LMFDB - Embedded newform 783.2.e.a.262.9

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			262.9
Character	$\chi$	$=$	783.262
Dual form			783.2.e.a.523.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764092 - 1.32345i) q^{2} +(-0.167673 - 0.290418i) q^{4} +(-0.0756080 - 0.130957i) q^{5} +(0.0289713 - 0.0501797i) q^{7} +2.54390 q^{8} -0.231086 q^{10} +(0.540786 - 0.936668i) q^{11} +(1.22647 + 2.12431i) q^{13} +(-0.0442735 - 0.0766839i) q^{14} +(2.27912 - 3.94755i) q^{16} +1.83487 q^{17} +2.89537 q^{19} +(-0.0253548 + 0.0439159i) q^{20} +(-0.826420 - 1.43140i) q^{22} +(-0.390679 - 0.676676i) q^{23} +(2.48857 - 4.31032i) q^{25} +3.74855 q^{26} -0.0194308 q^{28} +(-0.500000 + 0.866025i) q^{29} +(0.604509 + 1.04704i) q^{31} +(-0.939013 - 1.62642i) q^{32} +(1.40201 - 2.42836i) q^{34} -0.00876184 q^{35} -1.28794 q^{37} +(2.21233 - 3.83187i) q^{38} +(-0.192339 - 0.333141i) q^{40} +(-2.18597 - 3.78621i) q^{41} +(3.72209 - 6.44685i) q^{43} -0.362701 q^{44} -1.19406 q^{46} +(-2.93817 + 5.08906i) q^{47} +(3.49832 + 6.05927i) q^{49} +(-3.80299 - 6.58697i) q^{50} +(0.411292 - 0.712379i) q^{52} +0.0547103 q^{53} -0.163551 q^{55} +(0.0737000 - 0.127652i) q^{56} +(0.764092 + 1.32345i) q^{58} +(-3.61816 - 6.26684i) q^{59} +(2.02285 - 3.50368i) q^{61} +1.84760 q^{62} +6.24650 q^{64} +(0.185462 - 0.321230i) q^{65} +(2.16938 + 3.75748i) q^{67} +(-0.307659 - 0.532881i) q^{68} +(-0.00669485 + 0.0115958i) q^{70} -14.9063 q^{71} -3.30924 q^{73} +(-0.984108 + 1.70452i) q^{74} +(-0.485476 - 0.840869i) q^{76} +(-0.0313345 - 0.0542730i) q^{77} +(-1.60912 + 2.78708i) q^{79} -0.689278 q^{80} -6.68112 q^{82} +(-4.05392 + 7.02160i) q^{83} +(-0.138731 - 0.240289i) q^{85} +(-5.68804 - 9.85197i) q^{86} +(1.37570 - 2.38279i) q^{88} +3.75415 q^{89} +0.142130 q^{91} +(-0.131013 + 0.226921i) q^{92} +(4.49007 + 7.77702i) q^{94} +(-0.218913 - 0.379169i) q^{95} +(-7.78455 + 13.4832i) q^{97} +10.6922 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.764092	−	1.32345i	0.540295	−	0.935818i	−0.458592	−	0.888647i	$-0.651646\pi$
$2$	0.764092	−	1.32345i	0.540295	−	0.935818i	0.998887	−	0.0471709i	$-0.0150205\pi$
$3$		0			0
$3$		0			0
$4$	−0.167673	−	0.290418i	−0.0838365	−	0.145209i
$5$	−0.0756080	−	0.130957i	−0.0338129	−	0.0585657i	0.848624	−	0.528997i	$-0.177432\pi$
$5$	−0.0756080	−	0.130957i	−0.0338129	−	0.0585657i	−0.882437	+	0.470431i	$0.844098\pi$
$6$		0			0
$7$	0.0289713	−	0.0501797i	0.0109501	−	0.0189662i	−0.860498	−	0.509453i	$-0.829848\pi$
$7$	0.0289713	−	0.0501797i	0.0109501	−	0.0189662i	0.871449	+	0.490487i	$0.163181\pi$
$8$	2.54390			0.899404
$9$		0			0
$10$	−0.231086			−0.0730757
$11$	0.540786	−	0.936668i	0.163053	−	0.282416i	−0.772909	−	0.634517i	$-0.781199\pi$
$11$	0.540786	−	0.936668i	0.163053	−	0.282416i	0.935962	+	0.352101i	$0.114533\pi$
$12$		0			0
$13$	1.22647	+	2.12431i	0.340162	+	0.589178i	0.984463	−	0.175595i	$-0.0561848\pi$
$13$	1.22647	+	2.12431i	0.340162	+	0.589178i	−0.644301	+	0.764772i	$0.722851\pi$
$14$	−0.0442735	−	0.0766839i	−0.0118326	−	0.0204946i
$15$		0			0
$16$	2.27912	−	3.94755i	0.569779	−	0.986887i
$17$	1.83487			0.445022			0.222511	−	0.974930i	$-0.428575\pi$
$17$	1.83487			0.445022			0.222511	+	0.974930i	$0.428575\pi$
$18$		0			0
$19$	2.89537			0.664244			0.332122	−	0.943236i	$-0.392235\pi$
$19$	2.89537			0.664244			0.332122	+	0.943236i	$0.392235\pi$
$20$	−0.0253548	+	0.0439159i	−0.00566951	+	0.00981989i
$21$		0			0
$22$	−0.826420	−	1.43140i	−0.176193	−	0.305176i
$23$	−0.390679	−	0.676676i	−0.0814623	−	0.141097i	0.822416	−	0.568887i	$-0.192626\pi$
$23$	−0.390679	−	0.676676i	−0.0814623	−	0.141097i	−0.903878	+	0.427790i	$0.859292\pi$
$24$		0			0
$25$	2.48857	−	4.31032i	0.497713	−	0.862065i
$26$	3.74855			0.735150
$27$		0			0
$28$	−0.0194308			−0.00367208
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i
$30$		0			0
$31$	0.604509	+	1.04704i	0.108573	+	0.188054i	0.915192	−	0.403017i	$-0.132039\pi$
$31$	0.604509	+	1.04704i	0.108573	+	0.188054i	−0.806619	+	0.591071i	$0.798705\pi$
$32$	−0.939013	−	1.62642i	−0.165996	−	0.287513i
$33$		0			0
$34$	1.40201	−	2.42836i	0.240443	−	0.416460i
$35$	−0.00876184			−0.00148102
$36$		0			0
$37$	−1.28794			−0.211737			−0.105868	−	0.994380i	$-0.533762\pi$
$37$	−1.28794			−0.211737			−0.105868	+	0.994380i	$0.533762\pi$
$38$	2.21233	−	3.83187i	0.358888	−	0.621612i
$39$		0			0
$40$	−0.192339	−	0.333141i	−0.0304115	−	0.0526742i
$41$	−2.18597	−	3.78621i	−0.341391	−	0.591306i	0.643300	−	0.765614i	$-0.277565\pi$
$41$	−2.18597	−	3.78621i	−0.341391	−	0.591306i	−0.984691	+	0.174307i	$0.944231\pi$
$42$		0			0
$43$	3.72209	−	6.44685i	0.567613	−	0.983135i	−0.429188	−	0.903215i	$-0.641200\pi$
$43$	3.72209	−	6.44685i	0.567613	−	0.983135i	0.996801	−	0.0799197i	$-0.0254664\pi$
$44$	−0.362701			−0.0546792
$45$		0			0
$46$	−1.19406			−0.176054
$47$	−2.93817	+	5.08906i	−0.428576	+	0.742316i	−0.996747	−	0.0805948i	$-0.974318\pi$
$47$	−2.93817	+	5.08906i	−0.428576	+	0.742316i	0.568171	+	0.822911i	$0.307651\pi$
$48$		0			0
$49$	3.49832	+	6.05927i	0.499760	+	0.865610i
$50$	−3.80299	−	6.58697i	−0.537824	−	0.931538i
$51$		0			0
$52$	0.411292	−	0.712379i	0.0570360	−	0.0987892i
$53$	0.0547103			0.00751503			0.00375752	−	0.999993i	$-0.498804\pi$
$53$	0.0547103			0.00751503			0.00375752	+	0.999993i	$0.498804\pi$
$54$		0			0
$55$	−0.163551			−0.0220532
$56$	0.0737000	−	0.127652i	0.00984857	−	0.0170582i
$57$		0			0
$58$	0.764092	+	1.32345i	0.100330	+	0.173777i
$59$	−3.61816	−	6.26684i	−0.471045	−	0.815873i	0.528407	−	0.848991i	$-0.322790\pi$
$59$	−3.61816	−	6.26684i	−0.471045	−	0.815873i	−0.999451	+	0.0331179i	$0.989456\pi$
$60$		0			0
$61$	2.02285	−	3.50368i	0.258999	−	0.448600i	−0.706975	−	0.707239i	$-0.749941\pi$
$61$	2.02285	−	3.50368i	0.258999	−	0.448600i	0.965974	+	0.258639i	$0.0832740\pi$
$62$	1.84760			0.234646
$63$		0			0
$64$	6.24650			0.780812
$65$	0.185462	−	0.321230i	0.0230037	−	0.0398436i
$66$		0			0
$67$	2.16938	+	3.75748i	0.265032	+	0.459050i	0.967572	−	0.252595i	$-0.0812840\pi$
$67$	2.16938	+	3.75748i	0.265032	+	0.459050i	−0.702540	+	0.711645i	$0.747951\pi$
$68$	−0.307659	−	0.532881i	−0.0373091	−	0.0646213i
$69$		0			0
$70$	−0.00669485	+	0.0115958i	−0.000800188	+	0.00138597i
$71$	−14.9063			−1.76905			−0.884527	−	0.466489i	$-0.845519\pi$
$71$	−14.9063			−1.76905			−0.884527	+	0.466489i	$0.845519\pi$
$72$		0			0
$73$	−3.30924			−0.387317			−0.193658	−	0.981069i	$-0.562035\pi$
$73$	−3.30924			−0.387317			−0.193658	+	0.981069i	$0.562035\pi$
$74$	−0.984108	+	1.70452i	−0.114400	+	0.198147i
$75$		0			0
$76$	−0.485476	−	0.840869i	−0.0556879	−	0.0964543i
$77$	−0.0313345	−	0.0542730i	−0.00357090	−	0.00618498i
$78$		0			0
$79$	−1.60912	+	2.78708i	−0.181040	+	0.313570i	−0.942235	−	0.334953i	$-0.891280\pi$
$79$	−1.60912	+	2.78708i	−0.181040	+	0.313570i	0.761195	+	0.648523i	$0.224613\pi$
$80$	−0.689278			−0.0770636
$81$		0			0
$82$	−6.68112			−0.737807
$83$	−4.05392	+	7.02160i	−0.444976	+	0.770721i	−0.998051	−	0.0624110i	$-0.980121\pi$
$83$	−4.05392	+	7.02160i	−0.444976	+	0.770721i	0.553075	+	0.833132i	$0.313454\pi$
$84$		0			0
$85$	−0.138731	−	0.240289i	−0.0150475	−	0.0260630i
$86$	−5.68804	−	9.85197i	−0.613357	−	1.06236i
$87$		0			0
$88$	1.37570	−	2.38279i	0.146650	−	0.254006i
$89$	3.75415			0.397939			0.198970	−	0.980006i	$-0.436241\pi$
$89$	3.75415			0.397939			0.198970	+	0.980006i	$0.436241\pi$
$90$		0			0
$91$	0.142130			0.0148992
$92$	−0.131013	+	0.226921i	−0.0136590	+	0.0236581i
$93$		0			0
$94$	4.49007	+	7.77702i	0.463115	+	0.802139i
$95$	−0.218913	−	0.379169i	−0.0224600	−	0.0389019i
$96$		0			0
$97$	−7.78455	+	13.4832i	−0.790402	+	1.36902i	0.135317	+	0.990802i	$0.456795\pi$
$97$	−7.78455	+	13.4832i	−0.790402	+	1.36902i	−0.925718	+	0.378214i	$0.876538\pi$
$98$	10.6922			1.08007
$99$		0			0
$100$	−1.66906			−0.166906
$101$	−5.99585	+	10.3851i	−0.596609	+	1.03336i	0.396708	+	0.917945i	$0.370152\pi$
$101$	−5.99585	+	10.3851i	−0.596609	+	1.03336i	−0.993318	+	0.115413i	$0.963181\pi$
$102$		0			0
$103$	−5.47078	−	9.47568i	−0.539052	−	0.933666i	−0.998955	−	0.0456970i	$-0.985449\pi$
$103$	−5.47078	−	9.47568i	−0.539052	−	0.933666i	0.459903	−	0.887969i	$-0.347884\pi$
$104$	3.12002	+	5.40403i	0.305943	+	0.529908i
$105$		0			0
$106$	0.0418037	−	0.0724061i	0.00406033	−	0.00703270i
$107$	−3.86363			−0.373511			−0.186756	−	0.982406i	$-0.559797\pi$
$107$	−3.86363			−0.373511			−0.186756	+	0.982406i	$0.559797\pi$
$108$		0			0
$109$	−15.3103			−1.46646			−0.733230	−	0.679980i	$-0.761988\pi$
$109$	−15.3103			−1.46646			−0.733230	+	0.679980i	$0.761988\pi$
$110$	−0.124968	+	0.216451i	−0.0119152	+	0.0206378i
$111$		0			0
$112$	−0.132058	−	0.228731i	−0.0124783	−	0.0216131i
$113$	4.58543	+	7.94219i	0.431361	+	0.747139i	0.996991	−	0.0775204i	$-0.0247003\pi$
$113$	4.58543	+	7.94219i	0.431361	+	0.747139i	−0.565630	+	0.824659i	$0.691367\pi$
$114$		0			0
$115$	−0.0590769	+	0.102324i	−0.00550895	+	0.00954179i
$116$	0.335346			0.0311361
$117$		0			0
$118$	−11.0584			−1.01801
$119$	0.0531587	−	0.0920735i	0.00487305	−	0.00844036i
$120$		0			0
$121$	4.91510	+	8.51321i	0.446827	+	0.773928i
$122$	−3.09128	−	5.35426i	−0.279872	−	0.484752i
$123$		0			0
$124$	0.202720	−	0.351121i	0.0182048	−	0.0315316i
$125$	−1.50870			−0.134942
$126$		0			0
$127$	−12.5497			−1.11360			−0.556801	−	0.830646i	$-0.687972\pi$
$127$	−12.5497			−1.11360			−0.556801	+	0.830646i	$0.687972\pi$
$128$	6.65093	−	11.5197i	0.587864	−	1.01821i
$129$		0			0
$130$	−0.283420	−	0.490898i	−0.0248576	−	0.0430546i
$131$	9.22384	+	15.9762i	0.805891	+	1.39584i	0.915688	+	0.401890i	$0.131647\pi$
$131$	9.22384	+	15.9762i	0.805891	+	1.39584i	−0.109797	+	0.993954i	$0.535020\pi$
$132$		0			0
$133$	0.0838827	−	0.145289i	0.00727355	−	0.0125982i
$134$	6.63044			0.572782
$135$		0			0
$136$	4.66773			0.400255
$137$	8.59757	−	14.8914i	0.734540	−	1.27226i	−0.220385	−	0.975413i	$-0.570731\pi$
$137$	8.59757	−	14.8914i	0.734540	−	1.27226i	0.954925	−	0.296848i	$-0.0959354\pi$
$138$		0			0
$139$	−0.817007	−	1.41510i	−0.0692976	−	0.120027i	0.829295	−	0.558812i	$-0.188742\pi$
$139$	−0.817007	−	1.41510i	−0.0692976	−	0.120027i	−0.898592	+	0.438785i	$0.855409\pi$
$140$	0.00146912	+	0.00254460i	0.000124164	+	0.000215058i
$141$		0			0
$142$	−11.3898	+	19.7277i	−0.955810	+	1.65551i
$143$	2.65303			0.221858
$144$		0			0
$145$	0.151216			0.0125578
$146$	−2.52856	+	4.37960i	−0.209265	+	0.362458i
$147$		0			0
$148$	0.215953	+	0.374042i	0.0177513	+	0.0307461i
$149$	2.54709	+	4.41169i	0.208666	+	0.361419i	0.951294	−	0.308284i	$-0.0997546\pi$
$149$	2.54709	+	4.41169i	0.208666	+	0.361419i	−0.742629	+	0.669703i	$0.766421\pi$
$150$		0			0
$151$	8.81217	−	15.2631i	0.717124	−	1.24210i	−0.245010	−	0.969521i	$-0.578791\pi$
$151$	8.81217	−	15.2631i	0.717124	−	1.24210i	0.962134	−	0.272575i	$-0.0878754\pi$
$152$	7.36553			0.597424
$153$		0			0
$154$	−0.0957698			−0.00771735
$155$	0.0914115	−	0.158329i	0.00734235	−	0.0127173i
$156$		0			0
$157$	−0.737082	−	1.27666i	−0.0588256	−	0.101889i	0.835113	−	0.550079i	$-0.185402\pi$
$157$	−0.737082	−	1.27666i	−0.0588256	−	0.101889i	−0.893938	+	0.448190i	$0.852069\pi$
$158$	2.45903	+	4.25916i	0.195630	+	0.338841i
$159$		0			0
$160$	−0.141994	+	0.245940i	−0.0112256	+	0.0194433i
$161$	−0.0452739			−0.00356809
$162$		0			0
$163$	−14.2857			−1.11894			−0.559469	−	0.828851i	$-0.688995\pi$
$163$	−14.2857			−1.11894			−0.559469	+	0.828851i	$0.688995\pi$
$164$	−0.733056	+	1.26969i	−0.0572421	+	0.0991462i
$165$		0			0
$166$	6.19514	+	10.7303i	0.480836	+	0.832832i
$167$	7.16948	+	12.4179i	0.554791	+	0.960927i	0.997920	+	0.0644685i	$0.0205352\pi$
$167$	7.16948	+	12.4179i	0.554791	+	0.960927i	−0.443129	+	0.896458i	$0.646131\pi$
$168$		0			0
$169$	3.49154	−	6.04752i	0.268580	−	0.465194i
$170$	−0.424013			−0.0325203
$171$		0			0
$172$	−2.49638			−0.190347
$173$	−3.52672	+	6.10846i	−0.268132	+	0.464417i	−0.968379	−	0.249482i	$-0.919740\pi$
$173$	−3.52672	+	6.10846i	−0.268132	+	0.464417i	0.700248	+	0.713900i	$0.253073\pi$
$174$		0			0
$175$	−0.144194	−	0.249751i	−0.0109000	−	0.0188794i
$176$	−2.46503	−	4.26955i	−0.185809	−	0.321830i
$177$		0			0
$178$	2.86852	−	4.96841i	0.215004	−	0.372398i
$179$	−11.7051			−0.874878			−0.437439	−	0.899248i	$-0.644114\pi$
$179$	−11.7051			−0.874878			−0.437439	+	0.899248i	$0.644114\pi$
$180$		0			0
$181$	−7.15646			−0.531936			−0.265968	−	0.963982i	$-0.585691\pi$
$181$	−7.15646			−0.531936			−0.265968	+	0.963982i	$0.585691\pi$
$182$	0.108600	−	0.188101i	0.00804998	−	0.0139430i
$183$		0			0
$184$	−0.993848	−	1.72140i	−0.0732675	−	0.126903i
$185$	0.0973788	+	0.168665i	0.00715943	+	0.0124005i
$186$		0			0
$187$	0.992274	−	1.71867i	0.0725622	−	0.125681i
$188$	1.97061			0.143721
$189$		0			0
$190$	−0.669080			−0.0485401
$191$	−11.4273	+	19.7927i	−0.826853	+	1.43215i	0.0736417	+	0.997285i	$0.476538\pi$
$191$	−11.4273	+	19.7927i	−0.826853	+	1.43215i	−0.900495	+	0.434867i	$0.856795\pi$
$192$		0			0
$193$	−0.283851	−	0.491645i	−0.0204321	−	0.0353894i	0.855629	−	0.517590i	$-0.173171\pi$
$193$	−0.283851	−	0.491645i	−0.0204321	−	0.0353894i	−0.876061	+	0.482201i	$0.839838\pi$
$194$	11.8962	+	20.6049i	0.854100	+	1.47934i
$195$		0			0
$196$	1.17315	−	2.03195i	0.0837963	−	0.145139i
$197$	−7.85018			−0.559302			−0.279651	−	0.960102i	$-0.590219\pi$
$197$	−7.85018			−0.559302			−0.279651	+	0.960102i	$0.590219\pi$
$198$		0			0
$199$	15.9248			1.12888			0.564441	−	0.825473i	$-0.309092\pi$
$199$	15.9248			1.12888			0.564441	+	0.825473i	$0.309092\pi$
$200$	6.33066	−	10.9650i	0.447645	−	0.775344i
$201$		0			0
$202$	9.16276	+	15.8704i	0.644690	+	1.11664i
$203$	0.0289713	+	0.0501797i	0.00203339	+	0.00352193i
$204$		0			0
$205$	−0.330553	+	0.572535i	−0.0230868	+	0.0399876i
$206$	−16.7207			−1.16499
$207$		0			0
$208$	11.1811			0.775269
$209$	1.56578	−	2.71201i	0.108307	−	0.187593i
$210$		0			0
$211$	−10.0564	−	17.4181i	−0.692308	−	1.19911i	−0.971080	−	0.238755i	$-0.923261\pi$
$211$	−10.0564	−	17.4181i	−0.692308	−	1.19911i	0.278772	−	0.960357i	$-0.410073\pi$
$212$	−0.00917344	−	0.0158889i	−0.000630034	−	0.00109125i
$213$		0			0
$214$	−2.95217	+	5.11331i	−0.201806	+	0.349539i
$215$	−1.12568			−0.0767706
$216$		0			0
$217$	0.0700537			0.00475555
$218$	−11.6985	+	20.2624i	−0.792321	+	1.37234i
$219$		0			0
$220$	0.0274231	+	0.0474981i	0.00184886	+	0.00320232i
$221$	2.25042	+	3.89784i	0.151380	+	0.262197i
$222$		0			0
$223$	12.2271	−	21.1780i	0.818790	−	1.41819i	−0.0877845	−	0.996139i	$-0.527979\pi$
$223$	12.2271	−	21.1780i	0.818790	−	1.41819i	0.906574	−	0.422046i	$-0.138688\pi$
$224$	−0.108818			−0.00727069
$225$		0			0
$226$	14.0148			0.932248
$227$	14.2157	−	24.6223i	0.943527	−	1.63424i	0.184854	−	0.982766i	$-0.440819\pi$
$227$	14.2157	−	24.6223i	0.943527	−	1.63424i	0.758674	−	0.651471i	$-0.225848\pi$
$228$		0			0
$229$	7.17659	+	12.4302i	0.474242	+	0.821412i	0.999565	−	0.0294912i	$-0.00938869\pi$
$229$	7.17659	+	12.4302i	0.474242	+	0.821412i	−0.525323	+	0.850903i	$0.676055\pi$
$230$	0.0902804	+	0.156370i	0.00595291	+	0.0103108i
$231$		0			0
$232$	−1.27195	+	2.20308i	−0.0835075	+	0.144639i
$233$	3.54955			0.232539			0.116269	−	0.993218i	$-0.462906\pi$
$233$	3.54955			0.232539			0.116269	+	0.993218i	$0.462906\pi$
$234$		0			0
$235$	0.888597			0.0579657
$236$	−1.21334	+	2.10156i	−0.0789815	+	0.136800i
$237$		0			0
$238$	−0.0812362	−	0.140705i	−0.00526576	−	0.00912057i
$239$	6.97252	+	12.0768i	0.451015	+	0.781180i	0.998449	−	0.0556682i	$-0.0177289\pi$
$239$	6.97252	+	12.0768i	0.451015	+	0.781180i	−0.547435	+	0.836848i	$0.684396\pi$
$240$		0			0
$241$	−10.5625	+	18.2947i	−0.680389	+	1.17847i	0.294473	+	0.955660i	$0.404856\pi$
$241$	−10.5625	+	18.2947i	−0.680389	+	1.17847i	−0.974862	+	0.222808i	$0.928478\pi$
$242$	15.0224			0.965674
$243$		0			0
$244$	−1.35671			−0.0868543
$245$	0.529002	−	0.916258i	0.0337967	−	0.0585376i
$246$		0			0
$247$	3.55109	+	6.15067i	0.225951	+	0.391358i
$248$	1.53781	+	2.66357i	0.0976510	+	0.169137i
$249$		0			0
$250$	−1.15279	+	1.99669i	−0.0729086	+	0.126281i
$251$	−6.98888			−0.441134			−0.220567	−	0.975372i	$-0.570791\pi$
$251$	−6.98888			−0.441134			−0.220567	+	0.975372i	$0.570791\pi$
$252$		0			0
$253$	−0.845095			−0.0531307
$254$	−9.58910	+	16.6088i	−0.601673	+	1.04213i
$255$		0			0
$256$	−3.91734	−	6.78503i	−0.244834	−	0.424065i
$257$	−0.816339	−	1.41394i	−0.0509218	−	0.0881992i	0.839441	−	0.543451i	$-0.182883\pi$
$257$	−0.816339	−	1.41394i	−0.0509218	−	0.0881992i	−0.890363	+	0.455252i	$0.849549\pi$
$258$		0			0
$259$	−0.0373134	+	0.0646287i	−0.00231854	+	0.00401583i
$260$	−0.124388			−0.00771421
$261$		0			0
$262$	28.1915			1.74167
$263$	8.25965	−	14.3061i	0.509312	−	0.882153i	−0.490630	−	0.871368i	$-0.663233\pi$
$263$	8.25965	−	14.3061i	0.509312	−	0.882153i	0.999942	−	0.0107856i	$-0.00343324\pi$
$264$		0			0
$265$	−0.00413653	−	0.00716468i	−0.000254105	−	0.000440123i
$266$	−0.128188	−	0.222028i	−0.00785972	−	0.0136134i
$267$		0			0
$268$	0.727494	−	1.26006i	0.0444388	−	0.0769703i
$269$	−4.33854			−0.264525			−0.132263	−	0.991215i	$-0.542224\pi$
$269$	−4.33854			−0.264525			−0.132263	+	0.991215i	$0.542224\pi$
$270$		0			0
$271$	−18.7332			−1.13796			−0.568980	−	0.822351i	$-0.692662\pi$
$271$	−18.7332			−1.13796			−0.568980	+	0.822351i	$0.692662\pi$
$272$	4.18189	−	7.24325i	0.253565	−	0.439187i
$273$		0			0
$274$	−13.1387	−	22.7568i	−0.793736	−	1.37479i
$275$	−2.69156	−	4.66192i	−0.162307	−	0.281125i
$276$		0			0
$277$	−6.21884	+	10.7713i	−0.373654	+	0.647187i	−0.990125	−	0.140190i	$-0.955229\pi$
$277$	−6.21884	+	10.7713i	−0.373654	+	0.647187i	0.616471	+	0.787378i	$0.288562\pi$
$278$	−2.49707			−0.149765
$279$		0			0
$280$	−0.0222892			−0.00133204
$281$	−0.0725462	+	0.125654i	−0.00432774	+	0.00749587i	−0.868181	−	0.496247i	$-0.834711\pi$
$281$	−0.0725462	+	0.125654i	−0.00432774	+	0.00749587i	0.863853	+	0.503743i	$0.168044\pi$
$282$		0			0
$283$	−4.05504	−	7.02354i	−0.241047	−	0.417506i	0.719966	−	0.694010i	$-0.244158\pi$
$283$	−4.05504	−	7.02354i	−0.241047	−	0.417506i	−0.961013	+	0.276504i	$0.910824\pi$
$284$	2.49939	+	4.32906i	0.148311	+	0.256883i
$285$		0			0
$286$	2.02716	−	3.51114i	0.119869	−	0.207618i
$287$	−0.253321			−0.0149531
$288$		0			0
$289$	−13.6332			−0.801955
$290$	0.115543	−	0.200126i	0.00678491	−	0.0117518i
$291$		0			0
$292$	0.554870	+	0.961063i	0.0324713	+	0.0562419i
$293$	9.46566	+	16.3950i	0.552990	+	0.957806i	0.998057	+	0.0623090i	$0.0198464\pi$
$293$	9.46566	+	16.3950i	0.552990	+	0.957806i	−0.445067	+	0.895497i	$0.646820\pi$
$294$		0			0
$295$	−0.547124	+	0.947646i	−0.0318548	+	0.0551741i
$296$	−3.27640			−0.190437
$297$		0			0
$298$	7.78484			0.450964
$299$	0.958314	−	1.65985i	0.0554207	−	0.0959915i
$300$		0			0
$301$	−0.215667	−	0.373547i	−0.0124309	−	0.0215309i
$302$	−13.4666	−	23.3249i	−0.774917	−	1.34220i
$303$		0			0
$304$	6.59890	−	11.4296i	0.378473	−	0.655534i
$305$	−0.611774			−0.0350301
$306$		0			0
$307$	−19.9124			−1.13646			−0.568230	−	0.822870i	$-0.692372\pi$
$307$	−19.9124			−1.13646			−0.568230	+	0.822870i	$0.692372\pi$
$308$	−0.0105079	+	0.0182002i	−0.000598744	+	0.00103705i
$309$		0			0
$310$	−0.139694	−	0.241956i	−0.00793406	−	0.0137422i
$311$	−13.8828	−	24.0457i	−0.787222	−	1.36351i	−0.927663	−	0.373419i	$-0.878185\pi$
$311$	−13.8828	−	24.0457i	−0.787222	−	1.36351i	0.140441	−	0.990089i	$-0.455148\pi$
$312$		0			0
$313$	4.65543	−	8.06345i	0.263141	−	0.455773i	−0.703934	−	0.710265i	$-0.748575\pi$
$313$	4.65543	−	8.06345i	0.263141	−	0.455773i	0.967075	+	0.254492i	$0.0819083\pi$
$314$	−2.25279			−0.127133
$315$		0			0
$316$	1.07922			0.0607110
$317$	6.13808	−	10.6315i	0.344749	−	0.597123i	−0.640559	−	0.767909i	$-0.721297\pi$
$317$	6.13808	−	10.6315i	0.344749	−	0.597123i	0.985308	+	0.170786i	$0.0546307\pi$
$318$		0			0
$319$	0.540786	+	0.936668i	0.0302782	+	0.0524434i
$320$	−0.472285	−	0.818022i	−0.0264015	−	0.0457288i
$321$		0			0
$322$	−0.0345934	+	0.0599176i	−0.00192782	+	0.00333908i
$323$	5.31265			0.295604
$324$		0			0
$325$	12.2086			0.677212
$326$	−10.9156	+	18.9063i	−0.604557	+	1.04712i
$327$		0			0
$328$	−5.56088	−	9.63173i	−0.307048	−	0.531823i
$329$	0.170245	+	0.294873i	0.00938592	+	0.0162569i
$330$		0			0
$331$	10.8883	−	18.8590i	0.598472	−	1.03658i	−0.394574	−	0.918864i	$-0.629108\pi$
$331$	10.8883	−	18.8590i	0.598472	−	1.03658i	0.993047	−	0.117721i	$-0.0375587\pi$
$332$	2.71893			0.149221
$333$		0			0
$334$	21.9126			1.19900
$335$	0.328045	−	0.568191i	0.0179230	−	0.0310436i
$336$		0			0
$337$	5.96522	+	10.3321i	0.324946	+	0.562823i	0.981501	−	0.191455i	$-0.0613205\pi$
$337$	5.96522	+	10.3321i	0.324946	+	0.562823i	−0.656555	+	0.754278i	$0.727987\pi$
$338$	−5.33571	−	9.24172i	−0.290224	−	0.502684i
$339$		0			0
$340$	−0.0465229	+	0.0805801i	−0.00252306	+	0.00437007i
$341$	1.30764			0.0708127
$342$		0			0
$343$	0.811001			0.0437900
$344$	9.46861	−	16.4001i	0.510513	−	0.884235i
$345$		0			0
$346$	5.38948	+	9.33485i	0.289740	+	0.501844i
$347$	6.07938	+	10.5298i	0.326358	+	0.565269i	0.981786	−	0.189989i	$-0.0608451\pi$
$347$	6.07938	+	10.5298i	0.326358	+	0.565269i	−0.655428	+	0.755258i	$0.727512\pi$
$348$		0			0
$349$	−5.06632	+	8.77513i	−0.271194	+	0.469722i	−0.969168	−	0.246401i	$-0.920752\pi$
$349$	−5.06632	+	8.77513i	−0.271194	+	0.469722i	0.697974	+	0.716123i	$0.254085\pi$
$350$	−0.440710			−0.0235569
$351$		0			0
$352$	−2.03122			−0.108264
$353$	6.18340	−	10.7100i	0.329109	−	0.570034i	−0.653226	−	0.757163i	$-0.726585\pi$
$353$	6.18340	−	10.7100i	0.329109	−	0.570034i	0.982335	+	0.187129i	$0.0599183\pi$
$354$		0			0
$355$	1.12704	+	1.95208i	0.0598168	+	0.103606i
$356$	−0.629470	−	1.09027i	−0.0333618	−	0.0577844i
$357$		0			0
$358$	−8.94375	+	15.4910i	−0.472692	+	0.818726i
$359$	−19.6499			−1.03708			−0.518541	−	0.855053i	$-0.673525\pi$
$359$	−19.6499			−1.03708			−0.518541	+	0.855053i	$0.673525\pi$
$360$		0			0
$361$	−10.6168			−0.558779
$362$	−5.46819	+	9.47119i	−0.287402	+	0.497795i
$363$		0			0
$364$	−0.0238313	−	0.0412771i	−0.00124910	−	0.00216351i
$365$	0.250205	+	0.433367i	0.0130963	+	0.0226835i
$366$		0			0
$367$	−4.93147	+	8.54155i	−0.257421	+	0.445865i	−0.965550	−	0.260217i	$-0.916206\pi$
$367$	−4.93147	+	8.54155i	−0.257421	+	0.445865i	0.708130	+	0.706082i	$0.249539\pi$
$368$	−3.56162			−0.185662
$369$		0			0
$370$	0.297625			0.0154728
$371$	0.00158503	−	0.00274535i	8.22905e−5	−	0.000142531i
$372$		0			0
$373$	−10.4428	−	18.0874i	−0.540705	−	0.936529i	−0.998864	−	0.0476584i	$-0.984824\pi$
$373$	−10.4428	−	18.0874i	−0.540705	−	0.936529i	0.458158	−	0.888871i	$-0.348509\pi$
$374$	−1.51638	−	2.62644i	−0.0784100	−	0.135810i
$375$		0			0
$376$	−7.47441	+	12.9461i	−0.385463	+	0.667642i
$377$	−2.45294			−0.126333
$378$		0			0
$379$	−29.3384			−1.50701			−0.753506	−	0.657442i	$-0.771639\pi$
$379$	−29.3384			−1.50701			−0.753506	+	0.657442i	$0.771639\pi$
$380$	−0.0734117	+	0.127153i	−0.00376594	+	0.00652280i
$381$		0			0
$382$	17.4631	+	30.2469i	0.893489	+	1.54757i
$383$	−16.3193	−	28.2659i	−0.833879	−	1.44432i	−0.894940	−	0.446187i	$-0.852782\pi$
$383$	−16.3193	−	28.2659i	−0.833879	−	1.44432i	0.0610603	−	0.998134i	$-0.480552\pi$
$384$		0			0
$385$	−0.00473828	+	0.00820694i	−0.000241485	+	0.000418264i
$386$	−0.867554			−0.0441573
$387$		0			0
$388$	5.22104			0.265058
$389$	16.9326	−	29.3282i	0.858518	−	1.48700i	−0.0148249	−	0.999890i	$-0.504719\pi$
$389$	16.9326	−	29.3282i	0.858518	−	1.48700i	0.873343	−	0.487106i	$-0.161948\pi$
$390$		0			0
$391$	−0.716847	−	1.24162i	−0.0362525	−	0.0627912i
$392$	8.89937	+	15.4142i	0.449486	+	0.778533i
$393$		0			0
$394$	−5.99826	+	10.3893i	−0.302188	+	0.523405i
$395$	0.486649			0.0244860
$396$		0			0
$397$	30.3217			1.52180			0.760902	−	0.648867i	$-0.224757\pi$
$397$	30.3217			1.52180			0.760902	+	0.648867i	$0.224757\pi$
$398$	12.1680	−	21.0757i	0.609929	−	1.05643i
$399$		0			0
$400$	−11.3435	−	19.6475i	−0.567174	−	0.982374i
$401$	−17.3296	−	30.0157i	−0.865397	−	1.49891i	−0.866653	−	0.498912i	$-0.833733\pi$
$401$	−17.3296	−	30.0157i	−0.865397	−	1.49891i	0.00125608	−	0.999999i	$-0.499600\pi$
$402$		0			0
$403$	−1.48283	+	2.56833i	−0.0738649	+	0.127938i
$404$	4.02137			0.200071
$405$		0			0
$406$	0.0885469			0.00439451
$407$	−0.696502	+	1.20638i	−0.0345243	+	0.0597979i
$408$		0			0
$409$	6.67231	+	11.5568i	0.329925	+	0.571446i	0.982497	−	0.186281i	$-0.0596433\pi$
$409$	6.67231	+	11.5568i	0.329925	+	0.571446i	−0.652572	+	0.757727i	$0.726310\pi$
$410$	0.505146	+	0.874939i	0.0249474	+	0.0432102i
$411$		0			0
$412$	−1.83461	+	3.17763i	−0.0903846	+	0.156551i
$413$	−0.419291			−0.0206320
$414$		0			0
$415$	1.22604			0.0601837
$416$	2.30335	−	3.98951i	0.112931	−	0.195602i
$417$		0			0
$418$	−2.39280	−	4.14444i	−0.117035	−	0.202711i
$419$	2.20776	+	3.82395i	0.107856	+	0.186812i	0.914902	−	0.403677i	$-0.132268\pi$
$419$	2.20776	+	3.82395i	0.107856	+	0.186812i	−0.807045	+	0.590489i	$0.798935\pi$
$420$		0			0
$421$	−8.56811	+	14.8404i	−0.417584	+	0.723277i	−0.995696	−	0.0926806i	$-0.970456\pi$
$421$	−8.56811	+	14.8404i	−0.417584	+	0.723277i	0.578112	+	0.815958i	$0.303790\pi$
$422$	−30.7359			−1.49620
$423$		0			0
$424$	0.139177			0.00675905
$425$	4.56621	−	7.90890i	0.221494	−	0.383638i
$426$		0			0
$427$	−0.117209	−	0.203012i	−0.00567214	−	0.00982444i
$428$	0.647827	+	1.12207i	0.0313139	+	0.0542373i
$429$		0			0
$430$	−0.860122	+	1.48977i	−0.0414787	+	0.0718433i
$431$	−12.9834			−0.625388			−0.312694	−	0.949854i	$-0.601231\pi$
$431$	−12.9834			−0.625388			−0.312694	+	0.949854i	$0.601231\pi$
$432$		0			0
$433$	24.6959			1.18681			0.593404	−	0.804905i	$-0.297784\pi$
$433$	24.6959			1.18681			0.593404	+	0.804905i	$0.297784\pi$
$434$	0.0535274	−	0.0927123i	0.00256940	−	0.00445033i
$435$		0			0
$436$	2.56712	+	4.44639i	0.122943	+	0.212943i
$437$	−1.13116	−	1.95923i	−0.0541109	−	0.0937227i
$438$		0			0
$439$	17.5325	−	30.3672i	0.836781	−	1.44935i	−0.0557905	−	0.998442i	$-0.517768\pi$
$439$	17.5325	−	30.3672i	0.836781	−	1.44935i	0.892572	−	0.450905i	$-0.148899\pi$
$440$	−0.416057			−0.0198347
$441$		0			0
$442$	6.87811			0.327158
$443$	1.72283	−	2.98404i	0.0818544	−	0.141776i	−0.822192	−	0.569210i	$-0.807249\pi$
$443$	1.72283	−	2.98404i	0.0818544	−	0.141776i	0.904046	+	0.427434i	$0.140582\pi$
$444$		0			0
$445$	−0.283844	−	0.491632i	−0.0134555	−	0.0233056i
$446$	−18.6853	−	32.3639i	−0.884776	−	1.53248i
$447$		0			0
$448$	0.180969	−	0.313448i	0.00854999	−	0.0148090i
$449$	2.91179			0.137416			0.0687079	−	0.997637i	$-0.478112\pi$
$449$	2.91179			0.137416			0.0687079	+	0.997637i	$0.478112\pi$
$450$		0			0
$451$	−4.72856			−0.222659
$452$	1.53771	−	2.66338i	0.0723276	−	0.125275i
$453$		0			0
$454$	−21.7242	−	37.6273i	−1.01957	−	1.76594i
$455$	−0.0107461	−	0.0186129i	−0.000503787	−	0.000872585i
$456$		0			0
$457$	−14.4898	+	25.0971i	−0.677805	+	1.17399i	0.297835	+	0.954617i	$0.403735\pi$
$457$	−14.4898	+	25.0971i	−0.677805	+	1.17399i	−0.975640	+	0.219376i	$0.929598\pi$
$458$	21.9343			1.02492
$459$		0			0
$460$	0.0396224			0.00184741
$461$	−10.8729	+	18.8324i	−0.506402	+	0.877114i	0.493570	+	0.869706i	$0.335692\pi$
$461$	−10.8729	+	18.8324i	−0.506402	+	0.877114i	−0.999973	+	0.00740849i	$0.997642\pi$
$462$		0			0
$463$	−10.4419	−	18.0860i	−0.485278	−	0.840526i	0.514579	−	0.857443i	$-0.327948\pi$
$463$	−10.4419	−	18.0860i	−0.485278	−	0.840526i	−0.999857	+	0.0169169i	$0.994615\pi$
$464$	2.27912	+	3.94755i	0.105805	+	0.183260i
$465$		0			0
$466$	2.71218	−	4.69764i	0.125639	−	0.217614i
$467$	18.3950			0.851221			0.425610	−	0.904906i	$-0.360059\pi$
$467$	18.3950			0.851221			0.425610	+	0.904906i	$0.360059\pi$
$468$		0			0
$469$	0.251399			0.0116085
$470$	0.678970	−	1.17601i	0.0313185	−	0.0542453i
$471$		0			0
$472$	−9.20424	−	15.9422i	−0.423659	−	0.733799i
$473$	−4.02570	−	6.97272i	−0.185102	−	0.320606i
$474$		0			0
$475$	7.20533	−	12.4800i	0.330603	−	0.572622i
$476$	−0.0356531			−0.00163416
$477$		0			0
$478$	21.3106			0.974723
$479$	−4.65458	+	8.06197i	−0.212673	+	0.368361i	−0.952550	−	0.304381i	$-0.901550\pi$
$479$	−4.65458	+	8.06197i	−0.212673	+	0.368361i	0.739877	+	0.672742i	$0.234884\pi$
$480$		0			0
$481$	−1.57963	−	2.73599i	−0.0720247	−	0.124751i
$482$	16.1414	+	27.9577i	0.735221	+	1.27344i
$483$		0			0
$484$	1.64826	−	2.85487i	0.0749209	−	0.129767i
$485$	2.35430			0.106903
$486$		0			0
$487$	20.2090			0.915755			0.457877	−	0.889015i	$-0.348610\pi$
$487$	20.2090			0.915755			0.457877	+	0.889015i	$0.348610\pi$
$488$	5.14592	−	8.91299i	0.232945	−	0.403472i
$489$		0			0
$490$	−0.808412	−	1.40021i	−0.0365203	−	0.0632551i
$491$	−4.75578	−	8.23725i	−0.214625	−	0.371742i	0.738531	−	0.674219i	$-0.235520\pi$
$491$	−4.75578	−	8.23725i	−0.214625	−	0.371742i	−0.953157	+	0.302477i	$0.902186\pi$
$492$		0			0
$493$	−0.917437	+	1.58905i	−0.0413193	+	0.0715671i
$494$	10.8534			0.488320
$495$		0			0
$496$	5.51099			0.247451
$497$	−0.431855	+	0.747995i	−0.0193713	+	0.0335521i
$498$		0			0
$499$	2.29072	+	3.96765i	0.102547	+	0.177616i	0.912733	−	0.408556i	$-0.133968\pi$
$499$	2.29072	+	3.96765i	0.102547	+	0.177616i	−0.810186	+	0.586172i	$0.800634\pi$
$500$	0.252969	+	0.438154i	0.0113131	+	0.0195949i
$501$		0			0
$502$	−5.34015	+	9.24941i	−0.238342	+	0.412821i
$503$	−8.85873			−0.394991			−0.197496	−	0.980304i	$-0.563281\pi$
$503$	−8.85873			−0.394991			−0.197496	+	0.980304i	$0.563281\pi$
$504$		0			0
$505$	1.81334			0.0806924
$506$	−0.645730	+	1.11844i	−0.0287062	+	0.0497206i
$507$		0			0
$508$	2.10424	+	3.64465i	0.0933606	+	0.161705i
$509$	13.8720	+	24.0270i	0.614865	+	1.06498i	0.990408	+	0.138173i	$0.0441229\pi$
$509$	13.8720	+	24.0270i	0.614865	+	1.06498i	−0.375543	+	0.926805i	$0.622544\pi$
$510$		0			0
$511$	−0.0958728	+	0.166057i	−0.00424116	+	0.00734591i
$512$	14.6309			0.646599
$513$		0			0
$514$	−2.49503			−0.110051
$515$	−0.827270	+	1.43287i	−0.0364539	+	0.0631399i
$516$		0			0
$517$	3.17784	+	5.50418i	0.139761	+	0.242074i
$518$	0.0570217	+	0.0987645i	0.00250539	+	0.00433946i
$519$		0			0
$520$	0.471796	−	0.817175i	0.0206896	−	0.0358355i
$521$	25.4524			1.11509			0.557546	−	0.830146i	$-0.311743\pi$
$521$	25.4524			1.11509			0.557546	+	0.830146i	$0.311743\pi$
$522$		0			0
$523$	25.8717			1.13129			0.565646	−	0.824648i	$-0.308627\pi$
$523$	25.8717			1.13129			0.565646	+	0.824648i	$0.308627\pi$
$524$	3.09318	−	5.35755i	0.135126	−	0.234045i
$525$		0			0
$526$	−12.6223	−	21.8624i	−0.550357	−	0.953246i
$527$	1.10920	+	1.92119i	0.0483175	+	0.0836883i
$528$		0			0
$529$	11.1947	−	19.3899i	0.486728	−	0.843037i
$530$	−0.0126428			−0.000549167
$531$		0			0
$532$	−0.0562595			−0.00243916
$533$	5.36205	−	9.28735i	0.232256	−	0.402280i
$534$		0			0
$535$	0.292121	+	0.505969i	0.0126295	+	0.0218750i
$536$	5.51869	+	9.55865i	0.238371	+	0.412871i
$537$		0			0
$538$	−3.31504	+	5.74182i	−0.142922	+	0.247547i
$539$	7.56737			0.325950
$540$		0			0
$541$	4.29297			0.184569			0.0922845	−	0.995733i	$-0.470583\pi$
$541$	4.29297			0.184569			0.0922845	+	0.995733i	$0.470583\pi$
$542$	−14.3139	+	24.7924i	−0.614834	+	1.06492i
$543$		0			0
$544$	−1.72297	−	2.98427i	−0.0738718	−	0.127950i
$545$	1.15758	+	2.00499i	0.0495853	+	0.0858843i
$546$		0			0
$547$	9.26196	−	16.0422i	0.396013	−	0.685914i	−0.597217	−	0.802080i	$-0.703727\pi$
$547$	9.26196	−	16.0422i	0.396013	−	0.685914i	0.993230	+	0.116165i	$0.0370602\pi$
$548$	−5.76632			−0.246325
$549$		0			0
$550$	−8.22641			−0.350775
$551$	−1.44769	+	2.50747i	−0.0616735	+	0.106822i
$552$		0			0
$553$	0.0932365	+	0.161490i	0.00396482	+	0.00686727i
$554$	9.50353	+	16.4606i	0.403766	+	0.699344i
$555$		0			0
$556$	−0.273980	+	0.474547i	−0.0116193	+	0.0201253i
$557$	25.5627			1.08313			0.541564	−	0.840660i	$-0.317833\pi$
$557$	25.5627			1.08313			0.541564	+	0.840660i	$0.317833\pi$
$558$		0			0
$559$	18.2601			0.772321
$560$	−0.0199693	+	0.0345878i	−0.000843855	+	0.00146160i
$561$		0			0
$562$	0.110864	+	0.192022i	0.00467651	+	0.00809995i
$563$	−18.8929	−	32.7235i	−0.796242	−	1.37913i	−0.922047	−	0.387077i	$-0.873485\pi$
$563$	−18.8929	−	32.7235i	−0.796242	−	1.37913i	0.125805	−	0.992055i	$-0.459849\pi$
$564$		0			0
$565$	0.693390	−	1.20099i	0.0291711	−	0.0505259i
$566$	−12.3937			−0.520946
$567$		0			0
$568$	−37.9201			−1.59109
$569$	−18.7639	+	32.5000i	−0.786622	+	1.36247i	0.141403	+	0.989952i	$0.454839\pi$
$569$	−18.7639	+	32.5000i	−0.786622	+	1.36247i	−0.928025	+	0.372517i	$0.878495\pi$
$570$		0			0
$571$	5.07055	+	8.78244i	0.212196	+	0.367534i	0.952401	−	0.304847i	$-0.0986052\pi$
$571$	5.07055	+	8.78244i	0.212196	+	0.367534i	−0.740206	+	0.672381i	$0.765272\pi$
$572$	−0.444842	−	0.770489i	−0.0185998	−	0.0322158i
$573$		0			0
$574$	−0.193561	+	0.335257i	−0.00807907	+	0.0139934i
$575$	−3.88893			−0.162179
$576$		0			0
$577$	42.3619			1.76355			0.881775	−	0.471670i	$-0.156349\pi$
$577$	42.3619			1.76355			0.881775	+	0.471670i	$0.156349\pi$
$578$	−10.4170	+	18.0429i	−0.433292	+	0.750484i
$579$		0			0
$580$	−0.0253548	−	0.0439159i	−0.00105280	−	0.00182351i
$581$	0.234895	+	0.406849i	0.00974507	+	0.0168790i
$582$		0			0
$583$	0.0295865	−	0.0512454i	0.00122535	−	0.00212237i
$584$	−8.41836			−0.348354
$585$		0			0
$586$	28.9305			1.19511
$587$	−20.6611	+	35.7861i	−0.852775	+	1.47705i	0.0259199	+	0.999664i	$0.491749\pi$
$587$	−20.6611	+	35.7861i	−0.852775	+	1.47705i	−0.878694	+	0.477385i	$0.841585\pi$
$588$		0			0
$589$	1.75028	+	3.03158i	0.0721191	+	0.124914i
$590$	0.836106	+	1.44818i	0.0344219	+	0.0596205i
$591$		0			0
$592$	−2.93538	+	5.08422i	−0.120643	+	0.208960i
$593$	27.3325			1.12241			0.561206	−	0.827676i	$-0.310338\pi$
$593$	27.3325			1.12241			0.561206	+	0.827676i	$0.310338\pi$
$594$		0			0
$595$	−0.0160769			−0.000659088
$596$	0.854156	−	1.47944i	0.0349876	−	0.0606003i
$597$		0			0
$598$	−1.46448	−	2.53655i	−0.0598870	−	0.103727i
$599$	−8.29376	−	14.3652i	−0.338874	−	0.586947i	0.645347	−	0.763889i	$-0.276713\pi$
$599$	−8.29376	−	14.3652i	−0.338874	−	0.586947i	−0.984221	+	0.176943i	$0.943379\pi$
$600$		0			0
$601$	14.9920	−	25.9669i	0.611536	−	1.05921i	−0.379446	−	0.925214i	$-0.623885\pi$
$601$	14.9920	−	25.9669i	0.611536	−	1.05921i	0.990982	−	0.133997i	$-0.0427813\pi$
$602$	−0.659159			−0.0268653
$603$		0			0
$604$	−5.91025			−0.240485
$605$	0.743242	−	1.28733i	0.0302171	−	0.0523375i
$606$		0			0
$607$	16.3214	+	28.2694i	0.662464	+	1.14742i	0.979966	+	0.199164i	$0.0638225\pi$
$607$	16.3214	+	28.2694i	0.662464	+	1.14742i	−0.317502	+	0.948257i	$0.602844\pi$
$608$	−2.71880	−	4.70909i	−0.110262	−	0.190979i
$609$		0			0
$610$	−0.467451	+	0.809649i	−0.0189266	+	0.0327817i
$611$	−14.4143			−0.583141
$612$		0			0
$613$	25.4682			1.02865			0.514325	−	0.857596i	$-0.328043\pi$
$613$	25.4682			1.02865			0.514325	+	0.857596i	$0.328043\pi$
$614$	−15.2149	+	26.3530i	−0.614023	+	1.06352i
$615$		0			0
$616$	−0.0797118	−	0.138065i	−0.00321168	−	0.00556279i
$617$	2.79406	+	4.83945i	0.112484	+	0.194829i	0.916771	−	0.399412i	$-0.130786\pi$
$617$	2.79406	+	4.83945i	0.112484	+	0.194829i	−0.804287	+	0.594241i	$0.797452\pi$
$618$		0			0
$619$	−17.9962	+	31.1704i	−0.723329	+	1.25284i	0.236329	+	0.971673i	$0.424056\pi$
$619$	−17.9962	+	31.1704i	−0.723329	+	1.25284i	−0.959658	+	0.281169i	$0.909278\pi$
$620$	−0.0613090			−0.00246223
$621$		0			0
$622$	−42.4310			−1.70133
$623$	0.108763	−	0.188382i	0.00435748	−	0.00754738i
$624$		0			0
$625$	−12.3288	−	21.3540i	−0.493151	−	0.854162i
$626$	−7.11436	−	12.3224i	−0.284347	−	0.492503i
$627$		0			0
$628$	−0.247178	+	0.428124i	−0.00986346	+	0.0170840i
$629$	−2.36322			−0.0942276
$630$		0			0
$631$	−1.71845			−0.0684105			−0.0342053	−	0.999415i	$-0.510890\pi$
$631$	−1.71845			−0.0684105			−0.0342053	+	0.999415i	$0.510890\pi$
$632$	−4.09343	+	7.09003i	−0.162828	+	0.282026i
$633$		0			0
$634$	−9.38012	−	16.2468i	−0.372532	−	0.645244i
$635$	0.948854	+	1.64346i	0.0376541	+	0.0652189i
$636$		0			0
$637$	−8.58118	+	14.8630i	−0.339999	+	0.588895i
$638$	1.65284			0.0654366
$639$		0			0
$640$	−2.01145			−0.0795096
$641$	2.41368	−	4.18062i	0.0953347	−	0.165124i	−0.814414	−	0.580285i	$-0.802941\pi$
$641$	2.41368	−	4.18062i	0.0953347	−	0.165124i	0.909748	+	0.415160i	$0.136275\pi$
$642$		0			0
$643$	16.5082	+	28.5930i	0.651020	+	1.12760i	0.982876	+	0.184269i	$0.0589919\pi$
$643$	16.5082	+	28.5930i	0.651020	+	1.12760i	−0.331856	+	0.943330i	$0.607675\pi$
$644$	0.00759122	+	0.0131484i	0.000299136	+	0.000518118i
$645$		0			0
$646$	4.05935	−	7.03100i	0.159713	−	0.276631i
$647$	7.25011			0.285031			0.142516	−	0.989793i	$-0.454481\pi$
$647$	7.25011			0.285031			0.142516	+	0.989793i	$0.454481\pi$
$648$		0			0
$649$	−7.82660			−0.307221
$650$	9.32851	−	16.1575i	0.365894	−	0.633747i
$651$		0			0
$652$	2.39532	+	4.14881i	0.0938079	+	0.162480i
$653$	20.1301	+	34.8663i	0.787751	+	1.36442i	0.927342	+	0.374216i	$0.122088\pi$
$653$	20.1301	+	34.8663i	0.787751	+	1.36442i	−0.139591	+	0.990209i	$0.544579\pi$
$654$		0			0
$655$	1.39479	−	2.41585i	0.0544990	−	0.0943951i
$656$	−19.9283			−0.778070
$657$		0			0
$658$	0.520332			0.0202847
$659$	17.2360	−	29.8536i	0.671418	−	1.16293i	−0.306085	−	0.952004i	$-0.599019\pi$
$659$	17.2360	−	29.8536i	0.671418	−	1.16293i	0.977502	−	0.210925i	$-0.0676476\pi$
$660$		0			0
$661$	15.9747	+	27.6690i	0.621344	+	1.07620i	0.989236	+	0.146330i	$0.0467463\pi$
$661$	15.9747	+	27.6690i	0.621344	+	1.07620i	−0.367892	+	0.929869i	$0.619920\pi$
$662$	−16.6392	−	28.8200i	−0.646703	−	1.12012i
$663$		0			0
$664$	−10.3128	+	17.8622i	−0.400213	+	0.693189i
$665$	−0.0253688			−0.000983760
$666$		0			0
$667$	0.781359			0.0302543
$668$	2.40426	−	4.16430i	0.0930235	−	0.161121i
$669$		0			0
$670$	−0.501314	−	0.868301i	−0.0193674	−	0.0335454i
$671$	−2.18785	−	3.78948i	−0.0844612	−	0.146291i
$672$		0			0
$673$	−11.4286	+	19.7948i	−0.440538	+	0.763035i	−0.997729	−	0.0673494i	$-0.978546\pi$
$673$	−11.4286	+	19.7948i	−0.440538	+	0.763035i	0.557191	+	0.830384i	$0.311879\pi$
$674$	18.2319			0.702267
$675$		0			0
$676$	−2.34175			−0.0900672
$677$	−21.3136	+	36.9163i	−0.819150	+	1.41881i	0.0871600	+	0.996194i	$0.472221\pi$
$677$	−21.3136	+	36.9163i	−0.819150	+	1.41881i	−0.906310	+	0.422614i	$0.861112\pi$
$678$		0			0
$679$	0.451057	+	0.781254i	0.0173100	+	0.0299818i
$680$	−0.352918	−	0.611271i	−0.0135338	−	0.0234412i
$681$		0			0
$682$	0.999157	−	1.73059i	0.0382597	−	0.0662678i
$683$	41.5204			1.58873			0.794367	−	0.607438i	$-0.207803\pi$
$683$	41.5204			1.58873			0.794367	+	0.607438i	$0.207803\pi$
$684$		0			0
$685$	−2.60018			−0.0993478
$686$	0.619680	−	1.07332i	0.0236595	−	0.0409794i
$687$		0			0
$688$	−16.9662	−	29.3862i	−0.646829	−	1.12034i
$689$	0.0671006	+	0.116222i	0.00255633	+	0.00442769i
$690$		0			0
$691$	8.11414	−	14.0541i	0.308676	−	0.534643i	−0.669397	−	0.742905i	$-0.733447\pi$
$691$	8.11414	−	14.0541i	0.308676	−	0.534643i	0.978073	+	0.208262i	$0.0667806\pi$
$692$	2.36534			0.0899169
$693$		0			0
$694$	18.5808			0.705318
$695$	−0.123544	+	0.213985i	−0.00468631	+	0.00811693i
$696$		0			0
$697$	−4.01098	−	6.94722i	−0.151927	−	0.263145i
$698$	7.74227	+	13.4100i	0.293049	+	0.507576i
$699$		0			0
$700$	−0.0483549	+	0.0837531i	−0.00182764	+	0.00316557i
$701$	48.6772			1.83851			0.919257	−	0.393658i	$-0.128791\pi$
$701$	48.6772			1.83851			0.919257	+	0.393658i	$0.128791\pi$
$702$		0			0
$703$	−3.72908			−0.140645
$704$	3.37802	−	5.85090i	0.127314	−	0.220514i
$705$		0			0
$706$	−9.44937	−	16.3668i	−0.355632	−	0.615972i
$707$	0.347415	+	0.601740i	0.0130659	+	0.0226308i
$708$		0			0
$709$	−25.5541	+	44.2609i	−0.959703	+	1.66225i	−0.236484	+	0.971635i	$0.575995\pi$
$709$	−25.5541	+	44.2609i	−0.959703	+	1.66225i	−0.723219	+	0.690619i	$0.757338\pi$
$710$	3.44464			0.129275
$711$		0			0
$712$	9.55017			0.357908
$713$	0.472339	−	0.818115i	0.0176892	−	0.0306386i
$714$		0			0
$715$	−0.200590	−	0.347433i	−0.00750165	−	0.0129932i
$716$	1.96262	+	3.39936i	0.0733467	+	0.127040i
$717$		0			0
$718$	−15.0143	+	26.0056i	−0.560330	+	0.970520i
$719$	−33.1064			−1.23466			−0.617330	−	0.786704i	$-0.711786\pi$
$719$	−33.1064			−1.23466			−0.617330	+	0.786704i	$0.711786\pi$
$720$		0			0
$721$	−0.633983			−0.0236107
$722$	−8.11222	+	14.0508i	−0.301906	+	0.522916i
$723$		0			0
$724$	1.19995	+	2.07837i	0.0445956	+	0.0772419i
$725$	2.48857	+	4.31032i	0.0924231	+	0.160081i
$726$		0			0
$727$	7.51504	−	13.0164i	0.278717	−	0.482752i	−0.692349	−	0.721563i	$-0.743424\pi$
$727$	7.51504	−	13.0164i	0.278717	−	0.482752i	0.971066	+	0.238810i	$0.0767574\pi$
$728$	0.361564			0.0134004
$729$		0			0
$730$	0.764717			0.0283035
$731$	6.82956	−	11.8292i	0.252601	−	0.437517i
$732$		0			0
$733$	−18.5309	−	32.0965i	−0.684454	−	1.18551i	−0.973608	−	0.228227i	$-0.926707\pi$
$733$	−18.5309	−	32.0965i	−0.684454	−	1.18551i	0.289153	−	0.957283i	$-0.406626\pi$
$734$	7.53619	+	13.0531i	0.278166	+	0.481797i
$735$		0			0
$736$	−0.733706	+	1.27082i	−0.0270448	+	0.0468429i
$737$	4.69269			0.172857
$738$		0			0
$739$	−32.1984			−1.18444			−0.592219	−	0.805777i	$-0.701748\pi$
$739$	−32.1984			−1.18444			−0.592219	+	0.805777i	$0.701748\pi$
$740$	0.0326556	−	0.0565612i	0.00120044	−	0.00207923i
$741$		0			0
$742$	−0.00242221	−	0.00419540i	−8.89222e−5	−	0.000154018i
$743$	−4.46821	−	7.73916i	−0.163923	−	0.283922i	0.772350	−	0.635198i	$-0.219081\pi$
$743$	−4.46821	−	7.73916i	−0.163923	−	0.283922i	−0.936272	+	0.351275i	$0.885748\pi$
$744$		0			0
$745$	0.385160	−	0.667117i	0.0141112	−	0.0244413i
$746$	−31.9169			−1.16856
$747$		0			0
$748$	−0.665510			−0.0243335
$749$	−0.111934	+	0.193876i	−0.00408999	+	0.00708408i
$750$		0			0
$751$	0.386579	+	0.669575i	0.0141065	+	0.0244331i	0.872992	−	0.487734i	$-0.162176\pi$
$751$	0.386579	+	0.669575i	0.0141065	+	0.0244331i	−0.858886	+	0.512167i	$0.828843\pi$
$752$	13.3929	+	23.1971i	0.488388	+	0.845913i
$753$		0			0
$754$	−1.87427	+	3.24634i	−0.0682570	+	0.118225i
$755$	−2.66508			−0.0969922
$756$		0			0
$757$	−36.5342			−1.32786			−0.663929	−	0.747796i	$-0.731112\pi$
$757$	−36.5342			−1.32786			−0.663929	+	0.747796i	$0.731112\pi$
$758$	−22.4172	+	38.8278i	−0.814230	+	1.41029i
$759$		0			0
$760$	−0.556893	−	0.964567i	−0.0202006	−	0.0349885i
$761$	3.25115	+	5.63116i	0.117854	+	0.204130i	0.918917	−	0.394451i	$-0.129065\pi$
$761$	3.25115	+	5.63116i	0.117854	+	0.204130i	−0.801063	+	0.598580i	$0.795732\pi$
$762$		0			0
$763$	−0.443559	+	0.768267i	−0.0160579	+	0.0278131i
$764$	7.66423			0.277282
$765$		0			0
$766$	−49.8779			−1.80216
$767$	8.87514	−	15.3722i	0.320463	−	0.555058i
$768$		0			0
$769$	18.0717	+	31.3012i	0.651683	+	1.12875i	0.982714	+	0.185129i	$0.0592703\pi$
$769$	18.0717	+	31.3012i	0.651683	+	1.12875i	−0.331031	+	0.943620i	$0.607396\pi$
$770$	0.00724096	+	0.0125417i	0.000260946	+	0.000451972i
$771$		0			0
$772$	−0.0951884	+	0.164871i	−0.00342591	+	0.00593384i
$773$	3.21379			0.115592			0.0577959	−	0.998328i	$-0.481593\pi$
$773$	3.21379			0.115592			0.0577959	+	0.998328i	$0.481593\pi$
$774$		0			0
$775$	6.01745			0.216153
$776$	−19.8031	+	34.3000i	−0.710890	+	1.23130i
$777$		0			0
$778$	−25.8762	−	44.8188i	−0.927705	−	1.60683i
$779$	−6.32920	−	10.9625i	−0.226767	−	0.392772i
$780$		0			0
$781$	−8.06112	+	13.9623i	−0.288450	+	0.499609i
$782$	−2.19095			−0.0783482
$783$		0			0
$784$	31.8923			1.13901
$785$	−0.111459	+	0.193052i	−0.00397813	+	0.00689032i
$786$		0			0
$787$	14.5789	+	25.2513i	0.519680	+	0.900112i	0.999738	+	0.0228755i	$0.00728213\pi$
$787$	14.5789	+	25.2513i	0.519680	+	0.900112i	−0.480058	+	0.877237i	$0.659385\pi$
$788$	1.31626	+	2.27984i	0.0468900	+	0.0812158i
$789$		0			0
$790$	0.371844	−	0.644053i	0.0132296	−	0.0229144i
$791$	0.531383			0.0188938
$792$		0			0
$793$	9.92386			0.352407
$794$	23.1686	−	40.1291i	0.822222	−	1.42413i
$795$		0			0
$796$	−2.67017	−	4.62487i	−0.0946416	−	0.163924i
$797$	8.17998	+	14.1681i	0.289750	+	0.501862i	0.973750	−	0.227620i	$-0.0730945\pi$
$797$	8.17998	+	14.1681i	0.289750	+	0.501862i	−0.684000	+	0.729482i	$0.739761\pi$
$798$		0			0
$799$	−5.39117	+	9.33779i	−0.190726	+	0.330347i
$800$	−9.34719			−0.330473
$801$		0			0
$802$	−52.9655			−1.87028
$803$	−1.78959	+	3.09966i	−0.0631532	+	0.109385i
$804$		0			0
$805$	0.00342307	+	0.00592893i	0.000120647	+	0.000208967i
$806$	2.26603	+	3.92488i	0.0798176	+	0.138248i
$807$		0			0
$808$	−15.2528	+	26.4187i	−0.536593	+	0.929406i
$809$	−0.968702			−0.0340577			−0.0170289	−	0.999855i	$-0.505421\pi$
$809$	−0.968702			−0.0340577			−0.0170289	+	0.999855i	$0.505421\pi$
$810$		0			0
$811$	−32.8852			−1.15476			−0.577378	−	0.816477i	$-0.695924\pi$
$811$	−32.8852			−1.15476			−0.577378	+	0.816477i	$0.695924\pi$
$812$	0.00971541	−	0.0168276i	0.000340944	−	0.000590532i
$813$		0			0
$814$	1.06438	+	1.84356i	0.0373066	+	0.0646169i
$815$	1.08011	+	1.87080i	0.0378346	+	0.0655314i
$816$		0			0
$817$	10.7768	−	18.6660i	0.377034	−	0.653042i
$818$	20.3930			0.713026
$819$		0			0
$820$	0.221700			0.00774208
$821$	−6.92247	+	11.9901i	−0.241596	+	0.418456i	−0.961169	−	0.275960i	$-0.911004\pi$
$821$	−6.92247	+	11.9901i	−0.241596	+	0.418456i	0.719573	+	0.694417i	$0.244337\pi$
$822$		0			0
$823$	−9.93757	−	17.2124i	−0.346402	−	0.599986i	0.639206	−	0.769036i	$-0.279263\pi$
$823$	−9.93757	−	17.2124i	−0.346402	−	0.599986i	−0.985607	+	0.169050i	$0.945930\pi$
$824$	−13.9171	−	24.1051i	−0.484826	−	0.839743i
$825$		0			0
$826$	−0.320377	+	0.554910i	−0.0111473	+	0.0193078i
$827$	−24.5929			−0.855181			−0.427590	−	0.903973i	$-0.640637\pi$
$827$	−24.5929			−0.855181			−0.427590	+	0.903973i	$0.640637\pi$
$828$		0			0
$829$	−44.4191			−1.54274			−0.771370	−	0.636387i	$-0.780428\pi$
$829$	−44.4191			−1.54274			−0.771370	+	0.636387i	$0.780428\pi$
$830$	0.936804	−	1.62259i	0.0325169	−	0.0563210i
$831$		0			0
$832$	7.66115	+	13.2695i	0.265603	+	0.460037i
$833$	6.41898	+	11.1180i	0.222404	+	0.385216i
$834$		0			0
$835$	1.08414	−	1.87779i	0.0375182	−	0.0649835i
$836$	−1.05015			−0.0363203
$837$		0			0
$838$	6.74773			0.233096
$839$	−9.48394	+	16.4267i	−0.327422	+	0.567112i	−0.982000	−	0.188883i	$-0.939513\pi$
$839$	−9.48394	+	16.4267i	−0.327422	+	0.567112i	0.654578	+	0.755995i	$0.272847\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.0172414	−	0.0298629i
$842$	13.0936	+	22.6789i	0.451237	+	0.781565i
$843$		0			0
$844$	−3.37236	+	5.84110i	−0.116081	+	0.201059i
$845$	−1.05595			−0.0363259
$846$		0			0
$847$	0.569587			0.0195712
$848$	0.124691	−	0.215971i	0.00428191	−	0.00741649i
$849$		0			0
$850$	−6.97800	−	12.0863i	−0.239344	−	0.414555i
$851$	0.503173	+	0.871521i	0.0172485	+	0.0298754i
$852$		0			0
$853$	3.09105	−	5.35385i	0.105835	−	0.183312i	−0.808244	−	0.588848i	$-0.799582\pi$
$853$	3.09105	−	5.35385i	0.105835	−	0.183312i	0.914079	+	0.405536i	$0.132915\pi$
$854$	−0.358234			−0.0122585
$855$		0			0
$856$	−9.82869			−0.335938
$857$	13.3423	−	23.1095i	0.455763	−	0.789404i	−0.542969	−	0.839753i	$-0.682700\pi$
$857$	13.3423	−	23.1095i	0.455763	−	0.789404i	0.998732	+	0.0503484i	$0.0160332\pi$
$858$		0			0
$859$	21.8620	+	37.8661i	0.745922	+	1.29198i	0.949763	+	0.312971i	$0.101324\pi$
$859$	21.8620	+	37.8661i	0.745922	+	1.29198i	−0.203841	+	0.979004i	$0.565342\pi$
$860$	0.188746	+	0.326917i	0.00643618	+	0.0111478i
$861$		0			0
$862$	−9.92051	+	17.1828i	−0.337894	+	0.585250i
$863$	32.7025			1.11320			0.556602	−	0.830779i	$-0.312105\pi$
$863$	32.7025			1.11320			0.556602	+	0.830779i	$0.312105\pi$
$864$		0			0
$865$	1.06659			0.0362652
$866$	18.8699	−	32.6837i	0.641226	−	1.11064i
$867$		0			0
$868$	−0.0117461	−	0.0203449i	−0.000398689	−	0.000690550i
$869$	1.74038	+	3.01442i	0.0590382	+	0.102257i
$870$		0			0
$871$	−5.32137	+	9.21689i	−0.180308	+	0.312302i
$872$	−38.9478			−1.31894
$873$		0			0
$874$	−3.45725			−0.116943
$875$	−0.0437090	+	0.0757062i	−0.00147763	+	0.00255934i
$876$		0			0
$877$	11.5542	+	20.0125i	0.390159	+	0.675774i	0.992470	−	0.122487i	$-0.0390869\pi$
$877$	11.5542	+	20.0125i	0.390159	+	0.675774i	−0.602312	+	0.798261i	$0.705754\pi$
$878$	−26.7929	−	46.4067i	−0.904217	−	1.56615i
$879$		0			0
$880$	−0.372752	+	0.645625i	−0.0125655	+	0.0217640i
$881$	−42.3370			−1.42637			−0.713184	−	0.700976i	$-0.752748\pi$
$881$	−42.3370			−1.42637			−0.713184	+	0.700976i	$0.752748\pi$
$882$		0			0
$883$	−40.9401			−1.37774			−0.688872	−	0.724883i	$-0.741894\pi$
$883$	−40.9401			−1.37774			−0.688872	+	0.724883i	$0.741894\pi$
$884$	0.754670	−	1.30713i	0.0253823	−	0.0439634i
$885$		0			0
$886$	−2.63281	−	4.56016i	−0.0884509	−	0.153202i
$887$	5.97110	+	10.3423i	0.200490	+	0.347259i	0.948686	−	0.316218i	$-0.102413\pi$
$887$	5.97110	+	10.3423i	0.200490	+	0.347259i	−0.748196	+	0.663477i	$0.769080\pi$
$888$		0			0
$889$	−0.363580	+	0.629739i	−0.0121941	+	0.0211208i
$890$	−0.867531			−0.0290797
$891$		0			0
$892$	−8.20065			−0.274578
$893$	−8.50710	+	14.7347i	−0.284679	+	0.493079i
$894$		0			0
$895$	0.884996	+	1.53286i	0.0295822	+	0.0512378i
$896$	−0.385372	−	0.667484i	−0.0128744	−	0.0222991i
$897$		0			0
$898$	2.22487	−	3.85360i	0.0742450	−	0.128596i
$899$	−1.20902			−0.0403230
$900$		0			0
$901$	0.100386			0.00334436
$902$	−3.61306	+	6.25800i	−0.120302	+	0.208369i
$903$		0			0
$904$	11.6649	+	20.2041i	0.387967	+	0.671979i
$905$	0.541086	+	0.937188i	0.0179863	+	0.0311532i
$906$		0			0
$907$	−8.48976	+	14.7047i	−0.281898	+	0.488261i	−0.971852	−	0.235592i	$-0.924297\pi$
$907$	−8.48976	+	14.7047i	−0.281898	+	0.488261i	0.689954	+	0.723853i	$0.257631\pi$
$908$	−9.53434			−0.316408
$909$		0			0
$910$	−0.0328442			−0.00108877
$911$	14.5434	−	25.1899i	0.481844	−	0.834578i	−0.517939	−	0.855417i	$-0.673301\pi$
$911$	14.5434	−	25.1899i	0.481844	−	0.834578i	0.999783	+	0.0208399i	$0.00663401\pi$
$912$		0			0
$913$	4.38461	+	7.59436i	0.145109	+	0.251337i
$914$	22.1431	+	38.3530i	0.732429	+	1.26860i
$915$		0			0
$916$	2.40664	−	4.16843i	0.0795177	−	0.137729i
$917$	1.06891			0.0352984
$918$		0			0
$919$	56.7951			1.87350			0.936749	−	0.350002i	$-0.113819\pi$
$919$	56.7951			1.87350			0.936749	+	0.350002i	$0.113819\pi$
$920$	−0.150286	+	0.260302i	−0.00495477	+	0.00858192i
$921$		0			0
$922$	16.6158	+	28.7794i	0.547213	+	0.947800i
$923$	−18.2822	−	31.6656i	−0.601765	−	1.04229i
$924$		0			0
$925$	−3.20513	+	5.55146i	−0.105384	+	0.182531i
$926$	−31.9144			−1.04877
$927$		0			0
$928$	1.87803			0.0616493
$929$	−2.61328	+	4.52634i	−0.0857391	+	0.148504i	−0.905706	−	0.423907i	$-0.860658\pi$
$929$	−2.61328	+	4.52634i	−0.0857391	+	0.148504i	0.819967	+	0.572411i	$0.193992\pi$
$930$		0			0
$931$	10.1289	+	17.5439i	0.331963	+	0.574977i
$932$	−0.595164	−	1.03085i	−0.0194952	−	0.0337667i
$933$		0			0
$934$	14.0555	−	24.3448i	0.459910	−	0.796588i
$935$	−0.300095			−0.00981416
$936$		0			0
$937$	24.4385			0.798372			0.399186	−	0.916870i	$-0.369293\pi$
$937$	24.4385			0.798372			0.399186	+	0.916870i	$0.369293\pi$
$938$	0.192092	−	0.332714i	0.00627203	−	0.0108635i
$939$		0			0
$940$	−0.148994	−	0.258065i	−0.00485964	−	0.00841714i
$941$	−10.9756	−	19.0102i	−0.357793	−	0.619716i	0.629799	−	0.776758i	$-0.283137\pi$
$941$	−10.9756	−	19.0102i	−0.357793	−	0.619716i	−0.987592	+	0.157043i	$0.949804\pi$
$942$		0			0
$943$	−1.70803	+	2.95839i	−0.0556210	+	0.0963383i
$944$	−32.9849			−1.07357
$945$		0			0
$946$	−12.3040			−0.400039
$947$	1.14714	−	1.98691i	0.0372771	−	0.0645659i	−0.846785	−	0.531935i	$-0.821465\pi$
$947$	1.14714	−	1.98691i	0.0372771	−	0.0645659i	0.884062	+	0.467370i	$0.154798\pi$
$948$		0			0
$949$	−4.05868	−	7.02984i	−0.131750	−	0.228198i
$950$	−11.0111	−	19.0717i	−0.357246	−	0.618769i
$951$		0			0
$952$	0.135230	−	0.234226i	0.00438284	−	0.00759129i
$953$	−3.38896			−0.109779			−0.0548896	−	0.998492i	$-0.517481\pi$
$953$	−3.38896			−0.109779			−0.0548896	+	0.998492i	$0.517481\pi$
$954$		0			0
$955$	3.45599			0.111833
$956$	2.33821	−	4.04989i	0.0756230	−	0.130983i
$957$		0			0
$958$	7.11306	+	12.3202i	0.229812	+	0.398047i
$959$	−0.498165	−	0.862848i	−0.0160866	−	0.0278628i
$960$		0			0
$961$	14.7691	−	25.5809i	0.476424	−	0.825190i
$962$	−4.82792			−0.155658
$963$		0			0
$964$	7.08417			0.228166
$965$	−0.0429228	+	0.0743446i	−0.00138174	+	0.00239324i
$966$		0			0
$967$	−11.1626	−	19.3342i	−0.358965	−	0.621745i	0.628824	−	0.777548i	$-0.283537\pi$
$967$	−11.1626	−	19.3342i	−0.358965	−	0.621745i	−0.987788	+	0.155803i	$0.950203\pi$
$968$	12.5035	+	21.6567i	0.401878	+	0.696073i
$969$		0			0
$970$	1.79890	−	3.11579i	0.0577592	−	0.100042i
$971$	25.9936			0.834174			0.417087	−	0.908867i	$-0.363051\pi$
$971$	25.9936			0.834174			0.417087	+	0.908867i	$0.363051\pi$
$972$		0			0
$973$	−0.0946790			−0.00303527
$974$	15.4415	−	26.7455i	0.494777	−	0.856980i
$975$		0			0
$976$	−9.22062	−	15.9706i	−0.295145	−	0.511206i
$977$	2.79814	+	4.84652i	0.0895204	+	0.155054i	0.907309	−	0.420466i	$-0.138133\pi$
$977$	2.79814	+	4.84652i	0.0895204	+	0.155054i	−0.817788	+	0.575519i	$0.804800\pi$
$978$		0			0
$979$	2.03019	−	3.51639i	0.0648852	−	0.112384i
$980$	−0.354797			−0.0113336
$981$		0			0
$982$	−14.5354			−0.463844
$983$	−23.5817	+	40.8448i	−0.752141	+	1.30275i	0.194642	+	0.980874i	$0.437645\pi$
$983$	−23.5817	+	40.8448i	−0.752141	+	1.30275i	−0.946783	+	0.321872i	$0.895688\pi$
$984$		0			0
$985$	0.593536	+	1.02804i	0.0189116	+	0.0327559i
$986$	1.40201	+	2.42836i	0.0446492	+	0.0773346i
$987$		0			0
$988$	1.19084	−	2.06260i	0.0378858	−	0.0656202i
$989$	−5.81657			−0.184956
$990$		0			0
$991$	21.3455			0.678061			0.339030	−	0.940775i	$-0.389901\pi$
$991$	21.3455			0.678061			0.339030	+	0.940775i	$0.389901\pi$
$992$	1.13529	−	1.96637i	0.0360453	−	0.0624324i
$993$		0			0
$994$	0.659954	+	1.14307i	0.0209325	+	0.0362561i
$995$	−1.20405	−	2.08547i	−0.0381708	−	0.0661138i
$996$		0			0
$997$	19.2428	−	33.3294i	0.609424	−	1.05555i	−0.381911	−	0.924199i	$-0.624734\pi$
$997$	19.2428	−	33.3294i	0.609424	−	1.05555i	0.991335	−	0.131355i	$-0.0419328\pi$
$998$	7.00129			0.221622
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.e.a.262.9		22
3.2	odd	2		261.2.e.a.88.3	✓	22
9.2	odd	6		2349.2.a.f.1.9		11
9.4	even	3	inner	783.2.e.a.523.9		22
9.5	odd	6		261.2.e.a.175.3	yes	22
9.7	even	3		2349.2.a.e.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.3	✓	22	3.2	odd	2
261.2.e.a.175.3	yes	22	9.5	odd	6
783.2.e.a.262.9		22	1.1	even	1	trivial
783.2.e.a.523.9		22	9.4	even	3	inner
2349.2.a.e.1.3		11	9.7	even	3
2349.2.a.f.1.9		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)

\(f(q)\)	\(=\)	\(q+(0.764092 - 1.32345i) q^{2} +(-0.167673 - 0.290418i) q^{4} +(-0.0756080 - 0.130957i) q^{5} +(0.0289713 - 0.0501797i) q^{7} +2.54390 q^{8} -0.231086 q^{10} +(0.540786 - 0.936668i) q^{11} +(1.22647 + 2.12431i) q^{13} +(-0.0442735 - 0.0766839i) q^{14} +(2.27912 - 3.94755i) q^{16} +1.83487 q^{17} +2.89537 q^{19} +(-0.0253548 + 0.0439159i) q^{20} +(-0.826420 - 1.43140i) q^{22} +(-0.390679 - 0.676676i) q^{23} +(2.48857 - 4.31032i) q^{25} +3.74855 q^{26} -0.0194308 q^{28} +(-0.500000 + 0.866025i) q^{29} +(0.604509 + 1.04704i) q^{31} +(-0.939013 - 1.62642i) q^{32} +(1.40201 - 2.42836i) q^{34} -0.00876184 q^{35} -1.28794 q^{37} +(2.21233 - 3.83187i) q^{38} +(-0.192339 - 0.333141i) q^{40} +(-2.18597 - 3.78621i) q^{41} +(3.72209 - 6.44685i) q^{43} -0.362701 q^{44} -1.19406 q^{46} +(-2.93817 + 5.08906i) q^{47} +(3.49832 + 6.05927i) q^{49} +(-3.80299 - 6.58697i) q^{50} +(0.411292 - 0.712379i) q^{52} +0.0547103 q^{53} -0.163551 q^{55} +(0.0737000 - 0.127652i) q^{56} +(0.764092 + 1.32345i) q^{58} +(-3.61816 - 6.26684i) q^{59} +(2.02285 - 3.50368i) q^{61} +1.84760 q^{62} +6.24650 q^{64} +(0.185462 - 0.321230i) q^{65} +(2.16938 + 3.75748i) q^{67} +(-0.307659 - 0.532881i) q^{68} +(-0.00669485 + 0.0115958i) q^{70} -14.9063 q^{71} -3.30924 q^{73} +(-0.984108 + 1.70452i) q^{74} +(-0.485476 - 0.840869i) q^{76} +(-0.0313345 - 0.0542730i) q^{77} +(-1.60912 + 2.78708i) q^{79} -0.689278 q^{80} -6.68112 q^{82} +(-4.05392 + 7.02160i) q^{83} +(-0.138731 - 0.240289i) q^{85} +(-5.68804 - 9.85197i) q^{86} +(1.37570 - 2.38279i) q^{88} +3.75415 q^{89} +0.142130 q^{91} +(-0.131013 + 0.226921i) q^{92} +(4.49007 + 7.77702i) q^{94} +(-0.218913 - 0.379169i) q^{95} +(-7.78455 + 13.4832i) q^{97} +10.6922 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 5 q^{4} - q^{5} + 7 q^{7} - 6 q^{8} - 20 q^{10} + 3 q^{11} + 7 q^{13} - 10 q^{14} + 7 q^{16} - 2 q^{17} - 56 q^{19} - 4 q^{20} + 13 q^{22} + 4 q^{23} + 4 q^{25} + 12 q^{26} - 32 q^{28}+ \cdots - 86 q^{98}+O(q^{100}) \) 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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