LMFDB - Embedded newform 1386.2.k.q.991.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1386,2,Mod(793,1386)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1386.793"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1386, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,-2,0,-2,4,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.q.793.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.20711 - 2.09077i) q^{5} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-1.20711 + 2.09077i) q^{10} +(-0.500000 + 0.866025i) q^{11} -6.82843 q^{13} +(-2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.91421 - 6.77962i) q^{17} +(2.41421 + 4.18154i) q^{19} +2.41421 q^{20} +1.00000 q^{22} +(-2.62132 - 4.54026i) q^{23} +(-0.414214 + 0.717439i) q^{25} +(3.41421 + 5.91359i) q^{26} +(1.00000 + 2.44949i) q^{28} -2.82843 q^{29} +(-5.24264 + 9.08052i) q^{31} +(-0.500000 + 0.866025i) q^{32} -7.82843 q^{34} +(-6.32843 - 0.866025i) q^{35} +(0.828427 + 1.43488i) q^{37} +(2.41421 - 4.18154i) q^{38} +(-1.20711 - 2.09077i) q^{40} -6.65685 q^{41} +2.82843 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-2.62132 + 4.54026i) q^{46} +(0.378680 + 0.655892i) q^{47} +(-1.74264 - 6.77962i) q^{49} +0.828427 q^{50} +(3.41421 - 5.91359i) q^{52} +(5.41421 - 9.37769i) q^{53} +2.41421 q^{55} +(1.62132 - 2.09077i) q^{56} +(1.41421 + 2.44949i) q^{58} +(-3.82843 + 6.63103i) q^{59} +(2.20711 + 3.82282i) q^{61} +10.4853 q^{62} +1.00000 q^{64} +(8.24264 + 14.2767i) q^{65} +(-1.74264 + 3.01834i) q^{67} +(3.91421 + 6.77962i) q^{68} +(2.41421 + 5.91359i) q^{70} -9.31371 q^{71} +(-0.414214 + 0.717439i) q^{73} +(0.828427 - 1.43488i) q^{74} -4.82843 q^{76} +(1.00000 + 2.44949i) q^{77} +(-6.62132 - 11.4685i) q^{79} +(-1.20711 + 2.09077i) q^{80} +(3.32843 + 5.76500i) q^{82} -4.17157 q^{83} -18.8995 q^{85} +(-1.41421 - 2.44949i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(2.24264 + 3.88437i) q^{89} +(-11.0711 + 14.2767i) q^{91} +5.24264 q^{92} +(0.378680 - 0.655892i) q^{94} +(5.82843 - 10.0951i) q^{95} -15.8284 q^{97} +(-5.00000 + 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{11} - 16 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 2 q^{23} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 4 q^{31}+ \cdots - 20 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^11 - 16 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 - 2 * q^23 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 4 * q^31 - 2 * q^32 - 20 * q^34 - 14 * q^35 - 8 * q^37 + 4 * q^38 - 2 * q^40 - 4 * q^41 - 2 * q^44 - 2 * q^46 + 10 * q^47 + 10 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^53 + 4 * q^55 - 2 * q^56 - 4 * q^59 + 6 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^65 + 10 * q^67 + 10 * q^68 + 4 * q^70 + 8 * q^71 + 4 * q^73 - 8 * q^74 - 8 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 + 2 * q^82 - 28 * q^83 - 36 * q^85 - 2 * q^88 - 8 * q^89 - 16 * q^91 + 4 * q^92 + 10 * q^94 + 12 * q^95 - 52 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.20711	−	2.09077i	−0.539835	−	0.935021i	−0.998912	−	0.0466249i	$-0.985153\pi$
$5$	−1.20711	−	2.09077i	−0.539835	−	0.935021i	0.459078	−	0.888396i	$-0.348180\pi$
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.20711	+	2.09077i	−0.381721	+	0.661160i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−6.82843			−1.89386			−0.946932	−	0.321433i	$-0.895836\pi$
$13$	−6.82843			−1.89386			−0.946932	+	0.321433i	$0.895836\pi$
$14$	−2.62132	−	0.358719i	−0.700577	−	0.0958718i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.91421	−	6.77962i	0.949336	−	1.64430i	0.202509	−	0.979280i	$-0.435090\pi$
$17$	3.91421	−	6.77962i	0.949336	−	1.64430i	0.746827	−	0.665018i	$-0.231576\pi$
$18$		0			0
$19$	2.41421	+	4.18154i	0.553859	+	0.959311i	0.997991	+	0.0633502i	$0.0201785\pi$
$19$	2.41421	+	4.18154i	0.553859	+	0.959311i	−0.444133	+	0.895961i	$0.646488\pi$
$20$	2.41421			0.539835
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.62132	−	4.54026i	−0.546583	−	0.946710i	−0.998505	−	0.0546524i	$-0.982595\pi$
$23$	−2.62132	−	4.54026i	−0.546583	−	0.946710i	0.451922	−	0.892057i	$-0.350738\pi$
$24$		0			0
$25$	−0.414214	+	0.717439i	−0.0828427	+	0.143488i
$26$	3.41421	+	5.91359i	0.669582	+	1.15975i
$27$		0			0
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		0			0
$31$	−5.24264	+	9.08052i	−0.941606	+	1.63091i	−0.179198	+	0.983813i	$0.557350\pi$
$31$	−5.24264	+	9.08052i	−0.941606	+	1.63091i	−0.762408	+	0.647097i	$0.775983\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−7.82843			−1.34256
$35$	−6.32843	−	0.866025i	−1.06970	−	0.146385i
$36$		0			0
$37$	0.828427	+	1.43488i	0.136193	+	0.235892i	0.926052	−	0.377395i	$-0.123180\pi$
$37$	0.828427	+	1.43488i	0.136193	+	0.235892i	−0.789860	+	0.613287i	$0.789847\pi$
$38$	2.41421	−	4.18154i	0.391637	−	0.678335i
$39$		0			0
$40$	−1.20711	−	2.09077i	−0.190860	−	0.330580i
$41$	−6.65685			−1.03963			−0.519813	−	0.854280i	$-0.673998\pi$
$41$	−6.65685			−1.03963			−0.519813	+	0.854280i	$0.673998\pi$
$42$		0			0
$43$	2.82843			0.431331			0.215666	−	0.976467i	$-0.430808\pi$
$43$	2.82843			0.431331			0.215666	+	0.976467i	$0.430808\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	−2.62132	+	4.54026i	−0.386493	+	0.669425i
$47$	0.378680	+	0.655892i	0.0552361	+	0.0956717i	0.892321	−	0.451401i	$-0.149076\pi$
$47$	0.378680	+	0.655892i	0.0552361	+	0.0956717i	−0.837085	+	0.547073i	$0.815742\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	0.828427			0.117157
$51$		0			0
$52$	3.41421	−	5.91359i	0.473466	−	0.820068i
$53$	5.41421	−	9.37769i	0.743699	−	1.28813i	−0.207101	−	0.978320i	$-0.566403\pi$
$53$	5.41421	−	9.37769i	0.743699	−	1.28813i	0.950800	−	0.309806i	$-0.100264\pi$
$54$		0			0
$55$	2.41421			0.325532
$56$	1.62132	−	2.09077i	0.216658	−	0.279391i
$57$		0			0
$58$	1.41421	+	2.44949i	0.185695	+	0.321634i
$59$	−3.82843	+	6.63103i	−0.498419	+	0.863287i	−0.999998	−	0.00182490i	$-0.999419\pi$
$59$	−3.82843	+	6.63103i	−0.498419	+	0.863287i	0.501580	+	0.865112i	$0.332752\pi$
$60$		0			0
$61$	2.20711	+	3.82282i	0.282591	+	0.489462i	0.972022	−	0.234889i	$-0.0754727\pi$
$61$	2.20711	+	3.82282i	0.282591	+	0.489462i	−0.689431	+	0.724351i	$0.742139\pi$
$62$	10.4853			1.33163
$63$		0			0
$64$	1.00000			0.125000
$65$	8.24264	+	14.2767i	1.02237	+	1.77080i
$66$		0			0
$67$	−1.74264	+	3.01834i	−0.212897	+	0.368749i	−0.952620	−	0.304163i	$-0.901623\pi$
$67$	−1.74264	+	3.01834i	−0.212897	+	0.368749i	0.739723	+	0.672912i	$0.234957\pi$
$68$	3.91421	+	6.77962i	0.474668	+	0.822149i
$69$		0			0
$70$	2.41421	+	5.91359i	0.288554	+	0.706809i
$71$	−9.31371			−1.10533			−0.552667	−	0.833402i	$-0.686390\pi$
$71$	−9.31371			−1.10533			−0.552667	+	0.833402i	$0.686390\pi$
$72$		0			0
$73$	−0.414214	+	0.717439i	−0.0484800	+	0.0839699i	−0.889247	−	0.457427i	$-0.848771\pi$
$73$	−0.414214	+	0.717439i	−0.0484800	+	0.0839699i	0.840767	+	0.541397i	$0.182104\pi$
$74$	0.828427	−	1.43488i	0.0963027	−	0.166801i
$75$		0			0
$76$	−4.82843			−0.553859
$77$	1.00000	+	2.44949i	0.113961	+	0.279145i
$78$		0			0
$79$	−6.62132	−	11.4685i	−0.744957	−	1.29030i	−0.950215	−	0.311595i	$-0.899137\pi$
$79$	−6.62132	−	11.4685i	−0.744957	−	1.29030i	0.205258	−	0.978708i	$-0.434197\pi$
$80$	−1.20711	+	2.09077i	−0.134959	+	0.233755i
$81$		0			0
$82$	3.32843	+	5.76500i	0.367563	+	0.636638i
$83$	−4.17157			−0.457890			−0.228945	−	0.973439i	$-0.573528\pi$
$83$	−4.17157			−0.457890			−0.228945	+	0.973439i	$0.573528\pi$
$84$		0			0
$85$	−18.8995			−2.04994
$86$	−1.41421	−	2.44949i	−0.152499	−	0.264135i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	2.24264	+	3.88437i	0.237719	+	0.411742i	0.960060	−	0.279796i	$-0.0902668\pi$
$89$	2.24264	+	3.88437i	0.237719	+	0.411742i	−0.722340	+	0.691538i	$0.756933\pi$
$90$		0			0
$91$	−11.0711	+	14.2767i	−1.16056	+	1.49660i
$92$	5.24264			0.546583
$93$		0			0
$94$	0.378680	−	0.655892i	0.0390578	−	0.0676501i
$95$	5.82843	−	10.0951i	0.597984	−	1.03574i
$96$		0			0
$97$	−15.8284			−1.60713			−0.803567	−	0.595215i	$-0.797067\pi$
$97$	−15.8284			−1.60713			−0.803567	+	0.595215i	$0.797067\pi$
$98$	−5.00000	+	4.89898i	−0.505076	+	0.494872i
$99$		0			0
$100$	−0.414214	−	0.717439i	−0.0414214	−	0.0717439i
$101$	−7.07107	+	12.2474i	−0.703598	+	1.21867i	0.263598	+	0.964633i	$0.415091\pi$
$101$	−7.07107	+	12.2474i	−0.703598	+	1.21867i	−0.967195	+	0.254034i	$0.918242\pi$
$102$		0			0
$103$	7.41421	+	12.8418i	0.730544	+	1.26534i	0.956651	+	0.291237i	$0.0940669\pi$
$103$	7.41421	+	12.8418i	0.730544	+	1.26534i	−0.226107	+	0.974103i	$0.572600\pi$
$104$	−6.82843			−0.669582
$105$		0			0
$106$	−10.8284			−1.05175
$107$	2.67157	+	4.62730i	0.258271	+	0.447338i	0.965779	−	0.259367i	$-0.0835140\pi$
$107$	2.67157	+	4.62730i	0.258271	+	0.447338i	−0.707508	+	0.706705i	$0.750181\pi$
$108$		0			0
$109$	2.62132	−	4.54026i	0.251077	−	0.434878i	−0.712746	−	0.701423i	$-0.752549\pi$
$109$	2.62132	−	4.54026i	0.251077	−	0.434878i	0.963823	+	0.266545i	$0.0858819\pi$
$110$	−1.20711	−	2.09077i	−0.115093	−	0.199347i
$111$		0			0
$112$	−2.62132	−	0.358719i	−0.247691	−	0.0338958i
$113$	−7.65685			−0.720296			−0.360148	−	0.932895i	$-0.617274\pi$
$113$	−7.65685			−0.720296			−0.360148	+	0.932895i	$0.617274\pi$
$114$		0			0
$115$	−6.32843	+	10.9612i	−0.590129	+	1.02213i
$116$	1.41421	−	2.44949i	0.131306	−	0.227429i
$117$		0			0
$118$	7.65685			0.704871
$119$	−7.82843	−	19.1757i	−0.717631	−	1.75783i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.20711	−	3.82282i	0.199822	−	0.346102i
$123$		0			0
$124$	−5.24264	−	9.08052i	−0.470803	−	0.815455i
$125$	−10.0711			−0.900784
$126$		0			0
$127$	−7.24264			−0.642680			−0.321340	−	0.946964i	$-0.604133\pi$
$127$	−7.24264			−0.642680			−0.321340	+	0.946964i	$0.604133\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	8.24264	−	14.2767i	0.722927	−	1.25215i
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	0.980384	−	0.197097i	$-0.0631514\pi$
$131$	3.65685	+	6.33386i	0.319501	+	0.553392i	−0.660883	+	0.750489i	$0.729818\pi$
$132$		0			0
$133$	12.6569	+	1.73205i	1.09749	+	0.150188i
$134$	3.48528			0.301082
$135$		0			0
$136$	3.91421	−	6.77962i	0.335641	−	0.581347i
$137$	−0.414214	+	0.717439i	−0.0353887	+	0.0612949i	−0.883177	−	0.469039i	$-0.844600\pi$
$137$	−0.414214	+	0.717439i	−0.0353887	+	0.0612949i	0.847789	+	0.530334i	$0.177934\pi$
$138$		0			0
$139$	−6.00000			−0.508913			−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000			−0.508913			−0.254457	+	0.967084i	$0.581897\pi$
$140$	3.91421	−	5.04757i	0.330811	−	0.426597i
$141$		0			0
$142$	4.65685	+	8.06591i	0.390795	+	0.676876i
$143$	3.41421	−	5.91359i	0.285511	−	0.494519i
$144$		0			0
$145$	3.41421	+	5.91359i	0.283535	+	0.491097i
$146$	0.828427			0.0685611
$147$		0			0
$148$	−1.65685			−0.136193
$149$	5.65685	+	9.79796i	0.463428	+	0.802680i	0.999129	−	0.0417274i	$-0.0132861\pi$
$149$	5.65685	+	9.79796i	0.463428	+	0.802680i	−0.535701	+	0.844407i	$0.679953\pi$
$150$		0			0
$151$	3.62132	−	6.27231i	0.294699	−	0.510433i	−0.680216	−	0.733012i	$-0.738114\pi$
$151$	3.62132	−	6.27231i	0.294699	−	0.510433i	0.974915	+	0.222578i	$0.0714473\pi$
$152$	2.41421	+	4.18154i	0.195819	+	0.339168i
$153$		0			0
$154$	1.62132	−	2.09077i	0.130650	−	0.168479i
$155$	25.3137			2.03325
$156$		0			0
$157$	7.41421	−	12.8418i	0.591719	−	1.02489i	−0.402282	−	0.915516i	$-0.631783\pi$
$157$	7.41421	−	12.8418i	0.591719	−	1.02489i	0.994001	−	0.109371i	$-0.0348837\pi$
$158$	−6.62132	+	11.4685i	−0.526764	+	0.912382i
$159$		0			0
$160$	2.41421			0.190860
$161$	−13.7426	−	1.88064i	−1.08307	−	0.148215i
$162$		0			0
$163$	−1.50000	−	2.59808i	−0.117489	−	0.203497i	0.801283	−	0.598286i	$-0.204151\pi$
$163$	−1.50000	−	2.59808i	−0.117489	−	0.203497i	−0.918772	+	0.394789i	$0.870818\pi$
$164$	3.32843	−	5.76500i	0.259906	−	0.450171i
$165$		0			0
$166$	2.08579	+	3.61269i	0.161888	+	0.280399i
$167$	0.485281			0.0375522			0.0187761	−	0.999824i	$-0.494023\pi$
$167$	0.485281			0.0375522			0.0187761	+	0.999824i	$0.494023\pi$
$168$		0			0
$169$	33.6274			2.58672
$170$	9.44975	+	16.3674i	0.724763	+	1.25533i
$171$		0			0
$172$	−1.41421	+	2.44949i	−0.107833	+	0.186772i
$173$	−8.07107	−	13.9795i	−0.613632	−	1.06284i	−0.990623	−	0.136625i	$-0.956375\pi$
$173$	−8.07107	−	13.9795i	−0.613632	−	1.06284i	0.376991	−	0.926217i	$-0.376959\pi$
$174$		0			0
$175$	0.828427	+	2.02922i	0.0626232	+	0.153395i
$176$	1.00000			0.0753778
$177$		0			0
$178$	2.24264	−	3.88437i	0.168093	−	0.291146i
$179$	4.41421	−	7.64564i	0.329934	−	0.571462i	−0.652565	−	0.757733i	$-0.726307\pi$
$179$	4.41421	−	7.64564i	0.329934	−	0.571462i	0.982498	+	0.186271i	$0.0596402\pi$
$180$		0			0
$181$	−13.6569			−1.01511			−0.507553	−	0.861621i	$-0.669450\pi$
$181$	−13.6569			−1.01511			−0.507553	+	0.861621i	$0.669450\pi$
$182$	17.8995	+	2.44949i	1.32680	+	0.181568i
$183$		0			0
$184$	−2.62132	−	4.54026i	−0.193246	−	0.334712i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	3.91421	+	6.77962i	0.286236	+	0.495775i
$188$	−0.757359			−0.0552361
$189$		0			0
$190$	−11.6569			−0.845677
$191$	−6.65685	−	11.5300i	−0.481673	−	0.834282i	0.518106	−	0.855317i	$-0.326637\pi$
$191$	−6.65685	−	11.5300i	−0.481673	−	0.834282i	−0.999779	+	0.0210344i	$0.993304\pi$
$192$		0			0
$193$	7.41421	−	12.8418i	0.533687	−	0.924373i	−0.465539	−	0.885027i	$-0.654139\pi$
$193$	7.41421	−	12.8418i	0.533687	−	0.924373i	0.999226	−	0.0393452i	$-0.0125272\pi$
$194$	7.91421	+	13.7078i	0.568207	+	0.984164i
$195$		0			0
$196$	6.74264	+	1.88064i	0.481617	+	0.134331i
$197$	−20.4853			−1.45952			−0.729758	−	0.683706i	$-0.760367\pi$
$197$	−20.4853			−1.45952			−0.729758	+	0.683706i	$0.760367\pi$
$198$		0			0
$199$	9.82843	−	17.0233i	0.696719	−	1.20675i	−0.272879	−	0.962048i	$-0.587976\pi$
$199$	9.82843	−	17.0233i	0.696719	−	1.20675i	0.969598	−	0.244704i	$-0.0786908\pi$
$200$	−0.414214	+	0.717439i	−0.0292893	+	0.0507306i
$201$		0			0
$202$	14.1421			0.995037
$203$	−4.58579	+	5.91359i	−0.321859	+	0.415053i
$204$		0			0
$205$	8.03553	+	13.9180i	0.561226	+	0.972072i
$206$	7.41421	−	12.8418i	0.516573	−	0.894730i
$207$		0			0
$208$	3.41421	+	5.91359i	0.236733	+	0.410034i
$209$	−4.82843			−0.333989
$210$		0			0
$211$	9.17157			0.631397			0.315699	−	0.948860i	$-0.397761\pi$
$211$	9.17157			0.631397			0.315699	+	0.948860i	$0.397761\pi$
$212$	5.41421	+	9.37769i	0.371850	+	0.644063i
$213$		0			0
$214$	2.67157	−	4.62730i	0.182625	−	0.316316i
$215$	−3.41421	−	5.91359i	−0.232847	−	0.403304i
$216$		0			0
$217$	10.4853	+	25.6836i	0.711787	+	1.74352i
$218$	−5.24264			−0.355076
$219$		0			0
$220$	−1.20711	+	2.09077i	−0.0813831	+	0.140960i
$221$	−26.7279	+	46.2941i	−1.79791	+	3.11408i
$222$		0			0
$223$	9.31371			0.623692			0.311846	−	0.950133i	$-0.399053\pi$
$223$	9.31371			0.623692			0.311846	+	0.950133i	$0.399053\pi$
$224$	1.00000	+	2.44949i	0.0668153	+	0.163663i
$225$		0			0
$226$	3.82843	+	6.63103i	0.254663	+	0.441090i
$227$	5.15685	−	8.93193i	0.342272	−	0.592833i	−0.642582	−	0.766217i	$-0.722137\pi$
$227$	5.15685	−	8.93193i	0.342272	−	0.592833i	0.984854	+	0.173384i	$0.0554701\pi$
$228$		0			0
$229$	−5.65685	−	9.79796i	−0.373815	−	0.647467i	0.616334	−	0.787485i	$-0.288617\pi$
$229$	−5.65685	−	9.79796i	−0.373815	−	0.647467i	−0.990149	+	0.140018i	$0.955284\pi$
$230$	12.6569			0.834568
$231$		0			0
$232$	−2.82843			−0.185695
$233$	7.15685	+	12.3960i	0.468861	+	0.812091i	0.999366	−	0.0355903i	$-0.0113311\pi$
$233$	7.15685	+	12.3960i	0.468861	+	0.812091i	−0.530505	+	0.847682i	$0.677998\pi$
$234$		0			0
$235$	0.914214	−	1.58346i	0.0596367	−	0.103294i
$236$	−3.82843	−	6.63103i	−0.249209	−	0.431643i
$237$		0			0
$238$	−12.6924	+	16.3674i	−0.822725	+	1.06094i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	4.48528	−	7.76874i	0.288922	−	0.500428i	−0.684630	−	0.728890i	$-0.740036\pi$
$241$	4.48528	−	7.76874i	0.288922	−	0.500428i	0.973553	+	0.228462i	$0.0733697\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	−4.41421			−0.282591
$245$	−12.0711	+	11.8272i	−0.771192	+	0.755611i
$246$		0			0
$247$	−16.4853	−	28.5533i	−1.04893	−	1.81681i
$248$	−5.24264	+	9.08052i	−0.332908	+	0.576614i
$249$		0			0
$250$	5.03553	+	8.72180i	0.318475	+	0.551615i
$251$	−2.14214			−0.135210			−0.0676052	−	0.997712i	$-0.521536\pi$
$251$	−2.14214			−0.135210			−0.0676052	+	0.997712i	$0.521536\pi$
$252$		0			0
$253$	5.24264			0.329602
$254$	3.62132	+	6.27231i	0.227222	+	0.393560i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.4142	−	26.6982i	−0.961512	−	1.66539i	−0.718707	−	0.695313i	$-0.755266\pi$
$257$	−15.4142	−	26.6982i	−0.961512	−	1.66539i	−0.242805	−	0.970075i	$-0.578068\pi$
$258$		0			0
$259$	4.34315	+	0.594346i	0.269870	+	0.0369309i
$260$	−16.4853			−1.02237
$261$		0			0
$262$	3.65685	−	6.33386i	0.225921	−	0.391307i
$263$	6.65685	−	11.5300i	0.410479	−	0.710971i	−0.584463	−	0.811420i	$-0.698695\pi$
$263$	6.65685	−	11.5300i	0.410479	−	0.710971i	0.994942	+	0.100450i	$0.0320281\pi$
$264$		0			0
$265$	−26.1421			−1.60590
$266$	−4.82843	−	11.8272i	−0.296050	−	0.725171i
$267$		0			0
$268$	−1.74264	−	3.01834i	−0.106449	−	0.184375i
$269$	−3.03553	+	5.25770i	−0.185080	+	0.320568i	−0.943603	−	0.331078i	$-0.892588\pi$
$269$	−3.03553	+	5.25770i	−0.185080	+	0.320568i	0.758524	+	0.651646i	$0.225921\pi$
$270$		0			0
$271$	−4.65685	−	8.06591i	−0.282884	−	0.489969i	0.689210	−	0.724562i	$-0.257958\pi$
$271$	−4.65685	−	8.06591i	−0.282884	−	0.489969i	−0.972094	+	0.234593i	$0.924624\pi$
$272$	−7.82843			−0.474668
$273$		0			0
$274$	0.828427			0.0500471
$275$	−0.414214	−	0.717439i	−0.0249780	−	0.0432632i
$276$		0			0
$277$	0.585786	−	1.01461i	0.0351965	−	0.0609621i	−0.847891	−	0.530171i	$-0.822128\pi$
$277$	0.585786	−	1.01461i	0.0351965	−	0.0609621i	0.883087	+	0.469209i	$0.155461\pi$
$278$	3.00000	+	5.19615i	0.179928	+	0.311645i
$279$		0			0
$280$	−6.32843	−	0.866025i	−0.378196	−	0.0517549i
$281$	19.4853			1.16239			0.581197	−	0.813763i	$-0.302584\pi$
$281$	19.4853			1.16239			0.581197	+	0.813763i	$0.302584\pi$
$282$		0			0
$283$	15.0711	−	26.1039i	0.895882	−	1.55171i	0.0631728	−	0.998003i	$-0.479878\pi$
$283$	15.0711	−	26.1039i	0.895882	−	1.55171i	0.832709	−	0.553711i	$-0.186789\pi$
$284$	4.65685	−	8.06591i	0.276333	−	0.478624i
$285$		0			0
$286$	−6.82843			−0.403773
$287$	−10.7929	+	13.9180i	−0.637084	+	0.821551i
$288$		0			0
$289$	−22.1421	−	38.3513i	−1.30248	−	2.25596i
$290$	3.41421	−	5.91359i	0.200490	−	0.347258i
$291$		0			0
$292$	−0.414214	−	0.717439i	−0.0242400	−	0.0419849i
$293$	7.17157			0.418968			0.209484	−	0.977812i	$-0.432822\pi$
$293$	7.17157			0.418968			0.209484	+	0.977812i	$0.432822\pi$
$294$		0			0
$295$	18.4853			1.07625
$296$	0.828427	+	1.43488i	0.0481513	+	0.0834006i
$297$		0			0
$298$	5.65685	−	9.79796i	0.327693	−	0.567581i
$299$	17.8995	+	31.0028i	1.03515	+	1.79294i
$300$		0			0
$301$	4.58579	−	5.91359i	0.264320	−	0.340854i
$302$	−7.24264			−0.416767
$303$		0			0
$304$	2.41421	−	4.18154i	0.138465	−	0.239828i
$305$	5.32843	−	9.22911i	0.305105	−	0.528457i
$306$		0			0
$307$	10.6274			0.606539			0.303269	−	0.952905i	$-0.401922\pi$
$307$	10.6274			0.606539			0.303269	+	0.952905i	$0.401922\pi$
$308$	−2.62132	−	0.358719i	−0.149364	−	0.0204399i
$309$		0			0
$310$	−12.6569	−	21.9223i	−0.718861	−	1.24510i
$311$	16.1066	−	27.8975i	0.913322	−	1.58192i	0.103981	−	0.994579i	$-0.466842\pi$
$311$	16.1066	−	27.8975i	0.913322	−	1.58192i	0.809340	−	0.587340i	$-0.199825\pi$
$312$		0			0
$313$	3.34315	+	5.79050i	0.188966	+	0.327298i	0.944906	−	0.327343i	$-0.106153\pi$
$313$	3.34315	+	5.79050i	0.188966	+	0.327298i	−0.755940	+	0.654641i	$0.772820\pi$
$314$	−14.8284			−0.836817
$315$		0			0
$316$	13.2426			0.744957
$317$	−9.93503	−	17.2080i	−0.558007	−	0.966496i	−0.997663	−	0.0683299i	$-0.978233\pi$
$317$	−9.93503	−	17.2080i	−0.558007	−	0.966496i	0.439656	−	0.898166i	$-0.355100\pi$
$318$		0			0
$319$	1.41421	−	2.44949i	0.0791808	−	0.137145i
$320$	−1.20711	−	2.09077i	−0.0674793	−	0.116878i
$321$		0			0
$322$	5.24264	+	12.8418i	0.292161	+	0.715645i
$323$	37.7990			2.10319
$324$		0			0
$325$	2.82843	−	4.89898i	0.156893	−	0.271746i
$326$	−1.50000	+	2.59808i	−0.0830773	+	0.143894i
$327$		0			0
$328$	−6.65685			−0.367563
$329$	1.98528	+	0.271680i	0.109452	+	0.0149782i
$330$		0			0
$331$	8.15685	+	14.1281i	0.448341	+	0.776550i	0.998278	−	0.0586563i	$-0.0186816\pi$
$331$	8.15685	+	14.1281i	0.448341	+	0.776550i	−0.549937	+	0.835206i	$0.685348\pi$
$332$	2.08579	−	3.61269i	0.114472	−	0.198272i
$333$		0			0
$334$	−0.242641	−	0.420266i	−0.0132767	−	0.0229959i
$335$	8.41421			0.459718
$336$		0			0
$337$	26.4853			1.44275			0.721373	−	0.692547i	$-0.243512\pi$
$337$	26.4853			1.44275			0.721373	+	0.692547i	$0.243512\pi$
$338$	−16.8137	−	29.1222i	−0.914545	−	1.58404i
$339$		0			0
$340$	9.44975	−	16.3674i	0.512485	−	0.887649i
$341$	−5.24264	−	9.08052i	−0.283905	−	0.491738i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	2.82843			0.152499
$345$		0			0
$346$	−8.07107	+	13.9795i	−0.433903	+	0.751543i
$347$	−16.5711	+	28.7019i	−0.889582	+	1.54080i	−0.0492108	+	0.998788i	$0.515671\pi$
$347$	−16.5711	+	28.7019i	−0.889582	+	1.54080i	−0.840371	+	0.542012i	$0.817663\pi$
$348$		0			0
$349$	9.72792			0.520724			0.260362	−	0.965511i	$-0.416158\pi$
$349$	9.72792			0.520724			0.260362	+	0.965511i	$0.416158\pi$
$350$	1.34315	−	1.73205i	0.0717942	−	0.0925820i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	5.58579	−	9.67487i	0.297301	−	0.514941i	−0.678216	−	0.734862i	$-0.737247\pi$
$353$	5.58579	−	9.67487i	0.297301	−	0.514941i	0.975518	+	0.219921i	$0.0705800\pi$
$354$		0			0
$355$	11.2426	+	19.4728i	0.596697	+	1.03351i
$356$	−4.48528			−0.237719
$357$		0			0
$358$	−8.82843			−0.466597
$359$	−4.24264	−	7.34847i	−0.223918	−	0.387837i	0.732076	−	0.681223i	$-0.238551\pi$
$359$	−4.24264	−	7.34847i	−0.223918	−	0.387837i	−0.955994	+	0.293385i	$0.905218\pi$
$360$		0			0
$361$	−2.15685	+	3.73578i	−0.113519	+	0.196620i
$362$	6.82843	+	11.8272i	0.358894	+	0.621623i
$363$		0			0
$364$	−6.82843	−	16.7262i	−0.357907	−	0.876689i
$365$	2.00000			0.104685
$366$		0			0
$367$	−11.2426	+	19.4728i	−0.586861	+	1.01647i	0.407780	+	0.913080i	$0.366303\pi$
$367$	−11.2426	+	19.4728i	−0.586861	+	1.01647i	−0.994641	+	0.103393i	$0.967030\pi$
$368$	−2.62132	+	4.54026i	−0.136646	+	0.236677i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	−10.8284	−	26.5241i	−0.562184	−	1.37706i
$372$		0			0
$373$	−4.86396	−	8.42463i	−0.251846	−	0.436211i	0.712188	−	0.701989i	$-0.247704\pi$
$373$	−4.86396	−	8.42463i	−0.251846	−	0.436211i	−0.964034	+	0.265778i	$0.914371\pi$
$374$	3.91421	−	6.77962i	0.202399	−	0.350566i
$375$		0			0
$376$	0.378680	+	0.655892i	0.0195289	+	0.0338251i
$377$	19.3137			0.994707
$378$		0			0
$379$	30.6569			1.57474			0.787368	−	0.616483i	$-0.211443\pi$
$379$	30.6569			1.57474			0.787368	+	0.616483i	$0.211443\pi$
$380$	5.82843	+	10.0951i	0.298992	+	0.517869i
$381$		0			0
$382$	−6.65685	+	11.5300i	−0.340594	+	0.589927i
$383$	−11.1421	−	19.2987i	−0.569337	−	0.986120i	−0.996632	−	0.0820076i	$-0.973867\pi$
$383$	−11.1421	−	19.2987i	−0.569337	−	0.986120i	0.427295	−	0.904112i	$-0.359467\pi$
$384$		0			0
$385$	3.91421	−	5.04757i	0.199487	−	0.257248i
$386$	−14.8284			−0.754747
$387$		0			0
$388$	7.91421	−	13.7078i	0.401783	−	0.695909i
$389$	−11.8640	+	20.5490i	−0.601527	+	1.04187i	0.391063	+	0.920364i	$0.372107\pi$
$389$	−11.8640	+	20.5490i	−0.601527	+	1.04187i	−0.992590	+	0.121511i	$0.961226\pi$
$390$		0			0
$391$	−41.0416			−2.07556
$392$	−1.74264	−	6.77962i	−0.0880166	−	0.342422i
$393$		0			0
$394$	10.2426	+	17.7408i	0.516017	+	0.893767i
$395$	−15.9853	+	27.6873i	−0.804307	+	1.39310i
$396$		0			0
$397$	2.24264	+	3.88437i	0.112555	+	0.194951i	0.916800	−	0.399347i	$-0.130763\pi$
$397$	2.24264	+	3.88437i	0.112555	+	0.194951i	−0.804245	+	0.594298i	$0.797430\pi$
$398$	−19.6569			−0.985309
$399$		0			0
$400$	0.828427			0.0414214
$401$	−11.8995	−	20.6105i	−0.594232	−	1.02924i	−0.993655	−	0.112474i	$-0.964123\pi$
$401$	−11.8995	−	20.6105i	−0.594232	−	1.02924i	0.399422	−	0.916767i	$-0.369211\pi$
$402$		0			0
$403$	35.7990	−	62.0057i	1.78327	−	3.08872i
$404$	−7.07107	−	12.2474i	−0.351799	−	0.609333i
$405$		0			0
$406$	7.41421	+	1.01461i	0.367961	+	0.0503543i
$407$	−1.65685			−0.0821272
$408$		0			0
$409$	−19.7279	+	34.1698i	−0.975483	+	1.68959i	−0.297151	+	0.954831i	$0.596036\pi$
$409$	−19.7279	+	34.1698i	−0.975483	+	1.68959i	−0.678332	+	0.734756i	$0.737297\pi$
$410$	8.03553	−	13.9180i	0.396847	−	0.687359i
$411$		0			0
$412$	−14.8284			−0.730544
$413$	7.65685	+	18.7554i	0.376769	+	0.922892i
$414$		0			0
$415$	5.03553	+	8.72180i	0.247185	+	0.428136i
$416$	3.41421	−	5.91359i	0.167396	−	0.289938i
$417$		0			0
$418$	2.41421	+	4.18154i	0.118083	+	0.204526i
$419$	13.7990			0.674125			0.337062	−	0.941482i	$-0.390567\pi$
$419$	13.7990			0.674125			0.337062	+	0.941482i	$0.390567\pi$
$420$		0			0
$421$	9.17157			0.446995			0.223498	−	0.974704i	$-0.428253\pi$
$421$	9.17157			0.446995			0.223498	+	0.974704i	$0.428253\pi$
$422$	−4.58579	−	7.94282i	−0.223233	−	0.386650i
$423$		0			0
$424$	5.41421	−	9.37769i	0.262937	−	0.455421i
$425$	3.24264	+	5.61642i	0.157291	+	0.272436i
$426$		0			0
$427$	11.5711	+	1.58346i	0.559963	+	0.0766292i
$428$	−5.34315			−0.258271
$429$		0			0
$430$	−3.41421	+	5.91359i	−0.164648	+	0.285179i
$431$	12.4142	−	21.5020i	0.597972	−	1.03572i	−0.395149	−	0.918617i	$-0.629307\pi$
$431$	12.4142	−	21.5020i	0.597972	−	1.03572i	0.993120	−	0.117100i	$-0.0373598\pi$
$432$		0			0
$433$	−15.3431			−0.737345			−0.368672	−	0.929559i	$-0.620188\pi$
$433$	−15.3431			−0.737345			−0.368672	+	0.929559i	$0.620188\pi$
$434$	17.0000	−	21.9223i	0.816026	−	1.05230i
$435$		0			0
$436$	2.62132	+	4.54026i	0.125538	+	0.217439i
$437$	12.6569	−	21.9223i	0.605459	−	1.04869i
$438$		0			0
$439$	16.6924	+	28.9121i	0.796684	+	1.37990i	0.921764	+	0.387751i	$0.126748\pi$
$439$	16.6924	+	28.9121i	0.796684	+	1.37990i	−0.125080	+	0.992147i	$0.539919\pi$
$440$	2.41421			0.115093
$441$		0			0
$442$	53.4558			2.54264
$443$	−12.8284	−	22.2195i	−0.609497	−	1.05568i	−0.991323	−	0.131446i	$-0.958038\pi$
$443$	−12.8284	−	22.2195i	−0.609497	−	1.05568i	0.381826	−	0.924234i	$-0.375295\pi$
$444$		0			0
$445$	5.41421	−	9.37769i	0.256658	−	0.444545i
$446$	−4.65685	−	8.06591i	−0.220508	−	0.381932i
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$	−39.1127			−1.84584			−0.922921	−	0.384989i	$-0.874205\pi$
$449$	−39.1127			−1.84584			−0.922921	+	0.384989i	$0.874205\pi$
$450$		0			0
$451$	3.32843	−	5.76500i	0.156730	−	0.271463i
$452$	3.82843	−	6.63103i	0.180074	−	0.311897i
$453$		0			0
$454$	−10.3137			−0.484046
$455$	43.2132	+	5.91359i	2.02587	+	0.277233i
$456$		0			0
$457$	5.31371	+	9.20361i	0.248565	+	0.430527i	0.963128	−	0.269044i	$-0.0867078\pi$
$457$	5.31371	+	9.20361i	0.248565	+	0.430527i	−0.714563	+	0.699571i	$0.753374\pi$
$458$	−5.65685	+	9.79796i	−0.264327	+	0.457829i
$459$		0			0
$460$	−6.32843	−	10.9612i	−0.295064	−	0.511067i
$461$	−12.3431			−0.574878			−0.287439	−	0.957799i	$-0.592804\pi$
$461$	−12.3431			−0.574878			−0.287439	+	0.957799i	$0.592804\pi$
$462$		0			0
$463$	−39.1127			−1.81772			−0.908861	−	0.417100i	$-0.863046\pi$
$463$	−39.1127			−1.81772			−0.908861	+	0.417100i	$0.863046\pi$
$464$	1.41421	+	2.44949i	0.0656532	+	0.113715i
$465$		0			0
$466$	7.15685	−	12.3960i	0.331535	−	0.574235i
$467$	−15.4853	−	26.8213i	−0.716573	−	1.24114i	−0.962350	−	0.271815i	$-0.912376\pi$
$467$	−15.4853	−	26.8213i	−0.716573	−	1.24114i	0.245776	−	0.969327i	$-0.420957\pi$
$468$		0			0
$469$	3.48528	+	8.53716i	0.160935	+	0.394209i
$470$	−1.82843			−0.0843391
$471$		0			0
$472$	−3.82843	+	6.63103i	−0.176218	+	0.305218i
$473$	−1.41421	+	2.44949i	−0.0650256	+	0.112628i
$474$		0			0
$475$	−4.00000			−0.183533
$476$	20.5208	+	2.80821i	0.940570	+	0.128714i
$477$		0			0
$478$	−10.0000	−	17.3205i	−0.457389	−	0.792222i
$479$	−5.41421	+	9.37769i	−0.247382	+	0.428478i	−0.962799	−	0.270220i	$-0.912904\pi$
$479$	−5.41421	+	9.37769i	−0.247382	+	0.428478i	0.715417	+	0.698698i	$0.246237\pi$
$480$		0			0
$481$	−5.65685	−	9.79796i	−0.257930	−	0.446748i
$482$	−8.97056			−0.408598
$483$		0			0
$484$	1.00000			0.0454545
$485$	19.1066	+	33.0936i	0.867586	+	1.50270i
$486$		0			0
$487$	−0.656854	+	1.13770i	−0.0297649	+	0.0515543i	−0.880524	−	0.474001i	$-0.842809\pi$
$487$	−0.656854	+	1.13770i	−0.0297649	+	0.0515543i	0.850759	+	0.525556i	$0.176143\pi$
$488$	2.20711	+	3.82282i	0.0999110	+	0.173051i
$489$		0			0
$490$	16.2782	+	4.54026i	0.735373	+	0.205108i
$491$	29.6274			1.33707			0.668533	−	0.743682i	$-0.266922\pi$
$491$	29.6274			1.33707			0.668533	+	0.743682i	$0.266922\pi$
$492$		0			0
$493$	−11.0711	+	19.1757i	−0.498616	+	0.863628i
$494$	−16.4853	+	28.5533i	−0.741708	+	1.28468i
$495$		0			0
$496$	10.4853			0.470803
$497$	−15.1005	+	19.4728i	−0.677350	+	0.873476i
$498$		0			0
$499$	−12.8284	−	22.2195i	−0.574279	−	0.994681i	−0.996120	−	0.0880107i	$-0.971949\pi$
$499$	−12.8284	−	22.2195i	−0.574279	−	0.994681i	0.421840	−	0.906670i	$-0.361384\pi$
$500$	5.03553	−	8.72180i	0.225196	−	0.390051i
$501$		0			0
$502$	1.07107	+	1.85514i	0.0478041	+	0.0827991i
$503$	−24.9706			−1.11338			−0.556691	−	0.830720i	$-0.687929\pi$
$503$	−24.9706			−1.11338			−0.556691	+	0.830720i	$0.687929\pi$
$504$		0			0
$505$	34.1421			1.51931
$506$	−2.62132	−	4.54026i	−0.116532	−	0.201839i
$507$		0			0
$508$	3.62132	−	6.27231i	0.160670	−	0.278289i
$509$	−15.4142	−	26.6982i	−0.683223	−	1.18338i	−0.973992	−	0.226584i	$-0.927244\pi$
$509$	−15.4142	−	26.6982i	−0.683223	−	1.18338i	0.290769	−	0.956793i	$-0.406089\pi$
$510$		0			0
$511$	0.828427	+	2.02922i	0.0366475	+	0.0897676i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−15.4142	+	26.6982i	−0.679892	+	1.17761i
$515$	17.8995	−	31.0028i	0.788746	−	1.36615i
$516$		0			0
$517$	−0.757359			−0.0333086
$518$	−1.65685	−	4.05845i	−0.0727980	−	0.178318i
$519$		0			0
$520$	8.24264	+	14.2767i	0.361464	+	0.626074i
$521$	−3.34315	+	5.79050i	−0.146466	+	0.253686i	−0.929919	−	0.367765i	$-0.880123\pi$
$521$	−3.34315	+	5.79050i	−0.146466	+	0.253686i	0.783453	+	0.621451i	$0.213457\pi$
$522$		0			0
$523$	−9.72792	−	16.8493i	−0.425372	−	0.736766i	0.571083	−	0.820892i	$-0.306524\pi$
$523$	−9.72792	−	16.8493i	−0.425372	−	0.736766i	−0.996455	+	0.0841260i	$0.973190\pi$
$524$	−7.31371			−0.319501
$525$		0			0
$526$	−13.3137			−0.580505
$527$	41.0416	+	71.0862i	1.78780	+	3.09656i
$528$		0			0
$529$	−2.24264	+	3.88437i	−0.0975061	+	0.168886i
$530$	13.0711	+	22.6398i	0.567771	+	0.983408i
$531$		0			0
$532$	−7.82843	+	10.0951i	−0.339405	+	0.437679i
$533$	45.4558			1.96891
$534$		0			0
$535$	6.44975	−	11.1713i	0.278847	−	0.482977i
$536$	−1.74264	+	3.01834i	−0.0752706	+	0.130373i
$537$		0			0
$538$	6.07107			0.261742
$539$	6.74264	+	1.88064i	0.290426	+	0.0810048i
$540$		0			0
$541$	18.2782	+	31.6587i	0.785840	+	1.36111i	0.928496	+	0.371343i	$0.121102\pi$
$541$	18.2782	+	31.6587i	0.785840	+	1.36111i	−0.142656	+	0.989772i	$0.545564\pi$
$542$	−4.65685	+	8.06591i	−0.200029	+	0.346460i
$543$		0			0
$544$	3.91421	+	6.77962i	0.167821	+	0.290674i
$545$	−12.6569			−0.542160
$546$		0			0
$547$	−7.85786			−0.335978			−0.167989	−	0.985789i	$-0.553727\pi$
$547$	−7.85786			−0.335978			−0.167989	+	0.985789i	$0.553727\pi$
$548$	−0.414214	−	0.717439i	−0.0176943	−	0.0306475i
$549$		0			0
$550$	−0.414214	+	0.717439i	−0.0176621	+	0.0305917i
$551$	−6.82843	−	11.8272i	−0.290901	−	0.503855i
$552$		0			0
$553$	−34.7132	−	4.75039i	−1.47616	−	0.202007i
$554$	−1.17157			−0.0497754
$555$		0			0
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−6.24264	+	10.8126i	−0.264509	+	0.458143i	−0.967435	−	0.253120i	$-0.918543\pi$
$557$	−6.24264	+	10.8126i	−0.264509	+	0.458143i	0.702926	+	0.711263i	$0.251877\pi$
$558$		0			0
$559$	−19.3137			−0.816883
$560$	2.41421	+	5.91359i	0.102019	+	0.249895i
$561$		0			0
$562$	−9.74264	−	16.8747i	−0.410968	−	0.711818i
$563$	−7.17157	+	12.4215i	−0.302246	+	0.523505i	−0.976644	−	0.214863i	$-0.931070\pi$
$563$	−7.17157	+	12.4215i	−0.302246	+	0.523505i	0.674399	+	0.738368i	$0.264403\pi$
$564$		0			0
$565$	9.24264	+	16.0087i	0.388841	+	0.673492i
$566$	−30.1421			−1.26697
$567$		0			0
$568$	−9.31371			−0.390795
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	0.999018	−	0.0443003i	$-0.0141058\pi$
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	−0.537874	+	0.843025i	$0.680772\pi$
$570$		0			0
$571$	5.17157	−	8.95743i	0.216424	−	0.374857i	−0.737288	−	0.675578i	$-0.763894\pi$
$571$	5.17157	−	8.95743i	0.216424	−	0.374857i	0.953712	+	0.300721i	$0.0972274\pi$
$572$	3.41421	+	5.91359i	0.142755	+	0.247260i
$573$		0			0
$574$	17.4497	+	2.38794i	0.728338	+	0.0996708i
$575$	4.34315			0.181122
$576$		0			0
$577$	11.5711	−	20.0417i	0.481710	−	0.834346i	−0.518070	−	0.855338i	$-0.673349\pi$
$577$	11.5711	−	20.0417i	0.481710	−	0.834346i	0.999780	+	0.0209924i	$0.00668258\pi$
$578$	−22.1421	+	38.3513i	−0.920991	+	1.59520i
$579$		0			0
$580$	−6.82843			−0.283535
$581$	−6.76346	+	8.72180i	−0.280595	+	0.361841i
$582$		0			0
$583$	5.41421	+	9.37769i	0.224234	+	0.388384i
$584$	−0.414214	+	0.717439i	−0.0171403	+	0.0296878i
$585$		0			0
$586$	−3.58579	−	6.21076i	−0.148127	−	0.256564i
$587$	0.142136			0.00586657			0.00293328	−	0.999996i	$-0.499066\pi$
$587$	0.142136			0.00586657			0.00293328	+	0.999996i	$0.499066\pi$
$588$		0			0
$589$	−50.6274			−2.08607
$590$	−9.24264	−	16.0087i	−0.380513	−	0.659069i
$591$		0			0
$592$	0.828427	−	1.43488i	0.0340481	−	0.0589731i
$593$	13.9706	+	24.1977i	0.573702	+	0.993681i	0.996181	+	0.0873088i	$0.0278267\pi$
$593$	13.9706	+	24.1977i	0.573702	+	0.993681i	−0.422479	+	0.906373i	$0.638840\pi$
$594$		0			0
$595$	−30.6421	+	39.5145i	−1.25621	+	1.61994i
$596$	−11.3137			−0.463428
$597$		0			0
$598$	17.8995	−	31.0028i	0.731965	−	1.26780i
$599$	9.52082	−	16.4905i	0.389010	−	0.673785i	−0.603307	−	0.797509i	$-0.706150\pi$
$599$	9.52082	−	16.4905i	0.389010	−	0.673785i	0.992317	+	0.123724i	$0.0394838\pi$
$600$		0			0
$601$	−20.0000			−0.815817			−0.407909	−	0.913023i	$-0.633742\pi$
$601$	−20.0000			−0.815817			−0.407909	+	0.913023i	$0.633742\pi$
$602$	−7.41421	−	1.01461i	−0.302181	−	0.0413525i
$603$		0			0
$604$	3.62132	+	6.27231i	0.147349	+	0.255217i
$605$	−1.20711	+	2.09077i	−0.0490759	+	0.0850019i
$606$		0			0
$607$	−1.89340	−	3.27946i	−0.0768507	−	0.133109i	0.825039	−	0.565076i	$-0.191153\pi$
$607$	−1.89340	−	3.27946i	−0.0768507	−	0.133109i	−0.901890	+	0.431967i	$0.857820\pi$
$608$	−4.82843			−0.195819
$609$		0			0
$610$	−10.6569			−0.431483
$611$	−2.58579	−	4.47871i	−0.104610	−	0.181189i
$612$		0			0
$613$	5.55025	−	9.61332i	0.224173	−	0.388278i	−0.731898	−	0.681414i	$-0.761365\pi$
$613$	5.55025	−	9.61332i	0.224173	−	0.388278i	0.956071	+	0.293136i	$0.0946987\pi$
$614$	−5.31371	−	9.20361i	−0.214444	−	0.371428i
$615$		0			0
$616$	1.00000	+	2.44949i	0.0402911	+	0.0986928i
$617$	−7.51472			−0.302531			−0.151266	−	0.988493i	$-0.548335\pi$
$617$	−7.51472			−0.302531			−0.151266	+	0.988493i	$0.548335\pi$
$618$		0			0
$619$	−8.74264	+	15.1427i	−0.351396	+	0.608636i	−0.986494	−	0.163795i	$-0.947626\pi$
$619$	−8.74264	+	15.1427i	−0.351396	+	0.608636i	0.635098	+	0.772432i	$0.280960\pi$
$620$	−12.6569	+	21.9223i	−0.508311	+	0.880421i
$621$		0			0
$622$	−32.2132			−1.29163
$623$	11.7574	+	1.60896i	0.471049	+	0.0644615i
$624$		0			0
$625$	14.2279	+	24.6435i	0.569117	+	0.985739i
$626$	3.34315	−	5.79050i	0.133619	−	0.231435i
$627$		0			0
$628$	7.41421	+	12.8418i	0.295859	+	0.512443i
$629$	12.9706			0.517170
$630$		0			0
$631$	−34.9706			−1.39216			−0.696078	−	0.717966i	$-0.745073\pi$
$631$	−34.9706			−1.39216			−0.696078	+	0.717966i	$0.745073\pi$
$632$	−6.62132	−	11.4685i	−0.263382	−	0.456191i
$633$		0			0
$634$	−9.93503	+	17.2080i	−0.394570	+	0.683416i
$635$	8.74264	+	15.1427i	0.346941	+	0.600920i
$636$		0			0
$637$	11.8995	+	46.2941i	0.471475	+	1.83424i
$638$	−2.82843			−0.111979
$639$		0			0
$640$	−1.20711	+	2.09077i	−0.0477151	+	0.0826450i
$641$	2.34315	−	4.05845i	0.0925487	−	0.160299i	−0.816034	−	0.578004i	$-0.803832\pi$
$641$	2.34315	−	4.05845i	0.0925487	−	0.160299i	0.908583	+	0.417705i	$0.137165\pi$
$642$		0			0
$643$	6.34315			0.250149			0.125075	−	0.992147i	$-0.460083\pi$
$643$	6.34315			0.250149			0.125075	+	0.992147i	$0.460083\pi$
$644$	8.50000	−	10.9612i	0.334947	−	0.431930i
$645$		0			0
$646$	−18.8995	−	32.7349i	−0.743591	−	1.28794i
$647$	8.34924	−	14.4613i	0.328243	−	0.568533i	−0.653921	−	0.756563i	$-0.726877\pi$
$647$	8.34924	−	14.4613i	0.328243	−	0.568533i	0.982163	+	0.188030i	$0.0602103\pi$
$648$		0			0
$649$	−3.82843	−	6.63103i	−0.150279	−	0.260291i
$650$	−5.65685			−0.221880
$651$		0			0
$652$	3.00000			0.117489
$653$	13.1777	+	22.8244i	0.515682	+	0.893188i	0.999834	+	0.0182037i	$0.00579475\pi$
$653$	13.1777	+	22.8244i	0.515682	+	0.893188i	−0.484152	+	0.874984i	$0.660872\pi$
$654$		0			0
$655$	8.82843	−	15.2913i	0.344955	−	0.597480i
$656$	3.32843	+	5.76500i	0.129953	+	0.225086i
$657$		0			0
$658$	−0.757359	−	1.85514i	−0.0295249	−	0.0723210i
$659$	30.9411			1.20530			0.602648	−	0.798007i	$-0.294112\pi$
$659$	30.9411			1.20530			0.602648	+	0.798007i	$0.294112\pi$
$660$		0			0
$661$	2.51472	−	4.35562i	0.0978112	−	0.169414i	−0.812967	−	0.582309i	$-0.802149\pi$
$661$	2.51472	−	4.35562i	0.0978112	−	0.169414i	0.910778	+	0.412895i	$0.135483\pi$
$662$	8.15685	−	14.1281i	0.317025	−	0.549104i
$663$		0			0
$664$	−4.17157			−0.161888
$665$	−11.6569	−	28.5533i	−0.452033	−	1.10725i
$666$		0			0
$667$	7.41421	+	12.8418i	0.287079	+	0.497236i
$668$	−0.242641	+	0.420266i	−0.00938805	+	0.0162606i
$669$		0			0
$670$	−4.20711	−	7.28692i	−0.162535	−	0.281518i
$671$	−4.41421			−0.170409
$672$		0			0
$673$	−20.6274			−0.795128			−0.397564	−	0.917574i	$-0.630144\pi$
$673$	−20.6274			−0.795128			−0.397564	+	0.917574i	$0.630144\pi$
$674$	−13.2426	−	22.9369i	−0.510087	−	0.883497i
$675$		0			0
$676$	−16.8137	+	29.1222i	−0.646681	+	1.12008i
$677$	15.3848	+	26.6472i	0.591285	+	1.02414i	0.994060	+	0.108836i	$0.0347125\pi$
$677$	15.3848	+	26.6472i	0.591285	+	1.02414i	−0.402775	+	0.915299i	$0.631954\pi$
$678$		0			0
$679$	−25.6630	+	33.0936i	−0.984854	+	1.27002i
$680$	−18.8995			−0.724763
$681$		0			0
$682$	−5.24264	+	9.08052i	−0.200751	+	0.347711i
$683$	−3.17157	+	5.49333i	−0.121357	+	0.210196i	−0.920303	−	0.391206i	$-0.872058\pi$
$683$	−3.17157	+	5.49333i	−0.121357	+	0.210196i	0.798946	+	0.601403i	$0.205391\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$	2.13604	+	18.3967i	0.0815543	+	0.702388i
$687$		0			0
$688$	−1.41421	−	2.44949i	−0.0539164	−	0.0933859i
$689$	−36.9706	+	64.0349i	−1.40847	+	2.43954i
$690$		0			0
$691$	−0.428932	−	0.742932i	−0.0163173	−	0.0282625i	0.857751	−	0.514065i	$-0.171861\pi$
$691$	−0.428932	−	0.742932i	−0.0163173	−	0.0282625i	−0.874069	+	0.485802i	$0.838528\pi$
$692$	16.1421			0.613632
$693$		0			0
$694$	33.1421			1.25806
$695$	7.24264	+	12.5446i	0.274729	+	0.475845i
$696$		0			0
$697$	−26.0563	+	45.1309i	−0.986955	+	1.70946i
$698$	−4.86396	−	8.42463i	−0.184104	−	0.318877i
$699$		0			0
$700$	−2.17157	−	0.297173i	−0.0820777	−	0.0112321i
$701$	−0.142136			−0.00536839			−0.00268419	−	0.999996i	$-0.500854\pi$
$701$	−0.142136			−0.00536839			−0.00268419	+	0.999996i	$0.500854\pi$
$702$		0			0
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−11.1716			−0.420448
$707$	14.1421	+	34.6410i	0.531870	+	1.30281i
$708$		0			0
$709$	−16.0711	−	27.8359i	−0.603562	−	1.04540i	−0.992277	−	0.124042i	$-0.960414\pi$
$709$	−16.0711	−	27.8359i	−0.603562	−	1.04540i	0.388715	−	0.921358i	$-0.372919\pi$
$710$	11.2426	−	19.4728i	0.421929	−	0.730802i
$711$		0			0
$712$	2.24264	+	3.88437i	0.0840465	+	0.145573i
$713$	54.9706			2.05866
$714$		0			0
$715$	−16.4853			−0.616515
$716$	4.41421	+	7.64564i	0.164967	+	0.285731i
$717$		0			0
$718$	−4.24264	+	7.34847i	−0.158334	+	0.274242i
$719$	−13.1066	−	22.7013i	−0.488794	−	0.846616i	0.511123	−	0.859508i	$-0.329230\pi$
$719$	−13.1066	−	22.7013i	−0.488794	−	0.846616i	−0.999917	+	0.0128919i	$0.995896\pi$
$720$		0			0
$721$	38.8701	+	5.31925i	1.44760	+	0.198099i
$722$	4.31371			0.160540
$723$		0			0
$724$	6.82843	−	11.8272i	0.253776	−	0.439554i
$725$	1.17157	−	2.02922i	0.0435111	−	0.0753635i
$726$		0			0
$727$	−15.5147			−0.575409			−0.287705	−	0.957719i	$-0.592892\pi$
$727$	−15.5147			−0.575409			−0.287705	+	0.957719i	$0.592892\pi$
$728$	−11.0711	+	14.2767i	−0.410321	+	0.529129i
$729$		0			0
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	11.0711	−	19.1757i	0.409478	−	0.709237i
$732$		0			0
$733$	11.6213	+	20.1287i	0.429243	+	0.743471i	0.996806	−	0.0798589i	$-0.0254470\pi$
$733$	11.6213	+	20.1287i	0.429243	+	0.743471i	−0.567563	+	0.823330i	$0.692114\pi$
$734$	22.4853			0.829947
$735$		0			0
$736$	5.24264			0.193246
$737$	−1.74264	−	3.01834i	−0.0641910	−	0.111182i
$738$		0			0
$739$	17.0000	−	29.4449i	0.625355	−	1.08315i	−0.363117	−	0.931744i	$-0.618287\pi$
$739$	17.0000	−	29.4449i	0.625355	−	1.08315i	0.988472	−	0.151403i	$-0.0483792\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−17.5563	+	22.6398i	−0.644514	+	0.831132i
$743$	−2.34315			−0.0859617			−0.0429808	−	0.999076i	$-0.513685\pi$
$743$	−2.34315			−0.0859617			−0.0429808	+	0.999076i	$0.513685\pi$
$744$		0			0
$745$	13.6569	−	23.6544i	0.500348	−	0.866629i
$746$	−4.86396	+	8.42463i	−0.178082	+	0.308448i
$747$		0			0
$748$	−7.82843			−0.286236
$749$	14.0061	+	1.91669i	0.511772	+	0.0700343i
$750$		0			0
$751$	4.89949	+	8.48617i	0.178785	+	0.309665i	0.941465	−	0.337112i	$-0.109450\pi$
$751$	4.89949	+	8.48617i	0.178785	+	0.309665i	−0.762680	+	0.646777i	$0.776117\pi$
$752$	0.378680	−	0.655892i	0.0138090	−	0.0239179i
$753$		0			0
$754$	−9.65685	−	16.7262i	−0.351682	−	0.609131i
$755$	−17.4853			−0.636355
$756$		0			0
$757$	8.34315			0.303237			0.151618	−	0.988439i	$-0.451552\pi$
$757$	8.34315			0.303237			0.151618	+	0.988439i	$0.451552\pi$
$758$	−15.3284	−	26.5496i	−0.556754	−	0.964325i
$759$		0			0
$760$	5.82843	−	10.0951i	0.211419	−	0.366189i
$761$	13.2279	+	22.9114i	0.479512	+	0.830539i	0.999724	−	0.0234983i	$-0.00748043\pi$
$761$	13.2279	+	22.9114i	0.479512	+	0.830539i	−0.520212	+	0.854037i	$0.674147\pi$
$762$		0			0
$763$	−5.24264	−	12.8418i	−0.189796	−	0.464904i
$764$	13.3137			0.481673
$765$		0			0
$766$	−11.1421	+	19.2987i	−0.402582	+	0.697292i
$767$	26.1421	−	45.2795i	0.943938	−	1.63495i
$768$		0			0
$769$	9.51472			0.343110			0.171555	−	0.985175i	$-0.445121\pi$
$769$	9.51472			0.343110			0.171555	+	0.985175i	$0.445121\pi$
$770$	−6.32843	−	0.866025i	−0.228061	−	0.0312094i
$771$		0			0
$772$	7.41421	+	12.8418i	0.266843	+	0.462186i
$773$	−11.3787	+	19.7085i	−0.409263	+	0.708864i	−0.994807	−	0.101776i	$-0.967547\pi$
$773$	−11.3787	+	19.7085i	−0.409263	+	0.708864i	0.585545	+	0.810640i	$0.300881\pi$
$774$		0			0
$775$	−4.34315	−	7.52255i	−0.156010	−	0.270218i
$776$	−15.8284			−0.568207
$777$		0			0
$778$	23.7279			0.850687
$779$	−16.0711	−	27.8359i	−0.575806	−	0.997325i
$780$		0			0
$781$	4.65685	−	8.06591i	0.166635	−	0.288621i
$782$	20.5208	+	35.5431i	0.733823	+	1.27102i
$783$		0			0
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$	−35.7990			−1.27772
$786$		0			0
$787$	−17.3848	+	30.1113i	−0.619700	+	1.07335i	0.369840	+	0.929095i	$0.379413\pi$
$787$	−17.3848	+	30.1113i	−0.619700	+	1.07335i	−0.989540	+	0.144257i	$0.953921\pi$
$788$	10.2426	−	17.7408i	0.364879	−	0.631989i
$789$		0			0
$790$	31.9706			1.13746
$791$	−12.4142	+	16.0087i	−0.441399	+	0.569205i
$792$		0			0
$793$	−15.0711	−	26.1039i	−0.535189	−	0.926975i
$794$	2.24264	−	3.88437i	0.0795883	−	0.137851i
$795$		0			0
$796$	9.82843	+	17.0233i	0.348359	+	0.603376i
$797$	33.1005			1.17248			0.586240	−	0.810137i	$-0.300608\pi$
$797$	33.1005			1.17248			0.586240	+	0.810137i	$0.300608\pi$
$798$		0			0
$799$	5.92893			0.209751
$800$	−0.414214	−	0.717439i	−0.0146447	−	0.0253653i
$801$		0			0
$802$	−11.8995	+	20.6105i	−0.420186	+	0.727783i
$803$	−0.414214	−	0.717439i	−0.0146173	−	0.0253179i
$804$		0			0
$805$	12.6569	+	31.0028i	0.446095	+	1.09271i
$806$	−71.5980			−2.52193
$807$		0			0
$808$	−7.07107	+	12.2474i	−0.248759	+	0.430864i
$809$	10.3284	−	17.8894i	0.363128	−	0.628956i	−0.625346	−	0.780348i	$-0.715042\pi$
$809$	10.3284	−	17.8894i	0.363128	−	0.628956i	0.988474	+	0.151391i	$0.0483754\pi$
$810$		0			0
$811$	3.65685			0.128410			0.0642048	−	0.997937i	$-0.479549\pi$
$811$	3.65685			0.128410			0.0642048	+	0.997937i	$0.479549\pi$
$812$	−2.82843	−	6.92820i	−0.0992583	−	0.243132i
$813$		0			0
$814$	0.828427	+	1.43488i	0.0290364	+	0.0502924i
$815$	−3.62132	+	6.27231i	−0.126849	+	0.219709i
$816$		0			0
$817$	6.82843	+	11.8272i	0.238896	+	0.413781i
$818$	39.4558			1.37954
$819$		0			0
$820$	−16.0711			−0.561226
$821$	−19.2426	−	33.3292i	−0.671573	−	1.16320i	−0.977458	−	0.211130i	$-0.932286\pi$
$821$	−19.2426	−	33.3292i	−0.671573	−	1.16320i	0.305885	−	0.952068i	$-0.401048\pi$
$822$		0			0
$823$	19.2426	−	33.3292i	0.670756	−	1.16178i	−0.306934	−	0.951731i	$-0.599303\pi$
$823$	19.2426	−	33.3292i	0.670756	−	1.16178i	0.977690	−	0.210053i	$-0.0673637\pi$
$824$	7.41421	+	12.8418i	0.258286	+	0.447365i
$825$		0			0
$826$	12.4142	−	16.0087i	0.431946	−	0.557015i
$827$	7.82843			0.272221			0.136111	−	0.990694i	$-0.456540\pi$
$827$	7.82843			0.272221			0.136111	+	0.990694i	$0.456540\pi$
$828$		0			0
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	−0.513635	−	0.858009i	$-0.671701\pi$
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	0.999875	+	0.0158163i	$0.00503471\pi$
$830$	5.03553	−	8.72180i	0.174786	−	0.302738i
$831$		0			0
$832$	−6.82843			−0.236733
$833$	−52.7843	−	14.7224i	−1.82887	−	0.510102i
$834$		0			0
$835$	−0.585786	−	1.01461i	−0.0202720	−	0.0351121i
$836$	2.41421	−	4.18154i	0.0834973	−	0.144622i
$837$		0			0
$838$	−6.89949	−	11.9503i	−0.238339	−	0.412815i
$839$	−34.2132			−1.18117			−0.590585	−	0.806975i	$-0.701103\pi$
$839$	−34.2132			−1.18117			−0.590585	+	0.806975i	$0.701103\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	−4.58579	−	7.94282i	−0.158037	−	0.273727i
$843$		0			0
$844$	−4.58579	+	7.94282i	−0.157849	+	0.273403i
$845$	−40.5919	−	70.3072i	−1.39640	−	2.41864i
$846$		0			0
$847$	−2.62132	−	0.358719i	−0.0900696	−	0.0123257i
$848$	−10.8284			−0.371850
$849$		0			0
$850$	3.24264	−	5.61642i	0.111222	−	0.192642i
$851$	4.34315	−	7.52255i	0.148881	−	0.257870i
$852$		0			0
$853$	−14.7574			−0.505282			−0.252641	−	0.967560i	$-0.581299\pi$
$853$	−14.7574			−0.505282			−0.252641	+	0.967560i	$0.581299\pi$
$854$	−4.41421	−	10.8126i	−0.151051	−	0.369999i
$855$		0			0
$856$	2.67157	+	4.62730i	0.0913125	+	0.158158i
$857$	−22.1569	+	38.3768i	−0.756864	+	1.31093i	0.187579	+	0.982250i	$0.439936\pi$
$857$	−22.1569	+	38.3768i	−0.756864	+	1.31093i	−0.944442	+	0.328677i	$0.893397\pi$
$858$		0			0
$859$	−8.47056	−	14.6714i	−0.289012	−	0.500583i	0.684562	−	0.728954i	$-0.259993\pi$
$859$	−8.47056	−	14.6714i	−0.289012	−	0.500583i	−0.973574	+	0.228371i	$0.926660\pi$
$860$	6.82843			0.232847
$861$		0			0
$862$	−24.8284			−0.845660
$863$	−18.5919	−	32.2021i	−0.632875	−	1.09617i	−0.986961	−	0.160959i	$-0.948541\pi$
$863$	−18.5919	−	32.2021i	−0.632875	−	1.09617i	0.354086	−	0.935213i	$-0.384792\pi$
$864$		0			0
$865$	−19.4853	+	33.7495i	−0.662519	+	1.14752i
$866$	7.67157	+	13.2876i	0.260691	+	0.451529i
$867$		0			0
$868$	−27.4853	−	3.76127i	−0.932911	−	0.127666i
$869$	13.2426			0.449226
$870$		0			0
$871$	11.8995	−	20.6105i	0.403199	−	0.698361i
$872$	2.62132	−	4.54026i	0.0887691	−	0.153753i
$873$		0			0
$874$	−25.3137			−0.856249
$875$	−16.3284	+	21.0563i	−0.552002	+	0.711832i
$876$		0			0
$877$	3.27817	+	5.67796i	0.110696	+	0.191731i	0.916051	−	0.401062i	$-0.131359\pi$
$877$	3.27817	+	5.67796i	0.110696	+	0.191731i	−0.805355	+	0.592793i	$0.798025\pi$
$878$	16.6924	−	28.9121i	0.563341	−	0.975735i
$879$		0			0
$880$	−1.20711	−	2.09077i	−0.0406916	−	0.0704799i
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	17.4853			0.588427			0.294213	−	0.955740i	$-0.404942\pi$
$883$	17.4853			0.588427			0.294213	+	0.955740i	$0.404942\pi$
$884$	−26.7279	−	46.2941i	−0.898957	−	1.55704i
$885$		0			0
$886$	−12.8284	+	22.2195i	−0.430979	+	0.746478i
$887$	−9.82843	−	17.0233i	−0.330006	−	0.571588i	0.652506	−	0.757783i	$-0.273718\pi$
$887$	−9.82843	−	17.0233i	−0.330006	−	0.571588i	−0.982513	+	0.186196i	$0.940384\pi$
$888$		0			0
$889$	−11.7426	+	15.1427i	−0.393836	+	0.507870i
$890$	−10.8284			−0.362970
$891$		0			0
$892$	−4.65685	+	8.06591i	−0.155923	+	0.270067i
$893$	−1.82843	+	3.16693i	−0.0611860	+	0.105977i
$894$		0			0
$895$	−21.3137			−0.712439
$896$	−2.62132	−	0.358719i	−0.0875722	−	0.0119840i
$897$		0			0
$898$	19.5563	+	33.8726i	0.652604	+	1.13034i
$899$	14.8284	−	25.6836i	0.494556	−	0.856596i
$900$		0			0
$901$	−42.3848	−	73.4126i	−1.41204	−	2.44573i
$902$	−6.65685			−0.221649
$903$		0			0
$904$	−7.65685			−0.254663
$905$	16.4853	+	28.5533i	0.547989	+	0.949145i
$906$		0			0
$907$	−19.5711	+	33.8981i	−0.649847	+	1.12557i	0.333313	+	0.942816i	$0.391834\pi$
$907$	−19.5711	+	33.8981i	−0.649847	+	1.12557i	−0.983159	+	0.182751i	$0.941500\pi$
$908$	5.15685	+	8.93193i	0.171136	+	0.296417i
$909$		0			0
$910$	−16.4853	−	40.3805i	−0.546482	−	1.33860i
$911$	7.78680			0.257988			0.128994	−	0.991645i	$-0.458825\pi$
$911$	7.78680			0.257988			0.128994	+	0.991645i	$0.458825\pi$
$912$		0			0
$913$	2.08579	−	3.61269i	0.0690295	−	0.119563i
$914$	5.31371	−	9.20361i	0.175762	−	0.304428i
$915$		0			0
$916$	11.3137			0.373815
$917$	19.1716	+	2.62357i	0.633101	+	0.0866379i
$918$		0			0
$919$	1.55025	+	2.68512i	0.0511381	+	0.0885738i	0.890461	−	0.455059i	$-0.150382\pi$
$919$	1.55025	+	2.68512i	0.0511381	+	0.0885738i	−0.839323	+	0.543633i	$0.817048\pi$
$920$	−6.32843	+	10.9612i	−0.208642	+	0.361379i
$921$		0			0
$922$	6.17157	+	10.6895i	0.203250	+	0.352039i
$923$	63.5980			2.09335
$924$		0			0
$925$	−1.37258			−0.0451303
$926$	19.5563	+	33.8726i	0.642662	+	1.11312i
$927$		0			0
$928$	1.41421	−	2.44949i	0.0464238	−	0.0804084i
$929$	21.7279	+	37.6339i	0.712870	+	1.23473i	0.963775	+	0.266715i	$0.0859384\pi$
$929$	21.7279	+	37.6339i	0.712870	+	1.23473i	−0.250905	+	0.968012i	$0.580728\pi$
$930$		0			0
$931$	24.1421	−	23.6544i	0.791227	−	0.775241i
$932$	−14.3137			−0.468861
$933$		0			0
$934$	−15.4853	+	26.8213i	−0.506694	+	0.877620i
$935$	9.44975	−	16.3674i	0.309040	−	0.535273i
$936$		0			0
$937$	0.343146			0.0112101			0.00560504	−	0.999984i	$-0.498216\pi$
$937$	0.343146			0.0112101			0.00560504	+	0.999984i	$0.498216\pi$
$938$	5.65076	−	7.28692i	0.184504	−	0.237926i
$939$		0			0
$940$	0.914214	+	1.58346i	0.0298184	+	0.0516469i
$941$	−28.3137	+	49.0408i	−0.923001	+	1.59868i	−0.128255	+	0.991741i	$0.540938\pi$
$941$	−28.3137	+	49.0408i	−0.923001	+	1.59868i	−0.794746	+	0.606943i	$0.792396\pi$
$942$		0			0
$943$	17.4497	+	30.2238i	0.568242	+	0.984224i
$944$	7.65685			0.249209
$945$		0			0
$946$	2.82843			0.0919601
$947$	16.3137	+	28.2562i	0.530124	+	0.918202i	0.999382	+	0.0351411i	$0.0111881\pi$
$947$	16.3137	+	28.2562i	0.530124	+	0.918202i	−0.469258	+	0.883061i	$0.655479\pi$
$948$		0			0
$949$	2.82843	−	4.89898i	0.0918146	−	0.159028i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$		0			0
$952$	−7.82843	−	19.1757i	−0.253721	−	0.621486i
$953$	16.3137			0.528453			0.264226	−	0.964461i	$-0.414883\pi$
$953$	16.3137			0.528453			0.264226	+	0.964461i	$0.414883\pi$
$954$		0			0
$955$	−16.0711	+	27.8359i	−0.520048	+	0.900749i
$956$	−10.0000	+	17.3205i	−0.323423	+	0.560185i
$957$		0			0
$958$	10.8284			0.349851
$959$	0.828427	+	2.02922i	0.0267513	+	0.0655271i
$960$		0			0
$961$	−39.4706	−	68.3650i	−1.27324	−	2.20532i
$962$	−5.65685	+	9.79796i	−0.182384	+	0.315899i
$963$		0			0
$964$	4.48528	+	7.76874i	0.144461	+	0.250214i
$965$	−35.7990			−1.15241
$966$		0			0
$967$	22.8995			0.736398			0.368199	−	0.929747i	$-0.379974\pi$
$967$	22.8995			0.736398			0.368199	+	0.929747i	$0.379974\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	19.1066	−	33.0936i	0.613476	−	1.06257i
$971$	5.00000	+	8.66025i	0.160458	+	0.277921i	0.935033	−	0.354561i	$-0.115370\pi$
$971$	5.00000	+	8.66025i	0.160458	+	0.277921i	−0.774575	+	0.632482i	$0.782036\pi$
$972$		0			0
$973$	−9.72792	+	12.5446i	−0.311863	+	0.402162i
$974$	1.31371			0.0420939
$975$		0			0
$976$	2.20711	−	3.82282i	0.0706478	−	0.122366i
$977$	17.9706	−	31.1259i	0.574929	−	0.995807i	−0.421120	−	0.907005i	$-0.638363\pi$
$977$	17.9706	−	31.1259i	0.574929	−	0.995807i	0.996049	−	0.0888018i	$-0.0283038\pi$
$978$		0			0
$979$	−4.48528			−0.143350
$980$	−4.20711	−	16.3674i	−0.134391	−	0.522839i
$981$		0			0
$982$	−14.8137	−	25.6581i	−0.472724	−	0.818783i
$983$	−22.6213	+	39.1813i	−0.721508	+	1.24969i	0.238887	+	0.971047i	$0.423217\pi$
$983$	−22.6213	+	39.1813i	−0.721508	+	1.24969i	−0.960395	+	0.278641i	$0.910116\pi$
$984$		0			0
$985$	24.7279	+	42.8300i	0.787897	+	1.36468i
$986$	22.1421			0.705149
$987$		0			0
$988$	32.9706			1.04893
$989$	−7.41421	−	12.8418i	−0.235758	−	0.408345i
$990$		0			0
$991$	−16.8284	+	29.1477i	−0.534573	+	0.925907i	0.464611	+	0.885515i	$0.346194\pi$
$991$	−16.8284	+	29.1477i	−0.534573	+	0.925907i	−0.999184	+	0.0403922i	$0.987139\pi$
$992$	−5.24264	−	9.08052i	−0.166454	−	0.288307i
$993$		0			0
$994$	24.4142	+	3.34101i	0.774372	+	0.105970i
$995$	−47.4558			−1.50445
$996$		0			0
$997$	−4.10051	+	7.10228i	−0.129864	+	0.224932i	−0.923624	−	0.383300i	$-0.874788\pi$
$997$	−4.10051	+	7.10228i	−0.129864	+	0.224932i	0.793760	+	0.608232i	$0.208121\pi$
$998$	−12.8284	+	22.2195i	−0.406077	+	0.703346i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.q.991.1	yes	4
3.2	odd	2		1386.2.k.u.991.2	yes	4
7.2	even	3	inner	1386.2.k.q.793.1	✓	4
7.3	odd	6		9702.2.a.da.1.1		2
7.4	even	3		9702.2.a.ds.1.2		2
21.2	odd	6		1386.2.k.u.793.2	yes	4
21.11	odd	6		9702.2.a.cj.1.1		2
21.17	even	6		9702.2.a.cv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.q.793.1	✓	4	7.2	even	3	inner
1386.2.k.q.991.1	yes	4	1.1	even	1	trivial
1386.2.k.u.793.2	yes	4	21.2	odd	6
1386.2.k.u.991.2	yes	4	3.2	odd	2
9702.2.a.cj.1.1		2	21.11	odd	6
9702.2.a.cv.1.2		2	21.17	even	6
9702.2.a.da.1.1		2	7.3	odd	6
9702.2.a.ds.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.20711 - 2.09077i) q^{5} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-1.20711 + 2.09077i) q^{10} +(-0.500000 + 0.866025i) q^{11} -6.82843 q^{13} +(-2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.91421 - 6.77962i) q^{17} +(2.41421 + 4.18154i) q^{19} +2.41421 q^{20} +1.00000 q^{22} +(-2.62132 - 4.54026i) q^{23} +(-0.414214 + 0.717439i) q^{25} +(3.41421 + 5.91359i) q^{26} +(1.00000 + 2.44949i) q^{28} -2.82843 q^{29} +(-5.24264 + 9.08052i) q^{31} +(-0.500000 + 0.866025i) q^{32} -7.82843 q^{34} +(-6.32843 - 0.866025i) q^{35} +(0.828427 + 1.43488i) q^{37} +(2.41421 - 4.18154i) q^{38} +(-1.20711 - 2.09077i) q^{40} -6.65685 q^{41} +2.82843 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-2.62132 + 4.54026i) q^{46} +(0.378680 + 0.655892i) q^{47} +(-1.74264 - 6.77962i) q^{49} +0.828427 q^{50} +(3.41421 - 5.91359i) q^{52} +(5.41421 - 9.37769i) q^{53} +2.41421 q^{55} +(1.62132 - 2.09077i) q^{56} +(1.41421 + 2.44949i) q^{58} +(-3.82843 + 6.63103i) q^{59} +(2.20711 + 3.82282i) q^{61} +10.4853 q^{62} +1.00000 q^{64} +(8.24264 + 14.2767i) q^{65} +(-1.74264 + 3.01834i) q^{67} +(3.91421 + 6.77962i) q^{68} +(2.41421 + 5.91359i) q^{70} -9.31371 q^{71} +(-0.414214 + 0.717439i) q^{73} +(0.828427 - 1.43488i) q^{74} -4.82843 q^{76} +(1.00000 + 2.44949i) q^{77} +(-6.62132 - 11.4685i) q^{79} +(-1.20711 + 2.09077i) q^{80} +(3.32843 + 5.76500i) q^{82} -4.17157 q^{83} -18.8995 q^{85} +(-1.41421 - 2.44949i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(2.24264 + 3.88437i) q^{89} +(-11.0711 + 14.2767i) q^{91} +5.24264 q^{92} +(0.378680 - 0.655892i) q^{94} +(5.82843 - 10.0951i) q^{95} -15.8284 q^{97} +(-5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{11} - 16 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 2 q^{23} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 4 q^{31}+ \cdots - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^11 - 16 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 - 2 * q^23 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 4 * q^31 - 2 * q^32 - 20 * q^34 - 14 * q^35 - 8 * q^37 + 4 * q^38 - 2 * q^40 - 4 * q^41 - 2 * q^44 - 2 * q^46 + 10 * q^47 + 10 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^53 + 4 * q^55 - 2 * q^56 - 4 * q^59 + 6 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^65 + 10 * q^67 + 10 * q^68 + 4 * q^70 + 8 * q^71 + 4 * q^73 - 8 * q^74 - 8 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 + 2 * q^82 - 28 * q^83 - 36 * q^85 - 2 * q^88 - 8 * q^89 - 16 * q^91 + 4 * q^92 + 10 * q^94 + 12 * q^95 - 52 * q^97 - 20 * q^98

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