LMFDB - Embedded newform 900.3.f.f.199.6

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} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 12x^12 + 25x^10 + 53x^8 + 100x^6 + 192x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{28} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$0.422403 - 1.34966i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.f.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.696577 + 1.87477i) q^{2} +(-3.02956 - 2.61185i) q^{4} -5.46770 q^{7} +(7.00695 - 3.86039i) q^{8} +O(q^{10})$	\(q+(-0.696577 + 1.87477i) q^{2} +(-3.02956 - 2.61185i) q^{4} -5.46770 q^{7} +(7.00695 - 3.86039i) q^{8} +11.0403i q^{11} +10.1242i q^{13} +(3.80867 - 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} -24.4146i q^{17} +23.7757i q^{19} +(-20.6981 - 7.69043i) q^{22} +37.2526 q^{23} +(-18.9806 - 7.05227i) q^{26} +(16.5647 + 14.2808i) q^{28} -25.7726 q^{29} +4.83647i q^{31} +(-31.3108 - 6.60580i) q^{32} +(45.7719 + 17.0066i) q^{34} -35.6493i q^{37} +(-44.5741 - 16.5616i) q^{38} +9.30410 q^{41} -70.0287 q^{43} +(28.8356 - 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} -38.0223 q^{47} -19.1043 q^{49} +(26.4428 - 30.6718i) q^{52} -55.7762i q^{53} +(-38.3119 + 21.1075i) q^{56} +(17.9526 - 48.3179i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(-9.06729 - 3.36897i) q^{62} +(34.1947 - 54.0992i) q^{64} -104.493 q^{67} +(-63.7673 + 73.9656i) q^{68} +76.7471i q^{71} -93.5215i q^{73} +(66.8344 + 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} -60.3651i q^{77} -49.3762i q^{79} +(-6.48102 + 17.4431i) q^{82} -72.3768 q^{83} +(48.7804 - 131.288i) q^{86} +(42.6199 + 77.3589i) q^{88} +115.691 q^{89} -55.3560i q^{91} +(-112.859 - 97.2980i) q^{92} +(26.4854 - 71.2832i) q^{94} +72.9589i q^{97} +(13.3076 - 35.8162i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4}+O(q^{10}) $ 16 * q - 20 * q^4	$ 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) $ 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * 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 $

$2$	−0.696577	+	1.87477i	−0.348288	+	0.937387i
$2$	−0.696577	+	1.87477i	−0.348288	+	0.937387i
$3$		0			0
$3$		0			0
$4$	−3.02956	−	2.61185i	−0.757390	−	0.652962i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−5.46770			−0.781100			−0.390550	−	0.920582i	$-0.627715\pi$
$7$	−5.46770			−0.781100			−0.390550	+	0.920582i	$0.627715\pi$
$8$	7.00695	−	3.86039i	0.875869	−	0.482549i
$9$		0			0
$10$		0			0
$11$			11.0403i			1.00366i	0.864965	+	0.501832i	$0.167341\pi$
$11$			11.0403i			1.00366i	−0.864965	+	0.501832i	$0.832659\pi$
$12$		0			0
$13$			10.1242i			0.778784i	0.921072	+	0.389392i	$0.127315\pi$
$13$			10.1242i			0.778784i	−0.921072	+	0.389392i	$0.872685\pi$
$14$	3.80867	−	10.2507i	0.272048	−	0.732193i
$15$		0			0
$16$	2.35649	+	15.8255i	0.147280	+	0.989095i
$17$		−	24.4146i		−	1.43615i	−0.695964	−	0.718077i	$-0.745023\pi$
$17$		−	24.4146i		−	1.43615i	0.695964	−	0.718077i	$-0.254977\pi$
$18$		0			0
$19$			23.7757i			1.25135i	0.780082	+	0.625677i	$0.215177\pi$
$19$			23.7757i			1.25135i	−0.780082	+	0.625677i	$0.784823\pi$
$20$		0			0
$21$		0			0
$22$	−20.6981	−	7.69043i	−0.940823	−	0.349565i
$23$	37.2526			1.61968			0.809838	−	0.586653i	$-0.199555\pi$
$23$	37.2526			1.61968			0.809838	+	0.586653i	$0.199555\pi$
$24$		0			0
$25$		0			0
$26$	−18.9806	−	7.05227i	−0.730022	−	0.271241i
$27$		0			0
$28$	16.5647	+	14.2808i	0.591598	+	0.510029i
$29$	−25.7726			−0.888712			−0.444356	−	0.895850i	$-0.646567\pi$
$29$	−25.7726			−0.888712			−0.444356	+	0.895850i	$0.646567\pi$
$30$		0			0
$31$			4.83647i			0.156015i	0.996953	+	0.0780076i	$0.0248558\pi$
$31$			4.83647i			0.156015i	−0.996953	+	0.0780076i	$0.975144\pi$
$32$	−31.3108	−	6.60580i	−0.978461	−	0.206431i
$33$		0			0
$34$	45.7719	+	17.0066i	1.34623	+	0.500196i
$35$		0			0
$36$		0			0
$37$		−	35.6493i		−	0.963495i	−0.876310	−	0.481747i	$-0.840002\pi$
$37$		−	35.6493i		−	0.963495i	0.876310	−	0.481747i	$-0.159998\pi$
$38$	−44.5741	−	16.5616i	−1.17300	−	0.435832i
$39$		0			0
$40$		0			0
$41$	9.30410			0.226929			0.113465	−	0.993542i	$-0.463805\pi$
$41$	9.30410			0.226929			0.113465	+	0.993542i	$0.463805\pi$
$42$		0			0
$43$	−70.0287			−1.62857			−0.814287	−	0.580462i	$-0.802872\pi$
$43$	−70.0287			−1.62857			−0.814287	+	0.580462i	$0.802872\pi$
$44$	28.8356	−	33.4473i	0.655355	−	0.760166i
$45$		0			0
$46$	−25.9493	+	69.8401i	−0.564114	+	1.51826i
$47$	−38.0223			−0.808984			−0.404492	−	0.914542i	$-0.632552\pi$
$47$	−38.0223			−0.808984			−0.404492	+	0.914542i	$0.632552\pi$
$48$		0			0
$49$	−19.1043			−0.389883
$50$		0			0
$51$		0			0
$52$	26.4428	−	30.6718i	0.508516	−	0.589843i
$53$		−	55.7762i		−	1.05238i	−0.850366	−	0.526191i	$-0.823620\pi$
$53$		−	55.7762i		−	1.05238i	0.850366	−	0.526191i	$-0.176380\pi$
$54$		0			0
$55$		0			0
$56$	−38.3119	+	21.1075i	−0.684141	+	0.376919i
$57$		0			0
$58$	17.9526	−	48.3179i	0.309528	−	0.833067i
$59$		−	55.5411i		−	0.941374i	−0.882300	−	0.470687i	$-0.844006\pi$
$59$		−	55.5411i		−	0.941374i	0.882300	−	0.470687i	$-0.155994\pi$
$60$		0			0
$61$	−82.2412			−1.34822			−0.674108	−	0.738633i	$-0.735472\pi$
$61$	−82.2412			−1.34822			−0.674108	+	0.738633i	$0.735472\pi$
$62$	−9.06729	−	3.36897i	−0.146247	−	0.0543383i
$63$		0			0
$64$	34.1947	−	54.0992i	0.534293	−	0.845299i
$65$		0			0
$66$		0			0
$67$	−104.493			−1.55960			−0.779802	−	0.626026i	$-0.784680\pi$
$67$	−104.493			−1.55960			−0.779802	+	0.626026i	$0.784680\pi$
$68$	−63.7673	+	73.9656i	−0.937754	+	1.08773i
$69$		0			0
$70$		0			0
$71$			76.7471i			1.08094i	0.841362	+	0.540472i	$0.181754\pi$
$71$			76.7471i			1.08094i	−0.841362	+	0.540472i	$0.818246\pi$
$72$		0			0
$73$		−	93.5215i		−	1.28112i	−0.767910	−	0.640558i	$-0.778703\pi$
$73$		−	93.5215i		−	1.28112i	0.767910	−	0.640558i	$-0.221297\pi$
$74$	66.8344	+	24.8325i	0.903168	+	0.335574i
$75$		0			0
$76$	62.0986	−	72.0300i	0.817087	−	0.947764i
$77$		−	60.3651i		−	0.783963i
$78$		0			0
$79$		−	49.3762i		−	0.625016i	−0.949915	−	0.312508i	$-0.898831\pi$
$79$		−	49.3762i		−	0.625016i	0.949915	−	0.312508i	$-0.101169\pi$
$80$		0			0
$81$		0			0
$82$	−6.48102	+	17.4431i	−0.0790368	+	0.212721i
$83$	−72.3768			−0.872010			−0.436005	−	0.899944i	$-0.643607\pi$
$83$	−72.3768			−0.872010			−0.436005	+	0.899944i	$0.643607\pi$
$84$		0			0
$85$		0			0
$86$	48.7804	−	131.288i	0.567214	−	1.52661i
$87$		0			0
$88$	42.6199	+	77.3589i	0.484318	+	0.879079i
$89$	115.691			1.29990			0.649950	−	0.759977i	$-0.274790\pi$
$89$	115.691			1.29990			0.649950	+	0.759977i	$0.274790\pi$
$90$		0			0
$91$		−	55.3560i		−	0.608308i
$92$	−112.859	−	97.2980i	−1.22673	−	1.05759i
$93$		0			0
$94$	26.4854	−	71.2832i	0.281760	−	0.758332i
$95$		0			0
$96$		0			0
$97$			72.9589i			0.752154i	0.926588	+	0.376077i	$0.122727\pi$
$97$			72.9589i			0.752154i	−0.926588	+	0.376077i	$0.877273\pi$
$98$	13.3076	−	35.8162i	0.135792	−	0.365471i
$99$		0			0
$100$		0			0
$101$	−29.4092			−0.291180			−0.145590	−	0.989345i	$-0.546508\pi$
$101$	−29.4092			−0.291180			−0.145590	+	0.989345i	$0.546508\pi$
$102$		0			0
$103$	−28.1884			−0.273673			−0.136837	−	0.990594i	$-0.543694\pi$
$103$	−28.1884			−0.273673			−0.136837	+	0.990594i	$0.543694\pi$
$104$	39.0833	+	70.9397i	0.375801	+	0.682112i
$105$		0			0
$106$	104.568	+	38.8524i	0.986490	+	0.366532i
$107$	−4.50700			−0.0421215			−0.0210607	−	0.999778i	$-0.506704\pi$
$107$	−4.50700			−0.0421215			−0.0210607	+	0.999778i	$0.506704\pi$
$108$		0			0
$109$	−193.315			−1.77353			−0.886767	−	0.462217i	$-0.847054\pi$
$109$	−193.315			−1.77353			−0.886767	+	0.462217i	$0.847054\pi$
$110$		0			0
$111$		0			0
$112$	−12.8846	−	86.5292i	−0.115041	−	0.772582i
$113$		−	75.5727i		−	0.668785i	−0.942434	−	0.334392i	$-0.891469\pi$
$113$		−	75.5727i		−	0.668785i	0.942434	−	0.334392i	$-0.108531\pi$
$114$		0			0
$115$		0			0
$116$	78.0798	+	67.3142i	0.673102	+	0.580295i
$117$		0			0
$118$	104.127	+	38.6886i	0.882432	+	0.327870i
$119$			133.492i			1.12178i
$120$		0			0
$121$	−0.888544			−0.00734334
$122$	57.2873	−	154.184i	0.469568	−	1.26380i
$123$		0			0
$124$	12.6321	−	14.6524i	0.101872	−	0.118164i
$125$		0			0
$126$		0			0
$127$	131.306			1.03390			0.516951	−	0.856015i	$-0.327067\pi$
$127$	131.306			1.03390			0.516951	+	0.856015i	$0.327067\pi$
$128$	77.6045	+	101.792i	0.606285	+	0.795247i
$129$		0			0
$130$		0			0
$131$		−	75.7533i		−	0.578270i	−0.957288	−	0.289135i	$-0.906632\pi$
$131$		−	75.7533i		−	0.578270i	0.957288	−	0.289135i	$-0.0933676\pi$
$132$		0			0
$133$		−	129.999i		−	0.977433i
$134$	72.7877	−	195.902i	0.543192	−	1.46195i
$135$		0			0
$136$	−94.2500	−	171.072i	−0.693014	−	1.25788i
$137$			66.7927i			0.487538i	0.969833	+	0.243769i	$0.0783839\pi$
$137$			66.7927i			0.487538i	−0.969833	+	0.243769i	$0.921616\pi$
$138$		0			0
$139$			38.1214i			0.274255i	0.990553	+	0.137127i	$0.0437869\pi$
$139$			38.1214i			0.274255i	−0.990553	+	0.137127i	$0.956213\pi$
$140$		0			0
$141$		0			0
$142$	−143.884	−	53.4602i	−1.01326	−	0.376481i
$143$	−111.774			−0.781638
$144$		0			0
$145$		0			0
$146$	175.332	+	65.1449i	1.20090	+	0.446198i
$147$		0			0
$148$	−93.1106	+	108.002i	−0.629126	+	0.729742i
$149$	−126.717			−0.850449			−0.425225	−	0.905088i	$-0.639805\pi$
$149$	−126.717			−0.850449			−0.425225	+	0.905088i	$0.639805\pi$
$150$		0			0
$151$			68.4403i			0.453247i	0.973982	+	0.226623i	$0.0727687\pi$
$151$			68.4403i			0.453247i	−0.973982	+	0.226623i	$0.927231\pi$
$152$	91.7836	+	166.595i	0.603840	+	1.09602i
$153$		0			0
$154$	113.171	+	42.0489i	0.734877	+	0.273045i
$155$		0			0
$156$		0			0
$157$		−	25.5777i		−	0.162915i	−0.996677	−	0.0814577i	$-0.974042\pi$
$157$		−	25.5777i		−	0.162915i	0.996677	−	0.0814577i	$-0.0259575\pi$
$158$	92.5693	+	34.3943i	0.585882	+	0.217686i
$159$		0			0
$160$		0			0
$161$	−203.686			−1.26513
$162$		0			0
$163$	63.4771			0.389430			0.194715	−	0.980860i	$-0.437622\pi$
$163$	63.4771			0.389430			0.194715	+	0.980860i	$0.437622\pi$
$164$	−28.1873	−	24.3009i	−0.171874	−	0.148176i
$165$		0			0
$166$	50.4160	−	135.690i	0.303711	−	0.817411i
$167$	12.3771			0.0741144			0.0370572	−	0.999313i	$-0.488202\pi$
$167$	12.3771			0.0741144			0.0370572	+	0.999313i	$0.488202\pi$
$168$		0			0
$169$	66.5008			0.393496
$170$		0			0
$171$		0			0
$172$	212.156	+	182.904i	1.23347	+	1.06340i
$173$		−	59.3729i		−	0.343196i	−0.985167	−	0.171598i	$-0.945107\pi$
$173$		−	59.3729i		−	0.343196i	0.985167	−	0.171598i	$-0.0548930\pi$
$174$		0			0
$175$		0			0
$176$	−174.719	+	26.0164i	−0.992720	+	0.147820i
$177$		0			0
$178$	−80.5877	+	216.895i	−0.452740	+	1.21851i
$179$		−	252.782i		−	1.41219i	−0.708118	−	0.706094i	$-0.750455\pi$
$179$		−	252.782i		−	1.41219i	0.708118	−	0.706094i	$-0.249545\pi$
$180$		0			0
$181$	125.373			0.692670			0.346335	−	0.938111i	$-0.387426\pi$
$181$	125.373			0.692670			0.346335	+	0.938111i	$0.387426\pi$
$182$	103.780	+	38.5597i	0.570220	+	0.211867i
$183$		0			0
$184$	261.027	−	143.809i	1.41862	−	0.781573i
$185$		0			0
$186$		0			0
$187$	269.545			1.44142
$188$	115.191	+	99.3084i	0.612717	+	0.528236i
$189$		0			0
$190$		0			0
$191$		−	97.4640i		−	0.510283i	−0.966904	−	0.255141i	$-0.917878\pi$
$191$		−	97.4640i		−	0.510283i	0.966904	−	0.255141i	$-0.0821220\pi$
$192$		0			0
$193$		−	342.376i		−	1.77397i	−0.461798	−	0.886985i	$-0.652796\pi$
$193$		−	342.376i		−	1.77397i	0.461798	−	0.886985i	$-0.347204\pi$
$194$	−136.782	−	50.8215i	−0.705060	−	0.261966i
$195$		0			0
$196$	57.8775	+	49.8974i	0.295293	+	0.254579i
$197$			74.4829i			0.378086i	0.981969	+	0.189043i	$0.0605386\pi$
$197$			74.4829i			0.378086i	−0.981969	+	0.189043i	$0.939461\pi$
$198$		0			0
$199$			178.027i			0.894606i	0.894382	+	0.447303i	$0.147615\pi$
$199$			178.027i			0.894606i	−0.894382	+	0.447303i	$0.852385\pi$
$200$		0			0
$201$		0			0
$202$	20.4858	−	55.1356i	0.101415	−	0.272949i
$203$	140.917			0.694173
$204$		0			0
$205$		0			0
$206$	19.6354	−	52.8468i	0.0953172	−	0.256538i
$207$		0			0
$208$	−160.220	+	23.8575i	−0.770291	+	0.114700i
$209$	−262.491			−1.25594
$210$		0			0
$211$			185.893i			0.881008i	0.897751	+	0.440504i	$0.145200\pi$
$211$			185.893i			0.881008i	−0.897751	+	0.440504i	$0.854800\pi$
$212$	−145.679	+	168.978i	−0.687166	+	0.797064i
$213$		0			0
$214$	3.13947	−	8.44961i	0.0146704	−	0.0394842i
$215$		0			0
$216$		0			0
$217$		−	26.4444i		−	0.121863i
$218$	134.659	−	362.422i	0.617701	−	1.66249i
$219$		0			0
$220$		0			0
$221$	247.178			1.11845
$222$		0			0
$223$	202.724			0.909074			0.454537	−	0.890728i	$-0.349805\pi$
$223$	202.724			0.909074			0.454537	+	0.890728i	$0.349805\pi$
$224$	171.198	+	36.1186i	0.764276	+	0.161244i
$225$		0			0
$226$	141.682	+	52.6422i	0.626910	+	0.232930i
$227$	51.2708			0.225863			0.112931	−	0.993603i	$-0.463976\pi$
$227$	51.2708			0.225863			0.112931	+	0.993603i	$0.463976\pi$
$228$		0			0
$229$	−337.056			−1.47186			−0.735930	−	0.677058i	$-0.763255\pi$
$229$	−337.056			−1.47186			−0.735930	+	0.677058i	$0.763255\pi$
$230$		0			0
$231$		0			0
$232$	−180.588	+	99.4925i	−0.778395	+	0.428847i
$233$			80.2851i			0.344571i	0.985047	+	0.172286i	$0.0551152\pi$
$233$			80.2851i			0.344571i	−0.985047	+	0.172286i	$0.944885\pi$
$234$		0			0
$235$		0			0
$236$	−145.065	+	168.265i	−0.614682	+	0.712988i
$237$		0			0
$238$	−250.267	−	92.9873i	−1.05154	−	0.390703i
$239$			330.808i			1.38413i	0.721834	+	0.692066i	$0.243299\pi$
$239$			330.808i			1.38413i	−0.721834	+	0.692066i	$0.756701\pi$
$240$		0			0
$241$	−359.914			−1.49342			−0.746710	−	0.665150i	$-0.768368\pi$
$241$	−359.914			−1.49342			−0.746710	+	0.665150i	$0.768368\pi$
$242$	0.618939	−	1.66582i	0.00255760	−	0.00688355i
$243$		0			0
$244$	249.155	+	214.802i	1.02113	+	0.880334i
$245$		0			0
$246$		0			0
$247$	−240.710			−0.974534
$248$	18.6707	+	33.8889i	0.0752850	+	0.136649i
$249$		0			0
$250$		0			0
$251$		−	312.213i		−	1.24388i	−0.783067	−	0.621938i	$-0.786346\pi$
$251$		−	312.213i		−	1.24388i	0.783067	−	0.621938i	$-0.213654\pi$
$252$		0			0
$253$			411.280i			1.62561i
$254$	−91.4645	+	246.169i	−0.360096	+	0.969167i
$255$		0			0
$256$	−244.894	+	74.5853i	−0.956617	+	0.291349i
$257$			80.2592i			0.312293i	0.987734	+	0.156146i	$0.0499072\pi$
$257$			80.2592i			0.312293i	−0.987734	+	0.156146i	$0.950093\pi$
$258$		0			0
$259$			194.920i			0.752586i
$260$		0			0
$261$		0			0
$262$	142.020	+	52.7680i	0.542063	+	0.201405i
$263$	−487.967			−1.85539			−0.927694	−	0.373342i	$-0.878212\pi$
$263$	−487.967			−1.85539			−0.927694	+	0.373342i	$0.878212\pi$
$264$		0			0
$265$		0			0
$266$	243.718	+	90.5540i	0.916233	+	0.340428i
$267$		0			0
$268$	316.569	+	272.921i	1.18123	+	1.01836i
$269$	−309.553			−1.15076			−0.575378	−	0.817888i	$-0.695145\pi$
$269$	−309.553			−1.15076			−0.575378	+	0.817888i	$0.695145\pi$
$270$		0			0
$271$			48.9693i			0.180698i	0.995910	+	0.0903492i	$0.0287983\pi$
$271$			48.9693i			0.180698i	−0.995910	+	0.0903492i	$0.971202\pi$
$272$	386.374	−	57.5327i	1.42049	−	0.211517i
$273$		0			0
$274$	−125.221	−	46.5262i	−0.457012	−	0.169804i
$275$		0			0
$276$		0			0
$277$			199.644i			0.720736i	0.932810	+	0.360368i	$0.117349\pi$
$277$			199.644i			0.720736i	−0.932810	+	0.360368i	$0.882651\pi$
$278$	−71.4690	−	26.5545i	−0.257083	−	0.0955197i
$279$		0			0
$280$		0			0
$281$	−61.1598			−0.217650			−0.108825	−	0.994061i	$-0.534709\pi$
$281$	−61.1598			−0.217650			−0.108825	+	0.994061i	$0.534709\pi$
$282$		0			0
$283$	−432.506			−1.52829			−0.764145	−	0.645044i	$-0.776839\pi$
$283$	−432.506			−1.52829			−0.764145	+	0.645044i	$0.776839\pi$
$284$	200.452	−	232.510i	0.705816	−	0.818697i
$285$		0			0
$286$	77.8593	−	209.551i	0.272235	−	0.732697i
$287$	−50.8720			−0.177254
$288$		0			0
$289$	−307.073			−1.06254
$290$		0			0
$291$		0			0
$292$	−244.264	+	283.329i	−0.836521	+	0.970305i
$293$			283.234i			0.966668i	0.875436	+	0.483334i	$0.160574\pi$
$293$			283.234i			0.966668i	−0.875436	+	0.483334i	$0.839426\pi$
$294$		0			0
$295$		0			0
$296$	−137.620	−	249.793i	−0.464933	−	0.843895i
$297$		0			0
$298$	88.2681	−	237.566i	0.296202	−	0.797200i
$299$			377.152i			1.26138i
$300$		0			0
$301$	382.896			1.27208
$302$	−128.310	−	47.6739i	−0.424868	−	0.157861i
$303$		0			0
$304$	−376.263	+	56.0272i	−1.23771	+	0.184300i
$305$		0			0
$306$		0			0
$307$	−100.077			−0.325983			−0.162992	−	0.986627i	$-0.552114\pi$
$307$	−100.077			−0.325983			−0.162992	+	0.986627i	$0.552114\pi$
$308$	−157.665	+	182.880i	−0.511898	+	0.593766i
$309$		0			0
$310$		0			0
$311$			404.185i			1.29963i	0.760092	+	0.649815i	$0.225154\pi$
$311$			404.185i			1.29963i	−0.760092	+	0.649815i	$0.774846\pi$
$312$		0			0
$313$		−	128.579i		−	0.410795i	−0.978679	−	0.205398i	$-0.934151\pi$
$313$		−	128.579i		−	0.410795i	0.978679	−	0.205398i	$-0.0658487\pi$
$314$	47.9525	+	17.8168i	0.152715	+	0.0567415i
$315$		0			0
$316$	−128.963	+	149.588i	−0.408112	+	0.473381i
$317$			85.9315i			0.271077i	0.990772	+	0.135539i	$0.0432765\pi$
$317$			85.9315i			0.271077i	−0.990772	+	0.135539i	$0.956724\pi$
$318$		0			0
$319$		−	284.538i		−	0.891969i
$320$		0			0
$321$		0			0
$322$	141.883	−	381.865i	0.440630	−	1.18592i
$323$	580.475			1.79714
$324$		0			0
$325$		0			0
$326$	−44.2167	+	119.005i	−0.135634	+	0.365047i
$327$		0			0
$328$	65.1934	−	35.9175i	0.198760	−	0.109505i
$329$	207.894			0.631898
$330$		0			0
$331$			183.391i			0.554052i	0.960862	+	0.277026i	$0.0893488\pi$
$331$			183.391i			0.554052i	−0.960862	+	0.277026i	$0.910651\pi$
$332$	219.270	+	189.037i	0.660452	+	0.569390i
$333$		0			0
$334$	−8.62160	+	23.2043i	−0.0258132	+	0.0694739i
$335$		0			0
$336$		0			0
$337$		−	168.130i		−	0.498901i	−0.968388	−	0.249451i	$-0.919750\pi$
$337$		−	168.130i		−	0.498901i	0.968388	−	0.249451i	$-0.0802500\pi$
$338$	−46.3229	+	124.674i	−0.137050	+	0.368858i
$339$		0			0
$340$		0			0
$341$	−53.3962			−0.156587
$342$		0			0
$343$	372.374			1.08564
$344$	−490.688	+	270.338i	−1.42642	+	0.785867i
$345$		0			0
$346$	111.311	+	41.3578i	0.321708	+	0.119531i
$347$	137.414			0.396006			0.198003	−	0.980201i	$-0.436554\pi$
$347$	137.414			0.396006			0.198003	+	0.980201i	$0.436554\pi$
$348$		0			0
$349$	13.4893			0.0386513			0.0193256	−	0.999813i	$-0.493848\pi$
$349$	13.4893			0.0386513			0.0193256	+	0.999813i	$0.493848\pi$
$350$		0			0
$351$		0			0
$352$	72.9301	−	345.681i	0.207188	−	0.982047i
$353$		−	243.547i		−	0.689935i	−0.938615	−	0.344968i	$-0.887890\pi$
$353$		−	243.547i		−	0.689935i	0.938615	−	0.344968i	$-0.112110\pi$
$354$		0			0
$355$		0			0
$356$	−350.493	−	302.168i	−0.984532	−	0.848786i
$357$		0			0
$358$	473.909	+	176.082i	1.32377	+	0.491849i
$359$			17.9166i			0.0499068i	0.999689	+	0.0249534i	$0.00794374\pi$
$359$			17.9166i			0.0499068i	−0.999689	+	0.0249534i	$0.992056\pi$
$360$		0			0
$361$	−204.285			−0.565887
$362$	−87.3321	+	235.047i	−0.241249	+	0.649300i
$363$		0			0
$364$	−144.582	+	167.704i	−0.397202	+	0.460727i
$365$		0			0
$366$		0			0
$367$	−238.417			−0.649637			−0.324818	−	0.945776i	$-0.605303\pi$
$367$	−238.417			−0.649637			−0.324818	+	0.945776i	$0.605303\pi$
$368$	87.7852	+	589.541i	0.238547	+	1.60201i
$369$		0			0
$370$		0			0
$371$			304.968i			0.822016i
$372$		0			0
$373$		−	181.271i		−	0.485981i	−0.970029	−	0.242990i	$-0.921872\pi$
$373$		−	181.271i		−	0.485981i	0.970029	−	0.242990i	$-0.0781283\pi$
$374$	−187.759	+	505.336i	−0.502029	+	1.35117i
$375$		0			0
$376$	−266.420	+	146.781i	−0.708564	+	0.390375i
$377$		−	260.927i		−	0.692114i
$378$		0			0
$379$			306.206i			0.807931i	0.914774	+	0.403965i	$0.132368\pi$
$379$			306.206i			0.807931i	−0.914774	+	0.403965i	$0.867632\pi$
$380$		0			0
$381$		0			0
$382$	182.723	+	67.8912i	0.478333	+	0.177726i
$383$	144.027			0.376050			0.188025	−	0.982164i	$-0.439791\pi$
$383$	144.027			0.376050			0.188025	+	0.982164i	$0.439791\pi$
$384$		0			0
$385$		0			0
$386$	641.878	+	238.491i	1.66290	+	0.617853i
$387$		0			0
$388$	190.558	−	221.034i	0.491128	−	0.569674i
$389$	14.0099			0.0360152			0.0180076	−	0.999838i	$-0.494268\pi$
$389$	14.0099			0.0360152			0.0180076	+	0.999838i	$0.494268\pi$
$390$		0			0
$391$		−	909.506i		−	2.32610i
$392$	−133.863	+	73.7499i	−0.341486	+	0.188138i
$393$		0			0
$394$	−139.639	−	51.8831i	−0.354413	−	0.131683i
$395$		0			0
$396$		0			0
$397$		−	39.1084i		−	0.0985098i	−0.998786	−	0.0492549i	$-0.984315\pi$
$397$		−	39.1084i		−	0.0985098i	0.998786	−	0.0492549i	$-0.0156847\pi$
$398$	−333.760	−	124.009i	−0.838592	−	0.311581i
$399$		0			0
$400$		0			0
$401$	121.067			0.301913			0.150957	−	0.988540i	$-0.451765\pi$
$401$	121.067			0.301913			0.150957	+	0.988540i	$0.451765\pi$
$402$		0			0
$403$	−48.9653			−0.121502
$404$	89.0970	+	76.8124i	0.220537	+	0.190130i
$405$		0			0
$406$	−98.1595	+	264.188i	−0.241772	+	0.650709i
$407$	393.579			0.967026
$408$		0			0
$409$	541.795			1.32468			0.662342	−	0.749202i	$-0.269563\pi$
$409$	541.795			1.32468			0.662342	+	0.749202i	$0.269563\pi$
$410$		0			0
$411$		0			0
$412$	85.3983	+	73.6237i	0.207278	+	0.178698i
$413$			303.682i			0.735307i
$414$		0			0
$415$		0			0
$416$	66.8784	−	316.996i	0.160765	−	0.762009i
$417$		0			0
$418$	182.845	−	492.112i	0.437429	−	1.17730i
$419$		−	687.825i		−	1.64159i	−0.571224	−	0.820794i	$-0.693531\pi$
$419$		−	687.825i		−	1.64159i	0.571224	−	0.820794i	$-0.306469\pi$
$420$		0			0
$421$	−454.396			−1.07932			−0.539662	−	0.841882i	$-0.681448\pi$
$421$	−454.396			−1.07932			−0.539662	+	0.841882i	$0.681448\pi$
$422$	−348.507	−	129.489i	−0.825846	−	0.306845i
$423$		0			0
$424$	−215.318	−	390.821i	−0.507826	−	0.921749i
$425$		0			0
$426$		0			0
$427$	449.670			1.05309
$428$	13.6542	+	11.7716i	0.0319024	+	0.0275037i
$429$		0			0
$430$		0			0
$431$			466.145i			1.08154i	0.841169	+	0.540772i	$0.181868\pi$
$431$			466.145i			1.08154i	−0.841169	+	0.540772i	$0.818132\pi$
$432$		0			0
$433$			457.094i			1.05565i	0.849355	+	0.527823i	$0.176991\pi$
$433$			457.094i			1.05565i	−0.849355	+	0.527823i	$0.823009\pi$
$434$	49.5772	+	18.4205i	0.114233	+	0.0424436i
$435$		0			0
$436$	585.660	+	504.910i	1.34326	+	1.15805i
$437$			885.706i			2.02679i
$438$		0			0
$439$		−	777.467i		−	1.77100i	−0.464644	−	0.885498i	$-0.653818\pi$
$439$		−	777.467i		−	1.77100i	0.464644	−	0.885498i	$-0.346182\pi$
$440$		0			0
$441$		0			0
$442$	−172.178	+	463.403i	−0.389544	+	1.04842i
$443$	247.484			0.558654			0.279327	−	0.960196i	$-0.409889\pi$
$443$	247.484			0.558654			0.279327	+	0.960196i	$0.409889\pi$
$444$		0			0
$445$		0			0
$446$	−141.213	+	380.061i	−0.316620	+	0.852155i
$447$		0			0
$448$	−186.967	+	295.798i	−0.417336	+	0.660263i
$449$	412.508			0.918726			0.459363	−	0.888249i	$-0.348078\pi$
$449$	412.508			0.918726			0.459363	+	0.888249i	$0.348078\pi$
$450$		0			0
$451$			102.720i			0.227761i
$452$	−197.384	+	228.952i	−0.436691	+	0.506531i
$453$		0			0
$454$	−35.7141	+	96.1213i	−0.0786654	+	0.211721i
$455$		0			0
$456$		0			0
$457$			745.400i			1.63107i	0.578706	+	0.815537i	$0.303558\pi$
$457$			745.400i			1.63107i	−0.578706	+	0.815537i	$0.696442\pi$
$458$	234.785	−	631.904i	0.512631	−	1.37970i
$459$		0			0
$460$		0			0
$461$	−81.6151			−0.177039			−0.0885196	−	0.996074i	$-0.528214\pi$
$461$	−81.6151			−0.177039			−0.0885196	+	0.996074i	$0.528214\pi$
$462$		0			0
$463$	−292.248			−0.631205			−0.315603	−	0.948891i	$-0.602207\pi$
$463$	−292.248			−0.631205			−0.315603	+	0.948891i	$0.602207\pi$
$464$	−60.7329	−	407.865i	−0.130890	−	0.879020i
$465$		0			0
$466$	−150.517	−	55.9248i	−0.322997	−	0.120010i
$467$	51.4163			0.110099			0.0550495	−	0.998484i	$-0.482468\pi$
$467$	51.4163			0.110099			0.0550495	+	0.998484i	$0.482468\pi$
$468$		0			0
$469$	571.339			1.21821
$470$		0			0
$471$		0			0
$472$	−214.410	−	389.174i	−0.454259	−	0.824520i
$473$		−	773.139i		−	1.63454i
$474$		0			0
$475$		0			0
$476$	348.660	−	404.422i	0.732480	−	0.849625i
$477$		0			0
$478$	−620.190	−	230.433i	−1.29747	−	0.482077i
$479$			122.593i			0.255935i	0.991778	+	0.127967i	$0.0408453\pi$
$479$			122.593i			0.255935i	−0.991778	+	0.127967i	$0.959155\pi$
$480$		0			0
$481$	360.920			0.750354
$482$	250.708	−	674.758i	0.520141	−	1.39991i
$483$		0			0
$484$	2.69190	+	2.32074i	0.00556177	+	0.00479492i
$485$		0			0
$486$		0			0
$487$	65.9859			0.135495			0.0677474	−	0.997703i	$-0.478419\pi$
$487$	65.9859			0.135495			0.0677474	+	0.997703i	$0.478419\pi$
$488$	−576.260	+	317.483i	−1.18086	+	0.650580i
$489$		0			0
$490$		0			0
$491$		−	361.163i		−	0.735567i	−0.929911	−	0.367783i	$-0.880117\pi$
$491$		−	361.163i		−	0.735567i	0.929911	−	0.367783i	$-0.119883\pi$
$492$		0			0
$493$			629.229i			1.27633i
$494$	167.673	−	451.277i	0.339419	−	0.913516i
$495$		0			0
$496$	−76.5396	+	11.3971i	−0.154314	+	0.0229780i
$497$		−	419.630i		−	0.844326i
$498$		0			0
$499$			711.138i			1.42513i	0.701608	+	0.712564i	$0.252466\pi$
$499$			711.138i			1.42513i	−0.701608	+	0.712564i	$0.747534\pi$
$500$		0			0
$501$		0			0
$502$	585.328	+	217.480i	1.16599	+	0.433227i
$503$	353.756			0.703292			0.351646	−	0.936133i	$-0.385622\pi$
$503$	353.756			0.703292			0.351646	+	0.936133i	$0.385622\pi$
$504$		0			0
$505$		0			0
$506$	−771.057	−	286.488i	−1.52383	−	0.566182i
$507$		0			0
$508$	−397.799	−	342.951i	−0.783068	−	0.675100i
$509$	478.049			0.939192			0.469596	−	0.882881i	$-0.344400\pi$
$509$	478.049			0.939192			0.469596	+	0.882881i	$0.344400\pi$
$510$		0			0
$511$			511.348i			1.00068i
$512$	30.7568	−	511.075i	0.0600720	−	0.998194i
$513$		0			0
$514$	−150.468	−	55.9067i	−0.292739	−	0.108768i
$515$		0			0
$516$		0			0
$517$		−	419.778i		−	0.811949i
$518$	−365.431	−	135.777i	−0.705464	−	0.262117i
$519$		0			0
$520$		0			0
$521$	35.7365			0.0685921			0.0342960	−	0.999412i	$-0.489081\pi$
$521$	35.7365			0.0685921			0.0342960	+	0.999412i	$0.489081\pi$
$522$		0			0
$523$	−733.562			−1.40260			−0.701302	−	0.712864i	$-0.747398\pi$
$523$	−733.562			−1.40260			−0.701302	+	0.712864i	$0.747398\pi$
$524$	−197.856	+	229.499i	−0.377588	+	0.437976i
$525$		0			0
$526$	339.906	−	914.828i	0.646210	−	1.73922i
$527$	118.081			0.224062
$528$		0			0
$529$	858.753			1.62335
$530$		0			0
$531$		0			0
$532$	−339.537	+	393.839i	−0.638227	+	0.740298i
$533$			94.1965i			0.176729i
$534$		0			0
$535$		0			0
$536$	−732.181	+	403.386i	−1.36601	+	0.752585i
$537$		0			0
$538$	215.628	−	580.342i	0.400795	−	1.07870i
$539$		−	210.917i		−	0.391312i
$540$		0			0
$541$	608.939			1.12558			0.562790	−	0.826600i	$-0.309728\pi$
$541$	608.939			1.12558			0.562790	+	0.826600i	$0.309728\pi$
$542$	−91.8064	−	34.1109i	−0.169384	−	0.0629352i
$543$		0			0
$544$	−161.278	+	764.440i	−0.296467	+	1.40522i
$545$		0			0
$546$		0			0
$547$	−78.5868			−0.143669			−0.0718344	−	0.997417i	$-0.522885\pi$
$547$	−78.5868			−0.143669			−0.0718344	+	0.997417i	$0.522885\pi$
$548$	174.452	−	202.353i	0.318344	−	0.369257i
$549$		0			0
$550$		0			0
$551$		−	612.763i		−	1.11209i
$552$		0			0
$553$			269.974i			0.488200i
$554$	−374.287	−	139.067i	−0.675609	−	0.251024i
$555$		0			0
$556$	99.5673	−	115.491i	0.179078	−	0.207718i
$557$		−	928.488i		−	1.66694i	−0.552561	−	0.833472i	$-0.686349\pi$
$557$		−	928.488i		−	1.66694i	0.552561	−	0.833472i	$-0.313651\pi$
$558$		0			0
$559$		−	708.984i		−	1.26831i
$560$		0			0
$561$		0			0
$562$	42.6025	−	114.661i	0.0758051	−	0.204023i
$563$	−447.978			−0.795697			−0.397849	−	0.917451i	$-0.630243\pi$
$563$	−447.978			−0.795697			−0.397849	+	0.917451i	$0.630243\pi$
$564$		0			0
$565$		0			0
$566$	301.274	−	810.852i	0.532286	−	1.43260i
$567$		0			0
$568$	296.274	+	537.763i	0.521609	+	0.946766i
$569$	571.441			1.00429			0.502145	−	0.864783i	$-0.332544\pi$
$569$	571.441			1.00429			0.502145	+	0.864783i	$0.332544\pi$
$570$		0			0
$571$		−	990.801i		−	1.73520i	−0.497260	−	0.867602i	$-0.665660\pi$
$571$		−	990.801i		−	1.73520i	0.497260	−	0.867602i	$-0.334340\pi$
$572$	338.627	+	291.937i	0.592005	+	0.510380i
$573$		0			0
$574$	35.4363	−	95.3736i	0.0617357	−	0.166156i
$575$		0			0
$576$		0			0
$577$		−	826.638i		−	1.43265i	−0.697768	−	0.716324i	$-0.745823\pi$
$577$		−	826.638i		−	1.43265i	0.697768	−	0.716324i	$-0.254177\pi$
$578$	213.900	−	575.693i	0.370069	−	0.996008i
$579$		0			0
$580$		0			0
$581$	395.735			0.681127
$582$		0			0
$583$	615.787			1.05624
$584$	−361.030	−	655.301i	−0.618202	−	1.12209i
$585$		0			0
$586$	−530.999	−	197.294i	−0.906142	−	0.336679i
$587$	−900.009			−1.53323			−0.766617	−	0.642104i	$-0.778062\pi$
$587$	−900.009			−1.53323			−0.766617	+	0.642104i	$0.778062\pi$
$588$		0			0
$589$	−114.991			−0.195230
$590$		0			0
$591$		0			0
$592$	564.169	−	84.0071i	0.952987	−	0.141904i
$593$			704.088i			1.18733i	0.804711	+	0.593666i	$0.202320\pi$
$593$			704.088i			1.18733i	−0.804711	+	0.593666i	$0.797680\pi$
$594$		0			0
$595$		0			0
$596$	383.897	+	330.965i	0.644122	+	0.555311i
$597$		0			0
$598$	−707.075	−	262.715i	−1.18240	−	0.439323i
$599$		−	376.098i		−	0.627876i	−0.949444	−	0.313938i	$-0.898352\pi$
$599$		−	376.098i		−	0.627876i	0.949444	−	0.313938i	$-0.101648\pi$
$600$		0			0
$601$	430.191			0.715791			0.357896	−	0.933762i	$-0.383494\pi$
$601$	430.191			0.715791			0.357896	+	0.933762i	$0.383494\pi$
$602$	−266.716	+	717.844i	−0.443051	+	1.19243i
$603$		0			0
$604$	178.756	−	207.344i	0.295953	−	0.343285i
$605$		0			0
$606$		0			0
$607$	−93.4019			−0.153875			−0.0769373	−	0.997036i	$-0.524514\pi$
$607$	−93.4019			−0.153875			−0.0769373	+	0.997036i	$0.524514\pi$
$608$	157.058	−	744.436i	0.258319	−	1.22440i
$609$		0			0
$610$		0			0
$611$		−	384.944i		−	0.630024i
$612$		0			0
$613$		−	156.506i		−	0.255312i	−0.991818	−	0.127656i	$-0.959255\pi$
$613$		−	156.506i		−	0.255312i	0.991818	−	0.127656i	$-0.0407454\pi$
$614$	69.7113	−	187.622i	0.113536	−	0.305573i
$615$		0			0
$616$	−233.033	−	422.976i	−0.378301	−	0.686649i
$617$		−	553.493i		−	0.897072i	−0.893765	−	0.448536i	$-0.851946\pi$
$617$		−	553.493i		−	0.897072i	0.893765	−	0.448536i	$-0.148054\pi$
$618$		0			0
$619$			14.4398i			0.0233276i	0.999932	+	0.0116638i	$0.00371278\pi$
$619$			14.4398i			0.0233276i	−0.999932	+	0.0116638i	$0.996287\pi$
$620$		0			0
$621$		0			0
$622$	−757.756	−	281.546i	−1.21826	−	0.452646i
$623$	−632.564			−1.01535
$624$		0			0
$625$		0			0
$626$	241.056	+	89.5651i	0.385074	+	0.143075i
$627$		0			0
$628$	−66.8051	+	77.4893i	−0.106378	+	0.123391i
$629$	−870.364			−1.38373
$630$		0			0
$631$		−	352.389i		−	0.558460i	−0.960224	−	0.279230i	$-0.909921\pi$
$631$		−	352.389i		−	0.558460i	0.960224	−	0.279230i	$-0.0900793\pi$
$632$	−190.612	−	345.977i	−0.301601	−	0.547432i
$633$		0			0
$634$	−161.102	−	59.8579i	−0.254104	−	0.0944130i
$635$		0			0
$636$		0			0
$637$		−	193.415i		−	0.303634i
$638$	533.445	+	198.203i	0.836120	+	0.310662i
$639$		0			0
$640$		0			0
$641$	545.742			0.851391			0.425696	−	0.904866i	$-0.360029\pi$
$641$	545.742			0.851391			0.425696	+	0.904866i	$0.360029\pi$
$642$		0			0
$643$	757.447			1.17799			0.588995	−	0.808137i	$-0.299524\pi$
$643$	757.447			1.17799			0.588995	+	0.808137i	$0.299524\pi$
$644$	617.079	+	531.997i	0.958197	+	0.826082i
$645$		0			0
$646$	−404.345	+	1088.26i	−0.625922	+	1.68461i
$647$	−1161.36			−1.79500			−0.897499	−	0.441016i	$-0.854618\pi$
$647$	−1161.36			−1.79500			−0.897499	+	0.441016i	$0.854618\pi$
$648$		0			0
$649$	613.191			0.944824
$650$		0			0
$651$		0			0
$652$	−192.308	−	165.793i	−0.294950	−	0.254283i
$653$			621.231i			0.951348i	0.879622	+	0.475674i	$0.157796\pi$
$653$			621.231i			0.951348i	−0.879622	+	0.475674i	$0.842204\pi$
$654$		0			0
$655$		0			0
$656$	21.9250	+	147.242i	0.0334223	+	0.224455i
$657$		0			0
$658$	−144.814	+	389.755i	−0.220083	+	0.592333i
$659$		−	736.047i		−	1.11692i	−0.829533	−	0.558458i	$-0.811393\pi$
$659$		−	736.047i		−	1.11692i	0.829533	−	0.558458i	$-0.188607\pi$
$660$		0			0
$661$	383.845			0.580704			0.290352	−	0.956920i	$-0.406228\pi$
$661$	383.845			0.580704			0.290352	+	0.956920i	$0.406228\pi$
$662$	−343.817	−	127.746i	−0.519362	−	0.192970i
$663$		0			0
$664$	−507.141	+	279.403i	−0.763766	+	0.420788i
$665$		0			0
$666$		0			0
$667$	−960.096			−1.43942
$668$	−37.4972	−	32.3271i	−0.0561335	−	0.0483939i
$669$		0			0
$670$		0			0
$671$		−	907.968i		−	1.35316i
$672$		0			0
$673$			984.464i			1.46280i	0.681949	+	0.731400i	$0.261133\pi$
$673$			984.464i			1.46280i	−0.681949	+	0.731400i	$0.738867\pi$
$674$	315.205	+	117.115i	0.467664	+	0.173761i
$675$		0			0
$676$	−201.468	−	173.690i	−0.298030	−	0.256938i
$677$			673.154i			0.994319i	0.867659	+	0.497160i	$0.165624\pi$
$677$			673.154i			0.994319i	−0.867659	+	0.497160i	$0.834376\pi$
$678$		0			0
$679$		−	398.918i		−	0.587507i
$680$		0			0
$681$		0			0
$682$	37.1945	−	100.106i	0.0545374	−	0.146783i
$683$	−291.192			−0.426343			−0.213171	−	0.977015i	$-0.568379\pi$
$683$	−291.192			−0.426343			−0.213171	+	0.977015i	$0.568379\pi$
$684$		0			0
$685$		0			0
$686$	−259.387	+	698.117i	−0.378115	+	1.01766i
$687$		0			0
$688$	−165.022	−	1108.24i	−0.239857	−	1.61081i
$689$	564.689			0.819578
$690$		0			0
$691$			943.693i			1.36569i	0.730563	+	0.682846i	$0.239258\pi$
$691$			943.693i			1.36569i	−0.730563	+	0.682846i	$0.760742\pi$
$692$	−155.073	+	179.874i	−0.224094	+	0.259933i
$693$		0			0
$694$	−95.7193	+	257.620i	−0.137924	+	0.371211i
$695$		0			0
$696$		0			0
$697$		−	227.156i		−	0.325905i
$698$	−9.39633	+	25.2894i	−0.0134618	+	0.0362312i
$699$		0			0
$700$		0			0
$701$	−885.681			−1.26345			−0.631727	−	0.775191i	$-0.717654\pi$
$701$	−885.681			−1.26345			−0.631727	+	0.775191i	$0.717654\pi$
$702$		0			0
$703$	847.588			1.20567
$704$	597.272	+	377.521i	0.848397	+	0.536251i
$705$		0			0
$706$	456.596	+	169.649i	0.646737	+	0.240296i
$707$	160.801			0.227441
$708$		0			0
$709$	286.183			0.403644			0.201822	−	0.979422i	$-0.435314\pi$
$709$	286.183			0.403644			0.201822	+	0.979422i	$0.435314\pi$
$710$		0			0
$711$		0			0
$712$	810.642	−	446.613i	1.13854	−	0.627266i
$713$			180.171i			0.252694i
$714$		0			0
$715$		0			0
$716$	−660.228	+	765.818i	−0.922106	+	1.06958i
$717$		0			0
$718$	−33.5895	−	12.4803i	−0.0467820	−	0.0173820i
$719$			666.163i			0.926513i	0.886224	+	0.463257i	$0.153319\pi$
$719$			666.163i			0.926513i	−0.886224	+	0.463257i	$0.846681\pi$
$720$		0			0
$721$	154.125			0.213766
$722$	142.300	−	382.989i	0.197092	−	0.530455i
$723$		0			0
$724$	−379.826	−	327.456i	−0.524622	−	0.452287i
$725$		0			0
$726$		0			0
$727$	856.270			1.17781			0.588907	−	0.808201i	$-0.299559\pi$
$727$	856.270			1.17781			0.588907	+	0.808201i	$0.299559\pi$
$728$	−213.696	−	387.877i	−0.293538	−	0.532798i
$729$		0			0
$730$		0			0
$731$			1709.72i			2.33888i
$732$		0			0
$733$		−	769.487i		−	1.04978i	−0.851171	−	0.524889i	$-0.824107\pi$
$733$		−	769.487i		−	1.04978i	0.851171	−	0.524889i	$-0.175893\pi$
$734$	166.076	−	446.978i	0.226261	−	0.608961i
$735$		0			0
$736$	−1166.41	−	246.083i	−1.58479	−	0.334352i
$737$		−	1153.64i		−	1.56532i
$738$		0			0
$739$		−	1156.70i		−	1.56522i	−0.622511	−	0.782611i	$-0.713887\pi$
$739$		−	1156.70i		−	1.56522i	0.622511	−	0.782611i	$-0.286113\pi$
$740$		0			0
$741$		0			0
$742$	−571.746	−	212.433i	−0.770547	−	0.286298i
$743$	−426.794			−0.574421			−0.287210	−	0.957868i	$-0.592728\pi$
$743$	−426.794			−0.574421			−0.287210	+	0.957868i	$0.592728\pi$
$744$		0			0
$745$		0			0
$746$	339.842	+	126.269i	0.455552	+	0.169261i
$747$		0			0
$748$	−816.603	−	704.011i	−1.09172	−	0.941191i
$749$	24.6429			0.0329011
$750$		0			0
$751$			1222.03i			1.62721i	0.581420	+	0.813604i	$0.302497\pi$
$751$			1222.03i			1.62721i	−0.581420	+	0.813604i	$0.697503\pi$
$752$	−89.5990	−	601.722i	−0.119148	−	0.800162i
$753$		0			0
$754$	489.179	+	181.756i	0.648779	+	0.241055i
$755$		0			0
$756$		0			0
$757$			1312.95i			1.73442i	0.497945	+	0.867209i	$0.334088\pi$
$757$			1312.95i			1.73442i	−0.497945	+	0.867209i	$0.665912\pi$
$758$	−574.067	−	213.296i	−0.757344	−	0.281393i
$759$		0			0
$760$		0			0
$761$	189.584			0.249124			0.124562	−	0.992212i	$-0.460247\pi$
$761$	189.584			0.249124			0.124562	+	0.992212i	$0.460247\pi$
$762$		0			0
$763$	1056.99			1.38531
$764$	−254.561	+	295.273i	−0.333195	+	0.386483i
$765$		0			0
$766$	−100.326	+	270.019i	−0.130974	+	0.352505i
$767$	562.308			0.733127
$768$		0			0
$769$	−254.995			−0.331594			−0.165797	−	0.986160i	$-0.553020\pi$
$769$	−254.995			−0.331594			−0.165797	+	0.986160i	$0.553020\pi$
$770$		0			0
$771$		0			0
$772$	−894.235	+	1037.25i	−1.15834	+	1.34359i
$773$		−	23.2536i		−	0.0300823i	−0.999887	−	0.0150411i	$-0.995212\pi$
$773$		−	23.2536i		−	0.0300823i	0.999887	−	0.0150411i	$-0.00478793\pi$
$774$		0			0
$775$		0			0
$776$	281.650	+	511.220i	0.362951	+	0.658788i
$777$		0			0
$778$	−9.75897	+	26.2654i	−0.0125437	+	0.0337602i
$779$			221.212i			0.283969i
$780$		0			0
$781$	−847.312			−1.08491
$782$	1705.12	+	633.541i	2.18046	+	0.810155i
$783$		0			0
$784$	−45.0189	−	302.335i	−0.0574221	−	0.385631i
$785$		0			0
$786$		0			0
$787$	−220.593			−0.280296			−0.140148	−	0.990131i	$-0.544758\pi$
$787$	−220.593			−0.280296			−0.140148	+	0.990131i	$0.544758\pi$
$788$	194.538	−	225.651i	0.246876	−	0.286359i
$789$		0			0
$790$		0			0
$791$			413.209i			0.522388i
$792$		0			0
$793$		−	832.625i		−	1.04997i
$794$	73.3194	+	27.2420i	0.0923418	+	0.0343098i
$795$		0			0
$796$	464.979	−	539.343i	0.584144	−	0.677566i
$797$			1010.38i			1.26773i	0.773442	+	0.633867i	$0.218533\pi$
$797$			1010.38i			1.26773i	−0.773442	+	0.633867i	$0.781467\pi$
$798$		0			0
$799$			928.298i			1.16183i
$800$		0			0
$801$		0			0
$802$	−84.3327	+	226.974i	−0.105153	+	0.283010i
$803$	1032.51			1.28581
$804$		0			0
$805$		0			0
$806$	34.1081	−	91.7990i	0.0423178	−	0.113894i
$807$		0			0
$808$	−206.069	+	113.531i	−0.255036	+	0.140509i
$809$	1410.37			1.74335			0.871674	−	0.490086i	$-0.163035\pi$
$809$	1410.37			1.74335			0.871674	+	0.490086i	$0.163035\pi$
$810$		0			0
$811$			950.157i			1.17159i	0.810460	+	0.585793i	$0.199217\pi$
$811$			950.157i			1.17159i	−0.810460	+	0.585793i	$0.800783\pi$
$812$	−426.917	−	368.054i	−0.525760	−	0.453269i
$813$		0			0
$814$	−274.158	+	737.873i	−0.336804	+	0.906478i
$815$		0			0
$816$		0			0
$817$		−	1664.98i		−	2.03792i
$818$	−377.402	+	1015.74i	−0.461372	+	1.24174i
$819$		0			0
$820$		0			0
$821$	−77.3347			−0.0941957			−0.0470979	−	0.998890i	$-0.514997\pi$
$821$	−77.3347			−0.0941957			−0.0470979	+	0.998890i	$0.514997\pi$
$822$		0			0
$823$	−1260.16			−1.53118			−0.765591	−	0.643328i	$-0.777553\pi$
$823$	−1260.16			−1.53118			−0.765591	+	0.643328i	$0.777553\pi$
$824$	−197.514	+	108.818i	−0.239702	+	0.132061i
$825$		0			0
$826$	−569.335	−	211.538i	−0.689268	−	0.256099i
$827$	−438.047			−0.529681			−0.264841	−	0.964292i	$-0.585319\pi$
$827$	−438.047			−0.529681			−0.264841	+	0.964292i	$0.585319\pi$
$828$		0			0
$829$	−361.388			−0.435933			−0.217966	−	0.975956i	$-0.569942\pi$
$829$	−361.388			−0.435933			−0.217966	+	0.975956i	$0.569942\pi$
$830$		0			0
$831$		0			0
$832$	547.710	+	346.194i	0.658305	+	0.416098i
$833$			466.423i			0.559931i
$834$		0			0
$835$		0			0
$836$	795.234	+	685.588i	0.951237	+	0.820082i
$837$		0			0
$838$	1289.52	+	479.123i	1.53880	+	0.571746i
$839$			785.017i			0.935658i	0.883819	+	0.467829i	$0.154964\pi$
$839$			785.017i			0.935658i	−0.883819	+	0.467829i	$0.845036\pi$
$840$		0			0
$841$	−176.771			−0.210192
$842$	316.521	−	851.890i	0.375916	−	1.01175i
$843$		0			0
$844$	485.524	−	563.173i	0.575265	−	0.667267i
$845$		0			0
$846$		0			0
$847$	4.85829			0.00573588
$848$	882.688	−	131.436i	1.04091	−	0.154995i
$849$		0			0
$850$		0			0
$851$		−	1328.03i		−	1.56055i
$852$		0			0
$853$			1113.79i			1.30573i	0.757474	+	0.652865i	$0.226433\pi$
$853$			1113.79i			1.30573i	−0.757474	+	0.652865i	$0.773567\pi$
$854$	−313.230	+	843.030i	−0.366780	+	0.987155i
$855$		0			0
$856$	−31.5803	+	17.3988i	−0.0368929	+	0.0203257i
$857$		−	306.591i		−	0.357749i	−0.983872	−	0.178875i	$-0.942754\pi$
$857$		−	306.591i		−	0.357749i	0.983872	−	0.178875i	$-0.0572456\pi$
$858$		0			0
$859$		−	204.542i		−	0.238116i	−0.992887	−	0.119058i	$-0.962013\pi$
$859$		−	204.542i		−	0.238116i	0.992887	−	0.119058i	$-0.0379875\pi$
$860$		0			0
$861$		0			0
$862$	−873.918	−	324.706i	−1.01383	−	0.376689i
$863$	−654.384			−0.758266			−0.379133	−	0.925342i	$-0.623778\pi$
$863$	−654.384			−0.758266			−0.379133	+	0.925342i	$0.623778\pi$
$864$		0			0
$865$		0			0
$866$	−856.949	−	318.401i	−0.989549	−	0.367669i
$867$		0			0
$868$	−69.0687	+	80.1149i	−0.0795722	+	0.0922982i
$869$	545.129			0.627306
$870$		0			0
$871$		−	1057.91i		−	1.21459i
$872$	−1354.55	+	746.272i	−1.55338	+	0.855817i
$873$		0			0
$874$	−1660.50	−	616.963i	−1.89989	−	0.705907i
$875$		0			0
$876$		0			0
$877$			604.453i			0.689228i	0.938744	+	0.344614i	$0.111990\pi$
$877$			604.453i			0.689228i	−0.938744	+	0.344614i	$0.888010\pi$
$878$	1457.58	+	541.565i	1.66011	+	0.616817i
$879$		0			0
$880$		0			0
$881$	−1436.81			−1.63089			−0.815445	−	0.578834i	$-0.803508\pi$
$881$	−1436.81			−1.63089			−0.815445	+	0.578834i	$0.803508\pi$
$882$		0			0
$883$	−120.993			−0.137025			−0.0685123	−	0.997650i	$-0.521825\pi$
$883$	−120.993			−0.137025			−0.0685123	+	0.997650i	$0.521825\pi$
$884$	−748.841	−	645.592i	−0.847105	−	0.730307i
$885$		0			0
$886$	−172.392	+	463.977i	−0.194573	+	0.523676i
$887$	286.448			0.322941			0.161470	−	0.986878i	$-0.448376\pi$
$887$	286.448			0.322941			0.161470	+	0.986878i	$0.448376\pi$
$888$		0			0
$889$	−717.940			−0.807582
$890$		0			0
$891$		0			0
$892$	−614.164	−	529.483i	−0.688524	−	0.593591i
$893$		−	904.007i		−	1.01233i
$894$		0			0
$895$		0			0
$896$	−424.318	−	556.566i	−0.473569	−	0.621168i
$897$		0			0
$898$	−287.344	+	773.360i	−0.319982	+	0.861203i
$899$		−	124.649i		−	0.138652i
$900$		0			0
$901$	−1361.75			−1.51138
$902$	−192.577	−	71.5525i	−0.213500	−	0.0793265i
$903$		0			0
$904$	−291.740	−	529.534i	−0.322721	−	0.585768i
$905$		0			0
$906$		0			0
$907$	234.706			0.258772			0.129386	−	0.991594i	$-0.458699\pi$
$907$	234.706			0.258772			0.129386	+	0.991594i	$0.458699\pi$
$908$	−155.328	−	133.912i	−0.171066	−	0.147480i
$909$		0			0
$910$		0			0
$911$		−	491.244i		−	0.539236i	−0.962967	−	0.269618i	$-0.913103\pi$
$911$		−	491.244i		−	0.539236i	0.962967	−	0.269618i	$-0.0868974\pi$
$912$		0			0
$913$		−	799.063i		−	0.875206i
$914$	−1397.46	−	519.229i	−1.52895	−	0.568084i
$915$		0			0
$916$	1021.13	+	880.339i	1.11477	+	0.961069i
$917$			414.197i			0.451687i
$918$		0			0
$919$			356.091i			0.387477i	0.981053	+	0.193738i	$0.0620613\pi$
$919$			356.091i			0.387477i	−0.981053	+	0.193738i	$0.937939\pi$
$920$		0			0
$921$		0			0
$922$	56.8511	−	153.010i	0.0616607	−	0.165954i
$923$	−777.002			−0.841822
$924$		0			0
$925$		0			0
$926$	203.573	−	547.899i	0.219841	−	0.591684i
$927$		0			0
$928$	806.961	+	170.249i	0.869570	+	0.183458i
$929$	−916.019			−0.986027			−0.493014	−	0.870022i	$-0.664105\pi$
$929$	−916.019			−0.986027			−0.493014	+	0.870022i	$0.664105\pi$
$930$		0			0
$931$		−	454.217i		−	0.487881i
$932$	209.693	−	243.229i	0.224992	−	0.260975i
$933$		0			0
$934$	−35.8154	+	96.3939i	−0.0383462	+	0.103205i
$935$		0			0
$936$		0			0
$937$		−	143.818i		−	0.153488i	−0.997051	−	0.0767440i	$-0.975548\pi$
$937$		−	143.818i		−	0.153488i	0.997051	−	0.0767440i	$-0.0244524\pi$
$938$	−397.981	+	1071.13i	−0.424287	+	1.14193i
$939$		0			0
$940$		0			0
$941$	1488.04			1.58133			0.790667	−	0.612246i	$-0.209734\pi$
$941$	1488.04			1.58133			0.790667	+	0.612246i	$0.209734\pi$
$942$		0			0
$943$	346.602			0.367552
$944$	878.966	−	130.882i	0.931108	−	0.138646i
$945$		0			0
$946$	1449.46	+	538.551i	1.53220	+	0.569292i
$947$	1095.51			1.15682			0.578411	−	0.815745i	$-0.303673\pi$
$947$	1095.51			1.15682			0.578411	+	0.815745i	$0.303673\pi$
$948$		0			0
$949$	946.829			0.997713
$950$		0			0
$951$		0			0
$952$	515.331	+	935.370i	0.541314	+	0.982532i
$953$		−	1277.86i		−	1.34089i	−0.741961	−	0.670443i	$-0.766104\pi$
$953$		−	1277.86i		−	1.34089i	0.741961	−	0.670443i	$-0.233896\pi$
$954$		0			0
$955$		0			0
$956$	864.020	−	1002.20i	0.903786	−	1.04833i
$957$		0			0
$958$	−229.834	−	85.3953i	−0.239910	−	0.0891392i
$959$		−	365.202i		−	0.380816i
$960$		0			0
$961$	937.609			0.975659
$962$	−251.409	+	676.644i	−0.261339	+	0.703372i
$963$		0			0
$964$	1090.38	+	940.041i	1.13110	+	0.975146i
$965$		0			0
$966$		0			0
$967$	−237.958			−0.246079			−0.123039	−	0.992402i	$-0.539264\pi$
$967$	−237.958			−0.246079			−0.123039	+	0.992402i	$0.539264\pi$
$968$	−6.22598	+	3.43013i	−0.00643180	+	0.00354352i
$969$		0			0
$970$		0			0
$971$			1602.10i			1.64995i	0.565169	+	0.824975i	$0.308811\pi$
$971$			1602.10i			1.64995i	−0.565169	+	0.824975i	$0.691189\pi$
$972$		0			0
$973$		−	208.436i		−	0.214220i
$974$	−45.9643	+	123.709i	−0.0471912	+	0.127011i
$975$		0			0
$976$	−193.800	−	1301.51i	−0.198566	−	1.33351i
$977$			918.977i			0.940611i	0.882504	+	0.470305i	$0.155856\pi$
$977$			918.977i			0.940611i	−0.882504	+	0.470305i	$0.844144\pi$
$978$		0			0
$979$			1277.27i			1.30466i
$980$		0			0
$981$		0			0
$982$	677.100	+	251.578i	0.689511	+	0.256189i
$983$	1162.30			1.18240			0.591200	−	0.806525i	$-0.298654\pi$
$983$	1162.30			1.18240			0.591200	+	0.806525i	$0.298654\pi$
$984$		0			0
$985$		0			0
$986$	−1179.66	−	438.306i	−1.19641	−	0.444530i
$987$		0			0
$988$	729.245	+	628.698i	0.738103	+	0.636334i
$989$	−2608.75			−2.63776
$990$		0			0
$991$		−	491.614i		−	0.496079i	−0.968750	−	0.248040i	$-0.920214\pi$
$991$		−	491.614i		−	0.496079i	0.968750	−	0.248040i	$-0.0797863\pi$
$992$	31.9488	−	151.434i	0.0322064	−	0.152655i
$993$		0			0
$994$	786.712	+	292.305i	0.791461	+	0.294069i
$995$		0			0
$996$		0			0
$997$			1262.51i			1.26630i	0.774027	+	0.633152i	$0.218239\pi$
$997$			1262.51i			1.26630i	−0.774027	+	0.633152i	$0.781761\pi$
$998$	−1333.22	−	495.363i	−1.33590	−	0.496355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.f.199.6		16
3.2	odd	2		300.3.f.b.199.11		16
4.3	odd	2	inner	900.3.f.f.199.12		16
5.2	odd	4		180.3.c.b.91.1		8
5.3	odd	4		900.3.c.u.451.8		8
5.4	even	2	inner	900.3.f.f.199.11		16
12.11	even	2		300.3.f.b.199.5		16
15.2	even	4		60.3.c.a.31.8	yes	8
15.8	even	4		300.3.c.d.151.1		8
15.14	odd	2		300.3.f.b.199.6		16
20.3	even	4		900.3.c.u.451.7		8
20.7	even	4		180.3.c.b.91.2		8
20.19	odd	2	inner	900.3.f.f.199.5		16
40.27	even	4		2880.3.e.j.2431.3		8
40.37	odd	4		2880.3.e.j.2431.2		8
60.23	odd	4		300.3.c.d.151.2		8
60.47	odd	4		60.3.c.a.31.7	✓	8
60.59	even	2		300.3.f.b.199.12		16
120.77	even	4		960.3.e.c.511.3		8
120.107	odd	4		960.3.e.c.511.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.7	✓	8	60.47	odd	4
60.3.c.a.31.8	yes	8	15.2	even	4
180.3.c.b.91.1		8	5.2	odd	4
180.3.c.b.91.2		8	20.7	even	4
300.3.c.d.151.1		8	15.8	even	4
300.3.c.d.151.2		8	60.23	odd	4
300.3.f.b.199.5		16	12.11	even	2
300.3.f.b.199.6		16	15.14	odd	2
300.3.f.b.199.11		16	3.2	odd	2
300.3.f.b.199.12		16	60.59	even	2
900.3.c.u.451.7		8	20.3	even	4
900.3.c.u.451.8		8	5.3	odd	4
900.3.f.f.199.5		16	20.19	odd	2	inner
900.3.f.f.199.6		16	1.1	even	1	trivial
900.3.f.f.199.11		16	5.4	even	2	inner
900.3.f.f.199.12		16	4.3	odd	2	inner
960.3.e.c.511.3		8	120.77	even	4
960.3.e.c.511.8		8	120.107	odd	4
2880.3.e.j.2431.2		8	40.37	odd	4
2880.3.e.j.2431.3		8	40.27	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)

\(f(q)\)	\(=\)	\(q+(-0.696577 + 1.87477i) q^{2} +(-3.02956 - 2.61185i) q^{4} -5.46770 q^{7} +(7.00695 - 3.86039i) q^{8} +O(q^{10})\)	\(q+(-0.696577 + 1.87477i) q^{2} +(-3.02956 - 2.61185i) q^{4} -5.46770 q^{7} +(7.00695 - 3.86039i) q^{8} +11.0403i q^{11} +10.1242i q^{13} +(3.80867 - 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} -24.4146i q^{17} +23.7757i q^{19} +(-20.6981 - 7.69043i) q^{22} +37.2526 q^{23} +(-18.9806 - 7.05227i) q^{26} +(16.5647 + 14.2808i) q^{28} -25.7726 q^{29} +4.83647i q^{31} +(-31.3108 - 6.60580i) q^{32} +(45.7719 + 17.0066i) q^{34} -35.6493i q^{37} +(-44.5741 - 16.5616i) q^{38} +9.30410 q^{41} -70.0287 q^{43} +(28.8356 - 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} -38.0223 q^{47} -19.1043 q^{49} +(26.4428 - 30.6718i) q^{52} -55.7762i q^{53} +(-38.3119 + 21.1075i) q^{56} +(17.9526 - 48.3179i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(-9.06729 - 3.36897i) q^{62} +(34.1947 - 54.0992i) q^{64} -104.493 q^{67} +(-63.7673 + 73.9656i) q^{68} +76.7471i q^{71} -93.5215i q^{73} +(66.8344 + 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} -60.3651i q^{77} -49.3762i q^{79} +(-6.48102 + 17.4431i) q^{82} -72.3768 q^{83} +(48.7804 - 131.288i) q^{86} +(42.6199 + 77.3589i) q^{88} +115.691 q^{89} -55.3560i q^{91} +(-112.859 - 97.2980i) q^{92} +(26.4854 - 71.2832i) q^{94} +72.9589i q^{97} +(13.3076 - 35.8162i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4}+O(q^{10}) \) 16 * q - 20 * q^4	\( 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) \) 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * q^94

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