LMFDB - Embedded newform 900.3.f.i.199.4

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			199.4
Root			$-1.97048 - 0.960405i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.i.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97048 + 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(-6.95801 + 3.94792i) q^{8} +O(q^{10})$	\(q+(-1.97048 + 0.342371i) q^{2} +(3.76556 - 1.34927i) q^{4} +11.5108 q^{7} +(-6.95801 + 3.94792i) q^{8} +9.97507i q^{11} -14.1245i q^{13} +(-22.6817 + 3.94096i) q^{14} +(12.3590 - 10.1615i) q^{16} -30.5776i q^{17} -12.2274i q^{19} +(-3.41517 - 19.6556i) q^{22} +15.7638 q^{23} +(4.83582 + 27.8320i) q^{26} +(43.3446 - 15.5311i) q^{28} +18.8943 q^{29} +35.2490i q^{31} +(-20.8740 + 24.2544i) q^{32} +(10.4689 + 60.2524i) q^{34} -50.1245i q^{37} +(4.18631 + 24.0938i) q^{38} -28.8444 q^{41} -24.4548 q^{43} +(13.4590 + 37.5618i) q^{44} +(-31.0623 + 5.39707i) q^{46} -55.6641 q^{47} +83.4981 q^{49} +(-19.0578 - 53.1868i) q^{52} -2.46054i q^{53} +(-80.0921 + 45.4437i) q^{56} +(-37.2309 + 6.46887i) q^{58} -64.6577i q^{59} -30.2490 q^{61} +(-12.0682 - 69.4573i) q^{62} +(32.8278 - 54.9394i) q^{64} +66.1981 q^{67} +(-41.2574 - 115.142i) q^{68} -11.5775i q^{71} +2.24903i q^{73} +(17.1612 + 98.7692i) q^{74} +(-16.4981 - 46.0431i) q^{76} +114.821i q^{77} +78.4256i q^{79} +(56.8373 - 9.87548i) q^{82} +146.061 q^{83} +(48.1877 - 8.37262i) q^{86} +(-39.3808 - 69.4066i) q^{88} -87.4311 q^{89} -162.584i q^{91} +(59.3597 - 21.2696i) q^{92} +(109.685 - 19.0578i) q^{94} -126.747i q^{97} +(-164.531 + 28.5873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.149793\pi$
$11$			9.97507i			0.906824i	−0.891301	+	0.453412i	$0.850207\pi$
$12$		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	$-0.644047\pi$
$17$		−	30.5776i		−	1.79868i	0.437249	−	0.899341i	$-0.355953\pi$
$18$		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	$-0.388661\pi$
$23$	15.7638			0.685384			0.342692	+	0.939448i	$0.388661\pi$
$24$		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	$-0.394378\pi$
$29$	18.8943			0.651529			0.325765	+	0.945451i	$0.394378\pi$
$30$		0			0
$31$			35.2490i			1.13706i	0.822661	+	0.568532i	$0.192488\pi$
$31$			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	$-0.614417\pi$
$41$	−28.8444			−0.703522			−0.351761	+	0.936090i	$0.614417\pi$
$42$		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	$-0.701729\pi$
$47$	−55.6641			−1.18434			−0.592171	+	0.805812i	$0.701729\pi$
$48$		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	$-0.992611\pi$
$53$		−	2.46054i		−	0.0464253i	0.999731	−	0.0232127i	$-0.00738948\pi$
$54$		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	$-0.815410\pi$
$59$		−	64.6577i		−	1.09589i	0.836513	−	0.547947i	$-0.184590\pi$
$60$		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	$-0.974019\pi$
$71$		−	11.5775i		−	0.163064i	0.996671	−	0.0815318i	$-0.0259812\pi$
$72$		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	$-0.157620\pi$
$83$	146.061			1.75977			0.879884	+	0.475189i	$0.157620\pi$
$84$		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	$-0.663436\pi$
$89$	−87.4311			−0.982372			−0.491186	+	0.871055i	$0.663436\pi$
$90$		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	$-0.393745\pi$
$101$	66.1841			0.655289			0.327644	+	0.944801i	$0.393745\pi$
$102$		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	$-0.396720\pi$
$107$	68.2230			0.637598			0.318799	+	0.947822i	$0.396720\pi$
$108$		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	$0.219791\pi$
$113$			143.944i			1.27384i	−0.770931	+	0.636919i	$0.780209\pi$
$114$		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	$-0.606714\pi$
$131$		−	247.414i		−	1.88866i	0.329007	−	0.944328i	$-0.393286\pi$
$132$		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	$-0.827432\pi$
$137$		−	141.375i		−	1.03194i	0.856608	−	0.515968i	$-0.172568\pi$
$138$		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	$-0.149984\pi$
$149$	265.527			1.78206			0.891029	+	0.453947i	$0.149984\pi$
$150$		0			0
$151$			217.988i			1.44363i	0.692086	+	0.721815i	$0.256692\pi$
$151$			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	$-0.454778\pi$
$167$	47.2915			0.283182			0.141591	+	0.989925i	$0.454778\pi$
$168$		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	$-0.769116\pi$
$173$		−	229.534i		−	1.32678i	0.748272	−	0.663392i	$-0.230884\pi$
$174$		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	$-0.861532\pi$
$179$		−	150.868i		−	0.842838i	0.906866	−	0.421419i	$-0.138468\pi$
$180$		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	$-0.798631\pi$
$191$		−	225.861i		−	1.18252i	0.806481	−	0.591260i	$-0.201369\pi$
$192$		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	$-0.987082\pi$
$197$		−	15.9849i		−	0.0811414i	0.999177	−	0.0405707i	$-0.0129176\pi$
$198$		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	$-0.528011\pi$
$227$	−39.9003			−0.175772			−0.0878860	+	0.996131i	$0.528011\pi$
$228$		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	$0.0839454\pi$
$233$			121.475i			0.521352i	−0.965426	+	0.260676i	$0.916055\pi$
$234$		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	$-0.890760\pi$
$239$		−	160.843i		−	0.672984i	0.941686	−	0.336492i	$-0.109240\pi$
$240$		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	$0.216437\pi$
$251$			315.637i			1.25752i	−0.777601	+	0.628759i	$0.783563\pi$
$252$		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	$0.0540196\pi$
$257$			86.8117i			0.337789i	−0.985634	+	0.168894i	$0.945980\pi$
$258$		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	$-0.281788\pi$
$263$	333.003			1.26617			0.633086	+	0.774082i	$0.281788\pi$
$264$		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	$-0.615565\pi$
$269$	−191.063			−0.710271			−0.355136	+	0.934815i	$0.615565\pi$
$270$		0			0
$271$			261.165i			0.963708i	0.876252	+	0.481854i	$0.160036\pi$
$271$			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	$-0.196055\pi$
$281$	458.726			1.63248			0.816239	+	0.577714i	$0.196055\pi$
$282$		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	$0.140086\pi$
$293$			249.650i			0.852046i	−0.904712	+	0.426023i	$0.859914\pi$
$294$		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	$0.0853395\pi$
$311$			164.769i			0.529803i	−0.964275	+	0.264902i	$0.914661\pi$
$312$		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	$0.0863217\pi$
$317$			169.833i			0.535752i	−0.963453	+	0.267876i	$0.913678\pi$
$318$		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	$-0.577816\pi$
$347$	−167.974			−0.484074			−0.242037	+	0.970267i	$0.577816\pi$
$348$		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	$0.0919304\pi$
$353$			201.076i			0.569619i	−0.958584	+	0.284810i	$0.908070\pi$
$354$		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	$0.409478\pi$
$359$			689.161i			1.91967i	−0.280567	+	0.959835i	$0.590522\pi$
$360$		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	$-0.695973\pi$
$383$	−442.368			−1.15501			−0.577504	+	0.816388i	$0.695973\pi$
$384$		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	$-0.348520\pi$
$389$	356.424			0.916257			0.458129	+	0.888886i	$0.348520\pi$
$390$		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	$-0.504127\pi$
$401$	−10.3990			−0.0259327			−0.0129664	+	0.999916i	$0.504127\pi$
$402$		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	$0.0788823\pi$
$419$			205.551i			0.490574i	−0.969450	+	0.245287i	$0.921118\pi$
$420$		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	$0.136987\pi$
$431$			359.624i			0.834394i	−0.908816	+	0.417197i	$0.863013\pi$
$432$		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	$-0.423890\pi$
$443$	209.837			0.473672			0.236836	+	0.971550i	$0.423890\pi$
$444$		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	$-0.258816\pi$
$449$	617.155			1.37451			0.687255	+	0.726416i	$0.258816\pi$
$450$		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	$-0.506449\pi$
$461$	−18.6785			−0.0405174			−0.0202587	+	0.999795i	$0.506449\pi$
$462$		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	$-0.586599\pi$
$467$	−250.979			−0.537428			−0.268714	+	0.963220i	$0.586599\pi$
$468$		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	$0.127360\pi$
$479$			373.164i			0.779048i	−0.921016	+	0.389524i	$0.872640\pi$
$480$		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	$-0.861678\pi$
$491$		−	413.425i		−	0.842005i	0.907059	−	0.421003i	$-0.138322\pi$
$492$		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	$-0.635453\pi$
$503$	−415.288			−0.825622			−0.412811	+	0.910817i	$0.635453\pi$
$504$		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	$-0.372818\pi$
$509$	396.009			0.778013			0.389006	+	0.921235i	$0.372818\pi$
$510$		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	$-0.611048\pi$
$521$	−356.191			−0.683668			−0.341834	+	0.939760i	$0.611048\pi$
$522$		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	$0.219571\pi$
$557$			708.933i			1.27277i	−0.771372	+	0.636385i	$0.780429\pi$
$558$		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	$-0.924620\pi$
$563$	−1094.57			−1.94418			−0.972090	+	0.234607i	$0.924620\pi$
$564$		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	$-0.736210\pi$
$569$	−769.082			−1.35164			−0.675819	+	0.737068i	$0.736210\pi$
$570$		0			0
$571$			871.192i			1.52573i	0.646558	+	0.762865i	$0.276208\pi$
$571$			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	$-0.459759\pi$
$587$	148.024			0.252170			0.126085	+	0.992019i	$0.459759\pi$
$588$		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	$-0.972463\pi$
$593$		−	102.473i		−	0.172804i	0.996260	−	0.0864020i	$-0.0275370\pi$
$594$		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	$0.0952651\pi$
$599$			353.214i			0.589673i	−0.955548	+	0.294836i	$0.904735\pi$
$600$		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	$-0.990235\pi$
$617$		−	37.8513i		−	0.0613473i	0.999529	−	0.0306737i	$-0.00976526\pi$
$618$		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	$-0.823099\pi$
$641$	−1089.06			−1.69901			−0.849504	+	0.527582i	$0.823099\pi$
$642$		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	$-0.801216\pi$
$647$	−1049.77			−1.62251			−0.811257	+	0.584690i	$0.801216\pi$
$648$		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	$-0.973156\pi$
$653$		−	110.008i		−	0.168465i	0.996446	−	0.0842325i	$-0.0268438\pi$
$654$		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	$0.0888635\pi$
$659$			363.189i			0.551121i	−0.961284	+	0.275561i	$0.911137\pi$
$660$		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	$0.0709159\pi$
$677$			299.167i			0.441901i	−0.975285	+	0.220950i	$0.929084\pi$
$678$		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	$-0.579991\pi$
$683$	−339.673			−0.497326			−0.248663	+	0.968590i	$0.579991\pi$
$684$		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	$-0.570529\pi$
$701$	−308.111			−0.439531			−0.219765	+	0.975553i	$0.570529\pi$
$702$		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	$0.179078\pi$
$719$			766.999i			1.06676i	−0.845876	+	0.533379i	$0.820922\pi$
$720$		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	$-0.259859\pi$
$743$	1017.72			1.36974			0.684870	+	0.728665i	$0.259859\pi$
$744$		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	$-0.453445\pi$
$761$	221.811			0.291473			0.145737	+	0.989323i	$0.453445\pi$
$762$		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	$0.0835296\pi$
$773$			401.055i			0.518829i	−0.965766	+	0.259415i	$0.916470\pi$
$774$		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	$-0.765496\pi$
$797$		−	1070.94i		−	1.34372i	0.740679	−	0.671859i	$-0.234504\pi$
$798$		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	$-0.214274\pi$
$809$	1265.04			1.56371			0.781854	+	0.623461i	$0.214274\pi$
$810$		0			0
$811$			966.144i			1.19130i	0.803244	+	0.595650i	$0.203105\pi$
$811$			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	$-0.679674\pi$
$821$	−878.408			−1.06992			−0.534962	+	0.844876i	$0.679674\pi$
$822$		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	$-0.515842\pi$
$827$	−82.2846			−0.0994977			−0.0497489	+	0.998762i	$0.515842\pi$
$828$		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	$-0.966860\pi$
$839$		−	174.383i		−	0.207847i	0.994585	−	0.103923i	$-0.0331397\pi$
$840$		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	$-0.929547\pi$
$857$		−	376.279i		−	0.439065i	0.975605	−	0.219533i	$-0.0704532\pi$
$858$		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	$-0.480724\pi$
$863$	104.458			0.121041			0.0605204	+	0.998167i	$0.480724\pi$
$864$		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	$-0.606476\pi$
$881$	−578.468			−0.656604			−0.328302	+	0.944573i	$0.606476\pi$
$882$		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	$-0.491068\pi$
$887$	49.7756			0.0561168			0.0280584	+	0.999606i	$0.491068\pi$
$888$		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	$-0.878476\pi$
$911$		−	678.826i		−	0.745144i	0.928003	−	0.372572i	$-0.121524\pi$
$912$		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	$-0.421241\pi$
$929$	455.044			0.489821			0.244911	+	0.969546i	$0.421241\pi$
$930$		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	$-0.486913\pi$
$941$	77.3558			0.0822060			0.0411030	+	0.999155i	$0.486913\pi$
$942$		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	$-0.564777\pi$
$947$	−382.779			−0.404201			−0.202101	+	0.979365i	$0.564777\pi$
$948$		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	$0.196089\pi$
$953$			1101.29i			1.15560i	−0.816178	+	0.577800i	$0.803911\pi$
$954$		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	$0.0474725\pi$
$971$			288.556i			0.297174i	−0.988899	+	0.148587i	$0.952527\pi$
$972$		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	$0.365067\pi$
$977$			1781.05i			1.82298i	−0.411322	+	0.911490i	$0.634933\pi$
$978$		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	$-0.704768\pi$
$983$	−1179.28			−1.19968			−0.599838	+	0.800122i	$0.704768\pi$
$984$		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.199.4		16
3.2	odd	2	inner	900.3.f.i.199.14		16
4.3	odd	2	inner	900.3.f.i.199.15		16
5.2	odd	4		180.3.c.c.91.3	✓	8
5.3	odd	4		900.3.c.o.451.6		8
5.4	even	2	inner	900.3.f.i.199.13		16
12.11	even	2	inner	900.3.f.i.199.1		16
15.2	even	4		180.3.c.c.91.6	yes	8
15.8	even	4		900.3.c.o.451.3		8
15.14	odd	2	inner	900.3.f.i.199.3		16
20.3	even	4		900.3.c.o.451.5		8
20.7	even	4		180.3.c.c.91.4	yes	8
20.19	odd	2	inner	900.3.f.i.199.2		16
40.27	even	4		2880.3.e.i.2431.1		8
40.37	odd	4		2880.3.e.i.2431.4		8
60.23	odd	4		900.3.c.o.451.4		8
60.47	odd	4		180.3.c.c.91.5	yes	8
60.59	even	2	inner	900.3.f.i.199.16		16
120.77	even	4		2880.3.e.i.2431.8		8
120.107	odd	4		2880.3.e.i.2431.5		8

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