LMFDB - Embedded newform 900.3.c.o.451.4

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:	8.0.15012375625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} + 28x^{4} + 112x^{2} + 256 $ x^8 + 7x^6 + 28x^4 + 112*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.4
Root			$-0.342371 + 1.97048i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.o.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342371 + 1.97048i) q^{2} +(-3.76556 - 1.34927i) q^{4} +11.5108i q^{7} +(3.94792 - 6.95801i) q^{8} +O(q^{10})$	\(q+(-0.342371 + 1.97048i) q^{2} +(-3.76556 - 1.34927i) q^{4} +11.5108i q^{7} +(3.94792 - 6.95801i) q^{8} +9.97507i q^{11} +14.1245 q^{13} +(-22.6817 - 3.94096i) q^{14} +(12.3590 + 10.1615i) q^{16} +30.5776 q^{17} -12.2274i q^{19} +(-19.6556 - 3.41517i) q^{22} +15.7638i q^{23} +(-4.83582 + 27.8320i) q^{26} +(15.5311 - 43.3446i) q^{28} +18.8943 q^{29} -35.2490i q^{31} +(-24.2544 + 20.8740i) q^{32} +(-10.4689 + 60.2524i) q^{34} -50.1245 q^{37} +(24.0938 + 4.18631i) q^{38} +28.8444 q^{41} +24.4548i q^{43} +(13.4590 - 37.5618i) q^{44} +(-31.0623 - 5.39707i) q^{46} +55.6641i q^{47} -83.4981 q^{49} +(-53.1868 - 19.0578i) q^{52} -2.46054 q^{53} +(80.0921 + 45.4437i) q^{56} +(-6.46887 + 37.2309i) q^{58} +64.6577i q^{59} -30.2490 q^{61} +(69.4573 + 12.0682i) q^{62} +(-32.8278 - 54.9394i) q^{64} +66.1981i q^{67} +(-115.142 - 41.2574i) q^{68} -11.5775i q^{71} -2.24903 q^{73} +(17.1612 - 98.7692i) q^{74} +(-16.4981 + 46.0431i) q^{76} -114.821 q^{77} +78.4256i q^{79} +(-9.87548 + 56.8373i) q^{82} +146.061i q^{83} +(-48.1877 - 8.37262i) q^{86} +(69.4066 + 39.3808i) q^{88} -87.4311 q^{89} +162.584i q^{91} +(21.2696 - 59.3597i) q^{92} +(-109.685 - 19.0578i) q^{94} -126.747 q^{97} +(28.5873 - 164.531i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 14 q^{4}+O(q^{10}) $ 8 * q - 14 * q^4	$ 8 q - 14 q^{4} - 16 q^{13} - 14 q^{16} + 4 q^{22} + 92 q^{28} - 116 q^{34} - 272 q^{37} - 184 q^{46} - 152 q^{49} - 232 q^{52} - 84 q^{58} + 16 q^{61} - 182 q^{64} + 240 q^{73} + 384 q^{76} - 208 q^{82} + 652 q^{88} - 168 q^{94} - 240 q^{97}+O(q^{100}) $ 8 * q - 14 * q^4 - 16 * q^13 - 14 * q^16 + 4 * q^22 + 92 * q^28 - 116 * q^34 - 272 * q^37 - 184 * q^46 - 152 * q^49 - 232 * q^52 - 84 * q^58 + 16 * q^61 - 182 * q^64 + 240 * q^73 + 384 * q^76 - 208 * q^82 + 652 * q^88 - 168 * q^94 - 240 * 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 $

$2$	−0.342371	+	1.97048i	−0.171185	+	0.985239i
$2$	−0.342371	+	1.97048i	−0.171185	+	0.985239i
$3$		0			0
$3$		0			0
$4$	−3.76556	−	1.34927i	−0.941391	−	0.337317i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			11.5108i			1.64440i	0.569201	+	0.822199i	$0.307253\pi$
$7$			11.5108i			1.64440i	−0.569201	+	0.822199i	$0.692747\pi$
$8$	3.94792	−	6.95801i	0.493490	−	0.869751i
$9$		0			0
$10$		0			0
$11$			9.97507i			0.906824i	0.891301	+	0.453412i	$0.149793\pi$
$11$			9.97507i			0.906824i	−0.891301	+	0.453412i	$0.850207\pi$
$12$		0			0
$13$	14.1245			1.08650			0.543251	−	0.839571i	$-0.317193\pi$
$13$	14.1245			1.08650			0.543251	+	0.839571i	$0.317193\pi$
$14$	−22.6817	−	3.94096i	−1.62012	−	0.281497i
$15$		0			0
$16$	12.3590	+	10.1615i	0.772434	+	0.635095i
$17$	30.5776			1.79868			0.899341	−	0.437249i	$-0.144047\pi$
$17$	30.5776			1.79868			0.899341	+	0.437249i	$0.144047\pi$
$18$		0			0
$19$		−	12.2274i		−	0.643548i	−0.946816	−	0.321774i	$-0.895721\pi$
$19$		−	12.2274i		−	0.643548i	0.946816	−	0.321774i	$-0.104279\pi$
$20$		0			0
$21$		0			0
$22$	−19.6556	−	3.41517i	−0.893438	−	0.155235i
$23$			15.7638i			0.685384i	0.939448	+	0.342692i	$0.111339\pi$
$23$			15.7638i			0.685384i	−0.939448	+	0.342692i	$0.888661\pi$
$24$		0			0
$25$		0			0
$26$	−4.83582	+	27.8320i	−0.185993	+	1.07046i
$27$		0			0
$28$	15.5311	−	43.3446i	0.554683	−	1.54802i
$29$	18.8943			0.651529			0.325765	−	0.945451i	$-0.394378\pi$
$29$	18.8943			0.651529			0.325765	+	0.945451i	$0.394378\pi$
$30$		0			0
$31$		−	35.2490i		−	1.13706i	−0.822661	−	0.568532i	$-0.807512\pi$
$31$		−	35.2490i		−	1.13706i	0.822661	−	0.568532i	$-0.192488\pi$
$32$	−24.2544	+	20.8740i	−0.757949	+	0.652313i
$33$		0			0
$34$	−10.4689	+	60.2524i	−0.307908	+	1.77213i
$35$		0			0
$36$		0			0
$37$	−50.1245			−1.35472			−0.677358	−	0.735653i	$-0.736875\pi$
$37$	−50.1245			−1.35472			−0.677358	+	0.735653i	$0.736875\pi$
$38$	24.0938	+	4.18631i	0.634049	+	0.110166i
$39$		0			0
$40$		0			0
$41$	28.8444			0.703522			0.351761	−	0.936090i	$-0.385583\pi$
$41$	28.8444			0.703522			0.351761	+	0.936090i	$0.385583\pi$
$42$		0			0
$43$			24.4548i			0.568717i	0.958718	+	0.284359i	$0.0917806\pi$
$43$			24.4548i			0.568717i	−0.958718	+	0.284359i	$0.908219\pi$
$44$	13.4590	−	37.5618i	0.305887	−	0.853676i
$45$		0			0
$46$	−31.0623	−	5.39707i	−0.675266	−	0.117328i
$47$			55.6641i			1.18434i	0.805812	+	0.592171i	$0.201729\pi$
$47$			55.6641i			1.18434i	−0.805812	+	0.592171i	$0.798271\pi$
$48$		0			0
$49$	−83.4981			−1.70404
$50$		0			0
$51$		0			0
$52$	−53.1868	−	19.0578i	−1.02282	−	0.366495i
$53$	−2.46054			−0.0464253			−0.0232127	−	0.999731i	$-0.507389\pi$
$53$	−2.46054			−0.0464253			−0.0232127	+	0.999731i	$0.507389\pi$
$54$		0			0
$55$		0			0
$56$	80.0921	+	45.4437i	1.43022	+	0.811494i
$57$		0			0
$58$	−6.46887	+	37.2309i	−0.111532	+	0.641912i
$59$			64.6577i			1.09589i	0.836513	+	0.547947i	$0.184590\pi$
$59$			64.6577i			1.09589i	−0.836513	+	0.547947i	$0.815410\pi$
$60$		0			0
$61$	−30.2490			−0.495886			−0.247943	−	0.968775i	$-0.579755\pi$
$61$	−30.2490			−0.495886			−0.247943	+	0.968775i	$0.579755\pi$
$62$	69.4573	+	12.0682i	1.12028	+	0.194649i
$63$		0			0
$64$	−32.8278	−	54.9394i	−0.512935	−	0.858428i
$65$		0			0
$66$		0			0
$67$			66.1981i			0.988032i	0.869453	+	0.494016i	$0.164472\pi$
$67$			66.1981i			0.988032i	−0.869453	+	0.494016i	$0.835528\pi$
$68$	−115.142	−	41.2574i	−1.69326	−	0.606726i
$69$		0			0
$70$		0			0
$71$		−	11.5775i		−	0.163064i	−0.996671	−	0.0815318i	$-0.974019\pi$
$71$		−	11.5775i		−	0.163064i	0.996671	−	0.0815318i	$-0.0259812\pi$
$72$		0			0
$73$	−2.24903			−0.0308086			−0.0154043	−	0.999881i	$-0.504904\pi$
$73$	−2.24903			−0.0308086			−0.0154043	+	0.999881i	$0.504904\pi$
$74$	17.1612	−	98.7692i	0.231908	−	1.33472i
$75$		0			0
$76$	−16.4981	+	46.0431i	−0.217080	+	0.605831i
$77$	−114.821			−1.49118
$78$		0			0
$79$			78.4256i			0.992729i	0.868114	+	0.496364i	$0.165332\pi$
$79$			78.4256i			0.992729i	−0.868114	+	0.496364i	$0.834668\pi$
$80$		0			0
$81$		0			0
$82$	−9.87548	+	56.8373i	−0.120433	+	0.693137i
$83$			146.061i			1.75977i	0.475189	+	0.879884i	$0.342380\pi$
$83$			146.061i			1.75977i	−0.475189	+	0.879884i	$0.657620\pi$
$84$		0			0
$85$		0			0
$86$	−48.1877	−	8.37262i	−0.560322	−	0.0973561i
$87$		0			0
$88$	69.4066	+	39.3808i	0.788712	+	0.447509i
$89$	−87.4311			−0.982372			−0.491186	−	0.871055i	$-0.663436\pi$
$89$	−87.4311			−0.982372			−0.491186	+	0.871055i	$0.663436\pi$
$90$		0			0
$91$			162.584i			1.78664i
$92$	21.2696	−	59.3597i	0.231192	−	0.645214i
$93$		0			0
$94$	−109.685	−	19.0578i	−1.16686	−	0.202742i
$95$		0			0
$96$		0			0
$97$	−126.747			−1.30667			−0.653336	−	0.757068i	$-0.726631\pi$
$97$	−126.747			−1.30667			−0.653336	+	0.757068i	$0.726631\pi$
$98$	28.5873	−	164.531i	0.291707	−	1.67889i
$99$		0			0
$100$		0			0
$101$	−66.1841			−0.655289			−0.327644	−	0.944801i	$-0.606255\pi$
$101$	−66.1841			−0.655289			−0.327644	+	0.944801i	$0.606255\pi$
$102$		0			0
$103$		−	105.030i		−	1.01971i	−0.860260	−	0.509856i	$-0.829699\pi$
$103$		−	105.030i		−	1.01971i	0.860260	−	0.509856i	$-0.170301\pi$
$104$	55.7625	−	98.2785i	0.536178	−	0.944986i
$105$		0			0
$106$	0.842418	−	4.84844i	0.00794734	−	0.0457400i
$107$		−	68.2230i		−	0.637598i	−0.947822	−	0.318799i	$-0.896720\pi$
$107$		−	68.2230i		−	0.637598i	0.947822	−	0.318799i	$-0.103280\pi$
$108$		0			0
$109$	−33.5019			−0.307357			−0.153679	−	0.988121i	$-0.549112\pi$
$109$	−33.5019			−0.307357			−0.153679	+	0.988121i	$0.549112\pi$
$110$		0			0
$111$		0			0
$112$	−116.967	+	142.261i	−1.04435	+	1.27019i
$113$	143.944			1.27384			0.636919	−	0.770931i	$-0.280209\pi$
$113$	143.944			1.27384			0.636919	+	0.770931i	$0.280209\pi$
$114$		0			0
$115$		0			0
$116$	−71.1479	−	25.4935i	−0.613344	−	0.219772i
$117$		0			0
$118$	−127.407	−	22.1369i	−1.07972	−	0.187601i
$119$			351.972i			2.95775i
$120$		0			0
$121$	21.4981			0.177670
$122$	10.3564	−	59.6050i	0.0848884	−	0.488566i
$123$		0			0
$124$	−47.5603	+	132.732i	−0.383551	+	1.07042i
$125$		0			0
$126$		0			0
$127$		−	199.983i		−	1.57467i	−0.616525	−	0.787335i	$-0.711460\pi$
$127$		−	199.983i		−	1.57467i	0.616525	−	0.787335i	$-0.288540\pi$
$128$	119.496	−	45.8769i	0.933563	−	0.358413i
$129$		0			0
$130$		0			0
$131$		−	247.414i		−	1.88866i	−0.329007	−	0.944328i	$-0.606714\pi$
$131$		−	247.414i		−	1.88866i	0.329007	−	0.944328i	$-0.393286\pi$
$132$		0			0
$133$	140.747			1.05825
$134$	−130.442	−	22.6643i	−0.973447	−	0.169137i
$135$		0			0
$136$	120.718	−	212.759i	0.887632	−	1.56441i
$137$	141.375			1.03194			0.515968	−	0.856608i	$-0.327432\pi$
$137$	141.375			1.03194			0.515968	+	0.856608i	$0.327432\pi$
$138$		0			0
$139$			58.2705i			0.419212i	0.977786	+	0.209606i	$0.0672182\pi$
$139$			58.2705i			0.419212i	−0.977786	+	0.209606i	$0.932782\pi$
$140$		0			0
$141$		0			0
$142$	22.8132	+	3.96380i	0.160657	+	0.0279141i
$143$			140.893i			0.985266i
$144$		0			0
$145$		0			0
$146$	0.770003	−	4.43167i	0.00527399	−	0.0303539i
$147$		0			0
$148$	188.747	+	67.6314i	1.27532	+	0.456969i
$149$	265.527			1.78206			0.891029	−	0.453947i	$-0.149984\pi$
$149$	265.527			1.78206			0.891029	+	0.453947i	$0.149984\pi$
$150$		0			0
$151$		−	217.988i		−	1.44363i	−0.692086	−	0.721815i	$-0.743308\pi$
$151$		−	217.988i		−	1.44363i	0.692086	−	0.721815i	$-0.256692\pi$
$152$	−85.0785	−	48.2729i	−0.559727	−	0.317585i
$153$		0			0
$154$	39.3113	−	226.252i	0.255268	−	1.46917i
$155$		0			0
$156$		0			0
$157$	−66.3735			−0.422761			−0.211381	−	0.977404i	$-0.567796\pi$
$157$	−66.3735			−0.422761			−0.211381	+	0.977404i	$0.567796\pi$
$158$	−154.536	−	26.8506i	−0.978075	−	0.169941i
$159$		0			0
$160$		0			0
$161$	−181.454			−1.12704
$162$		0			0
$163$		−	93.5195i		−	0.573739i	−0.957970	−	0.286870i	$-0.907385\pi$
$163$		−	93.5195i		−	0.573739i	0.957970	−	0.286870i	$-0.0926147\pi$
$164$	−108.615	−	38.9188i	−0.662290	−	0.237310i
$165$		0			0
$166$	−287.809	−	50.0069i	−1.73379	−	0.301247i
$167$		−	47.2915i		−	0.283182i	−0.989925	−	0.141591i	$-0.954778\pi$
$167$		−	47.2915i		−	0.283182i	0.989925	−	0.141591i	$-0.0452219\pi$
$168$		0			0
$169$	30.5019			0.180485
$170$		0			0
$171$		0			0
$172$	32.9961	−	92.0862i	0.191838	−	0.535385i
$173$	−229.534			−1.32678			−0.663392	−	0.748272i	$-0.730884\pi$
$173$	−229.534			−1.32678			−0.663392	+	0.748272i	$0.730884\pi$
$174$		0			0
$175$		0			0
$176$	−101.362	+	123.281i	−0.575919	+	0.700462i
$177$		0			0
$178$	29.9339	−	172.281i	0.168168	−	0.967871i
$179$			150.868i			0.842838i	0.906866	+	0.421419i	$0.138468\pi$
$179$			150.868i			0.842838i	−0.906866	+	0.421419i	$0.861532\pi$
$180$		0			0
$181$	54.4981			0.301094			0.150547	−	0.988603i	$-0.451896\pi$
$181$	54.4981			0.301094			0.150547	+	0.988603i	$0.451896\pi$
$182$	−320.369	−	55.6641i	−1.76027	−	0.305847i
$183$		0			0
$184$	109.685	+	62.2343i	0.596113	+	0.338230i
$185$		0			0
$186$		0			0
$187$			305.013i			1.63109i
$188$	75.1058	−	209.607i	0.399499	−	1.11493i
$189$		0			0
$190$		0			0
$191$		−	225.861i		−	1.18252i	−0.806481	−	0.591260i	$-0.798631\pi$
$191$		−	225.861i		−	1.18252i	0.806481	−	0.591260i	$-0.201369\pi$
$192$		0			0
$193$	−174.498			−0.904135			−0.452068	−	0.891984i	$-0.649313\pi$
$193$	−174.498			−0.904135			−0.452068	+	0.891984i	$0.649313\pi$
$194$	43.3945	−	249.752i	0.223683	−	1.28738i
$195$		0			0
$196$	314.417	+	112.661i	1.60417	+	0.574802i
$197$	15.9849			0.0811414			0.0405707	−	0.999177i	$-0.487082\pi$
$197$	15.9849			0.0811414			0.0405707	+	0.999177i	$0.487082\pi$
$198$		0			0
$199$		−	30.9492i		−	0.155523i	−0.996972	−	0.0777617i	$-0.975223\pi$
$199$		−	30.9492i		−	0.155523i	0.996972	−	0.0777617i	$-0.0247773\pi$
$200$		0			0
$201$		0			0
$202$	22.6595	−	130.414i	0.112176	−	0.645616i
$203$			217.489i			1.07137i
$204$		0			0
$205$		0			0
$206$	206.960	+	35.9593i	1.00466	+	0.174560i
$207$		0			0
$208$	174.564	+	143.526i	0.839251	+	0.690031i
$209$	121.969			0.583585
$210$		0			0
$211$			190.667i			0.903634i	0.892111	+	0.451817i	$0.149224\pi$
$211$			190.667i			0.903634i	−0.892111	+	0.451817i	$0.850776\pi$
$212$	9.26533	+	3.31993i	0.0437044	+	0.0156600i
$213$		0			0
$214$	134.432	+	23.3576i	0.628187	+	0.109148i
$215$		0			0
$216$		0			0
$217$	405.743			1.86978
$218$	11.4701	−	66.0148i	0.0526151	−	0.302820i
$219$		0			0
$220$		0			0
$221$	431.893			1.95427
$222$		0			0
$223$			317.957i			1.42582i	0.701257	+	0.712909i	$0.252623\pi$
$223$			317.957i			1.42582i	−0.701257	+	0.712909i	$0.747377\pi$
$224$	−240.276	−	279.187i	−1.07266	−	1.24637i
$225$		0			0
$226$	−49.2821	+	283.638i	−0.218062	+	1.25503i
$227$			39.9003i			0.175772i	0.996131	+	0.0878860i	$0.0280111\pi$
$227$			39.9003i			0.175772i	−0.996131	+	0.0878860i	$0.971989\pi$
$228$		0			0
$229$	13.7510			0.0600479			0.0300239	−	0.999549i	$-0.490442\pi$
$229$	13.7510			0.0600479			0.0300239	+	0.999549i	$0.490442\pi$
$230$		0			0
$231$		0			0
$232$	74.5934	−	131.467i	0.321523	−	0.566668i
$233$	121.475			0.521352			0.260676	−	0.965426i	$-0.416055\pi$
$233$	121.475			0.521352			0.260676	+	0.965426i	$0.416055\pi$
$234$		0			0
$235$		0			0
$236$	87.2406	−	243.473i	0.369664	−	1.03166i
$237$		0			0
$238$	−693.553	−	120.505i	−2.91409	−	0.506323i
$239$			160.843i			0.672984i	0.941686	+	0.336492i	$0.109240\pi$
$239$			160.843i			0.672984i	−0.941686	+	0.336492i	$0.890760\pi$
$240$		0			0
$241$	−3.49419			−0.0144987			−0.00724935	−	0.999974i	$-0.502308\pi$
$241$	−3.49419			−0.0144987			−0.00724935	+	0.999974i	$0.502308\pi$
$242$	−7.36031	+	42.3615i	−0.0304145	+	0.175047i
$243$		0			0
$244$	113.905	+	40.8141i	0.466822	+	0.167271i
$245$		0			0
$246$		0			0
$247$		−	172.706i		−	0.699216i
$248$	−245.263	−	139.160i	−0.988963	−	0.561130i
$249$		0			0
$250$		0			0
$251$			315.637i			1.25752i	0.777601	+	0.628759i	$0.216437\pi$
$251$			315.637i			1.25752i	−0.777601	+	0.628759i	$0.783563\pi$
$252$		0			0
$253$	−157.245			−0.621522
$254$	394.062	+	68.4684i	1.55143	+	0.269561i
$255$		0			0
$256$	49.4873	+	251.171i	0.193310	+	0.981138i
$257$	−86.8117			−0.337789			−0.168894	−	0.985634i	$-0.554020\pi$
$257$	−86.8117			−0.337789			−0.168894	+	0.985634i	$0.554020\pi$
$258$		0			0
$259$		−	576.972i		−	2.22769i
$260$		0			0
$261$		0			0
$262$	487.523	+	84.7073i	1.86078	+	0.323310i
$263$			333.003i			1.26617i	0.774082	+	0.633086i	$0.218212\pi$
$263$			333.003i			1.26617i	−0.774082	+	0.633086i	$0.781788\pi$
$264$		0			0
$265$		0			0
$266$	−48.1877	+	277.339i	−0.181157	+	1.04263i
$267$		0			0
$268$	89.3190	−	249.273i	0.333280	−	0.930124i
$269$	−191.063			−0.710271			−0.355136	−	0.934815i	$-0.615565\pi$
$269$	−191.063			−0.710271			−0.355136	+	0.934815i	$0.615565\pi$
$270$		0			0
$271$		−	261.165i		−	0.963708i	−0.876252	−	0.481854i	$-0.839964\pi$
$271$		−	261.165i		−	0.963708i	0.876252	−	0.481854i	$-0.160036\pi$
$272$	377.907	+	310.714i	1.38936	+	1.14233i
$273$		0			0
$274$	−48.4027	+	278.577i	−0.176652	+	1.01670i
$275$		0			0
$276$		0			0
$277$	204.615			0.738682			0.369341	−	0.929294i	$-0.379583\pi$
$277$	204.615			0.738682			0.369341	+	0.929294i	$0.379583\pi$
$278$	−114.821	−	19.9501i	−0.413024	−	0.0717631i
$279$		0			0
$280$		0			0
$281$	−458.726			−1.63248			−0.816239	−	0.577714i	$-0.803945\pi$
$281$	−458.726			−1.63248			−0.816239	+	0.577714i	$0.803945\pi$
$282$		0			0
$283$			336.724i			1.18984i	0.803786	+	0.594918i	$0.202816\pi$
$283$			336.724i			1.18984i	−0.803786	+	0.594918i	$0.797184\pi$
$284$	−15.6212	+	43.5959i	−0.0550041	+	0.153507i
$285$		0			0
$286$	−277.626	−	48.2376i	−0.970722	−	0.168663i
$287$			332.022i			1.15687i
$288$		0			0
$289$	645.988			2.23525
$290$		0			0
$291$		0			0
$292$	8.46887	+	3.03455i	0.0290030	+	0.0103923i
$293$	249.650			0.852046			0.426023	−	0.904712i	$-0.359914\pi$
$293$	249.650			0.852046			0.426023	+	0.904712i	$0.359914\pi$
$294$		0			0
$295$		0			0
$296$	−197.888	+	348.767i	−0.668539	+	1.17827i
$297$		0			0
$298$	−90.9086	+	523.214i	−0.305062	+	1.75575i
$299$			222.656i			0.744670i
$300$		0			0
$301$	−281.494			−0.935197
$302$	429.541	+	74.6328i	1.42232	+	0.247128i
$303$		0			0
$304$	124.249	−	151.118i	0.408714	−	0.497099i
$305$		0			0
$306$		0			0
$307$		−	156.851i		−	0.510916i	−0.966820	−	0.255458i	$-0.917774\pi$
$307$		−	156.851i		−	0.510916i	0.966820	−	0.255458i	$-0.0822262\pi$
$308$	432.365	+	154.924i	1.40378	+	0.503000i
$309$		0			0
$310$		0			0
$311$			164.769i			0.529803i	0.964275	+	0.264902i	$0.0853395\pi$
$311$			164.769i			0.529803i	−0.964275	+	0.264902i	$0.914661\pi$
$312$		0			0
$313$	131.992			0.421700			0.210850	−	0.977518i	$-0.432377\pi$
$313$	131.992			0.421700			0.210850	+	0.977518i	$0.432377\pi$
$314$	22.7244	−	130.788i	0.0723706	−	0.416521i
$315$		0			0
$316$	105.817	−	295.316i	0.334864	−	0.934546i
$317$	−169.833			−0.535752			−0.267876	−	0.963453i	$-0.586322\pi$
$317$	−169.833			−0.535752			−0.267876	+	0.963453i	$0.586322\pi$
$318$		0			0
$319$			188.472i			0.590822i
$320$		0			0
$321$		0			0
$322$	62.1245	−	357.551i	0.192933	−	1.11041i
$323$		−	373.885i		−	1.15754i
$324$		0			0
$325$		0			0
$326$	184.278	+	32.0184i	0.565270	+	0.0982158i
$327$		0			0
$328$	113.875	−	200.700i	0.347181	−	0.611889i
$329$	−640.737			−1.94753
$330$		0			0
$331$		−	171.945i		−	0.519472i	−0.965680	−	0.259736i	$-0.916365\pi$
$331$		−	171.945i		−	0.519472i	0.965680	−	0.259736i	$-0.0836355\pi$
$332$	197.075	−	550.001i	0.593600	−	1.65663i
$333$		0			0
$334$	93.1868	+	16.1912i	0.279002	+	0.0484767i
$335$		0			0
$336$		0			0
$337$	470.249			1.39540			0.697699	−	0.716391i	$-0.254207\pi$
$337$	470.249			1.39540			0.697699	+	0.716391i	$0.254207\pi$
$338$	−10.4430	+	60.1034i	−0.0308964	+	0.177821i
$339$		0			0
$340$		0			0
$341$	351.611			1.03112
$342$		0			0
$343$		−	397.100i		−	1.15772i
$344$	170.157	+	96.5458i	0.494642	+	0.280656i
$345$		0			0
$346$	78.5856	−	452.291i	0.227126	−	1.30720i
$347$			167.974i			0.484074i	0.970267	+	0.242037i	$0.0778155\pi$
$347$			167.974i			0.484074i	−0.970267	+	0.242037i	$0.922184\pi$
$348$		0			0
$349$	−158.747			−0.454863			−0.227431	−	0.973794i	$-0.573033\pi$
$349$	−158.747			−0.454863			−0.227431	+	0.973794i	$0.573033\pi$
$350$		0			0
$351$		0			0
$352$	−208.220	−	241.939i	−0.591534	−	0.687327i
$353$	201.076			0.569619			0.284810	−	0.958584i	$-0.408070\pi$
$353$	201.076			0.569619			0.284810	+	0.958584i	$0.408070\pi$
$354$		0			0
$355$		0			0
$356$	329.228	+	117.968i	0.924796	+	0.331371i
$357$		0			0
$358$	−297.282	−	51.6528i	−0.830397	−	0.144282i
$359$		−	689.161i		−	1.91967i	−0.280567	−	0.959835i	$-0.590522\pi$
$359$		−	689.161i		−	1.91967i	0.280567	−	0.959835i	$-0.409478\pi$
$360$		0			0
$361$	211.490			0.585846
$362$	−18.6585	+	107.387i	−0.0515429	+	0.296650i
$363$		0			0
$364$	219.370	−	612.221i	0.602664	−	1.68193i
$365$		0			0
$366$		0			0
$367$			11.5108i			0.0313645i	0.999877	+	0.0156823i	$0.00499202\pi$
$367$			11.5108i			0.0313645i	−0.999877	+	0.0156823i	$0.995008\pi$
$368$	−160.184	+	194.824i	−0.435283	+	0.529414i
$369$		0			0
$370$		0			0
$371$		−	28.3228i		−	0.0763417i
$372$		0			0
$373$	−356.864			−0.956740			−0.478370	−	0.878159i	$-0.658772\pi$
$373$	−356.864			−0.956740			−0.478370	+	0.878159i	$0.658772\pi$
$374$	−601.022	−	104.428i	−1.60701	−	0.279218i
$375$		0			0
$376$	387.311	+	219.757i	1.03008	+	0.584461i
$377$	266.873			0.707887
$378$		0			0
$379$			554.623i			1.46338i	0.681635	+	0.731692i	$0.261269\pi$
$379$			554.623i			1.46338i	−0.681635	+	0.731692i	$0.738731\pi$
$380$		0			0
$381$		0			0
$382$	445.055	+	77.3283i	1.16506	+	0.202430i
$383$		−	442.368i		−	1.15501i	−0.816388	−	0.577504i	$-0.804027\pi$
$383$		−	442.368i		−	1.15501i	0.816388	−	0.577504i	$-0.195973\pi$
$384$		0			0
$385$		0			0
$386$	59.7430	−	343.845i	0.154775	−	0.890789i
$387$		0			0
$388$	477.274	+	171.016i	1.23009	+	0.440762i
$389$	356.424			0.916257			0.458129	−	0.888886i	$-0.348520\pi$
$389$	356.424			0.916257			0.458129	+	0.888886i	$0.348520\pi$
$390$		0			0
$391$			482.020i			1.23279i
$392$	−329.644	+	580.980i	−0.840928	+	1.48209i
$393$		0			0
$394$	−5.47275	+	31.4978i	−0.0138902	+	0.0799436i
$395$		0			0
$396$		0			0
$397$	−512.864			−1.29185			−0.645924	−	0.763402i	$-0.723528\pi$
$397$	−512.864			−1.29185			−0.645924	+	0.763402i	$0.723528\pi$
$398$	60.9846	+	10.5961i	0.153228	+	0.0266233i
$399$		0			0
$400$		0			0
$401$	10.3990			0.0259327			0.0129664	−	0.999916i	$-0.495873\pi$
$401$	10.3990			0.0259327			0.0129664	+	0.999916i	$0.495873\pi$
$402$		0			0
$403$		−	497.875i		−	1.23542i
$404$	249.221	+	89.3002i	0.616883	+	0.221040i
$405$		0			0
$406$	−428.556	−	74.4618i	−1.05556	−	0.183403i
$407$		−	499.995i		−	1.22849i
$408$		0			0
$409$	251.494			0.614900			0.307450	−	0.951564i	$-0.400524\pi$
$409$	251.494			0.614900			0.307450	+	0.951564i	$0.400524\pi$
$410$		0			0
$411$		0			0
$412$	−141.714	+	395.498i	−0.343966	+	0.959947i
$413$	−744.261			−1.80208
$414$		0			0
$415$		0			0
$416$	−342.581	+	294.836i	−0.823513	+	0.708739i
$417$		0			0
$418$	−41.7587	+	240.338i	−0.0999012	+	0.574971i
$419$		−	205.551i		−	0.490574i	−0.969450	−	0.245287i	$-0.921118\pi$
$419$		−	205.551i		−	0.490574i	0.969450	−	0.245287i	$-0.0788823\pi$
$420$		0			0
$421$	811.230			1.92691			0.963456	−	0.267868i	$-0.0863191\pi$
$421$	811.230			1.92691			0.963456	+	0.267868i	$0.0863191\pi$
$422$	−375.705	−	65.2788i	−0.890296	−	0.154689i
$423$		0			0
$424$	−9.71403	+	17.1205i	−0.0229104	+	0.0403785i
$425$		0			0
$426$		0			0
$427$		−	348.190i		−	0.815433i
$428$	−92.0511	+	256.898i	−0.215073	+	0.600229i
$429$		0			0
$430$		0			0
$431$			359.624i			0.834394i	0.908816	+	0.417197i	$0.136987\pi$
$431$			359.624i			0.834394i	−0.908816	+	0.417197i	$0.863013\pi$
$432$		0			0
$433$	198.747			0.459000			0.229500	−	0.973309i	$-0.426291\pi$
$433$	198.747			0.459000			0.229500	+	0.973309i	$0.426291\pi$
$434$	−138.915	+	799.508i	−0.320080	+	1.84218i
$435$		0			0
$436$	126.154	+	45.2031i	0.289343	+	0.103677i
$437$	192.751			0.441077
$438$		0			0
$439$		−	353.251i		−	0.804672i	−0.915492	−	0.402336i	$-0.868198\pi$
$439$		−	353.251i		−	0.804672i	0.915492	−	0.402336i	$-0.131802\pi$
$440$		0			0
$441$		0			0
$442$	−147.868	+	851.036i	−0.334542	+	1.92542i
$443$			209.837i			0.473672i	0.971550	+	0.236836i	$0.0761104\pi$
$443$			209.837i			0.473672i	−0.971550	+	0.236836i	$0.923890\pi$
$444$		0			0
$445$		0			0
$446$	−626.528	−	108.859i	−1.40477	−	0.244079i
$447$		0			0
$448$	632.395	−	377.874i	1.41160	−	0.843468i
$449$	617.155			1.37451			0.687255	−	0.726416i	$-0.258816\pi$
$449$	617.155			1.37451			0.687255	+	0.726416i	$0.258816\pi$
$450$		0			0
$451$			287.725i			0.637971i
$452$	−542.029	−	194.219i	−1.19918	−	0.429687i
$453$		0			0
$454$	−78.6226	−	13.6607i	−0.173177	−	0.0300896i
$455$		0			0
$456$		0			0
$457$	129.253			0.282829			0.141415	−	0.989950i	$-0.454835\pi$
$457$	129.253			0.282829			0.141415	+	0.989950i	$0.454835\pi$
$458$	−4.70793	+	27.0960i	−0.0102793	+	0.0591615i
$459$		0			0
$460$		0			0
$461$	18.6785			0.0405174			0.0202587	−	0.999795i	$-0.493551\pi$
$461$	18.6785			0.0405174			0.0202587	+	0.999795i	$0.493551\pi$
$462$		0			0
$463$			109.419i			0.236327i	0.992994	+	0.118163i	$0.0377007\pi$
$463$			109.419i			0.236327i	−0.992994	+	0.118163i	$0.962299\pi$
$464$	233.514	+	191.995i	0.503263	+	0.413782i
$465$		0			0
$466$	−41.5895	+	239.364i	−0.0892479	+	0.513656i
$467$			250.979i			0.537428i	0.963220	+	0.268714i	$0.0865987\pi$
$467$			250.979i			0.537428i	−0.963220	+	0.268714i	$0.913401\pi$
$468$		0			0
$469$	−761.992			−1.62472
$470$		0			0
$471$		0			0
$472$	449.889	+	255.264i	0.953155	+	0.540813i
$473$	−243.939			−0.515726
$474$		0			0
$475$		0			0
$476$	474.904	−	1325.37i	0.997698	−	2.78440i
$477$		0			0
$478$	−316.938	−	55.0680i	−0.663050	−	0.115205i
$479$		−	373.164i		−	0.779048i	−0.921016	−	0.389524i	$-0.872640\pi$
$479$		−	373.164i		−	0.779048i	0.921016	−	0.389524i	$-0.127360\pi$
$480$		0			0
$481$	−707.984			−1.47190
$482$	1.19631	−	6.88522i	0.00248197	−	0.0142847i
$483$		0			0
$484$	−80.9523	−	29.0066i	−0.167257	−	0.0599311i
$485$		0			0
$486$		0			0
$487$			182.784i			0.375326i	0.982233	+	0.187663i	$0.0600913\pi$
$487$			182.784i			0.375326i	−0.982233	+	0.187663i	$0.939909\pi$
$488$	−119.421	+	210.473i	−0.244715	+	0.431297i
$489$		0			0
$490$		0			0
$491$		−	413.425i		−	0.842005i	−0.907059	−	0.421003i	$-0.861678\pi$
$491$		−	413.425i		−	0.842005i	0.907059	−	0.421003i	$-0.138322\pi$
$492$		0			0
$493$	577.743			1.17189
$494$	340.314	+	59.1296i	0.688895	+	0.119696i
$495$		0			0
$496$	358.183	−	435.640i	0.722143	−	0.878307i
$497$	133.266			0.268141
$498$		0			0
$499$			92.8475i			0.186067i	0.995663	+	0.0930336i	$0.0296564\pi$
$499$			92.8475i			0.186067i	−0.995663	+	0.0930336i	$0.970344\pi$
$500$		0			0
$501$		0			0
$502$	−621.955	−	108.065i	−1.23895	−	0.215269i
$503$		−	415.288i		−	0.825622i	−0.910817	−	0.412811i	$-0.864547\pi$
$503$		−	415.288i		−	0.825622i	0.910817	−	0.412811i	$-0.135453\pi$
$504$		0			0
$505$		0			0
$506$	53.8362	−	309.848i	0.106396	−	0.612348i
$507$		0			0
$508$	−269.831	+	753.049i	−0.531163	+	1.48238i
$509$	396.009			0.778013			0.389006	−	0.921235i	$-0.372818\pi$
$509$	396.009			0.778013			0.389006	+	0.921235i	$0.372818\pi$
$510$		0			0
$511$		−	25.8881i		−	0.0506616i
$512$	−511.870	+	11.5200i	−0.999747	+	0.0225000i
$513$		0			0
$514$	29.7218	−	171.060i	0.0578245	−	0.332802i
$515$		0			0
$516$		0			0
$517$	−555.253			−1.07399
$518$	1136.91	+	197.538i	2.19481	+	0.381348i
$519$		0			0
$520$		0			0
$521$	356.191			0.683668			0.341834	−	0.939760i	$-0.388952\pi$
$521$	356.191			0.683668			0.341834	+	0.939760i	$0.388952\pi$
$522$		0			0
$523$			261.837i			0.500644i	0.968163	+	0.250322i	$0.0805365\pi$
$523$			261.837i			0.500644i	−0.968163	+	0.250322i	$0.919464\pi$
$524$	−333.828	+	931.653i	−0.637075	+	1.77796i
$525$		0			0
$526$	−656.175	−	114.011i	−1.24748	−	0.216750i
$527$		−	1077.83i		−	2.04522i
$528$		0			0
$529$	280.502			0.530249
$530$		0			0
$531$		0			0
$532$	−529.992	−	189.906i	−0.996226	−	0.356965i
$533$	407.413			0.764378
$534$		0			0
$535$		0			0
$536$	460.607	+	261.345i	0.859342	+	0.487584i
$537$		0			0
$538$	65.4144	−	376.485i	0.121588	−	0.699787i
$539$		−	832.899i		−	1.54527i
$540$		0			0
$541$	−581.984			−1.07576			−0.537878	−	0.843022i	$-0.680774\pi$
$541$	−581.984			−1.07576			−0.537878	+	0.843022i	$0.680774\pi$
$542$	514.619	+	89.4152i	0.949482	+	0.164973i
$543$		0			0
$544$	−741.640	+	638.277i	−1.36331	+	1.17330i
$545$		0			0
$546$		0			0
$547$		−	84.8307i		−	0.155083i	−0.996989	−	0.0775417i	$-0.975293\pi$
$547$		−	84.8307i		−	0.155083i	0.996989	−	0.0775417i	$-0.0247071\pi$
$548$	−532.357	−	190.753i	−0.971455	−	0.348089i
$549$		0			0
$550$		0			0
$551$		−	231.029i		−	0.419290i
$552$		0			0
$553$	−902.739			−1.63244
$554$	−70.0541	+	403.189i	−0.126452	+	0.727778i
$555$		0			0
$556$	78.6226	−	219.421i	0.141408	−	0.394643i
$557$	−708.933			−1.27277			−0.636385	−	0.771372i	$-0.719571\pi$
$557$	−708.933			−1.27277			−0.636385	+	0.771372i	$0.719571\pi$
$558$		0			0
$559$			345.413i			0.617912i
$560$		0			0
$561$		0			0
$562$	157.055	−	903.910i	0.279456	−	1.60838i
$563$		−	1094.57i		−	1.94418i	−0.234607	−	0.972090i	$-0.575380\pi$
$563$		−	1094.57i		−	1.94418i	0.234607	−	0.972090i	$-0.424620\pi$
$564$		0			0
$565$		0			0
$566$	−663.507	−	115.284i	−1.17227	−	0.203683i
$567$		0			0
$568$	−80.5564	−	45.7071i	−0.141825	−	0.0804703i
$569$	−769.082			−1.35164			−0.675819	−	0.737068i	$-0.736210\pi$
$569$	−769.082			−1.35164			−0.675819	+	0.737068i	$0.736210\pi$
$570$		0			0
$571$		−	871.192i		−	1.52573i	−0.646558	−	0.762865i	$-0.723792\pi$
$571$		−	871.192i		−	1.52573i	0.646558	−	0.762865i	$-0.276208\pi$
$572$	190.102	−	530.542i	0.332347	−	0.927520i
$573$		0			0
$574$	−654.241	−	113.675i	−1.13979	−	0.198039i
$575$		0			0
$576$		0			0
$577$	−216.739			−0.375631			−0.187816	−	0.982204i	$-0.560141\pi$
$577$	−216.739			−0.375631			−0.187816	+	0.982204i	$0.560141\pi$
$578$	−221.168	+	1272.91i	−0.382643	+	2.20226i
$579$		0			0
$580$		0			0
$581$	−1681.27			−2.89376
$582$		0			0
$583$		−	24.5441i		−	0.0420996i
$584$	−8.87900	+	15.6488i	−0.0152038	+	0.0267959i
$585$		0			0
$586$	−85.4727	+	491.929i	−0.145858	+	0.839469i
$587$		−	148.024i		−	0.252170i	−0.992019	−	0.126085i	$-0.959759\pi$
$587$		−	148.024i		−	0.252170i	0.992019	−	0.126085i	$-0.0402411\pi$
$588$		0			0
$589$	−431.004			−0.731755
$590$		0			0
$591$		0			0
$592$	−619.486	−	509.341i	−1.04643	−	0.860373i
$593$	−102.473			−0.172804			−0.0864020	−	0.996260i	$-0.527537\pi$
$593$	−102.473			−0.172804			−0.0864020	+	0.996260i	$0.527537\pi$
$594$		0			0
$595$		0			0
$596$	−999.857	−	358.267i	−1.67761	−	0.601118i
$597$		0			0
$598$	−438.739	−	76.2310i	−0.733678	−	0.127477i
$599$		−	353.214i		−	0.589673i	−0.955548	−	0.294836i	$-0.904735\pi$
$599$		−	353.214i		−	0.589673i	0.955548	−	0.294836i	$-0.0952651\pi$
$600$		0			0
$601$	422.498			0.702992			0.351496	−	0.936189i	$-0.385673\pi$
$601$	422.498			0.702992			0.351496	+	0.936189i	$0.385673\pi$
$602$	96.3754	−	554.678i	0.160092	−	0.921392i
$603$		0			0
$604$	−294.125	+	820.849i	−0.486961	+	1.35902i
$605$		0			0
$606$		0			0
$607$			958.261i			1.57868i	0.613954	+	0.789342i	$0.289578\pi$
$607$			958.261i			1.57868i	−0.613954	+	0.789342i	$0.710422\pi$
$608$	255.235	+	296.568i	0.419795	+	0.487777i
$609$		0			0
$610$		0			0
$611$			786.228i			1.28679i
$612$		0			0
$613$	885.611			1.44472			0.722358	−	0.691519i	$-0.243058\pi$
$613$	885.611			1.44472			0.722358	+	0.691519i	$0.243058\pi$
$614$	309.072	+	53.7012i	0.503374	+	0.0874613i
$615$		0			0
$616$	−453.304	+	798.924i	−0.735882	+	1.29695i
$617$	37.8513			0.0613473			0.0306737	−	0.999529i	$-0.490235\pi$
$617$	37.8513			0.0613473			0.0306737	+	0.999529i	$0.490235\pi$
$618$		0			0
$619$			544.679i			0.879934i	0.898014	+	0.439967i	$0.145010\pi$
$619$			544.679i			0.879934i	−0.898014	+	0.439967i	$0.854990\pi$
$620$		0			0
$621$		0			0
$622$	−324.673	−	56.4120i	−0.521983	−	0.0906946i
$623$		−	1006.40i		−	1.61541i
$624$		0			0
$625$		0			0
$626$	−45.1903	+	260.088i	−0.0721890	+	0.415476i
$627$		0			0
$628$	249.934	+	89.5557i	0.397984	+	0.142605i
$629$	−1532.69			−2.43670
$630$		0			0
$631$			665.520i			1.05471i	0.849646	+	0.527353i	$0.176816\pi$
$631$			665.520i			1.05471i	−0.849646	+	0.527353i	$0.823184\pi$
$632$	545.686	+	309.618i	0.863427	+	0.489902i
$633$		0			0
$634$	58.1460	−	334.653i	0.0917129	−	0.527843i
$635$		0			0
$636$		0			0
$637$	−1179.37			−1.85144
$638$	−371.380	−	64.5274i	−0.582101	−	0.101140i
$639$		0			0
$640$		0			0
$641$	1089.06			1.69901			0.849504	−	0.527582i	$-0.176901\pi$
$641$	1089.06			1.69901			0.849504	+	0.527582i	$0.176901\pi$
$642$		0			0
$643$			277.692i			0.431869i	0.976408	+	0.215935i	$0.0692798\pi$
$643$			277.692i			0.431869i	−0.976408	+	0.215935i	$0.930720\pi$
$644$	683.276	+	244.830i	1.06099	+	0.380171i
$645$		0			0
$646$	736.732	+	128.007i	1.14045	+	0.198154i
$647$			1049.77i			1.62251i	0.584690	+	0.811257i	$0.301216\pi$
$647$			1049.77i			1.62251i	−0.584690	+	0.811257i	$0.698784\pi$
$648$		0			0
$649$	−644.965			−0.993783
$650$		0			0
$651$		0			0
$652$	−126.183	+	352.154i	−0.193532	+	0.540113i
$653$	−110.008			−0.168465			−0.0842325	−	0.996446i	$-0.526844\pi$
$653$	−110.008			−0.168465			−0.0842325	+	0.996446i	$0.526844\pi$
$654$		0			0
$655$		0			0
$656$	356.487	+	293.103i	0.543425	+	0.446803i
$657$		0			0
$658$	219.370	−	1262.56i	0.333389	−	1.91878i
$659$		−	363.189i		−	0.551121i	−0.961284	−	0.275561i	$-0.911137\pi$
$659$		−	363.189i		−	0.551121i	0.961284	−	0.275561i	$-0.0888635\pi$
$660$		0			0
$661$	−801.735			−1.21291			−0.606456	−	0.795117i	$-0.707410\pi$
$661$	−801.735			−1.21291			−0.606456	+	0.795117i	$0.707410\pi$
$662$	338.814	+	58.8690i	0.511803	+	0.0889259i
$663$		0			0
$664$	1016.29	+	576.636i	1.53056	+	0.868428i
$665$		0			0
$666$		0			0
$667$			297.847i			0.446547i
$668$	−63.8089	+	178.079i	−0.0955223	+	0.266585i
$669$		0			0
$670$		0			0
$671$		−	301.736i		−	0.449681i
$672$		0			0
$673$	447.743			0.665295			0.332647	−	0.943051i	$-0.392058\pi$
$673$	447.743			0.665295			0.332647	+	0.943051i	$0.392058\pi$
$674$	−161.000	+	926.615i	−0.238872	+	1.37480i
$675$		0			0
$676$	−114.857	−	41.1553i	−0.169907	−	0.0608806i
$677$	−299.167			−0.441901			−0.220950	−	0.975285i	$-0.570916\pi$
$677$	−299.167			−0.441901			−0.220950	+	0.975285i	$0.570916\pi$
$678$		0			0
$679$		−	1458.96i		−	2.14869i
$680$		0			0
$681$		0			0
$682$	−120.381	+	692.841i	−0.176512	+	1.01590i
$683$		−	339.673i		−	0.497326i	−0.968590	−	0.248663i	$-0.920009\pi$
$683$		−	339.673i		−	0.497326i	0.968590	−	0.248663i	$-0.0799911\pi$
$684$		0			0
$685$		0			0
$686$	782.476	+	135.955i	1.14064	+	0.198186i
$687$		0			0
$688$	−248.498	+	302.236i	−0.361189	+	0.439297i
$689$	−34.7540			−0.0504412
$690$		0			0
$691$		−	764.773i		−	1.10676i	−0.832928	−	0.553381i	$-0.813337\pi$
$691$		−	764.773i		−	1.10676i	0.832928	−	0.553381i	$-0.186663\pi$
$692$	864.324	+	309.702i	1.24902	+	0.447547i
$693$		0			0
$694$	−330.988	−	57.5093i	−0.476928	−	0.0828664i
$695$		0			0
$696$		0			0
$697$	881.992			1.26541
$698$	54.3504	−	312.808i	0.0778659	−	0.448148i
$699$		0			0
$700$		0			0
$701$	308.111			0.439531			0.219765	−	0.975553i	$-0.429471\pi$
$701$	308.111			0.439531			0.219765	+	0.975553i	$0.429471\pi$
$702$		0			0
$703$			612.893i			0.871825i
$704$	548.024	−	327.460i	0.778443	−	0.465142i
$705$		0			0
$706$	−68.8424	+	396.215i	−0.0975105	+	0.561211i
$707$		−	761.831i		−	1.07755i
$708$		0			0
$709$	−882.249			−1.24436			−0.622178	−	0.782875i	$-0.713752\pi$
$709$	−882.249			−1.24436			−0.622178	+	0.782875i	$0.713752\pi$
$710$		0			0
$711$		0			0
$712$	−345.171	+	608.347i	−0.484791	+	0.854420i
$713$	555.659			0.779325
$714$		0			0
$715$		0			0
$716$	203.561	−	568.103i	0.284304	−	0.793440i
$717$		0			0
$718$	1357.98	+	235.949i	1.89133	+	0.328619i
$719$		−	766.999i		−	1.06676i	−0.845876	−	0.533379i	$-0.820922\pi$
$719$		−	766.999i		−	1.06676i	0.845876	−	0.533379i	$-0.179078\pi$
$720$		0			0
$721$	1208.98			1.67681
$722$	−72.4081	+	416.737i	−0.100288	+	0.577198i
$723$		0			0
$724$	−205.216	−	73.5325i	−0.283447	−	0.101564i
$725$		0			0
$726$		0			0
$727$			735.301i			1.01142i	0.862704	+	0.505709i	$0.168769\pi$
$727$			735.301i			1.01142i	−0.862704	+	0.505709i	$0.831231\pi$
$728$	1131.26	+	641.870i	1.55393	+	0.881689i
$729$		0			0
$730$		0			0
$731$			747.770i			1.02294i
$732$		0			0
$733$	−269.377			−0.367500			−0.183750	−	0.982973i	$-0.558824\pi$
$733$	−269.377			−0.367500			−0.183750	+	0.982973i	$0.558824\pi$
$734$	−22.6817	−	3.94096i	−0.0309015	−	0.00536915i
$735$		0			0
$736$	−329.055	−	382.342i	−0.447085	−	0.519486i
$737$	−660.331			−0.895971
$738$		0			0
$739$		−	807.949i		−	1.09330i	−0.837361	−	0.546650i	$-0.815903\pi$
$739$		−	807.949i		−	1.09330i	0.837361	−	0.546650i	$-0.184097\pi$
$740$		0			0
$741$		0			0
$742$	55.8094	+	9.69688i	0.0752148	+	0.0130686i
$743$			1017.72i			1.36974i	0.728665	+	0.684870i	$0.240141\pi$
$743$			1017.72i			1.36974i	−0.728665	+	0.684870i	$0.759859\pi$
$744$		0			0
$745$		0			0
$746$	122.180	−	703.192i	0.163780	−	0.942617i
$747$		0			0
$748$	411.545	−	1148.55i	0.550194	−	1.53549i
$749$	785.300			1.04846
$750$		0			0
$751$			551.845i			0.734814i	0.930060	+	0.367407i	$0.119754\pi$
$751$			551.845i			0.734814i	−0.930060	+	0.367407i	$0.880246\pi$
$752$	−565.631	+	687.950i	−0.752169	+	0.914827i
$753$		0			0
$754$	−91.3697	+	525.868i	−0.121180	+	0.697438i
$755$		0			0
$756$		0			0
$757$	−1168.86			−1.54407			−0.772037	−	0.635578i	$-0.780762\pi$
$757$	−1168.86			−1.54407			−0.772037	+	0.635578i	$0.780762\pi$
$758$	−1092.87	−	189.887i	−1.44178	−	0.250510i
$759$		0			0
$760$		0			0
$761$	−221.811			−0.291473			−0.145737	−	0.989323i	$-0.546555\pi$
$761$	−221.811			−0.291473			−0.145737	+	0.989323i	$0.546555\pi$
$762$		0			0
$763$		−	385.633i		−	0.505417i
$764$	−304.747	+	850.495i	−0.398884	+	1.11321i
$765$		0			0
$766$	871.677	+	151.454i	1.13796	+	0.197721i
$767$			913.259i			1.19069i
$768$		0			0
$769$	34.5136			0.0448811			0.0224406	−	0.999748i	$-0.492856\pi$
$769$	34.5136			0.0448811			0.0224406	+	0.999748i	$0.492856\pi$
$770$		0			0
$771$		0			0
$772$	657.084	+	235.445i	0.851145	+	0.304980i
$773$	401.055			0.518829			0.259415	−	0.965766i	$-0.416470\pi$
$773$	401.055			0.518829			0.259415	+	0.965766i	$0.416470\pi$
$774$		0			0
$775$		0			0
$776$	−500.388	+	881.908i	−0.644829	+	1.13648i
$777$		0			0
$778$	−122.029	+	702.326i	−0.156850	+	0.902732i
$779$		−	352.693i		−	0.452750i
$780$		0			0
$781$	115.486			0.147870
$782$	−949.809	−	165.029i	−1.21459	−	0.211035i
$783$		0			0
$784$	−1031.95	−	848.467i	−1.31626	−	1.08223i
$785$		0			0
$786$		0			0
$787$		−	1030.24i		−	1.30907i	−0.756032	−	0.654534i	$-0.772865\pi$
$787$		−	1030.24i		−	1.30907i	0.756032	−	0.654534i	$-0.227135\pi$
$788$	−60.1920	−	21.5679i	−0.0763858	−	0.0273704i
$789$		0			0
$790$		0			0
$791$			1656.90i			2.09469i
$792$		0			0
$793$	−427.253			−0.538780
$794$	175.590	−	1010.59i	0.221146	−	1.27278i
$795$		0			0
$796$	−41.7587	+	116.541i	−0.0524607	+	0.146408i
$797$	1070.94			1.34372			0.671859	−	0.740679i	$-0.265496\pi$
$797$	1070.94			1.34372			0.671859	+	0.740679i	$0.265496\pi$
$798$		0			0
$799$			1702.07i			2.13025i
$800$		0			0
$801$		0			0
$802$	−3.56032	+	20.4910i	−0.00443930	+	0.0255499i
$803$		−	22.4342i		−	0.0279380i
$804$		0			0
$805$		0			0
$806$	981.051	+	170.458i	1.21718	+	0.211486i
$807$		0			0
$808$	−261.290	+	460.510i	−0.323379	+	0.569938i
$809$	1265.04			1.56371			0.781854	−	0.623461i	$-0.214274\pi$
$809$	1265.04			1.56371			0.781854	+	0.623461i	$0.214274\pi$
$810$		0			0
$811$		−	966.144i		−	1.19130i	−0.803244	−	0.595650i	$-0.796895\pi$
$811$		−	966.144i		−	1.19130i	0.803244	−	0.595650i	$-0.203105\pi$
$812$	293.450	−	818.967i	0.361392	−	1.00858i
$813$		0			0
$814$	985.230	+	171.184i	1.21036	+	0.210300i
$815$		0			0
$816$		0			0
$817$	299.019			0.365997
$818$	−86.1043	+	495.564i	−0.105262	+	0.605824i
$819$		0			0
$820$		0			0
$821$	878.408			1.06992			0.534962	−	0.844876i	$-0.320326\pi$
$821$	878.408			1.06992			0.534962	+	0.844876i	$0.320326\pi$
$822$		0			0
$823$		−	887.674i		−	1.07858i	−0.842119	−	0.539292i	$-0.818692\pi$
$823$		−	887.674i		−	1.07858i	0.842119	−	0.539292i	$-0.181308\pi$
$824$	−730.802	−	414.651i	−0.886895	−	0.503218i
$825$		0			0
$826$	254.813	−	1466.55i	0.308491	−	1.77548i
$827$			82.2846i			0.0994977i	0.998762	+	0.0497489i	$0.0158421\pi$
$827$			82.2846i			0.0994977i	−0.998762	+	0.0497489i	$0.984158\pi$
$828$		0			0
$829$	348.475			0.420356			0.210178	−	0.977663i	$-0.432596\pi$
$829$	348.475			0.420356			0.210178	+	0.977663i	$0.432596\pi$
$830$		0			0
$831$		0			0
$832$	−463.677	−	775.992i	−0.557304	−	0.932683i
$833$	−2553.17			−3.06503
$834$		0			0
$835$		0			0
$836$	−459.283	−	164.569i	−0.549382	−	0.196853i
$837$		0			0
$838$	405.033	+	70.3746i	0.483333	+	0.0839792i
$839$			174.383i			0.207847i	0.994585	+	0.103923i	$0.0331397\pi$
$839$			174.383i			0.207847i	−0.994585	+	0.103923i	$0.966860\pi$
$840$		0			0
$841$	−484.004			−0.575510
$842$	−277.741	+	1598.51i	−0.329859	+	1.89847i
$843$		0			0
$844$	257.261	−	717.968i	0.304811	−	0.850673i
$845$		0			0
$846$		0			0
$847$			247.459i			0.292160i
$848$	−30.4097	−	25.0028i	−0.0358605	−	0.0294845i
$849$		0			0
$850$		0			0
$851$		−	790.154i		−	0.928500i
$852$		0			0
$853$	1549.11			1.81608			0.908038	−	0.418888i	$-0.137580\pi$
$853$	1549.11			1.81608			0.908038	+	0.418888i	$0.137580\pi$
$854$	686.101	+	119.210i	0.803396	+	0.139590i
$855$		0			0
$856$	−474.696	−	269.339i	−0.554552	−	0.314649i
$857$	376.279			0.439065			0.219533	−	0.975605i	$-0.429547\pi$
$857$	376.279			0.439065			0.219533	+	0.975605i	$0.429547\pi$
$858$		0			0
$859$			1495.73i			1.74124i	0.491952	+	0.870622i	$0.336284\pi$
$859$			1495.73i			1.74124i	−0.491952	+	0.870622i	$0.663716\pi$
$860$		0			0
$861$		0			0
$862$	−708.630	−	123.125i	−0.822077	−	0.142836i
$863$			104.458i			0.121041i	0.998167	+	0.0605204i	$0.0192760\pi$
$863$			104.458i			0.121041i	−0.998167	+	0.0605204i	$0.980724\pi$
$864$		0			0
$865$		0			0
$866$	−68.0452	+	391.627i	−0.0785741	+	0.452225i
$867$		0			0
$868$	−1527.85	−	547.456i	−1.76020	−	0.630710i
$869$	−782.300			−0.900230
$870$		0			0
$871$			935.017i			1.07350i
$872$	−132.263	+	233.107i	−0.151678	+	0.267324i
$873$		0			0
$874$	−65.9922	+	379.811i	−0.0755060	+	0.434567i
$875$		0			0
$876$		0			0
$877$	282.607			0.322243			0.161121	−	0.986935i	$-0.448489\pi$
$877$	282.607			0.322243			0.161121	+	0.986935i	$0.448489\pi$
$878$	696.073	+	120.943i	0.792794	+	0.137748i
$879$		0			0
$880$		0			0
$881$	578.468			0.656604			0.328302	−	0.944573i	$-0.393524\pi$
$881$	578.468			0.656604			0.328302	+	0.944573i	$0.393524\pi$
$882$		0			0
$883$		−	1267.53i		−	1.43548i	−0.696311	−	0.717741i	$-0.745176\pi$
$883$		−	1267.53i		−	1.43548i	0.696311	−	0.717741i	$-0.254824\pi$
$884$	−1626.32	−	582.740i	−1.83973	−	0.659208i
$885$		0			0
$886$	−413.479	−	71.8420i	−0.466680	−	0.0810858i
$887$		−	49.7756i		−	0.0561168i	−0.999606	−	0.0280584i	$-0.991068\pi$
$887$		−	49.7756i		−	0.0561168i	0.999606	−	0.0280584i	$-0.00893243\pi$
$888$		0			0
$889$	2301.96			2.58938
$890$		0			0
$891$		0			0
$892$	429.010	−	1197.29i	0.480953	−	1.34225i
$893$	680.628			0.762181
$894$		0			0
$895$		0			0
$896$	528.078	+	1375.49i	0.589373	+	1.53515i
$897$		0			0
$898$	−211.296	+	1216.09i	−0.235296	+	1.35422i
$899$		−	666.006i		−	0.740830i
$900$		0			0
$901$	−75.2374			−0.0835043
$902$	−566.955	−	98.5086i	−0.628554	−	0.109211i
$903$		0			0
$904$	568.278	−	1001.56i	0.628626	−	1.10792i
$905$		0			0
$906$		0			0
$907$		−	1487.71i		−	1.64026i	−0.572180	−	0.820128i	$-0.693902\pi$
$907$		−	1487.71i		−	1.64026i	0.572180	−	0.820128i	$-0.306098\pi$
$908$	53.8362	−	150.247i	0.0592909	−	0.165470i
$909$		0			0
$910$		0			0
$911$		−	678.826i		−	0.745144i	−0.928003	−	0.372572i	$-0.878476\pi$
$911$		−	678.826i		−	0.745144i	0.928003	−	0.372572i	$-0.121524\pi$
$912$		0			0
$913$	−1456.97			−1.59580
$914$	−44.2524	+	254.690i	−0.0484162	+	0.278654i
$915$		0			0
$916$	−51.7802	−	18.5537i	−0.0565286	−	0.0202552i
$917$	2847.93			3.10570
$918$		0			0
$919$		−	820.849i		−	0.893198i	−0.894734	−	0.446599i	$-0.852635\pi$
$919$		−	820.849i		−	0.893198i	0.894734	−	0.446599i	$-0.147365\pi$
$920$		0			0
$921$		0			0
$922$	−6.39499	+	36.8056i	−0.00693599	+	0.0399193i
$923$		−	163.527i		−	0.177169i
$924$		0			0
$925$		0			0
$926$	−215.608	−	37.4620i	−0.232838	−	0.0404557i
$927$		0			0
$928$	−458.270	+	394.401i	−0.493826	+	0.425001i
$929$	455.044			0.489821			0.244911	−	0.969546i	$-0.421241\pi$
$929$	455.044			0.489821			0.244911	+	0.969546i	$0.421241\pi$
$930$		0			0
$931$			1020.97i			1.09663i
$932$	−457.422	−	163.902i	−0.490796	−	0.175861i
$933$		0			0
$934$	−494.549	−	85.9279i	−0.529495	−	0.0919999i
$935$		0			0
$936$		0			0
$937$	1705.49			1.82016			0.910078	−	0.414437i	$-0.136021\pi$
$937$	1705.49			1.82016			0.910078	+	0.414437i	$0.136021\pi$
$938$	260.884	−	1501.49i	0.278128	−	1.60073i
$939$		0			0
$940$		0			0
$941$	−77.3558			−0.0822060			−0.0411030	−	0.999155i	$-0.513087\pi$
$941$	−77.3558			−0.0822060			−0.0411030	+	0.999155i	$0.513087\pi$
$942$		0			0
$943$			454.698i			0.482183i
$944$	−657.020	+	799.102i	−0.695996	+	0.846506i
$945$		0			0
$946$	83.5174	−	480.675i	0.0882848	−	0.508114i
$947$			382.779i			0.404201i	0.979365	+	0.202101i	$0.0647768\pi$
$947$			382.779i			0.404201i	−0.979365	+	0.202101i	$0.935223\pi$
$948$		0			0
$949$	−31.7665			−0.0334736
$950$		0			0
$951$		0			0
$952$	2449.02	+	1389.56i	2.57250	+	1.45962i
$953$	1101.29			1.15560			0.577800	−	0.816178i	$-0.303911\pi$
$953$	1101.29			1.15560			0.577800	+	0.816178i	$0.303911\pi$
$954$		0			0
$955$		0			0
$956$	217.020	−	605.665i	0.227009	−	0.633541i
$957$		0			0
$958$	735.311	+	127.760i	0.767548	+	0.133362i
$959$			1627.34i			1.69691i
$960$		0			0
$961$	−281.490			−0.292914
$962$	242.393	−	1395.07i	0.251968	−	1.45017i
$963$		0			0
$964$	13.1576	+	4.71459i	0.0136489	+	0.00489066i
$965$		0			0
$966$		0			0
$967$		−	1339.59i		−	1.38531i	−0.721269	−	0.692655i	$-0.756441\pi$
$967$		−	1339.59i		−	1.38531i	0.721269	−	0.692655i	$-0.243559\pi$
$968$	84.8727	−	149.584i	0.0876784	−	0.154529i
$969$		0			0
$970$		0			0
$971$			288.556i			0.297174i	0.988899	+	0.148587i	$0.0474725\pi$
$971$			288.556i			0.297174i	−0.988899	+	0.148587i	$0.952527\pi$
$972$		0			0
$973$	−670.739			−0.689352
$974$	−360.171	−	62.5799i	−0.369786	−	0.0642504i
$975$		0			0
$976$	−373.846	−	307.376i	−0.383039	−	0.314934i
$977$	−1781.05			−1.82298			−0.911490	−	0.411322i	$-0.865067\pi$
$977$	−1781.05			−1.82298			−0.911490	+	0.411322i	$0.865067\pi$
$978$		0			0
$979$		−	872.131i		−	0.890839i
$980$		0			0
$981$		0			0
$982$	814.644	+	141.545i	0.829576	+	0.144139i
$983$		−	1179.28i		−	1.19968i	−0.800122	−	0.599838i	$-0.795232\pi$
$983$		−	1179.28i		−	1.19968i	0.800122	−	0.599838i	$-0.204768\pi$
$984$		0			0
$985$		0			0
$986$	−197.802	+	1138.43i	−0.200611	+	1.15459i
$987$		0			0
$988$	−233.027	+	650.337i	−0.235857	+	0.658236i
$989$	−385.502			−0.389789
$990$		0			0
$991$		−	363.373i		−	0.366673i	−0.983050	−	0.183337i	$-0.941310\pi$
$991$		−	363.373i		−	0.366673i	0.983050	−	0.183337i	$-0.0586898\pi$
$992$	735.788	+	854.942i	0.741722	+	0.861837i
$993$		0			0
$994$	−45.6265	+	262.598i	−0.0459019	+	0.264183i
$995$		0			0
$996$		0			0
$997$	−412.630			−0.413872			−0.206936	−	0.978354i	$-0.566349\pi$
$997$	−412.630			−0.413872			−0.206936	+	0.978354i	$0.566349\pi$
$998$	−182.954	−	31.7883i	−0.183321	−	0.0318520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.o.451.4		8
3.2	odd	2	inner	900.3.c.o.451.5		8
4.3	odd	2	inner	900.3.c.o.451.3		8
5.2	odd	4		900.3.f.i.199.1		16
5.3	odd	4		900.3.f.i.199.16		16
5.4	even	2		180.3.c.c.91.5	yes	8
12.11	even	2	inner	900.3.c.o.451.6		8
15.2	even	4		900.3.f.i.199.15		16
15.8	even	4		900.3.f.i.199.2		16
15.14	odd	2		180.3.c.c.91.4	yes	8
20.3	even	4		900.3.f.i.199.3		16
20.7	even	4		900.3.f.i.199.14		16
20.19	odd	2		180.3.c.c.91.6	yes	8
40.19	odd	2		2880.3.e.i.2431.8		8
40.29	even	2		2880.3.e.i.2431.5		8
60.23	odd	4		900.3.f.i.199.13		16
60.47	odd	4		900.3.f.i.199.4		16
60.59	even	2		180.3.c.c.91.3	✓	8
120.29	odd	2		2880.3.e.i.2431.1		8
120.59	even	2		2880.3.e.i.2431.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.3	✓	8	60.59	even	2
180.3.c.c.91.4	yes	8	15.14	odd	2
180.3.c.c.91.5	yes	8	5.4	even	2
180.3.c.c.91.6	yes	8	20.19	odd	2
900.3.c.o.451.3		8	4.3	odd	2	inner
900.3.c.o.451.4		8	1.1	even	1	trivial
900.3.c.o.451.5		8	3.2	odd	2	inner
900.3.c.o.451.6		8	12.11	even	2	inner
900.3.f.i.199.1		16	5.2	odd	4
900.3.f.i.199.2		16	15.8	even	4
900.3.f.i.199.3		16	20.3	even	4
900.3.f.i.199.4		16	60.47	odd	4
900.3.f.i.199.13		16	60.23	odd	4
900.3.f.i.199.14		16	20.7	even	4
900.3.f.i.199.15		16	15.2	even	4
900.3.f.i.199.16		16	5.3	odd	4
2880.3.e.i.2431.1		8	120.29	odd	2
2880.3.e.i.2431.4		8	120.59	even	2
2880.3.e.i.2431.5		8	40.29	even	2
2880.3.e.i.2431.8		8	40.19	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.342371 + 1.97048i) q^{2} +(-3.76556 - 1.34927i) q^{4} +11.5108i q^{7} +(3.94792 - 6.95801i) q^{8} +O(q^{10})\)	\(q+(-0.342371 + 1.97048i) q^{2} +(-3.76556 - 1.34927i) q^{4} +11.5108i q^{7} +(3.94792 - 6.95801i) q^{8} +9.97507i q^{11} +14.1245 q^{13} +(-22.6817 - 3.94096i) q^{14} +(12.3590 + 10.1615i) q^{16} +30.5776 q^{17} -12.2274i q^{19} +(-19.6556 - 3.41517i) q^{22} +15.7638i q^{23} +(-4.83582 + 27.8320i) q^{26} +(15.5311 - 43.3446i) q^{28} +18.8943 q^{29} -35.2490i q^{31} +(-24.2544 + 20.8740i) q^{32} +(-10.4689 + 60.2524i) q^{34} -50.1245 q^{37} +(24.0938 + 4.18631i) q^{38} +28.8444 q^{41} +24.4548i q^{43} +(13.4590 - 37.5618i) q^{44} +(-31.0623 - 5.39707i) q^{46} +55.6641i q^{47} -83.4981 q^{49} +(-53.1868 - 19.0578i) q^{52} -2.46054 q^{53} +(80.0921 + 45.4437i) q^{56} +(-6.46887 + 37.2309i) q^{58} +64.6577i q^{59} -30.2490 q^{61} +(69.4573 + 12.0682i) q^{62} +(-32.8278 - 54.9394i) q^{64} +66.1981i q^{67} +(-115.142 - 41.2574i) q^{68} -11.5775i q^{71} -2.24903 q^{73} +(17.1612 - 98.7692i) q^{74} +(-16.4981 + 46.0431i) q^{76} -114.821 q^{77} +78.4256i q^{79} +(-9.87548 + 56.8373i) q^{82} +146.061i q^{83} +(-48.1877 - 8.37262i) q^{86} +(69.4066 + 39.3808i) q^{88} -87.4311 q^{89} +162.584i q^{91} +(21.2696 - 59.3597i) q^{92} +(-109.685 - 19.0578i) q^{94} -126.747 q^{97} +(28.5873 - 164.531i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 14 q^{4}+O(q^{10}) \) 8 * q - 14 * q^4	\( 8 q - 14 q^{4} - 16 q^{13} - 14 q^{16} + 4 q^{22} + 92 q^{28} - 116 q^{34} - 272 q^{37} - 184 q^{46} - 152 q^{49} - 232 q^{52} - 84 q^{58} + 16 q^{61} - 182 q^{64} + 240 q^{73} + 384 q^{76} - 208 q^{82} + 652 q^{88} - 168 q^{94} - 240 q^{97}+O(q^{100}) \) 8 * q - 14 * q^4 - 16 * q^13 - 14 * q^16 + 4 * q^22 + 92 * q^28 - 116 * q^34 - 272 * q^37 - 184 * q^46 - 152 * q^49 - 232 * q^52 - 84 * q^58 + 16 * q^61 - 182 * q^64 + 240 * q^73 + 384 * q^76 - 208 * q^82 + 652 * q^88 - 168 * q^94 - 240 * q^97

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