LMFDB - Embedded newform 297.2.e.e.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$0.947217 + 0.807294i$ of defining polynomial
Character	$\chi$	$=$	297.100
Dual form			297.2.e.e.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.447217 + 0.774602i) q^{2} +(0.599994 + 1.03922i) q^{4} +(1.87447 + 3.24667i) q^{5} +(-0.725528 + 1.25665i) q^{7} -2.86218 q^{8} +O(q^{10})$	\(q+(-0.447217 + 0.774602i) q^{2} +(0.599994 + 1.03922i) q^{4} +(1.87447 + 3.24667i) q^{5} +(-0.725528 + 1.25665i) q^{7} -2.86218 q^{8} -3.35317 q^{10} +(0.500000 - 0.866025i) q^{11} +(-2.87831 - 4.98537i) q^{13} +(-0.648937 - 1.12399i) q^{14} +(0.0800260 - 0.138609i) q^{16} +4.79655 q^{17} +0.702126 q^{19} +(-2.24934 + 3.89597i) q^{20} +(0.447217 + 0.774602i) q^{22} +(-0.825523 - 1.42985i) q^{23} +(-4.52724 + 7.84141i) q^{25} +5.14891 q^{26} -1.74125 q^{28} +(-2.15278 + 3.72872i) q^{29} +(1.65278 + 2.86269i) q^{31} +(-2.79060 - 4.83346i) q^{32} +(-2.14510 + 3.71542i) q^{34} -5.43991 q^{35} +9.73779 q^{37} +(-0.314002 + 0.543868i) q^{38} +(-5.36505 - 9.29255i) q^{40} +(2.12380 + 3.67853i) q^{41} +(2.05278 - 3.55552i) q^{43} +1.19999 q^{44} +1.47675 q^{46} +(0.898274 - 1.55586i) q^{47} +(2.44722 + 4.23870i) q^{49} +(-4.04932 - 7.01363i) q^{50} +(3.45393 - 5.98239i) q^{52} +1.15318 q^{53} +3.74893 q^{55} +(2.07659 - 3.59676i) q^{56} +(-1.92552 - 3.33509i) q^{58} +(-2.32552 - 4.02792i) q^{59} +(-1.27447 + 2.20745i) q^{61} -2.95660 q^{62} +5.31212 q^{64} +(10.7906 - 18.6898i) q^{65} +(-4.47062 - 7.74334i) q^{67} +(2.87790 + 4.98467i) q^{68} +(2.43282 - 4.21377i) q^{70} -5.14204 q^{71} +10.5378 q^{73} +(-4.35490 + 7.54291i) q^{74} +(0.421271 + 0.729663i) q^{76} +(0.725528 + 1.25665i) q^{77} +(0.543371 - 0.941146i) q^{79} +0.600024 q^{80} -3.79920 q^{82} +(-1.90171 + 3.29386i) q^{83} +(8.99096 + 15.5728i) q^{85} +(1.83608 + 3.18018i) q^{86} +(-1.43109 + 2.47872i) q^{88} +4.01536 q^{89} +8.35317 q^{91} +(0.990617 - 1.71580i) q^{92} +(0.803446 + 1.39161i) q^{94} +(1.31611 + 2.27957i) q^{95} +(-1.64550 + 2.85009i) q^{97} -4.37775 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7}+O(q^{10}) $ 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7	$ 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 6 q^{37} + 3 q^{38} - 12 q^{40} - 2 q^{41} + 21 q^{43} - 22 q^{44} + 4 q^{46} - 7 q^{47} + 15 q^{49} + 23 q^{50} + 10 q^{52} + 12 q^{53} + 8 q^{55} + 18 q^{56} + 21 q^{58} + 2 q^{59} - 15 q^{61} + 40 q^{62} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} + 38 q^{70} + 6 q^{71} + 44 q^{73} - 36 q^{74} - 42 q^{76} + q^{77} - 11 q^{79} + 68 q^{80} - 34 q^{82} + 18 q^{83} - 13 q^{85} - 24 q^{86} + 12 q^{89} + 38 q^{91} + 67 q^{92} + 19 q^{94} - 30 q^{95} - 26 q^{97} - 30 q^{98}+O(q^{100}) $ 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.447217	+	0.774602i	−0.316230	+	0.547727i	−0.979698	−	0.200478i	$-0.935750\pi$
$2$	−0.447217	+	0.774602i	−0.316230	+	0.547727i	0.663468	+	0.748205i	$0.269084\pi$
$3$		0			0
$3$		0			0
$4$	0.599994	+	1.03922i	0.299997	+	0.519610i
$5$	1.87447	+	3.24667i	0.838287	+	1.45195i	0.891326	+	0.453362i	$0.149776\pi$
$5$	1.87447	+	3.24667i	0.838287	+	1.45195i	−0.0530397	+	0.998592i	$0.516891\pi$
$6$		0			0
$7$	−0.725528	+	1.25665i	−0.274224	+	0.474970i	−0.969939	−	0.243348i	$-0.921754\pi$
$7$	−0.725528	+	1.25665i	−0.274224	+	0.474970i	0.695715	+	0.718318i	$0.255088\pi$
$8$	−2.86218			−1.01193
$9$		0			0
$10$	−3.35317			−1.06037
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−2.87831	−	4.98537i	−0.798298	−	1.38269i	−0.920724	−	0.390216i	$-0.872400\pi$
$13$	−2.87831	−	4.98537i	−0.798298	−	1.38269i	0.122425	−	0.992478i	$-0.460933\pi$
$14$	−0.648937	−	1.12399i	−0.173436	−	0.300400i
$15$		0			0
$16$	0.0800260	−	0.138609i	0.0200065	−	0.0346523i
$17$	4.79655			1.16333			0.581667	−	0.813427i	$-0.302401\pi$
$17$	4.79655			1.16333			0.581667	+	0.813427i	$0.302401\pi$
$18$		0			0
$19$	0.702126			0.161079			0.0805393	−	0.996751i	$-0.474336\pi$
$19$	0.702126			0.161079			0.0805393	+	0.996751i	$0.474336\pi$
$20$	−2.24934	+	3.89597i	−0.502967	+	0.871164i
$21$		0			0
$22$	0.447217	+	0.774602i	0.0953470	+	0.165146i
$23$	−0.825523	−	1.42985i	−0.172133	−	0.298144i	0.767032	−	0.641609i	$-0.221733\pi$
$23$	−0.825523	−	1.42985i	−0.172133	−	0.298144i	−0.939165	+	0.343465i	$0.888399\pi$
$24$		0			0
$25$	−4.52724	+	7.84141i	−0.905449	+	1.56828i
$26$	5.14891			1.00978
$27$		0			0
$28$	−1.74125			−0.329066
$29$	−2.15278	+	3.72872i	−0.399761	+	0.692406i	−0.993696	−	0.112107i	$-0.964240\pi$
$29$	−2.15278	+	3.72872i	−0.399761	+	0.692406i	0.593935	+	0.804513i	$0.297573\pi$
$30$		0			0
$31$	1.65278	+	2.86269i	0.296848	+	0.514155i	0.975413	−	0.220385i	$-0.0707313\pi$
$31$	1.65278	+	2.86269i	0.296848	+	0.514155i	−0.678565	+	0.734540i	$0.737398\pi$
$32$	−2.79060	−	4.83346i	−0.493313	−	0.854443i
$33$		0			0
$34$	−2.14510	+	3.71542i	−0.367881	+	0.637189i
$35$	−5.43991			−0.919513
$36$		0			0
$37$	9.73779			1.60088			0.800441	−	0.599411i	$-0.204599\pi$
$37$	9.73779			1.60088			0.800441	+	0.599411i	$0.204599\pi$
$38$	−0.314002	+	0.543868i	−0.0509379	+	0.0882271i
$39$		0			0
$40$	−5.36505	−	9.29255i	−0.848289	−	1.46928i
$41$	2.12380	+	3.67853i	0.331682	+	0.574490i	0.982842	−	0.184450i	$-0.0590505\pi$
$41$	2.12380	+	3.67853i	0.331682	+	0.574490i	−0.651160	+	0.758941i	$0.725717\pi$
$42$		0			0
$43$	2.05278	−	3.55552i	0.313046	−	0.542212i	−0.665974	−	0.745975i	$-0.731984\pi$
$43$	2.05278	−	3.55552i	0.313046	−	0.542212i	0.979020	+	0.203763i	$0.0653171\pi$
$44$	1.19999			0.180905
$45$		0			0
$46$	1.47675			0.217735
$47$	0.898274	−	1.55586i	0.131027	−	0.226945i	−0.793046	−	0.609162i	$-0.791506\pi$
$47$	0.898274	−	1.55586i	0.131027	−	0.226945i	0.924073	+	0.382217i	$0.124839\pi$
$48$		0			0
$49$	2.44722	+	4.23870i	0.349602	+	0.605529i
$50$	−4.04932	−	7.01363i	−0.572660	−	0.991877i
$51$		0			0
$52$	3.45393	−	5.98239i	0.478974	−	0.829608i
$53$	1.15318			0.158402			0.0792009	−	0.996859i	$-0.474763\pi$
$53$	1.15318			0.158402			0.0792009	+	0.996859i	$0.474763\pi$
$54$		0			0
$55$	3.74893			0.505506
$56$	2.07659	−	3.59676i	0.277496	−	0.480637i
$57$		0			0
$58$	−1.92552	−	3.33509i	−0.252833	−	0.437919i
$59$	−2.32552	−	4.02792i	−0.302757	−	0.524391i	0.674002	−	0.738729i	$-0.264574\pi$
$59$	−2.32552	−	4.02792i	−0.302757	−	0.524391i	−0.976759	+	0.214338i	$0.931240\pi$
$60$		0			0
$61$	−1.27447	+	2.20745i	−0.163179	+	0.282635i	−0.936007	−	0.351981i	$-0.885508\pi$
$61$	−1.27447	+	2.20745i	−0.163179	+	0.282635i	0.772828	+	0.634616i	$0.218842\pi$
$62$	−2.95660			−0.375489
$63$		0			0
$64$	5.31212			0.664015
$65$	10.7906	−	18.6898i	1.33841	−	2.31819i
$66$		0			0
$67$	−4.47062	−	7.74334i	−0.546173	−	0.946000i	−0.998532	−	0.0541636i	$-0.982751\pi$
$67$	−4.47062	−	7.74334i	−0.546173	−	0.946000i	0.452359	−	0.891836i	$-0.350583\pi$
$68$	2.87790	+	4.98467i	0.348997	+	0.604480i
$69$		0			0
$70$	2.43282	−	4.21377i	0.290778	−	0.503642i
$71$	−5.14204			−0.610248			−0.305124	−	0.952313i	$-0.598698\pi$
$71$	−5.14204			−0.610248			−0.305124	+	0.952313i	$0.598698\pi$
$72$		0			0
$73$	10.5378			1.23336			0.616678	−	0.787215i	$-0.288478\pi$
$73$	10.5378			1.23336			0.616678	+	0.787215i	$0.288478\pi$
$74$	−4.35490	+	7.54291i	−0.506247	+	0.876846i
$75$		0			0
$76$	0.421271	+	0.729663i	0.0483231	+	0.0836981i
$77$	0.725528	+	1.25665i	0.0826816	+	0.143209i
$78$		0			0
$79$	0.543371	−	0.941146i	0.0611340	−	0.105887i	−0.833839	−	0.552008i	$-0.813862\pi$
$79$	0.543371	−	0.941146i	0.0611340	−	0.105887i	0.894973	+	0.446121i	$0.147195\pi$
$80$	0.600024			0.0670847
$81$		0			0
$82$	−3.79920			−0.419552
$83$	−1.90171	+	3.29386i	−0.208740	+	0.361548i	−0.951318	−	0.308212i	$-0.900269\pi$
$83$	−1.90171	+	3.29386i	−0.208740	+	0.361548i	0.742578	+	0.669759i	$0.233603\pi$
$84$		0			0
$85$	8.99096	+	15.5728i	0.975207	+	1.68911i
$86$	1.83608	+	3.18018i	0.197989	+	0.342928i
$87$		0			0
$88$	−1.43109	+	2.47872i	−0.152555	+	0.264232i
$89$	4.01536			0.425627			0.212814	−	0.977093i	$-0.431737\pi$
$89$	4.01536			0.425627			0.212814	+	0.977093i	$0.431737\pi$
$90$		0			0
$91$	8.35317			0.875650
$92$	0.990617	−	1.71580i	0.103279	−	0.178884i
$93$		0			0
$94$	0.803446	+	1.39161i	0.0828692	+	0.143534i
$95$	1.31611	+	2.27957i	0.135030	+	0.233879i
$96$		0			0
$97$	−1.64550	+	2.85009i	−0.167075	+	0.289383i	−0.937390	−	0.348280i	$-0.886766\pi$
$97$	−1.64550	+	2.85009i	−0.167075	+	0.289383i	0.770315	+	0.637664i	$0.220099\pi$
$98$	−4.37775			−0.442219
$99$		0			0
$100$	−10.8653			−1.08653
$101$	7.09653	−	12.2916i	0.706131	−	1.22305i	−0.260151	−	0.965568i	$-0.583772\pi$
$101$	7.09653	−	12.2916i	0.706131	−	1.22305i	0.966282	−	0.257487i	$-0.0828944\pi$
$102$		0			0
$103$	−9.58885	−	16.6084i	−0.944817	−	1.63647i	−0.756116	−	0.654437i	$-0.772906\pi$
$103$	−9.58885	−	16.6084i	−0.944817	−	1.63647i	−0.188701	−	0.982035i	$-0.560428\pi$
$104$	8.23822	+	14.2690i	0.807824	+	1.39919i
$105$		0			0
$106$	−0.515723	+	0.893258i	−0.0500914	+	0.0867609i
$107$	10.0034			0.967066			0.483533	−	0.875326i	$-0.339353\pi$
$107$	10.0034			0.967066			0.483533	+	0.875326i	$0.339353\pi$
$108$		0			0
$109$	−7.40766			−0.709525			−0.354762	−	0.934956i	$-0.615438\pi$
$109$	−7.40766			−0.709525			−0.354762	+	0.934956i	$0.615438\pi$
$110$	−1.67659	+	2.90393i	−0.159856	+	0.276879i
$111$		0			0
$112$	0.116122	+	0.201130i	0.0109725	+	0.0190050i
$113$	0.821683	+	1.42320i	0.0772974	+	0.133883i	0.902083	−	0.431563i	$-0.142038\pi$
$113$	0.821683	+	1.42320i	0.0772974	+	0.133883i	−0.824786	+	0.565446i	$0.808704\pi$
$114$		0			0
$115$	3.09483	−	5.36040i	0.288594	−	0.499860i
$116$	−5.16661			−0.479708
$117$		0			0
$118$	4.16005			0.382964
$119$	−3.48003	+	6.02759i	−0.319014	+	0.552548i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−1.13993	−	1.97442i	−0.103204	−	0.178755i
$123$		0			0
$124$	−1.98331	+	3.43520i	−0.178107	+	0.308490i
$125$	−15.2000			−1.35953
$126$		0			0
$127$	−22.3309			−1.98155			−0.990773	−	0.135534i	$-0.956725\pi$
$127$	−22.3309			−1.98155			−0.990773	+	0.135534i	$0.956725\pi$
$128$	3.20553	−	5.55214i	0.283332	−	0.490745i
$129$		0			0
$130$	9.65145	+	16.7168i	0.846488	+	1.46616i
$131$	−4.89443	−	8.47741i	−0.427629	−	0.740675i	0.569033	−	0.822315i	$-0.307318\pi$
$131$	−4.89443	−	8.47741i	−0.427629	−	0.740675i	−0.996662	+	0.0816400i	$0.973984\pi$
$132$		0			0
$133$	−0.509412	+	0.882328i	−0.0441716	+	0.0765075i
$134$	7.99735			0.690866
$135$		0			0
$136$	−13.7286			−1.17722
$137$	−1.18811	+	2.05786i	−0.101507	+	0.175815i	−0.912306	−	0.409510i	$-0.865700\pi$
$137$	−1.18811	+	2.05786i	−0.101507	+	0.175815i	0.810799	+	0.585325i	$0.199033\pi$
$138$		0			0
$139$	5.74336	+	9.94779i	0.487145	+	0.843761i	0.999891	−	0.0147802i	$-0.00470485\pi$
$139$	5.74336	+	9.94779i	0.487145	+	0.843761i	−0.512745	+	0.858541i	$0.671372\pi$
$140$	−3.26392	−	5.65327i	−0.275851	−	0.477788i
$141$		0			0
$142$	2.29961	−	3.98304i	0.192979	−	0.334249i
$143$	−5.75661			−0.481392
$144$		0			0
$145$	−16.1412			−1.34046
$146$	−4.71268	+	8.16260i	−0.390024	+	0.675542i
$147$		0			0
$148$	5.84261	+	10.1197i	0.480260	+	0.831835i
$149$	−0.350657	−	0.607357i	−0.0287270	−	0.0497566i	0.851305	−	0.524672i	$-0.175812\pi$
$149$	−0.350657	−	0.607357i	−0.0287270	−	0.0497566i	−0.880031	+	0.474915i	$0.842479\pi$
$150$		0			0
$151$	1.25277	−	2.16986i	0.101949	−	0.176581i	−0.810539	−	0.585685i	$-0.800825\pi$
$151$	1.25277	−	2.16986i	0.101949	−	0.176581i	0.912488	+	0.409104i	$0.134159\pi$
$152$	−2.00961			−0.163001
$153$		0			0
$154$	−1.29787			−0.104586
$155$	−6.19615	+	10.7320i	−0.497687	+	0.862018i
$156$		0			0
$157$	−2.21785	−	3.84143i	−0.177004	−	0.306579i	0.763849	−	0.645395i	$-0.223307\pi$
$157$	−2.21785	−	3.84143i	−0.177004	−	0.306579i	−0.940853	+	0.338816i	$0.889974\pi$
$158$	0.486009	+	0.841793i	0.0386648	+	0.0669694i
$159$		0			0
$160$	10.4618	−	18.1203i	0.827075	−	1.43254i
$161$	2.39576			0.188812
$162$		0			0
$163$	17.6986			1.38626			0.693131	−	0.720812i	$-0.256231\pi$
$163$	17.6986			1.38626			0.693131	+	0.720812i	$0.256231\pi$
$164$	−2.54854	+	4.41420i	−0.199007	+	0.344691i
$165$		0			0
$166$	−1.70095	−	2.94614i	−0.132020	−	0.228664i
$167$	−4.45065	−	7.70875i	−0.344402	−	0.596521i	0.640843	−	0.767672i	$-0.278585\pi$
$167$	−4.45065	−	7.70875i	−0.344402	−	0.596521i	−0.985245	+	0.171151i	$0.945252\pi$
$168$		0			0
$169$	−10.0693	+	17.4405i	−0.774561	+	1.34158i
$170$	−16.0836			−1.23356
$171$		0			0
$172$	4.92663			0.375652
$173$	−12.3654	+	21.4176i	−0.940126	+	1.62835i	−0.174899	+	0.984586i	$0.555960\pi$
$173$	−12.3654	+	21.4176i	−0.940126	+	1.62835i	−0.765228	+	0.643760i	$0.777374\pi$
$174$		0			0
$175$	−6.56929	−	11.3783i	−0.496591	−	0.860122i
$176$	−0.0800260	−	0.138609i	−0.00603218	−	0.0104480i
$177$		0			0
$178$	−1.79574	+	3.11031i	−0.134596	+	0.233127i
$179$	11.8587			0.886362			0.443181	−	0.896432i	$-0.353850\pi$
$179$	11.8587			0.886362			0.443181	+	0.896432i	$0.353850\pi$
$180$		0			0
$181$	−4.94546			−0.367593			−0.183796	−	0.982964i	$-0.558839\pi$
$181$	−4.94546			−0.367593			−0.183796	+	0.982964i	$0.558839\pi$
$182$	−3.73568	+	6.47039i	−0.276907	+	0.479617i
$183$		0			0
$184$	2.36279	+	4.09248i	0.174187	+	0.301701i
$185$	18.2531	+	31.6154i	1.34200	+	2.32441i
$186$		0			0
$187$	2.39827	−	4.15393i	0.175379	−	0.303766i
$188$	2.15584			0.157230
$189$		0			0
$190$	−2.35435			−0.170802
$191$	0.161784	−	0.280218i	0.0117063	−	0.0202759i	−0.860113	−	0.510104i	$-0.829607\pi$
$191$	0.161784	−	0.280218i	0.0117063	−	0.0202759i	0.871819	+	0.489828i	$0.162940\pi$
$192$		0			0
$193$	−7.20767	−	12.4840i	−0.518819	−	0.898621i	−0.999761	−	0.0218687i	$-0.993038\pi$
$193$	−7.20767	−	12.4840i	−0.518819	−	0.898621i	0.480942	−	0.876753i	$-0.340295\pi$
$194$	−1.47179	−	2.54922i	−0.105669	−	0.183023i
$195$		0			0
$196$	−2.93663	+	5.08639i	−0.209759	+	0.363314i
$197$	18.3267			1.30572			0.652860	−	0.757478i	$-0.273569\pi$
$197$	18.3267			1.30572			0.652860	+	0.757478i	$0.273569\pi$
$198$		0			0
$199$	−1.51211			−0.107190			−0.0535951	−	0.998563i	$-0.517068\pi$
$199$	−1.51211			−0.107190			−0.0535951	+	0.998563i	$0.517068\pi$
$200$	12.9578	−	22.4435i	0.916253	−	1.58700i
$201$		0			0
$202$	6.34738	+	10.9940i	0.446600	+	0.773534i
$203$	−3.12380	−	5.41058i	−0.219248	−	0.379749i
$204$		0			0
$205$	−7.96199	+	13.7906i	−0.556089	+	0.963175i
$206$	17.1532			1.19512
$207$		0			0
$208$	−0.921357			−0.0638846
$209$	0.351063	−	0.608059i	0.0242835	−	0.0420603i
$210$		0			0
$211$	5.51111	+	9.54553i	0.379401	+	0.657141i	0.990975	−	0.134045i	$-0.0427968\pi$
$211$	5.51111	+	9.54553i	0.379401	+	0.657141i	−0.611574	+	0.791187i	$0.709463\pi$
$212$	0.691903	+	1.19841i	0.0475201	+	0.0823072i
$213$		0			0
$214$	−4.47369	+	7.74866i	−0.305815	+	0.529688i
$215$	15.3915			1.04969
$216$		0			0
$217$	−4.79655			−0.325611
$218$	3.31283	−	5.73799i	0.224373	−	0.388626i
$219$		0			0
$220$	2.24934	+	3.89597i	0.151650	+	0.262666i
$221$	−13.8059	−	23.9126i	−0.928687	−	1.60853i
$222$		0			0
$223$	11.6566	−	20.1899i	0.780585	−	1.35201i	−0.151017	−	0.988531i	$-0.548255\pi$
$223$	11.6566	−	20.1899i	0.780585	−	1.35201i	0.931601	−	0.363481i	$-0.118412\pi$
$224$	8.09864			0.541113
$225$		0			0
$226$	−1.46988			−0.0977750
$227$	2.98944	−	5.17787i	0.198416	−	0.343667i	−0.749599	−	0.661893i	$-0.769754\pi$
$227$	2.98944	−	5.17787i	0.198416	−	0.343667i	0.948015	+	0.318225i	$0.103087\pi$
$228$		0			0
$229$	−4.71228	−	8.16190i	−0.311396	−	0.539354i	0.667269	−	0.744817i	$-0.267463\pi$
$229$	−4.71228	−	8.16190i	−0.311396	−	0.539354i	−0.978665	+	0.205463i	$0.934130\pi$
$230$	2.76812	+	4.79452i	0.182524	+	0.316141i
$231$		0			0
$232$	6.16163	−	10.6723i	0.404531	−	0.700668i
$233$	−27.1685			−1.77987			−0.889933	−	0.456091i	$-0.849249\pi$
$233$	−27.1685			−1.77987			−0.889933	+	0.456091i	$0.849249\pi$
$234$		0			0
$235$	6.73513			0.439352
$236$	2.79060	−	4.83346i	0.181653	−	0.314631i
$237$		0			0
$238$	−3.11266	−	5.39128i	−0.201764	−	0.349465i
$239$	0.121289	+	0.210079i	0.00784553	+	0.0135889i	0.869922	−	0.493190i	$-0.164169\pi$
$239$	0.121289	+	0.210079i	0.00784553	+	0.0135889i	−0.862076	+	0.506779i	$0.830836\pi$
$240$		0			0
$241$	6.35528	−	11.0077i	0.409379	−	0.709066i	−0.585441	−	0.810715i	$-0.699079\pi$
$241$	6.35528	−	11.0077i	0.409379	−	0.709066i	0.994820	+	0.101649i	$0.0324119\pi$
$242$	0.894434			0.0574964
$243$		0			0
$244$	−3.05870			−0.195813
$245$	−9.17445	+	15.8906i	−0.586134	+	1.01521i
$246$		0			0
$247$	−2.02093	−	3.50036i	−0.128589	−	0.222722i
$248$	−4.73054	−	8.19354i	−0.300390	−	0.520290i
$249$		0			0
$250$	6.79769	−	11.7739i	0.429924	−	0.744650i
$251$	−23.6134			−1.49046			−0.745232	−	0.666805i	$-0.767661\pi$
$251$	−23.6134			−1.49046			−0.745232	+	0.666805i	$0.767661\pi$
$252$		0			0
$253$	−1.65105			−0.103800
$254$	9.98675	−	17.2976i	0.626624	−	1.08535i
$255$		0			0
$256$	8.17925	+	14.1669i	0.511203	+	0.885430i
$257$	2.05836	+	3.56518i	0.128397	+	0.222390i	0.923056	−	0.384667i	$-0.125684\pi$
$257$	2.05836	+	3.56518i	0.128397	+	0.222390i	−0.794659	+	0.607056i	$0.792350\pi$
$258$		0			0
$259$	−7.06504	+	12.2370i	−0.439000	+	0.760371i
$260$	25.8971			1.60607
$261$		0			0
$262$	8.75549			0.540916
$263$	−5.79614	+	10.0392i	−0.357405	+	0.619044i	−0.987527	−	0.157452i	$-0.949672\pi$
$263$	−5.79614	+	10.0392i	−0.357405	+	0.619044i	0.630121	+	0.776497i	$0.283005\pi$
$264$		0			0
$265$	2.16160	+	3.74400i	0.132786	+	0.229992i
$266$	−0.455635	−	0.789184i	−0.0279368	−	0.0483880i
$267$		0			0
$268$	5.36469	−	9.29192i	0.327701	−	0.567594i
$269$	6.82534			0.416148			0.208074	−	0.978113i	$-0.433280\pi$
$269$	6.82534			0.416148			0.208074	+	0.978113i	$0.433280\pi$
$270$		0			0
$271$	−7.57539			−0.460172			−0.230086	−	0.973170i	$-0.573901\pi$
$271$	−7.57539			−0.460172			−0.230086	+	0.973170i	$0.573901\pi$
$272$	0.383848	−	0.664845i	0.0232742	−	0.0403121i
$273$		0			0
$274$	−1.06268	−	1.84062i	−0.0641989	−	0.111196i
$275$	4.52724	+	7.84141i	0.273003	+	0.472855i
$276$		0			0
$277$	9.40168	−	16.2842i	0.564892	−	0.978422i	−0.432168	−	0.901793i	$-0.642251\pi$
$277$	9.40168	−	16.2842i	0.564892	−	0.978422i	0.997060	−	0.0766286i	$-0.0244156\pi$
$278$	−10.2741			−0.616200
$279$		0			0
$280$	15.5700			0.930485
$281$	12.4416	−	21.5495i	0.742205	−	1.28554i	−0.209285	−	0.977855i	$-0.567114\pi$
$281$	12.4416	−	21.5495i	0.742205	−	1.28554i	0.951489	−	0.307681i	$-0.0995530\pi$
$282$		0			0
$283$	9.07061	+	15.7108i	0.539192	+	0.933908i	0.998948	+	0.0458626i	$0.0146036\pi$
$283$	9.07061	+	15.7108i	0.539192	+	0.933908i	−0.459756	+	0.888045i	$0.652063\pi$
$284$	−3.08519	−	5.34371i	−0.183073	−	0.317091i
$285$		0			0
$286$	2.57445	−	4.45908i	0.152231	−	0.263671i
$287$	−6.16352			−0.363821
$288$		0			0
$289$	6.00687			0.353345
$290$	7.21863	−	12.5030i	0.423893	−	0.734203i
$291$		0			0
$292$	6.32262	+	10.9511i	0.370003	+	0.640864i
$293$	−8.03876	−	13.9235i	−0.469630	−	0.813422i	0.529768	−	0.848143i	$-0.322279\pi$
$293$	−8.03876	−	13.9235i	−0.469630	−	0.813422i	−0.999397	+	0.0347207i	$0.988946\pi$
$294$		0			0
$295$	8.71822	−	15.1004i	0.507595	−	0.879180i
$296$	−27.8713			−1.61998
$297$		0			0
$298$	0.627280			0.0363373
$299$	−4.75221	+	8.23107i	−0.274828	+	0.476015i
$300$		0			0
$301$	2.97871	+	5.15927i	0.171690	+	0.297375i
$302$	1.12052	+	1.94080i	0.0644787	+	0.111680i
$303$		0			0
$304$	0.0561883	−	0.0973209i	0.00322262	−	0.00558174i
$305$	−9.55581			−0.547164
$306$		0			0
$307$	−20.1343			−1.14913			−0.574563	−	0.818461i	$-0.694828\pi$
$307$	−20.1343			−1.14913			−0.574563	+	0.818461i	$0.694828\pi$
$308$	−0.870626	+	1.50797i	−0.0496085	+	0.0859244i
$309$		0			0
$310$	−5.54204	−	9.59910i	−0.314767	−	0.545192i
$311$	−6.51226	−	11.2796i	−0.369276	−	0.639605i	0.620176	−	0.784462i	$-0.287061\pi$
$311$	−6.51226	−	11.2796i	−0.369276	−	0.639605i	−0.989453	+	0.144857i	$0.953728\pi$
$312$		0			0
$313$	−5.12591	+	8.87834i	−0.289734	+	0.501833i	−0.973746	−	0.227637i	$-0.926900\pi$
$313$	−5.12591	+	8.87834i	−0.289734	+	0.501833i	0.684012	+	0.729470i	$0.260233\pi$
$314$	3.96744			0.223895
$315$		0			0
$316$	1.30408			0.0733601
$317$	−5.50882	+	9.54156i	−0.309406	+	0.535908i	−0.978233	−	0.207511i	$-0.933464\pi$
$317$	−5.50882	+	9.54156i	−0.309406	+	0.535908i	0.668826	+	0.743419i	$0.266797\pi$
$318$		0			0
$319$	2.15278	+	3.72872i	0.120532	+	0.208768i
$320$	9.95738	+	17.2467i	0.556635	+	0.964119i
$321$		0			0
$322$	−1.07142	+	1.85576i	−0.0597082	+	0.103418i
$323$	3.36778			0.187388
$324$		0			0
$325$	52.1232			2.89127
$326$	−7.91511	+	13.7094i	−0.438378	+	0.759292i
$327$		0			0
$328$	−6.07870	−	10.5286i	−0.335640	−	0.581346i
$329$	1.30345	+	2.25764i	0.0718613	+	0.124467i
$330$		0			0
$331$	9.07216	−	15.7134i	0.498651	−	0.863689i	−0.501348	−	0.865246i	$-0.667162\pi$
$331$	9.07216	−	15.7134i	0.498651	−	0.863689i	0.999999	+	0.00155679i	$0.000495541\pi$
$332$	−4.56406			−0.250485
$333$		0			0
$334$	7.96163			0.435641
$335$	16.7600	−	29.0293i	0.915699	−	1.58604i
$336$		0			0
$337$	0.839543	+	1.45413i	0.0457328	+	0.0792115i	0.887986	−	0.459871i	$-0.152104\pi$
$337$	0.839543	+	1.45413i	0.0457328	+	0.0792115i	−0.842253	+	0.539083i	$0.818771\pi$
$338$	−9.00631	−	15.5994i	−0.489879	−	0.848495i
$339$		0			0
$340$	−10.7891	+	18.6872i	−0.585118	+	1.01345i
$341$	3.30555			0.179006
$342$		0			0
$343$	−17.2595			−0.931925
$344$	−5.87543	+	10.1765i	−0.316782	+	0.548682i
$345$		0			0
$346$	−11.0601	−	19.1566i	−0.594592	−	1.02986i
$347$	−9.39059	−	16.2650i	−0.504113	−	0.873150i	−0.999989	−	0.00475637i	$-0.998486\pi$
$347$	−9.39059	−	16.2650i	−0.504113	−	0.873150i	0.495875	−	0.868394i	$-0.334847\pi$
$348$		0			0
$349$	−16.2545	+	28.1536i	−0.870082	+	1.50703i	−0.00817109	+	0.999967i	$0.502601\pi$
$349$	−16.2545	+	28.1536i	−0.870082	+	1.50703i	−0.861911	+	0.507060i	$0.830732\pi$
$350$	11.7516			0.628149
$351$		0			0
$352$	−5.58120			−0.297479
$353$	3.35487	−	5.81081i	0.178562	−	0.309278i	−0.762826	−	0.646603i	$-0.776189\pi$
$353$	3.35487	−	5.81081i	0.178562	−	0.309278i	0.941388	+	0.337325i	$0.109522\pi$
$354$		0			0
$355$	−9.63857	−	16.6945i	−0.511562	−	0.886052i
$356$	2.40919	+	4.17284i	0.127687	+	0.221160i
$357$		0			0
$358$	−5.30342	+	9.18579i	−0.280294	+	0.485484i
$359$	−14.7797			−0.780040			−0.390020	−	0.920806i	$-0.627532\pi$
$359$	−14.7797			−0.780040			−0.390020	+	0.920806i	$0.627532\pi$
$360$		0			0
$361$	−18.5070			−0.974054
$362$	2.21169	−	3.83076i	0.116244	−	0.201340i
$363$		0			0
$364$	5.01185	+	8.68078i	0.262692	+	0.454997i
$365$	19.7527	+	34.2128i	1.03391	+	1.79078i
$366$		0			0
$367$	−13.2934	+	23.0249i	−0.693912	+	1.20189i	0.276634	+	0.960975i	$0.410781\pi$
$367$	−13.2934	+	23.0249i	−0.693912	+	1.20189i	−0.970546	+	0.240916i	$0.922552\pi$
$368$	−0.264253			−0.0137751
$369$		0			0
$370$	−32.6525			−1.69752
$371$	−0.836667	+	1.44915i	−0.0434376	+	0.0752361i
$372$		0			0
$373$	−11.7781	−	20.4003i	−0.609848	−	1.05629i	−0.991265	−	0.131885i	$-0.957897\pi$
$373$	−11.7781	−	20.4003i	−0.609848	−	1.05629i	0.381417	−	0.924403i	$-0.375436\pi$
$374$	2.14510	+	3.71542i	0.110920	+	0.192120i
$375$		0			0
$376$	−2.57102	+	4.45314i	−0.132590	+	0.229653i
$377$	24.7854			1.27651
$378$		0			0
$379$	31.6536			1.62594			0.812969	−	0.582307i	$-0.197850\pi$
$379$	31.6536			1.62594			0.812969	+	0.582307i	$0.197850\pi$
$380$	−1.57932	+	2.73546i	−0.0810173	+	0.140326i
$381$		0			0
$382$	0.144705	+	0.250637i	0.00740375	+	0.0128237i
$383$	−17.9220	−	31.0419i	−0.915773	−	1.58616i	−0.805766	−	0.592234i	$-0.798246\pi$
$383$	−17.9220	−	31.0419i	−0.915773	−	1.58616i	−0.110006	−	0.993931i	$-0.535087\pi$
$384$		0			0
$385$	−2.71996	+	4.71110i	−0.138622	+	0.240100i
$386$	12.8936			0.656265
$387$		0			0
$388$	−3.94917			−0.200489
$389$	1.96084	−	3.39628i	0.0994188	−	0.172198i	−0.812025	−	0.583622i	$-0.801635\pi$
$389$	1.96084	−	3.39628i	0.0994188	−	0.172198i	0.911444	+	0.411424i	$0.134968\pi$
$390$		0			0
$391$	−3.95966	−	6.85833i	−0.200249	−	0.346841i
$392$	−7.00437	−	12.1319i	−0.353774	−	0.612755i
$393$		0			0
$394$	−8.19599	+	14.1959i	−0.412908	+	0.715178i
$395$	4.07412			0.204991
$396$		0			0
$397$	−3.90292			−0.195882			−0.0979411	−	0.995192i	$-0.531226\pi$
$397$	−3.90292			−0.195882			−0.0979411	+	0.995192i	$0.531226\pi$
$398$	0.676239	−	1.17128i	0.0338968	−	0.0587110i
$399$		0			0
$400$	0.724594	+	1.25503i	0.0362297	+	0.0627517i
$401$	15.8378	+	27.4318i	0.790900	+	1.36988i	0.925411	+	0.378966i	$0.123720\pi$
$401$	15.8378	+	27.4318i	0.790900	+	1.36988i	−0.134511	+	0.990912i	$0.542946\pi$
$402$		0			0
$403$	9.51440	−	16.4794i	0.473946	−	0.820898i
$404$	17.0315			0.847349
$405$		0			0
$406$	5.58807			0.277331
$407$	4.86889	−	8.43317i	0.241342	−	0.418017i
$408$		0			0
$409$	6.45815	+	11.1858i	0.319335	+	0.553104i	0.980349	−	0.197269i	$-0.0632072\pi$
$409$	6.45815	+	11.1858i	0.319335	+	0.553104i	−0.661015	+	0.750373i	$0.729874\pi$
$410$	−7.12147	−	12.3348i	−0.351704	−	0.609170i
$411$		0			0
$412$	11.5065	−	19.9299i	0.566885	−	0.981873i
$413$	6.74893			0.332093
$414$		0			0
$415$	−14.2587			−0.699934
$416$	−16.0644	+	27.8244i	−0.787622	+	1.36420i
$417$		0			0
$418$	0.314002	+	0.543868i	0.0153584	+	0.0266015i
$419$	13.6804	+	23.6951i	0.668331	+	1.15758i	0.978371	+	0.206860i	$0.0663244\pi$
$419$	13.6804	+	23.6951i	0.668331	+	1.15758i	−0.310040	+	0.950724i	$0.600342\pi$
$420$		0			0
$421$	9.78884	−	16.9548i	0.477079	−	0.826325i	−0.522576	−	0.852593i	$-0.675029\pi$
$421$	9.78884	−	16.9548i	0.477079	−	0.826325i	0.999655	+	0.0262679i	$0.00836230\pi$
$422$	−9.85865			−0.479912
$423$		0			0
$424$	−3.30061			−0.160292
$425$	−21.7151	+	37.6117i	−1.05334	+	1.82444i
$426$		0			0
$427$	−1.84933	−	3.20313i	−0.0894954	−	0.155011i
$428$	6.00198	+	10.3957i	0.290117	+	0.502497i
$429$		0			0
$430$	−6.88333	+	11.9223i	−0.331944	+	0.574943i
$431$	−9.80495			−0.472288			−0.236144	−	0.971718i	$-0.575884\pi$
$431$	−9.80495			−0.472288			−0.236144	+	0.971718i	$0.575884\pi$
$432$		0			0
$433$	−1.98391			−0.0953409			−0.0476704	−	0.998863i	$-0.515180\pi$
$433$	−1.98391			−0.0953409			−0.0476704	+	0.998863i	$0.515180\pi$
$434$	2.14510	−	3.71542i	0.102968	−	0.178346i
$435$		0			0
$436$	−4.44455	−	7.69819i	−0.212855	−	0.368676i
$437$	−0.579621	−	1.00393i	−0.0277270	−	0.0480246i
$438$		0			0
$439$	−17.5309	+	30.3644i	−0.836703	+	1.44921i	0.0559337	+	0.998434i	$0.482186\pi$
$439$	−17.5309	+	30.3644i	−0.836703	+	1.44921i	−0.892636	+	0.450777i	$0.851147\pi$
$440$	−10.7301			−0.511538
$441$		0			0
$442$	24.6970			1.17472
$443$	11.8560	−	20.5353i	0.563298	−	0.975660i	−0.433908	−	0.900957i	$-0.642866\pi$
$443$	11.8560	−	20.5353i	0.563298	−	0.975660i	0.997206	−	0.0747032i	$-0.0238009\pi$
$444$		0			0
$445$	7.52665	+	13.0365i	0.356798	+	0.617992i
$446$	10.4261	+	18.0585i	0.493689	+	0.855094i
$447$		0			0
$448$	−3.85409	+	6.67548i	−0.182089	+	0.315387i
$449$	11.6575			0.550154			0.275077	−	0.961422i	$-0.411297\pi$
$449$	11.6575			0.550154			0.275077	+	0.961422i	$0.411297\pi$
$450$		0			0
$451$	4.24760			0.200012
$452$	−0.986009	+	1.70782i	−0.0463780	+	0.0803290i
$453$		0			0
$454$	2.67386	+	4.63126i	0.125490	+	0.217356i
$455$	15.6577	+	27.1200i	0.734046	+	1.27140i
$456$		0			0
$457$	−6.60015	+	11.4318i	−0.308742	+	0.534757i	−0.978087	−	0.208195i	$-0.933241\pi$
$457$	−6.60015	+	11.4318i	−0.308742	+	0.534757i	0.669346	+	0.742951i	$0.266575\pi$
$458$	8.42964			0.393891
$459$		0			0
$460$	7.42751			0.346310
$461$	−15.1456	+	26.2330i	−0.705402	+	1.22179i	0.261144	+	0.965300i	$0.415900\pi$
$461$	−15.1456	+	26.2330i	−0.705402	+	1.22179i	−0.966546	+	0.256493i	$0.917433\pi$
$462$		0			0
$463$	13.6059	+	23.5662i	0.632322	+	1.09521i	0.987076	+	0.160254i	$0.0512313\pi$
$463$	13.6059	+	23.5662i	0.632322	+	1.09521i	−0.354754	+	0.934960i	$0.615435\pi$
$464$	0.344556	+	0.596789i	0.0159956	+	0.0277052i
$465$		0			0
$466$	12.1502	−	21.0448i	0.562847	−	0.974880i
$467$	−31.1873			−1.44318			−0.721588	−	0.692322i	$-0.756588\pi$
$467$	−31.1873			−1.44318			−0.721588	+	0.692322i	$0.756588\pi$
$468$		0			0
$469$	12.9742			0.599095
$470$	−3.01207	+	5.21705i	−0.138936	+	0.240645i
$471$		0			0
$472$	6.65606	+	11.5286i	0.306370	+	0.530648i
$473$	−2.05278	−	3.55552i	−0.0943871	−	0.163483i
$474$		0			0
$475$	−3.17869	+	5.50566i	−0.145848	+	0.252617i
$476$	−8.35199			−0.382813
$477$		0			0
$478$	−0.216970			−0.00992397
$479$	−19.1386	+	33.1490i	−0.874464	+	1.51462i	−0.0171309	+	0.999853i	$0.505453\pi$
$479$	−19.1386	+	33.1490i	−0.874464	+	1.51462i	−0.857333	+	0.514762i	$0.827880\pi$
$480$		0			0
$481$	−28.0283	−	48.5465i	−1.27798	−	2.21353i
$482$	5.68438	+	9.84563i	0.258916	+	0.448456i
$483$		0			0
$484$	0.599994	−	1.03922i	0.0272725	−	0.0472373i
$485$	−12.3378			−0.560228
$486$		0			0
$487$	−15.8602			−0.718697			−0.359348	−	0.933204i	$-0.617001\pi$
$487$	−15.8602			−0.718697			−0.359348	+	0.933204i	$0.617001\pi$
$488$	3.64776	−	6.31811i	0.165127	−	0.286008i
$489$		0			0
$490$	−8.20594	−	14.2131i	−0.370706	−	0.642082i
$491$	−3.50114	−	6.06416i	−0.158004	−	0.273672i	0.776145	−	0.630555i	$-0.217173\pi$
$491$	−3.50114	−	6.06416i	−0.158004	−	0.273672i	−0.934149	+	0.356883i	$0.883839\pi$
$492$		0			0
$493$	−10.3259	+	17.8850i	−0.465055	+	0.805499i
$494$	3.61518			0.162655
$495$		0			0
$496$	0.529060			0.0237555
$497$	3.73070	−	6.46175i	0.167345	−	0.289849i
$498$		0			0
$499$	−12.3353	−	21.3653i	−0.552202	−	0.956443i	−0.998115	−	0.0613663i	$-0.980454\pi$
$499$	−12.3353	−	21.3653i	−0.552202	−	0.956443i	0.445913	−	0.895076i	$-0.352879\pi$
$500$	−9.11990	−	15.7961i	−0.407854	−	0.706425i
$501$		0			0
$502$	10.5603	−	18.2910i	0.471330	−	0.816367i
$503$	−6.05183			−0.269838			−0.134919	−	0.990857i	$-0.543077\pi$
$503$	−6.05183			−0.269838			−0.134919	+	0.990857i	$0.543077\pi$
$504$		0			0
$505$	53.2088			2.36776
$506$	0.738375	−	1.27890i	0.0328248	−	0.0568542i
$507$		0			0
$508$	−13.3984	−	23.2067i	−0.594458	−	1.02963i
$509$	−10.0280	−	17.3690i	−0.444482	−	0.769866i	0.553534	−	0.832827i	$-0.313279\pi$
$509$	−10.0280	−	17.3690i	−0.444482	−	0.769866i	−0.998016	+	0.0629607i	$0.979946\pi$
$510$		0			0
$511$	−7.64547	+	13.2423i	−0.338216	+	0.585807i
$512$	−1.80948			−0.0799683
$513$		0			0
$514$	−3.68212			−0.162412
$515$	35.9479	−	62.2637i	1.58406	−	2.74366i
$516$		0			0
$517$	−0.898274	−	1.55586i	−0.0395060	−	0.0684265i
$518$	−6.31921	−	10.9452i	−0.277650	−	0.480904i
$519$		0			0
$520$	−30.8845	+	53.4936i	−1.35438	+	2.34585i
$521$	−18.8721			−0.826804			−0.413402	−	0.910549i	$-0.635660\pi$
$521$	−18.8721			−0.826804			−0.413402	+	0.910549i	$0.635660\pi$
$522$		0			0
$523$	−16.0568			−0.702114			−0.351057	−	0.936354i	$-0.614178\pi$
$523$	−16.0568			−0.702114			−0.351057	+	0.936354i	$0.614178\pi$
$524$	5.87326	−	10.1728i	0.256575	−	0.444400i
$525$		0			0
$526$	−5.18427	−	8.97941i	−0.226045	−	0.391521i
$527$	7.92762	+	13.7310i	0.345333	+	0.598134i
$528$		0			0
$529$	10.1370	−	17.5578i	0.440740	−	0.763384i
$530$	−3.86682			−0.167964
$531$		0			0
$532$	−1.22258			−0.0530054
$533$	12.2259	−	21.1759i	0.529563	−	0.917230i
$534$		0			0
$535$	18.7510	+	32.4778i	0.810678	+	1.40414i
$536$	12.7957	+	22.1628i	0.552690	+	0.957288i
$537$		0			0
$538$	−3.05241	+	5.28692i	−0.131599	+	0.227935i
$539$	4.89443			0.210818
$540$		0			0
$541$	18.4357			0.792614			0.396307	−	0.918118i	$-0.370292\pi$
$541$	18.4357			0.792614			0.396307	+	0.918118i	$0.370292\pi$
$542$	3.38784	−	5.86791i	0.145520	−	0.252048i
$543$		0			0
$544$	−13.3852	−	23.1839i	−0.573888	−	0.994002i
$545$	−13.8854	−	24.0502i	−0.594785	−	1.03020i
$546$		0			0
$547$	14.4834	−	25.0860i	0.619267	−	1.07260i	−0.370353	−	0.928891i	$-0.620763\pi$
$547$	14.4834	−	25.0860i	0.619267	−	1.07260i	0.989620	−	0.143711i	$-0.0459035\pi$
$548$	−2.85143			−0.121807
$549$		0			0
$550$	−8.09864			−0.345327
$551$	−1.51152	+	2.61803i	−0.0643929	+	0.111532i
$552$		0			0
$553$	0.788462	+	1.36566i	0.0335288	+	0.0580736i
$554$	8.40918	+	14.5651i	0.357272	+	0.618813i
$555$		0			0
$556$	−6.89196	+	11.9372i	−0.292284	+	0.506251i
$557$	11.7584			0.498219			0.249110	−	0.968475i	$-0.419862\pi$
$557$	11.7584			0.498219			0.249110	+	0.968475i	$0.419862\pi$
$558$		0			0
$559$	−23.6341			−0.999618
$560$	−0.435334	+	0.754021i	−0.0183962	+	0.0318632i
$561$		0			0
$562$	11.1282	+	19.2746i	0.469415	+	0.813050i
$563$	−0.282557	−	0.489403i	−0.0119084	−	0.0206259i	0.860010	−	0.510277i	$-0.170457\pi$
$563$	−0.282557	−	0.489403i	−0.0119084	−	0.0206259i	−0.871918	+	0.489652i	$0.837124\pi$
$564$		0			0
$565$	−3.08043	+	5.33546i	−0.129595	+	0.224465i
$566$	−16.2261			−0.682035
$567$		0			0
$568$	14.7174			0.617530
$569$	3.11671	−	5.39830i	0.130659	−	0.226309i	−0.793272	−	0.608868i	$-0.791624\pi$
$569$	3.11671	−	5.39830i	0.130659	−	0.226309i	0.923931	+	0.382559i	$0.124957\pi$
$570$		0			0
$571$	14.1967	+	24.5894i	0.594114	+	1.02904i	0.993671	+	0.112327i	$0.0358304\pi$
$571$	14.1967	+	24.5894i	0.594114	+	1.02904i	−0.399558	+	0.916708i	$0.630836\pi$
$572$	−3.45393	−	5.98239i	−0.144416	−	0.250136i
$573$		0			0
$574$	2.75643	−	4.77427i	0.115051	−	0.199274i
$575$	14.9494			0.623432
$576$		0			0
$577$	−25.5623			−1.06417			−0.532087	−	0.846690i	$-0.678592\pi$
$577$	−25.5623			−1.06417			−0.532087	+	0.846690i	$0.678592\pi$
$578$	−2.68637	+	4.65294i	−0.111738	+	0.193537i
$579$		0			0
$580$	−9.68464	−	16.7743i	−0.402133	−	0.696515i
$581$	−2.75949	−	4.77957i	−0.114483	−	0.198290i
$582$		0			0
$583$	0.576591	−	0.998685i	0.0238800	−	0.0413613i
$584$	−30.1611			−1.24807
$585$		0			0
$586$	14.3803			0.594044
$587$	−17.5932	+	30.4724i	−0.726151	+	1.25773i	0.232347	+	0.972633i	$0.425359\pi$
$587$	−17.5932	+	30.4724i	−0.726151	+	1.25773i	−0.958498	+	0.285098i	$0.907974\pi$
$588$		0			0
$589$	1.16046	+	2.00997i	0.0478158	+	0.0828194i
$590$	7.79787	+	13.5063i	0.321033	+	0.556046i
$591$		0			0
$592$	0.779276	−	1.34975i	0.0320280	−	0.0554742i
$593$	40.8141			1.67604			0.838018	−	0.545643i	$-0.183714\pi$
$593$	40.8141			1.67604			0.838018	+	0.545643i	$0.183714\pi$
$594$		0			0
$595$	−26.0928			−1.06970
$596$	0.420785	−	0.728821i	0.0172360	−	0.0298537i
$597$		0			0
$598$	−4.25054	−	7.36215i	−0.173817	−	0.301061i
$599$	23.2063	+	40.1945i	0.948184	+	1.64230i	0.749247	+	0.662291i	$0.230416\pi$
$599$	23.2063	+	40.1945i	0.948184	+	1.64230i	0.198938	+	0.980012i	$0.436251\pi$
$600$		0			0
$601$	−7.64723	+	13.2454i	−0.311937	+	0.540291i	−0.978782	−	0.204906i	$-0.934311\pi$
$601$	−7.64723	+	13.2454i	−0.311937	+	0.540291i	0.666844	+	0.745197i	$0.267645\pi$
$602$	−5.32851			−0.217174
$603$		0			0
$604$	3.00662			0.122338
$605$	1.87447	−	3.24667i	0.0762079	−	0.131996i
$606$		0			0
$607$	17.2474	+	29.8734i	0.700051	+	1.21252i	0.968448	+	0.249216i	$0.0801729\pi$
$607$	17.2474	+	29.8734i	0.700051	+	1.21252i	−0.268397	+	0.963308i	$0.586494\pi$
$608$	−1.95935	−	3.39370i	−0.0794622	−	0.137633i
$609$		0			0
$610$	4.27352	−	7.40196i	0.173030	−	0.299696i
$611$	−10.3420			−0.418394
$612$		0			0
$613$	19.6568			0.793931			0.396965	−	0.917834i	$-0.370063\pi$
$613$	19.6568			0.793931			0.396965	+	0.917834i	$0.370063\pi$
$614$	9.00440	−	15.5961i	0.363388	−	0.629406i
$615$		0			0
$616$	−2.07659	−	3.59676i	−0.0836682	−	0.144918i
$617$	−18.0267	−	31.2231i	−0.725726	−	1.25699i	−0.958675	−	0.284505i	$-0.908171\pi$
$617$	−18.0267	−	31.2231i	−0.725726	−	1.25699i	0.232949	−	0.972489i	$-0.425163\pi$
$618$		0			0
$619$	4.40997	−	7.63830i	0.177252	−	0.307009i	−0.763686	−	0.645587i	$-0.776613\pi$
$619$	4.40997	−	7.63830i	0.177252	−	0.307009i	0.940938	+	0.338578i	$0.109946\pi$
$620$	−14.8706			−0.597218
$621$		0			0
$622$	11.6496			0.467105
$623$	−2.91326	+	5.04591i	−0.116717	+	0.202160i
$624$		0			0
$625$	−5.85564	−	10.1423i	−0.234226	−	0.405691i
$626$	−4.58479	−	7.94108i	−0.183245	−	0.317390i
$627$		0			0
$628$	2.66139	−	4.60967i	0.106201	−	0.183946i
$629$	46.7078			1.86236
$630$		0			0
$631$	−0.823111			−0.0327675			−0.0163838	−	0.999866i	$-0.505215\pi$
$631$	−0.823111			−0.0327675			−0.0163838	+	0.999866i	$0.505215\pi$
$632$	−1.55522	+	2.69373i	−0.0618635	+	0.107151i
$633$		0			0
$634$	−4.92728	−	8.53430i	−0.195687	−	0.338940i
$635$	−41.8585	−	72.5010i	−1.66110	−	2.87711i
$636$		0			0
$637$	14.0877	−	24.4006i	0.558174	−	0.966786i
$638$	−3.85103			−0.152464
$639$		0			0
$640$	24.0346			0.950052
$641$	15.5236	−	26.8877i	0.613145	−	1.06200i	−0.377562	−	0.925984i	$-0.623237\pi$
$641$	15.5236	−	26.8877i	0.613145	−	1.06200i	0.990707	−	0.136014i	$-0.0434293\pi$
$642$		0			0
$643$	0.282962	+	0.490105i	0.0111589	+	0.0193279i	0.871551	−	0.490305i	$-0.163115\pi$
$643$	0.282962	+	0.490105i	0.0111589	+	0.0193279i	−0.860392	+	0.509633i	$0.829781\pi$
$644$	1.43744	+	2.48972i	0.0566432	+	0.0981088i
$645$		0			0
$646$	−1.50613	+	2.60869i	−0.0592578	+	0.102638i
$647$	32.7343			1.28692			0.643458	−	0.765481i	$-0.277499\pi$
$647$	32.7343			1.28692			0.643458	+	0.765481i	$0.277499\pi$
$648$		0			0
$649$	−4.65105			−0.182569
$650$	−23.3104	+	40.3747i	−0.914307	+	1.58363i
$651$		0			0
$652$	10.6191	+	18.3927i	0.415874	+	0.720316i
$653$	−3.61631	−	6.26362i	−0.141517	−	0.245115i	0.786551	−	0.617525i	$-0.211865\pi$
$653$	−3.61631	−	6.26362i	−0.141517	−	0.245115i	−0.928068	+	0.372411i	$0.878531\pi$
$654$		0			0
$655$	18.3489	−	31.7812i	0.716951	−	1.24180i
$656$	0.679837			0.0265432
$657$		0			0
$658$	−2.33169			−0.0908989
$659$	18.2545	−	31.6177i	0.711093	−	1.23165i	−0.253354	−	0.967374i	$-0.581534\pi$
$659$	18.2545	−	31.6177i	0.711093	−	1.23165i	0.964447	−	0.264276i	$-0.0851330\pi$
$660$		0			0
$661$	−7.07158	−	12.2483i	−0.275053	−	0.476405i	0.695096	−	0.718917i	$-0.255362\pi$
$661$	−7.07158	−	12.2483i	−0.275053	−	0.476405i	−0.970148	+	0.242512i	$0.922029\pi$
$662$	8.11445	+	14.0546i	0.315377	+	0.546249i
$663$		0			0
$664$	5.44303	−	9.42760i	0.211230	−	0.365862i
$665$	−3.81950			−0.148114
$666$		0			0
$667$	7.10866			0.275249
$668$	5.34073	−	9.25041i	0.206639	−	0.357909i
$669$		0			0
$670$	14.9908	+	25.9647i	0.579143	+	1.00311i
$671$	1.27447	+	2.20745i	0.0492004	+	0.0852176i
$672$		0			0
$673$	−7.78212	+	13.4790i	−0.299979	+	0.519578i	−0.976131	−	0.217184i	$-0.930313\pi$
$673$	−7.78212	+	13.4790i	−0.299979	+	0.519578i	0.676152	+	0.736762i	$0.263646\pi$
$674$	−1.50183			−0.0578484
$675$		0			0
$676$	−24.1661			−0.929464
$677$	−17.0779	+	29.5798i	−0.656357	+	1.13684i	0.325195	+	0.945647i	$0.394570\pi$
$677$	−17.0779	+	29.5798i	−0.656357	+	1.13684i	−0.981552	+	0.191196i	$0.938763\pi$
$678$		0			0
$679$	−2.38772	−	4.13565i	−0.0916322	−	0.158712i
$680$	−25.7337	−	44.5721i	−0.986844	−	1.70926i
$681$		0			0
$682$	−1.47830	+	2.56049i	−0.0566070	+	0.0980462i
$683$	48.8978			1.87102			0.935512	−	0.353295i	$-0.114939\pi$
$683$	48.8978			1.87102			0.935512	+	0.353295i	$0.114939\pi$
$684$		0			0
$685$	−8.90825			−0.340367
$686$	7.71874	−	13.3693i	0.294703	−	0.510440i
$687$		0			0
$688$	−0.328552	−	0.569068i	−0.0125259	−	0.0216955i
$689$	−3.31921	−	5.74904i	−0.126452	−	0.219021i
$690$		0			0
$691$	17.0662	−	29.5596i	0.649230	−	1.12450i	−0.334077	−	0.942546i	$-0.608425\pi$
$691$	17.0662	−	29.5596i	0.649230	−	1.12450i	0.983307	−	0.181954i	$-0.0582420\pi$
$692$	−29.6767			−1.12814
$693$		0			0
$694$	16.7985			0.637663
$695$	−21.5315	+	37.2936i	−0.816735	+	1.41463i
$696$		0			0
$697$	10.1869	+	17.6443i	0.385857	+	0.668324i
$698$	−14.5386	−	25.1815i	−0.550292	−	0.953134i
$699$		0			0
$700$	7.88307	−	13.6539i	0.297952	−	0.516068i
$701$	22.2291			0.839581			0.419791	−	0.907621i	$-0.362104\pi$
$701$	22.2291			0.839581			0.419791	+	0.907621i	$0.362104\pi$
$702$		0			0
$703$	6.83715			0.257868
$704$	2.65606	−	4.60043i	0.100104	−	0.173385i
$705$		0			0
$706$	3.00071	+	5.19739i	0.112933	+	0.195606i
$707$	10.2975	+	17.8357i	0.387276	+	0.670782i
$708$		0			0
$709$	10.2198	−	17.7012i	0.383812	−	0.664781i	−0.607792	−	0.794096i	$-0.707945\pi$
$709$	10.2198	−	17.7012i	0.383812	−	0.664781i	0.991604	+	0.129315i	$0.0412779\pi$
$710$	17.2421			0.647086
$711$		0			0
$712$	−11.4927			−0.430706
$713$	2.72881	−	4.72644i	0.102195	−	0.177006i
$714$		0			0
$715$	−10.7906	−	18.6898i	−0.403544	−	0.698959i
$716$	7.11516	+	12.3238i	0.265906	+	0.460563i
$717$		0			0
$718$	6.60971	−	11.4484i	0.246672	−	0.427249i
$719$	−19.8844			−0.741563			−0.370782	−	0.928720i	$-0.620910\pi$
$719$	−19.8844			−0.741563			−0.370782	+	0.928720i	$0.620910\pi$
$720$		0			0
$721$	27.8279			1.03637
$722$	8.27665	−	14.3356i	0.308025	−	0.533515i
$723$		0			0
$724$	−2.96724	−	5.13942i	−0.110277	−	0.191005i
$725$	−19.4923	−	33.7616i	−0.723925	−	1.25388i
$726$		0			0
$727$	−0.143365	+	0.248316i	−0.00531712	+	0.00920951i	−0.868672	−	0.495388i	$-0.835026\pi$
$727$	−0.143365	+	0.248316i	−0.00531712	+	0.00920951i	0.863355	+	0.504598i	$0.168359\pi$
$728$	−23.9083			−0.886099
$729$		0			0
$730$	−35.3350			−1.30781
$731$	9.84627	−	17.0542i	0.364178	−	0.630774i
$732$		0			0
$733$	−5.10058	−	8.83447i	−0.188394	−	0.326309i	0.756321	−	0.654201i	$-0.226995\pi$
$733$	−5.10058	−	8.83447i	−0.188394	−	0.326309i	−0.944715	+	0.327892i	$0.893662\pi$
$734$	−11.8901	−	20.5943i	−0.438872	−	0.760148i
$735$		0			0
$736$	−4.60741	+	7.98026i	−0.169831	+	0.294156i
$737$	−8.94124			−0.329355
$738$		0			0
$739$	29.3420			1.07936			0.539681	−	0.841870i	$-0.318545\pi$
$739$	29.3420			1.07936			0.539681	+	0.841870i	$0.318545\pi$
$740$	−21.9036	+	37.9381i	−0.805191	+	1.39463i
$741$		0			0
$742$	−0.748343	−	1.29617i	−0.0274725	−	0.0475838i
$743$	23.9113	+	41.4155i	0.877219	+	1.51939i	0.854380	+	0.519650i	$0.173937\pi$
$743$	23.9113	+	41.4155i	0.877219	+	1.51939i	0.0228399	+	0.999739i	$0.492729\pi$
$744$		0			0
$745$	1.31459	−	2.27694i	0.0481629	−	0.0834205i
$746$	21.0695			0.771410
$747$		0			0
$748$	5.75580			0.210453
$749$	−7.25776	+	12.5708i	−0.265193	+	0.459327i
$750$		0			0
$751$	10.0234	+	17.3610i	0.365758	+	0.633512i	0.988898	−	0.148599i	$-0.0474764\pi$
$751$	10.0234	+	17.3610i	0.365758	+	0.633512i	−0.623139	+	0.782111i	$0.714143\pi$
$752$	−0.143770	−	0.249018i	−0.00524277	−	0.00908074i
$753$		0			0
$754$	−11.0845	+	19.1988i	−0.403672	+	0.699180i
$755$	9.39311			0.341850
$756$		0			0
$757$	−34.7845			−1.26427			−0.632133	−	0.774860i	$-0.717820\pi$
$757$	−34.7845			−1.26427			−0.632133	+	0.774860i	$0.717820\pi$
$758$	−14.1560	+	24.5190i	−0.514171	+	0.890570i
$759$		0			0
$760$	−3.76694	−	6.52453i	−0.136641	−	0.236670i
$761$	−3.27617	−	5.67450i	−0.118761	−	0.205700i	0.800516	−	0.599312i	$-0.204559\pi$
$761$	−3.27617	−	5.67450i	−0.118761	−	0.205700i	−0.919277	+	0.393611i	$0.871226\pi$
$762$		0			0
$763$	5.37447	−	9.30885i	0.194569	−	0.337003i
$764$	0.388278			0.0140474
$765$		0			0
$766$	32.0601			1.15838
$767$	−13.3871	+	23.1872i	−0.483381	+	0.837241i
$768$		0			0
$769$	17.0111	+	29.4641i	0.613435	+	1.06250i	0.990657	+	0.136378i	$0.0435462\pi$
$769$	17.0111	+	29.4641i	0.613435	+	1.06250i	−0.377221	+	0.926123i	$0.623120\pi$
$770$	−2.43282	−	4.21377i	−0.0876728	−	0.151854i
$771$		0			0
$772$	8.64912	−	14.9807i	0.311289	−	0.539168i
$773$	−5.09752			−0.183345			−0.0916725	−	0.995789i	$-0.529221\pi$
$773$	−5.09752			−0.183345			−0.0916725	+	0.995789i	$0.529221\pi$
$774$		0			0
$775$	−29.9301			−1.07512
$776$	4.70972	−	8.15747i	0.169069	−	0.292836i
$777$		0			0
$778$	1.75385	+	3.03775i	0.0628784	+	0.108909i
$779$	1.49118	+	2.58279i	0.0534269	+	0.0925382i
$780$		0			0
$781$	−2.57102	+	4.45314i	−0.0919983	+	0.159346i
$782$	7.08330			0.253298
$783$		0			0
$784$	0.783363			0.0279773
$785$	8.31456	−	14.4012i	0.296759	−	0.514002i
$786$		0			0
$787$	12.5535	+	21.7433i	0.447485	+	0.775066i	0.998222	−	0.0596127i	$-0.0189866\pi$
$787$	12.5535	+	21.7433i	0.447485	+	0.775066i	−0.550737	+	0.834679i	$0.685653\pi$
$788$	10.9959	+	19.0454i	0.391712	+	0.678466i
$789$		0			0
$790$	−1.82202	+	3.15582i	−0.0648244	+	0.112279i
$791$	−2.38462			−0.0847872
$792$		0			0
$793$	14.6733			0.521063
$794$	1.74545	−	3.02321i	0.0619438	−	0.107290i
$795$		0			0
$796$	−0.907254	−	1.57141i	−0.0321568	−	0.0556972i
$797$	−3.39784	−	5.88523i	−0.120358	−	0.208466i	0.799551	−	0.600598i	$-0.205071\pi$
$797$	−3.39784	−	5.88523i	−0.120358	−	0.208466i	−0.919909	+	0.392133i	$0.871737\pi$
$798$		0			0
$799$	4.30861	−	7.46274i	0.152428	−	0.264013i
$800$	50.5349			1.78668
$801$		0			0
$802$	−28.3316			−1.00042
$803$	5.26890	−	9.12600i	0.185935	−	0.322050i
$804$		0			0
$805$	4.49077	+	7.77824i	0.158279	+	0.274147i
$806$	8.51000	+	14.7397i	0.299752	+	0.519185i
$807$		0			0
$808$	−20.3115	+	35.1806i	−0.714557	+	1.23765i
$809$	−17.0314			−0.598792			−0.299396	−	0.954129i	$-0.596785\pi$
$809$	−17.0314			−0.598792			−0.299396	+	0.954129i	$0.596785\pi$
$810$		0			0
$811$	2.28561			0.0802587			0.0401294	−	0.999194i	$-0.487223\pi$
$811$	2.28561			0.0802587			0.0401294	+	0.999194i	$0.487223\pi$
$812$	3.74853	−	6.49264i	0.131547	−	0.227847i
$813$		0			0
$814$	4.35490	+	7.54291i	0.152639	+	0.264379i
$815$	33.1754	+	57.4615i	1.16208	+	2.01279i
$816$		0			0
$817$	1.44131	−	2.49643i	0.0504251	−	0.0873389i
$818$	−11.5528			−0.403933
$819$		0			0
$820$	−19.1086			−0.667301
$821$	11.0263	−	19.0981i	0.384821	−	0.666530i	−0.606923	−	0.794761i	$-0.707596\pi$
$821$	11.0263	−	19.0981i	0.384821	−	0.666530i	0.991744	+	0.128231i	$0.0409297\pi$
$822$		0			0
$823$	12.3556	+	21.4006i	0.430691	+	0.745978i	0.996933	−	0.0782608i	$-0.0249367\pi$
$823$	12.3556	+	21.4006i	0.430691	+	0.745978i	−0.566242	+	0.824239i	$0.691603\pi$
$824$	27.4450	+	47.5361i	0.956092	+	1.65600i
$825$		0			0
$826$	−3.01824	+	5.22774i	−0.105018	+	0.181896i
$827$	−19.8452			−0.690085			−0.345043	−	0.938587i	$-0.612136\pi$
$827$	−19.8452			−0.690085			−0.345043	+	0.938587i	$0.612136\pi$
$828$		0			0
$829$	32.9988			1.14610			0.573048	−	0.819522i	$-0.305761\pi$
$829$	32.9988			1.14610			0.573048	+	0.819522i	$0.305761\pi$
$830$	6.37675	−	11.0449i	0.221340	−	0.383373i
$831$		0			0
$832$	−15.2899	−	26.4829i	−0.530082	−	0.918129i
$833$	11.7382	+	20.3311i	0.406704	+	0.704432i
$834$		0			0
$835$	16.6852	−	28.8996i	0.577415	−	1.00011i
$836$	0.842543			0.0291399
$837$		0			0
$838$	−24.4724			−0.845386
$839$	−10.1382	+	17.5598i	−0.350008	+	0.606232i	−0.986251	−	0.165257i	$-0.947155\pi$
$839$	−10.1382	+	17.5598i	−0.350008	+	0.606232i	0.636242	+	0.771489i	$0.280488\pi$
$840$		0			0
$841$	5.23110	+	9.06053i	0.180383	+	0.312432i
$842$	8.75547	+	15.1649i	0.301733	+	0.522617i
$843$		0			0
$844$	−6.61327	+	11.4545i	−0.227638	+	0.394281i
$845$	−75.4981			−2.59721
$846$		0			0
$847$	1.45106			0.0498589
$848$	0.0922845	−	0.159842i	0.00316906	−	0.00548898i
$849$		0			0
$850$	−19.4228	−	33.6412i	−0.666195	−	1.15388i
$851$	−8.03876	−	13.9235i	−0.275565	−	0.477293i
$852$		0			0
$853$	3.76447	−	6.52026i	0.128893	−	0.223249i	−0.794355	−	0.607454i	$-0.792191\pi$
$853$	3.76447	−	6.52026i	0.128893	−	0.223249i	0.923248	+	0.384205i	$0.125524\pi$
$854$	3.30821			0.113205
$855$		0			0
$856$	−28.6315			−0.978605
$857$	−5.76395	+	9.98345i	−0.196893	+	0.341028i	−0.947519	−	0.319699i	$-0.896418\pi$
$857$	−5.76395	+	9.98345i	−0.196893	+	0.341028i	0.750627	+	0.660727i	$0.229752\pi$
$858$		0			0
$859$	1.31075	+	2.27029i	0.0447222	+	0.0774612i	0.887520	−	0.460769i	$-0.152426\pi$
$859$	1.31075	+	2.27029i	0.0447222	+	0.0774612i	−0.842798	+	0.538230i	$0.819093\pi$
$860$	9.23480	+	15.9951i	0.314904	+	0.545430i
$861$		0			0
$862$	4.38494	−	7.59494i	0.149352	−	0.258685i
$863$	−29.7385			−1.01231			−0.506156	−	0.862442i	$-0.668934\pi$
$863$	−29.7385			−1.01231			−0.506156	+	0.862442i	$0.668934\pi$
$864$		0			0
$865$	−92.7143			−3.15238
$866$	0.887240	−	1.53675i	0.0301496	−	0.0522207i
$867$		0			0
$868$	−2.87790	−	4.98467i	−0.0976823	−	0.169191i
$869$	−0.543371	−	0.941146i	−0.0184326	−	0.0319262i
$870$		0			0
$871$	−25.7356	+	44.5754i	−0.872018	+	1.51038i
$872$	21.2020			0.717991
$873$		0			0
$874$	1.03686			0.0350725
$875$	11.0280	−	19.1011i	0.372815	−	0.645735i
$876$		0			0
$877$	−1.06123	−	1.83811i	−0.0358352	−	0.0620684i	0.847552	−	0.530713i	$-0.178076\pi$
$877$	−1.06123	−	1.83811i	−0.0358352	−	0.0620684i	−0.883387	+	0.468645i	$0.844742\pi$
$878$	−15.6802	−	27.1589i	−0.529181	−	0.916569i
$879$		0			0
$880$	0.300012	−	0.519636i	0.0101134	−	0.0175169i
$881$	−14.0627			−0.473783			−0.236892	−	0.971536i	$-0.576129\pi$
$881$	−14.0627			−0.473783			−0.236892	+	0.971536i	$0.576129\pi$
$882$		0			0
$883$	−20.5227			−0.690645			−0.345323	−	0.938484i	$-0.612231\pi$
$883$	−20.5227			−0.690645			−0.345323	+	0.938484i	$0.612231\pi$
$884$	16.5670	−	28.6948i	0.557207	−	0.965111i
$885$		0			0
$886$	10.6044	+	18.3674i	0.356263	+	0.617066i
$887$	1.25686	+	2.17695i	0.0422013	+	0.0730949i	0.886355	−	0.463007i	$-0.153230\pi$
$887$	1.25686	+	2.17695i	0.0422013	+	0.0730949i	−0.844153	+	0.536102i	$0.819896\pi$
$888$		0			0
$889$	16.2017	−	28.0622i	0.543387	−	0.941174i
$890$	−13.4642			−0.451321
$891$		0			0
$892$	27.9756			0.936693
$893$	0.630701	−	1.09241i	0.0211056	−	0.0365560i
$894$		0			0
$895$	22.2288	+	38.5013i	0.743025	+	1.28696i
$896$	4.65141	+	8.05647i	0.155393	+	0.269148i
$897$		0			0
$898$	−5.21345	+	9.02997i	−0.173975	+	0.301334i
$899$	−14.2322			−0.474672
$900$		0			0
$901$	5.53130			0.184274
$902$	−1.89960	+	3.29020i	−0.0632498	+	0.109552i
$903$		0			0
$904$	−2.35180	−	4.07344i	−0.0782197	−	0.135481i
$905$	−9.27009	−	16.0563i	−0.308148	−	0.533728i
$906$		0			0
$907$	−16.6153	+	28.7786i	−0.551703	+	0.955577i	0.446449	+	0.894809i	$0.352688\pi$
$907$	−16.6153	+	28.7786i	−0.551703	+	0.955577i	−0.998152	+	0.0607683i	$0.980645\pi$
$908$	7.17460			0.238097
$909$		0			0
$910$	−28.0096			−0.928509
$911$	2.77447	−	4.80553i	0.0919223	−	0.159214i	−0.816398	−	0.577490i	$-0.804032\pi$
$911$	2.77447	−	4.80553i	0.0919223	−	0.159214i	0.908320	+	0.418276i	$0.137366\pi$
$912$		0			0
$913$	1.90171	+	3.29386i	0.0629374	+	0.109011i
$914$	−5.90339	−	10.2250i	−0.195267	−	0.338212i
$915$		0			0
$916$	5.65468	−	9.79419i	0.186836	−	0.323609i
$917$	14.2042			0.469064
$918$		0			0
$919$	−46.9009			−1.54712			−0.773560	−	0.633724i	$-0.781526\pi$
$919$	−46.9009			−1.54712			−0.773560	+	0.633724i	$0.781526\pi$
$920$	−8.85795	+	15.3424i	−0.292038	+	0.505824i
$921$		0			0
$922$	−13.5468	−	23.4637i	−0.446139	−	0.772735i
$923$	14.8004	+	25.6350i	0.487160	+	0.843785i
$924$		0			0
$925$	−44.0853	+	76.3580i	−1.44952	+	2.51064i
$926$	−24.3392			−0.799837
$927$		0			0
$928$	24.0302			0.788829
$929$	−15.5050	+	26.8554i	−0.508702	+	0.881098i	0.491247	+	0.871020i	$0.336541\pi$
$929$	−15.5050	+	26.8554i	−0.508702	+	0.881098i	−0.999949	+	0.0100775i	$0.996792\pi$
$930$		0			0
$931$	1.71825	+	2.97610i	0.0563135	+	0.0975378i
$932$	−16.3009	−	28.2340i	−0.533955	−	0.924837i
$933$		0			0
$934$	13.9475	−	24.1578i	0.456376	−	0.790466i
$935$	17.9819			0.588072
$936$		0			0
$937$	−44.0640			−1.43951			−0.719755	−	0.694229i	$-0.755746\pi$
$937$	−44.0640			−1.43951			−0.719755	+	0.694229i	$0.755746\pi$
$938$	−5.80230	+	10.0499i	−0.189452	+	0.328140i
$939$		0			0
$940$	4.04104	+	6.99929i	0.131804	+	0.228292i
$941$	1.06028	+	1.83646i	0.0345642	+	0.0598669i	0.882790	−	0.469768i	$-0.155662\pi$
$941$	1.06028	+	1.83646i	0.0345642	+	0.0598669i	−0.848226	+	0.529635i	$0.822329\pi$
$942$		0			0
$943$	3.50649	−	6.07342i	0.114187	−	0.197778i
$944$	−0.744409			−0.0242284
$945$		0			0
$946$	3.67216			0.119392
$947$	−7.66234	+	13.2716i	−0.248993	+	0.431268i	−0.963247	−	0.268619i	$-0.913433\pi$
$947$	−7.66234	+	13.2716i	−0.248993	+	0.431268i	0.714254	+	0.699887i	$0.246766\pi$
$948$		0			0
$949$	−30.3310	−	52.5348i	−0.984586	−	1.70535i
$950$	−2.84313	−	4.92445i	−0.0922433	−	0.159770i
$951$		0			0
$952$	9.96047	−	17.2520i	0.322821	−	0.559142i
$953$	−31.7696			−1.02912			−0.514559	−	0.857455i	$-0.672045\pi$
$953$	−31.7696			−1.02912			−0.514559	+	0.857455i	$0.672045\pi$
$954$		0			0
$955$	1.21303			0.0392529
$956$	−0.145545	+	0.252092i	−0.00470727	+	0.00815323i
$957$		0			0
$958$	−17.1182	−	29.6496i	−0.553064	−	0.957934i
$959$	−1.72401	−	2.98607i	−0.0556711	−	0.0964253i
$960$		0			0
$961$	10.0367	−	17.3840i	0.323763	−	0.560774i
$962$	50.1390			1.61655
$963$		0			0
$964$	15.2525			0.491251
$965$	27.0211	−	46.8018i	0.869838	−	1.50660i
$966$		0			0
$967$	−2.35911	−	4.08609i	−0.0758637	−	0.131400i	0.825598	−	0.564259i	$-0.190838\pi$
$967$	−2.35911	−	4.08609i	−0.0758637	−	0.131400i	−0.901462	+	0.432859i	$0.857505\pi$
$968$	1.43109	+	2.47872i	0.0459969	+	0.0796690i
$969$		0			0
$970$	5.51765	−	9.55685i	0.177161	−	0.306852i
$971$	2.48946			0.0798905			0.0399452	−	0.999202i	$-0.487282\pi$
$971$	2.48946			0.0798905			0.0399452	+	0.999202i	$0.487282\pi$
$972$		0			0
$973$	−16.6679			−0.534348
$974$	7.09297	−	12.2854i	0.227273	−	0.393649i
$975$		0			0
$976$	0.203982	+	0.353306i	0.00652929	+	0.0113091i
$977$	23.9951	+	41.5608i	0.767672	+	1.32965i	0.938822	+	0.344403i	$0.111919\pi$
$977$	23.9951	+	41.5608i	0.767672	+	1.32965i	−0.171150	+	0.985245i	$0.554748\pi$
$978$		0			0
$979$	2.00768	−	3.47740i	0.0641657	−	0.111138i
$980$	−22.0185			−0.703354
$981$		0			0
$982$	6.26308			0.199863
$983$	−0.248569	+	0.430534i	−0.00792811	+	0.0137319i	−0.869962	−	0.493118i	$-0.835857\pi$
$983$	−0.248569	+	0.430534i	−0.00792811	+	0.0137319i	0.862034	+	0.506850i	$0.169190\pi$
$984$		0			0
$985$	34.3527	+	59.5006i	1.09457	+	1.89585i
$986$	−9.23583	−	15.9969i	−0.294129	−	0.509446i
$987$		0			0
$988$	2.42509	−	4.20039i	0.0771525	−	0.133632i
$989$	−6.77848			−0.215543
$990$		0			0
$991$	56.7182			1.80171			0.900856	−	0.434118i	$-0.142940\pi$
$991$	56.7182			1.80171			0.900856	+	0.434118i	$0.142940\pi$
$992$	9.22448	−	15.9773i	0.292878	−	0.507279i
$993$		0			0
$994$	3.33686	+	5.77961i	0.105839	+	0.183318i
$995$	−2.83439	−	4.90931i	−0.0898562	−	0.155635i
$996$		0			0
$997$	−25.5948	+	44.3314i	−0.810594	+	1.40399i	0.101855	+	0.994799i	$0.467522\pi$
$997$	−25.5948	+	44.3314i	−0.810594	+	1.40399i	−0.912449	+	0.409191i	$0.865811\pi$
$998$	22.0662			0.698492
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.e.100.2		8
3.2	odd	2		99.2.e.e.34.3	✓	8
9.2	odd	6		891.2.a.q.1.2		4
9.4	even	3	inner	297.2.e.e.199.2		8
9.5	odd	6		99.2.e.e.67.3	yes	8
9.7	even	3		891.2.a.p.1.3		4
33.32	even	2		1089.2.e.i.727.2		8
99.32	even	6		1089.2.e.i.364.2		8
99.43	odd	6		9801.2.a.bl.1.2		4
99.65	even	6		9801.2.a.bi.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.3	✓	8	3.2	odd	2
99.2.e.e.67.3	yes	8	9.5	odd	6
297.2.e.e.100.2		8	1.1	even	1	trivial
297.2.e.e.199.2		8	9.4	even	3	inner
891.2.a.p.1.3		4	9.7	even	3
891.2.a.q.1.2		4	9.2	odd	6
1089.2.e.i.364.2		8	99.32	even	6
1089.2.e.i.727.2		8	33.32	even	2
9801.2.a.bi.1.3		4	99.65	even	6
9801.2.a.bl.1.2		4	99.43	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.447217 + 0.774602i) q^{2} +(0.599994 + 1.03922i) q^{4} +(1.87447 + 3.24667i) q^{5} +(-0.725528 + 1.25665i) q^{7} -2.86218 q^{8} +O(q^{10})\)	\(q+(-0.447217 + 0.774602i) q^{2} +(0.599994 + 1.03922i) q^{4} +(1.87447 + 3.24667i) q^{5} +(-0.725528 + 1.25665i) q^{7} -2.86218 q^{8} -3.35317 q^{10} +(0.500000 - 0.866025i) q^{11} +(-2.87831 - 4.98537i) q^{13} +(-0.648937 - 1.12399i) q^{14} +(0.0800260 - 0.138609i) q^{16} +4.79655 q^{17} +0.702126 q^{19} +(-2.24934 + 3.89597i) q^{20} +(0.447217 + 0.774602i) q^{22} +(-0.825523 - 1.42985i) q^{23} +(-4.52724 + 7.84141i) q^{25} +5.14891 q^{26} -1.74125 q^{28} +(-2.15278 + 3.72872i) q^{29} +(1.65278 + 2.86269i) q^{31} +(-2.79060 - 4.83346i) q^{32} +(-2.14510 + 3.71542i) q^{34} -5.43991 q^{35} +9.73779 q^{37} +(-0.314002 + 0.543868i) q^{38} +(-5.36505 - 9.29255i) q^{40} +(2.12380 + 3.67853i) q^{41} +(2.05278 - 3.55552i) q^{43} +1.19999 q^{44} +1.47675 q^{46} +(0.898274 - 1.55586i) q^{47} +(2.44722 + 4.23870i) q^{49} +(-4.04932 - 7.01363i) q^{50} +(3.45393 - 5.98239i) q^{52} +1.15318 q^{53} +3.74893 q^{55} +(2.07659 - 3.59676i) q^{56} +(-1.92552 - 3.33509i) q^{58} +(-2.32552 - 4.02792i) q^{59} +(-1.27447 + 2.20745i) q^{61} -2.95660 q^{62} +5.31212 q^{64} +(10.7906 - 18.6898i) q^{65} +(-4.47062 - 7.74334i) q^{67} +(2.87790 + 4.98467i) q^{68} +(2.43282 - 4.21377i) q^{70} -5.14204 q^{71} +10.5378 q^{73} +(-4.35490 + 7.54291i) q^{74} +(0.421271 + 0.729663i) q^{76} +(0.725528 + 1.25665i) q^{77} +(0.543371 - 0.941146i) q^{79} +0.600024 q^{80} -3.79920 q^{82} +(-1.90171 + 3.29386i) q^{83} +(8.99096 + 15.5728i) q^{85} +(1.83608 + 3.18018i) q^{86} +(-1.43109 + 2.47872i) q^{88} +4.01536 q^{89} +8.35317 q^{91} +(0.990617 - 1.71580i) q^{92} +(0.803446 + 1.39161i) q^{94} +(1.31611 + 2.27957i) q^{95} +(-1.64550 + 2.85009i) q^{97} -4.37775 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7}+O(q^{10}) \) 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7	\( 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 6 q^{37} + 3 q^{38} - 12 q^{40} - 2 q^{41} + 21 q^{43} - 22 q^{44} + 4 q^{46} - 7 q^{47} + 15 q^{49} + 23 q^{50} + 10 q^{52} + 12 q^{53} + 8 q^{55} + 18 q^{56} + 21 q^{58} + 2 q^{59} - 15 q^{61} + 40 q^{62} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} + 38 q^{70} + 6 q^{71} + 44 q^{73} - 36 q^{74} - 42 q^{76} + q^{77} - 11 q^{79} + 68 q^{80} - 34 q^{82} + 18 q^{83} - 13 q^{85} - 24 q^{86} + 12 q^{89} + 38 q^{91} + 67 q^{92} + 19 q^{94} - 30 q^{95} - 26 q^{97} - 30 q^{98}+O(q^{100}) \) 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

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