LMFDB - Embedded newform 900.3.f.i.199.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(199,900)]

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, 1]))

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

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

chi := DirichletCharacter("900.199");

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.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 138x^{12} - 1000x^{10} + 5291x^{8} - 17800x^{6} + 39458x^{4} - 53588x^{2} + 32761 $ x^16 - 12x^14 + 138x^12 - 1000x^10 + 5291x^8 - 17800x^6 + 39458x^4 - 53588*x^2 + 32761
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{28} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.14
Root			$1.97048 + 1.96040i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.i.199.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97048 - 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(6.95801 - 3.94792i) q^{8} +O(q^{10})$	\(q+(1.97048 - 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(6.95801 - 3.94792i) q^{8} -9.97507i q^{11} -14.1245i q^{13} +(22.6817 - 3.94096i) q^{14} +(12.3590 - 10.1615i) q^{16} +30.5776i q^{17} -12.2274i q^{19} +(-3.41517 - 19.6556i) q^{22} -15.7638 q^{23} +(-4.83582 - 27.8320i) q^{26} +(43.3446 - 15.5311i) q^{28} -18.8943 q^{29} +35.2490i q^{31} +(20.8740 - 24.2544i) q^{32} +(10.4689 + 60.2524i) q^{34} -50.1245i q^{37} +(-4.18631 - 24.0938i) q^{38} +28.8444 q^{41} -24.4548 q^{43} +(-13.4590 - 37.5618i) q^{44} +(-31.0623 + 5.39707i) q^{46} +55.6641 q^{47} +83.4981 q^{49} +(-19.0578 - 53.1868i) q^{52} +2.46054i q^{53} +(80.0921 - 45.4437i) q^{56} +(-37.2309 + 6.46887i) q^{58} +64.6577i q^{59} -30.2490 q^{61} +(12.0682 + 69.4573i) q^{62} +(32.8278 - 54.9394i) q^{64} +66.1981 q^{67} +(41.2574 + 115.142i) q^{68} +11.5775i q^{71} +2.24903i q^{73} +(-17.1612 - 98.7692i) q^{74} +(-16.4981 - 46.0431i) q^{76} -114.821i q^{77} +78.4256i q^{79} +(56.8373 - 9.87548i) q^{82} -146.061 q^{83} +(-48.1877 + 8.37262i) q^{86} +(-39.3808 - 69.4066i) q^{88} +87.4311 q^{89} -162.584i q^{91} +(-59.3597 + 21.2696i) q^{92} +(109.685 - 19.0578i) q^{94} -126.747i q^{97} +(164.531 - 28.5873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{4}+O(q^{10}) $ 16 * q + 28 * q^4	$ 16 q + 28 q^{4} - 28 q^{16} + 232 q^{34} - 368 q^{46} + 304 q^{49} + 32 q^{61} + 364 q^{64} + 768 q^{76} + 336 q^{94}+O(q^{100}) $ 16 * q + 28 * q^4 - 28 * q^16 + 232 * q^34 - 368 * q^46 + 304 * q^49 + 32 * q^61 + 364 * q^64 + 768 * q^76 + 336 * q^94

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 $

$2$	1.97048	−	0.342371i	0.985239	−	0.171185i
$2$	1.97048	−	0.342371i	0.985239	−	0.171185i
$3$		0			0
$3$		0			0
$4$	3.76556	−	1.34927i	0.941391	−	0.337317i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	11.5108			1.64440			0.822199	−	0.569201i	$-0.192747\pi$
$7$	11.5108			1.64440			0.822199	+	0.569201i	$0.192747\pi$
$8$	6.95801	−	3.94792i	0.869751	−	0.493490i
$9$		0			0
$10$		0			0
$11$		−	9.97507i		−	0.906824i	−0.891301	−	0.453412i	$-0.850207\pi$
$11$		−	9.97507i		−	0.906824i	0.891301	−	0.453412i	$-0.149793\pi$
$12$		0			0
$13$		−	14.1245i		−	1.08650i	−0.839571	−	0.543251i	$-0.817193\pi$
$13$		−	14.1245i		−	1.08650i	0.839571	−	0.543251i	$-0.182807\pi$
$14$	22.6817	−	3.94096i	1.62012	−	0.281497i
$15$		0			0
$16$	12.3590	−	10.1615i	0.772434	−	0.635095i
$17$			30.5776i			1.79868i	0.437249	+	0.899341i	$0.355953\pi$
$17$			30.5776i			1.79868i	−0.437249	+	0.899341i	$0.644047\pi$
$18$		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
$22$	−3.41517	−	19.6556i	−0.155235	−	0.893438i
$23$	−15.7638			−0.685384			−0.342692	−	0.939448i	$-0.611339\pi$
$23$	−15.7638			−0.685384			−0.342692	+	0.939448i	$0.611339\pi$
$24$		0			0
$25$		0			0
$26$	−4.83582	−	27.8320i	−0.185993	−	1.07046i
$27$		0			0
$28$	43.3446	−	15.5311i	1.54802	−	0.554683i
$29$	−18.8943			−0.651529			−0.325765	−	0.945451i	$-0.605622\pi$
$29$	−18.8943			−0.651529			−0.325765	+	0.945451i	$0.605622\pi$
$30$		0			0
$31$			35.2490i			1.13706i	0.822661	+	0.568532i	$0.192488\pi$
$31$			35.2490i			1.13706i	−0.822661	+	0.568532i	$0.807512\pi$
$32$	20.8740	−	24.2544i	0.652313	−	0.757949i
$33$		0			0
$34$	10.4689	+	60.2524i	0.307908	+	1.77213i
$35$		0			0
$36$		0			0
$37$		−	50.1245i		−	1.35472i	−0.735653	−	0.677358i	$-0.763125\pi$
$37$		−	50.1245i		−	1.35472i	0.735653	−	0.677358i	$-0.236875\pi$
$38$	−4.18631	−	24.0938i	−0.110166	−	0.634049i
$39$		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
$43$	−24.4548			−0.568717			−0.284359	−	0.958718i	$-0.591781\pi$
$43$	−24.4548			−0.568717			−0.284359	+	0.958718i	$0.591781\pi$
$44$	−13.4590	−	37.5618i	−0.305887	−	0.853676i
$45$		0			0
$46$	−31.0623	+	5.39707i	−0.675266	+	0.117328i
$47$	55.6641			1.18434			0.592171	−	0.805812i	$-0.298271\pi$
$47$	55.6641			1.18434			0.592171	+	0.805812i	$0.298271\pi$
$48$		0			0
$49$	83.4981			1.70404
$50$		0			0
$51$		0			0
$52$	−19.0578	−	53.1868i	−0.366495	−	1.02282i
$53$			2.46054i			0.0464253i	0.999731	+	0.0232127i	$0.00738948\pi$
$53$			2.46054i			0.0464253i	−0.999731	+	0.0232127i	$0.992611\pi$
$54$		0			0
$55$		0			0
$56$	80.0921	−	45.4437i	1.43022	−	0.811494i
$57$		0			0
$58$	−37.2309	+	6.46887i	−0.641912	+	0.111532i
$59$			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	$0.579755\pi$
$62$	12.0682	+	69.4573i	0.194649	+	1.12028i
$63$		0			0
$64$	32.8278	−	54.9394i	0.512935	−	0.858428i
$65$		0			0
$66$		0			0
$67$	66.1981			0.988032			0.494016	−	0.869453i	$-0.335528\pi$
$67$	66.1981			0.988032			0.494016	+	0.869453i	$0.335528\pi$
$68$	41.2574	+	115.142i	0.606726	+	1.69326i
$69$		0			0
$70$		0			0
$71$			11.5775i			0.163064i	0.996671	+	0.0815318i	$0.0259812\pi$
$71$			11.5775i			0.163064i	−0.996671	+	0.0815318i	$0.974019\pi$
$72$		0			0
$73$			2.24903i			0.0308086i	0.999881	+	0.0154043i	$0.00490354\pi$
$73$			2.24903i			0.0308086i	−0.999881	+	0.0154043i	$0.995096\pi$
$74$	−17.1612	−	98.7692i	−0.231908	−	1.33472i
$75$		0			0
$76$	−16.4981	−	46.0431i	−0.217080	−	0.605831i
$77$		−	114.821i		−	1.49118i
$78$		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
$82$	56.8373	−	9.87548i	0.693137	−	0.120433i
$83$	−146.061			−1.75977			−0.879884	−	0.475189i	$-0.842380\pi$
$83$	−146.061			−1.75977			−0.879884	+	0.475189i	$0.842380\pi$
$84$		0			0
$85$		0			0
$86$	−48.1877	+	8.37262i	−0.560322	+	0.0973561i
$87$		0			0
$88$	−39.3808	−	69.4066i	−0.447509	−	0.788712i
$89$	87.4311			0.982372			0.491186	−	0.871055i	$-0.336564\pi$
$89$	87.4311			0.982372			0.491186	+	0.871055i	$0.336564\pi$
$90$		0			0
$91$		−	162.584i		−	1.78664i
$92$	−59.3597	+	21.2696i	−0.645214	+	0.231192i
$93$		0			0
$94$	109.685	−	19.0578i	1.16686	−	0.202742i
$95$		0			0
$96$		0			0
$97$		−	126.747i		−	1.30667i	−0.757068	−	0.653336i	$-0.773369\pi$
$97$		−	126.747i		−	1.30667i	0.757068	−	0.653336i	$-0.226631\pi$
$98$	164.531	−	28.5873i	1.67889	−	0.291707i
$99$		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
$103$	105.030			1.01971			0.509856	−	0.860260i	$-0.329699\pi$
$103$	105.030			1.01971			0.509856	+	0.860260i	$0.329699\pi$
$104$	−55.7625	−	98.2785i	−0.536178	−	0.944986i
$105$		0			0
$106$	0.842418	+	4.84844i	0.00794734	+	0.0457400i
$107$	−68.2230			−0.637598			−0.318799	−	0.947822i	$-0.603280\pi$
$107$	−68.2230			−0.637598			−0.318799	+	0.947822i	$0.603280\pi$
$108$		0			0
$109$	33.5019			0.307357			0.153679	−	0.988121i	$-0.450888\pi$
$109$	33.5019			0.307357			0.153679	+	0.988121i	$0.450888\pi$
$110$		0			0
$111$		0			0
$112$	142.261	−	116.967i	1.27019	−	1.04435i
$113$		−	143.944i		−	1.27384i	−0.770931	−	0.636919i	$-0.780209\pi$
$113$		−	143.944i		−	1.27384i	0.770931	−	0.636919i	$-0.219791\pi$
$114$		0			0
$115$		0			0
$116$	−71.1479	+	25.4935i	−0.613344	+	0.219772i
$117$		0			0
$118$	22.1369	+	127.407i	0.187601	+	1.07972i
$119$			351.972i			2.95775i
$120$		0			0
$121$	21.4981			0.177670
$122$	−59.6050	+	10.3564i	−0.488566	+	0.0848884i
$123$		0			0
$124$	47.5603	+	132.732i	0.383551	+	1.07042i
$125$		0			0
$126$		0			0
$127$	−199.983			−1.57467			−0.787335	−	0.616525i	$-0.788540\pi$
$127$	−199.983			−1.57467			−0.787335	+	0.616525i	$0.788540\pi$
$128$	45.8769	−	119.496i	0.358413	−	0.933563i
$129$		0			0
$130$		0			0
$131$			247.414i			1.88866i	0.329007	+	0.944328i	$0.393286\pi$
$131$			247.414i			1.88866i	−0.329007	+	0.944328i	$0.606714\pi$
$132$		0			0
$133$		−	140.747i		−	1.05825i
$134$	130.442	−	22.6643i	0.973447	−	0.169137i
$135$		0			0
$136$	120.718	+	212.759i	0.887632	+	1.56441i
$137$			141.375i			1.03194i	0.856608	+	0.515968i	$0.172568\pi$
$137$			141.375i			1.03194i	−0.856608	+	0.515968i	$0.827432\pi$
$138$		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
$142$	3.96380	+	22.8132i	0.0279141	+	0.160657i
$143$	−140.893			−0.985266
$144$		0			0
$145$		0			0
$146$	0.770003	+	4.43167i	0.00527399	+	0.0303539i
$147$		0			0
$148$	−67.6314	−	188.747i	−0.456969	−	1.27532i
$149$	−265.527			−1.78206			−0.891029	−	0.453947i	$-0.850016\pi$
$149$	−265.527			−1.78206			−0.891029	+	0.453947i	$0.850016\pi$
$150$		0			0
$151$			217.988i			1.44363i	0.692086	+	0.721815i	$0.256692\pi$
$151$			217.988i			1.44363i	−0.692086	+	0.721815i	$0.743308\pi$
$152$	−48.2729	−	85.0785i	−0.317585	−	0.559727i
$153$		0			0
$154$	−39.3113	−	226.252i	−0.255268	−	1.46917i
$155$		0			0
$156$		0			0
$157$		−	66.3735i		−	0.422761i	−0.977404	−	0.211381i	$-0.932204\pi$
$157$		−	66.3735i		−	0.422761i	0.977404	−	0.211381i	$-0.0677960\pi$
$158$	26.8506	+	154.536i	0.169941	+	0.978075i
$159$		0			0
$160$		0			0
$161$	−181.454			−1.12704
$162$		0			0
$163$	93.5195			0.573739			0.286870	−	0.957970i	$-0.407385\pi$
$163$	93.5195			0.573739			0.286870	+	0.957970i	$0.407385\pi$
$164$	108.615	−	38.9188i	0.662290	−	0.237310i
$165$		0			0
$166$	−287.809	+	50.0069i	−1.73379	+	0.301247i
$167$	−47.2915			−0.283182			−0.141591	−	0.989925i	$-0.545222\pi$
$167$	−47.2915			−0.283182			−0.141591	+	0.989925i	$0.545222\pi$
$168$		0			0
$169$	−30.5019			−0.180485
$170$		0			0
$171$		0			0
$172$	−92.0862	+	32.9961i	−0.535385	+	0.191838i
$173$			229.534i			1.32678i	0.748272	+	0.663392i	$0.230884\pi$
$173$			229.534i			1.32678i	−0.748272	+	0.663392i	$0.769116\pi$
$174$		0			0
$175$		0			0
$176$	−101.362	−	123.281i	−0.575919	−	0.700462i
$177$		0			0
$178$	172.281	−	29.9339i	0.967871	−	0.168168i
$179$			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	$0.451896\pi$
$182$	−55.6641	−	320.369i	−0.305847	−	1.76027i
$183$		0			0
$184$	−109.685	+	62.2343i	−0.596113	+	0.338230i
$185$		0			0
$186$		0			0
$187$	305.013			1.63109
$188$	209.607	−	75.1058i	1.11493	−	0.399499i
$189$		0			0
$190$		0			0
$191$			225.861i			1.18252i	0.806481	+	0.591260i	$0.201369\pi$
$191$			225.861i			1.18252i	−0.806481	+	0.591260i	$0.798631\pi$
$192$		0			0
$193$			174.498i			0.904135i	0.891984	+	0.452068i	$0.149313\pi$
$193$			174.498i			0.904135i	−0.891984	+	0.452068i	$0.850687\pi$
$194$	−43.3945	−	249.752i	−0.223683	−	1.28738i
$195$		0			0
$196$	314.417	−	112.661i	1.60417	−	0.574802i
$197$			15.9849i			0.0811414i	0.999177	+	0.0405707i	$0.0129176\pi$
$197$			15.9849i			0.0811414i	−0.999177	+	0.0405707i	$0.987082\pi$
$198$		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
$202$	−130.414	+	22.6595i	−0.645616	+	0.112176i
$203$	−217.489			−1.07137
$204$		0			0
$205$		0			0
$206$	206.960	−	35.9593i	1.00466	−	0.174560i
$207$		0			0
$208$	−143.526	−	174.564i	−0.690031	−	0.839251i
$209$	−121.969			−0.583585
$210$		0			0
$211$		−	190.667i		−	0.903634i	−0.892111	−	0.451817i	$-0.850776\pi$
$211$		−	190.667i		−	0.903634i	0.892111	−	0.451817i	$-0.149224\pi$
$212$	3.31993	+	9.26533i	0.0156600	+	0.0437044i
$213$		0			0
$214$	−134.432	+	23.3576i	−0.628187	+	0.109148i
$215$		0			0
$216$		0			0
$217$			405.743i			1.86978i
$218$	66.0148	−	11.4701i	0.302820	−	0.0526151i
$219$		0			0
$220$		0			0
$221$	431.893			1.95427
$222$		0			0
$223$	−317.957			−1.42582			−0.712909	−	0.701257i	$-0.752623\pi$
$223$	−317.957			−1.42582			−0.712909	+	0.701257i	$0.752623\pi$
$224$	240.276	−	279.187i	1.07266	−	1.24637i
$225$		0			0
$226$	−49.2821	−	283.638i	−0.218062	−	1.25503i
$227$	39.9003			0.175772			0.0878860	−	0.996131i	$-0.471989\pi$
$227$	39.9003			0.175772			0.0878860	+	0.996131i	$0.471989\pi$
$228$		0			0
$229$	−13.7510			−0.0600479			−0.0300239	−	0.999549i	$-0.509558\pi$
$229$	−13.7510			−0.0600479			−0.0300239	+	0.999549i	$0.509558\pi$
$230$		0			0
$231$		0			0
$232$	−131.467	+	74.5934i	−0.566668	+	0.321523i
$233$		−	121.475i		−	0.521352i	−0.965426	−	0.260676i	$-0.916055\pi$
$233$		−	121.475i		−	0.521352i	0.965426	−	0.260676i	$-0.0839454\pi$
$234$		0			0
$235$		0			0
$236$	87.2406	+	243.473i	0.369664	+	1.03166i
$237$		0			0
$238$	120.505	+	693.553i	0.506323	+	2.91409i
$239$			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	$0.502308\pi$
$242$	42.3615	−	7.36031i	0.175047	−	0.0304145i
$243$		0			0
$244$	−113.905	+	40.8141i	−0.466822	+	0.167271i
$245$		0			0
$246$		0			0
$247$	−172.706			−0.699216
$248$	139.160	+	245.263i	0.561130	+	0.988963i
$249$		0			0
$250$		0			0
$251$		−	315.637i		−	1.25752i	−0.777601	−	0.628759i	$-0.783563\pi$
$251$		−	315.637i		−	1.25752i	0.777601	−	0.628759i	$-0.216437\pi$
$252$		0			0
$253$			157.245i			0.621522i
$254$	−394.062	+	68.4684i	−1.55143	+	0.269561i
$255$		0			0
$256$	49.4873	−	251.171i	0.193310	−	0.981138i
$257$		−	86.8117i		−	0.337789i	−0.985634	−	0.168894i	$-0.945980\pi$
$257$		−	86.8117i		−	0.337789i	0.985634	−	0.168894i	$-0.0540196\pi$
$258$		0			0
$259$		−	576.972i		−	2.22769i
$260$		0			0
$261$		0			0
$262$	84.7073	+	487.523i	0.323310	+	1.86078i
$263$	−333.003			−1.26617			−0.633086	−	0.774082i	$-0.718212\pi$
$263$	−333.003			−1.26617			−0.633086	+	0.774082i	$0.718212\pi$
$264$		0			0
$265$		0			0
$266$	−48.1877	−	277.339i	−0.181157	−	1.04263i
$267$		0			0
$268$	249.273	−	89.3190i	0.930124	−	0.333280i
$269$	191.063			0.710271			0.355136	−	0.934815i	$-0.384435\pi$
$269$	191.063			0.710271			0.355136	+	0.934815i	$0.384435\pi$
$270$		0			0
$271$			261.165i			0.963708i	0.876252	+	0.481854i	$0.160036\pi$
$271$			261.165i			0.963708i	−0.876252	+	0.481854i	$0.839964\pi$
$272$	310.714	+	377.907i	1.14233	+	1.38936i
$273$		0			0
$274$	48.4027	+	278.577i	0.176652	+	1.01670i
$275$		0			0
$276$		0			0
$277$			204.615i			0.738682i	0.929294	+	0.369341i	$0.120417\pi$
$277$			204.615i			0.738682i	−0.929294	+	0.369341i	$0.879583\pi$
$278$	19.9501	+	114.821i	0.0717631	+	0.413024i
$279$		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
$283$	−336.724			−1.18984			−0.594918	−	0.803786i	$-0.702816\pi$
$283$	−336.724			−1.18984			−0.594918	+	0.803786i	$0.702816\pi$
$284$	15.6212	+	43.5959i	0.0550041	+	0.153507i
$285$		0			0
$286$	−277.626	+	48.2376i	−0.970722	+	0.168663i
$287$	332.022			1.15687
$288$		0			0
$289$	−645.988			−2.23525
$290$		0			0
$291$		0			0
$292$	3.03455	+	8.46887i	0.0103923	+	0.0290030i
$293$		−	249.650i		−	0.852046i	−0.904712	−	0.426023i	$-0.859914\pi$
$293$		−	249.650i		−	0.852046i	0.904712	−	0.426023i	$-0.140086\pi$
$294$		0			0
$295$		0			0
$296$	−197.888	−	348.767i	−0.668539	−	1.17827i
$297$		0			0
$298$	−523.214	+	90.9086i	−1.75575	+	0.305062i
$299$			222.656i			0.744670i
$300$		0			0
$301$	−281.494			−0.935197
$302$	74.6328	+	429.541i	0.247128	+	1.42232i
$303$		0			0
$304$	−124.249	−	151.118i	−0.408714	−	0.497099i
$305$		0			0
$306$		0			0
$307$	−156.851			−0.510916			−0.255458	−	0.966820i	$-0.582226\pi$
$307$	−156.851			−0.510916			−0.255458	+	0.966820i	$0.582226\pi$
$308$	−154.924	−	432.365i	−0.503000	−	1.40378i
$309$		0			0
$310$		0			0
$311$		−	164.769i		−	0.529803i	−0.964275	−	0.264902i	$-0.914661\pi$
$311$		−	164.769i		−	0.529803i	0.964275	−	0.264902i	$-0.0853395\pi$
$312$		0			0
$313$		−	131.992i		−	0.421700i	−0.977518	−	0.210850i	$-0.932377\pi$
$313$		−	131.992i		−	0.421700i	0.977518	−	0.210850i	$-0.0676232\pi$
$314$	−22.7244	−	130.788i	−0.0723706	−	0.416521i
$315$		0			0
$316$	105.817	+	295.316i	0.334864	+	0.934546i
$317$		−	169.833i		−	0.535752i	−0.963453	−	0.267876i	$-0.913678\pi$
$317$		−	169.833i		−	0.535752i	0.963453	−	0.267876i	$-0.0863217\pi$
$318$		0			0
$319$			188.472i			0.590822i
$320$		0			0
$321$		0			0
$322$	−357.551	+	62.1245i	−1.11041	+	0.192933i
$323$	373.885			1.15754
$324$		0			0
$325$		0			0
$326$	184.278	−	32.0184i	0.565270	−	0.0982158i
$327$		0			0
$328$	200.700	−	113.875i	0.611889	−	0.347181i
$329$	640.737			1.94753
$330$		0			0
$331$			171.945i			0.519472i	0.965680	+	0.259736i	$0.0836355\pi$
$331$			171.945i			0.519472i	−0.965680	+	0.259736i	$0.916365\pi$
$332$	−550.001	+	197.075i	−1.65663	+	0.593600i
$333$		0			0
$334$	−93.1868	+	16.1912i	−0.279002	+	0.0484767i
$335$		0			0
$336$		0			0
$337$			470.249i			1.39540i	0.716391	+	0.697699i	$0.245793\pi$
$337$			470.249i			1.39540i	−0.716391	+	0.697699i	$0.754207\pi$
$338$	−60.1034	+	10.4430i	−0.177821	+	0.0308964i
$339$		0			0
$340$		0			0
$341$	351.611			1.03112
$342$		0			0
$343$	397.100			1.15772
$344$	−170.157	+	96.5458i	−0.494642	+	0.280656i
$345$		0			0
$346$	78.5856	+	452.291i	0.227126	+	1.30720i
$347$	167.974			0.484074			0.242037	−	0.970267i	$-0.422184\pi$
$347$	167.974			0.484074			0.242037	+	0.970267i	$0.422184\pi$
$348$		0			0
$349$	158.747			0.454863			0.227431	−	0.973794i	$-0.426967\pi$
$349$	158.747			0.454863			0.227431	+	0.973794i	$0.426967\pi$
$350$		0			0
$351$		0			0
$352$	−241.939	−	208.220i	−0.687327	−	0.591534i
$353$		−	201.076i		−	0.569619i	−0.958584	−	0.284810i	$-0.908070\pi$
$353$		−	201.076i		−	0.569619i	0.958584	−	0.284810i	$-0.0919304\pi$
$354$		0			0
$355$		0			0
$356$	329.228	−	117.968i	0.924796	−	0.331371i
$357$		0			0
$358$	51.6528	+	297.282i	0.144282	+	0.830397i
$359$		−	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
$362$	107.387	−	18.6585i	0.296650	−	0.0515429i
$363$		0			0
$364$	−219.370	−	612.221i	−0.602664	−	1.68193i
$365$		0			0
$366$		0			0
$367$	11.5108			0.0313645			0.0156823	−	0.999877i	$-0.495008\pi$
$367$	11.5108			0.0313645			0.0156823	+	0.999877i	$0.495008\pi$
$368$	−194.824	+	160.184i	−0.529414	+	0.435283i
$369$		0			0
$370$		0			0
$371$			28.3228i			0.0763417i
$372$		0			0
$373$			356.864i			0.956740i	0.878159	+	0.478370i	$0.158772\pi$
$373$			356.864i			0.956740i	−0.878159	+	0.478370i	$0.841228\pi$
$374$	601.022	−	104.428i	1.60701	−	0.279218i
$375$		0			0
$376$	387.311	−	219.757i	1.03008	−	0.584461i
$377$			266.873i			0.707887i
$378$		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
$382$	77.3283	+	445.055i	0.202430	+	1.16506i
$383$	442.368			1.15501			0.577504	−	0.816388i	$-0.304027\pi$
$383$	442.368			1.15501			0.577504	+	0.816388i	$0.304027\pi$
$384$		0			0
$385$		0			0
$386$	59.7430	+	343.845i	0.154775	+	0.890789i
$387$		0			0
$388$	−171.016	−	477.274i	−0.440762	−	1.23009i
$389$	−356.424			−0.916257			−0.458129	−	0.888886i	$-0.651480\pi$
$389$	−356.424			−0.916257			−0.458129	+	0.888886i	$0.651480\pi$
$390$		0			0
$391$		−	482.020i		−	1.23279i
$392$	580.980	−	329.644i	1.48209	−	0.840928i
$393$		0			0
$394$	5.47275	+	31.4978i	0.0138902	+	0.0799436i
$395$		0			0
$396$		0			0
$397$		−	512.864i		−	1.29185i	−0.763402	−	0.645924i	$-0.776472\pi$
$397$		−	512.864i		−	1.29185i	0.763402	−	0.645924i	$-0.223528\pi$
$398$	−10.5961	−	60.9846i	−0.0266233	−	0.153228i
$399$		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
$403$	497.875			1.23542
$404$	−249.221	+	89.3002i	−0.616883	+	0.221040i
$405$		0			0
$406$	−428.556	+	74.4618i	−1.05556	+	0.183403i
$407$	−499.995			−1.22849
$408$		0			0
$409$	−251.494			−0.614900			−0.307450	−	0.951564i	$-0.599476\pi$
$409$	−251.494			−0.614900			−0.307450	+	0.951564i	$0.599476\pi$
$410$		0			0
$411$		0			0
$412$	395.498	−	141.714i	0.959947	−	0.343966i
$413$			744.261i			1.80208i
$414$		0			0
$415$		0			0
$416$	−342.581	−	294.836i	−0.823513	−	0.708739i
$417$		0			0
$418$	−240.338	+	41.7587i	−0.574971	+	0.0999012i
$419$		−	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	$0.0863191\pi$
$422$	−65.2788	−	375.705i	−0.154689	−	0.890296i
$423$		0			0
$424$	9.71403	+	17.1205i	0.0229104	+	0.0403785i
$425$		0			0
$426$		0			0
$427$	−348.190			−0.815433
$428$	−256.898	+	92.0511i	−0.600229	+	0.215073i
$429$		0			0
$430$		0			0
$431$		−	359.624i		−	0.834394i	−0.908816	−	0.417197i	$-0.863013\pi$
$431$		−	359.624i		−	0.834394i	0.908816	−	0.417197i	$-0.136987\pi$
$432$		0			0
$433$		−	198.747i		−	0.459000i	−0.973309	−	0.229500i	$-0.926291\pi$
$433$		−	198.747i		−	0.459000i	0.973309	−	0.229500i	$-0.0737091\pi$
$434$	138.915	+	799.508i	0.320080	+	1.84218i
$435$		0			0
$436$	126.154	−	45.2031i	0.289343	−	0.103677i
$437$			192.751i			0.441077i
$438$		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
$442$	851.036	−	147.868i	1.92542	−	0.334542i
$443$	−209.837			−0.473672			−0.236836	−	0.971550i	$-0.576110\pi$
$443$	−209.837			−0.473672			−0.236836	+	0.971550i	$0.576110\pi$
$444$		0			0
$445$		0			0
$446$	−626.528	+	108.859i	−1.40477	+	0.244079i
$447$		0			0
$448$	377.874	−	632.395i	0.843468	−	1.41160i
$449$	−617.155			−1.37451			−0.687255	−	0.726416i	$-0.741184\pi$
$449$	−617.155			−1.37451			−0.687255	+	0.726416i	$0.741184\pi$
$450$		0			0
$451$		−	287.725i		−	0.637971i
$452$	−194.219	−	542.029i	−0.429687	−	1.19918i
$453$		0			0
$454$	78.6226	−	13.6607i	0.173177	−	0.0300896i
$455$		0			0
$456$		0			0
$457$			129.253i			0.282829i	0.989950	+	0.141415i	$0.0451650\pi$
$457$			129.253i			0.282829i	−0.989950	+	0.141415i	$0.954835\pi$
$458$	−27.0960	+	4.70793i	−0.0591615	+	0.0102793i
$459$		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
$463$	−109.419			−0.236327			−0.118163	−	0.992994i	$-0.537701\pi$
$463$	−109.419			−0.236327			−0.118163	+	0.992994i	$0.537701\pi$
$464$	−233.514	+	191.995i	−0.503263	+	0.413782i
$465$		0			0
$466$	−41.5895	−	239.364i	−0.0892479	−	0.513656i
$467$	250.979			0.537428			0.268714	−	0.963220i	$-0.413401\pi$
$467$	250.979			0.537428			0.268714	+	0.963220i	$0.413401\pi$
$468$		0			0
$469$	761.992			1.62472
$470$		0			0
$471$		0			0
$472$	255.264	+	449.889i	0.540813	+	0.953155i
$473$			243.939i			0.515726i
$474$		0			0
$475$		0			0
$476$	474.904	+	1325.37i	0.997698	+	2.78440i
$477$		0			0
$478$	55.0680	+	316.938i	0.115205	+	0.663050i
$479$		−	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
$482$	−6.88522	+	1.19631i	−0.0142847	+	0.00248197i
$483$		0			0
$484$	80.9523	−	29.0066i	0.167257	−	0.0599311i
$485$		0			0
$486$		0			0
$487$	182.784			0.375326			0.187663	−	0.982233i	$-0.439909\pi$
$487$	182.784			0.375326			0.187663	+	0.982233i	$0.439909\pi$
$488$	−210.473	+	119.421i	−0.431297	+	0.244715i
$489$		0			0
$490$		0			0
$491$			413.425i			0.842005i	0.907059	+	0.421003i	$0.138322\pi$
$491$			413.425i			0.842005i	−0.907059	+	0.421003i	$0.861678\pi$
$492$		0			0
$493$		−	577.743i		−	1.17189i
$494$	−340.314	+	59.1296i	−0.688895	+	0.119696i
$495$		0			0
$496$	358.183	+	435.640i	0.722143	+	0.878307i
$497$			133.266i			0.268141i
$498$		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
$502$	−108.065	−	621.955i	−0.215269	−	1.23895i
$503$	415.288			0.825622			0.412811	−	0.910817i	$-0.364547\pi$
$503$	415.288			0.825622			0.412811	+	0.910817i	$0.364547\pi$
$504$		0			0
$505$		0			0
$506$	53.8362	+	309.848i	0.106396	+	0.612348i
$507$		0			0
$508$	−753.049	+	269.831i	−1.48238	+	0.531163i
$509$	−396.009			−0.778013			−0.389006	−	0.921235i	$-0.627182\pi$
$509$	−396.009			−0.778013			−0.389006	+	0.921235i	$0.627182\pi$
$510$		0			0
$511$			25.8881i			0.0506616i
$512$	11.5200	−	511.870i	0.0225000	−	0.999747i
$513$		0			0
$514$	−29.7218	−	171.060i	−0.0578245	−	0.332802i
$515$		0			0
$516$		0			0
$517$		−	555.253i		−	1.07399i
$518$	−197.538	−	1136.91i	−0.381348	−	2.19481i
$519$		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
$523$	−261.837			−0.500644			−0.250322	−	0.968163i	$-0.580536\pi$
$523$	−261.837			−0.500644			−0.250322	+	0.968163i	$0.580536\pi$
$524$	333.828	+	931.653i	0.637075	+	1.77796i
$525$		0			0
$526$	−656.175	+	114.011i	−1.24748	+	0.216750i
$527$	−1077.83			−2.04522
$528$		0			0
$529$	−280.502			−0.530249
$530$		0			0
$531$		0			0
$532$	−189.906	−	529.992i	−0.356965	−	0.996226i
$533$		−	407.413i		−	0.764378i
$534$		0			0
$535$		0			0
$536$	460.607	−	261.345i	0.859342	−	0.487584i
$537$		0			0
$538$	376.485	−	65.4144i	0.699787	−	0.121588i
$539$		−	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	$0.680774\pi$
$542$	89.4152	+	514.619i	0.164973	+	0.949482i
$543$		0			0
$544$	741.640	+	638.277i	1.36331	+	1.17330i
$545$		0			0
$546$		0			0
$547$	−84.8307			−0.155083			−0.0775417	−	0.996989i	$-0.524707\pi$
$547$	−84.8307			−0.155083			−0.0775417	+	0.996989i	$0.524707\pi$
$548$	190.753	+	532.357i	0.348089	+	0.971455i
$549$		0			0
$550$		0			0
$551$			231.029i			0.419290i
$552$		0			0
$553$			902.739i			1.63244i
$554$	70.0541	+	403.189i	0.126452	+	0.727778i
$555$		0			0
$556$	78.6226	+	219.421i	0.141408	+	0.394643i
$557$		−	708.933i		−	1.27277i	−0.771372	−	0.636385i	$-0.780429\pi$
$557$		−	708.933i		−	1.27277i	0.771372	−	0.636385i	$-0.219571\pi$
$558$		0			0
$559$			345.413i			0.617912i
$560$		0			0
$561$		0			0
$562$	−903.910	+	157.055i	−1.60838	+	0.279456i
$563$	1094.57			1.94418			0.972090	−	0.234607i	$-0.0753804\pi$
$563$	1094.57			1.94418			0.972090	+	0.234607i	$0.0753804\pi$
$564$		0			0
$565$		0			0
$566$	−663.507	+	115.284i	−1.17227	+	0.203683i
$567$		0			0
$568$	45.7071	+	80.5564i	0.0804703	+	0.141825i
$569$	769.082			1.35164			0.675819	−	0.737068i	$-0.263790\pi$
$569$	769.082			1.35164			0.675819	+	0.737068i	$0.263790\pi$
$570$		0			0
$571$			871.192i			1.52573i	0.646558	+	0.762865i	$0.276208\pi$
$571$			871.192i			1.52573i	−0.646558	+	0.762865i	$0.723792\pi$
$572$	−530.542	+	190.102i	−0.927520	+	0.332347i
$573$		0			0
$574$	654.241	−	113.675i	1.13979	−	0.198039i
$575$		0			0
$576$		0			0
$577$		−	216.739i		−	0.375631i	−0.982204	−	0.187816i	$-0.939859\pi$
$577$		−	216.739i		−	0.375631i	0.982204	−	0.187816i	$-0.0601408\pi$
$578$	−1272.91	+	221.168i	−2.20226	+	0.382643i
$579$		0			0
$580$		0			0
$581$	−1681.27			−2.89376
$582$		0			0
$583$	24.5441			0.0420996
$584$	8.87900	+	15.6488i	0.0152038	+	0.0267959i
$585$		0			0
$586$	−85.4727	−	491.929i	−0.145858	−	0.839469i
$587$	−148.024			−0.252170			−0.126085	−	0.992019i	$-0.540241\pi$
$587$	−148.024			−0.252170			−0.126085	+	0.992019i	$0.540241\pi$
$588$		0			0
$589$	431.004			0.731755
$590$		0			0
$591$		0			0
$592$	−509.341	−	619.486i	−0.860373	−	1.04643i
$593$			102.473i			0.172804i	0.996260	+	0.0864020i	$0.0275370\pi$
$593$			102.473i			0.172804i	−0.996260	+	0.0864020i	$0.972463\pi$
$594$		0			0
$595$		0			0
$596$	−999.857	+	358.267i	−1.67761	+	0.601118i
$597$		0			0
$598$	76.2310	+	438.739i	0.127477	+	0.733678i
$599$		−	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	$0.385673\pi$
$602$	−554.678	+	96.3754i	−0.921392	+	0.160092i
$603$		0			0
$604$	294.125	+	820.849i	0.486961	+	1.35902i
$605$		0			0
$606$		0			0
$607$	958.261			1.57868			0.789342	−	0.613954i	$-0.210422\pi$
$607$	958.261			1.57868			0.789342	+	0.613954i	$0.210422\pi$
$608$	−296.568	−	255.235i	−0.487777	−	0.419795i
$609$		0			0
$610$		0			0
$611$		−	786.228i		−	1.28679i
$612$		0			0
$613$		−	885.611i		−	1.44472i	−0.691519	−	0.722358i	$-0.743058\pi$
$613$		−	885.611i		−	1.44472i	0.691519	−	0.722358i	$-0.256942\pi$
$614$	−309.072	+	53.7012i	−0.503374	+	0.0874613i
$615$		0			0
$616$	−453.304	−	798.924i	−0.735882	−	1.29695i
$617$			37.8513i			0.0613473i	0.999529	+	0.0306737i	$0.00976526\pi$
$617$			37.8513i			0.0613473i	−0.999529	+	0.0306737i	$0.990235\pi$
$618$		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
$622$	−56.4120	−	324.673i	−0.0906946	−	0.521983i
$623$	1006.40			1.61541
$624$		0			0
$625$		0			0
$626$	−45.1903	−	260.088i	−0.0721890	−	0.415476i
$627$		0			0
$628$	−89.5557	−	249.934i	−0.142605	−	0.397984i
$629$	1532.69			2.43670
$630$		0			0
$631$		−	665.520i		−	1.05471i	−0.849646	−	0.527353i	$-0.823184\pi$
$631$		−	665.520i		−	1.05471i	0.849646	−	0.527353i	$-0.176816\pi$
$632$	309.618	+	545.686i	0.489902	+	0.863427i
$633$		0			0
$634$	−58.1460	−	334.653i	−0.0917129	−	0.527843i
$635$		0			0
$636$		0			0
$637$		−	1179.37i		−	1.85144i
$638$	64.5274	+	371.380i	0.101140	+	0.582101i
$639$		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
$643$	−277.692			−0.431869			−0.215935	−	0.976408i	$-0.569280\pi$
$643$	−277.692			−0.431869			−0.215935	+	0.976408i	$0.569280\pi$
$644$	−683.276	+	244.830i	−1.06099	+	0.380171i
$645$		0			0
$646$	736.732	−	128.007i	1.14045	−	0.198154i
$647$	1049.77			1.62251			0.811257	−	0.584690i	$-0.198784\pi$
$647$	1049.77			1.62251			0.811257	+	0.584690i	$0.198784\pi$
$648$		0			0
$649$	644.965			0.993783
$650$		0			0
$651$		0			0
$652$	352.154	−	126.183i	0.540113	−	0.193532i
$653$			110.008i			0.168465i	0.996446	+	0.0842325i	$0.0268438\pi$
$653$			110.008i			0.168465i	−0.996446	+	0.0842325i	$0.973156\pi$
$654$		0			0
$655$		0			0
$656$	356.487	−	293.103i	0.543425	−	0.446803i
$657$		0			0
$658$	1262.56	−	219.370i	1.91878	−	0.333389i
$659$		−	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	$0.707410\pi$
$662$	58.8690	+	338.814i	0.0889259	+	0.511803i
$663$		0			0
$664$	−1016.29	+	576.636i	−1.53056	+	0.868428i
$665$		0			0
$666$		0			0
$667$	297.847			0.446547
$668$	−178.079	+	63.8089i	−0.266585	+	0.0955223i
$669$		0			0
$670$		0			0
$671$			301.736i			0.449681i
$672$		0			0
$673$		−	447.743i		−	0.665295i	−0.943051	−	0.332647i	$-0.892058\pi$
$673$		−	447.743i		−	0.665295i	0.943051	−	0.332647i	$-0.107942\pi$
$674$	161.000	+	926.615i	0.238872	+	1.37480i
$675$		0			0
$676$	−114.857	+	41.1553i	−0.169907	+	0.0608806i
$677$		−	299.167i		−	0.441901i	−0.975285	−	0.220950i	$-0.929084\pi$
$677$		−	299.167i		−	0.441901i	0.975285	−	0.220950i	$-0.0709159\pi$
$678$		0			0
$679$		−	1458.96i		−	2.14869i
$680$		0			0
$681$		0			0
$682$	692.841	−	120.381i	1.01590	−	0.176512i
$683$	339.673			0.497326			0.248663	−	0.968590i	$-0.420009\pi$
$683$	339.673			0.497326			0.248663	+	0.968590i	$0.420009\pi$
$684$		0			0
$685$		0			0
$686$	782.476	−	135.955i	1.14064	−	0.198186i
$687$		0			0
$688$	−302.236	+	248.498i	−0.439297	+	0.361189i
$689$	34.7540			0.0504412
$690$		0			0
$691$			764.773i			1.10676i	0.832928	+	0.553381i	$0.186663\pi$
$691$			764.773i			1.10676i	−0.832928	+	0.553381i	$0.813337\pi$
$692$	309.702	+	864.324i	0.447547	+	1.24902i
$693$		0			0
$694$	330.988	−	57.5093i	0.476928	−	0.0828664i
$695$		0			0
$696$		0			0
$697$			881.992i			1.26541i
$698$	312.808	−	54.3504i	0.448148	−	0.0778659i
$699$		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
$703$	−612.893			−0.871825
$704$	−548.024	−	327.460i	−0.778443	−	0.465142i
$705$		0			0
$706$	−68.8424	−	396.215i	−0.0975105	−	0.561211i
$707$	−761.831			−1.07755
$708$		0			0
$709$	882.249			1.24436			0.622178	−	0.782875i	$-0.286248\pi$
$709$	882.249			1.24436			0.622178	+	0.782875i	$0.286248\pi$
$710$		0			0
$711$		0			0
$712$	608.347	−	345.171i	0.854420	−	0.484791i
$713$		−	555.659i		−	0.779325i
$714$		0			0
$715$		0			0
$716$	203.561	+	568.103i	0.284304	+	0.793440i
$717$		0			0
$718$	−235.949	−	1357.98i	−0.328619	−	1.89133i
$719$		−	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
$722$	416.737	−	72.4081i	0.577198	−	0.100288i
$723$		0			0
$724$	205.216	−	73.5325i	0.283447	−	0.101564i
$725$		0			0
$726$		0			0
$727$	735.301			1.01142			0.505709	−	0.862704i	$-0.331231\pi$
$727$	735.301			1.01142			0.505709	+	0.862704i	$0.331231\pi$
$728$	−641.870	−	1131.26i	−0.881689	−	1.55393i
$729$		0			0
$730$		0			0
$731$		−	747.770i		−	1.02294i
$732$		0			0
$733$			269.377i			0.367500i	0.982973	+	0.183750i	$0.0588237\pi$
$733$			269.377i			0.367500i	−0.982973	+	0.183750i	$0.941176\pi$
$734$	22.6817	−	3.94096i	0.0309015	−	0.00536915i
$735$		0			0
$736$	−329.055	+	382.342i	−0.447085	+	0.519486i
$737$		−	660.331i		−	0.895971i
$738$		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
$742$	9.69688	+	55.8094i	0.0130686	+	0.0752148i
$743$	−1017.72			−1.36974			−0.684870	−	0.728665i	$-0.740141\pi$
$743$	−1017.72			−1.36974			−0.684870	+	0.728665i	$0.740141\pi$
$744$		0			0
$745$		0			0
$746$	122.180	+	703.192i	0.163780	+	0.942617i
$747$		0			0
$748$	1148.55	−	411.545i	1.53549	−	0.550194i
$749$	−785.300			−1.04846
$750$		0			0
$751$		−	551.845i		−	0.734814i	−0.930060	−	0.367407i	$-0.880246\pi$
$751$		−	551.845i		−	0.734814i	0.930060	−	0.367407i	$-0.119754\pi$
$752$	687.950	−	565.631i	0.914827	−	0.752169i
$753$		0			0
$754$	91.3697	+	525.868i	0.121180	+	0.697438i
$755$		0			0
$756$		0			0
$757$		−	1168.86i		−	1.54407i	−0.635578	−	0.772037i	$-0.719238\pi$
$757$		−	1168.86i		−	1.54407i	0.635578	−	0.772037i	$-0.280762\pi$
$758$	189.887	+	1092.87i	0.250510	+	1.44178i
$759$		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
$763$	385.633			0.505417
$764$	304.747	+	850.495i	0.398884	+	1.11321i
$765$		0			0
$766$	871.677	−	151.454i	1.13796	−	0.197721i
$767$	913.259			1.19069
$768$		0			0
$769$	−34.5136			−0.0448811			−0.0224406	−	0.999748i	$-0.507144\pi$
$769$	−34.5136			−0.0448811			−0.0224406	+	0.999748i	$0.507144\pi$
$770$		0			0
$771$		0			0
$772$	235.445	+	657.084i	0.304980	+	0.851145i
$773$		−	401.055i		−	0.518829i	−0.965766	−	0.259415i	$-0.916470\pi$
$773$		−	401.055i		−	0.518829i	0.965766	−	0.259415i	$-0.0835296\pi$
$774$		0			0
$775$		0			0
$776$	−500.388	−	881.908i	−0.644829	−	1.13648i
$777$		0			0
$778$	−702.326	+	122.029i	−0.902732	+	0.156850i
$779$		−	352.693i		−	0.452750i
$780$		0			0
$781$	115.486			0.147870
$782$	−165.029	−	949.809i	−0.211035	−	1.21459i
$783$		0			0
$784$	1031.95	−	848.467i	1.31626	−	1.08223i
$785$		0			0
$786$		0			0
$787$	−1030.24			−1.30907			−0.654534	−	0.756032i	$-0.727135\pi$
$787$	−1030.24			−1.30907			−0.654534	+	0.756032i	$0.727135\pi$
$788$	21.5679	+	60.1920i	0.0273704	+	0.0763858i
$789$		0			0
$790$		0			0
$791$		−	1656.90i		−	2.09469i
$792$		0			0
$793$			427.253i			0.538780i
$794$	−175.590	−	1010.59i	−0.221146	−	1.27278i
$795$		0			0
$796$	−41.7587	−	116.541i	−0.0524607	−	0.146408i
$797$			1070.94i			1.34372i	0.740679	+	0.671859i	$0.234504\pi$
$797$			1070.94i			1.34372i	−0.740679	+	0.671859i	$0.765496\pi$
$798$		0			0
$799$			1702.07i			2.13025i
$800$		0			0
$801$		0			0
$802$	20.4910	−	3.56032i	0.0255499	−	0.00443930i
$803$	22.4342			0.0279380
$804$		0			0
$805$		0			0
$806$	981.051	−	170.458i	1.21718	−	0.211486i
$807$		0			0
$808$	−460.510	+	261.290i	−0.569938	+	0.323379i
$809$	−1265.04			−1.56371			−0.781854	−	0.623461i	$-0.785726\pi$
$809$	−1265.04			−1.56371			−0.781854	+	0.623461i	$0.785726\pi$
$810$		0			0
$811$			966.144i			1.19130i	0.803244	+	0.595650i	$0.203105\pi$
$811$			966.144i			1.19130i	−0.803244	+	0.595650i	$0.796895\pi$
$812$	−818.967	+	293.450i	−1.00858	+	0.361392i
$813$		0			0
$814$	−985.230	+	171.184i	−1.21036	+	0.210300i
$815$		0			0
$816$		0			0
$817$			299.019i			0.365997i
$818$	−495.564	+	86.1043i	−0.605824	+	0.105262i
$819$		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
$823$	887.674			1.07858			0.539292	−	0.842119i	$-0.318692\pi$
$823$	887.674			1.07858			0.539292	+	0.842119i	$0.318692\pi$
$824$	730.802	−	414.651i	0.886895	−	0.503218i
$825$		0			0
$826$	254.813	+	1466.55i	0.308491	+	1.77548i
$827$	82.2846			0.0994977			0.0497489	−	0.998762i	$-0.484158\pi$
$827$	82.2846			0.0994977			0.0497489	+	0.998762i	$0.484158\pi$
$828$		0			0
$829$	−348.475			−0.420356			−0.210178	−	0.977663i	$-0.567404\pi$
$829$	−348.475			−0.420356			−0.210178	+	0.977663i	$0.567404\pi$
$830$		0			0
$831$		0			0
$832$	−775.992	−	463.677i	−0.932683	−	0.557304i
$833$			2553.17i			3.06503i
$834$		0			0
$835$		0			0
$836$	−459.283	+	164.569i	−0.549382	+	0.196853i
$837$		0			0
$838$	−70.3746	−	405.033i	−0.0839792	−	0.483333i
$839$			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
$842$	1598.51	−	277.741i	1.89847	−	0.329859i
$843$		0			0
$844$	−257.261	−	717.968i	−0.304811	−	0.850673i
$845$		0			0
$846$		0			0
$847$	247.459			0.292160
$848$	25.0028	+	30.4097i	0.0294845	+	0.0358605i
$849$		0			0
$850$		0			0
$851$			790.154i			0.928500i
$852$		0			0
$853$		−	1549.11i		−	1.81608i	−0.418888	−	0.908038i	$-0.637580\pi$
$853$		−	1549.11i		−	1.81608i	0.418888	−	0.908038i	$-0.362420\pi$
$854$	−686.101	+	119.210i	−0.803396	+	0.139590i
$855$		0			0
$856$	−474.696	+	269.339i	−0.554552	+	0.314649i
$857$			376.279i			0.439065i	0.975605	+	0.219533i	$0.0704532\pi$
$857$			376.279i			0.439065i	−0.975605	+	0.219533i	$0.929547\pi$
$858$		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
$862$	−123.125	−	708.630i	−0.142836	−	0.822077i
$863$	−104.458			−0.121041			−0.0605204	−	0.998167i	$-0.519276\pi$
$863$	−104.458			−0.121041			−0.0605204	+	0.998167i	$0.519276\pi$
$864$		0			0
$865$		0			0
$866$	−68.0452	−	391.627i	−0.0785741	−	0.452225i
$867$		0			0
$868$	547.456	+	1527.85i	0.630710	+	1.76020i
$869$	782.300			0.900230
$870$		0			0
$871$		−	935.017i		−	1.07350i
$872$	233.107	−	132.263i	0.267324	−	0.151678i
$873$		0			0
$874$	65.9922	+	379.811i	0.0755060	+	0.434567i
$875$		0			0
$876$		0			0
$877$			282.607i			0.322243i	0.986935	+	0.161121i	$0.0515111\pi$
$877$			282.607i			0.322243i	−0.986935	+	0.161121i	$0.948489\pi$
$878$	−120.943	−	696.073i	−0.137748	−	0.792794i
$879$		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
$883$	1267.53			1.43548			0.717741	−	0.696311i	$-0.245176\pi$
$883$	1267.53			1.43548			0.717741	+	0.696311i	$0.245176\pi$
$884$	1626.32	−	582.740i	1.83973	−	0.659208i
$885$		0			0
$886$	−413.479	+	71.8420i	−0.466680	+	0.0810858i
$887$	−49.7756			−0.0561168			−0.0280584	−	0.999606i	$-0.508932\pi$
$887$	−49.7756			−0.0561168			−0.0280584	+	0.999606i	$0.508932\pi$
$888$		0			0
$889$	−2301.96			−2.58938
$890$		0			0
$891$		0			0
$892$	−1197.29	+	429.010i	−1.34225	+	0.480953i
$893$		−	680.628i		−	0.762181i
$894$		0			0
$895$		0			0
$896$	528.078	−	1375.49i	0.589373	−	1.53515i
$897$		0			0
$898$	−1216.09	+	211.296i	−1.35422	+	0.235296i
$899$		−	666.006i		−	0.740830i
$900$		0			0
$901$	−75.2374			−0.0835043
$902$	−98.5086	−	566.955i	−0.109211	−	0.628554i
$903$		0			0
$904$	−568.278	−	1001.56i	−0.628626	−	1.10792i
$905$		0			0
$906$		0			0
$907$	−1487.71			−1.64026			−0.820128	−	0.572180i	$-0.806098\pi$
$907$	−1487.71			−1.64026			−0.820128	+	0.572180i	$0.806098\pi$
$908$	150.247	−	53.8362i	0.165470	−	0.0592909i
$909$		0			0
$910$		0			0
$911$			678.826i			0.745144i	0.928003	+	0.372572i	$0.121524\pi$
$911$			678.826i			0.745144i	−0.928003	+	0.372572i	$0.878476\pi$
$912$		0			0
$913$			1456.97i			1.59580i
$914$	44.2524	+	254.690i	0.0484162	+	0.278654i
$915$		0			0
$916$	−51.7802	+	18.5537i	−0.0565286	+	0.0202552i
$917$			2847.93i			3.10570i
$918$		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
$922$	36.8056	−	6.39499i	0.0399193	−	0.00693599i
$923$	163.527			0.177169
$924$		0			0
$925$		0			0
$926$	−215.608	+	37.4620i	−0.232838	+	0.0404557i
$927$		0			0
$928$	−394.401	+	458.270i	−0.425001	+	0.493826i
$929$	−455.044			−0.489821			−0.244911	−	0.969546i	$-0.578759\pi$
$929$	−455.044			−0.489821			−0.244911	+	0.969546i	$0.578759\pi$
$930$		0			0
$931$		−	1020.97i		−	1.09663i
$932$	−163.902	−	457.422i	−0.175861	−	0.490796i
$933$		0			0
$934$	494.549	−	85.9279i	0.529495	−	0.0919999i
$935$		0			0
$936$		0			0
$937$			1705.49i			1.82016i	0.414437	+	0.910078i	$0.363979\pi$
$937$			1705.49i			1.82016i	−0.414437	+	0.910078i	$0.636021\pi$
$938$	1501.49	−	260.884i	1.60073	−	0.278128i
$939$		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
$943$	−454.698			−0.482183
$944$	657.020	+	799.102i	0.695996	+	0.846506i
$945$		0			0
$946$	83.5174	+	480.675i	0.0882848	+	0.508114i
$947$	382.779			0.404201			0.202101	−	0.979365i	$-0.435223\pi$
$947$	382.779			0.404201			0.202101	+	0.979365i	$0.435223\pi$
$948$		0			0
$949$	31.7665			0.0334736
$950$		0			0
$951$		0			0
$952$	1389.56	+	2449.02i	1.45962	+	2.57250i
$953$		−	1101.29i		−	1.15560i	−0.816178	−	0.577800i	$-0.803911\pi$
$953$		−	1101.29i		−	1.15560i	0.816178	−	0.577800i	$-0.196089\pi$
$954$		0			0
$955$		0			0
$956$	217.020	+	605.665i	0.227009	+	0.633541i
$957$		0			0
$958$	−127.760	−	735.311i	−0.133362	−	0.767548i
$959$			1627.34i			1.69691i
$960$		0			0
$961$	−281.490			−0.292914
$962$	−1395.07	+	242.393i	−1.45017	+	0.251968i
$963$		0			0
$964$	−13.1576	+	4.71459i	−0.0136489	+	0.00489066i
$965$		0			0
$966$		0			0
$967$	−1339.59			−1.38531			−0.692655	−	0.721269i	$-0.743559\pi$
$967$	−1339.59			−1.38531			−0.692655	+	0.721269i	$0.743559\pi$
$968$	149.584	−	84.8727i	0.154529	−	0.0876784i
$969$		0			0
$970$		0			0
$971$		−	288.556i		−	0.297174i	−0.988899	−	0.148587i	$-0.952527\pi$
$971$		−	288.556i		−	0.297174i	0.988899	−	0.148587i	$-0.0474725\pi$
$972$		0			0
$973$			670.739i			0.689352i
$974$	360.171	−	62.5799i	0.369786	−	0.0642504i
$975$		0			0
$976$	−373.846	+	307.376i	−0.383039	+	0.314934i
$977$		−	1781.05i		−	1.82298i	−0.411322	−	0.911490i	$-0.634933\pi$
$977$		−	1781.05i		−	1.82298i	0.411322	−	0.911490i	$-0.365067\pi$
$978$		0			0
$979$		−	872.131i		−	0.890839i
$980$		0			0
$981$		0			0
$982$	141.545	+	814.644i	0.144139	+	0.829576i
$983$	1179.28			1.19968			0.599838	−	0.800122i	$-0.295232\pi$
$983$	1179.28			1.19968			0.599838	+	0.800122i	$0.295232\pi$
$984$		0			0
$985$		0			0
$986$	−197.802	−	1138.43i	−0.200611	−	1.15459i
$987$		0			0
$988$	−650.337	+	233.027i	−0.658236	+	0.235857i
$989$	385.502			0.389789
$990$		0			0
$991$			363.373i			0.366673i	0.983050	+	0.183337i	$0.0586898\pi$
$991$			363.373i			0.366673i	−0.983050	+	0.183337i	$0.941310\pi$
$992$	854.942	+	735.788i	0.861837	+	0.741722i
$993$		0			0
$994$	45.6265	+	262.598i	0.0459019	+	0.264183i
$995$		0			0
$996$		0			0
$997$		−	412.630i		−	0.413872i	−0.978354	−	0.206936i	$-0.933651\pi$
$997$		−	412.630i		−	0.413872i	0.978354	−	0.206936i	$-0.0663492\pi$
$998$	31.7883	+	182.954i	0.0318520	+	0.183321i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.3	✓	8	15.2	even	4
180.3.c.c.91.4	yes	8	60.47	odd	4
180.3.c.c.91.5	yes	8	20.7	even	4
180.3.c.c.91.6	yes	8	5.2	odd	4
900.3.c.o.451.3		8	5.3	odd	4
900.3.c.o.451.4		8	20.3	even	4
900.3.c.o.451.5		8	60.23	odd	4
900.3.c.o.451.6		8	15.8	even	4
900.3.f.i.199.1		16	4.3	odd	2	inner
900.3.f.i.199.2		16	60.59	even	2	inner
900.3.f.i.199.3		16	5.4	even	2	inner
900.3.f.i.199.4		16	3.2	odd	2	inner
900.3.f.i.199.13		16	15.14	odd	2	inner
900.3.f.i.199.14		16	1.1	even	1	trivial
900.3.f.i.199.15		16	12.11	even	2	inner
900.3.f.i.199.16		16	20.19	odd	2	inner
2880.3.e.i.2431.1		8	120.107	odd	4
2880.3.e.i.2431.4		8	120.77	even	4
2880.3.e.i.2431.5		8	40.27	even	4
2880.3.e.i.2431.8		8	40.37	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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.97048 - 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(6.95801 - 3.94792i) q^{8} +O(q^{10})\)	\(q+(1.97048 - 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(6.95801 - 3.94792i) q^{8} -9.97507i q^{11} -14.1245i q^{13} +(22.6817 - 3.94096i) q^{14} +(12.3590 - 10.1615i) q^{16} +30.5776i q^{17} -12.2274i q^{19} +(-3.41517 - 19.6556i) q^{22} -15.7638 q^{23} +(-4.83582 - 27.8320i) q^{26} +(43.3446 - 15.5311i) q^{28} -18.8943 q^{29} +35.2490i q^{31} +(20.8740 - 24.2544i) q^{32} +(10.4689 + 60.2524i) q^{34} -50.1245i q^{37} +(-4.18631 - 24.0938i) q^{38} +28.8444 q^{41} -24.4548 q^{43} +(-13.4590 - 37.5618i) q^{44} +(-31.0623 + 5.39707i) q^{46} +55.6641 q^{47} +83.4981 q^{49} +(-19.0578 - 53.1868i) q^{52} +2.46054i q^{53} +(80.0921 - 45.4437i) q^{56} +(-37.2309 + 6.46887i) q^{58} +64.6577i q^{59} -30.2490 q^{61} +(12.0682 + 69.4573i) q^{62} +(32.8278 - 54.9394i) q^{64} +66.1981 q^{67} +(41.2574 + 115.142i) q^{68} +11.5775i q^{71} +2.24903i q^{73} +(-17.1612 - 98.7692i) q^{74} +(-16.4981 - 46.0431i) q^{76} -114.821i q^{77} +78.4256i q^{79} +(56.8373 - 9.87548i) q^{82} -146.061 q^{83} +(-48.1877 + 8.37262i) q^{86} +(-39.3808 - 69.4066i) q^{88} +87.4311 q^{89} -162.584i q^{91} +(-59.3597 + 21.2696i) q^{92} +(109.685 - 19.0578i) q^{94} -126.747i q^{97} +(164.531 - 28.5873i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{4}+O(q^{10}) \) 16 * q + 28 * q^4	\( 16 q + 28 q^{4} - 28 q^{16} + 232 q^{34} - 368 q^{46} + 304 q^{49} + 32 q^{61} + 364 q^{64} + 768 q^{76} + 336 q^{94}+O(q^{100}) \) 16 * q + 28 * q^4 - 28 * q^16 + 232 * q^34 - 368 * q^46 + 304 * q^49 + 32 * q^61 + 364 * q^64 + 768 * q^76 + 336 * q^94

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