LMFDB - Embedded newform 504.2.bl.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(17,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("504.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bl (of order $6$, degree $2$, 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:	$4.02446026187$
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} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Root			$1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	504.89
Dual form			504.2.bl.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01089 + 1.75092i) q^{5} +(0.561961 - 2.58538i) q^{7} +O(q^{10})$	$q+(-1.01089 + 1.75092i) q^{5} +(0.561961 - 2.58538i) q^{7} +(3.14000 - 1.81288i) q^{11} -4.74306i q^{13} +(1.71936 + 2.97801i) q^{17} +(4.34657 + 2.50950i) q^{19} +(6.02091 + 3.47617i) q^{23} +(0.456187 + 0.790140i) q^{25} -2.03630i q^{29} +(-0.266467 + 0.153845i) q^{31} +(3.95871 + 3.59749i) q^{35} +(5.84841 - 10.1298i) q^{37} -8.77283 q^{41} +3.21155 q^{43} +(0.192181 - 0.332867i) q^{47} +(-6.36840 - 2.90577i) q^{49} +(-5.53113 + 3.19340i) q^{53} +7.33052i q^{55} +(-4.25743 - 7.37408i) q^{59} +(1.05676 + 0.610120i) q^{61} +(8.30472 + 4.79473i) q^{65} +(-0.0419737 - 0.0727006i) q^{67} -8.41789i q^{71} +(-9.11304 + 5.26142i) q^{73} +(-2.92243 - 9.13687i) q^{77} +(-0.821159 + 1.42229i) q^{79} +10.3595 q^{83} -6.95235 q^{85} +(-4.30155 + 7.45051i) q^{89} +(-12.2626 - 2.66541i) q^{91} +(-8.78785 + 5.07367i) q^{95} +12.7477i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) $ 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.01089	+	1.75092i	−0.452085	+	0.783035i	−0.998515	−	0.0544698i	$-0.982653\pi$
$5$	−1.01089	+	1.75092i	−0.452085	+	0.783035i	0.546430	+	0.837505i	$0.315986\pi$
$6$		0			0
$7$	0.561961	−	2.58538i	0.212401	−	0.977183i
$7$	0.561961	−	2.58538i	0.212401	−	0.977183i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.14000	−	1.81288i	0.946746	−	0.546604i	0.0546772	−	0.998504i	$-0.482587\pi$
$11$	3.14000	−	1.81288i	0.946746	−	0.546604i	0.892069	+	0.451900i	$0.149254\pi$
$12$		0			0
$13$		−	4.74306i		−	1.31549i	−0.753241	−	0.657744i	$-0.771511\pi$
$13$		−	4.74306i		−	1.31549i	0.753241	−	0.657744i	$-0.228489\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.71936	+	2.97801i	0.417005	+	0.722274i	0.995637	−	0.0933149i	$-0.0297463\pi$
$17$	1.71936	+	2.97801i	0.417005	+	0.722274i	−0.578631	+	0.815589i	$0.696413\pi$
$18$		0			0
$19$	4.34657	+	2.50950i	0.997173	+	0.575718i	0.907411	−	0.420245i	$-0.138056\pi$
$19$	4.34657	+	2.50950i	0.997173	+	0.575718i	0.0897621	+	0.995963i	$0.471389\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.02091	+	3.47617i	1.25545	+	0.724832i	0.972186	−	0.234211i	$-0.0752505\pi$
$23$	6.02091	+	3.47617i	1.25545	+	0.724832i	0.283261	+	0.959043i	$0.408584\pi$
$24$		0			0
$25$	0.456187	+	0.790140i	0.0912375	+	0.158028i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	2.03630i		−	0.378131i	−0.981965	−	0.189065i	$-0.939454\pi$
$29$		−	2.03630i		−	0.378131i	0.981965	−	0.189065i	$-0.0605458\pi$
$30$		0			0
$31$	−0.266467	+	0.153845i	−0.0478588	+	0.0276313i	−0.523738	−	0.851879i	$-0.675463\pi$
$31$	−0.266467	+	0.153845i	−0.0478588	+	0.0276313i	0.475880	+	0.879510i	$0.342130\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.95871	+	3.59749i	0.669145	+	0.608088i
$36$		0			0
$37$	5.84841	−	10.1298i	0.961473	−	1.66532i	0.242668	−	0.970109i	$-0.421977\pi$
$37$	5.84841	−	10.1298i	0.961473	−	1.66532i	0.718806	−	0.695211i	$-0.244689\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.77283			−1.37009			−0.685043	−	0.728503i	$-0.740217\pi$
$41$	−8.77283			−1.37009			−0.685043	+	0.728503i	$0.740217\pi$
$42$		0			0
$43$	3.21155			0.489756			0.244878	−	0.969554i	$-0.421252\pi$
$43$	3.21155			0.489756			0.244878	+	0.969554i	$0.421252\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.192181	−	0.332867i	0.0280324	−	0.0485536i	−0.851669	−	0.524080i	$-0.824409\pi$
$47$	0.192181	−	0.332867i	0.0280324	−	0.0485536i	0.879701	+	0.475527i	$0.157742\pi$
$48$		0			0
$49$	−6.36840	−	2.90577i	−0.909772	−	0.415109i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.53113	+	3.19340i	−0.759759	+	0.438647i	−0.829209	−	0.558938i	$-0.811209\pi$
$53$	−5.53113	+	3.19340i	−0.759759	+	0.438647i	0.0694502	+	0.997585i	$0.477875\pi$
$54$		0			0
$55$			7.33052i			0.988447i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.25743	−	7.37408i	−0.554270	−	0.960023i	−0.997960	−	0.0638431i	$-0.979664\pi$
$59$	−4.25743	−	7.37408i	−0.554270	−	0.960023i	0.443690	−	0.896180i	$-0.353669\pi$
$60$		0			0
$61$	1.05676	+	0.610120i	0.135304	+	0.0781179i	0.566124	−	0.824320i	$-0.308442\pi$
$61$	1.05676	+	0.610120i	0.135304	+	0.0781179i	−0.430820	+	0.902438i	$0.641776\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.30472	+	4.79473i	1.03007	+	0.594713i
$66$		0			0
$67$	−0.0419737	−	0.0727006i	−0.00512791	−	0.00888180i	0.863450	−	0.504434i	$-0.168299\pi$
$67$	−0.0419737	−	0.0727006i	−0.00512791	−	0.00888180i	−0.868578	+	0.495553i	$0.834966\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.41789i		−	0.999020i	−0.866308	−	0.499510i	$-0.833513\pi$
$71$		−	8.41789i		−	0.999020i	0.866308	−	0.499510i	$-0.166487\pi$
$72$		0			0
$73$	−9.11304	+	5.26142i	−1.06660	+	0.615802i	−0.927251	−	0.374441i	$-0.877835\pi$
$73$	−9.11304	+	5.26142i	−1.06660	+	0.615802i	−0.139350	+	0.990243i	$0.544501\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.92243	−	9.13687i	−0.333042	−	1.04124i
$78$		0			0
$79$	−0.821159	+	1.42229i	−0.0923876	+	0.160020i	−0.908515	−	0.417852i	$-0.862783\pi$
$79$	−0.821159	+	1.42229i	−0.0923876	+	0.160020i	0.816128	+	0.577872i	$0.196117\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.3595			1.13710			0.568550	−	0.822648i	$-0.307504\pi$
$83$	10.3595			1.13710			0.568550	+	0.822648i	$0.307504\pi$
$84$		0			0
$85$	−6.95235			−0.754088
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.30155	+	7.45051i	−0.455964	+	0.789752i	−0.998743	−	0.0501230i	$-0.984039\pi$
$89$	−4.30155	+	7.45051i	−0.455964	+	0.789752i	0.542779	+	0.839875i	$0.317372\pi$
$90$		0			0
$91$	−12.2626	−	2.66541i	−1.28547	−	0.279411i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.78785	+	5.07367i	−0.901615	+	0.520547i
$96$		0			0
$97$			12.7477i			1.29433i	0.762350	+	0.647165i	$0.224046\pi$
$97$			12.7477i			1.29433i	−0.762350	+	0.647165i	$0.775954\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.80000	−	11.7779i	−0.676625	−	1.17195i	−0.975991	−	0.217811i	$-0.930108\pi$
$101$	−6.80000	−	11.7779i	−0.676625	−	1.17195i	0.299366	−	0.954138i	$-0.403225\pi$
$102$		0			0
$103$	15.5709	+	8.98987i	1.53425	+	0.885798i	0.999159	+	0.0410016i	$0.0130549\pi$
$103$	15.5709	+	8.98987i	1.53425	+	0.885798i	0.535088	+	0.844796i	$0.320278\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.05871	−	3.49800i	−0.585718	−	0.338164i	0.177685	−	0.984087i	$-0.443139\pi$
$107$	−6.05871	−	3.49800i	−0.585718	−	0.338164i	−0.763402	+	0.645923i	$0.776473\pi$
$108$		0			0
$109$	6.45987	+	11.1888i	0.618743	+	1.07169i	0.989715	+	0.143050i	$0.0456911\pi$
$109$	6.45987	+	11.1888i	0.618743	+	1.07169i	−0.370973	+	0.928644i	$0.620976\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			8.61440i			0.810375i	0.914234	+	0.405187i	$0.132794\pi$
$113$			8.61440i			0.810375i	−0.914234	+	0.405187i	$0.867206\pi$
$114$		0			0
$115$	−12.1730	+	7.02809i	−1.13514	+	0.655372i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.66551	−	2.77167i	0.794366	−	0.254078i
$120$		0			0
$121$	1.07307	−	1.85861i	0.0975516	−	0.168964i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.9536			−1.06916
$126$		0			0
$127$	−18.8607			−1.67362			−0.836809	−	0.547495i	$-0.815582\pi$
$127$	−18.8607			−1.67362			−0.836809	+	0.547495i	$0.815582\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.58615	+	11.4075i	−0.575435	+	0.996682i	0.420560	+	0.907265i	$0.361834\pi$
$131$	−6.58615	+	11.4075i	−0.575435	+	0.996682i	−0.995994	+	0.0894170i	$0.971500\pi$
$132$		0			0
$133$	8.93061	−	9.82732i	0.774382	−	0.852137i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	18.8310	−	10.8721i	1.60884	−	0.928864i	0.619210	−	0.785225i	$-0.287453\pi$
$137$	18.8310	−	10.8721i	1.60884	−	0.928864i	0.989630	−	0.143639i	$-0.0458804\pi$
$138$		0			0
$139$			6.59355i			0.559258i	0.960108	+	0.279629i	$0.0902114\pi$
$139$			6.59355i			0.559258i	−0.960108	+	0.279629i	$0.909789\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.59860	−	14.8932i	−0.719051	−	1.24543i
$144$		0			0
$145$	3.56539	+	2.05848i	0.296090	+	0.170947i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.3161	−	5.95603i	−0.845131	−	0.487937i	0.0138740	−	0.999904i	$-0.495584\pi$
$149$	−10.3161	−	5.95603i	−0.845131	−	0.487937i	−0.859005	+	0.511967i	$0.828917\pi$
$150$		0			0
$151$	−7.51999	−	13.0250i	−0.611968	−	1.05996i	−0.990908	−	0.134538i	$-0.957045\pi$
$151$	−7.51999	−	13.0250i	−0.611968	−	1.05996i	0.378941	−	0.925421i	$-0.376288\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	0.622082i		−	0.0499668i
$156$		0			0
$157$	−15.6968	+	9.06257i	−1.25274	+	0.723272i	−0.971653	−	0.236410i	$-0.924029\pi$
$157$	−15.6968	+	9.06257i	−1.25274	+	0.723272i	−0.281090	+	0.959681i	$0.590696\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.3708	−	13.6129i	0.974952	−	1.07285i
$162$		0			0
$163$	10.1844	−	17.6398i	0.797700	−	1.38166i	−0.123410	−	0.992356i	$-0.539383\pi$
$163$	10.1844	−	17.6398i	0.797700	−	1.38166i	0.921110	−	0.389302i	$-0.127284\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.1056			−0.859377			−0.429688	−	0.902977i	$-0.641377\pi$
$167$	−11.1056			−0.859377			−0.429688	+	0.902977i	$0.641377\pi$
$168$		0			0
$169$	−9.49664			−0.730511
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.64460	+	4.58059i	−0.201065	+	0.348255i	−0.948872	−	0.315661i	$-0.897774\pi$
$173$	−2.64460	+	4.58059i	−0.201065	+	0.348255i	0.747807	+	0.663917i	$0.231107\pi$
$174$		0			0
$175$	2.29917	−	0.735391i	0.173801	−	0.0555903i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−21.6741	+	12.5135i	−1.62000	+	0.935306i	−0.633080	+	0.774087i	$0.718209\pi$
$179$	−21.6741	+	12.5135i	−1.62000	+	0.935306i	−0.986919	+	0.161220i	$0.948457\pi$
$180$		0			0
$181$			1.10023i			0.0817793i	0.999164	+	0.0408896i	$0.0130192\pi$
$181$			1.10023i			0.0817793i	−0.999164	+	0.0408896i	$0.986981\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	11.8243	+	20.4802i	0.869336	+	1.50573i
$186$		0			0
$187$	10.7976	+	6.23397i	0.789596	+	0.455873i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	20.5966	+	11.8915i	1.49032	+	0.860436i	0.999939	−	0.0110722i	$-0.00352447\pi$
$191$	20.5966	+	11.8915i	1.49032	+	0.860436i	0.490381	+	0.871508i	$0.336858\pi$
$192$		0			0
$193$	4.53630	+	7.85709i	0.326530	+	0.565566i	0.981821	−	0.189810i	$-0.0607873\pi$
$193$	4.53630	+	7.85709i	0.326530	+	0.565566i	−0.655291	+	0.755376i	$0.727454\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.34682i		−	0.380945i	−0.981692	−	0.190473i	$-0.938998\pi$
$197$		−	5.34682i		−	0.380945i	0.981692	−	0.190473i	$-0.0610021\pi$
$198$		0			0
$199$	11.2592	−	6.50050i	0.798143	−	0.460808i	−0.0446781	−	0.999001i	$-0.514226\pi$
$199$	11.2592	−	6.50050i	0.798143	−	0.460808i	0.842822	+	0.538193i	$0.180893\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.26460	−	1.14432i	−0.369503	−	0.0803154i
$204$		0			0
$205$	8.86840	−	15.3605i	0.619396	−	1.07283i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	18.1977			1.25876
$210$		0			0
$211$	4.77710			0.328869			0.164434	−	0.986388i	$-0.447420\pi$
$211$	4.77710			0.328869			0.164434	+	0.986388i	$0.447420\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.24653	+	5.62316i	−0.221412	+	0.383496i
$216$		0			0
$217$	0.248003	+	0.775373i	0.0168356	+	0.0526357i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.1249	−	8.15502i	0.950144	−	0.548566i
$222$		0			0
$223$			7.26700i			0.486634i	0.969947	+	0.243317i	$0.0782356\pi$
$223$			7.26700i			0.486634i	−0.969947	+	0.243317i	$0.921764\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.40875	−	4.17209i	−0.159875	−	0.276911i	0.774949	−	0.632024i	$-0.217776\pi$
$227$	−2.40875	−	4.17209i	−0.159875	−	0.276911i	−0.934823	+	0.355113i	$0.884442\pi$
$228$		0			0
$229$	11.0654	+	6.38861i	0.731222	+	0.422171i	0.818869	−	0.573981i	$-0.194602\pi$
$229$	11.0654	+	6.38861i	0.731222	+	0.422171i	−0.0876474	+	0.996152i	$0.527935\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.6622	+	9.04257i	1.02606	+	0.592399i	0.915855	−	0.401510i	$-0.131514\pi$
$233$	15.6622	+	9.04257i	1.02606	+	0.592399i	0.110210	+	0.993908i	$0.464848\pi$
$234$		0			0
$235$	0.388549	+	0.672986i	0.0253461	+	0.0439008i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			6.01256i			0.388920i	0.980910	+	0.194460i	$0.0622954\pi$
$239$			6.01256i			0.388920i	−0.980910	+	0.194460i	$0.937705\pi$
$240$		0			0
$241$	−8.45282	+	4.88024i	−0.544494	+	0.314364i	−0.746898	−	0.664938i	$-0.768458\pi$
$241$	−8.45282	+	4.88024i	−0.544494	+	0.314364i	0.202404	+	0.979302i	$0.435125\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.5255	−	8.21314i	0.736340	−	0.524718i
$246$		0			0
$247$	11.9027	−	20.6161i	0.757350	−	1.31177i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.2692			0.900666			0.450333	−	0.892861i	$-0.351305\pi$
$251$	14.2692			0.900666			0.450333	+	0.892861i	$0.351305\pi$
$252$		0			0
$253$	25.2075			1.58478
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.28900	+	12.6249i	−0.454675	+	0.787520i	−0.998669	−	0.0515686i	$-0.983578\pi$
$257$	−7.28900	+	12.6249i	−0.454675	+	0.787520i	0.543994	+	0.839089i	$0.316911\pi$
$258$		0			0
$259$	−22.9027	−	20.8129i	−1.42310	−	1.29325i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.0919	+	7.55860i	−0.807280	+	0.466083i	−0.846010	−	0.533167i	$-0.821002\pi$
$263$	−13.0919	+	7.55860i	−0.807280	+	0.466083i	0.0387306	+	0.999250i	$0.487669\pi$
$264$		0			0
$265$		−	12.9127i		−	0.793224i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.851686	+	1.47516i	0.0519282	+	0.0899423i	0.890821	−	0.454354i	$-0.150130\pi$
$269$	0.851686	+	1.47516i	0.0519282	+	0.0899423i	−0.838893	+	0.544297i	$0.816797\pi$
$270$		0			0
$271$	−24.7312	−	14.2786i	−1.50231	−	0.867361i	−0.999996	−	0.00267828i	$-0.999147\pi$
$271$	−24.7312	−	14.2786i	−1.50231	−	0.867361i	−0.502318	−	0.864683i	$-0.667519\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.86486	+	1.65403i	0.172757	+	0.0997415i
$276$		0			0
$277$	1.24464	+	2.15578i	0.0747832	+	0.129528i	0.900992	−	0.433836i	$-0.142840\pi$
$277$	1.24464	+	2.15578i	0.0747832	+	0.129528i	−0.826209	+	0.563364i	$0.809507\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	0.670935i		−	0.0400246i	−0.999800	−	0.0200123i	$-0.993629\pi$
$281$		−	0.670935i		−	0.0400246i	0.999800	−	0.0200123i	$-0.00637054\pi$
$282$		0			0
$283$	17.9849	−	10.3836i	1.06909	−	0.617240i	0.141158	−	0.989987i	$-0.454917\pi$
$283$	17.9849	−	10.3836i	1.06909	−	0.617240i	0.927933	+	0.372747i	$0.121584\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.92998	+	22.6811i	−0.291008	+	1.33882i
$288$		0			0
$289$	2.58763	−	4.48190i	0.152213	−	0.263641i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−20.9828			−1.22583			−0.612914	−	0.790149i	$-0.710003\pi$
$293$	−20.9828			−1.22583			−0.612914	+	0.790149i	$0.710003\pi$
$294$		0			0
$295$	17.2152			1.00231
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.4877	−	28.5576i	0.953509	−	1.65153i
$300$		0			0
$301$	1.80476	−	8.30307i	0.104025	−	0.478581i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.13654	+	1.23353i	−0.122338	+	0.0706319i
$306$		0			0
$307$		−	4.77897i		−	0.272750i	−0.990657	−	0.136375i	$-0.956455\pi$
$307$		−	4.77897i		−	0.272750i	0.990657	−	0.136375i	$-0.0435452\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.6987	−	21.9948i	−0.720078	−	1.24721i	−0.960968	−	0.276660i	$-0.910773\pi$
$311$	−12.6987	−	21.9948i	−0.720078	−	1.24721i	0.240890	−	0.970553i	$-0.422561\pi$
$312$		0			0
$313$	24.5723	+	14.1868i	1.38891	+	0.801886i	0.993192	−	0.116488i	$-0.0371636\pi$
$313$	24.5723	+	14.1868i	1.38891	+	0.801886i	0.395715	+	0.918374i	$0.370497\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.2783	+	5.93420i	0.577289	+	0.333298i	0.760055	−	0.649858i	$-0.225172\pi$
$317$	10.2783	+	5.93420i	0.577289	+	0.333298i	−0.182766	+	0.983156i	$0.558505\pi$
$318$		0			0
$319$	−3.69156	−	6.39397i	−0.206688	−	0.357994i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			17.2589i			0.960310i
$324$		0			0
$325$	3.74768	−	2.16372i	0.207884	−	0.120022i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.752590	−	0.683919i	−0.0414916	−	0.0377057i
$330$		0			0
$331$	−7.17325	+	12.4244i	−0.394278	+	0.682909i	−0.993009	−	0.118041i	$-0.962338\pi$
$331$	−7.17325	+	12.4244i	−0.394278	+	0.682909i	0.598731	+	0.800950i	$0.295672\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.169724			0.00927301
$336$		0			0
$337$	−26.8167			−1.46080			−0.730401	−	0.683019i	$-0.760667\pi$
$337$	−26.8167			−1.46080			−0.730401	+	0.683019i	$0.760667\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.557803	+	0.966144i	−0.0302068	+	0.0523196i
$342$		0			0
$343$	−11.0913	+	14.8318i	−0.598874	+	0.800843i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.35617	−	3.66973i	0.341217	−	0.197002i	−0.319593	−	0.947555i	$-0.603546\pi$
$347$	6.35617	−	3.66973i	0.341217	−	0.197002i	0.660810	+	0.750553i	$0.270213\pi$
$348$		0			0
$349$		−	22.9882i		−	1.23053i	−0.788320	−	0.615265i	$-0.789049\pi$
$349$		−	22.9882i		−	1.23053i	0.788320	−	0.615265i	$-0.210951\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.82129	+	10.0828i	0.309836	+	0.536652i	0.978326	−	0.207069i	$-0.0663925\pi$
$353$	5.82129	+	10.0828i	0.309836	+	0.536652i	−0.668490	+	0.743721i	$0.733059\pi$
$354$		0			0
$355$	14.7391	+	8.50959i	0.782268	+	0.451642i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.0093	+	10.3977i	0.950493	+	0.548767i	0.893234	−	0.449592i	$-0.148431\pi$
$359$	18.0093	+	10.3977i	0.950493	+	0.548767i	0.0572588	+	0.998359i	$0.481764\pi$
$360$		0			0
$361$	3.09514	+	5.36094i	0.162902	+	0.282155i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	21.2749i		−	1.11358i
$366$		0			0
$367$	4.05124	−	2.33899i	0.211473	−	0.122094i	−0.390523	−	0.920593i	$-0.627706\pi$
$367$	4.05124	−	2.33899i	0.211473	−	0.122094i	0.601996	+	0.798499i	$0.294372\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.14788	+	16.0946i	0.267265	+	0.835592i
$372$		0			0
$373$	−9.44851	+	16.3653i	−0.489225	+	0.847363i	−0.999923	−	0.0123972i	$-0.996054\pi$
$373$	−9.44851	+	16.3653i	−0.489225	+	0.847363i	0.510698	+	0.859760i	$0.329387\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.65828			−0.497427
$378$		0			0
$379$	5.99600			0.307994			0.153997	−	0.988071i	$-0.450785\pi$
$379$	5.99600			0.307994			0.153997	+	0.988071i	$0.450785\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.0490	+	22.6015i	−0.666773	+	1.15488i	0.312029	+	0.950073i	$0.398991\pi$
$383$	−13.0490	+	22.6015i	−0.666773	+	1.15488i	−0.978801	+	0.204811i	$0.934342\pi$
$384$		0			0
$385$	18.9522	+	4.11946i	0.965893	+	0.209947i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.1808	−	9.34197i	0.820398	−	0.473657i	−0.0301558	−	0.999545i	$-0.509600\pi$
$389$	16.1808	−	9.34197i	0.820398	−	0.473657i	0.850554	+	0.525888i	$0.176267\pi$
$390$		0			0
$391$			23.9071i			1.20904i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.66021	−	2.87557i	−0.0835342	−	0.144685i
$396$		0			0
$397$	−8.41621	−	4.85910i	−0.422398	−	0.243871i	0.273705	−	0.961814i	$-0.411751\pi$
$397$	−8.41621	−	4.85910i	−0.422398	−	0.243871i	−0.696103	+	0.717942i	$0.745084\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.1872	−	14.5418i	−1.25779	−	0.726183i	−0.285143	−	0.958485i	$-0.592041\pi$
$401$	−25.1872	−	14.5418i	−1.25779	−	0.726183i	−0.972644	+	0.232302i	$0.925374\pi$
$402$		0			0
$403$	0.729694	+	1.26387i	0.0363487	+	0.0629577i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	42.4099i		−	2.10218i
$408$		0			0
$409$	−22.2509	+	12.8466i	−1.10024	+	0.635221i	−0.936283	−	0.351247i	$-0.885758\pi$
$409$	−22.2509	+	12.8466i	−1.10024	+	0.635221i	−0.163953	+	0.986468i	$0.552424\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−21.4573	+	6.86313i	−1.05585	+	0.337713i
$414$		0			0
$415$	−10.4723	+	18.1386i	−0.514067	+	0.890390i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.33235			−0.309356			−0.154678	−	0.987965i	$-0.549434\pi$
$419$	−6.33235			−0.309356			−0.154678	+	0.987965i	$0.549434\pi$
$420$		0			0
$421$	−21.0541			−1.02611			−0.513056	−	0.858355i	$-0.671487\pi$
$421$	−21.0541			−1.02611			−0.513056	+	0.858355i	$0.671487\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.56870	+	2.71706i	−0.0760930	+	0.131797i
$426$		0			0
$427$	2.17125	−	2.38926i	0.105074	−	0.115625i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.93915	−	1.11957i	0.0934056	−	0.0539277i	−0.452570	−	0.891729i	$-0.649493\pi$
$431$	1.93915	−	1.11957i	0.0934056	−	0.0539277i	0.545975	+	0.837801i	$0.316159\pi$
$432$		0			0
$433$			1.93460i			0.0929709i	0.998919	+	0.0464855i	$0.0148021\pi$
$433$			1.93460i			0.0929709i	−0.998919	+	0.0464855i	$0.985198\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.4469	+	30.2189i	0.834598	+	1.44557i
$438$		0			0
$439$	−4.91797	−	2.83939i	−0.234722	−	0.135517i	0.378027	−	0.925795i	$-0.376603\pi$
$439$	−4.91797	−	2.83939i	−0.234722	−	0.135517i	−0.612748	+	0.790278i	$0.709936\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.4243	−	11.7920i	−0.970387	−	0.560253i	−0.0710331	−	0.997474i	$-0.522630\pi$
$443$	−20.4243	−	11.7920i	−0.970387	−	0.560253i	−0.899354	+	0.437221i	$0.855963\pi$
$444$		0			0
$445$	−8.69683	−	15.0633i	−0.412269	−	0.714071i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.991121i		−	0.0467739i	−0.999726	−	0.0233869i	$-0.992555\pi$
$449$		−	0.991121i		−	0.0467739i	0.999726	−	0.0233869i	$-0.00744497\pi$
$450$		0			0
$451$	−27.5467	+	15.9041i	−1.29712	+	0.748894i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	17.0631	−	18.7764i	0.799932	−	0.880252i
$456$		0			0
$457$	−8.33211	+	14.4316i	−0.389759	+	0.675083i	−0.992417	−	0.122917i	$-0.960775\pi$
$457$	−8.33211	+	14.4316i	−0.389759	+	0.675083i	0.602658	+	0.798000i	$0.294109\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−21.9318			−1.02147			−0.510734	−	0.859739i	$-0.670626\pi$
$461$	−21.9318			−1.02147			−0.510734	+	0.859739i	$0.670626\pi$
$462$		0			0
$463$	14.5144			0.674541			0.337271	−	0.941408i	$-0.390496\pi$
$463$	14.5144			0.674541			0.337271	+	0.941408i	$0.390496\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.2497	−	35.0736i	0.937046	−	1.62301i	0.166102	−	0.986109i	$-0.446882\pi$
$467$	20.2497	−	35.0736i	0.937046	−	1.62301i	0.770944	−	0.636903i	$-0.219785\pi$
$468$		0			0
$469$	−0.211546	+	0.0676632i	−0.00976831	+	0.00312440i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.0843	−	5.82215i	0.463675	−	0.267703i
$474$		0			0
$475$			4.57920i			0.210108i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.828048	+	1.43422i	0.0378345	+	0.0655312i	0.884323	−	0.466876i	$-0.154621\pi$
$479$	0.828048	+	1.43422i	0.0378345	+	0.0655312i	−0.846488	+	0.532408i	$0.821287\pi$
$480$		0			0
$481$	−48.0460	−	27.7394i	−2.19071	−	1.26481i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.3202	−	12.8865i	−1.01351	−	0.585148i
$486$		0			0
$487$	3.74089	+	6.47941i	0.169516	+	0.293610i	0.938250	−	0.345959i	$-0.112446\pi$
$487$	3.74089	+	6.47941i	0.169516	+	0.293610i	−0.768734	+	0.639569i	$0.779113\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	0.518074i		−	0.0233804i	−0.999932	−	0.0116902i	$-0.996279\pi$
$491$		−	0.518074i		−	0.0233804i	0.999932	−	0.0116902i	$-0.00372119\pi$
$492$		0			0
$493$	6.06412	−	3.50112i	0.273114	−	0.157682i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.7635	−	4.73052i	−0.976225	−	0.212193i
$498$		0			0
$499$	−9.53093	+	16.5081i	−0.426663	+	0.739002i	−0.996574	−	0.0827042i	$-0.973644\pi$
$499$	−9.53093	+	16.5081i	−0.426663	+	0.739002i	0.569911	+	0.821706i	$0.306978\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.7859			0.748448			0.374224	−	0.927338i	$-0.377909\pi$
$503$	16.7859			0.748448			0.374224	+	0.927338i	$0.377909\pi$
$504$		0			0
$505$	27.4963			1.22357
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.72937	+	11.6556i	−0.298274	+	0.516626i	−0.975741	−	0.218927i	$-0.929744\pi$
$509$	−6.72937	+	11.6556i	−0.298274	+	0.516626i	0.677467	+	0.735553i	$0.263078\pi$
$510$		0			0
$511$	8.48160	+	26.5174i	0.375204	+	1.17306i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−31.4811	+	18.1756i	−1.38722	+	0.800913i
$516$		0			0
$517$		−	1.39360i		−	0.0612906i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.0558	−	36.4697i	−0.922471	−	1.59777i	−0.795579	−	0.605850i	$-0.792833\pi$
$521$	−21.0558	−	36.4697i	−0.922471	−	1.59777i	−0.126892	−	0.991917i	$-0.540500\pi$
$522$		0			0
$523$	16.2844	+	9.40179i	0.712067	+	0.411112i	0.811826	−	0.583900i	$-0.198474\pi$
$523$	16.2844	+	9.40179i	0.712067	+	0.411112i	−0.0997592	+	0.995012i	$0.531807\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.916302	−	0.529027i	−0.0399148	−	0.0230448i
$528$		0			0
$529$	12.6676	+	21.9409i	0.550764	+	0.953951i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			41.6101i			1.80233i
$534$		0			0
$535$	12.2494	−	7.07221i	0.529589	−	0.305758i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−25.2646	+	2.42104i	−1.08822	+	0.104282i
$540$		0			0
$541$	−3.81212	+	6.60278i	−0.163896	+	0.283876i	−0.936263	−	0.351301i	$-0.885739\pi$
$541$	−3.81212	+	6.60278i	−0.163896	+	0.283876i	0.772367	+	0.635177i	$0.219073\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−26.1210			−1.11890
$546$		0			0
$547$	−29.4627			−1.25974			−0.629868	−	0.776702i	$-0.716891\pi$
$547$	−29.4627			−1.25974			−0.629868	+	0.776702i	$0.716891\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.11008	−	8.85091i	0.217697	−	0.377062i
$552$		0			0
$553$	3.21570	+	2.92228i	0.136746	+	0.124268i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.94246	+	1.12148i	−0.0823048	+	0.0475187i	−0.540588	−	0.841288i	$-0.681798\pi$
$557$	−1.94246	+	1.12148i	−0.0823048	+	0.0475187i	0.458283	+	0.888806i	$0.348465\pi$
$558$		0			0
$559$		−	15.2326i		−	0.644269i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.7328	+	39.3744i	0.958075	+	1.65943i	0.727169	+	0.686458i	$0.240836\pi$
$563$	22.7328	+	39.3744i	0.958075	+	1.65943i	0.230906	+	0.972976i	$0.425831\pi$
$564$		0			0
$565$	−15.0831	−	8.70825i	−0.634552	−	0.366359i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.5789	−	9.57183i	−0.695023	−	0.401272i	0.110468	−	0.993880i	$-0.464765\pi$
$569$	−16.5789	−	9.57183i	−0.695023	−	0.401272i	−0.805491	+	0.592608i	$0.798098\pi$
$570$		0			0
$571$	−0.602095	−	1.04286i	−0.0251969	−	0.0436423i	0.853152	−	0.521662i	$-0.174688\pi$
$571$	−0.602095	−	1.04286i	−0.0251969	−	0.0436423i	−0.878349	+	0.478020i	$0.841355\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.34315i			0.264527i
$576$		0			0
$577$	17.4229	−	10.0591i	0.725325	−	0.418767i	−0.0913843	−	0.995816i	$-0.529129\pi$
$577$	17.4229	−	10.0591i	0.725325	−	0.418767i	0.816710	+	0.577049i	$0.195796\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.82162	−	26.7832i	0.241521	−	1.11115i
$582$		0			0
$583$	−11.5785	+	20.0545i	−0.479532	+	0.830574i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	44.9416			1.85494			0.927470	−	0.373898i	$-0.121979\pi$
$587$	44.9416			1.85494			0.927470	+	0.373898i	$0.121979\pi$
$588$		0			0
$589$	−1.54429			−0.0636313
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.55552	−	13.0865i	0.310268	−	0.537400i	−0.668152	−	0.744025i	$-0.732915\pi$
$593$	7.55552	−	13.0865i	0.310268	−	0.537400i	0.978420	+	0.206624i	$0.0662478\pi$
$594$		0			0
$595$	−3.90695	+	17.9745i	−0.160169	+	0.736882i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	31.5433	−	18.2115i	1.28883	−	0.744104i	0.310381	−	0.950612i	$-0.399544\pi$
$599$	31.5433	−	18.2115i	1.28883	−	0.744104i	0.978445	+	0.206509i	$0.0662102\pi$
$600$		0			0
$601$		−	26.5993i		−	1.08501i	−0.840053	−	0.542504i	$-0.817476\pi$
$601$		−	26.5993i		−	1.08501i	0.840053	−	0.542504i	$-0.182524\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.16952	+	3.75771i	0.0882033	+	0.152773i
$606$		0			0
$607$	−19.2701	−	11.1256i	−0.782151	−	0.451575i	0.0550410	−	0.998484i	$-0.482471\pi$
$607$	−19.2701	−	11.1256i	−0.782151	−	0.451575i	−0.837192	+	0.546909i	$0.815804\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.57881	−	0.911525i	−0.0638717	−	0.0368764i
$612$		0			0
$613$	8.25327	+	14.2951i	0.333346	+	0.577373i	0.983166	−	0.182716i	$-0.0584888\pi$
$613$	8.25327	+	14.2951i	0.333346	+	0.577373i	−0.649819	+	0.760089i	$0.725155\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			24.1547i			0.972431i	0.873839	+	0.486216i	$0.161623\pi$
$617$			24.1547i			0.972431i	−0.873839	+	0.486216i	$0.838377\pi$
$618$		0			0
$619$	24.1670	−	13.9528i	0.971354	−	0.560811i	0.0717051	−	0.997426i	$-0.477156\pi$
$619$	24.1670	−	13.9528i	0.971354	−	0.560811i	0.899649	+	0.436614i	$0.143823\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.8451	+	15.3081i	0.674885	+	0.613304i
$624$		0			0
$625$	9.80285	−	16.9790i	0.392114	−	0.679161i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	40.2220			1.60376
$630$		0			0
$631$	−13.9089			−0.553703			−0.276852	−	0.960913i	$-0.589291\pi$
$631$	−13.9089			−0.553703			−0.276852	+	0.960913i	$0.589291\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.0662	−	33.0236i	0.756619	−	1.31050i
$636$		0			0
$637$	−13.7822	+	30.2057i	−0.546072	+	1.19679i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−26.5365	+	15.3208i	−1.04813	+	0.605137i	−0.922125	−	0.386893i	$-0.873548\pi$
$641$	−26.5365	+	15.3208i	−1.04813	+	0.605137i	−0.126003	+	0.992030i	$0.540215\pi$
$642$		0			0
$643$			15.4008i			0.607348i	0.952776	+	0.303674i	$0.0982133\pi$
$643$			15.4008i			0.607348i	−0.952776	+	0.303674i	$0.901787\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.9006	−	36.2009i	−0.821688	−	1.42321i	−0.904424	−	0.426634i	$-0.859699\pi$
$647$	−20.9006	−	36.2009i	−0.821688	−	1.42321i	0.0827358	−	0.996572i	$-0.473634\pi$
$648$		0			0
$649$	−26.7366	−	15.4364i	−1.04950	−	0.605932i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.78703	+	3.91849i	0.265597	+	0.153342i	0.626885	−	0.779112i	$-0.284330\pi$
$653$	6.78703	+	3.91849i	0.265597	+	0.153342i	−0.361288	+	0.932454i	$0.617663\pi$
$654$		0			0
$655$	−13.3158	−	23.0636i	−0.520291	−	0.901171i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			11.6341i			0.453202i	0.973988	+	0.226601i	$0.0727613\pi$
$659$			11.6341i			0.453202i	−0.973988	+	0.226601i	$0.927239\pi$
$660$		0			0
$661$	19.5416	−	11.2823i	0.760079	−	0.438832i	−0.0692453	−	0.997600i	$-0.522059\pi$
$661$	19.5416	−	11.2823i	0.760079	−	0.438832i	0.829324	+	0.558768i	$0.188726\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.17895	+	25.5712i	0.317166	+	0.991607i
$666$		0			0
$667$	7.07852	−	12.2604i	0.274081	−	0.474723i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.42430			0.170798
$672$		0			0
$673$	24.6415			0.949860			0.474930	−	0.880024i	$-0.342473\pi$
$673$	24.6415			0.949860			0.474930	+	0.880024i	$0.342473\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.87418	−	6.71027i	0.148897	−	0.257897i	−0.781923	−	0.623375i	$-0.785761\pi$
$677$	3.87418	−	6.71027i	0.148897	−	0.257897i	0.930820	+	0.365478i	$0.119094\pi$
$678$		0			0
$679$	32.9576	+	7.16369i	1.26480	+	0.274917i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.58568	−	5.53430i	0.366786	−	0.211764i	−0.305267	−	0.952267i	$-0.598746\pi$
$683$	9.58568	−	5.53430i	0.366786	−	0.211764i	0.672053	+	0.740503i	$0.265413\pi$
$684$		0			0
$685$			43.9621i			1.67970i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	15.1465	+	26.2345i	0.577035	+	0.999454i
$690$		0			0
$691$	−13.4729	−	7.77857i	−0.512532	−	0.295911i	0.221342	−	0.975196i	$-0.428956\pi$
$691$	−13.4729	−	7.77857i	−0.512532	−	0.295911i	−0.733874	+	0.679286i	$0.762290\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.5448	−	6.66538i	−0.437918	−	0.252832i
$696$		0			0
$697$	−15.0836	−	26.1256i	−0.571333	−	0.989578i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			15.1353i			0.571652i	0.958282	+	0.285826i	$0.0922679\pi$
$701$			15.1353i			0.571652i	−0.958282	+	0.285826i	$0.907732\pi$
$702$		0			0
$703$	50.8411	−	29.3531i	1.91751	−	1.10707i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−34.2718	+	10.9619i	−1.28892	+	0.412263i
$708$		0			0
$709$	0.430771	−	0.746118i	0.0161780	−	0.0280210i	−0.857823	−	0.513945i	$-0.828184\pi$
$709$	0.430771	−	0.746118i	0.0161780	−	0.0280210i	0.874001	+	0.485924i	$0.161517\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.13916			−0.0801122
$714$		0			0
$715$	34.7691			1.30029
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−16.9554	+	29.3675i	−0.632328	+	1.09522i	0.354746	+	0.934963i	$0.384567\pi$
$719$	−16.9554	+	29.3675i	−0.632328	+	1.09522i	−0.987075	+	0.160262i	$0.948766\pi$
$720$		0			0
$721$	31.9925	−	35.2048i	1.19146	−	1.31109i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.60896	−	0.928932i	0.0597552	−	0.0344997i
$726$		0			0
$727$		−	26.5949i		−	0.986351i	−0.869930	−	0.493176i	$-0.835836\pi$
$727$		−	26.5949i		−	0.986351i	0.869930	−	0.493176i	$-0.164164\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.52179	+	9.56403i	0.204231	+	0.353738i
$732$		0			0
$733$	−1.80172	−	1.04022i	−0.0665479	−	0.0384214i	0.466357	−	0.884597i	$-0.345566\pi$
$733$	−1.80172	−	1.04022i	−0.0665479	−	0.0384214i	−0.532905	+	0.846175i	$0.678900\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.263595	−	0.152187i	−0.00970965	−	0.00560587i
$738$		0			0
$739$	−19.9101	−	34.4852i	−0.732403	−	1.26856i	−0.955853	−	0.293844i	$-0.905065\pi$
$739$	−19.9101	−	34.4852i	−0.732403	−	1.26856i	0.223450	−	0.974715i	$-0.428268\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			12.2940i			0.451022i	0.974241	+	0.225511i	$0.0724052\pi$
$743$			12.2940i			0.451022i	−0.974241	+	0.225511i	$0.927595\pi$
$744$		0			0
$745$	20.8570	−	12.0418i	0.764143	−	0.441178i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.4484	+	13.6984i	−0.454856	+	0.500527i
$750$		0			0
$751$	−24.1272	+	41.7895i	−0.880414	+	1.52492i	−0.0295319	+	0.999564i	$0.509402\pi$
$751$	−24.1272	+	41.7895i	−0.880414	+	1.52492i	−0.850882	+	0.525357i	$0.823932\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	30.4076			1.10665
$756$		0			0
$757$	−9.77773			−0.355378			−0.177689	−	0.984087i	$-0.556862\pi$
$757$	−9.77773			−0.355378			−0.177689	+	0.984087i	$0.556862\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.8030	−	44.6921i	0.935358	−	1.62009i	0.161363	−	0.986895i	$-0.448411\pi$
$761$	25.8030	−	44.6921i	0.935358	−	1.62009i	0.773994	−	0.633192i	$-0.218256\pi$
$762$		0			0
$763$	32.5576	−	10.4135i	1.17866	−	0.376996i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−34.9757	+	20.1932i	−1.26290	+	0.729136i
$768$		0			0
$769$		−	21.8208i		−	0.786877i	−0.919351	−	0.393438i	$-0.871285\pi$
$769$		−	21.8208i		−	0.786877i	0.919351	−	0.393438i	$-0.128715\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.9682	+	32.8539i	0.682239	+	1.18167i	0.974296	+	0.225272i	$0.0723269\pi$
$773$	18.9682	+	32.8539i	0.682239	+	1.18167i	−0.292057	+	0.956401i	$0.594340\pi$
$774$		0			0
$775$	−0.243117	−	0.140364i	−0.00873303	−	0.00504202i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−38.1318	−	22.0154i	−1.36621	−	0.788783i
$780$		0			0
$781$	−15.2606	−	26.4322i	−0.546068	−	0.945818i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	36.6452i		−	1.30792i
$786$		0			0
$787$	4.28284	−	2.47270i	0.152667	−	0.0881422i	−0.421721	−	0.906726i	$-0.638574\pi$
$787$	4.28284	−	2.47270i	0.152667	−	0.0881422i	0.574387	+	0.818584i	$0.305240\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	22.2715	+	4.84095i	0.791884	+	0.172125i
$792$		0			0
$793$	2.89384	−	5.01227i	0.102763	−	0.177991i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	47.6012			1.68612			0.843061	−	0.537819i	$-0.180752\pi$
$797$	47.6012			1.68612			0.843061	+	0.537819i	$0.180752\pi$
$798$		0			0
$799$	1.32171			0.0467587
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.0766	+	33.0417i	−0.673200	+	1.16602i
$804$		0			0
$805$	11.3295	+	35.4214i	0.399314	+	1.24844i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.94662	+	2.27858i	−0.138756	+	0.0801108i	−0.567771	−	0.823187i	$-0.692194\pi$
$809$	−3.94662	+	2.27858i	−0.138756	+	0.0801108i	0.429015	+	0.903297i	$0.358861\pi$
$810$		0			0
$811$		−	15.6097i		−	0.548131i	−0.961711	−	0.274065i	$-0.911632\pi$
$811$		−	15.6097i		−	0.548131i	0.961711	−	0.274065i	$-0.0883685\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	20.5906	+	35.6640i	0.721258	+	1.24925i
$816$		0			0
$817$	13.9592	+	8.05936i	0.488372	+	0.281961i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.24732	+	1.87484i	0.113332	+	0.0654324i	0.555595	−	0.831453i	$-0.312491\pi$
$821$	3.24732	+	1.87484i	0.113332	+	0.0654324i	−0.442262	+	0.896886i	$0.645824\pi$
$822$		0			0
$823$	11.9161	+	20.6392i	0.415367	+	0.719438i	0.995467	−	0.0951081i	$-0.0303197\pi$
$823$	11.9161	+	20.6392i	0.415367	+	0.719438i	−0.580099	+	0.814546i	$0.696986\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	6.30470i		−	0.219236i	−0.993974	−	0.109618i	$-0.965037\pi$
$827$		−	6.30470i		−	0.219236i	0.993974	−	0.109618i	$-0.0349627\pi$
$828$		0			0
$829$	−13.3705	+	7.71946i	−0.464376	+	0.268108i	−0.713883	−	0.700265i	$-0.753065\pi$
$829$	−13.3705	+	7.71946i	−0.464376	+	0.268108i	0.249506	+	0.968373i	$0.419732\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.29614	−	23.9612i	−0.0795567	−	0.830207i
$834$		0			0
$835$	11.2266	−	19.4450i	0.388512	−	0.672922i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−26.0853			−0.900566			−0.450283	−	0.892886i	$-0.648677\pi$
$839$	−26.0853			−0.900566			−0.450283	+	0.892886i	$0.648677\pi$
$840$		0			0
$841$	24.8535			0.857017
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.60009	−	16.6278i	0.330253	−	0.572015i
$846$		0			0
$847$	−4.20219	−	3.81876i	−0.144389	−	0.131214i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	70.4255	−	40.6602i	2.41416	−	1.39381i
$852$		0			0
$853$		−	24.7463i		−	0.847297i	−0.905827	−	0.423649i	$-0.860749\pi$
$853$		−	24.7463i		−	0.847297i	0.905827	−	0.423649i	$-0.139251\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.79032	−	15.2253i	−0.300272	−	0.520086i	0.675926	−	0.736970i	$-0.263744\pi$
$857$	−8.79032	−	15.2253i	−0.300272	−	0.520086i	−0.976197	+	0.216884i	$0.930411\pi$
$858$		0			0
$859$	0.359931	+	0.207806i	0.0122807	+	0.00709026i	0.506128	−	0.862459i	$-0.331076\pi$
$859$	0.359931	+	0.207806i	0.0122807	+	0.00709026i	−0.493847	+	0.869549i	$0.664410\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.22335	+	4.17040i	0.245886	+	0.141962i	0.617879	−	0.786273i	$-0.287992\pi$
$863$	7.22335	+	4.17040i	0.245886	+	0.141962i	−0.371993	+	0.928235i	$0.621326\pi$
$864$		0			0
$865$	−5.34682	−	9.26097i	−0.181797	−	0.314882i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			5.95465i			0.201998i
$870$		0			0
$871$	−0.344824	+	0.199084i	−0.0116839	+	0.00674570i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.71743	+	30.9045i	−0.227091	+	1.04476i
$876$		0			0
$877$	−23.4450	+	40.6079i	−0.791681	+	1.37123i	0.133245	+	0.991083i	$0.457460\pi$
$877$	−23.4450	+	40.6079i	−0.791681	+	1.37123i	−0.924926	+	0.380148i	$0.875873\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	16.9745			0.571885			0.285942	−	0.958247i	$-0.407693\pi$
$881$	16.9745			0.571885			0.285942	+	0.958247i	$0.407693\pi$
$882$		0			0
$883$	−25.2950			−0.851244			−0.425622	−	0.904901i	$-0.639945\pi$
$883$	−25.2950			−0.851244			−0.425622	+	0.904901i	$0.639945\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.82443	+	6.62411i	−0.128412	+	0.222416i	−0.923061	−	0.384652i	$-0.874321\pi$
$887$	−3.82443	+	6.62411i	−0.128412	+	0.222416i	0.794650	+	0.607068i	$0.207655\pi$
$888$		0			0
$889$	−10.5990	+	48.7622i	−0.355478	+	1.63543i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.67066	−	0.964554i	0.0559064	−	0.0322776i
$894$		0			0
$895$		−	50.5995i		−	1.69135i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.313273	+	0.542605i	0.0104482	+	0.0180969i
$900$		0			0
$901$	−19.0200	−	10.9812i	−0.633647	−	0.365836i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.92641	−	1.11221i	−0.0640360	−	0.0369712i
$906$		0			0
$907$	11.2777	+	19.5335i	0.374469	+	0.648599i	0.990247	−	0.139320i	$-0.0444918\pi$
$907$	11.2777	+	19.5335i	0.374469	+	0.648599i	−0.615779	+	0.787919i	$0.711158\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			39.6484i			1.31361i	0.754060	+	0.656805i	$0.228093\pi$
$911$			39.6484i			1.31361i	−0.754060	+	0.656805i	$0.771907\pi$
$912$		0			0
$913$	32.5288	−	18.7805i	1.07655	−	0.621544i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.7917	+	23.4383i	0.851717	+	0.774001i
$918$		0			0
$919$	−21.1733	+	36.6731i	−0.698441	+	1.20974i	0.270566	+	0.962702i	$0.412789\pi$
$919$	−21.1733	+	36.6731i	−0.698441	+	1.20974i	−0.969007	+	0.247034i	$0.920544\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−39.9266			−1.31420
$924$		0			0
$925$	10.6719			0.350890
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.03550	−	1.79353i	0.0339735	−	0.0588438i	−0.848539	−	0.529133i	$-0.822517\pi$
$929$	1.03550	−	1.79353i	0.0339735	−	0.0588438i	0.882512	+	0.470289i	$0.155850\pi$
$930$		0			0
$931$	−20.3887	−	28.6116i	−0.668213	−	0.937707i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−21.8304	+	12.6038i	−0.713930	+	0.412187i
$936$		0			0
$937$		−	13.4301i		−	0.438741i	−0.975642	−	0.219371i	$-0.929600\pi$
$937$		−	13.4301i		−	0.438741i	0.975642	−	0.219371i	$-0.0704004\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.2101	+	26.3447i	0.495836	+	0.858814i	0.999988	−	0.00480105i	$-0.00152823\pi$
$941$	15.2101	+	26.3447i	0.495836	+	0.858814i	−0.504152	+	0.863615i	$0.668195\pi$
$942$		0			0
$943$	−52.8204	−	30.4959i	−1.72007	−	0.993083i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.8185	−	27.6080i	−1.55389	−	0.897140i	−0.997819	−	0.0660075i	$-0.978974\pi$
$947$	−47.8185	−	27.6080i	−1.55389	−	0.897140i	−0.556074	−	0.831133i	$-0.687693\pi$
$948$		0			0
$949$	24.9552	+	43.2237i	0.810081	+	1.40310i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	23.7985i		−	0.770910i	−0.922727	−	0.385455i	$-0.874044\pi$
$953$		−	23.7985i		−	0.770910i	0.922727	−	0.385455i	$-0.125956\pi$
$954$		0			0
$955$	−41.6420	+	24.0420i	−1.34750	+	0.777981i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.5262	−	54.7950i	−0.565951	−	1.76942i
$960$		0			0
$961$	−15.4527	+	26.7648i	−0.498473	+	0.863381i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−18.3429			−0.590477
$966$		0			0
$967$	35.2186			1.13255			0.566277	−	0.824215i	$-0.308383\pi$
$967$	35.2186			1.13255			0.566277	+	0.824215i	$0.308383\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.2261	−	47.1570i	0.873728	−	1.51334i	0.0156154	−	0.999878i	$-0.495029\pi$
$971$	27.2261	−	47.1570i	0.873728	−	1.51334i	0.858112	−	0.513462i	$-0.171637\pi$
$972$		0			0
$973$	17.0469	+	3.70532i	0.546497	+	0.118787i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	34.3637	−	19.8399i	1.09939	−	0.634735i	0.163332	−	0.986571i	$-0.447776\pi$
$977$	34.3637	−	19.8399i	1.09939	−	0.634735i	0.936062	+	0.351836i	$0.114443\pi$
$978$		0			0
$979$			31.1928i			0.996926i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.4610	−	26.7793i	−0.493130	−	0.854125i	0.506839	−	0.862041i	$-0.330814\pi$
$983$	−15.4610	−	26.7793i	−0.493130	−	0.854125i	−0.999969	+	0.00791519i	$0.997480\pi$
$984$		0			0
$985$	9.36186	+	5.40507i	0.298294	+	0.172220i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	19.3364	+	11.1639i	0.614863	+	0.354991i
$990$		0			0
$991$	−4.71177	−	8.16103i	−0.149674	−	0.259244i	0.781433	−	0.623990i	$-0.214489\pi$
$991$	−4.71177	−	8.16103i	−0.149674	−	0.259244i	−0.931107	+	0.364746i	$0.881156\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			26.2853i			0.833299i
$996$		0			0
$997$	11.6863	−	6.74707i	0.370108	−	0.213682i	−0.303398	−	0.952864i	$-0.598121\pi$
$997$	11.6863	−	6.74707i	0.370108	−	0.213682i	0.673506	+	0.739182i	$0.264788\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bl.a.89.2	yes	16
3.2	odd	2	inner	504.2.bl.a.89.7	yes	16
4.3	odd	2		1008.2.bt.d.593.2		16
7.2	even	3		3528.2.k.b.881.14		16
7.3	odd	6	inner	504.2.bl.a.17.7	yes	16
7.4	even	3		3528.2.bl.a.521.2		16
7.5	odd	6		3528.2.k.b.881.4		16
7.6	odd	2		3528.2.bl.a.1097.7		16
12.11	even	2		1008.2.bt.d.593.7		16
21.2	odd	6		3528.2.k.b.881.3		16
21.5	even	6		3528.2.k.b.881.13		16
21.11	odd	6		3528.2.bl.a.521.7		16
21.17	even	6	inner	504.2.bl.a.17.2	✓	16
21.20	even	2		3528.2.bl.a.1097.2		16
28.3	even	6		1008.2.bt.d.17.7		16
28.19	even	6		7056.2.k.h.881.3		16
28.23	odd	6		7056.2.k.h.881.13		16
84.23	even	6		7056.2.k.h.881.4		16
84.47	odd	6		7056.2.k.h.881.14		16
84.59	odd	6		1008.2.bt.d.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bl.a.17.2	✓	16	21.17	even	6	inner
504.2.bl.a.17.7	yes	16	7.3	odd	6	inner
504.2.bl.a.89.2	yes	16	1.1	even	1	trivial
504.2.bl.a.89.7	yes	16	3.2	odd	2	inner
1008.2.bt.d.17.2		16	84.59	odd	6
1008.2.bt.d.17.7		16	28.3	even	6
1008.2.bt.d.593.2		16	4.3	odd	2
1008.2.bt.d.593.7		16	12.11	even	2
3528.2.k.b.881.3		16	21.2	odd	6
3528.2.k.b.881.4		16	7.5	odd	6
3528.2.k.b.881.13		16	21.5	even	6
3528.2.k.b.881.14		16	7.2	even	3
3528.2.bl.a.521.2		16	7.4	even	3
3528.2.bl.a.521.7		16	21.11	odd	6
3528.2.bl.a.1097.2		16	21.20	even	2
3528.2.bl.a.1097.7		16	7.6	odd	2
7056.2.k.h.881.3		16	28.19	even	6
7056.2.k.h.881.4		16	84.23	even	6
7056.2.k.h.881.13		16	28.23	odd	6
7056.2.k.h.881.14		16	84.47	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01089 + 1.75092i) q^{5} +(0.561961 - 2.58538i) q^{7} +O(q^{10})\)	\(q+(-1.01089 + 1.75092i) q^{5} +(0.561961 - 2.58538i) q^{7} +(3.14000 - 1.81288i) q^{11} -4.74306i q^{13} +(1.71936 + 2.97801i) q^{17} +(4.34657 + 2.50950i) q^{19} +(6.02091 + 3.47617i) q^{23} +(0.456187 + 0.790140i) q^{25} -2.03630i q^{29} +(-0.266467 + 0.153845i) q^{31} +(3.95871 + 3.59749i) q^{35} +(5.84841 - 10.1298i) q^{37} -8.77283 q^{41} +3.21155 q^{43} +(0.192181 - 0.332867i) q^{47} +(-6.36840 - 2.90577i) q^{49} +(-5.53113 + 3.19340i) q^{53} +7.33052i q^{55} +(-4.25743 - 7.37408i) q^{59} +(1.05676 + 0.610120i) q^{61} +(8.30472 + 4.79473i) q^{65} +(-0.0419737 - 0.0727006i) q^{67} -8.41789i q^{71} +(-9.11304 + 5.26142i) q^{73} +(-2.92243 - 9.13687i) q^{77} +(-0.821159 + 1.42229i) q^{79} +10.3595 q^{83} -6.95235 q^{85} +(-4.30155 + 7.45051i) q^{89} +(-12.2626 - 2.66541i) q^{91} +(-8.78785 + 5.07367i) q^{95} +12.7477i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) \) 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

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