LMFDB - Embedded newform 243.2.e.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 1.27297i$ of defining polynomial
Character	$\chi$	$=$	243.109
Dual form			243.2.e.d.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.614005 + 0.515212i) q^{2} +(-0.235737 + 1.33693i) q^{4} +(2.58401 - 0.940501i) q^{5} +(0.412733 + 2.34072i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(-1.10204 + 1.90878i) q^{10} +(0.235072 + 0.0855594i) q^{11} +(2.00090 + 1.67895i) q^{13} +(-1.45939 - 1.22457i) q^{14} +(-0.524408 - 0.190869i) q^{16} +(0.146688 - 0.254072i) q^{17} +(1.39237 + 2.41166i) q^{19} +(0.648239 + 3.67635i) q^{20} +(-0.188417 + 0.0685781i) q^{22} +(-1.16168 + 6.58821i) q^{23} +(1.96232 - 1.64658i) q^{25} -2.09357 q^{26} -3.22668 q^{28} +(-0.271990 + 0.228226i) q^{29} +(0.480218 - 2.72345i) q^{31} +(5.47807 - 1.99386i) q^{32} +(0.0408333 + 0.231577i) q^{34} +(3.26796 + 5.66027i) q^{35} +(3.49619 - 6.05558i) q^{37} +(-2.09744 - 0.763405i) q^{38} +(-5.66895 - 4.75682i) q^{40} +(-7.44412 - 6.24636i) q^{41} +(-0.244984 - 0.0891669i) q^{43} +(-0.169802 + 0.294106i) q^{44} +(-2.68104 - 4.64370i) q^{46} +(-1.98403 - 11.2520i) q^{47} +(1.26921 - 0.461953i) q^{49} +(-0.356537 + 2.02202i) q^{50} +(-2.71632 + 2.27927i) q^{52} +5.43137 q^{53} +0.687897 q^{55} +(4.89998 - 4.11157i) q^{56} +(0.0494182 - 0.280264i) q^{58} +(-5.61647 + 2.04423i) q^{59} +(-2.05717 - 11.6668i) q^{61} +(1.10830 + 1.91963i) q^{62} +(-1.77824 + 3.08001i) q^{64} +(6.74938 + 2.45657i) q^{65} +(1.38677 + 1.16364i) q^{67} +(0.305096 + 0.256006i) q^{68} +(-4.92278 - 1.79175i) q^{70} +(0.185255 - 0.320871i) q^{71} +(-2.51339 - 4.35333i) q^{73} +(0.973225 + 5.51943i) q^{74} +(-3.55246 + 1.29299i) q^{76} +(-0.103249 + 0.585553i) q^{77} +(0.614997 - 0.516044i) q^{79} -1.53459 q^{80} +7.78892 q^{82} +(-2.11095 + 1.77130i) q^{83} +(0.140089 - 0.794483i) q^{85} +(0.196361 - 0.0714696i) q^{86} +(-0.116903 - 0.662992i) q^{88} +(-5.22533 - 9.05054i) q^{89} +(-3.10412 + 5.37650i) q^{91} +(-8.53412 - 3.10617i) q^{92} +(7.01535 + 5.88658i) q^{94} +(5.86607 + 4.92221i) q^{95} +(13.9400 + 5.07373i) q^{97} +(-0.541296 + 0.937552i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} + 3 q^{13} - 21 q^{14} + 9 q^{16} + 9 q^{17} - 3 q^{19} + 24 q^{20} + 12 q^{22} - 12 q^{23} + 12 q^{25} - 30 q^{26} - 12 q^{28}+ \cdots - 45 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 + 3 * q^13 - 21 * q^14 + 9 * q^16 + 9 * q^17 - 3 * q^19 + 24 * q^20 + 12 * q^22 - 12 * q^23 + 12 * q^25 - 30 * q^26 - 12 * q^28 - 24 * q^29 + 12 * q^31 + 27 * q^32 + 12 * q^35 - 3 * q^37 - 30 * q^38 - 15 * q^40 + 6 * q^41 - 15 * q^43 + 3 * q^44 - 3 * q^46 + 12 * q^47 - 33 * q^49 + 21 * q^50 - 45 * q^52 - 18 * q^53 - 12 * q^55 + 30 * q^56 - 51 * q^58 - 3 * q^59 - 33 * q^61 - 12 * q^62 + 12 * q^64 + 21 * q^65 - 6 * q^67 + 9 * q^68 - 15 * q^70 + 27 * q^71 + 6 * q^73 - 21 * q^74 + 6 * q^76 - 12 * q^77 + 21 * q^79 + 42 * q^80 - 12 * q^82 - 6 * q^83 + 36 * q^85 - 21 * q^86 + 42 * q^88 + 9 * q^89 + 6 * q^91 - 3 * q^92 + 48 * q^94 + 3 * q^95 + 39 * q^97 - 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.614005	+	0.515212i	−0.434167	+	0.364310i	−0.833521	−	0.552487i	$-0.813679\pi$
$2$	−0.614005	+	0.515212i	−0.434167	+	0.364310i	0.399354	+	0.916797i	$0.369234\pi$
$3$		0			0
$3$		0			0
$4$	−0.235737	+	1.33693i	−0.117868	+	0.668465i
$5$	2.58401	−	0.940501i	1.15560	−	0.420605i	0.308078	−	0.951361i	$-0.400314\pi$
$5$	2.58401	−	0.940501i	1.15560	−	0.420605i	0.847524	+	0.530756i	$0.178092\pi$
$6$		0			0
$7$	0.412733	+	2.34072i	0.155998	+	0.884711i	0.957867	+	0.287211i	$0.0927280\pi$
$7$	0.412733	+	2.34072i	0.155998	+	0.884711i	−0.801869	+	0.597500i	$0.796161\pi$
$8$	−1.34559	−	2.33062i	−0.475736	−	0.823999i
$9$		0			0
$10$	−1.10204	+	1.90878i	−0.348494	+	0.603610i
$11$	0.235072	+	0.0855594i	0.0708770	+	0.0257971i	0.377215	−	0.926126i	$-0.376882\pi$
$11$	0.235072	+	0.0855594i	0.0708770	+	0.0257971i	−0.306338	+	0.951923i	$0.599104\pi$
$12$		0			0
$13$	2.00090	+	1.67895i	0.554948	+	0.465657i	0.876613	−	0.481197i	$-0.159798\pi$
$13$	2.00090	+	1.67895i	0.554948	+	0.465657i	−0.321664	+	0.946854i	$0.604242\pi$
$14$	−1.45939	−	1.22457i	−0.390038	−	0.327281i
$15$		0			0
$16$	−0.524408	−	0.190869i	−0.131102	−	0.0477173i
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	−0.847689	−	0.530494i	$-0.822006\pi$
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	0.883266	+	0.468873i	$0.155340\pi$
$18$		0			0
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	0.980370	−	0.197168i	$-0.0631745\pi$
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	−0.660937	+	0.750441i	$0.729841\pi$
$20$	0.648239	+	3.67635i	0.144951	+	0.822056i
$21$		0			0
$22$	−0.188417	+	0.0685781i	−0.0401706	+	0.0146209i
$23$	−1.16168	+	6.58821i	−0.242227	+	1.37374i	0.584619	+	0.811308i	$0.301244\pi$
$23$	−1.16168	+	6.58821i	−0.242227	+	1.37374i	−0.826846	+	0.562428i	$0.809867\pi$
$24$		0			0
$25$	1.96232	−	1.64658i	0.392464	−	0.329316i
$26$	−2.09357			−0.410584
$27$		0			0
$28$	−3.22668			−0.609786
$29$	−0.271990	+	0.228226i	−0.0505072	+	0.0423806i	−0.667692	−	0.744438i	$-0.732718\pi$
$29$	−0.271990	+	0.228226i	−0.0505072	+	0.0423806i	0.617185	+	0.786818i	$0.288273\pi$
$30$		0			0
$31$	0.480218	−	2.72345i	0.0862497	−	0.489146i	−0.910830	−	0.412781i	$-0.864557\pi$
$31$	0.480218	−	2.72345i	0.0862497	−	0.489146i	0.997080	−	0.0763652i	$-0.0243315\pi$
$32$	5.47807	−	1.99386i	0.968396	−	0.352467i
$33$		0			0
$34$	0.0408333	+	0.231577i	0.00700285	+	0.0397151i
$35$	3.26796	+	5.66027i	0.552386	+	0.956760i
$36$		0			0
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	−0.421297	−	0.906923i	$-0.638425\pi$
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	0.996067	−	0.0886080i	$-0.0282418\pi$
$38$	−2.09744	−	0.763405i	−0.340250	−	0.123841i
$39$		0			0
$40$	−5.66895	−	4.75682i	−0.896340	−	0.752119i
$41$	−7.44412	−	6.24636i	−1.16258	−	0.975517i	−0.162638	−	0.986686i	$-0.552000\pi$
$41$	−7.44412	−	6.24636i	−1.16258	−	0.975517i	−0.999938	+	0.0111686i	$0.996445\pi$
$42$		0			0
$43$	−0.244984	−	0.0891669i	−0.0373597	−	0.0135978i	0.323273	−	0.946306i	$-0.395217\pi$
$43$	−0.244984	−	0.0891669i	−0.0373597	−	0.0135978i	−0.360632	+	0.932708i	$0.617439\pi$
$44$	−0.169802	+	0.294106i	−0.0255986	+	0.0443381i
$45$		0			0
$46$	−2.68104	−	4.64370i	−0.395298	−	0.684677i
$47$	−1.98403	−	11.2520i	−0.289400	−	1.64127i	−0.689131	−	0.724637i	$-0.742007\pi$
$47$	−1.98403	−	11.2520i	−0.289400	−	1.64127i	0.399731	−	0.916633i	$-0.369104\pi$
$48$		0			0
$49$	1.26921	−	0.461953i	0.181315	−	0.0659933i
$50$	−0.356537	+	2.02202i	−0.0504219	+	0.285957i
$51$		0			0
$52$	−2.71632	+	2.27927i	−0.376686	+	0.316077i
$53$	5.43137			0.746056			0.373028	−	0.927820i	$-0.378320\pi$
$53$	5.43137			0.746056			0.373028	+	0.927820i	$0.378320\pi$
$54$		0			0
$55$	0.687897			0.0927560
$56$	4.89998	−	4.11157i	0.654787	−	0.549431i
$57$		0			0
$58$	0.0494182	−	0.280264i	0.00648892	−	0.0368005i
$59$	−5.61647	+	2.04423i	−0.731203	+	0.266136i	−0.680674	−	0.732587i	$-0.738313\pi$
$59$	−5.61647	+	2.04423i	−0.731203	+	0.266136i	−0.0505288	+	0.998723i	$0.516091\pi$
$60$		0			0
$61$	−2.05717	−	11.6668i	−0.263393	−	1.49378i	−0.773571	−	0.633709i	$-0.781532\pi$
$61$	−2.05717	−	11.6668i	−0.263393	−	1.49378i	0.510178	−	0.860069i	$-0.329580\pi$
$62$	1.10830	+	1.91963i	0.140754	+	0.243793i
$63$		0			0
$64$	−1.77824	+	3.08001i	−0.222281	+	0.385001i
$65$	6.74938	+	2.45657i	0.837157	+	0.304700i
$66$		0			0
$67$	1.38677	+	1.16364i	0.169421	+	0.142161i	0.723556	−	0.690266i	$-0.242506\pi$
$67$	1.38677	+	1.16364i	0.169421	+	0.142161i	−0.554135	+	0.832427i	$0.686951\pi$
$68$	0.305096	+	0.256006i	0.0369984	+	0.0310453i
$69$		0			0
$70$	−4.92278	−	1.79175i	−0.588385	−	0.214154i
$71$	0.185255	−	0.320871i	0.0219857	−	0.0380804i	−0.854823	−	0.518919i	$-0.826334\pi$
$71$	0.185255	−	0.320871i	0.0219857	−	0.0380804i	0.876809	+	0.480839i	$0.159668\pi$
$72$		0			0
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	0.680621	−	0.732636i	$-0.261710\pi$
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	−0.974792	+	0.223117i	$0.928377\pi$
$74$	0.973225	+	5.51943i	0.113135	+	0.641621i
$75$		0			0
$76$	−3.55246	+	1.29299i	−0.407495	+	0.148316i
$77$	−0.103249	+	0.585553i	−0.0117663	+	0.0667299i
$78$		0			0
$79$	0.614997	−	0.516044i	0.0691926	−	0.0580595i	−0.607535	−	0.794293i	$-0.707842\pi$
$79$	0.614997	−	0.516044i	0.0691926	−	0.0580595i	0.676728	+	0.736233i	$0.263397\pi$
$80$	−1.53459			−0.171572
$81$		0			0
$82$	7.78892			0.860143
$83$	−2.11095	+	1.77130i	−0.231707	+	0.194425i	−0.751248	−	0.660021i	$-0.770548\pi$
$83$	−2.11095	+	1.77130i	−0.231707	+	0.194425i	0.519541	+	0.854446i	$0.326103\pi$
$84$		0			0
$85$	0.140089	−	0.794483i	0.0151948	−	0.0861738i
$86$	0.196361	−	0.0714696i	0.0211742	−	0.00770677i
$87$		0			0
$88$	−0.116903	−	0.662992i	−0.0124619	−	0.0706752i
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	−0.997989	−	0.0633809i	$-0.979812\pi$
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	0.444105	−	0.895975i	$-0.353522\pi$
$90$		0			0
$91$	−3.10412	+	5.37650i	−0.325401	+	0.563611i
$92$	−8.53412	−	3.10617i	−0.889744	−	0.323840i
$93$		0			0
$94$	7.01535	+	5.88658i	0.723578	+	0.607154i
$95$	5.86607	+	4.92221i	0.601846	+	0.505009i
$96$		0			0
$97$	13.9400	+	5.07373i	1.41539	+	0.515160i	0.932707	−	0.360636i	$-0.117440\pi$
$97$	13.9400	+	5.07373i	1.41539	+	0.515160i	0.482683	+	0.875795i	$0.339662\pi$
$98$	−0.541296	+	0.937552i	−0.0546791	+	0.0947070i
$99$		0			0
$100$	1.73877	+	3.01164i	0.173877	+	0.301164i
$101$	0.695518	+	3.94448i	0.0692066	+	0.392490i	0.999660	+	0.0260796i	$0.00830233\pi$
$101$	0.695518	+	3.94448i	0.0692066	+	0.392490i	−0.930453	+	0.366411i	$0.880587\pi$
$102$		0			0
$103$	5.56238	−	2.02454i	0.548078	−	0.199484i	−0.0531146	−	0.998588i	$-0.516915\pi$
$103$	5.56238	−	2.02454i	0.548078	−	0.199484i	0.601192	+	0.799105i	$0.294693\pi$
$104$	1.22062	−	6.92250i	0.119692	−	0.678807i
$105$		0			0
$106$	−3.33489	+	2.79830i	−0.323913	+	0.271795i
$107$	−0.258978			−0.0250364			−0.0125182	−	0.999922i	$-0.503985\pi$
$107$	−0.258978			−0.0250364			−0.0125182	+	0.999922i	$0.503985\pi$
$108$		0			0
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$	−0.422372	+	0.354413i	−0.0402716	+	0.0337919i
$111$		0			0
$112$	0.230331	−	1.30627i	0.0217643	−	0.123431i
$113$	2.93107	−	1.06682i	0.275732	−	0.100358i	−0.200453	−	0.979703i	$-0.564241\pi$
$113$	2.93107	−	1.06682i	0.275732	−	0.100358i	0.476185	+	0.879345i	$0.342019\pi$
$114$		0			0
$115$	3.19443	+	18.1165i	0.297882	+	1.68937i
$116$	−0.241005	−	0.417432i	−0.0223767	−	0.0387576i
$117$		0			0
$118$	2.39533	−	4.14884i	0.220508	−	0.381932i
$119$	0.655255	+	0.238493i	0.0600671	+	0.0218627i
$120$		0			0
$121$	−8.37855	−	7.03044i	−0.761686	−	0.639131i
$122$	7.27397	+	6.10359i	0.658555	+	0.552593i
$123$		0			0
$124$	3.52786	+	1.28404i	0.316811	+	0.115310i
$125$	−3.35257	+	5.80682i	−0.299863	+	0.519378i
$126$		0			0
$127$	9.22726	+	15.9821i	0.818787	+	1.41818i	0.906576	+	0.422042i	$0.138686\pi$
$127$	9.22726	+	15.9821i	0.818787	+	1.41818i	−0.0877893	+	0.996139i	$0.527980\pi$
$128$	1.52961	+	8.67484i	0.135200	+	0.766755i
$129$		0			0
$130$	−5.40981	+	1.96901i	−0.474472	+	0.172694i
$131$	2.47023	−	14.0094i	0.215825	−	1.22400i	−0.663645	−	0.748048i	$-0.730991\pi$
$131$	2.47023	−	14.0094i	0.215825	−	1.22400i	0.879470	−	0.475955i	$-0.157898\pi$
$132$		0			0
$133$	−5.07035	+	4.25453i	−0.439655	+	0.368915i
$134$	−1.45101			−0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	−15.0800	+	12.6536i	−1.28837	+	1.08107i	−0.296343	+	0.955082i	$0.595767\pi$
$137$	−15.0800	+	12.6536i	−1.28837	+	1.08107i	−0.992031	+	0.125993i	$0.959788\pi$
$138$		0			0
$139$	−3.11021	+	17.6388i	−0.263804	+	1.49611i	0.508615	+	0.860994i	$0.330158\pi$
$139$	−3.11021	+	17.6388i	−0.263804	+	1.49611i	−0.772419	+	0.635113i	$0.780953\pi$
$140$	−8.33776	+	3.03470i	−0.704670	+	0.256479i
$141$		0			0
$142$	0.0515689	+	0.292462i	0.00432757	+	0.0245429i
$143$	0.326705	+	0.565870i	0.0273205	+	0.0473205i
$144$		0			0
$145$	−0.488175	+	0.845544i	−0.0405408	+	0.0702186i
$146$	3.78612	+	1.37804i	0.313342	+	0.114047i
$147$		0			0
$148$	7.27171	+	6.10169i	0.597730	+	0.501555i
$149$	12.4784	+	10.4707i	1.02227	+	0.857790i	0.989912	−	0.141686i	$-0.0452524\pi$
$149$	12.4784	+	10.4707i	1.02227	+	0.857790i	0.0323628	+	0.999476i	$0.489697\pi$
$150$		0			0
$151$	−13.4140	−	4.88229i	−1.09161	−	0.397315i	−0.267396	−	0.963587i	$-0.586163\pi$
$151$	−13.4140	−	4.88229i	−1.09161	−	0.397315i	−0.824219	+	0.566271i	$0.808385\pi$
$152$	3.74711	−	6.49019i	0.303931	−	0.526424i
$153$		0			0
$154$	−0.238288	−	0.412728i	−0.0192018	−	0.0332585i
$155$	−1.32052	−	7.48906i	−0.106067	−	0.601536i
$156$		0			0
$157$	−0.717319	+	0.261083i	−0.0572483	+	0.0208367i	−0.370486	−	0.928838i	$-0.620809\pi$
$157$	−0.717319	+	0.261083i	−0.0572483	+	0.0208367i	0.313237	+	0.949675i	$0.398586\pi$
$158$	−0.111740	+	0.633707i	−0.00888953	+	0.0504150i
$159$		0			0
$160$	12.2801	−	10.3043i	0.970831	−	0.814624i
$161$	−15.9006			−1.25315
$162$		0			0
$163$	5.12834			0.401682			0.200841	−	0.979624i	$-0.435632\pi$
$163$	5.12834			0.401682			0.200841	+	0.979624i	$0.435632\pi$
$164$	10.1058	−	8.47977i	0.789130	−	0.662159i
$165$		0			0
$166$	0.383542	−	2.17517i	0.0297686	−	0.168826i
$167$	−8.36432	+	3.04436i	−0.647251	+	0.235580i	−0.644722	−	0.764417i	$-0.723027\pi$
$167$	−8.36432	+	3.04436i	−0.647251	+	0.235580i	−0.00252824	+	0.999997i	$0.500805\pi$
$168$		0			0
$169$	−1.07272	−	6.08369i	−0.0825169	−	0.467976i
$170$	0.323312	+	0.559992i	0.0247969	+	0.0429495i
$171$		0			0
$172$	0.176962	−	0.306507i	0.0134932	−	0.0233709i
$173$	6.40047	+	2.32958i	0.486619	+	0.177115i	0.573666	−	0.819089i	$-0.305521\pi$
$173$	6.40047	+	2.32958i	0.486619	+	0.177115i	−0.0870471	+	0.996204i	$0.527743\pi$
$174$		0			0
$175$	4.66411	+	3.91365i	0.352573	+	0.295844i
$176$	−0.106943	−	0.0897361i	−0.00806115	−	0.00676411i
$177$		0			0
$178$	7.87133	+	2.86493i	0.589981	+	0.214735i
$179$	9.17382	−	15.8895i	0.685684	−	1.18764i	−0.287538	−	0.957769i	$-0.592837\pi$
$179$	9.17382	−	15.8895i	0.685684	−	1.18764i	0.973221	−	0.229870i	$-0.0738301\pi$
$180$		0			0
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	0.575115	−	0.818073i	$-0.304957\pi$
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	−0.996029	+	0.0890276i	$0.971624\pi$
$182$	−0.864087	−	4.90048i	−0.0640504	−	0.363248i
$183$		0			0
$184$	16.9178	−	6.15756i	1.24719	−	0.453941i
$185$	3.33890	−	18.9358i	0.245480	−	1.39219i
$186$		0			0
$187$	0.0562206	−	0.0471747i	0.00411126	−	0.00344976i
$188$	15.5108			1.13124
$189$		0			0
$190$	−6.13778			−0.445281
$191$	5.25385	−	4.40850i	0.380155	−	0.318988i	−0.432608	−	0.901582i	$-0.642407\pi$
$191$	5.25385	−	4.40850i	0.380155	−	0.318988i	0.812763	+	0.582594i	$0.197962\pi$
$192$		0			0
$193$	3.54465	−	20.1027i	0.255149	−	1.44702i	−0.540540	−	0.841318i	$-0.681780\pi$
$193$	3.54465	−	20.1027i	0.255149	−	1.44702i	0.795690	−	0.605705i	$-0.207109\pi$
$194$	−11.1733	+	4.06673i	−0.802193	+	0.291975i
$195$		0			0
$196$	0.318401	+	1.80574i	0.0227429	+	0.128981i
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	0.806875	−	0.590723i	$-0.201157\pi$
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	−0.915018	+	0.403413i	$0.867824\pi$
$198$		0			0
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	−0.823141	−	0.567837i	$-0.807780\pi$
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	0.903332	+	0.428942i	$0.141114\pi$
$200$	−6.47803	−	2.35781i	−0.458066	−	0.166722i
$201$		0			0
$202$	−2.45929	−	2.06359i	−0.173035	−	0.145194i
$203$	−0.646474	−	0.542456i	−0.0453736	−	0.0380729i
$204$		0			0
$205$	−25.1103	−	9.13942i	−1.75378	−	0.638325i
$206$	−2.37226	+	4.10888i	−0.165283	+	0.286279i
$207$		0			0
$208$	−0.728826	−	1.26236i	−0.0505350	−	0.0875292i
$209$	0.120968	+	0.686045i	0.00836755	+	0.0474547i
$210$		0			0
$211$	−23.8971	+	8.69785i	−1.64515	+	0.598785i	−0.987928	−	0.154915i	$-0.950490\pi$
$211$	−23.8971	+	8.69785i	−1.64515	+	0.598785i	−0.657219	+	0.753700i	$0.728267\pi$
$212$	−1.28037	+	7.26136i	−0.0879364	+	0.498712i
$213$		0			0
$214$	0.159014	−	0.133429i	0.0108700	−	0.00912100i
$215$	−0.716901			−0.0488923
$216$		0			0
$217$	6.57305			0.446208
$218$	5.25458	−	4.40911i	0.355885	−	0.298623i
$219$		0			0
$220$	−0.162163	+	0.919670i	−0.0109330	+	0.0620042i
$221$	0.720082	−	0.262088i	0.0484380	−	0.0176300i
$222$		0			0
$223$	−0.665305	−	3.77313i	−0.0445521	−	0.252668i	0.954395	−	0.298547i	$-0.0965020\pi$
$223$	−0.665305	−	3.77313i	−0.0445521	−	0.252668i	−0.998947	+	0.0458797i	$0.985391\pi$
$224$	6.92805	+	11.9997i	0.462900	+	0.801766i
$225$		0			0
$226$	−1.25005	+	2.16515i	−0.0831523	+	0.144024i
$227$	−2.36426	−	0.860520i	−0.156921	−	0.0571147i	0.262365	−	0.964969i	$-0.415498\pi$
$227$	−2.36426	−	0.860520i	−0.156921	−	0.0571147i	−0.419287	+	0.907854i	$0.637720\pi$
$228$		0			0
$229$	−12.2105	−	10.2458i	−0.806890	−	0.677061i	0.142974	−	0.989727i	$-0.454334\pi$
$229$	−12.2105	−	10.2458i	−0.806890	−	0.677061i	−0.949863	+	0.312666i	$0.898778\pi$
$230$	−11.2952	−	9.47783i	−0.744786	−	0.624950i
$231$		0			0
$232$	0.897894	+	0.326807i	0.0589496	+	0.0214559i
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.124077	+	0.992273i	$0.539597\pi$
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.797295	+	0.603590i	$0.793736\pi$
$234$		0			0
$235$	−15.7092	−	27.2092i	−1.02476	−	1.77493i
$236$	−1.40898	−	7.99073i	−0.0917169	−	0.520153i
$237$		0			0
$238$	−0.525205	+	0.191159i	−0.0340440	+	0.0123910i
$239$	−2.55363	+	14.4824i	−0.165181	+	0.936787i	0.783697	+	0.621143i	$0.213332\pi$
$239$	−2.55363	+	14.4824i	−0.165181	+	0.936787i	−0.948878	+	0.315644i	$0.897780\pi$
$240$		0			0
$241$	6.46767	−	5.42702i	0.416619	−	0.349585i	−0.410256	−	0.911970i	$-0.634561\pi$
$241$	6.46767	−	5.42702i	0.416619	−	0.349585i	0.826875	+	0.562385i	$0.190116\pi$
$242$	8.76664			0.563541
$243$		0			0
$244$	16.0826			1.02958
$245$	2.84517	−	2.38738i	0.181771	−	0.152524i
$246$		0			0
$247$	−1.26307	+	7.16320i	−0.0803670	+	0.455784i
$248$	−6.99351	+	2.54543i	−0.444088	+	0.161635i
$249$		0			0
$250$	−0.933246	−	5.29270i	−0.0590237	−	0.334740i
$251$	11.6102	+	20.1095i	0.732832	+	1.26930i	0.955668	+	0.294447i	$0.0951354\pi$
$251$	11.6102	+	20.1095i	0.732832	+	1.26930i	−0.222835	+	0.974856i	$0.571531\pi$
$252$		0			0
$253$	−0.836762	+	1.44931i	−0.0526067	+	0.0911176i
$254$	−13.8997	−	5.05909i	−0.872147	−	0.317436i
$255$		0			0
$256$	−10.8574	−	9.11046i	−0.678589	−	0.569404i
$257$	5.25905	+	4.41286i	0.328050	+	0.275267i	0.791905	−	0.610644i	$-0.209090\pi$
$257$	5.25905	+	4.41286i	0.328050	+	0.275267i	−0.463855	+	0.885911i	$0.653534\pi$
$258$		0			0
$259$	15.6174	+	5.68428i	0.970420	+	0.353204i
$260$	−4.87534	+	8.44434i	−0.302356	+	0.523696i
$261$		0			0
$262$	5.70105	+	9.87451i	0.352212	+	0.610049i
$263$	0.582232	+	3.30200i	0.0359019	+	0.203610i	0.997483	−	0.0709128i	$-0.0225912\pi$
$263$	0.582232	+	3.30200i	0.0359019	+	0.203610i	−0.961581	+	0.274523i	$0.911480\pi$
$264$		0			0
$265$	14.0347	−	5.10821i	0.862144	−	0.313795i
$266$	0.921240	−	5.22461i	0.0564848	−	0.320341i
$267$		0			0
$268$	−1.88262	+	1.57970i	−0.114999	+	0.0964958i
$269$	12.7416			0.776869			0.388434	−	0.921476i	$-0.373016\pi$
$269$	12.7416			0.776869			0.388434	+	0.921476i	$0.373016\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	−0.125419	+	0.105239i	−0.00760465	+	0.00638106i
$273$		0			0
$274$	2.73991	−	15.5388i	0.165524	−	0.938734i
$275$	0.602168	−	0.219171i	0.0363121	−	0.0132165i
$276$		0			0
$277$	0.726061	+	4.11770i	0.0436248	+	0.247408i	0.998820	−	0.0485686i	$-0.0154660\pi$
$277$	0.726061	+	4.11770i	0.0436248	+	0.247408i	−0.955195	+	0.295977i	$0.904355\pi$
$278$	−7.17806	−	12.4328i	−0.430511	−	0.745667i
$279$		0			0
$280$	8.79463	−	15.2327i	0.525580	−	0.910331i
$281$	20.3312	+	7.39995i	1.21286	+	0.441444i	0.867694	−	0.497098i	$-0.165601\pi$
$281$	20.3312	+	7.39995i	1.21286	+	0.441444i	0.345164	+	0.938542i	$0.387823\pi$
$282$		0			0
$283$	4.00437	+	3.36007i	0.238035	+	0.199735i	0.754000	−	0.656875i	$-0.228122\pi$
$283$	4.00437	+	3.36007i	0.238035	+	0.199735i	−0.515965	+	0.856610i	$0.672566\pi$
$284$	0.385311	+	0.323314i	0.0228640	+	0.0191852i
$285$		0			0
$286$	−0.492142	−	0.179125i	−0.0291010	−	0.0105919i
$287$	11.5486	−	20.0027i	0.681690	−	1.18072i
$288$		0			0
$289$	8.45697	+	14.6479i	0.497469	+	0.861641i
$290$	−0.135892	−	0.770682i	−0.00797986	−	0.0452560i
$291$		0			0
$292$	6.41259	−	2.33399i	0.375269	−	0.136587i
$293$	−1.06658	+	6.04885i	−0.0623100	+	0.353378i	0.937673	+	0.347519i	$0.112976\pi$
$293$	−1.06658	+	6.04885i	−0.0623100	+	0.353378i	−0.999983	+	0.00585836i	$0.998135\pi$
$294$		0			0
$295$	−12.5904	+	10.5646i	−0.733041	+	0.615095i
$296$	−18.8177			−1.09376
$297$		0			0
$298$	−13.0564			−0.756339
$299$	−13.3857	+	11.2319i	−0.774113	+	0.649558i
$300$		0			0
$301$	0.107602	−	0.610242i	0.00620208	−	0.0351738i
$302$	10.7517	−	3.91329i	0.618689	−	0.225184i
$303$		0			0
$304$	−0.269861	−	1.53046i	−0.0154776	−	0.0877776i
$305$	−16.2884	−	28.2123i	−0.932669	−	1.61543i
$306$		0			0
$307$	−9.50194	+	16.4578i	−0.542304	+	0.939298i	0.456467	+	0.889740i	$0.349115\pi$
$307$	−9.50194	+	16.4578i	−0.542304	+	0.939298i	−0.998771	+	0.0495580i	$0.984219\pi$
$308$	−0.758504	−	0.276073i	−0.0432198	−	0.0157307i
$309$		0			0
$310$	4.66926	+	3.91797i	0.265196	+	0.222526i
$311$	−16.5059	−	13.8501i	−0.935963	−	0.785366i	0.0409150	−	0.999163i	$-0.486973\pi$
$311$	−16.5059	−	13.8501i	−0.935963	−	0.785366i	−0.976878	+	0.213796i	$0.931417\pi$
$312$		0			0
$313$	3.58363	+	1.30433i	0.202559	+	0.0737253i	0.441307	−	0.897356i	$-0.354515\pi$
$313$	3.58363	+	1.30433i	0.202559	+	0.0737253i	−0.238749	+	0.971081i	$0.576737\pi$
$314$	0.305925	−	0.529877i	0.0172643	−	0.0299027i
$315$		0			0
$316$	0.544937	+	0.943859i	0.0306551	+	0.0530962i
$317$	0.738784	+	4.18985i	0.0414942	+	0.235325i	0.998501	−	0.0547416i	$-0.0174335\pi$
$317$	0.738784	+	4.18985i	0.0414942	+	0.235325i	−0.957006	+	0.290067i	$0.906322\pi$
$318$		0			0
$319$	−0.0834641	+	0.0303785i	−0.00467309	+	0.00170087i
$320$	−1.69824	+	9.63120i	−0.0949346	+	0.538401i
$321$		0			0
$322$	9.76308	−	8.19219i	0.544075	−	0.456533i
$323$	0.816980			0.0454580
$324$		0			0
$325$	6.69092			0.371146
$326$	−3.14883	+	2.64218i	−0.174397	+	0.146337i
$327$		0			0
$328$	−4.54120	+	25.7544i	−0.250746	+	1.42205i
$329$	25.5189	−	9.28812i	1.40690	−	0.512071i
$330$		0			0
$331$	−2.48209	−	14.0766i	−0.136428	−	0.773722i	−0.973855	−	0.227172i	$-0.927052\pi$
$331$	−2.48209	−	14.0766i	−0.136428	−	0.773722i	0.837427	−	0.546550i	$-0.184059\pi$
$332$	−1.87047	−	3.23976i	−0.102656	−	0.177805i
$333$		0			0
$334$	3.56725	−	6.17865i	0.195191	−	0.338081i
$335$	4.67783	+	1.70259i	0.255577	+	0.0930225i
$336$		0			0
$337$	27.3620	+	22.9594i	1.49050	+	1.25068i	0.894000	+	0.448066i	$0.147887\pi$
$337$	27.3620	+	22.9594i	1.49050	+	1.25068i	0.596500	+	0.802613i	$0.296557\pi$
$338$	3.79304	+	3.18274i	0.206314	+	0.173118i
$339$		0			0
$340$	1.02914	+	0.374578i	0.0558132	+	0.0203143i
$341$	0.345903	−	0.599121i	0.0187317	−	0.0324442i
$342$		0			0
$343$	9.92407	+	17.1890i	0.535849	+	0.928118i
$344$	0.121833	+	0.690947i	0.00656877	+	0.0372533i
$345$		0			0
$346$	−5.13015	+	1.86722i	−0.275799	+	0.100382i
$347$	−3.37599	+	19.1462i	−0.181232	+	1.02782i	0.749469	+	0.662040i	$0.230309\pi$
$347$	−3.37599	+	19.1462i	−0.181232	+	1.02782i	−0.930701	+	0.365780i	$0.880802\pi$
$348$		0			0
$349$	−6.14422	+	5.15561i	−0.328892	+	0.275973i	−0.792248	−	0.610199i	$-0.791090\pi$
$349$	−6.14422	+	5.15561i	−0.328892	+	0.275973i	0.463356	+	0.886172i	$0.346645\pi$
$350$	−4.88014			−0.260855
$351$		0			0
$352$	1.45834			0.0777296
$353$	6.70581	−	5.62684i	0.356914	−	0.299487i	−0.446645	−	0.894711i	$-0.647381\pi$
$353$	6.70581	−	5.62684i	0.356914	−	0.299487i	0.803559	+	0.595225i	$0.202937\pi$
$354$		0			0
$355$	0.176920	−	1.00336i	0.00938995	−	0.0532531i
$356$	13.3317	−	4.85236i	0.706581	−	0.257175i
$357$		0			0
$358$	2.55369	+	14.4827i	0.134967	+	0.765435i
$359$	4.13896	+	7.16888i	0.218446	+	0.378359i	0.954333	−	0.298745i	$-0.0965680\pi$
$359$	4.13896	+	7.16888i	0.218446	+	0.378359i	−0.735887	+	0.677104i	$0.763235\pi$
$360$		0			0
$361$	5.62260	−	9.73862i	0.295926	−	0.512559i
$362$	8.53035	+	3.10479i	0.448345	+	0.163184i
$363$		0			0
$364$	−6.45625	−	5.41744i	−0.338400	−	0.283951i
$365$	−10.5889	−	8.88517i	−0.554250	−	0.465071i
$366$		0			0
$367$	13.9073	+	5.06185i	0.725956	+	0.264226i	0.678452	−	0.734645i	$-0.262651\pi$
$367$	13.9073	+	5.06185i	0.725956	+	0.264226i	0.0475039	+	0.998871i	$0.484873\pi$
$368$	1.86668	−	3.23318i	0.0973074	−	0.168541i
$369$		0			0
$370$	7.70585	+	13.3469i	0.400608	+	0.693874i
$371$	2.24170	+	12.7133i	0.116383	+	0.660044i
$372$		0			0
$373$	−23.9935	+	8.73294i	−1.24234	+	0.452174i	−0.877806	−	0.479016i	$-0.840993\pi$
$373$	−23.9935	+	8.73294i	−1.24234	+	0.452174i	−0.364533	+	0.931191i	$0.618771\pi$
$374$	−0.0102148	+	0.0579310i	−0.000528195	+	0.00299554i
$375$		0			0
$376$	−23.5544	+	19.7645i	−1.21473	+	1.01928i
$377$	−0.927403			−0.0477637
$378$		0			0
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$	−7.96351	+	6.68218i	−0.408519	+	0.342788i
$381$		0			0
$382$	−0.954579	+	5.41369i	−0.0488405	+	0.276988i
$383$	22.4222	−	8.16103i	1.14572	−	0.417009i	0.301746	−	0.953388i	$-0.402431\pi$
$383$	22.4222	−	8.16103i	1.14572	−	0.417009i	0.843977	+	0.536379i	$0.180208\pi$
$384$		0			0
$385$	0.283918	+	1.61018i	0.0144698	+	0.0820622i
$386$	8.18070	+	14.1694i	0.416387	+	0.721203i
$387$		0			0
$388$	−10.0694	+	17.4407i	−0.511196	+	0.885418i
$389$	−35.6832	−	12.9876i	−1.80921	−	0.658499i	−0.997193	−	0.0748675i	$-0.976147\pi$
$389$	−35.6832	−	12.9876i	−1.80921	−	0.658499i	−0.812018	−	0.583632i	$-0.801631\pi$
$390$		0			0
$391$	1.50347	+	1.26156i	0.0760339	+	0.0638000i
$392$	−2.78446	−	2.33644i	−0.140637	−	0.118008i
$393$		0			0
$394$	2.28648	+	0.832210i	0.115191	+	0.0419261i
$395$	1.10382	−	1.91187i	0.0555390	−	0.0961964i
$396$		0			0
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	−0.999924	−	0.0123433i	$-0.996071\pi$
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	0.489272	−	0.872131i	$-0.337262\pi$
$398$	0.314899	+	1.78588i	0.0157845	+	0.0895182i
$399$		0			0
$400$	−1.34334	+	0.488935i	−0.0671669	+	0.0244468i
$401$	1.20598	−	6.83946i	0.0602238	−	0.341546i	−0.939776	−	0.341791i	$-0.888967\pi$
$401$	1.20598	−	6.83946i	0.0602238	−	0.341546i	1.00000		0.000244329i	$7.77724e-5\pi$
$402$		0			0
$403$	5.53341	−	4.64308i	0.275639	−	0.231288i
$404$	−5.43745			−0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	1.33997	−	1.12437i	0.0664198	−	0.0557328i
$408$		0			0
$409$	−1.89380	+	10.7403i	−0.0936423	+	0.531072i	0.901513	+	0.432753i	$0.142458\pi$
$409$	−1.89380	+	10.7403i	−0.0936423	+	0.531072i	−0.995155	+	0.0983191i	$0.968653\pi$
$410$	20.1266	−	7.32549i	0.993983	−	0.361780i
$411$		0			0
$412$	1.39541	+	7.91377i	0.0687470	+	0.389884i
$413$	−7.10308	−	12.3029i	−0.349520	−	0.605386i
$414$		0			0
$415$	−3.78880	+	6.56240i	−0.185985	+	0.322135i
$416$	14.3086	+	5.20792i	0.701539	+	0.255339i
$417$		0			0
$418$	−0.427734	−	0.358911i	−0.0209211	−	0.0175549i
$419$	−7.71344	−	6.47235i	−0.376826	−	0.316195i	0.434629	−	0.900610i	$-0.356880\pi$
$419$	−7.71344	−	6.47235i	−0.376826	−	0.316195i	−0.811455	+	0.584415i	$0.801324\pi$
$420$		0			0
$421$	2.92016	+	1.06285i	0.142320	+	0.0518001i	0.412198	−	0.911094i	$-0.364761\pi$
$421$	2.92016	+	1.06285i	0.142320	+	0.0518001i	−0.269878	+	0.962894i	$0.586983\pi$
$422$	10.1917	−	17.6526i	0.496126	−	0.859315i
$423$		0			0
$424$	−7.30837	−	12.6585i	−0.354926	−	0.614750i
$425$	−0.130500	−	0.740104i	−0.00633020	−	0.0359003i
$426$		0			0
$427$	26.4597	−	9.63053i	1.28047	−	0.466054i
$428$	0.0610508	−	0.346236i	0.00295100	−	0.0167360i
$429$		0			0
$430$	0.440181	−	0.369356i	0.0212274	−	0.0178119i
$431$	−28.0701			−1.35209			−0.676044	−	0.736862i	$-0.736307\pi$
$431$	−28.0701			−1.35209			−0.676044	+	0.736862i	$0.736307\pi$
$432$		0			0
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$	−4.03589	+	3.38651i	−0.193729	+	0.162558i
$435$		0			0
$436$	2.01741	−	11.4413i	0.0966162	−	0.547938i
$437$	−17.5060	+	6.37167i	−0.837426	+	0.304798i
$438$		0			0
$439$	2.54040	+	14.4073i	0.121247	+	0.687624i	0.983467	+	0.181090i	$0.0579625\pi$
$439$	2.54040	+	14.4073i	0.121247	+	0.687624i	−0.862220	+	0.506534i	$0.830926\pi$
$440$	−0.925624	−	1.60323i	−0.0441274	−	0.0764309i
$441$		0			0
$442$	−0.307103	+	0.531918i	−0.0146074	+	0.0253008i
$443$	−17.2489	−	6.27810i	−0.819522	−	0.298282i	−0.101971	−	0.994787i	$-0.532515\pi$
$443$	−17.2489	−	6.27810i	−0.819522	−	0.298282i	−0.717551	+	0.696506i	$0.754737\pi$
$444$		0			0
$445$	−22.0143	−	18.4722i	−1.04358	−	0.875667i
$446$	2.35246	+	1.97395i	0.111392	+	0.0934692i
$447$		0			0
$448$	−7.94339	−	2.89116i	−0.375290	−	0.136594i
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	−0.981922	−	0.189288i	$-0.939382\pi$
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	0.654889	+	0.755725i	$0.272715\pi$
$450$		0			0
$451$	−1.21547	−	2.10526i	−0.0572344	−	0.0991328i
$452$	0.735305	+	4.17012i	0.0345859	+	0.196146i
$453$		0			0
$454$	1.89502	−	0.689730i	0.0889375	−	0.0323706i
$455$	−2.96447	+	16.8123i	−0.138976	+	0.788175i
$456$		0			0
$457$	13.5193	−	11.3440i	0.632404	−	0.530650i	−0.269271	−	0.963064i	$-0.586783\pi$
$457$	13.5193	−	11.3440i	0.632404	−	0.530650i	0.901675	+	0.432415i	$0.142338\pi$
$458$	12.7760			0.596985
$459$		0			0
$460$	−24.9736			−1.16440
$461$	19.6399	−	16.4798i	0.914720	−	0.767541i	−0.0582911	−	0.998300i	$-0.518565\pi$
$461$	19.6399	−	16.4798i	0.914720	−	0.767541i	0.973011	+	0.230758i	$0.0741207\pi$
$462$		0			0
$463$	3.18600	−	18.0687i	0.148066	−	0.839723i	−0.816788	−	0.576937i	$-0.804248\pi$
$463$	3.18600	−	18.0687i	0.148066	−	0.839723i	0.964854	−	0.262786i	$-0.0846412\pi$
$464$	0.186195	−	0.0677694i	0.00864388	−	0.00314612i
$465$		0			0
$466$	−3.91500	−	22.2030i	−0.181359	−	1.02854i
$467$	8.13092	+	14.0832i	0.376254	+	0.651692i	0.990514	−	0.137412i	$-0.0438786\pi$
$467$	8.13092	+	14.0832i	0.376254	+	0.651692i	−0.614260	+	0.789104i	$0.710545\pi$
$468$		0			0
$469$	−2.15139	+	3.72632i	−0.0993421	+	0.172066i
$470$	23.6640	+	8.61301i	1.09154	+	0.397288i
$471$		0			0
$472$	12.3218	+	10.3392i	0.567155	+	0.475900i
$473$	−0.0499599	−	0.0419213i	−0.00229716	−	0.00192755i
$474$		0			0
$475$	6.70328	+	2.43979i	0.307567	+	0.111945i
$476$	−0.473317	+	0.819809i	−0.0216944	+	0.0375759i
$477$		0			0
$478$	−5.89354	−	10.2079i	−0.269564	−	0.466899i
$479$	−1.64475	−	9.32781i	−0.0751503	−	0.426199i	−0.999051	−	0.0435653i	$-0.986128\pi$
$479$	−1.64475	−	9.32781i	−0.0751503	−	0.426199i	0.923900	−	0.382633i	$-0.124983\pi$
$480$		0			0
$481$	17.1625	−	6.24665i	0.782544	−	0.284823i
$482$	−1.17512	+	6.66444i	−0.0535253	+	0.303557i
$483$		0			0
$484$	11.3743	−	9.54420i	0.517015	−	0.433827i
$485$	40.7928			1.85231
$486$		0			0
$487$	−0.467564			−0.0211874			−0.0105937	−	0.999944i	$-0.503372\pi$
$487$	−0.467564			−0.0211874			−0.0105937	+	0.999944i	$0.503372\pi$
$488$	−24.4228	+	20.4931i	−1.10557	+	0.927680i
$489$		0			0
$490$	−0.516943	+	2.93173i	−0.0233531	+	0.132442i
$491$	−23.5365	+	8.56657i	−1.06219	+	0.386604i	−0.813249	−	0.581916i	$-0.802303\pi$
$491$	−23.5365	+	8.56657i	−1.06219	+	0.386604i	−0.248937	+	0.968520i	$0.580081\pi$
$492$		0			0
$493$	0.0180882	+	0.102583i	0.000814649	+	0.00462011i
$494$	−2.91504	−	5.04899i	−0.131154	−	0.227165i
$495$		0			0
$496$	−0.771653	+	1.33654i	−0.0346482	+	0.0600125i
$497$	0.827531	+	0.301197i	0.0371198	+	0.0135105i
$498$		0			0
$499$	−10.7508	−	9.02098i	−0.481271	−	0.403835i	0.369615	−	0.929185i	$-0.379490\pi$
$499$	−10.7508	−	9.02098i	−0.481271	−	0.403835i	−0.850886	+	0.525351i	$0.823934\pi$
$500$	−6.97299	−	5.85103i	−0.311842	−	0.261666i
$501$		0			0
$502$	−17.4894	−	6.36563i	−0.780591	−	0.284112i
$503$	−14.1558	+	24.5186i	−0.631176	+	1.09323i	0.356136	+	0.934434i	$0.384094\pi$
$503$	−14.1558	+	24.5186i	−0.631176	+	1.09323i	−0.987312	+	0.158794i	$0.949239\pi$
$504$		0			0
$505$	5.50701	+	9.53842i	0.245059	+	0.424454i
$506$	−0.232927	−	1.32100i	−0.0103549	−	0.0587254i
$507$		0			0
$508$	−23.5421	+	8.56864i	−1.04451	+	0.380172i
$509$	−4.98152	+	28.2516i	−0.220802	+	1.25223i	0.649747	+	0.760150i	$0.274875\pi$
$509$	−4.98152	+	28.2516i	−0.220802	+	1.25223i	−0.870549	+	0.492081i	$0.836236\pi$
$510$		0			0
$511$	9.15258	−	7.67992i	0.404886	−	0.339740i
$512$	−6.25700			−0.276523
$513$		0			0
$514$	−5.50264			−0.242711
$515$	12.4691	−	10.4628i	0.549456	−	0.461048i
$516$		0			0
$517$	0.496322	−	2.81478i	0.0218282	−	0.123794i
$518$	−12.5178	+	4.55610i	−0.550000	+	0.200184i
$519$		0			0
$520$	−3.35652	−	19.0358i	−0.147193	−	0.834774i
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	0.998565	+	0.0535462i	$0.0170525\pi$
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	−0.452910	+	0.891556i	$0.649614\pi$
$522$		0			0
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	−0.431510	−	0.902108i	$-0.642019\pi$
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	0.997004	−	0.0773554i	$-0.0246476\pi$
$524$	18.1472	+	6.60504i	0.792765	+	0.288543i
$525$		0			0
$526$	−2.05872	−	1.72747i	−0.0897645	−	0.0753214i
$527$	−0.621510	−	0.521509i	−0.0270734	−	0.0227173i
$528$		0			0
$529$	−20.4421	−	7.44030i	−0.888785	−	0.323491i
$530$	−5.98556	+	10.3673i	−0.259996	+	0.450327i
$531$		0			0
$532$	−4.49274	−	7.78166i	−0.194785	−	0.337378i
$533$	−4.40758	−	24.9966i	−0.190913	−	1.08272i
$534$		0			0
$535$	−0.669202	+	0.243569i	−0.0289321	+	0.0105304i
$536$	0.845985	−	4.79782i	0.0365410	−	0.207234i
$537$		0			0
$538$	−7.82341	+	6.56462i	−0.337291	+	0.283021i
$539$	0.337880			0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	14.4639	−	12.1366i	0.621277	−	0.521313i
$543$		0			0
$544$	0.296987	−	1.68430i	0.0127332	−	0.0722137i
$545$	−22.1136	+	8.04869i	−0.947242	+	0.344768i
$546$		0			0
$547$	−1.73232	−	9.82449i	−0.0740688	−	0.420065i	−0.999184	−	0.0403794i	$-0.987143\pi$
$547$	−1.73232	−	9.82449i	−0.0740688	−	0.420065i	0.925116	−	0.379685i	$-0.123968\pi$
$548$	−13.3621	−	23.1439i	−0.570802	−	0.988658i
$549$		0			0
$550$	−0.256815	+	0.444816i	−0.0109506	+	0.0189670i
$551$	−0.929115	−	0.338170i	−0.0395816	−	0.0144065i
$552$		0			0
$553$	1.46175	+	1.22655i	0.0621598	+	0.0521582i
$554$	−2.56729	−	2.15421i	−0.109074	−	0.0915237i
$555$		0			0
$556$	−22.8487	−	8.31625i	−0.969002	−	0.352688i
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	−0.600162	−	0.799879i	$-0.704897\pi$
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	0.992796	+	0.119816i	$0.0382305\pi$
$558$		0			0
$559$	−0.340480	−	0.589729i	−0.0144008	−	0.0249429i
$560$	−0.633374	−	3.59204i	−0.0267649	−	0.151792i
$561$		0			0
$562$	−16.2960	+	5.93126i	−0.687406	+	0.250195i
$563$	7.58549	−	43.0194i	0.319690	−	1.81305i	−0.224935	−	0.974374i	$-0.572217\pi$
$563$	7.58549	−	43.0194i	0.319690	−	1.81305i	0.544625	−	0.838680i	$-0.316672\pi$
$564$		0			0
$565$	6.57055	−	5.51335i	0.276425	−	0.231948i
$566$	−4.18985			−0.176113
$567$		0			0
$568$	−0.997105			−0.0418376
$569$	10.3927	−	8.72050i	0.435684	−	0.365582i	−0.398407	−	0.917209i	$-0.630437\pi$
$569$	10.3927	−	8.72050i	0.435684	−	0.365582i	0.834091	+	0.551626i	$0.185993\pi$
$570$		0			0
$571$	4.12392	−	23.3879i	0.172581	−	0.978754i	−0.768319	−	0.640068i	$-0.778906\pi$
$571$	4.12392	−	23.3879i	0.172581	−	0.978754i	0.940899	−	0.338686i	$-0.109983\pi$
$572$	−0.833546	+	0.303386i	−0.0348523	+	0.0126852i
$573$		0			0
$574$	3.21474	+	18.2317i	0.134181	+	0.760977i
$575$	8.56844	+	14.8410i	0.357329	+	0.618911i
$576$		0			0
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	−0.769069	−	0.639166i	$-0.779280\pi$
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	0.938068	+	0.346450i	$0.112613\pi$
$578$	−12.7394	−	4.63676i	−0.529889	−	0.192864i
$579$		0			0
$580$	−1.01535	−	0.851982i	−0.0421602	−	0.0353766i
$581$	−5.01738	−	4.21008i	−0.208156	−	0.174664i
$582$		0			0
$583$	1.27677	+	0.464704i	0.0528782	+	0.0192461i
$584$	−6.76397	+	11.7155i	−0.279895	+	0.484793i
$585$		0			0
$586$	−2.46156	−	4.26354i	−0.101686	−	0.176125i
$587$	−0.641108	−	3.63590i	−0.0264614	−	0.150070i	0.968714	−	0.248178i	$-0.0798319\pi$
$587$	−0.641108	−	3.63590i	−0.0264614	−	0.150070i	−0.995176	+	0.0981085i	$0.968721\pi$
$588$		0			0
$589$	7.23668	−	2.63394i	0.298182	−	0.108530i
$590$	2.28757	−	12.9734i	0.0941777	−	0.534108i
$591$		0			0
$592$	−2.98925	+	2.50828i	−0.122858	+	0.103090i
$593$	29.4590			1.20974			0.604869	−	0.796325i	$-0.293226\pi$
$593$	29.4590			1.20974			0.604869	+	0.796325i	$0.293226\pi$
$594$		0			0
$595$	1.91749			0.0786093
$596$	−16.9402	+	14.2145i	−0.693897	+	0.582248i
$597$		0			0
$598$	2.43206	−	13.7929i	0.0994544	−	0.564034i
$599$	20.5561	−	7.48182i	0.839901	−	0.305699i	0.113985	−	0.993482i	$-0.463638\pi$
$599$	20.5561	−	7.48182i	0.839901	−	0.305699i	0.725916	+	0.687783i	$0.241416\pi$
$600$		0			0
$601$	6.34175	+	35.9658i	0.258685	+	1.46708i	0.786433	+	0.617676i	$0.211926\pi$
$601$	6.34175	+	35.9658i	0.258685	+	1.46708i	−0.527748	+	0.849401i	$0.676963\pi$
$602$	0.248335	+	0.430130i	0.0101214	+	0.0175308i
$603$		0			0
$604$	9.68946	−	16.7826i	0.394258	−	0.682876i
$605$	−28.2624	−	10.2867i	−1.14903	−	0.418212i
$606$		0			0
$607$	−5.04120	−	4.23007i	−0.204616	−	0.171693i	0.534721	−	0.845029i	$-0.320417\pi$
$607$	−5.04120	−	4.23007i	−0.204616	−	0.171693i	−0.739337	+	0.673335i	$0.764861\pi$
$608$	12.4360	+	10.4351i	0.504347	+	0.423198i
$609$		0			0
$610$	24.5364	+	8.93053i	0.993451	+	0.361586i
$611$	14.9217	−	25.8451i	0.603667	−	1.04558i
$612$		0			0
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	0.929136	−	0.369737i	$-0.120552\pi$
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	−0.784770	+	0.619787i	$0.787219\pi$
$614$	−2.64503	−	15.0007i	−0.106745	−	0.605379i
$615$		0			0
$616$	1.50363	−	0.547277i	0.0605831	−	0.0220504i
$617$	2.87170	−	16.2862i	0.115610	−	0.655659i	−0.870836	−	0.491574i	$-0.836422\pi$
$617$	2.87170	−	16.2862i	0.115610	−	0.655659i	0.986446	−	0.164085i	$-0.0524672\pi$
$618$		0			0
$619$	−1.14857	+	0.963764i	−0.0461649	+	0.0387369i	−0.665578	−	0.746328i	$-0.731815\pi$
$619$	−1.14857	+	0.963764i	−0.0461649	+	0.0387369i	0.619413	+	0.785065i	$0.287371\pi$
$620$	10.3236			0.414608
$621$		0			0
$622$	17.2704			0.692481
$623$	19.0282	−	15.9665i	0.762347	−	0.639685i
$624$		0			0
$625$	−5.42585	+	30.7715i	−0.217034	+	1.23086i
$626$	−2.87237	+	1.04546i	−0.114803	+	0.0417849i
$627$		0			0
$628$	−0.179951	−	1.02055i	−0.00718082	−	0.0407244i
$629$	−1.02570	−	1.77657i	−0.0408974	−	0.0708363i
$630$		0			0
$631$	17.9456	−	31.0827i	0.714404	−	1.23738i	−0.248785	−	0.968559i	$-0.580031\pi$
$631$	17.9456	−	31.0827i	0.714404	−	1.23738i	0.963189	−	0.268826i	$-0.0866356\pi$
$632$	−2.03023	−	0.738945i	−0.0807584	−	0.0293936i
$633$		0			0
$634$	−2.61228	−	2.19196i	−0.103747	−	0.0870539i
$635$	38.8745	+	32.6195i	1.54269	+	1.29447i
$636$		0			0
$637$	3.31515	+	1.20661i	0.131351	+	0.0478078i
$638$	0.0355961	−	0.0616542i	0.00140926	−	0.00244091i
$639$		0			0
$640$	12.1112	+	20.9772i	0.478738	+	0.829198i
$641$	6.81186	+	38.6320i	0.269052	+	1.52587i	0.757242	+	0.653134i	$0.226546\pi$
$641$	6.81186	+	38.6320i	0.269052	+	1.52587i	−0.488190	+	0.872738i	$0.662343\pi$
$642$		0			0
$643$	9.79019	−	3.56334i	0.386087	−	0.140524i	−0.141682	−	0.989912i	$-0.545251\pi$
$643$	9.79019	−	3.56334i	0.386087	−	0.140524i	0.527769	+	0.849388i	$0.323029\pi$
$644$	3.74837	−	21.2580i	0.147706	−	0.837684i
$645$		0			0
$646$	−0.501630	+	0.420917i	−0.0197364	+	0.0165608i
$647$	−39.1517			−1.53921			−0.769606	−	0.638519i	$-0.779547\pi$
$647$	−39.1517			−1.53921			−0.769606	+	0.638519i	$0.779547\pi$
$648$		0			0
$649$	−1.49518			−0.0586910
$650$	−4.10826	+	3.44724i	−0.161139	+	0.135212i
$651$		0			0
$652$	−1.20894	+	6.85623i	−0.0473457	+	0.268511i
$653$	−30.9252	+	11.2558i	−1.21020	+	0.440475i	−0.866772	−	0.498705i	$-0.833809\pi$
$653$	−30.9252	+	11.2558i	−1.21020	+	0.440475i	−0.343424	+	0.939180i	$0.611587\pi$
$654$		0			0
$655$	−6.79273	−	38.5235i	−0.265414	−	1.50524i
$656$	2.71152	+	4.69649i	0.105867	+	0.183367i
$657$		0			0
$658$	−10.8834	+	18.8506i	−0.424279	+	0.734873i
$659$	20.2677	+	7.37683i	0.789517	+	0.287361i	0.705135	−	0.709073i	$-0.250886\pi$
$659$	20.2677	+	7.37683i	0.789517	+	0.287361i	0.0843816	+	0.996434i	$0.473109\pi$
$660$		0			0
$661$	20.1442	+	16.9030i	0.783518	+	0.657450i	0.944132	−	0.329568i	$-0.106903\pi$
$661$	20.1442	+	16.9030i	0.783518	+	0.657450i	−0.160614	+	0.987017i	$0.551347\pi$
$662$	8.77646	+	7.36433i	0.341107	+	0.286223i
$663$		0			0
$664$	6.96869	+	2.53640i	0.270438	+	0.0984313i
$665$	−9.10043	+	15.7624i	−0.352900	+	0.611240i
$666$		0			0
$667$	−1.18764	−	2.05705i	−0.0459855	−	0.0796493i
$668$	−2.09832	−	11.9002i	−0.0811866	−	0.460432i
$669$		0			0
$670$	−3.74941	+	1.36467i	−0.144852	+	0.0527219i
$671$	0.514619	−	2.91855i	0.0198666	−	0.112669i
$672$		0			0
$673$	8.82645	−	7.40627i	0.340235	−	0.285491i	−0.456620	−	0.889662i	$-0.650940\pi$
$673$	8.82645	−	7.40627i	0.340235	−	0.285491i	0.796855	+	0.604171i	$0.206496\pi$
$674$	−28.6293			−1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	−25.9881	+	21.8066i	−0.998803	+	0.838095i	−0.986818	−	0.161833i	$-0.948259\pi$
$677$	−25.9881	+	21.8066i	−0.998803	+	0.838095i	−0.0119845	+	0.999928i	$0.503815\pi$
$678$		0			0
$679$	−6.12273	+	34.7237i	−0.234969	+	1.33257i
$680$	−2.04014	+	0.742551i	−0.0782359	+	0.0284755i
$681$		0			0
$682$	0.0962881	+	0.546077i	0.00368706	+	0.0209104i
$683$	−18.3777	−	31.8310i	−0.703201	−	1.21798i	−0.967337	−	0.253495i	$-0.918420\pi$
$683$	−18.3777	−	31.8310i	−0.703201	−	1.21798i	0.264135	−	0.964486i	$-0.414913\pi$
$684$		0			0
$685$	−27.0661	+	46.8799i	−1.03414	+	1.79119i
$686$	−14.9494	−	5.44113i	−0.570771	−	0.207743i
$687$		0			0
$688$	0.111452	+	0.0935197i	0.00424908	+	0.00356540i
$689$	10.8676	+	9.11900i	0.414023	+	0.347406i
$690$		0			0
$691$	−12.5713	−	4.57559i	−0.478236	−	0.174064i	0.0916438	−	0.995792i	$-0.470788\pi$
$691$	−12.5713	−	4.57559i	−0.478236	−	0.174064i	−0.569879	+	0.821728i	$0.693010\pi$
$692$	−4.62331	+	8.00781i	−0.175752	+	0.304411i
$693$		0			0
$694$	−7.79146	−	13.4952i	−0.295760	−	0.512271i
$695$	8.55257	+	48.5040i	0.324417	+	1.83986i
$696$		0			0
$697$	−2.67899	+	0.975072i	−0.101474	+	0.0369335i
$698$	1.11635	−	6.33114i	0.0422545	−	0.239637i
$699$		0			0
$700$	−6.33178	+	5.31299i	−0.239319	+	0.200812i
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$		0			0
$703$	19.4720			0.734400
$704$	−0.681540	+	0.571880i	−0.0256865	+	0.0215535i
$705$		0			0
$706$	−1.21839	+	6.90982i	−0.0458546	+	0.260055i
$707$	−8.94587	+	3.25603i	−0.336444	+	0.122456i
$708$		0			0
$709$	2.97700	+	16.8834i	0.111804	+	0.634069i	0.988283	+	0.152631i	$0.0487745\pi$
$709$	2.97700	+	16.8834i	0.111804	+	0.634069i	−0.876480	+	0.481439i	$0.840114\pi$
$710$	0.408315	+	0.707223i	0.0153238	+	0.0265416i
$711$		0			0
$712$	−14.0623	+	24.3566i	−0.527006	+	0.912800i
$713$	17.3848	+	6.32755i	0.651066	+	0.236969i
$714$		0			0
$715$	1.37641	+	1.15495i	0.0514748	+	0.0431925i
$716$	19.0806	+	16.0105i	0.713075	+	0.598341i
$717$		0			0
$718$	−6.23483	−	2.26929i	−0.232682	−	0.0846893i
$719$	21.6760	−	37.5439i	0.808377	−	1.40015i	−0.105610	−	0.994408i	$-0.533680\pi$
$719$	21.6760	−	37.5439i	0.808377	−	1.40015i	0.913987	−	0.405742i	$-0.132987\pi$
$720$		0			0
$721$	7.03467	+	12.1844i	0.261985	+	0.453771i
$722$	1.56515	+	8.87639i	0.0582488	+	0.330345i
$723$		0			0
$724$	14.4479	−	5.25862i	0.536954	−	0.195435i
$725$	−0.157937	+	0.895706i	−0.00586564	+	0.0332657i
$726$		0			0
$727$	−27.8410	+	23.3614i	−1.03257	+	0.866427i	−0.991154	−	0.132715i	$-0.957630\pi$
$727$	−27.8410	+	23.3614i	−1.03257	+	0.866427i	−0.0414130	+	0.999142i	$0.513186\pi$
$728$	16.7075			0.619220
$729$		0			0
$730$	11.0794			0.410067
$731$	−0.0585911	+	0.0491638i	−0.00216707	+	0.00181839i
$732$		0			0
$733$	0.672992	−	3.81673i	0.0248575	−	0.140974i	−0.969853	−	0.243690i	$-0.921642\pi$
$733$	0.672992	−	3.81673i	0.0248575	−	0.140974i	0.994711	+	0.102716i	$0.0327532\pi$
$734$	−11.1471	+	4.05721i	−0.411447	+	0.149754i
$735$		0			0
$736$	6.77217	+	38.4069i	0.249626	+	1.41570i
$737$	0.226432	+	0.392191i	0.00834071	+	0.0144465i
$738$		0			0
$739$	−13.2241	+	22.9048i	−0.486456	+	0.842567i	−0.999879	−	0.0155689i	$-0.995044\pi$
$739$	−13.2241	+	22.9048i	−0.486456	+	0.842567i	0.513422	+	0.858136i	$0.328377\pi$
$740$	24.5288	+	8.92774i	0.901695	+	0.328190i
$741$		0			0
$742$	−7.92648	−	6.65110i	−0.290990	−	0.244170i
$743$	−10.3135	−	8.65408i	−0.378367	−	0.317487i	0.433694	−	0.901060i	$-0.357210\pi$
$743$	−10.3135	−	8.65408i	−0.378367	−	0.317487i	−0.812061	+	0.583573i	$0.801654\pi$
$744$		0			0
$745$	42.0921	+	15.3203i	1.54213	+	0.561291i
$746$	10.2329	−	17.7238i	0.374651	−	0.648915i
$747$		0			0
$748$	0.0498160	+	0.0862839i	0.00182145	+	0.00315485i
$749$	−0.106889	−	0.606197i	−0.00390564	−	0.0221500i
$750$		0			0
$751$	−3.54105	+	1.28884i	−0.129215	+	0.0470303i	−0.405818	−	0.913954i	$-0.633013\pi$
$751$	−3.54105	+	1.28884i	−0.129215	+	0.0470303i	0.276603	+	0.960984i	$0.410791\pi$
$752$	−1.10721	+	6.27932i	−0.0403759	+	0.228983i
$753$		0			0
$754$	0.569430	−	0.477809i	0.0207374	−	0.0174008i
$755$	−39.2536			−1.42859
$756$		0			0
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$	−12.3565	+	10.3683i	−0.448808	+	0.376595i
$759$		0			0
$760$	3.57853	−	20.2948i	0.129807	−	0.736171i
$761$	9.07314	−	3.30235i	0.328901	−	0.119710i	−0.172292	−	0.985046i	$-0.555117\pi$
$761$	9.07314	−	3.30235i	0.328901	−	0.119710i	0.501192	+	0.865336i	$0.332895\pi$
$762$		0			0
$763$	−3.53211	−	20.0316i	−0.127871	−	0.725193i
$764$	4.65533	+	8.06327i	0.168424	+	0.291719i
$765$		0			0
$766$	−9.56272	+	16.5631i	−0.345515	+	0.598450i
$767$	−14.6701	−	5.33949i	−0.529708	−	0.192798i
$768$		0			0
$769$	29.6544	+	24.8830i	1.06936	+	0.897302i	0.994995	−	0.0999284i	$-0.0318614\pi$
$769$	29.6544	+	24.8830i	1.06936	+	0.897302i	0.0743687	+	0.997231i	$0.476306\pi$
$770$	−1.00391	−	0.842380i	−0.0361784	−	0.0303573i
$771$		0			0
$772$	26.0403	+	9.47789i	0.937210	+	0.341117i
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	−0.997462	−	0.0711944i	$-0.977319\pi$
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	0.560387	+	0.828231i	$0.310652\pi$
$774$		0			0
$775$	−3.54205	−	6.13500i	−0.127234	−	0.220376i
$776$	−6.93246	−	39.3159i	−0.248861	−	1.41136i
$777$		0			0
$778$	28.6011	−	10.4099i	1.02540	−	0.373214i
$779$	4.69910	−	26.6499i	0.168363	−	0.954833i
$780$		0			0
$781$	0.0710018	−	0.0595776i	0.00254065	−	0.00213185i
$782$	−1.57311			−0.0562544
$783$		0			0
$784$	−0.753755			−0.0269198
$785$	−1.60801	+	1.34928i	−0.0573922	+	0.0481578i
$786$		0			0
$787$	3.63630	−	20.6225i	0.129620	−	0.735112i	−0.848836	−	0.528656i	$-0.822696\pi$
$787$	3.63630	−	20.6225i	0.129620	−	0.735112i	0.978456	−	0.206456i	$-0.0661929\pi$
$788$	3.87263	−	1.40952i	0.137957	−	0.0502121i
$789$		0			0
$790$	0.307266	+	1.74259i	0.0109320	+	0.0619987i
$791$	3.70688	+	6.42051i	0.131802	+	0.228287i
$792$		0			0
$793$	15.4718	−	26.7979i	0.549419	−	0.951621i
$794$	15.3269	+	5.57853i	0.543931	+	0.197975i
$795$		0			0
$796$	2.35285	+	1.97428i	0.0833946	+	0.0699764i
$797$	9.14409	+	7.67280i	0.323900	+	0.271785i	0.790209	−	0.612837i	$-0.209972\pi$
$797$	9.14409	+	7.67280i	0.323900	+	0.271785i	−0.466309	+	0.884622i	$0.654416\pi$
$798$		0			0
$799$	−3.14984	−	1.14645i	−0.111433	−	0.0405585i
$800$	7.46668	−	12.9327i	0.263987	−	0.457239i
$801$		0			0
$802$	2.78329	+	4.82080i	0.0982814	+	0.170228i
$803$	−0.218362	−	1.23839i	−0.00770582	−	0.0437019i
$804$		0			0
$805$	−41.0873	+	14.9546i	−1.44814	+	0.527079i
$806$	−1.00537	+	5.70175i	−0.0354127	+	0.200836i
$807$		0			0
$808$	8.25721	−	6.92862i	0.290488	−	0.243748i
$809$	8.60808			0.302644			0.151322	−	0.988485i	$-0.451647\pi$
$809$	8.60808			0.302644			0.151322	+	0.988485i	$0.451647\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	0.877624	−	0.736414i	0.0307985	−	0.0258431i
$813$		0			0
$814$	−0.243461	+	1.38074i	−0.00853330	+	0.0483948i
$815$	13.2517	−	4.82321i	0.464185	−	0.168950i
$816$		0			0
$817$	−0.126069	−	0.714972i	−0.00441059	−	0.0250137i
$818$	−4.37071	−	7.57029i	−0.152818	−	0.264689i
$819$		0			0
$820$	18.1382	−	31.4163i	0.633413	−	1.09710i
$821$	−27.2288	−	9.91047i	−0.950291	−	0.345878i	−0.180069	−	0.983654i	$-0.557632\pi$
$821$	−27.2288	−	9.91047i	−0.950291	−	0.345878i	−0.770222	+	0.637776i	$0.779854\pi$
$822$		0			0
$823$	−8.62318	−	7.23571i	−0.300585	−	0.252221i	0.480003	−	0.877267i	$-0.340636\pi$
$823$	−8.62318	−	7.23571i	−0.300585	−	0.252221i	−0.780588	+	0.625046i	$0.785080\pi$
$824$	−12.2031	−	10.2396i	−0.425115	−	0.356714i
$825$		0			0
$826$	10.6999	+	3.89445i	0.372298	+	0.135505i
$827$	−15.4640	+	26.7844i	−0.537734	+	0.931383i	0.461291	+	0.887249i	$0.347386\pi$
$827$	−15.4640	+	26.7844i	−0.537734	+	0.931383i	−0.999026	+	0.0441346i	$0.985947\pi$
$828$		0			0
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	0.938698	−	0.344739i	$-0.112033\pi$
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	−0.767902	+	0.640567i	$0.778699\pi$
$830$	−1.05468	−	5.98138i	−0.0366084	−	0.207617i
$831$		0			0
$832$	−8.72927	+	3.17719i	−0.302633	+	0.110149i
$833$	0.0688086	−	0.390233i	0.00238408	−	0.0135208i
$834$		0			0
$835$	−18.7502	+	15.7333i	−0.648878	+	0.544473i
$836$	−0.945711			−0.0327081
$837$		0			0
$838$	8.07072			0.278798
$839$	−10.0683	+	8.44829i	−0.347596	+	0.291667i	−0.799824	−	0.600235i	$-0.795074\pi$
$839$	−10.0683	+	8.44829i	−0.347596	+	0.291667i	0.452228	+	0.891902i	$0.350629\pi$
$840$		0			0
$841$	−5.01391	+	28.4353i	−0.172893	+	0.980527i
$842$	−2.34058	+	0.851903i	−0.0806618	+	0.0293585i
$843$		0			0
$844$	−5.99498	−	33.9992i	−0.206356	−	1.17030i
$845$	−8.49363	−	14.7114i	−0.292190	−	0.506088i
$846$		0			0
$847$	12.9982	−	22.5136i	0.446624	−	0.773575i
$848$	−2.84825	−	1.03668i	−0.0978095	−	0.0355997i
$849$		0			0
$850$	0.461438	+	0.387193i	0.0158272	+	0.0132806i
$851$	35.8340	+	30.0683i	1.22837	+	1.03073i
$852$		0			0
$853$	−14.5110	−	5.28159i	−0.496849	−	0.180838i	0.0814274	−	0.996679i	$-0.474052\pi$
$853$	−14.5110	−	5.28159i	−0.496849	−	0.180838i	−0.578276	+	0.815841i	$0.696274\pi$
$854$	−11.2846	+	19.5455i	−0.386151	+	0.668834i
$855$		0			0
$856$	0.348478	+	0.603581i	0.0119107	+	0.0206300i
$857$	3.81726	+	21.6488i	0.130395	+	0.739508i	0.977956	+	0.208810i	$0.0669590\pi$
$857$	3.81726	+	21.6488i	0.130395	+	0.739508i	−0.847561	+	0.530698i	$0.821930\pi$
$858$		0			0
$859$	−18.3867	+	6.69220i	−0.627345	+	0.228335i	−0.636075	−	0.771627i	$-0.719443\pi$
$859$	−18.3867	+	6.69220i	−0.627345	+	0.228335i	0.00873053	+	0.999962i	$0.497221\pi$
$860$	0.169000	−	0.958447i	0.00576286	−	0.0326828i
$861$		0			0
$862$	17.2352	−	14.4620i	0.587032	−	0.492578i
$863$	21.8676			0.744383			0.372191	−	0.928156i	$-0.378607\pi$
$863$	21.8676			0.744383			0.372191	+	0.928156i	$0.378607\pi$
$864$		0			0
$865$	18.7298			0.636833
$866$	−11.9885	+	10.0596i	−0.407386	+	0.341838i
$867$		0			0
$868$	−1.54951	+	8.78771i	−0.0525938	+	0.298274i
$869$	0.188721	−	0.0686889i	0.00640193	−	0.00233011i
$870$		0			0
$871$	0.821092	+	4.65664i	0.0278216	+	0.157784i
$872$	11.5153	+	19.9452i	0.389959	+	0.675428i
$873$		0			0
$874$	7.46602	−	12.9315i	0.252542	−	0.437416i
$875$	−14.9759	−	5.45078i	−0.506277	−	0.184270i
$876$		0			0
$877$	−29.9522	−	25.1329i	−1.01142	−	0.848678i	−0.0228908	−	0.999738i	$-0.507287\pi$
$877$	−29.9522	−	25.1329i	−1.01142	−	0.848678i	−0.988525	+	0.151060i	$0.951731\pi$
$878$	−8.98264	−	7.53733i	−0.303149	−	0.254372i
$879$		0			0
$880$	−0.360739	−	0.131298i	−0.0121605	−	0.00442606i
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	−0.797915	−	0.602771i	$-0.794063\pi$
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	0.920972	+	0.389629i	$0.127397\pi$
$882$		0			0
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	0.893915	−	0.448237i	$-0.147948\pi$
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	−0.835142	+	0.550035i	$0.814614\pi$
$884$	0.180644	+	1.02448i	0.00607572	+	0.0344571i
$885$		0			0
$886$	13.8255	−	5.03207i	0.464477	−	0.169056i
$887$	4.93530	−	27.9895i	0.165711	−	0.939795i	−0.782617	−	0.622504i	$-0.786115\pi$
$887$	4.93530	−	27.9895i	0.165711	−	0.939795i	0.948328	−	0.317292i	$-0.102773\pi$
$888$		0			0
$889$	−33.6013	+	28.1948i	−1.12695	+	0.945623i
$890$	23.0340			0.772102
$891$		0			0
$892$	5.20125			0.174151
$893$	24.3734	−	20.4517i	0.815626	−	0.684392i
$894$		0			0
$895$	8.76109	−	49.6866i	0.292851	−	1.66084i
$896$	−19.6741	+	7.16078i	−0.657265	+	0.239225i
$897$		0			0
$898$	−1.92900	−	10.9399i	−0.0643716	−	0.365069i
$899$	0.490949	+	0.850349i	0.0163741	+	0.0283607i
$900$		0			0
$901$	0.796719	−	1.37996i	0.0265426	−	0.0459731i
$902$	1.83096	+	0.666415i	0.0609643	+	0.0221892i
$903$		0			0
$904$	−6.43036	−	5.39571i	−0.213871	−	0.179459i
$905$	−23.8575	−	20.0188i	−0.793050	−	0.665448i
$906$		0			0
$907$	−49.9134	−	18.1670i	−1.65735	−	0.603225i	−0.667403	−	0.744696i	$-0.732594\pi$
$907$	−49.9134	−	18.1670i	−1.65735	−	0.603225i	−0.989942	+	0.141472i	$0.954817\pi$
$908$	1.70780	−	2.95799i	0.0566753	−	0.0981644i
$909$		0			0
$910$	−6.84171	−	11.8502i	−0.226801	−	0.392830i
$911$	−1.40236	−	7.95320i	−0.0464624	−	0.263501i	0.952724	−	0.303838i	$-0.0982681\pi$
$911$	−1.40236	−	7.95320i	−0.0464624	−	0.263501i	−0.999186	+	0.0403366i	$0.987157\pi$
$912$		0			0
$913$	−0.647778	+	0.235772i	−0.0214383	+	0.00780291i
$914$	−2.45633	+	13.9305i	−0.0812482	+	0.460782i
$915$		0			0
$916$	16.5764	−	13.9092i	0.547698	−	0.459574i
$917$	33.8116			1.11656
$918$		0			0
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$	37.9244	−	31.8223i	1.25033	−	1.04915i
$921$		0			0
$922$	−3.56840	+	20.2374i	−0.117519	+	0.666483i
$923$	0.909402	−	0.330995i	0.0299333	−	0.0108948i
$924$		0			0
$925$	−3.11036	−	17.6397i	−0.102268	−	0.579991i
$926$	7.35298	+	12.7357i	0.241634	+	0.418522i
$927$		0			0
$928$	−1.03493	+	1.79255i	−0.0339732	+	0.0588433i
$929$	27.2454	+	9.91651i	0.893892	+	0.325350i	0.747802	−	0.663921i	$-0.231109\pi$
$929$	27.2454	+	9.91651i	0.893892	+	0.325350i	0.146090	+	0.989271i	$0.453331\pi$
$930$		0			0
$931$	2.88128	+	2.41768i	0.0944302	+	0.0792364i
$932$	−29.2519	−	24.5453i	−0.958178	−	0.804007i
$933$		0			0
$934$	−12.2482	−	4.45800i	−0.400775	−	0.145870i
$935$	0.100907	−	0.174775i	0.00330000	−	0.00571576i
$936$		0			0
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	0.822031	−	0.569443i	$-0.192841\pi$
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	−0.904168	+	0.427178i	$0.859508\pi$
$938$	−0.598878	−	3.39641i	−0.0195541	−	0.110897i
$939$		0			0
$940$	40.0800	−	14.5879i	1.30727	−	0.475806i
$941$	−9.69670	+	54.9927i	−0.316103	+	1.79271i	0.249861	+	0.968282i	$0.419615\pi$
$941$	−9.69670	+	54.9927i	−0.316103	+	1.79271i	−0.565965	+	0.824430i	$0.691496\pi$
$942$		0			0
$943$	49.8000	−	41.7871i	1.62171	−	1.36078i
$944$	3.33551			0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	32.5794	−	27.3373i	1.05869	−	0.888345i	0.0647076	−	0.997904i	$-0.479389\pi$
$947$	32.5794	−	27.3373i	1.05869	−	0.888345i	0.993980	+	0.109560i	$0.0349441\pi$
$948$		0			0
$949$	2.27998	−	12.9304i	0.0740113	−	0.419739i
$950$	−5.37286	+	1.95556i	−0.174318	+	0.0634467i
$951$		0			0
$952$	−0.325864	−	1.84807i	−0.0105613	−	0.0598961i
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	0.633505	−	0.773739i	$-0.281616\pi$
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	−0.986830	+	0.161762i	$0.948282\pi$
$954$		0			0
$955$	9.42977	−	16.3328i	0.305140	−	0.528518i
$956$	−18.7599	−	6.82806i	−0.606740	−	0.220835i
$957$		0			0
$958$	5.81568	+	4.87993i	0.187896	+	0.157664i
$959$	−35.8427	−	30.0756i	−1.15742	−	0.971192i
$960$		0			0
$961$	21.9439	+	7.98692i	0.707867	+	0.257643i
$962$	−7.31954	+	12.6778i	−0.235991	+	0.408749i
$963$		0			0
$964$	5.73088	+	9.92618i	0.184579	+	0.319701i
$965$	−9.74721	−	55.2792i	−0.313774	−	1.77950i
$966$		0			0
$967$	−4.34945	+	1.58307i	−0.139869	+	0.0509081i	−0.411006	−	0.911633i	$-0.634823\pi$
$967$	−4.34945	+	1.58307i	−0.139869	+	0.0509081i	0.271137	+	0.962541i	$0.412600\pi$
$968$	−5.11124	+	28.9873i	−0.164282	+	0.931687i
$969$		0			0
$970$	−25.0470	+	21.0169i	−0.804211	+	0.674813i
$971$	−21.6509			−0.694809			−0.347405	−	0.937715i	$-0.612937\pi$
$971$	−21.6509			−0.694809			−0.347405	+	0.937715i	$0.612937\pi$
$972$		0			0
$973$	−42.5714			−1.36478
$974$	0.287087	−	0.240895i	0.00919886	−	0.00771876i
$975$		0			0
$976$	−1.14803	+	6.51081i	−0.0367476	+	0.208406i
$977$	20.7529	−	7.55345i	0.663945	−	0.241656i	0.0120065	−	0.999928i	$-0.496178\pi$
$977$	20.7529	−	7.55345i	0.663945	−	0.241656i	0.651939	+	0.758272i	$0.273956\pi$
$978$		0			0
$979$	−0.453973	−	2.57461i	−0.0145090	−	0.0822849i
$980$	2.52105	+	4.36659i	0.0805320	+	0.139485i
$981$		0			0
$982$	10.0379	−	17.3862i	0.320323	−	0.554815i
$983$	13.0270	+	4.74144i	0.415497	+	0.151229i	0.541305	−	0.840826i	$-0.317930\pi$
$983$	13.0270	+	4.74144i	0.415497	+	0.151229i	−0.125809	+	0.992055i	$0.540152\pi$
$984$		0			0
$985$	−6.39476	−	5.36584i	−0.203754	−	0.170970i
$986$	−0.0639582	−	0.0536673i	−0.00203684	−	0.00170911i
$987$		0			0
$988$	−9.27895	−	3.37726i	−0.295203	−	0.107445i
$989$	0.872042	−	1.51042i	0.0277293	−	0.0480286i
$990$		0			0
$991$	−17.4112	−	30.1570i	−0.553084	−	0.957970i	−0.998050	−	0.0624224i	$-0.980117\pi$
$991$	−17.4112	−	30.1570i	−0.553084	−	0.957970i	0.444966	−	0.895548i	$-0.353216\pi$
$992$	−2.79950	−	15.8768i	−0.0888842	−	0.504088i
$993$		0			0
$994$	−0.663289	+	0.241417i	−0.0210382	+	0.00765729i
$995$	1.08034	−	6.12692i	0.0342491	−	0.194236i
$996$		0			0
$997$	−18.9594	+	15.9088i	−0.600451	+	0.503838i	−0.891590	−	0.452843i	$-0.850410\pi$
$997$	−18.9594	+	15.9088i	−0.600451	+	0.503838i	0.291140	+	0.956681i	$0.405966\pi$
$998$	11.2488			0.356073
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.d.109.1		12
3.2	odd	2		243.2.e.a.109.2		12
9.2	odd	6		81.2.e.a.64.1		12
9.4	even	3		243.2.e.c.28.1		12
9.5	odd	6		243.2.e.b.28.2		12
9.7	even	3		27.2.e.a.4.2	✓	12
27.2	odd	18		81.2.e.a.19.1		12
27.4	even	9		729.2.a.a.1.3		6
27.5	odd	18		729.2.c.b.244.3		12
27.7	even	9		243.2.e.c.217.1		12
27.11	odd	18		243.2.e.a.136.2		12
27.13	even	9		729.2.c.e.487.4		12
27.14	odd	18		729.2.c.b.487.3		12
27.16	even	9	inner	243.2.e.d.136.1		12
27.20	odd	18		243.2.e.b.217.2		12
27.22	even	9		729.2.c.e.244.4		12
27.23	odd	18		729.2.a.d.1.4		6
27.25	even	9		27.2.e.a.7.2	yes	12
36.7	odd	6		432.2.u.c.193.2		12
45.7	odd	12		675.2.u.b.274.2		24
45.34	even	6		675.2.l.c.301.1		12
45.43	odd	12		675.2.u.b.274.3		24
108.79	odd	18		432.2.u.c.385.2		12
135.52	odd	36		675.2.u.b.574.3		24
135.79	even	18		675.2.l.c.601.1		12
135.133	odd	36		675.2.u.b.574.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	9.7	even	3
27.2.e.a.7.2	yes	12	27.25	even	9
81.2.e.a.19.1		12	27.2	odd	18
81.2.e.a.64.1		12	9.2	odd	6
243.2.e.a.109.2		12	3.2	odd	2
243.2.e.a.136.2		12	27.11	odd	18
243.2.e.b.28.2		12	9.5	odd	6
243.2.e.b.217.2		12	27.20	odd	18
243.2.e.c.28.1		12	9.4	even	3
243.2.e.c.217.1		12	27.7	even	9
243.2.e.d.109.1		12	1.1	even	1	trivial
243.2.e.d.136.1		12	27.16	even	9	inner
432.2.u.c.193.2		12	36.7	odd	6
432.2.u.c.385.2		12	108.79	odd	18
675.2.l.c.301.1		12	45.34	even	6
675.2.l.c.601.1		12	135.79	even	18
675.2.u.b.274.2		24	45.7	odd	12
675.2.u.b.274.3		24	45.43	odd	12
675.2.u.b.574.2		24	135.133	odd	36
675.2.u.b.574.3		24	135.52	odd	36
729.2.a.a.1.3		6	27.4	even	9
729.2.a.d.1.4		6	27.23	odd	18
729.2.c.b.244.3		12	27.5	odd	18
729.2.c.b.487.3		12	27.14	odd	18
729.2.c.e.244.4		12	27.22	even	9
729.2.c.e.487.4		12	27.13	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.614005 + 0.515212i) q^{2} +(-0.235737 + 1.33693i) q^{4} +(2.58401 - 0.940501i) q^{5} +(0.412733 + 2.34072i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(-1.10204 + 1.90878i) q^{10} +(0.235072 + 0.0855594i) q^{11} +(2.00090 + 1.67895i) q^{13} +(-1.45939 - 1.22457i) q^{14} +(-0.524408 - 0.190869i) q^{16} +(0.146688 - 0.254072i) q^{17} +(1.39237 + 2.41166i) q^{19} +(0.648239 + 3.67635i) q^{20} +(-0.188417 + 0.0685781i) q^{22} +(-1.16168 + 6.58821i) q^{23} +(1.96232 - 1.64658i) q^{25} -2.09357 q^{26} -3.22668 q^{28} +(-0.271990 + 0.228226i) q^{29} +(0.480218 - 2.72345i) q^{31} +(5.47807 - 1.99386i) q^{32} +(0.0408333 + 0.231577i) q^{34} +(3.26796 + 5.66027i) q^{35} +(3.49619 - 6.05558i) q^{37} +(-2.09744 - 0.763405i) q^{38} +(-5.66895 - 4.75682i) q^{40} +(-7.44412 - 6.24636i) q^{41} +(-0.244984 - 0.0891669i) q^{43} +(-0.169802 + 0.294106i) q^{44} +(-2.68104 - 4.64370i) q^{46} +(-1.98403 - 11.2520i) q^{47} +(1.26921 - 0.461953i) q^{49} +(-0.356537 + 2.02202i) q^{50} +(-2.71632 + 2.27927i) q^{52} +5.43137 q^{53} +0.687897 q^{55} +(4.89998 - 4.11157i) q^{56} +(0.0494182 - 0.280264i) q^{58} +(-5.61647 + 2.04423i) q^{59} +(-2.05717 - 11.6668i) q^{61} +(1.10830 + 1.91963i) q^{62} +(-1.77824 + 3.08001i) q^{64} +(6.74938 + 2.45657i) q^{65} +(1.38677 + 1.16364i) q^{67} +(0.305096 + 0.256006i) q^{68} +(-4.92278 - 1.79175i) q^{70} +(0.185255 - 0.320871i) q^{71} +(-2.51339 - 4.35333i) q^{73} +(0.973225 + 5.51943i) q^{74} +(-3.55246 + 1.29299i) q^{76} +(-0.103249 + 0.585553i) q^{77} +(0.614997 - 0.516044i) q^{79} -1.53459 q^{80} +7.78892 q^{82} +(-2.11095 + 1.77130i) q^{83} +(0.140089 - 0.794483i) q^{85} +(0.196361 - 0.0714696i) q^{86} +(-0.116903 - 0.662992i) q^{88} +(-5.22533 - 9.05054i) q^{89} +(-3.10412 + 5.37650i) q^{91} +(-8.53412 - 3.10617i) q^{92} +(7.01535 + 5.88658i) q^{94} +(5.86607 + 4.92221i) q^{95} +(13.9400 + 5.07373i) q^{97} +(-0.541296 + 0.937552i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} + 3 q^{13} - 21 q^{14} + 9 q^{16} + 9 q^{17} - 3 q^{19} + 24 q^{20} + 12 q^{22} - 12 q^{23} + 12 q^{25} - 30 q^{26} - 12 q^{28}+ \cdots - 45 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 + 3 * q^13 - 21 * q^14 + 9 * q^16 + 9 * q^17 - 3 * q^19 + 24 * q^20 + 12 * q^22 - 12 * q^23 + 12 * q^25 - 30 * q^26 - 12 * q^28 - 24 * q^29 + 12 * q^31 + 27 * q^32 + 12 * q^35 - 3 * q^37 - 30 * q^38 - 15 * q^40 + 6 * q^41 - 15 * q^43 + 3 * q^44 - 3 * q^46 + 12 * q^47 - 33 * q^49 + 21 * q^50 - 45 * q^52 - 18 * q^53 - 12 * q^55 + 30 * q^56 - 51 * q^58 - 3 * q^59 - 33 * q^61 - 12 * q^62 + 12 * q^64 + 21 * q^65 - 6 * q^67 + 9 * q^68 - 15 * q^70 + 27 * q^71 + 6 * q^73 - 21 * q^74 + 6 * q^76 - 12 * q^77 + 21 * q^79 + 42 * q^80 - 12 * q^82 - 6 * q^83 + 36 * q^85 - 21 * q^86 + 42 * q^88 + 9 * q^89 + 6 * q^91 - 3 * q^92 + 48 * q^94 + 3 * q^95 + 39 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more