LMFDB - Embedded newform 700.5.o.c.549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, degree $2$, 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:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.1
Character	$\chi$	$=$	700.549
Dual form			700.5.o.c.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.52174 + 14.7601i) q^{3} +(40.1198 + 28.1318i) q^{7} +(-104.740 - 181.415i) q^{9} +(-93.3277 + 161.648i) q^{11} +200.942 q^{13} +(-55.0227 + 95.3020i) q^{17} +(226.158 - 130.572i) q^{19} +(-757.119 + 352.440i) q^{21} +(-385.090 + 222.332i) q^{23} +2189.75 q^{27} -734.572 q^{29} +(-406.469 - 234.675i) q^{31} +(-1590.63 - 2755.05i) q^{33} +(-1743.27 + 1006.48i) q^{37} +(-1712.38 + 2965.92i) q^{39} +46.3418i q^{41} -2748.95i q^{43} +(-2145.32 - 3715.80i) q^{47} +(818.201 + 2257.29i) q^{49} +(-937.777 - 1624.28i) q^{51} +(-2851.55 - 1646.34i) q^{53} +4450.82i q^{57} +(207.675 + 119.901i) q^{59} +(-2363.68 + 1364.67i) q^{61} +(901.384 - 10224.9i) q^{63} +(4326.27 + 2497.77i) q^{67} -7578.62i q^{69} -2966.43 q^{71} +(-2081.39 + 3605.08i) q^{73} +(-8291.75 + 3859.82i) q^{77} +(1760.95 + 3050.05i) q^{79} +(-10176.5 + 17626.2i) q^{81} -2158.50 q^{83} +(6259.83 - 10842.3i) q^{87} +(-8809.09 + 5085.93i) q^{89} +(8061.77 + 5652.87i) q^{91} +(6927.64 - 3999.68i) q^{93} +12024.1 q^{97} +39100.6 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) $ 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−8.52174	+	14.7601i	−0.946860	+	1.64001i	−0.194876	+	0.980828i	$0.562430\pi$
$3$	−8.52174	+	14.7601i	−0.946860	+	1.64001i	−0.751984	+	0.659181i	$0.770903\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	40.1198	+	28.1318i	0.818772	+	0.574119i
$7$	40.1198	+	28.1318i	0.818772	+	0.574119i
$8$		0			0
$9$	−104.740	−	181.415i	−1.29309	−	2.23969i
$10$		0			0
$11$	−93.3277	+	161.648i	−0.771303	+	1.33594i	0.165546	+	0.986202i	$0.447061\pi$
$11$	−93.3277	+	161.648i	−0.771303	+	1.33594i	−0.936849	+	0.349734i	$0.886272\pi$
$12$		0			0
$13$	200.942			1.18901			0.594504	−	0.804093i	$-0.297349\pi$
$13$	200.942			1.18901			0.594504	+	0.804093i	$0.297349\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−55.0227	+	95.3020i	−0.190390	+	0.329765i	−0.945379	−	0.325972i	$-0.894309\pi$
$17$	−55.0227	+	95.3020i	−0.190390	+	0.329765i	0.754990	+	0.655737i	$0.227642\pi$
$18$		0			0
$19$	226.158	−	130.572i	0.626477	−	0.361696i	−0.152910	−	0.988240i	$-0.548864\pi$
$19$	226.158	−	130.572i	0.626477	−	0.361696i	0.779386	+	0.626544i	$0.215531\pi$
$20$		0			0
$21$	−757.119	+	352.440i	−1.71682	+	0.799184i
$22$		0			0
$23$	−385.090	+	222.332i	−0.727959	+	0.420287i	−0.817675	−	0.575680i	$-0.804737\pi$
$23$	−385.090	+	222.332i	−0.727959	+	0.420287i	0.0897163	+	0.995967i	$0.471404\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2189.75			3.00377
$28$		0			0
$29$	−734.572			−0.873450			−0.436725	−	0.899595i	$-0.643862\pi$
$29$	−734.572			−0.873450			−0.436725	+	0.899595i	$0.643862\pi$
$30$		0			0
$31$	−406.469	−	234.675i	−0.422965	−	0.244199i	0.273380	−	0.961906i	$-0.411858\pi$
$31$	−406.469	−	234.675i	−0.422965	−	0.244199i	−0.696345	+	0.717707i	$0.745192\pi$
$32$		0			0
$33$	−1590.63	−	2755.05i	−1.46063	−	2.52989i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1743.27	+	1006.48i	−1.27339	+	0.735194i	−0.975625	−	0.219445i	$-0.929575\pi$
$37$	−1743.27	+	1006.48i	−1.27339	+	0.735194i	−0.297768	+	0.954638i	$0.596242\pi$
$38$		0			0
$39$	−1712.38	+	2965.92i	−1.12582	+	1.94998i
$40$		0			0
$41$			46.3418i			0.0275680i	0.999905	+	0.0137840i	$0.00438772\pi$
$41$			46.3418i			0.0275680i	−0.999905	+	0.0137840i	$0.995612\pi$
$42$		0			0
$43$		−	2748.95i		−	1.48672i	−0.668890	−	0.743361i	$-0.733230\pi$
$43$		−	2748.95i		−	1.48672i	0.668890	−	0.743361i	$-0.266770\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2145.32	−	3715.80i	−0.971171	−	1.68212i	−0.692033	−	0.721866i	$-0.743285\pi$
$47$	−2145.32	−	3715.80i	−0.971171	−	1.68212i	−0.279138	−	0.960251i	$-0.590049\pi$
$48$		0			0
$49$	818.201	+	2257.29i	0.340775	+	0.940145i
$50$		0			0
$51$	−937.777	−	1624.28i	−0.360545	−	0.624482i
$52$		0			0
$53$	−2851.55	−	1646.34i	−1.01515	−	0.586096i	−0.102454	−	0.994738i	$-0.532669\pi$
$53$	−2851.55	−	1646.34i	−1.01515	−	0.586096i	−0.912695	+	0.408641i	$0.866003\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			4450.82i			1.36990i
$58$		0			0
$59$	207.675	+	119.901i	0.0596596	+	0.0344445i	0.529533	−	0.848289i	$-0.322367\pi$
$59$	207.675	+	119.901i	0.0596596	+	0.0344445i	−0.469873	+	0.882734i	$0.655700\pi$
$60$		0			0
$61$	−2363.68	+	1364.67i	−0.635226	+	0.366748i	−0.782773	−	0.622307i	$-0.786195\pi$
$61$	−2363.68	+	1364.67i	−0.635226	+	0.366748i	0.147547	+	0.989055i	$0.452862\pi$
$62$		0			0
$63$	901.384	−	10224.9i	0.227106	−	2.57618i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4326.27	+	2497.77i	0.963749	+	0.556421i	0.897325	−	0.441371i	$-0.145508\pi$
$67$	4326.27	+	2497.77i	0.963749	+	0.556421i	0.0664243	+	0.997791i	$0.478841\pi$
$68$		0			0
$69$		−	7578.62i		−	1.59181i
$70$		0			0
$71$	−2966.43			−0.588461			−0.294231	−	0.955734i	$-0.595063\pi$
$71$	−2966.43			−0.588461			−0.294231	+	0.955734i	$0.595063\pi$
$72$		0			0
$73$	−2081.39	+	3605.08i	−0.390579	+	0.676502i	−0.992526	−	0.122034i	$-0.961058\pi$
$73$	−2081.39	+	3605.08i	−0.390579	+	0.676502i	0.601947	+	0.798536i	$0.294392\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8291.75	+	3859.82i	−1.39851	+	0.651007i
$78$		0			0
$79$	1760.95	+	3050.05i	0.282158	+	0.488712i	0.971916	−	0.235328i	$-0.0756164\pi$
$79$	1760.95	+	3050.05i	0.282158	+	0.488712i	−0.689758	+	0.724040i	$0.742283\pi$
$80$		0			0
$81$	−10176.5	+	17626.2i	−1.55106	+	2.68651i
$82$		0			0
$83$	−2158.50			−0.313326			−0.156663	−	0.987652i	$-0.550074\pi$
$83$	−2158.50			−0.313326			−0.156663	+	0.987652i	$0.550074\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6259.83	−	10842.3i	0.827035	−	1.43247i
$88$		0			0
$89$	−8809.09	+	5085.93i	−1.11212	+	0.642082i	−0.939377	−	0.342885i	$-0.888596\pi$
$89$	−8809.09	+	5085.93i	−1.11212	+	0.642082i	−0.172742	+	0.984967i	$0.555263\pi$
$90$		0			0
$91$	8061.77	+	5652.87i	0.973526	+	0.682632i
$92$		0			0
$93$	6927.64	−	3999.68i	0.800976	−	0.462444i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12024.1			1.27794			0.638970	−	0.769231i	$-0.279361\pi$
$97$	12024.1			1.27794			0.638970	+	0.769231i	$0.279361\pi$
$98$		0			0
$99$	39100.6			3.98945
$100$		0			0
$101$	−7742.92	−	4470.38i	−0.759035	−	0.438229i	0.0699141	−	0.997553i	$-0.477727\pi$
$101$	−7742.92	−	4470.38i	−0.759035	−	0.438229i	−0.828949	+	0.559324i	$0.811061\pi$
$102$		0			0
$103$	6771.73	+	11729.0i	0.638301	+	1.10557i	0.985806	+	0.167891i	$0.0536958\pi$
$103$	6771.73	+	11729.0i	0.638301	+	1.10557i	−0.347505	+	0.937678i	$0.612971\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	17736.7	−	10240.3i	1.54919	−	0.894428i	0.550991	−	0.834511i	$-0.314250\pi$
$107$	17736.7	−	10240.3i	1.54919	−	0.894428i	0.998203	−	0.0599162i	$-0.0190833\pi$
$108$		0			0
$109$	6936.88	−	12015.0i	0.583863	−	1.01128i	−0.411153	−	0.911566i	$-0.634874\pi$
$109$	6936.88	−	12015.0i	0.583863	−	1.01128i	0.995016	−	0.0997145i	$-0.0317929\pi$
$110$		0			0
$111$		−	34307.8i		−	2.78450i
$112$		0			0
$113$		−	14984.4i		−	1.17350i	−0.809769	−	0.586748i	$-0.800408\pi$
$113$		−	14984.4i		−	1.17350i	0.809769	−	0.586748i	$-0.199592\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−21046.7	−	36453.9i	−1.53749	−	2.66301i
$118$		0			0
$119$	−4888.52	+	2275.61i	−0.345210	+	0.160696i
$120$		0			0
$121$	−10099.6	−	17493.0i	−0.689817	−	1.19480i
$122$		0			0
$123$	−684.009	−	394.913i	−0.0452118	−	0.0261030i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			5331.98i			0.330583i	0.986245	+	0.165292i	$0.0528566\pi$
$127$			5331.98i			0.330583i	−0.986245	+	0.165292i	$0.947143\pi$
$128$		0			0
$129$	40574.7	+	23425.8i	2.43824	+	1.40772i
$130$		0			0
$131$	8943.10	−	5163.30i	0.521129	−	0.300874i	−0.216267	−	0.976334i	$-0.569388\pi$
$131$	8943.10	−	5163.30i	0.521129	−	0.300874i	0.737397	+	0.675460i	$0.236055\pi$
$132$		0			0
$133$	12746.7	+	1123.70i	0.720598	+	0.0635251i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−27056.4	−	15621.0i	−1.44155	−	0.832277i	−0.443593	−	0.896228i	$-0.646296\pi$
$137$	−27056.4	−	15621.0i	−1.44155	−	0.832277i	−0.997953	+	0.0639513i	$0.979630\pi$
$138$		0			0
$139$		−	35302.9i		−	1.82718i	−0.406640	−	0.913588i	$-0.633300\pi$
$139$		−	35302.9i		−	1.82718i	0.406640	−	0.913588i	$-0.366700\pi$
$140$		0			0
$141$	73127.3			3.67825
$142$		0			0
$143$	−18753.5	+	32482.0i	−0.917085	+	1.58844i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−40290.2	−	7159.30i	−1.86451	−	0.331311i
$148$		0			0
$149$	4953.80	+	8580.23i	0.223134	+	0.386480i	0.955758	−	0.294154i	$-0.0950379\pi$
$149$	4953.80	+	8580.23i	0.223134	+	0.386480i	−0.732624	+	0.680634i	$0.761705\pi$
$150$		0			0
$151$	−8963.08	+	15524.5i	−0.393100	+	0.680869i	−0.992857	−	0.119313i	$-0.961931\pi$
$151$	−8963.08	+	15524.5i	−0.393100	+	0.680869i	0.599757	+	0.800183i	$0.295264\pi$
$152$		0			0
$153$	23052.3			0.984762
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7322.38	−	12682.7i	0.297066	−	0.514534i	−0.678397	−	0.734695i	$-0.737325\pi$
$157$	7322.38	−	12682.7i	0.297066	−	0.514534i	0.975463	+	0.220162i	$0.0706585\pi$
$158$		0			0
$159$	48600.4	−	28059.4i	1.92241	−	1.10990i
$160$		0			0
$161$	−21704.3	−	1913.37i	−0.837327	−	0.0738154i
$162$		0			0
$163$	7552.29	−	4360.32i	0.284252	−	0.164113i	−0.351095	−	0.936340i	$-0.614191\pi$
$163$	7552.29	−	4360.32i	0.284252	−	0.164113i	0.635347	+	0.772227i	$0.280857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	44129.3			1.58232			0.791160	−	0.611610i	$-0.209478\pi$
$167$	44129.3			1.58232			0.791160	+	0.611610i	$0.209478\pi$
$168$		0			0
$169$	11816.8			0.413738
$170$		0			0
$171$	−47375.6	−	27352.3i	−1.62018	−	0.935410i
$172$		0			0
$173$	−4885.29	−	8461.56i	−0.163229	−	0.282721i	0.772796	−	0.634655i	$-0.218858\pi$
$173$	−4885.29	−	8461.56i	−0.163229	−	0.282721i	−0.936025	+	0.351933i	$0.885524\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3539.51	+	2043.54i	−0.112979	+	0.0652282i
$178$		0			0
$179$	7694.67	−	13327.6i	0.240151	−	0.415953i	−0.720606	−	0.693344i	$-0.756136\pi$
$179$	7694.67	−	13327.6i	0.240151	−	0.415953i	0.960757	+	0.277391i	$0.0894698\pi$
$180$		0			0
$181$			54639.8i			1.66783i	0.551892	+	0.833916i	$0.313906\pi$
$181$			54639.8i			1.66783i	−0.551892	+	0.833916i	$0.686094\pi$
$182$		0			0
$183$		−	46517.4i		−	1.38903i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10270.3	−	17788.6i	−0.293697	−	0.508697i
$188$		0			0
$189$	87852.2	+	61601.6i	2.45940	+	1.72452i
$190$		0			0
$191$	22397.2	+	38793.1i	0.613941	+	1.06338i	0.990569	+	0.137013i	$0.0437501\pi$
$191$	22397.2	+	38793.1i	0.613941	+	1.06338i	−0.376628	+	0.926365i	$0.622917\pi$
$192$		0			0
$193$	55391.5	+	31980.3i	1.48706	+	0.858555i	0.999891	−	0.0147531i	$-0.00469622\pi$
$193$	55391.5	+	31980.3i	1.48706	+	0.858555i	0.487169	+	0.873308i	$0.338030\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	25491.2i		−	0.656837i	−0.944532	−	0.328419i	$-0.893484\pi$
$197$		−	25491.2i		−	0.656837i	0.944532	−	0.328419i	$-0.106516\pi$
$198$		0			0
$199$	2236.98	+	1291.52i	0.0564879	+	0.0326133i	0.527978	−	0.849258i	$-0.322950\pi$
$199$	2236.98	+	1291.52i	0.0564879	+	0.0326133i	−0.471490	+	0.881871i	$0.656284\pi$
$200$		0			0
$201$	−73734.7	+	42570.7i	−1.82507	+	1.05371i
$202$		0			0
$203$	−29470.9	−	20664.8i	−0.715157	−	0.501464i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	80668.7	+	46574.1i	1.88263	+	1.08694i
$208$		0			0
$209$			48744.1i			1.11591i
$210$		0			0
$211$	−14510.3			−0.325920			−0.162960	−	0.986633i	$-0.552104\pi$
$211$	−14510.3			−0.325920			−0.162960	+	0.986633i	$0.552104\pi$
$212$		0			0
$213$	25279.2	−	43784.8i	0.557190	−	0.965082i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9705.63	−	20849.8i	−0.206112	−	0.442775i
$218$		0			0
$219$	−35474.2	−	61443.1i	−0.739646	−	1.28110i
$220$		0			0
$221$	−11056.4	+	19150.2i	−0.226375	+	0.392093i
$222$		0			0
$223$	−61440.5			−1.23551			−0.617753	−	0.786372i	$-0.711957\pi$
$223$	−61440.5			−1.23551			−0.617753	+	0.786372i	$0.711957\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5698.60	+	9870.26i	−0.110590	+	0.191548i	−0.916008	−	0.401159i	$-0.868607\pi$
$227$	−5698.60	+	9870.26i	−0.110590	+	0.191548i	0.805418	+	0.592707i	$0.201941\pi$
$228$		0			0
$229$	−38838.2	+	22423.2i	−0.740607	+	0.427590i	−0.822290	−	0.569069i	$-0.807304\pi$
$229$	−38838.2	+	22423.2i	−0.740607	+	0.427590i	0.0816828	+	0.996658i	$0.473971\pi$
$230$		0			0
$231$	13688.8	−	155279.i	0.256532	−	2.90998i
$232$		0			0
$233$	41439.1	−	23924.9i	0.763306	−	0.440695i	−0.0671757	−	0.997741i	$-0.521399\pi$
$233$	41439.1	−	23924.9i	0.763306	−	0.440695i	0.830481	+	0.557046i	$0.188065\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−60025.3			−1.06866
$238$		0			0
$239$	−39249.0			−0.687120			−0.343560	−	0.939131i	$-0.611633\pi$
$239$	−39249.0			−0.687120			−0.343560	+	0.939131i	$0.611633\pi$
$240$		0			0
$241$	−95527.7	−	55152.9i	−1.64473	−	0.949586i	−0.979119	−	0.203289i	$-0.934837\pi$
$241$	−95527.7	−	55152.9i	−1.64473	−	0.949586i	−0.665613	−	0.746297i	$-0.731830\pi$
$242$		0			0
$243$	−84758.2	−	146806.i	−1.43539	−	2.48617i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	45444.7	−	26237.5i	0.744885	−	0.430060i
$248$		0			0
$249$	18394.2	−	31859.6i	0.296675	−	0.513857i
$250$		0			0
$251$		−	31065.0i		−	0.493088i	−0.969132	−	0.246544i	$-0.920705\pi$
$251$		−	31065.0i		−	0.493088i	0.969132	−	0.246544i	$-0.0792950\pi$
$252$		0			0
$253$		−	82998.9i		−	1.29667i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	36797.6	+	63735.4i	0.557126	+	0.964971i	0.997735	+	0.0672717i	$0.0214294\pi$
$257$	36797.6	+	63735.4i	0.557126	+	0.964971i	−0.440608	+	0.897699i	$0.645237\pi$
$258$		0			0
$259$	−98254.0	−	8661.69i	−1.46471	−	0.129123i
$260$		0			0
$261$	76939.0	+	133262.i	1.12945	+	1.95626i
$262$		0			0
$263$	−62913.7	−	36323.3i	−0.909566	−	0.525138i	−0.0292743	−	0.999571i	$-0.509320\pi$
$263$	−62913.7	−	36323.3i	−0.909566	−	0.525138i	−0.880291	+	0.474433i	$0.842653\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	173364.i		−	2.43185i
$268$		0			0
$269$	−6852.82	−	3956.48i	−0.0947032	−	0.0546769i	0.451900	−	0.892068i	$-0.350746\pi$
$269$	−6852.82	−	3956.48i	−0.0947032	−	0.0546769i	−0.546604	+	0.837391i	$0.684080\pi$
$270$		0			0
$271$	85123.4	−	49146.0i	1.15907	−	0.669190i	0.207990	−	0.978131i	$-0.433308\pi$
$271$	85123.4	−	49146.0i	1.15907	−	0.669190i	0.951081	+	0.308941i	$0.0999745\pi$
$272$		0			0
$273$	−152137.	+	70820.1i	−2.04131	+	0.950235i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5986.07	−	3456.06i	−0.0780157	−	0.0450424i	0.460485	−	0.887668i	$-0.347676\pi$
$277$	−5986.07	−	3456.06i	−0.0780157	−	0.0450424i	−0.538500	+	0.842625i	$0.681009\pi$
$278$		0			0
$279$			98319.5i			1.26308i
$280$		0			0
$281$	−92240.8			−1.16818			−0.584091	−	0.811688i	$-0.698549\pi$
$281$	−92240.8			−1.16818			−0.584091	+	0.811688i	$0.698549\pi$
$282$		0			0
$283$	−16206.8	+	28071.0i	−0.202360	+	0.350497i	−0.949288	−	0.314407i	$-0.898194\pi$
$283$	−16206.8	+	28071.0i	−0.202360	+	0.350497i	0.746929	+	0.664904i	$0.231528\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1303.68	+	1859.23i	−0.0158273	+	0.0225719i
$288$		0			0
$289$	35705.5	+	61843.8i	0.427503	+	0.740458i
$290$		0			0
$291$	−102467.	+	177477.i	−1.21003	+	2.09583i
$292$		0			0
$293$	−75728.6			−0.882114			−0.441057	−	0.897479i	$-0.645396\pi$
$293$	−75728.6			−0.882114			−0.441057	+	0.897479i	$0.645396\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−204364.	+	353969.i	−2.31681	+	4.01284i
$298$		0			0
$299$	−77380.9	+	44675.9i	−0.865548	+	0.499724i
$300$		0			0
$301$	77333.0	−	110287.i	0.853555	−	1.21729i
$302$		0			0
$303$	131966.	−	76190.7i	1.43740	−	0.829883i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−8913.62			−0.0945753			−0.0472876	−	0.998881i	$-0.515058\pi$
$307$	−8913.62			−0.0945753			−0.0472876	+	0.998881i	$0.515058\pi$
$308$		0			0
$309$	−230828.			−2.41753
$310$		0			0
$311$	−93267.8	−	53848.2i	−0.964298	−	0.556737i	−0.0668045	−	0.997766i	$-0.521280\pi$
$311$	−93267.8	−	53848.2i	−0.964298	−	0.556737i	−0.897493	+	0.441029i	$0.854614\pi$
$312$		0			0
$313$	2739.86	+	4745.58i	0.0279666	+	0.0484396i	0.879670	−	0.475585i	$-0.157763\pi$
$313$	2739.86	+	4745.58i	0.0279666	+	0.0484396i	−0.851703	+	0.524024i	$0.824430\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	125839.	−	72653.4i	1.25227	−	0.722999i	0.280711	−	0.959792i	$-0.409430\pi$
$317$	125839.	−	72653.4i	1.25227	−	0.722999i	0.971560	+	0.236794i	$0.0760965\pi$
$318$		0			0
$319$	68555.9	−	118742.i	0.673695	−	1.16687i
$320$		0			0
$321$			349061.i			3.38759i
$322$		0			0
$323$			28737.8i			0.275453i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	118229.	+	204778.i	1.10567	+	1.91508i
$328$		0			0
$329$	18462.4	−	209429.i	0.170568	−	1.93484i
$330$		0			0
$331$	−57649.3	−	99851.6i	−0.526185	−	0.911379i	−0.999535	−	0.0305044i	$-0.990289\pi$
$331$	−57649.3	−	99851.6i	−0.526185	−	0.911379i	0.473350	−	0.880875i	$-0.343045\pi$
$332$		0			0
$333$	365181.	+	210837.i	3.29321	+	1.90134i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	155840.i		−	1.37220i	−0.727506	−	0.686101i	$-0.759321\pi$
$337$		−	155840.i		−	1.37220i	0.727506	−	0.686101i	$-0.240679\pi$
$338$		0			0
$339$	221171.	+	127693.i	1.92454	+	1.11114i
$340$		0			0
$341$	75869.6	−	43803.3i	0.652468	−	0.376702i
$342$		0			0
$343$	−30675.5	+	113579.i	−0.260738	+	0.965410i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	134819.	+	77837.8i	1.11968	+	0.646445i	0.941318	−	0.337520i	$-0.109588\pi$
$347$	134819.	+	77837.8i	1.11968	+	0.646445i	0.178358	+	0.983966i	$0.442922\pi$
$348$		0			0
$349$			16897.8i			0.138733i	0.997591	+	0.0693665i	$0.0220978\pi$
$349$			16897.8i			0.138733i	−0.997591	+	0.0693665i	$0.977902\pi$
$350$		0			0
$351$	440013.			3.57150
$352$		0			0
$353$	−91030.7	+	157670.i	−0.730531	+	1.26532i	0.226126	+	0.974098i	$0.427394\pi$
$353$	−91030.7	+	157670.i	−0.730531	+	1.26532i	−0.956657	+	0.291218i	$0.905940\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8070.44	−	91547.1i	0.0633229	−	0.718304i
$358$		0			0
$359$	26246.3	+	45459.9i	0.203647	+	0.352727i	0.949701	−	0.313158i	$-0.101387\pi$
$359$	26246.3	+	45459.9i	0.203647	+	0.352727i	−0.746054	+	0.665886i	$0.768054\pi$
$360$		0			0
$361$	−31062.2	+	53801.3i	−0.238351	+	0.412837i
$362$		0			0
$363$	344265.			2.61264
$364$		0			0
$365$		0			0
$366$		0			0
$367$	27031.5	−	46819.9i	0.200695	−	0.347615i	−0.748057	−	0.663634i	$-0.769013\pi$
$367$	27031.5	−	46819.9i	0.200695	−	0.347615i	0.948753	+	0.316020i	$0.102347\pi$
$368$		0			0
$369$	8407.10	−	4853.84i	0.0617438	−	0.0356478i
$370$		0			0
$371$	−68089.1	−	146270.i	−0.494686	−	1.06270i
$372$		0			0
$373$	−61750.1	+	35651.4i	−0.443833	+	0.256247i	−0.705222	−	0.708986i	$-0.749153\pi$
$373$	−61750.1	+	35651.4i	−0.443833	+	0.256247i	0.261389	+	0.965234i	$0.415819\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−147606.			−1.03854
$378$		0			0
$379$	−200433.			−1.39537			−0.697686	−	0.716403i	$-0.745787\pi$
$379$	−200433.			−1.39537			−0.697686	+	0.716403i	$0.745787\pi$
$380$		0			0
$381$	−78700.4	−	45437.7i	−0.542160	−	0.313016i
$382$		0			0
$383$	41013.3	+	71037.1i	0.279594	+	0.484270i	0.971284	−	0.237924i	$-0.0764669\pi$
$383$	41013.3	+	71037.1i	0.279594	+	0.484270i	−0.691690	+	0.722194i	$0.743134\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−498701.	+	287925.i	−3.32980	+	1.92246i
$388$		0			0
$389$	47546.9	−	82353.6i	0.314212	−	0.544231i	−0.665058	−	0.746792i	$-0.731593\pi$
$389$	47546.9	−	82353.6i	0.314212	−	0.544231i	0.979270	+	0.202561i	$0.0649264\pi$
$390$		0			0
$391$		−	48933.2i		−	0.320074i
$392$		0			0
$393$			176001.i			1.13954i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−66430.0	−	115060.i	−0.421486	−	0.730035i	0.574599	−	0.818435i	$-0.305158\pi$
$397$	−66430.0	−	115060.i	−0.421486	−	0.730035i	−0.996085	+	0.0883998i	$0.971825\pi$
$398$		0			0
$399$	−125210.	+	178566.i	−0.786487	+	1.12164i
$400$		0			0
$401$	−3695.08	−	6400.06i	−0.0229792	−	0.0398011i	0.854307	−	0.519769i	$-0.173982\pi$
$401$	−3695.08	−	6400.06i	−0.0229792	−	0.0398011i	−0.877286	+	0.479967i	$0.840648\pi$
$402$		0			0
$403$	−81676.8	−	47156.1i	−0.502908	−	0.290354i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	375730.i		−	2.26823i
$408$		0			0
$409$	−145297.	−	83887.2i	−0.868580	−	0.501475i	−0.00170409	−	0.999999i	$-0.500542\pi$
$409$	−145297.	−	83887.2i	−0.868580	−	0.501475i	−0.866876	+	0.498523i	$0.833876\pi$
$410$		0			0
$411$	461135.	−	266236.i	2.72988	−	1.57610i
$412$		0			0
$413$	4958.85	+	10652.7i	0.0290724	+	0.0624539i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	521073.	+	300842.i	2.99659	+	1.73008i
$418$		0			0
$419$		−	107092.i		−	0.609998i	−0.952353	−	0.304999i	$-0.901344\pi$
$419$		−	107092.i		−	0.609998i	0.952353	−	0.304999i	$-0.0986561\pi$
$420$		0			0
$421$	189741.			1.07053			0.535264	−	0.844685i	$-0.320212\pi$
$421$	189741.			1.07053			0.535264	+	0.844685i	$0.320212\pi$
$422$		0			0
$423$	−449401.	+	778385.i	−2.51162	+	4.35025i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−133221.	−	11744.2i	−0.730662	−	0.0644123i
$428$		0			0
$429$	−319624.	−	553606.i	−1.73670	−	3.00806i
$430$		0			0
$431$	−57533.3	+	99650.6i	−0.309717	+	0.536445i	−0.978300	−	0.207192i	$-0.933568\pi$
$431$	−57533.3	+	99650.6i	−0.309717	+	0.536445i	0.668584	+	0.743637i	$0.266901\pi$
$432$		0			0
$433$	−71376.7			−0.380698			−0.190349	−	0.981716i	$-0.560962\pi$
$433$	−71376.7			−0.380698			−0.190349	+	0.981716i	$0.560962\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−58060.8	+	100564.i	−0.304033	+	0.526600i
$438$		0			0
$439$	−41314.4	+	23852.9i	−0.214374	+	0.123769i	−0.603343	−	0.797482i	$-0.706165\pi$
$439$	−41314.4	+	23852.9i	−0.214374	+	0.123769i	0.388969	+	0.921251i	$0.372831\pi$
$440$		0			0
$441$	323808.	−	384862.i	1.66498	−	1.97892i
$442$		0			0
$443$	−53111.5	+	30663.9i	−0.270633	+	0.156250i	−0.629175	−	0.777263i	$-0.716607\pi$
$443$	−53111.5	+	30663.9i	−0.270633	+	0.156250i	0.358542	+	0.933514i	$0.383274\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−168860.			−0.845107
$448$		0			0
$449$	1671.86			0.00829293			0.00414646	−	0.999991i	$-0.498680\pi$
$449$	1671.86			0.00829293			0.00414646	+	0.999991i	$0.498680\pi$
$450$		0			0
$451$	−7491.07	−	4324.97i	−0.0368291	−	0.0212633i
$452$		0			0
$453$	−152762.	−	264591.i	−0.744421	−	1.28938i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	331100.	−	191160.i	1.58535	−	0.915305i	0.591296	−	0.806454i	$-0.298616\pi$
$457$	331100.	−	191160.i	1.58535	−	0.915305i	0.994058	−	0.108850i	$-0.0347169\pi$
$458$		0			0
$459$	−120486.	+	208687.i	−0.571887	+	0.990537i
$460$		0			0
$461$		−	140500.i		−	0.661112i	−0.943786	−	0.330556i	$-0.892764\pi$
$461$		−	140500.i		−	0.661112i	0.943786	−	0.330556i	$-0.107236\pi$
$462$		0			0
$463$			75338.7i			0.351444i	0.984440	+	0.175722i	$0.0562260\pi$
$463$			75338.7i			0.351444i	−0.984440	+	0.175722i	$0.943774\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−119774.	−	207455.i	−0.549199	−	0.951240i	−0.998330	−	0.0577740i	$-0.981600\pi$
$467$	−119774.	−	207455.i	−0.549199	−	0.951240i	0.449131	−	0.893466i	$-0.351734\pi$
$468$		0			0
$469$	103302.	+	221916.i	0.469639	+	1.00889i
$470$		0			0
$471$	124799.	+	216158.i	0.562560	+	0.974382i
$472$		0			0
$473$	444363.	+	256553.i	1.98617	+	1.14671i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			689753.i			3.03149i
$478$		0			0
$479$	39339.0	+	22712.4i	0.171456	+	0.0989900i	0.583272	−	0.812277i	$-0.301772\pi$
$479$	39339.0	+	22712.4i	0.171456	+	0.0989900i	−0.411816	+	0.911267i	$0.635105\pi$
$480$		0			0
$481$	−350297.	+	202244.i	−1.51407	+	0.874151i
$482$		0			0
$483$	213200.	−	304053.i	0.913889	−	1.30333i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−125334.	−	72361.8i	−0.528460	−	0.305107i	0.211929	−	0.977285i	$-0.432025\pi$
$487$	−125334.	−	72361.8i	−0.528460	−	0.305107i	−0.740389	+	0.672179i	$0.765359\pi$
$488$		0			0
$489$			148630.i			0.621568i
$490$		0			0
$491$	15374.4			0.0637729			0.0318865	−	0.999491i	$-0.489849\pi$
$491$	15374.4			0.0637729			0.0318865	+	0.999491i	$0.489849\pi$
$492$		0			0
$493$	40418.1	−	70006.2i	0.166296	−	0.288033i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−119013.	−	83451.2i	−0.481816	−	0.337847i
$498$		0			0
$499$	−80710.7	−	139795.i	−0.324138	−	0.561424i	0.657199	−	0.753717i	$-0.271741\pi$
$499$	−80710.7	−	139795.i	−0.324138	−	0.561424i	−0.981338	+	0.192293i	$0.938408\pi$
$500$		0			0
$501$	−376058.	+	651352.i	−1.49823	+	2.59502i
$502$		0			0
$503$	102790.			0.406270			0.203135	−	0.979151i	$-0.434887\pi$
$503$	102790.			0.406270			0.203135	+	0.979151i	$0.434887\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−100700.	+	174417.i	−0.391752	+	0.678535i
$508$		0			0
$509$	−239227.	+	138118.i	−0.923366	+	0.533106i	−0.884707	−	0.466147i	$-0.845642\pi$
$509$	−239227.	+	138118.i	−0.923366	+	0.533106i	−0.0386588	+	0.999252i	$0.512309\pi$
$510$		0			0
$511$	−184923.	+	86081.8i	−0.708187	+	0.329662i
$512$		0			0
$513$	495229.	−	285920.i	1.88179	−	1.08645i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	800869.			2.99627
$518$		0			0
$519$	166524.			0.618221
$520$		0			0
$521$	−213489.	−	123258.i	−0.786503	−	0.454088i	0.0522272	−	0.998635i	$-0.483368\pi$
$521$	−213489.	−	123258.i	−0.786503	−	0.454088i	−0.838730	+	0.544548i	$0.816701\pi$
$522$		0			0
$523$	50667.2	+	87758.2i	0.185235	+	0.320837i	0.943656	−	0.330929i	$-0.107362\pi$
$523$	50667.2	+	87758.2i	0.185235	+	0.320837i	−0.758420	+	0.651766i	$0.774029\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	44730.0	−	25824.9i	0.161056	−	0.0929859i
$528$		0			0
$529$	−41057.6	+	71113.8i	−0.146718	+	0.254122i
$530$		0			0
$531$		−	50233.9i		−	0.178159i
$532$		0			0
$533$			9312.03i			0.0327786i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	131144.	+	227148.i	0.454778	+	0.787699i
$538$		0			0
$539$	−441247.	−	78406.6i	−1.51881	−	0.269883i
$540$		0			0
$541$	−13098.2	−	22686.7i	−0.0447523	−	0.0775133i	0.842782	−	0.538256i	$-0.180917\pi$
$541$	−13098.2	−	22686.7i	−0.0447523	−	0.0775133i	−0.887534	+	0.460742i	$0.847583\pi$
$542$		0			0
$543$	−806488.	−	465626.i	−2.73526	−	1.57920i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			483160.i			1.61479i	0.590012	+	0.807395i	$0.299123\pi$
$547$			483160.i			1.61479i	−0.590012	+	0.807395i	$0.700877\pi$
$548$		0			0
$549$	495143.	+	285871.i	1.64280	+	0.948473i
$550$		0			0
$551$	−166129.	+	95914.8i	−0.547196	+	0.315924i
$552$		0			0
$553$	−15154.6	+	171906.i	−0.0495557	+	0.562136i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	79228.5	+	45742.6i	0.255371	+	0.147438i	0.622221	−	0.782842i	$-0.286231\pi$
$557$	79228.5	+	45742.6i	0.255371	+	0.147438i	−0.366850	+	0.930280i	$0.619564\pi$
$558$		0			0
$559$		−	552380.i		−	1.76772i
$560$		0			0
$561$	350082.			1.11236
$562$		0			0
$563$	−106624.	+	184678.i	−0.336386	+	0.582638i	−0.983750	−	0.179543i	$-0.942538\pi$
$563$	−106624.	+	184678.i	−0.336386	+	0.582638i	0.647364	+	0.762181i	$0.275871\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−904137.	+	420877.i	−2.81234	+	1.30915i
$568$		0			0
$569$	−8033.59	−	13914.6i	−0.0248133	−	0.0429780i	0.853352	−	0.521335i	$-0.174566\pi$
$569$	−8033.59	−	13914.6i	−0.0248133	−	0.0429780i	−0.878165	+	0.478357i	$0.841232\pi$
$570$		0			0
$571$	−213022.	+	368965.i	−0.653360	+	1.13165i	0.328943	+	0.944350i	$0.393308\pi$
$571$	−213022.	+	368965.i	−0.653360	+	1.13165i	−0.982302	+	0.187302i	$0.940026\pi$
$572$		0			0
$573$	−763452.			−2.32526
$574$		0			0
$575$		0			0
$576$		0			0
$577$	214913.	−	372240.i	0.645521	−	1.11808i	−0.338660	−	0.940909i	$-0.609974\pi$
$577$	214913.	−	372240.i	0.645521	−	1.11808i	0.984181	−	0.177166i	$-0.0566931\pi$
$578$		0			0
$579$	−944064.	+	545055.i	−2.81607	+	1.62586i
$580$		0			0
$581$	−86598.6	−	60722.5i	−0.256542	−	0.179886i
$582$		0			0
$583$	532257.	−	307299.i	1.56597	−	0.904116i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	72375.4			0.210046			0.105023	−	0.994470i	$-0.466508\pi$
$587$	72375.4			0.210046			0.105023	+	0.994470i	$0.466508\pi$
$588$		0			0
$589$	−122568.			−0.353303
$590$		0			0
$591$	376252.	+	217229.i	1.07722	+	0.621933i
$592$		0			0
$593$	−186483.	−	322998.i	−0.530311	−	0.918525i	−0.999375	−	0.0353606i	$-0.988742\pi$
$593$	−186483.	−	322998.i	−0.530311	−	0.918525i	0.469064	−	0.883164i	$-0.344591\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−38125.9	+	22012.0i	−0.106972	+	0.0617605i
$598$		0			0
$599$	−278948.	+	483153.i	−0.777446	+	1.34658i	0.155963	+	0.987763i	$0.450152\pi$
$599$	−278948.	+	483153.i	−0.777446	+	1.34658i	−0.933409	+	0.358813i	$0.883182\pi$
$600$		0			0
$601$			68122.4i			0.188600i	0.995544	+	0.0942999i	$0.0300613\pi$
$601$			68122.4i			0.188600i	−0.995544	+	0.0942999i	$0.969939\pi$
$602$		0			0
$603$		−	1.04647e6i		−	2.87800i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−182260.	−	315683.i	−0.494667	−	0.856788i	0.505314	−	0.862935i	$-0.331377\pi$
$607$	−182260.	−	315683.i	−0.494667	−	0.856788i	−0.999981	+	0.00614713i	$0.998043\pi$
$608$		0			0
$609$	556158.	−	258892.i	1.49956	−	0.698047i
$610$		0			0
$611$	−431085.	−	746661.i	−1.15473	−	2.00005i
$612$		0			0
$613$	−202893.	−	117140.i	−0.539940	−	0.311735i	0.205114	−	0.978738i	$-0.434243\pi$
$613$	−202893.	−	117140.i	−0.539940	−	0.311735i	−0.745055	+	0.667003i	$0.767577\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	335125.i		−	0.880312i	−0.897921	−	0.440156i	$-0.854923\pi$
$617$		−	335125.i		−	0.880312i	0.897921	−	0.440156i	$-0.145077\pi$
$618$		0			0
$619$	−129011.	−	74484.6i	−0.336702	−	0.194395i	0.322111	−	0.946702i	$-0.395608\pi$
$619$	−129011.	−	74484.6i	−0.336702	−	0.194395i	−0.658813	+	0.752307i	$0.728941\pi$
$620$		0			0
$621$	−843250.	+	486850.i	−2.18662	+	1.26244i
$622$		0			0
$623$	−496496.	−	43769.1i	−1.27920	−	0.112770i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−719467.	−	415384.i	−1.83010	−	1.05661i
$628$		0			0
$629$		−	221517.i		−	0.559893i
$630$		0			0
$631$	681456.			1.71151			0.855754	−	0.517383i	$-0.173094\pi$
$631$	681456.			1.71151			0.855754	+	0.517383i	$0.173094\pi$
$632$		0			0
$633$	123653.	−	214173.i	0.308601	−	0.534513i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	164411.	+	453584.i	0.405184	+	1.11784i
$638$		0			0
$639$	310704.	+	538156.i	0.760932	+	1.31797i
$640$		0			0
$641$	385755.	−	668147.i	0.938848	−	1.62613i	0.171225	−	0.985232i	$-0.445228\pi$
$641$	385755.	−	668147.i	0.938848	−	1.62613i	0.767624	−	0.640901i	$-0.221439\pi$
$642$		0			0
$643$	−199260.			−0.481945			−0.240973	−	0.970532i	$-0.577466\pi$
$643$	−199260.			−0.481945			−0.240973	+	0.970532i	$0.577466\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	203005.	−	351615.i	0.484951	−	0.839960i	−0.514899	−	0.857251i	$-0.672171\pi$
$647$	203005.	−	351615.i	0.484951	−	0.839960i	0.999851	+	0.0172904i	$0.00550399\pi$
$648$		0			0
$649$	−38763.7	+	22380.2i	−0.0920313	+	0.0531343i
$650$		0			0
$651$	390454.	+	34420.9i	0.921315	+	0.0812195i
$652$		0			0
$653$	−547579.	+	316145.i	−1.28416	+	0.741412i	−0.977607	−	0.210441i	$-0.932510\pi$
$653$	−547579.	+	316145.i	−1.28416	+	0.741412i	−0.306556	+	0.951852i	$0.599177\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	872021.			2.02021
$658$		0			0
$659$	645822.			1.48711			0.743554	−	0.668676i	$-0.233139\pi$
$659$	645822.			1.48711			0.743554	+	0.668676i	$0.233139\pi$
$660$		0			0
$661$	−551042.	−	318145.i	−1.26119	−	0.728151i	−0.287889	−	0.957664i	$-0.592953\pi$
$661$	−551042.	−	318145.i	−1.26119	−	0.728151i	−0.973306	+	0.229513i	$0.926287\pi$
$662$		0			0
$663$	−188439.	−	326386.i	−0.428691	−	0.742514i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	282876.	−	163319.i	0.635836	−	0.367100i
$668$		0			0
$669$	523580.	−	906867.i	1.16985	−	2.02624i
$670$		0			0
$671$		−	509445.i		−	1.13149i
$672$		0			0
$673$		−	190181.i		−	0.419891i	−0.977713	−	0.209946i	$-0.932671\pi$
$673$		−	190181.i		−	0.419891i	0.977713	−	0.209946i	$-0.0673287\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	34152.8	+	59154.4i	0.0745159	+	0.129065i	0.900876	−	0.434077i	$-0.142926\pi$
$677$	34152.8	+	59154.4i	0.0745159	+	0.129065i	−0.826360	+	0.563143i	$0.809592\pi$
$678$		0			0
$679$	482406.	+	338261.i	1.04634	+	0.733690i
$680$		0			0
$681$	−97123.9	−	168223.i	−0.209427	−	0.362737i
$682$		0			0
$683$	274448.	+	158452.i	0.588326	+	0.339670i	0.764435	−	0.644700i	$-0.223018\pi$
$683$	274448.	+	158452.i	0.588326	+	0.339670i	−0.176109	+	0.984371i	$0.556351\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	764340.i		−	1.61947i
$688$		0			0
$689$	−572997.	−	330820.i	−1.20702	−	0.696873i
$690$		0			0
$691$	−474220.	+	273791.i	−0.993171	+	0.573408i	−0.906221	−	0.422805i	$-0.861046\pi$
$691$	−474220.	+	273791.i	−0.993171	+	0.573408i	−0.0869506	+	0.996213i	$0.527712\pi$
$692$		0			0
$693$	1.56871e6	+	1.09997e6i	3.26645	+	2.29042i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−4416.47	−	2549.85i	−0.00909096	−	0.00524867i
$698$		0			0
$699$			815526.i			1.66910i
$700$		0			0
$701$	−429632.			−0.874301			−0.437150	−	0.899388i	$-0.644012\pi$
$701$	−429632.			−0.874301			−0.437150	+	0.899388i	$0.644012\pi$
$702$		0			0
$703$	−262837.	+	455247.i	−0.531834	+	0.921163i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−184885.	−	397173.i	−0.369881	−	0.794586i
$708$		0			0
$709$	−461346.	−	799074.i	−0.917771	−	1.58963i	−0.802793	−	0.596257i	$-0.796654\pi$
$709$	−461346.	−	799074.i	−0.917771	−	1.58963i	−0.114977	−	0.993368i	$-0.536679\pi$
$710$		0			0
$711$	368883.	−	638925.i	0.729709	−	1.26389i
$712$		0			0
$713$	208703.			0.410534
$714$		0			0
$715$		0			0
$716$		0			0
$717$	334470.	−	579318.i	0.650607	−	1.12688i
$718$		0			0
$719$	849653.	−	490547.i	1.64355	−	0.948906i	0.663997	−	0.747736i	$-0.268859\pi$
$719$	849653.	−	490547.i	1.64355	−	0.948906i	0.979556	−	0.201170i	$-0.0644744\pi$
$720$		0			0
$721$	−58277.0	+	661066.i	−0.112105	+	1.27167i
$722$		0			0
$723$	1.62812e6	−	939997.i	3.11466	−	1.79825i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−206124.			−0.389995			−0.194997	−	0.980804i	$-0.562470\pi$
$727$	−206124.			−0.389995			−0.194997	+	0.980804i	$0.562470\pi$
$728$		0			0
$729$	1.24056e6			2.33433
$730$		0			0
$731$	261981.	+	151255.i	0.490269	+	0.283057i
$732$		0			0
$733$	−3647.88	−	6318.31i	−0.00678942	−	0.0117596i	0.862611	−	0.505868i	$-0.168828\pi$
$733$	−3647.88	−	6318.31i	−0.00678942	−	0.0117596i	−0.869400	+	0.494109i	$0.835494\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−807521.	+	466223.i	−1.48669	+	0.858338i
$738$		0			0
$739$	−7878.12	+	13645.3i	−0.0144256	+	0.0249859i	−0.873148	−	0.487455i	$-0.837925\pi$
$739$	−7878.12	+	13645.3i	−0.0144256	+	0.0249859i	0.858722	+	0.512441i	$0.171259\pi$
$740$		0			0
$741$			894357.i			1.62882i
$742$		0			0
$743$			918563.i			1.66392i	0.554839	+	0.831958i	$0.312780\pi$
$743$			918563.i			1.66392i	−0.554839	+	0.831958i	$0.687220\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	226081.	+	391584.i	0.405157	+	0.701753i
$748$		0			0
$749$	999673.	+	88127.2i	1.78194	+	0.157089i
$750$		0			0
$751$	324544.	+	562127.i	0.575432	+	0.996678i	0.995995	+	0.0894142i	$0.0284995\pi$
$751$	324544.	+	562127.i	0.575432	+	0.996678i	−0.420562	+	0.907264i	$0.638167\pi$
$752$		0			0
$753$	458523.	+	264728.i	0.808669	+	0.466885i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			361330.i			0.630540i	0.949002	+	0.315270i	$0.102095\pi$
$757$			361330.i			0.630540i	−0.949002	+	0.315270i	$0.897905\pi$
$758$		0			0
$759$	1.22507e6	+	707294.i	2.12656	+	1.22777i
$760$		0			0
$761$	−352574.	+	203559.i	−0.608810	+	0.351496i	−0.772499	−	0.635015i	$-0.780994\pi$
$761$	−352574.	+	203559.i	−0.608810	+	0.351496i	0.163690	+	0.986512i	$0.447660\pi$
$762$		0			0
$763$	616311.	−	286894.i	1.05865	−	0.492802i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	41730.7	+	24093.2i	0.0709357	+	0.0409548i
$768$		0			0
$769$		−	3720.24i		−	0.00629098i	−0.999995	−	0.00314549i	$-0.998999\pi$
$769$		−	3720.24i		−	0.00629098i	0.999995	−	0.00314549i	$-0.00100124\pi$
$770$		0			0
$771$	−1.25432e6			−2.11008
$772$		0			0
$773$	64914.4	−	112435.i	0.108638	−	0.188167i	−0.806581	−	0.591124i	$-0.798684\pi$
$773$	64914.4	−	112435.i	0.108638	−	0.188167i	0.915219	+	0.402957i	$0.132018\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	965142.	−	1.37642e6i	1.59863	−	2.27987i
$778$		0			0
$779$	6050.96	+	10480.6i	0.00997125	+	0.0172707i
$780$		0			0
$781$	276850.	−	479519.i	0.453882	−	0.786147i
$782$		0			0
$783$	−1.60853e6			−2.62364
$784$		0			0
$785$		0			0
$786$		0			0
$787$	301911.	−	522925.i	0.487450	−	0.844287i	−0.512446	−	0.858719i	$-0.671261\pi$
$787$	301911.	−	522925.i	0.487450	−	0.844287i	0.999896	+	0.0144319i	$0.00459398\pi$
$788$		0			0
$789$	1.07227e6	−	619075.i	1.72246	−	0.994464i
$790$		0			0
$791$	421538.	−	601171.i	0.673726	−	0.960826i
$792$		0			0
$793$	−474962.	+	274220.i	−0.755288	+	0.436066i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−981302.			−1.54485			−0.772425	−	0.635106i	$-0.780956\pi$
$797$	−981302.			−1.54485			−0.772425	+	0.635106i	$0.780956\pi$
$798$		0			0
$799$	472164.			0.739604
$800$		0			0
$801$	1.84533e6	+	1.06540e6i	2.87613	+	1.66054i
$802$		0			0
$803$	−388503.	−	672907.i	−0.602509	−	1.04358i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	116796.	−	67432.1i	0.179341	−	0.103543i
$808$		0			0
$809$	−540742.	+	936593.i	−0.826216	+	1.43105i	0.0747711	+	0.997201i	$0.476177\pi$
$809$	−540742.	+	936593.i	−0.826216	+	1.43105i	−0.900987	+	0.433847i	$0.857156\pi$
$810$		0			0
$811$		−	976385.i		−	1.48450i	−0.670125	−	0.742249i	$-0.733759\pi$
$811$		−	976385.i		−	1.48450i	0.670125	−	0.742249i	$-0.266241\pi$
$812$		0			0
$813$			1.67524e6i			2.53452i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−358937.	−	621697.i	−0.537742	−	0.931397i
$818$		0			0
$819$	181126.	−	2.05461e6i	0.270031	−	3.06310i
$820$		0			0
$821$	−88380.7	−	153080.i	−0.131121	−	0.227108i	0.792988	−	0.609237i	$-0.208524\pi$
$821$	−88380.7	−	153080.i	−0.131121	−	0.227108i	−0.924109	+	0.382129i	$0.875191\pi$
$822$		0			0
$823$	317321.	+	183205.i	0.468488	+	0.270482i	0.715607	−	0.698503i	$-0.246150\pi$
$823$	317321.	+	183205.i	0.468488	+	0.270482i	−0.247118	+	0.968985i	$0.579484\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			674908.i			0.986811i	0.869799	+	0.493405i	$0.164248\pi$
$827$			674908.i			0.986811i	−0.869799	+	0.493405i	$0.835752\pi$
$828$		0			0
$829$	245500.	+	141739.i	0.357225	+	0.206244i	0.667863	−	0.744284i	$-0.267209\pi$
$829$	245500.	+	141739.i	0.357225	+	0.206244i	−0.310638	+	0.950528i	$0.600543\pi$
$830$		0			0
$831$	102023.	−	58903.2i	0.147740	−	0.0852977i
$832$		0			0
$833$	−260144.	−	46225.7i	−0.374907	−	0.0666184i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−890064.	−	513879.i	−1.27049	−	0.733516i
$838$		0			0
$839$			1.03574e6i			1.47138i	0.677317	+	0.735691i	$0.263142\pi$
$839$			1.03574e6i			1.47138i	−0.677317	+	0.735691i	$0.736858\pi$
$840$		0			0
$841$	−167686.			−0.237085
$842$		0			0
$843$	786052.	−	1.36148e6i	1.10610	−	1.91583i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	86916.4	−	985938.i	0.121153	−	1.37430i
$848$		0			0
$849$	−276220.	−	478427.i	−0.383213	−	0.663744i
$850$		0			0
$851$	447545.	−	775171.i	0.617985	−	1.07038i
$852$		0			0
$853$	998779.			1.37269			0.686344	−	0.727277i	$-0.259215\pi$
$853$	998779.			1.37269			0.686344	+	0.727277i	$0.259215\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−578029.	+	1.00118e6i	−0.787024	+	1.36317i	0.140759	+	0.990044i	$0.455046\pi$
$857$	−578029.	+	1.00118e6i	−0.787024	+	1.36317i	−0.927783	+	0.373121i	$0.878288\pi$
$858$		0			0
$859$	−807360.	+	466129.i	−1.09416	+	0.631713i	−0.934681	−	0.355488i	$-0.884315\pi$
$859$	−807360.	+	466129.i	−1.09416	+	0.631713i	−0.159479	+	0.987201i	$0.550981\pi$
$860$		0			0
$861$	−16332.7	−	35086.2i	−0.0220319	−	0.0473294i
$862$		0			0
$863$	−378841.	+	218724.i	−0.508669	+	0.293680i	−0.732286	−	0.680997i	$-0.761547\pi$
$863$	−378841.	+	218724.i	−0.508669	+	0.293680i	0.223618	+	0.974677i	$0.428213\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.21709e6			−1.61914
$868$		0			0
$869$	−657381.			−0.870517
$870$		0			0
$871$	869330.	+	501908.i	1.14590	+	0.661589i
$872$		0			0
$873$	−1.25941e6	−	2.18136e6i	−1.65249	−	2.86219i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−941044.	+	543312.i	−1.22352	+	0.706399i	−0.965666	−	0.259785i	$-0.916348\pi$
$877$	−941044.	+	543312.i	−1.22352	+	0.706399i	−0.257853	+	0.966184i	$0.583015\pi$
$878$		0			0
$879$	645339.	−	1.11776e6i	0.835238	−	1.44667i
$880$		0			0
$881$			878341.i			1.13165i	0.824526	+	0.565824i	$0.191442\pi$
$881$			878341.i			1.13165i	−0.824526	+	0.565824i	$0.808558\pi$
$882$		0			0
$883$			627160.i			0.804373i	0.915558	+	0.402186i	$0.131750\pi$
$883$			627160.i			0.804373i	−0.915558	+	0.402186i	$0.868250\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	693541.	+	1.20125e6i	0.881505	+	1.52681i	0.849668	+	0.527319i	$0.176803\pi$
$887$	693541.	+	1.20125e6i	0.881505	+	1.52681i	0.0318376	+	0.999493i	$0.489864\pi$
$888$		0			0
$889$	−149998.	+	213918.i	−0.189794	+	0.270672i
$890$		0			0
$891$	−1.89950e6	−	3.29003e6i	−2.39267	−	4.14423i
$892$		0			0
$893$	−970361.	−	560238.i	−1.21683	−	0.702538i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	1.52286e6i		−	1.89268i
$898$		0			0
$899$	298581.	+	172386.i	0.369439	+	0.213295i
$900$		0			0
$901$	313800.	−	181173.i	0.386548	−	0.223174i
$902$		0			0
$903$	968840.	+	2.08128e6i	1.18816	+	2.55244i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−238143.	−	137492.i	−0.289483	−	0.167133i	0.348226	−	0.937411i	$-0.386784\pi$
$907$	−238143.	−	137492.i	−0.289483	−	0.167133i	−0.637709	+	0.770278i	$0.720118\pi$
$908$		0			0
$909$			1.87291e6i			2.26667i
$910$		0			0
$911$	−1.33223e6			−1.60525			−0.802625	−	0.596484i	$-0.796564\pi$
$911$	−1.33223e6			−1.60525			−0.802625	+	0.596484i	$0.796564\pi$
$912$		0			0
$913$	201448.	−	348918.i	0.241669	−	0.418583i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	504049.	+	44435.0i	0.599424	+	0.0528429i
$918$		0			0
$919$	444678.	+	770204.i	0.526519	+	0.911958i	0.999523	+	0.0308975i	$0.00983653\pi$
$919$	444678.	+	770204.i	0.526519	+	0.911958i	−0.473003	+	0.881061i	$0.656830\pi$
$920$		0			0
$921$	75959.6	−	131566.i	0.0895495	−	0.155104i
$922$		0			0
$923$	−596082.			−0.699685
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.41854e6	−	2.45699e6i	1.65076	−	2.85919i
$928$		0			0
$929$	641891.	−	370596.i	0.743755	−	0.429407i	−0.0796781	−	0.996821i	$-0.525389\pi$
$929$	641891.	−	370596.i	0.743755	−	0.429407i	0.823433	+	0.567414i	$0.192056\pi$
$930$		0			0
$931$	479782.	+	403669.i	0.553535	+	0.465722i
$932$		0			0
$933$	1.58961e6	−	917760.i	1.82611	−	1.05430i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	792567.			0.902728			0.451364	−	0.892340i	$-0.350938\pi$
$937$	792567.			0.902728			0.451364	+	0.892340i	$0.350938\pi$
$938$		0			0
$939$	−93393.4			−0.105922
$940$		0			0
$941$	421649.	+	243439.i	0.476181	+	0.274923i	0.718824	−	0.695192i	$-0.244681\pi$
$941$	421649.	+	243439.i	0.476181	+	0.274923i	−0.242642	+	0.970116i	$0.578014\pi$
$942$		0			0
$943$	−10303.3	−	17845.8i	−0.0115865	−	0.0200684i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	715538.	−	413116.i	0.797871	−	0.460651i	−0.0448553	−	0.998993i	$-0.514283\pi$
$947$	715538.	−	413116.i	0.797871	−	0.460651i	0.842726	+	0.538343i	$0.180949\pi$
$948$		0			0
$949$	−418240.	+	724413.i	−0.464401	+	0.804366i
$950$		0			0
$951$			2.47653e6i			2.73831i
$952$		0			0
$953$		−	553288.i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$953$		−	553288.i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.16843e6	+	2.02378e6i	1.27579	+	2.20973i
$958$		0			0
$959$	−646050.	−	1.38786e6i	−0.702472	−	1.50906i
$960$		0			0
$961$	−351616.	−	609016.i	−0.380734	−	0.659451i
$962$		0			0
$963$	−3.71549e6	−	2.14514e6i	−4.00648	−	2.31314i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			113775.i			0.121673i	0.998148	+	0.0608366i	$0.0193769\pi$
$967$			113775.i			0.121673i	−0.998148	+	0.0608366i	$0.980623\pi$
$968$		0			0
$969$	−424172.	−	244896.i	−0.451746	−	0.260816i
$970$		0			0
$971$	−309016.	+	178411.i	−0.327750	+	0.189227i	−0.654842	−	0.755766i	$-0.727265\pi$
$971$	−309016.	+	178411.i	−0.327750	+	0.189227i	0.327092	+	0.944993i	$0.393931\pi$
$972$		0			0
$973$	993134.	−	1.41635e6i	1.04902	−	1.49604i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	812051.	+	468838.i	0.850735	+	0.491172i	0.860899	−	0.508776i	$-0.169902\pi$
$977$	812051.	+	468838.i	0.850735	+	0.491172i	−0.0101640	+	0.999948i	$0.503235\pi$
$978$		0			0
$979$		−	1.89863e6i		−	1.98096i
$980$		0			0
$981$	−2.90628e6			−3.01994
$982$		0			0
$983$	−140607.	+	243538.i	−0.145512	+	0.252035i	−0.929564	−	0.368661i	$-0.879816\pi$
$983$	−140607.	+	243538.i	−0.145512	+	0.252035i	0.784052	+	0.620696i	$0.213150\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.93385e6	+	2.05720e6i	3.01165	+	2.11175i
$988$		0			0
$989$	611179.	+	1.05859e6i	0.624850	+	1.08227i
$990$		0			0
$991$	−58992.2	+	102178.i	−0.0600686	+	0.104042i	−0.894496	−	0.447076i	$-0.852465\pi$
$991$	−58992.2	+	102178.i	−0.0600686	+	0.104042i	0.834427	+	0.551118i	$0.185799\pi$
$992$		0			0
$993$	1.96509e6			1.99289
$994$		0			0
$995$		0			0
$996$		0			0
$997$	258634.	−	447967.i	0.260193	−	0.450667i	−0.706100	−	0.708112i	$-0.749547\pi$
$997$	258634.	−	447967.i	0.260193	−	0.450667i	0.966293	+	0.257445i	$0.0828806\pi$
$998$		0			0
$999$	−3.81733e6	+	2.20394e6i	−3.82497	+	2.20835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.c.549.1		44
5.2	odd	4		700.5.s.c.101.11	✓	22
5.3	odd	4		700.5.s.d.101.1	yes	22
5.4	even	2	inner	700.5.o.c.549.22		44
7.5	odd	6	inner	700.5.o.c.649.22		44
35.12	even	12		700.5.s.c.201.11	yes	22
35.19	odd	6	inner	700.5.o.c.649.1		44
35.33	even	12		700.5.s.d.201.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.5.o.c.549.1		44	1.1	even	1	trivial
700.5.o.c.549.22		44	5.4	even	2	inner
700.5.o.c.649.1		44	35.19	odd	6	inner
700.5.o.c.649.22		44	7.5	odd	6	inner
700.5.s.c.101.11	✓	22	5.2	odd	4
700.5.s.c.201.11	yes	22	35.12	even	12
700.5.s.d.101.1	yes	22	5.3	odd	4
700.5.s.d.201.1	yes	22	35.33	even	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.52174 + 14.7601i) q^{3} +(40.1198 + 28.1318i) q^{7} +(-104.740 - 181.415i) q^{9} +(-93.3277 + 161.648i) q^{11} +200.942 q^{13} +(-55.0227 + 95.3020i) q^{17} +(226.158 - 130.572i) q^{19} +(-757.119 + 352.440i) q^{21} +(-385.090 + 222.332i) q^{23} +2189.75 q^{27} -734.572 q^{29} +(-406.469 - 234.675i) q^{31} +(-1590.63 - 2755.05i) q^{33} +(-1743.27 + 1006.48i) q^{37} +(-1712.38 + 2965.92i) q^{39} +46.3418i q^{41} -2748.95i q^{43} +(-2145.32 - 3715.80i) q^{47} +(818.201 + 2257.29i) q^{49} +(-937.777 - 1624.28i) q^{51} +(-2851.55 - 1646.34i) q^{53} +4450.82i q^{57} +(207.675 + 119.901i) q^{59} +(-2363.68 + 1364.67i) q^{61} +(901.384 - 10224.9i) q^{63} +(4326.27 + 2497.77i) q^{67} -7578.62i q^{69} -2966.43 q^{71} +(-2081.39 + 3605.08i) q^{73} +(-8291.75 + 3859.82i) q^{77} +(1760.95 + 3050.05i) q^{79} +(-10176.5 + 17626.2i) q^{81} -2158.50 q^{83} +(6259.83 - 10842.3i) q^{87} +(-8809.09 + 5085.93i) q^{89} +(8061.77 + 5652.87i) q^{91} +(6927.64 - 3999.68i) q^{93} +12024.1 q^{97} +39100.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) \) 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Introduction

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