LMFDB - Embedded newform 819.2.ct.b.316.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.5
Root			$-0.485989i$ of defining polynomial
Character	$\chi$	$=$	819.316
Dual form			819.2.ct.b.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.420879 + 0.242995i) q^{2} +(-0.881907 - 1.52751i) q^{4} -1.06536i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.82917i q^{8} +(0.258876 - 0.448387i) q^{10} +(-4.98494 - 2.87806i) q^{11} +(1.77592 + 3.13785i) q^{13} -0.485989 q^{14} +(-1.31934 + 2.28516i) q^{16} +(-1.17266 - 2.03111i) q^{17} +(-5.36979 + 3.10025i) q^{19} +(-1.62734 + 0.939548i) q^{20} +(-1.39870 - 2.42263i) q^{22} +(-2.75674 + 4.77481i) q^{23} +3.86501 q^{25} +(-0.0150320 + 1.75219i) q^{26} +(1.52751 + 0.881907i) q^{28} +(2.80215 - 4.85347i) q^{29} +5.46420i q^{31} +(-4.27878 + 2.47036i) q^{32} -1.13980i q^{34} +(0.532679 + 0.922628i) q^{35} +(-4.08375 - 2.35775i) q^{37} -3.01337 q^{38} -1.94873 q^{40} +(-7.69141 - 4.44064i) q^{41} +(-4.77851 - 8.27662i) q^{43} +10.1527i q^{44} +(-2.32051 + 1.33975i) q^{46} +5.21864i q^{47} +(0.500000 - 0.866025i) q^{49} +(1.62670 + 0.939177i) q^{50} +(3.22689 - 5.48003i) q^{52} -1.52870 q^{53} +(-3.06616 + 5.31075i) q^{55} +(0.914587 + 1.58411i) q^{56} +(2.35873 - 1.36181i) q^{58} +(9.06406 - 5.23314i) q^{59} +(-3.82305 - 6.62171i) q^{61} +(-1.32777 + 2.29977i) q^{62} +2.87621 q^{64} +(3.34294 - 1.89199i) q^{65} +(2.83779 + 1.63840i) q^{67} +(-2.06836 + 3.58251i) q^{68} +0.517753i q^{70} +(-7.50761 + 4.33452i) q^{71} -7.63941i q^{73} +(-1.14584 - 1.98466i) q^{74} +(9.47131 + 5.46826i) q^{76} +5.75611 q^{77} -15.6147 q^{79} +(2.43451 + 1.40557i) q^{80} +(-2.15810 - 3.73794i) q^{82} +2.63313i q^{83} +(-2.16387 + 1.24931i) q^{85} -4.64461i q^{86} +(-5.26447 + 9.11832i) q^{88} +(-10.4502 - 6.03343i) q^{89} +(-3.10692 - 1.82950i) q^{91} +9.72476 q^{92} +(-1.26810 + 2.19642i) q^{94} +(3.30288 + 5.72075i) q^{95} +(14.5156 - 8.38057i) q^{97} +(0.420879 - 0.242995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40}+ \cdots - 54 q^{97}+O(q^{100}) $ 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.420879	+	0.242995i	0.297606	+	0.171823i	0.641367	−	0.767234i	$-0.278368\pi$
$2$	0.420879	+	0.242995i	0.297606	+	0.171823i	−0.343761	+	0.939057i	$0.611701\pi$
$3$		0			0
$3$		0			0
$4$	−0.881907	−	1.52751i	−0.440954	−	0.763754i
$5$		−	1.06536i		−	0.476443i	−0.971211	−	0.238221i	$-0.923436\pi$
$5$		−	1.06536i		−	0.476443i	0.971211	−	0.238221i	$-0.0765644\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	1.82917i		−	0.646710i
$9$		0			0
$10$	0.258876	−	0.448387i	0.0818639	−	0.141792i
$11$	−4.98494	−	2.87806i	−1.50302	−	0.867767i	−0.999994	−	0.00349358i	$-0.998888\pi$
$11$	−4.98494	−	2.87806i	−1.50302	−	0.867767i	−0.503022	−	0.864273i	$-0.667779\pi$
$12$		0			0
$13$	1.77592	+	3.13785i	0.492552	+	0.870283i
$13$	1.77592	+	3.13785i	0.492552	+	0.870283i
$14$	−0.485989			−0.129886
$15$		0			0
$16$	−1.31934	+	2.28516i	−0.329834	+	0.571289i
$17$	−1.17266	−	2.03111i	−0.284413	−	0.492618i	0.688054	−	0.725660i	$-0.258465\pi$
$17$	−1.17266	−	2.03111i	−0.284413	−	0.492618i	−0.972467	+	0.233042i	$0.925132\pi$
$18$		0			0
$19$	−5.36979	+	3.10025i	−1.23191	+	0.711246i	−0.967429	−	0.253144i	$-0.918535\pi$
$19$	−5.36979	+	3.10025i	−1.23191	+	0.711246i	−0.264485	+	0.964390i	$0.585202\pi$
$20$	−1.62734	+	0.939548i	−0.363885	+	0.210089i
$21$		0			0
$22$	−1.39870	−	2.42263i	−0.298205	−	0.516506i
$23$	−2.75674	+	4.77481i	−0.574820	+	0.995618i	0.421241	+	0.906949i	$0.361595\pi$
$23$	−2.75674	+	4.77481i	−0.574820	+	0.995618i	−0.996061	+	0.0886690i	$0.971739\pi$
$24$		0			0
$25$	3.86501			0.773002
$26$	−0.0150320	+	1.75219i	−0.00294801	+	0.343634i
$27$		0			0
$28$	1.52751	+	0.881907i	0.288672	+	0.166665i
$29$	2.80215	−	4.85347i	0.520346	−	0.901266i	−0.479374	−	0.877611i	$-0.659136\pi$
$29$	2.80215	−	4.85347i	0.520346	−	0.901266i	0.999720	−	0.0236554i	$-0.00753046\pi$
$30$		0			0
$31$			5.46420i			0.981400i	0.871329	+	0.490700i	$0.163259\pi$
$31$			5.46420i			0.981400i	−0.871329	+	0.490700i	$0.836741\pi$
$32$	−4.27878	+	2.47036i	−0.756389	+	0.436701i
$33$		0			0
$34$		−	1.13980i		−	0.195475i
$35$	0.532679	+	0.922628i	0.0900393	+	0.155953i
$36$		0			0
$37$	−4.08375	−	2.35775i	−0.671364	−	0.387612i	0.125229	−	0.992128i	$-0.460033\pi$
$37$	−4.08375	−	2.35775i	−0.671364	−	0.387612i	−0.796593	+	0.604515i	$0.793367\pi$
$38$	−3.01337			−0.488834
$39$		0			0
$40$	−1.94873			−0.308121
$41$	−7.69141	−	4.44064i	−1.20120	−	0.693511i	−0.240375	−	0.970680i	$-0.577270\pi$
$41$	−7.69141	−	4.44064i	−1.20120	−	0.693511i	−0.960821	+	0.277169i	$0.910604\pi$
$42$		0			0
$43$	−4.77851	−	8.27662i	−0.728716	−	1.26217i	−0.957426	−	0.288679i	$-0.906784\pi$
$43$	−4.77851	−	8.27662i	−0.728716	−	1.26217i	0.228710	−	0.973495i	$-0.426549\pi$
$44$			10.1527i			1.53058i
$45$		0			0
$46$	−2.32051	+	1.33975i	−0.342140	+	0.197535i
$47$			5.21864i			0.761217i	0.924736	+	0.380608i	$0.124285\pi$
$47$			5.21864i			0.761217i	−0.924736	+	0.380608i	$0.875715\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	1.62670	+	0.939177i	0.230050	+	0.132820i
$51$		0			0
$52$	3.22689	−	5.48003i	0.447489	−	0.759943i
$53$	−1.52870			−0.209982			−0.104991	−	0.994473i	$-0.533481\pi$
$53$	−1.52870			−0.209982			−0.104991	+	0.994473i	$0.533481\pi$
$54$		0			0
$55$	−3.06616	+	5.31075i	−0.413441	+	0.716102i
$56$	0.914587	+	1.58411i	0.122217	+	0.211686i
$57$		0			0
$58$	2.35873	−	1.36181i	0.309717	−	0.178815i
$59$	9.06406	−	5.23314i	1.18004	−	0.681297i	0.224016	−	0.974585i	$-0.428083\pi$
$59$	9.06406	−	5.23314i	1.18004	−	0.681297i	0.956024	+	0.293289i	$0.0947497\pi$
$60$		0			0
$61$	−3.82305	−	6.62171i	−0.489491	−	0.847823i	0.510436	−	0.859916i	$-0.329484\pi$
$61$	−3.82305	−	6.62171i	−0.489491	−	0.847823i	−0.999927	+	0.0120926i	$0.996151\pi$
$62$	−1.32777	+	2.29977i	−0.168627	+	0.292071i
$63$		0			0
$64$	2.87621			0.359526
$65$	3.34294	−	1.89199i	0.414640	−	0.234673i
$66$		0			0
$67$	2.83779	+	1.63840i	0.346691	+	0.200162i	0.663227	−	0.748418i	$-0.269186\pi$
$67$	2.83779	+	1.63840i	0.346691	+	0.200162i	−0.316536	+	0.948581i	$0.602520\pi$
$68$	−2.06836	+	3.58251i	−0.250826	+	0.434443i
$69$		0			0
$70$			0.517753i			0.0618833i
$71$	−7.50761	+	4.33452i	−0.890990	+	0.514413i	−0.874266	−	0.485447i	$-0.838657\pi$
$71$	−7.50761	+	4.33452i	−0.890990	+	0.514413i	−0.0167238	+	0.999860i	$0.505324\pi$
$72$		0			0
$73$		−	7.63941i		−	0.894126i	−0.894503	−	0.447063i	$-0.852470\pi$
$73$		−	7.63941i		−	0.894126i	0.894503	−	0.447063i	$-0.147530\pi$
$74$	−1.14584	−	1.98466i	−0.133202	−	0.230712i
$75$		0			0
$76$	9.47131	+	5.46826i	1.08643	+	0.627253i
$77$	5.75611			0.655970
$78$		0			0
$79$	−15.6147			−1.75679			−0.878397	−	0.477932i	$-0.841387\pi$
$79$	−15.6147			−1.75679			−0.878397	+	0.477932i	$0.841387\pi$
$80$	2.43451	+	1.40557i	0.272187	+	0.157147i
$81$		0			0
$82$	−2.15810	−	3.73794i	−0.238322	−	0.412786i
$83$			2.63313i			0.289024i	0.989503	+	0.144512i	$0.0461612\pi$
$83$			2.63313i			0.289024i	−0.989503	+	0.144512i	$0.953839\pi$
$84$		0			0
$85$	−2.16387	+	1.24931i	−0.234704	+	0.135507i
$86$		−	4.64461i		−	0.500841i
$87$		0			0
$88$	−5.26447	+	9.11832i	−0.561194	+	0.972016i
$89$	−10.4502	−	6.03343i	−1.10772	−	0.639542i	−0.169481	−	0.985533i	$-0.554209\pi$
$89$	−10.4502	−	6.03343i	−1.10772	−	0.639542i	−0.938238	+	0.345991i	$0.887543\pi$
$90$		0			0
$91$	−3.10692	−	1.82950i	−0.325694	−	0.191783i
$92$	9.72476			1.01388
$93$		0			0
$94$	−1.26810	+	2.19642i	−0.130795	+	0.226543i
$95$	3.30288	+	5.72075i	0.338868	+	0.586936i
$96$		0			0
$97$	14.5156	−	8.38057i	1.47383	−	0.850918i	0.474268	−	0.880381i	$-0.342713\pi$
$97$	14.5156	−	8.38057i	1.47383	−	0.850918i	0.999566	+	0.0294624i	$0.00937954\pi$
$98$	0.420879	−	0.242995i	0.0425152	−	0.0245462i
$99$		0			0
$100$	−3.40858	−	5.90384i	−0.340858	−	0.590384i
$101$	1.28815	−	2.23115i	0.128176	−	0.222008i	−0.794794	−	0.606880i	$-0.792421\pi$
$101$	1.28815	−	2.23115i	0.128176	−	0.222008i	0.922970	+	0.384872i	$0.125754\pi$
$102$		0			0
$103$	10.3824			1.02301			0.511506	−	0.859280i	$-0.329088\pi$
$103$	10.3824			1.02301			0.511506	+	0.859280i	$0.329088\pi$
$104$	5.73967	−	3.24847i	0.562821	−	0.318539i
$105$		0			0
$106$	−0.643396	−	0.371465i	−0.0624921	−	0.0360798i
$107$	8.51774	−	14.7532i	0.823441	−	1.42624i	−0.0796637	−	0.996822i	$-0.525385\pi$
$107$	8.51774	−	14.7532i	0.823441	−	1.42624i	0.903105	−	0.429420i	$-0.141282\pi$
$108$		0			0
$109$			1.86126i			0.178276i	0.996019	+	0.0891380i	$0.0284112\pi$
$109$			1.86126i			0.178276i	−0.996019	+	0.0891380i	$0.971589\pi$
$110$	−2.58097	+	1.49012i	−0.246086	+	0.142078i
$111$		0			0
$112$		−	2.63867i		−	0.249331i
$113$	−2.38371	−	4.12870i	−0.224240	−	0.388396i	0.731851	−	0.681465i	$-0.238657\pi$
$113$	−2.38371	−	4.12870i	−0.224240	−	0.388396i	−0.956091	+	0.293069i	$0.905323\pi$
$114$		0			0
$115$	5.08689	+	2.93692i	0.474355	+	0.273869i
$116$	−9.88495			−0.917794
$117$		0			0
$118$	5.08650			0.468250
$119$	2.03111	+	1.17266i	0.186192	+	0.107498i
$120$		0			0
$121$	11.0664	+	19.1676i	1.00604	+	1.74251i
$122$		−	3.71592i		−	0.336423i
$123$		0			0
$124$	8.34662	−	4.81892i	0.749548	−	0.432752i
$125$		−	9.44442i		−	0.844734i
$126$		0			0
$127$	−0.593804	+	1.02850i	−0.0526916	+	0.0912645i	−0.891168	−	0.453673i	$-0.850113\pi$
$127$	−0.593804	+	1.02850i	−0.0526916	+	0.0912645i	0.838477	+	0.544938i	$0.183447\pi$
$128$	9.76810	+	5.63962i	0.863386	+	0.498476i
$129$		0			0
$130$	1.86672	+	0.0160144i	0.163722	+	0.00140456i
$131$	14.8261			1.29537			0.647683	−	0.761910i	$-0.275738\pi$
$131$	14.8261			1.29537			0.647683	+	0.761910i	$0.275738\pi$
$132$		0			0
$133$	3.10025	−	5.36979i	0.268826	−	0.465619i
$134$	0.796244	+	1.37914i	0.0687850	+	0.119139i
$135$		0			0
$136$	−3.71526	+	2.14501i	−0.318581	+	0.183933i
$137$	−5.69247	+	3.28655i	−0.486341	+	0.280789i	−0.723055	−	0.690790i	$-0.757263\pi$
$137$	−5.69247	+	3.28655i	−0.486341	+	0.280789i	0.236714	+	0.971579i	$0.423929\pi$
$138$		0			0
$139$	0.367315	+	0.636208i	0.0311553	+	0.0539625i	0.881183	−	0.472776i	$-0.156748\pi$
$139$	0.367315	+	0.636208i	0.0311553	+	0.0539625i	−0.850027	+	0.526739i	$0.823415\pi$
$140$	0.939548	−	1.62734i	0.0794063	−	0.137536i
$141$		0			0
$142$	−4.21306			−0.353552
$143$	0.178040	−	20.7532i	0.0148885	−	1.73547i
$144$		0			0
$145$	−5.17068	−	2.98530i	−0.429402	−	0.247915i
$146$	1.85634	−	3.21527i	0.153631	−	0.266097i
$147$		0			0
$148$			8.31728i			0.683676i
$149$	−19.6065	+	11.3198i	−1.60622	+	0.927354i	−0.616019	+	0.787732i	$0.711255\pi$
$149$	−19.6065	+	11.3198i	−1.60622	+	0.927354i	−0.990205	+	0.139622i	$0.955411\pi$
$150$		0			0
$151$		−	7.94508i		−	0.646561i	−0.946303	−	0.323281i	$-0.895214\pi$
$151$		−	7.94508i		−	0.646561i	0.946303	−	0.323281i	$-0.104786\pi$
$152$	5.67089	+	9.82227i	0.459970	+	0.796691i
$153$		0			0
$154$	2.42263	+	1.39870i	0.195221	+	0.112711i
$155$	5.82134			0.467581
$156$		0			0
$157$	15.4868			1.23598			0.617991	−	0.786185i	$-0.287947\pi$
$157$	15.4868			1.23598			0.617991	+	0.786185i	$0.287947\pi$
$158$	−6.57191	−	3.79429i	−0.522833	−	0.301858i
$159$		0			0
$160$	2.63182	+	4.55844i	0.208063	+	0.360376i
$161$		−	5.51348i		−	0.434523i
$162$		0			0
$163$	5.10619	−	2.94806i	0.399947	−	0.230910i	−0.286514	−	0.958076i	$-0.592496\pi$
$163$	5.10619	−	2.94806i	0.399947	−	0.230910i	0.686461	+	0.727166i	$0.259163\pi$
$164$			15.6649i			1.22322i
$165$		0			0
$166$	−0.639837	+	1.10823i	−0.0496609	+	0.0860153i
$167$	−8.23496	−	4.75446i	−0.637241	−	0.367911i	0.146310	−	0.989239i	$-0.453260\pi$
$167$	−8.23496	−	4.75446i	−0.637241	−	0.367911i	−0.783551	+	0.621328i	$0.786594\pi$
$168$		0			0
$169$	−6.69220	+	11.1452i	−0.514784	+	0.857320i
$170$	−1.21430			−0.0931326
$171$		0			0
$172$	−8.42841	+	14.5984i	−0.642660	+	1.11312i
$173$	0.812324	+	1.40699i	0.0617599	+	0.106971i	0.895252	−	0.445560i	$-0.146995\pi$
$173$	0.812324	+	1.40699i	0.0617599	+	0.106971i	−0.833492	+	0.552531i	$0.813662\pi$
$174$		0			0
$175$	−3.34720	+	1.93251i	−0.253024	+	0.146084i
$176$	13.1536	−	7.59424i	0.991491	−	0.572438i
$177$		0			0
$178$	−2.93218	−	5.07869i	−0.219776	−	0.380664i
$179$	−9.87735	+	17.1081i	−0.738268	+	1.27872i	0.215007	+	0.976612i	$0.431023\pi$
$179$	−9.87735	+	17.1081i	−0.738268	+	1.27872i	−0.953275	+	0.302105i	$0.902311\pi$
$180$		0			0
$181$	−0.589428			−0.0438118			−0.0219059	−	0.999760i	$-0.506973\pi$
$181$	−0.589428			−0.0438118			−0.0219059	+	0.999760i	$0.506973\pi$
$182$	−0.863079	−	1.52496i	−0.0639757	−	0.113038i
$183$		0			0
$184$	8.73396	+	5.04256i	0.643876	+	0.371742i
$185$	−2.51185	+	4.35066i	−0.184675	+	0.319867i
$186$		0			0
$187$			13.5000i			0.987217i
$188$	7.97152	−	4.60236i	0.581383	−	0.335661i
$189$		0			0
$190$			3.21032i			0.232901i
$191$	4.58812	+	7.94686i	0.331985	+	0.575015i	0.982901	−	0.184135i	$-0.0589484\pi$
$191$	4.58812	+	7.94686i	0.331985	+	0.575015i	−0.650916	+	0.759150i	$0.725615\pi$
$192$		0			0
$193$	−2.84691	−	1.64367i	−0.204925	−	0.118314i	0.394025	−	0.919100i	$-0.371082\pi$
$193$	−2.84691	−	1.64367i	−0.204925	−	0.118314i	−0.598951	+	0.800786i	$0.704416\pi$
$194$	8.14574			0.584830
$195$		0			0
$196$	−1.76381			−0.125987
$197$	13.2678	+	7.66017i	0.945292	+	0.545765i	0.891615	−	0.452793i	$-0.149573\pi$
$197$	13.2678	+	7.66017i	0.945292	+	0.545765i	0.0536771	+	0.998558i	$0.482906\pi$
$198$		0			0
$199$	−7.26150	−	12.5773i	−0.514754	−	0.891581i	−0.999853	−	0.0171214i	$-0.994550\pi$
$199$	−7.26150	−	12.5773i	−0.514754	−	0.891581i	0.485099	−	0.874459i	$-0.338784\pi$
$200$		−	7.06977i		−	0.499909i
$201$		0			0
$202$	1.08431	−	0.626029i	0.0762921	−	0.0440473i
$203$			5.60430i			0.393345i
$204$		0			0
$205$	−4.73087	+	8.19411i	−0.330418	+	0.572301i
$206$	4.36975	+	2.52288i	0.304455	+	0.175777i
$207$		0			0
$208$	−9.51351	−	0.0816157i	−0.659643	−	0.00565903i
$209$	35.6908			2.46878
$210$		0			0
$211$	8.26364	−	14.3130i	0.568892	−	0.985350i	−0.427783	−	0.903881i	$-0.640705\pi$
$211$	8.26364	−	14.3130i	0.568892	−	0.985350i	0.996676	−	0.0814692i	$-0.0259612\pi$
$212$	1.34817	+	2.33509i	0.0925925	+	0.160375i
$213$		0			0
$214$	7.16988	−	4.13953i	0.490123	−	0.282972i
$215$	−8.81757	+	5.09083i	−0.601354	+	0.347192i
$216$		0			0
$217$	−2.73210	−	4.73214i	−0.185467	−	0.321239i
$218$	−0.452275	+	0.783363i	−0.0306319	+	0.0530561i
$219$		0			0
$220$	10.8163			0.729234
$221$	4.29077	−	7.28675i	0.288628	−	0.490160i
$222$		0			0
$223$	−18.7844	−	10.8452i	−1.25789	−	0.726246i	−0.285230	−	0.958459i	$-0.592070\pi$
$223$	−18.7844	−	10.8452i	−1.25789	−	0.726246i	−0.972665	+	0.232213i	$0.925403\pi$
$224$	2.47036	−	4.27878i	0.165058	−	0.285888i
$225$		0			0
$226$		−	2.31691i		−	0.154119i
$227$	4.70729	−	2.71776i	0.312434	−	0.180384i	−0.335581	−	0.942011i	$-0.608933\pi$
$227$	4.70729	−	2.71776i	0.312434	−	0.180384i	0.648015	+	0.761627i	$0.275599\pi$
$228$		0			0
$229$			9.99668i			0.660599i	0.943876	+	0.330300i	$0.107150\pi$
$229$			9.99668i			0.660599i	−0.943876	+	0.330300i	$0.892850\pi$
$230$	1.42731	+	2.47217i	0.0941141	+	0.163010i
$231$		0			0
$232$	−8.87783	−	5.12562i	−0.582858	−	0.336513i
$233$	−1.72553			−0.113043			−0.0565217	−	0.998401i	$-0.518001\pi$
$233$	−1.72553			−0.113043			−0.0565217	+	0.998401i	$0.518001\pi$
$234$		0			0
$235$	5.55972			0.362676
$236$	−15.9873	−	9.23029i	−1.04069	−	0.600840i
$237$		0			0
$238$	0.569902	+	0.987100i	0.0369413	+	0.0639842i
$239$			5.80837i			0.375712i	0.982197	+	0.187856i	$0.0601539\pi$
$239$			5.80837i			0.375712i	−0.982197	+	0.187856i	$0.939846\pi$
$240$		0			0
$241$	9.63038	−	5.56010i	0.620348	−	0.358158i	−0.156657	−	0.987653i	$-0.550072\pi$
$241$	9.63038	−	5.56010i	0.620348	−	0.358158i	0.777004	+	0.629495i	$0.216738\pi$
$242$			10.7563i			0.691443i
$243$		0			0
$244$	−6.74315	+	11.6795i	−0.431686	+	0.747701i
$245$	−0.922628	−	0.532679i	−0.0589445	−	0.0340316i
$246$		0			0
$247$	−19.2644	−	11.3438i	−1.22577	−	0.721787i
$248$	9.99498			0.634682
$249$		0			0
$250$	2.29494	−	3.97496i	0.145145	−	0.251398i
$251$	−4.87634	−	8.44607i	−0.307792	−	0.533111i	0.670087	−	0.742283i	$-0.266257\pi$
$251$	−4.87634	−	8.44607i	−0.307792	−	0.533111i	−0.977879	+	0.209171i	$0.932923\pi$
$252$		0			0
$253$	27.4844	−	15.8681i	1.72793	−	0.997620i
$254$	−0.499839	+	0.288582i	−0.0313627	+	0.0181073i
$255$		0			0
$256$	−0.135416	−	0.234547i	−0.00846350	−	0.0146592i
$257$	−5.19710	+	9.00164i	−0.324186	+	0.561507i	−0.981347	−	0.192243i	$-0.938424\pi$
$257$	−5.19710	+	9.00164i	−0.324186	+	0.561507i	0.657161	+	0.753750i	$0.271757\pi$
$258$		0			0
$259$	4.71551			0.293007
$260$	−5.83820	−	3.43780i	−0.362070	−	0.213203i
$261$		0			0
$262$	6.24001	+	3.60267i	0.385509	+	0.222574i
$263$	−12.2395	+	21.1994i	−0.754717	+	1.30721i	0.190798	+	0.981629i	$0.438893\pi$
$263$	−12.2395	+	21.1994i	−0.754717	+	1.30721i	−0.945515	+	0.325579i	$0.894441\pi$
$264$		0			0
$265$			1.62861i			0.100045i
$266$	2.60966	−	1.50669i	0.160008	−	0.0923809i
$267$		0			0
$268$		−	5.77966i		−	0.353049i
$269$	2.52910	+	4.38052i	0.154202	+	0.267085i	0.932768	−	0.360477i	$-0.117386\pi$
$269$	2.52910	+	4.38052i	0.154202	+	0.267085i	−0.778566	+	0.627562i	$0.784053\pi$
$270$		0			0
$271$	11.7523	+	6.78518i	0.713900	+	0.412170i	0.812503	−	0.582957i	$-0.198104\pi$
$271$	11.7523	+	6.78518i	0.713900	+	0.412170i	−0.0986037	+	0.995127i	$0.531438\pi$
$272$	6.18855			0.375236
$273$		0			0
$274$	−3.19446			−0.192984
$275$	−19.2669	−	11.1237i	−1.16183	−	0.670786i
$276$		0			0
$277$	−11.7870	−	20.4156i	−0.708210	−	1.22666i	−0.965521	−	0.260327i	$-0.916170\pi$
$277$	−11.7870	−	20.4156i	−0.708210	−	1.22666i	0.257311	−	0.966329i	$-0.417164\pi$
$278$			0.357022i			0.0214128i
$279$		0			0
$280$	1.68765	−	0.974363i	0.100856	−	0.0582293i
$281$		−	14.8688i		−	0.886996i	−0.896275	−	0.443498i	$-0.853737\pi$
$281$		−	14.8688i		−	0.886996i	0.896275	−	0.443498i	$-0.146263\pi$
$282$		0			0
$283$	−10.4948	+	18.1776i	−0.623852	+	1.08054i	0.364910	+	0.931043i	$0.381100\pi$
$283$	−10.4948	+	18.1776i	−0.623852	+	1.08054i	−0.988762	+	0.149500i	$0.952233\pi$
$284$	13.2420	+	7.64530i	0.785770	+	0.453665i
$285$		0			0
$286$	5.11785	−	8.69132i	0.302625	−	0.513929i
$287$	8.88127			0.524245
$288$		0			0
$289$	5.74972	−	9.95880i	0.338219	−	0.585812i
$290$	−1.45082	−	2.51290i	−0.0851952	−	0.147562i
$291$		0			0
$292$	−11.6693	+	6.73725i	−0.682892	+	0.394268i
$293$	−6.39182	+	3.69032i	−0.373414	+	0.215591i	−0.674949	−	0.737864i	$-0.735834\pi$
$293$	−6.39182	+	3.69032i	−0.373414	+	0.215591i	0.301535	+	0.953455i	$0.402501\pi$
$294$		0			0
$295$	−5.57517	−	9.65648i	−0.324599	−	0.562222i
$296$	−4.31274	+	7.46989i	−0.250673	+	0.434178i
$297$		0			0
$298$	−11.0026			−0.637363
$299$	−19.8784	−	0.170535i	−1.14960	−	0.00986232i
$300$		0			0
$301$	8.27662	+	4.77851i	0.477057	+	0.275429i
$302$	1.93061	−	3.34392i	0.111094	−	0.192421i
$303$		0			0
$304$		−	16.3611i		−	0.938371i
$305$	−7.05450	+	4.07292i	−0.403939	+	0.233215i
$306$		0			0
$307$		−	26.2172i		−	1.49629i	−0.663534	−	0.748146i	$-0.730944\pi$
$307$		−	26.2172i		−	1.49629i	0.663534	−	0.748146i	$-0.269056\pi$
$308$	−5.07636	−	8.79251i	−0.289252	−	0.501000i
$309$		0			0
$310$	2.45008	+	1.41455i	0.139155	+	0.0803413i
$311$	23.3730			1.32536			0.662681	−	0.748902i	$-0.269419\pi$
$311$	23.3730			1.32536			0.662681	+	0.748902i	$0.269419\pi$
$312$		0			0
$313$	−20.5337			−1.16064			−0.580318	−	0.814390i	$-0.697072\pi$
$313$	−20.5337			−1.16064			−0.580318	+	0.814390i	$0.697072\pi$
$314$	6.51807	+	3.76321i	0.367836	+	0.212370i
$315$		0			0
$316$	13.7707	+	23.8516i	0.774665	+	1.34176i
$317$			2.73722i			0.153738i	0.997041	+	0.0768689i	$0.0244923\pi$
$317$			2.73722i			0.153738i	−0.997041	+	0.0768689i	$0.975508\pi$
$318$		0			0
$319$	−27.9371	+	16.1295i	−1.56418	+	0.903079i
$320$		−	3.06419i		−	0.171294i
$321$		0			0
$322$	1.33975	−	2.32051i	0.0746611	−	0.129317i
$323$	12.5939	+	7.27110i	0.700744	+	0.404575i
$324$		0			0
$325$	6.86396	+	12.1278i	0.380744	+	0.672730i
$326$	2.86545			0.158703
$327$		0			0
$328$	−8.12269	+	14.0689i	−0.448501	+	0.776826i
$329$	−2.60932	−	4.51947i	−0.143856	−	0.249167i
$330$		0			0
$331$	−8.35843	+	4.82574i	−0.459421	+	0.265247i	−0.711801	−	0.702382i	$-0.752120\pi$
$331$	−8.35843	+	4.82574i	−0.459421	+	0.265247i	0.252380	+	0.967628i	$0.418787\pi$
$332$	4.02213	−	2.32218i	0.220743	−	0.127446i
$333$		0			0
$334$	−2.31062	−	4.00210i	−0.126431	−	0.218985i
$335$	1.74548	−	3.02327i	0.0953659	−	0.165179i
$336$		0			0
$337$	11.3368			0.617555			0.308778	−	0.951134i	$-0.400080\pi$
$337$	11.3368			0.617555			0.308778	+	0.951134i	$0.400080\pi$
$338$	−5.52482	+	3.06459i	−0.300511	+	0.166692i
$339$		0			0
$340$	3.81666	+	2.20355i	0.206987	+	0.119504i
$341$	15.7263	−	27.2387i	0.851627	−	1.47506i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−15.1394	+	8.74072i	−0.816261	+	0.471268i
$345$		0			0
$346$			0.789562i			0.0424471i
$347$	−9.83667	−	17.0376i	−0.528060	−	0.914627i	−0.999465	−	0.0327100i	$-0.989586\pi$
$347$	−9.83667	−	17.0376i	−0.528060	−	0.914627i	0.471405	−	0.881917i	$-0.343747\pi$
$348$		0			0
$349$	6.82990	+	3.94324i	0.365596	+	0.211077i	0.671533	−	0.740975i	$-0.265636\pi$
$349$	6.82990	+	3.94324i	0.365596	+	0.211077i	−0.305937	+	0.952052i	$0.598970\pi$
$350$	−1.87835			−0.100402
$351$		0			0
$352$	28.4393			1.51582
$353$	−12.7151	−	7.34104i	−0.676754	−	0.390724i	0.121877	−	0.992545i	$-0.461109\pi$
$353$	−12.7151	−	7.34104i	−0.676754	−	0.390724i	−0.798631	+	0.601821i	$0.794442\pi$
$354$		0			0
$355$	4.61782	+	7.99830i	0.245089	+	0.424506i
$356$			21.2837i			1.12803i
$357$		0			0
$358$	−8.31434	+	4.80028i	−0.439426	+	0.253703i
$359$		−	16.7725i		−	0.885220i	−0.896714	−	0.442610i	$-0.854053\pi$
$359$		−	16.7725i		−	0.885220i	0.896714	−	0.442610i	$-0.145947\pi$
$360$		0			0
$361$	9.72307	−	16.8408i	0.511740	−	0.886360i
$362$	−0.248078	−	0.143228i	−0.0130387	−	0.00752789i
$363$		0			0
$364$	−0.0545559	+	6.35929i	−0.00285951	+	0.333317i
$365$	−8.13871			−0.426000
$366$		0			0
$367$	5.47023	−	9.47471i	0.285543	−	0.494576i	−0.687197	−	0.726471i	$-0.741159\pi$
$367$	5.47023	−	9.47471i	0.285543	−	0.494576i	0.972741	+	0.231895i	$0.0744926\pi$
$368$	−7.27413	−	12.5992i	−0.379190	−	0.656777i
$369$		0			0
$370$	−2.11437	+	1.22073i	−0.109921	+	0.0634629i
$371$	1.32389	−	0.764348i	0.0687329	−	0.0396830i
$372$		0			0
$373$	3.61767	+	6.26599i	0.187316	+	0.324441i	0.944354	−	0.328930i	$-0.106688\pi$
$373$	3.61767	+	6.26599i	0.187316	+	0.324441i	−0.757039	+	0.653370i	$0.773355\pi$
$374$	−3.28042	+	5.68186i	−0.169627	+	0.293802i
$375$		0			0
$376$	9.54580			0.492287
$377$	20.2059	+	0.173345i	1.04065	+	0.00892770i
$378$		0			0
$379$	2.28182	+	1.31741i	0.117209	+	0.0676707i	0.557458	−	0.830205i	$-0.311777\pi$
$379$	2.28182	+	1.31741i	0.117209	+	0.0676707i	−0.440249	+	0.897876i	$0.645110\pi$
$380$	5.82566	−	10.0903i	0.298850	−	0.517623i
$381$		0			0
$382$			4.45956i			0.228171i
$383$	−7.45530	+	4.30432i	−0.380948	+	0.219941i	−0.678231	−	0.734849i	$-0.737253\pi$
$383$	−7.45530	+	4.30432i	−0.380948	+	0.219941i	0.297283	+	0.954790i	$0.403920\pi$
$384$		0			0
$385$		−	6.13233i		−	0.312532i
$386$	−0.798804	−	1.38357i	−0.0406581	−	0.0704218i
$387$		0			0
$388$	−25.6028	−	14.7818i	−1.29978	−	0.750431i
$389$	−19.9726			−1.01265			−0.506325	−	0.862343i	$-0.668996\pi$
$389$	−19.9726			−1.01265			−0.506325	+	0.862343i	$0.668996\pi$
$390$		0			0
$391$	12.9309			0.653945
$392$	−1.58411	−	0.914587i	−0.0800097	−	0.0461936i
$393$		0			0
$394$	3.72276	+	6.44801i	0.187550	+	0.324846i
$395$			16.6353i			0.837012i
$396$		0			0
$397$	−2.47610	+	1.42958i	−0.124272	+	0.0717485i	−0.560847	−	0.827919i	$-0.689525\pi$
$397$	−2.47610	+	1.42958i	−0.124272	+	0.0717485i	0.436575	+	0.899668i	$0.356191\pi$
$398$		−	7.05802i		−	0.353787i
$399$		0			0
$400$	−5.09924	+	8.83215i	−0.254962	+	0.441608i
$401$	−15.6107	−	9.01285i	−0.779562	−	0.450080i	0.0567132	−	0.998391i	$-0.481938\pi$
$401$	−15.6107	−	9.01285i	−0.779562	−	0.450080i	−0.836275	+	0.548310i	$0.815271\pi$
$402$		0			0
$403$	−17.1459	+	9.70400i	−0.854096	+	0.483391i
$404$	−4.54413			−0.226079
$405$		0			0
$406$	−1.36181	+	2.35873i	−0.0675857	+	0.117062i
$407$	13.5715	+	23.5065i	0.672714	+	1.16518i
$408$		0			0
$409$	−7.58420	+	4.37874i	−0.375015	+	0.216515i	−0.675647	−	0.737225i	$-0.736136\pi$
$409$	−7.58420	+	4.37874i	−0.375015	+	0.216515i	0.300632	+	0.953740i	$0.402802\pi$
$410$	−3.98225	+	2.29915i	−0.196669	+	0.113547i
$411$		0			0
$412$	−9.15635	−	15.8593i	−0.451101	−	0.781330i
$413$	−5.23314	+	9.06406i	−0.257506	+	0.446013i
$414$		0			0
$415$	2.80523			0.137703
$416$	−15.3504	−	9.03901i	−0.752615	−	0.443174i
$417$		0			0
$418$	15.0215	+	8.67266i	0.734725	+	0.424194i
$419$	−0.864446	+	1.49726i	−0.0422310	+	0.0731462i	−0.886368	−	0.462981i	$-0.846780\pi$
$419$	−0.864446	+	1.49726i	−0.0422310	+	0.0731462i	0.844137	+	0.536127i	$0.180113\pi$
$420$		0			0
$421$			25.6427i			1.24975i	0.780726	+	0.624874i	$0.214850\pi$
$421$			25.6427i			1.24975i	−0.780726	+	0.624874i	$0.785150\pi$
$422$	6.95598	−	4.01604i	0.338612	−	0.195498i
$423$		0			0
$424$			2.79625i			0.135798i
$425$	−4.53236	−	7.85028i	−0.219852	−	0.380795i
$426$		0			0
$427$	6.62171	+	3.82305i	0.320447	+	0.185010i
$428$	−30.0474			−1.45240
$429$		0			0
$430$	−4.94818			−0.238622
$431$	−0.222971	−	0.128733i	−0.0107402	−	0.00620083i	0.494620	−	0.869109i	$-0.335307\pi$
$431$	−0.222971	−	0.128733i	−0.0107402	−	0.00620083i	−0.505360	+	0.862908i	$0.668640\pi$
$432$		0			0
$433$	−12.1641	−	21.0688i	−0.584570	−	1.01250i	−0.994929	−	0.100580i	$-0.967930\pi$
$433$	−12.1641	−	21.0688i	−0.584570	−	1.01250i	0.410359	−	0.911924i	$-0.365403\pi$
$434$		−	2.65554i		−	0.127470i
$435$		0			0
$436$	2.84308	−	1.64145i	0.136159	−	0.0786114i
$437$		−	34.1863i		−	1.63535i
$438$		0			0
$439$	8.50900	−	14.7380i	0.406112	−	0.703407i	−0.588338	−	0.808615i	$-0.700218\pi$
$439$	8.50900	−	14.7380i	0.406112	−	0.703407i	0.994450	+	0.105208i	$0.0335509\pi$
$440$	9.71428	+	5.60854i	0.463110	+	0.267377i
$441$		0			0
$442$	3.57654	−	2.02421i	0.170118	−	0.0962816i
$443$	−38.1564			−1.81287			−0.906433	−	0.422349i	$-0.861206\pi$
$443$	−38.1564			−1.81287			−0.906433	+	0.422349i	$0.861206\pi$
$444$		0			0
$445$	−6.42776	+	11.1332i	−0.304705	+	0.527765i
$446$	−5.27063	−	9.12900i	−0.249572	−	0.432271i
$447$		0			0
$448$	−2.49087	+	1.43810i	−0.117683	+	0.0679440i
$449$	−35.7959	+	20.6668i	−1.68931	+	0.975325i	−0.734270	+	0.678858i	$0.762475\pi$
$449$	−35.7959	+	20.6668i	−1.68931	+	0.975325i	−0.955043	+	0.296468i	$0.904191\pi$
$450$		0			0
$451$	25.5608	+	44.2726i	1.20361	+	2.08472i
$452$	−4.20442	+	7.28227i	−0.197759	+	0.342529i
$453$		0			0
$454$	2.64160			0.123976
$455$	−1.94907	+	3.30998i	−0.0913738	+	0.155174i
$456$		0			0
$457$	−16.1281	−	9.31158i	−0.754442	−	0.435578i	0.0728544	−	0.997343i	$-0.476789\pi$
$457$	−16.1281	−	9.31158i	−0.754442	−	0.435578i	−0.827297	+	0.561765i	$0.810123\pi$
$458$	−2.42914	+	4.20739i	−0.113506	+	0.196599i
$459$		0			0
$460$		−	10.3604i		−	0.483054i
$461$	6.58984	−	3.80465i	0.306919	−	0.177200i	−0.338628	−	0.940920i	$-0.609963\pi$
$461$	6.58984	−	3.80465i	0.306919	−	0.177200i	0.645547	+	0.763720i	$0.276629\pi$
$462$		0			0
$463$			25.2029i			1.17128i	0.810571	+	0.585640i	$0.199157\pi$
$463$			25.2029i			1.17128i	−0.810571	+	0.585640i	$0.800843\pi$
$464$	7.39395	+	12.8067i	0.343256	+	0.594536i
$465$		0			0
$466$	−0.726241	−	0.419295i	−0.0336425	−	0.0194235i
$467$	−18.6005			−0.860727			−0.430364	−	0.902656i	$-0.641615\pi$
$467$	−18.6005			−0.860727			−0.430364	+	0.902656i	$0.641615\pi$
$468$		0			0
$469$	−3.27680			−0.151308
$470$	2.33997	+	1.35098i	0.107935	+	0.0623162i
$471$		0			0
$472$	−9.57232	−	16.5797i	−0.440602	−	0.763144i
$473$			55.0113i			2.52942i
$474$		0			0
$475$	−20.7543	+	11.9825i	−0.952272	+	0.549794i
$476$		−	4.13673i		−	0.189607i
$477$		0			0
$478$	−1.41140	+	2.44462i	−0.0645561	+	0.111814i
$479$	21.2514	+	12.2695i	0.971001	+	0.560608i	0.899541	−	0.436836i	$-0.143901\pi$
$479$	21.2514	+	12.2695i	0.971001	+	0.560608i	0.0714598	+	0.997443i	$0.477234\pi$
$480$		0			0
$481$	0.145854	−	17.0014i	0.00665035	−	0.775196i
$482$	5.40430			0.246159
$483$		0			0
$484$	19.5191	−	33.8081i	0.887233	−	1.53673i
$485$	−8.92832	−	15.4643i	−0.405414	−	0.702198i
$486$		0			0
$487$	−26.6423	+	15.3819i	−1.20728	+	0.697022i	−0.962164	−	0.272472i	$-0.912159\pi$
$487$	−26.6423	+	15.3819i	−1.20728	+	0.697022i	−0.245114	+	0.969494i	$0.578825\pi$
$488$	−12.1123	+	6.99301i	−0.548296	+	0.316559i
$489$		0			0
$490$	−0.258876	−	0.448387i	−0.0116948	−	0.0202561i
$491$	9.60159	−	16.6304i	0.433313	−	0.750521i	−0.563843	−	0.825882i	$-0.690678\pi$
$491$	9.60159	−	16.6304i	0.433313	−	0.750521i	0.997156	+	0.0753611i	$0.0240110\pi$
$492$		0			0
$493$	−13.1439			−0.591973
$494$	−5.35152	−	9.45551i	−0.240776	−	0.425424i
$495$		0			0
$496$	−12.4866	−	7.20912i	−0.560663	−	0.323699i
$497$	4.33452	−	7.50761i	0.194430	−	0.336763i
$498$		0			0
$499$			14.0592i			0.629376i	0.949195	+	0.314688i	$0.101900\pi$
$499$			14.0592i			0.629376i	−0.949195	+	0.314688i	$0.898100\pi$
$500$	−14.4264	+	8.32910i	−0.645169	+	0.372489i
$501$		0			0
$502$		−	4.73970i		−	0.211543i
$503$	−0.301296	−	0.521861i	−0.0134341	−	0.0232686i	0.859230	−	0.511589i	$-0.170943\pi$
$503$	−0.301296	−	0.521861i	−0.0134341	−	0.0232686i	−0.872664	+	0.488321i	$0.837610\pi$
$504$		0			0
$505$	−2.37697	−	1.37235i	−0.105774	−	0.0610686i
$506$	15.4235			0.685657
$507$		0			0
$508$	2.09472			0.0929382
$509$	6.81860	+	3.93672i	0.302229	+	0.174492i	0.643444	−	0.765493i	$-0.277505\pi$
$509$	6.81860	+	3.93672i	0.302229	+	0.174492i	−0.341215	+	0.939985i	$0.610838\pi$
$510$		0			0
$511$	3.81971	+	6.61593i	0.168974	+	0.292671i
$512$		−	22.6901i		−	1.00277i
$513$		0			0
$514$	−4.37470	+	2.52573i	−0.192960	+	0.111405i
$515$		−	11.0610i		−	0.487407i
$516$		0			0
$517$	15.0195	−	26.0146i	0.660559	−	1.14412i
$518$	1.98466	+	1.14584i	0.0872009	+	0.0503455i
$519$		0			0
$520$	−3.46079	−	6.11481i	−0.151766	−	0.268152i
$521$	26.5275			1.16219			0.581096	−	0.813835i	$-0.302624\pi$
$521$	26.5275			1.16219			0.581096	+	0.813835i	$0.302624\pi$
$522$		0			0
$523$	3.77968	−	6.54661i	0.165274	−	0.286263i	−0.771479	−	0.636255i	$-0.780482\pi$
$523$	3.77968	−	6.54661i	0.165274	−	0.286263i	0.936753	+	0.349992i	$0.113816\pi$
$524$	−13.0753	−	22.6471i	−0.571197	−	0.989341i
$525$		0			0
$526$	−10.3027	+	5.94824i	−0.449217	+	0.259356i
$527$	11.0984	−	6.40768i	0.483455	−	0.279123i
$528$		0			0
$529$	−3.69924	−	6.40727i	−0.160836	−	0.278577i
$530$	−0.395743	+	0.685447i	−0.0171900	+	0.0297739i
$531$		0			0
$532$	−10.9365			−0.474158
$533$	0.274703	−	32.0207i	0.0118987	−	1.38697i
$534$		0			0
$535$	−15.7174	−	9.07445i	−0.679523	−	0.392323i
$536$	2.99692	−	5.19081i	0.129447	−	0.224209i
$537$		0			0
$538$			2.45823i			0.105982i
$539$	−4.98494	+	2.87806i	−0.214717	+	0.123967i
$540$		0			0
$541$		−	13.8116i		−	0.593807i	−0.954907	−	0.296904i	$-0.904046\pi$
$541$		−	13.8116i		−	0.593807i	0.954907	−	0.296904i	$-0.0959540\pi$
$542$	3.29752	+	5.71148i	0.141641	+	0.245329i
$543$		0			0
$544$	10.0352	+	5.79380i	0.430254	+	0.248407i
$545$	1.98291			0.0849383
$546$		0			0
$547$	15.3668			0.657039			0.328519	−	0.944497i	$-0.393450\pi$
$547$	15.3668			0.657039			0.328519	+	0.944497i	$0.393450\pi$
$548$	10.0405	+	5.79687i	0.428908	+	0.247630i
$549$		0			0
$550$	−5.40601	−	9.36348i	−0.230513	−	0.399260i
$551$			34.7494i			1.48038i
$552$		0			0
$553$	13.5228	−	7.80736i	0.575046	−	0.332003i
$554$		−	11.4567i		−	0.486747i
$555$		0			0
$556$	0.647876	−	1.12215i	0.0274760	−	0.0475899i
$557$	22.5868	+	13.0405i	0.957032	+	0.552542i	0.895258	−	0.445548i	$-0.146991\pi$
$557$	22.5868	+	13.0405i	0.957032	+	0.552542i	0.0617734	+	0.998090i	$0.480324\pi$
$558$		0			0
$559$	17.4845	−	29.6929i	0.739517	−	1.25588i
$560$	−2.81113			−0.118792
$561$		0			0
$562$	3.61303	−	6.25795i	0.152406	−	0.263976i
$563$	6.43529	+	11.1462i	0.271215	+	0.469758i	0.969173	−	0.246380i	$-0.0792412\pi$
$563$	6.43529	+	11.1462i	0.271215	+	0.469758i	−0.697958	+	0.716138i	$0.745908\pi$
$564$		0			0
$565$	−4.39855	+	2.53950i	−0.185048	+	0.106838i
$566$	−8.83409	+	5.10037i	−0.371325	+	0.214384i
$567$		0			0
$568$	7.92859	+	13.7327i	0.332676	+	0.576212i
$569$	2.47488	−	4.28662i	0.103752	−	0.179704i	−0.809475	−	0.587154i	$-0.800248\pi$
$569$	2.47488	−	4.28662i	0.103752	−	0.179704i	0.913228	+	0.407449i	$0.133582\pi$
$570$		0			0
$571$	28.2860			1.18373			0.591865	−	0.806037i	$-0.298392\pi$
$571$	28.2860			1.18373			0.591865	+	0.806037i	$0.298392\pi$
$572$	−31.8577	+	18.0304i	−1.33204	+	0.753891i
$573$		0			0
$574$	3.73794	+	2.15810i	0.156019	+	0.0900774i
$575$	−10.6548	+	18.4547i	−0.444337	+	0.769615i
$576$		0			0
$577$			30.1903i			1.25684i	0.777875	+	0.628419i	$0.216298\pi$
$577$			30.1903i			1.25684i	−0.777875	+	0.628419i	$0.783702\pi$
$578$	4.83987	−	2.79430i	0.201312	−	0.116228i
$579$		0			0
$580$			10.5310i			0.437277i
$581$	−1.31657	−	2.28036i	−0.0546203	−	0.0946052i
$582$		0			0
$583$	7.62046	+	4.39967i	0.315607	+	0.182216i
$584$	−13.9738			−0.578240
$585$		0			0
$586$	−3.58691			−0.148174
$587$	22.5606	+	13.0253i	0.931174	+	0.537614i	0.887183	−	0.461418i	$-0.152659\pi$
$587$	22.5606	+	13.0253i	0.931174	+	0.537614i	0.0439914	+	0.999032i	$0.485993\pi$
$588$		0			0
$589$	−16.9404	−	29.3416i	−0.698016	−	1.20900i
$590$		−	5.41895i		−	0.223094i
$591$		0			0
$592$	10.7757	−	6.22134i	0.442877	−	0.255695i
$593$		−	10.6780i		−	0.438494i	−0.975669	−	0.219247i	$-0.929640\pi$
$593$		−	10.6780i		−	0.438494i	0.975669	−	0.219247i	$-0.0703601\pi$
$594$		0			0
$595$	1.24931	−	2.16387i	0.0512167	−	0.0887099i
$596$	34.5822	+	19.9660i	1.41654	+	0.817840i
$597$		0			0
$598$	−8.32497	−	4.90212i	−0.340433	−	0.200463i
$599$	13.3791			0.546655			0.273327	−	0.961921i	$-0.411876\pi$
$599$	13.3791			0.546655			0.273327	+	0.961921i	$0.411876\pi$
$600$		0			0
$601$	−17.4475	+	30.2199i	−0.711697	+	1.23270i	0.252522	+	0.967591i	$0.418740\pi$
$601$	−17.4475	+	30.2199i	−0.711697	+	1.23270i	−0.964220	+	0.265105i	$0.914593\pi$
$602$	2.32230	+	4.02235i	0.0946501	+	0.163939i
$603$		0			0
$604$	−12.1362	+	7.00682i	−0.493814	+	0.285104i
$605$	20.4204	−	11.7897i	0.830207	−	0.479320i
$606$		0			0
$607$	17.4463	+	30.2179i	0.708123	+	1.22651i	0.965553	+	0.260208i	$0.0837912\pi$
$607$	17.4463	+	30.2179i	0.708123	+	1.22651i	−0.257429	+	0.966297i	$0.582875\pi$
$608$	15.3174	−	26.5306i	0.621204	−	1.07596i
$609$		0			0
$610$	−3.95879			−0.160287
$611$	−16.3753	+	9.26790i	−0.662474	+	0.374939i
$612$		0			0
$613$	−3.51431	−	2.02899i	−0.141942	−	0.0819500i	0.427347	−	0.904087i	$-0.359448\pi$
$613$	−3.51431	−	2.02899i	−0.141942	−	0.0819500i	−0.569289	+	0.822137i	$0.692781\pi$
$614$	6.37063	−	11.0343i	0.257098	−	0.445306i
$615$		0			0
$616$		−	10.5289i		−	0.424223i
$617$	1.33035	−	0.768080i	0.0535580	−	0.0309217i	−0.472982	−	0.881072i	$-0.656822\pi$
$617$	1.33035	−	0.768080i	0.0535580	−	0.0309217i	0.526540	+	0.850150i	$0.323489\pi$
$618$		0			0
$619$		−	15.0023i		−	0.602993i	−0.953467	−	0.301496i	$-0.902514\pi$
$619$		−	15.0023i		−	0.602993i	0.953467	−	0.301496i	$-0.0974861\pi$
$620$	−5.13388	−	8.89214i	−0.206182	−	0.357117i
$621$		0			0
$622$	9.83721	+	5.67951i	0.394436	+	0.227728i
$623$	12.0669			0.483448
$624$		0			0
$625$	9.26336			0.370534
$626$	−8.64222	−	4.98959i	−0.345412	−	0.199424i
$627$		0			0
$628$	−13.6579	−	23.6562i	−0.545011	−	0.943986i
$629$			11.0594i			0.440968i
$630$		0			0
$631$	−8.08574	+	4.66831i	−0.321888	+	0.185842i	−0.652234	−	0.758018i	$-0.726168\pi$
$631$	−8.08574	+	4.66831i	−0.321888	+	0.185842i	0.330346	+	0.943860i	$0.392835\pi$
$632$			28.5620i			1.13614i
$633$		0			0
$634$	−0.665131	+	1.15204i	−0.0264157	+	0.0457534i
$635$	1.09572	+	0.632614i	0.0434823	+	0.0251045i
$636$		0			0
$637$	3.60542	+	0.0309306i	0.142852	+	0.00122552i
$638$	−15.6775			−0.620679
$639$		0			0
$640$	6.00821	−	10.4065i	0.237495	−	0.411354i
$641$	6.54834	+	11.3421i	0.258644	+	0.447984i	0.965879	−	0.258994i	$-0.0833911\pi$
$641$	6.54834	+	11.3421i	0.258644	+	0.447984i	−0.707235	+	0.706979i	$0.750058\pi$
$642$		0			0
$643$	−12.0111	+	6.93458i	−0.473670	+	0.273473i	−0.717775	−	0.696276i	$-0.754839\pi$
$643$	−12.0111	+	6.93458i	−0.473670	+	0.273473i	0.244105	+	0.969749i	$0.421506\pi$
$644$	−8.42189	+	4.86238i	−0.331869	+	0.191605i
$645$		0			0
$646$	3.53368	+	6.12051i	0.139031	+	0.240808i
$647$	−5.83908	+	10.1136i	−0.229558	+	0.397606i	−0.957677	−	0.287845i	$-0.907061\pi$
$647$	−5.83908	+	10.1136i	−0.229558	+	0.397606i	0.728119	+	0.685450i	$0.240395\pi$
$648$		0			0
$649$	−60.2451			−2.36483
$650$	−0.0580987	+	6.77225i	−0.00227882	+	0.265630i
$651$		0			0
$652$	−9.00637	−	5.19983i	−0.352716	−	0.203641i
$653$	4.34307	−	7.52242i	0.169958	−	0.294375i	−0.768447	−	0.639913i	$-0.778970\pi$
$653$	4.34307	−	7.52242i	0.169958	−	0.294375i	0.938405	+	0.345538i	$0.112304\pi$
$654$		0			0
$655$		−	15.7952i		−	0.617168i
$656$	20.2951	−	11.7174i	0.792390	−	0.457487i
$657$		0			0
$658$		−	2.53620i		−	0.0988715i
$659$	−24.1981	−	41.9124i	−0.942626	−	1.63268i	−0.760436	−	0.649413i	$-0.775015\pi$
$659$	−24.1981	−	41.9124i	−0.942626	−	1.63268i	−0.182190	−	0.983263i	$-0.558319\pi$
$660$		0			0
$661$	−22.0611	−	12.7370i	−0.858076	−	0.495410i	0.00529178	−	0.999986i	$-0.498316\pi$
$661$	−22.0611	−	12.7370i	−0.858076	−	0.495410i	−0.863367	+	0.504576i	$0.831649\pi$
$662$	−4.69051			−0.182302
$663$		0			0
$664$	4.81645			0.186915
$665$	−5.72075	−	3.30288i	−0.221841	−	0.128080i
$666$		0			0
$667$	15.4496	+	26.7595i	0.598211	+	1.03613i
$668$			16.7720i			0.648927i
$669$		0			0
$670$	1.46927	−	0.848286i	0.0567630	−	0.0327721i
$671$			44.0118i			1.69906i
$672$		0			0
$673$	−0.655263	+	1.13495i	−0.0252585	+	0.0437491i	−0.878378	−	0.477966i	$-0.841374\pi$
$673$	−0.655263	+	1.13495i	−0.0252585	+	0.0437491i	0.853120	+	0.521715i	$0.174708\pi$
$674$	4.77142	+	2.75478i	0.183788	+	0.106110i
$675$		0			0
$676$	22.9262	+	0.393394i	0.881777	+	0.0151305i
$677$	47.4782			1.82473			0.912367	−	0.409373i	$-0.134253\pi$
$677$	47.4782			1.82473			0.912367	+	0.409373i	$0.134253\pi$
$678$		0			0
$679$	−8.38057	+	14.5156i	−0.321617	+	0.557057i
$680$	2.28520	+	3.95809i	0.0876335	+	0.151786i
$681$		0			0
$682$	13.2377	−	7.64281i	0.506899	−	0.292658i
$683$	−11.4380	+	6.60376i	−0.437665	+	0.252686i	−0.702607	−	0.711579i	$-0.747981\pi$
$683$	−11.4380	+	6.60376i	−0.437665	+	0.252686i	0.264942	+	0.964264i	$0.414647\pi$
$684$		0			0
$685$	3.50136	+	6.06453i	0.133780	+	0.231714i
$686$	−0.242995	+	0.420879i	−0.00927758	+	0.0160692i
$687$		0			0
$688$	25.2178			0.961421
$689$	−2.71484	−	4.79682i	−0.103427	−	0.182744i
$690$		0			0
$691$	−5.74831	−	3.31879i	−0.218676	−	0.126253i	0.386661	−	0.922222i	$-0.373628\pi$
$691$	−5.74831	−	3.31879i	−0.218676	−	0.126253i	−0.605337	+	0.795969i	$0.706962\pi$
$692$	1.43279	−	2.48166i	0.0544665	−	0.0943387i
$693$		0			0
$694$		−	9.56103i		−	0.362932i
$695$	0.677790	−	0.391322i	0.0257100	−	0.0148437i
$696$		0			0
$697$			20.8295i			0.788974i
$698$	1.91637	+	3.31926i	0.0725358	+	0.125636i
$699$		0			0
$700$	5.90384	+	3.40858i	0.223144	+	0.128832i
$701$	49.2722			1.86099			0.930494	−	0.366308i	$-0.119378\pi$
$701$	49.2722			1.86099			0.930494	+	0.366308i	$0.119378\pi$
$702$		0			0
$703$	29.2385			1.10275
$704$	−14.3377	−	8.27789i	−0.540373	−	0.311985i
$705$		0			0
$706$	−3.56767	−	6.17938i	−0.134271	−	0.232564i
$707$			2.57631i			0.0968921i
$708$		0			0
$709$	−10.0225	+	5.78651i	−0.376404	+	0.217317i	−0.676253	−	0.736670i	$-0.736397\pi$
$709$	−10.0225	+	5.78651i	−0.376404	+	0.217317i	0.299848	+	0.953987i	$0.403064\pi$
$710$			4.48842i			0.168448i
$711$		0			0
$712$	−11.0362	+	19.1152i	−0.413598	+	0.716373i
$713$	−26.0906	−	15.0634i	−0.977099	−	0.564129i
$714$		0			0
$715$	−22.1096	−	0.189677i	−0.826852	−	0.00709351i
$716$	34.8436			1.30217
$717$		0			0
$718$	4.07563	−	7.05920i	0.152101	−	0.263447i
$719$	6.02564	+	10.4367i	0.224718	+	0.389224i	0.956235	−	0.292600i	$-0.0945204\pi$
$719$	6.02564	+	10.4367i	0.224718	+	0.389224i	−0.731516	+	0.681824i	$0.761187\pi$
$720$		0			0
$721$	−8.99146	+	5.19122i	−0.334860	+	0.193331i
$722$	8.18447	−	4.72531i	0.304594	−	0.175858i
$723$		0			0
$724$	0.519821	+	0.900356i	0.0193190	+	0.0334615i
$725$	10.8303	−	18.7587i	0.402229	−	0.696681i
$726$		0			0
$727$	−35.1133			−1.30228			−0.651139	−	0.758958i	$-0.725709\pi$
$727$	−35.1133			−1.30228			−0.651139	+	0.758958i	$0.725709\pi$
$728$	−3.34647	+	5.68309i	−0.124028	+	0.210629i
$729$		0			0
$730$	−3.42541	−	1.97766i	−0.126780	−	0.0731966i
$731$	−11.2072	+	19.4114i	−0.414513	+	0.717957i
$732$		0			0
$733$		−	4.72292i		−	0.174445i	−0.996189	−	0.0872225i	$-0.972201\pi$
$733$		−	4.72292i		−	0.174445i	0.996189	−	0.0872225i	$-0.0277991\pi$
$734$	4.60461	−	2.65847i	0.169959	−	0.0981259i
$735$		0			0
$736$		−	27.2405i		−	1.00410i
$737$	−9.43081	−	16.3346i	−0.347388	−	0.601694i
$738$		0			0
$739$	5.24267	+	3.02686i	0.192855	+	0.111345i	0.593318	−	0.804968i	$-0.297818\pi$
$739$	5.24267	+	3.02686i	0.192855	+	0.111345i	−0.400464	+	0.916313i	$0.631151\pi$
$740$	8.86089			0.325733
$741$		0			0
$742$	0.742930			0.0272738
$743$	−20.5317	−	11.8540i	−0.753235	−	0.434880i	0.0736267	−	0.997286i	$-0.476543\pi$
$743$	−20.5317	−	11.8540i	−0.753235	−	0.434880i	−0.826862	+	0.562406i	$0.809876\pi$
$744$		0			0
$745$	12.0596	+	20.8879i	0.441831	+	0.765274i
$746$			3.51630i			0.128741i
$747$		0			0
$748$	20.6213	−	11.9057i	0.753991	−	0.435317i
$749$			17.0355i			0.622463i
$750$		0			0
$751$	12.0552	−	20.8801i	0.439899	−	0.761927i	−0.557782	−	0.829987i	$-0.688348\pi$
$751$	12.0552	−	20.8801i	0.439899	−	0.761927i	0.997681	+	0.0680602i	$0.0216810\pi$
$752$	−11.9254	−	6.88514i	−0.434875	−	0.251075i
$753$		0			0
$754$	8.46210	+	4.98287i	0.308171	+	0.181465i
$755$	−8.46436			−0.308050
$756$		0			0
$757$	18.0820	−	31.3189i	0.657200	−	1.13830i	−0.324137	−	0.946010i	$-0.605074\pi$
$757$	18.0820	−	31.3189i	0.657200	−	1.13830i	0.981337	−	0.192294i	$-0.0615927\pi$
$758$	0.640246	+	1.10894i	0.0232548	+	0.0402785i
$759$		0			0
$760$	10.4642	−	6.04153i	0.379578	−	0.219149i
$761$	11.8683	−	6.85216i	0.430225	−	0.248390i	−0.269218	−	0.963079i	$-0.586765\pi$
$761$	11.8683	−	6.85216i	0.430225	−	0.248390i	0.699442	+	0.714689i	$0.253432\pi$
$762$		0			0
$763$	−0.930628	−	1.61189i	−0.0336910	−	0.0583545i
$764$	8.09260	−	14.0168i	0.292780	−	0.507110i
$765$		0			0
$766$	−4.18371			−0.151163
$767$	32.5179	+	19.1480i	1.17415	+	0.691395i
$768$		0			0
$769$	36.7196	+	21.2001i	1.32414	+	0.764494i	0.984387	−	0.176019i	$-0.0563221\pi$
$769$	36.7196	+	21.2001i	1.32414	+	0.764494i	0.339756	+	0.940513i	$0.389655\pi$
$770$	1.49012	−	2.58097i	0.0537003	−	0.0930116i
$771$		0			0
$772$			5.79825i			0.208683i
$773$	3.66142	−	2.11392i	0.131692	−	0.0760325i	−0.432707	−	0.901535i	$-0.642441\pi$
$773$	3.66142	−	2.11392i	0.131692	−	0.0760325i	0.564399	+	0.825502i	$0.309108\pi$
$774$		0			0
$775$			21.1192i			0.758624i
$776$	−15.3295	−	26.5515i	−0.550298	−	0.953144i
$777$		0			0
$778$	−8.40604	−	4.85323i	−0.301371	−	0.173997i
$779$	55.0683			1.97303
$780$		0			0
$781$	49.9000			1.78556
$782$	5.44236	+	3.14215i	0.194618	+	0.112363i
$783$		0			0
$784$	1.31934	+	2.28516i	0.0471191	+	0.0816127i
$785$		−	16.4990i		−	0.588875i
$786$		0			0
$787$	13.3645	−	7.71598i	0.476392	−	0.275045i	−0.242520	−	0.970147i	$-0.577974\pi$
$787$	13.3645	−	7.71598i	0.476392	−	0.275045i	0.718912	+	0.695101i	$0.244641\pi$
$788$		−	27.0223i		−	0.962628i
$789$		0			0
$790$	−4.04229	+	7.00144i	−0.143818	+	0.249100i
$791$	4.12870	+	2.38371i	0.146800	+	0.0847549i
$792$		0			0
$793$	13.9885	−	23.7558i	0.496746	−	0.843593i
$794$	−1.38952			−0.0493122
$795$		0			0
$796$	−12.8079	+	22.1840i	−0.453966	+	0.786291i
$797$	−10.0729	−	17.4467i	−0.356799	−	0.617994i	0.630625	−	0.776088i	$-0.282799\pi$
$797$	−10.0729	−	17.4467i	−0.356799	−	0.617994i	−0.987424	+	0.158094i	$0.949465\pi$
$798$		0			0
$799$	10.5997	−	6.11972i	0.374989	−	0.216500i
$800$	−16.5375	+	9.54795i	−0.584690	+	0.337571i
$801$		0			0
$802$	−4.38015	−	7.58664i	−0.154668	−	0.267893i
$803$	−21.9867	+	38.0820i	−0.775893	+	1.34389i
$804$		0			0
$805$	−5.87384			−0.207026
$806$	−9.57435	−	0.0821377i	−0.337242	−	0.00289318i
$807$		0			0
$808$	−4.08116	−	2.35626i	−0.143575	−	0.0828929i
$809$	17.0108	−	29.4635i	0.598067	−	1.03588i	−0.395040	−	0.918664i	$-0.629269\pi$
$809$	17.0108	−	29.4635i	0.598067	−	1.03588i	0.993106	−	0.117218i	$-0.0373975\pi$
$810$		0			0
$811$			30.0516i			1.05525i	0.849477	+	0.527626i	$0.176918\pi$
$811$			30.0516i			1.05525i	−0.849477	+	0.527626i	$0.823082\pi$
$812$	8.56062	−	4.94247i	0.300419	−	0.173447i
$813$		0			0
$814$			13.1912i			0.462352i
$815$	−3.14074	−	5.43992i	−0.110015	−	0.190552i
$816$		0			0
$817$	51.3192	+	29.6291i	1.79543	+	1.03659i
$818$	−4.25604			−0.148809
$819$		0			0
$820$	16.6888			0.582797
$821$	−11.7870	−	6.80525i	−0.411370	−	0.237505i	0.280008	−	0.959998i	$-0.409663\pi$
$821$	−11.7870	−	6.80525i	−0.411370	−	0.237505i	−0.691378	+	0.722493i	$0.742996\pi$
$822$		0			0
$823$	20.1300	+	34.8662i	0.701688	+	1.21536i	0.967874	+	0.251437i	$0.0809032\pi$
$823$	20.1300	+	34.8662i	0.701688	+	1.21536i	−0.266186	+	0.963922i	$0.585763\pi$
$824$		−	18.9913i		−	0.661593i
$825$		0			0
$826$	−4.40504	+	2.54325i	−0.153271	+	0.0884910i
$827$		−	16.6662i		−	0.579541i	−0.957096	−	0.289771i	$-0.906421\pi$
$827$		−	16.6662i		−	0.579541i	0.957096	−	0.289771i	$-0.0935790\pi$
$828$		0			0
$829$	6.11891	−	10.5983i	0.212518	−	0.368093i	−0.739984	−	0.672625i	$-0.765167\pi$
$829$	6.11891	−	10.5983i	0.212518	−	0.368093i	0.952502	+	0.304532i	$0.0985001\pi$
$830$	1.18066	+	0.681655i	0.0409814	+	0.0236606i
$831$		0			0
$832$	5.10792	+	9.02511i	0.177085	+	0.312889i
$833$	−2.34533			−0.0812608
$834$		0			0
$835$	−5.06520	+	8.77319i	−0.175289	+	0.303609i
$836$	−31.4759	−	54.5179i	−1.08862	−	1.88554i
$837$		0			0
$838$	−0.727654	+	0.420111i	−0.0251364	+	0.0145125i
$839$	−40.5002	+	23.3828i	−1.39822	+	0.807265i	−0.994206	−	0.107487i	$-0.965720\pi$
$839$	−40.5002	+	23.3828i	−1.39822	+	0.807265i	−0.404017	+	0.914752i	$0.632386\pi$
$840$		0			0
$841$	−1.20410	−	2.08555i	−0.0415205	−	0.0719157i
$842$	−6.23103	+	10.7925i	−0.214736	+	0.371933i
$843$		0			0
$844$	−29.1511			−1.00342
$845$	11.8736	+	7.12959i	0.408464	+	0.245265i
$846$		0			0
$847$	−19.1676	−	11.0664i	−0.658607	−	0.380247i
$848$	2.01686	−	3.49331i	0.0692593	−	0.119961i
$849$		0			0
$850$		−	4.40536i		−	0.151103i
$851$	22.5157	−	12.9994i	0.771827	−	0.445615i
$852$		0			0
$853$		−	4.23317i		−	0.144941i	−0.997371	−	0.0724704i	$-0.976912\pi$
$853$		−	4.23317i		−	0.144941i	0.997371	−	0.0724704i	$-0.0230883\pi$
$854$	1.85796	+	3.21808i	0.0635781	+	0.110120i
$855$		0			0
$856$	−26.9861	−	15.5804i	−0.922366	−	0.532528i
$857$	−12.7087			−0.434122			−0.217061	−	0.976158i	$-0.569647\pi$
$857$	−12.7087			−0.434122			−0.217061	+	0.976158i	$0.569647\pi$
$858$		0			0
$859$	12.6692			0.432266			0.216133	−	0.976364i	$-0.430655\pi$
$859$	12.6692			0.432266			0.216133	+	0.976364i	$0.430655\pi$
$860$	15.5526	+	8.97928i	0.530338	+	0.306191i
$861$		0			0
$862$	−0.0625626	−	0.108362i	−0.00213089	−	0.00369081i
$863$			27.6136i			0.939979i	0.882672	+	0.469989i	$0.155742\pi$
$863$			27.6136i			0.939979i	−0.882672	+	0.469989i	$0.844258\pi$
$864$		0			0
$865$	1.49895	−	0.865417i	0.0509657	−	0.0294251i
$866$		−	11.8232i		−	0.401770i
$867$		0			0
$868$	−4.81892	+	8.34662i	−0.163565	+	0.283303i
$869$	77.8385	+	44.9401i	2.64049	+	1.52449i
$870$		0			0
$871$	−0.101353	+	11.8142i	−0.00343423	+	0.400310i
$872$	3.40456			0.115293
$873$		0			0
$874$	8.30709	−	14.3883i	0.280991	−	0.486692i
$875$	4.72221	+	8.17911i	0.159640	+	0.276504i
$876$		0			0
$877$	−2.23965	+	1.29306i	−0.0756275	+	0.0436636i	−0.537337	−	0.843368i	$-0.680570\pi$
$877$	−2.23965	+	1.29306i	−0.0756275	+	0.0436636i	0.461709	+	0.887031i	$0.347236\pi$
$878$	7.16252	−	4.13528i	0.241723	−	0.139559i
$879$		0			0
$880$	−8.09060	−	14.0133i	−0.272734	−	0.472389i
$881$	−7.62486	+	13.2067i	−0.256888	+	0.444943i	−0.965407	−	0.260749i	$-0.916031\pi$
$881$	−7.62486	+	13.2067i	−0.256888	+	0.444943i	0.708518	+	0.705692i	$0.249364\pi$
$882$		0			0
$883$	20.9880			0.706304			0.353152	−	0.935566i	$-0.385110\pi$
$883$	20.9880			0.706304			0.353152	+	0.935566i	$0.385110\pi$
$884$	−14.9146	−	0.127952i	−0.501633	−	0.00430348i
$885$		0			0
$886$	−16.0592	−	9.27180i	−0.539521	−	0.311492i
$887$	0.684569	−	1.18571i	0.0229856	−	0.0398122i	−0.854304	−	0.519774i	$-0.826016\pi$
$887$	0.684569	−	1.18571i	0.0229856	−	0.0398122i	0.877289	+	0.479962i	$0.159349\pi$
$888$		0			0
$889$		−	1.18761i		−	0.0398311i
$890$	−5.41062	+	3.12382i	−0.181364	+	0.104711i
$891$		0			0
$892$			38.2577i			1.28096i
$893$	−16.1791	−	28.0230i	−0.541412	−	0.937753i
$894$		0			0
$895$	18.2262	+	10.5229i	0.609236	+	0.351742i
$896$	−11.2792			−0.376813
$897$		0			0
$898$	−20.0877			−0.670334
$899$	26.5203	+	15.3115i	0.884503	+	0.510668i
$900$		0			0
$901$	1.79265	+	3.10496i	0.0597217	+	0.103441i
$902$			24.8446i			0.827233i
$903$		0			0
$904$	−7.55211	+	4.36021i	−0.251180	+	0.145019i
$905$			0.627952i			0.0208738i
$906$		0			0
$907$	−14.3349	+	24.8288i	−0.475984	+	0.824428i	−0.999621	−	0.0275130i	$-0.991241\pi$
$907$	−14.3349	+	24.8288i	−0.475984	+	0.824428i	0.523638	+	0.851941i	$0.324575\pi$
$908$	−8.30279	−	4.79362i	−0.275538	−	0.159082i
$909$		0			0
$910$	−1.62463	+	0.919489i	−0.0538560	+	0.0304808i
$911$	−11.9761			−0.396784			−0.198392	−	0.980123i	$-0.563572\pi$
$911$	−11.9761			−0.396784			−0.198392	+	0.980123i	$0.563572\pi$
$912$		0			0
$913$	7.57830	−	13.1260i	0.250805	−	0.434407i
$914$	−4.52533	−	7.83810i	−0.149685	−	0.259261i
$915$		0			0
$916$	15.2700	−	8.81614i	0.504535	−	0.291294i
$917$	−12.8398	+	7.41307i	−0.424008	+	0.244801i
$918$		0			0
$919$	−13.0048	−	22.5249i	−0.428988	−	0.743029i	0.567796	−	0.823169i	$-0.307796\pi$
$919$	−13.0048	−	22.5249i	−0.428988	−	0.743029i	−0.996784	+	0.0801408i	$0.974463\pi$
$920$	5.37213	−	9.30480i	0.177114	−	0.306770i
$921$		0			0
$922$	3.69803			0.121788
$923$	−26.9340	−	15.8600i	−0.886544	−	0.522038i
$924$		0			0
$925$	−15.7837	−	9.11274i	−0.518966	−	0.299625i
$926$	−6.12418	+	10.6074i	−0.201253	+	0.348580i
$927$		0			0
$928$			27.6892i			0.908944i
$929$	24.7855	−	14.3099i	0.813185	−	0.469492i	−0.0348760	−	0.999392i	$-0.511104\pi$
$929$	24.7855	−	14.3099i	0.813185	−	0.469492i	0.848061	+	0.529899i	$0.177770\pi$
$930$		0			0
$931$			6.20049i			0.203213i
$932$	1.52176	+	2.63577i	0.0498469	+	0.0863374i
$933$		0			0
$934$	−7.82855	−	4.51982i	−0.256158	−	0.147893i
$935$	14.3823			0.470352
$936$		0			0
$937$	−45.1573			−1.47522			−0.737612	−	0.675225i	$-0.764047\pi$
$937$	−45.1573			−1.47522			−0.737612	+	0.675225i	$0.764047\pi$
$938$	−1.37914	−	0.796244i	−0.0450304	−	0.0259983i
$939$		0			0
$940$	−4.90316	−	8.49252i	−0.159923	−	0.276996i
$941$			33.5054i			1.09224i	0.837705	+	0.546122i	$0.183897\pi$
$941$			33.5054i			1.09224i	−0.837705	+	0.546122i	$0.816103\pi$
$942$		0			0
$943$	42.4064	−	24.4834i	1.38094	−	0.797288i
$944$			27.6171i			0.898859i
$945$		0			0
$946$	−13.3675	+	23.1531i	−0.434613	+	0.752772i
$947$	−35.4712	−	20.4793i	−1.15266	−	0.665488i	−0.203125	−	0.979153i	$-0.565110\pi$
$947$	−35.4712	−	20.4793i	−1.15266	−	0.665488i	−0.949534	+	0.313665i	$0.898443\pi$
$948$		0			0
$949$	23.9713	−	13.5670i	0.778142	−	0.440404i
$950$	−11.6467			−0.377870
$951$		0			0
$952$	2.14501	−	3.71526i	0.0695201	−	0.120412i
$953$	13.5406	+	23.4530i	0.438622	+	0.759716i	0.997584	−	0.0694777i	$-0.0221333\pi$
$953$	13.5406	+	23.4530i	0.438622	+	0.759716i	−0.558961	+	0.829194i	$0.688800\pi$
$954$		0			0
$955$	8.46626	−	4.88800i	0.273962	−	0.158172i
$956$	8.87233	−	5.12244i	0.286952	−	0.165672i
$957$		0			0
$958$	5.96284	+	10.3279i	0.192651	+	0.333681i
$959$	3.28655	−	5.69247i	0.106128	−	0.183820i
$960$		0			0
$961$	1.14247			0.0368538
$962$	4.19263	−	7.12008i	0.135176	−	0.229561i
$963$		0			0
$964$	−16.9862	−	9.80699i	−0.547089	−	0.315862i
$965$	−1.75109	+	3.03298i	−0.0563697	+	0.0976352i
$966$		0			0
$967$		−	57.7720i		−	1.85782i	−0.370301	−	0.928912i	$-0.620746\pi$
$967$		−	57.7720i		−	1.85782i	0.370301	−	0.928912i	$-0.379254\pi$
$968$	35.0609	−	20.2424i	1.12690	−	0.650616i
$969$		0			0
$970$		−	8.67813i		−	0.278638i
$971$	27.8843	+	48.2970i	0.894849	+	1.54992i	0.833992	+	0.551777i	$0.186050\pi$
$971$	27.8843	+	48.2970i	0.894849	+	1.54992i	0.0608566	+	0.998147i	$0.480617\pi$
$972$		0			0
$973$	−0.636208	−	0.367315i	−0.0203959	−	0.0117756i
$974$	−14.9509			−0.479058
$975$		0			0
$976$	20.1755			0.645803
$977$	25.4683	+	14.7042i	0.814804	+	0.470427i	0.848621	−	0.529001i	$-0.177433\pi$
$977$	25.4683	+	14.7042i	0.814804	+	0.470427i	−0.0338172	+	0.999428i	$0.510766\pi$
$978$		0			0
$979$	34.7291	+	60.1526i	1.10995	+	1.92248i
$980$			1.87910i			0.0600255i
$981$		0			0
$982$	8.08221	−	4.66627i	0.257914	−	0.148907i
$983$		−	43.0253i		−	1.37229i	−0.727464	−	0.686146i	$-0.759301\pi$
$983$		−	43.0253i		−	1.37229i	0.727464	−	0.686146i	$-0.240699\pi$
$984$		0			0
$985$	8.16083	−	14.1350i	0.260026	−	0.450378i
$986$	−5.53201	−	3.19390i	−0.176175	−	0.101715i
$987$		0			0
$988$	−0.338274	+	39.4307i	−0.0107619	+	1.25446i
$989$	52.6925			1.67552
$990$		0			0
$991$	25.9615	−	44.9666i	0.824693	−	1.42841i	−0.0774611	−	0.996995i	$-0.524681\pi$
$991$	25.9615	−	44.9666i	0.824693	−	1.42841i	0.902154	−	0.431414i	$-0.141985\pi$
$992$	−13.4985	−	23.3801i	−0.428579	−	0.742320i
$993$		0			0
$994$	3.64862	−	2.10653i	0.115727	−	0.0668151i
$995$	−13.3993	+	7.73611i	−0.424787	+	0.245251i
$996$		0			0
$997$	4.05357	+	7.02099i	0.128378	+	0.222357i	0.923048	−	0.384684i	$-0.125690\pi$
$997$	4.05357	+	7.02099i	0.128378	+	0.222357i	−0.794670	+	0.607041i	$0.792356\pi$
$998$	−3.41631	+	5.91722i	−0.108141	+	0.187306i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.b.316.5		16
3.2	odd	2		273.2.bd.a.43.4	✓	16
13.10	even	6	inner	819.2.ct.b.127.5		16
39.20	even	12		3549.2.a.bb.1.4		8
39.23	odd	6		273.2.bd.a.127.4	yes	16
39.32	even	12		3549.2.a.bd.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.4	✓	16	3.2	odd	2
273.2.bd.a.127.4	yes	16	39.23	odd	6
819.2.ct.b.127.5		16	13.10	even	6	inner
819.2.ct.b.316.5		16	1.1	even	1	trivial
3549.2.a.bb.1.4		8	39.20	even	12
3549.2.a.bd.1.5		8	39.32	even	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.420879 + 0.242995i) q^{2} +(-0.881907 - 1.52751i) q^{4} -1.06536i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.82917i q^{8} +(0.258876 - 0.448387i) q^{10} +(-4.98494 - 2.87806i) q^{11} +(1.77592 + 3.13785i) q^{13} -0.485989 q^{14} +(-1.31934 + 2.28516i) q^{16} +(-1.17266 - 2.03111i) q^{17} +(-5.36979 + 3.10025i) q^{19} +(-1.62734 + 0.939548i) q^{20} +(-1.39870 - 2.42263i) q^{22} +(-2.75674 + 4.77481i) q^{23} +3.86501 q^{25} +(-0.0150320 + 1.75219i) q^{26} +(1.52751 + 0.881907i) q^{28} +(2.80215 - 4.85347i) q^{29} +5.46420i q^{31} +(-4.27878 + 2.47036i) q^{32} -1.13980i q^{34} +(0.532679 + 0.922628i) q^{35} +(-4.08375 - 2.35775i) q^{37} -3.01337 q^{38} -1.94873 q^{40} +(-7.69141 - 4.44064i) q^{41} +(-4.77851 - 8.27662i) q^{43} +10.1527i q^{44} +(-2.32051 + 1.33975i) q^{46} +5.21864i q^{47} +(0.500000 - 0.866025i) q^{49} +(1.62670 + 0.939177i) q^{50} +(3.22689 - 5.48003i) q^{52} -1.52870 q^{53} +(-3.06616 + 5.31075i) q^{55} +(0.914587 + 1.58411i) q^{56} +(2.35873 - 1.36181i) q^{58} +(9.06406 - 5.23314i) q^{59} +(-3.82305 - 6.62171i) q^{61} +(-1.32777 + 2.29977i) q^{62} +2.87621 q^{64} +(3.34294 - 1.89199i) q^{65} +(2.83779 + 1.63840i) q^{67} +(-2.06836 + 3.58251i) q^{68} +0.517753i q^{70} +(-7.50761 + 4.33452i) q^{71} -7.63941i q^{73} +(-1.14584 - 1.98466i) q^{74} +(9.47131 + 5.46826i) q^{76} +5.75611 q^{77} -15.6147 q^{79} +(2.43451 + 1.40557i) q^{80} +(-2.15810 - 3.73794i) q^{82} +2.63313i q^{83} +(-2.16387 + 1.24931i) q^{85} -4.64461i q^{86} +(-5.26447 + 9.11832i) q^{88} +(-10.4502 - 6.03343i) q^{89} +(-3.10692 - 1.82950i) q^{91} +9.72476 q^{92} +(-1.26810 + 2.19642i) q^{94} +(3.30288 + 5.72075i) q^{95} +(14.5156 - 8.38057i) q^{97} +(0.420879 - 0.242995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40}+ \cdots - 54 q^{97}+O(q^{100}) \) 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

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