LMFDB - Embedded newform 300.4.i.d.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,4,Mod(257,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("300.257");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	300.i (of order $4$, degree $2$, 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:	$17.7005730017$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7965941760000.54
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 42x^{6} - 112x^{5} + 613x^{4} - 1044x^{3} + 2484x^{2} - 1980x + 7785 $ x^8 - 4x^7 + 42x^6 - 112x^5 + 613x^4 - 1044x^3 + 2484x^2 - 1980*x + 7785
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.1
Root			$1.72474 - 1.73330i$ of defining polynomial
Character	$\chi$	$=$	300.293
Dual form			300.4.i.d.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.23522 + 3.01047i) q^{3} +(-7.34847 + 7.34847i) q^{7} +(8.87412 - 25.5000i) q^{9} -17.7482i q^{11} +(-39.1918 - 39.1918i) q^{13} +(65.2112 + 65.2112i) q^{17} -47.0000i q^{19} +(9.00000 - 53.2447i) q^{21} +(-43.4741 + 43.4741i) q^{23} +(39.1832 + 134.713i) q^{27} +283.972 q^{29} -26.0000 q^{31} +(53.4306 + 75.1676i) q^{33} +(222.904 - 222.904i) q^{37} +(283.972 + 48.0000i) q^{39} -408.210i q^{41} +(144.520 + 144.520i) q^{43} +(347.793 + 347.793i) q^{47} +235.000i q^{49} +(-472.500 - 79.8671i) q^{51} +(43.4741 - 43.4741i) q^{53} +(141.492 + 199.055i) q^{57} +674.433 q^{59} +614.000 q^{61} +(122.175 + 252.597i) q^{63} +(170.240 - 170.240i) q^{67} +(53.2447 - 315.000i) q^{69} +283.972i q^{71} +(-515.618 - 515.618i) q^{73} +(130.422 + 130.422i) q^{77} -586.000i q^{79} +(-571.500 - 452.580i) q^{81} +(-413.004 + 413.004i) q^{83} +(-1202.68 + 854.889i) q^{87} -1082.64 q^{89} +576.000 q^{91} +(110.116 - 78.2723i) q^{93} +(690.756 - 690.756i) q^{97} +(-452.580 - 157.500i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 72 q^{21} - 208 q^{31} - 3780 q^{51} + 4912 q^{61} - 4572 q^{81} + 4608 q^{91}+O(q^{100}) $ 8 * q + 72 * q^21 - 208 * q^31 - 3780 * q^51 + 4912 * q^61 - 4572 * q^81 + 4608 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−4.23522	+	3.01047i	−0.815068	+	0.579366i
$3$	−4.23522	+	3.01047i	−0.815068	+	0.579366i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−7.34847	+	7.34847i	−0.396780	+	0.396780i	−0.877096	−	0.480316i	$-0.840522\pi$
$7$	−7.34847	+	7.34847i	−0.396780	+	0.396780i	0.480316	+	0.877096i	$0.340522\pi$
$8$		0			0
$9$	8.87412	−	25.5000i	0.328671	−	0.944444i
$10$		0			0
$11$		−	17.7482i		−	0.486481i	−0.969966	−	0.243241i	$-0.921790\pi$
$11$		−	17.7482i		−	0.486481i	0.969966	−	0.243241i	$-0.0782105\pi$
$12$		0			0
$13$	−39.1918	−	39.1918i	−0.836143	−	0.836143i	0.152206	−	0.988349i	$-0.451362\pi$
$13$	−39.1918	−	39.1918i	−0.836143	−	0.836143i	−0.988349	+	0.152206i	$0.951362\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	65.2112	+	65.2112i	0.930355	+	0.930355i	0.997728	−	0.0673727i	$-0.0214617\pi$
$17$	65.2112	+	65.2112i	0.930355	+	0.930355i	−0.0673727	+	0.997728i	$0.521462\pi$
$18$		0			0
$19$		−	47.0000i		−	0.567502i	−0.958898	−	0.283751i	$-0.908421\pi$
$19$		−	47.0000i		−	0.567502i	0.958898	−	0.283751i	$-0.0915789\pi$
$20$		0			0
$21$	9.00000	−	53.2447i	0.0935220	−	0.553283i
$22$		0			0
$23$	−43.4741	+	43.4741i	−0.394130	+	0.394130i	−0.876156	−	0.482027i	$-0.839901\pi$
$23$	−43.4741	+	43.4741i	−0.394130	+	0.394130i	0.482027	+	0.876156i	$0.339901\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	39.1832	+	134.713i	0.279289	+	0.960207i
$28$		0			0
$29$	283.972			1.81835			0.909177	−	0.416411i	$-0.136712\pi$
$29$	283.972			1.81835			0.909177	+	0.416411i	$0.136712\pi$
$30$		0			0
$31$	−26.0000			−0.150637			−0.0753184	−	0.997160i	$-0.523997\pi$
$31$	−26.0000			−0.150637			−0.0753184	+	0.997160i	$0.523997\pi$
$32$		0			0
$33$	53.4306	+	75.1676i	0.281851	+	0.396515i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	222.904	−	222.904i	0.990409	−	0.990409i	−0.00954577	−	0.999954i	$-0.503039\pi$
$37$	222.904	−	222.904i	0.990409	−	0.990409i	0.999954	+	0.00954577i	$0.00303856\pi$
$38$		0			0
$39$	283.972	+	48.0000i	1.16595	+	0.197081i
$40$		0			0
$41$		−	408.210i		−	1.55492i	−0.628934	−	0.777459i	$-0.716508\pi$
$41$		−	408.210i		−	1.55492i	0.628934	−	0.777459i	$-0.283492\pi$
$42$		0			0
$43$	144.520	+	144.520i	0.512537	+	0.512537i	0.915303	−	0.402766i	$-0.131951\pi$
$43$	144.520	+	144.520i	0.512537	+	0.512537i	−0.402766	+	0.915303i	$0.631951\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	347.793	+	347.793i	1.07938	+	1.07938i	0.996565	+	0.0828144i	$0.0263909\pi$
$47$	347.793	+	347.793i	1.07938	+	1.07938i	0.0828144	+	0.996565i	$0.473609\pi$
$48$		0			0
$49$			235.000i			0.685131i
$50$		0			0
$51$	−472.500	−	79.8671i	−1.29732	−	0.219287i
$52$		0			0
$53$	43.4741	−	43.4741i	0.112672	−	0.112672i	−0.648523	−	0.761195i	$-0.724613\pi$
$53$	43.4741	−	43.4741i	0.112672	−	0.112672i	0.761195	+	0.648523i	$0.224613\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	141.492	+	199.055i	0.328791	+	0.462553i
$58$		0			0
$59$	674.433			1.48820			0.744099	−	0.668069i	$-0.232879\pi$
$59$	674.433			1.48820			0.744099	+	0.668069i	$0.232879\pi$
$60$		0			0
$61$	614.000			1.28876			0.644382	−	0.764703i	$-0.277115\pi$
$61$	614.000			1.28876			0.644382	+	0.764703i	$0.277115\pi$
$62$		0			0
$63$	122.175	+	252.597i	0.244327	+	0.505147i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	170.240	−	170.240i	0.310419	−	0.310419i	−0.534653	−	0.845072i	$-0.679558\pi$
$67$	170.240	−	170.240i	0.310419	−	0.310419i	0.845072	+	0.534653i	$0.179558\pi$
$68$		0			0
$69$	53.2447	−	315.000i	0.0928973	−	0.549588i
$70$		0			0
$71$			283.972i			0.474666i	0.971428	+	0.237333i	$0.0762732\pi$
$71$			283.972i			0.474666i	−0.971428	+	0.237333i	$0.923727\pi$
$72$		0			0
$73$	−515.618	−	515.618i	−0.826691	−	0.826691i	0.160366	−	0.987058i	$-0.448732\pi$
$73$	−515.618	−	515.618i	−0.826691	−	0.826691i	−0.987058	+	0.160366i	$0.948732\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	130.422	+	130.422i	0.193026	+	0.193026i
$78$		0			0
$79$		−	586.000i		−	0.834559i	−0.908778	−	0.417279i	$-0.862984\pi$
$79$		−	586.000i		−	0.834559i	0.908778	−	0.417279i	$-0.137016\pi$
$80$		0			0
$81$	−571.500	−	452.580i	−0.783951	−	0.620823i
$82$		0			0
$83$	−413.004	+	413.004i	−0.546182	+	0.546182i	−0.925334	−	0.379152i	$-0.876216\pi$
$83$	−413.004	+	413.004i	−0.546182	+	0.546182i	0.379152	+	0.925334i	$0.376216\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1202.68	+	854.889i	−1.48208	+	1.05349i
$88$		0			0
$89$	−1082.64			−1.28944			−0.644718	−	0.764420i	$-0.723025\pi$
$89$	−1082.64			−1.28944			−0.644718	+	0.764420i	$0.723025\pi$
$90$		0			0
$91$	576.000			0.663530
$92$		0			0
$93$	110.116	−	78.2723i	0.122779	−	0.0872737i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	690.756	−	690.756i	0.723048	−	0.723048i	−0.246177	−	0.969225i	$-0.579174\pi$
$97$	690.756	−	690.756i	0.723048	−	0.723048i	0.969225	+	0.246177i	$0.0791744\pi$
$98$		0			0
$99$	−452.580	−	157.500i	−0.459455	−	0.159892i
$100$		0			0
$101$		−	390.461i		−	0.384677i	−0.981329	−	0.192338i	$-0.938393\pi$
$101$		−	390.461i		−	0.384677i	0.981329	−	0.192338i	$-0.0616071\pi$
$102$		0			0
$103$	−950.402	−	950.402i	−0.909183	−	0.909183i	0.0870229	−	0.996206i	$-0.472265\pi$
$103$	−950.402	−	950.402i	−0.909183	−	0.909183i	−0.996206	+	0.0870229i	$0.972265\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1021.64	−	1021.64i	−0.923045	−	0.923045i	0.0741981	−	0.997244i	$-0.476360\pi$
$107$	−1021.64	−	1021.64i	−0.923045	−	0.923045i	−0.997244	+	0.0741981i	$0.976360\pi$
$108$		0			0
$109$			638.000i			0.560636i	0.959907	+	0.280318i	$0.0904399\pi$
$109$			638.000i			0.560636i	−0.959907	+	0.280318i	$0.909560\pi$
$110$		0			0
$111$	−273.000	+	1615.09i	−0.233442	+	1.38106i
$112$		0			0
$113$	1021.64	−	1021.64i	0.850513	−	0.850513i	−0.139683	−	0.990196i	$-0.544608\pi$
$113$	1021.64	−	1021.64i	0.850513	−	0.850513i	0.990196	+	0.139683i	$0.0446083\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1347.18	+	651.599i	−1.06451	+	0.514875i
$118$		0			0
$119$	−958.405			−0.738293
$120$		0			0
$121$	1016.00			0.763336
$122$		0			0
$123$	1228.90	+	1728.86i	0.900866	+	1.26736i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1080.22	−	1080.22i	0.754760	−	0.754760i	−0.220604	−	0.975363i	$-0.570803\pi$
$127$	1080.22	−	1080.22i	0.754760	−	0.754760i	0.975363	+	0.220604i	$0.0708028\pi$
$128$		0			0
$129$	−1047.15	−	177.000i	−0.714698	−	0.120806i
$130$		0			0
$131$			2733.23i			1.82293i	0.411382	+	0.911463i	$0.365046\pi$
$131$			2733.23i			1.82293i	−0.411382	+	0.911463i	$0.634954\pi$
$132$		0			0
$133$	345.378	+	345.378i	0.225173	+	0.225173i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1282.49	−	1282.49i	−0.799783	−	0.799783i	0.183278	−	0.983061i	$-0.441329\pi$
$137$	−1282.49	−	1282.49i	−0.799783	−	0.799783i	−0.983061	+	0.183278i	$0.941329\pi$
$138$		0			0
$139$			2359.00i			1.43948i	0.694244	+	0.719740i	$0.255739\pi$
$139$			2359.00i			1.43948i	−0.694244	+	0.719740i	$0.744261\pi$
$140$		0			0
$141$	−2520.00	−	425.958i	−1.50512	−	0.254412i
$142$		0			0
$143$	−695.586	+	695.586i	−0.406768	+	0.406768i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−707.461	−	995.276i	−0.396941	−	0.558428i
$148$		0			0
$149$	−2342.77			−1.28810			−0.644050	−	0.764983i	$-0.722747\pi$
$149$	−2342.77			−1.28810			−0.644050	+	0.764983i	$0.722747\pi$
$150$		0			0
$151$	2554.00			1.37643			0.688217	−	0.725505i	$-0.258394\pi$
$151$	2554.00			1.37643			0.688217	+	0.725505i	$0.258394\pi$
$152$		0			0
$153$	2241.58	−	1084.19i	1.18445	−	0.572888i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	605.024	−	605.024i	0.307555	−	0.307555i	−0.536405	−	0.843961i	$-0.680218\pi$
$157$	605.024	−	605.024i	0.307555	−	0.307555i	0.843961	+	0.536405i	$0.180218\pi$
$158$		0			0
$159$	−53.2447	+	315.000i	−0.0265571	+	0.157114i
$160$		0			0
$161$		−	638.937i		−	0.312766i
$162$		0			0
$163$	−633.193	−	633.193i	−0.304267	−	0.304267i	0.538414	−	0.842681i	$-0.319024\pi$
$163$	−633.193	−	633.193i	−0.304267	−	0.304267i	−0.842681	+	0.538414i	$0.819024\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1304.22	−	1304.22i	−0.604335	−	0.604335i	0.337125	−	0.941460i	$-0.390545\pi$
$167$	−1304.22	−	1304.22i	−0.604335	−	0.604335i	−0.941460	+	0.337125i	$0.890545\pi$
$168$		0			0
$169$			875.000i			0.398270i
$170$		0			0
$171$	−1198.50	−	417.084i	−0.535974	−	0.186522i
$172$		0			0
$173$	1652.02	−	1652.02i	0.726015	−	0.726015i	−0.243809	−	0.969823i	$-0.578397\pi$
$173$	1652.02	−	1652.02i	0.726015	−	0.726015i	0.969823	+	0.243809i	$0.0783969\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2856.37	+	2030.36i	−1.21298	+	0.862211i
$178$		0			0
$179$	1189.13			0.496536			0.248268	−	0.968691i	$-0.420139\pi$
$179$	1189.13			0.496536			0.248268	+	0.968691i	$0.420139\pi$
$180$		0			0
$181$	−26.0000			−0.0106772			−0.00533858	−	0.999986i	$-0.501699\pi$
$181$	−26.0000			−0.0106772			−0.00533858	+	0.999986i	$0.501699\pi$
$182$		0			0
$183$	−2600.42	+	1848.43i	−1.05043	+	0.746666i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1157.38	−	1157.38i	0.452600	−	0.452600i
$188$		0			0
$189$	−1277.87	−	702.000i	−0.491807	−	0.270175i
$190$		0			0
$191$			1526.35i			0.578234i	0.957294	+	0.289117i	$0.0933617\pi$
$191$			1526.35i			0.578234i	−0.957294	+	0.289117i	$0.906638\pi$
$192$		0			0
$193$	−290.265	−	290.265i	−0.108258	−	0.108258i	0.650903	−	0.759161i	$-0.274390\pi$
$193$	−290.265	−	290.265i	−0.108258	−	0.108258i	−0.759161	+	0.650903i	$0.774390\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2738.87	+	2738.87i	0.990540	+	0.990540i	0.999956	−	0.00941546i	$-0.00299708\pi$
$197$	2738.87	+	2738.87i	0.990540	+	0.990540i	−0.00941546	+	0.999956i	$0.502997\pi$
$198$		0			0
$199$		−	5392.00i		−	1.92075i	−0.278715	−	0.960374i	$-0.589909\pi$
$199$		−	5392.00i		−	1.92075i	0.278715	−	0.960374i	$-0.410091\pi$
$200$		0			0
$201$	−208.500	+	1233.50i	−0.0731664	+	0.432859i
$202$		0			0
$203$	−2086.76	+	2086.76i	−0.721486	+	0.721486i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	722.796	+	1494.38i	0.242695	+	0.501773i
$208$		0			0
$209$	−834.167			−0.276079
$210$		0			0
$211$	3599.00			1.17424			0.587122	−	0.809499i	$-0.300261\pi$
$211$	3599.00			1.17424			0.587122	+	0.809499i	$0.300261\pi$
$212$		0			0
$213$	−854.889	−	1202.68i	−0.275005	−	0.386885i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	191.060	−	191.060i	0.0597696	−	0.0597696i
$218$		0			0
$219$	3736.00	+	631.500i	1.15277	+	0.194853i
$220$		0			0
$221$		−	5111.49i		−	1.55582i
$222$		0			0
$223$	−2635.65	−	2635.65i	−0.791463	−	0.791463i	0.190269	−	0.981732i	$-0.439064\pi$
$223$	−2635.65	−	2635.65i	−0.791463	−	0.791463i	−0.981732	+	0.190269i	$0.939064\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1304.22	+	1304.22i	0.381341	+	0.381341i	0.871585	−	0.490244i	$-0.163092\pi$
$227$	1304.22	+	1304.22i	0.381341	+	0.381341i	−0.490244	+	0.871585i	$0.663092\pi$
$228$		0			0
$229$			208.000i			0.0600220i	0.999550	+	0.0300110i	$0.00955422\pi$
$229$			208.000i			0.0600220i	−0.999550	+	0.0300110i	$0.990446\pi$
$230$		0			0
$231$	−945.000	−	159.734i	−0.269162	−	0.0454967i
$232$		0			0
$233$	391.267	−	391.267i	0.110012	−	0.110012i	−0.649958	−	0.759970i	$-0.725214\pi$
$233$	391.267	−	391.267i	0.110012	−	0.110012i	0.759970	+	0.649958i	$0.225214\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1764.14	+	2481.84i	0.483515	+	0.680222i
$238$		0			0
$239$	5324.47			1.44105			0.720526	−	0.693428i	$-0.243900\pi$
$239$	5324.47			1.44105			0.720526	+	0.693428i	$0.243900\pi$
$240$		0			0
$241$	−4681.00			−1.25116			−0.625580	−	0.780160i	$-0.715138\pi$
$241$	−4681.00			−1.25116			−0.625580	+	0.780160i	$0.715138\pi$
$242$		0			0
$243$	3782.91	+	196.290i	0.998656	+	0.0518190i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1842.02	+	1842.02i	−0.474513	+	0.474513i
$248$		0			0
$249$	505.825	−	2992.50i	0.128736	−	0.761614i
$250$		0			0
$251$		−	1011.65i		−	0.254401i	−0.991877	−	0.127201i	$-0.959401\pi$
$251$		−	1011.65i		−	0.254401i	0.991877	−	0.127201i	$-0.0405992\pi$
$252$		0			0
$253$	771.589	+	771.589i	0.191737	+	0.191737i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1608.54	+	1608.54i	0.390421	+	0.390421i	0.874837	−	0.484417i	$-0.160968\pi$
$257$	1608.54	+	1608.54i	0.390421	+	0.390421i	−0.484417	+	0.874837i	$0.660968\pi$
$258$		0			0
$259$			3276.00i			0.785949i
$260$		0			0
$261$	2520.00	−	7241.28i	0.597640	−	1.71733i
$262$		0			0
$263$	−2304.13	+	2304.13i	−0.540223	+	0.540223i	−0.923594	−	0.383371i	$-0.874763\pi$
$263$	−2304.13	+	2304.13i	−0.540223	+	0.540223i	0.383371	+	0.923594i	$0.374763\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4585.23	−	3259.26i	1.05098	−	0.747055i
$268$		0			0
$269$	6744.33			1.52866			0.764329	−	0.644826i	$-0.223070\pi$
$269$	6744.33			1.52866			0.764329	+	0.644826i	$0.223070\pi$
$270$		0			0
$271$	−658.000			−0.147493			−0.0737466	−	0.997277i	$-0.523496\pi$
$271$	−658.000			−0.147493			−0.0737466	+	0.997277i	$0.523496\pi$
$272$		0			0
$273$	−2439.48	+	1734.03i	−0.540822	+	0.384426i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3164.74	−	3164.74i	0.686465	−	0.686465i	−0.274984	−	0.961449i	$-0.588672\pi$
$277$	3164.74	−	3164.74i	0.686465	−	0.686465i	0.961449	+	0.274984i	$0.0886725\pi$
$278$		0			0
$279$	−230.727	+	663.000i	−0.0495099	+	0.142268i
$280$		0			0
$281$		−	1490.85i		−	0.316501i	−0.987399	−	0.158250i	$-0.949415\pi$
$281$		−	1490.85i		−	0.316501i	0.987399	−	0.158250i	$-0.0505854\pi$
$282$		0			0
$283$	4033.08	+	4033.08i	0.847145	+	0.847145i	0.989776	−	0.142631i	$-0.0455562\pi$
$283$	4033.08	+	4033.08i	0.847145	+	0.847145i	−0.142631	+	0.989776i	$0.545556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2999.71	+	2999.71i	0.616960	+	0.616960i
$288$		0			0
$289$			3592.00i			0.731122i
$290$		0			0
$291$	−846.000	+	5005.00i	−0.170424	+	1.00824i
$292$		0			0
$293$	1173.80	−	1173.80i	0.234042	−	0.234042i	−0.580336	−	0.814377i	$-0.697079\pi$
$293$	1173.80	−	1173.80i	0.234042	−	0.234042i	0.814377	+	0.580336i	$0.197079\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2390.92	−	695.433i	0.467123	−	0.135869i
$298$		0			0
$299$	3407.66			0.659098
$300$		0			0
$301$	−2124.00			−0.406729
$302$		0			0
$303$	1175.47	+	1653.69i	0.222868	+	0.313538i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−3528.49	+	3528.49i	−0.655966	+	0.655966i	−0.954423	−	0.298457i	$-0.903528\pi$
$307$	−3528.49	+	3528.49i	−0.655966	+	0.655966i	0.298457	+	0.954423i	$0.403528\pi$
$308$		0			0
$309$	6886.32	+	1164.00i	1.26780	+	0.214297i
$310$		0			0
$311$		−	603.440i		−	0.110026i	−0.998486	−	0.0550128i	$-0.982480\pi$
$311$		−	603.440i		−	0.110026i	0.998486	−	0.0550128i	$-0.0175200\pi$
$312$		0			0
$313$	4051.46	+	4051.46i	0.731635	+	0.731635i	0.970944	−	0.239308i	$-0.0769207\pi$
$313$	4051.46	+	4051.46i	0.731635	+	0.731635i	−0.239308	+	0.970944i	$0.576921\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1130.33	+	1130.33i	0.200270	+	0.200270i	0.800116	−	0.599846i	$-0.204771\pi$
$317$	1130.33	+	1130.33i	0.200270	+	0.200270i	−0.599846	+	0.800116i	$0.704771\pi$
$318$		0			0
$319$		−	5040.00i		−	0.884595i
$320$		0			0
$321$	7402.50	+	1251.25i	1.28713	+	0.217564i
$322$		0			0
$323$	3064.93	−	3064.93i	0.527978	−	0.527978i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1920.68	−	2702.07i	−0.324813	−	0.456956i
$328$		0			0
$329$	−5111.49			−0.856552
$330$		0			0
$331$	−9613.00			−1.59631			−0.798154	−	0.602453i	$-0.794190\pi$
$331$	−9613.00			−1.59631			−0.798154	+	0.602453i	$0.794190\pi$
$332$		0			0
$333$	−3705.97	−	7662.11i	−0.609867	−	1.26090i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	513.168	−	513.168i	0.0829497	−	0.0829497i	−0.664415	−	0.747364i	$-0.731319\pi$
$337$	513.168	−	513.168i	0.0829497	−	0.0829497i	0.747364	+	0.664415i	$0.231319\pi$
$338$		0			0
$339$	−1251.25	+	7402.50i	−0.200468	+	1.18598i
$340$		0			0
$341$			461.454i			0.0732820i
$342$		0			0
$343$	−4247.42	−	4247.42i	−0.668626	−	0.668626i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1021.64	+	1021.64i	0.158054	+	0.158054i	0.781704	−	0.623650i	$-0.214351\pi$
$347$	1021.64	+	1021.64i	0.158054	+	0.158054i	−0.623650	+	0.781704i	$0.714351\pi$
$348$		0			0
$349$		−	1106.00i		−	0.169636i	−0.996396	−	0.0848178i	$-0.972969\pi$
$349$		−	1106.00i		−	0.169636i	0.996396	−	0.0848178i	$-0.0270308\pi$
$350$		0			0
$351$	3744.00	−	6815.32i	0.569345	−	1.03640i
$352$		0			0
$353$	−1434.65	+	1434.65i	−0.216313	+	0.216313i	−0.806943	−	0.590630i	$-0.798879\pi$
$353$	−1434.65	+	1434.65i	−0.216313	+	0.216313i	0.590630	+	0.806943i	$0.298879\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4059.05	−	2885.25i	0.601759	−	0.427741i
$358$		0			0
$359$	−7489.76			−1.10110			−0.550549	−	0.834803i	$-0.685582\pi$
$359$	−7489.76			−1.10110			−0.550549	+	0.834803i	$0.685582\pi$
$360$		0			0
$361$	4650.00			0.677941
$362$		0			0
$363$	−4302.98	+	3058.64i	−0.622170	+	0.442250i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8911.24	+	8911.24i	−1.26747	+	1.26747i	−0.320086	+	0.947388i	$0.603712\pi$
$367$	−8911.24	+	8911.24i	−1.26747	+	1.26747i	−0.947388	+	0.320086i	$0.896288\pi$
$368$		0			0
$369$	−10409.3	−	3622.50i	−1.46853	−	0.511056i
$370$		0			0
$371$			638.937i			0.0894122i
$372$		0			0
$373$	3696.28	+	3696.28i	0.513100	+	0.513100i	0.915475	−	0.402375i	$-0.131815\pi$
$373$	3696.28	+	3696.28i	0.513100	+	0.513100i	−0.402375	+	0.915475i	$0.631815\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11129.4	−	11129.4i	−1.52040	−	1.52040i
$378$		0			0
$379$		−	13427.0i		−	1.81979i	−0.414844	−	0.909893i	$-0.636164\pi$
$379$		−	13427.0i		−	1.81979i	0.414844	−	0.909893i	$-0.363836\pi$
$380$		0			0
$381$	−1323.00	+	7826.97i	−0.177899	+	1.05246i
$382$		0			0
$383$	−2043.28	+	2043.28i	−0.272603	+	0.272603i	−0.830147	−	0.557544i	$-0.811744\pi$
$383$	−2043.28	+	2043.28i	−0.272603	+	0.272603i	0.557544	+	0.830147i	$0.311744\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4967.74	−	2402.77i	0.652518	−	0.315606i
$388$		0			0
$389$	2449.26			0.319235			0.159617	−	0.987179i	$-0.448974\pi$
$389$	2449.26			0.319235			0.159617	+	0.987179i	$0.448974\pi$
$390$		0			0
$391$	−5670.00			−0.733361
$392$		0			0
$393$	−8228.31	−	11575.8i	−1.05614	−	1.48581i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7857.96	+	7857.96i	−0.993400	+	0.993400i	−0.999978	−	0.00657821i	$-0.997906\pi$
$397$	−7857.96	+	7857.96i	−0.993400	+	0.993400i	0.00657821	+	0.999978i	$0.497906\pi$
$398$		0			0
$399$	−2502.50	−	423.000i	−0.313989	−	0.0530739i
$400$		0			0
$401$			10915.2i			1.35930i	0.733539	+	0.679648i	$0.237867\pi$
$401$			10915.2i			1.35930i	−0.733539	+	0.679648i	$0.762133\pi$
$402$		0			0
$403$	1018.99	+	1018.99i	0.125954	+	0.125954i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3956.15	−	3956.15i	−0.481815	−	0.481815i
$408$		0			0
$409$			8083.00i			0.977209i	0.872505	+	0.488605i	$0.162494\pi$
$409$			8083.00i			0.977209i	−0.872505	+	0.488605i	$0.837506\pi$
$410$		0			0
$411$	9292.50	+	1570.72i	1.11524	+	0.188511i
$412$		0			0
$413$	−4956.05	+	4956.05i	−0.590487	+	0.590487i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7101.70	−	9990.88i	−0.833985	−	1.17327i
$418$		0			0
$419$	−12406.0			−1.44648			−0.723238	−	0.690599i	$-0.757347\pi$
$419$	−12406.0			−1.44648			−0.723238	+	0.690599i	$0.757347\pi$
$420$		0			0
$421$	1972.00			0.228288			0.114144	−	0.993464i	$-0.463587\pi$
$421$	1972.00			0.228288			0.114144	+	0.993464i	$0.463587\pi$
$422$		0			0
$423$	11955.1	−	5782.37i	1.37417	−	0.664653i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4511.96	+	4511.96i	−0.511356	+	0.511356i
$428$		0			0
$429$	851.915	−	5040.00i	0.0958761	−	0.567211i
$430$		0			0
$431$			2094.29i			0.234057i	0.993129	+	0.117028i	$0.0373369\pi$
$431$			2094.29i			0.234057i	−0.993129	+	0.117028i	$0.962663\pi$
$432$		0			0
$433$	836.501	+	836.501i	0.0928399	+	0.0928399i	0.752001	−	0.659162i	$-0.229089\pi$
$433$	836.501	+	836.501i	0.0928399	+	0.0928399i	−0.659162	+	0.752001i	$0.729089\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2043.28	+	2043.28i	0.223669	+	0.223669i
$438$		0			0
$439$			8108.00i			0.881489i	0.897633	+	0.440745i	$0.145286\pi$
$439$			8108.00i			0.881489i	−0.897633	+	0.440745i	$0.854714\pi$
$440$		0			0
$441$	5992.50	+	2085.42i	0.647068	+	0.225183i
$442$		0			0
$443$	11238.1	−	11238.1i	1.20527	−	1.20527i	0.232734	−	0.972541i	$-0.425233\pi$
$443$	11238.1	−	11238.1i	1.20527	−	1.20527i	0.972541	−	0.232734i	$-0.0747671\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9922.13	−	7052.84i	1.04989	−	0.746281i
$448$		0			0
$449$	−13115.9			−1.37857			−0.689287	−	0.724488i	$-0.742076\pi$
$449$	−13115.9			−1.37857			−0.689287	+	0.724488i	$0.742076\pi$
$450$		0			0
$451$	−7245.00			−0.756438
$452$		0			0
$453$	−10816.7	+	7688.74i	−1.12189	+	0.797459i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	694.430	−	694.430i	0.0710811	−	0.0710811i	−0.670672	−	0.741754i	$-0.733994\pi$
$457$	694.430	−	694.430i	0.0710811	−	0.0710811i	0.741754	+	0.670672i	$0.233994\pi$
$458$		0			0
$459$	−6229.63	+	11340.0i	−0.633495	+	1.15317i
$460$		0			0
$461$			1987.80i			0.200827i	0.994946	+	0.100413i	$0.0320166\pi$
$461$			1987.80i			0.200827i	−0.994946	+	0.100413i	$0.967983\pi$
$462$		0			0
$463$	−240.050	−	240.050i	−0.0240952	−	0.0240952i	0.694957	−	0.719052i	$-0.255424\pi$
$463$	−240.050	−	240.050i	−0.0240952	−	0.0240952i	−0.719052	+	0.694957i	$0.755424\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8086.19	−	8086.19i	−0.801251	−	0.801251i	0.182040	−	0.983291i	$-0.441730\pi$
$467$	−8086.19	−	8086.19i	−0.801251	−	0.801251i	−0.983291	+	0.182040i	$0.941730\pi$
$468$		0			0
$469$			2502.00i			0.246336i
$470$		0			0
$471$	−741.000	+	4383.82i	−0.0724915	+	0.428865i
$472$		0			0
$473$	2564.97	−	2564.97i	0.249340	−	0.249340i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−722.796	−	1494.38i	−0.0693806	−	0.143445i
$478$		0			0
$479$	−5288.98			−0.504508			−0.252254	−	0.967661i	$-0.581172\pi$
$479$	−5288.98			−0.504508			−0.252254	+	0.967661i	$0.581172\pi$
$480$		0			0
$481$	−17472.0			−1.65625
$482$		0			0
$483$	1923.50	+	2706.03i	0.181206	+	0.254925i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1207.60	+	1207.60i	−0.112364	+	0.112364i	−0.761054	−	0.648689i	$-0.775318\pi$
$487$	−1207.60	+	1207.60i	−0.112364	+	0.112364i	0.648689	+	0.761054i	$0.275318\pi$
$488$		0			0
$489$	4587.92	+	775.500i	0.424280	+	0.0717164i
$490$		0			0
$491$		−	6211.88i		−	0.570954i	−0.958386	−	0.285477i	$-0.907848\pi$
$491$		−	6211.88i		−	0.570954i	0.958386	−	0.285477i	$-0.0921520\pi$
$492$		0			0
$493$	18518.1	+	18518.1i	1.69171	+	1.69171i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2086.76	−	2086.76i	−0.188338	−	0.188338i
$498$		0			0
$499$		−	6292.00i		−	0.564466i	−0.959346	−	0.282233i	$-0.908925\pi$
$499$		−	6292.00i		−	0.564466i	0.959346	−	0.282233i	$-0.0910751\pi$
$500$		0			0
$501$	9450.00	+	1597.34i	0.842704	+	0.142443i
$502$		0			0
$503$	5999.43	−	5999.43i	0.531812	−	0.531812i	−0.389299	−	0.921111i	$-0.627283\pi$
$503$	5999.43	−	5999.43i	0.531812	−	0.531812i	0.921111	+	0.389299i	$0.127283\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2634.16	−	3705.81i	−0.230744	−	0.324617i
$508$		0			0
$509$	20339.5			1.77118			0.885591	−	0.464466i	$-0.153754\pi$
$509$	20339.5			1.77118			0.885591	+	0.464466i	$0.153754\pi$
$510$		0			0
$511$	7578.00			0.656029
$512$		0			0
$513$	6331.53	−	1841.61i	0.544919	−	0.158497i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6172.71	−	6172.71i	0.525098	−	0.525098i
$518$		0			0
$519$	−2023.30	+	11970.0i	−0.171123	+	1.01238i
$520$		0			0
$521$			17304.5i			1.45514i	0.686036	+	0.727568i	$0.259349\pi$
$521$			17304.5i			1.45514i	−0.686036	+	0.727568i	$0.740651\pi$
$522$		0			0
$523$	−13884.9	−	13884.9i	−1.16089	−	1.16089i	−0.984281	−	0.176609i	$-0.943487\pi$
$523$	−13884.9	−	13884.9i	−1.16089	−	1.16089i	−0.176609	−	0.984281i	$-0.556513\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1695.49	−	1695.49i	−0.140146	−	0.140146i
$528$		0			0
$529$			8387.00i			0.689324i
$530$		0			0
$531$	5985.00	−	17198.0i	0.489128	−	1.40552i
$532$		0			0
$533$	−15998.5	+	15998.5i	−1.30013	+	1.30013i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5036.23	+	3579.85i	−0.404710	+	0.287676i
$538$		0			0
$539$	4170.84			0.333304
$540$		0			0
$541$	−8296.00			−0.659284			−0.329642	−	0.944106i	$-0.606928\pi$
$541$	−8296.00			−0.659284			−0.329642	+	0.944106i	$0.606928\pi$
$542$		0			0
$543$	110.116	−	78.2723i	0.00870260	−	0.00618597i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	2323.34	−	2323.34i	0.181607	−	0.181607i	−0.610449	−	0.792056i	$-0.709011\pi$
$547$	2323.34	−	2323.34i	0.181607	−	0.181607i	0.792056	+	0.610449i	$0.209011\pi$
$548$		0			0
$549$	5448.71	−	15657.0i	0.423580	−	1.21717i
$550$		0			0
$551$		−	13346.7i		−	1.03192i
$552$		0			0
$553$	4306.20	+	4306.20i	0.331136	+	0.331136i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15998.5	+	15998.5i	1.21701	+	1.21701i	0.968672	+	0.248343i	$0.0798859\pi$
$557$	15998.5	+	15998.5i	1.21701	+	1.21701i	0.248343	+	0.968672i	$0.420114\pi$
$558$		0			0
$559$		−	11328.0i		−	0.857108i
$560$		0			0
$561$	−1417.50	+	8386.04i	−0.106679	+	0.631121i
$562$		0			0
$563$	−2260.65	+	2260.65i	−0.169228	+	0.169228i	−0.786640	−	0.617412i	$-0.788181\pi$
$563$	−2260.65	+	2260.65i	−0.169228	+	0.169228i	0.617412	+	0.786640i	$0.288181\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7525.42	−	873.879i	0.557386	−	0.0647257i
$568$		0			0
$569$	−3638.39			−0.268065			−0.134033	−	0.990977i	$-0.542793\pi$
$569$	−3638.39			−0.268065			−0.134033	+	0.990977i	$0.542793\pi$
$570$		0			0
$571$	5564.00			0.407787			0.203893	−	0.978993i	$-0.434640\pi$
$571$	5564.00			0.407787			0.203893	+	0.978993i	$0.434640\pi$
$572$		0			0
$573$	−4595.03	−	6464.42i	−0.335009	−	0.471300i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15788.2	+	15788.2i	−1.13912	+	1.13912i	−0.150509	+	0.988609i	$0.548091\pi$
$577$	−15788.2	+	15788.2i	−1.13912	+	1.13912i	−0.988609	+	0.150509i	$0.951909\pi$
$578$		0			0
$579$	2103.17	+	355.500i	0.150958	+	0.0255165i
$580$		0			0
$581$		−	6069.90i		−	0.433428i
$582$		0			0
$583$	−771.589	−	771.589i	−0.0548130	−	0.0548130i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14368.2	+	14368.2i	1.01029	+	1.01029i	0.999947	+	0.0103415i	$0.00329187\pi$
$587$	14368.2	+	14368.2i	1.01029	+	1.01029i	0.0103415	+	0.999947i	$0.496708\pi$
$588$		0			0
$589$			1222.00i			0.0854866i
$590$		0			0
$591$	−19845.0	−	3354.42i	−1.38124	−	0.233473i
$592$		0			0
$593$	543.427	−	543.427i	0.0376321	−	0.0376321i	−0.688040	−	0.725672i	$-0.741529\pi$
$593$	543.427	−	543.427i	0.0376321	−	0.0376321i	0.725672	+	0.688040i	$0.241529\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	16232.5	+	22836.3i	1.11281	+	1.56554i
$598$		0			0
$599$	7844.72			0.535103			0.267551	−	0.963544i	$-0.413785\pi$
$599$	7844.72			0.535103			0.267551	+	0.963544i	$0.413785\pi$
$600$		0			0
$601$	7579.00			0.514399			0.257200	−	0.966358i	$-0.417200\pi$
$601$	7579.00			0.514399			0.257200	+	0.966358i	$0.417200\pi$
$602$		0			0
$603$	−2830.38	−	5851.83i	−0.191148	−	0.395199i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9371.75	−	9371.75i	0.626668	−	0.626668i	−0.320560	−	0.947228i	$-0.603871\pi$
$607$	9371.75	−	9371.75i	0.626668	−	0.626668i	0.947228	+	0.320560i	$0.103871\pi$
$608$		0			0
$609$	2555.75	−	15120.0i	0.170056	−	1.00606i
$610$		0			0
$611$		−	27261.3i		−	1.80503i
$612$		0			0
$613$	−14728.8	−	14728.8i	−0.970457	−	0.970457i	0.0291193	−	0.999576i	$-0.490730\pi$
$613$	−14728.8	−	14728.8i	−0.970457	−	0.970457i	−0.999576	+	0.0291193i	$0.990730\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12564.0	−	12564.0i	−0.819787	−	0.819787i	0.166290	−	0.986077i	$-0.446821\pi$
$617$	−12564.0	−	12564.0i	−0.819787	−	0.819787i	−0.986077	+	0.166290i	$0.946821\pi$
$618$		0			0
$619$		−	11212.0i		−	0.728026i	−0.931394	−	0.364013i	$-0.881406\pi$
$619$		−	11212.0i		−	0.728026i	0.931394	−	0.364013i	$-0.118594\pi$
$620$		0			0
$621$	−7560.00	−	4153.09i	−0.488522	−	0.268370i
$622$		0			0
$623$	7955.77	−	7955.77i	0.511623	−	0.511623i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3532.88	−	2511.24i	0.225023	−	0.159951i
$628$		0			0
$629$	29071.6			1.84286
$630$		0			0
$631$	21734.0			1.37118			0.685592	−	0.727986i	$-0.259544\pi$
$631$	21734.0			1.37118			0.685592	+	0.727986i	$0.259544\pi$
$632$		0			0
$633$	−15242.5	+	10834.7i	−0.957088	+	0.680316i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9210.08	−	9210.08i	0.572868	−	0.572868i
$638$		0			0
$639$	7241.28	+	2520.00i	0.448295	+	0.156009i
$640$		0			0
$641$			11145.9i			0.686796i	0.939190	+	0.343398i	$0.111578\pi$
$641$			11145.9i			0.686796i	−0.939190	+	0.343398i	$0.888422\pi$
$642$		0			0
$643$	−6988.39	−	6988.39i	−0.428609	−	0.428609i	0.459546	−	0.888154i	$-0.348012\pi$
$643$	−6988.39	−	6988.39i	−0.428609	−	0.428609i	−0.888154	+	0.459546i	$0.848012\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22258.8	+	22258.8i	1.35252	+	1.35252i	0.882830	+	0.469692i	$0.155635\pi$
$647$	22258.8	+	22258.8i	1.35252	+	1.35252i	0.469692	+	0.882830i	$0.344365\pi$
$648$		0			0
$649$		−	11970.0i		−	0.723981i
$650$		0			0
$651$	−234.000	+	1384.36i	−0.0140878	+	0.0833448i
$652$		0			0
$653$	−3086.66	+	3086.66i	−0.184978	+	0.184978i	−0.793521	−	0.608543i	$-0.791754\pi$
$653$	−3086.66	+	3086.66i	−0.184978	+	0.184978i	0.608543	+	0.793521i	$0.291754\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−17723.9	+	8572.60i	−1.05247	+	0.509055i
$658$		0			0
$659$	2608.99			0.154221			0.0771107	−	0.997023i	$-0.475431\pi$
$659$	2608.99			0.154221			0.0771107	+	0.997023i	$0.475431\pi$
$660$		0			0
$661$	−1988.00			−0.116981			−0.0584903	−	0.998288i	$-0.518629\pi$
$661$	−1988.00			−0.116981			−0.0584903	+	0.998288i	$0.518629\pi$
$662$		0			0
$663$	15388.0	+	21648.3i	0.901389	+	1.26810i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12345.4	+	12345.4i	−0.716667	+	0.716667i
$668$		0			0
$669$	19097.1	+	3228.00i	1.10364	+	0.186550i
$670$		0			0
$671$		−	10897.4i		−	0.626960i
$672$		0			0
$673$	15191.7	+	15191.7i	0.870131	+	0.870131i	0.992486	−	0.122355i	$-0.0390447\pi$
$673$	15191.7	+	15191.7i	0.870131	+	0.870131i	−0.122355	+	0.992486i	$0.539045\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3738.78	+	3738.78i	0.212249	+	0.212249i	0.805222	−	0.592973i	$-0.202046\pi$
$677$	3738.78	+	3738.78i	0.212249	+	0.212249i	−0.592973	+	0.805222i	$0.702046\pi$
$678$		0			0
$679$			10152.0i			0.573782i
$680$		0			0
$681$	−9450.00	−	1597.34i	−0.531754	−	0.0898829i
$682$		0			0
$683$	−19193.8	+	19193.8i	−1.07530	+	1.07530i	−0.0783786	+	0.996924i	$0.524974\pi$
$683$	−19193.8	+	19193.8i	−1.07530	+	1.07530i	−0.996924	+	0.0783786i	$0.975026\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−626.178	−	880.925i	−0.0347747	−	0.0489220i
$688$		0			0
$689$	−3407.66			−0.188420
$690$		0			0
$691$	−1883.00			−0.103665			−0.0518326	−	0.998656i	$-0.516506\pi$
$691$	−1883.00			−0.103665			−0.0518326	+	0.998656i	$0.516506\pi$
$692$		0			0
$693$	4483.15	−	2168.39i	0.245745	−	0.118860i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	26619.8	−	26619.8i	1.44663	−	1.44663i
$698$		0			0
$699$	−479.202	+	2835.00i	−0.0259300	+	0.153404i
$700$		0			0
$701$		−	13701.6i		−	0.738237i	−0.929382	−	0.369118i	$-0.879660\pi$
$701$		−	13701.6i		−	0.738237i	0.929382	−	0.369118i	$-0.120340\pi$
$702$		0			0
$703$	−10476.5	−	10476.5i	−0.562059	−	0.562059i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2869.29	+	2869.29i	0.152632	+	0.152632i
$708$		0			0
$709$			23848.0i			1.26323i	0.775282	+	0.631615i	$0.217608\pi$
$709$			23848.0i			1.26323i	−0.775282	+	0.631615i	$0.782392\pi$
$710$		0			0
$711$	−14943.0	−	5200.23i	−0.788194	−	0.274295i
$712$		0			0
$713$	1130.33	−	1130.33i	0.0593704	−	0.0593704i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−22550.3	+	16029.2i	−1.17456	+	0.834896i
$718$		0			0
$719$	8554.65			0.443720			0.221860	−	0.975079i	$-0.428787\pi$
$719$	8554.65			0.443720			0.221860	+	0.975079i	$0.428787\pi$
$720$		0			0
$721$	13968.0			0.721492
$722$		0			0
$723$	19825.0	−	14092.0i	1.01978	−	0.724879i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	23862.9	−	23862.9i	1.21737	−	1.21737i	0.248819	−	0.968550i	$-0.419958\pi$
$727$	23862.9	−	23862.9i	1.21737	−	1.21737i	0.968550	−	0.248819i	$-0.0800423\pi$
$728$		0			0
$729$	−16612.4	+	10557.0i	−0.843995	+	0.536351i
$730$		0			0
$731$			18848.6i			0.953682i
$732$		0			0
$733$	12301.3	+	12301.3i	0.619864	+	0.619864i	0.945496	−	0.325632i	$-0.105577\pi$
$733$	12301.3	+	12301.3i	0.619864	+	0.619864i	−0.325632	+	0.945496i	$0.605577\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3021.45	−	3021.45i	−0.151013	−	0.151013i
$738$		0			0
$739$		−	17516.0i		−	0.871903i	−0.899970	−	0.435952i	$-0.856412\pi$
$739$		−	17516.0i		−	0.871903i	0.899970	−	0.435952i	$-0.143588\pi$
$740$		0			0
$741$	2256.00	−	13346.7i	0.111844	−	0.661677i
$742$		0			0
$743$	22389.2	−	22389.2i	1.10549	−	1.10549i	0.111754	−	0.993736i	$-0.464353\pi$
$743$	22389.2	−	22389.2i	1.10549	−	1.10549i	0.993736	−	0.111754i	$-0.0356470\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6866.56	+	14196.7i	0.336324	+	0.695353i
$748$		0			0
$749$	15015.0			0.732492
$750$		0			0
$751$	−3428.00			−0.166564			−0.0832820	−	0.996526i	$-0.526540\pi$
$751$	−3428.00			−0.166564			−0.0832820	+	0.996526i	$0.526540\pi$
$752$		0			0
$753$	3045.54	+	4284.56i	0.147391	+	0.207354i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	19502.8	−	19502.8i	0.936384	−	0.936384i	−0.0617101	−	0.998094i	$-0.519655\pi$
$757$	19502.8	−	19502.8i	0.936384	−	0.936384i	0.998094	+	0.0617101i	$0.0196554\pi$
$758$		0			0
$759$	−5590.70	−	945.000i	−0.267364	−	0.0451928i
$760$		0			0
$761$			22025.6i			1.04918i	0.851355	+	0.524590i	$0.175781\pi$
$761$			22025.6i			1.04918i	−0.851355	+	0.524590i	$0.824219\pi$
$762$		0			0
$763$	−4688.32	−	4688.32i	−0.222449	−	0.222449i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−26432.3	−	26432.3i	−1.24435	−	1.24435i
$768$		0			0
$769$			22283.0i			1.04492i	0.852663	+	0.522461i	$0.174986\pi$
$769$			22283.0i			1.04492i	−0.852663	+	0.522461i	$0.825014\pi$
$770$		0			0
$771$	−11655.0	−	1970.05i	−0.544416	−	0.0920231i
$772$		0			0
$773$	12259.7	−	12259.7i	0.570441	−	0.570441i	−0.361811	−	0.932252i	$-0.617841\pi$
$773$	12259.7	−	12259.7i	0.570441	−	0.570441i	0.932252	+	0.361811i	$0.117841\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−9862.31	−	13874.6i	−0.455352	−	0.640602i
$778$		0			0
$779$	−19185.8			−0.882419
$780$		0			0
$781$	5040.00			0.230916
$782$		0			0
$783$	11126.9	+	38254.8i	0.507847	+	1.74600i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−18745.9	+	18745.9i	−0.849073	+	0.849073i	−0.990018	−	0.140944i	$-0.954986\pi$
$787$	−18745.9	+	18745.9i	−0.849073	+	0.849073i	0.140944	+	0.990018i	$0.454986\pi$
$788$		0			0
$789$	2821.97	−	16695.0i	0.127332	−	0.753305i
$790$		0			0
$791$			15015.0i			0.674933i
$792$		0			0
$793$	−24063.8	−	24063.8i	−1.07759	−	1.07759i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19172.1	+	19172.1i	0.852083	+	0.852083i	0.990390	−	0.138306i	$-0.0441658\pi$
$797$	19172.1	+	19172.1i	0.852083	+	0.852083i	−0.138306	+	0.990390i	$0.544166\pi$
$798$		0			0
$799$			45360.0i			2.00841i
$800$		0			0
$801$	−9607.50	+	27607.4i	−0.423801	+	1.21780i
$802$		0			0
$803$	−9151.30	+	9151.30i	−0.402170	+	0.402170i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28563.7	+	20303.6i	−1.24596	+	0.885652i
$808$		0			0
$809$	−40395.0			−1.75552			−0.877758	−	0.479104i	$-0.840962\pi$
$809$	−40395.0			−1.75552			−0.877758	+	0.479104i	$0.840962\pi$
$810$		0			0
$811$	13564.0			0.587295			0.293648	−	0.955914i	$-0.405131\pi$
$811$	13564.0			0.587295			0.293648	+	0.955914i	$0.405131\pi$
$812$		0			0
$813$	2786.77	−	1980.89i	0.120217	−	0.0854525i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	6792.44	−	6792.44i	0.290866	−	0.290866i
$818$		0			0
$819$	5111.49	−	14688.0i	0.218083	−	0.626667i
$820$		0			0
$821$		−	30065.5i		−	1.27807i	−0.769179	−	0.639034i	$-0.779334\pi$
$821$		−	30065.5i		−	1.27807i	0.769179	−	0.639034i	$-0.220666\pi$
$822$		0			0
$823$	−1018.99	−	1018.99i	−0.0431588	−	0.0431588i	0.685198	−	0.728357i	$-0.259716\pi$
$823$	−1018.99	−	1018.99i	−0.0431588	−	0.0431588i	−0.728357	+	0.685198i	$0.759716\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28106.0	−	28106.0i	−1.18179	−	1.18179i	−0.979280	−	0.202513i	$-0.935089\pi$
$827$	−28106.0	−	28106.0i	−1.18179	−	1.18179i	−0.202513	−	0.979280i	$-0.564911\pi$
$828$		0			0
$829$		−	35756.0i		−	1.49802i	−0.662560	−	0.749009i	$-0.730530\pi$
$829$		−	35756.0i		−	1.49802i	0.662560	−	0.749009i	$-0.269470\pi$
$830$		0			0
$831$	−3876.00	+	22930.7i	−0.161801	+	0.957230i
$832$		0			0
$833$	−15324.6	+	15324.6i	−0.637415	+	0.637415i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1018.76	−	3502.55i	−0.0420712	−	0.144642i
$838$		0			0
$839$	−24350.6			−1.00200			−0.500999	−	0.865448i	$-0.667034\pi$
$839$	−24350.6			−1.00200			−0.500999	+	0.865448i	$0.667034\pi$
$840$		0			0
$841$	56251.0			2.30641
$842$		0			0
$843$	4488.17	+	6314.08i	0.183370	+	0.257970i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−7466.04	+	7466.04i	−0.302876	+	0.302876i
$848$		0			0
$849$	−29222.5	−	4939.50i	−1.18129	−	0.199674i
$850$		0			0
$851$			19381.1i			0.780699i
$852$		0			0
$853$	−10069.9	−	10069.9i	−0.404203	−	0.404203i	0.475508	−	0.879711i	$-0.342264\pi$
$853$	−10069.9	−	10069.9i	−0.404203	−	0.404203i	−0.879711	+	0.475508i	$0.842264\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21280.6	−	21280.6i	−0.848228	−	0.848228i	0.141684	−	0.989912i	$-0.454748\pi$
$857$	−21280.6	−	21280.6i	−0.848228	−	0.848228i	−0.989912	+	0.141684i	$0.954748\pi$
$858$		0			0
$859$		−	11431.0i		−	0.454040i	−0.973890	−	0.227020i	$-0.927102\pi$
$859$		−	11431.0i		−	0.454040i	0.973890	−	0.227020i	$-0.0728983\pi$
$860$		0			0
$861$	−21735.0	−	3673.89i	−0.860310	−	0.145419i
$862$		0			0
$863$	−4521.31	+	4521.31i	−0.178340	+	0.178340i	−0.790632	−	0.612292i	$-0.790248\pi$
$863$	−4521.31	+	4521.31i	−0.178340	+	0.178340i	0.612292	+	0.790632i	$0.290248\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10813.6	−	15212.9i	−0.423587	−	0.595914i
$868$		0			0
$869$	−10400.5			−0.405997
$870$		0			0
$871$	−13344.0			−0.519109
$872$		0			0
$873$	−11484.4	−	23744.1i	−0.445234	−	0.920524i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−778.938	+	778.938i	−0.0299919	+	0.0299919i	−0.721944	−	0.691952i	$-0.756751\pi$
$877$	−778.938	+	778.938i	−0.0299919	+	0.0299919i	0.691952	+	0.721944i	$0.256751\pi$
$878$		0			0
$879$	−1437.61	+	8505.00i	−0.0551642	+	0.326356i
$880$		0			0
$881$		−	3904.61i		−	0.149319i	−0.997209	−	0.0746593i	$-0.976213\pi$
$881$		−	3904.61i		−	0.149319i	0.997209	−	0.0746593i	$-0.0237869\pi$
$882$		0			0
$883$	−29647.4	−	29647.4i	−1.12991	−	1.12991i	−0.990191	−	0.139724i	$-0.955379\pi$
$883$	−29647.4	−	29647.4i	−1.12991	−	1.12991i	−0.139724	−	0.990191i	$-0.544621\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1043.38	−	1043.38i	−0.0394963	−	0.0394963i	0.687083	−	0.726579i	$-0.258891\pi$
$887$	−1043.38	−	1043.38i	−0.0394963	−	0.0394963i	−0.726579	+	0.687083i	$0.758891\pi$
$888$		0			0
$889$			15876.0i			0.598947i
$890$		0			0
$891$	−8032.50	+	10143.1i	−0.302019	+	0.381377i
$892$		0			0
$893$	16346.3	−	16346.3i	0.612550	−	0.612550i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−14432.2	+	10258.7i	−0.537209	+	0.381858i
$898$		0			0
$899$	−7383.27			−0.273911
$900$		0			0
$901$	5670.00			0.209650
$902$		0			0
$903$	8995.60	−	6394.24i	0.331511	−	0.235645i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4852.44	−	4852.44i	0.177643	−	0.177643i	−0.612684	−	0.790328i	$-0.709910\pi$
$907$	4852.44	−	4852.44i	0.177643	−	0.177643i	0.790328	+	0.612684i	$0.209910\pi$
$908$		0			0
$909$	−9956.76	−	3465.00i	−0.363306	−	0.126432i
$910$		0			0
$911$			28823.1i			1.04825i	0.851642	+	0.524124i	$0.175607\pi$
$911$			28823.1i			1.04825i	−0.851642	+	0.524124i	$0.824393\pi$
$912$		0			0
$913$	7330.10	+	7330.10i	0.265707	+	0.265707i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20085.0	−	20085.0i	−0.723301	−	0.723301i
$918$		0			0
$919$		−	52802.0i		−	1.89530i	−0.319316	−	0.947648i	$-0.603453\pi$
$919$		−	52802.0i		−	1.89530i	0.319316	−	0.947648i	$-0.396547\pi$
$920$		0			0
$921$	4321.50	−	25566.3i	0.154613	−	0.914701i
$922$		0			0
$923$	11129.4	−	11129.4i	0.396888	−	0.396888i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−32669.2	+	15801.3i	−1.15750	+	0.559851i
$928$		0			0
$929$	−31662.9			−1.11822			−0.559109	−	0.829094i	$-0.688857\pi$
$929$	−31662.9			−1.11822			−0.559109	+	0.829094i	$0.688857\pi$
$930$		0			0
$931$	11045.0			0.388813
$932$		0			0
$933$	1816.64	+	2555.70i	0.0637450	+	0.0896783i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2267.00	+	2267.00i	−0.0790392	+	0.0790392i	−0.745521	−	0.666482i	$-0.767799\pi$
$937$	−2267.00	+	2267.00i	−0.0790392	+	0.0790392i	0.666482	+	0.745521i	$0.267799\pi$
$938$		0			0
$939$	−29355.6	−	4962.00i	−1.02022	−	0.172448i
$940$		0			0
$941$		−	1490.85i		−	0.0516476i	−0.999667	−	0.0258238i	$-0.991779\pi$
$941$		−	1490.85i		−	0.0516476i	0.999667	−	0.0258238i	$-0.00822088\pi$
$942$		0			0
$943$	17746.6	+	17746.6i	0.612839	+	0.612839i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31301.4	+	31301.4i	1.07408	+	1.07408i	0.997027	+	0.0770578i	$0.0245526\pi$
$947$	31301.4	+	31301.4i	1.07408	+	1.07408i	0.0770578	+	0.997027i	$0.475447\pi$
$948$		0			0
$949$			40416.0i			1.38246i
$950$		0			0
$951$	−8190.00	−	1384.36i	−0.279263	−	0.0472040i
$952$		0			0
$953$	11629.3	−	11629.3i	0.395290	−	0.395290i	−0.481278	−	0.876568i	$-0.659827\pi$
$953$	11629.3	−	11629.3i	0.395290	−	0.395290i	0.876568	+	0.481278i	$0.159827\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	15172.8	+	21345.5i	0.512504	+	0.721005i
$958$		0			0
$959$	18848.6			0.634676
$960$		0			0
$961$	−29115.0			−0.977309
$962$		0			0
$963$	−35118.0	+	16985.7i	−1.17514	+	0.568387i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	21055.8	−	21055.8i	0.700216	−	0.700216i	−0.264240	−	0.964457i	$-0.585121\pi$
$967$	21055.8	−	21055.8i	0.700216	−	0.700216i	0.964457	+	0.264240i	$0.0851212\pi$
$968$		0			0
$969$	−3753.75	+	22207.5i	−0.124446	+	0.736231i
$970$		0			0
$971$			48009.0i			1.58670i	0.608768	+	0.793348i	$0.291664\pi$
$971$			48009.0i			1.58670i	−0.608768	+	0.793348i	$0.708336\pi$
$972$		0			0
$973$	−17335.0	−	17335.0i	−0.571157	−	0.571157i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25193.3	−	25193.3i	−0.824978	−	0.824978i	0.161839	−	0.986817i	$-0.448257\pi$
$977$	−25193.3	−	25193.3i	−0.824978	−	0.824978i	−0.986817	+	0.161839i	$0.948257\pi$
$978$		0			0
$979$			19215.0i			0.627287i
$980$		0			0
$981$	16269.0	+	5661.69i	0.529489	+	0.184265i
$982$		0			0
$983$	−36300.9	+	36300.9i	−1.17784	+	1.17784i	−0.197549	+	0.980293i	$0.563298\pi$
$983$	−36300.9	+	36300.9i	−1.17784	+	1.17784i	−0.980293	+	0.197549i	$0.936702\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	21648.3	−	15388.0i	0.698148	−	0.496257i
$988$		0			0
$989$	−12565.8			−0.404012
$990$		0			0
$991$	51374.0			1.64677			0.823385	−	0.567483i	$-0.192083\pi$
$991$	51374.0			1.64677			0.823385	+	0.567483i	$0.192083\pi$
$992$		0			0
$993$	40713.1	−	28939.7i	1.30110	−	0.924846i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	16622.2	−	16622.2i	0.528016	−	0.528016i	−0.391965	−	0.919980i	$-0.628204\pi$
$997$	16622.2	−	16622.2i	0.528016	−	0.528016i	0.919980	+	0.391965i	$0.128204\pi$
$998$		0			0
$999$	38762.2	+	21294.0i	1.22761	+	0.674387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.4.i.d.293.1	yes	8
3.2	odd	2	inner	300.4.i.d.293.3	yes	8
5.2	odd	4	inner	300.4.i.d.257.3	yes	8
5.3	odd	4	inner	300.4.i.d.257.2	yes	8
5.4	even	2	inner	300.4.i.d.293.4	yes	8
15.2	even	4	inner	300.4.i.d.257.1	✓	8
15.8	even	4	inner	300.4.i.d.257.4	yes	8
15.14	odd	2	inner	300.4.i.d.293.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.4.i.d.257.1	✓	8	15.2	even	4	inner
300.4.i.d.257.2	yes	8	5.3	odd	4	inner
300.4.i.d.257.3	yes	8	5.2	odd	4	inner
300.4.i.d.257.4	yes	8	15.8	even	4	inner
300.4.i.d.293.1	yes	8	1.1	even	1	trivial
300.4.i.d.293.2	yes	8	15.14	odd	2	inner
300.4.i.d.293.3	yes	8	3.2	odd	2	inner
300.4.i.d.293.4	yes	8	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	300.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.23522 + 3.01047i) q^{3} +(-7.34847 + 7.34847i) q^{7} +(8.87412 - 25.5000i) q^{9} -17.7482i q^{11} +(-39.1918 - 39.1918i) q^{13} +(65.2112 + 65.2112i) q^{17} -47.0000i q^{19} +(9.00000 - 53.2447i) q^{21} +(-43.4741 + 43.4741i) q^{23} +(39.1832 + 134.713i) q^{27} +283.972 q^{29} -26.0000 q^{31} +(53.4306 + 75.1676i) q^{33} +(222.904 - 222.904i) q^{37} +(283.972 + 48.0000i) q^{39} -408.210i q^{41} +(144.520 + 144.520i) q^{43} +(347.793 + 347.793i) q^{47} +235.000i q^{49} +(-472.500 - 79.8671i) q^{51} +(43.4741 - 43.4741i) q^{53} +(141.492 + 199.055i) q^{57} +674.433 q^{59} +614.000 q^{61} +(122.175 + 252.597i) q^{63} +(170.240 - 170.240i) q^{67} +(53.2447 - 315.000i) q^{69} +283.972i q^{71} +(-515.618 - 515.618i) q^{73} +(130.422 + 130.422i) q^{77} -586.000i q^{79} +(-571.500 - 452.580i) q^{81} +(-413.004 + 413.004i) q^{83} +(-1202.68 + 854.889i) q^{87} -1082.64 q^{89} +576.000 q^{91} +(110.116 - 78.2723i) q^{93} +(690.756 - 690.756i) q^{97} +(-452.580 - 157.500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 72 q^{21} - 208 q^{31} - 3780 q^{51} + 4912 q^{61} - 4572 q^{81} + 4608 q^{91}+O(q^{100}) \) 8 * q + 72 * q^21 - 208 * q^31 - 3780 * q^51 + 4912 * q^61 - 4572 * q^81 + 4608 * q^91

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