LMFDB - Embedded newform 1296.3.o.n.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,3,Mod(271,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1296.271");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1296.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$35.3134422611$
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 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1296.271
Dual form			1296.3.o.n.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00000 - 5.19615i) q^{5} +(-6.00000 + 3.46410i) q^{7} +O(q^{10})$	$q+(3.00000 - 5.19615i) q^{5} +(-6.00000 + 3.46410i) q^{7} +(-18.0000 + 10.3923i) q^{11} +(7.00000 - 12.1244i) q^{13} +6.00000 q^{17} +6.92820i q^{19} +(-5.50000 - 9.52628i) q^{25} +(15.0000 + 25.9808i) q^{29} +(18.0000 + 10.3923i) q^{31} +41.5692i q^{35} +26.0000 q^{37} +(-27.0000 + 46.7654i) q^{41} +(18.0000 - 10.3923i) q^{43} +(36.0000 - 20.7846i) q^{47} +(-0.500000 + 0.866025i) q^{49} +18.0000 q^{53} +124.708i q^{55} +(-18.0000 - 10.3923i) q^{59} +(35.0000 + 60.6218i) q^{61} +(-42.0000 - 72.7461i) q^{65} +(102.000 + 58.8897i) q^{67} -83.1384i q^{71} +82.0000 q^{73} +(72.0000 - 124.708i) q^{77} +(-66.0000 + 38.1051i) q^{79} +(18.0000 - 10.3923i) q^{83} +(18.0000 - 31.1769i) q^{85} -114.000 q^{89} +96.9948i q^{91} +(36.0000 + 20.7846i) q^{95} +(-17.0000 - 29.4449i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{5} - 12 q^{7}+O(q^{10}) $ 2 * q + 6 * q^5 - 12 * q^7	$ 2 q + 6 q^{5} - 12 q^{7} - 36 q^{11} + 14 q^{13} + 12 q^{17} - 11 q^{25} + 30 q^{29} + 36 q^{31} + 52 q^{37} - 54 q^{41} + 36 q^{43} + 72 q^{47} - q^{49} + 36 q^{53} - 36 q^{59} + 70 q^{61} - 84 q^{65} + 204 q^{67} + 164 q^{73} + 144 q^{77} - 132 q^{79} + 36 q^{83} + 36 q^{85} - 228 q^{89} + 72 q^{95} - 34 q^{97}+O(q^{100}) $ 2 * q + 6 * q^5 - 12 * q^7 - 36 * q^11 + 14 * q^13 + 12 * q^17 - 11 * q^25 + 30 * q^29 + 36 * q^31 + 52 * q^37 - 54 * q^41 + 36 * q^43 + 72 * q^47 - q^49 + 36 * q^53 - 36 * q^59 + 70 * q^61 - 84 * q^65 + 204 * q^67 + 164 * q^73 + 144 * q^77 - 132 * q^79 + 36 * q^83 + 36 * q^85 - 228 * q^89 + 72 * q^95 - 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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
$5$	3.00000	−	5.19615i	0.600000	−	1.03923i	−0.392820	−	0.919615i	$-0.628501\pi$
$5$	3.00000	−	5.19615i	0.600000	−	1.03923i	0.992820	−	0.119615i	$-0.0381661\pi$
$6$		0			0
$7$	−6.00000	+	3.46410i	−0.857143	+	0.494872i	−0.863054	−	0.505111i	$-0.831452\pi$
$7$	−6.00000	+	3.46410i	−0.857143	+	0.494872i	0.00591161	+	0.999983i	$0.498118\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−18.0000	+	10.3923i	−1.63636	+	0.944755i	−0.654293	+	0.756241i	$0.727034\pi$
$11$	−18.0000	+	10.3923i	−1.63636	+	0.944755i	−0.982071	+	0.188514i	$0.939633\pi$
$12$		0			0
$13$	7.00000	−	12.1244i	0.538462	−	0.932643i	−0.460526	−	0.887646i	$-0.652339\pi$
$13$	7.00000	−	12.1244i	0.538462	−	0.932643i	0.998987	−	0.0449963i	$-0.0143276\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.00000			0.352941			0.176471	−	0.984306i	$-0.443532\pi$
$17$	6.00000			0.352941			0.176471	+	0.984306i	$0.443532\pi$
$18$		0			0
$19$			6.92820i			0.364642i	0.983239	+	0.182321i	$0.0583610\pi$
$19$			6.92820i			0.364642i	−0.983239	+	0.182321i	$0.941639\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	15.0000	+	25.9808i	0.517241	+	0.895888i	0.999799	+	0.0200244i	$0.00637439\pi$
$29$	15.0000	+	25.9808i	0.517241	+	0.895888i	−0.482558	+	0.875864i	$0.660292\pi$
$30$		0			0
$31$	18.0000	+	10.3923i	0.580645	+	0.335236i	0.761390	−	0.648294i	$-0.224517\pi$
$31$	18.0000	+	10.3923i	0.580645	+	0.335236i	−0.180745	+	0.983530i	$0.557851\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			41.5692i			1.18769i
$36$		0			0
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−27.0000	+	46.7654i	−0.658537	+	1.14062i	0.322458	+	0.946584i	$0.395491\pi$
$41$	−27.0000	+	46.7654i	−0.658537	+	1.14062i	−0.980995	+	0.194035i	$0.937842\pi$
$42$		0			0
$43$	18.0000	−	10.3923i	0.418605	−	0.241682i	−0.275875	−	0.961193i	$-0.588968\pi$
$43$	18.0000	−	10.3923i	0.418605	−	0.241682i	0.694480	+	0.719512i	$0.255634\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	36.0000	−	20.7846i	0.765957	−	0.442226i	−0.0654732	−	0.997854i	$-0.520856\pi$
$47$	36.0000	−	20.7846i	0.765957	−	0.442226i	0.831431	+	0.555629i	$0.187522\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0102041	+	0.0176740i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	18.0000			0.339623			0.169811	−	0.985477i	$-0.445684\pi$
$53$	18.0000			0.339623			0.169811	+	0.985477i	$0.445684\pi$
$54$		0			0
$55$			124.708i			2.26741i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−18.0000	−	10.3923i	−0.305085	−	0.176141i	0.339640	−	0.940555i	$-0.389695\pi$
$59$	−18.0000	−	10.3923i	−0.305085	−	0.176141i	−0.644725	+	0.764415i	$0.723028\pi$
$60$		0			0
$61$	35.0000	+	60.6218i	0.573770	+	0.993800i	0.996174	+	0.0873918i	$0.0278532\pi$
$61$	35.0000	+	60.6218i	0.573770	+	0.993800i	−0.422404	+	0.906408i	$0.638813\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−42.0000	−	72.7461i	−0.646154	−	1.11917i
$66$		0			0
$67$	102.000	+	58.8897i	1.52239	+	0.878951i	0.999650	+	0.0264578i	$0.00842278\pi$
$67$	102.000	+	58.8897i	1.52239	+	0.878951i	0.522738	+	0.852493i	$0.324911\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	83.1384i		−	1.17096i	−0.810685	−	0.585482i	$-0.800905\pi$
$71$		−	83.1384i		−	1.17096i	0.810685	−	0.585482i	$-0.199095\pi$
$72$		0			0
$73$	82.0000			1.12329			0.561644	−	0.827379i	$-0.310169\pi$
$73$	82.0000			1.12329			0.561644	+	0.827379i	$0.310169\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	72.0000	−	124.708i	0.935065	−	1.61958i
$78$		0			0
$79$	−66.0000	+	38.1051i	−0.835443	+	0.482343i	−0.855713	−	0.517451i	$-0.826881\pi$
$79$	−66.0000	+	38.1051i	−0.835443	+	0.482343i	0.0202696	+	0.999795i	$0.493548\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	18.0000	−	10.3923i	0.216867	−	0.125208i	−0.387631	−	0.921814i	$-0.626707\pi$
$83$	18.0000	−	10.3923i	0.216867	−	0.125208i	0.604499	+	0.796606i	$0.293373\pi$
$84$		0			0
$85$	18.0000	−	31.1769i	0.211765	−	0.366787i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−114.000			−1.28090			−0.640449	−	0.768000i	$-0.721252\pi$
$89$	−114.000			−1.28090			−0.640449	+	0.768000i	$0.721252\pi$
$90$		0			0
$91$			96.9948i			1.06588i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	36.0000	+	20.7846i	0.378947	+	0.218785i
$96$		0			0
$97$	−17.0000	−	29.4449i	−0.175258	−	0.303555i	0.764993	−	0.644039i	$-0.222743\pi$
$97$	−17.0000	−	29.4449i	−0.175258	−	0.303555i	−0.940250	+	0.340484i	$0.889409\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.0891089	−	0.154341i	0.818026	−	0.575182i	$-0.195069\pi$
$101$	−9.00000	−	15.5885i	−0.0891089	−	0.154341i	−0.907135	+	0.420840i	$0.861735\pi$
$102$		0			0
$103$	114.000	+	65.8179i	1.10680	+	0.639009i	0.937998	−	0.346642i	$-0.112678\pi$
$103$	114.000	+	65.8179i	1.10680	+	0.639009i	0.168798	+	0.985651i	$0.446011\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	145.492i		−	1.35974i	−0.733332	−	0.679870i	$-0.762036\pi$
$107$		−	145.492i		−	1.35974i	0.733332	−	0.679870i	$-0.237964\pi$
$108$		0			0
$109$	34.0000			0.311927			0.155963	−	0.987763i	$-0.450152\pi$
$109$	34.0000			0.311927			0.155963	+	0.987763i	$0.450152\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−39.0000	+	67.5500i	−0.345133	+	0.597787i	−0.985378	−	0.170383i	$-0.945499\pi$
$113$	−39.0000	+	67.5500i	−0.345133	+	0.597787i	0.640245	+	0.768171i	$0.278833\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−36.0000	+	20.7846i	−0.302521	+	0.174661i
$120$		0			0
$121$	155.500	−	269.334i	1.28512	−	2.22590i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	84.0000			0.672000
$126$		0			0
$127$			103.923i			0.818292i	0.912469	+	0.409146i	$0.134173\pi$
$127$			103.923i			0.818292i	−0.912469	+	0.409146i	$0.865827\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	90.0000	+	51.9615i	0.687023	+	0.396653i	0.802496	−	0.596658i	$-0.203505\pi$
$131$	90.0000	+	51.9615i	0.687023	+	0.396653i	−0.115473	+	0.993311i	$0.536838\pi$
$132$		0			0
$133$	−24.0000	−	41.5692i	−0.180451	−	0.312551i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	93.0000	+	161.081i	0.678832	+	1.17577i	0.975333	+	0.220739i	$0.0708469\pi$
$137$	93.0000	+	161.081i	0.678832	+	1.17577i	−0.296501	+	0.955033i	$0.595820\pi$
$138$		0			0
$139$	42.0000	+	24.2487i	0.302158	+	0.174451i	0.643412	−	0.765520i	$-0.277518\pi$
$139$	42.0000	+	24.2487i	0.302158	+	0.174451i	−0.341254	+	0.939971i	$0.610852\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			290.985i			2.03486i
$144$		0			0
$145$	180.000			1.24138
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−93.0000	+	161.081i	−0.624161	+	1.08108i	0.364541	+	0.931187i	$0.381226\pi$
$149$	−93.0000	+	161.081i	−0.624161	+	1.08108i	−0.988702	+	0.149892i	$0.952108\pi$
$150$		0			0
$151$	−30.0000	+	17.3205i	−0.198675	+	0.114705i	−0.596038	−	0.802957i	$-0.703259\pi$
$151$	−30.0000	+	17.3205i	−0.198675	+	0.114705i	0.397362	+	0.917662i	$0.369926\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	108.000	−	62.3538i	0.696774	−	0.402283i
$156$		0			0
$157$	−85.0000	+	147.224i	−0.541401	+	0.937735i	0.457423	+	0.889249i	$0.348773\pi$
$157$	−85.0000	+	147.224i	−0.541401	+	0.937735i	−0.998824	+	0.0484851i	$0.984561\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$			284.056i			1.74268i	0.490683	+	0.871338i	$0.336747\pi$
$163$			284.056i			1.74268i	−0.490683	+	0.871338i	$0.663253\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−180.000	−	103.923i	−1.07784	−	0.622294i	−0.147530	−	0.989058i	$-0.547132\pi$
$167$	−180.000	−	103.923i	−1.07784	−	0.622294i	−0.930314	+	0.366764i	$0.880466\pi$
$168$		0			0
$169$	−13.5000	−	23.3827i	−0.0798817	−	0.138359i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−21.0000	−	36.3731i	−0.121387	−	0.210249i	0.798928	−	0.601427i	$-0.205401\pi$
$173$	−21.0000	−	36.3731i	−0.121387	−	0.210249i	−0.920315	+	0.391178i	$0.872068\pi$
$174$		0			0
$175$	66.0000	+	38.1051i	0.377143	+	0.217744i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			145.492i			0.812806i	0.913694	+	0.406403i	$0.133217\pi$
$179$			145.492i			0.812806i	−0.913694	+	0.406403i	$0.866783\pi$
$180$		0			0
$181$	82.0000			0.453039			0.226519	−	0.974007i	$-0.427265\pi$
$181$	82.0000			0.453039			0.226519	+	0.974007i	$0.427265\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	78.0000	−	135.100i	0.421622	−	0.730270i
$186$		0			0
$187$	−108.000	+	62.3538i	−0.577540	+	0.333443i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−288.000	+	166.277i	−1.50785	+	0.870560i	−0.507895	+	0.861419i	$0.669576\pi$
$191$	−288.000	+	166.277i	−1.50785	+	0.870560i	−0.999958	+	0.00914069i	$0.997090\pi$
$192$		0			0
$193$	47.0000	−	81.4064i	0.243523	−	0.421795i	−0.718192	−	0.695845i	$-0.755030\pi$
$193$	47.0000	−	81.4064i	0.243523	−	0.421795i	0.961715	+	0.274050i	$0.0883634\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	258.000			1.30964			0.654822	−	0.755783i	$-0.272743\pi$
$197$	258.000			1.30964			0.654822	+	0.755783i	$0.272743\pi$
$198$		0			0
$199$			117.779i			0.591857i	0.955210	+	0.295928i	$0.0956289\pi$
$199$			117.779i			0.591857i	−0.955210	+	0.295928i	$0.904371\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−180.000	−	103.923i	−0.886700	−	0.511936i
$204$		0			0
$205$	162.000	+	280.592i	0.790244	+	1.36874i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−72.0000	−	124.708i	−0.344498	−	0.596687i
$210$		0			0
$211$	78.0000	+	45.0333i	0.369668	+	0.213428i	0.673314	−	0.739357i	$-0.264870\pi$
$211$	78.0000	+	45.0333i	0.369668	+	0.213428i	−0.303645	+	0.952785i	$0.598204\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	124.708i		−	0.580036i
$216$		0			0
$217$	−144.000			−0.663594
$218$		0			0
$219$		0			0
$220$		0			0
$221$	42.0000	−	72.7461i	0.190045	−	0.329168i
$222$		0			0
$223$	306.000	−	176.669i	1.37220	−	0.792238i	0.380993	−	0.924578i	$-0.375582\pi$
$223$	306.000	−	176.669i	1.37220	−	0.792238i	0.991204	+	0.132339i	$0.0422489\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−126.000	+	72.7461i	−0.555066	+	0.320468i	−0.751163	−	0.660117i	$-0.770507\pi$
$227$	−126.000	+	72.7461i	−0.555066	+	0.320468i	0.196097	+	0.980585i	$0.437173\pi$
$228$		0			0
$229$	−113.000	+	195.722i	−0.493450	+	0.854680i	−0.999972	−	0.00754710i	$-0.997598\pi$
$229$	−113.000	+	195.722i	−0.493450	+	0.854680i	0.506522	+	0.862227i	$0.330931\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−114.000			−0.489270			−0.244635	−	0.969615i	$-0.578668\pi$
$233$	−114.000			−0.489270			−0.244635	+	0.969615i	$0.578668\pi$
$234$		0			0
$235$		−	249.415i		−	1.06134i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	288.000	+	166.277i	1.20502	+	0.695719i	0.961667	−	0.274219i	$-0.0884192\pi$
$239$	288.000	+	166.277i	1.20502	+	0.695719i	0.243354	+	0.969938i	$0.421752\pi$
$240$		0			0
$241$	−89.0000	−	154.153i	−0.369295	−	0.639637i	0.620161	−	0.784475i	$-0.287067\pi$
$241$	−89.0000	−	154.153i	−0.369295	−	0.639637i	−0.989455	+	0.144838i	$0.953734\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.00000	+	5.19615i	0.0122449	+	0.0212088i
$246$		0			0
$247$	84.0000	+	48.4974i	0.340081	+	0.196346i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	103.923i		−	0.414036i	−0.978337	−	0.207018i	$-0.933624\pi$
$251$		−	103.923i		−	0.414036i	0.978337	−	0.207018i	$-0.0663759\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	129.000	−	223.435i	0.501946	−	0.869395i	−0.498052	−	0.867147i	$-0.665951\pi$
$257$	129.000	−	223.435i	0.501946	−	0.869395i	0.999997	−	0.00224796i	$-0.000715548\pi$
$258$		0			0
$259$	−156.000	+	90.0666i	−0.602317	+	0.347748i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	324.000	−	187.061i	1.23194	−	0.711260i	0.264505	−	0.964384i	$-0.414791\pi$
$263$	324.000	−	187.061i	1.23194	−	0.711260i	0.967434	+	0.253124i	$0.0814580\pi$
$264$		0			0
$265$	54.0000	−	93.5307i	0.203774	−	0.352946i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−510.000			−1.89591			−0.947955	−	0.318403i	$-0.896853\pi$
$269$	−510.000			−1.89591			−0.947955	+	0.318403i	$0.896853\pi$
$270$		0			0
$271$		−	450.333i		−	1.66175i	−0.556462	−	0.830873i	$-0.687842\pi$
$271$		−	450.333i		−	1.66175i	0.556462	−	0.830873i	$-0.312158\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	198.000	+	114.315i	0.720000	+	0.415692i
$276$		0			0
$277$	7.00000	+	12.1244i	0.0252708	+	0.0437702i	0.878384	−	0.477955i	$-0.158622\pi$
$277$	7.00000	+	12.1244i	0.0252708	+	0.0437702i	−0.853113	+	0.521725i	$0.825289\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	177.000	+	306.573i	0.629893	+	1.09101i	0.987573	+	0.157163i	$0.0502347\pi$
$281$	177.000	+	306.573i	0.629893	+	1.09101i	−0.357679	+	0.933844i	$0.616432\pi$
$282$		0			0
$283$	−126.000	−	72.7461i	−0.445230	−	0.257053i	0.260584	−	0.965451i	$-0.416085\pi$
$283$	−126.000	−	72.7461i	−0.445230	−	0.257053i	−0.705813	+	0.708398i	$0.749418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	374.123i		−	1.30356i
$288$		0			0
$289$	−253.000			−0.875433
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−249.000	+	431.281i	−0.849829	+	1.47195i	0.0315309	+	0.999503i	$0.489962\pi$
$293$	−249.000	+	431.281i	−0.849829	+	1.47195i	−0.881360	+	0.472445i	$0.843372\pi$
$294$		0			0
$295$	−108.000	+	62.3538i	−0.366102	+	0.211369i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−72.0000	+	124.708i	−0.239203	+	0.414311i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	420.000			1.37705
$306$		0			0
$307$			187.061i			0.609321i	0.952461	+	0.304660i	$0.0985430\pi$
$307$			187.061i			0.609321i	−0.952461	+	0.304660i	$0.901457\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−36.0000	−	20.7846i	−0.115756	−	0.0668315i	0.441004	−	0.897505i	$-0.354622\pi$
$311$	−36.0000	−	20.7846i	−0.115756	−	0.0668315i	−0.556760	+	0.830673i	$0.687956\pi$
$312$		0			0
$313$	−145.000	−	251.147i	−0.463259	−	0.802388i	0.535862	−	0.844305i	$-0.319987\pi$
$313$	−145.000	−	251.147i	−0.463259	−	0.802388i	−0.999121	+	0.0419176i	$0.986653\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−105.000	−	181.865i	−0.331230	−	0.573708i	0.651523	−	0.758629i	$-0.274130\pi$
$317$	−105.000	−	181.865i	−0.331230	−	0.573708i	−0.982753	+	0.184921i	$0.940797\pi$
$318$		0			0
$319$	−540.000	−	311.769i	−1.69279	−	0.977333i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			41.5692i			0.128697i
$324$		0			0
$325$	−154.000			−0.473846
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−144.000	+	249.415i	−0.437690	+	0.758101i
$330$		0			0
$331$	174.000	−	100.459i	0.525680	−	0.303501i	−0.213576	−	0.976927i	$-0.568511\pi$
$331$	174.000	−	100.459i	0.525680	−	0.303501i	0.739255	+	0.673425i	$0.235178\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	612.000	−	353.338i	1.82687	−	1.05474i
$336$		0			0
$337$	151.000	−	261.540i	0.448071	−	0.776082i	−0.550189	−	0.835040i	$-0.685444\pi$
$337$	151.000	−	261.540i	0.448071	−	0.776082i	0.998260	+	0.0589579i	$0.0187778\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−432.000			−1.26686
$342$		0			0
$343$		−	346.410i		−	1.00994i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−54.0000	−	31.1769i	−0.155620	−	0.0898470i	0.420168	−	0.907446i	$-0.361971\pi$
$347$	−54.0000	−	31.1769i	−0.155620	−	0.0898470i	−0.575788	+	0.817599i	$0.695304\pi$
$348$		0			0
$349$	179.000	+	310.037i	0.512894	+	0.888358i	0.999888	+	0.0149532i	$0.00475994\pi$
$349$	179.000	+	310.037i	0.512894	+	0.888358i	−0.486994	+	0.873405i	$0.661907\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−279.000	−	483.242i	−0.790368	−	1.36896i	−0.925739	−	0.378163i	$-0.876556\pi$
$353$	−279.000	−	483.242i	−0.790368	−	1.36896i	0.135371	−	0.990795i	$-0.456777\pi$
$354$		0			0
$355$	−432.000	−	249.415i	−1.21690	−	0.702578i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			83.1384i			0.231583i	0.993274	+	0.115792i	$0.0369405\pi$
$359$			83.1384i			0.231583i	−0.993274	+	0.115792i	$0.963059\pi$
$360$		0			0
$361$	313.000			0.867036
$362$		0			0
$363$		0			0
$364$		0			0
$365$	246.000	−	426.084i	0.673973	−	1.16735i
$366$		0			0
$367$	−186.000	+	107.387i	−0.506812	+	0.292608i	−0.731522	−	0.681818i	$-0.761190\pi$
$367$	−186.000	+	107.387i	−0.506812	+	0.292608i	0.224710	+	0.974426i	$0.427856\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−108.000	+	62.3538i	−0.291105	+	0.168070i
$372$		0			0
$373$	−277.000	+	479.778i	−0.742627	+	1.28627i	0.208668	+	0.977987i	$0.433087\pi$
$373$	−277.000	+	479.778i	−0.742627	+	1.28627i	−0.951295	+	0.308282i	$0.900246\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	420.000			1.11406
$378$		0			0
$379$		−	533.472i		−	1.40758i	−0.710410	−	0.703788i	$-0.751490\pi$
$379$		−	533.472i		−	1.40758i	0.710410	−	0.703788i	$-0.248510\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−432.000	−	249.415i	−1.12794	−	0.651215i	−0.184522	−	0.982828i	$-0.559074\pi$
$383$	−432.000	−	249.415i	−1.12794	−	0.651215i	−0.943415	+	0.331613i	$0.892407\pi$
$384$		0			0
$385$	−432.000	−	748.246i	−1.12208	−	1.94350i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	99.0000	+	171.473i	0.254499	+	0.440805i	0.964759	−	0.263134i	$-0.0847562\pi$
$389$	99.0000	+	171.473i	0.254499	+	0.440805i	−0.710261	+	0.703939i	$0.751423\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$			457.261i			1.15762i
$396$		0			0
$397$	−646.000			−1.62720			−0.813602	−	0.581422i	$-0.802496\pi$
$397$	−646.000			−1.62720			−0.813602	+	0.581422i	$0.802496\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	165.000	−	285.788i	0.411471	−	0.712689i	−0.583580	−	0.812056i	$-0.698348\pi$
$401$	165.000	−	285.788i	0.411471	−	0.712689i	0.995051	+	0.0993667i	$0.0316817\pi$
$402$		0			0
$403$	252.000	−	145.492i	0.625310	−	0.361023i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−468.000	+	270.200i	−1.14988	+	0.663882i
$408$		0			0
$409$	−65.0000	+	112.583i	−0.158924	+	0.275265i	−0.934481	−	0.356013i	$-0.884136\pi$
$409$	−65.0000	+	112.583i	−0.158924	+	0.275265i	0.775557	+	0.631278i	$0.217469\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	144.000			0.348668
$414$		0			0
$415$		−	124.708i		−	0.300500i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−306.000	−	176.669i	−0.730310	−	0.421645i	0.0882254	−	0.996101i	$-0.471880\pi$
$419$	−306.000	−	176.669i	−0.730310	−	0.421645i	−0.818536	+	0.574456i	$0.805214\pi$
$420$		0			0
$421$	199.000	+	344.678i	0.472684	+	0.818713i	0.999511	−	0.0312596i	$-0.00995185\pi$
$421$	199.000	+	344.678i	0.472684	+	0.818713i	−0.526827	+	0.849972i	$0.676619\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−33.0000	−	57.1577i	−0.0776471	−	0.134489i
$426$		0			0
$427$	−420.000	−	242.487i	−0.983607	−	0.567886i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			124.708i			0.289345i	0.989480	+	0.144672i	$0.0462128\pi$
$431$			124.708i			0.289345i	−0.989480	+	0.144672i	$0.953787\pi$
$432$		0			0
$433$	−142.000			−0.327945			−0.163972	−	0.986465i	$-0.552431\pi$
$433$	−142.000			−0.327945			−0.163972	+	0.986465i	$0.552431\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	486.000	−	280.592i	1.10706	−	0.639162i	0.168995	−	0.985617i	$-0.445948\pi$
$439$	486.000	−	280.592i	1.10706	−	0.639162i	0.938067	+	0.346455i	$0.112615\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−378.000	+	218.238i	−0.853273	+	0.492637i	−0.861754	−	0.507327i	$-0.830634\pi$
$443$	−378.000	+	218.238i	−0.853273	+	0.492637i	0.00848075	+	0.999964i	$0.497300\pi$
$444$		0			0
$445$	−342.000	+	592.361i	−0.768539	+	1.33115i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	198.000			0.440980			0.220490	−	0.975389i	$-0.429234\pi$
$449$	198.000			0.440980			0.220490	+	0.975389i	$0.429234\pi$
$450$		0			0
$451$		−	1122.37i		−	2.48862i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	504.000	+	290.985i	1.10769	+	0.639526i
$456$		0			0
$457$	223.000	+	386.247i	0.487965	+	0.845180i	0.999904	−	0.0138415i	$-0.00440603\pi$
$457$	223.000	+	386.247i	0.487965	+	0.845180i	−0.511939	+	0.859022i	$0.671073\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	171.000	+	296.181i	0.370933	+	0.642474i	0.989709	−	0.143093i	$-0.0457047\pi$
$461$	171.000	+	296.181i	0.370933	+	0.642474i	−0.618777	+	0.785567i	$0.712371\pi$
$462$		0			0
$463$	−138.000	−	79.6743i	−0.298056	−	0.172083i	0.343513	−	0.939148i	$-0.388383\pi$
$463$	−138.000	−	79.6743i	−0.298056	−	0.172083i	−0.641569	+	0.767065i	$0.721716\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	394.908i		−	0.845627i	−0.906217	−	0.422813i	$-0.861043\pi$
$467$		−	394.908i		−	0.845627i	0.906217	−	0.422813i	$-0.138957\pi$
$468$		0			0
$469$	−816.000			−1.73987
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−216.000	+	374.123i	−0.456660	+	0.790958i
$474$		0			0
$475$	66.0000	−	38.1051i	0.138947	−	0.0802213i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−684.000	+	394.908i	−1.42797	+	0.824442i	−0.996961	−	0.0779035i	$-0.975177\pi$
$479$	−684.000	+	394.908i	−1.42797	+	0.824442i	−0.431014	+	0.902345i	$0.641844\pi$
$480$		0			0
$481$	182.000	−	315.233i	0.378378	−	0.655371i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−204.000			−0.420619
$486$		0			0
$487$		−	6.92820i		−	0.0142263i	−0.999975	−	0.00711315i	$-0.997736\pi$
$487$		−	6.92820i		−	0.0142263i	0.999975	−	0.00711315i	$-0.00226420\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	558.000	+	322.161i	1.13646	+	0.656133i	0.945551	−	0.325475i	$-0.105524\pi$
$491$	558.000	+	322.161i	1.13646	+	0.656133i	0.190906	+	0.981608i	$0.438858\pi$
$492$		0			0
$493$	90.0000	+	155.885i	0.182556	+	0.316196i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	288.000	+	498.831i	0.579477	+	1.00368i
$498$		0			0
$499$	702.000	+	405.300i	1.40681	+	0.812224i	0.995079	−	0.0990798i	$-0.0315899\pi$
$499$	702.000	+	405.300i	1.40681	+	0.812224i	0.411734	+	0.911304i	$0.364923\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			332.554i			0.661141i	0.943781	+	0.330570i	$0.107241\pi$
$503$			332.554i			0.661141i	−0.943781	+	0.330570i	$0.892759\pi$
$504$		0			0
$505$	−108.000			−0.213861
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−153.000	+	265.004i	−0.300589	+	0.520636i	−0.976270	−	0.216559i	$-0.930517\pi$
$509$	−153.000	+	265.004i	−0.300589	+	0.520636i	0.675680	+	0.737195i	$0.263850\pi$
$510$		0			0
$511$	−492.000	+	284.056i	−0.962818	+	0.555883i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	684.000	−	394.908i	1.32816	−	0.766811i
$516$		0			0
$517$	−432.000	+	748.246i	−0.835590	+	1.44728i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−522.000			−1.00192			−0.500960	−	0.865471i	$-0.667020\pi$
$521$	−522.000			−1.00192			−0.500960	+	0.865471i	$0.667020\pi$
$522$		0			0
$523$			48.4974i			0.0927293i	0.998925	+	0.0463646i	$0.0147636\pi$
$523$			48.4974i			0.0927293i	−0.998925	+	0.0463646i	$0.985236\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	108.000	+	62.3538i	0.204934	+	0.118318i
$528$		0			0
$529$	−264.500	−	458.127i	−0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	378.000	+	654.715i	0.709193	+	1.22836i
$534$		0			0
$535$	−756.000	−	436.477i	−1.41308	−	0.815844i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	20.7846i		−	0.0385614i
$540$		0			0
$541$	802.000			1.48244			0.741220	−	0.671262i	$-0.234248\pi$
$541$	802.000			1.48244			0.741220	+	0.671262i	$0.234248\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	102.000	−	176.669i	0.187156	−	0.324164i
$546$		0			0
$547$	30.0000	−	17.3205i	0.0548446	−	0.0316645i	−0.472327	−	0.881423i	$-0.656586\pi$
$547$	30.0000	−	17.3205i	0.0548446	−	0.0316645i	0.527172	+	0.849759i	$0.323253\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−180.000	+	103.923i	−0.326679	+	0.188608i
$552$		0			0
$553$	264.000	−	457.261i	0.477396	−	0.826874i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	474.000			0.850987			0.425494	−	0.904961i	$-0.360100\pi$
$557$	474.000			0.850987			0.425494	+	0.904961i	$0.360100\pi$
$558$		0			0
$559$		−	290.985i		−	0.520545i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−594.000	−	342.946i	−1.05506	−	0.609140i	−0.131000	−	0.991382i	$-0.541819\pi$
$563$	−594.000	−	342.946i	−1.05506	−	0.609140i	−0.924062	+	0.382242i	$0.875152\pi$
$564$		0			0
$565$	234.000	+	405.300i	0.414159	+	0.717345i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−75.0000	−	129.904i	−0.131810	−	0.228302i	0.792564	−	0.609788i	$-0.208746\pi$
$569$	−75.0000	−	129.904i	−0.131810	−	0.228302i	−0.924374	+	0.381487i	$0.875412\pi$
$570$		0			0
$571$	−582.000	−	336.018i	−1.01926	−	0.588473i	−0.105374	−	0.994433i	$-0.533604\pi$
$571$	−582.000	−	336.018i	−1.01926	−	0.588473i	−0.913891	+	0.405960i	$0.866937\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−46.0000			−0.0797227			−0.0398614	−	0.999205i	$-0.512692\pi$
$577$	−46.0000			−0.0797227			−0.0398614	+	0.999205i	$0.512692\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−72.0000	+	124.708i	−0.123924	+	0.214643i
$582$		0			0
$583$	−324.000	+	187.061i	−0.555746	+	0.320860i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	306.000	−	176.669i	0.521295	−	0.300970i	−0.216170	−	0.976356i	$-0.569356\pi$
$587$	306.000	−	176.669i	0.521295	−	0.300970i	0.737464	+	0.675386i	$0.236023\pi$
$588$		0			0
$589$	−72.0000	+	124.708i	−0.122241	+	0.211728i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−114.000			−0.192243			−0.0961214	−	0.995370i	$-0.530644\pi$
$593$	−114.000			−0.192243			−0.0961214	+	0.995370i	$0.530644\pi$
$594$		0			0
$595$			249.415i			0.419185i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−216.000	−	124.708i	−0.360601	−	0.208193i	0.308743	−	0.951145i	$-0.400092\pi$
$599$	−216.000	−	124.708i	−0.360601	−	0.208193i	−0.669344	+	0.742952i	$0.733425\pi$
$600$		0			0
$601$	−313.000	−	542.132i	−0.520799	−	0.902050i	−0.999707	−	0.0241851i	$-0.992301\pi$
$601$	−313.000	−	542.132i	−0.520799	−	0.902050i	0.478909	−	0.877865i	$-0.341032\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−933.000	−	1616.00i	−1.54215	−	2.67108i
$606$		0			0
$607$	582.000	+	336.018i	0.958814	+	0.553571i	0.895808	−	0.444442i	$-0.146598\pi$
$607$	582.000	+	336.018i	0.958814	+	0.553571i	0.0630061	+	0.998013i	$0.479931\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	581.969i		−	0.952486i
$612$		0			0
$613$	−694.000			−1.13214			−0.566069	−	0.824358i	$-0.691536\pi$
$613$	−694.000			−1.13214			−0.566069	+	0.824358i	$0.691536\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.0000	+	25.9808i	−0.0243112	+	0.0421082i	−0.877925	−	0.478798i	$-0.841073\pi$
$617$	−15.0000	+	25.9808i	−0.0243112	+	0.0421082i	0.853614	+	0.520906i	$0.174406\pi$
$618$		0			0
$619$	294.000	−	169.741i	0.474960	−	0.274218i	−0.243354	−	0.969938i	$-0.578248\pi$
$619$	294.000	−	169.741i	0.474960	−	0.274218i	0.718314	+	0.695719i	$0.244914\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	684.000	−	394.908i	1.09791	−	0.633881i
$624$		0			0
$625$	389.500	−	674.634i	0.623200	−	1.07941i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	156.000			0.248013
$630$		0			0
$631$			464.190i			0.735641i	0.929897	+	0.367821i	$0.119896\pi$
$631$			464.190i			0.735641i	−0.929897	+	0.367821i	$0.880104\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	540.000	+	311.769i	0.850394	+	0.490975i
$636$		0			0
$637$	7.00000	+	12.1244i	0.0109890	+	0.0190335i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−195.000	−	337.750i	−0.304212	−	0.526911i	0.672873	−	0.739758i	$-0.265060\pi$
$641$	−195.000	−	337.750i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931727\pi$
$642$		0			0
$643$	−702.000	−	405.300i	−1.09176	−	0.630326i	−0.157714	−	0.987485i	$-0.550412\pi$
$643$	−702.000	−	405.300i	−1.09176	−	0.630326i	−0.934044	+	0.357158i	$0.883746\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			581.969i			0.899489i	0.893157	+	0.449744i	$0.148485\pi$
$647$			581.969i			0.899489i	−0.893157	+	0.449744i	$0.851515\pi$
$648$		0			0
$649$	432.000			0.665639
$650$		0			0
$651$		0			0
$652$		0			0
$653$	387.000	−	670.304i	0.592649	−	1.02650i	−0.401225	−	0.915980i	$-0.631415\pi$
$653$	387.000	−	670.304i	0.592649	−	1.02650i	0.993874	−	0.110519i	$-0.0352513\pi$
$654$		0			0
$655$	540.000	−	311.769i	0.824427	−	0.475983i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	198.000	−	114.315i	0.300455	−	0.173468i	−0.342192	−	0.939630i	$-0.611169\pi$
$659$	198.000	−	114.315i	0.300455	−	0.173468i	0.642647	+	0.766162i	$0.277836\pi$
$660$		0			0
$661$	227.000	−	393.176i	0.343419	−	0.594819i	−0.641646	−	0.767001i	$-0.721748\pi$
$661$	227.000	−	393.176i	0.343419	−	0.594819i	0.985065	+	0.172182i	$0.0550816\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−288.000			−0.433083
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1260.00	−	727.461i	−1.87779	−	1.08415i
$672$		0			0
$673$	−217.000	−	375.855i	−0.322437	−	0.558477i	0.658553	−	0.752534i	$-0.271169\pi$
$673$	−217.000	−	375.855i	−0.322437	−	0.558477i	−0.980990	+	0.194057i	$0.937835\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−117.000	−	202.650i	−0.172821	−	0.299335i	0.766584	−	0.642144i	$-0.221955\pi$
$677$	−117.000	−	202.650i	−0.172821	−	0.299335i	−0.939405	+	0.342809i	$0.888622\pi$
$678$		0			0
$679$	204.000	+	117.779i	0.300442	+	0.173460i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	270.200i		−	0.395608i	−0.980242	−	0.197804i	$-0.936619\pi$
$683$		−	270.200i		−	0.395608i	0.980242	−	0.197804i	$-0.0633809\pi$
$684$		0			0
$685$	1116.00			1.62920
$686$		0			0
$687$		0			0
$688$		0			0
$689$	126.000	−	218.238i	0.182874	−	0.316747i
$690$		0			0
$691$	−18.0000	+	10.3923i	−0.0260492	+	0.0150395i	−0.512968	−	0.858408i	$-0.671454\pi$
$691$	−18.0000	+	10.3923i	−0.0260492	+	0.0150395i	0.486919	+	0.873447i	$0.338121\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	252.000	−	145.492i	0.362590	−	0.209341i
$696$		0			0
$697$	−162.000	+	280.592i	−0.232425	+	0.402571i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1074.00			1.53210			0.766049	−	0.642783i	$-0.222220\pi$
$701$	1074.00			1.53210			0.766049	+	0.642783i	$0.222220\pi$
$702$		0			0
$703$			180.133i			0.256235i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	108.000	+	62.3538i	0.152758	+	0.0881949i
$708$		0			0
$709$	−449.000	−	777.691i	−0.633286	−	1.09688i	−0.986875	−	0.161483i	$-0.948372\pi$
$709$	−449.000	−	777.691i	−0.633286	−	1.09688i	0.353589	−	0.935401i	$-0.384961\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	1512.00	+	872.954i	2.11469	+	1.22091i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	956.092i		−	1.32975i	−0.746954	−	0.664876i	$-0.768484\pi$
$719$		−	956.092i		−	1.32975i	0.746954	−	0.664876i	$-0.231516\pi$
$720$		0			0
$721$	−912.000			−1.26491
$722$		0			0
$723$		0			0
$724$		0			0
$725$	165.000	−	285.788i	0.227586	−	0.394191i
$726$		0			0
$727$	−702.000	+	405.300i	−0.965612	+	0.557496i	−0.897896	−	0.440208i	$-0.854905\pi$
$727$	−702.000	+	405.300i	−0.965612	+	0.557496i	−0.0677164	+	0.997705i	$0.521571\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	108.000	−	62.3538i	0.147743	−	0.0852994i
$732$		0			0
$733$	−185.000	+	320.429i	−0.252387	+	0.437148i	−0.964183	−	0.265239i	$-0.914549\pi$
$733$	−185.000	+	320.429i	−0.252387	+	0.437148i	0.711795	+	0.702387i	$0.247882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2448.00			−3.32157
$738$		0			0
$739$			852.169i			1.15314i	0.817048	+	0.576569i	$0.195609\pi$
$739$			852.169i			1.15314i	−0.817048	+	0.576569i	$0.804391\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1188.00	+	685.892i	1.59892	+	0.923139i	0.991695	+	0.128611i	$0.0410520\pi$
$743$	1188.00	+	685.892i	1.59892	+	0.923139i	0.607228	+	0.794527i	$0.292281\pi$
$744$		0			0
$745$	558.000	+	966.484i	0.748993	+	1.29729i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	504.000	+	872.954i	0.672897	+	1.16549i
$750$		0			0
$751$	66.0000	+	38.1051i	0.0878828	+	0.0507392i	0.543297	−	0.839540i	$-0.317176\pi$
$751$	66.0000	+	38.1051i	0.0878828	+	0.0507392i	−0.455415	+	0.890279i	$0.650509\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			207.846i			0.275293i
$756$		0			0
$757$	514.000			0.678996			0.339498	−	0.940607i	$-0.389743\pi$
$757$	514.000			0.678996			0.339498	+	0.940607i	$0.389743\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−483.000	+	836.581i	−0.634691	+	1.09932i	0.351889	+	0.936042i	$0.385539\pi$
$761$	−483.000	+	836.581i	−0.634691	+	1.09932i	−0.986580	+	0.163276i	$0.947794\pi$
$762$		0			0
$763$	−204.000	+	117.779i	−0.267366	+	0.154364i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−252.000	+	145.492i	−0.328553	+	0.189690i
$768$		0			0
$769$	479.000	−	829.652i	0.622887	−	1.07887i	−0.366059	−	0.930592i	$-0.619293\pi$
$769$	479.000	−	829.652i	0.622887	−	1.07887i	0.988945	−	0.148280i	$-0.0473736\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	546.000			0.706339			0.353169	−	0.935559i	$-0.385104\pi$
$773$	546.000			0.706339			0.353169	+	0.935559i	$0.385104\pi$
$774$		0			0
$775$		−	228.631i		−	0.295007i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−324.000	−	187.061i	−0.415918	−	0.240130i
$780$		0			0
$781$	864.000	+	1496.49i	1.10627	+	1.91612i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	510.000	+	883.346i	0.649682	+	1.12528i
$786$		0			0
$787$	210.000	+	121.244i	0.266836	+	0.154058i	0.627449	−	0.778658i	$-0.284099\pi$
$787$	210.000	+	121.244i	0.266836	+	0.154058i	−0.360613	+	0.932716i	$0.617432\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	540.400i		−	0.683186i
$792$		0			0
$793$	980.000			1.23581
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−669.000	+	1158.74i	−0.839398	+	1.45388i	0.0510012	+	0.998699i	$0.483759\pi$
$797$	−669.000	+	1158.74i	−0.839398	+	1.45388i	−0.890399	+	0.455181i	$0.849575\pi$
$798$		0			0
$799$	216.000	−	124.708i	0.270338	−	0.156080i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1476.00	+	852.169i	−1.83811	+	1.06123i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	966.000			1.19407			0.597033	−	0.802216i	$-0.296346\pi$
$809$	966.000			1.19407			0.597033	+	0.802216i	$0.296346\pi$
$810$		0			0
$811$			1517.28i			1.87087i	0.353497	+	0.935436i	$0.384992\pi$
$811$			1517.28i			1.87087i	−0.353497	+	0.935436i	$0.615008\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1476.00	+	852.169i	1.81104	+	1.04561i
$816$		0			0
$817$	72.0000	+	124.708i	0.0881273	+	0.152641i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	111.000	+	192.258i	0.135201	+	0.234175i	0.925674	−	0.378322i	$-0.123499\pi$
$821$	111.000	+	192.258i	0.135201	+	0.234175i	−0.790473	+	0.612497i	$0.790165\pi$
$822$		0			0
$823$	1110.00	+	640.859i	1.34872	+	0.778686i	0.988069	−	0.154013i	$-0.0492197\pi$
$823$	1110.00	+	640.859i	1.34872	+	0.778686i	0.360655	+	0.932699i	$0.382553\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1434.14i			1.73415i	0.498182	+	0.867073i	$0.334001\pi$
$827$			1434.14i			1.73415i	−0.498182	+	0.867073i	$0.665999\pi$
$828$		0			0
$829$	226.000			0.272618			0.136309	−	0.990666i	$-0.456476\pi$
$829$	226.000			0.272618			0.136309	+	0.990666i	$0.456476\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.00000	+	5.19615i	−0.00360144	+	0.00623788i
$834$		0			0
$835$	−1080.00	+	623.538i	−1.29341	+	0.746752i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	432.000	−	249.415i	0.514899	−	0.297277i	−0.219946	−	0.975512i	$-0.570588\pi$
$839$	432.000	−	249.415i	0.514899	−	0.297277i	0.734845	+	0.678235i	$0.237255\pi$
$840$		0			0
$841$	−29.5000	+	51.0955i	−0.0350773	+	0.0607556i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−162.000			−0.191716
$846$		0			0
$847$			2154.67i			2.54389i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	35.0000	+	60.6218i	0.0410317	+	0.0710689i	0.885812	−	0.464044i	$-0.153602\pi$
$853$	35.0000	+	60.6218i	0.0410317	+	0.0710689i	−0.844780	+	0.535113i	$0.820269\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0000	+	36.3731i	0.0245041	+	0.0424423i	0.878017	−	0.478629i	$-0.158866\pi$
$857$	21.0000	+	36.3731i	0.0245041	+	0.0424423i	−0.853513	+	0.521071i	$0.825533\pi$
$858$		0			0
$859$	798.000	+	460.726i	0.928987	+	0.536351i	0.886491	−	0.462746i	$-0.153136\pi$
$859$	798.000	+	460.726i	0.928987	+	0.536351i	0.0424961	+	0.999097i	$0.486469\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	166.277i		−	0.192673i	−0.995349	−	0.0963365i	$-0.969287\pi$
$863$		−	166.277i		−	0.192673i	0.995349	−	0.0963365i	$-0.0307125\pi$
$864$		0			0
$865$	−252.000			−0.291329
$866$		0			0
$867$		0			0
$868$		0			0
$869$	792.000	−	1371.78i	0.911392	−	1.57858i
$870$		0			0
$871$	1428.00	−	824.456i	1.63949	−	0.946563i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−504.000	+	290.985i	−0.576000	+	0.332554i
$876$		0			0
$877$	83.0000	−	143.760i	0.0946408	−	0.163923i	−0.814818	−	0.579717i	$-0.803163\pi$
$877$	83.0000	−	143.760i	0.0946408	−	0.163923i	0.909459	+	0.415794i	$0.136496\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	702.000			0.796822			0.398411	−	0.917207i	$-0.369562\pi$
$881$	702.000			0.796822			0.398411	+	0.917207i	$0.369562\pi$
$882$		0			0
$883$		−	630.466i		−	0.714005i	−0.934103	−	0.357003i	$-0.883799\pi$
$883$		−	630.466i		−	0.714005i	0.934103	−	0.357003i	$-0.116201\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1116.00	−	644.323i	−1.25817	−	0.726407i	−0.285454	−	0.958392i	$-0.592144\pi$
$887$	−1116.00	−	644.323i	−1.25817	−	0.726407i	−0.972719	+	0.231985i	$0.925478\pi$
$888$		0			0
$889$	−360.000	−	623.538i	−0.404949	−	0.701393i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	144.000	+	249.415i	0.161254	+	0.279300i
$894$		0			0
$895$	756.000	+	436.477i	0.844693	+	0.487684i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			623.538i			0.693591i
$900$		0			0
$901$	108.000			0.119867
$902$		0			0
$903$		0			0
$904$		0			0
$905$	246.000	−	426.084i	0.271823	−	0.470812i
$906$		0			0
$907$	−1254.00	+	723.997i	−1.38258	+	0.798233i	−0.992464	−	0.122533i	$-0.960898\pi$
$907$	−1254.00	+	723.997i	−1.38258	+	0.798233i	−0.390115	+	0.920766i	$0.627565\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−288.000	+	166.277i	−0.316136	+	0.182521i	−0.649669	−	0.760217i	$-0.725093\pi$
$911$	−288.000	+	166.277i	−0.316136	+	0.182521i	0.333533	+	0.942738i	$0.391759\pi$
$912$		0			0
$913$	−216.000	+	374.123i	−0.236583	+	0.409773i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−720.000			−0.785169
$918$		0			0
$919$		−	561.184i		−	0.610647i	−0.952249	−	0.305323i	$-0.901235\pi$
$919$		−	561.184i		−	0.610647i	0.952249	−	0.305323i	$-0.0987646\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1008.00	−	581.969i	−1.09209	−	0.630519i
$924$		0			0
$925$	−143.000	−	247.683i	−0.154595	−	0.267766i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−219.000	−	379.319i	−0.235737	−	0.408309i	0.723749	−	0.690063i	$-0.242417\pi$
$929$	−219.000	−	379.319i	−0.235737	−	0.408309i	−0.959487	+	0.281754i	$0.909084\pi$
$930$		0			0
$931$	−6.00000	−	3.46410i	−0.00644468	−	0.00372084i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			748.246i			0.800263i
$936$		0			0
$937$	1826.00			1.94877			0.974386	−	0.224881i	$-0.0721992\pi$
$937$	1826.00			1.94877			0.974386	+	0.224881i	$0.0721992\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−165.000	+	285.788i	−0.175345	+	0.303707i	−0.940281	−	0.340400i	$-0.889438\pi$
$941$	−165.000	+	285.788i	−0.175345	+	0.303707i	0.764935	+	0.644107i	$0.222771\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−162.000	+	93.5307i	−0.171067	+	0.0987653i	−0.583089	−	0.812409i	$-0.698156\pi$
$947$	−162.000	+	93.5307i	−0.171067	+	0.0987653i	0.412022	+	0.911174i	$0.364823\pi$
$948$		0			0
$949$	574.000	−	994.197i	0.604847	−	1.04763i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1110.00			1.16474			0.582371	−	0.812923i	$-0.302125\pi$
$953$	1110.00			1.16474			0.582371	+	0.812923i	$0.302125\pi$
$954$		0			0
$955$			1995.32i			2.08934i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1116.00	−	644.323i	−1.16371	−	0.671870i
$960$		0			0
$961$	−264.500	−	458.127i	−0.275234	−	0.476719i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−282.000	−	488.438i	−0.292228	−	0.506154i
$966$		0			0
$967$	−654.000	−	377.587i	−0.676319	−	0.390473i	0.122148	−	0.992512i	$-0.461022\pi$
$967$	−654.000	−	377.587i	−0.676319	−	0.390473i	−0.798467	+	0.602039i	$0.794355\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			394.908i			0.406702i	0.979106	+	0.203351i	$0.0651832\pi$
$971$			394.908i			0.406702i	−0.979106	+	0.203351i	$0.934817\pi$
$972$		0			0
$973$	−336.000			−0.345324
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−459.000	+	795.011i	−0.469806	+	0.813727i	−0.999404	−	0.0345214i	$-0.989009\pi$
$977$	−459.000	+	795.011i	−0.469806	+	0.813727i	0.529598	+	0.848248i	$0.322343\pi$
$978$		0			0
$979$	2052.00	−	1184.72i	2.09602	−	1.21014i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−36.0000	+	20.7846i	−0.0366226	+	0.0211441i	−0.518200	−	0.855260i	$-0.673398\pi$
$983$	−36.0000	+	20.7846i	−0.0366226	+	0.0211441i	0.481577	+	0.876404i	$0.340064\pi$
$984$		0			0
$985$	774.000	−	1340.61i	0.785787	−	1.36102i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		−	48.4974i		−	0.0489379i	−0.999701	−	0.0244689i	$-0.992211\pi$
$991$		−	48.4974i		−	0.0489379i	0.999701	−	0.0244689i	$-0.00778948\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	612.000	+	353.338i	0.615075	+	0.355114i
$996$		0			0
$997$	−277.000	−	479.778i	−0.277834	−	0.481222i	0.693013	−	0.720925i	$-0.256283\pi$
$997$	−277.000	−	479.778i	−0.277834	−	0.481222i	−0.970846	+	0.239704i	$0.922950\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.3.o.n.271.1		2
3.2	odd	2		1296.3.o.a.271.1		2
4.3	odd	2		1296.3.o.p.271.1		2
9.2	odd	6		1296.3.o.c.703.1		2
9.4	even	3		144.3.g.b.127.1		2
9.5	odd	6		48.3.g.a.31.1	✓	2
9.7	even	3		1296.3.o.p.703.1		2
12.11	even	2		1296.3.o.c.271.1		2
36.7	odd	6	inner	1296.3.o.n.703.1		2
36.11	even	6		1296.3.o.a.703.1		2
36.23	even	6		48.3.g.a.31.2	yes	2
36.31	odd	6		144.3.g.b.127.2		2
45.4	even	6		3600.3.e.t.3151.2		2
45.13	odd	12		3600.3.j.i.1999.1		4
45.14	odd	6		1200.3.e.h.751.2		2
45.22	odd	12		3600.3.j.i.1999.3		4
45.23	even	12		1200.3.j.a.799.4		4
45.32	even	12		1200.3.j.a.799.2		4
63.41	even	6		2352.3.m.a.1471.2		2
72.5	odd	6		192.3.g.a.127.2		2
72.13	even	6		576.3.g.i.127.1		2
72.59	even	6		192.3.g.a.127.1		2
72.67	odd	6		576.3.g.i.127.2		2
144.5	odd	12		768.3.b.b.127.2		4
144.13	even	12		2304.3.b.n.127.4		4
144.59	even	12		768.3.b.b.127.4		4
144.67	odd	12		2304.3.b.n.127.3		4
144.77	odd	12		768.3.b.b.127.3		4
144.85	even	12		2304.3.b.n.127.2		4
144.131	even	12		768.3.b.b.127.1		4
144.139	odd	12		2304.3.b.n.127.1		4
180.23	odd	12		1200.3.j.a.799.1		4
180.59	even	6		1200.3.e.h.751.1		2
180.67	even	12		3600.3.j.i.1999.2		4
180.103	even	12		3600.3.j.i.1999.4		4
180.139	odd	6		3600.3.e.t.3151.1		2
180.167	odd	12		1200.3.j.a.799.3		4
252.167	odd	6		2352.3.m.a.1471.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.g.a.31.1	✓	2	9.5	odd	6
48.3.g.a.31.2	yes	2	36.23	even	6
144.3.g.b.127.1		2	9.4	even	3
144.3.g.b.127.2		2	36.31	odd	6
192.3.g.a.127.1		2	72.59	even	6
192.3.g.a.127.2		2	72.5	odd	6
576.3.g.i.127.1		2	72.13	even	6
576.3.g.i.127.2		2	72.67	odd	6
768.3.b.b.127.1		4	144.131	even	12
768.3.b.b.127.2		4	144.5	odd	12
768.3.b.b.127.3		4	144.77	odd	12
768.3.b.b.127.4		4	144.59	even	12
1200.3.e.h.751.1		2	180.59	even	6
1200.3.e.h.751.2		2	45.14	odd	6
1200.3.j.a.799.1		4	180.23	odd	12
1200.3.j.a.799.2		4	45.32	even	12
1200.3.j.a.799.3		4	180.167	odd	12
1200.3.j.a.799.4		4	45.23	even	12
1296.3.o.a.271.1		2	3.2	odd	2
1296.3.o.a.703.1		2	36.11	even	6
1296.3.o.c.271.1		2	12.11	even	2
1296.3.o.c.703.1		2	9.2	odd	6
1296.3.o.n.271.1		2	1.1	even	1	trivial
1296.3.o.n.703.1		2	36.7	odd	6	inner
1296.3.o.p.271.1		2	4.3	odd	2
1296.3.o.p.703.1		2	9.7	even	3
2304.3.b.n.127.1		4	144.139	odd	12
2304.3.b.n.127.2		4	144.85	even	12
2304.3.b.n.127.3		4	144.67	odd	12
2304.3.b.n.127.4		4	144.13	even	12
2352.3.m.a.1471.1		2	252.167	odd	6
2352.3.m.a.1471.2		2	63.41	even	6
3600.3.e.t.3151.1		2	180.139	odd	6
3600.3.e.t.3151.2		2	45.4	even	6
3600.3.j.i.1999.1		4	45.13	odd	12
3600.3.j.i.1999.2		4	180.67	even	12
3600.3.j.i.1999.3		4	45.22	odd	12
3600.3.j.i.1999.4		4	180.103	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1296.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 - 5.19615i) q^{5} +(-6.00000 + 3.46410i) q^{7} +O(q^{10})\)	\(q+(3.00000 - 5.19615i) q^{5} +(-6.00000 + 3.46410i) q^{7} +(-18.0000 + 10.3923i) q^{11} +(7.00000 - 12.1244i) q^{13} +6.00000 q^{17} +6.92820i q^{19} +(-5.50000 - 9.52628i) q^{25} +(15.0000 + 25.9808i) q^{29} +(18.0000 + 10.3923i) q^{31} +41.5692i q^{35} +26.0000 q^{37} +(-27.0000 + 46.7654i) q^{41} +(18.0000 - 10.3923i) q^{43} +(36.0000 - 20.7846i) q^{47} +(-0.500000 + 0.866025i) q^{49} +18.0000 q^{53} +124.708i q^{55} +(-18.0000 - 10.3923i) q^{59} +(35.0000 + 60.6218i) q^{61} +(-42.0000 - 72.7461i) q^{65} +(102.000 + 58.8897i) q^{67} -83.1384i q^{71} +82.0000 q^{73} +(72.0000 - 124.708i) q^{77} +(-66.0000 + 38.1051i) q^{79} +(18.0000 - 10.3923i) q^{83} +(18.0000 - 31.1769i) q^{85} -114.000 q^{89} +96.9948i q^{91} +(36.0000 + 20.7846i) q^{95} +(-17.0000 - 29.4449i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{5} - 12 q^{7}+O(q^{10}) \) 2 * q + 6 * q^5 - 12 * q^7	\( 2 q + 6 q^{5} - 12 q^{7} - 36 q^{11} + 14 q^{13} + 12 q^{17} - 11 q^{25} + 30 q^{29} + 36 q^{31} + 52 q^{37} - 54 q^{41} + 36 q^{43} + 72 q^{47} - q^{49} + 36 q^{53} - 36 q^{59} + 70 q^{61} - 84 q^{65} + 204 q^{67} + 164 q^{73} + 144 q^{77} - 132 q^{79} + 36 q^{83} + 36 q^{85} - 228 q^{89} + 72 q^{95} - 34 q^{97}+O(q^{100}) \) 2 * q + 6 * q^5 - 12 * q^7 - 36 * q^11 + 14 * q^13 + 12 * q^17 - 11 * q^25 + 30 * q^29 + 36 * q^31 + 52 * q^37 - 54 * q^41 + 36 * q^43 + 72 * q^47 - q^49 + 36 * q^53 - 36 * q^59 + 70 * q^61 - 84 * q^65 + 204 * q^67 + 164 * q^73 + 144 * q^77 - 132 * q^79 + 36 * q^83 + 36 * q^85 - 228 * q^89 + 72 * q^95 - 34 * q^97

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