LMFDB - Embedded newform 783.2.e.a.262.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(262,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.262"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			262.10
Character	$\chi$	$=$	783.262
Dual form			783.2.e.a.523.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10224 - 1.90914i) q^{2} +(-1.42988 - 2.47662i) q^{4} +(0.463291 + 0.802444i) q^{5} +(2.26860 - 3.92934i) q^{7} -1.89533 q^{8} +2.04264 q^{10} +(-1.20435 + 2.08600i) q^{11} +(-0.371618 - 0.643660i) q^{13} +(-5.00111 - 8.66217i) q^{14} +(0.770648 - 1.33480i) q^{16} +5.13650 q^{17} -5.36170 q^{19} +(1.32490 - 2.29480i) q^{20} +(2.65498 + 4.59856i) q^{22} +(-0.335860 - 0.581727i) q^{23} +(2.07072 - 3.58660i) q^{25} -1.63845 q^{26} -12.9753 q^{28} +(-0.500000 + 0.866025i) q^{29} +(-1.44652 - 2.50544i) q^{31} +(-3.59421 - 6.22535i) q^{32} +(5.66167 - 9.80630i) q^{34} +4.20410 q^{35} +4.90470 q^{37} +(-5.90990 + 10.2362i) q^{38} +(-0.878089 - 1.52089i) q^{40} +(1.06714 + 1.84833i) q^{41} +(-5.53316 + 9.58372i) q^{43} +6.88832 q^{44} -1.48080 q^{46} +(-4.29186 + 7.43372i) q^{47} +(-6.79313 - 11.7660i) q^{49} +(-4.56488 - 7.90660i) q^{50} +(-1.06274 + 1.84071i) q^{52} -10.5674 q^{53} -2.23186 q^{55} +(-4.29975 + 7.44738i) q^{56} +(1.10224 + 1.90914i) q^{58} +(4.71055 + 8.15891i) q^{59} +(4.51517 - 7.82051i) q^{61} -6.37765 q^{62} -12.7642 q^{64} +(0.344334 - 0.596405i) q^{65} +(3.04601 + 5.27585i) q^{67} +(-7.34458 - 12.7212i) q^{68} +(4.63394 - 8.02621i) q^{70} +12.8590 q^{71} +0.359617 q^{73} +(5.40617 - 9.36376i) q^{74} +(7.66659 + 13.2789i) q^{76} +(5.46440 + 9.46461i) q^{77} +(-1.69119 + 2.92923i) q^{79} +1.42814 q^{80} +4.70497 q^{82} +(3.23863 - 5.60948i) q^{83} +(2.37970 + 4.12175i) q^{85} +(12.1978 + 21.1272i) q^{86} +(2.28264 - 3.95365i) q^{88} -0.921884 q^{89} -3.37221 q^{91} +(-0.960479 + 1.66360i) q^{92} +(9.46134 + 16.3875i) q^{94} +(-2.48403 - 4.30246i) q^{95} +(1.17421 - 2.03379i) q^{97} -29.9507 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 5 q^{4} - q^{5} + 7 q^{7} - 6 q^{8} - 20 q^{10} + 3 q^{11} + 7 q^{13} - 10 q^{14} + 7 q^{16} - 2 q^{17} - 56 q^{19} - 4 q^{20} + 13 q^{22} + 4 q^{23} + 4 q^{25} + 12 q^{26} - 32 q^{28}+ \cdots - 86 q^{98}+O(q^{100}) $ 22 * q + q^2 - 5 * q^4 - q^5 + 7 * q^7 - 6 * q^8 - 20 * q^10 + 3 * q^11 + 7 * q^13 - 10 * q^14 + 7 * q^16 - 2 * q^17 - 56 * q^19 - 4 * q^20 + 13 * q^22 + 4 * q^23 + 4 * q^25 + 12 * q^26 - 32 * q^28 - 11 * q^29 + 27 * q^31 + 7 * q^32 + 19 * q^34 + 22 * q^35 - 28 * q^37 - 5 * q^38 + 24 * q^40 - 9 * q^41 + 25 * q^43 - 46 * q^44 - 20 * q^46 + 6 * q^47 + 12 * q^49 + 41 * q^50 + 20 * q^52 + 12 * q^53 - 70 * q^55 - 10 * q^56 + q^58 + 25 * q^61 + 12 * q^62 - 50 * q^64 + 5 * q^65 + 29 * q^67 - 50 * q^68 + 7 * q^70 + 2 * q^71 - 26 * q^73 + 14 * q^74 + 38 * q^76 + 9 * q^77 + 27 * q^79 + 74 * q^80 - 34 * q^82 - 12 * q^83 + 7 * q^85 + q^86 - 5 * q^88 - 46 * q^89 - 86 * q^91 + 19 * q^92 - 10 * q^94 + 8 * q^95 + 36 * q^97 - 86 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.10224	−	1.90914i	0.779404	−	1.34997i	−0.152882	−	0.988244i	$-0.548856\pi$
$2$	1.10224	−	1.90914i	0.779404	−	1.34997i	0.932286	−	0.361722i	$-0.117811\pi$
$3$		0			0
$3$		0			0
$4$	−1.42988	−	2.47662i	−0.714940	−	1.23831i
$5$	0.463291	+	0.802444i	0.207190	+	0.358864i	0.950828	−	0.309718i	$-0.100235\pi$
$5$	0.463291	+	0.802444i	0.207190	+	0.358864i	−0.743638	+	0.668582i	$0.766901\pi$
$6$		0			0
$7$	2.26860	−	3.92934i	0.857452	−	1.48515i	−0.0169002	−	0.999857i	$-0.505380\pi$
$7$	2.26860	−	3.92934i	0.857452	−	1.48515i	0.874352	−	0.485293i	$-0.161287\pi$
$8$	−1.89533			−0.670099
$9$		0			0
$10$	2.04264			0.645939
$11$	−1.20435	+	2.08600i	−0.363126	+	0.628953i	−0.988474	−	0.151394i	$-0.951624\pi$
$11$	−1.20435	+	2.08600i	−0.363126	+	0.628953i	0.625348	+	0.780346i	$0.284957\pi$
$12$		0			0
$13$	−0.371618	−	0.643660i	−0.103068	−	0.178519i	0.809879	−	0.586597i	$-0.199533\pi$
$13$	−0.371618	−	0.643660i	−0.103068	−	0.178519i	−0.912947	+	0.408078i	$0.866199\pi$
$14$	−5.00111	−	8.66217i	−1.33660	−	2.31506i
$15$		0			0
$16$	0.770648	−	1.33480i	0.192662	−	0.333700i
$17$	5.13650			1.24578			0.622892	−	0.782308i	$-0.285958\pi$
$17$	5.13650			1.24578			0.622892	+	0.782308i	$0.285958\pi$
$18$		0			0
$19$	−5.36170			−1.23006			−0.615029	−	0.788504i	$-0.710856\pi$
$19$	−5.36170			−1.23006			−0.615029	+	0.788504i	$0.710856\pi$
$20$	1.32490	−	2.29480i	0.296257	−	0.513132i
$21$		0			0
$22$	2.65498	+	4.59856i	0.566043	+	0.980416i
$23$	−0.335860	−	0.581727i	−0.0700317	−	0.121298i	0.828883	−	0.559422i	$-0.188977\pi$
$23$	−0.335860	−	0.581727i	−0.0700317	−	0.121298i	−0.898915	+	0.438123i	$0.855643\pi$
$24$		0			0
$25$	2.07072	−	3.58660i	0.414144	−	0.717319i
$26$	−1.63845			−0.321327
$27$		0			0
$28$	−12.9753			−2.45211
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i
$30$		0			0
$31$	−1.44652	−	2.50544i	−0.259802	−	0.449990i	0.706387	−	0.707826i	$-0.250324\pi$
$31$	−1.44652	−	2.50544i	−0.259802	−	0.449990i	−0.966189	+	0.257836i	$0.916991\pi$
$32$	−3.59421	−	6.22535i	−0.635373	−	1.10050i
$33$		0			0
$34$	5.66167	−	9.80630i	0.970969	−	1.68177i
$35$	4.20410			0.710622
$36$		0			0
$37$	4.90470			0.806327			0.403164	−	0.915128i	$-0.367911\pi$
$37$	4.90470			0.806327			0.403164	+	0.915128i	$0.367911\pi$
$38$	−5.90990	+	10.2362i	−0.958712	+	1.66054i
$39$		0			0
$40$	−0.878089	−	1.52089i	−0.138838	−	0.240474i
$41$	1.06714	+	1.84833i	0.166659	+	0.288661i	0.937243	−	0.348677i	$-0.113369\pi$
$41$	1.06714	+	1.84833i	0.166659	+	0.288661i	−0.770584	+	0.637338i	$0.780036\pi$
$42$		0			0
$43$	−5.53316	+	9.58372i	−0.843799	+	1.46150i	0.0428610	+	0.999081i	$0.486353\pi$
$43$	−5.53316	+	9.58372i	−0.843799	+	1.46150i	−0.886660	+	0.462422i	$0.846981\pi$
$44$	6.88832			1.03845
$45$		0			0
$46$	−1.48080			−0.218332
$47$	−4.29186	+	7.43372i	−0.626032	+	1.08432i	0.362308	+	0.932058i	$0.381989\pi$
$47$	−4.29186	+	7.43372i	−0.626032	+	1.08432i	−0.988340	+	0.152261i	$0.951345\pi$
$48$		0			0
$49$	−6.79313	−	11.7660i	−0.970447	−	1.68086i
$50$	−4.56488	−	7.90660i	−0.645571	−	1.11816i
$51$		0			0
$52$	−1.06274	+	1.84071i	−0.147375	+	0.255261i
$53$	−10.5674			−1.45154			−0.725771	−	0.687936i	$-0.758517\pi$
$53$	−10.5674			−1.45154			−0.725771	+	0.687936i	$0.758517\pi$
$54$		0			0
$55$	−2.23186			−0.300944
$56$	−4.29975	+	7.44738i	−0.574578	+	0.995198i
$57$		0			0
$58$	1.10224	+	1.90914i	0.144732	+	0.250682i
$59$	4.71055	+	8.15891i	0.613262	+	1.06220i	0.990687	+	0.136160i	$0.0434762\pi$
$59$	4.71055	+	8.15891i	0.613262	+	1.06220i	−0.377425	+	0.926040i	$0.623191\pi$
$60$		0			0
$61$	4.51517	−	7.82051i	0.578109	−	1.00131i	−0.417587	−	0.908637i	$-0.637124\pi$
$61$	4.51517	−	7.82051i	0.578109	−	1.00131i	0.995696	−	0.0926771i	$-0.0295424\pi$
$62$	−6.37765			−0.809962
$63$		0			0
$64$	−12.7642			−1.59552
$65$	0.344334	−	0.596405i	0.0427094	−	0.0739749i
$66$		0			0
$67$	3.04601	+	5.27585i	0.372130	+	0.644548i	0.989893	−	0.141817i	$-0.0452943\pi$
$67$	3.04601	+	5.27585i	0.372130	+	0.644548i	−0.617763	+	0.786364i	$0.711961\pi$
$68$	−7.34458	−	12.7212i	−0.890661	−	1.54267i
$69$		0			0
$70$	4.63394	−	8.02621i	0.553861	−	0.959316i
$71$	12.8590			1.52608			0.763039	−	0.646353i	$-0.223707\pi$
$71$	12.8590			1.52608			0.763039	+	0.646353i	$0.223707\pi$
$72$		0			0
$73$	0.359617			0.0420899			0.0210450	−	0.999779i	$-0.493301\pi$
$73$	0.359617			0.0420899			0.0210450	+	0.999779i	$0.493301\pi$
$74$	5.40617	−	9.36376i	0.628454	−	1.08852i
$75$		0			0
$76$	7.66659	+	13.2789i	0.879418	+	1.52320i
$77$	5.46440	+	9.46461i	0.622726	+	1.07859i
$78$		0			0
$79$	−1.69119	+	2.92923i	−0.190274	+	0.329564i	−0.945341	−	0.326083i	$-0.894271\pi$
$79$	−1.69119	+	2.92923i	−0.190274	+	0.329564i	0.755067	+	0.655648i	$0.227604\pi$
$80$	1.42814			0.159671
$81$		0			0
$82$	4.70497			0.519577
$83$	3.23863	−	5.60948i	0.355486	−	0.615720i	−0.631715	−	0.775201i	$-0.717649\pi$
$83$	3.23863	−	5.60948i	0.355486	−	0.615720i	0.987201	+	0.159481i	$0.0509820\pi$
$84$		0			0
$85$	2.37970	+	4.12175i	0.258114	+	0.447067i
$86$	12.1978	+	21.1272i	1.31532	+	2.27820i
$87$		0			0
$88$	2.28264	−	3.95365i	0.243330	−	0.421461i
$89$	−0.921884			−0.0977195			−0.0488598	−	0.998806i	$-0.515559\pi$
$89$	−0.921884			−0.0977195			−0.0488598	+	0.998806i	$0.515559\pi$
$90$		0			0
$91$	−3.37221			−0.353504
$92$	−0.960479	+	1.66360i	−0.100137	+	0.173442i
$93$		0			0
$94$	9.46134	+	16.3875i	0.975863	+	1.69024i
$95$	−2.48403	−	4.30246i	−0.254856	−	0.441424i
$96$		0			0
$97$	1.17421	−	2.03379i	0.119223	−	0.206500i	−0.800237	−	0.599684i	$-0.795293\pi$
$97$	1.17421	−	2.03379i	0.119223	−	0.206500i	0.919460	+	0.393184i	$0.128626\pi$
$98$	−29.9507			−3.02548
$99$		0			0
$100$	−11.8435			−1.18435
$101$	−3.27997	+	5.68107i	−0.326369	+	0.565288i	−0.981788	−	0.189977i	$-0.939159\pi$
$101$	−3.27997	+	5.68107i	−0.326369	+	0.565288i	0.655419	+	0.755265i	$0.272492\pi$
$102$		0			0
$103$	6.89267	+	11.9385i	0.679155	+	1.17633i	0.975236	+	0.221169i	$0.0709871\pi$
$103$	6.89267	+	11.9385i	0.679155	+	1.17633i	−0.296080	+	0.955163i	$0.595680\pi$
$104$	0.704337	+	1.21995i	0.0690659	+	0.119626i
$105$		0			0
$106$	−11.6478	+	20.1746i	−1.13134	+	1.95953i
$107$	4.16667			0.402807			0.201404	−	0.979508i	$-0.435450\pi$
$107$	4.16667			0.402807			0.201404	+	0.979508i	$0.435450\pi$
$108$		0			0
$109$	17.2935			1.65642			0.828210	−	0.560418i	$-0.189359\pi$
$109$	17.2935			1.65642			0.828210	+	0.560418i	$0.189359\pi$
$110$	−2.46006	+	4.26094i	−0.234557	+	0.406265i
$111$		0			0
$112$	−3.49659	−	6.05627i	−0.330397	−	0.572264i
$113$	−2.72887	−	4.72655i	−0.256711	−	0.444636i	0.708648	−	0.705562i	$-0.249305\pi$
$113$	−2.72887	−	4.72655i	−0.256711	−	0.444636i	−0.965359	+	0.260926i	$0.915972\pi$
$114$		0			0
$115$	0.311202	−	0.539018i	0.0290197	−	0.0502637i
$116$	2.85976			0.265522
$117$		0			0
$118$	20.7687			1.91191
$119$	11.6527	−	20.1830i	1.06820	−	1.85018i
$120$		0			0
$121$	2.59907	+	4.50172i	0.236279	+	0.409247i
$122$	−9.95364	−	17.2402i	−0.901160	−	1.56086i
$123$		0			0
$124$	−4.13669	+	7.16495i	−0.371485	+	0.643431i
$125$	8.47030			0.757607
$126$		0			0
$127$	−2.77140			−0.245922			−0.122961	−	0.992411i	$-0.539239\pi$
$127$	−2.77140			−0.245922			−0.122961	+	0.992411i	$0.539239\pi$
$128$	−6.88081	+	11.9179i	−0.608183	+	1.05340i
$129$		0			0
$130$	−0.759080	−	1.31477i	−0.0665757	−	0.115313i
$131$	10.1056	+	17.5034i	0.882928	+	1.52928i	0.848070	+	0.529884i	$0.177765\pi$
$131$	10.1056	+	17.5034i	0.882928	+	1.52928i	0.0348584	+	0.999392i	$0.488902\pi$
$132$		0			0
$133$	−12.1636	+	21.0679i	−1.05472	+	1.82682i
$134$	13.4298			1.16016
$135$		0			0
$136$	−9.73535			−0.834799
$137$	−8.17049	+	14.1517i	−0.698052	+	1.20906i	0.271089	+	0.962554i	$0.412616\pi$
$137$	−8.17049	+	14.1517i	−0.698052	+	1.20906i	−0.969141	+	0.246508i	$0.920717\pi$
$138$		0			0
$139$	10.1406	+	17.5641i	0.860118	+	1.48977i	0.871814	+	0.489836i	$0.162943\pi$
$139$	10.1406	+	17.5641i	0.860118	+	1.48977i	−0.0116965	+	0.999932i	$0.503723\pi$
$140$	−6.01135	−	10.4120i	−0.508052	−	0.879972i
$141$		0			0
$142$	14.1737	−	24.5496i	1.18943	−	2.06015i
$143$	1.79023			0.149707
$144$		0			0
$145$	−0.926583			−0.0769485
$146$	0.396385	−	0.686559i	0.0328051	−	0.0568200i
$147$		0			0
$148$	−7.01313	−	12.1471i	−0.576476	−	0.998485i
$149$	−3.65821	−	6.33621i	−0.299693	−	0.519083i	0.676373	−	0.736559i	$-0.263551\pi$
$149$	−3.65821	−	6.33621i	−0.299693	−	0.519083i	−0.976066	+	0.217477i	$0.930217\pi$
$150$		0			0
$151$	7.24188	−	12.5433i	0.589336	−	1.02076i	−0.404983	−	0.914324i	$-0.632723\pi$
$151$	7.24188	−	12.5433i	0.589336	−	1.02076i	0.994320	−	0.106436i	$-0.0339440\pi$
$152$	10.1622			0.824261
$153$		0			0
$154$	24.0924			1.94142
$155$	1.34032	−	2.32150i	0.107657	−	0.186467i
$156$		0			0
$157$	−1.86899	−	3.23719i	−0.149162	−	0.258356i	0.781756	−	0.623584i	$-0.214324\pi$
$157$	−1.86899	−	3.23719i	−0.149162	−	0.258356i	−0.930918	+	0.365229i	$0.880991\pi$
$158$	3.72821	+	6.45745i	0.296601	+	0.513727i
$159$		0			0
$160$	3.33033	−	5.76830i	0.263286	−	0.456025i
$161$	−3.04773			−0.240195
$162$		0			0
$163$	−14.2825			−1.11869			−0.559344	−	0.828936i	$-0.688947\pi$
$163$	−14.2825			−1.11869			−0.559344	+	0.828936i	$0.688947\pi$
$164$	3.05175	−	5.28579i	0.238302	−	0.412751i
$165$		0			0
$166$	−7.13952	−	12.3660i	−0.554134	−	0.959789i
$167$	1.78844	+	3.09767i	0.138394	+	0.239705i	0.926889	−	0.375336i	$-0.122473\pi$
$167$	1.78844	+	3.09767i	0.138394	+	0.239705i	−0.788495	+	0.615041i	$0.789139\pi$
$168$		0			0
$169$	6.22380	−	10.7799i	0.478754	−	0.829226i
$170$	10.4920			0.804701
$171$		0			0
$172$	31.6470			2.41306
$173$	11.1252	−	19.2693i	0.845830	−	1.46502i	−0.0390687	−	0.999237i	$-0.512439\pi$
$173$	11.1252	−	19.2693i	0.845830	−	1.46502i	0.884899	−	0.465784i	$-0.154228\pi$
$174$		0			0
$175$	−9.39530	−	16.2731i	−0.710218	−	1.23013i
$176$	1.85626	+	3.21514i	0.139921	+	0.242350i
$177$		0			0
$178$	−1.01614	+	1.76001i	−0.0761629	+	0.131918i
$179$	−16.9360			−1.26585			−0.632927	−	0.774212i	$-0.718147\pi$
$179$	−16.9360			−1.26585			−0.632927	+	0.774212i	$0.718147\pi$
$180$		0			0
$181$	−0.223217			−0.0165916			−0.00829581	−	0.999966i	$-0.502641\pi$
$181$	−0.223217			−0.0165916			−0.00829581	+	0.999966i	$0.502641\pi$
$182$	−3.71700	+	6.43803i	−0.275522	+	0.477218i
$183$		0			0
$184$	0.636565	+	1.10256i	0.0469282	+	0.0812820i
$185$	2.27230	+	3.93575i	0.167063	+	0.289362i
$186$		0			0
$187$	−6.18616	+	10.7147i	−0.452377	+	0.783539i
$188$	24.5474			1.79030
$189$		0			0
$190$	−10.9520			−0.794543
$191$	0.851901	−	1.47554i	0.0616414	−	0.106766i	−0.833558	−	0.552432i	$-0.813700\pi$
$191$	0.851901	−	1.47554i	0.0616414	−	0.106766i	0.895199	+	0.445666i	$0.147033\pi$
$192$		0			0
$193$	−11.6175	−	20.1221i	−0.836245	−	1.44842i	−0.893012	−	0.450032i	$-0.851413\pi$
$193$	−11.6175	−	20.1221i	−0.836245	−	1.44842i	0.0567668	−	0.998387i	$-0.481921\pi$
$194$	−2.58853	−	4.48347i	−0.185846	−	0.321894i
$195$		0			0
$196$	−19.4267	+	33.6480i	−1.38762	+	2.40343i
$197$	−3.11364			−0.221838			−0.110919	−	0.993829i	$-0.535379\pi$
$197$	−3.11364			−0.221838			−0.110919	+	0.993829i	$0.535379\pi$
$198$		0			0
$199$	−25.7334			−1.82419			−0.912096	−	0.409977i	$-0.865537\pi$
$199$	−25.7334			−1.82419			−0.912096	+	0.409977i	$0.865537\pi$
$200$	−3.92470	+	6.79777i	−0.277518	+	0.480675i
$201$		0			0
$202$	7.23064	+	12.5238i	0.508746	+	0.881175i
$203$	2.26860	+	3.92934i	0.159225	+	0.275785i
$204$		0			0
$205$	−0.988790	+	1.71263i	−0.0690601	+	0.119616i
$206$	30.3896			2.11734
$207$		0			0
$208$	−1.14555			−0.0794293
$209$	6.45738	−	11.1845i	0.446666	−	0.773648i
$210$		0			0
$211$	5.60533	+	9.70871i	0.385887	+	0.668375i	0.991892	−	0.127085i	$-0.0405622\pi$
$211$	5.60533	+	9.70871i	0.385887	+	0.668375i	−0.606005	+	0.795461i	$0.707229\pi$
$212$	15.1101	+	26.1715i	1.03777	+	1.79746i
$213$		0			0
$214$	4.59268	−	7.95476i	0.313949	−	0.543776i
$215$	−10.2539			−0.699307
$216$		0			0
$217$	−13.1263			−0.891070
$218$	19.0617	−	33.0158i	1.29102	−	2.23611i
$219$		0			0
$220$	3.19130	+	5.52749i	0.215157	+	0.372663i
$221$	−1.90881	−	3.30616i	−0.128401	−	0.222396i
$222$		0			0
$223$	−3.38054	+	5.85527i	−0.226378	+	0.392098i	−0.956732	−	0.290971i	$-0.906022\pi$
$223$	−3.38054	+	5.85527i	−0.226378	+	0.392098i	0.730354	+	0.683069i	$0.239355\pi$
$224$	−32.6154			−2.17920
$225$		0			0
$226$	−12.0315			−0.800326
$227$	−10.9012	+	18.8815i	−0.723541	+	1.25321i	0.236031	+	0.971745i	$0.424153\pi$
$227$	−10.9012	+	18.8815i	−0.723541	+	1.25321i	−0.959572	+	0.281464i	$0.909180\pi$
$228$		0			0
$229$	3.56571	+	6.17600i	0.235629	+	0.408121i	0.959455	−	0.281861i	$-0.0909517\pi$
$229$	3.56571	+	6.17600i	0.235629	+	0.408121i	−0.723826	+	0.689982i	$0.757618\pi$
$230$	−0.686041	−	1.18826i	−0.0452362	−	0.0783514i
$231$		0			0
$232$	0.947664	−	1.64140i	0.0622172	−	0.107763i
$233$	−15.6138			−1.02289			−0.511447	−	0.859315i	$-0.670890\pi$
$233$	−15.6138			−1.02289			−0.511447	+	0.859315i	$0.670890\pi$
$234$		0			0
$235$	−7.95352			−0.518831
$236$	13.4710	−	23.3325i	0.876890	−	1.51882i
$237$		0			0
$238$	−25.6882	−	44.4932i	−1.66512	−	2.88407i
$239$	−0.805993	−	1.39602i	−0.0521353	−	0.0903011i	0.838780	−	0.544471i	$-0.183269\pi$
$239$	−0.805993	−	1.39602i	−0.0521353	−	0.0903011i	−0.890915	+	0.454169i	$0.849936\pi$
$240$		0			0
$241$	−3.96719	+	6.87137i	−0.255549	+	0.442624i	−0.965045	−	0.262086i	$-0.915590\pi$
$241$	−3.96719	+	6.87137i	−0.255549	+	0.442624i	0.709495	+	0.704710i	$0.248923\pi$
$242$	11.4592			0.736627
$243$		0			0
$244$	−25.8246			−1.65325
$245$	6.29439	−	10.9022i	0.402134	−	0.696516i
$246$		0			0
$247$	1.99250	+	3.45111i	0.126780	+	0.219589i
$248$	2.74162	+	4.74863i	0.174093	+	0.301538i
$249$		0			0
$250$	9.33633	−	16.1710i	0.590482	−	1.02274i
$251$	−15.2548			−0.962878			−0.481439	−	0.876480i	$-0.659886\pi$
$251$	−15.2548			−0.962878			−0.481439	+	0.876480i	$0.659886\pi$
$252$		0			0
$253$	1.61798			0.101721
$254$	−3.05476	+	5.29100i	−0.191673	+	0.331987i
$255$		0			0
$256$	2.40447	+	4.16466i	0.150279	+	0.260291i
$257$	7.86293	+	13.6190i	0.490476	+	0.849529i	0.999940	−	0.0109627i	$-0.00348962\pi$
$257$	7.86293	+	13.6190i	0.490476	+	0.849529i	−0.509464	+	0.860492i	$0.670156\pi$
$258$		0			0
$259$	11.1268	−	19.2722i	0.691387	−	1.19752i
$260$	−1.96943			−0.122139
$261$		0			0
$262$	44.5552			2.75263
$263$	−3.64686	+	6.31655i	−0.224875	+	0.389495i	−0.956282	−	0.292446i	$-0.905531\pi$
$263$	−3.64686	+	6.31655i	−0.224875	+	0.389495i	0.731407	+	0.681941i	$0.238864\pi$
$264$		0			0
$265$	−4.89578	−	8.47974i	−0.300745	−	0.520906i
$266$	26.8144	+	46.4440i	1.64410	+	2.84766i
$267$		0			0
$268$	8.71086	−	15.0877i	0.532101	−	0.921626i
$269$	−13.9167			−0.848516			−0.424258	−	0.905541i	$-0.639465\pi$
$269$	−13.9167			−0.848516			−0.424258	+	0.905541i	$0.639465\pi$
$270$		0			0
$271$	−5.89268			−0.357955			−0.178978	−	0.983853i	$-0.557279\pi$
$271$	−5.89268			−0.357955			−0.178978	+	0.983853i	$0.557279\pi$
$272$	3.95843	−	6.85621i	0.240015	−	0.415719i
$273$		0			0
$274$	18.0117	+	31.1972i	1.08813	+	1.88469i
$275$	4.98776	+	8.63905i	0.300773	+	0.520954i
$276$		0			0
$277$	−4.07099	+	7.05117i	−0.244602	+	0.423664i	−0.962020	−	0.272980i	$-0.911991\pi$
$277$	−4.07099	+	7.05117i	−0.244602	+	0.423664i	0.717417	+	0.696644i	$0.245324\pi$
$278$	44.7098			2.68152
$279$		0			0
$280$	−7.96814			−0.476187
$281$	10.0913	−	17.4787i	0.601999	−	1.04269i	−0.390519	−	0.920595i	$-0.627704\pi$
$281$	10.0913	−	17.4787i	0.601999	−	1.04269i	0.992518	−	0.122098i	$-0.0389624\pi$
$282$		0			0
$283$	13.7058	+	23.7391i	0.814725	+	1.41114i	0.909526	+	0.415648i	$0.136445\pi$
$283$	13.7058	+	23.7391i	0.814725	+	1.41114i	−0.0948010	+	0.995496i	$0.530221\pi$
$284$	−18.3868	−	31.8468i	−1.09105	−	1.88976i
$285$		0			0
$286$	1.97327	−	3.41781i	0.116682	−	0.202099i
$287$	9.68364			0.571607
$288$		0			0
$289$	9.38363			0.551978
$290$	−1.02132	+	1.76898i	−0.0599739	+	0.103878i
$291$		0			0
$292$	−0.514209	−	0.890635i	−0.0300918	−	0.0521205i
$293$	3.21385	+	5.56655i	0.187755	+	0.325201i	0.944501	−	0.328507i	$-0.106546\pi$
$293$	3.21385	+	5.56655i	0.187755	+	0.325201i	−0.756746	+	0.653709i	$0.773212\pi$
$294$		0			0
$295$	−4.36471	+	7.55991i	−0.254124	+	0.440155i
$296$	−9.29601			−0.540319
$297$		0			0
$298$	−16.1290			−0.934326
$299$	−0.249623	+	0.432360i	−0.0144361	+	0.0250040i
$300$		0			0
$301$	25.1051	+	43.4833i	1.44703	+	2.50634i
$302$	−15.9646	−	27.6516i	−0.918661	−	1.59117i
$303$		0			0
$304$	−4.13198	+	7.15680i	−0.236985	+	0.410471i
$305$	8.36736			0.479114
$306$		0			0
$307$	13.2099			0.753928			0.376964	−	0.926228i	$-0.376968\pi$
$307$	13.2099			0.753928			0.376964	+	0.926228i	$0.376968\pi$
$308$	15.6269	−	27.0665i	0.890423	−	1.54226i
$309$		0			0
$310$	−2.95471	−	5.11770i	−0.167816	−	0.290666i
$311$	−7.98502	−	13.8305i	−0.452789	−	0.784254i	0.545769	−	0.837936i	$-0.316238\pi$
$311$	−7.98502	−	13.8305i	−0.452789	−	0.784254i	−0.998558	+	0.0536819i	$0.982904\pi$
$312$		0			0
$313$	11.1558	−	19.3225i	0.630564	−	1.09217i	−0.356872	−	0.934153i	$-0.616157\pi$
$313$	11.1558	−	19.3225i	0.630564	−	1.09217i	0.987436	−	0.158016i	$-0.0505099\pi$
$314$	−8.24033			−0.465028
$315$		0			0
$316$	9.67281			0.544138
$317$	1.57365	−	2.72565i	0.0883852	−	0.153088i	−0.818443	−	0.574587i	$-0.805163\pi$
$317$	1.57365	−	2.72565i	0.0883852	−	0.153088i	0.906829	+	0.421499i	$0.138496\pi$
$318$		0			0
$319$	−1.20435	−	2.08600i	−0.0674308	−	0.116794i
$320$	−5.91353	−	10.2425i	−0.330577	−	0.572575i
$321$		0			0
$322$	−3.35934	+	5.81855i	−0.187209	+	0.324255i
$323$	−27.5404			−1.53239
$324$		0			0
$325$	−3.07807			−0.170740
$326$	−15.7427	+	27.2672i	−0.871909	+	1.51019i
$327$		0			0
$328$	−2.02257	−	3.50320i	−0.111678	−	0.193432i
$329$	19.4731	+	33.7283i	1.07358	+	1.85950i
$330$		0			0
$331$	8.92523	−	15.4590i	0.490575	−	0.849701i	−0.509366	−	0.860550i	$-0.670120\pi$
$331$	8.92523	−	15.4590i	0.490575	−	0.849701i	0.999941	+	0.0108490i	$0.00345342\pi$
$332$	−18.5234			−1.01660
$333$		0			0
$334$	7.88518			0.431458
$335$	−2.82238	+	4.88851i	−0.154203	+	0.267088i
$336$		0			0
$337$	15.8508	+	27.4544i	0.863447	+	1.49553i	0.868581	+	0.495547i	$0.165032\pi$
$337$	15.8508	+	27.4544i	0.863447	+	1.49553i	−0.00513407	+	0.999987i	$0.501634\pi$
$338$	−13.7203	−	23.7642i	−0.746285	−	1.29260i
$339$		0			0
$340$	6.80536	−	11.7872i	0.369072	−	0.639252i
$341$	6.96846			0.377363
$342$		0			0
$343$	−29.8832			−1.61354
$344$	10.4871	−	18.1643i	0.565429	−	0.979352i
$345$		0			0
$346$	−24.5252	−	42.4790i	−1.31849	−	2.28368i
$347$	−16.2161	−	28.0871i	−0.870527	−	1.50780i	−0.861453	−	0.507837i	$-0.830445\pi$
$347$	−16.2161	−	28.0871i	−0.870527	−	1.50780i	−0.00907365	−	0.999959i	$-0.502888\pi$
$348$		0			0
$349$	−0.514758	+	0.891588i	−0.0275544	+	0.0477256i	−0.879474	−	0.475947i	$-0.842105\pi$
$349$	−0.514758	+	0.891588i	−0.0275544	+	0.0477256i	0.851919	+	0.523673i	$0.175439\pi$
$350$	−41.4236			−2.21418
$351$		0			0
$352$	17.3148			0.922881
$353$	−10.0761	+	17.4522i	−0.536294	+	0.928889i	0.462805	+	0.886460i	$0.346843\pi$
$353$	−10.0761	+	17.4522i	−0.536294	+	0.928889i	−0.999099	+	0.0424286i	$0.986490\pi$
$354$		0			0
$355$	5.95744	+	10.3186i	0.316188	+	0.547654i
$356$	1.31818	+	2.28316i	0.0698636	+	0.121007i
$357$		0			0
$358$	−18.6675	+	32.3331i	−0.986611	+	1.70886i
$359$	−27.8483			−1.46978			−0.734890	−	0.678187i	$-0.762766\pi$
$359$	−27.8483			−1.46978			−0.734890	+	0.678187i	$0.762766\pi$
$360$		0			0
$361$	9.74783			0.513044
$362$	−0.246040	+	0.426153i	−0.0129316	+	0.0223981i
$363$		0			0
$364$	4.82186	+	8.35170i	0.252734	+	0.437748i
$365$	0.166607	+	0.288572i	0.00872062	+	0.0151046i
$366$		0			0
$367$	6.87873	−	11.9143i	0.359067	−	0.621922i	−0.628738	−	0.777617i	$-0.716428\pi$
$367$	6.87873	−	11.9143i	0.359067	−	0.621922i	0.987805	+	0.155695i	$0.0497617\pi$
$368$	−1.03532			−0.0539698
$369$		0			0
$370$	10.0185			0.520838
$371$	−23.9732	+	41.5228i	−1.24463	+	2.15576i
$372$		0			0
$373$	−10.5133	−	18.2096i	−0.544358	−	0.942855i	−0.998647	−	0.0520011i	$-0.983440\pi$
$373$	−10.5133	−	18.2096i	−0.544358	−	0.942855i	0.454289	−	0.890854i	$-0.349893\pi$
$374$	13.6373	+	23.6205i	0.705168	+	1.22139i
$375$		0			0
$376$	8.13448	−	14.0893i	0.419504	−	0.726602i
$377$	0.743235			0.0382786
$378$		0			0
$379$	−31.3041			−1.60799			−0.803993	−	0.594639i	$-0.797295\pi$
$379$	−31.3041			−1.60799			−0.803993	+	0.594639i	$0.797295\pi$
$380$	−7.10372	+	12.3040i	−0.364413	+	0.631183i
$381$		0			0
$382$	−1.87801	−	3.25280i	−0.0960871	−	0.166428i
$383$	−9.32276	−	16.1475i	−0.476371	−	0.825099i	0.523262	−	0.852172i	$-0.324715\pi$
$383$	−9.32276	−	16.1475i	−0.476371	−	0.825099i	−0.999633	+	0.0270728i	$0.991381\pi$
$384$		0			0
$385$	−5.06321	+	8.76975i	−0.258045	+	0.446948i
$386$	−51.2212			−2.60709
$387$		0			0
$388$	−6.71592			−0.340949
$389$	−0.703182	+	1.21795i	−0.0356528	+	0.0617524i	−0.883301	−	0.468806i	$-0.844684\pi$
$389$	−0.703182	+	1.21795i	−0.0356528	+	0.0617524i	0.847648	+	0.530558i	$0.178018\pi$
$390$		0			0
$391$	−1.72515	−	2.98804i	−0.0872443	−	0.151112i
$392$	12.8752	+	22.3005i	0.650296	+	1.12634i
$393$		0			0
$394$	−3.43199	+	5.94438i	−0.172901	+	0.299474i
$395$	−3.13406			−0.157692
$396$		0			0
$397$	11.0056			0.552353			0.276177	−	0.961107i	$-0.410933\pi$
$397$	11.0056			0.552353			0.276177	+	0.961107i	$0.410933\pi$
$398$	−28.3644	+	49.1287i	−1.42178	+	2.46260i
$399$		0			0
$400$	−3.19160	−	5.52801i	−0.159580	−	0.276400i
$401$	−7.25219	−	12.5612i	−0.362157	−	0.627274i	0.626159	−	0.779696i	$-0.284626\pi$
$401$	−7.25219	−	12.5612i	−0.362157	−	0.627274i	−0.988316	+	0.152421i	$0.951293\pi$
$402$		0			0
$403$	−1.07510	+	1.86213i	−0.0535546	+	0.0927593i
$404$	18.7598			0.933337
$405$		0			0
$406$	10.0022			0.496401
$407$	−5.90699	+	10.2312i	−0.292798	+	0.507142i
$408$		0			0
$409$	1.77259	+	3.07022i	0.0876490	+	0.151812i	0.906517	−	0.422169i	$-0.138731\pi$
$409$	1.77259	+	3.07022i	0.0876490	+	0.151812i	−0.818868	+	0.573982i	$0.805398\pi$
$410$	2.17977	+	3.77548i	0.107651	+	0.186458i
$411$		0			0
$412$	19.7114	−	34.1411i	0.971110	−	1.68201i
$413$	42.7455			2.10337
$414$		0			0
$415$	6.00172			0.294613
$416$	−2.67134	+	4.62690i	−0.130973	+	0.226852i
$417$		0			0
$418$	−14.2352	−	24.6561i	−0.696266	−	1.20597i
$419$	7.86579	+	13.6239i	0.384269	+	0.665573i	0.991667	−	0.128824i	$-0.0411202\pi$
$419$	7.86579	+	13.6239i	0.384269	+	0.665573i	−0.607399	+	0.794397i	$0.707787\pi$
$420$		0			0
$421$	−4.05975	+	7.03170i	−0.197860	+	0.342704i	−0.947834	−	0.318763i	$-0.896733\pi$
$421$	−4.05975	+	7.03170i	−0.197860	+	0.342704i	0.749974	+	0.661467i	$0.230066\pi$
$422$	24.7137			1.20305
$423$		0			0
$424$	20.0287			0.972678
$425$	10.6363	−	18.4226i	0.515935	−	0.893625i
$426$		0			0
$427$	−20.4863	−	35.4833i	−0.991401	−	1.71716i
$428$	−5.95784	−	10.3193i	−0.287983	−	0.498801i
$429$		0			0
$430$	−11.3022	+	19.5761i	−0.545043	+	0.944042i
$431$	−12.1165			−0.583629			−0.291815	−	0.956475i	$-0.594259\pi$
$431$	−12.1165			−0.583629			−0.291815	+	0.956475i	$0.594259\pi$
$432$		0			0
$433$	3.43459			0.165056			0.0825279	−	0.996589i	$-0.473701\pi$
$433$	3.43459			0.165056			0.0825279	+	0.996589i	$0.473701\pi$
$434$	−14.4684	+	25.0599i	−0.694503	+	1.20291i
$435$		0			0
$436$	−24.7277	−	42.8296i	−1.18424	−	2.05117i
$437$	1.80078	+	3.11904i	0.0861430	+	0.149204i
$438$		0			0
$439$	16.4846	−	28.5522i	0.786768	−	1.36272i	−0.141169	−	0.989986i	$-0.545086\pi$
$439$	16.4846	−	28.5522i	0.786768	−	1.36272i	0.927937	−	0.372737i	$-0.121581\pi$
$440$	4.23011			0.201663
$441$		0			0
$442$	−8.41590			−0.400304
$443$	11.2896	−	19.5541i	0.536384	−	0.929045i	−0.462711	−	0.886509i	$-0.653123\pi$
$443$	11.2896	−	19.5541i	0.536384	−	0.929045i	0.999095	−	0.0425353i	$-0.0135435\pi$
$444$		0			0
$445$	−0.427101	−	0.739760i	−0.0202465	−	0.0350680i
$446$	7.45235	+	12.9079i	0.352879	+	0.611205i
$447$		0			0
$448$	−28.9569	+	50.1548i	−1.36808	+	2.36959i
$449$	−21.7754			−1.02764			−0.513821	−	0.857897i	$-0.671771\pi$
$449$	−21.7754			−1.02764			−0.513821	+	0.857897i	$0.671771\pi$
$450$		0			0
$451$	−5.14083			−0.242072
$452$	−7.80392	+	13.5168i	−0.367066	+	0.635776i
$453$		0			0
$454$	24.0316	+	41.6240i	1.12786	+	1.95351i
$455$	−1.56232	−	2.70601i	−0.0732425	−	0.126860i
$456$		0			0
$457$	−12.2382	+	21.1972i	−0.572480	+	0.991565i	0.423830	+	0.905742i	$0.360685\pi$
$457$	−12.2382	+	21.1972i	−0.572480	+	0.991565i	−0.996310	+	0.0858232i	$0.972648\pi$
$458$	15.7211			0.734600
$459$		0			0
$460$	−1.77993			−0.0829895
$461$	−0.667074	+	1.15541i	−0.0310688	+	0.0538127i	−0.881142	−	0.472852i	$-0.843224\pi$
$461$	−0.667074	+	1.15541i	−0.0310688	+	0.0538127i	0.850073	+	0.526665i	$0.176558\pi$
$462$		0			0
$463$	4.98373	+	8.63207i	0.231613	+	0.401166i	0.958283	−	0.285821i	$-0.0922662\pi$
$463$	4.98373	+	8.63207i	0.231613	+	0.401166i	−0.726670	+	0.686987i	$0.758933\pi$
$464$	0.770648	+	1.33480i	0.0357764	+	0.0619666i
$465$		0			0
$466$	−17.2102	+	29.8090i	−0.797248	+	1.38087i
$467$	−25.1146			−1.16217			−0.581084	−	0.813844i	$-0.697371\pi$
$467$	−25.1146			−1.16217			−0.581084	+	0.813844i	$0.697371\pi$
$468$		0			0
$469$	27.6408			1.27633
$470$	−8.76672	+	15.1844i	−0.404378	+	0.700404i
$471$		0			0
$472$	−8.92804	−	15.4638i	−0.410946	−	0.711780i
$473$	−13.3278	−	23.0843i	−0.612811	−	1.06142i
$474$		0			0
$475$	−11.1026	+	19.2303i	−0.509422	+	0.882345i
$476$	−66.6477			−3.05479
$477$		0			0
$478$	−3.55360			−0.162538
$479$	9.65158	−	16.7170i	0.440992	−	0.763821i	−0.556771	−	0.830666i	$-0.687960\pi$
$479$	9.65158	−	16.7170i	0.440992	−	0.763821i	0.997763	+	0.0668451i	$0.0212933\pi$
$480$		0			0
$481$	−1.82267	−	3.15696i	−0.0831067	−	0.143945i
$482$	8.74561	+	15.1478i	0.398352	+	0.689965i
$483$		0			0
$484$	7.43272	−	12.8738i	0.337851	−	0.585175i
$485$	2.17601			0.0988073
$486$		0			0
$487$	−28.4814			−1.29061			−0.645307	−	0.763923i	$-0.723271\pi$
$487$	−28.4814			−1.29061			−0.645307	+	0.763923i	$0.723271\pi$
$488$	−8.55773	+	14.8224i	−0.387390	+	0.670980i
$489$		0			0
$490$	−13.8759	−	24.0338i	−0.626849	−	1.08573i
$491$	2.06270	+	3.57271i	0.0930886	+	0.161234i	0.908809	−	0.417212i	$-0.136993\pi$
$491$	2.06270	+	3.57271i	0.0930886	+	0.161234i	−0.815721	+	0.578446i	$0.803659\pi$
$492$		0			0
$493$	−2.56825	+	4.44834i	−0.115668	+	0.200343i
$494$	8.78488			0.395251
$495$		0			0
$496$	−4.45902			−0.200216
$497$	29.1719	−	50.5272i	1.30854	−	2.26645i
$498$		0			0
$499$	−5.24487	−	9.08438i	−0.234793	−	0.406673i	0.724420	−	0.689359i	$-0.242108\pi$
$499$	−5.24487	−	9.08438i	−0.234793	−	0.406673i	−0.959212	+	0.282686i	$0.908774\pi$
$500$	−12.1115	−	20.9778i	−0.541643	−	0.938154i
$501$		0			0
$502$	−16.8146	+	29.1237i	−0.750470	+	1.29985i
$503$	39.1480			1.74552			0.872762	−	0.488146i	$-0.162327\pi$
$503$	39.1480			1.74552			0.872762	+	0.488146i	$0.162327\pi$
$504$		0			0
$505$	−6.07832			−0.270482
$506$	1.78340	−	3.08894i	0.0792819	−	0.137320i
$507$		0			0
$508$	3.96277	+	6.86372i	0.175820	+	0.304528i
$509$	−11.0100	−	19.0698i	−0.488009	−	0.845256i	0.511896	−	0.859047i	$-0.328943\pi$
$509$	−11.0100	−	19.0698i	−0.488009	−	0.845256i	−0.999905	+	0.0137913i	$0.995610\pi$
$510$		0			0
$511$	0.815828	−	1.41305i	0.0360901	−	0.0625099i
$512$	−16.9220			−0.747854
$513$		0			0
$514$	34.6674			1.52911
$515$	−6.38663	+	11.0620i	−0.281429	+	0.487449i
$516$		0			0
$517$	−10.3378	−	17.9056i	−0.454657	−	0.787489i
$518$	−24.5289	−	42.4853i	−1.07774	−	1.86670i
$519$		0			0
$520$	−0.652626	+	1.13038i	−0.0286196	+	0.0495705i
$521$	24.1240			1.05689			0.528445	−	0.848967i	$-0.322775\pi$
$521$	24.1240			1.05689			0.528445	+	0.848967i	$0.322775\pi$
$522$		0			0
$523$	−13.5138			−0.590916			−0.295458	−	0.955356i	$-0.595472\pi$
$523$	−13.5138			−0.590916			−0.295458	+	0.955356i	$0.595472\pi$
$524$	28.8995	−	50.0554i	1.26248	−	2.18668i
$525$		0			0
$526$	8.03945	+	13.9247i	0.350537	+	0.607148i
$527$	−7.43003	−	12.8692i	−0.323657	−	0.560590i
$528$		0			0
$529$	11.2744	−	19.5278i	0.490191	−	0.849036i
$530$	−21.5854			−0.937608
$531$		0			0
$532$	69.5698			3.01623
$533$	0.793133	−	1.37375i	0.0343544	−	0.0595036i
$534$		0			0
$535$	1.93038	+	3.34352i	0.0834577	+	0.144553i
$536$	−5.77319	−	9.99946i	−0.249364	−	0.431911i
$537$		0			0
$538$	−15.3396	+	26.5689i	−0.661336	+	1.14547i
$539$	32.7253			1.40958
$540$		0			0
$541$	35.5004			1.52628			0.763141	−	0.646232i	$-0.223656\pi$
$541$	35.5004			1.52628			0.763141	+	0.646232i	$0.223656\pi$
$542$	−6.49517	+	11.2500i	−0.278991	+	0.483227i
$543$		0			0
$544$	−18.4617	−	31.9765i	−0.791537	−	1.37098i
$545$	8.01195	+	13.8771i	0.343194	+	0.594429i
$546$		0			0
$547$	−19.0752	+	33.0391i	−0.815595	+	1.41265i	0.0933055	+	0.995638i	$0.470257\pi$
$547$	−19.0752	+	33.0391i	−0.815595	+	1.41265i	−0.908900	+	0.417014i	$0.863077\pi$
$548$	46.7313			1.99626
$549$		0			0
$550$	21.9909			0.937695
$551$	2.68085	−	4.64337i	0.114208	−	0.197814i
$552$		0			0
$553$	7.67330	+	13.2905i	0.326302	+	0.565171i
$554$	8.97445	+	15.5442i	0.381288	+	0.660410i
$555$		0			0
$556$	28.9998	−	50.2291i	1.22987	−	2.13019i
$557$	−15.9537			−0.675981			−0.337991	−	0.941149i	$-0.609747\pi$
$557$	−15.9537			−0.675981			−0.337991	+	0.941149i	$0.609747\pi$
$558$		0			0
$559$	8.22488			0.347875
$560$	3.23988	−	5.61163i	0.136910	−	0.237135i
$561$		0			0
$562$	−22.2462	−	38.5316i	−0.938401	−	1.62536i
$563$	−9.23784	−	16.0004i	−0.389328	−	0.674337i	0.603031	−	0.797718i	$-0.293960\pi$
$563$	−9.23784	−	16.0004i	−0.389328	−	0.674337i	−0.992359	+	0.123381i	$0.960626\pi$
$564$		0			0
$565$	2.52853	−	4.37954i	0.106376	−	0.184249i
$566$	60.4284			2.54000
$567$		0			0
$568$	−24.3719			−1.02262
$569$	−6.68412	+	11.5772i	−0.280213	+	0.485343i	−0.971437	−	0.237297i	$-0.923738\pi$
$569$	−6.68412	+	11.5772i	−0.280213	+	0.485343i	0.691224	+	0.722640i	$0.257072\pi$
$570$		0			0
$571$	−22.1698	−	38.3993i	−0.927779	−	1.60696i	−0.787029	−	0.616915i	$-0.788382\pi$
$571$	−22.1698	−	38.3993i	−0.927779	−	1.60696i	−0.140750	−	0.990045i	$-0.544951\pi$
$572$	−2.55982	−	4.43374i	−0.107031	−	0.185384i
$573$		0			0
$574$	10.6737	−	18.4874i	0.445512	−	0.771650i
$575$	−2.78189			−0.116013
$576$		0			0
$577$	29.9400			1.24642			0.623209	−	0.782055i	$-0.285829\pi$
$577$	29.9400			1.24642			0.623209	+	0.782055i	$0.285829\pi$
$578$	10.3430	−	17.9147i	0.430214	−	0.745152i
$579$		0			0
$580$	1.32490	+	2.29480i	0.0550135	+	0.0952862i
$581$	−14.6943	−	25.4514i	−0.609624	−	1.05590i
$582$		0			0
$583$	12.7269	−	22.0436i	0.527093	−	0.912951i
$584$	−0.681591			−0.0282044
$585$		0			0
$586$	14.1698			0.585348
$587$	11.3491	−	19.6573i	0.468429	−	0.811343i	−0.530920	−	0.847422i	$-0.678154\pi$
$587$	11.3491	−	19.6573i	0.468429	−	0.811343i	0.999349	+	0.0360792i	$0.0114868\pi$
$588$		0			0
$589$	7.75578	+	13.4334i	0.319571	+	0.553514i
$590$	9.62195	+	16.6657i	0.396130	+	0.686116i
$591$		0			0
$592$	3.77980	−	6.54680i	0.155349	−	0.269072i
$593$	−14.8743			−0.610816			−0.305408	−	0.952222i	$-0.598793\pi$
$593$	−14.8743			−0.610816			−0.305408	+	0.952222i	$0.598793\pi$
$594$		0			0
$595$	21.5943			0.885282
$596$	−10.4616	+	18.1200i	−0.428524	+	0.742226i
$597$		0			0
$598$	0.550290	+	0.953131i	0.0225030	+	0.0389764i
$599$	4.98070	+	8.62682i	0.203506	+	0.352482i	0.949656	−	0.313296i	$-0.101433\pi$
$599$	4.98070	+	8.62682i	0.203506	+	0.352482i	−0.746150	+	0.665778i	$0.768100\pi$
$600$		0			0
$601$	0.588301	−	1.01897i	0.0239973	−	0.0415645i	−0.853777	−	0.520638i	$-0.825694\pi$
$601$	0.588301	−	1.01897i	0.0239973	−	0.0415645i	0.877775	+	0.479074i	$0.159027\pi$
$602$	110.688			4.51129
$603$		0			0
$604$	−41.4201			−1.68536
$605$	−2.40825	+	4.17122i	−0.0979094	+	0.169584i
$606$		0			0
$607$	−11.8473	−	20.5201i	−0.480866	−	0.832884i	0.518893	−	0.854839i	$-0.326344\pi$
$607$	−11.8473	−	20.5201i	−0.480866	−	0.832884i	−0.999759	+	0.0219552i	$0.993011\pi$
$608$	19.2711	+	33.3785i	0.781545	+	1.35368i
$609$		0			0
$610$	9.22287	−	15.9745i	0.373423	−	0.646788i
$611$	6.37972			0.258096
$612$		0			0
$613$	−37.9295			−1.53196			−0.765979	−	0.642865i	$-0.777746\pi$
$613$	−37.9295			−1.53196			−0.765979	+	0.642865i	$0.777746\pi$
$614$	14.5605	−	25.2195i	0.587614	−	1.01778i
$615$		0			0
$616$	−10.3568	−	17.9385i	−0.417288	−	0.722764i
$617$	6.46731	+	11.2017i	0.260364	+	0.450964i	0.966339	−	0.257273i	$-0.0828240\pi$
$617$	6.46731	+	11.2017i	0.260364	+	0.450964i	−0.705974	+	0.708237i	$0.749491\pi$
$618$		0			0
$619$	−1.91618	+	3.31891i	−0.0770176	+	0.133398i	−0.901962	−	0.431816i	$-0.857873\pi$
$619$	−1.91618	+	3.31891i	−0.0770176	+	0.133398i	0.824944	+	0.565214i	$0.191206\pi$
$620$	−7.66596			−0.307872
$621$		0			0
$622$	−35.2058			−1.41162
$623$	−2.09139	+	3.62239i	−0.0837898	+	0.145128i
$624$		0			0
$625$	−6.42939	−	11.1360i	−0.257176	−	0.445441i
$626$	−24.5929	−	42.5961i	−0.982928	−	1.70248i
$627$		0			0
$628$	−5.34486	+	9.25757i	−0.213283	+	0.369417i
$629$	25.1930			1.00451
$630$		0			0
$631$	22.0032			0.875933			0.437967	−	0.898991i	$-0.355699\pi$
$631$	22.0032			0.875933			0.437967	+	0.898991i	$0.355699\pi$
$632$	3.20536	−	5.55185i	0.127503	−	0.220841i
$633$		0			0
$634$	−3.46910	−	6.00866i	−0.137776	−	0.238634i
$635$	−1.28397	−	2.22389i	−0.0509526	−	0.0882526i
$636$		0			0
$637$	−5.04889	+	8.74493i	−0.200044	+	0.346487i
$638$	−5.30996			−0.210223
$639$		0			0
$640$	−12.7513			−0.504038
$641$	−2.51413	+	4.35460i	−0.0993022	+	0.171997i	−0.911396	−	0.411530i	$-0.864994\pi$
$641$	−2.51413	+	4.35460i	−0.0993022	+	0.171997i	0.812094	+	0.583527i	$0.198328\pi$
$642$		0			0
$643$	−6.36545	−	11.0253i	−0.251029	−	0.434795i	0.712781	−	0.701387i	$-0.247436\pi$
$643$	−6.36545	−	11.0253i	−0.251029	−	0.434795i	−0.963809	+	0.266593i	$0.914102\pi$
$644$	4.35789	+	7.54809i	0.171725	+	0.297436i
$645$		0			0
$646$	−30.3562	+	52.5785i	−1.19435	+	2.06867i
$647$	43.9990			1.72978			0.864889	−	0.501963i	$-0.167389\pi$
$647$	43.9990			1.72978			0.864889	+	0.501963i	$0.167389\pi$
$648$		0			0
$649$	−22.6927			−0.890765
$650$	−3.39278	+	5.87646i	−0.133076	+	0.230494i
$651$		0			0
$652$	20.4222	+	35.3723i	0.799795	+	1.38528i
$653$	8.74258	+	15.1426i	0.342123	+	0.592575i	0.984827	−	0.173540i	$-0.0555206\pi$
$653$	8.74258	+	15.1426i	0.342123	+	0.592575i	−0.642703	+	0.766115i	$0.722187\pi$
$654$		0			0
$655$	−9.36365	+	16.2183i	−0.365868	+	0.633702i
$656$	3.28954			0.128435
$657$		0			0
$658$	85.8562			3.34702
$659$	1.04543	−	1.81073i	0.0407241	−	0.0705361i	−0.844945	−	0.534853i	$-0.820367\pi$
$659$	1.04543	−	1.81073i	0.0407241	−	0.0705361i	0.885669	+	0.464317i	$0.153700\pi$
$660$		0			0
$661$	−5.99363	−	10.3813i	−0.233125	−	0.403785i	0.725601	−	0.688116i	$-0.241562\pi$
$661$	−5.99363	−	10.3813i	−0.233125	−	0.403785i	−0.958726	+	0.284331i	$0.908229\pi$
$662$	−19.6755	−	34.0790i	−0.764712	−	1.32452i
$663$		0			0
$664$	−6.13827	+	10.6318i	−0.238211	+	0.412594i
$665$	−22.5411			−0.874107
$666$		0			0
$667$	0.671720			0.0260091
$668$	5.11451	−	8.85858i	0.197886	−	0.342749i
$669$		0			0
$670$	6.22190	+	10.7767i	0.240373	+	0.416338i
$671$	10.8757	+	18.8373i	0.419853	+	0.727206i
$672$		0			0
$673$	2.82920	−	4.90033i	0.109058	−	0.188894i	−0.806331	−	0.591465i	$-0.798550\pi$
$673$	2.82920	−	4.90033i	0.109058	−	0.188894i	0.915389	+	0.402571i	$0.131883\pi$
$674$	69.8856			2.69189
$675$		0			0
$676$	−35.5971			−1.36912
$677$	−14.2753	+	24.7255i	−0.548643	+	0.950278i	0.449724	+	0.893167i	$0.351522\pi$
$677$	−14.2753	+	24.7255i	−0.548643	+	0.950278i	−0.998368	+	0.0571109i	$0.981811\pi$
$678$		0			0
$679$	−5.32763	−	9.22773i	−0.204456	−	0.354128i
$680$	−4.51030	−	7.81207i	−0.172962	−	0.299579i
$681$		0			0
$682$	7.68093	−	13.3038i	0.294118	−	0.509428i
$683$	−30.2589			−1.15782			−0.578912	−	0.815390i	$-0.696523\pi$
$683$	−30.2589			−1.15782			−0.578912	+	0.815390i	$0.696523\pi$
$684$		0			0
$685$	−15.1413			−0.578518
$686$	−32.9385	+	57.0512i	−1.25760	+	2.17823i
$687$		0			0
$688$	8.52824	+	14.7713i	0.325136	+	0.563152i
$689$	3.92703	+	6.80181i	0.149608	+	0.259128i
$690$		0			0
$691$	16.6414	−	28.8237i	0.633068	−	1.09651i	−0.353853	−	0.935301i	$-0.615129\pi$
$691$	16.6414	−	28.8237i	0.633068	−	1.09651i	0.986921	−	0.161205i	$-0.0515381\pi$
$692$	−63.6305			−2.41887
$693$		0			0
$694$	−71.4964			−2.71397
$695$	−9.39614	+	16.2746i	−0.356416	+	0.617331i
$696$		0			0
$697$	5.48134	+	9.49397i	0.207621	+	0.359610i
$698$	1.13478	+	1.96549i	0.0429520	+	0.0743950i
$699$		0			0
$700$	−26.8683	+	46.5372i	−1.01553	+	1.75894i
$701$	−9.14819			−0.345522			−0.172761	−	0.984964i	$-0.555269\pi$
$701$	−9.14819			−0.345522			−0.172761	+	0.984964i	$0.555269\pi$
$702$		0			0
$703$	−26.2975			−0.991830
$704$	15.3726	−	26.6261i	0.579376	−	1.00351i
$705$		0			0
$706$	22.2125	+	38.4732i	0.835979	+	1.44796i
$707$	14.8819	+	25.7762i	0.559691	+	0.969414i
$708$		0			0
$709$	23.4677	−	40.6472i	0.881346	−	1.52654i	0.0315017	−	0.999504i	$-0.489971\pi$
$709$	23.4677	−	40.6472i	0.881346	−	1.52654i	0.849845	−	0.527033i	$-0.176696\pi$
$710$	26.2662			0.985753
$711$		0			0
$712$	1.74727			0.0654818
$713$	−0.971654	+	1.68295i	−0.0363887	+	0.0630271i
$714$		0			0
$715$	0.829400	+	1.43656i	0.0310178	+	0.0537244i
$716$	24.2164	+	41.9440i	0.905009	+	1.56752i
$717$		0			0
$718$	−30.6956	+	53.1664i	−1.14555	+	1.98415i
$719$	23.1046			0.861658			0.430829	−	0.902434i	$-0.358221\pi$
$719$	23.1046			0.861658			0.430829	+	0.902434i	$0.358221\pi$
$720$		0			0
$721$	62.5470			2.32937
$722$	10.7445	−	18.6100i	0.399868	−	0.692592i
$723$		0			0
$724$	0.319174	+	0.552825i	0.0118620	+	0.0205456i
$725$	2.07072	+	3.58660i	0.0769047	+	0.133203i
$726$		0			0
$727$	13.5030	−	23.3879i	0.500800	−	0.867410i	−0.499200	−	0.866487i	$-0.666373\pi$
$727$	13.5030	−	23.3879i	0.500800	−	0.867410i	1.00000		0.000923514i	$-0.000293964\pi$
$728$	6.39144			0.236883
$729$		0			0
$730$	0.734567			0.0271875
$731$	−28.4211	+	49.2268i	−1.05119	+	1.82072i
$732$		0			0
$733$	−2.02103	−	3.50053i	−0.0746485	−	0.129295i	0.826285	−	0.563252i	$-0.190450\pi$
$733$	−2.02103	−	3.50053i	−0.0746485	−	0.129295i	−0.900933	+	0.433957i	$0.857117\pi$
$734$	−15.1641	−	26.2649i	−0.559716	−	0.969456i
$735$		0			0
$736$	−2.41430	+	4.18170i	−0.0889924	+	0.154139i
$737$	−14.6739			−0.540520
$738$		0			0
$739$	24.7100			0.908974			0.454487	−	0.890753i	$-0.349823\pi$
$739$	24.7100			0.908974			0.454487	+	0.890753i	$0.349823\pi$
$740$	6.49824	−	11.2553i	0.238880	−	0.413753i
$741$		0			0
$742$	52.8486	+	91.5365i	1.94013	+	3.36041i
$743$	9.23046	+	15.9876i	0.338633	+	0.586529i	0.984176	−	0.177195i	$-0.0567023\pi$
$743$	9.23046	+	15.9876i	0.338633	+	0.586529i	−0.645543	+	0.763724i	$0.723369\pi$
$744$		0			0
$745$	3.38964	−	5.87102i	0.124187	−	0.215098i
$746$	−46.3528			−1.69710
$747$		0			0
$748$	35.3818			1.29369
$749$	9.45253	−	16.3723i	0.345388	−	0.598229i
$750$		0			0
$751$	12.6844	+	21.9700i	0.462861	+	0.801698i	0.999102	−	0.0423666i	$-0.0134897\pi$
$751$	12.6844	+	21.9700i	0.462861	+	0.801698i	−0.536242	+	0.844065i	$0.680156\pi$
$752$	6.61502	+	11.4576i	0.241225	+	0.417814i
$753$		0			0
$754$	0.819226	−	1.41894i	0.0298344	−	0.0516748i
$755$	13.4204			0.488419
$756$		0			0
$757$	31.0623			1.12898			0.564490	−	0.825440i	$-0.309073\pi$
$757$	31.0623			1.12898			0.564490	+	0.825440i	$0.309073\pi$
$758$	−34.5048	+	59.7640i	−1.25327	+	2.17073i
$759$		0			0
$760$	4.70805	+	8.15458i	0.170779	+	0.295798i
$761$	−18.7325	−	32.4457i	−0.679054	−	1.17616i	−0.975266	−	0.221034i	$-0.929057\pi$
$761$	−18.7325	−	32.4457i	−0.679054	−	1.17616i	0.296212	−	0.955122i	$-0.404276\pi$
$762$		0			0
$763$	39.2322	−	67.9521i	1.42030	−	2.46003i
$764$	−4.87247			−0.176280
$765$		0			0
$766$	−41.1038			−1.48514
$767$	3.50105	−	6.06399i	0.126415	−	0.218958i
$768$		0			0
$769$	12.4824	+	21.6202i	0.450128	+	0.779645i	0.998394	−	0.0566593i	$-0.0180449\pi$
$769$	12.4824	+	21.6202i	0.450128	+	0.779645i	−0.548265	+	0.836305i	$0.684712\pi$
$770$	11.1618	+	19.3328i	0.402243	+	0.696705i
$771$		0			0
$772$	−33.2232	+	57.5443i	−1.19573	+	2.07107i
$773$	14.4493			0.519705			0.259853	−	0.965648i	$-0.416326\pi$
$773$	14.4493			0.519705			0.259853	+	0.965648i	$0.416326\pi$
$774$		0			0
$775$	−11.9813			−0.430382
$776$	−2.22551	+	3.85470i	−0.0798912	+	0.138376i
$777$		0			0
$778$	1.55016	+	2.68495i	0.0555758	+	0.0962601i
$779$	−5.72166	−	9.91021i	−0.205000	−	0.355070i
$780$		0			0
$781$	−15.4867	+	26.8238i	−0.554158	+	0.959830i
$782$	−7.60612			−0.271994
$783$		0			0
$784$	−20.9404			−0.747873
$785$	1.73177	−	2.99952i	0.0618097	−	0.107057i
$786$		0			0
$787$	−15.5870	−	26.9974i	−0.555615	−	0.962353i	−0.997855	−	0.0654568i	$-0.979150\pi$
$787$	−15.5870	−	26.9974i	−0.555615	−	0.962353i	0.442240	−	0.896897i	$-0.354184\pi$
$788$	4.45213	+	7.71132i	0.158601	+	0.274704i
$789$		0			0
$790$	−3.45450	+	5.98336i	−0.122905	+	0.212879i
$791$	−24.7629			−0.880469
$792$		0			0
$793$	−6.71167			−0.238338
$794$	12.1308	−	21.0112i	0.430506	−	0.745658i
$795$		0			0
$796$	36.7956	+	63.7319i	1.30419	+	2.25892i
$797$	−6.58939	−	11.4131i	−0.233408	−	0.404275i	0.725401	−	0.688327i	$-0.241654\pi$
$797$	−6.58939	−	11.4131i	−0.233408	−	0.404275i	−0.958809	+	0.284052i	$0.908321\pi$
$798$		0			0
$799$	−22.0451	+	38.1833i	−0.779901	+	1.35083i
$800$	−29.7704			−1.05254
$801$		0			0
$802$	−31.9747			−1.12907
$803$	−0.433105	+	0.750160i	−0.0152839	+	0.0264726i
$804$		0			0
$805$	−1.41199	−	2.44564i	−0.0497661	−	0.0861973i
$806$	2.37005	+	4.10504i	0.0834813	+	0.144594i
$807$		0			0
$808$	6.21661	−	10.7675i	0.218700	−	0.378799i
$809$	20.3684			0.716113			0.358057	−	0.933700i	$-0.383440\pi$
$809$	20.3684			0.716113			0.358057	+	0.933700i	$0.383440\pi$
$810$		0			0
$811$	−6.64714			−0.233413			−0.116706	−	0.993166i	$-0.537234\pi$
$811$	−6.64714			−0.233413			−0.116706	+	0.993166i	$0.537234\pi$
$812$	6.48766	−	11.2370i	0.227672	−	0.394340i
$813$		0			0
$814$	13.0219	+	22.5545i	0.456416	+	0.790536i
$815$	−6.61694	−	11.4609i	−0.231781	−	0.401457i
$816$		0			0
$817$	29.6671	−	51.3850i	1.03792	−	1.79773i
$818$	7.81530			0.273256
$819$		0			0
$820$	5.65540			0.197495
$821$	−22.7247	+	39.3603i	−0.793097	+	1.37368i	0.130944	+	0.991390i	$0.458199\pi$
$821$	−22.7247	+	39.3603i	−0.793097	+	1.37368i	−0.924041	+	0.382294i	$0.875134\pi$
$822$		0			0
$823$	3.04646	+	5.27662i	0.106193	+	0.183932i	0.914225	−	0.405207i	$-0.132801\pi$
$823$	3.04646	+	5.27662i	0.106193	+	0.183932i	−0.808032	+	0.589139i	$0.799467\pi$
$824$	−13.0639	−	22.6273i	−0.455102	−	0.788259i
$825$		0			0
$826$	47.1159	−	81.6072i	1.63937	−	2.83948i
$827$	−13.6049			−0.473090			−0.236545	−	0.971621i	$-0.576015\pi$
$827$	−13.6049			−0.473090			−0.236545	+	0.971621i	$0.576015\pi$
$828$		0			0
$829$	−12.7936			−0.444340			−0.222170	−	0.975008i	$-0.571314\pi$
$829$	−12.7936			−0.444340			−0.222170	+	0.975008i	$0.571314\pi$
$830$	6.61536	−	11.4581i	0.229622	−	0.397718i
$831$		0			0
$832$	4.74339	+	8.21580i	0.164448	+	0.284832i
$833$	−34.8929	−	60.4363i	−1.20897	−	2.09399i
$834$		0			0
$835$	−1.65714	+	2.87025i	−0.0573476	+	0.0993289i
$836$	−36.9331			−1.27736
$837$		0			0
$838$	34.6800			1.19800
$839$	−15.4668	+	26.7892i	−0.533972	+	0.924866i	0.465241	+	0.885184i	$0.345968\pi$
$839$	−15.4668	+	26.7892i	−0.533972	+	0.924866i	−0.999212	+	0.0396818i	$0.987366\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.0172414	−	0.0298629i
$842$	8.94967	+	15.5013i	0.308426	+	0.534210i
$843$		0			0
$844$	16.0299	−	27.7646i	0.551771	−	0.955696i
$845$	11.5337			0.396772
$846$		0			0
$847$	23.5850			0.810392
$848$	−8.14374	+	14.1054i	−0.279657	+	0.484380i
$849$		0			0
$850$	−23.4475	−	40.6123i	−0.804243	−	1.39299i
$851$	−1.64729	−	2.85319i	−0.0564685	−	0.0978062i
$852$		0			0
$853$	−27.9653	+	48.4373i	−0.957514	+	1.65846i	−0.229005	+	0.973425i	$0.573547\pi$
$853$	−27.9653	+	48.4373i	−0.957514	+	1.65846i	−0.728508	+	0.685037i	$0.759786\pi$
$854$	−90.3235			−3.09081
$855$		0			0
$856$	−7.89721			−0.269921
$857$	5.92568	−	10.2636i	0.202417	−	0.350597i	−0.746889	−	0.664948i	$-0.768454\pi$
$857$	5.92568	−	10.2636i	0.202417	−	0.350597i	0.949307	+	0.314351i	$0.101787\pi$
$858$		0			0
$859$	12.7090	+	22.0126i	0.433625	+	0.751060i	0.997182	−	0.0750168i	$-0.0239010\pi$
$859$	12.7090	+	22.0126i	0.433625	+	0.751060i	−0.563558	+	0.826077i	$0.690568\pi$
$860$	14.6618	+	25.3950i	0.499963	+	0.865961i
$861$		0			0
$862$	−13.3553	+	23.1320i	−0.454883	+	0.787880i
$863$	−23.3768			−0.795755			−0.397878	−	0.917438i	$-0.630253\pi$
$863$	−23.3768			−0.795755			−0.397878	+	0.917438i	$0.630253\pi$
$864$		0			0
$865$	20.6167			0.700991
$866$	3.78575	−	6.55711i	0.128645	−	0.222820i
$867$		0			0
$868$	18.7690	+	32.5089i	0.637061	+	1.10342i
$869$	−4.07359	−	7.05566i	−0.138187	−	0.239347i
$870$		0			0
$871$	2.26390	−	3.92120i	0.0767095	−	0.132865i
$872$	−32.7769			−1.10997
$873$		0			0
$874$	7.93959			0.268561
$875$	19.2158	−	33.2827i	0.649611	−	1.12516i
$876$		0			0
$877$	−1.67270	−	2.89720i	−0.0564830	−	0.0978314i	0.836401	−	0.548117i	$-0.184655\pi$
$877$	−1.67270	−	2.89720i	−0.0564830	−	0.0978314i	−0.892884	+	0.450286i	$0.851322\pi$
$878$	−36.3401	−	62.9429i	−1.22642	−	2.12422i
$879$		0			0
$880$	−1.71998	+	2.97910i	−0.0579806	+	0.100425i
$881$	41.5838			1.40099			0.700496	−	0.713656i	$-0.252962\pi$
$881$	41.5838			1.40099			0.700496	+	0.713656i	$0.252962\pi$
$882$		0			0
$883$	14.9366			0.502657			0.251328	−	0.967902i	$-0.419133\pi$
$883$	14.9366			0.502657			0.251328	+	0.967902i	$0.419133\pi$
$884$	−5.45875	+	9.45483i	−0.183598	+	0.318000i
$885$		0			0
$886$	−24.8877	−	43.1068i	−0.836119	−	1.44820i
$887$	−0.186039	−	0.322230i	−0.00624659	−	0.0108194i	0.862885	−	0.505400i	$-0.168655\pi$
$887$	−0.186039	−	0.322230i	−0.00624659	−	0.0108194i	−0.869132	+	0.494581i	$0.835322\pi$
$888$		0			0
$889$	−6.28721	+	10.8898i	−0.210866	+	0.365231i
$890$	−1.88308			−0.0631209
$891$		0			0
$892$	19.3351			0.647386
$893$	23.0117	−	39.8574i	0.770056	−	1.33378i
$894$		0			0
$895$	−7.84628	−	13.5902i	−0.262272	−	0.454269i
$896$	31.2197	+	54.0740i	1.04298	+	1.80649i
$897$		0			0
$898$	−24.0017	+	41.5722i	−0.800949	+	1.38728i
$899$	2.89303			0.0964880
$900$		0			0
$901$	−54.2794			−1.80831
$902$	−5.66645	+	9.81457i	−0.188672	+	0.326790i
$903$		0			0
$904$	5.17211	+	8.95836i	0.172022	+	0.297950i
$905$	−0.103415	−	0.179119i	−0.00343762	−	0.00595413i
$906$		0			0
$907$	0.385152	−	0.667102i	0.0127887	−	0.0221508i	−0.859560	−	0.511034i	$-0.829262\pi$
$907$	0.385152	−	0.667102i	0.0127887	−	0.0221508i	0.872349	+	0.488884i	$0.162596\pi$
$908$	62.3498			2.06915
$909$		0			0
$910$	−6.88821			−0.228342
$911$	−13.2921	+	23.0225i	−0.440385	+	0.762770i	−0.997718	−	0.0675194i	$-0.978492\pi$
$911$	−13.2921	+	23.0225i	−0.440385	+	0.762770i	0.557332	+	0.830289i	$0.311825\pi$
$912$		0			0
$913$	7.80091	+	13.5116i	0.258172	+	0.447168i
$914$	26.9790	+	46.7290i	0.892386	+	1.54566i
$915$		0			0
$916$	10.1971	−	17.6619i	0.336921	−	0.583564i
$917$	91.7022			3.02827
$918$		0			0
$919$	−5.15934			−0.170191			−0.0850954	−	0.996373i	$-0.527120\pi$
$919$	−5.15934			−0.170191			−0.0850954	+	0.996373i	$0.527120\pi$
$920$	−0.589830	+	1.02162i	−0.0194461	+	0.0336817i
$921$		0			0
$922$	1.47056	+	2.54708i	0.0484302	+	0.0838836i
$923$	−4.77861	−	8.27680i	−0.157290	−	0.272434i
$924$		0			0
$925$	10.1563	−	17.5912i	0.333936	−	0.578394i
$926$	21.9731			0.722082
$927$		0			0
$928$	7.18842			0.235971
$929$	−19.6030	+	33.9534i	−0.643153	+	1.11397i	0.341572	+	0.939856i	$0.389041\pi$
$929$	−19.6030	+	33.9534i	−0.643153	+	1.11397i	−0.984725	+	0.174118i	$0.944293\pi$
$930$		0			0
$931$	36.4227	+	63.0860i	1.19371	+	2.06756i
$932$	22.3259	+	38.6695i	0.731308	+	1.26666i
$933$		0			0
$934$	−27.6824	+	47.9474i	−0.905797	+	1.56889i
$935$	−11.4640			−0.374912
$936$		0			0
$937$	−29.3931			−0.960232			−0.480116	−	0.877205i	$-0.659405\pi$
$937$	−29.3931			−0.960232			−0.480116	+	0.877205i	$0.659405\pi$
$938$	30.4669	−	52.7702i	0.994779	−	1.72301i
$939$		0			0
$940$	11.3726	+	19.6979i	0.370933	+	0.642474i
$941$	10.1080	+	17.5075i	0.329511	+	0.570729i	0.982415	−	0.186711i	$-0.0597829\pi$
$941$	10.1080	+	17.5075i	0.329511	+	0.570729i	−0.652904	+	0.757440i	$0.726450\pi$
$942$		0			0
$943$	0.716817	−	1.24156i	0.0233428	−	0.0404309i
$944$	14.5207			0.472609
$945$		0			0
$946$	−58.7617			−1.91051
$947$	16.6473	−	28.8340i	0.540965	−	0.936979i	−0.457884	−	0.889012i	$-0.651392\pi$
$947$	16.6473	−	28.8340i	0.540965	−	0.936979i	0.998849	−	0.0479670i	$-0.0152742\pi$
$948$		0			0
$949$	−0.133640	−	0.231471i	−0.00433813	−	0.00751387i
$950$	24.4755	+	42.3928i	0.794090	+	1.37541i
$951$		0			0
$952$	−22.0856	+	38.2535i	−0.715800	+	1.23980i
$953$	−22.6156			−0.732592			−0.366296	−	0.930498i	$-0.619374\pi$
$953$	−22.6156			−0.732592			−0.366296	+	0.930498i	$0.619374\pi$
$954$		0			0
$955$	1.57871			0.0510860
$956$	−2.30495	+	3.99228i	−0.0745473	+	0.129120i
$957$		0			0
$958$	−21.2768	−	36.8525i	−0.687422	−	1.19065i
$959$	37.0712	+	64.2092i	1.19709	+	2.07342i
$960$		0			0
$961$	11.3152	−	19.5985i	0.365006	−	0.632209i
$962$	−8.03611			−0.259095
$963$		0			0
$964$	22.6904			0.730809
$965$	10.7646	−	18.6448i	0.346524	−	0.600197i
$966$		0			0
$967$	−3.44661	−	5.96971i	−0.110836	−	0.191973i	0.805272	−	0.592906i	$-0.202019\pi$
$967$	−3.44661	−	5.96971i	−0.110836	−	0.191973i	−0.916107	+	0.400933i	$0.868686\pi$
$968$	−4.92609	−	8.53224i	−0.158330	−	0.274236i
$969$		0			0
$970$	2.39849	−	4.15430i	0.0770108	−	0.133387i
$971$	0.238354			0.00764915			0.00382457	−	0.999993i	$-0.498783\pi$
$971$	0.238354			0.00764915			0.00382457	+	0.999993i	$0.498783\pi$
$972$		0			0
$973$	92.0204			2.95004
$974$	−31.3934	+	54.3750i	−1.00591	+	1.74229i
$975$		0			0
$976$	−6.95922	−	12.0537i	−0.222759	−	0.385830i
$977$	−2.93440	−	5.08252i	−0.0938796	−	0.162604i	0.815261	−	0.579094i	$-0.196594\pi$
$977$	−2.93440	−	5.08252i	−0.0938796	−	0.162604i	−0.909140	+	0.416490i	$0.863260\pi$
$978$		0			0
$979$	1.11027	−	1.92305i	0.0354845	−	0.0614609i
$980$	−36.0009			−1.15001
$981$		0			0
$982$	9.09441			0.290214
$983$	8.31197	−	14.3968i	0.265111	−	0.459185i	−0.702482	−	0.711702i	$-0.747925\pi$
$983$	8.31197	−	14.3968i	0.265111	−	0.459185i	0.967593	+	0.252516i	$0.0812582\pi$
$984$		0			0
$985$	−1.44252	−	2.49852i	−0.0459626	−	0.0796096i
$986$	5.66167	+	9.80630i	0.180304	+	0.312296i
$987$		0			0
$988$	5.69807	−	9.86936i	0.181280	−	0.313986i
$989$	7.43347			0.236371
$990$		0			0
$991$	0.420562			0.0133596			0.00667980	−	0.999978i	$-0.497874\pi$
$991$	0.420562			0.0133596			0.00667980	+	0.999978i	$0.497874\pi$
$992$	−10.3982	+	18.0101i	−0.330142	+	0.571823i
$993$		0			0
$994$	−64.3090	−	111.386i	−2.03976	−	3.53296i
$995$	−11.9221	−	20.6496i	−0.377954	−	0.654636i
$996$		0			0
$997$	9.77079	−	16.9235i	0.309444	−	0.535973i	−0.668797	−	0.743445i	$-0.733190\pi$
$997$	9.77079	−	16.9235i	0.309444	−	0.535973i	0.978241	+	0.207473i	$0.0665238\pi$
$998$	−23.1245			−0.731992
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.e.a.262.10		22
3.2	odd	2		261.2.e.a.88.2	✓	22
9.2	odd	6		2349.2.a.f.1.10		11
9.4	even	3	inner	783.2.e.a.523.10		22
9.5	odd	6		261.2.e.a.175.2	yes	22
9.7	even	3		2349.2.a.e.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.2	✓	22	3.2	odd	2
261.2.e.a.175.2	yes	22	9.5	odd	6
783.2.e.a.262.10		22	1.1	even	1	trivial
783.2.e.a.523.10		22	9.4	even	3	inner
2349.2.a.e.1.2		11	9.7	even	3
2349.2.a.f.1.10		11	9.2	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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10224 - 1.90914i) q^{2} +(-1.42988 - 2.47662i) q^{4} +(0.463291 + 0.802444i) q^{5} +(2.26860 - 3.92934i) q^{7} -1.89533 q^{8} +2.04264 q^{10} +(-1.20435 + 2.08600i) q^{11} +(-0.371618 - 0.643660i) q^{13} +(-5.00111 - 8.66217i) q^{14} +(0.770648 - 1.33480i) q^{16} +5.13650 q^{17} -5.36170 q^{19} +(1.32490 - 2.29480i) q^{20} +(2.65498 + 4.59856i) q^{22} +(-0.335860 - 0.581727i) q^{23} +(2.07072 - 3.58660i) q^{25} -1.63845 q^{26} -12.9753 q^{28} +(-0.500000 + 0.866025i) q^{29} +(-1.44652 - 2.50544i) q^{31} +(-3.59421 - 6.22535i) q^{32} +(5.66167 - 9.80630i) q^{34} +4.20410 q^{35} +4.90470 q^{37} +(-5.90990 + 10.2362i) q^{38} +(-0.878089 - 1.52089i) q^{40} +(1.06714 + 1.84833i) q^{41} +(-5.53316 + 9.58372i) q^{43} +6.88832 q^{44} -1.48080 q^{46} +(-4.29186 + 7.43372i) q^{47} +(-6.79313 - 11.7660i) q^{49} +(-4.56488 - 7.90660i) q^{50} +(-1.06274 + 1.84071i) q^{52} -10.5674 q^{53} -2.23186 q^{55} +(-4.29975 + 7.44738i) q^{56} +(1.10224 + 1.90914i) q^{58} +(4.71055 + 8.15891i) q^{59} +(4.51517 - 7.82051i) q^{61} -6.37765 q^{62} -12.7642 q^{64} +(0.344334 - 0.596405i) q^{65} +(3.04601 + 5.27585i) q^{67} +(-7.34458 - 12.7212i) q^{68} +(4.63394 - 8.02621i) q^{70} +12.8590 q^{71} +0.359617 q^{73} +(5.40617 - 9.36376i) q^{74} +(7.66659 + 13.2789i) q^{76} +(5.46440 + 9.46461i) q^{77} +(-1.69119 + 2.92923i) q^{79} +1.42814 q^{80} +4.70497 q^{82} +(3.23863 - 5.60948i) q^{83} +(2.37970 + 4.12175i) q^{85} +(12.1978 + 21.1272i) q^{86} +(2.28264 - 3.95365i) q^{88} -0.921884 q^{89} -3.37221 q^{91} +(-0.960479 + 1.66360i) q^{92} +(9.46134 + 16.3875i) q^{94} +(-2.48403 - 4.30246i) q^{95} +(1.17421 - 2.03379i) q^{97} -29.9507 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 5 q^{4} - q^{5} + 7 q^{7} - 6 q^{8} - 20 q^{10} + 3 q^{11} + 7 q^{13} - 10 q^{14} + 7 q^{16} - 2 q^{17} - 56 q^{19} - 4 q^{20} + 13 q^{22} + 4 q^{23} + 4 q^{25} + 12 q^{26} - 32 q^{28}+ \cdots - 86 q^{98}+O(q^{100}) \) 22 * q + q^2 - 5 * q^4 - q^5 + 7 * q^7 - 6 * q^8 - 20 * q^10 + 3 * q^11 + 7 * q^13 - 10 * q^14 + 7 * q^16 - 2 * q^17 - 56 * q^19 - 4 * q^20 + 13 * q^22 + 4 * q^23 + 4 * q^25 + 12 * q^26 - 32 * q^28 - 11 * q^29 + 27 * q^31 + 7 * q^32 + 19 * q^34 + 22 * q^35 - 28 * q^37 - 5 * q^38 + 24 * q^40 - 9 * q^41 + 25 * q^43 - 46 * q^44 - 20 * q^46 + 6 * q^47 + 12 * q^49 + 41 * q^50 + 20 * q^52 + 12 * q^53 - 70 * q^55 - 10 * q^56 + q^58 + 25 * q^61 + 12 * q^62 - 50 * q^64 + 5 * q^65 + 29 * q^67 - 50 * q^68 + 7 * q^70 + 2 * q^71 - 26 * q^73 + 14 * q^74 + 38 * q^76 + 9 * q^77 + 27 * q^79 + 74 * q^80 - 34 * q^82 - 12 * q^83 + 7 * q^85 + q^86 - 5 * q^88 - 46 * q^89 - 86 * q^91 + 19 * q^92 - 10 * q^94 + 8 * q^95 + 36 * q^97 - 86 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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