LMFDB - Embedded newform 729.2.i.a.10.10

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			10.10
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.593472 - 0.0928174i) q^{2} +(-1.56090 - 0.500483i) q^{4} +(0.621532 + 0.282521i) q^{5} +(-0.302306 - 2.21327i) q^{7} +(1.95348 + 0.981077i) q^{8} +O(q^{10})$	\(q+(-0.593472 - 0.0928174i) q^{2} +(-1.56090 - 0.500483i) q^{4} +(0.621532 + 0.282521i) q^{5} +(-0.302306 - 2.21327i) q^{7} +(1.95348 + 0.981077i) q^{8} +(-0.342639 - 0.225357i) q^{10} +(0.636509 - 0.0494734i) q^{11} +(0.868078 + 2.53705i) q^{13} +(-0.0260198 + 1.34157i) q^{14} +(1.59883 + 1.14278i) q^{16} +(-0.980238 + 2.27245i) q^{17} +(4.56909 - 6.13736i) q^{19} +(-0.828753 - 0.752053i) q^{20} +(-0.382342 - 0.0297180i) q^{22} +(-6.28672 - 4.87257i) q^{23} +(-2.98112 - 3.41599i) q^{25} +(-0.279697 - 1.58624i) q^{26} +(-0.635834 + 3.60599i) q^{28} +(-0.325480 + 0.196428i) q^{29} +(-2.13959 + 0.0830257i) q^{31} +(-3.96410 - 3.88796i) q^{32} +(0.792666 - 1.25765i) q^{34} +(0.437402 - 1.46102i) q^{35} +(6.21694 - 6.58957i) q^{37} +(-3.28128 + 3.21826i) q^{38} +(0.936978 + 1.16167i) q^{40} +(2.39445 - 6.20179i) q^{41} +(0.0198074 + 0.0768969i) q^{43} +(-1.01829 - 0.241339i) q^{44} +(3.27873 + 3.47525i) q^{46} +(-5.96737 - 0.231561i) q^{47} +(1.93643 - 0.539042i) q^{49} +(1.45215 + 2.30399i) q^{50} +(-0.0852321 - 4.39455i) q^{52} +(9.73666 - 3.54385i) q^{53} +(0.409588 + 0.149078i) q^{55} +(1.58084 - 4.62017i) q^{56} +(0.211395 - 0.0863643i) q^{58} +(-5.28596 - 11.0546i) q^{59} +(6.26787 - 2.00971i) q^{61} +(1.27749 + 0.149317i) q^{62} +(-0.355417 - 0.477408i) q^{64} +(-0.177232 + 1.82211i) q^{65} +(-6.40602 - 3.86605i) q^{67} +(2.66738 - 3.05647i) q^{68} +(-0.395194 + 0.826479i) q^{70} +(-0.264891 + 4.54800i) q^{71} +(-8.34451 + 5.48827i) q^{73} +(-4.30121 + 3.33369i) q^{74} +(-10.2036 + 7.29306i) q^{76} +(-0.301918 - 1.39381i) q^{77} +(1.76774 - 2.19166i) q^{79} +(0.670867 + 1.16198i) q^{80} +(-1.99667 + 3.45834i) q^{82} +(-1.69478 - 4.38960i) q^{83} +(-1.25126 + 1.13546i) q^{85} +(-0.00461775 - 0.0474747i) q^{86} +(1.29195 + 0.527819i) q^{88} +(0.399193 + 6.85388i) q^{89} +(5.35275 - 2.68825i) q^{91} +(7.37431 + 10.7520i) q^{92} +(3.51998 + 0.691301i) q^{94} +(4.57377 - 2.52370i) q^{95} +(-0.870033 + 0.395479i) q^{97} +(-1.19925 + 0.140172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.593472	−	0.0928174i	−0.419648	−	0.0656318i	−0.0588302	−	0.998268i	$-0.518737\pi$
$2$	−0.593472	−	0.0928174i	−0.419648	−	0.0656318i	−0.360818	+	0.932636i	$0.617502\pi$
$3$		0			0
$3$		0			0
$4$	−1.56090	−	0.500483i	−0.780451	−	0.250241i
$5$	0.621532	+	0.282521i	0.277958	+	0.126347i	0.547939	−	0.836518i	$-0.315413\pi$
$5$	0.621532	+	0.282521i	0.277958	+	0.126347i	−0.269981	+	0.962866i	$0.587018\pi$
$6$		0			0
$7$	−0.302306	−	2.21327i	−0.114261	−	0.836537i	−0.955316	−	0.295587i	$-0.904485\pi$
$7$	−0.302306	−	2.21327i	−0.114261	−	0.836537i	0.841055	−	0.540950i	$-0.181935\pi$
$8$	1.95348	+	0.981077i	0.690661	+	0.346863i
$9$		0			0
$10$	−0.342639	−	0.225357i	−0.108352	−	0.0712642i
$11$	0.636509	−	0.0494734i	0.191915	−	0.0149168i	0.0188247	−	0.999823i	$-0.494008\pi$
$11$	0.636509	−	0.0494734i	0.191915	−	0.0149168i	0.173090	+	0.984906i	$0.444625\pi$
$12$		0			0
$13$	0.868078	+	2.53705i	0.240761	+	0.703652i	0.998683	+	0.0513060i	$0.0163384\pi$
$13$	0.868078	+	2.53705i	0.240761	+	0.703652i	−0.757922	+	0.652346i	$0.773785\pi$
$14$	−0.0260198	+	1.34157i	−0.00695407	+	0.358550i
$15$		0			0
$16$	1.59883	+	1.14278i	0.399708	+	0.285694i
$17$	−0.980238	+	2.27245i	−0.237743	+	0.551149i	−0.994759	−	0.102246i	$-0.967397\pi$
$17$	−0.980238	+	2.27245i	−0.237743	+	0.551149i	0.757016	+	0.653396i	$0.226656\pi$
$18$		0			0
$19$	4.56909	−	6.13736i	1.04822	−	1.40801i	0.139688	−	0.990196i	$-0.455390\pi$
$19$	4.56909	−	6.13736i	1.04822	−	1.40801i	0.908534	−	0.417811i	$-0.137203\pi$
$20$	−0.828753	−	0.752053i	−0.185315	−	0.168164i
$21$		0			0
$22$	−0.382342	−	0.0297180i	−0.0815157	−	0.00633590i
$23$	−6.28672	−	4.87257i	−1.31087	−	1.01600i	−0.997802	−	0.0662720i	$-0.978890\pi$
$23$	−6.28672	−	4.87257i	−1.31087	−	1.01600i	−0.313070	−	0.949730i	$-0.601357\pi$
$24$		0			0
$25$	−2.98112	−	3.41599i	−0.596225	−	0.683198i
$26$	−0.279697	−	1.58624i	−0.0548532	−	0.311088i
$27$		0			0
$28$	−0.635834	+	3.60599i	−0.120161	+	0.681468i
$29$	−0.325480	+	0.196428i	−0.0604400	+	0.0364757i	−0.546597	−	0.837396i	$-0.684077\pi$
$29$	−0.325480	+	0.196428i	−0.0604400	+	0.0364757i	0.486157	+	0.873871i	$0.338398\pi$
$30$		0			0
$31$	−2.13959	+	0.0830257i	−0.384281	+	0.0149119i	−0.230192	−	0.973145i	$-0.573936\pi$
$31$	−2.13959	+	0.0830257i	−0.384281	+	0.0149119i	−0.154089	+	0.988057i	$0.549244\pi$
$32$	−3.96410	−	3.88796i	−0.700760	−	0.687301i
$33$		0			0
$34$	0.792666	−	1.25765i	0.135941	−	0.215685i
$35$	0.437402	−	1.46102i	0.0739344	−	0.246958i
$36$		0			0
$37$	6.21694	−	6.58957i	1.02206	−	1.08332i	0.0255631	−	0.999673i	$-0.491862\pi$
$37$	6.21694	−	6.58957i	1.02206	−	1.08332i	0.996496	−	0.0836457i	$-0.0266564\pi$
$38$	−3.28128	+	3.21826i	−0.532295	+	0.522071i
$39$		0			0
$40$	0.936978	+	1.16167i	0.148149	+	0.183676i
$41$	2.39445	−	6.20179i	0.373951	−	0.968556i	−0.610362	−	0.792123i	$-0.708976\pi$
$41$	2.39445	−	6.20179i	0.373951	−	0.968556i	0.984313	−	0.176434i	$-0.0564561\pi$
$42$		0			0
$43$	0.0198074	+	0.0768969i	0.00302060	+	0.0117267i	0.969883	−	0.243573i	$-0.0783196\pi$
$43$	0.0198074	+	0.0768969i	0.00302060	+	0.0117267i	−0.966862	+	0.255300i	$0.917826\pi$
$44$	−1.01829	−	0.241339i	−0.153513	−	0.0363832i
$45$		0			0
$46$	3.27873	+	3.47525i	0.483423	+	0.512398i
$47$	−5.96737	−	0.231561i	−0.870431	−	0.0337767i	−0.400311	−	0.916379i	$-0.631098\pi$
$47$	−5.96737	−	0.231561i	−0.870431	−	0.0337767i	−0.470120	+	0.882603i	$0.655789\pi$
$48$		0			0
$49$	1.93643	−	0.539042i	0.276633	−	0.0770060i
$50$	1.45215	+	2.30399i	0.205365	+	0.325834i
$51$		0			0
$52$	−0.0852321	−	4.39455i	−0.0118196	−	0.609414i
$53$	9.73666	−	3.54385i	1.33743	−	0.486786i	0.428430	−	0.903575i	$-0.359067\pi$
$53$	9.73666	−	3.54385i	1.33743	−	0.486786i	0.909003	+	0.416789i	$0.136845\pi$
$54$		0			0
$55$	0.409588	+	0.149078i	0.0552288	+	0.0201016i
$56$	1.58084	−	4.62017i	0.211248	−	0.617396i
$57$		0			0
$58$	0.211395	−	0.0863643i	0.0277575	−	0.0113402i
$59$	−5.28596	−	11.0546i	−0.688173	−	1.43919i	−0.888226	−	0.459407i	$-0.848062\pi$
$59$	−5.28596	−	11.0546i	−0.688173	−	1.43919i	0.200053	−	0.979785i	$-0.435889\pi$
$60$		0			0
$61$	6.26787	−	2.00971i	0.802519	−	0.257317i	0.124364	−	0.992237i	$-0.460311\pi$
$61$	6.26787	−	2.00971i	0.802519	−	0.257317i	0.678155	+	0.734919i	$0.262780\pi$
$62$	1.27749	+	0.149317i	0.162242	+	0.0189633i
$63$		0			0
$64$	−0.355417	−	0.477408i	−0.0444271	−	0.0596760i
$65$	−0.177232	+	1.82211i	−0.0219830	+	0.226005i
$66$		0			0
$67$	−6.40602	−	3.86605i	−0.782620	−	0.472314i	0.0682638	−	0.997667i	$-0.478254\pi$
$67$	−6.40602	−	3.86605i	−0.782620	−	0.472314i	−0.850884	+	0.525354i	$0.823933\pi$
$68$	2.66738	−	3.05647i	0.323467	−	0.370652i
$69$		0			0
$70$	−0.395194	+	0.826479i	−0.0472348	+	0.0987831i
$71$	−0.264891	+	4.54800i	−0.0314368	+	0.539748i	0.945420	+	0.325854i	$0.105652\pi$
$71$	−0.264891	+	4.54800i	−0.0314368	+	0.539748i	−0.976857	+	0.213894i	$0.931385\pi$
$72$		0			0
$73$	−8.34451	+	5.48827i	−0.976651	+	0.642353i	−0.934202	−	0.356745i	$-0.883886\pi$
$73$	−8.34451	+	5.48827i	−0.976651	+	0.642353i	−0.0424490	+	0.999099i	$0.513516\pi$
$74$	−4.30121	+	3.33369i	−0.500005	+	0.387533i
$75$		0			0
$76$	−10.2036	+	7.29306i	−1.17043	+	0.836571i
$77$	−0.301918	−	1.39381i	−0.0344068	−	0.158839i
$78$		0			0
$79$	1.76774	−	2.19166i	0.198887	−	0.246581i	−0.669095	−	0.743177i	$-0.733318\pi$
$79$	1.76774	−	2.19166i	0.198887	−	0.246581i	0.867982	+	0.496596i	$0.165417\pi$
$80$	0.670867	+	1.16198i	0.0750052	+	0.129913i
$81$		0			0
$82$	−1.99667	+	3.45834i	−0.220496	+	0.381910i
$83$	−1.69478	−	4.38960i	−0.186027	−	0.481821i	0.808227	−	0.588871i	$-0.200427\pi$
$83$	−1.69478	−	4.38960i	−0.186027	−	0.481821i	−0.994254	+	0.107050i	$0.965860\pi$
$84$		0			0
$85$	−1.25126	+	1.13546i	−0.135719	+	0.123158i
$86$	−0.00461775	−	0.0474747i	−0.000497945	−	0.00511932i
$87$		0			0
$88$	1.29195	+	0.527819i	0.137722	+	0.0562657i
$89$	0.399193	+	6.85388i	0.0423144	+	0.726510i	0.951031	+	0.309096i	$0.100026\pi$
$89$	0.399193	+	6.85388i	0.0423144	+	0.726510i	−0.908717	+	0.417414i	$0.862937\pi$
$90$		0			0
$91$	5.35275	−	2.68825i	0.561121	−	0.281805i
$92$	7.37431	+	10.7520i	0.768825	+	1.12097i
$93$		0			0
$94$	3.51998	+	0.691301i	0.363058	+	0.0713023i
$95$	4.57377	−	2.52370i	0.469259	−	0.258926i
$96$		0			0
$97$	−0.870033	+	0.395479i	−0.0883385	+	0.0401548i	−0.457493	−	0.889213i	$-0.651252\pi$
$97$	−0.870033	+	0.395479i	−0.0883385	+	0.0401548i	0.369154	+	0.929368i	$0.379647\pi$
$98$	−1.19925	+	0.140172i	−0.121143	+	0.0141595i
$99$		0			0
$100$	2.94360	+	6.82402i	0.294360	+	0.682402i
$101$	0.0952048	−	0.439514i	0.00947324	−	0.0437333i	−0.972353	−	0.233518i	$-0.924976\pi$
$101$	0.0952048	−	0.439514i	0.00947324	−	0.0437333i	0.981826	+	0.189784i	$0.0607788\pi$
$102$		0			0
$103$	1.72545	−	2.51577i	0.170013	−	0.247886i	−0.730301	−	0.683125i	$-0.760620\pi$
$103$	1.72545	−	2.51577i	0.170013	−	0.247886i	0.900315	+	0.435240i	$0.143336\pi$
$104$	−0.793267	+	5.80774i	−0.0777862	+	0.569496i
$105$		0			0
$106$	−6.10737	+	1.19945i	−0.593200	+	0.116501i
$107$	8.81049	−	7.39288i	0.851742	−	0.714697i	−0.108430	−	0.994104i	$-0.534582\pi$
$107$	8.81049	−	7.39288i	0.851742	−	0.714697i	0.960173	+	0.279407i	$0.0901380\pi$
$108$		0			0
$109$	−3.20590	−	2.69007i	−0.307070	−	0.257662i	0.476210	−	0.879332i	$-0.342010\pi$
$109$	−3.20590	−	2.69007i	−0.307070	−	0.257662i	−0.783280	+	0.621670i	$0.786455\pi$
$110$	−0.229242	−	0.126490i	−0.0218574	−	0.0120604i
$111$		0			0
$112$	2.04593	−	3.88411i	0.193323	−	0.367014i
$113$	−4.51883	+	17.5432i	−0.425096	+	1.65032i	0.294292	+	0.955716i	$0.404916\pi$
$113$	−4.51883	+	17.5432i	−0.425096	+	1.65032i	−0.719388	+	0.694609i	$0.755578\pi$
$114$		0			0
$115$	−2.53079	−	4.80459i	−0.235998	−	0.448030i
$116$	0.606350	−	0.143708i	0.0562982	−	0.0133429i
$117$		0			0
$118$	2.11101	+	7.05125i	0.194334	+	0.649120i
$119$	5.32586	+	1.48256i	0.488221	+	0.135906i
$120$		0			0
$121$	−10.4652	+	1.63673i	−0.951381	+	0.148793i
$122$	−3.90635	+	0.610941i	−0.353664	+	0.0553120i
$123$		0			0
$124$	3.38124	+	0.941232i	0.303644	+	0.0845251i
$125$	−1.86682	−	6.23561i	−0.166974	−	0.557730i
$126$		0			0
$127$	13.2376	−	3.13738i	1.17465	−	0.278397i	0.403457	−	0.914999i	$-0.367808\pi$
$127$	13.2376	−	3.13738i	1.17465	−	0.278397i	0.771193	+	0.636601i	$0.219660\pi$
$128$	5.34204	+	10.1416i	0.472174	+	0.896400i
$129$		0			0
$130$	0.274306	−	1.06492i	0.0240582	−	0.0933997i
$131$	−2.64715	+	5.02550i	−0.231283	+	0.439080i	−0.972733	−	0.231928i	$-0.925496\pi$
$131$	−2.64715	+	5.02550i	−0.231283	+	0.439080i	0.741450	+	0.671008i	$0.234138\pi$
$132$		0			0
$133$	−14.9649	−	8.25727i	−1.29762	−	0.715996i
$134$	3.44296	+	2.88899i	0.297426	+	0.249570i
$135$		0			0
$136$	−4.14432	+	3.47750i	−0.355373	+	0.298193i
$137$	−1.74442	+	0.342593i	−0.149036	+	0.0292697i	−0.266674	−	0.963787i	$-0.585925\pi$
$137$	−1.74442	+	0.342593i	−0.149036	+	0.0292697i	0.117638	+	0.993057i	$0.462468\pi$
$138$		0			0
$139$	−0.456046	+	3.33885i	−0.0386813	+	0.283197i	0.961289	+	0.275541i	$0.0888569\pi$
$139$	−0.456046	+	3.33885i	−0.0386813	+	0.283197i	−0.999971	+	0.00765659i	$0.997563\pi$
$140$	−1.41396	+	2.06160i	−0.119501	+	0.174237i
$141$		0			0
$142$	0.579339	−	2.67452i	0.0486170	−	0.224441i
$143$	0.678056	+	1.57191i	0.0567019	+	0.131450i
$144$		0			0
$145$	−0.257791	+	0.0301314i	−0.0214084	+	0.00250228i
$146$	5.46164	−	2.48262i	0.452009	−	0.205463i
$147$		0			0
$148$	−13.0020	+	7.17420i	−1.06876	+	0.589716i
$149$	−0.527487	−	0.103595i	−0.0432134	−	0.00848683i	0.171059	−	0.985261i	$-0.445281\pi$
$149$	−0.527487	−	0.103595i	−0.0432134	−	0.00848683i	−0.214272	+	0.976774i	$0.568738\pi$
$150$		0			0
$151$	11.6317	+	16.9594i	0.946573	+	1.38014i	0.924833	+	0.380373i	$0.124204\pi$
$151$	11.6317	+	16.9594i	0.946573	+	1.38014i	0.0217398	+	0.999764i	$0.493079\pi$
$152$	14.9469	−	7.50660i	1.21235	−	0.608866i
$153$		0			0
$154$	0.0498103	+	0.855210i	0.00401383	+	0.0689148i
$155$	−1.35328	−	0.552875i	−0.108698	−	0.0444080i
$156$		0			0
$157$	−0.627832	−	6.45467i	−0.0501064	−	0.515139i	−0.986451	−	0.164057i	$-0.947542\pi$
$157$	−0.627832	−	6.45467i	−0.0501064	−	0.515139i	0.936345	−	0.351083i	$-0.114186\pi$
$158$	−1.25253	+	1.13661i	−0.0996459	+	0.0904238i
$159$		0			0
$160$	−1.36538	−	3.53643i	−0.107943	−	0.279580i
$161$	−8.88380	+	15.3872i	−0.700142	+	1.21268i
$162$		0			0
$163$	6.62321	+	11.4717i	0.518770	+	0.898536i	0.999762	+	0.0218113i	$0.00694331\pi$
$163$	6.62321	+	11.4717i	0.518770	+	0.898536i	−0.480992	+	0.876725i	$0.659723\pi$
$164$	−6.84139	+	8.48200i	−0.534223	+	0.662333i
$165$		0			0
$166$	0.598376	+	2.76241i	0.0464430	+	0.214405i
$167$	15.7591	−	11.2639i	1.21948	−	0.871630i	0.224773	−	0.974411i	$-0.427836\pi$
$167$	15.7591	−	11.2639i	1.21948	−	0.871630i	0.994704	+	0.102781i	$0.0327742\pi$
$168$		0			0
$169$	4.59203	−	3.55909i	0.353233	−	0.273776i
$170$	0.847980	−	0.557725i	0.0650371	−	0.0427756i
$171$		0			0
$172$	0.00756825	−	0.129942i	0.000577073	−	0.00990797i
$173$	−10.1600	+	21.2478i	−0.772448	+	1.61544i	0.0156413	+	0.999878i	$0.495021\pi$
$173$	−10.1600	+	21.2478i	−0.772448	+	1.61544i	−0.788089	+	0.615561i	$0.788930\pi$
$174$		0			0
$175$	−6.65929	+	7.63070i	−0.503395	+	0.576826i
$176$	1.07421	+	0.648288i	0.0809715	+	0.0488665i
$177$		0			0
$178$	0.399249	−	4.10464i	0.0299250	−	0.307656i
$179$	−2.58401	−	3.47092i	−0.193138	−	0.259429i	0.694997	−	0.719013i	$-0.255406\pi$
$179$	−2.58401	−	3.47092i	−0.193138	−	0.259429i	−0.888134	+	0.459584i	$0.847998\pi$
$180$		0			0
$181$	9.42933	+	1.10213i	0.700876	+	0.0819207i	0.459065	−	0.888403i	$-0.348184\pi$
$181$	9.42933	+	1.10213i	0.700876	+	0.0819207i	0.241811	+	0.970323i	$0.422259\pi$
$182$	−3.42623	+	1.09858i	−0.253969	+	0.0814318i
$183$		0			0
$184$	−7.50064	−	15.6863i	−0.552954	−	1.15641i
$185$	5.72572	−	2.33921i	0.420963	−	0.171982i
$186$		0			0
$187$	−0.511505	+	1.49493i	−0.0374049	+	0.109320i
$188$	9.19859	+	3.34801i	0.670876	+	0.244179i
$189$		0			0
$190$	−2.94865	+	1.07322i	−0.213917	+	0.0778596i
$191$	−0.403393	−	20.7989i	−0.0291885	−	1.50495i	−0.672928	−	0.739708i	$-0.734964\pi$
$191$	−0.403393	−	20.7989i	−0.0291885	−	1.50495i	0.643739	−	0.765245i	$-0.277382\pi$
$192$		0			0
$193$	10.9009	+	17.2955i	0.784668	+	1.24496i	0.965231	+	0.261397i	$0.0841830\pi$
$193$	10.9009	+	17.2955i	0.784668	+	1.24496i	−0.180564	+	0.983563i	$0.557792\pi$
$194$	0.553048	−	0.153951i	0.0397065	−	0.0110531i
$195$		0			0
$196$	−3.29236	−	0.127758i	−0.235168	−	0.00912561i
$197$	2.15466	+	2.28380i	0.153513	+	0.162714i	0.799566	−	0.600578i	$-0.205063\pi$
$197$	2.15466	+	2.28380i	0.153513	+	0.162714i	−0.646053	+	0.763293i	$0.723581\pi$
$198$		0			0
$199$	−13.8285	−	3.27741i	−0.980274	−	0.232329i	−0.290915	−	0.956749i	$-0.593960\pi$
$199$	−13.8285	−	3.27741i	−0.980274	−	0.232329i	−0.689359	+	0.724420i	$0.742108\pi$
$200$	−2.47223	−	9.59779i	−0.174813	−	0.678666i
$201$		0			0
$202$	−0.0972960	+	0.252003i	−0.00684572	+	0.0177309i
$203$	0.533142	+	0.660992i	0.0374192	+	0.0463925i
$204$		0			0
$205$	3.24036	−	3.17813i	0.226317	−	0.221970i
$206$	−1.25751	+	1.33289i	−0.0876150	+	0.0928665i
$207$		0			0
$208$	−1.51137	+	5.04834i	−0.104795	+	0.350039i
$209$	2.60463	−	4.13253i	0.180166	−	0.285853i
$210$		0			0
$211$	18.4274	+	18.0735i	1.26860	+	1.24423i	0.955665	+	0.294456i	$0.0951383\pi$
$211$	18.4274	+	18.0735i	1.26860	+	1.24423i	0.312932	+	0.949776i	$0.398689\pi$
$212$	−16.9716	+	0.658575i	−1.16561	+	0.0452311i
$213$		0			0
$214$	−5.91497	+	3.56970i	−0.404339	+	0.244020i
$215$	−0.00941408	+	0.0533899i	−0.000642035	+	0.00364116i
$216$		0			0
$217$	0.830567	+	4.71038i	0.0563826	+	0.319761i
$218$	1.65293	+	1.89405i	0.111950	+	0.128281i
$219$		0			0
$220$	−0.564716	−	0.437688i	−0.0380731	−	0.0295089i
$221$	−6.61624	−	0.514255i	−0.445056	−	0.0345925i
$222$		0			0
$223$	0.487750	+	0.442610i	0.0326622	+	0.0296393i	0.688176	−	0.725544i	$-0.258412\pi$
$223$	0.487750	+	0.442610i	0.0326622	+	0.0296393i	−0.655513	+	0.755184i	$0.727548\pi$
$224$	−7.40673	+	9.94897i	−0.494883	+	0.664743i
$225$		0			0
$226$	4.31011	−	9.99197i	0.286705	−	0.664656i
$227$	16.8907	+	12.0728i	1.12108	+	0.801297i	0.981981	−	0.188981i	$-0.0605186\pi$
$227$	16.8907	+	12.0728i	1.12108	+	0.801297i	0.139096	+	0.990279i	$0.455580\pi$
$228$		0			0
$229$	−0.147969	+	7.62922i	−0.00977804	+	0.504153i	0.962624	+	0.270841i	$0.0873019\pi$
$229$	−0.147969	+	7.62922i	−0.00977804	+	0.504153i	−0.972402	+	0.233312i	$0.925044\pi$
$230$	1.05601	+	3.08629i	0.0696309	+	0.203504i
$231$		0			0
$232$	−0.828530	+	0.0643984i	−0.0543957	+	0.00422797i
$233$	−14.9551	−	9.83612i	−0.979741	−	0.644386i	−0.0447279	−	0.998999i	$-0.514242\pi$
$233$	−14.9551	−	9.83612i	−0.979741	−	0.644386i	−0.935013	+	0.354613i	$0.884612\pi$
$234$		0			0
$235$	−3.64349	−	1.82983i	−0.237675	−	0.119365i
$236$	2.71820	+	19.9007i	0.176940	+	1.29543i
$237$		0			0
$238$	−3.02315	−	1.37419i	−0.195961	−	0.0890754i
$239$	13.8597	+	4.44394i	0.896511	+	0.287455i	0.717637	−	0.696417i	$-0.245224\pi$
$239$	13.8597	+	4.44394i	0.896511	+	0.287455i	0.178874	+	0.983872i	$0.442755\pi$
$240$		0			0
$241$	−1.31610	−	0.205834i	−0.0847774	−	0.0132589i	0.111988	−	0.993710i	$-0.464278\pi$
$241$	−1.31610	−	0.205834i	−0.0847774	−	0.0132589i	−0.196765	+	0.980451i	$0.563044\pi$
$242$	6.36272			0.409011
$243$		0			0
$244$	−10.7894			−0.690718
$245$	1.35584	+	0.212050i	0.0866217	+	0.0135474i
$246$		0			0
$247$	19.5371	+	6.26433i	1.24312	+	0.398590i
$248$	−4.26110	−	1.93691i	−0.270580	−	0.122994i
$249$		0			0
$250$	0.529133	+	3.87394i	0.0334653	+	0.245009i
$251$	−12.4303	−	6.24273i	−0.784593	−	0.394037i	0.0109457	−	0.999940i	$-0.496516\pi$
$251$	−12.4303	−	6.24273i	−0.784593	−	0.394037i	−0.795539	+	0.605903i	$0.792812\pi$
$252$		0			0
$253$	−4.24262	−	2.79041i	−0.266731	−	0.175432i
$254$	−8.14737	+	0.633264i	−0.511212	+	0.0397345i
$255$		0			0
$256$	−1.84367	−	5.38834i	−0.115230	−	0.336771i
$257$	0.346537	−	17.8673i	0.0216164	−	1.11453i	−0.819299	−	0.573367i	$-0.805637\pi$
$257$	0.346537	−	17.8673i	0.0216164	−	1.11453i	0.840915	−	0.541167i	$-0.182017\pi$
$258$		0			0
$259$	−16.4639	−	11.7677i	−1.02302	−	0.731209i
$260$	1.18858	−	2.75543i	0.0737124	−	0.170885i
$261$		0			0
$262$	2.03747	−	2.73679i	0.125875	−	0.169080i
$263$	−16.0239	−	14.5409i	−0.988074	−	0.896629i	0.00657133	−	0.999978i	$-0.497908\pi$
$263$	−16.0239	−	14.5409i	−0.988074	−	0.896629i	−0.994645	+	0.103349i	$0.967044\pi$
$264$		0			0
$265$	7.05286	+	0.548191i	0.433253	+	0.0336751i
$266$	8.11482	+	6.28946i	0.497552	+	0.385632i
$267$		0			0
$268$	8.06428	+	9.24064i	0.492604	+	0.564462i
$269$	−0.375001	−	2.12673i	−0.0228642	−	0.129669i	0.971239	−	0.238106i	$-0.0765266\pi$
$269$	−0.375001	−	2.12673i	−0.0228642	−	0.129669i	−0.994103	+	0.108437i	$0.965415\pi$
$270$		0			0
$271$	−2.60975	+	14.8006i	−0.158531	+	0.899073i	0.796956	+	0.604038i	$0.206442\pi$
$271$	−2.60975	+	14.8006i	−0.158531	+	0.899073i	−0.955486	+	0.295035i	$0.904669\pi$
$272$	−4.16413	+	2.51307i	−0.252488	+	0.152377i
$273$		0			0
$274$	1.06707	−	0.0414070i	0.0644638	−	0.00250149i
$275$	−2.06651	−	2.02682i	−0.124615	−	0.122222i
$276$		0			0
$277$	−1.90799	+	3.02723i	−0.114640	+	0.181888i	−0.898404	−	0.439170i	$-0.855272\pi$
$277$	−1.90799	+	3.02723i	−0.114640	+	0.181888i	0.783764	+	0.621059i	$0.213297\pi$
$278$	0.580554	−	1.93919i	0.0348193	−	0.116305i
$279$		0			0
$280$	2.28783	−	2.42496i	0.136724	−	0.144919i
$281$	10.5445	−	10.3419i	0.629030	−	0.616948i	−0.314093	−	0.949392i	$-0.601700\pi$
$281$	10.5445	−	10.3419i	0.629030	−	0.616948i	0.943123	+	0.332444i	$0.107873\pi$
$282$		0			0
$283$	−14.4983	−	17.9751i	−0.861836	−	1.06851i	−0.996978	−	0.0776833i	$-0.975248\pi$
$283$	−14.4983	−	17.9751i	−0.861836	−	1.06851i	0.135142	−	0.990826i	$-0.456851\pi$
$284$	2.68966	−	6.96641i	0.159602	−	0.413380i
$285$		0			0
$286$	−0.256507	−	0.995820i	−0.0151676	−	0.0588841i
$287$	−14.4501	−	3.42473i	−0.852961	−	0.202155i
$288$		0			0
$289$	7.46296	+	7.91028i	0.438998	+	0.465310i
$290$	0.155788	+	0.00604530i	0.00914821	+	0.000354992i
$291$		0			0
$292$	15.7717	−	4.39036i	0.922971	−	0.256927i
$293$	9.07525	+	14.3989i	0.530182	+	0.841191i	0.999116	−	0.0420426i	$-0.0133865\pi$
$293$	9.07525	+	14.3989i	0.530182	+	0.841191i	−0.468934	+	0.883233i	$0.655362\pi$
$294$		0			0
$295$	−0.162224	−	8.36421i	−0.00944502	−	0.486983i
$296$	18.6096	−	6.77333i	1.08166	−	0.393692i
$297$		0			0
$298$	0.303433	+	0.110441i	0.0175774	+	0.00639766i
$299$	6.90462	−	20.1795i	0.399304	−	1.16701i
$300$		0			0
$301$	0.164206	−	0.0670854i	0.00946465	−	0.00386674i
$302$	−5.32895	−	11.1446i	−0.306647	−	0.641297i
$303$		0			0
$304$	14.3188	−	4.59115i	0.821242	−	0.263321i
$305$	4.46347	+	0.521705i	0.255578	+	0.0298727i
$306$		0			0
$307$	−1.30425	−	1.75191i	−0.0744375	−	0.0999869i	0.763345	−	0.645991i	$-0.223556\pi$
$307$	−1.30425	−	1.75191i	−0.0744375	−	0.0999869i	−0.837782	+	0.546004i	$0.816148\pi$
$308$	−0.226313	+	2.32670i	−0.0128954	+	0.132576i
$309$		0			0
$310$	0.751817	+	0.453724i	0.0427003	+	0.0257698i
$311$	20.0615	−	22.9879i	1.13758	−	1.30353i	0.190810	−	0.981627i	$-0.438889\pi$
$311$	20.0615	−	22.9879i	1.13758	−	1.30353i	0.946774	−	0.321899i	$-0.104321\pi$
$312$		0			0
$313$	−12.0785	+	25.2600i	−0.682717	+	1.42778i	0.210245	+	0.977649i	$0.432574\pi$
$313$	−12.0785	+	25.2600i	−0.682717	+	1.42778i	−0.892962	+	0.450132i	$0.851377\pi$
$314$	−0.226505	+	3.88894i	−0.0127824	+	0.219466i
$315$		0			0
$316$	−3.85616	+	2.53624i	−0.216926	+	0.142674i
$317$	−23.5957	+	18.2880i	−1.32526	+	1.02716i	−0.328692	+	0.944437i	$0.606608\pi$
$317$	−23.5957	+	18.2880i	−1.32526	+	1.02716i	−0.996573	+	0.0827204i	$0.973639\pi$
$318$		0			0
$319$	−0.197453	+	0.141131i	−0.0110552	+	0.00790180i
$320$	−0.0860253	−	0.397137i	−0.00480896	−	0.0222006i
$321$		0			0
$322$	6.70049	−	8.30730i	0.373404	−	0.462948i
$323$	9.46802	+	16.3991i	0.526815	+	0.912470i
$324$		0			0
$325$	6.07869	−	10.5286i	0.337185	−	0.584022i
$326$	−2.86592	−	7.42291i	−0.158728	−	0.411117i
$327$		0			0
$328$	10.7620	−	9.76595i	0.594229	−	0.539234i
$329$	1.29146	+	13.2774i	0.0712006	+	0.732007i
$330$		0			0
$331$	−9.90764	−	4.04771i	−0.544573	−	0.222483i	0.0891835	−	0.996015i	$-0.471574\pi$
$331$	−9.90764	−	4.04771i	−0.544573	−	0.222483i	−0.633756	+	0.773533i	$0.718488\pi$
$332$	0.448471	+	7.69994i	0.0246130	+	0.422589i
$333$		0			0
$334$	−10.3981	+	5.22212i	−0.568958	+	0.285741i
$335$	−2.88931	−	4.21271i	−0.157860	−	0.230165i
$336$		0			0
$337$	−1.86093	−	0.365475i	−0.101371	−	0.0199087i	0.141769	−	0.989900i	$-0.454721\pi$
$337$	−1.86093	−	0.365475i	−0.101371	−	0.0199087i	−0.243141	+	0.969991i	$0.578178\pi$
$338$	−3.05559	+	1.68600i	−0.166202	+	0.0917064i
$339$		0			0
$340$	2.52138	−	1.14611i	0.136741	−	0.0621563i
$341$	−1.35776	+	0.158699i	−0.0735268	+	0.00859405i
$342$		0			0
$343$	−7.97183	−	18.4808i	−0.430438	−	0.997868i
$344$	−0.0367484	+	0.169650i	−0.00198134	+	0.00914689i
$345$		0			0
$346$	8.00182	−	11.6669i	0.430181	−	0.627219i
$347$	−1.27885	+	9.36285i	−0.0686524	+	0.502624i	0.924072	+	0.382218i	$0.124840\pi$
$347$	−1.27885	+	9.36285i	−0.0686524	+	0.502624i	−0.992725	+	0.120407i	$0.961580\pi$
$348$		0			0
$349$	0.872067	−	0.171268i	0.0466807	−	0.00916778i	−0.169317	−	0.985562i	$-0.554156\pi$
$349$	0.872067	−	0.171268i	0.0466807	−	0.00916778i	0.215998	+	0.976394i	$0.430700\pi$
$350$	4.66036	−	3.91051i	0.249107	−	0.209025i
$351$		0			0
$352$	−2.71554	−	2.27861i	−0.144739	−	0.121450i
$353$	13.2301	+	7.30008i	0.704169	+	0.388544i	0.794415	−	0.607375i	$-0.207778\pi$
$353$	13.2301	+	7.30008i	0.704169	+	0.388544i	−0.0902456	+	0.995920i	$0.528765\pi$
$354$		0			0
$355$	−1.44954	+	2.75189i	−0.0769337	+	0.146055i
$356$	2.80715	−	10.8980i	0.148779	−	0.577594i
$357$		0			0
$358$	1.21137	+	2.29974i	0.0640231	+	0.121545i
$359$	−16.0300	+	3.79917i	−0.846029	+	0.200513i	−0.630698	−	0.776029i	$-0.717231\pi$
$359$	−16.0300	+	3.79917i	−0.846029	+	0.200513i	−0.215331	+	0.976541i	$0.569083\pi$
$360$		0			0
$361$	−11.3413	−	37.8825i	−0.596910	−	1.99382i
$362$	−5.49375	−	1.52929i	−0.288745	−	0.0803777i
$363$		0			0
$364$	−9.70054	+	1.51714i	−0.508447	+	0.0795196i
$365$	−6.73693	+	1.05364i	−0.352627	+	0.0551498i
$366$		0			0
$367$	18.5784	+	5.17165i	0.969784	+	0.269958i	0.716619	−	0.697465i	$-0.245689\pi$
$367$	18.5784	+	5.17165i	0.969784	+	0.269958i	0.253165	+	0.967423i	$0.418528\pi$
$368$	−4.48314	−	14.9747i	−0.233700	−	0.780612i
$369$		0			0
$370$	−3.61517	+	0.856812i	−0.187944	+	0.0445435i
$371$	−10.7869	−	20.4785i	−0.560030	−	1.06319i
$372$		0			0
$373$	7.67432	−	29.7935i	0.397361	−	1.54265i	−0.386842	−	0.922146i	$-0.626434\pi$
$373$	7.67432	−	29.7935i	0.397361	−	1.54265i	0.784203	−	0.620504i	$-0.213072\pi$
$374$	0.442319	−	0.839722i	0.0228718	−	0.0434210i
$375$		0			0
$376$	−11.4300	−	6.30680i	−0.589457	−	0.325249i
$377$	−0.780889	−	0.655244i	−0.0402178	−	0.0337468i
$378$		0			0
$379$	9.96446	−	8.36118i	0.511840	−	0.429485i	−0.349936	−	0.936774i	$-0.613797\pi$
$379$	9.96446	−	8.36118i	0.511840	−	0.429485i	0.861776	+	0.507289i	$0.169352\pi$
$380$	−8.40227	+	1.65015i	−0.431028	+	0.0846510i
$381$		0			0
$382$	−1.69109	+	12.3810i	−0.0865238	+	0.633466i
$383$	−10.7690	+	15.7015i	−0.550268	+	0.802310i	−0.995664	−	0.0930236i	$-0.970347\pi$
$383$	−10.7690	+	15.7015i	−0.550268	+	0.802310i	0.445396	+	0.895334i	$0.353063\pi$
$384$		0			0
$385$	0.206128	−	0.951595i	0.0105053	−	0.0484978i
$386$	−4.86409	−	11.2762i	−0.247575	−	0.573944i
$387$		0			0
$388$	1.55597	−	0.181866i	0.0789922	−	0.00923287i
$389$	5.19017	−	2.35922i	0.263152	−	0.119617i	−0.277890	−	0.960613i	$-0.589635\pi$
$389$	5.19017	−	2.35922i	0.263152	−	0.119617i	0.541042	+	0.840996i	$0.318030\pi$
$390$		0			0
$391$	17.2351	−	9.50995i	0.871619	−	0.480939i
$392$	4.31163	+	0.846776i	0.217770	+	0.0427687i
$393$		0			0
$394$	−1.06675	−	1.55536i	−0.0537422	−	0.0783580i
$395$	1.71790	−	0.862760i	0.0864368	−	0.0434102i
$396$		0			0
$397$	−1.61784	−	27.7772i	−0.0811969	−	1.39410i	−0.755261	−	0.655424i	$-0.772490\pi$
$397$	−1.61784	−	27.7772i	−0.0811969	−	1.39410i	0.674064	−	0.738673i	$-0.264547\pi$
$398$	7.90261	+	3.22857i	0.396122	+	0.161834i
$399$		0			0
$400$	−0.862604	−	8.86835i	−0.0431302	−	0.443417i
$401$	4.85002	−	4.40116i	0.242199	−	0.219784i	−0.541863	−	0.840467i	$-0.682281\pi$
$401$	4.85002	−	4.40116i	0.242199	−	0.219784i	0.784061	+	0.620684i	$0.213145\pi$
$402$		0			0
$403$	−2.06797	−	5.35617i	−0.103013	−	0.266810i
$404$	−0.368575	+	0.638390i	−0.0183373	+	0.0317611i
$405$		0			0
$406$	−0.255053	−	0.441765i	−0.0126581	−	0.0219244i
$407$	3.63113	−	4.50190i	0.179988	−	0.223151i
$408$		0			0
$409$	−3.16926	−	14.6309i	−0.156710	−	0.723452i	−0.986284	−	0.165056i	$-0.947219\pi$
$409$	−3.16926	−	14.6309i	−0.156710	−	0.723452i	0.829575	−	0.558396i	$-0.188583\pi$
$410$	−2.21805	+	1.58537i	−0.109542	+	0.0782957i
$411$		0			0
$412$	−3.95235	+	3.06330i	−0.194718	+	0.150918i
$413$	−22.8689	+	15.0411i	−1.12531	+	0.740125i
$414$		0			0
$415$	0.186792	−	3.20709i	0.00916924	−	0.157430i
$416$	6.42282	−	13.4322i	0.314904	−	0.658567i
$417$		0			0
$418$	−1.92935	+	2.21079i	−0.0943675	+	0.108133i
$419$	29.4847	+	17.7941i	1.44042	+	0.869300i	0.999600	−	0.0282935i	$-0.00900732\pi$
$419$	29.4847	+	17.7941i	1.44042	+	0.869300i	0.440824	+	0.897594i	$0.354686\pi$
$420$		0			0
$421$	−0.794306	+	8.16618i	−0.0387121	+	0.397995i	0.955850	+	0.293854i	$0.0949378\pi$
$421$	−0.794306	+	8.16618i	−0.0387121	+	0.397995i	−0.994563	+	0.104141i	$0.966791\pi$
$422$	−9.25864	−	12.4365i	−0.450703	−	0.605400i
$423$		0			0
$424$	22.4972	+	2.62955i	1.09256	+	0.127702i
$425$	10.6849	−	3.42596i	0.518292	−	0.166184i
$426$		0			0
$427$	−6.34285	−	13.2649i	−0.306952	−	0.641935i
$428$	−17.4523	+	7.13006i	−0.843590	+	0.344644i
$429$		0			0
$430$	0.0105425	−	0.0308116i	0.000508405	−	0.00148587i
$431$	−31.3862	−	11.4236i	−1.51182	−	0.550257i	−0.552730	−	0.833360i	$-0.686414\pi$
$431$	−31.3862	−	11.4236i	−1.51182	−	0.550257i	−0.959089	+	0.283103i	$0.908636\pi$
$432$		0			0
$433$	−32.9219	+	11.9826i	−1.58213	+	0.575847i	−0.975665	−	0.219266i	$-0.929634\pi$
$433$	−32.9219	+	11.9826i	−1.58213	+	0.575847i	−0.606461	+	0.795113i	$0.707411\pi$
$434$	−0.0557134	−	2.87257i	−0.00267433	−	0.137888i
$435$		0			0
$436$	3.65776	+	5.80344i	0.175175	+	0.277934i
$437$	−58.6294	+	16.3206i	−2.80462	+	0.780720i
$438$		0			0
$439$	20.6171	+	0.800038i	0.984002	+	0.0381838i	0.525750	−	0.850639i	$-0.323785\pi$
$439$	20.6171	+	0.800038i	0.984002	+	0.0381838i	0.458251	+	0.888823i	$0.348476\pi$
$440$	0.653867	+	0.693058i	0.0311719	+	0.0330403i
$441$		0			0
$442$	3.87882	+	0.919298i	0.184497	+	0.0437265i
$443$	−3.07922	−	11.9543i	−0.146298	−	0.567965i	−0.998964	−	0.0455080i	$-0.985509\pi$
$443$	−3.07922	−	11.9543i	−0.146298	−	0.567965i	0.852666	−	0.522457i	$-0.174984\pi$
$444$		0			0
$445$	−1.68825	+	4.37268i	−0.0800309	+	0.207285i
$446$	−0.248384	−	0.307948i	−0.0117613	−	0.0145818i
$447$		0			0
$448$	−0.949187	+	0.930956i	−0.0448449	+	0.0439835i
$449$	23.7722	−	25.1971i	1.12188	−	1.18912i	0.141933	−	0.989876i	$-0.454668\pi$
$449$	23.7722	−	25.1971i	1.12188	−	1.18912i	0.979949	−	0.199249i	$-0.0638501\pi$
$450$		0			0
$451$	1.21727	−	4.06595i	0.0573189	−	0.191458i
$452$	15.8335	−	25.1216i	0.744746	−	1.18162i
$453$		0			0
$454$	−8.90361	−	8.73260i	−0.417867	−	0.409841i
$455$	4.08639	−	0.158571i	0.191573	−	0.00743391i
$456$		0			0
$457$	−14.1645	+	8.54834i	−0.662589	+	0.399874i	−0.807743	−	0.589535i	$-0.799311\pi$
$457$	−14.1645	+	8.54834i	−0.662589	+	0.399874i	0.145154	+	0.989409i	$0.453632\pi$
$458$	0.795939	−	4.51400i	0.0371918	−	0.210925i
$459$		0			0
$460$	1.54570	+	8.76611i	0.0720687	+	0.408722i
$461$	−0.206139	−	0.236209i	−0.00960084	−	0.0110013i	0.748615	−	0.663005i	$-0.230719\pi$
$461$	−0.206139	−	0.236209i	−0.00960084	−	0.0110013i	−0.758216	+	0.652003i	$0.773929\pi$
$462$		0			0
$463$	2.21341	+	1.71552i	0.102866	+	0.0797271i	0.662735	−	0.748854i	$-0.269396\pi$
$463$	2.21341	+	1.71552i	0.102866	+	0.0797271i	−0.559869	+	0.828581i	$0.689149\pi$
$464$	−0.744860	−	0.0578951i	−0.0345793	−	0.00268771i
$465$		0			0
$466$	7.96247	+	7.22556i	0.368854	+	0.334717i
$467$	−9.75674	+	13.1056i	−0.451488	+	0.606454i	−0.968344	−	0.249618i	$-0.919695\pi$
$467$	−9.75674	+	13.1056i	−0.451488	+	0.606454i	0.516856	+	0.856072i	$0.327102\pi$
$468$		0			0
$469$	−6.62004	+	15.3470i	−0.305685	+	0.708657i
$470$	1.99247	+	1.42413i	0.0919059	+	0.0656904i
$471$		0			0
$472$	0.519417	−	26.7810i	0.0239081	−	1.23270i
$473$	0.0164119	+	0.0479657i	0.000754621	+	0.00220546i
$474$		0			0
$475$	−34.5862	+	2.68825i	−1.58692	+	0.123345i
$476$	−7.57116	−	4.97963i	−0.347023	−	0.228241i
$477$		0			0
$478$	−7.81289	−	3.92378i	−0.357353	−	0.179470i
$479$	−3.50896	−	25.6901i	−0.160328	−	1.17381i	−0.878429	−	0.477873i	$-0.841408\pi$
$479$	−3.50896	−	25.6901i	−0.160328	−	1.17381i	0.718101	−	0.695939i	$-0.245012\pi$
$480$		0			0
$481$	22.1149	+	10.0524i	1.00835	+	0.458352i
$482$	0.761963	+	0.244314i	0.0347065	+	0.0111282i
$483$		0			0
$484$	17.1543	+	2.68288i	0.779740	+	0.121949i
$485$	−0.652484			−0.0296278
$486$		0			0
$487$	32.7166			1.48253			0.741266	−	0.671211i	$-0.234225\pi$
$487$	32.7166			1.48253			0.741266	+	0.671211i	$0.234225\pi$
$488$	14.2159	+	2.22332i	0.643523	+	0.100645i
$489$		0			0
$490$	−0.784974	−	0.251692i	−0.0354615	−	0.0113703i
$491$	14.8780	+	6.76288i	0.671435	+	0.305205i	0.720363	−	0.693598i	$-0.243975\pi$
$491$	14.8780	+	6.76288i	0.671435	+	0.305205i	−0.0489276	+	0.998802i	$0.515580\pi$
$492$		0			0
$493$	−0.127325	−	0.932181i	−0.00573441	−	0.0419833i
$494$	−11.0133	−	5.53109i	−0.495512	−	0.248855i
$495$		0			0
$496$	−3.51572	−	2.31232i	−0.157860	−	0.103826i
$497$	10.1460	−	0.788611i	0.455111	−	0.0353740i
$498$		0			0
$499$	11.1551	+	32.6019i	0.499369	+	1.45946i	0.851921	+	0.523670i	$0.175437\pi$
$499$	11.1551	+	32.6019i	0.499369	+	1.45946i	−0.352552	+	0.935792i	$0.614686\pi$
$500$	−0.206896	+	10.6675i	−0.00925266	+	0.477065i
$501$		0			0
$502$	6.79760	+	4.85863i	0.303392	+	0.216851i
$503$	−9.69373	+	22.4726i	−0.432222	+	1.00200i	0.553381	+	0.832928i	$0.313337\pi$
$503$	−9.69373	+	22.4726i	−0.432222	+	1.00200i	−0.985603	+	0.169075i	$0.945922\pi$
$504$		0			0
$505$	0.183345	−	0.246275i	0.00815874	−	0.0109591i
$506$	2.25888	+	2.04982i	0.100419	+	0.0911257i
$507$		0			0
$508$	−22.2328	−	1.72807i	−0.986423	−	0.0766709i
$509$	31.0823	+	24.0906i	1.37770	+	1.06780i	0.989235	+	0.146335i	$0.0467478\pi$
$509$	31.0823	+	24.0906i	1.37770	+	1.06780i	0.388465	+	0.921463i	$0.373005\pi$
$510$		0			0
$511$	14.6696	+	16.8095i	0.648945	+	0.743608i
$512$	−3.38686	−	19.2078i	−0.149679	−	0.848874i
$513$		0			0
$514$	−1.86406	+	10.5716i	−0.0822201	+	0.466293i
$515$	1.78318	−	1.07615i	0.0785762	−	0.0474210i
$516$		0			0
$517$	−3.80974	+	0.147835i	−0.167552	+	0.00650179i
$518$	8.67862	+	8.51193i	0.381317	+	0.373993i
$519$		0			0
$520$	−2.13385	+	3.38558i	−0.0935755	+	0.148468i
$521$	10.7720	−	35.9808i	0.471928	−	1.57635i	−0.308577	−	0.951199i	$-0.599853\pi$
$521$	10.7720	−	35.9808i	0.471928	−	1.57635i	0.780505	−	0.625149i	$-0.214962\pi$
$522$		0			0
$523$	−13.0246	+	13.8052i	−0.569524	+	0.603660i	−0.946556	−	0.322540i	$-0.895463\pi$
$523$	−13.0246	+	13.8052i	−0.569524	+	0.603660i	0.377032	+	0.926200i	$0.376945\pi$
$524$	6.64712	−	6.51945i	0.290381	−	0.284804i
$525$		0			0
$526$	8.16007	+	10.1169i	0.355796	+	0.441118i
$527$	1.90863	−	4.94348i	0.0831413	−	0.215341i
$528$		0			0
$529$	10.0437	+	38.9920i	0.436683	+	1.69531i
$530$	−4.13479	−	0.979964i	−0.179604	−	0.0425669i
$531$		0			0
$532$	19.2261	+	20.3785i	0.833556	+	0.883518i
$533$	17.8128	+	0.691219i	0.771559	+	0.0299400i
$534$		0			0
$535$	7.56464	−	2.10576i	0.327048	−	0.0910400i
$536$	−8.72117	−	13.8371i	−0.376697	−	0.597671i
$537$		0			0
$538$	0.0251546	+	1.29696i	0.00108449	+	0.0559161i
$539$	1.20589	−	0.438907i	0.0519412	−	0.0189051i
$540$		0			0
$541$	−19.6121	−	7.13823i	−0.843191	−	0.306896i	−0.115930	−	0.993257i	$-0.536985\pi$
$541$	−19.6121	−	7.13823i	−0.843191	−	0.306896i	−0.727261	+	0.686361i	$0.759207\pi$
$542$	2.92257	−	8.54152i	0.125535	−	0.366890i
$543$		0			0
$544$	12.7209	−	5.19708i	0.545406	−	0.222823i
$545$	−1.23257	−	2.57770i	−0.0527975	−	0.110417i
$546$		0			0
$547$	30.6535	−	9.82864i	1.31065	−	0.420242i	0.433799	−	0.901010i	$-0.357173\pi$
$547$	30.6535	−	9.82864i	1.31065	−	0.420242i	0.876848	+	0.480768i	$0.159642\pi$
$548$	2.89433	+	0.338299i	0.123640	+	0.0144514i
$549$		0			0
$550$	1.03829	+	1.39467i	0.0442730	+	0.0594689i
$551$	−0.281598	+	2.89508i	−0.0119965	+	0.123335i
$552$		0			0
$553$	−5.38512	−	3.24994i	−0.228999	−	0.138201i
$554$	1.41332	−	1.61948i	0.0600460	−	0.0688051i
$555$		0			0
$556$	2.38288	−	4.98337i	0.101057	−	0.211342i
$557$	−2.64446	+	45.4037i	−0.112050	+	1.92382i	0.211092	+	0.977466i	$0.432298\pi$
$557$	−2.64446	+	45.4037i	−0.112050	+	1.92382i	−0.323142	+	0.946351i	$0.604739\pi$
$558$		0			0
$559$	−0.177897	+	0.117005i	−0.00752425	+	0.00494878i
$560$	2.36896	−	1.83608i	0.100107	−	0.0775885i
$561$		0			0
$562$	−7.21775	+	5.15894i	−0.304463	+	0.217617i
$563$	4.12026	+	19.0213i	0.173648	+	0.801650i	0.978183	+	0.207745i	$0.0666123\pi$
$563$	4.12026	+	19.0213i	0.173648	+	0.801650i	−0.804535	+	0.593906i	$0.797585\pi$
$564$		0			0
$565$	−7.76492	+	9.62699i	−0.326672	+	0.405010i
$566$	6.93596	+	12.0134i	0.291540	+	0.504962i
$567$		0			0
$568$	−4.97940	+	8.62457i	−0.208931	+	0.361879i
$569$	11.8394	+	30.6649i	0.496334	+	1.28554i	0.924274	+	0.381730i	$0.124672\pi$
$569$	11.8394	+	30.6649i	0.496334	+	1.28554i	−0.427939	+	0.903807i	$0.640760\pi$
$570$		0			0
$571$	4.67732	−	4.24444i	0.195740	−	0.177624i	−0.568243	−	0.822861i	$-0.692377\pi$
$571$	4.67732	−	4.24444i	0.195740	−	0.177624i	0.763983	+	0.645236i	$0.223241\pi$
$572$	−0.271664	−	2.79295i	−0.0113589	−	0.116779i
$573$		0			0
$574$	8.25784	+	3.37370i	0.344676	+	0.140815i
$575$	2.09683	+	36.0011i	0.0874437	+	1.50135i
$576$		0			0
$577$	−21.4902	+	10.7928i	−0.894649	+	0.449310i	−0.835848	−	0.548960i	$-0.815024\pi$
$577$	−21.4902	+	10.7928i	−0.894649	+	0.449310i	−0.0588004	+	0.998270i	$0.518728\pi$
$578$	−3.69485	−	5.38722i	−0.153685	−	0.224079i
$579$		0			0
$580$	0.417466	+	0.0819877i	0.0173344	+	0.00340436i
$581$	−9.20302	+	5.07801i	−0.381805	+	0.210671i
$582$		0			0
$583$	6.02214	−	2.73740i	0.249412	−	0.113372i
$584$	−21.6853	+	2.53465i	−0.897343	+	0.104884i
$585$		0			0
$586$	−4.04944	−	9.38767i	−0.167281	−	0.387801i
$587$	−5.61322	+	25.9135i	−0.231682	+	1.06956i	0.702199	+	0.711981i	$0.252202\pi$
$587$	−5.61322	+	25.9135i	−0.231682	+	1.06956i	−0.933881	+	0.357584i	$0.883601\pi$
$588$		0			0
$589$	−9.26642	+	13.5108i	−0.381816	+	0.556701i
$590$	−0.680068	+	4.97898i	−0.0279980	+	0.204981i
$591$		0			0
$592$	17.4702	−	3.43104i	0.718023	−	0.141015i
$593$	−18.4262	+	15.4615i	−0.756675	+	0.634926i	−0.937259	−	0.348634i	$-0.886646\pi$
$593$	−18.4262	+	15.4615i	−0.756675	+	0.634926i	0.180584	+	0.983560i	$0.442201\pi$
$594$		0			0
$595$	2.89134	+	2.42612i	0.118533	+	0.0994614i
$596$	0.771507	+	0.425700i	0.0316022	+	0.0174373i
$597$		0			0
$598$	−5.97071	+	11.3351i	−0.244160	+	0.463527i
$599$	6.87026	−	26.6720i	0.280711	−	1.08979i	−0.660188	−	0.751100i	$-0.729523\pi$
$599$	6.87026	−	26.6720i	0.280711	−	1.08979i	0.940899	−	0.338687i	$-0.109983\pi$
$600$		0			0
$601$	−0.184385	−	0.350046i	−0.00752122	−	0.0142787i	0.880972	−	0.473168i	$-0.156890\pi$
$601$	−0.184385	−	0.350046i	−0.00752122	−	0.0142787i	−0.888494	+	0.458889i	$0.848248\pi$
$602$	−0.103678	+	0.0245722i	−0.00422561	+	0.00100149i
$603$		0			0
$604$	−9.66802	−	32.2934i	−0.393386	−	1.31400i
$605$	−6.96686	−	1.93936i	−0.283243	−	0.0788461i
$606$		0			0
$607$	−6.64394	+	1.03909i	−0.269669	+	0.0421755i	−0.287908	−	0.957658i	$-0.592960\pi$
$607$	−6.64394	+	1.03909i	−0.269669	+	0.0421755i	0.0182386	+	0.999834i	$0.494194\pi$
$608$	−41.9742	+	6.56464i	−1.70228	+	0.266231i
$609$		0			0
$610$	−2.60052	−	0.723905i	−0.105292	−	0.0293100i
$611$	−4.59266	−	15.3406i	−0.185799	−	0.620612i
$612$		0			0
$613$	−22.6183	+	5.36063i	−0.913543	+	0.216514i	−0.660399	−	0.750915i	$-0.729613\pi$
$613$	−22.6183	+	5.36063i	−0.913543	+	0.216514i	−0.253144	+	0.967429i	$0.581465\pi$
$614$	0.611428	+	1.16077i	0.0246752	+	0.0468448i
$615$		0			0
$616$	0.777641	−	3.01899i	0.0313321	−	0.121639i
$617$	−14.5930	+	27.7041i	−0.587491	+	1.11532i	0.393143	+	0.919477i	$0.371388\pi$
$617$	−14.5930	+	27.7041i	−0.587491	+	1.11532i	−0.980634	+	0.195847i	$0.937254\pi$
$618$		0			0
$619$	−8.39797	−	4.63380i	−0.337543	−	0.186248i	0.305281	−	0.952262i	$-0.401250\pi$
$619$	−8.39797	−	4.63380i	−0.337543	−	0.186248i	−0.642824	+	0.766014i	$0.722237\pi$
$620$	1.83563	+	1.54028i	0.0737206	+	0.0618590i
$621$		0			0
$622$	−14.0396	+	11.7806i	−0.562938	+	0.472361i
$623$	15.0488	−	2.95549i	0.602917	−	0.118409i
$624$		0			0
$625$	−2.46648	+	18.0578i	−0.0986591	+	0.722312i
$626$	9.51282	−	13.8700i	0.380209	−	0.554358i
$627$		0			0
$628$	−2.25047	+	10.3893i	−0.0898036	+	0.414579i
$629$	8.88037	+	20.5870i	0.354084	+	0.820858i
$630$		0			0
$631$	11.7156	−	1.36935i	0.466389	−	0.0545130i	0.120346	−	0.992732i	$-0.461599\pi$
$631$	11.7156	−	1.36935i	0.466389	−	0.0545130i	0.346042	+	0.938219i	$0.387525\pi$
$632$	5.60344	−	2.54708i	0.222893	−	0.101317i
$633$		0			0
$634$	15.7008	−	8.66335i	0.623559	−	0.344065i
$635$	9.11399	+	1.78993i	0.361677	+	0.0710311i
$636$		0			0
$637$	3.04855	+	4.44489i	0.120788	+	0.176113i
$638$	0.130282	−	0.0654301i	0.00515792	−	0.00259040i
$639$		0			0
$640$	0.455030	+	7.81257i	0.0179867	+	0.308819i
$641$	16.4097	+	6.70409i	0.648143	+	0.264796i	0.678340	−	0.734748i	$-0.262700\pi$
$641$	16.4097	+	6.70409i	0.648143	+	0.264796i	−0.0301967	+	0.999544i	$0.509613\pi$
$642$		0			0
$643$	−0.409753	−	4.21262i	−0.0161591	−	0.166130i	0.983751	−	0.179538i	$-0.0574603\pi$
$643$	−0.409753	−	4.21262i	−0.0161591	−	0.166130i	−0.999910	+	0.0134083i	$0.995732\pi$
$644$	21.5678	−	19.5717i	0.849889	−	0.771233i
$645$		0			0
$646$	−4.09689	−	10.6112i	−0.161190	−	0.417492i
$647$	−4.14009	+	7.17084i	−0.162764	+	0.281915i	−0.935859	−	0.352375i	$-0.885374\pi$
$647$	−4.14009	+	7.17084i	−0.162764	+	0.281915i	0.773095	+	0.634290i	$0.218707\pi$
$648$		0			0
$649$	−3.91147	−	6.77487i	−0.153539	−	0.265937i
$650$	−4.58477	+	5.68423i	−0.179830	+	0.222954i
$651$		0			0
$652$	−4.59677	−	21.2211i	−0.180024	−	0.831081i
$653$	12.6552	−	9.04536i	0.495234	−	0.353972i	−0.306286	−	0.951939i	$-0.599086\pi$
$653$	12.6552	−	9.04536i	0.495234	−	0.353972i	0.801521	+	0.597967i	$0.204025\pi$
$654$		0			0
$655$	−3.06510	+	2.37563i	−0.119763	+	0.0928236i
$656$	10.9156	−	7.17929i	0.426182	−	0.280304i
$657$		0			0
$658$	0.465926	−	7.99964i	0.0181637	−	0.311858i
$659$	−5.95423	+	12.4522i	−0.231944	+	0.485070i	−0.984927	−	0.172970i	$-0.944664\pi$
$659$	−5.95423	+	12.4522i	−0.231944	+	0.485070i	0.752983	+	0.658040i	$0.228614\pi$
$660$		0			0
$661$	10.4314	−	11.9531i	0.405736	−	0.464922i	−0.513810	−	0.857904i	$-0.671766\pi$
$661$	10.4314	−	11.9531i	0.405736	−	0.464922i	0.919546	+	0.392982i	$0.128557\pi$
$662$	5.50421	+	3.32181i	0.213927	+	0.129106i
$663$		0			0
$664$	0.995801	−	10.2377i	0.0386446	−	0.397301i
$665$	−6.96830	−	9.36005i	−0.270219	−	0.362967i
$666$		0			0
$667$	3.00331	+	0.351036i	0.116289	+	0.0135922i
$668$	−30.2358	+	9.69473i	−1.16986	+	0.375100i
$669$		0			0
$670$	1.32371	+	2.76831i	0.0511394	+	0.106949i
$671$	3.89013	−	1.58929i	0.150177	−	0.0613540i
$672$		0			0
$673$	−15.8355	+	46.2811i	−0.610415	+	1.78401i	0.0102721	+	0.999947i	$0.496730\pi$
$673$	−15.8355	+	46.2811i	−0.610415	+	1.78401i	−0.620687	+	0.784058i	$0.713146\pi$
$674$	1.07049	+	0.389626i	0.0412337	+	0.0150078i
$675$		0			0
$676$	−8.94897	+	3.25716i	−0.344191	+	0.125275i
$677$	−0.887227	−	45.7452i	−0.0340989	−	1.75813i	−0.493356	−	0.869828i	$-0.664230\pi$
$677$	−0.887227	−	45.7452i	−0.0340989	−	1.75813i	0.459257	−	0.888303i	$-0.348116\pi$
$678$		0			0
$679$	1.13832	+	1.80606i	0.0436846	+	0.0693103i
$680$	−3.55830	+	0.990519i	−0.136454	+	0.0379847i
$681$		0			0
$682$	0.820522	+	0.0318400i	0.0314194	+	0.00121922i
$683$	2.30170	+	2.43965i	0.0880719	+	0.0933508i	0.769910	−	0.638152i	$-0.220301\pi$
$683$	2.30170	+	2.43965i	0.0880719	+	0.0933508i	−0.681839	+	0.731503i	$0.738819\pi$
$684$		0			0
$685$	−1.18100	−	0.279903i	−0.0451238	−	0.0106945i
$686$	3.01572	+	11.7078i	0.115141	+	0.447004i
$687$		0			0
$688$	−0.0562073	+	0.145581i	−0.00214288	+	0.00555021i
$689$	17.4431	+	21.6261i	0.664530	+	0.823888i
$690$		0			0
$691$	−23.3879	+	22.9387i	−0.889717	+	0.872628i	−0.992521	−	0.122073i	$-0.961046\pi$
$691$	−23.3879	+	22.9387i	−0.889717	+	0.872628i	0.102804	+	0.994702i	$0.467219\pi$
$692$	26.4929	−	28.0808i	1.00711	−	1.06747i
$693$		0			0
$694$	1.62800	−	5.43789i	0.0617980	−	0.206420i
$695$	−1.22674	+	1.94636i	−0.0465330	+	0.0738296i
$696$		0			0
$697$	11.7461	+	11.5205i	0.444915	+	0.436370i
$698$	−0.533444	+	0.0207001i	−0.0201912	+	0.000783509i
$699$		0			0
$700$	14.2135	−	8.57791i	0.537221	−	0.324214i
$701$	3.68077	−	20.8747i	0.139021	−	0.788426i	−0.832954	−	0.553342i	$-0.813352\pi$
$701$	3.68077	−	20.8747i	0.139021	−	0.788426i	0.971975	−	0.235084i	$-0.0755366\pi$
$702$		0			0
$703$	−12.0368	−	68.2640i	−0.453976	−	2.57462i
$704$	−0.249845	−	0.286291i	−0.00941639	−	0.0107900i
$705$		0			0
$706$	−7.17415	−	5.56038i	−0.270003	−	0.209268i
$707$	−1.00154	−	0.0778462i	−0.0376669	−	0.00292771i
$708$		0			0
$709$	−26.5128	−	24.0590i	−0.995707	−	0.903556i	−0.000368821	−	1.00000i	$-0.500117\pi$
$709$	−26.5128	−	24.0590i	−0.995707	−	0.903556i	−0.995338	+	0.0964438i	$0.969253\pi$
$710$	1.11569	−	1.49863i	0.0418710	−	0.0562425i
$711$		0			0
$712$	−5.94436	+	13.7806i	−0.222774	+	0.516449i
$713$	13.8555	+	9.90334i	0.518894	+	0.370883i
$714$		0			0
$715$	−0.0226641	+	1.16856i	−0.000847591	+	0.0437016i
$716$	2.29624	+	6.71102i	0.0858146	+	0.250803i
$717$		0			0
$718$	9.86597	−	0.766843i	0.368195	−	0.0286183i
$719$	21.9701	+	14.4500i	0.819347	+	0.538893i	0.888588	−	0.458707i	$-0.151687\pi$
$719$	21.9701	+	14.4500i	0.819347	+	0.538893i	−0.0692405	+	0.997600i	$0.522058\pi$
$720$		0			0
$721$	−6.08967	−	3.05835i	−0.226791	−	0.113899i
$722$	3.21458	+	23.5349i	0.119634	+	0.875879i
$723$		0			0
$724$	−14.1667	−	6.43954i	−0.526500	−	0.239323i
$725$	1.64129	+	0.526258i	0.0609560	+	0.0195447i
$726$		0			0
$727$	−38.9681	−	6.09450i	−1.44525	−	0.226032i	−0.617251	−	0.786767i	$-0.711753\pi$
$727$	−38.9681	−	6.09450i	−1.44525	−	0.226032i	−0.827996	+	0.560734i	$0.810519\pi$
$728$	13.0939			0.485292
$729$		0			0
$730$	4.09598			0.151599
$731$	−0.194160	−	0.0303661i	−0.00718127	−	0.00112313i
$732$		0			0
$733$	7.01185	+	2.24826i	0.258988	+	0.0830413i	0.431984	−	0.901881i	$-0.357814\pi$
$733$	7.01185	+	2.24826i	0.258988	+	0.0830413i	−0.172995	+	0.984923i	$0.555345\pi$
$734$	−10.5457	−	4.79363i	−0.389250	−	0.176936i
$735$		0			0
$736$	5.97680	+	43.7579i	0.220308	+	1.61294i
$737$	−4.26876	−	2.14385i	−0.157242	−	0.0789698i
$738$		0			0
$739$	7.73122	+	5.08490i	0.284397	+	0.187051i	0.683690	−	0.729772i	$-0.260374\pi$
$739$	7.73122	+	5.08490i	0.284397	+	0.187051i	−0.399293	+	0.916823i	$0.630744\pi$
$740$	−10.1080	+	0.785657i	−0.371578	+	0.0288813i
$741$		0			0
$742$	4.50099	+	13.1546i	0.165237	+	0.482922i
$743$	−0.231358	+	11.9287i	−0.00848769	+	0.437623i	0.971331	+	0.237733i	$0.0764043\pi$
$743$	−0.231358	+	11.9287i	−0.00848769	+	0.437623i	−0.979818	+	0.199890i	$0.935941\pi$
$744$		0			0
$745$	−0.298582	−	0.213414i	−0.0109392	−	0.00781887i
$746$	−7.31985	+	16.9693i	−0.267999	+	0.621291i
$747$		0			0
$748$	1.54659	−	2.07744i	0.0565491	−	0.0759586i
$749$	−19.0259	−	17.2651i	−0.695191	−	0.630852i
$750$		0			0
$751$	9.96117	+	0.774243i	0.363488	+	0.0282525i	0.257938	−	0.966161i	$-0.416957\pi$
$751$	9.96117	+	0.774243i	0.363488	+	0.0282525i	0.105550	+	0.994414i	$0.466340\pi$
$752$	−9.27620	−	7.18960i	−0.338268	−	0.262178i
$753$		0			0
$754$	0.402618	+	0.461349i	0.0146625	+	0.0168013i
$755$	2.43807	+	13.8270i	0.0887306	+	0.503216i
$756$		0			0
$757$	−4.97343	+	28.2057i	−0.180763	+	1.02516i	0.750517	+	0.660851i	$0.229804\pi$
$757$	−4.97343	+	28.2057i	−0.180763	+	1.02516i	−0.931280	+	0.364305i	$0.881307\pi$
$758$	−6.68969	+	4.03725i	−0.242981	+	0.146640i
$759$		0			0
$760$	11.4107	−	0.442788i	0.413911	−	0.0160616i
$761$	24.2557	+	23.7898i	0.879267	+	0.862379i	0.991340	−	0.131321i	$-0.0419218\pi$
$761$	24.2557	+	23.7898i	0.879267	+	0.862379i	−0.112073	+	0.993700i	$0.535749\pi$
$762$		0			0
$763$	−4.98469	+	7.90874i	−0.180458	+	0.286316i
$764$	−9.77982	+	32.6669i	−0.353821	+	1.18185i
$765$		0			0
$766$	7.84845	−	8.31887i	0.283576	−	0.300573i
$767$	23.4576	−	23.0070i	0.847004	−	0.830736i
$768$		0			0
$769$	−29.8468	−	37.0043i	−1.07630	−	1.33441i	−0.939015	−	0.343877i	$-0.888260\pi$
$769$	−29.8468	−	37.0043i	−1.07630	−	1.33441i	−0.137289	−	0.990531i	$-0.543839\pi$
$770$	−0.210656	+	0.545613i	−0.00759152	+	0.0196625i
$771$		0			0
$772$	−8.35919	−	32.4524i	−0.300854	−	1.16799i
$773$	1.66745	+	0.395193i	0.0599740	+	0.0142141i	0.260493	−	0.965476i	$-0.416115\pi$
$773$	1.66745	+	0.395193i	0.0599740	+	0.0142141i	−0.200519	+	0.979690i	$0.564263\pi$
$774$		0			0
$775$	6.66199	+	7.06129i	0.239306	+	0.253649i
$776$	−2.08759	−	0.0810081i	−0.0749402	−	0.00290802i
$777$		0			0
$778$	−3.29920	+	0.918396i	−0.118282	+	0.0329261i
$779$	−27.1221	−	43.0322i	−0.971750	−	1.54179i
$780$		0			0
$781$	0.0563996	+	2.90795i	0.00201814	+	0.104055i
$782$	−11.1113	+	4.04417i	−0.397338	+	0.144619i
$783$		0			0
$784$	3.71203	+	1.35107i	0.132573	+	0.0482525i
$785$	1.43336	−	4.18916i	0.0511589	−	0.149518i
$786$		0			0
$787$	−42.6657	+	17.4308i	−1.52087	+	0.621343i	−0.976115	−	0.217254i	$-0.930290\pi$
$787$	−42.6657	+	17.4308i	−1.52087	+	0.621343i	−0.544752	+	0.838597i	$0.683376\pi$
$788$	−2.22020	−	4.64316i	−0.0790914	−	0.165406i
$789$		0			0
$790$	−1.09960	+	0.352574i	−0.0391221	+	0.0125440i
$791$	40.1938	+	4.69799i	1.42913	+	0.167041i
$792$		0			0
$793$	10.5397	+	14.1573i	0.374277	+	0.502742i
$794$	−1.61806	+	16.6352i	−0.0574230	+	0.590360i
$795$		0			0
$796$	19.9446	+	12.0366i	0.706917	+	0.426627i
$797$	24.1461	−	27.6684i	0.855300	−	0.980065i	−0.144656	−	0.989482i	$-0.546208\pi$
$797$	24.1461	−	27.6684i	0.855300	−	0.980065i	0.999956	+	0.00941743i	$0.00299771\pi$
$798$		0			0
$799$	6.37566	−	13.3336i	0.225555	−	0.471707i
$800$	−1.46376	+	25.1318i	−0.0517518	+	0.888543i
$801$		0			0
$802$	−3.28686	+	2.16180i	−0.116063	+	0.0763358i
$803$	−5.03983	+	3.90616i	−0.177852	+	0.137846i
$804$		0			0
$805$	−9.86877	+	7.05377i	−0.347829	+	0.248613i
$806$	0.730136	+	3.37068i	0.0257179	+	0.118727i
$807$		0			0
$808$	0.617179	−	0.765181i	0.0217123	−	0.0269190i
$809$	−12.7169	−	22.0263i	−0.447102	−	0.774403i	0.551094	−	0.834443i	$-0.314210\pi$
$809$	−12.7169	−	22.0263i	−0.447102	−	0.774403i	−0.998196	+	0.0600401i	$0.980877\pi$
$810$		0			0
$811$	25.9217	−	44.8978i	0.910235	−	1.57657i	0.0965042	−	0.995333i	$-0.469234\pi$
$811$	25.9217	−	44.8978i	0.910235	−	1.57657i	0.813731	−	0.581241i	$-0.197433\pi$
$812$	−0.501367	−	1.29857i	−0.0175945	−	0.0455709i
$813$		0			0
$814$	−2.57283	+	2.33472i	−0.0901776	+	0.0818318i
$815$	0.875532	+	9.00125i	0.0306685	+	0.315300i
$816$		0			0
$817$	0.562446	+	0.229784i	0.0196775	+	0.00803914i
$818$	0.522862	+	8.97720i	0.0182815	+	0.313880i
$819$		0			0
$820$	−6.64848	+	3.33899i	−0.232175	+	0.116603i
$821$	9.76933	+	14.2440i	0.340952	+	0.497120i	0.956801	−	0.290744i	$-0.0939028\pi$
$821$	9.76933	+	14.2440i	0.340952	+	0.497120i	−0.615849	+	0.787864i	$0.711187\pi$
$822$		0			0
$823$	16.5589	+	3.25207i	0.577208	+	0.113360i	0.472793	−	0.881174i	$-0.343246\pi$
$823$	16.5589	+	3.25207i	0.577208	+	0.113360i	0.104416	+	0.994534i	$0.466703\pi$
$824$	5.83879	−	3.22171i	0.203404	−	0.112234i
$825$		0			0
$826$	14.9681	−	6.80386i	0.520808	−	0.236736i
$827$	37.0475	−	4.33023i	1.28827	−	0.150577i	0.555764	−	0.831340i	$-0.312426\pi$
$827$	37.0475	−	4.33023i	1.28827	−	0.150577i	0.732504	+	0.680763i	$0.238352\pi$
$828$		0			0
$829$	14.6790	+	34.0296i	0.509821	+	1.18190i	0.957691	+	0.287799i	$0.0929236\pi$
$829$	14.6790	+	34.0296i	0.509821	+	1.18190i	−0.447870	+	0.894099i	$0.647817\pi$
$830$	−0.408529	+	1.88598i	−0.0141803	+	0.0654633i
$831$		0			0
$832$	0.902679	−	1.31614i	0.0312948	−	0.0456289i
$833$	−0.673218	+	4.92882i	−0.0233256	+	0.170774i
$834$		0			0
$835$	12.9771	−	2.54862i	0.449091	−	0.0881986i
$836$	−6.13384	+	5.14690i	−0.212143	+	0.178009i
$837$		0			0
$838$	−15.8468	−	13.2970i	−0.547417	−	0.459338i
$839$	−35.7127	−	19.7054i	−1.23294	−	0.680307i	−0.273404	−	0.961899i	$-0.588150\pi$
$839$	−35.7127	−	19.7054i	−1.23294	−	0.680307i	−0.959534	+	0.281592i	$0.909137\pi$
$840$		0			0
$841$	−13.4479	+	25.5302i	−0.463721	+	0.880353i
$842$	1.22936	−	4.77267i	0.0423666	−	0.164477i
$843$		0			0
$844$	−19.7179	−	37.4336i	−0.678719	−	1.28852i
$845$	3.85961	−	0.914744i	0.132775	−	0.0314682i
$846$		0			0
$847$	6.78620	+	22.6675i	0.233177	+	0.778864i
$848$	19.6171	+	5.46079i	0.673654	+	0.187524i
$849$		0			0
$850$	−6.65916	+	1.04147i	−0.228407	+	0.0357222i
$851$	−71.1923	+	11.1343i	−2.44044	+	0.381678i
$852$		0			0
$853$	31.5882	+	8.79318i	1.08156	+	0.301073i	0.762716	−	0.646734i	$-0.223866\pi$
$853$	31.5882	+	8.79318i	1.08156	+	0.301073i	0.318845	+	0.947807i	$0.396705\pi$
$854$	2.53309	+	8.46110i	0.0866804	+	0.289533i
$855$		0			0
$856$	24.4641	−	5.79811i	0.836167	−	0.198175i
$857$	−5.52496	−	10.4889i	−0.188729	−	0.358293i	0.772071	−	0.635537i	$-0.219221\pi$
$857$	−5.52496	−	10.4889i	−0.188729	−	0.358293i	−0.960800	+	0.277243i	$0.910579\pi$
$858$		0			0
$859$	−7.59915	+	29.5017i	−0.259280	+	1.00659i	0.697691	+	0.716399i	$0.254211\pi$
$859$	−7.59915	+	29.5017i	−0.259280	+	1.00659i	−0.956970	+	0.290186i	$0.906283\pi$
$860$	0.0414152	−	0.0786248i	0.00141225	−	0.00268108i
$861$		0			0
$862$	17.5665	+	9.69279i	0.598318	+	0.330138i
$863$	2.37311	+	1.99128i	0.0807816	+	0.0677838i	0.682284	−	0.731087i	$-0.260987\pi$
$863$	2.37311	+	1.99128i	0.0807816	+	0.0677838i	−0.601503	+	0.798871i	$0.705431\pi$
$864$		0			0
$865$	−12.3177	+	10.3358i	−0.418814	+	0.351427i
$866$	20.6504	−	4.05561i	0.701730	−	0.137815i
$867$		0			0
$868$	1.06103	−	7.76812i	0.0360138	−	0.263667i
$869$	1.01676	−	1.48247i	0.0344911	−	0.0502892i
$870$		0			0
$871$	4.24746	−	19.6085i	0.143920	−	0.664407i
$872$	−3.62351	−	8.40025i	−0.122708	−	0.284468i
$873$		0			0
$874$	36.3097	−	4.24400i	1.22819	−	0.143555i
$875$	−13.2367	+	6.01683i	−0.447483	+	0.203406i
$876$		0			0
$877$	17.9218	−	9.88882i	0.605175	−	0.333922i	−0.150758	−	0.988571i	$-0.548171\pi$
$877$	17.9218	−	9.88882i	0.605175	−	0.333922i	0.755933	+	0.654649i	$0.227184\pi$
$878$	−12.1614	−	2.38843i	−0.410429	−	0.0806055i
$879$		0			0
$880$	0.484500	+	0.706418i	0.0163325	+	0.0238133i
$881$	18.5379	−	9.31010i	0.624559	−	0.313665i	−0.108226	−	0.994126i	$-0.534517\pi$
$881$	18.5379	−	9.31010i	0.624559	−	0.313665i	0.732784	+	0.680461i	$0.238221\pi$
$882$		0			0
$883$	1.14669	+	19.6879i	0.0385891	+	0.662550i	0.961036	+	0.276425i	$0.0891497\pi$
$883$	1.14669	+	19.6879i	0.0385891	+	0.662550i	−0.922446	+	0.386125i	$0.873813\pi$
$884$	10.0699	+	4.11402i	0.338688	+	0.138369i
$885$		0			0
$886$	0.717869	+	7.38034i	0.0241173	+	0.247947i
$887$	23.1669	−	21.0229i	0.777869	−	0.705878i	−0.182930	−	0.983126i	$-0.558558\pi$
$887$	23.1669	−	21.0229i	0.777869	−	0.705878i	0.960798	+	0.277248i	$0.0894223\pi$
$888$		0			0
$889$	−10.9457	−	28.3500i	−0.367106	−	0.950828i
$890$	1.40779	−	2.43837i	0.0471893	−	0.0817343i
$891$		0			0
$892$	−0.539811	−	0.934981i	−0.0180742	−	0.0313055i
$893$	−28.6867	+	35.5659i	−0.959963	+	1.19017i
$894$		0			0
$895$	−0.625434	−	2.88732i	−0.0209060	−	0.0965126i
$896$	20.8312	−	14.8892i	0.695920	−	0.497414i
$897$		0			0
$898$	−16.4469	+	12.7473i	−0.548840	+	0.425383i
$899$	0.680083	−	0.447298i	0.0226820	−	0.0149182i
$900$		0			0
$901$	−1.49102	+	25.5999i	−0.0496731	+	0.852855i
$902$	−1.09981	+	2.30005i	−0.0366195	+	0.0765832i
$903$		0			0
$904$	−26.0387	+	29.8370i	−0.866034	+	0.992365i
$905$	5.54925	+	3.34899i	0.184463	+	0.111324i
$906$		0			0
$907$	3.52996	−	36.2912i	0.117210	−	1.20503i	−0.733610	−	0.679571i	$-0.762166\pi$
$907$	3.52996	−	36.2912i	0.117210	−	1.20503i	0.850820	−	0.525457i	$-0.176106\pi$
$908$	−20.3225	−	27.2979i	−0.674427	−	0.905913i
$909$		0			0
$910$	−2.43988	−	0.285181i	−0.0808812	−	0.00945366i
$911$	−23.7738	+	7.62276i	−0.787661	+	0.252553i	−0.671820	−	0.740714i	$-0.734487\pi$
$911$	−23.7738	+	7.62276i	−0.787661	+	0.252553i	−0.115841	+	0.993268i	$0.536956\pi$
$912$		0			0
$913$	−1.29591	−	2.71017i	−0.0428885	−	0.0896936i
$914$	9.19969	−	3.75849i	0.304299	−	0.124320i
$915$		0			0
$916$	4.04926	−	11.8344i	0.133791	−	0.391020i
$917$	11.9230	+	4.33963i	0.393733	+	0.143307i
$918$		0			0
$919$	31.1295	−	11.3302i	1.02687	−	0.373750i	0.226981	−	0.973899i	$-0.427114\pi$
$919$	31.1295	−	11.3302i	1.02687	−	0.373750i	0.799888	+	0.600150i	$0.204892\pi$
$920$	−0.230191	−	11.8686i	−0.00758918	−	0.391296i
$921$		0			0
$922$	0.100413	+	0.159317i	0.00330694	+	0.00524682i
$923$	−11.7685	+	3.27597i	−0.387363	+	0.107830i
$924$		0			0
$925$	−41.0434	−	1.59267i	−1.34950	−	0.0523666i
$926$	−1.15437	−	1.22356i	−0.0379349	−	0.0402086i
$927$		0			0
$928$	2.05394	+	0.486792i	0.0674238	+	0.0159797i
$929$	−2.46573	−	9.57254i	−0.0808979	−	0.314065i	0.915124	−	0.403172i	$-0.132092\pi$
$929$	−2.46573	−	9.57254i	−0.0808979	−	0.314065i	−0.996022	+	0.0891073i	$0.971599\pi$
$930$		0			0
$931$	5.53944	−	14.3475i	0.181548	−	0.470220i
$932$	18.4206	+	22.8380i	0.603387	+	0.748083i
$933$		0			0
$934$	7.00678	−	6.87220i	0.229269	−	0.224865i
$935$	−0.740265	+	0.784635i	−0.0242093	+	0.0256603i
$936$		0			0
$937$	−7.03420	+	23.4959i	−0.229797	+	0.767577i	0.762854	+	0.646570i	$0.223797\pi$
$937$	−7.03420	+	23.4959i	−0.229797	+	0.767577i	−0.992652	+	0.121006i	$0.961388\pi$
$938$	5.35327	−	8.49355i	0.174791	−	0.277324i
$939$		0			0
$940$	4.77133	+	4.67969i	0.155624	+	0.152635i
$941$	1.12897	−	0.0438091i	0.0368033	−	0.00142814i	−0.0203672	−	0.999793i	$-0.506484\pi$
$941$	1.12897	−	0.0438091i	0.0368033	−	0.00142814i	0.0571704	+	0.998364i	$0.481792\pi$
$942$		0			0
$943$	−45.2719	+	27.3217i	−1.47426	+	0.889718i
$944$	4.18163	−	23.7152i	0.136100	−	0.771863i
$945$		0			0
$946$	−0.00528798	−	0.0299896i	−0.000171927	−	0.000975046i
$947$	18.6666	+	21.3895i	0.606582	+	0.695066i	0.971787	−	0.235861i	$-0.0757911\pi$
$947$	18.6666	+	21.3895i	0.606582	+	0.695066i	−0.365204	+	0.930927i	$0.619001\pi$
$948$		0			0
$949$	−21.1677	−	16.4062i	−0.687133	−	0.532568i
$950$	20.7755	+	1.61480i	0.674045	+	0.0523909i
$951$		0			0
$952$	8.94949	+	8.12123i	0.290055	+	0.263211i
$953$	18.4163	−	24.7373i	0.596561	−	0.801321i	−0.396610	−	0.917987i	$-0.629813\pi$
$953$	18.4163	−	24.7373i	0.596561	−	0.801321i	0.993171	+	0.116666i	$0.0372208\pi$
$954$		0			0
$955$	5.62539	−	13.0411i	0.182033	−	0.422001i
$956$	−19.4096	−	13.8731i	−0.627750	−	0.448689i
$957$		0			0
$958$	−0.302020	+	15.5721i	−0.00975782	+	0.503111i
$959$	1.28560	+	3.75731i	0.0415142	+	0.121330i
$960$		0			0
$961$	−26.3358	+	2.04698i	−0.849543	+	0.0660317i
$962$	−12.1915	−	8.01849i	−0.393070	−	0.258526i
$963$		0			0
$964$	1.95128	+	0.979972i	0.0628466	+	0.0315628i
$965$	1.88894	+	13.8295i	0.0608071	+	0.445186i
$966$		0			0
$967$	−34.4018	−	15.6375i	−1.10629	−	0.502869i	−0.224480	−	0.974479i	$-0.572068\pi$
$967$	−34.4018	−	15.6375i	−1.10629	−	0.502869i	−0.881807	+	0.471610i	$0.843673\pi$
$968$	−22.0493	−	7.06984i	−0.708693	−	0.227233i
$969$		0			0
$970$	0.387231	+	0.0605619i	0.0124333	+	0.00194452i
$971$	−51.0109			−1.63702			−0.818509	−	0.574493i	$-0.805199\pi$
$971$	−51.0109			−1.63702			−0.818509	+	0.574493i	$0.805199\pi$
$972$		0			0
$973$	7.52763			0.241325
$974$	−19.4164	−	3.03667i	−0.622142	−	0.0973013i
$975$		0			0
$976$	12.3179	+	3.94958i	0.394287	+	0.126423i
$977$	1.25977	+	0.572637i	0.0403037	+	0.0183203i	0.433861	−	0.900980i	$-0.357151\pi$
$977$	1.25977	+	0.572637i	0.0403037	+	0.0183203i	−0.393557	+	0.919300i	$0.628756\pi$
$978$		0			0
$979$	0.593175	+	4.34281i	0.0189579	+	0.138797i
$980$	−2.01021	−	1.00957i	−0.0642138	−	0.0322494i
$981$		0			0
$982$	−8.20197	−	5.39452i	−0.261735	−	0.172146i
$983$	−43.1324	+	3.35251i	−1.37571	+	0.106929i	−0.743949	−	0.668236i	$-0.767050\pi$
$983$	−43.1324	+	3.35251i	−1.37571	+	0.106929i	−0.631759	+	0.775165i	$0.717667\pi$
$984$		0			0
$985$	0.693966	+	2.02819i	0.0221116	+	0.0646235i
$986$	−0.0109590	+	0.565041i	−0.000349005	+	0.0179946i
$987$		0			0
$988$	−27.3603	−	19.5560i	−0.870449	−	0.622159i
$989$	0.250163	−	0.579942i	0.00795471	−	0.0184411i
$990$		0			0
$991$	−5.51236	+	7.40438i	−0.175106	+	0.235208i	−0.881008	−	0.473101i	$-0.843134\pi$
$991$	−5.51236	+	7.40438i	−0.175106	+	0.235208i	0.705902	+	0.708309i	$0.250542\pi$
$992$	8.80434	+	7.98951i	0.279538	+	0.253667i
$993$		0			0
$994$	−6.09458	−	0.473708i	−0.193308	−	0.0150251i
$995$	−7.66890	−	5.94384i	−0.243120	−	0.188432i
$996$		0			0
$997$	11.7447	+	13.4580i	0.371960	+	0.426219i	0.908649	−	0.417562i	$-0.137115\pi$
$997$	11.7447	+	13.4580i	0.371960	+	0.426219i	−0.536689	+	0.843780i	$0.680325\pi$
$998$	−3.59420	−	20.3837i	−0.113772	−	0.645235i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.10		1404
3.2	odd	2		243.2.i.a.13.17	✓	1404
243.56	odd	162		243.2.i.a.187.17	yes	1404
243.187	even	81	inner	729.2.i.a.73.10		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.17	✓	1404	3.2	odd	2
243.2.i.a.187.17	yes	1404	243.56	odd	162
729.2.i.a.10.10		1404	1.1	even	1	trivial
729.2.i.a.73.10		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)

\(f(q)\)	\(=\)	\(q+(-0.593472 - 0.0928174i) q^{2} +(-1.56090 - 0.500483i) q^{4} +(0.621532 + 0.282521i) q^{5} +(-0.302306 - 2.21327i) q^{7} +(1.95348 + 0.981077i) q^{8} +O(q^{10})\)	\(q+(-0.593472 - 0.0928174i) q^{2} +(-1.56090 - 0.500483i) q^{4} +(0.621532 + 0.282521i) q^{5} +(-0.302306 - 2.21327i) q^{7} +(1.95348 + 0.981077i) q^{8} +(-0.342639 - 0.225357i) q^{10} +(0.636509 - 0.0494734i) q^{11} +(0.868078 + 2.53705i) q^{13} +(-0.0260198 + 1.34157i) q^{14} +(1.59883 + 1.14278i) q^{16} +(-0.980238 + 2.27245i) q^{17} +(4.56909 - 6.13736i) q^{19} +(-0.828753 - 0.752053i) q^{20} +(-0.382342 - 0.0297180i) q^{22} +(-6.28672 - 4.87257i) q^{23} +(-2.98112 - 3.41599i) q^{25} +(-0.279697 - 1.58624i) q^{26} +(-0.635834 + 3.60599i) q^{28} +(-0.325480 + 0.196428i) q^{29} +(-2.13959 + 0.0830257i) q^{31} +(-3.96410 - 3.88796i) q^{32} +(0.792666 - 1.25765i) q^{34} +(0.437402 - 1.46102i) q^{35} +(6.21694 - 6.58957i) q^{37} +(-3.28128 + 3.21826i) q^{38} +(0.936978 + 1.16167i) q^{40} +(2.39445 - 6.20179i) q^{41} +(0.0198074 + 0.0768969i) q^{43} +(-1.01829 - 0.241339i) q^{44} +(3.27873 + 3.47525i) q^{46} +(-5.96737 - 0.231561i) q^{47} +(1.93643 - 0.539042i) q^{49} +(1.45215 + 2.30399i) q^{50} +(-0.0852321 - 4.39455i) q^{52} +(9.73666 - 3.54385i) q^{53} +(0.409588 + 0.149078i) q^{55} +(1.58084 - 4.62017i) q^{56} +(0.211395 - 0.0863643i) q^{58} +(-5.28596 - 11.0546i) q^{59} +(6.26787 - 2.00971i) q^{61} +(1.27749 + 0.149317i) q^{62} +(-0.355417 - 0.477408i) q^{64} +(-0.177232 + 1.82211i) q^{65} +(-6.40602 - 3.86605i) q^{67} +(2.66738 - 3.05647i) q^{68} +(-0.395194 + 0.826479i) q^{70} +(-0.264891 + 4.54800i) q^{71} +(-8.34451 + 5.48827i) q^{73} +(-4.30121 + 3.33369i) q^{74} +(-10.2036 + 7.29306i) q^{76} +(-0.301918 - 1.39381i) q^{77} +(1.76774 - 2.19166i) q^{79} +(0.670867 + 1.16198i) q^{80} +(-1.99667 + 3.45834i) q^{82} +(-1.69478 - 4.38960i) q^{83} +(-1.25126 + 1.13546i) q^{85} +(-0.00461775 - 0.0474747i) q^{86} +(1.29195 + 0.527819i) q^{88} +(0.399193 + 6.85388i) q^{89} +(5.35275 - 2.68825i) q^{91} +(7.37431 + 10.7520i) q^{92} +(3.51998 + 0.691301i) q^{94} +(4.57377 - 2.52370i) q^{95} +(-0.870033 + 0.395479i) q^{97} +(-1.19925 + 0.140172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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