LMFDB - Embedded newform 567.2.ba.a.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34473 + 1.60259i) q^{2} +(-0.412694 - 2.34051i) q^{4} +(-0.275976 + 0.231571i) q^{5} +(2.18789 + 1.48767i) q^{7} +(0.682329 + 0.393943i) q^{8} +O(q^{10})$	\(q+(-1.34473 + 1.60259i) q^{2} +(-0.412694 - 2.34051i) q^{4} +(-0.275976 + 0.231571i) q^{5} +(2.18789 + 1.48767i) q^{7} +(0.682329 + 0.393943i) q^{8} -0.753678i q^{10} +(4.02242 - 4.79373i) q^{11} +(-0.429890 + 1.18111i) q^{13} +(-5.32625 + 1.50578i) q^{14} +(2.91769 - 1.06195i) q^{16} +0.937219 q^{17} -7.64344i q^{19} +(0.655887 + 0.550354i) q^{20} +(2.27331 + 12.8926i) q^{22} +(0.584919 - 1.60705i) q^{23} +(-0.845703 + 4.79622i) q^{25} +(-1.31476 - 2.27722i) q^{26} +(2.57896 - 5.73471i) q^{28} +(0.731568 + 2.00997i) q^{29} +(5.71494 - 1.00770i) q^{31} +(-2.76059 + 7.58465i) q^{32} +(-1.26031 + 1.50198i) q^{34} +(-0.948304 + 0.0960919i) q^{35} +(1.66757 - 2.88831i) q^{37} +(12.2493 + 10.2784i) q^{38} +(-0.279532 + 0.0492890i) q^{40} +(8.66669 + 3.15442i) q^{41} +(-0.688669 + 3.90564i) q^{43} +(-12.8798 - 7.43615i) q^{44} +(1.78889 + 3.09844i) q^{46} +(-0.876005 + 4.96807i) q^{47} +(2.57370 + 6.50969i) q^{49} +(-6.54914 - 7.80496i) q^{50} +(2.94182 + 0.518722i) q^{52} +(3.01037 + 1.73804i) q^{53} +2.25443i q^{55} +(0.906803 + 1.87698i) q^{56} +(-4.20492 - 1.53047i) q^{58} +(-6.00562 - 2.18587i) q^{59} +(-10.3015 - 1.81644i) q^{61} +(-6.07015 + 10.5138i) q^{62} +(-5.33790 - 9.24552i) q^{64} +(-0.154873 - 0.425509i) q^{65} +(-0.222678 + 0.186849i) q^{67} +(-0.386785 - 2.19357i) q^{68} +(1.12122 - 1.64896i) q^{70} +(4.18316 - 2.41515i) q^{71} +(-3.19638 + 1.84543i) q^{73} +(2.38635 + 6.55643i) q^{74} +(-17.8895 + 3.15440i) q^{76} +(15.9321 - 4.50413i) q^{77} +(7.90824 + 6.63581i) q^{79} +(-0.559294 + 0.968725i) q^{80} +(-16.7096 + 9.64732i) q^{82} +(-6.06917 + 2.20900i) q^{83} +(-0.258650 + 0.217033i) q^{85} +(-5.33306 - 6.35570i) q^{86} +(4.63307 - 1.68630i) q^{88} -5.12391 q^{89} +(-2.69765 + 1.94461i) q^{91} +(-4.00271 - 0.705785i) q^{92} +(-6.78379 - 8.08461i) q^{94} +(1.77000 + 2.10940i) q^{95} +(-7.91567 - 1.39575i) q^{97} +(-13.8933 - 4.62921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.34473	+	1.60259i	−0.950871	+	1.13320i	0.0401094	+	0.999195i	$0.487229\pi$
$2$	−1.34473	+	1.60259i	−0.950871	+	1.13320i	−0.990980	+	0.134008i	$0.957215\pi$
$3$		0			0
$3$		0			0
$4$	−0.412694	−	2.34051i	−0.206347	−	1.17025i
$5$	−0.275976	+	0.231571i	−0.123420	+	0.103562i	−0.702409	−	0.711774i	$-0.747892\pi$
$5$	−0.275976	+	0.231571i	−0.123420	+	0.103562i	0.578989	+	0.815336i	$0.303448\pi$
$6$		0			0
$7$	2.18789	+	1.48767i	0.826944	+	0.562285i
$7$	2.18789	+	1.48767i	0.826944	+	0.562285i
$8$	0.682329	+	0.393943i	0.241240	+	0.139280i
$9$		0			0
$10$		−	0.753678i		−	0.238334i
$11$	4.02242	−	4.79373i	1.21281	−	1.44536i	0.352327	−	0.935877i	$-0.385390\pi$
$11$	4.02242	−	4.79373i	1.21281	−	1.44536i	0.860478	−	0.509488i	$-0.170165\pi$
$12$		0			0
$13$	−0.429890	+	1.18111i	−0.119230	+	0.327582i	−0.984923	−	0.172994i	$-0.944656\pi$
$13$	−0.429890	+	1.18111i	−0.119230	+	0.327582i	0.865693	+	0.500576i	$0.166878\pi$
$14$	−5.32625	+	1.50578i	−1.42350	+	0.402435i
$15$		0			0
$16$	2.91769	−	1.06195i	0.729422	−	0.265488i
$17$	0.937219			0.227309			0.113654	−	0.993520i	$-0.463744\pi$
$17$	0.937219			0.227309			0.113654	+	0.993520i	$0.463744\pi$
$18$		0			0
$19$		−	7.64344i		−	1.75352i	−0.480924	−	0.876762i	$-0.659699\pi$
$19$		−	7.64344i		−	1.75352i	0.480924	−	0.876762i	$-0.340301\pi$
$20$	0.655887	+	0.550354i	0.146661	+	0.123063i
$21$		0			0
$22$	2.27331	+	12.8926i	0.484672	+	2.74871i
$23$	0.584919	−	1.60705i	0.121964	−	0.335093i	−0.863653	−	0.504086i	$-0.831829\pi$
$23$	0.584919	−	1.60705i	0.121964	−	0.335093i	0.985617	+	0.168993i	$0.0540515\pi$
$24$		0			0
$25$	−0.845703	+	4.79622i	−0.169141	+	0.959245i
$26$	−1.31476	−	2.27722i	−0.257845	−	0.446600i
$27$		0			0
$28$	2.57896	−	5.73471i	0.487378	−	1.08376i
$29$	0.731568	+	2.00997i	0.135849	+	0.373241i	0.988899	−	0.148587i	$-0.0474725\pi$
$29$	0.731568	+	2.00997i	0.135849	+	0.373241i	−0.853051	+	0.521828i	$0.825250\pi$
$30$		0			0
$31$	5.71494	−	1.00770i	1.02643	−	0.180988i	0.365013	−	0.931002i	$-0.381065\pi$
$31$	5.71494	−	1.00770i	1.02643	−	0.180988i	0.661421	+	0.750014i	$0.269953\pi$
$32$	−2.76059	+	7.58465i	−0.488007	+	1.34079i
$33$		0			0
$34$	−1.26031	+	1.50198i	−0.216141	+	0.257587i
$35$	−0.948304	+	0.0960919i	−0.160293	+	0.0162425i
$36$		0			0
$37$	1.66757	−	2.88831i	0.274146	−	0.474835i	−0.695773	−	0.718261i	$-0.744938\pi$
$37$	1.66757	−	2.88831i	0.274146	−	0.474835i	0.969919	+	0.243427i	$0.0782715\pi$
$38$	12.2493	+	10.2784i	1.98710	+	1.66738i
$39$		0			0
$40$	−0.279532	+	0.0492890i	−0.0441978	+	0.00779327i
$41$	8.66669	+	3.15442i	1.35351	+	0.492637i	0.914041	−	0.405621i	$-0.132945\pi$
$41$	8.66669	+	3.15442i	1.35351	+	0.492637i	0.439468	+	0.898258i	$0.355167\pi$
$42$		0			0
$43$	−0.688669	+	3.90564i	−0.105021	+	0.595604i	0.886191	+	0.463320i	$0.153342\pi$
$43$	−0.688669	+	3.90564i	−0.105021	+	0.595604i	−0.991212	+	0.132284i	$0.957769\pi$
$44$	−12.8798	−	7.43615i	−1.94170	−	1.12104i
$45$		0			0
$46$	1.78889	+	3.09844i	0.263757	+	0.456841i
$47$	−0.876005	+	4.96807i	−0.127778	+	0.724667i	0.851840	+	0.523802i	$0.175487\pi$
$47$	−0.876005	+	4.96807i	−0.127778	+	0.724667i	−0.979619	+	0.200866i	$0.935624\pi$
$48$		0			0
$49$	2.57370	+	6.50969i	0.367672	+	0.929956i
$50$	−6.54914	−	7.80496i	−0.926189	−	1.10379i
$51$		0			0
$52$	2.94182	+	0.518722i	0.407957	+	0.0719338i
$53$	3.01037	+	1.73804i	0.413506	+	0.238738i	0.692295	−	0.721614i	$-0.256600\pi$
$53$	3.01037	+	1.73804i	0.413506	+	0.238738i	−0.278789	+	0.960352i	$0.589933\pi$
$54$		0			0
$55$			2.25443i			0.303987i
$56$	0.906803	+	1.87698i	0.121177	+	0.250822i
$57$		0			0
$58$	−4.20492	−	1.53047i	−0.552133	−	0.200960i
$59$	−6.00562	−	2.18587i	−0.781866	−	0.284576i	−0.0799153	−	0.996802i	$-0.525465\pi$
$59$	−6.00562	−	2.18587i	−0.781866	−	0.284576i	−0.701950	+	0.712226i	$0.747687\pi$
$60$		0			0
$61$	−10.3015	−	1.81644i	−1.31898	−	0.232571i	−0.530525	−	0.847669i	$-0.678005\pi$
$61$	−10.3015	−	1.81644i	−1.31898	−	0.232571i	−0.788451	+	0.615098i	$0.789116\pi$
$62$	−6.07015	+	10.5138i	−0.770910	+	1.33526i
$63$		0			0
$64$	−5.33790	−	9.24552i	−0.667238	−	1.15569i
$65$	−0.154873	−	0.425509i	−0.0192096	−	0.0527779i
$66$		0			0
$67$	−0.222678	+	0.186849i	−0.0272045	+	0.0228273i	−0.656289	−	0.754510i	$-0.727875\pi$
$67$	−0.222678	+	0.186849i	−0.0272045	+	0.0228273i	0.629084	+	0.777337i	$0.283430\pi$
$68$	−0.386785	−	2.19357i	−0.0469046	−	0.266009i
$69$		0			0
$70$	1.12122	−	1.64896i	0.134011	−	0.197089i
$71$	4.18316	−	2.41515i	0.496450	−	0.286625i	−0.230797	−	0.973002i	$-0.574133\pi$
$71$	4.18316	−	2.41515i	0.496450	−	0.286625i	0.727246	+	0.686377i	$0.240800\pi$
$72$		0			0
$73$	−3.19638	+	1.84543i	−0.374108	+	0.215992i	−0.675252	−	0.737587i	$-0.735965\pi$
$73$	−3.19638	+	1.84543i	−0.374108	+	0.215992i	0.301143	+	0.953579i	$0.402632\pi$
$74$	2.38635	+	6.55643i	0.277407	+	0.762170i
$75$		0			0
$76$	−17.8895	+	3.15440i	−2.05207	+	0.361835i
$77$	15.9321	−	4.50413i	1.81563	−	0.513293i
$78$		0			0
$79$	7.90824	+	6.63581i	0.889747	+	0.746586i	0.968159	−	0.250335i	$-0.0805406\pi$
$79$	7.90824	+	6.63581i	0.889747	+	0.746586i	−0.0784124	+	0.996921i	$0.524985\pi$
$80$	−0.559294	+	0.968725i	−0.0625309	+	0.108307i
$81$		0			0
$82$	−16.7096	+	9.64732i	−1.84527	+	1.06537i
$83$	−6.06917	+	2.20900i	−0.666178	+	0.242469i	−0.652901	−	0.757443i	$-0.726448\pi$
$83$	−6.06917	+	2.20900i	−0.666178	+	0.242469i	−0.0132766	+	0.999912i	$0.504226\pi$
$84$		0			0
$85$	−0.258650	+	0.217033i	−0.0280545	+	0.0235405i
$86$	−5.33306	−	6.35570i	−0.575079	−	0.685353i
$87$		0			0
$88$	4.63307	−	1.68630i	0.493887	−	0.179760i
$89$	−5.12391			−0.543133			−0.271566	−	0.962420i	$-0.587542\pi$
$89$	−5.12391			−0.543133			−0.271566	+	0.962420i	$0.587542\pi$
$90$		0			0
$91$	−2.69765	+	1.94461i	−0.282791	+	0.203851i
$92$	−4.00271	−	0.705785i	−0.417311	−	0.0735832i
$93$		0			0
$94$	−6.78379	−	8.08461i	−0.699695	−	0.833864i
$95$	1.77000	+	2.10940i	0.181598	+	0.216420i
$96$		0			0
$97$	−7.91567	−	1.39575i	−0.803714	−	0.141717i	−0.243324	−	0.969945i	$-0.578238\pi$
$97$	−7.91567	−	1.39575i	−0.803714	−	0.141717i	−0.560390	+	0.828229i	$0.689349\pi$
$98$	−13.8933	−	4.62921i	−1.40344	−	0.467621i
$99$		0			0
$100$	11.5746			1.15746
$101$	13.3809	−	4.87023i	1.33145	−	0.484606i	0.424337	−	0.905504i	$-0.360507\pi$
$101$	13.3809	−	4.87023i	1.33145	−	0.484606i	0.907108	+	0.420898i	$0.138285\pi$
$102$		0			0
$103$	4.11263	+	4.90124i	0.405230	+	0.482934i	0.929607	−	0.368552i	$-0.120146\pi$
$103$	4.11263	+	4.90124i	0.405230	+	0.482934i	−0.524377	+	0.851486i	$0.675702\pi$
$104$	−0.758617	+	0.636556i	−0.0743886	+	0.0624194i
$105$		0			0
$106$	−6.83352	+	2.48720i	−0.663730	+	0.241578i
$107$	2.81413	−	1.62474i	0.272053	−	0.157070i	−0.357767	−	0.933811i	$-0.616462\pi$
$107$	2.81413	−	1.62474i	0.272053	−	0.157070i	0.629820	+	0.776741i	$0.283129\pi$
$108$		0			0
$109$	6.30335	−	10.9177i	0.603751	−	1.04573i	−0.388496	−	0.921450i	$-0.627005\pi$
$109$	6.30335	−	10.9177i	0.603751	−	1.04573i	0.992247	−	0.124278i	$-0.0396613\pi$
$110$	−3.61293	−	3.03161i	−0.344479	−	0.289052i
$111$		0			0
$112$	7.96340	+	2.01711i	0.752471	+	0.190599i
$113$	14.5530	−	2.56609i	1.36903	−	0.241397i	0.559674	−	0.828713i	$-0.310926\pi$
$113$	14.5530	−	2.56609i	1.36903	−	0.241397i	0.809358	+	0.587315i	$0.199815\pi$
$114$		0			0
$115$	0.210723	+	0.578957i	0.0196500	+	0.0539880i
$116$	4.40242	−	2.54174i	0.408755	−	0.235995i
$117$		0			0
$118$	11.5790	−	6.68515i	1.06594	−	0.615418i
$119$	2.05053	+	1.39427i	0.187972	+	0.127812i
$120$		0			0
$121$	−4.88989	−	27.7319i	−0.444535	−	2.52108i
$122$	16.7638	−	14.0665i	1.51773	−	1.27352i
$123$		0			0
$124$	−4.71705	−	12.9600i	−0.423604	−	1.16384i
$125$	−1.77792	−	3.07945i	−0.159022	−	0.275435i
$126$		0			0
$127$	7.01123	−	12.1438i	0.622146	−	1.07759i	−0.366939	−	0.930245i	$-0.619594\pi$
$127$	7.01123	−	12.1438i	0.622146	−	1.07759i	0.989085	−	0.147344i	$-0.0470724\pi$
$128$	6.09727	+	1.07511i	0.538928	+	0.0950275i
$129$		0			0
$130$	0.890179	+	0.323999i	0.0780739	+	0.0284166i
$131$	−2.46411	−	0.896863i	−0.215290	−	0.0783593i	0.232123	−	0.972686i	$-0.425433\pi$
$131$	−2.46411	−	0.896863i	−0.215290	−	0.0783593i	−0.447414	+	0.894327i	$0.647655\pi$
$132$		0			0
$133$	11.3709	−	16.7230i	0.985980	−	1.45007i
$134$		−	0.608125i		−	0.0525340i
$135$		0			0
$136$	0.639491	+	0.369210i	0.0548359	+	0.0316595i
$137$	−9.59321	−	1.69154i	−0.819603	−	0.144518i	−0.251902	−	0.967753i	$-0.581056\pi$
$137$	−9.59321	−	1.69154i	−0.819603	−	0.144518i	−0.567701	+	0.823235i	$0.692167\pi$
$138$		0			0
$139$	0.0836111	+	0.0996438i	0.00709180	+	0.00845168i	0.769579	−	0.638552i	$-0.220466\pi$
$139$	0.0836111	+	0.0996438i	0.00709180	+	0.00845168i	−0.762487	+	0.647004i	$0.776022\pi$
$140$	0.616263	+	2.17985i	0.0520837	+	0.184231i
$141$		0			0
$142$	−1.75474	+	9.95163i	−0.147255	+	0.835122i
$143$	3.93274	+	6.81171i	0.328873	+	0.569624i
$144$		0			0
$145$	−0.667345	−	0.385292i	−0.0554199	−	0.0319967i
$146$	1.34081	−	7.60411i	0.110966	−	0.629321i
$147$		0			0
$148$	−7.44829	−	2.71096i	−0.612246	−	0.222839i
$149$	−14.1676	+	2.49814i	−1.16066	+	0.204655i	−0.720624	−	0.693326i	$-0.756145\pi$
$149$	−14.1676	+	2.49814i	−1.16066	+	0.204655i	−0.440034	+	0.897981i	$0.645034\pi$
$150$		0			0
$151$	15.5163	+	13.0197i	1.26269	+	1.05953i	0.995390	+	0.0959147i	$0.0305776\pi$
$151$	15.5163	+	13.0197i	1.26269	+	1.05953i	0.267305	+	0.963612i	$0.413867\pi$
$152$	3.01107	−	5.21533i	0.244230	−	0.423019i
$153$		0			0
$154$	−14.2061	+	31.5895i	−1.14476	+	2.54555i
$155$	−1.34383	+	1.60152i	−0.107939	+	0.128637i
$156$		0			0
$157$	−1.35670	+	3.72752i	−0.108277	+	0.297488i	−0.981984	−	0.188964i	$-0.939487\pi$
$157$	−1.35670	+	3.72752i	−0.108277	+	0.297488i	0.873707	+	0.486452i	$0.161709\pi$
$158$	−21.2690	+	3.75029i	−1.69207	+	0.298357i
$159$		0			0
$160$	−0.994530	−	2.73245i	−0.0786245	−	0.216019i
$161$	3.67049	−	2.64588i	0.289275	−	0.208525i
$162$		0			0
$163$	−8.65872	−	14.9973i	−0.678203	−	1.17468i	−0.975522	−	0.219904i	$-0.929426\pi$
$163$	−8.65872	−	14.9973i	−0.678203	−	1.17468i	0.297318	−	0.954778i	$-0.403908\pi$
$164$	3.80624	−	21.5863i	0.297217	−	1.68560i
$165$		0			0
$166$	4.62130	−	12.6969i	0.358682	−	0.985472i
$167$	−2.13178	−	12.0899i	−0.164962	−	0.935548i	−0.949103	−	0.314965i	$-0.898007\pi$
$167$	−2.13178	−	12.0899i	−0.164962	−	0.935548i	0.784141	−	0.620583i	$-0.213104\pi$
$168$		0			0
$169$	8.74835	+	7.34074i	0.672950	+	0.564672i
$170$		−	0.706361i		−	0.0541754i
$171$		0			0
$172$	9.42537			0.718678
$173$	−19.8439	+	7.22261i	−1.50871	+	0.549125i	−0.958298	−	0.285771i	$-0.907750\pi$
$173$	−19.8439	+	7.22261i	−1.50871	+	0.549125i	−0.550409	+	0.834895i	$0.685528\pi$
$174$		0			0
$175$	−8.98548	+	9.23547i	−0.679238	+	0.698136i
$176$	6.64546	−	18.2582i	0.500920	−	1.37627i
$177$		0			0
$178$	6.89029	−	8.21153i	0.516449	−	0.615480i
$179$			9.39393i			0.702135i	0.936350	+	0.351068i	$0.114181\pi$
$179$			9.39393i			0.702135i	−0.936350	+	0.351068i	$0.885819\pi$
$180$		0			0
$181$	−8.05463	−	4.65035i	−0.598696	−	0.345657i	0.169832	−	0.985473i	$-0.445677\pi$
$181$	−8.05463	−	4.65035i	−0.598696	−	0.345657i	−0.768529	+	0.639816i	$0.779011\pi$
$182$	0.511210	−	6.93822i	0.0378934	−	0.514295i
$183$		0			0
$184$	1.03219	−	0.866113i	0.0760943	−	0.0638507i
$185$	0.208641	+	1.18326i	0.0153396	+	0.0869952i
$186$		0			0
$187$	3.76989	−	4.49278i	0.275681	−	0.328544i
$188$	11.9893			0.874411
$189$		0			0
$190$	−5.76069			−0.417924
$191$	5.86657	−	6.99151i	0.424490	−	0.505888i	−0.510834	−	0.859679i	$-0.670663\pi$
$191$	5.86657	−	6.99151i	0.424490	−	0.505888i	0.935324	+	0.353791i	$0.115108\pi$
$192$		0			0
$193$	−0.608638	−	3.45176i	−0.0438107	−	0.248463i	0.955035	−	0.296492i	$-0.0958169\pi$
$193$	−0.608638	−	3.45176i	−0.0438107	−	0.248463i	−0.998846	+	0.0480295i	$0.984706\pi$
$194$	12.8813	−	10.8087i	0.924822	−	0.776018i
$195$		0			0
$196$	14.1738	−	8.71028i	1.01242	−	0.622163i
$197$	17.0883	+	9.86593i	1.21749	+	0.702918i	0.964380	−	0.264519i	$-0.0852132\pi$
$197$	17.0883	+	9.86593i	1.21749	+	0.702918i	0.253110	+	0.967438i	$0.418547\pi$
$198$		0			0
$199$			11.1409i			0.789757i	0.918733	+	0.394878i	$0.129213\pi$
$199$			11.1409i			0.789757i	−0.918733	+	0.394878i	$0.870787\pi$
$200$	−2.46648	+	2.93944i	−0.174407	+	0.207850i
$201$		0			0
$202$	−10.1887	+	27.9932i	−0.716875	+	1.96960i
$203$	−1.38957	+	5.48591i	−0.0975286	+	0.385035i
$204$		0			0
$205$	−3.12227	+	1.13641i	−0.218069	+	0.0793705i
$206$	−13.3851			−0.932584
$207$		0			0
$208$			3.90265i			0.270600i
$209$	−36.6406	−	30.7451i	−2.53448	−	2.12668i
$210$		0			0
$211$	−1.40219	−	7.95221i	−0.0965307	−	0.547453i	−0.994268	−	0.106921i	$-0.965901\pi$
$211$	−1.40219	−	7.95221i	−0.0965307	−	0.547453i	0.897737	−	0.440532i	$-0.145210\pi$
$212$	2.82553	−	7.76307i	0.194058	−	0.533170i
$213$		0			0
$214$	−1.18047	+	6.69475i	−0.0806950	+	0.457644i
$215$	−0.714376	−	1.23734i	−0.0487201	−	0.0843856i
$216$		0			0
$217$	14.0028	+	6.29720i	0.950570	+	0.427481i
$218$	9.02032	+	24.7831i	0.610933	+	1.67853i
$219$		0			0
$220$	5.27650	−	0.930390i	0.355742	−	0.0627269i
$221$	−0.402901	+	1.10696i	−0.0271021	+	0.0744623i
$222$		0			0
$223$	4.16647	−	4.96540i	0.279007	−	0.332508i	−0.608282	−	0.793721i	$-0.708141\pi$
$223$	4.16647	−	4.96540i	0.279007	−	0.332508i	0.887290	+	0.461213i	$0.152586\pi$
$224$	−17.3233	+	12.4875i	−1.15746	+	0.834358i
$225$		0			0
$226$	−15.4575	+	26.7733i	−1.02822	+	1.78093i
$227$	−5.31375	−	4.45877i	−0.352686	−	0.295939i	0.449181	−	0.893441i	$-0.351716\pi$
$227$	−5.31375	−	4.45877i	−0.352686	−	0.295939i	−0.801868	+	0.597502i	$0.796160\pi$
$228$		0			0
$229$	−18.1760	+	3.20491i	−1.20110	+	0.211787i	−0.738175	−	0.674610i	$-0.764312\pi$
$229$	−18.1760	+	3.20491i	−1.20110	+	0.211787i	−0.462927	+	0.886396i	$0.653201\pi$
$230$	−1.21120	−	0.440840i	−0.0798641	−	0.0290682i
$231$		0			0
$232$	−0.292641	+	1.65965i	−0.0192129	+	0.108962i
$233$	−20.8367	−	12.0300i	−1.36505	−	0.788115i	−0.374763	−	0.927121i	$-0.622276\pi$
$233$	−20.8367	−	12.0300i	−1.36505	−	0.788115i	−0.990292	+	0.139006i	$0.955609\pi$
$234$		0			0
$235$	−0.908705	−	1.57392i	−0.0592774	−	0.102671i
$236$	−2.63755	+	14.9583i	−0.171690	+	0.973702i
$237$		0			0
$238$	−4.99186	+	1.41124i	−0.323574	+	0.0914772i
$239$	3.56306	+	4.24628i	0.230475	+	0.274669i	0.868871	−	0.495039i	$-0.164846\pi$
$239$	3.56306	+	4.24628i	0.230475	+	0.274669i	−0.638396	+	0.769708i	$0.720402\pi$
$240$		0			0
$241$	−10.0391	−	1.77016i	−0.646673	−	0.114026i	−0.159314	−	0.987228i	$-0.550928\pi$
$241$	−10.0391	−	1.77016i	−0.646673	−	0.114026i	−0.487358	+	0.873202i	$0.662039\pi$
$242$	51.0185	+	29.4556i	3.27960	+	1.89348i
$243$		0			0
$244$			24.8604i			1.59153i
$245$	−2.21773	−	1.20052i	−0.141686	−	0.0766985i
$246$		0			0
$247$	9.02777	+	3.28584i	0.574423	+	0.209073i
$248$	4.29645	+	1.56378i	0.272825	+	0.0993000i
$249$		0			0
$250$	7.32595	+	1.29176i	0.463333	+	0.0816982i
$251$	−10.3890	+	17.9942i	−0.655746	+	1.13579i	0.325960	+	0.945384i	$0.394312\pi$
$251$	−10.3890	+	17.9942i	−0.655746	+	1.13579i	−0.981706	+	0.190402i	$0.939021\pi$
$252$		0			0
$253$	−5.35099	−	9.26818i	−0.336414	−	0.582685i
$254$	10.0333	+	27.5663i	0.629547	+	1.72967i
$255$		0			0
$256$	6.43410	−	5.39885i	0.402132	−	0.337428i
$257$	4.40206	+	24.9653i	0.274593	+	1.55729i	0.740251	+	0.672330i	$0.234706\pi$
$257$	4.40206	+	24.9653i	0.274593	+	1.55729i	−0.465658	+	0.884965i	$0.654182\pi$
$258$		0			0
$259$	7.94528	−	3.83851i	0.493696	−	0.238514i
$260$	−0.931991	+	0.538085i	−0.0577996	+	0.0333706i
$261$		0			0
$262$	4.75088	−	2.74292i	0.293510	−	0.169458i
$263$	1.35880	+	3.73327i	0.0837872	+	0.230203i	0.974510	−	0.224343i	$-0.0720236\pi$
$263$	1.35880	+	3.73327i	0.0837872	+	0.230203i	−0.890723	+	0.454546i	$0.849801\pi$
$264$		0			0
$265$	−1.23327	+	0.217458i	−0.0757591	+	0.0133584i
$266$	11.5093	+	40.7108i	0.705680	+	2.49614i
$267$		0			0
$268$	0.529220	+	0.444068i	0.0323272	+	0.0271258i
$269$	2.35052	−	4.07121i	0.143313	−	0.248226i	−0.785429	−	0.618952i	$-0.787558\pi$
$269$	2.35052	−	4.07121i	0.143313	−	0.248226i	0.928742	+	0.370726i	$0.120891\pi$
$270$		0			0
$271$	−7.44995	+	4.30123i	−0.452552	+	0.261281i	−0.708907	−	0.705302i	$-0.750812\pi$
$271$	−7.44995	+	4.30123i	−0.452552	+	0.261281i	0.256355	+	0.966583i	$0.417478\pi$
$272$	2.73451	−	0.995282i	0.165804	−	0.0603478i
$273$		0			0
$274$	15.6112	−	13.0993i	0.943105	−	0.791359i
$275$	19.5900	+	23.3465i	1.18132	+	1.40785i
$276$		0			0
$277$	−14.9283	+	5.43344i	−0.896952	+	0.326464i	−0.749031	−	0.662535i	$-0.769480\pi$
$277$	−14.9283	+	5.43344i	−0.896952	+	0.326464i	−0.147921	+	0.988999i	$0.547258\pi$
$278$	−0.272123			−0.0163209
$279$		0			0
$280$	−0.684909	−	0.308011i	−0.0409312	−	0.0184072i
$281$	−21.2686	−	3.75023i	−1.26878	−	0.223720i	−0.501569	−	0.865118i	$-0.667244\pi$
$281$	−21.2686	−	3.75023i	−1.26878	−	0.223720i	−0.767208	+	0.641398i	$0.778355\pi$
$282$		0			0
$283$	−2.92239	−	3.48277i	−0.173718	−	0.207029i	0.672159	−	0.740407i	$-0.265367\pi$
$283$	−2.92239	−	3.48277i	−0.173718	−	0.207029i	−0.845877	+	0.533377i	$0.820923\pi$
$284$	−7.37903	−	8.79399i	−0.437865	−	0.521827i
$285$		0			0
$286$	−16.2049	−	2.85736i	−0.958216	−	0.168959i
$287$	14.2690	+	19.7946i	0.842274	+	1.16844i
$288$		0			0
$289$	−16.1216			−0.948331
$290$	1.51487	−	0.551366i	0.0889560	−	0.0323773i
$291$		0			0
$292$	5.63837	+	6.71955i	0.329961	+	0.393232i
$293$	6.06074	−	5.08556i	0.354072	−	0.297102i	−0.448351	−	0.893858i	$-0.647988\pi$
$293$	6.06074	−	5.08556i	0.354072	−	0.297102i	0.802423	+	0.596756i	$0.203544\pi$
$294$		0			0
$295$	2.16359	−	0.787482i	0.125969	−	0.0458490i
$296$	2.27565	−	1.31385i	0.132270	−	0.0763660i
$297$		0			0
$298$	15.0482	−	26.0643i	0.871720	−	1.50986i
$299$	1.64666	+	1.38171i	0.0952288	+	0.0799064i
$300$		0			0
$301$	−7.31701	+	7.52058i	−0.421746	+	0.433479i
$302$	−41.7305	+	7.35821i	−2.40132	+	0.423417i
$303$		0			0
$304$	−8.11696	−	22.3012i	−0.465540	−	1.27906i
$305$	3.26361	−	1.88424i	0.186873	−	0.107891i
$306$		0			0
$307$	16.6860	−	9.63367i	0.952321	−	0.549823i	0.0585197	−	0.998286i	$-0.481362\pi$
$307$	16.6860	−	9.63367i	0.952321	−	0.549823i	0.893801	+	0.448464i	$0.148029\pi$
$308$	−17.1170	−	35.4303i	−0.975333	−	2.01883i
$309$		0			0
$310$	−0.759480	−	4.30723i	−0.0431356	−	0.244634i
$311$	−10.1814	+	8.54323i	−0.577336	+	0.484442i	−0.884071	−	0.467353i	$-0.845208\pi$
$311$	−10.1814	+	8.54323i	−0.577336	+	0.484442i	0.306735	+	0.951795i	$0.400763\pi$
$312$		0			0
$313$	5.11582	+	14.0556i	0.289163	+	0.794470i	0.996184	+	0.0872770i	$0.0278165\pi$
$313$	5.11582	+	14.0556i	0.289163	+	0.794470i	−0.707021	+	0.707193i	$0.749961\pi$
$314$	−4.14928	−	7.18676i	−0.234157	−	0.405573i
$315$		0			0
$316$	12.2675	−	21.2479i	0.690098	−	1.19528i
$317$	16.3443	+	2.88195i	0.917990	+	0.161866i	0.612629	−	0.790370i	$-0.290112\pi$
$317$	16.3443	+	2.88195i	0.917990	+	0.161866i	0.305361	+	0.952237i	$0.401223\pi$
$318$		0			0
$319$	12.5779	+	4.57798i	0.704228	+	0.256318i
$320$	3.61412	+	1.31543i	0.202036	+	0.0735350i
$321$		0			0
$322$	−0.695564	+	9.44031i	−0.0387623	+	0.526088i
$323$		−	7.16357i		−	0.398592i
$324$		0			0
$325$	−5.30133	−	3.06072i	−0.294065	−	0.169778i
$326$	35.6783	+	6.29105i	1.97604	+	0.348429i
$327$		0			0
$328$	4.67087	+	5.56653i	0.257906	+	0.307360i
$329$	−9.30743	+	9.56637i	−0.513135	+	0.527411i
$330$		0			0
$331$	−3.98781	+	22.6160i	−0.219190	+	1.24309i	0.654297	+	0.756238i	$0.272965\pi$
$331$	−3.98781	+	22.6160i	−0.219190	+	1.24309i	−0.873486	+	0.486848i	$0.838146\pi$
$332$	7.67488	+	13.2933i	0.421214	+	0.729564i
$333$		0			0
$334$	22.2419	+	12.8414i	1.21702	+	0.702649i
$335$	0.0181849	−	0.103132i	0.000993547	−	0.00563469i
$336$		0			0
$337$	25.8190	+	9.39733i	1.40645	+	0.511905i	0.930085	−	0.367344i	$-0.119733\pi$
$337$	25.8190	+	9.39733i	1.40645	+	0.511905i	0.476363	+	0.879249i	$0.341955\pi$
$338$	−23.5284	+	4.14870i	−1.27978	+	0.225659i
$339$		0			0
$340$	0.614710	+	0.515803i	0.0333373	+	0.0279733i
$341$	18.1573	−	31.4493i	0.983271	−	1.70308i
$342$		0			0
$343$	−4.05327	+	18.0713i	−0.218856	+	0.975757i
$344$	−2.00849	+	2.39363i	−0.108291	+	0.129056i
$345$		0			0
$346$	15.1099	−	41.5142i	0.812316	−	2.23182i
$347$	−9.82099	+	1.73171i	−0.527218	+	0.0929628i	−0.430921	−	0.902390i	$-0.641811\pi$
$347$	−9.82099	+	1.73171i	−0.527218	+	0.0929628i	−0.0962976	+	0.995353i	$0.530700\pi$
$348$		0			0
$349$	−9.55483	−	26.2517i	−0.511458	−	1.40522i	−0.879717	−	0.475497i	$-0.842268\pi$
$349$	−9.55483	−	26.2517i	−0.511458	−	1.40522i	0.368259	−	0.929723i	$-0.379954\pi$
$350$	−2.71761	−	26.8193i	−0.145262	−	1.43355i
$351$		0			0
$352$	25.2545	+	43.7421i	1.34607	+	2.33146i
$353$	−4.10320	+	23.2704i	−0.218392	+	1.23856i	0.656532	+	0.754298i	$0.272023\pi$
$353$	−4.10320	+	23.2704i	−0.218392	+	1.23856i	−0.874923	+	0.484262i	$0.839088\pi$
$354$		0			0
$355$	−0.595172	+	1.63522i	−0.0315884	+	0.0867885i
$356$	2.11461	+	11.9925i	0.112074	+	0.635603i
$357$		0			0
$358$	−15.0546	−	12.6323i	−0.795662	−	0.667640i
$359$		−	0.0297974i		−	0.00157265i	−1.00000		0.000786324i	$-0.999750\pi$
$359$		−	0.0297974i		−	0.00157265i	1.00000		0.000786324i	$-0.000250295\pi$
$360$		0			0
$361$	−39.4221			−2.07485
$362$	18.2839	−	6.65481i	0.960983	−	0.349769i
$363$		0			0
$364$	5.66468	+	5.51134i	0.296910	+	0.288873i
$365$	0.454775	−	1.24948i	0.0238040	−	0.0654010i
$366$		0			0
$367$	−10.0778	+	12.0103i	−0.526059	+	0.626933i	−0.962002	−	0.273041i	$-0.911970\pi$
$367$	−10.0778	+	12.0103i	−0.526059	+	0.626933i	0.435943	+	0.899974i	$0.356415\pi$
$368$		−	5.31003i		−	0.276805i
$369$		0			0
$370$	−2.17685	−	1.25681i	−0.113169	−	0.0653383i
$371$	4.00073	+	8.28106i	0.207708	+	0.429931i
$372$		0			0
$373$	11.7396	−	9.85066i	0.607852	−	0.510048i	−0.286107	−	0.958198i	$-0.592361\pi$
$373$	11.7396	−	9.85066i	0.607852	−	0.510048i	0.893959	+	0.448150i	$0.147917\pi$
$374$	2.13059	+	12.0832i	0.110170	+	0.624807i
$375$		0			0
$376$	−2.55486	+	3.04476i	−0.131757	+	0.157021i
$377$	−2.68849			−0.138464
$378$		0			0
$379$	17.9559			0.922330			0.461165	−	0.887314i	$-0.347432\pi$
$379$	17.9559			0.922330			0.461165	+	0.887314i	$0.347432\pi$
$380$	4.20660	−	5.01323i	0.215794	−	0.257173i
$381$		0			0
$382$	3.31556	+	18.8034i	0.169639	+	0.962068i
$383$	26.4748	−	22.2150i	1.35280	−	1.13513i	0.374665	−	0.927160i	$-0.377758\pi$
$383$	26.4748	−	22.2150i	1.35280	−	1.13513i	0.978135	−	0.207973i	$-0.0666866\pi$
$384$		0			0
$385$	−3.35384	+	4.93244i	−0.170927	+	0.251380i
$386$	6.35021	+	3.66630i	0.323217	+	0.186610i
$387$		0			0
$388$			19.1027i			0.969792i
$389$	−0.222028	+	0.264602i	−0.0112573	+	0.0134159i	−0.771644	−	0.636055i	$-0.780565\pi$
$389$	−0.222028	+	0.264602i	−0.0112573	+	0.0134159i	0.760386	+	0.649471i	$0.225010\pi$
$390$		0			0
$391$	0.548197	−	1.50616i	0.0277235	−	0.0761697i
$392$	−0.808334	+	5.45564i	−0.0408270	+	0.275551i
$393$		0			0
$394$	−38.7903	+	14.1185i	−1.95423	+	0.711280i
$395$	−3.71914			−0.187130
$396$		0			0
$397$		−	2.62188i		−	0.131589i	−0.997833	−	0.0657943i	$-0.979042\pi$
$397$		−	2.62188i		−	0.131589i	0.997833	−	0.0657943i	$-0.0209581\pi$
$398$	−17.8543	−	14.9815i	−0.894955	−	0.750956i
$399$		0			0
$400$	2.62586	+	14.8920i	0.131293	+	0.744599i
$401$	5.90492	−	16.2236i	0.294878	−	0.810169i	−0.700458	−	0.713694i	$-0.747021\pi$
$401$	5.90492	−	16.2236i	0.294878	−	0.810169i	0.995335	−	0.0964756i	$-0.0307570\pi$
$402$		0			0
$403$	−1.26659	+	7.18320i	−0.0630934	+	0.357821i
$404$	−16.9210	−	29.3081i	−0.841852	−	1.45813i
$405$		0			0
$406$	−6.92307	−	9.60400i	−0.343586	−	0.476638i
$407$	−7.13813	−	19.6118i	−0.353824	−	0.972123i
$408$		0			0
$409$	−22.7379	+	4.00930i	−1.12432	+	0.198247i	−0.704735	−	0.709471i	$-0.748934\pi$
$409$	−22.7379	+	4.00930i	−1.12432	+	0.198247i	−0.419581	+	0.907718i	$0.637823\pi$
$410$	2.37741	−	6.53189i	0.117412	−	0.322587i
$411$		0			0
$412$	9.77413	−	11.6484i	0.481537	−	0.573873i
$413$	−9.88779	−	13.7168i	−0.486546	−	0.674959i
$414$		0			0
$415$	1.16340	−	2.01507i	0.0571092	−	0.0989161i
$416$	−7.77158	−	6.52113i	−0.381033	−	0.319725i
$417$		0			0
$418$	98.5437	−	17.3759i	4.81993	−	0.849884i
$419$	−21.7961	−	7.93314i	−1.06481	−	0.387559i	−0.250577	−	0.968097i	$-0.580620\pi$
$419$	−21.7961	−	7.93314i	−1.06481	−	0.387559i	−0.814234	+	0.580537i	$0.802843\pi$
$420$		0			0
$421$	−3.28202	+	18.6133i	−0.159956	+	0.907156i	0.794158	+	0.607712i	$0.207912\pi$
$421$	−3.28202	+	18.6133i	−0.159956	+	0.907156i	−0.954114	+	0.299444i	$0.903199\pi$
$422$	14.6297	+	8.44647i	0.712163	+	0.411168i
$423$		0			0
$424$	1.36937	+	2.37183i	0.0665027	+	0.115186i
$425$	−0.792609	+	4.49511i	−0.0384472	+	0.218045i
$426$		0			0
$427$	−19.8363	−	19.2994i	−0.959947	−	0.933963i
$428$	−4.96409	−	5.91598i	−0.239949	−	0.285959i
$429$		0			0
$430$	2.94359	+	0.519035i	0.141953	+	0.0250301i
$431$	−35.0297	−	20.2244i	−1.68732	−	0.974175i	−0.956557	−	0.291545i	$-0.905831\pi$
$431$	−35.0297	−	20.2244i	−1.68732	−	0.974175i	−0.730764	−	0.682630i	$-0.760836\pi$
$432$		0			0
$433$			5.57490i			0.267912i	0.990987	+	0.133956i	$0.0427681\pi$
$433$			5.57490i			0.267912i	−0.990987	+	0.133956i	$0.957232\pi$
$434$	−28.9218	+	13.9727i	−1.38829	+	0.670710i
$435$		0			0
$436$	−28.1543	−	10.2473i	−1.34835	−	0.490759i
$437$	−12.2834	−	4.47079i	−0.587594	−	0.213867i
$438$		0			0
$439$	−33.6601	−	5.93518i	−1.60651	−	0.283271i	−0.702789	−	0.711398i	$-0.748062\pi$
$439$	−33.6601	−	5.93518i	−1.60651	−	0.283271i	−0.903718	+	0.428127i	$0.859174\pi$
$440$	−0.888115	+	1.53826i	−0.0423392	+	0.0733337i
$441$		0			0
$442$	−1.23221	−	2.13426i	−0.0586104	−	0.101516i
$443$	4.54519	+	12.4878i	0.215949	+	0.593314i	0.999611	−	0.0278724i	$-0.00887321\pi$
$443$	4.54519	+	12.4878i	0.215949	+	0.593314i	−0.783663	+	0.621186i	$0.786651\pi$
$444$		0			0
$445$	1.41407	−	1.18655i	0.0670335	−	0.0562478i
$446$	2.35472	+	13.3543i	0.111499	+	0.632344i
$447$		0			0
$448$	2.07551	−	28.1692i	0.0980587	−	1.33087i
$449$	10.5259	−	6.07712i	0.496747	−	0.286797i	−0.230622	−	0.973043i	$-0.574076\pi$
$449$	10.5259	−	6.07712i	0.496747	−	0.286797i	0.727369	+	0.686247i	$0.240743\pi$
$450$		0			0
$451$	49.9825	−	28.8574i	2.35358	−	1.35884i
$452$	−12.0119	−	33.0024i	−0.564992	−	1.55230i
$453$		0			0
$454$	14.2912	−	2.51992i	0.670718	−	0.118266i
$455$	0.294171	−	1.16136i	0.0137910	−	0.0544456i
$456$		0			0
$457$	−10.9634	−	9.19939i	−0.512846	−	0.430329i	0.349283	−	0.937017i	$-0.386425\pi$
$457$	−10.9634	−	9.19939i	−0.512846	−	0.430329i	−0.862129	+	0.506688i	$0.830870\pi$
$458$	19.3057	−	33.4384i	0.902095	−	1.56248i
$459$		0			0
$460$	1.26809	−	0.732131i	0.0591249	−	0.0341358i
$461$	23.2811	−	8.47362i	1.08431	−	0.394656i	0.262798	−	0.964851i	$-0.415355\pi$
$461$	23.2811	−	8.47362i	1.08431	−	0.394656i	0.821509	+	0.570195i	$0.193132\pi$
$462$		0			0
$463$	−13.5051	+	11.3321i	−0.627634	+	0.526647i	−0.900193	−	0.435492i	$-0.856574\pi$
$463$	−13.5051	+	11.3321i	−0.627634	+	0.526647i	0.272559	+	0.962139i	$0.412130\pi$
$464$	4.26897	+	5.08756i	0.198182	+	0.236184i
$465$		0			0
$466$	47.2990	−	17.2154i	2.19108	−	0.797490i
$467$	−3.57088			−0.165240			−0.0826202	−	0.996581i	$-0.526329\pi$
$467$	−3.57088			−0.165240			−0.0826202	+	0.996581i	$0.526329\pi$
$468$		0			0
$469$	−0.765164	+	0.0775343i	−0.0353320	+	0.00358020i
$470$	3.74432	+	0.660225i	0.172713	+	0.0304539i
$471$		0			0
$472$	−3.23670	−	3.85735i	−0.148981	−	0.177549i
$473$	15.9525	+	19.0114i	0.733495	+	0.874145i
$474$		0			0
$475$	36.6596	+	6.46408i	1.68206	+	0.296592i
$476$	2.41705	−	5.37468i	0.110785	−	0.246348i
$477$		0			0
$478$	−11.5964			−0.530408
$479$	−6.03889	+	2.19798i	−0.275924	+	0.100428i	−0.476276	−	0.879296i	$-0.658014\pi$
$479$	−6.03889	+	2.19798i	−0.275924	+	0.100428i	0.200352	+	0.979724i	$0.435791\pi$
$480$		0			0
$481$	2.69455	+	3.21124i	0.122861	+	0.146420i
$482$	16.3367	−	13.7081i	0.744117	−	0.624388i
$483$		0			0
$484$	−62.8887	+	22.8896i	−2.85858	+	1.04044i
$485$	2.50775	−	1.44785i	0.113871	−	0.0657434i
$486$		0			0
$487$	8.85684	−	15.3405i	0.401342	−	0.695144i	−0.592546	−	0.805536i	$-0.701877\pi$
$487$	8.85684	−	15.3405i	0.401342	−	0.695144i	0.993888	+	0.110392i	$0.0352107\pi$
$488$	−6.31346	−	5.29762i	−0.285797	−	0.239812i
$489$		0			0
$490$	4.90621	−	1.93974i	0.221640	−	0.0876286i
$491$	−12.0720	+	2.12862i	−0.544803	+	0.0960634i	−0.439274	−	0.898353i	$-0.644764\pi$
$491$	−12.0720	+	2.12862i	−0.544803	+	0.0960634i	−0.105528	+	0.994416i	$0.533653\pi$
$492$		0			0
$493$	0.685639	+	1.88378i	0.0308796	+	0.0848411i
$494$	−17.4058	+	10.0492i	−0.783124	+	0.452137i
$495$		0			0
$496$	15.6043	−	9.00915i	0.700654	−	0.404523i
$497$	12.7452	+	0.939070i	0.571701	+	0.0421231i
$498$		0			0
$499$	0.866807	+	4.91590i	0.0388036	+	0.220066i	0.998043	−	0.0625278i	$-0.0199162\pi$
$499$	0.866807	+	4.91590i	0.0388036	+	0.220066i	−0.959240	+	0.282594i	$0.908805\pi$
$500$	−6.47374	+	5.43212i	−0.289515	+	0.242932i
$501$		0			0
$502$	−14.8670	−	40.8467i	−0.663547	−	1.82308i
$503$	10.5236	+	18.2273i	0.469222	+	0.812717i	0.999381	−	0.0351814i	$-0.0112009\pi$
$503$	10.5236	+	18.2273i	0.469222	+	0.812717i	−0.530158	+	0.847899i	$0.677868\pi$
$504$		0			0
$505$	−2.56499	+	4.44269i	−0.114140	+	0.197697i
$506$	22.0488	+	3.88779i	0.980187	+	0.172833i
$507$		0			0
$508$	−31.3162	−	11.3981i	−1.38943	−	0.505711i
$509$	−25.7085	−	9.35714i	−1.13951	−	0.414748i	−0.297774	−	0.954636i	$-0.596244\pi$
$509$	−25.7085	−	9.35714i	−1.13951	−	0.414748i	−0.841737	+	0.539888i	$0.818466\pi$
$510$		0			0
$511$	−9.73871	−	0.717551i	−0.430815	−	0.0317426i
$512$			29.9539i			1.32379i
$513$		0			0
$514$	−45.9289	−	26.5170i	−2.02583	−	1.16962i
$515$	−2.26997	−	0.400257i	−0.100027	−	0.0176374i
$516$		0			0
$517$	20.2919	+	24.1830i	0.892438	+	1.06357i
$518$	−4.53272	+	17.8948i	−0.199156	+	0.786253i
$519$		0			0
$520$	0.0619521	−	0.351348i	0.00271678	−	0.0154076i
$521$	−18.9952	−	32.9006i	−0.832194	−	1.44140i	−0.896295	−	0.443458i	$-0.853751\pi$
$521$	−18.9952	−	32.9006i	−0.832194	−	1.44140i	0.0641012	−	0.997943i	$-0.479582\pi$
$522$		0			0
$523$	−0.735757	−	0.424789i	−0.0321724	−	0.0185747i	0.483828	−	0.875163i	$-0.339246\pi$
$523$	−0.735757	−	0.424789i	−0.0321724	−	0.0185747i	−0.516000	+	0.856589i	$0.672580\pi$
$524$	−1.08219	+	6.13740i	−0.0472756	+	0.268113i
$525$		0			0
$526$	−7.81014	−	2.84266i	−0.340538	−	0.123946i
$527$	5.35615	−	0.944435i	0.233318	−	0.0411402i
$528$		0			0
$529$	15.3785	+	12.9041i	0.668632	+	0.561049i
$530$	1.30992	−	2.26885i	0.0568993	−	0.0985525i
$531$		0			0
$532$	−43.8329	−	19.7121i	−1.90040	−	0.854629i
$533$	−7.45145	+	8.88030i	−0.322758	+	0.384648i
$534$		0			0
$535$	−0.400389	+	1.10006i	−0.0173103	+	0.0475598i
$536$	−0.225548	+	0.0397701i	−0.00974217	+	0.00171781i
$537$		0			0
$538$	3.36367	+	9.24162i	0.145018	+	0.398434i
$539$	41.5582	+	13.8471i	1.79004	+	0.596435i
$540$		0			0
$541$	20.4690	+	35.4533i	0.880031	+	1.52426i	0.851305	+	0.524671i	$0.175812\pi$
$541$	20.4690	+	35.4533i	0.880031	+	1.52426i	0.0287257	+	0.999587i	$0.490855\pi$
$542$	3.12508	−	17.7232i	0.134234	−	0.761278i
$543$		0			0
$544$	−2.58727	+	7.10848i	−0.110928	+	0.304773i
$545$	0.788657	+	4.47270i	0.0337824	+	0.191589i
$546$		0			0
$547$	−9.03807	−	7.58384i	−0.386440	−	0.324262i	0.428784	−	0.903407i	$-0.358942\pi$
$547$	−9.03807	−	7.58384i	−0.386440	−	0.324262i	−0.815224	+	0.579145i	$0.803386\pi$
$548$			23.1510i			0.988964i
$549$		0			0
$550$	−63.7583			−2.71866
$551$	15.3630	−	5.59169i	0.654487	−	0.238214i
$552$		0			0
$553$	7.43049	+	26.2832i	0.315977	+	1.11768i
$554$	11.3670	−	31.2304i	0.482935	−	1.32685i
$555$		0			0
$556$	0.198711	−	0.236815i	0.00842723	−	0.0100432i
$557$		−	31.2086i		−	1.32235i	−0.750232	−	0.661175i	$-0.770058\pi$
$557$		−	31.2086i		−	1.32235i	0.750232	−	0.661175i	$-0.229942\pi$
$558$		0			0
$559$	−4.31695	−	2.49239i	−0.182587	−	0.105417i
$560$	−2.66481	+	1.28742i	−0.112609	+	0.0544034i
$561$		0			0
$562$	34.6107	−	29.0418i	1.45996	−	1.22505i
$563$	2.88191	+	16.3441i	0.121458	+	0.688824i	0.983349	+	0.181729i	$0.0581694\pi$
$563$	2.88191	+	16.3441i	0.121458	+	0.688824i	−0.861890	+	0.507095i	$0.830719\pi$
$564$		0			0
$565$	−3.42205	+	4.07824i	−0.143967	+	0.171573i
$566$	9.51130			0.399790
$567$		0			0
$568$	3.80572			0.159684
$569$	8.45351	−	10.0745i	0.354389	−	0.422345i	−0.559168	−	0.829054i	$-0.688879\pi$
$569$	8.45351	−	10.0745i	0.354389	−	0.422345i	0.913558	+	0.406709i	$0.133324\pi$
$570$		0			0
$571$	2.47480	+	14.0353i	0.103567	+	0.587359i	0.991783	+	0.127932i	$0.0408340\pi$
$571$	2.47480	+	14.0353i	0.103567	+	0.587359i	−0.888216	+	0.459427i	$0.848055\pi$
$572$	14.3198	−	12.0158i	0.598742	−	0.502404i
$573$		0			0
$574$	−50.9108	−	3.75112i	−2.12498	−	0.156569i
$575$	7.21311	+	4.16449i	0.300807	+	0.173671i
$576$		0			0
$577$		−	0.548136i		−	0.0228192i	−0.999935	−	0.0114096i	$-0.996368\pi$
$577$		−	0.548136i		−	0.0228192i	0.999935	−	0.0114096i	$-0.00363187\pi$
$578$	21.6793	−	25.8364i	0.901740	−	1.07465i
$579$		0			0
$580$	−0.626368	+	1.72093i	−0.0260085	+	0.0714578i
$581$	−16.5649	−	4.19586i	−0.687228	−	0.174074i
$582$		0			0
$583$	20.4407	−	7.43979i	0.846566	−	0.308125i
$584$	−2.90798			−0.120333
$585$		0			0
$586$			16.5516i			0.683741i
$587$	19.8533	+	16.6589i	0.819432	+	0.687585i	0.952839	−	0.303476i	$-0.0981474\pi$
$587$	19.8533	+	16.6589i	0.819432	+	0.687585i	−0.133407	+	0.991061i	$0.542592\pi$
$588$		0			0
$589$	−7.70228	−	43.6818i	−0.317367	−	1.79988i
$590$	−1.64744	+	4.52631i	−0.0678241	+	0.186345i
$591$		0			0
$592$	1.79819	−	10.1981i	0.0739053	−	0.419138i
$593$	1.71212	+	2.96547i	0.0703082	+	0.121777i	0.899036	−	0.437874i	$-0.144268\pi$
$593$	1.71212	+	2.96547i	0.0703082	+	0.121777i	−0.828728	+	0.559651i	$0.810935\pi$
$594$		0			0
$595$	−0.888768	+	0.0900591i	−0.0364359	+	0.00369206i
$596$	11.6938	+	32.1285i	0.478997	+	1.31603i
$597$		0			0
$598$	−4.42864	+	0.780889i	−0.181101	+	0.0319329i
$599$	−9.51273	+	26.1360i	−0.388680	+	1.06789i	0.578917	+	0.815387i	$0.303476\pi$
$599$	−9.51273	+	26.1360i	−0.388680	+	1.06789i	−0.967596	+	0.252502i	$0.918747\pi$
$600$		0			0
$601$	4.26455	−	5.08229i	0.173955	−	0.207311i	−0.672022	−	0.740531i	$-0.734574\pi$
$601$	4.26455	−	5.08229i	0.173955	−	0.207311i	0.845976	+	0.533220i	$0.179018\pi$
$602$	−2.21299	−	21.8394i	−0.0901947	−	0.890106i
$603$		0			0
$604$	24.0692	−	41.6890i	0.979361	−	1.69630i
$605$	7.77140	+	6.52098i	0.315952	+	0.265115i
$606$		0			0
$607$	−36.0153	+	6.35047i	−1.46182	+	0.257758i	−0.847287	−	0.531136i	$-0.821765\pi$
$607$	−36.0153	+	6.35047i	−1.46182	+	0.257758i	−0.614530	+	0.788894i	$0.710654\pi$
$608$	57.9728	+	21.1004i	2.35111	+	0.855733i
$609$		0			0
$610$	−1.36901	+	7.76403i	−0.0554295	+	0.314357i
$611$	−5.49127	−	3.17039i	−0.222153	−	0.128260i
$612$		0			0
$613$	7.90264	+	13.6878i	0.319185	+	0.552844i	0.980318	−	0.197424i	$-0.0632577\pi$
$613$	7.90264	+	13.6878i	0.319185	+	0.552844i	−0.661134	+	0.750268i	$0.729924\pi$
$614$	−6.99940	+	39.6956i	−0.282473	+	1.60198i
$615$		0			0
$616$	12.6453	+	3.20302i	0.509493	+	0.129053i
$617$	−10.9448	−	13.0434i	−0.440619	−	0.525109i	0.499336	−	0.866409i	$-0.333577\pi$
$617$	−10.9448	−	13.0434i	−0.440619	−	0.525109i	−0.939955	+	0.341299i	$0.889133\pi$
$618$		0			0
$619$	23.4106	+	4.12792i	0.940952	+	0.165915i	0.623027	−	0.782200i	$-0.285903\pi$
$619$	23.4106	+	4.12792i	0.940952	+	0.165915i	0.317925	+	0.948116i	$0.397014\pi$
$620$	4.30295	+	2.48431i	0.172811	+	0.0997722i
$621$		0			0
$622$		−	27.8050i		−	1.11488i
$623$	−11.2105	−	7.62266i	−0.449140	−	0.305395i
$624$		0			0
$625$	−21.6787	−	7.89041i	−0.867149	−	0.315617i
$626$	−29.4048	−	10.7025i	−1.17525	−	0.427757i
$627$		0			0
$628$	9.28418	+	1.63705i	0.370479	+	0.0653254i
$629$	1.56287	−	2.70698i	0.0623158	−	0.107934i
$630$		0			0
$631$	21.9990	+	38.1033i	0.875765	+	1.51687i	0.855946	+	0.517066i	$0.172976\pi$
$631$	21.9990	+	38.1033i	0.875765	+	1.51687i	0.0198191	+	0.999804i	$0.493691\pi$
$632$	2.78189	+	7.64319i	0.110658	+	0.304030i
$633$		0			0
$634$	−26.5974	+	22.3179i	−1.05632	+	0.886356i
$635$	0.877226	+	4.97499i	0.0348116	+	0.197427i
$636$		0			0
$637$	−8.79509	+	0.241382i	−0.348474	+	0.00956392i
$638$	−24.2506	+	14.0011i	−0.960090	+	0.554308i
$639$		0			0
$640$	−1.93166	+	1.11525i	−0.0763557	+	0.0440840i
$641$	9.08443	+	24.9593i	0.358813	+	0.985831i	0.979442	+	0.201727i	$0.0646553\pi$
$641$	9.08443	+	24.9593i	0.358813	+	0.985831i	−0.620629	+	0.784105i	$0.713123\pi$
$642$		0			0
$643$	−21.8428	+	3.85147i	−0.861394	+	0.151887i	−0.586858	−	0.809690i	$-0.699635\pi$
$643$	−21.8428	+	3.85147i	−0.861394	+	0.151887i	−0.274536	+	0.961577i	$0.588524\pi$
$644$	−7.70750	−	7.49887i	−0.303718	−	0.295497i
$645$		0			0
$646$	11.4803	+	9.63310i	0.451686	+	0.379009i
$647$	6.41692	−	11.1144i	0.252275	−	0.436954i	−0.711877	−	0.702305i	$-0.752154\pi$
$647$	6.41692	−	11.1144i	0.252275	−	0.436954i	0.964152	+	0.265351i	$0.0854878\pi$
$648$		0			0
$649$	−34.6356	+	19.9969i	−1.35957	+	0.784946i
$650$	12.0340	−	4.38000i	0.472011	−	0.171798i
$651$		0			0
$652$	−31.5280	+	26.4551i	−1.23473	+	1.03606i
$653$	−6.85654	−	8.17131i	−0.268317	−	0.319768i	0.615015	−	0.788515i	$-0.289150\pi$
$653$	−6.85654	−	8.17131i	−0.268317	−	0.319768i	−0.883332	+	0.468747i	$0.844706\pi$
$654$		0			0
$655$	0.887722	−	0.323104i	0.0346862	−	0.0126247i
$656$	28.6366			1.11807
$657$		0			0
$658$	−2.81498	−	27.7802i	−0.109739	−	1.08299i
$659$	−12.4568	−	2.19647i	−0.485248	−	0.0855623i	−0.0743281	−	0.997234i	$-0.523681\pi$
$659$	−12.4568	−	2.19647i	−0.485248	−	0.0855623i	−0.410920	+	0.911672i	$0.634792\pi$
$660$		0			0
$661$	21.3936	+	25.4959i	0.832115	+	0.991677i	0.999983	+	0.00586698i	$0.00186753\pi$
$661$	21.3936	+	25.4959i	0.832115	+	0.991677i	−0.167867	+	0.985810i	$0.553688\pi$
$662$	−30.8816	−	36.8033i	−1.20025	−	1.43040i
$663$		0			0
$664$	−5.01139	−	0.883643i	−0.194479	−	0.0342920i
$665$	0.734472	+	7.24830i	0.0284816	+	0.281077i
$666$		0			0
$667$	3.65803			0.141639
$668$	−27.4168	+	9.97890i	−1.06079	+	0.386095i
$669$		0			0
$670$	0.140824	+	0.167828i	0.00544051	+	0.00648375i
$671$	−50.1446	+	42.0763i	−1.93581	+	1.62434i
$672$		0			0
$673$	21.0468	−	7.66040i	0.811294	−	0.295287i	0.0971357	−	0.995271i	$-0.469032\pi$
$673$	21.0468	−	7.66040i	0.811294	−	0.295287i	0.714158	+	0.699984i	$0.246810\pi$
$674$	−49.7797	+	28.7403i	−1.91744	+	1.10704i
$675$		0			0
$676$	13.5706	−	23.5051i	0.521948	−	0.904040i
$677$	−35.4418	−	29.7392i	−1.36214	−	1.14297i	−0.975316	−	0.220814i	$-0.929129\pi$
$677$	−35.4418	−	29.7392i	−1.36214	−	1.14297i	−0.386821	−	0.922155i	$-0.626427\pi$
$678$		0			0
$679$	−15.2422	−	14.8296i	−0.584941	−	0.569108i
$680$	−0.261982	+	0.0461946i	−0.0100466	+	0.00177148i
$681$		0			0
$682$	25.9837	+	71.3896i	0.994968	+	2.73365i
$683$	7.53532	−	4.35052i	0.288331	−	0.166468i	−0.348858	−	0.937176i	$-0.613430\pi$
$683$	7.53532	−	4.35052i	0.288331	−	0.166468i	0.637189	+	0.770708i	$0.280097\pi$
$684$		0			0
$685$	3.03920	−	1.75468i	0.116122	−	0.0670431i
$686$	−23.5103	−	30.7968i	−0.897628	−	1.17583i
$687$		0			0
$688$	2.13828	+	12.1268i	0.0815210	+	0.462329i
$689$	−3.34695	+	2.80842i	−0.127509	+	0.106992i
$690$		0			0
$691$	3.89200	+	10.6932i	0.148059	+	0.406787i	0.991446	−	0.130519i	$-0.0416642\pi$
$691$	3.89200	+	10.6932i	0.148059	+	0.406787i	−0.843387	+	0.537306i	$0.819442\pi$
$692$	25.0940	+	43.4641i	0.953932	+	1.65226i
$693$		0			0
$694$	10.4314	−	18.0677i	0.395971	−	0.685841i
$695$	−0.0461492	−	0.00813736i	−0.00175054	−	0.000308667i
$696$		0			0
$697$	8.12259	+	2.95638i	0.307665	+	0.111981i
$698$	54.9194	+	19.9890i	2.07873	+	0.756596i
$699$		0			0
$700$	25.3239	+	17.2191i	0.957155	+	0.650822i
$701$			19.8586i			0.750050i	0.927015	+	0.375025i	$0.122366\pi$
$701$			19.8586i			0.750050i	−0.927015	+	0.375025i	$0.877634\pi$
$702$		0			0
$703$	−22.0766	−	12.7459i	−0.832634	−	0.480722i
$704$	−65.7918	−	11.6009i	−2.47962	−	0.437224i
$705$		0			0
$706$	−31.7753	−	37.8683i	−1.19588	−	1.42519i
$707$	36.5211	+	9.25072i	1.37352	+	0.347909i
$708$		0			0
$709$	3.55338	−	20.1522i	0.133450	−	0.756831i	−0.842477	−	0.538733i	$-0.818903\pi$
$709$	3.55338	−	20.1522i	0.133450	−	0.756831i	0.975927	−	0.218099i	$-0.0699855\pi$
$710$	−1.82024	−	3.15275i	−0.0683125	−	0.118321i
$711$		0			0
$712$	−3.49619	−	2.01852i	−0.131025	−	0.0756474i
$713$	1.72335	−	9.77363i	0.0645402	−	0.366025i
$714$		0			0
$715$	−2.66274	−	0.969157i	−0.0995807	−	0.0362444i
$716$	21.9866	−	3.87682i	0.821676	−	0.144884i
$717$		0			0
$718$	0.0477531	+	0.0400696i	0.00178213	+	0.00149538i
$719$	−11.1854	+	19.3737i	−0.417146	+	0.722518i	−0.995651	−	0.0931608i	$-0.970303\pi$
$719$	−11.1854	+	19.3737i	−0.417146	+	0.722518i	0.578505	+	0.815679i	$0.303636\pi$
$720$		0			0
$721$	1.70656	+	16.8416i	0.0635557	+	0.627214i
$722$	53.0123	−	63.1776i	1.97291	−	2.35123i
$723$		0			0
$724$	−7.56006	+	20.7711i	−0.280967	+	0.771951i
$725$	−10.2589	+	1.80893i	−0.381007	+	0.0671818i
$726$		0			0
$727$	−2.58356	−	7.09828i	−0.0958190	−	0.263261i	0.882518	−	0.470278i	$-0.155846\pi$
$727$	−2.58356	−	7.09828i	−0.0958190	−	0.263261i	−0.978337	+	0.207018i	$0.933624\pi$
$728$	−2.60675	+	0.264143i	−0.0966126	+	0.00978978i
$729$		0			0
$730$	1.39086	+	2.40904i	0.0514781	+	0.0891627i
$731$	−0.645434	+	3.66044i	−0.0238722	+	0.135386i
$732$		0			0
$733$	5.82499	−	16.0040i	0.215151	−	0.591123i	−0.784425	−	0.620223i	$-0.787042\pi$
$733$	5.82499	−	16.0040i	0.215151	−	0.591123i	0.999576	+	0.0291005i	$0.00926428\pi$
$734$	−5.69560	−	32.3013i	−0.210228	−	1.19226i
$735$		0			0
$736$	10.5742	+	8.87281i	0.389770	+	0.327056i
$737$			1.81905i			0.0670054i
$738$		0			0
$739$	6.98225			0.256846			0.128423	−	0.991719i	$-0.459008\pi$
$739$	6.98225			0.256846			0.128423	+	0.991719i	$0.459008\pi$
$740$	2.68333	−	0.976651i	0.0986411	−	0.0359024i
$741$		0			0
$742$	−18.6511	−	4.72428i	−0.684703	−	0.173434i
$743$	0.493042	−	1.35462i	0.0180880	−	0.0496962i	−0.930320	−	0.366749i	$-0.880471\pi$
$743$	0.493042	−	1.35462i	0.0180880	−	0.0496962i	0.948408	+	0.317052i	$0.102693\pi$
$744$		0			0
$745$	3.33143	−	3.97024i	0.122054	−	0.145458i
$746$			32.0603i			1.17381i
$747$		0			0
$748$	−12.0712	−	6.96930i	−0.441366	−	0.254823i
$749$	8.57408	+	0.631740i	0.313290	+	0.0230833i
$750$		0			0
$751$	−14.3786	+	12.0651i	−0.524683	+	0.440261i	−0.866261	−	0.499592i	$-0.833483\pi$
$751$	−14.3786	+	12.0651i	−0.524683	+	0.440261i	0.341578	+	0.939854i	$0.389039\pi$
$752$	2.71994	+	15.4256i	0.0991861	+	0.562512i
$753$		0			0
$754$	3.61531	−	4.30855i	0.131662	−	0.156908i
$755$	−7.29709			−0.265568
$756$		0			0
$757$	−6.53601			−0.237555			−0.118778	−	0.992921i	$-0.537898\pi$
$757$	−6.53601			−0.237555			−0.118778	+	0.992921i	$0.537898\pi$
$758$	−24.1458	+	28.7759i	−0.877017	+	1.04519i
$759$		0			0
$760$	0.376737	+	2.13658i	0.0136657	+	0.0775020i
$761$	2.71646	−	2.27938i	0.0984717	−	0.0826276i	−0.592223	−	0.805774i	$-0.701749\pi$
$761$	2.71646	−	2.27938i	0.0984717	−	0.0826276i	0.690694	+	0.723147i	$0.257305\pi$
$762$		0			0
$763$	30.0329	−	14.5095i	1.08727	−	0.525278i
$764$	−18.7848	−	10.8454i	−0.679609	−	0.392373i
$765$		0			0
$766$			72.3016i			2.61236i
$767$	5.16352	−	6.15364i	0.186444	−	0.222195i
$768$		0			0
$769$	3.05429	−	8.39159i	0.110141	−	0.302609i	−0.872361	−	0.488862i	$-0.837412\pi$
$769$	3.05429	−	8.39159i	0.110141	−	0.302609i	0.982502	+	0.186253i	$0.0596345\pi$
$770$	−3.39466	−	12.0076i	−0.122335	−	0.432726i
$771$		0			0
$772$	−7.82767	+	2.84904i	−0.281724	+	0.102539i
$773$	−1.68056			−0.0604455			−0.0302227	−	0.999543i	$-0.509622\pi$
$773$	−1.68056			−0.0604455			−0.0302227	+	0.999543i	$0.509622\pi$
$774$		0			0
$775$			28.2624i			1.01521i
$776$	−4.85124	−	4.07068i	−0.174149	−	0.146129i
$777$		0			0
$778$	−0.125481	−	0.711640i	−0.00449872	−	0.0255135i
$779$	24.1106	−	66.2433i	0.863851	−	2.37341i
$780$		0			0
$781$	5.24885	−	29.7677i	0.187818	−	1.06517i
$782$	1.67658	+	2.90392i	0.0599543	+	0.103844i
$783$		0			0
$784$	14.4222	+	16.2601i	0.515080	+	0.580718i
$785$	−0.488767	−	1.34288i	−0.0174449	−	0.0479293i
$786$		0			0
$787$	−19.3925	+	3.41942i	−0.691268	+	0.121889i	−0.508236	−	0.861218i	$-0.669702\pi$
$787$	−19.3925	+	3.41942i	−0.691268	+	0.121889i	−0.183032	+	0.983107i	$0.558591\pi$
$788$	16.0390	−	44.0669i	0.571367	−	1.56982i
$789$		0			0
$790$	5.00126	−	5.96027i	0.177937	−	0.212057i
$791$	35.6578	+	16.0357i	1.26785	+	0.570164i
$792$		0			0
$793$	6.57395	−	11.3864i	0.233448	−	0.404343i
$794$	4.20181	+	3.52574i	0.149117	+	0.125124i
$795$		0			0
$796$	26.0753	−	4.59778i	0.924215	−	0.162964i
$797$	6.04013	+	2.19843i	0.213952	+	0.0778723i	0.446773	−	0.894647i	$-0.352573\pi$
$797$	6.04013	+	2.19843i	0.213952	+	0.0778723i	−0.232820	+	0.972520i	$0.574795\pi$
$798$		0			0
$799$	−0.821008	+	4.65617i	−0.0290452	+	0.164723i
$800$	−34.0430	−	19.6548i	−1.20360	−	0.694900i
$801$		0			0
$802$	18.0593	+	31.2797i	0.637697	+	1.10452i
$803$	−4.01068	+	22.7457i	−0.141534	+	0.802678i
$804$		0			0
$805$	−0.400256	+	1.58018i	−0.0141072	+	0.0556940i
$806$	−9.80851	−	11.6893i	−0.345490	−	0.411739i
$807$		0			0
$808$	11.0487	+	1.94819i	0.388693	+	0.0685371i
$809$	−18.3341	−	10.5852i	−0.644592	−	0.372155i	0.141789	−	0.989897i	$-0.454715\pi$
$809$	−18.3341	−	10.5852i	−0.644592	−	0.372155i	−0.786381	+	0.617741i	$0.788048\pi$
$810$		0			0
$811$			36.0138i			1.26461i	0.774718	+	0.632307i	$0.217892\pi$
$811$			36.0138i			1.26461i	−0.774718	+	0.632307i	$0.782108\pi$
$812$	13.4133	+	0.988292i	0.470713	+	0.0346823i
$813$		0			0
$814$	41.0287	+	14.9332i	1.43805	+	0.523409i
$815$	5.86254	+	2.13379i	0.205356	+	0.0747435i
$816$		0			0
$817$	29.8525	+	5.26380i	1.04441	+	0.184157i
$818$	24.1511	−	41.8310i	0.844424	−	1.46259i
$819$		0			0
$820$	3.94832	+	6.83869i	0.137881	+	0.238818i
$821$	9.84670	+	27.0536i	0.343652	+	0.944177i	0.984325	+	0.176363i	$0.0564333\pi$
$821$	9.84670	+	27.0536i	0.343652	+	0.944177i	−0.640673	+	0.767814i	$0.721344\pi$
$822$		0			0
$823$	−15.0019	+	12.5881i	−0.522933	+	0.438793i	−0.865653	−	0.500645i	$-0.833096\pi$
$823$	−15.0019	+	12.5881i	−0.522933	+	0.438793i	0.342720	+	0.939438i	$0.388652\pi$
$824$	0.875358	+	4.96440i	0.0304945	+	0.172943i
$825$		0			0
$826$	35.2789	+	2.59936i	1.22751	+	0.0904432i
$827$	−13.9928	+	8.07875i	−0.486577	+	0.280925i	−0.723153	−	0.690687i	$-0.757308\pi$
$827$	−13.9928	+	8.07875i	−0.486577	+	0.280925i	0.236576	+	0.971613i	$0.423975\pi$
$828$		0			0
$829$	27.8116	−	16.0570i	0.965936	−	0.557683i	0.0679412	−	0.997689i	$-0.478357\pi$
$829$	27.8116	−	16.0570i	0.965936	−	0.557683i	0.897995	+	0.440006i	$0.145024\pi$
$830$	1.66487	+	4.57420i	0.0577886	+	0.158773i
$831$		0			0
$832$	13.2147	−	2.33011i	0.458138	−	0.0807821i
$833$	2.41212	+	6.10100i	0.0835751	+	0.211387i
$834$		0			0
$835$	3.38800	+	2.84287i	0.117247	+	0.0983816i
$836$	−56.8377	+	98.4458i	−1.96577	+	3.40482i
$837$		0			0
$838$	42.0236	−	24.2623i	1.45168	−	0.838128i
$839$	4.91418	−	1.78862i	0.169656	−	0.0617499i	−0.255795	−	0.966731i	$-0.582337\pi$
$839$	4.91418	−	1.78862i	0.169656	−	0.0617499i	0.425452	+	0.904981i	$0.360115\pi$
$840$		0			0
$841$	18.7105	−	15.7000i	0.645190	−	0.541379i
$842$	−25.4161	−	30.2897i	−0.875895	−	1.04385i
$843$		0			0
$844$	−18.0335	+	6.56366i	−0.620739	+	0.225931i
$845$	−4.11423			−0.141534
$846$		0			0
$847$	30.5573	−	67.9488i	1.04996	−	2.33475i
$848$	10.6290	+	1.87419i	0.365003	+	0.0643598i
$849$		0			0
$850$	−6.13798	−	7.31496i	−0.210531	−	0.250901i
$851$	−3.66627	−	4.36929i	−0.125678	−	0.149777i
$852$		0			0
$853$	−39.1762	−	6.90782i	−1.34137	−	0.236519i	−0.543529	−	0.839391i	$-0.682912\pi$
$853$	−39.1762	−	6.90782i	−1.34137	−	0.236519i	−0.797838	+	0.602871i	$0.794023\pi$
$854$	57.6037	−	5.83699i	1.97116	−	0.199738i
$855$		0			0
$856$	2.56022			0.0875065
$857$	−40.7035	+	14.8148i	−1.39040	+	0.506066i	−0.925315	−	0.379199i	$-0.876200\pi$
$857$	−40.7035	+	14.8148i	−1.39040	+	0.506066i	−0.465088	+	0.885264i	$0.653977\pi$
$858$		0			0
$859$	−8.80914	−	10.4983i	−0.300564	−	0.358198i	0.594532	−	0.804072i	$-0.297337\pi$
$859$	−8.80914	−	10.4983i	−0.300564	−	0.358198i	−0.895096	+	0.445874i	$0.852893\pi$
$860$	−2.60117	+	2.18264i	−0.0886993	+	0.0744275i
$861$		0			0
$862$	79.5171	−	28.9419i	2.70836	−	0.985764i
$863$	−24.1671	+	13.9529i	−0.822659	+	0.474962i	−0.851333	−	0.524626i	$-0.824205\pi$
$863$	−24.1671	+	13.9529i	−0.822659	+	0.474962i	0.0286735	+	0.999589i	$0.490872\pi$
$864$		0			0
$865$	3.80390	−	6.58855i	0.129336	−	0.224017i
$866$	−8.93428	−	7.49675i	−0.303599	−	0.254750i
$867$		0			0
$868$	8.95976	−	35.3724i	0.304114	−	1.20062i
$869$	63.6205	−	11.2180i	2.15818	−	0.380545i
$870$		0			0
$871$	−0.124963	−	0.343333i	−0.00423421	−	0.0116334i
$872$	8.60191	−	4.96631i	0.291297	−	0.168181i
$873$		0			0
$874$	23.6828	−	13.6732i	0.801081	−	0.462504i
$875$	0.691302	−	9.38246i	0.0233703	−	0.317185i
$876$		0			0
$877$	−6.39579	−	36.2723i	−0.215970	−	1.22483i	−0.879215	−	0.476426i	$-0.841932\pi$
$877$	−6.39579	−	36.2723i	−0.215970	−	1.22483i	0.663244	−	0.748403i	$-0.269179\pi$
$878$	54.7755	−	45.9621i	1.84858	−	1.55115i
$879$		0			0
$880$	2.39410	+	6.57772i	0.0807049	+	0.221735i
$881$	−23.0421	−	39.9101i	−0.776309	−	1.34461i	−0.934056	−	0.357127i	$-0.883756\pi$
$881$	−23.0421	−	39.9101i	−0.776309	−	1.34461i	0.157747	−	0.987480i	$-0.449577\pi$
$882$		0			0
$883$	−18.9002	+	32.7361i	−0.636043	+	1.10166i	0.350251	+	0.936656i	$0.386096\pi$
$883$	−18.9002	+	32.7361i	−0.636043	+	1.10166i	−0.986293	+	0.165002i	$0.947237\pi$
$884$	2.75713	+	0.486156i	0.0927322	+	0.0163512i
$885$		0			0
$886$	−26.1249	−	9.50870i	−0.877685	−	0.319451i
$887$	1.27960	+	0.465737i	0.0429648	+	0.0156379i	0.363413	−	0.931628i	$-0.381611\pi$
$887$	1.27960	+	0.465737i	0.0429648	+	0.0156379i	−0.320448	+	0.947266i	$0.603834\pi$
$888$		0			0
$889$	33.4057	−	16.1389i	1.12039	−	0.541282i
$890$			3.86177i			0.129447i
$891$		0			0
$892$	−13.3410	−	7.70245i	−0.446691	−	0.257897i
$893$	37.9731	+	6.69569i	1.27072	+	0.224063i
$894$		0			0
$895$	−2.17536	−	2.59250i	−0.0727143	−	0.0866576i
$896$	11.7407	+	11.4229i	0.392230	+	0.381613i
$897$		0			0
$898$	−4.41537	+	25.0408i	−0.147343	+	0.835622i
$899$	6.20631	+	10.7496i	0.206992	+	0.358521i
$900$		0			0
$901$	2.82138	+	1.62892i	0.0939937	+	0.0542673i
$902$	−20.9665	+	118.907i	−0.698109	+	3.95917i
$903$		0			0
$904$	10.9408	+	3.98214i	0.363887	+	0.132444i
$905$	3.29977	−	0.581838i	0.109688	−	0.0193410i
$906$		0			0
$907$	−24.0479	−	20.1786i	−0.798497	−	0.670019i	0.149336	−	0.988787i	$-0.452287\pi$
$907$	−24.0479	−	20.1786i	−0.798497	−	0.670019i	−0.947833	+	0.318768i	$0.896731\pi$
$908$	−8.24282	+	14.2770i	−0.273548	+	0.473798i
$909$		0			0
$910$	1.46561	+	2.03316i	0.0485845	+	0.0673987i
$911$	23.0479	−	27.4674i	0.763610	−	0.910034i	−0.234461	−	0.972126i	$-0.575332\pi$
$911$	23.0479	−	27.4674i	0.763610	−	0.910034i	0.998070	+	0.0620911i	$0.0197769\pi$
$912$		0			0
$913$	−13.8234	+	37.9795i	−0.457488	+	1.25694i
$914$	29.4857	−	5.19913i	0.975301	−	0.171972i
$915$		0			0
$916$	15.0022	+	41.2183i	0.495688	+	1.36189i
$917$	−4.05697	−	5.62801i	−0.133973	−	0.185853i
$918$		0			0
$919$	−10.7450	−	18.6110i	−0.354446	−	0.613919i	0.632577	−	0.774498i	$-0.281997\pi$
$919$	−10.7450	−	18.6110i	−0.354446	−	0.613919i	−0.987023	+	0.160579i	$0.948664\pi$
$920$	−0.0842934	+	0.478052i	−0.00277907	+	0.0157609i
$921$		0			0
$922$	−17.7271	+	48.7048i	−0.583811	+	1.60401i
$923$	1.05427	+	5.97904i	0.0347016	+	0.196802i
$924$		0			0
$925$	12.4427	+	10.4407i	0.409113	+	0.343287i
$926$		−	36.8818i		−	1.21201i
$927$		0			0
$928$	−17.2644			−0.566733
$929$	−36.9931	+	13.4644i	−1.21371	+	0.441753i	−0.867988	−	0.496586i	$-0.834587\pi$
$929$	−36.9931	+	13.4644i	−1.21371	+	0.441753i	−0.345718	+	0.938338i	$0.612365\pi$
$930$		0			0
$931$	49.7564	−	19.6719i	1.63070	−	0.644721i
$932$	−19.5572	+	53.7330i	−0.640618	+	1.76008i
$933$		0			0
$934$	4.80188	−	5.72266i	0.157122	−	0.187251i
$935$			2.11289i			0.0690990i
$936$		0			0
$937$	−42.7796	−	24.6988i	−1.39755	−	0.806875i	−0.403413	−	0.915018i	$-0.632176\pi$
$937$	−42.7796	−	24.6988i	−1.39755	−	0.806875i	−0.994135	+	0.108143i	$0.965510\pi$
$938$	0.904687	−	1.33051i	0.0295391	−	0.0434427i
$939$		0			0
$940$	−3.30876	+	2.77638i	−0.107920	+	0.0905555i
$941$	−2.65678	−	15.0673i	−0.0866085	−	0.491181i	−0.996998	−	0.0774286i	$-0.975329\pi$
$941$	−2.65678	−	15.0673i	−0.0866085	−	0.491181i	0.910389	−	0.413752i	$-0.135782\pi$
$942$		0			0
$943$	10.1386	−	12.0827i	0.330159	−	0.393468i
$944$	−19.8438			−0.645862
$945$		0			0
$946$	−51.9193			−1.68804
$947$	5.35115	−	6.37725i	0.173889	−	0.207233i	−0.672060	−	0.740497i	$-0.734590\pi$
$947$	5.35115	−	6.37725i	0.173889	−	0.207233i	0.845949	+	0.533264i	$0.179035\pi$
$948$		0			0
$949$	−0.805572	−	4.56862i	−0.0261500	−	0.148304i
$950$	−59.6567	+	50.0579i	−1.93552	+	1.62409i
$951$		0			0
$952$	0.849873	+	1.75914i	0.0275445	+	0.0570141i
$953$	11.5050	+	6.64241i	0.372683	+	0.215169i	0.674630	−	0.738156i	$-0.264303\pi$
$953$	11.5050	+	6.64241i	0.372683	+	0.215169i	−0.301947	+	0.953325i	$0.597637\pi$
$954$		0			0
$955$			3.28801i			0.106398i
$956$	8.46800	−	10.0918i	0.273875	−	0.326391i
$957$		0			0
$958$	4.59825	−	12.6336i	0.148563	−	0.408172i
$959$	−18.4724	−	17.9724i	−0.596505	−	0.580359i
$960$		0			0
$961$	2.51466	−	0.915263i	0.0811182	−	0.0295246i
$962$	−8.76976			−0.282748
$963$		0			0
$964$			24.2270i			0.780300i
$965$	0.967296	+	0.811658i	0.0311384	+	0.0261282i
$966$		0			0
$967$	−2.63510	−	14.9444i	−0.0847390	−	0.480579i	−0.997413	−	0.0718894i	$-0.977097\pi$
$967$	−2.63510	−	14.9444i	−0.0847390	−	0.480579i	0.912674	−	0.408689i	$-0.134014\pi$
$968$	7.58827	−	20.8486i	0.243896	−	0.670100i
$969$		0			0
$970$	−1.05194	+	5.96586i	−0.0337758	+	0.191552i
$971$	1.28302	+	2.22225i	0.0411740	+	0.0713155i	0.885878	−	0.463918i	$-0.153557\pi$
$971$	1.28302	+	2.22225i	0.0411740	+	0.0713155i	−0.844704	+	0.535234i	$0.820224\pi$
$972$		0			0
$973$	0.0346950	+	0.342395i	0.00111227	+	0.0109767i
$974$	12.6745	+	34.8228i	0.406116	+	1.11579i
$975$		0			0
$976$	−31.9856	+	5.63993i	−1.02384	+	0.180530i
$977$	3.81094	−	10.4705i	0.121923	−	0.334980i	−0.863684	−	0.504034i	$-0.831849\pi$
$977$	3.81094	−	10.4705i	0.121923	−	0.334980i	0.985607	+	0.169053i	$0.0540710\pi$
$978$		0			0
$979$	−20.6105	+	24.5626i	−0.658714	+	0.785025i
$980$	−1.89458	+	5.68607i	−0.0605201	+	0.181635i
$981$		0			0
$982$	12.8223	−	22.2090i	0.409177	−	0.708716i
$983$	36.7166	+	30.8089i	1.17108	+	0.982651i	0.999997	−	0.00260591i	$-0.000829489\pi$
$983$	36.7166	+	30.8089i	1.17108	+	0.982651i	0.171081	+	0.985257i	$0.445274\pi$
$984$		0			0
$985$	−7.00062	+	1.23440i	−0.223058	+	0.0393312i
$986$	−3.94093	−	1.43438i	−0.125505	−	0.0456800i
$987$		0			0
$988$	3.96482	−	22.4856i	0.126138	−	0.715362i
$989$	5.87374	+	3.39121i	0.186774	+	0.107834i
$990$		0			0
$991$	−11.3476	−	19.6547i	−0.360470	−	0.624352i	0.627568	−	0.778561i	$-0.284050\pi$
$991$	−11.3476	−	19.6547i	−0.360470	−	0.624352i	−0.988038	+	0.154209i	$0.950717\pi$
$992$	−8.13356	+	46.1277i	−0.258241	+	1.46456i
$993$		0			0
$994$	−18.6439	+	19.1626i	−0.591348	+	0.607800i
$995$	−2.57991	−	3.07461i	−0.0817885	−	0.0974718i
$996$		0			0
$997$	−19.7591	−	3.48405i	−0.625775	−	0.110341i	−0.148237	−	0.988952i	$-0.547360\pi$
$997$	−19.7591	−	3.48405i	−0.625775	−	0.110341i	−0.477539	+	0.878611i	$0.658471\pi$
$998$	−9.04381	−	5.22145i	−0.286277	−	0.165282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.4		132
3.2	odd	2		189.2.ba.a.101.19	✓	132
7.5	odd	6		567.2.bd.a.467.19		132
21.5	even	6		189.2.bd.a.47.4	yes	132
27.4	even	9		189.2.bd.a.185.4	yes	132
27.23	odd	18		567.2.bd.a.17.19		132
189.131	even	18	inner	567.2.ba.a.341.4		132
189.166	odd	18		189.2.ba.a.131.19	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.19	✓	132	3.2	odd	2
189.2.ba.a.131.19	yes	132	189.166	odd	18
189.2.bd.a.47.4	yes	132	21.5	even	6
189.2.bd.a.185.4	yes	132	27.4	even	9
567.2.ba.a.143.4		132	1.1	even	1	trivial
567.2.ba.a.341.4		132	189.131	even	18	inner
567.2.bd.a.17.19		132	27.23	odd	18
567.2.bd.a.467.19		132	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34473 + 1.60259i) q^{2} +(-0.412694 - 2.34051i) q^{4} +(-0.275976 + 0.231571i) q^{5} +(2.18789 + 1.48767i) q^{7} +(0.682329 + 0.393943i) q^{8} +O(q^{10})\)	\(q+(-1.34473 + 1.60259i) q^{2} +(-0.412694 - 2.34051i) q^{4} +(-0.275976 + 0.231571i) q^{5} +(2.18789 + 1.48767i) q^{7} +(0.682329 + 0.393943i) q^{8} -0.753678i q^{10} +(4.02242 - 4.79373i) q^{11} +(-0.429890 + 1.18111i) q^{13} +(-5.32625 + 1.50578i) q^{14} +(2.91769 - 1.06195i) q^{16} +0.937219 q^{17} -7.64344i q^{19} +(0.655887 + 0.550354i) q^{20} +(2.27331 + 12.8926i) q^{22} +(0.584919 - 1.60705i) q^{23} +(-0.845703 + 4.79622i) q^{25} +(-1.31476 - 2.27722i) q^{26} +(2.57896 - 5.73471i) q^{28} +(0.731568 + 2.00997i) q^{29} +(5.71494 - 1.00770i) q^{31} +(-2.76059 + 7.58465i) q^{32} +(-1.26031 + 1.50198i) q^{34} +(-0.948304 + 0.0960919i) q^{35} +(1.66757 - 2.88831i) q^{37} +(12.2493 + 10.2784i) q^{38} +(-0.279532 + 0.0492890i) q^{40} +(8.66669 + 3.15442i) q^{41} +(-0.688669 + 3.90564i) q^{43} +(-12.8798 - 7.43615i) q^{44} +(1.78889 + 3.09844i) q^{46} +(-0.876005 + 4.96807i) q^{47} +(2.57370 + 6.50969i) q^{49} +(-6.54914 - 7.80496i) q^{50} +(2.94182 + 0.518722i) q^{52} +(3.01037 + 1.73804i) q^{53} +2.25443i q^{55} +(0.906803 + 1.87698i) q^{56} +(-4.20492 - 1.53047i) q^{58} +(-6.00562 - 2.18587i) q^{59} +(-10.3015 - 1.81644i) q^{61} +(-6.07015 + 10.5138i) q^{62} +(-5.33790 - 9.24552i) q^{64} +(-0.154873 - 0.425509i) q^{65} +(-0.222678 + 0.186849i) q^{67} +(-0.386785 - 2.19357i) q^{68} +(1.12122 - 1.64896i) q^{70} +(4.18316 - 2.41515i) q^{71} +(-3.19638 + 1.84543i) q^{73} +(2.38635 + 6.55643i) q^{74} +(-17.8895 + 3.15440i) q^{76} +(15.9321 - 4.50413i) q^{77} +(7.90824 + 6.63581i) q^{79} +(-0.559294 + 0.968725i) q^{80} +(-16.7096 + 9.64732i) q^{82} +(-6.06917 + 2.20900i) q^{83} +(-0.258650 + 0.217033i) q^{85} +(-5.33306 - 6.35570i) q^{86} +(4.63307 - 1.68630i) q^{88} -5.12391 q^{89} +(-2.69765 + 1.94461i) q^{91} +(-4.00271 - 0.705785i) q^{92} +(-6.78379 - 8.08461i) q^{94} +(1.77000 + 2.10940i) q^{95} +(-7.91567 - 1.39575i) q^{97} +(-13.8933 - 4.62921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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