LMFDB - Embedded newform 315.4.d.c.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(64,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("315.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.d (of order $2$, degree $1$, 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:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.1
Root			$-4.31366i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.c.64.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.31366i q^{2} -20.2350 q^{4} +(2.32771 - 10.9353i) q^{5} +7.00000i q^{7} +65.0123i q^{8} +(-58.1067 - 12.3686i) q^{10} -25.5420 q^{11} +64.1014i q^{13} +37.1956 q^{14} +183.574 q^{16} +27.6952i q^{17} -0.792436 q^{19} +(-47.1011 + 221.276i) q^{20} +135.721i q^{22} +108.606i q^{23} +(-114.164 - 50.9086i) q^{25} +340.613 q^{26} -141.645i q^{28} -234.000 q^{29} +129.204 q^{31} -455.349i q^{32} +147.163 q^{34} +(76.5474 + 16.2940i) q^{35} +38.3108i q^{37} +4.21073i q^{38} +(710.932 + 151.330i) q^{40} +403.216 q^{41} -172.895i q^{43} +516.840 q^{44} +577.097 q^{46} -206.943i q^{47} -49.0000 q^{49} +(-270.511 + 606.626i) q^{50} -1297.09i q^{52} +144.031i q^{53} +(-59.4542 + 279.310i) q^{55} -455.086 q^{56} +1243.40i q^{58} -679.086 q^{59} -574.717 q^{61} -686.544i q^{62} -950.977 q^{64} +(700.971 + 149.209i) q^{65} +515.640i q^{67} -560.411i q^{68} +(86.5805 - 406.747i) q^{70} -556.612 q^{71} +173.243i q^{73} +203.571 q^{74} +16.0349 q^{76} -178.794i q^{77} -79.3290 q^{79} +(427.306 - 2007.44i) q^{80} -2142.55i q^{82} +1043.56i q^{83} +(302.856 + 64.4663i) q^{85} -918.703 q^{86} -1660.54i q^{88} +652.060 q^{89} -448.710 q^{91} -2197.65i q^{92} -1099.62 q^{94} +(-1.84456 + 8.66556i) q^{95} +515.714i q^{97} +260.369i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 36 q^{4} - 6 q^{5} - 16 q^{10} - 84 q^{11} + 56 q^{14} + 148 q^{16} + 72 q^{19} + 68 q^{20} - 362 q^{25} + 620 q^{26} - 88 q^{29} + 120 q^{31} + 964 q^{34} + 28 q^{35} + 1396 q^{40} + 852 q^{41}+ \cdots + 1628 q^{95}+O(q^{100}) $ 10 * q - 36 * q^4 - 6 * q^5 - 16 * q^10 - 84 * q^11 + 56 * q^14 + 148 * q^16 + 72 * q^19 + 68 * q^20 - 362 * q^25 + 620 * q^26 - 88 * q^29 + 120 * q^31 + 964 * q^34 + 28 * q^35 + 1396 * q^40 + 852 * q^41 + 1424 * q^44 + 176 * q^46 - 490 * q^49 - 1644 * q^50 - 1136 * q^55 - 588 * q^56 - 864 * q^59 - 884 * q^61 - 2724 * q^64 - 520 * q^65 + 756 * q^70 - 880 * q^71 - 3024 * q^74 - 2672 * q^76 - 3580 * q^79 + 2316 * q^80 + 1572 * q^85 - 2432 * q^86 + 1492 * q^89 + 476 * q^91 + 1652 * q^94 + 1628 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	5.31366i		−	1.87866i	−0.343013	−	0.939331i	$-0.611447\pi$
$2$		−	5.31366i		−	1.87866i	0.343013	−	0.939331i	$-0.388553\pi$
$3$		0			0
$3$		0			0
$4$	−20.2350			−2.52937
$5$	2.32771	−	10.9353i	0.208197	−	0.978087i
$5$	2.32771	−	10.9353i	0.208197	−	0.978087i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			65.0123i			2.87317i
$9$		0			0
$10$	−58.1067	−	12.3686i	−1.83749	−	0.391131i
$11$	−25.5420			−0.700108			−0.350054	−	0.936730i	$-0.613837\pi$
$11$	−25.5420			−0.700108			−0.350054	+	0.936730i	$0.613837\pi$
$12$		0			0
$13$			64.1014i			1.36758i	0.729679	+	0.683790i	$0.239670\pi$
$13$			64.1014i			1.36758i	−0.729679	+	0.683790i	$0.760330\pi$
$14$	37.1956			0.710067
$15$		0			0
$16$	183.574			2.86834
$17$			27.6952i			0.395122i	0.980291	+	0.197561i	$0.0633020\pi$
$17$			27.6952i			0.395122i	−0.980291	+	0.197561i	$0.936698\pi$
$18$		0			0
$19$	−0.792436			−0.00956828			−0.00478414	−	0.999989i	$-0.501523\pi$
$19$	−0.792436			−0.00956828			−0.00478414	+	0.999989i	$0.501523\pi$
$20$	−47.1011	+	221.276i	−0.526606	+	2.47394i
$21$		0			0
$22$			135.721i			1.31527i
$23$			108.606i			0.984609i	0.870423	+	0.492305i	$0.163845\pi$
$23$			108.606i			0.984609i	−0.870423	+	0.492305i	$0.836155\pi$
$24$		0			0
$25$	−114.164	−	50.9086i	−0.913308	−	0.407269i
$26$	340.613			2.56922
$27$		0			0
$28$		−	141.645i		−	0.956012i
$29$	−234.000			−1.49837			−0.749186	−	0.662360i	$-0.769555\pi$
$29$	−234.000			−1.49837			−0.749186	+	0.662360i	$0.769555\pi$
$30$		0			0
$31$	129.204			0.748570			0.374285	−	0.927314i	$-0.377888\pi$
$31$	129.204			0.748570			0.374285	+	0.927314i	$0.377888\pi$
$32$		−	455.349i		−	2.51547i
$33$		0			0
$34$	147.163			0.742300
$35$	76.5474	+	16.2940i	0.369682	+	0.0786909i
$36$		0			0
$37$			38.3108i			0.170223i	0.996371	+	0.0851116i	$0.0271247\pi$
$37$			38.3108i			0.170223i	−0.996371	+	0.0851116i	$0.972875\pi$
$38$			4.21073i			0.0179756i
$39$		0			0
$40$	710.932	+	151.330i	2.81021	+	0.598183i
$41$	403.216			1.53590			0.767949	−	0.640511i	$-0.221278\pi$
$41$	403.216			1.53590			0.767949	+	0.640511i	$0.221278\pi$
$42$		0			0
$43$		−	172.895i		−	0.613167i	−0.951844	−	0.306584i	$-0.900814\pi$
$43$		−	172.895i		−	0.613167i	0.951844	−	0.306584i	$-0.0991859\pi$
$44$	516.840			1.77083
$45$		0			0
$46$	577.097			1.84975
$47$		−	206.943i		−	0.642250i	−0.947037	−	0.321125i	$-0.895939\pi$
$47$		−	206.943i		−	0.642250i	0.947037	−	0.321125i	$-0.104061\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−270.511	+	606.626i	−0.765120	+	1.71580i
$51$		0			0
$52$		−	1297.09i		−	3.45911i
$53$			144.031i			0.373287i	0.982428	+	0.186643i	$0.0597609\pi$
$53$			144.031i			0.373287i	−0.982428	+	0.186643i	$0.940239\pi$
$54$		0			0
$55$	−59.4542	+	279.310i	−0.145760	+	0.684767i
$56$	−455.086			−1.08595
$57$		0			0
$58$			1243.40i			2.81493i
$59$	−679.086			−1.49846			−0.749232	−	0.662307i	$-0.769577\pi$
$59$	−679.086			−1.49846			−0.749232	+	0.662307i	$0.769577\pi$
$60$		0			0
$61$	−574.717			−1.20631			−0.603155	−	0.797624i	$-0.706090\pi$
$61$	−574.717			−1.20631			−0.603155	+	0.797624i	$0.706090\pi$
$62$		−	686.544i		−	1.40631i
$63$		0			0
$64$	−950.977			−1.85738
$65$	700.971	+	149.209i	1.33761	+	0.284725i
$66$		0			0
$67$			515.640i			0.940230i	0.882605	+	0.470115i	$0.155788\pi$
$67$			515.640i			0.940230i	−0.882605	+	0.470115i	$0.844212\pi$
$68$		−	560.411i		−	0.999409i
$69$		0			0
$70$	86.5805	−	406.747i	0.147834	−	0.694508i
$71$	−556.612			−0.930391			−0.465195	−	0.885208i	$-0.654016\pi$
$71$	−556.612			−0.930391			−0.465195	+	0.885208i	$0.654016\pi$
$72$		0			0
$73$			173.243i			0.277762i	0.990309	+	0.138881i	$0.0443505\pi$
$73$			173.243i			0.277762i	−0.990309	+	0.138881i	$0.955650\pi$
$74$	203.571			0.319792
$75$		0			0
$76$	16.0349			0.0242017
$77$		−	178.794i		−	0.264616i
$78$		0			0
$79$	−79.3290			−0.112977			−0.0564887	−	0.998403i	$-0.517990\pi$
$79$	−79.3290			−0.112977			−0.0564887	+	0.998403i	$0.517990\pi$
$80$	427.306	−	2007.44i	0.597178	−	2.80548i
$81$		0			0
$82$		−	2142.55i		−	2.88543i
$83$			1043.56i			1.38007i	0.723777	+	0.690034i	$0.242404\pi$
$83$			1043.56i			1.38007i	−0.723777	+	0.690034i	$0.757596\pi$
$84$		0			0
$85$	302.856	+	64.4663i	0.386463	+	0.0822630i
$86$	−918.703			−1.15193
$87$		0			0
$88$		−	1660.54i		−	2.01153i
$89$	652.060			0.776609			0.388304	−	0.921531i	$-0.373061\pi$
$89$	652.060			0.776609			0.388304	+	0.921531i	$0.373061\pi$
$90$		0			0
$91$	−448.710			−0.516897
$92$		−	2197.65i		−	2.49044i
$93$		0			0
$94$	−1099.62			−1.20657
$95$	−1.84456	+	8.66556i	−0.00199208	+	0.00935861i
$96$		0			0
$97$			515.714i			0.539823i	0.962885	+	0.269912i	$0.0869945\pi$
$97$			515.714i			0.539823i	−0.962885	+	0.269912i	$0.913005\pi$
$98$			260.369i			0.268380i
$99$		0			0
$100$	2310.09	+	1030.13i	2.31009	+	1.03013i
$101$	536.339			0.528394			0.264197	−	0.964469i	$-0.414893\pi$
$101$	536.339			0.528394			0.264197	+	0.964469i	$0.414893\pi$
$102$		0			0
$103$		−	381.693i		−	0.365139i	−0.983193	−	0.182570i	$-0.941559\pi$
$103$		−	381.693i		−	0.365139i	0.983193	−	0.182570i	$-0.0584415\pi$
$104$	−4167.38			−3.92928
$105$		0			0
$106$	765.332			0.701279
$107$			1381.12i			1.24783i	0.781492	+	0.623915i	$0.214459\pi$
$107$			1381.12i			1.24783i	−0.781492	+	0.623915i	$0.785541\pi$
$108$		0			0
$109$	390.582			0.343220			0.171610	−	0.985165i	$-0.445103\pi$
$109$	390.582			0.343220			0.171610	+	0.985165i	$0.445103\pi$
$110$	1484.16	+	315.919i	1.28644	+	0.273834i
$111$		0			0
$112$			1285.02i			1.08413i
$113$			1643.15i			1.36792i	0.729521	+	0.683958i	$0.239743\pi$
$113$			1643.15i			1.36792i	−0.729521	+	0.683958i	$0.760257\pi$
$114$		0			0
$115$	1187.65	+	252.804i	0.963033	+	0.204992i
$116$	4734.99			3.78994
$117$		0			0
$118$			3608.43i			2.81511i
$119$	−193.866			−0.149342
$120$		0			0
$121$	−678.609			−0.509849
$122$			3053.85i			2.26625i
$123$		0			0
$124$	−2614.43			−1.89341
$125$	−822.443	+	1129.92i	−0.588492	+	0.808503i
$126$		0			0
$127$		−	192.032i		−	0.134174i	−0.997747	−	0.0670869i	$-0.978630\pi$
$127$		−	192.032i		−	0.134174i	0.997747	−	0.0670869i	$-0.0213705\pi$
$128$			1410.38i			0.973914i
$129$		0			0
$130$	792.848	−	3724.72i	0.534903	−	2.51292i
$131$	−2082.90			−1.38919			−0.694594	−	0.719402i	$-0.744416\pi$
$131$	−2082.90			−1.38919			−0.694594	+	0.719402i	$0.744416\pi$
$132$		0			0
$133$		−	5.54705i		−	0.00361647i
$134$	2739.93			1.76637
$135$		0			0
$136$	−1800.53			−1.13525
$137$			78.1709i			0.0487488i	0.999703	+	0.0243744i	$0.00775939\pi$
$137$			78.1709i			0.0487488i	−0.999703	+	0.0243744i	$0.992241\pi$
$138$		0			0
$139$	−1393.67			−0.850426			−0.425213	−	0.905093i	$-0.639801\pi$
$139$	−1393.67			−0.850426			−0.425213	+	0.905093i	$0.639801\pi$
$140$	−1548.93	−	329.707i	−0.935062	−	0.199038i
$141$		0			0
$142$			2957.65i			1.74789i
$143$		−	1637.28i		−	0.957454i
$144$		0			0
$145$	−544.685	+	2558.88i	−0.311956	+	1.46554i
$146$	920.556			0.521820
$147$		0			0
$148$		−	775.217i		−	0.430557i
$149$	32.5002			0.0178693			0.00893463	−	0.999960i	$-0.497156\pi$
$149$	32.5002			0.0178693			0.00893463	+	0.999960i	$0.497156\pi$
$150$		0			0
$151$	466.762			0.251553			0.125777	−	0.992059i	$-0.459858\pi$
$151$	466.762			0.251553			0.125777	+	0.992059i	$0.459858\pi$
$152$		−	51.5181i		−	0.0274913i
$153$		0			0
$154$	−950.048			−0.497124
$155$	300.749	−	1412.89i	0.155850	−	0.732167i
$156$		0			0
$157$			1673.50i			0.850701i	0.905029	+	0.425351i	$0.139849\pi$
$157$			1673.50i			0.850701i	−0.905029	+	0.425351i	$0.860151\pi$
$158$			421.527i			0.212246i
$159$		0			0
$160$	−4979.39	−	1059.92i	−2.46035	−	0.523712i
$161$	−760.245			−0.372147
$162$		0			0
$163$		−	1869.36i		−	0.898279i	−0.893462	−	0.449139i	$-0.851731\pi$
$163$		−	1869.36i		−	0.898279i	0.893462	−	0.449139i	$-0.148269\pi$
$164$	−8159.06			−3.88485
$165$		0			0
$166$	5545.12			2.59268
$167$		−	46.5250i		−	0.0215581i	−0.999942	−	0.0107791i	$-0.996569\pi$
$167$		−	46.5250i		−	0.0215581i	0.999942	−	0.0107791i	$-0.00343115\pi$
$168$		0			0
$169$	−1911.99			−0.870275
$170$	342.552	−	1609.28i	0.154544	−	0.726034i
$171$		0			0
$172$			3498.52i			1.55093i
$173$			2496.28i			1.09704i	0.836137	+	0.548521i	$0.184809\pi$
$173$			2496.28i			1.09704i	−0.836137	+	0.548521i	$0.815191\pi$
$174$		0			0
$175$	356.360	−	799.145i	0.153933	−	0.345198i
$176$	−4688.83			−2.00815
$177$		0			0
$178$		−	3464.82i		−	1.45898i
$179$	2975.70			1.24254			0.621269	−	0.783598i	$-0.286618\pi$
$179$	2975.70			1.24254			0.621269	+	0.783598i	$0.286618\pi$
$180$		0			0
$181$	966.273			0.396809			0.198405	−	0.980120i	$-0.436424\pi$
$181$	966.273			0.396809			0.198405	+	0.980120i	$0.436424\pi$
$182$			2384.29i			0.971074i
$183$		0			0
$184$	−7060.76			−2.82895
$185$	418.942	+	89.1764i	0.166493	+	0.0354399i
$186$		0			0
$187$		−	707.389i		−	0.276628i
$188$			4187.48i			1.62449i
$189$		0			0
$190$	46.0458	+	9.80136i	0.0175817	+	0.00374245i
$191$	1545.50			0.585488			0.292744	−	0.956191i	$-0.405432\pi$
$191$	1545.50			0.585488			0.292744	+	0.956191i	$0.405432\pi$
$192$		0			0
$193$			2304.05i			0.859322i	0.902990	+	0.429661i	$0.141367\pi$
$193$			2304.05i			0.859322i	−0.902990	+	0.429661i	$0.858633\pi$
$194$	2740.33			1.01415
$195$		0			0
$196$	991.513			0.361338
$197$			222.021i			0.0802960i	0.999194	+	0.0401480i	$0.0127829\pi$
$197$			222.021i			0.0802960i	−0.999194	+	0.0401480i	$0.987217\pi$
$198$		0			0
$199$	−3580.56			−1.27547			−0.637736	−	0.770255i	$-0.720129\pi$
$199$	−3580.56			−1.27547			−0.637736	+	0.770255i	$0.720129\pi$
$200$	3309.69	−	7422.04i	1.17015	−	2.62409i
$201$		0			0
$202$		−	2849.92i		−	0.992673i
$203$		−	1638.00i		−	0.566331i
$204$		0			0
$205$	938.570	−	4409.31i	0.319769	−	1.50224i
$206$	−2028.19			−0.685973
$207$		0			0
$208$			11767.3i			3.92268i
$209$	20.2404			0.00669883
$210$		0			0
$211$	−4181.04			−1.36415			−0.682073	−	0.731284i	$-0.738921\pi$
$211$	−4181.04			−1.36415			−0.682073	+	0.731284i	$0.738921\pi$
$212$		−	2914.46i		−	0.944180i
$213$		0			0
$214$	7338.79			2.34425
$215$	−1890.66	−	402.449i	−0.599731	−	0.127659i
$216$		0			0
$217$			904.426i			0.282933i
$218$		−	2075.42i		−	0.644794i
$219$		0			0
$220$	1203.05	−	5651.83i	0.368681	−	1.73203i
$221$	−1775.30			−0.540361
$222$		0			0
$223$		−	2361.52i		−	0.709145i	−0.935028	−	0.354573i	$-0.884626\pi$
$223$		−	2361.52i		−	0.709145i	0.935028	−	0.354573i	$-0.115374\pi$
$224$	3187.44			0.950758
$225$		0			0
$226$	8731.14			2.56985
$227$		−	586.877i		−	0.171596i	−0.996313	−	0.0857982i	$-0.972656\pi$
$227$		−	586.877i		−	0.171596i	0.996313	−	0.0857982i	$-0.0273440\pi$
$228$		0			0
$229$	4619.55			1.33305			0.666526	−	0.745482i	$-0.267781\pi$
$229$	4619.55			1.33305			0.666526	+	0.745482i	$0.267781\pi$
$230$	1343.31	−	6310.76i	0.385111	−	1.80921i
$231$		0			0
$232$		−	15212.9i		−	4.30507i
$233$		−	5120.44i		−	1.43971i	−0.694127	−	0.719853i	$-0.744209\pi$
$233$		−	5120.44i		−	1.43971i	0.694127	−	0.719853i	$-0.255791\pi$
$234$		0			0
$235$	−2262.99	−	481.703i	−0.628176	−	0.133714i
$236$	13741.3			3.79017
$237$		0			0
$238$			1030.14i			0.280563i
$239$	1127.51			0.305158			0.152579	−	0.988291i	$-0.451242\pi$
$239$	1127.51			0.305158			0.152579	+	0.988291i	$0.451242\pi$
$240$		0			0
$241$	−3549.53			−0.948736			−0.474368	−	0.880327i	$-0.657323\pi$
$241$	−3549.53			−0.948736			−0.474368	+	0.880327i	$0.657323\pi$
$242$			3605.89i			0.957833i
$243$		0			0
$244$	11629.4			3.05120
$245$	−114.058	+	535.832i	−0.0297424	+	0.139727i
$246$		0			0
$247$		−	50.7963i		−	0.0130854i
$248$			8399.84i			2.15077i
$249$		0			0
$250$	6003.99	+	4370.18i	1.51890	+	1.10558i
$251$	−4717.19			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$251$	−4717.19			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$252$		0			0
$253$		−	2774.02i		−	0.689333i
$254$	−1020.39			−0.252067
$255$		0			0
$256$	−113.552			−0.0277227
$257$		−	6260.31i		−	1.51948i	−0.650224	−	0.759742i	$-0.725325\pi$
$257$		−	6260.31i		−	1.51948i	0.650224	−	0.759742i	$-0.274675\pi$
$258$		0			0
$259$	−268.176			−0.0643383
$260$	−14184.1	−	3019.25i	−3.38331	−	0.720176i
$261$		0			0
$262$			11067.8i			2.60981i
$263$		−	5753.04i		−	1.34885i	−0.738344	−	0.674425i	$-0.764392\pi$
$263$		−	5753.04i		−	1.34885i	0.738344	−	0.674425i	$-0.235608\pi$
$264$		0			0
$265$	1575.03	+	335.262i	0.365107	+	0.0777170i
$266$	−29.4751			−0.00679412
$267$		0			0
$268$		−	10433.9i		−	2.37819i
$269$	−7059.21			−1.60003			−0.800014	−	0.599982i	$-0.795174\pi$
$269$	−7059.21			−1.60003			−0.800014	+	0.599982i	$0.795174\pi$
$270$		0			0
$271$	−8534.52			−1.91305			−0.956523	−	0.291658i	$-0.905793\pi$
$271$	−8534.52			−1.91305			−0.956523	+	0.291658i	$0.905793\pi$
$272$			5084.11i			1.13334i
$273$		0			0
$274$	415.373			0.0915826
$275$	2915.96	+	1300.30i	0.639415	+	0.285132i
$276$		0			0
$277$		−	1313.94i		−	0.285008i	−0.989794	−	0.142504i	$-0.954485\pi$
$277$		−	1313.94i		−	0.285008i	0.989794	−	0.142504i	$-0.0455154\pi$
$278$			7405.47i			1.59766i
$279$		0			0
$280$	−1059.31	+	4976.53i	−0.226092	+	1.06216i
$281$	247.229			0.0524856			0.0262428	−	0.999656i	$-0.491646\pi$
$281$	247.229			0.0524856			0.0262428	+	0.999656i	$0.491646\pi$
$282$		0			0
$283$			9074.90i			1.90617i	0.302697	+	0.953087i	$0.402113\pi$
$283$			9074.90i			1.90617i	−0.302697	+	0.953087i	$0.597887\pi$
$284$	11263.0			2.35330
$285$		0			0
$286$	−8699.92			−1.79873
$287$			2822.51i			0.580515i
$288$		0			0
$289$	4145.98			0.843879
$290$	13597.0	+	2894.27i	2.75325	+	0.586060i
$291$		0			0
$292$		−	3505.57i		−	0.702562i
$293$		−	2740.72i		−	0.546466i	−0.961948	−	0.273233i	$-0.911907\pi$
$293$		−	2740.72i		−	0.546466i	0.961948	−	0.273233i	$-0.0880930\pi$
$294$		0			0
$295$	−1580.71	+	7426.04i	−0.311975	+	1.46563i
$296$	−2490.68			−0.489080
$297$		0			0
$298$		−	172.695i		−	0.0335703i
$299$	−6961.83			−1.34653
$300$		0			0
$301$	1210.26			0.231755
$302$		−	2480.21i		−	0.472584i
$303$		0			0
$304$	−145.470			−0.0274451
$305$	−1337.77	+	6284.73i	−0.251150	+	1.17988i
$306$		0			0
$307$		−	6985.46i		−	1.29864i	−0.760517	−	0.649318i	$-0.775054\pi$
$307$		−	6985.46i		−	1.29864i	0.760517	−	0.649318i	$-0.224946\pi$
$308$			3617.88i			0.669311i
$309$		0			0
$310$	−7507.60	−	1598.08i	−1.37549	−	0.292789i
$311$	356.841			0.0650630			0.0325315	−	0.999471i	$-0.489643\pi$
$311$	356.841			0.0650630			0.0325315	+	0.999471i	$0.489643\pi$
$312$		0			0
$313$		−	6630.12i		−	1.19731i	−0.801009	−	0.598653i	$-0.795703\pi$
$313$		−	6630.12i		−	1.19731i	0.801009	−	0.598653i	$-0.204297\pi$
$314$	8892.42			1.59818
$315$		0			0
$316$	1605.22			0.285762
$317$		−	2494.05i		−	0.441891i	−0.975286	−	0.220946i	$-0.929086\pi$
$317$		−	2494.05i		−	0.441891i	0.975286	−	0.220946i	$-0.0709144\pi$
$318$		0			0
$319$	5976.83			1.04902
$320$	−2213.60	+	10399.3i	−0.386700	+	1.81668i
$321$		0			0
$322$			4039.68i			0.699139i
$323$		−	21.9467i		−	0.00378063i
$324$		0			0
$325$	3263.31	−	7318.05i	0.556973	−	1.24902i
$326$	−9933.13			−1.68756
$327$		0			0
$328$			26214.0i			4.41289i
$329$	1448.60			0.242748
$330$		0			0
$331$	−4682.47			−0.777558			−0.388779	−	0.921331i	$-0.627103\pi$
$331$	−4682.47			−0.777558			−0.388779	+	0.921331i	$0.627103\pi$
$332$		−	21116.4i		−	3.49070i
$333$		0			0
$334$	−247.218			−0.0405005
$335$	5638.70	+	1200.26i	0.919627	+	0.195753i
$336$		0			0
$337$		−	3596.60i		−	0.581363i	−0.956820	−	0.290681i	$-0.906118\pi$
$337$		−	3596.60i		−	0.581363i	0.956820	−	0.290681i	$-0.0938820\pi$
$338$			10159.7i			1.63495i
$339$		0			0
$340$	−6128.28	−	1304.47i	−0.977509	−	0.208073i
$341$	−3300.12			−0.524080
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	11240.3			1.76173
$345$		0			0
$346$	13264.4			2.06097
$347$			1899.51i			0.293865i	0.989147	+	0.146932i	$0.0469400\pi$
$347$			1899.51i			0.293865i	−0.989147	+	0.146932i	$0.953060\pi$
$348$		0			0
$349$	1037.55			0.159137			0.0795683	−	0.996829i	$-0.474646\pi$
$349$	1037.55			0.159137			0.0795683	+	0.996829i	$0.474646\pi$
$350$	−4246.38	−	1893.58i	−0.648510	−	0.289188i
$351$		0			0
$352$			11630.5i			1.76110i
$353$			4087.08i			0.616242i	0.951347	+	0.308121i	$0.0997001\pi$
$353$			4087.08i			0.616242i	−0.951347	+	0.308121i	$0.900300\pi$
$354$		0			0
$355$	−1295.63	+	6086.75i	−0.193704	+	0.910003i
$356$	−13194.4			−1.96433
$357$		0			0
$358$		−	15811.8i		−	2.33431i
$359$	3472.67			0.510530			0.255265	−	0.966871i	$-0.417837\pi$
$359$	3472.67			0.510530			0.255265	+	0.966871i	$0.417837\pi$
$360$		0			0
$361$	−6858.37			−0.999908
$362$		−	5134.44i		−	0.745470i
$363$		0			0
$364$	9079.63			1.30742
$365$	1894.48	+	403.260i	0.271675	+	0.0578290i
$366$		0			0
$367$		−	8769.14i		−	1.24726i	−0.781719	−	0.623631i	$-0.785657\pi$
$367$		−	8769.14i		−	1.24726i	0.781719	−	0.623631i	$-0.214343\pi$
$368$			19937.3i			2.82419i
$369$		0			0
$370$	473.853	−	2226.11i	0.0665796	−	0.312784i
$371$	−1008.22			−0.141089
$372$		0			0
$373$			11368.9i			1.57817i	0.614284	+	0.789085i	$0.289445\pi$
$373$			11368.9i			1.57817i	−0.614284	+	0.789085i	$0.710555\pi$
$374$	−3758.82			−0.519690
$375$		0			0
$376$	13453.8			1.84529
$377$		−	14999.8i		−	2.04914i
$378$		0			0
$379$	12137.4			1.64500			0.822501	−	0.568764i	$-0.192578\pi$
$379$	12137.4			1.64500			0.822501	+	0.568764i	$0.192578\pi$
$380$	37.3246	−	175.347i	0.00503871	−	0.0236714i
$381$		0			0
$382$		−	8212.24i		−	1.09993i
$383$			9869.61i			1.31675i	0.752692	+	0.658373i	$0.228755\pi$
$383$			9869.61i			1.31675i	−0.752692	+	0.658373i	$0.771245\pi$
$384$		0			0
$385$	−1955.17	−	416.180i	−0.258817	−	0.0550921i
$386$	12242.9			1.61438
$387$		0			0
$388$		−	10435.5i		−	1.36541i
$389$	57.1166			0.00744454			0.00372227	−	0.999993i	$-0.498815\pi$
$389$	57.1166			0.00744454			0.00372227	+	0.999993i	$0.498815\pi$
$390$		0			0
$391$	−3007.88			−0.389041
$392$		−	3185.60i		−	0.410452i
$393$		0			0
$394$	1179.74			0.150849
$395$	−184.655	+	867.490i	−0.0235215	+	0.110502i
$396$		0			0
$397$			7436.17i			0.940078i	0.882646	+	0.470039i	$0.155760\pi$
$397$			7436.17i			0.940078i	−0.882646	+	0.470039i	$0.844240\pi$
$398$			19025.8i			2.39618i
$399$		0			0
$400$	−20957.4	−	9345.47i	−2.61968	−	1.16818i
$401$	12465.0			1.55230			0.776149	−	0.630550i	$-0.217171\pi$
$401$	12465.0			1.55230			0.776149	+	0.630550i	$0.217171\pi$
$402$		0			0
$403$			8282.15i			1.02373i
$404$	−10852.8			−1.33650
$405$		0			0
$406$	−8703.79			−1.06394
$407$		−	978.533i		−	0.119175i
$408$		0			0
$409$	1708.72			0.206578			0.103289	−	0.994651i	$-0.467063\pi$
$409$	1708.72			0.206578			0.103289	+	0.994651i	$0.467063\pi$
$410$	−23429.6	−	4987.24i	−2.82220	−	0.600737i
$411$		0			0
$412$			7723.54i			0.923571i
$413$		−	4753.60i		−	0.566366i
$414$		0			0
$415$	11411.7	+	2429.10i	1.34983	+	0.287325i
$416$	29188.5			3.44011
$417$		0			0
$418$		−	107.550i		−	0.0125848i
$419$	10618.8			1.23810			0.619050	−	0.785352i	$-0.287518\pi$
$419$	10618.8			1.23810			0.619050	+	0.785352i	$0.287518\pi$
$420$		0			0
$421$	13273.5			1.53661			0.768304	−	0.640085i	$-0.221101\pi$
$421$	13273.5			1.53661			0.768304	+	0.640085i	$0.221101\pi$
$422$			22216.6i			2.56277i
$423$		0			0
$424$	−9363.80			−1.07251
$425$	1409.92	−	3161.78i	0.160921	−	0.360868i
$426$		0			0
$427$		−	4023.02i		−	0.455943i
$428$		−	27946.9i		−	3.15622i
$429$		0			0
$430$	−2138.47	+	10046.3i	−0.239829	+	1.12669i
$431$	−7918.20			−0.884934			−0.442467	−	0.896785i	$-0.645897\pi$
$431$	−7918.20			−0.884934			−0.442467	+	0.896785i	$0.645897\pi$
$432$		0			0
$433$		−	4433.34i		−	0.492038i	−0.969265	−	0.246019i	$-0.920877\pi$
$433$		−	4433.34i		−	0.492038i	0.969265	−	0.246019i	$-0.0791226\pi$
$434$	4805.81			0.531535
$435$		0			0
$436$	−7903.40			−0.868129
$437$		−	86.0637i		−	0.00942102i
$438$		0			0
$439$	−12958.4			−1.40882			−0.704408	−	0.709796i	$-0.748787\pi$
$439$	−12958.4			−1.40882			−0.704408	+	0.709796i	$0.748787\pi$
$440$	−18158.6	−	3865.26i	−1.96745	−	0.418793i
$441$		0			0
$442$			9433.34i			1.01515i
$443$		−	12040.4i		−	1.29133i	−0.763621	−	0.645664i	$-0.776580\pi$
$443$		−	12040.4i		−	1.29133i	0.763621	−	0.645664i	$-0.223420\pi$
$444$		0			0
$445$	1517.80	−	7130.50i	0.161687	−	0.759591i
$446$	−12548.3			−1.33224
$447$		0			0
$448$		−	6656.84i		−	0.702023i
$449$	11586.3			1.21780			0.608899	−	0.793247i	$-0.291611\pi$
$449$	11586.3			1.21780			0.608899	+	0.793247i	$0.291611\pi$
$450$		0			0
$451$	−10298.9			−1.07529
$452$		−	33249.1i		−	3.45997i
$453$		0			0
$454$	−3118.46			−0.322371
$455$	−1044.47	+	4906.80i	−0.107616	+	0.505570i
$456$		0			0
$457$			9734.34i			0.996396i	0.867063	+	0.498198i	$0.166005\pi$
$457$			9734.34i			0.996396i	−0.867063	+	0.498198i	$0.833995\pi$
$458$		−	24546.7i		−	2.50435i
$459$		0			0
$460$	−24032.0	−	5115.48i	−2.43587	−	0.518501i
$461$	1343.41			0.135724			0.0678621	−	0.997695i	$-0.478382\pi$
$461$	1343.41			0.135724			0.0678621	+	0.997695i	$0.478382\pi$
$462$		0			0
$463$			6613.72i			0.663857i	0.943305	+	0.331929i	$0.107699\pi$
$463$			6613.72i			0.663857i	−0.943305	+	0.331929i	$0.892301\pi$
$464$	−42956.3			−4.29784
$465$		0			0
$466$	−27208.3			−2.70472
$467$			14688.9i			1.45551i	0.685838	+	0.727755i	$0.259436\pi$
$467$			14688.9i			1.45551i	−0.685838	+	0.727755i	$0.740564\pi$
$468$		0			0
$469$	−3609.48			−0.355374
$470$	−2559.60	+	12024.8i	−0.251204	+	1.18013i
$471$		0			0
$472$		−	44148.9i		−	4.30534i
$473$			4416.07i			0.429283i
$474$		0			0
$475$	90.4673	+	40.3418i	0.00873879	+	0.00389686i
$476$	3922.88			0.377741
$477$		0			0
$478$		−	5991.22i		−	0.573288i
$479$	−15298.6			−1.45931			−0.729657	−	0.683813i	$-0.760320\pi$
$479$	−15298.6			−1.45931			−0.729657	+	0.683813i	$0.760320\pi$
$480$		0			0
$481$	−2455.78			−0.232794
$482$			18861.0i			1.78235i
$483$		0			0
$484$	13731.6			1.28960
$485$	5639.52	+	1200.43i	0.527994	+	0.112389i
$486$		0			0
$487$		−	9653.80i		−	0.898266i	−0.893465	−	0.449133i	$-0.851733\pi$
$487$		−	9653.80i		−	0.898266i	0.893465	−	0.449133i	$-0.148267\pi$
$488$		−	37363.7i		−	3.46593i
$489$		0			0
$490$	2847.23	+	606.064i	0.262499	+	0.0558758i
$491$	−20142.6			−1.85137			−0.925684	−	0.378297i	$-0.876510\pi$
$491$	−20142.6			−1.85137			−0.925684	+	0.378297i	$0.876510\pi$
$492$		0			0
$493$		−	6480.69i		−	0.592039i
$494$	−269.914			−0.0245830
$495$		0			0
$496$	23718.4			2.14715
$497$		−	3896.29i		−	0.351655i
$498$		0			0
$499$	1309.29			0.117459			0.0587293	−	0.998274i	$-0.481295\pi$
$499$	1309.29			0.117459			0.0587293	+	0.998274i	$0.481295\pi$
$500$	16642.1	−	22863.8i	1.48851	−	2.04500i
$501$		0			0
$502$			25065.5i			2.22855i
$503$			2186.17i			0.193791i	0.995295	+	0.0968953i	$0.0308912\pi$
$503$			2186.17i			0.193791i	−0.995295	+	0.0968953i	$0.969109\pi$
$504$		0			0
$505$	1248.44	−	5865.06i	0.110010	−	0.516815i
$506$	−14740.2			−1.29502
$507$		0			0
$508$			3885.76i			0.339375i
$509$	3591.11			0.312718			0.156359	−	0.987700i	$-0.450024\pi$
$509$	3591.11			0.312718			0.156359	+	0.987700i	$0.450024\pi$
$510$		0			0
$511$	−1212.70			−0.104984
$512$			11886.4i			1.02600i
$513$		0			0
$514$	−33265.2			−2.85460
$515$	−4173.94	−	888.470i	−0.357138	−	0.0760207i
$516$		0			0
$517$			5285.73i			0.449644i
$518$			1424.99i			0.120870i
$519$		0			0
$520$	−9700.46	+	45571.8i	−0.818064	+	3.84318i
$521$	8605.34			0.723621			0.361811	−	0.932252i	$-0.382159\pi$
$521$	8605.34			0.723621			0.361811	+	0.932252i	$0.382159\pi$
$522$		0			0
$523$		−	22536.4i		−	1.88423i	−0.335297	−	0.942113i	$-0.608837\pi$
$523$		−	22536.4i		−	1.88423i	0.335297	−	0.942113i	$-0.391163\pi$
$524$	42147.3			3.51377
$525$		0			0
$526$	−30569.7			−2.53403
$527$			3578.32i			0.295776i
$528$		0			0
$529$	371.637			0.0305447
$530$	1781.47	−	8369.17i	0.146004	−	0.685912i
$531$		0			0
$532$			112.244i			0.00914738i
$533$			25846.7i			2.10046i
$534$		0			0
$535$	15103.0	+	3214.84i	1.22049	+	0.259794i
$536$	−33522.9			−2.70144
$537$		0			0
$538$			37510.2i			3.00591i
$539$	1251.56			0.100015
$540$		0			0
$541$	8782.44			0.697942			0.348971	−	0.937134i	$-0.386531\pi$
$541$	8782.44			0.697942			0.348971	+	0.937134i	$0.386531\pi$
$542$			45349.5i			3.59396i
$543$		0			0
$544$	12611.0			0.993917
$545$	909.161	−	4271.15i	0.0714572	−	0.335699i
$546$		0			0
$547$			22593.0i			1.76601i	0.469366	+	0.883004i	$0.344482\pi$
$547$			22593.0i			1.76601i	−0.469366	+	0.883004i	$0.655518\pi$
$548$		−	1581.78i		−	0.123304i
$549$		0			0
$550$	6909.37	−	15494.4i	0.535667	−	1.20124i
$551$	185.430			0.0143368
$552$		0			0
$553$		−	555.303i		−	0.0427014i
$554$	−6981.84			−0.535433
$555$		0			0
$556$	28200.8			2.15104
$557$			7264.13i			0.552587i	0.961073	+	0.276294i	$0.0891062\pi$
$557$			7264.13i			0.552587i	−0.961073	+	0.276294i	$0.910894\pi$
$558$		0			0
$559$	11082.8			0.838555
$560$	14052.1	+	2991.14i	1.06037	+	0.225712i
$561$		0			0
$562$		−	1313.69i		−	0.0986027i
$563$			3851.42i			0.288309i	0.989555	+	0.144154i	$0.0460462\pi$
$563$			3851.42i			0.288309i	−0.989555	+	0.144154i	$0.953954\pi$
$564$		0			0
$565$	17968.4	+	3824.78i	1.33794	+	0.284796i
$566$	48220.9			3.58105
$567$		0			0
$568$		−	36186.7i		−	2.67317i
$569$	16580.3			1.22158			0.610792	−	0.791791i	$-0.290851\pi$
$569$	16580.3			1.22158			0.610792	+	0.791791i	$0.290851\pi$
$570$		0			0
$571$	6385.86			0.468021			0.234010	−	0.972234i	$-0.424815\pi$
$571$	6385.86			0.468021			0.234010	+	0.972234i	$0.424815\pi$
$572$			33130.2i			2.42175i
$573$		0			0
$574$	14997.9			1.09059
$575$	5529.00	−	12398.9i	0.401001	−	0.899252i
$576$		0			0
$577$		−	11059.1i		−	0.797912i	−0.916970	−	0.398956i	$-0.869373\pi$
$577$		−	11059.1i		−	0.797912i	0.916970	−	0.398956i	$-0.130627\pi$
$578$		−	22030.3i		−	1.58536i
$579$		0			0
$580$	11021.7	−	51778.7i	0.789052	−	3.70689i
$581$	−7304.92			−0.521617
$582$		0			0
$583$		−	3678.84i		−	0.261341i
$584$	−11263.0			−0.798055
$585$		0			0
$586$	−14563.2			−1.02662
$587$			7871.25i			0.553461i	0.960948	+	0.276730i	$0.0892509\pi$
$587$			7871.25i			0.553461i	−0.960948	+	0.276730i	$0.910749\pi$
$588$		0			0
$589$	−102.386			−0.00716253
$590$	39459.4	+	8399.37i	2.75342	+	0.586096i
$591$		0			0
$592$			7032.85i			0.488258i
$593$		−	2018.06i		−	0.139750i	−0.997556	−	0.0698750i	$-0.977740\pi$
$593$		−	2018.06i		−	0.139750i	0.997556	−	0.0698750i	$-0.0222600\pi$
$594$		0			0
$595$	−451.264	+	2120.00i	−0.0310925	+	0.146069i
$596$	−657.640			−0.0451980
$597$		0			0
$598$			36992.8i			2.52968i
$599$	−1356.67			−0.0925409			−0.0462705	−	0.998929i	$-0.514734\pi$
$599$	−1356.67			−0.0925409			−0.0462705	+	0.998929i	$0.514734\pi$
$600$		0			0
$601$	11178.7			0.758715			0.379358	−	0.925250i	$-0.376145\pi$
$601$	11178.7			0.758715			0.379358	+	0.925250i	$0.376145\pi$
$602$		−	6430.92i		−	0.435390i
$603$		0			0
$604$	−9444.91			−0.636272
$605$	−1579.60	+	7420.82i	−0.106149	+	0.498676i
$606$		0			0
$607$			9404.67i			0.628870i	0.949279	+	0.314435i	$0.101815\pi$
$607$			9404.67i			0.628870i	−0.949279	+	0.314435i	$0.898185\pi$
$608$			360.835i			0.0240687i
$609$		0			0
$610$	33394.9	+	7108.47i	2.21659	+	0.471825i
$611$	13265.3			0.878328
$612$		0			0
$613$			18938.0i			1.24779i	0.781507	+	0.623897i	$0.214452\pi$
$613$			18938.0i			1.24779i	−0.781507	+	0.623897i	$0.785548\pi$
$614$	−37118.4			−2.43970
$615$		0			0
$616$	11623.8			0.760286
$617$		−	17716.9i		−	1.15600i	−0.816036	−	0.578001i	$-0.803833\pi$
$617$		−	17716.9i		−	1.15600i	0.816036	−	0.578001i	$-0.196167\pi$
$618$		0			0
$619$	6240.33			0.405202			0.202601	−	0.979261i	$-0.435061\pi$
$619$	6240.33			0.405202			0.202601	+	0.979261i	$0.435061\pi$
$620$	−6085.63	+	28589.7i	−0.394202	+	1.85192i
$621$		0			0
$622$		−	1896.13i		−	0.122231i
$623$			4564.42i			0.293531i
$624$		0			0
$625$	10441.6	+	11623.8i	0.668264	+	0.743924i
$626$	−35230.2			−2.24933
$627$		0			0
$628$		−	33863.2i		−	2.15174i
$629$	−1061.03			−0.0672589
$630$		0			0
$631$	−25887.7			−1.63323			−0.816617	−	0.577179i	$-0.804153\pi$
$631$	−25887.7			−1.63323			−0.816617	+	0.577179i	$0.804153\pi$
$632$		−	5157.37i		−	0.324603i
$633$		0			0
$634$	−13252.5			−0.830165
$635$	−2099.94	−	446.994i	−0.131234	−	0.0279345i
$636$		0			0
$637$		−	3140.97i		−	0.195369i
$638$		−	31758.8i		−	1.97076i
$639$		0			0
$640$	15423.0	+	3282.95i	0.952573	+	0.202766i
$641$	−18798.4			−1.15834			−0.579168	−	0.815208i	$-0.696622\pi$
$641$	−18798.4			−1.15834			−0.579168	+	0.815208i	$0.696622\pi$
$642$		0			0
$643$			2287.70i			0.140308i	0.997536	+	0.0701541i	$0.0223491\pi$
$643$			2287.70i			0.140308i	−0.997536	+	0.0701541i	$0.977651\pi$
$644$	15383.5			0.941298
$645$		0			0
$646$	−116.617			−0.00710253
$647$		−	1769.31i		−	0.107510i	−0.998554	−	0.0537548i	$-0.982881\pi$
$647$		−	1769.31i		−	0.107510i	0.998554	−	0.0537548i	$-0.0171189\pi$
$648$		0			0
$649$	17345.2			1.04909
$650$	−38885.6	−	17340.1i	−2.34649	−	1.04636i
$651$		0			0
$652$			37826.4i			2.27208i
$653$			3891.48i			0.233209i	0.993178	+	0.116604i	$0.0372010\pi$
$653$			3891.48i			0.233209i	−0.993178	+	0.116604i	$0.962799\pi$
$654$		0			0
$655$	−4848.38	+	22777.2i	−0.289224	+	1.35875i
$656$	74019.8			4.40547
$657$		0			0
$658$		−	7697.37i		−	0.456040i
$659$	20097.6			1.18800			0.594001	−	0.804465i	$-0.297548\pi$
$659$	20097.6			1.18800			0.594001	+	0.804465i	$0.297548\pi$
$660$		0			0
$661$	−27167.9			−1.59865			−0.799326	−	0.600898i	$-0.794810\pi$
$661$	−27167.9			−1.59865			−0.799326	+	0.600898i	$0.794810\pi$
$662$			24881.0i			1.46077i
$663$		0			0
$664$	−67844.3			−3.96516
$665$	−60.6589	−	12.9119i	−0.00353722	−	0.000752937i
$666$		0			0
$667$		−	25414.0i		−	1.47531i
$668$			941.430i			0.0545285i
$669$		0			0
$670$	6377.77	−	29962.1i	0.367753	−	1.72767i
$671$	14679.4			0.844548
$672$		0			0
$673$		−	25909.7i		−	1.48402i	−0.670389	−	0.742010i	$-0.733873\pi$
$673$		−	25909.7i		−	1.48402i	0.670389	−	0.742010i	$-0.266127\pi$
$674$	−19111.1			−1.09218
$675$		0			0
$676$	38689.1			2.20125
$677$		−	4359.22i		−	0.247472i	−0.992315	−	0.123736i	$-0.960512\pi$
$677$		−	4359.22i		−	0.247472i	0.992315	−	0.123736i	$-0.0394875\pi$
$678$		0			0
$679$	−3610.00			−0.204034
$680$	−4191.11	+	19689.4i	−0.236355	+	1.11037i
$681$		0			0
$682$			17535.7i			0.984569i
$683$			29721.9i			1.66512i	0.553937	+	0.832559i	$0.313125\pi$
$683$			29721.9i			1.66512i	−0.553937	+	0.832559i	$0.686875\pi$
$684$		0			0
$685$	854.826	+	181.959i	0.0476806	+	0.0101493i
$686$	−1822.58			−0.101438
$687$		0			0
$688$		−	31738.9i		−	1.75877i
$689$	−9232.60			−0.510499
$690$		0			0
$691$	−4929.13			−0.271365			−0.135682	−	0.990752i	$-0.543323\pi$
$691$	−4929.13			−0.271365			−0.135682	+	0.990752i	$0.543323\pi$
$692$		−	50512.0i		−	2.77482i
$693$		0			0
$694$	10093.4			0.552073
$695$	−3244.05	+	15240.2i	−0.177056	+	0.831791i
$696$		0			0
$697$			11167.1i			0.606866i
$698$		−	5513.18i		−	0.298964i
$699$		0			0
$700$	−7210.93	+	16170.7i	−0.389354	+	0.873133i
$701$	19358.8			1.04304			0.521520	−	0.853239i	$-0.325365\pi$
$701$	19358.8			1.04304			0.521520	+	0.853239i	$0.325365\pi$
$702$		0			0
$703$		−	30.3589i		−	0.00162874i
$704$	24289.8			1.30036
$705$		0			0
$706$	21717.3			1.15771
$707$			3754.38i			0.199714i
$708$		0			0
$709$	17186.3			0.910359			0.455180	−	0.890400i	$-0.349575\pi$
$709$	17186.3			0.910359			0.455180	+	0.890400i	$0.349575\pi$
$710$	32342.9	+	6884.54i	1.70959	+	0.363905i
$711$		0			0
$712$			42391.9i			2.23133i
$713$			14032.4i			0.737049i
$714$		0			0
$715$	−17904.2	−	3811.10i	−0.936473	−	0.199339i
$716$	−60213.1			−3.14284
$717$		0			0
$718$		−	18452.6i		−	0.959113i
$719$	−15107.3			−0.783598			−0.391799	−	0.920051i	$-0.628147\pi$
$719$	−15107.3			−0.783598			−0.391799	+	0.920051i	$0.628147\pi$
$720$		0			0
$721$	2671.85			0.138010
$722$			36443.0i			1.87849i
$723$		0			0
$724$	−19552.5			−1.00368
$725$	26714.3	+	11912.6i	1.36848	+	0.610240i
$726$		0			0
$727$		−	15840.9i		−	0.808124i	−0.914732	−	0.404062i	$-0.867598\pi$
$727$		−	15840.9i		−	0.808124i	0.914732	−	0.404062i	$-0.132402\pi$
$728$		−	29171.7i		−	1.48513i
$729$		0			0
$730$	2142.79	−	10066.6i	0.108641	−	0.510385i
$731$	4788.35			0.242276
$732$		0			0
$733$			27639.7i			1.39276i	0.717671	+	0.696382i	$0.245208\pi$
$733$			27639.7i			1.39276i	−0.717671	+	0.696382i	$0.754792\pi$
$734$	−46596.2			−2.34318
$735$		0			0
$736$	49453.8			2.47675
$737$		−	13170.4i		−	0.658263i
$738$		0			0
$739$	−34874.4			−1.73596			−0.867982	−	0.496597i	$-0.834583\pi$
$739$	−34874.4			−1.73596			−0.867982	+	0.496597i	$0.834583\pi$
$740$	−8477.27	−	1804.48i	−0.421123	−	0.0896406i
$741$		0			0
$742$			5357.32i			0.265059i
$743$		−	27686.7i		−	1.36706i	−0.729922	−	0.683530i	$-0.760444\pi$
$743$		−	27686.7i		−	1.36706i	0.729922	−	0.683530i	$-0.239556\pi$
$744$		0			0
$745$	75.6510	−	355.401i	0.00372032	−	0.0174777i
$746$	60410.2			2.96485
$747$		0			0
$748$			14314.0i			0.699694i
$749$	−9667.83			−0.471635
$750$		0			0
$751$	4806.85			0.233561			0.116781	−	0.993158i	$-0.462743\pi$
$751$	4806.85			0.233561			0.116781	+	0.993158i	$0.462743\pi$
$752$		−	37989.3i		−	1.84219i
$753$		0			0
$754$	−79703.6			−3.84965
$755$	1086.49	−	5104.21i	0.0523726	−	0.246041i
$756$		0			0
$757$		−	40166.6i		−	1.92851i	−0.264983	−	0.964253i	$-0.585366\pi$
$757$		−	40166.6i		−	1.92851i	0.264983	−	0.964253i	$-0.414634\pi$
$758$		−	64493.9i		−	3.09040i
$759$		0			0
$760$	−563.368	−	119.919i	−0.0268888	−	0.00572359i
$761$	−25912.3			−1.23432			−0.617162	−	0.786836i	$-0.711718\pi$
$761$	−25912.3			−1.23432			−0.617162	+	0.786836i	$0.711718\pi$
$762$		0			0
$763$			2734.07i			0.129725i
$764$	−31273.1			−1.48092
$765$		0			0
$766$	52443.7			2.47372
$767$		−	43530.4i		−	2.04927i
$768$		0			0
$769$	23231.3			1.08939			0.544697	−	0.838633i	$-0.316645\pi$
$769$	23231.3			1.08939			0.544697	+	0.838633i	$0.316645\pi$
$770$	−2211.44	+	10389.1i	−0.103499	+	0.486230i
$771$		0			0
$772$		−	46622.4i		−	2.17354i
$773$			836.306i			0.0389131i	0.999811	+	0.0194566i	$0.00619360\pi$
$773$			836.306i			0.0389131i	−0.999811	+	0.0194566i	$0.993806\pi$
$774$		0			0
$775$	−14750.4	−	6577.58i	−0.683675	−	0.304869i
$776$	−33527.8			−1.55100
$777$		0			0
$778$		−	303.498i		−	0.0139858i
$779$	−319.523			−0.0146959
$780$		0			0
$781$	14217.0			0.651374
$782$			15982.8i			0.730875i
$783$		0			0
$784$	−8995.11			−0.409763
$785$	18300.3	+	3895.43i	0.832060	+	0.177113i
$786$		0			0
$787$			31945.6i			1.44693i	0.690359	+	0.723467i	$0.257453\pi$
$787$			31945.6i			1.44693i	−0.690359	+	0.723467i	$0.742547\pi$
$788$		−	4492.58i		−	0.203098i
$789$		0			0
$790$	4609.55	+	981.193i	0.207595	+	0.0441890i
$791$	−11502.1			−0.517024
$792$		0			0
$793$		−	36840.2i		−	1.64973i
$794$	39513.3			1.76609
$795$		0			0
$796$	72452.4			3.22614
$797$		−	5628.83i		−	0.250168i	−0.992146	−	0.125084i	$-0.960080\pi$
$797$		−	5628.83i		−	0.250168i	0.992146	−	0.125084i	$-0.0399200\pi$
$798$		0			0
$799$	5731.32			0.253767
$800$	−23181.2	+	51984.2i	−1.02447	+	2.29740i
$801$		0			0
$802$		−	66234.6i		−	2.91624i
$803$		−	4424.97i		−	0.194463i
$804$		0			0
$805$	−1769.63	+	8313.54i	−0.0774798	+	0.363992i
$806$	44008.5			1.92324
$807$		0			0
$808$			34868.7i			1.51816i
$809$	−27890.7			−1.21210			−0.606048	−	0.795428i	$-0.707246\pi$
$809$	−27890.7			−1.21210			−0.606048	+	0.795428i	$0.707246\pi$
$810$		0			0
$811$	−12170.3			−0.526949			−0.263474	−	0.964666i	$-0.584868\pi$
$811$	−12170.3			−0.526949			−0.263474	+	0.964666i	$0.584868\pi$
$812$			33144.9i			1.43246i
$813$		0			0
$814$	−5199.59			−0.223889
$815$	−20442.1	−	4351.32i	−0.878595	−	0.187019i
$816$		0			0
$817$			137.008i			0.00586696i
$818$		−	9079.53i		−	0.388091i
$819$		0			0
$820$	−18991.9	+	89222.1i	−0.808813	+	3.79972i
$821$	30932.3			1.31491			0.657457	−	0.753492i	$-0.271632\pi$
$821$	30932.3			1.31491			0.657457	+	0.753492i	$0.271632\pi$
$822$		0			0
$823$			25949.0i			1.09906i	0.835475	+	0.549528i	$0.185193\pi$
$823$			25949.0i			1.09906i	−0.835475	+	0.549528i	$0.814807\pi$
$824$	24814.7			1.04911
$825$		0			0
$826$	−25259.0			−1.06401
$827$		−	27728.5i		−	1.16592i	−0.812502	−	0.582959i	$-0.801895\pi$
$827$		−	27728.5i		−	1.16592i	0.812502	−	0.582959i	$-0.198105\pi$
$828$		0			0
$829$	10650.1			0.446194			0.223097	−	0.974796i	$-0.428383\pi$
$829$	10650.1			0.446194			0.223097	+	0.974796i	$0.428383\pi$
$830$	12907.4	−	60637.8i	0.539787	−	2.53587i
$831$		0			0
$832$		−	60959.0i		−	2.54011i
$833$		−	1357.06i		−	0.0564460i
$834$		0			0
$835$	−508.767	−	108.297i	−0.0210857	−	0.00448833i
$836$	−409.563			−0.0169438
$837$		0			0
$838$		−	56424.8i		−	2.32597i
$839$	29761.9			1.22466			0.612332	−	0.790601i	$-0.290232\pi$
$839$	29761.9			1.22466			0.612332	+	0.790601i	$0.290232\pi$
$840$		0			0
$841$	30367.2			1.24512
$842$		−	70531.0i		−	2.88677i
$843$		0			0
$844$	84603.2			3.45043
$845$	−4450.57	+	20908.3i	−0.181188	+	0.851205i
$846$		0			0
$847$		−	4750.26i		−	0.192705i
$848$			26440.3i			1.07071i
$849$		0			0
$850$	−16800.6	−	7491.85i	−0.677949	−	0.302316i
$851$	−4160.80			−0.167603
$852$		0			0
$853$			24410.2i			0.979824i	0.871772	+	0.489912i	$0.162971\pi$
$853$			24410.2i			0.979824i	−0.871772	+	0.489912i	$0.837029\pi$
$854$	−21376.9			−0.856562
$855$		0			0
$856$	−89789.8			−3.58522
$857$		−	15189.3i		−	0.605433i	−0.953081	−	0.302717i	$-0.902106\pi$
$857$		−	15189.3i		−	0.605433i	0.953081	−	0.302717i	$-0.0978936\pi$
$858$		0			0
$859$	10339.1			0.410668			0.205334	−	0.978692i	$-0.434172\pi$
$859$	10339.1			0.410668			0.205334	+	0.978692i	$0.434172\pi$
$860$	38257.5	+	8143.53i	1.51694	+	0.322898i
$861$		0			0
$862$			42074.6i			1.66249i
$863$			27566.6i			1.08734i	0.839298	+	0.543671i	$0.182966\pi$
$863$			27566.6i			1.08734i	−0.839298	+	0.543671i	$0.817034\pi$
$864$		0			0
$865$	27297.6	+	5810.60i	1.07300	+	0.228400i
$866$	−23557.2			−0.924373
$867$		0			0
$868$		−	18301.0i		−	0.715642i
$869$	2026.22			0.0790964
$870$		0			0
$871$	−33053.2			−1.28584
$872$			25392.6i			0.986127i
$873$		0			0
$874$	−457.313			−0.0176989
$875$	−7909.42	−	5757.10i	−0.305585	−	0.222429i
$876$		0			0
$877$		−	6032.49i		−	0.232272i	−0.993233	−	0.116136i	$-0.962949\pi$
$877$		−	6032.49i		−	0.232272i	0.993233	−	0.116136i	$-0.0370508\pi$
$878$			68856.4i			2.64669i
$879$		0			0
$880$	−10914.2	+	51274.0i	−0.418089	+	1.96414i
$881$	−44253.2			−1.69231			−0.846156	−	0.532935i	$-0.821089\pi$
$881$	−44253.2			−1.69231			−0.846156	+	0.532935i	$0.821089\pi$
$882$		0			0
$883$			7744.13i			0.295142i	0.989051	+	0.147571i	$0.0471456\pi$
$883$			7744.13i			0.295142i	−0.989051	+	0.147571i	$0.952854\pi$
$884$	35923.1			1.36677
$885$		0			0
$886$	−63978.8			−2.42597
$887$		−	18632.5i		−	0.705318i	−0.935752	−	0.352659i	$-0.885278\pi$
$887$		−	18632.5i		−	0.705318i	0.935752	−	0.352659i	$-0.114722\pi$
$888$		0			0
$889$	1344.22			0.0507130
$890$	−37889.0	−	8065.09i	−1.42701	−	0.303756i
$891$		0			0
$892$			47785.3i			1.79369i
$893$			163.989i			0.00614522i
$894$		0			0
$895$	6926.56	−	32540.3i	0.258692	−	1.21531i
$896$	−9872.65			−0.368105
$897$		0			0
$898$		−	61565.7i		−	2.28783i
$899$	−30233.7			−1.12164
$900$		0			0
$901$	−3988.97			−0.147494
$902$			54725.0i			2.02011i
$903$		0			0
$904$	−106825.			−3.93025
$905$	2249.20	−	10566.5i	0.0826143	−	0.388114i
$906$		0			0
$907$			1258.19i			0.0460612i	0.999735	+	0.0230306i	$0.00733151\pi$
$907$			1258.19i			0.0460612i	−0.999735	+	0.0230306i	$0.992668\pi$
$908$			11875.4i			0.434030i
$909$		0			0
$910$	26073.0	+	5549.94i	0.949795	+	0.202174i
$911$	−27133.6			−0.986800			−0.493400	−	0.869802i	$-0.664246\pi$
$911$	−27133.6			−0.986800			−0.493400	+	0.869802i	$0.664246\pi$
$912$		0			0
$913$		−	26654.6i		−	0.966197i
$914$	51724.9			1.87189
$915$		0			0
$916$	−93476.5			−3.37178
$917$		−	14580.3i		−	0.525064i
$918$		0			0
$919$	−42534.1			−1.52673			−0.763367	−	0.645965i	$-0.776455\pi$
$919$	−42534.1			−1.52673			−0.763367	+	0.645965i	$0.776455\pi$
$920$	−16435.4	+	77211.8i	−0.588977	+	2.76696i
$921$		0			0
$922$		−	7138.42i		−	0.254980i
$923$		−	35679.7i		−	1.27238i
$924$		0			0
$925$	1950.35	−	4373.70i	0.0693266	−	0.155466i
$926$	35143.1			1.24716
$927$		0			0
$928$			106552.i			3.76911i
$929$	41849.0			1.47795			0.738977	−	0.673730i	$-0.235309\pi$
$929$	41849.0			1.47795			0.738977	+	0.673730i	$0.235309\pi$
$930$		0			0
$931$	38.8294			0.00136690
$932$			103612.i			3.64155i
$933$		0			0
$934$	78051.9			2.73441
$935$	−7735.54	−	1646.60i	−0.270566	−	0.0575930i
$936$		0			0
$937$		−	33281.9i		−	1.16038i	−0.814482	−	0.580188i	$-0.802979\pi$
$937$		−	33281.9i		−	1.16038i	0.814482	−	0.580188i	$-0.197021\pi$
$938$			19179.5i			0.667627i
$939$		0			0
$940$	45791.5	+	9747.24i	1.58889	+	0.338213i
$941$	−12740.6			−0.441373			−0.220687	−	0.975345i	$-0.570830\pi$
$941$	−12740.6			−0.441373			−0.220687	+	0.975345i	$0.570830\pi$
$942$		0			0
$943$			43791.9i			1.51226i
$944$	−124662.			−4.29810
$945$		0			0
$946$	23465.5			0.806478
$947$		−	20681.5i		−	0.709670i	−0.934929	−	0.354835i	$-0.884537\pi$
$947$		−	20681.5i		−	0.709670i	0.934929	−	0.354835i	$-0.115463\pi$
$948$		0			0
$949$	−11105.1			−0.379861
$950$	214.363	−	480.712i	0.00732088	−	0.0164172i
$951$		0			0
$952$		−	12603.7i		−	0.429084i
$953$			6702.50i			0.227823i	0.993491	+	0.113912i	$0.0363380\pi$
$953$			6702.50i			0.227823i	−0.993491	+	0.113912i	$0.963662\pi$
$954$		0			0
$955$	3597.47	−	16900.6i	0.121897	−	0.572659i
$956$	−22815.2			−0.771857
$957$		0			0
$958$			81291.6i			2.74156i
$959$	−547.196			−0.0184253
$960$		0			0
$961$	−13097.4			−0.439643
$962$			13049.2i			0.437341i
$963$		0			0
$964$	71824.6			2.39970
$965$	25195.6	+	5363.16i	0.840492	+	0.178908i
$966$		0			0
$967$		−	36459.9i		−	1.21248i	−0.795280	−	0.606242i	$-0.792676\pi$
$967$		−	36459.9i		−	1.21248i	0.795280	−	0.606242i	$-0.207324\pi$
$968$		−	44117.9i		−	1.46488i
$969$		0			0
$970$	6378.69	−	29966.5i	0.211142	−	0.991922i
$971$	15789.7			0.521850			0.260925	−	0.965359i	$-0.415973\pi$
$971$	15789.7			0.521850			0.260925	+	0.965359i	$0.415973\pi$
$972$		0			0
$973$		−	9755.67i		−	0.321431i
$974$	−51297.0			−1.68754
$975$		0			0
$976$	−105503.			−3.46011
$977$			34429.2i			1.12742i	0.825974	+	0.563709i	$0.190626\pi$
$977$			34429.2i			1.12742i	−0.825974	+	0.563709i	$0.809374\pi$
$978$		0			0
$979$	−16654.9			−0.543710
$980$	2307.95	−	10842.5i	0.0752294	−	0.353420i
$981$		0			0
$982$			107031.i			3.47809i
$983$		−	21047.5i		−	0.682922i	−0.939896	−	0.341461i	$-0.889078\pi$
$983$		−	21047.5i		−	0.682922i	0.939896	−	0.341461i	$-0.110922\pi$
$984$		0			0
$985$	2427.87	+	516.799i	0.0785365	+	0.0167174i
$986$	−34436.1			−1.11224
$987$		0			0
$988$			1027.86i			0.0330978i
$989$	18777.5			0.603730
$990$		0			0
$991$	23839.1			0.764150			0.382075	−	0.924131i	$-0.375210\pi$
$991$	23839.1			0.764150			0.382075	+	0.924131i	$0.375210\pi$
$992$		−	58832.7i		−	1.88301i
$993$		0			0
$994$	−20703.5			−0.660640
$995$	−8334.49	+	39154.6i	−0.265549	+	1.24752i
$996$		0			0
$997$			7853.62i			0.249475i	0.992190	+	0.124738i	$0.0398089\pi$
$997$			7853.62i			0.249475i	−0.992190	+	0.124738i	$0.960191\pi$
$998$		−	6957.12i		−	0.220665i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.c.64.1		10
3.2	odd	2		35.4.b.a.29.10	yes	10
5.2	odd	4		1575.4.a.bq.1.5		5
5.3	odd	4		1575.4.a.bn.1.1		5
5.4	even	2	inner	315.4.d.c.64.10		10
12.11	even	2		560.4.g.f.449.6		10
15.2	even	4		175.4.a.i.1.1		5
15.8	even	4		175.4.a.j.1.5		5
15.14	odd	2		35.4.b.a.29.1	✓	10
21.2	odd	6		245.4.j.e.214.10		20
21.5	even	6		245.4.j.f.214.10		20
21.11	odd	6		245.4.j.e.79.1		20
21.17	even	6		245.4.j.f.79.1		20
21.20	even	2		245.4.b.d.99.10		10
60.59	even	2		560.4.g.f.449.5		10
105.44	odd	6		245.4.j.e.214.1		20
105.59	even	6		245.4.j.f.79.10		20
105.62	odd	4		1225.4.a.be.1.1		5
105.74	odd	6		245.4.j.e.79.10		20
105.83	odd	4		1225.4.a.bh.1.5		5
105.89	even	6		245.4.j.f.214.1		20
105.104	even	2		245.4.b.d.99.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.1	✓	10	15.14	odd	2
35.4.b.a.29.10	yes	10	3.2	odd	2
175.4.a.i.1.1		5	15.2	even	4
175.4.a.j.1.5		5	15.8	even	4
245.4.b.d.99.1		10	105.104	even	2
245.4.b.d.99.10		10	21.20	even	2
245.4.j.e.79.1		20	21.11	odd	6
245.4.j.e.79.10		20	105.74	odd	6
245.4.j.e.214.1		20	105.44	odd	6
245.4.j.e.214.10		20	21.2	odd	6
245.4.j.f.79.1		20	21.17	even	6
245.4.j.f.79.10		20	105.59	even	6
245.4.j.f.214.1		20	105.89	even	6
245.4.j.f.214.10		20	21.5	even	6
315.4.d.c.64.1		10	1.1	even	1	trivial
315.4.d.c.64.10		10	5.4	even	2	inner
560.4.g.f.449.5		10	60.59	even	2
560.4.g.f.449.6		10	12.11	even	2
1225.4.a.be.1.1		5	105.62	odd	4
1225.4.a.bh.1.5		5	105.83	odd	4
1575.4.a.bn.1.1		5	5.3	odd	4
1575.4.a.bq.1.5		5	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.31366i q^{2} -20.2350 q^{4} +(2.32771 - 10.9353i) q^{5} +7.00000i q^{7} +65.0123i q^{8} +(-58.1067 - 12.3686i) q^{10} -25.5420 q^{11} +64.1014i q^{13} +37.1956 q^{14} +183.574 q^{16} +27.6952i q^{17} -0.792436 q^{19} +(-47.1011 + 221.276i) q^{20} +135.721i q^{22} +108.606i q^{23} +(-114.164 - 50.9086i) q^{25} +340.613 q^{26} -141.645i q^{28} -234.000 q^{29} +129.204 q^{31} -455.349i q^{32} +147.163 q^{34} +(76.5474 + 16.2940i) q^{35} +38.3108i q^{37} +4.21073i q^{38} +(710.932 + 151.330i) q^{40} +403.216 q^{41} -172.895i q^{43} +516.840 q^{44} +577.097 q^{46} -206.943i q^{47} -49.0000 q^{49} +(-270.511 + 606.626i) q^{50} -1297.09i q^{52} +144.031i q^{53} +(-59.4542 + 279.310i) q^{55} -455.086 q^{56} +1243.40i q^{58} -679.086 q^{59} -574.717 q^{61} -686.544i q^{62} -950.977 q^{64} +(700.971 + 149.209i) q^{65} +515.640i q^{67} -560.411i q^{68} +(86.5805 - 406.747i) q^{70} -556.612 q^{71} +173.243i q^{73} +203.571 q^{74} +16.0349 q^{76} -178.794i q^{77} -79.3290 q^{79} +(427.306 - 2007.44i) q^{80} -2142.55i q^{82} +1043.56i q^{83} +(302.856 + 64.4663i) q^{85} -918.703 q^{86} -1660.54i q^{88} +652.060 q^{89} -448.710 q^{91} -2197.65i q^{92} -1099.62 q^{94} +(-1.84456 + 8.66556i) q^{95} +515.714i q^{97} +260.369i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 36 q^{4} - 6 q^{5} - 16 q^{10} - 84 q^{11} + 56 q^{14} + 148 q^{16} + 72 q^{19} + 68 q^{20} - 362 q^{25} + 620 q^{26} - 88 q^{29} + 120 q^{31} + 964 q^{34} + 28 q^{35} + 1396 q^{40} + 852 q^{41}+ \cdots + 1628 q^{95}+O(q^{100}) \) 10 * q - 36 * q^4 - 6 * q^5 - 16 * q^10 - 84 * q^11 + 56 * q^14 + 148 * q^16 + 72 * q^19 + 68 * q^20 - 362 * q^25 + 620 * q^26 - 88 * q^29 + 120 * q^31 + 964 * q^34 + 28 * q^35 + 1396 * q^40 + 852 * q^41 + 1424 * q^44 + 176 * q^46 - 490 * q^49 - 1644 * q^50 - 1136 * q^55 - 588 * q^56 - 864 * q^59 - 884 * q^61 - 2724 * q^64 - 520 * q^65 + 756 * q^70 - 880 * q^71 - 3024 * q^74 - 2672 * q^76 - 3580 * q^79 + 2316 * q^80 + 1572 * q^85 - 2432 * q^86 + 1492 * q^89 + 476 * q^91 + 1652 * q^94 + 1628 * q^95

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