LMFDB - Embedded newform 392.2.e.c.195.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(195,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.195"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.5
Root			$-0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	392.195
Dual form			392.2.e.c.195.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} -2.61313i q^{3} +(-1.00000 - 1.73205i) q^{4} +3.20041 q^{5} +(-3.20041 - 1.84776i) q^{6} -2.82843 q^{8} -3.82843 q^{9} +(2.26303 - 3.91969i) q^{10} -2.00000 q^{11} +(-4.52607 + 2.61313i) q^{12} +5.07517 q^{13} -8.36308i q^{15} +(-2.00000 + 3.46410i) q^{16} +0.317025i q^{17} +(-2.70711 + 4.68885i) q^{18} +4.77791i q^{19} +(-3.20041 - 5.54328i) q^{20} +(-1.41421 + 2.44949i) q^{22} +1.43488i q^{23} +7.39104i q^{24} +5.24264 q^{25} +(3.58869 - 6.21579i) q^{26} +2.16478i q^{27} +9.37769i q^{29} +(-10.2426 - 5.91359i) q^{30} -2.65131 q^{31} +(2.82843 + 4.89898i) q^{32} +5.22625i q^{33} +(0.388275 + 0.224171i) q^{34} +(3.82843 + 6.63103i) q^{36} -2.44949i q^{37} +(5.85172 + 3.37849i) q^{38} -13.2621i q^{39} -9.05213 q^{40} -4.46088i q^{41} -8.82843 q^{43} +(2.00000 + 3.46410i) q^{44} -12.2525 q^{45} +(1.75736 + 1.01461i) q^{46} +5.30262 q^{47} +(9.05213 + 5.22625i) q^{48} +(3.70711 - 6.42090i) q^{50} +0.828427 q^{51} +(-5.07517 - 8.79045i) q^{52} -3.46410i q^{53} +(2.65131 + 1.53073i) q^{54} -6.40083 q^{55} +12.4853 q^{57} +(11.4853 + 6.63103i) q^{58} -2.61313i q^{59} +(-14.4853 + 8.36308i) q^{60} -3.97696 q^{61} +(-1.87476 + 3.24718i) q^{62} +8.00000 q^{64} +16.2426 q^{65} +(6.40083 + 3.69552i) q^{66} +12.0000 q^{67} +(0.549104 - 0.317025i) q^{68} +3.74952 q^{69} +10.8284 q^{72} -1.39942i q^{73} +(-3.00000 - 1.73205i) q^{74} -13.6997i q^{75} +(8.27558 - 4.77791i) q^{76} +(-16.2426 - 9.37769i) q^{78} -11.8272i q^{79} +(-6.40083 + 11.0866i) q^{80} -5.82843 q^{81} +(-5.46345 - 3.15432i) q^{82} +8.47343i q^{83} +1.01461i q^{85} +(-6.24264 + 10.8126i) q^{86} +24.5051 q^{87} +5.65685 q^{88} -9.87285i q^{89} +(-8.66386 + 15.0062i) q^{90} +(2.48528 - 1.43488i) q^{92} +6.92820i q^{93} +(3.74952 - 6.49435i) q^{94} +15.2913i q^{95} +(12.8017 - 7.39104i) q^{96} +3.82683i q^{97} +7.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{18} + 8 q^{25} - 48 q^{30} + 8 q^{36} - 48 q^{43} + 16 q^{44} + 48 q^{46} + 24 q^{50} - 16 q^{51} + 32 q^{57} + 24 q^{58} - 48 q^{60} + 64 q^{64}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^18 + 8 * q^25 - 48 * q^30 + 8 * q^36 - 48 * q^43 + 16 * q^44 + 48 * q^46 + 24 * q^50 - 16 * q^51 + 32 * q^57 + 24 * q^58 - 48 * q^60 + 64 * q^64 + 96 * q^65 + 96 * q^67 + 64 * q^72 - 24 * q^74 - 96 * q^78 - 24 * q^81 - 16 * q^86 - 48 * q^92 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$3$		−	2.61313i		−	1.50869i	−0.656479	−	0.754344i	$-0.727955\pi$
$3$		−	2.61313i		−	1.50869i	0.656479	−	0.754344i	$-0.272045\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	3.20041			1.43127			0.715634	−	0.698475i	$-0.246138\pi$
$5$	3.20041			1.43127			0.715634	+	0.698475i	$0.246138\pi$
$6$	−3.20041	−	1.84776i	−1.30656	−	0.754344i
$7$		0			0
$7$		0			0
$8$	−2.82843			−1.00000
$9$	−3.82843			−1.27614
$10$	2.26303	−	3.91969i	0.715634	−	1.23951i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	−4.52607	+	2.61313i	−1.30656	+	0.754344i
$13$	5.07517			1.40760			0.703800	−	0.710399i	$-0.251485\pi$
$13$	5.07517			1.40760			0.703800	+	0.710399i	$0.251485\pi$
$14$		0			0
$15$		−	8.36308i		−	2.15934i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$			0.317025i			0.0768899i	0.999261	+	0.0384450i	$0.0122404\pi$
$17$			0.317025i			0.0768899i	−0.999261	+	0.0384450i	$0.987760\pi$
$18$	−2.70711	+	4.68885i	−0.638071	+	1.10517i
$19$			4.77791i			1.09613i	0.836436	+	0.548064i	$0.184635\pi$
$19$			4.77791i			1.09613i	−0.836436	+	0.548064i	$0.815365\pi$
$20$	−3.20041	−	5.54328i	−0.715634	−	1.23951i
$21$		0			0
$22$	−1.41421	+	2.44949i	−0.301511	+	0.522233i
$23$			1.43488i			0.299193i	0.988747	+	0.149596i	$0.0477974\pi$
$23$			1.43488i			0.299193i	−0.988747	+	0.149596i	$0.952203\pi$
$24$			7.39104i			1.50869i
$25$	5.24264			1.04853
$26$	3.58869	−	6.21579i	0.703800	−	1.21902i
$27$			2.16478i			0.416613i
$28$		0			0
$29$			9.37769i			1.74139i	0.491820	+	0.870697i	$0.336332\pi$
$29$			9.37769i			1.74139i	−0.491820	+	0.870697i	$0.663668\pi$
$30$	−10.2426	−	5.91359i	−1.87004	−	1.07967i
$31$	−2.65131			−0.476189			−0.238095	−	0.971242i	$-0.576523\pi$
$31$	−2.65131			−0.476189			−0.238095	+	0.971242i	$0.576523\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$			5.22625i			0.909774i
$34$	0.388275	+	0.224171i	0.0665886	+	0.0384450i
$35$		0			0
$36$	3.82843	+	6.63103i	0.638071	+	1.10517i
$37$		−	2.44949i		−	0.402694i	−0.979520	−	0.201347i	$-0.935468\pi$
$37$		−	2.44949i		−	0.402694i	0.979520	−	0.201347i	$-0.0645318\pi$
$38$	5.85172	+	3.37849i	0.949275	+	0.548064i
$39$		−	13.2621i		−	2.12363i
$40$	−9.05213			−1.43127
$41$		−	4.46088i		−	0.696673i	−0.937370	−	0.348337i	$-0.886747\pi$
$41$		−	4.46088i		−	0.696673i	0.937370	−	0.348337i	$-0.113253\pi$
$42$		0			0
$43$	−8.82843			−1.34632			−0.673161	−	0.739496i	$-0.735064\pi$
$43$	−8.82843			−1.34632			−0.673161	+	0.739496i	$0.735064\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	−12.2525			−1.82650
$46$	1.75736	+	1.01461i	0.259108	+	0.149596i
$47$	5.30262			0.773466			0.386733	−	0.922192i	$-0.373603\pi$
$47$	5.30262			0.773466			0.386733	+	0.922192i	$0.373603\pi$
$48$	9.05213	+	5.22625i	1.30656	+	0.754344i
$49$		0			0
$50$	3.70711	−	6.42090i	0.524264	−	0.908052i
$51$	0.828427			0.116003
$52$	−5.07517	−	8.79045i	−0.703800	−	1.21902i
$53$		−	3.46410i		−	0.475831i	−0.971286	−	0.237915i	$-0.923536\pi$
$53$		−	3.46410i		−	0.475831i	0.971286	−	0.237915i	$-0.0764641\pi$
$54$	2.65131	+	1.53073i	0.360797	+	0.208306i
$55$	−6.40083			−0.863087
$56$		0			0
$57$	12.4853			1.65372
$58$	11.4853	+	6.63103i	1.50809	+	0.870697i
$59$		−	2.61313i		−	0.340200i	−0.985427	−	0.170100i	$-0.945591\pi$
$59$		−	2.61313i		−	0.340200i	0.985427	−	0.170100i	$-0.0544091\pi$
$60$	−14.4853	+	8.36308i	−1.87004	+	1.07967i
$61$	−3.97696			−0.509198			−0.254599	−	0.967047i	$-0.581943\pi$
$61$	−3.97696			−0.509198			−0.254599	+	0.967047i	$0.581943\pi$
$62$	−1.87476	+	3.24718i	−0.238095	+	0.412392i
$63$		0			0
$64$	8.00000			1.00000
$65$	16.2426			2.01465
$66$	6.40083	+	3.69552i	0.787887	+	0.454887i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	0.549104	−	0.317025i	0.0665886	−	0.0384450i
$69$	3.74952			0.451389
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	10.8284			1.27614
$73$		−	1.39942i		−	0.163789i	−0.996641	−	0.0818947i	$-0.973903\pi$
$73$		−	1.39942i		−	0.163789i	0.996641	−	0.0818947i	$-0.0260971\pi$
$74$	−3.00000	−	1.73205i	−0.348743	−	0.201347i
$75$		−	13.6997i		−	1.58190i
$76$	8.27558	−	4.77791i	0.949275	−	0.548064i
$77$		0			0
$78$	−16.2426	−	9.37769i	−1.83912	−	1.06181i
$79$		−	11.8272i		−	1.33066i	−0.746548	−	0.665331i	$-0.768290\pi$
$79$		−	11.8272i		−	1.33066i	0.746548	−	0.665331i	$-0.231710\pi$
$80$	−6.40083	+	11.0866i	−0.715634	+	1.23951i
$81$	−5.82843			−0.647603
$82$	−5.46345	−	3.15432i	−0.603337	−	0.348337i
$83$			8.47343i			0.930080i	0.885290	+	0.465040i	$0.153960\pi$
$83$			8.47343i			0.930080i	−0.885290	+	0.465040i	$0.846040\pi$
$84$		0			0
$85$			1.01461i			0.110050i
$86$	−6.24264	+	10.8126i	−0.673161	+	1.16595i
$87$	24.5051			2.62722
$88$	5.65685			0.603023
$89$		−	9.87285i		−	1.04652i	−0.852173	−	0.523260i	$-0.824716\pi$
$89$		−	9.87285i		−	1.04652i	0.852173	−	0.523260i	$-0.175284\pi$
$90$	−8.66386	+	15.0062i	−0.913251	+	1.58180i
$91$		0			0
$92$	2.48528	−	1.43488i	0.259108	−	0.149596i
$93$			6.92820i			0.718421i
$94$	3.74952	−	6.49435i	0.386733	−	0.669841i
$95$			15.2913i			1.56885i
$96$	12.8017	−	7.39104i	1.30656	−	0.754344i
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$	7.65685			0.769543
$100$	−5.24264	−	9.08052i	−0.524264	−	0.908052i
$101$	−7.72648			−0.768813			−0.384407	−	0.923164i	$-0.625594\pi$
$101$	−7.72648			−0.768813			−0.384407	+	0.923164i	$0.625594\pi$
$102$	0.585786	−	1.01461i	0.0580015	−	0.100462i
$103$	15.4530			1.52263			0.761313	−	0.648385i	$-0.224555\pi$
$103$	15.4530			1.52263			0.761313	+	0.648385i	$0.224555\pi$
$104$	−14.3548			−1.40760
$105$		0			0
$106$	−4.24264	−	2.44949i	−0.412082	−	0.237915i
$107$	−8.48528			−0.820303			−0.410152	−	0.912017i	$-0.634524\pi$
$107$	−8.48528			−0.820303			−0.410152	+	0.912017i	$0.634524\pi$
$108$	3.74952	−	2.16478i	0.360797	−	0.208306i
$109$			0.420266i			0.0402542i	0.999797	+	0.0201271i	$0.00640708\pi$
$109$			0.420266i			0.0402542i	−0.999797	+	0.0201271i	$0.993593\pi$
$110$	−4.52607	+	7.83938i	−0.431544	+	0.747455i
$111$	−6.40083			−0.607539
$112$		0			0
$113$	−16.4853			−1.55080			−0.775402	−	0.631467i	$-0.782453\pi$
$113$	−16.4853			−1.55080			−0.775402	+	0.631467i	$0.782453\pi$
$114$	8.82843	−	15.2913i	0.826858	−	1.43216i
$115$			4.59220i			0.428225i
$116$	16.2426	−	9.37769i	1.50809	−	0.870697i
$117$	−19.4299			−1.79630
$118$	−3.20041	−	1.84776i	−0.294622	−	0.170100i
$119$		0			0
$120$			23.6544i			2.15934i
$121$	−7.00000			−0.636364
$122$	−2.81214	+	4.87076i	−0.254599	+	0.440978i
$123$	−11.6569			−1.05106
$124$	2.65131	+	4.59220i	0.238095	+	0.412392i
$125$	0.776550			0.0694568
$126$		0			0
$127$		−	5.49333i		−	0.487454i	−0.969844	−	0.243727i	$-0.921630\pi$
$127$		−	5.49333i		−	0.487454i	0.969844	−	0.243727i	$-0.0783701\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$			23.0698i			2.03118i
$130$	11.4853	−	19.8931i	1.00733	−	1.74474i
$131$		−	3.50981i		−	0.306653i	−0.988176	−	0.153327i	$-0.951001\pi$
$131$		−	3.50981i		−	0.306653i	0.988176	−	0.153327i	$-0.0489987\pi$
$132$	9.05213	−	5.22625i	0.787887	−	0.454887i
$133$		0			0
$134$	8.48528	−	14.6969i	0.733017	−	1.26962i
$135$			6.92820i			0.596285i
$136$		−	0.896683i		−	0.0768899i
$137$	0.242641			0.0207302			0.0103651	−	0.999946i	$-0.496701\pi$
$137$	0.242641			0.0207302			0.0103651	+	0.999946i	$0.496701\pi$
$138$	2.65131	−	4.59220i	0.225694	−	0.390914i
$139$			5.04054i			0.427533i	0.976885	+	0.213767i	$0.0685732\pi$
$139$			5.04054i			0.427533i	−0.976885	+	0.213767i	$0.931427\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	−10.1503			−0.848814
$144$	7.65685	−	13.2621i	0.638071	−	1.10517i
$145$			30.0125i			2.49240i
$146$	−1.71393	−	0.989538i	−0.141846	−	0.0818947i
$147$		0			0
$148$	−4.24264	+	2.44949i	−0.348743	+	0.201347i
$149$			20.1903i			1.65405i	0.562165	+	0.827025i	$0.309969\pi$
$149$			20.1903i			1.65405i	−0.562165	+	0.827025i	$0.690031\pi$
$150$	−16.7786	−	9.68714i	−1.36997	−	0.790951i
$151$			15.2913i			1.24439i	0.782863	+	0.622194i	$0.213758\pi$
$151$			15.2913i			1.24439i	−0.782863	+	0.622194i	$0.786242\pi$
$152$		−	13.5140i		−	1.09613i
$153$		−	1.21371i		−	0.0981225i
$154$		0			0
$155$	−8.48528			−0.681554
$156$	−22.9706	+	13.2621i	−1.83912	+	1.06181i
$157$	23.9560			1.91190			0.955948	−	0.293536i	$-0.0948321\pi$
$157$	23.9560			1.91190			0.955948	+	0.293536i	$0.0948321\pi$
$158$	−14.4853	−	8.36308i	−1.15239	−	0.665331i
$159$	−9.05213			−0.717881
$160$	9.05213	+	15.6788i	0.715634	+	1.23951i
$161$		0			0
$162$	−4.12132	+	7.13834i	−0.323802	+	0.560841i
$163$	8.14214			0.637741			0.318871	−	0.947798i	$-0.396696\pi$
$163$	8.14214			0.637741			0.318871	+	0.947798i	$0.396696\pi$
$164$	−7.72648	+	4.46088i	−0.603337	+	0.348337i
$165$			16.7262i			1.30213i
$166$	10.3778	+	5.99162i	0.805473	+	0.465040i
$167$	14.3548			1.11080			0.555402	−	0.831582i	$-0.312564\pi$
$167$	14.3548			1.11080			0.555402	+	0.831582i	$0.312564\pi$
$168$		0			0
$169$	12.7574			0.981335
$170$	1.24264	+	0.717439i	0.0953062	+	0.0550251i
$171$		−	18.2919i		−	1.39882i
$172$	8.82843	+	15.2913i	0.673161	+	1.16595i
$173$	−6.94993			−0.528393			−0.264197	−	0.964469i	$-0.585107\pi$
$173$	−6.94993			−0.528393			−0.264197	+	0.964469i	$0.585107\pi$
$174$	17.3277	−	30.0125i	1.31361	−	2.27524i
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	−6.82843			−0.513256
$178$	−12.0917	−	6.98116i	−0.906313	−	0.523260i
$179$	−20.4853			−1.53114			−0.765571	−	0.643352i	$-0.777543\pi$
$179$	−20.4853			−1.53114			−0.765571	+	0.643352i	$0.777543\pi$
$180$	12.2525	+	21.2220i	0.913251	+	1.58180i
$181$	2.10220			0.156256			0.0781278	−	0.996943i	$-0.475106\pi$
$181$	2.10220			0.156256			0.0781278	+	0.996943i	$0.475106\pi$
$182$		0			0
$183$			10.3923i			0.768221i
$184$		−	4.05845i		−	0.299193i
$185$		−	7.83938i		−	0.576363i
$186$	8.48528	+	4.89898i	0.622171	+	0.359211i
$187$		−	0.634051i		−	0.0463664i
$188$	−5.30262	−	9.18440i	−0.386733	−	0.669841i
$189$		0			0
$190$	18.7279	+	10.8126i	1.35867	+	0.784426i
$191$		−	11.8272i		−	0.855785i	−0.903830	−	0.427892i	$-0.859256\pi$
$191$		−	11.8272i		−	0.855785i	0.903830	−	0.427892i	$-0.140744\pi$
$192$		−	20.9050i		−	1.50869i
$193$	−14.1421			−1.01797			−0.508987	−	0.860774i	$-0.669980\pi$
$193$	−14.1421			−1.01797			−0.508987	+	0.860774i	$0.669980\pi$
$194$	4.68690	+	2.70598i	0.336500	+	0.194278i
$195$		−	42.4441i		−	3.03948i
$196$		0			0
$197$			26.5241i			1.88977i	0.327409	+	0.944883i	$0.393824\pi$
$197$			26.5241i			1.88977i	−0.327409	+	0.944883i	$0.606176\pi$
$198$	5.41421	−	9.37769i	0.384771	−	0.666444i
$199$	−2.65131			−0.187946			−0.0939731	−	0.995575i	$-0.529957\pi$
$199$	−2.65131			−0.187946			−0.0939731	+	0.995575i	$0.529957\pi$
$200$	−14.8284			−1.04853
$201$		−	31.3575i		−	2.21179i
$202$	−5.46345	+	9.46297i	−0.384407	+	0.665812i
$203$		0			0
$204$	−0.828427	−	1.43488i	−0.0580015	−	0.100462i
$205$		−	14.2767i		−	0.997126i
$206$	10.9269	−	18.9259i	0.761313	−	1.31863i
$207$		−	5.49333i		−	0.381813i
$208$	−10.1503	+	17.5809i	−0.703800	+	1.21902i
$209$		−	9.55582i		−	0.660990i
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$	−6.00000	+	3.46410i	−0.412082	+	0.237915i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−28.2546			−1.92695
$216$		−	6.12293i		−	0.416613i
$217$		0			0
$218$	0.514719	+	0.297173i	0.0348611	+	0.0201271i
$219$	−3.65685			−0.247107
$220$	6.40083	+	11.0866i	0.431544	+	0.747455i
$221$			1.60896i			0.108230i
$222$	−4.52607	+	7.83938i	−0.303770	+	0.526145i
$223$	−24.5051			−1.64098			−0.820491	−	0.571659i	$-0.806300\pi$
$223$	−24.5051			−1.64098			−0.820491	+	0.571659i	$0.806300\pi$
$224$		0			0
$225$	−20.0711			−1.33807
$226$	−11.6569	+	20.1903i	−0.775402	+	1.34304i
$227$			23.2555i			1.54352i	0.635913	+	0.771761i	$0.280624\pi$
$227$			23.2555i			1.54352i	−0.635913	+	0.771761i	$0.719376\pi$
$228$	−12.4853	−	21.6251i	−0.826858	−	1.43216i
$229$	17.5552			1.16008			0.580039	−	0.814589i	$-0.303037\pi$
$229$	17.5552			1.16008			0.580039	+	0.814589i	$0.303037\pi$
$230$	5.62427	+	3.24718i	0.370854	+	0.214112i
$231$		0			0
$232$		−	26.5241i		−	1.74139i
$233$	−20.2426			−1.32614			−0.663070	−	0.748558i	$-0.730747\pi$
$233$	−20.2426			−1.32614			−0.663070	+	0.748558i	$0.730747\pi$
$234$	−13.7390	+	23.7967i	−0.898148	+	1.55564i
$235$	16.9706			1.10704
$236$	−4.52607	+	2.61313i	−0.294622	+	0.170100i
$237$	−30.9059			−2.00756
$238$		0			0
$239$			13.2621i			0.857851i	0.903340	+	0.428926i	$0.141108\pi$
$239$			13.2621i			0.857851i	−0.903340	+	0.428926i	$0.858892\pi$
$240$	28.9706	+	16.7262i	1.87004	+	1.07967i
$241$		−	22.1187i		−	1.42479i	−0.701778	−	0.712396i	$-0.747610\pi$
$241$		−	22.1187i		−	1.42479i	0.701778	−	0.712396i	$-0.252390\pi$
$242$	−4.94975	+	8.57321i	−0.318182	+	0.551107i
$243$			21.7248i			1.39364i
$244$	3.97696	+	6.88830i	0.254599	+	0.440978i
$245$		0			0
$246$	−8.24264	+	14.2767i	−0.525532	+	0.910247i
$247$			24.2487i			1.54291i
$248$	7.49903			0.476189
$249$	22.1421			1.40320
$250$	0.549104	−	0.951076i	0.0347284	−	0.0601513i
$251$			19.1886i			1.21117i	0.795780	+	0.605586i	$0.207061\pi$
$251$			19.1886i			1.21117i	−0.795780	+	0.605586i	$0.792939\pi$
$252$		0			0
$253$		−	2.86976i		−	0.180420i
$254$	−6.72792	−	3.88437i	−0.422147	−	0.243727i
$255$	2.65131			0.166031
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		−	8.15640i		−	0.508782i	−0.967101	−	0.254391i	$-0.918125\pi$
$257$		−	8.15640i		−	0.508782i	0.967101	−	0.254391i	$-0.0818751\pi$
$258$	28.2546	+	16.3128i	1.75906	+	1.01559i
$259$		0			0
$260$	−16.2426	−	28.1331i	−1.00733	−	1.74474i
$261$		−	35.9018i		−	2.22227i
$262$	−4.29862	−	2.48181i	−0.265570	−	0.153327i
$263$		−	8.95743i		−	0.552339i	−0.961109	−	0.276169i	$-0.910935\pi$
$263$		−	8.95743i		−	0.552339i	0.961109	−	0.276169i	$-0.0890651\pi$
$264$		−	14.7821i		−	0.909774i
$265$		−	11.0866i		−	0.681042i
$266$		0			0
$267$	−25.7990			−1.57887
$268$	−12.0000	−	20.7846i	−0.733017	−	1.26962i
$269$	2.42386			0.147785			0.0738927	−	0.997266i	$-0.476458\pi$
$269$	2.42386			0.147785			0.0738927	+	0.997266i	$0.476458\pi$
$270$	8.48528	+	4.89898i	0.516398	+	0.298142i
$271$	−13.2565			−0.805278			−0.402639	−	0.915359i	$-0.631907\pi$
$271$	−13.2565			−0.805278			−0.402639	+	0.915359i	$0.631907\pi$
$272$	−1.09821	−	0.634051i	−0.0665886	−	0.0384450i
$273$		0			0
$274$	0.171573	−	0.297173i	0.0103651	−	0.0179529i
$275$	−10.4853			−0.632286
$276$	−3.74952	−	6.49435i	−0.225694	−	0.390914i
$277$		−	16.7262i		−	1.00498i	−0.864584	−	0.502489i	$-0.832418\pi$
$277$		−	16.7262i		−	1.00498i	0.864584	−	0.502489i	$-0.167582\pi$
$278$	6.17338	+	3.56420i	0.370255	+	0.213767i
$279$	10.1503			0.607685
$280$		0			0
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$	−16.9706	−	9.79796i	−1.01058	−	0.583460i
$283$		−	0.185709i		−	0.0110393i	−0.999985	−	0.00551963i	$-0.998243\pi$
$283$		−	0.185709i		−	0.0110393i	0.999985	−	0.00551963i	$-0.00175696\pi$
$284$		0			0
$285$	39.9581			2.36691
$286$	−7.17738	+	12.4316i	−0.424407	+	0.735095i
$287$		0			0
$288$	−10.8284	−	18.7554i	−0.638071	−	1.10517i
$289$	16.8995			0.994088
$290$	36.7576	+	21.2220i	2.15848	+	1.24620i
$291$	10.0000			0.586210
$292$	−2.42386	+	1.39942i	−0.141846	+	0.0818947i
$293$	−5.07517			−0.296495			−0.148247	−	0.988950i	$-0.547363\pi$
$293$	−5.07517			−0.296495			−0.148247	+	0.988950i	$0.547363\pi$
$294$		0			0
$295$		−	8.36308i		−	0.486917i
$296$			6.92820i			0.402694i
$297$		−	4.32957i		−	0.251227i
$298$	24.7279	+	14.2767i	1.43245	+	0.827025i
$299$			7.28225i			0.421143i
$300$	−23.7285	+	13.6997i	−1.36997	+	0.790951i
$301$		0			0
$302$	18.7279	+	10.8126i	1.07767	+	0.622194i
$303$			20.1903i			1.15990i
$304$	−16.5512	−	9.55582i	−0.949275	−	0.548064i
$305$	−12.7279			−0.728799
$306$	−1.48648	−	0.858221i	−0.0849766	−	0.0490613i
$307$			6.04601i			0.345064i	0.985004	+	0.172532i	$0.0551948\pi$
$307$			6.04601i			0.345064i	−0.985004	+	0.172532i	$0.944805\pi$
$308$		0			0
$309$		−	40.3805i		−	2.29717i
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−27.1564			−1.53990			−0.769949	−	0.638105i	$-0.779718\pi$
$311$	−27.1564			−1.53990			−0.769949	+	0.638105i	$0.779718\pi$
$312$			37.5108i			2.12363i
$313$		−	10.5838i		−	0.598233i	−0.954217	−	0.299116i	$-0.903308\pi$
$313$		−	10.5838i		−	0.598233i	0.954217	−	0.299116i	$-0.0966919\pi$
$314$	16.9394	−	29.3400i	0.955948	−	1.65575i
$315$		0			0
$316$	−20.4853	+	11.8272i	−1.15239	+	0.665331i
$317$		−	4.05845i		−	0.227945i	−0.993484	−	0.113973i	$-0.963642\pi$
$317$		−	4.05845i		−	0.227945i	0.993484	−	0.113973i	$-0.0363576\pi$
$318$	−6.40083	+	11.0866i	−0.358940	+	0.621703i
$319$		−	18.7554i		−	1.05010i
$320$	25.6033			1.43127
$321$			22.1731i			1.23758i
$322$		0			0
$323$	−1.51472			−0.0842812
$324$	5.82843	+	10.0951i	0.323802	+	0.560841i
$325$	26.6073			1.47591
$326$	5.75736	−	9.97204i	0.318871	−	0.552300i
$327$	1.09821			0.0607310
$328$			12.6173i			0.696673i
$329$		0			0
$330$	20.4853	+	11.8272i	1.12768	+	0.651065i
$331$	20.8284			1.14483			0.572417	−	0.819963i	$-0.306006\pi$
$331$	20.8284			1.14483			0.572417	+	0.819963i	$0.306006\pi$
$332$	14.6764	−	8.47343i	0.805473	−	0.465040i
$333$			9.37769i			0.513894i
$334$	10.1503	−	17.5809i	0.555402	−	0.961984i
$335$	38.4050			2.09829
$336$		0			0
$337$	4.24264			0.231111			0.115556	−	0.993301i	$-0.463135\pi$
$337$	4.24264			0.231111			0.115556	+	0.993301i	$0.463135\pi$
$338$	9.02082	−	15.6245i	0.490668	−	0.849861i
$339$			43.0781i			2.33968i
$340$	1.75736	−	1.01461i	0.0953062	−	0.0550251i
$341$	5.30262			0.287153
$342$	−22.4029	−	12.9343i	−1.21141	−	0.699408i
$343$		0			0
$344$	24.9706			1.34632
$345$	12.0000			0.646058
$346$	−4.91434	+	8.51189i	−0.264197	+	0.457602i
$347$	6.97056			0.374199			0.187100	−	0.982341i	$-0.440091\pi$
$347$	6.97056			0.374199			0.187100	+	0.982341i	$0.440091\pi$
$348$	−24.5051	−	42.4441i	−1.31361	−	2.27524i
$349$	22.4029			1.19920			0.599600	−	0.800300i	$-0.295327\pi$
$349$	22.4029			1.19920			0.599600	+	0.800300i	$0.295327\pi$
$350$		0			0
$351$			10.9867i			0.586424i
$352$	−5.65685	−	9.79796i	−0.301511	−	0.522233i
$353$		−	13.1200i		−	0.698308i	−0.937065	−	0.349154i	$-0.886469\pi$
$353$		−	13.1200i		−	0.698308i	0.937065	−	0.349154i	$-0.113531\pi$
$354$	−4.82843	+	8.36308i	−0.256628	+	0.444493i
$355$		0			0
$356$	−17.1003	+	9.87285i	−0.906313	+	0.523260i
$357$		0			0
$358$	−14.4853	+	25.0892i	−0.765571	+	1.32601i
$359$		−	17.3205i		−	0.914141i	−0.889430	−	0.457071i	$-0.848899\pi$
$359$		−	17.3205i		−	0.914141i	0.889430	−	0.457071i	$-0.151101\pi$
$360$	34.6554			1.82650
$361$	−3.82843			−0.201496
$362$	1.48648	−	2.57466i	0.0781278	−	0.135321i
$363$			18.2919i			0.960075i
$364$		0			0
$365$		−	4.47871i		−	0.234427i
$366$	12.7279	+	7.34847i	0.665299	+	0.384111i
$367$	−17.0061			−0.887709			−0.443855	−	0.896099i	$-0.646389\pi$
$367$	−17.0061			−0.887709			−0.443855	+	0.896099i	$0.646389\pi$
$368$	−4.97056	−	2.86976i	−0.259108	−	0.149596i
$369$			17.0782i			0.889054i
$370$	−9.60124	−	5.54328i	−0.499145	−	0.288181i
$371$		0			0
$372$	12.0000	−	6.92820i	0.622171	−	0.359211i
$373$			9.20361i			0.476545i	0.971198	+	0.238273i	$0.0765811\pi$
$373$			9.20361i			0.476545i	−0.971198	+	0.238273i	$0.923419\pi$
$374$	−0.776550	−	0.448342i	−0.0401545	−	0.0231832i
$375$		−	2.02922i		−	0.104789i
$376$	−14.9981			−0.773466
$377$			47.5934i			2.45118i
$378$		0			0
$379$	17.3137			0.889345			0.444673	−	0.895693i	$-0.353320\pi$
$379$	17.3137			0.889345			0.444673	+	0.895693i	$0.353320\pi$
$380$	26.4853	−	15.2913i	1.35867	−	0.784426i
$381$	−14.3548			−0.735416
$382$	−14.4853	−	8.36308i	−0.741131	−	0.427892i
$383$	5.30262			0.270951			0.135476	−	0.990781i	$-0.456744\pi$
$383$	5.30262			0.270951			0.135476	+	0.990781i	$0.456744\pi$
$384$	−25.6033	−	14.7821i	−1.30656	−	0.754344i
$385$		0			0
$386$	−10.0000	+	17.3205i	−0.508987	+	0.881591i
$387$	33.7990			1.71810
$388$	6.62827	−	3.82683i	0.336500	−	0.194278i
$389$			3.63818i			0.184463i	0.995738	+	0.0922316i	$0.0294000\pi$
$389$			3.63818i			0.184463i	−0.995738	+	0.0922316i	$0.970600\pi$
$390$	−51.9832	−	30.0125i	−2.63227	−	1.51974i
$391$	−0.454893			−0.0230049
$392$		0			0
$393$	−9.17157			−0.462645
$394$	32.4853	+	18.7554i	1.63658	+	0.944883i
$395$		−	37.8519i		−	1.90453i
$396$	−7.65685	−	13.2621i	−0.384771	−	0.666444i
$397$	−24.2776			−1.21846			−0.609230	−	0.792994i	$-0.708521\pi$
$397$	−24.2776			−1.21846			−0.609230	+	0.792994i	$0.708521\pi$
$398$	−1.87476	+	3.24718i	−0.0939731	+	0.162766i
$399$		0			0
$400$	−10.4853	+	18.1610i	−0.524264	+	0.908052i
$401$	7.75736			0.387384			0.193692	−	0.981062i	$-0.437954\pi$
$401$	7.75736			0.387384			0.193692	+	0.981062i	$0.437954\pi$
$402$	−38.4050	−	22.1731i	−1.91546	−	1.10589i
$403$	−13.4558			−0.670283
$404$	7.72648	+	13.3827i	0.384407	+	0.665812i
$405$	−18.6534			−0.926893
$406$		0			0
$407$			4.89898i			0.242833i
$408$	−2.34315			−0.116003
$409$		−	3.82683i		−	0.189225i	−0.995514	−	0.0946124i	$-0.969839\pi$
$409$		−	3.82683i		−	0.189225i	0.995514	−	0.0946124i	$-0.0301612\pi$
$410$	−17.4853	−	10.0951i	−0.863536	−	0.498563i
$411$		−	0.634051i		−	0.0312754i
$412$	−15.4530	−	26.7653i	−0.761313	−	1.31863i
$413$		0			0
$414$	−6.72792	−	3.88437i	−0.330659	−	0.190906i
$415$			27.1185i			1.33119i
$416$	14.3548	+	24.8632i	0.703800	+	1.21902i
$417$	13.1716			0.645015
$418$	−11.7034	−	6.75699i	−0.572434	−	0.330495i
$419$		−	39.8309i		−	1.94587i	−0.231082	−	0.972934i	$-0.574226\pi$
$419$		−	39.8309i		−	1.94587i	0.231082	−	0.972934i	$-0.425774\pi$
$420$		0			0
$421$		−	26.5241i		−	1.29271i	−0.763038	−	0.646353i	$-0.776293\pi$
$421$		−	26.5241i		−	1.29271i	0.763038	−	0.646353i	$-0.223707\pi$
$422$	14.4853	−	25.0892i	0.705132	−	1.22133i
$423$	−20.3007			−0.987053
$424$			9.79796i			0.475831i
$425$			1.66205i			0.0806213i
$426$		0			0
$427$		0			0
$428$	8.48528	+	14.6969i	0.410152	+	0.710403i
$429$			26.5241i			1.28060i
$430$	−19.9790	+	34.6047i	−0.963474	+	1.66879i
$431$			7.52255i			0.362348i	0.983451	+	0.181174i	$0.0579898\pi$
$431$			7.52255i			0.362348i	−0.983451	+	0.181174i	$0.942010\pi$
$432$	−7.49903	−	4.32957i	−0.360797	−	0.208306i
$433$		−	5.17186i		−	0.248544i	−0.992248	−	0.124272i	$-0.960341\pi$
$433$		−	5.17186i		−	0.248544i	0.992248	−	0.124272i	$-0.0396595\pi$
$434$		0			0
$435$	78.4264			3.76026
$436$	0.727922	−	0.420266i	0.0348611	−	0.0201271i
$437$	−6.85572			−0.327953
$438$	−2.58579	+	4.47871i	−0.123554	+	0.214001i
$439$	35.7536			1.70643			0.853214	−	0.521561i	$-0.174650\pi$
$439$	35.7536			1.70643			0.853214	+	0.521561i	$0.174650\pi$
$440$	18.1043			0.863087
$441$		0			0
$442$	1.97056	+	1.13770i	0.0937301	+	0.0541151i
$443$	−28.2843			−1.34383			−0.671913	−	0.740630i	$-0.734527\pi$
$443$	−28.2843			−1.34383			−0.671913	+	0.740630i	$0.734527\pi$
$444$	6.40083	+	11.0866i	0.303770	+	0.526145i
$445$		−	31.5972i		−	1.49785i
$446$	−17.3277	+	30.0125i	−0.820491	+	1.42113i
$447$	52.7597			2.49545
$448$		0			0
$449$	−5.65685			−0.266963			−0.133482	−	0.991051i	$-0.542616\pi$
$449$	−5.65685			−0.266963			−0.133482	+	0.991051i	$0.542616\pi$
$450$	−14.1924	+	24.5819i	−0.669036	+	1.15880i
$451$			8.92177i			0.420110i
$452$	16.4853	+	28.5533i	0.775402	+	1.34304i
$453$	39.9581			1.87739
$454$	28.4821	+	16.4441i	1.33673	+	0.771761i
$455$		0			0
$456$	−35.3137			−1.65372
$457$	−21.1716			−0.990364			−0.495182	−	0.868789i	$-0.664899\pi$
$457$	−21.1716			−0.990364			−0.495182	+	0.868789i	$0.664899\pi$
$458$	12.4134	−	21.5006i	0.580039	−	1.00466i
$459$	−0.686292			−0.0320333
$460$	7.95393	−	4.59220i	0.370854	−	0.214112i
$461$	26.6073			1.23923			0.619613	−	0.784908i	$-0.287290\pi$
$461$	26.6073			1.23923			0.619613	+	0.784908i	$0.287290\pi$
$462$		0			0
$463$			18.7554i			0.871637i	0.900035	+	0.435818i	$0.143541\pi$
$463$			18.7554i			0.871637i	−0.900035	+	0.435818i	$0.856459\pi$
$464$	−32.4853	−	18.7554i	−1.50809	−	0.870697i
$465$			22.1731i			1.02825i
$466$	−14.3137	+	24.7921i	−0.663070	+	1.14847i
$467$		−	0.0769232i		−	0.00355958i	−0.999998	−	0.00177979i	$-0.999433\pi$
$467$		−	0.0769232i		−	0.00355958i	0.999998	−	0.00177979i	$-0.000566526\pi$
$468$	19.4299	+	33.6536i	0.898148	+	1.55564i
$469$		0			0
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$		−	62.6000i		−	2.88446i
$472$			7.39104i			0.340200i
$473$	17.6569			0.811863
$474$	−21.8538	+	37.8519i	−1.00378	+	1.73859i
$475$			25.0489i			1.14932i
$476$		0			0
$477$			13.2621i			0.607228i
$478$	16.2426	+	9.37769i	0.742921	+	0.428926i
$479$	11.7034			0.534744			0.267372	−	0.963593i	$-0.413845\pi$
$479$	11.7034			0.534744			0.267372	+	0.963593i	$0.413845\pi$
$480$	40.9706	−	23.6544i	1.87004	−	1.07967i
$481$		−	12.4316i		−	0.566831i
$482$	−27.0898	−	15.6403i	−1.23391	−	0.712396i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$			12.2474i			0.556128i
$486$	26.6073	+	15.3617i	1.20693	+	0.696822i
$487$			34.0467i			1.54280i	0.636349	+	0.771401i	$0.280444\pi$
$487$			34.0467i			1.54280i	−0.636349	+	0.771401i	$0.719556\pi$
$488$	11.2485			0.509198
$489$		−	21.2764i		−	0.962153i
$490$		0			0
$491$	−31.7990			−1.43507			−0.717534	−	0.696523i	$-0.754729\pi$
$491$	−31.7990			−1.43507			−0.717534	+	0.696523i	$0.754729\pi$
$492$	11.6569	+	20.1903i	0.525532	+	0.910247i
$493$	−2.97297			−0.133896
$494$	29.6985	+	17.1464i	1.33620	+	0.771454i
$495$	24.5051			1.10142
$496$	5.30262	−	9.18440i	0.238095	−	0.412392i
$497$		0			0
$498$	15.6569	−	27.1185i	0.701600	−	1.21521i
$499$	−8.48528			−0.379853			−0.189927	−	0.981798i	$-0.560825\pi$
$499$	−8.48528			−0.379853			−0.189927	+	0.981798i	$0.560825\pi$
$500$	−0.776550	−	1.34502i	−0.0347284	−	0.0601513i
$501$		−	37.5108i		−	1.67586i
$502$	23.5011	+	13.5684i	1.04891	+	0.605586i
$503$	−24.5051			−1.09263			−0.546314	−	0.837580i	$-0.683969\pi$
$503$	−24.5051			−1.09263			−0.546314	+	0.837580i	$0.683969\pi$
$504$		0			0
$505$	−24.7279			−1.10038
$506$	−3.51472	−	2.02922i	−0.156248	−	0.0902100i
$507$		−	33.3366i		−	1.48053i
$508$	−9.51472	+	5.49333i	−0.422147	+	0.243727i
$509$	−14.1273			−0.626182			−0.313091	−	0.949723i	$-0.601364\pi$
$509$	−14.1273			−0.626182			−0.313091	+	0.949723i	$0.601364\pi$
$510$	1.87476	−	3.24718i	0.0830157	−	0.143787i
$511$		0			0
$512$	−22.6274			−1.00000
$513$	−10.3431			−0.456661
$514$	−9.98951	−	5.76745i	−0.440619	−	0.254391i
$515$	49.4558			2.17928
$516$	39.9581	−	23.0698i	1.75906	−	1.01559i
$517$	−10.6052			−0.466418
$518$		0			0
$519$			18.1610i			0.797181i
$520$	−45.9411			−2.01465
$521$			18.6089i			0.815271i	0.913145	+	0.407636i	$0.133647\pi$
$521$			18.6089i			0.815271i	−0.913145	+	0.407636i	$0.866353\pi$
$522$	−43.9706	−	25.3864i	−1.92454	−	1.11113i
$523$		−	32.8113i		−	1.43474i	−0.696693	−	0.717369i	$-0.745346\pi$
$523$		−	32.8113i		−	1.43474i	0.696693	−	0.717369i	$-0.254654\pi$
$524$	−6.07917	+	3.50981i	−0.265570	+	0.153327i
$525$		0			0
$526$	−10.9706	−	6.33386i	−0.478339	−	0.276169i
$527$		−	0.840532i		−	0.0366141i
$528$	−18.1043	−	10.4525i	−0.787887	−	0.454887i
$529$	20.9411			0.910484
$530$	−13.5782	−	7.83938i	−0.589799	−	0.340521i
$531$			10.0042i			0.434144i
$532$		0			0
$533$		−	22.6398i		−	0.980637i
$534$	−18.2426	+	31.5972i	−0.789436	+	1.36734i
$535$	−27.1564			−1.17407
$536$	−33.9411			−1.46603
$537$			53.5306i			2.31002i
$538$	1.71393	−	2.96861i	0.0738927	−	0.127986i
$539$		0			0
$540$	12.0000	−	6.92820i	0.516398	−	0.298142i
$541$		−	32.8580i		−	1.41267i	−0.707875	−	0.706337i	$-0.750346\pi$
$541$		−	32.8580i		−	1.41267i	0.707875	−	0.706337i	$-0.249654\pi$
$542$	−9.37379	+	16.2359i	−0.402639	+	0.697391i
$543$		−	5.49333i		−	0.235741i
$544$	−1.55310	+	0.896683i	−0.0665886	+	0.0384450i
$545$			1.34502i			0.0576145i
$546$		0			0
$547$	−15.1716			−0.648690			−0.324345	−	0.945939i	$-0.605144\pi$
$547$	−15.1716			−0.648690			−0.324345	+	0.945939i	$0.605144\pi$
$548$	−0.242641	−	0.420266i	−0.0103651	−	0.0179529i
$549$	15.2255			0.649809
$550$	−7.41421	+	12.8418i	−0.316143	+	0.547576i
$551$	−44.8058			−1.90879
$552$	−10.6052			−0.451389
$553$		0			0
$554$	−20.4853	−	11.8272i	−0.870336	−	0.502489i
$555$	−20.4853			−0.869552
$556$	8.73048	−	5.04054i	0.370255	−	0.213767i
$557$		−	16.7262i		−	0.708710i	−0.935111	−	0.354355i	$-0.884700\pi$
$557$		−	16.7262i		−	0.708710i	0.935111	−	0.354355i	$-0.115300\pi$
$558$	7.17738	−	12.4316i	0.303843	−	0.526271i
$559$	−44.8058			−1.89508
$560$		0			0
$561$	−1.65685			−0.0699524
$562$	6.17157	−	10.6895i	0.260332	−	0.450908i
$563$		−	16.7611i		−	0.706398i	−0.935548	−	0.353199i	$-0.885094\pi$
$563$		−	16.7611i		−	0.706398i	0.935548	−	0.353199i	$-0.114906\pi$
$564$	−24.0000	+	13.8564i	−1.01058	+	0.583460i
$565$	−52.7597			−2.21962
$566$	−0.227446	−	0.131316i	−0.00956028	−	0.00551963i
$567$		0			0
$568$		0			0
$569$	14.1005			0.591124			0.295562	−	0.955324i	$-0.404493\pi$
$569$	14.1005			0.591124			0.295562	+	0.955324i	$0.404493\pi$
$570$	28.2546	−	48.9384i	1.18346	−	2.04980i
$571$	−23.6569			−0.990009			−0.495004	−	0.868891i	$-0.664834\pi$
$571$	−23.6569			−0.990009			−0.495004	+	0.868891i	$0.664834\pi$
$572$	10.1503	+	17.5809i	0.424407	+	0.735095i
$573$	−30.9059			−1.29111
$574$		0			0
$575$			7.52255i			0.313712i
$576$	−30.6274			−1.27614
$577$		−	2.11039i		−	0.0878567i	−0.999035	−	0.0439284i	$-0.986013\pi$
$577$		−	2.11039i		−	0.0878567i	0.999035	−	0.0439284i	$-0.0139873\pi$
$578$	11.9497	−	20.6976i	0.497044	−	0.860905i
$579$			36.9552i			1.53580i
$580$	51.9832	−	30.0125i	2.15848	−	1.24620i
$581$		0			0
$582$	7.07107	−	12.2474i	0.293105	−	0.507673i
$583$			6.92820i			0.286937i
$584$			3.95815i			0.163789i
$585$	−62.1838			−2.57098
$586$	−3.58869	+	6.21579i	−0.148247	+	0.256772i
$587$		−	43.2638i		−	1.78569i	−0.450365	−	0.892845i	$-0.648706\pi$
$587$		−	43.2638i		−	1.78569i	0.450365	−	0.892845i	$-0.351294\pi$
$588$		0			0
$589$		−	12.6677i		−	0.521964i
$590$	−10.2426	−	5.91359i	−0.421683	−	0.243459i
$591$	69.3109			2.85107
$592$	8.48528	+	4.89898i	0.348743	+	0.201347i
$593$		−	12.3003i		−	0.505111i	−0.967582	−	0.252556i	$-0.918729\pi$
$593$		−	12.3003i		−	0.505111i	0.967582	−	0.252556i	$-0.0812711\pi$
$594$	−5.30262	−	3.06147i	−0.217569	−	0.125614i
$595$		0			0
$596$	34.9706	−	20.1903i	1.43245	−	0.827025i
$597$			6.92820i			0.283552i
$598$	8.91890	+	5.14933i	0.364721	+	0.210572i
$599$		−	35.4815i		−	1.44974i	−0.688887	−	0.724868i	$-0.741901\pi$
$599$		−	35.4815i		−	1.44974i	0.688887	−	0.724868i	$-0.258099\pi$
$600$			38.7485i			1.58190i
$601$		−	35.1843i		−	1.43520i	−0.696456	−	0.717600i	$-0.745241\pi$
$601$		−	35.1843i		−	1.43520i	0.696456	−	0.717600i	$-0.254759\pi$
$602$		0			0
$603$	−45.9411			−1.87087
$604$	26.4853	−	15.2913i	1.07767	−	0.622194i
$605$	−22.4029			−0.910807
$606$	24.7279	+	14.2767i	1.00450	+	0.579950i
$607$	25.6033			1.03921			0.519603	−	0.854408i	$-0.326080\pi$
$607$	25.6033			1.03921			0.519603	+	0.854408i	$0.326080\pi$
$608$	−23.4069	+	13.5140i	−0.949275	+	0.548064i
$609$		0			0
$610$	−9.00000	+	15.5885i	−0.364399	+	0.631158i
$611$	26.9117			1.08873
$612$	−2.10220	+	1.21371i	−0.0849766	+	0.0490613i
$613$			26.9444i			1.08827i	0.838997	+	0.544137i	$0.183143\pi$
$613$			26.9444i			1.08827i	−0.838997	+	0.544137i	$0.816857\pi$
$614$	7.40482	+	4.27518i	0.298834	+	0.172532i
$615$	−37.3067			−1.50435
$616$		0			0
$617$	−9.21320			−0.370910			−0.185455	−	0.982653i	$-0.559376\pi$
$617$	−9.21320			−0.370910			−0.185455	+	0.982653i	$0.559376\pi$
$618$	−49.4558	−	28.5533i	−1.98941	−	1.14858i
$619$			29.1158i			1.17026i	0.810938	+	0.585131i	$0.198957\pi$
$619$			29.1158i			1.17026i	−0.810938	+	0.585131i	$0.801043\pi$
$620$	8.48528	+	14.6969i	0.340777	+	0.590243i
$621$	−3.10620			−0.124648
$622$	−19.2025	+	33.2597i	−0.769949	+	1.33359i
$623$		0			0
$624$	45.9411	+	26.5241i	1.83912	+	1.06181i
$625$	−23.7279			−0.949117
$626$	−12.9625	−	7.48389i	−0.518085	−	0.299116i
$627$	−24.9706			−0.997228
$628$	−23.9560	−	41.4930i	−0.955948	−	1.65575i
$629$	0.776550			0.0309631
$630$		0			0
$631$		−	29.7420i		−	1.18401i	−0.805934	−	0.592006i	$-0.798336\pi$
$631$		−	29.7420i		−	1.18401i	0.805934	−	0.592006i	$-0.201664\pi$
$632$			33.4523i			1.33066i
$633$		−	53.5306i		−	2.12765i
$634$	−4.97056	−	2.86976i	−0.197406	−	0.113973i
$635$		−	17.5809i		−	0.697677i
$636$	9.05213	+	15.6788i	0.358940	+	0.621703i
$637$		0			0
$638$	−22.9706	−	13.2621i	−0.909413	−	0.525050i
$639$		0			0
$640$	18.1043	−	31.3575i	0.715634	−	1.23951i
$641$	−16.9289			−0.668653			−0.334326	−	0.942457i	$-0.608509\pi$
$641$	−16.9289			−0.668653			−0.334326	+	0.942457i	$0.608509\pi$
$642$	27.1564	+	15.6788i	1.07178	+	0.618791i
$643$		−	36.3981i		−	1.43540i	−0.696353	−	0.717700i	$-0.745195\pi$
$643$		−	36.3981i		−	1.43540i	0.696353	−	0.717700i	$-0.254805\pi$
$644$		0			0
$645$			73.8329i			2.90717i
$646$	−1.07107	+	1.85514i	−0.0421406	+	0.0729897i
$647$	11.7034			0.460110			0.230055	−	0.973178i	$-0.426109\pi$
$647$	11.7034			0.460110			0.230055	+	0.973178i	$0.426109\pi$
$648$	16.4853			0.647603
$649$			5.22625i			0.205148i
$650$	18.8142	−	32.5872i	0.737954	−	1.27817i
$651$		0			0
$652$	−8.14214	−	14.1026i	−0.318871	−	0.552300i
$653$			35.0613i			1.37205i	0.727576	+	0.686027i	$0.240647\pi$
$653$			35.0613i			1.37205i	−0.727576	+	0.686027i	$0.759353\pi$
$654$	0.776550	−	1.34502i	0.0303655	−	0.0525946i
$655$		−	11.2328i		−	0.438903i
$656$	15.4530	+	8.92177i	0.603337	+	0.348337i
$657$			5.35757i			0.209019i
$658$		0			0
$659$	25.5147			0.993912			0.496956	−	0.867776i	$-0.334451\pi$
$659$	25.5147			0.993912			0.496956	+	0.867776i	$0.334451\pi$
$660$	28.9706	−	16.7262i	1.12768	−	0.651065i
$661$	−20.8498			−0.810963			−0.405481	−	0.914103i	$-0.632896\pi$
$661$	−20.8498			−0.810963			−0.405481	+	0.914103i	$0.632896\pi$
$662$	14.7279	−	25.5095i	0.572417	−	0.991455i
$663$	4.20441			0.163286
$664$		−	23.9665i		−	0.930080i
$665$		0			0
$666$	11.4853	+	6.63103i	0.445046	+	0.256947i
$667$	−13.4558			−0.521012
$668$	−14.3548	−	24.8632i	−0.555402	−	0.961984i
$669$			64.0349i			2.47573i
$670$	27.1564	−	47.0363i	1.04914	−	1.81717i
$671$	7.95393			0.307058
$672$		0			0
$673$	30.3848			1.17125			0.585624	−	0.810583i	$-0.300850\pi$
$673$	30.3848			1.17125			0.585624	+	0.810583i	$0.300850\pi$
$674$	3.00000	−	5.19615i	0.115556	−	0.200148i
$675$			11.3492i			0.436830i
$676$	−12.7574	−	22.0964i	−0.490668	−	0.849861i
$677$	−1.00400			−0.0385867			−0.0192934	−	0.999814i	$-0.506142\pi$
$677$	−1.00400			−0.0385867			−0.0192934	+	0.999814i	$0.506142\pi$
$678$	52.7597	+	30.4608i	2.02622	+	1.16984i
$679$		0			0
$680$		−	2.86976i		−	0.110050i
$681$	60.7696			2.32869
$682$	3.74952	−	6.49435i	0.143576	−	0.248682i
$683$	−14.1421			−0.541134			−0.270567	−	0.962701i	$-0.587211\pi$
$683$	−14.1421			−0.541134			−0.270567	+	0.962701i	$0.587211\pi$
$684$	−31.6825	+	18.2919i	−1.21141	+	0.699408i
$685$	0.776550			0.0296705
$686$		0			0
$687$		−	45.8739i		−	1.75020i
$688$	17.6569	−	30.5826i	0.673161	−	1.16595i
$689$		−	17.5809i		−	0.669779i
$690$	8.48528	−	14.6969i	0.323029	−	0.559503i
$691$			19.9314i			0.758226i	0.925350	+	0.379113i	$0.123771\pi$
$691$			19.9314i			0.758226i	−0.925350	+	0.379113i	$0.876229\pi$
$692$	6.94993	+	12.0376i	0.264197	+	0.457602i
$693$		0			0
$694$	4.92893	−	8.53716i	0.187100	−	0.324066i
$695$			16.1318i			0.611915i
$696$	−69.3109			−2.62722
$697$	1.41421			0.0535672
$698$	15.8412	−	27.4378i	0.599600	−	1.03854i
$699$			52.8966i			2.00073i
$700$		0			0
$701$			6.15978i			0.232652i	0.993211	+	0.116326i	$0.0371117\pi$
$701$			6.15978i			0.232652i	−0.993211	+	0.116326i	$0.962888\pi$
$702$	13.4558	+	7.76874i	0.507858	+	0.293212i
$703$	11.7034			0.441404
$704$	−16.0000			−0.603023
$705$		−	44.3462i		−	1.67018i
$706$	−16.0687	−	9.27726i	−0.604753	−	0.349154i
$707$		0			0
$708$	6.82843	+	11.8272i	0.256628	+	0.444493i
$709$		−	36.7423i		−	1.37989i	−0.723863	−	0.689944i	$-0.757635\pi$
$709$		−	36.7423i		−	1.37989i	0.723863	−	0.689944i	$-0.242365\pi$
$710$		0			0
$711$			45.2795i			1.69811i
$712$			27.9246i			1.04652i
$713$		−	3.80430i		−	0.142472i
$714$		0			0
$715$	−32.4853			−1.21488
$716$	20.4853	+	35.4815i	0.765571	+	1.32601i
$717$	34.6554			1.29423
$718$	−21.2132	−	12.2474i	−0.791670	−	0.457071i
$719$	−29.3528			−1.09468			−0.547338	−	0.836912i	$-0.684359\pi$
$719$	−29.3528			−1.09468			−0.547338	+	0.836912i	$0.684359\pi$
$720$	24.5051	−	42.4441i	0.913251	−	1.58180i
$721$		0			0
$722$	−2.70711	+	4.68885i	−0.100748	+	0.174501i
$723$	−57.7990			−2.14957
$724$	−2.10220	−	3.64113i	−0.0781278	−	0.135321i
$725$			49.1639i			1.82590i
$726$	22.4029	+	12.9343i	0.831449	+	0.480037i
$727$	43.0643			1.59716			0.798582	−	0.601886i	$-0.205584\pi$
$727$	43.0643			1.59716			0.798582	+	0.601886i	$0.205584\pi$
$728$		0			0
$729$	39.2843			1.45497
$730$	−5.48528	−	3.16693i	−0.203019	−	0.117213i
$731$		−	2.79884i		−	0.103519i
$732$	18.0000	−	10.3923i	0.665299	−	0.384111i
$733$	7.40482			0.273503			0.136752	−	0.990605i	$-0.456334\pi$
$733$	7.40482			0.273503			0.136752	+	0.990605i	$0.456334\pi$
$734$	−12.0251	+	20.8281i	−0.443855	+	0.768779i
$735$		0			0
$736$	−7.02944	+	4.05845i	−0.259108	+	0.149596i
$737$	−24.0000			−0.884051
$738$	20.9164	+	12.0761i	0.769944	+	0.444527i
$739$	15.1716			0.558095			0.279048	−	0.960277i	$-0.409981\pi$
$739$	15.1716			0.558095			0.279048	+	0.960277i	$0.409981\pi$
$740$	−13.5782	+	7.83938i	−0.499145	+	0.288181i
$741$	63.3649			2.32777
$742$		0			0
$743$		−	13.2621i		−	0.486538i	−0.969959	−	0.243269i	$-0.921780\pi$
$743$		−	13.2621i		−	0.486538i	0.969959	−	0.243269i	$-0.0782197\pi$
$744$		−	19.5959i		−	0.718421i
$745$			64.6172i			2.36739i
$746$	11.2721	+	6.50794i	0.412700	+	0.238273i
$747$		−	32.4399i		−	1.18691i
$748$	−1.09821	+	0.634051i	−0.0401545	+	0.0231832i
$749$		0			0
$750$	−2.48528	−	1.43488i	−0.0907496	−	0.0523943i
$751$			35.7277i			1.30372i	0.758338	+	0.651862i	$0.226012\pi$
$751$			35.7277i			1.30372i	−0.758338	+	0.651862i	$0.773988\pi$
$752$	−10.6052	+	18.3688i	−0.386733	+	0.669841i
$753$	50.1421			1.82728
$754$	58.2898	+	33.6536i	2.12279	+	1.22559i
$755$			48.9384i			1.78105i
$756$		0			0
$757$			35.9018i			1.30487i	0.757843	+	0.652437i	$0.226253\pi$
$757$			35.9018i			1.30487i	−0.757843	+	0.652437i	$0.773747\pi$
$758$	12.2426	−	21.2049i	0.444673	−	0.770196i
$759$	−7.49903			−0.272198
$760$		−	43.2503i		−	1.56885i
$761$			21.8561i			0.792282i	0.918190	+	0.396141i	$0.129651\pi$
$761$			21.8561i			0.792282i	−0.918190	+	0.396141i	$0.870349\pi$
$762$	−10.1503	+	17.5809i	−0.367708	+	0.636889i
$763$		0			0
$764$	−20.4853	+	11.8272i	−0.741131	+	0.427892i
$765$		−	3.88437i		−	0.140440i
$766$	3.74952	−	6.49435i	0.135476	−	0.234651i
$767$		−	13.2621i		−	0.478865i
$768$	−36.2085	+	20.9050i	−1.30656	+	0.754344i
$769$		−	46.1940i		−	1.66580i	−0.553425	−	0.832899i	$-0.686680\pi$
$769$		−	46.1940i		−	1.66580i	0.553425	−	0.832899i	$-0.313320\pi$
$770$		0			0
$771$	−21.3137			−0.767594
$772$	14.1421	+	24.4949i	0.508987	+	0.881591i
$773$	−31.0001			−1.11500			−0.557499	−	0.830178i	$-0.688239\pi$
$773$	−31.0001			−1.11500			−0.557499	+	0.830178i	$0.688239\pi$
$774$	23.8995	−	41.3951i	0.859050	−	1.48792i
$775$	−13.8999			−0.499298
$776$		−	10.8239i		−	0.388556i
$777$		0			0
$778$	4.45584	+	2.57258i	0.159750	+	0.0922316i
$779$	21.3137			0.763643
$780$	−73.5153	+	42.4441i	−2.63227	+	1.51974i
$781$		0			0
$782$	−0.321658	+	0.557127i	−0.0115025	+	0.0199228i
$783$	−20.3007			−0.725487
$784$		0			0
$785$	76.6690			2.73644
$786$	−6.48528	+	11.2328i	−0.231322	+	0.400662i
$787$			38.8255i			1.38398i	0.721908	+	0.691989i	$0.243265\pi$
$787$			38.8255i			1.38398i	−0.721908	+	0.691989i	$0.756735\pi$
$788$	45.9411	−	26.5241i	1.63658	−	0.944883i
$789$	−23.4069			−0.833307
$790$	−46.3589	−	26.7653i	−1.64937	−	0.952267i
$791$		0			0
$792$	−21.6569			−0.769543
$793$	−20.1838			−0.716747
$794$	−17.1669	+	29.7339i	−0.609230	+	1.05522i
$795$	−28.9706			−1.02748
$796$	2.65131	+	4.59220i	0.0939731	+	0.162766i
$797$	−13.4840			−0.477627			−0.238814	−	0.971065i	$-0.576759\pi$
$797$	−13.4840			−0.477627			−0.238814	+	0.971065i	$0.576759\pi$
$798$		0			0
$799$			1.68106i			0.0594718i
$800$	14.8284	+	25.6836i	0.524264	+	0.908052i
$801$			37.7975i			1.33551i
$802$	5.48528	−	9.50079i	0.193692	−	0.335484i
$803$			2.79884i			0.0987687i
$804$	−54.3128	+	31.3575i	−1.91546	+	1.10589i
$805$		0			0
$806$	−9.51472	+	16.4800i	−0.335142	+	0.580482i
$807$		−	6.33386i		−	0.222962i
$808$	21.8538			0.768813
$809$	−15.4558			−0.543399			−0.271699	−	0.962382i	$-0.587586\pi$
$809$	−15.4558			−0.543399			−0.271699	+	0.962382i	$0.587586\pi$
$810$	−13.1899	+	22.8456i	−0.463447	+	0.802713i
$811$			28.4818i			1.00013i	0.865988	+	0.500065i	$0.166690\pi$
$811$			28.4818i			1.00013i	−0.865988	+	0.500065i	$0.833310\pi$
$812$		0			0
$813$			34.6410i			1.21491i
$814$	6.00000	+	3.46410i	0.210300	+	0.121417i
$815$	26.0582			0.912779
$816$	−1.65685	+	2.86976i	−0.0580015	+	0.100462i
$817$		−	42.1814i		−	1.47574i
$818$	−4.68690	−	2.70598i	−0.163873	−	0.0946124i
$819$		0			0
$820$	−24.7279	+	14.2767i	−0.863536	+	0.498563i
$821$			17.9149i			0.625233i	0.949879	+	0.312616i	$0.101205\pi$
$821$			17.9149i			0.625233i	−0.949879	+	0.312616i	$0.898795\pi$
$822$	−0.776550	−	0.448342i	−0.0270853	−	0.0156377i
$823$			20.7846i			0.724506i	0.932080	+	0.362253i	$0.117992\pi$
$823$			20.7846i			0.724506i	−0.932080	+	0.362253i	$0.882008\pi$
$824$	−43.7076			−1.52263
$825$			27.3994i			0.953923i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−9.51472	+	5.49333i	−0.330659	+	0.190906i
$829$	16.7786			0.582745			0.291373	−	0.956610i	$-0.405888\pi$
$829$	16.7786			0.582745			0.291373	+	0.956610i	$0.405888\pi$
$830$	33.2132	+	19.1757i	1.15285	+	0.665597i
$831$	−43.7076			−1.51620
$832$	40.6014			1.40760
$833$		0			0
$834$	9.31371	−	16.1318i	0.322507	−	0.558599i
$835$	45.9411			1.58986
$836$	−16.5512	+	9.55582i	−0.572434	+	0.330495i
$837$		−	5.73951i		−	0.198387i
$838$	−48.7827	−	28.1647i	−1.68517	−	0.972934i
$839$	−30.4510			−1.05129			−0.525643	−	0.850705i	$-0.676175\pi$
$839$	−30.4510			−1.05129			−0.525643	+	0.850705i	$0.676175\pi$
$840$		0			0
$841$	−58.9411			−2.03245
$842$	−32.4853	−	18.7554i	−1.11952	−	0.646353i
$843$		−	22.8072i		−	0.785520i
$844$	−20.4853	−	35.4815i	−0.705132	−	1.22133i
$845$	40.8288			1.40455
$846$	−14.3548	+	24.8632i	−0.493527	+	0.854813i
$847$		0			0
$848$	12.0000	+	6.92820i	0.412082	+	0.237915i
$849$	−0.485281			−0.0166548
$850$	2.03559	+	1.17525i	0.0698201	+	0.0403106i
$851$	3.51472			0.120483
$852$		0			0
$853$	32.5532			1.11460			0.557301	−	0.830311i	$-0.311837\pi$
$853$	32.5532			1.11460			0.557301	+	0.830311i	$0.311837\pi$
$854$		0			0
$855$		−	58.5416i		−	2.00208i
$856$	24.0000			0.820303
$857$			34.4734i			1.17759i	0.808283	+	0.588794i	$0.200397\pi$
$857$			34.4734i			1.17759i	−0.808283	+	0.588794i	$0.799603\pi$
$858$	32.4853	+	18.7554i	1.10903	+	0.640298i
$859$		−	44.5319i		−	1.51941i	−0.650268	−	0.759705i	$-0.725343\pi$
$859$		−	44.5319i		−	1.51941i	0.650268	−	0.759705i	$-0.274657\pi$
$860$	28.2546	+	48.9384i	0.963474	+	1.66879i
$861$		0			0
$862$	9.21320	+	5.31925i	0.313803	+	0.181174i
$863$		−	4.05845i		−	0.138151i	−0.997611	−	0.0690756i	$-0.977995\pi$
$863$		−	4.05845i		−	0.138151i	0.997611	−	0.0690756i	$-0.0220050\pi$
$864$	−10.6052	+	6.12293i	−0.360797	+	0.208306i
$865$	−22.2426			−0.756272
$866$	−6.33421	−	3.65706i	−0.215245	−	0.124272i
$867$		−	44.1605i		−	1.49977i
$868$		0			0
$869$			23.6544i			0.802419i
$870$	55.4558	−	96.0523i	1.88013	−	3.25648i
$871$	60.9021			2.06359
$872$		−	1.18869i		−	0.0402542i
$873$		−	14.6508i		−	0.495853i
$874$	−4.84772	+	8.39651i	−0.163977	+	0.284016i
$875$		0			0
$876$	3.65685	+	6.33386i	0.123554	+	0.214001i
$877$		−	32.1915i		−	1.08703i	−0.839399	−	0.543515i	$-0.817093\pi$
$877$		−	32.1915i		−	1.08703i	0.839399	−	0.543515i	$-0.182907\pi$
$878$	25.2816	−	43.7891i	0.853214	−	1.47781i
$879$			13.2621i			0.447318i
$880$	12.8017	−	22.1731i	0.431544	−	0.747455i
$881$			34.8448i			1.17395i	0.809605	+	0.586975i	$0.199681\pi$
$881$			34.8448i			1.17395i	−0.809605	+	0.586975i	$0.800319\pi$
$882$		0			0
$883$	38.4264			1.29315			0.646576	−	0.762850i	$-0.276200\pi$
$883$	38.4264			1.29315			0.646576	+	0.762850i	$0.276200\pi$
$884$	2.78680	−	1.60896i	0.0937301	−	0.0541151i
$885$	−21.8538			−0.734607
$886$	−20.0000	+	34.6410i	−0.671913	+	1.16379i
$887$	39.9581			1.34166			0.670830	−	0.741611i	$-0.265938\pi$
$887$	39.9581			1.34166			0.670830	+	0.741611i	$0.265938\pi$
$888$	18.1043			0.607539
$889$		0			0
$890$	−38.6985	−	22.3426i	−1.29718	−	0.748925i
$891$	11.6569			0.390519
$892$	24.5051	+	42.4441i	0.820491	+	1.42113i
$893$			25.3354i			0.847818i
$894$	37.3067	−	64.6172i	1.24772	−	2.16112i
$895$	−65.5614			−2.19147
$896$		0			0
$897$	19.0294			0.635374
$898$	−4.00000	+	6.92820i	−0.133482	+	0.231197i
$899$		−	24.8632i		−	0.829233i
$900$	20.0711	+	34.7641i	0.669036	+	1.15880i
$901$	1.09821			0.0365866
$902$	10.9269	+	6.30864i	0.363826	+	0.210055i
$903$		0			0
$904$	46.6274			1.55080
$905$	6.72792			0.223644
$906$	28.2546	−	48.9384i	0.938697	−	1.62587i
$907$	−16.0000			−0.531271			−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$	40.2797	−	23.2555i	1.33673	−	0.771761i
$909$	29.5803			0.981115
$910$		0			0
$911$			5.49333i			0.182002i	0.995851	+	0.0910010i	$0.0290066\pi$
$911$			5.49333i			0.182002i	−0.995851	+	0.0910010i	$0.970993\pi$
$912$	−24.9706	+	43.2503i	−0.826858	+	1.43216i
$913$		−	16.9469i		−	0.560859i
$914$	−14.9706	+	25.9298i	−0.495182	+	0.857681i
$915$			33.2597i			1.09953i
$916$	−17.5552	−	30.4064i	−0.580039	−	1.00466i
$917$		0			0
$918$	−0.485281	+	0.840532i	−0.0160167	+	0.0277417i
$919$			17.9149i			0.590957i	0.955349	+	0.295478i	$0.0954790\pi$
$919$			17.9149i			0.590957i	−0.955349	+	0.295478i	$0.904521\pi$
$920$		−	12.9887i		−	0.428225i
$921$	15.7990			0.520594
$922$	18.8142	−	32.5872i	0.619613	−	1.07320i
$923$		0			0
$924$		0			0
$925$		−	12.8418i		−	0.422236i
$926$	22.9706	+	13.2621i	0.754860	+	0.435818i
$927$	−59.1605			−1.94309
$928$	−45.9411	+	26.5241i	−1.50809	+	0.870697i
$929$		−	1.58513i		−	0.0520063i	−0.999662	−	0.0260032i	$-0.991722\pi$
$929$		−	1.58513i		−	0.0520063i	0.999662	−	0.0260032i	$-0.00827800\pi$
$930$	27.1564	+	15.6788i	0.890493	+	0.514127i
$931$		0			0
$932$	20.2426	+	35.0613i	0.663070	+	1.14847i
$933$			70.9631i			2.32323i
$934$	−0.0942114	−	0.0543929i	−0.00308269	−	0.00177979i
$935$		−	2.02922i		−	0.0663627i
$936$	54.9561			1.79630
$937$			16.9694i			0.554366i	0.960817	+	0.277183i	$0.0894008\pi$
$937$			16.9694i			0.554366i	−0.960817	+	0.277183i	$0.910599\pi$
$938$		0			0
$939$	−27.6569			−0.902547
$940$	−16.9706	−	29.3939i	−0.553519	−	0.958723i
$941$	2.42386			0.0790157			0.0395078	−	0.999219i	$-0.487421\pi$
$941$	2.42386			0.0790157			0.0395078	+	0.999219i	$0.487421\pi$
$942$	−76.6690	−	44.2649i	−2.49801	−	1.44223i
$943$	6.40083			0.208440
$944$	9.05213	+	5.22625i	0.294622	+	0.170100i
$945$		0			0
$946$	12.4853	−	21.6251i	0.405932	−	0.703094i
$947$	51.4558			1.67209			0.836045	−	0.548661i	$-0.184862\pi$
$947$	51.4558			1.67209			0.836045	+	0.548661i	$0.184862\pi$
$948$	30.9059	+	53.5306i	1.00378	+	1.73859i
$949$		−	7.10228i		−	0.230550i
$950$	30.6785	+	17.7122i	0.995341	+	0.574660i
$951$	−10.6052			−0.343898
$952$		0			0
$953$	−41.3137			−1.33828			−0.669141	−	0.743135i	$-0.733338\pi$
$953$	−41.3137			−1.33828			−0.669141	+	0.743135i	$0.733338\pi$
$954$	16.2426	+	9.37769i	0.525875	+	0.303614i
$955$		−	37.8519i		−	1.22486i
$956$	22.9706	−	13.2621i	0.742921	−	0.428926i
$957$	−49.0102			−1.58427
$958$	8.27558	−	14.3337i	0.267372	−	0.463102i
$959$		0			0
$960$		−	66.9046i		−	2.15934i
$961$	−23.9706			−0.773244
$962$	−15.2255	−	8.79045i	−0.490890	−	0.283416i
$963$	32.4853			1.04682
$964$	−38.3107	+	22.1187i	−1.23391	+	0.712396i
$965$	−45.2607			−1.45699
$966$		0			0
$967$		−	21.0308i		−	0.676305i	−0.941091	−	0.338152i	$-0.890198\pi$
$967$		−	21.0308i		−	0.676305i	0.941091	−	0.338152i	$-0.109802\pi$
$968$	19.7990			0.636364
$969$			3.95815i			0.127154i
$970$	15.0000	+	8.66025i	0.481621	+	0.278064i
$971$			24.7862i			0.795428i	0.917509	+	0.397714i	$0.130196\pi$
$971$			24.7862i			0.795428i	−0.917509	+	0.397714i	$0.869804\pi$
$972$	37.6284	−	21.7248i	1.20693	−	0.696822i
$973$		0			0
$974$	41.6985	+	24.0746i	1.33611	+	0.771401i
$975$		−	69.5282i		−	2.22669i
$976$	7.95393	−	13.7766i	0.254599	−	0.440978i
$977$	37.2132			1.19056			0.595278	−	0.803520i	$-0.297042\pi$
$977$	37.2132			1.19056			0.595278	+	0.803520i	$0.297042\pi$
$978$	−26.0582	−	15.0447i	−0.833249	−	0.481077i
$979$			19.7457i			0.631075i
$980$		0			0
$981$		−	1.60896i		−	0.0513701i
$982$	−22.4853	+	38.9456i	−0.717534	+	1.24281i
$983$	26.0582			0.831127			0.415564	−	0.909564i	$-0.363584\pi$
$983$	26.0582			0.831127			0.415564	+	0.909564i	$0.363584\pi$
$984$	32.9706			1.05106
$985$			84.8881i			2.70476i
$986$	−2.10220	+	3.64113i	−0.0669478	+	0.115957i
$987$		0			0
$988$	42.0000	−	24.2487i	1.33620	−	0.771454i
$989$		−	12.6677i		−	0.402810i
$990$	17.3277	−	30.0125i	0.550711	−	0.953859i
$991$		−	32.2636i		−	1.02489i	−0.858721	−	0.512444i	$-0.828740\pi$
$991$		−	32.2636i		−	1.02489i	0.858721	−	0.512444i	$-0.171260\pi$
$992$	−7.49903	−	12.9887i	−0.238095	−	0.412392i
$993$		−	54.4273i		−	1.72720i
$994$		0			0
$995$	−8.48528			−0.269002
$996$	−22.1421	−	38.3513i	−0.701600	−	1.21521i
$997$	5.39683			0.170919			0.0854596	−	0.996342i	$-0.472764\pi$
$997$	5.39683			0.170919			0.0854596	+	0.996342i	$0.472764\pi$
$998$	−6.00000	+	10.3923i	−0.189927	+	0.328963i
$999$	5.30262			0.167767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.e.c.195.5	✓	8
4.3	odd	2		1568.2.e.c.783.8		8
7.2	even	3		392.2.m.e.227.2		8
7.3	odd	6		392.2.m.c.19.4		8
7.4	even	3		392.2.m.c.19.3		8
7.5	odd	6		392.2.m.e.227.1		8
7.6	odd	2	inner	392.2.e.c.195.6	yes	8
8.3	odd	2	inner	392.2.e.c.195.7	yes	8
8.5	even	2		1568.2.e.c.783.7		8
28.3	even	6		1568.2.q.c.1391.1		8
28.11	odd	6		1568.2.q.c.1391.4		8
28.19	even	6		1568.2.q.d.815.4		8
28.23	odd	6		1568.2.q.d.815.1		8
28.27	even	2		1568.2.e.c.783.1		8
56.3	even	6		392.2.m.e.19.2		8
56.5	odd	6		1568.2.q.c.815.4		8
56.11	odd	6		392.2.m.e.19.1		8
56.13	odd	2		1568.2.e.c.783.2		8
56.19	even	6		392.2.m.c.227.3		8
56.27	even	2	inner	392.2.e.c.195.8	yes	8
56.37	even	6		1568.2.q.c.815.1		8
56.45	odd	6		1568.2.q.d.1391.1		8
56.51	odd	6		392.2.m.c.227.4		8
56.53	even	6		1568.2.q.d.1391.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.c.195.5	✓	8	1.1	even	1	trivial
392.2.e.c.195.6	yes	8	7.6	odd	2	inner
392.2.e.c.195.7	yes	8	8.3	odd	2	inner
392.2.e.c.195.8	yes	8	56.27	even	2	inner
392.2.m.c.19.3		8	7.4	even	3
392.2.m.c.19.4		8	7.3	odd	6
392.2.m.c.227.3		8	56.19	even	6
392.2.m.c.227.4		8	56.51	odd	6
392.2.m.e.19.1		8	56.11	odd	6
392.2.m.e.19.2		8	56.3	even	6
392.2.m.e.227.1		8	7.5	odd	6
392.2.m.e.227.2		8	7.2	even	3
1568.2.e.c.783.1		8	28.27	even	2
1568.2.e.c.783.2		8	56.13	odd	2
1568.2.e.c.783.7		8	8.5	even	2
1568.2.e.c.783.8		8	4.3	odd	2
1568.2.q.c.815.1		8	56.37	even	6
1568.2.q.c.815.4		8	56.5	odd	6
1568.2.q.c.1391.1		8	28.3	even	6
1568.2.q.c.1391.4		8	28.11	odd	6
1568.2.q.d.815.1		8	28.23	odd	6
1568.2.q.d.815.4		8	28.19	even	6
1568.2.q.d.1391.1		8	56.45	odd	6
1568.2.q.d.1391.4		8	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} -2.61313i q^{3} +(-1.00000 - 1.73205i) q^{4} +3.20041 q^{5} +(-3.20041 - 1.84776i) q^{6} -2.82843 q^{8} -3.82843 q^{9} +(2.26303 - 3.91969i) q^{10} -2.00000 q^{11} +(-4.52607 + 2.61313i) q^{12} +5.07517 q^{13} -8.36308i q^{15} +(-2.00000 + 3.46410i) q^{16} +0.317025i q^{17} +(-2.70711 + 4.68885i) q^{18} +4.77791i q^{19} +(-3.20041 - 5.54328i) q^{20} +(-1.41421 + 2.44949i) q^{22} +1.43488i q^{23} +7.39104i q^{24} +5.24264 q^{25} +(3.58869 - 6.21579i) q^{26} +2.16478i q^{27} +9.37769i q^{29} +(-10.2426 - 5.91359i) q^{30} -2.65131 q^{31} +(2.82843 + 4.89898i) q^{32} +5.22625i q^{33} +(0.388275 + 0.224171i) q^{34} +(3.82843 + 6.63103i) q^{36} -2.44949i q^{37} +(5.85172 + 3.37849i) q^{38} -13.2621i q^{39} -9.05213 q^{40} -4.46088i q^{41} -8.82843 q^{43} +(2.00000 + 3.46410i) q^{44} -12.2525 q^{45} +(1.75736 + 1.01461i) q^{46} +5.30262 q^{47} +(9.05213 + 5.22625i) q^{48} +(3.70711 - 6.42090i) q^{50} +0.828427 q^{51} +(-5.07517 - 8.79045i) q^{52} -3.46410i q^{53} +(2.65131 + 1.53073i) q^{54} -6.40083 q^{55} +12.4853 q^{57} +(11.4853 + 6.63103i) q^{58} -2.61313i q^{59} +(-14.4853 + 8.36308i) q^{60} -3.97696 q^{61} +(-1.87476 + 3.24718i) q^{62} +8.00000 q^{64} +16.2426 q^{65} +(6.40083 + 3.69552i) q^{66} +12.0000 q^{67} +(0.549104 - 0.317025i) q^{68} +3.74952 q^{69} +10.8284 q^{72} -1.39942i q^{73} +(-3.00000 - 1.73205i) q^{74} -13.6997i q^{75} +(8.27558 - 4.77791i) q^{76} +(-16.2426 - 9.37769i) q^{78} -11.8272i q^{79} +(-6.40083 + 11.0866i) q^{80} -5.82843 q^{81} +(-5.46345 - 3.15432i) q^{82} +8.47343i q^{83} +1.01461i q^{85} +(-6.24264 + 10.8126i) q^{86} +24.5051 q^{87} +5.65685 q^{88} -9.87285i q^{89} +(-8.66386 + 15.0062i) q^{90} +(2.48528 - 1.43488i) q^{92} +6.92820i q^{93} +(3.74952 - 6.49435i) q^{94} +15.2913i q^{95} +(12.8017 - 7.39104i) q^{96} +3.82683i q^{97} +7.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{18} + 8 q^{25} - 48 q^{30} + 8 q^{36} - 48 q^{43} + 16 q^{44} + 48 q^{46} + 24 q^{50} - 16 q^{51} + 32 q^{57} + 24 q^{58} - 48 q^{60} + 64 q^{64}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^18 + 8 * q^25 - 48 * q^30 + 8 * q^36 - 48 * q^43 + 16 * q^44 + 48 * q^46 + 24 * q^50 - 16 * q^51 + 32 * q^57 + 24 * q^58 - 48 * q^60 + 64 * q^64 + 96 * q^65 + 96 * q^67 + 64 * q^72 - 24 * q^74 - 96 * q^78 - 24 * q^81 - 16 * q^86 - 48 * q^92 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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