LMFDB - Embedded newform 648.4.i.k.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,4,Mod(217,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("648.217");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	648.i (of order $3$, 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:	$38.2332376837$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	648.217
Dual form			648.4.i.k.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.00000 + 12.1244i) q^{5} +(12.0000 - 20.7846i) q^{7} +O(q^{10})$	$q+(7.00000 + 12.1244i) q^{5} +(12.0000 - 20.7846i) q^{7} +(-14.0000 + 24.2487i) q^{11} +(37.0000 + 64.0859i) q^{13} -82.0000 q^{17} +92.0000 q^{19} +(4.00000 + 6.92820i) q^{23} +(-35.5000 + 61.4878i) q^{25} +(-69.0000 + 119.512i) q^{29} +(-40.0000 - 69.2820i) q^{31} +336.000 q^{35} +30.0000 q^{37} +(141.000 + 244.219i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(120.000 - 207.846i) q^{47} +(-116.500 - 201.784i) q^{49} +130.000 q^{53} -392.000 q^{55} +(298.000 + 516.151i) q^{59} +(109.000 - 188.794i) q^{61} +(-518.000 + 897.202i) q^{65} +(218.000 + 377.587i) q^{67} -856.000 q^{71} -998.000 q^{73} +(336.000 + 581.969i) q^{77} +(16.0000 - 27.7128i) q^{79} +(-754.000 + 1305.97i) q^{83} +(-574.000 - 994.197i) q^{85} +246.000 q^{89} +1776.00 q^{91} +(644.000 + 1115.44i) q^{95} +(-433.000 + 749.978i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 14 q^{5} + 24 q^{7}+O(q^{10}) $ 2 * q + 14 * q^5 + 24 * q^7	$ 2 q + 14 q^{5} + 24 q^{7} - 28 q^{11} + 74 q^{13} - 164 q^{17} + 184 q^{19} + 8 q^{23} - 71 q^{25} - 138 q^{29} - 80 q^{31} + 672 q^{35} + 60 q^{37} + 282 q^{41} - 4 q^{43} + 240 q^{47} - 233 q^{49} + 260 q^{53} - 784 q^{55} + 596 q^{59} + 218 q^{61} - 1036 q^{65} + 436 q^{67} - 1712 q^{71} - 1996 q^{73} + 672 q^{77} + 32 q^{79} - 1508 q^{83} - 1148 q^{85} + 492 q^{89} + 3552 q^{91} + 1288 q^{95} - 866 q^{97}+O(q^{100}) $ 2 * q + 14 * q^5 + 24 * q^7 - 28 * q^11 + 74 * q^13 - 164 * q^17 + 184 * q^19 + 8 * q^23 - 71 * q^25 - 138 * q^29 - 80 * q^31 + 672 * q^35 + 60 * q^37 + 282 * q^41 - 4 * q^43 + 240 * q^47 - 233 * q^49 + 260 * q^53 - 784 * q^55 + 596 * q^59 + 218 * q^61 - 1036 * q^65 + 436 * q^67 - 1712 * q^71 - 1996 * q^73 + 672 * q^77 + 32 * q^79 - 1508 * q^83 - 1148 * q^85 + 492 * q^89 + 3552 * q^91 + 1288 * q^95 - 866 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	7.00000	+	12.1244i	0.626099	+	1.08444i	0.988327	+	0.152346i	$0.0486828\pi$
$5$	7.00000	+	12.1244i	0.626099	+	1.08444i	−0.362228	+	0.932089i	$0.617984\pi$
$6$		0			0
$7$	12.0000	−	20.7846i	0.647939	−	1.12226i	−0.335675	−	0.941978i	$-0.608964\pi$
$7$	12.0000	−	20.7846i	0.647939	−	1.12226i	0.983614	−	0.180286i	$-0.0577022\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−14.0000	+	24.2487i	−0.383742	+	0.664660i	−0.991594	−	0.129390i	$-0.958698\pi$
$11$	−14.0000	+	24.2487i	−0.383742	+	0.664660i	0.607852	+	0.794050i	$0.292031\pi$
$12$		0			0
$13$	37.0000	+	64.0859i	0.789381	+	1.36725i	0.926347	+	0.376672i	$0.122932\pi$
$13$	37.0000	+	64.0859i	0.789381	+	1.36725i	−0.136966	+	0.990576i	$0.543735\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−82.0000			−1.16988			−0.584939	−	0.811077i	$-0.698882\pi$
$17$	−82.0000			−1.16988			−0.584939	+	0.811077i	$0.698882\pi$
$18$		0			0
$19$	92.0000			1.11086			0.555428	−	0.831565i	$-0.312555\pi$
$19$	92.0000			1.11086			0.555428	+	0.831565i	$0.312555\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.00000	+	6.92820i	0.0362634	+	0.0628100i	0.883587	−	0.468266i	$-0.155121\pi$
$23$	4.00000	+	6.92820i	0.0362634	+	0.0628100i	−0.847324	+	0.531076i	$0.821788\pi$
$24$		0			0
$25$	−35.5000	+	61.4878i	−0.284000	+	0.491902i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−69.0000	+	119.512i	−0.441827	+	0.765267i	−0.997825	−	0.0659169i	$-0.979003\pi$
$29$	−69.0000	+	119.512i	−0.441827	+	0.765267i	0.555998	+	0.831183i	$0.312336\pi$
$30$		0			0
$31$	−40.0000	−	69.2820i	−0.231749	−	0.401401i	0.726574	−	0.687088i	$-0.241111\pi$
$31$	−40.0000	−	69.2820i	−0.231749	−	0.401401i	−0.958323	+	0.285688i	$0.907778\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	336.000			1.62270
$36$		0			0
$37$	30.0000			0.133296			0.0666482	−	0.997777i	$-0.478769\pi$
$37$	30.0000			0.133296			0.0666482	+	0.997777i	$0.478769\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	141.000	+	244.219i	0.537085	+	0.930259i	0.999059	+	0.0433656i	$0.0138080\pi$
$41$	141.000	+	244.219i	0.537085	+	0.930259i	−0.461974	+	0.886894i	$0.652859\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.00709296	+	0.0122854i	−0.869550	−	0.493845i	$-0.835591\pi$
$43$	−2.00000	+	3.46410i	−0.00709296	+	0.0122854i	0.862457	+	0.506130i	$0.168924\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	120.000	−	207.846i	0.372421	−	0.645053i	−0.617516	−	0.786558i	$-0.711861\pi$
$47$	120.000	−	207.846i	0.372421	−	0.645053i	0.989937	+	0.141506i	$0.0451943\pi$
$48$		0			0
$49$	−116.500	−	201.784i	−0.339650	−	0.588291i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	130.000			0.336922			0.168461	−	0.985708i	$-0.446120\pi$
$53$	130.000			0.336922			0.168461	+	0.985708i	$0.446120\pi$
$54$		0			0
$55$	−392.000			−0.961041
$56$		0			0
$57$		0			0
$58$		0			0
$59$	298.000	+	516.151i	0.657564	+	1.13893i	0.981244	+	0.192768i	$0.0617465\pi$
$59$	298.000	+	516.151i	0.657564	+	1.13893i	−0.323680	+	0.946167i	$0.604920\pi$
$60$		0			0
$61$	109.000	−	188.794i	0.228787	−	0.396271i	−0.728662	−	0.684874i	$-0.759857\pi$
$61$	109.000	−	188.794i	0.228787	−	0.396271i	0.957449	+	0.288603i	$0.0931907\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−518.000	+	897.202i	−0.988461	+	1.71207i
$66$		0			0
$67$	218.000	+	377.587i	0.397507	+	0.688502i	0.993418	−	0.114549i	$-0.0365423\pi$
$67$	218.000	+	377.587i	0.397507	+	0.688502i	−0.595911	+	0.803050i	$0.703209\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−856.000			−1.43082			−0.715412	−	0.698703i	$-0.753761\pi$
$71$	−856.000			−1.43082			−0.715412	+	0.698703i	$0.753761\pi$
$72$		0			0
$73$	−998.000			−1.60010			−0.800048	−	0.599935i	$-0.795193\pi$
$73$	−998.000			−1.60010			−0.800048	+	0.599935i	$0.795193\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	336.000	+	581.969i	0.497283	+	0.861319i
$78$		0			0
$79$	16.0000	−	27.7128i	0.0227866	−	0.0394675i	−0.854407	−	0.519604i	$-0.826080\pi$
$79$	16.0000	−	27.7128i	0.0227866	−	0.0394675i	0.877194	+	0.480136i	$0.159413\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−754.000	+	1305.97i	−0.997136	+	1.72709i	−0.433066	+	0.901362i	$0.642568\pi$
$83$	−754.000	+	1305.97i	−0.997136	+	1.72709i	−0.564070	+	0.825727i	$0.690765\pi$
$84$		0			0
$85$	−574.000	−	994.197i	−0.732459	−	1.26866i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	246.000			0.292988			0.146494	−	0.989212i	$-0.453201\pi$
$89$	246.000			0.292988			0.146494	+	0.989212i	$0.453201\pi$
$90$		0			0
$91$	1776.00			2.04588
$92$		0			0
$93$		0			0
$94$		0			0
$95$	644.000	+	1115.44i	0.695505	+	1.20465i
$96$		0			0
$97$	−433.000	+	749.978i	−0.453242	+	0.785038i	−0.998585	−	0.0531745i	$-0.983066\pi$
$97$	−433.000	+	749.978i	−0.453242	+	0.785038i	0.545343	+	0.838213i	$0.316399\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	135.000	−	233.827i	0.133000	−	0.230363i	−0.791832	−	0.610739i	$-0.790872\pi$
$101$	135.000	−	233.827i	0.133000	−	0.230363i	0.924832	+	0.380377i	$0.124206\pi$
$102$		0			0
$103$	748.000	+	1295.57i	0.715560	+	1.23939i	0.962743	+	0.270417i	$0.0871615\pi$
$103$	748.000	+	1295.57i	0.715560	+	1.23939i	−0.247184	+	0.968969i	$0.579505\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1692.00			1.52871			0.764354	−	0.644797i	$-0.223058\pi$
$107$	1692.00			1.52871			0.764354	+	0.644797i	$0.223058\pi$
$108$		0			0
$109$	406.000			0.356768			0.178384	−	0.983961i	$-0.442913\pi$
$109$	406.000			0.356768			0.178384	+	0.983961i	$0.442913\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	393.000	+	680.696i	0.327171	+	0.566677i	0.981949	−	0.189144i	$-0.0605713\pi$
$113$	393.000	+	680.696i	0.327171	+	0.566677i	−0.654778	+	0.755821i	$0.727238\pi$
$114$		0			0
$115$	−56.0000	+	96.9948i	−0.0454089	+	0.0786506i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−984.000	+	1704.34i	−0.758010	+	1.31291i
$120$		0			0
$121$	273.500	+	473.716i	0.205485	+	0.355910i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	756.000			0.540950
$126$		0			0
$127$	1744.00			1.21854			0.609272	−	0.792962i	$-0.291462\pi$
$127$	1744.00			1.21854			0.609272	+	0.792962i	$0.291462\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	326.000	+	564.649i	0.217426	+	0.376592i	0.954020	−	0.299742i	$-0.0969007\pi$
$131$	326.000	+	564.649i	0.217426	+	0.376592i	−0.736595	+	0.676335i	$0.763567\pi$
$132$		0			0
$133$	1104.00	−	1912.18i	0.719766	−	1.24667i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	765.000	−	1325.02i	0.477068	−	0.826307i	−0.522586	−	0.852586i	$-0.675033\pi$
$137$	765.000	−	1325.02i	0.477068	−	0.826307i	0.999655	+	0.0262798i	$0.00836609\pi$
$138$		0			0
$139$	−258.000	−	446.869i	−0.157434	−	0.272683i	0.776509	−	0.630106i	$-0.216989\pi$
$139$	−258.000	−	446.869i	−0.157434	−	0.272683i	−0.933943	+	0.357423i	$0.883655\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2072.00			−1.21167
$144$		0			0
$145$	−1932.00			−1.10651
$146$		0			0
$147$		0			0
$148$		0			0
$149$	671.000	+	1162.21i	0.368929	+	0.639004i	0.989398	−	0.145227i	$-0.0463911\pi$
$149$	671.000	+	1162.21i	0.368929	+	0.639004i	−0.620469	+	0.784231i	$0.713058\pi$
$150$		0			0
$151$	212.000	−	367.195i	0.114254	−	0.197893i	−0.803227	−	0.595672i	$-0.796886\pi$
$151$	212.000	−	367.195i	0.114254	−	0.197893i	0.917481	+	0.397779i	$0.130219\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	560.000	−	969.948i	0.290195	−	0.502633i
$156$		0			0
$157$	−131.000	−	226.899i	−0.0665920	−	0.115341i	0.830807	−	0.556560i	$-0.187879\pi$
$157$	−131.000	−	226.899i	−0.0665920	−	0.115341i	−0.897399	+	0.441220i	$0.854546\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	192.000			0.0939858
$162$		0			0
$163$	−2292.00			−1.10137			−0.550685	−	0.834713i	$-0.685633\pi$
$163$	−2292.00			−1.10137			−0.550685	+	0.834713i	$0.685633\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−948.000	−	1641.98i	−0.439272	−	0.760842i	0.558361	−	0.829598i	$-0.311430\pi$
$167$	−948.000	−	1641.98i	−0.439272	−	0.760842i	−0.997633	+	0.0687562i	$0.978097\pi$
$168$		0			0
$169$	−1639.50	+	2839.70i	−0.746245	+	1.29253i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1437.00	+	2488.96i	−0.631521	+	1.09383i	0.355720	+	0.934592i	$0.384236\pi$
$173$	−1437.00	+	2488.96i	−0.631521	+	1.09383i	−0.987241	+	0.159234i	$0.949098\pi$
$174$		0			0
$175$	852.000	+	1475.71i	0.368029	+	0.637446i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1188.00			0.496063			0.248032	−	0.968752i	$-0.420216\pi$
$179$	1188.00			0.496063			0.248032	+	0.968752i	$0.420216\pi$
$180$		0			0
$181$	−3474.00			−1.42663			−0.713316	−	0.700843i	$-0.752808\pi$
$181$	−3474.00			−1.42663			−0.713316	+	0.700843i	$0.752808\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	210.000	+	363.731i	0.0834568	+	0.144551i
$186$		0			0
$187$	1148.00	−	1988.39i	0.448931	−	0.777571i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	96.0000	−	166.277i	0.0363681	−	0.0629915i	−0.847268	−	0.531165i	$-0.821754\pi$
$191$	96.0000	−	166.277i	0.0363681	−	0.0629915i	0.883637	+	0.468173i	$0.155088\pi$
$192$		0			0
$193$	−2401.00	−	4158.65i	−0.895481	−	1.55102i	−0.833209	−	0.552959i	$-0.813499\pi$
$193$	−2401.00	−	4158.65i	−0.895481	−	1.55102i	−0.0622720	−	0.998059i	$-0.519835\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1518.00			−0.549000			−0.274500	−	0.961587i	$-0.588512\pi$
$197$	−1518.00			−0.549000			−0.274500	+	0.961587i	$0.588512\pi$
$198$		0			0
$199$	5128.00			1.82670			0.913352	−	0.407170i	$-0.133484\pi$
$199$	5128.00			1.82670			0.913352	+	0.407170i	$0.133484\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1656.00	+	2868.28i	0.572554	+	0.991692i
$204$		0			0
$205$	−1974.00	+	3419.07i	−0.672537	+	1.16487i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1288.00	+	2230.88i	−0.426281	+	0.738341i
$210$		0			0
$211$	−542.000	−	938.772i	−0.176838	−	0.306292i	0.763958	−	0.645266i	$-0.223254\pi$
$211$	−542.000	−	938.772i	−0.176838	−	0.306292i	−0.940796	+	0.338974i	$0.889920\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−56.0000			−0.0177636
$216$		0			0
$217$	−1920.00			−0.600636
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3034.00	−	5255.04i	−0.923479	−	1.59951i
$222$		0			0
$223$	−344.000	+	595.825i	−0.103300	+	0.178921i	−0.913042	−	0.407865i	$-0.866274\pi$
$223$	−344.000	+	595.825i	−0.103300	+	0.178921i	0.809742	+	0.586786i	$0.199607\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2406.00	−	4167.31i	0.703488	−	1.21848i	−0.263746	−	0.964592i	$-0.584958\pi$
$227$	2406.00	−	4167.31i	0.703488	−	1.21848i	0.967234	−	0.253885i	$-0.0817086\pi$
$228$		0			0
$229$	−1247.00	−	2159.87i	−0.359843	−	0.623267i	0.628091	−	0.778140i	$-0.283836\pi$
$229$	−1247.00	−	2159.87i	−0.359843	−	0.623267i	−0.987934	+	0.154873i	$0.950503\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−698.000			−0.196255			−0.0981277	−	0.995174i	$-0.531285\pi$
$233$	−698.000			−0.196255			−0.0981277	+	0.995174i	$0.531285\pi$
$234$		0			0
$235$	3360.00			0.932690
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3160.00	−	5473.28i	−0.855244	−	1.48133i	−0.876418	−	0.481551i	$-0.840074\pi$
$239$	−3160.00	−	5473.28i	−0.855244	−	1.48133i	0.0211737	−	0.999776i	$-0.493260\pi$
$240$		0			0
$241$	3255.00	−	5637.83i	0.870012	−	1.50691i	0.00802978	−	0.999968i	$-0.497444\pi$
$241$	3255.00	−	5637.83i	0.870012	−	1.50691i	0.861983	−	0.506938i	$-0.169223\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1631.00	−	2824.97i	0.425309	−	0.736657i
$246$		0			0
$247$	3404.00	+	5895.90i	0.876888	+	1.51881i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−628.000			−0.157924			−0.0789622	−	0.996878i	$-0.525161\pi$
$251$	−628.000			−0.157924			−0.0789622	+	0.996878i	$0.525161\pi$
$252$		0			0
$253$	−224.000			−0.0556631
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2431.00	−	4210.62i	−0.590045	−	1.02199i	−0.994226	−	0.107309i	$-0.965777\pi$
$257$	−2431.00	−	4210.62i	−0.590045	−	1.02199i	0.404181	−	0.914679i	$-0.367557\pi$
$258$		0			0
$259$	360.000	−	623.538i	0.0863680	−	0.149594i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2908.00	−	5036.80i	0.681806	−	1.18092i	−0.292623	−	0.956228i	$-0.594528\pi$
$263$	2908.00	−	5036.80i	0.681806	−	1.18092i	0.974429	−	0.224695i	$-0.0721385\pi$
$264$		0			0
$265$	910.000	+	1576.17i	0.210947	+	0.365370i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3526.00			−0.799197			−0.399599	−	0.916690i	$-0.630850\pi$
$269$	−3526.00			−0.799197			−0.399599	+	0.916690i	$0.630850\pi$
$270$		0			0
$271$	−256.000			−0.0573834			−0.0286917	−	0.999588i	$-0.509134\pi$
$271$	−256.000			−0.0573834			−0.0286917	+	0.999588i	$0.509134\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−994.000	−	1721.66i	−0.217965	−	0.377527i
$276$		0			0
$277$	−71.0000	+	122.976i	−0.0154006	+	0.0266747i	−0.873623	−	0.486603i	$-0.838236\pi$
$277$	−71.0000	+	122.976i	−0.0154006	+	0.0266747i	0.858222	+	0.513278i	$0.171569\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4421.00	−	7657.40i	0.938558	−	1.62563i	0.170394	−	0.985376i	$-0.445496\pi$
$281$	4421.00	−	7657.40i	0.938558	−	1.62563i	0.768163	−	0.640254i	$-0.221171\pi$
$282$		0			0
$283$	3590.00	+	6218.06i	0.754075	+	1.30610i	0.945833	+	0.324655i	$0.105248\pi$
$283$	3590.00	+	6218.06i	0.754075	+	1.30610i	−0.191757	+	0.981442i	$0.561419\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6768.00			1.39199
$288$		0			0
$289$	1811.00			0.368614
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3687.00	+	6386.07i	0.735143	+	1.27330i	0.954661	+	0.297696i	$0.0962182\pi$
$293$	3687.00	+	6386.07i	0.735143	+	1.27330i	−0.219518	+	0.975608i	$0.570448\pi$
$294$		0			0
$295$	−4172.00	+	7226.12i	−0.823401	+	1.42617i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−296.000	+	512.687i	−0.0572512	+	0.0991621i
$300$		0			0
$301$	48.0000	+	83.1384i	0.00919161	+	0.0159203i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3052.00			0.572974
$306$		0			0
$307$	1500.00			0.278858			0.139429	−	0.990232i	$-0.455473\pi$
$307$	1500.00			0.278858			0.139429	+	0.990232i	$0.455473\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3804.00	−	6588.72i	−0.693585	−	1.20133i	−0.970655	−	0.240475i	$-0.922697\pi$
$311$	−3804.00	−	6588.72i	−0.693585	−	1.20133i	0.277070	−	0.960850i	$-0.410637\pi$
$312$		0			0
$313$	2379.00	−	4120.55i	0.429614	−	0.744112i	−0.567225	−	0.823563i	$-0.691983\pi$
$313$	2379.00	−	4120.55i	0.429614	−	0.744112i	0.996839	+	0.0794502i	$0.0253165\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2187.00	−	3788.00i	0.387489	−	0.671151i	−0.604622	−	0.796513i	$-0.706676\pi$
$317$	2187.00	−	3788.00i	0.387489	−	0.671151i	0.992111	+	0.125361i	$0.0400090\pi$
$318$		0			0
$319$	−1932.00	−	3346.32i	−0.339095	−	0.587329i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7544.00			−1.29956
$324$		0			0
$325$	−5254.00			−0.896737
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2880.00	−	4988.31i	−0.482613	−	0.835910i
$330$		0			0
$331$	3902.00	−	6758.46i	0.647956	−	1.12229i	−0.335655	−	0.941985i	$-0.608958\pi$
$331$	3902.00	−	6758.46i	0.647956	−	1.12229i	0.983610	−	0.180307i	$-0.0577091\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3052.00	+	5286.22i	−0.497757	+	0.862140i
$336$		0			0
$337$	−2553.00	−	4421.93i	−0.412673	−	0.714770i	0.582508	−	0.812825i	$-0.302071\pi$
$337$	−2553.00	−	4421.93i	−0.412673	−	0.714770i	−0.995181	+	0.0980544i	$0.968738\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2240.00			0.355727
$342$		0			0
$343$	2640.00			0.415588
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2358.00	−	4084.18i	−0.364796	−	0.631845i	0.623948	−	0.781466i	$-0.285528\pi$
$347$	−2358.00	−	4084.18i	−0.364796	−	0.631845i	−0.988743	+	0.149622i	$0.952194\pi$
$348$		0			0
$349$	−3651.00	+	6323.72i	−0.559982	+	0.969916i	0.437516	+	0.899211i	$0.355858\pi$
$349$	−3651.00	+	6323.72i	−0.559982	+	0.969916i	−0.997497	+	0.0707057i	$0.977475\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2191.00	+	3794.92i	−0.330355	+	0.572191i	−0.982581	−	0.185833i	$-0.940502\pi$
$353$	−2191.00	+	3794.92i	−0.330355	+	0.572191i	0.652227	+	0.758024i	$0.273835\pi$
$354$		0			0
$355$	−5992.00	−	10378.4i	−0.895838	−	1.55164i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7224.00			−1.06203			−0.531014	−	0.847363i	$-0.678189\pi$
$359$	−7224.00			−1.06203			−0.531014	+	0.847363i	$0.678189\pi$
$360$		0			0
$361$	1605.00			0.233999
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6986.00	−	12100.1i	−1.00182	−	1.73520i
$366$		0			0
$367$	−704.000	+	1219.36i	−0.100132	+	0.173434i	−0.911739	−	0.410770i	$-0.865260\pi$
$367$	−704.000	+	1219.36i	−0.100132	+	0.173434i	0.811607	+	0.584204i	$0.198593\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1560.00	−	2702.00i	0.218305	−	0.378115i
$372$		0			0
$373$	857.000	+	1484.37i	0.118965	+	0.206053i	0.919358	−	0.393423i	$-0.128709\pi$
$373$	857.000	+	1484.37i	0.118965	+	0.206053i	−0.800393	+	0.599476i	$0.795376\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10212.0			−1.39508
$378$		0			0
$379$	884.000			0.119810			0.0599051	−	0.998204i	$-0.480920\pi$
$379$	884.000			0.119810			0.0599051	+	0.998204i	$0.480920\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5184.00	+	8978.95i	0.691619	+	1.19792i	0.971307	+	0.237828i	$0.0764355\pi$
$383$	5184.00	+	8978.95i	0.691619	+	1.19792i	−0.279688	+	0.960091i	$0.590231\pi$
$384$		0			0
$385$	−4704.00	+	8147.57i	−0.622696	+	1.07854i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	199.000	−	344.678i	0.0259375	−	0.0449251i	−0.852765	−	0.522294i	$-0.825076\pi$
$389$	199.000	−	344.678i	0.0259375	−	0.0449251i	0.878703	+	0.477369i	$0.158410\pi$
$390$		0			0
$391$	−328.000	−	568.113i	−0.0424237	−	0.0734800i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	448.000			0.0570666
$396$		0			0
$397$	−5098.00			−0.644487			−0.322243	−	0.946657i	$-0.604437\pi$
$397$	−5098.00			−0.644487			−0.322243	+	0.946657i	$0.604437\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5001.00	+	8661.99i	0.622788	+	1.07870i	0.988964	+	0.148155i	$0.0473335\pi$
$401$	5001.00	+	8661.99i	0.622788	+	1.07870i	−0.366176	+	0.930546i	$0.619333\pi$
$402$		0			0
$403$	2960.00	−	5126.87i	0.365876	−	0.633716i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−420.000	+	727.461i	−0.0511514	+	0.0885969i
$408$		0			0
$409$	4635.00	+	8028.06i	0.560357	+	0.970567i	0.997465	+	0.0711578i	$0.0226694\pi$
$409$	4635.00	+	8028.06i	0.560357	+	0.970567i	−0.437108	+	0.899409i	$0.643997\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14304.0			1.70425
$414$		0			0
$415$	−21112.0			−2.49722
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3258.00	−	5643.02i	−0.379866	−	0.657947i	0.611177	−	0.791494i	$-0.290696\pi$
$419$	−3258.00	−	5643.02i	−0.379866	−	0.657947i	−0.991042	+	0.133548i	$0.957363\pi$
$420$		0			0
$421$	1313.00	−	2274.18i	0.151999	−	0.263271i	−0.779963	−	0.625826i	$-0.784762\pi$
$421$	1313.00	−	2274.18i	0.151999	−	0.263271i	0.931962	+	0.362555i	$0.118096\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2911.00	−	5042.00i	0.332245	−	0.575466i
$426$		0			0
$427$	−2616.00	−	4531.04i	−0.296480	−	0.513519i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4304.00			0.481012			0.240506	−	0.970648i	$-0.422687\pi$
$431$	4304.00			0.481012			0.240506	+	0.970648i	$0.422687\pi$
$432$		0			0
$433$	11794.0			1.30897			0.654484	−	0.756076i	$-0.272886\pi$
$433$	11794.0			1.30897			0.654484	+	0.756076i	$0.272886\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	368.000	+	637.395i	0.0402834	+	0.0697728i
$438$		0			0
$439$	2772.00	−	4801.24i	0.301368	−	0.521984i	−0.675078	−	0.737746i	$-0.735890\pi$
$439$	2772.00	−	4801.24i	0.301368	−	0.521984i	0.976446	+	0.215762i	$0.0692236\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1894.00	+	3280.50i	−0.203130	+	0.351832i	−0.949535	−	0.313660i	$-0.898445\pi$
$443$	−1894.00	+	3280.50i	−0.203130	+	0.351832i	0.746405	+	0.665492i	$0.231778\pi$
$444$		0			0
$445$	1722.00	+	2982.59i	0.183440	+	0.317727i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	13342.0			1.40233			0.701167	−	0.712997i	$-0.252663\pi$
$449$	13342.0			1.40233			0.701167	+	0.712997i	$0.252663\pi$
$450$		0			0
$451$	−7896.00			−0.824408
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12432.0	+	21532.9i	1.28093	+	2.21863i
$456$		0			0
$457$	2195.00	−	3801.85i	0.224678	−	0.389153i	−0.731545	−	0.681793i	$-0.761200\pi$
$457$	2195.00	−	3801.85i	0.224678	−	0.389153i	0.956223	+	0.292640i	$0.0945337\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2899.00	−	5021.22i	0.292885	−	0.507291i	−0.681606	−	0.731720i	$-0.738718\pi$
$461$	2899.00	−	5021.22i	0.292885	−	0.507291i	0.974491	+	0.224428i	$0.0720514\pi$
$462$		0			0
$463$	7328.00	+	12692.5i	0.735553	+	1.27402i	0.954480	+	0.298274i	$0.0964109\pi$
$463$	7328.00	+	12692.5i	0.735553	+	1.27402i	−0.218927	+	0.975741i	$0.570256\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8412.00			−0.833535			−0.416768	−	0.909013i	$-0.636837\pi$
$467$	−8412.00			−0.833535			−0.416768	+	0.909013i	$0.636837\pi$
$468$		0			0
$469$	10464.0			1.03024
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−56.0000	−	96.9948i	−0.00544373	−	0.00942881i
$474$		0			0
$475$	−3266.00	+	5656.88i	−0.315483	+	0.546432i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7424.00	−	12858.7i	0.708165	−	1.22658i	−0.257372	−	0.966313i	$-0.582856\pi$
$479$	7424.00	−	12858.7i	0.708165	−	1.22658i	0.965537	−	0.260266i	$-0.0838102\pi$
$480$		0			0
$481$	1110.00	+	1922.58i	0.105222	+	0.182249i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12124.0			−1.13510
$486$		0			0
$487$	18568.0			1.72771			0.863857	−	0.503738i	$-0.168042\pi$
$487$	18568.0			1.72771			0.863857	+	0.503738i	$0.168042\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7182.00	−	12439.6i	−0.660120	−	1.14336i	−0.980584	−	0.196101i	$-0.937172\pi$
$491$	−7182.00	−	12439.6i	−0.660120	−	1.14336i	0.320463	−	0.947261i	$-0.396161\pi$
$492$		0			0
$493$	5658.00	−	9799.94i	0.516883	−	0.895268i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10272.0	+	17791.6i	−0.927087	+	1.60576i
$498$		0			0
$499$	−10830.0	−	18758.1i	−0.971578	−	1.68282i	−0.690794	−	0.723051i	$-0.742739\pi$
$499$	−10830.0	−	18758.1i	−0.971578	−	1.68282i	−0.280783	−	0.959771i	$-0.590594\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	17112.0			1.51687			0.758436	−	0.651748i	$-0.225964\pi$
$503$	17112.0			1.51687			0.758436	+	0.651748i	$0.225964\pi$
$504$		0			0
$505$	3780.00			0.333085
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5739.00	+	9940.24i	0.499758	+	0.865606i	1.00000		0.000279686i	$-8.90267e-5\pi$
$509$	5739.00	+	9940.24i	0.499758	+	0.865606i	−0.500242	+	0.865886i	$0.666756\pi$
$510$		0			0
$511$	−11976.0	+	20743.0i	−1.03677	+	1.79573i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10472.0	+	18138.0i	−0.896022	+	1.55196i
$516$		0			0
$517$	3360.00	+	5819.69i	0.285827	+	0.495067i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13114.0			−1.10275			−0.551377	−	0.834256i	$-0.685897\pi$
$521$	−13114.0			−1.10275			−0.551377	+	0.834256i	$0.685897\pi$
$522$		0			0
$523$	−4508.00			−0.376905			−0.188452	−	0.982082i	$-0.560347\pi$
$523$	−4508.00			−0.376905			−0.188452	+	0.982082i	$0.560347\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3280.00	+	5681.13i	0.271118	+	0.469590i
$528$		0			0
$529$	6051.50	−	10481.5i	0.497370	−	0.861470i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−10434.0	+	18072.2i	−0.847930	+	1.46866i
$534$		0			0
$535$	11844.0	+	20514.4i	0.957123	+	1.65779i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6524.00			0.521352
$540$		0			0
$541$	22950.0			1.82384			0.911920	−	0.410368i	$-0.134600\pi$
$541$	22950.0			1.82384			0.911920	+	0.410368i	$0.134600\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2842.00	+	4922.49i	0.223372	+	0.386892i
$546$		0			0
$547$	3290.00	−	5698.45i	0.257167	−	0.445426i	−0.708315	−	0.705897i	$-0.750544\pi$
$547$	3290.00	−	5698.45i	0.257167	−	0.445426i	0.965482	+	0.260471i	$0.0838777\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6348.00	+	10995.1i	−0.490806	+	0.850100i
$552$		0			0
$553$	−384.000	−	665.108i	−0.0295286	−	0.0511451i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7046.00			−0.535994			−0.267997	−	0.963420i	$-0.586362\pi$
$557$	−7046.00			−0.535994			−0.267997	+	0.963420i	$0.586362\pi$
$558$		0			0
$559$	−296.000			−0.0223962
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4126.00	+	7146.44i	0.308864	+	0.534967i	0.978114	−	0.208070i	$-0.0667180\pi$
$563$	4126.00	+	7146.44i	0.308864	+	0.534967i	−0.669251	+	0.743037i	$0.733385\pi$
$564$		0			0
$565$	−5502.00	+	9529.74i	−0.409683	+	0.709592i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3419.00	+	5921.88i	−0.251901	+	0.436306i	−0.964049	−	0.265723i	$-0.914389\pi$
$569$	−3419.00	+	5921.88i	−0.251901	+	0.436306i	0.712148	+	0.702030i	$0.247723\pi$
$570$		0			0
$571$	−11658.0	−	20192.2i	−0.854417	−	1.47989i	−0.877185	−	0.480153i	$-0.840581\pi$
$571$	−11658.0	−	20192.2i	−0.854417	−	1.47989i	0.0227678	−	0.999741i	$-0.492752\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−568.000			−0.0411952
$576$		0			0
$577$	−10558.0			−0.761760			−0.380880	−	0.924625i	$-0.624379\pi$
$577$	−10558.0			−0.761760			−0.380880	+	0.924625i	$0.624379\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18096.0	+	31343.2i	1.29217	+	2.23810i
$582$		0			0
$583$	−1820.00	+	3152.33i	−0.129291	+	0.223939i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	514.000	−	890.274i	0.0361415	−	0.0625989i	−0.847389	−	0.530973i	$-0.821827\pi$
$587$	514.000	−	890.274i	0.0361415	−	0.0625989i	0.883530	+	0.468374i	$0.155160\pi$
$588$		0			0
$589$	−3680.00	−	6373.95i	−0.257439	−	0.445898i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1202.00			−0.0832382			−0.0416191	−	0.999134i	$-0.513252\pi$
$593$	−1202.00			−0.0832382			−0.0416191	+	0.999134i	$0.513252\pi$
$594$		0			0
$595$	−27552.0			−1.89836
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1788.00	−	3096.91i	−0.121963	−	0.211246i	0.798579	−	0.601890i	$-0.205586\pi$
$599$	−1788.00	−	3096.91i	−0.121963	−	0.211246i	−0.920542	+	0.390644i	$0.872252\pi$
$600$		0			0
$601$	−4325.00	+	7491.12i	−0.293545	+	0.508435i	−0.974645	−	0.223755i	$-0.928168\pi$
$601$	−4325.00	+	7491.12i	−0.293545	+	0.508435i	0.681101	+	0.732190i	$0.261502\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3829.00	+	6632.02i	−0.257307	+	0.445670i
$606$		0			0
$607$	−6328.00	−	10960.4i	−0.423139	−	0.732899i	0.573105	−	0.819482i	$-0.305739\pi$
$607$	−6328.00	−	10960.4i	−0.423139	−	0.732899i	−0.996245	+	0.0865829i	$0.972405\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17760.0			1.17593
$612$		0			0
$613$	−3298.00			−0.217300			−0.108650	−	0.994080i	$-0.534653\pi$
$613$	−3298.00			−0.217300			−0.108650	+	0.994080i	$0.534653\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2685.00	+	4650.56i	0.175193	+	0.303443i	0.940228	−	0.340546i	$-0.110612\pi$
$617$	2685.00	+	4650.56i	0.175193	+	0.303443i	−0.765035	+	0.643989i	$0.777278\pi$
$618$		0			0
$619$	8110.00	−	14046.9i	0.526605	−	0.912106i	−0.472915	−	0.881108i	$-0.656798\pi$
$619$	8110.00	−	14046.9i	0.526605	−	0.912106i	0.999519	−	0.0309981i	$-0.00986859\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2952.00	−	5113.01i	0.189838	−	0.328810i
$624$		0			0
$625$	9729.50	+	16852.0i	0.622688	+	1.07853i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2460.00			−0.155941
$630$		0			0
$631$	−20360.0			−1.28450			−0.642249	−	0.766496i	$-0.721999\pi$
$631$	−20360.0			−1.28450			−0.642249	+	0.766496i	$0.721999\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12208.0	+	21144.9i	0.762929	+	1.32143i
$636$		0			0
$637$	8621.00	−	14932.0i	0.536227	−	0.928772i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	7249.00	−	12555.6i	0.446674	−	0.773663i	−0.551493	−	0.834180i	$-0.685942\pi$
$641$	7249.00	−	12555.6i	0.446674	−	0.773663i	0.998167	+	0.0605169i	$0.0192749\pi$
$642$		0			0
$643$	−10806.0	−	18716.5i	−0.662748	−	1.14791i	−0.979891	−	0.199536i	$-0.936057\pi$
$643$	−10806.0	−	18716.5i	−0.662748	−	1.14791i	0.317142	−	0.948378i	$-0.397277\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12184.0			−0.740344			−0.370172	−	0.928963i	$-0.620701\pi$
$647$	−12184.0			−0.740344			−0.370172	+	0.928963i	$0.620701\pi$
$648$		0			0
$649$	−16688.0			−1.00934
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−14061.0	−	24354.4i	−0.842648	−	1.45951i	−0.887648	−	0.460523i	$-0.847662\pi$
$653$	−14061.0	−	24354.4i	−0.842648	−	1.45951i	0.0449993	−	0.998987i	$-0.485671\pi$
$654$		0			0
$655$	−4564.00	+	7905.08i	−0.272260	+	0.471568i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2850.00	+	4936.34i	−0.168468	+	0.291795i	−0.937881	−	0.346956i	$-0.887215\pi$
$659$	−2850.00	+	4936.34i	−0.168468	+	0.291795i	0.769414	+	0.638751i	$0.220549\pi$
$660$		0			0
$661$	14729.0	+	25511.4i	0.866705	+	1.50118i	0.865345	+	0.501177i	$0.167100\pi$
$661$	14729.0	+	25511.4i	0.866705	+	1.50118i	0.00135988	+	0.999999i	$0.499567\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30912.0			1.80258
$666$		0			0
$667$	−1104.00			−0.0640885
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3052.00	+	5286.22i	0.175590	+	0.304131i
$672$		0			0
$673$	−9905.00	+	17156.0i	−0.567325	+	0.982636i	0.429504	+	0.903065i	$0.358688\pi$
$673$	−9905.00	+	17156.0i	−0.567325	+	0.982636i	−0.996829	+	0.0795708i	$0.974645\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5225.00	+	9049.97i	−0.296622	+	0.513764i	−0.975361	−	0.220615i	$-0.929193\pi$
$677$	−5225.00	+	9049.97i	−0.296622	+	0.513764i	0.678739	+	0.734380i	$0.262527\pi$
$678$		0			0
$679$	10392.0	+	17999.5i	0.587347	+	1.01731i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23300.0			−1.30534			−0.652672	−	0.757641i	$-0.726352\pi$
$683$	−23300.0			−1.30534			−0.652672	+	0.757641i	$0.726352\pi$
$684$		0			0
$685$	21420.0			1.19477
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4810.00	+	8331.16i	0.265960	+	0.460656i
$690$		0			0
$691$	7106.00	−	12308.0i	0.391208	−	0.677593i	−0.601401	−	0.798947i	$-0.705391\pi$
$691$	7106.00	−	12308.0i	0.391208	−	0.677593i	0.992609	+	0.121355i	$0.0387238\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3612.00	−	6256.17i	0.197138	−	0.341453i
$696$		0			0
$697$	−11562.0	−	20026.0i	−0.628324	−	1.08829i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15978.0			0.860885			0.430443	−	0.902618i	$-0.358357\pi$
$701$	15978.0			0.860885			0.430443	+	0.902618i	$0.358357\pi$
$702$		0			0
$703$	2760.00			0.148073
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3240.00	−	5611.84i	−0.172352	−	0.298522i
$708$		0			0
$709$	4433.00	−	7678.18i	0.234816	−	0.406714i	−0.724403	−	0.689377i	$-0.757884\pi$
$709$	4433.00	−	7678.18i	0.234816	−	0.406714i	0.959219	+	0.282663i	$0.0912178\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	320.000	−	554.256i	0.0168080	−	0.0291123i
$714$		0			0
$715$	−14504.0	−	25121.7i	−0.758628	−	1.31398i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7760.00			−0.402502			−0.201251	−	0.979540i	$-0.564501\pi$
$719$	−7760.00			−0.402502			−0.201251	+	0.979540i	$0.564501\pi$
$720$		0			0
$721$	35904.0			1.85456
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4899.00	−	8485.32i	−0.250958	−	0.434671i
$726$		0			0
$727$	−6540.00	+	11327.6i	−0.333638	+	0.577879i	−0.983222	−	0.182411i	$-0.941610\pi$
$727$	−6540.00	+	11327.6i	−0.333638	+	0.577879i	0.649584	+	0.760290i	$0.274943\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	164.000	−	284.056i	0.00829789	−	0.0143724i
$732$		0			0
$733$	−8467.00	−	14665.3i	−0.426652	−	0.738983i	0.569921	−	0.821699i	$-0.306974\pi$
$733$	−8467.00	−	14665.3i	−0.426652	−	0.738983i	−0.996573	+	0.0827167i	$0.973640\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12208.0			−0.610159
$738$		0			0
$739$	−7060.00			−0.351429			−0.175715	−	0.984441i	$-0.556224\pi$
$739$	−7060.00			−0.351429			−0.175715	+	0.984441i	$0.556224\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6260.00	−	10842.6i	−0.309094	−	0.535367i	0.669070	−	0.743199i	$-0.266693\pi$
$743$	−6260.00	−	10842.6i	−0.309094	−	0.535367i	−0.978165	+	0.207832i	$0.933359\pi$
$744$		0			0
$745$	−9394.00	+	16270.9i	−0.461973	+	0.800160i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	20304.0	−	35167.6i	0.990510	−	1.71561i
$750$		0			0
$751$	4896.00	+	8480.12i	0.237893	+	0.412043i	0.960109	−	0.279624i	$-0.0902099\pi$
$751$	4896.00	+	8480.12i	0.237893	+	0.412043i	−0.722217	+	0.691667i	$0.756877\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5936.00			0.286137
$756$		0			0
$757$	13166.0			0.632135			0.316068	−	0.948737i	$-0.397637\pi$
$757$	13166.0			0.632135			0.316068	+	0.948737i	$0.397637\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11611.0	−	20110.8i	−0.553086	−	0.957973i	−0.998050	−	0.0624244i	$-0.980117\pi$
$761$	−11611.0	−	20110.8i	−0.553086	−	0.957973i	0.444964	−	0.895549i	$-0.353217\pi$
$762$		0			0
$763$	4872.00	−	8438.55i	0.231164	−	0.400388i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22052.0	+	38195.2i	−1.03814	+	1.79811i
$768$		0			0
$769$	19967.0	+	34583.9i	0.936318	+	1.62175i	0.772267	+	0.635298i	$0.219123\pi$
$769$	19967.0	+	34583.9i	0.936318	+	1.62175i	0.164051	+	0.986452i	$0.447544\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17106.0			0.795938			0.397969	−	0.917399i	$-0.369715\pi$
$773$	17106.0			0.795938			0.397969	+	0.917399i	$0.369715\pi$
$774$		0			0
$775$	5680.00			0.263267
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12972.0	+	22468.2i	0.596624	+	1.03338i
$780$		0			0
$781$	11984.0	−	20756.9i	0.549067	−	0.951012i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1834.00	−	3176.58i	0.0833863	−	0.144429i
$786$		0			0
$787$	4978.00	+	8622.15i	0.225472	+	0.390529i	0.956461	−	0.291860i	$-0.0942742\pi$
$787$	4978.00	+	8622.15i	0.225472	+	0.390529i	−0.730989	+	0.682389i	$0.760941\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18864.0			0.847948
$792$		0			0
$793$	16132.0			0.722401
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4565.00	−	7906.81i	−0.202887	−	0.351410i	0.746571	−	0.665306i	$-0.231699\pi$
$797$	−4565.00	−	7906.81i	−0.202887	−	0.351410i	−0.949457	+	0.313896i	$0.898366\pi$
$798$		0			0
$799$	−9840.00	+	17043.4i	−0.435687	+	0.754633i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13972.0	−	24200.2i	0.614024	−	1.06352i
$804$		0			0
$805$	1344.00	+	2327.88i	0.0588444	+	0.101922i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11482.0			−0.498993			−0.249497	−	0.968376i	$-0.580265\pi$
$809$	−11482.0			−0.498993			−0.249497	+	0.968376i	$0.580265\pi$
$810$		0			0
$811$	4612.00			0.199691			0.0998454	−	0.995003i	$-0.468165\pi$
$811$	4612.00			0.199691			0.0998454	+	0.995003i	$0.468165\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16044.0	−	27789.0i	−0.689567	−	1.19436i
$816$		0			0
$817$	−184.000	+	318.697i	−0.00787925	+	0.0136473i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17505.0	+	30319.5i	−0.744128	+	1.28887i	0.206474	+	0.978452i	$0.433801\pi$
$821$	−17505.0	+	30319.5i	−0.744128	+	1.28887i	−0.950601	+	0.310415i	$0.899532\pi$
$822$		0			0
$823$	−6844.00	−	11854.2i	−0.289875	−	0.502078i	0.683905	−	0.729571i	$-0.260280\pi$
$823$	−6844.00	−	11854.2i	−0.289875	−	0.502078i	−0.973780	+	0.227493i	$0.926947\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11668.0			−0.490612			−0.245306	−	0.969446i	$-0.578888\pi$
$827$	−11668.0			−0.490612			−0.245306	+	0.969446i	$0.578888\pi$
$828$		0			0
$829$	−29306.0			−1.22779			−0.613896	−	0.789387i	$-0.710399\pi$
$829$	−29306.0			−1.22779			−0.613896	+	0.789387i	$0.710399\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9553.00	+	16546.3i	0.397349	+	0.688229i
$834$		0			0
$835$	13272.0	−	22987.8i	0.550056	−	0.952724i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1332.00	+	2307.09i	−0.0548102	+	0.0949340i	−0.892129	−	0.451781i	$-0.850789\pi$
$839$	−1332.00	+	2307.09i	−0.0548102	+	0.0949340i	0.837318	+	0.546715i	$0.184122\pi$
$840$		0			0
$841$	2672.50	+	4628.91i	0.109578	+	0.189795i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−45906.0			−1.86889
$846$		0			0
$847$	13128.0			0.532566
$848$		0			0
$849$		0			0
$850$		0			0
$851$	120.000	+	207.846i	0.00483378	+	0.00837235i
$852$		0			0
$853$	−13015.0	+	22542.6i	−0.522421	+	0.904860i	0.477239	+	0.878774i	$0.341638\pi$
$853$	−13015.0	+	22542.6i	−0.522421	+	0.904860i	−0.999660	+	0.0260860i	$0.991696\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22101.0	−	38280.1i	0.880929	−	1.52581i	0.0306184	−	0.999531i	$-0.490252\pi$
$857$	22101.0	−	38280.1i	0.880929	−	1.52581i	0.850310	−	0.526282i	$-0.176414\pi$
$858$		0			0
$859$	16374.0	+	28360.6i	0.650377	+	1.12649i	0.983031	+	0.183437i	$0.0587223\pi$
$859$	16374.0	+	28360.6i	0.650377	+	1.12649i	−0.332655	+	0.943049i	$0.607944\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−45344.0			−1.78856			−0.894280	−	0.447507i	$-0.852312\pi$
$863$	−45344.0			−1.78856			−0.894280	+	0.447507i	$0.852312\pi$
$864$		0			0
$865$	−40236.0			−1.58158
$866$		0			0
$867$		0			0
$868$		0			0
$869$	448.000	+	775.959i	0.0174883	+	0.0302907i
$870$		0			0
$871$	−16132.0	+	27941.4i	−0.627568	+	1.08698i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9072.00	−	15713.2i	0.350502	−	0.607088i
$876$		0			0
$877$	4389.00	+	7601.97i	0.168992	+	0.292703i	0.938066	−	0.346457i	$-0.112615\pi$
$877$	4389.00	+	7601.97i	0.168992	+	0.292703i	−0.769074	+	0.639160i	$0.779282\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4142.00			0.158397			0.0791984	−	0.996859i	$-0.474764\pi$
$881$	4142.00			0.158397			0.0791984	+	0.996859i	$0.474764\pi$
$882$		0			0
$883$	22076.0			0.841355			0.420678	−	0.907210i	$-0.361792\pi$
$883$	22076.0			0.841355			0.420678	+	0.907210i	$0.361792\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20188.0	−	34966.6i	−0.764201	−	1.32364i	−0.940668	−	0.339329i	$-0.889800\pi$
$887$	−20188.0	−	34966.6i	−0.764201	−	1.32364i	0.176466	−	0.984307i	$-0.443533\pi$
$888$		0			0
$889$	20928.0	−	36248.4i	0.789542	−	1.36753i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11040.0	−	19121.8i	0.413706	−	0.716560i
$894$		0			0
$895$	8316.00	+	14403.7i	0.310585	+	0.537948i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11040.0			0.409571
$900$		0			0
$901$	−10660.0			−0.394158
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24318.0	−	42120.0i	−0.893213	−	1.54709i
$906$		0			0
$907$	13198.0	−	22859.6i	0.483167	−	0.836870i	−0.516646	−	0.856199i	$-0.672820\pi$
$907$	13198.0	−	22859.6i	0.483167	−	0.836870i	0.999813	+	0.0193293i	$0.00615309\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12184.0	−	21103.3i	0.443111	−	0.767490i	−0.554808	−	0.831979i	$-0.687208\pi$
$911$	12184.0	−	21103.3i	0.443111	−	0.767490i	0.997918	+	0.0644882i	$0.0205415\pi$
$912$		0			0
$913$	−21112.0	−	36567.1i	−0.765285	−	1.32551i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15648.0			0.563514
$918$		0			0
$919$	−5096.00			−0.182918			−0.0914589	−	0.995809i	$-0.529153\pi$
$919$	−5096.00			−0.182918			−0.0914589	+	0.995809i	$0.529153\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−31672.0	−	54857.5i	−1.12947	−	1.95629i
$924$		0			0
$925$	−1065.00	+	1844.63i	−0.0378562	+	0.0655689i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9247.00	+	16016.3i	−0.326571	+	0.565637i	−0.981829	−	0.189768i	$-0.939226\pi$
$929$	−9247.00	+	16016.3i	−0.326571	+	0.565637i	0.655258	+	0.755405i	$0.272560\pi$
$930$		0			0
$931$	−10718.0	−	18564.1i	−0.377302	−	0.653506i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	32144.0			1.12430
$936$		0			0
$937$	−33222.0			−1.15829			−0.579144	−	0.815225i	$-0.696613\pi$
$937$	−33222.0			−1.15829			−0.579144	+	0.815225i	$0.696613\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	13923.0	+	24115.3i	0.482335	+	0.835428i	0.999794	−	0.0202796i	$-0.00645562\pi$
$941$	13923.0	+	24115.3i	0.482335	+	0.835428i	−0.517460	+	0.855708i	$0.673122\pi$
$942$		0			0
$943$	−1128.00	+	1953.75i	−0.0389531	+	0.0674687i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20526.0	−	35552.1i	0.704335	−	1.21994i	−0.262596	−	0.964906i	$-0.584579\pi$
$947$	20526.0	−	35552.1i	0.704335	−	1.21994i	0.966931	−	0.255038i	$-0.0820881\pi$
$948$		0			0
$949$	−36926.0	−	63957.7i	−1.26309	−	2.18773i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5706.00			−0.193951			−0.0969756	−	0.995287i	$-0.530917\pi$
$953$	−5706.00			−0.193951			−0.0969756	+	0.995287i	$0.530917\pi$
$954$		0			0
$955$	2688.00			0.0910802
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−18360.0	−	31800.5i	−0.618222	−	1.07079i
$960$		0			0
$961$	11695.5	−	20257.2i	0.392585	−	0.679977i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	33614.0	−	58221.2i	1.12132	−	1.94218i
$966$		0			0
$967$	19676.0	+	34079.8i	0.654330	+	1.13333i	0.982061	+	0.188562i	$0.0603828\pi$
$967$	19676.0	+	34079.8i	0.654330	+	1.13333i	−0.327731	+	0.944771i	$0.606284\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	33180.0			1.09660			0.548299	−	0.836282i	$-0.315276\pi$
$971$	33180.0			1.09660			0.548299	+	0.836282i	$0.315276\pi$
$972$		0			0
$973$	−12384.0			−0.408030
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2007.00	−	3476.23i	−0.0657212	−	0.113832i	0.831292	−	0.555835i	$-0.187601\pi$
$977$	−2007.00	−	3476.23i	−0.0657212	−	0.113832i	−0.897014	+	0.442003i	$0.854268\pi$
$978$		0			0
$979$	−3444.00	+	5965.18i	−0.112432	+	0.194738i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10164.0	−	17604.6i	0.329788	−	0.571209i	−0.652682	−	0.757632i	$-0.726356\pi$
$983$	10164.0	−	17604.6i	0.329788	−	0.571209i	0.982470	+	0.186423i	$0.0596895\pi$
$984$		0			0
$985$	−10626.0	−	18404.8i	−0.343728	−	0.595355i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.0000			−0.00102886
$990$		0			0
$991$	11728.0			0.375936			0.187968	−	0.982175i	$-0.439810\pi$
$991$	11728.0			0.375936			0.187968	+	0.982175i	$0.439810\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	35896.0	+	62173.7i	1.14370	+	1.98094i
$996$		0			0
$997$	−25487.0	+	44144.8i	−0.809610	+	1.40229i	0.103524	+	0.994627i	$0.466988\pi$
$997$	−25487.0	+	44144.8i	−0.809610	+	1.40229i	−0.913134	+	0.407659i	$0.866345\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.4.i.k.217.1		2
3.2	odd	2		648.4.i.b.217.1		2
9.2	odd	6		24.4.a.a.1.1	✓	1
9.4	even	3	inner	648.4.i.k.433.1		2
9.5	odd	6		648.4.i.b.433.1		2
9.7	even	3		72.4.a.b.1.1		1
36.7	odd	6		144.4.a.b.1.1		1
36.11	even	6		48.4.a.b.1.1		1
45.2	even	12		600.4.f.b.49.1		2
45.7	odd	12		1800.4.f.q.649.1		2
45.29	odd	6		600.4.a.h.1.1		1
45.34	even	6		1800.4.a.bg.1.1		1
45.38	even	12		600.4.f.b.49.2		2
45.43	odd	12		1800.4.f.q.649.2		2
63.20	even	6		1176.4.a.a.1.1		1
72.11	even	6		192.4.a.g.1.1		1
72.29	odd	6		192.4.a.a.1.1		1
72.43	odd	6		576.4.a.v.1.1		1
72.61	even	6		576.4.a.u.1.1		1
144.11	even	12		768.4.d.b.385.2		2
144.29	odd	12		768.4.d.o.385.2		2
144.83	even	12		768.4.d.b.385.1		2
144.101	odd	12		768.4.d.o.385.1		2
180.47	odd	12		1200.4.f.p.49.2		2
180.83	odd	12		1200.4.f.p.49.1		2
180.119	even	6		1200.4.a.u.1.1		1
252.83	odd	6		2352.4.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.a.a.1.1	✓	1	9.2	odd	6
48.4.a.b.1.1		1	36.11	even	6
72.4.a.b.1.1		1	9.7	even	3
144.4.a.b.1.1		1	36.7	odd	6
192.4.a.a.1.1		1	72.29	odd	6
192.4.a.g.1.1		1	72.11	even	6
576.4.a.u.1.1		1	72.61	even	6
576.4.a.v.1.1		1	72.43	odd	6
600.4.a.h.1.1		1	45.29	odd	6
600.4.f.b.49.1		2	45.2	even	12
600.4.f.b.49.2		2	45.38	even	12
648.4.i.b.217.1		2	3.2	odd	2
648.4.i.b.433.1		2	9.5	odd	6
648.4.i.k.217.1		2	1.1	even	1	trivial
648.4.i.k.433.1		2	9.4	even	3	inner
768.4.d.b.385.1		2	144.83	even	12
768.4.d.b.385.2		2	144.11	even	12
768.4.d.o.385.1		2	144.101	odd	12
768.4.d.o.385.2		2	144.29	odd	12
1176.4.a.a.1.1		1	63.20	even	6
1200.4.a.u.1.1		1	180.119	even	6
1200.4.f.p.49.1		2	180.83	odd	12
1200.4.f.p.49.2		2	180.47	odd	12
1800.4.a.bg.1.1		1	45.34	even	6
1800.4.f.q.649.1		2	45.7	odd	12
1800.4.f.q.649.2		2	45.43	odd	12
2352.4.a.w.1.1		1	252.83	odd	6

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(7.00000 + 12.1244i) q^{5} +(12.0000 - 20.7846i) q^{7} +O(q^{10})\)	\(q+(7.00000 + 12.1244i) q^{5} +(12.0000 - 20.7846i) q^{7} +(-14.0000 + 24.2487i) q^{11} +(37.0000 + 64.0859i) q^{13} -82.0000 q^{17} +92.0000 q^{19} +(4.00000 + 6.92820i) q^{23} +(-35.5000 + 61.4878i) q^{25} +(-69.0000 + 119.512i) q^{29} +(-40.0000 - 69.2820i) q^{31} +336.000 q^{35} +30.0000 q^{37} +(141.000 + 244.219i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(120.000 - 207.846i) q^{47} +(-116.500 - 201.784i) q^{49} +130.000 q^{53} -392.000 q^{55} +(298.000 + 516.151i) q^{59} +(109.000 - 188.794i) q^{61} +(-518.000 + 897.202i) q^{65} +(218.000 + 377.587i) q^{67} -856.000 q^{71} -998.000 q^{73} +(336.000 + 581.969i) q^{77} +(16.0000 - 27.7128i) q^{79} +(-754.000 + 1305.97i) q^{83} +(-574.000 - 994.197i) q^{85} +246.000 q^{89} +1776.00 q^{91} +(644.000 + 1115.44i) q^{95} +(-433.000 + 749.978i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 14 q^{5} + 24 q^{7}+O(q^{10}) \) 2 * q + 14 * q^5 + 24 * q^7	\( 2 q + 14 q^{5} + 24 q^{7} - 28 q^{11} + 74 q^{13} - 164 q^{17} + 184 q^{19} + 8 q^{23} - 71 q^{25} - 138 q^{29} - 80 q^{31} + 672 q^{35} + 60 q^{37} + 282 q^{41} - 4 q^{43} + 240 q^{47} - 233 q^{49} + 260 q^{53} - 784 q^{55} + 596 q^{59} + 218 q^{61} - 1036 q^{65} + 436 q^{67} - 1712 q^{71} - 1996 q^{73} + 672 q^{77} + 32 q^{79} - 1508 q^{83} - 1148 q^{85} + 492 q^{89} + 3552 q^{91} + 1288 q^{95} - 866 q^{97}+O(q^{100}) \) 2 * q + 14 * q^5 + 24 * q^7 - 28 * q^11 + 74 * q^13 - 164 * q^17 + 184 * q^19 + 8 * q^23 - 71 * q^25 - 138 * q^29 - 80 * q^31 + 672 * q^35 + 60 * q^37 + 282 * q^41 - 4 * q^43 + 240 * q^47 - 233 * q^49 + 260 * q^53 - 784 * q^55 + 596 * q^59 + 218 * q^61 - 1036 * q^65 + 436 * q^67 - 1712 * q^71 - 1996 * q^73 + 672 * q^77 + 32 * q^79 - 1508 * q^83 - 1148 * q^85 + 492 * q^89 + 3552 * q^91 + 1288 * q^95 - 866 * q^97

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