LMFDB - Embedded newform 729.2.g.d.514.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$729 = 3^{6}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	729.g (of order $27$ , degree $18$ , 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			514.5
Character	$\chi$	$=$	729.514
Dual form			729.2.g.d.217.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0454430 + 0.780226i) q^{2} +(1.37979 - 0.161274i) q^{4} +(-1.44081 - 0.341479i) q^{5} +(-2.26996 + 3.04908i) q^{7} +(0.459961 + 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(-3.46856 - 3.67646i) q^{11} +(-4.01443 + 2.01612i) q^{13} +(-2.48212 - 1.63252i) q^{14} +(0.689105 - 0.163321i) q^{16} +(-4.30582 + 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(-2.04309 - 0.238803i) q^{20} +(2.71085 - 2.87333i) q^{22} +(-2.06314 - 2.77128i) q^{23} +(-2.50883 - 1.25998i) q^{25} +(-1.75546 - 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(-0.545523 + 0.358796i) q^{29} +(0.260680 - 0.604325i) q^{31} +(1.67812 + 5.60530i) q^{32} +(-1.41843 - 3.28829i) q^{34} +(4.31178 - 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(-1.00072 + 3.34263i) q^{38} +(0.228053 - 3.91553i) q^{40} +(0.0397020 - 0.681658i) q^{41} +(-2.40716 + 8.04048i) q^{43} +(-5.37881 - 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(3.14280 + 7.28584i) q^{47} +(-2.13657 - 7.13664i) q^{49} +(0.869061 - 2.01471i) q^{50} +(-5.21392 + 3.42925i) q^{52} +(-2.07469 + 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(-8.99782 - 4.51888i) q^{56} +(-0.304732 - 0.409326i) q^{58} +(-3.61647 + 3.83324i) q^{59} +(6.74505 + 0.788383i) q^{61} +(0.483356 + 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(6.47250 - 1.53401i) q^{65} +(-4.42909 - 2.91306i) q^{67} +(-5.68837 + 2.85681i) q^{68} +(3.01881 + 3.19975i) q^{70} +(-1.06500 + 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(-0.466781 + 0.626996i) q^{74} +(6.03481 + 1.43028i) q^{76} +(19.0833 - 2.23052i) q^{77} +(-0.653695 - 11.2235i) q^{79} -1.04864 q^{80} +0.533651 q^{82} +(-0.0942903 - 1.61890i) q^{83} +(6.73904 - 0.787681i) q^{85} +(-6.38278 - 1.51275i) q^{86} +(7.99490 - 10.7390i) q^{88} +(-0.181087 - 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(-3.29364 - 3.49105i) q^{92} +(-5.54178 + 2.78318i) q^{94} +(-5.52314 - 3.63263i) q^{95} +(4.85369 - 1.15034i) q^{97} +(5.47110 - 1.99132i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100})$ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.0454430	+	0.780226i	0.0321330	+	0.551703i	0.975507	+	0.219970i	$0.0705961\pi$
$2$	0.0454430	+	0.780226i	0.0321330	+	0.551703i	−0.943374	+	0.331732i	$0.892367\pi$
$3$		0			0
$3$		0			0
$4$	1.37979	−	0.161274i	0.689895	−	0.0806371i
$5$	−1.44081	−	0.341479i	−0.644351	−	0.152714i	−0.104568	−	0.994518i	$-0.533346\pi$
$5$	−1.44081	−	0.341479i	−0.644351	−	0.152714i	−0.539784	+	0.841804i	$0.681494\pi$
$6$		0			0
$7$	−2.26996	+	3.04908i	−0.857963	+	1.15244i	0.129024	+	0.991642i	$0.458816\pi$
$7$	−2.26996	+	3.04908i	−0.857963	+	1.15244i	−0.986987	+	0.160803i	$0.948592\pi$
$8$	0.459961	+	2.60857i	0.162621	+	0.922268i
$9$		0			0
$10$	0.200956	−	1.13968i	0.0635478	−	0.360398i
$11$	−3.46856	−	3.67646i	−1.04581	−	1.10850i	−0.993949	−	0.109841i	$-0.964966\pi$
$11$	−3.46856	−	3.67646i	−1.04581	−	1.10850i	−0.0518624	−	0.998654i	$-0.516516\pi$
$12$		0			0
$13$	−4.01443	+	2.01612i	−1.11340	+	0.559171i	−0.907774	−	0.419459i	$-0.862220\pi$
$13$	−4.01443	+	2.01612i	−1.11340	+	0.559171i	−0.205627	+	0.978630i	$0.565924\pi$
$14$	−2.48212	−	1.63252i	−0.663376	−	0.436309i
$15$		0			0
$16$	0.689105	−	0.163321i	0.172276	−	0.0408303i
$17$	−4.30582	+	1.56719i	−1.04431	+	0.380099i	−0.806514	−	0.591215i	$-0.798648\pi$
$17$	−4.30582	+	1.56719i	−1.04431	+	0.380099i	−0.237800	+	0.971314i	$0.576426\pi$
$18$		0			0
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.774995	−	0.631967i	$-0.217752\pi$
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.187460	+	0.982272i	$0.439975\pi$
$20$	−2.04309	−	0.238803i	−0.456849	−	0.0533980i
$21$		0			0
$22$	2.71085	−	2.87333i	0.577955	−	0.612597i
$23$	−2.06314	−	2.77128i	−0.430195	−	0.577852i	0.533183	−	0.846000i	$-0.320996\pi$
$23$	−2.06314	−	2.77128i	−0.430195	−	0.577852i	−0.963378	+	0.268148i	$0.913588\pi$
$24$		0			0
$25$	−2.50883	−	1.25998i	−0.501766	−	0.251996i
$26$	−1.75546	−	3.04054i	−0.344273	−	0.596299i
$27$		0			0
$28$	−2.64032	+	4.57318i	−0.498974	+	0.864249i
$29$	−0.545523	+	0.358796i	−0.101301	+	0.0666267i	−0.599149	−	0.800638i	$-0.704494\pi$
$29$	−0.545523	+	0.358796i	−0.101301	+	0.0666267i	0.497848	+	0.867264i	$0.334124\pi$
$30$		0			0
$31$	0.260680	−	0.604325i	0.0468196	−	0.108540i	−0.893201	−	0.449657i	$-0.851546\pi$
$31$	0.260680	−	0.604325i	0.0468196	−	0.108540i	0.940021	+	0.341117i	$0.110805\pi$
$32$	1.67812	+	5.60530i	0.296652	+	0.990886i
$33$		0			0
$34$	−1.41843	−	3.28829i	−0.243259	−	0.563937i
$35$	4.31178	−	3.61801i	0.728824	−	0.611556i
$36$		0			0
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	0.703590	−	0.710606i	$-0.251579\pi$
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	−0.577633	+	0.816296i	$0.696024\pi$
$38$	−1.00072	+	3.34263i	−0.162338	+	0.542245i
$39$		0			0
$40$	0.228053	−	3.91553i	0.0360584	−	0.619099i
$41$	0.0397020	−	0.681658i	0.00620042	−	0.106457i	−0.993788	−	0.111291i	$-0.964502\pi$
$41$	0.0397020	−	0.681658i	0.00620042	−	0.106457i	0.999988	+	0.00483359i	$0.00153858\pi$
$42$		0			0
$43$	−2.40716	+	8.04048i	−0.367089	+	1.22616i	0.552578	+	0.833461i	$0.313644\pi$
$43$	−2.40716	+	8.04048i	−0.367089	+	1.22616i	−0.919666	+	0.392700i	$0.871541\pi$
$44$	−5.37881	−	4.51336i	−0.810886	−	0.680414i
$45$		0			0
$46$	2.06847	−	1.73565i	0.304979	−	0.255908i
$47$	3.14280	+	7.28584i	0.458425	+	1.06275i	0.978053	+	0.208356i	$0.0668112\pi$
$47$	3.14280	+	7.28584i	0.458425	+	1.06275i	−0.519628	+	0.854392i	$0.673930\pi$
$48$		0			0
$49$	−2.13657	−	7.13664i	−0.305224	−	1.01952i
$50$	0.869061	−	2.01471i	0.122904	−	0.284923i
$51$		0			0
$52$	−5.21392	+	3.42925i	−0.723040	+	0.475551i
$53$	−2.07469	+	3.59347i	−0.284981	+	0.493601i	−0.972605	−	0.232466i	$-0.925321\pi$
$53$	−2.07469	+	3.59347i	−0.284981	+	0.493601i	0.687624	+	0.726067i	$0.258654\pi$
$54$		0			0
$55$	3.74212	+	6.48154i	0.504587	+	0.873971i
$56$	−8.99782	−	4.51888i	−1.20238	−	0.603860i
$57$		0			0
$58$	−0.304732	−	0.409326i	−0.0400133	−	0.0537471i
$59$	−3.61647	+	3.83324i	−0.470825	+	0.499045i	−0.918648	−	0.395077i	$-0.870718\pi$
$59$	−3.61647	+	3.83324i	−0.470825	+	0.499045i	0.447823	+	0.894122i	$0.352199\pi$
$60$		0			0
$61$	6.74505	+	0.788383i	0.863615	+	0.100942i	0.536355	−	0.843992i	$-0.319801\pi$
$61$	6.74505	+	0.788383i	0.863615	+	0.100942i	0.327260	+	0.944934i	$0.393875\pi$
$62$	0.483356	+	0.175927i	0.0613862	+	0.0223428i
$63$		0			0
$64$	−2.96617	+	1.07960i	−0.370771	+	0.134950i
$65$	6.47250	−	1.53401i	0.802815	−	0.190271i
$66$		0			0
$67$	−4.42909	−	2.91306i	−0.541099	−	0.355886i	0.249351	−	0.968413i	$-0.419783\pi$
$67$	−4.42909	−	2.91306i	−0.541099	−	0.355886i	−0.790450	+	0.612527i	$0.790153\pi$
$68$	−5.68837	+	2.85681i	−0.689817	+	0.346439i
$69$		0			0
$70$	3.01881	+	3.19975i	0.360816	+	0.382443i
$71$	−1.06500	+	6.03991i	−0.126392	+	0.716805i	0.854079	+	0.520143i	$0.174121\pi$
$71$	−1.06500	+	6.03991i	−0.126392	+	0.716805i	−0.980471	+	0.196662i	$0.936990\pi$
$72$		0			0
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	−0.996306	−	0.0858796i	$-0.972630\pi$
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	0.906848	−	0.421457i	$-0.138481\pi$
$74$	−0.466781	+	0.626996i	−0.0542622	+	0.0728868i
$75$		0			0
$76$	6.03481	+	1.43028i	0.692240	+	0.164064i
$77$	19.0833	−	2.23052i	2.17475	−	0.254191i
$78$		0			0
$79$	−0.653695	−	11.2235i	−0.0735465	−	1.26274i	−0.810070	−	0.586333i	$-0.800571\pi$
$79$	−0.653695	−	11.2235i	−0.0735465	−	1.26274i	0.736524	−	0.676412i	$-0.236466\pi$
$80$	−1.04864			−0.117242
$81$		0			0
$82$	0.533651			0.0589319
$83$	−0.0942903	−	1.61890i	−0.0103497	−	0.177698i	−0.999521	−	0.0309347i	$-0.990152\pi$
$83$	−0.0942903	−	1.61890i	−0.0103497	−	0.177698i	0.989172	−	0.146763i	$-0.0468854\pi$
$84$		0			0
$85$	6.73904	−	0.787681i	0.730952	−	0.0854360i
$86$	−6.38278	−	1.51275i	−0.688273	−	0.163124i
$87$		0			0
$88$	7.99490	−	10.7390i	0.852259	−	1.14478i
$89$	−0.181087	−	1.02699i	−0.0191952	−	0.108861i	0.973705	−	0.227813i	$-0.0731576\pi$
$89$	−0.181087	−	1.02699i	−0.0191952	−	0.108861i	−0.992900	+	0.118952i	$0.962046\pi$
$90$		0			0
$91$	2.96526	−	16.8168i	0.310844	−	1.76288i
$92$	−3.29364	−	3.49105i	−0.343385	−	0.363967i
$93$		0			0
$94$	−5.54178	+	2.78318i	−0.571591	+	0.287064i
$95$	−5.52314	−	3.63263i	−0.566662	−	0.372700i
$96$		0			0
$97$	4.85369	−	1.15034i	0.492817	−	0.116800i	0.0233097	−	0.999728i	$-0.492580\pi$
$97$	4.85369	−	1.15034i	0.492817	−	0.116800i	0.469508	+	0.882928i	$0.344431\pi$
$98$	5.47110	−	1.99132i	0.552664	−	0.201153i
$99$		0			0
$100$	−3.66486	−	1.33390i	−0.366486	−	0.133390i
$101$	9.50577	+	1.11107i	0.945859	+	0.110555i	0.575018	−	0.818141i	$-0.304995\pi$
$101$	9.50577	+	1.11107i	0.945859	+	0.110555i	0.370842	+	0.928696i	$0.379069\pi$
$102$		0			0
$103$	−2.23381	+	2.36770i	−0.220104	+	0.233297i	−0.828011	−	0.560711i	$-0.810528\pi$
$103$	−2.23381	+	2.36770i	−0.220104	+	0.233297i	0.607907	+	0.794008i	$0.292009\pi$
$104$	−7.10567	−	9.54457i	−0.696768	−	0.935922i
$105$		0			0
$106$	−2.89800	−	1.45543i	−0.281479	−	0.141364i
$107$	−8.40680	−	14.5610i	−0.812716	−	1.40767i	−0.910956	−	0.412503i	$-0.864655\pi$
$107$	−8.40680	−	14.5610i	−0.812716	−	1.40767i	0.0982402	−	0.995163i	$-0.468679\pi$
$108$		0			0
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	−0.988884	−	0.148691i	$-0.952494\pi$
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	0.623212	+	0.782053i	$0.285827\pi$
$110$	−4.88701	+	3.21424i	−0.465958	+	0.306465i
$111$		0			0
$112$	−1.06626	+	2.47187i	−0.100752	+	0.233570i
$113$	2.87359	+	9.59845i	0.270324	+	0.902947i	0.980098	+	0.198516i	$0.0636123\pi$
$113$	2.87359	+	9.59845i	0.270324	+	0.902947i	−0.709773	+	0.704430i	$0.751203\pi$
$114$		0			0
$115$	2.02627	+	4.69742i	0.188950	+	0.438036i
$116$	−0.694842	+	0.583042i	−0.0645144	+	0.0541340i
$117$		0			0
$118$	−3.15514	−	2.64747i	−0.290454	−	0.243720i
$119$	4.99553	−	16.6862i	0.457940	−	1.52962i
$120$		0			0
$121$	−0.845852	+	14.5227i	−0.0768956	+	1.32025i
$122$	−0.308602	+	5.29849i	−0.0279395	+	0.479703i
$123$		0			0
$124$	0.262222	−	0.875882i	0.0235482	−	0.0786565i
$125$	8.85601	+	7.43107i	0.792105	+	0.664655i
$126$		0			0
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	−0.501096	−	0.865392i	$-0.667070\pi$
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	0.765230	+	0.643757i	$0.222625\pi$
$128$	3.65789	+	8.47994i	0.323315	+	0.749528i
$129$		0			0
$130$	1.49100	+	4.98030i	0.130770	+	0.436801i
$131$	−6.59441	+	15.2876i	−0.576157	+	1.33568i	0.342088	+	0.939668i	$0.388866\pi$
$131$	−6.59441	+	15.2876i	−0.576157	+	1.33568i	−0.918245	+	0.396013i	$0.870393\pi$
$132$		0			0
$133$	−14.1788	+	9.32554i	−1.22946	+	0.808627i
$134$	2.07157	−	3.58807i	0.178956	−	0.309962i
$135$		0			0
$136$	−6.06863	−	10.5112i	−0.520380	−	0.901325i
$137$	8.28923	+	4.16301i	0.708197	+	0.355670i	0.766161	−	0.642649i	$-0.222165\pi$
$137$	8.28923	+	4.16301i	0.708197	+	0.355670i	−0.0579639	+	0.998319i	$0.518461\pi$
$138$		0			0
$139$	9.50746	+	12.7707i	0.806412	+	1.08320i	0.994874	+	0.101119i	$0.0322422\pi$
$139$	9.50746	+	12.7707i	0.806412	+	1.08320i	−0.188462	+	0.982080i	$0.560350\pi$
$140$	5.36586	−	5.68748i	0.453498	−	0.480680i
$141$		0			0
$142$	−4.76089	−	0.556468i	−0.399525	−	0.0466978i
$143$	21.3365	+	7.76585i	1.78425	+	0.649413i
$144$		0			0
$145$	0.908517	−	0.330673i	0.0754483	−	0.0274609i
$146$	3.34730	−	0.793325i	0.277025	−	0.0656560i
$147$		0			0
$148$	1.16083	+	0.763489i	0.0954195	+	0.0627584i
$149$	20.8590	−	10.4758i	1.70883	−	0.858208i	0.722924	−	0.690928i	$-0.242798\pi$
$149$	20.8590	−	10.4758i	1.70883	−	0.858208i	0.985909	−	0.167281i	$-0.0534986\pi$
$150$		0			0
$151$	1.60038	+	1.69630i	0.130237	+	0.138043i	0.789210	−	0.614123i	$-0.210490\pi$
$151$	1.60038	+	1.69630i	0.130237	+	0.138043i	−0.658973	+	0.752167i	$0.729009\pi$
$152$	−2.05349	+	11.6459i	−0.166560	+	0.944608i
$153$		0			0
$154$	2.60751	+	14.7879i	0.210119	+	1.19165i
$155$	−0.581956	+	0.781702i	−0.0467438	+	0.0627878i
$156$		0			0
$157$	−19.1527	−	4.53927i	−1.52855	−	0.362273i	−0.621541	−	0.783382i	$-0.713493\pi$
$157$	−19.1527	−	4.53927i	−1.52855	−	0.362273i	−0.907010	+	0.421109i	$0.861641\pi$
$158$	8.72717	−	1.02006i	0.694296	−	0.0811516i
$159$		0			0
$160$	−0.503760	−	8.64923i	−0.0398257	−	0.683782i
$161$	13.1331			1.03503
$162$		0			0
$163$	−17.6622			−1.38341			−0.691707	−	0.722179i	$-0.743141\pi$
$163$	−17.6622			−1.38341			−0.691707	+	0.722179i	$0.743141\pi$
$164$	−0.0551534	−	0.946947i	−0.00430676	−	0.0739442i
$165$		0			0
$166$	1.25882	−	0.147135i	0.0977037	−	0.0114199i
$167$	3.29876	+	0.781820i	0.255266	+	0.0604991i	0.356256	−	0.934388i	$-0.384053\pi$
$167$	3.29876	+	0.781820i	0.255266	+	0.0604991i	−0.100991	+	0.994887i	$0.532201\pi$
$168$		0			0
$169$	4.28782	−	5.75954i	0.329832	−	0.443042i
$170$	0.920811	+	5.22218i	0.0706230	+	0.400523i
$171$		0			0
$172$	−2.02465	+	11.4824i	−0.154378	+	0.875524i
$173$	12.8183	+	13.5866i	0.974557	+	1.03297i	0.999446	+	0.0332802i	$0.0105954\pi$
$173$	12.8183	+	13.5866i	0.974557	+	1.03297i	−0.0248887	+	0.999690i	$0.507923\pi$
$174$		0			0
$175$	9.53672	−	4.78952i	0.720908	−	0.362054i
$176$	−2.99065	−	1.96698i	−0.225429	−	0.148267i
$177$		0			0
$178$	0.793058	−	0.187958i	0.0594422	−	0.0140881i
$179$	−11.1678	+	4.06476i	−0.834723	+	0.303814i	−0.723796	−	0.690014i	$-0.757604\pi$
$179$	−11.1678	+	4.06476i	−0.834723	+	0.303814i	−0.110927	+	0.993829i	$0.535382\pi$
$180$		0			0
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.828244	−	0.560367i	$-0.189340\pi$
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.274275	+	0.961651i	$0.411562\pi$
$182$	13.2557	+	1.54937i	0.982575	+	0.114847i
$183$		0			0
$184$	6.28011	−	6.65652i	0.462976	−	0.490725i
$185$	−0.884368	−	1.18791i	−0.0650200	−	0.0873370i
$186$		0			0
$187$	20.6967	+	10.3943i	1.51349	+	0.760105i
$188$	5.51142	+	9.54607i	0.401962	+	0.696219i
$189$		0			0
$190$	2.58328	−	4.47437i	0.187411	−	0.324605i
$191$	−4.81793	+	3.16881i	−0.348614	+	0.229287i	−0.711724	−	0.702459i	$-0.752085\pi$
$191$	−4.81793	+	3.16881i	−0.348614	+	0.229287i	0.363110	+	0.931746i	$0.381715\pi$
$192$		0			0
$193$	0.0696139	−	0.161383i	0.00501092	−	0.0116166i	−0.915692	−	0.401880i	$-0.868357\pi$
$193$	0.0696139	−	0.161383i	0.00501092	−	0.0116166i	0.920703	+	0.390264i	$0.127616\pi$
$194$	1.11809	+	3.73470i	0.0802745	+	0.268136i
$195$		0			0
$196$	−4.09897	−	9.50249i	−0.292784	−	0.678749i
$197$	8.59155	−	7.20917i	0.612123	−	0.513632i	−0.283194	−	0.959063i	$-0.591394\pi$
$197$	8.59155	−	7.20917i	0.612123	−	0.513632i	0.895316	+	0.445431i	$0.146950\pi$
$198$		0			0
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.113866	−	0.993496i	$-0.536324\pi$
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.998175	+	0.0603824i	$0.980768\pi$
$200$	2.13278	−	7.12399i	0.150811	−	0.503742i
$201$		0			0
$202$	−0.434911	+	7.46714i	−0.0306002	+	0.525386i
$203$	0.144315	−	2.47779i	0.0101289	−	0.173907i
$204$		0			0
$205$	−0.289975	+	0.968584i	−0.0202527	+	0.0676489i
$206$	−1.94885	−	1.63528i	−0.135783	−	0.113935i
$207$		0			0
$208$	−2.43709	+	2.04496i	−0.168982	+	0.141792i
$209$	−8.93772	−	20.7200i	−0.618235	−	1.43323i
$210$		0			0
$211$	−0.341693	−	1.14134i	−0.0235231	−	0.0785728i	0.945422	−	0.325848i	$-0.105650\pi$
$211$	−0.341693	−	1.14134i	−0.0235231	−	0.0785728i	−0.968945	+	0.247276i	$0.920465\pi$
$212$	−2.28310	+	5.29283i	−0.156804	+	0.363513i
$213$		0			0
$214$	10.9788	−	7.22090i	0.750498	−	0.493610i
$215$	6.21393	−	10.7628i	0.423786	−	0.734019i
$216$		0			0
$217$	1.25090	+	2.16663i	0.0849168	+	0.147080i
$218$	−5.33272	−	2.67819i	−0.361177	−	0.181390i
$219$		0			0
$220$	6.20864	+	8.33965i	0.418587	+	0.562259i
$221$	14.1257	−	14.9724i	0.950200	−	1.00715i
$222$		0			0
$223$	14.7991	+	1.72977i	0.991024	+	0.115834i	0.596126	−	0.802891i	$-0.296706\pi$
$223$	14.7991	+	1.72977i	0.991024	+	0.115834i	0.394898	+	0.918725i	$0.370780\pi$
$224$	−20.9003	−	7.60707i	−1.39646	−	0.508269i
$225$		0			0
$226$	−7.35838	+	2.67823i	−0.489472	+	0.178153i
$227$	−23.9357	+	5.67287i	−1.58867	+	0.376522i	−0.927532	−	0.373743i	$-0.878074\pi$
$227$	−23.9357	+	5.67287i	−1.58867	+	0.376522i	−0.661138	+	0.750265i	$0.729926\pi$
$228$		0			0
$229$	−1.27577	−	0.839089i	−0.0843054	−	0.0554486i	0.506656	−	0.862148i	$-0.330881\pi$
$229$	−1.27577	−	0.839089i	−0.0843054	−	0.0554486i	−0.590962	+	0.806699i	$0.701252\pi$
$230$	−3.57297	+	1.79441i	−0.235594	+	0.118320i
$231$		0			0
$232$	−1.18686	−	1.25800i	−0.0779213	−	0.0825918i
$233$	2.44148	−	13.8463i	0.159946	−	0.907101i	−0.794177	−	0.607687i	$-0.792098\pi$
$233$	2.44148	−	13.8463i	0.159946	−	0.907101i	0.954123	−	0.299414i	$-0.0967912\pi$
$234$		0			0
$235$	−2.04023	−	11.5707i	−0.133090	−	0.754791i
$236$	−4.37177	+	5.87231i	−0.284578	+	0.382255i
$237$		0			0
$238$	13.2460	+	3.13937i	0.858613	+	0.203495i
$239$	22.7624	−	2.66054i	1.47238	−	0.172096i	0.658258	−	0.752793i	$-0.271294\pi$
$239$	22.7624	−	2.66054i	1.47238	−	0.172096i	0.814120	+	0.580696i	$0.197220\pi$
$240$		0			0
$241$	0.411011	+	7.05678i	0.0264755	+	0.454567i	0.985329	+	0.170666i	$0.0545918\pi$
$241$	0.411011	+	7.05678i	0.0264755	+	0.454567i	−0.958853	+	0.283902i	$0.908371\pi$
$242$	−11.3694			−0.730855
$243$		0			0
$244$	9.43390			0.603943
$245$	0.641385	+	11.0122i	0.0409766	+	0.703541i
$246$		0			0
$247$	−19.9200	+	2.32831i	−1.26748	+	0.148147i
$248$	1.69632	+	0.402036i	0.107717	+	0.0255293i
$249$		0			0
$250$	−5.39547	+	7.24737i	−0.341239	+	0.458364i
$251$	0.0115419	+	0.0654574i	0.000728518	+	0.00413163i	0.985170	−	0.171582i	$-0.0548878\pi$
$251$	0.0115419	+	0.0654574i	0.000728518	+	0.00413163i	−0.984441	+	0.175714i	$0.943777\pi$
$252$		0			0
$253$	−3.03237	+	17.1974i	−0.190644	+	1.08119i
$254$	2.08404	+	2.20895i	0.130764	+	0.138602i
$255$		0			0
$256$	−12.0916	+	6.07263i	−0.755725	+	0.379539i
$257$	−16.1614	−	10.6295i	−1.00812	−	0.663052i	−0.0658251	−	0.997831i	$-0.520968\pi$
$257$	−16.1614	−	10.6295i	−1.00812	−	0.663052i	−0.942297	+	0.334779i	$0.891338\pi$
$258$		0			0
$259$	−3.69938	+	0.876770i	−0.229868	+	0.0544798i
$260$	8.68330	−	3.16046i	0.538515	−	0.196003i
$261$		0			0
$262$	−12.2274	−	4.45042i	−0.755413	−	0.274948i
$263$	−14.9583	−	1.74837i	−0.922367	−	0.107809i	−0.358364	−	0.933582i	$-0.616665\pi$
$263$	−14.9583	−	1.74837i	−0.922367	−	0.107809i	−0.564003	+	0.825773i	$0.690739\pi$
$264$		0			0
$265$	4.21634	−	4.46906i	0.259008	−	0.274532i
$266$	−7.92035	−	10.6389i	−0.485628	−	0.652312i
$267$		0			0
$268$	−6.58101	−	3.30511i	−0.401999	−	0.201892i
$269$	5.86823	+	10.1641i	0.357792	+	0.619715i	0.987592	−	0.157043i	$-0.0501962\pi$
$269$	5.86823	+	10.1641i	0.357792	+	0.619715i	−0.629799	+	0.776758i	$0.716863\pi$
$270$		0			0
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	−0.818964	−	0.573844i	$-0.805451\pi$
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	0.906446	+	0.422322i	$0.138785\pi$
$272$	−2.71121	+	1.78319i	−0.164391	+	0.108122i
$273$		0			0
$274$	−2.87140	+	6.65665i	−0.173468	+	0.402143i
$275$	4.06976	+	13.5939i	0.245416	+	0.819746i
$276$		0			0
$277$	−0.911389	−	2.11284i	−0.0547601	−	0.126948i	0.888640	−	0.458606i	$-0.151651\pi$
$277$	−0.911389	−	2.11284i	−0.0547601	−	0.126948i	−0.943400	+	0.331658i	$0.892392\pi$
$278$	−9.53200	+	7.99830i	−0.571692	+	0.479706i
$279$		0			0
$280$	11.4211	+	9.58343i	0.682540	+	0.572719i
$281$	−1.81991	+	6.07893i	−0.108567	+	0.362639i	−0.994957	−	0.100300i	$-0.968020\pi$
$281$	−1.81991	+	6.07893i	−0.108567	+	0.362639i	0.886390	+	0.462939i	$0.153205\pi$
$282$		0			0
$283$	0.853670	−	14.6569i	0.0507454	−	0.871265i	−0.872872	−	0.487949i	$-0.837745\pi$
$283$	0.853670	−	14.6569i	0.0507454	−	0.871265i	0.923617	−	0.383316i	$-0.125218\pi$
$284$	−0.495393	+	8.50556i	−0.0293961	+	0.504712i
$285$		0			0
$286$	−5.08952	+	17.0002i	−0.300950	+	1.00524i
$287$	1.98831	+	1.66839i	0.117366	+	0.0984819i
$288$		0			0
$289$	3.06122	−	2.56867i	0.180072	−	0.151098i
$290$	0.299285	+	0.693822i	0.0175746	+	0.0407426i
$291$		0			0
$292$	−1.75368	−	5.85769i	−0.102626	−	0.342795i
$293$	−10.0427	+	23.2816i	−0.586701	+	1.36013i	0.323606	+	0.946192i	$0.395105\pi$
$293$	−10.0427	+	23.2816i	−0.586701	+	1.36013i	−0.910307	+	0.413934i	$0.864155\pi$
$294$		0			0
$295$	6.51964	−	4.28803i	0.379588	−	0.249659i
$296$	−1.32461	+	2.29430i	−0.0769916	+	0.133353i
$297$		0			0
$298$	9.12136	+	15.7987i	0.528386	+	0.915191i
$299$	13.8696	+	6.96556i	0.802098	+	0.402829i
$300$		0			0
$301$	−19.0519	−	25.5912i	−1.09813	−	1.47505i
$302$	−1.25077	+	1.32574i	−0.0719739	+	0.0762879i
$303$		0			0
$304$	3.14035	+	0.367054i	0.180111	+	0.0210520i
$305$	−9.44914	−	3.43921i	−0.541056	−	0.196928i
$306$		0			0
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.00601852	−	0.999982i	$-0.498084\pi$
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.647386	+	0.762162i	$0.275862\pi$
$308$	25.9713	−	6.15530i	1.47985	−	0.350731i
$309$		0			0
$310$	−0.636350	−	0.418534i	−0.0361422	−	0.0237711i
$311$	−22.4620	+	11.2809i	−1.27370	+	0.639679i	−0.951691	−	0.307056i	$-0.900656\pi$
$311$	−22.4620	+	11.2809i	−1.27370	+	0.639679i	−0.322014	+	0.946735i	$0.604360\pi$
$312$		0			0
$313$	−20.2873	−	21.5033i	−1.14671	−	1.21544i	−0.973041	−	0.230632i	$-0.925921\pi$
$313$	−20.2873	−	21.5033i	−1.14671	−	1.21544i	−0.173664	−	0.984805i	$-0.555561\pi$
$314$	2.67130	−	15.1497i	0.150750	−	0.854947i
$315$		0			0
$316$	−2.71203	−	15.3807i	−0.152563	−	0.865230i
$317$	2.56069	−	3.43961i	0.143823	−	0.193188i	−0.724374	−	0.689407i	$-0.757871\pi$
$317$	2.56069	−	3.43961i	0.143823	−	0.193188i	0.868197	+	0.496219i	$0.165279\pi$
$318$		0			0
$319$	3.21128	+	0.761087i	0.179797	+	0.0426127i
$320$	4.64235	−	0.542613i	0.259515	−	0.0303330i
$321$		0			0
$322$	0.596807	+	10.2468i	0.0332588	+	0.571031i
$323$	−20.4570			−1.13826
$324$		0			0
$325$	12.6118			0.699576
$326$	−0.802624	−	13.7805i	−0.0444533	−	0.763233i
$327$		0			0
$328$	1.79641	−	0.209970i	0.0991902	−	0.0115937i
$329$	−29.3491	−	6.95587i	−1.61807	−	0.383490i
$330$		0			0
$331$	−16.6197	+	22.3242i	−0.913503	+	1.22705i	0.0599599	+	0.998201i	$0.480903\pi$
$331$	−16.6197	+	22.3242i	−0.913503	+	1.22705i	−0.973463	+	0.228846i	$0.926505\pi$
$332$	−0.391188	−	2.21854i	−0.0214692	−	0.121758i
$333$		0			0
$334$	−0.460091	+	2.60930i	−0.0251750	+	0.142775i
$335$	5.38674	+	5.70961i	0.294309	+	0.311949i
$336$		0			0
$337$	24.0402	−	12.0735i	1.30956	−	0.657683i	0.349354	−	0.936991i	$-0.386401\pi$
$337$	24.0402	−	12.0735i	1.30956	−	0.657683i	0.960202	+	0.279307i	$0.0901049\pi$
$338$	4.68859	+	3.08374i	0.255026	+	0.167733i
$339$		0			0
$340$	9.17143	−	2.17367i	0.497390	−	0.117884i
$341$	−3.12596	+	1.13776i	−0.169280	+	0.0616130i
$342$		0			0
$343$	1.60598	+	0.584529i	0.0867148	+	0.0315616i
$344$	−22.0813	−	2.58094i	−1.19055	−	0.139155i
$345$		0			0
$346$	−10.0181	+	10.6186i	−0.538577	+	0.570859i
$347$	−18.2126	−	24.4638i	−0.977703	−	1.31328i	−0.949529	−	0.313680i	$-0.898438\pi$
$347$	−18.2126	−	24.4638i	−0.977703	−	1.31328i	−0.0281743	−	0.999603i	$-0.508969\pi$
$348$		0			0
$349$	−7.12702	−	3.57932i	−0.381500	−	0.191597i	0.247705	−	0.968835i	$-0.420323\pi$
$349$	−7.12702	−	3.57932i	−0.381500	−	0.191597i	−0.629206	+	0.777239i	$0.716620\pi$
$350$	4.17028	+	7.22314i	0.222911	+	0.386093i
$351$		0			0
$352$	14.7870	−	25.6119i	0.788151	−	1.36512i
$353$	18.2389	−	11.9959i	0.970756	−	0.638476i	0.0381118	−	0.999273i	$-0.487866\pi$
$353$	18.2389	−	11.9959i	0.970756	−	0.638476i	0.932644	+	0.360797i	$0.117495\pi$
$354$		0			0
$355$	3.59697	−	8.33871i	0.190907	−	0.442573i
$356$	−0.415490	−	1.38783i	−0.0220209	−	0.0735549i
$357$		0			0
$358$	−3.67893	−	8.52871i	−0.194437	−	0.450757i
$359$	−13.2606	+	11.1269i	−0.699866	+	0.587258i	−0.921736	−	0.387819i	$-0.873229\pi$
$359$	−13.2606	+	11.1269i	−0.699866	+	0.587258i	0.221869	+	0.975076i	$0.428784\pi$
$360$		0			0
$361$	0.713665	+	0.598836i	0.0375613	+	0.0315177i
$362$	−3.53818	+	11.8183i	−0.185962	+	0.621158i
$363$		0			0
$364$	1.37931	−	23.6819i	0.0722957	−	1.24127i
$365$	−0.378959	+	6.50647i	−0.0198356	+	0.340564i
$366$		0			0
$367$	6.85653	−	22.9024i	0.357908	−	1.19550i	−0.569672	−	0.821872i	$-0.692930\pi$
$367$	6.85653	−	22.9024i	0.357908	−	1.19550i	0.927580	−	0.373624i	$-0.121885\pi$
$368$	−1.87433	−	1.57275i	−0.0977062	−	0.0819853i
$369$		0			0
$370$	0.886651	−	0.743989i	0.0460948	−	0.0386781i
$371$	−6.24733	−	14.4829i	−0.324345	−	0.751916i
$372$		0			0
$373$	3.30709	+	11.0464i	0.171235	+	0.571963i	0.999925	+	0.0122560i	$0.00390131\pi$
$373$	3.30709	+	11.0464i	0.171235	+	0.571963i	−0.828690	+	0.559707i	$0.810914\pi$
$374$	−7.16937	+	16.6205i	−0.370719	+	0.859423i
$375$		0			0
$376$	−17.5600	+	11.5494i	−0.905589	+	0.595615i
$377$	1.46658	−	2.54020i	0.0755329	−	0.130827i
$378$		0			0
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	−0.999282	−	0.0378763i	$-0.987941\pi$
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	0.466839	−	0.884342i	$-0.345393\pi$
$380$	−8.20663	−	4.12152i	−0.420991	−	0.211430i
$381$		0			0
$382$	−2.69132	−	3.61508i	−0.137700	−	0.184963i
$383$	10.8805	−	11.5326i	0.555967	−	0.589290i	−0.387040	−	0.922063i	$-0.626503\pi$
$383$	10.8805	−	11.5326i	0.555967	−	0.589290i	0.943007	+	0.332772i	$0.107984\pi$
$384$		0			0
$385$	−28.2572	−	3.30279i	−1.44012	−	0.168326i
$386$	0.129079	+	0.0469808i	0.00656994	+	0.00239126i
$387$		0			0
$388$	6.51155	−	2.37001i	0.330574	−	0.120319i
$389$	−27.7406	+	6.57464i	−1.40650	+	0.333347i	−0.862636	−	0.505825i	$-0.831188\pi$
$389$	−27.7406	+	6.57464i	−1.40650	+	0.333347i	−0.543866	+	0.839172i	$0.683040\pi$
$390$		0			0
$391$	13.2266	+	8.69929i	0.668899	+	0.439942i
$392$	17.6337	−	8.85596i	0.890635	−	0.447293i
$393$		0			0
$394$	6.01520	+	6.37574i	0.303041	+	0.321205i
$395$	−2.89074	+	16.3942i	−0.145449	+	0.824882i
$396$		0			0
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	0.737117	+	0.675765i	$0.236187\pi$
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	−0.461538	+	0.887120i	$0.652702\pi$
$398$	9.55738	−	12.8378i	0.479068	−	0.643500i
$399$		0			0
$400$	−1.93463	−	0.458515i	−0.0967314	−	0.0229258i
$401$	−16.9325	+	1.97912i	−0.845568	+	0.0988328i	−0.527835	−	0.849347i	$-0.676996\pi$
$401$	−16.9325	+	1.97912i	−0.845568	+	0.0988328i	−0.317734	+	0.948180i	$0.602922\pi$
$402$		0			0
$403$	0.171910	+	2.95158i	0.00856345	+	0.147029i
$404$	13.2952			0.661458
$405$		0			0
$406$	1.93980			0.0962705
$407$	−0.293936	−	5.04668i	−0.0145698	−	0.250155i
$408$		0			0
$409$	23.6758	−	2.76730i	1.17069	−	0.136834i	0.491555	−	0.870846i	$-0.336429\pi$
$409$	23.6758	−	2.76730i	1.17069	−	0.136834i	0.679136	+	0.734012i	$0.262354\pi$
$410$	−0.768892	−	0.182231i	−0.0379728	−	0.00899973i
$411$		0			0
$412$	−2.70034	+	3.62719i	−0.133036	+	0.178699i
$413$	−3.47862	−	19.7282i	−0.171172	−	0.970762i
$414$		0			0
$415$	−0.416966	+	2.36473i	−0.0204681	+	0.116080i
$416$	−18.0376	−	19.1188i	−0.884368	−	0.937375i
$417$		0			0
$418$	15.7601	−	7.91501i	0.770851	−	0.387136i
$419$	13.1474	+	8.64720i	0.642294	+	0.422443i	0.828439	−	0.560079i	$-0.189229\pi$
$419$	13.1474	+	8.64720i	0.642294	+	0.422443i	−0.186146	+	0.982522i	$0.559600\pi$
$420$		0			0
$421$	−22.9228	+	5.43281i	−1.11719	+	0.264779i	−0.747425	−	0.664346i	$-0.768710\pi$
$421$	−22.9228	+	5.43281i	−1.11719	+	0.264779i	−0.369766	+	0.929125i	$0.620562\pi$
$422$	0.874971	−	0.318464i	0.0425929	−	0.0155026i
$423$		0			0
$424$	−10.3281	−	3.75912i	−0.501577	−	0.182559i
$425$	12.7772	+	1.49344i	0.619784	+	0.0724424i
$426$		0			0
$427$	−17.7148	+	18.7766i	−0.857280	+	0.908664i
$428$	−13.9479	−	18.7353i	−0.674199	−	0.905606i
$429$		0			0
$430$	8.67982	+	4.35917i	0.418578	+	0.210218i
$431$	0.705848	+	1.22256i	0.0339995	+	0.0588888i	0.882524	−	0.470267i	$-0.155842\pi$
$431$	0.705848	+	1.22256i	0.0339995	+	0.0588888i	−0.848525	+	0.529155i	$0.822509\pi$
$432$		0			0
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	−0.978929	−	0.204200i	$-0.934541\pi$
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	0.666307	+	0.745677i	$0.267874\pi$
$434$	−1.63361	+	1.07444i	−0.0784159	+	0.0515750i
$435$		0			0
$436$	−4.20123	+	9.73954i	−0.201202	+	0.466440i
$437$	−4.42379	−	14.7765i	−0.211619	−	0.706856i
$438$		0			0
$439$	8.21406	+	19.0423i	0.392036	+	0.908840i	0.993904	+	0.110246i	$0.0351637\pi$
$439$	8.21406	+	19.0423i	0.392036	+	0.908840i	−0.601869	+	0.798595i	$0.705577\pi$
$440$	−15.1863	+	12.7428i	−0.723979	+	0.607490i
$441$		0			0
$442$	12.3238	+	10.3409i	0.586182	+	0.491865i
$443$	−9.74198	+	32.5405i	−0.462855	+	1.54604i	0.334417	+	0.942425i	$0.391461\pi$
$443$	−9.74198	+	32.5405i	−0.462855	+	1.54604i	−0.797273	+	0.603619i	$0.793725\pi$
$444$		0			0
$445$	−0.0897847	+	1.54154i	−0.00425621	+	0.0730762i
$446$	−0.677095	+	11.6253i	−0.0320614	+	0.550473i
$447$		0			0
$448$	3.44129	−	11.4947i	0.162586	−	0.543075i
$449$	0.919709	+	0.771727i	0.0434038	+	0.0364201i	0.664231	−	0.747527i	$-0.268759\pi$
$449$	0.919709	+	0.771727i	0.0434038	+	0.0364201i	−0.620828	+	0.783947i	$0.713203\pi$
$450$		0			0
$451$	−2.64380	+	2.21841i	−0.124492	+	0.104461i
$452$	5.51293	+	12.7804i	0.259306	+	0.601140i
$453$		0			0
$454$	−5.51383	−	18.4175i	−0.258777	−	0.864375i
$455$	−10.0150	+	23.2173i	−0.469509	+	1.08844i
$456$		0			0
$457$	26.7801	−	17.6135i	1.25272	−	0.823926i	0.262702	−	0.964877i	$-0.415386\pi$
$457$	26.7801	−	17.6135i	1.25272	−	0.823926i	0.990017	+	0.140951i	$0.0450161\pi$
$458$	0.596704	−	1.03352i	0.0278821	−	0.0482933i
$459$		0			0
$460$	3.55340	+	6.15466i	0.165678	+	0.286963i
$461$	0.300873	+	0.151104i	0.0140130	+	0.00703761i	0.455792	−	0.890086i	$-0.349356\pi$
$461$	0.300873	+	0.151104i	0.0140130	+	0.00703761i	−0.441779	+	0.897124i	$0.645652\pi$
$462$		0			0
$463$	−1.76325	−	2.36845i	−0.0819451	−	0.110071i	0.759260	−	0.650787i	$-0.225561\pi$
$463$	−1.76325	−	2.36845i	−0.0819451	−	0.110071i	−0.841205	+	0.540716i	$0.818153\pi$
$464$	−0.317324	+	0.336343i	−0.0147314	+	0.0156144i
$465$		0			0
$466$	10.9142	+	1.27568i	0.505590	+	0.0590950i
$467$	−3.55605	−	1.29430i	−0.164554	−	0.0598929i	0.258429	−	0.966030i	$-0.416795\pi$
$467$	−3.55605	−	1.29430i	−0.164554	−	0.0598929i	−0.422984	+	0.906137i	$0.639017\pi$
$468$		0			0
$469$	18.9360	−	6.89213i	0.874382	−	0.318249i
$470$	8.93506	−	2.11765i	0.412144	−	0.0976799i
$471$		0			0
$472$	−11.6627	−	7.67068i	−0.536819	−	0.353072i
$473$	37.9099	−	19.0391i	1.74310	−	0.875418i
$474$		0			0
$475$	−8.60123	−	9.11677i	−0.394651	−	0.418306i
$476$	4.20172	−	23.8292i	0.192586	−	1.09221i
$477$		0			0
$478$	3.11022	+	17.6389i	0.142258	+	0.806785i
$479$	−1.89106	+	2.54013i	−0.0864047	+	0.116062i	−0.843224	−	0.537563i	$-0.819345\pi$
$479$	−1.89106	+	2.54013i	−0.0864047	+	0.116062i	0.756819	+	0.653625i	$0.226752\pi$
$480$		0			0
$481$	−4.37186	−	1.03615i	−0.199339	−	0.0472443i
$482$	−5.48721	+	0.641362i	−0.249935	+	0.0292133i
$483$		0			0
$484$	1.17504	+	20.1747i	0.0534110	+	0.917032i
$485$	−7.38607			−0.335384
$486$		0			0
$487$	1.22501			0.0555106			0.0277553	−	0.999615i	$-0.491164\pi$
$487$	1.22501			0.0555106			0.0277553	+	0.999615i	$0.491164\pi$
$488$	1.04591	+	17.9575i	0.0473460	+	0.812900i
$489$		0			0
$490$	−8.56282	+	1.00085i	−0.386829	+	0.0452138i
$491$	−39.4547	−	9.35094i	−1.78057	−	0.422002i	−0.797212	−	0.603700i	$-0.793693\pi$
$491$	−39.4547	−	9.35094i	−1.78057	−	0.422002i	−0.983354	+	0.181698i	$0.941841\pi$
$492$		0			0
$493$	1.78662	−	2.39985i	0.0804653	−	0.108084i
$494$	−2.72183	−	15.4363i	−0.122461	−	0.694512i
$495$		0			0
$496$	0.0809373	−	0.459018i	0.00363419	−	0.0206105i
$497$	−15.9987	−	16.9576i	−0.717639	−	0.760652i
$498$		0			0
$499$	−36.7745	+	18.4688i	−1.64625	+	0.826778i	−0.648396	+	0.761303i	$0.724560\pi$
$499$	−36.7745	+	18.4688i	−1.64625	+	0.826778i	−0.997854	+	0.0654753i	$0.979144\pi$
$500$	13.4179	+	8.82507i	0.600065	+	0.394669i
$501$		0			0
$502$	−0.0505470	+	0.0119799i	−0.00225602	+	0.000534687i
$503$	9.54144	−	3.47280i	0.425432	−	0.154845i	−0.120426	−	0.992722i	$-0.538426\pi$
$503$	9.54144	−	3.47280i	0.425432	−	0.154845i	0.545858	+	0.837878i	$0.316204\pi$
$504$		0			0
$505$	−13.3166	−	4.84686i	−0.592582	−	0.215682i
$506$	−13.5557	−	1.58443i	−0.602623	−	0.0704366i
$507$		0			0
$508$	3.70433	−	3.92636i	0.164353	−	0.174204i
$509$	14.4794	+	19.4492i	0.641789	+	0.862073i	0.997363	−	0.0725757i	$-0.0231219\pi$
$509$	14.4794	+	19.4492i	0.641789	+	0.862073i	−0.355574	+	0.934648i	$0.615714\pi$
$510$		0			0
$511$	14.9518	+	7.50907i	0.661428	+	0.332182i
$512$	3.94773	+	6.83768i	0.174467	+	0.302186i
$513$		0			0
$514$	7.55901	−	13.0926i	0.333414	−	0.577490i
$515$	4.02703	−	2.64862i	0.177452	−	0.116712i
$516$		0			0
$517$	15.8851	−	36.8258i	0.698626	−	1.61960i
$518$	−0.852189	−	2.84651i	−0.0374430	−	0.125068i
$519$		0			0
$520$	6.97867	+	16.1784i	0.306035	+	0.709469i
$521$	−4.86477	+	4.08202i	−0.213129	+	0.178837i	−0.743102	−	0.669178i	$-0.766646\pi$
$521$	−4.86477	+	4.08202i	−0.213129	+	0.178837i	0.529973	+	0.848014i	$0.322202\pi$
$522$		0			0
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	0.977862	−	0.209250i	$-0.0671024\pi$
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	−0.0362674	+	0.999342i	$0.511547\pi$
$524$	−6.63341	+	22.1571i	−0.289782	+	0.967939i
$525$		0			0
$526$	0.684376	−	11.7503i	0.0298402	−	0.512337i
$527$	−0.175350	+	3.01065i	−0.00763838	+	0.131146i
$528$		0			0
$529$	3.17303	−	10.5987i	0.137958	−	0.460812i
$530$	3.67848	+	3.08661i	0.159783	+	0.134074i
$531$		0			0
$532$	−18.0598	+	15.1540i	−0.782991	+	0.657008i
$533$	1.21492	+	2.81651i	0.0526242	+	0.121997i
$534$		0			0
$535$	7.14035	+	23.8504i	0.308704	+	1.03114i
$536$	5.56170	−	12.8935i	0.240229	−	0.556913i
$537$		0			0
$538$	−7.66360	+	5.04043i	−0.330401	+	0.217308i
$539$	−18.8268	+	32.6089i	−0.810926	+	1.40457i
$540$		0			0
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	0.835689	−	0.549203i	$-0.185068\pi$
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	−0.893468	+	0.449127i	$0.851735\pi$
$542$	2.01162	+	1.01028i	0.0864066	+	0.0433950i
$543$		0			0
$544$	−16.0102	−	21.5055i	−0.686433	−	0.922039i
$545$	7.75865	−	8.22369i	0.332344	−	0.352264i
$546$		0			0
$547$	−32.5857	−	3.80872i	−1.39326	−	0.162849i	−0.613881	−	0.789399i	$-0.710392\pi$
$547$	−32.5857	−	3.80872i	−1.39326	−	0.162849i	−0.779381	+	0.626550i	$0.784466\pi$
$548$	12.1088	+	4.40724i	0.517262	+	0.188268i
$549$		0			0
$550$	−10.4214	+	3.79308i	−0.444370	+	0.161737i
$551$	−2.83646	+	0.672254i	−0.120837	+	0.0286390i
$552$		0			0
$553$	35.7053	+	23.4837i	1.51834	+	0.998630i
$554$	1.60707	−	0.807103i	0.0682780	−	0.0342905i
$555$		0			0
$556$	15.1779	+	16.0876i	0.643686	+	0.682267i
$557$	1.71906	−	9.74928i	0.0728390	−	0.413090i	−0.926485	−	0.376331i	$-0.877185\pi$
$557$	1.71906	−	9.74928i	0.0728390	−	0.413090i	0.999324	−	0.0367591i	$-0.0117034\pi$
$558$		0			0
$559$	−6.54721	−	37.1311i	−0.276917	−	1.57048i
$560$	2.38037	−	3.19740i	0.100589	−	0.135115i
$561$		0			0
$562$	−4.82564	−	1.14370i	−0.203557	−	0.0482440i
$563$	6.98793	−	0.816772i	0.294506	−	0.0344228i	0.0324431	−	0.999474i	$-0.489671\pi$
$563$	6.98793	−	0.816772i	0.294506	−	0.0344228i	0.262063	+	0.965051i	$0.415597\pi$
$564$		0			0
$565$	−0.862634	−	14.8108i	−0.0362913	−	0.623097i
$566$	11.4745			0.482310
$567$		0			0
$568$	−16.2454			−0.681640
$569$	−0.228981	−	3.93146i	−0.00959940	−	0.164815i	−0.999701	−	0.0244612i	$-0.992213\pi$
$569$	−0.228981	−	3.93146i	−0.00959940	−	0.164815i	0.990101	−	0.140354i	$-0.0448241\pi$
$570$		0			0
$571$	−25.3946	+	2.96820i	−1.06273	+	0.124215i	−0.629448	−	0.777043i	$-0.716719\pi$
$571$	−25.3946	+	2.96820i	−1.06273	+	0.124215i	−0.433282	+	0.901258i	$0.642645\pi$
$572$	30.6923	+	7.27421i	1.28331	+	0.304150i
$573$		0			0
$574$	−1.21136	+	1.62715i	−0.0505614	+	0.0679157i
$575$	1.68431	+	9.55219i	0.0702405	+	0.398354i
$576$		0			0
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	−0.963099	−	0.269149i	$-0.913258\pi$
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	0.997071	+	0.0764818i	$0.0243687\pi$
$578$	2.14325	+	2.27172i	0.0891476	+	0.0944909i
$579$		0			0
$580$	1.20023	−	0.602780i	0.0498370	−	0.0250291i
$581$	5.15020	+	3.38734i	0.213666	+	0.140530i
$582$		0			0
$583$	20.4075	−	4.83666i	0.845191	−	0.200314i
$584$	10.9558	−	3.98757i	0.453353	−	0.165007i
$585$		0			0
$586$	−18.6213	−	6.77759i	−0.769238	−	0.279980i
$587$	−27.5853	−	3.22426i	−1.13857	−	0.133079i	−0.474152	−	0.880443i	$-0.657245\pi$
$587$	−27.5853	−	3.22426i	−1.13857	−	0.133079i	−0.664415	+	0.747363i	$0.731319\pi$
$588$		0			0
$589$	2.01639	−	2.13725i	0.0830838	−	0.0880637i
$590$	3.64190	+	4.89193i	0.149935	+	0.201397i
$591$		0			0
$592$	0.632966	+	0.317887i	0.0260147	+	0.0130651i
$593$	7.16631	+	12.4124i	0.294285	+	0.509717i	0.974818	−	0.223000i	$-0.0715851\pi$
$593$	7.16631	+	12.4124i	0.294285	+	0.509717i	−0.680533	+	0.732717i	$0.738252\pi$
$594$		0			0
$595$	−12.8956	+	22.3359i	−0.528669	+	0.915682i
$596$	27.0915	−	17.8184i	1.10971	−	0.729869i
$597$		0			0
$598$	−4.80443	+	11.1379i	−0.196468	+	0.455464i
$599$	−7.88798	−	26.3477i	−0.322294	−	1.07654i	−0.953618	−	0.301018i	$-0.902674\pi$
$599$	−7.88798	−	26.3477i	−0.322294	−	1.07654i	0.631324	−	0.775519i	$-0.282512\pi$
$600$		0			0
$601$	7.42657	+	17.2167i	0.302936	+	0.702285i	0.999890	−	0.0148309i	$-0.00472101\pi$
$601$	7.42657	+	17.2167i	0.302936	+	0.702285i	−0.696954	+	0.717116i	$0.745462\pi$
$602$	19.1011	−	16.0277i	0.778503	−	0.653242i
$603$		0			0
$604$	2.48176	+	2.08244i	0.100981	+	0.0847333i
$605$	6.17792	−	20.6357i	0.251168	−	0.838960i
$606$		0			0
$607$	−1.53553	+	26.3640i	−0.0623252	+	1.07008i	0.811660	+	0.584130i	$0.198564\pi$
$607$	−1.53553	+	26.3640i	−0.0623252	+	1.07008i	−0.873985	+	0.485952i	$0.838473\pi$
$608$	−1.51887	+	26.0780i	−0.0615983	+	1.05760i
$609$		0			0
$610$	2.25396	−	7.52875i	0.0912602	−	0.304830i
$611$	−27.3057	−	22.9122i	−1.10467	−	0.926928i
$612$		0			0
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.996062	−	0.0886553i	$-0.971743\pi$
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.0856560	+	0.996325i	$0.527299\pi$
$614$	3.77141	+	8.74312i	0.152202	+	0.352843i
$615$		0			0
$616$	14.5960	+	48.7542i	0.588092	+	1.96436i
$617$	−2.83253	+	6.56654i	−0.114033	+	0.264359i	−0.965669	−	0.259775i	$-0.916352\pi$
$617$	−2.83253	+	6.56654i	−0.114033	+	0.264359i	0.851636	+	0.524134i	$0.175611\pi$
$618$		0			0
$619$	15.7252	−	10.3426i	0.632050	−	0.415706i	−0.192657	−	0.981266i	$-0.561710\pi$
$619$	15.7252	−	10.3426i	0.632050	−	0.415706i	0.824707	+	0.565560i	$0.191340\pi$
$620$	−0.676908	+	1.17244i	−0.0271853	+	0.0470863i
$621$		0			0
$622$	−9.82235	−	17.0128i	−0.393841	−	0.682152i
$623$	3.54245	+	1.77908i	0.141925	+	0.0712775i
$624$		0			0
$625$	−1.83983	−	2.47133i	−0.0735934	−	0.0988530i
$626$	15.8555	−	16.8058i	0.633713	−	0.671696i
$627$		0			0
$628$	−27.1587	−	3.17440i	−1.08375	−	0.126672i
$629$	−4.30649	−	1.56744i	−0.171711	−	0.0624978i
$630$		0			0
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.741548	−	0.670900i	$-0.765908\pi$
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.136813	+	0.990597i	$0.543686\pi$
$632$	28.9766	−	6.86759i	1.15263	−	0.273178i
$633$		0			0
$634$	2.80004	+	1.84161i	0.111204	+	0.0731398i
$635$	−5.14171	+	2.58226i	−0.204042	+	0.102474i
$636$		0			0
$637$	22.9654	+	24.3419i	0.909923	+	0.964463i
$638$	−0.447890	+	2.54011i	−0.0177321	+	0.100564i
$639$		0			0
$640$	−2.37461	−	13.4671i	−0.0938648	−	0.532334i
$641$	−2.60302	+	3.49646i	−0.102813	+	0.138102i	−0.850552	−	0.525891i	$-0.823732\pi$
$641$	−2.60302	+	3.49646i	−0.102813	+	0.138102i	0.747739	+	0.663993i	$0.231139\pi$
$642$		0			0
$643$	18.4995	+	4.38447i	0.729550	+	0.172906i	0.578573	−	0.815631i	$-0.303610\pi$
$643$	18.4995	+	4.38447i	0.729550	+	0.172906i	0.150977	+	0.988537i	$0.451758\pi$
$644$	18.1209	−	2.11803i	0.714064	−	0.0834621i
$645$		0			0
$646$	−0.929625	−	15.9610i	−0.0365756	−	0.627979i
$647$	−20.6268			−0.810924			−0.405462	−	0.914112i	$-0.632889\pi$
$647$	−20.6268			−0.810924			−0.405462	+	0.914112i	$0.632889\pi$
$648$		0			0
$649$	26.6367			1.04558
$650$	0.573117	+	9.84004i	0.0224795	+	0.385958i
$651$		0			0
$652$	−24.3702	+	2.84846i	−0.954410	+	0.111554i
$653$	5.82928	+	1.38157i	0.228117	+	0.0540648i	0.343085	−	0.939304i	$-0.388528\pi$
$653$	5.82928	+	1.38157i	0.228117	+	0.0540648i	−0.114967	+	0.993369i	$0.536676\pi$
$654$		0			0
$655$	14.7217	−	19.7747i	0.575225	−	0.772661i
$656$	−0.0839701	−	0.476218i	−0.00327848	−	0.0185932i
$657$		0			0
$658$	4.09344	−	23.2150i	0.159579	−	0.905016i
$659$	26.6529	+	28.2504i	1.03825	+	1.10048i	0.994843	+	0.101423i	$0.0323394\pi$
$659$	26.6529	+	28.2504i	1.03825	+	1.10048i	0.0434061	+	0.999058i	$0.486179\pi$
$660$		0			0
$661$	27.6987	−	13.9108i	1.07736	−	0.541068i	0.180583	−	0.983560i	$-0.442202\pi$
$661$	27.6987	−	13.9108i	1.07736	−	0.541068i	0.896773	+	0.442491i	$0.145905\pi$
$662$	−18.1731	−	11.9527i	−0.706319	−	0.464553i
$663$		0			0
$664$	4.17964	−	0.990594i	0.162202	−	0.0384425i
$665$	23.6135	−	8.59460i	0.915691	−	0.333284i
$666$		0			0
$667$	2.11981	+	0.771549i	0.0820795	+	0.0298745i
$668$	4.67768	+	0.546743i	0.180985	+	0.0211541i
$669$		0			0
$670$	−4.21000	+	4.46233i	−0.162646	+	0.172395i
$671$	−20.4972	−	27.5325i	−0.791285	−	1.06288i
$672$		0			0
$673$	−34.4849	−	17.3190i	−1.32930	−	0.667598i	−0.364650	−	0.931145i	$-0.618811\pi$
$673$	−34.4849	−	17.3190i	−1.32930	−	0.667598i	−0.964646	+	0.263547i	$0.915108\pi$
$674$	10.5125	+	18.2082i	0.404926	+	0.701352i
$675$		0			0
$676$	4.98742	−	8.63847i	0.191824	−	0.332249i
$677$	−3.33250	+	2.19182i	−0.128078	+	0.0842386i	−0.611932	−	0.790911i	$-0.709607\pi$
$677$	−3.33250	+	2.19182i	−0.128078	+	0.0842386i	0.483853	+	0.875149i	$0.339237\pi$
$678$		0			0
$679$	−7.51016	+	17.4105i	−0.288214	+	0.668154i
$680$	5.15441	+	17.2169i	0.197663	+	0.660239i
$681$		0			0
$682$	−1.02976	−	2.38725i	−0.0394316	−	0.0914127i
$683$	32.2624	−	27.0713i	1.23449	−	1.03586i	0.236551	−	0.971619i	$-0.423983\pi$
$683$	32.2624	−	27.0713i	1.23449	−	1.03586i	0.997935	−	0.0642370i	$-0.0204614\pi$
$684$		0			0
$685$	−10.5217	−	8.82872i	−0.402012	−	0.337328i
$686$	−0.383084	+	1.27959i	−0.0146262	+	0.0488550i
$687$		0			0
$688$	−0.345609	+	5.93388i	−0.0131762	+	0.226227i
$689$	1.08383	−	18.6086i	0.0412905	−	0.708930i
$690$		0			0
$691$	2.45234	−	8.19140i	0.0932916	−	0.311616i	−0.898589	−	0.438792i	$-0.855406\pi$
$691$	2.45234	−	8.19140i	0.0932916	−	0.311616i	0.991880	+	0.127177i	$0.0405916\pi$
$692$	19.8777	+	16.6794i	0.755638	+	0.634056i
$693$		0			0
$694$	18.2596	−	15.3216i	0.693125	−	0.581601i
$695$	−9.33753	−	21.6468i	−0.354193	−	0.821111i
$696$		0			0
$697$	0.897337	+	2.99731i	0.0339891	+	0.113531i
$698$	2.46881	−	5.72333i	0.0934457	−	0.216631i
$699$		0			0
$700$	12.3862	−	8.14656i	0.468156	−	0.307911i
$701$	−0.440975	+	0.763791i	−0.0166554	+	0.0288480i	−0.874233	−	0.485507i	$-0.838635\pi$
$701$	−0.440975	+	0.763791i	−0.0166554	+	0.0288480i	0.857578	+	0.514355i	$0.171968\pi$
$702$		0			0
$703$	2.23259	+	3.86697i	0.0842039	+	0.145845i
$704$	14.2574	+	7.16036i	0.537348	+	0.269866i
$705$		0			0
$706$	10.1883	+	13.6853i	0.383443	+	0.515053i
$707$	−24.9654	+	26.4618i	−0.938921	+	0.995198i
$708$		0			0
$709$	39.9617	+	4.67085i	1.50079	+	0.175417i	0.826453	−	0.563005i	$-0.190355\pi$
$709$	39.9617	+	4.67085i	1.50079	+	0.175417i	0.674338	+	0.738423i	$0.264429\pi$
$710$	6.66953	+	2.42751i	0.250303	+	0.0911028i
$711$		0			0
$712$	2.59569	−	0.944754i	0.0972777	−	0.0354062i
$713$	−2.21257	+	0.524390i	−0.0828615	+	0.0196385i
$714$		0			0
$715$	−28.0900	−	18.4751i	−1.05051	−	0.690930i
$716$	−14.7537	+	7.40960i	−0.551372	+	0.276910i
$717$		0			0
$718$	−9.28413	−	9.84060i	−0.346481	−	0.367248i
$719$	−2.39151	+	13.5629i	−0.0891883	+	0.505812i	0.907186	+	0.420730i	$0.138226\pi$
$719$	−2.39151	+	13.5629i	−0.0891883	+	0.505812i	−0.996374	+	0.0850815i	$0.972885\pi$
$720$		0			0
$721$	−2.14866	−	12.1857i	−0.0800203	−	0.453817i
$722$	−0.434796	+	0.584032i	−0.0161814	+	0.0217354i
$723$		0			0
$724$	21.3369	+	5.05695i	0.792981	+	0.187940i
$725$	1.82070	−	0.212809i	0.0676190	−	0.00790353i
$726$		0			0
$727$	0.725932	+	12.4638i	0.0269233	+	0.462256i	0.984646	+	0.174563i	$0.0558512\pi$
$727$	0.725932	+	12.4638i	0.0269233	+	0.462256i	−0.957723	+	0.287693i	$0.907112\pi$
$728$	45.2317			1.67640
$729$		0			0
$730$	−5.09374			−0.188528
$731$	−2.23616	−	38.3933i	−0.0827072	−	1.42003i
$732$		0			0
$733$	26.6912	−	3.11976i	0.985864	−	0.115231i	0.392145	−	0.919903i	$-0.371733\pi$
$733$	26.6912	−	3.11976i	0.985864	−	0.115231i	0.593719	+	0.804673i	$0.297659\pi$
$734$	18.1806	+	4.30889i	0.671059	+	0.159044i
$735$		0			0
$736$	12.0717	−	16.2151i	0.444967	−	0.597695i
$737$	4.65283	+	26.3875i	0.171389	+	0.971996i
$738$		0			0
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	0.802365	+	0.596833i	$0.203575\pi$
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	−0.958106	+	0.286415i	$0.907536\pi$
$740$	−1.41182	−	1.49644i	−0.0518996	−	0.0550103i
$741$		0			0
$742$	11.0161	−	5.53247i	0.404412	−	0.203103i
$743$	30.1360	+	19.8208i	1.10558	+	0.727154i	0.964826	−	0.262890i	$-0.0846757\pi$
$743$	30.1360	+	19.8208i	1.10558	+	0.727154i	0.140758	+	0.990044i	$0.455046\pi$
$744$		0			0
$745$	−33.6311	+	7.97072i	−1.23215	+	0.292025i
$746$	−8.46844	+	3.08226i	−0.310052	+	0.112850i
$747$		0			0
$748$	30.2335	+	11.0041i	1.10544	+	0.402349i
$749$	63.4808	+	7.41984i	2.31954	+	0.271115i
$750$		0			0
$751$	1.60334	−	1.69945i	0.0585069	−	0.0620137i	−0.697459	−	0.716625i	$-0.745686\pi$
$751$	1.60334	−	1.69945i	0.0585069	−	0.0620137i	0.755966	+	0.654611i	$0.227168\pi$
$752$	3.35565	+	4.50742i	0.122368	+	0.164369i
$753$		0			0
$754$	2.04857	+	1.02883i	0.0746047	+	0.0374679i
$755$	−1.72660	−	2.99055i	−0.0628372	−	0.108837i
$756$		0			0
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	−0.680823	−	0.732448i	$-0.738378\pi$
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	0.974730	+	0.223386i	$0.0717109\pi$
$758$	13.5369	−	8.90334i	0.491681	−	0.323384i
$759$		0			0
$760$	6.93553	−	16.0784i	0.251578	−	0.583223i
$761$	13.0085	+	43.4514i	0.471557	+	1.57511i	0.781215	+	0.624262i	$0.214600\pi$
$761$	13.0085	+	43.4514i	0.471557	+	1.57511i	−0.309657	+	0.950848i	$0.600214\pi$
$762$		0			0
$763$	−11.4959	−	26.6506i	−0.416181	−	0.964817i
$764$	−6.13669	+	5.14929i	−0.222018	+	0.186295i
$765$		0			0
$766$	9.49250	+	7.96515i	0.342978	+	0.287793i
$767$	6.78980	−	22.6795i	0.245165	−	0.818910i
$768$		0			0
$769$	−1.06788	+	18.3348i	−0.0385087	+	0.661168i	0.922729	+	0.385448i	$0.125953\pi$
$769$	−1.06788	+	18.3348i	−0.0385087	+	0.661168i	−0.961238	+	0.275720i	$0.911084\pi$
$770$	1.29283	−	22.1971i	0.0465904	−	0.799927i
$771$		0			0
$772$	0.0700256	−	0.233902i	0.00252028	−	0.00841831i
$773$	22.5821	+	18.9486i	0.812222	+	0.681536i	0.951137	−	0.308769i	$-0.0999169\pi$
$773$	22.5821	+	18.9486i	0.812222	+	0.681536i	−0.138915	+	0.990304i	$0.544361\pi$
$774$		0			0
$775$	−1.41544	+	1.18769i	−0.0508441	+	0.0426633i
$776$	5.23326	+	12.1321i	0.187863	+	0.435515i
$777$		0			0
$778$	−6.39031	−	21.3451i	−0.229104	−	0.765260i
$779$	1.20741	−	2.79910i	0.0432601	−	0.100288i
$780$		0			0
$781$	25.8995	−	17.0344i	0.926758	−	0.609538i
$782$	−6.18635	+	10.7151i	−0.221224	+	0.383170i
$783$		0			0
$784$	−2.63788	−	4.56895i	−0.0942102	−	0.163177i
$785$	26.0454	+	13.0805i	0.929599	+	0.466862i
$786$		0			0
$787$	19.1430	+	25.7135i	0.682375	+	0.916588i	0.999494	−	0.0317973i	$-0.0101231\pi$
$787$	19.1430	+	25.7135i	0.682375	+	0.916588i	−0.317120	+	0.948386i	$0.602716\pi$
$788$	10.6919	−	11.3327i	0.380882	−	0.403712i
$789$		0			0
$790$	−12.9225	−	1.51043i	−0.459764	−	0.0537387i
$791$	−35.7894	−	13.0263i	−1.27252	−	0.463161i
$792$		0			0
$793$	−28.6670	+	10.4339i	−1.01799	+	0.370520i
$794$	−24.0469	+	5.69922i	−0.853393	+	0.202258i
$795$		0			0
$796$	−23.7680	−	15.6325i	−0.842435	−	0.554079i
$797$	10.5327	−	5.28974i	0.373088	−	0.187372i	−0.252368	−	0.967631i	$-0.581209\pi$
$797$	10.5327	−	5.28974i	0.373088	−	0.187372i	0.625456	+	0.780259i	$0.284913\pi$
$798$		0			0
$799$	−24.9506	−	26.4461i	−0.882689	−	0.935596i
$800$	2.85246	−	16.1771i	0.100850	−	0.571948i
$801$		0			0
$802$	−2.31363	−	13.1212i	−0.0816970	−	0.463327i
$803$	−13.2852	+	17.8451i	−0.468825	+	0.629741i
$804$		0			0
$805$	−18.9223	−	4.48468i	−0.666925	−	0.158064i
$806$	−2.29509	+	0.268257i	−0.0808410	+	0.00944895i
$807$		0			0
$808$	1.47399	+	25.3075i	0.0518549	+	0.890314i
$809$	21.4155			0.752929			0.376464	−	0.926431i	$-0.377140\pi$
$809$	21.4155			0.752929			0.376464	+	0.926431i	$0.377140\pi$
$810$		0			0
$811$	1.73790			0.0610258			0.0305129	−	0.999534i	$-0.490286\pi$
$811$	1.73790			0.0610258			0.0305129	+	0.999534i	$0.490286\pi$
$812$	−0.200480	−	3.44211i	−0.00703547	−	0.120794i
$813$		0			0
$814$	3.92419	−	0.458672i	0.137543	−	0.0160765i
$815$	25.4480	+	6.03128i	0.891404	+	0.211267i
$816$		0			0
$817$	−22.3760	+	30.0562i	−0.782837	+	1.05153i
$818$	3.23502	+	18.3467i	0.113110	+	0.641477i
$819$		0			0
$820$	−0.243897	+	1.38321i	−0.00851725	+	0.0483037i
$821$	6.12045	+	6.48730i	0.213605	+	0.226408i	0.825313	−	0.564675i	$-0.190999\pi$
$821$	6.12045	+	6.48730i	0.213605	+	0.226408i	−0.611708	+	0.791084i	$0.709517\pi$
$822$		0			0
$823$	1.65516	−	0.831255i	0.0576954	−	0.0289757i	−0.419718	−	0.907655i	$-0.637871\pi$
$823$	1.65516	−	0.831255i	0.0576954	−	0.0289757i	0.477413	+	0.878679i	$0.341575\pi$
$824$	−7.20378	−	4.73800i	−0.250955	−	0.165056i
$825$		0			0
$826$	15.2344	−	3.61061i	0.530072	−	0.125629i
$827$	−19.7686	+	7.19517i	−0.687420	+	0.250200i	−0.662030	−	0.749477i	$-0.730305\pi$
$827$	−19.7686	+	7.19517i	−0.687420	+	0.250200i	−0.0253900	+	0.999678i	$0.508083\pi$
$828$		0			0
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	0.247792	−	0.968813i	$-0.420295\pi$
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	−0.432921	+	0.901432i	$0.642517\pi$
$830$	−1.86397	−	0.217867i	−0.0646995	−	0.00756228i
$831$		0			0
$832$	9.73087	−	10.3141i	0.337357	−	0.357578i
$833$	20.3841	+	27.3807i	0.706269	+	0.948683i
$834$		0			0
$835$	−4.48592	−	2.25291i	−0.155242	−	0.0779653i
$836$	−15.6738	−	27.1478i	−0.542089	−	0.938925i
$837$		0			0
$838$	−6.14931	+	10.6509i	−0.212424	+	0.367930i
$839$	−19.9919	+	13.1489i	−0.690196	+	0.453949i	−0.845540	−	0.533911i	$-0.820722\pi$
$839$	−19.9919	+	13.1489i	−0.690196	+	0.453949i	0.155345	+	0.987860i	$0.450351\pi$
$840$		0			0
$841$	−11.3175	+	26.2368i	−0.390257	+	0.904717i
$842$	−5.28050	−	17.6381i	−0.181978	−	0.607849i
$843$		0			0
$844$	−0.655533	−	1.51970i	−0.0225644	−	0.0523101i
$845$	−8.14471	+	6.83422i	−0.280186	+	0.235104i
$846$		0			0
$847$	−42.3609	−	35.5450i	−1.45554	−	1.22134i
$848$	−0.842792	+	2.81512i	−0.0289416	+	0.0966717i
$849$		0			0
$850$	−0.584586	+	10.0370i	−0.0200511	+	0.344265i
$851$	0.200918	−	3.44963i	0.00688738	−	0.118252i
$852$		0			0
$853$	−1.93688	+	6.46964i	−0.0663176	+	0.221516i	−0.984724	−	0.174122i	$-0.944291\pi$
$853$	−1.93688	+	6.46964i	−0.0663176	+	0.221516i	0.918406	+	0.395638i	$0.129477\pi$
$854$	−15.4550	−	12.9683i	−0.528860	−	0.443766i
$855$		0			0
$856$	34.1166	−	28.6272i	1.16608	−	0.978457i
$857$	−7.46865	−	17.3143i	−0.255124	−	0.591444i	0.741730	−	0.670698i	$-0.234005\pi$
$857$	−7.46865	−	17.3143i	−0.255124	−	0.591444i	−0.996854	+	0.0792539i	$0.974746\pi$
$858$		0			0
$859$	−9.29717	−	31.0547i	−0.317215	−	1.05957i	−0.956774	−	0.290831i	$-0.906068\pi$
$859$	−9.29717	−	31.0547i	−0.317215	−	1.05957i	0.639559	−	0.768742i	$-0.279117\pi$
$860$	6.83814	−	15.8526i	0.233179	−	0.540569i
$861$		0			0
$862$	−0.921800	+	0.606277i	−0.0313966	+	0.0206499i
$863$	23.6121	−	40.8973i	0.803765	−	1.39216i	−0.113357	−	0.993554i	$-0.536160\pi$
$863$	23.6121	−	40.8973i	0.803765	−	1.39216i	0.917122	−	0.398607i	$-0.130506\pi$
$864$		0			0
$865$	−13.8292	−	23.9529i	−0.470208	−	0.814424i
$866$	−9.08673	−	4.56353i	−0.308780	−	0.155075i
$867$		0			0
$868$	2.07540	+	2.78775i	0.0704438	+	0.0946224i
$869$	−38.9955	+	41.3328i	−1.32283	+	1.40212i
$870$		0			0
$871$	23.6533	+	2.76468i	0.801462	+	0.0936775i
$872$	−19.0051	−	6.91730i	−0.643595	−	0.234249i
$873$		0			0
$874$	11.3280	−	4.12304i	0.383174	−	0.139464i
$875$	−42.7607	+	10.1345i	−1.44558	+	0.342608i
$876$		0			0
$877$	−4.70518	−	3.09464i	−0.158883	−	0.104499i	0.467578	−	0.883952i	$-0.345127\pi$
$877$	−4.70518	−	3.09464i	−0.158883	−	0.104499i	−0.626461	+	0.779453i	$0.715497\pi$
$878$	−14.4840	+	7.27416i	−0.488813	+	0.245491i
$879$		0			0
$880$	3.63729	+	3.85530i	0.122613	+	0.129962i
$881$	−0.984686	+	5.58443i	−0.0331749	+	0.188144i	−0.996892	−	0.0787820i	$-0.974897\pi$
$881$	−0.984686	+	5.58443i	−0.0331749	+	0.188144i	0.963717	+	0.266926i	$0.0860080\pi$
$882$		0			0
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	0.904437	+	0.426606i	$0.140291\pi$
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	−0.703985	+	0.710215i	$0.748598\pi$
$884$	17.0759	−	22.9369i	0.574324	−	0.771452i
$885$		0			0
$886$	−25.8316	−	6.12221i	−0.867830	−	0.205680i
$887$	−26.7020	+	3.12102i	−0.896567	+	0.104794i	−0.551879	−	0.833924i	$-0.686089\pi$
$887$	−26.7020	+	3.12102i	−0.896567	+	0.104794i	−0.344687	+	0.938718i	$0.612015\pi$
$888$		0			0
$889$	0.858840	+	14.7457i	0.0288046	+	0.494556i
$890$	−1.20683			−0.0404531
$891$		0			0
$892$	20.6987			0.693043
$893$	2.05976	+	35.3647i	0.0689273	+	1.18344i
$894$		0			0
$895$	17.4788	−	2.04298i	0.584252	−	0.0682892i
$896$	−34.1593	−	8.09590i	−1.14118	−	0.270465i
$897$		0			0
$898$	−0.560327	+	0.752650i	−0.0186984	+	0.0251163i
$899$	0.0746222	+	0.423204i	0.00248879	+	0.0141146i
$900$		0			0
$901$	3.30159	−	18.7243i	0.109992	−	0.623796i
$902$	−1.85100	−	1.96195i	−0.0616317	−	0.0653258i
$903$		0			0
$904$	−23.7165	+	11.9109i	−0.788798	+	0.396149i
$905$	−19.5279	−	12.8437i	−0.649128	−	0.426938i
$906$		0			0
$907$	29.6181	−	7.01961i	0.983452	−	0.233082i	0.292724	−	0.956197i	$-0.405438\pi$
$907$	29.6181	−	7.01961i	0.983452	−	0.233082i	0.690728	+	0.723115i	$0.257290\pi$
$908$	−32.1114	+	11.6876i	−1.06565	+	0.387866i
$909$		0			0
$910$	−18.5699	−	6.75888i	−0.615585	−	0.224055i
$911$	−13.9708	−	1.63296i	−0.462875	−	0.0541023i	−0.118540	−	0.992949i	$-0.537821\pi$
$911$	−13.9708	−	1.63296i	−0.462875	−	0.0541023i	−0.344335	+	0.938847i	$0.611895\pi$
$912$		0			0
$913$	−5.62478	+	5.96192i	−0.186153	+	0.197311i
$914$	14.9595	+	20.0941i	0.494816	+	0.664653i
$915$		0			0
$916$	−1.89562	−	0.952017i	−0.0626331	−	0.0314555i
$917$	−31.6440	−	54.8090i	−1.04498	−	1.80995i
$918$		0			0
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	−0.999691	−	0.0248384i	$-0.992093\pi$
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	0.521356	+	0.853339i	$0.325426\pi$
$920$	−11.3215	+	7.44628i	−0.373260	+	0.245497i
$921$		0			0
$922$	−0.104223	+	0.241615i	−0.00343239	+	0.00795717i
$923$	−7.90183	−	26.3939i	−0.260092	−	0.868767i
$924$		0			0
$925$	−1.11215	−	2.57825i	−0.0365672	−	0.0847724i
$926$	1.76780	−	1.48336i	0.0580935	−	0.0487462i
$927$		0			0
$928$	−2.92661	−	2.45572i	−0.0960706	−	0.0806128i
$929$	12.7796	−	42.6869i	0.419286	−	1.40051i	−0.444104	−	0.895975i	$-0.646478\pi$
$929$	12.7796	−	42.6869i	0.419286	−	1.40051i	0.863390	−	0.504537i	$-0.168337\pi$
$930$		0			0
$931$	1.93382	−	33.2024i	0.0633783	−	1.08816i
$932$	1.13567	−	19.4987i	0.0372002	−	0.638702i
$933$		0			0
$934$	0.848246	−	2.83334i	0.0277555	−	0.0927097i
$935$	−26.2707	−	22.0437i	−0.859143	−	0.720907i
$936$		0			0
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	−0.862999	−	0.505206i	$-0.831416\pi$
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	0.347673	+	0.937616i	$0.386972\pi$
$938$	6.23793	+	14.4611i	0.203676	+	0.472173i
$939$		0			0
$940$	−4.68115	−	15.6361i	−0.152682	−	0.509995i
$941$	22.4902	−	52.1381i	0.733160	−	1.69966i	0.0188529	−	0.999822i	$-0.493999\pi$
$941$	22.4902	−	52.1381i	0.733160	−	1.69966i	0.714307	−	0.699833i	$-0.246742\pi$
$942$		0			0
$943$	−1.97098	+	1.29633i	−0.0641838	+	0.0422144i
$944$	−1.86608	+	3.23215i	−0.0607359	+	0.105198i
$945$		0			0
$946$	16.5775	+	28.7131i	0.538982	+	0.933544i
$947$	−14.0976	−	7.08007i	−0.458110	−	0.230071i	0.204751	−	0.978814i	$-0.434362\pi$
$947$	−14.0976	−	7.08007i	−0.458110	−	0.230071i	−0.662861	+	0.748743i	$0.730658\pi$
$948$		0			0
$949$	11.8076	+	15.8603i	0.383290	+	0.514848i
$950$	6.72227	−	7.12519i	0.218099	−	0.231172i
$951$		0			0
$952$	45.8249	+	5.35617i	1.48519	+	0.173594i
$953$	47.3933	+	17.2497i	1.53522	+	0.558774i	0.964893	−	0.262645i	$-0.0845947\pi$
$953$	47.3933	+	17.2497i	1.53522	+	0.558774i	0.570326	+	0.821418i	$0.306817\pi$
$954$		0			0
$955$	8.02382	−	2.92043i	0.259645	−	0.0945030i
$956$	30.9783	−	7.34198i	1.00191	−	0.237457i
$957$		0			0
$958$	−2.06781	−	1.36002i	−0.0668080	−	0.0439403i
$959$	−31.5096	+	15.8247i	−1.01750	+	0.511006i
$960$		0			0
$961$	20.9762	+	22.2335i	0.676653	+	0.717210i
$962$	0.609760	−	3.45812i	0.0196594	−	0.111494i
$963$		0			0
$964$	1.70519	+	9.67059i	0.0549203	+	0.311469i
$965$	−0.155410	+	0.208751i	−0.00500281	+	0.00671994i
$966$		0			0
$967$	21.3040	+	5.04915i	0.685092	+	0.162370i	0.558399	−	0.829572i	$-0.311416\pi$
$967$	21.3040	+	5.04915i	0.685092	+	0.162370i	0.126692	+	0.991942i	$0.459564\pi$
$968$	−38.2725	+	4.47342i	−1.23013	+	0.143781i
$969$		0			0
$970$	−0.335645	−	5.76280i	−0.0107769	−	0.185032i
$971$	−21.3313			−0.684555			−0.342277	−	0.939599i	$-0.611198\pi$
$971$	−21.3313			−0.684555			−0.342277	+	0.939599i	$0.611198\pi$
$972$		0			0
$973$	−60.5205			−1.94020
$974$	0.0556682	+	0.955786i	0.00178372	+	0.0306254i
$975$		0			0
$976$	4.77681	−	0.558329i	0.152902	−	0.0178717i
$977$	6.97799	+	1.65381i	0.223246	+	0.0529102i	0.340716	−	0.940166i	$-0.389330\pi$
$977$	6.97799	+	1.65381i	0.223246	+	0.0529102i	−0.117471	+	0.993076i	$0.537479\pi$
$978$		0			0
$979$	−3.14760	+	4.22796i	−0.100598	+	0.135126i
$980$	2.66095	+	15.0910i	0.0850011	+	0.482065i
$981$		0			0
$982$	5.50290	−	31.2085i	0.175605	−	0.995904i
$983$	28.4197	+	30.1231i	0.906447	+	0.960777i	0.999391	−	0.0348939i	$-0.0111093\pi$
$983$	28.4197	+	30.1231i	0.906447	+	0.960777i	−0.0929443	+	0.995671i	$0.529628\pi$
$984$		0			0
$985$	−14.8406	+	7.45323i	−0.472861	+	0.237480i
$986$	1.95361	+	1.28491i	0.0622156	+	0.0409199i
$987$		0			0
$988$	−27.1099	+	6.42517i	−0.862481	+	0.204412i
$989$	27.2487	−	9.91773i	0.866460	−	0.315365i
$990$		0			0
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.985105	−	0.171953i	$-0.0550079\pi$
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.644105	+	0.764937i	$0.277230\pi$
$992$	3.82487	+	0.447063i	0.121440	+	0.0141943i
$993$		0			0
$994$	12.5037	−	13.2532i	0.396594	−	0.420365i
$995$	18.1075	+	24.3226i	0.574046	+	0.771077i
$996$		0			0
$997$	−23.6921	−	11.8986i	−0.750338	−	0.376834i	0.0321637	−	0.999483i	$-0.489760\pi$
$997$	−23.6921	−	11.8986i	−0.750338	−	0.376834i	−0.782501	+	0.622649i	$0.786056\pi$
$998$	−16.0810	−	27.8531i	−0.509035	−	0.881674i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.514.5		144
3.2	odd	2		729.2.g.a.514.4		144
9.2	odd	6		729.2.g.b.28.4		144
9.4	even	3		81.2.g.a.13.4	✓	144
9.5	odd	6		243.2.g.a.10.5		144
9.7	even	3		729.2.g.c.28.5		144
81.2	odd	54		729.2.g.a.217.4		144
81.22	even	27		6561.2.a.c.1.30		72
81.25	even	27		729.2.g.c.703.5		144
81.29	odd	54		243.2.g.a.73.5		144
81.52	even	27		81.2.g.a.25.4	yes	144
81.56	odd	54		729.2.g.b.703.4		144
81.59	odd	54		6561.2.a.d.1.43		72
81.79	even	27	inner	729.2.g.d.217.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.4	✓	144	9.4	even	3
81.2.g.a.25.4	yes	144	81.52	even	27
243.2.g.a.10.5		144	9.5	odd	6
243.2.g.a.73.5		144	81.29	odd	54
729.2.g.a.217.4		144	81.2	odd	54
729.2.g.a.514.4		144	3.2	odd	2
729.2.g.b.28.4		144	9.2	odd	6
729.2.g.b.703.4		144	81.56	odd	54
729.2.g.c.28.5		144	9.7	even	3
729.2.g.c.703.5		144	81.25	even	27
729.2.g.d.217.5		144	81.79	even	27	inner
729.2.g.d.514.5		144	1.1	even	1	trivial
6561.2.a.c.1.30		72	81.22	even	27
6561.2.a.d.1.43		72	81.59	odd	54

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	729.2.g.d.514.5

Level	$729$
Weight	$2$
Character	729.514
Analytic conductor	$5.821$
Analytic rank	$0$
Dimension	$144$
Inner twists	$2$