LMFDB - Embedded newform 605.2.b.g.364.5

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			364.5
Root			$0.802699i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.g.364.4

$q$-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	$0.0915942\pi$
$2$			0.802699i			0.567594i	−0.958884	+	0.283797i	$0.908406\pi$
$3$		−	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	$0.0356927\pi$
$7$			0.592103i			0.223794i	−0.993720	+	0.111897i	$0.964307\pi$
$8$			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	$0.0800712\pi$
$13$			1.79489i			0.497813i	−0.968528	+	0.248906i	$0.919929\pi$
$14$	−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	$0.328433\pi$
$17$			7.07712i			1.71645i	−0.513271	+	0.858226i	$0.671567\pi$
$18$		−	0.0804405i		−	0.0189600i
$19$	2.28684			0.524637			0.262319	−	0.964981i	$-0.415513\pi$
$19$	2.28684			0.524637			0.262319	+	0.964981i	$0.415513\pi$
$20$	−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	$-0.607715\pi$
$29$	−3.57549			−0.663952			−0.331976	+	0.943288i	$0.607715\pi$
$30$	−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	$-0.271941\pi$
$41$	8.41020			1.31345			0.656726	+	0.754129i	$0.271941\pi$
$42$			0.836847i			0.129128i
$43$		−	9.51936i		−	1.45169i	−0.687859	−	0.725844i	$-0.741449\pi$
$43$		−	9.51936i		−	1.45169i	0.687859	−	0.725844i	$-0.258551\pi$
$44$		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	$-0.570712\pi$
$61$	−3.44158			−0.440649			−0.220325	+	0.975427i	$0.570712\pi$
$62$			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	$-0.869263\pi$
$73$		−	6.82275i		−	0.798543i	0.916833	−	0.399271i	$-0.130737\pi$
$74$	−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	$-0.581947\pi$
$79$	−4.52605			−0.509221			−0.254610	+	0.967044i	$0.581947\pi$
$80$	−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	$-0.894251\pi$
$83$		−	5.94262i		−	0.652288i	0.945320	−	0.326144i	$-0.105749\pi$
$84$	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	$-0.664503\pi$
$101$	−9.93130			−0.988201			−0.494101	+	0.869405i	$0.664503\pi$
$102$			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	$-0.912679\pi$
$107$		−	5.60440i		−	0.541798i	0.962608	−	0.270899i	$-0.0873209\pi$
$108$		−	6.92177i		−	0.666048i
$109$	−18.6001			−1.78157			−0.890784	−	0.454428i	$-0.849844\pi$
$109$	−18.6001			−1.78157			−0.890784	+	0.454428i	$0.849844\pi$
$110$		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	$-0.747610\pi$
$127$		−	16.0566i		−	1.42479i	0.701777	−	0.712397i	$-0.252390\pi$
$128$			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	$-0.211310\pi$
$131$	18.0296			1.57525			0.787625	+	0.616154i	$0.211310\pi$
$132$		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	$-0.609248\pi$
$139$	−7.93492			−0.673031			−0.336516	+	0.941678i	$0.609248\pi$
$140$	−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	$-0.671116\pi$
$149$	−12.5009			−1.02411			−0.512056	+	0.858952i	$0.671116\pi$
$150$	−3.04009	−	6.37938i	−0.248222	−	0.520874i
$151$	8.40248			0.683784			0.341892	−	0.939739i	$-0.388932\pi$
$151$	8.40248			0.683784			0.341892	+	0.939739i	$0.388932\pi$
$152$			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	$-0.890375\pi$
$167$		−	8.72628i		−	0.675260i	0.941279	−	0.337630i	$-0.109625\pi$
$168$			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	$-0.886549\pi$
$173$		−	9.17861i		−	0.697837i	0.937153	−	0.348918i	$-0.113451\pi$
$174$	−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	$-0.949747\pi$
$193$		−	4.36836i		−	0.314442i	0.987563	−	0.157221i	$-0.0502534\pi$
$194$	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	$-0.811723\pi$
$197$		−	15.6525i		−	1.11520i	0.830111	−	0.557599i	$-0.188277\pi$
$198$		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	$-0.403406\pi$
$211$	8.68130			0.597646			0.298823	+	0.954309i	$0.403406\pi$
$212$		−	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	$0.0118001\pi$
$227$			1.11681i			0.0741252i	−0.999313	+	0.0370626i	$0.988200\pi$
$228$		−	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	$-0.928719\pi$
$233$		−	6.77947i		−	0.444138i	0.975031	−	0.222069i	$-0.0712810\pi$
$234$	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	$-0.545432\pi$
$239$	−4.39808			−0.284488			−0.142244	+	0.989832i	$0.545432\pi$
$240$	1.82850	+	1.15414i	0.118029	+	0.0744996i
$241$	−9.61218			−0.619175			−0.309587	−	0.950871i	$-0.600191\pi$
$241$	−9.61218			−0.619175			−0.309587	+	0.950871i	$0.600191\pi$
$242$		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	$0.274572\pi$
$263$			24.6351i			1.51906i	−0.650471	+	0.759531i	$0.725428\pi$
$264$		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	$-0.249323\pi$
$271$	23.3303			1.41722			0.708609	+	0.705602i	$0.249323\pi$
$272$			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	$0.228530\pi$
$277$			21.8973i			1.31568i	−0.753158	+	0.657840i	$0.771470\pi$
$278$		−	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	$-0.344058\pi$
$281$	15.7754			0.941084			0.470542	+	0.882378i	$0.344058\pi$
$282$			2.73009i			0.162575i
$283$			22.6091i			1.34397i	0.740563	+	0.671987i	$0.234559\pi$
$283$			22.6091i			1.34397i	−0.740563	+	0.671987i	$0.765441\pi$
$284$	−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	$-0.873402\pi$
$293$		−	13.2596i		−	0.774635i	0.921946	−	0.387317i	$-0.126598\pi$
$294$	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	$-0.907732\pi$
$307$		−	10.0161i		−	0.571650i	0.958282	−	0.285825i	$-0.0922676\pi$
$308$		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	$-0.788754\pi$
$337$		−	22.6164i		−	1.23199i	0.787750	−	0.615996i	$-0.211246\pi$
$338$			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	$0.00155836\pi$
$347$			0.182395i			0.00979145i	−0.999988	+	0.00489573i	$0.998442\pi$
$348$			8.53468i			0.457507i
$349$	15.4273			0.825803			0.412902	−	0.910776i	$-0.364515\pi$
$349$	15.4273			0.825803			0.412902	+	0.910776i	$0.364515\pi$
$350$	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	$-0.425682\pi$
$359$	8.76734			0.462723			0.231361	+	0.972868i	$0.425682\pi$
$360$	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	$-0.973397\pi$
$373$		−	3.22450i		−	0.166958i	0.996510	−	0.0834792i	$-0.0266032\pi$
$374$		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	$-0.138438\pi$
$409$	36.6821			1.81381			0.906906	+	0.421333i	$0.138438\pi$
$410$	−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	$-0.333257\pi$
$431$	20.7691			1.00041			0.500207	+	0.865906i	$0.333257\pi$
$432$		−	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	$-0.418434\pi$
$439$	10.6208			0.506905			0.253452	+	0.967348i	$0.418434\pi$
$440$		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	$0.102256\pi$
$457$			13.4999i			0.631498i	−0.948843	+	0.315749i	$0.897744\pi$
$458$			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	$-0.415073\pi$
$461$	11.3217			0.527303			0.263652	+	0.964618i	$0.415073\pi$
$462$		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	$-0.949621\pi$
$479$	−43.2250			−1.97500			−0.987501	+	0.157611i	$0.949621\pi$
$480$	−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	$-0.565535\pi$
$491$	−9.05983			−0.408864			−0.204432	+	0.978881i	$0.565535\pi$
$492$		−	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	$0.131933\pi$
$503$			18.0638i			0.805426i	−0.915326	+	0.402713i	$0.868067\pi$
$504$	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	$-0.818356\pi$
$523$		−	24.7070i		−	1.08036i	0.841549	−	0.540181i	$-0.181644\pi$
$524$	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	$-0.586895\pi$
$541$	−12.5420			−0.539221			−0.269610	+	0.962970i	$0.586895\pi$
$542$			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	$-0.771745\pi$
$547$		−	30.7407i		−	1.31438i	0.753726	−	0.657189i	$-0.228255\pi$
$548$		−	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	$-0.908169\pi$
$557$		−	13.4294i		−	0.569021i	0.958673	−	0.284510i	$-0.0918310\pi$
$558$		−	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	$0.222542\pi$
$563$			30.5401i			1.28711i	−0.765399	+	0.643556i	$0.777458\pi$
$564$	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	$-0.681246\pi$
$569$	−25.7204			−1.07826			−0.539128	+	0.842224i	$0.681246\pi$
$570$	−3.85760	+	6.11157i	−0.161577	+	0.255985i
$571$	−27.1115			−1.13458			−0.567291	−	0.823518i	$-0.692008\pi$
$571$	−27.1115			−1.13458			−0.567291	+	0.823518i	$0.692008\pi$
$572$		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	$-0.960072\pi$
$593$		−	6.09322i		−	0.250219i	0.992143	−	0.125109i	$-0.0399282\pi$
$594$		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	$-0.572340\pi$
$601$	−11.0471			−0.450621			−0.225310	+	0.974287i	$0.572340\pi$
$602$			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	$-0.999251\pi$
$607$		−	0.115912i		−	0.00470474i	0.999997	−	0.00235237i	$-0.000748784\pi$
$608$			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	$-0.874339\pi$
$613$		−	19.0445i		−	0.769202i	0.923083	−	0.384601i	$-0.125661\pi$
$614$	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	$-0.599494\pi$
$659$	−15.7879			−0.615011			−0.307505	+	0.951546i	$0.599494\pi$
$660$		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	$0.196047\pi$
$673$			29.9733i			1.15539i	−0.816254	+	0.577693i	$0.803953\pi$
$674$	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	$-0.976999\pi$
$677$		−	3.75709i		−	0.144397i	0.997390	−	0.0721984i	$-0.0230015\pi$
$678$			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	$-0.723772\pi$
$701$	−34.2344			−1.29302			−0.646509	+	0.762907i	$0.723772\pi$
$702$			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	$0.359373\pi$
$733$			48.9490i			1.80797i	−0.427561	+	0.903987i	$0.640627\pi$
$734$	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	$-0.375912\pi$
$739$	20.6622			0.760072			0.380036	+	0.924972i	$0.375912\pi$
$740$	−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	$0.186627\pi$
$743$			30.1631i			1.10658i	−0.832990	+	0.553288i	$0.813373\pi$
$744$	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	$-0.376675\pi$
$761$	20.8450			0.755631			0.377816	+	0.925881i	$0.376675\pi$
$762$		−	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	$-0.561896\pi$
$769$	−10.7167			−0.386455			−0.193228	+	0.981154i	$0.561896\pi$
$770$		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	$-0.918424\pi$
$787$		−	14.2222i		−	0.506967i	0.967340	−	0.253484i	$-0.0815764\pi$
$788$		−	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	$-0.637251\pi$
$809$	−23.7753			−0.835896			−0.417948	+	0.908471i	$0.637251\pi$
$810$	14.1015	+	8.90079i	0.495475	+	0.312742i
$811$	−8.19869			−0.287895			−0.143948	−	0.989585i	$-0.545980\pi$
$811$	−8.19869			−0.287895			−0.143948	+	0.989585i	$0.545980\pi$
$812$		−	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	$-0.773816\pi$
$821$	−43.4373			−1.51597			−0.757986	+	0.652271i	$0.773816\pi$
$822$		−	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	$-0.854971\pi$
$827$		−	25.3079i		−	0.880042i	0.897987	−	0.440021i	$-0.145029\pi$
$828$			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	$0.263368\pi$
$853$			43.0014i			1.47234i	−0.676797	+	0.736170i	$0.736632\pi$
$854$	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	$-0.621940\pi$
$857$		−	54.3052i		−	1.85503i	0.373784	−	0.927516i	$-0.378060\pi$
$858$		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	$0.259314\pi$
$877$			43.0882i			1.45499i	−0.686116	+	0.727493i	$0.740686\pi$
$878$			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	$0.0118221\pi$
$887$			2.21174i			0.0742631i	−0.999310	+	0.0371315i	$0.988178\pi$
$888$			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	$-0.337219\pi$
$919$	29.6718			0.978781			0.489391	+	0.872065i	$0.337219\pi$
$920$	−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	$0.164460\pi$
$937$			30.2421i			0.987967i	−0.869471	+	0.493983i	$0.835540\pi$
$938$		−	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	$-0.531215\pi$
$941$	−6.00672			−0.195813			−0.0979067	+	0.995196i	$0.531215\pi$
$942$		−	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	$-0.949359\pi$
$953$		−	9.78136i		−	0.316849i	0.987371	−	0.158425i	$-0.0506415\pi$
$954$	−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	$0.00627695\pi$
$967$			1.22635i			0.0394367i	−0.999806	+	0.0197184i	$0.993723\pi$
$968$		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	$-0.900917\pi$
$997$		−	19.3415i		−	0.612552i	0.951943	−	0.306276i	$-0.0990831\pi$
$998$		−	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.g.364.5		8
5.2	odd	4		3025.2.a.bl.1.4		8
5.3	odd	4		3025.2.a.bl.1.5		8
5.4	even	2	inner	605.2.b.g.364.4		8
11.2	odd	10		605.2.j.g.444.2		16
11.3	even	5		55.2.j.a.9.3	yes	16
11.4	even	5		55.2.j.a.49.2	yes	16
11.5	even	5		605.2.j.h.124.2		16
11.6	odd	10		605.2.j.g.124.3		16
11.7	odd	10		605.2.j.d.269.3		16
11.8	odd	10		605.2.j.d.9.2		16
11.9	even	5		605.2.j.h.444.3		16
11.10	odd	2		605.2.b.f.364.4		8
33.14	odd	10		495.2.ba.a.64.2		16
33.26	odd	10		495.2.ba.a.379.3		16
44.3	odd	10		880.2.cd.c.449.2		16
44.15	odd	10		880.2.cd.c.49.3		16
55.3	odd	20		275.2.h.d.251.3		16
55.4	even	10		55.2.j.a.49.3	yes	16
55.9	even	10		605.2.j.h.444.2		16
55.14	even	10		55.2.j.a.9.2	✓	16
55.19	odd	10		605.2.j.d.9.3		16
55.24	odd	10		605.2.j.g.444.3		16
55.29	odd	10		605.2.j.d.269.2		16
55.32	even	4		3025.2.a.bk.1.5		8
55.37	odd	20		275.2.h.d.126.2		16
55.39	odd	10		605.2.j.g.124.2		16
55.43	even	4		3025.2.a.bk.1.4		8
55.47	odd	20		275.2.h.d.251.2		16
55.48	odd	20		275.2.h.d.126.3		16
55.49	even	10		605.2.j.h.124.3		16
55.54	odd	2		605.2.b.f.364.5		8
165.14	odd	10		495.2.ba.a.64.3		16
165.59	odd	10		495.2.ba.a.379.2		16
220.59	odd	10		880.2.cd.c.49.2		16
220.179	odd	10		880.2.cd.c.449.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	55.14	even	10
55.2.j.a.9.3	yes	16	11.3	even	5
55.2.j.a.49.2	yes	16	11.4	even	5
55.2.j.a.49.3	yes	16	55.4	even	10
275.2.h.d.126.2		16	55.37	odd	20
275.2.h.d.126.3		16	55.48	odd	20
275.2.h.d.251.2		16	55.47	odd	20
275.2.h.d.251.3		16	55.3	odd	20
495.2.ba.a.64.2		16	33.14	odd	10
495.2.ba.a.64.3		16	165.14	odd	10
495.2.ba.a.379.2		16	165.59	odd	10
495.2.ba.a.379.3		16	33.26	odd	10
605.2.b.f.364.4		8	11.10	odd	2
605.2.b.f.364.5		8	55.54	odd	2
605.2.b.g.364.4		8	5.4	even	2	inner
605.2.b.g.364.5		8	1.1	even	1	trivial
605.2.j.d.9.2		16	11.8	odd	10
605.2.j.d.9.3		16	55.19	odd	10
605.2.j.d.269.2		16	55.29	odd	10
605.2.j.d.269.3		16	11.7	odd	10
605.2.j.g.124.2		16	55.39	odd	10
605.2.j.g.124.3		16	11.6	odd	10
605.2.j.g.444.2		16	11.2	odd	10
605.2.j.g.444.3		16	55.24	odd	10
605.2.j.h.124.2		16	11.5	even	5
605.2.j.h.124.3		16	55.49	even	10
605.2.j.h.444.2		16	55.9	even	10
605.2.j.h.444.3		16	11.9	even	5
880.2.cd.c.49.2		16	220.59	odd	10
880.2.cd.c.49.3		16	44.15	odd	10
880.2.cd.c.449.2		16	44.3	odd	10
880.2.cd.c.449.3		16	220.179	odd	10
3025.2.a.bk.1.4		8	55.43	even	4
3025.2.a.bk.1.5		8	55.32	even	4
3025.2.a.bl.1.4		8	5.2	odd	4
3025.2.a.bl.1.5		8	5.3	odd	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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