LMFDB - Embedded newform 729.2.e.u.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, 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("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			568.1
Root			$-1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.u.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48321 - 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(-0.291470 + 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(1.19062 + 2.06222i) q^{8} +O(q^{10})$	\(q+(-1.48321 - 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(-0.291470 + 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(1.19062 + 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(0.720852 + 4.08816i) q^{11} +(-6.46137 + 2.35175i) q^{13} +(-4.12227 + 1.50038i) q^{14} +(-0.823316 - 4.66925i) q^{16} +(0.488276 - 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(-0.631796 + 0.530140i) q^{20} +(1.13780 - 6.45276i) q^{22} +(-1.23576 - 1.03693i) q^{23} +(2.05098 + 0.746497i) q^{25} +10.8532 q^{26} +1.36563 q^{28} +(-7.73168 - 2.81410i) q^{29} +(0.799803 + 0.671115i) q^{31} +(-0.472527 + 2.67984i) q^{32} +(-1.18078 + 0.990788i) q^{34} +(2.33252 + 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(0.736003 + 4.17408i) q^{38} +(-3.75589 + 1.36703i) q^{40} +(-4.55579 + 1.65817i) q^{41} +(1.70874 + 9.69073i) q^{43} +(-1.01987 + 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(-9.57379 + 8.03337i) q^{47} +(0.125792 - 0.713402i) q^{49} +(-2.63906 - 2.21443i) q^{50} +(-3.17486 - 1.15555i) q^{52} -7.34280 q^{53} -6.96786 q^{55} +(6.21903 + 2.26354i) q^{56} +(9.94855 + 8.34783i) q^{58} +(-1.57184 + 8.91436i) q^{59} +(-0.984935 + 0.826459i) q^{61} +(-0.823982 - 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(-2.00416 - 11.3662i) q^{65} +(4.36609 - 1.58913i) q^{67} +(0.450900 - 0.164114i) q^{68} +(-1.27863 - 7.25146i) q^{70} +(2.81187 - 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(-1.58196 + 1.32742i) q^{74} +(0.229119 - 1.29940i) q^{76} +(8.83817 + 7.41611i) q^{77} +(-4.37596 - 1.59272i) q^{79} +7.95828 q^{80} +7.65237 q^{82} +(5.41676 + 1.97154i) q^{83} +(1.25566 + 1.05362i) q^{85} +(2.69708 - 15.2959i) q^{86} +(-7.57240 + 6.35400i) q^{88} +(2.27221 + 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(-0.137642 - 0.780605i) q^{92} +(18.5368 - 6.74683i) q^{94} +(4.23546 - 1.54158i) q^{95} +(1.48911 + 8.44516i) q^{97} +(-0.571704 + 0.990221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.48321	−	0.539846i	−1.04879	−	0.381729i	−0.240585	−	0.970628i	$-0.577339\pi$
$2$	−1.48321	−	0.539846i	−1.04879	−	0.381729i	−0.808206	+	0.588899i	$0.799561\pi$
$3$		0			0
$3$		0			0
$4$	0.376403	+	0.315840i	0.188202	+	0.157920i
$5$	−0.291470	+	1.65301i	−0.130349	+	0.739247i	0.847637	+	0.530577i	$0.178025\pi$
$5$	−0.291470	+	1.65301i	−0.130349	+	0.739247i	−0.977986	+	0.208670i	$0.933086\pi$
$6$		0			0
$7$	2.12905	−	1.78649i	0.804707	−	0.675229i	−0.144632	−	0.989486i	$-0.546200\pi$
$7$	2.12905	−	1.78649i	0.804707	−	0.675229i	0.949338	+	0.314257i	$0.101755\pi$
$8$	1.19062	+	2.06222i	0.420948	+	0.729104i
$9$		0			0
$10$	1.32468	−	2.29442i	0.418901	−	0.725558i
$11$	0.720852	+	4.08816i	0.217345	+	1.23263i	0.876790	+	0.480873i	$0.159680\pi$
$11$	0.720852	+	4.08816i	0.217345	+	1.23263i	−0.659445	+	0.751753i	$0.729209\pi$
$12$		0			0
$13$	−6.46137	+	2.35175i	−1.79206	+	0.652257i	−0.792987	+	0.609239i	$0.791475\pi$
$13$	−6.46137	+	2.35175i	−1.79206	+	0.652257i	−0.999074	+	0.0430184i	$0.986303\pi$
$14$	−4.12227	+	1.50038i	−1.10172	+	0.400995i
$15$		0			0
$16$	−0.823316	−	4.66925i	−0.205829	−	1.16731i
$17$	0.488276	−	0.845718i	0.118424	−	0.205117i	−0.800719	−	0.599040i	$-0.795549\pi$
$17$	0.488276	−	0.845718i	0.118424	−	0.205117i	0.919143	+	0.393923i	$0.128882\pi$
$18$		0			0
$19$	−1.34264	−	2.32553i	−0.308024	−	0.533513i	0.669906	−	0.742446i	$-0.266334\pi$
$19$	−1.34264	−	2.32553i	−0.308024	−	0.533513i	−0.977930	+	0.208933i	$0.933001\pi$
$20$	−0.631796	+	0.530140i	−0.141274	+	0.118543i
$21$		0			0
$22$	1.13780	−	6.45276i	0.242579	−	1.37573i
$23$	−1.23576	−	1.03693i	−0.257674	−	0.216214i	0.504795	−	0.863239i	$-0.331568\pi$
$23$	−1.23576	−	1.03693i	−0.257674	−	0.216214i	−0.762468	+	0.647026i	$0.776013\pi$
$24$		0			0
$25$	2.05098	+	0.746497i	0.410197	+	0.149299i
$26$	10.8532			2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	−7.73168	−	2.81410i	−1.43574	−	0.522565i	−0.497166	−	0.867655i	$-0.665626\pi$
$29$	−7.73168	−	2.81410i	−1.43574	−	0.522565i	−0.938570	+	0.345090i	$0.887848\pi$
$30$		0			0
$31$	0.799803	+	0.671115i	0.143649	+	0.120536i	0.711780	−	0.702402i	$-0.247889\pi$
$31$	0.799803	+	0.671115i	0.143649	+	0.120536i	−0.568132	+	0.822938i	$0.692334\pi$
$32$	−0.472527	+	2.67984i	−0.0835318	+	0.473733i
$33$		0			0
$34$	−1.18078	+	0.990788i	−0.202501	+	0.169919i
$35$	2.33252	+	4.04005i	0.394268	+	0.682893i
$36$		0			0
$37$	0.654172	−	1.13306i	0.107545	−	0.186274i	−0.807230	−	0.590237i	$-0.799034\pi$
$37$	0.654172	−	1.13306i	0.107545	−	0.186274i	0.914775	+	0.403963i	$0.132368\pi$
$38$	0.736003	+	4.17408i	0.119395	+	0.677125i
$39$		0			0
$40$	−3.75589	+	1.36703i	−0.593859	+	0.216147i
$41$	−4.55579	+	1.65817i	−0.711495	+	0.258963i	−0.672311	−	0.740269i	$-0.734698\pi$
$41$	−4.55579	+	1.65817i	−0.711495	+	0.258963i	−0.0391841	+	0.999232i	$0.512476\pi$
$42$		0			0
$43$	1.70874	+	9.69073i	0.260580	+	1.47782i	0.781332	+	0.624115i	$0.214540\pi$
$43$	1.70874	+	9.69073i	0.260580	+	1.47782i	−0.520752	+	0.853708i	$0.674348\pi$
$44$	−1.01987	+	1.76647i	−0.153751	+	0.266305i
$45$		0			0
$46$	1.27312	+	2.20510i	0.187711	+	0.325125i
$47$	−9.57379	+	8.03337i	−1.39648	+	1.17179i	−0.433846	+	0.900987i	$0.642844\pi$
$47$	−9.57379	+	8.03337i	−1.39648	+	1.17179i	−0.962636	+	0.270800i	$0.912712\pi$
$48$		0			0
$49$	0.125792	−	0.713402i	0.0179703	−	0.101915i
$50$	−2.63906	−	2.21443i	−0.373219	−	0.313168i
$51$		0			0
$52$	−3.17486	−	1.15555i	−0.440273	−	0.160246i
$53$	−7.34280			−1.00861			−0.504305	−	0.863525i	$-0.668251\pi$
$53$	−7.34280			−1.00861			−0.504305	+	0.863525i	$0.668251\pi$
$54$		0			0
$55$	−6.96786			−0.939546
$56$	6.21903	+	2.26354i	0.831052	+	0.302478i
$57$		0			0
$58$	9.94855	+	8.34783i	1.30631	+	1.09612i
$59$	−1.57184	+	8.91436i	−0.204636	+	1.16055i	0.693375	+	0.720577i	$0.256123\pi$
$59$	−1.57184	+	8.91436i	−0.204636	+	1.16055i	−0.898011	+	0.439973i	$0.854988\pi$
$60$		0			0
$61$	−0.984935	+	0.826459i	−0.126108	+	0.105817i	−0.703660	−	0.710536i	$-0.748452\pi$
$61$	−0.984935	+	0.826459i	−0.126108	+	0.105817i	0.577552	+	0.816354i	$0.304008\pi$
$62$	−0.823982	−	1.42718i	−0.104646	−	0.181252i
$63$		0			0
$64$	−2.59373	+	4.49247i	−0.324216	+	0.561558i
$65$	−2.00416	−	11.3662i	−0.248585	−	1.40980i
$66$		0			0
$67$	4.36609	−	1.58913i	0.533403	−	0.194143i	−0.0612541	−	0.998122i	$-0.519510\pi$
$67$	4.36609	−	1.58913i	0.533403	−	0.194143i	0.594657	+	0.803979i	$0.297288\pi$
$68$	0.450900	−	0.164114i	0.0546797	−	0.0199018i
$69$		0			0
$70$	−1.27863	−	7.25146i	−0.152825	−	0.866716i
$71$	2.81187	−	4.87030i	0.333707	−	0.577998i	−0.649528	−	0.760337i	$-0.725034\pi$
$71$	2.81187	−	4.87030i	0.333707	−	0.577998i	0.983236	+	0.182339i	$0.0583670\pi$
$72$		0			0
$73$	2.28072	+	3.95033i	0.266938	+	0.462351i	0.968070	−	0.250681i	$-0.0806547\pi$
$73$	2.28072	+	3.95033i	0.266938	+	0.462351i	−0.701131	+	0.713032i	$0.747321\pi$
$74$	−1.58196	+	1.32742i	−0.183899	+	0.154309i
$75$		0			0
$76$	0.229119	−	1.29940i	0.0262817	−	0.149051i
$77$	8.83817	+	7.41611i	1.00720	+	0.845144i
$78$		0			0
$79$	−4.37596	−	1.59272i	−0.492334	−	0.179195i	0.0839088	−	0.996473i	$-0.473260\pi$
$79$	−4.37596	−	1.59272i	−0.492334	−	0.179195i	−0.576243	+	0.817278i	$0.695482\pi$
$80$	7.95828			0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	5.41676	+	1.97154i	0.594566	+	0.216404i	0.621737	−	0.783226i	$-0.286427\pi$
$83$	5.41676	+	1.97154i	0.594566	+	0.216404i	−0.0271703	+	0.999631i	$0.508650\pi$
$84$		0			0
$85$	1.25566	+	1.05362i	0.136196	+	0.114282i
$86$	2.69708	−	15.2959i	0.290833	−	1.64940i
$87$		0			0
$88$	−7.57240	+	6.35400i	−0.807221	+	0.677339i
$89$	2.27221	+	3.93558i	0.240854	+	0.417171i	0.960958	−	0.276695i	$-0.0892393\pi$
$89$	2.27221	+	3.93558i	0.240854	+	0.417171i	−0.720104	+	0.693866i	$0.755906\pi$
$90$		0			0
$91$	−9.55523	+	16.5502i	−1.00166	+	1.73493i
$92$	−0.137642	−	0.780605i	−0.0143501	−	0.0813837i
$93$		0			0
$94$	18.5368	−	6.74683i	1.91192	−	0.695883i
$95$	4.23546	−	1.54158i	0.434549	−	0.158163i
$96$		0			0
$97$	1.48911	+	8.44516i	0.151196	+	0.857476i	0.962181	+	0.272410i	$0.0878205\pi$
$97$	1.48911	+	8.44516i	0.151196	+	0.857476i	−0.810985	+	0.585067i	$0.801068\pi$
$98$	−0.571704	+	0.990221i	−0.0577508	+	0.100027i
$99$		0			0
$100$	0.536224	+	0.928767i	0.0536224	+	0.0928767i
$101$	5.97952	−	5.01741i	0.594984	−	0.499251i	−0.294845	−	0.955545i	$-0.595268\pi$
$101$	5.97952	−	5.01741i	0.594984	−	0.499251i	0.889829	+	0.456294i	$0.150824\pi$
$102$		0			0
$103$	−0.376148	+	2.13324i	−0.0370629	+	0.210194i	−0.997715	−	0.0675594i	$-0.978479\pi$
$103$	−0.376148	+	2.13324i	−0.0370629	+	0.210194i	0.960652	+	0.277754i	$0.0895899\pi$
$104$	−12.5429	−	10.5247i	−1.22993	−	1.03203i
$105$		0			0
$106$	10.8909	+	3.96398i	1.05782	+	0.385016i
$107$	−12.5849			−1.21663			−0.608317	−	0.793695i	$-0.708155\pi$
$107$	−12.5849			−1.21663			−0.608317	+	0.793695i	$0.708155\pi$
$108$		0			0
$109$	−12.2140			−1.16989			−0.584945	−	0.811073i	$-0.698884\pi$
$109$	−12.2140			−1.16989			−0.584945	+	0.811073i	$0.698884\pi$
$110$	10.3348	+	3.76157i	0.985387	+	0.358652i
$111$		0			0
$112$	−10.0944	−	8.47025i	−0.953836	−	0.800363i
$113$	−0.0782863	+	0.443984i	−0.00736456	+	0.0417665i	−0.988269	−	0.152726i	$-0.951195\pi$
$113$	−0.0782863	+	0.443984i	−0.00736456	+	0.0417665i	0.980904	+	0.194492i	$0.0623060\pi$
$114$		0			0
$115$	2.07423	−	1.74049i	0.193423	−	0.162301i
$116$	−2.02142	−	3.50121i	−0.187685	−	0.325079i
$117$		0			0
$118$	7.14376	−	12.3734i	0.657636	−	1.13906i
$119$	−0.471300	−	2.67288i	−0.0432040	−	0.245022i
$120$		0			0
$121$	−5.85677	+	2.13169i	−0.532434	+	0.193790i
$122$	1.90703	−	0.694103i	0.172655	−	0.0628411i
$123$		0			0
$124$	0.0890839	+	0.505220i	0.00799997	+	0.0453701i
$125$	−6.02803	+	10.4409i	−0.539164	+	0.933859i
$126$		0			0
$127$	0.265534	+	0.459919i	0.0235624	+	0.0408112i	0.877566	−	0.479456i	$-0.159166\pi$
$127$	0.265534	+	0.459919i	0.0235624	+	0.0408112i	−0.854004	+	0.520267i	$0.825833\pi$
$128$	10.4414	−	8.76136i	0.922896	−	0.774402i
$129$		0			0
$130$	−3.16337	+	17.9404i	−0.277446	+	1.57348i
$131$	8.74519	+	7.33809i	0.764071	+	0.641132i	0.939183	−	0.343417i	$-0.111584\pi$
$131$	8.74519	+	7.33809i	0.764071	+	0.641132i	−0.175112	+	0.984548i	$0.556029\pi$
$132$		0			0
$133$	−7.01309	−	2.55256i	−0.608112	−	0.221335i
$134$	−7.33374			−0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	−3.97419	−	1.44649i	−0.339538	−	0.123582i	0.166623	−	0.986021i	$-0.446714\pi$
$137$	−3.97419	−	1.44649i	−0.339538	−	0.123582i	−0.506161	+	0.862439i	$0.668936\pi$
$138$		0			0
$139$	−8.54563	−	7.17064i	−0.724831	−	0.608205i	0.203886	−	0.978995i	$-0.434643\pi$
$139$	−8.54563	−	7.17064i	−0.724831	−	0.608205i	−0.928717	+	0.370789i	$0.879087\pi$
$140$	−0.398039	+	2.25739i	−0.0336404	+	0.190784i
$141$		0			0
$142$	−6.79981	+	5.70572i	−0.570628	+	0.478813i
$143$	−14.2720	−	24.7198i	−1.19348	−	2.06718i
$144$		0			0
$145$	6.90528	−	11.9603i	0.573452	−	0.993248i
$146$	−1.25023	−	7.09042i	−0.103470	−	0.586807i
$147$		0			0
$148$	0.604098	−	0.219874i	0.0496566	−	0.0180735i
$149$	18.3030	−	6.66176i	1.49944	−	0.545753i	0.543527	−	0.839391i	$-0.317088\pi$
$149$	18.3030	−	6.66176i	1.49944	−	0.545753i	0.955917	+	0.293639i	$0.0948662\pi$
$150$		0			0
$151$	−0.215820	−	1.22398i	−0.0175632	−	0.0996059i	0.974766	−	0.223229i	$-0.0716598\pi$
$151$	−0.215820	−	1.22398i	−0.0175632	−	0.0996059i	−0.992329	+	0.123623i	$0.960549\pi$
$152$	3.19716	−	5.53765i	0.259324	−	0.449163i
$153$		0			0
$154$	−9.10535	−	15.7709i	−0.733730	−	1.27086i
$155$	−1.34248	+	1.12647i	−0.107830	+	0.0904803i
$156$		0			0
$157$	−0.613523	+	3.47946i	−0.0489645	+	0.277691i	−0.999453	−	0.0330680i	$-0.989472\pi$
$157$	−0.613523	+	3.47946i	−0.0489645	+	0.277691i	0.950489	+	0.310759i	$0.100583\pi$
$158$	5.63067	+	4.72469i	0.447952	+	0.375876i
$159$		0			0
$160$	−4.29206	−	1.56218i	−0.339317	−	0.123501i
$161$	−4.48345			−0.353346
$162$		0			0
$163$	15.9509			1.24937			0.624685	−	0.780877i	$-0.285228\pi$
$163$	15.9509			1.24937			0.624685	+	0.780877i	$0.285228\pi$
$164$	−2.23853	−	0.814759i	−0.174800	−	0.0636220i
$165$		0			0
$166$	−6.96989	−	5.84843i	−0.540968	−	0.453926i
$167$	2.51523	−	14.2646i	0.194635	−	1.10383i	−0.718304	−	0.695730i	$-0.755081\pi$
$167$	2.51523	−	14.2646i	0.194635	−	1.10383i	0.912938	−	0.408098i	$-0.133808\pi$
$168$		0			0
$169$	26.2600	−	22.0348i	2.02000	−	1.69498i
$170$	−1.29362	−	2.24061i	−0.0992161	−	0.171847i
$171$		0			0
$172$	−2.41755	+	4.18731i	−0.184336	+	0.319280i
$173$	2.19099	+	12.4257i	0.166578	+	0.944709i	0.947423	+	0.319984i	$0.103678\pi$
$173$	2.19099	+	12.4257i	0.166578	+	0.944709i	−0.780845	+	0.624725i	$0.785211\pi$
$174$		0			0
$175$	5.70026	−	2.07473i	0.430900	−	0.156835i
$176$	18.4952	−	6.73168i	1.39412	−	0.507420i
$177$		0			0
$178$	−1.24557	−	7.06396i	−0.0933591	−	0.529466i
$179$	−0.147949	+	0.256256i	−0.0110582	+	0.0191534i	−0.871502	−	0.490393i	$-0.836853\pi$
$179$	−0.147949	+	0.256256i	−0.0110582	+	0.0191534i	0.860443	+	0.509546i	$0.170187\pi$
$180$		0			0
$181$	−0.710251	−	1.23019i	−0.0527925	−	0.0914393i	0.838421	−	0.545022i	$-0.183479\pi$
$181$	−0.710251	−	1.23019i	−0.0527925	−	0.0914393i	−0.891214	+	0.453583i	$0.850146\pi$
$182$	23.1070	−	19.3891i	1.71280	−	1.43721i
$183$		0			0
$184$	0.667044	−	3.78299i	0.0491751	−	0.278886i
$185$	1.68228	+	1.41160i	0.123684	+	0.103783i
$186$		0			0
$187$	3.80940	+	1.38651i	0.278571	+	0.101392i
$188$	−6.14087			−0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	−19.3803	−	7.05385i	−1.40231	−	0.510399i	−0.473446	−	0.880823i	$-0.656990\pi$
$191$	−19.3803	−	7.05385i	−1.40231	−	0.510399i	−0.928863	+	0.370424i	$0.879212\pi$
$192$		0			0
$193$	−16.0532	−	13.4702i	−1.15553	−	0.969608i	−0.155699	−	0.987805i	$-0.549763\pi$
$193$	−16.0532	−	13.4702i	−1.15553	−	0.969608i	−0.999834	+	0.0181970i	$0.994207\pi$
$194$	2.35042	−	13.3299i	0.168750	−	0.957029i
$195$		0			0
$196$	0.272670	−	0.228797i	0.0194764	−	0.0163426i
$197$	4.79810	+	8.31056i	0.341851	+	0.592103i	0.984776	−	0.173826i	$-0.0556129\pi$
$197$	4.79810	+	8.31056i	0.341851	+	0.592103i	−0.642926	+	0.765929i	$0.722280\pi$
$198$		0			0
$199$	5.34583	−	9.25925i	0.378956	−	0.656371i	−0.611955	−	0.790893i	$-0.709616\pi$
$199$	5.34583	−	9.25925i	0.378956	−	0.656371i	0.990911	+	0.134522i	$0.0429498\pi$
$200$	0.902507	+	5.11837i	0.0638169	+	0.361924i
$201$		0			0
$202$	−11.5775	+	4.21388i	−0.814592	+	0.296487i
$203$	−21.4885	+	7.82118i	−1.50820	+	0.548939i
$204$		0			0
$205$	−1.41310	−	8.01406i	−0.0986948	−	0.559726i
$206$	1.70953	−	2.96099i	0.119108	−	0.206302i
$207$		0			0
$208$	16.3006	+	28.2335i	1.13025	+	1.95764i
$209$	8.53927	−	7.16530i	0.590674	−	0.495634i
$210$		0			0
$211$	−2.61345	+	14.8216i	−0.179917	+	1.02036i	0.752397	+	0.658710i	$0.228898\pi$
$211$	−2.61345	+	14.8216i	−0.179917	+	1.02036i	−0.932314	+	0.361650i	$0.882213\pi$
$212$	−2.76385	−	2.31915i	−0.189822	−	0.159280i
$213$		0			0
$214$	18.6662	+	6.79394i	1.27599	+	0.464424i
$215$	−16.5169			−1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	18.1160	+	6.59368i	1.22697	+	0.446580i
$219$		0			0
$220$	−2.62273	−	2.20073i	−0.176824	−	0.148373i
$221$	−1.16601	+	6.61280i	−0.0784346	+	0.444825i
$222$		0			0
$223$	−9.41324	+	7.89864i	−0.630357	+	0.528932i	−0.901040	−	0.433736i	$-0.857195\pi$
$223$	−9.41324	+	7.89864i	−0.630357	+	0.528932i	0.270683	+	0.962669i	$0.412751\pi$
$224$	3.78146	+	6.54968i	0.252659	+	0.437619i
$225$		0			0
$226$	0.355798	−	0.616261i	0.0236674	−	0.0409931i
$227$	0.651625	+	3.69555i	0.0432499	+	0.245282i	0.998766	−	0.0496553i	$-0.0158123\pi$
$227$	0.651625	+	3.69555i	0.0432499	+	0.245282i	−0.955517	+	0.294938i	$0.904701\pi$
$228$		0			0
$229$	17.4806	−	6.36240i	1.15515	−	0.420439i	0.307786	−	0.951456i	$-0.400412\pi$
$229$	17.4806	−	6.36240i	1.15515	−	0.420439i	0.847362	+	0.531016i	$0.178190\pi$
$230$	−4.01613	+	1.46175i	−0.264816	+	0.0963850i
$231$		0			0
$232$	−3.40222	−	19.2949i	−0.223366	−	1.26677i
$233$	−0.272892	+	0.472663i	−0.0178777	+	0.0309652i	−0.874826	−	0.484438i	$-0.839024\pi$
$233$	−0.272892	+	0.472663i	−0.0178777	+	0.0309652i	0.856948	+	0.515403i	$0.172358\pi$
$234$		0			0
$235$	−10.4887	−	18.1670i	−0.684210	−	1.18509i
$236$	−3.40716	+	2.85894i	−0.221787	+	0.186101i
$237$		0			0
$238$	−0.743903	+	4.21888i	−0.0482200	+	0.273469i
$239$	−15.3935	−	12.9167i	−0.995721	−	0.835509i	−0.00933493	−	0.999956i	$-0.502971\pi$
$239$	−15.3935	−	12.9167i	−0.995721	−	0.835509i	−0.986386	+	0.164448i	$0.947416\pi$
$240$		0			0
$241$	−14.3691	−	5.22993i	−0.925597	−	0.336890i	−0.165134	−	0.986271i	$-0.552806\pi$
$241$	−14.3691	−	5.22993i	−0.925597	−	0.336890i	−0.760463	+	0.649382i	$0.775028\pi$
$242$	9.83763			0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	1.14259	+	0.415871i	0.0729977	+	0.0265690i
$246$		0			0
$247$	14.1444	+	11.8685i	0.899985	+	0.755177i
$248$	−0.431721	+	2.44841i	−0.0274143	+	0.155474i
$249$		0			0
$250$	14.5773	−	12.2318i	0.921951	−	0.773609i
$251$	−6.37816	−	11.0473i	−0.402586	−	0.697299i	0.591451	−	0.806341i	$-0.298555\pi$
$251$	−6.37816	−	11.0473i	−0.402586	−	0.697299i	−0.994037	+	0.109042i	$0.965222\pi$
$252$		0			0
$253$	3.34831	−	5.79945i	0.210507	−	0.364608i
$254$	−0.145559	−	0.825506i	−0.00913319	−	0.0517969i
$255$		0			0
$256$	−10.4674	+	3.80981i	−0.654210	+	0.238113i
$257$	12.3144	−	4.48207i	0.768151	−	0.279584i	0.0719281	−	0.997410i	$-0.477085\pi$
$257$	12.3144	−	4.48207i	0.768151	−	0.279584i	0.696223	+	0.717826i	$0.254863\pi$
$258$		0			0
$259$	−0.631430	−	3.58102i	−0.0392351	−	0.222513i
$260$	2.83551	−	4.91125i	0.175851	−	0.304583i
$261$		0			0
$262$	−9.00956	−	15.6050i	−0.556613	−	0.964081i
$263$	−7.28828	+	6.11559i	−0.449415	+	0.377104i	−0.839219	−	0.543794i	$-0.816987\pi$
$263$	−7.28828	+	6.11559i	−0.449415	+	0.377104i	0.389804	+	0.920898i	$0.372543\pi$
$264$		0			0
$265$	2.14020	−	12.1377i	0.131472	−	0.745613i
$266$	9.02393	+	7.57198i	0.553293	+	0.464268i
$267$		0			0
$268$	2.14532	+	0.780834i	0.131046	+	0.0476970i
$269$	22.1408			1.34995			0.674973	−	0.737842i	$-0.264155\pi$
$269$	22.1408			1.34995			0.674973	+	0.737842i	$0.264155\pi$
$270$		0			0
$271$	27.9627			1.69861			0.849307	−	0.527899i	$-0.177020\pi$
$271$	27.9627			1.69861			0.849307	+	0.527899i	$0.177020\pi$
$272$	−4.35088	−	1.58359i	−0.263811	−	0.0960193i
$273$		0			0
$274$	5.11369	+	4.29090i	0.308930	+	0.259223i
$275$	−1.57334	+	8.92286i	−0.0948760	+	0.538069i
$276$		0			0
$277$	−14.4657	+	12.1382i	−0.869162	+	0.729313i	−0.963921	−	0.266187i	$-0.914236\pi$
$277$	−14.4657	+	12.1382i	−0.869162	+	0.729313i	0.0947596	+	0.995500i	$0.469792\pi$
$278$	8.80397	+	15.2489i	0.528027	+	0.914569i
$279$		0			0
$280$	−5.55431	+	9.62034i	−0.331933	+	0.574925i
$281$	−3.47327	−	19.6979i	−0.207198	−	1.17508i	−0.893944	−	0.448179i	$-0.852073\pi$
$281$	−3.47327	−	19.6979i	−0.207198	−	1.17508i	0.686746	−	0.726897i	$-0.259038\pi$
$282$		0			0
$283$	−15.7352	+	5.72714i	−0.935360	+	0.340443i	−0.764332	−	0.644823i	$-0.776931\pi$
$283$	−15.7352	+	5.72714i	−0.935360	+	0.340443i	−0.171028	+	0.985266i	$0.554709\pi$
$284$	2.59663	−	0.945097i	0.154082	−	0.0560812i
$285$		0			0
$286$	7.82354	+	44.3695i	0.462615	+	2.62362i
$287$	−6.73722	+	11.6692i	−0.397685	+	0.688811i
$288$		0			0
$289$	8.02317	+	13.8965i	0.471951	+	0.817444i
$290$	−16.6987	+	14.0119i	−0.980583	+	0.822807i
$291$		0			0
$292$	−0.389199	+	2.20726i	−0.0227762	+	0.129170i
$293$	14.9930	+	12.5806i	0.875902	+	0.734969i	0.965332	−	0.261024i	$-0.0840602\pi$
$293$	14.9930	+	12.5806i	0.875902	+	0.734969i	−0.0894304	+	0.995993i	$0.528505\pi$
$294$		0			0
$295$	−14.2774	−	5.19653i	−0.831260	−	0.302554i
$296$	3.11549			0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	10.4233	+	3.79377i	0.602794	+	0.219399i
$300$		0			0
$301$	20.9504	+	17.5794i	1.20756	+	1.01326i
$302$	−0.340652	+	1.93193i	−0.0196023	+	0.111170i
$303$		0			0
$304$	−9.75306	+	8.18379i	−0.559377	+	0.469373i
$305$	−1.07906	−	1.86899i	−0.0617870	−	0.107018i
$306$		0			0
$307$	−7.44973	+	12.9033i	−0.425179	+	0.736431i	−0.996437	−	0.0843392i	$-0.973122\pi$
$307$	−7.44973	+	12.9033i	−0.425179	+	0.736431i	0.571258	+	0.820770i	$0.306455\pi$
$308$	0.984416	+	5.58290i	0.0560923	+	0.318115i
$309$		0			0
$310$	2.59930	−	0.946068i	0.147630	−	0.0537331i
$311$	−4.31541	+	1.57068i	−0.244704	+	0.0890651i	−0.461461	−	0.887161i	$-0.652674\pi$
$311$	−4.31541	+	1.57068i	−0.244704	+	0.0890651i	0.216756	+	0.976226i	$0.430452\pi$
$312$		0			0
$313$	2.06098	+	11.6884i	0.116493	+	0.660666i	0.986000	+	0.166745i	$0.0533257\pi$
$313$	2.06098	+	11.6884i	0.116493	+	0.660666i	−0.869507	+	0.493921i	$0.835563\pi$
$314$	2.78836	−	4.82958i	0.157356	−	0.272549i
$315$		0			0
$316$	−1.14408	−	1.98161i	−0.0643597	−	0.111474i
$317$	−11.1209	+	9.33157i	−0.624614	+	0.524113i	−0.899250	−	0.437435i	$-0.855887\pi$
$317$	−11.1209	+	9.33157i	−0.624614	+	0.524113i	0.274636	+	0.961548i	$0.411443\pi$
$318$		0			0
$319$	5.93108	−	33.6368i	0.332077	−	1.88330i
$320$	−6.67009	−	5.59687i	−0.372869	−	0.312874i
$321$		0			0
$322$	6.64992	+	2.42037i	0.370586	+	0.134882i
$323$	−2.62232			−0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−23.6586	−	8.61102i	−1.31033	−	0.476920i
$327$		0			0
$328$	−8.84373	−	7.42077i	−0.488314	−	0.409744i
$329$	−6.03161	+	34.2069i	−0.332533	+	1.88589i
$330$		0			0
$331$	−6.20933	+	5.21024i	−0.341296	+	0.286381i	−0.797284	−	0.603605i	$-0.793730\pi$
$331$	−6.20933	+	5.21024i	−0.341296	+	0.286381i	0.455988	+	0.889986i	$0.349286\pi$
$332$	1.41620	+	2.45292i	0.0777238	+	0.134622i
$333$		0			0
$334$	−11.4313	+	19.7996i	−0.625494	+	1.08339i
$335$	1.35426	+	7.68037i	0.0739909	+	0.419623i
$336$		0			0
$337$	17.6737	−	6.43270i	0.962748	−	0.350412i	0.187638	−	0.982238i	$-0.439917\pi$
$337$	17.6737	−	6.43270i	0.962748	−	0.350412i	0.775110	+	0.631827i	$0.217695\pi$
$338$	−50.8446	+	18.5059i	−2.76558	+	1.00659i
$339$		0			0
$340$	0.139858	+	0.793176i	0.00758488	+	0.0430160i
$341$	−2.16708	+	3.75350i	−0.117354	+	0.203263i
$342$		0			0
$343$	8.72082	+	15.1049i	0.470880	+	0.815588i
$344$	−17.9499	+	15.0618i	−0.967796	+	0.812077i
$345$		0			0
$346$	3.45826	−	19.6128i	0.185917	−	1.05439i
$347$	−13.4959	−	11.3244i	−0.724497	−	0.607925i	0.204128	−	0.978944i	$-0.434564\pi$
$347$	−13.4959	−	11.3244i	−0.724497	−	0.607925i	−0.928625	+	0.371019i	$0.879009\pi$
$348$		0			0
$349$	15.9647	+	5.81068i	0.854572	+	0.311039i	0.731903	−	0.681409i	$-0.238633\pi$
$349$	15.9647	+	5.81068i	0.854572	+	0.311039i	0.122669	+	0.992448i	$0.460855\pi$
$350$	−9.57475			−0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	14.2416	+	5.18352i	0.758004	+	0.275891i	0.691970	−	0.721926i	$-0.256743\pi$
$353$	14.2416	+	5.18352i	0.758004	+	0.275891i	0.0660343	+	0.997817i	$0.478965\pi$
$354$		0			0
$355$	7.23106	+	6.06758i	0.383785	+	0.322034i
$356$	−0.387747	+	2.19902i	−0.0205505	+	0.116548i
$357$		0			0
$358$	0.357779	−	0.300212i	0.0189092	−	0.0158667i
$359$	−1.22548	−	2.12259i	−0.0646783	−	0.112026i	0.831873	−	0.554966i	$-0.187269\pi$
$359$	−1.22548	−	2.12259i	−0.0646783	−	0.112026i	−0.896551	+	0.442940i	$0.853935\pi$
$360$		0			0
$361$	5.89461	−	10.2098i	0.310243	−	0.537356i
$362$	0.389341	+	2.20806i	0.0204633	+	0.116053i
$363$		0			0
$364$	−8.82382	+	3.21161i	−0.462494	+	0.168334i
$365$	−7.19468	+	2.61865i	−0.376587	+	0.137066i
$366$		0			0
$367$	−0.228093	−	1.29358i	−0.0119063	−	0.0675242i	0.978276	−	0.207308i	$-0.0664703\pi$
$367$	−0.228093	−	1.29358i	−0.0119063	−	0.0675242i	−0.990182	+	0.139784i	$0.955359\pi$
$368$	−3.82425	+	6.62379i	−0.199353	+	0.345289i
$369$		0			0
$370$	−1.73314	−	3.00189i	−0.0901017	−	0.156061i
$371$	−15.6332	+	13.1178i	−0.811636	+	0.681043i
$372$		0			0
$373$	−1.67157	+	9.47993i	−0.0865505	+	0.490852i	0.910461	+	0.413595i	$0.135727\pi$
$373$	−1.67157	+	9.47993i	−0.0865505	+	0.490852i	−0.997011	+	0.0772566i	$0.975384\pi$
$374$	−4.90166	−	4.11298i	−0.253459	−	0.212677i
$375$		0			0
$376$	−27.9653	−	10.1785i	−1.44220	−	0.524918i
$377$	56.5753			2.91377
$378$		0			0
$379$	−8.56311			−0.439857			−0.219929	−	0.975516i	$-0.570582\pi$
$379$	−8.56311			−0.439857			−0.219929	+	0.975516i	$0.570582\pi$
$380$	2.08113	+	0.757470i	0.106760	+	0.0388574i
$381$		0			0
$382$	24.9372	+	20.9248i	1.27590	+	1.07060i
$383$	5.84059	−	33.1236i	0.298440	−	1.69254i	−0.354441	−	0.935078i	$-0.615329\pi$
$383$	5.84059	−	33.1236i	0.298440	−	1.69254i	0.652881	−	0.757460i	$-0.273560\pi$
$384$		0			0
$385$	−14.8349	+	12.4480i	−0.756059	+	0.634409i
$386$	16.5385	+	28.6455i	0.841786	+	1.45802i
$387$		0			0
$388$	−2.10681	+	3.64911i	−0.106957	+	0.185255i
$389$	−2.59673	−	14.7268i	−0.131660	−	0.746678i	−0.977128	−	0.212653i	$-0.931790\pi$
$389$	−2.59673	−	14.7268i	−0.131660	−	0.746678i	0.845468	−	0.534026i	$-0.179321\pi$
$390$		0			0
$391$	−1.48034	+	0.538799i	−0.0748639	+	0.0272482i
$392$	1.62096	−	0.589982i	0.0818709	−	0.0297986i
$393$		0			0
$394$	−2.63020	−	14.9166i	−0.132507	−	0.751487i
$395$	3.90824	−	6.76927i	0.196645	−	0.340599i
$396$		0			0
$397$	8.38938	+	14.5308i	0.421051	+	0.729282i	0.996043	−	0.0888774i	$-0.0283279\pi$
$397$	8.38938	+	14.5308i	0.421051	+	0.729282i	−0.574991	+	0.818159i	$0.694995\pi$
$398$	−12.9276	+	10.8475i	−0.648001	+	0.543738i
$399$		0			0
$400$	1.79698	−	10.1912i	0.0898489	−	0.509559i
$401$	10.0553	+	8.43742i	0.502139	+	0.421345i	0.858353	−	0.513060i	$-0.171488\pi$
$401$	10.0553	+	8.43742i	0.502139	+	0.421345i	−0.356214	+	0.934404i	$0.615933\pi$
$402$		0			0
$403$	−6.74612	−	2.45539i	−0.336048	−	0.122311i
$404$	3.83541			0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	5.10369	+	1.85759i	0.252980	+	0.0920773i
$408$		0			0
$409$	19.4962	+	16.3593i	0.964026	+	0.808914i	0.981603	−	0.190932i	$-0.0611509\pi$
$409$	19.4962	+	16.3593i	0.964026	+	0.808914i	−0.0175773	+	0.999846i	$0.505595\pi$
$410$	−2.23044	+	12.6494i	−0.110153	+	0.624711i
$411$		0			0
$412$	−0.815345	+	0.684156i	−0.0401692	+	0.0337059i
$413$	12.5789	+	21.7872i	0.618965	+	1.07208i
$414$		0			0
$415$	−4.83779	+	8.37929i	−0.237478	+	0.411323i
$416$	−3.24912	−	18.4267i	−0.159301	−	0.903442i
$417$		0			0
$418$	−16.5337	+	6.01779i	−0.808692	+	0.294340i
$419$	11.9060	−	4.33341i	0.581644	−	0.211701i	−0.0344063	−	0.999408i	$-0.510954\pi$
$419$	11.9060	−	4.33341i	0.581644	−	0.211701i	0.616050	+	0.787707i	$0.288732\pi$
$420$		0			0
$421$	−3.06962	−	17.4087i	−0.149604	−	0.848447i	−0.963554	−	0.267513i	$-0.913798\pi$
$421$	−3.06962	−	17.4087i	−0.149604	−	0.848447i	0.813950	−	0.580935i	$-0.197313\pi$
$422$	11.8777	−	20.5727i	0.578196	−	1.00147i
$423$		0			0
$424$	−8.74249	−	15.1424i	−0.424573	−	0.735382i
$425$	1.63277	−	1.37006i	0.0792011	−	0.0664576i
$426$		0			0
$427$	−0.620521	+	3.51915i	−0.0300291	+	0.170304i
$428$	−4.73702	−	3.97483i	−0.228972	−	0.192131i
$429$		0			0
$430$	24.4981	+	8.91658i	1.18140	+	0.429996i
$431$	15.6974			0.756117			0.378059	−	0.925782i	$-0.376592\pi$
$431$	15.6974			0.756117			0.378059	+	0.925782i	$0.376592\pi$
$432$		0			0
$433$	−12.6258			−0.606759			−0.303380	−	0.952870i	$-0.598115\pi$
$433$	−12.6258			−0.606759			−0.303380	+	0.952870i	$0.598115\pi$
$434$	−4.30394	−	1.56651i	−0.206596	−	0.0751947i
$435$		0			0
$436$	−4.59739	−	3.85767i	−0.220175	−	0.184749i
$437$	−0.752214	+	4.26602i	−0.0359833	+	0.204071i
$438$		0			0
$439$	20.6349	−	17.3147i	0.984849	−	0.826386i	3.49262e−5	−	1.00000i	$-0.499989\pi$
$439$	20.6349	−	17.3147i	0.984849	−	0.826386i	0.984814	+	0.173614i	$0.0555444\pi$
$440$	−8.29608	−	14.3692i	−0.395500	−	0.685027i
$441$		0			0
$442$	5.29934	−	9.17873i	0.252064	−	0.436588i
$443$	6.03044	+	34.2003i	0.286515	+	1.62491i	0.699824	+	0.714315i	$0.253262\pi$
$443$	6.03044	+	34.2003i	0.286515	+	1.62491i	−0.413310	+	0.910591i	$0.635627\pi$
$444$		0			0
$445$	−7.16783	+	2.60888i	−0.339788	+	0.123673i
$446$	18.2259	−	6.63369i	0.863022	−	0.314114i
$447$		0			0
$448$	2.50355	+	14.1984i	0.118282	+	0.670810i
$449$	10.3731	−	17.9667i	0.489535	−	0.847900i	−0.510392	−	0.859942i	$-0.670500\pi$
$449$	10.3731	−	17.9667i	0.489535	−	0.847900i	0.999927	+	0.0120419i	$0.00383314\pi$
$450$		0			0
$451$	−10.0629	−	17.4295i	−0.473844	−	0.820722i
$452$	−0.169695	+	0.142391i	−0.00798179	+	0.00669752i
$453$		0			0
$454$	1.02853	−	5.83307i	0.0482712	−	0.273760i
$455$	−24.5725	−	20.6187i	−1.15197	−	0.966621i
$456$		0			0
$457$	6.77305	+	2.46519i	0.316830	+	0.115317i	0.495540	−	0.868585i	$-0.334970\pi$
$457$	6.77305	+	2.46519i	0.316830	+	0.115317i	−0.178710	+	0.983902i	$0.557192\pi$
$458$	−29.3621			−1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	−21.7321	−	7.90984i	−1.01217	−	0.368398i	−0.217902	−	0.975971i	$-0.569921\pi$
$461$	−21.7321	−	7.90984i	−1.01217	−	0.368398i	−0.794264	+	0.607573i	$0.792143\pi$
$462$		0			0
$463$	3.81172	+	3.19841i	0.177145	+	0.148643i	0.727049	−	0.686585i	$-0.240891\pi$
$463$	3.81172	+	3.19841i	0.177145	+	0.148643i	−0.549904	+	0.835228i	$0.685336\pi$
$464$	−6.77414	+	38.4180i	−0.314481	+	1.78351i
$465$		0			0
$466$	0.659922	−	0.553741i	0.0305703	−	0.0256515i
$467$	6.24068	+	10.8092i	0.288784	+	0.500189i	0.973520	−	0.228602i	$-0.0734156\pi$
$467$	6.24068	+	10.8092i	0.288784	+	0.500189i	−0.684735	+	0.728792i	$0.740082\pi$
$468$		0			0
$469$	6.45669	−	11.1833i	0.298142	−	0.516397i
$470$	5.74966	+	32.6079i	0.265212	+	1.50409i
$471$		0			0
$472$	−20.2548	+	7.37215i	−0.932303	+	0.339331i
$473$	−38.3855	+	13.9712i	−1.76497	+	0.642395i
$474$		0			0
$475$	−1.01774	−	5.77190i	−0.0466972	−	0.264833i
$476$	0.666803	−	1.15494i	0.0305628	−	0.0529364i
$477$		0			0
$478$	15.8588	+	27.4683i	0.725365	+	1.25637i
$479$	21.8103	−	18.3010i	0.996536	−	0.836193i	0.0100353	−	0.999950i	$-0.496806\pi$
$479$	21.8103	−	18.3010i	0.996536	−	0.836193i	0.986501	+	0.163757i	$0.0523612\pi$
$480$		0			0
$481$	−1.56218	+	8.85956i	−0.0712293	+	0.403961i
$482$	18.4891	+	15.5142i	0.842157	+	0.706654i
$483$		0			0
$484$	−2.87778	−	1.04743i	−0.130808	−	0.0476103i
$485$	−14.3939			−0.653595
$486$		0			0
$487$	29.6841			1.34511			0.672557	−	0.740045i	$-0.265196\pi$
$487$	29.6841			1.34511			0.672557	+	0.740045i	$0.265196\pi$
$488$	−2.87702	−	1.04715i	−0.130237	−	0.0474023i
$489$		0			0
$490$	−1.47021	−	1.23365i	−0.0664172	−	0.0557307i
$491$	2.15410	−	12.2165i	0.0972131	−	0.551323i	−0.896834	−	0.442368i	$-0.854139\pi$
$491$	2.15410	−	12.2165i	0.0972131	−	0.551323i	0.994047	−	0.108955i	$-0.0347503\pi$
$492$		0			0
$493$	−6.15512	+	5.16476i	−0.277213	+	0.232609i
$494$	−14.5720	−	25.2394i	−0.655623	−	1.13557i
$495$		0			0
$496$	2.47512	−	4.28702i	0.111136	−	0.192493i
$497$	−2.71411	−	15.3925i	−0.121745	−	0.690448i
$498$		0			0
$499$	2.14233	−	0.779745i	0.0959040	−	0.0349062i	−0.293623	−	0.955921i	$-0.594861\pi$
$499$	2.14233	−	0.779745i	0.0959040	−	0.0349062i	0.389527	+	0.921015i	$0.372639\pi$
$500$	−5.56662	+	2.02608i	−0.248947	+	0.0906092i
$501$		0			0
$502$	3.49634	+	19.8287i	0.156049	+	0.885000i
$503$	−20.6406	+	35.7506i	−0.920320	+	1.59404i	−0.121399	+	0.992604i	$0.538738\pi$
$503$	−20.6406	+	35.7506i	−0.920320	+	1.59404i	−0.798920	+	0.601437i	$0.794595\pi$
$504$		0			0
$505$	6.55097	+	11.3466i	0.291514	+	0.504917i
$506$	−8.09708	+	6.79425i	−0.359959	+	0.302041i
$507$		0			0
$508$	−0.0453128	+	0.256982i	−0.00201043	+	0.0114017i
$509$	12.5816	+	10.5572i	0.557671	+	0.467941i	0.877529	−	0.479524i	$-0.159191\pi$
$509$	12.5816	+	10.5572i	0.557671	+	0.467941i	−0.319858	+	0.947466i	$0.603635\pi$
$510$		0			0
$511$	11.9130	+	4.33597i	0.527000	+	0.191812i
$512$	−9.67844			−0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	−3.41662	−	1.24355i	−0.150554	−	0.0547973i
$516$		0			0
$517$	−39.7429	−	33.3483i	−1.74789	−	1.46666i
$518$	−0.996651	+	5.65229i	−0.0437903	+	0.248347i
$519$		0			0
$520$	21.0533	−	17.6658i	0.923248	−	0.774697i
$521$	4.64836	+	8.05119i	0.203648	+	0.352729i	0.949701	−	0.313157i	$-0.101387\pi$
$521$	4.64836	+	8.05119i	0.203648	+	0.352729i	−0.746053	+	0.665887i	$0.768053\pi$
$522$		0			0
$523$	11.3736	−	19.6996i	0.497331	−	0.861402i	−0.502664	−	0.864482i	$-0.667647\pi$
$523$	11.3736	−	19.6996i	0.497331	−	0.861402i	0.999995	+	0.00307938i	$0.000980199\pi$
$524$	0.974059	+	5.52416i	0.0425520	+	0.241324i
$525$		0			0
$526$	14.1116	−	5.13619i	0.615293	−	0.223949i
$527$	0.958098	−	0.348719i	0.0417354	−	0.0151905i
$528$		0			0
$529$	−3.54202	−	20.0878i	−0.154001	−	0.873382i
$530$	−9.72687	+	16.8474i	−0.422508	+	0.731806i
$531$		0			0
$532$	−1.83355	−	3.17581i	−0.0794946	−	0.137689i
$533$	25.5370	−	21.4281i	1.10613	−	0.928155i
$534$		0			0
$535$	3.66813	−	20.8030i	0.158587	−	0.899393i
$536$	8.47549	+	7.11178i	0.366086	+	0.307182i
$537$		0			0
$538$	−32.8395	−	11.9526i	−1.41581	−	0.515314i
$539$	3.00718			0.129528
$540$		0			0
$541$	2.38959			0.102737			0.0513683	−	0.998680i	$-0.483642\pi$
$541$	2.38959			0.102737			0.0513683	+	0.998680i	$0.483642\pi$
$542$	−41.4747	−	15.0956i	−1.78149	−	0.648410i
$543$		0			0
$544$	2.03566	+	1.70812i	0.0872783	+	0.0732352i
$545$	3.56001	−	20.1898i	0.152494	−	0.864837i
$546$		0			0
$547$	22.7261	−	19.0694i	0.971697	−	0.815350i	−0.0111192	−	0.999938i	$-0.503539\pi$
$547$	22.7261	−	19.0694i	0.971697	−	0.815350i	0.982816	+	0.184588i	$0.0590950\pi$
$548$	−1.03904	−	1.79967i	−0.0443856	−	0.0768781i
$549$		0			0
$550$	7.15057	−	12.3852i	0.304901	−	0.528105i
$551$	3.83662	+	21.7586i	0.163446	+	0.926946i
$552$		0			0
$553$	−12.1620	+	4.42662i	−0.517182	+	0.188239i
$554$	28.0085	−	10.1943i	1.18997	−	0.433113i
$555$		0			0
$556$	−0.951832	−	5.39811i	−0.0403667	−	0.228931i
$557$	−4.20706	+	7.28685i	−0.178259	+	0.308754i	−0.941284	−	0.337615i	$-0.890380\pi$
$557$	−4.20706	+	7.28685i	−0.178259	+	0.308754i	0.763025	+	0.646369i	$0.223713\pi$
$558$		0			0
$559$	−33.8309	−	58.5969i	−1.43090	−	2.47838i
$560$	16.9436	−	14.2174i	0.715998	−	0.600794i
$561$		0			0
$562$	−5.48222	+	31.0912i	−0.231253	+	1.31150i
$563$	−20.8567	−	17.5009i	−0.879006	−	0.737573i	0.0869687	−	0.996211i	$-0.472282\pi$
$563$	−20.8567	−	17.5009i	−0.879006	−	0.737573i	−0.965974	+	0.258638i	$0.916726\pi$
$564$		0			0
$565$	−0.711090	−	0.258816i	−0.0299158	−	0.0108885i
$566$	26.4304			1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	20.6256	+	7.50711i	0.864670	+	0.314714i	0.736007	−	0.676974i	$-0.236709\pi$
$569$	20.6256	+	7.50711i	0.864670	+	0.314714i	0.128664	+	0.991688i	$0.458931\pi$
$570$		0			0
$571$	−34.3597	−	28.8313i	−1.43791	−	1.20655i	−0.940845	−	0.338837i	$-0.889966\pi$
$571$	−34.3597	−	28.8313i	−1.43791	−	1.20655i	−0.497066	−	0.867713i	$-0.665589\pi$
$572$	2.43548	−	13.8123i	0.101833	−	0.577521i
$573$		0			0
$574$	16.2923	−	13.6709i	0.680028	−	0.570611i
$575$	−1.76046	−	3.04921i	−0.0734163	−	0.127161i
$576$		0			0
$577$	−6.00955	+	10.4088i	−0.250181	+	0.433326i	−0.963575	−	0.267437i	$-0.913823\pi$
$577$	−6.00955	+	10.4088i	−0.250181	+	0.433326i	0.713395	+	0.700762i	$0.247157\pi$
$578$	−4.39810	−	24.9428i	−0.182937	−	1.03749i
$579$		0			0
$580$	6.37671	−	2.32093i	0.264778	−	0.0963715i
$581$	15.0547	−	5.47946i	0.624574	−	0.227326i
$582$		0			0
$583$	−5.29307	−	30.0185i	−0.219217	−	1.24324i
$584$	−5.43095	+	9.40669i	−0.224734	+	0.389252i
$585$		0			0
$586$	−15.4463	−	26.7537i	−0.638079	−	1.10519i
$587$	−13.0456	+	10.9466i	−0.538451	+	0.451814i	−0.871008	−	0.491269i	$-0.836533\pi$
$587$	−13.0456	+	10.9466i	−0.538451	+	0.451814i	0.332557	+	0.943083i	$0.392089\pi$
$588$		0			0
$589$	0.486845	−	2.76103i	0.0200601	−	0.113766i
$590$	18.3711	+	15.4151i	0.756324	+	0.634631i
$591$		0			0
$592$	−5.82913	−	2.12163i	−0.239576	−	0.0871985i
$593$	−14.9284			−0.613037			−0.306519	−	0.951865i	$-0.599164\pi$
$593$	−14.9284			−0.613037			−0.306519	+	0.951865i	$0.599164\pi$
$594$		0			0
$595$	4.55566			0.186764
$596$	8.99338	+	3.27332i	0.368383	+	0.134081i
$597$		0			0
$598$	−13.4119	−	11.2539i	−0.548454	−	0.460208i
$599$	2.35029	−	13.3292i	0.0960304	−	0.544615i	−0.898396	−	0.439186i	$-0.855267\pi$
$599$	2.35029	−	13.3292i	0.0960304	−	0.544615i	0.994427	−	0.105430i	$-0.0336218\pi$
$600$		0			0
$601$	−34.7150	+	29.1294i	−1.41606	+	1.18821i	−0.462642	+	0.886545i	$0.653099\pi$
$601$	−34.7150	+	29.1294i	−1.41606	+	1.18821i	−0.953413	+	0.301667i	$0.902457\pi$
$602$	−21.5837	−	37.3841i	−0.879686	−	1.52366i
$603$		0			0
$604$	0.305346	−	0.528874i	0.0124243	−	0.0215196i
$605$	−1.81663	−	10.3026i	−0.0738564	−	0.418861i
$606$		0			0
$607$	−22.9631	+	8.35787i	−0.932042	+	0.339236i	−0.763019	−	0.646376i	$-0.776284\pi$
$607$	−22.9631	+	8.35787i	−0.932042	+	0.339236i	−0.169024	+	0.985612i	$0.554061\pi$
$608$	6.86647	−	2.49919i	0.278472	−	0.101356i
$609$		0			0
$610$	0.591515	+	3.35465i	0.0239497	+	0.135826i
$611$	42.9674	−	74.4217i	1.73827	−	3.01078i
$612$		0			0
$613$	12.5998	+	21.8235i	0.508901	+	0.881443i	0.999947	+	0.0103088i	$0.00328145\pi$
$613$	12.5998	+	21.8235i	0.508901	+	0.881443i	−0.491046	+	0.871134i	$0.663385\pi$
$614$	18.0154	−	15.1167i	0.727041	−	0.610059i
$615$		0			0
$616$	−4.77071	+	27.0560i	−0.192217	+	1.09012i
$617$	3.09624	+	2.59805i	0.124650	+	0.104594i	0.702982	−	0.711208i	$-0.251852\pi$
$617$	3.09624	+	2.59805i	0.124650	+	0.104594i	−0.578332	+	0.815802i	$0.696296\pi$
$618$		0			0
$619$	42.0700	+	15.3122i	1.69094	+	0.615451i	0.994743	−	0.102403i	$-0.0326530\pi$
$619$	42.0700	+	15.3122i	1.69094	+	0.615451i	0.696194	+	0.717853i	$0.254875\pi$
$620$	−0.861097			−0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	11.8685	+	4.31979i	0.475502	+	0.173069i
$624$		0			0
$625$	−7.14194	−	5.99280i	−0.285678	−	0.239712i
$626$	3.25305	−	18.4490i	0.130018	−	0.737369i
$627$		0			0
$628$	−1.32989	+	1.11591i	−0.0530682	+	0.0445295i
$629$	−0.638833	−	1.10649i	−0.0254719	−	0.0441187i
$630$		0			0
$631$	−15.7058	+	27.2033i	−0.625238	+	1.08294i	0.363256	+	0.931689i	$0.381665\pi$
$631$	−15.7058	+	27.2033i	−0.625238	+	1.08294i	−0.988495	+	0.151255i	$0.951668\pi$
$632$	−1.92558	−	10.9205i	−0.0765955	−	0.434395i
$633$		0			0
$634$	21.5323	−	7.83713i	0.855159	−	0.311252i
$635$	−0.837645	+	0.304878i	−0.0332409	+	0.0120987i
$636$		0			0
$637$	0.864952	+	4.90539i	0.0342707	+	0.194359i
$638$	−26.9558	+	46.6888i	−1.06719	+	1.84843i
$639$		0			0
$640$	11.4392	+	19.8133i	0.452176	+	0.783191i
$641$	37.2609	−	31.2656i	1.47172	−	1.23492i	0.557192	−	0.830384i	$-0.311879\pi$
$641$	37.2609	−	31.2656i	1.47172	−	1.23492i	0.914524	−	0.404533i	$-0.132566\pi$
$642$		0			0
$643$	−4.86777	+	27.6065i	−0.191966	+	1.08869i	0.724708	+	0.689057i	$0.241975\pi$
$643$	−4.86777	+	27.6065i	−0.191966	+	1.08869i	−0.916674	+	0.399637i	$0.869136\pi$
$644$	−1.68759	−	1.41605i	−0.0665003	−	0.0558003i
$645$		0			0
$646$	3.88947	+	1.41565i	0.153029	+	0.0556980i
$647$	−37.5519			−1.47632			−0.738159	−	0.674627i	$-0.764304\pi$
$647$	−37.5519			−1.47632			−0.738159	+	0.674627i	$0.764304\pi$
$648$		0			0
$649$	−37.5763			−1.47500
$650$	22.2597	+	8.10187i	0.873097	+	0.317781i
$651$		0			0
$652$	6.00397	+	5.03793i	0.235134	+	0.197300i
$653$	−0.887728	+	5.03455i	−0.0347395	+	0.197017i	−0.997238	−	0.0742686i	$-0.976338\pi$
$653$	−0.887728	+	5.03455i	−0.0347395	+	0.197017i	0.962499	+	0.271286i	$0.0874489\pi$
$654$		0			0
$655$	−14.6789	+	12.3170i	−0.573551	+	0.481266i
$656$	11.4933	+	19.9069i	0.448737	+	0.777236i
$657$		0			0
$658$	27.4126	−	47.4801i	1.06866	−	1.85097i
$659$	6.07871	+	34.4741i	0.236793	+	1.34292i	0.838805	+	0.544433i	$0.183255\pi$
$659$	6.07871	+	34.4741i	0.236793	+	1.34292i	−0.602012	+	0.798487i	$0.705634\pi$
$660$		0			0
$661$	−1.25304	+	0.456071i	−0.0487378	+	0.0177391i	−0.366274	−	0.930507i	$-0.619367\pi$
$661$	−1.25304	+	0.456071i	−0.0487378	+	0.0177391i	0.317536	+	0.948246i	$0.397144\pi$
$662$	12.0225	−	4.37583i	0.467268	−	0.170071i
$663$		0			0
$664$	2.38357	+	13.5179i	0.0925004	+	0.524596i
$665$	6.26350	−	10.8487i	0.242888	−	0.420694i
$666$		0			0
$667$	6.63648	+	11.4947i	0.256966	+	0.445077i
$668$	5.45207	−	4.57483i	0.210947	−	0.177006i
$669$		0			0
$670$	2.13756	−	12.1227i	0.0825813	−	0.468342i
$671$	−4.08869	−	3.43081i	−0.157842	−	0.132445i
$672$		0			0
$673$	3.36366	+	1.22427i	0.129659	+	0.0471922i	0.406035	−	0.913858i	$-0.366911\pi$
$673$	3.36366	+	1.22427i	0.129659	+	0.0471922i	−0.276375	+	0.961050i	$0.589133\pi$
$674$	−29.6866			−1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	34.7112	+	12.6338i	1.33406	+	0.485558i	0.907937	−	0.419107i	$-0.137657\pi$
$677$	34.7112	+	12.6338i	1.33406	+	0.485558i	0.426123	+	0.904665i	$0.359879\pi$
$678$		0			0
$679$	18.2576	+	15.3199i	0.700661	+	0.587925i
$680$	−0.677786	+	3.84391i	−0.0259919	+	0.147407i
$681$		0			0
$682$	5.24056	−	4.39735i	0.200671	−	0.168383i
$683$	−19.0083	−	32.9233i	−0.727332	−	1.25978i	−0.958007	−	0.286745i	$-0.907427\pi$
$683$	−19.0083	−	32.9233i	−0.727332	−	1.25978i	0.230675	−	0.973031i	$-0.425907\pi$
$684$		0			0
$685$	3.54941	−	6.14775i	0.135616	−	0.234894i
$686$	−4.78053	−	27.1117i	−0.182521	−	1.03513i
$687$		0			0
$688$	43.8417	−	15.9571i	1.67145	−	0.608357i
$689$	47.4445	−	17.2684i	1.80749	−	0.657873i
$690$		0			0
$691$	0.0955871	+	0.542101i	0.00363630	+	0.0206225i	0.986572	−	0.163327i	$-0.0522227\pi$
$691$	0.0955871	+	0.542101i	0.00363630	+	0.0206225i	−0.982936	+	0.183950i	$0.941112\pi$
$692$	−3.09984	+	5.36908i	−0.117838	+	0.204102i
$693$		0			0
$694$	13.9039	+	24.0822i	0.527784	+	0.914148i
$695$	14.3439	−	12.0360i	0.544095	−	0.456550i
$696$		0			0
$697$	−0.822135	+	4.66256i	−0.0311406	+	0.176607i
$698$	−20.5422	−	17.2370i	−0.777535	−	0.652429i
$699$		0			0
$700$	2.80088	+	1.01944i	0.105863	+	0.0385311i
$701$	19.0242			0.718534			0.359267	−	0.933235i	$-0.383027\pi$
$701$	19.0242			0.718534			0.359267	+	0.933235i	$0.383027\pi$
$702$		0			0
$703$	−3.51328			−0.132506
$704$	−20.2356	−	7.36515i	−0.762658	−	0.277585i
$705$		0			0
$706$	−18.3251	−	15.3765i	−0.689673	−	0.578704i
$707$	3.76717	−	21.3647i	0.141679	−	0.803501i
$708$		0			0
$709$	9.31264	−	7.81423i	0.349743	−	0.293470i	−0.450944	−	0.892552i	$-0.648912\pi$
$709$	9.31264	−	7.81423i	0.349743	−	0.293470i	0.800687	+	0.599083i	$0.204468\pi$
$710$	−7.44966	−	12.9032i	−0.279581	−	0.484248i
$711$		0			0
$712$	−5.41068	+	9.37158i	−0.202774	+	0.351215i
$713$	−0.292469	−	1.65867i	−0.0109530	−	0.0621178i
$714$		0			0
$715$	45.0219	−	16.3866i	1.68372	−	0.612825i
$716$	−0.136624	+	0.0497272i	−0.00510589	+	0.00185839i
$717$		0			0
$718$	0.671776	+	3.80983i	0.0250704	+	0.142182i
$719$	−4.88834	+	8.46685i	−0.182304	+	0.315760i	−0.942665	−	0.333741i	$-0.891689\pi$
$719$	−4.88834	+	8.46685i	−0.182304	+	0.315760i	0.760361	+	0.649501i	$0.225022\pi$
$720$		0			0
$721$	3.01017	+	5.21376i	0.112104	+	0.194171i
$722$	−14.2547	+	11.9611i	−0.530504	+	0.445146i
$723$		0			0
$724$	0.121203	−	0.687374i	0.00450446	−	0.0255460i
$725$	−13.7568	−	11.5434i	−0.510916	−	0.428709i
$726$		0			0
$727$	−4.07350	−	1.48263i	−0.151078	−	0.0549878i	0.265374	−	0.964145i	$-0.414504\pi$
$727$	−4.07350	−	1.48263i	−0.151078	−	0.0549878i	−0.416452	+	0.909158i	$0.636727\pi$
$728$	−45.5067			−1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	9.02996	+	3.28664i	0.333985	+	0.121561i
$732$		0			0
$733$	22.3636	+	18.7653i	0.826020	+	0.693113i	0.954374	−	0.298615i	$-0.0965248\pi$
$733$	22.3636	+	18.7653i	0.826020	+	0.693113i	−0.128354	+	0.991728i	$0.540969\pi$
$734$	−0.360022	+	2.04179i	−0.0132887	+	0.0753638i
$735$		0			0
$736$	3.36272	−	2.82166i	0.123952	−	0.104008i
$737$	9.64391	+	16.7037i	0.355238	+	0.615290i
$738$		0			0
$739$	−20.7777	+	35.9880i	−0.764319	+	1.32384i	0.176287	+	0.984339i	$0.443591\pi$
$739$	−20.7777	+	35.9880i	−0.764319	+	1.32384i	−0.940606	+	0.339501i	$0.889742\pi$
$740$	0.187377	+	1.06267i	0.00688810	+	0.0390644i
$741$		0			0
$742$	30.2690	−	11.0170i	1.11121	−	0.404447i
$743$	−20.0881	+	7.31149i	−0.736963	+	0.268232i	−0.683109	−	0.730316i	$-0.739373\pi$
$743$	−20.0881	+	7.31149i	−0.736963	+	0.268232i	−0.0538536	+	0.998549i	$0.517150\pi$
$744$		0			0
$745$	5.67716	+	32.1968i	0.207995	+	1.17960i
$746$	7.59699	−	13.1584i	0.278146	−	0.481763i
$747$		0			0
$748$	0.995957	+	1.72505i	0.0364158	+	0.0630740i
$749$	−26.7940	+	22.4829i	−0.979033	+	0.821506i
$750$		0			0
$751$	−6.94030	+	39.3604i	−0.253255	+	1.43628i	0.547256	+	0.836965i	$0.315672\pi$
$751$	−6.94030	+	39.3604i	−0.253255	+	1.43628i	−0.800512	+	0.599317i	$0.795439\pi$
$752$	45.3921	+	38.0885i	1.65528	+	1.38894i
$753$		0			0
$754$	−83.9132	−	30.5419i	−3.05594	−	1.11227i
$755$	2.08615			0.0759228
$756$		0			0
$757$	6.68348			0.242915			0.121458	−	0.992597i	$-0.461243\pi$
$757$	6.68348			0.242915			0.121458	+	0.992597i	$0.461243\pi$
$758$	12.7009	+	4.62276i	0.461319	+	0.167906i
$759$		0			0
$760$	8.22190	+	6.89899i	0.298240	+	0.250253i
$761$	7.29757	−	41.3866i	0.264537	−	1.50026i	−0.505815	−	0.862642i	$-0.668808\pi$
$761$	7.29757	−	41.3866i	0.264537	−	1.50026i	0.770351	−	0.637620i	$-0.220081\pi$
$762$		0			0
$763$	−26.0043	+	21.8202i	−0.941417	+	0.789943i
$764$	−5.06692	−	8.77617i	−0.183315	−	0.317511i
$765$		0			0
$766$	−26.5445	+	45.9764i	−0.959092	+	1.66120i
$767$	−10.8081	−	61.2955i	−0.390256	−	2.21325i
$768$		0			0
$769$	−2.26770	+	0.825374i	−0.0817752	+	0.0297637i	−0.382584	−	0.923921i	$-0.624966\pi$
$769$	−2.26770	+	0.825374i	−0.0817752	+	0.0297637i	0.300809	+	0.953685i	$0.402743\pi$
$770$	28.7234	−	10.4545i	1.03512	−	0.376753i
$771$		0			0
$772$	−1.78804	−	10.1405i	−0.0643529	−	0.364964i
$773$	−0.698900	+	1.21053i	−0.0251377	+	0.0435398i	−0.878321	−	0.478072i	$-0.841336\pi$
$773$	−0.698900	+	1.21053i	−0.0251377	+	0.0435398i	0.853183	+	0.521612i	$0.174669\pi$
$774$		0			0
$775$	1.13940	+	1.97350i	0.0409284	+	0.0708901i
$776$	−15.6428	+	13.1259i	−0.561544	+	0.471191i
$777$		0			0
$778$	−4.09869	+	23.2448i	−0.146945	+	0.833368i
$779$	9.97293	+	8.36828i	0.357317	+	0.299825i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.48321 - 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(-0.291470 + 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(1.19062 + 2.06222i) q^{8} +O(q^{10})\)	\(q+(-1.48321 - 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(-0.291470 + 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(1.19062 + 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(0.720852 + 4.08816i) q^{11} +(-6.46137 + 2.35175i) q^{13} +(-4.12227 + 1.50038i) q^{14} +(-0.823316 - 4.66925i) q^{16} +(0.488276 - 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(-0.631796 + 0.530140i) q^{20} +(1.13780 - 6.45276i) q^{22} +(-1.23576 - 1.03693i) q^{23} +(2.05098 + 0.746497i) q^{25} +10.8532 q^{26} +1.36563 q^{28} +(-7.73168 - 2.81410i) q^{29} +(0.799803 + 0.671115i) q^{31} +(-0.472527 + 2.67984i) q^{32} +(-1.18078 + 0.990788i) q^{34} +(2.33252 + 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(0.736003 + 4.17408i) q^{38} +(-3.75589 + 1.36703i) q^{40} +(-4.55579 + 1.65817i) q^{41} +(1.70874 + 9.69073i) q^{43} +(-1.01987 + 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(-9.57379 + 8.03337i) q^{47} +(0.125792 - 0.713402i) q^{49} +(-2.63906 - 2.21443i) q^{50} +(-3.17486 - 1.15555i) q^{52} -7.34280 q^{53} -6.96786 q^{55} +(6.21903 + 2.26354i) q^{56} +(9.94855 + 8.34783i) q^{58} +(-1.57184 + 8.91436i) q^{59} +(-0.984935 + 0.826459i) q^{61} +(-0.823982 - 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(-2.00416 - 11.3662i) q^{65} +(4.36609 - 1.58913i) q^{67} +(0.450900 - 0.164114i) q^{68} +(-1.27863 - 7.25146i) q^{70} +(2.81187 - 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(-1.58196 + 1.32742i) q^{74} +(0.229119 - 1.29940i) q^{76} +(8.83817 + 7.41611i) q^{77} +(-4.37596 - 1.59272i) q^{79} +7.95828 q^{80} +7.65237 q^{82} +(5.41676 + 1.97154i) q^{83} +(1.25566 + 1.05362i) q^{85} +(2.69708 - 15.2959i) q^{86} +(-7.57240 + 6.35400i) q^{88} +(2.27221 + 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(-0.137642 - 0.780605i) q^{92} +(18.5368 - 6.74683i) q^{94} +(4.23546 - 1.54158i) q^{95} +(1.48911 + 8.44516i) q^{97} +(-0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more