LMFDB - Embedded newform 864.2.r.b.145.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(145,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("864.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.r (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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.7
Root			$0.820200 - 1.15207i$ of defining polynomial
Character	$\chi$	$=$	864.145
Dual form			864.2.r.b.721.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97542 + 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +O(q^{10})$	$q+(1.97542 + 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(-4.24153 + 2.44885i) q^{11} +(4.00895 + 2.31457i) q^{13} -1.92788 q^{17} +2.12907i q^{19} +(-1.15765 + 2.00511i) q^{23} +(0.101535 + 0.175863i) q^{25} +(-3.16440 + 1.82697i) q^{29} +(2.65800 - 4.60379i) q^{31} +4.14154i q^{35} +7.98438i q^{37} +(2.36240 - 4.09180i) q^{41} +(2.20800 - 1.27479i) q^{43} +(-2.02005 - 3.49884i) q^{47} +(1.85171 - 3.20726i) q^{49} +8.95958i q^{53} -11.1718 q^{55} +(3.05255 + 1.76239i) q^{59} +(1.71675 - 0.991165i) q^{61} +(5.27959 + 9.14451i) q^{65} +(7.72723 + 4.46132i) q^{67} +13.3561 q^{71} -11.5592 q^{73} +(-7.70112 - 4.44625i) q^{77} +(4.97330 + 8.61401i) q^{79} +(3.12153 - 1.80221i) q^{83} +(-3.80838 - 2.19877i) q^{85} -2.49965 q^{89} +8.40489i q^{91} +(-2.42823 + 4.20582i) q^{95} +(6.99370 + 12.1134i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) $ 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.97542	+	1.14051i	0.883437	+	0.510052i	0.871790	−	0.489880i	$-0.162959\pi$
$5$	1.97542	+	1.14051i	0.883437	+	0.510052i	0.0116467	+	0.999932i	$0.496293\pi$
$6$		0			0
$7$	0.907824	+	1.57240i	0.343125	+	0.594311i	0.985011	−	0.172490i	$-0.0551811\pi$
$7$	0.907824	+	1.57240i	0.343125	+	0.594311i	−0.641886	+	0.766800i	$0.721848\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.24153	+	2.44885i	−1.27887	+	0.738355i	−0.976640	−	0.214880i	$-0.931064\pi$
$11$	−4.24153	+	2.44885i	−1.27887	+	0.738355i	−0.302228	+	0.953236i	$0.597730\pi$
$12$		0			0
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.939317	−	0.343052i	$-0.111461\pi$
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.172567	+	0.984998i	$0.444794\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.92788			−0.467579			−0.233790	−	0.972287i	$-0.575113\pi$
$17$	−1.92788			−0.467579			−0.233790	+	0.972287i	$0.575113\pi$
$18$		0			0
$19$			2.12907i			0.488442i	0.969720	+	0.244221i	$0.0785322\pi$
$19$			2.12907i			0.488442i	−0.969720	+	0.244221i	$0.921468\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.15765	+	2.00511i	−0.241387	+	0.418094i	−0.961109	−	0.276168i	$-0.910936\pi$
$23$	−1.15765	+	2.00511i	−0.241387	+	0.418094i	0.719723	+	0.694261i	$0.244269\pi$
$24$		0			0
$25$	0.101535	+	0.175863i	0.0203069	+	0.0351726i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.16440	+	1.82697i	−0.587615	+	0.339260i	−0.764154	−	0.645034i	$-0.776843\pi$
$29$	−3.16440	+	1.82697i	−0.587615	+	0.339260i	0.176539	+	0.984294i	$0.443510\pi$
$30$		0			0
$31$	2.65800	−	4.60379i	0.477391	−	0.826865i	−0.522273	−	0.852778i	$-0.674916\pi$
$31$	2.65800	−	4.60379i	0.477391	−	0.826865i	0.999664	+	0.0259130i	$0.00824928\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			4.14154i			0.700048i
$36$		0			0
$37$			7.98438i			1.31262i	0.754489	+	0.656312i	$0.227885\pi$
$37$			7.98438i			1.31262i	−0.754489	+	0.656312i	$0.772115\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.36240	−	4.09180i	0.368946	−	0.639033i	−0.620455	−	0.784242i	$-0.713052\pi$
$41$	2.36240	−	4.09180i	0.368946	−	0.639033i	0.989401	+	0.145209i	$0.0463855\pi$
$42$		0			0
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	−0.322102	−	0.946705i	$-0.604390\pi$
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	0.658819	+	0.752301i	$0.271056\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.02005	−	3.49884i	−0.294655	−	0.510358i	0.680249	−	0.732981i	$-0.261871\pi$
$47$	−2.02005	−	3.49884i	−0.294655	−	0.510358i	−0.974905	+	0.222623i	$0.928538\pi$
$48$		0			0
$49$	1.85171	−	3.20726i	0.264530	−	0.458179i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			8.95958i			1.23069i	0.788257	+	0.615347i	$0.210984\pi$
$53$			8.95958i			1.23069i	−0.788257	+	0.615347i	$0.789016\pi$
$54$		0			0
$55$	−11.1718			−1.50640
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.05255	+	1.76239i	0.397408	+	0.229444i	0.685365	−	0.728200i	$-0.259643\pi$
$59$	3.05255	+	1.76239i	0.397408	+	0.229444i	−0.287957	+	0.957643i	$0.592976\pi$
$60$		0			0
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	−0.386054	−	0.922476i	$-0.626162\pi$
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	0.605861	+	0.795571i	$0.292829\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.27959	+	9.14451i	0.654852	+	1.13424i
$66$		0			0
$67$	7.72723	+	4.46132i	0.944031	+	0.545036i	0.891222	−	0.453568i	$-0.149849\pi$
$67$	7.72723	+	4.46132i	0.944031	+	0.545036i	0.0528093	+	0.998605i	$0.483182\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.3561			1.58508			0.792539	−	0.609821i	$-0.208759\pi$
$71$	13.3561			1.58508			0.792539	+	0.609821i	$0.208759\pi$
$72$		0			0
$73$	−11.5592			−1.35290			−0.676450	−	0.736489i	$-0.736482\pi$
$73$	−11.5592			−1.35290			−0.676450	+	0.736489i	$0.736482\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.70112	−	4.44625i	−0.877625	−	0.506697i
$78$		0			0
$79$	4.97330	+	8.61401i	0.559540	+	0.969151i	0.997535	+	0.0701739i	$0.0223554\pi$
$79$	4.97330	+	8.61401i	0.559540	+	0.969151i	−0.437995	+	0.898977i	$0.644311\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.12153	−	1.80221i	0.342632	−	0.197819i	−0.318803	−	0.947821i	$-0.603281\pi$
$83$	3.12153	−	1.80221i	0.342632	−	0.197819i	0.661435	+	0.750002i	$0.269948\pi$
$84$		0			0
$85$	−3.80838	−	2.19877i	−0.413077	−	0.238490i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.49965			−0.264962			−0.132481	−	0.991186i	$-0.542294\pi$
$89$	−2.49965			−0.264962			−0.132481	+	0.991186i	$0.542294\pi$
$90$		0			0
$91$			8.40489i			0.881072i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.42823	+	4.20582i	−0.249131	+	0.431508i
$96$		0			0
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	0.964818	+	0.262918i	$0.0846849\pi$
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	−0.254715	+	0.967016i	$0.581982\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.13087	−	0.652911i	0.112526	−	0.0649671i	−0.442681	−	0.896679i	$-0.645972\pi$
$101$	1.13087	−	0.652911i	0.112526	−	0.0649671i	0.555207	+	0.831712i	$0.312639\pi$
$102$		0			0
$103$	3.22312	−	5.58261i	0.317584	−	0.550071i	−0.662400	−	0.749151i	$-0.730462\pi$
$103$	3.22312	−	5.58261i	0.317584	−	0.550071i	0.979983	+	0.199080i	$0.0637952\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	3.10427i		−	0.300101i	−0.988678	−	0.150051i	$-0.952056\pi$
$107$		−	3.10427i		−	0.300101i	0.988678	−	0.150051i	$-0.0479437\pi$
$108$		0			0
$109$		−	18.0837i		−	1.73210i	−0.499955	−	0.866051i	$-0.666650\pi$
$109$		−	18.0837i		−	1.73210i	0.499955	−	0.866051i	$-0.333350\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.41718	−	2.45463i	0.133317	−	0.230913i	−0.791636	−	0.610993i	$-0.790770\pi$
$113$	1.41718	−	2.45463i	0.133317	−	0.230913i	0.924953	+	0.380080i	$0.124104\pi$
$114$		0			0
$115$	−4.57370	+	2.64063i	−0.426500	+	0.246240i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.75018	−	3.03139i	−0.160438	−	0.277887i
$120$		0			0
$121$	6.49370	−	11.2474i	0.590337	−	1.02249i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	10.9419i		−	0.978674i
$126$		0			0
$127$	7.44962			0.661047			0.330523	−	0.943798i	$-0.392775\pi$
$127$	7.44962			0.661047			0.330523	+	0.943798i	$0.392775\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.12153	−	1.80221i	−0.272729	−	0.157460i	0.357398	−	0.933952i	$-0.383664\pi$
$131$	−3.12153	−	1.80221i	−0.272729	−	0.157460i	−0.630127	+	0.776492i	$0.716997\pi$
$132$		0			0
$133$	−3.34774	+	1.93282i	−0.290286	+	0.167597i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.88147	−	10.1870i	−0.502488	−	0.870335i	−0.999996	−	0.00287543i	$-0.999085\pi$
$137$	−5.88147	−	10.1870i	−0.502488	−	0.870335i	0.497508	−	0.867460i	$-0.334249\pi$
$138$		0			0
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.0475703	−	0.998868i	$-0.515148\pi$
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.888830	+	0.458237i	$0.848481\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−22.6721			−1.89594
$144$		0			0
$145$	−8.33472			−0.692161
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.59790	+	3.80930i	0.540521	+	0.312070i	0.745290	−	0.666740i	$-0.232311\pi$
$149$	6.59790	+	3.80930i	0.540521	+	0.312070i	−0.204769	+	0.978810i	$0.565644\pi$
$150$		0			0
$151$	−2.26988	−	3.93155i	−0.184720	−	0.319945i	0.758762	−	0.651368i	$-0.225805\pi$
$151$	−2.26988	−	3.93155i	−0.184720	−	0.319945i	−0.943482	+	0.331423i	$0.892471\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.5014	−	6.06296i	0.843489	−	0.486989i
$156$		0			0
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.0300161	−	0.999549i	$-0.509556\pi$
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.880643	+	0.473780i	$0.842889\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.20377			−0.331303
$162$		0			0
$163$		−	20.5911i		−	1.61282i	−0.591358	−	0.806409i	$-0.701408\pi$
$163$		−	20.5911i		−	1.61282i	0.591358	−	0.806409i	$-0.298592\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.53912	−	4.39789i	0.196483	−	0.340319i	−0.750903	−	0.660413i	$-0.770381\pi$
$167$	2.53912	−	4.39789i	0.196483	−	0.340319i	0.947386	+	0.320094i	$0.103715\pi$
$168$		0			0
$169$	4.21446	+	7.29967i	0.324190	+	0.561513i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.0398	−	6.37385i	0.839343	−	0.484595i	−0.0176977	−	0.999843i	$-0.505634\pi$
$173$	11.0398	−	6.37385i	0.839343	−	0.484595i	0.857041	+	0.515248i	$0.172300\pi$
$174$		0			0
$175$	−0.184351	+	0.319306i	−0.0139356	+	0.0241372i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	8.82019i		−	0.659252i	−0.944112	−	0.329626i	$-0.893077\pi$
$179$		−	8.82019i		−	0.659252i	0.944112	−	0.329626i	$-0.106923\pi$
$180$		0			0
$181$			15.4369i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$181$			15.4369i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.10628	+	15.7725i	−0.669507	+	1.15962i
$186$		0			0
$187$	8.17715	−	4.72108i	0.597972	−	0.345239i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.81698	+	8.34326i	0.348545	+	0.603697i	0.985991	−	0.166797i	$-0.0533426\pi$
$191$	4.81698	+	8.34326i	0.348545	+	0.603697i	−0.637446	+	0.770495i	$0.720009\pi$
$192$		0			0
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	−0.712470	−	0.701702i	$-0.752424\pi$
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	0.963927	+	0.266166i	$0.0857570\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	4.31842i		−	0.307675i	−0.988096	−	0.153837i	$-0.950837\pi$
$197$		−	4.31842i		−	0.307675i	0.988096	−	0.153837i	$-0.0491632\pi$
$198$		0			0
$199$	−5.90649			−0.418700			−0.209350	−	0.977841i	$-0.567135\pi$
$199$	−5.90649			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.74544	−	3.31713i	−0.403251	−	0.232817i
$204$		0			0
$205$	9.33350	−	5.38870i	0.651880	−	0.376363i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.21376	−	9.03050i	−0.360644	−	0.624653i
$210$		0			0
$211$	−15.8781	−	9.16723i	−1.09309	−	0.631098i	−0.158696	−	0.987328i	$-0.550729\pi$
$211$	−15.8781	−	9.16723i	−1.09309	−	0.631098i	−0.934399	+	0.356229i	$0.884062\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.81565			0.396624
$216$		0			0
$217$	9.65199			0.655220
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.72877	−	4.46221i	−0.519893	−	0.300161i
$222$		0			0
$223$	2.63263	+	4.55986i	0.176294	+	0.305350i	0.940608	−	0.339494i	$-0.110256\pi$
$223$	2.63263	+	4.55986i	0.176294	+	0.305350i	−0.764314	+	0.644844i	$0.776922\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.53638	+	0.887027i	−0.101973	+	0.0588741i	−0.550119	−	0.835086i	$-0.685418\pi$
$227$	−1.53638	+	0.887027i	−0.101973	+	0.0588741i	0.448146	+	0.893960i	$0.352084\pi$
$228$		0			0
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	0.605267	−	0.796023i	$-0.293066\pi$
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	−0.386742	+	0.922188i	$0.626400\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.3207			1.33125			0.665627	−	0.746284i	$-0.268164\pi$
$233$	20.3207			1.33125			0.665627	+	0.746284i	$0.268164\pi$
$234$		0			0
$235$		−	9.21558i		−	0.601158i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.69811	−	15.0656i	0.562634	−	0.974510i	−0.434632	−	0.900608i	$-0.643121\pi$
$239$	8.69811	−	15.0656i	0.562634	−	0.974510i	0.997266	−	0.0739020i	$-0.0235452\pi$
$240$		0			0
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	0.556171	−	0.831068i	$-0.312270\pi$
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	−0.997811	+	0.0661240i	$0.978937\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.31583	−	4.22379i	0.467391	−	0.269848i
$246$		0			0
$247$	−4.92788	+	8.53534i	−0.313553	+	0.543090i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	4.50751i		−	0.284512i	−0.989830	−	0.142256i	$-0.954564\pi$
$251$		−	4.50751i		−	0.284512i	0.989830	−	0.142256i	$-0.0454356\pi$
$252$		0			0
$253$		−	11.3396i		−	0.712916i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.11258	−	7.12320i	0.256536	−	0.444333i	−0.708776	−	0.705434i	$-0.750752\pi$
$257$	4.11258	−	7.12320i	0.256536	−	0.444333i	0.965311	+	0.261101i	$0.0840856\pi$
$258$		0			0
$259$	−12.5546	+	7.24842i	−0.780106	+	0.450395i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.51376	+	4.35395i	0.155005	+	0.268476i	0.933061	−	0.359719i	$-0.117127\pi$
$263$	2.51376	+	4.35395i	0.155005	+	0.268476i	−0.778056	+	0.628195i	$0.783794\pi$
$264$		0			0
$265$	−10.2185	+	17.6990i	−0.627718	+	1.08724i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	23.1577i		−	1.41195i	−0.708236	−	0.705976i	$-0.750509\pi$
$269$		−	23.1577i		−	1.41195i	0.708236	−	0.705976i	$-0.249491\pi$
$270$		0			0
$271$	−20.9367			−1.27181			−0.635906	−	0.771766i	$-0.719373\pi$
$271$	−20.9367			−1.27181			−0.635906	+	0.771766i	$0.719373\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.861323	−	0.497285i	−0.0519398	−	0.0299874i
$276$		0			0
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.950763	−	0.309920i	$-0.899698\pi$
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.206983	+	0.978345i	$0.566364\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.28029	+	16.0739i	0.553616	+	0.958890i	0.998010	+	0.0630590i	$0.0200856\pi$
$281$	9.28029	+	16.0739i	0.553616	+	0.958890i	−0.444394	+	0.895831i	$0.646581\pi$
$282$		0			0
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	0.551387	−	0.834250i	$-0.314099\pi$
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	−0.446788	+	0.894640i	$0.647432\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.57859			0.506378
$288$		0			0
$289$	−13.2833			−0.781370
$290$		0			0
$291$		0			0
$292$		0			0
$293$	29.5484	+	17.0598i	1.72623	+	0.996642i	0.904057	+	0.427411i	$0.140574\pi$
$293$	29.5484	+	17.0598i	1.72623	+	0.996642i	0.822178	+	0.569231i	$0.192759\pi$
$294$		0			0
$295$	4.02005	+	6.96294i	0.234057	+	0.405398i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.28192	+	5.35892i	−0.536787	+	0.309914i
$300$		0			0
$301$	4.00895	+	2.31457i	0.231072	+	0.133410i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.52174			0.258914
$306$		0			0
$307$			4.77588i			0.272574i	0.990669	+	0.136287i	$0.0435169\pi$
$307$			4.77588i			0.272574i	−0.990669	+	0.136287i	$0.956483\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.1771	+	19.3592i	−0.633793	+	1.09776i	0.352976	+	0.935632i	$0.385170\pi$
$311$	−11.1771	+	19.3592i	−0.633793	+	1.09776i	−0.986769	+	0.162130i	$0.948164\pi$
$312$		0			0
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	0.898545	−	0.438881i	$-0.144625\pi$
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	−0.829355	+	0.558723i	$0.811292\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.2886	+	8.24953i	−0.802528	+	0.463340i	−0.844354	−	0.535785i	$-0.820016\pi$
$317$	−14.2886	+	8.24953i	−0.802528	+	0.463340i	0.0418263	+	0.999125i	$0.486682\pi$
$318$		0			0
$319$	8.94793	−	15.4983i	0.500988	−	0.867737i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	4.10459i		−	0.228385i
$324$		0			0
$325$			0.940035i			0.0521438i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.66771	−	6.35266i	0.202207	−	0.350233i
$330$		0			0
$331$	−0.329200	+	0.190064i	−0.0180945	+	0.0104469i	−0.509020	−	0.860755i	$-0.669992\pi$
$331$	−0.329200	+	0.190064i	−0.0180945	+	0.0104469i	0.490925	+	0.871202i	$0.336659\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.1764	+	17.6260i	0.555994	+	0.963010i
$336$		0			0
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	−0.926437	−	0.376450i	$-0.877145\pi$
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	0.789234	+	0.614093i	$0.210478\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			26.0361i			1.40994i
$342$		0			0
$343$	19.4337			1.04932
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.40337	+	4.85169i	0.451116	+	0.260452i	0.708302	−	0.705910i	$-0.249462\pi$
$347$	8.40337	+	4.85169i	0.451116	+	0.260452i	−0.257185	+	0.966362i	$0.582795\pi$
$348$		0			0
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.404158	−	0.914689i	$-0.367564\pi$
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.994223	+	0.107333i	$0.0342312\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.2376	−	22.9282i	−0.704565	−	1.22034i	−0.966848	−	0.255352i	$-0.917809\pi$
$353$	−13.2376	−	22.9282i	−0.704565	−	1.22034i	0.262283	−	0.964991i	$-0.415525\pi$
$354$		0			0
$355$	26.3840	+	15.2328i	1.40032	+	0.808473i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.4619			−1.23827			−0.619135	−	0.785285i	$-0.712517\pi$
$359$	−23.4619			−1.23827			−0.619135	+	0.785285i	$0.712517\pi$
$360$		0			0
$361$	14.4671			0.761424
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−22.8343	−	13.1834i	−1.19520	−	0.690050i
$366$		0			0
$367$	−9.62599	−	16.6727i	−0.502472	−	0.870308i	−0.999996	−	0.00285720i	$-0.999091\pi$
$367$	−9.62599	−	16.6727i	−0.502472	−	0.870308i	0.497524	−	0.867450i	$-0.334243\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−14.0880	+	8.13373i	−0.731414	+	0.422282i
$372$		0			0
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	0.716562	−	0.697524i	$-0.245715\pi$
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	−0.245793	+	0.969322i	$0.579048\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−16.9146			−0.871145
$378$		0			0
$379$			35.5203i			1.82455i	0.409574	+	0.912277i	$0.365677\pi$
$379$			35.5203i			1.82455i	−0.409574	+	0.912277i	$0.634323\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.0395	−	31.2453i	0.921774	−	1.59656i	0.125105	−	0.992144i	$-0.460073\pi$
$383$	18.0395	−	31.2453i	0.921774	−	1.59656i	0.796669	−	0.604416i	$-0.206593\pi$
$384$		0			0
$385$	−10.1420	−	17.5664i	−0.516884	−	0.895269i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.5243	+	10.1177i	−0.888519	+	0.512987i	−0.873458	−	0.486900i	$-0.838128\pi$
$389$	−17.5243	+	10.1177i	−0.888519	+	0.512987i	−0.0150612	+	0.999887i	$0.504794\pi$
$390$		0			0
$391$	2.23181	−	3.86560i	0.112867	−	0.195492i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			22.6884i			1.14158i
$396$		0			0
$397$		−	3.99499i		−	0.200503i	−0.994962	−	0.100251i	$-0.968035\pi$
$397$		−	3.99499i		−	0.200503i	0.994962	−	0.100251i	$-0.0319647\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.0124	+	24.2702i	−0.699747	+	1.21200i	0.268807	+	0.963194i	$0.413371\pi$
$401$	−14.0124	+	24.2702i	−0.699747	+	1.21200i	−0.968554	+	0.248803i	$0.919963\pi$
$402$		0			0
$403$	21.3116	−	12.3042i	1.06161	−	0.612918i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−19.5525	−	33.8660i	−0.969183	−	1.67867i
$408$		0			0
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	−0.587826	−	0.808987i	$-0.700016\pi$
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	0.994517	+	0.104579i	$0.0333494\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			6.39976i			0.314912i
$414$		0			0
$415$	8.22179			0.403592
$416$		0			0
$417$		0			0
$418$		0			0
$419$	20.5573	+	11.8688i	1.00429	+	0.579827i	0.909515	−	0.415672i	$-0.136453\pi$
$419$	20.5573	+	11.8688i	1.00429	+	0.579827i	0.0947752	+	0.995499i	$0.469787\pi$
$420$		0			0
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.973910	−	0.226935i	$-0.927130\pi$
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.290424	+	0.956898i	$0.593796\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.195746	−	0.339043i	−0.00949509	−	0.0164460i
$426$		0			0
$427$	3.11701	+	1.79961i	0.150843	+	0.0870891i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.0367			−0.531621			−0.265810	−	0.964025i	$-0.585640\pi$
$431$	−11.0367			−0.531621			−0.265810	+	0.964025i	$0.585640\pi$
$432$		0			0
$433$	34.9394			1.67908			0.839541	−	0.543297i	$-0.182824\pi$
$433$	34.9394			1.67908			0.839541	+	0.543297i	$0.182824\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.26901	−	2.46472i	−0.204215	−	0.117903i
$438$		0			0
$439$	6.58518	+	11.4059i	0.314293	+	0.544372i	0.979287	−	0.202477i	$-0.0648991\pi$
$439$	6.58518	+	11.4059i	0.314293	+	0.544372i	−0.664994	+	0.746849i	$0.731566\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.6849	−	13.6745i	1.12530	−	0.649694i	0.182554	−	0.983196i	$-0.441564\pi$
$443$	23.6849	−	13.6745i	1.12530	−	0.649694i	0.942749	+	0.333502i	$0.108230\pi$
$444$		0			0
$445$	−4.93787	−	2.85088i	−0.234077	−	0.135145i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	13.8225			0.652323			0.326161	−	0.945314i	$-0.394245\pi$
$449$	13.8225			0.652323			0.326161	+	0.945314i	$0.394245\pi$
$450$		0			0
$451$			23.1407i			1.08965i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.58588	+	16.6032i	−0.449393	+	0.778371i
$456$		0			0
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	0.791288	−	0.611443i	$-0.209411\pi$
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	−0.925170	+	0.379554i	$0.876077\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.3717	+	11.1843i	−0.902231	+	0.520903i	−0.877923	−	0.478801i	$-0.841071\pi$
$461$	−19.3717	+	11.1843i	−0.902231	+	0.520903i	−0.0243074	+	0.999705i	$0.507738\pi$
$462$		0			0
$463$	−18.5733	+	32.1699i	−0.863174	+	1.49506i	0.00567564	+	0.999984i	$0.498193\pi$
$463$	−18.5733	+	32.1699i	−0.863174	+	1.49506i	−0.868849	+	0.495077i	$0.835140\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			22.6850i			1.04974i	0.851184	+	0.524868i	$0.175885\pi$
$467$			22.6850i			1.04974i	−0.851184	+	0.524868i	$0.824115\pi$
$468$		0			0
$469$			16.2004i			0.748063i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.24353	+	10.8141i	−0.287078	+	0.497233i
$474$		0			0
$475$	−0.374425	+	0.216174i	−0.0171798	+	0.00991875i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.1576	+	22.7897i	0.601188	+	1.04129i	0.992641	+	0.121091i	$0.0386392\pi$
$479$	13.1576	+	22.7897i	0.601188	+	1.04129i	−0.391453	+	0.920198i	$0.628027\pi$
$480$		0			0
$481$	−18.4804	+	32.0090i	−0.842634	+	1.45948i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			31.9056i			1.44876i
$486$		0			0
$487$	24.0388			1.08930			0.544652	−	0.838662i	$-0.316662\pi$
$487$	24.0388			1.08930			0.544652	+	0.838662i	$0.316662\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−27.2256	−	15.7187i	−1.22867	−	0.709374i	−0.261920	−	0.965090i	$-0.584356\pi$
$491$	−27.2256	−	15.7187i	−1.22867	−	0.709374i	−0.966752	+	0.255715i	$0.917689\pi$
$492$		0			0
$493$	6.10058	−	3.52217i	0.274756	−	0.158631i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.1250	+	21.0011i	0.543881	+	0.942029i
$498$		0			0
$499$	5.08156	+	2.93384i	0.227482	+	0.131337i	0.609410	−	0.792855i	$-0.291406\pi$
$499$	5.08156	+	2.93384i	0.227482	+	0.131337i	−0.381928	+	0.924192i	$0.624740\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	32.4317			1.44606			0.723029	−	0.690818i	$-0.242749\pi$
$503$	32.4317			1.44606			0.723029	+	0.690818i	$0.242749\pi$
$504$		0			0
$505$	2.97861			0.132546
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.6855	−	7.90133i	−0.606599	−	0.350220i	0.165034	−	0.986288i	$-0.447227\pi$
$509$	−13.6855	−	7.90133i	−0.606599	−	0.350220i	−0.771633	+	0.636068i	$0.780560\pi$
$510$		0			0
$511$	−10.4937	−	18.1756i	−0.464214	−	0.804042i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.7341	−	7.35202i	0.561130	−	0.323969i
$516$		0			0
$517$	17.1362	+	9.89361i	0.753650	+	0.435120i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.50310			−0.241095			−0.120548	−	0.992708i	$-0.538465\pi$
$521$	−5.50310			−0.241095			−0.120548	+	0.992708i	$0.538465\pi$
$522$		0			0
$523$		−	38.5894i		−	1.68740i	−0.536818	−	0.843698i	$-0.680374\pi$
$523$		−	38.5894i		−	1.68740i	0.536818	−	0.843698i	$-0.319626\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.12430	+	8.87555i	−0.223218	+	0.386625i
$528$		0			0
$529$	8.81970	+	15.2762i	0.383465	+	0.664181i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.9415	−	10.9359i	0.820449	−	0.473686i
$534$		0			0
$535$	3.54046	−	6.13225i	0.153067	−	0.265120i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			18.1382i			0.781268i
$540$		0			0
$541$			22.5666i			0.970214i	0.874455	+	0.485107i	$0.161219\pi$
$541$			22.5666i			0.970214i	−0.874455	+	0.485107i	$0.838781\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	20.6246	−	35.7229i	0.883463	−	1.53020i
$546$		0			0
$547$	−11.2679	+	6.50552i	−0.481780	+	0.278156i	−0.721158	−	0.692770i	$-0.756390\pi$
$547$	−11.2679	+	6.50552i	−0.481780	+	0.278156i	0.239378	+	0.970927i	$0.423057\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.88974	−	6.73723i	−0.165709	−	0.287016i
$552$		0			0
$553$	−9.02976	+	15.6400i	−0.383985	+	0.665081i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			5.73693i			0.243081i	0.992586	+	0.121541i	$0.0387835\pi$
$557$			5.73693i			0.243081i	−0.992586	+	0.121541i	$0.961217\pi$
$558$		0			0
$559$	11.8024			0.499186
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−13.2510	−	7.65045i	−0.558462	−	0.322428i	0.194066	−	0.980988i	$-0.437832\pi$
$563$	−13.2510	−	7.65045i	−0.558462	−	0.322428i	−0.752528	+	0.658560i	$0.771166\pi$
$564$		0			0
$565$	5.59908	−	3.23263i	0.235555	−	0.135998i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.63095	−	11.4851i	−0.277984	−	0.481482i	0.692900	−	0.721034i	$-0.256333\pi$
$569$	−6.63095	−	11.4851i	−0.277984	−	0.481482i	−0.970884	+	0.239552i	$0.922999\pi$
$570$		0			0
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.902378	−	0.430946i	$-0.141820\pi$
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.0779788	+	0.996955i	$0.475153\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.470166			−0.0196073
$576$		0			0
$577$	−4.78434			−0.199174			−0.0995872	−	0.995029i	$-0.531752\pi$
$577$	−4.78434			−0.199174			−0.0995872	+	0.995029i	$0.531752\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.66760	+	3.27219i	0.235132	+	0.135753i
$582$		0			0
$583$	−21.9406	−	38.0023i	−0.908689	−	1.57390i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−37.0796	+	21.4079i	−1.53044	+	0.883598i	−0.531095	+	0.847312i	$0.678219\pi$
$587$	−37.0796	+	21.4079i	−1.53044	+	0.883598i	−0.999341	+	0.0362861i	$0.988447\pi$
$588$		0			0
$589$	9.80179	+	5.65906i	0.403876	+	0.233178i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.825572			0.0339022			0.0169511	−	0.999856i	$-0.494604\pi$
$593$	0.825572			0.0339022			0.0169511	+	0.999856i	$0.494604\pi$
$594$		0			0
$595$		−	7.98438i		−	0.327328i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.961228	+	1.66490i	−0.0392747	+	0.0680258i	−0.884995	−	0.465601i	$-0.845838\pi$
$599$	−0.961228	+	1.66490i	−0.0392747	+	0.0680258i	0.845720	+	0.533627i	$0.179171\pi$
$600$		0			0
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.850425	−	0.526096i	$-0.823655\pi$
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.0303994	−	0.999538i	$-0.509678\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	25.6556	−	14.8123i	1.04305	−	0.602205i
$606$		0			0
$607$	−20.5078	+	35.5206i	−0.832386	+	1.44174i	0.0637546	+	0.997966i	$0.479693\pi$
$607$	−20.5078	+	35.5206i	−0.832386	+	1.44174i	−0.896141	+	0.443770i	$0.853641\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	18.7022i		−	0.756611i
$612$		0			0
$613$		−	5.05878i		−	0.204322i	−0.994768	−	0.102161i	$-0.967424\pi$
$613$		−	5.05878i		−	0.204322i	0.994768	−	0.102161i	$-0.0325757\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.0739	−	27.8408i	0.647112	−	1.12083i	−0.336698	−	0.941613i	$-0.609310\pi$
$617$	16.0739	−	27.8408i	0.647112	−	1.12083i	0.983809	−	0.179217i	$-0.0573566\pi$
$618$		0			0
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.936100	−	0.351734i	$-0.885592\pi$
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.163440	+	0.986553i	$0.552259\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.26924	−	3.93044i	−0.0909153	−	0.157470i
$624$		0			0
$625$	12.9871	−	22.4942i	0.519482	−	0.899770i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	15.3929i		−	0.613756i
$630$		0			0
$631$	15.4885			0.616586			0.308293	−	0.951292i	$-0.400242\pi$
$631$	15.4885			0.616586			0.308293	+	0.951292i	$0.400242\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.7162	+	8.49638i	0.583993	+	0.337168i
$636$		0			0
$637$	14.8468	−	8.57182i	0.588253	−	0.339628i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.2248	+	26.3701i	0.601344	+	1.04156i	0.992618	+	0.121284i	$0.0387011\pi$
$641$	15.2248	+	26.3701i	0.601344	+	1.04156i	−0.391274	+	0.920274i	$0.627966\pi$
$642$		0			0
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	0.183893	−	0.982946i	$-0.441130\pi$
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	−0.759310	+	0.650729i	$0.774463\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.6734			0.734126			0.367063	−	0.930196i	$-0.380363\pi$
$647$	18.6734			0.734126			0.367063	+	0.930196i	$0.380363\pi$
$648$		0			0
$649$	−17.2633			−0.677644
$650$		0			0
$651$		0			0
$652$		0			0
$653$	31.4276	+	18.1448i	1.22986	+	0.710059i	0.967000	−	0.254775i	$-0.0820015\pi$
$653$	31.4276	+	18.1448i	1.22986	+	0.710059i	0.262858	+	0.964834i	$0.415335\pi$
$654$		0			0
$655$	−4.11089	−	7.12028i	−0.160626	−	0.278212i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.3088	+	11.1480i	−0.752166	+	0.434263i	−0.826476	−	0.562972i	$-0.809658\pi$
$659$	−19.3088	+	11.1480i	−0.752166	+	0.434263i	0.0743103	+	0.997235i	$0.476324\pi$
$660$		0			0
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	0.395494	−	0.918469i	$-0.370573\pi$
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	−0.597670	+	0.801742i	$0.703907\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.81762			−0.341933
$666$		0			0
$667$		−	8.45996i		−	0.327571i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.85442	+	8.40810i	−0.187403	+	0.324591i
$672$		0			0
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	0.785753	−	0.618541i	$-0.212276\pi$
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	−0.928548	+	0.371211i	$0.878943\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.57613	−	4.95143i	0.329607	−	0.190299i	−0.326059	−	0.945349i	$-0.605721\pi$
$677$	8.57613	−	4.95143i	0.329607	−	0.190299i	0.655667	+	0.755050i	$0.272388\pi$
$678$		0			0
$679$	−12.6981	+	21.9938i	−0.487309	+	0.844043i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	39.0736i		−	1.49511i	−0.664200	−	0.747555i	$-0.731228\pi$
$683$		−	39.0736i		−	1.49511i	0.664200	−	0.747555i	$-0.268772\pi$
$684$		0			0
$685$		−	26.8316i		−	1.02518i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−20.7376	+	35.9185i	−0.790039	+	1.36839i
$690$		0			0
$691$	2.07502	−	1.19801i	0.0789375	−	0.0455746i	−0.460012	−	0.887913i	$-0.652155\pi$
$691$	2.07502	−	1.19801i	0.0789375	−	0.0455746i	0.538949	+	0.842338i	$0.318821\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.5391	−	25.1825i	−0.551500	−	0.955227i
$696$		0			0
$697$	−4.55443	+	7.88850i	−0.172511	+	0.298798i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	30.9184i		−	1.16777i	−0.811836	−	0.583885i	$-0.801532\pi$
$701$		−	30.9184i		−	1.16777i	0.811836	−	0.583885i	$-0.198468\pi$
$702$		0			0
$703$	−16.9993			−0.641141
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.05327	+	1.18546i	0.0772212	+	0.0445837i
$708$		0			0
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	−0.413717	−	0.910406i	$-0.635770\pi$
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	0.581576	+	0.813492i	$0.302436\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.15406	+	10.6591i	0.230471	+	0.399188i
$714$		0			0
$715$	−44.7870	−	25.8578i	−1.67494	−	0.967027i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.7871			0.551465			0.275733	−	0.961234i	$-0.411080\pi$
$719$	14.7871			0.551465			0.275733	+	0.961234i	$0.411080\pi$
$720$		0			0
$721$	11.7041			0.435884
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.642593	−	0.371001i	−0.0238653	−	0.0137786i
$726$		0			0
$727$	1.06681	+	1.84777i	0.0395658	+	0.0685299i	0.885130	−	0.465344i	$-0.154069\pi$
$727$	1.06681	+	1.84777i	0.0395658	+	0.0685299i	−0.845564	+	0.533873i	$0.820736\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.25675	+	2.45764i	−0.157442	+	0.0908990i
$732$		0			0
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	0.0297113	−	0.999559i	$-0.490541\pi$
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	−0.850787	+	0.525510i	$0.823875\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−43.7003			−1.60972
$738$		0			0
$739$			5.46282i			0.200953i	0.994939	+	0.100476i	$0.0320367\pi$
$739$			5.46282i			0.200953i	−0.994939	+	0.100476i	$0.967963\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.8170	+	29.1279i	−0.616955	+	1.06860i	0.373083	+	0.927798i	$0.378301\pi$
$743$	−16.8170	+	29.1279i	−0.616955	+	1.06860i	−0.990038	+	0.140800i	$0.955033\pi$
$744$		0			0
$745$	8.68910	+	15.0500i	0.318344	+	0.551388i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.88115	−	2.81813i	0.178353	−	0.102972i
$750$		0			0
$751$	12.6727	−	21.9498i	0.462435	−	0.800961i	−0.536647	−	0.843807i	$-0.680309\pi$
$751$	12.6727	−	21.9498i	0.462435	−	0.800961i	0.999082	+	0.0428462i	$0.0136426\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	10.3553i		−	0.376868i
$756$		0			0
$757$			3.95103i			0.143603i	0.997419	+	0.0718014i	$0.0228748\pi$
$757$			3.95103i			0.143603i	−0.997419	+	0.0718014i	$0.977125\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.3979	−	40.5264i	0.848175	−	1.46908i	−0.0346607	−	0.999399i	$-0.511035\pi$
$761$	23.3979	−	40.5264i	0.848175	−	1.46908i	0.882835	−	0.469682i	$-0.155632\pi$
$762$		0			0
$763$	28.4347	−	16.4168i	1.02941	−	0.594328i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.15835	+	14.1307i	0.294581	+	0.510229i
$768$		0			0
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	−0.815314	−	0.579019i	$-0.803436\pi$
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	0.909102	+	0.416573i	$0.136769\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	38.8477i		−	1.39725i	−0.715486	−	0.698627i	$-0.753795\pi$
$773$		−	38.8477i		−	1.39725i	0.715486	−	0.698627i	$-0.246205\pi$
$774$		0			0
$775$	1.07952			0.0387773
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.71173	+	5.02972i	0.312130	+	0.180209i
$780$		0			0
$781$	−56.6503	+	32.7071i	−2.02711	+	1.17035i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.0271	−	26.0277i	−0.536340	−	0.928968i
$786$		0			0
$787$	−40.8579	−	23.5893i	−1.45643	−	0.840869i	−0.457595	−	0.889161i	$-0.651289\pi$
$787$	−40.8579	−	23.5893i	−1.45643	−	0.840869i	−0.998833	+	0.0482918i	$0.984622\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.14621			0.182978
$792$		0			0
$793$	9.17648			0.325866
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.35645	+	3.66990i	0.225157	+	0.129995i	0.608336	−	0.793680i	$-0.291837\pi$
$797$	6.35645	+	3.66990i	0.225157	+	0.129995i	−0.383179	+	0.923674i	$0.625171\pi$
$798$		0			0
$799$	3.89442	+	6.74533i	0.137775	+	0.238633i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	49.0286	−	28.3067i	1.73018	−	0.998920i
$804$		0			0
$805$	−8.30423	−	4.79445i	−0.292686	−	0.168982i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.25520			−0.0792887			−0.0396443	−	0.999214i	$-0.512622\pi$
$809$	−2.25520			−0.0792887			−0.0396443	+	0.999214i	$0.512622\pi$
$810$		0			0
$811$		−	15.9986i		−	0.561785i	−0.959739	−	0.280893i	$-0.909369\pi$
$811$		−	15.9986i		−	0.561785i	0.959739	−	0.280893i	$-0.0906305\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.4844	−	40.6761i	0.822622	−	1.42482i
$816$		0			0
$817$	2.71411	+	4.70098i	0.0949548	+	0.164467i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.2413	+	14.5731i	−0.880928	+	0.508604i	−0.870964	−	0.491347i	$-0.836505\pi$
$821$	−25.2413	+	14.5731i	−0.880928	+	0.508604i	−0.00996351	+	0.999950i	$0.503172\pi$
$822$		0			0
$823$	4.15695	−	7.20005i	0.144902	−	0.250978i	−0.784434	−	0.620212i	$-0.787047\pi$
$823$	4.15695	−	7.20005i	0.144902	−	0.250978i	0.929336	+	0.369234i	$0.120380\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	43.5035i		−	1.51277i	−0.654129	−	0.756383i	$-0.726965\pi$
$827$		−	43.5035i		−	1.51277i	0.654129	−	0.756383i	$-0.273035\pi$
$828$		0			0
$829$		−	15.9248i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$829$		−	15.9248i		−	0.553092i	0.961001	−	0.276546i	$-0.0891897\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.56987	+	6.18320i	−0.123689	+	0.214235i
$834$		0			0
$835$	10.0317	−	5.79180i	0.347161	−	0.200433i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.0582	−	36.4739i	−0.727009	−	1.25922i	−0.958142	−	0.286295i	$-0.907576\pi$
$839$	−21.0582	−	36.4739i	−0.727009	−	1.25922i	0.231132	−	0.972922i	$-0.425757\pi$
$840$		0			0
$841$	−7.82437	+	13.5522i	−0.269806	+	0.467318i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			19.2266i			0.661415i
$846$		0			0
$847$	23.5806			0.810238
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.0095	−	9.24311i	−0.548800	−	0.316850i
$852$		0			0
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.217108	−	0.976148i	$-0.430338\pi$
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.953923	+	0.300053i	$0.0970043\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.6170	+	21.8532i	0.430988	+	0.746493i	0.996959	−	0.0779326i	$-0.0248319\pi$
$857$	12.6170	+	21.8532i	0.430988	+	0.746493i	−0.565971	+	0.824425i	$0.691499\pi$
$858$		0			0
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.986244	+	0.165297i	$0.0528584\pi$
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.636274	+	0.771463i	$0.280475\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−54.3877			−1.85138			−0.925689	−	0.378285i	$-0.876514\pi$
$863$	−54.3877			−1.85138			−0.925689	+	0.378285i	$0.876514\pi$
$864$		0			0
$865$	29.0778			0.988675
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−42.1888	−	24.3577i	−1.43116	−	0.826278i
$870$		0			0
$871$	20.6521	+	35.7704i	0.699768	+	1.21203i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	17.2050	−	9.93334i	0.581637	−	0.335808i
$876$		0			0
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	0.397067	−	0.917790i	$-0.370028\pi$
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	−0.596296	+	0.802765i	$0.703361\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	43.2881			1.45841			0.729207	−	0.684293i	$-0.239889\pi$
$881$	43.2881			1.45841			0.729207	+	0.684293i	$0.239889\pi$
$882$		0			0
$883$		−	31.1510i		−	1.04832i	−0.851621	−	0.524158i	$-0.824380\pi$
$883$		−	31.1510i		−	1.04832i	0.851621	−	0.524158i	$-0.175620\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.8886	+	43.1083i	−0.835677	+	1.44743i	0.0578015	+	0.998328i	$0.481591\pi$
$887$	−24.8886	+	43.1083i	−0.835677	+	1.44743i	−0.893478	+	0.449107i	$0.851742\pi$
$888$		0			0
$889$	6.76295	+	11.7138i	0.226822	+	0.392867i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.44926	−	4.30083i	0.249280	−	0.143922i
$894$		0			0
$895$	10.0595	−	17.4236i	0.336253	−	0.582407i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			19.4243i			0.647838i
$900$		0			0
$901$		−	17.2730i		−	0.575447i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.6059	+	30.4944i	−0.585241	+	1.01367i
$906$		0			0
$907$	−16.6712	+	9.62515i	−0.553559	+	0.319598i	−0.750556	−	0.660806i	$-0.770214\pi$
$907$	−16.6712	+	9.62515i	−0.553559	+	0.319598i	0.196997	+	0.980404i	$0.436881\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.1396	+	19.2944i	0.369072	+	0.639252i	0.989421	−	0.145074i	$-0.0463421\pi$
$911$	11.1396	+	19.2944i	0.369072	+	0.639252i	−0.620348	+	0.784326i	$0.713009\pi$
$912$		0			0
$913$	−8.82669	+	15.2883i	−0.292121	+	0.505968i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	6.54438i		−	0.216114i
$918$		0			0
$919$	−28.0122			−0.924039			−0.462019	−	0.886870i	$-0.652875\pi$
$919$	−28.0122			−0.924039			−0.462019	+	0.886870i	$0.652875\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	53.5440	+	30.9136i	1.76242	+	1.01753i
$924$		0			0
$925$	−1.40416	+	0.810691i	−0.0461684	+	0.0266554i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.94220	+	6.82809i	0.129339	+	0.224022i	0.923421	−	0.383789i	$-0.125381\pi$
$929$	3.94220	+	6.82809i	0.129339	+	0.224022i	−0.794081	+	0.607811i	$0.792048\pi$
$930$		0			0
$931$	6.82847	+	3.94242i	0.223794	+	0.129208i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	21.5378			0.704361
$936$		0			0
$937$	−8.98600			−0.293560			−0.146780	−	0.989169i	$-0.546891\pi$
$937$	−8.98600			−0.293560			−0.146780	+	0.989169i	$0.546891\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−21.0227	−	12.1375i	−0.685322	−	0.395671i	0.116535	−	0.993187i	$-0.462821\pi$
$941$	−21.0227	−	12.1375i	−0.685322	−	0.395671i	−0.801857	+	0.597516i	$0.796155\pi$
$942$		0			0
$943$	5.46967	+	9.47375i	0.178117	+	0.308508i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.71382	−	0.989473i	0.0556916	−	0.0321536i	−0.471896	−	0.881654i	$-0.656430\pi$
$947$	1.71382	−	0.989473i	0.0556916	−	0.0321536i	0.527587	+	0.849501i	$0.323097\pi$
$948$		0			0
$949$	−46.3402	−	26.7545i	−1.50427	−	0.868488i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.9674			−0.938347			−0.469173	−	0.883106i	$-0.655448\pi$
$953$	−28.9674			−0.938347			−0.469173	+	0.883106i	$0.655448\pi$
$954$		0			0
$955$			21.9753i			0.711104i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10.6787	−	18.4960i	0.344833	−	0.597268i
$960$		0			0
$961$	1.37008	+	2.37304i	0.0441961	+	0.0765498i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.8017	−	7.96842i	0.444293	−	0.256512i
$966$		0			0
$967$	−0.00531192	+	0.00920052i	−0.000170820	+	0.000295869i	−0.866111	−	0.499852i	$-0.833388\pi$
$967$	−0.00531192	+	0.00920052i	−0.000170820	+	0.000295869i	0.865940	+	0.500148i	$0.166721\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			17.0984i			0.548715i	0.961628	+	0.274357i	$0.0884651\pi$
$971$			17.0984i			0.548715i	−0.961628	+	0.274357i	$0.911535\pi$
$972$		0			0
$973$		−	23.1457i		−	0.742017i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.50612	−	9.53688i	0.176156	−	0.305112i	−0.764404	−	0.644737i	$-0.776967\pi$
$977$	5.50612	−	9.53688i	0.176156	−	0.305112i	0.940561	+	0.339625i	$0.110300\pi$
$978$		0			0
$979$	10.6023	−	6.12126i	0.338852	−	0.195636i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.7443	+	39.3943i	0.725432	+	1.25648i	0.958796	+	0.284095i	$0.0916932\pi$
$983$	22.7443	+	39.3943i	0.725432	+	1.25648i	−0.233364	+	0.972389i	$0.574973\pi$
$984$		0			0
$985$	4.92521	−	8.53071i	0.156930	−	0.271811i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			5.90304i			0.187706i
$990$		0			0
$991$	−3.93737			−0.125075			−0.0625374	−	0.998043i	$-0.519919\pi$
$991$	−3.93737			−0.125075			−0.0625374	+	0.998043i	$0.519919\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.6678	−	6.73642i	−0.369895	−	0.213559i
$996$		0			0
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	−0.533900	−	0.845547i	$-0.679274\pi$
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	0.465316	+	0.885145i	$0.345941\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.r.b.145.7		16
3.2	odd	2		288.2.r.b.49.1		16
4.3	odd	2		216.2.n.b.37.4		16
8.3	odd	2		216.2.n.b.37.3		16
8.5	even	2	inner	864.2.r.b.145.2		16
9.2	odd	6		288.2.r.b.241.8		16
9.4	even	3		2592.2.d.k.1297.2		8
9.5	odd	6		2592.2.d.j.1297.7		8
9.7	even	3	inner	864.2.r.b.721.2		16
12.11	even	2		72.2.n.b.13.5	✓	16
24.5	odd	2		288.2.r.b.49.8		16
24.11	even	2		72.2.n.b.13.6	yes	16
36.7	odd	6		216.2.n.b.181.3		16
36.11	even	6		72.2.n.b.61.6	yes	16
36.23	even	6		648.2.d.j.325.1		8
36.31	odd	6		648.2.d.k.325.8		8
72.5	odd	6		2592.2.d.j.1297.2		8
72.11	even	6		72.2.n.b.61.5	yes	16
72.13	even	6		2592.2.d.k.1297.7		8
72.29	odd	6		288.2.r.b.241.1		16
72.43	odd	6		216.2.n.b.181.4		16
72.59	even	6		648.2.d.j.325.2		8
72.61	even	6	inner	864.2.r.b.721.7		16
72.67	odd	6		648.2.d.k.325.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.5	✓	16	12.11	even	2
72.2.n.b.13.6	yes	16	24.11	even	2
72.2.n.b.61.5	yes	16	72.11	even	6
72.2.n.b.61.6	yes	16	36.11	even	6
216.2.n.b.37.3		16	8.3	odd	2
216.2.n.b.37.4		16	4.3	odd	2
216.2.n.b.181.3		16	36.7	odd	6
216.2.n.b.181.4		16	72.43	odd	6
288.2.r.b.49.1		16	3.2	odd	2
288.2.r.b.49.8		16	24.5	odd	2
288.2.r.b.241.1		16	72.29	odd	6
288.2.r.b.241.8		16	9.2	odd	6
648.2.d.j.325.1		8	36.23	even	6
648.2.d.j.325.2		8	72.59	even	6
648.2.d.k.325.7		8	72.67	odd	6
648.2.d.k.325.8		8	36.31	odd	6
864.2.r.b.145.2		16	8.5	even	2	inner
864.2.r.b.145.7		16	1.1	even	1	trivial
864.2.r.b.721.2		16	9.7	even	3	inner
864.2.r.b.721.7		16	72.61	even	6	inner
2592.2.d.j.1297.2		8	72.5	odd	6
2592.2.d.j.1297.7		8	9.5	odd	6
2592.2.d.k.1297.2		8	9.4	even	3
2592.2.d.k.1297.7		8	72.13	even	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.97542 + 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +O(q^{10})\)	\(q+(1.97542 + 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(-4.24153 + 2.44885i) q^{11} +(4.00895 + 2.31457i) q^{13} -1.92788 q^{17} +2.12907i q^{19} +(-1.15765 + 2.00511i) q^{23} +(0.101535 + 0.175863i) q^{25} +(-3.16440 + 1.82697i) q^{29} +(2.65800 - 4.60379i) q^{31} +4.14154i q^{35} +7.98438i q^{37} +(2.36240 - 4.09180i) q^{41} +(2.20800 - 1.27479i) q^{43} +(-2.02005 - 3.49884i) q^{47} +(1.85171 - 3.20726i) q^{49} +8.95958i q^{53} -11.1718 q^{55} +(3.05255 + 1.76239i) q^{59} +(1.71675 - 0.991165i) q^{61} +(5.27959 + 9.14451i) q^{65} +(7.72723 + 4.46132i) q^{67} +13.3561 q^{71} -11.5592 q^{73} +(-7.70112 - 4.44625i) q^{77} +(4.97330 + 8.61401i) q^{79} +(3.12153 - 1.80221i) q^{83} +(-3.80838 - 2.19877i) q^{85} -2.49965 q^{89} +8.40489i q^{91} +(-2.42823 + 4.20582i) q^{95} +(6.99370 + 12.1134i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) \) 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

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