LMFDB - Embedded newform 297.2.g.b.98.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(98,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.98"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
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} + 15x^{14} + 150x^{12} + 837x^{10} + 3372x^{8} + 8010x^{6} + 13761x^{4} + 13392x^{2} + 8649 $ x^16 + 15x^14 + 150x^12 + 837x^10 + 3372x^8 + 8010x^6 + 13761x^4 + 13392*x^2 + 8649
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			98.1
Root			$-1.29716 - 2.24675i$ of defining polynomial
Character	$\chi$	$=$	297.98
Dual form			297.2.g.b.197.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29716 - 2.24675i) q^{2} +(-2.36526 + 4.09675i) q^{4} +(0.137404 + 0.0793301i) q^{5} +(2.91814 - 1.68479i) q^{7} +7.08384 q^{8} -0.411616i q^{10} +(1.95143 - 2.68177i) q^{11} +(0.897990 + 0.518455i) q^{13} +(-7.57060 - 4.37089i) q^{14} +(-4.45837 - 7.72212i) q^{16} -5.02413 q^{17} -5.11879i q^{19} +(-0.649990 + 0.375272i) q^{20} +(-8.55660 - 0.905691i) q^{22} +(4.02970 + 2.32655i) q^{23} +(-2.48741 - 4.30833i) q^{25} -2.69008i q^{26} +15.9398i q^{28} +(0.673383 + 1.16633i) q^{29} +(1.62482 - 2.81427i) q^{31} +(-4.48261 + 7.76411i) q^{32} +(6.51711 + 11.2880i) q^{34} +0.534618 q^{35} +3.04356 q^{37} +(-11.5007 + 6.63990i) q^{38} +(0.973346 + 0.561961i) q^{40} +(0.940692 - 1.62933i) q^{41} +(-8.24914 + 4.76264i) q^{43} +(6.37090 + 14.3376i) q^{44} -12.0716i q^{46} +(0.996127 - 0.575114i) q^{47} +(2.17703 - 3.77072i) q^{49} +(-6.45316 + 11.1772i) q^{50} +(-4.24795 + 2.45256i) q^{52} -9.36720i q^{53} +(0.480880 - 0.213678i) q^{55} +(20.6716 - 11.9348i) q^{56} +(1.74697 - 3.02585i) q^{58} +(4.69477 + 2.71052i) q^{59} +(9.61807 - 5.55299i) q^{61} -8.43060 q^{62} +5.42521 q^{64} +(0.0822581 + 0.142475i) q^{65} +(-2.67969 + 4.64135i) q^{67} +(11.8834 - 20.5826i) q^{68} +(-0.693486 - 1.20115i) q^{70} +0.558344i q^{71} +6.24053i q^{73} +(-3.94799 - 6.83812i) q^{74} +(20.9704 + 12.1073i) q^{76} +(1.17634 - 11.1135i) q^{77} +(3.72007 - 2.14778i) q^{79} -1.41473i q^{80} -4.88092 q^{82} +(4.61447 + 7.99250i) q^{83} +(-0.690334 - 0.398565i) q^{85} +(21.4009 + 12.3558i) q^{86} +(13.8236 - 18.9972i) q^{88} +1.98314i q^{89} +3.49395 q^{91} +(-19.0625 + 11.0058i) q^{92} +(-2.58428 - 1.49203i) q^{94} +(0.406074 - 0.703341i) q^{95} +(0.917466 + 1.58910i) q^{97} -11.2958 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{4} + 12 q^{11} + 6 q^{14} - 2 q^{16} - 36 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{25} - 4 q^{31} - 28 q^{37} - 66 q^{38} + 30 q^{47} + 10 q^{49} + 20 q^{55} + 120 q^{56} - 6 q^{58} + 36 q^{59}+ \cdots - 4 q^{97}+O(q^{100}) $ 16 * q - 14 * q^4 + 12 * q^11 + 6 * q^14 - 2 * q^16 - 36 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^25 - 4 * q^31 - 28 * q^37 - 66 * q^38 + 30 * q^47 + 10 * q^49 + 20 * q^55 + 120 * q^56 - 6 * q^58 + 36 * q^59 + 40 * q^64 + 8 * q^67 - 72 * q^77 + 12 * q^82 + 72 * q^86 - 6 * q^88 - 12 * q^91 - 18 * q^92 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.29716	−	2.24675i	−0.917232	−	1.58869i	−0.803600	−	0.595169i	$-0.797085\pi$
$2$	−1.29716	−	2.24675i	−0.917232	−	1.58869i	−0.113631	−	0.993523i	$-0.536248\pi$
$3$		0			0
$3$		0			0
$4$	−2.36526	+	4.09675i	−1.18263	+	2.04837i
$5$	0.137404	+	0.0793301i	0.0614488	+	0.0354775i	0.530410	−	0.847741i	$-0.322038\pi$
$5$	0.137404	+	0.0793301i	0.0614488	+	0.0354775i	−0.468961	+	0.883219i	$0.655371\pi$
$6$		0			0
$7$	2.91814	−	1.68479i	1.10295	−	0.636790i	0.165958	−	0.986133i	$-0.446928\pi$
$7$	2.91814	−	1.68479i	1.10295	−	0.636790i	0.936995	+	0.349343i	$0.113595\pi$
$8$	7.08384			2.50451
$9$		0			0
$10$		−	0.411616i		−	0.130164i
$11$	1.95143	−	2.68177i	0.588380	−	0.808585i
$11$	1.95143	−	2.68177i	0.588380	−	0.808585i
$12$		0			0
$13$	0.897990	+	0.518455i	0.249058	+	0.143794i	0.619333	−	0.785129i	$-0.287403\pi$
$13$	0.897990	+	0.518455i	0.249058	+	0.143794i	−0.370275	+	0.928922i	$0.620737\pi$
$14$	−7.57060	−	4.37089i	−2.02333	−	1.16817i
$15$		0			0
$16$	−4.45837	−	7.72212i	−1.11459	−	1.93053i
$17$	−5.02413			−1.21853			−0.609265	−	0.792966i	$-0.708536\pi$
$17$	−5.02413			−1.21853			−0.609265	+	0.792966i	$0.708536\pi$
$18$		0			0
$19$		−	5.11879i		−	1.17433i	−0.809467	−	0.587166i	$-0.800244\pi$
$19$		−	5.11879i		−	1.17433i	0.809467	−	0.587166i	$-0.199756\pi$
$20$	−0.649990	+	0.375272i	−0.145342	+	0.0839134i
$21$		0			0
$22$	−8.55660	−	0.905691i	−1.82427	−	0.193094i
$23$	4.02970	+	2.32655i	0.840250	+	0.485118i	0.857349	−	0.514735i	$-0.172110\pi$
$23$	4.02970	+	2.32655i	0.840250	+	0.485118i	−0.0170993	+	0.999854i	$0.505443\pi$
$24$		0			0
$25$	−2.48741	−	4.30833i	−0.497483	−	0.861665i
$26$		−	2.69008i		−	0.527568i
$27$		0			0
$28$			15.9398i			3.01235i
$29$	0.673383	+	1.16633i	0.125044	+	0.216583i	0.921750	−	0.387784i	$-0.126759\pi$
$29$	0.673383	+	1.16633i	0.125044	+	0.216583i	−0.796706	+	0.604367i	$0.793426\pi$
$30$		0			0
$31$	1.62482	−	2.81427i	0.291826	−	0.505457i	−0.682416	−	0.730964i	$-0.739071\pi$
$31$	1.62482	−	2.81427i	0.291826	−	0.505457i	0.974242	+	0.225507i	$0.0724039\pi$
$32$	−4.48261	+	7.76411i	−0.792421	+	1.37251i
$33$		0			0
$34$	6.51711	+	11.2880i	1.11768	+	1.93587i
$35$	0.534618			0.0903669
$36$		0			0
$37$	3.04356			0.500359			0.250179	−	0.968200i	$-0.419510\pi$
$37$	3.04356			0.500359			0.250179	+	0.968200i	$0.419510\pi$
$38$	−11.5007	+	6.63990i	−1.86565	+	1.07713i
$39$		0			0
$40$	0.973346	+	0.561961i	0.153899	+	0.0888539i
$41$	0.940692	−	1.62933i	0.146911	−	0.254458i	−0.783173	−	0.621804i	$-0.786400\pi$
$41$	0.940692	−	1.62933i	0.146911	−	0.254458i	0.930084	+	0.367346i	$0.119733\pi$
$42$		0			0
$43$	−8.24914	+	4.76264i	−1.25798	+	0.726296i	−0.972682	−	0.232143i	$-0.925426\pi$
$43$	−8.24914	+	4.76264i	−1.25798	+	0.726296i	−0.285300	+	0.958438i	$0.592093\pi$
$44$	6.37090	+	14.3376i	0.960449	+	2.16148i
$45$		0			0
$46$		−	12.0716i		−	1.77986i
$47$	0.996127	−	0.575114i	0.145300	−	0.0838890i	−0.425588	−	0.904917i	$-0.639933\pi$
$47$	0.996127	−	0.575114i	0.145300	−	0.0838890i	0.570888	+	0.821028i	$0.306599\pi$
$48$		0			0
$49$	2.17703	−	3.77072i	0.311004	−	0.538674i
$50$	−6.45316	+	11.1772i	−0.912614	+	1.58069i
$51$		0			0
$52$	−4.24795	+	2.45256i	−0.589085	+	0.340109i
$53$		−	9.36720i		−	1.28668i	−0.765579	−	0.643342i	$-0.777547\pi$
$53$		−	9.36720i		−	1.28668i	0.765579	−	0.643342i	$-0.222453\pi$
$54$		0			0
$55$	0.480880	−	0.213678i	0.0648418	−	0.0288124i
$56$	20.6716	−	11.9348i	2.76236	−	1.59485i
$57$		0			0
$58$	1.74697	−	3.02585i	0.229389	−	0.397313i
$59$	4.69477	+	2.71052i	0.611206	+	0.352880i	0.773437	−	0.633873i	$-0.218536\pi$
$59$	4.69477	+	2.71052i	0.611206	+	0.352880i	−0.162231	+	0.986753i	$0.551869\pi$
$60$		0			0
$61$	9.61807	−	5.55299i	1.23147	−	0.710988i	0.264132	−	0.964487i	$-0.414915\pi$
$61$	9.61807	−	5.55299i	1.23147	−	0.710988i	0.967336	+	0.253498i	$0.0815813\pi$
$62$	−8.43060			−1.07069
$63$		0			0
$64$	5.42521			0.678152
$65$	0.0822581	+	0.142475i	0.0102029	+	0.0176719i
$66$		0			0
$67$	−2.67969	+	4.64135i	−0.327376	+	0.567032i	−0.981990	−	0.188931i	$-0.939498\pi$
$67$	−2.67969	+	4.64135i	−0.327376	+	0.567032i	0.654614	+	0.755963i	$0.272831\pi$
$68$	11.8834	−	20.5826i	1.44107	−	2.49600i
$69$		0			0
$70$	−0.693486	−	1.20115i	−0.0828874	−	0.143565i
$71$			0.558344i			0.0662633i	0.999451	+	0.0331316i	$0.0105481\pi$
$71$			0.558344i			0.0662633i	−0.999451	+	0.0331316i	$0.989452\pi$
$72$		0			0
$73$			6.24053i			0.730398i	0.930929	+	0.365199i	$0.118999\pi$
$73$			6.24053i			0.730398i	−0.930929	+	0.365199i	$0.881001\pi$
$74$	−3.94799	−	6.83812i	−0.458945	−	0.794916i
$75$		0			0
$76$	20.9704	+	12.1073i	2.40547	+	1.38880i
$77$	1.17634	−	11.1135i	0.134056	−	1.26651i
$78$		0			0
$79$	3.72007	−	2.14778i	0.418540	−	0.241644i	−0.275912	−	0.961183i	$-0.588980\pi$
$79$	3.72007	−	2.14778i	0.418540	−	0.241644i	0.694453	+	0.719539i	$0.255647\pi$
$80$		−	1.41473i		−	0.158172i
$81$		0			0
$82$	−4.88092			−0.539007
$83$	4.61447	+	7.99250i	0.506504	+	0.877291i	0.999972	+	0.00752676i	$0.00239586\pi$
$83$	4.61447	+	7.99250i	0.506504	+	0.877291i	−0.493467	+	0.869764i	$0.664271\pi$
$84$		0			0
$85$	−0.690334	−	0.398565i	−0.0748773	−	0.0432304i
$86$	21.4009	+	12.3558i	2.30772	+	1.33236i
$87$		0			0
$88$	13.8236	−	18.9972i	1.47360	−	2.02511i
$89$			1.98314i			0.210212i	0.994461	+	0.105106i	$0.0335182\pi$
$89$			1.98314i			0.210212i	−0.994461	+	0.105106i	$0.966482\pi$
$90$		0			0
$91$	3.49395			0.366265
$92$	−19.0625	+	11.0058i	−1.98741	+	1.14743i
$93$		0			0
$94$	−2.58428	−	1.49203i	−0.266548	−	0.153891i
$95$	0.406074	−	0.703341i	0.0416623	−	0.0721613i
$96$		0			0
$97$	0.917466	+	1.58910i	0.0931545	+	0.161348i	0.908837	−	0.417152i	$-0.136972\pi$
$97$	0.917466	+	1.58910i	0.0931545	+	0.161348i	−0.815682	+	0.578500i	$0.803638\pi$
$98$	−11.2958			−1.14105
$99$		0			0
$100$	23.5335			2.35335
$101$	8.92252	+	15.4543i	0.887824	+	1.53776i	0.842443	+	0.538786i	$0.181117\pi$
$101$	8.92252	+	15.4543i	0.887824	+	1.53776i	0.0453812	+	0.998970i	$0.485550\pi$
$102$		0			0
$103$	−4.40350	+	7.62708i	−0.433890	+	0.751519i	−0.997204	−	0.0747237i	$-0.976193\pi$
$103$	−4.40350	+	7.62708i	−0.433890	+	0.751519i	0.563315	+	0.826242i	$0.309526\pi$
$104$	6.36122	+	3.67265i	0.623768	+	0.360133i
$105$		0			0
$106$	−21.0457	+	12.1508i	−2.04414	+	1.18019i
$107$	−14.3322			−1.38554			−0.692772	−	0.721156i	$-0.743611\pi$
$107$	−14.3322			−1.38554			−0.692772	+	0.721156i	$0.743611\pi$
$108$		0			0
$109$			7.45146i			0.713721i	0.934158	+	0.356860i	$0.116153\pi$
$109$			7.45146i			0.713721i	−0.934158	+	0.356860i	$0.883847\pi$
$110$	−1.10386	−	0.803241i	−0.105249	−	0.0765860i
$111$		0			0
$112$	−26.0203	−	15.0228i	−2.45868	−	1.41952i
$113$	0.0916620	+	0.0529211i	0.00862284	+	0.00497840i	0.504305	−	0.863525i	$-0.331749\pi$
$113$	0.0916620	+	0.0529211i	0.00862284	+	0.00497840i	−0.495682	+	0.868504i	$0.665082\pi$
$114$		0			0
$115$	0.369130	+	0.639352i	0.0344216	+	0.0596199i
$116$	−6.37090			−0.591523
$117$		0			0
$118$		−	14.0640i		−	1.29469i
$119$	−14.6611	+	8.46460i	−1.34398	+	0.775948i
$120$		0			0
$121$	−3.38381	−	10.4666i	−0.307619	−	0.951510i
$122$	−24.9524	−	14.4063i	−2.25908	−	1.30428i
$123$		0			0
$124$	7.68622	+	13.3129i	0.690243	+	1.19554i
$125$		−	1.58261i		−	0.141553i
$126$		0			0
$127$			13.7812i			1.22288i	0.791290	+	0.611441i	$0.209410\pi$
$127$			13.7812i			1.22288i	−0.791290	+	0.611441i	$0.790590\pi$
$128$	1.92784	+	3.33912i	0.170399	+	0.295139i
$129$		0			0
$130$	0.213404	−	0.369627i	0.0187168	−	0.0324184i
$131$	1.24756	−	2.16083i	0.109000	−	0.188793i	−0.806366	−	0.591417i	$-0.798569\pi$
$131$	1.24756	−	2.16083i	0.109000	−	0.188793i	0.915365	+	0.402625i	$0.131902\pi$
$132$		0			0
$133$	−8.62409	−	14.9374i	−0.747803	−	1.29523i
$134$	13.9039			1.20112
$135$		0			0
$136$	−35.5901			−3.05183
$137$	9.87123	−	5.69916i	0.843356	−	0.486912i	−0.0150476	−	0.999887i	$-0.504790\pi$
$137$	9.87123	−	5.69916i	0.843356	−	0.486912i	0.858404	+	0.512975i	$0.171457\pi$
$138$		0			0
$139$	10.4200	+	6.01599i	0.883812	+	0.510269i	0.871914	−	0.489660i	$-0.162879\pi$
$139$	10.4200	+	6.01599i	0.883812	+	0.510269i	0.0118989	+	0.999929i	$0.496212\pi$
$140$	−1.26451	+	2.19019i	−0.106870	+	0.185105i
$141$		0			0
$142$	1.25446	−	0.724263i	0.105272	−	0.0607788i
$143$	3.14275	−	1.39648i	0.262810	−	0.116779i
$144$		0			0
$145$			0.213678i			0.0177450i
$146$	14.0209	−	8.09497i	1.16038	−	0.669945i
$147$		0			0
$148$	−7.19881	+	12.4687i	−0.591738	+	1.02492i
$149$	−1.16530	+	2.01836i	−0.0954650	+	0.165350i	−0.909803	−	0.415041i	$-0.863767\pi$
$149$	−1.16530	+	2.01836i	−0.0954650	+	0.165350i	0.814338	+	0.580392i	$0.197100\pi$
$150$		0			0
$151$	−6.60387	+	3.81274i	−0.537415	+	0.310277i	−0.744031	−	0.668146i	$-0.767088\pi$
$151$	−6.60387	+	3.81274i	−0.537415	+	0.310277i	0.206616	+	0.978422i	$0.433755\pi$
$152$		−	36.2607i		−	2.94113i
$153$		0			0
$154$	−26.4952	+	11.7731i	−2.13505	+	0.948706i
$155$	0.446512	−	0.257794i	0.0358647	−	0.0207065i
$156$		0			0
$157$	−8.15839	+	14.1307i	−0.651110	+	1.12776i	0.331744	+	0.943370i	$0.392363\pi$
$157$	−8.15839	+	14.1307i	−0.651110	+	1.12776i	−0.982854	+	0.184386i	$0.940970\pi$
$158$	−9.65105	−	5.57204i	−0.767797	−	0.443288i
$159$		0			0
$160$	−1.23185	+	0.711212i	−0.0973867	+	0.0562262i
$161$	15.6790			1.23567
$162$		0			0
$163$	15.5456			1.21762			0.608812	−	0.793314i	$-0.291646\pi$
$163$	15.5456			1.21762			0.608812	+	0.793314i	$0.291646\pi$
$164$	4.44996	+	7.70755i	0.347483	+	0.601859i
$165$		0			0
$166$	11.9714	−	20.7351i	0.929164	−	1.60936i
$167$	−5.69751	+	9.86838i	−0.440887	+	0.763638i	−0.997756	−	0.0669621i	$-0.978669\pi$
$167$	−5.69751	+	9.86838i	−0.440887	+	0.763638i	0.556869	+	0.830601i	$0.312003\pi$
$168$		0			0
$169$	−5.96241	−	10.3272i	−0.458647	−	0.794400i
$170$			2.06801i			0.158609i
$171$		0			0
$172$		−	45.0595i		−	3.43575i
$173$	−1.55757	−	2.69779i	−0.118420	−	0.205109i	0.800722	−	0.599036i	$-0.204449\pi$
$173$	−1.55757	−	2.69779i	−0.118420	−	0.205109i	−0.919142	+	0.393927i	$0.871116\pi$
$174$		0			0
$175$	−14.5172	−	8.38153i	−1.09740	−	0.633584i
$176$	−29.4092	−	3.11288i	−2.21680	−	0.234642i
$177$		0			0
$178$	4.45561	−	2.57245i	0.333962	−	0.192813i
$179$			15.9590i			1.19283i	0.802676	+	0.596415i	$0.203409\pi$
$179$			15.9590i			1.19283i	−0.802676	+	0.596415i	$0.796591\pi$
$180$		0			0
$181$	−10.2550			−0.762245			−0.381122	−	0.924525i	$-0.624462\pi$
$181$	−10.2550			−0.762245			−0.381122	+	0.924525i	$0.624462\pi$
$182$	−4.53221	−	7.85003i	−0.335950	−	0.581883i
$183$		0			0
$184$	28.5457	+	16.4809i	2.10442	+	1.21499i
$185$	0.418197	+	0.241446i	0.0307464	+	0.0177515i
$186$		0			0
$187$	−9.80426	+	13.4736i	−0.716958	+	0.985285i
$188$			5.44117i			0.396838i
$189$		0			0
$190$	−2.10698			−0.152856
$191$	−7.29468	+	4.21159i	−0.527824	+	0.304740i	−0.740130	−	0.672464i	$-0.765236\pi$
$191$	−7.29468	+	4.21159i	−0.527824	+	0.304740i	0.212306	+	0.977203i	$0.431903\pi$
$192$		0			0
$193$	−7.93368	−	4.58051i	−0.571079	−	0.329713i	0.186501	−	0.982455i	$-0.440285\pi$
$193$	−7.93368	−	4.58051i	−0.571079	−	0.329713i	−0.757580	+	0.652742i	$0.773618\pi$
$194$	2.38020	−	4.12263i	0.170889	−	0.295988i
$195$		0			0
$196$	10.2985	+	17.8374i	0.735604	+	1.27410i
$197$	6.82011			0.485913			0.242956	−	0.970037i	$-0.421883\pi$
$197$	6.82011			0.485913			0.242956	+	0.970037i	$0.421883\pi$
$198$		0			0
$199$	−11.6395			−0.825102			−0.412551	−	0.910934i	$-0.635362\pi$
$199$	−11.6395			−0.825102			−0.412551	+	0.910934i	$0.635362\pi$
$200$	−17.6204	−	30.5195i	−1.24595	−	2.15805i
$201$		0			0
$202$	23.1479	−	40.0933i	1.62868	−	2.82096i
$203$	3.93005	+	2.26902i	0.275836	+	0.159254i
$204$		0			0
$205$	0.258509	−	0.149250i	0.0180551	−	0.0104241i
$206$	22.8482			1.59191
$207$		0			0
$208$		−	9.24585i		−	0.641084i
$209$	−13.7274	−	9.98899i	−0.949547	−	0.690953i
$210$		0			0
$211$	16.6264	+	9.59924i	1.14461	+	0.660839i	0.947567	−	0.319556i	$-0.103534\pi$
$211$	16.6264	+	9.59924i	1.14461	+	0.660839i	0.197040	+	0.980396i	$0.436867\pi$
$212$	38.3750	+	22.1558i	2.63561	+	1.52167i
$213$		0			0
$214$	18.5912	+	32.2008i	1.27087	+	2.20120i
$215$	−1.51128			−0.103069
$216$		0			0
$217$		−	10.9499i		−	0.743327i
$218$	16.7416	−	9.66575i	1.13388	−	0.654647i
$219$		0			0
$220$	−0.262019	+	2.47544i	−0.0176653	+	0.166894i
$221$	−4.51162	−	2.60478i	−0.303484	−	0.175217i
$222$		0			0
$223$	7.35920	+	12.7465i	0.492809	+	0.853570i	0.999966	−	0.00828390i	$-0.00263688\pi$
$223$	7.35920	+	12.7465i	0.492809	+	0.853570i	−0.507157	+	0.861854i	$0.669304\pi$
$224$			30.2090i			2.01842i
$225$		0			0
$226$		−	0.274589i		−	0.0182654i
$227$	1.47531	+	2.55531i	0.0979197	+	0.169602i	0.910823	−	0.412796i	$-0.135448\pi$
$227$	1.47531	+	2.55531i	0.0979197	+	0.169602i	−0.812904	+	0.582398i	$0.802114\pi$
$228$		0			0
$229$	−5.54107	+	9.59742i	−0.366164	+	0.634215i	−0.988962	−	0.148168i	$-0.952662\pi$
$229$	−5.54107	+	9.59742i	−0.366164	+	0.634215i	0.622798	+	0.782383i	$0.285996\pi$
$230$	0.957643	−	1.65869i	0.0631451	−	0.109371i
$231$		0			0
$232$	4.77014	+	8.26212i	0.313175	+	0.542435i
$233$	−7.80394			−0.511253			−0.255627	−	0.966776i	$-0.582282\pi$
$233$	−7.80394			−0.511253			−0.255627	+	0.966776i	$0.582282\pi$
$234$		0			0
$235$	0.182495			0.0119047
$236$	−22.2087	+	12.8222i	−1.44566	+	0.834652i
$237$		0			0
$238$	38.0357	+	21.9599i	2.46549	+	1.42345i
$239$	7.95608	−	13.7803i	0.514636	−	0.891375i	−0.485220	−	0.874392i	$-0.661260\pi$
$239$	7.95608	−	13.7803i	0.514636	−	0.891375i	0.999856	−	0.0169832i	$-0.00540617\pi$
$240$		0			0
$241$	12.0653	−	6.96588i	0.777192	−	0.448712i	−0.0582422	−	0.998302i	$-0.518550\pi$
$241$	12.0653	−	6.96588i	0.777192	−	0.448712i	0.835434	+	0.549590i	$0.185216\pi$
$242$	−19.1265	+	21.1795i	−1.22950	+	1.36147i
$243$		0			0
$244$			52.5370i			3.36334i
$245$	0.598263	−	0.345407i	0.0382216	−	0.0220673i
$246$		0			0
$247$	2.65386	−	4.59663i	0.168861	−	0.292476i
$248$	11.5099	−	19.9358i	0.730882	−	1.26592i
$249$		0			0
$250$	−3.55572	+	2.05290i	−0.224884	+	0.129837i
$251$			7.70054i			0.486054i	0.970020	+	0.243027i	$0.0781403\pi$
$251$			7.70054i			0.486054i	−0.970020	+	0.243027i	$0.921860\pi$
$252$		0			0
$253$	14.1030	−	6.26663i	0.886645	−	0.393980i
$254$	30.9629	−	17.8764i	1.94278	−	1.12167i
$255$		0			0
$256$	10.4267	−	18.0595i	0.651666	−	1.12872i
$257$	4.87372	+	2.81384i	0.304014	+	0.175523i	0.644245	−	0.764819i	$-0.277172\pi$
$257$	4.87372	+	2.81384i	0.304014	+	0.175523i	−0.340231	+	0.940342i	$0.610505\pi$
$258$		0			0
$259$	8.88154	−	5.12776i	0.551872	−	0.318623i
$260$	−0.778246			−0.0482648
$261$		0			0
$262$	−6.47313			−0.399912
$263$	−13.0451	−	22.5947i	−0.804394	−	1.39325i	−0.916700	−	0.399577i	$-0.869157\pi$
$263$	−13.0451	−	22.5947i	−0.804394	−	1.39325i	0.112306	−	0.993674i	$-0.464176\pi$
$264$		0			0
$265$	0.743100	−	1.28709i	0.0456483	−	0.0790652i
$266$	−22.3737	+	38.7523i	−1.37182	+	2.37606i
$267$		0			0
$268$	−12.6763	−	21.9560i	−0.774328	−	1.34118i
$269$		−	18.1739i		−	1.10808i	−0.832489	−	0.554042i	$-0.813085\pi$
$269$		−	18.1739i		−	1.10808i	0.832489	−	0.554042i	$-0.186915\pi$
$270$		0			0
$271$		−	17.8451i		−	1.08402i	−0.840374	−	0.542008i	$-0.817664\pi$
$271$		−	17.8451i		−	1.08402i	0.840374	−	0.542008i	$-0.182336\pi$
$272$	22.3994	+	38.7969i	1.35816	+	2.35241i
$273$		0			0
$274$	−25.6092	−	14.7855i	−1.54711	−	0.893222i
$275$	−16.4080	−	1.73674i	−0.989438	−	0.104729i
$276$		0			0
$277$	15.9596	−	9.21430i	0.958921	−	0.553633i	0.0630804	−	0.998008i	$-0.479908\pi$
$277$	15.9596	−	9.21430i	0.958921	−	0.553633i	0.895841	+	0.444375i	$0.146574\pi$
$278$		−	31.2148i		−	1.87214i
$279$		0			0
$280$	3.78714			0.226325
$281$	−6.61767	−	11.4621i	−0.394777	−	0.683774i	0.598296	−	0.801276i	$-0.295845\pi$
$281$	−6.61767	−	11.4621i	−0.394777	−	0.683774i	−0.993073	+	0.117501i	$0.962512\pi$
$282$		0			0
$283$	−14.7366	−	8.50820i	−0.876002	−	0.505760i	−0.00666371	−	0.999978i	$-0.502121\pi$
$283$	−14.7366	−	8.50820i	−0.876002	−	0.505760i	−0.869338	+	0.494218i	$0.835454\pi$
$284$	−2.28739	−	1.32063i	−0.135732	−	0.0783648i
$285$		0			0
$286$	−7.21418	−	5.24951i	−0.426583	−	0.310410i
$287$		−	6.33947i		−	0.374207i
$288$		0			0
$289$	8.24189			0.484817
$290$	0.480081	−	0.277175i	0.0281914	−	0.0162763i
$291$		0			0
$292$	−25.5658	−	14.7604i	−1.49613	−	0.863790i
$293$	−13.2439	+	22.9392i	−0.773719	+	1.34012i	0.161793	+	0.986825i	$0.448272\pi$
$293$	−13.2439	+	22.9392i	−0.773719	+	1.34012i	−0.935512	+	0.353295i	$0.885061\pi$
$294$		0			0
$295$	0.430052	+	0.744872i	0.0250386	+	0.0433681i
$296$	21.5601			1.25316
$297$		0			0
$298$	6.04632			0.350254
$299$	2.41242	+	4.17843i	0.139514	+	0.241645i
$300$		0			0
$301$	−16.0481	+	27.7961i	−0.924996	+	1.60214i
$302$	17.1326	+	9.89149i	0.985868	+	0.569191i
$303$		0			0
$304$	−39.5279	+	22.8215i	−2.26708	+	1.30890i
$305$	1.76208			0.100896
$306$		0			0
$307$		−	0.641034i		−	0.0365858i	−0.999833	−	0.0182929i	$-0.994177\pi$
$307$		−	0.641034i		−	0.0365858i	0.999833	−	0.0182929i	$-0.00582313\pi$
$308$	42.7470	+	31.1055i	2.43574	+	1.77240i
$309$		0			0
$310$	−1.15840	−	0.668800i	−0.0657925	−	0.0379853i
$311$	−10.5744	−	6.10513i	−0.599619	−	0.346190i	0.169273	−	0.985569i	$-0.445858\pi$
$311$	−10.5744	−	6.10513i	−0.599619	−	0.346190i	−0.768892	+	0.639379i	$0.779191\pi$
$312$		0			0
$313$	−13.3275	−	23.0839i	−0.753315	−	1.30478i	−0.946208	−	0.323560i	$-0.895120\pi$
$313$	−13.3275	−	23.0839i	−0.753315	−	1.30478i	0.192893	−	0.981220i	$-0.438213\pi$
$314$	42.3310			2.38888
$315$		0			0
$316$			20.3202i			1.14310i
$317$	15.1631	−	8.75445i	0.851647	−	0.491699i	−0.00955915	−	0.999954i	$-0.503043\pi$
$317$	15.1631	−	8.75445i	0.851647	−	0.491699i	0.861206	+	0.508256i	$0.169709\pi$
$318$		0			0
$319$	4.44191	+	0.470163i	0.248699	+	0.0263241i
$320$	0.745444	+	0.430382i	0.0416716	+	0.0240591i
$321$		0			0
$322$	−20.3381	−	35.2267i	−1.13340	−	1.96311i
$323$			25.7175i			1.43096i
$324$		0			0
$325$		−	5.15845i		−	0.286139i
$326$	−20.1651	−	34.9271i	−1.11684	−	1.93443i
$327$		0			0
$328$	6.66371	−	11.5419i	0.367942	−	0.637294i
$329$	1.93789	−	3.35653i	0.106839	−	0.185051i
$330$		0			0
$331$	12.5699	+	21.7716i	0.690902	+	1.19668i	0.971543	+	0.236865i	$0.0761199\pi$
$331$	12.5699	+	21.7716i	0.690902	+	1.19668i	−0.280640	+	0.959813i	$0.590547\pi$
$332$	−43.6577			−2.39603
$333$		0			0
$334$	29.5624			1.61758
$335$	−0.736398	+	0.425159i	−0.0402337	+	0.0232289i
$336$		0			0
$337$	9.87559	+	5.70168i	0.537958	+	0.310590i	0.744251	−	0.667900i	$-0.232807\pi$
$337$	9.87559	+	5.70168i	0.537958	+	0.310590i	−0.206293	+	0.978490i	$0.566140\pi$
$338$	−15.4684	+	26.7921i	−0.841371	+	1.45730i
$339$		0			0
$340$	3.26564	−	1.88542i	0.177104	−	0.102251i
$341$	−4.37650	−	9.84924i	−0.237001	−	0.533367i
$342$		0			0
$343$			8.91573i			0.481404i
$344$	−58.4355	+	33.7378i	−3.15063	+	1.81902i
$345$		0			0
$346$	−4.04083	+	6.99893i	−0.217237	+	0.376265i
$347$	4.94187	−	8.55957i	0.265294	−	0.459502i	−0.702347	−	0.711835i	$-0.747864\pi$
$347$	4.94187	−	8.55957i	0.265294	−	0.459502i	0.967641	+	0.252333i	$0.0811978\pi$
$348$		0			0
$349$	−31.3513	+	18.1007i	−1.67820	+	0.968906i	−0.715384	+	0.698732i	$0.753748\pi$
$349$	−31.3513	+	18.1007i	−1.67820	+	0.968906i	−0.962811	+	0.270175i	$0.912919\pi$
$350$			43.4888i			2.32457i
$351$		0			0
$352$	12.0741	+	27.1725i	0.643549	+	1.44830i
$353$	−13.3548	+	7.71038i	−0.710803	+	0.410382i	−0.811358	−	0.584549i	$-0.801271\pi$
$353$	−13.3548	+	7.71038i	−0.710803	+	0.410382i	0.100556	+	0.994931i	$0.467938\pi$
$354$		0			0
$355$	−0.0442935	+	0.0767186i	−0.00235085	+	0.00407180i
$356$	−8.12440	−	4.69063i	−0.430592	−	0.248603i
$357$		0			0
$358$	35.8558	−	20.7014i	1.89504	−	1.09410i
$359$	−22.5845			−1.19196			−0.595981	−	0.802998i	$-0.703237\pi$
$359$	−22.5845			−1.19196			−0.595981	+	0.802998i	$0.703237\pi$
$360$		0			0
$361$	−7.20205			−0.379055
$362$	13.3023	+	23.0403i	0.699155	+	1.21097i
$363$		0			0
$364$	−8.26408	+	14.3138i	−0.433156	+	0.750248i
$365$	−0.495061	+	0.857472i	−0.0259127	+	0.0448821i
$366$		0			0
$367$	10.4584	+	18.1144i	0.545922	+	0.945565i	0.998548	+	0.0538647i	$0.0171540\pi$
$367$	10.4584	+	18.1144i	0.545922	+	0.945565i	−0.452626	+	0.891700i	$0.649513\pi$
$368$		−	41.4904i		−	2.16284i
$369$		0			0
$370$		−	1.25278i		−	0.0651288i
$371$	−15.7817	−	27.3348i	−0.819348	−	1.41915i
$372$		0			0
$373$	−21.2836	−	12.2881i	−1.10202	−	0.636252i	−0.165270	−	0.986248i	$-0.552849\pi$
$373$	−21.2836	−	12.2881i	−1.10202	−	0.636252i	−0.936751	+	0.349997i	$0.886183\pi$
$374$	42.9895	+	4.55031i	2.22293	+	0.235291i
$375$		0			0
$376$	7.05640	−	4.07401i	0.363906	−	0.210101i
$377$			1.39648i			0.0719221i
$378$		0			0
$379$	26.7013			1.37155			0.685777	−	0.727811i	$-0.259462\pi$
$379$	26.7013			1.37155			0.685777	+	0.727811i	$0.259462\pi$
$380$	1.92094	+	3.32717i	0.0985422	+	0.170680i
$381$		0			0
$382$	18.9248	+	10.9262i	0.968275	+	0.559034i
$383$	−24.3065	−	14.0334i	−1.24201	−	0.717072i	−0.272504	−	0.962155i	$-0.587852\pi$
$383$	−24.3065	−	14.0334i	−1.24201	−	0.717072i	−0.969502	+	0.245082i	$0.921185\pi$
$384$		0			0
$385$	1.04327	−	1.43372i	0.0531700	−	0.0730693i
$386$			23.7667i			1.20969i
$387$		0			0
$388$	−8.68017			−0.440669
$389$	22.3706	−	12.9157i	1.13423	−	0.654850i	0.189237	−	0.981931i	$-0.439398\pi$
$389$	22.3706	−	12.9157i	1.13423	−	0.654850i	0.944996	+	0.327081i	$0.106065\pi$
$390$		0			0
$391$	−20.2457	−	11.6889i	−1.02387	−	0.591132i
$392$	15.4217	−	26.7112i	0.778913	−	1.34912i
$393$		0			0
$394$	−8.84679	−	15.3231i	−0.445695	−	0.771966i
$395$	0.681535			0.0342917
$396$		0			0
$397$	6.26174			0.314268			0.157134	−	0.987577i	$-0.449775\pi$
$397$	6.26174			0.314268			0.157134	+	0.987577i	$0.449775\pi$
$398$	15.0983	+	26.1511i	0.756810	+	1.31083i
$399$		0			0
$400$	−22.1796	+	38.4162i	−1.10898	+	1.92081i
$401$	−21.0664	−	12.1627i	−1.05201	−	0.607376i	−0.128796	−	0.991671i	$-0.541111\pi$
$401$	−21.0664	−	12.1627i	−1.05201	−	0.607376i	−0.923210	+	0.384295i	$0.874445\pi$
$402$		0			0
$403$	2.91814	−	1.68479i	0.145363	−	0.0839253i
$404$	−84.4162			−4.19986
$405$		0			0
$406$		−	11.7731i		−	0.584290i
$407$	5.93931	−	8.16214i	0.294401	−	0.404582i
$408$		0			0
$409$	31.1436	+	17.9808i	1.53995	+	0.889092i	0.998841	+	0.0481417i	$0.0153299\pi$
$409$	31.1436	+	17.9808i	1.53995	+	0.889092i	0.541112	+	0.840950i	$0.318003\pi$
$410$	−0.670656	−	0.387204i	−0.0331214	−	0.0191226i
$411$		0			0
$412$	−20.8308	−	36.0800i	−1.02626	−	1.77753i
$413$	18.2666			0.898843
$414$		0			0
$415$			1.46427i			0.0718780i
$416$	−8.05068	+	4.64806i	−0.394717	+	0.227890i
$417$		0			0
$418$	−4.63605	+	43.7995i	−0.226757	+	2.14230i
$419$	32.8419	+	18.9613i	1.60443	+	0.926318i	0.990586	+	0.136891i	$0.0437109\pi$
$419$	32.8419	+	18.9613i	1.60443	+	0.926318i	0.613844	+	0.789427i	$0.289622\pi$
$420$		0			0
$421$	−3.52098	−	6.09852i	−0.171602	−	0.297224i	0.767378	−	0.641195i	$-0.221561\pi$
$421$	−3.52098	−	6.09852i	−0.171602	−	0.297224i	−0.938980	+	0.343971i	$0.888228\pi$
$422$		−	49.8071i		−	2.42457i
$423$		0			0
$424$		−	66.3557i		−	3.22252i
$425$	12.4971	+	21.6456i	0.606198	+	1.04997i
$426$		0			0
$427$	18.7112	−	32.4088i	0.905501	−	1.56837i
$428$	33.8993	−	58.7153i	1.63858	−	2.83811i
$429$		0			0
$430$	1.96038	+	3.39547i	0.0945378	+	0.163744i
$431$	38.2910			1.84441			0.922207	−	0.386696i	$-0.126384\pi$
$431$	38.2910			1.84441			0.922207	+	0.386696i	$0.126384\pi$
$432$		0			0
$433$	−22.1866			−1.06622			−0.533109	−	0.846047i	$-0.678976\pi$
$433$	−22.1866			−1.06622			−0.533109	+	0.846047i	$0.678976\pi$
$434$	−24.6017	+	14.2038i	−1.18092	+	0.681803i
$435$		0			0
$436$	−30.5267	−	17.6246i	−1.46197	−	0.844066i
$437$	11.9091	−	20.6272i	0.569690	−	0.986732i
$438$		0			0
$439$	19.1579	−	11.0608i	0.914357	−	0.527904i	0.0325264	−	0.999471i	$-0.489645\pi$
$439$	19.1579	−	11.0608i	0.914357	−	0.527904i	0.881830	+	0.471567i	$0.156311\pi$
$440$	3.40647	−	1.51366i	0.162397	−	0.0721610i
$441$		0			0
$442$			13.5153i			0.642858i
$443$	−16.1301	+	9.31270i	−0.766363	+	0.442460i	−0.831576	−	0.555412i	$-0.812561\pi$
$443$	−16.1301	+	9.31270i	−0.766363	+	0.442460i	0.0652128	+	0.997871i	$0.479227\pi$
$444$		0			0
$445$	−0.157322	+	0.272490i	−0.00745779	+	0.0129173i
$446$	19.0922	−	33.0686i	0.904040	−	1.56584i
$447$		0			0
$448$	15.8315	−	9.14034i	0.747969	−	0.431840i
$449$		−	17.9495i		−	0.847088i	−0.905876	−	0.423544i	$-0.860786\pi$
$449$		−	17.9495i		−	0.847088i	0.905876	−	0.423544i	$-0.139214\pi$
$450$		0			0
$451$	−2.53378	−	5.70225i	−0.119311	−	0.268508i
$452$	−0.433609	+	0.250344i	−0.0203952	+	0.0117752i
$453$		0			0
$454$	3.82743	−	6.62930i	0.179630	−	0.311129i
$455$	0.480081	+	0.277175i	0.0225066	+	0.0129942i
$456$		0			0
$457$	5.18506	−	2.99360i	0.242547	−	0.140035i	−0.373800	−	0.927509i	$-0.621945\pi$
$457$	5.18506	−	2.99360i	0.242547	−	0.140035i	0.616347	+	0.787475i	$0.288612\pi$
$458$	28.7507			1.34343
$459$		0			0
$460$	−3.49235			−0.162832
$461$	−4.80832	−	8.32826i	−0.223946	−	0.387886i	0.732057	−	0.681244i	$-0.238561\pi$
$461$	−4.80832	−	8.32826i	−0.223946	−	0.387886i	−0.956003	+	0.293358i	$0.905227\pi$
$462$		0			0
$463$	−4.99782	+	8.65648i	−0.232268	+	0.402301i	−0.958475	−	0.285176i	$-0.907948\pi$
$463$	−4.99782	+	8.65648i	−0.232268	+	0.402301i	0.726207	+	0.687476i	$0.241281\pi$
$464$	6.00438	−	10.3999i	0.278746	−	0.482803i
$465$		0			0
$466$	10.1230	+	17.5335i	0.468938	+	0.812224i
$467$			18.1972i			0.842066i	0.907045	+	0.421033i	$0.138332\pi$
$467$			18.1972i			0.842066i	−0.907045	+	0.421033i	$0.861668\pi$
$468$		0			0
$469$			18.0588i			0.833879i
$470$	−0.236726	−	0.410021i	−0.0109194	−	0.0189129i
$471$		0			0
$472$	33.2569	+	19.2009i	1.53078	+	0.883793i
$473$	−3.32532	+	31.4163i	−0.152899	+	1.44452i
$474$		0			0
$475$	−22.0534	+	12.7326i	−1.01188	+	0.584210i
$476$		−	80.0838i		−	3.67064i
$477$		0			0
$478$	−41.2813			−1.88816
$479$	9.41443	+	16.3063i	0.430156	+	0.745053i	0.996886	−	0.0788507i	$-0.0251250\pi$
$479$	9.41443	+	16.3063i	0.430156	+	0.745053i	−0.566730	+	0.823904i	$0.691792\pi$
$480$		0			0
$481$	2.73309	+	1.57795i	0.124618	+	0.0719483i
$482$	−31.3012	−	18.0718i	−1.42573	−	0.823146i
$483$		0			0
$484$	50.8826	+	10.8936i	2.31285	+	0.495164i
$485$			0.291130i			0.0132196i
$486$		0			0
$487$	−40.2338			−1.82317			−0.911585	−	0.411112i	$-0.865140\pi$
$487$	−40.2338			−1.82317			−0.911585	+	0.411112i	$0.865140\pi$
$488$	68.1328	−	39.3365i	3.08423	−	1.78068i
$489$		0			0
$490$	−1.55209	−	0.896098i	−0.0701162	−	0.0404816i
$491$	−4.10919	+	7.11732i	−0.185445	+	0.321200i	−0.943726	−	0.330727i	$-0.892706\pi$
$491$	−4.10919	+	7.11732i	−0.185445	+	0.321200i	0.758281	+	0.651927i	$0.226039\pi$
$492$		0			0
$493$	−3.38316	−	5.85981i	−0.152370	−	0.263913i
$494$	−13.7700			−0.619540
$495$		0			0
$496$	−28.9761			−1.30107
$497$	0.940692	+	1.62933i	0.0421958	+	0.0730853i
$498$		0			0
$499$	15.2562	−	26.4246i	0.682963	−	1.18293i	−0.291109	−	0.956690i	$-0.594024\pi$
$499$	15.2562	−	26.4246i	0.682963	−	1.18293i	0.974072	−	0.226237i	$-0.0726423\pi$
$500$	6.48354	+	3.74327i	0.289953	+	0.167404i
$501$		0			0
$502$	17.3012	−	9.98884i	0.772190	−	0.445824i
$503$	16.3781			0.730263			0.365131	−	0.930956i	$-0.381024\pi$
$503$	16.3781			0.730263			0.365131	+	0.930956i	$0.381024\pi$
$504$		0			0
$505$			2.83130i			0.125991i
$506$	−32.3734	−	23.5570i	−1.43917	−	1.04724i
$507$		0			0
$508$	−56.4580	−	32.5961i	−2.50492	−	1.44622i
$509$	14.4224	+	8.32681i	0.639264	+	0.369079i	0.784331	−	0.620343i	$-0.213006\pi$
$509$	14.4224	+	8.32681i	0.639264	+	0.369079i	−0.145067	+	0.989422i	$0.546340\pi$
$510$		0			0
$511$	10.5140	+	18.2107i	0.465111	+	0.805595i
$512$	−46.3889			−2.05012
$513$		0			0
$514$		−	14.6000i		−	0.643980i
$515$	−1.21011	+	0.698660i	−0.0533240	+	0.0307866i
$516$		0			0
$517$	0.401550	−	3.79368i	0.0176602	−	0.166846i
$518$	−23.0416	−	13.3031i	−1.01239	−	0.584503i
$519$		0			0
$520$	0.582703	+	1.00927i	0.0255532	+	0.0442595i
$521$			41.8433i			1.83319i	0.399818	+	0.916595i	$0.369073\pi$
$521$			41.8433i			1.83319i	−0.399818	+	0.916595i	$0.630927\pi$
$522$		0			0
$523$			39.5791i			1.73067i	0.501192	+	0.865336i	$0.332895\pi$
$523$			39.5791i			1.73067i	−0.501192	+	0.865336i	$0.667105\pi$
$524$	5.90159	+	10.2218i	0.257812	+	0.446543i
$525$		0			0
$526$	−33.8431	+	58.6180i	−1.47563	+	2.55587i
$527$	−8.16329	+	14.1392i	−0.355599	+	0.615915i
$528$		0			0
$529$	−0.674365	−	1.16803i	−0.0293202	−	0.0507841i
$530$	−3.85569			−0.167480
$531$		0			0
$532$	81.5927			3.53749
$533$	1.68946	−	0.975413i	0.0731788	−	0.0422498i
$534$		0			0
$535$	−1.96930	−	1.13697i	−0.0851401	−	0.0491557i
$536$	−18.9825	+	32.8786i	−0.819917	+	1.42014i
$537$		0			0
$538$	−40.8323	+	23.5745i	−1.76040	+	1.01637i
$539$	−5.86389	−	13.1966i	−0.252576	−	0.568418i
$540$		0			0
$541$		−	29.7471i		−	1.27893i	−0.768821	−	0.639464i	$-0.779156\pi$
$541$		−	29.7471i		−	1.27893i	0.768821	−	0.639464i	$-0.220844\pi$
$542$	−40.0936	+	23.1480i	−1.72217	+	0.994293i
$543$		0			0
$544$	22.5212	−	39.0079i	0.965589	−	1.67245i
$545$	−0.591125	+	1.02386i	−0.0253210	+	0.0438573i
$546$		0			0
$547$	0.0889871	−	0.0513767i	0.00380481	−	0.00219671i	−0.498096	−	0.867122i	$-0.665967\pi$
$547$	0.0889871	−	0.0513767i	0.00380481	−	0.00219671i	0.501901	+	0.864925i	$0.332634\pi$
$548$			53.9199i			2.30334i
$549$		0			0
$550$	17.3818	+	39.1174i	0.741162	+	1.66797i
$551$	5.97022	−	3.44691i	0.254340	−	0.146843i
$552$		0			0
$553$	7.23711	−	12.5351i	0.307753	−	0.533045i
$554$	−41.4044	−	23.9049i	−1.75911	−	1.01562i
$555$		0			0
$556$	−49.2919	+	28.4587i	−2.09044	+	1.20692i
$557$	21.3570			0.904926			0.452463	−	0.891783i	$-0.350546\pi$
$557$	21.3570			0.904926			0.452463	+	0.891783i	$0.350546\pi$
$558$		0			0
$559$	−9.87686			−0.417746
$560$	−2.38352	−	4.12838i	−0.100722	−	0.174456i
$561$		0			0
$562$	−17.1684	+	29.7365i	−0.724204	+	1.25436i
$563$	−18.9075	+	32.7488i	−0.796858	+	1.38020i	0.124795	+	0.992183i	$0.460173\pi$
$563$	−18.9075	+	32.7488i	−0.796858	+	1.38020i	−0.921653	+	0.388016i	$0.873161\pi$
$564$		0			0
$565$	0.00839647	+	0.0145431i	0.000353242	+	0.000611833i
$566$			44.1460i			1.85560i
$567$		0			0
$568$			3.95522i			0.165957i
$569$	8.58131	+	14.8633i	0.359747	+	0.623101i	0.987918	−	0.154975i	$-0.0495295\pi$
$569$	8.58131	+	14.8633i	0.359747	+	0.623101i	−0.628171	+	0.778075i	$0.716196\pi$
$570$		0			0
$571$	32.6430	+	18.8464i	1.36607	+	0.788698i	0.990423	−	0.138067i	$-0.0440889\pi$
$571$	32.6430	+	18.8464i	1.36607	+	0.788698i	0.375642	+	0.926765i	$0.377422\pi$
$572$	−1.71240	+	16.1781i	−0.0715991	+	0.676438i
$573$		0			0
$574$	−14.2432	+	8.22332i	−0.594500	+	0.343235i
$575$		−	23.1483i		−	0.965352i
$576$		0			0
$577$	18.2232			0.758642			0.379321	−	0.925265i	$-0.376158\pi$
$577$	18.2232			0.758642			0.379321	+	0.925265i	$0.376158\pi$
$578$	−10.6911	−	18.5175i	−0.444690	−	0.770225i
$579$		0			0
$580$	−0.875385	−	0.505404i	−0.0363484	−	0.0209857i
$581$	26.9314	+	15.5488i	1.11730	+	0.645074i
$582$		0			0
$583$	−25.1207	−	18.2795i	−1.04039	−	0.757058i
$584$			44.2069i			1.82929i
$585$		0			0
$586$	68.7181			2.83872
$587$	0.250861	−	0.144835i	0.0103541	−	0.00597797i	−0.494814	−	0.868999i	$-0.664764\pi$
$587$	0.250861	−	0.144835i	0.0103541	−	0.00597797i	0.505168	+	0.863021i	$0.331430\pi$
$588$		0			0
$589$	−14.4056	−	8.31710i	−0.593574	−	0.342700i
$590$	1.11569	−	1.93244i	0.0459324	−	0.0795573i
$591$		0			0
$592$	−13.5693	−	23.5027i	−0.557696	−	0.965957i
$593$	−10.5590			−0.433606			−0.216803	−	0.976215i	$-0.569563\pi$
$593$	−10.5590			−0.433606			−0.216803	+	0.976215i	$0.569563\pi$
$594$		0			0
$595$	−2.68599			−0.110115
$596$	−5.51246	−	9.54787i	−0.225799	−	0.391096i
$597$		0			0
$598$	6.25859	−	10.8402i	0.255933	−	0.443289i
$599$	−11.0356	−	6.37143i	−0.450904	−	0.260330i	0.257308	−	0.966330i	$-0.417165\pi$
$599$	−11.0356	−	6.37143i	−0.450904	−	0.260330i	−0.708212	+	0.706000i	$0.750498\pi$
$600$		0			0
$601$	15.4925	−	8.94459i	0.631952	−	0.364857i	−0.149556	−	0.988753i	$-0.547784\pi$
$601$	15.4925	−	8.94459i	0.631952	−	0.364857i	0.781507	+	0.623896i	$0.214451\pi$
$602$	83.2678			3.39374
$603$		0			0
$604$		−	36.0725i		−	1.46777i
$605$	0.365368	−	1.70659i	0.0148543	−	0.0693827i
$606$		0			0
$607$	21.3132	+	12.3052i	0.865077	+	0.499453i	0.865709	−	0.500547i	$-0.166868\pi$
$607$	21.3132	+	12.3052i	0.865077	+	0.499453i	−0.000631871		1.00000i	$0.500201\pi$
$608$	39.7429	+	22.9456i	1.61179	+	0.930565i
$609$		0			0
$610$	−2.28570	−	3.95895i	−0.0925453	−	0.160293i
$611$	1.19268			0.0482508
$612$		0			0
$613$			15.3836i			0.621339i	0.950518	+	0.310669i	$0.100553\pi$
$613$			15.3836i			0.621339i	−0.950518	+	0.310669i	$0.899447\pi$
$614$	−1.44024	+	0.831525i	−0.0581235	+	0.0335576i
$615$		0			0
$616$	8.33298	−	78.7265i	0.335745	−	3.17198i
$617$	−2.83696	−	1.63792i	−0.114212	−	0.0659402i	0.441806	−	0.897111i	$-0.354338\pi$
$617$	−2.83696	−	1.63792i	−0.114212	−	0.0659402i	−0.556018	+	0.831170i	$0.687671\pi$
$618$		0			0
$619$	−4.01397	−	6.95240i	−0.161335	−	0.279440i	0.774013	−	0.633170i	$-0.218247\pi$
$619$	−4.01397	−	6.95240i	−0.161335	−	0.279440i	−0.935348	+	0.353730i	$0.884913\pi$
$620$			2.43899i			0.0979524i
$621$		0			0
$622$			31.6773i			1.27015i
$623$	3.34117	+	5.78707i	0.133861	+	0.231854i
$624$		0			0
$625$	−12.3115	+	21.3242i	−0.492461	+	0.852967i
$626$	−34.5758	+	59.8871i	−1.38193	+	2.39357i
$627$		0			0
$628$	−38.5934	−	66.8457i	−1.54004	−	2.66743i
$629$	−15.2913			−0.609702
$630$		0			0
$631$	−40.1130			−1.59687			−0.798436	−	0.602080i	$-0.794339\pi$
$631$	−40.1130			−1.59687			−0.798436	+	0.602080i	$0.794339\pi$
$632$	26.3523	−	15.2145i	1.04824	−	0.605202i
$633$		0			0
$634$	−39.3381	−	22.7119i	−1.56232	−	0.902003i
$635$	−1.09326	+	1.89359i	−0.0433848	+	0.0751447i
$636$		0			0
$637$	3.90990	−	2.25738i	0.154916	−	0.0894406i
$638$	−4.70553	−	10.5897i	−0.186294	−	0.419251i
$639$		0			0
$640$			0.611744i			0.0241813i
$641$	1.91439	−	1.10527i	0.0756137	−	0.0436556i	−0.461716	−	0.887028i	$-0.652766\pi$
$641$	1.91439	−	1.10527i	0.0756137	−	0.0436556i	0.537330	+	0.843372i	$0.319433\pi$
$642$		0			0
$643$	11.3784	−	19.7080i	0.448720	−	0.777206i	−0.549583	−	0.835439i	$-0.685213\pi$
$643$	11.3784	−	19.7080i	0.448720	−	0.777206i	0.998303	+	0.0582333i	$0.0185467\pi$
$644$	−37.0848	+	64.2327i	−1.46134	+	2.53112i
$645$		0			0
$646$	57.7808	−	33.3597i	2.27335	−	1.31252i
$647$		−	12.2576i		−	0.481897i	−0.970538	−	0.240948i	$-0.922542\pi$
$647$		−	12.2576i		−	0.481897i	0.970538	−	0.240948i	$-0.0774584\pi$
$648$		0			0
$649$	16.4305	−	7.30088i	0.644955	−	0.286585i
$650$	−11.5897	+	6.69134i	−0.454587	+	0.262456i
$651$		0			0
$652$	−36.7693	+	63.6863i	−1.44000	+	2.49415i
$653$	−19.6458	−	11.3425i	−0.768798	−	0.443866i	0.0636475	−	0.997972i	$-0.479727\pi$
$653$	−19.6458	−	11.3425i	−0.768798	−	0.443866i	−0.832446	+	0.554107i	$0.813060\pi$
$654$		0			0
$655$	0.342838	−	0.197938i	0.0133958	−	0.00773406i
$656$	−16.7758			−0.654985
$657$		0			0
$658$	−10.0550			−0.391986
$659$	12.3240	+	21.3458i	0.480074	+	0.831513i	0.999739	−	0.0228574i	$-0.00727637\pi$
$659$	12.3240	+	21.3458i	0.480074	+	0.831513i	−0.519664	+	0.854370i	$0.673943\pi$
$660$		0			0
$661$	12.8269	−	22.2168i	0.498907	−	0.864133i	−0.501092	−	0.865394i	$-0.667068\pi$
$661$	12.8269	−	22.2168i	0.498907	−	0.864133i	0.999999	+	0.00126123i	$0.000401463\pi$
$662$	32.6103	−	56.4827i	1.26744	−	2.19526i
$663$		0			0
$664$	32.6882	+	56.6176i	1.26855	+	2.19719i
$665$		−	2.73660i		−	0.106121i
$666$		0			0
$667$			6.26663i			0.242645i
$668$	−26.9522	−	46.6825i	−1.04281	−	1.80620i
$669$		0			0
$670$	1.91045	+	1.10300i	0.0738073	+	0.0426127i
$671$	3.87716	−	36.6298i	0.149676	−	1.41408i
$672$		0			0
$673$	−27.3002	+	15.7618i	−1.05235	+	0.607572i	−0.923305	−	0.384067i	$-0.874523\pi$
$673$	−27.3002	+	15.7618i	−1.05235	+	0.607572i	−0.129041	+	0.991639i	$0.541190\pi$
$674$		−	29.5840i		−	1.13953i
$675$		0			0
$676$	56.4105			2.16964
$677$	−4.38509	−	7.59519i	−0.168533	−	0.291907i	0.769372	−	0.638802i	$-0.220570\pi$
$677$	−4.38509	−	7.59519i	−0.168533	−	0.291907i	−0.937904	+	0.346895i	$0.887236\pi$
$678$		0			0
$679$	5.35459	+	3.09147i	0.205490	+	0.118640i
$680$	−4.89021	−	2.82337i	−0.187531	−	0.108271i
$681$		0			0
$682$	−16.4518	+	22.6090i	−0.629971	+	0.865742i
$683$		−	22.5674i		−	0.863516i	−0.901990	−	0.431758i	$-0.857894\pi$
$683$		−	22.5674i		−	0.863516i	0.901990	−	0.431758i	$-0.142106\pi$
$684$		0			0
$685$	1.80846			0.0690976
$686$	20.0314	−	11.5651i	0.764803	−	0.441559i
$687$		0			0
$688$	73.5553	+	42.4672i	2.80427	+	1.61905i
$689$	4.85647	−	8.41165i	0.185017	−	0.320458i
$690$		0			0
$691$	−9.54293	−	16.5288i	−0.363030	−	0.628787i	0.625428	−	0.780282i	$-0.284925\pi$
$691$	−9.54293	−	16.5288i	−0.363030	−	0.628787i	−0.988458	+	0.151495i	$0.951591\pi$
$692$	14.7362			0.560186
$693$		0			0
$694$	−25.6416			−0.973343
$695$	0.954497	+	1.65324i	0.0362062	+	0.0627109i
$696$		0			0
$697$	−4.72616	+	8.18595i	−0.179016	+	0.310065i
$698$	81.3353	+	46.9590i	3.07859	+	1.77742i
$699$		0			0
$700$	68.6740	−	39.6490i	2.59563	−	1.49859i
$701$	−18.2771			−0.690315			−0.345158	−	0.938545i	$-0.612175\pi$
$701$	−18.2771			−0.690315			−0.345158	+	0.938545i	$0.612175\pi$
$702$		0			0
$703$		−	15.5794i		−	0.587587i
$704$	10.5869	−	14.5492i	0.399010	−	0.548343i
$705$		0			0
$706$	34.6466	+	20.0032i	1.30394	+	0.752831i
$707$	52.0743	+	30.0651i	1.95846	+	1.13072i
$708$		0			0
$709$	−6.09028	−	10.5487i	−0.228725	−	0.396164i	0.728705	−	0.684827i	$-0.240122\pi$
$709$	−6.09028	−	10.5487i	−0.228725	−	0.396164i	−0.957431	+	0.288664i	$0.906789\pi$
$710$	0.229823			0.00862511
$711$		0			0
$712$			14.0482i			0.526479i
$713$	13.0950	−	7.56042i	0.490413	−	0.283140i
$714$		0			0
$715$	0.542608	+	0.0574335i	0.0202924	+	0.00214789i
$716$	−65.3799	−	37.7471i	−2.44336	−	1.41067i
$717$		0			0
$718$	29.2957	+	50.7417i	1.09331	+	1.89366i
$719$			8.08637i			0.301571i	0.988567	+	0.150785i	$0.0481802\pi$
$719$			8.08637i			0.301571i	−0.988567	+	0.150785i	$0.951820\pi$
$720$		0			0
$721$			29.6759i			1.10519i
$722$	9.34222	+	16.1812i	0.347682	+	0.602202i
$723$		0			0
$724$	24.2556	−	42.0119i	0.901452	−	1.56136i
$725$	3.34996	−	5.80231i	0.124415	−	0.215492i
$726$		0			0
$727$	−0.752397	−	1.30319i	−0.0279049	−	0.0483326i	0.851736	−	0.523972i	$-0.175550\pi$
$727$	−0.752397	−	1.30319i	−0.0279049	−	0.0483326i	−0.879641	+	0.475639i	$0.842217\pi$
$728$	24.7506			0.917316
$729$		0			0
$730$	2.56870			0.0950718
$731$	41.4447	−	23.9281i	1.53289	−	0.885014i
$732$		0			0
$733$	−2.84468	−	1.64238i	−0.105071	−	0.0606626i	0.446544	−	0.894762i	$-0.352655\pi$
$733$	−2.84468	−	1.64238i	−0.105071	−	0.0606626i	−0.551615	+	0.834099i	$0.685988\pi$
$734$	27.1324	−	46.9947i	1.00147	−	1.73461i
$735$		0			0
$736$	−36.1271	+	20.8580i	−1.33166	+	0.768836i
$737$	7.21782	+	16.2436i	0.265872	+	0.598341i
$738$		0			0
$739$		−	45.1813i		−	1.66202i	−0.556257	−	0.831010i	$-0.687763\pi$
$739$		−	45.1813i		−	1.66202i	0.556257	−	0.831010i	$-0.312237\pi$
$740$	−1.97829	+	1.14216i	−0.0727232	+	0.0419868i
$741$		0			0
$742$	−40.9430	+	70.9153i	−1.50306	+	2.60338i
$743$	−3.06363	+	5.30637i	−0.112394	+	0.194672i	−0.916735	−	0.399496i	$-0.869185\pi$
$743$	−3.06363	+	5.30637i	−0.112394	+	0.194672i	0.804341	+	0.594168i	$0.202518\pi$
$744$		0			0
$745$	−0.320233	+	0.184887i	−0.0117324	+	0.00677372i
$746$			63.7584i			2.33436i
$747$		0			0
$748$	−32.0082	−	72.0340i	−1.17034	−	2.63382i
$749$	−41.8233	+	24.1467i	−1.52819	+	0.882302i
$750$		0			0
$751$	−10.0212	+	17.3573i	−0.365679	+	0.633375i	−0.988885	−	0.148683i	$-0.952497\pi$
$751$	−10.0212	+	17.3573i	−0.365679	+	0.633375i	0.623205	+	0.782058i	$0.285830\pi$
$752$	−8.88220	−	5.12814i	−0.323900	−	0.187004i
$753$		0			0
$754$	3.13753	−	1.81145i	0.114262	−	0.0659693i
$755$	−1.20986			−0.0440314
$756$		0			0
$757$	38.1828			1.38778			0.693889	−	0.720082i	$-0.255896\pi$
$757$	38.1828			1.38778			0.693889	+	0.720082i	$0.255896\pi$
$758$	−34.6359	−	59.9912i	−1.25803	−	2.17898i
$759$		0			0
$760$	2.87656	−	4.98236i	0.104344	−	0.180729i
$761$	18.8711	−	32.6858i	0.684078	−	1.18486i	−0.289648	−	0.957133i	$-0.593538\pi$
$761$	18.8711	−	32.6858i	0.684078	−	1.18486i	0.973726	−	0.227725i	$-0.0731286\pi$
$762$		0			0
$763$	12.5541	+	21.7444i	0.454490	+	0.787200i
$764$		−	39.8459i		−	1.44158i
$765$		0			0
$766$			72.8143i			2.63089i
$767$	2.81057	+	4.86805i	0.101484	+	0.175775i
$768$		0			0
$769$	−21.6668	−	12.5093i	−0.781326	−	0.451099i	0.0555743	−	0.998455i	$-0.482301\pi$
$769$	−21.6668	−	12.5093i	−0.781326	−	0.451099i	−0.836900	+	0.547356i	$0.815634\pi$
$770$	−4.57451	−	0.484199i	−0.164854	−	0.0174493i
$771$		0			0
$772$	37.5304	−	21.6682i	1.35075	−	0.779855i
$773$			55.3377i			1.99036i	0.0980708	+	0.995179i	$0.468733\pi$
$773$			55.3377i			1.99036i	−0.0980708	+	0.995179i	$0.531267\pi$
$774$		0			0
$775$	−16.1664			−0.580713
$776$	6.49918	+	11.2569i	0.233307	+	0.404099i
$777$		0			0
$778$	−58.0365	−	33.5074i	−2.08071	−	1.20130i
$779$	−8.34019	−	4.81521i	−0.298818	−	0.172523i
$780$		0			0
$781$	1.49735	+	1.08957i	0.0535795	+	0.0389879i
$782$			60.6494i			2.16882i
$783$		0			0
$784$	−38.8239			−1.38657
$785$	−2.24199	+	1.29441i	−0.0800199	+	0.0461995i
$786$		0			0
$787$	15.5326	+	8.96774i	0.553677	+	0.319665i	0.750604	−	0.660753i	$-0.229763\pi$
$787$	15.5326	+	8.96774i	0.553677	+	0.319665i	−0.196927	+	0.980418i	$0.563096\pi$
$788$	−16.1313	+	27.9403i	−0.574654	+	0.995330i
$789$		0			0
$790$	−0.884061	−	1.53124i	−0.0314535	−	0.0544790i
$791$	0.356643			0.0126808
$792$		0			0
$793$	11.5159			0.408942
$794$	−8.12249	−	14.0686i	−0.288256	−	0.499275i
$795$		0			0
$796$	27.5304	−	47.6841i	0.975790	−	1.69012i
$797$	−29.9676	−	17.3018i	−1.06151	−	0.612862i	−0.135659	−	0.990756i	$-0.543315\pi$
$797$	−29.9676	−	17.3018i	−1.06151	−	0.612862i	−0.925849	+	0.377893i	$0.876649\pi$
$798$		0			0
$799$	−5.00467	+	2.88945i	−0.177053	+	0.102221i
$800$	44.6004			1.57686
$801$		0			0
$802$			63.1079i			2.22842i
$803$	16.7357	+	12.1780i	0.590589	+	0.429751i
$804$		0			0
$805$	2.15435	+	1.24381i	0.0759308	+	0.0438386i
$806$	−7.57060	−	4.37089i	−0.266663	−	0.153958i
$807$		0			0
$808$	63.2057	+	109.475i	2.22357	+	3.85133i
$809$	−6.72470			−0.236428			−0.118214	−	0.992988i	$-0.537717\pi$
$809$	−6.72470			−0.236428			−0.118214	+	0.992988i	$0.537717\pi$
$810$		0			0
$811$		−	26.0937i		−	0.916275i	−0.888881	−	0.458137i	$-0.848517\pi$
$811$		−	26.0937i		−	0.916275i	0.888881	−	0.458137i	$-0.151483\pi$
$812$	−18.5912	+	10.7336i	−0.652422	+	0.376676i
$813$		0			0
$814$	−26.0425	−	2.75653i	−0.912791	−	0.0966163i
$815$	2.13602	+	1.23323i	0.0748216	+	0.0431983i
$816$		0			0
$817$	24.3790	+	42.2256i	0.852912	+	1.47729i
$818$		−	93.2959i		−	3.26201i
$819$		0			0
$820$			1.41206i			0.0493113i
$821$	−19.5583	−	33.8760i	−0.682590	−	1.18228i	−0.974188	−	0.225740i	$-0.927520\pi$
$821$	−19.5583	−	33.8760i	−0.682590	−	1.18228i	0.291598	−	0.956541i	$-0.405813\pi$
$822$		0			0
$823$	15.3692	−	26.6203i	0.535737	−	0.927924i	−0.463390	−	0.886154i	$-0.653367\pi$
$823$	15.3692	−	26.6203i	0.535737	−	0.927924i	0.999127	−	0.0417697i	$-0.0132996\pi$
$824$	−31.1937	+	54.0290i	−1.08668	+	1.88219i
$825$		0			0
$826$	−23.6948	−	41.0406i	−0.824447	−	1.42798i
$827$	−22.0427			−0.766499			−0.383250	−	0.923645i	$-0.625195\pi$
$827$	−22.0427			−0.766499			−0.383250	+	0.923645i	$0.625195\pi$
$828$		0			0
$829$	13.2009			0.458486			0.229243	−	0.973369i	$-0.426375\pi$
$829$	13.2009			0.458486			0.229243	+	0.973369i	$0.426375\pi$
$830$	3.28984	−	1.89939i	0.114192	−	0.0659288i
$831$		0			0
$832$	4.87179	+	2.81273i	0.168899	+	0.0975138i
$833$	−10.9377	+	18.9446i	−0.378968	+	0.656391i
$834$		0			0
$835$	−1.56572	+	0.903968i	−0.0541839	+	0.0312831i
$836$	73.3913	−	32.6113i	2.53829	−	1.12789i
$837$		0			0
$838$		−	98.3833i		−	3.39859i
$839$	35.2755	−	20.3663i	1.21785	−	0.703124i	0.253390	−	0.967364i	$-0.418455\pi$
$839$	35.2755	−	20.3663i	1.21785	−	0.703124i	0.964457	+	0.264240i	$0.0851212\pi$
$840$		0			0
$841$	13.5931	−	23.5440i	0.468728	−	0.811861i
$842$	−9.13457	+	15.8215i	−0.314798	+	0.545246i
$843$		0			0
$844$	−78.6513	+	45.4094i	−2.70729	+	1.56305i
$845$		−	1.89199i		−	0.0650866i
$846$		0			0
$847$	−27.5084	−	24.8420i	−0.945202	−	0.853582i
$848$	−72.3346	+	41.7624i	−2.48398	+	1.43413i
$849$		0			0
$850$	32.4215	−	56.1557i	1.11205	−	1.92612i
$851$	12.2646	+	7.08099i	0.420426	+	0.242733i
$852$		0			0
$853$	23.8885	−	13.7921i	0.817928	−	0.472231i	−0.0317735	−	0.999495i	$-0.510116\pi$
$853$	23.8885	−	13.7921i	0.817928	−	0.472231i	0.849701	+	0.527264i	$0.176782\pi$
$854$	−97.0860			−3.32222
$855$		0			0
$856$	−101.527			−3.47012
$857$	9.73781	+	16.8664i	0.332637	+	0.576145i	0.983028	−	0.183455i	$-0.0587282\pi$
$857$	9.73781	+	16.8664i	0.332637	+	0.576145i	−0.650391	+	0.759600i	$0.725395\pi$
$858$		0			0
$859$	2.28915	−	3.96493i	0.0781050	−	0.135282i	−0.824327	−	0.566113i	$-0.808446\pi$
$859$	2.28915	−	3.96493i	0.0781050	−	0.135282i	0.902432	+	0.430832i	$0.141780\pi$
$860$	3.57457	−	6.19134i	0.121892	−	0.211123i
$861$		0			0
$862$	−49.6697	−	86.0304i	−1.69176	−	2.93021i
$863$		−	47.3061i		−	1.61032i	−0.593059	−	0.805159i	$-0.702080\pi$
$863$		−	47.3061i		−	1.61032i	0.593059	−	0.805159i	$-0.297920\pi$
$864$		0			0
$865$		−	0.494248i		−	0.0168049i
$866$	28.7796	+	49.8476i	0.977969	+	1.69389i
$867$		0			0
$868$	44.8589	+	25.8993i	1.52261	+	0.879080i
$869$	1.49960	−	14.1676i	0.0508705	−	0.480604i
$870$		0			0
$871$	−4.81266	+	2.77859i	−0.163071	+	0.0941490i
$872$			52.7849i			1.78752i
$873$		0			0
$874$	−61.7922			−2.09015
$875$	−2.66636	−	4.61827i	−0.0901394	−	0.156126i
$876$		0			0
$877$	4.42115	+	2.55255i	0.149292	+	0.0861936i	0.572785	−	0.819706i	$-0.305863\pi$
$877$	4.42115	+	2.55255i	0.149292	+	0.0861936i	−0.423493	+	0.905899i	$0.639196\pi$
$878$	−49.7018	−	28.6953i	−1.67735	−	0.968421i
$879$		0			0
$880$	−3.79399	−	2.76075i	−0.127895	−	0.0930650i
$881$		−	46.1405i		−	1.55451i	−0.629184	−	0.777257i	$-0.716611\pi$
$881$		−	46.1405i		−	1.55451i	0.629184	−	0.777257i	$-0.283389\pi$
$882$		0			0
$883$	−27.9137			−0.939370			−0.469685	−	0.882834i	$-0.655633\pi$
$883$	−27.9137			−0.939370			−0.469685	+	0.882834i	$0.655633\pi$
$884$	21.3423	−	12.3220i	0.717819	−	0.414433i
$885$		0			0
$886$	41.8466	+	24.1602i	1.40586	+	0.811676i
$887$	20.7680	−	35.9712i	0.697320	−	1.20779i	−0.272073	−	0.962277i	$-0.587709\pi$
$887$	20.7680	−	35.9712i	0.697320	−	1.20779i	0.969392	−	0.245516i	$-0.0789575\pi$
$888$		0			0
$889$	23.2184	+	40.2154i	0.778720	+	1.34878i
$890$	0.816290			0.0273621
$891$		0			0
$892$	−69.6256			−2.33124
$893$	−2.94389	−	5.09897i	−0.0985135	−	0.170630i
$894$		0			0
$895$	−1.26603	+	2.19282i	−0.0423186	+	0.0732980i
$896$	11.2514	+	6.49602i	0.375884	+	0.217017i
$897$		0			0
$898$	−40.3280	+	23.2834i	−1.34576	+	0.776976i
$899$	4.37650			0.145964
$900$		0			0
$901$			47.0620i			1.56786i
$902$	−9.52479	+	13.0895i	−0.317141	+	0.435833i
$903$		0			0
$904$	0.649319	+	0.374884i	0.0215960	+	0.0124685i
$905$	−1.40907	−	0.813526i	−0.0468390	−	0.0270425i
$906$		0			0
$907$	3.43330	+	5.94664i	0.114001	+	0.197455i	0.917380	−	0.398013i	$-0.130300\pi$
$907$	3.43330	+	5.94664i	0.114001	+	0.197455i	−0.803379	+	0.595468i	$0.796967\pi$
$908$	−13.9579			−0.463211
$909$		0			0
$910$		−	1.43816i		−	0.0476747i
$911$	−29.0235	+	16.7567i	−0.961591	+	0.555175i	−0.896662	−	0.442715i	$-0.854015\pi$
$911$	−29.0235	+	16.7567i	−0.961591	+	0.555175i	−0.0649284	+	0.997890i	$0.520682\pi$
$912$		0			0
$913$	30.4389	+	3.22187i	1.00738	+	0.106628i
$914$	−13.4517	−	7.76636i	−0.444944	−	0.256888i
$915$		0			0
$916$	−26.2121	−	45.4007i	−0.866073	−	1.50008i
$917$		−	8.40748i		−	0.277639i
$918$		0			0
$919$		−	46.0840i		−	1.52017i	−0.649824	−	0.760085i	$-0.725157\pi$
$919$		−	46.0840i		−	1.52017i	0.649824	−	0.760085i	$-0.274843\pi$
$920$	2.61486	+	4.52907i	0.0862093	+	0.149319i
$921$		0			0
$922$	−12.4743	+	21.6062i	−0.410821	+	0.711562i
$923$	−0.289476	+	0.501388i	−0.00952823	+	0.0165034i
$924$		0			0
$925$	−7.57060	−	13.1127i	−0.248920	−	0.431142i
$926$	25.9319			0.852176
$927$		0			0
$928$	−12.0741			−0.396350
$929$	−50.3776	+	29.0855i	−1.65283	+	0.954265i	−0.676936	+	0.736042i	$0.736692\pi$
$929$	−50.3776	+	29.0855i	−1.65283	+	0.954265i	−0.975899	+	0.218222i	$0.929974\pi$
$930$		0			0
$931$	−19.3015	−	11.1437i	−0.632582	−	0.365222i
$932$	18.4583	−	31.9708i	0.604623	−	1.04724i
$933$		0			0
$934$	40.8845	−	23.6047i	1.33778	−	0.772370i
$935$	−2.41600	+	1.07355i	−0.0790117	+	0.0351087i
$936$		0			0
$937$		−	6.36938i		−	0.208079i	−0.994573	−	0.104039i	$-0.966823\pi$
$937$		−	6.36938i		−	0.208079i	0.994573	−	0.104039i	$-0.0331768\pi$
$938$	40.5737	−	23.4252i	1.32478	−	0.764860i
$939$		0			0
$940$	−0.431648	+	0.747637i	−0.0140788	+	0.0243852i
$941$	−6.87117	+	11.9012i	−0.223994	+	0.387969i	−0.956017	−	0.293311i	$-0.905243\pi$
$941$	−6.87117	+	11.9012i	−0.223994	+	0.387969i	0.732023	+	0.681280i	$0.238576\pi$
$942$		0			0
$943$	7.58141	−	4.37713i	0.246885	−	0.142539i
$944$		−	48.3380i		−	1.57327i
$945$		0			0
$946$	74.8980	−	33.2808i	2.43514	−	1.08205i
$947$	9.90101	−	5.71635i	0.321739	−	0.185756i	−0.330428	−	0.943831i	$-0.607193\pi$
$947$	9.90101	−	5.71635i	0.321739	−	0.185756i	0.652168	+	0.758075i	$0.273860\pi$
$948$		0			0
$949$	−3.23543	+	5.60393i	−0.105027	+	0.181911i
$950$	57.2137	+	33.0324i	1.85626	+	1.07171i
$951$		0			0
$952$	−103.857	+	59.9618i	−3.36602	+	1.94337i
$953$	−39.5826			−1.28221			−0.641103	−	0.767455i	$-0.721523\pi$
$953$	−39.5826			−1.28221			−0.641103	+	0.767455i	$0.721523\pi$
$954$		0			0
$955$	−1.33642			−0.0432456
$956$	37.6363	+	65.1880i	1.21725	+	2.10833i
$957$		0			0
$958$	24.4241	−	42.3038i	0.789106	−	1.36677i
$959$	19.2037	−	33.2619i	0.620121	−	1.07408i
$960$		0			0
$961$	10.2199	+	17.7015i	0.329675	+	0.571015i
$962$		−	8.18742i		−	0.263973i
$963$		0			0
$964$			65.9044i			2.12264i
$965$	−0.726745	−	1.25876i	−0.0233947	−	0.0405209i
$966$		0			0
$967$	−32.1259	−	18.5479i	−1.03310	−	0.596461i	−0.115229	−	0.993339i	$-0.536760\pi$
$967$	−32.1259	−	18.5479i	−1.03310	−	0.596461i	−0.917871	+	0.396878i	$0.870094\pi$
$968$	−23.9704	−	74.1437i	−0.770437	−	2.38307i
$969$		0			0
$970$	0.654097	−	0.377643i	0.0210018	−	0.0121254i
$971$		−	31.6598i		−	1.01601i	−0.861354	−	0.508005i	$-0.830383\pi$
$971$		−	31.6598i		−	1.01601i	0.861354	−	0.508005i	$-0.169617\pi$
$972$		0			0
$973$	40.5427			1.29974
$974$	52.1898	+	90.3954i	1.67227	+	2.89646i
$975$		0			0
$976$	−85.7618	−	49.5146i	−2.74517	−	1.58492i
$977$	28.4797	+	16.4427i	0.911145	+	0.526050i	0.880799	−	0.473489i	$-0.157006\pi$
$977$	28.4797	+	16.4427i	0.911145	+	0.526050i	0.0303458	+	0.999539i	$0.490339\pi$
$978$		0			0
$979$	5.31832	+	3.86996i	0.169974	+	0.123684i
$980$			3.26791i			0.104389i
$981$		0			0
$982$	21.3211			0.680385
$983$	−24.9856	+	14.4254i	−0.796916	+	0.460100i	−0.842392	−	0.538866i	$-0.818853\pi$
$983$	−24.9856	+	14.4254i	−0.796916	+	0.460100i	0.0454757	+	0.998965i	$0.485520\pi$
$984$		0			0
$985$	0.937109	+	0.541040i	0.0298588	+	0.0172390i
$986$	−8.77702	+	15.2023i	−0.279517	+	0.484138i
$987$		0			0
$988$	12.5541	+	21.7444i	0.399400	+	0.691782i
$989$	−44.3220			−1.40936
$990$		0			0
$991$	−11.8746			−0.377209			−0.188605	−	0.982053i	$-0.560396\pi$
$991$	−11.8746			−0.377209			−0.188605	+	0.982053i	$0.560396\pi$
$992$	14.5668	+	25.2305i	0.462498	+	0.801070i
$993$		0			0
$994$	2.44046	−	4.22700i	0.0774067	−	0.134072i
$995$	−1.59931	−	0.923363i	−0.0507016	−	0.0292726i
$996$		0			0
$997$	3.56706	−	2.05944i	0.112970	−	0.0652232i	−0.442450	−	0.896793i	$-0.645891\pi$
$997$	3.56706	−	2.05944i	0.112970	−	0.0652232i	0.555420	+	0.831570i	$0.312557\pi$
$998$	−79.1592			−2.50574
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.g.b.98.1		16
3.2	odd	2		99.2.g.b.32.8	yes	16
9.2	odd	6	inner	297.2.g.b.197.8		16
9.4	even	3		891.2.d.b.890.15		16
9.5	odd	6		891.2.d.b.890.2		16
9.7	even	3		99.2.g.b.65.1	yes	16
11.10	odd	2	inner	297.2.g.b.98.8		16
33.32	even	2		99.2.g.b.32.1	✓	16
99.32	even	6		891.2.d.b.890.16		16
99.43	odd	6		99.2.g.b.65.8	yes	16
99.65	even	6	inner	297.2.g.b.197.1		16
99.76	odd	6		891.2.d.b.890.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.1	✓	16	33.32	even	2
99.2.g.b.32.8	yes	16	3.2	odd	2
99.2.g.b.65.1	yes	16	9.7	even	3
99.2.g.b.65.8	yes	16	99.43	odd	6
297.2.g.b.98.1		16	1.1	even	1	trivial
297.2.g.b.98.8		16	11.10	odd	2	inner
297.2.g.b.197.1		16	99.65	even	6	inner
297.2.g.b.197.8		16	9.2	odd	6	inner
891.2.d.b.890.1		16	99.76	odd	6
891.2.d.b.890.2		16	9.5	odd	6
891.2.d.b.890.15		16	9.4	even	3
891.2.d.b.890.16		16	99.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29716 - 2.24675i) q^{2} +(-2.36526 + 4.09675i) q^{4} +(0.137404 + 0.0793301i) q^{5} +(2.91814 - 1.68479i) q^{7} +7.08384 q^{8} -0.411616i q^{10} +(1.95143 - 2.68177i) q^{11} +(0.897990 + 0.518455i) q^{13} +(-7.57060 - 4.37089i) q^{14} +(-4.45837 - 7.72212i) q^{16} -5.02413 q^{17} -5.11879i q^{19} +(-0.649990 + 0.375272i) q^{20} +(-8.55660 - 0.905691i) q^{22} +(4.02970 + 2.32655i) q^{23} +(-2.48741 - 4.30833i) q^{25} -2.69008i q^{26} +15.9398i q^{28} +(0.673383 + 1.16633i) q^{29} +(1.62482 - 2.81427i) q^{31} +(-4.48261 + 7.76411i) q^{32} +(6.51711 + 11.2880i) q^{34} +0.534618 q^{35} +3.04356 q^{37} +(-11.5007 + 6.63990i) q^{38} +(0.973346 + 0.561961i) q^{40} +(0.940692 - 1.62933i) q^{41} +(-8.24914 + 4.76264i) q^{43} +(6.37090 + 14.3376i) q^{44} -12.0716i q^{46} +(0.996127 - 0.575114i) q^{47} +(2.17703 - 3.77072i) q^{49} +(-6.45316 + 11.1772i) q^{50} +(-4.24795 + 2.45256i) q^{52} -9.36720i q^{53} +(0.480880 - 0.213678i) q^{55} +(20.6716 - 11.9348i) q^{56} +(1.74697 - 3.02585i) q^{58} +(4.69477 + 2.71052i) q^{59} +(9.61807 - 5.55299i) q^{61} -8.43060 q^{62} +5.42521 q^{64} +(0.0822581 + 0.142475i) q^{65} +(-2.67969 + 4.64135i) q^{67} +(11.8834 - 20.5826i) q^{68} +(-0.693486 - 1.20115i) q^{70} +0.558344i q^{71} +6.24053i q^{73} +(-3.94799 - 6.83812i) q^{74} +(20.9704 + 12.1073i) q^{76} +(1.17634 - 11.1135i) q^{77} +(3.72007 - 2.14778i) q^{79} -1.41473i q^{80} -4.88092 q^{82} +(4.61447 + 7.99250i) q^{83} +(-0.690334 - 0.398565i) q^{85} +(21.4009 + 12.3558i) q^{86} +(13.8236 - 18.9972i) q^{88} +1.98314i q^{89} +3.49395 q^{91} +(-19.0625 + 11.0058i) q^{92} +(-2.58428 - 1.49203i) q^{94} +(0.406074 - 0.703341i) q^{95} +(0.917466 + 1.58910i) q^{97} -11.2958 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4} + 12 q^{11} + 6 q^{14} - 2 q^{16} - 36 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{25} - 4 q^{31} - 28 q^{37} - 66 q^{38} + 30 q^{47} + 10 q^{49} + 20 q^{55} + 120 q^{56} - 6 q^{58} + 36 q^{59}+ \cdots - 4 q^{97}+O(q^{100}) \) 16 * q - 14 * q^4 + 12 * q^11 + 6 * q^14 - 2 * q^16 - 36 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^25 - 4 * q^31 - 28 * q^37 - 66 * q^38 + 30 * q^47 + 10 * q^49 + 20 * q^55 + 120 * q^56 - 6 * q^58 + 36 * q^59 + 40 * q^64 + 8 * q^67 - 72 * q^77 + 12 * q^82 + 72 * q^86 - 6 * q^88 - 12 * q^91 - 18 * q^92 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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