LMFDB - Embedded newform 297.2.t.a.8.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			8.6
Character	$\chi$	$=$	297.8
Dual form			297.2.t.a.260.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0653389 + 0.621658i) q^{2} +(1.57411 - 0.334586i) q^{4} +(1.26871 + 0.133347i) q^{5} +(-3.59877 + 3.24034i) q^{7} +(0.697171 + 2.14567i) q^{8} +0.797419i q^{10} +(3.12186 + 1.11982i) q^{11} +(0.339621 - 0.762800i) q^{13} +(-2.24953 - 2.02548i) q^{14} +(1.65196 - 0.735502i) q^{16} +(-0.199958 - 0.145278i) q^{17} +(2.08556 - 0.677640i) q^{19} +(2.04171 - 0.214592i) q^{20} +(-0.492168 + 2.01390i) q^{22} +(4.19803 - 2.42373i) q^{23} +(-3.29889 - 0.701200i) q^{25} +(0.496392 + 0.161287i) q^{26} +(-4.58066 + 6.30474i) q^{28} +(-5.19962 - 5.77477i) q^{29} +(1.60265 + 0.713544i) q^{31} +(2.82126 + 4.88657i) q^{32} +(0.0772482 - 0.133798i) q^{34} +(-4.99790 + 3.63118i) q^{35} +(0.106959 - 0.329187i) q^{37} +(0.557529 + 1.25223i) q^{38} +(0.598391 + 2.81521i) q^{40} +(-3.25297 + 3.61279i) q^{41} +(-0.366648 - 0.211684i) q^{43} +(5.28881 + 0.718188i) q^{44} +(1.78103 + 2.45137i) q^{46} +(-1.54628 + 7.27468i) q^{47} +(1.71959 - 16.3608i) q^{49} +(0.220361 - 2.09659i) q^{50} +(0.279376 - 1.31436i) q^{52} +(-6.95271 - 9.56959i) q^{53} +(3.81142 + 1.83703i) q^{55} +(-9.46167 - 5.46270i) q^{56} +(3.25019 - 3.60971i) q^{58} +(-1.09220 - 5.13837i) q^{59} +(-5.66802 - 12.7306i) q^{61} +(-0.338865 + 1.04292i) q^{62} +(0.0724543 - 0.0526411i) q^{64} +(0.532599 - 0.922488i) q^{65} +(-0.252454 - 0.437263i) q^{67} +(-0.363363 - 0.161780i) q^{68} +(-2.58391 - 2.86973i) q^{70} +(6.95402 - 9.57138i) q^{71} +(3.85174 + 1.25150i) q^{73} +(0.211631 + 0.0449835i) q^{74} +(3.05616 - 1.76448i) q^{76} +(-14.8635 + 6.08591i) q^{77} +(2.20083 - 0.231316i) q^{79} +(2.19395 - 0.712856i) q^{80} +(-2.45847 - 1.78618i) q^{82} +(3.77042 - 1.67870i) q^{83} +(-0.234317 - 0.210980i) q^{85} +(0.107639 - 0.241761i) q^{86} +(-0.226303 + 7.47919i) q^{88} +13.5225i q^{89} +(1.24952 + 3.84563i) q^{91} +(5.79719 - 5.21981i) q^{92} +(-4.62340 - 0.485939i) q^{94} +(2.73634 - 0.581627i) q^{95} +(0.830936 + 7.90582i) q^{97} +10.2832 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.0653389	+	0.621658i	0.0462016	+	0.439579i	0.993032	+	0.117845i	$0.0375988\pi$
$2$	0.0653389	+	0.621658i	0.0462016	+	0.439579i	−0.946830	+	0.321733i	$0.895735\pi$
$3$		0			0
$3$		0			0
$4$	1.57411	−	0.334586i	0.787053	−	0.167293i
$5$	1.26871	+	0.133347i	0.567386	+	0.0596347i	0.383878	−	0.923384i	$-0.374588\pi$
$5$	1.26871	+	0.133347i	0.567386	+	0.0596347i	0.183508	+	0.983018i	$0.441255\pi$
$6$		0			0
$7$	−3.59877	+	3.24034i	−1.36021	+	1.22474i	−0.410396	+	0.911907i	$0.634610\pi$
$7$	−3.59877	+	3.24034i	−1.36021	+	1.22474i	−0.949810	+	0.312828i	$0.898724\pi$
$8$	0.697171	+	2.14567i	0.246487	+	0.758609i
$9$		0			0
$10$			0.797419i			0.252166i
$11$	3.12186	+	1.11982i	0.941276	+	0.337639i
$11$	3.12186	+	1.11982i	0.941276	+	0.337639i
$12$		0			0
$13$	0.339621	−	0.762800i	0.0941938	−	0.211563i	−0.860304	−	0.509782i	$-0.829726\pi$
$13$	0.339621	−	0.762800i	0.0941938	−	0.211563i	0.954497	+	0.298219i	$0.0963927\pi$
$14$	−2.24953	−	2.02548i	−0.601211	−	0.541333i
$15$		0			0
$16$	1.65196	−	0.735502i	0.412991	−	0.183875i
$17$	−0.199958	−	0.145278i	−0.0484969	−	0.0352351i	0.563273	−	0.826271i	$-0.309542\pi$
$17$	−0.199958	−	0.145278i	−0.0484969	−	0.0352351i	−0.611770	+	0.791036i	$0.709542\pi$
$18$		0			0
$19$	2.08556	−	0.677640i	0.478461	−	0.155461i	−0.0598507	−	0.998207i	$-0.519062\pi$
$19$	2.08556	−	0.677640i	0.478461	−	0.155461i	0.538311	+	0.842746i	$0.319062\pi$
$20$	2.04171	−	0.214592i	0.456539	−	0.0479842i
$21$		0			0
$22$	−0.492168	+	2.01390i	−0.104931	+	0.429364i
$23$	4.19803	−	2.42373i	0.875349	−	0.505383i	0.00622685	−	0.999981i	$-0.498018\pi$
$23$	4.19803	−	2.42373i	0.875349	−	0.505383i	0.869122	+	0.494598i	$0.164685\pi$
$24$		0			0
$25$	−3.29889	−	0.701200i	−0.659777	−	0.140240i
$26$	0.496392	+	0.161287i	0.0973504	+	0.0316311i
$27$		0			0
$28$	−4.58066	+	6.30474i	−0.865664	+	1.19148i
$29$	−5.19962	−	5.77477i	−0.965546	−	1.07235i	−0.997343	−	0.0728530i	$-0.976790\pi$
$29$	−5.19962	−	5.77477i	−0.965546	−	1.07235i	0.0317968	−	0.999494i	$-0.489877\pi$
$30$		0			0
$31$	1.60265	+	0.713544i	0.287844	+	0.128156i	0.545579	−	0.838059i	$-0.316310\pi$
$31$	1.60265	+	0.713544i	0.287844	+	0.128156i	−0.257736	+	0.966215i	$0.582976\pi$
$32$	2.82126	+	4.88657i	0.498733	+	0.863831i
$33$		0			0
$34$	0.0772482	−	0.133798i	0.0132480	−	0.0229461i
$35$	−4.99790	+	3.63118i	−0.844799	+	0.613782i
$36$		0			0
$37$	0.106959	−	0.329187i	0.0175840	−	0.0541180i	−0.941879	−	0.335951i	$-0.890942\pi$
$37$	0.106959	−	0.329187i	0.0175840	−	0.0541180i	0.959464	+	0.281833i	$0.0909424\pi$
$38$	0.557529	+	1.25223i	0.0904431	+	0.203139i
$39$		0			0
$40$	0.598391	+	2.81521i	0.0946139	+	0.445124i
$41$	−3.25297	+	3.61279i	−0.508029	+	0.564224i	−0.941530	−	0.336930i	$-0.890612\pi$
$41$	−3.25297	+	3.61279i	−0.508029	+	0.564224i	0.433501	+	0.901153i	$0.357278\pi$
$42$		0			0
$43$	−0.366648	−	0.211684i	−0.0559133	−	0.0322816i	0.471783	−	0.881715i	$-0.343611\pi$
$43$	−0.366648	−	0.211684i	−0.0559133	−	0.0322816i	−0.527696	+	0.849433i	$0.676944\pi$
$44$	5.28881	+	0.718188i	0.797318	+	0.108271i
$45$		0			0
$46$	1.78103	+	2.45137i	0.262598	+	0.361435i
$47$	−1.54628	+	7.27468i	−0.225548	+	1.06112i	0.708979	+	0.705230i	$0.249156\pi$
$47$	−1.54628	+	7.27468i	−0.225548	+	1.06112i	−0.934527	+	0.355891i	$0.884177\pi$
$48$		0			0
$49$	1.71959	−	16.3608i	0.245656	−	2.33726i
$50$	0.220361	−	2.09659i	0.0311638	−	0.296503i
$51$		0			0
$52$	0.279376	−	1.31436i	0.0387425	−	0.182269i
$53$	−6.95271	−	9.56959i	−0.955029	−	1.31448i	−0.949257	−	0.314501i	$-0.898163\pi$
$53$	−6.95271	−	9.56959i	−0.955029	−	1.31448i	−0.00577155	−	0.999983i	$-0.501837\pi$
$54$		0			0
$55$	3.81142	+	1.83703i	0.513932	+	0.247704i
$56$	−9.46167	−	5.46270i	−1.26437	−	0.729984i
$57$		0			0
$58$	3.25019	−	3.60971i	0.426771	−	0.473978i
$59$	−1.09220	−	5.13837i	−0.142192	−	0.668959i	−0.990278	−	0.139101i	$-0.955579\pi$
$59$	−1.09220	−	5.13837i	−0.142192	−	0.668959i	0.848086	−	0.529858i	$-0.177755\pi$
$60$		0			0
$61$	−5.66802	−	12.7306i	−0.725715	−	1.62998i	−0.775597	−	0.631228i	$-0.782551\pi$
$61$	−5.66802	−	12.7306i	−0.725715	−	1.62998i	0.0498815	−	0.998755i	$-0.484116\pi$
$62$	−0.338865	+	1.04292i	−0.0430359	+	0.132451i
$63$		0			0
$64$	0.0724543	−	0.0526411i	0.00905678	−	0.00658014i
$65$	0.532599	−	0.922488i	0.0660607	−	0.114421i
$66$		0			0
$67$	−0.252454	−	0.437263i	−0.0308421	−	0.0534201i	0.850192	−	0.526472i	$-0.176486\pi$
$67$	−0.252454	−	0.437263i	−0.0308421	−	0.0534201i	−0.881034	+	0.473052i	$0.843152\pi$
$68$	−0.363363	−	0.161780i	−0.0440642	−	0.0196187i
$69$		0			0
$70$	−2.58391	−	2.86973i	−0.308837	−	0.342998i
$71$	6.95402	−	9.57138i	0.825290	−	1.13591i	−0.163491	−	0.986545i	$-0.552276\pi$
$71$	6.95402	−	9.57138i	0.825290	−	1.13591i	0.988781	−	0.149370i	$-0.0477244\pi$
$72$		0			0
$73$	3.85174	+	1.25150i	0.450812	+	0.146478i	0.525618	−	0.850720i	$-0.323834\pi$
$73$	3.85174	+	1.25150i	0.450812	+	0.146478i	−0.0748068	+	0.997198i	$0.523834\pi$
$74$	0.211631	+	0.0449835i	0.0246016	+	0.00522922i
$75$		0			0
$76$	3.05616	−	1.76448i	0.350566	−	0.202399i
$77$	−14.8635	+	6.08591i	−1.69385	+	0.693554i
$78$		0			0
$79$	2.20083	−	0.231316i	0.247613	−	0.0260251i	0.0200909	−	0.999798i	$-0.493604\pi$
$79$	2.20083	−	0.231316i	0.247613	−	0.0260251i	0.227522	+	0.973773i	$0.426938\pi$
$80$	2.19395	−	0.712856i	0.245291	−	0.0796998i
$81$		0			0
$82$	−2.45847	−	1.78618i	−0.271492	−	0.197251i
$83$	3.77042	−	1.67870i	0.413857	−	0.184261i	−0.189236	−	0.981932i	$-0.560601\pi$
$83$	3.77042	−	1.67870i	0.413857	−	0.184261i	0.603094	+	0.797670i	$0.293935\pi$
$84$		0			0
$85$	−0.234317	−	0.210980i	−0.0254152	−	0.0228840i
$86$	0.107639	−	0.241761i	0.0116070	−	0.0260698i
$87$		0			0
$88$	−0.226303	+	7.47919i	−0.0241240	+	0.797284i
$89$			13.5225i			1.43338i	0.697393	+	0.716689i	$0.254343\pi$
$89$			13.5225i			1.43338i	−0.697393	+	0.716689i	$0.745657\pi$
$90$		0			0
$91$	1.24952	+	3.84563i	0.130985	+	0.403131i
$92$	5.79719	−	5.21981i	0.604399	−	0.544203i
$93$		0			0
$94$	−4.62340	−	0.485939i	−0.476867	−	0.0501207i
$95$	2.73634	−	0.581627i	0.280743	−	0.0596737i
$96$		0			0
$97$	0.830936	+	7.90582i	0.0843687	+	0.802715i	0.952122	+	0.305719i	$0.0988969\pi$
$97$	0.830936	+	7.90582i	0.0843687	+	0.802715i	−0.867753	+	0.496996i	$0.834436\pi$
$98$	10.2832			1.03876
$99$		0			0
$100$	−5.42741			−0.542741
$101$	0.563906	+	5.36520i	0.0561107	+	0.533858i	0.986086	+	0.166236i	$0.0531613\pi$
$101$	0.563906	+	5.36520i	0.0561107	+	0.533858i	−0.929975	+	0.367622i	$0.880172\pi$
$102$		0			0
$103$	−16.0974	+	3.42161i	−1.58612	+	0.337141i	−0.914764	−	0.403989i	$-0.867623\pi$
$103$	−16.0974	+	3.42161i	−1.58612	+	0.337141i	−0.671361	+	0.741131i	$0.734290\pi$
$104$	1.87349	+	0.196912i	0.183711	+	0.0193088i
$105$		0			0
$106$	5.49473	−	4.94748i	0.533695	−	0.480542i
$107$	−0.705070	−	2.16998i	−0.0681617	−	0.209780i	0.911174	−	0.412022i	$-0.135177\pi$
$107$	−0.705070	−	2.16998i	−0.0681617	−	0.209780i	−0.979336	+	0.202242i	$0.935177\pi$
$108$		0			0
$109$		−	8.89941i		−	0.852409i	−0.904627	−	0.426205i	$-0.859850\pi$
$109$		−	8.89941i		−	0.852409i	0.904627	−	0.426205i	$-0.140150\pi$
$110$	−0.892968	+	2.48943i	−0.0851411	+	0.237358i
$111$		0			0
$112$	−3.56176	+	7.99983i	−0.336554	+	0.755913i
$113$	5.38119	+	4.84525i	0.506220	+	0.455803i	0.882234	−	0.470811i	$-0.156039\pi$
$113$	5.38119	+	4.84525i	0.506220	+	0.455803i	−0.376014	+	0.926614i	$0.622705\pi$
$114$		0			0
$115$	5.64929	−	2.51523i	0.526799	−	0.234546i
$116$	−10.1169	−	7.35037i	−0.939332	−	0.682465i
$117$		0			0
$118$	3.12295	−	1.01471i	0.287491	−	0.0934114i
$119$	1.19035	−	0.125111i	0.109119	−	0.0114689i
$120$		0			0
$121$	8.49199	+	6.99185i	0.771999	+	0.635623i
$122$	7.54373	−	4.35537i	0.682977	−	0.394317i
$123$		0			0
$124$	2.76148	+	0.586970i	0.247988	+	0.0527114i
$125$	−10.1582	−	3.30059i	−0.908574	−	0.295213i
$126$		0			0
$127$	1.69280	−	2.32994i	0.150212	−	0.206749i	−0.727279	−	0.686341i	$-0.759216\pi$
$127$	1.69280	−	2.32994i	0.150212	−	0.206749i	0.877491	+	0.479593i	$0.159216\pi$
$128$	7.58863	+	8.42802i	0.670746	+	0.744939i
$129$		0			0
$130$	0.608271	+	0.270820i	0.0533489	+	0.0237525i
$131$	0.281682	+	0.487887i	0.0246106	+	0.0426269i	0.878068	−	0.478535i	$-0.158832\pi$
$131$	0.281682	+	0.487887i	0.0246106	+	0.0426269i	−0.853458	+	0.521162i	$0.825499\pi$
$132$		0			0
$133$	−5.30966	+	9.19661i	−0.460406	+	0.797447i
$134$	0.255333	−	0.185510i	0.0220574	−	0.0160256i
$135$		0			0
$136$	0.172314	−	0.530328i	0.0147758	−	0.0454752i
$137$	−1.88819	−	4.24095i	−0.161319	−	0.362329i	0.814742	−	0.579823i	$-0.196878\pi$
$137$	−1.88819	−	4.24095i	−0.161319	−	0.362329i	−0.976062	+	0.217494i	$0.930212\pi$
$138$		0			0
$139$	2.18480	+	10.2787i	0.185312	+	0.871825i	0.968300	+	0.249788i	$0.0803611\pi$
$139$	2.18480	+	10.2787i	0.185312	+	0.871825i	−0.782988	+	0.622036i	$0.786306\pi$
$140$	−6.65227	+	7.38809i	−0.562219	+	0.624408i
$141$		0			0
$142$	6.40450	+	3.69764i	0.537453	+	0.310299i
$143$	1.91445	−	2.00104i	0.160094	−	0.167335i
$144$		0			0
$145$	−5.82678	−	8.01988i	−0.483888	−	0.666015i
$146$	−0.526340	+	2.47623i	−0.0435602	+	0.204935i
$147$		0			0
$148$	0.0582238	−	0.553963i	0.00478597	−	0.0455354i
$149$	1.59142	−	15.1413i	0.130374	−	1.24042i	−0.712252	−	0.701924i	$-0.752325\pi$
$149$	1.59142	−	15.1413i	0.130374	−	1.24042i	0.842625	−	0.538500i	$-0.181009\pi$
$150$		0			0
$151$	−1.58872	+	7.47434i	−0.129288	+	0.608253i	0.865022	+	0.501733i	$0.167304\pi$
$151$	−1.58872	+	7.47434i	−0.129288	+	0.608253i	−0.994311	+	0.106520i	$0.966029\pi$
$152$	2.90799	+	4.00250i	0.235869	+	0.324646i
$153$		0			0
$154$	−4.75452	−	8.84234i	−0.383130	−	0.712536i
$155$	1.93815	+	1.11899i	0.155676	+	0.0898795i
$156$		0			0
$157$	−2.89738	+	3.21787i	−0.231236	+	0.256814i	−0.847585	−	0.530659i	$-0.821944\pi$
$157$	−2.89738	+	3.21787i	−0.231236	+	0.256814i	0.616349	+	0.787473i	$0.288611\pi$
$158$	0.287599	+	1.35305i	0.0228802	+	0.107643i
$159$		0			0
$160$	2.92776	+	6.57586i	0.231460	+	0.519867i
$161$	−7.25399	+	22.3255i	−0.571695	+	1.75950i
$162$		0			0
$163$	−5.76502	+	4.18853i	−0.451551	+	0.328071i	−0.790208	−	0.612839i	$-0.790027\pi$
$163$	−5.76502	+	4.18853i	−0.451551	+	0.328071i	0.338657	+	0.940910i	$0.390027\pi$
$164$	−3.91173	+	6.77532i	−0.305455	+	0.529064i
$165$		0			0
$166$	1.28993	+	2.23423i	0.100118	+	0.173410i
$167$	−7.47107	−	3.32634i	−0.578129	−	0.257400i	0.0967737	−	0.995306i	$-0.469148\pi$
$167$	−7.47107	−	3.32634i	−0.578129	−	0.257400i	−0.674903	+	0.737907i	$0.735814\pi$
$168$		0			0
$169$	8.23218	+	9.14276i	0.633244	+	0.703289i
$170$	0.115847	−	0.159450i	0.00888509	−	0.0122293i
$171$		0			0
$172$	−0.647970	−	0.210538i	−0.0494072	−	0.0160534i
$173$	6.61744	+	1.40658i	0.503114	+	0.106940i	0.452476	−	0.891777i	$-0.350541\pi$
$173$	6.61744	+	1.40658i	0.503114	+	0.106940i	0.0506387	+	0.998717i	$0.483874\pi$
$174$		0			0
$175$	14.1440	−	8.16607i	1.06919	−	0.617297i
$176$	5.98083	−	0.446225i	0.450822	−	0.0336355i
$177$		0			0
$178$	−8.40634	+	0.883542i	−0.630082	+	0.0662243i
$179$	6.85049	−	2.22586i	0.512030	−	0.166369i	−0.0415954	−	0.999135i	$-0.513244\pi$
$179$	6.85049	−	2.22586i	0.512030	−	0.166369i	0.553625	+	0.832766i	$0.313244\pi$
$180$		0			0
$181$	0.383330	+	0.278506i	0.0284927	+	0.0207012i	0.601940	−	0.798541i	$-0.294394\pi$
$181$	0.383330	+	0.278506i	0.0284927	+	0.0207012i	−0.573448	+	0.819242i	$0.694394\pi$
$182$	−2.30902	+	1.02804i	−0.171156	+	0.0762037i
$183$		0			0
$184$	8.12727	+	7.31783i	0.599151	+	0.539478i
$185$	0.179597	−	0.403382i	0.0132042	−	0.0296572i
$186$		0			0
$187$	−0.461555	−	0.677454i	−0.0337522	−	0.0495404i
$188$			11.9685i			0.872891i
$189$		0			0
$190$	0.540363	+	1.66307i	0.0392020	+	0.120651i
$191$	−0.0301700	+	0.0271652i	−0.00218303	+	0.00196561i	−0.670221	−	0.742161i	$-0.733801\pi$
$191$	−0.0301700	+	0.0271652i	−0.00218303	+	0.00196561i	0.668038	+	0.744127i	$0.267134\pi$
$192$		0			0
$193$	−11.1756	−	1.17460i	−0.804436	−	0.0845496i	−0.306619	−	0.951832i	$-0.599198\pi$
$193$	−11.1756	−	1.17460i	−0.804436	−	0.0845496i	−0.497816	+	0.867283i	$0.665865\pi$
$194$	−4.86043	+	1.03312i	−0.348958	+	0.0741734i
$195$		0			0
$196$	−2.76729	−	26.3290i	−0.197664	−	1.88065i
$197$	20.8150			1.48301			0.741504	−	0.670948i	$-0.234113\pi$
$197$	20.8150			1.48301			0.741504	+	0.670948i	$0.234113\pi$
$198$		0			0
$199$	14.4111			1.02158			0.510788	−	0.859707i	$-0.329354\pi$
$199$	14.4111			1.02158			0.510788	+	0.859707i	$0.329354\pi$
$200$	−0.795343	−	7.56718i	−0.0562392	−	0.535080i
$201$		0			0
$202$	−3.29848	+	0.701113i	−0.232080	+	0.0493302i
$203$	37.4245	+	3.93347i	2.62668	+	0.276076i
$204$		0			0
$205$	−4.60885	+	4.14983i	−0.321896	+	0.289836i
$206$	−3.17886	−	9.78352i	−0.221482	−	0.681650i
$207$		0			0
$208$		−	1.50991i		−	0.104693i
$209$	7.26966	+	0.219963i	0.502853	+	0.0152152i
$210$		0			0
$211$	−7.39314	+	16.6053i	−0.508965	+	1.14315i	0.458164	+	0.888868i	$0.348507\pi$
$211$	−7.39314	+	16.6053i	−0.508965	+	1.14315i	−0.967129	+	0.254286i	$0.918159\pi$
$212$	−14.1462	−	12.7373i	−0.971562	−	0.874799i
$213$		0			0
$214$	1.30292	−	0.580097i	0.0890658	−	0.0396546i
$215$	−0.436944	−	0.317458i	−0.0297993	−	0.0216505i
$216$		0			0
$217$	−8.07968	+	2.62525i	−0.548484	+	0.178213i
$218$	5.53239	−	0.581478i	0.374701	−	0.0393827i
$219$		0			0
$220$	6.61422	+	1.61642i	0.445930	+	0.108979i
$221$	−0.178728	+	0.103189i	−0.0120225	+	0.00694122i
$222$		0			0
$223$	−0.737985	−	0.156863i	−0.0494191	−	0.0105044i	0.183136	−	0.983088i	$-0.441375\pi$
$223$	−0.737985	−	0.156863i	−0.0494191	−	0.0105044i	−0.232555	+	0.972583i	$0.574709\pi$
$224$	−25.9872	−	8.44376i	−1.73634	−	0.564172i
$225$		0			0
$226$	−2.66049	+	3.66185i	−0.176973	+	0.243582i
$227$	−11.1196	−	12.3496i	−0.738037	−	0.819673i	0.250899	−	0.968013i	$-0.419274\pi$
$227$	−11.1196	−	12.3496i	−0.738037	−	0.819673i	−0.988936	+	0.148340i	$0.952607\pi$
$228$		0			0
$229$	−20.0961	−	8.94735i	−1.32799	−	0.591258i	−0.384640	−	0.923067i	$-0.625674\pi$
$229$	−20.0961	−	8.94735i	−1.32799	−	0.591258i	−0.943347	+	0.331809i	$0.892341\pi$
$230$	1.93273	+	3.34759i	0.127440	+	0.220733i
$231$		0			0
$232$	8.76573	−	15.1827i	0.575498	−	0.996792i
$233$	12.5102	−	9.08916i	0.819568	−	0.595451i	−0.0970210	−	0.995282i	$-0.530931\pi$
$233$	12.5102	−	9.08916i	0.819568	−	0.595451i	0.916589	+	0.399832i	$0.130931\pi$
$234$		0			0
$235$	−2.93185	+	9.02329i	−0.191252	+	0.588615i
$236$	−3.43846	−	7.72291i	−0.223825	−	0.502719i
$237$		0			0
$238$	0.155553	+	0.731818i	0.0100830	+	0.0474367i
$239$	−12.5862	+	13.9784i	−0.814132	+	0.904185i	−0.996877	−	0.0789751i	$-0.974835\pi$
$239$	−12.5862	+	13.9784i	−0.814132	+	0.904185i	0.182744	+	0.983160i	$0.441502\pi$
$240$		0			0
$241$	13.4825	+	7.78412i	0.868483	+	0.501419i	0.866844	−	0.498580i	$-0.166145\pi$
$241$	13.4825	+	7.78412i	0.868483	+	0.501419i	0.00163940	+	0.999999i	$0.499478\pi$
$242$	−3.79169	+	5.73596i	−0.243739	+	0.368721i
$243$		0			0
$244$	−13.1815	−	18.1428i	−0.843862	−	1.16148i
$245$	4.36334	−	20.5279i	0.278764	−	1.31148i
$246$		0			0
$247$	0.191396	−	1.82101i	0.0121782	−	0.115868i
$248$	−0.413713	+	3.93621i	−0.0262708	+	0.249950i
$249$		0			0
$250$	1.38811	−	6.53056i	0.0877920	−	0.413029i
$251$	8.32155	+	11.4536i	0.525252	+	0.722947i	0.986397	−	0.164378i	$-0.0525616\pi$
$251$	8.32155	+	11.4536i	0.525252	+	0.722947i	−0.461146	+	0.887324i	$0.652562\pi$
$252$		0			0
$253$	15.8198	−	2.86550i	0.994582	−	0.180152i
$254$	1.55903	+	0.900107i	0.0978223	+	0.0564778i
$255$		0			0
$256$	−4.62367	+	5.13510i	−0.288979	+	0.320944i
$257$	3.09474	+	14.5596i	0.193045	+	0.908204i	0.962873	+	0.269953i	$0.0870083\pi$
$257$	3.09474	+	14.5596i	0.193045	+	0.908204i	−0.769829	+	0.638250i	$0.779658\pi$
$258$		0			0
$259$	0.681758	+	1.53125i	0.0423624	+	0.0951475i
$260$	0.529714	−	1.63029i	0.0328515	−	0.101106i
$261$		0			0
$262$	−0.284894	+	0.206988i	−0.0176008	+	0.0127877i
$263$	−11.9506	+	20.6991i	−0.736906	+	1.27636i	0.216976	+	0.976177i	$0.430381\pi$
$263$	−11.9506	+	20.6991i	−0.736906	+	1.27636i	−0.953882	+	0.300181i	$0.902953\pi$
$264$		0			0
$265$	−7.54492	−	13.0682i	−0.463481	−	0.802773i
$266$	−6.06407	−	2.69990i	−0.371812	−	0.165541i
$267$		0			0
$268$	−0.543691	−	0.603830i	−0.0332112	−	0.0368848i
$269$	−4.62668	+	6.36807i	−0.282093	+	0.388268i	−0.926426	−	0.376477i	$-0.877135\pi$
$269$	−4.62668	+	6.36807i	−0.282093	+	0.388268i	0.644332	+	0.764745i	$0.277135\pi$
$270$		0			0
$271$	−4.67871	−	1.52020i	−0.284211	−	0.0923458i	0.163442	−	0.986553i	$-0.447740\pi$
$271$	−4.67871	−	1.52020i	−0.284211	−	0.0923458i	−0.447654	+	0.894207i	$0.647740\pi$
$272$	−0.437176	−	0.0929245i	−0.0265077	−	0.00563438i
$273$		0			0
$274$	2.51305	−	1.45091i	0.151819	−	0.0876527i
$275$	−9.51343	−	5.88321i	−0.573682	−	0.354771i
$276$		0			0
$277$	26.2641	−	2.76046i	1.57805	−	0.165860i	0.725397	−	0.688331i	$-0.241656\pi$
$277$	26.2641	−	2.76046i	1.57805	−	0.165860i	0.852657	+	0.522471i	$0.174990\pi$
$278$	−6.24706	+	2.02979i	−0.374674	+	0.121739i
$279$		0			0
$280$	−11.2757	−	8.19229i	−0.673853	−	0.489583i
$281$	−14.5196	+	6.46453i	−0.866165	+	0.385641i	−0.791209	−	0.611546i	$-0.790548\pi$
$281$	−14.5196	+	6.46453i	−0.866165	+	0.385641i	−0.0749554	+	0.997187i	$0.523881\pi$
$282$		0			0
$283$	8.18244	+	7.36750i	0.486396	+	0.437953i	0.875483	−	0.483248i	$-0.160543\pi$
$283$	8.18244	+	7.36750i	0.486396	+	0.437953i	−0.389088	+	0.921201i	$0.627210\pi$
$284$	7.74390	−	17.3931i	0.459516	−	1.03209i
$285$		0			0
$286$	1.36905	+	1.05939i	0.0809537	+	0.0626429i
$287$		−	23.5424i		−	1.38966i
$288$		0			0
$289$	−5.23441	−	16.1099i	−0.307907	−	0.947639i
$290$	4.60491	−	4.14628i	0.270410	−	0.243478i
$291$		0			0
$292$	6.48177	+	0.681262i	0.379317	+	0.0398678i
$293$	−13.8586	+	2.94575i	−0.809631	+	0.172092i	−0.594086	−	0.804402i	$-0.702486\pi$
$293$	−13.8586	+	2.94575i	−0.809631	+	0.172092i	−0.215545	+	0.976494i	$0.569153\pi$
$294$		0			0
$295$	−0.700495	−	6.66477i	−0.0407844	−	0.388038i
$296$	0.780897			0.0453887
$297$		0			0
$298$	9.51670			0.551288
$299$	−0.423087	−	4.02540i	−0.0244678	−	0.232795i
$300$		0			0
$301$	2.00541	−	0.426264i	0.115590	−	0.0245694i
$302$	−4.75029	−	0.499276i	−0.273348	−	0.0287301i
$303$		0			0
$304$	2.94687	−	2.65337i	0.169014	−	0.152181i
$305$	−5.49351	−	16.9073i	−0.314557	−	0.968108i
$306$		0			0
$307$		−	11.5389i		−	0.658559i	−0.944233	−	0.329279i	$-0.893194\pi$
$307$		−	11.5389i		−	0.658559i	0.944233	−	0.329279i	$-0.106806\pi$
$308$	−21.3604	+	14.5530i	−1.21712	+	0.829233i
$309$		0			0
$310$	−0.568993	+	1.27798i	−0.0323166	+	0.0725844i
$311$	20.3343	+	18.3091i	1.15305	+	1.03821i	0.998740	+	0.0501904i	$0.0159828\pi$
$311$	20.3343	+	18.3091i	1.15305	+	1.03821i	0.154312	+	0.988022i	$0.450684\pi$
$312$		0			0
$313$	7.59123	−	3.37983i	0.429081	−	0.191039i	−0.180821	−	0.983516i	$-0.557875\pi$
$313$	7.59123	−	3.37983i	0.429081	−	0.191039i	0.609902	+	0.792477i	$0.291209\pi$
$314$	−2.18973	−	1.59093i	−0.123573	−	0.0897814i
$315$		0			0
$316$	3.38694	−	1.10048i	0.190530	−	0.0619071i
$317$	−15.1108	+	1.58821i	−0.848707	+	0.0892027i	−0.518889	−	0.854842i	$-0.673654\pi$
$317$	−15.1108	+	1.58821i	−0.848707	+	0.0892027i	−0.329818	+	0.944044i	$0.606987\pi$
$318$		0			0
$319$	−9.76577	−	23.8507i	−0.546778	−	1.33538i
$320$	0.0989432	−	0.0571249i	0.00553110	−	0.00319338i
$321$		0			0
$322$	−14.3528	−	3.05078i	−0.799850	−	0.170013i
$323$	−0.515471	−	0.167487i	−0.0286816	−	0.00931920i
$324$		0			0
$325$	−1.65524	+	2.27825i	−0.0918165	+	0.126375i
$326$	−2.98052	−	3.31020i	−0.165076	−	0.183335i
$327$		0			0
$328$	−10.0197	−	4.46108i	−0.553248	−	0.246322i
$329$	−18.0078	−	31.1904i	−0.992800	−	1.71958i
$330$		0			0
$331$	−7.20722	+	12.4833i	−0.396145	+	0.686142i	−0.993247	−	0.116023i	$-0.962985\pi$
$331$	−7.20722	+	12.4833i	−0.396145	+	0.686142i	0.597102	+	0.802165i	$0.296319\pi$
$332$	5.37337	−	3.90398i	0.294902	−	0.214259i
$333$		0			0
$334$	1.57969	−	4.86179i	0.0864369	−	0.266025i
$335$	−0.261984	−	0.588425i	−0.0143137	−	0.0321491i
$336$		0			0
$337$	−1.60984	−	7.57372i	−0.0876938	−	0.412567i	−0.999995	−	0.00304781i	$-0.999030\pi$
$337$	−1.60984	−	7.57372i	−0.0876938	−	0.412567i	0.912302	−	0.409519i	$-0.134303\pi$
$338$	−5.14579	+	5.71498i	−0.279894	+	0.310854i
$339$		0			0
$340$	−0.439431	−	0.253705i	−0.0238315	−	0.0137591i
$341$	4.20419	+	4.02226i	0.227670	+	0.217818i
$342$		0			0
$343$	26.9014	+	37.0266i	1.45254	+	1.99925i
$344$	0.198589	−	0.934287i	0.0107072	−	0.0503734i
$345$		0			0
$346$	−0.442036	+	4.20569i	−0.0237640	+	0.226099i
$347$	0.905345	−	8.61378i	0.0486014	−	0.462412i	−0.942973	−	0.332870i	$-0.891983\pi$
$347$	0.905345	−	8.61378i	0.0486014	−	0.462412i	0.991574	−	0.129541i	$-0.0413505\pi$
$348$		0			0
$349$	−3.48542	+	16.3976i	−0.186570	+	0.877745i	0.780879	+	0.624682i	$0.214771\pi$
$349$	−3.48542	+	16.3976i	−0.186570	+	0.877745i	−0.967450	+	0.253063i	$0.918562\pi$
$350$	6.00066	+	8.25920i	0.320749	+	0.441473i
$351$		0			0
$352$	3.33549	+	18.4145i	0.177782	+	0.981495i
$353$	−10.1385	−	5.85345i	−0.539617	−	0.311548i	0.205307	−	0.978698i	$-0.434181\pi$
$353$	−10.1385	−	5.85345i	−0.539617	−	0.311548i	−0.744924	+	0.667150i	$0.767514\pi$
$354$		0			0
$355$	10.0990	−	11.2160i	0.535998	−	0.595286i
$356$	4.52443	+	21.2858i	0.239794	+	1.12814i
$357$		0			0
$358$	1.83133	+	4.11323i	0.0967887	+	0.217391i
$359$	−5.55436	+	17.0946i	−0.293148	+	0.902217i	0.690689	+	0.723152i	$0.257307\pi$
$359$	−5.55436	+	17.0946i	−0.293148	+	0.902217i	−0.983837	+	0.179065i	$0.942693\pi$
$360$		0			0
$361$	−11.4810	+	8.34140i	−0.604261	+	0.439021i
$362$	−0.148089	+	0.256498i	−0.00778339	+	0.0134812i
$363$		0			0
$364$	3.25357	+	5.63535i	0.170534	+	0.295373i
$365$	4.71986	+	2.10142i	0.247049	+	0.109993i
$366$		0			0
$367$	−18.3798	−	20.4128i	−0.959418	−	1.06554i	−0.997801	−	0.0662788i	$-0.978887\pi$
$367$	−18.3798	−	20.4128i	−0.959418	−	1.06554i	0.0383829	−	0.999263i	$-0.487779\pi$
$368$	5.15233	−	7.09157i	0.268584	−	0.369674i
$369$		0			0
$370$	0.262500	+	0.0852915i	0.0136467	+	0.00443409i
$371$	56.0300	+	11.9095i	2.90893	+	0.618312i
$372$		0			0
$373$	−14.6976	+	8.48568i	−0.761015	+	0.439372i	−0.829660	−	0.558269i	$-0.811466\pi$
$373$	−14.6976	+	8.48568i	−0.761015	+	0.439372i	0.0686452	+	0.997641i	$0.478132\pi$
$374$	0.390988	−	0.331193i	0.0202175	−	0.0171256i
$375$		0			0
$376$	−16.6871	+	1.75388i	−0.860571	+	0.0904497i
$377$	−6.17089	+	2.00505i	−0.317817	+	0.103265i
$378$		0			0
$379$	12.4374	+	9.03634i	0.638869	+	0.464165i	0.859461	−	0.511201i	$-0.170799\pi$
$379$	12.4374	+	9.03634i	0.638869	+	0.464165i	−0.220593	+	0.975366i	$0.570799\pi$
$380$	4.11269	−	1.83109i	0.210976	−	0.0939327i
$381$		0			0
$382$	−0.0188588	−	0.0169805i	−0.000964898	−	0.000868798i
$383$	−3.37198	+	7.57359i	−0.172300	+	0.386993i	−0.978968	−	0.204012i	$-0.934602\pi$
$383$	−3.37198	+	7.57359i	−0.172300	+	0.386993i	0.806668	+	0.591005i	$0.201268\pi$
$384$		0			0
$385$	−19.6690	+	5.73928i	−1.00243	+	0.292501i
$386$		−	7.02414i		−	0.357519i
$387$		0			0
$388$	3.95316	+	12.1666i	0.200691	+	0.617665i
$389$	18.7155	−	16.8515i	0.948912	−	0.854405i	−0.0405525	−	0.999177i	$-0.512912\pi$
$389$	18.7155	−	16.8515i	0.948912	−	0.854405i	0.989465	+	0.144773i	$0.0462451\pi$
$390$		0			0
$391$	−1.19154	−	0.125236i	−0.0602589	−	0.00633347i
$392$	36.3038	−	7.71662i	1.83362	−	0.389748i
$393$		0			0
$394$	1.36003	+	12.9398i	0.0685173	+	0.651899i
$395$	2.82307			0.142044
$396$		0			0
$397$	−26.0948			−1.30966			−0.654830	−	0.755776i	$-0.727260\pi$
$397$	−26.0948			−1.30966			−0.654830	+	0.755776i	$0.727260\pi$
$398$	0.941605	+	8.95878i	0.0471984	+	0.449063i
$399$		0			0
$400$	−5.96537	+	1.26798i	−0.298269	+	0.0633990i
$401$	−4.20361	−	0.441818i	−0.209918	−	0.0220633i	−0.00101451	−	0.999999i	$-0.500323\pi$
$401$	−4.20361	−	0.441818i	−0.209918	−	0.0220633i	−0.208904	+	0.977936i	$0.566990\pi$
$402$		0			0
$403$	1.08858	−	0.980164i	0.0542262	−	0.0488255i
$404$	2.68277	+	8.25672i	0.133473	+	0.410787i
$405$		0			0
$406$			23.5222i			1.16739i
$407$	0.702543	−	0.907900i	0.0348238	−	0.0450029i
$408$		0			0
$409$	10.2885	−	23.1083i	0.508733	−	1.14263i	−0.458488	−	0.888700i	$-0.651609\pi$
$409$	10.2885	−	23.1083i	0.508733	−	1.14263i	0.967222	−	0.253933i	$-0.0817244\pi$
$410$	−2.88091	−	2.59398i	−0.142278	−	0.128108i
$411$		0			0
$412$	−24.1942	+	10.7719i	−1.19196	+	0.530696i
$413$	20.5807	+	14.9527i	1.01271	+	0.735775i
$414$		0			0
$415$	5.00743	−	1.62701i	0.245805	−	0.0798669i
$416$	4.68563	−	0.492480i	0.229732	−	0.0241458i
$417$		0			0
$418$	0.338250	+	4.53362i	0.0165443	+	0.221746i
$419$	−13.4153	+	7.74533i	−0.655381	+	0.378384i	−0.790515	−	0.612443i	$-0.790187\pi$
$419$	−13.4153	+	7.74533i	−0.655381	+	0.378384i	0.135134	+	0.990827i	$0.456854\pi$
$420$		0			0
$421$	28.3961	+	6.03577i	1.38394	+	0.294165i	0.838919	−	0.544257i	$-0.183188\pi$
$421$	28.3961	+	6.03577i	1.38394	+	0.294165i	0.545021	+	0.838422i	$0.316522\pi$
$422$	−10.8059	−	3.51104i	−0.526021	−	0.170915i
$423$		0			0
$424$	15.6860	−	21.5899i	0.761778	−	1.04850i
$425$	0.557769	+	0.619466i	0.0270558	+	0.0300485i
$426$		0			0
$427$	61.6493	+	27.4481i	2.98342	+	1.32830i
$428$	−1.83590	−	3.17988i	−0.0887417	−	0.153705i
$429$		0			0
$430$	0.168801	−	0.292372i	0.00814032	−	0.0140994i
$431$	3.88324	−	2.82134i	0.187049	−	0.135899i	−0.490320	−	0.871542i	$-0.663120\pi$
$431$	3.88324	−	2.82134i	0.187049	−	0.135899i	0.677369	+	0.735643i	$0.263120\pi$
$432$		0			0
$433$	8.34981	−	25.6981i	0.401266	−	1.23497i	−0.522706	−	0.852513i	$-0.675078\pi$
$433$	8.34981	−	25.6981i	0.401266	−	1.23497i	0.923973	−	0.382458i	$-0.124922\pi$
$434$	−2.15992	−	4.85127i	−0.103680	−	0.232868i
$435$		0			0
$436$	−2.97762	−	14.0086i	−0.142602	−	0.670891i
$437$	7.11282	−	7.89959i	0.340252	−	0.377889i
$438$		0			0
$439$	−27.6193	−	15.9460i	−1.31820	−	0.761061i	−0.334758	−	0.942304i	$-0.608654\pi$
$439$	−27.6193	−	15.9460i	−1.31820	−	0.761061i	−0.983438	+	0.181243i	$0.941988\pi$
$440$	−1.28444	+	9.45877i	−0.0612334	+	0.450929i
$441$		0			0
$442$	−0.0758259	−	0.104365i	−0.00360667	−	0.00496416i
$443$	−2.32617	+	10.9438i	−0.110520	+	0.519954i	0.887706	+	0.460410i	$0.152298\pi$
$443$	−2.32617	+	10.9438i	−0.110520	+	0.519954i	−0.998226	+	0.0595433i	$0.981036\pi$
$444$		0			0
$445$	−1.80318	+	17.1561i	−0.0854790	+	0.813278i
$446$	0.0492964	−	0.469024i	0.00233425	−	0.0222089i
$447$		0			0
$448$	−0.0901707	+	0.424220i	−0.00426017	+	0.0200425i
$449$	−14.9366	−	20.5585i	−0.704903	−	0.970216i	−0.999892	−	0.0147150i	$-0.995316\pi$
$449$	−14.9366	−	20.5585i	−0.704903	−	0.970216i	0.294989	−	0.955501i	$-0.404684\pi$
$450$		0			0
$451$	−14.2010	+	7.63587i	−0.668699	+	0.359559i
$452$	10.0917	+	5.82646i	0.474675	+	0.274054i
$453$		0			0
$454$	6.95070	−	7.71953i	0.326212	−	0.362296i
$455$	1.07248	+	5.04562i	0.0502786	+	0.236542i
$456$		0			0
$457$	−6.07199	−	13.6379i	−0.284036	−	0.637955i	0.714030	−	0.700115i	$-0.246868\pi$
$457$	−6.07199	−	13.6379i	−0.284036	−	0.637955i	−0.998066	+	0.0621597i	$0.980201\pi$
$458$	4.24914	−	13.0775i	0.198549	−	0.611072i
$459$		0			0
$460$	8.05102	−	5.84941i	0.375381	−	0.272730i
$461$	6.50819	−	11.2725i	0.303117	−	0.525013i	−0.673724	−	0.738983i	$-0.735306\pi$
$461$	6.50819	−	11.2725i	0.303117	−	0.525013i	0.976840	+	0.213970i	$0.0686395\pi$
$462$		0			0
$463$	2.01632	+	3.49236i	0.0937062	+	0.162304i	0.909068	−	0.416648i	$-0.136795\pi$
$463$	2.01632	+	3.49236i	0.0937062	+	0.162304i	−0.815362	+	0.578952i	$0.803462\pi$
$464$	−12.8369	−	5.71538i	−0.595940	−	0.265330i
$465$		0			0
$466$	6.46775	+	7.18317i	0.299613	+	0.332754i
$467$	−24.7492	+	34.0643i	−1.14525	+	1.57631i	−0.390085	+	0.920779i	$0.627554\pi$
$467$	−24.7492	+	34.0643i	−1.14525	+	1.57631i	−0.755170	+	0.655529i	$0.772446\pi$
$468$		0			0
$469$	2.32540	+	0.755569i	0.107377	+	0.0348889i
$470$	−5.80097	−	1.23303i	−0.267579	−	0.0568756i
$471$		0			0
$472$	10.2638	−	5.92582i	0.472430	−	0.272758i
$473$	−0.907575	−	1.07143i	−0.0417303	−	0.0492644i
$474$		0			0
$475$	−7.35519	+	0.773062i	−0.337479	+	0.0354705i
$476$	1.83188	−	0.595214i	0.0839641	−	0.0272816i
$477$		0			0
$478$	−9.51213	−	6.91097i	−0.435075	−	0.316100i
$479$	−6.79274	+	3.02432i	−0.310368	+	0.138185i	−0.556009	−	0.831176i	$-0.687668\pi$
$479$	−6.79274	+	3.02432i	−0.310368	+	0.138185i	0.245641	+	0.969361i	$0.421001\pi$
$480$		0			0
$481$	−0.214779	−	0.193387i	−0.00979306	−	0.00881771i
$482$	−3.95813	+	8.89010i	−0.180288	+	0.404933i
$483$		0			0
$484$	15.7067	+	8.16461i	0.713940	+	0.371119i
$485$			10.1410i			0.460480i
$486$		0			0
$487$	4.00699	+	12.3322i	0.181574	+	0.558827i	0.999873	−	0.0159664i	$-0.00508249\pi$
$487$	4.00699	+	12.3322i	0.181574	+	0.558827i	−0.818299	+	0.574793i	$0.805082\pi$
$488$	23.3641	−	21.0371i	1.05764	−	0.952305i
$489$		0			0
$490$	13.0464	+	1.37124i	0.589378	+	0.0619461i
$491$	31.4996	−	6.69545i	1.42156	−	0.302162i	0.567944	−	0.823067i	$-0.307739\pi$
$491$	31.4996	−	6.69545i	1.42156	−	0.302162i	0.853614	+	0.520905i	$0.174406\pi$
$492$		0			0
$493$	0.200760	+	1.91010i	0.00904176	+	0.0860266i
$494$	1.14455			0.0514957
$495$		0			0
$496$	3.17233			0.142442
$497$	5.98869	+	56.9786i	0.268630	+	2.55584i
$498$		0			0
$499$	25.3022	−	5.37816i	1.13268	−	0.240759i	0.396825	−	0.917894i	$-0.370112\pi$
$499$	25.3022	−	5.37816i	1.13268	−	0.240759i	0.735859	+	0.677135i	$0.236779\pi$
$500$	−17.0943	−	1.79669i	−0.764482	−	0.0803503i
$501$		0			0
$502$	−6.57652	+	5.92153i	−0.293525	+	0.264291i
$503$	0.339066	+	1.04354i	0.0151182	+	0.0465290i	0.958331	−	0.285660i	$-0.0922128\pi$
$503$	0.339066	+	1.04354i	0.0151182	+	0.0465290i	−0.943213	+	0.332189i	$0.892213\pi$
$504$		0			0
$505$			6.88210i			0.306250i
$506$	2.81501	+	9.64727i	0.125142	+	0.428874i
$507$		0			0
$508$	1.88508	−	4.23396i	0.0836369	−	0.187852i
$509$	−5.20389	−	4.68561i	−0.230658	−	0.207686i	0.545695	−	0.837984i	$-0.316266\pi$
$509$	−5.20389	−	4.68561i	−0.230658	−	0.207686i	−0.776353	+	0.630298i	$0.782933\pi$
$510$		0			0
$511$	−17.9168	+	7.97708i	−0.792593	+	0.352885i
$512$	14.8558	+	10.7934i	0.656539	+	0.477003i
$513$		0			0
$514$	−8.84890	+	2.87518i	−0.390308	+	0.126819i
$515$	−20.8793	+	2.19450i	−0.920050	+	0.0967012i
$516$		0			0
$517$	−12.9736	+	20.9790i	−0.570579	+	0.922653i
$518$	−0.907371	+	0.523871i	−0.0398676	+	0.0230176i
$519$		0			0
$520$	2.35067	+	0.499650i	0.103084	+	0.0219111i
$521$	7.27467	+	2.36368i	0.318709	+	0.103555i	0.464003	−	0.885834i	$-0.346413\pi$
$521$	7.27467	+	2.36368i	0.318709	+	0.103555i	−0.145294	+	0.989389i	$0.546413\pi$
$522$		0			0
$523$	−18.3418	+	25.2453i	−0.802029	+	1.10390i	0.190476	+	0.981692i	$0.438997\pi$
$523$	−18.3418	+	25.2453i	−0.802029	+	1.10390i	−0.992505	+	0.122206i	$0.961003\pi$
$524$	0.606637	+	0.673739i	0.0265011	+	0.0294324i
$525$		0			0
$526$	−13.6486	−	6.07674i	−0.595106	−	0.264958i
$527$	−0.216799	−	0.375508i	−0.00944393	−	0.0163574i
$528$		0			0
$529$	0.248947	−	0.431189i	0.0108238	−	0.0187473i
$530$	7.63097	−	5.54423i	0.331468	−	0.240826i
$531$		0			0
$532$	−5.28091	+	16.2530i	−0.228956	+	0.704656i
$533$	1.65106	+	3.70835i	0.0715155	+	0.160626i
$534$		0			0
$535$	−0.605171	−	2.84711i	−0.0261638	−	0.123091i
$536$	0.762218	−	0.846529i	0.0329228	−	0.0365645i
$537$		0			0
$538$	−4.26107	−	2.46013i	−0.183708	−	0.106064i
$539$	23.6896	−	49.1506i	1.02038	−	2.11707i
$540$		0			0
$541$	−16.7402	−	23.0409i	−0.719717	−	0.990605i	−0.999533	−	0.0305514i	$-0.990274\pi$
$541$	−16.7402	−	23.0409i	−0.719717	−	0.990605i	0.279817	−	0.960053i	$-0.409726\pi$
$542$	0.639346	−	3.00789i	0.0274623	−	0.129200i
$543$		0			0
$544$	0.145777	−	1.38697i	0.00625013	−	0.0594661i
$545$	1.18671	−	11.2908i	0.0508331	−	0.483645i
$546$		0			0
$547$	8.39019	−	39.4727i	0.358739	−	1.68773i	−0.315265	−	0.949004i	$-0.602093\pi$
$547$	8.39019	−	39.4727i	0.358739	−	1.68773i	0.674003	−	0.738729i	$-0.264573\pi$
$548$	−4.39118	−	6.04394i	−0.187582	−	0.258185i
$549$		0			0
$550$	3.03575	−	6.29851i	0.129445	−	0.268569i
$551$	−14.7573	−	8.52016i	−0.628684	−	0.362971i
$552$		0			0
$553$	−7.17073	+	7.96390i	−0.304930	+	0.338659i
$554$	3.43213	+	16.1469i	0.145817	+	0.686016i
$555$		0			0
$556$	6.87820	+	15.4487i	0.291701	+	0.655171i
$557$	5.23145	−	16.1007i	0.221664	−	0.682211i	−0.776950	−	0.629563i	$-0.783234\pi$
$557$	5.23145	−	16.1007i	0.221664	−	0.682211i	0.998613	−	0.0526476i	$-0.0167660\pi$
$558$		0			0
$559$	−0.285994	+	0.207787i	−0.0120963	+	0.00878845i
$560$	−5.58560	+	9.67455i	−0.236035	+	0.408824i
$561$		0			0
$562$	−4.96742	−	8.60382i	−0.209538	−	0.362930i
$563$	−21.2668	−	9.46858i	−0.896288	−	0.399053i	−0.0937095	−	0.995600i	$-0.529872\pi$
$563$	−21.2668	−	9.46858i	−0.896288	−	0.399053i	−0.802579	+	0.596546i	$0.796539\pi$
$564$		0			0
$565$	6.18109	+	6.86480i	0.260041	+	0.288804i
$566$	−4.04544	+	5.56807i	−0.170042	+	0.234043i
$567$		0			0
$568$	25.3852	+	8.24815i	1.06514	+	0.346085i
$569$	−22.2560	−	4.73066i	−0.933020	−	0.198320i	−0.283768	−	0.958893i	$-0.591585\pi$
$569$	−22.2560	−	4.73066i	−0.933020	−	0.198320i	−0.649252	+	0.760573i	$0.724918\pi$
$570$		0			0
$571$	−25.0248	+	14.4481i	−1.04726	+	0.604634i	−0.921880	−	0.387475i	$-0.873347\pi$
$571$	−25.0248	+	14.4481i	−1.04726	+	0.604634i	−0.125377	+	0.992109i	$0.540014\pi$
$572$	2.34402	−	3.79040i	0.0980085	−	0.158484i
$573$		0			0
$574$	14.6353	−	1.53823i	0.610866	−	0.0642046i
$575$	−15.5483	+	5.05196i	−0.648410	+	0.210681i
$576$		0			0
$577$	25.9942	+	18.8859i	1.08215	+	0.786229i	0.978057	−	0.208339i	$-0.0668056\pi$
$577$	25.9942	+	18.8859i	1.08215	+	0.786229i	0.104094	+	0.994567i	$0.466806\pi$
$578$	9.67282	−	4.30662i	0.402336	−	0.179132i
$579$		0			0
$580$	−11.8553	−	10.6746i	−0.492265	−	0.443238i
$581$	−8.12930	+	18.2587i	−0.337260	+	0.757499i
$582$		0			0
$583$	−10.9891	−	37.6607i	−0.455124	−	1.55975i
$584$			9.13707i			0.378095i
$585$		0			0
$586$	−2.73676	−	8.42287i	−0.113054	−	0.347945i
$587$	−2.75704	+	2.48245i	−0.113795	+	0.102462i	−0.724064	−	0.689733i	$-0.757728\pi$
$587$	−2.75704	+	2.48245i	−0.113795	+	0.102462i	0.610269	+	0.792194i	$0.291061\pi$
$588$		0			0
$589$	3.82594	+	0.402123i	0.157645	+	0.0165692i
$590$	4.09744	−	0.870937i	0.168689	−	0.0358559i
$591$		0			0
$592$	−0.0654247	−	0.622474i	−0.00268894	−	0.0255835i
$593$	−38.2706			−1.57159			−0.785793	−	0.618490i	$-0.787745\pi$
$593$	−38.2706			−1.57159			−0.785793	+	0.618490i	$0.787745\pi$
$594$		0			0
$595$	1.52690			0.0625968
$596$	−2.56102	−	24.3665i	−0.104903	−	0.998090i
$597$		0			0
$598$	2.47478	−	0.526031i	0.101201	−	0.0215110i
$599$	−12.4319	−	1.30664i	−0.507953	−	0.0533880i	−0.152914	−	0.988240i	$-0.548866\pi$
$599$	−12.4319	−	1.30664i	−0.507953	−	0.0533880i	−0.355039	+	0.934852i	$0.615532\pi$
$600$		0			0
$601$	−16.9896	+	15.2975i	−0.693021	+	0.623998i	−0.938450	−	0.345416i	$-0.887738\pi$
$601$	−16.9896	+	15.2975i	−0.693021	+	0.623998i	0.245429	+	0.969415i	$0.421071\pi$
$602$	0.396022	+	1.21883i	0.0161406	+	0.0496758i
$603$		0			0
$604$			12.2970i			0.500356i
$605$	9.84156	+	10.0030i	0.400116	+	0.406682i
$606$		0			0
$607$	12.3631	−	27.7681i	0.501805	−	1.12707i	−0.468120	−	0.883665i	$-0.655068\pi$
$607$	12.3631	−	27.7681i	0.501805	−	1.12707i	0.969924	−	0.243407i	$-0.0782650\pi$
$608$	9.19525	+	8.27944i	0.372916	+	0.335775i
$609$		0			0
$610$	10.1516	−	4.51979i	0.411026	−	0.183001i
$611$	5.02398	+	3.65013i	0.203248	+	0.147669i
$612$		0			0
$613$	1.41405	−	0.459451i	0.0571128	−	0.0185571i	−0.280321	−	0.959906i	$-0.590441\pi$
$613$	1.41405	−	0.459451i	0.0571128	−	0.0185571i	0.337434	+	0.941349i	$0.390441\pi$
$614$	7.17324	−	0.753938i	0.289488	−	0.0304265i
$615$		0			0
$616$	−23.4207	−	27.6492i	−0.943649	−	1.11402i
$617$	29.1210	−	16.8130i	1.17237	−	0.676867i	0.218132	−	0.975919i	$-0.430004\pi$
$617$	29.1210	−	16.8130i	1.17237	−	0.676867i	0.954237	+	0.299052i	$0.0966705\pi$
$618$		0			0
$619$	−2.76364	−	0.587430i	−0.111080	−	0.0236108i	0.152036	−	0.988375i	$-0.451417\pi$
$619$	−2.76364	−	0.587430i	−0.111080	−	0.0236108i	−0.263116	+	0.964764i	$0.584750\pi$
$620$	3.42525	+	1.11293i	0.137561	+	0.0446964i
$621$		0			0
$622$	−10.0534	+	13.8373i	−0.403103	+	0.554824i
$623$	−43.8174	−	48.6642i	−1.75551	−	1.94969i
$624$		0			0
$625$	2.95737	+	1.31671i	0.118295	+	0.0526683i
$626$	2.59710	+	4.49831i	0.103801	+	0.179789i
$627$		0			0
$628$	−3.48413	+	6.03469i	−0.139032	+	0.240810i
$629$	−0.0692110	+	0.0502848i	−0.00275962	+	0.00200498i
$630$		0			0
$631$	2.32895	−	7.16777i	0.0927140	−	0.285344i	−0.893937	−	0.448192i	$-0.852068\pi$
$631$	2.32895	−	7.16777i	0.0927140	−	0.285344i	0.986651	+	0.162848i	$0.0520680\pi$
$632$	2.03068	+	4.56099i	0.0807762	+	0.181426i
$633$		0			0
$634$	−1.97465	−	9.28998i	−0.0784232	−	0.368952i
$635$	2.45837	−	2.73030i	0.0975574	−	0.108348i
$636$		0			0
$637$	−11.8960	−	6.86818i	−0.471338	−	0.272127i
$638$	14.1889	−	7.62935i	0.561743	−	0.302049i
$639$		0			0
$640$	8.50394	+	11.7047i	0.336148	+	0.462668i
$641$	4.00545	−	18.8441i	0.158206	−	0.744299i	−0.825484	−	0.564425i	$-0.809098\pi$
$641$	4.00545	−	18.8441i	0.158206	−	0.744299i	0.983690	−	0.179874i	$-0.0575689\pi$
$642$		0			0
$643$	1.96220	−	18.6691i	0.0773816	−	0.736237i	−0.885194	−	0.465222i	$-0.845974\pi$
$643$	1.96220	−	18.6691i	0.0773816	−	0.736237i	0.962575	−	0.271014i	$-0.0873590\pi$
$644$	−3.94874	+	37.5698i	−0.155602	+	1.48046i
$645$		0			0
$646$	0.0704391	−	0.331390i	0.00277139	−	0.0130384i
$647$	1.43599	+	1.97647i	0.0564545	+	0.0777030i	0.836311	−	0.548256i	$-0.184708\pi$
$647$	1.43599	+	1.97647i	0.0564545	+	0.0777030i	−0.779856	+	0.625959i	$0.784708\pi$
$648$		0			0
$649$	2.34439	−	17.2643i	0.0920254	−	0.677685i
$650$	−1.52444	−	0.880138i	−0.0597936	−	0.0345219i
$651$		0			0
$652$	−7.67332	+	8.52209i	−0.300511	+	0.333751i
$653$	4.15170	+	19.5322i	0.162469	+	0.764355i	0.981630	+	0.190792i	$0.0611057\pi$
$653$	4.15170	+	19.5322i	0.162469	+	0.764355i	−0.819162	+	0.573563i	$0.805561\pi$
$654$		0			0
$655$	0.292315	+	0.656550i	0.0114217	+	0.0256535i
$656$	−2.71658	+	8.36077i	−0.106065	+	0.326433i
$657$		0			0
$658$	18.2131	−	13.2326i	0.710022	−	0.515861i
$659$	17.8420	−	30.9032i	0.695024	−	1.20382i	−0.275148	−	0.961402i	$-0.588727\pi$
$659$	17.8420	−	30.9032i	0.695024	−	1.20382i	0.970172	−	0.242416i	$-0.0779398\pi$
$660$		0			0
$661$	4.45874	+	7.72277i	0.173425	+	0.300381i	0.939615	−	0.342233i	$-0.111183\pi$
$661$	4.45874	+	7.72277i	0.173425	+	0.300381i	−0.766190	+	0.642614i	$0.777850\pi$
$662$	−8.23124	−	3.66478i	−0.319916	−	0.142436i
$663$		0			0
$664$	6.23056	+	6.91974i	0.241793	+	0.268538i
$665$	−7.96278	+	10.9598i	−0.308783	+	0.425004i
$666$		0			0
$667$	−35.8246	−	11.6401i	−1.38714	−	0.450708i
$668$	−12.8732	−	2.73628i	−0.498079	−	0.105870i
$669$		0			0
$670$	0.348681	−	0.201311i	0.0134707	−	0.00777733i
$671$	−3.43876	−	46.0902i	−0.132752	−	1.77929i
$672$		0			0
$673$	10.8735	−	1.14285i	0.419142	−	0.0440536i	0.107390	−	0.994217i	$-0.465751\pi$
$673$	10.8735	−	1.14285i	0.419142	−	0.0440536i	0.311752	+	0.950163i	$0.399084\pi$
$674$	4.60308	−	1.49563i	0.177304	−	0.0576096i
$675$		0			0
$676$	16.0174	+	11.6373i	0.616052	+	0.447588i
$677$	−21.7120	+	9.66682i	−0.834461	+	0.371526i	−0.779069	−	0.626939i	$-0.784308\pi$
$677$	−21.7120	+	9.66682i	−0.834461	+	0.371526i	−0.0553924	+	0.998465i	$0.517641\pi$
$678$		0			0
$679$	−28.6079	−	25.7587i	−1.09787	−	0.988528i
$680$	0.289335	−	0.649856i	0.0110955	−	0.0249208i
$681$		0			0
$682$	−2.22577	+	2.87638i	−0.0852293	+	0.110142i
$683$			24.2759i			0.928892i	0.885602	+	0.464446i	$0.153746\pi$
$683$			24.2759i			0.928892i	−0.885602	+	0.464446i	$0.846254\pi$
$684$		0			0
$685$	−1.83006	−	5.63234i	−0.0699229	−	0.215201i
$686$	−21.2602	+	19.1428i	−0.811717	+	0.730874i
$687$		0			0
$688$	−0.761384	−	0.0800247i	−0.0290275	−	0.00305091i
$689$	−9.66097	+	2.05350i	−0.368054	+	0.0782322i
$690$		0			0
$691$	3.41070	+	32.4506i	0.129749	+	1.23448i	0.844675	+	0.535280i	$0.179794\pi$
$691$	3.41070	+	32.4506i	0.129749	+	1.23448i	−0.714926	+	0.699200i	$0.753540\pi$
$692$	10.8872			0.413868
$693$		0			0
$694$	5.41398			0.205512
$695$	1.40125	+	13.3320i	0.0531525	+	0.505712i
$696$		0			0
$697$	1.17532	−	0.249821i	0.0445183	−	0.00946266i
$698$	−10.4215	−	1.09534i	−0.394458	−	0.0414592i
$699$		0			0
$700$	19.5320	−	17.5867i	0.738239	−	0.664713i
$701$	−11.0658	−	34.0571i	−0.417951	−	1.28632i	−0.909585	−	0.415518i	$-0.863600\pi$
$701$	−11.0658	−	34.0571i	−0.417951	−	1.28632i	0.491634	−	0.870802i	$-0.336400\pi$
$702$		0			0
$703$		−	0.759020i		−	0.0286270i
$704$	0.285141	−	0.0832021i	0.0107466	−	0.00313580i
$705$		0			0
$706$	2.97641	−	6.68513i	0.112019	−	0.251598i
$707$	−19.4145	−	17.4809i	−0.730157	−	0.657436i
$708$		0			0
$709$	3.35991	−	1.49593i	0.126184	−	0.0561807i	−0.342673	−	0.939455i	$-0.611332\pi$
$709$	3.35991	−	1.49593i	0.126184	−	0.0561807i	0.468857	+	0.883274i	$0.344666\pi$
$710$	7.63240	+	5.54527i	0.286439	+	0.208110i
$711$		0			0
$712$	−29.0147	+	9.42746i	−1.08737	+	0.353309i
$713$	8.45739	−	0.888907i	0.316732	−	0.0332898i
$714$		0			0
$715$	2.69572	−	2.28346i	0.100814	−	0.0853966i
$716$	10.0387	−	5.79582i	0.375162	−	0.216600i
$717$		0			0
$718$	−10.9899	−	2.33597i	−0.410139	−	0.0871778i
$719$	−12.2052	−	3.96571i	−0.455177	−	0.147896i	0.0724502	−	0.997372i	$-0.476918\pi$
$719$	−12.2052	−	3.96571i	−0.455177	−	0.147896i	−0.527627	+	0.849476i	$0.676918\pi$
$720$		0			0
$721$	46.8436	−	64.4747i	1.74455	−	2.40116i
$722$	−5.93565	−	6.59221i	−0.220902	−	0.245337i
$723$		0			0
$724$	0.696587	+	0.310140i	0.0258884	+	0.0115263i
$725$	13.1037	+	22.6963i	0.486659	+	0.842918i
$726$		0			0
$727$	20.9562	−	36.2973i	0.777224	−	1.34619i	−0.156312	−	0.987708i	$-0.549961\pi$
$727$	20.9562	−	36.2973i	0.777224	−	1.34619i	0.933536	−	0.358484i	$-0.116706\pi$
$728$	−7.38033	+	5.36212i	−0.273533	+	0.198733i
$729$		0			0
$730$	−0.997974	+	3.07145i	−0.0369367	+	0.113679i
$731$	0.0425611	+	0.0955939i	0.00157418	+	0.00353567i
$732$		0			0
$733$	5.40762	+	25.4408i	0.199735	+	0.939679i	0.957786	+	0.287483i	$0.0928186\pi$
$733$	5.40762	+	25.4408i	0.199735	+	0.939679i	−0.758051	+	0.652196i	$0.773848\pi$
$734$	11.4889	−	12.7597i	0.424063	−	0.470970i
$735$		0			0
$736$	23.6875	+	13.6760i	0.873131	+	0.504102i
$737$	−0.298468	−	1.64777i	−0.0109942	−	0.0606966i
$738$		0			0
$739$	−17.3756	−	23.9154i	−0.639171	−	0.879744i	0.359400	−	0.933184i	$-0.382981\pi$
$739$	−17.3756	−	23.9154i	−0.639171	−	0.879744i	−0.998571	+	0.0534398i	$0.982981\pi$
$740$	0.147739	−	0.695056i	0.00543098	−	0.0255508i
$741$		0			0
$742$	−3.74272	+	35.6096i	−0.137400	+	1.30727i
$743$	−1.56007	+	14.8431i	−0.0572334	+	0.544539i	0.927910	+	0.372805i	$0.121604\pi$
$743$	−1.56007	+	14.8431i	−0.0572334	+	0.544539i	−0.985143	+	0.171735i	$0.945063\pi$
$744$		0			0
$745$	4.03810	−	18.9978i	0.147945	−	0.696024i
$746$	−6.23552	−	8.58246i	−0.228299	−	0.314226i
$747$		0			0
$748$	−0.953203	−	0.911955i	−0.0348525	−	0.0333444i
$749$	9.56888	+	5.52460i	0.349639	+	0.201864i
$750$		0			0
$751$	−12.1248	+	13.4659i	−0.442439	+	0.491378i	−0.922576	−	0.385815i	$-0.873920\pi$
$751$	−12.1248	+	13.4659i	−0.442439	+	0.491378i	0.480137	+	0.877194i	$0.340587\pi$
$752$	2.79614	+	13.1548i	0.101965	+	0.479706i
$753$		0			0
$754$	−1.64965	−	3.70518i	−0.0600768	−	0.134935i
$755$	−3.01231	+	9.27095i	−0.109629	+	0.337404i
$756$		0			0
$757$	5.28836	−	3.84222i	0.192209	−	0.139648i	−0.487519	−	0.873112i	$-0.662098\pi$
$757$	5.28836	−	3.84222i	0.192209	−	0.139648i	0.679728	+	0.733465i	$0.262098\pi$
$758$	−4.80486	+	8.32227i	−0.174520	+	0.302278i
$759$		0			0
$760$	3.15568	+	5.46580i	0.114469	+	0.198265i
$761$	29.7819	+	13.2597i	1.07959	+	0.480665i	0.867934	−	0.496679i	$-0.165447\pi$
$761$	29.7819	+	13.2597i	1.07959	+	0.480665i	0.211657	+	0.977344i	$0.432114\pi$
$762$		0			0
$763$	28.8372	+	32.0269i	1.04398	+	1.15945i
$764$	−0.0384017	+	0.0528554i	−0.00138932	+	0.00191224i
$765$		0			0
$766$	−4.92851	−	1.60137i	−0.178074	−	0.0578598i
$767$	−4.29049	−	0.911971i	−0.154920	−	0.0329294i
$768$		0			0
$769$	−34.9046	+	20.1522i	−1.25869	+	0.726707i	−0.972821	−	0.231560i	$-0.925617\pi$
$769$	−34.9046	+	20.1522i	−1.25869	+	0.726707i	−0.285873	+	0.958268i	$0.592284\pi$
$770$	−4.85302	−	11.8524i	−0.174891	−	0.427131i
$771$		0			0
$772$	−17.9845	+	1.89025i	−0.647278	+	0.0680316i
$773$	9.02009	−	2.93080i	0.324430	−	0.105414i	−0.142274	−	0.989827i	$-0.545441\pi$
$773$	9.02009	−	2.93080i	0.324430	−	0.105414i	0.466704	+	0.884414i	$0.345441\pi$
$774$		0			0
$775$	−4.78661	−	3.47767i	−0.171940	−	0.124922i
$776$	−16.3840	+	7.29463i	−0.588151	+	0.261862i
$777$		0			0
$778$	11.6987	+	10.5336i	0.419419	+	0.377647i
$779$	−4.33610	+	9.73905i	−0.155357	+	0.348938i
$780$		0			0
$781$	32.4277	−	22.0932i	1.16035	−	0.790558i
$782$		−	0.748915i		−	0.0267812i
$783$		0			0
$784$	−9.19272	−	28.2923i	−0.328311	−	1.01044i
$785$	−4.10504	+	3.69620i	−0.146515	+	0.131923i
$786$		0			0
$787$	41.0059	+	4.30989i	1.46170	+	0.153631i	0.801742	−	0.597670i	$-0.203907\pi$
$787$	41.0059	+	4.30989i	1.46170	+	0.153631i	0.659959	+	0.751301i	$0.270574\pi$
$788$	32.7650	−	6.96442i	1.16721	−	0.248097i
$789$		0			0
$790$	0.184456	+	1.75498i	0.00656265	+	0.0624395i
$791$	−35.0659			−1.24680
$792$		0			0
$793$	−11.6359			−0.413202
$794$	−1.70501	−	16.2221i	−0.0605084	−	0.575699i
$795$		0			0
$796$	22.6846	−	4.82176i	0.804034	−	0.170903i
$797$	−12.7001	−	1.33483i	−0.449861	−	0.0472823i	−0.123110	−	0.992393i	$-0.539287\pi$
$797$	−12.7001	−	1.33483i	−0.449861	−	0.0472823i	−0.326750	+	0.945111i	$0.605954\pi$
$798$		0			0
$799$	1.36604	−	1.22999i	0.0483271	−	0.0435139i
$800$	−5.88056	−	18.0985i	−0.207909	−	0.639878i
$801$		0			0
$802$		−	2.64208i		−	0.0932950i
$803$	10.6231	+	8.22028i	0.374881	+	0.290087i
$804$		0			0
$805$	−12.1803	+	27.3574i	−0.429298	+	0.964220i
$806$	0.680454	+	0.612684i	0.0239680	+	0.0215809i
$807$		0			0
$808$	−11.1188	+	4.95042i	−0.391159	+	0.174155i
$809$	33.5935	+	24.4071i	1.18108	+	0.858107i	0.992293	−	0.123910i	$-0.0395435\pi$
$809$	33.5935	+	24.4071i	1.18108	+	0.858107i	0.188790	+	0.982017i	$0.439543\pi$
$810$		0			0
$811$	5.10222	−	1.65781i	0.179163	−	0.0582137i	−0.218061	−	0.975935i	$-0.569973\pi$
$811$	5.10222	−	1.65781i	0.179163	−	0.0582137i	0.397225	+	0.917721i	$0.369973\pi$
$812$	60.2262	−	6.33002i	2.11352	−	0.222140i
$813$		0			0
$814$	0.610307	+	0.377421i	0.0213913	+	0.0132286i
$815$	−7.87269	+	4.54530i	−0.275768	+	0.159215i
$816$		0			0
$817$	−0.908113	−	0.193025i	−0.0317709	−	0.00675310i
$818$	15.0377	+	4.88605i	0.525782	+	0.170837i
$819$		0			0
$820$	−5.86634	+	8.07432i	−0.204861	+	0.281968i
$821$	21.3407	+	23.7013i	0.744797	+	0.827181i	0.989818	−	0.142337i	$-0.0454617\pi$
$821$	21.3407	+	23.7013i	0.744797	+	0.827181i	−0.245022	+	0.969518i	$0.578795\pi$
$822$		0			0
$823$	−23.8606	−	10.6234i	−0.831727	−	0.370309i	−0.0537135	−	0.998556i	$-0.517106\pi$
$823$	−23.8606	−	10.6234i	−0.831727	−	0.370309i	−0.778013	+	0.628248i	$0.783772\pi$
$824$	−18.5643	−	32.1543i	−0.646718	−	1.12015i
$825$		0			0
$826$	−7.95077	+	13.7711i	−0.276643	+	0.479159i
$827$	31.8832	−	23.1645i	1.10869	−	0.805508i	0.126231	−	0.992001i	$-0.459712\pi$
$827$	31.8832	−	23.1645i	1.10869	−	0.805508i	0.982456	+	0.186493i	$0.0597120\pi$
$828$		0			0
$829$	−10.5153	+	32.3627i	−0.365211	+	1.12400i	0.584638	+	0.811294i	$0.301237\pi$
$829$	−10.5153	+	32.3627i	−0.365211	+	1.12400i	−0.949849	+	0.312710i	$0.898763\pi$
$830$	1.33863	+	3.00660i	0.0464644	+	0.104361i
$831$		0			0
$832$	−0.0155477	−	0.0731461i	−0.000539019	−	0.00253589i
$833$	−2.72072	+	3.02166i	−0.0942672	+	0.104694i
$834$		0			0
$835$	−9.03509	−	5.21641i	−0.312672	−	0.180521i
$836$	11.5168	−	2.08609i	0.398317	−	0.0721488i
$837$		0			0
$838$	−5.69149	−	7.83367i	−0.196609	−	0.270610i
$839$	−11.8515	+	55.7569i	−0.409159	+	1.92494i	−0.0301584	+	0.999545i	$0.509601\pi$
$839$	−11.8515	+	55.7569i	−0.409159	+	1.92494i	−0.379001	+	0.925396i	$0.623732\pi$
$840$		0			0
$841$	−3.28052	+	31.2121i	−0.113122	+	1.07628i
$842$	−1.89682	+	18.0470i	−0.0653687	+	0.621941i
$843$		0			0
$844$	−6.08169	+	28.6121i	−0.209340	+	0.984869i
$845$	9.22511	+	12.6973i	0.317353	+	0.436800i
$846$		0			0
$847$	−53.2167	+	2.35493i	−1.82855	+	0.0809163i
$848$	−18.5241	−	10.6949i	−0.636120	−	0.367264i
$849$		0			0
$850$	−0.348652	+	0.387217i	−0.0119587	+	0.0132814i
$851$	−0.348843	−	1.64118i	−0.0119582	−	0.0562588i
$852$		0			0
$853$	13.1547	+	29.5460i	0.450410	+	1.01164i	0.985937	+	0.167118i	$0.0534462\pi$
$853$	13.1547	+	29.5460i	0.450410	+	1.01164i	−0.535527	+	0.844518i	$0.679887\pi$
$854$	−13.0352	+	40.1182i	−0.446056	+	1.37282i
$855$		0			0
$856$	4.16452	−	3.02570i	0.142340	−	0.103416i
$857$	16.8286	−	29.1480i	0.574855	−	0.995678i	−0.421202	−	0.906967i	$-0.638392\pi$
$857$	16.8286	−	29.1480i	0.574855	−	0.995678i	0.996057	−	0.0887115i	$-0.0282749\pi$
$858$		0			0
$859$	19.0213	+	32.9458i	0.648998	+	1.12410i	0.983363	+	0.181653i	$0.0581449\pi$
$859$	19.0213	+	32.9458i	0.648998	+	1.12410i	−0.334365	+	0.942444i	$0.608522\pi$
$860$	−0.794013	−	0.353517i	−0.0270756	−	0.0120548i
$861$		0			0
$862$	2.00763	+	2.22970i	0.0683803	+	0.0759440i
$863$	−9.20216	+	12.6657i	−0.313245	+	0.431145i	−0.936390	−	0.350962i	$-0.885855\pi$
$863$	−9.20216	+	12.6657i	−0.313245	+	0.431145i	0.623145	+	0.782107i	$0.285855\pi$
$864$		0			0
$865$	8.20807	+	2.66696i	0.279083	+	0.0906795i
$866$	16.5210	+	3.51165i	0.561406	+	0.119331i
$867$		0			0
$868$	−11.8399	+	6.83576i	−0.401872	+	0.232021i
$869$	7.12971	+	1.74240i	0.241859	+	0.0591069i
$870$		0			0
$871$	−0.419282	+	0.0440684i	−0.0142068	+	0.00149320i
$872$	19.0952	−	6.20441i	0.646646	−	0.210108i
$873$		0			0
$874$	5.37559	+	3.90559i	0.181832	+	0.132109i
$875$	47.2519	−	21.0379i	1.59741	−	0.711211i
$876$		0			0
$877$	−10.9549	−	9.86381i	−0.369920	−	0.333077i	0.463115	−	0.886298i	$-0.346732\pi$
$877$	−10.9549	−	9.86381i	−0.369920	−	0.333077i	−0.833034	+	0.553221i	$0.813398\pi$
$878$	8.10835	−	18.2116i	0.273643	−	0.614613i
$879$		0			0
$880$	7.64746	+	0.231395i	0.257796	+	0.00780031i
$881$			29.1468i			0.981981i	0.871165	+	0.490990i	$0.163365\pi$
$881$			29.1468i			0.981981i	−0.871165	+	0.490990i	$0.836635\pi$
$882$		0			0
$883$	0.109578	+	0.337245i	0.00368758	+	0.0113492i	0.952883	−	0.303337i	$-0.0981008\pi$
$883$	0.109578	+	0.337245i	0.00368758	+	0.0113492i	−0.949196	+	0.314686i	$0.898101\pi$
$884$	−0.246811	+	0.222230i	−0.00830115	+	0.00747439i
$885$		0			0
$886$	−6.95527	−	0.731028i	−0.233667	−	0.0245594i
$887$	2.52234	−	0.536141i	0.0846920	−	0.0180018i	−0.165371	−	0.986231i	$-0.552882\pi$
$887$	2.52234	−	0.536141i	0.0846920	−	0.0180018i	0.250063	+	0.968230i	$0.419549\pi$
$888$		0			0
$889$	1.45781	+	13.8702i	0.0488935	+	0.465190i
$890$	−10.7831			−0.361449
$891$		0			0
$892$	−1.21415			−0.0406528
$893$	1.70475	+	16.2196i	0.0570473	+	0.542769i
$894$		0			0
$895$	8.98812	−	1.91048i	0.300440	−	0.0638605i
$896$	−54.6194	−	5.74073i	−1.82471	−	0.191784i
$897$		0			0
$898$	11.8044	−	10.6287i	0.393919	−	0.354686i
$899$	−4.21260	−	12.9651i	−0.140498	−	0.432409i
$900$		0			0
$901$			2.92359i			0.0973989i
$902$	−5.67478	−	8.32926i	−0.188950	−	0.277334i
$903$		0			0
$904$	−6.64470	+	14.9242i	−0.220999	+	0.496373i
$905$	0.449198	+	0.404460i	0.0149319	+	0.0134447i
$906$		0			0
$907$	17.1306	−	7.62703i	0.568812	−	0.253251i	−0.102118	−	0.994772i	$-0.532562\pi$
$907$	17.1306	−	7.62703i	0.568812	−	0.253251i	0.670930	+	0.741521i	$0.265895\pi$
$908$	−21.6355	−	15.7191i	−0.718000	−	0.521657i
$909$		0			0
$910$	−3.06658	+	0.996391i	−0.101656	+	0.0330301i
$911$	−12.1823	+	1.28041i	−0.403619	+	0.0424220i	−0.304163	−	0.952620i	$-0.598377\pi$
$911$	−12.1823	+	1.28041i	−0.403619	+	0.0424220i	−0.0994555	+	0.995042i	$0.531710\pi$
$912$		0			0
$913$	13.6506	−	1.01846i	0.451768	−	0.0337060i
$914$	8.08139	−	4.66579i	0.267309	−	0.154331i
$915$		0			0
$916$	−34.6270	−	7.36020i	−1.14411	−	0.243188i
$917$	−2.59463	−	0.843046i	−0.0856822	−	0.0278398i
$918$		0			0
$919$	−14.4656	+	19.9102i	−0.477175	+	0.656775i	−0.977959	−	0.208797i	$-0.933045\pi$
$919$	−14.4656	+	19.9102i	−0.477175	+	0.656775i	0.500784	+	0.865572i	$0.333045\pi$
$920$	9.33537	+	10.3680i	0.307778	+	0.341822i
$921$		0			0
$922$	7.43289	+	3.30934i	0.244789	+	0.108987i
$923$	−4.93933	−	8.55517i	−0.162580	−	0.281597i
$924$		0			0
$925$	−0.583673	+	1.01095i	−0.0191910	+	0.0332399i
$926$	−2.03931	+	1.48165i	−0.0670160	+	0.0486899i
$927$		0			0
$928$	13.5493	−	41.7004i	0.444777	−	1.36888i
$929$	−7.85739	−	17.6480i	−0.257793	−	0.579012i	0.737563	−	0.675278i	$-0.235977\pi$
$929$	−7.85739	−	17.6480i	−0.257793	−	0.579012i	−0.995356	+	0.0962666i	$0.969310\pi$
$930$		0			0
$931$	−7.50044	−	35.2868i	−0.245817	−	1.15648i
$932$	16.6512	−	18.4930i	0.545428	−	0.605759i
$933$		0			0
$934$	−22.7934	−	13.1598i	−0.745824	−	0.430602i
$935$	−0.495244	−	0.921043i	−0.0161962	−	0.0301213i
$936$		0			0
$937$	29.8196	+	41.0432i	0.974165	+	1.34082i	0.939915	+	0.341409i	$0.110904\pi$
$937$	29.8196	+	41.0432i	0.974165	+	1.34082i	0.0342499	+	0.999413i	$0.489096\pi$
$938$	−0.317767	+	1.49497i	−0.0103754	+	0.0488126i
$939$		0			0
$940$	−1.59596	+	15.1846i	−0.0520546	+	0.495266i
$941$	3.15903	−	30.0561i	0.102981	−	0.979802i	−0.813998	−	0.580867i	$-0.802713\pi$
$941$	3.15903	−	30.0561i	0.102981	−	0.979802i	0.916979	−	0.398934i	$-0.130620\pi$
$942$		0			0
$943$	−4.89963	+	23.0509i	−0.159554	+	0.750642i
$944$	−5.58355	−	7.68510i	−0.181729	−	0.250129i
$945$		0			0
$946$	0.606763	−	0.634207i	0.0197276	−	0.0206199i
$947$	9.86510	+	5.69562i	0.320573	+	0.185083i	0.651648	−	0.758522i	$-0.274078\pi$
$947$	9.86510	+	5.69562i	0.320573	+	0.185083i	−0.331075	+	0.943604i	$0.607411\pi$
$948$		0			0
$949$	2.26278	−	2.51307i	0.0734529	−	0.0815777i
$950$	−0.961160	−	4.52190i	−0.0311842	−	0.146710i
$951$		0			0
$952$	1.09833	+	2.46688i	0.0355970	+	0.0799521i
$953$	14.8543	−	45.7168i	0.481178	−	1.48091i	−0.356263	−	0.934386i	$-0.615949\pi$
$953$	14.8543	−	45.7168i	0.481178	−	1.48091i	0.837441	−	0.546527i	$-0.184051\pi$
$954$		0			0
$955$	−0.0418995	+	0.0304418i	−0.00135584	+	0.000985073i
$956$	−15.1350	+	26.2146i	−0.489501	+	0.847840i
$957$		0			0
$958$	−2.32392	−	4.02515i	−0.0750826	−	0.130047i
$959$	20.5373	+	9.14381i	0.663185	+	0.295269i
$960$		0			0
$961$	−18.6837	−	20.7504i	−0.602701	−	0.669367i
$962$	0.106188	−	0.146155i	0.00342362	−	0.00471221i
$963$		0			0
$964$	23.8273	+	7.74196i	0.767426	+	0.249352i
$965$	−14.0220	−	2.98046i	−0.451383	−	0.0959445i
$966$		0			0
$967$	11.4552	−	6.61368i	0.368375	−	0.212681i	−0.304373	−	0.952553i	$-0.598447\pi$
$967$	11.4552	−	6.61368i	0.368375	−	0.212681i	0.672748	+	0.739871i	$0.265114\pi$
$968$	−9.08185	+	23.0955i	−0.291902	+	0.742319i
$969$		0			0
$970$	−6.30425	+	0.662604i	−0.202417	+	0.0212749i
$971$	−25.6742	+	8.34206i	−0.823925	+	0.267710i	−0.690484	−	0.723347i	$-0.742603\pi$
$971$	−25.6742	+	8.34206i	−0.823925	+	0.267710i	−0.133441	+	0.991057i	$0.542603\pi$
$972$		0			0
$973$	−41.1690	−	29.9110i	−1.31982	−	0.958903i
$974$	−7.40462	+	3.29675i	−0.237259	+	0.105635i
$975$		0			0
$976$	−18.7267	−	16.8616i	−0.599428	−	0.539727i
$977$	−16.0691	+	36.0917i	−0.514095	+	1.15468i	0.450940	+	0.892554i	$0.351089\pi$
$977$	−16.0691	+	36.0917i	−0.514095	+	1.15468i	−0.965035	+	0.262122i	$0.915578\pi$
$978$		0			0
$979$	−15.1427	+	42.2152i	−0.483964	+	1.34920i
$980$		−	33.7730i		−	1.07884i
$981$		0			0
$982$	6.22044	+	19.1445i	0.198502	+	0.610927i
$983$	24.8132	−	22.3419i	0.791419	−	0.712597i	−0.170671	−	0.985328i	$-0.554594\pi$
$983$	24.8132	−	22.3419i	0.791419	−	0.712597i	0.962090	+	0.272731i	$0.0879269\pi$
$984$		0			0
$985$	26.4083	+	2.77562i	0.841438	+	0.0884387i
$986$	−1.17431	+	0.249608i	−0.0373977	+	0.00794913i
$987$		0			0
$988$	−0.308008	−	2.93050i	−0.00979903	−	0.0932315i
$989$	−2.05226			−0.0652582
$990$		0			0
$991$	0.780068			0.0247797			0.0123898	−	0.999923i	$-0.496056\pi$
$991$	0.780068			0.0247797			0.0123898	+	0.999923i	$0.496056\pi$
$992$	1.03470	+	9.84453i	0.0328518	+	0.312564i
$993$		0			0
$994$	−35.0299	+	7.44584i	−1.11108	+	0.236168i
$995$	18.2836	+	1.92168i	0.579628	+	0.0609213i
$996$		0			0
$997$	32.6031	−	29.3560i	1.03255	−	0.929714i	0.0349820	−	0.999388i	$-0.488863\pi$
$997$	32.6031	−	29.3560i	1.03255	−	0.929714i	0.997570	+	0.0696741i	$0.0221959\pi$
$998$	4.99660	+	15.3779i	0.158164	+	0.486780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.8.6		80
3.2	odd	2		99.2.p.a.74.5	yes	80
9.2	odd	6		891.2.k.a.404.8		80
9.4	even	3		99.2.p.a.41.5	yes	80
9.5	odd	6	inner	297.2.t.a.206.6		80
9.7	even	3		891.2.k.a.404.13		80
11.7	odd	10	inner	297.2.t.a.62.6		80
33.29	even	10		99.2.p.a.29.5	✓	80
99.7	odd	30		891.2.k.a.161.8		80
99.29	even	30		891.2.k.a.161.13		80
99.40	odd	30		99.2.p.a.95.5	yes	80
99.95	even	30	inner	297.2.t.a.260.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.5	✓	80	33.29	even	10
99.2.p.a.41.5	yes	80	9.4	even	3
99.2.p.a.74.5	yes	80	3.2	odd	2
99.2.p.a.95.5	yes	80	99.40	odd	30
297.2.t.a.8.6		80	1.1	even	1	trivial
297.2.t.a.62.6		80	11.7	odd	10	inner
297.2.t.a.206.6		80	9.5	odd	6	inner
297.2.t.a.260.6		80	99.95	even	30	inner
891.2.k.a.161.8		80	99.7	odd	30
891.2.k.a.161.13		80	99.29	even	30
891.2.k.a.404.8		80	9.2	odd	6
891.2.k.a.404.13		80	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0653389 + 0.621658i) q^{2} +(1.57411 - 0.334586i) q^{4} +(1.26871 + 0.133347i) q^{5} +(-3.59877 + 3.24034i) q^{7} +(0.697171 + 2.14567i) q^{8} +0.797419i q^{10} +(3.12186 + 1.11982i) q^{11} +(0.339621 - 0.762800i) q^{13} +(-2.24953 - 2.02548i) q^{14} +(1.65196 - 0.735502i) q^{16} +(-0.199958 - 0.145278i) q^{17} +(2.08556 - 0.677640i) q^{19} +(2.04171 - 0.214592i) q^{20} +(-0.492168 + 2.01390i) q^{22} +(4.19803 - 2.42373i) q^{23} +(-3.29889 - 0.701200i) q^{25} +(0.496392 + 0.161287i) q^{26} +(-4.58066 + 6.30474i) q^{28} +(-5.19962 - 5.77477i) q^{29} +(1.60265 + 0.713544i) q^{31} +(2.82126 + 4.88657i) q^{32} +(0.0772482 - 0.133798i) q^{34} +(-4.99790 + 3.63118i) q^{35} +(0.106959 - 0.329187i) q^{37} +(0.557529 + 1.25223i) q^{38} +(0.598391 + 2.81521i) q^{40} +(-3.25297 + 3.61279i) q^{41} +(-0.366648 - 0.211684i) q^{43} +(5.28881 + 0.718188i) q^{44} +(1.78103 + 2.45137i) q^{46} +(-1.54628 + 7.27468i) q^{47} +(1.71959 - 16.3608i) q^{49} +(0.220361 - 2.09659i) q^{50} +(0.279376 - 1.31436i) q^{52} +(-6.95271 - 9.56959i) q^{53} +(3.81142 + 1.83703i) q^{55} +(-9.46167 - 5.46270i) q^{56} +(3.25019 - 3.60971i) q^{58} +(-1.09220 - 5.13837i) q^{59} +(-5.66802 - 12.7306i) q^{61} +(-0.338865 + 1.04292i) q^{62} +(0.0724543 - 0.0526411i) q^{64} +(0.532599 - 0.922488i) q^{65} +(-0.252454 - 0.437263i) q^{67} +(-0.363363 - 0.161780i) q^{68} +(-2.58391 - 2.86973i) q^{70} +(6.95402 - 9.57138i) q^{71} +(3.85174 + 1.25150i) q^{73} +(0.211631 + 0.0449835i) q^{74} +(3.05616 - 1.76448i) q^{76} +(-14.8635 + 6.08591i) q^{77} +(2.20083 - 0.231316i) q^{79} +(2.19395 - 0.712856i) q^{80} +(-2.45847 - 1.78618i) q^{82} +(3.77042 - 1.67870i) q^{83} +(-0.234317 - 0.210980i) q^{85} +(0.107639 - 0.241761i) q^{86} +(-0.226303 + 7.47919i) q^{88} +13.5225i q^{89} +(1.24952 + 3.84563i) q^{91} +(5.79719 - 5.21981i) q^{92} +(-4.62340 - 0.485939i) q^{94} +(2.73634 - 0.581627i) q^{95} +(0.830936 + 7.90582i) q^{97} +10.2832 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

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