LMFDB - Embedded newform 297.2.n.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	297.37
Dual form			297.2.n.b.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0694404 + 0.660681i) q^{2} +(1.52462 + 0.324067i) q^{4} +(0.116719 + 1.11051i) q^{5} +(-2.61265 + 2.90164i) q^{7} +(-0.730548 + 2.24840i) q^{8} -0.741796 q^{10} +(-3.27403 + 0.529836i) q^{11} +(2.44648 - 1.08924i) q^{13} +(-1.73564 - 1.92762i) q^{14} +(1.41310 + 0.629154i) q^{16} +(4.48727 - 3.26019i) q^{17} +(-1.58598 + 4.88115i) q^{19} +(-0.181927 + 1.73092i) q^{20} +(-0.122703 - 2.19988i) q^{22} +(1.05719 - 1.83110i) q^{23} +(3.67114 - 0.780324i) q^{25} +(0.549758 + 1.69198i) q^{26} +(-4.92362 + 3.57722i) q^{28} +(-0.724696 + 0.804856i) q^{29} +(-0.392973 + 0.174963i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +(-3.52724 - 2.56269i) q^{35} +(-2.69024 - 8.27970i) q^{37} +(-3.11475 - 1.38678i) q^{38} +(-2.58213 - 0.548848i) q^{40} +(1.95324 + 2.16930i) q^{41} +(1.11628 + 1.93346i) q^{43} +(-5.16335 - 0.253209i) q^{44} +(1.13637 + 0.825618i) q^{46} +(12.5550 - 2.66864i) q^{47} +(-0.861884 - 8.20028i) q^{49} +(0.260620 + 2.47964i) q^{50} +(4.08293 - 0.867854i) q^{52} +(4.56381 + 3.31581i) q^{53} +(-0.970527 - 3.57399i) q^{55} +(-4.61537 - 7.99405i) q^{56} +(-0.481430 - 0.534682i) q^{58} +(-2.32346 - 0.493867i) q^{59} +(-3.73133 - 1.66130i) q^{61} +(-0.0883065 - 0.271779i) q^{62} +(-0.590604 - 0.429099i) q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(7.89789 - 3.51637i) q^{68} +(1.93805 - 2.15242i) q^{70} +(5.11062 - 3.71308i) q^{71} +(-3.60705 - 11.1014i) q^{73} +(5.65706 - 1.20244i) q^{74} +(-3.99983 + 6.92792i) q^{76} +(7.01650 - 10.8843i) q^{77} +(-0.471916 + 4.48998i) q^{79} +(-0.533744 + 1.64269i) q^{80} +(-1.56885 + 1.13983i) q^{82} +(-0.440332 - 0.196049i) q^{83} +(4.14421 + 4.60261i) q^{85} +(-1.35492 + 0.603248i) q^{86} +(1.20056 - 7.74839i) q^{88} -16.0830 q^{89} +(-3.23120 + 9.94461i) q^{91} +(2.20521 - 2.44913i) q^{92} +(0.891300 + 8.48015i) q^{94} +(-5.60566 - 1.19152i) q^{95} +(-0.837864 + 7.97174i) q^{97} +5.47762 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.0694404	+	0.660681i	−0.0491018	+	0.467172i	0.942150	+	0.335191i	$0.108801\pi$
$2$	−0.0694404	+	0.660681i	−0.0491018	+	0.467172i	−0.991252	+	0.131982i	$0.957866\pi$
$3$		0			0
$3$		0			0
$4$	1.52462	+	0.324067i	0.762309	+	0.162034i
$5$	0.116719	+	1.11051i	0.0521983	+	0.496634i	0.989122	+	0.147099i	$0.0469936\pi$
$5$	0.116719	+	1.11051i	0.0521983	+	0.496634i	−0.936923	+	0.349535i	$0.886340\pi$
$6$		0			0
$7$	−2.61265	+	2.90164i	−0.987488	+	1.09672i	0.00782061	+	0.999969i	$0.497511\pi$
$7$	−2.61265	+	2.90164i	−0.987488	+	1.09672i	−0.995309	+	0.0967475i	$0.969156\pi$
$8$	−0.730548	+	2.24840i	−0.258288	+	0.794928i
$9$		0			0
$10$	−0.741796			−0.234576
$11$	−3.27403	+	0.529836i	−0.987157	+	0.159752i
$11$	−3.27403	+	0.529836i	−0.987157	+	0.159752i
$12$		0			0
$13$	2.44648	−	1.08924i	0.678531	−	0.302101i	−0.0383829	−	0.999263i	$-0.512221\pi$
$13$	2.44648	−	1.08924i	0.678531	−	0.302101i	0.716914	+	0.697162i	$0.245554\pi$
$14$	−1.73564	−	1.92762i	−0.463868	−	0.515178i
$15$		0			0
$16$	1.41310	+	0.629154i	0.353276	+	0.157289i
$17$	4.48727	−	3.26019i	1.08832	−	0.790713i	0.109207	−	0.994019i	$-0.465169\pi$
$17$	4.48727	−	3.26019i	1.08832	−	0.790713i	0.979115	+	0.203306i	$0.0651688\pi$
$18$		0			0
$19$	−1.58598	+	4.88115i	−0.363849	+	1.11981i	0.586850	+	0.809696i	$0.300368\pi$
$19$	−1.58598	+	4.88115i	−0.363849	+	1.11981i	−0.950699	+	0.310116i	$0.899632\pi$
$20$	−0.181927	+	1.73092i	−0.0406802	+	0.387046i
$21$		0			0
$22$	−0.122703	−	2.19988i	−0.0261603	−	0.469017i
$23$	1.05719	−	1.83110i	0.220439	−	0.381812i	−0.734502	−	0.678606i	$-0.762584\pi$
$23$	1.05719	−	1.83110i	0.220439	−	0.381812i	0.954941	+	0.296795i	$0.0959176\pi$
$24$		0			0
$25$	3.67114	−	0.780324i	0.734227	−	0.156065i
$26$	0.549758	+	1.69198i	0.107816	+	0.331825i
$27$		0			0
$28$	−4.92362	+	3.57722i	−0.930476	+	0.676030i
$29$	−0.724696	+	0.804856i	−0.134573	+	0.149458i	−0.806664	−	0.591010i	$-0.798729\pi$
$29$	−0.724696	+	0.804856i	−0.134573	+	0.149458i	0.672092	+	0.740468i	$0.265396\pi$
$30$		0			0
$31$	−0.392973	+	0.174963i	−0.0705800	+	0.0314243i	−0.441723	−	0.897151i	$-0.645633\pi$
$31$	−0.392973	+	0.174963i	−0.0705800	+	0.0314243i	0.371143	+	0.928576i	$0.378966\pi$
$32$	−2.87790	+	4.98467i	−0.508746	+	0.881173i
$33$		0			0
$34$	1.84235	+	3.19104i	0.315960	+	0.547259i
$35$	−3.52724	−	2.56269i	−0.596212	−	0.433173i
$36$		0			0
$37$	−2.69024	−	8.27970i	−0.442273	−	1.36118i	−0.885447	−	0.464740i	$-0.846148\pi$
$37$	−2.69024	−	8.27970i	−0.442273	−	1.36118i	0.443175	−	0.896435i	$-0.353852\pi$
$38$	−3.11475	−	1.38678i	−0.505279	−	0.224965i
$39$		0			0
$40$	−2.58213	−	0.548848i	−0.408270	−	0.0867805i
$41$	1.95324	+	2.16930i	0.305045	+	0.338787i	0.876104	−	0.482122i	$-0.160134\pi$
$41$	1.95324	+	2.16930i	0.305045	+	0.338787i	−0.571059	+	0.820909i	$0.693467\pi$
$42$		0			0
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	0.938501	−	0.345277i	$-0.112215\pi$
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	−0.768269	+	0.640127i	$0.778882\pi$
$44$	−5.16335	−	0.253209i	−0.778404	−	0.0381728i
$45$		0			0
$46$	1.13637	+	0.825618i	0.167548	+	0.121731i
$47$	12.5550	−	2.66864i	1.83133	−	0.389262i	0.842549	−	0.538619i	$-0.181054\pi$
$47$	12.5550	−	2.66864i	1.83133	−	0.389262i	0.988783	+	0.149357i	$0.0477205\pi$
$48$		0			0
$49$	−0.861884	−	8.20028i	−0.123126	−	1.17147i
$50$	0.260620	+	2.47964i	0.0368573	+	0.350674i
$51$		0			0
$52$	4.08293	−	0.867854i	0.566201	−	0.120350i
$53$	4.56381	+	3.31581i	0.626888	+	0.455461i	0.855321	−	0.518099i	$-0.173360\pi$
$53$	4.56381	+	3.31581i	0.626888	+	0.455461i	−0.228433	+	0.973560i	$0.573360\pi$
$54$		0			0
$55$	−0.970527	−	3.57399i	−0.130866	−	0.481917i
$56$	−4.61537	−	7.99405i	−0.616755	−	1.06825i
$57$		0			0
$58$	−0.481430	−	0.534682i	−0.0632149	−	0.0702072i
$59$	−2.32346	−	0.493867i	−0.302489	−	0.0642960i	0.0541667	−	0.998532i	$-0.482750\pi$
$59$	−2.32346	−	0.493867i	−0.302489	−	0.0642960i	−0.356656	+	0.934236i	$0.616083\pi$
$60$		0			0
$61$	−3.73133	−	1.66130i	−0.477748	−	0.212707i	0.153712	−	0.988116i	$-0.450877\pi$
$61$	−3.73133	−	1.66130i	−0.477748	−	0.212707i	−0.631460	+	0.775408i	$0.717544\pi$
$62$	−0.0883065	−	0.271779i	−0.0112149	−	0.0345160i
$63$		0			0
$64$	−0.590604	−	0.429099i	−0.0738255	−	0.0536374i
$65$	1.49516	+	2.58969i	0.185452	+	0.321212i
$66$		0			0
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	−0.397772	−	0.917484i	$-0.630216\pi$
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	0.993451	−	0.114262i	$-0.0364503\pi$
$68$	7.89789	−	3.51637i	0.957760	−	0.426422i
$69$		0			0
$70$	1.93805	−	2.15242i	0.231641	−	0.257264i
$71$	5.11062	−	3.71308i	0.606519	−	0.440662i	−0.241668	−	0.970359i	$-0.577694\pi$
$71$	5.11062	−	3.71308i	0.606519	−	0.440662i	0.848187	+	0.529697i	$0.177694\pi$
$72$		0			0
$73$	−3.60705	−	11.1014i	−0.422174	−	1.29932i	−0.905675	−	0.423973i	$-0.860635\pi$
$73$	−3.60705	−	11.1014i	−0.422174	−	1.29932i	0.483501	−	0.875344i	$-0.339365\pi$
$74$	5.65706	−	1.20244i	0.657620	−	0.139781i
$75$		0			0
$76$	−3.99983	+	6.92792i	−0.458812	+	0.794686i
$77$	7.01650	−	10.8843i	0.799604	−	1.24038i
$78$		0			0
$79$	−0.471916	+	4.48998i	−0.0530946	+	0.505162i	0.935366	+	0.353682i	$0.115071\pi$
$79$	−0.471916	+	4.48998i	−0.0530946	+	0.505162i	−0.988460	+	0.151480i	$0.951596\pi$
$80$	−0.533744	+	1.64269i	−0.0596744	+	0.183659i
$81$		0			0
$82$	−1.56885	+	1.13983i	−0.173250	+	0.125874i
$83$	−0.440332	−	0.196049i	−0.0483327	−	0.0215191i	0.382428	−	0.923985i	$-0.375088\pi$
$83$	−0.440332	−	0.196049i	−0.0483327	−	0.0215191i	−0.430761	+	0.902466i	$0.641755\pi$
$84$		0			0
$85$	4.14421	+	4.60261i	0.449503	+	0.499224i
$86$	−1.35492	+	0.603248i	−0.146104	+	0.0650499i
$87$		0			0
$88$	1.20056	−	7.74839i	0.127980	−	0.825981i
$89$	−16.0830			−1.70480			−0.852399	−	0.522891i	$-0.824853\pi$
$89$	−16.0830			−1.70480			−0.852399	+	0.522891i	$0.824853\pi$
$90$		0			0
$91$	−3.23120	+	9.94461i	−0.338722	+	1.04248i
$92$	2.20521	−	2.44913i	0.229909	−	0.255340i
$93$		0			0
$94$	0.891300	+	8.48015i	0.0919306	+	0.874661i
$95$	−5.60566	−	1.19152i	−0.575128	−	0.122247i
$96$		0			0
$97$	−0.837864	+	7.97174i	−0.0850722	+	0.809408i	0.865918	+	0.500186i	$0.166735\pi$
$97$	−0.837864	+	7.97174i	−0.0850722	+	0.809408i	−0.950990	+	0.309222i	$0.899932\pi$
$98$	5.47762			0.553323
$99$		0			0
$100$	5.84996			0.584996
$101$	0.184108	−	1.75167i	0.0183194	−	0.174297i	−0.981536	−	0.191275i	$-0.938738\pi$
$101$	0.184108	−	1.75167i	0.0183194	−	0.174297i	0.999856	+	0.0169777i	$0.00540443\pi$
$102$		0			0
$103$	−2.62893	−	0.558797i	−0.259036	−	0.0550599i	0.0765627	−	0.997065i	$-0.475605\pi$
$103$	−2.62893	−	0.558797i	−0.259036	−	0.0550599i	−0.335599	+	0.942005i	$0.608939\pi$
$104$	0.661778	+	6.29640i	0.0648927	+	0.617412i
$105$		0			0
$106$	−2.50760	+	2.78498i	−0.243560	+	0.270501i
$107$	3.17558	−	9.77342i	0.306995	−	0.944833i	−0.671931	−	0.740614i	$-0.734535\pi$
$107$	3.17558	−	9.77342i	0.306995	−	0.944833i	0.978925	−	0.204219i	$-0.0654653\pi$
$108$		0			0
$109$	2.36284			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$109$	2.36284			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$110$	2.42866	−	0.393030i	0.231564	−	0.0374739i
$111$		0			0
$112$	−5.51752	+	2.45656i	−0.521357	+	0.232123i
$113$	−1.02540	−	1.13882i	−0.0964613	−	0.107131i	0.692981	−	0.720956i	$-0.256297\pi$
$113$	−1.02540	−	1.13882i	−0.0964613	−	0.107131i	−0.789442	+	0.613825i	$0.789630\pi$
$114$		0			0
$115$	2.15685	+	0.960290i	0.201127	+	0.0895475i
$116$	−1.36571	+	0.992247i	−0.126803	+	0.0921279i
$117$		0			0
$118$	0.487631	−	1.50077i	0.0448901	−	0.138157i
$119$	−2.26375	+	21.5382i	−0.207518	+	1.97440i
$120$		0			0
$121$	10.4385	−	3.46940i	0.948959	−	0.315400i
$122$	1.35669	−	2.34986i	0.122829	−	0.212746i
$123$		0			0
$124$	−0.655833	+	0.139402i	−0.0588956	+	0.0125186i
$125$	3.02032	+	9.29560i	0.270146	+	0.831424i
$126$		0			0
$127$	6.19006	−	4.49734i	0.549279	−	0.399074i	−0.278241	−	0.960511i	$-0.589751\pi$
$127$	6.19006	−	4.49734i	0.549279	−	0.399074i	0.827519	+	0.561437i	$0.189751\pi$
$128$	−7.37825	+	8.19438i	−0.652152	+	0.724288i
$129$		0			0
$130$	−1.81479	+	0.807995i	−0.159167	+	0.0708659i
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	−0.959015	−	0.283356i	$-0.908552\pi$
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	0.724901	+	0.688853i	$0.241886\pi$
$132$		0			0
$133$	−10.0197	−	17.3547i	−0.868820	−	1.50484i
$134$	5.24101	+	3.80782i	0.452754	+	0.328945i
$135$		0			0
$136$	4.05203	+	12.4709i	0.347459	+	1.06937i
$137$	−15.2847	−	6.80519i	−1.30586	−	0.581407i	−0.368455	−	0.929646i	$-0.620113\pi$
$137$	−15.2847	−	6.80519i	−1.30586	−	0.581407i	−0.937406	+	0.348239i	$0.886780\pi$
$138$		0			0
$139$	−13.4399	−	2.85673i	−1.13995	−	0.242305i	−0.401011	−	0.916073i	$-0.631341\pi$
$139$	−13.4399	−	2.85673i	−1.13995	−	0.242305i	−0.738943	+	0.673768i	$0.764675\pi$
$140$	−4.54720	−	5.05018i	−0.384309	−	0.426818i
$141$		0			0
$142$	2.09828	+	3.63433i	0.176084	+	0.304986i
$143$	−7.43273	+	4.86244i	−0.621556	+	0.406618i
$144$		0			0
$145$	−0.978384	−	0.710837i	−0.0812503	−	0.0590318i
$146$	7.58494	−	1.61223i	0.627734	−	0.133429i
$147$		0			0
$148$	−1.41840	−	13.4952i	−0.116592	−	1.10930i
$149$	0.581142	+	5.52920i	0.0476090	+	0.452970i	0.992194	+	0.124703i	$0.0397978\pi$
$149$	0.581142	+	5.52920i	0.0476090	+	0.452970i	−0.944585	+	0.328267i	$0.893536\pi$
$150$		0			0
$151$	0.160326	−	0.0340783i	0.0130471	−	0.00277325i	−0.201384	−	0.979512i	$-0.564544\pi$
$151$	0.160326	−	0.0340783i	0.0130471	−	0.00277325i	0.214431	+	0.976739i	$0.431210\pi$
$152$	−9.81611	−	7.13182i	−0.796192	−	0.578467i
$153$		0			0
$154$	6.70385	+	5.39148i	0.540211	+	0.434458i
$155$	−0.240165	−	0.415978i	−0.0192905	−	0.0334121i
$156$		0			0
$157$	15.9608	+	17.7262i	1.27381	+	1.41471i	0.864752	+	0.502200i	$0.167476\pi$
$157$	15.9608	+	17.7262i	1.27381	+	1.41471i	0.409058	+	0.912509i	$0.365858\pi$
$158$	−2.93367	−	0.623572i	−0.233391	−	0.0496087i
$159$		0			0
$160$	−5.87141	−	2.61412i	−0.464176	−	0.206664i
$161$	2.55114	+	7.85161i	0.201058	+	0.618794i
$162$		0			0
$163$	3.39466	+	2.46636i	0.265890	+	0.193180i	0.712740	−	0.701429i	$-0.247454\pi$
$163$	3.39466	+	2.46636i	0.265890	+	0.193180i	−0.446850	+	0.894609i	$0.647454\pi$
$164$	2.27495	+	3.94033i	0.177644	+	0.307688i
$165$		0			0
$166$	0.160102	−	0.277306i	0.0124264	−	0.0215231i
$167$	−14.4709	+	6.44287i	−1.11979	+	0.498564i	−0.881289	−	0.472577i	$-0.843324\pi$
$167$	−14.4709	+	6.44287i	−1.11979	+	0.498564i	−0.238504	+	0.971141i	$0.576657\pi$
$168$		0			0
$169$	−3.89989	+	4.33127i	−0.299992	+	0.333174i
$170$	−3.32864	+	2.41840i	−0.255295	+	0.185482i
$171$		0			0
$172$	1.07533	+	3.30954i	0.0819935	+	0.252350i
$173$	−2.54601	+	0.541171i	−0.193569	+	0.0411445i	−0.303676	−	0.952775i	$-0.598214\pi$
$173$	−2.54601	+	0.541171i	−0.193569	+	0.0411445i	0.110107	+	0.993920i	$0.464881\pi$
$174$		0			0
$175$	−7.32717	+	12.6910i	−0.553882	+	0.959352i
$176$	−4.95989	−	1.31116i	−0.373866	−	0.0988322i
$177$		0			0
$178$	1.11681	−	10.6258i	0.0837087	−	0.796435i
$179$	−2.34483	+	7.21663i	−0.175261	+	0.539396i	−0.999645	−	0.0266334i	$-0.991521\pi$
$179$	−2.34483	+	7.21663i	−0.175261	+	0.539396i	0.824385	+	0.566030i	$0.191521\pi$
$180$		0			0
$181$	1.94179	−	1.41080i	0.144332	−	0.104864i	−0.513276	−	0.858224i	$-0.671568\pi$
$181$	1.94179	−	1.41080i	0.144332	−	0.104864i	0.657608	+	0.753360i	$0.271568\pi$
$182$	−6.34584	−	2.82535i	−0.470385	−	0.209429i
$183$		0			0
$184$	3.34472	+	3.71469i	0.246576	+	0.273850i
$185$	8.88066	−	3.95393i	0.652919	−	0.290698i
$186$		0			0
$187$	−12.9641	+	13.0515i	−0.948028	+	0.954419i
$188$	20.0064			1.45911
$189$		0			0
$190$	1.17647	−	3.62081i	0.0853504	−	0.262681i
$191$	11.0529	−	12.2754i	0.799757	−	0.888220i	−0.195966	−	0.980611i	$-0.562784\pi$
$191$	11.0529	−	12.2754i	0.799757	−	0.888220i	0.995723	+	0.0923909i	$0.0294509\pi$
$192$		0			0
$193$	0.850335	+	8.09040i	0.0612085	+	0.582360i	0.981545	+	0.191232i	$0.0612482\pi$
$193$	0.850335	+	8.09040i	0.0612085	+	0.582360i	−0.920336	+	0.391128i	$0.872085\pi$
$194$	−5.20860	−	1.10712i	−0.373956	−	0.0794867i
$195$		0			0
$196$	1.34340	−	12.7816i	0.0959571	−	0.912971i
$197$	22.9072			1.63207			0.816035	−	0.578003i	$-0.196168\pi$
$197$	22.9072			1.63207			0.816035	+	0.578003i	$0.196168\pi$
$198$		0			0
$199$	9.27177			0.657259			0.328629	−	0.944459i	$-0.393413\pi$
$199$	9.27177			0.657259			0.328629	+	0.944459i	$0.393413\pi$
$200$	−0.927464	+	8.82423i	−0.0655816	+	0.623967i
$201$		0			0
$202$	1.14451	+	0.243273i	0.0805273	+	0.0171166i
$203$	−0.442028	−	4.20561i	−0.0310243	−	0.295176i
$204$		0			0
$205$	−2.18104	+	2.42229i	−0.152330	+	0.169180i
$206$	0.551741	−	1.69808i	0.0384416	−	0.118311i
$207$		0			0
$208$	4.14243			0.287226
$209$	2.60634	−	16.8213i	0.180284	−	1.16356i
$210$		0			0
$211$	3.84655	−	1.71260i	0.264808	−	0.117900i	−0.270038	−	0.962850i	$-0.587036\pi$
$211$	3.84655	−	1.71260i	0.264808	−	0.117900i	0.534846	+	0.844950i	$0.320370\pi$
$212$	5.88353	+	6.53432i	0.404082	+	0.448779i
$213$		0			0
$214$	6.23661	+	2.77672i	0.426326	+	0.189812i
$215$	−2.01683	+	1.46531i	−0.137547	+	0.0999334i
$216$		0			0
$217$	0.519021	−	1.59738i	0.0352335	−	0.108437i
$218$	−0.164077	+	1.56109i	−0.0111127	+	0.105730i
$219$		0			0
$220$	−0.321469	−	5.76348i	−0.0216735	−	0.388574i
$221$	7.42687	−	12.8637i	0.499585	−	0.865307i
$222$		0			0
$223$	6.70917	−	1.42608i	0.449280	−	0.0954973i	0.0222853	−	0.999752i	$-0.492906\pi$
$223$	6.70917	−	1.42608i	0.449280	−	0.0954973i	0.426994	+	0.904254i	$0.359572\pi$
$224$	−6.94477	−	21.3738i	−0.464017	−	1.42810i
$225$		0			0
$226$	0.823601	−	0.598381i	0.0547851	−	0.0398037i
$227$	−18.8226	+	20.9046i	−1.24930	+	1.38749i	−0.358221	+	0.933637i	$0.616617\pi$
$227$	−18.8226	+	20.9046i	−1.24930	+	1.38749i	−0.891078	+	0.453850i	$0.850050\pi$
$228$		0			0
$229$	−12.8213	+	5.70843i	−0.847258	+	0.377223i	−0.783990	−	0.620773i	$-0.786819\pi$
$229$	−12.8213	+	5.70843i	−0.847258	+	0.377223i	−0.0632674	+	0.997997i	$0.520152\pi$
$230$	−0.784218	+	1.35831i	−0.0517098	+	0.0895640i
$231$		0			0
$232$	−1.28021	−	2.21739i	−0.0840499	−	0.145579i
$233$	−11.7385	−	8.52854i	−0.769017	−	0.558723i	0.132646	−	0.991163i	$-0.457653\pi$
$233$	−11.7385	−	8.52854i	−0.769017	−	0.558723i	−0.901663	+	0.432440i	$0.857653\pi$
$234$		0			0
$235$	4.42895	+	13.6309i	0.288913	+	0.889182i
$236$	−3.38235	−	1.50592i	−0.220172	−	0.0980269i
$237$		0			0
$238$	−14.0727	−	2.99124i	−0.912196	−	0.193893i
$239$	16.8274	+	18.6887i	1.08847	+	1.20887i	0.976581	+	0.215151i	$0.0690244\pi$
$239$	16.8274	+	18.6887i	1.08847	+	1.20887i	0.111892	+	0.993720i	$0.464309\pi$
$240$		0			0
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	−0.996419	−	0.0845570i	$-0.973053\pi$
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	0.424981	−	0.905202i	$-0.360281\pi$
$242$	1.56731	+	7.13747i	0.100750	+	0.458814i
$243$		0			0
$244$	−5.15048	−	3.74205i	−0.329726	−	0.239560i
$245$	9.00586	−	1.91426i	0.575364	−	0.122297i
$246$		0			0
$247$	1.43668	+	13.6691i	0.0914140	+	0.869746i
$248$	−0.106300	−	1.01138i	−0.00675006	−	0.0642225i
$249$		0			0
$250$	−6.35116	+	1.34998i	−0.401683	+	0.0853803i
$251$	−17.6993	−	12.8593i	−1.11717	−	0.811670i	−0.133390	−	0.991064i	$-0.542586\pi$
$251$	−17.6993	−	12.8593i	−1.11717	−	0.811670i	−0.983777	+	0.179394i	$0.942586\pi$
$252$		0			0
$253$	−2.49108	+	6.55523i	−0.156613	+	0.412124i
$254$	2.54147	+	4.40195i	0.159466	+	0.276203i
$255$		0			0
$256$	−5.87849	−	6.52873i	−0.367406	−	0.408045i
$257$	5.05088	+	1.07360i	0.315065	+	0.0669691i	0.362730	−	0.931894i	$-0.381845\pi$
$257$	5.05088	+	1.07360i	0.315065	+	0.0669691i	−0.0476651	+	0.998863i	$0.515178\pi$
$258$		0			0
$259$	31.0534	+	13.8259i	1.92956	+	0.859097i
$260$	1.44031	+	4.43283i	0.0893244	+	0.274912i
$261$		0			0
$262$	−2.88024	−	2.09262i	−0.177942	−	0.129282i
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	−0.871798	−	0.489866i	$-0.837046\pi$
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	0.0116625	−	0.999932i	$-0.496288\pi$
$264$		0			0
$265$	−3.14954	+	5.45516i	−0.193475	+	0.335108i
$266$	12.1617	−	5.41473i	0.745680	−	0.331998i
$267$		0			0
$268$	10.1706	−	11.2956i	0.621269	−	0.689989i
$269$	2.44290	−	1.77487i	0.148946	−	0.108216i	−0.510816	−	0.859690i	$-0.670657\pi$
$269$	2.44290	−	1.77487i	0.148946	−	0.108216i	0.659763	+	0.751474i	$0.270657\pi$
$270$		0			0
$271$	−7.84125	−	24.1329i	−0.476322	−	1.46597i	−0.844167	−	0.536081i	$-0.819904\pi$
$271$	−7.84125	−	24.1329i	−0.476322	−	1.46597i	0.367845	−	0.929887i	$-0.380096\pi$
$272$	8.39214	−	1.78380i	0.508848	−	0.108159i
$273$		0			0
$274$	5.55744	−	9.62577i	0.335737	−	0.581514i
$275$	−11.6060	+	4.49991i	−0.699866	+	0.271355i
$276$		0			0
$277$	1.10428	−	10.5065i	0.0663497	−	0.631275i	−0.909930	−	0.414762i	$-0.863865\pi$
$277$	1.10428	−	10.5065i	0.0663497	−	0.631275i	0.976280	−	0.216513i	$-0.0694684\pi$
$278$	2.82066	−	8.68109i	0.169172	−	0.520657i
$279$		0			0
$280$	8.33875	−	6.05845i	0.498335	−	0.362062i
$281$	20.6192	+	9.18026i	1.23004	+	0.547648i	0.915776	−	0.401688i	$-0.131576\pi$
$281$	20.6192	+	9.18026i	1.23004	+	0.547648i	0.314261	+	0.949336i	$0.398243\pi$
$282$		0			0
$283$	−3.93264	−	4.36763i	−0.233771	−	0.259629i	0.614833	−	0.788657i	$-0.289223\pi$
$283$	−3.93264	−	4.36763i	−0.233771	−	0.259629i	−0.848604	+	0.529028i	$0.822557\pi$
$284$	8.99503	−	4.00484i	0.533757	−	0.237644i
$285$		0			0
$286$	−2.69639	−	5.24831i	−0.159441	−	0.310339i
$287$	−11.3977			−0.672782
$288$		0			0
$289$	4.25344	−	13.0907i	0.250202	−	0.770044i
$290$	0.537576	−	0.597039i	0.0315676	−	0.0350593i
$291$		0			0
$292$	−1.90178	−	18.0943i	−0.111294	−	1.05889i
$293$	6.93909	+	1.47495i	0.405386	+	0.0861674i	0.406092	−	0.913832i	$-0.366891\pi$
$293$	6.93909	+	1.47495i	0.405386	+	0.0861674i	−0.000705925		1.00000i	$0.500225\pi$
$294$		0			0
$295$	0.277251	−	2.63786i	0.0161422	−	0.153582i
$296$	20.5814			1.19627
$297$		0			0
$298$	−3.69339			−0.213953
$299$	0.591873	−	5.63129i	0.0342289	−	0.325666i
$300$		0			0
$301$	−8.52666	−	1.81240i	−0.491469	−	0.104465i
$302$	0.0113818	+	0.108291i	0.000654949	+	0.00623143i
$303$		0			0
$304$	−5.31215	+	5.89974i	−0.304673	+	0.338373i
$305$	1.40936	−	4.33757i	0.0806999	−	0.248369i
$306$		0			0
$307$	−18.5370			−1.05796			−0.528981	−	0.848633i	$-0.677426\pi$
$307$	−18.5370			−1.05796			−0.528981	+	0.848633i	$0.677426\pi$
$308$	14.2247	−	14.3206i	0.810529	−	0.815993i
$309$		0			0
$310$	0.291506	−	0.129787i	0.0165564	−	0.00737139i
$311$	−4.60110	−	5.11004i	−0.260905	−	0.289764i	0.598433	−	0.801173i	$-0.295790\pi$
$311$	−4.60110	−	5.11004i	−0.260905	−	0.289764i	−0.859337	+	0.511409i	$0.829124\pi$
$312$		0			0
$313$	−23.1363	−	10.3009i	−1.30774	−	0.582243i	−0.369822	−	0.929103i	$-0.620581\pi$
$313$	−23.1363	−	10.3009i	−1.30774	−	0.582243i	−0.937917	+	0.346860i	$0.887248\pi$
$314$	−12.8197	+	9.31407i	−0.723459	+	0.525624i
$315$		0			0
$316$	−2.17455	+	6.69256i	−0.122328	+	0.376486i
$317$	1.14765	−	10.9191i	0.0644582	−	0.613279i	−0.913840	−	0.406075i	$-0.866897\pi$
$317$	1.14765	−	10.9191i	0.0644582	−	0.613279i	0.978298	−	0.207204i	$-0.0664363\pi$
$318$		0			0
$319$	1.94623	−	3.01909i	0.108968	−	0.169037i
$320$	0.407582	−	0.705953i	0.0227845	−	0.0394640i
$321$		0			0
$322$	−5.36457	+	1.14027i	−0.298956	+	0.0635450i
$323$	8.79675	+	27.0736i	0.489464	+	1.50642i
$324$		0			0
$325$	8.13140	−	5.90780i	0.451049	−	0.327706i
$326$	−1.86520	+	2.07152i	−0.103304	+	0.114731i
$327$		0			0
$328$	−6.30437	+	2.80689i	−0.348101	+	0.154984i
$329$	−25.0583	+	43.4023i	−1.38151	+	2.39284i
$330$		0			0
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	0.912495	−	0.409088i	$-0.134153\pi$
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	−0.810528	+	0.585700i	$0.800820\pi$
$332$	−0.607805	−	0.441596i	−0.0333576	−	0.0242357i
$333$		0			0
$334$	−3.25182	−	10.0081i	−0.177931	−	0.547617i
$335$	9.94756	+	4.42894i	0.543493	+	0.241979i
$336$		0			0
$337$	31.4916	+	6.69375i	1.71546	+	0.364632i	0.957670	−	0.287869i	$-0.0929469\pi$
$337$	31.4916	+	6.69375i	1.71546	+	0.364632i	0.757788	+	0.652501i	$0.226280\pi$
$338$	−2.59078	−	2.87735i	−0.140920	−	0.156507i
$339$		0			0
$340$	4.82678	+	8.36023i	0.261769	+	0.453397i
$341$	1.19390	−	0.781045i	0.0646535	−	0.0422960i
$342$		0			0
$343$	3.93417	+	2.85834i	0.212425	+	0.154336i
$344$	−5.16268	+	1.09736i	−0.278353	+	0.0591658i
$345$		0			0
$346$	−0.180746	−	1.71968i	−0.00971694	−	0.0924505i
$347$	−2.24971	−	21.4046i	−0.120771	−	1.14906i	−0.872167	−	0.489207i	$-0.837286\pi$
$347$	−2.24971	−	21.4046i	−0.120771	−	1.14906i	0.751397	−	0.659851i	$-0.229381\pi$
$348$		0			0
$349$	16.4524	−	3.49707i	0.880677	−	0.187194i	0.254686	−	0.967024i	$-0.418028\pi$
$349$	16.4524	−	3.49707i	0.880677	−	0.187194i	0.625991	+	0.779830i	$0.284695\pi$
$350$	−7.87593	−	5.72219i	−0.420986	−	0.305864i
$351$		0			0
$352$	6.78127	−	17.8448i	0.361443	−	0.951129i
$353$	1.56543	+	2.71140i	0.0833193	+	0.144313i	0.904674	−	0.426105i	$-0.140115\pi$
$353$	1.56543	+	2.71140i	0.0833193	+	0.144313i	−0.821355	+	0.570418i	$0.806781\pi$
$354$		0			0
$355$	4.71991	+	5.24199i	0.250507	+	0.278216i
$356$	−24.5205	−	5.21199i	−1.29958	−	0.276235i
$357$		0			0
$358$	−4.60507	−	2.05031i	−0.243385	−	0.108362i
$359$	−2.62315	−	8.07323i	−0.138445	−	0.426089i	0.857665	−	0.514208i	$-0.171914\pi$
$359$	−2.62315	−	8.07323i	−0.138445	−	0.426089i	−0.996110	+	0.0881197i	$0.971914\pi$
$360$		0			0
$361$	−5.93893	−	4.31489i	−0.312575	−	0.227099i
$362$	0.797247	+	1.38087i	0.0419024	+	0.0725770i
$363$		0			0
$364$	−8.14907	+	14.1146i	−0.427127	+	0.739806i
$365$	11.9071	−	5.30140i	0.623248	−	0.277488i
$366$		0			0
$367$	−7.36777	+	8.18274i	−0.384595	+	0.427136i	−0.904093	−	0.427336i	$-0.859452\pi$
$367$	−7.36777	+	8.18274i	−0.384595	+	0.427136i	0.519498	+	0.854471i	$0.326119\pi$
$368$	2.64596	−	1.92241i	0.137930	−	0.100212i
$369$		0			0
$370$	1.99561	+	6.14185i	0.103747	+	0.319300i
$371$	−21.5449	+	4.57951i	−1.11856	+	0.237756i
$372$		0			0
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	−0.972599	−	0.232491i	$-0.925312\pi$
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	0.687642	+	0.726050i	$0.258646\pi$
$374$	−7.72264	−	9.47143i	−0.399328	−	0.489756i
$375$		0			0
$376$	−3.17185	+	30.1781i	−0.163576	+	1.55632i
$377$	−0.896269	+	2.75843i	−0.0461602	+	0.142067i
$378$		0			0
$379$	−20.5384	+	14.9220i	−1.05499	+	0.766492i	−0.973154	−	0.230154i	$-0.926077\pi$
$379$	−20.5384	+	14.9220i	−1.05499	+	0.766492i	−0.0818315	+	0.996646i	$0.526077\pi$
$380$	−8.16035	−	3.63322i	−0.418617	−	0.186380i
$381$		0			0
$382$	7.34264	+	8.15483i	0.375682	+	0.417237i
$383$	11.0674	−	4.92751i	0.565516	−	0.251784i	−0.104006	−	0.994577i	$-0.533166\pi$
$383$	11.0674	−	4.92751i	0.565516	−	0.251784i	0.669521	+	0.742793i	$0.266499\pi$
$384$		0			0
$385$	12.9061	+	6.52146i	0.657755	+	0.332364i
$386$	−5.40422			−0.275068
$387$		0			0
$388$	−3.86080	+	11.8823i	−0.196003	+	0.603234i
$389$	−9.60275	+	10.6649i	−0.486879	+	0.540734i	−0.935658	−	0.352909i	$-0.885192\pi$
$389$	−9.60275	+	10.6649i	−0.486879	+	0.540734i	0.448779	+	0.893643i	$0.351859\pi$
$390$		0			0
$391$	−1.22586	−	11.6633i	−0.0619945	−	0.589838i
$392$	19.0671	+	4.05284i	0.963035	+	0.204699i
$393$		0			0
$394$	−1.59068	+	15.1344i	−0.0801375	+	0.762458i
$395$	−5.04123			−0.253652
$396$		0			0
$397$	−5.03882			−0.252891			−0.126446	−	0.991974i	$-0.540357\pi$
$397$	−5.03882			−0.252891			−0.126446	+	0.991974i	$0.540357\pi$
$398$	−0.643836	+	6.12569i	−0.0322726	+	0.307053i
$399$		0			0
$400$	5.67864	+	1.20703i	0.283932	+	0.0603516i
$401$	−1.90244	−	18.1005i	−0.0950032	−	0.903895i	−0.933401	−	0.358836i	$-0.883174\pi$
$401$	−1.90244	−	18.1005i	−0.0950032	−	0.903895i	0.838398	−	0.545059i	$-0.183493\pi$
$402$		0			0
$403$	−0.770823	+	0.856086i	−0.0383974	+	0.0426447i
$404$	0.848352	−	2.61096i	0.0422071	−	0.129900i
$405$		0			0
$406$	2.80926			0.139421
$407$	13.1948	+	25.6826i	0.654042	+	1.27304i
$408$		0			0
$409$	15.0100	−	6.68287i	0.742195	−	0.330447i	−0.000568948	−	1.00000i	$-0.500181\pi$
$409$	15.0100	−	6.68287i	0.742195	−	0.330447i	0.742764	+	0.669553i	$0.233514\pi$
$410$	−1.44891	−	1.60917i	−0.0715564	−	0.0794715i
$411$		0			0
$412$	−3.82703	−	1.70390i	−0.188544	−	0.0839453i
$413$	7.50342	−	5.45155i	0.369219	−	0.268253i
$414$		0			0
$415$	0.166318	−	0.511874i	0.00816423	−	0.0251269i
$416$	−1.61121	+	15.3296i	−0.0789960	+	0.751596i
$417$		0			0
$418$	10.9326	+	2.89004i	0.534729	+	0.141357i
$419$	−8.70324	+	15.0745i	−0.425181	+	0.736435i	−0.996437	−	0.0843365i	$-0.973123\pi$
$419$	−8.70324	+	15.0745i	−0.425181	+	0.736435i	0.571256	+	0.820772i	$0.306456\pi$
$420$		0			0
$421$	−4.44925	+	0.945717i	−0.216843	+	0.0460914i	−0.315052	−	0.949074i	$-0.602022\pi$
$421$	−4.44925	+	0.945717i	−0.216843	+	0.0460914i	0.0982090	+	0.995166i	$0.468689\pi$
$422$	0.864374	+	2.66027i	0.0420771	+	0.129500i
$423$		0			0
$424$	−10.7893	+	7.83890i	−0.523976	+	0.380691i
$425$	13.9294	−	15.4701i	0.675674	−	0.750412i
$426$		0			0
$427$	14.5692	−	6.48660i	0.705051	−	0.313909i
$428$	8.00879	−	13.8716i	0.387120	−	0.670511i
$429$		0			0
$430$	−0.828055	−	1.43423i	−0.0399323	−	0.0691648i
$431$	10.1004	+	7.33838i	0.486520	+	0.353477i	0.803844	−	0.594840i	$-0.202784\pi$
$431$	10.1004	+	7.33838i	0.486520	+	0.353477i	−0.317325	+	0.948317i	$0.602784\pi$
$432$		0			0
$433$	8.86451	+	27.2822i	0.426001	+	1.31110i	0.902032	+	0.431668i	$0.142075\pi$
$433$	8.86451	+	27.2822i	0.426001	+	1.31110i	−0.476031	+	0.879428i	$0.657925\pi$
$434$	1.01932	+	0.453830i	0.0489289	+	0.0217846i
$435$		0			0
$436$	3.60243	+	0.765720i	0.172525	+	0.0366713i
$437$	7.26121	+	8.06439i	0.347351	+	0.385772i
$438$		0			0
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	0.910871	−	0.412692i	$-0.135411\pi$
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	−0.812837	+	0.582491i	$0.802078\pi$
$440$	8.74476	+	0.428841i	0.416890	+	0.0204442i
$441$		0			0
$442$	7.98309	+	5.80005i	0.379717	+	0.275880i
$443$	−20.7658	+	4.41390i	−0.986612	+	0.209711i	−0.672840	−	0.739788i	$-0.734926\pi$
$443$	−20.7658	+	4.41390i	−0.986612	+	0.209711i	−0.313772	+	0.949498i	$0.601593\pi$
$444$		0			0
$445$	−1.87720	−	17.8603i	−0.0889876	−	0.846660i
$446$	0.476296	+	4.53165i	0.0225533	+	0.214580i
$447$		0			0
$448$	2.78813	−	0.592635i	0.131727	−	0.0279994i
$449$	20.9494	+	15.2206i	0.988663	+	0.718306i	0.959628	−	0.281273i	$-0.0907566\pi$
$449$	20.9494	+	15.2206i	0.988663	+	0.718306i	0.0290350	+	0.999578i	$0.490757\pi$
$450$		0			0
$451$	−7.54435	−	6.06744i	−0.355249	−	0.285705i
$452$	−1.19428	−	2.06856i	−0.0561744	−	0.0972970i
$453$		0			0
$454$	−12.5042	−	13.8874i	−0.586853	−	0.651766i
$455$	−11.4207	−	2.42754i	−0.535410	−	0.113805i
$456$		0			0
$457$	−9.41304	−	4.19096i	−0.440323	−	0.196045i	0.174587	−	0.984642i	$-0.444141\pi$
$457$	−9.41304	−	4.19096i	−0.440323	−	0.196045i	−0.614910	+	0.788597i	$0.710808\pi$
$458$	−2.88113	−	8.86721i	−0.134626	−	0.414338i
$459$		0			0
$460$	2.97717	+	2.16304i	0.138811	+	0.100852i
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	−0.993862	−	0.110628i	$-0.964714\pi$
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	0.401124	−	0.916024i	$-0.368620\pi$
$462$		0			0
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.136368	−	0.990658i	$-0.456457\pi$
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.789751	−	0.613427i	$-0.210210\pi$
$464$	−1.53045	+	0.681400i	−0.0710493	+	0.0316332i
$465$		0			0
$466$	6.44977	−	7.16320i	0.298780	−	0.331829i
$467$	−14.0582	+	10.2139i	−0.650537	+	0.472643i	−0.863454	−	0.504427i	$-0.831704\pi$
$467$	−14.0582	+	10.2139i	−0.650537	+	0.472643i	0.212917	+	0.977070i	$0.431704\pi$
$468$		0			0
$469$	11.7661	+	36.2123i	0.543308	+	1.67213i
$470$	−9.31323	+	1.97959i	−0.429587	+	0.0913116i
$471$		0			0
$472$	2.80781	−	4.86327i	0.129240	−	0.223850i
$473$	−4.67916	−	5.73876i	−0.215148	−	0.263868i
$474$		0			0
$475$	−2.01348	+	19.1569i	−0.0923846	+	0.878980i
$476$	−10.4312	+	32.1039i	−0.478112	+	1.47148i
$477$		0			0
$478$	−13.5158	+	9.81979i	−0.618197	+	0.449147i
$479$	20.0030	+	8.90589i	0.913959	+	0.406921i	0.809170	−	0.587574i	$-0.199917\pi$
$479$	20.0030	+	8.90589i	0.913959	+	0.406921i	0.104788	+	0.994495i	$0.466584\pi$
$480$		0			0
$481$	−15.6002	−	17.3258i	−0.711309	−	0.789988i
$482$	10.7675	−	4.79400i	0.490447	−	0.218361i
$483$		0			0
$484$	17.0391	−	1.90671i	0.774505	−	0.0866687i
$485$	−8.95046			−0.406420
$486$		0			0
$487$	1.01084	−	3.11106i	0.0458057	−	0.140975i	−0.925538	−	0.378655i	$-0.876387\pi$
$487$	1.01084	−	3.11106i	0.0458057	−	0.140975i	0.971344	+	0.237679i	$0.0763867\pi$
$488$	6.46117	−	7.17586i	0.292483	−	0.324836i
$489$		0			0
$490$	0.639342	+	6.08293i	0.0288825	+	0.274799i
$491$	−7.06604	−	1.50193i	−0.318886	−	0.0677813i	0.0456879	−	0.998956i	$-0.485452\pi$
$491$	−7.06604	−	1.50193i	−0.318886	−	0.0677813i	−0.364574	+	0.931174i	$0.618785\pi$
$492$		0			0
$493$	−0.627919	+	5.97425i	−0.0282801	+	0.269067i
$494$	−9.13071			−0.410810
$495$		0			0
$496$	−0.665390			−0.0298769
$497$	−2.57822	+	24.5302i	−0.115649	+	1.10033i
$498$		0			0
$499$	−14.5103	−	3.08427i	−0.649572	−	0.138071i	−0.128670	−	0.991687i	$-0.541071\pi$
$499$	−14.5103	−	3.08427i	−0.649572	−	0.138071i	−0.520902	+	0.853617i	$0.674404\pi$
$500$	1.59244	+	15.1510i	0.0712159	+	0.677574i
$501$		0			0
$502$	9.72492	−	10.8006i	0.434044	−	0.482055i
$503$	10.1918	−	31.3671i	0.454430	−	1.39859i	−0.417374	−	0.908735i	$-0.637049\pi$
$503$	10.1918	−	31.3671i	0.454430	−	1.39859i	0.871803	−	0.489856i	$-0.162951\pi$
$504$		0			0
$505$	1.96673			0.0875181
$506$	−4.15794	−	2.10101i	−0.184843	−	0.0934013i
$507$		0			0
$508$	10.8949	−	4.85073i	0.483383	−	0.215216i
$509$	−25.8749	−	28.7370i	−1.14688	−	1.27374i	−0.956402	−	0.292052i	$-0.905662\pi$
$509$	−25.8749	−	28.7370i	−1.14688	−	1.27374i	−0.190481	−	0.981691i	$-0.561005\pi$
$510$		0			0
$511$	41.6361	+	18.5376i	1.84187	+	0.820055i
$512$	−13.1198	+	9.53213i	−0.579821	+	0.421264i
$513$		0			0
$514$	−1.06004	+	3.26247i	−0.0467564	+	0.143901i
$515$	0.313701	−	2.98467i	0.0138233	−	0.131520i
$516$		0			0
$517$	−39.6915	+	15.3893i	−1.74563	+	0.676821i
$518$	−11.2908	+	19.5563i	−0.496091	+	0.859255i
$519$		0			0
$520$	−6.91494	+	1.46982i	−0.303240	+	0.0644557i
$521$	5.40297	+	16.6286i	0.236708	+	0.728514i	0.996890	+	0.0788032i	$0.0251099\pi$
$521$	5.40297	+	16.6286i	0.236708	+	0.728514i	−0.760182	+	0.649710i	$0.774890\pi$
$522$		0			0
$523$	−11.7211	+	8.51591i	−0.512530	+	0.372375i	−0.813782	−	0.581170i	$-0.802595\pi$
$523$	−11.7211	+	8.51591i	−0.512530	+	0.372375i	0.301253	+	0.953544i	$0.402595\pi$
$524$	−5.58934	+	6.20760i	−0.244172	+	0.271180i
$525$		0			0
$526$	16.9310	−	7.53816i	0.738226	−	0.328680i
$527$	−1.19296	+	2.06627i	−0.0519663	+	0.0900082i
$528$		0			0
$529$	9.26470	+	16.0469i	0.402813	+	0.697693i
$530$	−3.38542	−	2.45965i	−0.147053	−	0.106840i
$531$		0			0
$532$	−9.65216	−	29.7063i	−0.418474	−	1.28793i
$533$	7.14146	+	3.17958i	0.309331	+	0.137723i
$534$		0			0
$535$	11.2241	+	2.38576i	0.485260	+	0.103145i
$536$	15.4261	+	17.1325i	0.666307	+	0.740009i
$537$		0			0
$538$	1.00299	+	1.73722i	0.0432418	+	0.0748971i
$539$	7.16664	+	26.3913i	0.308689	+	1.13675i
$540$		0			0
$541$	−26.7771	−	19.4547i	−1.15124	−	0.836422i	−0.162591	−	0.986694i	$-0.551985\pi$
$541$	−26.7771	−	19.4547i	−1.15124	−	0.836422i	−0.988645	+	0.150272i	$0.951985\pi$
$542$	16.4886	−	3.50477i	0.708248	−	0.150543i
$543$		0			0
$544$	3.33706	+	31.7500i	0.143075	+	1.36127i
$545$	0.275788	+	2.62395i	0.0118135	+	0.112398i
$546$		0			0
$547$	−9.01278	+	1.91573i	−0.385359	+	0.0819105i	−0.396517	−	0.918027i	$-0.629781\pi$
$547$	−9.01278	+	1.91573i	−0.385359	+	0.0819105i	0.0111586	+	0.999938i	$0.496448\pi$
$548$	−21.0980	−	15.3286i	−0.901262	−	0.654805i
$549$		0			0
$550$	−2.16708	−	7.98032i	−0.0924046	−	0.340282i
$551$	−2.77927	−	4.81383i	−0.118401	−	0.205076i
$552$		0			0
$553$	−11.7953	−	13.1001i	−0.501589	−	0.557071i
$554$	6.86477	+	1.45915i	0.291656	+	0.0619935i
$555$		0			0
$556$	−19.5649	−	8.71084i	−0.829735	−	0.369422i
$557$	−11.4496	−	35.2384i	−0.485137	−	1.49310i	−0.831782	−	0.555102i	$-0.812679\pi$
$557$	−11.4496	−	35.2384i	−0.485137	−	1.49310i	0.346645	−	0.937996i	$-0.387321\pi$
$558$		0			0
$559$	4.83697	+	3.51427i	0.204582	+	0.148638i
$560$	−3.37202	−	5.84052i	−0.142494	−	0.246807i
$561$		0			0
$562$	−7.49703	+	12.9852i	−0.316243	+	0.547749i
$563$	24.6603	−	10.9795i	1.03931	−	0.462730i	0.185132	−	0.982714i	$-0.440729\pi$
$563$	24.6603	−	10.9795i	1.03931	−	0.462730i	0.854176	+	0.519984i	$0.174062\pi$
$564$		0			0
$565$	1.14498	−	1.27163i	0.0481698	−	0.0534980i
$566$	3.15870	−	2.29493i	0.132770	−	0.0964630i
$567$		0			0
$568$	4.61492	+	14.2033i	0.193638	+	0.595956i
$569$	−26.8753	+	5.71252i	−1.12667	+	0.239481i	−0.733305	−	0.679900i	$-0.762023\pi$
$569$	−26.8753	+	5.71252i	−1.12667	+	0.239481i	−0.393367	+	0.919382i	$0.628690\pi$
$570$		0			0
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	−0.0921492	−	0.995745i	$-0.529374\pi$
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	0.908415	−	0.418069i	$-0.137293\pi$
$572$	−12.9078	+	5.00466i	−0.539703	+	0.209256i
$573$		0			0
$574$	0.791458	−	7.53022i	0.0330348	−	0.314305i
$575$	2.45223	−	7.54719i	0.102265	−	0.314739i
$576$		0			0
$577$	23.5957	−	17.1433i	0.982302	−	0.713684i	0.0240800	−	0.999710i	$-0.492334\pi$
$577$	23.5957	−	17.1433i	0.982302	−	0.713684i	0.958222	+	0.286026i	$0.0923344\pi$
$578$	8.35345	+	3.71920i	0.347458	+	0.154698i
$579$		0			0
$580$	−1.26130	−	1.40082i	−0.0523727	−	0.0581658i
$581$	1.71930	−	0.765480i	0.0713284	−	0.0317575i
$582$		0			0
$583$	−16.6989	−	8.43797i	−0.691598	−	0.349465i
$584$	27.5954			1.14191
$585$		0			0
$586$	−1.45632	+	4.48210i	−0.0601602	+	0.185154i
$587$	3.40449	−	3.78107i	0.140518	−	0.156062i	−0.668778	−	0.743463i	$-0.733182\pi$
$587$	3.40449	−	3.78107i	0.140518	−	0.156062i	0.809296	+	0.587401i	$0.199849\pi$
$588$		0			0
$589$	−0.230772	−	2.19565i	−0.00950878	−	0.0904700i
$590$	1.72353	+	0.366349i	0.0709568	+	0.0150823i
$591$		0			0
$592$	1.40762	−	13.3927i	0.0578530	−	0.550435i
$593$	−3.46422			−0.142258			−0.0711292	−	0.997467i	$-0.522660\pi$
$593$	−3.46422			−0.142258			−0.0711292	+	0.997467i	$0.522660\pi$
$594$		0			0
$595$	−24.1825			−0.991386
$596$	−0.905814	+	8.61825i	−0.0371036	+	0.353017i
$597$		0			0
$598$	3.67939	+	0.782079i	0.150461	+	0.0319816i
$599$	2.60013	+	24.7386i	0.106238	+	1.01079i	0.909653	+	0.415370i	$0.136348\pi$
$599$	2.60013	+	24.7386i	0.106238	+	1.01079i	−0.803414	+	0.595421i	$0.796985\pi$
$600$		0			0
$601$	7.40602	−	8.22522i	0.302098	−	0.335514i	−0.572914	−	0.819616i	$-0.694187\pi$
$601$	7.40602	−	8.22522i	0.302098	−	0.335514i	0.875012	+	0.484102i	$0.160854\pi$
$602$	1.78951	−	5.50755i	0.0729351	−	0.224471i
$603$		0			0
$604$	0.255479			0.0103953
$605$	5.07116	+	11.1871i	0.206172	+	0.454821i
$606$		0			0
$607$	−25.5436	+	11.3728i	−1.03678	+	0.461606i	−0.853302	−	0.521417i	$-0.825404\pi$
$607$	−25.5436	+	11.3728i	−1.03678	+	0.461606i	−0.183483	+	0.983023i	$0.558737\pi$
$608$	−19.7666	−	21.9530i	−0.801642	−	0.890313i
$609$		0			0
$610$	2.76789	+	1.23234i	0.112068	+	0.0498961i
$611$	27.8087	−	20.2042i	1.12502	−	0.817375i
$612$		0			0
$613$	3.39680	−	10.4543i	0.137196	−	0.422245i	−0.858729	−	0.512429i	$-0.828746\pi$
$613$	3.39680	−	10.4543i	0.137196	−	0.422245i	0.995925	+	0.0901845i	$0.0287457\pi$
$614$	1.28722	−	12.2471i	0.0519479	−	0.494251i
$615$		0			0
$616$	19.3464	+	23.7274i	0.779489	+	0.956004i
$617$	9.31311	−	16.1308i	0.374932	−	0.649401i	−0.615385	−	0.788227i	$-0.710999\pi$
$617$	9.31311	−	16.1308i	0.374932	−	0.649401i	0.990317	+	0.138826i	$0.0443328\pi$
$618$		0			0
$619$	−2.62973	+	0.558967i	−0.105698	+	0.0224668i	−0.260457	−	0.965485i	$-0.583873\pi$
$619$	−2.62973	+	0.558967i	−0.105698	+	0.0224668i	0.154759	+	0.987952i	$0.450540\pi$
$620$	−0.231355	−	0.712036i	−0.00929142	−	0.0285961i
$621$		0			0
$622$	3.69561	−	2.68502i	0.148180	−	0.107659i
$623$	42.0193	−	46.6672i	1.68347	−	1.86968i
$624$		0			0
$625$	7.17308	−	3.19366i	0.286923	−	0.127746i
$626$	8.41222	−	14.5704i	0.336220	−	0.582350i
$627$		0			0
$628$	18.5896	+	32.1981i	0.741805	+	1.28484i
$629$	−39.0652	−	28.3826i	−1.55763	−	1.13169i
$630$		0			0
$631$	−12.1224	−	37.3089i	−0.482585	−	1.48524i	−0.835448	−	0.549569i	$-0.814792\pi$
$631$	−12.1224	−	37.3089i	−0.482585	−	1.48524i	0.352863	−	0.935675i	$-0.385208\pi$
$632$	−9.75049	−	4.34120i	−0.387853	−	0.172683i
$633$		0			0
$634$	7.13437	+	1.51646i	0.283342	+	0.0602262i
$635$	5.71682	+	6.34917i	0.226865	+	0.251959i
$636$		0			0
$637$	−11.0407	−	19.1230i	−0.437447	−	0.757681i
$638$	1.85951	+	1.49549i	0.0736187	+	0.0592069i
$639$		0			0
$640$	−9.96109	−	7.23716i	−0.393747	−	0.286074i
$641$	25.1863	−	5.35351i	0.994799	−	0.211451i	0.318376	−	0.947965i	$-0.396863\pi$
$641$	25.1863	−	5.35351i	0.994799	−	0.211451i	0.676423	+	0.736514i	$0.263529\pi$
$642$		0			0
$643$	1.39358	+	13.2590i	0.0549574	+	0.522885i	0.987021	+	0.160590i	$0.0513398\pi$
$643$	1.39358	+	13.2590i	0.0549574	+	0.522885i	−0.932064	+	0.362294i	$0.881993\pi$
$644$	1.34507	+	12.7975i	0.0530030	+	0.504290i
$645$		0			0
$646$	−18.4979	+	3.93185i	−0.727789	+	0.154696i
$647$	19.2955	+	14.0190i	0.758585	+	0.551145i	0.898476	−	0.439022i	$-0.144675\pi$
$647$	19.2955	+	14.0190i	0.758585	+	0.551145i	−0.139891	+	0.990167i	$0.544675\pi$
$648$		0			0
$649$	7.86876	+	0.385882i	0.308876	+	0.0151472i
$650$	3.33853	+	5.78250i	0.130948	+	0.226808i
$651$		0			0
$652$	4.37628	+	4.86035i	0.171388	+	0.190346i
$653$	12.4469	+	2.64566i	0.487083	+	0.103533i	0.444906	−	0.895577i	$-0.353237\pi$
$653$	12.4469	+	2.64566i	0.487083	+	0.103533i	0.0421776	+	0.999110i	$0.486570\pi$
$654$		0			0
$655$	−5.46676	−	2.43396i	−0.213604	−	0.0951027i
$656$	1.39531	+	4.29433i	0.0544778	+	0.167666i
$657$		0			0
$658$	−26.9350	−	19.5694i	−1.05004	−	0.762896i
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	−0.999354	−	0.0359452i	$-0.988556\pi$
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	0.468547	−	0.883438i	$-0.344777\pi$
$660$		0			0
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	0.0335234	+	0.999438i	$0.489327\pi$
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	−0.882300	+	0.470687i	$0.844006\pi$
$662$	−2.25170	+	1.00252i	−0.0875150	+	0.0389642i
$663$		0			0
$664$	0.762478	−	0.846818i	0.0295899	−	0.0328629i
$665$	18.1030	−	13.1526i	0.702003	−	0.510035i
$666$		0			0
$667$	0.707636	+	2.17788i	0.0273998	+	0.0843278i
$668$	−24.1505	+	5.13336i	−0.934413	+	0.198616i
$669$		0			0
$670$	−3.61688	+	6.26462i	−0.139732	+	0.242023i
$671$	13.0967	+	3.46214i	0.505593	+	0.133654i
$672$		0			0
$673$	2.78952	−	26.5405i	0.107528	−	1.02306i	−0.799120	−	0.601172i	$-0.794701\pi$
$673$	2.78952	−	26.5405i	0.107528	−	1.02306i	0.906648	−	0.421889i	$-0.138633\pi$
$674$	−6.60922	+	20.3411i	−0.254578	+	0.783510i
$675$		0			0
$676$	−7.34946	+	5.33970i	−0.282672	+	0.205373i
$677$	−24.7416	−	11.0157i	−0.950897	−	0.423367i	−0.128138	−	0.991756i	$-0.540900\pi$
$677$	−24.7416	−	11.0157i	−0.950897	−	0.423367i	−0.822759	+	0.568390i	$0.807567\pi$
$678$		0			0
$679$	−20.9421	−	23.2585i	−0.803683	−	0.892581i
$680$	−13.3760	+	5.95540i	−0.512948	+	0.228379i
$681$		0			0
$682$	0.433117	+	0.843026i	0.0165849	+	0.0322811i
$683$	16.7343			0.640322			0.320161	−	0.947363i	$-0.396263\pi$
$683$	16.7343			0.640322			0.320161	+	0.947363i	$0.396263\pi$
$684$		0			0
$685$	5.77319	−	17.7681i	0.220582	−	0.678883i
$686$	−2.16165	+	2.40075i	−0.0825320	+	0.0916611i
$687$		0			0
$688$	0.360980	+	3.43449i	0.0137622	+	0.130939i
$689$	14.7770	+	3.14095i	0.562958	+	0.119661i
$690$		0			0
$691$	3.92186	−	37.3140i	0.149195	−	1.41949i	−0.622062	−	0.782968i	$-0.713705\pi$
$691$	3.92186	−	37.3140i	0.149195	−	1.41949i	0.771256	−	0.636525i	$-0.219629\pi$
$692$	−4.05707			−0.154226
$693$		0			0
$694$	14.2978			0.542738
$695$	1.60373	−	15.2585i	0.0608330	−	0.578787i
$696$		0			0
$697$	15.8370	+	3.36627i	0.599871	+	0.127507i
$698$	1.16798	+	11.1126i	0.0442089	+	0.420619i
$699$		0			0
$700$	−15.2839	+	16.9745i	−0.577676	+	0.641575i
$701$	−3.15219	+	9.70143i	−0.119056	+	0.366418i	−0.992771	−	0.120020i	$-0.961704\pi$
$701$	−3.15219	+	9.70143i	−0.119056	+	0.366418i	0.873715	+	0.486438i	$0.161704\pi$
$702$		0			0
$703$	44.6811			1.68518
$704$	2.16101	+	1.09196i	0.0814460	+	0.0411548i
$705$		0			0
$706$	−1.90007	+	0.845967i	−0.0715102	+	0.0318384i
$707$	4.60170	+	5.11070i	0.173065	+	0.192208i
$708$		0			0
$709$	−13.2443	−	5.89673i	−0.497399	−	0.221457i	0.142675	−	0.989770i	$-0.454430\pi$
$709$	−13.2443	−	5.89673i	−0.497399	−	0.221457i	−0.640074	+	0.768313i	$0.721096\pi$
$710$	−3.79104	+	2.75435i	−0.142275	+	0.103369i
$711$		0			0
$712$	11.7494	−	36.1610i	0.440329	−	1.35519i
$713$	−0.0950714	+	0.904544i	−0.00356045	+	0.0338754i
$714$		0			0
$715$	−6.26732	−	7.68655i	−0.234384	−	0.287461i
$716$	−5.91364	+	10.2427i	−0.221003	+	0.382789i
$717$		0			0
$718$	5.51598	−	1.17246i	0.205855	−	0.0437558i
$719$	−5.94135	−	18.2856i	−0.221575	−	0.681938i	−0.998621	−	0.0524943i	$-0.983283\pi$
$719$	−5.94135	−	18.2856i	−0.221575	−	0.681938i	0.777046	−	0.629444i	$-0.216717\pi$
$720$		0			0
$721$	8.48991	−	6.16828i	0.316181	−	0.229719i
$722$	3.26317	−	3.62411i	0.121442	−	0.134876i
$723$		0			0
$724$	3.41768	−	1.52165i	0.127017	−	0.0565517i
$725$	−2.03241	+	3.52023i	−0.0754818	+	0.130738i
$726$		0			0
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	0.859208	−	0.511627i	$-0.170957\pi$
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	−0.872686	+	0.488282i	$0.837624\pi$
$728$	−19.9989	−	14.5300i	−0.741207	−	0.538519i
$729$		0			0
$730$	2.67570	+	8.23495i	0.0990320	+	0.304789i
$731$	11.3125	+	5.03666i	0.418408	+	0.186287i
$732$		0			0
$733$	1.83490	+	0.390019i	0.0677734	+	0.0144057i	0.241674	−	0.970358i	$-0.422304\pi$
$733$	1.83490	+	0.390019i	0.0677734	+	0.0144057i	−0.173900	+	0.984763i	$0.555637\pi$
$734$	−4.89456	−	5.43596i	−0.180662	−	0.200645i
$735$		0			0
$736$	6.08497	+	10.5395i	0.224295	+	0.388490i
$737$	−11.4891	+	30.2333i	−0.423206	+	1.11366i
$738$		0			0
$739$	42.5402	+	30.9073i	1.56487	+	1.13694i	0.931873	+	0.362784i	$0.118174\pi$
$739$	42.5402	+	30.9073i	1.56487	+	1.13694i	0.632993	+	0.774157i	$0.281826\pi$
$740$	14.8210	−	3.15029i	0.544829	−	0.115807i
$741$		0			0
$742$	−1.52951	−	14.5523i	−0.0561501	−	0.534233i
$743$	−3.48423	−	33.1502i	−0.127824	−	1.21616i	−0.850875	−	0.525368i	$-0.823928\pi$
$743$	−3.48423	−	33.1502i	−0.127824	−	1.21616i	0.723051	−	0.690795i	$-0.242739\pi$
$744$		0			0
$745$	−6.07238	+	1.29072i	−0.222475	+	0.0472885i
$746$	−5.91558	−	4.29792i	−0.216585	−	0.157358i
$747$		0			0
$748$	−23.9948	+	15.6973i	−0.877338	+	0.573949i
$749$	20.0623	+	34.7489i	0.733060	+	1.26970i
$750$		0			0
$751$	−15.6336	−	17.3629i	−0.570479	−	0.633581i	0.387002	−	0.922079i	$-0.373511\pi$
$751$	−15.6336	−	17.3629i	−0.570479	−	0.633581i	−0.957480	+	0.288498i	$0.906844\pi$
$752$	19.4205	+	4.12795i	0.708192	+	0.150531i
$753$		0			0
$754$	−1.76021	−	0.783695i	−0.0641030	−	0.0285405i
$755$	0.0565572	+	0.174065i	0.00205833	+	0.00633488i
$756$		0			0
$757$	27.3472	+	19.8689i	0.993952	+	0.722148i	0.960783	−	0.277302i	$-0.0894401\pi$
$757$	27.3472	+	19.8689i	0.993952	+	0.722148i	0.0331687	+	0.999450i	$0.489440\pi$
$758$	−8.43250	−	14.6055i	−0.306282	−	0.530496i
$759$		0			0
$760$	6.77421	−	11.7333i	0.245726	−	0.425611i
$761$	−18.3731	+	8.18025i	−0.666026	+	0.296534i	−0.711763	−	0.702420i	$-0.752103\pi$
$761$	−18.3731	+	8.18025i	−0.666026	+	0.296534i	0.0457371	+	0.998954i	$0.485436\pi$
$762$		0			0
$763$	−6.17328	+	6.85612i	−0.223488	+	0.248208i
$764$	20.8294	−	15.1335i	0.753583	−	0.547510i
$765$		0			0
$766$	2.48699	+	7.65417i	0.0898586	+	0.276556i
$767$	−6.22224	+	1.32258i	−0.224672	+	0.0477555i
$768$		0			0
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	−0.871623	−	0.490178i	$-0.836932\pi$
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	0.860318	+	0.509759i	$0.170265\pi$
$770$	−5.20481	+	8.07395i	−0.187568	+	0.290965i
$771$		0			0
$772$	−1.32540	+	12.6103i	−0.0477021	+	0.453856i
$773$	−8.88046	+	27.3313i	−0.319408	+	0.983037i	0.654494	+	0.756067i	$0.272882\pi$
$773$	−8.88046	+	27.3313i	−0.319408	+	0.983037i	−0.973902	+	0.226970i	$0.927118\pi$
$774$		0			0
$775$	−1.30613	+	0.948959i	−0.0469176	+	0.0340876i
$776$	−17.3115	−	7.70759i	−0.621448	−	0.276686i
$777$		0			0
$778$	−6.37930	−	7.08493i	−0.228709	−	0.254007i
$779$	−13.6865	+	6.09360i	−0.490368	+	0.218326i
$780$		0			0
$781$	−14.7650	+	14.8645i	−0.528333	+	0.531895i
$782$	7.79085			0.278600
$783$		0			0
$784$	3.94131	−	12.1301i	0.140761	−	0.433218i
$785$	−17.8222	+	19.7935i	−0.636101	+	0.706462i
$786$		0			0
$787$	1.47416	+	14.0257i	0.0525481	+	0.499962i	0.988866	+	0.148808i	$0.0475437\pi$
$787$	1.47416	+	14.0257i	0.0525481	+	0.499962i	−0.936318	+	0.351153i	$0.885790\pi$
$788$	34.9247	+	7.42347i	1.24414	+	0.264450i
$789$		0			0
$790$	0.350065	−	3.33065i	0.0124548	−	0.118499i
$791$	5.98345			0.212747
$792$		0			0
$793$	−10.9382			−0.388426
$794$	0.349898	−	3.32906i	0.0124174	−	0.118144i
$795$		0			0
$796$	14.1359	+	3.00468i	0.501034	+	0.106498i
$797$	2.73391	+	26.0114i	0.0968400	+	0.921371i	0.929807	+	0.368048i	$0.119974\pi$
$797$	2.73391	+	26.0114i	0.0968400	+	0.921371i	−0.832967	+	0.553323i	$0.813359\pi$
$798$		0			0
$799$	47.6373	−	52.9066i	1.68529	−	1.87170i
$800$	−6.67551	+	20.5451i	−0.236015	+	0.726379i
$801$		0			0
$802$	12.0908			0.426939
$803$	17.6915	+	34.4351i	0.624320	+	1.21519i
$804$		0			0
$805$	−8.42150	+	3.74949i	−0.296819	+	0.132152i
$806$	−0.512074	−	0.568715i	−0.0180370	−	0.0200321i
$807$		0			0
$808$	3.80394	+	1.69362i	0.133822	+	0.0595814i
$809$	12.8256	−	9.31836i	0.450925	−	0.327616i	−0.339036	−	0.940773i	$-0.610101\pi$
$809$	12.8256	−	9.31836i	0.450925	−	0.327616i	0.789961	+	0.613157i	$0.210101\pi$
$810$		0			0
$811$	−11.2255	+	34.5484i	−0.394179	+	1.21316i	0.535420	+	0.844586i	$0.320154\pi$
$811$	−11.2255	+	34.5484i	−0.394179	+	1.21316i	−0.929599	+	0.368573i	$0.879846\pi$
$812$	0.688979	−	6.55520i	0.0241784	−	0.230042i
$813$		0			0
$814$	−17.8843	+	6.93415i	−0.626844	+	0.243042i
$815$	−2.34269	+	4.05766i	−0.0820608	+	0.142134i
$816$		0			0
$817$	−11.2079	+	2.38231i	−0.392115	+	0.0833466i
$818$	3.37295	+	10.3809i	0.117932	+	0.362958i
$819$		0			0
$820$	−4.11023	+	2.98626i	−0.143535	+	0.104285i
$821$	10.9448	−	12.1554i	0.381976	−	0.424227i	−0.521242	−	0.853409i	$-0.674531\pi$
$821$	10.9448	−	12.1554i	0.381976	−	0.424227i	0.903218	+	0.429181i	$0.141198\pi$
$822$		0			0
$823$	−23.9116	+	10.6461i	−0.833506	+	0.371101i	−0.778700	−	0.627396i	$-0.784121\pi$
$823$	−23.9116	+	10.6461i	−0.833506	+	0.371101i	−0.0548060	+	0.998497i	$0.517454\pi$
$824$	3.17696	−	5.50265i	0.110675	−	0.191694i
$825$		0			0
$826$	3.08070	+	5.33592i	0.107191	+	0.185661i
$827$	4.48139	+	3.25592i	0.155833	+	0.113219i	0.662969	−	0.748647i	$-0.269296\pi$
$827$	4.48139	+	3.25592i	0.155833	+	0.113219i	−0.507136	+	0.861866i	$0.669296\pi$
$828$		0			0
$829$	5.71784	+	17.5977i	0.198589	+	0.611194i	0.999916	+	0.0129672i	$0.00412771\pi$
$829$	5.71784	+	17.5977i	0.198589	+	0.611194i	−0.801327	+	0.598227i	$0.795872\pi$
$830$	0.326637	+	0.145428i	0.0113377	+	0.00504788i
$831$		0			0
$832$	−1.91229	−	0.406470i	−0.0662968	−	0.0140918i
$833$	−30.6020	−	33.9869i	−1.06030	−	1.17758i
$834$		0			0
$835$	−8.84388	−	15.3180i	−0.306055	−	0.530103i
$836$	9.42492	−	24.8015i	0.325968	−	0.857776i
$837$		0			0
$838$	−9.35505	−	6.79684i	−0.323165	−	0.234793i
$839$	−17.5727	+	3.73519i	−0.606677	+	0.128953i	−0.501000	−	0.865447i	$-0.667034\pi$
$839$	−17.5727	+	3.73519i	−0.606677	+	0.128953i	−0.105677	+	0.994400i	$0.533701\pi$
$840$		0			0
$841$	2.90872	+	27.6746i	0.100301	+	0.954296i
$842$	−0.315860	−	3.00520i	−0.0108852	−	0.103566i
$843$		0			0
$844$	6.41952	−	1.36451i	0.220969	−	0.0469684i
$845$	−5.26509	−	3.82531i	−0.181125	−	0.131595i
$846$		0			0
$847$	−17.2053	+	39.3532i	−0.591182	+	1.35219i
$848$	4.36299	+	7.55692i	0.149826	+	0.259506i
$849$		0			0
$850$	9.25357	+	10.2771i	0.317395	+	0.352503i
$851$	−18.0051	−	3.82710i	−0.617207	−	0.131191i
$852$		0			0
$853$	25.4999	+	11.3533i	0.873099	+	0.388729i	0.793841	−	0.608125i	$-0.208078\pi$
$853$	25.4999	+	11.3533i	0.873099	+	0.388729i	0.0792581	+	0.996854i	$0.474745\pi$
$854$	3.27389	+	10.0760i	0.112030	+	0.344794i
$855$		0			0
$856$	19.6546	+	14.2799i	0.671781	+	0.488077i
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	0.784265	−	0.620426i	$-0.213040\pi$
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	−0.929437	+	0.368981i	$0.879707\pi$
$858$		0			0
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	−0.999595	−	0.0284667i	$-0.990938\pi$
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	0.524450	+	0.851441i	$0.324271\pi$
$860$	−3.54975	+	1.58045i	−0.121046	+	0.0538929i
$861$		0			0
$862$	−5.54971	+	6.16357i	−0.189024	+	0.209932i
$863$	10.9978	−	7.99035i	0.374368	−	0.271995i	−0.384652	−	0.923062i	$-0.625678\pi$
$863$	10.9978	−	7.99035i	0.374368	−	0.271995i	0.759020	+	0.651067i	$0.225678\pi$
$864$		0			0
$865$	−0.898141	−	2.76419i	−0.0305377	−	0.0939854i
$866$	−18.6404	+	3.96213i	−0.633425	+	0.134639i
$867$		0			0
$868$	1.30897	−	2.26720i	0.0444293	−	0.0769538i
$869$	−0.833885	−	14.9504i	−0.0282876	−	0.507156i
$870$		0			0
$871$	2.72977	−	25.9720i	0.0924946	−	0.880028i
$872$	−1.72617	+	5.31260i	−0.0584555	+	0.179907i
$873$		0			0
$874$	−5.83221	+	4.23735i	−0.197278	+	0.143331i
$875$	−34.8635	−	15.5222i	−1.17860	−	0.524748i
$876$		0			0
$877$	24.2078	+	26.8855i	0.817439	+	0.907858i	0.997118	−	0.0758674i	$-0.0241726\pi$
$877$	24.2078	+	26.8855i	0.817439	+	0.907858i	−0.179679	+	0.983725i	$0.557506\pi$
$878$	−2.49314	+	1.11002i	−0.0841392	+	0.0374612i
$879$		0			0
$880$	0.877135	−	5.66103i	0.0295682	−	0.190833i
$881$	−26.6423			−0.897601			−0.448800	−	0.893632i	$-0.648149\pi$
$881$	−26.6423			−0.897601			−0.448800	+	0.893632i	$0.648149\pi$
$882$		0			0
$883$	−6.32757	+	19.4743i	−0.212940	+	0.655361i	0.786354	+	0.617776i	$0.211966\pi$
$883$	−6.32757	+	19.4743i	−0.212940	+	0.655361i	−0.999293	+	0.0375844i	$0.988034\pi$
$884$	15.4918	−	17.2054i	0.521047	−	0.578681i
$885$		0			0
$886$	−1.47420	−	14.0261i	−0.0495267	−	0.471215i
$887$	−31.3019	−	6.65342i	−1.05101	−	0.223400i	−0.350149	−	0.936694i	$-0.613869\pi$
$887$	−31.3019	−	6.65342i	−1.05101	−	0.223400i	−0.700865	+	0.713294i	$0.747202\pi$
$888$		0			0
$889$	−3.12278	+	29.7113i	−0.104735	+	0.996484i
$890$	11.9303			0.399906
$891$		0			0
$892$	10.6911			0.357963
$893$	−6.88592	+	65.5151i	−0.230428	+	2.19238i
$894$		0			0
$895$	−8.28780	−	1.76163i	−0.277031	−	0.0588847i
$896$	−4.50036	−	42.8181i	−0.150347	−	1.43045i
$897$		0			0
$898$	−11.5107	+	12.7839i	−0.384118	+	0.426606i
$899$	0.143966	−	0.443082i	0.00480153	−	0.0147776i
$900$		0			0
$901$	31.2892			1.04239
$902$	4.53253	−	4.56308i	0.150917	−	0.151934i
$903$		0			0
$904$	3.30962	−	1.47354i	0.110076	−	0.0490091i
$905$	1.79334	+	1.99171i	0.0596127	+	0.0662066i
$906$		0			0
$907$	−44.8096	−	19.9505i	−1.48788	−	0.662447i	−0.507877	−	0.861430i	$-0.669569\pi$
$907$	−44.8096	−	19.9505i	−1.48788	−	0.662447i	−0.980003	+	0.198983i	$0.936236\pi$
$908$	−35.4717	+	25.7717i	−1.17717	+	0.855265i
$909$		0			0
$910$	2.39689	−	7.37687i	0.0794561	−	0.244541i
$911$	−2.44401	+	23.2532i	−0.0809736	+	0.770413i	0.876405	+	0.481576i	$0.159935\pi$
$911$	−2.44401	+	23.2532i	−0.0809736	+	0.770413i	−0.957378	+	0.288837i	$0.906731\pi$
$912$		0			0
$913$	1.54553	+	0.408565i	0.0511497	+	0.0135215i
$914$	3.42253	−	5.92800i	0.113207	−	0.196081i
$915$		0			0
$916$	−21.3975	+	4.54819i	−0.706995	+	0.150276i
$917$	−6.46615	−	19.9008i	−0.213531	−	0.657181i
$918$		0			0
$919$	6.14797	−	4.46676i	0.202803	−	0.147345i	−0.481749	−	0.876309i	$-0.659998\pi$
$919$	6.14797	−	4.46676i	0.202803	−	0.147345i	0.684551	+	0.728965i	$0.259998\pi$
$920$	−3.73479	+	4.14791i	−0.123132	+	0.136752i
$921$		0			0
$922$	15.4472	−	6.87755i	0.508728	−	0.226500i
$923$	8.45857	−	14.6507i	0.278417	−	0.482233i
$924$		0			0
$925$	−16.3371	−	28.2967i	−0.537160	−	0.930389i
$926$	21.4202	+	15.5627i	0.703910	+	0.511421i
$927$		0			0
$928$	−1.92634	−	5.92866i	−0.0632352	−	0.194618i
$929$	13.5906	+	6.05092i	0.445893	+	0.198524i	0.617385	−	0.786661i	$-0.288192\pi$
$929$	13.5906	+	6.05092i	0.445893	+	0.198524i	−0.171492	+	0.985185i	$0.554859\pi$
$930$		0			0
$931$	41.3937	+	8.79850i	1.35662	+	0.288359i
$932$	−15.1329	−	16.8068i	−0.495696	−	0.550526i
$933$		0			0
$934$	−5.77192	−	9.99727i	−0.188863	−	0.327121i
$935$	−16.0069	−	12.8733i	−0.523482	−	0.421003i
$936$		0			0
$937$	−14.4192	−	10.4762i	−0.471056	−	0.342242i	0.326797	−	0.945095i	$-0.394031\pi$
$937$	−14.4192	−	10.4762i	−0.471056	−	0.342242i	−0.797853	+	0.602853i	$0.794031\pi$
$938$	−24.7418	+	5.25904i	−0.807850	+	0.171714i
$939$		0			0
$940$	2.33512	+	22.2172i	0.0761633	+	0.724645i
$941$	4.45909	+	42.4254i	0.145362	+	1.38303i	0.787441	+	0.616391i	$0.211406\pi$
$941$	4.45909	+	42.4254i	0.145362	+	1.38303i	−0.642078	+	0.766639i	$0.721928\pi$
$942$		0			0
$943$	6.03716	−	1.28324i	0.196597	−	0.0417879i
$944$	−2.97257	−	2.15970i	−0.0967491	−	0.0702923i
$945$		0			0
$946$	4.11641	−	2.69293i	0.133836	−	0.0875548i
$947$	3.44670	+	5.96986i	0.112003	+	0.193994i	0.916578	−	0.399857i	$-0.130940\pi$
$947$	3.44670	+	5.96986i	0.112003	+	0.193994i	−0.804575	+	0.593851i	$0.797607\pi$
$948$		0			0
$949$	−20.9167	−	23.2303i	−0.678984	−	0.754088i
$950$	−12.5168	−	2.66053i	−0.406099	−	0.0863190i
$951$		0			0
$952$	−46.7725	−	20.8245i	−1.51591	−	0.674925i
$953$	7.31766	+	22.5214i	0.237042	+	0.729541i	0.996844	+	0.0793863i	$0.0252960\pi$
$953$	7.31766	+	22.5214i	0.237042	+	0.729541i	−0.759802	+	0.650155i	$0.774704\pi$
$954$		0			0
$955$	14.9220	+	10.8415i	0.482866	+	0.350822i
$956$	19.5989	+	33.9463i	0.633874	+	1.09790i
$957$		0			0
$958$	−7.27297	+	12.5972i	−0.234979	+	0.406996i
$959$	59.6798	−	26.5712i	1.92716	−	0.858027i
$960$		0			0
$961$	−20.6192	+	22.9000i	−0.665137	+	0.738709i
$962$	12.5301	−	9.10366i	0.403987	−	0.293514i
$963$		0			0
$964$	−8.54567	−	26.3009i	−0.275238	−	0.847094i
$965$	−8.88519	+	1.88860i	−0.286024	+	0.0607963i
$966$		0			0
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	−0.499303	−	0.866427i	$-0.666411\pi$
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	1.00000		0.000804082i	$-0.000255947\pi$
$968$	0.174718	+	26.0045i	0.00561565	+	0.835818i
$969$		0			0
$970$	0.621524	−	5.91340i	0.0199559	−	0.189868i
$971$	−4.12687	+	12.7012i	−0.132438	+	0.407601i	−0.995183	−	0.0980383i	$-0.968743\pi$
$971$	−4.12687	+	12.7012i	−0.132438	+	0.407601i	0.862745	+	0.505639i	$0.168743\pi$
$972$		0			0
$973$	43.4028	−	31.5340i	1.39143	−	1.01093i
$974$	1.98522	+	0.883879i	0.0636107	+	0.0283213i
$975$		0			0
$976$	−4.22755	−	4.69517i	−0.135321	−	0.150289i
$977$	8.14511	−	3.62644i	0.260585	−	0.116020i	−0.272286	−	0.962216i	$-0.587780\pi$
$977$	8.14511	−	3.62644i	0.260585	−	0.116020i	0.532871	+	0.846196i	$0.321113\pi$
$978$		0			0
$979$	52.6564	−	8.52137i	1.68290	−	0.272344i
$980$	14.3508			0.458421
$981$		0			0
$982$	1.48297	−	4.56411i	0.0473234	−	0.145647i
$983$	11.2806	−	12.5283i	0.359794	−	0.399592i	−0.535886	−	0.844290i	$-0.680022\pi$
$983$	11.2806	−	12.5283i	0.359794	−	0.399592i	0.895680	+	0.444698i	$0.146689\pi$
$984$		0			0
$985$	2.67370	+	25.4386i	0.0851912	+	0.810541i
$986$	−3.90347	−	0.829709i	−0.124312	−	0.0264233i
$987$		0			0
$988$	−2.23933	+	21.3058i	−0.0712425	+	0.677827i
$989$	4.72049			0.150103
$990$		0			0
$991$	−33.5356			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$991$	−33.5356			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$992$	0.258805	−	2.46237i	0.00821707	−	0.0781802i
$993$		0			0
$994$	−16.0276	−	3.40677i	−0.508364	−	0.108056i
$995$	1.08219	+	10.2964i	0.0343078	+	0.326417i
$996$		0			0
$997$	−2.17044	+	2.41052i	−0.0687385	+	0.0763419i	−0.776533	−	0.630076i	$-0.783024\pi$
$997$	−2.17044	+	2.41052i	−0.0687385	+	0.0763419i	0.707795	+	0.706418i	$0.249690\pi$
$998$	3.04532	−	9.37254i	0.0963980	−	0.296682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.37.4		72
3.2	odd	2		99.2.m.b.4.6	✓	72
9.2	odd	6		99.2.m.b.70.4	yes	72
9.4	even	3		891.2.f.e.730.4		36
9.5	odd	6		891.2.f.f.730.6		36
9.7	even	3	inner	297.2.n.b.235.6		72
11.3	even	5	inner	297.2.n.b.91.6		72
33.5	odd	10		1089.2.e.p.364.11		36
33.14	odd	10		99.2.m.b.58.4	yes	72
33.17	even	10		1089.2.e.o.364.8		36
99.5	odd	30		9801.2.a.cm.1.8		18
99.14	odd	30		891.2.f.f.487.6		36
99.25	even	15	inner	297.2.n.b.289.4		72
99.38	odd	30		1089.2.e.p.727.11		36
99.47	odd	30		99.2.m.b.25.6	yes	72
99.49	even	15		9801.2.a.cp.1.11		18
99.50	even	30		9801.2.a.co.1.11		18
99.58	even	15		891.2.f.e.487.4		36
99.83	even	30		1089.2.e.o.727.8		36
99.94	odd	30		9801.2.a.cn.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	3.2	odd	2
99.2.m.b.25.6	yes	72	99.47	odd	30
99.2.m.b.58.4	yes	72	33.14	odd	10
99.2.m.b.70.4	yes	72	9.2	odd	6
297.2.n.b.37.4		72	1.1	even	1	trivial
297.2.n.b.91.6		72	11.3	even	5	inner
297.2.n.b.235.6		72	9.7	even	3	inner
297.2.n.b.289.4		72	99.25	even	15	inner
891.2.f.e.487.4		36	99.58	even	15
891.2.f.e.730.4		36	9.4	even	3
891.2.f.f.487.6		36	99.14	odd	30
891.2.f.f.730.6		36	9.5	odd	6
1089.2.e.o.364.8		36	33.17	even	10
1089.2.e.o.727.8		36	99.83	even	30
1089.2.e.p.364.11		36	33.5	odd	10
1089.2.e.p.727.11		36	99.38	odd	30
9801.2.a.cm.1.8		18	99.5	odd	30
9801.2.a.cn.1.8		18	99.94	odd	30
9801.2.a.co.1.11		18	99.50	even	30
9801.2.a.cp.1.11		18	99.49	even	15

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0694404 + 0.660681i) q^{2} +(1.52462 + 0.324067i) q^{4} +(0.116719 + 1.11051i) q^{5} +(-2.61265 + 2.90164i) q^{7} +(-0.730548 + 2.24840i) q^{8} -0.741796 q^{10} +(-3.27403 + 0.529836i) q^{11} +(2.44648 - 1.08924i) q^{13} +(-1.73564 - 1.92762i) q^{14} +(1.41310 + 0.629154i) q^{16} +(4.48727 - 3.26019i) q^{17} +(-1.58598 + 4.88115i) q^{19} +(-0.181927 + 1.73092i) q^{20} +(-0.122703 - 2.19988i) q^{22} +(1.05719 - 1.83110i) q^{23} +(3.67114 - 0.780324i) q^{25} +(0.549758 + 1.69198i) q^{26} +(-4.92362 + 3.57722i) q^{28} +(-0.724696 + 0.804856i) q^{29} +(-0.392973 + 0.174963i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +(-3.52724 - 2.56269i) q^{35} +(-2.69024 - 8.27970i) q^{37} +(-3.11475 - 1.38678i) q^{38} +(-2.58213 - 0.548848i) q^{40} +(1.95324 + 2.16930i) q^{41} +(1.11628 + 1.93346i) q^{43} +(-5.16335 - 0.253209i) q^{44} +(1.13637 + 0.825618i) q^{46} +(12.5550 - 2.66864i) q^{47} +(-0.861884 - 8.20028i) q^{49} +(0.260620 + 2.47964i) q^{50} +(4.08293 - 0.867854i) q^{52} +(4.56381 + 3.31581i) q^{53} +(-0.970527 - 3.57399i) q^{55} +(-4.61537 - 7.99405i) q^{56} +(-0.481430 - 0.534682i) q^{58} +(-2.32346 - 0.493867i) q^{59} +(-3.73133 - 1.66130i) q^{61} +(-0.0883065 - 0.271779i) q^{62} +(-0.590604 - 0.429099i) q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(7.89789 - 3.51637i) q^{68} +(1.93805 - 2.15242i) q^{70} +(5.11062 - 3.71308i) q^{71} +(-3.60705 - 11.1014i) q^{73} +(5.65706 - 1.20244i) q^{74} +(-3.99983 + 6.92792i) q^{76} +(7.01650 - 10.8843i) q^{77} +(-0.471916 + 4.48998i) q^{79} +(-0.533744 + 1.64269i) q^{80} +(-1.56885 + 1.13983i) q^{82} +(-0.440332 - 0.196049i) q^{83} +(4.14421 + 4.60261i) q^{85} +(-1.35492 + 0.603248i) q^{86} +(1.20056 - 7.74839i) q^{88} -16.0830 q^{89} +(-3.23120 + 9.94461i) q^{91} +(2.20521 - 2.44913i) q^{92} +(0.891300 + 8.48015i) q^{94} +(-5.60566 - 1.19152i) q^{95} +(-0.837864 + 7.97174i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

L-functions

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