LMFDB - Embedded newform 455.2.d.b.246.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [455,2,Mod(246,455)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(455, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("455.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 455 = 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	455.d (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:	$3.63319329197$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 365x^{14} + 2316x^{12} + 8212x^{10} + 16209x^{8} + 16722x^{6} + 7737x^{4} + 1248x^{2} + 64 $ x^18 + 30x^16 + 365x^14 + 2316x^12 + 8212x^10 + 16209x^8 + 16722x^6 + 7737x^4 + 1248x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			246.6
Root			$-1.46507i$ of defining polynomial
Character	$\chi$	$=$	455.246
Dual form			455.2.d.b.246.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46507i q^{2} +2.66524 q^{3} -0.146416 q^{4} +1.00000i q^{5} -3.90476i q^{6} -1.00000i q^{7} -2.71562i q^{8} +4.10353 q^{9} +O(q^{10})$	\(q-1.46507i q^{2} +2.66524 q^{3} -0.146416 q^{4} +1.00000i q^{5} -3.90476i q^{6} -1.00000i q^{7} -2.71562i q^{8} +4.10353 q^{9} +1.46507 q^{10} +4.62772i q^{11} -0.390233 q^{12} +(-1.07610 - 3.44122i) q^{13} -1.46507 q^{14} +2.66524i q^{15} -4.27139 q^{16} +1.28033 q^{17} -6.01194i q^{18} +1.72407i q^{19} -0.146416i q^{20} -2.66524i q^{21} +6.77992 q^{22} -7.52949 q^{23} -7.23780i q^{24} -1.00000 q^{25} +(-5.04162 + 1.57655i) q^{26} +2.94117 q^{27} +0.146416i q^{28} +10.1125 q^{29} +3.90476 q^{30} +1.48695i q^{31} +0.826626i q^{32} +12.3340i q^{33} -1.87577i q^{34} +1.00000 q^{35} -0.600821 q^{36} +2.08630i q^{37} +2.52587 q^{38} +(-2.86806 - 9.17170i) q^{39} +2.71562 q^{40} +1.12814i q^{41} -3.90476 q^{42} -7.90335 q^{43} -0.677571i q^{44} +4.10353i q^{45} +11.0312i q^{46} -1.21990i q^{47} -11.3843 q^{48} -1.00000 q^{49} +1.46507i q^{50} +3.41240 q^{51} +(0.157557 + 0.503849i) q^{52} -1.03088 q^{53} -4.30901i q^{54} -4.62772 q^{55} -2.71562 q^{56} +4.59507i q^{57} -14.8155i q^{58} +14.0082i q^{59} -0.390233i q^{60} -12.8043 q^{61} +2.17847 q^{62} -4.10353i q^{63} -7.33173 q^{64} +(3.44122 - 1.07610i) q^{65} +18.0701 q^{66} -11.5301i q^{67} -0.187461 q^{68} -20.0679 q^{69} -1.46507i q^{70} -7.23666i q^{71} -11.1436i q^{72} -6.70200i q^{73} +3.05657 q^{74} -2.66524 q^{75} -0.252431i q^{76} +4.62772 q^{77} +(-13.4371 + 4.20189i) q^{78} +11.9357 q^{79} -4.27139i q^{80} -4.47164 q^{81} +1.65280 q^{82} +16.2863i q^{83} +0.390233i q^{84} +1.28033i q^{85} +11.5789i q^{86} +26.9523 q^{87} +12.5671 q^{88} -3.09148i q^{89} +6.01194 q^{90} +(-3.44122 + 1.07610i) q^{91} +1.10243 q^{92} +3.96308i q^{93} -1.78723 q^{94} -1.72407 q^{95} +2.20316i q^{96} +9.18205i q^{97} +1.46507i q^{98} +18.9900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{3} - 24 q^{4} + 26 q^{9}+O(q^{10}) $ 18 * q + 4 * q^3 - 24 * q^4 + 26 * q^9	$ 18 q + 4 q^{3} - 24 q^{4} + 26 q^{9} + 10 q^{12} - 4 q^{13} + 52 q^{16} - 12 q^{17} - 8 q^{22} - 24 q^{23} - 18 q^{25} - 38 q^{26} + 28 q^{27} + 44 q^{29} - 24 q^{30} + 18 q^{35} - 40 q^{36} + 38 q^{38} + 14 q^{39} + 24 q^{42} - 20 q^{43} - 120 q^{48} - 18 q^{49} - 44 q^{51} - 14 q^{52} + 44 q^{53} + 16 q^{55} + 16 q^{61} + 28 q^{62} - 92 q^{64} + 4 q^{65} - 4 q^{66} + 140 q^{68} - 60 q^{69} - 88 q^{74} - 4 q^{75} - 16 q^{77} - 20 q^{78} - 4 q^{79} + 66 q^{81} - 2 q^{82} - 80 q^{87} - 16 q^{88} + 2 q^{90} - 4 q^{91} + 100 q^{92} + 80 q^{94} - 12 q^{95}+O(q^{100}) $ 18 * q + 4 * q^3 - 24 * q^4 + 26 * q^9 + 10 * q^12 - 4 * q^13 + 52 * q^16 - 12 * q^17 - 8 * q^22 - 24 * q^23 - 18 * q^25 - 38 * q^26 + 28 * q^27 + 44 * q^29 - 24 * q^30 + 18 * q^35 - 40 * q^36 + 38 * q^38 + 14 * q^39 + 24 * q^42 - 20 * q^43 - 120 * q^48 - 18 * q^49 - 44 * q^51 - 14 * q^52 + 44 * q^53 + 16 * q^55 + 16 * q^61 + 28 * q^62 - 92 * q^64 + 4 * q^65 - 4 * q^66 + 140 * q^68 - 60 * q^69 - 88 * q^74 - 4 * q^75 - 16 * q^77 - 20 * q^78 - 4 * q^79 + 66 * q^81 - 2 * q^82 - 80 * q^87 - 16 * q^88 + 2 * q^90 - 4 * q^91 + 100 * q^92 + 80 * q^94 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/455\mathbb{Z}\right)^\times$.

$n$	$66$	$92$	$106$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.46507i		−	1.03596i	−0.855394	−	0.517979i	$-0.826685\pi$
$2$		−	1.46507i		−	1.03596i	0.855394	−	0.517979i	$-0.173315\pi$
$3$	2.66524			1.53878			0.769390	−	0.638780i	$-0.220560\pi$
$3$	2.66524			1.53878			0.769390	+	0.638780i	$0.220560\pi$
$4$	−0.146416			−0.0732078
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	3.90476i		−	1.59411i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	2.71562i		−	0.960117i
$9$	4.10353			1.36784
$10$	1.46507			0.463294
$11$			4.62772i			1.39531i	0.716433	+	0.697656i	$0.245773\pi$
$11$			4.62772i			1.39531i	−0.716433	+	0.697656i	$0.754227\pi$
$12$	−0.390233			−0.112651
$13$	−1.07610	−	3.44122i	−0.298455	−	0.954424i
$13$	−1.07610	−	3.44122i	−0.298455	−	0.954424i
$14$	−1.46507			−0.391555
$15$			2.66524i			0.688163i
$16$	−4.27139			−1.06785
$17$	1.28033			0.310526			0.155263	−	0.987873i	$-0.450377\pi$
$17$	1.28033			0.310526			0.155263	+	0.987873i	$0.450377\pi$
$18$		−	6.01194i		−	1.41703i
$19$			1.72407i			0.395529i	0.980250	+	0.197764i	$0.0633681\pi$
$19$			1.72407i			0.395529i	−0.980250	+	0.197764i	$0.936632\pi$
$20$		−	0.146416i		−	0.0327395i
$21$		−	2.66524i		−	0.581604i
$22$	6.77992			1.44548
$23$	−7.52949			−1.57001			−0.785003	−	0.619492i	$-0.787339\pi$
$23$	−7.52949			−1.57001			−0.785003	+	0.619492i	$0.787339\pi$
$24$		−	7.23780i		−	1.47741i
$25$	−1.00000			−0.200000
$26$	−5.04162	+	1.57655i	−0.988742	+	0.309187i
$27$	2.94117			0.566029
$28$			0.146416i			0.0276699i
$29$	10.1125			1.87785			0.938923	−	0.344128i	$-0.111825\pi$
$29$	10.1125			1.87785			0.938923	+	0.344128i	$0.111825\pi$
$30$	3.90476			0.712908
$31$			1.48695i			0.267064i	0.991045	+	0.133532i	$0.0426318\pi$
$31$			1.48695i			0.267064i	−0.991045	+	0.133532i	$0.957368\pi$
$32$			0.826626i			0.146128i
$33$			12.3340i			2.14708i
$34$		−	1.87577i		−	0.321692i
$35$	1.00000			0.169031
$36$	−0.600821			−0.100137
$37$			2.08630i			0.342986i	0.985185	+	0.171493i	$0.0548592\pi$
$37$			2.08630i			0.342986i	−0.985185	+	0.171493i	$0.945141\pi$
$38$	2.52587			0.409751
$39$	−2.86806	−	9.17170i	−0.459257	−	1.46865i
$40$	2.71562			0.429378
$41$			1.12814i			0.176186i	0.996112	+	0.0880930i	$0.0280773\pi$
$41$			1.12814i			0.176186i	−0.996112	+	0.0880930i	$0.971923\pi$
$42$	−3.90476			−0.602517
$43$	−7.90335			−1.20525			−0.602625	−	0.798025i	$-0.705878\pi$
$43$	−7.90335			−1.20525			−0.602625	+	0.798025i	$0.705878\pi$
$44$		−	0.677571i		−	0.102148i
$45$			4.10353i			0.611718i
$46$			11.0312i			1.62646i
$47$		−	1.21990i		−	0.177940i	−0.996034	−	0.0889702i	$-0.971642\pi$
$47$		−	1.21990i		−	0.177940i	0.996034	−	0.0889702i	$-0.0283576\pi$
$48$	−11.3843			−1.64318
$49$	−1.00000			−0.142857
$50$			1.46507i			0.207191i
$51$	3.41240			0.477832
$52$	0.157557	+	0.503849i	0.0218493	+	0.0698712i
$53$	−1.03088			−0.141603			−0.0708014	−	0.997490i	$-0.522556\pi$
$53$	−1.03088			−0.141603			−0.0708014	+	0.997490i	$0.522556\pi$
$54$		−	4.30901i		−	0.586382i
$55$	−4.62772			−0.624002
$56$	−2.71562			−0.362890
$57$			4.59507i			0.608632i
$58$		−	14.8155i		−	1.94537i
$59$			14.0082i			1.82371i	0.410512	+	0.911855i	$0.365350\pi$
$59$			14.0082i			1.82371i	−0.410512	+	0.911855i	$0.634650\pi$
$60$		−	0.390233i		−	0.0503789i
$61$	−12.8043			−1.63943			−0.819714	−	0.572773i	$-0.805868\pi$
$61$	−12.8043			−1.63943			−0.819714	+	0.572773i	$0.805868\pi$
$62$	2.17847			0.276667
$63$		−	4.10353i		−	0.516996i
$64$	−7.33173			−0.916466
$65$	3.44122	−	1.07610i	0.426831	−	0.133473i
$66$	18.0701			2.22428
$67$		−	11.5301i		−	1.40862i	−0.709890	−	0.704312i	$-0.751255\pi$
$67$		−	11.5301i		−	1.40862i	0.709890	−	0.704312i	$-0.248745\pi$
$68$	−0.187461			−0.0227329
$69$	−20.0679			−2.41589
$70$		−	1.46507i		−	0.175109i
$71$		−	7.23666i		−	0.858833i	−0.903107	−	0.429417i	$-0.858719\pi$
$71$		−	7.23666i		−	0.858833i	0.903107	−	0.429417i	$-0.141281\pi$
$72$		−	11.1436i		−	1.31329i
$73$		−	6.70200i		−	0.784409i	−0.919878	−	0.392205i	$-0.871713\pi$
$73$		−	6.70200i		−	0.784409i	0.919878	−	0.392205i	$-0.128287\pi$
$74$	3.05657			0.355319
$75$	−2.66524			−0.307756
$76$		−	0.252431i		−	0.0289558i
$77$	4.62772			0.527378
$78$	−13.4371	+	4.20189i	−1.52146	+	0.475771i
$79$	11.9357			1.34287			0.671437	−	0.741062i	$-0.265678\pi$
$79$	11.9357			1.34287			0.671437	+	0.741062i	$0.265678\pi$
$80$		−	4.27139i		−	0.477556i
$81$	−4.47164			−0.496849
$82$	1.65280			0.182521
$83$			16.2863i			1.78766i	0.448409	+	0.893829i	$0.351991\pi$
$83$			16.2863i			1.78766i	−0.448409	+	0.893829i	$0.648009\pi$
$84$			0.390233i			0.0425779i
$85$			1.28033i			0.138872i
$86$			11.5789i			1.24859i
$87$	26.9523			2.88959
$88$	12.5671			1.33966
$89$		−	3.09148i		−	0.327696i	−0.986486	−	0.163848i	$-0.947609\pi$
$89$		−	3.09148i		−	0.327696i	0.986486	−	0.163848i	$-0.0523907\pi$
$90$	6.01194			0.633714
$91$	−3.44122	+	1.07610i	−0.360738	+	0.112806i
$92$	1.10243			0.114937
$93$			3.96308i			0.410952i
$94$	−1.78723			−0.184339
$95$	−1.72407			−0.176886
$96$			2.20316i			0.224859i
$97$			9.18205i			0.932296i	0.884707	+	0.466148i	$0.154359\pi$
$97$			9.18205i			0.932296i	−0.884707	+	0.466148i	$0.845641\pi$
$98$			1.46507i			0.147994i
$99$			18.9900i			1.90857i
$100$	0.146416			0.0146416
$101$	−1.07146			−0.106614			−0.0533071	−	0.998578i	$-0.516976\pi$
$101$	−1.07146			−0.106614			−0.0533071	+	0.998578i	$0.516976\pi$
$102$		−	4.99939i		−	0.495013i
$103$	−8.28838			−0.816679			−0.408339	−	0.912830i	$-0.633892\pi$
$103$	−8.28838			−0.816679			−0.408339	+	0.912830i	$0.633892\pi$
$104$	−9.34506	+	2.92227i	−0.916359	+	0.286552i
$105$	2.66524			0.260101
$106$			1.51031i			0.146695i
$107$	12.5948			1.21759			0.608794	−	0.793329i	$-0.291654\pi$
$107$	12.5948			1.21759			0.608794	+	0.793329i	$0.291654\pi$
$108$	−0.430634			−0.0414378
$109$			2.14944i			0.205879i	0.994688	+	0.102940i	$0.0328249\pi$
$109$			2.14944i			0.205879i	−0.994688	+	0.102940i	$0.967175\pi$
$110$			6.77992i			0.646440i
$111$			5.56051i			0.527780i
$112$			4.27139i			0.403609i
$113$	8.99642			0.846312			0.423156	−	0.906057i	$-0.360922\pi$
$113$	8.99642			0.846312			0.423156	+	0.906057i	$0.360922\pi$
$114$	6.73207			0.630516
$115$		−	7.52949i		−	0.702128i
$116$	−1.48063			−0.137473
$117$	−4.41579	−	14.1212i	−0.408240	−	1.30550i
$118$	20.5229			1.88929
$119$		−	1.28033i		−	0.117368i
$120$	7.23780			0.660717
$121$	−10.4158			−0.946893
$122$			18.7592i			1.69838i
$123$			3.00677i			0.271111i
$124$		−	0.217712i		−	0.0195511i
$125$		−	1.00000i		−	0.0894427i
$126$	−6.01194			−0.535586
$127$	−3.62461			−0.321632			−0.160816	−	0.986984i	$-0.551413\pi$
$127$	−3.62461			−0.321632			−0.160816	+	0.986984i	$0.551413\pi$
$128$			12.3947i			1.09555i
$129$	−21.0644			−1.85461
$130$	−1.57655	−	5.04162i	−0.138273	−	0.442179i
$131$	18.2622			1.59558			0.797788	−	0.602938i	$-0.206003\pi$
$131$	18.2622			1.59558			0.797788	+	0.602938i	$0.206003\pi$
$132$		−	1.80589i		−	0.157183i
$133$	1.72407			0.149496
$134$	−16.8923			−1.45928
$135$			2.94117i			0.253136i
$136$		−	3.47690i		−	0.298142i
$137$			0.567292i			0.0484671i	0.999706	+	0.0242335i	$0.00771453\pi$
$137$			0.567292i			0.0484671i	−0.999706	+	0.0242335i	$0.992285\pi$
$138$			29.4008i			2.50276i
$139$	−8.48359			−0.719569			−0.359784	−	0.933035i	$-0.617150\pi$
$139$	−8.48359			−0.719569			−0.359784	+	0.933035i	$0.617150\pi$
$140$	−0.146416			−0.0123744
$141$		−	3.25133i		−	0.273811i
$142$	−10.6022			−0.889715
$143$	15.9250	−	4.97987i	1.33172	−	0.416438i
$144$	−17.5278			−1.46065
$145$			10.1125i			0.839798i
$146$	−9.81886			−0.812615
$147$	−2.66524			−0.219826
$148$		−	0.305467i		−	0.0251093i
$149$		−	8.05515i		−	0.659904i	−0.943998	−	0.329952i	$-0.892967\pi$
$149$		−	8.05515i		−	0.659904i	0.943998	−	0.329952i	$-0.107033\pi$
$150$			3.90476i			0.318822i
$151$		−	5.48140i		−	0.446070i	−0.974810	−	0.223035i	$-0.928404\pi$
$151$		−	5.48140i		−	0.446070i	0.974810	−	0.223035i	$-0.0715964\pi$
$152$	4.68192			0.379754
$153$	5.25388			0.424751
$154$		−	6.77992i		−	0.546341i
$155$	−1.48695			−0.119435
$156$	0.419929	+	1.34288i	0.0336212	+	0.107516i
$157$	20.8873			1.66699			0.833493	−	0.552531i	$-0.186338\pi$
$157$	20.8873			1.66699			0.833493	+	0.552531i	$0.186338\pi$
$158$		−	17.4866i		−	1.39116i
$159$	−2.74756			−0.217896
$160$	−0.826626			−0.0653505
$161$			7.52949i			0.593407i
$162$			6.55124i			0.514714i
$163$		−	18.6553i		−	1.46120i	−0.682806	−	0.730599i	$-0.739241\pi$
$163$		−	18.6553i		−	1.46120i	0.682806	−	0.730599i	$-0.260759\pi$
$164$		−	0.165177i		−	0.0128982i
$165$	−12.3340			−0.960202
$166$	23.8605			1.85194
$167$			5.32179i			0.411813i	0.978572	+	0.205906i	$0.0660142\pi$
$167$			5.32179i			0.411813i	−0.978572	+	0.205906i	$0.933986\pi$
$168$	−7.23780			−0.558408
$169$	−10.6840	+	7.40617i	−0.821849	+	0.569706i
$170$	1.87577			0.143865
$171$			7.07477i			0.541021i
$172$	1.15717			0.0882336
$173$	10.4086			0.791351			0.395676	−	0.918390i	$-0.370510\pi$
$173$	10.4086			0.791351			0.395676	+	0.918390i	$0.370510\pi$
$174$		−	39.4869i		−	2.99349i
$175$			1.00000i			0.0755929i
$176$		−	19.7668i		−	1.48998i
$177$			37.3352i			2.80629i
$178$	−4.52922			−0.339479
$179$	3.51830			0.262970			0.131485	−	0.991318i	$-0.458025\pi$
$179$	3.51830			0.262970			0.131485	+	0.991318i	$0.458025\pi$
$180$		−	0.600821i		−	0.0447825i
$181$	15.9978			1.18911			0.594555	−	0.804055i	$-0.297328\pi$
$181$	15.9978			1.18911			0.594555	+	0.804055i	$0.297328\pi$
$182$	1.57655	+	5.04162i	0.116862	+	0.373709i
$183$	−34.1267			−2.52272
$184$			20.4472i			1.50739i
$185$	−2.08630			−0.153388
$186$	5.80617			0.425729
$187$			5.92503i			0.433281i
$188$			0.178612i			0.0130266i
$189$		−	2.94117i		−	0.213939i
$190$			2.52587i			0.183246i
$191$	−21.1989			−1.53390			−0.766951	−	0.641706i	$-0.778227\pi$
$191$	−21.1989			−1.53390			−0.766951	+	0.641706i	$0.778227\pi$
$192$	−19.5408			−1.41024
$193$		−	16.2263i		−	1.16800i	−0.811754	−	0.583999i	$-0.801487\pi$
$193$		−	16.2263i		−	1.16800i	0.811754	−	0.583999i	$-0.198513\pi$
$194$	13.4523			0.965819
$195$	9.17170	−	2.86806i	0.656799	−	0.205386i
$196$	0.146416			0.0104583
$197$		−	2.30728i		−	0.164387i	−0.996616	−	0.0821935i	$-0.973807\pi$
$197$		−	2.30728i		−	0.164387i	0.996616	−	0.0821935i	$-0.0261925\pi$
$198$	27.8216			1.97719
$199$	17.6911			1.25409			0.627044	−	0.778984i	$-0.284265\pi$
$199$	17.6911			1.25409			0.627044	+	0.778984i	$0.284265\pi$
$200$			2.71562i			0.192023i
$201$		−	30.7305i		−	2.16756i
$202$			1.56976i			0.110448i
$203$		−	10.1125i		−	0.709759i
$204$	−0.499628			−0.0349810
$205$	−1.12814			−0.0787928
$206$			12.1430i			0.846044i
$207$	−30.8975			−2.14752
$208$	4.59643	+	14.6988i	0.318705	+	1.01918i
$209$	−7.97852			−0.551886
$210$		−	3.90476i		−	0.269454i
$211$	−6.22460			−0.428519			−0.214259	−	0.976777i	$-0.568734\pi$
$211$	−6.22460			−0.428519			−0.214259	+	0.976777i	$0.568734\pi$
$212$	0.150938			0.0103664
$213$		−	19.2875i		−	1.32155i
$214$		−	18.4522i		−	1.26137i
$215$		−	7.90335i		−	0.539004i
$216$		−	7.98712i		−	0.543455i
$217$	1.48695			0.100941
$218$	3.14908			0.213282
$219$		−	17.8625i		−	1.20703i
$220$	0.677571			0.0456818
$221$	−1.37776	−	4.40591i	−0.0926782	−	0.296374i
$222$	8.14651			0.546758
$223$		−	5.32179i		−	0.356374i	−0.983997	−	0.178187i	$-0.942977\pi$
$223$		−	5.32179i		−	0.356374i	0.983997	−	0.178187i	$-0.0570231\pi$
$224$	0.826626			0.0552313
$225$	−4.10353			−0.273569
$226$		−	13.1803i		−	0.876743i
$227$			12.9412i			0.858937i	0.903082	+	0.429469i	$0.141299\pi$
$227$			12.9412i			0.858937i	−0.903082	+	0.429469i	$0.858701\pi$
$228$		−	0.672789i		−	0.0445566i
$229$		−	26.8927i		−	1.77712i	−0.458763	−	0.888559i	$-0.651707\pi$
$229$		−	26.8927i		−	1.77712i	0.458763	−	0.888559i	$-0.348293\pi$
$230$	−11.0312			−0.727375
$231$	12.3340			0.811519
$232$		−	27.4617i		−	1.80295i
$233$	0.643475			0.0421554			0.0210777	−	0.999778i	$-0.493290\pi$
$233$	0.643475			0.0421554			0.0210777	+	0.999778i	$0.493290\pi$
$234$	−20.6884	+	6.46942i	−1.35244	+	0.422919i
$235$	1.21990			0.0795774
$236$		−	2.05102i		−	0.133510i
$237$	31.8116			2.06639
$238$	−1.87577			−0.121588
$239$		−	24.1040i		−	1.55916i	−0.626306	−	0.779578i	$-0.715434\pi$
$239$		−	24.1040i		−	1.55916i	0.626306	−	0.779578i	$-0.284566\pi$
$240$		−	11.3843i		−	0.734854i
$241$		−	0.781343i		−	0.0503307i	−0.999683	−	0.0251654i	$-0.991989\pi$
$241$		−	0.781343i		−	0.0503307i	0.999683	−	0.0251654i	$-0.00801123\pi$
$242$			15.2599i			0.980941i
$243$	−20.7415			−1.33057
$244$	1.87475			0.120019
$245$		−	1.00000i		−	0.0638877i
$246$	4.40511			0.280860
$247$	5.93291	−	1.85526i	0.377502	−	0.118048i
$248$	4.03799			0.256412
$249$			43.4071i			2.75081i
$250$	−1.46507			−0.0926588
$251$	−12.4807			−0.787772			−0.393886	−	0.919159i	$-0.628870\pi$
$251$	−12.4807			−0.787772			−0.393886	+	0.919159i	$0.628870\pi$
$252$			0.600821i			0.0378481i
$253$		−	34.8444i		−	2.19065i
$254$			5.31028i			0.333197i
$255$			3.41240i			0.213693i
$256$	3.49560			0.218475
$257$	−7.89115			−0.492237			−0.246118	−	0.969240i	$-0.579155\pi$
$257$	−7.89115			−0.492237			−0.246118	+	0.969240i	$0.579155\pi$
$258$			30.8606i			1.92130i
$259$	2.08630			0.129637
$260$	−0.503849	+	0.157557i	−0.0312474	+	0.00977128i
$261$	41.4970			2.56860
$262$		−	26.7553i		−	1.65295i
$263$	11.9743			0.738364			0.369182	−	0.929357i	$-0.379638\pi$
$263$	11.9743			0.738364			0.369182	+	0.929357i	$0.379638\pi$
$264$	33.4945			2.06145
$265$		−	1.03088i		−	0.0633267i
$266$		−	2.52587i		−	0.154871i
$267$		−	8.23955i		−	0.504252i
$268$			1.68818i			0.103122i
$269$	1.44411			0.0880492			0.0440246	−	0.999030i	$-0.485982\pi$
$269$	1.44411			0.0880492			0.0440246	+	0.999030i	$0.485982\pi$
$270$	4.30901			0.262238
$271$		−	18.9486i		−	1.15104i	−0.817786	−	0.575522i	$-0.804799\pi$
$271$		−	18.9486i		−	1.15104i	0.817786	−	0.575522i	$-0.195201\pi$
$272$	−5.46881			−0.331595
$273$	−9.17170	+	2.86806i	−0.555097	+	0.173583i
$274$	0.831120			0.0502098
$275$		−	4.62772i		−	0.279062i
$276$	2.93826			0.176862
$277$	−10.7652			−0.646815			−0.323408	−	0.946260i	$-0.604828\pi$
$277$	−10.7652			−0.646815			−0.323408	+	0.946260i	$0.604828\pi$
$278$			12.4290i			0.745443i
$279$			6.10173i			0.365301i
$280$		−	2.71562i		−	0.162289i
$281$		−	13.8013i		−	0.823314i	−0.911339	−	0.411657i	$-0.864950\pi$
$281$		−	13.8013i		−	0.823314i	0.911339	−	0.411657i	$-0.135050\pi$
$282$	−4.76341			−0.283657
$283$	−9.66944			−0.574789			−0.287394	−	0.957812i	$-0.592789\pi$
$283$	−9.66944			−0.574789			−0.287394	+	0.957812i	$0.592789\pi$
$284$			1.05956i			0.0628733i
$285$	−4.59507			−0.272188
$286$	−7.29584	−	23.3312i	−0.431412	−	1.37960i
$287$	1.12814			0.0665920
$288$			3.39208i			0.199880i
$289$	−15.3607			−0.903573
$290$	14.8155			0.869995
$291$			24.4724i			1.43460i
$292$			0.981276i			0.0574249i
$293$			20.3650i			1.18974i	0.803822	+	0.594869i	$0.202796\pi$
$293$			20.3650i			1.18974i	−0.803822	+	0.594869i	$0.797204\pi$
$294$			3.90476i			0.227730i
$295$	−14.0082			−0.815588
$296$	5.66561			0.329307
$297$			13.6109i			0.789787i
$298$	−11.8013			−0.683632
$299$	8.10245	+	25.9106i	0.468577	+	1.49845i
$300$	0.390233			0.0225301
$301$			7.90335i			0.455541i
$302$	−8.03060			−0.462109
$303$	−2.85570			−0.164056
$304$		−	7.36418i		−	0.422365i
$305$		−	12.8043i		−	0.733174i
$306$		−	7.69728i		−	0.440024i
$307$			5.66548i			0.323346i	0.986844	+	0.161673i	$0.0516889\pi$
$307$			5.66548i			0.323346i	−0.986844	+	0.161673i	$0.948311\pi$
$308$	−0.677571			−0.0386082
$309$	−22.0906			−1.25669
$310$			2.17847i			0.123729i
$311$	−25.9435			−1.47112			−0.735562	−	0.677458i	$-0.763082\pi$
$311$	−25.9435			−1.47112			−0.735562	+	0.677458i	$0.763082\pi$
$312$	−24.9069	+	7.78856i	−1.41007	+	0.440941i
$313$	−16.9839			−0.959987			−0.479994	−	0.877272i	$-0.659361\pi$
$313$	−16.9839			−0.959987			−0.479994	+	0.877272i	$0.659361\pi$
$314$		−	30.6012i		−	1.72693i
$315$	4.10353			0.231208
$316$	−1.74758			−0.0983088
$317$		−	3.76355i		−	0.211382i	−0.994399	−	0.105691i	$-0.966295\pi$
$317$		−	3.76355i		−	0.211382i	0.994399	−	0.105691i	$-0.0337055\pi$
$318$			4.02535i			0.225731i
$319$			46.7979i			2.62018i
$320$		−	7.33173i		−	0.409856i
$321$	33.5683			1.87360
$322$	11.0312			0.614744
$323$			2.20738i			0.122822i
$324$	0.654717			0.0363732
$325$	1.07610	+	3.44122i	0.0596911	+	0.190885i
$326$	−27.3313			−1.51374
$327$			5.72879i			0.316803i
$328$	3.06360			0.169159
$329$	−1.21990			−0.0672552
$330$			18.0701i			0.994728i
$331$			25.4467i			1.39868i	0.714790	+	0.699339i	$0.246522\pi$
$331$			25.4467i			1.39868i	−0.714790	+	0.699339i	$0.753478\pi$
$332$		−	2.38457i		−	0.130870i
$333$			8.56121i			0.469152i
$334$	7.79677			0.426620
$335$	11.5301			0.629956
$336$			11.3843i			0.621065i
$337$	27.2139			1.48244			0.741218	−	0.671264i	$-0.234248\pi$
$337$	27.2139			1.48244			0.741218	+	0.671264i	$0.234248\pi$
$338$	10.8505	+	15.6528i	0.590191	+	0.851400i
$339$	23.9777			1.30229
$340$		−	0.187461i		−	0.0101665i
$341$	−6.88118			−0.372637
$342$	10.3650			0.560475
$343$			1.00000i			0.0539949i
$344$			21.4625i			1.15718i
$345$		−	20.0679i		−	1.08042i
$346$		−	15.2493i		−	0.819806i
$347$	−16.4371			−0.882388			−0.441194	−	0.897412i	$-0.645445\pi$
$347$	−16.4371			−0.882388			−0.441194	+	0.897412i	$0.645445\pi$
$348$	−3.94624			−0.211540
$349$			3.51452i			0.188128i	0.995566	+	0.0940641i	$0.0299859\pi$
$349$			3.51452i			0.188128i	−0.995566	+	0.0940641i	$0.970014\pi$
$350$	1.46507			0.0783110
$351$	−3.16499	−	10.1212i	−0.168934	−	0.540232i
$352$	−3.82540			−0.203894
$353$			3.76145i			0.200202i	0.994977	+	0.100101i	$0.0319166\pi$
$353$			3.76145i			0.200202i	−0.994977	+	0.100101i	$0.968083\pi$
$354$	54.6986			2.90720
$355$	7.23666			0.384082
$356$			0.452640i			0.0239899i
$357$		−	3.41240i		−	0.180603i
$358$		−	5.15454i		−	0.272426i
$359$			5.51209i			0.290917i	0.989364	+	0.145459i	$0.0464657\pi$
$359$			5.51209i			0.290917i	−0.989364	+	0.145459i	$0.953534\pi$
$360$	11.1436			0.587321
$361$	16.0276			0.843557
$362$		−	23.4379i		−	1.23187i
$363$	−27.7607			−1.45706
$364$	0.503849	−	0.157557i	0.0264088	−	0.00825824i
$365$	6.70200			0.350798
$366$			49.9978i			2.61343i
$367$	30.0369			1.56791			0.783957	−	0.620815i	$-0.213198\pi$
$367$	30.0369			1.56791			0.783957	+	0.620815i	$0.213198\pi$
$368$	32.1614			1.67653
$369$			4.62936i			0.240995i
$370$			3.05657i			0.158904i
$371$			1.03088i			0.0535208i
$372$		−	0.580256i		−	0.0300849i
$373$	13.9391			0.721738			0.360869	−	0.932616i	$-0.382480\pi$
$373$	13.9391			0.721738			0.360869	+	0.932616i	$0.382480\pi$
$374$	8.68055			0.448860
$375$		−	2.66524i		−	0.137633i
$376$	−3.31278			−0.170844
$377$	−10.8820	−	34.7994i	−0.560453	−	1.79226i
$378$	−4.30901			−0.221632
$379$			20.7459i			1.06565i	0.846227	+	0.532823i	$0.178869\pi$
$379$			20.7459i			1.06565i	−0.846227	+	0.532823i	$0.821131\pi$
$380$	0.252431			0.0129494
$381$	−9.66046			−0.494921
$382$			31.0578i			1.58906i
$383$			2.49658i			0.127569i	0.997964	+	0.0637847i	$0.0203171\pi$
$383$			2.49658i			0.127569i	−0.997964	+	0.0637847i	$0.979683\pi$
$384$			33.0349i			1.68581i
$385$			4.62772i			0.235851i
$386$	−23.7726			−1.21000
$387$	−32.4316			−1.64859
$388$		−	1.34440i		−	0.0682513i
$389$	10.5511			0.534960			0.267480	−	0.963563i	$-0.413809\pi$
$389$	10.5511			0.534960			0.267480	+	0.963563i	$0.413809\pi$
$390$	−4.20189	−	13.4371i	−0.212771	−	0.680416i
$391$	−9.64025			−0.487528
$392$			2.71562i			0.137160i
$393$	48.6733			2.45524
$394$	−3.38032			−0.170298
$395$			11.9357i			0.600551i
$396$		−	2.78043i		−	0.139722i
$397$		−	20.3192i		−	1.01979i	−0.860236	−	0.509897i	$-0.829684\pi$
$397$		−	20.3192i		−	1.01979i	0.860236	−	0.509897i	$-0.170316\pi$
$398$		−	25.9186i		−	1.29918i
$399$	4.59507			0.230041
$400$	4.27139			0.213570
$401$		−	12.4731i		−	0.622878i	−0.950266	−	0.311439i	$-0.899189\pi$
$401$		−	12.4731i		−	0.622878i	0.950266	−	0.311439i	$-0.100811\pi$
$402$	−45.0222			−2.24550
$403$	5.11692	−	1.60010i	0.254892	−	0.0797066i
$404$	0.156878			0.00780500
$405$		−	4.47164i		−	0.222197i
$406$	−14.8155			−0.735280
$407$	−9.65484			−0.478573
$408$		−	9.26679i		−	0.458774i
$409$			10.6684i			0.527518i	0.964589	+	0.263759i	$0.0849624\pi$
$409$			10.6684i			0.527518i	−0.964589	+	0.263759i	$0.915038\pi$
$410$			1.65280i			0.0816259i
$411$			1.51197i			0.0745801i
$412$	1.21355			0.0597872
$413$	14.0082			0.689298
$414$			45.2668i			2.22474i
$415$	−16.2863			−0.799465
$416$	2.84460	−	0.889529i	0.139468	−	0.0436127i
$417$	−22.6108			−1.10726
$418$			11.6890i			0.571730i
$419$	29.6841			1.45017			0.725083	−	0.688662i	$-0.241802\pi$
$419$	29.6841			1.45017			0.725083	+	0.688662i	$0.241802\pi$
$420$	−0.390233			−0.0190414
$421$		−	13.4500i		−	0.655514i	−0.944762	−	0.327757i	$-0.893707\pi$
$421$		−	13.4500i		−	0.655514i	0.944762	−	0.327757i	$-0.106293\pi$
$422$			9.11944i			0.443927i
$423$		−	5.00589i		−	0.243395i
$424$			2.79949i			0.135955i
$425$	−1.28033			−0.0621053
$426$	−28.2574			−1.36907
$427$			12.8043i			0.619645i
$428$	−1.84408			−0.0891369
$429$	42.4441	−	13.2726i	2.04922	−	0.640806i
$430$	−11.5789			−0.558385
$431$		−	33.0749i		−	1.59316i	−0.604532	−	0.796581i	$-0.706640\pi$
$431$		−	33.0749i		−	1.59316i	0.604532	−	0.796581i	$-0.293360\pi$
$432$	−12.5629			−0.604434
$433$	−13.4972			−0.648635			−0.324318	−	0.945948i	$-0.605135\pi$
$433$	−13.4972			−0.648635			−0.324318	+	0.945948i	$0.605135\pi$
$434$		−	2.17847i		−	0.104570i
$435$			26.9523i			1.29226i
$436$		−	0.314712i		−	0.0150720i
$437$		−	12.9814i		−	0.620983i
$438$	−26.1697			−1.25043
$439$	10.8985			0.520159			0.260079	−	0.965587i	$-0.416251\pi$
$439$	10.8985			0.520159			0.260079	+	0.965587i	$0.416251\pi$
$440$			12.5671i			0.599115i
$441$	−4.10353			−0.195406
$442$	−6.45495	+	2.01851i	−0.307030	+	0.0960107i
$443$	−33.5921			−1.59601			−0.798003	−	0.602653i	$-0.794110\pi$
$443$	−33.5921			−1.59601			−0.798003	+	0.602653i	$0.794110\pi$
$444$		−	0.814146i		−	0.0386376i
$445$	3.09148			0.146550
$446$	−7.79677			−0.369188
$447$		−	21.4690i		−	1.01545i
$448$			7.33173i			0.346392i
$449$		−	33.7493i		−	1.59273i	−0.604817	−	0.796364i	$-0.706754\pi$
$449$		−	33.7493i		−	1.59273i	0.604817	−	0.796364i	$-0.293246\pi$
$450$			6.01194i			0.283405i
$451$	−5.22072			−0.245834
$452$	−1.31722			−0.0619566
$453$		−	14.6093i		−	0.686403i
$454$	18.9597			0.889822
$455$	−1.07610	−	3.44122i	−0.0504482	−	0.161327i
$456$	12.4785			0.584358
$457$		−	11.2789i		−	0.527604i	−0.964577	−	0.263802i	$-0.915024\pi$
$457$		−	11.2789i		−	0.527604i	0.964577	−	0.263802i	$-0.0849765\pi$
$458$	−39.3995			−1.84102
$459$	3.76568			0.175767
$460$			1.10243i			0.0514013i
$461$			38.8671i			1.81022i	0.425178	+	0.905110i	$0.360211\pi$
$461$			38.8671i			1.81022i	−0.425178	+	0.905110i	$0.639789\pi$
$462$		−	18.0701i		−	0.840699i
$463$			10.8599i			0.504704i	0.967636	+	0.252352i	$0.0812041\pi$
$463$			10.8599i			0.504704i	−0.967636	+	0.252352i	$0.918796\pi$
$464$	−43.1945			−2.00525
$465$	−3.96308			−0.183783
$466$		−	0.942732i		−	0.0436712i
$467$	−30.7494			−1.42291			−0.711455	−	0.702731i	$-0.751964\pi$
$467$	−30.7494			−1.42291			−0.711455	+	0.702731i	$0.751964\pi$
$468$	0.646541	+	2.06756i	0.0298863	+	0.0955729i
$469$	−11.5301			−0.532410
$470$		−	1.78723i		−	0.0824388i
$471$	55.6697			2.56512
$472$	38.0409			1.75098
$473$		−	36.5745i		−	1.68170i
$474$		−	46.6061i		−	2.14069i
$475$		−	1.72407i		−	0.0791058i
$476$			0.187461i			0.00859224i
$477$	−4.23026			−0.193690
$478$	−35.3139			−1.61522
$479$			31.6605i			1.44660i	0.690532	+	0.723302i	$0.257376\pi$
$479$			31.6605i			1.44660i	−0.690532	+	0.723302i	$0.742624\pi$
$480$	−2.20316			−0.100560
$481$	7.17944	−	2.24506i	0.327354	−	0.102366i
$482$	−1.14472			−0.0521405
$483$			20.0679i			0.913122i
$484$	1.52504			0.0693199
$485$	−9.18205			−0.416935
$486$			30.3877i			1.37841i
$487$			7.89192i			0.357617i	0.983884	+	0.178808i	$0.0572242\pi$
$487$			7.89192i			0.357617i	−0.983884	+	0.178808i	$0.942776\pi$
$488$			34.7717i			1.57404i
$489$		−	49.7210i		−	2.24846i
$490$	−1.46507			−0.0661849
$491$	41.8887			1.89041			0.945206	−	0.326474i	$-0.105861\pi$
$491$	41.8887			1.89041			0.945206	+	0.326474i	$0.105861\pi$
$492$		−	0.440238i		−	0.0198475i
$493$	12.9474			0.583120
$494$	−2.71808	−	8.69210i	−0.122292	−	0.391076i
$495$	−18.9900			−0.853537
$496$		−	6.35134i		−	0.285184i
$497$	−7.23666			−0.324608
$498$	63.5942			2.84972
$499$		−	1.13318i		−	0.0507281i	−0.999678	−	0.0253640i	$-0.991926\pi$
$499$		−	1.13318i		−	0.0507281i	0.999678	−	0.0253640i	$-0.00807449\pi$
$500$			0.146416i			0.00654790i
$501$			14.1839i			0.633689i
$502$			18.2850i			0.816099i
$503$	−33.4180			−1.49004			−0.745018	−	0.667044i	$-0.767559\pi$
$503$	−33.4180			−1.49004			−0.745018	+	0.667044i	$0.767559\pi$
$504$	−11.1436			−0.496377
$505$		−	1.07146i		−	0.0476794i
$506$	−51.0493			−2.26942
$507$	−28.4756	+	19.7393i	−1.26464	+	0.876652i
$508$	0.530699			0.0235460
$509$		−	26.3711i		−	1.16888i	−0.811437	−	0.584440i	$-0.801314\pi$
$509$		−	26.3711i		−	1.16888i	0.811437	−	0.584440i	$-0.198686\pi$
$510$	4.99939			0.221377
$511$	−6.70200			−0.296479
$512$			19.6681i			0.869217i
$513$			5.07079i			0.223881i
$514$			11.5611i			0.509936i
$515$		−	8.28838i		−	0.365230i
$516$	3.08415			0.135772
$517$	5.64535			0.248282
$518$		−	3.05657i		−	0.134298i
$519$	27.7415			1.21772
$520$	−2.92227	−	9.34506i	−0.128150	−	0.409808i
$521$	−4.74619			−0.207934			−0.103967	−	0.994581i	$-0.533154\pi$
$521$	−4.74619			−0.207934			−0.103967	+	0.994581i	$0.533154\pi$
$522$		−	60.7958i		−	2.66096i
$523$	13.2476			0.579278			0.289639	−	0.957136i	$-0.406465\pi$
$523$	13.2476			0.579278			0.289639	+	0.957136i	$0.406465\pi$
$524$	−2.67387			−0.116809
$525$			2.66524i			0.116321i
$526$		−	17.5431i		−	0.764914i
$527$			1.90379i			0.0829303i
$528$		−	52.6834i		−	2.29275i
$529$	33.6932			1.46492
$530$	−1.51031			−0.0656038
$531$			57.4830i			2.49455i
$532$	−0.252431			−0.0109443
$533$	3.88218	−	1.21399i	0.168156	−	0.0525836i
$534$	−12.0715			−0.522384
$535$			12.5948i			0.544522i
$536$	−31.3114			−1.35244
$537$	9.37713			0.404653
$538$		−	2.11572i		−	0.0912152i
$539$		−	4.62772i		−	0.199330i
$540$		−	0.430634i		−	0.0185315i
$541$		−	31.6007i		−	1.35862i	−0.733852	−	0.679310i	$-0.762279\pi$
$541$		−	31.6007i		−	1.35862i	0.733852	−	0.679310i	$-0.237721\pi$
$542$	−27.7609			−1.19243
$543$	42.6382			1.82978
$544$			1.05836i			0.0453766i
$545$	−2.14944			−0.0920721
$546$	4.20189	+	13.4371i	0.179824	+	0.575056i
$547$	15.0005			0.641376			0.320688	−	0.947185i	$-0.396086\pi$
$547$	15.0005			0.641376			0.320688	+	0.947185i	$0.396086\pi$
$548$		−	0.0830604i		−	0.00354817i
$549$	−52.5430			−2.24248
$550$	−6.77992			−0.289097
$551$			17.4347i			0.742742i
$552$			54.4969i			2.31954i
$553$		−	11.9357i		−	0.507558i
$554$			15.7716i			0.670073i
$555$	−5.56051			−0.236031
$556$	1.24213			0.0526780
$557$		−	0.755865i		−	0.0320270i	−0.999872	−	0.0160135i	$-0.994903\pi$
$557$		−	0.755865i		−	0.0320270i	0.999872	−	0.0160135i	$-0.00509748\pi$
$558$	8.93943			0.378436
$559$	8.50476	+	27.1972i	0.359713	+	1.15032i
$560$	−4.27139			−0.180499
$561$			15.7916i			0.666724i
$562$	−20.2197			−0.852919
$563$	14.0829			0.593522			0.296761	−	0.954952i	$-0.404093\pi$
$563$	14.0829			0.593522			0.296761	+	0.954952i	$0.404093\pi$
$564$			0.476045i			0.0200451i
$565$			8.99642i			0.378482i
$566$			14.1664i			0.595457i
$567$			4.47164i			0.187791i
$568$	−19.6520			−0.824580
$569$	20.0727			0.841493			0.420746	−	0.907178i	$-0.361768\pi$
$569$	20.0727			0.841493			0.420746	+	0.907178i	$0.361768\pi$
$570$			6.73207i			0.281976i
$571$	39.6025			1.65731			0.828656	−	0.559758i	$-0.189106\pi$
$571$	39.6025			1.65731			0.828656	+	0.559758i	$0.189106\pi$
$572$	−2.33167	+	0.729131i	−0.0974921	+	0.0304865i
$573$	−56.5004			−2.36034
$574$		−	1.65280i		−	0.0689865i
$575$	7.52949			0.314001
$576$	−30.0860			−1.25358
$577$		−	20.3402i		−	0.846775i	−0.905949	−	0.423387i	$-0.860841\pi$
$577$		−	20.3402i		−	0.846775i	0.905949	−	0.423387i	$-0.139159\pi$
$578$			22.5045i			0.936064i
$579$		−	43.2472i		−	1.79729i
$580$		−	1.48063i		−	0.0614797i
$581$	16.2863			0.675671
$582$	35.8537			1.48618
$583$		−	4.77065i		−	0.197580i
$584$	−18.2001			−0.753125
$585$	14.1212	−	4.41579i	0.583838	−	0.182571i
$586$	29.8361			1.23252
$587$		−	27.7622i		−	1.14587i	−0.819602	−	0.572934i	$-0.805805\pi$
$587$		−	27.7622i		−	1.14587i	0.819602	−	0.572934i	$-0.194195\pi$
$588$	0.390233			0.0160929
$589$	−2.56360			−0.105631
$590$			20.5229i			0.844915i
$591$		−	6.14947i		−	0.252955i
$592$		−	8.91143i		−	0.366257i
$593$			22.4330i			0.921211i	0.887605	+	0.460605i	$0.152368\pi$
$593$			22.4330i			0.921211i	−0.887605	+	0.460605i	$0.847632\pi$
$594$	19.9409			0.818186
$595$	1.28033			0.0524885
$596$			1.17940i			0.0483101i
$597$	47.1511			1.92977
$598$	37.9608	−	11.8706i	1.55233	−	0.485426i
$599$	45.5527			1.86123			0.930617	−	0.365996i	$-0.119271\pi$
$599$	45.5527			1.86123			0.930617	+	0.365996i	$0.119271\pi$
$600$			7.23780i			0.295482i
$601$	−8.47654			−0.345765			−0.172883	−	0.984942i	$-0.555308\pi$
$601$	−8.47654			−0.345765			−0.172883	+	0.984942i	$0.555308\pi$
$602$	11.5789			0.471921
$603$		−	47.3141i		−	1.92678i
$604$			0.802562i			0.0326558i
$605$		−	10.4158i		−	0.423463i
$606$			4.18379i			0.169955i
$607$	−31.5717			−1.28145			−0.640727	−	0.767769i	$-0.721367\pi$
$607$	−31.5717			−1.28145			−0.640727	+	0.767769i	$0.721367\pi$
$608$	−1.42516			−0.0577979
$609$		−	26.9523i		−	1.09216i
$610$	−18.7592			−0.759537
$611$	−4.19794	+	1.31273i	−0.169831	+	0.0531073i
$612$	−0.769250			−0.0310951
$613$			13.4748i			0.544244i	0.962263	+	0.272122i	$0.0877254\pi$
$613$			13.4748i			0.544244i	−0.962263	+	0.272122i	$0.912275\pi$
$614$	8.30029			0.334972
$615$	−3.00677			−0.121245
$616$		−	12.5671i		−	0.506345i
$617$			36.6834i			1.47682i	0.674352	+	0.738410i	$0.264423\pi$
$617$			36.6834i			1.47682i	−0.674352	+	0.738410i	$0.735577\pi$
$618$			32.3641i			1.30188i
$619$			35.3137i			1.41938i	0.704516	+	0.709688i	$0.251164\pi$
$619$			35.3137i			1.41938i	−0.704516	+	0.709688i	$0.748836\pi$
$620$	0.217712			0.00874353
$621$	−22.1455			−0.888670
$622$			38.0090i			1.52402i
$623$	−3.09148			−0.123857
$624$	12.2506	+	39.1759i	0.490417	+	1.56829i
$625$	1.00000			0.0400000
$626$			24.8825i			0.994506i
$627$	−21.2647			−0.849230
$628$	−3.05822			−0.122036
$629$			2.67116i			0.106506i
$630$		−	6.01194i		−	0.239521i
$631$			34.7223i			1.38227i	0.722723	+	0.691137i	$0.242890\pi$
$631$			34.7223i			1.38227i	−0.722723	+	0.691137i	$0.757110\pi$
$632$		−	32.4129i		−	1.28932i
$633$	−16.5901			−0.659396
$634$	−5.51385			−0.218983
$635$		−	3.62461i		−	0.143838i
$636$	0.402285			0.0159517
$637$	1.07610	+	3.44122i	0.0426365	+	0.136346i
$638$	68.5619			2.71439
$639$		−	29.6958i		−	1.17475i
$640$	−12.3947			−0.489944
$641$	−12.9368			−0.510971			−0.255485	−	0.966813i	$-0.582235\pi$
$641$	−12.9368			−0.510971			−0.255485	+	0.966813i	$0.582235\pi$
$642$		−	49.1797i		−	1.94097i
$643$			25.9004i			1.02141i	0.859755	+	0.510707i	$0.170616\pi$
$643$			25.9004i			1.02141i	−0.859755	+	0.510707i	$0.829384\pi$
$644$		−	1.10243i		−	0.0434420i
$645$		−	21.0644i		−	0.829408i
$646$	3.23396			0.127238
$647$	14.5044			0.570228			0.285114	−	0.958494i	$-0.407969\pi$
$647$	14.5044			0.570228			0.285114	+	0.958494i	$0.407969\pi$
$648$			12.1433i			0.477033i
$649$	−64.8260			−2.54464
$650$	5.04162	−	1.57655i	0.197748	−	0.0618374i
$651$	3.96308			0.155325
$652$			2.73143i			0.106971i
$653$	23.2408			0.909481			0.454741	−	0.890624i	$-0.349732\pi$
$653$	23.2408			0.909481			0.454741	+	0.890624i	$0.349732\pi$
$654$	8.39306			0.328194
$655$			18.2622i			0.713564i
$656$		−	4.81873i		−	0.188140i
$657$		−	27.5018i		−	1.07295i
$658$			1.78723i			0.0696735i
$659$	−33.2905			−1.29681			−0.648407	−	0.761294i	$-0.724564\pi$
$659$	−33.2905			−1.29681			−0.648407	+	0.761294i	$0.724564\pi$
$660$	1.80589			0.0702942
$661$		−	9.24842i		−	0.359722i	−0.983692	−	0.179861i	$-0.942435\pi$
$661$		−	9.24842i		−	0.359722i	0.983692	−	0.179861i	$-0.0575648\pi$
$662$	37.2811			1.44897
$663$	−3.67207	−	11.7428i	−0.142611	−	0.456054i
$664$	44.2275			1.71636
$665$			1.72407i			0.0668566i
$666$	12.5427			0.486021
$667$	−76.1420			−2.94823
$668$		−	0.779193i		−	0.0301479i
$669$		−	14.1839i		−	0.548380i
$670$		−	16.8923i		−	0.652608i
$671$		−	59.2549i		−	2.28751i
$672$	2.20316			0.0849888
$673$	−0.808875			−0.0311798			−0.0155899	−	0.999878i	$-0.504963\pi$
$673$	−0.808875			−0.0311798			−0.0155899	+	0.999878i	$0.504963\pi$
$674$		−	39.8702i		−	1.53574i
$675$	−2.94117			−0.113206
$676$	1.56431	−	1.08438i	0.0601657	−	0.0417069i
$677$	−16.7684			−0.644462			−0.322231	−	0.946661i	$-0.604433\pi$
$677$	−16.7684			−0.644462			−0.322231	+	0.946661i	$0.604433\pi$
$678$		−	35.1288i		−	1.34911i
$679$	9.18205			0.352375
$680$	3.47690			0.133333
$681$			34.4914i			1.32171i
$682$			10.0814i			0.386036i
$683$			28.8879i			1.10536i	0.833392	+	0.552682i	$0.186396\pi$
$683$			28.8879i			1.10536i	−0.833392	+	0.552682i	$0.813604\pi$
$684$		−	1.03586i		−	0.0396070i
$685$	−0.567292			−0.0216751
$686$	1.46507			0.0559364
$687$		−	71.6755i		−	2.73459i
$688$	33.7583			1.28702
$689$	1.10933	+	3.54750i	0.0422621	+	0.135149i
$690$	−29.4008			−1.11927
$691$			20.5225i			0.780712i	0.920664	+	0.390356i	$0.127648\pi$
$691$			20.5225i			0.780712i	−0.920664	+	0.390356i	$0.872352\pi$
$692$	−1.52398			−0.0579331
$693$	18.9900			0.721370
$694$			24.0814i			0.914117i
$695$		−	8.48359i		−	0.321801i
$696$		−	73.1923i		−	2.77435i
$697$			1.44440i			0.0547104i
$698$	5.14901			0.194893
$699$	1.71502			0.0648679
$700$		−	0.146416i		−	0.00553399i
$701$	18.5376			0.700154			0.350077	−	0.936721i	$-0.386155\pi$
$701$	18.5376			0.700154			0.350077	+	0.936721i	$0.386155\pi$
$702$	−14.8283	+	4.63691i	−0.559657	+	0.175009i
$703$	−3.59694			−0.135661
$704$		−	33.9292i		−	1.27875i
$705$	3.25133			0.122452
$706$	5.51077			0.207401
$707$			1.07146i			0.0402964i
$708$		−	5.46646i		−	0.205442i
$709$		−	8.56864i		−	0.321802i	−0.986971	−	0.160901i	$-0.948560\pi$
$709$		−	8.56864i		−	0.321802i	0.986971	−	0.160901i	$-0.0514400\pi$
$710$		−	10.6022i		−	0.397892i
$711$	48.9786			1.83684
$712$	−8.39528			−0.314627
$713$		−	11.1960i		−	0.419292i
$714$	−4.99939			−0.187097
$715$	4.97987	+	15.9250i	0.186237	+	0.595562i
$716$	−0.515134			−0.0192514
$717$		−	64.2429i		−	2.39920i
$718$	8.07557			0.301378
$719$	10.7670			0.401541			0.200771	−	0.979638i	$-0.435655\pi$
$719$	10.7670			0.401541			0.200771	+	0.979638i	$0.435655\pi$
$720$		−	17.5278i		−	0.653222i
$721$			8.28838i			0.308675i
$722$		−	23.4815i		−	0.873889i
$723$		−	2.08247i		−	0.0774479i
$724$	−2.34233			−0.0870521
$725$	−10.1125			−0.375569
$726$			40.6712i			1.50945i
$727$	18.2670			0.677487			0.338743	−	0.940879i	$-0.389998\pi$
$727$	18.2670			0.677487			0.338743	+	0.940879i	$0.389998\pi$
$728$	2.92227	+	9.34506i	0.108307	+	0.346351i
$729$	−41.8663			−1.55061
$730$		−	9.81886i		−	0.363412i
$731$	−10.1189			−0.374262
$732$	4.99668			0.184683
$733$			13.1869i			0.487069i	0.969892	+	0.243534i	$0.0783069\pi$
$733$			13.1869i			0.487069i	−0.969892	+	0.243534i	$0.921693\pi$
$734$		−	44.0060i		−	1.62429i
$735$		−	2.66524i		−	0.0983090i
$736$		−	6.22407i		−	0.229422i
$737$	53.3581			1.96547
$738$	6.78231			0.249660
$739$		−	2.22164i		−	0.0817243i	−0.999165	−	0.0408621i	$-0.986990\pi$
$739$		−	2.22164i		−	0.0817243i	0.999165	−	0.0408621i	$-0.0130104\pi$
$740$	0.305467			0.0112292
$741$	15.8127	−	4.94473i	0.580892	−	0.181649i
$742$	1.51031			0.0554453
$743$			22.2034i			0.814564i	0.913302	+	0.407282i	$0.133523\pi$
$743$			22.2034i			0.814564i	−0.913302	+	0.407282i	$0.866477\pi$
$744$	10.7622			0.394562
$745$	8.05515			0.295118
$746$		−	20.4217i		−	0.747690i
$747$			66.8314i			2.44523i
$748$		−	0.867516i		−	0.0317195i
$749$		−	12.5948i		−	0.460205i
$750$	−3.90476			−0.142582
$751$	−46.9512			−1.71327			−0.856637	−	0.515920i	$-0.827450\pi$
$751$	−46.9512			−1.71327			−0.856637	+	0.515920i	$0.827450\pi$
$752$			5.21067i			0.190013i
$753$	−33.2640			−1.21221
$754$	−50.9834	+	15.9429i	−1.85670	+	0.580605i
$755$	5.48140			0.199488
$756$			0.430634i			0.0156620i
$757$	−38.0694			−1.38366			−0.691828	−	0.722062i	$-0.743195\pi$
$757$	−38.0694			−1.38366			−0.691828	+	0.722062i	$0.743195\pi$
$758$	30.3941			1.10396
$759$		−	92.8688i		−	3.37092i
$760$			4.68192i			0.169831i
$761$			35.6231i			1.29134i	0.763619	+	0.645668i	$0.223421\pi$
$761$			35.6231i			1.29134i	−0.763619	+	0.645668i	$0.776579\pi$
$762$			14.1532i			0.512717i
$763$	2.14944			0.0778151
$764$	3.10386			0.112294
$765$			5.25388i			0.189955i
$766$	3.65765			0.132156
$767$	48.2053	−	15.0742i	1.74059	−	0.544296i
$768$	9.31663			0.336185
$769$		−	5.26155i		−	0.189736i	−0.995490	−	0.0948681i	$-0.969757\pi$
$769$		−	5.26155i		−	0.189736i	0.995490	−	0.0948681i	$-0.0302429\pi$
$770$	6.77992			0.244331
$771$	−21.0319			−0.757444
$772$			2.37579i			0.0855065i
$773$			41.1018i			1.47833i	0.673525	+	0.739165i	$0.264780\pi$
$773$			41.1018i			1.47833i	−0.673525	+	0.739165i	$0.735220\pi$
$774$			47.5144i			1.70787i
$775$		−	1.48695i		−	0.0534127i
$776$	24.9350			0.895114
$777$	5.56051			0.199482
$778$		−	15.4580i		−	0.554195i
$779$	−1.94499			−0.0696866
$780$	−1.34288	+	0.419929i	−0.0480828	+	0.0150359i
$781$	33.4892			1.19834
$782$			14.1236i			0.505059i
$783$	29.7426			1.06292
$784$	4.27139			0.152550
$785$			20.8873i			0.745498i
$786$		−	71.3095i		−	2.54353i
$787$			7.99614i			0.285032i	0.989793	+	0.142516i	$0.0455192\pi$
$787$			7.99614i			0.285032i	−0.989793	+	0.142516i	$0.954481\pi$
$788$			0.337822i			0.0120344i
$789$	31.9143			1.13618
$790$	17.4866			0.622145
$791$		−	8.99642i		−	0.319876i
$792$	51.5696			1.83245
$793$	13.7787	+	44.0626i	0.489296	+	1.56471i
$794$	−29.7690			−1.05646
$795$		−	2.74756i		−	0.0974459i
$796$	−2.59025			−0.0918090
$797$	−18.2780			−0.647439			−0.323720	−	0.946153i	$-0.604933\pi$
$797$	−18.2780			−0.647439			−0.323720	+	0.946153i	$0.604933\pi$
$798$		−	6.73207i		−	0.238313i
$799$		−	1.56188i		−	0.0552552i
$800$		−	0.826626i		−	0.0292256i
$801$		−	12.6860i		−	0.448237i
$802$	−18.2739			−0.645275
$803$	31.0150			1.09449
$804$			4.49943i			0.158682i
$805$	−7.52949			−0.265380
$806$	−2.34425	−	7.49662i	−0.0825726	−	0.264057i
$807$	3.84892			0.135488
$808$			2.90968i			0.102362i
$809$	−37.3141			−1.31189			−0.655946	−	0.754808i	$-0.727730\pi$
$809$	−37.3141			−1.31189			−0.655946	+	0.754808i	$0.727730\pi$
$810$	−6.55124			−0.230187
$811$			25.5479i			0.897110i	0.893755	+	0.448555i	$0.148061\pi$
$811$			25.5479i			0.897110i	−0.893755	+	0.448555i	$0.851939\pi$
$812$			1.48063i			0.0519599i
$813$		−	50.5026i		−	1.77120i
$814$			14.1450i			0.495781i
$815$	18.6553			0.653468
$816$	−14.5757			−0.510252
$817$		−	13.6259i		−	0.476711i
$818$	15.6299			0.546487
$819$	−14.1212	+	4.41579i	−0.493433	+	0.154300i
$820$	0.165177			0.00576824
$821$			46.1178i			1.60952i	0.593598	+	0.804762i	$0.297707\pi$
$821$			46.1178i			1.60952i	−0.593598	+	0.804762i	$0.702293\pi$
$822$	2.21514			0.0772618
$823$	−8.81111			−0.307136			−0.153568	−	0.988138i	$-0.549076\pi$
$823$	−8.81111			−0.307136			−0.153568	+	0.988138i	$0.549076\pi$
$824$			22.5081i			0.784107i
$825$		−	12.3340i		−	0.429415i
$826$		−	20.5229i		−	0.714083i
$827$		−	29.5559i		−	1.02776i	−0.857862	−	0.513879i	$-0.828208\pi$
$827$		−	29.5559i		−	1.02776i	0.857862	−	0.513879i	$-0.171792\pi$
$828$	4.52387			0.157215
$829$	−9.76643			−0.339202			−0.169601	−	0.985513i	$-0.554248\pi$
$829$	−9.76643			−0.339202			−0.169601	+	0.985513i	$0.554248\pi$
$830$			23.8605i			0.828211i
$831$	−28.6918			−0.995306
$832$	7.88964	+	25.2301i	0.273524	+	0.874697i
$833$	−1.28033			−0.0443609
$834$			33.1264i			1.14707i
$835$	−5.32179			−0.184168
$836$	1.16818			0.0404023
$837$			4.37337i			0.151166i
$838$		−	43.4892i		−	1.50231i
$839$			30.3025i			1.04616i	0.852284	+	0.523080i	$0.175217\pi$
$839$			30.3025i			1.04616i	−0.852284	+	0.523080i	$0.824783\pi$
$840$		−	7.23780i		−	0.249728i
$841$	73.2628			2.52630
$842$	−19.7052			−0.679085
$843$		−	36.7837i		−	1.26690i
$844$	0.911378			0.0313709
$845$	−7.40617	−	10.6840i	−0.254780	−	0.367542i
$846$	−7.33395			−0.252146
$847$			10.4158i			0.357892i
$848$	4.40331			0.151210
$849$	−25.7714			−0.884473
$850$			1.87577i			0.0643384i
$851$		−	15.7088i		−	0.538491i
$852$			2.82398i			0.0967481i
$853$			11.5388i			0.395082i	0.980295	+	0.197541i	$0.0632955\pi$
$853$			11.5388i			0.395082i	−0.980295	+	0.197541i	$0.936705\pi$
$854$	18.7592			0.641926
$855$	−7.07477			−0.241952
$856$		−	34.2028i		−	1.16903i
$857$	30.0981			1.02813			0.514066	−	0.857750i	$-0.328139\pi$
$857$	30.0981			1.02813			0.514066	+	0.857750i	$0.328139\pi$
$858$	−19.4452	−	62.1834i	−0.663848	−	2.12290i
$859$	17.0420			0.581467			0.290733	−	0.956804i	$-0.406101\pi$
$859$	17.0420			0.581467			0.290733	+	0.956804i	$0.406101\pi$
$860$			1.15717i			0.0394593i
$861$	3.00677			0.102470
$862$	−48.4569			−1.65045
$863$		−	15.0579i		−	0.512577i	−0.966600	−	0.256288i	$-0.917500\pi$
$863$		−	15.0579i		−	0.512577i	0.966600	−	0.256288i	$-0.0824997\pi$
$864$			2.43125i			0.0827128i
$865$			10.4086i			0.353903i
$866$			19.7743i			0.671958i
$867$	−40.9402			−1.39040
$868$	−0.217712			−0.00738964
$869$			55.2352i			1.87373i
$870$	39.4869			1.33873
$871$	−39.6776	+	12.4075i	−1.34442	+	0.420412i
$872$	5.83708			0.197668
$873$			37.6788i			1.27523i
$874$	−19.0185			−0.643312
$875$	−1.00000			−0.0338062
$876$			2.61534i			0.0883642i
$877$		−	23.9557i		−	0.808926i	−0.914554	−	0.404463i	$-0.867459\pi$
$877$		−	23.9557i		−	0.808926i	0.914554	−	0.404463i	$-0.132541\pi$
$878$		−	15.9671i		−	0.538862i
$879$			54.2778i			1.83075i
$880$	19.7668			0.666340
$881$	−44.6031			−1.50272			−0.751359	−	0.659894i	$-0.770601\pi$
$881$	−44.6031			−1.50272			−0.751359	+	0.659894i	$0.770601\pi$
$882$			6.01194i			0.202432i
$883$	−53.9903			−1.81692			−0.908459	−	0.417974i	$-0.862740\pi$
$883$	−53.9903			−1.81692			−0.908459	+	0.417974i	$0.862740\pi$
$884$	0.201726	+	0.645094i	0.00678477	+	0.0216969i
$885$	−37.3352			−1.25501
$886$			49.2146i			1.65340i
$887$	−8.51255			−0.285823			−0.142912	−	0.989735i	$-0.545646\pi$
$887$	−8.51255			−0.285823			−0.142912	+	0.989735i	$0.545646\pi$
$888$	15.1002			0.506731
$889$			3.62461i			0.121565i
$890$		−	4.52922i		−	0.151820i
$891$		−	20.6935i		−	0.693258i
$892$			0.779193i			0.0260893i
$893$	2.10319			0.0703806
$894$	−31.4534			−1.05196
$895$			3.51830i			0.117604i
$896$	12.3947			0.414078
$897$	21.5950	+	69.0582i	0.721037	+	2.30579i
$898$	−49.4449			−1.65000
$899$			15.0368i			0.501504i
$900$	0.600821			0.0200274
$901$	−1.31987			−0.0439714
$902$			7.64870i			0.254674i
$903$			21.0644i			0.700978i
$904$		−	24.4309i		−	0.812559i
$905$			15.9978i			0.531786i
$906$	−21.4035			−0.711084
$907$	31.8891			1.05886			0.529431	−	0.848353i	$-0.322406\pi$
$907$	31.8891			1.05886			0.529431	+	0.848353i	$0.322406\pi$
$908$		−	1.89479i		−	0.0628809i
$909$	−4.39677			−0.145832
$910$	−5.04162	+	1.57655i	−0.167128	+	0.0522621i
$911$	−32.7163			−1.08394			−0.541970	−	0.840398i	$-0.682322\pi$
$911$	−32.7163			−1.08394			−0.541970	+	0.840398i	$0.682322\pi$
$912$		−	19.6273i		−	0.649926i
$913$	−75.3686			−2.49434
$914$	−16.5243			−0.546575
$915$		−	34.1267i		−	1.12819i
$916$			3.93750i			0.130099i
$917$		−	18.2622i		−	0.603071i
$918$		−	5.51697i		−	0.182087i
$919$	−34.3802			−1.13410			−0.567050	−	0.823684i	$-0.691915\pi$
$919$	−34.3802			−1.13410			−0.567050	+	0.823684i	$0.691915\pi$
$920$	−20.4472			−0.674126
$921$			15.0999i			0.497558i
$922$	56.9428			1.87531
$923$	−24.9029	+	7.78734i	−0.819691	+	0.256323i
$924$	−1.80589			−0.0594095
$925$		−	2.08630i		−	0.0685973i
$926$	15.9105			0.522852
$927$	−34.0116			−1.11709
$928$			8.35926i			0.274406i
$929$			16.1622i			0.530265i	0.964212	+	0.265132i	$0.0854156\pi$
$929$			16.1622i			0.530265i	−0.964212	+	0.265132i	$0.914584\pi$
$930$			5.80617i			0.190392i
$931$		−	1.72407i		−	0.0565041i
$932$	−0.0942147			−0.00308611
$933$	−69.1459			−2.26373
$934$			45.0498i			1.47407i
$935$	−5.92503			−0.193769
$936$	−38.3477	+	11.9916i	−1.25343	+	0.391958i
$937$	31.0608			1.01471			0.507356	−	0.861737i	$-0.330623\pi$
$937$	31.0608			1.01471			0.507356	+	0.861737i	$0.330623\pi$
$938$			16.8923i			0.551554i
$939$	−45.2663			−1.47721
$940$	−0.178612			−0.00582568
$941$		−	60.4279i		−	1.96989i	−0.172858	−	0.984947i	$-0.555300\pi$
$941$		−	60.4279i		−	1.96989i	0.172858	−	0.984947i	$-0.444700\pi$
$942$		−	81.5597i		−	2.65736i
$943$		−	8.49432i		−	0.276613i
$944$		−	59.8345i		−	1.94745i
$945$	2.94117			0.0956764
$946$	−53.5840			−1.74217
$947$			32.7981i			1.06580i	0.846180	+	0.532898i	$0.178897\pi$
$947$			32.7981i			1.06580i	−0.846180	+	0.532898i	$0.821103\pi$
$948$	−4.65772			−0.151276
$949$	−23.0631	+	7.21199i	−0.748659	+	0.234111i
$950$	−2.52587			−0.0819502
$951$		−	10.0308i		−	0.325270i
$952$	−3.47690			−0.112687
$953$	−11.5855			−0.375290			−0.187645	−	0.982237i	$-0.560085\pi$
$953$	−11.5855			−0.375290			−0.187645	+	0.982237i	$0.560085\pi$
$954$			6.19761i			0.200655i
$955$		−	21.1989i		−	0.685982i
$956$			3.52919i			0.114142i
$957$			124.728i			4.03188i
$958$	46.3846			1.49862
$959$	0.567292			0.0183188
$960$		−	19.5408i		−	0.630678i
$961$	28.7890			0.928677
$962$	−3.28917	−	10.5183i	−0.106047	−	0.339125i
$963$	51.6832			1.66547
$964$			0.114401i			0.00368460i
$965$	16.2263			0.522344
$966$	29.4008			0.945956
$967$			47.3045i			1.52121i	0.649216	+	0.760604i	$0.275097\pi$
$967$			47.3045i			1.52121i	−0.649216	+	0.760604i	$0.724903\pi$
$968$			28.2854i			0.909128i
$969$			5.88322i			0.188996i
$970$			13.4523i			0.431927i
$971$	25.7962			0.827840			0.413920	−	0.910313i	$-0.364159\pi$
$971$	25.7962			0.827840			0.413920	+	0.910313i	$0.364159\pi$
$972$	3.03688			0.0974081
$973$			8.48359i			0.271971i
$974$	11.5622			0.370476
$975$	2.86806	+	9.17170i	0.0918514	+	0.293730i
$976$	54.6924			1.75066
$977$			21.5667i			0.689980i	0.938606	+	0.344990i	$0.112118\pi$
$977$			21.5667i			0.689980i	−0.938606	+	0.344990i	$0.887882\pi$
$978$	−72.8445			−2.32931
$979$	14.3065			0.457238
$980$			0.146416i			0.00467707i
$981$			8.82031i			0.281611i
$982$		−	61.3697i		−	1.95839i
$983$			40.2239i			1.28294i	0.767147	+	0.641472i	$0.221676\pi$
$983$			40.2239i			1.28294i	−0.767147	+	0.641472i	$0.778324\pi$
$984$	8.16525			0.260299
$985$	2.30728			0.0735161
$986$		−	18.9687i		−	0.604088i
$987$	−3.25133			−0.103491
$988$	−0.868670	+	0.271640i	−0.0276361	+	0.00864201i
$989$	59.5081			1.89225
$990$			27.8216i			0.884228i
$991$	−17.2351			−0.547490			−0.273745	−	0.961802i	$-0.588262\pi$
$991$	−17.2351			−0.547490			−0.273745	+	0.961802i	$0.588262\pi$
$992$	−1.22915			−0.0390255
$993$			67.8217i			2.15226i
$994$			10.6022i			0.336280i
$995$			17.6911i			0.560845i
$996$		−	6.35547i		−	0.201381i
$997$	0.332018			0.0105151			0.00525755	−	0.999986i	$-0.498326\pi$
$997$	0.332018			0.0105151			0.00525755	+	0.999986i	$0.498326\pi$
$998$	−1.66018			−0.0525521
$999$			6.13619i			0.194140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	455.2.d.b.246.6	✓	18
13.5	odd	4		5915.2.a.bd.1.3		9
13.8	odd	4		5915.2.a.bc.1.7		9
13.12	even	2	inner	455.2.d.b.246.13	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.d.b.246.6	✓	18	1.1	even	1	trivial
455.2.d.b.246.13	yes	18	13.12	even	2	inner
5915.2.a.bc.1.7		9	13.8	odd	4
5915.2.a.bd.1.3		9	13.5	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:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.46507i q^{2} +2.66524 q^{3} -0.146416 q^{4} +1.00000i q^{5} -3.90476i q^{6} -1.00000i q^{7} -2.71562i q^{8} +4.10353 q^{9} +O(q^{10})\)	\(q-1.46507i q^{2} +2.66524 q^{3} -0.146416 q^{4} +1.00000i q^{5} -3.90476i q^{6} -1.00000i q^{7} -2.71562i q^{8} +4.10353 q^{9} +1.46507 q^{10} +4.62772i q^{11} -0.390233 q^{12} +(-1.07610 - 3.44122i) q^{13} -1.46507 q^{14} +2.66524i q^{15} -4.27139 q^{16} +1.28033 q^{17} -6.01194i q^{18} +1.72407i q^{19} -0.146416i q^{20} -2.66524i q^{21} +6.77992 q^{22} -7.52949 q^{23} -7.23780i q^{24} -1.00000 q^{25} +(-5.04162 + 1.57655i) q^{26} +2.94117 q^{27} +0.146416i q^{28} +10.1125 q^{29} +3.90476 q^{30} +1.48695i q^{31} +0.826626i q^{32} +12.3340i q^{33} -1.87577i q^{34} +1.00000 q^{35} -0.600821 q^{36} +2.08630i q^{37} +2.52587 q^{38} +(-2.86806 - 9.17170i) q^{39} +2.71562 q^{40} +1.12814i q^{41} -3.90476 q^{42} -7.90335 q^{43} -0.677571i q^{44} +4.10353i q^{45} +11.0312i q^{46} -1.21990i q^{47} -11.3843 q^{48} -1.00000 q^{49} +1.46507i q^{50} +3.41240 q^{51} +(0.157557 + 0.503849i) q^{52} -1.03088 q^{53} -4.30901i q^{54} -4.62772 q^{55} -2.71562 q^{56} +4.59507i q^{57} -14.8155i q^{58} +14.0082i q^{59} -0.390233i q^{60} -12.8043 q^{61} +2.17847 q^{62} -4.10353i q^{63} -7.33173 q^{64} +(3.44122 - 1.07610i) q^{65} +18.0701 q^{66} -11.5301i q^{67} -0.187461 q^{68} -20.0679 q^{69} -1.46507i q^{70} -7.23666i q^{71} -11.1436i q^{72} -6.70200i q^{73} +3.05657 q^{74} -2.66524 q^{75} -0.252431i q^{76} +4.62772 q^{77} +(-13.4371 + 4.20189i) q^{78} +11.9357 q^{79} -4.27139i q^{80} -4.47164 q^{81} +1.65280 q^{82} +16.2863i q^{83} +0.390233i q^{84} +1.28033i q^{85} +11.5789i q^{86} +26.9523 q^{87} +12.5671 q^{88} -3.09148i q^{89} +6.01194 q^{90} +(-3.44122 + 1.07610i) q^{91} +1.10243 q^{92} +3.96308i q^{93} -1.78723 q^{94} -1.72407 q^{95} +2.20316i q^{96} +9.18205i q^{97} +1.46507i q^{98} +18.9900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{3} - 24 q^{4} + 26 q^{9}+O(q^{10}) \) 18 * q + 4 * q^3 - 24 * q^4 + 26 * q^9	\( 18 q + 4 q^{3} - 24 q^{4} + 26 q^{9} + 10 q^{12} - 4 q^{13} + 52 q^{16} - 12 q^{17} - 8 q^{22} - 24 q^{23} - 18 q^{25} - 38 q^{26} + 28 q^{27} + 44 q^{29} - 24 q^{30} + 18 q^{35} - 40 q^{36} + 38 q^{38} + 14 q^{39} + 24 q^{42} - 20 q^{43} - 120 q^{48} - 18 q^{49} - 44 q^{51} - 14 q^{52} + 44 q^{53} + 16 q^{55} + 16 q^{61} + 28 q^{62} - 92 q^{64} + 4 q^{65} - 4 q^{66} + 140 q^{68} - 60 q^{69} - 88 q^{74} - 4 q^{75} - 16 q^{77} - 20 q^{78} - 4 q^{79} + 66 q^{81} - 2 q^{82} - 80 q^{87} - 16 q^{88} + 2 q^{90} - 4 q^{91} + 100 q^{92} + 80 q^{94} - 12 q^{95}+O(q^{100}) \) 18 * q + 4 * q^3 - 24 * q^4 + 26 * q^9 + 10 * q^12 - 4 * q^13 + 52 * q^16 - 12 * q^17 - 8 * q^22 - 24 * q^23 - 18 * q^25 - 38 * q^26 + 28 * q^27 + 44 * q^29 - 24 * q^30 + 18 * q^35 - 40 * q^36 + 38 * q^38 + 14 * q^39 + 24 * q^42 - 20 * q^43 - 120 * q^48 - 18 * q^49 - 44 * q^51 - 14 * q^52 + 44 * q^53 + 16 * q^55 + 16 * q^61 + 28 * q^62 - 92 * q^64 + 4 * q^65 - 4 * q^66 + 140 * q^68 - 60 * q^69 - 88 * q^74 - 4 * q^75 - 16 * q^77 - 20 * q^78 - 4 * q^79 + 66 * q^81 - 2 * q^82 - 80 * q^87 - 16 * q^88 + 2 * q^90 - 4 * q^91 + 100 * q^92 + 80 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more