LMFDB - Embedded newform 1638.2.r.x.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.x.1387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.27492 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.13746 - 3.70219i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-3.27492 + 5.67232i) q^{19} +(2.13746 - 3.70219i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-2.63746 - 4.56821i) q^{23} +13.2749 q^{25} +(2.50000 + 2.59808i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(4.13746 + 7.16629i) q^{29} -1.27492 q^{31} +(0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +(2.13746 - 3.70219i) q^{35} +(-0.137459 - 0.238085i) q^{37} -6.54983 q^{38} +4.27492 q^{40} +(4.13746 + 7.16629i) q^{41} +(5.91238 - 10.2405i) q^{43} +4.00000 q^{44} +(2.63746 - 4.56821i) q^{46} +6.54983 q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.63746 + 11.4964i) q^{50} +(-1.00000 + 3.46410i) q^{52} +3.54983 q^{53} +(8.54983 + 14.8087i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-4.13746 + 7.16629i) q^{58} +(-5.91238 + 10.2405i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-0.637459 - 1.10411i) q^{62} +1.00000 q^{64} +(-14.9622 + 3.70219i) q^{65} +(1.36254 + 2.35999i) q^{67} +(1.50000 + 2.59808i) q^{68} +4.27492 q^{70} +(2.63746 - 4.56821i) q^{71} +5.72508 q^{73} +(0.137459 - 0.238085i) q^{74} +(-3.27492 - 5.67232i) q^{76} +4.00000 q^{77} -8.00000 q^{79} +(2.13746 + 3.70219i) q^{80} +(-4.13746 + 7.16629i) q^{82} +11.8248 q^{83} +(-6.41238 + 11.1066i) q^{85} +11.8248 q^{86} +(2.00000 + 3.46410i) q^{88} +(0.362541 + 0.627940i) q^{89} +(-1.00000 + 3.46410i) q^{91} +5.27492 q^{92} +(3.27492 + 5.67232i) q^{94} +(14.0000 - 24.2487i) q^{95} +(0.274917 - 0.476171i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} - q^{10} - 8 q^{11} + 14 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} + q^{20} + 8 q^{22} - 3 q^{23} + 38 q^{25} + 10 q^{26} - 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 - q^10 - 8 * q^11 + 14 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 + q^20 + 8 * q^22 - 3 * q^23 + 38 * q^25 + 10 * q^26 - 2 * q^28 + 9 * q^29 + 10 * q^31 + 2 * q^32 + 12 * q^34 + q^35 + 7 * q^37 + 4 * q^38 + 2 * q^40 + 9 * q^41 + q^43 + 16 * q^44 + 3 * q^46 - 4 * q^47 - 2 * q^49 + 19 * q^50 - 4 * q^52 - 16 * q^53 + 4 * q^55 + 2 * q^56 - 9 * q^58 - q^59 + 18 * q^61 + 5 * q^62 + 4 * q^64 - 7 * q^65 + 13 * q^67 + 6 * q^68 + 2 * q^70 + 3 * q^71 + 38 * q^73 - 7 * q^74 + 2 * q^76 + 16 * q^77 - 32 * q^79 + q^80 - 9 * q^82 + 2 * q^83 - 3 * q^85 + 2 * q^86 + 8 * q^88 + 9 * q^89 - 4 * q^91 + 6 * q^92 - 2 * q^94 + 56 * q^95 - 14 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	+	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
$5$	−4.27492			−1.91180			−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−4.27492			−1.91180			−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.13746	−	3.70219i	−0.675924	−	1.17073i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−3.27492	+	5.67232i	−0.751318	+	1.30132i	0.195867	+	0.980631i	$0.437248\pi$
$19$	−3.27492	+	5.67232i	−0.751318	+	1.30132i	−0.947184	+	0.320690i	$0.896085\pi$
$20$	2.13746	−	3.70219i	0.477950	−	0.827834i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	−2.63746	−	4.56821i	−0.549948	−	0.952538i	−0.998277	−	0.0586697i	$-0.981314\pi$
$23$	−2.63746	−	4.56821i	−0.549948	−	0.952538i	0.448329	−	0.893868i	$-0.352019\pi$
$24$		0			0
$25$	13.2749			2.65498
$26$	2.50000	+	2.59808i	0.490290	+	0.509525i
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	4.13746	+	7.16629i	0.768307	+	1.33075i	0.938480	+	0.345332i	$0.112234\pi$
$29$	4.13746	+	7.16629i	0.768307	+	1.33075i	−0.170174	+	0.985414i	$0.554433\pi$
$30$		0			0
$31$	−1.27492			−0.228982			−0.114491	−	0.993424i	$-0.536524\pi$
$31$	−1.27492			−0.228982			−0.114491	+	0.993424i	$0.536524\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	2.13746	−	3.70219i	0.361296	−	0.625784i
$36$		0			0
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	0.854505	−	0.519443i	$-0.173860\pi$
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	−0.877103	+	0.480302i	$0.840527\pi$
$38$	−6.54983			−1.06252
$39$		0			0
$40$	4.27492			0.675924
$41$	4.13746	+	7.16629i	0.646162	+	1.11919i	0.984032	+	0.177993i	$0.0569605\pi$
$41$	4.13746	+	7.16629i	0.646162	+	1.11919i	−0.337869	+	0.941193i	$0.609706\pi$
$42$		0			0
$43$	5.91238	−	10.2405i	0.901629	−	1.56167i	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	5.91238	−	10.2405i	0.901629	−	1.56167i	0.825380	−	0.564578i	$-0.190961\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	2.63746	−	4.56821i	0.388872	−	0.673546i
$47$	6.54983			0.955392			0.477696	−	0.878525i	$-0.341472\pi$
$47$	6.54983			0.955392			0.477696	+	0.878525i	$0.341472\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	6.63746	+	11.4964i	0.938678	+	1.62584i
$51$		0			0
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	3.54983			0.487607			0.243804	−	0.969825i	$-0.421605\pi$
$53$	3.54983			0.487607			0.243804	+	0.969825i	$0.421605\pi$
$54$		0			0
$55$	8.54983	+	14.8087i	1.15286	+	1.99681i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	−4.13746	+	7.16629i	−0.543275	+	0.940980i
$59$	−5.91238	+	10.2405i	−0.769726	+	1.33320i	0.167986	+	0.985789i	$0.446274\pi$
$59$	−5.91238	+	10.2405i	−0.769726	+	1.33320i	−0.937712	+	0.347415i	$0.887060\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$	−0.637459	−	1.10411i	−0.0809573	−	0.140222i
$63$		0			0
$64$	1.00000			0.125000
$65$	−14.9622	+	3.70219i	−1.85583	+	0.459200i
$66$		0			0
$67$	1.36254	+	2.35999i	0.166461	+	0.288319i	0.937173	−	0.348865i	$-0.113433\pi$
$67$	1.36254	+	2.35999i	0.166461	+	0.288319i	−0.770712	+	0.637183i	$0.780099\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	4.27492			0.510950
$71$	2.63746	−	4.56821i	0.313009	−	0.542147i	−0.666003	−	0.745949i	$-0.731996\pi$
$71$	2.63746	−	4.56821i	0.313009	−	0.542147i	0.979012	+	0.203802i	$0.0653297\pi$
$72$		0			0
$73$	5.72508			0.670070			0.335035	−	0.942206i	$-0.391252\pi$
$73$	5.72508			0.670070			0.335035	+	0.942206i	$0.391252\pi$
$74$	0.137459	−	0.238085i	0.0159792	−	0.0276769i
$75$		0			0
$76$	−3.27492	−	5.67232i	−0.375659	−	0.650660i
$77$	4.00000			0.455842
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	2.13746	+	3.70219i	0.238975	+	0.413917i
$81$		0			0
$82$	−4.13746	+	7.16629i	−0.456906	+	0.791384i
$83$	11.8248			1.29794			0.648968	−	0.760816i	$-0.275201\pi$
$83$	11.8248			1.29794			0.648968	+	0.760816i	$0.275201\pi$
$84$		0			0
$85$	−6.41238	+	11.1066i	−0.695520	+	1.20468i
$86$	11.8248			1.27510
$87$		0			0
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	0.362541	+	0.627940i	0.0384293	+	0.0665615i	0.884600	−	0.466350i	$-0.154431\pi$
$89$	0.362541	+	0.627940i	0.0384293	+	0.0665615i	−0.846171	+	0.532911i	$0.821098\pi$
$90$		0			0
$91$	−1.00000	+	3.46410i	−0.104828	+	0.363137i
$92$	5.27492			0.549948
$93$		0			0
$94$	3.27492	+	5.67232i	0.337782	+	0.585055i
$95$	14.0000	−	24.2487i	1.43637	−	2.48787i
$96$		0			0
$97$	0.274917	−	0.476171i	0.0279136	−	0.0483478i	−0.851731	−	0.523979i	$-0.824447\pi$
$97$	0.274917	−	0.476171i	0.0279136	−	0.0483478i	0.879645	+	0.475631i	$0.157780\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$		0			0
$100$	−6.63746	+	11.4964i	−0.663746	+	1.14964i
$101$	0.862541	+	1.49397i	0.0858261	+	0.148655i	0.905743	−	0.423828i	$-0.139314\pi$
$101$	0.862541	+	1.49397i	0.0858261	+	0.148655i	−0.819917	+	0.572483i	$0.805980\pi$
$102$		0			0
$103$	5.27492			0.519753			0.259877	−	0.965642i	$-0.416318\pi$
$103$	5.27492			0.519753			0.259877	+	0.965642i	$0.416318\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$		0			0
$106$	1.77492	+	3.07425i	0.172395	+	0.298597i
$107$	1.27492	+	2.20822i	0.123251	+	0.213477i	0.921048	−	0.389449i	$-0.127335\pi$
$107$	1.27492	+	2.20822i	0.123251	+	0.213477i	−0.797797	+	0.602926i	$0.794001\pi$
$108$		0			0
$109$	−4.54983			−0.435795			−0.217898	−	0.975972i	$-0.569920\pi$
$109$	−4.54983			−0.435795			−0.217898	+	0.975972i	$0.569920\pi$
$110$	−8.54983	+	14.8087i	−0.815195	+	1.41196i
$111$		0			0
$112$	1.00000			0.0944911
$113$	7.41238	−	12.8386i	0.697298	−	1.20775i	−0.272102	−	0.962268i	$-0.587719\pi$
$113$	7.41238	−	12.8386i	0.697298	−	1.20775i	0.969400	−	0.245487i	$-0.0789478\pi$
$114$		0			0
$115$	11.2749	+	19.5287i	1.05139	+	1.82106i
$116$	−8.27492			−0.768307
$117$		0			0
$118$	−11.8248			−1.08856
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	9.00000			0.814822
$123$		0			0
$124$	0.637459	−	1.10411i	0.0572455	−	0.0991521i
$125$	−35.3746			−3.16400
$126$		0			0
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−10.6873	−	11.1066i	−0.937338	−	0.974110i
$131$	2.72508			0.238092			0.119046	−	0.992889i	$-0.462016\pi$
$131$	2.72508			0.238092			0.119046	+	0.992889i	$0.462016\pi$
$132$		0			0
$133$	−3.27492	−	5.67232i	−0.283971	−	0.491853i
$134$	−1.36254	+	2.35999i	−0.117706	+	0.203872i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	11.4124	−	19.7668i	0.975025	−	1.68879i	0.295173	−	0.955444i	$-0.404623\pi$
$137$	11.4124	−	19.7668i	0.975025	−	1.68879i	0.679852	−	0.733349i	$-0.262044\pi$
$138$		0			0
$139$	4.54983	−	7.88054i	0.385912	−	0.668419i	−0.605983	−	0.795477i	$-0.707220\pi$
$139$	4.54983	−	7.88054i	0.385912	−	0.668419i	0.991895	+	0.127058i	$0.0405535\pi$
$140$	2.13746	+	3.70219i	0.180648	+	0.312892i
$141$		0			0
$142$	5.27492			0.442661
$143$	−10.0000	−	10.3923i	−0.836242	−	0.869048i
$144$		0			0
$145$	−17.6873	−	30.6353i	−1.46885	−	2.54412i
$146$	2.86254	+	4.95807i	0.236906	+	0.410333i
$147$		0			0
$148$	0.274917			0.0225981
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	13.0997			1.06604			0.533018	−	0.846104i	$-0.321058\pi$
$151$	13.0997			1.06604			0.533018	+	0.846104i	$0.321058\pi$
$152$	3.27492	−	5.67232i	0.265631	−	0.460086i
$153$		0			0
$154$	2.00000	+	3.46410i	0.161165	+	0.279145i
$155$	5.45017			0.437768
$156$		0			0
$157$	−3.72508			−0.297294			−0.148647	−	0.988890i	$-0.547492\pi$
$157$	−3.72508			−0.297294			−0.148647	+	0.988890i	$0.547492\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$		0			0
$160$	−2.13746	+	3.70219i	−0.168981	+	0.292684i
$161$	5.27492			0.415722
$162$		0			0
$163$	6.63746	−	11.4964i	0.519886	−	0.900469i	−0.479847	−	0.877352i	$-0.659308\pi$
$163$	6.63746	−	11.4964i	0.519886	−	0.900469i	0.999733	−	0.0231165i	$-0.00735887\pi$
$164$	−8.27492			−0.646162
$165$		0			0
$166$	5.91238	+	10.2405i	0.458889	+	0.794820i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−12.8248			−0.983614
$171$		0			0
$172$	5.91238	+	10.2405i	0.450814	+	0.780833i
$173$	−2.27492	+	3.94027i	−0.172959	+	0.299573i	−0.939453	−	0.342678i	$-0.888666\pi$
$173$	−2.27492	+	3.94027i	−0.172959	+	0.299573i	0.766494	+	0.642251i	$0.221999\pi$
$174$		0			0
$175$	−6.63746	+	11.4964i	−0.501745	+	0.869047i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	−0.362541	+	0.627940i	−0.0271736	+	0.0470661i
$179$	0.725083	+	1.25588i	0.0541952	+	0.0938689i	0.891850	−	0.452331i	$-0.149407\pi$
$179$	0.725083	+	1.25588i	0.0541952	+	0.0938689i	−0.837655	+	0.546200i	$0.816074\pi$
$180$		0			0
$181$	−16.8248			−1.25057			−0.625287	−	0.780395i	$-0.715018\pi$
$181$	−16.8248			−1.25057			−0.625287	+	0.780395i	$0.715018\pi$
$182$	−3.50000	+	0.866025i	−0.259437	+	0.0641941i
$183$		0			0
$184$	2.63746	+	4.56821i	0.194436	+	0.336773i
$185$	0.587624	+	1.01779i	0.0432030	+	0.0748298i
$186$		0			0
$187$	−12.0000			−0.877527
$188$	−3.27492	+	5.67232i	−0.238848	+	0.413697i
$189$		0			0
$190$	28.0000			2.03133
$191$	3.36254	−	5.82409i	0.243305	−	0.421417i	−0.718349	−	0.695683i	$-0.755102\pi$
$191$	3.36254	−	5.82409i	0.243305	−	0.421417i	0.961654	+	0.274267i	$0.0884351\pi$
$192$		0			0
$193$	12.4124	+	21.4989i	0.893462	+	1.54752i	0.835696	+	0.549192i	$0.185064\pi$
$193$	12.4124	+	21.4989i	0.893462	+	1.54752i	0.0577662	+	0.998330i	$0.481602\pi$
$194$	0.549834			0.0394758
$195$		0			0
$196$	1.00000			0.0714286
$197$	−10.9124	−	18.9008i	−0.777475	−	1.34663i	−0.933393	−	0.358856i	$-0.883167\pi$
$197$	−10.9124	−	18.9008i	−0.777475	−	1.34663i	0.155919	−	0.987770i	$-0.450166\pi$
$198$		0			0
$199$	−5.91238	+	10.2405i	−0.419117	+	0.725932i	−0.995851	−	0.0909999i	$-0.970994\pi$
$199$	−5.91238	+	10.2405i	−0.419117	+	0.725932i	0.576734	+	0.816932i	$0.304327\pi$
$200$	−13.2749			−0.938678
$201$		0			0
$202$	−0.862541	+	1.49397i	−0.0606882	+	0.105115i
$203$	−8.27492			−0.580785
$204$		0			0
$205$	−17.6873	−	30.6353i	−1.23533	−	2.13966i
$206$	2.63746	+	4.56821i	0.183760	+	0.318282i
$207$		0			0
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	26.1993			1.81225
$210$		0			0
$211$	−10.5498	−	18.2728i	−0.726281	−	1.25795i	−0.958445	−	0.285278i	$-0.907914\pi$
$211$	−10.5498	−	18.2728i	−0.726281	−	1.25795i	0.232164	−	0.972677i	$-0.425419\pi$
$212$	−1.77492	+	3.07425i	−0.121902	+	0.211140i
$213$		0			0
$214$	−1.27492	+	2.20822i	−0.0871515	+	0.150951i
$215$	−25.2749	+	43.7774i	−1.72374	+	2.98560i
$216$		0			0
$217$	0.637459	−	1.10411i	0.0432735	−	0.0749519i
$218$	−2.27492	−	3.94027i	−0.154077	−	0.266869i
$219$		0			0
$220$	−17.0997			−1.15286
$221$	3.00000	−	10.3923i	0.201802	−	0.699062i
$222$		0			0
$223$	−5.36254	−	9.28819i	−0.359102	−	0.621983i	0.628709	−	0.777641i	$-0.283584\pi$
$223$	−5.36254	−	9.28819i	−0.359102	−	0.621983i	−0.987811	+	0.155657i	$0.950250\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	14.8248			0.986128
$227$	−10.5498	+	18.2728i	−0.700217	+	1.21281i	0.268173	+	0.963371i	$0.413580\pi$
$227$	−10.5498	+	18.2728i	−0.700217	+	1.21281i	−0.968390	+	0.249441i	$0.919753\pi$
$228$		0			0
$229$	12.7251			0.840897			0.420449	−	0.907316i	$-0.361873\pi$
$229$	12.7251			0.840897			0.420449	+	0.907316i	$0.361873\pi$
$230$	−11.2749	+	19.5287i	−0.743446	+	1.28769i
$231$		0			0
$232$	−4.13746	−	7.16629i	−0.271637	−	0.470490i
$233$	−7.45017			−0.488077			−0.244038	−	0.969766i	$-0.578472\pi$
$233$	−7.45017			−0.488077			−0.244038	+	0.969766i	$0.578472\pi$
$234$		0			0
$235$	−28.0000			−1.82652
$236$	−5.91238	−	10.2405i	−0.384863	−	0.666602i
$237$		0			0
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	5.27492			0.341206			0.170603	−	0.985340i	$-0.445428\pi$
$239$	5.27492			0.341206			0.170603	+	0.985340i	$0.445428\pi$
$240$		0			0
$241$	7.86254	−	13.6183i	0.506471	−	0.877233i	−0.493501	−	0.869745i	$-0.664283\pi$
$241$	7.86254	−	13.6183i	0.506471	−	0.877233i	0.999972	−	0.00748804i	$-0.00238354\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	4.50000	+	7.79423i	0.288083	+	0.498974i
$245$	2.13746	+	3.70219i	0.136557	+	0.236524i
$246$		0			0
$247$	−6.54983	+	22.6893i	−0.416756	+	1.44369i
$248$	1.27492			0.0809573
$249$		0			0
$250$	−17.6873	−	30.6353i	−1.11864	−	1.93755i
$251$	6.63746	−	11.4964i	0.418953	−	0.725647i	−0.576882	−	0.816828i	$-0.695731\pi$
$251$	6.63746	−	11.4964i	0.418953	−	0.725647i	0.995834	+	0.0911804i	$0.0290640\pi$
$252$		0			0
$253$	−10.5498	+	18.2728i	−0.663262	+	1.14880i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$		0			0
$259$	0.274917			0.0170825
$260$	4.27492	−	14.8087i	0.265119	−	0.918400i
$261$		0			0
$262$	1.36254	+	2.35999i	0.0841781	+	0.145801i
$263$	10.5498	+	18.2728i	0.650531	+	1.12675i	0.982994	+	0.183636i	$0.0587868\pi$
$263$	10.5498	+	18.2728i	0.650531	+	1.12675i	−0.332464	+	0.943116i	$0.607880\pi$
$264$		0			0
$265$	−15.1752			−0.932208
$266$	3.27492	−	5.67232i	0.200798	−	0.347792i
$267$		0			0
$268$	−2.72508			−0.166461
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	−0.938823	−	0.344400i	$-0.888082\pi$
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	0.171152	−	0.985245i	$-0.445251\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	22.8248			1.37889
$275$	−26.5498	−	45.9857i	−1.60102	−	2.77304i
$276$		0			0
$277$	−7.41238	+	12.8386i	−0.445366	+	0.771397i	−0.998078	−	0.0619755i	$-0.980260\pi$
$277$	−7.41238	+	12.8386i	−0.445366	+	0.771397i	0.552711	+	0.833373i	$0.313593\pi$
$278$	9.09967			0.545762
$279$		0			0
$280$	−2.13746	+	3.70219i	−0.127738	+	0.221248i
$281$	20.8248			1.24230			0.621150	−	0.783691i	$-0.286666\pi$
$281$	20.8248			1.24230			0.621150	+	0.783691i	$0.286666\pi$
$282$		0			0
$283$	4.72508	+	8.18408i	0.280877	+	0.486493i	0.971601	−	0.236625i	$-0.0760414\pi$
$283$	4.72508	+	8.18408i	0.280877	+	0.486493i	−0.690724	+	0.723119i	$0.742708\pi$
$284$	2.63746	+	4.56821i	0.156504	+	0.271074i
$285$		0			0
$286$	4.00000	−	13.8564i	0.236525	−	0.819346i
$287$	−8.27492			−0.488453
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	17.6873	−	30.6353i	1.03863	−	1.79897i
$291$		0			0
$292$	−2.86254	+	4.95807i	−0.167518	+	0.290149i
$293$	−9.13746	+	15.8265i	−0.533816	+	0.924596i	0.465404	+	0.885099i	$0.345909\pi$
$293$	−9.13746	+	15.8265i	−0.533816	+	0.924596i	−0.999220	+	0.0394979i	$0.987424\pi$
$294$		0			0
$295$	25.2749	−	43.7774i	1.47156	−	2.54882i
$296$	0.137459	+	0.238085i	0.00798962	+	0.0138384i
$297$		0			0
$298$	−1.00000			−0.0579284
$299$	−13.1873	−	13.7046i	−0.762641	−	0.792560i
$300$		0			0
$301$	5.91238	+	10.2405i	0.340784	+	0.590255i
$302$	6.54983	+	11.3446i	0.376901	+	0.652811i
$303$		0			0
$304$	6.54983			0.375659
$305$	−19.2371	+	33.3197i	−1.10151	+	1.90788i
$306$		0			0
$307$	−1.45017			−0.0827653			−0.0413827	−	0.999143i	$-0.513176\pi$
$307$	−1.45017			−0.0827653			−0.0413827	+	0.999143i	$0.513176\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$		0			0
$310$	2.72508	+	4.71998i	0.154774	+	0.268077i
$311$	2.54983			0.144588			0.0722939	−	0.997383i	$-0.476968\pi$
$311$	2.54983			0.144588			0.0722939	+	0.997383i	$0.476968\pi$
$312$		0			0
$313$	17.6495			0.997609			0.498804	−	0.866715i	$-0.333773\pi$
$313$	17.6495			0.997609			0.498804	+	0.866715i	$0.333773\pi$
$314$	−1.86254	−	3.22602i	−0.105109	−	0.182055i
$315$		0			0
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	7.54983			0.424041			0.212020	−	0.977265i	$-0.431996\pi$
$317$	7.54983			0.424041			0.212020	+	0.977265i	$0.431996\pi$
$318$		0			0
$319$	16.5498	−	28.6652i	0.926613	−	1.60494i
$320$	−4.27492			−0.238975
$321$		0			0
$322$	2.63746	+	4.56821i	0.146980	+	0.254577i
$323$	9.82475	+	17.0170i	0.546664	+	0.946849i
$324$		0			0
$325$	46.4622	−	11.4964i	2.57726	−	0.637706i
$326$	13.2749			0.735230
$327$		0			0
$328$	−4.13746	−	7.16629i	−0.228453	−	0.395692i
$329$	−3.27492	+	5.67232i	−0.180552	+	0.312725i
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	−5.91238	+	10.2405i	−0.324484	+	0.562022i
$333$		0			0
$334$		0			0
$335$	−5.82475	−	10.0888i	−0.318240	−	0.551208i
$336$		0			0
$337$	0.274917			0.0149757			0.00748785	−	0.999972i	$-0.497617\pi$
$337$	0.274917			0.0149757			0.00748785	+	0.999972i	$0.497617\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$		0			0
$340$	−6.41238	−	11.1066i	−0.347760	−	0.602338i
$341$	2.54983	+	4.41644i	0.138081	+	0.239164i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−5.91238	+	10.2405i	−0.318774	+	0.552133i
$345$		0			0
$346$	−4.54983			−0.244601
$347$	15.2749	−	26.4569i	0.820001	−	1.42028i	−0.0856804	−	0.996323i	$-0.527306\pi$
$347$	15.2749	−	26.4569i	0.820001	−	1.42028i	0.905681	−	0.423960i	$-0.139360\pi$
$348$		0			0
$349$	17.4622	+	30.2454i	0.934731	+	1.61900i	0.775113	+	0.631822i	$0.217693\pi$
$349$	17.4622	+	30.2454i	0.934731	+	1.61900i	0.159617	+	0.987179i	$0.448974\pi$
$350$	−13.2749			−0.709574
$351$		0			0
$352$	−4.00000			−0.213201
$353$	−9.77492	−	16.9307i	−0.520266	−	0.901128i	−0.999722	−	0.0235618i	$-0.992499\pi$
$353$	−9.77492	−	16.9307i	−0.520266	−	0.901128i	0.479456	−	0.877566i	$-0.340834\pi$
$354$		0			0
$355$	−11.2749	+	19.5287i	−0.598410	+	1.03648i
$356$	−0.725083			−0.0384293
$357$		0			0
$358$	−0.725083	+	1.25588i	−0.0383218	+	0.0663753i
$359$	1.09967			0.0580383			0.0290192	−	0.999579i	$-0.490762\pi$
$359$	1.09967			0.0580383			0.0290192	+	0.999579i	$0.490762\pi$
$360$		0			0
$361$	−11.9502	−	20.6983i	−0.628956	−	1.08938i
$362$	−8.41238	−	14.5707i	−0.442145	−	0.765817i
$363$		0			0
$364$	−2.50000	−	2.59808i	−0.131036	−	0.136176i
$365$	−24.4743			−1.28104
$366$		0			0
$367$	−6.63746	−	11.4964i	−0.346473	−	0.600108i	0.639148	−	0.769084i	$-0.279287\pi$
$367$	−6.63746	−	11.4964i	−0.346473	−	0.600108i	−0.985620	+	0.168976i	$0.945954\pi$
$368$	−2.63746	+	4.56821i	−0.137487	+	0.238135i
$369$		0			0
$370$	−0.587624	+	1.01779i	−0.0305491	+	0.0529126i
$371$	−1.77492	+	3.07425i	−0.0921491	+	0.159607i
$372$		0			0
$373$	−13.4124	+	23.2309i	−0.694466	+	1.20285i	0.275894	+	0.961188i	$0.411026\pi$
$373$	−13.4124	+	23.2309i	−0.694466	+	1.20285i	−0.970360	+	0.241663i	$0.922307\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$		0			0
$376$	−6.54983			−0.337782
$377$	20.6873	+	21.4989i	1.06545	+	1.10725i
$378$		0			0
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$	14.0000	+	24.2487i	0.718185	+	1.24393i
$381$		0			0
$382$	6.72508			0.344085
$383$	11.0997	−	19.2252i	0.567167	−	0.982361i	−0.429678	−	0.902982i	$-0.641373\pi$
$383$	11.0997	−	19.2252i	0.567167	−	0.982361i	0.996844	−	0.0793791i	$-0.0252938\pi$
$384$		0			0
$385$	−17.0997			−0.871480
$386$	−12.4124	+	21.4989i	−0.631773	+	1.09426i
$387$		0			0
$388$	0.274917	+	0.476171i	0.0139568	+	0.0241739i
$389$	24.6495			1.24978			0.624890	−	0.780713i	$-0.285144\pi$
$389$	24.6495			1.24978			0.624890	+	0.780713i	$0.285144\pi$
$390$		0			0
$391$	−15.8248			−0.800292
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	10.9124	−	18.9008i	0.549758	−	0.952208i
$395$	34.1993			1.72076
$396$		0			0
$397$	−11.6375	+	20.1567i	−0.584067	+	1.01163i	0.410924	+	0.911670i	$0.365206\pi$
$397$	−11.6375	+	20.1567i	−0.584067	+	1.01163i	−0.994991	+	0.0999645i	$0.968127\pi$
$398$	−11.8248			−0.592721
$399$		0			0
$400$	−6.63746	−	11.4964i	−0.331873	−	0.574821i
$401$	−1.13746	−	1.97014i	−0.0568020	−	0.0983839i	0.836226	−	0.548385i	$-0.184757\pi$
$401$	−1.13746	−	1.97014i	−0.0568020	−	0.0983839i	−0.893028	+	0.450001i	$0.851424\pi$
$402$		0			0
$403$	−4.46221	+	1.10411i	−0.222279	+	0.0549997i
$404$	−1.72508			−0.0858261
$405$		0			0
$406$	−4.13746	−	7.16629i	−0.205339	−	0.355657i
$407$	−0.549834	+	0.952341i	−0.0272543	+	0.0472058i
$408$		0			0
$409$	14.9622	−	25.9153i	0.739834	−	1.28143i	−0.212736	−	0.977110i	$-0.568238\pi$
$409$	14.9622	−	25.9153i	0.739834	−	1.28143i	0.952570	−	0.304320i	$-0.0984292\pi$
$410$	17.6873	−	30.6353i	0.873513	−	1.51297i
$411$		0			0
$412$	−2.63746	+	4.56821i	−0.129938	+	0.225060i
$413$	−5.91238	−	10.2405i	−0.290929	−	0.503904i
$414$		0			0
$415$	−50.5498			−2.48139
$416$	1.00000	−	3.46410i	0.0490290	−	0.169842i
$417$		0			0
$418$	13.0997	+	22.6893i	0.640726	+	1.10977i
$419$	−11.1873	−	19.3770i	−0.546535	−	0.946626i	−0.998509	−	0.0545951i	$-0.982613\pi$
$419$	−11.1873	−	19.3770i	−0.546535	−	0.946626i	0.451974	−	0.892031i	$-0.350720\pi$
$420$		0			0
$421$	8.27492			0.403295			0.201647	−	0.979458i	$-0.435370\pi$
$421$	8.27492			0.403295			0.201647	+	0.979458i	$0.435370\pi$
$422$	10.5498	−	18.2728i	0.513558	−	0.889508i
$423$		0			0
$424$	−3.54983			−0.172395
$425$	19.9124	−	34.4892i	0.965892	−	1.67297i
$426$		0			0
$427$	4.50000	+	7.79423i	0.217770	+	0.377189i
$428$	−2.54983			−0.123251
$429$		0			0
$430$	−50.5498			−2.43773
$431$	−6.63746	−	11.4964i	−0.319715	−	0.553763i	0.660713	−	0.750638i	$-0.270254\pi$
$431$	−6.63746	−	11.4964i	−0.319715	−	0.553763i	−0.980429	+	0.196875i	$0.936921\pi$
$432$		0			0
$433$	5.13746	−	8.89834i	0.246891	−	0.427627i	−0.715771	−	0.698335i	$-0.753925\pi$
$433$	5.13746	−	8.89834i	0.246891	−	0.427627i	0.962661	+	0.270708i	$0.0872579\pi$
$434$	1.27492			0.0611980
$435$		0			0
$436$	2.27492	−	3.94027i	0.108949	−	0.188705i
$437$	34.5498			1.65274
$438$		0			0
$439$	−6.54983	−	11.3446i	−0.312607	−	0.541450i	0.666319	−	0.745667i	$-0.267869\pi$
$439$	−6.54983	−	11.3446i	−0.312607	−	0.541450i	−0.978926	+	0.204216i	$0.934535\pi$
$440$	−8.54983	−	14.8087i	−0.407597	−	0.705979i
$441$		0			0
$442$	10.5000	−	2.59808i	0.499434	−	0.123578i
$443$	−34.5498			−1.64151			−0.820756	−	0.571279i	$-0.806448\pi$
$443$	−34.5498			−1.64151			−0.820756	+	0.571279i	$0.806448\pi$
$444$		0			0
$445$	−1.54983	−	2.68439i	−0.0734692	−	0.127252i
$446$	5.36254	−	9.28819i	0.253924	−	0.439809i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−9.54983	+	16.5408i	−0.450685	+	0.780609i	−0.998429	−	0.0560374i	$-0.982153\pi$
$449$	−9.54983	+	16.5408i	−0.450685	+	0.780609i	0.547744	+	0.836646i	$0.315487\pi$
$450$		0			0
$451$	16.5498	−	28.6652i	0.779301	−	1.34979i
$452$	7.41238	+	12.8386i	0.348649	+	0.603877i
$453$		0			0
$454$	−21.0997			−0.990257
$455$	4.27492	−	14.8087i	0.200411	−	0.694245i
$456$		0			0
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$	6.36254	+	11.0202i	0.297302	+	0.514942i
$459$		0			0
$460$	−22.5498			−1.05139
$461$	−9.68729	+	16.7789i	−0.451182	+	0.781471i	−0.998460	−	0.0554807i	$-0.982331\pi$
$461$	−9.68729	+	16.7789i	−0.451182	+	0.781471i	0.547278	+	0.836951i	$0.315664\pi$
$462$		0			0
$463$	−10.5498			−0.490292			−0.245146	−	0.969486i	$-0.578836\pi$
$463$	−10.5498			−0.490292			−0.245146	+	0.969486i	$0.578836\pi$
$464$	4.13746	−	7.16629i	0.192077	−	0.332687i
$465$		0			0
$466$	−3.72508	−	6.45203i	−0.172561	−	0.298885i
$467$	8.17525			0.378305			0.189153	−	0.981948i	$-0.439426\pi$
$467$	8.17525			0.378305			0.189153	+	0.981948i	$0.439426\pi$
$468$		0			0
$469$	−2.72508			−0.125833
$470$	−14.0000	−	24.2487i	−0.645772	−	1.11851i
$471$		0			0
$472$	5.91238	−	10.2405i	0.272139	−	0.471359i
$473$	−47.2990			−2.17481
$474$		0			0
$475$	−43.4743	+	75.2996i	−1.99474	+	3.45498i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	2.63746	+	4.56821i	0.120635	+	0.208945i
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$		0			0
$481$	−0.687293	−	0.714256i	−0.0313379	−	0.0325673i
$482$	15.7251			0.716258
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−1.17525	+	2.03559i	−0.0533653	+	0.0924314i
$486$		0			0
$487$	0.549834	−	0.952341i	0.0249154	−	0.0431547i	−0.853299	−	0.521422i	$-0.825402\pi$
$487$	0.549834	−	0.952341i	0.0249154	−	0.0431547i	0.878214	+	0.478267i	$0.158735\pi$
$488$	−4.50000	+	7.79423i	−0.203705	+	0.352828i
$489$		0			0
$490$	−2.13746	+	3.70219i	−0.0965605	+	0.167248i
$491$	12.5498	+	21.7370i	0.566366	+	0.980975i	0.996921	+	0.0784105i	$0.0249845\pi$
$491$	12.5498	+	21.7370i	0.566366	+	0.980975i	−0.430555	+	0.902564i	$0.641682\pi$
$492$		0			0
$493$	24.8248			1.11805
$494$	−22.9244	+	5.67232i	−1.03142	+	0.255210i
$495$		0			0
$496$	0.637459	+	1.10411i	0.0286227	+	0.0495760i
$497$	2.63746	+	4.56821i	0.118306	+	0.204912i
$498$		0			0
$499$	−31.8248			−1.42467			−0.712336	−	0.701839i	$-0.752363\pi$
$499$	−31.8248			−1.42467			−0.712336	+	0.701839i	$0.752363\pi$
$500$	17.6873	−	30.6353i	0.791000	−	1.37005i
$501$		0			0
$502$	13.2749			0.592489
$503$	−10.5498	+	18.2728i	−0.470394	+	0.814746i	−0.999427	−	0.0338552i	$-0.989221\pi$
$503$	−10.5498	+	18.2728i	−0.470394	+	0.814746i	0.529033	+	0.848601i	$0.322555\pi$
$504$		0			0
$505$	−3.68729	−	6.38658i	−0.164082	−	0.284199i
$506$	−21.0997			−0.937995
$507$		0			0
$508$	8.00000			0.354943
$509$	−6.58762	−	11.4101i	−0.291991	−	0.505744i	0.682289	−	0.731082i	$-0.260985\pi$
$509$	−6.58762	−	11.4101i	−0.291991	−	0.505744i	−0.974281	+	0.225339i	$0.927651\pi$
$510$		0			0
$511$	−2.86254	+	4.95807i	−0.126631	+	0.219332i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	−22.5498			−0.993664
$516$		0			0
$517$	−13.0997	−	22.6893i	−0.576123	−	0.997874i
$518$	0.137459	+	0.238085i	0.00603958	+	0.0104609i
$519$		0			0
$520$	14.9622	−	3.70219i	0.656136	−	0.162352i
$521$	20.8248			0.912349			0.456174	−	0.889890i	$-0.349219\pi$
$521$	20.8248			0.912349			0.456174	+	0.889890i	$0.349219\pi$
$522$		0			0
$523$	13.0997	+	22.6893i	0.572809	+	0.992133i	0.996276	+	0.0862221i	$0.0274795\pi$
$523$	13.0997	+	22.6893i	0.572809	+	0.992133i	−0.423467	+	0.905911i	$0.639187\pi$
$524$	−1.36254	+	2.35999i	−0.0595229	+	0.103097i
$525$		0			0
$526$	−10.5498	+	18.2728i	−0.459995	+	0.796734i
$527$	−1.91238	+	3.31233i	−0.0833044	+	0.144287i
$528$		0			0
$529$	−2.41238	+	4.17836i	−0.104886	+	0.181668i
$530$	−7.58762	−	13.1422i	−0.329585	−	0.570859i
$531$		0			0
$532$	6.54983			0.283971
$533$	20.6873	+	21.4989i	0.896066	+	0.931219i
$534$		0			0
$535$	−5.45017	−	9.43996i	−0.235631	−	0.408125i
$536$	−1.36254	−	2.35999i	−0.0588528	−	0.101936i
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−2.00000	+	3.46410i	−0.0861461	+	0.149209i
$540$		0			0
$541$	25.3746			1.09094			0.545469	−	0.838131i	$-0.316351\pi$
$541$	25.3746			1.09094			0.545469	+	0.838131i	$0.316351\pi$
$542$	12.6375	−	21.8887i	0.542825	−	0.940201i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	19.4502			0.833154
$546$		0			0
$547$	2.90033			0.124009			0.0620046	−	0.998076i	$-0.480251\pi$
$547$	2.90033			0.124009			0.0620046	+	0.998076i	$0.480251\pi$
$548$	11.4124	+	19.7668i	0.487513	+	0.844396i
$549$		0			0
$550$	26.5498	−	45.9857i	1.13209	−	1.96084i
$551$	−54.1993			−2.30897
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	−14.8248			−0.629843
$555$		0			0
$556$	4.54983	+	7.88054i	0.192956	+	0.334210i
$557$	−17.5997	−	30.4835i	−0.745722	−	1.29163i	−0.949857	−	0.312685i	$-0.898771\pi$
$557$	−17.5997	−	30.4835i	−0.745722	−	1.29163i	0.204135	−	0.978943i	$-0.434562\pi$
$558$		0			0
$559$	11.8248	−	40.9621i	0.500134	−	1.73251i
$560$	−4.27492			−0.180648
$561$		0			0
$562$	10.4124	+	18.0348i	0.439220	+	0.760751i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	−31.6873	+	54.8840i	−1.33309	+	2.30899i
$566$	−4.72508	+	8.18408i	−0.198610	+	0.344003i
$567$		0			0
$568$	−2.63746	+	4.56821i	−0.110665	+	0.191678i
$569$	2.45017	+	4.24381i	0.102716	+	0.177910i	0.912803	−	0.408400i	$-0.133913\pi$
$569$	2.45017	+	4.24381i	0.102716	+	0.177910i	−0.810087	+	0.586310i	$0.800580\pi$
$570$		0			0
$571$	−14.7251			−0.616226			−0.308113	−	0.951350i	$-0.599697\pi$
$571$	−14.7251			−0.616226			−0.308113	+	0.951350i	$0.599697\pi$
$572$	14.0000	−	3.46410i	0.585369	−	0.144841i
$573$		0			0
$574$	−4.13746	−	7.16629i	−0.172694	−	0.299115i
$575$	−35.0120	−	60.6426i	−1.46010	−	2.52897i
$576$		0			0
$577$	9.37459			0.390269			0.195135	−	0.980776i	$-0.437486\pi$
$577$	9.37459			0.390269			0.195135	+	0.980776i	$0.437486\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		0			0
$580$	35.3746			1.46885
$581$	−5.91238	+	10.2405i	−0.245287	+	0.424849i
$582$		0			0
$583$	−7.09967	−	12.2970i	−0.294038	−	0.509289i
$584$	−5.72508			−0.236906
$585$		0			0
$586$	−18.2749			−0.754930
$587$	4.46221	+	7.72877i	0.184175	+	0.319001i	0.943298	−	0.331946i	$-0.107705\pi$
$587$	4.46221	+	7.72877i	0.184175	+	0.319001i	−0.759123	+	0.650947i	$0.774372\pi$
$588$		0			0
$589$	4.17525	−	7.23174i	0.172038	−	0.297979i
$590$	50.5498			2.08110
$591$		0			0
$592$	−0.137459	+	0.238085i	−0.00564951	+	0.00978525i
$593$	−4.45017			−0.182746			−0.0913732	−	0.995817i	$-0.529126\pi$
$593$	−4.45017			−0.182746			−0.0913732	+	0.995817i	$0.529126\pi$
$594$		0			0
$595$	−6.41238	−	11.1066i	−0.262882	−	0.455325i
$596$	−0.500000	−	0.866025i	−0.0204808	−	0.0354738i
$597$		0			0
$598$	5.27492	−	18.2728i	0.215707	−	0.747232i
$599$	10.7251			0.438215			0.219108	−	0.975701i	$-0.429685\pi$
$599$	10.7251			0.438215			0.219108	+	0.975701i	$0.429685\pi$
$600$		0			0
$601$	3.86254	+	6.69012i	0.157556	+	0.272896i	0.933987	−	0.357307i	$-0.116305\pi$
$601$	3.86254	+	6.69012i	0.157556	+	0.272896i	−0.776431	+	0.630203i	$0.782972\pi$
$602$	−5.91238	+	10.2405i	−0.240970	+	0.417373i
$603$		0			0
$604$	−6.54983	+	11.3446i	−0.266509	+	0.461607i
$605$	10.6873	−	18.5109i	0.434500	−	0.752577i
$606$		0			0
$607$	−7.36254	+	12.7523i	−0.298836	+	0.517600i	−0.975870	−	0.218352i	$-0.929932\pi$
$607$	−7.36254	+	12.7523i	−0.298836	+	0.517600i	0.677034	+	0.735952i	$0.263265\pi$
$608$	3.27492	+	5.67232i	0.132815	+	0.230043i
$609$		0			0
$610$	−38.4743			−1.55778
$611$	22.9244	−	5.67232i	0.927423	−	0.229478i
$612$		0			0
$613$	−14.6873	−	25.4391i	−0.593214	−	1.02748i	−0.993796	−	0.111216i	$-0.964525\pi$
$613$	−14.6873	−	25.4391i	−0.593214	−	1.02748i	0.400582	−	0.916261i	$-0.368808\pi$
$614$	−0.725083	−	1.25588i	−0.0292620	−	0.0506832i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	19.9622	−	34.5756i	0.803648	−	1.39196i	−0.113551	−	0.993532i	$-0.536223\pi$
$617$	19.9622	−	34.5756i	0.803648	−	1.39196i	0.917200	−	0.398428i	$-0.130444\pi$
$618$		0			0
$619$	−15.6495			−0.629007			−0.314503	−	0.949256i	$-0.601838\pi$
$619$	−15.6495			−0.629007			−0.314503	+	0.949256i	$0.601838\pi$
$620$	−2.72508	+	4.71998i	−0.109442	+	0.189559i
$621$		0			0
$622$	1.27492	+	2.20822i	0.0511195	+	0.0885416i
$623$	−0.725083			−0.0290498
$624$		0			0
$625$	84.8488			3.39395
$626$	8.82475	+	15.2849i	0.352708	+	0.610908i
$627$		0			0
$628$	1.86254	−	3.22602i	0.0743235	−	0.128732i
$629$	−0.824752			−0.0328850
$630$		0			0
$631$	14.5498	−	25.2011i	0.579220	−	1.00324i	−0.416349	−	0.909205i	$-0.636691\pi$
$631$	14.5498	−	25.2011i	0.579220	−	1.00324i	0.995569	−	0.0940333i	$-0.0299760\pi$
$632$	8.00000			0.318223
$633$		0			0
$634$	3.77492	+	6.53835i	0.149921	+	0.259671i
$635$	17.0997	+	29.6175i	0.678580	+	1.17533i
$636$		0			0
$637$	−2.50000	−	2.59808i	−0.0990536	−	0.102940i
$638$	33.0997			1.31043
$639$		0			0
$640$	−2.13746	−	3.70219i	−0.0844905	−	0.146342i
$641$	9.41238	−	16.3027i	0.371766	−	0.643918i	−0.618071	−	0.786122i	$-0.712086\pi$
$641$	9.41238	−	16.3027i	0.371766	−	0.643918i	0.989837	+	0.142204i	$0.0454189\pi$
$642$		0			0
$643$	16.3746	−	28.3616i	0.645751	−	1.11847i	−0.338377	−	0.941011i	$-0.609878\pi$
$643$	16.3746	−	28.3616i	0.645751	−	1.11847i	0.984128	−	0.177462i	$-0.0567888\pi$
$644$	−2.63746	+	4.56821i	−0.103930	+	0.180013i
$645$		0			0
$646$	−9.82475	+	17.0170i	−0.386550	+	0.669524i
$647$	4.72508	+	8.18408i	0.185762	+	0.321750i	0.943833	−	0.330423i	$-0.107191\pi$
$647$	4.72508	+	8.18408i	0.185762	+	0.321750i	−0.758071	+	0.652172i	$0.773858\pi$
$648$		0			0
$649$	47.2990			1.85665
$650$	33.1873	+	34.4892i	1.30171	+	1.35278i
$651$		0			0
$652$	6.63746	+	11.4964i	0.259943	+	0.450234i
$653$	16.7371	+	28.9896i	0.654974	+	1.13445i	0.981900	+	0.189399i	$0.0606539\pi$
$653$	16.7371	+	28.9896i	0.654974	+	1.13445i	−0.326926	+	0.945050i	$0.606013\pi$
$654$		0			0
$655$	−11.6495			−0.455184
$656$	4.13746	−	7.16629i	0.161541	−	0.279797i
$657$		0			0
$658$	−6.54983			−0.255339
$659$	−6.72508	+	11.6482i	−0.261972	+	0.453749i	−0.966766	−	0.255663i	$-0.917706\pi$
$659$	−6.72508	+	11.6482i	−0.261972	+	0.453749i	0.704794	+	0.709412i	$0.251039\pi$
$660$		0			0
$661$	−4.95017	−	8.57394i	−0.192539	−	0.333488i	0.753552	−	0.657388i	$-0.228339\pi$
$661$	−4.95017	−	8.57394i	−0.192539	−	0.333488i	−0.946091	+	0.323901i	$0.895006\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	−11.8248			−0.458889
$665$	14.0000	+	24.2487i	0.542897	+	0.940325i
$666$		0			0
$667$	21.8248	−	37.8016i	0.845058	−	1.46368i
$668$		0			0
$669$		0			0
$670$	5.82475	−	10.0888i	0.225030	−	0.389763i
$671$	−36.0000			−1.38976
$672$		0			0
$673$	9.04983	+	15.6748i	0.348845	+	0.604218i	0.986045	−	0.166481i	$-0.0532405\pi$
$673$	9.04983	+	15.6748i	0.348845	+	0.604218i	−0.637199	+	0.770699i	$0.719907\pi$
$674$	0.137459	+	0.238085i	0.00529471	+	0.00917070i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	33.6495			1.29326			0.646628	−	0.762806i	$-0.276179\pi$
$677$	33.6495			1.29326			0.646628	+	0.762806i	$0.276179\pi$
$678$		0			0
$679$	0.274917	+	0.476171i	0.0105504	+	0.0182738i
$680$	6.41238	−	11.1066i	0.245903	−	0.425917i
$681$		0			0
$682$	−2.54983	+	4.41644i	−0.0976382	+	0.169114i
$683$	−2.17525	+	3.76764i	−0.0832336	+	0.144165i	−0.904637	−	0.426183i	$-0.859858\pi$
$683$	−2.17525	+	3.76764i	−0.0832336	+	0.144165i	0.821404	+	0.570347i	$0.193191\pi$
$684$		0			0
$685$	−48.7870	+	84.5015i	−1.86405	+	3.22864i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−11.8248			−0.450814
$689$	12.4244	−	3.07425i	0.473333	−	0.117119i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−2.27492	−	3.94027i	−0.0864794	−	0.149787i
$693$		0			0
$694$	30.5498			1.15966
$695$	−19.4502	+	33.6887i	−0.737787	+	1.27788i
$696$		0			0
$697$	24.8248			0.940305
$698$	−17.4622	+	30.2454i	−0.660954	+	1.14481i
$699$		0			0
$700$	−6.63746	−	11.4964i	−0.250872	−	0.434524i
$701$	−14.9244			−0.563688			−0.281844	−	0.959460i	$-0.590946\pi$
$701$	−14.9244			−0.563688			−0.281844	+	0.959460i	$0.590946\pi$
$702$		0			0
$703$	1.80066			0.0679133
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	9.77492	−	16.9307i	0.367884	−	0.637194i
$707$	−1.72508			−0.0648784
$708$		0			0
$709$	23.6873	−	41.0276i	0.889595	−	1.54082i	0.0492402	−	0.998787i	$-0.484320\pi$
$709$	23.6873	−	41.0276i	0.889595	−	1.54082i	0.840355	−	0.542037i	$-0.182347\pi$
$710$	−22.5498			−0.846280
$711$		0			0
$712$	−0.362541	−	0.627940i	−0.0135868	−	0.0235331i
$713$	3.36254	+	5.82409i	0.125928	+	0.218114i
$714$		0			0
$715$	42.7492	+	44.4262i	1.59873	+	1.66145i
$716$	−1.45017			−0.0541952
$717$		0			0
$718$	0.549834	+	0.952341i	0.0205196	+	0.0355411i
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	−0.930923	−	0.365216i	$-0.880995\pi$
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	0.781748	+	0.623595i	$0.214328\pi$
$720$		0			0
$721$	−2.63746	+	4.56821i	−0.0982241	+	0.170129i
$722$	11.9502	−	20.6983i	0.444739	−	0.770311i
$723$		0			0
$724$	8.41238	−	14.5707i	0.312643	−	0.541514i
$725$	54.9244	+	95.1319i	2.03984	+	3.53311i
$726$		0			0
$727$	19.8248			0.735259			0.367630	−	0.929972i	$-0.380169\pi$
$727$	19.8248			0.735259			0.367630	+	0.929972i	$0.380169\pi$
$728$	1.00000	−	3.46410i	0.0370625	−	0.128388i
$729$		0			0
$730$	−12.2371	−	21.1953i	−0.452916	−	0.784474i
$731$	−17.7371	−	30.7216i	−0.656031	−	1.13628i
$732$		0			0
$733$	−32.6495			−1.20594			−0.602968	−	0.797765i	$-0.706016\pi$
$733$	−32.6495			−1.20594			−0.602968	+	0.797765i	$0.706016\pi$
$734$	6.63746	−	11.4964i	0.244993	−	0.424340i
$735$		0			0
$736$	−5.27492			−0.194436
$737$	5.45017	−	9.43996i	0.200759	−	0.347726i
$738$		0			0
$739$	24.6375	+	42.6733i	0.906304	+	1.56976i	0.819158	+	0.573568i	$0.194441\pi$
$739$	24.6375	+	42.6733i	0.906304	+	1.56976i	0.0871458	+	0.996196i	$0.472225\pi$
$740$	−1.17525			−0.0432030
$741$		0			0
$742$	−3.54983			−0.130319
$743$	−2.08762	−	3.61587i	−0.0765875	−	0.132653i	0.825188	−	0.564858i	$-0.191069\pi$
$743$	−2.08762	−	3.61587i	−0.0765875	−	0.132653i	−0.901776	+	0.432205i	$0.857736\pi$
$744$		0			0
$745$	2.13746	−	3.70219i	0.0783104	−	0.135638i
$746$	−26.8248			−0.982124
$747$		0			0
$748$	6.00000	−	10.3923i	0.219382	−	0.379980i
$749$	−2.54983			−0.0931689
$750$		0			0
$751$	9.27492	+	16.0646i	0.338447	+	0.586207i	0.984141	−	0.177390i	$-0.0567652\pi$
$751$	9.27492	+	16.0646i	0.338447	+	0.586207i	−0.645694	+	0.763596i	$0.723432\pi$
$752$	−3.27492	−	5.67232i	−0.119424	−	0.206848i
$753$		0			0
$754$	−8.27492	+	28.6652i	−0.301355	+	1.04392i
$755$	−56.0000			−2.03805
$756$		0			0
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$		0			0
$760$	−14.0000	+	24.2487i	−0.507833	+	0.879593i
$761$	10.0997	−	17.4931i	0.366113	−	0.634126i	−0.622841	−	0.782348i	$-0.714022\pi$
$761$	10.0997	−	17.4931i	0.366113	−	0.634126i	0.988954	+	0.148222i	$0.0473551\pi$
$762$		0			0
$763$	2.27492	−	3.94027i	0.0823575	−	0.142647i
$764$	3.36254	+	5.82409i	0.121652	+	0.210708i
$765$		0			0
$766$	22.1993			0.802095
$767$	−11.8248	+	40.9621i	−0.426967	+	1.47906i
$768$		0			0
$769$	−20.8248	−	36.0695i	−0.750960	−	1.30070i	−0.947358	−	0.320176i	$-0.896258\pi$
$769$	−20.8248	−	36.0695i	−0.750960	−	1.30070i	0.196398	−	0.980524i	$-0.437075\pi$
$770$	−8.54983	−	14.8087i	−0.308115	−	0.533670i
$771$		0			0
$772$	−24.8248			−0.893462
$773$	−10.4502	+	18.1002i	−0.375866	+	0.651020i	−0.990456	−	0.137827i	$-0.955988\pi$
$773$	−10.4502	+	18.1002i	−0.375866	+	0.651020i	0.614590	+	0.788847i	$0.289321\pi$
$774$		0			0
$775$	−16.9244			−0.607943
$776$	−0.274917	+	0.476171i	−0.00986895	+	0.0170935i
$777$		0			0
$778$	12.3248	+	21.3471i	0.441864	+	0.765330i
$779$	−54.1993			−1.94189
$780$		0			0
$781$	−21.0997			−0.755006
$782$	−7.91238	−	13.7046i	−0.282946	−	0.490077i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	15.9244			0.568367
$786$		0			0
$787$	−10.5498	+	18.2728i	−0.376061	+	0.651357i	−0.990485	−	0.137619i	$-0.956055\pi$
$787$	−10.5498	+	18.2728i	−0.376061	+	0.651357i	0.614424	+	0.788976i	$0.289388\pi$
$788$	21.8248			0.777475
$789$		0			0
$790$	17.0997	+	29.6175i	0.608379	+	1.05374i
$791$	7.41238	+	12.8386i	0.263554	+	0.456488i
$792$		0			0
$793$	9.00000	−	31.1769i	0.319599	−	1.10712i
$794$	−23.2749			−0.825996
$795$		0			0
$796$	−5.91238	−	10.2405i	−0.209559	−	0.362966i
$797$	8.27492	−	14.3326i	0.293113	−	0.507686i	−0.681431	−	0.731882i	$-0.738642\pi$
$797$	8.27492	−	14.3326i	0.293113	−	0.507686i	0.974544	+	0.224196i	$0.0719756\pi$
$798$		0			0
$799$	9.82475	−	17.0170i	0.347575	−	0.602017i
$800$	6.63746	−	11.4964i	0.234670	−	0.406460i
$801$		0			0
$802$	1.13746	−	1.97014i	0.0401651	−	0.0695679i
$803$	−11.4502	−	19.8323i	−0.404068	−	0.699866i
$804$		0			0
$805$	−22.5498			−0.794777
$806$	−3.18729	−	3.31233i	−0.112268	−	0.116672i
$807$		0			0
$808$	−0.862541	−	1.49397i	−0.0303441	−	0.0525575i
$809$	4.86254	+	8.42217i	0.170958	+	0.296108i	0.938755	−	0.344585i	$-0.111980\pi$
$809$	4.86254	+	8.42217i	0.170958	+	0.296108i	−0.767797	+	0.640693i	$0.778647\pi$
$810$		0			0
$811$	5.09967			0.179074			0.0895368	−	0.995984i	$-0.471461\pi$
$811$	5.09967			0.179074			0.0895368	+	0.995984i	$0.471461\pi$
$812$	4.13746	−	7.16629i	0.145196	−	0.251487i
$813$		0			0
$814$	−1.09967			−0.0385434
$815$	−28.3746	+	49.1462i	−0.993918	+	1.72152i
$816$		0			0
$817$	38.7251	+	67.0738i	1.35482	+	2.34662i
$818$	29.9244			1.04628
$819$		0			0
$820$	35.3746			1.23533
$821$	7.63746	+	13.2285i	0.266549	+	0.461677i	0.967968	−	0.251072i	$-0.0807832\pi$
$821$	7.63746	+	13.2285i	0.266549	+	0.461677i	−0.701419	+	0.712749i	$0.747450\pi$
$822$		0			0
$823$	3.45017	−	5.97586i	0.120265	−	0.208305i	−0.799607	−	0.600524i	$-0.794959\pi$
$823$	3.45017	−	5.97586i	0.120265	−	0.208305i	0.919872	+	0.392218i	$0.128292\pi$
$824$	−5.27492			−0.183760
$825$		0			0
$826$	5.91238	−	10.2405i	0.205718	−	0.356314i
$827$	−5.09967			−0.177333			−0.0886664	−	0.996061i	$-0.528261\pi$
$827$	−5.09967			−0.177333			−0.0886664	+	0.996061i	$0.528261\pi$
$828$		0			0
$829$	22.4124	+	38.8194i	0.778414	+	1.34825i	0.932856	+	0.360251i	$0.117309\pi$
$829$	22.4124	+	38.8194i	0.778414	+	1.34825i	−0.154442	+	0.988002i	$0.549358\pi$
$830$	−25.2749	−	43.7774i	−0.877305	−	1.51954i
$831$		0			0
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−3.00000			−0.103944
$834$		0			0
$835$		0			0
$836$	−13.0997	+	22.6893i	−0.453062	+	0.784726i
$837$		0			0
$838$	11.1873	−	19.3770i	0.386459	−	0.669366i
$839$	−10.3746	+	17.9693i	−0.358170	+	0.620369i	−0.987655	−	0.156643i	$-0.949933\pi$
$839$	−10.3746	+	17.9693i	−0.358170	+	0.620369i	0.629485	+	0.777013i	$0.283266\pi$
$840$		0			0
$841$	−19.7371	+	34.1857i	−0.680591	+	1.17882i
$842$	4.13746	+	7.16629i	0.142586	+	0.246967i
$843$		0			0
$844$	21.0997			0.726281
$845$	−49.1615	+	25.9153i	−1.69121	+	0.891514i
$846$		0			0
$847$	−2.50000	−	4.33013i	−0.0859010	−	0.148785i
$848$	−1.77492	−	3.07425i	−0.0609509	−	0.105570i
$849$		0			0
$850$	39.8248			1.36598
$851$	−0.725083	+	1.25588i	−0.0248555	+	0.0430510i
$852$		0			0
$853$	−14.4502			−0.494764			−0.247382	−	0.968918i	$-0.579570\pi$
$853$	−14.4502			−0.494764			−0.247382	+	0.968918i	$0.579570\pi$
$854$	−4.50000	+	7.79423i	−0.153987	+	0.266713i
$855$		0			0
$856$	−1.27492	−	2.20822i	−0.0435758	−	0.0754755i
$857$	36.8248			1.25791			0.628955	−	0.777442i	$-0.283483\pi$
$857$	36.8248			1.25791			0.628955	+	0.777442i	$0.283483\pi$
$858$		0			0
$859$	−27.6495			−0.943389			−0.471694	−	0.881762i	$-0.656357\pi$
$859$	−27.6495			−0.943389			−0.471694	+	0.881762i	$0.656357\pi$
$860$	−25.2749	−	43.7774i	−0.861868	−	1.49280i
$861$		0			0
$862$	6.63746	−	11.4964i	0.226073	−	0.391569i
$863$	−35.2990			−1.20159			−0.600796	−	0.799402i	$-0.705150\pi$
$863$	−35.2990			−1.20159			−0.600796	+	0.799402i	$0.705150\pi$
$864$		0			0
$865$	9.72508	−	16.8443i	0.330663	−	0.572725i
$866$	10.2749			0.349156
$867$		0			0
$868$	0.637459	+	1.10411i	0.0216368	+	0.0374760i
$869$	16.0000	+	27.7128i	0.542763	+	0.940093i
$870$		0			0
$871$	6.81271	+	7.07997i	0.230840	+	0.239896i
$872$	4.54983			0.154077
$873$		0			0
$874$	17.2749	+	29.9210i	0.584333	+	1.01209i
$875$	17.6873	−	30.6353i	0.597940	−	1.03566i
$876$		0			0
$877$	1.86254	−	3.22602i	0.0628936	−	0.108935i	−0.832864	−	0.553478i	$-0.813300\pi$
$877$	1.86254	−	3.22602i	0.0628936	−	0.108935i	0.895758	+	0.444543i	$0.146634\pi$
$878$	6.54983	−	11.3446i	0.221046	−	0.382863i
$879$		0			0
$880$	8.54983	−	14.8087i	0.288215	−	0.499203i
$881$	0.774917	+	1.34220i	0.0261076	+	0.0452197i	0.878784	−	0.477220i	$-0.158355\pi$
$881$	0.774917	+	1.34220i	0.0261076	+	0.0452197i	−0.852676	+	0.522439i	$0.825022\pi$
$882$		0			0
$883$	58.0241			1.95267			0.976333	−	0.216273i	$-0.0693900\pi$
$883$	58.0241			1.95267			0.976333	+	0.216273i	$0.0693900\pi$
$884$	7.50000	+	7.79423i	0.252252	+	0.262148i
$885$		0			0
$886$	−17.2749	−	29.9210i	−0.580362	−	1.00522i
$887$	23.2749	+	40.3133i	0.781495	+	1.35359i	0.931071	+	0.364839i	$0.118876\pi$
$887$	23.2749	+	40.3133i	0.781495	+	1.35359i	−0.149575	+	0.988750i	$0.547791\pi$
$888$		0			0
$889$	8.00000			0.268311
$890$	1.54983	−	2.68439i	0.0519506	−	0.0899810i
$891$		0			0
$892$	10.7251			0.359102
$893$	−21.4502	+	37.1528i	−0.717802	+	1.24327i
$894$		0			0
$895$	−3.09967	−	5.36878i	−0.103611	−	0.179459i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−19.0997			−0.637364
$899$	−5.27492	−	9.13642i	−0.175928	−	0.304717i
$900$		0			0
$901$	5.32475	−	9.22274i	0.177393	−	0.307254i
$902$	33.0997			1.10210
$903$		0			0
$904$	−7.41238	+	12.8386i	−0.246532	+	0.427006i
$905$	71.9244			2.39085
$906$		0			0
$907$	19.9124	+	34.4892i	0.661180	+	1.14520i	0.980306	+	0.197484i	$0.0632772\pi$
$907$	19.9124	+	34.4892i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$908$	−10.5498	−	18.2728i	−0.350109	−	0.606406i
$909$		0			0
$910$	14.9622	−	3.70219i	0.495992	−	0.122726i
$911$	25.0997			0.831589			0.415795	−	0.909459i	$-0.363504\pi$
$911$	25.0997			0.831589			0.415795	+	0.909459i	$0.363504\pi$
$912$		0			0
$913$	−23.6495	−	40.9621i	−0.782684	−	1.35565i
$914$	−8.50000	+	14.7224i	−0.281155	+	0.486975i
$915$		0			0
$916$	−6.36254	+	11.0202i	−0.210224	+	0.364119i
$917$	−1.36254	+	2.35999i	−0.0449951	+	0.0779338i
$918$		0			0
$919$	−19.8248	+	34.3375i	−0.653958	+	1.13269i	0.328196	+	0.944610i	$0.393559\pi$
$919$	−19.8248	+	34.3375i	−0.653958	+	1.13269i	−0.982154	+	0.188079i	$0.939774\pi$
$920$	−11.2749	−	19.5287i	−0.371723	−	0.643843i
$921$		0			0
$922$	−19.3746			−0.638068
$923$	5.27492	−	18.2728i	0.173626	−	0.601458i
$924$		0			0
$925$	−1.82475	−	3.16056i	−0.0599975	−	0.103919i
$926$	−5.27492	−	9.13642i	−0.173345	−	0.300242i
$927$		0			0
$928$	8.27492			0.271637
$929$	26.7749	−	46.3755i	0.878457	−	1.52153i	0.0254221	−	0.999677i	$-0.491907\pi$
$929$	26.7749	−	46.3755i	0.878457	−	1.52153i	0.853034	−	0.521855i	$-0.174760\pi$
$930$		0			0
$931$	6.54983			0.214662
$932$	3.72508	−	6.45203i	0.122019	−	0.211343i
$933$		0			0
$934$	4.08762	+	7.07997i	0.133751	+	0.231664i
$935$	51.2990			1.67766
$936$		0			0
$937$	19.1752			0.626428			0.313214	−	0.949683i	$-0.398594\pi$
$937$	19.1752			0.626428			0.313214	+	0.949683i	$0.398594\pi$
$938$	−1.36254	−	2.35999i	−0.0444886	−	0.0770564i
$939$		0			0
$940$	14.0000	−	24.2487i	0.456630	−	0.790906i
$941$	−37.6495			−1.22734			−0.613669	−	0.789563i	$-0.710307\pi$
$941$	−37.6495			−1.22734			−0.613669	+	0.789563i	$0.710307\pi$
$942$		0			0
$943$	21.8248	−	37.8016i	0.710712	−	1.23099i
$944$	11.8248			0.384863
$945$		0			0
$946$	−23.6495	−	40.9621i	−0.768912	−	1.33179i
$947$	−4.54983	−	7.88054i	−0.147850	−	0.256083i	0.782583	−	0.622547i	$-0.213902\pi$
$947$	−4.54983	−	7.88054i	−0.147850	−	0.256083i	−0.930433	+	0.366463i	$0.880569\pi$
$948$		0			0
$949$	20.0378	−	4.95807i	0.650454	−	0.160946i
$950$	−86.9485			−2.82098
$951$		0			0
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	−5.54983	+	9.61260i	−0.179777	+	0.311383i	−0.941804	−	0.336162i	$-0.890871\pi$
$953$	−5.54983	+	9.61260i	−0.179777	+	0.311383i	0.762027	+	0.647545i	$0.224204\pi$
$954$		0			0
$955$	−14.3746	+	24.8975i	−0.465151	+	0.805665i
$956$	−2.63746	+	4.56821i	−0.0853015	+	0.147747i
$957$		0			0
$958$	−10.0000	+	17.3205i	−0.323085	+	0.559600i
$959$	11.4124	+	19.7668i	0.368525	+	0.638304i
$960$		0			0
$961$	−29.3746			−0.947567
$962$	0.274917	−	0.952341i	0.00886369	−	0.0307047i
$963$		0			0
$964$	7.86254	+	13.6183i	0.253235	+	0.438617i
$965$	−53.0619	−	91.9059i	−1.70812	−	2.95855i
$966$		0			0
$967$	−18.5498			−0.596522			−0.298261	−	0.954484i	$-0.596407\pi$
$967$	−18.5498			−0.596522			−0.298261	+	0.954484i	$0.596407\pi$
$968$	2.50000	−	4.33013i	0.0803530	−	0.139176i
$969$		0			0
$970$	−2.35050			−0.0754699
$971$	24.2870	−	42.0663i	0.779406	−	1.34997i	−0.152879	−	0.988245i	$-0.548854\pi$
$971$	24.2870	−	42.0663i	0.779406	−	1.34997i	0.932285	−	0.361725i	$-0.117812\pi$
$972$		0			0
$973$	4.54983	+	7.88054i	0.145861	+	0.252639i
$974$	1.09967			0.0352357
$975$		0			0
$976$	−9.00000			−0.288083
$977$	12.3127	+	21.3262i	0.393918	+	0.682287i	0.992962	−	0.118429i	$-0.0377859\pi$
$977$	12.3127	+	21.3262i	0.393918	+	0.682287i	−0.599044	+	0.800716i	$0.704453\pi$
$978$		0			0
$979$	1.45017	−	2.51176i	0.0463475	−	0.0802762i
$980$	−4.27492			−0.136557
$981$		0			0
$982$	−12.5498	+	21.7370i	−0.400481	+	0.693654i
$983$	−53.8488			−1.71751			−0.858756	−	0.512385i	$-0.828762\pi$
$983$	−53.8488			−1.71751			−0.858756	+	0.512385i	$0.828762\pi$
$984$		0			0
$985$	46.6495	+	80.7993i	1.48638	+	2.57448i
$986$	12.4124	+	21.4989i	0.395291	+	0.684663i
$987$		0			0
$988$	−16.3746	−	17.0170i	−0.520945	−	0.541382i
$989$	−62.3746			−1.98340
$990$		0			0
$991$	18.3746	+	31.8257i	0.583688	+	1.01098i	0.995038	+	0.0994996i	$0.0317242\pi$
$991$	18.3746	+	31.8257i	0.583688	+	1.01098i	−0.411350	+	0.911478i	$0.634942\pi$
$992$	−0.637459	+	1.10411i	−0.0202393	+	0.0350555i
$993$		0			0
$994$	−2.63746	+	4.56821i	−0.0836551	+	0.144895i
$995$	25.2749	−	43.7774i	0.801269	−	1.38784i
$996$		0			0
$997$	1.95017	−	3.37779i	0.0617624	−	0.106976i	−0.833491	−	0.552533i	$-0.813661\pi$
$997$	1.95017	−	3.37779i	0.0617624	−	0.106976i	0.895253	+	0.445558i	$0.146995\pi$
$998$	−15.9124	−	27.5610i	−0.503697	−	0.872430i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.x.757.1		4
3.2	odd	2		546.2.l.j.211.2	✓	4
13.9	even	3	inner	1638.2.r.x.1387.1		4
39.23	odd	6		7098.2.a.bm.1.1		2
39.29	odd	6		7098.2.a.ca.1.2		2
39.35	odd	6		546.2.l.j.295.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.j.211.2	✓	4	3.2	odd	2
546.2.l.j.295.2	yes	4	39.35	odd	6
1638.2.r.x.757.1		4	1.1	even	1	trivial
1638.2.r.x.1387.1		4	13.9	even	3	inner
7098.2.a.bm.1.1		2	39.23	odd	6
7098.2.a.ca.1.2		2	39.29	odd	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.27492 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.13746 - 3.70219i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-3.27492 + 5.67232i) q^{19} +(2.13746 - 3.70219i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-2.63746 - 4.56821i) q^{23} +13.2749 q^{25} +(2.50000 + 2.59808i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(4.13746 + 7.16629i) q^{29} -1.27492 q^{31} +(0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +(2.13746 - 3.70219i) q^{35} +(-0.137459 - 0.238085i) q^{37} -6.54983 q^{38} +4.27492 q^{40} +(4.13746 + 7.16629i) q^{41} +(5.91238 - 10.2405i) q^{43} +4.00000 q^{44} +(2.63746 - 4.56821i) q^{46} +6.54983 q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.63746 + 11.4964i) q^{50} +(-1.00000 + 3.46410i) q^{52} +3.54983 q^{53} +(8.54983 + 14.8087i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-4.13746 + 7.16629i) q^{58} +(-5.91238 + 10.2405i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-0.637459 - 1.10411i) q^{62} +1.00000 q^{64} +(-14.9622 + 3.70219i) q^{65} +(1.36254 + 2.35999i) q^{67} +(1.50000 + 2.59808i) q^{68} +4.27492 q^{70} +(2.63746 - 4.56821i) q^{71} +5.72508 q^{73} +(0.137459 - 0.238085i) q^{74} +(-3.27492 - 5.67232i) q^{76} +4.00000 q^{77} -8.00000 q^{79} +(2.13746 + 3.70219i) q^{80} +(-4.13746 + 7.16629i) q^{82} +11.8248 q^{83} +(-6.41238 + 11.1066i) q^{85} +11.8248 q^{86} +(2.00000 + 3.46410i) q^{88} +(0.362541 + 0.627940i) q^{89} +(-1.00000 + 3.46410i) q^{91} +5.27492 q^{92} +(3.27492 + 5.67232i) q^{94} +(14.0000 - 24.2487i) q^{95} +(0.274917 - 0.476171i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} - q^{10} - 8 q^{11} + 14 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} + q^{20} + 8 q^{22} - 3 q^{23} + 38 q^{25} + 10 q^{26} - 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 - q^10 - 8 * q^11 + 14 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 + q^20 + 8 * q^22 - 3 * q^23 + 38 * q^25 + 10 * q^26 - 2 * q^28 + 9 * q^29 + 10 * q^31 + 2 * q^32 + 12 * q^34 + q^35 + 7 * q^37 + 4 * q^38 + 2 * q^40 + 9 * q^41 + q^43 + 16 * q^44 + 3 * q^46 - 4 * q^47 - 2 * q^49 + 19 * q^50 - 4 * q^52 - 16 * q^53 + 4 * q^55 + 2 * q^56 - 9 * q^58 - q^59 + 18 * q^61 + 5 * q^62 + 4 * q^64 - 7 * q^65 + 13 * q^67 + 6 * q^68 + 2 * q^70 + 3 * q^71 + 38 * q^73 - 7 * q^74 + 2 * q^76 + 16 * q^77 - 32 * q^79 + q^80 - 9 * q^82 + 2 * q^83 - 3 * q^85 + 2 * q^86 + 8 * q^88 + 9 * q^89 - 4 * q^91 + 6 * q^92 - 2 * q^94 + 56 * q^95 - 14 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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