LMFDB - Embedded newform 1998.2.t.a.397.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(307,1998)] 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("1998.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1998, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			397.33
Character	$\chi$	$=$	1998.397
Dual form			1998.2.t.a.307.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.323001 - 0.186485i) q^{5} -0.0420982 q^{7} -1.00000i q^{8} -0.372969 q^{10} +(-1.29042 + 2.23507i) q^{11} +(-1.93306 - 1.11605i) q^{13} +(-0.0364581 + 0.0210491i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.25134 + 1.29981i) q^{17} +(5.14372 - 2.96973i) q^{19} +(-0.323001 + 0.186485i) q^{20} +2.58084i q^{22} +(3.66709 - 2.11720i) q^{23} +(-2.43045 - 4.20966i) q^{25} -2.23210 q^{26} +(-0.0210491 + 0.0364581i) q^{28} +(-0.672857 - 0.388474i) q^{29} +(8.09859 - 4.67573i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.59962 q^{34} +(0.0135978 + 0.00785067i) q^{35} +(5.51271 - 2.57099i) q^{37} +(2.96973 - 5.14372i) q^{38} +(-0.186485 + 0.323001i) q^{40} +(3.61683 - 6.26454i) q^{41} +(-9.57847 - 5.53013i) q^{43} +(1.29042 + 2.23507i) q^{44} +(2.11720 - 3.66709i) q^{46} +(5.02395 - 8.70173i) q^{47} -6.99823 q^{49} +(-4.20966 - 2.43045i) q^{50} +(-1.93306 + 1.11605i) q^{52} +(-3.61144 + 6.25519i) q^{53} +(0.833612 - 0.481286i) q^{55} +0.0420982i q^{56} -0.776949 q^{58} +12.5360i q^{59} -9.35171i q^{61} +(4.67573 - 8.09859i) q^{62} -1.00000 q^{64} +(0.416253 + 0.720971i) q^{65} +(-1.16092 + 2.01077i) q^{67} +(2.25134 - 1.29981i) q^{68} +0.0157013 q^{70} +(0.342015 + 0.592387i) q^{71} +13.1748 q^{73} +(3.48865 - 4.98290i) q^{74} -5.93946i q^{76} +(0.0543243 - 0.0940925i) q^{77} +3.92502i q^{79} +0.372969i q^{80} -7.23366i q^{82} +(-4.18421 - 7.24727i) q^{83} +(-0.484789 - 0.839680i) q^{85} -11.0603 q^{86} +(2.23507 + 1.29042i) q^{88} +(-5.63029 - 3.25065i) q^{89} +(0.0813784 + 0.0469838i) q^{91} -4.23439i q^{92} -10.0479i q^{94} -2.21523 q^{95} +(5.13338 + 2.96376i) q^{97} +(-6.06064 + 3.49911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1998\mathbb{Z}\right)^\times$.

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.323001	−	0.186485i	−0.144450	−	0.0833985i	0.426033	−	0.904708i	$-0.359911\pi$
$5$	−0.323001	−	0.186485i	−0.144450	−	0.0833985i	−0.570483	+	0.821309i	$0.693244\pi$
$6$		0			0
$7$	−0.0420982			−0.0159116			−0.00795582	−	0.999968i	$-0.502532\pi$
$7$	−0.0420982			−0.0159116			−0.00795582	+	0.999968i	$0.502532\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.372969			−0.117943
$11$	−1.29042	+	2.23507i	−0.389076	+	0.673899i	−0.992325	−	0.123653i	$-0.960539\pi$
$11$	−1.29042	+	2.23507i	−0.389076	+	0.673899i	0.603250	+	0.797552i	$0.293872\pi$
$12$		0			0
$13$	−1.93306	−	1.11605i	−0.536134	−	0.309537i	0.207377	−	0.978261i	$-0.433507\pi$
$13$	−1.93306	−	1.11605i	−0.536134	−	0.309537i	−0.743511	+	0.668724i	$0.766841\pi$
$14$	−0.0364581	+	0.0210491i	−0.00974385	+	0.00562561i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.25134	+	1.29981i	0.546030	+	0.315250i	0.747519	−	0.664240i	$-0.231245\pi$
$17$	2.25134	+	1.29981i	0.546030	+	0.315250i	−0.201489	+	0.979491i	$0.564578\pi$
$18$		0			0
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.224024	−	0.974584i	$-0.428081\pi$
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.956026	+	0.293281i	$0.0947472\pi$
$20$	−0.323001	+	0.186485i	−0.0722252	+	0.0416992i
$21$		0			0
$22$			2.58084i			0.550236i
$23$	3.66709	−	2.11720i	0.764641	−	0.441466i	−0.0663185	−	0.997799i	$-0.521125\pi$
$23$	3.66709	−	2.11720i	0.764641	−	0.441466i	0.830960	+	0.556333i	$0.187792\pi$
$24$		0			0
$25$	−2.43045	−	4.20966i	−0.486089	−	0.841932i
$26$	−2.23210			−0.437751
$27$		0			0
$28$	−0.0210491	+	0.0364581i	−0.00397791	+	0.00688994i
$29$	−0.672857	−	0.388474i	−0.124946	−	0.0721379i	0.436224	−	0.899838i	$-0.356315\pi$
$29$	−0.672857	−	0.388474i	−0.124946	−	0.0721379i	−0.561171	+	0.827700i	$0.689649\pi$
$30$		0			0
$31$	8.09859	−	4.67573i	1.45455	−	0.839785i	0.455816	−	0.890074i	$-0.349348\pi$
$31$	8.09859	−	4.67573i	1.45455	−	0.839785i	0.998735	+	0.0502891i	$0.0160143\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	2.59962			0.445831
$35$	0.0135978	+	0.00785067i	0.00229844	+	0.00132701i
$36$		0			0
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$38$	2.96973	−	5.14372i	0.481754	−	0.834422i
$39$		0			0
$40$	−0.186485	+	0.323001i	−0.0294858	+	0.0510709i
$41$	3.61683	−	6.26454i	0.564854	−	0.978356i	−0.432209	−	0.901773i	$-0.642266\pi$
$41$	3.61683	−	6.26454i	0.564854	−	0.978356i	0.997063	−	0.0765828i	$-0.0244010\pi$
$42$		0			0
$43$	−9.57847	−	5.53013i	−1.46070	−	0.843337i	−0.461659	−	0.887057i	$-0.652746\pi$
$43$	−9.57847	−	5.53013i	−1.46070	−	0.843337i	−0.999044	+	0.0437202i	$0.986079\pi$
$44$	1.29042	+	2.23507i	0.194538	+	0.336949i
$45$		0			0
$46$	2.11720	−	3.66709i	0.312163	−	0.540683i
$47$	5.02395	−	8.70173i	0.732818	−	1.26928i	−0.222856	−	0.974851i	$-0.571538\pi$
$47$	5.02395	−	8.70173i	0.732818	−	1.26928i	0.955674	−	0.294427i	$-0.0951287\pi$
$48$		0			0
$49$	−6.99823			−0.999747
$50$	−4.20966	−	2.43045i	−0.595335	−	0.343717i
$51$		0			0
$52$	−1.93306	+	1.11605i	−0.268067	+	0.154769i
$53$	−3.61144	+	6.25519i	−0.496069	+	0.859217i	−0.999990	−	0.00453324i	$-0.998557\pi$
$53$	−3.61144	+	6.25519i	−0.496069	+	0.859217i	0.503921	+	0.863750i	$0.331890\pi$
$54$		0			0
$55$	0.833612	−	0.481286i	0.112404	−	0.0648966i
$56$			0.0420982i			0.00562561i
$57$		0			0
$58$	−0.776949			−0.102018
$59$			12.5360i			1.63205i	0.578016	+	0.816025i	$0.303827\pi$
$59$			12.5360i			1.63205i	−0.578016	+	0.816025i	$0.696173\pi$
$60$		0			0
$61$		−	9.35171i		−	1.19736i	−0.800987	−	0.598682i	$-0.795691\pi$
$61$		−	9.35171i		−	1.19736i	0.800987	−	0.598682i	$-0.204309\pi$
$62$	4.67573	−	8.09859i	0.593818	−	1.02852i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.416253	+	0.720971i	0.0516298	+	0.0894255i
$66$		0			0
$67$	−1.16092	+	2.01077i	−0.141829	+	0.245655i	−0.928185	−	0.372118i	$-0.878632\pi$
$67$	−1.16092	+	2.01077i	−0.141829	+	0.245655i	0.786356	+	0.617773i	$0.211965\pi$
$68$	2.25134	−	1.29981i	0.273015	−	0.157625i
$69$		0			0
$70$	0.0157013			0.00187667
$71$	0.342015	+	0.592387i	0.0405897	+	0.0703034i	0.885607	−	0.464436i	$-0.153743\pi$
$71$	0.342015	+	0.592387i	0.0405897	+	0.0703034i	−0.845017	+	0.534740i	$0.820410\pi$
$72$		0			0
$73$	13.1748			1.54199			0.770995	−	0.636841i	$-0.219759\pi$
$73$	13.1748			1.54199			0.770995	+	0.636841i	$0.219759\pi$
$74$	3.48865	−	4.98290i	0.405547	−	0.579251i
$75$		0			0
$76$		−	5.93946i		−	0.681302i
$77$	0.0543243	−	0.0940925i	0.00619083	−	0.0107228i
$78$		0			0
$79$			3.92502i			0.441599i	0.975319	+	0.220800i	$0.0708667\pi$
$79$			3.92502i			0.441599i	−0.975319	+	0.220800i	$0.929133\pi$
$80$			0.372969i			0.0416992i
$81$		0			0
$82$		−	7.23366i		−	0.798825i
$83$	−4.18421	−	7.24727i	−0.459277	−	0.795491i	0.539646	−	0.841892i	$-0.318558\pi$
$83$	−4.18421	−	7.24727i	−0.459277	−	0.795491i	−0.998923	+	0.0464012i	$0.985225\pi$
$84$		0			0
$85$	−0.484789	−	0.839680i	−0.0525828	−	0.0910761i
$86$	−11.0603			−1.19266
$87$		0			0
$88$	2.23507	+	1.29042i	0.238259	+	0.137559i
$89$	−5.63029	−	3.25065i	−0.596809	−	0.344568i	0.170976	−	0.985275i	$-0.445308\pi$
$89$	−5.63029	−	3.25065i	−0.596809	−	0.344568i	−0.767785	+	0.640707i	$0.778641\pi$
$90$		0			0
$91$	0.0813784	+	0.0469838i	0.00853077	+	0.00492524i
$92$		−	4.23439i		−	0.441466i
$93$		0			0
$94$		−	10.0479i		−	1.03636i
$95$	−2.21523			−0.227278
$96$		0			0
$97$	5.13338	+	2.96376i	0.521216	+	0.300924i	0.737432	−	0.675421i	$-0.236038\pi$
$97$	5.13338	+	2.96376i	0.521216	+	0.300924i	−0.216216	+	0.976346i	$0.569372\pi$
$98$	−6.06064	+	3.49911i	−0.612217	+	0.353464i
$99$		0			0
$100$	−4.86089			−0.486089
$101$	−4.82354	+	8.35461i	−0.479960	+	0.831315i	−0.999736	−	0.0229877i	$-0.992682\pi$
$101$	−4.82354	+	8.35461i	−0.479960	+	0.831315i	0.519776	+	0.854303i	$0.326015\pi$
$102$		0			0
$103$	−0.515555	+	0.297656i	−0.0507991	+	0.0293289i	−0.525184	−	0.850988i	$-0.676004\pi$
$103$	−0.515555	+	0.297656i	−0.0507991	+	0.0293289i	0.474385	+	0.880317i	$0.342670\pi$
$104$	−1.11605	+	1.93306i	−0.109438	+	0.189552i
$105$		0			0
$106$			7.22287i			0.701547i
$107$	−4.79286	−	8.30148i	−0.463343	−	0.802534i	0.535782	−	0.844357i	$-0.320017\pi$
$107$	−4.79286	−	8.30148i	−0.463343	−	0.802534i	−0.999125	+	0.0418223i	$0.986684\pi$
$108$		0			0
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	0.831911	−	0.554909i	$-0.187247\pi$
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	−0.0646094	+	0.997911i	$0.520580\pi$
$110$	0.481286	−	0.833612i	0.0458888	−	0.0794818i
$111$		0			0
$112$	0.0210491	+	0.0364581i	0.00198895	+	0.00344497i
$113$			15.3597i			1.44492i	0.691411	+	0.722462i	$0.256989\pi$
$113$			15.3597i			1.44492i	−0.691411	+	0.722462i	$0.743011\pi$
$114$		0			0
$115$	−1.57930			−0.147270
$116$	−0.672857	+	0.388474i	−0.0624732	+	0.0360689i
$117$		0			0
$118$	6.26801	+	10.8565i	0.577017	+	0.999423i
$119$	−0.0947774	−	0.0547197i	−0.00868823	−	0.00501615i
$120$		0			0
$121$	2.16964	+	3.75793i	0.197240	+	0.341630i
$122$	−4.67586	−	8.09882i	−0.423332	−	0.733233i
$123$		0			0
$124$		−	9.35145i		−	0.839785i
$125$			3.67781i			0.328953i
$126$		0			0
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	−0.917079	−	0.398707i	$-0.869459\pi$
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	0.803829	+	0.594860i	$0.202792\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	0.720971	+	0.416253i	0.0632334	+	0.0365078i
$131$		−	11.3397i		−	0.990756i	−0.868677	−	0.495378i	$-0.835030\pi$
$131$		−	11.3397i		−	0.990756i	0.868677	−	0.495378i	$-0.164970\pi$
$132$		0			0
$133$	−0.216542	+	0.125020i	−0.0187765	+	0.0108406i
$134$			2.32184i			0.200576i
$135$		0			0
$136$	1.29981	−	2.25134i	0.111458	−	0.193051i
$137$	7.60904	−	13.1792i	0.650084	−	1.12598i	−0.333018	−	0.942921i	$-0.608067\pi$
$137$	7.60904	−	13.1792i	0.650084	−	1.12598i	0.983102	−	0.183058i	$-0.0585997\pi$
$138$		0			0
$139$	−16.2052			−1.37451			−0.687254	−	0.726417i	$-0.741184\pi$
$139$	−16.2052			−1.37451			−0.687254	+	0.726417i	$0.741184\pi$
$140$	0.0135978	−	0.00785067i	0.00114922	−	0.000663503i
$141$		0			0
$142$	0.592387	+	0.342015i	0.0497120	+	0.0287013i
$143$	4.98891	−	2.88035i	0.417193	−	0.240867i
$144$		0			0
$145$	0.144889	+	0.250955i	0.0120324	+	0.0208407i
$146$	11.4097	−	6.58738i	0.944272	−	0.545176i
$147$		0			0
$148$	0.529810	−	6.05965i	0.0435501	−	0.498100i
$149$	−0.177156	−	0.306844i	−0.0145132	−	0.0251376i	0.858678	−	0.512516i	$-0.171287\pi$
$149$	−0.177156	−	0.306844i	−0.0145132	−	0.0251376i	−0.873191	+	0.487379i	$0.837953\pi$
$150$		0			0
$151$	6.89360			0.560993			0.280496	−	0.959855i	$-0.409501\pi$
$151$	6.89360			0.560993			0.280496	+	0.959855i	$0.409501\pi$
$152$	−2.96973	−	5.14372i	−0.240877	−	0.417211i
$153$		0			0
$154$		−	0.108649i		−	0.00875516i
$155$	−3.48780			−0.280147
$156$		0			0
$157$	11.5596			0.922553			0.461276	−	0.887257i	$-0.347392\pi$
$157$	11.5596			0.922553			0.461276	+	0.887257i	$0.347392\pi$
$158$	1.96251	+	3.39917i	0.156129	+	0.270423i
$159$		0			0
$160$	0.186485	+	0.323001i	0.0147429	+	0.0255355i
$161$	−0.154378	+	0.0891302i	−0.0121667	+	0.00702444i
$162$		0			0
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.905911	−	0.423468i	$-0.139187\pi$
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.0862213	+	0.996276i	$0.472521\pi$
$164$	−3.61683	−	6.26454i	−0.282427	−	0.489178i
$165$		0			0
$166$	−7.24727	−	4.18421i	−0.562497	−	0.324758i
$167$	−10.1001	−	5.83129i	−0.781569	−	0.451239i	0.0554171	−	0.998463i	$-0.482351\pi$
$167$	−10.1001	−	5.83129i	−0.781569	−	0.451239i	−0.836986	+	0.547224i	$0.815684\pi$
$168$		0			0
$169$	−4.00886	−	6.94354i	−0.308374	−	0.534119i
$170$	−0.839680	−	0.484789i	−0.0644005	−	0.0371816i
$171$		0			0
$172$	−9.57847	+	5.53013i	−0.730351	+	0.421669i
$173$	−0.0292353	−	0.0506371i	−0.00222272	−	0.00384987i	0.864912	−	0.501924i	$-0.167374\pi$
$173$	−0.0292353	−	0.0506371i	−0.00222272	−	0.00384987i	−0.867135	+	0.498074i	$0.834041\pi$
$174$		0			0
$175$	0.102318	+	0.177219i	0.00773448	+	0.0133965i
$176$	2.58084			0.194538
$177$		0			0
$178$	−6.50129			−0.487293
$179$		−	8.49336i		−	0.634823i	−0.948288	−	0.317412i	$-0.897186\pi$
$179$		−	8.49336i		−	0.634823i	0.948288	−	0.317412i	$-0.102814\pi$
$180$		0			0
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	0.993136	+	0.116967i	$0.0373171\pi$
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	−0.395272	+	0.918564i	$0.629350\pi$
$182$	0.0939676			0.00696534
$183$		0			0
$184$	−2.11720	−	3.66709i	−0.156082	−	0.270341i
$185$	−2.26006	−	0.197603i	−0.166163	−	0.0145280i
$186$		0			0
$187$	−5.81033	+	3.35460i	−0.424894	+	0.245313i
$188$	−5.02395	−	8.70173i	−0.366409	−	0.634639i
$189$		0			0
$190$	−1.91845	+	1.10762i	−0.139179	+	0.0803550i
$191$	−7.11315	−	4.10678i	−0.514689	−	0.297156i	0.220070	−	0.975484i	$-0.429372\pi$
$191$	−7.11315	−	4.10678i	−0.514689	−	0.297156i	−0.734759	+	0.678328i	$0.762705\pi$
$192$		0			0
$193$	16.6788	−	9.62948i	1.20056	−	0.693145i	0.239883	−	0.970802i	$-0.422891\pi$
$193$	16.6788	−	9.62948i	1.20056	−	0.693145i	0.960680	+	0.277656i	$0.0895577\pi$
$194$	5.92752			0.425571
$195$		0			0
$196$	−3.49911	+	6.06064i	−0.249937	+	0.432903i
$197$	0.245783	−	0.425708i	0.0175113	−	0.0303304i	−0.857137	−	0.515089i	$-0.827759\pi$
$197$	0.245783	−	0.425708i	0.0175113	−	0.0303304i	0.874648	+	0.484758i	$0.161092\pi$
$198$		0			0
$199$			10.8937i			0.772236i	0.922449	+	0.386118i	$0.126184\pi$
$199$			10.8937i			0.772236i	−0.922449	+	0.386118i	$0.873816\pi$
$200$	−4.20966	+	2.43045i	−0.297668	+	0.171859i
$201$		0			0
$202$			9.64708i			0.678766i
$203$	0.0283261	+	0.0163541i	0.00198810	+	0.00114783i
$204$		0			0
$205$	−2.33648	+	1.34897i	−0.163187	+	0.0942159i
$206$	−0.297656	+	0.515555i	−0.0207387	+	0.0359204i
$207$		0			0
$208$			2.23210i			0.154769i
$209$			15.3288i			1.06031i
$210$		0			0
$211$	6.38957	+	11.0671i	0.439876	+	0.761888i	0.997680	−	0.0680853i	$-0.0216890\pi$
$211$	6.38957	+	11.0671i	0.439876	+	0.761888i	−0.557803	+	0.829973i	$0.688356\pi$
$212$	3.61144	+	6.25519i	0.248034	+	0.429608i
$213$		0			0
$214$	−8.30148	−	4.79286i	−0.567477	−	0.327633i
$215$	2.06257	+	3.57247i	0.140666	+	0.243641i
$216$		0			0
$217$	−0.340937	+	0.196840i	−0.0231443	+	0.0133624i
$218$	9.25015			0.626499
$219$		0			0
$220$		−	0.962572i		−	0.0648966i
$221$	−2.90131	−	5.02522i	−0.195163	−	0.338033i
$222$		0			0
$223$	−14.1726	+	24.5477i	−0.949067	+	1.64383i	−0.201673	+	0.979453i	$0.564638\pi$
$223$	−14.1726	+	24.5477i	−0.949067	+	1.64383i	−0.747395	+	0.664380i	$0.768696\pi$
$224$	0.0364581	+	0.0210491i	0.00243596	+	0.00140640i
$225$		0			0
$226$	7.67987	+	13.3019i	0.510858	+	0.884831i
$227$		−	0.818681i		−	0.0543377i	−0.999631	−	0.0271689i	$-0.991351\pi$
$227$		−	0.818681i		−	0.0543377i	0.999631	−	0.0271689i	$-0.00864918\pi$
$228$		0			0
$229$	8.65599	−	14.9926i	0.572004	−	0.990740i	−0.424356	−	0.905495i	$-0.639499\pi$
$229$	8.65599	−	14.9926i	0.572004	−	0.990740i	0.996360	−	0.0852446i	$-0.0271672\pi$
$230$	−1.36771	+	0.789649i	−0.0901842	+	0.0520679i
$231$		0			0
$232$	−0.388474	+	0.672857i	−0.0255046	+	0.0441752i
$233$	9.20929			0.603320			0.301660	−	0.953416i	$-0.402459\pi$
$233$	9.20929			0.603320			0.301660	+	0.953416i	$0.402459\pi$
$234$		0			0
$235$	−3.24548	+	1.87378i	−0.211712	+	0.122232i
$236$	10.8565	+	6.26801i	0.706699	+	0.408013i
$237$		0			0
$238$	−0.109439			−0.00709391
$239$			2.31920i			0.150017i	0.997183	+	0.0750084i	$0.0238983\pi$
$239$			2.31920i			0.150017i	−0.997183	+	0.0750084i	$0.976102\pi$
$240$		0			0
$241$			6.64422i			0.427992i	0.976835	+	0.213996i	$0.0686479\pi$
$241$			6.64422i			0.427992i	−0.976835	+	0.213996i	$0.931352\pi$
$242$	3.75793	+	2.16964i	0.241569	+	0.139470i
$243$		0			0
$244$	−8.09882	−	4.67586i	−0.518474	−	0.299341i
$245$	2.26043	+	1.30506i	0.144414	+	0.0833773i
$246$		0			0
$247$	−13.2575			−0.843553
$248$	−4.67573	−	8.09859i	−0.296909	−	0.514261i
$249$		0			0
$250$	1.83890	+	3.18508i	0.116303	+	0.201442i
$251$			26.2916i			1.65951i	0.558128	+	0.829755i	$0.311520\pi$
$251$			26.2916i			1.65951i	−0.558128	+	0.829755i	$0.688480\pi$
$252$		0			0
$253$			10.9283i			0.687054i
$254$			2.55251i			0.160158i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			7.33555i			0.457579i	0.973476	+	0.228789i	$0.0734767\pi$
$257$			7.33555i			0.457579i	−0.973476	+	0.228789i	$0.926523\pi$
$258$		0			0
$259$	−0.232075	+	0.108234i	−0.0144205	+	0.00672535i
$260$	0.832506			0.0516298
$261$		0			0
$262$	−5.66986	−	9.82049i	−0.350285	−	0.606712i
$263$	−20.5544			−1.26744			−0.633719	−	0.773563i	$-0.718472\pi$
$263$	−20.5544			−1.26744			−0.633719	+	0.773563i	$0.718472\pi$
$264$		0			0
$265$	2.33299	−	1.34695i	0.143315	−	0.0827428i
$266$	−0.125020	+	0.216542i	−0.00766549	+	0.0132770i
$267$		0			0
$268$	1.16092	+	2.01077i	0.0709145	+	0.122828i
$269$	−25.4958			−1.55450			−0.777252	−	0.629189i	$-0.783387\pi$
$269$	−25.4958			−1.55450			−0.777252	+	0.629189i	$0.783387\pi$
$270$		0			0
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	−0.345062	−	0.938580i	$-0.612142\pi$
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	0.985365	−	0.170457i	$-0.0545245\pi$
$272$		−	2.59962i		−	0.157625i
$273$		0			0
$274$		−	15.2181i		−	0.919358i
$275$	12.5452			0.756502
$276$		0			0
$277$			16.5281i			0.993079i	0.868014	+	0.496540i	$0.165396\pi$
$277$			16.5281i			0.993079i	−0.868014	+	0.496540i	$0.834604\pi$
$278$	−14.0341	+	8.10261i	−0.841711	+	0.485962i
$279$		0			0
$280$	0.00785067	−	0.0135978i	0.000469168	−	0.000812622i
$281$	−1.81247	+	1.04643i	−0.108123	+	0.0624247i	−0.553086	−	0.833124i	$-0.686550\pi$
$281$	−1.81247	+	1.04643i	−0.108123	+	0.0624247i	0.444963	+	0.895549i	$0.353217\pi$
$282$		0			0
$283$	8.44984	+	4.87852i	0.502291	+	0.289998i	0.729659	−	0.683811i	$-0.239679\pi$
$283$	8.44984	+	4.87852i	0.502291	+	0.289998i	−0.227368	+	0.973809i	$0.573012\pi$
$284$	0.684030			0.0405897
$285$		0			0
$286$	2.88035	−	4.98891i	0.170318	−	0.295000i
$287$	−0.152262	+	0.263726i	−0.00898776	+	0.0155673i
$288$		0			0
$289$	−5.12098	−	8.86981i	−0.301234	−	0.521753i
$290$	0.250955	+	0.144889i	0.0147366	+	0.00850817i
$291$		0			0
$292$	6.58738	−	11.4097i	0.385497	−	0.667701i
$293$	−0.690674	+	1.19628i	−0.0403496	+	0.0698876i	−0.885495	−	0.464649i	$-0.846181\pi$
$293$	−0.690674	+	1.19628i	−0.0403496	+	0.0698876i	0.845145	+	0.534537i	$0.179514\pi$
$294$		0			0
$295$	2.33777	−	4.04914i	0.136110	−	0.235750i
$296$	−2.57099	−	5.51271i	−0.149436	−	0.320420i
$297$		0			0
$298$	−0.306844	−	0.177156i	−0.0177750	−	0.0102624i
$299$	−9.45160			−0.546600
$300$		0			0
$301$	0.403237	+	0.232809i	0.0232422	+	0.0134189i
$302$	5.97003	−	3.44680i	0.343537	−	0.198341i
$303$		0			0
$304$	−5.14372	−	2.96973i	−0.295013	−	0.170326i
$305$	−1.74395	+	3.02061i	−0.0998583	+	0.172960i
$306$		0			0
$307$	−22.3771			−1.27713			−0.638564	−	0.769569i	$-0.720471\pi$
$307$	−22.3771			−1.27713			−0.638564	+	0.769569i	$0.720471\pi$
$308$	−0.0543243	−	0.0940925i	−0.00309542	−	0.00536142i
$309$		0			0
$310$	−3.02053	+	1.74390i	−0.171554	+	0.0990470i
$311$			28.3659i			1.60848i	0.594303	+	0.804241i	$0.297428\pi$
$311$			28.3659i			1.60848i	−0.594303	+	0.804241i	$0.702572\pi$
$312$		0			0
$313$	11.9592	−	6.90465i	0.675974	−	0.390274i	−0.122362	−	0.992485i	$-0.539047\pi$
$313$	11.9592	−	6.90465i	0.675974	−	0.390274i	0.798336	+	0.602212i	$0.205714\pi$
$314$	10.0109	−	5.77978i	0.564946	−	0.326172i
$315$		0			0
$316$	3.39917	+	1.96251i	0.191218	+	0.110400i
$317$	3.66038	+	6.33996i	0.205587	+	0.356088i	0.950320	−	0.311276i	$-0.100756\pi$
$317$	3.66038	+	6.33996i	0.205587	+	0.356088i	−0.744732	+	0.667363i	$0.767423\pi$
$318$		0			0
$319$	1.73653	−	1.00259i	0.0972273	−	0.0561342i
$320$	0.323001	+	0.186485i	0.0180563	+	0.0104248i
$321$		0			0
$322$	−0.0891302	+	0.154378i	−0.00496703	+	0.00860315i
$323$	15.4403			0.859123
$324$		0			0
$325$			10.8500i			0.601851i
$326$	14.6262			0.810073
$327$		0			0
$328$	−6.26454	−	3.61683i	−0.345901	−	0.199706i
$329$	−0.211499	+	0.366328i	−0.0116603	+	0.0201963i
$330$		0			0
$331$	11.5078	−	6.64402i	0.632524	−	0.365188i	−0.149205	−	0.988806i	$-0.547671\pi$
$331$	11.5078	−	6.64402i	0.632524	−	0.365188i	0.781729	+	0.623618i	$0.214338\pi$
$332$	−8.36842			−0.459277
$333$		0			0
$334$	−11.6626			−0.638148
$335$	0.749956	−	0.432988i	0.0409745	−	0.0236566i
$336$		0			0
$337$	4.98122	−	8.62772i	0.271344	−	0.469982i	−0.697862	−	0.716232i	$-0.745865\pi$
$337$	4.98122	−	8.62772i	0.271344	−	0.469982i	0.969206	+	0.246250i	$0.0791985\pi$
$338$	−6.94354	−	4.00886i	−0.377679	−	0.218053i
$339$		0			0
$340$	−0.969579			−0.0525828
$341$			24.1346i			1.30696i
$342$		0			0
$343$	0.589301			0.0318193
$344$	−5.53013	+	9.57847i	−0.298165	+	0.516436i
$345$		0			0
$346$	−0.0506371	−	0.0292353i	−0.00272227	−	0.00157170i
$347$	18.1956	−	10.5053i	0.976793	−	0.563952i	0.0754928	−	0.997146i	$-0.475947\pi$
$347$	18.1956	−	10.5053i	0.976793	−	0.563952i	0.901300	+	0.433195i	$0.142614\pi$
$348$		0			0
$349$	15.3871	+	26.6512i	0.823652	+	1.42661i	0.902945	+	0.429756i	$0.141401\pi$
$349$	15.3871	+	26.6512i	0.823652	+	1.42661i	−0.0792924	+	0.996851i	$0.525266\pi$
$350$	0.177219	+	0.102318i	0.00947276	+	0.00546910i
$351$		0			0
$352$	2.23507	−	1.29042i	0.119130	−	0.0687795i
$353$	−0.249511	+	0.144055i	−0.0132801	+	0.00766729i	−0.506625	−	0.862166i	$-0.669107\pi$
$353$	−0.249511	+	0.144055i	−0.0132801	+	0.00766729i	0.493345	+	0.869834i	$0.335774\pi$
$354$		0			0
$355$		−	0.255122i		−	0.0135405i
$356$	−5.63029	+	3.25065i	−0.298405	+	0.172284i
$357$		0			0
$358$	−4.24668	−	7.35546i	−0.224444	−	0.388748i
$359$	6.45640			0.340756			0.170378	−	0.985379i	$-0.445501\pi$
$359$	6.45640			0.340756			0.170378	+	0.985379i	$0.445501\pi$
$360$		0			0
$361$	8.13857	−	14.0964i	0.428346	−	0.741917i
$362$	13.9316	+	8.04344i	0.732231	+	0.422754i
$363$		0			0
$364$	0.0813784	−	0.0469838i	0.00426538	−	0.00246262i
$365$	−4.25546	−	2.45689i	−0.222741	−	0.128600i
$366$		0			0
$367$	−36.5491			−1.90785			−0.953924	−	0.300048i	$-0.902997\pi$
$367$	−36.5491			−1.90785			−0.953924	+	0.300048i	$0.902997\pi$
$368$	−3.66709	−	2.11720i	−0.191160	−	0.110366i
$369$		0			0
$370$	−2.05607	+	0.958902i	−0.106890	+	0.0498509i
$371$	0.152035	−	0.263333i	0.00789327	−	0.0136715i
$372$		0			0
$373$	−1.47138	+	2.54850i	−0.0761851	+	0.131956i	−0.901601	−	0.432569i	$-0.857607\pi$
$373$	−1.47138	+	2.54850i	−0.0761851	+	0.131956i	0.825416	+	0.564525i	$0.190941\pi$
$374$	−3.35460	+	5.81033i	−0.173462	+	0.300445i
$375$		0			0
$376$	−8.70173	−	5.02395i	−0.448758	−	0.259090i
$377$	0.867115	+	1.50189i	0.0446587	+	0.0773511i
$378$		0			0
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	−0.907597	−	0.419842i	$-0.862086\pi$
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	0.817392	+	0.576081i	$0.195419\pi$
$380$	−1.10762	+	1.91845i	−0.0568196	+	0.0984144i
$381$		0			0
$382$	−8.21356			−0.420242
$383$	14.9439	+	8.62785i	0.763596	+	0.440863i	0.830585	−	0.556891i	$-0.188006\pi$
$383$	14.9439	+	8.62785i	0.763596	+	0.440863i	−0.0669892	+	0.997754i	$0.521339\pi$
$384$		0			0
$385$	−0.0350936	+	0.0202613i	−0.00178854	+	0.00103261i
$386$	9.62948	−	16.6788i	0.490128	−	0.848926i
$387$		0			0
$388$	5.13338	−	2.96376i	0.260608	−	0.150462i
$389$			18.8091i			0.953659i	0.878996	+	0.476830i	$0.158214\pi$
$389$			18.8091i			0.953659i	−0.878996	+	0.476830i	$0.841786\pi$
$390$		0			0
$391$	11.0078			0.556689
$392$			6.99823i			0.353464i
$393$		0			0
$394$		−	0.491565i		−	0.0247647i
$395$	0.731956	−	1.26778i	0.0368287	−	0.0637891i
$396$		0			0
$397$	7.41696			0.372246			0.186123	−	0.982526i	$-0.440408\pi$
$397$	7.41696			0.372246			0.186123	+	0.982526i	$0.440408\pi$
$398$	5.44686	+	9.43424i	0.273026	+	0.472896i
$399$		0			0
$400$	−2.43045	+	4.20966i	−0.121522	+	0.210483i
$401$	−17.6319	+	10.1798i	−0.880496	+	0.508354i	−0.870822	−	0.491599i	$-0.836413\pi$
$401$	−17.6319	+	10.1798i	−0.880496	+	0.508354i	−0.00967393	+	0.999953i	$0.503079\pi$
$402$		0			0
$403$	−20.8734			−1.03978
$404$	4.82354	+	8.35461i	0.239980	+	0.415658i
$405$		0			0
$406$	0.0327082			0.00162328
$407$	−1.36735	+	15.6390i	−0.0677771	+	0.775194i
$408$		0			0
$409$		−	7.62313i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$409$		−	7.62313i		−	0.376940i	0.982079	−	0.188470i	$-0.0603528\pi$
$410$	−1.34897	+	2.33648i	−0.0666207	+	0.115391i
$411$		0			0
$412$			0.595311i			0.0293289i
$413$		−	0.527744i		−	0.0259686i
$414$		0			0
$415$			3.12116i			0.153212i
$416$	1.11605	+	1.93306i	0.0547189	+	0.0947760i
$417$		0			0
$418$	7.66438	+	13.2751i	0.374877	+	0.649306i
$419$	34.5568			1.68821			0.844106	−	0.536176i	$-0.180132\pi$
$419$	34.5568			1.68821			0.844106	+	0.536176i	$0.180132\pi$
$420$		0			0
$421$	−16.1271	−	9.31096i	−0.785985	−	0.453789i	0.0525623	−	0.998618i	$-0.483261\pi$
$421$	−16.1271	−	9.31096i	−0.785985	−	0.453789i	−0.838547	+	0.544829i	$0.816595\pi$
$422$	11.0671	+	6.38957i	0.538736	+	0.311039i
$423$		0			0
$424$	6.25519	+	3.61144i	0.303779	+	0.175387i
$425$		−	12.6365i		−	0.612959i
$426$		0			0
$427$			0.393691i			0.0190520i
$428$	−9.58572			−0.463343
$429$		0			0
$430$	3.57247	+	2.06257i	0.172280	+	0.0994659i
$431$	−18.6073	+	10.7429i	−0.896281	+	0.517468i	−0.875992	−	0.482326i	$-0.839792\pi$
$431$	−18.6073	+	10.7429i	−0.896281	+	0.517468i	−0.0202895	+	0.999794i	$0.506459\pi$
$432$		0			0
$433$	−30.8001			−1.48016			−0.740080	−	0.672519i	$-0.765212\pi$
$433$	−30.8001			−1.48016			−0.740080	+	0.672519i	$0.765212\pi$
$434$	−0.196840	+	0.340937i	−0.00944861	+	0.0163655i
$435$		0			0
$436$	8.01087	−	4.62508i	0.383651	−	0.221501i
$437$	12.5750	−	21.7805i	0.601543	−	1.04190i
$438$		0			0
$439$			29.6094i			1.41318i	0.707623	+	0.706590i	$0.249768\pi$
$439$			29.6094i			1.41318i	−0.707623	+	0.706590i	$0.750232\pi$
$440$	−0.481286	−	0.833612i	−0.0229444	−	0.0397409i
$441$		0			0
$442$	−5.02522	−	2.90131i	−0.239025	−	0.138001i
$443$	−0.902430	+	1.56305i	−0.0428758	+	0.0742630i	−0.886667	−	0.462409i	$-0.846985\pi$
$443$	−0.902430	+	1.56305i	−0.0428758	+	0.0742630i	0.843791	+	0.536672i	$0.180319\pi$
$444$		0			0
$445$	1.21239	+	2.09992i	0.0574729	+	0.0995459i
$446$			28.3452i			1.34218i
$447$		0			0
$448$	0.0420982			0.00198895
$449$	32.7760	−	18.9232i	1.54679	−	0.893042i	0.548410	−	0.836210i	$-0.315233\pi$
$449$	32.7760	−	18.9232i	1.54679	−	0.893042i	0.998384	−	0.0568322i	$-0.0181000\pi$
$450$		0			0
$451$	9.33445	+	16.1677i	0.439542	+	0.761309i
$452$	13.3019	+	7.67987i	0.625670	+	0.361231i
$453$		0			0
$454$	−0.409340	−	0.708998i	−0.0192113	−	0.0332749i
$455$	−0.0175235	−	0.0303516i	−0.000821515	−	0.00142291i
$456$		0			0
$457$		−	14.9856i		−	0.700995i	−0.936564	−	0.350497i	$-0.886013\pi$
$457$		−	14.9856i		−	0.700995i	0.936564	−	0.350497i	$-0.113987\pi$
$458$		−	17.3120i		−	0.808936i
$459$		0			0
$460$	−0.789649	+	1.36771i	−0.0368176	+	0.0637699i
$461$	−15.4306	+	8.90884i	−0.718673	+	0.414926i	−0.814264	−	0.580494i	$-0.802859\pi$
$461$	−15.4306	+	8.90884i	−0.718673	+	0.414926i	0.0955909	+	0.995421i	$0.469526\pi$
$462$		0			0
$463$	−20.1534	−	11.6356i	−0.936610	−	0.540752i	−0.0477138	−	0.998861i	$-0.515194\pi$
$463$	−20.1534	−	11.6356i	−0.936610	−	0.540752i	−0.888896	+	0.458109i	$0.848527\pi$
$464$			0.776949i			0.0360689i
$465$		0			0
$466$	7.97547	−	4.60464i	0.369457	−	0.213306i
$467$			17.6430i			0.816422i	0.912888	+	0.408211i	$0.133847\pi$
$467$			17.6430i			0.816422i	−0.912888	+	0.408211i	$0.866153\pi$
$468$		0			0
$469$	0.0488727	−	0.0846500i	0.00225673	−	0.00390877i
$470$	−1.87378	+	3.24548i	−0.0864309	+	0.149703i
$471$		0			0
$472$	12.5360			0.577017
$473$	24.7205	−	14.2724i	1.13665	−	0.656244i
$474$		0			0
$475$	−25.0031	−	14.4355i	−1.14722	−	0.662348i
$476$	−0.0947774	+	0.0547197i	−0.00434411	+	0.00250808i
$477$		0			0
$478$	1.15960	+	2.00849i	0.0530389	+	0.0918661i
$479$	−1.62166	+	0.936267i	−0.0740956	+	0.0427791i	−0.536590	−	0.843843i	$-0.680288\pi$
$479$	−1.62166	+	0.936267i	−0.0740956	+	0.0427791i	0.462494	+	0.886622i	$0.346955\pi$
$480$		0			0
$481$	−13.5258	−	1.18259i	−0.616721	−	0.0539215i
$482$	3.32211	+	5.75406i	0.151318	+	0.262090i
$483$		0			0
$484$	4.33928			0.197240
$485$	−1.10539	−	1.91459i	−0.0501932	−	0.0869372i
$486$		0			0
$487$		−	5.36851i		−	0.243270i	−0.992575	−	0.121635i	$-0.961186\pi$
$487$		−	5.36851i		−	0.243270i	0.992575	−	0.121635i	$-0.0388138\pi$
$488$	−9.35171			−0.423332
$489$		0			0
$490$	2.61012			0.117913
$491$	−19.2176	−	33.2859i	−0.867279	−	1.50217i	−0.864766	−	0.502175i	$-0.832533\pi$
$491$	−19.2176	−	33.2859i	−0.867279	−	1.50217i	−0.00251360	−	0.999997i	$-0.500800\pi$
$492$		0			0
$493$	−1.00989	−	1.74917i	−0.0454830	−	0.0787788i
$494$	−11.4813	+	6.62874i	−0.516569	+	0.298241i
$495$		0			0
$496$	−8.09859	−	4.67573i	−0.363638	−	0.209946i
$497$	−0.0143982	−	0.0249385i	−0.000645849	−	0.00111864i
$498$		0			0
$499$	−2.88148	−	1.66362i	−0.128993	−	0.0744740i	0.434115	−	0.900857i	$-0.357061\pi$
$499$	−2.88148	−	1.66362i	−0.128993	−	0.0744740i	−0.563108	+	0.826383i	$0.690394\pi$
$500$	3.18508	+	1.83890i	0.142441	+	0.0822383i
$501$		0			0
$502$	13.1458	+	22.7692i	0.586725	+	1.01624i
$503$	−10.6045	−	6.12250i	−0.472830	−	0.272989i	0.244594	−	0.969626i	$-0.421345\pi$
$503$	−10.6045	−	6.12250i	−0.472830	−	0.272989i	−0.717424	+	0.696637i	$0.754679\pi$
$504$		0			0
$505$	3.11601	−	1.79903i	0.138661	−	0.0800558i
$506$	5.46413	+	9.46416i	0.242910	+	0.420733i
$507$		0			0
$508$	1.27625	+	2.21054i	0.0566246	+	0.0980766i
$509$	1.73398			0.0768572			0.0384286	−	0.999261i	$-0.487765\pi$
$509$	1.73398			0.0768572			0.0384286	+	0.999261i	$0.487765\pi$
$510$		0			0
$511$	−0.554634			−0.0245356
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.66777	+	6.35277i	0.161779	+	0.280209i
$515$	0.222033			0.00978393
$516$		0			0
$517$	12.9660	+	22.4577i	0.570243	+	0.987691i
$518$	−0.146866	+	0.209771i	−0.00645293	+	0.00921683i
$519$		0			0
$520$	0.720971	−	0.416253i	0.0316167	−	0.0182539i
$521$	−3.37632	−	5.84796i	−0.147919	−	0.256204i	0.782539	−	0.622602i	$-0.213924\pi$
$521$	−3.37632	−	5.84796i	−0.147919	−	0.256204i	−0.930458	+	0.366398i	$0.880591\pi$
$522$		0			0
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.927966	−	0.372666i	$-0.878444\pi$
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.141245	+	0.989975i	$0.545110\pi$
$524$	−9.82049	−	5.66986i	−0.429010	−	0.247689i
$525$		0			0
$526$	−17.8006	+	10.2772i	−0.776144	+	0.448107i
$527$	24.3102			1.05897
$528$		0			0
$529$	−2.53497	+	4.39069i	−0.110216	+	0.190900i
$530$	1.34695	−	2.33299i	0.0585080	−	0.101339i
$531$		0			0
$532$			0.250041i			0.0108406i
$533$	−13.9831	+	8.07314i	−0.605675	+	0.349687i
$534$		0			0
$535$			3.57518i			0.154568i
$536$	2.01077	+	1.16092i	0.0868522	+	0.0501441i
$537$		0			0
$538$	−22.0800	+	12.7479i	−0.951936	+	0.549600i
$539$	9.03064	−	15.6415i	0.388977	−	0.673728i
$540$		0			0
$541$			13.9031i			0.597741i	0.954294	+	0.298870i	$0.0966098\pi$
$541$			13.9031i			0.597741i	−0.954294	+	0.298870i	$0.903390\pi$
$542$		−	21.0814i		−	0.905525i
$543$		0			0
$544$	−1.29981	−	2.25134i	−0.0557289	−	0.0965253i
$545$	−1.72501	−	2.98781i	−0.0738913	−	0.127984i
$546$		0			0
$547$	6.72089	+	3.88031i	0.287365	+	0.165910i	0.636753	−	0.771068i	$-0.280277\pi$
$547$	6.72089	+	3.88031i	0.287365	+	0.165910i	−0.349388	+	0.936978i	$0.613611\pi$
$548$	−7.60904	−	13.1792i	−0.325042	−	0.562989i
$549$		0			0
$550$	10.8644	−	6.27259i	0.463261	−	0.267464i
$551$	−4.61465			−0.196591
$552$		0			0
$553$		−	0.165236i		−	0.00702657i
$554$	8.26407	+	14.3138i	0.351106	+	0.608134i
$555$		0			0
$556$	−8.10261	+	14.0341i	−0.343627	+	0.595180i
$557$	19.0159	+	10.9788i	0.805730	+	0.465189i	0.845471	−	0.534021i	$-0.179320\pi$
$557$	19.0159	+	10.9788i	0.805730	+	0.465189i	−0.0397407	+	0.999210i	$0.512653\pi$
$558$		0			0
$559$	12.3438	+	21.3801i	0.522088	+	0.904283i
$560$		−	0.0157013i		−	0.000663503i
$561$		0			0
$562$	−1.04643	+	1.81247i	−0.0441409	+	0.0764543i
$563$	−9.39056	+	5.42164i	−0.395765	+	0.228495i	−0.684655	−	0.728867i	$-0.740047\pi$
$563$	−9.39056	+	5.42164i	−0.395765	+	0.228495i	0.288890	+	0.957362i	$0.406714\pi$
$564$		0			0
$565$	2.86436	−	4.96121i	0.120504	−	0.208720i
$566$	9.75704			0.410119
$567$		0			0
$568$	0.592387	−	0.342015i	0.0248560	−	0.0143506i
$569$	7.21399	+	4.16500i	0.302426	+	0.174606i	0.643532	−	0.765419i	$-0.277468\pi$
$569$	7.21399	+	4.16500i	0.302426	+	0.174606i	−0.341106	+	0.940025i	$0.610802\pi$
$570$		0			0
$571$	−13.2737			−0.555487			−0.277744	−	0.960655i	$-0.589587\pi$
$571$	−13.2737			−0.555487			−0.277744	+	0.960655i	$0.589587\pi$
$572$		−	5.76069i		−	0.240867i
$573$		0			0
$574$			0.304525i			0.0127106i
$575$	−17.8253	−	10.2915i	−0.743368	−	0.429184i
$576$		0			0
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.919134	−	0.393944i	$-0.128890\pi$
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.118402	+	0.992966i	$0.462223\pi$
$578$	−8.86981	−	5.12098i	−0.368935	−	0.213005i
$579$		0			0
$580$	0.289778			0.0120324
$581$	0.176148	+	0.305097i	0.00730785	+	0.0126576i
$582$		0			0
$583$	−9.32053	−	16.1436i	−0.386017	−	0.668601i
$584$		−	13.1748i		−	0.545176i
$585$		0			0
$586$			1.38135i			0.0570630i
$587$		−	24.4935i		−	1.01096i	−0.862839	−	0.505478i	$-0.831316\pi$
$587$		−	24.4935i		−	1.01096i	0.862839	−	0.505478i	$-0.168684\pi$
$588$		0			0
$589$	27.7713	−	48.1012i	1.14430	−	1.98198i
$590$		−	4.67555i		−	0.192489i
$591$		0			0
$592$	−4.98290	−	3.48865i	−0.204796	−	0.143383i
$593$	33.7386			1.38548			0.692740	−	0.721188i	$-0.256403\pi$
$593$	33.7386			1.38548			0.692740	+	0.721188i	$0.256403\pi$
$594$		0			0
$595$	0.0204088	+	0.0353490i	0.000836678	+	0.00144917i
$596$	−0.354313			−0.0145132
$597$		0			0
$598$	−8.18532	+	4.72580i	−0.334723	+	0.193252i
$599$	−9.87519	+	17.1043i	−0.403489	+	0.698864i	−0.994144	−	0.108060i	$-0.965536\pi$
$599$	−9.87519	+	17.1043i	−0.403489	+	0.698864i	0.590655	+	0.806924i	$0.298869\pi$
$600$		0			0
$601$	6.85144	+	11.8670i	0.279476	+	0.484067i	0.971255	−	0.238043i	$-0.0765059\pi$
$601$	6.85144	+	11.8670i	0.279476	+	0.484067i	−0.691778	+	0.722110i	$0.743173\pi$
$602$	0.465618			0.0189772
$603$		0			0
$604$	3.44680	−	5.97003i	0.140248	−	0.242917i
$605$		−	1.61842i		−	0.0657981i
$606$		0			0
$607$		−	10.8253i		−	0.439385i	−0.975569	−	0.219692i	$-0.929495\pi$
$607$		−	10.8253i		−	0.439385i	0.975569	−	0.219692i	$-0.0705054\pi$
$608$	−5.93946			−0.240877
$609$		0			0
$610$			3.48790i			0.141221i
$611$	−19.4232	+	11.2140i	−0.785777	+	0.453669i
$612$		0			0
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	−0.580887	−	0.813984i	$-0.697294\pi$
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	0.995375	+	0.0960708i	$0.0306275\pi$
$614$	−19.3791	+	11.1885i	−0.782078	+	0.451533i
$615$		0			0
$616$	−0.0940925	−	0.0543243i	−0.00379109	−	0.00218879i
$617$	15.4306			0.621211			0.310605	−	0.950539i	$-0.399468\pi$
$617$	15.4306			0.621211			0.310605	+	0.950539i	$0.399468\pi$
$618$		0			0
$619$	−6.19852	+	10.7361i	−0.249139	+	0.431522i	−0.963287	−	0.268473i	$-0.913481\pi$
$619$	−6.19852	+	10.7361i	−0.249139	+	0.431522i	0.714148	+	0.699995i	$0.246814\pi$
$620$	−1.74390	+	3.02053i	−0.0700368	+	0.121307i
$621$		0			0
$622$	14.1829	+	24.5656i	0.568684	+	0.984990i
$623$	0.237025	+	0.136847i	0.00949621	+	0.00548264i
$624$		0			0
$625$	−11.4664	+	19.8604i	−0.458655	+	0.794414i
$626$	6.90465	−	11.9592i	0.275965	−	0.477986i
$627$		0			0
$628$	5.77978	−	10.0109i	0.230638	−	0.399477i
$629$	15.7528	+	1.37730i	0.628105	+	0.0549167i
$630$		0			0
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.283658	−	0.958925i	$-0.591548\pi$
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.972283	+	0.233808i	$0.924881\pi$
$632$	3.92502			0.156129
$633$		0			0
$634$	6.33996	+	3.66038i	0.251792	+	0.145372i
$635$	0.824462	−	0.476003i	0.0327178	−	0.0188896i
$636$		0			0
$637$	13.5280	+	7.81038i	0.535998	+	0.309459i
$638$	1.00259	−	1.73653i	0.0396929	−	0.0687501i
$639$		0			0
$640$	0.372969			0.0147429
$641$	24.2444	+	41.9925i	0.957596	+	1.65860i	0.728312	+	0.685245i	$0.240305\pi$
$641$	24.2444	+	41.9925i	0.957596	+	1.65860i	0.229283	+	0.973360i	$0.426362\pi$
$642$		0			0
$643$	−18.1536	+	10.4810i	−0.715907	+	0.413329i	−0.813244	−	0.581922i	$-0.802301\pi$
$643$	−18.1536	+	10.4810i	−0.715907	+	0.413329i	0.0973375	+	0.995251i	$0.468967\pi$
$644$			0.178260i			0.00702444i
$645$		0			0
$646$	13.3717	−	7.72017i	0.526103	−	0.303746i
$647$	33.9152	−	19.5810i	1.33334	−	0.769807i	0.347534	−	0.937667i	$-0.387019\pi$
$647$	33.9152	−	19.5810i	1.33334	−	0.769807i	0.985811	+	0.167861i	$0.0536859\pi$
$648$		0			0
$649$	−28.0189	−	16.1767i	−1.09984	−	0.634991i
$650$	5.42501	+	9.39639i	0.212786	+	0.368557i
$651$		0			0
$652$	12.6667	−	7.31312i	0.496066	−	0.286404i
$653$	−33.8074	−	19.5187i	−1.32298	−	0.763825i	−0.338780	−	0.940866i	$-0.610014\pi$
$653$	−33.8074	−	19.5187i	−1.32298	−	0.763825i	−0.984204	+	0.177040i	$0.943348\pi$
$654$		0			0
$655$	−2.11468	+	3.66274i	−0.0826275	+	0.143115i
$656$	−7.23366			−0.282427
$657$		0			0
$658$			0.422999i			0.0164902i
$659$	−46.4734			−1.81035			−0.905174	−	0.425041i	$-0.860260\pi$
$659$	−46.4734			−1.81035			−0.905174	+	0.425041i	$0.860260\pi$
$660$		0			0
$661$	−34.9133	−	20.1572i	−1.35797	−	0.784024i	−0.368620	−	0.929580i	$-0.620170\pi$
$661$	−34.9133	−	20.1572i	−1.35797	−	0.784024i	−0.989350	+	0.145556i	$0.953503\pi$
$662$	6.64402	−	11.5078i	0.258227	−	0.447262i
$663$		0			0
$664$	−7.24727	+	4.18421i	−0.281248	+	0.162379i
$665$	0.0932575			0.00361637
$666$		0			0
$667$	−3.28990			−0.127386
$668$	−10.1001	+	5.83129i	−0.390784	+	0.225620i
$669$		0			0
$670$	0.432988	−	0.749956i	0.0167278	−	0.0289733i
$671$	20.9017	+	12.0676i	0.806902	+	0.465865i
$672$		0			0
$673$	46.1767			1.77998			0.889990	−	0.455979i	$-0.150711\pi$
$673$	46.1767			1.77998			0.889990	+	0.455979i	$0.150711\pi$
$674$		−	9.96243i		−	0.383738i
$675$		0			0
$676$	−8.01771			−0.308374
$677$	−21.2133	+	36.7426i	−0.815294	+	1.41213i	0.0938220	+	0.995589i	$0.470092\pi$
$677$	−21.2133	+	36.7426i	−0.815294	+	1.41213i	−0.909116	+	0.416542i	$0.863242\pi$
$678$		0			0
$679$	−0.216106	−	0.124769i	−0.00829340	−	0.00478820i
$680$	−0.839680	+	0.484789i	−0.0322003	+	0.0185908i
$681$		0			0
$682$	12.0673	+	20.9011i	0.462080	+	0.800346i
$683$	−44.0035	−	25.4054i	−1.68375	−	0.972112i	−0.959132	−	0.282960i	$-0.908684\pi$
$683$	−44.0035	−	25.4054i	−1.68375	−	0.972112i	−0.724616	−	0.689153i	$-0.757983\pi$
$684$		0			0
$685$	−4.91545	+	2.83794i	−0.187810	+	0.108432i
$686$	0.510349	−	0.294650i	0.0194852	−	0.0112498i
$687$		0			0
$688$			11.0603i			0.421669i
$689$	13.9622	−	8.06110i	0.531919	−	0.307103i
$690$		0			0
$691$	2.16910	+	3.75700i	0.0825166	+	0.142923i	0.904330	−	0.426833i	$-0.140371\pi$
$691$	2.16910	+	3.75700i	0.0825166	+	0.142923i	−0.821814	+	0.569756i	$0.807038\pi$
$692$	−0.0584707			−0.00222272
$693$		0			0
$694$	10.5053	−	18.1956i	0.398774	−	0.690697i
$695$	5.23430	+	3.02202i	0.198548	+	0.114632i
$696$		0			0
$697$	16.2854	−	9.40239i	0.616854	−	0.356141i
$698$	26.6512	+	15.3871i	1.00876	+	0.582410i
$699$		0			0
$700$	0.204635			0.00773448
$701$	39.9218	+	23.0488i	1.50782	+	0.870542i	0.999959	+	0.00910594i	$0.00289855\pi$
$701$	39.9218	+	23.0488i	1.50782	+	0.870542i	0.507865	+	0.861437i	$0.330435\pi$
$702$		0			0
$703$	20.7207	−	29.5957i	0.781496	−	1.11622i
$704$	1.29042	−	2.23507i	0.0486345	−	0.0842374i
$705$		0			0
$706$	−0.144055	+	0.249511i	−0.00542160	+	0.00939048i
$707$	0.203062	−	0.351714i	0.00763695	−	0.0132276i
$708$		0			0
$709$	39.1822	+	22.6218i	1.47152	+	0.849581i	0.999488	−	0.0320017i	$-0.0101882\pi$
$709$	39.1822	+	22.6218i	1.47152	+	0.849581i	0.472030	+	0.881583i	$0.343522\pi$
$710$	−0.127561	−	0.220942i	−0.00478728	−	0.00829181i
$711$		0			0
$712$	−3.25065	+	5.63029i	−0.121823	+	0.211004i
$713$	19.7989	−	34.2926i	0.741473	−	1.28427i
$714$		0			0
$715$	−2.14856			−0.0803516
$716$	−7.35546	−	4.24668i	−0.274887	−	0.158706i
$717$		0			0
$718$	5.59141	−	3.22820i	0.208670	−	0.120475i
$719$	1.96437	−	3.40238i	0.0732585	−	0.126887i	−0.827069	−	0.562100i	$-0.809994\pi$
$719$	1.96437	−	3.40238i	0.0732585	−	0.126887i	0.900328	+	0.435213i	$0.143327\pi$
$720$		0			0
$721$	0.0217039	−	0.0125308i	0.000808297	−	0.000466671i
$722$		−	16.2771i		−	0.605773i
$723$		0			0
$724$	16.0869			0.597864
$725$			3.77666i			0.140262i
$726$		0			0
$727$		−	42.2670i		−	1.56760i	−0.621015	−	0.783798i	$-0.713280\pi$
$727$		−	42.2670i		−	1.56760i	0.621015	−	0.783798i	$-0.286720\pi$
$728$	0.0469838	−	0.0813784i	0.00174134	−	0.00301608i
$729$		0			0
$730$	−4.91378			−0.181867
$731$	−14.3762	−	24.9004i	−0.531725	−	0.920974i
$732$		0			0
$733$	2.04764	−	3.54661i	0.0756312	−	0.130997i	−0.825729	−	0.564066i	$-0.809236\pi$
$733$	2.04764	−	3.54661i	0.0756312	−	0.130997i	0.901361	+	0.433069i	$0.142569\pi$
$734$	−31.6525	+	18.2746i	−1.16831	+	0.674526i
$735$		0			0
$736$	−4.23439			−0.156082
$737$	−2.99615	−	5.18948i	−0.110364	−	0.191157i
$738$		0			0
$739$	43.9364			1.61623			0.808114	−	0.589027i	$-0.200489\pi$
$739$	43.9364			1.61623			0.808114	+	0.589027i	$0.200489\pi$
$740$	−1.30116	+	1.85847i	−0.0478316	+	0.0683187i
$741$		0			0
$742$		−	0.304070i		−	0.0111628i
$743$	−8.94276	+	15.4893i	−0.328078	+	0.568248i	−0.982130	−	0.188202i	$-0.939734\pi$
$743$	−8.94276	+	15.4893i	−0.328078	+	0.568248i	0.654053	+	0.756449i	$0.273068\pi$
$744$		0			0
$745$			0.132148i			0.00484152i
$746$			2.94276i			0.107742i
$747$		0			0
$748$			6.70920i			0.245313i
$749$	0.201771	+	0.349478i	0.00737255	+	0.0127696i
$750$		0			0
$751$	8.35475	+	14.4709i	0.304869	+	0.528049i	0.977232	−	0.212173i	$-0.0680539\pi$
$751$	8.35475	+	14.4709i	0.304869	+	0.528049i	−0.672363	+	0.740222i	$0.734721\pi$
$752$	−10.0479			−0.366409
$753$		0			0
$754$	1.50189	+	0.867115i	0.0546955	+	0.0315785i
$755$	−2.22664	−	1.28555i	−0.0810356	−	0.0467859i
$756$		0			0
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	0.633213	−	0.773978i	$-0.281736\pi$
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	−0.353678	+	0.935367i	$0.615069\pi$
$758$			3.51220i			0.127569i
$759$		0			0
$760$			2.21523i			0.0803550i
$761$	−28.1061			−1.01885			−0.509423	−	0.860516i	$-0.670141\pi$
$761$	−28.1061			−1.01885			−0.509423	+	0.860516i	$0.670141\pi$
$762$		0			0
$763$	−0.337243	−	0.194708i	−0.0122090	−	0.00704889i
$764$	−7.11315	+	4.10678i	−0.257345	+	0.148578i
$765$		0			0
$766$	17.2557			0.623474
$767$	13.9908	−	24.2329i	0.505180	−	0.874998i
$768$		0			0
$769$	−8.59532	+	4.96251i	−0.309955	+	0.178953i	−0.646906	−	0.762569i	$-0.723938\pi$
$769$	−8.59532	+	4.96251i	−0.309955	+	0.178953i	0.336951	+	0.941522i	$0.390604\pi$
$770$	−0.0202613	+	0.0350936i	−0.000730167	+	0.00126469i
$771$		0			0
$772$		−	19.2590i		−	0.693145i
$773$	18.3764	+	31.8289i	0.660954	+	1.14481i	0.980365	+	0.197190i	$0.0631815\pi$
$773$	18.3764	+	31.8289i	0.660954	+	1.14481i	−0.319411	+	0.947616i	$0.603485\pi$
$774$		0			0
$775$	−39.3664	−	22.7282i	−1.41408	−	0.816421i
$776$	2.96376	−	5.13338i	0.106393	−	0.184278i
$777$		0			0
$778$	9.40455	+	16.2892i	0.337169	+	0.583995i
$779$		−	42.9640i		−	1.53935i
$780$		0			0
$781$	−1.76537			−0.0631699
$782$	9.53305	−	5.50391i	0.340901	−	0.196819i
$783$		0			0
$784$	3.49911	+	6.06064i	0.124968	+	0.216452i
$785$	−3.73374	−	2.15568i	−0.133263	−	0.0769395i
$786$		0			0
$787$	−1.31315	−	2.27445i	−0.0468088	−	0.0810752i	0.841672	−	0.539990i	$-0.181572\pi$
$787$	−1.31315	−	2.27445i	−0.0468088	−	0.0810752i	−0.888481	+	0.458914i	$0.848238\pi$
$788$	−0.245783	−	0.425708i	−0.00875565	−	0.0151652i
$789$		0			0
$790$		−	1.46391i		−	0.0520836i
$791$		−	0.646618i		−	0.0229911i
$792$		0			0
$793$	−10.4370	+	18.0774i	−0.370628	+	0.641947i
$794$	6.42327	−	3.70848i	0.227953	−	0.131609i
$795$		0			0
$796$	9.43424	+	5.44686i	0.334388	+	0.193059i
$797$		−	29.5312i		−	1.04605i	−0.852318	−	0.523024i	$-0.824804\pi$
$797$		−	29.5312i		−	1.04605i	0.852318	−	0.523024i	$-0.175196\pi$
$798$		0			0
$799$	22.6212	−	13.0604i	0.800281	−	0.462042i
$800$			4.86089i			0.171859i
$801$		0			0
$802$	−10.1798	+	17.6319i	−0.359461	+	0.622605i
$803$	−17.0010	+	29.4465i	−0.599951	+	1.03915i
$804$		0			0
$805$	0.0664856			0.00234331
$806$	−18.0769	+	10.4367i	−0.636732	+	0.367617i
$807$		0			0
$808$	8.35461	+	4.82354i	0.293914	+	0.169691i
$809$	−10.2145	+	5.89735i	−0.359123	+	0.207340i	−0.668696	−	0.743536i	$-0.733147\pi$
$809$	−10.2145	+	5.89735i	−0.359123	+	0.207340i	0.309573	+	0.950876i	$0.399814\pi$
$810$		0			0
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	0.995194	−	0.0979192i	$-0.0312187\pi$
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	−0.582398	+	0.812904i	$0.697885\pi$
$812$	0.0283261	−	0.0163541i	0.000994051	−	0.000573916i
$813$		0			0
$814$	6.63531	+	14.2274i	0.232568	+	0.498670i
$815$	−2.72757	−	4.72429i	−0.0955426	−	0.165485i
$816$		0			0
$817$	−65.6920			−2.29827
$818$	−3.81157	−	6.60183i	−0.133268	−	0.230828i
$819$		0			0
$820$			2.69793i			0.0942159i
$821$	33.9326			1.18425			0.592127	−	0.805845i	$-0.298288\pi$
$821$	33.9326			1.18425			0.592127	+	0.805845i	$0.298288\pi$
$822$		0			0
$823$	19.8667			0.692509			0.346255	−	0.938141i	$-0.387453\pi$
$823$	19.8667			0.692509			0.346255	+	0.938141i	$0.387453\pi$
$824$	0.297656	+	0.515555i	0.0103693	+	0.0179602i
$825$		0			0
$826$	−0.263872	−	0.457040i	−0.00918129	−	0.0159025i
$827$	15.8162	−	9.13148i	0.549982	−	0.317533i	−0.199132	−	0.979973i	$-0.563812\pi$
$827$	15.8162	−	9.13148i	0.549982	−	0.317533i	0.749115	+	0.662440i	$0.230479\pi$
$828$		0			0
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.391331	−	0.920250i	$-0.627985\pi$
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.992625	+	0.121223i	$0.961319\pi$
$830$	1.56058	+	2.70301i	0.0541686	+	0.0938227i
$831$		0			0
$832$	1.93306	+	1.11605i	0.0670167	+	0.0386921i
$833$	−15.7554	−	9.09637i	−0.545891	−	0.315171i
$834$		0			0
$835$	2.17489	+	3.76703i	0.0752653	+	0.130363i
$836$	13.2751	+	7.66438i	0.459129	+	0.265078i
$837$		0			0
$838$	29.9271	−	17.2784i	1.03381	−	0.596873i
$839$	−6.11933	−	10.5990i	−0.211263	−	0.365918i	0.740847	−	0.671673i	$-0.234424\pi$
$839$	−6.11933	−	10.5990i	−0.211263	−	0.365918i	−0.952110	+	0.305756i	$0.901091\pi$
$840$		0			0
$841$	−14.1982	−	24.5920i	−0.489592	−	0.847999i
$842$	−18.6219			−0.641754
$843$		0			0
$844$	12.7791			0.439876
$845$			2.99036i			0.102872i
$846$		0			0
$847$	−0.0913381	−	0.158202i	−0.00313842	−	0.00543589i
$848$	7.22287			0.248034
$849$		0			0
$850$	−6.31824	−	10.9435i	−0.216714	−	0.375359i
$851$	14.7723	−	21.0996i	0.506388	−	0.723283i
$852$		0			0
$853$	−15.5546	+	8.98046i	−0.532580	+	0.307485i	−0.742066	−	0.670327i	$-0.766154\pi$
$853$	−15.5546	+	8.98046i	−0.532580	+	0.307485i	0.209487	+	0.977812i	$0.432821\pi$
$854$	0.196845	+	0.340946i	0.00673591	+	0.0116669i
$855$		0			0
$856$	−8.30148	+	4.79286i	−0.283739	+	0.163817i
$857$	44.5684	+	25.7316i	1.52243	+	0.878975i	0.999649	+	0.0265070i	$0.00843842\pi$
$857$	44.5684	+	25.7316i	1.52243	+	0.878975i	0.522780	+	0.852468i	$0.324895\pi$
$858$		0			0
$859$	6.87771	−	3.97085i	0.234664	−	0.135484i	−0.378058	−	0.925782i	$-0.623408\pi$
$859$	6.87771	−	3.97085i	0.234664	−	0.135484i	0.612722	+	0.790299i	$0.290075\pi$
$860$	4.12514			0.140666
$861$		0			0
$862$	−10.7429	+	18.6073i	−0.365905	+	0.633767i
$863$	−12.2981	+	21.3010i	−0.418634	+	0.725095i	−0.995802	−	0.0915301i	$-0.970824\pi$
$863$	−12.2981	+	21.3010i	−0.418634	+	0.725095i	0.577169	+	0.816625i	$0.304158\pi$
$864$		0			0
$865$			0.0218078i			0.000741486i
$866$	−26.6737	+	15.4001i	−0.906409	+	0.523315i
$867$		0			0
$868$			0.393680i			0.0133624i
$869$	−8.77269	−	5.06491i	−0.297593	−	0.171815i
$870$		0			0
$871$	4.48825	−	2.59129i	0.152079	−	0.0878026i
$872$	4.62508	−	8.01087i	0.156625	−	0.271282i
$873$		0			0
$874$		−	25.1500i		−	0.850711i
$875$		−	0.154829i		−	0.00523419i
$876$		0			0
$877$	−6.30917	−	10.9278i	−0.213046	−	0.369006i	0.739621	−	0.673024i	$-0.235005\pi$
$877$	−6.30917	−	10.9278i	−0.213046	−	0.369006i	−0.952666	+	0.304018i	$0.901672\pi$
$878$	14.8047	+	25.6425i	0.499635	+	0.865393i
$879$		0			0
$880$	−0.833612	−	0.481286i	−0.0281011	−	0.0162242i
$881$	6.02320	+	10.4325i	0.202927	+	0.351480i	0.949470	−	0.313857i	$-0.101621\pi$
$881$	6.02320	+	10.4325i	0.202927	+	0.351480i	−0.746543	+	0.665337i	$0.768288\pi$
$882$		0			0
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	−0.663903	−	0.747819i	$-0.731101\pi$
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	0.315679	+	0.948866i	$0.397768\pi$
$884$	−5.80262			−0.195163
$885$		0			0
$886$			1.80486i			0.0606355i
$887$	−20.6333	−	35.7380i	−0.692800	−	1.19996i	−0.970917	−	0.239417i	$-0.923044\pi$
$887$	−20.6333	−	35.7380i	−0.692800	−	1.19996i	0.278117	−	0.960547i	$-0.410290\pi$
$888$		0			0
$889$	0.0537280	−	0.0930596i	0.00180198	−	0.00312112i
$890$	2.09992	+	1.21239i	0.0703896	+	0.0406394i
$891$		0			0
$892$	14.1726	+	24.5477i	0.474534	+	0.821917i
$893$		−	59.6790i		−	1.99708i
$894$		0			0
$895$	−1.58388	+	2.74336i	−0.0529433	+	0.0917005i
$896$	0.0364581	−	0.0210491i	0.00121798	−	0.000703202i
$897$		0			0
$898$	18.9232	−	32.7760i	0.631476	−	1.09375i
$899$	−7.26560			−0.242321
$900$		0			0
$901$	−16.2611	+	9.38837i	−0.541737	+	0.312772i
$902$	16.1677	+	9.33445i	0.538327	+	0.310803i
$903$		0			0
$904$	15.3597			0.510858
$905$		−	5.99991i		−	0.199444i
$906$		0			0
$907$			22.3722i			0.742855i	0.928462	+	0.371428i	$0.121132\pi$
$907$			22.3722i			0.742855i	−0.928462	+	0.371428i	$0.878868\pi$
$908$	−0.708998	−	0.409340i	−0.0235289	−	0.0135844i
$909$		0			0
$910$	−0.0303516	−	0.0175235i	−0.00100615	−	0.000580899i
$911$	−42.7829	−	24.7007i	−1.41746	−	0.818371i	−0.421384	−	0.906882i	$-0.638456\pi$
$911$	−42.7829	−	24.7007i	−1.41746	−	0.818371i	−0.996075	+	0.0885116i	$0.971789\pi$
$912$		0			0
$913$	21.5975			0.714774
$914$	−7.49278	−	12.9779i	−0.247839	−	0.429270i
$915$		0			0
$916$	−8.65599	−	14.9926i	−0.286002	−	0.495370i
$917$			0.477382i			0.0157646i
$918$		0			0
$919$		−	23.9475i		−	0.789956i	−0.918691	−	0.394978i	$-0.870752\pi$
$919$		−	23.9475i		−	0.789956i	0.918691	−	0.394978i	$-0.129248\pi$
$920$			1.57930i			0.0520679i
$921$		0			0
$922$	−8.90884	+	15.4306i	−0.293397	+	0.508179i
$923$		−	1.52683i		−	0.0502561i
$924$		0			0
$925$	−24.2214	−	16.9580i	−0.796393	−	0.557574i
$926$	−23.2712			−0.764739
$927$		0			0
$928$	0.388474	+	0.672857i	0.0127523	+	0.0220876i
$929$	11.7665			0.386047			0.193024	−	0.981194i	$-0.438171\pi$
$929$	11.7665			0.386047			0.193024	+	0.981194i	$0.438171\pi$
$930$		0			0
$931$	−35.9969	+	20.7828i	−1.17975	+	0.681130i
$932$	4.60464	−	7.97547i	0.150830	−	0.261245i
$933$		0			0
$934$	8.82151	+	15.2793i	0.288649	+	0.499954i
$935$	2.50232			0.0818347
$936$		0			0
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	−0.911482	−	0.411341i	$-0.865061\pi$
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	0.811973	+	0.583696i	$0.198394\pi$
$938$		−	0.0977454i		−	0.00319150i
$939$		0			0
$940$			3.74756i			0.122232i
$941$	8.03681			0.261992			0.130996	−	0.991383i	$-0.458182\pi$
$941$	8.03681			0.261992			0.130996	+	0.991383i	$0.458182\pi$
$942$		0			0
$943$		−	30.6302i		−	0.997455i
$944$	10.8565	−	6.26801i	0.353349	−	0.204006i
$945$		0			0
$946$	14.2724	−	24.7205i	0.464035	−	0.803731i
$947$	18.0551	−	10.4241i	0.586712	−	0.338738i	−0.177084	−	0.984196i	$-0.556667\pi$
$947$	18.0551	−	10.4241i	0.586712	−	0.338738i	0.763796	+	0.645457i	$0.223333\pi$
$948$		0			0
$949$	−25.4676	−	14.7037i	−0.826713	−	0.477303i
$950$	−28.8711			−0.936701
$951$		0			0
$952$	−0.0547197	+	0.0947774i	−0.00177348	+	0.00307175i
$953$	−20.3122	+	35.1818i	−0.657978	+	1.13965i	0.323161	+	0.946344i	$0.395255\pi$
$953$	−20.3122	+	35.1818i	−0.657978	+	1.13965i	−0.981138	+	0.193307i	$0.938079\pi$
$954$		0			0
$955$	1.53170	+	2.65299i	0.0495647	+	0.0858486i
$956$	2.00849	+	1.15960i	0.0649591	+	0.0375042i
$957$		0			0
$958$	−0.936267	+	1.62166i	−0.0302494	+	0.0523935i
$959$	−0.320327	+	0.554823i	−0.0103439	+	0.0179162i
$960$		0			0
$961$	28.2248	−	48.8868i	0.910478	−	1.57699i
$962$	−12.3049	+	5.73872i	−0.396727	+	0.185024i
$963$		0			0
$964$	5.75406	+	3.32211i	0.185326	+	0.106998i
$965$	−7.18300			−0.231229
$966$		0			0
$967$	−0.514288	−	0.296924i	−0.0165384	−	0.00954843i	0.491708	−	0.870760i	$-0.336373\pi$
$967$	−0.514288	−	0.296924i	−0.0165384	−	0.00954843i	−0.508246	+	0.861212i	$0.669706\pi$
$968$	3.75793	−	2.16964i	0.120784	−	0.0697349i
$969$		0			0
$970$	−1.91459	−	1.10539i	−0.0614739	−	0.0354920i
$971$	−3.85800	+	6.68226i	−0.123809	+	0.214444i	−0.921267	−	0.388931i	$-0.872844\pi$
$971$	−3.85800	+	6.68226i	−0.123809	+	0.214444i	0.797458	+	0.603375i	$0.206178\pi$
$972$		0			0
$973$	0.682211			0.0218707
$974$	−2.68425	−	4.64926i	−0.0860090	−	0.148972i
$975$		0			0
$976$	−8.09882	+	4.67586i	−0.259237	+	0.149670i
$977$		−	30.0532i		−	0.961486i	−0.876862	−	0.480743i	$-0.840367\pi$
$977$		−	30.0532i		−	0.961486i	0.876862	−	0.480743i	$-0.159633\pi$
$978$		0			0
$979$	14.5308	−	8.38939i	0.464408	−	0.268126i
$980$	2.26043	−	1.30506i	0.0722069	−	0.0416887i
$981$		0			0
$982$	−33.2859	−	19.2176i	−1.06220	−	0.613259i
$983$	6.77861	+	11.7409i	0.216204	+	0.374476i	0.953644	−	0.300936i	$-0.0972990\pi$
$983$	6.77861	+	11.7409i	0.216204	+	0.374476i	−0.737440	+	0.675412i	$0.763966\pi$
$984$		0			0
$985$	−0.158776	+	0.0916694i	−0.00505902	+	0.00292083i
$986$	−1.74917	−	1.00989i	−0.0557050	−	0.0321613i
$987$		0			0
$988$	−6.62874	+	11.4813i	−0.210888	+	0.365269i
$989$	−46.8335			−1.48922
$990$		0			0
$991$		−	16.5362i		−	0.525288i	−0.964893	−	0.262644i	$-0.915405\pi$
$991$		−	16.5362i		−	0.525288i	0.964893	−	0.262644i	$-0.0845945\pi$
$992$	−9.35145			−0.296909
$993$		0			0
$994$	−0.0249385	−	0.0143982i	−0.000791000	−	0.000456684i
$995$	2.03151	−	3.51868i	0.0644032	−	0.111550i
$996$		0			0
$997$	−17.5565	+	10.1363i	−0.556021	+	0.321019i	−0.751547	−	0.659680i	$-0.770692\pi$
$997$	−17.5565	+	10.1363i	−0.556021	+	0.321019i	0.195526	+	0.980698i	$0.437359\pi$
$998$	−3.32725			−0.105322
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.t.a.397.33		76
3.2	odd	2		666.2.t.a.619.13	yes	76
9.4	even	3		1998.2.k.a.1063.32		76
9.5	odd	6		666.2.k.a.175.1	✓	76
37.11	even	6		1998.2.k.a.1639.7		76
111.11	odd	6		666.2.k.a.529.20	yes	76
333.85	even	6	inner	1998.2.t.a.307.33		76
333.122	odd	6		666.2.t.a.85.13	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.1	✓	76	9.5	odd	6
666.2.k.a.529.20	yes	76	111.11	odd	6
666.2.t.a.85.13	yes	76	333.122	odd	6
666.2.t.a.619.13	yes	76	3.2	odd	2
1998.2.k.a.1063.32		76	9.4	even	3
1998.2.k.a.1639.7		76	37.11	even	6
1998.2.t.a.307.33		76	333.85	even	6	inner
1998.2.t.a.397.33		76	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1998 = 2 \cdot 3^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1998.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.323001 - 0.186485i) q^{5} -0.0420982 q^{7} -1.00000i q^{8} -0.372969 q^{10} +(-1.29042 + 2.23507i) q^{11} +(-1.93306 - 1.11605i) q^{13} +(-0.0364581 + 0.0210491i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.25134 + 1.29981i) q^{17} +(5.14372 - 2.96973i) q^{19} +(-0.323001 + 0.186485i) q^{20} +2.58084i q^{22} +(3.66709 - 2.11720i) q^{23} +(-2.43045 - 4.20966i) q^{25} -2.23210 q^{26} +(-0.0210491 + 0.0364581i) q^{28} +(-0.672857 - 0.388474i) q^{29} +(8.09859 - 4.67573i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.59962 q^{34} +(0.0135978 + 0.00785067i) q^{35} +(5.51271 - 2.57099i) q^{37} +(2.96973 - 5.14372i) q^{38} +(-0.186485 + 0.323001i) q^{40} +(3.61683 - 6.26454i) q^{41} +(-9.57847 - 5.53013i) q^{43} +(1.29042 + 2.23507i) q^{44} +(2.11720 - 3.66709i) q^{46} +(5.02395 - 8.70173i) q^{47} -6.99823 q^{49} +(-4.20966 - 2.43045i) q^{50} +(-1.93306 + 1.11605i) q^{52} +(-3.61144 + 6.25519i) q^{53} +(0.833612 - 0.481286i) q^{55} +0.0420982i q^{56} -0.776949 q^{58} +12.5360i q^{59} -9.35171i q^{61} +(4.67573 - 8.09859i) q^{62} -1.00000 q^{64} +(0.416253 + 0.720971i) q^{65} +(-1.16092 + 2.01077i) q^{67} +(2.25134 - 1.29981i) q^{68} +0.0157013 q^{70} +(0.342015 + 0.592387i) q^{71} +13.1748 q^{73} +(3.48865 - 4.98290i) q^{74} -5.93946i q^{76} +(0.0543243 - 0.0940925i) q^{77} +3.92502i q^{79} +0.372969i q^{80} -7.23366i q^{82} +(-4.18421 - 7.24727i) q^{83} +(-0.484789 - 0.839680i) q^{85} -11.0603 q^{86} +(2.23507 + 1.29042i) q^{88} +(-5.63029 - 3.25065i) q^{89} +(0.0813784 + 0.0469838i) q^{91} -4.23439i q^{92} -10.0479i q^{94} -2.21523 q^{95} +(5.13338 + 2.96376i) q^{97} +(-6.06064 + 3.49911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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