LMFDB - Embedded newform 729.2.e.g.406.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.g.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 + 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(3.64543 + 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(1.41875 - 2.45734i) q^{8} +O(q^{10})$	\(q+(0.673648 + 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(3.64543 + 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(1.41875 - 2.45734i) q^{8} +(1.70574 + 2.95442i) q^{10} +(0.152704 - 0.0555796i) q^{11} +(1.84730 - 1.55007i) q^{13} +(-1.47178 + 1.23497i) q^{14} +(0.0393628 - 0.0143269i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.79813 + 3.11446i) q^{19} +(0.826352 - 4.68647i) q^{20} +(0.134285 + 0.0488759i) q^{22} +(-0.492726 - 2.79439i) q^{23} +(7.69846 + 6.45978i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(-5.14543 - 4.31753i) q^{29} +(-0.900330 - 5.10602i) q^{31} +(-5.29813 - 1.92836i) q^{32} +(-0.458111 + 2.59808i) q^{34} +(-4.23783 + 7.34013i) q^{35} +(3.31908 + 5.74881i) q^{37} +(-2.97178 + 1.08164i) q^{38} +(8.43242 - 7.07564i) q^{40} +(4.44356 - 3.72859i) q^{41} +(5.85117 - 2.12965i) q^{43} +(-0.0996702 - 0.172634i) q^{44} +(1.24763 - 2.16095i) q^{46} +(-1.28446 + 7.28455i) q^{47} +(2.09240 + 0.761570i) q^{49} +(1.53462 + 8.70323i) q^{50} +(-2.26604 - 1.90144i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(4.74897 + 3.98486i) q^{56} +(-1.02569 - 5.81699i) q^{58} +(-4.81180 - 1.75135i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(2.27972 - 3.94858i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(8.79086 - 3.19961i) q^{65} +(-4.49273 + 3.76984i) q^{67} +(2.81908 - 2.36549i) q^{68} +(-7.00387 + 2.54920i) q^{70} +(-7.65910 - 13.2660i) q^{71} +(-4.34002 + 7.51714i) q^{73} +(-1.01367 + 5.74881i) q^{74} +(4.14543 + 1.50881i) q^{76} +(0.0616516 + 0.349643i) q^{77} +(-0.971782 - 0.815422i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(6.49273 + 5.44804i) q^{83} +(2.02094 + 11.4613i) q^{85} +(5.14543 + 1.87278i) q^{86} +(0.0800699 - 0.454099i) q^{88} +(3.86097 - 6.68739i) q^{89} +(2.63429 + 4.56272i) q^{91} +(-3.27079 + 1.19047i) q^{92} +(-4.98293 + 4.18117i) q^{94} +(-10.6873 + 8.96773i) q^{95} +(3.67112 - 1.33618i) q^{97} +(0.979055 + 1.69577i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29} + 9 q^{31} - 18 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} - 3 q^{38} + 27 q^{40} - 3 q^{41} + 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} + 9 q^{49} - 15 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 3 q^{56} - 36 q^{58} + 6 q^{59} + 18 q^{61} - 12 q^{62} - 12 q^{64} + 21 q^{65} - 9 q^{67} - 18 q^{70} - 9 q^{71} - 6 q^{73} + 15 q^{74} + 9 q^{76} - 3 q^{77} + 9 q^{79} + 6 q^{80} + 36 q^{82} + 21 q^{83} + 9 q^{85} + 15 q^{86} + 9 q^{88} + 6 q^{91} - 48 q^{92} - 9 q^{94} - 42 q^{95} + 36 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.673648	+	0.565258i	0.476341	+	0.399698i	0.849101	−	0.528230i	$-0.177144\pi$
$2$	0.673648	+	0.565258i	0.476341	+	0.399698i	−0.372760	+	0.927928i	$0.621589\pi$
$3$		0			0
$3$		0			0
$4$	−0.213011	−	1.20805i	−0.106506	−	0.604023i
$5$	3.64543	+	1.32683i	1.63029	+	0.593375i	0.985302	−	0.170821i	$-0.0546420\pi$
$5$	3.64543	+	1.32683i	1.63029	+	0.593375i	0.644984	+	0.764196i	$0.276864\pi$
$6$		0			0
$7$	−0.379385	+	2.15160i	−0.143394	+	0.813229i	0.825248	+	0.564770i	$0.191035\pi$
$7$	−0.379385	+	2.15160i	−0.143394	+	0.813229i	−0.968643	+	0.248459i	$0.920076\pi$
$8$	1.41875	−	2.45734i	0.501603	−	0.868802i
$9$		0			0
$10$	1.70574	+	2.95442i	0.539401	+	0.934271i
$11$	0.152704	−	0.0555796i	0.0460419	−	0.0167579i	−0.318897	−	0.947790i	$-0.603312\pi$
$11$	0.152704	−	0.0555796i	0.0460419	−	0.0167579i	0.364938	+	0.931032i	$0.381090\pi$
$12$		0			0
$13$	1.84730	−	1.55007i	0.512348	−	0.429911i	−0.349607	−	0.936897i	$-0.613685\pi$
$13$	1.84730	−	1.55007i	0.512348	−	0.429911i	0.861954	+	0.506986i	$0.169240\pi$
$14$	−1.47178	+	1.23497i	−0.393350	+	0.330060i
$15$		0			0
$16$	0.0393628	−	0.0143269i	0.00984071	−	0.00358173i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	−0.995165	−	0.0982214i	$-0.968685\pi$
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	0.582645	+	0.812727i	$0.302018\pi$
$20$	0.826352	−	4.68647i	0.184778	−	1.04793i
$21$		0			0
$22$	0.134285	+	0.0488759i	0.0286297	+	0.0104204i
$23$	−0.492726	−	2.79439i	−0.102740	−	0.582670i	−0.992099	−	0.125459i	$-0.959960\pi$
$23$	−0.492726	−	2.79439i	−0.102740	−	0.582670i	0.889358	−	0.457211i	$-0.151152\pi$
$24$		0			0
$25$	7.69846	+	6.45978i	1.53969	+	1.29196i
$26$	2.12061			0.415887
$27$		0			0
$28$	2.68004			0.506481
$29$	−5.14543	−	4.31753i	−0.955482	−	0.801745i	0.0247300	−	0.999694i	$-0.492127\pi$
$29$	−5.14543	−	4.31753i	−0.955482	−	0.801745i	−0.980212	+	0.197949i	$0.936572\pi$
$30$		0			0
$31$	−0.900330	−	5.10602i	−0.161704	−	0.917069i	−0.952398	−	0.304857i	$-0.901391\pi$
$31$	−0.900330	−	5.10602i	−0.161704	−	0.917069i	0.790694	−	0.612212i	$-0.209720\pi$
$32$	−5.29813	−	1.92836i	−0.936587	−	0.340890i
$33$		0			0
$34$	−0.458111	+	2.59808i	−0.0785654	+	0.445566i
$35$	−4.23783	+	7.34013i	−0.716323	+	1.24071i
$36$		0			0
$37$	3.31908	+	5.74881i	0.545653	+	0.945099i	0.998566	+	0.0535438i	$0.0170517\pi$
$37$	3.31908	+	5.74881i	0.545653	+	0.945099i	−0.452912	+	0.891555i	$0.649615\pi$
$38$	−2.97178	+	1.08164i	−0.482087	+	0.175465i
$39$		0			0
$40$	8.43242	−	7.07564i	1.33328	−	1.11876i
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	−0.226082	−	0.974108i	$-0.572592\pi$
$41$	4.44356	−	3.72859i	0.693968	−	0.582308i	0.920050	+	0.391800i	$0.128147\pi$
$42$		0			0
$43$	5.85117	−	2.12965i	0.892295	−	0.324769i	0.145134	−	0.989412i	$-0.453639\pi$
$43$	5.85117	−	2.12965i	0.892295	−	0.324769i	0.747161	+	0.664643i	$0.231417\pi$
$44$	−0.0996702	−	0.172634i	−0.0150259	−	0.0260255i
$45$		0			0
$46$	1.24763	−	2.16095i	0.183952	−	0.318615i
$47$	−1.28446	+	7.28455i	−0.187358	+	1.06256i	0.735530	+	0.677492i	$0.236933\pi$
$47$	−1.28446	+	7.28455i	−0.187358	+	1.06256i	−0.922888	+	0.385069i	$0.874178\pi$
$48$		0			0
$49$	2.09240	+	0.761570i	0.298914	+	0.108796i
$50$	1.53462	+	8.70323i	0.217027	+	1.23082i
$51$		0			0
$52$	−2.26604	−	1.90144i	−0.314244	−	0.263682i
$53$	−1.40373			−0.192818			−0.0964088	−	0.995342i	$-0.530736\pi$
$53$	−1.40373			−0.192818			−0.0964088	+	0.995342i	$0.530736\pi$
$54$		0			0
$55$	0.630415			0.0850051
$56$	4.74897	+	3.98486i	0.634608	+	0.532499i
$57$		0			0
$58$	−1.02569	−	5.81699i	−0.134680	−	0.763808i
$59$	−4.81180	−	1.75135i	−0.626444	−	0.228007i	0.00923910	−	0.999957i	$-0.497059\pi$
$59$	−4.81180	−	1.75135i	−0.626444	−	0.228007i	−0.635683	+	0.771951i	$0.719281\pi$
$60$		0			0
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	0.913489	+	0.406864i	$0.133378\pi$
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	−0.997554	+	0.0698959i	$0.977733\pi$
$62$	2.27972	−	3.94858i	0.289524	−	0.501470i
$63$		0			0
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$	8.79086	−	3.19961i	1.09037	−	0.396863i
$66$		0			0
$67$	−4.49273	+	3.76984i	−0.548874	+	0.460560i	−0.874559	−	0.484918i	$-0.838849\pi$
$67$	−4.49273	+	3.76984i	−0.548874	+	0.460560i	0.325686	+	0.945478i	$0.394405\pi$
$68$	2.81908	−	2.36549i	0.341863	−	0.286857i
$69$		0			0
$70$	−7.00387	+	2.54920i	−0.837123	+	0.304688i
$71$	−7.65910	−	13.2660i	−0.908968	−	1.57438i	−0.815500	−	0.578756i	$-0.803538\pi$
$71$	−7.65910	−	13.2660i	−0.908968	−	1.57438i	−0.0934675	−	0.995622i	$-0.529795\pi$
$72$		0			0
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	0.491996	+	0.870597i	$0.336267\pi$
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	−0.999958	+	0.00921733i	$0.997066\pi$
$74$	−1.01367	+	5.74881i	−0.117837	+	0.668286i
$75$		0			0
$76$	4.14543	+	1.50881i	0.475513	+	0.173073i
$77$	0.0616516	+	0.349643i	0.00702585	+	0.0398456i
$78$		0			0
$79$	−0.971782	−	0.815422i	−0.109334	−	0.0917421i	0.586482	−	0.809962i	$-0.300513\pi$
$79$	−0.971782	−	0.815422i	−0.109334	−	0.0917421i	−0.695816	+	0.718220i	$0.744957\pi$
$80$	0.162504			0.0181685
$81$		0			0
$82$	5.10101			0.563313
$83$	6.49273	+	5.44804i	0.712669	+	0.598001i	0.925347	−	0.379122i	$-0.123774\pi$
$83$	6.49273	+	5.44804i	0.712669	+	0.598001i	−0.212677	+	0.977122i	$0.568218\pi$
$84$		0			0
$85$	2.02094	+	11.4613i	0.219202	+	1.24316i
$86$	5.14543	+	1.87278i	0.554846	+	0.201947i
$87$		0			0
$88$	0.0800699	−	0.454099i	0.00853548	−	0.0484071i
$89$	3.86097	−	6.68739i	0.409262	−	0.708862i	−0.585546	−	0.810640i	$-0.699120\pi$
$89$	3.86097	−	6.68739i	0.409262	−	0.708862i	0.994807	+	0.101778i	$0.0324530\pi$
$90$		0			0
$91$	2.63429	+	4.56272i	0.276148	+	0.478303i
$92$	−3.27079	+	1.19047i	−0.341004	+	0.124115i
$93$		0			0
$94$	−4.98293	+	4.18117i	−0.513950	+	0.431255i
$95$	−10.6873	+	8.96773i	−1.09650	+	0.920069i
$96$		0			0
$97$	3.67112	−	1.33618i	0.372746	−	0.135668i	−0.148853	−	0.988859i	$-0.547558\pi$
$97$	3.67112	−	1.33618i	0.372746	−	0.135668i	0.521599	+	0.853191i	$0.325336\pi$
$98$	0.979055	+	1.69577i	0.0988995	+	0.171299i
$99$		0			0
$100$	6.16385	−	10.6761i	0.616385	−	1.06761i
$101$	1.40895	−	7.99054i	0.140196	−	0.795089i	−0.830904	−	0.556415i	$-0.812176\pi$
$101$	1.40895	−	7.99054i	0.140196	−	0.795089i	0.971100	−	0.238673i	$-0.0767125\pi$
$102$		0			0
$103$	−17.5214	−	6.37727i	−1.72644	−	0.628371i	−0.728069	−	0.685503i	$-0.759582\pi$
$103$	−17.5214	−	6.37727i	−1.72644	−	0.628371i	−0.998367	+	0.0571322i	$0.981804\pi$
$104$	−1.18820	−	6.73859i	−0.116512	−	0.660774i
$105$		0			0
$106$	−0.945622	−	0.793471i	−0.0918470	−	0.0770688i
$107$	−7.59627			−0.734359			−0.367179	−	0.930150i	$-0.619676\pi$
$107$	−7.59627			−0.734359			−0.367179	+	0.930150i	$0.619676\pi$
$108$		0			0
$109$	−15.6382			−1.49786			−0.748932	−	0.662647i	$-0.769433\pi$
$109$	−15.6382			−1.49786			−0.748932	+	0.662647i	$0.769433\pi$
$110$	0.424678	+	0.356347i	0.0404914	+	0.0339764i
$111$		0			0
$112$	0.0158921	+	0.0901285i	0.00150166	+	0.00851635i
$113$	−2.17365	−	0.791143i	−0.204480	−	0.0744245i	0.237750	−	0.971326i	$-0.423590\pi$
$113$	−2.17365	−	0.791143i	−0.204480	−	0.0744245i	−0.442230	+	0.896902i	$0.645812\pi$
$114$		0			0
$115$	1.91147	−	10.8405i	0.178246	−	1.01088i
$116$	−4.11974	+	7.13559i	−0.382508	+	0.662523i
$117$		0			0
$118$	−2.25150	−	3.89971i	−0.207267	−	0.358997i
$119$	−6.15910	+	2.24173i	−0.564604	+	0.205499i
$120$		0			0
$121$	−8.40626	+	7.05369i	−0.764205	+	0.641244i
$122$	−2.54710	+	2.13727i	−0.230604	+	0.193500i
$123$		0			0
$124$	−5.97653	+	2.17528i	−0.536708	+	0.195346i
$125$	9.79473	+	16.9650i	0.876067	+	1.51739i
$126$		0			0
$127$	−0.0209445	+	0.0362770i	−0.00185853	+	0.00321906i	−0.866953	−	0.498390i	$-0.833925\pi$
$127$	−0.0209445	+	0.0362770i	−0.00185853	+	0.00321906i	0.865095	+	0.501609i	$0.167258\pi$
$128$	−1.18820	+	6.73859i	−0.105023	+	0.595613i
$129$		0			0
$130$	7.73055	+	2.81369i	0.678014	+	0.246777i
$131$	−3.18614	−	18.0695i	−0.278374	−	1.57874i	−0.728036	−	0.685539i	$-0.759567\pi$
$131$	−3.18614	−	18.0695i	−0.278374	−	1.57874i	0.449662	−	0.893199i	$-0.351544\pi$
$132$		0			0
$133$	−6.01889	−	5.05044i	−0.521904	−	0.437929i
$134$	−5.15745			−0.445536
$135$		0			0
$136$	8.51249			0.729940
$137$	−10.9645	−	9.20031i	−0.936761	−	0.786036i	0.0402576	−	0.999189i	$-0.487182\pi$
$137$	−10.9645	−	9.20031i	−0.936761	−	0.786036i	−0.977019	+	0.213153i	$0.931627\pi$
$138$		0			0
$139$	1.82248	+	10.3358i	0.154581	+	0.876672i	0.959168	+	0.282837i	$0.0912755\pi$
$139$	1.82248	+	10.3358i	0.154581	+	0.876672i	−0.804587	+	0.593835i	$0.797613\pi$
$140$	9.76991	+	3.55596i	0.825709	+	0.300533i
$141$		0			0
$142$	2.33915	−	13.2660i	0.196297	−	1.11325i
$143$	0.195937	−	0.339373i	0.0163851	−	0.0283798i
$144$		0			0
$145$	−13.0287	−	22.5663i	−1.08197	−	1.87403i
$146$	−7.17277	+	2.61068i	−0.593623	+	0.216061i
$147$		0			0
$148$	6.23783	−	5.23416i	0.512746	−	0.430245i
$149$	0.973841	−	0.817150i	0.0797802	−	0.0669435i	−0.602025	−	0.798477i	$-0.705639\pi$
$149$	0.973841	−	0.817150i	0.0797802	−	0.0669435i	0.681806	+	0.731533i	$0.261195\pi$
$150$		0			0
$151$	−7.38326	+	2.68729i	−0.600841	+	0.218688i	−0.624491	−	0.781032i	$-0.714693\pi$
$151$	−7.38326	+	2.68729i	−0.600841	+	0.218688i	0.0236500	+	0.999720i	$0.492471\pi$
$152$	5.10220	+	8.83726i	0.413843	+	0.716797i
$153$		0			0
$154$	−0.156107	+	0.270386i	−0.0125795	+	0.0217883i
$155$	3.49273	−	19.8082i	0.280543	−	1.59104i
$156$		0			0
$157$	11.6074	+	4.22475i	0.926372	+	0.337172i	0.760771	−	0.649021i	$-0.224821\pi$
$157$	11.6074	+	4.22475i	0.926372	+	0.337172i	0.165602	+	0.986193i	$0.447043\pi$
$158$	−0.193715	−	1.09861i	−0.0154112	−	0.0874011i
$159$		0			0
$160$	−16.7554	−	14.0594i	−1.32463	−	1.11149i
$161$	6.19934			0.488576
$162$		0			0
$163$	−13.7469			−1.07674			−0.538371	−	0.842708i	$-0.680960\pi$
$163$	−13.7469			−1.07674			−0.538371	+	0.842708i	$0.680960\pi$
$164$	−5.45084	−	4.57380i	−0.425639	−	0.357153i
$165$		0			0
$166$	1.29426	+	7.34013i	0.100454	+	0.569705i
$167$	−3.49273	−	1.27125i	−0.270275	−	0.0983721i	0.203327	−	0.979111i	$-0.434824\pi$
$167$	−3.49273	−	1.27125i	−0.270275	−	0.0983721i	−0.473603	+	0.880739i	$0.657047\pi$
$168$		0			0
$169$	−1.24763	+	7.07564i	−0.0959712	+	0.544280i
$170$	−5.11721	+	8.86327i	−0.392472	+	0.679782i
$171$		0			0
$172$	−3.81908	−	6.61484i	−0.291202	−	0.504377i
$173$	−1.46538	+	0.533356i	−0.111411	+	0.0405503i	−0.397124	−	0.917765i	$-0.629992\pi$
$173$	−1.46538	+	0.533356i	−0.111411	+	0.0405503i	0.285713	+	0.958315i	$0.407770\pi$
$174$		0			0
$175$	−16.8195	+	14.1133i	−1.27144	+	1.06686i
$176$	0.00521457	−	0.00437554i	0.000393063	−	0.000329819i
$177$		0			0
$178$	6.38103	−	2.32251i	0.478279	−	0.174079i
$179$	−6.09627	−	10.5590i	−0.455656	−	0.789220i	0.543069	−	0.839688i	$-0.317262\pi$
$179$	−6.09627	−	10.5590i	−0.455656	−	0.789220i	−0.998726	+	0.0504679i	$0.983929\pi$
$180$		0			0
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	−0.361073	−	0.932537i	$-0.617590\pi$
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	0.988138	−	0.153570i	$-0.0490771\pi$
$182$	−0.804530	+	4.56272i	−0.0596357	+	0.338211i
$183$		0			0
$184$	−7.56583	−	2.75374i	−0.557760	−	0.203008i
$185$	4.47178	+	25.3607i	0.328772	+	1.86456i
$186$		0			0
$187$	0.373455	+	0.313366i	0.0273098	+	0.0229156i
$188$	9.07367			0.661766
$189$		0			0
$190$	−12.2686			−0.890056
$191$	13.3871	+	11.2331i	0.968658	+	0.812801i	0.982340	−	0.187105i	$-0.0599106\pi$
$191$	13.3871	+	11.2331i	0.968658	+	0.812801i	−0.0136814	+	0.999906i	$0.504355\pi$
$192$		0			0
$193$	−0.345952	−	1.96199i	−0.0249022	−	0.141227i	0.969822	−	0.243815i	$-0.0783989\pi$
$193$	−0.345952	−	1.96199i	−0.0249022	−	0.141227i	−0.994724	+	0.102588i	$0.967288\pi$
$194$	3.22833	+	1.17502i	0.231781	+	0.0843612i
$195$		0			0
$196$	0.474308	−	2.68993i	0.0338791	−	0.192138i
$197$	10.5963	−	18.3533i	0.754953	−	1.30762i	−0.190445	−	0.981698i	$-0.560993\pi$
$197$	10.5963	−	18.3533i	0.754953	−	1.30762i	0.945398	−	0.325919i	$-0.105674\pi$
$198$		0			0
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	0.915488	−	0.402346i	$-0.131805\pi$
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	−0.806186	+	0.591662i	$0.798472\pi$
$200$	26.7961	−	9.75297i	1.89477	−	0.689639i
$201$		0			0
$202$	5.46585	−	4.58639i	0.384576	−	0.322698i
$203$	11.2417	−	9.43290i	0.789012	−	0.662060i
$204$		0			0
$205$	21.1459	−	7.69648i	1.47689	−	0.537545i
$206$	−8.19846	−	14.2002i	−0.571214	−	0.989372i
$207$		0			0
$208$	0.0505072	−	0.0874810i	0.00350204	−	0.00606572i
$209$	−0.101481	+	0.575529i	−0.00701960	+	0.0398101i
$210$		0			0
$211$	−0.946967	−	0.344668i	−0.0651919	−	0.0237279i	0.309218	−	0.950991i	$-0.399933\pi$
$211$	−0.946967	−	0.344668i	−0.0651919	−	0.0237279i	−0.374410	+	0.927263i	$0.622155\pi$
$212$	0.299011	+	1.69577i	0.0205361	+	0.116466i
$213$		0			0
$214$	−5.11721	−	4.29385i	−0.349805	−	0.293522i
$215$	24.1557			1.64740
$216$		0			0
$217$	11.3277			0.768974
$218$	−10.5346	−	8.83959i	−0.713494	−	0.598693i
$219$		0			0
$220$	−0.134285	−	0.761570i	−0.00905352	−	0.0513450i
$221$	6.79813	+	2.47432i	0.457292	+	0.166441i
$222$		0			0
$223$	3.17499	−	18.0063i	0.212613	−	1.20579i	−0.672387	−	0.740199i	$-0.734731\pi$
$223$	3.17499	−	18.0063i	0.212613	−	1.20579i	0.885001	−	0.465590i	$-0.154158\pi$
$224$	6.15910	−	10.6679i	0.411522	−	0.712777i
$225$		0			0
$226$	−1.01707	−	1.76162i	−0.0676548	−	0.117181i
$227$	−2.48545	+	0.904631i	−0.164965	+	0.0600424i	−0.423183	−	0.906044i	$-0.639087\pi$
$227$	−2.48545	+	0.904631i	−0.164965	+	0.0600424i	0.258217	+	0.966087i	$0.416865\pi$
$228$		0			0
$229$	−2.65270	+	2.22588i	−0.175296	+	0.147090i	−0.726214	−	0.687469i	$-0.758722\pi$
$229$	−2.65270	+	2.22588i	−0.175296	+	0.147090i	0.550919	+	0.834559i	$0.314277\pi$
$230$	7.41534	−	6.22221i	0.488953	−	0.410281i
$231$		0			0
$232$	−17.9097	+	6.51860i	−1.17583	+	0.427967i
$233$	3.06283	+	5.30498i	0.200653	+	0.347541i	0.948739	−	0.316061i	$-0.102360\pi$
$233$	3.06283	+	5.30498i	0.200653	+	0.347541i	−0.748086	+	0.663602i	$0.769027\pi$
$234$		0			0
$235$	−14.3478	+	24.8511i	−0.935945	+	1.62110i
$236$	−1.09075	+	6.18594i	−0.0710016	+	0.402670i
$237$		0			0
$238$	−5.41622	−	1.97134i	−0.351082	−	0.127783i
$239$	5.02734	+	28.5115i	0.325192	+	1.84425i	0.508325	+	0.861165i	$0.330265\pi$
$239$	5.02734	+	28.5115i	0.325192	+	1.84425i	−0.183133	+	0.983088i	$0.558624\pi$
$240$		0			0
$241$	17.1027	+	14.3508i	1.10168	+	0.924419i	0.997537	−	0.0701436i	$-0.0223458\pi$
$241$	17.1027	+	14.3508i	1.10168	+	0.924419i	0.104142	+	0.994562i	$0.466790\pi$
$242$	−9.65002			−0.620326
$243$		0			0
$244$	4.63816			0.296927
$245$	6.61721	+	5.55250i	0.422758	+	0.354736i
$246$		0			0
$247$	1.50593	+	8.54055i	0.0958200	+	0.543422i
$248$	−13.8246	−	5.03174i	−0.877863	−	0.319516i
$249$		0			0
$250$	−2.99138	+	16.9650i	−0.189192	+	1.07296i
$251$	−11.3610	+	19.6778i	−0.717098	+	1.24205i	0.245047	+	0.969511i	$0.421197\pi$
$251$	−11.3610	+	19.6778i	−0.717098	+	1.24205i	−0.962145	+	0.272539i	$0.912137\pi$
$252$		0			0
$253$	−0.230552	−	0.399328i	−0.0144947	−	0.0251055i
$254$	−0.0346151	+	0.0125989i	−0.00217194	+	0.000790523i
$255$		0			0
$256$	−12.3341	+	10.3495i	−0.770881	+	0.646846i
$257$	15.0064	−	12.5919i	0.936073	−	0.785459i	−0.0408244	−	0.999166i	$-0.512998\pi$
$257$	15.0064	−	12.5919i	0.936073	−	0.785459i	0.976898	+	0.213708i	$0.0685540\pi$
$258$		0			0
$259$	−13.6284	+	4.96032i	−0.846825	+	0.308219i
$260$	−5.73783	−	9.93821i	−0.355845	−	0.616341i
$261$		0			0
$262$	8.06758	−	13.9735i	0.498417	−	0.863283i
$263$	−3.09105	+	17.5302i	−0.190602	+	1.08096i	0.727941	+	0.685640i	$0.240477\pi$
$263$	−3.09105	+	17.5302i	−0.190602	+	1.08096i	−0.918543	+	0.395320i	$0.870634\pi$
$264$		0			0
$265$	−5.11721	−	1.86251i	−0.314348	−	0.114413i
$266$	−1.19981	−	6.80445i	−0.0735649	−	0.417207i
$267$		0			0
$268$	5.51114	+	4.62440i	0.336647	+	0.282480i
$269$	−22.7888			−1.38946			−0.694729	−	0.719272i	$-0.744476\pi$
$269$	−22.7888			−1.38946			−0.694729	+	0.719272i	$0.744476\pi$
$270$		0			0
$271$	−3.44562			−0.209307			−0.104653	−	0.994509i	$-0.533373\pi$
$271$	−3.44562			−0.209307			−0.104653	+	0.994509i	$0.533373\pi$
$272$	0.0962667	+	0.0807773i	0.00583702	+	0.00489784i
$273$		0			0
$274$	−2.18567	−	12.3955i	−0.132041	−	0.748843i
$275$	1.53462	+	0.558554i	0.0925408	+	0.0336821i
$276$		0			0
$277$	−0.453830	+	2.57380i	−0.0272680	+	0.154645i	−0.995402	−	0.0957898i	$-0.969462\pi$
$277$	−0.453830	+	2.57380i	−0.0272680	+	0.154645i	0.968134	+	0.250434i	$0.0805734\pi$
$278$	−4.61468	+	7.99287i	−0.276770	+	0.479380i
$279$		0			0
$280$	12.0248	+	20.8276i	0.718620	+	1.24469i
$281$	−12.8598	+	4.68058i	−0.767150	+	0.279220i	−0.695804	−	0.718232i	$-0.744952\pi$
$281$	−12.8598	+	4.68058i	−0.767150	+	0.279220i	−0.0713464	+	0.997452i	$0.522730\pi$
$282$		0			0
$283$	17.5273	−	14.7072i	1.04189	−	0.874251i	0.0496744	−	0.998765i	$-0.484182\pi$
$283$	17.5273	−	14.7072i	1.04189	−	0.874251i	0.992218	+	0.124514i	$0.0397372\pi$
$284$	−14.3944	+	12.0783i	−0.854150	+	0.716717i
$285$		0			0
$286$	0.323826	−	0.117863i	0.0191482	−	0.00696938i
$287$	6.33662	+	10.9753i	0.374039	+	0.647854i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	3.97906	−	22.5663i	0.233658	−	1.32514i
$291$		0			0
$292$	10.0055	+	3.64171i	0.585529	+	0.213115i
$293$	−4.21641	−	23.9125i	−0.246326	−	1.39698i	−0.817394	−	0.576079i	$-0.804582\pi$
$293$	−4.21641	−	23.9125i	−0.246326	−	1.39698i	0.571068	−	0.820903i	$-0.306529\pi$
$294$		0			0
$295$	−15.2173	−	12.7689i	−0.885988	−	0.743432i
$296$	18.8357			1.09481
$297$		0			0
$298$	1.11793			0.0647597
$299$	−5.24170	−	4.39831i	−0.303135	−	0.254361i
$300$		0			0
$301$	2.36231	+	13.3973i	0.136161	+	0.772209i
$302$	−6.49273	−	2.36316i	−0.373614	−	0.135985i
$303$		0			0
$304$	−0.0261591	+	0.148356i	−0.00150033	+	0.00850878i
$305$	−7.33409	+	12.7030i	−0.419949	+	0.727373i
$306$		0			0
$307$	8.07444	+	13.9853i	0.460833	+	0.798186i	0.999003	−	0.0446505i	$-0.0142174\pi$
$307$	8.07444	+	13.9853i	0.460833	+	0.798186i	−0.538170	+	0.842836i	$0.680884\pi$
$308$	0.409253	−	0.148956i	0.0233193	−	0.00848754i
$309$		0			0
$310$	13.5496	−	11.3695i	0.769567	−	0.645744i
$311$	−14.3327	+	12.0266i	−0.812736	+	0.681966i	−0.951259	−	0.308393i	$-0.900209\pi$
$311$	−14.3327	+	12.0266i	−0.812736	+	0.681966i	0.138523	+	0.990359i	$0.455764\pi$
$312$		0			0
$313$	−2.60607	+	0.948531i	−0.147304	+	0.0536141i	−0.414620	−	0.909995i	$-0.636085\pi$
$313$	−2.60607	+	0.948531i	−0.147304	+	0.0536141i	0.267316	+	0.963609i	$0.413863\pi$
$314$	5.43124	+	9.40718i	0.306502	+	0.530878i
$315$		0			0
$316$	−0.778066	+	1.34765i	−0.0437696	+	0.0758112i
$317$	−3.03580	+	17.2169i	−0.170507	+	0.966995i	0.772695	+	0.634777i	$0.218908\pi$
$317$	−3.03580	+	17.2169i	−0.170507	+	0.966995i	−0.943203	+	0.332218i	$0.892203\pi$
$318$		0			0
$319$	−1.02569	−	0.373321i	−0.0574277	−	0.0209020i
$320$	−3.39646	−	19.2623i	−0.189868	−	1.07679i
$321$		0			0
$322$	4.17617	+	3.50423i	0.232729	+	0.195283i
$323$	−10.7888			−0.600305
$324$		0			0
$325$	24.2344			1.34428
$326$	−9.26058	−	7.77055i	−0.512896	−	0.430371i
$327$		0			0
$328$	−2.85814	−	16.2093i	−0.157814	−	0.895009i
$329$	−15.1861	−	5.52730i	−0.837239	−	0.304730i
$330$		0			0
$331$	−5.63651	+	31.9662i	−0.309810	+	1.75702i	0.290139	+	0.956984i	$0.406298\pi$
$331$	−5.63651	+	31.9662i	−0.309810	+	1.75702i	−0.599950	+	0.800038i	$0.704813\pi$
$332$	5.19846	−	9.00400i	0.285303	−	0.494159i
$333$		0			0
$334$	−1.63429	−	2.83067i	−0.0894241	−	0.154887i
$335$	−21.3799	+	7.78163i	−1.16811	+	0.425156i
$336$		0			0
$337$	6.34730	−	5.32601i	0.345759	−	0.290126i	−0.453325	−	0.891345i	$-0.649762\pi$
$337$	6.34730	−	5.32601i	0.345759	−	0.290126i	0.799085	+	0.601219i	$0.205318\pi$
$338$	−4.84002	+	4.06126i	−0.263263	+	0.220903i
$339$		0			0
$340$	13.4153	−	4.88279i	0.727549	−	0.264806i
$341$	−0.421274	−	0.729669i	−0.0228133	−	0.0395138i
$342$		0			0
$343$	−10.0792	+	17.4577i	−0.544225	+	0.942626i
$344$	3.06805	−	17.3998i	0.165418	−	0.938132i
$345$		0			0
$346$	−1.28864	−	0.469026i	−0.0692776	−	0.0252150i
$347$	−2.59833	−	14.7358i	−0.139485	−	0.791061i	−0.971631	−	0.236503i	$-0.923999\pi$
$347$	−2.59833	−	14.7358i	−0.139485	−	0.791061i	0.832145	−	0.554558i	$-0.187113\pi$
$348$		0			0
$349$	25.7743	+	21.6272i	1.37966	+	1.15768i	0.969336	+	0.245737i	$0.0790301\pi$
$349$	25.7743	+	21.6272i	1.37966	+	1.15768i	0.410328	+	0.911938i	$0.365414\pi$
$350$	−19.3081			−1.03206
$351$		0			0
$352$	−0.916222			−0.0488348
$353$	12.0680	+	10.1263i	0.642317	+	0.538968i	0.904729	−	0.425988i	$-0.140073\pi$
$353$	12.0680	+	10.1263i	0.642317	+	0.538968i	−0.262412	+	0.964956i	$0.584518\pi$
$354$		0			0
$355$	−10.3191	−	58.5224i	−0.547680	−	3.10605i
$356$	−8.90110	−	3.23974i	−0.471757	−	0.171706i
$357$		0			0
$358$	1.86184	−	10.5590i	0.0984015	−	0.558063i
$359$	9.06283	−	15.6973i	0.478318	−	0.828471i	−0.521373	−	0.853329i	$-0.674580\pi$
$359$	9.06283	−	15.6973i	0.478318	−	0.828471i	0.999691	+	0.0248577i	$0.00791328\pi$
$360$		0			0
$361$	3.03343	+	5.25406i	0.159654	+	0.276529i
$362$	13.9427	−	5.07472i	0.732811	−	0.266721i
$363$		0			0
$364$	4.95084	−	4.15425i	0.259494	−	0.217742i
$365$	−25.7952	+	21.6447i	−1.35018	+	1.13294i
$366$		0			0
$367$	17.9884	−	6.54726i	0.938989	−	0.341764i	0.173223	−	0.984883i	$-0.444582\pi$
$367$	17.9884	−	6.54726i	0.938989	−	0.341764i	0.765767	+	0.643119i	$0.222360\pi$
$368$	−0.0594300	−	0.102936i	−0.00309800	−	0.00536590i
$369$		0			0
$370$	−11.3229	+	19.6119i	−0.588652	+	1.01958i
$371$	0.532556	−	3.02027i	0.0276489	−	0.156805i
$372$		0			0
$373$	14.3302	+	5.21577i	0.741991	+	0.270063i	0.685231	−	0.728325i	$-0.259701\pi$
$373$	14.3302	+	5.21577i	0.741991	+	0.270063i	0.0567593	+	0.998388i	$0.481923\pi$
$374$	0.0744448	+	0.422197i	0.00384945	+	0.0218313i
$375$		0			0
$376$	16.0783	+	13.4913i	0.829176	+	0.695761i
$377$	−16.1976			−0.834218
$378$		0			0
$379$	9.84760			0.505837			0.252919	−	0.967488i	$-0.418610\pi$
$379$	9.84760			0.505837			0.252919	+	0.967488i	$0.418610\pi$
$380$	13.1099	+	11.0005i	0.672526	+	0.564316i
$381$		0			0
$382$	2.66860	+	15.1344i	0.136537	+	0.774341i
$383$	26.6780	+	9.70999i	1.36318	+	0.496157i	0.917036	−	0.398803i	$-0.130574\pi$
$383$	26.6780	+	9.70999i	1.36318	+	0.496157i	0.446145	+	0.894961i	$0.352797\pi$
$384$		0			0
$385$	−0.239170	+	1.35640i	−0.0121892	+	0.0691286i
$386$	0.875982	−	1.51724i	0.0445863	−	0.0772257i
$387$		0			0
$388$	−2.39615	−	4.15026i	−0.121646	−	0.210698i
$389$	10.2280	−	3.72270i	0.518581	−	0.188748i	−0.0694513	−	0.997585i	$-0.522125\pi$
$389$	10.2280	−	3.72270i	0.518581	−	0.188748i	0.588033	+	0.808837i	$0.299903\pi$
$390$		0			0
$391$	6.52094	−	5.47172i	0.329778	−	0.276717i
$392$	4.84002	−	4.06126i	0.244458	−	0.205125i
$393$		0			0
$394$	17.5125	−	6.37402i	0.882266	−	0.321119i
$395$	−2.46064	−	4.26195i	−0.123808	−	0.214442i
$396$		0			0
$397$	9.05350	−	15.6811i	0.454382	−	0.787013i	−0.544270	−	0.838910i	$-0.683193\pi$
$397$	9.05350	−	15.6811i	0.454382	−	0.787013i	0.998652	+	0.0518969i	$0.0165267\pi$
$398$	−0.470904	+	2.67063i	−0.0236043	+	0.133867i
$399$		0			0
$400$	0.395582	+	0.143980i	0.0197791	+	0.00719900i
$401$	−0.248970	−	1.41198i	−0.0124330	−	0.0705110i	0.977960	−	0.208792i	$-0.0669533\pi$
$401$	−0.248970	−	1.41198i	−0.0124330	−	0.0705110i	−0.990393	+	0.138281i	$0.955842\pi$
$402$		0			0
$403$	−9.57785	−	8.03677i	−0.477107	−	0.400340i
$404$	−9.95306			−0.495183
$405$		0			0
$406$	12.9050			0.640463
$407$	0.826352	+	0.693392i	0.0409607	+	0.0343701i
$408$		0			0
$409$	1.49407	+	8.47329i	0.0738770	+	0.418977i	0.999207	+	0.0398148i	$0.0126768\pi$
$409$	1.49407	+	8.47329i	0.0738770	+	0.418977i	−0.925330	+	0.379163i	$0.876212\pi$
$410$	18.5954	+	6.76817i	0.918361	+	0.334256i
$411$		0			0
$412$	−3.97178	+	22.5251i	−0.195676	+	1.10973i
$413$	5.59374	−	9.68864i	0.275250	−	0.476747i
$414$		0			0
$415$	16.4402	+	28.4752i	0.807016	+	1.39779i
$416$	−12.7763	+	4.65020i	−0.626410	+	0.227995i
$417$		0			0
$418$	−0.393685	+	0.330341i	−0.0192558	+	0.0161575i
$419$	9.43107	−	7.91361i	0.460738	−	0.386605i	−0.382664	−	0.923887i	$-0.624993\pi$
$419$	9.43107	−	7.91361i	0.460738	−	0.386605i	0.843403	+	0.537282i	$0.180549\pi$
$420$		0			0
$421$	−10.4461	+	3.80207i	−0.509111	+	0.185301i	−0.583788	−	0.811906i	$-0.698430\pi$
$421$	−10.4461	+	3.80207i	−0.509111	+	0.185301i	0.0746763	+	0.997208i	$0.476208\pi$
$422$	−0.443096	−	0.767465i	−0.0215696	−	0.0373596i
$423$		0			0
$424$	−1.99154	+	3.44946i	−0.0967179	+	0.167520i
$425$	−5.23530	+	29.6909i	−0.253949	+	1.44022i
$426$		0			0
$427$	−7.76264	−	2.82537i	−0.375661	−	0.136729i
$428$	1.61809	+	9.17664i	0.0782133	+	0.443569i
$429$		0			0
$430$	16.2724	+	13.6542i	0.784727	+	0.658464i
$431$	36.8958			1.77721			0.888604	−	0.458675i	$-0.151676\pi$
$431$	36.8958			1.77721			0.888604	+	0.458675i	$0.151676\pi$
$432$		0			0
$433$	−37.9982			−1.82608			−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−37.9982			−1.82608			−0.913040	+	0.407871i	$0.866271\pi$
$434$	7.63088	+	6.40307i	0.366294	+	0.307357i
$435$		0			0
$436$	3.33110	+	18.8916i	0.159531	+	0.904744i
$437$	9.58899	+	3.49011i	0.458704	+	0.166955i
$438$		0			0
$439$	0.0350819	−	0.198960i	0.00167437	−	0.00949582i	−0.983959	−	0.178394i	$-0.942910\pi$
$439$	0.0350819	−	0.198960i	0.00167437	−	0.00949582i	0.985633	+	0.168898i	$0.0540209\pi$
$440$	0.894400	−	1.54915i	0.0426388	−	0.0738526i
$441$		0			0
$442$	3.18092	+	5.50952i	0.151301	+	0.262061i
$443$	19.9491	−	7.26087i	0.947810	−	0.344974i	0.178564	−	0.983928i	$-0.442855\pi$
$443$	19.9491	−	7.26087i	0.947810	−	0.344974i	0.769245	+	0.638954i	$0.220632\pi$
$444$		0			0
$445$	22.9479	−	19.2556i	1.08783	−	0.912802i
$446$	12.3170	−	10.3352i	0.583228	−	0.489386i
$447$		0			0
$448$	10.3512	−	3.76752i	0.489047	−	0.177998i
$449$	−16.6297	−	28.8035i	−0.784804	−	1.35932i	−0.929116	−	0.369788i	$-0.879430\pi$
$449$	−16.6297	−	28.8035i	−0.784804	−	1.35932i	0.144312	−	0.989532i	$-0.453903\pi$
$450$		0			0
$451$	0.471315	−	0.816341i	0.0221933	−	0.0384400i
$452$	−0.492726	+	2.79439i	−0.0231759	+	0.131437i
$453$		0			0
$454$	−2.18567	−	0.795519i	−0.102579	−	0.0373355i
$455$	3.54916	+	20.1283i	0.166387	+	0.943629i
$456$		0			0
$457$	−0.0261591	−	0.0219501i	−0.00122367	−	0.00102678i	0.642176	−	0.766558i	$-0.278032\pi$
$457$	−0.0261591	−	0.0219501i	−0.00122367	−	0.00102678i	−0.643399	+	0.765531i	$0.722476\pi$
$458$	−3.04519			−0.142292
$459$		0			0
$460$	−13.5030			−0.629580
$461$	11.4802	+	9.63306i	0.534688	+	0.448656i	0.869717	−	0.493551i	$-0.164302\pi$
$461$	11.4802	+	9.63306i	0.534688	+	0.448656i	−0.335029	+	0.942208i	$0.608746\pi$
$462$		0			0
$463$	−5.28627	−	29.9799i	−0.245674	−	1.39329i	−0.818922	−	0.573905i	$-0.805428\pi$
$463$	−5.28627	−	29.9799i	−0.245674	−	1.39329i	0.573248	−	0.819382i	$-0.305683\pi$
$464$	−0.264396	−	0.0962321i	−0.0122743	−	0.00446746i
$465$		0			0
$466$	−0.935412	+	5.30498i	−0.0433321	+	0.245749i
$467$	−0.255367	+	0.442308i	−0.0118170	+	0.0204676i	−0.871873	−	0.489731i	$-0.837095\pi$
$467$	−0.255367	+	0.442308i	−0.0118170	+	0.0204676i	0.860056	+	0.510199i	$0.170428\pi$
$468$		0			0
$469$	−6.40673	−	11.0968i	−0.295835	−	0.512401i
$470$	−23.7126	+	8.63068i	−1.09378	+	0.398104i
$471$		0			0
$472$	−11.1304	+	9.33953i	−0.512319	+	0.429887i
$473$	0.775129	−	0.650411i	0.0356405	−	0.0299059i
$474$		0			0
$475$	−33.9616	+	12.3610i	−1.55826	+	0.567162i
$476$	4.02007	+	6.96296i	0.184259	+	0.319147i
$477$		0			0
$478$	−12.7297	+	22.0484i	−0.582242	+	1.00847i
$479$	2.68298	−	15.2159i	0.122589	−	0.695234i	−0.860122	−	0.510088i	$-0.829613\pi$
$479$	2.68298	−	15.2159i	0.122589	−	0.695234i	0.982711	−	0.185147i	$-0.0592760\pi$
$480$		0			0
$481$	15.0424	+	5.47497i	0.685872	+	0.249637i
$482$	3.40925	+	19.3348i	0.155287	+	0.880677i
$483$		0			0
$484$	10.3118	+	8.65263i	0.468718	+	0.393301i
$485$	15.1557			0.688185
$486$		0			0
$487$	29.5107			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$487$	29.5107			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$488$	8.21869	+	6.89630i	0.372043	+	0.312181i
$489$		0			0
$490$	1.31908	+	7.48086i	0.0595899	+	0.337951i
$491$	2.02734	+	0.737892i	0.0914926	+	0.0333006i	0.387361	−	0.921928i	$-0.373387\pi$
$491$	2.02734	+	0.737892i	0.0914926	+	0.0333006i	−0.295868	+	0.955229i	$0.595609\pi$
$492$		0			0
$493$	3.49912	−	19.8445i	0.157593	−	0.893752i
$494$	−3.81315	+	6.60457i	−0.171562	+	0.297153i
$495$		0			0
$496$	−0.108593	−	0.188089i	−0.00487597	−	0.00844543i
$497$	31.4488	−	11.4464i	1.41067	−	0.513442i
$498$		0			0
$499$	5.74170	−	4.81786i	0.257034	−	0.215677i	−0.505160	−	0.863025i	$-0.668567\pi$
$499$	5.74170	−	4.81786i	0.257034	−	0.215677i	0.762194	+	0.647349i	$0.224122\pi$
$500$	18.4081	−	15.4462i	0.823234	−	0.690775i
$501$		0			0
$502$	−18.7763	+	6.83402i	−0.838028	+	0.305017i
$503$	14.2981	+	24.7651i	0.637522	+	1.10422i	0.985975	+	0.166894i	$0.0533739\pi$
$503$	14.2981	+	24.7651i	0.637522	+	1.10422i	−0.348453	+	0.937326i	$0.613293\pi$
$504$		0			0
$505$	15.7383	−	27.2595i	0.700345	−	1.21303i
$506$	0.0704123	−	0.399328i	0.00313021	−	0.0177523i
$507$		0			0
$508$	0.0482857	+	0.0175745i	0.00214233	+	0.000779745i
$509$	0.293796	+	1.66620i	0.0130223	+	0.0738530i	0.990626	−	0.136600i	$-0.0436174\pi$
$509$	0.293796	+	1.66620i	0.0130223	+	0.0738530i	−0.977604	+	0.210453i	$0.932506\pi$
$510$		0			0
$511$	−14.5273	−	12.1899i	−0.642652	−	0.539249i
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	17.2267			0.759836
$515$	−55.4115	−	46.4958i	−2.44172	−	2.04885i
$516$		0			0
$517$	0.208730	+	1.18377i	0.00917994	+	0.0520620i
$518$	−11.9846	−	4.36203i	−0.526572	−	0.191657i
$519$		0			0
$520$	4.60947	−	26.1416i	0.202139	−	1.14639i
$521$	−11.2019	+	19.4022i	−0.490763	+	0.850026i	−0.999943	−	0.0106337i	$-0.996615\pi$
$521$	−11.2019	+	19.4022i	−0.490763	+	0.850026i	0.509181	+	0.860660i	$0.329948\pi$
$522$		0			0
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	0.838254	−	0.545281i	$-0.183577\pi$
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	−0.891354	+	0.453309i	$0.850244\pi$
$524$	−21.1501	+	7.69800i	−0.923945	+	0.336289i
$525$		0			0
$526$	−11.9914	+	10.0620i	−0.522849	+	0.438722i
$527$	11.9153	−	9.99816i	0.519041	−	0.435527i
$528$		0			0
$529$	14.0471	−	5.11273i	0.610744	−	0.222293i
$530$	−2.39440	−	4.14722i	−0.104006	−	0.180144i
$531$		0			0
$532$	−4.81908	+	8.34689i	−0.208934	+	0.361883i
$533$	2.42902	−	13.7756i	0.105212	−	0.596689i
$534$		0			0
$535$	−27.6917	−	10.0789i	−1.19721	−	0.435751i
$536$	2.88976	+	16.3886i	0.124819	+	0.707881i
$537$		0			0
$538$	−15.3516	−	12.8816i	−0.661856	−	0.555363i
$539$	0.361844			0.0155857
$540$		0			0
$541$	38.9394			1.67414			0.837069	−	0.547098i	$-0.184267\pi$
$541$	38.9394			1.67414			0.837069	+	0.547098i	$0.184267\pi$
$542$	−2.32114	−	1.94767i	−0.0997014	−	0.0836594i
$543$		0			0
$544$	−2.93717	−	16.6575i	−0.125930	−	0.714184i
$545$	−57.0078	−	20.7491i	−2.44195	−	0.888796i
$546$		0			0
$547$	−2.54782	+	14.4494i	−0.108937	+	0.617812i	0.880638	+	0.473790i	$0.157115\pi$
$547$	−2.54782	+	14.4494i	−0.108937	+	0.617812i	−0.989575	+	0.144021i	$0.953997\pi$
$548$	−8.77884	+	15.2054i	−0.375013	+	0.649542i
$549$		0			0
$550$	0.718063	+	1.24372i	0.0306183	+	0.0530325i
$551$	22.6989	−	8.26173i	0.967007	−	0.351962i
$552$		0			0
$553$	2.12314	−	1.78153i	0.0902851	−	0.0757582i
$554$	−1.76058	+	1.47730i	−0.0747999	+	0.0627646i
$555$		0			0
$556$	12.0979	−	4.40328i	0.513066	−	0.186741i
$557$	−5.55350	−	9.61894i	−0.235309	−	0.407568i	0.724053	−	0.689744i	$-0.242277\pi$
$557$	−5.55350	−	9.61894i	−0.235309	−	0.407568i	−0.959363	+	0.282176i	$0.908944\pi$
$558$		0			0
$559$	7.50774	−	13.0038i	0.317544	−	0.550002i
$560$	−0.0616516	+	0.349643i	−0.00260525	+	0.0147751i
$561$		0			0
$562$	−11.3087	−	4.11603i	−0.477029	−	0.173624i
$563$	−2.83187	−	16.0603i	−0.119349	−	0.676863i	−0.984505	−	0.175359i	$-0.943891\pi$
$563$	−2.83187	−	16.0603i	−0.119349	−	0.676863i	0.865155	−	0.501504i	$-0.167220\pi$
$564$		0			0
$565$	−6.87417	−	5.76811i	−0.289199	−	0.242666i
$566$	20.1206			0.845733
$567$		0			0
$568$	−43.4653			−1.82376
$569$	−27.5902	−	23.1509i	−1.15664	−	0.970536i	−0.156786	−	0.987633i	$-0.550113\pi$
$569$	−27.5902	−	23.1509i	−1.15664	−	0.970536i	−0.999854	+	0.0170961i	$0.994558\pi$
$570$		0			0
$571$	6.79978	+	38.5635i	0.284562	+	1.61383i	0.706846	+	0.707368i	$0.250117\pi$
$571$	6.79978	+	38.5635i	0.284562	+	1.61383i	−0.422284	+	0.906464i	$0.638771\pi$
$572$	−0.451714	−	0.164411i	−0.0188871	−	0.00687435i
$573$		0			0
$574$	−1.93525	+	10.9753i	−0.0807758	+	0.458102i
$575$	14.2579	−	24.6954i	0.594595	−	1.02987i
$576$		0			0
$577$	−5.90286	−	10.2240i	−0.245739	−	0.425633i	0.716600	−	0.697484i	$-0.245697\pi$
$577$	−5.90286	−	10.2240i	−0.245739	−	0.425633i	−0.962339	+	0.271852i	$0.912364\pi$
$578$	6.61081	−	2.40614i	0.274974	−	0.100082i
$579$		0			0
$580$	−24.4859	+	20.5461i	−1.01672	+	0.853131i
$581$	−14.1853	+	11.9028i	−0.588504	+	0.493813i
$582$		0			0
$583$	−0.214355	+	0.0780189i	−0.00887769	+	0.00323121i
$584$	12.3148	+	21.3299i	0.509590	+	0.882636i
$585$		0			0
$586$	10.6763	−	18.4920i	0.441035	−	0.763896i
$587$	6.93923	−	39.3543i	0.286413	−	1.62433i	−0.413783	−	0.910375i	$-0.635793\pi$
$587$	6.93923	−	39.3543i	0.286413	−	1.62433i	0.700196	−	0.713951i	$-0.253096\pi$
$588$		0			0
$589$	17.5214	+	6.37727i	0.721957	+	0.262771i
$590$	−3.03343	−	17.2035i	−0.124884	−	0.708255i
$591$		0			0
$592$	0.213011	+	0.178737i	0.00875470	+	0.00734606i
$593$	29.2995			1.20319			0.601594	−	0.798802i	$-0.294533\pi$
$593$	29.2995			1.20319			0.601594	+	0.798802i	$0.294533\pi$
$594$		0			0
$595$	−25.4270			−1.04240
$596$	−1.19459	−	1.00238i	−0.0489324	−	0.0410592i
$597$		0			0
$598$	−1.04488	−	5.92582i	−0.0427284	−	0.242325i
$599$	9.46451	+	3.44480i	0.386709	+	0.140751i	0.528056	−	0.849209i	$-0.322921\pi$
$599$	9.46451	+	3.44480i	0.386709	+	0.140751i	−0.141347	+	0.989960i	$0.545143\pi$
$600$		0			0
$601$	−5.28224	+	29.9571i	−0.215467	+	1.22197i	0.664627	+	0.747175i	$0.268590\pi$
$601$	−5.28224	+	29.9571i	−0.215467	+	1.22197i	−0.880094	+	0.474799i	$0.842521\pi$
$602$	−5.98158	+	10.3604i	−0.243791	+	0.422259i
$603$		0			0
$604$	4.81908	+	8.34689i	0.196085	+	0.339630i
$605$	−40.0035	+	14.5601i	−1.62637	+	0.591951i
$606$		0			0
$607$	−17.6759	+	14.8319i	−0.717444	+	0.602007i	−0.926677	−	0.375859i	$-0.877348\pi$
$607$	−17.6759	+	14.8319i	−0.717444	+	0.602007i	0.209233	+	0.977866i	$0.432903\pi$
$608$	15.5326	−	13.0334i	0.629928	−	0.528573i
$609$		0			0
$610$	−12.1211	+	4.41171i	−0.490768	+	0.178625i
$611$	8.91875	+	15.4477i	0.360814	+	0.624948i
$612$		0			0
$613$	−0.382789	+	0.663010i	−0.0154607	+	0.0267787i	−0.873652	−	0.486551i	$-0.838255\pi$
$613$	−0.382789	+	0.663010i	−0.0154607	+	0.0267787i	0.858192	+	0.513330i	$0.171588\pi$
$614$	−2.46599	+	13.9853i	−0.0995194	+	0.564403i
$615$		0			0
$616$	0.946662	+	0.344557i	0.0381421	+	0.0138826i
$617$	1.61287	+	9.14706i	0.0649319	+	0.368247i	0.999908	+	0.0135372i	$0.00430917\pi$
$617$	1.61287	+	9.14706i	0.0649319	+	0.368247i	−0.934977	+	0.354710i	$0.884580\pi$
$618$		0			0
$619$	−26.8746	−	22.5505i	−1.08018	−	0.906381i	−0.0842469	−	0.996445i	$-0.526848\pi$
$619$	−26.8746	−	22.5505i	−1.08018	−	0.906381i	−0.995936	+	0.0900639i	$0.971293\pi$
$620$	−24.6732			−0.990901
$621$		0			0
$622$	−16.4534			−0.659720
$623$	12.9238	+	10.8444i	0.517781	+	0.434470i
$624$		0			0
$625$	4.47090	+	25.3558i	0.178836	+	1.01423i
$626$	−2.29174	−	0.834124i	−0.0915962	−	0.0333383i
$627$		0			0
$628$	2.63119	−	14.9222i	0.104996	−	0.595461i
$629$	−9.95723	+	17.2464i	−0.397021	+	0.687660i
$630$		0			0
$631$	−17.8810	−	30.9709i	−0.711833	−	1.23293i	−0.964168	−	0.265291i	$-0.914532\pi$
$631$	−17.8810	−	30.9709i	−0.711833	−	1.23293i	0.252336	−	0.967640i	$-0.418801\pi$
$632$	−3.38248	+	1.23112i	−0.134548	+	0.0489715i
$633$		0			0
$634$	−11.7770	+	9.88210i	−0.467725	+	0.392468i
$635$	−0.124485	+	0.104455i	−0.00494004	+	0.00414519i
$636$		0			0
$637$	5.04576	−	1.83651i	0.199920	−	0.0727650i
$638$	−0.479933	−	0.831268i	−0.0190007	−	0.0329102i
$639$		0			0
$640$	−13.2724	+	22.9885i	−0.524639	+	0.908702i
$641$	−0.508151	+	2.88187i	−0.0200708	+	0.113827i	−0.993197	−	0.116444i	$-0.962850\pi$
$641$	−0.508151	+	2.88187i	−0.0200708	+	0.113827i	0.973126	+	0.230271i	$0.0739614\pi$
$642$		0			0
$643$	19.0303	+	6.92648i	0.750483	+	0.273154i	0.688809	−	0.724943i	$-0.258134\pi$
$643$	19.0303	+	6.92648i	0.750483	+	0.273154i	0.0616741	+	0.998096i	$0.480356\pi$
$644$	−1.32053	−	7.48909i	−0.0520361	−	0.295111i
$645$		0			0
$646$	−7.26786	−	6.09845i	−0.285950	−	0.239940i
$647$	−10.7219			−0.421523			−0.210761	−	0.977538i	$-0.567594\pi$
$647$	−10.7219			−0.421523			−0.210761	+	0.977538i	$0.567594\pi$
$648$		0			0
$649$	−0.832119			−0.0326635
$650$	16.3255	+	13.6987i	0.640338	+	0.537307i
$651$		0			0
$652$	2.92824	+	16.6069i	0.114679	+	0.650376i
$653$	33.5724	+	12.2193i	1.31379	+	0.478180i	0.901463	−	0.432856i	$-0.142494\pi$
$653$	33.5724	+	12.2193i	1.31379	+	0.478180i	0.412326	+	0.911036i	$0.364716\pi$
$654$		0			0
$655$	12.3603	−	70.0985i	0.482955	−	2.73897i
$656$	0.121492	−	0.210430i	0.00474347	−	0.00821593i
$657$		0			0
$658$	−7.10576	−	12.3075i	−0.277011	−	0.479798i
$659$	29.0043	−	10.5567i	1.12985	−	0.411231i	0.291611	−	0.956537i	$-0.405809\pi$
$659$	29.0043	−	10.5567i	1.12985	−	0.411231i	0.838237	+	0.545306i	$0.183586\pi$
$660$		0			0
$661$	−7.54395	+	6.33012i	−0.293426	+	0.246213i	−0.777602	−	0.628757i	$-0.783564\pi$
$661$	−7.54395	+	6.33012i	−0.293426	+	0.246213i	0.484176	+	0.874971i	$0.339119\pi$
$662$	−21.8662	+	18.3479i	−0.849853	+	0.713112i
$663$		0			0
$664$	22.5993	−	8.22546i	0.877021	−	0.319210i
$665$	−15.2404	−	26.3971i	−0.590996	−	1.02363i
$666$		0			0
$667$	−9.52956	+	16.5057i	−0.368986	+	0.639103i
$668$	−0.791737	+	4.49016i	−0.0306332	+	0.173730i
$669$		0			0
$670$	−18.8011	−	6.84305i	−0.726351	−	0.264370i
$671$	0.106696	+	0.605102i	0.00411895	+	0.0233597i
$672$		0			0
$673$	−15.0890	−	12.6612i	−0.581638	−	0.488052i	0.303847	−	0.952721i	$-0.401729\pi$
$673$	−15.0890	−	12.6612i	−0.581638	−	0.488052i	−0.885485	+	0.464669i	$0.846173\pi$
$674$	7.28642			0.280662
$675$		0			0
$676$	8.81345			0.338979
$677$	21.7993	+	18.2918i	0.837816	+	0.703011i	0.957071	−	0.289853i	$-0.0936063\pi$
$677$	21.7993	+	18.2918i	0.837816	+	0.703011i	−0.119256	+	0.992864i	$0.538051\pi$
$678$		0			0
$679$	1.48215	+	8.40571i	0.0568799	+	0.322582i
$680$	31.0317	+	11.2946i	1.19001	+	0.433128i
$681$		0			0
$682$	0.128660	−	0.729669i	0.00492666	−	0.0279405i
$683$	6.25537	−	10.8346i	0.239355	−	0.414575i	−0.721174	−	0.692754i	$-0.756397\pi$
$683$	6.25537	−	10.8346i	0.239355	−	0.414575i	0.960529	+	0.278179i	$0.0897307\pi$
$684$		0			0
$685$	−27.7631	−	48.0871i	−1.06077	−	1.83731i
$686$	−16.6579	+	6.06299i	−0.636002	+	0.231486i
$687$		0			0
$688$	0.199807	−	0.167658i	0.00761758	−	0.00639191i
$689$	−2.59311	+	2.17588i	−0.0987897	+	0.0828944i
$690$		0			0
$691$	−40.0548	+	14.5788i	−1.52376	+	0.554603i	−0.962083	−	0.272756i	$-0.912065\pi$
$691$	−40.0548	+	14.5788i	−1.52376	+	0.554603i	−0.561675	+	0.827358i	$0.689843\pi$
$692$	0.956462	+	1.65664i	0.0363592	+	0.0629760i
$693$		0			0
$694$	6.57919	−	11.3955i	0.249743	−	0.432567i
$695$	−7.07011	+	40.0966i	−0.268184	+	1.52095i
$696$		0			0
$697$	16.3525	+	5.95183i	0.619396	+	0.225442i
$698$	5.13785	+	29.1382i	0.194471	+	1.10290i
$699$		0			0
$700$	20.6322	+	17.3125i	0.779825	+	0.654351i
$701$	−51.7701			−1.95533			−0.977665	−	0.210167i	$-0.932599\pi$
$701$	−51.7701			−1.95533			−0.977665	+	0.210167i	$0.932599\pi$
$702$		0			0
$703$	−23.8726			−0.900371
$704$	−0.627640	−	0.526653i	−0.0236551	−	0.0198490i
$705$		0			0
$706$	2.40565	+	13.6431i	0.0905378	+	0.513466i
$707$	16.6579	+	6.06299i	0.626485	+	0.228022i
$708$		0			0
$709$	2.63223	−	14.9281i	0.0988553	−	0.560636i	−0.894642	−	0.446783i	$-0.852570\pi$
$709$	2.63223	−	14.9281i	0.0988553	−	0.560636i	0.993498	−	0.113853i	$-0.0363194\pi$
$710$	26.1288	−	45.2564i	0.980597	−	1.69844i
$711$		0			0
$712$	−10.9555	−	18.9754i	−0.410574	−	0.711135i
$713$	−13.8246	+	5.03174i	−0.517735	+	0.188440i
$714$		0			0
$715$	1.16456	−	0.977185i	0.0435522	−	0.0365446i
$716$	−11.4572	+	9.61376i	−0.428177	+	0.359283i
$717$		0			0
$718$	14.9782	−	5.45161i	0.558981	−	0.203452i
$719$	−1.30747	−	2.26460i	−0.0487603	−	0.0844553i	0.840615	−	0.541633i	$-0.182194\pi$
$719$	−1.30747	−	2.26460i	−0.0487603	−	0.0844553i	−0.889375	+	0.457178i	$0.848860\pi$
$720$		0			0
$721$	20.3687	−	35.2796i	0.758570	−	1.31388i
$722$	−0.926433	+	5.25406i	−0.0344783	+	0.195536i
$723$		0			0
$724$	−19.4491	−	7.07889i	−0.722819	−	0.263085i
$725$	−11.7216	−	66.4767i	−0.435330	−	2.46888i
$726$		0			0
$727$	−3.14022	−	2.63495i	−0.116464	−	0.0977250i	0.582696	−	0.812690i	$-0.301998\pi$
$727$	−3.14022	−	2.63495i	−0.116464	−	0.0977250i	−0.699160	+	0.714965i	$0.746442\pi$
$728$	14.9495			0.554067
$729$		0			0
$730$	−29.6117			−1.09598
$731$	14.3097	+	12.0073i	0.529265	+	0.444106i
$732$		0			0
$733$	−6.63475	−	37.6275i	−0.245060	−	1.38981i	−0.820353	−	0.571858i	$-0.806223\pi$
$733$	−6.63475	−	37.6275i	−0.245060	−	1.38981i	0.575293	−	0.817948i	$-0.304888\pi$
$734$	15.8188	+	5.75756i	0.583882	+	0.212516i
$735$		0			0
$736$	−2.77807	+	15.7552i	−0.102401	+	0.580744i
$737$	−0.476529	+	0.825373i	−0.0175532	+	0.0304030i
$738$		0			0
$739$	12.1047	+	20.9660i	0.445279	+	0.771247i	0.998072	−	0.0620725i	$-0.0197710\pi$
$739$	12.1047	+	20.9660i	0.445279	+	0.771247i	−0.552792	+	0.833319i	$0.686438\pi$
$740$	29.6844	−	10.8042i	1.09122	−	0.397171i
$741$		0			0
$742$	2.06599	−	1.73357i	0.0758448	−	0.0636414i
$743$	2.53667	−	2.12852i	0.0930616	−	0.0780879i	−0.595070	−	0.803674i	$-0.702876\pi$
$743$	2.53667	−	2.12852i	0.0930616	−	0.0780879i	0.688131	+	0.725586i	$0.258431\pi$
$744$		0			0
$745$	4.63429	−	1.68674i	0.169787	−	0.0617974i
$746$	6.70527	+	11.6139i	0.245497	+	0.425214i
$747$		0			0
$748$	0.299011	−	0.517902i	0.0109329	−	0.0189364i
$749$	2.88191	−	16.3441i	0.105303	−	0.597202i
$750$		0			0
$751$	−12.8841	−	4.68944i	−0.470149	−	0.171120i	0.0960710	−	0.995374i	$-0.469372\pi$
$751$	−12.8841	−	4.68944i	−0.470149	−	0.171120i	−0.566220	+	0.824254i	$0.691595\pi$
$752$	0.0538049	+	0.305143i	0.00196206	+	0.0111274i
$753$		0			0
$754$	−10.9115	−	9.15581i	−0.397372	−	0.333435i
$755$	−30.4807			−1.10931
$756$		0			0
$757$	12.3833			0.450079			0.225040	−	0.974350i	$-0.427749\pi$
$757$	12.3833			0.450079			0.225040	+	0.974350i	$0.427749\pi$
$758$	6.63382	+	5.56643i	0.240951	+	0.202182i
$759$		0			0
$760$	6.87417	+	38.9854i	0.249352	+	1.41415i
$761$	7.12536	+	2.59342i	0.258294	+	0.0940114i	0.467922	−	0.883770i	$-0.345003\pi$
$761$	7.12536	+	2.59342i	0.258294	+	0.0940114i	−0.209628	+	0.977781i	$0.567225\pi$
$762$		0			0
$763$	5.93289	−	33.6471i	0.214785	−	1.21811i
$764$	10.7185	−	18.5650i	0.387783	−	0.671660i
$765$		0			0
$766$	12.4829	+	21.6211i	0.451026	+	0.781201i
$767$	−11.6035	+	4.22334i	−0.418980	+	0.152496i
$768$		0			0
$769$	2.46451	−	2.06797i	0.0888724	−	0.0745728i	−0.597269	−	0.802041i	$-0.703748\pi$
$769$	2.46451	−	2.06797i	0.0888724	−	0.0745728i	0.686141	+	0.727468i	$0.259303\pi$
$770$	−0.927833	+	0.778544i	−0.0334368	+	0.0280568i
$771$		0			0
$772$	−2.29648	+	0.835852i	−0.0826523	+	0.0300830i
$773$	−0.0922341	−	0.159754i	−0.00331743	−	0.00574596i	0.864362	−	0.502870i	$-0.167723\pi$
$773$	−0.0922341	−	0.159754i	−0.00331743	−	0.00574596i	−0.867679	+	0.497124i	$0.834389\pi$
$774$		0			0
$775$	26.0526	−	45.1245i	0.935838	−	1.62092i
$776$	1.92495	−	10.9169i	0.0691015	−	0.391894i
$777$		0			0
$778$	8.99437	+	3.27368i	0.322464	+	0.117367i

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)

\(f(q)\)	\(=\)	\(q+(0.673648 + 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(3.64543 + 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(1.41875 - 2.45734i) q^{8} +O(q^{10})\)	\(q+(0.673648 + 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(3.64543 + 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(1.41875 - 2.45734i) q^{8} +(1.70574 + 2.95442i) q^{10} +(0.152704 - 0.0555796i) q^{11} +(1.84730 - 1.55007i) q^{13} +(-1.47178 + 1.23497i) q^{14} +(0.0393628 - 0.0143269i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.79813 + 3.11446i) q^{19} +(0.826352 - 4.68647i) q^{20} +(0.134285 + 0.0488759i) q^{22} +(-0.492726 - 2.79439i) q^{23} +(7.69846 + 6.45978i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(-5.14543 - 4.31753i) q^{29} +(-0.900330 - 5.10602i) q^{31} +(-5.29813 - 1.92836i) q^{32} +(-0.458111 + 2.59808i) q^{34} +(-4.23783 + 7.34013i) q^{35} +(3.31908 + 5.74881i) q^{37} +(-2.97178 + 1.08164i) q^{38} +(8.43242 - 7.07564i) q^{40} +(4.44356 - 3.72859i) q^{41} +(5.85117 - 2.12965i) q^{43} +(-0.0996702 - 0.172634i) q^{44} +(1.24763 - 2.16095i) q^{46} +(-1.28446 + 7.28455i) q^{47} +(2.09240 + 0.761570i) q^{49} +(1.53462 + 8.70323i) q^{50} +(-2.26604 - 1.90144i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(4.74897 + 3.98486i) q^{56} +(-1.02569 - 5.81699i) q^{58} +(-4.81180 - 1.75135i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(2.27972 - 3.94858i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(8.79086 - 3.19961i) q^{65} +(-4.49273 + 3.76984i) q^{67} +(2.81908 - 2.36549i) q^{68} +(-7.00387 + 2.54920i) q^{70} +(-7.65910 - 13.2660i) q^{71} +(-4.34002 + 7.51714i) q^{73} +(-1.01367 + 5.74881i) q^{74} +(4.14543 + 1.50881i) q^{76} +(0.0616516 + 0.349643i) q^{77} +(-0.971782 - 0.815422i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(6.49273 + 5.44804i) q^{83} +(2.02094 + 11.4613i) q^{85} +(5.14543 + 1.87278i) q^{86} +(0.0800699 - 0.454099i) q^{88} +(3.86097 - 6.68739i) q^{89} +(2.63429 + 4.56272i) q^{91} +(-3.27079 + 1.19047i) q^{92} +(-4.98293 + 4.18117i) q^{94} +(-10.6873 + 8.96773i) q^{95} +(3.67112 - 1.33618i) q^{97} +(0.979055 + 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29} + 9 q^{31} - 18 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} - 3 q^{38} + 27 q^{40} - 3 q^{41} + 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} + 9 q^{49} - 15 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 3 q^{56} - 36 q^{58} + 6 q^{59} + 18 q^{61} - 12 q^{62} - 12 q^{64} + 21 q^{65} - 9 q^{67} - 18 q^{70} - 9 q^{71} - 6 q^{73} + 15 q^{74} + 9 q^{76} - 3 q^{77} + 9 q^{79} + 6 q^{80} + 36 q^{82} + 21 q^{83} + 9 q^{85} + 15 q^{86} + 9 q^{88} + 6 q^{91} - 48 q^{92} - 9 q^{94} - 42 q^{95} + 36 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more