LMFDB - Embedded newform 605.2.b.f.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (of order $2$, degree $1$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1480160000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 $ x^8 + 9x^6 + 27x^4 + 31*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.4
Root			$-0.802699i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.f.364.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.802699i q^{2} -1.76074i q^{3} +1.35567 q^{4} +(-1.19353 + 1.89090i) q^{5} -1.41335 q^{6} -0.592103i q^{7} -2.69360i q^{8} -0.100212 q^{9} +O(q^{10})$	\(q-0.802699i q^{2} -1.76074i q^{3} +1.35567 q^{4} +(-1.19353 + 1.89090i) q^{5} -1.41335 q^{6} -0.592103i q^{7} -2.69360i q^{8} -0.100212 q^{9} +(1.51782 + 0.958043i) q^{10} -2.38699i q^{12} -1.79489i q^{13} -0.475281 q^{14} +(3.32938 + 2.10149i) q^{15} +0.549201 q^{16} -7.07712i q^{17} +0.0804405i q^{18} -2.28684 q^{19} +(-1.61803 + 2.56344i) q^{20} -1.04254 q^{21} -1.49081i q^{23} -4.74273 q^{24} +(-2.15099 - 4.51367i) q^{25} -1.44076 q^{26} -5.10578i q^{27} -0.802699i q^{28} +3.57549 q^{29} +(1.68687 - 2.67249i) q^{30} +6.16724 q^{31} -5.82804i q^{32} -5.68079 q^{34} +(1.11961 + 0.706691i) q^{35} -0.135855 q^{36} +7.33743i q^{37} +1.83565i q^{38} -3.16034 q^{39} +(5.09331 + 3.21488i) q^{40} -8.41020 q^{41} +0.836847i q^{42} +9.51936i q^{43} +(0.119606 - 0.189492i) q^{45} -1.19667 q^{46} +1.93165i q^{47} -0.967002i q^{48} +6.64941 q^{49} +(-3.62312 + 1.72659i) q^{50} -12.4610 q^{51} -2.43329i q^{52} -2.38291i q^{53} -4.09840 q^{54} -1.59489 q^{56} +4.02654i q^{57} -2.87004i q^{58} +0.0382778 q^{59} +(4.51356 + 2.84894i) q^{60} +3.44158 q^{61} -4.95043i q^{62} +0.0593361i q^{63} -3.57976 q^{64} +(3.39395 + 2.14225i) q^{65} +6.79162i q^{67} -9.59426i q^{68} -2.62493 q^{69} +(0.567260 - 0.898707i) q^{70} -11.7935 q^{71} +0.269932i q^{72} +6.82275i q^{73} +5.88974 q^{74} +(-7.94742 + 3.78733i) q^{75} -3.10021 q^{76} +2.53680i q^{78} +4.52605 q^{79} +(-0.655487 + 1.03848i) q^{80} -9.29059 q^{81} +6.75086i q^{82} +5.94262i q^{83} -1.41335 q^{84} +(13.3821 + 8.44673i) q^{85} +7.64118 q^{86} -6.29552i q^{87} +6.21375 q^{89} +(-0.152105 - 0.0960079i) q^{90} -1.06276 q^{91} -2.02105i q^{92} -10.8589i q^{93} +1.55054 q^{94} +(2.72941 - 4.32418i) q^{95} -10.2617 q^{96} -5.37571i q^{97} -5.33748i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} + 12 q^{19} - 4 q^{20} - 4 q^{21} + 2 q^{24} - 8 q^{25} + 10 q^{26} + 24 q^{29} + 22 q^{30} + 14 q^{31} - 8 q^{34} + 14 q^{35} + 20 q^{36} + 30 q^{39} + 24 q^{40} - 34 q^{41} + 6 q^{45} - 24 q^{46} + 30 q^{49} + 16 q^{50} - 54 q^{51} + 20 q^{54} - 10 q^{56} + 6 q^{59} + 34 q^{60} - 20 q^{61} - 14 q^{64} + 20 q^{65} - 32 q^{69} + 8 q^{70} - 42 q^{71} - 4 q^{74} - 20 q^{75} - 28 q^{76} + 16 q^{79} - 28 q^{80} - 36 q^{81} - 6 q^{84} - 4 q^{85} + 46 q^{86} + 12 q^{89} + 46 q^{90} + 20 q^{91} - 42 q^{94} + 26 q^{95} + 8 q^{96}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 + 12 * q^19 - 4 * q^20 - 4 * q^21 + 2 * q^24 - 8 * q^25 + 10 * q^26 + 24 * q^29 + 22 * q^30 + 14 * q^31 - 8 * q^34 + 14 * q^35 + 20 * q^36 + 30 * q^39 + 24 * q^40 - 34 * q^41 + 6 * q^45 - 24 * q^46 + 30 * q^49 + 16 * q^50 - 54 * q^51 + 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 - 20 * q^61 - 14 * q^64 + 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 - 4 * q^74 - 20 * q^75 - 28 * q^76 + 16 * q^79 - 28 * q^80 - 36 * q^81 - 6 * q^84 - 4 * q^85 + 46 * q^86 + 12 * q^89 + 46 * q^90 + 20 * q^91 - 42 * q^94 + 26 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.802699i		−	0.567594i	−0.958884	−	0.283797i	$-0.908406\pi$
$2$		−	0.802699i		−	0.567594i	0.958884	−	0.283797i	$-0.0915942\pi$
$3$		−	1.76074i		−	1.01656i	−0.861190	−	0.508282i	$-0.830281\pi$
$3$		−	1.76074i		−	1.01656i	0.861190	−	0.508282i	$-0.169719\pi$
$4$	1.35567			0.677837
$5$	−1.19353	+	1.89090i	−0.533762	+	0.845635i
$5$	−1.19353	+	1.89090i	−0.533762	+	0.845635i
$6$	−1.41335			−0.576996
$7$		−	0.592103i		−	0.223794i	−0.993720	−	0.111897i	$-0.964307\pi$
$7$		−	0.592103i		−	0.223794i	0.993720	−	0.111897i	$-0.0356927\pi$
$8$		−	2.69360i		−	0.952330i
$9$	−0.100212			−0.0334042
$10$	1.51782	+	0.958043i	0.479977	+	0.302960i
$11$		0			0
$11$		0			0
$12$		−	2.38699i		−	0.689065i
$13$		−	1.79489i		−	0.497813i	−0.968528	−	0.248906i	$-0.919929\pi$
$13$		−	1.79489i		−	0.497813i	0.968528	−	0.248906i	$-0.0800712\pi$
$14$	−0.475281			−0.127024
$15$	3.32938	+	2.10149i	0.859643	+	0.542603i
$16$	0.549201			0.137300
$17$		−	7.07712i		−	1.71645i	−0.513271	−	0.858226i	$-0.671567\pi$
$17$		−	7.07712i		−	1.71645i	0.513271	−	0.858226i	$-0.328433\pi$
$18$			0.0804405i			0.0189600i
$19$	−2.28684			−0.524637			−0.262319	−	0.964981i	$-0.584487\pi$
$19$	−2.28684			−0.524637			−0.262319	+	0.964981i	$0.584487\pi$
$20$	−1.61803	+	2.56344i	−0.361803	+	0.573203i
$21$	−1.04254			−0.227501
$22$		0			0
$23$		−	1.49081i		−	0.310855i	−0.987847	−	0.155428i	$-0.950324\pi$
$23$		−	1.49081i		−	0.310855i	0.987847	−	0.155428i	$-0.0496756\pi$
$24$	−4.74273			−0.968105
$25$	−2.15099	−	4.51367i	−0.430197	−	0.902735i
$26$	−1.44076			−0.282556
$27$		−	5.10578i		−	0.982607i
$28$		−	0.802699i		−	0.151696i
$29$	3.57549			0.663952			0.331976	−	0.943288i	$-0.392285\pi$
$29$	3.57549			0.663952			0.331976	+	0.943288i	$0.392285\pi$
$30$	1.68687	−	2.67249i	0.307978	−	0.487928i
$31$	6.16724			1.10767			0.553834	−	0.832627i	$-0.313164\pi$
$31$	6.16724			1.10767			0.553834	+	0.832627i	$0.313164\pi$
$32$		−	5.82804i		−	1.03026i
$33$		0			0
$34$	−5.68079			−0.974248
$35$	1.11961	+	0.706691i	0.189248	+	0.119453i
$36$	−0.135855			−0.0226426
$37$			7.33743i			1.20627i	0.797641	+	0.603133i	$0.206081\pi$
$37$			7.33743i			1.20627i	−0.797641	+	0.603133i	$0.793919\pi$
$38$			1.83565i			0.297781i
$39$	−3.16034			−0.506059
$40$	5.09331	+	3.21488i	0.805324	+	0.508317i
$41$	−8.41020			−1.31345			−0.656726	−	0.754129i	$-0.728059\pi$
$41$	−8.41020			−1.31345			−0.656726	+	0.754129i	$0.728059\pi$
$42$			0.836847i			0.129128i
$43$			9.51936i			1.45169i	0.687859	+	0.725844i	$0.258551\pi$
$43$			9.51936i			1.45169i	−0.687859	+	0.725844i	$0.741449\pi$
$44$		0			0
$45$	0.119606	−	0.189492i	0.0178299	−	0.0282477i
$46$	−1.19667			−0.176440
$47$			1.93165i			0.281761i	0.990027	+	0.140880i	$0.0449933\pi$
$47$			1.93165i			0.281761i	−0.990027	+	0.140880i	$0.955007\pi$
$48$		−	0.967002i		−	0.139575i
$49$	6.64941			0.949916
$50$	−3.62312	+	1.72659i	−0.512387	+	0.244177i
$51$	−12.4610			−1.74489
$52$		−	2.43329i		−	0.337436i
$53$		−	2.38291i		−	0.327318i	−0.986517	−	0.163659i	$-0.947670\pi$
$53$		−	2.38291i		−	0.327318i	0.986517	−	0.163659i	$-0.0523296\pi$
$54$	−4.09840			−0.557722
$55$		0			0
$56$	−1.59489			−0.213126
$57$			4.02654i			0.533328i
$58$		−	2.87004i		−	0.376855i
$59$	0.0382778			0.00498334			0.00249167	−	0.999997i	$-0.499207\pi$
$59$	0.0382778			0.00498334			0.00249167	+	0.999997i	$0.499207\pi$
$60$	4.51356	+	2.84894i	0.582698	+	0.367797i
$61$	3.44158			0.440649			0.220325	−	0.975427i	$-0.429288\pi$
$61$	3.44158			0.440649			0.220325	+	0.975427i	$0.429288\pi$
$62$		−	4.95043i		−	0.628706i
$63$			0.0593361i			0.00747565i
$64$	−3.57976			−0.447470
$65$	3.39395	+	2.14225i	0.420968	+	0.265713i
$66$		0			0
$67$			6.79162i			0.829728i	0.909883	+	0.414864i	$0.136171\pi$
$67$			6.79162i			0.829728i	−0.909883	+	0.414864i	$0.863829\pi$
$68$		−	9.59426i		−	1.16348i
$69$	−2.62493			−0.316005
$70$	0.567260	−	0.898707i	0.0678006	−	0.107416i
$71$	−11.7935			−1.39963			−0.699816	−	0.714324i	$-0.746735\pi$
$71$	−11.7935			−1.39963			−0.699816	+	0.714324i	$0.746735\pi$
$72$			0.269932i			0.0318118i
$73$			6.82275i			0.798543i	0.916833	+	0.399271i	$0.130737\pi$
$73$			6.82275i			0.798543i	−0.916833	+	0.399271i	$0.869263\pi$
$74$	5.88974			0.684669
$75$	−7.94742	+	3.78733i	−0.917689	+	0.437323i
$76$	−3.10021			−0.355619
$77$		0			0
$78$			2.53680i			0.287236i
$79$	4.52605			0.509221			0.254610	−	0.967044i	$-0.418053\pi$
$79$	4.52605			0.509221			0.254610	+	0.967044i	$0.418053\pi$
$80$	−0.655487	+	1.03848i	−0.0732856	+	0.116106i
$81$	−9.29059			−1.03229
$82$			6.75086i			0.745508i
$83$			5.94262i			0.652288i	0.945320	+	0.326144i	$0.105749\pi$
$83$			5.94262i			0.652288i	−0.945320	+	0.326144i	$0.894251\pi$
$84$	−1.41335			−0.154209
$85$	13.3821	+	8.44673i	1.45149	+	0.916176i
$86$	7.64118			0.823970
$87$		−	6.29552i		−	0.674951i
$88$		0			0
$89$	6.21375			0.658656			0.329328	−	0.944216i	$-0.393178\pi$
$89$	6.21375			0.658656			0.329328	+	0.944216i	$0.393178\pi$
$90$	−0.152105	−	0.0960079i	−0.0160332	−	0.0101201i
$91$	−1.06276			−0.111407
$92$		−	2.02105i		−	0.210709i
$93$		−	10.8589i		−	1.12602i
$94$	1.55054			0.159926
$95$	2.72941	−	4.32418i	0.280031	−	0.443652i
$96$	−10.2617			−1.04733
$97$		−	5.37571i		−	0.545821i	−0.962039	−	0.272910i	$-0.912014\pi$
$97$		−	5.37571i		−	0.545821i	0.962039	−	0.272910i	$-0.0879862\pi$
$98$		−	5.33748i		−	0.539167i
$99$		0			0
$100$	−2.91604	−	6.11907i	−0.291604	−	0.611907i
$101$	9.93130			0.988201			0.494101	−	0.869405i	$-0.335497\pi$
$101$	9.93130			0.988201			0.494101	+	0.869405i	$0.335497\pi$
$102$			10.0024i			0.990386i
$103$		−	13.5214i		−	1.33230i	−0.745818	−	0.666150i	$-0.767941\pi$
$103$		−	13.5214i		−	1.33230i	0.745818	−	0.666150i	$-0.232059\pi$
$104$	−4.83471			−0.474082
$105$	1.24430	−	1.97134i	0.121431	−	0.192383i
$106$	−1.91276			−0.185784
$107$			5.60440i			0.541798i	0.962608	+	0.270899i	$0.0873209\pi$
$107$			5.60440i			0.541798i	−0.962608	+	0.270899i	$0.912679\pi$
$108$		−	6.92177i		−	0.666048i
$109$	18.6001			1.78157			0.890784	−	0.454428i	$-0.150156\pi$
$109$	18.6001			1.78157			0.890784	+	0.454428i	$0.150156\pi$
$110$		0			0
$111$	12.9193			1.22625
$112$		−	0.325184i		−	0.0307270i
$113$			11.8014i			1.11018i	0.831790	+	0.555091i	$0.187316\pi$
$113$			11.8014i			1.11018i	−0.831790	+	0.555091i	$0.812684\pi$
$114$	3.23210			0.302714
$115$	2.81897	+	1.77932i	0.262870	+	0.165923i
$116$	4.84720			0.450052
$117$			0.179870i			0.0166290i
$118$		−	0.0307255i		−	0.00282851i
$119$	−4.19038			−0.384132
$120$	5.66057	−	8.96801i	0.516737	−	0.818664i
$121$		0			0
$122$		−	2.76255i		−	0.250110i
$123$			14.8082i			1.33521i
$124$	8.36076			0.750819
$125$	11.1022	+	1.31990i	0.993007	+	0.118055i
$126$	0.0476291			0.00424313
$127$			16.0566i			1.42479i	0.701777	+	0.712397i	$0.252390\pi$
$127$			16.0566i			1.42479i	−0.701777	+	0.712397i	$0.747610\pi$
$128$		−	8.78261i		−	0.776280i
$129$	16.7611			1.47574
$130$	1.71958	−	2.72432i	0.150817	−	0.238939i
$131$	−18.0296			−1.57525			−0.787625	−	0.616154i	$-0.788690\pi$
$131$	−18.0296			−1.57525			−0.787625	+	0.616154i	$0.788690\pi$
$132$		0			0
$133$			1.35405i			0.117411i
$134$	5.45162			0.470949
$135$	9.65450	+	6.09388i	0.830927	+	0.524478i
$136$	−19.0629			−1.63463
$137$		−	4.03208i		−	0.344483i	−0.985055	−	0.172242i	$-0.944899\pi$
$137$		−	4.03208i		−	0.344483i	0.985055	−	0.172242i	$-0.0551010\pi$
$138$			2.10703i			0.179362i
$139$	7.93492			0.673031			0.336516	−	0.941678i	$-0.390752\pi$
$139$	7.93492			0.673031			0.336516	+	0.941678i	$0.390752\pi$
$140$	1.51782	+	0.958043i	0.128279	+	0.0809694i
$141$	3.40114			0.286428
$142$			9.46663i			0.794422i
$143$		0			0
$144$	−0.0550368			−0.00458640
$145$	−4.26745	+	6.76089i	−0.354392	+	0.561461i
$146$	5.47662			0.453248
$147$		−	11.7079i		−	0.965652i
$148$			9.94716i			0.817652i
$149$	12.5009			1.02411			0.512056	−	0.858952i	$-0.328884\pi$
$149$	12.5009			1.02411			0.512056	+	0.858952i	$0.328884\pi$
$150$	3.04009	+	6.37938i	0.248222	+	0.520874i
$151$	−8.40248			−0.683784			−0.341892	−	0.939739i	$-0.611068\pi$
$151$	−8.40248			−0.683784			−0.341892	+	0.939739i	$0.611068\pi$
$152$			6.15983i			0.499628i
$153$			0.709215i			0.0573367i
$154$		0			0
$155$	−7.36076	+	11.6616i	−0.591231	+	0.936683i
$156$	−4.28439			−0.343026
$157$		−	13.9959i		−	1.11699i	−0.829507	−	0.558496i	$-0.811379\pi$
$157$		−	13.9959i		−	1.11699i	0.829507	−	0.558496i	$-0.188621\pi$
$158$		−	3.63306i		−	0.289031i
$159$	−4.19569			−0.332740
$160$	11.0202	+	6.95592i	0.871225	+	0.549914i
$161$	−0.882713			−0.0695676
$162$			7.45755i			0.585921i
$163$			11.8415i			0.927496i	0.885967	+	0.463748i	$0.153496\pi$
$163$			11.8415i			0.927496i	−0.885967	+	0.463748i	$0.846504\pi$
$164$	−11.4015			−0.890307
$165$		0			0
$166$	4.77014			0.370235
$167$			8.72628i			0.675260i	0.941279	+	0.337630i	$0.109625\pi$
$167$			8.72628i			0.675260i	−0.941279	+	0.337630i	$0.890375\pi$
$168$			2.80818i			0.216656i
$169$	9.77837			0.752182
$170$	6.78018	−	10.7418i	0.520016	−	0.823858i
$171$	0.229170			0.0175251
$172$			12.9052i			0.984009i
$173$			9.17861i			0.697837i	0.937153	+	0.348918i	$0.113451\pi$
$173$			9.17861i			0.697837i	−0.937153	+	0.348918i	$0.886549\pi$
$174$	−5.05341			−0.383098
$175$	−2.67256	+	1.27361i	−0.202027	+	0.0962755i
$176$		0			0
$177$		−	0.0673973i		−	0.00506589i
$178$		−	4.98777i		−	0.373849i
$179$	−1.44816			−0.108241			−0.0541204	−	0.998534i	$-0.517235\pi$
$179$	−1.44816			−0.108241			−0.0541204	+	0.998534i	$0.517235\pi$
$180$	0.162147	−	0.256889i	0.0120857	−	0.0191474i
$181$	0.793502			0.0589806			0.0294903	−	0.999565i	$-0.490612\pi$
$181$	0.793502			0.0589806			0.0294903	+	0.999565i	$0.490612\pi$
$182$			0.853076i			0.0632342i
$183$		−	6.05974i		−	0.447949i
$184$	−4.01564			−0.296037
$185$	−13.8743	−	8.75742i	−1.02006	−	0.643858i
$186$	−8.71644			−0.639120
$187$		0			0
$188$			2.61869i			0.190988i
$189$	−3.02315			−0.219902
$190$	−3.47102	−	2.19089i	−0.251814	−	0.158944i
$191$	−8.15029			−0.589735			−0.294867	−	0.955538i	$-0.595275\pi$
$191$	−8.15029			−0.589735			−0.294867	+	0.955538i	$0.595275\pi$
$192$			6.30303i			0.454882i
$193$			4.36836i			0.314442i	0.987563	+	0.157221i	$0.0502534\pi$
$193$			4.36836i			0.314442i	−0.987563	+	0.157221i	$0.949747\pi$
$194$	−4.31508			−0.309804
$195$	3.77195	−	5.97587i	0.270115	−	0.427941i
$196$	9.01444			0.643889
$197$			15.6525i			1.11520i	0.830111	+	0.557599i	$0.188277\pi$
$197$			15.6525i			1.11520i	−0.830111	+	0.557599i	$0.811723\pi$
$198$		0			0
$199$	−1.43830			−0.101959			−0.0509793	−	0.998700i	$-0.516234\pi$
$199$	−1.43830			−0.101959			−0.0509793	+	0.998700i	$0.516234\pi$
$200$	−12.1580	+	5.79389i	−0.859702	+	0.409690i
$201$	11.9583			0.843472
$202$		−	7.97185i		−	0.560897i
$203$		−	2.11706i		−	0.148589i
$204$	−16.8930			−1.18275
$205$	10.0378	−	15.9028i	0.701071	−	1.11070i
$206$	−10.8536			−0.756206
$207$			0.149398i			0.0103839i
$208$		−	0.985756i		−	0.0683499i
$209$		0			0
$210$	−1.58239	−	0.998799i	−0.109195	−	0.0689237i
$211$	−8.68130			−0.597646			−0.298823	−	0.954309i	$-0.596594\pi$
$211$	−8.68130			−0.597646			−0.298823	+	0.954309i	$0.596594\pi$
$212$		−	3.23045i		−	0.221868i
$213$			20.7653i			1.42282i
$214$	4.49864			0.307521
$215$	−18.0001	−	11.3616i	−1.22760	−	0.774856i
$216$	−13.7529			−0.935767
$217$		−	3.65164i		−	0.247889i
$218$		−	14.9303i		−	1.01121i
$219$	12.0131			0.811770
$220$		0			0
$221$	−12.7026			−0.854472
$222$		−	10.3703i		−	0.696010i
$223$		−	6.30604i		−	0.422284i	−0.977455	−	0.211142i	$-0.932282\pi$
$223$		−	6.30604i		−	0.422284i	0.977455	−	0.211142i	$-0.0677182\pi$
$224$	−3.45080			−0.230566
$225$	0.215556	+	0.452327i	0.0143704	+	0.0301551i
$226$	9.47296			0.630132
$227$		−	1.11681i		−	0.0741252i	−0.999313	−	0.0370626i	$-0.988200\pi$
$227$		−	1.11681i		−	0.0741252i	0.999313	−	0.0370626i	$-0.0118001\pi$
$228$			5.45867i			0.361510i
$229$	4.19616			0.277290			0.138645	−	0.990342i	$-0.455725\pi$
$229$	4.19616			0.277290			0.138645	+	0.990342i	$0.455725\pi$
$230$	1.42826	−	2.26278i	0.0941767	−	0.149204i
$231$		0			0
$232$		−	9.63094i		−	0.632302i
$233$			6.77947i			0.444138i	0.975031	+	0.222069i	$0.0712810\pi$
$233$			6.77947i			0.444138i	−0.975031	+	0.222069i	$0.928719\pi$
$234$	0.144382			0.00943853
$235$	−3.65256	−	2.30548i	−0.238267	−	0.150393i
$236$	0.0518922			0.00337789
$237$		−	7.96921i		−	0.517656i
$238$			3.36362i			0.218031i
$239$	4.39808			0.284488			0.142244	−	0.989832i	$-0.454568\pi$
$239$	4.39808			0.284488			0.142244	+	0.989832i	$0.454568\pi$
$240$	1.82850	+	1.15414i	0.118029	+	0.0744996i
$241$	9.61218			0.619175			0.309587	−	0.950871i	$-0.399809\pi$
$241$	9.61218			0.619175			0.309587	+	0.950871i	$0.399809\pi$
$242$		0			0
$243$			1.04101i			0.0667807i
$244$	4.66566			0.298688
$245$	−7.93626	+	12.5734i	−0.507029	+	0.803282i
$246$	11.8865			0.757857
$247$			4.10463i			0.261171i
$248$		−	16.6120i		−	1.05487i
$249$	10.4634			0.663093
$250$	1.05948	−	8.91169i	0.0670075	−	0.563625i
$251$	13.4206			0.847100			0.423550	−	0.905873i	$-0.360784\pi$
$251$	13.4206			0.847100			0.423550	+	0.905873i	$0.360784\pi$
$252$			0.0804405i			0.00506727i
$253$		0			0
$254$	12.8886			0.808704
$255$	14.8725	−	23.5624i	0.931353	−	1.47554i
$256$	−14.2093			−0.888081
$257$			10.8174i			0.674769i	0.941367	+	0.337384i	$0.109542\pi$
$257$			10.8174i			0.674769i	−0.941367	+	0.337384i	$0.890458\pi$
$258$		−	13.4541i		−	0.837619i
$259$	4.34451			0.269955
$260$	4.60109	+	2.90419i	0.285348	+	0.180110i
$261$	−0.358309			−0.0221788
$262$			14.4723i			0.894103i
$263$		−	24.6351i		−	1.51906i	−0.650471	−	0.759531i	$-0.725428\pi$
$263$		−	24.6351i		−	1.51906i	0.650471	−	0.759531i	$-0.274572\pi$
$264$		0			0
$265$	4.50584	+	2.84407i	0.276791	+	0.174710i
$266$	1.08689			0.0666416
$267$		−	10.9408i		−	0.669566i
$268$			9.20722i			0.562420i
$269$	4.80101			0.292723			0.146361	−	0.989231i	$-0.453244\pi$
$269$	4.80101			0.292723			0.146361	+	0.989231i	$0.453244\pi$
$270$	4.89155	−	7.74966i	0.297691	−	0.471629i
$271$	−23.3303			−1.41722			−0.708609	−	0.705602i	$-0.750677\pi$
$271$	−23.3303			−1.41722			−0.708609	+	0.705602i	$0.750677\pi$
$272$		−	3.88676i		−	0.235670i
$273$			1.87125i			0.113253i
$274$	−3.23654			−0.195527
$275$		0			0
$276$	−3.55855			−0.214200
$277$		−	21.8973i		−	1.31568i	−0.753158	−	0.657840i	$-0.771470\pi$
$277$		−	21.8973i		−	1.31568i	0.753158	−	0.657840i	$-0.228530\pi$
$278$		−	6.36935i		−	0.382008i
$279$	−0.618034			−0.0370007
$280$	1.90354	−	3.01577i	0.113758	−	0.180227i
$281$	−15.7754			−0.941084			−0.470542	−	0.882378i	$-0.655942\pi$
$281$	−15.7754			−0.941084			−0.470542	+	0.882378i	$0.655942\pi$
$282$		−	2.73009i		−	0.162575i
$283$		−	22.6091i		−	1.34397i	−0.740563	−	0.671987i	$-0.765441\pi$
$283$		−	22.6091i		−	1.34397i	0.740563	−	0.671987i	$-0.234559\pi$
$284$	−15.9881			−0.948722
$285$	−7.61377	−	4.80578i	−0.451001	−	0.284670i
$286$		0			0
$287$			4.97971i			0.293943i
$288$			0.584042i			0.0344150i
$289$	−33.0856			−1.94621
$290$	5.42696	+	3.42548i	0.318682	+	0.201151i
$291$	−9.46524			−0.554862
$292$			9.24943i			0.541282i
$293$			13.2596i			0.774635i	0.921946	+	0.387317i	$0.126598\pi$
$293$			13.2596i			0.774635i	−0.921946	+	0.387317i	$0.873402\pi$
$294$	−9.39792			−0.548098
$295$	−0.0456855	+	0.0723793i	−0.00265992	+	0.00421409i
$296$	19.7641			1.14876
$297$		0			0
$298$		−	10.0344i		−	0.581280i
$299$	−2.67584			−0.154748
$300$	−10.7741	+	5.13439i	−0.622043	+	0.296434i
$301$	5.63644			0.324879
$302$			6.74466i			0.388112i
$303$		−	17.4865i		−	1.00457i
$304$	−1.25594			−0.0720329
$305$	−4.10762	+	6.50768i	−0.235202	+	0.372628i
$306$	0.569286			0.0325439
$307$			10.0161i			0.571650i	0.958282	+	0.285825i	$0.0922676\pi$
$307$			10.0161i			0.571650i	−0.958282	+	0.285825i	$0.907732\pi$
$308$		0			0
$309$	−23.8076			−1.35437
$310$	9.36076	+	5.90848i	0.531656	+	0.335579i
$311$	−3.40826			−0.193265			−0.0966323	−	0.995320i	$-0.530807\pi$
$311$	−3.40826			−0.193265			−0.0966323	+	0.995320i	$0.530807\pi$
$312$			8.51267i			0.481935i
$313$			24.5008i			1.38487i	0.721481	+	0.692434i	$0.243462\pi$
$313$			24.5008i			1.38487i	−0.721481	+	0.692434i	$0.756538\pi$
$314$	−11.2345			−0.633998
$315$	−0.112199	−	0.0708193i	−0.00632167	−	0.00399021i
$316$	6.13586			0.345169
$317$		−	6.98851i		−	0.392514i	−0.980553	−	0.196257i	$-0.937121\pi$
$317$		−	6.98851i		−	0.392514i	0.980553	−	0.196257i	$-0.0628786\pi$
$318$			3.36787i			0.188861i
$319$		0			0
$320$	4.27254	−	6.76895i	0.238842	−	0.378396i
$321$	9.86790			0.550772
$322$			0.708553i			0.0394861i
$323$			16.1842i			0.900515i
$324$	−12.5950			−0.699723
$325$	−8.10155	+	3.86078i	−0.449393	+	0.214158i
$326$	9.50514			0.526441
$327$		−	32.7500i		−	1.81108i
$328$			22.6537i			1.25084i
$329$	1.14374			0.0630563
$330$		0			0
$331$	5.64321			0.310179			0.155089	−	0.987900i	$-0.450433\pi$
$331$	5.64321			0.310179			0.155089	+	0.987900i	$0.450433\pi$
$332$			8.05626i			0.442145i
$333$		−	0.735302i		−	0.0402943i
$334$	7.00458			0.383273
$335$	−12.8422	−	8.10598i	−0.701647	−	0.442877i
$336$	−0.572565			−0.0312360
$337$			22.6164i			1.23199i	0.787750	+	0.615996i	$0.211246\pi$
$337$			22.6164i			1.23199i	−0.787750	+	0.615996i	$0.788754\pi$
$338$		−	7.84909i		−	0.426934i
$339$	20.7792			1.12857
$340$	18.1418	+	11.4510i	0.983876	+	0.621018i
$341$		0			0
$342$		−	0.183955i		−	0.00994713i
$343$		−	8.08186i		−	0.436379i
$344$	25.6413			1.38249
$345$	3.13293	−	4.96348i	0.168671	−	0.267225i
$346$	7.36766			0.396088
$347$		−	0.182395i		−	0.00979145i	−0.999988	−	0.00489573i	$-0.998442\pi$
$347$		−	0.182395i		−	0.00979145i	0.999988	−	0.00489573i	$-0.00155836\pi$
$348$		−	8.53468i		−	0.457507i
$349$	−15.4273			−0.825803			−0.412902	−	0.910776i	$-0.635485\pi$
$349$	−15.4273			−0.825803			−0.412902	+	0.910776i	$0.635485\pi$
$350$	1.02232	+	2.14526i	0.0546454	+	0.114669i
$351$	−9.16431			−0.489155
$352$		0			0
$353$		−	23.9103i		−	1.27262i	−0.771435	−	0.636308i	$-0.780461\pi$
$353$		−	23.9103i		−	1.27262i	0.771435	−	0.636308i	$-0.219539\pi$
$354$	−0.0540997			−0.00287537
$355$	14.0759	−	22.3003i	0.747069	−	1.18358i
$356$	8.42382			0.446461
$357$			7.37818i			0.390495i
$358$			1.16244i			0.0614368i
$359$	−8.76734			−0.462723			−0.231361	−	0.972868i	$-0.574318\pi$
$359$	−8.76734			−0.462723			−0.231361	+	0.972868i	$0.574318\pi$
$360$	−0.510414	−	0.322171i	−0.0269012	−	0.0169799i
$361$	−13.7704			−0.724756
$362$		−	0.636943i		−	0.0334770i
$363$		0			0
$364$	−1.44076			−0.0755161
$365$	−12.9011	−	8.14314i	−0.675276	−	0.426231i
$366$	−4.86414			−0.254253
$367$		−	5.38232i		−	0.280955i	−0.990084	−	0.140477i	$-0.955136\pi$
$367$		−	5.38232i		−	0.280955i	0.990084	−	0.140477i	$-0.0448637\pi$
$368$		−	0.818755i		−	0.0426806i
$369$	0.842807			0.0438748
$370$	−7.02957	+	11.1369i	−0.365450	+	0.578980i
$371$	−1.41093			−0.0732517
$372$		−	14.7211i		−	0.763256i
$373$			3.22450i			0.166958i	0.996510	+	0.0834792i	$0.0266032\pi$
$373$			3.22450i			0.166958i	−0.996510	+	0.0834792i	$0.973397\pi$
$374$		0			0
$375$	2.32400	−	19.5480i	0.120011	−	1.00946i
$376$	5.20309			0.268329
$377$		−	6.41762i		−	0.330524i
$378$			2.42668i			0.124815i
$379$	19.6634			1.01004			0.505020	−	0.863108i	$-0.331485\pi$
$379$	19.6634			1.01004			0.505020	+	0.863108i	$0.331485\pi$
$380$	3.70019	−	5.86218i	0.189816	−	0.300724i
$381$	28.2716			1.44840
$382$			6.54223i			0.334730i
$383$			27.9751i			1.42946i	0.699400	+	0.714731i	$0.253451\pi$
$383$			27.9751i			1.42946i	−0.699400	+	0.714731i	$0.746549\pi$
$384$	−15.4639			−0.789139
$385$		0			0
$386$	3.50648			0.178475
$387$		−	0.953959i		−	0.0484924i
$388$		−	7.28771i		−	0.369977i
$389$	−13.0400			−0.661154			−0.330577	−	0.943779i	$-0.607243\pi$
$389$	−13.0400			−0.661154			−0.330577	+	0.943779i	$0.607243\pi$
$390$	−4.79683	−	3.02774i	−0.242897	−	0.153316i
$391$	−10.5506			−0.533569
$392$		−	17.9108i		−	0.904634i
$393$			31.7454i			1.60134i
$394$	12.5643			0.632980
$395$	−5.40197	+	8.55830i	−0.271803	+	0.430615i
$396$		0			0
$397$			1.82243i			0.0914651i	0.998954	+	0.0457325i	$0.0145622\pi$
$397$			1.82243i			0.0914651i	−0.998954	+	0.0457325i	$0.985438\pi$
$398$			1.15452i			0.0578711i
$399$	2.38413			0.119356
$400$	−1.18132	−	2.47892i	−0.0590662	−	0.123946i
$401$	5.38085			0.268707			0.134353	−	0.990933i	$-0.457104\pi$
$401$	5.38085			0.268707			0.134353	+	0.990933i	$0.457104\pi$
$402$		−	9.59890i		−	0.478750i
$403$		−	11.0695i		−	0.551411i
$404$	13.4636			0.669840
$405$	11.0886	−	17.5676i	0.550996	−	0.872939i
$406$	−1.69936			−0.0843379
$407$		0			0
$408$			33.5648i			1.66171i
$409$	−36.6821			−1.81381			−0.906906	−	0.421333i	$-0.861562\pi$
$409$	−36.6821			−1.81381			−0.906906	+	0.421333i	$0.861562\pi$
$410$	−12.7652	−	8.05733i	−0.630428	−	0.397923i
$411$	−7.09944			−0.350190
$412$		−	18.3306i		−	0.903083i
$413$		−	0.0226644i		−	0.00111524i
$414$	0.119921			0.00589382
$415$	−11.2369	−	7.09268i	−0.551597	−	0.348166i
$416$	−10.4607			−0.512877
$417$		−	13.9713i		−	0.684180i
$418$		0			0
$419$	−2.86630			−0.140028			−0.0700141	−	0.997546i	$-0.522304\pi$
$419$	−2.86630			−0.140028			−0.0700141	+	0.997546i	$0.522304\pi$
$420$	1.68687	−	2.67249i	0.0823107	−	0.130404i
$421$	4.65975			0.227102			0.113551	−	0.993532i	$-0.463777\pi$
$421$	4.65975			0.227102			0.113551	+	0.993532i	$0.463777\pi$
$422$			6.96847i			0.339220i
$423$		−	0.193576i		−	0.00941198i
$424$	−6.41859			−0.311714
$425$	−31.9438	+	15.2228i	−1.54950	+	0.738413i
$426$	16.6683			0.807582
$427$		−	2.03777i		−	0.0986147i
$428$			7.59774i			0.367250i
$429$		0			0
$430$	−9.11996	+	14.4487i	−0.439803	+	0.696778i
$431$	−20.7691			−1.00041			−0.500207	−	0.865906i	$-0.666743\pi$
$431$	−20.7691			−1.00041			−0.500207	+	0.865906i	$0.666743\pi$
$432$		−	2.80410i		−	0.134912i
$433$		−	12.7972i		−	0.614993i	−0.951549	−	0.307496i	$-0.900509\pi$
$433$		−	12.7972i		−	0.614993i	0.951549	−	0.307496i	$-0.0994912\pi$
$434$	−2.93117			−0.140701
$435$	11.9042	+	7.51387i	0.570762	+	0.360263i
$436$	25.2157			1.20761
$437$			3.40925i			0.163086i
$438$		−	9.64291i		−	0.460756i
$439$	−10.6208			−0.506905			−0.253452	−	0.967348i	$-0.581566\pi$
$439$	−10.6208			−0.506905			−0.253452	+	0.967348i	$0.581566\pi$
$440$		0			0
$441$	−0.666354			−0.0317312
$442$			10.1964i			0.484993i
$443$			6.59894i			0.313525i	0.987636	+	0.156763i	$0.0501057\pi$
$443$			6.59894i			0.313525i	−0.987636	+	0.156763i	$0.949894\pi$
$444$	17.5144			0.831196
$445$	−7.41627	+	11.7496i	−0.351565	+	0.556982i
$446$	−5.06185			−0.239686
$447$		−	22.0108i		−	1.04108i
$448$			2.11958i			0.100141i
$449$	−13.6281			−0.643147			−0.321574	−	0.946885i	$-0.604212\pi$
$449$	−13.6281			−0.643147			−0.321574	+	0.946885i	$0.604212\pi$
$450$	0.363082	−	0.173026i	0.0171159	−	0.00815654i
$451$		0			0
$452$			15.9988i			0.752522i
$453$			14.7946i			0.695111i
$454$	−0.896462			−0.0420730
$455$	1.26843	−	2.00957i	0.0594650	−	0.0942101i
$456$	10.8459			0.507904
$457$		−	13.4999i		−	0.631498i	−0.948843	−	0.315749i	$-0.897744\pi$
$457$		−	13.4999i		−	0.631498i	0.948843	−	0.315749i	$-0.102256\pi$
$458$		−	3.36825i		−	0.157388i
$459$	−36.1342			−1.68660
$460$	3.82160	+	2.41218i	0.178183	+	0.112469i
$461$	−11.3217			−0.527303			−0.263652	−	0.964618i	$-0.584927\pi$
$461$	−11.3217			−0.527303			−0.263652	+	0.964618i	$0.584927\pi$
$462$		0			0
$463$		−	4.82990i		−	0.224464i	−0.993682	−	0.112232i	$-0.964200\pi$
$463$		−	4.82990i		−	0.224464i	0.993682	−	0.112232i	$-0.0358001\pi$
$464$	1.96367			0.0911609
$465$	20.5331	+	12.9604i	0.952199	+	0.601024i
$466$	5.44187			0.252090
$467$		−	24.0173i		−	1.11139i	−0.831387	−	0.555694i	$-0.812453\pi$
$467$		−	24.0173i		−	1.11139i	0.831387	−	0.555694i	$-0.187547\pi$
$468$			0.243846i			0.0112718i
$469$	4.02134			0.185688
$470$	−1.85061	+	2.93191i	−0.0853621	+	0.135239i
$471$	−24.6431			−1.13550
$472$		−	0.103105i		−	0.00474579i
$473$		0			0
$474$	−6.39688			−0.293818
$475$	4.91896	+	10.3221i	0.225698	+	0.473609i
$476$	−5.68079			−0.260379
$477$			0.238797i			0.0109338i
$478$		−	3.53034i		−	0.161474i
$479$	43.2250			1.97500			0.987501	−	0.157611i	$-0.0503792\pi$
$479$	43.2250			1.97500			0.987501	+	0.157611i	$0.0503792\pi$
$480$	12.2476	−	19.4038i	0.559023	−	0.885657i
$481$	13.1699			0.600494
$482$		−	7.71569i		−	0.351440i
$483$			1.55423i			0.0707199i
$484$		0			0
$485$	10.1649	+	6.41606i	0.461565	+	0.291338i
$486$	0.835616			0.0379043
$487$			41.9609i			1.90143i	0.310067	+	0.950715i	$0.399648\pi$
$487$			41.9609i			1.90143i	−0.310067	+	0.950715i	$0.600352\pi$
$488$		−	9.27023i		−	0.419644i
$489$	20.8498			0.942860
$490$	10.0926	+	6.37042i	0.455938	+	0.287786i
$491$	9.05983			0.408864			0.204432	−	0.978881i	$-0.434465\pi$
$491$	9.05983			0.408864			0.204432	+	0.978881i	$0.434465\pi$
$492$			20.0751i			0.905055i
$493$		−	25.3042i		−	1.13964i
$494$	3.29478			0.148239
$495$		0			0
$496$	3.38705			0.152083
$497$			6.98297i			0.313229i
$498$		−	8.39898i		−	0.376367i
$499$	−30.2793			−1.35549			−0.677744	−	0.735298i	$-0.737042\pi$
$499$	−30.2793			−1.35549			−0.677744	+	0.735298i	$0.737042\pi$
$500$	15.0509	+	1.78935i	0.673097	+	0.0800223i
$501$	15.3647			0.686446
$502$		−	10.7727i		−	0.480809i
$503$		−	18.0638i		−	0.805426i	−0.915326	−	0.402713i	$-0.868067\pi$
$503$		−	18.0638i		−	0.805426i	0.915326	−	0.402713i	$-0.131933\pi$
$504$	0.159828			0.00711929
$505$	−11.8533	+	18.7791i	−0.527464	+	0.835658i
$506$		0			0
$507$		−	17.2172i		−	0.764642i
$508$			21.7675i			0.965778i
$509$	24.9157			1.10437			0.552184	−	0.833722i	$-0.313794\pi$
$509$	24.9157			1.10437			0.552184	+	0.833722i	$0.313794\pi$
$510$	−18.9135	−	11.9381i	−0.837505	−	0.528630i
$511$	4.03977			0.178709
$512$		−	6.15942i		−	0.272210i
$513$			11.6761i			0.515513i
$514$	8.68309			0.382995
$515$	25.5675	+	16.1381i	1.12664	+	0.711131i
$516$	22.7226			1.00031
$517$		0			0
$518$		−	3.48734i		−	0.153225i
$519$	16.1612			0.709396
$520$	5.77036	−	9.14194i	0.253047	−	0.400900i
$521$	36.2831			1.58959			0.794797	−	0.606876i	$-0.207578\pi$
$521$	36.2831			1.58959			0.794797	+	0.606876i	$0.207578\pi$
$522$			0.287614i			0.0125885i
$523$			24.7070i			1.08036i	0.841549	+	0.540181i	$0.181644\pi$
$523$			24.7070i			1.08036i	−0.841549	+	0.540181i	$0.818356\pi$
$524$	−24.4422			−1.06776
$525$	2.24249	+	4.70569i	0.0978703	+	0.205373i
$526$	−19.7745			−0.862211
$527$		−	43.6462i		−	1.90126i
$528$		0			0
$529$	20.7775			0.903369
$530$	2.28293	−	3.61683i	0.0991641	−	0.157105i
$531$	−0.00383591			−0.000166464
$532$			1.83565i			0.0795853i
$533$			15.0954i			0.653854i
$534$	−8.78217			−0.380042
$535$	−10.5973	−	6.68900i	−0.458163	−	0.289191i
$536$	18.2939			0.790175
$537$			2.54984i			0.110034i
$538$		−	3.85376i		−	0.166148i
$539$		0			0
$540$	13.0884	+	8.26132i	0.563233	+	0.355511i
$541$	12.5420			0.539221			0.269610	−	0.962970i	$-0.413105\pi$
$541$	12.5420			0.539221			0.269610	+	0.962970i	$0.413105\pi$
$542$			18.7272i			0.804404i
$543$		−	1.39715i		−	0.0599576i
$544$	−41.2457			−1.76839
$545$	−22.1997	+	35.1709i	−0.950932	+	1.50656i
$546$	1.50205			0.0642817
$547$			30.7407i			1.31438i	0.753726	+	0.657189i	$0.228255\pi$
$547$			30.7407i			1.31438i	−0.753726	+	0.657189i	$0.771745\pi$
$548$		−	5.46618i		−	0.233504i
$549$	−0.344889			−0.0147195
$550$		0			0
$551$	−8.17659			−0.348334
$552$			7.07051i			0.300941i
$553$		−	2.67989i		−	0.113961i
$554$	−17.5769			−0.746772
$555$	−15.4196	+	24.4291i	−0.654524	+	1.03696i
$556$	10.7572			0.456206
$557$			13.4294i			0.569021i	0.958673	+	0.284510i	$0.0918310\pi$
$557$			13.4294i			0.569021i	−0.958673	+	0.284510i	$0.908169\pi$
$558$			0.496095i			0.0210014i
$559$	17.0862			0.722669
$560$	0.614889	+	0.388116i	0.0259838	+	0.0164009i
$561$		0			0
$562$			12.6629i			0.534154i
$563$		−	30.5401i		−	1.28711i	−0.765399	−	0.643556i	$-0.777458\pi$
$563$		−	30.5401i		−	1.28711i	0.765399	−	0.643556i	$-0.222542\pi$
$564$	4.61084			0.194152
$565$	−22.3152	−	14.0853i	−0.938808	−	0.592572i
$566$	−18.1483			−0.762831
$567$			5.50099i			0.231020i
$568$			31.7669i			1.33291i
$569$	25.7204			1.07826			0.539128	−	0.842224i	$-0.318754\pi$
$569$	25.7204			1.07826			0.539128	+	0.842224i	$0.318754\pi$
$570$	−3.85760	+	6.11157i	−0.161577	+	0.255985i
$571$	27.1115			1.13458			0.567291	−	0.823518i	$-0.307992\pi$
$571$	27.1115			1.13458			0.567291	+	0.823518i	$0.307992\pi$
$572$		0			0
$573$			14.3506i			0.599504i
$574$	3.99721			0.166840
$575$	−6.72903	+	3.20671i	−0.280620	+	0.133729i
$576$	0.358736			0.0149473
$577$		−	2.87015i		−	0.119486i	−0.998214	−	0.0597430i	$-0.980972\pi$
$577$		−	2.87015i		−	0.119486i	0.998214	−	0.0597430i	$-0.0190281\pi$
$578$			26.5578i			1.10466i
$579$	7.69156			0.319650
$580$	−5.78527	+	9.16557i	−0.240220	+	0.380579i
$581$	3.51865			0.145978
$582$			7.59774i			0.314936i
$583$		0			0
$584$	18.3777			0.760476
$585$	−0.340116	−	0.214680i	−0.0140621	−	0.00887593i
$586$	10.6435			0.439678
$587$		−	44.8360i		−	1.85058i	−0.379262	−	0.925289i	$-0.623822\pi$
$587$		−	44.8360i		−	1.85058i	0.379262	−	0.925289i	$-0.376178\pi$
$588$		−	15.8721i		−	0.654554i
$589$	−14.1035			−0.581124
$590$	0.0580988	+	0.0366717i	0.00239189	+	0.00150975i
$591$	27.5601			1.13367
$592$			4.02972i			0.165621i
$593$			6.09322i			0.250219i	0.992143	+	0.125109i	$0.0399282\pi$
$593$			6.09322i			0.250219i	−0.992143	+	0.125109i	$0.960072\pi$
$594$		0			0
$595$	5.00133	−	7.92358i	0.205035	−	0.324835i
$596$	16.9471			0.694181
$597$			2.53248i			0.103648i
$598$			2.14789i			0.0878339i
$599$	12.9337			0.528457			0.264229	−	0.964460i	$-0.414883\pi$
$599$	12.9337			0.528457			0.264229	+	0.964460i	$0.414883\pi$
$600$	10.2015	+	21.4071i	0.416476	+	0.873943i
$601$	11.0471			0.450621			0.225310	−	0.974287i	$-0.427660\pi$
$601$	11.0471			0.450621			0.225310	+	0.974287i	$0.427660\pi$
$602$		−	4.52437i		−	0.184399i
$603$		−	0.680605i		−	0.0277164i
$604$	−11.3910			−0.463494
$605$		0			0
$606$	−14.0364			−0.570188
$607$			0.115912i			0.00470474i	0.999997	+	0.00235237i	$0.000748784\pi$
$607$			0.115912i			0.00470474i	−0.999997	+	0.00235237i	$0.999251\pi$
$608$			13.3278i			0.540514i
$609$	−3.72760			−0.151050
$610$	5.22371	+	3.29718i	0.211502	+	0.133499i
$611$	3.46710			0.140264
$612$			0.961465i			0.0388649i
$613$			19.0445i			0.769202i	0.923083	+	0.384601i	$0.125661\pi$
$613$			19.0445i			0.769202i	−0.923083	+	0.384601i	$0.874339\pi$
$614$	8.03993			0.324465
$615$	−28.0008	−	17.6740i	−1.12910	−	0.712684i
$616$		0			0
$617$		−	30.8894i		−	1.24356i	−0.783192	−	0.621780i	$-0.786410\pi$
$617$		−	30.8894i		−	1.24356i	0.783192	−	0.621780i	$-0.213590\pi$
$618$			19.1104i			0.768732i
$619$	−33.5697			−1.34928			−0.674639	−	0.738148i	$-0.735701\pi$
$619$	−33.5697			−1.34928			−0.674639	+	0.738148i	$0.735701\pi$
$620$	−9.97880	+	15.8093i	−0.400758	+	0.634919i
$621$	−7.61174			−0.305449
$622$			2.73581i			0.109696i
$623$		−	3.67918i		−	0.147403i
$624$	−1.73566			−0.0694821
$625$	−15.7465	+	19.4177i	−0.629861	+	0.776708i
$626$	19.6668			0.786043
$627$		0			0
$628$		−	18.9738i		−	0.757139i
$629$	51.9278			2.07050
$630$	−0.0568466	+	0.0900617i	−0.00226482	+	0.00358814i
$631$	24.6573			0.981590			0.490795	−	0.871275i	$-0.336706\pi$
$631$	24.6573			0.981590			0.490795	+	0.871275i	$0.336706\pi$
$632$		−	12.1914i		−	0.484946i
$633$			15.2855i			0.607546i
$634$	−5.60967			−0.222788
$635$	−30.3614	−	19.1640i	−1.20486	−	0.760500i
$636$	−5.68799			−0.225543
$637$		−	11.9350i		−	0.472880i
$638$		0			0
$639$	1.18186			0.0467535
$640$	16.6070	+	10.4823i	0.656450	+	0.414348i
$641$	7.01647			0.277134			0.138567	−	0.990353i	$-0.455750\pi$
$641$	7.01647			0.277134			0.138567	+	0.990353i	$0.455750\pi$
$642$		−	7.92095i		−	0.312615i
$643$			12.2525i			0.483192i	0.970377	+	0.241596i	$0.0776709\pi$
$643$			12.2525i			0.483192i	−0.970377	+	0.241596i	$0.922329\pi$
$644$	−1.19667			−0.0471555
$645$	−20.0049	+	31.6936i	−0.787691	+	1.24793i
$646$	12.9911			0.511127
$647$		−	6.12014i		−	0.240608i	−0.992737	−	0.120304i	$-0.961613\pi$
$647$		−	6.12014i		−	0.240608i	0.992737	−	0.120304i	$-0.0383869\pi$
$648$			25.0251i			0.983079i
$649$		0			0
$650$	3.09905	+	6.50310i	0.121555	+	0.255073i
$651$	−6.42960			−0.251996
$652$			16.0532i			0.628691i
$653$		−	38.0316i		−	1.48829i	−0.668018	−	0.744145i	$-0.732857\pi$
$653$		−	38.0316i		−	1.48829i	0.668018	−	0.744145i	$-0.267143\pi$
$654$	−26.2884			−1.02796
$655$	21.5188	−	34.0921i	0.840808	−	1.33209i
$656$	−4.61889			−0.180338
$657$		−	0.683725i		−	0.0266746i
$658$		−	0.918077i		−	0.0357904i
$659$	15.7879			0.615011			0.307505	−	0.951546i	$-0.400506\pi$
$659$	15.7879			0.615011			0.307505	+	0.951546i	$0.400506\pi$
$660$		0			0
$661$	−24.5794			−0.956027			−0.478014	−	0.878352i	$-0.658643\pi$
$661$	−24.5794			−0.956027			−0.478014	+	0.878352i	$0.658643\pi$
$662$		−	4.52980i		−	0.176056i
$663$			22.3661i			0.868626i
$664$	16.0070			0.621193
$665$	−2.56036	−	1.61609i	−0.0992866	−	0.0626693i
$666$	−0.590226			−0.0228708
$667$		−	5.33038i		−	0.206393i
$668$			11.8300i			0.457716i
$669$	−11.1033			−0.429279
$670$	−6.50666	+	10.3085i	−0.251374	+	0.398251i
$671$		0			0
$672$			6.07597i			0.234385i
$673$		−	29.9733i		−	1.15539i	−0.816254	−	0.577693i	$-0.803953\pi$
$673$		−	29.9733i		−	1.15539i	0.816254	−	0.577693i	$-0.196047\pi$
$674$	18.1541			0.699271
$675$	−23.0458	+	10.9825i	−0.887034	+	0.422715i
$676$	13.2563			0.509857
$677$			3.75709i			0.144397i	0.997390	+	0.0721984i	$0.0230015\pi$
$677$			3.75709i			0.144397i	−0.997390	+	0.0721984i	$0.976999\pi$
$678$		−	16.6794i		−	0.640570i
$679$	−3.18297			−0.122151
$680$	22.7521	−	36.0460i	0.872502	−	1.38230i
$681$	−1.96641			−0.0753531
$682$		0			0
$683$			21.0157i			0.804144i	0.915608	+	0.402072i	$0.131710\pi$
$683$			21.0157i			0.804144i	−0.915608	+	0.402072i	$0.868290\pi$
$684$	0.310680			0.0118791
$685$	7.62424	+	4.81239i	0.291307	+	0.183872i
$686$	−6.48730			−0.247686
$687$		−	7.38836i		−	0.281883i
$688$			5.22805i			0.199317i
$689$	−4.27706			−0.162943
$690$	−3.98418	−	2.51480i	−0.151675	−	0.0957367i
$691$	−38.2825			−1.45633			−0.728167	−	0.685399i	$-0.759628\pi$
$691$	−38.2825			−1.45633			−0.728167	+	0.685399i	$0.759628\pi$
$692$			12.4432i			0.473020i
$693$		0			0
$694$	−0.146408			−0.00555757
$695$	−9.47054	+	15.0041i	−0.359238	+	0.569139i
$696$	−16.9576			−0.642776
$697$			59.5200i			2.25448i
$698$			12.3835i			0.468721i
$699$	11.9369			0.451495
$700$	−3.62312	+	1.72659i	−0.136941	+	0.0652591i
$701$	34.2344			1.29302			0.646509	−	0.762907i	$-0.276228\pi$
$701$	34.2344			1.29302			0.646509	+	0.762907i	$0.276228\pi$
$702$			7.35618i			0.277641i
$703$		−	16.7795i		−	0.632852i
$704$		0			0
$705$	−4.05936	+	6.43121i	−0.152884	+	0.242214i
$706$	−19.1928			−0.722329
$707$		−	5.88035i		−	0.221153i
$708$		−	0.0913687i		−	0.00343385i
$709$	4.12477			0.154909			0.0774545	−	0.996996i	$-0.475321\pi$
$709$	4.12477			0.154909			0.0774545	+	0.996996i	$0.475321\pi$
$710$	−17.9004	−	11.2987i	−0.671791	−	0.424032i
$711$	−0.453567			−0.0170101
$712$		−	16.7373i		−	0.627258i
$713$		−	9.19418i		−	0.344325i
$714$	5.92246			0.221642
$715$		0			0
$716$	−1.96324			−0.0733697
$717$		−	7.74389i		−	0.289201i
$718$			7.03754i			0.262639i
$719$	−29.3596			−1.09493			−0.547463	−	0.836830i	$-0.684406\pi$
$719$	−29.3596			−1.09493			−0.547463	+	0.836830i	$0.684406\pi$
$720$	0.0656880	−	0.104069i	0.00244805	−	0.00387842i
$721$	−8.00605			−0.298161
$722$			11.0535i			0.411367i
$723$		−	16.9246i		−	0.629431i
$724$	1.07573			0.0399792
$725$	−7.69084	−	16.1386i	−0.285630	−	0.599373i
$726$		0			0
$727$			44.0893i			1.63518i	0.575799	+	0.817591i	$0.304691\pi$
$727$			44.0893i			1.63518i	−0.575799	+	0.817591i	$0.695309\pi$
$728$			2.86265i			0.106097i
$729$	−26.0388			−0.964401
$730$	−6.53649	+	10.3557i	−0.241926	+	0.383282i
$731$	67.3696			2.49176
$732$		−	8.21503i		−	0.303636i
$733$		−	48.9490i		−	1.80797i	−0.427561	−	0.903987i	$-0.640627\pi$
$733$		−	48.9490i		−	1.80797i	0.427561	−	0.903987i	$-0.359373\pi$
$734$	−4.32038			−0.159468
$735$	22.1384	+	13.9737i	0.816589	+	0.515428i
$736$	−8.68849			−0.320262
$737$		0			0
$738$		−	0.676520i		−	0.0249031i
$739$	−20.6622			−0.760072			−0.380036	−	0.924972i	$-0.624088\pi$
$739$	−20.6622			−0.760072			−0.380036	+	0.924972i	$0.624088\pi$
$740$	−18.8091	−	11.8722i	−0.691435	−	0.436431i
$741$	7.22719			0.265498
$742$			1.13255i			0.0415772i
$743$		−	30.1631i		−	1.10658i	−0.832990	−	0.553288i	$-0.813373\pi$
$743$		−	30.1631i		−	1.10658i	0.832990	−	0.553288i	$-0.186627\pi$
$744$	−29.2495			−1.07234
$745$	−14.9201	+	23.6379i	−0.546632	+	0.866025i
$746$	2.58830			0.0947645
$747$		−	0.595525i		−	0.0217891i
$748$		0			0
$749$	3.31838			0.121251
$750$	−15.6912	−	1.86547i	−0.572961	−	0.0681175i
$751$	12.0966			0.441412			0.220706	−	0.975340i	$-0.429164\pi$
$751$	12.0966			0.441412			0.220706	+	0.975340i	$0.429164\pi$
$752$			1.06087i			0.0386858i
$753$		−	23.6302i		−	0.861133i
$754$	−5.15141			−0.187603
$755$	10.0286	−	15.8882i	0.364978	−	0.578232i
$756$	−4.09840			−0.149057
$757$		−	20.6101i		−	0.749086i	−0.927210	−	0.374543i	$-0.877800\pi$
$757$		−	20.6101i		−	0.749086i	0.927210	−	0.374543i	$-0.122200\pi$
$758$		−	15.7838i		−	0.573293i
$759$		0			0
$760$	−11.6476	−	7.35192i	−0.422503	−	0.266682i
$761$	−20.8450			−0.755631			−0.377816	−	0.925881i	$-0.623325\pi$
$761$	−20.8450			−0.755631			−0.377816	+	0.925881i	$0.623325\pi$
$762$		−	22.6935i		−	0.822100i
$763$		−	11.0132i		−	0.398704i
$764$	−11.0491			−0.399744
$765$	−1.34105	−	0.846468i	−0.0484859	−	0.0306041i
$766$	22.4556			0.811354
$767$		−	0.0687044i		−	0.00248077i
$768$			25.0189i			0.902792i
$769$	10.7167			0.386455			0.193228	−	0.981154i	$-0.438104\pi$
$769$	10.7167			0.386455			0.193228	+	0.981154i	$0.438104\pi$
$770$		0			0
$771$	19.0466			0.685946
$772$			5.92207i			0.213140i
$773$		−	20.3563i		−	0.732164i	−0.930583	−	0.366082i	$-0.880699\pi$
$773$		−	20.3563i		−	0.732164i	0.930583	−	0.366082i	$-0.119301\pi$
$774$	−0.765742			−0.0275240
$775$	−13.2656	−	27.8369i	−0.476516	−	0.999931i
$776$	−14.4800			−0.519801
$777$		−	7.64957i		−	0.274427i
$778$			10.4672i			0.375267i
$779$	19.2328			0.689087
$780$	5.11353	−	8.10134i	0.183094	−	0.290074i
$781$		0			0
$782$			8.46898i			0.302850i
$783$		−	18.2557i		−	0.652405i
$784$	3.65187			0.130424
$785$	26.4648	+	16.7045i	0.944568	+	0.596208i
$786$	25.4820			0.908914
$787$			14.2222i			0.506967i	0.967340	+	0.253484i	$0.0815764\pi$
$787$			14.2222i			0.506967i	−0.967340	+	0.253484i	$0.918424\pi$
$788$			21.2198i			0.755923i
$789$	−43.3760			−1.54423
$790$	6.86974	+	4.33615i	0.244414	+	0.154273i
$791$	6.98764			0.248452
$792$		0			0
$793$		−	6.17726i		−	0.219361i
$794$	1.46286			0.0519150
$795$	5.00767	−	7.93361i	0.177604	−	0.281376i
$796$	−1.94987			−0.0691113
$797$			45.0384i			1.59534i	0.603093	+	0.797671i	$0.293935\pi$
$797$			45.0384i			1.59534i	−0.603093	+	0.797671i	$0.706065\pi$
$798$		−	1.91374i		−	0.0677455i
$799$	13.6705			0.483629
$800$	−26.3059	+	12.5360i	−0.930053	+	0.443215i
$801$	−0.622695			−0.0220018
$802$		−	4.31920i		−	0.152516i
$803$		0			0
$804$	16.2115			0.571737
$805$	1.05354	−	1.66912i	0.0371325	−	0.0588288i
$806$	−8.88548			−0.312978
$807$		−	8.45334i		−	0.297572i
$808$		−	26.7509i		−	0.941094i
$809$	23.7753			0.835896			0.417948	−	0.908471i	$-0.362749\pi$
$809$	23.7753			0.835896			0.417948	+	0.908471i	$0.362749\pi$
$810$	−14.1015	−	8.90079i	−0.495475	−	0.312742i
$811$	8.19869			0.287895			0.143948	−	0.989585i	$-0.454020\pi$
$811$	8.19869			0.287895			0.143948	+	0.989585i	$0.454020\pi$
$812$		−	2.87004i		−	0.100719i
$813$			41.0787i			1.44069i
$814$		0			0
$815$	−22.3910	−	14.1331i	−0.784323	−	0.495062i
$816$	−6.84358			−0.239573
$817$		−	21.7693i		−	0.761610i
$818$			29.4447i			1.02951i
$819$	0.106502			0.00372147
$820$	13.6080	−	21.5591i	0.475212	−	0.752875i
$821$	43.4373			1.51597			0.757986	−	0.652271i	$-0.226184\pi$
$821$	43.4373			1.51597			0.757986	+	0.652271i	$0.226184\pi$
$822$			5.69872i			0.198766i
$823$		−	51.6801i		−	1.80145i	−0.434386	−	0.900727i	$-0.643034\pi$
$823$		−	51.6801i		−	1.80145i	0.434386	−	0.900727i	$-0.356966\pi$
$824$	−36.4211			−1.26879
$825$		0			0
$826$	−0.0181927			−0.000633004
$827$			25.3079i			0.880042i	0.897987	+	0.440021i	$0.145029\pi$
$827$			25.3079i			0.880042i	−0.897987	+	0.440021i	$0.854971\pi$
$828$			0.202535i			0.00703857i
$829$	41.8760			1.45441			0.727207	−	0.686418i	$-0.240818\pi$
$829$	41.8760			1.45441			0.727207	+	0.686418i	$0.240818\pi$
$830$	−5.69329	+	9.01984i	−0.197617	+	0.313083i
$831$	−38.5555			−1.33747
$832$			6.42527i			0.222756i
$833$		−	47.0587i		−	1.63049i
$834$	−11.2148			−0.388336
$835$	−16.5005	−	10.4151i	−0.571024	−	0.360428i
$836$		0			0
$837$		−	31.4885i		−	1.08840i
$838$			2.30078i			0.0794791i
$839$	14.3848			0.496619			0.248309	−	0.968681i	$-0.420125\pi$
$839$	14.3848			0.496619			0.248309	+	0.968681i	$0.420125\pi$
$840$	−5.30999	−	3.35164i	−0.183212	−	0.115643i
$841$	−16.2158			−0.559167
$842$		−	3.74038i		−	0.128902i
$843$			27.7765i			0.956673i
$844$	−11.7690			−0.405106
$845$	−11.6708	+	18.4899i	−0.401486	+	0.636072i
$846$	−0.155383			−0.00534218
$847$		0			0
$848$		−	1.30870i		−	0.0449408i
$849$	−39.8088			−1.36624
$850$	12.2193	+	25.6413i	0.419119	+	0.879488i
$851$	10.9387			0.374974
$852$			28.1510i			0.964437i
$853$		−	43.0014i		−	1.47234i	−0.676797	−	0.736170i	$-0.736632\pi$
$853$		−	43.0014i		−	1.47234i	0.676797	−	0.736170i	$-0.263368\pi$
$854$	−1.63572			−0.0559731
$855$	−0.273521	+	0.433337i	−0.00935421	+	0.0148198i
$856$	15.0960			0.515970
$857$			54.3052i			1.85503i	0.373784	+	0.927516i	$0.378060\pi$
$857$			54.3052i			1.85503i	−0.373784	+	0.927516i	$0.621940\pi$
$858$		0			0
$859$	−24.3361			−0.830336			−0.415168	−	0.909745i	$-0.636277\pi$
$859$	−24.3361			−0.830336			−0.415168	+	0.909745i	$0.636277\pi$
$860$	−24.4023	−	15.4026i	−0.832112	−	0.525226i
$861$	8.76798			0.298812
$862$			16.6714i			0.567828i
$863$		−	39.1501i		−	1.33268i	−0.745646	−	0.666342i	$-0.767859\pi$
$863$		−	39.1501i		−	1.33268i	0.745646	−	0.666342i	$-0.232141\pi$
$864$	−29.7567			−1.01234
$865$	−17.3558	−	10.9549i	−0.590115	−	0.372478i
$866$	−10.2723			−0.349066
$867$			58.2551i			1.97845i
$868$		−	4.95043i		−	0.168029i
$869$		0			0
$870$	6.03138	−	9.55548i	0.204483	−	0.323961i
$871$	12.1902			0.413049
$872$		−	50.1012i		−	1.69664i
$873$			0.538713i			0.0182327i
$874$	2.73660			0.0925668
$875$	0.781516	−	6.57362i	0.0264201	−	0.222229i
$876$	16.2859			0.550248
$877$		−	43.0882i		−	1.45499i	−0.686116	−	0.727493i	$-0.740686\pi$
$877$		−	43.0882i		−	1.45499i	0.686116	−	0.727493i	$-0.259314\pi$
$878$			8.52534i			0.287716i
$879$	23.3468			0.787466
$880$		0			0
$881$	−38.1083			−1.28390			−0.641950	−	0.766746i	$-0.721874\pi$
$881$	−38.1083			−1.28390			−0.641950	+	0.766746i	$0.721874\pi$
$882$			0.534882i			0.0180104i
$883$		−	29.0261i		−	0.976805i	−0.872618	−	0.488403i	$-0.837580\pi$
$883$		−	29.0261i		−	0.976805i	0.872618	−	0.488403i	$-0.162420\pi$
$884$	−17.2206			−0.579193
$885$	0.127441	+	0.0804405i	0.00428389	+	0.00270398i
$886$	5.29696			0.177955
$887$		−	2.21174i		−	0.0742631i	−0.999310	−	0.0371315i	$-0.988178\pi$
$887$		−	2.21174i		−	0.0742631i	0.999310	−	0.0371315i	$-0.0118221\pi$
$888$		−	34.7994i		−	1.16779i
$889$	9.50717			0.318860
$890$	9.43136	+	5.95304i	0.316140	+	0.199546i
$891$		0			0
$892$		−	8.54894i		−	0.286240i
$893$		−	4.41739i		−	0.147822i
$894$	−17.6681			−0.590909
$895$	1.72842	−	2.73833i	0.0577748	−	0.0915323i
$896$	−5.20021			−0.173727
$897$			4.71146i			0.157311i
$898$			10.9392i			0.365047i
$899$	22.0509			0.735439
$900$	0.292223	+	0.613207i	0.00974078	+	0.0204402i
$901$	−16.8641			−0.561825
$902$		0			0
$903$		−	9.92432i		−	0.330261i
$904$	31.7882			1.05726
$905$	−0.947066	+	1.50043i	−0.0314816	+	0.0498760i
$906$	11.8756			0.394541
$907$			26.6863i			0.886106i	0.896496	+	0.443053i	$0.146105\pi$
$907$			26.6863i			0.886106i	−0.896496	+	0.443053i	$0.853895\pi$
$908$		−	1.51403i		−	0.0502448i
$909$	−0.995240			−0.0330100
$910$	−1.61308	−	1.01817i	−0.0534731	−	0.0337520i
$911$	−36.2736			−1.20180			−0.600899	−	0.799325i	$-0.705191\pi$
$911$	−36.2736			−1.20180			−0.600899	+	0.799325i	$0.705191\pi$
$912$			2.21138i			0.0732261i
$913$		0			0
$914$	−10.8363			−0.358434
$915$	11.4583	+	7.23246i	0.378801	+	0.239098i
$916$	5.68863			0.187958
$917$			10.6754i			0.352532i
$918$			29.0049i			0.957303i
$919$	−29.6718			−0.978781			−0.489391	−	0.872065i	$-0.662781\pi$
$919$	−29.6718			−0.978781			−0.489391	+	0.872065i	$0.662781\pi$
$920$	4.79278	−	7.59316i	0.158013	−	0.250339i
$921$	17.6358			0.581119
$922$			9.08790i			0.299294i
$923$			21.1680i			0.696754i
$924$		0			0
$925$	33.1188	−	15.7827i	1.08894	−	0.518932i
$926$	−3.87696			−0.127405
$927$			1.35501i			0.0445044i
$928$		−	20.8381i		−	0.684044i
$929$	−27.7726			−0.911189			−0.455595	−	0.890187i	$-0.650573\pi$
$929$	−27.7726			−0.911189			−0.455595	+	0.890187i	$0.650573\pi$
$930$	10.4033	−	16.4819i	0.341138	−	0.540462i
$931$	−15.2062			−0.498362
$932$			9.19075i			0.301053i
$933$			6.00106i			0.196466i
$934$	−19.2786			−0.630817
$935$		0			0
$936$	0.484498			0.0158363
$937$		−	30.2421i		−	0.987967i	−0.869471	−	0.493983i	$-0.835540\pi$
$937$		−	30.2421i		−	0.987967i	0.869471	−	0.493983i	$-0.164460\pi$
$938$		−	3.22792i		−	0.105395i
$939$	43.1396			1.40781
$940$	−4.95168	−	3.12548i	−0.161506	−	0.101942i
$941$	6.00672			0.195813			0.0979067	−	0.995196i	$-0.468785\pi$
$941$	6.00672			0.195813			0.0979067	+	0.995196i	$0.468785\pi$
$942$			19.7810i			0.644500i
$943$			12.5380i			0.408294i
$944$	0.0210222			0.000684214
$945$	3.60821	−	5.71646i	0.117375	−	0.185956i
$946$		0			0
$947$		−	10.0218i		−	0.325665i	−0.986654	−	0.162833i	$-0.947937\pi$
$947$		−	10.0218i		−	0.325665i	0.986654	−	0.162833i	$-0.0520630\pi$
$948$		−	10.8037i		−	0.350887i
$949$	12.2461			0.397525
$950$	8.28551	−	3.94845i	0.268817	−	0.128105i
$951$	−12.3050			−0.399016
$952$			11.2872i			0.365820i
$953$			9.78136i			0.316849i	0.987371	+	0.158425i	$0.0506415\pi$
$953$			9.78136i			0.316849i	−0.987371	+	0.158425i	$0.949359\pi$
$954$	0.191682			0.00620594
$955$	9.72760	−	15.4114i	0.314778	−	0.498700i
$956$	5.96237			0.192837
$957$		0			0
$958$		−	34.6967i		−	1.12100i
$959$	−2.38740			−0.0770933
$960$	−11.9184	−	7.52283i	−0.384664	−	0.242798i
$961$	7.03479			0.226929
$962$		−	10.5714i		−	0.340837i
$963$		−	0.561631i		−	0.0180983i
$964$	13.0310			0.419700
$965$	−8.26012	−	5.21376i	−0.265903	−	0.167837i
$966$	1.24758			0.0401402
$967$		−	1.22635i		−	0.0394367i	−0.999806	−	0.0197184i	$-0.993723\pi$
$967$		−	1.22635i		−	0.0394367i	0.999806	−	0.0197184i	$-0.00627695\pi$
$968$		0			0
$969$	28.4963			0.915432
$970$	5.15016	−	8.15937i	0.165362	−	0.261982i
$971$	−44.6467			−1.43278			−0.716390	−	0.697700i	$-0.754207\pi$
$971$	−44.6467			−1.43278			−0.716390	+	0.697700i	$0.754207\pi$
$972$			1.41127i			0.0452664i
$973$		−	4.69829i		−	0.150620i
$974$	33.6820			1.07924
$975$	6.79784	+	14.2647i	0.217705	+	0.456837i
$976$	1.89012			0.0605013
$977$			47.2451i			1.51151i	0.654857	+	0.755753i	$0.272729\pi$
$977$			47.2451i			1.51151i	−0.654857	+	0.755753i	$0.727271\pi$
$978$		−	16.7361i		−	0.535162i
$979$		0			0
$980$	−10.7590	+	17.0454i	−0.343683	+	0.544495i
$981$	−1.86396			−0.0595118
$982$		−	7.27232i		−	0.232069i
$983$			13.9351i			0.444459i	0.974994	+	0.222230i	$0.0713335\pi$
$983$			13.9351i			0.444459i	−0.974994	+	0.222230i	$0.928667\pi$
$984$	39.8873			1.27156
$985$	−29.5974	−	18.6817i	−0.943050	−	0.595250i
$986$	−20.3116			−0.646854
$987$		−	2.01383i		−	0.0641008i
$988$			5.56454i			0.177032i
$989$	14.1916			0.451265
$990$		0			0
$991$	36.5755			1.16186			0.580930	−	0.813953i	$-0.302689\pi$
$991$	36.5755			1.16186			0.580930	+	0.813953i	$0.302689\pi$
$992$		−	35.9429i		−	1.14119i
$993$		−	9.93623i		−	0.315317i
$994$	5.60522			0.177787
$995$	1.71665	−	2.71968i	0.0544216	−	0.0862197i
$996$	14.1850			0.449469
$997$			19.3415i			0.612552i	0.951943	+	0.306276i	$0.0990831\pi$
$997$			19.3415i			0.612552i	−0.951943	+	0.306276i	$0.900917\pi$
$998$			24.3052i			0.769367i
$999$	37.4633			1.18529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.f.364.4		8
5.2	odd	4		3025.2.a.bk.1.5		8
5.3	odd	4		3025.2.a.bk.1.4		8
5.4	even	2	inner	605.2.b.f.364.5		8
11.2	odd	10		605.2.j.h.444.3		16
11.3	even	5		605.2.j.d.9.2		16
11.4	even	5		605.2.j.d.269.3		16
11.5	even	5		605.2.j.g.124.3		16
11.6	odd	10		605.2.j.h.124.2		16
11.7	odd	10		55.2.j.a.49.2	yes	16
11.8	odd	10		55.2.j.a.9.3	yes	16
11.9	even	5		605.2.j.g.444.2		16
11.10	odd	2		605.2.b.g.364.5		8
33.8	even	10		495.2.ba.a.64.2		16
33.29	even	10		495.2.ba.a.379.3		16
44.7	even	10		880.2.cd.c.49.3		16
44.19	even	10		880.2.cd.c.449.2		16
55.4	even	10		605.2.j.d.269.2		16
55.7	even	20		275.2.h.d.126.2		16
55.8	even	20		275.2.h.d.251.3		16
55.9	even	10		605.2.j.g.444.3		16
55.14	even	10		605.2.j.d.9.3		16
55.18	even	20		275.2.h.d.126.3		16
55.19	odd	10		55.2.j.a.9.2	✓	16
55.24	odd	10		605.2.j.h.444.2		16
55.29	odd	10		55.2.j.a.49.3	yes	16
55.32	even	4		3025.2.a.bl.1.4		8
55.39	odd	10		605.2.j.h.124.3		16
55.43	even	4		3025.2.a.bl.1.5		8
55.49	even	10		605.2.j.g.124.2		16
55.52	even	20		275.2.h.d.251.2		16
55.54	odd	2		605.2.b.g.364.4		8
165.29	even	10		495.2.ba.a.379.2		16
165.74	even	10		495.2.ba.a.64.3		16
220.19	even	10		880.2.cd.c.449.3		16
220.139	even	10		880.2.cd.c.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	55.19	odd	10
55.2.j.a.9.3	yes	16	11.8	odd	10
55.2.j.a.49.2	yes	16	11.7	odd	10
55.2.j.a.49.3	yes	16	55.29	odd	10
275.2.h.d.126.2		16	55.7	even	20
275.2.h.d.126.3		16	55.18	even	20
275.2.h.d.251.2		16	55.52	even	20
275.2.h.d.251.3		16	55.8	even	20
495.2.ba.a.64.2		16	33.8	even	10
495.2.ba.a.64.3		16	165.74	even	10
495.2.ba.a.379.2		16	165.29	even	10
495.2.ba.a.379.3		16	33.29	even	10
605.2.b.f.364.4		8	1.1	even	1	trivial
605.2.b.f.364.5		8	5.4	even	2	inner
605.2.b.g.364.4		8	55.54	odd	2
605.2.b.g.364.5		8	11.10	odd	2
605.2.j.d.9.2		16	11.3	even	5
605.2.j.d.9.3		16	55.14	even	10
605.2.j.d.269.2		16	55.4	even	10
605.2.j.d.269.3		16	11.4	even	5
605.2.j.g.124.2		16	55.49	even	10
605.2.j.g.124.3		16	11.5	even	5
605.2.j.g.444.2		16	11.9	even	5
605.2.j.g.444.3		16	55.9	even	10
605.2.j.h.124.2		16	11.6	odd	10
605.2.j.h.124.3		16	55.39	odd	10
605.2.j.h.444.2		16	55.24	odd	10
605.2.j.h.444.3		16	11.2	odd	10
880.2.cd.c.49.2		16	220.139	even	10
880.2.cd.c.49.3		16	44.7	even	10
880.2.cd.c.449.2		16	44.19	even	10
880.2.cd.c.449.3		16	220.19	even	10
3025.2.a.bk.1.4		8	5.3	odd	4
3025.2.a.bk.1.5		8	5.2	odd	4
3025.2.a.bl.1.4		8	55.32	even	4
3025.2.a.bl.1.5		8	55.43	even	4

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.802699i q^{2} -1.76074i q^{3} +1.35567 q^{4} +(-1.19353 + 1.89090i) q^{5} -1.41335 q^{6} -0.592103i q^{7} -2.69360i q^{8} -0.100212 q^{9} +O(q^{10})\)	\(q-0.802699i q^{2} -1.76074i q^{3} +1.35567 q^{4} +(-1.19353 + 1.89090i) q^{5} -1.41335 q^{6} -0.592103i q^{7} -2.69360i q^{8} -0.100212 q^{9} +(1.51782 + 0.958043i) q^{10} -2.38699i q^{12} -1.79489i q^{13} -0.475281 q^{14} +(3.32938 + 2.10149i) q^{15} +0.549201 q^{16} -7.07712i q^{17} +0.0804405i q^{18} -2.28684 q^{19} +(-1.61803 + 2.56344i) q^{20} -1.04254 q^{21} -1.49081i q^{23} -4.74273 q^{24} +(-2.15099 - 4.51367i) q^{25} -1.44076 q^{26} -5.10578i q^{27} -0.802699i q^{28} +3.57549 q^{29} +(1.68687 - 2.67249i) q^{30} +6.16724 q^{31} -5.82804i q^{32} -5.68079 q^{34} +(1.11961 + 0.706691i) q^{35} -0.135855 q^{36} +7.33743i q^{37} +1.83565i q^{38} -3.16034 q^{39} +(5.09331 + 3.21488i) q^{40} -8.41020 q^{41} +0.836847i q^{42} +9.51936i q^{43} +(0.119606 - 0.189492i) q^{45} -1.19667 q^{46} +1.93165i q^{47} -0.967002i q^{48} +6.64941 q^{49} +(-3.62312 + 1.72659i) q^{50} -12.4610 q^{51} -2.43329i q^{52} -2.38291i q^{53} -4.09840 q^{54} -1.59489 q^{56} +4.02654i q^{57} -2.87004i q^{58} +0.0382778 q^{59} +(4.51356 + 2.84894i) q^{60} +3.44158 q^{61} -4.95043i q^{62} +0.0593361i q^{63} -3.57976 q^{64} +(3.39395 + 2.14225i) q^{65} +6.79162i q^{67} -9.59426i q^{68} -2.62493 q^{69} +(0.567260 - 0.898707i) q^{70} -11.7935 q^{71} +0.269932i q^{72} +6.82275i q^{73} +5.88974 q^{74} +(-7.94742 + 3.78733i) q^{75} -3.10021 q^{76} +2.53680i q^{78} +4.52605 q^{79} +(-0.655487 + 1.03848i) q^{80} -9.29059 q^{81} +6.75086i q^{82} +5.94262i q^{83} -1.41335 q^{84} +(13.3821 + 8.44673i) q^{85} +7.64118 q^{86} -6.29552i q^{87} +6.21375 q^{89} +(-0.152105 - 0.0960079i) q^{90} -1.06276 q^{91} -2.02105i q^{92} -10.8589i q^{93} +1.55054 q^{94} +(2.72941 - 4.32418i) q^{95} -10.2617 q^{96} -5.37571i q^{97} -5.33748i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} + 12 q^{19} - 4 q^{20} - 4 q^{21} + 2 q^{24} - 8 q^{25} + 10 q^{26} + 24 q^{29} + 22 q^{30} + 14 q^{31} - 8 q^{34} + 14 q^{35} + 20 q^{36} + 30 q^{39} + 24 q^{40} - 34 q^{41} + 6 q^{45} - 24 q^{46} + 30 q^{49} + 16 q^{50} - 54 q^{51} + 20 q^{54} - 10 q^{56} + 6 q^{59} + 34 q^{60} - 20 q^{61} - 14 q^{64} + 20 q^{65} - 32 q^{69} + 8 q^{70} - 42 q^{71} - 4 q^{74} - 20 q^{75} - 28 q^{76} + 16 q^{79} - 28 q^{80} - 36 q^{81} - 6 q^{84} - 4 q^{85} + 46 q^{86} + 12 q^{89} + 46 q^{90} + 20 q^{91} - 42 q^{94} + 26 q^{95} + 8 q^{96}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 + 12 * q^19 - 4 * q^20 - 4 * q^21 + 2 * q^24 - 8 * q^25 + 10 * q^26 + 24 * q^29 + 22 * q^30 + 14 * q^31 - 8 * q^34 + 14 * q^35 + 20 * q^36 + 30 * q^39 + 24 * q^40 - 34 * q^41 + 6 * q^45 - 24 * q^46 + 30 * q^49 + 16 * q^50 - 54 * q^51 + 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 - 20 * q^61 - 14 * q^64 + 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 - 4 * q^74 - 20 * q^75 - 28 * q^76 + 16 * q^79 - 28 * q^80 - 36 * q^81 - 6 * q^84 - 4 * q^85 + 46 * q^86 + 12 * q^89 + 46 * q^90 + 20 * q^91 - 42 * q^94 + 26 * q^95 + 8 * q^96

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