LMFDB - Embedded newform 729.2.i.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

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("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66910 - 0.417440i) q^{2} +(5.04536 + 1.61773i) q^{4} +(2.30401 + 1.04730i) q^{5} +(0.333383 + 2.44079i) q^{7} +(-7.96289 - 3.99911i) q^{8} +O(q^{10})$	\(q+(-2.66910 - 0.417440i) q^{2} +(5.04536 + 1.61773i) q^{4} +(2.30401 + 1.04730i) q^{5} +(0.333383 + 2.44079i) q^{7} +(-7.96289 - 3.99911i) q^{8} +(-5.71246 - 3.75714i) q^{10} +(2.51287 - 0.195316i) q^{11} +(-0.870322 - 2.54361i) q^{13} +(0.129052 - 6.65389i) q^{14} +(10.9634 + 7.83616i) q^{16} +(2.69059 - 6.23748i) q^{17} +(4.40120 - 5.91184i) q^{19} +(9.93032 + 9.01128i) q^{20} +(-6.78865 - 0.527655i) q^{22} +(-1.96035 - 1.51938i) q^{23} +(0.924025 + 1.05882i) q^{25} +(1.26117 + 7.15247i) q^{26} +(-2.26651 + 12.8540i) q^{28} +(3.92297 - 2.36752i) q^{29} +(0.332893 - 0.0129178i) q^{31} +(-13.2681 - 13.0132i) q^{32} +(-9.78522 + 15.5253i) q^{34} +(-1.78813 + 5.97277i) q^{35} +(-1.45474 + 1.54193i) q^{37} +(-14.2151 + 13.9421i) q^{38} +(-14.1583 - 17.5536i) q^{40} +(-2.52421 + 6.53786i) q^{41} +(-0.0847579 - 0.329050i) q^{43} +(12.9943 + 3.07971i) q^{44} +(4.59812 + 4.87372i) q^{46} +(9.02289 + 0.350129i) q^{47} +(0.897270 - 0.249772i) q^{49} +(-2.02433 - 3.21181i) q^{50} +(-0.276211 - 14.2414i) q^{52} +(-10.0630 + 3.66262i) q^{53} +(5.99424 + 2.18173i) q^{55} +(7.10632 - 20.7690i) q^{56} +(-11.4591 + 4.68156i) q^{58} +(2.19593 + 4.59239i) q^{59} +(4.43170 - 1.42097i) q^{61} +(-0.893919 - 0.104484i) q^{62} +(13.8870 + 18.6535i) q^{64} +(0.658698 - 6.77200i) q^{65} +(1.54194 + 0.930564i) q^{67} +(23.6655 - 27.1177i) q^{68} +(7.26598 - 15.1955i) q^{70} +(-0.147599 + 2.53418i) q^{71} +(9.68672 - 6.37106i) q^{73} +(4.52651 - 3.50831i) q^{74} +(31.7694 - 22.7074i) q^{76} +(1.31447 + 6.06829i) q^{77} +(-6.76355 + 8.38549i) q^{79} +(17.0530 + 29.5366i) q^{80} +(9.46653 - 16.3965i) q^{82} +(2.49030 + 6.45004i) q^{83} +(12.7317 - 11.5534i) q^{85} +(0.0888687 + 0.913651i) q^{86} +(-20.7908 - 8.49398i) q^{88} +(-0.465562 - 7.99339i) q^{89} +(5.91828 - 2.97227i) q^{91} +(-7.43270 - 10.8371i) q^{92} +(-23.9369 - 4.70105i) q^{94} +(16.3319 - 9.01156i) q^{95} +(-5.56831 + 2.53111i) q^{97} +(-2.49917 + 0.292111i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	−2.66910	−	0.417440i	−1.88734	−	0.295175i	−0.897910	−	0.440180i	$-0.854915\pi$
$2$	−2.66910	−	0.417440i	−1.88734	−	0.295175i	−0.989431	+	0.145005i	$0.953680\pi$
$3$		0			0
$3$		0			0
$4$	5.04536	+	1.61773i	2.52268	+	0.808865i
$5$	2.30401	+	1.04730i	1.03039	+	0.468368i	0.856363	−	0.516374i	$-0.172719\pi$
$5$	2.30401	+	1.04730i	1.03039	+	0.468368i	0.174023	+	0.984742i	$0.444323\pi$
$6$		0			0
$7$	0.333383	+	2.44079i	0.126007	+	0.922533i	0.939883	+	0.341495i	$0.110933\pi$
$7$	0.333383	+	2.44079i	0.126007	+	0.922533i	−0.813877	+	0.581038i	$0.802647\pi$
$8$	−7.96289	−	3.99911i	−2.81531	−	1.41390i
$9$		0			0
$10$	−5.71246	−	3.75714i	−1.80644	−	1.18811i
$11$	2.51287	−	0.195316i	0.757659	−	0.0588899i	0.307149	−	0.951661i	$-0.400625\pi$
$11$	2.51287	−	0.195316i	0.757659	−	0.0588899i	0.450510	+	0.892771i	$0.351242\pi$
$12$		0			0
$13$	−0.870322	−	2.54361i	−0.241384	−	0.705471i	−0.998629	−	0.0523406i	$-0.983332\pi$
$13$	−0.870322	−	2.54361i	−0.241384	−	0.705471i	0.757245	−	0.653130i	$-0.226545\pi$
$14$	0.129052	−	6.65389i	0.0344906	−	1.77833i
$15$		0			0
$16$	10.9634	+	7.83616i	2.74085	+	1.95904i
$17$	2.69059	−	6.23748i	0.652563	−	1.51281i	−0.194268	−	0.980948i	$-0.562233\pi$
$17$	2.69059	−	6.23748i	0.652563	−	1.51281i	0.846831	−	0.531862i	$-0.178508\pi$
$18$		0			0
$19$	4.40120	−	5.91184i	1.00970	−	1.35627i	0.0764411	−	0.997074i	$-0.475644\pi$
$19$	4.40120	−	5.91184i	1.00970	−	1.35627i	0.933263	−	0.359194i	$-0.116948\pi$
$20$	9.93032	+	9.01128i	2.22049	+	2.01498i
$21$		0			0
$22$	−6.78865	−	0.527655i	−1.44734	−	0.112496i
$23$	−1.96035	−	1.51938i	−0.408761	−	0.316813i	0.387386	−	0.921918i	$-0.373378\pi$
$23$	−1.96035	−	1.51938i	−0.408761	−	0.316813i	−0.796146	+	0.605104i	$0.793131\pi$
$24$		0			0
$25$	0.924025	+	1.05882i	0.184805	+	0.211763i
$26$	1.26117	+	7.15247i	0.247336	+	1.40271i
$27$		0			0
$28$	−2.26651	+	12.8540i	−0.428329	+	2.42918i
$29$	3.92297	−	2.36752i	0.728477	−	0.439638i	−0.103370	−	0.994643i	$-0.532963\pi$
$29$	3.92297	−	2.36752i	0.728477	−	0.439638i	0.831847	+	0.555005i	$0.187284\pi$
$30$		0			0
$31$	0.332893	−	0.0129178i	0.0597894	−	0.00232010i	−0.00886332	−	0.999961i	$-0.502821\pi$
$31$	0.332893	−	0.0129178i	0.0597894	−	0.00232010i	0.0686527	+	0.997641i	$0.478130\pi$
$32$	−13.2681	−	13.0132i	−2.34548	−	2.30043i
$33$		0			0
$34$	−9.78522	+	15.5253i	−1.67815	+	2.66257i
$35$	−1.78813	+	5.97277i	−0.302249	+	1.00958i
$36$		0			0
$37$	−1.45474	+	1.54193i	−0.239158	+	0.253492i	−0.835824	−	0.548997i	$-0.815010\pi$
$37$	−1.45474	+	1.54193i	−0.239158	+	0.253492i	0.596667	+	0.802489i	$0.296491\pi$
$38$	−14.2151	+	13.9421i	−2.30599	+	2.26170i
$39$		0			0
$40$	−14.1583	−	17.5536i	−2.23863	−	2.77546i
$41$	−2.52421	+	6.53786i	−0.394215	+	1.02104i	0.583687	+	0.811979i	$0.301609\pi$
$41$	−2.52421	+	6.53786i	−0.394215	+	1.02104i	−0.977902	+	0.209064i	$0.932958\pi$
$42$		0			0
$43$	−0.0847579	−	0.329050i	−0.0129255	−	0.0501797i	0.961602	−	0.274447i	$-0.0884949\pi$
$43$	−0.0847579	−	0.329050i	−0.0129255	−	0.0501797i	−0.974528	+	0.224268i	$0.928001\pi$
$44$	12.9943	+	3.07971i	1.95897	+	0.464283i
$45$		0			0
$46$	4.59812	+	4.87372i	0.677955	+	0.718590i
$47$	9.02289	+	0.350129i	1.31612	+	0.0510716i	0.687242	−	0.726429i	$-0.258821\pi$
$47$	9.02289	+	0.350129i	1.31612	+	0.0510716i	0.628883	+	0.777500i	$0.283513\pi$
$48$		0			0
$49$	0.897270	−	0.249772i	0.128181	−	0.0356817i
$50$	−2.02433	−	3.21181i	−0.286283	−	0.454219i
$51$		0			0
$52$	−0.276211	−	14.2414i	−0.0383036	−	1.97492i
$53$	−10.0630	+	3.66262i	−1.38226	+	0.503100i	−0.922861	−	0.385133i	$-0.874156\pi$
$53$	−10.0630	+	3.66262i	−1.38226	+	0.503100i	−0.459394	+	0.888232i	$0.651934\pi$
$54$		0			0
$55$	5.99424	+	2.18173i	0.808264	+	0.294184i
$56$	7.10632	−	20.7690i	0.949622	−	2.77537i
$57$		0			0
$58$	−11.4591	+	4.68156i	−1.50465	+	0.614719i
$59$	2.19593	+	4.59239i	0.285885	+	0.597878i	0.994143	−	0.108076i	$-0.0344690\pi$
$59$	2.19593	+	4.59239i	0.285885	+	0.597878i	−0.708257	+	0.705954i	$0.750518\pi$
$60$		0			0
$61$	4.43170	−	1.42097i	0.567421	−	0.181936i	−0.00774942	−	0.999970i	$-0.502467\pi$
$61$	4.43170	−	1.42097i	0.567421	−	0.181936i	0.575170	+	0.818034i	$0.304936\pi$
$62$	−0.893919	−	0.104484i	−0.113528	−	0.0132695i
$63$		0			0
$64$	13.8870	+	18.6535i	1.73588	+	2.33169i
$65$	0.658698	−	6.77200i	0.0817014	−	0.839964i
$66$		0			0
$67$	1.54194	+	0.930564i	0.188378	+	0.113687i	0.607752	−	0.794127i	$-0.292071\pi$
$67$	1.54194	+	0.930564i	0.188378	+	0.113687i	−0.419374	+	0.907813i	$0.637750\pi$
$68$	23.6655	−	27.1177i	2.86987	−	3.28850i
$69$		0			0
$70$	7.26598	−	15.1955i	0.868450	−	1.81621i
$71$	−0.147599	+	2.53418i	−0.0175168	+	0.300752i	0.978159	+	0.207858i	$0.0666491\pi$
$71$	−0.147599	+	2.53418i	−0.0175168	+	0.300752i	−0.995676	+	0.0928948i	$0.970388\pi$
$72$		0			0
$73$	9.68672	−	6.37106i	1.13375	−	0.745676i	0.163199	−	0.986593i	$-0.447819\pi$
$73$	9.68672	−	6.37106i	1.13375	−	0.745676i	0.970546	+	0.240917i	$0.0774482\pi$
$74$	4.52651	−	3.50831i	0.526196	−	0.407833i
$75$		0			0
$76$	31.7694	−	22.7074i	3.64420	−	2.60472i
$77$	1.31447	+	6.06829i	0.149798	+	0.691545i
$78$		0			0
$79$	−6.76355	+	8.38549i	−0.760959	+	0.943441i	−0.999617	−	0.0276624i	$-0.991194\pi$
$79$	−6.76355	+	8.38549i	−0.760959	+	0.943441i	0.238658	+	0.971104i	$0.423292\pi$
$80$	17.0530	+	29.5366i	1.90658	+	3.30229i
$81$		0			0
$82$	9.46653	−	16.3965i	1.04540	−	1.81069i
$83$	2.49030	+	6.45004i	0.273346	+	0.707983i	0.999785	+	0.0207523i	$0.00660613\pi$
$83$	2.49030	+	6.45004i	0.273346	+	0.707983i	−0.726439	+	0.687231i	$0.758826\pi$
$84$		0			0
$85$	12.7317	−	11.5534i	1.38094	−	1.25314i
$86$	0.0888687	+	0.913651i	0.00958296	+	0.0985215i
$87$		0			0
$88$	−20.7908	−	8.49398i	−2.21631	−	0.905462i
$89$	−0.465562	−	7.99339i	−0.0493495	−	0.847297i	−0.928633	−	0.370999i	$-0.879015\pi$
$89$	−0.465562	−	7.99339i	−0.0493495	−	0.847297i	0.879284	−	0.476298i	$-0.158022\pi$
$90$		0			0
$91$	5.91828	−	2.97227i	0.620404	−	0.311579i
$92$	−7.43270	−	10.8371i	−0.774913	−	1.12985i
$93$		0			0
$94$	−23.9369	−	4.70105i	−2.46890	−	0.484876i
$95$	16.3319	−	9.01156i	1.67562	−	0.924566i
$96$		0			0
$97$	−5.56831	+	2.53111i	−0.565376	+	0.256995i	−0.676043	−	0.736863i	$-0.736306\pi$
$97$	−5.56831	+	2.53111i	−0.565376	+	0.256995i	0.110666	+	0.993858i	$0.464702\pi$
$98$	−2.49917	+	0.292111i	−0.252454	+	0.0295077i
$99$		0			0
$100$	2.94916	+	6.83693i	0.294916	+	0.683693i
$101$	−2.53434	+	11.6998i	−0.252177	+	1.16418i	0.658994	+	0.752148i	$0.270982\pi$
$101$	−2.53434	+	11.6998i	−0.252177	+	1.16418i	−0.911171	+	0.412029i	$0.864820\pi$
$102$		0			0
$103$	−4.16050	+	6.06616i	−0.409946	+	0.597716i	−0.973591	−	0.228301i	$-0.926683\pi$
$103$	−4.16050	+	6.06616i	−0.409946	+	0.597716i	0.563644	+	0.826018i	$0.309399\pi$
$104$	−3.24192	+	23.7350i	−0.317896	+	2.32741i
$105$		0			0
$106$	28.3880	−	5.57523i	2.75729	−	0.541514i
$107$	−1.02915	+	0.863563i	−0.0994921	+	0.0834838i	−0.691177	−	0.722686i	$-0.742907\pi$
$107$	−1.02915	+	0.863563i	−0.0994921	+	0.0834838i	0.591685	+	0.806169i	$0.298463\pi$
$108$		0			0
$109$	2.41801	+	2.02895i	0.231603	+	0.194338i	0.751202	−	0.660072i	$-0.229474\pi$
$109$	2.41801	+	2.02895i	0.231603	+	0.194338i	−0.519599	+	0.854410i	$0.673919\pi$
$110$	−15.0885	−	8.32549i	−1.43863	−	0.793804i
$111$		0			0
$112$	−15.4714	+	29.3718i	−1.46191	+	2.77537i
$113$	0.832231	−	3.23092i	0.0782897	−	0.303939i	−0.917246	−	0.398320i	$-0.869593\pi$
$113$	0.832231	−	3.23092i	0.0782897	−	0.303939i	0.995536	+	0.0943809i	$0.0300872\pi$
$114$		0			0
$115$	−2.92541	−	5.55375i	−0.272796	−	0.517890i
$116$	23.6228	−	5.59870i	2.19332	−	0.519827i
$117$		0			0
$118$	−3.94411	−	13.1742i	−0.363084	−	1.21279i
$119$	16.1214	+	4.48769i	1.47784	+	0.411386i
$120$		0			0
$121$	−4.59151	+	0.718099i	−0.417410	+	0.0652818i
$122$	−12.4218	+	1.94274i	−1.12462	+	0.175887i
$123$		0			0
$124$	1.70046	+	0.473356i	0.152706	+	0.0425086i
$125$	−2.60925	−	8.71549i	−0.233378	−	0.779537i
$126$		0			0
$127$	−1.15906	+	0.274702i	−0.102850	+	0.0243758i	−0.281718	−	0.959497i	$-0.590904\pi$
$127$	−1.15906	+	0.274702i	−0.102850	+	0.0243758i	0.178869	+	0.983873i	$0.442756\pi$
$128$	−11.9568	−	22.6993i	−1.05684	−	2.00636i
$129$		0			0
$130$	−4.58504	+	17.8002i	−0.402134	+	1.56118i
$131$	10.1186	−	19.2096i	0.884062	−	1.67835i	0.161696	−	0.986841i	$-0.448304\pi$
$131$	10.1186	−	19.2096i	0.884062	−	1.67835i	0.722366	−	0.691511i	$-0.243055\pi$
$132$		0			0
$133$	15.8968	+	8.77151i	1.37843	+	0.760586i
$134$	−3.72714	−	3.12744i	−0.321976	−	0.270170i
$135$		0			0
$136$	−46.3692	+	38.9084i	−3.97613	+	3.33637i
$137$	−20.4068	+	4.00776i	−1.74347	+	0.342406i	−0.960207	−	0.279288i	$-0.909902\pi$
$137$	−20.4068	+	4.00776i	−1.74347	+	0.342406i	−0.783260	+	0.621694i	$0.786445\pi$
$138$		0			0
$139$	−0.742600	+	5.43679i	−0.0629865	+	0.461143i	0.932105	+	0.362187i	$0.117970\pi$
$139$	−0.742600	+	5.43679i	−0.0629865	+	0.461143i	−0.995092	+	0.0989555i	$0.968450\pi$
$140$	−18.6841	+	27.2421i	−1.57909	+	2.30237i
$141$		0			0
$142$	1.45183	−	6.70239i	0.121835	−	0.562452i
$143$	−2.68382	−	6.22178i	−0.224432	−	0.520292i
$144$		0			0
$145$	11.5181	−	1.34627i	0.956525	−	0.111802i
$146$	−28.5144	+	12.9614i	−2.35987	+	1.07269i
$147$		0			0
$148$	−9.83411	+	5.42623i	−0.808359	+	0.446033i
$149$	−0.874907	−	0.171826i	−0.0716752	−	0.0140765i	0.156746	−	0.987639i	$-0.449900\pi$
$149$	−0.874907	−	0.171826i	−0.0716752	−	0.0140765i	−0.228421	+	0.973562i	$0.573356\pi$
$150$		0			0
$151$	−0.841874	−	1.22748i	−0.0685107	−	0.0998911i	0.788906	−	0.614514i	$-0.210648\pi$
$151$	−0.841874	−	1.22748i	−0.0685107	−	0.0998911i	−0.857417	+	0.514623i	$0.827932\pi$
$152$	−58.6884	+	29.4744i	−4.76025	+	2.39069i
$153$		0			0
$154$	−0.975320	−	16.7456i	−0.0785935	−	1.34940i
$155$	0.780519	+	0.318877i	0.0626928	+	0.0256128i
$156$		0			0
$157$	2.07963	+	21.3804i	0.165972	+	1.70635i	0.595552	+	0.803316i	$0.296933\pi$
$157$	2.07963	+	21.3804i	0.165972	+	1.70635i	−0.429580	+	0.903029i	$0.641338\pi$
$158$	21.5531	−	19.5584i	1.71467	−	1.55598i
$159$		0			0
$160$	−16.9410	−	43.8783i	−1.33930	−	3.46888i
$161$	3.05495	−	5.29134i	0.240764	−	0.417016i
$162$		0			0
$163$	1.53630	+	2.66095i	0.120332	+	0.208421i	0.919899	−	0.392156i	$-0.128271\pi$
$163$	1.53630	+	2.66095i	0.120332	+	0.208421i	−0.799567	+	0.600578i	$0.794937\pi$
$164$	−23.3120	+	28.9024i	−1.82036	+	2.25690i
$165$		0			0
$166$	−3.95436	−	18.2554i	−0.306918	−	1.41689i
$167$	2.31364	−	1.65369i	0.179035	−	0.127966i	−0.488444	−	0.872595i	$-0.662435\pi$
$167$	2.31364	−	1.65369i	0.179035	−	0.127966i	0.667479	+	0.744629i	$0.267374\pi$
$168$		0			0
$169$	4.56260	−	3.53628i	0.350969	−	0.272022i
$170$	−38.8050	+	25.5224i	−2.97621	+	1.95748i
$171$		0			0
$172$	0.104680	−	1.79729i	0.00798180	−	0.137042i
$173$	−1.10151	+	2.30361i	−0.0837463	+	0.175141i	−0.939780	−	0.341779i	$-0.888971\pi$
$173$	−1.10151	+	2.30361i	−0.0837463	+	0.175141i	0.856034	+	0.516919i	$0.172921\pi$
$174$		0			0
$175$	−2.27630	+	2.60835i	−0.172072	+	0.197172i
$176$	29.0801	+	17.5499i	2.19200	+	1.32288i
$177$		0			0
$178$	−2.09413	+	21.5295i	−0.156962	+	1.61371i
$179$	7.29880	+	9.80399i	0.545538	+	0.732785i	0.986322	−	0.164828i	$-0.0527070\pi$
$179$	7.29880	+	9.80399i	0.545538	+	0.732785i	−0.440784	+	0.897613i	$0.645300\pi$
$180$		0			0
$181$	−20.6616	−	2.41499i	−1.53576	−	0.179505i	−0.694246	−	0.719738i	$-0.744262\pi$
$181$	−20.6616	−	2.41499i	−1.53576	−	0.179505i	−0.841516	+	0.540233i	$0.818336\pi$
$182$	−17.0372	+	5.46277i	−1.26288	+	0.404928i
$183$		0			0
$184$	9.53384	+	19.9383i	0.702844	+	1.46987i
$185$	−4.96661	+	2.02908i	−0.365152	+	0.149181i
$186$		0			0
$187$	5.54282	−	16.1995i	0.405331	−	1.18462i
$188$	44.9573	+	16.3631i	3.27885	+	1.19340i
$189$		0			0
$190$	−47.3533	+	17.2352i	−3.43537	+	1.25037i
$191$	−0.135193	−	6.97052i	−0.00978223	−	0.504369i	−0.972376	−	0.233420i	$-0.925008\pi$
$191$	−0.135193	−	6.97052i	−0.00978223	−	0.504369i	0.962594	−	0.270949i	$-0.0873375\pi$
$192$		0			0
$193$	−11.9457	−	18.9531i	−0.859869	−	1.36428i	−0.930316	−	0.366760i	$-0.880467\pi$
$193$	−11.9457	−	18.9531i	−0.859869	−	1.36428i	0.0704468	−	0.997516i	$-0.477558\pi$
$194$	15.9190	−	4.43135i	1.14292	−	0.318152i
$195$		0			0
$196$	4.93111	+	0.191350i	0.352222	+	0.0136678i
$197$	−16.4821	−	17.4700i	−1.17430	−	1.24468i	−0.963663	−	0.267120i	$-0.913928\pi$
$197$	−16.4821	−	17.4700i	−1.17430	−	1.24468i	−0.210636	−	0.977565i	$-0.567553\pi$
$198$		0			0
$199$	6.23796	+	1.47842i	0.442197	+	0.104803i	0.445682	−	0.895191i	$-0.352961\pi$
$199$	6.23796	+	1.47842i	0.442197	+	0.104803i	−0.00348503	+	0.999994i	$0.501109\pi$
$200$	−3.12359	−	12.1265i	−0.220871	−	0.857474i
$201$		0			0
$202$	11.6484	−	30.1701i	0.819579	−	2.12276i
$203$	7.08648	+	8.78586i	0.497374	+	0.616647i
$204$		0			0
$205$	−12.6629	+	12.4197i	−0.884417	+	0.867430i
$206$	13.6371	−	14.4544i	0.950139	−	1.00709i
$207$		0			0
$208$	10.3905	−	34.7066i	0.720450	−	2.40647i
$209$	9.90497	−	15.7153i	0.685141	−	1.08705i
$210$		0			0
$211$	2.06913	+	2.02939i	0.142445	+	0.139709i	0.767947	−	0.640514i	$-0.221279\pi$
$211$	2.06913	+	2.02939i	0.142445	+	0.139709i	−0.625502	+	0.780223i	$0.715106\pi$
$212$	−56.6964	+	2.20008i	−3.89393	+	0.151102i
$213$		0			0
$214$	3.10740	−	1.87533i	0.212418	−	0.128195i
$215$	0.149332	−	0.846903i	0.0101844	−	0.0577583i
$216$		0			0
$217$	0.142510	+	0.808217i	0.00967424	+	0.0548653i
$218$	−5.60695	−	6.42486i	−0.379751	−	0.435146i
$219$		0			0
$220$	26.7137	+	20.7047i	1.80103	+	1.39591i
$221$	−18.2074	−	1.41519i	−1.22476	−	0.0951960i
$222$		0			0
$223$	13.2817	+	12.0525i	0.889407	+	0.807093i	0.982053	−	0.188606i	$-0.0603968\pi$
$223$	13.2817	+	12.0525i	0.889407	+	0.807093i	−0.0926463	+	0.995699i	$0.529533\pi$
$224$	27.3392	−	36.7230i	1.82668	−	2.45366i
$225$		0			0
$226$	−3.57002	+	8.27625i	−0.237474	+	0.550528i
$227$	18.2372	+	13.0351i	1.21044	+	0.865173i	0.993811	−	0.111081i	$-0.0354312\pi$
$227$	18.2372	+	13.0351i	1.21044	+	0.865173i	0.216632	+	0.976253i	$0.430493\pi$
$228$		0			0
$229$	−0.508218	+	26.2036i	−0.0335840	+	1.73158i	0.483237	+	0.875489i	$0.339461\pi$
$229$	−0.508218	+	26.2036i	−0.0335840	+	1.73158i	−0.516821	+	0.856093i	$0.672885\pi$
$230$	5.48986	+	16.0447i	0.361991	+	1.05796i
$231$		0			0
$232$	−40.7062	+	3.16393i	−2.67249	+	0.207722i
$233$	2.55358	+	1.67952i	0.167291	+	0.110029i	0.630393	−	0.776276i	$-0.282894\pi$
$233$	2.55358	+	1.67952i	0.167291	+	0.110029i	−0.463103	+	0.886305i	$0.653264\pi$
$234$		0			0
$235$	20.4222	+	10.2564i	1.33220	+	0.669054i
$236$	3.64999	+	26.7227i	0.237594	+	1.73950i
$237$		0			0
$238$	−41.1563	−	18.7078i	−2.66777	−	1.21265i
$239$	7.39082	+	2.36977i	0.478072	+	0.153288i	0.534586	−	0.845114i	$-0.320468\pi$
$239$	7.39082	+	2.36977i	0.478072	+	0.153288i	−0.0565137	+	0.998402i	$0.517998\pi$
$240$		0			0
$241$	−8.17598	−	1.27870i	−0.526661	−	0.0823683i	−0.114401	−	0.993435i	$-0.536495\pi$
$241$	−8.17598	−	1.27870i	−0.526661	−	0.0823683i	−0.412260	+	0.911066i	$0.635260\pi$
$242$	12.5550			0.807065
$243$		0			0
$244$	24.6582			1.57858
$245$	2.32891	+	0.364235i	0.148789	+	0.0232701i
$246$		0			0
$247$	−18.8679	−	6.04974i	−1.20053	−	0.384936i
$248$	−2.70245	−	1.22842i	−0.171606	−	0.0780044i
$249$		0			0
$250$	3.32615	+	24.3517i	0.210364	+	1.54014i
$251$	14.2793	+	7.17131i	0.901298	+	0.452649i	0.838203	−	0.545358i	$-0.183606\pi$
$251$	14.2793	+	7.17131i	0.901298	+	0.452649i	0.0630954	+	0.998007i	$0.479903\pi$
$252$		0			0
$253$	−5.22286	−	3.43513i	−0.328358	−	0.215965i
$254$	3.20831	−	0.249370i	0.201308	−	0.0156469i
$255$		0			0
$256$	7.38121	+	21.5724i	0.461326	+	1.34828i
$257$	0.0692553	−	3.57078i	0.00432003	−	0.222739i	−0.991430	−	0.130640i	$-0.958297\pi$
$257$	0.0692553	−	3.57078i	0.00432003	−	0.222739i	0.995750	−	0.0920991i	$-0.0293576\pi$
$258$		0			0
$259$	−4.24852	−	3.03666i	−0.263990	−	0.188689i
$260$	14.2786	−	33.1016i	0.885523	−	2.05287i
$261$		0			0
$262$	−35.0263	+	47.0485i	−2.16393	+	2.90667i
$263$	−8.59990	−	7.80400i	−0.530293	−	0.481215i	0.362311	−	0.932057i	$-0.381988\pi$
$263$	−8.59990	−	7.80400i	−0.530293	−	0.481215i	−0.892604	+	0.450842i	$0.851124\pi$
$264$		0			0
$265$	−27.0211	−	2.10025i	−1.65989	−	0.129017i
$266$	−38.7687	−	30.0480i	−2.37706	−	1.84236i
$267$		0			0
$268$	6.27423	+	7.18947i	0.383259	+	0.439167i
$269$	1.80904	+	10.2596i	0.110299	+	0.625538i	0.988971	+	0.148111i	$0.0473193\pi$
$269$	1.80904	+	10.2596i	0.110299	+	0.625538i	−0.878672	+	0.477427i	$0.841570\pi$
$270$		0			0
$271$	−0.242951	+	1.37784i	−0.0147582	+	0.0836979i	−0.991297	−	0.131642i	$-0.957975\pi$
$271$	−0.242951	+	1.37784i	−0.0147582	+	0.0836979i	0.976539	+	0.215340i	$0.0690861\pi$
$272$	78.3758	−	47.3000i	4.75223	−	2.86799i
$273$		0			0
$274$	56.1408	−	2.17852i	3.39159	−	0.131609i
$275$	2.52876	+	2.48019i	0.152490	+	0.149561i
$276$		0			0
$277$	7.26200	−	11.5219i	0.436331	−	0.692287i	−0.553766	−	0.832673i	$-0.686810\pi$
$277$	7.26200	−	11.5219i	0.436331	−	0.692287i	0.990097	+	0.140386i	$0.0448344\pi$
$278$	4.25161	−	14.2014i	0.254995	−	0.851741i
$279$		0			0
$280$	38.1245	−	40.4096i	2.27837	−	2.41493i
$281$	−4.26150	+	4.17965i	−0.254220	+	0.249337i	−0.816140	−	0.577855i	$-0.803890\pi$
$281$	−4.26150	+	4.17965i	−0.254220	+	0.249337i	0.561920	+	0.827192i	$0.310063\pi$
$282$		0			0
$283$	−13.4676	−	16.6972i	−0.800565	−	0.992545i	−0.999920	−	0.0126175i	$-0.995984\pi$
$283$	−13.4676	−	16.6972i	−0.800565	−	0.992545i	0.199356	−	0.979927i	$-0.436115\pi$
$284$	−4.84432	+	12.5471i	−0.287457	+	0.744533i
$285$		0			0
$286$	4.56616	+	17.7269i	0.270003	+	1.04821i
$287$	−16.7991	−	3.98146i	−0.991619	−	0.235018i
$288$		0			0
$289$	−20.0008	−	21.1996i	−1.17652	−	1.24703i
$290$	−31.3049	−	1.21477i	−1.83829	−	0.0713340i
$291$		0			0
$292$	59.1796	−	16.4738i	3.46323	−	0.964055i
$293$	0.331131	+	0.525375i	0.0193449	+	0.0306927i	0.855520	−	0.517770i	$-0.173238\pi$
$293$	0.331131	+	0.525375i	0.0193449	+	0.0306927i	−0.836175	+	0.548463i	$0.815213\pi$
$294$		0			0
$295$	0.249821	+	12.8807i	0.0145452	+	0.749945i
$296$	17.7503	−	6.46058i	1.03171	−	0.375513i
$297$		0			0
$298$	2.26349	+	0.823843i	0.131120	+	0.0477239i
$299$	−2.15859	+	6.30871i	−0.124834	+	0.364842i
$300$		0			0
$301$	0.774887	−	0.316576i	0.0446637	−	0.0182471i
$302$	1.73465	+	3.62771i	0.0998178	+	0.208751i
$303$		0			0
$304$	94.5781	−	30.3253i	5.42443	−	1.73927i
$305$	11.6989	+	1.36740i	0.669875	+	0.0782972i
$306$		0			0
$307$	−1.75959	−	2.36353i	−0.100425	−	0.134894i	0.749070	−	0.662491i	$-0.230501\pi$
$307$	−1.75959	−	2.36353i	−0.100425	−	0.134894i	−0.849495	+	0.527597i	$0.823093\pi$
$308$	−3.18485	+	32.7431i	−0.181474	+	1.86571i
$309$		0			0
$310$	−1.95017	−	1.17694i	−0.110762	−	0.0668455i
$311$	−5.62286	+	6.44309i	−0.318843	+	0.365354i	−0.890376	−	0.455225i	$-0.849559\pi$
$311$	−5.62286	+	6.44309i	−0.318843	+	0.365354i	0.571533	+	0.820579i	$0.306349\pi$
$312$		0			0
$313$	−9.91689	+	20.7394i	−0.560536	+	1.17226i	0.405558	+	0.914069i	$0.367077\pi$
$313$	−9.91689	+	20.7394i	−0.560536	+	1.17226i	−0.966094	+	0.258192i	$0.916873\pi$
$314$	3.37431	−	57.9347i	0.190424	−	3.26945i
$315$		0			0
$316$	−47.6900	+	31.3662i	−2.68277	+	1.76449i
$317$	−0.301281	+	0.233511i	−0.0169216	+	0.0131153i	−0.621026	−	0.783790i	$-0.713284\pi$
$317$	−0.301281	+	0.233511i	−0.0169216	+	0.0131153i	0.604105	+	0.796905i	$0.293531\pi$
$318$		0			0
$319$	9.39550	−	6.71550i	0.526047	−	0.375996i
$320$	12.4600	+	57.5218i	0.696536	+	3.21557i
$321$		0			0
$322$	−10.3628	+	12.8479i	−0.577496	+	0.715983i
$323$	−25.0331	−	43.3587i	−1.39288	−	2.41254i
$324$		0			0
$325$	1.88902	−	3.27187i	0.104784	−	0.181491i
$326$	−2.98975	−	7.74365i	−0.165587	−	0.428881i
$327$		0			0
$328$	46.2456	−	41.9657i	2.55349	−	2.31717i
$329$	2.15348	+	22.1397i	0.118725	+	1.22060i
$330$		0			0
$331$	−19.8274	−	8.10040i	−1.08981	−	0.445238i	−0.239169	−	0.970978i	$-0.576875\pi$
$331$	−19.8274	−	8.10040i	−1.08981	−	0.445238i	−0.850646	+	0.525740i	$0.823789\pi$
$332$	2.13004	+	36.5714i	0.116901	+	2.00711i
$333$		0			0
$334$	−6.86565	+	3.44806i	−0.375672	+	0.188669i
$335$	2.57806	+	3.75891i	0.140855	+	0.205371i
$336$		0			0
$337$	16.0612	+	3.15431i	0.874908	+	0.171826i	0.609956	−	0.792435i	$-0.291187\pi$
$337$	16.0612	+	3.15431i	0.874908	+	0.171826i	0.264952	+	0.964262i	$0.414644\pi$
$338$	−13.6542	+	7.53409i	−0.742693	+	0.409801i
$339$		0			0
$340$	82.9260	−	37.6945i	4.49730	−	2.04427i
$341$	0.833995	−	0.0974800i	0.0451634	−	0.00527884i
$342$		0			0
$343$	7.73885	+	17.9407i	0.417859	+	0.968705i
$344$	−0.640992	+	2.95915i	−0.0345600	+	0.159547i
$345$		0			0
$346$	3.90167	−	5.68877i	0.209755	−	0.305830i
$347$	0.430358	−	3.15078i	0.0231028	−	0.169143i	−0.975633	−	0.219409i	$-0.929587\pi$
$347$	0.430358	−	3.15078i	0.0231028	−	0.169143i	0.998736	+	0.0502661i	$0.0160069\pi$
$348$		0			0
$349$	−10.0778	+	1.97921i	−0.539452	+	0.105945i	−0.455015	−	0.890484i	$-0.650366\pi$
$349$	−10.0778	+	1.97921i	−0.539452	+	0.105945i	−0.0844371	+	0.996429i	$0.526909\pi$
$350$	7.16450	−	6.01173i	0.382958	−	0.321340i
$351$		0			0
$352$	−35.8826	−	30.1091i	−1.91255	−	1.60482i
$353$	1.66982	+	0.921368i	0.0888756	+	0.0490395i	0.526928	−	0.849910i	$-0.323344\pi$
$353$	1.66982	+	0.921368i	0.0888756	+	0.0490395i	−0.438052	+	0.898950i	$0.644331\pi$
$354$		0			0
$355$	−2.99413	+	5.68421i	−0.158912	+	0.301687i
$356$	10.5822	−	41.0827i	0.560856	−	2.17738i
$357$		0			0
$358$	−15.3887	−	29.2147i	−0.813316	−	1.54404i
$359$	19.8526	−	4.70515i	1.04778	−	0.248329i	0.329553	−	0.944137i	$-0.393102\pi$
$359$	19.8526	−	4.70515i	1.04778	−	0.248329i	0.718227	+	0.695808i	$0.244954\pi$
$360$		0			0
$361$	−10.1300	−	33.8365i	−0.533157	−	1.78087i
$362$	54.1397	+	15.0708i	2.84552	+	0.792105i
$363$		0			0
$364$	34.6682	−	5.42200i	1.81711	−	0.284190i
$365$	28.9908	−	4.53407i	1.51745	−	0.237324i
$366$		0			0
$367$	−6.23235	−	1.73489i	−0.325326	−	0.0905606i	0.101659	−	0.994819i	$-0.467585\pi$
$367$	−6.23235	−	1.73489i	−0.325326	−	0.0905606i	−0.426985	+	0.904259i	$0.640424\pi$
$368$	−9.58591	−	32.0192i	−0.499700	−	1.66912i
$369$		0			0
$370$	14.1034	−	3.34257i	0.733201	−	0.173772i
$371$	−12.2945	−	23.3406i	−0.638300	−	1.21178i
$372$		0			0
$373$	−6.32066	+	24.5383i	−0.327271	+	1.27055i	0.567260	+	0.823539i	$0.308004\pi$
$373$	−6.32066	+	24.5383i	−0.327271	+	1.27055i	−0.894531	+	0.447006i	$0.852490\pi$
$374$	−21.5567	+	40.9243i	−1.11467	+	2.11615i
$375$		0			0
$376$	−70.4481	−	38.8716i	−3.63308	−	2.00465i
$377$	−9.43631	−	7.91800i	−0.485995	−	0.407798i
$378$		0			0
$379$	27.9058	−	23.4157i	1.43342	−	1.20279i	0.489769	−	0.871852i	$-0.337081\pi$
$379$	27.9058	−	23.4157i	1.43342	−	1.20279i	0.943654	−	0.330933i	$-0.107363\pi$
$380$	96.9785	−	19.0460i	4.97489	−	0.977037i
$381$		0			0
$382$	−2.54893	+	18.6615i	−0.130415	+	0.954804i
$383$	−5.79523	+	8.44966i	−0.296123	+	0.431757i	−0.943979	−	0.330005i	$-0.892950\pi$
$383$	−5.79523	+	8.44966i	−0.296123	+	0.431757i	0.647857	+	0.761762i	$0.275666\pi$
$384$		0			0
$385$	−3.32676	+	15.3581i	−0.169548	+	0.782719i
$386$	23.9725	+	55.5744i	1.22017	+	2.82866i
$387$		0			0
$388$	−32.1888	+	3.76233i	−1.63414	+	0.191003i
$389$	−35.6409	+	16.2008i	−1.80707	+	0.821412i	−0.852938	+	0.522013i	$0.825181\pi$
$389$	−35.6409	+	16.2008i	−1.80707	+	0.821412i	−0.954128	+	0.299400i	$0.903214\pi$
$390$		0			0
$391$	−14.7516	+	8.13959i	−0.746020	+	0.411637i
$392$	−8.14373	−	1.59938i	−0.411321	−	0.0807807i
$393$		0			0
$394$	36.6997	+	53.5095i	1.84890	+	2.69577i
$395$	−24.3654	+	12.2368i	−1.22596	+	0.615700i
$396$		0			0
$397$	−1.07789	−	18.5067i	−0.0540978	−	0.928824i	−0.910757	−	0.412942i	$-0.864501\pi$
$397$	−1.07789	−	18.5067i	−0.0540978	−	0.928824i	0.856660	−	0.515882i	$-0.172536\pi$
$398$	−16.0326	−	6.55004i	−0.803642	−	0.328324i
$399$		0			0
$400$	1.83340	+	18.8490i	0.0916701	+	0.942451i
$401$	9.35293	−	8.48733i	0.467063	−	0.423837i	−0.404187	−	0.914676i	$-0.632446\pi$
$401$	9.35293	−	8.48733i	0.467063	−	0.423837i	0.871250	+	0.490839i	$0.163310\pi$
$402$		0			0
$403$	−0.322582	−	0.835509i	−0.0160690	−	0.0416196i
$404$	−31.7138	+	54.9300i	−1.57782	+	2.73287i
$405$		0			0
$406$	−15.2470	−	26.4086i	−0.756695	−	1.31063i
$407$	−3.35441	+	4.15881i	−0.166272	+	0.206145i
$408$		0			0
$409$	6.34151	+	29.2757i	0.313567	+	1.44759i	0.813521	+	0.581536i	$0.197548\pi$
$409$	6.34151	+	29.2757i	0.313567	+	1.44759i	−0.499953	+	0.866052i	$0.666649\pi$
$410$	38.9831	−	27.8635i	1.92524	−	1.37608i
$411$		0			0
$412$	−30.8046	+	23.8754i	−1.51763	+	1.17626i
$413$	−10.4770	+	6.89083i	−0.515539	+	0.339075i
$414$		0			0
$415$	−1.01746	+	17.4691i	−0.0499450	+	0.857522i
$416$	−21.5531	+	45.0745i	−1.05673	+	2.20996i
$417$		0			0
$418$	−32.9976	+	37.8110i	−1.61396	+	1.84940i
$419$	14.0220	+	8.46233i	0.685020	+	0.413412i	0.816061	−	0.577965i	$-0.196153\pi$
$419$	14.0220	+	8.46233i	0.685020	+	0.413412i	−0.131041	+	0.991377i	$0.541832\pi$
$420$		0			0
$421$	0.955467	−	9.82306i	0.0465666	−	0.478746i	−0.942806	−	0.333343i	$-0.891823\pi$
$421$	0.955467	−	9.82306i	0.0465666	−	0.478746i	0.989372	−	0.145404i	$-0.0464482\pi$
$422$	−4.67558	−	6.28039i	−0.227604	−	0.305725i
$423$		0			0
$424$	94.7776	+	11.0779i	4.60281	+	0.537991i
$425$	9.09051	−	2.91475i	0.440954	−	0.141386i
$426$		0			0
$427$	4.94574	+	10.3431i	0.239341	+	0.500539i
$428$	−6.58946	+	2.69209i	−0.318514	+	0.130127i
$429$		0			0
$430$	−0.752114	+	2.19813i	−0.0362701	+	0.106003i
$431$	−23.9902	−	8.73172i	−1.15557	−	0.420592i	−0.308056	−	0.951368i	$-0.599678\pi$
$431$	−23.9902	−	8.73172i	−1.15557	−	0.420592i	−0.847512	+	0.530776i	$0.821901\pi$
$432$		0			0
$433$	29.3575	−	10.6852i	1.41083	−	0.513500i	0.479456	−	0.877566i	$-0.340834\pi$
$433$	29.3575	−	10.6852i	1.41083	−	0.513500i	0.931373	+	0.364066i	$0.118612\pi$
$434$	−0.0429929	−	2.21670i	−0.00206373	−	0.106405i
$435$		0			0
$436$	8.91744	+	14.1485i	0.427068	+	0.677589i
$437$	−17.6102	+	4.90214i	−0.842411	+	0.234501i
$438$		0			0
$439$	2.11870	+	0.0822153i	0.101120	+	0.00392392i	0.0892857	−	0.996006i	$-0.471542\pi$
$439$	2.11870	+	0.0822153i	0.101120	+	0.00392392i	0.0118343	+	0.999930i	$0.496233\pi$
$440$	−39.0065	−	41.3445i	−1.85956	−	1.97102i
$441$		0			0
$442$	48.0067	+	11.3778i	2.28344	+	0.541186i
$443$	7.48787	+	29.0697i	0.355759	+	1.38114i	0.856769	+	0.515701i	$0.172468\pi$
$443$	7.48787	+	29.0697i	0.355759	+	1.38114i	−0.501009	+	0.865442i	$0.667038\pi$
$444$		0			0
$445$	7.29883	−	18.9045i	0.345998	−	0.896157i
$446$	−30.4190	−	37.7136i	−1.44038	−	1.78579i
$447$		0			0
$448$	−40.8997	+	40.1141i	−1.93233	+	1.89521i
$449$	−8.22207	+	8.71489i	−0.388024	+	0.411281i	−0.891711	−	0.452605i	$-0.850495\pi$
$449$	−8.22207	+	8.71489i	−0.388024	+	0.411281i	0.503688	+	0.863886i	$0.331976\pi$
$450$		0			0
$451$	−5.06606	+	16.9218i	−0.238552	+	0.796818i
$452$	9.42565	−	14.9548i	0.443345	−	0.703415i
$453$		0			0
$454$	−43.2355	−	42.4051i	−2.02914	−	1.99017i
$455$	16.7487	−	0.649924i	0.785189	−	0.0304689i
$456$		0			0
$457$	−0.725500	+	0.437841i	−0.0339375	+	0.0204814i	−0.533567	−	0.845758i	$-0.679149\pi$
$457$	−0.725500	+	0.437841i	−0.0339375	+	0.0204814i	0.499629	+	0.866239i	$0.333470\pi$
$458$	12.2949	−	69.7280i	0.574504	−	3.25817i
$459$		0			0
$460$	−5.77527	−	32.7532i	−0.269273	−	1.52713i
$461$	−10.2973	−	11.7994i	−0.479591	−	0.549551i	0.461748	−	0.887011i	$-0.347222\pi$
$461$	−10.2973	−	11.7994i	−0.479591	−	0.549551i	−0.941340	+	0.337460i	$0.890432\pi$
$462$		0			0
$463$	−1.86121	−	1.44255i	−0.0864980	−	0.0670410i	0.568434	−	0.822729i	$-0.307550\pi$
$463$	−1.86121	−	1.44255i	−0.0864980	−	0.0670410i	−0.654932	+	0.755688i	$0.727303\pi$
$464$	61.5613	+	4.78493i	2.85791	+	0.222135i
$465$		0			0
$466$	−6.11467	−	5.54877i	−0.283257	−	0.257042i
$467$	−18.6949	+	25.1116i	−0.865096	+	1.16203i	0.120467	+	0.992717i	$0.461561\pi$
$467$	−18.6949	+	25.1116i	−0.865096	+	1.16203i	−0.985563	+	0.169308i	$0.945847\pi$
$468$		0			0
$469$	−1.75726	+	4.07378i	−0.0811427	+	0.188110i
$470$	−50.2274	−	35.9004i	−2.31682	−	1.65596i
$471$		0			0
$472$	0.879571	−	45.3505i	0.0404856	−	2.08742i
$473$	−0.277254	−	0.810307i	−0.0127482	−	0.0372579i
$474$		0			0
$475$	10.3264	−	0.802628i	0.473806	−	0.0368271i
$476$	74.0783	+	48.7221i	3.39537	+	2.23317i
$477$		0			0
$478$	−18.7376	−	9.41038i	−0.857039	−	0.430421i
$479$	−3.89073	−	28.4852i	−0.177772	−	1.30152i	−0.836011	−	0.548713i	$-0.815118\pi$
$479$	−3.89073	−	28.4852i	−0.177772	−	1.30152i	0.658239	−	0.752809i	$-0.271302\pi$
$480$		0			0
$481$	5.18817	+	2.35831i	0.236560	+	0.107530i
$482$	21.2888	+	6.82597i	0.969677	+	0.310914i
$483$		0			0
$484$	−24.3275	−	3.80475i	−1.10580	−	0.172943i
$485$	−15.4803			−0.702924
$486$		0			0
$487$	8.26379			0.374468			0.187234	−	0.982315i	$-0.440048\pi$
$487$	8.26379			0.374468			0.187234	+	0.982315i	$0.440048\pi$
$488$	−40.9717	−	6.40786i	−1.85470	−	0.290070i
$489$		0			0
$490$	−6.06405	−	1.94436i	−0.273946	−	0.0878372i
$491$	−7.66751	−	3.48531i	−0.346030	−	0.157290i	0.233254	−	0.972416i	$-0.425063\pi$
$491$	−7.66751	−	3.48531i	−0.346030	−	0.157290i	−0.579284	+	0.815126i	$0.696668\pi$
$492$		0			0
$493$	−4.21229	−	30.8395i	−0.189712	−	1.38894i
$494$	47.8349	+	24.0236i	2.15219	+	1.08087i
$495$		0			0
$496$	3.75086	+	2.46698i	0.168419	+	0.110771i
$497$	−6.23463	+	0.484594i	−0.279661	+	0.0217370i
$498$		0			0
$499$	1.78516	+	5.21734i	0.0799149	+	0.233560i	0.978871	−	0.204479i	$-0.0655499\pi$
$499$	1.78516	+	5.21734i	0.0799149	+	0.233560i	−0.898956	+	0.438039i	$0.855673\pi$
$500$	0.934718	−	48.1938i	0.0418019	−	2.15529i
$501$		0			0
$502$	−35.1192	−	25.1017i	−1.56745	−	1.12034i
$503$	−6.44429	+	14.9396i	−0.287337	+	0.666122i	−0.999350	−	0.0360442i	$-0.988524\pi$
$503$	−6.44429	+	14.9396i	−0.287337	+	0.666122i	0.712013	+	0.702166i	$0.247784\pi$
$504$		0			0
$505$	−18.0924	+	24.3023i	−0.805102	+	1.08144i
$506$	12.5064	+	11.3489i	0.555977	+	0.504522i
$507$		0			0
$508$	−6.29225	−	0.489072i	−0.279174	−	0.0216991i
$509$	−24.0949	−	18.6749i	−1.06799	−	0.827751i	−0.0823442	−	0.996604i	$-0.526241\pi$
$509$	−24.0949	−	18.6749i	−1.06799	−	0.827751i	−0.985641	+	0.168853i	$0.945994\pi$
$510$		0			0
$511$	18.7798	+	21.5193i	0.830770	+	0.951957i
$512$	−1.78584	−	10.1280i	−0.0789237	−	0.447599i
$513$		0			0
$514$	−1.67544	+	9.50188i	−0.0739004	+	0.419110i
$515$	−15.9389	+	9.61920i	−0.702354	+	0.423873i
$516$		0			0
$517$	22.7418	−	0.882484i	1.00018	−	0.0388116i
$518$	10.0721	+	9.87867i	0.442544	+	0.434044i
$519$		0			0
$520$	−32.3272	+	51.2905i	−1.41764	+	2.24924i
$521$	−0.331882	+	1.10856i	−0.0145400	+	0.0485670i	−0.964952	−	0.262428i	$-0.915477\pi$
$521$	−0.331882	+	1.10856i	−0.0145400	+	0.0485670i	0.950412	+	0.310995i	$0.100662\pi$
$522$		0			0
$523$	−5.13660	+	5.44448i	−0.224608	+	0.238070i	−0.829871	−	0.557955i	$-0.811586\pi$
$523$	−5.13660	+	5.44448i	−0.224608	+	0.238070i	0.605263	+	0.796025i	$0.293068\pi$
$524$	82.1277	−	80.5503i	3.58776	−	3.51885i
$525$		0			0
$526$	19.6963	+	24.4196i	0.858801	+	1.06475i
$527$	0.815103	−	2.11117i	0.0355065	−	0.0919640i
$528$		0			0
$529$	−4.20271	−	16.3159i	−0.182727	−	0.709388i
$530$	71.2453	+	16.8855i	3.09470	+	0.733457i
$531$		0			0
$532$	66.0154	+	69.9722i	2.86213	+	3.03368i
$533$	18.8267	+	0.730560i	0.815473	+	0.0316441i
$534$		0			0
$535$	−3.27560	+	0.911825i	−0.141616	+	0.0394216i
$536$	−8.55685	−	13.5764i	−0.369600	−	0.586410i
$537$		0			0
$538$	−0.545756	−	28.1390i	−0.0235292	−	1.21316i
$539$	2.20594	−	0.802897i	0.0950166	−	0.0345832i
$540$		0			0
$541$	−8.62511	−	3.13928i	−0.370823	−	0.134968i	0.149885	−	0.988703i	$-0.452110\pi$
$541$	−8.62511	−	3.13928i	−0.370823	−	0.134968i	−0.520708	+	0.853735i	$0.674332\pi$
$542$	1.22363	−	3.57618i	0.0525593	−	0.153610i
$543$		0			0
$544$	−116.869	+	47.7461i	−5.01070	+	2.04710i
$545$	3.44620	+	7.20712i	0.147619	+	0.308719i
$546$		0			0
$547$	26.5440	−	8.51098i	1.13494	−	0.363903i	0.322280	−	0.946644i	$-0.395551\pi$
$547$	26.5440	−	8.51098i	1.13494	−	0.363903i	0.812658	+	0.582741i	$0.198020\pi$
$548$	−109.443	−	12.7920i	−4.67517	−	0.546449i
$549$		0			0
$550$	−5.71419	−	7.67549i	−0.243654	−	0.327284i
$551$	3.26935	−	33.6119i	0.139279	−	1.43191i
$552$		0			0
$553$	−22.7221	−	13.7129i	−0.966242	−	0.583130i
$554$	−24.1927	+	27.7218i	−1.02785	+	1.17779i
$555$		0			0
$556$	−12.5419	+	26.2292i	−0.531897	+	1.11237i
$557$	1.19625	−	20.5388i	0.0506867	−	0.870257i	−0.873146	−	0.487459i	$-0.837924\pi$
$557$	1.19625	−	20.5388i	0.0506867	−	0.870257i	0.923832	−	0.382797i	$-0.125039\pi$
$558$		0			0
$559$	−0.763210	+	0.501971i	−0.0322803	+	0.0212311i
$560$	−66.4076	+	51.4697i	−2.80623	+	2.17499i
$561$		0			0
$562$	13.1191	−	9.37700i	0.553398	−	0.395545i
$563$	0.329062	+	1.51912i	0.0138683	+	0.0640232i	0.983744	−	0.179579i	$-0.0574735\pi$
$563$	0.329062	+	1.51912i	0.0138683	+	0.0640232i	−0.969875	+	0.243602i	$0.921671\pi$
$564$		0			0
$565$	5.30122	−	6.57248i	0.223024	−	0.276506i
$566$	28.9763	+	50.1884i	1.21796	+	2.10958i
$567$		0			0
$568$	11.3098	−	19.5892i	0.474549	−	0.821943i
$569$	11.7813	+	30.5143i	0.493898	+	1.27923i	0.926041	+	0.377422i	$0.123189\pi$
$569$	11.7813	+	30.5143i	0.493898	+	1.27923i	−0.432144	+	0.901805i	$0.642243\pi$
$570$		0			0
$571$	−20.2486	+	18.3746i	−0.847378	+	0.768954i	−0.974844	−	0.222888i	$-0.928451\pi$
$571$	−20.2486	+	18.3746i	−0.847378	+	0.768954i	0.127466	+	0.991843i	$0.459316\pi$
$572$	−3.47565	−	35.7328i	−0.145324	−	1.49406i
$573$		0			0
$574$	43.1765	+	17.6395i	1.80215	+	0.736260i
$575$	−0.202663	−	3.47959i	−0.00845164	−	0.145109i
$576$		0			0
$577$	35.7632	−	17.9610i	1.48884	−	0.747725i	0.496132	−	0.868247i	$-0.334753\pi$
$577$	35.7632	−	17.9610i	1.48884	−	0.747725i	0.992711	+	0.120522i	$0.0384568\pi$
$578$	44.5346	+	64.9330i	1.85239	+	2.70086i
$579$		0			0
$580$	60.2908	+	11.8407i	2.50344	+	0.491659i
$581$	−14.9130	+	8.22863i	−0.618695	+	0.341381i
$582$		0			0
$583$	−24.5716	+	11.1692i	−1.01765	+	0.462579i
$584$	−102.613	+	11.9937i	−4.24615	+	0.496304i
$585$		0			0
$586$	−0.664510	−	1.54051i	−0.0274506	−	0.0636377i
$587$	5.91301	−	27.2975i	0.244056	−	1.12669i	−0.676612	−	0.736340i	$-0.736552\pi$
$587$	5.91301	−	27.2975i	0.244056	−	1.12669i	0.920668	−	0.390348i	$-0.127645\pi$
$588$		0			0
$589$	1.38876	−	2.02486i	0.0572229	−	0.0834331i
$590$	4.71013	−	34.4843i	0.193913	−	1.41969i
$591$		0			0
$592$	−28.0317	+	5.50525i	−1.15210	+	0.226264i
$593$	−16.7650	+	14.0675i	−0.688457	+	0.577684i	−0.918464	−	0.395505i	$-0.870570\pi$
$593$	−16.7650	+	14.0675i	−0.688457	+	0.577684i	0.230007	+	0.973189i	$0.426125\pi$
$594$		0			0
$595$	32.4439	+	27.2237i	1.33007	+	1.11606i
$596$	−4.13625	−	2.28229i	−0.169427	−	0.0934861i
$597$		0			0
$598$	8.39501	−	15.9375i	0.343297	−	0.651734i
$599$	−1.17707	+	4.56967i	−0.0480938	+	0.186712i	−0.987926	−	0.154924i	$-0.950487\pi$
$599$	−1.17707	+	4.56967i	−0.0480938	+	0.186712i	0.939833	+	0.341635i	$0.110981\pi$
$600$		0			0
$601$	−19.7149	−	37.4278i	−0.804187	−	1.52671i	−0.849410	−	0.527734i	$-0.823042\pi$
$601$	−19.7149	−	37.4278i	−0.804187	−	1.52671i	0.0452229	−	0.998977i	$-0.485600\pi$
$602$	−2.20040	+	0.521505i	−0.0896818	+	0.0212550i
$603$		0			0
$604$	−2.26182	−	7.55501i	−0.0920322	−	0.307409i
$605$	−11.3310	−	3.15419i	−0.460669	−	0.128236i
$606$		0			0
$607$	−34.6122	+	5.41326i	−1.40487	+	0.219717i	−0.811094	−	0.584915i	$-0.801128\pi$
$607$	−34.6122	+	5.41326i	−1.40487	+	0.219717i	−0.593773	+	0.804632i	$0.702362\pi$
$608$	−135.327	+	21.1648i	−5.48825	+	0.858347i
$609$		0			0
$610$	−30.6547	−	8.53331i	−1.24117	−	0.345504i
$611$	−6.96223	−	23.2555i	−0.281662	−	0.940816i
$612$		0			0
$613$	−1.10788	+	0.262571i	−0.0447467	+	0.0106052i	−0.252928	−	0.967485i	$-0.581394\pi$
$613$	−1.10788	+	0.262571i	−0.0447467	+	0.0106052i	0.208182	+	0.978090i	$0.433246\pi$
$614$	3.70988	+	7.04304i	0.149719	+	0.284234i
$615$		0			0
$616$	13.8008	−	53.5778i	0.556048	−	2.15871i
$617$	−4.49805	+	8.53933i	−0.181085	+	0.343781i	−0.958446	−	0.285273i	$-0.907916\pi$
$617$	−4.49805	+	8.53933i	−0.181085	+	0.343781i	0.777362	+	0.629054i	$0.216558\pi$
$618$		0			0
$619$	−21.8512	−	12.0570i	−0.878275	−	0.484612i	−0.0211836	−	0.999776i	$-0.506743\pi$
$619$	−21.8512	−	12.0570i	−0.878275	−	0.484612i	−0.857092	+	0.515164i	$0.827731\pi$
$620$	3.42214	+	2.87152i	0.137437	+	0.115323i
$621$		0			0
$622$	17.6976	−	14.8501i	0.709609	−	0.595433i
$623$	19.3550	−	3.80120i	0.775441	−	0.152292i
$624$		0			0
$625$	4.06693	−	29.7752i	0.162677	−	1.19101i
$626$	35.1267	−	51.2159i	1.40394	−	2.04700i
$627$		0			0
$628$	−24.0953	+	111.236i	−0.961507	+	4.43881i
$629$	5.70367	+	13.2226i	0.227420	+	0.527220i
$630$		0			0
$631$	−39.1073	+	4.57099i	−1.55684	+	0.181968i	−0.850526	−	0.525933i	$-0.823716\pi$
$631$	−39.1073	+	4.57099i	−1.55684	+	0.181968i	−0.706312	+	0.707901i	$0.749642\pi$
$632$	87.3919	−	39.7245i	3.47627	−	1.58016i
$633$		0			0
$634$	0.901627	−	0.497497i	0.0358082	−	0.0197581i
$635$	−2.95818	−	0.580967i	−0.117392	−	0.0230550i
$636$		0			0
$637$	−1.41624	−	2.06492i	−0.0561134	−	0.0818153i
$638$	−27.8809	+	14.0023i	−1.10381	+	0.554357i
$639$		0			0
$640$	−3.77544	−	64.8219i	−0.149238	−	2.56231i
$641$	13.7067	+	5.59979i	0.541381	+	0.221178i	0.632360	−	0.774674i	$-0.282086\pi$
$641$	13.7067	+	5.59979i	0.541381	+	0.221178i	−0.0909797	+	0.995853i	$0.529000\pi$
$642$		0			0
$643$	1.07485	+	11.0505i	0.0423881	+	0.435788i	0.992353	+	0.123431i	$0.0393899\pi$
$643$	1.07485	+	11.0505i	0.0423881	+	0.435788i	−0.949965	+	0.312356i	$0.898882\pi$
$644$	23.9733	−	21.7546i	0.944680	−	0.857251i
$645$		0			0
$646$	48.7164	+	126.179i	1.91672	+	4.96443i
$647$	13.6681	−	23.6739i	0.537350	−	0.930718i	−0.461695	−	0.887039i	$-0.652759\pi$
$647$	13.6681	−	23.6739i	0.537350	−	0.930718i	0.999046	−	0.0436794i	$-0.0139080\pi$
$648$		0			0
$649$	6.41505	+	11.1112i	0.251813	+	0.436152i
$650$	−6.40779	+	7.94441i	−0.251334	+	0.311606i
$651$		0			0
$652$	3.44648	+	15.9107i	0.134975	+	0.623113i
$653$	−18.5229	+	13.2394i	−0.724859	+	0.518098i	−0.883032	−	0.469314i	$-0.844501\pi$
$653$	−18.5229	+	13.2394i	−0.724859	+	0.518098i	0.158173	+	0.987411i	$0.449440\pi$
$654$		0			0
$655$	43.4316	−	33.6620i	1.69701	−	1.31528i
$656$	−78.9056	+	51.8970i	−3.08075	+	2.02624i
$657$		0			0
$658$	3.49415	−	59.9922i	0.136216	−	2.33874i
$659$	3.19289	−	6.67736i	0.124377	−	0.260113i	−0.830555	−	0.556936i	$-0.811977\pi$
$659$	3.19289	−	6.67736i	0.124377	−	0.260113i	0.954932	+	0.296823i	$0.0959273\pi$
$660$		0			0
$661$	25.2192	−	28.8979i	0.980911	−	1.12400i	−0.0113629	−	0.999935i	$-0.503617\pi$
$661$	25.2192	−	28.8979i	0.980911	−	1.12400i	0.992274	−	0.124064i	$-0.0395929\pi$
$662$	49.5401	+	29.8976i	1.92543	+	1.16200i
$663$		0			0
$664$	5.96445	−	61.3199i	0.231466	−	2.37967i
$665$	27.4401	+	36.8585i	1.06408	+	1.42931i
$666$		0			0
$667$	−11.2876	−	1.31933i	−0.437056	−	0.0510845i
$668$	14.3484	−	4.60061i	0.555154	−	0.178003i
$669$		0			0
$670$	−5.31200	−	11.1091i	−0.205220	−	0.429182i
$671$	10.8587	−	4.43629i	0.419197	−	0.171261i
$672$		0			0
$673$	−1.27652	+	3.73078i	−0.0492064	+	0.143811i	−0.968015	−	0.250892i	$-0.919276\pi$
$673$	−1.27652	+	3.73078i	−0.0492064	+	0.143811i	0.918809	+	0.394703i	$0.129153\pi$
$674$	−41.5522	−	15.1238i	−1.60053	−	0.582546i
$675$		0			0
$676$	28.7407	−	10.4608i	1.10541	−	0.402337i
$677$	−0.382827	−	19.7384i	−0.0147132	−	0.758610i	−0.932425	−	0.361363i	$-0.882311\pi$
$677$	−0.382827	−	19.7384i	−0.0147132	−	0.758610i	0.917712	−	0.397247i	$-0.130034\pi$
$678$		0			0
$679$	−8.03429	−	12.7473i	−0.308328	−	0.489195i
$680$	−147.584	+	41.0828i	−5.65959	+	1.57546i
$681$		0			0
$682$	−2.26671	−	0.0879587i	−0.0867968	−	0.00336811i
$683$	7.99736	+	8.47670i	0.306010	+	0.324352i	0.862069	−	0.506791i	$-0.169168\pi$
$683$	7.99736	+	8.47670i	0.306010	+	0.324352i	−0.556058	+	0.831143i	$0.687687\pi$
$684$		0			0
$685$	−51.2148	−	12.1381i	−1.95682	−	0.463774i
$686$	−13.1666	−	51.1160i	−0.502704	−	1.95162i
$687$		0			0
$688$	1.64926	−	4.27168i	0.0628773	−	0.162856i
$689$	18.0743	+	22.4086i	0.688577	+	0.853701i
$690$		0			0
$691$	−26.7299	+	26.2165i	−1.01685	+	0.997322i	−0.999997	−	0.00253636i	$-0.999193\pi$
$691$	−26.7299	+	26.2165i	−1.01685	+	0.997322i	−0.0168554	+	0.999858i	$0.505365\pi$
$692$	−9.28414	+	9.84062i	−0.352930	+	0.374084i
$693$		0			0
$694$	−2.46393	+	8.23010i	−0.0935296	+	0.312410i
$695$	−7.40492	+	11.7487i	−0.280885	+	0.445654i
$696$		0			0
$697$	33.9882	+	33.3354i	1.28739	+	1.26267i
$698$	27.7249	−	1.07585i	1.04940	−	0.0407216i
$699$		0			0
$700$	−15.7043	+	9.47761i	−0.593568	+	0.358220i
$701$	1.16383	−	6.60042i	0.0439574	−	0.249295i	−0.954909	−	0.296899i	$-0.904048\pi$
$701$	1.16383	−	6.60042i	0.0439574	−	0.249295i	0.998866	+	0.0476043i	$0.0151587\pi$
$702$		0			0
$703$	2.71306	+	15.3865i	0.102325	+	0.580314i
$704$	38.5396	+	44.1615i	1.45252	+	1.66440i
$705$		0			0
$706$	−4.07231	−	3.15628i	−0.153263	−	0.118788i
$707$	−29.4018	−	2.28529i	−1.10577	−	0.0859471i
$708$		0			0
$709$	−20.2128	−	18.3422i	−0.759109	−	0.688855i	0.197476	−	0.980308i	$-0.436726\pi$
$709$	−20.2128	−	18.3422i	−0.759109	−	0.688855i	−0.956585	+	0.291453i	$0.905861\pi$
$710$	10.3645	−	13.9219i	0.388971	−	0.522479i
$711$		0			0
$712$	−28.2593	+	65.5123i	−1.05906	+	2.45518i
$713$	−0.672213	−	0.480469i	−0.0251746	−	0.0179937i
$714$		0			0
$715$	0.332543	−	17.1458i	0.0124364	−	0.641218i
$716$	20.9649	+	61.2721i	0.783494	+	2.28985i
$717$		0			0
$718$	−54.9528	+	4.27127i	−2.05082	+	0.159402i
$719$	39.9392	+	26.2684i	1.48948	+	0.979647i	0.993805	+	0.111139i	$0.0354500\pi$
$719$	39.9392	+	26.2684i	1.48948	+	0.979647i	0.495676	+	0.868508i	$0.334920\pi$
$720$		0			0
$721$	−16.1933	−	8.13257i	−0.603069	−	0.302873i
$722$	12.9133	+	94.5418i	0.480582	+	3.51848i
$723$		0			0
$724$	−100.338	−	45.6093i	−3.72904	−	1.69506i
$725$	6.13169	+	1.96605i	0.227725	+	0.0730172i
$726$		0			0
$727$	−6.55086	−	1.02454i	−0.242958	−	0.0379979i	0.0318673	−	0.999492i	$-0.489855\pi$
$727$	−6.55086	−	1.02454i	−0.242958	−	0.0379979i	−0.274825	+	0.961494i	$0.588620\pi$
$728$	−59.0131			−2.18717
$729$		0			0
$730$	−79.2720			−2.93399
$731$	−2.28049	−	0.356662i	−0.0843471	−	0.0131916i
$732$		0			0
$733$	−0.531808	−	0.170517i	−0.0196428	−	0.00629820i	0.295488	−	0.955346i	$-0.404518\pi$
$733$	−0.531808	−	0.170517i	−0.0196428	−	0.00629820i	−0.315131	+	0.949048i	$0.602049\pi$
$734$	15.9106	+	7.23224i	0.587269	+	0.266947i
$735$		0			0
$736$	6.23793	+	45.6697i	0.229933	+	1.68341i
$737$	4.05645	+	2.03722i	0.149421	+	0.0750421i
$738$		0			0
$739$	23.0685	+	15.1724i	0.848590	+	0.558126i	0.897670	−	0.440669i	$-0.145259\pi$
$739$	23.0685	+	15.1724i	0.848590	+	0.558126i	−0.0490801	+	0.998795i	$0.515629\pi$
$740$	−28.3408	+	2.20282i	−1.04183	+	0.0809774i
$741$		0			0
$742$	23.0721	+	67.4306i	0.847002	+	2.47546i
$743$	−0.177368	+	9.14505i	−0.00650700	+	0.335499i	0.982385	+	0.186866i	$0.0598330\pi$
$743$	−0.177368	+	9.14505i	−0.00650700	+	0.335499i	−0.988892	+	0.148633i	$0.952513\pi$
$744$		0			0
$745$	−1.83584	−	1.31218i	−0.0672601	−	0.0480746i
$746$	27.1138	−	62.8568i	0.992705	−	2.30135i
$747$		0			0
$748$	54.1719	−	72.7655i	1.98072	−	2.66057i
$749$	−2.45088	−	2.22406i	−0.0895532	−	0.0812652i
$750$		0			0
$751$	20.3921	+	1.58500i	0.744118	+	0.0578374i	0.443953	−	0.896050i	$-0.353576\pi$
$751$	20.3921	+	1.58500i	0.744118	+	0.0578374i	0.300165	+	0.953887i	$0.402958\pi$
$752$	96.1778	+	74.5435i	3.50724	+	2.71832i
$753$		0			0
$754$	21.8812	+	25.0731i	0.796866	+	0.913107i
$755$	−0.654143	−	3.70983i	−0.0238067	−	0.135015i
$756$		0			0
$757$	−1.66040	+	9.41662i	−0.0603484	+	0.342253i	0.939652	+	0.342133i	$0.111149\pi$
$757$	−1.66040	+	9.41662i	−0.0603484	+	0.342253i	−1.00000		0.000119960i	$0.999962\pi$
$758$	−84.2581	+	50.8500i	−3.06039	+	1.84696i
$759$		0			0
$760$	−166.087	+	6.44495i	−6.02462	+	0.233783i
$761$	−33.4362	−	32.7940i	−1.21206	−	1.18878i	−0.976171	−	0.217004i	$-0.930372\pi$
$761$	−33.4362	−	32.7940i	−1.21206	−	1.18878i	−0.235892	−	0.971779i	$-0.575801\pi$
$762$		0			0
$763$	−4.14613	+	6.57828i	−0.150100	+	0.238150i
$764$	10.5943	−	35.3875i	0.383289	−	1.28027i
$765$		0			0
$766$	18.9953	−	20.1338i	0.686328	−	0.727465i
$767$	9.77010	−	9.58244i	0.352778	−	0.346002i
$768$		0			0
$769$	−7.77226	−	9.63609i	−0.280275	−	0.347486i	0.618589	−	0.785715i	$-0.287705\pi$
$769$	−7.77226	−	9.63609i	−0.280275	−	0.347486i	−0.898863	+	0.438229i	$0.855606\pi$
$770$	15.2905	−	39.6035i	0.551033	−	1.42721i
$771$		0			0
$772$	−29.6092	−	114.950i	−1.06566	−	4.13715i
$773$	34.8092	+	8.24994i	1.25200	+	0.296730i	0.802555	−	0.596578i	$-0.203473\pi$
$773$	34.8092	+	8.24994i	1.25200	+	0.296730i	0.449446	+	0.893308i	$0.351621\pi$
$774$		0			0
$775$	0.321279	+	0.340536i	0.0115407	+	0.0122324i
$776$	54.4620	+	2.11338i	1.95507	+	0.0758657i
$777$		0			0
$778$	101.892	−	28.3636i	3.65301	−	1.01688i
$779$	27.5412	+	43.6971i	0.986766	+	1.56561i
$780$		0			0
$781$	0.124068	+	6.39691i	0.00443950	+	0.228899i
$782$	42.7713	−	15.5675i	1.52950	−	0.556692i
$783$		0			0
$784$	11.7944	+	4.29280i	0.421228	+	0.153314i
$785$	−17.6003	+	51.4388i	−0.628182	+	1.83593i
$786$		0			0
$787$	32.5082	−	13.2811i	1.15879	−	0.473419i	0.284432	−	0.958696i	$-0.408195\pi$
$787$	32.5082	−	13.2811i	1.15879	−	0.473419i	0.874360	+	0.485277i	$0.161281\pi$
$788$	−54.8963	−	114.806i	−1.95560	−	4.08979i
$789$		0			0
$790$	70.1420	−	22.4901i	2.49554	−	0.800163i
$791$	8.16345	+	0.954171i	0.290259	+	0.0339264i
$792$		0			0
$793$	−7.47139	−	10.0358i	−0.265317	−	0.356382i
$794$	−4.84843	+	49.8462i	−0.172064	+	1.76898i
$795$		0			0
$796$	29.0810	+	17.5505i	1.03075	+	0.622061i
$797$	11.6012	−	13.2935i	0.410936	−	0.470880i	−0.510237	−	0.860034i	$-0.670442\pi$
$797$	11.6012	−	13.2935i	0.410936	−	0.470880i	0.921173	+	0.389154i	$0.127233\pi$
$798$		0			0
$799$	26.4608	−	55.3380i	0.936115	−	1.95772i
$800$	1.51858	−	26.0730i	0.0536899	−	0.921819i
$801$		0			0
$802$	−28.5069	+	18.7493i	−1.00661	+	0.662060i
$803$	23.0971	−	17.9016i	0.815080	−	0.631735i
$804$		0			0
$805$	12.5803	−	8.99185i	0.443397	−	0.316921i
$806$	0.512230	+	2.36472i	0.0180425	+	0.0832936i
$807$		0			0
$808$	66.9697	−	83.0294i	2.35599	−	2.92096i
$809$	0.489186	+	0.847295i	0.0171989	+	0.0297893i	0.874497	−	0.485031i	$-0.161192\pi$
$809$	0.489186	+	0.847295i	0.0171989	+	0.0297893i	−0.857298	+	0.514821i	$0.827858\pi$
$810$		0			0
$811$	20.4595	−	35.4369i	0.718431	−	1.24436i	−0.243190	−	0.969979i	$-0.578194\pi$
$811$	20.4595	−	35.4369i	0.718431	−	1.24436i	0.961621	−	0.274380i	$-0.0884727\pi$
$812$	21.5407	+	55.7918i	0.755931	+	1.95791i
$813$		0			0
$814$	10.6893	−	9.70004i	0.374660	−	0.339986i
$815$	0.752835	+	7.73982i	0.0263707	+	0.271114i
$816$		0			0
$817$	−2.31833	−	0.947141i	−0.0811080	−	0.0331363i
$818$	−4.70530	−	80.7870i	−0.164517	−	2.82465i
$819$		0			0
$820$	−83.9807	+	42.1767i	−2.93273	+	1.47287i
$821$	27.4812	+	40.0686i	0.959100	+	1.39840i	0.916822	+	0.399297i	$0.130746\pi$
$821$	27.4812	+	40.0686i	0.959100	+	1.39840i	0.0422786	+	0.999106i	$0.486538\pi$
$822$		0			0
$823$	5.29912	+	1.04071i	0.184716	+	0.0362770i	0.284215	−	0.958761i	$-0.408267\pi$
$823$	5.29912	+	1.04071i	0.184716	+	0.0362770i	−0.0994989	+	0.995038i	$0.531724\pi$
$824$	57.3889	−	31.6658i	1.99924	−	1.10313i
$825$		0			0
$826$	30.8407	−	14.0188i	1.07308	−	0.487777i
$827$	14.9714	−	1.74991i	0.520608	−	0.0608503i	0.148269	−	0.988947i	$-0.452630\pi$
$827$	14.9714	−	1.74991i	0.520608	−	0.0608503i	0.372339	+	0.928097i	$0.378556\pi$
$828$		0			0
$829$	−7.56307	−	17.5332i	−0.262676	−	0.608952i	0.734927	−	0.678146i	$-0.237216\pi$
$829$	−7.56307	−	17.5332i	−0.262676	−	0.608952i	−0.997603	+	0.0691945i	$0.977957\pi$
$830$	10.0080	−	46.2020i	0.347382	−	1.60369i
$831$		0			0
$832$	35.3611	−	51.5578i	1.22593	−	1.78744i
$833$	0.856233	−	6.26874i	0.0296667	−	0.217199i
$834$		0			0
$835$	7.06256	−	1.38704i	0.244410	−	0.0480006i
$836$	75.3972	−	63.2658i	2.60767	−	2.18809i
$837$		0			0
$838$	−33.8937	−	28.4402i	−1.17084	−	0.982449i
$839$	31.5676	+	17.4183i	1.08983	+	0.601345i	0.923062	−	0.384651i	$-0.125678\pi$
$839$	31.5676	+	17.4183i	1.08983	+	0.601345i	0.166772	+	0.985996i	$0.446666\pi$
$840$		0			0
$841$	−3.73075	+	7.08265i	−0.128646	+	0.244229i
$842$	−6.65078	+	25.8199i	−0.229201	+	0.889812i
$843$		0			0
$844$	7.15651	+	13.5863i	0.246337	+	0.467660i
$845$	14.2159	−	3.36922i	0.489040	−	0.115905i
$846$		0			0
$847$	−3.28346	−	10.9675i	−0.112821	−	0.376849i
$848$	−139.025	−	38.7003i	−4.77414	−	1.32897i
$849$		0			0
$850$	−25.4802	+	3.98504i	−0.873965	+	0.136686i
$851$	5.19458	−	0.812417i	0.178068	−	0.0278493i
$852$		0			0
$853$	45.6238	+	12.7002i	1.56213	+	0.434848i	0.938046	−	0.346511i	$-0.112634\pi$
$853$	45.6238	+	12.7002i	1.56213	+	0.434848i	0.624082	+	0.781359i	$0.285473\pi$
$854$	−8.88304	−	29.6714i	−0.303971	−	1.01534i
$855$		0			0
$856$	11.6485	−	2.76075i	0.398139	−	0.0943606i
$857$	0.529683	+	1.00558i	0.0180936	+	0.0343499i	0.893642	−	0.448781i	$-0.148142\pi$
$857$	0.529683	+	1.00558i	0.0180936	+	0.0343499i	−0.875548	+	0.483131i	$0.839500\pi$
$858$		0			0
$859$	6.44593	−	25.0246i	0.219932	−	0.853829i	−0.759242	−	0.650808i	$-0.774430\pi$
$859$	6.44593	−	25.0246i	0.219932	−	0.853829i	0.979174	−	0.203021i	$-0.0650760\pi$
$860$	2.12349	−	4.03135i	0.0724105	−	0.137468i
$861$		0			0
$862$	60.3874	+	33.3203i	2.05680	+	1.13490i
$863$	1.89218	+	1.58773i	0.0644105	+	0.0540468i	0.674425	−	0.738344i	$-0.264392\pi$
$863$	1.89218	+	1.58773i	0.0644105	+	0.0540468i	−0.610014	+	0.792391i	$0.708836\pi$
$864$		0			0
$865$	−4.95048	+	4.15394i	−0.168321	+	0.141238i
$866$	−82.8185	+	16.2650i	−2.81429	+	0.552708i
$867$		0			0
$868$	−0.588460	+	4.30829i	−0.0199736	+	0.146233i
$869$	−15.3581	+	22.3927i	−0.520989	+	0.759620i
$870$		0			0
$871$	1.02501	−	4.73198i	0.0347312	−	0.160337i
$872$	−11.1403	−	25.8262i	−0.377260	−	0.874586i
$873$		0			0
$874$	49.0498	−	5.73310i	1.65914	−	0.193925i
$875$	20.4028	−	9.27422i	0.689741	−	0.313526i
$876$		0			0
$877$	6.14726	−	3.39192i	0.207578	−	0.114537i	−0.375917	−	0.926653i	$-0.622672\pi$
$877$	6.14726	−	3.39192i	0.207578	−	0.114537i	0.583495	+	0.812116i	$0.301685\pi$
$878$	−5.62071	−	1.10387i	−0.189690	−	0.0372539i
$879$		0			0
$880$	48.6209	+	70.8910i	1.63901	+	2.38973i
$881$	9.67245	−	4.85768i	0.325873	−	0.163660i	−0.278340	−	0.960483i	$-0.589784\pi$
$881$	9.67245	−	4.85768i	0.325873	−	0.163660i	0.604213	+	0.796823i	$0.293488\pi$
$882$		0			0
$883$	1.49870	+	25.7318i	0.0504354	+	0.865943i	0.924748	+	0.380580i	$0.124276\pi$
$883$	1.49870	+	25.7318i	0.0504354	+	0.865943i	−0.874313	+	0.485363i	$0.838687\pi$
$884$	−89.5735	−	36.5948i	−3.01268	−	1.23082i
$885$		0			0
$886$	−7.85104	−	80.7157i	−0.263761	−	2.71170i
$887$	−34.3600	+	31.1801i	−1.15370	+	1.04692i	−0.155444	+	0.987845i	$0.549681\pi$
$887$	−34.3600	+	31.1801i	−1.15370	+	1.04692i	−0.998253	+	0.0590796i	$0.981183\pi$
$888$		0			0
$889$	−1.05690	−	2.73744i	−0.0354473	−	0.0918107i
$890$	−27.3728	+	47.4111i	−0.917539	+	1.58922i
$891$		0			0
$892$	47.5132	+	82.2952i	1.59086	+	2.75545i
$893$	41.7815	−	51.8009i	1.39816	−	1.73345i
$894$		0			0
$895$	6.54879	+	30.2326i	0.218902	+	1.01056i
$896$	51.4182	−	36.7515i	1.71776	−	1.22778i
$897$		0			0
$898$	25.5835	−	19.8287i	0.853732	−	0.661693i
$899$	1.27535	−	0.838809i	0.0425352	−	0.0279758i
$900$		0			0
$901$	−4.22976	+	72.6222i	−0.140914	+	2.41940i
$902$	20.5857	−	43.0513i	0.685428	−	1.43345i
$903$		0			0
$904$	−19.5478	+	22.3993i	−0.650149	+	0.744988i
$905$	−45.0753	−	27.2031i	−1.49835	−	0.904260i
$906$		0			0
$907$	−1.99051	+	20.4643i	−0.0660939	+	0.679504i	0.902472	+	0.430748i	$0.141750\pi$
$907$	−1.99051	+	20.4643i	−0.0660939	+	0.679504i	−0.968566	+	0.248756i	$0.919978\pi$
$908$	70.9257	+	95.2697i	2.35375	+	3.16164i
$909$		0			0
$910$	−44.9752	−	5.25685i	−1.49091	−	0.174263i
$911$	5.22621	−	1.67572i	0.173152	−	0.0555190i	−0.217485	−	0.976064i	$-0.569785\pi$
$911$	5.22621	−	1.67572i	0.173152	−	0.0555190i	0.390637	+	0.920545i	$0.372255\pi$
$912$		0			0
$913$	7.51760	+	15.7217i	0.248796	+	0.520313i
$914$	2.11921	−	0.865791i	0.0700971	−	0.0286378i
$915$		0			0
$916$	−44.9545	+	131.384i	−1.48534	+	4.34106i
$917$	50.2600	+	18.2932i	1.65973	+	0.604093i
$918$		0			0
$919$	−46.6919	+	16.9944i	−1.54022	+	0.560595i	−0.966099	−	0.258173i	$-0.916879\pi$
$919$	−46.6919	+	16.9944i	−1.54022	+	0.560595i	−0.574124	+	0.818769i	$0.694657\pi$
$920$	1.08463	+	55.9230i	0.0357590	+	1.84373i
$921$		0			0
$922$	22.5589	+	35.7922i	0.742939	+	1.17875i
$923$	6.57444	−	1.83012i	0.216400	−	0.0602392i
$924$		0			0
$925$	−2.97684	−	0.115515i	−0.0978779	−	0.00379811i
$926$	4.36559	+	4.62726i	0.143462	+	0.152061i
$927$		0			0
$928$	−82.8593	−	19.6380i	−2.71999	−	0.644650i
$929$	−2.14588	−	8.33082i	−0.0704040	−	0.273325i	0.923496	−	0.383607i	$-0.125318\pi$
$929$	−2.14588	−	8.33082i	−0.0704040	−	0.273325i	−0.993900	+	0.110282i	$0.964825\pi$
$930$		0			0
$931$	2.47245	−	6.40381i	0.0810313	−	0.209876i
$932$	10.1667	+	12.6048i	0.333022	+	0.412883i
$933$		0			0
$934$	60.3811	−	59.2214i	1.97573	−	1.93778i
$935$	29.7365	−	31.5188i	0.972487	−	1.03078i
$936$		0			0
$937$	0.910199	−	3.04028i	0.0297349	−	0.0993215i	−0.941834	−	0.336078i	$-0.890899\pi$
$937$	0.910199	−	3.04028i	0.0297349	−	0.0993215i	0.971569	+	0.236757i	$0.0760845\pi$
$938$	6.39087	−	10.1398i	0.208669	−	0.331076i
$939$		0			0
$940$	86.4451	+	84.7848i	2.81953	+	2.76537i
$941$	−51.5498	+	2.00037i	−1.68048	+	0.0652101i	−0.861224	−	0.508225i	$-0.830302\pi$
$941$	−51.5498	+	2.00037i	−1.68048	+	0.0652101i	−0.819251	+	0.573435i	$0.805610\pi$
$942$		0			0
$943$	14.8818	−	8.98123i	0.484619	−	0.292469i
$944$	−11.9119	+	67.5558i	−0.387700	+	2.19875i
$945$		0			0
$946$	0.401766	+	2.27853i	0.0130625	+	0.0740814i
$947$	−20.6435	−	23.6549i	−0.670825	−	0.768680i	0.312622	−	0.949878i	$-0.398793\pi$
$947$	−20.6435	−	23.6549i	−0.670825	−	0.768680i	−0.983447	+	0.181198i	$0.942003\pi$
$948$		0			0
$949$	−24.6361	−	19.0944i	−0.799721	−	0.619830i
$950$	−27.8972	−	2.16834i	−0.905104	−	0.0703502i
$951$		0			0
$952$	−110.426	−	100.206i	−3.57893	−	3.24770i
$953$	14.7972	−	19.8760i	0.479327	−	0.643848i	−0.495024	−	0.868879i	$-0.664841\pi$
$953$	14.7972	−	19.8760i	0.479327	−	0.643848i	0.974352	+	0.225031i	$0.0722483\pi$
$954$		0			0
$955$	6.98876	−	16.2018i	0.226151	−	0.524277i
$956$	33.4557	+	23.9127i	1.08203	+	0.773391i
$957$		0			0
$958$	−1.50610	+	77.6541i	−0.0486599	+	2.50889i
$959$	−16.5854	−	48.4726i	−0.535569	−	1.56526i
$960$		0			0
$961$	−30.7961	+	2.39366i	−0.993424	+	0.0772150i
$962$	−12.8633	−	8.46033i	−0.414730	−	0.272772i
$963$		0			0
$964$	−39.1822	−	19.6780i	−1.26197	−	0.633787i
$965$	−7.67336	−	56.1790i	−0.247014	−	1.80846i
$966$		0			0
$967$	28.3706	+	12.8960i	0.912336	+	0.414708i	0.814279	−	0.580473i	$-0.197132\pi$
$967$	28.3706	+	12.8960i	0.912336	+	0.414708i	0.0980566	+	0.995181i	$0.468737\pi$
$968$	39.4335	+	12.6438i	1.26744	+	0.406388i
$969$		0			0
$970$	41.3185	+	6.46209i	1.32666	+	0.207485i
$971$	−58.5739			−1.87972			−0.939862	−	0.341554i	$-0.889047\pi$
$971$	−58.5739			−1.87972			−0.939862	+	0.341554i	$0.889047\pi$
$972$		0			0
$973$	−13.5177			−0.433356
$974$	−22.0569	−	3.44964i	−0.706748	−	0.110533i
$975$		0			0
$976$	59.7213	+	19.1489i	1.91163	+	0.612941i
$977$	21.3458	+	9.70287i	0.682913	+	0.310422i	0.725057	−	0.688689i	$-0.241814\pi$
$977$	21.3458	+	9.70287i	0.682913	+	0.310422i	−0.0421431	+	0.999112i	$0.513419\pi$
$978$		0			0
$979$	−2.73113	−	19.9954i	−0.0872874	−	0.639057i
$980$	11.1609	+	5.60524i	0.356523	+	0.179053i
$981$		0			0
$982$	19.0105	+	12.5034i	0.606649	+	0.398999i
$983$	−34.8118	+	2.70579i	−1.11032	+	0.0863013i	−0.619529	−	0.784974i	$-0.712676\pi$
$983$	−34.8118	+	2.70579i	−1.11032	+	0.0863013i	−0.490795	+	0.871275i	$0.663294\pi$
$984$		0			0
$985$	−19.6786	−	57.5128i	−0.627011	−	1.83251i
$986$	−1.63058	+	84.0721i	−0.0519281	+	2.67740i
$987$		0			0
$988$	−85.4083	−	61.0462i	−2.71720	−	1.94214i
$989$	−0.333799	+	0.773832i	−0.0106142	+	0.0246064i
$990$		0			0
$991$	23.7815	−	31.9442i	0.755445	−	1.01474i	−0.243548	−	0.969889i	$-0.578311\pi$
$991$	23.7815	−	31.9442i	0.755445	−	1.01474i	0.998994	−	0.0448506i	$-0.0142812\pi$
$992$	−4.58495	−	4.16062i	−0.145572	−	0.132100i
$993$		0			0
$994$	16.8432	+	1.30915i	0.534232	+	0.0415238i
$995$	12.8240	+	9.93933i	0.406547	+	0.315098i
$996$		0			0
$997$	4.05236	+	4.64349i	0.128339	+	0.147061i	0.814009	−	0.580852i	$-0.197281\pi$
$997$	4.05236	+	4.64349i	0.128339	+	0.147061i	−0.685670	+	0.727913i	$0.740490\pi$
$998$	−2.58686	−	14.6708i	−0.0818856	−	0.464396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.1		1404
3.2	odd	2		243.2.i.a.13.26	✓	1404
243.56	odd	162		243.2.i.a.187.26	yes	1404
243.187	even	81	inner	729.2.i.a.73.1		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.26	✓	1404	3.2	odd	2
243.2.i.a.187.26	yes	1404	243.56	odd	162
729.2.i.a.10.1		1404	1.1	even	1	trivial
729.2.i.a.73.1		1404	243.187	even	81	inner

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.66910 - 0.417440i) q^{2} +(5.04536 + 1.61773i) q^{4} +(2.30401 + 1.04730i) q^{5} +(0.333383 + 2.44079i) q^{7} +(-7.96289 - 3.99911i) q^{8} +O(q^{10})\)	\(q+(-2.66910 - 0.417440i) q^{2} +(5.04536 + 1.61773i) q^{4} +(2.30401 + 1.04730i) q^{5} +(0.333383 + 2.44079i) q^{7} +(-7.96289 - 3.99911i) q^{8} +(-5.71246 - 3.75714i) q^{10} +(2.51287 - 0.195316i) q^{11} +(-0.870322 - 2.54361i) q^{13} +(0.129052 - 6.65389i) q^{14} +(10.9634 + 7.83616i) q^{16} +(2.69059 - 6.23748i) q^{17} +(4.40120 - 5.91184i) q^{19} +(9.93032 + 9.01128i) q^{20} +(-6.78865 - 0.527655i) q^{22} +(-1.96035 - 1.51938i) q^{23} +(0.924025 + 1.05882i) q^{25} +(1.26117 + 7.15247i) q^{26} +(-2.26651 + 12.8540i) q^{28} +(3.92297 - 2.36752i) q^{29} +(0.332893 - 0.0129178i) q^{31} +(-13.2681 - 13.0132i) q^{32} +(-9.78522 + 15.5253i) q^{34} +(-1.78813 + 5.97277i) q^{35} +(-1.45474 + 1.54193i) q^{37} +(-14.2151 + 13.9421i) q^{38} +(-14.1583 - 17.5536i) q^{40} +(-2.52421 + 6.53786i) q^{41} +(-0.0847579 - 0.329050i) q^{43} +(12.9943 + 3.07971i) q^{44} +(4.59812 + 4.87372i) q^{46} +(9.02289 + 0.350129i) q^{47} +(0.897270 - 0.249772i) q^{49} +(-2.02433 - 3.21181i) q^{50} +(-0.276211 - 14.2414i) q^{52} +(-10.0630 + 3.66262i) q^{53} +(5.99424 + 2.18173i) q^{55} +(7.10632 - 20.7690i) q^{56} +(-11.4591 + 4.68156i) q^{58} +(2.19593 + 4.59239i) q^{59} +(4.43170 - 1.42097i) q^{61} +(-0.893919 - 0.104484i) q^{62} +(13.8870 + 18.6535i) q^{64} +(0.658698 - 6.77200i) q^{65} +(1.54194 + 0.930564i) q^{67} +(23.6655 - 27.1177i) q^{68} +(7.26598 - 15.1955i) q^{70} +(-0.147599 + 2.53418i) q^{71} +(9.68672 - 6.37106i) q^{73} +(4.52651 - 3.50831i) q^{74} +(31.7694 - 22.7074i) q^{76} +(1.31447 + 6.06829i) q^{77} +(-6.76355 + 8.38549i) q^{79} +(17.0530 + 29.5366i) q^{80} +(9.46653 - 16.3965i) q^{82} +(2.49030 + 6.45004i) q^{83} +(12.7317 - 11.5534i) q^{85} +(0.0888687 + 0.913651i) q^{86} +(-20.7908 - 8.49398i) q^{88} +(-0.465562 - 7.99339i) q^{89} +(5.91828 - 2.97227i) q^{91} +(-7.43270 - 10.8371i) q^{92} +(-23.9369 - 4.70105i) q^{94} +(16.3319 - 9.01156i) q^{95} +(-5.56831 + 2.53111i) q^{97} +(-2.49917 + 0.292111i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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