LMFDB - Embedded newform 1008.2.bt.d.17.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(17,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			17.8
Root			$-1.45333 - 1.51725i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.2.bt.d.593.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45333 + 2.51725i) q^{5} +(2.64571 + 0.0146827i) q^{7} +(-1.08853 - 0.628464i) q^{11} +5.32679i q^{13} +(0.880708 - 1.52543i) q^{17} +(6.69849 - 3.86738i) q^{19} +(-4.43392 + 2.55992i) q^{23} +(-1.72435 + 2.98667i) q^{25} +8.74013i q^{29} +(-2.18272 - 1.26019i) q^{31} +(3.80814 + 6.68124i) q^{35} +(-3.66400 - 6.34623i) q^{37} -3.09603 q^{41} -1.15729 q^{43} +(-3.44334 - 5.96403i) q^{47} +(6.99957 + 0.0776922i) q^{49} +(11.3057 + 6.52735i) q^{53} -3.65347i q^{55} +(-3.13525 + 5.43042i) q^{59} +(2.19449 - 1.26699i) q^{61} +(-13.4088 + 7.74160i) q^{65} +(0.689860 - 1.19487i) q^{67} +8.65477i q^{71} +(4.38121 + 2.52949i) q^{73} +(-2.87071 - 1.67872i) q^{77} +(7.63142 + 13.2180i) q^{79} -3.75373 q^{83} +5.11985 q^{85} +(-3.55321 - 6.15434i) q^{89} +(-0.0782115 + 14.0931i) q^{91} +(19.4703 + 11.2412i) q^{95} +4.03874i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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

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
$5$	1.45333	+	2.51725i	0.649950	+	1.12575i	0.983134	+	0.182885i	$0.0585436\pi$
$5$	1.45333	+	2.51725i	0.649950	+	1.12575i	−0.333184	+	0.942862i	$0.608123\pi$
$6$		0			0
$7$	2.64571	+	0.0146827i	0.999985	+	0.00554953i
$7$	2.64571	+	0.0146827i	0.999985	+	0.00554953i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.08853	−	0.628464i	−0.328205	−	0.189489i	0.326839	−	0.945080i	$-0.394016\pi$
$11$	−1.08853	−	0.628464i	−0.328205	−	0.189489i	−0.655044	+	0.755591i	$0.727350\pi$
$12$		0			0
$13$			5.32679i			1.47739i	0.674042	+	0.738693i	$0.264557\pi$
$13$			5.32679i			1.47739i	−0.674042	+	0.738693i	$0.735443\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.880708	−	1.52543i	0.213603	−	0.369971i	−0.739236	−	0.673446i	$-0.764813\pi$
$17$	0.880708	−	1.52543i	0.213603	−	0.369971i	0.952840	+	0.303475i	$0.0981467\pi$
$18$		0			0
$19$	6.69849	−	3.86738i	1.53674	−	0.887237i	0.537712	−	0.843128i	$-0.319289\pi$
$19$	6.69849	−	3.86738i	1.53674	−	0.887237i	0.999027	−	0.0441085i	$-0.0140447\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.43392	+	2.55992i	−0.924536	+	0.533781i	−0.885079	−	0.465440i	$-0.845896\pi$
$23$	−4.43392	+	2.55992i	−0.924536	+	0.533781i	−0.0394566	+	0.999221i	$0.512563\pi$
$24$		0			0
$25$	−1.72435	+	2.98667i	−0.344871	+	0.597333i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			8.74013i			1.62300i	0.584352	+	0.811500i	$0.301349\pi$
$29$			8.74013i			1.62300i	−0.584352	+	0.811500i	$0.698651\pi$
$30$		0			0
$31$	−2.18272	−	1.26019i	−0.392027	−	0.226337i	0.291011	−	0.956720i	$-0.406008\pi$
$31$	−2.18272	−	1.26019i	−0.392027	−	0.226337i	−0.683038	+	0.730383i	$0.739342\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.80814	+	6.68124i	0.643693	+	1.12934i
$36$		0			0
$37$	−3.66400	−	6.34623i	−0.602358	−	1.04331i	−0.992463	−	0.122544i	$-0.960895\pi$
$37$	−3.66400	−	6.34623i	−0.602358	−	1.04331i	0.390106	−	0.920770i	$-0.372439\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.09603			−0.483519			−0.241760	−	0.970336i	$-0.577725\pi$
$41$	−3.09603			−0.483519			−0.241760	+	0.970336i	$0.577725\pi$
$42$		0			0
$43$	−1.15729			−0.176484			−0.0882422	−	0.996099i	$-0.528125\pi$
$43$	−1.15729			−0.176484			−0.0882422	+	0.996099i	$0.528125\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.44334	−	5.96403i	−0.502262	−	0.869944i	−0.999997	−	0.00261431i	$-0.999168\pi$
$47$	−3.44334	−	5.96403i	−0.502262	−	0.869944i	0.497734	−	0.867330i	$-0.334165\pi$
$48$		0			0
$49$	6.99957	+	0.0776922i	0.999938	+	0.0110989i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	11.3057	+	6.52735i	1.55296	+	0.896600i	0.997899	+	0.0647890i	$0.0206374\pi$
$53$	11.3057	+	6.52735i	1.55296	+	0.896600i	0.555058	+	0.831811i	$0.312696\pi$
$54$		0			0
$55$		−	3.65347i		−	0.492634i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.13525	+	5.43042i	−0.408175	+	0.706980i	−0.994685	−	0.102962i	$-0.967168\pi$
$59$	−3.13525	+	5.43042i	−0.408175	+	0.706980i	0.586510	+	0.809942i	$0.300501\pi$
$60$		0			0
$61$	2.19449	−	1.26699i	0.280976	−	0.162221i	−0.352889	−	0.935665i	$-0.614801\pi$
$61$	2.19449	−	1.26699i	0.280976	−	0.162221i	0.633865	+	0.773444i	$0.281467\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.4088	+	7.74160i	−1.66316	+	0.960227i
$66$		0			0
$67$	0.689860	−	1.19487i	0.0842798	−	0.145977i	−0.820804	−	0.571210i	$-0.806474\pi$
$67$	0.689860	−	1.19487i	0.0842798	−	0.145977i	0.905084	+	0.425233i	$0.139808\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8.65477i			1.02713i	0.858050	+	0.513566i	$0.171676\pi$
$71$			8.65477i			1.02713i	−0.858050	+	0.513566i	$0.828324\pi$
$72$		0			0
$73$	4.38121	+	2.52949i	0.512782	+	0.296055i	0.733976	−	0.679175i	$-0.237662\pi$
$73$	4.38121	+	2.52949i	0.512782	+	0.296055i	−0.221195	+	0.975230i	$0.570996\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.87071	−	1.67872i	−0.327148	−	0.191308i
$78$		0			0
$79$	7.63142	+	13.2180i	0.858602	+	1.48714i	0.873262	+	0.487250i	$0.162000\pi$
$79$	7.63142	+	13.2180i	0.858602	+	1.48714i	−0.0146603	+	0.999893i	$0.504667\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.75373			−0.412025			−0.206013	−	0.978549i	$-0.566049\pi$
$83$	−3.75373			−0.412025			−0.206013	+	0.978549i	$0.566049\pi$
$84$		0			0
$85$	5.11985			0.555326
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.55321	−	6.15434i	−0.376640	−	0.652359i	0.613931	−	0.789359i	$-0.289587\pi$
$89$	−3.55321	−	6.15434i	−0.376640	−	0.652359i	−0.990571	+	0.137001i	$0.956254\pi$
$90$		0			0
$91$	−0.0782115	+	14.0931i	−0.00819880	+	1.47736i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	19.4703	+	11.2412i	1.99761	+	1.15332i
$96$		0			0
$97$			4.03874i			0.410072i	0.978754	+	0.205036i	$0.0657311\pi$
$97$			4.03874i			0.410072i	−0.978754	+	0.205036i	$0.934269\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.39249	−	5.87597i	0.337565	−	0.584681i	−0.646409	−	0.762991i	$-0.723730\pi$
$101$	3.39249	−	5.87597i	0.337565	−	0.584681i	0.983974	+	0.178311i	$0.0570632\pi$
$102$		0			0
$103$	5.39758	−	3.11629i	0.531839	−	0.307057i	−0.209926	−	0.977717i	$-0.567322\pi$
$103$	5.39758	−	3.11629i	0.531839	−	0.307057i	0.741765	+	0.670660i	$0.233989\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.41950	−	4.86100i	0.813944	−	0.469931i	−0.0343796	−	0.999409i	$-0.510946\pi$
$107$	8.41950	−	4.86100i	0.813944	−	0.469931i	0.848324	+	0.529478i	$0.177612\pi$
$108$		0			0
$109$	7.34463	−	12.7213i	0.703488	−	1.21848i	−0.263746	−	0.964592i	$-0.584958\pi$
$109$	7.34463	−	12.7213i	0.703488	−	1.21848i	0.967234	−	0.253885i	$-0.0817086\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	19.1169i		−	1.79837i	−0.437572	−	0.899184i	$-0.644161\pi$
$113$		−	19.1169i		−	1.79837i	0.437572	−	0.899184i	$-0.355839\pi$
$114$		0			0
$115$	−12.8879	−	7.44084i	−1.20180	−	0.693862i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.35250	−	4.02292i	0.215653	−	0.368780i
$120$		0			0
$121$	−4.71007	−	8.15807i	−0.428188	−	0.741643i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.50909			0.403305
$126$		0			0
$127$	−14.2906			−1.26808			−0.634041	−	0.773299i	$-0.718605\pi$
$127$	−14.2906			−1.26808			−0.634041	+	0.773299i	$0.718605\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.07057	−	10.5145i	−0.530388	−	0.918659i	−0.999371	−	0.0354521i	$-0.988713\pi$
$131$	−6.07057	−	10.5145i	−0.530388	−	0.918659i	0.468983	−	0.883207i	$-0.344620\pi$
$132$		0			0
$133$	17.7791	−	10.1336i	1.54164	−	0.878695i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.986259	−	0.569417i	−0.0842618	−	0.0486486i	0.457277	−	0.889324i	$-0.348825\pi$
$137$	−0.986259	−	0.569417i	−0.0842618	−	0.0486486i	−0.541539	+	0.840676i	$0.682158\pi$
$138$		0			0
$139$			20.6610i			1.75245i	0.481906	+	0.876223i	$0.339945\pi$
$139$			20.6610i			1.75245i	−0.481906	+	0.876223i	$0.660055\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.34770	−	5.79838i	0.279948	−	0.484885i
$144$		0			0
$145$	−22.0011	+	12.7023i	−1.82709	+	1.05487i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.28425	+	3.05086i	−0.432903	+	0.249936i	−0.700582	−	0.713572i	$-0.747076\pi$
$149$	−5.28425	+	3.05086i	−0.432903	+	0.249936i	0.267680	+	0.963508i	$0.413743\pi$
$150$		0			0
$151$	3.66443	−	6.34698i	0.298207	−	0.516510i	−0.677519	−	0.735505i	$-0.736945\pi$
$151$	3.66443	−	6.34698i	0.298207	−	0.516510i	0.975726	+	0.218996i	$0.0702781\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	7.32591i		−	0.588432i
$156$		0			0
$157$	3.32800	+	1.92142i	0.265603	+	0.153346i	0.626888	−	0.779110i	$-0.284328\pi$
$157$	3.32800	+	1.92142i	0.265603	+	0.153346i	−0.361285	+	0.932456i	$0.617662\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.7685	+	6.70772i	−0.927484	+	0.528642i
$162$		0			0
$163$	−7.97206	−	13.8080i	−0.624420	−	1.08153i	−0.988653	−	0.150219i	$-0.952002\pi$
$163$	−7.97206	−	13.8080i	−0.624420	−	1.08153i	0.364233	−	0.931308i	$-0.381331\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−24.1419			−1.86816			−0.934079	−	0.357067i	$-0.883777\pi$
$167$	−24.1419			−1.86816			−0.934079	+	0.357067i	$0.883777\pi$
$168$		0			0
$169$	−15.3747			−1.18267
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.78641	+	11.7544i	0.515962	+	0.893672i	0.999828	+	0.0185299i	$0.00589860\pi$
$173$	6.78641	+	11.7544i	0.515962	+	0.893672i	−0.483867	+	0.875142i	$0.660768\pi$
$174$		0			0
$175$	−4.60599	+	7.87654i	−0.348180	+	0.595410i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.62646	−	0.939035i	−0.121567	−	0.0701868i	0.437983	−	0.898983i	$-0.355693\pi$
$179$	−1.62646	−	0.939035i	−0.121567	−	0.0701868i	−0.559550	+	0.828796i	$0.689026\pi$
$180$		0			0
$181$		−	5.36975i		−	0.399130i	−0.979885	−	0.199565i	$-0.936047\pi$
$181$		−	5.36975i		−	0.399130i	0.979885	−	0.199565i	$-0.0639530\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.6500	−	18.4464i	0.783005	−	1.35620i
$186$		0			0
$187$	−1.91736	+	1.10699i	−0.140211	+	0.0809509i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.3153	−	8.26495i	1.03582	−	0.598031i	0.117173	−	0.993111i	$-0.462617\pi$
$191$	14.3153	−	8.26495i	1.03582	−	0.598031i	0.918646	+	0.395081i	$0.129283\pi$
$192$		0			0
$193$	−6.24013	+	10.8082i	−0.449174	+	0.777993i	−0.998332	−	0.0577258i	$-0.981615\pi$
$193$	−6.24013	+	10.8082i	−0.449174	+	0.777993i	0.549158	+	0.835718i	$0.314948\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19.7258i		−	1.40541i	−0.711482	−	0.702704i	$-0.751976\pi$
$197$		−	19.7258i		−	1.40541i	0.711482	−	0.702704i	$-0.248024\pi$
$198$		0			0
$199$	−21.2771	−	12.2844i	−1.50830	−	0.870815i	−0.999953	−	0.00966023i	$-0.996925\pi$
$199$	−21.2771	−	12.2844i	−1.50830	−	0.870815i	−0.508343	−	0.861155i	$-0.669742\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.128328	+	23.1238i	−0.00900689	+	1.62298i
$204$		0			0
$205$	−4.49957	−	7.79348i	−0.314264	−	0.544320i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.72203			−0.672487
$210$		0			0
$211$	16.0173			1.10267			0.551337	−	0.834283i	$-0.314118\pi$
$211$	16.0173			1.10267			0.551337	+	0.834283i	$0.314118\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.68192	−	2.91317i	−0.114706	−	0.198677i
$216$		0			0
$217$	−5.75633	−	3.36615i	−0.390765	−	0.228509i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.12565	+	4.69135i	0.546590	+	0.315574i
$222$		0			0
$223$		−	24.7358i		−	1.65643i	−0.560410	−	0.828215i	$-0.689356\pi$
$223$		−	24.7358i		−	1.65643i	0.560410	−	0.828215i	$-0.310644\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.1431	−	19.3005i	0.739597	−	1.28102i	−0.213080	−	0.977035i	$-0.568350\pi$
$227$	11.1431	−	19.3005i	0.739597	−	1.28102i	0.952677	−	0.303984i	$-0.0983171\pi$
$228$		0			0
$229$	−14.5011	+	8.37219i	−0.958257	+	0.553250i	−0.895636	−	0.444788i	$-0.853279\pi$
$229$	−14.5011	+	8.37219i	−0.958257	+	0.553250i	−0.0626207	+	0.998037i	$0.519946\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.45707	−	0.841243i	0.0954561	−	0.0551116i	−0.451512	−	0.892265i	$-0.649115\pi$
$233$	1.45707	−	0.841243i	0.0954561	−	0.0551116i	0.546968	+	0.837153i	$0.315782\pi$
$234$		0			0
$235$	10.0086	−	17.3355i	0.652891	−	1.13084i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	7.79777i		−	0.504396i	−0.967676	−	0.252198i	$-0.918847\pi$
$239$		−	7.79777i		−	0.504396i	0.967676	−	0.252198i	$-0.0811534\pi$
$240$		0			0
$241$	−12.1503	−	7.01500i	−0.782672	−	0.451876i	0.0547042	−	0.998503i	$-0.482578\pi$
$241$	−12.1503	−	7.01500i	−0.782672	−	0.451876i	−0.837377	+	0.546627i	$0.815912\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.97713	+	17.7326i	0.637416	+	1.13289i
$246$		0			0
$247$	20.6007	+	35.6815i	1.31079	+	2.27036i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.34078			−0.589585			−0.294792	−	0.955561i	$-0.595251\pi$
$251$	−9.34078			−0.589585			−0.294792	+	0.955561i	$0.595251\pi$
$252$		0			0
$253$	6.43528			0.404583
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.12814	−	7.15016i	−0.257507	−	0.446015i	0.708067	−	0.706146i	$-0.249568\pi$
$257$	−4.12814	−	7.15016i	−0.257507	−	0.446015i	−0.965573	+	0.260131i	$0.916234\pi$
$258$		0			0
$259$	−9.60070	−	16.8441i	−0.596558	−	1.04664i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.7171	−	10.2290i	−1.09248	−	0.630746i	−0.158248	−	0.987399i	$-0.550584\pi$
$263$	−17.7171	−	10.2290i	−1.09248	−	0.630746i	−0.934237	+	0.356653i	$0.883918\pi$
$264$		0			0
$265$			37.9456i			2.33098i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.1726	−	26.2797i	0.925088	−	1.60230i	0.133668	−	0.991026i	$-0.457324\pi$
$269$	15.1726	−	26.2797i	0.925088	−	1.60230i	0.791420	−	0.611273i	$-0.209342\pi$
$270$		0			0
$271$	5.16870	−	2.98415i	0.313976	−	0.181274i	−0.334728	−	0.942315i	$-0.608645\pi$
$271$	5.16870	−	2.98415i	0.313976	−	0.181274i	0.648704	+	0.761041i	$0.275311\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.75403	−	2.16739i	0.226376	−	0.130698i
$276$		0			0
$277$	1.11836	−	1.93706i	0.0671958	−	0.116387i	−0.830470	−	0.557063i	$-0.811928\pi$
$277$	1.11836	−	1.93706i	0.0671958	−	0.116387i	0.897666	+	0.440677i	$0.145261\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			16.2683i			0.970484i	0.874380	+	0.485242i	$0.161268\pi$
$281$			16.2683i			0.970484i	−0.874380	+	0.485242i	$0.838732\pi$
$282$		0			0
$283$	−3.84235	−	2.21838i	−0.228404	−	0.131869i	0.381432	−	0.924397i	$-0.375431\pi$
$283$	−3.84235	−	2.21838i	−0.228404	−	0.131869i	−0.609836	+	0.792528i	$0.708765\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.19121	−	0.0454581i	−0.483512	−	0.00268331i
$288$		0			0
$289$	6.94871	+	12.0355i	0.408747	+	0.707971i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.48448			0.495669			0.247834	−	0.968802i	$-0.420281\pi$
$293$	8.48448			0.495669			0.247834	+	0.968802i	$0.420281\pi$
$294$		0			0
$295$	−18.2263			−1.06117
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.6362	−	23.6186i	−0.788601	−	1.36590i
$300$		0			0
$301$	−3.06184	−	0.0169920i	−0.176482	−	0.000979405i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.37865	+	3.68272i	0.365241	+	0.210872i
$306$		0			0
$307$			2.06321i			0.117753i	0.998265	+	0.0588767i	$0.0187519\pi$
$307$			2.06321i			0.117753i	−0.998265	+	0.0588767i	$0.981248\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.4339	−	23.2683i	0.761768	−	1.31942i	−0.180170	−	0.983635i	$-0.557665\pi$
$311$	13.4339	−	23.2683i	0.761768	−	1.31942i	0.941938	−	0.335786i	$-0.109002\pi$
$312$		0			0
$313$	−10.6333	+	6.13912i	−0.601028	+	0.347004i	−0.769446	−	0.638712i	$-0.779468\pi$
$313$	−10.6333	+	6.13912i	−0.601028	+	0.347004i	0.168418	+	0.985716i	$0.446134\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.29866	−	0.749784i	0.0729403	−	0.0421121i	−0.463086	−	0.886313i	$-0.653258\pi$
$317$	1.29866	−	0.749784i	0.0729403	−	0.0421121i	0.536027	+	0.844201i	$0.319925\pi$
$318$		0			0
$319$	5.49286	−	9.51391i	0.307541	−	0.532676i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	13.6241i		−	0.758066i
$324$		0			0
$325$	−15.9094	−	9.18527i	−0.882492	−	0.509507i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.02251	−	15.8297i	−0.497427	−	0.872718i
$330$		0			0
$331$	7.53641	+	13.0534i	0.414239	+	0.717482i	0.995348	−	0.0963430i	$-0.0307146\pi$
$331$	7.53641	+	13.0534i	0.414239	+	0.717482i	−0.581110	+	0.813825i	$0.697381\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.01039			0.219111
$336$		0			0
$337$	15.3414			0.835700			0.417850	−	0.908516i	$-0.362784\pi$
$337$	15.3414			0.835700			0.417850	+	0.908516i	$0.362784\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.58397	+	2.74352i	0.0857768	+	0.148570i
$342$		0			0
$343$	18.5177	+	0.308324i	0.999861	+	0.0166479i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.4995	+	7.79393i	0.724691	+	0.418400i	0.816477	−	0.577378i	$-0.195924\pi$
$347$	13.4995	+	7.79393i	0.724691	+	0.418400i	−0.0917861	+	0.995779i	$0.529258\pi$
$348$		0			0
$349$		−	1.35182i		−	0.0723613i	−0.999345	−	0.0361806i	$-0.988481\pi$
$349$		−	1.35182i		−	0.0723613i	0.999345	−	0.0361806i	$-0.0115192\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.91110	−	17.1665i	0.527515	−	0.913682i	−0.471971	−	0.881614i	$-0.656457\pi$
$353$	9.91110	−	17.1665i	0.527515	−	0.913682i	0.999486	−	0.0320680i	$-0.0102093\pi$
$354$		0			0
$355$	−21.7862	+	12.5783i	−1.15629	+	0.667585i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.9382	+	10.9340i	−0.999521	+	0.577074i	−0.908107	−	0.418739i	$-0.862472\pi$
$359$	−18.9382	+	10.9340i	−0.999521	+	0.577074i	−0.0914146	+	0.995813i	$0.529139\pi$
$360$		0			0
$361$	20.4132	−	35.3567i	1.07438	−	1.86088i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			14.7048i			0.769683i
$366$		0			0
$367$	−0.591012	−	0.341221i	−0.0308506	−	0.0178116i	0.484495	−	0.874794i	$-0.339003\pi$
$367$	−0.591012	−	0.341221i	−0.0308506	−	0.0178116i	−0.515346	+	0.856982i	$0.672337\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	29.8158	+	17.4355i	1.54796	+	0.905205i
$372$		0			0
$373$	12.5153	+	21.6772i	0.648020	+	1.12240i	0.983595	+	0.180390i	$0.0577360\pi$
$373$	12.5153	+	21.6772i	0.648020	+	1.12240i	−0.335575	+	0.942013i	$0.608931\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−46.5568			−2.39780
$378$		0			0
$379$	10.7220			0.550752			0.275376	−	0.961337i	$-0.411198\pi$
$379$	10.7220			0.550752			0.275376	+	0.961337i	$0.411198\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.8748	+	20.5677i	0.606772	+	1.05096i	0.991769	+	0.128042i	$0.0408692\pi$
$383$	11.8748	+	20.5677i	0.606772	+	1.05096i	−0.384997	+	0.922918i	$0.625797\pi$
$384$		0			0
$385$	0.0536427	−	9.66602i	0.00273389	−	0.492626i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.6648	+	7.88939i	0.692834	+	0.400008i	0.804673	−	0.593718i	$-0.202341\pi$
$389$	13.6648	+	7.88939i	0.692834	+	0.400008i	−0.111839	+	0.993726i	$0.535674\pi$
$390$		0			0
$391$			9.01818i			0.456069i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.1820	+	38.4203i	−1.11610	+	1.93314i
$396$		0			0
$397$	−13.9468	+	8.05218i	−0.699969	+	0.404127i	−0.807336	−	0.590092i	$-0.799091\pi$
$397$	−13.9468	+	8.05218i	−0.699969	+	0.404127i	0.107367	+	0.994219i	$0.465758\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.4857	−	8.36335i	0.723384	−	0.417646i	−0.0926131	−	0.995702i	$-0.529522\pi$
$401$	14.4857	−	8.36335i	0.723384	−	0.417646i	0.815997	+	0.578056i	$0.196189\pi$
$402$		0			0
$403$	6.71278	−	11.6269i	0.334387	−	0.579176i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			9.21076i			0.456561i
$408$		0			0
$409$	10.1106	+	5.83733i	0.499935	+	0.288637i	0.728687	−	0.684847i	$-0.240131\pi$
$409$	10.1106	+	5.83733i	0.499935	+	0.288637i	−0.228752	+	0.973485i	$0.573464\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.37471	+	14.3213i	−0.412092	+	0.704704i
$414$		0			0
$415$	−5.45542	−	9.44906i	−0.267796	−	0.463836i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.16399			0.398837			0.199419	−	0.979914i	$-0.436095\pi$
$419$	8.16399			0.398837			0.199419	+	0.979914i	$0.436095\pi$
$420$		0			0
$421$	−7.71744			−0.376125			−0.188063	−	0.982157i	$-0.560221\pi$
$421$	−7.71744			−0.376125			−0.188063	+	0.982157i	$0.560221\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.03730	+	5.26076i	0.147331	+	0.255185i
$426$		0			0
$427$	5.82459	−	3.31987i	0.281872	−	0.160660i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	24.1483	+	13.9420i	1.16318	+	0.671563i	0.952064	−	0.305898i	$-0.0989566\pi$
$431$	24.1483	+	13.9420i	1.16318	+	0.671563i	0.211117	+	0.977461i	$0.432290\pi$
$432$		0			0
$433$		−	19.8885i		−	0.955779i	−0.878420	−	0.477889i	$-0.841402\pi$
$433$		−	19.8885i		−	0.955779i	0.878420	−	0.477889i	$-0.158598\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−19.8004	+	34.2953i	−0.947180	+	1.64056i
$438$		0			0
$439$	−6.61654	+	3.82006i	−0.315790	+	0.182322i	−0.649515	−	0.760349i	$-0.725028\pi$
$439$	−6.61654	+	3.82006i	−0.315790	+	0.182322i	0.333724	+	0.942671i	$0.391695\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.4681	+	10.0852i	−0.829933	+	0.479162i	−0.853830	−	0.520553i	$-0.825726\pi$
$443$	−17.4681	+	10.0852i	−0.829933	+	0.479162i	0.0238969	+	0.999714i	$0.492393\pi$
$444$		0			0
$445$	10.3280	−	17.8886i	0.489594	−	0.848002i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	2.27122i		−	0.107185i	−0.998563	−	0.0535926i	$-0.982933\pi$
$449$		−	2.27122i		−	0.107185i	0.998563	−	0.0535926i	$-0.0170672\pi$
$450$		0			0
$451$	3.37013	+	1.94575i	0.158693	+	0.0916216i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−35.5896	+	20.2852i	−1.66847	+	0.950983i
$456$		0			0
$457$	−5.74056	−	9.94294i	−0.268532	−	0.465111i	0.699951	−	0.714191i	$-0.253205\pi$
$457$	−5.74056	−	9.94294i	−0.268532	−	0.465111i	−0.968483	+	0.249080i	$0.919872\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.2339			−1.17526			−0.587630	−	0.809130i	$-0.699939\pi$
$461$	−25.2339			−1.17526			−0.587630	+	0.809130i	$0.699939\pi$
$462$		0			0
$463$	−17.8323			−0.828736			−0.414368	−	0.910110i	$-0.635997\pi$
$463$	−17.8323			−0.828736			−0.414368	+	0.910110i	$0.635997\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.62598	−	4.54833i	−0.121516	−	0.210472i	0.798850	−	0.601531i	$-0.205442\pi$
$467$	−2.62598	−	4.54833i	−0.121516	−	0.210472i	−0.920366	+	0.391059i	$0.872109\pi$
$468$		0			0
$469$	1.84271	−	3.15116i	0.0850887	−	0.145507i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.25974	+	0.727312i	0.0579230	+	0.0334419i
$474$		0			0
$475$			26.6749i			1.22393i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.2216	−	29.8287i	0.786875	−	1.36291i	−0.140997	−	0.990010i	$-0.545031\pi$
$479$	17.2216	−	29.8287i	0.786875	−	1.36291i	0.927873	−	0.372898i	$-0.121636\pi$
$480$		0			0
$481$	33.8050	−	19.5173i	1.54138	−	0.889915i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.1665	+	5.86963i	−0.461637	+	0.266526i
$486$		0			0
$487$	−12.3207	+	21.3401i	−0.558304	+	0.967010i	0.439335	+	0.898324i	$0.355214\pi$
$487$	−12.3207	+	21.3401i	−0.558304	+	0.967010i	−0.997638	+	0.0686868i	$0.978119\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			6.90125i			0.311449i	0.987801	+	0.155725i	$0.0497712\pi$
$491$			6.90125i			0.311449i	−0.987801	+	0.155725i	$0.950229\pi$
$492$		0			0
$493$	13.3325	+	7.69750i	0.600464	+	0.346678i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.127075	+	22.8980i	−0.00570010	+	1.02712i
$498$		0			0
$499$	−3.72644	−	6.45437i	−0.166818	−	0.288938i	0.770481	−	0.637463i	$-0.220016\pi$
$499$	−3.72644	−	6.45437i	−0.166818	−	0.288938i	−0.937299	+	0.348525i	$0.886683\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.0638301			0.00284605			0.00142302	−	0.999999i	$-0.499547\pi$
$503$	0.0638301			0.00284605			0.00142302	+	0.999999i	$0.499547\pi$
$504$		0			0
$505$	19.7217			0.877603
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.76796	−	11.7225i	−0.299985	−	0.519588i	0.676148	−	0.736766i	$-0.263648\pi$
$509$	−6.76796	−	11.7225i	−0.299985	−	0.519588i	−0.976132	+	0.217178i	$0.930315\pi$
$510$		0			0
$511$	11.5543	+	6.75663i	0.511131	+	0.298896i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.6890	+	9.05802i	0.691338	+	0.399144i
$516$		0			0
$517$			8.65605i			0.380693i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.01202	+	10.4131i	−0.263391	+	0.456207i	−0.967141	−	0.254241i	$-0.918174\pi$
$521$	−6.01202	+	10.4131i	−0.263391	+	0.456207i	0.703750	+	0.710448i	$0.251508\pi$
$522$		0			0
$523$	−18.1014	+	10.4508i	−0.791517	+	0.456983i	−0.840496	−	0.541817i	$-0.817737\pi$
$523$	−18.1014	+	10.4508i	−0.791517	+	0.456983i	0.0489792	+	0.998800i	$0.484403\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.84467	+	2.21972i	−0.167477	+	0.0966926i
$528$		0			0
$529$	1.60642	−	2.78241i	0.0698445	−	0.120974i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	16.4919i		−	0.714345i
$534$		0			0
$535$	24.4727	+	14.1293i	1.05805	+	0.610863i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.57043	−	4.48355i	−0.326081	−	0.193120i
$540$		0			0
$541$	−5.07613	−	8.79211i	−0.218240	−	0.378003i	0.736030	−	0.676949i	$-0.236698\pi$
$541$	−5.07613	−	8.79211i	−0.218240	−	0.378003i	−0.954270	+	0.298946i	$0.903365\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	42.6968			1.82893
$546$		0			0
$547$	3.99041			0.170618			0.0853088	−	0.996355i	$-0.472812\pi$
$547$	3.99041			0.170618			0.0853088	+	0.996355i	$0.472812\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	33.8014	+	58.5457i	1.43999	+	2.49413i
$552$		0			0
$553$	19.9965	+	35.0831i	0.850336	+	1.49188i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.41758	+	3.70519i	0.271921	+	0.156994i	0.629760	−	0.776789i	$-0.283153\pi$
$557$	6.41758	+	3.70519i	0.271921	+	0.156994i	−0.357839	+	0.933783i	$0.616486\pi$
$558$		0			0
$559$		−	6.16462i		−	0.260736i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.851583	−	1.47499i	0.0358899	−	0.0621632i	−0.847522	−	0.530759i	$-0.821907\pi$
$563$	0.851583	−	1.47499i	0.0358899	−	0.0621632i	0.883412	+	0.468596i	$0.155240\pi$
$564$		0			0
$565$	48.1220	−	27.7832i	2.02451	−	1.16885i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.3339	+	8.27566i	−0.600907	+	0.346934i	−0.769398	−	0.638769i	$-0.779444\pi$
$569$	−14.3339	+	8.27566i	−0.600907	+	0.346934i	0.168491	+	0.985703i	$0.446110\pi$
$570$		0			0
$571$	−3.49034	+	6.04545i	−0.146066	+	0.252994i	−0.929770	−	0.368140i	$-0.879995\pi$
$571$	−3.49034	+	6.04545i	−0.146066	+	0.252994i	0.783704	+	0.621135i	$0.213328\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	17.6569i		−	0.736342i
$576$		0			0
$577$	−28.5904	−	16.5067i	−1.19023	−	0.687182i	−0.231875	−	0.972746i	$-0.574486\pi$
$577$	−28.5904	−	16.5067i	−1.19023	−	0.687182i	−0.958360	+	0.285564i	$0.907819\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.93128	−	0.0551148i	−0.412019	−	0.00228655i
$582$		0			0
$583$	−8.20441	−	14.2105i	−0.339792	−	0.588537i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.1690			−1.16266			−0.581330	−	0.813668i	$-0.697467\pi$
$587$	−28.1690			−1.16266			−0.581330	+	0.813668i	$0.697467\pi$
$588$		0			0
$589$	−19.4945			−0.803259
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.04923	−	12.2096i	−0.289477	−	0.501389i	0.684208	−	0.729287i	$-0.260148\pi$
$593$	−7.04923	−	12.2096i	−0.289477	−	0.501389i	−0.973685	+	0.227898i	$0.926815\pi$
$594$		0			0
$595$	13.5456	+	0.0751731i	0.555317	+	0.00308180i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	27.9852	+	16.1573i	1.14345	+	0.660169i	0.947282	−	0.320402i	$-0.103818\pi$
$599$	27.9852	+	16.1573i	1.14345	+	0.660169i	0.196164	+	0.980571i	$0.437151\pi$
$600$		0			0
$601$		−	11.9359i		−	0.486877i	−0.969916	−	0.243439i	$-0.921725\pi$
$601$		−	11.9359i		−	0.486877i	0.969916	−	0.243439i	$-0.0782754\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	13.6906	−	23.7128i	0.556602	−	0.964062i
$606$		0			0
$607$	19.8863	−	11.4813i	0.807159	−	0.466013i	−0.0388095	−	0.999247i	$-0.512357\pi$
$607$	19.8863	−	11.4813i	0.807159	−	0.466013i	0.845968	+	0.533233i	$0.179023\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	31.7692	−	18.3419i	1.28524	−	0.742035i
$612$		0			0
$613$	−18.5772	+	32.1766i	−0.750325	+	1.29960i	0.197339	+	0.980335i	$0.436770\pi$
$613$	−18.5772	+	32.1766i	−0.750325	+	1.29960i	−0.947665	+	0.319267i	$0.896563\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	2.34437i		−	0.0943806i	−0.998886	−	0.0471903i	$-0.984973\pi$
$617$		−	2.34437i		−	0.0943806i	0.998886	−	0.0471903i	$-0.0150267\pi$
$618$		0			0
$619$	25.9709	+	14.9943i	1.04386	+	0.602673i	0.920924	−	0.389742i	$-0.127436\pi$
$619$	25.9709	+	14.9943i	1.04386	+	0.602673i	0.122936	+	0.992415i	$0.460769\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.31040	−	16.3348i	−0.373013	−	0.654439i
$624$		0			0
$625$	15.1750	+	26.2838i	0.606999	+	1.05135i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.9077			−0.514662
$630$		0			0
$631$	43.6780			1.73879			0.869396	−	0.494116i	$-0.164508\pi$
$631$	43.6780			1.73879			0.869396	+	0.494116i	$0.164508\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−20.7689	−	35.9729i	−0.824190	−	1.42754i
$636$		0			0
$637$	−0.413850	+	37.2852i	−0.0163973	+	1.47729i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14.6850	+	8.47841i	0.580024	+	0.334877i	0.761143	−	0.648584i	$-0.224639\pi$
$641$	14.6850	+	8.47841i	0.580024	+	0.334877i	−0.181119	+	0.983461i	$0.557972\pi$
$642$		0			0
$643$			15.2731i			0.602311i	0.953575	+	0.301156i	$0.0973723\pi$
$643$			15.2731i			0.602311i	−0.953575	+	0.301156i	$0.902628\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.66472	+	2.88338i	−0.0654469	+	0.113357i	−0.896892	−	0.442249i	$-0.854181\pi$
$647$	−1.66472	+	2.88338i	−0.0654469	+	0.113357i	0.831445	+	0.555607i	$0.187514\pi$
$648$		0			0
$649$	6.82565	−	3.94079i	0.267930	−	0.154689i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.0441	−	6.37633i	0.432190	−	0.249525i	−0.268089	−	0.963394i	$-0.586392\pi$
$653$	11.0441	−	6.37633i	0.432190	−	0.249525i	0.700279	+	0.713869i	$0.253059\pi$
$654$		0			0
$655$	17.6451	−	30.5622i	0.689452	−	1.19417i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			45.3768i			1.76763i	0.467837	+	0.883815i	$0.345033\pi$
$659$			45.3768i			1.76763i	−0.467837	+	0.883815i	$0.654967\pi$
$660$		0			0
$661$	−12.0610	−	6.96341i	−0.469118	−	0.270845i	0.246753	−	0.969079i	$-0.420637\pi$
$661$	−12.0610	−	6.96341i	−0.469118	−	0.270845i	−0.715870	+	0.698233i	$0.753970\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	51.3477	+	30.0268i	1.99118	+	1.16439i
$666$		0			0
$667$	−22.3741	−	38.7530i	−0.866327	−	1.50052i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.18503			−0.122957
$672$		0			0
$673$	−26.2388			−1.01143			−0.505716	−	0.862700i	$-0.668772\pi$
$673$	−26.2388			−1.01143			−0.505716	+	0.862700i	$0.668772\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.6453	−	37.4908i	−0.831897	−	1.44089i	−0.896532	−	0.442980i	$-0.853921\pi$
$677$	−21.6453	−	37.4908i	−0.831897	−	1.44089i	0.0646342	−	0.997909i	$-0.479412\pi$
$678$		0			0
$679$	−0.0592995	+	10.6853i	−0.00227571	+	0.410066i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.5578	−	13.6011i	−0.901416	−	0.520433i	−0.0237567	−	0.999718i	$-0.507563\pi$
$683$	−23.5578	−	13.6011i	−0.901416	−	0.520433i	−0.877659	+	0.479285i	$0.840896\pi$
$684$		0			0
$685$		−	3.31021i		−	0.126477i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−34.7698	+	60.2231i	−1.32462	+	2.29432i
$690$		0			0
$691$	−3.16588	+	1.82782i	−0.120436	+	0.0695336i	−0.559008	−	0.829162i	$-0.688818\pi$
$691$	−3.16588	+	1.82782i	−0.120436	+	0.0695336i	0.438572	+	0.898696i	$0.355484\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−52.0089	+	30.0274i	−1.97281	+	1.13900i
$696$		0			0
$697$	−2.72670	+	4.72279i	−0.103281	+	0.178888i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			31.5686i			1.19233i	0.802863	+	0.596164i	$0.203309\pi$
$701$			31.5686i			1.19233i	−0.802863	+	0.596164i	$0.796691\pi$
$702$		0			0
$703$	−49.0865	−	28.3401i	−1.85133	−	1.06887i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.06182	−	15.4963i	0.340805	−	0.582798i
$708$		0			0
$709$	16.1056	+	27.8956i	0.604857	+	1.04764i	0.992074	+	0.125655i	$0.0401031\pi$
$709$	16.1056	+	27.8956i	0.604857	+	1.04764i	−0.387217	+	0.921989i	$0.626564\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.9040			0.483258
$714$		0			0
$715$	19.4613			0.727810
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.07969	+	3.60213i	0.0775595	+	0.134337i	0.902196	−	0.431325i	$-0.141954\pi$
$719$	2.07969	+	3.60213i	0.0775595	+	0.134337i	−0.824637	+	0.565662i	$0.808621\pi$
$720$		0			0
$721$	14.3262	−	8.16556i	0.533535	−	0.304101i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−26.1039	−	15.0711i	−0.969473	−	0.559725i
$726$		0			0
$727$			42.3925i			1.57225i	0.618067	+	0.786125i	$0.287916\pi$
$727$			42.3925i			1.57225i	−0.618067	+	0.786125i	$0.712084\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.01923	+	1.76536i	−0.0376976	+	0.0652942i
$732$		0			0
$733$	−11.7565	+	6.78764i	−0.434237	+	0.250707i	−0.701150	−	0.713014i	$-0.747330\pi$
$733$	−11.7565	+	6.78764i	−0.434237	+	0.250707i	0.266913	+	0.963721i	$0.413996\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.50187	+	0.867105i	−0.0553221	+	0.0319402i
$738$		0			0
$739$	−6.46273	+	11.1938i	−0.237735	+	0.411770i	−0.960064	−	0.279780i	$-0.909738\pi$
$739$	−6.46273	+	11.1938i	−0.237735	+	0.411770i	0.722329	+	0.691550i	$0.243072\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	18.9462i		−	0.695068i	−0.937667	−	0.347534i	$-0.887019\pi$
$743$		−	18.9462i		−	0.695068i	0.937667	−	0.347534i	$-0.112981\pi$
$744$		0			0
$745$	−15.3595	−	8.86784i	−0.562730	−	0.324892i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	22.3469	−	12.7372i	0.816539	−	0.465407i
$750$		0			0
$751$	−11.4733	−	19.8723i	−0.418666	−	0.725150i	0.577140	−	0.816645i	$-0.304169\pi$
$751$	−11.4733	−	19.8723i	−0.418666	−	0.725150i	−0.995806	+	0.0914950i	$0.970835\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	21.3025			0.775279
$756$		0			0
$757$	−6.87010			−0.249698			−0.124849	−	0.992176i	$-0.539845\pi$
$757$	−6.87010			−0.249698			−0.124849	+	0.992176i	$0.539845\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.6164	+	32.2445i	0.674843	+	1.16886i	0.976515	+	0.215451i	$0.0691221\pi$
$761$	18.6164	+	32.2445i	0.674843	+	1.16886i	−0.301671	+	0.953412i	$0.597545\pi$
$762$		0			0
$763$	19.6186	−	33.5490i	0.710239	−	1.21455i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−28.9267	−	16.7008i	−1.04448	−	0.603032i
$768$		0			0
$769$		−	18.5757i		−	0.669856i	−0.942244	−	0.334928i	$-0.891288\pi$
$769$		−	18.5757i		−	0.669856i	0.942244	−	0.334928i	$-0.108712\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.99548	−	5.18832i	0.107740	−	0.186611i	−0.807114	−	0.590395i	$-0.798972\pi$
$773$	2.99548	−	5.18832i	0.107740	−	0.186611i	0.914854	+	0.403784i	$0.132305\pi$
$774$		0			0
$775$	7.52755	−	4.34603i	0.270398	−	0.156114i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−20.7388	+	11.9735i	−0.743043	+	0.428996i
$780$		0			0
$781$	5.43921	−	9.42099i	0.194630	−	0.337110i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			11.1698i			0.398669i
$786$		0			0
$787$	21.5679	+	12.4522i	0.768813	+	0.443875i	0.832451	−	0.554098i	$-0.186937\pi$
$787$	21.5679	+	12.4522i	0.768813	+	0.443875i	−0.0636377	+	0.997973i	$0.520270\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.280687	−	50.5778i	0.00998009	−	1.79834i
$792$		0			0
$793$	6.74899	+	11.6896i	0.239664	+	0.415110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.4955			−0.442612			−0.221306	−	0.975204i	$-0.571032\pi$
$797$	−12.4955			−0.442612			−0.221306	+	0.975204i	$0.571032\pi$
$798$		0			0
$799$	−12.1303			−0.429139
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.17939	−	5.50686i	−0.112198	−	0.194333i
$804$		0			0
$805$	−33.9885	−	19.8755i	−1.19794	−	0.700521i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	32.8616	+	18.9727i	1.15535	+	0.667043i	0.950186	−	0.311684i	$-0.100893\pi$
$809$	32.8616	+	18.9727i	1.15535	+	0.667043i	0.205167	+	0.978727i	$0.434226\pi$
$810$		0			0
$811$		−	38.7451i		−	1.36053i	−0.732968	−	0.680263i	$-0.761866\pi$
$811$		−	38.7451i		−	1.36053i	0.732968	−	0.680263i	$-0.238134\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.1721	−	40.1353i	0.811683	−	1.40588i
$816$		0			0
$817$	−7.75207	+	4.47566i	−0.271210	+	0.156583i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.53706	−	3.77417i	0.228145	−	0.131720i	−0.381571	−	0.924340i	$-0.624617\pi$
$821$	6.53706	−	3.77417i	0.228145	−	0.131720i	0.609716	+	0.792620i	$0.291283\pi$
$822$		0			0
$823$	−10.6203	+	18.3949i	−0.370200	+	0.641205i	−0.989596	−	0.143874i	$-0.954044\pi$
$823$	−10.6203	+	18.3949i	−0.370200	+	0.641205i	0.619396	+	0.785078i	$0.287377\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			17.9188i			0.623098i	0.950230	+	0.311549i	$0.100848\pi$
$827$			17.9188i			0.623098i	−0.950230	+	0.311549i	$0.899152\pi$
$828$		0			0
$829$	−26.9593	−	15.5649i	−0.936334	−	0.540592i	−0.0475245	−	0.998870i	$-0.515133\pi$
$829$	−26.9593	−	15.5649i	−0.936334	−	0.540592i	−0.888809	+	0.458278i	$0.848467\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.28309	−	10.6089i	0.217696	−	0.367578i
$834$		0			0
$835$	−35.0862	−	60.7712i	−1.21421	−	2.10307i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.3438			0.633297			0.316649	−	0.948543i	$-0.397442\pi$
$839$	18.3438			0.633297			0.316649	+	0.948543i	$0.397442\pi$
$840$		0			0
$841$	−47.3898			−1.63413
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−22.3446	−	38.7019i	−0.768676	−	1.33139i
$846$		0			0
$847$	−12.3417	−	21.6531i	−0.424065	−	0.744008i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	32.4917	+	18.7591i	1.11380	+	0.643054i
$852$		0			0
$853$			45.2905i			1.55072i	0.631521	+	0.775359i	$0.282431\pi$
$853$			45.2905i			1.55072i	−0.631521	+	0.775359i	$0.717569\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.2703	−	36.8413i	0.726581	−	1.25847i	−0.231739	−	0.972778i	$-0.574442\pi$
$857$	21.2703	−	36.8413i	0.726581	−	1.25847i	0.958320	−	0.285697i	$-0.0922250\pi$
$858$		0			0
$859$	−20.5225	+	11.8487i	−0.700218	+	0.404271i	−0.807429	−	0.589965i	$-0.799141\pi$
$859$	−20.5225	+	11.8487i	−0.700218	+	0.404271i	0.107210	+	0.994236i	$0.465808\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.4202	+	18.7178i	−1.10360	+	0.637162i	−0.937163	−	0.348891i	$-0.886558\pi$
$863$	−32.4202	+	18.7178i	−1.10360	+	0.637162i	−0.166433	+	0.986053i	$0.553225\pi$
$864$		0			0
$865$	−19.7258	+	34.1662i	−0.670699	+	1.16168i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	19.1843i		−	0.650783i
$870$		0			0
$871$	6.36484	+	3.67474i	0.215664	+	0.124514i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.9298	+	0.0662055i	0.403299	+	0.00223816i
$876$		0			0
$877$	−0.532842	−	0.922910i	−0.0179928	−	0.0311645i	0.856889	−	0.515501i	$-0.172394\pi$
$877$	−0.532842	−	0.922910i	−0.0179928	−	0.0311645i	−0.874882	+	0.484337i	$0.839061\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	44.4036			1.49600			0.747998	−	0.663701i	$-0.231015\pi$
$881$	44.4036			1.49600			0.747998	+	0.663701i	$0.231015\pi$
$882$		0			0
$883$	−26.3117			−0.885458			−0.442729	−	0.896656i	$-0.645990\pi$
$883$	−26.3117			−0.885458			−0.442729	+	0.896656i	$0.645990\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.4691	−	35.4536i	−0.687286	−	1.19041i	−0.972713	−	0.232013i	$-0.925469\pi$
$887$	−20.4691	−	35.4536i	−0.687286	−	1.19041i	0.285427	−	0.958400i	$-0.407865\pi$
$888$		0			0
$889$	−37.8087	−	0.209824i	−1.26806	−	0.00703726i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−46.1303	−	26.6334i	−1.54369	−	0.891251i
$894$		0			0
$895$		−	5.45892i		−	0.182472i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.0142	−	19.0772i	0.367345	−	0.636261i
$900$		0			0
$901$	19.9140	−	11.4974i	0.663433	−	0.383033i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.5170	−	7.80404i	0.449320	−	0.259415i
$906$		0			0
$907$	−24.8508	+	43.0428i	−0.825156	+	1.42921i	0.0766447	+	0.997058i	$0.475579\pi$
$907$	−24.8508	+	43.0428i	−0.825156	+	1.42921i	−0.901800	+	0.432153i	$0.857754\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	14.2074i		−	0.470713i	−0.971909	−	0.235356i	$-0.924374\pi$
$911$		−	14.2074i		−	0.470713i	0.971909	−	0.235356i	$-0.0756257\pi$
$912$		0			0
$913$	4.08605	+	2.35908i	0.135229	+	0.0780743i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.9066	−	27.9075i	−0.525282	−	0.921588i
$918$		0			0
$919$	21.5364	+	37.3022i	0.710421	+	1.23048i	0.964699	+	0.263354i	$0.0848286\pi$
$919$	21.5364	+	37.3022i	0.710421	+	1.23048i	−0.254279	+	0.967131i	$0.581838\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−46.1022			−1.51747
$924$		0			0
$925$	25.2721			0.830942
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.8978	−	25.8038i	−0.488782	−	0.846595i	0.511135	−	0.859501i	$-0.329225\pi$
$929$	−14.8978	−	25.8038i	−0.488782	−	0.846595i	−0.999917	+	0.0129053i	$0.995892\pi$
$930$		0			0
$931$	47.1870	−	26.5495i	1.54649	−	0.870126i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.57312	−	3.21764i	−0.182260	−	0.105228i
$936$		0			0
$937$		−	45.6131i		−	1.49012i	−0.667000	−	0.745058i	$-0.732422\pi$
$937$		−	45.6131i		−	1.49012i	0.667000	−	0.745058i	$-0.267578\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.94839	+	13.7670i	−0.259110	+	0.448792i	−0.966004	−	0.258528i	$-0.916763\pi$
$941$	−7.94839	+	13.7670i	−0.259110	+	0.448792i	0.706894	+	0.707320i	$0.250096\pi$
$942$		0			0
$943$	13.7276	−	7.92561i	0.447031	−	0.258093i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	42.1286	−	24.3229i	1.36900	−	0.790390i	0.378195	−	0.925726i	$-0.376545\pi$
$947$	42.1286	−	24.3229i	1.36900	−	0.790390i	0.990800	+	0.135336i	$0.0432115\pi$
$948$		0			0
$949$	−13.4741	+	23.3378i	−0.437387	+	0.757576i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	3.50929i		−	0.113677i	−0.998383	−	0.0568386i	$-0.981898\pi$
$953$		−	3.50929i		−	0.113677i	0.998383	−	0.0568386i	$-0.0181020\pi$
$954$		0			0
$955$	41.6098	+	24.0234i	1.34646	+	0.777380i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.60100	−	1.52099i	−0.0839906	−	0.0491155i
$960$		0			0
$961$	−12.3238	−	21.3455i	−0.397543	−	0.688565i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−36.2759			−1.16776
$966$		0			0
$967$	−25.6422			−0.824599			−0.412299	−	0.911048i	$-0.635274\pi$
$967$	−25.6422			−0.824599			−0.412299	+	0.911048i	$0.635274\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.9164	+	37.9603i	0.703331	+	1.21820i	0.967291	+	0.253671i	$0.0816380\pi$
$971$	21.9164	+	37.9603i	0.703331	+	1.21820i	−0.263960	+	0.964534i	$0.585029\pi$
$972$		0			0
$973$	−0.303359	+	54.6631i	−0.00972525	+	1.75242i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.5853	−	10.7303i	−0.594598	−	0.343291i	0.172315	−	0.985042i	$-0.444875\pi$
$977$	−18.5853	−	10.7303i	−0.594598	−	0.343291i	−0.766913	+	0.641750i	$0.778208\pi$
$978$		0			0
$979$			8.93226i			0.285476i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.50371	+	16.4609i	−0.303121	+	0.525022i	−0.976841	−	0.213965i	$-0.931362\pi$
$983$	−9.50371	+	16.4609i	−0.303121	+	0.525022i	0.673720	+	0.738987i	$0.264695\pi$
$984$		0			0
$985$	49.6548	−	28.6682i	1.58213	−	0.913445i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.13131	−	2.96256i	0.163166	−	0.0942040i
$990$		0			0
$991$	−6.99686	+	12.1189i	−0.222262	+	0.384970i	−0.955495	−	0.295008i	$-0.904678\pi$
$991$	−6.99686	+	12.1189i	−0.222262	+	0.384970i	0.733232	+	0.679978i	$0.238011\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	71.4131i		−	2.26395i
$996$		0			0
$997$	−0.764764	−	0.441537i	−0.0242203	−	0.0139836i	0.487841	−	0.872933i	$-0.337785\pi$
$997$	−0.764764	−	0.441537i	−0.0242203	−	0.0139836i	−0.512061	+	0.858949i	$0.671118\pi$
$998$		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.17.8		16
3.2	odd	2	inner	1008.2.bt.d.17.1		16
4.3	odd	2		504.2.bl.a.17.8	yes	16
7.3	odd	6		7056.2.k.h.881.16		16
7.4	even	3		7056.2.k.h.881.2		16
7.5	odd	6	inner	1008.2.bt.d.593.1		16
12.11	even	2		504.2.bl.a.17.1	✓	16
21.5	even	6	inner	1008.2.bt.d.593.8		16
21.11	odd	6		7056.2.k.h.881.15		16
21.17	even	6		7056.2.k.h.881.1		16
28.3	even	6		3528.2.k.b.881.15		16
28.11	odd	6		3528.2.k.b.881.1		16
28.19	even	6		504.2.bl.a.89.1	yes	16
28.23	odd	6		3528.2.bl.a.1097.8		16
28.27	even	2		3528.2.bl.a.521.1		16
84.11	even	6		3528.2.k.b.881.16		16
84.23	even	6		3528.2.bl.a.1097.1		16
84.47	odd	6		504.2.bl.a.89.8	yes	16
84.59	odd	6		3528.2.k.b.881.2		16
84.83	odd	2		3528.2.bl.a.521.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bl.a.17.1	✓	16	12.11	even	2
504.2.bl.a.17.8	yes	16	4.3	odd	2
504.2.bl.a.89.1	yes	16	28.19	even	6
504.2.bl.a.89.8	yes	16	84.47	odd	6
1008.2.bt.d.17.1		16	3.2	odd	2	inner
1008.2.bt.d.17.8		16	1.1	even	1	trivial
1008.2.bt.d.593.1		16	7.5	odd	6	inner
1008.2.bt.d.593.8		16	21.5	even	6	inner
3528.2.k.b.881.1		16	28.11	odd	6
3528.2.k.b.881.2		16	84.59	odd	6
3528.2.k.b.881.15		16	28.3	even	6
3528.2.k.b.881.16		16	84.11	even	6
3528.2.bl.a.521.1		16	28.27	even	2
3528.2.bl.a.521.8		16	84.83	odd	2
3528.2.bl.a.1097.1		16	84.23	even	6
3528.2.bl.a.1097.8		16	28.23	odd	6
7056.2.k.h.881.1		16	21.17	even	6
7056.2.k.h.881.2		16	7.4	even	3
7056.2.k.h.881.15		16	21.11	odd	6
7056.2.k.h.881.16		16	7.3	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(1.45333 + 2.51725i) q^{5} +(2.64571 + 0.0146827i) q^{7} +(-1.08853 - 0.628464i) q^{11} +5.32679i q^{13} +(0.880708 - 1.52543i) q^{17} +(6.69849 - 3.86738i) q^{19} +(-4.43392 + 2.55992i) q^{23} +(-1.72435 + 2.98667i) q^{25} +8.74013i q^{29} +(-2.18272 - 1.26019i) q^{31} +(3.80814 + 6.68124i) q^{35} +(-3.66400 - 6.34623i) q^{37} -3.09603 q^{41} -1.15729 q^{43} +(-3.44334 - 5.96403i) q^{47} +(6.99957 + 0.0776922i) q^{49} +(11.3057 + 6.52735i) q^{53} -3.65347i q^{55} +(-3.13525 + 5.43042i) q^{59} +(2.19449 - 1.26699i) q^{61} +(-13.4088 + 7.74160i) q^{65} +(0.689860 - 1.19487i) q^{67} +8.65477i q^{71} +(4.38121 + 2.52949i) q^{73} +(-2.87071 - 1.67872i) q^{77} +(7.63142 + 13.2180i) q^{79} -3.75373 q^{83} +5.11985 q^{85} +(-3.55321 - 6.15434i) q^{89} +(-0.0782115 + 14.0931i) q^{91} +(19.4703 + 11.2412i) q^{95} +4.03874i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} - 12 q^{19} + 12 q^{25} - 24 q^{31} + 4 q^{37} - 8 q^{43} + 32 q^{49} + 28 q^{67} - 60 q^{73} + 32 q^{79} - 32 q^{85} + 84 q^{91}+O(q^{100}) \) 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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