LMFDB - Embedded newform 432.2.i.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.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:	$3.44953736732$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.2.i.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +(-2.50000 - 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +2.00000 q^{17} +4.00000 q^{19} +(0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-4.50000 - 7.79423i) q^{29} +(-0.500000 + 0.866025i) q^{31} +3.00000 q^{35} -6.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{47} +(-1.00000 + 1.73205i) q^{49} -2.00000 q^{53} +5.00000 q^{55} +(-5.50000 + 9.52628i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(2.50000 + 4.33013i) q^{65} +(-0.500000 + 0.866025i) q^{67} +4.00000 q^{71} -2.00000 q^{73} +(-7.50000 + 12.9904i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{83} +(-1.00000 + 1.73205i) q^{85} +18.0000 q^{89} -15.0000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(6.50000 + 11.2583i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} - 3 q^{7}+O(q^{10}) $ 2 * q - q^5 - 3 * q^7	$ 2 q - q^{5} - 3 q^{7} - 5 q^{11} + 5 q^{13} + 4 q^{17} + 8 q^{19} + q^{23} + 4 q^{25} - 9 q^{29} - q^{31} + 6 q^{35} - 12 q^{37} + 3 q^{41} + q^{43} + 3 q^{47} - 2 q^{49} - 4 q^{53} + 10 q^{55} - 11 q^{59} - 7 q^{61} + 5 q^{65} - q^{67} + 8 q^{71} - 4 q^{73} - 15 q^{77} + q^{79} - q^{83} - 2 q^{85} + 36 q^{89} - 30 q^{91} - 4 q^{95} + 13 q^{97}+O(q^{100}) $ 2 * q - q^5 - 3 * q^7 - 5 * q^11 + 5 * q^13 + 4 * q^17 + 8 * q^19 + q^23 + 4 * q^25 - 9 * q^29 - q^31 + 6 * q^35 - 12 * q^37 + 3 * q^41 + q^43 + 3 * q^47 - 2 * q^49 - 4 * q^53 + 10 * q^55 - 11 * q^59 - 7 * q^61 + 5 * q^65 - q^67 + 8 * q^71 - 4 * q^73 - 15 * q^77 + q^79 - q^83 - 2 * q^85 + 36 * q^89 - 30 * q^91 - 4 * q^95 + 13 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$		0			0
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	−0.894951	−	0.446165i	$-0.852789\pi$
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	0.833866	+	0.551967i	$0.186123\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.50000	+	12.9904i	−0.854704	+	1.48039i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.500000	−	0.866025i	−0.0548821	−	0.0950586i	0.837279	−	0.546776i	$-0.184145\pi$
$83$	−0.500000	−	0.866025i	−0.0548821	−	0.0950586i	−0.892161	+	0.451717i	$0.850812\pi$
$84$		0			0
$85$	−1.00000	+	1.73205i	−0.108465	+	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$		0			0
$91$	−15.0000			−1.57243
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	0.980622	+	0.195911i	$0.0627665\pi$
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	−0.320647	+	0.947199i	$0.603900\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	−0.735901	−	0.677089i	$-0.763241\pi$
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	0.954327	+	0.298764i	$0.0965744\pi$
$132$		0			0
$133$	−6.00000	−	10.3923i	−0.520266	−	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−25.0000			−2.09061
$144$		0			0
$145$	9.00000			0.747409
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.50000	−	16.4545i	0.778270	−	1.34800i	−0.154668	−	0.987967i	$-0.549431\pi$
$149$	9.50000	−	16.4545i	0.778270	−	1.34800i	0.932938	−	0.360037i	$-0.117236\pi$
$150$		0			0
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.500000	−	0.866025i	−0.0401610	−	0.0695608i
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000			−0.236433
$162$		0			0
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.5000	−	18.1865i	0.812514	−	1.40732i	−0.0985846	−	0.995129i	$-0.531432\pi$
$167$	10.5000	−	18.1865i	0.812514	−	1.40732i	0.911099	−	0.412188i	$-0.135235\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$		0			0
$175$	6.00000	−	10.3923i	0.453557	−	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	−5.00000	−	8.66025i	−0.365636	−	0.633300i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.5000	+	23.3827i	0.976826	+	1.69191i	0.673774	+	0.738938i	$0.264672\pi$
$191$	13.5000	+	23.3827i	0.976826	+	1.69191i	0.303052	+	0.952974i	$0.401994\pi$
$192$		0			0
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	−0.531446	−	0.847092i	$-0.678351\pi$
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	0.999326	+	0.0366998i	$0.0116845\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−13.5000	+	23.3827i	−0.947514	+	1.64114i
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.0000	−	17.3205i	−0.691714	−	1.19808i
$210$		0			0
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	−0.720035	−	0.693938i	$-0.755874\pi$
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	0.960985	+	0.276600i	$0.0892077\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.00000			−0.0681994
$216$		0			0
$217$	3.00000			0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.00000	−	8.66025i	0.336336	−	0.582552i
$222$		0			0
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	0.620994	−	0.783815i	$-0.286729\pi$
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	−0.989301	+	0.145889i	$0.953396\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$		0			0
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	−0.435653	−	0.900115i	$-0.643482\pi$
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	0.997349	−	0.0727709i	$-0.0231842\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.50000	−	14.7224i	0.549819	−	0.952315i	−0.448467	−	0.893799i	$-0.648030\pi$
$239$	8.50000	−	14.7224i	0.549819	−	0.952315i	0.998286	−	0.0585157i	$-0.0186368\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	10.0000	−	17.3205i	0.636285	−	1.10208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$	−5.00000			−0.314347
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	−0.735972	−	0.677012i	$-0.763274\pi$
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	0.954296	+	0.298864i	$0.0966077\pi$
$258$		0			0
$259$	9.00000	+	15.5885i	0.559233	+	0.968620i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.50000	+	6.06218i	0.215819	+	0.373810i	0.953526	−	0.301312i	$-0.0974245\pi$
$263$	3.50000	+	6.06218i	0.215819	+	0.373810i	−0.737706	+	0.675122i	$0.764091\pi$
$264$		0			0
$265$	1.00000	−	1.73205i	0.0614295	−	0.106399i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$		0			0
$277$	14.5000	+	25.1147i	0.871221	+	1.50900i	0.860735	+	0.509053i	$0.170004\pi$
$277$	14.5000	+	25.1147i	0.871221	+	1.50900i	0.0104855	+	0.999945i	$0.496662\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	0.996887	+	0.0788417i	$0.0251222\pi$
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	−0.430165	+	0.902750i	$0.641545\pi$
$282$		0			0
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.00000			−0.531253
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$	−5.50000	−	9.52628i	−0.320222	−	0.554641i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.50000	−	4.33013i	−0.144579	−	0.250418i
$300$		0			0
$301$	1.50000	−	2.59808i	0.0864586	−	0.149751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.00000			0.400819
$306$		0			0
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	−0.709771	−	0.704433i	$-0.751201\pi$
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	0.964942	+	0.262463i	$0.0845347\pi$
$312$		0			0
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	0.964720	−	0.263278i	$-0.0848035\pi$
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	−0.710365	+	0.703833i	$0.751470\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$		0			0
$319$	−22.5000	+	38.9711i	−1.25976	+	2.18197i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.00000			0.445132
$324$		0			0
$325$	20.0000			1.10940
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.50000	−	7.79423i	0.248093	−	0.429710i
$330$		0			0
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	−0.999667	−	0.0257885i	$-0.991790\pi$
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	0.477500	−	0.878632i	$-0.341543\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.500000	−	0.866025i	−0.0273179	−	0.0473160i
$336$		0			0
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	−0.717038	−	0.697034i	$-0.754502\pi$
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	0.962168	+	0.272456i	$0.0878358\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.00000			0.270765
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	10.5000	+	18.1865i	0.562052	+	0.973503i	0.997317	+	0.0732005i	$0.0233213\pi$
$349$	10.5000	+	18.1865i	0.562052	+	0.973503i	−0.435265	+	0.900302i	$0.643345\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	0.791794	−	0.610789i	$-0.209147\pi$
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	−0.924855	+	0.380319i	$0.875814\pi$
$354$		0			0
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$		0			0
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$	−17.5000	+	30.3109i	−0.906116	+	1.56944i	−0.0867031	+	0.996234i	$0.527633\pi$
$373$	−17.5000	+	30.3109i	−0.906116	+	1.56944i	−0.819413	+	0.573204i	$0.805700\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−45.0000			−2.31762
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	0.282079	+	0.959391i	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		0			0
$385$	−7.50000	−	12.9904i	−0.382235	−	0.662051i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	17.5000	+	30.3109i	0.887285	+	1.53682i	0.843072	+	0.537801i	$0.180745\pi$
$389$	17.5000	+	30.3109i	0.887285	+	1.53682i	0.0442134	+	0.999022i	$0.485922\pi$
$390$		0			0
$391$	1.00000	−	1.73205i	0.0505722	−	0.0875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.00000			−0.0503155
$396$		0			0
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	0.475253	+	0.879849i	$0.342356\pi$
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	−0.999598	+	0.0283431i	$0.990977\pi$
$402$		0			0
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	15.0000	+	25.9808i	0.743522	+	1.28782i
$408$		0			0
$409$	16.5000	−	28.5788i	0.815872	−	1.41313i	−0.0928272	−	0.995682i	$-0.529590\pi$
$409$	16.5000	−	28.5788i	0.815872	−	1.41313i	0.908700	−	0.417450i	$-0.137076\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	33.0000			1.62382
$414$		0			0
$415$	1.00000			0.0490881
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$		0			0
$427$	−10.5000	+	18.1865i	−0.508131	+	0.880108i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.00000			−0.385346			−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000			−0.385346			−0.192673	+	0.981263i	$0.561716\pi$
$432$		0			0
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.00000	−	3.46410i	0.0956730	−	0.165710i
$438$		0			0
$439$	16.5000	+	28.5788i	0.787502	+	1.36399i	0.927493	+	0.373841i	$0.121959\pi$
$439$	16.5000	+	28.5788i	0.787502	+	1.36399i	−0.139991	+	0.990153i	$0.544707\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.5000	+	19.9186i	0.546381	+	0.946360i	0.998519	+	0.0544120i	$0.0173284\pi$
$443$	11.5000	+	19.9186i	0.546381	+	0.946360i	−0.452137	+	0.891948i	$0.649338\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$		0			0
$451$	−15.0000			−0.706322
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.50000	−	12.9904i	0.351605	−	0.608998i
$456$		0			0
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.5000	−	21.6506i	−0.582183	−	1.00837i	−0.995220	−	0.0976564i	$-0.968865\pi$
$461$	−12.5000	−	21.6506i	−0.582183	−	1.00837i	0.413037	−	0.910714i	$-0.364468\pi$
$462$		0			0
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	0.999190	−	0.0402476i	$-0.0128147\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	3.00000			0.138527
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.50000	−	4.33013i	0.114950	−	0.199099i
$474$		0			0
$475$	8.00000	+	13.8564i	0.367065	+	0.635776i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	−15.0000	+	25.9808i	−0.683941	+	1.18462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.0000			−0.590300
$486$		0			0
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	−0.387812	−	0.921739i	$-0.626769\pi$
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	0.992155	−	0.125014i	$-0.0398977\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	3.00000	+	5.19615i	0.132712	+	0.229864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.50000	−	4.33013i	−0.110163	−	0.190808i
$516$		0			0
$517$	7.50000	−	12.9904i	0.329850	−	0.571316i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−40.0000			−1.74908			−0.874539	−	0.484955i	$-0.838836\pi$
$523$	−40.0000			−1.74908			−0.874539	+	0.484955i	$0.838836\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.00000	+	1.73205i	−0.0435607	+	0.0754493i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.50000	−	12.9904i	−0.324861	−	0.562676i
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.0000			0.430730
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.00000	+	8.66025i	−0.214176	+	0.370965i
$546$		0			0
$547$	−9.50000	−	16.4545i	−0.406191	−	0.703543i	0.588269	−	0.808666i	$-0.299810\pi$
$547$	−9.50000	−	16.4545i	−0.406191	−	0.703543i	−0.994459	+	0.105123i	$0.966476\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.0000	−	31.1769i	−0.766826	−	1.32818i
$552$		0			0
$553$	1.50000	−	2.59808i	0.0637865	−	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.0000			0.932170			0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000			0.932170			0.466085	+	0.884740i	$0.345664\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.500000	−	0.866025i	0.0210725	−	0.0364986i	−0.855297	−	0.518138i	$-0.826625\pi$
$563$	0.500000	−	0.866025i	0.0210725	−	0.0364986i	0.876369	+	0.481640i	$0.159959\pi$
$564$		0			0
$565$	−4.50000	−	7.79423i	−0.189316	−	0.327906i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	−0.999609	−	0.0279702i	$-0.991096\pi$
$569$	−12.5000	−	21.6506i	−0.524027	−	0.907642i	0.475581	−	0.879672i	$-0.342238\pi$
$570$		0			0
$571$	7.50000	−	12.9904i	0.313865	−	0.543631i	−0.665330	−	0.746549i	$-0.731709\pi$
$571$	7.50000	−	12.9904i	0.313865	−	0.543631i	0.979196	+	0.202919i	$0.0650427\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.50000	+	2.59808i	−0.0622305	+	0.107786i
$582$		0			0
$583$	5.00000	+	8.66025i	0.207079	+	0.358671i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.50000	−	14.7224i	−0.350833	−	0.607660i	0.635563	−	0.772049i	$-0.280768\pi$
$587$	−8.50000	−	14.7224i	−0.350833	−	0.607660i	−0.986396	+	0.164389i	$0.947435\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.5000	−	18.1865i	0.429018	−	0.743082i	−0.567768	−	0.823189i	$-0.692193\pi$
$599$	10.5000	−	18.1865i	0.429018	−	0.743082i	0.996786	+	0.0801071i	$0.0255262\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.0000			0.606835
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	−0.834251	−	0.551385i	$-0.814100\pi$
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	0.894639	+	0.446790i	$0.147433\pi$
$618$		0			0
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	0.734068	−	0.679076i	$-0.237620\pi$
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	−0.955131	+	0.296183i	$0.904286\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−27.0000	−	46.7654i	−1.08173	−	1.87362i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$		0			0
$637$	5.00000	+	8.66025i	0.198107	+	0.343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.500000	−	0.866025i	−0.0197488	−	0.0342059i	0.855982	−	0.517005i	$-0.172953\pi$
$641$	−0.500000	−	0.866025i	−0.0197488	−	0.0342059i	−0.875731	+	0.482800i	$0.839620\pi$
$642$		0			0
$643$	7.50000	−	12.9904i	0.295771	−	0.512291i	−0.679393	−	0.733775i	$-0.737757\pi$
$643$	7.50000	−	12.9904i	0.295771	−	0.512291i	0.975164	+	0.221484i	$0.0710901\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$		0			0
$649$	55.0000			2.15894
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	0.338446	+	0.940986i	$0.390099\pi$
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	−0.984141	+	0.177390i	$0.943234\pi$
$654$		0			0
$655$	2.50000	+	4.33013i	0.0976831	+	0.169192i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000			0.465340
$666$		0			0
$667$	−9.00000			−0.348481
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.5000	+	30.3109i	−0.675580	+	1.17014i
$672$		0			0
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	0.622770	−	0.782405i	$-0.286007\pi$
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	−0.988968	+	0.148132i	$0.952674\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.5000	+	30.3109i	0.672580	+	1.16494i	0.977170	+	0.212459i	$0.0681471\pi$
$677$	17.5000	+	30.3109i	0.672580	+	1.16494i	−0.304590	+	0.952483i	$0.598520\pi$
$678$		0			0
$679$	19.5000	−	33.7750i	0.748341	−	1.29617i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	−3.00000			−0.114624
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.00000	+	8.66025i	−0.190485	+	0.329929i
$690$		0			0
$691$	20.5000	+	35.5070i	0.779857	+	1.35075i	0.932024	+	0.362397i	$0.118041\pi$
$691$	20.5000	+	35.5070i	0.779857	+	1.35075i	−0.152167	+	0.988355i	$0.548625\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.50000	+	2.59808i	0.0568982	+	0.0985506i
$696$		0			0
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−24.0000			−0.905177
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.50000	−	7.79423i	0.169240	−	0.293132i
$708$		0			0
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.500000	+	0.866025i	0.0187251	+	0.0324329i
$714$		0			0
$715$	12.5000	−	21.6506i	0.467473	−	0.809688i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	32.0000			1.19340			0.596699	−	0.802465i	$-0.296479\pi$
$719$	32.0000			1.19340			0.596699	+	0.802465i	$0.296479\pi$
$720$		0			0
$721$	15.0000			0.558629
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	−19.5000	−	33.7750i	−0.723215	−	1.25265i	−0.959705	−	0.281011i	$-0.909330\pi$
$727$	−19.5000	−	33.7750i	−0.723215	−	1.25265i	0.236490	−	0.971634i	$-0.424003\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$		0			0
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.00000			0.184177
$738$		0			0
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.50000	+	9.52628i	−0.201775	+	0.349485i	−0.949101	−	0.314973i	$-0.898004\pi$
$743$	−5.50000	+	9.52628i	−0.201775	+	0.349485i	0.747325	+	0.664459i	$0.231338\pi$
$744$		0			0
$745$	9.50000	+	16.4545i	0.348053	+	0.602846i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.0000	−	31.1769i	−0.657706	−	1.13918i
$750$		0			0
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	−0.507342	−	0.861745i	$-0.669372\pi$
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	0.999964	+	0.00849853i	$0.00270520\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.0000			−0.618693
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.50000	+	4.33013i	−0.0906249	+	0.156967i	−0.907774	−	0.419459i	$-0.862220\pi$
$761$	−2.50000	+	4.33013i	−0.0906249	+	0.156967i	0.817149	+	0.576426i	$0.195553\pi$
$762$		0			0
$763$	−15.0000	−	25.9808i	−0.543036	−	0.940567i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.5000	+	47.6314i	0.992967	+	1.71987i
$768$		0			0
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	−10.0000	−	17.3205i	−0.357828	−	0.619777i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.50000	−	6.06218i	−0.124920	−	0.216368i
$786$		0			0
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.188119	+	0.982146i	$0.560239\pi$
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.756504	+	0.653989i	$0.773094\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	27.0000			0.960009
$792$		0			0
$793$	−35.0000			−1.24289
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.50000	+	11.2583i	−0.230242	+	0.398791i	−0.957879	−	0.287171i	$-0.907285\pi$
$797$	−6.50000	+	11.2583i	−0.230242	+	0.398791i	0.727637	+	0.685962i	$0.240618\pi$
$798$		0			0
$799$	3.00000	+	5.19615i	0.106132	+	0.183827i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$		0			0
$805$	1.50000	−	2.59808i	0.0528681	−	0.0915702i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	50.0000			1.75791			0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000			1.75791			0.878953	+	0.476908i	$0.158243\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.00000	+	10.3923i	−0.210171	+	0.364027i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	−0.995948	−	0.0899279i	$-0.971336\pi$
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	0.420094	−	0.907480i	$-0.361997\pi$
$822$		0			0
$823$	−24.5000	+	42.4352i	−0.854016	+	1.47920i	0.0235383	+	0.999723i	$0.492507\pi$
$823$	−24.5000	+	42.4352i	−0.854016	+	1.47920i	−0.877555	+	0.479477i	$0.840826\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−44.0000			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$827$	−44.0000			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$828$		0			0
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.00000	+	3.46410i	−0.0692959	+	0.120024i
$834$		0			0
$835$	10.5000	+	18.1865i	0.363367	+	0.629371i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.5000	−	18.1865i	−0.362500	−	0.627869i	0.625871	−	0.779926i	$-0.284743\pi$
$839$	−10.5000	−	18.1865i	−0.362500	−	0.627869i	−0.988372	+	0.152057i	$0.951410\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.0000			0.412813
$846$		0			0
$847$	42.0000			1.44314
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$		0			0
$853$	0.500000	+	0.866025i	0.0171197	+	0.0296521i	0.874458	−	0.485101i	$-0.161217\pi$
$853$	0.500000	+	0.866025i	0.0171197	+	0.0296521i	−0.857339	+	0.514753i	$0.827884\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	0.999019	−	0.0442921i	$-0.0141032\pi$
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	−0.537867	+	0.843029i	$0.680770\pi$
$858$		0			0
$859$	−4.50000	+	7.79423i	−0.153538	+	0.265936i	−0.932526	−	0.361104i	$-0.882400\pi$
$859$	−4.50000	+	7.79423i	−0.153538	+	0.265936i	0.778988	+	0.627039i	$0.215733\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	56.0000			1.90626			0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000			1.90626			0.953131	+	0.302558i	$0.0978405\pi$
$864$		0			0
$865$	−3.00000			−0.102003
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.50000	−	4.33013i	0.0848067	−	0.146889i
$870$		0			0
$871$	2.50000	+	4.33013i	0.0847093	+	0.146721i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.5000	+	23.3827i	0.456383	+	0.790479i
$876$		0			0
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	−0.890239	−	0.455493i	$-0.849463\pi$
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	0.839588	+	0.543224i	$0.182796\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.5000	+	47.6314i	−0.923360	+	1.59931i	−0.129181	+	0.991621i	$0.541235\pi$
$887$	−27.5000	+	47.6314i	−0.923360	+	1.59931i	−0.794178	+	0.607685i	$0.792098\pi$
$888$		0			0
$889$	24.0000	+	41.5692i	0.804934	+	1.39419i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.00000			0.300167
$900$		0			0
$901$	−4.00000			−0.133259
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$		0			0
$907$	24.5000	+	42.4352i	0.813509	+	1.40904i	0.910393	+	0.413744i	$0.135779\pi$
$907$	24.5000	+	42.4352i	0.813509	+	1.40904i	−0.0968843	+	0.995296i	$0.530888\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.5000	−	35.5070i	−0.679195	−	1.17640i	−0.975224	−	0.221222i	$-0.928996\pi$
$911$	−20.5000	−	35.5070i	−0.679195	−	1.17640i	0.296028	−	0.955179i	$-0.404338\pi$
$912$		0			0
$913$	−2.50000	+	4.33013i	−0.0827379	+	0.143306i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.0000			−0.495344
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.0000	−	17.3205i	0.329154	−	0.570111i
$924$		0			0
$925$	−12.0000	−	20.7846i	−0.394558	−	0.683394i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	0.523884	−	0.851790i	$-0.324483\pi$
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	−0.999613	+	0.0278019i	$0.991149\pi$
$930$		0			0
$931$	−4.00000	+	6.92820i	−0.131095	+	0.227063i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.0000			0.327035
$936$		0			0
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	0.461133	+	0.887331i	$0.347443\pi$
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	−0.999018	+	0.0443125i	$0.985890\pi$
$942$		0			0
$943$	−1.50000	−	2.59808i	−0.0488467	−	0.0846050i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$	−27.0000			−0.873699
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.50000	−	7.79423i	0.145313	−	0.251689i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.50000	+	11.2583i	0.209242	+	0.362418i
$966$		0			0
$967$	−12.5000	+	21.6506i	−0.401973	+	0.696237i	−0.993964	−	0.109707i	$-0.965009\pi$
$967$	−12.5000	+	21.6506i	−0.401973	+	0.696237i	0.591991	+	0.805945i	$0.298342\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	−9.00000			−0.288527
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.5000	−	33.7750i	0.623860	−	1.08056i	−0.364900	−	0.931047i	$-0.618897\pi$
$977$	19.5000	−	33.7750i	0.623860	−	1.08056i	0.988760	−	0.149511i	$-0.0477699\pi$
$978$		0			0
$979$	−45.0000	−	77.9423i	−1.43821	−	2.49105i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	0.960489	−	0.278319i	$-0.0897773\pi$
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	−0.721276	+	0.692648i	$0.756444\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.00000			0.0317982
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.0000	+	17.3205i	−0.317021	+	0.549097i
$996$		0			0
$997$	−9.50000	−	16.4545i	−0.300868	−	0.521119i	0.675465	−	0.737392i	$-0.263943\pi$
$997$	−9.50000	−	16.4545i	−0.300868	−	0.521119i	−0.976333	+	0.216274i	$0.930610\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.i.a.145.1		2
3.2	odd	2		144.2.i.b.49.1		2
4.3	odd	2		216.2.i.a.145.1		2
8.3	odd	2		1728.2.i.h.577.1		2
8.5	even	2		1728.2.i.g.577.1		2
9.2	odd	6		144.2.i.b.97.1		2
9.4	even	3		1296.2.a.i.1.1		1
9.5	odd	6		1296.2.a.e.1.1		1
9.7	even	3	inner	432.2.i.a.289.1		2
12.11	even	2		72.2.i.a.49.1	yes	2
24.5	odd	2		576.2.i.c.193.1		2
24.11	even	2		576.2.i.d.193.1		2
36.7	odd	6		216.2.i.a.73.1		2
36.11	even	6		72.2.i.a.25.1	✓	2
36.23	even	6		648.2.a.a.1.1		1
36.31	odd	6		648.2.a.c.1.1		1
72.5	odd	6		5184.2.a.x.1.1		1
72.11	even	6		576.2.i.d.385.1		2
72.13	even	6		5184.2.a.n.1.1		1
72.29	odd	6		576.2.i.c.385.1		2
72.43	odd	6		1728.2.i.h.1153.1		2
72.59	even	6		5184.2.a.s.1.1		1
72.61	even	6		1728.2.i.g.1153.1		2
72.67	odd	6		5184.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.i.a.25.1	✓	2	36.11	even	6
72.2.i.a.49.1	yes	2	12.11	even	2
144.2.i.b.49.1		2	3.2	odd	2
144.2.i.b.97.1		2	9.2	odd	6
216.2.i.a.73.1		2	36.7	odd	6
216.2.i.a.145.1		2	4.3	odd	2
432.2.i.a.145.1		2	1.1	even	1	trivial
432.2.i.a.289.1		2	9.7	even	3	inner
576.2.i.c.193.1		2	24.5	odd	2
576.2.i.c.385.1		2	72.29	odd	6
576.2.i.d.193.1		2	24.11	even	2
576.2.i.d.385.1		2	72.11	even	6
648.2.a.a.1.1		1	36.23	even	6
648.2.a.c.1.1		1	36.31	odd	6
1296.2.a.e.1.1		1	9.5	odd	6
1296.2.a.i.1.1		1	9.4	even	3
1728.2.i.g.577.1		2	8.5	even	2
1728.2.i.g.1153.1		2	72.61	even	6
1728.2.i.h.577.1		2	8.3	odd	2
1728.2.i.h.1153.1		2	72.43	odd	6
5184.2.a.i.1.1		1	72.67	odd	6
5184.2.a.n.1.1		1	72.13	even	6
5184.2.a.s.1.1		1	72.59	even	6
5184.2.a.x.1.1		1	72.5	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +(-2.50000 - 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +2.00000 q^{17} +4.00000 q^{19} +(0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-4.50000 - 7.79423i) q^{29} +(-0.500000 + 0.866025i) q^{31} +3.00000 q^{35} -6.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{47} +(-1.00000 + 1.73205i) q^{49} -2.00000 q^{53} +5.00000 q^{55} +(-5.50000 + 9.52628i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(2.50000 + 4.33013i) q^{65} +(-0.500000 + 0.866025i) q^{67} +4.00000 q^{71} -2.00000 q^{73} +(-7.50000 + 12.9904i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{83} +(-1.00000 + 1.73205i) q^{85} +18.0000 q^{89} -15.0000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(6.50000 + 11.2583i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} - 3 q^{7}+O(q^{10}) \) 2 * q - q^5 - 3 * q^7	\( 2 q - q^{5} - 3 q^{7} - 5 q^{11} + 5 q^{13} + 4 q^{17} + 8 q^{19} + q^{23} + 4 q^{25} - 9 q^{29} - q^{31} + 6 q^{35} - 12 q^{37} + 3 q^{41} + q^{43} + 3 q^{47} - 2 q^{49} - 4 q^{53} + 10 q^{55} - 11 q^{59} - 7 q^{61} + 5 q^{65} - q^{67} + 8 q^{71} - 4 q^{73} - 15 q^{77} + q^{79} - q^{83} - 2 q^{85} + 36 q^{89} - 30 q^{91} - 4 q^{95} + 13 q^{97}+O(q^{100}) \) 2 * q - q^5 - 3 * q^7 - 5 * q^11 + 5 * q^13 + 4 * q^17 + 8 * q^19 + q^23 + 4 * q^25 - 9 * q^29 - q^31 + 6 * q^35 - 12 * q^37 + 3 * q^41 + q^43 + 3 * q^47 - 2 * q^49 - 4 * q^53 + 10 * q^55 - 11 * q^59 - 7 * q^61 + 5 * q^65 - q^67 + 8 * q^71 - 4 * q^73 - 15 * q^77 + q^79 - q^83 - 2 * q^85 + 36 * q^89 - 30 * q^91 - 4 * q^95 + 13 * q^97

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