$
$223$	−21.1384			−1.41553			−0.707765	+	0.706448i	$0.750297\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.4885	+	14.4885i	−0.961634	+	0.961634i	−0.999291	−	0.0376566i	$-0.988011\pi$
$227$	−14.4885	+	14.4885i	−0.961634	+	0.961634i	0.0376566	+	0.999291i	$0.488011\pi$
$228$		0			0
$229$	−10.0956	−	10.0956i	−0.667138	−	0.667138i	0.289914	−	0.957053i	$-0.406373\pi$
$229$	−10.0956	−	10.0956i	−0.667138	−	0.667138i	−0.957053	+	0.289914i	$0.906373\pi$
$230$		0			0
$231$			0.110920i			0.00729799i
$232$		0			0
$233$		−	3.44995i		−	0.226014i	−0.993594	−	0.113007i	$-0.963952\pi$
$233$		−	3.44995i		−	0.226014i	0.993594	−	0.113007i	$-0.0360482\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.735793	−	0.735793i	0.0477949	−	0.0477949i
$238$		0			0
$239$	−18.0060			−1.16471			−0.582354	−	0.812935i	$-0.697868\pi$
$239$	−18.0060			−1.16471			−0.582354	+	0.812935i	$0.697868\pi$
$240$		0			0
$241$	12.6235			0.813154			0.406577	−	0.913617i	$-0.366722\pi$
$241$	12.6235			0.813154			0.406577	+	0.913617i	$0.366722\pi$
$242$		0			0
$243$	1.67686	−	1.67686i	0.107571	−	0.107571i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	8.29155i		−	0.527578i
$248$		0			0
$249$			1.32611i			0.0840386i
$250$		0			0
$251$	9.17919	+	9.17919i	0.579386	+	0.579386i	0.934734	−	0.355348i	$-0.115638\pi$
$251$	9.17919	+	9.17919i	0.579386	+	0.579386i	−0.355348	+	0.934734i	$0.615638\pi$
$252$		0			0
$253$	4.91929	−	4.91929i	0.309273	−	0.309273i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.2897			−1.01612			−0.508061	−	0.861321i	$-0.669637\pi$
$257$	−16.2897			−1.01612			−0.508061	+	0.861321i	$0.669637\pi$
$258$		0			0
$259$	−2.86648	+	2.86648i	−0.178115	+	0.178115i
$260$		0			0
$261$	7.64282	+	7.64282i	0.473079	+	0.473079i
$262$		0			0
$263$		−	10.4898i		−	0.646831i	−0.946257	−	0.323416i	$-0.895169\pi$
$263$		−	10.4898i		−	0.646831i	0.946257	−	0.323416i	$-0.104831\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.979132	−	0.979132i	−0.0599219	−	0.0599219i
$268$		0			0
$269$	−8.46636	+	8.46636i	−0.516203	+	0.516203i	−0.916420	−	0.400217i	$-0.868935\pi$
$269$	−8.46636	+	8.46636i	−0.516203	+	0.516203i	0.400217	+	0.916420i	$0.368935\pi$
$270$		0			0
$271$	8.92117			0.541923			0.270961	−	0.962590i	$-0.412658\pi$
$271$	8.92117			0.541923			0.270961	+	0.962590i	$0.412658\pi$
$272$		0			0
$273$	−0.0826631			−0.00500300
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.36430	−	9.36430i	−0.562646	−	0.562646i	0.367412	−	0.930058i	$-0.380244\pi$
$277$	−9.36430	−	9.36430i	−0.562646	−	0.562646i	−0.930058	+	0.367412i	$0.880244\pi$
$278$		0			0
$279$		−	25.4853i		−	1.52576i
$280$		0			0
$281$			3.12921i			0.186673i	0.995635	+	0.0933365i	$0.0297532\pi$
$281$			3.12921i			0.186673i	−0.995635	+	0.0933365i	$0.970247\pi$
$282$		0			0
$283$	−2.07308	−	2.07308i	−0.123232	−	0.123232i	0.642801	−	0.766033i	$-0.277772\pi$
$283$	−2.07308	−	2.07308i	−0.123232	−	0.123232i	−0.766033	+	0.642801i	$0.777772\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.41972			−0.0838035
$288$		0			0
$289$	4.61834			0.271667
$290$		0			0
$291$	−0.240571	+	0.240571i	−0.0141025	+	0.0141025i
$292$		0			0
$293$	−12.3528	−	12.3528i	−0.721659	−	0.721659i	0.247284	−	0.968943i	$-0.420462\pi$
$293$	−12.3528	−	12.3528i	−0.721659	−	0.721659i	−0.968943	+	0.247284i	$0.920462\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			1.76829i			0.102606i
$298$		0			0
$299$	3.66610	+	3.66610i	0.212016	+	0.212016i
$300$		0			0
$301$	−2.33491	+	2.33491i	−0.134582	+	0.134582i
$302$		0			0
$303$	0.856834			0.0492238
$304$		0			0
$305$		0			0
$306$		0			0
$307$	10.5938	−	10.5938i	0.604619	−	0.604619i	−0.336916	−	0.941535i	$-0.609384\pi$
$307$	10.5938	−	10.5938i	0.604619	−	0.604619i	0.941535	+	0.336916i	$0.109384\pi$
$308$		0			0
$309$	0.0719229	+	0.0719229i	0.00409155	+	0.00409155i
$310$		0			0
$311$		−	19.4153i		−	1.10094i	−0.834854	−	0.550471i	$-0.814448\pi$
$311$		−	19.4153i		−	1.10094i	0.834854	−	0.550471i	$-0.185552\pi$
$312$		0			0
$313$		−	2.56569i		−	0.145022i	−0.997368	−	0.0725108i	$-0.976899\pi$
$313$		−	2.56569i		−	0.145022i	0.997368	−	0.0725108i	$-0.0231012\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.32418	−	7.32418i	0.411367	−	0.411367i	−0.470848	−	0.882215i	$-0.656052\pi$
$317$	7.32418	−	7.32418i	0.411367	−	0.411367i	0.882215	+	0.470848i	$0.156052\pi$
$318$		0			0
$319$	−12.0945			−0.677163
$320$		0			0
$321$	−0.711000			−0.0396842
$322$		0			0
$323$	10.9248	−	10.9248i	0.607873	−	0.607873i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			1.39428i			0.0771038i
$328$		0			0
$329$			3.65238i			0.201362i
$330$		0			0
$331$	−4.17652	−	4.17652i	−0.229562	−	0.229562i	0.582948	−	0.812510i	$-0.301899\pi$
$331$	−4.17652	−	4.17652i	−0.229562	−	0.229562i	−0.812510	+	0.582948i	$0.801899\pi$
$332$		0			0
$333$	−22.8191	+	22.8191i	−1.25048	+	1.25048i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.4540			−0.678410			−0.339205	−	0.940712i	$-0.610158\pi$
$337$	−12.4540			−0.678410			−0.339205	+	0.940712i	$0.610158\pi$
$338$		0			0
$339$	−0.254371	+	0.254371i	−0.0138155	+	0.0138155i
$340$		0			0
$341$	20.1648	+	20.1648i	1.09199	+	1.09199i
$342$		0			0
$343$			5.20917i			0.281269i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.5107	−	17.5107i	−0.940024	−	0.940024i	0.0582766	−	0.998300i	$-0.481439\pi$
$347$	−17.5107	−	17.5107i	−0.940024	−	0.940024i	−0.998300	+	0.0582766i	$0.981439\pi$
$348$		0			0
$349$	8.42042	−	8.42042i	0.450735	−	0.450735i	−0.444863	−	0.895598i	$-0.646748\pi$
$349$	8.42042	−	8.42042i	0.450735	−	0.450735i	0.895598	+	0.444863i	$0.146748\pi$
$350$		0			0
$351$	−1.31782			−0.0703398
$352$		0			0
$353$	−9.71293			−0.516967			−0.258484	−	0.966016i	$-0.583223\pi$
$353$	−9.71293			−0.516967			−0.258484	+	0.966016i	$0.583223\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.108916	−	0.108916i	−0.00576443	−	0.00576443i
$358$		0			0
$359$			6.77551i			0.357598i	0.983886	+	0.178799i	$0.0572212\pi$
$359$			6.77551i			0.357598i	−0.983886	+	0.178799i	$0.942779\pi$
$360$		0			0
$361$			7.95830i			0.418858i
$362$		0			0
$363$	−0.0131274	−	0.0131274i	−0.000689012	−	0.000689012i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−34.4591			−1.79875			−0.899376	−	0.437176i	$-0.855979\pi$
$367$	−34.4591			−1.79875			−0.899376	+	0.437176i	$0.855979\pi$
$368$		0			0
$369$	−11.3019			−0.588355
$370$		0			0
$371$	1.14120	−	1.14120i	0.0592480	−	0.0592480i
$372$		0			0
$373$	−3.55187	−	3.55187i	−0.183909	−	0.183909i	0.609148	−	0.793057i	$-0.291512\pi$
$373$	−3.55187	−	3.55187i	−0.183909	−	0.183909i	−0.793057	+	0.609148i	$0.791512\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	9.01345i		−	0.464216i
$378$		0			0
$379$	−26.4464	−	26.4464i	−1.35846	−	1.35846i	−0.875817	−	0.482644i	$-0.839677\pi$
$379$	−26.4464	−	26.4464i	−1.35846	−	1.35846i	−0.482644	−	0.875817i	$-0.660323\pi$
$380$		0			0
$381$	−1.06518	+	1.06518i	−0.0545706	+	0.0545706i
$382$		0			0
$383$	30.8614			1.57695			0.788473	−	0.615069i	$-0.210872\pi$
$383$	30.8614			1.57695			0.788473	+	0.615069i	$0.210872\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−18.5875	+	18.5875i	−0.944854	+	0.944854i
$388$		0			0
$389$	9.50959	+	9.50959i	0.482155	+	0.482155i	0.905819	−	0.423664i	$-0.139256\pi$
$389$	9.50959	+	9.50959i	0.482155	+	0.482155i	−0.423664	+	0.905819i	$0.639256\pi$
$390$		0			0
$391$			9.66080i			0.488568i
$392$		0			0
$393$			0.444253i			0.0224096i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−24.8540	+	24.8540i	−1.24739	+	1.24739i	−0.290518	+	0.956870i	$0.593828\pi$
$397$	−24.8540	+	24.8540i	−1.24739	+	1.24739i	−0.956870	+	0.290518i	$0.906172\pi$
$398$		0			0
$399$	−0.110081			−0.00551094
$400$		0			0
$401$	4.69303			0.234359			0.117179	−	0.993111i	$-0.462615\pi$
$401$	4.69303			0.234359			0.117179	+	0.993111i	$0.462615\pi$
$402$		0			0
$403$	−15.0278	+	15.0278i	−0.748590	+	0.748590i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	36.1106i		−	1.78993i
$408$		0			0
$409$		−	28.2641i		−	1.39757i	−0.715331	−	0.698786i	$-0.753724\pi$
$409$		−	28.2641i		−	1.39757i	0.715331	−	0.698786i	$-0.246276\pi$
$410$		0			0
$411$	1.04073	+	1.04073i	0.0513352	+	0.0513352i
$412$		0			0
$413$	−3.05085	+	3.05085i	−0.150123	+	0.150123i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.942858			−0.0461720
$418$		0			0
$419$	−23.0355	+	23.0355i	−1.12536	+	1.12536i	−0.134433	+	0.990923i	$0.542921\pi$
$419$	−23.0355	+	23.0355i	−1.12536	+	1.12536i	−0.990923	+	0.134433i	$0.957079\pi$
$420$		0			0
$421$	5.40760	+	5.40760i	0.263550	+	0.263550i	0.826495	−	0.562945i	$-0.190332\pi$
$421$	5.40760	+	5.40760i	0.263550	+	0.263550i	−0.562945	+	0.826495i	$0.690332\pi$
$422$		0			0
$423$			29.0754i			1.41369i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.273762	+	0.273762i	0.0132483	+	0.0132483i
$428$		0			0
$429$	0.520675	−	0.520675i	0.0251384	−	0.0251384i
$430$		0			0
$431$	12.6839			0.610961			0.305481	−	0.952198i	$-0.401183\pi$
$431$	12.6839			0.610961			0.305481	+	0.952198i	$0.401183\pi$
$432$		0			0
$433$	−23.8511			−1.14621			−0.573104	−	0.819482i	$-0.694261\pi$
$433$	−23.8511			−1.14621			−0.573104	+	0.819482i	$0.694261\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.88208	+	4.88208i	0.233542	+	0.233542i
$438$		0			0
$439$			4.65878i			0.222352i	0.993801	+	0.111176i	$0.0354617\pi$
$439$			4.65878i			0.222352i	−0.993801	+	0.111176i	$0.964538\pi$
$440$		0			0
$441$			20.5229i			0.977280i
$442$		0			0
$443$	−8.74048	−	8.74048i	−0.415273	−	0.415273i	0.468298	−	0.883571i	$-0.344867\pi$
$443$	−8.74048	−	8.74048i	−0.415273	−	0.415273i	−0.883571	+	0.468298i	$0.844867\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.27810			0.0604520
$448$		0			0
$449$	−7.28525			−0.343812			−0.171906	−	0.985113i	$-0.554993\pi$
$449$	−7.28525			−0.343812			−0.171906	+	0.985113i	$0.554993\pi$
$450$		0			0
$451$	8.94247	−	8.94247i	0.421085	−	0.421085i
$452$		0			0
$453$	−1.18678	−	1.18678i	−0.0557596	−	0.0557596i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			25.2194i			1.17971i	0.807508	+	0.589857i	$0.200816\pi$
$457$			25.2194i			1.17971i	−0.807508	+	0.589857i	$0.799184\pi$
$458$		0			0
$459$	−1.73633	−	1.73633i	−0.0810451	−	0.0810451i
$460$		0			0
$461$	13.6698	−	13.6698i	0.636667	−	0.636667i	−0.313064	−	0.949732i	$-0.601356\pi$
$461$	13.6698	−	13.6698i	0.636667	−	0.636667i	0.949732	+	0.313064i	$0.101356\pi$
$462$		0			0
$463$	−2.77045			−0.128754			−0.0643768	−	0.997926i	$-0.520506\pi$
$463$	−2.77045			−0.128754			−0.0643768	+	0.997926i	$0.520506\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.9587	−	17.9587i	0.831031	−	0.831031i	−0.156627	−	0.987658i	$-0.550062\pi$
$467$	17.9587	−	17.9587i	0.831031	−	0.831031i	0.987658	+	0.156627i	$0.0500621\pi$
$468$		0			0
$469$	−0.364314	−	0.364314i	−0.0168225	−	0.0168225i
$470$		0			0
$471$		−	1.26306i		−	0.0581986i
$472$		0			0
$473$		−	29.4141i		−	1.35246i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.08470	−	9.08470i	0.415960	−	0.415960i
$478$		0			0
$479$	22.4540			1.02595			0.512975	−	0.858403i	$-0.328543\pi$
$479$	22.4540			1.02595			0.512975	+	0.858403i	$0.328543\pi$
$480$		0			0
$481$	26.9114			1.22705
$482$		0			0
$483$	0.0486722	−	0.0486722i	0.00221466	−	0.00221466i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			27.7615i			1.25799i	0.777408	+	0.628997i	$0.216534\pi$
$487$			27.7615i			1.25799i	−0.777408	+	0.628997i	$0.783466\pi$
$488$		0			0
$489$		−	0.916741i		−	0.0414565i
$490$		0			0
$491$	−16.8993	−	16.8993i	−0.762656	−	0.762656i	0.214146	−	0.976802i	$-0.431303\pi$
$491$	−16.8993	−	16.8993i	−0.762656	−	0.762656i	−0.976802	+	0.214146i	$0.931303\pi$
$492$		0			0
$493$	11.8760	−	11.8760i	0.534867	−	0.534867i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.43638			0.154143
$498$		0			0
$499$	1.81950	−	1.81950i	0.0814520	−	0.0814520i	−0.665207	−	0.746659i	$-0.731657\pi$
$499$	1.81950	−	1.81950i	0.0814520	−	0.0814520i	0.746659	+	0.665207i	$0.231657\pi$
$500$		0			0
$501$	−0.500397	−	0.500397i	−0.0223561	−	0.0223561i
$502$		0			0
$503$		−	42.2076i		−	1.88195i	−0.338482	−	0.940973i	$-0.609913\pi$
$503$		−	42.2076i		−	1.88195i	0.338482	−	0.940973i	$-0.390087\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.422139	−	0.422139i	−0.0187478	−	0.0187478i
$508$		0			0
$509$	−21.9831	+	21.9831i	−0.974382	+	0.974382i	−0.999680	−	0.0252980i	$-0.991947\pi$
$509$	−21.9831	+	21.9831i	−0.974382	+	0.974382i	0.0252980	+	0.999680i	$0.491947\pi$
$510$		0			0
$511$	−2.84461			−0.125838
$512$		0			0
$513$	−1.75491			−0.0774812
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−23.0054	−	23.0054i	−1.01178	−	1.01178i
$518$		0			0
$519$			1.30034i			0.0570786i
$520$		0			0
$521$		−	28.1418i		−	1.23291i	−0.787388	−	0.616457i	$-0.788567\pi$
$521$		−	28.1418i		−	1.23291i	0.787388	−	0.616457i	$-0.211433\pi$
$522$		0			0
$523$	9.58093	+	9.58093i	0.418945	+	0.418945i	0.884840	−	0.465895i	$-0.154268\pi$
$523$	9.58093	+	9.58093i	0.418945	+	0.418945i	−0.465895	+	0.884840i	$0.654268\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−39.6009			−1.72504
$528$		0			0
$529$	18.6828			0.812295
$530$		0			0
$531$	−24.2868	+	24.2868i	−1.05396	+	1.05396i
$532$		0			0
$533$	6.66438	+	6.66438i	0.288666	+	0.288666i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			1.03488i			0.0446582i
$538$		0			0
$539$	−16.2384	−	16.2384i	−0.699437	−	0.699437i
$540$		0			0
$541$	−26.9128	+	26.9128i	−1.15707	+	1.15707i	−0.171972	+	0.985102i	$0.555014\pi$
$541$	−26.9128	+	26.9128i	−1.15707	+	1.15707i	−0.985102	+	0.171972i	$0.944986\pi$
$542$		0			0
$543$	1.30590			0.0560415
$544$		0			0
$545$		0			0
$546$		0			0
$547$	10.6627	−	10.6627i	0.455902	−	0.455902i	−0.441406	−	0.897308i	$-0.645520\pi$
$547$	10.6627	−	10.6627i	0.455902	−	0.455902i	0.897308	+	0.441406i	$0.145520\pi$
$548$		0			0
$549$	2.17933	+	2.17933i	0.0930115	+	0.0930115i
$550$		0			0
$551$		−	12.0030i		−	0.511347i
$552$		0			0
$553$		−	4.43780i		−	0.188714i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.8060	−	22.8060i	0.966320	−	0.966320i	−0.0331307	−	0.999451i	$-0.510548\pi$
$557$	22.8060	−	22.8060i	0.966320	−	0.966320i	0.999451	+	0.0331307i	$0.0105477\pi$
$558$		0			0
$559$	21.9209			0.927153
$560$		0			0
$561$	1.37207			0.0579287
$562$		0			0
$563$	0.472513	−	0.472513i	0.0199140	−	0.0199140i	−0.697080	−	0.716994i	$-0.745518\pi$
$563$	0.472513	−	0.472513i	0.0199140	−	0.0199140i	0.716994	+	0.697080i	$0.245518\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	3.35664i		−	0.140965i
$568$		0			0
$569$		−	3.14792i		−	0.131967i	−0.997821	−	0.0659837i	$-0.978981\pi$
$569$		−	3.14792i		−	0.131967i	0.997821	−	0.0659837i	$-0.0210185\pi$
$570$		0			0
$571$	−5.78162	−	5.78162i	−0.241953	−	0.241953i	0.575704	−	0.817658i	$-0.304728\pi$
$571$	−5.78162	−	5.78162i	−0.241953	−	0.241953i	−0.817658	+	0.575704i	$0.804728\pi$
$572$		0			0
$573$	0.104748	−	0.104748i	0.00437593	−	0.00437593i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	29.0110			1.20774			0.603872	−	0.797081i	$-0.293624\pi$
$577$	29.0110			1.20774			0.603872	+	0.797081i	$0.293624\pi$
$578$		0			0
$579$	−0.100588	+	0.100588i	−0.00418029	+	0.00418029i
$580$		0			0
$581$	3.99908	+	3.99908i	0.165910	+	0.165910i
$582$		0			0
$583$			14.3762i			0.595403i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.4099	+	20.4099i	0.842408	+	0.842408i	0.989172	−	0.146764i	$-0.0468857\pi$
$587$	20.4099	+	20.4099i	0.842408	+	0.842408i	−0.146764	+	0.989172i	$0.546886\pi$
$588$		0			0
$589$	−20.0123	+	20.0123i	−0.824592	+	0.824592i
$590$		0			0
$591$	0.636074			0.0261646
$592$		0			0
$593$	28.9098			1.18718			0.593592	−	0.804766i	$-0.297709\pi$
$593$	28.9098			1.18718			0.593592	+	0.804766i	$0.297709\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.695161	−	0.695161i	−0.0284511	−	0.0284511i
$598$		0			0
$599$		−	11.7893i		−	0.481696i	−0.970563	−	0.240848i	$-0.922574\pi$
$599$		−	11.7893i		−	0.481696i	0.970563	−	0.240848i	$-0.0774256\pi$
$600$		0			0
$601$		−	17.7398i		−	0.723621i	−0.932252	−	0.361810i	$-0.882159\pi$
$601$		−	17.7398i		−	0.723621i	0.932252	−	0.361810i	$-0.117841\pi$
$602$		0			0
$603$	−2.90019	−	2.90019i	−0.118105	−	0.118105i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	25.8393			1.04878			0.524392	−	0.851477i	$-0.324293\pi$
$607$	25.8393			1.04878			0.524392	+	0.851477i	$0.324293\pi$
$608$		0			0
$609$	−0.119665			−0.00484907
$610$		0			0
$611$	17.1448	−	17.1448i	0.693605	−	0.693605i
$612$		0			0
$613$	31.5411	+	31.5411i	1.27393	+	1.27393i	0.944006	+	0.329929i	$0.107025\pi$
$613$	31.5411	+	31.5411i	1.27393	+	1.27393i	0.329929	+	0.944006i	$0.392975\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			15.0637i			0.606440i	0.952921	+	0.303220i	$0.0980618\pi$
$617$			15.0637i			0.606440i	−0.952921	+	0.303220i	$0.901938\pi$
$618$		0			0
$619$	10.4975	+	10.4975i	0.421929	+	0.421929i	0.885868	−	0.463938i	$-0.153564\pi$
$619$	10.4975	+	10.4975i	0.421929	+	0.421929i	−0.463938	+	0.885868i	$0.653564\pi$
$620$		0			0
$621$	0.775933	−	0.775933i	0.0311371	−	0.0311371i
$622$		0			0
$623$	−5.90545			−0.236597
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.693373	−	0.693373i	0.0276906	−	0.0276906i
$628$		0			0
$629$	35.4581	+	35.4581i	1.41381	+	1.41381i
$630$		0			0
$631$			43.6349i			1.73708i	0.495621	+	0.868539i	$0.334940\pi$
$631$			43.6349i			1.73708i	−0.495621	+	0.868539i	$0.665060\pi$
$632$		0			0
$633$			0.309581i			0.0123047i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	12.1017	−	12.1017i	0.479486	−	0.479486i
$638$		0			0
$639$	27.3559			1.08218
$640$		0			0
$641$	−34.2710			−1.35362			−0.676812	−	0.736156i	$-0.736639\pi$
$641$	−34.2710			−1.35362			−0.676812	+	0.736156i	$0.736639\pi$
$642$		0			0
$643$	−30.1937	+	30.1937i	−1.19072	+	1.19072i	−0.213857	+	0.976865i	$0.568603\pi$
$643$	−30.1937	+	30.1937i	−1.19072	+	1.19072i	−0.976865	+	0.213857i	$0.931397\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			15.7474i			0.619096i	0.950884	+	0.309548i	$0.100178\pi$
$647$			15.7474i			0.619096i	−0.950884	+	0.309548i	$0.899822\pi$
$648$		0			0
$649$		−	38.4331i		−	1.50863i
$650$		0			0
$651$	0.199514	+	0.199514i	0.00781956	+	0.00781956i
$652$		0			0
$653$	−5.80619	+	5.80619i	−0.227214	+	0.227214i	−0.811528	−	0.584314i	$-0.801364\pi$
$653$	−5.80619	+	5.80619i	−0.227214	+	0.227214i	0.584314	+	0.811528i	$0.301364\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−22.6450			−0.883465
$658$		0			0
$659$	−1.76782	+	1.76782i	−0.0688647	+	0.0688647i	−0.740700	−	0.671836i	$-0.765506\pi$
$659$	−1.76782	+	1.76782i	−0.0688647	+	0.0688647i	0.671836	+	0.740700i	$0.265506\pi$
$660$		0			0
$661$	−12.4824	−	12.4824i	−0.485509	−	0.485509i	0.421377	−	0.906886i	$-0.361547\pi$
$661$	−12.4824	−	12.4824i	−0.485509	−	0.485509i	−0.906886	+	0.421377i	$0.861547\pi$
$662$		0			0
$663$			1.02253i			0.0397119i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.30714	+	5.30714i	0.205493	+	0.205493i
$668$		0			0
$669$	1.31736	−	1.31736i	0.0509322	−	0.0509322i
$670$		0			0
$671$	−3.44872			−0.133136
$672$		0			0
$673$	14.1113			0.543950			0.271975	−	0.962304i	$-0.412323\pi$
$673$	14.1113			0.543950			0.271975	+	0.962304i	$0.412323\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.31191	+	8.31191i	0.319453	+	0.319453i	0.848557	−	0.529104i	$-0.177472\pi$
$677$	8.31191	+	8.31191i	0.319453	+	0.319453i	−0.529104	+	0.848557i	$0.677472\pi$
$678$		0			0
$679$			1.45096i			0.0556827i
$680$		0			0
$681$		−	1.80587i		−	0.0692011i
$682$		0			0
$683$	−30.0811	−	30.0811i	−1.15102	−	1.15102i	−0.986348	−	0.164673i	$-0.947343\pi$
$683$	−30.0811	−	30.0811i	−1.15102	−	1.15102i	−0.164673	−	0.986348i	$-0.552657\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.25834			0.0480086
$688$		0			0
$689$	−10.7139			−0.408167
$690$		0			0
$691$	−24.0212	+	24.0212i	−0.913810	+	0.913810i	−0.996570	−	0.0827600i	$-0.973627\pi$
$691$	−24.0212	+	24.0212i	−0.913810	+	0.913810i	0.0827600	+	0.996570i	$0.473627\pi$
$692$		0			0
$693$	2.66282	+	2.66282i	0.101152	+	0.101152i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			17.5618i			0.665200i
$698$		0			0
$699$	0.215004	+	0.215004i	0.00813219	+	0.00813219i
$700$		0			0
$701$	10.0971	−	10.0971i	0.381363	−	0.381363i	−0.490230	−	0.871593i	$-0.663087\pi$
$701$	10.0971	−	10.0971i	0.381363	−	0.381363i	0.871593	+	0.490230i	$0.163087\pi$
$702$		0			0
$703$	35.8375			1.35164
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.58392	−	2.58392i	0.0971782	−	0.0971782i
$708$		0			0
$709$	−4.67310	−	4.67310i	−0.175502	−	0.175502i	0.613890	−	0.789392i	$-0.289604\pi$
$709$	−4.67310	−	4.67310i	−0.175502	−	0.175502i	−0.789392	+	0.613890i	$0.789604\pi$
$710$		0			0
$711$		−	35.3279i		−	1.32490i
$712$		0			0
$713$		−	17.6968i		−	0.662752i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.12215	−	1.12215i	0.0419074	−	0.0419074i
$718$		0			0
$719$	23.5339			0.877667			0.438833	−	0.898568i	$-0.355392\pi$
$719$	23.5339			0.877667			0.438833	+	0.898568i	$0.355392\pi$
$720$		0			0
$721$	0.433789			0.0161552
$722$		0			0
$723$	−0.786710	+	0.786710i	−0.0292581	+	0.0292581i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			16.6692i			0.618226i	0.951025	+	0.309113i	$0.100032\pi$
$727$			16.6692i			0.618226i	−0.951025	+	0.309113i	$0.899968\pi$
$728$		0			0
$729$		−	26.5814i		−	0.984498i
$730$		0			0
$731$	28.8826	+	28.8826i	1.06826	+	1.06826i
$732$		0			0
$733$	−27.4684	+	27.4684i	−1.01457	+	1.01457i	−0.0146760	+	0.999892i	$0.504672\pi$
$733$	−27.4684	+	27.4684i	−1.01457	+	1.01457i	−0.999892	+	0.0146760i	$0.995328\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.58945			0.169055
$738$		0			0
$739$	−22.7939	+	22.7939i	−0.838486	+	0.838486i	−0.988660	−	0.150174i	$-0.952017\pi$
$739$	−22.7939	+	22.7939i	−0.838486	+	0.838486i	0.150174	+	0.988660i	$0.452017\pi$
$740$		0			0
$741$	0.516736	+	0.516736i	0.0189828	+	0.0189828i
$742$		0			0
$743$			16.4964i			0.605196i	0.953118	+	0.302598i	$0.0978539\pi$
$743$			16.4964i			0.605196i	−0.953118	+	0.302598i	$0.902146\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	31.8354	+	31.8354i	1.16480	+	1.16480i
$748$		0			0
$749$	−2.14413	+	2.14413i	−0.0783449	+	0.0783449i
$750$		0			0
$751$	21.6997			0.791833			0.395917	−	0.918286i	$-0.370427\pi$
$751$	21.6997			0.791833			0.395917	+	0.918286i	$0.370427\pi$
$752$		0			0
$753$	−1.14411			−0.0416937
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.73819	+	1.73819i	0.0631757	+	0.0631757i	0.737989	−	0.674813i	$-0.235776\pi$
$757$	1.73819	+	1.73819i	0.0631757	+	0.0631757i	−0.674813	+	0.737989i	$0.735776\pi$
$758$		0			0
$759$			0.613149i			0.0222559i
$760$		0			0
$761$		−	46.5311i		−	1.68675i	−0.537323	−	0.843376i	$-0.680565\pi$
$761$		−	46.5311i		−	1.68675i	0.537323	−	0.843376i	$-0.319435\pi$
$762$		0			0
$763$	4.20467	+	4.20467i	0.152219	+	0.152219i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	28.6423			1.03421
$768$		0			0
$769$	15.4731			0.557976			0.278988	−	0.960295i	$-0.410001\pi$
$769$	15.4731			0.557976			0.278988	+	0.960295i	$0.410001\pi$
$770$		0			0
$771$	1.01519	−	1.01519i	0.0365610	−	0.0365610i
$772$		0			0
$773$	−5.69848	−	5.69848i	−0.204960	−	0.204960i	0.597161	−	0.802121i	$-0.296295\pi$
$773$	−5.69848	−	5.69848i	−0.204960	−	0.204960i	−0.802121	+	0.597161i	$0.796295\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	0.357284i		−	0.0128175i
$778$		0			0
$779$	8.87484	+	8.87484i	0.317974	+	0.317974i
$780$		0			0
$781$	−21.6449	+	21.6449i	−0.774516	+	0.774516i
$782$		0			0
$783$	−1.90770			−0.0681757
$784$		0			0
$785$		0			0
$786$		0			0
$787$	18.1351	−	18.1351i	0.646448	−	0.646448i	−0.305685	−	0.952133i	$-0.598885\pi$
$787$	18.1351	−	18.1351i	0.646448	−	0.646448i	0.952133	+	0.305685i	$0.0988855\pi$
$788$		0			0
$789$	0.653736	+	0.653736i	0.0232736	+	0.0232736i
$790$		0			0
$791$			1.53419i			0.0545495i
$792$		0			0
$793$		−	2.57016i		−	0.0912690i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.51575	+	4.51575i	−0.159956	+	0.159956i	−0.782547	−	0.622591i	$-0.786080\pi$
$797$	−4.51575	+	4.51575i	−0.159956	+	0.159956i	0.622591	+	0.782547i	$0.286080\pi$
$798$		0			0
$799$	45.1795			1.59834
$800$		0			0
$801$	−47.0114			−1.66107
$802$		0			0
$803$	17.9175	−	17.9175i	0.632294	−	0.632294i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	1.05526i		−	0.0371470i
$808$		0			0
$809$		−	3.33368i		−	0.117206i	−0.998281	−	0.0586030i	$-0.981335\pi$
$809$		−	3.33368i		−	0.117206i	0.998281	−	0.0586030i	$-0.0186646\pi$
$810$		0			0
$811$	−37.1948	−	37.1948i	−1.30609	−	1.30609i	−0.924215	−	0.381873i	$-0.875279\pi$
$811$	−37.1948	−	37.1948i	−1.30609	−	1.30609i	−0.381873	−	0.924215i	$-0.624721\pi$
$812$		0			0
$813$	−0.555975	+	0.555975i	−0.0194989	+	0.0194989i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	29.1916			1.02129
$818$		0			0
$819$	−1.98446	+	1.98446i	−0.0693428	+	0.0693428i
$820$		0			0
$821$	−25.5278	−	25.5278i	−0.890926	−	0.890926i	0.103684	−	0.994610i	$-0.466937\pi$
$821$	−25.5278	−	25.5278i	−0.890926	−	0.890926i	−0.994610	+	0.103684i	$0.966937\pi$
$822$		0			0
$823$		−	16.8858i		−	0.588603i	−0.955713	−	0.294301i	$-0.904913\pi$
$823$		−	16.8858i		−	0.588603i	0.955713	−	0.294301i	$-0.0950870\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.5765	+	11.5765i	0.402556	+	0.402556i	0.879133	−	0.476577i	$-0.158123\pi$
$827$	11.5765	+	11.5765i	0.402556	+	0.402556i	−0.476577	+	0.879133i	$0.658123\pi$
$828$		0			0
$829$	5.97296	−	5.97296i	0.207449	−	0.207449i	−0.595733	−	0.803182i	$-0.703138\pi$
$829$	5.97296	−	5.97296i	0.207449	−	0.207449i	0.803182	+	0.595733i	$0.203138\pi$
$830$		0			0
$831$	1.16718			0.0404891
$832$		0			0
$833$	31.8900			1.10492
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.18065	+	3.18065i	0.109939	+	0.109939i
$838$		0			0
$839$			27.2960i			0.942362i	0.882037	+	0.471181i	$0.156172\pi$
$839$			27.2960i			0.942362i	−0.882037	+	0.471181i	$0.843828\pi$
$840$		0			0
$841$			15.9519i			0.550066i
$842$		0			0
$843$	−0.195015	−	0.195015i	−0.00671668	−	0.00671668i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.0791757			−0.00272051
$848$		0			0
$849$	0.258392			0.00886799
$850$		0			0
$851$	−15.8455	+	15.8455i	−0.543177	+	0.543177i
$852$		0			0
$853$	29.1167	+	29.1167i	0.996938	+	0.996938i	0.999995	−	0.00305738i	$-0.000973195\pi$
$853$	29.1167	+	29.1167i	0.996938	+	0.996938i	−0.00305738	+	0.999995i	$0.500973\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			22.0170i			0.752087i	0.926602	+	0.376044i	$0.122716\pi$
$857$			22.0170i			0.752087i	−0.926602	+	0.376044i	$0.877284\pi$
$858$		0			0
$859$	−16.8910	−	16.8910i	−0.576312	−	0.576312i	0.357573	−	0.933885i	$-0.383604\pi$
$859$	−16.8910	−	16.8910i	−0.576312	−	0.576312i	−0.933885	+	0.357573i	$0.883604\pi$
$860$		0			0
$861$	0.0884782	−	0.0884782i	0.00301533	−	0.00301533i
$862$		0			0
$863$	46.2073			1.57292			0.786458	−	0.617644i	$-0.211913\pi$
$863$	46.2073			1.57292			0.786458	+	0.617644i	$0.211913\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.287819	+	0.287819i	−0.00977484	+	0.00977484i
$868$		0			0
$869$	27.9526	+	27.9526i	0.948227	+	0.948227i
$870$		0			0
$871$			3.42029i			0.115892i
$872$		0			0
$873$			11.5506i			0.390929i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	21.6380	−	21.6380i	0.730664	−	0.730664i	−0.240087	−	0.970751i	$-0.577176\pi$
$877$	21.6380	−	21.6380i	0.730664	−	0.730664i	0.970751	+	0.240087i	$0.0771760\pi$
$878$		0			0
$879$	1.53968			0.0519320
$880$		0			0
$881$	−35.6649			−1.20158			−0.600790	−	0.799407i	$-0.705147\pi$
$881$	−35.6649			−1.20158			−0.600790	+	0.799407i	$0.705147\pi$
$882$		0			0
$883$	17.5681	−	17.5681i	0.591213	−	0.591213i	−0.346746	−	0.937959i	$-0.612713\pi$
$883$	17.5681	−	17.5681i	0.591213	−	0.591213i	0.937959	+	0.346746i	$0.112713\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	51.2454i		−	1.72065i	−0.509744	−	0.860326i	$-0.670260\pi$
$887$		−	51.2454i		−	1.72065i	0.509744	−	0.860326i	$-0.329740\pi$
$888$		0			0
$889$			6.42441i			0.215468i
$890$		0			0
$891$	21.1426	+	21.1426i	0.708305	+	0.708305i
$892$		0			0
$893$	22.8315	−	22.8315i	0.764025	−	0.764025i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.456949			−0.0152571
$898$		0			0
$899$	−21.7547	+	21.7547i	−0.725559	+	0.725559i
$900$		0			0
$901$	−14.1165	−	14.1165i	−0.470288	−	0.470288i
$902$		0			0
$903$		−	0.291028i		−	0.00968479i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	29.6745	+	29.6745i	0.985324	+	0.985324i	0.999894	−	0.0145695i	$-0.00463777\pi$
$907$	29.6745	+	29.6745i	0.985324	+	0.985324i	−0.0145695	+	0.999894i	$0.504638\pi$
$908$		0			0
$909$	20.5697	−	20.5697i	0.682255	−	0.682255i
$910$		0			0
$911$	24.9064			0.825187			0.412593	−	0.910915i	$-0.364623\pi$
$911$	24.9064			0.825187			0.412593	+	0.910915i	$0.364623\pi$
$912$		0			0
$913$	−50.3785			−1.66729
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.33971	+	1.33971i	0.0442413	+	0.0442413i
$918$		0			0
$919$			15.6940i			0.517696i	0.965918	+	0.258848i	$0.0833429\pi$
$919$			15.6940i			0.517696i	−0.965918	+	0.258848i	$0.916657\pi$
$920$		0			0
$921$			1.32043i			0.0435096i
$922$		0			0
$923$	−16.1309	−	16.1309i	−0.530954	−	0.530954i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.45326			0.113420
$928$		0			0
$929$	6.00598			0.197050			0.0985249	−	0.995135i	$-0.468588\pi$
$929$	6.00598			0.197050			0.0985249	+	0.995135i	$0.468588\pi$
$930$		0			0
$931$	16.1156	−	16.1156i	0.528167	−	0.528167i
$932$		0			0
$933$	1.20998	+	1.20998i	0.0396130	+	0.0396130i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	4.83037i		−	0.157801i	−0.996882	−	0.0789006i	$-0.974859\pi$
$937$		−	4.83037i		−	0.157801i	0.996882	−	0.0789006i	$-0.0251410\pi$
$938$		0			0
$939$	0.159896	+	0.159896i	0.00521802	+	0.00521802i
$940$		0			0
$941$	−3.63878	+	3.63878i	−0.118621	+	0.118621i	−0.763925	−	0.645305i	$-0.776730\pi$
$941$	−3.63878	+	3.63878i	−0.118621	+	0.118621i	0.645305	+	0.763925i	$0.276730\pi$
$942$		0			0
$943$	−7.84801			−0.255566
$944$		0			0
$945$		0			0
$946$		0			0
$947$	34.7720	−	34.7720i	1.12994	−	1.12994i	0.139751	−	0.990187i	$-0.455370\pi$
$947$	34.7720	−	34.7720i	1.12994	−	1.12994i	0.990187	−	0.139751i	$-0.0446302\pi$
$948$		0			0
$949$	13.3530	+	13.3530i	0.433457	+	0.433457i
$950$		0			0
$951$			0.912899i			0.0296028i
$952$		0			0
$953$			1.89827i			0.0614910i	0.999527	+	0.0307455i	$0.00978813\pi$
$953$			1.89827i			0.0614910i	−0.999527	+	0.0307455i	$0.990212\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.753741	−	0.753741i	0.0243650	−	0.0243650i
$958$		0			0
$959$	6.27694			0.202693
$960$		0			0
$961$	41.5417			1.34006
$962$		0			0
$963$	−17.0687	+	17.0687i	−0.550033	+	0.550033i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			61.5753i			1.98013i	0.140616	+	0.990064i	$0.455092\pi$
$967$			61.5753i			1.98013i	−0.140616	+	0.990064i	$0.544908\pi$
$968$		0			0
$969$			1.36169i			0.0437437i
$970$		0			0
$971$	−22.6595	−	22.6595i	−0.727179	−	0.727179i	0.242878	−	0.970057i	$-0.421909\pi$
$971$	−22.6595	−	22.6595i	−0.727179	−	0.727179i	−0.970057	+	0.242878i	$0.921909\pi$
$972$		0			0
$973$	−2.84334	+	2.84334i	−0.0911532	+	0.0911532i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.3240			0.810186			0.405093	−	0.914276i	$-0.367239\pi$
$977$	25.3240			0.810186			0.405093	+	0.914276i	$0.367239\pi$
$978$		0			0
$979$	37.1970	−	37.1970i	1.18882	−	1.18882i
$980$		0			0
$981$	33.4720	+	33.4720i	1.06868	+	1.06868i
$982$		0			0
$983$		−	5.01686i		−	0.160013i	−0.996794	−	0.0800065i	$-0.974506\pi$
$983$		−	5.01686i		−	0.160013i	0.996794	−	0.0800065i	$-0.0254941\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.227620	−	0.227620i	−0.00724521	−	0.00724521i
$988$		0			0
$989$	−12.9071	+	12.9071i	−0.410420	+	0.410420i
$990$		0			0
$991$	−41.2998			−1.31193			−0.655965	−	0.754791i	$-0.727738\pi$
$991$	−41.2998			−1.31193			−0.655965	+	0.754791i	$0.727738\pi$
$992$		0			0
$993$	0.520569			0.0165198
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.23850	−	1.23850i	−0.0392235	−	0.0392235i	0.687223	−	0.726447i	$-0.258830\pi$
$997$	−1.23850	−	1.23850i	−0.0392235	−	0.0392235i	−0.726447	+	0.687223i	$0.758830\pi$
$998$		0			0
$999$		−	5.69582i		−	0.180208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.f.1201.4		12
4.3	odd	2		400.2.l.g.101.2	yes	12
5.2	odd	4		1600.2.q.f.49.3		12
5.3	odd	4		1600.2.q.e.49.4		12
5.4	even	2		1600.2.l.g.1201.3		12
16.3	odd	4		400.2.l.g.301.2	yes	12
16.13	even	4	inner	1600.2.l.f.401.4		12
20.3	even	4		400.2.q.e.149.1		12
20.7	even	4		400.2.q.f.149.6		12
20.19	odd	2		400.2.l.f.101.5	✓	12
80.3	even	4		400.2.q.f.349.6		12
80.13	odd	4		1600.2.q.f.849.3		12
80.19	odd	4		400.2.l.f.301.5	yes	12
80.29	even	4		1600.2.l.g.401.3		12
80.67	even	4		400.2.q.e.349.1		12
80.77	odd	4		1600.2.q.e.849.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.5	✓	12	20.19	odd	2
400.2.l.f.301.5	yes	12	80.19	odd	4
400.2.l.g.101.2	yes	12	4.3	odd	2
400.2.l.g.301.2	yes	12	16.3	odd	4
400.2.q.e.149.1		12	20.3	even	4
400.2.q.e.349.1		12	80.67	even	4
400.2.q.f.149.6		12	20.7	even	4
400.2.q.f.349.6		12	80.3	even	4
1600.2.l.f.401.4		12	16.13	even	4	inner
1600.2.l.f.1201.4		12	1.1	even	1	trivial
1600.2.l.g.401.3		12	80.29	even	4
1600.2.l.g.1201.3		12	5.4	even	2
1600.2.q.e.49.4		12	5.3	odd	4
1600.2.q.e.849.4		12	80.77	odd	4
1600.2.q.f.49.3		12	5.2	odd	4
1600.2.q.f.849.3		12	80.13	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.0623209 + 0.0623209i) q^{3} +0.375877i q^{7} +2.99223i q^{9} +O(q^{10})\)	\(q+(-0.0623209 + 0.0623209i) q^{3} +0.375877i q^{7} +2.99223i q^{9} +(-2.36756 - 2.36756i) q^{11} +(1.76442 - 1.76442i) q^{13} +4.64955 q^{17} +(2.34965 - 2.34965i) q^{19} +(-0.0234250 - 0.0234250i) q^{21} +2.07779i q^{23} +(-0.373441 - 0.373441i) q^{27} +(2.55422 - 2.55422i) q^{29} -8.51714 q^{31} +0.295096 q^{33} +(7.62613 + 7.62613i) q^{37} +0.219921i q^{39} +3.77709i q^{41} +(6.21191 + 6.21191i) q^{43} +9.71696 q^{47} +6.85872 q^{49} +(-0.289764 + 0.289764i) q^{51} +(-3.03609 - 3.03609i) q^{53} +0.292864i q^{57} +(8.11663 + 8.11663i) q^{59} +(0.728329 - 0.728329i) q^{61} -1.12471 q^{63} +(-0.969239 + 0.969239i) q^{67} +(-0.129490 - 0.129490i) q^{69} -9.14230i q^{71} +7.56793i q^{73} +(0.889909 - 0.889909i) q^{77} -11.8065 q^{79} -8.93015 q^{81} +(10.6393 - 10.6393i) q^{83} +0.318363i q^{87} +15.7111i q^{89} +(0.663205 + 0.663205i) q^{91} +(0.530796 - 0.530796i) q^{93} +3.86020 q^{97} +(7.08428 - 7.08428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3}+O(q^{10}) \) 12 * q - 2 * q^3	\( 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * q^99

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