LMFDB - Embedded newform 900.3.c.p.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12239922073600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 32x^{2} + 256 $ x^8 - 2x^6 + 4x^4 - 32*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.1
Root			$-1.89639 + 0.635381i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.p.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89639 - 0.635381i) q^{2} +(3.19258 + 2.40986i) q^{4} +10.1035i q^{7} +(-4.52320 - 6.59853i) q^{8} +O(q^{10})$	\(q+(-1.89639 - 0.635381i) q^{2} +(3.19258 + 2.40986i) q^{4} +10.1035i q^{7} +(-4.52320 - 6.59853i) q^{8} -10.6555i q^{11} -11.7703 q^{13} +(6.41959 - 19.1602i) q^{14} +(4.38516 + 15.3873i) q^{16} +16.6320 q^{17} -0.464096i q^{19} +(-6.77033 + 20.2071i) q^{22} +42.1327i q^{23} +(22.3211 + 7.47864i) q^{26} +(-24.3481 + 32.2564i) q^{28} +19.5536 q^{29} -9.17534i q^{31} +(1.46084 - 31.9666i) q^{32} +(-31.5407 - 10.5676i) q^{34} -23.5407 q^{37} +(-0.294878 + 0.880107i) q^{38} -44.0525 q^{41} +58.3007i q^{43} +(25.6784 - 34.0187i) q^{44} +(26.7703 - 79.9000i) q^{46} -41.6433i q^{47} -53.0813 q^{49} +(-37.5777 - 28.3648i) q^{52} -80.2381 q^{53} +(66.6685 - 45.7003i) q^{56} +(-37.0813 - 12.4240i) q^{58} -63.9333i q^{59} +80.3923 q^{61} +(-5.82983 + 17.4000i) q^{62} +(-23.0813 + 59.6930i) q^{64} -22.5275i q^{67} +(53.0989 + 40.0807i) q^{68} +61.4860i q^{71} -137.703 q^{73} +(44.6422 + 14.9573i) q^{74} +(1.11841 - 1.48167i) q^{76} +107.659 q^{77} +138.665i q^{79} +(83.5407 + 27.9901i) q^{82} -86.2233i q^{83} +(37.0431 - 110.561i) q^{86} +(-70.3110 + 48.1972i) q^{88} -127.212 q^{89} -118.922i q^{91} +(-101.534 + 134.512i) q^{92} +(-26.4593 + 78.9719i) q^{94} -15.0000 q^{97} +(100.663 + 33.7269i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 8 q^{13} - 8 q^{16} + 32 q^{22} - 44 q^{28} - 80 q^{34} - 16 q^{37} + 128 q^{46} - 80 q^{49} - 236 q^{52} + 48 q^{58} + 40 q^{61} + 160 q^{64} - 240 q^{73} - 228 q^{76} + 496 q^{82} - 304 q^{88} - 384 q^{94} - 120 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^13 - 8 * q^16 + 32 * q^22 - 44 * q^28 - 80 * q^34 - 16 * q^37 + 128 * q^46 - 80 * q^49 - 236 * q^52 + 48 * q^58 + 40 * q^61 + 160 * q^64 - 240 * q^73 - 228 * q^76 + 496 * q^82 - 304 * q^88 - 384 * q^94 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.89639	−	0.635381i	−0.948194	−	0.317690i
$2$	−1.89639	−	0.635381i	−0.948194	−	0.317690i
$3$		0			0
$3$		0			0
$4$	3.19258	+	2.40986i	0.798146	+	0.602465i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			10.1035i			1.44336i	0.692226	+	0.721681i	$0.256630\pi$
$7$			10.1035i			1.44336i	−0.692226	+	0.721681i	$0.743370\pi$
$8$	−4.52320	−	6.59853i	−0.565400	−	0.824817i
$9$		0			0
$10$		0			0
$11$		−	10.6555i		−	0.968686i	−0.874878	−	0.484343i	$-0.839059\pi$
$11$		−	10.6555i		−	0.968686i	0.874878	−	0.484343i	$-0.160941\pi$
$12$		0			0
$13$	−11.7703			−0.905410			−0.452705	−	0.891660i	$-0.649541\pi$
$13$	−11.7703			−0.905410			−0.452705	+	0.891660i	$0.649541\pi$
$14$	6.41959	−	19.1602i	0.458542	−	1.36859i
$15$		0			0
$16$	4.38516	+	15.3873i	0.274073	+	0.961709i
$17$	16.6320			0.978350			0.489175	−	0.872186i	$-0.337298\pi$
$17$	16.6320			0.978350			0.489175	+	0.872186i	$0.337298\pi$
$18$		0			0
$19$		−	0.464096i		−	0.0244261i	−0.999925	−	0.0122131i	$-0.996112\pi$
$19$		−	0.464096i		−	0.0244261i	0.999925	−	0.0122131i	$-0.00388763\pi$
$20$		0			0
$21$		0			0
$22$	−6.77033	+	20.2071i	−0.307742	+	0.918503i
$23$			42.1327i			1.83186i	0.401340	+	0.915929i	$0.368544\pi$
$23$			42.1327i			1.83186i	−0.401340	+	0.915929i	$0.631456\pi$
$24$		0			0
$25$		0			0
$26$	22.3211	+	7.47864i	0.858505	+	0.287640i
$27$		0			0
$28$	−24.3481	+	32.2564i	−0.869574	+	1.15201i
$29$	19.5536			0.674264			0.337132	−	0.941457i	$-0.390543\pi$
$29$	19.5536			0.674264			0.337132	+	0.941457i	$0.390543\pi$
$30$		0			0
$31$		−	9.17534i		−	0.295979i	−0.988989	−	0.147989i	$-0.952720\pi$
$31$		−	9.17534i		−	0.295979i	0.988989	−	0.147989i	$-0.0472801\pi$
$32$	1.46084	−	31.9666i	0.0456514	−	0.998957i
$33$		0			0
$34$	−31.5407	−	10.5676i	−0.927666	−	0.310813i
$35$		0			0
$36$		0			0
$37$	−23.5407			−0.636234			−0.318117	−	0.948051i	$-0.603050\pi$
$37$	−23.5407			−0.636234			−0.318117	+	0.948051i	$0.603050\pi$
$38$	−0.294878	+	0.880107i	−0.00775994	+	0.0231607i
$39$		0			0
$40$		0			0
$41$	−44.0525			−1.07445			−0.537226	−	0.843439i	$-0.680528\pi$
$41$	−44.0525			−1.07445			−0.537226	+	0.843439i	$0.680528\pi$
$42$		0			0
$43$			58.3007i			1.35583i	0.735140	+	0.677915i	$0.237116\pi$
$43$			58.3007i			1.35583i	−0.735140	+	0.677915i	$0.762884\pi$
$44$	25.6784	−	34.0187i	0.583599	−	0.773152i
$45$		0			0
$46$	26.7703	−	79.9000i	0.581964	−	1.73696i
$47$		−	41.6433i		−	0.886027i	−0.896515	−	0.443014i	$-0.853909\pi$
$47$		−	41.6433i		−	0.886027i	0.896515	−	0.443014i	$-0.146091\pi$
$48$		0			0
$49$	−53.0813			−1.08329
$50$		0			0
$51$		0			0
$52$	−37.5777	−	28.3648i	−0.722649	−	0.545477i
$53$	−80.2381			−1.51393			−0.756963	−	0.653458i	$-0.773318\pi$
$53$	−80.2381			−1.51393			−0.756963	+	0.653458i	$0.773318\pi$
$54$		0			0
$55$		0			0
$56$	66.6685	−	45.7003i	1.19051	−	0.816077i
$57$		0			0
$58$	−37.0813	−	12.4240i	−0.639333	−	0.214207i
$59$		−	63.9333i		−	1.08361i	−0.840503	−	0.541807i	$-0.817740\pi$
$59$		−	63.9333i		−	1.08361i	0.840503	−	0.541807i	$-0.182260\pi$
$60$		0			0
$61$	80.3923			1.31791			0.658953	−	0.752184i	$-0.270999\pi$
$61$	80.3923			1.31791			0.658953	+	0.752184i	$0.270999\pi$
$62$	−5.82983	+	17.4000i	−0.0940296	+	0.280645i
$63$		0			0
$64$	−23.0813	+	59.6930i	−0.360646	+	0.932703i
$65$		0			0
$66$		0			0
$67$		−	22.5275i		−	0.336232i	−0.985767	−	0.168116i	$-0.946232\pi$
$67$		−	22.5275i		−	0.336232i	0.985767	−	0.168116i	$-0.0537683\pi$
$68$	53.0989	+	40.0807i	0.780866	+	0.589421i
$69$		0			0
$70$		0			0
$71$			61.4860i			0.866000i	0.901394	+	0.433000i	$0.142545\pi$
$71$			61.4860i			0.866000i	−0.901394	+	0.433000i	$0.857455\pi$
$72$		0			0
$73$	−137.703			−1.88635			−0.943173	−	0.332301i	$-0.892175\pi$
$73$	−137.703			−1.88635			−0.943173	+	0.332301i	$0.892175\pi$
$74$	44.6422	+	14.9573i	0.603274	+	0.202125i
$75$		0			0
$76$	1.11841	−	1.48167i	0.0147159	−	0.0194956i
$77$	107.659			1.39816
$78$		0			0
$79$			138.665i			1.75525i	0.479347	+	0.877626i	$0.340874\pi$
$79$			138.665i			1.75525i	−0.479347	+	0.877626i	$0.659126\pi$
$80$		0			0
$81$		0			0
$82$	83.5407	+	27.9901i	1.01879	+	0.341343i
$83$		−	86.2233i		−	1.03883i	−0.854521	−	0.519417i	$-0.826149\pi$
$83$		−	86.2233i		−	1.03883i	0.854521	−	0.519417i	$-0.173851\pi$
$84$		0			0
$85$		0			0
$86$	37.0431	−	110.561i	0.430734	−	1.28559i
$87$		0			0
$88$	−70.3110	+	48.1972i	−0.798989	+	0.547695i
$89$	−127.212			−1.42935			−0.714676	−	0.699456i	$-0.753426\pi$
$89$	−127.212			−1.42935			−0.714676	+	0.699456i	$0.753426\pi$
$90$		0			0
$91$		−	118.922i		−	1.30683i
$92$	−101.534	+	134.512i	−1.10363	+	1.46209i
$93$		0			0
$94$	−26.4593	+	78.9719i	−0.281482	+	0.840126i
$95$		0			0
$96$		0			0
$97$	−15.0000			−0.154639			−0.0773196	−	0.997006i	$-0.524636\pi$
$97$	−15.0000			−0.154639			−0.0773196	+	0.997006i	$0.524636\pi$
$98$	100.663	+	33.7269i	1.02717	+	0.344152i
$99$		0			0
$100$		0			0
$101$	−195.764			−1.93825			−0.969127	−	0.246563i	$-0.920699\pi$
$101$	−195.764			−1.93825			−0.969127	+	0.246563i	$0.920699\pi$
$102$		0			0
$103$			15.5661i			0.151127i	0.997141	+	0.0755636i	$0.0240756\pi$
$103$			15.5661i			0.151127i	−0.997141	+	0.0755636i	$0.975924\pi$
$104$	53.2396	+	77.6669i	0.511919	+	0.746797i
$105$		0			0
$106$	152.163	+	50.9817i	1.43550	+	0.480960i
$107$		−	51.3199i		−	0.479625i	−0.970819	−	0.239813i	$-0.922914\pi$
$107$		−	51.3199i		−	0.479625i	0.970819	−	0.239813i	$-0.0770860\pi$
$108$		0			0
$109$	−46.8516			−0.429832			−0.214916	−	0.976633i	$-0.568948\pi$
$109$	−46.8516			−0.429832			−0.214916	+	0.976633i	$0.568948\pi$
$110$		0			0
$111$		0			0
$112$	−155.466	+	44.3056i	−1.38809	+	0.395586i
$113$	−115.526			−1.02235			−0.511175	−	0.859477i	$-0.670790\pi$
$113$	−115.526			−1.02235			−0.511175	+	0.859477i	$0.670790\pi$
$114$		0			0
$115$		0			0
$116$	62.4266	+	47.1215i	0.538161	+	0.406220i
$117$		0			0
$118$	−40.6220	+	121.242i	−0.344254	+	1.02748i
$119$			168.041i			1.41211i
$120$		0			0
$121$	7.45934			0.0616474
$122$	−152.455	−	51.0797i	−1.24963	−	0.418686i
$123$		0			0
$124$	22.1113	−	29.2930i	0.178317	−	0.236234i
$125$		0			0
$126$		0			0
$127$			161.656i			1.27289i	0.771324	+	0.636443i	$0.219595\pi$
$127$			161.656i			1.27289i	−0.771324	+	0.636443i	$0.780405\pi$
$128$	81.6989	−	98.5357i	0.638273	−	0.769810i
$129$		0			0
$130$		0			0
$131$			197.561i			1.50810i	0.656818	+	0.754049i	$0.271902\pi$
$131$			197.561i			1.50810i	−0.656818	+	0.754049i	$0.728098\pi$
$132$		0			0
$133$	4.68901			0.0352557
$134$	−14.3136	+	42.7210i	−0.106818	+	0.318813i
$135$		0			0
$136$	−75.2297	−	109.747i	−0.553159	−	0.806960i
$137$	76.4182			0.557797			0.278899	−	0.960321i	$-0.410031\pi$
$137$	76.4182			0.557797			0.278899	+	0.960321i	$0.410031\pi$
$138$		0			0
$139$		−	223.206i		−	1.60580i	−0.596115	−	0.802899i	$-0.703290\pi$
$139$		−	223.206i		−	1.60580i	0.596115	−	0.802899i	$-0.296710\pi$
$140$		0			0
$141$		0			0
$142$	39.0670	−	116.601i	0.275120	−	0.821137i
$143$			125.419i			0.877058i
$144$		0			0
$145$		0			0
$146$	261.139	+	87.4940i	1.78862	+	0.599274i
$147$		0			0
$148$	−75.1555	−	56.7297i	−0.507807	−	0.383308i
$149$	−166.320			−1.11624			−0.558119	−	0.829761i	$-0.688477\pi$
$149$	−166.320			−1.11624			−0.558119	+	0.829761i	$0.688477\pi$
$150$		0			0
$151$			112.995i			0.748313i	0.927366	+	0.374156i	$0.122068\pi$
$151$			112.995i			0.748313i	−0.927366	+	0.374156i	$0.877932\pi$
$152$	−3.06236	+	2.09920i	−0.0201471	+	0.0138105i
$153$		0			0
$154$	−204.163	−	68.4042i	−1.32573	−	0.444183i
$155$		0			0
$156$		0			0
$157$	−75.9330			−0.483649			−0.241825	−	0.970320i	$-0.577746\pi$
$157$	−75.9330			−0.483649			−0.241825	+	0.970320i	$0.577746\pi$
$158$	88.1050	−	262.962i	0.557626	−	1.66432i
$159$		0			0
$160$		0			0
$161$	−425.689			−2.64403
$162$		0			0
$163$			184.184i			1.12996i	0.825103	+	0.564982i	$0.191117\pi$
$163$			184.184i			1.12996i	−0.825103	+	0.564982i	$0.808883\pi$
$164$	−140.641	−	106.160i	−0.857568	−	0.647319i
$165$		0			0
$166$	−54.7846	+	163.513i	−0.330028	+	0.985017i
$167$			193.268i			1.15729i	0.815578	+	0.578647i	$0.196419\pi$
$167$			193.268i			1.15729i	−0.815578	+	0.578647i	$0.803581\pi$
$168$		0			0
$169$	−30.4593			−0.180233
$170$		0			0
$171$		0			0
$172$	−140.496	+	186.130i	−0.816840	+	1.08215i
$173$	−56.8646			−0.328697			−0.164348	−	0.986402i	$-0.552552\pi$
$173$	−56.8646			−0.328697			−0.164348	+	0.986402i	$0.552552\pi$
$174$		0			0
$175$		0			0
$176$	163.961	−	46.7263i	0.931594	−	0.265490i
$177$		0			0
$178$	241.244	+	80.8282i	1.35530	+	0.454091i
$179$			272.150i			1.52039i	0.649695	+	0.760195i	$0.274896\pi$
$179$			272.150i			1.52039i	−0.649695	+	0.760195i	$0.725104\pi$
$180$		0			0
$181$	−50.2297			−0.277512			−0.138756	−	0.990327i	$-0.544310\pi$
$181$	−50.2297			−0.277512			−0.138756	+	0.990327i	$0.544310\pi$
$182$	−75.5607	+	225.522i	−0.415169	+	1.23913i
$183$		0			0
$184$	278.014	−	190.575i	1.51095	−	1.03573i
$185$		0			0
$186$		0			0
$187$		−	177.223i		−	0.947714i
$188$	100.354	−	132.950i	0.533800	−	0.707179i
$189$		0			0
$190$		0			0
$191$		−	194.247i		−	1.01700i	−0.861062	−	0.508500i	$-0.830200\pi$
$191$		−	194.247i		−	1.01700i	0.861062	−	0.508500i	$-0.169800\pi$
$192$		0			0
$193$	22.7033			0.117634			0.0588168	−	0.998269i	$-0.481267\pi$
$193$	22.7033			0.117634			0.0588168	+	0.998269i	$0.481267\pi$
$194$	28.4458	+	9.53071i	0.146628	+	0.0491274i
$195$		0			0
$196$	−169.466	−	127.918i	−0.864625	−	0.652645i
$197$	154.633			0.784938			0.392469	−	0.919765i	$-0.371621\pi$
$197$	154.633			0.784938			0.392469	+	0.919765i	$0.371621\pi$
$198$		0			0
$199$			236.094i			1.18640i	0.805054	+	0.593201i	$0.202136\pi$
$199$			236.094i			1.18640i	−0.805054	+	0.593201i	$0.797864\pi$
$200$		0			0
$201$		0			0
$202$	371.244	+	124.384i	1.83784	+	0.615765i
$203$			197.561i			0.973206i
$204$		0			0
$205$		0			0
$206$	9.89040	−	29.5194i	0.0480116	−	0.143298i
$207$		0			0
$208$	−51.6148	−	181.114i	−0.248148	−	0.870741i
$209$	−4.94520			−0.0236612
$210$		0			0
$211$			115.209i			0.546015i	0.962012	+	0.273007i	$0.0880183\pi$
$211$			115.209i			0.546015i	−0.962012	+	0.273007i	$0.911982\pi$
$212$	−256.167	−	193.362i	−1.20833	−	0.912087i
$213$		0			0
$214$	−32.6077	+	97.3225i	−0.152372	+	0.454778i
$215$		0			0
$216$		0			0
$217$	92.7033			0.427204
$218$	88.8489	+	29.7686i	0.407564	+	0.136553i
$219$		0			0
$220$		0			0
$221$	−195.764			−0.885808
$222$		0			0
$223$		−	425.170i		−	1.90659i	−0.302039	−	0.953296i	$-0.597667\pi$
$223$		−	425.170i		−	1.90659i	0.302039	−	0.953296i	$-0.402333\pi$
$224$	322.976	+	14.7597i	1.44186	+	0.0658915i
$225$		0			0
$226$	219.081	+	73.4027i	0.969386	+	0.324791i
$227$		−	178.208i		−	0.785055i	−0.919740	−	0.392528i	$-0.871601\pi$
$227$		−	178.208i		−	0.785055i	0.919740	−	0.392528i	$-0.128399\pi$
$228$		0			0
$229$	331.636			1.44819			0.724097	−	0.689699i	$-0.242257\pi$
$229$	331.636			1.44819			0.724097	+	0.689699i	$0.242257\pi$
$230$		0			0
$231$		0			0
$232$	−88.4451	−	129.025i	−0.381229	−	0.556144i
$233$	−182.952			−0.785200			−0.392600	−	0.919709i	$-0.628424\pi$
$233$	−182.952			−0.785200			−0.392600	+	0.919709i	$0.628424\pi$
$234$		0			0
$235$		0			0
$236$	154.070	−	204.112i	0.652840	−	0.864882i
$237$		0			0
$238$	106.770	−	318.672i	0.448615	−	1.33896i
$239$		−	210.664i		−	0.881438i	−0.897645	−	0.440719i	$-0.854724\pi$
$239$		−	210.664i		−	0.881438i	0.897645	−	0.440719i	$-0.145276\pi$
$240$		0			0
$241$	−3.62198			−0.0150290			−0.00751448	−	0.999972i	$-0.502392\pi$
$241$	−3.62198			−0.0150290			−0.00751448	+	0.999972i	$0.502392\pi$
$242$	−14.1458	−	4.73952i	−0.0584538	−	0.0195848i
$243$		0			0
$244$	256.659	+	193.734i	1.05188	+	0.793992i
$245$		0			0
$246$		0			0
$247$			5.46257i			0.0221157i
$248$	−60.5438	+	41.5019i	−0.244128	+	0.167346i
$249$		0			0
$250$		0			0
$251$			250.839i			0.999357i	0.866211	+	0.499678i	$0.166548\pi$
$251$			250.839i			0.999357i	−0.866211	+	0.499678i	$0.833452\pi$
$252$		0			0
$253$	448.947			1.77450
$254$	102.713	−	306.564i	0.404384	−	1.20694i
$255$		0			0
$256$	−217.541	+	134.952i	−0.849768	+	0.527157i
$257$	360.060			1.40101			0.700505	−	0.713647i	$-0.252958\pi$
$257$	360.060			1.40101			0.700505	+	0.713647i	$0.252958\pi$
$258$		0			0
$259$		−	237.844i		−	0.918316i
$260$		0			0
$261$		0			0
$262$	125.526	−	374.652i	0.479108	−	1.42997i
$263$		−	191.310i		−	0.727416i	−0.931513	−	0.363708i	$-0.881511\pi$
$263$		−	191.310i		−	0.727416i	0.931513	−	0.363708i	$-0.118489\pi$
$264$		0			0
$265$		0			0
$266$	−8.89219	−	2.97931i	−0.0334293	−	0.0112004i
$267$		0			0
$268$	54.2882	−	71.9210i	0.202568	−	0.268362i
$269$	−156.656			−0.582365			−0.291183	−	0.956667i	$-0.594049\pi$
$269$	−156.656			−0.582365			−0.291183	+	0.956667i	$0.594049\pi$
$270$		0			0
$271$		−	30.4172i		−	0.112241i	−0.998424	−	0.0561203i	$-0.982127\pi$
$271$		−	30.4172i		−	0.112241i	0.998424	−	0.0561203i	$-0.0178730\pi$
$272$	72.9339	+	255.922i	0.268139	+	0.940888i
$273$		0			0
$274$	−144.919	−	48.5547i	−0.528900	−	0.177207i
$275$		0			0
$276$		0			0
$277$	438.421			1.58275			0.791373	−	0.611333i	$-0.209366\pi$
$277$	438.421			1.58275			0.791373	+	0.611333i	$0.209366\pi$
$278$	−141.821	+	423.285i	−0.510146	+	1.52261i
$279$		0			0
$280$		0			0
$281$	239.589			0.852630			0.426315	−	0.904575i	$-0.359812\pi$
$281$	239.589			0.852630			0.426315	+	0.904575i	$0.359812\pi$
$282$		0			0
$283$		−	235.523i		−	0.832238i	−0.909310	−	0.416119i	$-0.863390\pi$
$283$		−	235.523i		−	0.832238i	0.909310	−	0.416119i	$-0.136610\pi$
$284$	−148.173	+	196.299i	−0.521734	+	0.691194i
$285$		0			0
$286$	79.6890	−	237.844i	0.278633	−	0.831622i
$287$		−	445.086i		−	1.55082i
$288$		0			0
$289$	−12.3780			−0.0428305
$290$		0			0
$291$		0			0
$292$	−439.629	−	331.845i	−1.50558	−	1.13646i
$293$	−271.955			−0.928173			−0.464086	−	0.885790i	$-0.653617\pi$
$293$	−271.955			−0.928173			−0.464086	+	0.885790i	$0.653617\pi$
$294$		0			0
$295$		0			0
$296$	106.479	+	155.334i	0.359727	+	0.524777i
$297$		0			0
$298$	315.407	+	105.676i	1.05841	+	0.354618i
$299$		−	495.916i		−	1.65858i
$300$		0			0
$301$	−589.043			−1.95695
$302$	71.7950	−	214.283i	0.237732	−	0.709546i
$303$		0			0
$304$	7.14121	−	2.03514i	0.0234908	−	0.00669454i
$305$		0			0
$306$		0			0
$307$		−	316.352i		−	1.03046i	−0.857052	−	0.515230i	$-0.827706\pi$
$307$		−	316.352i		−	1.03046i	0.857052	−	0.515230i	$-0.172294\pi$
$308$	343.709	+	259.442i	1.11594	+	0.842344i
$309$		0			0
$310$		0			0
$311$			298.355i			0.959342i	0.877448	+	0.479671i	$0.159244\pi$
$311$			298.355i			0.959342i	−0.877448	+	0.479671i	$0.840756\pi$
$312$		0			0
$313$	191.651			0.612302			0.306151	−	0.951983i	$-0.400959\pi$
$313$	191.651			0.612302			0.306151	+	0.951983i	$0.400959\pi$
$314$	143.998	+	48.2464i	0.458594	+	0.153651i
$315$		0			0
$316$	−334.163	+	442.699i	−1.05748	+	1.40095i
$317$	−232.847			−0.734534			−0.367267	−	0.930115i	$-0.619707\pi$
$317$	−232.847			−0.734534			−0.367267	+	0.930115i	$0.619707\pi$
$318$		0			0
$319$		−	208.355i		−	0.653150i
$320$		0			0
$321$		0			0
$322$	807.273	+	270.475i	2.50706	+	0.839984i
$323$		−	7.71883i		−	0.0238973i
$324$		0			0
$325$		0			0
$326$	117.027	−	349.285i	0.358979	−	1.07143i
$327$		0			0
$328$	199.258	+	290.682i	0.607495	+	0.886225i
$329$	420.744			1.27886
$330$		0			0
$331$		−	200.214i		−	0.604877i	−0.953169	−	0.302438i	$-0.902199\pi$
$331$		−	200.214i		−	0.604877i	0.953169	−	0.302438i	$-0.0978007\pi$
$332$	207.786	−	275.275i	0.625861	−	0.829141i
$333$		0			0
$334$	122.799	−	366.512i	0.367661	−	1.09734i
$335$		0			0
$336$		0			0
$337$	−451.029			−1.33836			−0.669182	−	0.743099i	$-0.733355\pi$
$337$	−451.029			−1.33836			−0.669182	+	0.743099i	$0.733355\pi$
$338$	57.7628	+	19.3533i	0.170896	+	0.0572582i
$339$		0			0
$340$		0			0
$341$	−97.7682			−0.286710
$342$		0			0
$343$		−	41.2357i		−	0.120221i
$344$	384.699	−	263.706i	1.11831	−	0.766586i
$345$		0			0
$346$	107.837	+	36.1307i	0.311669	+	0.104424i
$347$			128.845i			0.371313i	0.982615	+	0.185656i	$0.0594411\pi$
$347$			128.845i			0.371313i	−0.982615	+	0.185656i	$0.940559\pi$
$348$		0			0
$349$	0.756045			0.00216632			0.00108316	−	0.999999i	$-0.499655\pi$
$349$	0.756045			0.00216632			0.00108316	+	0.999999i	$0.499655\pi$
$350$		0			0
$351$		0			0
$352$	−340.622	−	15.5661i	−0.967676	−	0.0442219i
$353$	−55.7392			−0.157902			−0.0789508	−	0.996879i	$-0.525157\pi$
$353$	−55.7392			−0.157902			−0.0789508	+	0.996879i	$0.525157\pi$
$354$		0			0
$355$		0			0
$356$	−406.136	−	306.564i	−1.14083	−	0.861134i
$357$		0			0
$358$	172.919	−	516.102i	0.483013	−	1.44162i
$359$		−	194.247i		−	0.541078i	−0.962709	−	0.270539i	$-0.912798\pi$
$359$		−	194.247i		−	0.541078i	0.962709	−	0.270539i	$-0.0872019\pi$
$360$		0			0
$361$	360.785			0.999403
$362$	95.2550	+	31.9150i	0.263135	+	0.0881629i
$363$		0			0
$364$	286.585	−	379.668i	0.787321	−	1.04304i
$365$		0			0
$366$		0			0
$367$			24.0264i			0.0654671i	0.999464	+	0.0327335i	$0.0104213\pi$
$367$			24.0264i			0.0654671i	−0.999464	+	0.0327335i	$0.989579\pi$
$368$	−648.311	+	184.759i	−1.76171	+	0.502062i
$369$		0			0
$370$		0			0
$371$		−	810.688i		−	2.18514i
$372$		0			0
$373$	136.986			0.367254			0.183627	−	0.982996i	$-0.441216\pi$
$373$	136.986			0.367254			0.183627	+	0.982996i	$0.441216\pi$
$374$	−112.604	+	336.083i	−0.301080	+	0.898617i
$375$		0			0
$376$	−274.785	+	188.361i	−0.730810	+	0.500960i
$377$	−230.153			−0.610485
$378$		0			0
$379$		−	103.356i		−	0.272707i	−0.990660	−	0.136353i	$-0.956462\pi$
$379$		−	103.356i		−	0.272707i	0.990660	−	0.136353i	$-0.0435382\pi$
$380$		0			0
$381$		0			0
$382$	−123.421	+	368.368i	−0.323091	+	0.964314i
$383$			19.3533i			0.0505308i	0.999681	+	0.0252654i	$0.00804308\pi$
$383$			19.3533i			0.0505308i	−0.999681	+	0.0252654i	$0.991957\pi$
$384$		0			0
$385$		0			0
$386$	−43.0543	−	14.4252i	−0.111540	−	0.0373711i
$387$		0			0
$388$	−47.8887	−	36.1479i	−0.123425	−	0.0931646i
$389$	273.978			0.704314			0.352157	−	0.935941i	$-0.385448\pi$
$389$	273.978			0.704314			0.352157	+	0.935941i	$0.385448\pi$
$390$		0			0
$391$			700.750i			1.79220i
$392$	240.097	+	350.259i	0.612493	+	0.893518i
$393$		0			0
$394$	−293.244	−	98.2507i	−0.744274	−	0.249367i
$395$		0			0
$396$		0			0
$397$	218.230			0.549697			0.274848	−	0.961488i	$-0.411372\pi$
$397$	218.230			0.549697			0.274848	+	0.961488i	$0.411372\pi$
$398$	150.010	−	447.726i	0.376908	−	1.12494i
$399$		0			0
$400$		0			0
$401$	396.472			0.988709			0.494355	−	0.869260i	$-0.335404\pi$
$401$	396.472			0.988709			0.494355	+	0.869260i	$0.335404\pi$
$402$		0			0
$403$			107.997i			0.267982i
$404$	−624.991	−	471.763i	−1.54701	−	1.16773i
$405$		0			0
$406$	125.526	−	374.652i	0.309178	−	0.922789i
$407$			250.839i			0.616311i
$408$		0			0
$409$	301.976			0.738327			0.369164	−	0.929364i	$-0.379644\pi$
$409$	301.976			0.738327			0.369164	+	0.929364i	$0.379644\pi$
$410$		0			0
$411$		0			0
$412$	−37.5121	+	49.6960i	−0.0910488	+	0.120621i
$413$	645.952			1.56405
$414$		0			0
$415$		0			0
$416$	−17.1946	+	376.258i	−0.0413332	+	0.904466i
$417$		0			0
$418$	9.37802	+	3.14209i	0.0224355	+	0.00751695i
$419$			420.461i			1.00349i	0.865017	+	0.501743i	$0.167308\pi$
$419$			420.461i			1.00349i	−0.865017	+	0.501743i	$0.832692\pi$
$420$		0			0
$421$	−197.378			−0.468831			−0.234416	−	0.972136i	$-0.575318\pi$
$421$	−197.378			−0.468831			−0.234416	+	0.972136i	$0.575318\pi$
$422$	73.2017	−	218.481i	0.173464	−	0.517728i
$423$		0			0
$424$	362.933	+	529.454i	0.855974	+	1.24871i
$425$		0			0
$426$		0			0
$427$			812.246i			1.90222i
$428$	123.674	−	163.843i	0.288957	−	0.382811i
$429$		0			0
$430$		0			0
$431$			236.869i			0.549581i	0.961504	+	0.274790i	$0.0886084\pi$
$431$			236.869i			0.549581i	−0.961504	+	0.274790i	$0.911392\pi$
$432$		0			0
$433$	−364.378			−0.841520			−0.420760	−	0.907172i	$-0.638236\pi$
$433$	−364.378			−0.841520			−0.420760	+	0.907172i	$0.638236\pi$
$434$	−175.802	−	58.9019i	−0.405073	−	0.135719i
$435$		0			0
$436$	−149.578	−	112.906i	−0.343068	−	0.258958i
$437$	19.5536			0.0447452
$438$		0			0
$439$			72.3679i			0.164847i	0.996597	+	0.0824236i	$0.0262660\pi$
$439$			72.3679i			0.164847i	−0.996597	+	0.0824236i	$0.973734\pi$
$440$		0			0
$441$		0			0
$442$	371.244	+	124.384i	0.839918	+	0.281413i
$443$			240.295i			0.542428i	0.962519	+	0.271214i	$0.0874250\pi$
$443$			240.295i			0.542428i	−0.962519	+	0.271214i	$0.912575\pi$
$444$		0			0
$445$		0			0
$446$	−270.145	+	806.287i	−0.605706	+	1.80782i
$447$		0			0
$448$	−603.110	−	233.203i	−1.34623	−	0.520542i
$449$	−498.959			−1.11127			−0.555633	−	0.831427i	$-0.687524\pi$
$449$	−498.959			−1.11127			−0.555633	+	0.831427i	$0.687524\pi$
$450$		0			0
$451$			469.403i			1.04081i
$452$	−368.825	−	278.400i	−0.815984	−	0.615930i
$453$		0			0
$454$	−113.230	+	337.951i	−0.249405	+	0.744385i
$455$		0			0
$456$		0			0
$457$	171.866			0.376074			0.188037	−	0.982162i	$-0.439787\pi$
$457$	171.866			0.376074			0.188037	+	0.982162i	$0.439787\pi$
$458$	−628.911	−	210.715i	−1.37317	−	0.460077i
$459$		0			0
$460$		0			0
$461$	831.825			1.80439			0.902196	−	0.431326i	$-0.141954\pi$
$461$	831.825			1.80439			0.902196	+	0.431326i	$0.141954\pi$
$462$		0			0
$463$			370.011i			0.799160i	0.916698	+	0.399580i	$0.130844\pi$
$463$			370.011i			0.799160i	−0.916698	+	0.399580i	$0.869156\pi$
$464$	85.7460	+	300.879i	0.184797	+	0.648445i
$465$		0			0
$466$	346.947	+	116.244i	0.744522	+	0.249450i
$467$			527.770i			1.13013i	0.825047	+	0.565065i	$0.191149\pi$
$467$			527.770i			1.13013i	−0.825047	+	0.565065i	$0.808851\pi$
$468$		0			0
$469$	227.608			0.485304
$470$		0			0
$471$		0			0
$472$	−421.866	+	289.183i	−0.893784	+	0.612676i
$473$	621.226			1.31337
$474$		0			0
$475$		0			0
$476$	−404.956	+	536.486i	−0.850748	+	1.12707i
$477$		0			0
$478$	−133.852	+	399.500i	−0.280024	+	0.835775i
$479$			532.777i			1.11227i	0.831092	+	0.556135i	$0.187716\pi$
$479$			532.777i			1.11227i	−0.831092	+	0.556135i	$0.812284\pi$
$480$		0			0
$481$	277.081			0.576053
$482$	6.86868	+	2.30134i	0.0142504	+	0.00477455i
$483$		0			0
$484$	23.8146	+	17.9760i	0.0492036	+	0.0371404i
$485$		0			0
$486$		0			0
$487$		−	495.073i		−	1.01658i	−0.861187	−	0.508288i	$-0.830278\pi$
$487$		−	495.073i		−	1.01658i	0.861187	−	0.508288i	$-0.169722\pi$
$488$	−363.631	−	530.471i	−0.745144	−	1.08703i
$489$		0			0
$490$		0			0
$491$		−	518.094i		−	1.05518i	−0.849499	−	0.527590i	$-0.823096\pi$
$491$		−	518.094i		−	1.05518i	0.849499	−	0.527590i	$-0.176904\pi$
$492$		0			0
$493$	325.215			0.659666
$494$	3.47081	−	10.3592i	0.00702593	−	0.0209699i
$495$		0			0
$496$	141.184	−	40.2354i	0.284645	−	0.0811197i
$497$	−621.226			−1.24995
$498$		0			0
$499$			676.579i			1.35587i	0.735122	+	0.677935i	$0.237125\pi$
$499$			676.579i			1.35587i	−0.735122	+	0.677935i	$0.762875\pi$
$500$		0			0
$501$		0			0
$502$	159.378	−	475.688i	0.317486	−	0.947585i
$503$		−	35.2804i		−	0.0701399i	−0.999385	−	0.0350700i	$-0.988835\pi$
$503$		−	35.2804i		−	0.0701399i	0.999385	−	0.0350700i	$-0.0111654\pi$
$504$		0			0
$505$		0			0
$506$	−851.379	−	285.252i	−1.68257	−	0.563740i
$507$		0			0
$508$	−389.569	+	516.102i	−0.766869	+	1.01595i
$509$	538.520			1.05800			0.528998	−	0.848623i	$-0.322568\pi$
$509$	538.520			1.05800			0.528998	+	0.848623i	$0.322568\pi$
$510$		0			0
$511$		−	1391.29i		−	2.72268i
$512$	498.288	−	117.700i	0.973218	−	0.229884i
$513$		0			0
$514$	−682.813	−	228.775i	−1.32843	−	0.445088i
$515$		0			0
$516$		0			0
$517$	−443.732			−0.858282
$518$	−151.121	+	451.044i	−0.291740	+	0.870742i
$519$		0			0
$520$		0			0
$521$	73.7237			0.141504			0.0707521	−	0.997494i	$-0.477460\pi$
$521$	73.7237			0.141504			0.0707521	+	0.997494i	$0.477460\pi$
$522$		0			0
$523$		−	465.440i		−	0.889942i	−0.895545	−	0.444971i	$-0.853214\pi$
$523$		−	465.440i		−	0.889942i	0.895545	−	0.444971i	$-0.146786\pi$
$524$	−476.094	+	630.729i	−0.908576	+	1.20368i
$525$		0			0
$526$	−121.555	+	362.799i	−0.231093	+	0.689732i
$527$		−	152.604i		−	0.289571i
$528$		0			0
$529$	−1246.17			−2.35570
$530$		0			0
$531$		0			0
$532$	14.9701	+	11.2999i	0.0281392	+	0.0212403i
$533$	518.512			0.972819
$534$		0			0
$535$		0			0
$536$	−148.649	+	101.897i	−0.277330	+	0.190106i
$537$		0			0
$538$	297.081	+	99.5364i	0.552196	+	0.185012i
$539$			565.610i			1.04937i
$540$		0			0
$541$	−48.9857			−0.0905466			−0.0452733	−	0.998975i	$-0.514416\pi$
$541$	−48.9857			−0.0905466			−0.0452733	+	0.998975i	$0.514416\pi$
$542$	−19.3265	+	57.6828i	−0.0356577	+	0.106426i
$543$		0			0
$544$	24.2967	−	531.668i	0.0446631	−	0.977330i
$545$		0			0
$546$		0			0
$547$		−	500.536i		−	0.915056i	−0.889195	−	0.457528i	$-0.848735\pi$
$547$		−	500.536i		−	0.915056i	0.889195	−	0.457528i	$-0.151265\pi$
$548$	243.971	+	184.157i	0.445203	+	0.336053i
$549$		0			0
$550$		0			0
$551$		−	9.07478i		−	0.0164696i
$552$		0			0
$553$	−1401.00			−2.53346
$554$	−831.417	−	278.564i	−1.50075	−	0.502824i
$555$		0			0
$556$	537.895	−	712.603i	0.967436	−	1.28166i
$557$	−771.368			−1.38486			−0.692431	−	0.721484i	$-0.743460\pi$
$557$	−771.368			−1.38486			−0.692431	+	0.721484i	$0.743460\pi$
$558$		0			0
$559$		−	686.218i		−	1.22758i
$560$		0			0
$561$		0			0
$562$	−454.354	−	152.230i	−0.808459	−	0.270872i
$563$		−	535.602i		−	0.951335i	−0.879625	−	0.475667i	$-0.842207\pi$
$563$		−	535.602i		−	0.951335i	0.879625	−	0.475667i	$-0.157793\pi$
$564$		0			0
$565$		0			0
$566$	−149.647	+	446.644i	−0.264394	+	0.789123i
$567$		0			0
$568$	405.718	−	278.114i	0.714292	−	0.489637i
$569$	102.941			0.180915			0.0904575	−	0.995900i	$-0.471167\pi$
$569$	102.941			0.180915			0.0904575	+	0.995900i	$0.471167\pi$
$570$		0			0
$571$		−	642.662i		−	1.12550i	−0.826626	−	0.562752i	$-0.809743\pi$
$571$		−	642.662i		−	1.12550i	0.826626	−	0.562752i	$-0.190257\pi$
$572$	−302.243	+	400.411i	−0.528396	+	0.700020i
$573$		0			0
$574$	−282.799	+	844.056i	−0.492681	+	1.47048i
$575$		0			0
$576$		0			0
$577$	−397.919			−0.689634			−0.344817	−	0.938670i	$-0.612059\pi$
$577$	−397.919			−0.689634			−0.344817	+	0.938670i	$0.612059\pi$
$578$	23.4735	+	7.86476i	0.0406117	+	0.0136068i
$579$		0			0
$580$		0			0
$581$	871.159			1.49941
$582$		0			0
$583$			854.981i			1.46652i
$584$	622.860	+	908.640i	1.06654	+	1.55589i
$585$		0			0
$586$	515.732	+	172.795i	0.880089	+	0.294872i
$587$			813.625i			1.38607i	0.720903	+	0.693036i	$0.243727\pi$
$587$			813.625i			1.38607i	−0.720903	+	0.693036i	$0.756273\pi$
$588$		0			0
$589$	−4.25824			−0.00722961
$590$		0			0
$591$		0			0
$592$	−103.230	−	362.228i	−0.174374	−	0.611872i
$593$	731.362			1.23333			0.616663	−	0.787227i	$-0.288484\pi$
$593$	731.362			1.23333			0.616663	+	0.787227i	$0.288484\pi$
$594$		0			0
$595$		0			0
$596$	−530.989	−	400.807i	−0.890921	−	0.672494i
$597$		0			0
$598$	−315.096	+	940.450i	−0.526916	+	1.57266i
$599$		−	752.516i		−	1.25629i	−0.778098	−	0.628143i	$-0.783815\pi$
$599$		−	752.516i		−	1.25629i	0.778098	−	0.628143i	$-0.216185\pi$
$600$		0			0
$601$	1013.81			1.68688			0.843439	−	0.537226i	$-0.180528\pi$
$601$	1013.81			1.68688			0.843439	+	0.537226i	$0.180528\pi$
$602$	1117.05	+	374.267i	1.85557	+	0.621705i
$603$		0			0
$604$	−272.302	+	360.747i	−0.450832	+	0.597262i
$605$		0			0
$606$		0			0
$607$			432.276i			0.712151i	0.934457	+	0.356075i	$0.115885\pi$
$607$			432.276i			0.712151i	−0.934457	+	0.356075i	$0.884115\pi$
$608$	−14.8356	−	0.677973i	−0.0244007	−	0.00111509i
$609$		0			0
$610$		0			0
$611$			490.155i			0.802218i
$612$		0			0
$613$	213.971			0.349056			0.174528	−	0.984652i	$-0.444160\pi$
$613$	213.971			0.349056			0.174528	+	0.984652i	$0.444160\pi$
$614$	−201.004	+	599.926i	−0.327368	+	0.977077i
$615$		0			0
$616$	−486.962	−	710.389i	−0.790522	−	1.15323i
$617$	−814.966			−1.32085			−0.660426	−	0.750891i	$-0.729624\pi$
$617$	−814.966			−1.32085			−0.660426	+	0.750891i	$0.729624\pi$
$618$		0			0
$619$			1035.45i			1.67278i	0.548133	+	0.836391i	$0.315339\pi$
$619$			1035.45i			1.67278i	−0.548133	+	0.836391i	$0.684661\pi$
$620$		0			0
$621$		0			0
$622$	189.569	−	565.798i	0.304774	−	0.909643i
$623$		−	1285.29i		−	2.06307i
$624$		0			0
$625$		0			0
$626$	−363.444	−	121.771i	−0.580581	−	0.194522i
$627$		0			0
$628$	−242.422	−	182.988i	−0.386023	−	0.291382i
$629$	−391.527			−0.622460
$630$		0			0
$631$		−	67.7270i		−	0.107333i	−0.998559	−	0.0536664i	$-0.982909\pi$
$631$		−	67.7270i		−	0.107333i	0.998559	−	0.0536664i	$-0.0170907\pi$
$632$	914.985	−	627.209i	1.44776	−	0.992419i
$633$		0			0
$634$	441.569	+	147.947i	0.696481	+	0.233355i
$635$		0			0
$636$		0			0
$637$	624.785			0.980824
$638$	−132.385	+	395.122i	−0.207499	+	0.619313i
$639$		0			0
$640$		0			0
$641$	851.379			1.32820			0.664102	−	0.747642i	$-0.268814\pi$
$641$	851.379			1.32820			0.664102	+	0.747642i	$0.268814\pi$
$642$		0			0
$643$			562.800i			0.875272i	0.899152	+	0.437636i	$0.144184\pi$
$643$			562.800i			0.875272i	−0.899152	+	0.437636i	$0.855816\pi$
$644$	−1359.05	−	1025.85i	−2.11032	−	1.59294i
$645$		0			0
$646$	−4.90440	+	14.6379i	−0.00759195	+	0.0226593i
$647$			331.188i			0.511883i	0.966692	+	0.255942i	$0.0823855\pi$
$647$			331.188i			0.511883i	−0.966692	+	0.255942i	$0.917615\pi$
$648$		0			0
$649$	−681.244			−1.04968
$650$		0			0
$651$		0			0
$652$	−443.857	+	588.023i	−0.680763	+	0.901875i
$653$	−804.177			−1.23151			−0.615756	−	0.787937i	$-0.711149\pi$
$653$	−804.177			−1.23151			−0.615756	+	0.787937i	$0.711149\pi$
$654$		0			0
$655$		0			0
$656$	−193.177	−	677.851i	−0.294478	−	1.03331i
$657$		0			0
$658$	−797.895	−	267.333i	−1.21261	−	0.406281i
$659$		−	1061.53i		−	1.61081i	−0.592722	−	0.805407i	$-0.701947\pi$
$659$		−	1061.53i		−	1.61081i	0.592722	−	0.805407i	$-0.298053\pi$
$660$		0			0
$661$	−117.646			−0.177982			−0.0889910	−	0.996032i	$-0.528364\pi$
$661$	−117.646			−0.177982			−0.0889910	+	0.996032i	$0.528364\pi$
$662$	−127.212	+	379.684i	−0.192164	+	0.573541i
$663$		0			0
$664$	−568.947	+	390.005i	−0.856848	+	0.587357i
$665$		0			0
$666$		0			0
$667$			823.848i			1.23516i
$668$	−465.749	+	617.025i	−0.697229	+	0.923690i
$669$		0			0
$670$		0			0
$671$		−	856.624i		−	1.27664i
$672$		0			0
$673$	−984.785			−1.46328			−0.731638	−	0.681693i	$-0.761244\pi$
$673$	−984.785			−1.46328			−0.731638	+	0.681693i	$0.761244\pi$
$674$	855.326	+	286.575i	1.26903	+	0.425185i
$675$		0			0
$676$	−97.2440	−	73.4027i	−0.143852	−	0.108584i
$677$	99.5646			0.147067			0.0735337	−	0.997293i	$-0.476572\pi$
$677$	99.5646			0.147067			0.0735337	+	0.997293i	$0.476572\pi$
$678$		0			0
$679$		−	151.553i		−	0.223200i
$680$		0			0
$681$		0			0
$682$	185.407	+	62.1201i	0.271857	+	0.0910851i
$683$		−	434.807i		−	0.636614i	−0.947988	−	0.318307i	$-0.896886\pi$
$683$		−	434.807i		−	0.636614i	0.947988	−	0.318307i	$-0.103114\pi$
$684$		0			0
$685$		0			0
$686$	−26.2004	+	78.1990i	−0.0381930	+	0.113993i
$687$		0			0
$688$	−897.093	+	255.658i	−1.30391	+	0.371596i
$689$	944.429			1.37072
$690$		0			0
$691$			1153.87i			1.66986i	0.550358	+	0.834929i	$0.314491\pi$
$691$			1153.87i			1.66986i	−0.550358	+	0.834929i	$0.685509\pi$
$692$	−181.545	−	137.036i	−0.262348	−	0.198028i
$693$		0			0
$694$	81.8659	−	244.341i	0.117962	−	0.352077i
$695$		0			0
$696$		0			0
$697$	−732.679			−1.05119
$698$	−1.43375	−	0.480376i	−0.00205409	−	0.000688218i
$699$		0			0
$700$		0			0
$701$	479.405			0.683887			0.341944	−	0.939720i	$-0.388915\pi$
$701$	479.405			0.683887			0.341944	+	0.939720i	$0.388915\pi$
$702$		0			0
$703$			10.9251i			0.0155407i
$704$	636.061	+	245.944i	0.903496	+	0.349352i
$705$		0			0
$706$	105.703	+	35.4156i	0.149721	+	0.0501638i
$707$		−	1977.90i		−	2.79760i
$708$		0			0
$709$	932.880			1.31577			0.657884	−	0.753119i	$-0.271451\pi$
$709$	932.880			1.31577			0.657884	+	0.753119i	$0.271451\pi$
$710$		0			0
$711$		0			0
$712$	575.407	+	839.415i	0.808155	+	1.17895i
$713$	386.582			0.542191
$714$		0			0
$715$		0			0
$716$	−655.842	+	868.860i	−0.915981	+	1.21349i
$717$		0			0
$718$	−123.421	+	368.368i	−0.171895	+	0.513047i
$719$			141.836i			0.197268i	0.995124	+	0.0986341i	$0.0314473\pi$
$719$			141.836i			0.197268i	−0.995124	+	0.0986341i	$0.968553\pi$
$720$		0			0
$721$	−157.273			−0.218131
$722$	−684.188	−	229.236i	−0.947629	−	0.317501i
$723$		0			0
$724$	−160.362	−	121.046i	−0.221495	−	0.167191i
$725$		0			0
$726$		0			0
$727$		−	891.575i		−	1.22638i	−0.789937	−	0.613188i	$-0.789887\pi$
$727$		−	891.575i		−	1.22638i	0.789937	−	0.613188i	$-0.210113\pi$
$728$	−784.710	+	537.907i	−1.07790	+	0.738884i
$729$		0			0
$730$		0			0
$731$			969.655i			1.32648i
$732$		0			0
$733$	614.593			0.838463			0.419232	−	0.907879i	$-0.362300\pi$
$733$	614.593			0.838463			0.419232	+	0.907879i	$0.362300\pi$
$734$	15.2659	−	45.5634i	0.0207983	−	0.0620755i
$735$		0			0
$736$	1346.84	+	61.5494i	1.82995	+	0.0836269i
$737$	−240.043			−0.325703
$738$		0			0
$739$			817.138i			1.10573i	0.833269	+	0.552867i	$0.186466\pi$
$739$			817.138i			1.10573i	−0.833269	+	0.552867i	$0.813534\pi$
$740$		0			0
$741$		0			0
$742$	−515.096	+	1537.38i	−0.694199	+	2.07194i
$743$			868.860i			1.16939i	0.811252	+	0.584697i	$0.198787\pi$
$743$			868.860i			1.16939i	−0.811252	+	0.584697i	$0.801213\pi$
$744$		0			0
$745$		0			0
$746$	−259.778	−	87.0381i	−0.348228	−	0.116673i
$747$		0			0
$748$	427.081	−	565.798i	0.570964	−	0.756414i
$749$	518.512			0.692273
$750$		0			0
$751$			100.822i			0.134250i	0.997745	+	0.0671252i	$0.0213827\pi$
$751$			100.822i			0.134250i	−0.997745	+	0.0671252i	$0.978617\pi$
$752$	640.779	−	182.613i	0.852100	−	0.242836i
$753$		0			0
$754$	436.459	+	146.235i	0.578859	+	0.193945i
$755$		0			0
$756$		0			0
$757$	−33.6363			−0.0444336			−0.0222168	−	0.999753i	$-0.507072\pi$
$757$	−33.6363			−0.0444336			−0.0222168	+	0.999753i	$0.507072\pi$
$758$	−65.6703	+	196.003i	−0.0866363	+	0.258579i
$759$		0			0
$760$		0			0
$761$	685.059			0.900209			0.450105	−	0.892976i	$-0.351387\pi$
$761$	685.059			0.900209			0.450105	+	0.892976i	$0.351387\pi$
$762$		0			0
$763$		−	473.367i		−	0.620402i
$764$	468.108	−	620.150i	0.612707	−	0.811714i
$765$		0			0
$766$	12.2967	−	36.7013i	0.0160531	−	0.0479130i
$767$			752.516i			0.981116i
$768$		0			0
$769$	23.6505			0.0307549			0.0153775	−	0.999882i	$-0.495105\pi$
$769$	23.6505			0.0307549			0.0153775	+	0.999882i	$0.495105\pi$
$770$		0			0
$771$		0			0
$772$	72.4821	+	54.7117i	0.0938888	+	0.0708701i
$773$	947.350			1.22555			0.612775	−	0.790257i	$-0.290053\pi$
$773$	947.350			1.22555			0.612775	+	0.790257i	$0.290053\pi$
$774$		0			0
$775$		0			0
$776$	67.8480	+	98.9780i	0.0874330	+	0.127549i
$777$		0			0
$778$	−519.569	−	174.080i	−0.667827	−	0.223754i
$779$			20.4446i			0.0262447i
$780$		0			0
$781$	655.167			0.838882
$782$	445.243	−	1328.89i	0.569364	−	1.69935i
$783$		0			0
$784$	−232.770	−	816.780i	−0.296901	−	1.04181i
$785$		0			0
$786$		0			0
$787$			1054.73i			1.34019i	0.742275	+	0.670096i	$0.233747\pi$
$787$			1054.73i			1.34019i	−0.742275	+	0.670096i	$0.766253\pi$
$788$	493.678	+	372.643i	0.626495	+	0.472897i
$789$		0			0
$790$		0			0
$791$		−	1167.22i		−	1.47562i
$792$		0			0
$793$	−946.244			−1.19325
$794$	−413.848	−	138.659i	−0.521220	−	0.174633i
$795$		0			0
$796$	−568.953	+	753.749i	−0.714765	+	0.946921i
$797$	810.475			1.01691			0.508454	−	0.861089i	$-0.330217\pi$
$797$	810.475			1.01691			0.508454	+	0.861089i	$0.330217\pi$
$798$		0			0
$799$		−	692.609i		−	0.866845i
$800$		0			0
$801$		0			0
$802$	−751.866	−	251.911i	−0.937489	−	0.314103i
$803$			1467.30i			1.82728i
$804$		0			0
$805$		0			0
$806$	68.6191	−	204.804i	0.0851353	−	0.254099i
$807$		0			0
$808$	885.478	+	1291.75i	1.09589	+	1.59870i
$809$	−768.673			−0.950152			−0.475076	−	0.879945i	$-0.657579\pi$
$809$	−768.673			−0.950152			−0.475076	+	0.879945i	$0.657579\pi$
$810$		0			0
$811$		−	744.199i		−	0.917632i	−0.888531	−	0.458816i	$-0.848274\pi$
$811$		−	744.199i		−	0.917632i	0.888531	−	0.458816i	$-0.151726\pi$
$812$	−476.094	+	630.729i	−0.586322	+	0.776760i
$813$		0			0
$814$	159.378	−	475.688i	0.195796	−	0.584383i
$815$		0			0
$816$		0			0
$817$	27.0571			0.0331177
$818$	−572.664	−	191.870i	−0.700078	−	0.234559i
$819$		0			0
$820$		0			0
$821$	−205.427			−0.250215			−0.125108	−	0.992143i	$-0.539928\pi$
$821$	−205.427			−0.250215			−0.125108	+	0.992143i	$0.539928\pi$
$822$		0			0
$823$			1287.79i			1.56475i	0.622808	+	0.782375i	$0.285992\pi$
$823$			1287.79i			1.56475i	−0.622808	+	0.782375i	$0.714008\pi$
$824$	102.713	−	70.4086i	0.124652	−	0.0854473i
$825$		0			0
$826$	−1224.98	−	410.425i	−1.48302	−	0.496883i
$827$			255.621i			0.309094i	0.987985	+	0.154547i	$0.0493918\pi$
$827$			255.621i			0.309094i	−0.987985	+	0.154547i	$0.950608\pi$
$828$		0			0
$829$	−14.0286			−0.0169223			−0.00846114	−	0.999964i	$-0.502693\pi$
$829$	−14.0286			−0.0169223			−0.00846114	+	0.999964i	$0.502693\pi$
$830$		0			0
$831$		0			0
$832$	271.675	−	702.606i	0.326532	−	0.844479i
$833$	−882.846			−1.05984
$834$		0			0
$835$		0			0
$836$	−15.7880	−	11.9172i	−0.0188851	−	0.0142551i
$837$		0			0
$838$	267.153	−	797.357i	0.318798	−	0.951500i
$839$		−	333.636i		−	0.397659i	−0.980034	−	0.198829i	$-0.936286\pi$
$839$		−	333.636i		−	0.397659i	0.980034	−	0.198829i	$-0.0637140\pi$
$840$		0			0
$841$	−458.655			−0.545369
$842$	374.306	+	125.410i	0.444543	+	0.148943i
$843$		0			0
$844$	−277.638	+	367.815i	−0.328955	+	0.435799i
$845$		0			0
$846$		0			0
$847$			75.3657i			0.0889795i
$848$	−351.857	−	1234.65i	−0.414926	−	1.45596i
$849$		0			0
$850$		0			0
$851$		−	991.832i		−	1.16549i
$852$		0			0
$853$	1563.83			1.83333			0.916663	−	0.399661i	$-0.130872\pi$
$853$	1563.83			1.83333			0.916663	+	0.399661i	$0.130872\pi$
$854$	516.086	−	1540.33i	0.604316	−	1.80367i
$855$		0			0
$856$	−338.636	+	232.130i	−0.395603	+	0.271180i
$857$	1283.36			1.49750			0.748749	−	0.662854i	$-0.230655\pi$
$857$	1283.36			1.49750			0.748749	+	0.662854i	$0.230655\pi$
$858$		0			0
$859$		−	1448.91i		−	1.68674i	−0.537330	−	0.843372i	$-0.680567\pi$
$859$		−	1448.91i		−	1.68674i	0.537330	−	0.843372i	$-0.319433\pi$
$860$		0			0
$861$		0			0
$862$	150.502	−	449.196i	0.174597	−	0.521109i
$863$			755.677i			0.875640i	0.899063	+	0.437820i	$0.144249\pi$
$863$			755.677i			0.875640i	−0.899063	+	0.437820i	$0.855751\pi$
$864$		0			0
$865$		0			0
$866$	691.002	+	231.519i	0.797924	+	0.267343i
$867$		0			0
$868$	295.963	+	223.402i	0.340971	+	0.257375i
$869$	1477.55			1.70029
$870$		0			0
$871$			265.157i			0.304428i
$872$	211.919	+	309.152i	0.243027	+	0.354532i
$873$		0			0
$874$	−37.0813	−	12.4240i	−0.0424271	−	0.0142151i
$875$		0			0
$876$		0			0
$877$	−248.612			−0.283480			−0.141740	−	0.989904i	$-0.545270\pi$
$877$	−248.612			−0.283480			−0.141740	+	0.989904i	$0.545270\pi$
$878$	45.9812	−	137.238i	0.0523704	−	0.156307i
$879$		0			0
$880$		0			0
$881$	−460.306			−0.522481			−0.261240	−	0.965274i	$-0.584132\pi$
$881$	−460.306			−0.522481			−0.261240	+	0.965274i	$0.584132\pi$
$882$		0			0
$883$		−	554.195i		−	0.627628i	−0.949485	−	0.313814i	$-0.898393\pi$
$883$		−	554.195i		−	0.627628i	0.949485	−	0.313814i	$-0.101607\pi$
$884$	−624.991	−	471.763i	−0.707004	−	0.533668i
$885$		0			0
$886$	152.679	−	455.694i	0.172324	−	0.514327i
$887$		−	251.593i		−	0.283644i	−0.989892	−	0.141822i	$-0.954704\pi$
$887$		−	251.593i		−	0.283644i	0.989892	−	0.141822i	$-0.0452961\pi$
$888$		0			0
$889$	−1633.30			−1.83723
$890$		0			0
$891$		0			0
$892$	1024.60	−	1357.39i	1.14865	−	1.52174i
$893$	−19.3265			−0.0216422
$894$		0			0
$895$		0			0
$896$	995.558	+	825.448i	1.11111	+	0.921259i
$897$		0			0
$898$	946.220	+	317.029i	1.05370	+	0.353039i
$899$		−	179.411i		−	0.199568i
$900$		0			0
$901$	−1334.52			−1.48115
$902$	298.250	−	890.171i	0.330654	−	0.986886i
$903$		0			0
$904$	522.545	+	762.299i	0.578037	+	0.843251i
$905$		0			0
$906$		0			0
$907$		−	447.842i		−	0.493762i	−0.969046	−	0.246881i	$-0.920594\pi$
$907$		−	447.842i		−	0.493762i	0.969046	−	0.246881i	$-0.0794056\pi$
$908$	429.455	−	568.942i	0.472968	−	0.626588i
$909$		0			0
$910$		0			0
$911$			96.7664i			0.106220i	0.998589	+	0.0531100i	$0.0169134\pi$
$911$			96.7664i			0.106220i	−0.998589	+	0.0531100i	$0.983087\pi$
$912$		0			0
$913$	−918.756			−1.00630
$914$	−325.925	−	109.200i	−0.356592	−	0.119475i
$915$		0			0
$916$	1058.78	+	799.196i	1.15587	+	0.872485i
$917$	−1996.06			−2.17673
$918$		0			0
$919$		−	234.739i		−	0.255429i	−0.991811	−	0.127715i	$-0.959236\pi$
$919$		−	234.739i		−	0.255429i	0.991811	−	0.127715i	$-0.0407641\pi$
$920$		0			0
$921$		0			0
$922$	−1577.46	−	528.526i	−1.71092	−	0.573238i
$923$		−	723.711i		−	0.784085i
$924$		0			0
$925$		0			0
$926$	235.098	−	701.685i	0.253886	−	0.757759i
$927$		0			0
$928$	28.5648	−	625.064i	0.0307811	−	0.673561i
$929$	552.902			0.595158			0.297579	−	0.954697i	$-0.403821\pi$
$929$	552.902			0.595158			0.297579	+	0.954697i	$0.403821\pi$
$930$		0			0
$931$			24.6348i			0.0264606i
$932$	−584.088	−	440.887i	−0.626704	−	0.473055i
$933$		0			0
$934$	335.335	−	1000.86i	0.359031	−	1.07158i
$935$		0			0
$936$		0			0
$937$	957.870			1.02227			0.511137	−	0.859499i	$-0.329225\pi$
$937$	957.870			1.02227			0.511137	+	0.859499i	$0.329225\pi$
$938$	−431.633	−	144.618i	−0.460163	−	0.154177i
$939$		0			0
$940$		0			0
$941$	−1125.13			−1.19567			−0.597837	−	0.801618i	$-0.703973\pi$
$941$	−1125.13			−1.19567			−0.597837	+	0.801618i	$0.703973\pi$
$942$		0			0
$943$		−	1856.05i		−	1.96824i
$944$	983.763	−	280.358i	1.04212	−	0.296989i
$945$		0			0
$946$	−1178.09	−	394.715i	−1.24533	−	0.417246i
$947$			256.824i			0.271198i	0.990764	+	0.135599i	$0.0432959\pi$
$947$			256.824i			0.271198i	−0.990764	+	0.135599i	$0.956704\pi$
$948$		0			0
$949$	1620.81			1.70792
$950$		0			0
$951$		0			0
$952$	1108.83	−	760.085i	1.16473	−	0.798409i
$953$	−575.377			−0.603753			−0.301877	−	0.953347i	$-0.597613\pi$
$953$	−575.377			−0.603753			−0.301877	+	0.953347i	$0.597613\pi$
$954$		0			0
$955$		0			0
$956$	507.670	−	672.561i	0.531035	−	0.703516i
$957$		0			0
$958$	338.516	−	1010.35i	0.353357	−	1.05465i
$959$			772.094i			0.805103i
$960$		0			0
$961$	876.813			0.912397
$962$	−525.454	−	176.052i	−0.546210	−	0.183006i
$963$		0			0
$964$	−11.5635	−	8.72845i	−0.0119953	−	0.00905441i
$965$		0			0
$966$		0			0
$967$		−	860.976i		−	0.890358i	−0.895442	−	0.445179i	$-0.853140\pi$
$967$		−	860.976i		−	0.890358i	0.895442	−	0.445179i	$-0.146860\pi$
$968$	−33.7401	−	49.2207i	−0.0348555	−	0.0508478i
$969$		0			0
$970$		0			0
$971$			177.116i			0.182406i	0.995832	+	0.0912030i	$0.0290712\pi$
$971$			177.116i			0.182406i	−0.995832	+	0.0912030i	$0.970929\pi$
$972$		0			0
$973$	2255.17			2.31775
$974$	−314.560	+	938.851i	−0.322957	+	0.963913i
$975$		0			0
$976$	352.534	+	1237.02i	0.361202	+	1.26744i
$977$	755.634			0.773423			0.386711	−	0.922201i	$-0.373611\pi$
$977$	755.634			0.773423			0.386711	+	0.922201i	$0.373611\pi$
$978$		0			0
$979$			1355.52i			1.38459i
$980$		0			0
$981$		0			0
$982$	−329.187	+	982.507i	−0.335221	+	1.00052i
$983$			1108.93i			1.12811i	0.825738	+	0.564054i	$0.190759\pi$
$983$			1108.93i			1.12811i	−0.825738	+	0.564054i	$0.809241\pi$
$984$		0			0
$985$		0			0
$986$	−616.735	−	206.636i	−0.625492	−	0.209570i
$987$		0			0
$988$	−13.1640	+	17.4397i	−0.0133239	+	0.0176515i
$989$	−2456.37			−2.48369
$990$		0			0
$991$		−	516.421i		−	0.521111i	−0.965459	−	0.260556i	$-0.916094\pi$
$991$		−	516.421i		−	0.521111i	0.965459	−	0.260556i	$-0.0839058\pi$
$992$	−293.305	−	13.4037i	−0.295670	−	0.0135118i
$993$		0			0
$994$	1178.09	+	394.715i	1.18520	+	0.397098i
$995$		0			0
$996$		0			0
$997$	1127.03			1.13042			0.565212	−	0.824946i	$-0.308794\pi$
$997$	1127.03			1.13042			0.565212	+	0.824946i	$0.308794\pi$
$998$	429.885	−	1283.06i	0.430747	−	1.28563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.p.451.1	✓	8
3.2	odd	2	inner	900.3.c.p.451.8	yes	8
4.3	odd	2	inner	900.3.c.p.451.2	yes	8
5.2	odd	4		900.3.f.g.199.9		16
5.3	odd	4		900.3.f.g.199.8		16
5.4	even	2		900.3.c.q.451.8	yes	8
12.11	even	2	inner	900.3.c.p.451.7	yes	8
15.2	even	4		900.3.f.g.199.7		16
15.8	even	4		900.3.f.g.199.10		16
15.14	odd	2		900.3.c.q.451.1	yes	8
20.3	even	4		900.3.f.g.199.11		16
20.7	even	4		900.3.f.g.199.6		16
20.19	odd	2		900.3.c.q.451.7	yes	8
60.23	odd	4		900.3.f.g.199.5		16
60.47	odd	4		900.3.f.g.199.12		16
60.59	even	2		900.3.c.q.451.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.c.p.451.1	✓	8	1.1	even	1	trivial
900.3.c.p.451.2	yes	8	4.3	odd	2	inner
900.3.c.p.451.7	yes	8	12.11	even	2	inner
900.3.c.p.451.8	yes	8	3.2	odd	2	inner
900.3.c.q.451.1	yes	8	15.14	odd	2
900.3.c.q.451.2	yes	8	60.59	even	2
900.3.c.q.451.7	yes	8	20.19	odd	2
900.3.c.q.451.8	yes	8	5.4	even	2
900.3.f.g.199.5		16	60.23	odd	4
900.3.f.g.199.6		16	20.7	even	4
900.3.f.g.199.7		16	15.2	even	4
900.3.f.g.199.8		16	5.3	odd	4
900.3.f.g.199.9		16	5.2	odd	4
900.3.f.g.199.10		16	15.8	even	4
900.3.f.g.199.11		16	20.3	even	4
900.3.f.g.199.12		16	60.47	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89639 - 0.635381i) q^{2} +(3.19258 + 2.40986i) q^{4} +10.1035i q^{7} +(-4.52320 - 6.59853i) q^{8} +O(q^{10})\)	\(q+(-1.89639 - 0.635381i) q^{2} +(3.19258 + 2.40986i) q^{4} +10.1035i q^{7} +(-4.52320 - 6.59853i) q^{8} -10.6555i q^{11} -11.7703 q^{13} +(6.41959 - 19.1602i) q^{14} +(4.38516 + 15.3873i) q^{16} +16.6320 q^{17} -0.464096i q^{19} +(-6.77033 + 20.2071i) q^{22} +42.1327i q^{23} +(22.3211 + 7.47864i) q^{26} +(-24.3481 + 32.2564i) q^{28} +19.5536 q^{29} -9.17534i q^{31} +(1.46084 - 31.9666i) q^{32} +(-31.5407 - 10.5676i) q^{34} -23.5407 q^{37} +(-0.294878 + 0.880107i) q^{38} -44.0525 q^{41} +58.3007i q^{43} +(25.6784 - 34.0187i) q^{44} +(26.7703 - 79.9000i) q^{46} -41.6433i q^{47} -53.0813 q^{49} +(-37.5777 - 28.3648i) q^{52} -80.2381 q^{53} +(66.6685 - 45.7003i) q^{56} +(-37.0813 - 12.4240i) q^{58} -63.9333i q^{59} +80.3923 q^{61} +(-5.82983 + 17.4000i) q^{62} +(-23.0813 + 59.6930i) q^{64} -22.5275i q^{67} +(53.0989 + 40.0807i) q^{68} +61.4860i q^{71} -137.703 q^{73} +(44.6422 + 14.9573i) q^{74} +(1.11841 - 1.48167i) q^{76} +107.659 q^{77} +138.665i q^{79} +(83.5407 + 27.9901i) q^{82} -86.2233i q^{83} +(37.0431 - 110.561i) q^{86} +(-70.3110 + 48.1972i) q^{88} -127.212 q^{89} -118.922i q^{91} +(-101.534 + 134.512i) q^{92} +(-26.4593 + 78.9719i) q^{94} -15.0000 q^{97} +(100.663 + 33.7269i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 8 q^{13} - 8 q^{16} + 32 q^{22} - 44 q^{28} - 80 q^{34} - 16 q^{37} + 128 q^{46} - 80 q^{49} - 236 q^{52} + 48 q^{58} + 40 q^{61} + 160 q^{64} - 240 q^{73} - 228 q^{76} + 496 q^{82} - 304 q^{88} - 384 q^{94} - 120 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^13 - 8 * q^16 + 32 * q^22 - 44 * q^28 - 80 * q^34 - 16 * q^37 + 128 * q^46 - 80 * q^49 - 236 * q^52 + 48 * q^58 + 40 * q^61 + 160 * q^64 - 240 * q^73 - 228 * q^76 + 496 * q^82 - 304 * q^88 - 384 * q^94 - 120 * q^97

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