LMFDB - Embedded newform 1008.2.bt.d.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(17,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, 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("1008.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bt (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:	$8.04892052375$
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:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$1.01089 + 0.750919i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.2.bt.d.593.2

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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	0.546430	−	0.837505i	$-0.315986\pi$
$5$	−1.01089	−	1.75092i	−0.452085	−	0.783035i	−0.998515	+	0.0544698i	$0.982653\pi$
$6$		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	$-0.517413\pi$
$11$	−3.14000	−	1.81288i	−0.946746	−	0.546604i	−0.892069	+	0.451900i	$0.850746\pi$
$12$		0			0
$13$			4.74306i			1.31549i	0.753241	+	0.657744i	$0.228489\pi$
$13$			4.74306i			1.31549i	−0.753241	+	0.657744i	$0.771511\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.71936	−	2.97801i	0.417005	−	0.722274i	−0.578631	−	0.815589i	$-0.696413\pi$
$17$	1.71936	−	2.97801i	0.417005	−	0.722274i	0.995637	+	0.0933149i	$0.0297463\pi$
$18$		0			0
$19$	−4.34657	+	2.50950i	−0.997173	+	0.575718i	−0.907411	−	0.420245i	$-0.861944\pi$
$19$	−4.34657	+	2.50950i	−0.997173	+	0.575718i	−0.0897621	+	0.995963i	$0.528611\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.02091	+	3.47617i	−1.25545	+	0.724832i	−0.972186	−	0.234211i	$-0.924749\pi$
$23$	−6.02091	+	3.47617i	−1.25545	+	0.724832i	−0.283261	+	0.959043i	$0.591416\pi$
$24$		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	$0.0605458\pi$
$29$			2.03630i			0.378131i	−0.981965	+	0.189065i	$0.939454\pi$
$30$		0			0
$31$	0.266467	+	0.153845i	0.0478588	+	0.0276313i	0.523738	−	0.851879i	$-0.324537\pi$
$31$	0.266467	+	0.153845i	0.0478588	+	0.0276313i	−0.475880	+	0.879510i	$0.657870\pi$
$32$		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	0.718806	+	0.695211i	$0.244689\pi$
$37$	5.84841	+	10.1298i	0.961473	+	1.66532i	0.242668	+	0.970109i	$0.421977\pi$
$38$		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	$-0.578748\pi$
$43$	−3.21155			−0.489756			−0.244878	+	0.969554i	$0.578748\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.192181	−	0.332867i	−0.0280324	−	0.0485536i	0.851669	−	0.524080i	$-0.175591\pi$
$47$	−0.192181	−	0.332867i	−0.0280324	−	0.0485536i	−0.879701	+	0.475527i	$0.842258\pi$
$48$		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	0.0694502	−	0.997585i	$-0.477875\pi$
$53$	−5.53113	−	3.19340i	−0.759759	−	0.438647i	−0.829209	+	0.558938i	$0.811209\pi$
$54$		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	−0.443690	−	0.896180i	$-0.646331\pi$
$59$	4.25743	−	7.37408i	0.554270	−	0.960023i	0.997960	−	0.0638431i	$-0.0203357\pi$
$60$		0			0
$61$	1.05676	−	0.610120i	0.135304	−	0.0781179i	−0.430820	−	0.902438i	$-0.641776\pi$
$61$	1.05676	−	0.610120i	0.135304	−	0.0781179i	0.566124	+	0.824320i	$0.308442\pi$
$62$		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	$-0.831701\pi$
$67$	0.0419737	−	0.0727006i	0.00512791	−	0.00888180i	0.868578	+	0.495553i	$0.165034\pi$
$68$		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	−0.139350	−	0.990243i	$-0.544501\pi$
$73$	−9.11304	−	5.26142i	−1.06660	−	0.615802i	−0.927251	+	0.374441i	$0.877835\pi$
$74$		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	$-0.137217\pi$
$79$	0.821159	+	1.42229i	0.0923876	+	0.160020i	−0.816128	+	0.577872i	$0.803883\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.3595			−1.13710			−0.568550	−	0.822648i	$-0.692496\pi$
$83$	−10.3595			−1.13710			−0.568550	+	0.822648i	$0.692496\pi$
$84$		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	0.542779	−	0.839875i	$-0.317372\pi$
$89$	−4.30155	−	7.45051i	−0.455964	−	0.789752i	−0.998743	+	0.0501230i	$0.984039\pi$
$90$		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	$-0.775954\pi$
$97$		−	12.7477i		−	1.29433i	0.762350	−	0.647165i	$-0.224046\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.80000	+	11.7779i	−0.676625	+	1.17195i	0.299366	+	0.954138i	$0.403225\pi$
$101$	−6.80000	+	11.7779i	−0.676625	+	1.17195i	−0.975991	+	0.217811i	$0.930108\pi$
$102$		0			0
$103$	−15.5709	+	8.98987i	−1.53425	+	0.885798i	−0.535088	+	0.844796i	$0.679722\pi$
$103$	−15.5709	+	8.98987i	−1.53425	+	0.885798i	−0.999159	+	0.0410016i	$0.986945\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.05871	−	3.49800i	0.585718	−	0.338164i	−0.177685	−	0.984087i	$-0.556861\pi$
$107$	6.05871	−	3.49800i	0.585718	−	0.338164i	0.763402	+	0.645923i	$0.223527\pi$
$108$		0			0
$109$	6.45987	−	11.1888i	0.618743	−	1.07169i	−0.370973	−	0.928644i	$-0.620976\pi$
$109$	6.45987	−	11.1888i	0.618743	−	1.07169i	0.989715	−	0.143050i	$-0.0456911\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	8.61440i		−	0.810375i	−0.914234	−	0.405187i	$-0.867206\pi$
$113$		−	8.61440i		−	0.810375i	0.914234	−	0.405187i	$-0.132794\pi$
$114$		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	$-0.184418\pi$
$127$	18.8607			1.67362			0.836809	+	0.547495i	$0.184418\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.58615	+	11.4075i	0.575435	+	0.996682i	0.995994	+	0.0894170i	$0.0285004\pi$
$131$	6.58615	+	11.4075i	0.575435	+	0.996682i	−0.420560	+	0.907265i	$0.638166\pi$
$132$		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	0.989630	+	0.143639i	$0.0458804\pi$
$137$	18.8310	+	10.8721i	1.60884	+	0.928864i	0.619210	+	0.785225i	$0.287453\pi$
$138$		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	−0.859005	−	0.511967i	$-0.828917\pi$
$149$	−10.3161	+	5.95603i	−0.845131	+	0.487937i	0.0138740	+	0.999904i	$0.495584\pi$
$150$		0			0
$151$	7.51999	−	13.0250i	0.611968	−	1.05996i	−0.378941	−	0.925421i	$-0.623712\pi$
$151$	7.51999	−	13.0250i	0.611968	−	1.05996i	0.990908	−	0.134538i	$-0.0429552\pi$
$152$		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	−0.281090	−	0.959681i	$-0.590696\pi$
$157$	−15.6968	−	9.06257i	−1.25274	−	0.723272i	−0.971653	+	0.236410i	$0.924029\pi$
$158$		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	−0.921110	−	0.389302i	$-0.872716\pi$
$163$	−10.1844	−	17.6398i	−0.797700	−	1.38166i	0.123410	−	0.992356i	$-0.460617\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.1056			0.859377			0.429688	−	0.902977i	$-0.358623\pi$
$167$	11.1056			0.859377			0.429688	+	0.902977i	$0.358623\pi$
$168$		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	0.747807	−	0.663917i	$-0.231107\pi$
$173$	−2.64460	−	4.58059i	−0.201065	−	0.348255i	−0.948872	+	0.315661i	$0.897774\pi$
$174$		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	0.986919	+	0.161220i	$0.0515428\pi$
$179$	21.6741	+	12.5135i	1.62000	+	0.935306i	0.633080	+	0.774087i	$0.281791\pi$
$180$		0			0
$181$		−	1.10023i		−	0.0817793i	−0.999164	−	0.0408896i	$-0.986981\pi$
$181$		−	1.10023i		−	0.0817793i	0.999164	−	0.0408896i	$-0.0130192\pi$
$182$		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	$-0.996476\pi$
$191$	−20.5966	+	11.8915i	−1.49032	+	0.860436i	−0.490381	+	0.871508i	$0.663142\pi$
$192$		0			0
$193$	4.53630	−	7.85709i	0.326530	−	0.565566i	−0.655291	−	0.755376i	$-0.727454\pi$
$193$	4.53630	−	7.85709i	0.326530	−	0.565566i	0.981821	+	0.189810i	$0.0607873\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.34682i			0.380945i	0.981692	+	0.190473i	$0.0610021\pi$
$197$			5.34682i			0.380945i	−0.981692	+	0.190473i	$0.938998\pi$
$198$		0			0
$199$	−11.2592	−	6.50050i	−0.798143	−	0.460808i	0.0446781	−	0.999001i	$-0.485774\pi$
$199$	−11.2592	−	6.50050i	−0.798143	−	0.460808i	−0.842822	+	0.538193i	$0.819107\pi$
$200$		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	$-0.552580\pi$
$211$	−4.77710			−0.328869			−0.164434	+	0.986388i	$0.552580\pi$
$212$		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	$-0.782224\pi$
$227$	2.40875	−	4.17209i	0.159875	−	0.276911i	0.934823	+	0.355113i	$0.115558\pi$
$228$		0			0
$229$	11.0654	−	6.38861i	0.731222	−	0.422171i	−0.0876474	−	0.996152i	$-0.527935\pi$
$229$	11.0654	−	6.38861i	0.731222	−	0.422171i	0.818869	+	0.573981i	$0.194602\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.6622	−	9.04257i	1.02606	−	0.592399i	0.110210	−	0.993908i	$-0.464848\pi$
$233$	15.6622	−	9.04257i	1.02606	−	0.592399i	0.915855	+	0.401510i	$0.131514\pi$
$234$		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	0.202404	−	0.979302i	$-0.435125\pi$
$241$	−8.45282	−	4.88024i	−0.544494	−	0.314364i	−0.746898	+	0.664938i	$0.768458\pi$
$242$		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	$-0.648695\pi$
$251$	−14.2692			−0.900666			−0.450333	+	0.892861i	$0.648695\pi$
$252$		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	0.543994	−	0.839089i	$-0.316911\pi$
$257$	−7.28900	−	12.6249i	−0.454675	−	0.787520i	−0.998669	+	0.0515686i	$0.983578\pi$
$258$		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	$-0.178998\pi$
$263$	13.0919	+	7.55860i	0.807280	+	0.466083i	−0.0387306	+	0.999250i	$0.512331\pi$
$264$		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	−0.838893	−	0.544297i	$-0.816797\pi$
$269$	0.851686	−	1.47516i	0.0519282	−	0.0899423i	0.890821	+	0.454354i	$0.150130\pi$
$270$		0			0
$271$	24.7312	−	14.2786i	1.50231	−	0.867361i	0.502318	−	0.864683i	$-0.332481\pi$
$271$	24.7312	−	14.2786i	1.50231	−	0.867361i	0.999996	−	0.00267828i	$-0.000852524\pi$
$272$		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	−0.826209	−	0.563364i	$-0.809507\pi$
$277$	1.24464	−	2.15578i	0.0747832	−	0.129528i	0.900992	+	0.433836i	$0.142840\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			0.670935i			0.0400246i	0.999800	+	0.0200123i	$0.00637054\pi$
$281$			0.670935i			0.0400246i	−0.999800	+	0.0200123i	$0.993629\pi$
$282$		0			0
$283$	−17.9849	−	10.3836i	−1.06909	−	0.617240i	−0.141158	−	0.989987i	$-0.545083\pi$
$283$	−17.9849	−	10.3836i	−1.06909	−	0.617240i	−0.927933	+	0.372747i	$0.878416\pi$
$284$		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	−0.240890	−	0.970553i	$-0.577439\pi$
$311$	12.6987	−	21.9948i	0.720078	−	1.24721i	0.960968	−	0.276660i	$-0.0892275\pi$
$312$		0			0
$313$	24.5723	−	14.1868i	1.38891	−	0.801886i	0.395715	−	0.918374i	$-0.370497\pi$
$313$	24.5723	−	14.1868i	1.38891	−	0.801886i	0.993192	+	0.116488i	$0.0371636\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.2783	−	5.93420i	0.577289	−	0.333298i	−0.182766	−	0.983156i	$-0.558505\pi$
$317$	10.2783	−	5.93420i	0.577289	−	0.333298i	0.760055	+	0.649858i	$0.225172\pi$
$318$		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	$-0.0376615\pi$
$331$	7.17325	+	12.4244i	0.394278	+	0.682909i	−0.598731	+	0.800950i	$0.704328\pi$
$332$		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	$-0.396454\pi$
$347$	−6.35617	−	3.66973i	−0.341217	−	0.197002i	−0.660810	+	0.750553i	$0.729787\pi$
$348$		0			0
$349$			22.9882i			1.23053i	0.788320	+	0.615265i	$0.210951\pi$
$349$			22.9882i			1.23053i	−0.788320	+	0.615265i	$0.789049\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.82129	−	10.0828i	0.309836	−	0.536652i	−0.668490	−	0.743721i	$-0.733059\pi$
$353$	5.82129	−	10.0828i	0.309836	−	0.536652i	0.978326	+	0.207069i	$0.0663925\pi$
$354$		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	$-0.851569\pi$
$359$	−18.0093	+	10.3977i	−0.950493	+	0.548767i	−0.0572588	+	0.998359i	$0.518236\pi$
$360$		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	$-0.372294\pi$
$367$	−4.05124	−	2.33899i	−0.211473	−	0.122094i	−0.601996	+	0.798499i	$0.705628\pi$
$368$		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	0.510698	−	0.859760i	$-0.329387\pi$
$373$	−9.44851	−	16.3653i	−0.489225	−	0.847363i	−0.999923	+	0.0123972i	$0.996054\pi$
$374$		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	$-0.549215\pi$
$379$	−5.99600			−0.307994			−0.153997	+	0.988071i	$0.549215\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	13.0490	+	22.6015i	0.666773	+	1.15488i	0.978801	+	0.204811i	$0.0656581\pi$
$383$	13.0490	+	22.6015i	0.666773	+	1.15488i	−0.312029	+	0.950073i	$0.601009\pi$
$384$		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	0.850554	−	0.525888i	$-0.176267\pi$
$389$	16.1808	+	9.34197i	0.820398	+	0.473657i	−0.0301558	+	0.999545i	$0.509600\pi$
$390$		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	−0.696103	−	0.717942i	$-0.745084\pi$
$397$	−8.41621	+	4.85910i	−0.422398	+	0.243871i	0.273705	+	0.961814i	$0.411751\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.1872	+	14.5418i	−1.25779	+	0.726183i	−0.972644	−	0.232302i	$-0.925374\pi$
$401$	−25.1872	+	14.5418i	−1.25779	+	0.726183i	−0.285143	+	0.958485i	$0.592041\pi$
$402$		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	−0.163953	−	0.986468i	$-0.552424\pi$
$409$	−22.2509	−	12.8466i	−1.10024	−	0.635221i	−0.936283	+	0.351247i	$0.885758\pi$
$410$		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	$-0.450566\pi$
$419$	6.33235			0.309356			0.154678	+	0.987965i	$0.450566\pi$
$420$		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	$-0.350507\pi$
$431$	−1.93915	−	1.11957i	−0.0934056	−	0.0539277i	−0.545975	+	0.837801i	$0.683841\pi$
$432$		0			0
$433$		−	1.93460i		−	0.0929709i	−0.998919	−	0.0464855i	$-0.985198\pi$
$433$		−	1.93460i		−	0.0929709i	0.998919	−	0.0464855i	$-0.0148021\pi$
$434$		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	$-0.623397\pi$
$439$	4.91797	−	2.83939i	0.234722	−	0.135517i	0.612748	+	0.790278i	$0.290064\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	20.4243	−	11.7920i	0.970387	−	0.560253i	0.0710331	−	0.997474i	$-0.477370\pi$
$443$	20.4243	−	11.7920i	0.970387	−	0.560253i	0.899354	+	0.437221i	$0.144037\pi$
$444$		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	$0.00744497\pi$
$449$			0.991121i			0.0467739i	−0.999726	+	0.0233869i	$0.992555\pi$
$450$		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	0.602658	−	0.798000i	$-0.294109\pi$
$457$	−8.33211	−	14.4316i	−0.389759	−	0.675083i	−0.992417	+	0.122917i	$0.960775\pi$
$458$		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	$-0.609504\pi$
$463$	−14.5144			−0.674541			−0.337271	+	0.941408i	$0.609504\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.2497	−	35.0736i	−0.937046	−	1.62301i	−0.770944	−	0.636903i	$-0.780215\pi$
$467$	−20.2497	−	35.0736i	−0.937046	−	1.62301i	−0.166102	−	0.986109i	$-0.553118\pi$
$468$		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	$-0.845379\pi$
$479$	−0.828048	+	1.43422i	−0.0378345	+	0.0655312i	0.846488	+	0.532408i	$0.178713\pi$
$480$		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	$-0.887554\pi$
$487$	−3.74089	+	6.47941i	−0.169516	+	0.293610i	0.768734	+	0.639569i	$0.220887\pi$
$488$		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	$-0.0263557\pi$
$499$	9.53093	+	16.5081i	0.426663	+	0.739002i	−0.569911	+	0.821706i	$0.693022\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−16.7859			−0.748448			−0.374224	−	0.927338i	$-0.622091\pi$
$503$	−16.7859			−0.748448			−0.374224	+	0.927338i	$0.622091\pi$
$504$		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	0.677467	−	0.735553i	$-0.263078\pi$
$509$	−6.72937	−	11.6556i	−0.298274	−	0.516626i	−0.975741	+	0.218927i	$0.929744\pi$
$510$		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	−0.126892	+	0.991917i	$0.540500\pi$
$521$	−21.0558	+	36.4697i	−0.922471	+	1.59777i	−0.795579	+	0.605850i	$0.792833\pi$
$522$		0			0
$523$	−16.2844	+	9.40179i	−0.712067	+	0.411112i	−0.811826	−	0.583900i	$-0.801526\pi$
$523$	−16.2844	+	9.40179i	−0.712067	+	0.411112i	0.0997592	+	0.995012i	$0.468193\pi$
$524$		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	0.772367	−	0.635177i	$-0.219073\pi$
$541$	−3.81212	−	6.60278i	−0.163896	−	0.283876i	−0.936263	+	0.351301i	$0.885739\pi$
$542$		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	$-0.283109\pi$
$547$	29.4627			1.25974			0.629868	+	0.776702i	$0.283109\pi$
$548$		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	0.458283	−	0.888806i	$-0.348465\pi$
$557$	−1.94246	−	1.12148i	−0.0823048	−	0.0475187i	−0.540588	+	0.841288i	$0.681798\pi$
$558$		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	−0.230906	+	0.972976i	$0.574169\pi$
$563$	−22.7328	+	39.3744i	−0.958075	+	1.65943i	−0.727169	+	0.686458i	$0.759164\pi$
$564$		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	−0.805491	−	0.592608i	$-0.798098\pi$
$569$	−16.5789	+	9.57183i	−0.695023	+	0.401272i	0.110468	+	0.993880i	$0.464765\pi$
$570$		0			0
$571$	0.602095	−	1.04286i	0.0251969	−	0.0436423i	−0.853152	−	0.521662i	$-0.825312\pi$
$571$	0.602095	−	1.04286i	0.0251969	−	0.0436423i	0.878349	+	0.478020i	$0.158645\pi$
$572$		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	0.816710	−	0.577049i	$-0.195796\pi$
$577$	17.4229	+	10.0591i	0.725325	+	0.418767i	−0.0913843	+	0.995816i	$0.529129\pi$
$578$		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	$-0.878021\pi$
$587$	−44.9416			−1.85494			−0.927470	+	0.373898i	$0.878021\pi$
$588$		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	0.978420	−	0.206624i	$-0.0662478\pi$
$593$	7.55552	+	13.0865i	0.310268	+	0.537400i	−0.668152	+	0.744025i	$0.732915\pi$
$594$		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	$-0.600456\pi$
$599$	−31.5433	−	18.2115i	−1.28883	−	0.744104i	−0.978445	+	0.206509i	$0.933790\pi$
$600$		0			0
$601$			26.5993i			1.08501i	0.840053	+	0.542504i	$0.182524\pi$
$601$			26.5993i			1.08501i	−0.840053	+	0.542504i	$0.817476\pi$
$602$		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	$-0.517529\pi$
$607$	19.2701	−	11.1256i	0.782151	−	0.451575i	0.837192	+	0.546909i	$0.184196\pi$
$608$		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	−0.649819	−	0.760089i	$-0.725155\pi$
$613$	8.25327	−	14.2951i	0.333346	−	0.577373i	0.983166	+	0.182716i	$0.0584888\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	24.1547i		−	0.972431i	−0.873839	−	0.486216i	$-0.838377\pi$
$617$		−	24.1547i		−	0.972431i	0.873839	−	0.486216i	$-0.161623\pi$
$618$		0			0
$619$	−24.1670	−	13.9528i	−0.971354	−	0.560811i	−0.0717051	−	0.997426i	$-0.522844\pi$
$619$	−24.1670	−	13.9528i	−0.971354	−	0.560811i	−0.899649	+	0.436614i	$0.856177\pi$
$620$		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	$-0.410709\pi$
$631$	13.9089			0.553703			0.276852	+	0.960913i	$0.410709\pi$
$632$		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	−0.126003	−	0.992030i	$-0.540215\pi$
$641$	−26.5365	−	15.3208i	−1.04813	−	0.605137i	−0.922125	+	0.386893i	$0.873548\pi$
$642$		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	−0.0827358	−	0.996572i	$-0.526366\pi$
$647$	20.9006	−	36.2009i	0.821688	−	1.42321i	0.904424	−	0.426634i	$-0.140301\pi$
$648$		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	−0.361288	−	0.932454i	$-0.617663\pi$
$653$	6.78703	−	3.91849i	0.265597	−	0.153342i	0.626885	+	0.779112i	$0.284330\pi$
$654$		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	0.829324	−	0.558768i	$-0.188726\pi$
$661$	19.5416	+	11.2823i	0.760079	+	0.438832i	−0.0692453	+	0.997600i	$0.522059\pi$
$662$		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	0.930820	−	0.365478i	$-0.119094\pi$
$677$	3.87418	+	6.71027i	0.148897	+	0.257897i	−0.781923	+	0.623375i	$0.785761\pi$
$678$		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	$-0.401254\pi$
$683$	−9.58568	−	5.53430i	−0.366786	−	0.211764i	−0.672053	+	0.740503i	$0.734587\pi$
$684$		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	$-0.571044\pi$
$691$	13.4729	−	7.77857i	0.512532	−	0.295911i	0.733874	+	0.679286i	$0.237710\pi$
$692$		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	$-0.907732\pi$
$701$		−	15.1353i		−	0.571652i	0.958282	−	0.285826i	$-0.0922679\pi$
$702$		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	0.874001	−	0.485924i	$-0.161517\pi$
$709$	0.430771	+	0.746118i	0.0161780	+	0.0280210i	−0.857823	+	0.513945i	$0.828184\pi$
$710$		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	0.987075	+	0.160262i	$0.0512339\pi$
$719$	16.9554	+	29.3675i	0.632328	+	1.09522i	−0.354746	+	0.934963i	$0.615433\pi$
$720$		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	−0.532905	−	0.846175i	$-0.678900\pi$
$733$	−1.80172	+	1.04022i	−0.0665479	+	0.0384214i	0.466357	+	0.884597i	$0.345566\pi$
$734$		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	−0.223450	−	0.974715i	$-0.571732\pi$
$739$	19.9101	−	34.4852i	0.732403	−	1.26856i	0.955853	−	0.293844i	$-0.0949346\pi$
$740$		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	0.850882	+	0.525357i	$0.176068\pi$
$751$	24.1272	+	41.7895i	0.880414	+	1.52492i	0.0295319	+	0.999564i	$0.490598\pi$
$752$		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	0.773994	+	0.633192i	$0.218256\pi$
$761$	25.8030	+	44.6921i	0.935358	+	1.62009i	0.161363	+	0.986895i	$0.448411\pi$
$762$		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	$0.128715\pi$
$769$			21.8208i			0.786877i	−0.919351	+	0.393438i	$0.871285\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.9682	−	32.8539i	0.682239	−	1.18167i	−0.292057	−	0.956401i	$-0.594340\pi$
$773$	18.9682	−	32.8539i	0.682239	−	1.18167i	0.974296	−	0.225272i	$-0.0723269\pi$
$774$		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	$-0.361426\pi$
$787$	−4.28284	−	2.47270i	−0.152667	−	0.0881422i	−0.574387	+	0.818584i	$0.694760\pi$
$788$		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	0.429015	−	0.903297i	$-0.358861\pi$
$809$	−3.94662	−	2.27858i	−0.138756	−	0.0801108i	−0.567771	+	0.823187i	$0.692194\pi$
$810$		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	−0.442262	−	0.896886i	$-0.645824\pi$
$821$	3.24732	−	1.87484i	0.113332	−	0.0654324i	0.555595	+	0.831453i	$0.312491\pi$
$822$		0			0
$823$	−11.9161	+	20.6392i	−0.415367	+	0.719438i	−0.995467	−	0.0951081i	$-0.969680\pi$
$823$	−11.9161	+	20.6392i	−0.415367	+	0.719438i	0.580099	+	0.814546i	$0.303014\pi$
$824$		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	0.249506	−	0.968373i	$-0.419732\pi$
$829$	−13.3705	−	7.71946i	−0.464376	−	0.268108i	−0.713883	+	0.700265i	$0.753065\pi$
$830$		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	$-0.351323\pi$
$839$	26.0853			0.900566			0.450283	+	0.892886i	$0.351323\pi$
$840$		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	$0.139251\pi$
$853$			24.7463i			0.847297i	−0.905827	+	0.423649i	$0.860749\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.79032	+	15.2253i	−0.300272	+	0.520086i	−0.976197	−	0.216884i	$-0.930411\pi$
$857$	−8.79032	+	15.2253i	−0.300272	+	0.520086i	0.675926	+	0.736970i	$0.263744\pi$
$858$		0			0
$859$	−0.359931	+	0.207806i	−0.0122807	+	0.00709026i	−0.506128	−	0.862459i	$-0.668924\pi$
$859$	−0.359931	+	0.207806i	−0.0122807	+	0.00709026i	0.493847	+	0.869549i	$0.335590\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.22335	+	4.17040i	−0.245886	+	0.141962i	−0.617879	−	0.786273i	$-0.712008\pi$
$863$	−7.22335	+	4.17040i	−0.245886	+	0.141962i	0.371993	+	0.928235i	$0.378674\pi$
$864$		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	−0.924926	−	0.380148i	$-0.875873\pi$
$877$	−23.4450	−	40.6079i	−0.791681	−	1.37123i	0.133245	−	0.991083i	$-0.457460\pi$
$878$		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	$-0.360055\pi$
$883$	25.2950			0.851244			0.425622	+	0.904901i	$0.360055\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.82443	+	6.62411i	0.128412	+	0.222416i	0.923061	−	0.384652i	$-0.125679\pi$
$887$	3.82443	+	6.62411i	0.128412	+	0.222416i	−0.794650	+	0.607068i	$0.792345\pi$
$888$		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	$-0.955508\pi$
$907$	−11.2777	+	19.5335i	−0.374469	+	0.648599i	0.615779	+	0.787919i	$0.288842\pi$
$908$		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	0.969007	+	0.247034i	$0.0794559\pi$
$919$	21.1733	+	36.6731i	0.698441	+	1.20974i	−0.270566	+	0.962702i	$0.587211\pi$
$920$		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	0.882512	−	0.470289i	$-0.155850\pi$
$929$	1.03550	+	1.79353i	0.0339735	+	0.0588438i	−0.848539	+	0.529133i	$0.822517\pi$
$930$		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	$0.0704004\pi$
$937$			13.4301i			0.438741i	−0.975642	+	0.219371i	$0.929600\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.2101	−	26.3447i	0.495836	−	0.858814i	−0.504152	−	0.863615i	$-0.668195\pi$
$941$	15.2101	−	26.3447i	0.495836	−	0.858814i	0.999988	+	0.00480105i	$0.00152823\pi$
$942$		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	0.556074	−	0.831133i	$-0.312307\pi$
$947$	47.8185	−	27.6080i	1.55389	−	0.897140i	0.997819	−	0.0660075i	$-0.0210261\pi$
$948$		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	$0.125956\pi$
$953$			23.7985i			0.770910i	−0.922727	+	0.385455i	$0.874044\pi$
$954$		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	$-0.691617\pi$
$967$	−35.2186			−1.13255			−0.566277	+	0.824215i	$0.691617\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−27.2261	−	47.1570i	−0.873728	−	1.51334i	−0.858112	−	0.513462i	$-0.828363\pi$
$971$	−27.2261	−	47.1570i	−0.873728	−	1.51334i	−0.0156154	−	0.999878i	$-0.504971\pi$
$972$		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	0.936062	−	0.351836i	$-0.114443\pi$
$977$	34.3637	+	19.8399i	1.09939	+	0.634735i	0.163332	+	0.986571i	$0.447776\pi$
$978$		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	$-0.669186\pi$
$983$	15.4610	−	26.7793i	0.493130	−	0.854125i	0.999969	+	0.00791519i	$0.00251951\pi$
$984$		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	$-0.785511\pi$
$991$	4.71177	−	8.16103i	0.149674	−	0.259244i	0.931107	+	0.364746i	$0.118844\pi$
$992$		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	0.673506	−	0.739182i	$-0.264788\pi$
$997$	11.6863	+	6.74707i	0.370108	+	0.213682i	−0.303398	+	0.952864i	$0.598121\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bl.a.17.2	✓	16	4.3	odd	2
504.2.bl.a.17.7	yes	16	12.11	even	2
504.2.bl.a.89.2	yes	16	84.47	odd	6
504.2.bl.a.89.7	yes	16	28.19	even	6
1008.2.bt.d.17.2		16	1.1	even	1	trivial
1008.2.bt.d.17.7		16	3.2	odd	2	inner
1008.2.bt.d.593.2		16	21.5	even	6	inner
1008.2.bt.d.593.7		16	7.5	odd	6	inner
3528.2.k.b.881.3		16	28.3	even	6
3528.2.k.b.881.4		16	84.11	even	6
3528.2.k.b.881.13		16	28.11	odd	6
3528.2.k.b.881.14		16	84.59	odd	6
3528.2.bl.a.521.2		16	84.83	odd	2
3528.2.bl.a.521.7		16	28.27	even	2
3528.2.bl.a.1097.2		16	28.23	odd	6
3528.2.bl.a.1097.7		16	84.23	even	6
7056.2.k.h.881.3		16	21.11	odd	6
7056.2.k.h.881.4		16	7.3	odd	6
7056.2.k.h.881.13		16	21.17	even	6
7056.2.k.h.881.14		16	7.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bt (of order \(6\), degree \(2\), not 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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