LMFDB - Embedded newform 729.2.c.b.487.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.6
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.b.244.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.840456 - 1.45571i) q^{2} +(-0.412733 - 0.714874i) q^{4} +(-0.564772 - 0.978214i) q^{5} +(1.95446 - 3.38523i) q^{7} +1.97429 q^{8} +O(q^{10})$	\(q+(0.840456 - 1.45571i) q^{2} +(-0.412733 - 0.714874i) q^{4} +(-0.564772 - 0.978214i) q^{5} +(1.95446 - 3.38523i) q^{7} +1.97429 q^{8} -1.89866 q^{10} +(-0.935228 + 1.61986i) q^{11} +(0.366299 + 0.634448i) q^{13} +(-3.28528 - 5.69027i) q^{14} +(2.48477 - 4.30375i) q^{16} -1.88964 q^{17} +2.74286 q^{19} +(-0.466200 + 0.807482i) q^{20} +(1.57204 + 2.72285i) q^{22} +(-2.91385 - 5.04694i) q^{23} +(1.86207 - 3.22519i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(-2.65997 + 4.60720i) q^{29} +(-0.670300 - 1.16099i) q^{31} +(-2.20239 - 3.81465i) q^{32} +(-1.58816 + 2.75078i) q^{34} -4.41530 q^{35} +3.39611 q^{37} +(2.30525 - 3.99281i) q^{38} +(-1.11502 - 1.93128i) q^{40} +(0.898166 + 1.55567i) q^{41} +(-2.51508 + 4.35624i) q^{43} +1.54400 q^{44} -9.79585 q^{46} +(0.854339 - 1.47976i) q^{47} +(-4.13984 - 7.17041i) q^{49} +(-3.12997 - 5.42126i) q^{50} +(0.302367 - 0.523715i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(3.85867 - 6.68342i) q^{56} +(4.47117 + 7.74430i) q^{58} +(-5.63002 - 9.75149i) q^{59} +(-2.61545 + 4.53009i) q^{61} -2.25343 q^{62} +2.53503 q^{64} +(0.413751 - 0.716637i) q^{65} +(0.944514 + 1.63595i) q^{67} +(0.779918 + 1.35086i) q^{68} +(-3.71087 + 6.42741i) q^{70} +12.1839 q^{71} +9.88768 q^{73} +(2.85428 - 4.94376i) q^{74} +(-1.13207 - 1.96080i) q^{76} +(3.65573 + 6.33192i) q^{77} +(-6.17644 + 10.6979i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(-5.84158 + 10.1179i) q^{83} +(1.06722 + 1.84848i) q^{85} +(4.22762 + 7.32246i) q^{86} +(-1.84641 + 3.19808i) q^{88} +5.72873 q^{89} +2.86367 q^{91} +(-2.40528 + 4.16607i) q^{92} +(-1.43607 - 2.48734i) q^{94} +(-1.54909 - 2.68310i) q^{95} +(0.171689 - 0.297374i) q^{97} -13.9174 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.840456	−	1.45571i	0.594292	−	1.02934i	−0.399354	−	0.916797i	$-0.630766\pi$
$2$	0.840456	−	1.45571i	0.594292	−	1.02934i	0.993646	−	0.112548i	$-0.0359011\pi$
$3$		0			0
$3$		0			0
$4$	−0.412733	−	0.714874i	−0.206366	−	0.357437i
$5$	−0.564772	−	0.978214i	−0.252574	−	0.437471i	0.711660	−	0.702524i	$-0.247944\pi$
$5$	−0.564772	−	0.978214i	−0.252574	−	0.437471i	−0.964234	+	0.265054i	$0.914610\pi$
$6$		0			0
$7$	1.95446	−	3.38523i	0.738717	−	1.27950i	−0.214356	−	0.976756i	$-0.568765\pi$
$7$	1.95446	−	3.38523i	0.738717	−	1.27950i	0.953073	−	0.302740i	$-0.0979013\pi$
$8$	1.97429			0.698017
$9$		0			0
$10$	−1.89866			−0.600410
$11$	−0.935228	+	1.61986i	−0.281982	+	0.488407i	−0.971873	−	0.235506i	$-0.924325\pi$
$11$	−0.935228	+	1.61986i	−0.281982	+	0.488407i	0.689891	+	0.723913i	$0.257658\pi$
$12$		0			0
$13$	0.366299	+	0.634448i	0.101593	+	0.175964i	0.912341	−	0.409431i	$-0.134273\pi$
$13$	0.366299	+	0.634448i	0.101593	+	0.175964i	−0.810748	+	0.585395i	$0.800939\pi$
$14$	−3.28528	−	5.69027i	−0.878027	−	1.52079i
$15$		0			0
$16$	2.48477	−	4.30375i	0.621192	−	1.07594i
$17$	−1.88964			−0.458306			−0.229153	−	0.973390i	$-0.573596\pi$
$17$	−1.88964			−0.458306			−0.229153	+	0.973390i	$0.573596\pi$
$18$		0			0
$19$	2.74286			0.629254			0.314627	−	0.949215i	$-0.398121\pi$
$19$	2.74286			0.629254			0.314627	+	0.949215i	$0.398121\pi$
$20$	−0.466200	+	0.807482i	−0.104245	+	0.180558i
$21$		0			0
$22$	1.57204	+	2.72285i	0.335159	+	0.580513i
$23$	−2.91385	−	5.04694i	−0.607580	−	1.05236i	−0.991638	−	0.129050i	$-0.958807\pi$
$23$	−2.91385	−	5.04694i	−0.607580	−	1.05236i	0.384058	−	0.923309i	$-0.374526\pi$
$24$		0			0
$25$	1.86207	−	3.22519i	0.372413	−	0.645038i
$26$	1.23143			0.241504
$27$		0			0
$28$	−3.22668			−0.609786
$29$	−2.65997	+	4.60720i	−0.493944	+	0.855535i	−0.999976	−	0.00697928i	$-0.997778\pi$
$29$	−2.65997	+	4.60720i	−0.493944	+	0.855535i	0.506032	+	0.862515i	$0.331112\pi$
$30$		0			0
$31$	−0.670300	−	1.16099i	−0.120390	−	0.208521i	0.799532	−	0.600624i	$-0.205081\pi$
$31$	−0.670300	−	1.16099i	−0.120390	−	0.208521i	−0.919921	+	0.392103i	$0.871748\pi$
$32$	−2.20239	−	3.81465i	−0.389331	−	0.674341i
$33$		0			0
$34$	−1.58816	+	2.75078i	−0.272368	+	0.471755i
$35$	−4.41530			−0.746322
$36$		0			0
$37$	3.39611			0.558318			0.279159	−	0.960245i	$-0.409944\pi$
$37$	3.39611			0.558318			0.279159	+	0.960245i	$0.409944\pi$
$38$	2.30525	−	3.99281i	0.373961	−	0.647719i
$39$		0			0
$40$	−1.11502	−	1.93128i	−0.176301	−	0.305362i
$41$	0.898166	+	1.55567i	0.140270	+	0.242955i	0.927598	−	0.373579i	$-0.121870\pi$
$41$	0.898166	+	1.55567i	0.140270	+	0.242955i	−0.787328	+	0.616534i	$0.788536\pi$
$42$		0			0
$43$	−2.51508	+	4.35624i	−0.383546	+	0.664320i	−0.991566	−	0.129601i	$-0.958630\pi$
$43$	−2.51508	+	4.35624i	−0.383546	+	0.664320i	0.608021	+	0.793921i	$0.291964\pi$
$44$	1.54400			0.232766
$45$		0			0
$46$	−9.79585			−1.44432
$47$	0.854339	−	1.47976i	0.124618	−	0.215845i	−0.796965	−	0.604025i	$-0.793563\pi$
$47$	0.854339	−	1.47976i	0.124618	−	0.215845i	0.921584	+	0.388180i	$0.126896\pi$
$48$		0			0
$49$	−4.13984	−	7.17041i	−0.591405	−	1.02434i
$50$	−3.12997	−	5.42126i	−0.442644	−	0.766682i
$51$		0			0
$52$	0.302367	−	0.523715i	0.0419308	−	0.0726263i
$53$	−2.84494			−0.390783			−0.195391	−	0.980725i	$-0.562598\pi$
$53$	−2.84494			−0.390783			−0.195391	+	0.980725i	$0.562598\pi$
$54$		0			0
$55$	2.11276			0.284885
$56$	3.85867	−	6.68342i	0.515637	−	0.893109i
$57$		0			0
$58$	4.47117	+	7.74430i	0.587094	+	1.01688i
$59$	−5.63002	−	9.75149i	−0.732967	−	1.26954i	−0.955610	−	0.294635i	$-0.904802\pi$
$59$	−5.63002	−	9.75149i	−0.732967	−	1.26954i	0.222643	−	0.974900i	$-0.428531\pi$
$60$		0			0
$61$	−2.61545	+	4.53009i	−0.334874	+	0.580018i	−0.983461	−	0.181122i	$-0.942027\pi$
$61$	−2.61545	+	4.53009i	−0.334874	+	0.580018i	0.648587	+	0.761141i	$0.275360\pi$
$62$	−2.25343			−0.286186
$63$		0			0
$64$	2.53503			0.316879
$65$	0.413751	−	0.716637i	0.0513195	−	0.0888879i
$66$		0			0
$67$	0.944514	+	1.63595i	0.115391	+	0.199863i	0.917936	−	0.396729i	$-0.129855\pi$
$67$	0.944514	+	1.63595i	0.115391	+	0.199863i	−0.802545	+	0.596591i	$0.796521\pi$
$68$	0.779918	+	1.35086i	0.0945789	+	0.163816i
$69$		0			0
$70$	−3.71087	+	6.42741i	−0.443533	+	0.768222i
$71$	12.1839			1.44596			0.722980	−	0.690869i	$-0.242772\pi$
$71$	12.1839			1.44596			0.722980	+	0.690869i	$0.242772\pi$
$72$		0			0
$73$	9.88768			1.15727			0.578633	−	0.815588i	$-0.303587\pi$
$73$	9.88768			1.15727			0.578633	+	0.815588i	$0.303587\pi$
$74$	2.85428	−	4.94376i	0.331804	−	0.574701i
$75$		0			0
$76$	−1.13207	−	1.96080i	−0.129857	−	0.224919i
$77$	3.65573	+	6.33192i	0.416610	+	0.721589i
$78$		0			0
$79$	−6.17644	+	10.6979i	−0.694904	+	1.20361i	0.275310	+	0.961356i	$0.411220\pi$
$79$	−6.17644	+	10.6979i	−0.694904	+	1.20361i	−0.970213	+	0.242253i	$0.922114\pi$
$80$	−5.61331			−0.627587
$81$		0			0
$82$	3.01948			0.333445
$83$	−5.84158	+	10.1179i	−0.641197	+	1.11059i	0.343969	+	0.938981i	$0.388228\pi$
$83$	−5.84158	+	10.1179i	−0.641197	+	1.11059i	−0.985166	+	0.171605i	$0.945105\pi$
$84$		0			0
$85$	1.06722	+	1.84848i	0.115756	+	0.200495i
$86$	4.22762	+	7.32246i	0.455876	+	0.789601i
$87$		0			0
$88$	−1.84641	+	3.19808i	−0.196828	+	0.340916i
$89$	5.72873			0.607244			0.303622	−	0.952793i	$-0.401804\pi$
$89$	5.72873			0.607244			0.303622	+	0.952793i	$0.401804\pi$
$90$		0			0
$91$	2.86367			0.300194
$92$	−2.40528	+	4.16607i	−0.250768	+	0.434343i
$93$		0			0
$94$	−1.43607	−	2.48734i	−0.148119	−	0.256550i
$95$	−1.54909	−	2.68310i	−0.158933	−	0.275280i
$96$		0			0
$97$	0.171689	−	0.297374i	0.0174324	−	0.0301938i	−0.857178	−	0.515021i	$-0.827784\pi$
$97$	0.171689	−	0.297374i	0.0174324	−	0.0301938i	0.874610	+	0.484827i	$0.161117\pi$
$98$	−13.9174			−1.40587
$99$		0			0
$100$	−3.07414			−0.307414
$101$	−8.70113	+	15.0708i	−0.865794	+	1.49960i	0.000461665		1.00000i	$0.499853\pi$
$101$	−8.70113	+	15.0708i	−0.865794	+	1.49960i	−0.866256	+	0.499600i	$0.833480\pi$
$102$		0			0
$103$	7.90650	+	13.6945i	0.779051	+	1.34936i	0.932489	+	0.361197i	$0.117632\pi$
$103$	7.90650	+	13.6945i	0.779051	+	1.34936i	−0.153439	+	0.988158i	$0.549035\pi$
$104$	0.723180	+	1.25258i	0.0709136	+	0.122826i
$105$		0			0
$106$	−2.39105	+	4.14142i	−0.232239	+	0.402250i
$107$	16.5298			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$107$	16.5298			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	1.77568	−	3.07557i	0.169305	−	0.293245i
$111$		0			0
$112$	−9.71277	−	16.8230i	−0.917770	−	1.58963i
$113$	9.97241	+	17.2727i	0.938125	+	1.62488i	0.768964	+	0.639292i	$0.220772\pi$
$113$	9.97241	+	17.2727i	0.938125	+	1.62488i	0.169161	+	0.985588i	$0.445894\pi$
$114$		0			0
$115$	−3.29132	+	5.70074i	−0.306917	+	0.531596i
$116$	4.39142			0.407733
$117$		0			0
$118$	−18.9271			−1.74239
$119$	−3.69324	+	6.39687i	−0.338558	+	0.586400i
$120$		0			0
$121$	3.75070	+	6.49640i	0.340972	+	0.590582i
$122$	4.39634	+	7.61468i	0.398026	+	0.689401i
$123$		0			0
$124$	−0.553310	+	0.958361i	−0.0496887	+	0.0860634i
$125$	−9.85429			−0.881394
$126$		0			0
$127$	1.06946			0.0948989			0.0474495	−	0.998874i	$-0.484891\pi$
$127$	1.06946			0.0948989			0.0474495	+	0.998874i	$0.484891\pi$
$128$	6.53536	−	11.3196i	0.577650	−	1.00052i
$129$		0			0
$130$	−0.695479	−	1.20460i	−0.0609975	−	0.105651i
$131$	3.82015	+	6.61669i	0.333768	+	0.578103i	0.983247	−	0.182276i	$-0.0583465\pi$
$131$	3.82015	+	6.61669i	0.333768	+	0.578103i	−0.649479	+	0.760379i	$0.725013\pi$
$132$		0			0
$133$	5.36081	−	9.28519i	0.464841	−	0.805128i
$134$	3.17529			0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	7.82525	−	13.5537i	0.668556	−	1.15797i	−0.309752	−	0.950818i	$-0.600246\pi$
$137$	7.82525	−	13.5537i	0.668556	−	1.15797i	0.978308	−	0.207156i	$-0.0664208\pi$
$138$		0			0
$139$	−4.32847	−	7.49712i	−0.367136	−	0.635898i	0.621981	−	0.783033i	$-0.286328\pi$
$139$	−4.32847	−	7.49712i	−0.367136	−	0.635898i	−0.989116	+	0.147135i	$0.952995\pi$
$140$	1.82234	+	3.15638i	0.154016	+	0.266763i
$141$		0			0
$142$	10.2400	−	17.7362i	0.859322	−	1.48839i
$143$	−1.37029			−0.114590
$144$		0			0
$145$	6.00910			0.499029
$146$	8.31016	−	14.3936i	0.687754	−	1.19122i
$147$		0			0
$148$	−1.40169	−	2.42779i	−0.115218	−	0.199563i
$149$	−1.23191	−	2.13373i	−0.100922	−	0.174802i	0.811143	−	0.584848i	$-0.198846\pi$
$149$	−1.23191	−	2.13373i	−0.100922	−	0.174802i	−0.912065	+	0.410046i	$0.865513\pi$
$150$		0			0
$151$	5.25670	−	9.10488i	0.427785	−	0.740945i	−0.568891	−	0.822413i	$-0.692628\pi$
$151$	5.25670	−	9.10488i	0.427785	−	0.740945i	0.996676	+	0.0814681i	$0.0259609\pi$
$152$	5.41519			0.439230
$153$		0			0
$154$	12.2899			0.990351
$155$	−0.757134	+	1.31139i	−0.0608145	+	0.105334i
$156$		0			0
$157$	−0.179974	−	0.311725i	−0.0143635	−	0.0248783i	0.858754	−	0.512388i	$-0.171239\pi$
$157$	−0.179974	−	0.311725i	−0.0143635	−	0.0248783i	−0.873118	+	0.487509i	$0.837906\pi$
$158$	10.3820	+	17.9822i	0.825951	+	1.43059i
$159$		0			0
$160$	−2.48770	+	4.30882i	−0.196670	+	0.340642i
$161$	−22.7800			−1.79532
$162$		0			0
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	0.741405	−	1.28415i	0.0578940	−	0.100275i
$165$		0			0
$166$	9.81919	+	17.0073i	0.762117	+	1.32002i
$167$	1.08792	+	1.88434i	0.0841861	+	0.145815i	0.905044	−	0.425318i	$-0.139838\pi$
$167$	1.08792	+	1.88434i	0.0841861	+	0.145815i	−0.820858	+	0.571132i	$0.806504\pi$
$168$		0			0
$169$	6.23165	−	10.7935i	0.479358	−	0.830272i
$170$	3.58780			0.275172
$171$		0			0
$172$	4.15222			0.316604
$173$	−8.78351	+	15.2135i	−0.667798	+	1.15666i	0.310721	+	0.950501i	$0.399430\pi$
$173$	−8.78351	+	15.2135i	−0.667798	+	1.15666i	−0.978519	+	0.206159i	$0.933904\pi$
$174$		0			0
$175$	−7.27867	−	12.6070i	−0.550216	−	0.953001i
$176$	4.64765	+	8.04997i	0.350330	+	0.606789i
$177$		0			0
$178$	4.81475	−	8.33939i	0.360881	−	0.625064i
$179$	−1.00447			−0.0750777			−0.0375388	−	0.999295i	$-0.511952\pi$
$179$	−1.00447			−0.0750777			−0.0375388	+	0.999295i	$0.511952\pi$
$180$		0			0
$181$	−21.1732			−1.57380			−0.786898	−	0.617084i	$-0.788314\pi$
$181$	−21.1732			−1.57380			−0.786898	+	0.617084i	$0.788314\pi$
$182$	2.40679	−	4.16868i	0.178403	−	0.309003i
$183$		0			0
$184$	−5.75278	−	9.96411i	−0.424101	−	0.734564i
$185$	−1.91803	−	3.32212i	−0.141016	−	0.244247i
$186$		0			0
$187$	1.76725	−	3.06096i	0.129234	−	0.223840i
$188$	−1.41045			−0.102868
$189$		0			0
$190$	−5.20776			−0.377811
$191$	−4.91419	+	8.51163i	−0.355578	+	0.615880i	−0.987217	−	0.159383i	$-0.949049\pi$
$191$	−4.91419	+	8.51163i	−0.355578	+	0.615880i	0.631638	+	0.775263i	$0.282383\pi$
$192$		0			0
$193$	5.57804	+	9.66145i	0.401516	+	0.695447i	0.993909	−	0.110203i	$-0.0351500\pi$
$193$	5.57804	+	9.66145i	0.401516	+	0.695447i	−0.592393	+	0.805649i	$0.701817\pi$
$194$	−0.288594	−	0.499860i	−0.0207199	−	0.0358879i
$195$		0			0
$196$	−3.41729	+	5.91893i	−0.244092	+	0.422781i
$197$	−9.08994			−0.647631			−0.323816	−	0.946120i	$-0.604966\pi$
$197$	−9.08994			−0.647631			−0.323816	+	0.946120i	$0.604966\pi$
$198$		0			0
$199$	−14.6939			−1.04162			−0.520811	−	0.853672i	$-0.674370\pi$
$199$	−14.6939			−1.04162			−0.520811	+	0.853672i	$0.674370\pi$
$200$	3.67625	−	6.36746i	0.259950	−	0.450247i
$201$		0			0
$202$	14.6258	+	25.3327i	1.02907	+	1.78240i
$203$	10.3976	+	18.0092i	0.729769	+	1.26400i
$204$		0			0
$205$	1.01452	−	1.75720i	0.0708570	−	0.122728i
$206$	26.5803			1.85194
$207$		0			0
$208$	3.64067			0.252435
$209$	−2.56520	+	4.44305i	−0.177438	+	0.307332i
$210$		0			0
$211$	−3.92915	−	6.80549i	−0.270494	−	0.468509i	0.698495	−	0.715615i	$-0.253854\pi$
$211$	−3.92915	−	6.80549i	−0.270494	−	0.468509i	−0.968988	+	0.247106i	$0.920520\pi$
$212$	1.17420	+	2.03378i	0.0806445	+	0.139680i
$213$		0			0
$214$	13.8926	−	24.0627i	0.949678	−	1.64489i
$215$	5.68178			0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$	−3.96564	+	6.86869i	−0.268587	+	0.465207i
$219$		0			0
$220$	−0.872006	−	1.51036i	−0.0587907	−	0.101828i
$221$	−0.692174	−	1.19888i	−0.0465607	−	0.0806455i
$222$		0			0
$223$	4.37044	−	7.56983i	0.292666	−	0.506913i	−0.681773	−	0.731564i	$-0.738791\pi$
$223$	4.37044	−	7.56983i	0.292666	−	0.506913i	0.974439	+	0.224651i	$0.0721241\pi$
$224$	−17.2179			−1.15042
$225$		0			0
$226$	33.5255			2.23008
$227$	2.03421	−	3.52335i	0.135015	−	0.233853i	−0.790588	−	0.612348i	$-0.790225\pi$
$227$	2.03421	−	3.52335i	0.135015	−	0.233853i	0.925603	+	0.378495i	$0.123558\pi$
$228$		0			0
$229$	−8.07794	−	13.9914i	−0.533805	−	0.924577i	−0.999220	−	0.0394849i	$-0.987428\pi$
$229$	−8.07794	−	13.9914i	−0.533805	−	0.924577i	0.465415	−	0.885093i	$-0.345905\pi$
$230$	5.53242	+	9.58244i	0.364797	+	0.631847i
$231$		0			0
$232$	−5.25154	+	9.09594i	−0.344781	+	0.597178i
$233$	−17.2132			−1.12767			−0.563836	−	0.825887i	$-0.690675\pi$
$233$	−17.2132			−1.12767			−0.563836	+	0.825887i	$0.690675\pi$
$234$		0			0
$235$	−1.93003			−0.125901
$236$	−4.64739	+	8.04952i	−0.302519	+	0.523979i
$237$		0			0
$238$	6.20800	+	10.7526i	0.402405	+	0.696986i
$239$	−0.767720	−	1.32973i	−0.0496597	−	0.0860131i	0.840127	−	0.542390i	$-0.182480\pi$
$239$	−0.767720	−	1.32973i	−0.0496597	−	0.0860131i	−0.889787	+	0.456377i	$0.849147\pi$
$240$		0			0
$241$	2.76084	−	4.78191i	0.177841	−	0.308030i	−0.763300	−	0.646045i	$-0.776422\pi$
$241$	2.76084	−	4.78191i	0.177841	−	0.308030i	0.941141	+	0.338015i	$0.109755\pi$
$242$	12.6092			0.810549
$243$		0			0
$244$	4.31792			0.276427
$245$	−4.67613	+	8.09929i	−0.298747	+	0.517445i
$246$		0			0
$247$	1.00471	+	1.74020i	0.0639279	+	0.110726i
$248$	−1.32337	−	2.29214i	−0.0840339	−	0.145551i
$249$		0			0
$250$	−8.28210	+	14.3450i	−0.523806	+	0.907258i
$251$	21.4409			1.35334			0.676668	−	0.736288i	$-0.263423\pi$
$251$	21.4409			1.35334			0.676668	+	0.736288i	$0.263423\pi$
$252$		0			0
$253$	10.9005			0.685306
$254$	0.898831	−	1.55682i	0.0563977	−	0.0976837i
$255$		0			0
$256$	−8.45034	−	14.6364i	−0.528146	−	0.914776i
$257$	−7.39324	−	12.8055i	−0.461177	−	0.798783i	0.537843	−	0.843045i	$-0.319239\pi$
$257$	−7.39324	−	12.8055i	−0.461177	−	0.798783i	−0.999020	+	0.0442626i	$0.985906\pi$
$258$		0			0
$259$	6.63757	−	11.4966i	0.412439	−	0.714365i
$260$	−0.683074			−0.0423625
$261$		0			0
$262$	12.8427			0.793423
$263$	1.40138	−	2.42726i	0.0864127	−	0.149671i	−0.819580	−	0.572965i	$-0.805793\pi$
$263$	1.40138	−	2.42726i	0.0864127	−	0.149671i	0.905992	+	0.423294i	$0.139126\pi$
$264$		0			0
$265$	1.60674	+	2.78296i	0.0987015	+	0.170956i
$266$	−9.01104	−	15.6076i	−0.552503	−	0.956963i
$267$		0			0
$268$	0.779664	−	1.35042i	0.0476256	−	0.0824899i
$269$	0.356528			0.0217379			0.0108689	−	0.999941i	$-0.496540\pi$
$269$	0.356528			0.0217379			0.0108689	+	0.999941i	$0.496540\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	−4.69533	+	8.13255i	−0.284696	+	0.493108i
$273$		0			0
$274$	−13.1536	−	22.7826i	−0.794636	−	1.37635i
$275$	3.48291	+	6.03258i	0.210027	+	0.363778i
$276$		0			0
$277$	−12.4950	+	21.6419i	−0.750751	+	1.30034i	0.196709	+	0.980462i	$0.436975\pi$
$277$	−12.4950	+	21.6419i	−0.750751	+	1.30034i	−0.947459	+	0.319876i	$0.896359\pi$
$278$	−14.5515			−0.872744
$279$		0			0
$280$	−8.71708			−0.520945
$281$	3.66143	−	6.34179i	0.218423	−	0.378319i	−0.735903	−	0.677087i	$-0.763242\pi$
$281$	3.66143	−	6.34179i	0.218423	−	0.378319i	0.954326	+	0.298767i	$0.0965755\pi$
$282$		0			0
$283$	7.19404	+	12.4604i	0.427641	+	0.740697i	0.996663	−	0.0816258i	$-0.0260112\pi$
$283$	7.19404	+	12.4604i	0.427641	+	0.740697i	−0.569022	+	0.822323i	$0.692678\pi$
$284$	−5.02868	−	8.70993i	−0.298397	−	0.516839i
$285$		0			0
$286$	−1.15167	+	1.99475i	−0.0680997	+	0.117952i
$287$	7.02172			0.414479
$288$		0			0
$289$	−13.4292			−0.789956
$290$	5.05039	−	8.74752i	0.296569	−	0.513672i
$291$		0			0
$292$	−4.08097	−	7.06845i	−0.238821	−	0.413650i
$293$	−7.20776	−	12.4842i	−0.421082	−	0.729335i	0.574964	−	0.818179i	$-0.305016\pi$
$293$	−7.20776	−	12.4842i	−0.421082	−	0.729335i	−0.996046	+	0.0888441i	$0.971683\pi$
$294$		0			0
$295$	−6.35936	+	11.0147i	−0.370256	+	0.641303i
$296$	6.70491			0.389715
$297$		0			0
$298$	−4.14147			−0.239909
$299$	2.13468	−	3.69737i	0.123452	−	0.213825i
$300$		0			0
$301$	9.83124	+	17.0282i	0.566663	+	0.981489i
$302$	−8.83606	−	15.3045i	−0.508458	−	0.880675i
$303$		0			0
$304$	6.81536	−	11.8046i	0.390888	−	0.677038i
$305$	5.90853			0.338321
$306$		0			0
$307$	−30.4326			−1.73688			−0.868440	−	0.495795i	$-0.834877\pi$
$307$	−30.4326			−1.73688			−0.868440	+	0.495795i	$0.834877\pi$
$308$	3.01768	−	5.22678i	0.171948	−	0.297823i
$309$		0			0
$310$	1.27268	+	2.20434i	0.0722831	+	0.125198i
$311$	−6.99780	−	12.1206i	−0.396809	−	0.687293i	0.596521	−	0.802597i	$-0.296549\pi$
$311$	−6.99780	−	12.1206i	−0.396809	−	0.687293i	−0.993330	+	0.115304i	$0.963216\pi$
$312$		0			0
$313$	−11.0438	+	19.1284i	−0.624231	+	1.08120i	0.364457	+	0.931220i	$0.381254\pi$
$313$	−11.0438	+	19.1284i	−0.624231	+	1.08120i	−0.988689	+	0.149981i	$0.952079\pi$
$314$	−0.605042			−0.0341445
$315$		0			0
$316$	10.1969			0.573619
$317$	8.69436	−	15.0591i	0.488324	−	0.845802i	−0.511586	−	0.859232i	$-0.670942\pi$
$317$	8.69436	−	15.0591i	0.488324	−	0.845802i	0.999910	+	0.0134302i	$0.00427511\pi$
$318$		0			0
$319$	−4.97535	−	8.61756i	−0.278566	−	0.482491i
$320$	−1.43171	−	2.47980i	−0.0800352	−	0.138625i
$321$		0			0
$322$	−19.1456	+	33.1612i	−1.06694	+	1.84800i
$323$	−5.18302			−0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$	12.2863	−	21.2804i	0.680474	−	1.17861i
$327$		0			0
$328$	1.77324	+	3.07134i	0.0979108	+	0.169586i
$329$	−3.33954	−	5.78426i	−0.184115	−	0.318897i
$330$		0			0
$331$	−0.432074	+	0.748374i	−0.0237489	+	0.0411343i	−0.877656	−	0.479292i	$-0.840894\pi$
$331$	−0.432074	+	0.748374i	−0.0237489	+	0.0411343i	0.853907	+	0.520426i	$0.174227\pi$
$332$	9.64405			0.529286
$333$		0			0
$334$	3.65741			0.200124
$335$	1.06687	−	1.84787i	0.0582893	−	0.100960i
$336$		0			0
$337$	−0.209264	−	0.362457i	−0.0113994	−	0.0197443i	0.860269	−	0.509840i	$-0.170295\pi$
$337$	−0.209264	−	0.362457i	−0.0113994	−	0.0197443i	−0.871669	+	0.490095i	$0.836962\pi$
$338$	−10.4749	−	18.1430i	−0.569757	−	0.986848i
$339$		0			0
$340$	0.880952	−	1.52585i	0.0477763	−	0.0827510i
$341$	2.50753			0.135791
$342$		0			0
$343$	−5.00216			−0.270091
$344$	−4.96549	+	8.60048i	−0.267721	+	0.463707i
$345$		0			0
$346$	14.7643	+	25.5725i	0.793734	+	1.37479i
$347$	11.7049	+	20.2734i	0.628351	+	1.08834i	0.987883	+	0.155202i	$0.0496029\pi$
$347$	11.7049	+	20.2734i	0.628351	+	1.08834i	−0.359532	+	0.933133i	$0.617064\pi$
$348$		0			0
$349$	−10.5882	+	18.3393i	−0.566773	+	0.981680i	0.430109	+	0.902777i	$0.358475\pi$
$349$	−10.5882	+	18.3393i	−0.566773	+	0.981680i	−0.996882	+	0.0789033i	$0.974858\pi$
$350$	−24.4696			−1.30796
$351$		0			0
$352$	8.23894			0.439137
$353$	11.7722	−	20.3901i	0.626573	−	1.08526i	−0.361662	−	0.932309i	$-0.617791\pi$
$353$	11.7722	−	20.3901i	0.626573	−	1.08526i	0.988235	−	0.152946i	$-0.0488762\pi$
$354$		0			0
$355$	−6.88111	−	11.9184i	−0.365211	−	0.632565i
$356$	−2.36444	−	4.09532i	−0.125315	−	0.217052i
$357$		0			0
$358$	−0.844214	+	1.46222i	−0.0446181	+	0.0772808i
$359$	10.4609			0.552107			0.276053	−	0.961142i	$-0.410973\pi$
$359$	10.4609			0.552107			0.276053	+	0.961142i	$0.410973\pi$
$360$		0			0
$361$	−11.4767			−0.604039
$362$	−17.7952	+	30.8222i	−0.935294	+	1.61998i
$363$		0			0
$364$	−1.18193	−	2.04716i	−0.0619500	−	0.107301i
$365$	−5.58428	−	9.67227i	−0.292295	−	0.506269i
$366$		0			0
$367$	−10.6291	+	18.4102i	−0.554836	+	0.961005i	0.443080	+	0.896482i	$0.353886\pi$
$367$	−10.6291	+	18.4102i	−0.554836	+	0.961005i	−0.997916	+	0.0645226i	$0.979448\pi$
$368$	−28.9610			−1.50970
$369$		0			0
$370$	−6.44808			−0.335220
$371$	−5.56033	+	9.63077i	−0.288678	+	0.500005i
$372$		0			0
$373$	−1.15504	−	2.00059i	−0.0598059	−	0.103587i	0.834572	−	0.550898i	$-0.185715\pi$
$373$	−1.15504	−	2.00059i	−0.0598059	−	0.103587i	−0.894378	+	0.447312i	$0.852381\pi$
$374$	−2.97059	−	5.14521i	−0.153605	−	0.266052i
$375$		0			0
$376$	1.68671	−	2.92147i	0.0869855	−	0.150663i
$377$	−3.89737			−0.200725
$378$		0			0
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	−1.27872	+	2.21481i	−0.0655969	+	0.113617i
$381$		0			0
$382$	8.26032	+	14.3073i	0.422635	+	0.732025i
$383$	−9.82727	−	17.0213i	−0.502150	−	0.869749i	−0.999997	−	0.00248418i	$-0.999209\pi$
$383$	−9.82727	−	17.0213i	−0.502150	−	0.869749i	0.497847	−	0.867265i	$-0.334124\pi$
$384$		0			0
$385$	4.12931	−	7.15218i	0.210449	−	0.364509i
$386$	18.7524			0.954472
$387$		0			0
$388$	−0.283447			−0.0143898
$389$	−9.42129	+	16.3182i	−0.477679	+	0.827364i	−0.999673	−	0.0255856i	$-0.991855\pi$
$389$	−9.42129	+	16.3182i	−0.477679	+	0.827364i	0.521994	+	0.852949i	$0.325188\pi$
$390$		0			0
$391$	5.50614	+	9.53691i	0.278457	+	0.482302i
$392$	−8.17324	−	14.1565i	−0.412811	−	0.715009i
$393$		0			0
$394$	−7.63969	+	13.2323i	−0.384882	+	0.666636i
$395$	13.9531			0.702058
$396$		0			0
$397$	20.1178			1.00968			0.504841	−	0.863212i	$-0.331551\pi$
$397$	20.1178			1.00968			0.504841	+	0.863212i	$0.331551\pi$
$398$	−12.3496	+	21.3901i	−0.619028	+	1.07219i
$399$		0			0
$400$	−9.25360	−	16.0277i	−0.462680	−	0.801385i
$401$	−15.4028	−	26.6785i	−0.769181	−	1.33226i	−0.938007	−	0.346615i	$-0.887331\pi$
$401$	−15.4028	−	26.6785i	−0.769181	−	1.33226i	0.168826	−	0.985646i	$-0.446002\pi$
$402$		0			0
$403$	0.491061	−	0.850542i	0.0244615	−	0.0423685i
$404$	14.3650			0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	−3.17614	+	5.50124i	−0.157435	+	0.272686i
$408$		0			0
$409$	−19.8460	−	34.3743i	−0.981323	−	1.69970i	−0.657256	−	0.753667i	$-0.728283\pi$
$409$	−19.8460	−	34.3743i	−0.981323	−	1.69970i	−0.324067	−	0.946034i	$-0.605050\pi$
$410$	−1.70532	−	2.95369i	−0.0842196	−	0.145873i
$411$		0			0
$412$	6.52655	−	11.3043i	0.321540	−	0.556923i
$413$	−44.0146			−2.16582
$414$		0			0
$415$	13.1966			0.647798
$416$	1.61347	−	2.79460i	0.0791067	−	0.137017i
$417$		0			0
$418$	4.31187	+	7.46838i	0.210900	+	0.365290i
$419$	7.72057	+	13.3724i	0.377174	+	0.653285i	0.990650	−	0.136429i	$-0.0435624\pi$
$419$	7.72057	+	13.3724i	0.377174	+	0.653285i	−0.613476	+	0.789714i	$0.710229\pi$
$420$		0			0
$421$	9.04682	−	15.6696i	0.440915	−	0.763687i	−0.556843	−	0.830618i	$-0.687987\pi$
$421$	9.04682	−	15.6696i	0.440915	−	0.763687i	0.997758	+	0.0669307i	$0.0213206\pi$
$422$	−13.2091			−0.643009
$423$		0			0
$424$	−5.61674			−0.272773
$425$	−3.51864	+	6.09446i	−0.170679	+	0.295625i
$426$		0			0
$427$	10.2236	+	17.7078i	0.494754	+	0.856939i
$428$	−6.82240	−	11.8167i	−0.329773	−	0.571184i
$429$		0			0
$430$	4.77529	−	8.27104i	0.230285	−	0.398865i
$431$	28.9683			1.39535			0.697677	−	0.716412i	$-0.254217\pi$
$431$	28.9683			1.39535			0.697677	+	0.716412i	$0.254217\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	−4.40425	+	7.62838i	−0.211411	+	0.366174i
$435$		0			0
$436$	1.94746	+	3.37309i	0.0932662	+	0.161542i
$437$	−7.99227	−	13.8430i	−0.382322	−	0.662201i
$438$		0			0
$439$	−5.13177	+	8.88848i	−0.244926	+	0.424224i	−0.962111	−	0.272659i	$-0.912097\pi$
$439$	−5.13177	+	8.88848i	−0.244926	+	0.424224i	0.717185	+	0.696883i	$0.245430\pi$
$440$	4.17120			0.198854
$441$		0			0
$442$	−2.32697			−0.110683
$443$	10.9543	−	18.9733i	0.520452	−	0.901450i	−0.479265	−	0.877670i	$-0.659097\pi$
$443$	10.9543	−	18.9733i	0.520452	−	0.901450i	0.999717	−	0.0237794i	$-0.00756994\pi$
$444$		0			0
$445$	−3.23543	−	5.60393i	−0.153374	−	0.265652i
$446$	−7.34633	−	12.7242i	−0.347859	−	0.602509i
$447$		0			0
$448$	4.95462	−	8.58165i	0.234084	−	0.405445i
$449$	−9.97130			−0.470575			−0.235287	−	0.971926i	$-0.575603\pi$
$449$	−9.97130			−0.470575			−0.235287	+	0.971926i	$0.575603\pi$
$450$		0			0
$451$	−3.35996			−0.158214
$452$	8.23188	−	14.2580i	0.387195	−	0.670642i
$453$		0			0
$454$	−3.41932	−	5.92244i	−0.160477	−	0.277954i
$455$	−1.61732	−	2.80128i	−0.0758211	−	0.131326i
$456$		0			0
$457$	3.80905	−	6.59747i	0.178180	−	0.308617i	−0.763077	−	0.646307i	$-0.776312\pi$
$457$	3.80905	−	6.59747i	0.178180	−	0.308617i	0.941257	+	0.337691i	$0.109646\pi$
$458$	−27.1566			−1.26894
$459$		0			0
$460$	5.43375			0.253350
$461$	−11.4003	+	19.7458i	−0.530963	+	0.919656i	0.468384	+	0.883525i	$0.344836\pi$
$461$	−11.4003	+	19.7458i	−0.530963	+	0.919656i	−0.999347	+	0.0361304i	$0.988497\pi$
$462$		0			0
$463$	4.39787	+	7.61733i	0.204386	+	0.354007i	0.949937	−	0.312442i	$-0.101147\pi$
$463$	4.39787	+	7.61733i	0.204386	+	0.354007i	−0.745551	+	0.666449i	$0.767813\pi$
$464$	13.2188	+	22.8956i	0.613668	+	1.06290i
$465$		0			0
$466$	−14.4669	+	25.0574i	−0.670166	+	1.16076i
$467$	10.9976			0.508906			0.254453	−	0.967085i	$-0.418105\pi$
$467$	10.9976			0.508906			0.254453	+	0.967085i	$0.418105\pi$
$468$		0			0
$469$	7.38406			0.340964
$470$	−1.62210	+	2.80956i	−0.0748220	+	0.129596i
$471$		0			0
$472$	−11.1153	−	19.2523i	−0.511623	−	0.886157i
$473$	−4.70434	−	8.14816i	−0.216306	−	0.374653i
$474$		0			0
$475$	5.10738	−	8.84624i	0.234343	−	0.405893i
$476$	6.09728			0.279468
$477$		0			0
$478$	−2.58094			−0.118049
$479$	12.8463	−	22.2504i	0.586961	−	1.01665i	−0.407667	−	0.913131i	$-0.633658\pi$
$479$	12.8463	−	22.2504i	0.586961	−	1.01665i	0.994628	−	0.103515i	$-0.0330090\pi$
$480$		0			0
$481$	1.24399	+	2.15466i	0.0567212	+	0.0982440i
$482$	−4.64072	−	8.03797i	−0.211379	−	0.366119i
$483$		0			0
$484$	3.09607	−	5.36255i	0.140731	−	0.243752i
$485$	−0.387861			−0.0176119
$486$		0			0
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	−5.16365	+	8.94370i	−0.233747	+	0.404862i
$489$		0			0
$490$	7.86016	+	13.6142i	0.355086	+	0.615027i
$491$	4.35414	+	7.54159i	0.196499	+	0.340347i	0.947391	−	0.320078i	$-0.103709\pi$
$491$	4.35414	+	7.54159i	0.196499	+	0.340347i	−0.750892	+	0.660425i	$0.770376\pi$
$492$		0			0
$493$	5.02639	−	8.70596i	0.226377	−	0.392097i
$494$	3.37764			0.151967
$495$		0			0
$496$	−6.66217			−0.299140
$497$	23.8129	−	41.2451i	1.06815	−	1.85010i
$498$		0			0
$499$	−5.81774	−	10.0766i	−0.260438	−	0.451091i	0.705921	−	0.708291i	$-0.250534\pi$
$499$	−5.81774	−	10.0766i	−0.260438	−	0.451091i	−0.966358	+	0.257200i	$0.917200\pi$
$500$	4.06719	+	7.04458i	0.181890	+	0.315043i
$501$		0			0
$502$	18.0201	−	31.2118i	0.804277	−	1.39305i
$503$	37.7991			1.68538			0.842689	−	0.538400i	$-0.180971\pi$
$503$	37.7991			1.68538			0.842689	+	0.538400i	$0.180971\pi$
$504$		0			0
$505$	19.6566			0.874708
$506$	9.16135	−	15.8679i	0.407272	−	0.705416i
$507$		0			0
$508$	−0.441400	−	0.764527i	−0.0195840	−	0.0339204i
$509$	11.7868	+	20.4154i	0.522442	+	0.904896i	0.999659	+	0.0261103i	$0.00831211\pi$
$509$	11.7868	+	20.4154i	0.522442	+	0.904896i	−0.477217	+	0.878785i	$0.658355\pi$
$510$		0			0
$511$	19.3251	−	33.4720i	0.854891	−	1.48072i
$512$	−2.26711			−0.100193
$513$		0			0
$514$	−24.8548			−1.09630
$515$	8.93074	−	15.4685i	0.393536	−	0.681623i
$516$		0			0
$517$	1.59800	+	2.76782i	0.0702801	+	0.121729i
$518$	−11.1572	−	19.3248i	−0.490218	−	0.849083i
$519$		0			0
$520$	0.816864	−	1.41485i	0.0358218	−	0.0620453i
$521$	−7.86948			−0.344768			−0.172384	−	0.985030i	$-0.555147\pi$
$521$	−7.86948			−0.344768			−0.172384	+	0.985030i	$0.555147\pi$
$522$		0			0
$523$	33.2935			1.45582			0.727911	−	0.685672i	$-0.240491\pi$
$523$	33.2935			1.45582			0.727911	+	0.685672i	$0.240491\pi$
$524$	3.15340	−	5.46185i	0.137757	−	0.238602i
$525$		0			0
$526$	−2.35559	−	4.08001i	−0.102709	−	0.177897i
$527$	1.26663	+	2.19387i	0.0551752	+	0.0955663i
$528$		0			0
$529$	−5.48104	+	9.49344i	−0.238306	+	0.412758i
$530$	5.40159			0.234630
$531$		0			0
$532$	−8.85032			−0.383710
$533$	−0.657995	+	1.13968i	−0.0285009	+	0.0493650i
$534$		0			0
$535$	−9.33558	−	16.1697i	−0.403612	−	0.699077i
$536$	1.86474	+	3.22983i	0.0805447	+	0.139507i
$537$		0			0
$538$	0.299646	−	0.519002i	0.0129186	−	0.0223758i
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	−10.2087	+	17.6820i	−0.438503	+	0.759509i
$543$		0			0
$544$	4.16173	+	7.20833i	0.178433	+	0.309055i
$545$	2.66484	+	4.61564i	0.114149	+	0.197712i
$546$		0			0
$547$	10.4456	−	18.0923i	0.446621	−	0.773570i	−0.551543	−	0.834146i	$-0.685961\pi$
$547$	10.4456	−	18.0923i	0.446621	−	0.773570i	0.998164	+	0.0605770i	$0.0192941\pi$
$548$	−12.9190			−0.551870
$549$		0			0
$550$	11.7089			0.499271
$551$	−7.29591	+	12.6369i	−0.310816	+	0.538349i
$552$		0			0
$553$	24.1432	+	41.8173i	1.02667	+	1.77825i
$554$	21.0030	+	36.3782i	0.892330	+	1.54556i
$555$		0			0
$556$	−3.57300	+	6.18862i	−0.151529	+	0.262456i
$557$	−8.57840			−0.363478			−0.181739	−	0.983347i	$-0.558173\pi$
$557$	−8.57840			−0.363478			−0.181739	+	0.983347i	$0.558173\pi$
$558$		0			0
$559$	−3.68508			−0.155862
$560$	−10.9710	+	19.0023i	−0.463609	+	0.802995i
$561$		0			0
$562$	−6.15455	−	10.6600i	−0.259614	−	0.449665i
$563$	−7.85744	−	13.6095i	−0.331152	−	0.573571i	0.651586	−	0.758574i	$-0.274104\pi$
$563$	−7.85744	−	13.6095i	−0.331152	−	0.573571i	−0.982738	+	0.185003i	$0.940770\pi$
$564$		0			0
$565$	11.2643	−	19.5103i	0.473892	−	0.820804i
$566$	24.1851			1.01658
$567$		0			0
$568$	24.0545			1.00930
$569$	6.33639	−	10.9750i	0.265635	−	0.460094i	−0.702094	−	0.712084i	$-0.747752\pi$
$569$	6.33639	−	10.9750i	0.265635	−	0.460094i	0.967730	+	0.251990i	$0.0810849\pi$
$570$		0			0
$571$	13.1613	+	22.7961i	0.550785	+	0.953988i	0.998218	+	0.0596704i	$0.0190050\pi$
$571$	13.1613	+	22.7961i	0.550785	+	0.953988i	−0.447433	+	0.894317i	$0.647662\pi$
$572$	0.565565	+	0.979587i	0.0236474	+	0.0409586i
$573$		0			0
$574$	5.90145	−	10.2216i	0.246322	−	0.426642i
$575$	−21.7031			−0.905082
$576$		0			0
$577$	−22.1154			−0.920676			−0.460338	−	0.887744i	$-0.652272\pi$
$577$	−22.1154			−0.920676			−0.460338	+	0.887744i	$0.652272\pi$
$578$	−11.2867	+	19.5491i	−0.469465	+	0.813136i
$579$		0			0
$580$	−2.48015	−	4.29575i	−0.102983	−	0.178371i
$581$	22.8343	+	39.5502i	0.947326	+	1.64082i
$582$		0			0
$583$	2.66067	−	4.60842i	0.110194	−	0.190861i
$584$	19.5211			0.807790
$585$		0			0
$586$	−24.2312			−1.00098
$587$	7.15157	−	12.3869i	0.295177	−	0.511261i	−0.679849	−	0.733352i	$-0.737955\pi$
$587$	7.15157	−	12.3869i	0.295177	−	0.511261i	0.975026	+	0.222091i	$0.0712881\pi$
$588$		0			0
$589$	−1.83854	−	3.18444i	−0.0757556	−	0.131213i
$590$	10.6895	+	18.5148i	0.440081	+	0.762242i
$591$		0			0
$592$	8.43856	−	14.6160i	0.346823	−	0.600714i
$593$	−47.7300			−1.96004			−0.980018	−	0.198908i	$-0.936260\pi$
$593$	−47.7300			−1.96004			−0.980018	+	0.198908i	$0.936260\pi$
$594$		0			0
$595$	8.34334			0.342044
$596$	−1.01690	+	1.76132i	−0.0416539	+	0.0721466i
$597$		0			0
$598$	−3.58821	−	6.21496i	−0.146733	−	0.254149i
$599$	−0.249785	−	0.432640i	−0.0102059	−	0.0176772i	0.860877	−	0.508813i	$-0.169915\pi$
$599$	−0.249785	−	0.432640i	−0.0102059	−	0.0176772i	−0.871083	+	0.491135i	$0.836582\pi$
$600$		0			0
$601$	8.46354	−	14.6593i	0.345235	−	0.597965i	−0.640161	−	0.768240i	$-0.721133\pi$
$601$	8.46354	−	14.6593i	0.345235	−	0.597965i	0.985396	+	0.170276i	$0.0544659\pi$
$602$	33.0509			1.34705
$603$		0			0
$604$	−8.67846			−0.353121
$605$	4.23658	−	7.33797i	0.172241	−	0.298331i
$606$		0			0
$607$	−0.347316	−	0.601569i	−0.0140971	−	0.0244170i	0.858891	−	0.512159i	$-0.171154\pi$
$607$	−0.347316	−	0.601569i	−0.0140971	−	0.0244170i	−0.872988	+	0.487742i	$0.837821\pi$
$608$	−6.04084	−	10.4630i	−0.244988	−	0.424332i
$609$		0			0
$610$	4.96586	−	8.60112i	0.201062	−	0.348249i
$611$	1.25177			0.0506413
$612$		0			0
$613$	−32.6633			−1.31926			−0.659630	−	0.751590i	$-0.729287\pi$
$613$	−32.6633			−1.31926			−0.659630	+	0.751590i	$0.729287\pi$
$614$	−25.5772	+	44.3011i	−1.03221	+	1.78785i
$615$		0			0
$616$	7.21747	+	12.5010i	0.290800	+	0.503681i
$617$	11.4422	+	19.8185i	0.460646	+	0.797863i	0.998993	−	0.0448606i	$-0.0142844\pi$
$617$	11.4422	+	19.8185i	0.460646	+	0.797863i	−0.538347	+	0.842723i	$0.680951\pi$
$618$		0			0
$619$	−4.24287	+	7.34886i	−0.170535	+	0.295376i	−0.938607	−	0.344988i	$-0.887883\pi$
$619$	−4.24287	+	7.34886i	−0.170535	+	0.295376i	0.768072	+	0.640364i	$0.221216\pi$
$620$	1.24998			0.0502002
$621$		0			0
$622$	−23.5254			−0.943282
$623$	11.1966	−	19.3931i	0.448582	−	0.776966i
$624$		0			0
$625$	−3.74490	−	6.48635i	−0.149796	−	0.259454i
$626$	18.5636	+	32.1531i	0.741952	+	1.28510i
$627$		0			0
$628$	−0.148563	+	0.257318i	−0.00592829	+	0.0102681i
$629$	−6.41744			−0.255880
$630$		0			0
$631$	1.59173			0.0633657			0.0316829	−	0.999498i	$-0.489913\pi$
$631$	1.59173			0.0633657			0.0316829	+	0.999498i	$0.489913\pi$
$632$	−12.1941	+	21.1208i	−0.485054	+	0.840138i
$633$		0			0
$634$	−14.6145	−	25.3130i	−0.580414	−	1.00531i
$635$	−0.603999	−	1.04616i	−0.0239690	−	0.0415155i
$636$		0			0
$637$	3.03284	−	5.25303i	0.120165	−	0.208133i
$638$	−16.7263			−0.662199
$639$		0			0
$640$	−14.7640			−0.583597
$641$	10.8373	−	18.7708i	0.428049	−	0.741402i	−0.568651	−	0.822579i	$-0.692534\pi$
$641$	10.8373	−	18.7708i	0.428049	−	0.741402i	0.996700	+	0.0811767i	$0.0258678\pi$
$642$		0			0
$643$	3.45103	+	5.97736i	0.136095	+	0.235724i	0.926015	−	0.377486i	$-0.123211\pi$
$643$	3.45103	+	5.97736i	0.136095	+	0.235724i	−0.789920	+	0.613210i	$0.789878\pi$
$644$	9.40207	+	16.2849i	0.370493	+	0.641713i
$645$		0			0
$646$	−4.35610	+	7.54499i	−0.171388	+	0.296854i
$647$	6.18972			0.243343			0.121671	−	0.992570i	$-0.461175\pi$
$647$	6.18972			0.243343			0.121671	+	0.992570i	$0.461175\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$	2.29301	−	3.97161i	0.0899392	−	0.155779i
$651$		0			0
$652$	−6.03357	−	10.4504i	−0.236293	−	0.409271i
$653$	−13.6072	−	23.5684i	−0.532492	−	0.922304i	−0.999280	−	0.0379345i	$-0.987922\pi$
$653$	−13.6072	−	23.5684i	−0.532492	−	0.922304i	0.466788	−	0.884369i	$-0.345411\pi$
$654$		0			0
$655$	4.31503	−	7.47385i	0.168602	−	0.292027i
$656$	8.92694			0.348539
$657$		0			0
$658$	−11.2270			−0.437672
$659$	2.64100	−	4.57434i	0.102879	−	0.178191i	−0.809991	−	0.586443i	$-0.800528\pi$
$659$	2.64100	−	4.57434i	0.102879	−	0.178191i	0.912870	+	0.408251i	$0.133861\pi$
$660$		0			0
$661$	−5.83252	−	10.1022i	−0.226859	−	0.392931i	0.730017	−	0.683429i	$-0.239512\pi$
$661$	−5.83252	−	10.1022i	−0.226859	−	0.392931i	−0.956875	+	0.290498i	$0.906179\pi$
$662$	0.726278	+	1.25795i	0.0282276	+	0.0488916i
$663$		0			0
$664$	−11.5330	+	19.9757i	−0.447566	+	0.775207i
$665$	−12.1105			−0.469626
$666$		0			0
$667$	31.0030			1.20044
$668$	0.898044	−	1.55546i	0.0347464	−	0.0601824i
$669$		0			0
$670$	−1.79332	−	3.10611i	−0.0692818	−	0.120000i
$671$	−4.89208	−	8.47333i	−0.188857	−	0.327109i
$672$		0			0
$673$	−24.5512	+	42.5239i	−0.946380	+	1.63918i	−0.193415	+	0.981117i	$0.561956\pi$
$673$	−24.5512	+	42.5239i	−0.946380	+	1.63918i	−0.752965	+	0.658061i	$0.771377\pi$
$674$	−0.703510			−0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	−11.3095	+	19.5887i	−0.434660	+	0.752854i	−0.997268	−	0.0738704i	$-0.976465\pi$
$677$	−11.3095	+	19.5887i	−0.434660	+	0.752854i	0.562608	+	0.826724i	$0.309798\pi$
$678$		0			0
$679$	−0.671120	−	1.16241i	−0.0257552	−	0.0446093i
$680$	2.10700	+	3.64942i	0.0807996	+	0.139949i
$681$		0			0
$682$	2.10747	−	3.65025i	0.0806993	−	0.139775i
$683$	17.1386			0.655791			0.327896	−	0.944714i	$-0.393661\pi$
$683$	17.1386			0.655791			0.327896	+	0.944714i	$0.393661\pi$
$684$		0			0
$685$	−17.6779			−0.675439
$686$	−4.20409	+	7.28170i	−0.160513	+	0.278017i
$687$		0			0
$688$	12.4988	+	21.6485i	0.476511	+	0.825341i
$689$	−1.04210	−	1.80497i	−0.0397008	−	0.0687639i
$690$		0			0
$691$	−9.12796	+	15.8101i	−0.347244	+	0.601444i	−0.985759	−	0.168165i	$-0.946216\pi$
$691$	−9.12796	+	15.8101i	−0.347244	+	0.601444i	0.638515	+	0.769609i	$0.279549\pi$
$692$	14.5010			0.551244
$693$		0			0
$694$	39.3497			1.49370
$695$	−4.88919	+	8.46833i	−0.185458	+	0.321222i
$696$		0			0
$697$	−1.69721	−	2.93966i	−0.0642866	−	0.111348i
$698$	17.7978	+	30.8268i	0.673658	+	1.16681i
$699$		0			0
$700$	−6.00829	+	10.4067i	−0.227092	+	0.393335i
$701$	2.92075			0.110315			0.0551575	−	0.998478i	$-0.482434\pi$
$701$	2.92075			0.110315			0.0551575	+	0.998478i	$0.482434\pi$
$702$		0			0
$703$	9.31505			0.351324
$704$	−2.37083	+	4.10640i	−0.0893540	+	0.154766i
$705$		0			0
$706$	−19.7881	−	34.2740i	−0.744734	−	1.28992i
$707$	34.0120	+	58.9106i	1.27915	+	2.21556i
$708$		0			0
$709$	−15.0137	+	26.0044i	−0.563850	+	0.976617i	0.433306	+	0.901247i	$0.357347\pi$
$709$	−15.0137	+	26.0044i	−0.563850	+	0.976617i	−0.997156	+	0.0753698i	$0.975986\pi$
$710$	−23.1331			−0.868169
$711$		0			0
$712$	11.3102			0.423867
$713$	−3.90631	+	6.76593i	−0.146292	+	0.253386i
$714$		0			0
$715$	0.773903	+	1.34044i	0.0289423	+	0.0501296i
$716$	0.414578	+	0.718071i	0.0154935	+	0.0268356i
$717$		0			0
$718$	8.79195	−	15.2281i	0.328113	−	0.568308i
$719$	−40.0569			−1.49387			−0.746936	−	0.664896i	$-0.768476\pi$
$719$	−40.0569			−1.49387			−0.746936	+	0.664896i	$0.768476\pi$
$720$		0			0
$721$	61.8118			2.30199
$722$	−9.64570	+	16.7068i	−0.358976	+	0.621764i
$723$		0			0
$724$	8.73890	+	15.1362i	0.324779	+	0.562533i
$725$	9.90607	+	17.1578i	0.367902	+	0.637225i
$726$		0			0
$727$	0.769390	−	1.33262i	0.0285351	−	0.0494243i	−0.851405	−	0.524509i	$-0.824249\pi$
$727$	0.769390	−	1.33262i	0.0285351	−	0.0494243i	0.879940	+	0.475084i	$0.157582\pi$
$728$	5.65371			0.209540
$729$		0			0
$730$	−18.7734			−0.694834
$731$	4.75260	−	8.23174i	0.175781	−	0.304462i
$732$		0			0
$733$	0.755947	+	1.30934i	0.0279215	+	0.0483615i	0.879649	−	0.475624i	$-0.157778\pi$
$733$	0.755947	+	1.30934i	0.0279215	+	0.0483615i	−0.851727	+	0.523986i	$0.824444\pi$
$734$	17.8666	+	30.9459i	0.659470	+	1.14224i
$735$		0			0
$736$	−12.8349	+	22.2306i	−0.473099	+	0.819432i
$737$	−3.53334			−0.130152
$738$		0			0
$739$	21.3558			0.785584			0.392792	−	0.919627i	$-0.371509\pi$
$739$	21.3558			0.785584			0.392792	+	0.919627i	$0.371509\pi$
$740$	−1.58327	+	2.74230i	−0.0582021	+	0.100809i
$741$		0			0
$742$	9.34643	+	16.1885i	0.343118	+	0.594298i
$743$	−10.1644	−	17.6052i	−0.372895	−	0.645872i	0.617115	−	0.786873i	$-0.288301\pi$
$743$	−10.1644	−	17.6052i	−0.372895	−	0.645872i	−0.990009	+	0.141001i	$0.954968\pi$
$744$		0			0
$745$	−1.39150	+	2.41015i	−0.0509806	+	0.0883009i
$746$	−3.88305			−0.142169
$747$		0			0
$748$	−2.91760			−0.106678
$749$	32.3069	−	55.9572i	1.18047	−	2.04463i
$750$		0			0
$751$	−2.13158	−	3.69200i	−0.0777824	−	0.134723i	0.824510	−	0.565847i	$-0.191451\pi$
$751$	−2.13158	−	3.69200i	−0.0777824	−	0.134723i	−0.902293	+	0.431124i	$0.858117\pi$
$752$	−4.24567	−	7.35371i	−0.154824	−	0.268162i
$753$		0			0
$754$	−3.27557	+	5.67346i	−0.119289	+	0.206615i
$755$	−11.8754			−0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	10.5510	−	18.2748i	0.383229	−	0.663772i
$759$		0			0
$760$	−3.05835	−	5.29721i	−0.110938	−	0.192150i
$761$	9.08056	+	15.7280i	0.329170	+	0.570139i	0.982347	−	0.187066i	$-0.0598978\pi$
$761$	9.08056	+	15.7280i	0.329170	+	0.570139i	−0.653177	+	0.757205i	$0.726564\pi$
$762$		0			0
$763$	−9.22201	+	15.9730i	−0.333859	+	0.578261i
$764$	8.11299			0.293518
$765$		0			0
$766$	−33.0375			−1.19369
$767$	4.12454	−	7.14392i	0.148929	−	0.257952i
$768$		0			0
$769$	−12.4274	−	21.5248i	−0.448142	−	0.776205i	0.550123	−	0.835084i	$-0.314581\pi$
$769$	−12.4274	−	21.5248i	−0.448142	−	0.776205i	−0.998265	+	0.0588785i	$0.981248\pi$
$770$	−6.94101	−	12.0222i	−0.250137	−	0.433249i
$771$		0			0
$772$	4.60448	−	7.97520i	0.165719	−	0.287034i
$773$	−38.4832			−1.38414			−0.692071	−	0.721829i	$-0.743302\pi$
$773$	−38.4832			−1.38414			−0.692071	+	0.721829i	$0.743302\pi$
$774$		0			0
$775$	−4.99257			−0.179338
$776$	0.338964	−	0.587103i	0.0121681	−	0.0210758i
$777$		0			0
$778$	15.8364	+	27.4294i	0.567761	+	0.983391i
$779$	2.46354	+	4.26698i	0.0882655	+	0.152880i
$780$		0			0
$781$	−11.3947	+	19.7362i	−0.407734	+	0.706216i
$782$	18.5107			0.661940
$783$		0			0
$784$	−41.1462			−1.46951
$785$	−0.203289	+	0.352107i	−0.00725569	+	0.0125672i
$786$		0			0
$787$	0.536239	+	0.928794i	0.0191149	+	0.0331079i	0.875425	−	0.483355i	$-0.160582\pi$
$787$	0.536239	+	0.928794i	0.0191149	+	0.0331079i	−0.856310	+	0.516463i	$0.827249\pi$
$788$	3.75172	+	6.49816i	0.133649	+	0.231487i
$789$		0			0
$790$	11.7270	−	20.3117i	0.417227	−	0.722659i
$791$	77.9627			2.77204
$792$		0			0
$793$	−3.83214			−0.136083
$794$	16.9081	−	29.2857i	0.600046	−	1.03931i
$795$		0			0
$796$	6.06465	+	10.5043i	0.214956	+	0.372314i
$797$	12.6236	+	21.8647i	0.447151	+	0.774488i	0.998199	−	0.0599851i	$-0.0191053\pi$
$797$	12.6236	+	21.8647i	0.447151	+	0.774488i	−0.551048	+	0.834473i	$0.685772\pi$
$798$		0			0
$799$	−1.61440	+	2.79622i	−0.0571132	+	0.0989230i
$800$	−16.4040			−0.579968
$801$		0			0
$802$	−51.7817			−1.82847
$803$	−9.24723	+	16.0167i	−0.326328	+	0.565216i
$804$		0			0
$805$	12.8655	+	22.2837i	0.453450	+	0.785399i
$806$	−0.825430	−	1.42969i	−0.0290745	−	0.0503586i
$807$		0			0
$808$	−17.1785	+	29.7541i	−0.604339	+	1.04675i
$809$	11.7337			0.412536			0.206268	−	0.978495i	$-0.433868\pi$
$809$	11.7337			0.412536			0.206268	+	0.978495i	$0.433868\pi$
$810$		0			0
$811$	−38.4085			−1.34871			−0.674353	−	0.738409i	$-0.735577\pi$
$811$	−38.4085			−1.34871			−0.674353	+	0.738409i	$0.735577\pi$
$812$	8.58287	−	14.8660i	0.301200	−	0.521693i
$813$		0			0
$814$	5.33881	+	9.24709i	0.187125	+	0.324110i
$815$	−8.25616	−	14.3001i	−0.289201	−	0.500910i
$816$		0			0
$817$	−6.89849	+	11.9485i	−0.241348	+	0.418027i
$818$	−66.7189			−2.33277
$819$		0			0
$820$	−1.67490			−0.0584901
$821$	13.3660	−	23.1506i	0.466477	−	0.807963i	−0.532789	−	0.846248i	$-0.678856\pi$
$821$	13.3660	−	23.1506i	0.466477	−	0.807963i	0.999267	+	0.0382852i	$0.0121895\pi$
$822$		0			0
$823$	−2.18213	−	3.77956i	−0.0760643	−	0.131747i	0.825484	−	0.564425i	$-0.190902\pi$
$823$	−2.18213	−	3.77956i	−0.0760643	−	0.131747i	−0.901549	+	0.432678i	$0.857569\pi$
$824$	15.6097	+	27.0368i	0.543790	+	0.941872i
$825$		0			0
$826$	−36.9924	+	64.0727i	−1.28713	+	2.22937i
$827$	39.1454			1.36122			0.680610	−	0.732646i	$-0.261715\pi$
$827$	39.1454			1.36122			0.680610	+	0.732646i	$0.261715\pi$
$828$		0			0
$829$	−32.8867			−1.14220			−0.571101	−	0.820880i	$-0.693484\pi$
$829$	−32.8867			−1.14220			−0.571101	+	0.820880i	$0.693484\pi$
$830$	11.0912	−	19.2105i	0.384981	−	0.666807i
$831$		0			0
$832$	0.928579	+	1.60835i	0.0321927	+	0.0557594i
$833$	7.82282	+	13.5495i	0.271045	+	0.469463i
$834$		0			0
$835$	1.22886	−	2.12844i	0.0425264	−	0.0736578i
$836$	4.23496			0.146469
$837$		0			0
$838$	25.9552			0.896607
$839$	15.8202	−	27.4013i	0.546173	−	0.945999i	−0.452359	−	0.891836i	$-0.649418\pi$
$839$	15.8202	−	27.4013i	0.546173	−	0.945999i	0.998532	−	0.0541631i	$-0.0172491\pi$
$840$		0			0
$841$	0.349144	+	0.604736i	0.0120395	+	0.0208530i
$842$	−15.2069	−	26.3391i	−0.524065	−	0.907707i
$843$		0			0
$844$	−3.24338	+	5.61770i	−0.111642	+	0.193369i
$845$	−14.0778			−0.484293
$846$		0			0
$847$	29.3224			1.00753
$848$	−7.06902	+	12.2439i	−0.242751	+	0.420458i
$849$		0			0
$850$	5.91452	+	10.2443i	0.202866	+	0.351375i
$851$	−9.89576	−	17.1400i	−0.339222	−	0.587550i
$852$		0			0
$853$	2.82882	−	4.89967i	0.0968571	−	0.167761i	−0.813525	−	0.581530i	$-0.802454\pi$
$853$	2.82882	−	4.89967i	0.0968571	−	0.167761i	0.910382	+	0.413768i	$0.135788\pi$
$854$	34.3699			1.17611
$855$		0			0
$856$	32.6346			1.11543
$857$	−20.6052	+	35.6892i	−0.703859	+	1.21912i	0.263242	+	0.964730i	$0.415208\pi$
$857$	−20.6052	+	35.6892i	−0.703859	+	1.21912i	−0.967102	+	0.254391i	$0.918125\pi$
$858$		0			0
$859$	−17.9272	−	31.0508i	−0.611668	−	1.05944i	−0.990959	−	0.134163i	$-0.957165\pi$
$859$	−17.9272	−	31.0508i	−0.611668	−	1.05944i	0.379291	−	0.925277i	$-0.376168\pi$
$860$	−2.34506	−	4.06176i	−0.0799658	−	0.138505i
$861$		0			0
$862$	24.3466	−	42.1695i	0.829248	−	1.43630i
$863$	−20.9694			−0.713806			−0.356903	−	0.934142i	$-0.616167\pi$
$863$	−20.9694			−0.713806			−0.356903	+	0.934142i	$0.616167\pi$
$864$		0			0
$865$	19.8427			0.674673
$866$	−31.5929	+	54.7205i	−1.07357	+	1.85948i
$867$		0			0
$868$	2.16285	+	3.74616i	0.0734118	+	0.127153i
$869$	−11.5528	−	20.0100i	−0.391900	−	0.678791i
$870$		0			0
$871$	−0.691949	+	1.19849i	−0.0234458	+	0.0406093i
$872$	−9.31556			−0.315465
$873$		0			0
$874$	−26.8686			−0.908844
$875$	−19.2598	+	33.3590i	−0.651101	+	1.12774i
$876$		0			0
$877$	−10.2552	−	17.7625i	−0.346294	−	0.599798i	0.639294	−	0.768962i	$-0.279227\pi$
$877$	−10.2552	−	17.7625i	−0.346294	−	0.599798i	−0.985588	+	0.169164i	$0.945893\pi$
$878$	8.62605	+	14.9408i	0.291115	+	0.504226i
$879$		0			0
$880$	5.24973	−	9.09279i	0.176968	−	0.306518i
$881$	38.2877			1.28994			0.644972	−	0.764206i	$-0.276869\pi$
$881$	38.2877			1.28994			0.644972	+	0.764206i	$0.276869\pi$
$882$		0			0
$883$	−17.4465			−0.587122			−0.293561	−	0.955940i	$-0.594840\pi$
$883$	−17.4465			−0.587122			−0.293561	+	0.955940i	$0.594840\pi$
$884$	−0.571366	+	0.989635i	−0.0192171	+	0.0332850i
$885$		0			0
$886$	−18.4131	−	31.8925i	−0.618601	−	1.07145i
$887$	−27.1084	−	46.9532i	−0.910213	−	1.57653i	−0.813763	−	0.581196i	$-0.802585\pi$
$887$	−27.1084	−	46.9532i	−0.910213	−	1.57653i	−0.0964492	−	0.995338i	$-0.530749\pi$
$888$		0			0
$889$	2.09021	−	3.62035i	0.0701034	−	0.121423i
$890$	−10.8769			−0.364596
$891$		0			0
$892$	−7.21530			−0.241586
$893$	2.34333	−	4.05876i	0.0784165	−	0.135821i
$894$		0			0
$895$	0.567297	+	0.982588i	0.0189627	+	0.0328443i
$896$	−25.5462	−	44.2473i	−0.853439	−	1.47820i
$897$		0			0
$898$	−8.38044	+	14.5153i	−0.279659	+	0.484383i
$899$	7.13191			0.237862
$900$		0			0
$901$	5.37593			0.179098
$902$	−2.82390	+	4.89114i	−0.0940256	+	0.162857i
$903$		0			0
$904$	19.6884	+	34.1013i	0.654827	+	1.13419i
$905$	11.9581	+	20.7120i	0.397499	+	0.688489i
$906$		0			0
$907$	−14.3416	+	24.8403i	−0.476204	+	0.824810i	−0.999628	−	0.0272623i	$-0.991321\pi$
$907$	−14.3416	+	24.8403i	−0.476204	+	0.824810i	0.523424	+	0.852072i	$0.324654\pi$
$908$	−3.35834			−0.111450
$909$		0			0
$910$	−5.43715			−0.180240
$911$	−14.1908	+	24.5792i	−0.470162	+	0.814345i	−0.999418	−	0.0341177i	$-0.989138\pi$
$911$	−14.1908	+	24.5792i	−0.470162	+	0.814345i	0.529256	+	0.848462i	$0.322471\pi$
$912$		0			0
$913$	−10.9264	−	18.9251i	−0.361612	−	0.626330i
$914$	−6.40268	−	11.0898i	−0.211782	−	0.366817i
$915$		0			0
$916$	−6.66806	+	11.5494i	−0.220319	+	0.381603i
$917$	29.8653			0.986240
$918$		0			0
$919$	37.7786			1.24620			0.623101	−	0.782141i	$-0.285873\pi$
$919$	37.7786			1.24620			0.623101	+	0.782141i	$0.285873\pi$
$920$	−6.49802	+	11.2549i	−0.214233	+	0.371063i
$921$		0			0
$922$	19.1628	+	33.1910i	0.631095	+	1.09309i
$923$	4.46294	+	7.73004i	0.146899	+	0.254437i
$924$		0			0
$925$	6.32378	−	10.9531i	0.207925	−	0.360136i
$926$	14.7849			0.485861
$927$		0			0
$928$	23.4331			0.769230
$929$	−17.2884	+	29.9444i	−0.567215	+	0.982445i	0.429625	+	0.903007i	$0.358646\pi$
$929$	−17.2884	+	29.9444i	−0.567215	+	0.982445i	−0.996840	+	0.0794378i	$0.974688\pi$
$930$		0			0
$931$	−11.3550	−	19.6674i	−0.372144	−	0.644573i
$932$	7.10444	+	12.3052i	0.232714	+	0.403072i
$933$		0			0
$934$	9.24296	−	16.0093i	0.302439	−	0.523839i
$935$	−3.99237			−0.130564
$936$		0			0
$937$	−19.4368			−0.634972			−0.317486	−	0.948263i	$-0.602839\pi$
$937$	−19.4368			−0.634972			−0.317486	+	0.948263i	$0.602839\pi$
$938$	6.20598	−	10.7491i	0.202632	−	0.350970i
$939$		0			0
$940$	0.796585	+	1.37973i	0.0259817	+	0.0450017i
$941$	4.96923	+	8.60696i	0.161992	+	0.280579i	0.935583	−	0.353107i	$-0.114875\pi$
$941$	4.96923	+	8.60696i	0.161992	+	0.280579i	−0.773591	+	0.633685i	$0.781541\pi$
$942$		0			0
$943$	5.23424	−	9.06597i	0.170450	−	0.295229i
$944$	−55.9572			−1.82125
$945$		0			0
$946$	−15.8152			−0.514195
$947$	8.45535	−	14.6451i	0.274762	−	0.475902i	−0.695313	−	0.718707i	$-0.744734\pi$
$947$	8.45535	−	14.6451i	0.274762	−	0.475902i	0.970075	+	0.242805i	$0.0780676\pi$
$948$		0			0
$949$	3.62185	+	6.27322i	0.117570	+	0.203637i
$950$	−8.58505	−	14.8697i	−0.278536	−	0.482438i
$951$		0			0
$952$	−7.29151	+	12.6293i	−0.236319	+	0.409317i
$953$	−17.3573			−0.562259			−0.281129	−	0.959670i	$-0.590709\pi$
$953$	−17.3573			−0.562259			−0.281129	+	0.959670i	$0.590709\pi$
$954$		0			0
$955$	11.1016			0.359239
$956$	−0.633726	+	1.09765i	−0.0204962	+	0.0355004i
$957$		0			0
$958$	−21.5934	−	37.4009i	−0.697652	−	1.20837i
$959$	−30.5883	−	52.9805i	−0.987748	−	1.71083i
$960$		0			0
$961$	14.6014	−	25.2904i	0.471013	−	0.815818i
$962$	4.18208			0.134836
$963$		0			0
$964$	−4.55795			−0.146802
$965$	6.30065	−	10.9130i	0.202825	−	0.351303i
$966$		0			0
$967$	8.39168	+	14.5348i	0.269858	+	0.467408i	0.968825	−	0.247746i	$-0.0796899\pi$
$967$	8.39168	+	14.5348i	0.269858	+	0.467408i	−0.698967	+	0.715154i	$0.746357\pi$
$968$	7.40496	+	12.8258i	0.238004	+	0.412236i
$969$		0			0
$970$	−0.325980	+	0.564614i	−0.0104666	+	0.0181287i
$971$	33.4811			1.07446			0.537230	−	0.843436i	$-0.319471\pi$
$971$	33.4811			1.07446			0.537230	+	0.843436i	$0.319471\pi$
$972$		0			0
$973$	−33.8393			−1.08484
$974$	−25.5331	+	44.2246i	−0.818133	+	1.41705i
$975$		0			0
$976$	12.9976	+	22.5124i	0.416042	+	0.720606i
$977$	11.3674	+	19.6889i	0.363676	+	0.629905i	0.988563	−	0.150810i	$-0.0481882\pi$
$977$	11.3674	+	19.6889i	0.363676	+	0.629905i	−0.624887	+	0.780715i	$0.714855\pi$
$978$		0			0
$979$	−5.35767	+	9.27976i	−0.171232	+	0.296582i
$980$	7.71997			0.246605
$981$		0			0
$982$	14.6378			0.467112
$983$	23.5798	−	40.8414i	0.752078	−	1.30264i	−0.194735	−	0.980856i	$-0.562385\pi$
$983$	23.5798	−	40.8414i	0.752078	−	1.30264i	0.946814	−	0.321782i	$-0.104282\pi$
$984$		0			0
$985$	5.13374	+	8.89190i	0.163575	+	0.283320i
$986$	−8.44892	−	14.6340i	−0.269068	−	0.466040i
$987$		0			0
$988$	0.829350	−	1.43648i	0.0263851	−	0.0457004i
$989$	29.3142			0.932138
$990$		0			0
$991$	−4.37673			−0.139032			−0.0695158	−	0.997581i	$-0.522145\pi$
$991$	−4.37673			−0.139032			−0.0695158	+	0.997581i	$0.522145\pi$
$992$	−2.95252	+	5.11392i	−0.0937428	+	0.162367i
$993$		0			0
$994$	−40.0274	−	69.3295i	−1.26959	−	2.19900i
$995$	8.29869	+	14.3738i	0.263086	+	0.455679i
$996$		0			0
$997$	1.07225	−	1.85719i	0.0339585	−	0.0588179i	−0.848547	−	0.529121i	$-0.822522\pi$
$997$	1.07225	−	1.85719i	0.0339585	−	0.0588179i	0.882505	+	0.470303i	$0.155855\pi$
$998$	−19.5582			−0.619104
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.b.487.6		12
3.2	odd	2		729.2.c.e.487.1		12
9.2	odd	6		729.2.a.a.1.6		6
9.4	even	3	inner	729.2.c.b.244.6		12
9.5	odd	6		729.2.c.e.244.1		12
9.7	even	3		729.2.a.d.1.1		6
27.2	odd	18		243.2.e.d.109.2		12
27.4	even	9		81.2.e.a.19.2		12
27.5	odd	18		243.2.e.d.136.2		12
27.7	even	9		243.2.e.b.28.1		12
27.11	odd	18		27.2.e.a.4.1	✓	12
27.13	even	9		243.2.e.b.217.1		12
27.14	odd	18		243.2.e.c.217.2		12
27.16	even	9		81.2.e.a.64.2		12
27.20	odd	18		243.2.e.c.28.2		12
27.22	even	9		243.2.e.a.136.1		12
27.23	odd	18		27.2.e.a.7.1	yes	12
27.25	even	9		243.2.e.a.109.1		12
108.11	even	18		432.2.u.c.193.1		12
108.23	even	18		432.2.u.c.385.1		12
135.23	even	36		675.2.u.b.574.4		24
135.38	even	36		675.2.u.b.274.1		24
135.77	even	36		675.2.u.b.574.1		24
135.92	even	36		675.2.u.b.274.4		24
135.104	odd	18		675.2.l.c.601.2		12
135.119	odd	18		675.2.l.c.301.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	27.11	odd	18
27.2.e.a.7.1	yes	12	27.23	odd	18
81.2.e.a.19.2		12	27.4	even	9
81.2.e.a.64.2		12	27.16	even	9
243.2.e.a.109.1		12	27.25	even	9
243.2.e.a.136.1		12	27.22	even	9
243.2.e.b.28.1		12	27.7	even	9
243.2.e.b.217.1		12	27.13	even	9
243.2.e.c.28.2		12	27.20	odd	18
243.2.e.c.217.2		12	27.14	odd	18
243.2.e.d.109.2		12	27.2	odd	18
243.2.e.d.136.2		12	27.5	odd	18
432.2.u.c.193.1		12	108.11	even	18
432.2.u.c.385.1		12	108.23	even	18
675.2.l.c.301.2		12	135.119	odd	18
675.2.l.c.601.2		12	135.104	odd	18
675.2.u.b.274.1		24	135.38	even	36
675.2.u.b.274.4		24	135.92	even	36
675.2.u.b.574.1		24	135.77	even	36
675.2.u.b.574.4		24	135.23	even	36
729.2.a.a.1.6		6	9.2	odd	6
729.2.a.d.1.1		6	9.7	even	3
729.2.c.b.244.6		12	9.4	even	3	inner
729.2.c.b.487.6		12	1.1	even	1	trivial
729.2.c.e.244.1		12	9.5	odd	6
729.2.c.e.487.1		12	3.2	odd	2

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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.840456 - 1.45571i) q^{2} +(-0.412733 - 0.714874i) q^{4} +(-0.564772 - 0.978214i) q^{5} +(1.95446 - 3.38523i) q^{7} +1.97429 q^{8} +O(q^{10})\)	\(q+(0.840456 - 1.45571i) q^{2} +(-0.412733 - 0.714874i) q^{4} +(-0.564772 - 0.978214i) q^{5} +(1.95446 - 3.38523i) q^{7} +1.97429 q^{8} -1.89866 q^{10} +(-0.935228 + 1.61986i) q^{11} +(0.366299 + 0.634448i) q^{13} +(-3.28528 - 5.69027i) q^{14} +(2.48477 - 4.30375i) q^{16} -1.88964 q^{17} +2.74286 q^{19} +(-0.466200 + 0.807482i) q^{20} +(1.57204 + 2.72285i) q^{22} +(-2.91385 - 5.04694i) q^{23} +(1.86207 - 3.22519i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(-2.65997 + 4.60720i) q^{29} +(-0.670300 - 1.16099i) q^{31} +(-2.20239 - 3.81465i) q^{32} +(-1.58816 + 2.75078i) q^{34} -4.41530 q^{35} +3.39611 q^{37} +(2.30525 - 3.99281i) q^{38} +(-1.11502 - 1.93128i) q^{40} +(0.898166 + 1.55567i) q^{41} +(-2.51508 + 4.35624i) q^{43} +1.54400 q^{44} -9.79585 q^{46} +(0.854339 - 1.47976i) q^{47} +(-4.13984 - 7.17041i) q^{49} +(-3.12997 - 5.42126i) q^{50} +(0.302367 - 0.523715i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(3.85867 - 6.68342i) q^{56} +(4.47117 + 7.74430i) q^{58} +(-5.63002 - 9.75149i) q^{59} +(-2.61545 + 4.53009i) q^{61} -2.25343 q^{62} +2.53503 q^{64} +(0.413751 - 0.716637i) q^{65} +(0.944514 + 1.63595i) q^{67} +(0.779918 + 1.35086i) q^{68} +(-3.71087 + 6.42741i) q^{70} +12.1839 q^{71} +9.88768 q^{73} +(2.85428 - 4.94376i) q^{74} +(-1.13207 - 1.96080i) q^{76} +(3.65573 + 6.33192i) q^{77} +(-6.17644 + 10.6979i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(-5.84158 + 10.1179i) q^{83} +(1.06722 + 1.84848i) q^{85} +(4.22762 + 7.32246i) q^{86} +(-1.84641 + 3.19808i) q^{88} +5.72873 q^{89} +2.86367 q^{91} +(-2.40528 + 4.16607i) q^{92} +(-1.43607 - 2.48734i) q^{94} +(-1.54909 - 2.68310i) q^{95} +(0.171689 - 0.297374i) q^{97} -13.9174 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

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