LMFDB - Embedded newform 783.2.k.f.136.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(82,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,-10,0,0,4,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.3
Character	$\chi$	$=$	783.136
Dual form			783.2.k.f.190.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42552 + 0.686496i) q^{2} +(0.313861 - 0.393569i) q^{4} +(1.33026 - 0.640620i) q^{5} +(0.300750 + 0.377129i) q^{7} +(0.526918 - 2.30858i) q^{8} +(-1.45653 + 1.82644i) q^{10} +(-0.893763 - 3.91583i) q^{11} +(-0.713691 - 3.12688i) q^{13} +(-0.687624 - 0.331142i) q^{14} +(1.05773 + 4.63420i) q^{16} -6.16896 q^{17} +(-4.73505 + 5.93756i) q^{19} +(0.165388 - 0.724614i) q^{20} +(3.96228 + 4.96854i) q^{22} +(-1.48532 - 0.715295i) q^{23} +(-1.75825 + 2.20478i) q^{25} +(3.16398 + 3.96750i) q^{26} +0.242820 q^{28} +(-1.81488 - 5.07013i) q^{29} +(4.26937 - 2.05602i) q^{31} +(-1.73639 - 2.17737i) q^{32} +(8.79399 - 4.23496i) q^{34} +(0.641673 + 0.309013i) q^{35} +(-1.89985 + 8.32377i) q^{37} +(2.67381 - 11.7147i) q^{38} +(-0.777983 - 3.40856i) q^{40} -5.44168 q^{41} +(-9.14266 - 4.40287i) q^{43} +(-1.82167 - 0.877268i) q^{44} +2.60841 q^{46} +(2.17854 + 9.54479i) q^{47} +(1.50587 - 6.59765i) q^{49} +(0.992857 - 4.34999i) q^{50} +(-1.45464 - 0.700519i) q^{52} +(-6.97382 + 3.35842i) q^{53} +(-3.69750 - 4.63651i) q^{55} +(1.02910 - 0.495590i) q^{56} +(6.06778 + 5.98168i) q^{58} -2.25688 q^{59} +(1.67795 + 2.10409i) q^{61} +(-4.67464 + 5.86181i) q^{62} +(-4.59527 - 2.21297i) q^{64} +(-2.95254 - 3.70237i) q^{65} +(2.81867 - 12.3494i) q^{67} +(-1.93619 + 2.42791i) q^{68} -1.12686 q^{70} +(-0.734095 - 3.21628i) q^{71} +(-8.01113 - 3.85796i) q^{73} +(-3.00596 - 13.1700i) q^{74} +(0.850694 + 3.72713i) q^{76} +(1.20797 - 1.51475i) q^{77} +(0.235786 - 1.03305i) q^{79} +(4.37581 + 5.48710i) q^{80} +(7.75724 - 3.73569i) q^{82} +(7.42726 - 9.31349i) q^{83} +(-8.20632 + 3.95195i) q^{85} +16.0556 q^{86} -9.51095 q^{88} +(3.00588 - 1.44755i) q^{89} +(0.964596 - 1.20957i) q^{91} +(-0.747703 + 0.360075i) q^{92} +(-9.65801 - 12.1108i) q^{94} +(-2.49513 + 10.9319i) q^{95} +(8.15625 - 10.2276i) q^{97} +(2.38261 + 10.4389i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) $ 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Character values

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

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.42552	+	0.686496i	−1.00800	+	0.485426i	−0.863645	−	0.504100i	$-0.831824\pi$
$2$	−1.42552	+	0.686496i	−1.00800	+	0.485426i	−0.144352	+	0.989526i	$0.546110\pi$
$3$		0			0
$3$		0			0
$4$	0.313861	−	0.393569i	0.156930	−	0.196784i
$5$	1.33026	−	0.640620i	0.594910	−	0.286494i	−0.112100	−	0.993697i	$-0.535758\pi$
$5$	1.33026	−	0.640620i	0.594910	−	0.286494i	0.707010	+	0.707203i	$0.250043\pi$
$6$		0			0
$7$	0.300750	+	0.377129i	0.113673	+	0.142541i	0.835413	−	0.549623i	$-0.185229\pi$
$7$	0.300750	+	0.377129i	0.113673	+	0.142541i	−0.721740	+	0.692165i	$0.756657\pi$
$8$	0.526918	−	2.30858i	0.186294	−	0.816206i
$9$		0			0
$10$	−1.45653	+	1.82644i	−0.460597	+	0.577570i
$11$	−0.893763	−	3.91583i	−0.269480	−	1.18067i	−0.910620	−	0.413244i	$-0.864396\pi$
$11$	−0.893763	−	3.91583i	−0.269480	−	1.18067i	0.641141	−	0.767423i	$-0.278462\pi$
$12$		0			0
$13$	−0.713691	−	3.12688i	−0.197942	−	0.867242i	−0.972159	−	0.234321i	$-0.924713\pi$
$13$	−0.713691	−	3.12688i	−0.197942	−	0.867242i	0.774217	−	0.632920i	$-0.218144\pi$
$14$	−0.687624	−	0.331142i	−0.183775	−	0.0885016i
$15$		0			0
$16$	1.05773	+	4.63420i	0.264432	+	1.15855i
$17$	−6.16896			−1.49619			−0.748096	−	0.663591i	$-0.769032\pi$
$17$	−6.16896			−1.49619			−0.748096	+	0.663591i	$0.769032\pi$
$18$		0			0
$19$	−4.73505	+	5.93756i	−1.08629	+	1.36217i	−0.159242	+	0.987240i	$0.550905\pi$
$19$	−4.73505	+	5.93756i	−1.08629	+	1.36217i	−0.927053	+	0.374931i	$0.877667\pi$
$20$	0.165388	−	0.724614i	0.0369820	−	0.162029i
$21$		0			0
$22$	3.96228	+	4.96854i	0.844761	+	1.05930i
$23$	−1.48532	−	0.715295i	−0.309712	−	0.149149i	0.272571	−	0.962136i	$-0.412126\pi$
$23$	−1.48532	−	0.715295i	−0.309712	−	0.149149i	−0.582283	+	0.812986i	$0.697840\pi$
$24$		0			0
$25$	−1.75825	+	2.20478i	−0.351650	+	0.440955i
$26$	3.16398	+	3.96750i	0.620507	+	0.778091i
$27$		0			0
$28$	0.242820			0.0458887
$29$	−1.81488	−	5.07013i	−0.337015	−	0.941499i
$29$	−1.81488	−	5.07013i	−0.337015	−	0.941499i
$30$		0			0
$31$	4.26937	−	2.05602i	0.766801	−	0.369272i	−0.00923750	−	0.999957i	$-0.502940\pi$
$31$	4.26937	−	2.05602i	0.766801	−	0.369272i	0.776039	+	0.630685i	$0.217226\pi$
$32$	−1.73639	−	2.17737i	−0.306954	−	0.384908i
$33$		0			0
$34$	8.79399	−	4.23496i	1.50816	−	0.726290i
$35$	0.641673	+	0.309013i	0.108462	+	0.0522328i
$36$		0			0
$37$	−1.89985	+	8.32377i	−0.312333	+	1.36842i	0.538342	+	0.842727i	$0.319051\pi$
$37$	−1.89985	+	8.32377i	−0.312333	+	1.36842i	−0.850675	+	0.525693i	$0.823806\pi$
$38$	2.67381	−	11.7147i	0.433749	−	1.90038i
$39$		0			0
$40$	−0.777983	−	3.40856i	−0.123010	−	0.538941i
$41$	−5.44168			−0.849847			−0.424924	−	0.905229i	$-0.639699\pi$
$41$	−5.44168			−0.849847			−0.424924	+	0.905229i	$0.639699\pi$
$42$		0			0
$43$	−9.14266	−	4.40287i	−1.39424	−	0.671432i	−0.422257	−	0.906476i	$-0.638762\pi$
$43$	−9.14266	−	4.40287i	−1.39424	−	0.671432i	−0.971985	+	0.235044i	$0.924476\pi$
$44$	−1.82167	−	0.877268i	−0.274627	−	0.132253i
$45$		0			0
$46$	2.60841			0.384589
$47$	2.17854	+	9.54479i	0.317772	+	1.39225i	0.841450	+	0.540334i	$0.181702\pi$
$47$	2.17854	+	9.54479i	0.317772	+	1.39225i	−0.523678	+	0.851916i	$0.675441\pi$
$48$		0			0
$49$	1.50587	−	6.59765i	0.215124	−	0.942522i
$50$	0.992857	−	4.34999i	0.140411	−	0.615182i
$51$		0			0
$52$	−1.45464	−	0.700519i	−0.201723	−	0.0971446i
$53$	−6.97382	+	3.35842i	−0.957928	+	0.461314i	−0.846459	−	0.532454i	$-0.821270\pi$
$53$	−6.97382	+	3.35842i	−0.957928	+	0.461314i	−0.111469	+	0.993768i	$0.535556\pi$
$54$		0			0
$55$	−3.69750	−	4.63651i	−0.498570	−	0.625187i
$56$	1.02910	−	0.495590i	0.137520	−	0.0662260i
$57$		0			0
$58$	6.06778	+	5.98168i	0.796738	+	0.785433i
$59$	−2.25688			−0.293821			−0.146911	−	0.989150i	$-0.546933\pi$
$59$	−2.25688			−0.293821			−0.146911	+	0.989150i	$0.546933\pi$
$60$		0			0
$61$	1.67795	+	2.10409i	0.214840	+	0.269401i	0.877560	−	0.479466i	$-0.159170\pi$
$61$	1.67795	+	2.10409i	0.214840	+	0.269401i	−0.662720	+	0.748867i	$0.730598\pi$
$62$	−4.67464	+	5.86181i	−0.593679	+	0.744450i
$63$		0			0
$64$	−4.59527	−	2.21297i	−0.574409	−	0.276621i
$65$	−2.95254	−	3.70237i	−0.366217	−	0.459222i
$66$		0			0
$67$	2.81867	−	12.3494i	0.344355	−	1.50872i	−0.445420	−	0.895322i	$-0.646946\pi$
$67$	2.81867	−	12.3494i	0.344355	−	1.50872i	0.789775	−	0.613396i	$-0.210197\pi$
$68$	−1.93619	+	2.42791i	−0.234798	+	0.294427i
$69$		0			0
$70$	−1.12686			−0.134685
$71$	−0.734095	−	3.21628i	−0.0871210	−	0.381702i	0.912505	−	0.409067i	$-0.134146\pi$
$71$	−0.734095	−	3.21628i	−0.0871210	−	0.381702i	−0.999626	+	0.0273645i	$0.991289\pi$
$72$		0			0
$73$	−8.01113	−	3.85796i	−0.937632	−	0.451540i	−0.0982989	−	0.995157i	$-0.531340\pi$
$73$	−8.01113	−	3.85796i	−0.937632	−	0.451540i	−0.839333	+	0.543617i	$0.817054\pi$
$74$	−3.00596	−	13.1700i	−0.349436	−	1.53098i
$75$		0			0
$76$	0.850694	+	3.72713i	0.0975813	+	0.427532i
$77$	1.20797	−	1.51475i	0.137661	−	0.172622i
$78$		0			0
$79$	0.235786	−	1.03305i	0.0265280	−	0.116227i	−0.959930	−	0.280239i	$-0.909586\pi$
$79$	0.235786	−	1.03305i	0.0265280	−	0.116227i	0.986458	+	0.164012i	$0.0524435\pi$
$80$	4.37581	+	5.48710i	0.489231	+	0.613476i
$81$		0			0
$82$	7.75724	−	3.73569i	0.856644	−	0.412538i
$83$	7.42726	−	9.31349i	0.815248	−	1.02229i	−0.183977	−	0.982930i	$-0.558897\pi$
$83$	7.42726	−	9.31349i	0.815248	−	1.02229i	0.999225	−	0.0393578i	$-0.0125312\pi$
$84$		0			0
$85$	−8.20632	+	3.95195i	−0.890100	+	0.428650i
$86$	16.0556			1.73132
$87$		0			0
$88$	−9.51095			−1.01387
$89$	3.00588	−	1.44755i	0.318622	−	0.153440i	−0.267736	−	0.963492i	$-0.586275\pi$
$89$	3.00588	−	1.44755i	0.318622	−	0.153440i	0.586358	+	0.810052i	$0.300561\pi$
$90$		0			0
$91$	0.964596	−	1.20957i	0.101117	−	0.126797i
$92$	−0.747703	+	0.360075i	−0.0779534	+	0.0375404i
$93$		0			0
$94$	−9.65801	−	12.1108i	−0.996148	−	1.24913i
$95$	−2.49513	+	10.9319i	−0.255995	+	1.12159i
$96$		0			0
$97$	8.15625	−	10.2276i	0.828141	−	1.03846i	−0.170448	−	0.985367i	$-0.554522\pi$
$97$	8.15625	−	10.2276i	0.828141	−	1.03846i	0.998590	−	0.0530897i	$-0.0169069\pi$
$98$	2.38261	+	10.4389i	0.240680	+	1.05449i
$99$		0			0
$100$	0.315886	+	1.38398i	0.0315886	+	0.138398i
$101$	−9.81276	−	4.72558i	−0.976406	−	0.470212i	−0.123538	−	0.992340i	$-0.539424\pi$
$101$	−9.81276	−	4.72558i	−0.976406	−	0.470212i	−0.852867	+	0.522127i	$0.825139\pi$
$102$		0			0
$103$	−0.885718	−	3.88059i	−0.0872724	−	0.382365i	0.912363	−	0.409383i	$-0.134256\pi$
$103$	−0.885718	−	3.88059i	−0.0872724	−	0.382365i	−0.999635	+	0.0270178i	$0.991399\pi$
$104$	−7.59471			−0.744723
$105$		0			0
$106$	7.63581	−	9.57500i	0.741655	−	0.930006i
$107$	2.06932	−	9.06629i	0.200049	−	0.876471i	−0.770857	−	0.637009i	$-0.780172\pi$
$107$	2.06932	−	9.06629i	0.200049	−	0.876471i	0.970906	−	0.239463i	$-0.0769713\pi$
$108$		0			0
$109$	5.99903	+	7.52255i	0.574603	+	0.720529i	0.981182	−	0.193086i	$-0.0618498\pi$
$109$	5.99903	+	7.52255i	0.574603	+	0.720529i	−0.406579	+	0.913616i	$0.633278\pi$
$110$	8.45381	+	4.07114i	0.806039	+	0.388168i
$111$		0			0
$112$	−1.42958	+	1.79264i	−0.135083	+	0.169388i
$113$	9.95640	+	12.4849i	0.936620	+	1.17448i	0.984456	+	0.175629i	$0.0561958\pi$
$113$	9.95640	+	12.4849i	0.936620	+	1.17448i	−0.0478369	+	0.998855i	$0.515233\pi$
$114$		0			0
$115$	−2.43410			−0.226981
$116$	−2.56506	−	0.877034i	−0.238160	−	0.0814306i
$117$		0			0
$118$	3.21724	−	1.54934i	0.296171	−	0.142628i
$119$	−1.85532	−	2.32649i	−0.170077	−	0.213269i
$120$		0			0
$121$	−4.62427	+	2.22693i	−0.420388	+	0.202448i
$122$	−3.83641	−	1.84752i	−0.347332	−	0.167266i
$123$		0			0
$124$	0.530802	−	2.32559i	0.0476674	−	0.208844i
$125$	−2.56924	+	11.2566i	−0.229800	+	1.00682i
$126$		0			0
$127$	0.335991	+	1.47207i	0.0298144	+	0.130625i	0.987645	−	0.156708i	$-0.0500883\pi$
$127$	0.335991	+	1.47207i	0.0298144	+	0.130625i	−0.957831	+	0.287334i	$0.907231\pi$
$128$	13.6398			1.20560
$129$		0			0
$130$	6.75057	+	3.25090i	0.592064	+	0.285123i
$131$	−6.13008	−	2.95209i	−0.535587	−	0.257925i	0.146481	−	0.989213i	$-0.453205\pi$
$131$	−6.13008	−	2.95209i	−0.535587	−	0.257925i	−0.682069	+	0.731288i	$0.738919\pi$
$132$		0			0
$133$	−3.66330			−0.317648
$134$	4.45973	+	19.5393i	0.385262	+	1.68794i
$135$		0			0
$136$	−3.25053	+	14.2415i	−0.278731	+	1.22120i
$137$	−0.758827	+	3.32464i	−0.0648310	+	0.284043i	−0.996944	−	0.0781257i	$-0.975106\pi$
$137$	−0.758827	+	3.32464i	−0.0648310	+	0.284043i	0.932113	+	0.362169i	$0.117964\pi$
$138$		0			0
$139$	9.17098	+	4.41651i	0.777872	+	0.374603i	0.780309	−	0.625394i	$-0.215062\pi$
$139$	9.17098	+	4.41651i	0.777872	+	0.374603i	−0.00243744	+	0.999997i	$0.500776\pi$
$140$	0.323014	−	0.155555i	0.0272997	−	0.0131468i
$141$		0			0
$142$	3.25443	+	4.08093i	0.273106	+	0.342464i
$143$	−11.6065	+	5.58939i	−0.970583	+	0.467408i
$144$		0			0
$145$	−5.66229	−	5.58194i	−0.470227	−	0.463555i
$146$	14.0685			1.16432
$147$		0			0
$148$	2.67969	+	3.36022i	0.220269	+	0.276209i
$149$	−2.93241	+	3.67713i	−0.240233	+	0.301242i	−0.887302	−	0.461189i	$-0.847423\pi$
$149$	−2.93241	+	3.67713i	−0.240233	+	0.301242i	0.647069	+	0.762431i	$0.275994\pi$
$150$		0			0
$151$	13.6251	+	6.56152i	1.10880	+	0.533969i	0.896414	−	0.443218i	$-0.146163\pi$
$151$	13.6251	+	6.56152i	1.10880	+	0.533969i	0.212383	+	0.977186i	$0.431877\pi$
$152$	11.2123	+	14.0598i	0.909442	+	1.14040i
$153$		0			0
$154$	−0.682125	+	2.98858i	−0.0549672	+	0.240827i
$155$	4.36224	−	5.47008i	0.350384	−	0.439368i
$156$		0			0
$157$	−14.5184			−1.15870			−0.579349	−	0.815080i	$-0.696693\pi$
$157$	−14.5184			−1.15870			−0.579349	+	0.815080i	$0.696693\pi$
$158$	0.373063	+	1.63450i	0.0296793	+	0.130034i
$159$		0			0
$160$	−3.70472	−	1.78410i	−0.292884	−	0.141045i
$161$	−0.176954	−	0.775285i	−0.0139459	−	0.0611010i
$162$		0			0
$163$	−3.51230	−	15.3884i	−0.275105	−	1.20531i	−0.903901	−	0.427742i	$-0.859309\pi$
$163$	−3.51230	−	15.3884i	−0.275105	−	1.20531i	0.628796	−	0.777570i	$-0.283548\pi$
$164$	−1.70793	+	2.14168i	−0.133367	+	0.167237i
$165$		0			0
$166$	−4.19406	+	18.3754i	−0.325522	+	1.42621i
$167$	−9.36770	−	11.7467i	−0.724894	−	0.908988i	0.273710	−	0.961812i	$-0.411749\pi$
$167$	−9.36770	−	11.7467i	−0.724894	−	0.908988i	−0.998604	+	0.0528240i	$0.983178\pi$
$168$		0			0
$169$	2.44455	−	1.17723i	0.188042	−	0.0905563i
$170$	8.98530	−	11.2672i	0.689141	−	0.864155i
$171$		0			0
$172$	−4.60235	+	2.21638i	−0.350926	+	0.168997i
$173$	−17.3906			−1.32218			−0.661092	−	0.750305i	$-0.729907\pi$
$173$	−17.3906			−1.32218			−0.661092	+	0.750305i	$0.729907\pi$
$174$		0			0
$175$	−1.36028			−0.102827
$176$	17.2014	−	8.28376i	1.29660	−	0.624412i
$177$		0			0
$178$	−3.29121	+	4.12705i	−0.246687	+	0.309335i
$179$	7.67218	−	3.69473i	0.573446	−	0.276157i	−0.124604	−	0.992207i	$-0.539766\pi$
$179$	7.67218	−	3.69473i	0.573446	−	0.276157i	0.698049	+	0.716050i	$0.254052\pi$
$180$		0			0
$181$	12.0210	+	15.0739i	0.893515	+	1.12043i	0.992118	+	0.125306i	$0.0399912\pi$
$181$	12.0210	+	15.0739i	0.893515	+	1.12043i	−0.0986030	+	0.995127i	$0.531437\pi$
$182$	−0.544693	+	2.38646i	−0.0403753	+	0.176896i
$183$		0			0
$184$	−2.43396	+	3.05209i	−0.179434	+	0.225003i
$185$	2.80508	+	12.2899i	0.206234	+	0.903568i
$186$		0			0
$187$	5.51358	+	24.1566i	0.403193	+	1.76650i
$188$	4.44029	+	2.13833i	0.323841	+	0.155954i
$189$		0			0
$190$	−3.94782	−	17.2965i	−0.286405	−	1.25482i
$191$	9.51137			0.688219			0.344109	−	0.938930i	$-0.388181\pi$
$191$	9.51137			0.688219			0.344109	+	0.938930i	$0.388181\pi$
$192$		0			0
$193$	0.948724	−	1.18966i	0.0682907	−	0.0856338i	−0.746513	−	0.665371i	$-0.768273\pi$
$193$	0.948724	−	1.18966i	0.0682907	−	0.0856338i	0.814804	+	0.579737i	$0.196845\pi$
$194$	−4.60571	+	20.1789i	−0.330671	+	1.44876i
$195$		0			0
$196$	−2.12400	−	2.66341i	−0.151714	−	0.190243i
$197$	4.29152	+	2.06669i	0.305758	+	0.147245i	0.580471	−	0.814281i	$-0.302868\pi$
$197$	4.29152	+	2.06669i	0.305758	+	0.147245i	−0.274713	+	0.961526i	$0.588583\pi$
$198$		0			0
$199$	9.14811	−	11.4714i	0.648492	−	0.813184i	−0.343544	−	0.939137i	$-0.611627\pi$
$199$	9.14811	−	11.4714i	0.648492	−	0.813184i	0.992036	+	0.125953i	$0.0401988\pi$
$200$	4.16345	+	5.22080i	0.294400	+	0.369166i
$201$		0			0
$202$	17.2324			1.21247
$203$	1.36627	−	2.20929i	0.0958932	−	0.155062i
$204$		0			0
$205$	−7.23885	+	3.48605i	−0.505583	+	0.243476i
$206$	3.92662	+	4.92382i	0.273580	+	0.343059i
$207$		0			0
$208$	13.7357	−	6.61478i	0.952402	−	0.458652i
$209$	27.4825	+	13.2349i	1.90100	+	0.915476i
$210$		0			0
$211$	−2.48346	+	10.8807i	−0.170968	+	0.749060i	0.814634	+	0.579976i	$0.196938\pi$
$211$	−2.48346	+	10.8807i	−0.170968	+	0.749060i	−0.985602	+	0.169084i	$0.945919\pi$
$212$	−0.867041	+	3.79875i	−0.0595486	+	0.260900i
$213$		0			0
$214$	3.27410	+	14.3448i	0.223813	+	0.980589i
$215$	−14.9827			−1.02181
$216$		0			0
$217$	2.05940	+	0.991754i	0.139801	+	0.0673247i
$218$	−13.7160	−	6.60526i	−0.928962	−	0.447364i
$219$		0			0
$220$	−2.98529			−0.201268
$221$	4.40273	+	19.2896i	0.296159	+	1.29756i
$222$		0			0
$223$	−3.11807	+	13.6612i	−0.208802	+	0.914819i	0.756564	+	0.653919i	$0.226876\pi$
$223$	−3.11807	+	13.6612i	−0.208802	+	0.914819i	−0.965366	+	0.260900i	$0.915981\pi$
$224$	0.298928	−	1.30969i	0.0199730	−	0.0875073i
$225$		0			0
$226$	−22.7639	−	10.9625i	−1.51423	−	0.729217i
$227$	−13.5313	+	6.51631i	−0.898101	+	0.432503i	−0.825203	−	0.564837i	$-0.808939\pi$
$227$	−13.5313	+	6.51631i	−0.898101	+	0.432503i	−0.0728982	+	0.997339i	$0.523225\pi$
$228$		0			0
$229$	−4.97520	−	6.23870i	−0.328770	−	0.412265i	0.589783	−	0.807562i	$-0.299213\pi$
$229$	−4.97520	−	6.23870i	−0.328770	−	0.412265i	−0.918553	+	0.395297i	$0.870642\pi$
$230$	3.46987	−	1.67100i	0.228796	−	0.110182i
$231$		0			0
$232$	−12.6611	+	1.51825i	−0.831241	+	0.0996780i
$233$	−20.9476			−1.37232			−0.686161	−	0.727450i	$-0.740705\pi$
$233$	−20.9476			−1.37232			−0.686161	+	0.727450i	$0.740705\pi$
$234$		0			0
$235$	9.01260	+	11.3014i	0.587917	+	0.737225i
$236$	−0.708347	+	0.888239i	−0.0461095	+	0.0578194i
$237$		0			0
$238$	4.24192	+	2.04280i	0.274963	+	0.132415i
$239$	6.20784	+	7.78439i	0.401552	+	0.503530i	0.940962	−	0.338513i	$-0.109924\pi$
$239$	6.20784	+	7.78439i	0.401552	+	0.503530i	−0.539410	+	0.842043i	$0.681353\pi$
$240$		0			0
$241$	−0.0404502	+	0.177224i	−0.00260563	+	0.0114160i	−0.976214	−	0.216809i	$-0.930435\pi$
$241$	−0.0404502	+	0.177224i	−0.00260563	+	0.0114160i	0.973608	+	0.228225i	$0.0732922\pi$
$242$	5.06322	−	6.34908i	0.325476	−	0.408134i
$243$		0			0
$244$	1.35475			0.0867288
$245$	−2.22338	−	9.74128i	−0.142047	−	0.622348i
$246$		0			0
$247$	21.9454	+	10.5684i	1.39635	+	0.672449i
$248$	−2.49688	−	10.9395i	−0.158552	−	0.694661i
$249$		0			0
$250$	−4.06509	−	17.8103i	−0.257099	−	1.12642i
$251$	−12.1904	+	15.2863i	−0.769451	+	0.964861i	−0.999966	−	0.00820789i	$-0.997387\pi$
$251$	−12.1904	+	15.2863i	−0.769451	+	0.964861i	0.230516	+	0.973069i	$0.425959\pi$
$252$		0			0
$253$	−1.47345	+	6.45558i	−0.0926347	+	0.405859i
$254$	−1.48953	−	1.86782i	−0.0934617	−	0.117197i
$255$		0			0
$256$	−10.2533	+	4.93772i	−0.640830	+	0.308607i
$257$	11.8435	−	14.8513i	0.738780	−	0.926401i	−0.260456	−	0.965486i	$-0.583873\pi$
$257$	11.8435	−	14.8513i	0.738780	−	0.926401i	0.999236	+	0.0390848i	$0.0124442\pi$
$258$		0			0
$259$	−3.71052	+	1.78689i	−0.230560	+	0.111032i
$260$	−2.38382			−0.147838
$261$		0			0
$262$	10.7652			0.665074
$263$	16.7757	−	8.07875i	1.03443	−	0.498157i	0.161949	−	0.986799i	$-0.448222\pi$
$263$	16.7757	−	8.07875i	1.03443	−	0.498157i	0.872484	+	0.488642i	$0.162508\pi$
$264$		0			0
$265$	−7.12553	+	8.93514i	−0.437718	+	0.548881i
$266$	5.22211	−	2.51484i	0.320188	−	0.154195i
$267$		0			0
$268$	−3.97567	−	4.98533i	−0.242852	−	0.304527i
$269$	0.379197	−	1.66137i	0.0231200	−	0.101296i	−0.962051	−	0.272868i	$-0.912028\pi$
$269$	0.379197	−	1.66137i	0.0231200	−	0.101296i	0.985171	+	0.171573i	$0.0548848\pi$
$270$		0			0
$271$	10.3255	−	12.9478i	0.627230	−	0.786522i	−0.362111	−	0.932135i	$-0.617944\pi$
$271$	10.3255	−	12.9478i	0.627230	−	0.786522i	0.989342	+	0.145613i	$0.0465154\pi$
$272$	−6.52507	−	28.5882i	−0.395640	−	1.73341i
$273$		0			0
$274$	−1.20063	−	5.26028i	−0.0725324	−	0.317785i
$275$	10.2050	+	4.91446i	0.615384	+	0.296353i
$276$		0			0
$277$	1.11908	+	4.90299i	0.0672388	+	0.294592i	0.997356	−	0.0726705i	$-0.0231521\pi$
$277$	1.11908	+	4.90299i	0.0672388	+	0.294592i	−0.930117	+	0.367263i	$0.880295\pi$
$278$	−16.1054			−0.965935
$279$		0			0
$280$	1.05149	−	1.31853i	0.0628386	−	0.0787971i
$281$	−3.62478	+	15.8812i	−0.216237	+	0.947394i	0.743994	+	0.668186i	$0.232929\pi$
$281$	−3.62478	+	15.8812i	−0.216237	+	0.947394i	−0.960231	+	0.279208i	$0.909928\pi$
$282$		0			0
$283$	−18.5299	−	23.2357i	−1.10149	−	1.38122i	−0.917238	−	0.398340i	$-0.869586\pi$
$283$	−18.5299	−	23.2357i	−1.10149	−	1.38122i	−0.184248	−	0.982880i	$-0.558985\pi$
$284$	−1.49623	−	0.720547i	−0.0887850	−	0.0427566i
$285$		0			0
$286$	12.7082	−	15.9356i	0.751453	−	0.942292i
$287$	−1.63659	−	2.05222i	−0.0966047	−	0.121138i
$288$		0			0
$289$	21.0560			1.23859
$290$	11.9037	+	4.07006i	0.699010	+	0.239002i
$291$		0			0
$292$	−4.03275	+	1.94207i	−0.235999	+	0.113651i
$293$	−9.92035	−	12.4397i	−0.579553	−	0.726737i	0.402484	−	0.915427i	$-0.368147\pi$
$293$	−9.92035	−	12.4397i	−0.579553	−	0.726737i	−0.982037	+	0.188691i	$0.939576\pi$
$294$		0			0
$295$	−3.00224	+	1.44580i	−0.174797	+	0.0841779i
$296$	18.2150	+	8.77189i	1.05873	+	0.509856i
$297$		0			0
$298$	1.65589	−	7.25493i	0.0959231	−	0.420267i
$299$	−1.17658	+	5.15494i	−0.0680434	+	0.298118i
$300$		0			0
$301$	−1.08921	−	4.77213i	−0.0627809	−	0.275061i
$302$	−23.9274			−1.37687
$303$		0			0
$304$	−32.5243	−	15.6629i	−1.86539	−	0.898327i
$305$	3.58003	+	1.72405i	0.204992	+	0.0987190i
$306$		0			0
$307$	−1.68343			−0.0960784			−0.0480392	−	0.998845i	$-0.515297\pi$
$307$	−1.68343			−0.0960784			−0.0480392	+	0.998845i	$0.515297\pi$
$308$	−0.217024	−	0.950842i	−0.0123661	−	0.0541793i
$309$		0			0
$310$	−2.46329	+	10.7924i	−0.139906	+	0.612967i
$311$	6.24417	−	27.3575i	0.354074	−	1.55130i	−0.413598	−	0.910459i	$-0.635728\pi$
$311$	6.24417	−	27.3575i	0.354074	−	1.55130i	0.767673	−	0.640842i	$-0.221415\pi$
$312$		0			0
$313$	−9.38999	−	4.52198i	−0.530754	−	0.255597i	0.149259	−	0.988798i	$-0.452311\pi$
$313$	−9.38999	−	4.52198i	−0.530754	−	0.255597i	−0.680012	+	0.733201i	$0.738026\pi$
$314$	20.6964	−	9.96685i	1.16796	−	0.562462i
$315$		0			0
$316$	−0.332571	−	0.417031i	−0.0187086	−	0.0234598i
$317$	−24.3195	+	11.7117i	−1.36592	+	0.657792i	−0.965948	−	0.258736i	$-0.916694\pi$
$317$	−24.3195	+	11.7117i	−1.36592	+	0.657792i	−0.399971	+	0.916528i	$0.630980\pi$
$318$		0			0
$319$	−18.2317	+	11.6383i	−1.02078	+	0.651617i
$320$	−7.53058			−0.420972
$321$		0			0
$322$	0.784481	+	0.983708i	0.0437174	+	0.0548199i
$323$	29.2103	−	36.6286i	1.62530	−	2.03807i
$324$		0			0
$325$	8.14893	+	3.92432i	0.452021	+	0.217682i
$326$	15.5709	+	19.5253i	0.862395	+	1.08141i
$327$		0			0
$328$	−2.86732	+	12.5625i	−0.158321	+	0.693650i
$329$	−2.94442	+	3.69219i	−0.162331	+	0.203557i
$330$		0			0
$331$	21.7976			1.19810			0.599052	−	0.800710i	$-0.295544\pi$
$331$	21.7976			1.19810			0.599052	+	0.800710i	$0.295544\pi$
$332$	−1.33437	−	5.84628i	−0.0732333	−	0.320856i
$333$		0			0
$334$	21.4179	+	10.3143i	1.17194	+	0.564375i
$335$	−4.16170	−	18.2336i	−0.227378	−	0.996208i
$336$		0			0
$337$	−2.36853	−	10.3772i	−0.129022	−	0.565282i	−0.997570	−	0.0696762i	$-0.977803\pi$
$337$	−2.36853	−	10.3772i	−0.129022	−	0.565282i	0.868548	−	0.495605i	$-0.165054\pi$
$338$	−2.67659	+	3.35634i	−0.145587	+	0.182561i
$339$		0			0
$340$	−1.02027	+	4.47011i	−0.0553321	+	0.242426i
$341$	−11.8668	−	14.8805i	−0.642625	−	0.805826i
$342$		0			0
$343$	5.98324	−	2.88138i	0.323064	−	0.155580i
$344$	−14.9818	+	18.7866i	−0.807765	+	1.01291i
$345$		0			0
$346$	24.7907	−	11.9386i	1.33276	−	0.641822i
$347$	6.00830			0.322542			0.161271	−	0.986910i	$-0.448441\pi$
$347$	6.00830			0.322542			0.161271	+	0.986910i	$0.448441\pi$
$348$		0			0
$349$	22.1013			1.18305			0.591527	−	0.806285i	$-0.298525\pi$
$349$	22.1013			1.18305			0.591527	+	0.806285i	$0.298525\pi$
$350$	1.93911	−	0.933827i	0.103650	−	0.0499151i
$351$		0			0
$352$	−6.97429	+	8.74548i	−0.371731	+	0.466135i
$353$	−32.6352	+	15.7163i	−1.73699	+	0.836493i	−0.753063	+	0.657948i	$0.771425\pi$
$353$	−32.6352	+	15.7163i	−1.73699	+	0.836493i	−0.983932	+	0.178544i	$0.942861\pi$
$354$		0			0
$355$	−3.03695	−	3.80821i	−0.161184	−	0.202119i
$356$	0.373715	−	1.63735i	0.0198068	−	0.0867794i
$357$		0			0
$358$	−8.40046	+	10.5338i	−0.443978	+	0.556731i
$359$	−3.30493	−	14.4798i	−0.174427	−	0.764217i	−0.984141	−	0.177391i	$-0.943234\pi$
$359$	−3.30493	−	14.4798i	−0.174427	−	0.764217i	0.809713	−	0.586826i	$-0.199623\pi$
$360$		0			0
$361$	−8.60607	−	37.7057i	−0.452951	−	1.98451i
$362$	−27.4844	−	13.2358i	−1.44455	−	0.695658i
$363$		0			0
$364$	−0.173298	−	0.759270i	−0.00908331	−	0.0397966i
$365$	−13.1284			−0.687171
$366$		0			0
$367$	−5.19012	+	6.50821i	−0.270922	+	0.339726i	−0.898617	−	0.438734i	$-0.855427\pi$
$367$	−5.19012	+	6.50821i	−0.270922	+	0.339726i	0.627695	+	0.778459i	$0.283999\pi$
$368$	1.74375	−	7.63989i	0.0908995	−	0.398257i
$369$		0			0
$370$	−12.4356	−	15.5938i	−0.646498	−	0.810683i
$371$	−3.36394	−	1.61999i	−0.174647	−	0.0841055i
$372$		0			0
$373$	15.6555	−	19.6314i	0.810613	−	1.01648i	−0.188793	−	0.982017i	$-0.560458\pi$
$373$	15.6555	−	19.6314i	0.810613	−	1.01648i	0.999406	−	0.0344595i	$-0.0109710\pi$
$374$	−24.4431	−	30.6507i	−1.26392	−	1.58491i
$375$		0			0
$376$	23.1828			1.19556
$377$	−14.5584	+	9.29342i	−0.749798	+	0.478636i
$378$		0			0
$379$	−27.6833	+	13.3316i	−1.42200	+	0.684797i	−0.977490	−	0.210980i	$-0.932335\pi$
$379$	−27.6833	+	13.3316i	−1.42200	+	0.684797i	−0.444505	+	0.895777i	$0.646620\pi$
$380$	3.51932	+	4.41309i	0.180537	+	0.226387i
$381$		0			0
$382$	−13.5587	+	6.52952i	−0.693723	+	0.334079i
$383$	21.0128	+	10.1192i	1.07370	+	0.517068i	0.885298	−	0.465024i	$-0.153954\pi$
$383$	21.0128	+	10.1192i	1.07370	+	0.517068i	0.188404	+	0.982092i	$0.439668\pi$
$384$		0			0
$385$	0.636541	−	2.78887i	0.0324411	−	0.142134i
$386$	−0.535730	+	2.34719i	−0.0272679	+	0.119469i
$387$		0			0
$388$	−1.46534	−	6.42009i	−0.0743915	−	0.325931i
$389$	−7.51454			−0.381002			−0.190501	−	0.981687i	$-0.561011\pi$
$389$	−7.51454			−0.381002			−0.190501	+	0.981687i	$0.561011\pi$
$390$		0			0
$391$	9.16290	+	4.41262i	0.463388	+	0.223156i
$392$	−14.4377	−	6.95284i	−0.729215	−	0.351172i
$393$		0			0
$394$	−7.53643			−0.379680
$395$	−0.348133	−	1.52527i	−0.0175165	−	0.0767446i
$396$		0			0
$397$	1.10330	−	4.83387i	0.0553730	−	0.242605i	−0.939666	−	0.342094i	$-0.888864\pi$
$397$	1.10330	−	4.83387i	0.0553730	−	0.242605i	0.995039	+	0.0994894i	$0.0317209\pi$
$398$	−5.16580	+	22.6328i	−0.258938	+	1.13448i
$399$		0			0
$400$	−12.0771	−	5.81604i	−0.603857	−	0.290802i
$401$	2.33960	−	1.12669i	0.116834	−	0.0562642i	−0.374554	−	0.927205i	$-0.622204\pi$
$401$	2.33960	−	1.12669i	0.116834	−	0.0562642i	0.491388	+	0.870941i	$0.336490\pi$
$402$		0			0
$403$	−9.47594	−	11.8825i	−0.472030	−	0.591907i
$404$	−4.93968	+	2.37882i	−0.245758	+	0.118351i
$405$		0			0
$406$	−0.430979	+	4.08733i	−0.0213892	+	0.202851i
$407$	34.2925			1.69982
$408$		0			0
$409$	7.91495	+	9.92503i	0.391369	+	0.490761i	0.938011	−	0.346605i	$-0.112666\pi$
$409$	7.91495	+	9.92503i	0.391369	+	0.490761i	−0.546642	+	0.837366i	$0.684094\pi$
$410$	7.92599	−	9.93888i	0.391437	−	0.490846i
$411$		0			0
$412$	−1.80527	−	0.869372i	−0.0889392	−	0.0428309i
$413$	−0.678759	−	0.851137i	−0.0333995	−	0.0418817i
$414$		0			0
$415$	3.91379	−	17.1474i	0.192120	−	0.841733i
$416$	−5.56913	+	6.98347i	−0.273049	+	0.342393i
$417$		0			0
$418$	−48.2626			−2.36060
$419$	6.17368	+	27.0486i	0.301604	+	1.32141i	0.867706	+	0.497078i	$0.165594\pi$
$419$	6.17368	+	27.0486i	0.301604	+	1.32141i	−0.566102	+	0.824335i	$0.691549\pi$
$420$		0			0
$421$	−23.1671	−	11.1567i	−1.12910	−	0.543744i	−0.226404	−	0.974033i	$-0.572697\pi$
$421$	−23.1671	−	11.1567i	−1.12910	−	0.543744i	−0.902691	+	0.430290i	$0.858411\pi$
$422$	−3.92935	−	17.2156i	−0.191278	−	0.838043i
$423$		0			0
$424$	4.07854	+	17.8692i	0.198071	+	0.867807i
$425$	10.8466	−	13.6012i	0.526136	−	0.659753i
$426$		0			0
$427$	−0.288867	+	1.26561i	−0.0139793	+	0.0612472i
$428$	−2.91873	−	3.65997i	−0.141082	−	0.176911i
$429$		0			0
$430$	21.3582	−	10.2855i	1.02998	−	0.496013i
$431$	19.5331	−	24.4937i	0.940875	−	1.17982i	−0.0426573	−	0.999090i	$-0.513582\pi$
$431$	19.5331	−	24.4937i	0.940875	−	1.17982i	0.983533	−	0.180731i	$-0.0578462\pi$
$432$		0			0
$433$	−5.14684	+	2.47859i	−0.247341	+	0.119113i	−0.553447	−	0.832884i	$-0.686688\pi$
$433$	−5.14684	+	2.47859i	−0.247341	+	0.119113i	0.306106	+	0.951997i	$0.400974\pi$
$434$	−3.61656			−0.173600
$435$		0			0
$436$	4.84350			0.231962
$437$	11.2802	−	5.43225i	0.539605	−	0.259860i
$438$		0			0
$439$	−4.81335	+	6.03575i	−0.229729	+	0.288071i	−0.883314	−	0.468783i	$-0.844693\pi$
$439$	−4.81335	+	6.03575i	−0.229729	+	0.288071i	0.653585	+	0.756853i	$0.273264\pi$
$440$	−12.6520	+	6.09290i	−0.603162	+	0.290467i
$441$		0			0
$442$	−19.5184	−	24.4753i	−0.928397	−	1.16417i
$443$	0.179073	−	0.784568i	0.00850799	−	0.0372760i	−0.970496	−	0.241118i	$-0.922486\pi$
$443$	0.179073	−	0.784568i	0.00850799	−	0.0372760i	0.979004	+	0.203842i	$0.0653430\pi$
$444$		0			0
$445$	3.07127	−	3.85125i	0.145592	−	0.182567i
$446$	−4.93345	−	21.6149i	−0.233606	−	1.02349i
$447$		0			0
$448$	−0.547456	−	2.39856i	−0.0258649	−	0.113321i
$449$	−34.0196	−	16.3830i	−1.60548	−	0.773160i	−0.605737	−	0.795665i	$-0.707122\pi$
$449$	−34.0196	−	16.3830i	−1.60548	−	0.773160i	−0.999747	+	0.0225050i	$0.992836\pi$
$450$		0			0
$451$	4.86357	+	21.3087i	0.229017	+	1.00339i
$452$	8.03860			0.378104
$453$		0			0
$454$	14.8157	−	18.5783i	0.695335	−	0.871923i
$455$	0.508293	−	2.22698i	0.0238291	−	0.104402i
$456$		0			0
$457$	16.6023	+	20.8186i	0.776622	+	0.973853i	1.00000		0.000878959i	$-0.000279782\pi$
$457$	16.6023	+	20.8186i	0.776622	+	0.973853i	−0.223378	+	0.974732i	$0.571708\pi$
$458$	11.3751	+	5.47796i	0.531523	+	0.255968i
$459$		0			0
$460$	−0.763968	+	0.957986i	−0.0356202	+	0.0446663i
$461$	19.1192	+	23.9748i	0.890472	+	1.11662i	0.992550	+	0.121840i	$0.0388795\pi$
$461$	19.1192	+	23.9748i	0.890472	+	1.11662i	−0.102078	+	0.994776i	$0.532549\pi$
$462$		0			0
$463$	−12.1589			−0.565070			−0.282535	−	0.959257i	$-0.591175\pi$
$463$	−12.1589			−0.565070			−0.282535	+	0.959257i	$0.591175\pi$
$464$	21.5764	−	13.7733i	1.00166	−	0.639411i
$465$		0			0
$466$	29.8613	−	14.3804i	1.38330	−	0.666160i
$467$	−6.56520	−	8.23250i	−0.303801	−	0.380955i	0.606373	−	0.795180i	$-0.292624\pi$
$467$	−6.56520	−	8.23250i	−0.303801	−	0.380955i	−0.910174	+	0.414226i	$0.864052\pi$
$468$		0			0
$469$	5.50503	−	2.65108i	0.254199	−	0.122416i
$470$	−20.6061	−	9.92335i	−0.950487	−	0.457730i
$471$		0			0
$472$	−1.18919	+	5.21019i	−0.0547370	+	0.239819i
$473$	−9.06953	+	39.7362i	−0.417018	+	1.82707i
$474$		0			0
$475$	−4.76560	−	20.8794i	−0.218661	−	0.958014i
$476$	−1.49795			−0.0686582
$477$		0			0
$478$	−14.1934	−	6.83517i	−0.649190	−	0.312633i
$479$	−15.3524	−	7.39331i	−0.701468	−	0.337809i	0.0489239	−	0.998803i	$-0.484421\pi$
$479$	−15.3524	−	7.39331i	−0.701468	−	0.337809i	−0.750392	+	0.660993i	$0.770135\pi$
$480$		0			0
$481$	27.3834			1.24857
$482$	−0.0640008	−	0.280406i	−0.00291516	−	0.0127721i
$483$		0			0
$484$	−0.574925	+	2.51891i	−0.0261330	+	0.114496i
$485$	4.29792	−	18.8304i	0.195159	−	0.855046i
$486$		0			0
$487$	−11.2714	−	5.42800i	−0.510754	−	0.245966i	0.160712	−	0.987001i	$-0.448621\pi$
$487$	−11.2714	−	5.42800i	−0.510754	−	0.245966i	−0.671466	+	0.741035i	$0.734335\pi$
$488$	5.74160	−	2.76501i	0.259910	−	0.125166i
$489$		0			0
$490$	9.85684	+	12.3601i	0.445287	+	0.558372i
$491$	−10.4235	+	5.01971i	−0.470407	+	0.226536i	−0.654042	−	0.756458i	$-0.726928\pi$
$491$	−10.4235	+	5.01971i	−0.470407	+	0.226536i	0.183635	+	0.982995i	$0.441214\pi$
$492$		0			0
$493$	11.1959	+	31.2774i	0.504239	+	1.40866i
$494$	−38.5389			−1.73395
$495$		0			0
$496$	14.0438	+	17.6104i	0.630587	+	0.790731i
$497$	0.992173	−	1.24415i	0.0445051	−	0.0558076i
$498$		0			0
$499$	22.3283	+	10.7527i	0.999550	+	0.481358i	0.860786	−	0.508967i	$-0.169973\pi$
$499$	22.3283	+	10.7527i	0.999550	+	0.481358i	0.138764	+	0.990325i	$0.455687\pi$
$500$	3.62386	+	4.54418i	0.162064	+	0.203222i
$501$		0			0
$502$	6.88373	−	30.1596i	0.307236	−	1.34609i
$503$	21.0937	−	26.4506i	0.940521	−	1.17938i	−0.0430897	−	0.999071i	$-0.513720\pi$
$503$	21.0937	−	26.4506i	0.940521	−	1.17938i	0.983611	−	0.180305i	$-0.0577084\pi$
$504$		0			0
$505$	−16.0808			−0.715587
$506$	−2.33130	−	10.2141i	−0.103639	−	0.454072i
$507$		0			0
$508$	0.684816	+	0.329790i	0.0303838	+	0.0146321i
$509$	−6.36536	−	27.8885i	−0.282140	−	1.23613i	−0.895044	−	0.445978i	$-0.852856\pi$
$509$	−6.36536	−	27.8885i	−0.282140	−	1.23613i	0.612904	−	0.790157i	$-0.290001\pi$
$510$		0			0
$511$	−0.954404	−	4.18152i	−0.0422203	−	0.184979i
$512$	−5.78196	+	7.25035i	−0.255529	+	0.320423i
$513$		0			0
$514$	−6.68787	+	29.3015i	−0.294989	+	1.29243i
$515$	−3.66421	−	4.59478i	−0.161465	−	0.202470i
$516$		0			0
$517$	35.4287	−	17.0616i	1.55815	−	0.750366i
$518$	4.06273	−	5.09451i	0.178506	−	0.223840i
$519$		0			0
$520$	−10.1029	+	4.86532i	−0.443044	+	0.213359i
$521$	23.1052			1.01226			0.506128	−	0.862458i	$-0.331076\pi$
$521$	23.1052			1.01226			0.506128	+	0.862458i	$0.331076\pi$
$522$		0			0
$523$	−19.0757			−0.834120			−0.417060	−	0.908879i	$-0.636940\pi$
$523$	−19.0757			−0.834120			−0.417060	+	0.908879i	$0.636940\pi$
$524$	−3.08584	+	1.48606i	−0.134806	+	0.0649190i
$525$		0			0
$526$	−18.3681	+	23.0329i	−0.800888	+	1.00428i
$527$	−26.3375	+	12.6835i	−1.14728	+	0.552502i
$528$		0			0
$529$	−12.6457	−	15.8572i	−0.549814	−	0.689445i
$530$	4.02368	−	17.6289i	0.174777	−	0.765750i
$531$		0			0
$532$	−1.14976	+	1.44176i	−0.0498486	+	0.0625082i
$533$	3.88368	+	17.0155i	0.168221	+	0.737023i
$534$		0			0
$535$	−3.05531	−	13.3862i	−0.132092	−	0.578735i
$536$	−27.0243	−	13.0142i	−1.16727	−	0.562129i
$537$		0			0
$538$	0.599970	+	2.62864i	0.0258665	+	0.113329i
$539$	−27.1812			−1.17078
$540$		0			0
$541$	−0.981894	+	1.23126i	−0.0422149	+	0.0529359i	−0.802491	−	0.596664i	$-0.796492\pi$
$541$	−0.981894	+	1.23126i	−0.0422149	+	0.0529359i	0.760276	+	0.649600i	$0.225064\pi$
$542$	−5.83066	+	25.5458i	−0.250448	+	1.09729i
$543$		0			0
$544$	10.7117	+	13.4321i	0.459262	+	0.575896i
$545$	12.7994	+	6.16385i	0.548264	+	0.264030i
$546$		0			0
$547$	6.10809	−	7.65930i	0.261163	−	0.327488i	−0.633911	−	0.773406i	$-0.718551\pi$
$547$	6.10809	−	7.65930i	0.261163	−	0.327488i	0.895074	+	0.445918i	$0.147123\pi$
$548$	1.07031	+	1.34212i	0.0457213	+	0.0573327i
$549$		0			0
$550$	−17.9212			−0.764163
$551$	38.6978	+	13.2313i	1.64858	+	0.563674i
$552$		0			0
$553$	0.460505	−	0.221767i	0.0195827	−	0.00943051i
$554$	−4.96115	−	6.22109i	−0.210779	−	0.264309i
$555$		0			0
$556$	4.61661	−	2.22324i	0.195788	−	0.0942864i
$557$	6.73940	+	3.24553i	0.285558	+	0.137517i	0.571180	−	0.820825i	$-0.306486\pi$
$557$	6.73940	+	3.24553i	0.285558	+	0.137517i	−0.285622	+	0.958342i	$0.592200\pi$
$558$		0			0
$559$	−7.24224	+	31.7303i	−0.306314	+	1.34205i
$560$	−0.753316	+	3.30049i	−0.0318334	+	0.139471i
$561$		0			0
$562$	−5.73518	−	25.1274i	−0.241924	−	1.05994i
$563$	2.33889			0.0985724			0.0492862	−	0.998785i	$-0.484305\pi$
$563$	2.33889			0.0985724			0.0492862	+	0.998785i	$0.484305\pi$
$564$		0			0
$565$	21.2427	+	10.2299i	0.893687	+	0.430377i
$566$	42.3660	+	20.4024i	1.78077	+	0.857576i
$567$		0			0
$568$	−7.81184			−0.327778
$569$	8.92006	+	39.0814i	0.373949	+	1.63838i	0.715572	+	0.698539i	$0.246166\pi$
$569$	8.92006	+	39.0814i	0.373949	+	1.63838i	−0.341624	+	0.939837i	$0.610977\pi$
$570$		0			0
$571$	2.16612	−	9.49039i	0.0906493	−	0.397161i	−0.909165	−	0.416436i	$-0.863279\pi$
$571$	2.16612	−	9.49039i	0.0906493	−	0.397161i	0.999814	+	0.0192758i	$0.00613604\pi$
$572$	−1.44301	+	6.32224i	−0.0603353	+	0.264346i
$573$		0			0
$574$	3.74183	+	1.80197i	0.156181	+	0.0752128i
$575$	4.18864	−	2.01714i	0.174678	−	0.0841206i
$576$		0			0
$577$	24.4255	+	30.6286i	1.01685	+	1.27509i	0.960971	+	0.276649i	$0.0892240\pi$
$577$	24.4255	+	30.6286i	1.01685	+	1.27509i	0.0558768	+	0.998438i	$0.482205\pi$
$578$	−30.0158	+	14.4549i	−1.24849	+	0.601243i
$579$		0			0
$580$	−3.97405	+	0.476547i	−0.165013	+	0.0197875i
$581$	5.74614			0.238390
$582$		0			0
$583$	19.3839	+	24.3067i	0.802801	+	1.00668i
$584$	−13.1276	+	16.4615i	−0.543224	+	0.681182i
$585$		0			0
$586$	22.6815	+	10.9228i	0.936965	+	0.451218i
$587$	−13.0173	−	16.3232i	−0.537282	−	0.673731i	0.436896	−	0.899512i	$-0.356078\pi$
$587$	−13.0173	−	16.3232i	−0.537282	−	0.673731i	−0.974178	+	0.225781i	$0.927506\pi$
$588$		0			0
$589$	−8.00792	+	35.0850i	−0.329961	+	1.44565i
$590$	3.28723	−	4.12205i	0.135333	−	0.169702i
$591$		0			0
$592$	−40.5836			−1.66797
$593$	4.13674	+	18.1242i	0.169875	+	0.744273i	0.986048	+	0.166464i	$0.0532349\pi$
$593$	4.13674	+	18.1242i	0.169875	+	0.744273i	−0.816172	+	0.577809i	$0.803908\pi$
$594$		0			0
$595$	−3.95845	−	1.90629i	−0.162281	−	0.0781502i
$596$	0.526835	+	2.30821i	0.0215800	+	0.0945481i
$597$		0			0
$598$	−1.86160	−	8.15620i	−0.0761265	−	0.333532i
$599$	4.70831	−	5.90403i	0.192376	−	0.241232i	−0.676283	−	0.736642i	$-0.736411\pi$
$599$	4.70831	−	5.90403i	0.192376	−	0.241232i	0.868660	+	0.495409i	$0.164982\pi$
$600$		0			0
$601$	−7.99894	+	35.0457i	−0.326284	+	1.42954i	0.499871	+	0.866100i	$0.333381\pi$
$601$	−7.99894	+	35.0457i	−0.326284	+	1.42954i	−0.826155	+	0.563443i	$0.809477\pi$
$602$	4.82874	+	6.05504i	0.196805	+	0.246785i
$603$		0			0
$604$	6.85880	−	3.30302i	0.279081	−	0.134398i
$605$	−4.72486	+	5.92479i	−0.192093	+	0.240877i
$606$		0			0
$607$	−4.59961	+	2.21506i	−0.186692	+	0.0899063i	−0.524895	−	0.851167i	$-0.675895\pi$
$607$	−4.59961	+	2.21506i	−0.186692	+	0.0899063i	0.338203	+	0.941073i	$0.390181\pi$
$608$	21.1502			0.857753
$609$		0			0
$610$	−6.28698			−0.254552
$611$	28.2906	−	13.6241i	1.14452	−	0.551170i
$612$		0			0
$613$	−9.72405	+	12.1936i	−0.392751	+	0.492494i	−0.938415	−	0.345510i	$-0.887706\pi$
$613$	−9.72405	+	12.1936i	−0.392751	+	0.492494i	0.545664	+	0.838004i	$0.316277\pi$
$614$	2.39977	−	1.15567i	0.0968468	−	0.0466390i
$615$		0			0
$616$	−2.86042	−	3.58685i	−0.115250	−	0.144519i
$617$	0.643771	−	2.82055i	0.0259173	−	0.113551i	−0.960315	−	0.278919i	$-0.910024\pi$
$617$	0.643771	−	2.82055i	0.0259173	−	0.113551i	0.986232	+	0.165368i	$0.0528811\pi$
$618$		0			0
$619$	10.3979	−	13.0385i	0.417927	−	0.524063i	−0.527650	−	0.849462i	$-0.676927\pi$
$619$	10.3979	−	13.0385i	0.417927	−	0.524063i	0.945577	+	0.325398i	$0.105498\pi$
$620$	−0.783717	−	3.43369i	−0.0314748	−	0.137900i
$621$		0			0
$622$	9.87960	+	43.2853i	0.396136	+	1.73558i
$623$	1.44993	+	0.698252i	0.0580904	+	0.0279749i
$624$		0			0
$625$	0.655869	+	2.87355i	0.0262348	+	0.114942i
$626$	16.4900			0.659072
$627$		0			0
$628$	−4.55677	+	5.71401i	−0.181835	+	0.228014i
$629$	11.7201	−	51.3490i	0.467310	−	2.04742i
$630$		0			0
$631$	25.7057	+	32.2339i	1.02333	+	1.28321i	0.958432	+	0.285321i	$0.0921001\pi$
$631$	25.7057	+	32.2339i	1.02333	+	1.28321i	0.0648959	+	0.997892i	$0.479328\pi$
$632$	−2.26063	−	1.08866i	−0.0899230	−	0.0433046i
$633$		0			0
$634$	26.6280	−	33.3905i	1.05753	−	1.32611i
$635$	1.38999	+	1.74300i	0.0551602	+	0.0691687i
$636$		0			0
$637$	−21.7048			−0.859976
$638$	18.0001	−	29.1066i	0.712631	−	1.15234i
$639$		0			0
$640$	18.1445	−	8.73791i	0.717223	−	0.345396i
$641$	−5.63784	−	7.06963i	−0.222681	−	0.279234i	0.657924	−	0.753085i	$-0.271435\pi$
$641$	−5.63784	−	7.06963i	−0.222681	−	0.279234i	−0.880605	+	0.473851i	$0.842863\pi$
$642$		0			0
$643$	−20.0926	+	9.67607i	−0.792373	+	0.381587i	−0.785870	−	0.618392i	$-0.787784\pi$
$643$	−20.0926	+	9.67607i	−0.792373	+	0.381587i	−0.00650343	+	0.999979i	$0.502070\pi$
$644$	−0.360667	−	0.173688i	−0.0142123	−	0.00684426i
$645$		0			0
$646$	−16.4946	+	72.2676i	−0.648972	+	2.84333i
$647$	−8.67886	+	38.0246i	−0.341201	+	1.49490i	0.455341	+	0.890317i	$0.349517\pi$
$647$	−8.67886	+	38.0246i	−0.341201	+	1.49490i	−0.796542	+	0.604583i	$0.793340\pi$
$648$		0			0
$649$	2.01712	+	8.83758i	0.0791788	+	0.346905i
$650$	−14.3105			−0.561304
$651$		0			0
$652$	−7.15877	−	3.44748i	−0.280359	−	0.135014i
$653$	38.0768	+	18.3368i	1.49006	+	0.717575i	0.989011	−	0.147845i	$-0.0472336\pi$
$653$	38.0768	+	18.3368i	1.49006	+	0.717575i	0.501048	+	0.865419i	$0.332948\pi$
$654$		0			0
$655$	−10.0458			−0.392521
$656$	−5.75581	−	25.2179i	−0.224727	−	0.984592i
$657$		0			0
$658$	1.66267	−	7.28464i	0.0648176	−	0.283985i
$659$	0.302889	−	1.32704i	0.0117989	−	0.0516943i	−0.968686	−	0.248290i	$-0.920131\pi$
$659$	0.302889	−	1.32704i	0.0117989	−	0.0516943i	0.980485	+	0.196596i	$0.0629886\pi$
$660$		0			0
$661$	−28.3589	−	13.6569i	−1.10304	−	0.531194i	−0.208424	−	0.978039i	$-0.566833\pi$
$661$	−28.3589	−	13.6569i	−1.10304	−	0.531194i	−0.894611	+	0.446845i	$0.852548\pi$
$662$	−31.0730	+	14.9640i	−1.20769	+	0.581591i
$663$		0			0
$664$	−17.5874	−	22.0539i	−0.682522	−	0.855856i
$665$	−4.87314	+	2.34678i	−0.188972	+	0.0910042i
$666$		0			0
$667$	−0.930951	+	8.82896i	−0.0360465	+	0.341859i
$668$	−7.56329			−0.292633
$669$		0			0
$670$	18.4499	+	23.1354i	0.712781	+	0.893799i
$671$	6.73956	−	8.45114i	0.260178	−	0.326253i
$672$		0			0
$673$	−31.7011	−	15.2664i	−1.22199	−	0.588477i	−0.292122	−	0.956381i	$-0.594361\pi$
$673$	−31.7011	−	15.2664i	−1.22199	−	0.588477i	−0.929864	+	0.367904i	$0.880076\pi$
$674$	10.5003	+	13.1669i	0.404456	+	0.507172i
$675$		0			0
$676$	0.303925	−	1.33158i	0.0116894	−	0.0512148i
$677$	−6.16457	+	7.73013i	−0.236924	+	0.297093i	−0.886052	−	0.463586i	$-0.846562\pi$
$677$	−6.16457	+	7.73013i	−0.236924	+	0.297093i	0.649128	+	0.760679i	$0.275134\pi$
$678$		0			0
$679$	6.31012			0.242160
$680$	4.79934	+	21.0273i	0.184046	+	0.806359i
$681$		0			0
$682$	27.1319	+	13.0660i	1.03893	+	0.500324i
$683$	2.06518	+	9.04814i	0.0790219	+	0.346218i	0.998947	−	0.0458763i	$-0.0146080\pi$
$683$	2.06518	+	9.04814i	0.0790219	+	0.346218i	−0.919925	+	0.392094i	$0.871751\pi$
$684$		0			0
$685$	1.12039	+	4.90875i	0.0428079	+	0.187554i
$686$	−6.55119	+	8.21494i	−0.250126	+	0.313648i
$687$		0			0
$688$	10.7334	−	47.0260i	0.409206	−	1.79285i
$689$	15.4785	+	19.4095i	0.589685	+	0.739442i
$690$		0			0
$691$	13.5429	−	6.52192i	0.515196	−	0.248105i	−0.158174	−	0.987411i	$-0.550561\pi$
$691$	13.5429	−	6.52192i	0.515196	−	0.248105i	0.673370	+	0.739306i	$0.264846\pi$
$692$	−5.45823	+	6.84440i	−0.207491	+	0.260185i
$693$		0			0
$694$	−8.56497	+	4.12467i	−0.325122	+	0.156570i
$695$	15.0291			0.570086
$696$		0			0
$697$	33.5695			1.27153
$698$	−31.5059	+	15.1724i	−1.19252	+	0.574285i
$699$		0			0
$700$	−0.426938	+	0.535364i	−0.0161368	+	0.0202348i
$701$	18.8083	−	9.05758i	0.710378	−	0.342100i	−0.0435553	−	0.999051i	$-0.513868\pi$
$701$	18.8083	−	9.05758i	0.710378	−	0.342100i	0.753933	+	0.656951i	$0.228154\pi$
$702$		0			0
$703$	−40.4270	−	50.6939i	−1.52473	−	1.91196i
$704$	−4.55852	+	19.9722i	−0.171806	+	0.752730i
$705$		0			0
$706$	35.7330	−	44.8078i	1.34483	−	1.68636i
$707$	−1.16904	−	5.12190i	−0.0439663	−	0.192629i
$708$		0			0
$709$	−8.24606	−	36.1284i	−0.309687	−	1.35683i	−0.855014	−	0.518605i	$-0.826451\pi$
$709$	−8.24606	−	36.1284i	−0.309687	−	1.35683i	0.545326	−	0.838224i	$-0.316406\pi$
$710$	6.94356	+	3.34384i	0.260587	+	0.125492i
$711$		0			0
$712$	−1.75794	−	7.70205i	−0.0658817	−	0.288646i
$713$	−7.81206			−0.292564
$714$		0			0
$715$	−11.8590	+	14.8707i	−0.443500	+	0.556132i
$716$	0.953866	−	4.17916i	0.0356477	−	0.156183i
$717$		0			0
$718$	14.6516	+	18.3725i	0.546793	+	0.685657i
$719$	13.2393	+	6.37570i	0.493741	+	0.237773i	0.664149	−	0.747600i	$-0.268794\pi$
$719$	13.2393	+	6.37570i	0.493741	+	0.237773i	−0.170407	+	0.985374i	$0.554508\pi$
$720$		0			0
$721$	1.19710	−	1.50112i	0.0445824	−	0.0559046i
$722$	38.1529	+	47.8423i	1.41991	+	1.78050i
$723$		0			0
$724$	9.70553			0.360703
$725$	14.3695	+	4.91315i	0.533670	+	0.182470i
$726$		0			0
$727$	20.8128	−	10.0229i	0.771905	−	0.371730i	−0.00610522	−	0.999981i	$-0.501943\pi$
$727$	20.8128	−	10.0229i	0.771905	−	0.371730i	0.778010	+	0.628251i	$0.216229\pi$
$728$	−2.28411	−	2.86419i	−0.0846549	−	0.106154i
$729$		0			0
$730$	18.7148	−	9.01258i	0.692666	−	0.333570i
$731$	56.4006	+	27.1611i	2.08605	+	1.00459i
$732$		0			0
$733$	−1.74718	+	7.65491i	−0.0645337	+	0.282741i	−0.996891	−	0.0787987i	$-0.974892\pi$
$733$	−1.74718	+	7.65491i	−0.0645337	+	0.282741i	0.932357	+	0.361539i	$0.117749\pi$
$734$	2.93078	−	12.8406i	0.108177	−	0.473955i
$735$		0			0
$736$	1.02165	+	4.47613i	0.0376585	+	0.164992i
$737$	−50.8773			−1.87409
$738$		0			0
$739$	−31.4187	−	15.1305i	−1.15576	−	0.556583i	−0.244999	−	0.969523i	$-0.578788\pi$
$739$	−31.4187	−	15.1305i	−1.15576	−	0.556583i	−0.910758	+	0.412940i	$0.864502\pi$
$740$	5.71731	+	2.75331i	0.210172	+	0.101214i
$741$		0			0
$742$	5.90749			0.216871
$743$	−6.03657	−	26.4479i	−0.221460	−	0.970280i	−0.956380	−	0.292126i	$-0.905637\pi$
$743$	−6.03657	−	26.4479i	−0.221460	−	0.970280i	0.734920	−	0.678154i	$-0.237220\pi$
$744$		0			0
$745$	−1.54523	+	6.77010i	−0.0566129	+	0.248037i
$746$	−8.84044	+	38.7325i	−0.323672	+	1.41810i
$747$		0			0
$748$	11.2378	+	5.41183i	0.410894	+	0.197876i
$749$	4.04151	−	1.94629i	0.147674	−	0.0711159i
$750$		0			0
$751$	−13.2645	−	16.6332i	−0.484029	−	0.606953i	0.478515	−	0.878079i	$-0.341175\pi$
$751$	−13.2645	−	16.6332i	−0.484029	−	0.606953i	−0.962544	+	0.271127i	$0.912604\pi$
$752$	−41.9282	+	20.1916i	−1.52896	+	0.736310i
$753$		0			0
$754$	14.3735	−	23.2423i	0.523452	−	0.846435i
$755$	22.3284			0.812614
$756$		0			0
$757$	−23.5366	−	29.5140i	−0.855454	−	1.07271i	−0.996573	−	0.0827128i	$-0.973642\pi$
$757$	−23.5366	−	29.5140i	−0.855454	−	1.07271i	0.141119	−	0.989993i	$-0.454930\pi$
$758$	30.3111	−	38.0089i	1.10095	−	1.38055i
$759$		0			0
$760$	23.9224	+	11.5204i	0.867755	+	0.417889i
$761$	7.60038	+	9.53057i	0.275513	+	0.345483i	0.900266	−	0.435340i	$-0.143372\pi$
$761$	7.60038	+	9.53057i	0.275513	+	0.345483i	−0.624753	+	0.780823i	$0.714800\pi$
$762$		0			0
$763$	−1.03276	+	4.52482i	−0.0373884	+	0.163809i
$764$	2.98525	−	3.74338i	0.108002	−	0.135431i
$765$		0			0
$766$	−36.9010			−1.33329
$767$	1.61072	+	7.05701i	0.0581596	+	0.254814i
$768$		0			0
$769$	−4.19134	−	2.01844i	−0.151144	−	0.0727869i	0.356783	−	0.934187i	$-0.383874\pi$
$769$	−4.19134	−	2.01844i	−0.151144	−	0.0727869i	−0.507926	+	0.861400i	$0.669588\pi$
$770$	1.00714	+	4.41258i	0.0362949	+	0.159018i
$771$		0			0
$772$	−0.170447	−	0.746777i	−0.00613452	−	0.0268771i
$773$	−12.6382	+	15.8478i	−0.454565	+	0.570006i	−0.955317	−	0.295585i	$-0.904486\pi$
$773$	−12.6382	+	15.8478i	−0.454565	+	0.570006i	0.500752	+	0.865591i	$0.333057\pi$
$774$		0			0
$775$	−2.97355	+	13.0280i	−0.106813	+	0.467979i
$776$	−19.3136	−	24.2184i	−0.693317	−	0.869392i
$777$		0			0
$778$	10.7122	−	5.15870i	0.384049	−	0.184948i
$779$	25.7666	−	32.3103i	0.923185	−	1.15764i
$780$		0			0
$781$	−11.9383	+	5.74918i	−0.427186	+	0.205722i
$782$	−16.0912			−0.575419
$783$		0			0
$784$	32.1677			1.14885
$785$	−19.3133	+	9.30080i	−0.689322	+	0.331960i
$786$		0			0
$787$	20.9397	−	26.2575i	0.746418	−	0.935979i	−0.253087	−	0.967444i	$-0.581446\pi$
$787$	20.9397	−	26.2575i	0.746418	−	0.935979i	0.999505	+	0.0314648i	$0.0100172\pi$
$788$	2.16032	−	1.04036i	0.0769583	−	0.0370612i
$789$		0			0
$790$	1.54336	+	1.93532i	0.0549104	+	0.0688554i
$791$	−1.71404	+	7.50970i	−0.0609443	+	0.267014i
$792$		0			0
$793$	5.38170	−	6.74843i	0.191110	−	0.239644i
$794$	1.74565	+	7.64820i	0.0619509	+	0.271425i
$795$		0			0
$796$	−1.64354	−	7.20082i	−0.0582538	−	0.255226i
$797$	18.7917	+	9.04962i	0.665637	+	0.320554i	0.736014	−	0.676967i	$-0.236706\pi$
$797$	18.7917	+	9.04962i	0.665637	+	0.320554i	−0.0703767	+	0.997520i	$0.522420\pi$
$798$		0			0
$799$	−13.4393	−	58.8814i	−0.475448	−	2.08307i
$800$	7.85362			0.277668
$801$		0			0
$802$	−2.56168	+	3.21225i	−0.0904561	+	0.113428i
$803$	−7.94706	+	34.8183i	−0.280446	+	1.22871i
$804$		0			0
$805$	−0.732057	−	0.917970i	−0.0258016	−	0.0323542i
$806$	21.6654	+	10.4335i	0.763132	+	0.367505i
$807$		0			0
$808$	−16.0799	+	20.1635i	−0.565688	+	0.709351i
$809$	34.6369	+	43.4333i	1.21777	+	1.52703i	0.777118	+	0.629355i	$0.216681\pi$
$809$	34.6369	+	43.4333i	1.21777	+	1.52703i	0.440650	+	0.897679i	$0.354748\pi$
$810$		0			0
$811$	30.6586			1.07657			0.538284	−	0.842764i	$-0.319073\pi$
$811$	30.6586			1.07657			0.538284	+	0.842764i	$0.319073\pi$
$812$	−0.440689	−	1.23113i	−0.0154652	−	0.0432042i
$813$		0			0
$814$	−48.8847	+	23.5417i	−1.71341	+	0.825135i
$815$	−14.5304	−	18.2205i	−0.508977	−	0.638237i
$816$		0			0
$817$	69.4332	−	33.4373i	2.42916	−	1.16982i
$818$	−18.0964	−	8.71478i	−0.632727	−	0.304705i
$819$		0			0
$820$	−0.899991	+	3.94312i	−0.0314290	+	0.137700i
$821$	7.59977	−	33.2968i	0.265234	−	1.16207i	−0.650253	−	0.759718i	$-0.725337\pi$
$821$	7.59977	−	33.2968i	0.265234	−	1.16207i	0.915487	−	0.402348i	$-0.131806\pi$
$822$		0			0
$823$	−5.37768	−	23.5612i	−0.187454	−	0.821291i	−0.977953	−	0.208827i	$-0.933036\pi$
$823$	−5.37768	−	23.5612i	−0.187454	−	0.821291i	0.790498	−	0.612464i	$-0.209822\pi$
$824$	−9.42534			−0.328347
$825$		0			0
$826$	1.55189	+	0.747350i	0.0539971	+	0.0260036i
$827$	−26.9529	−	12.9798i	−0.937244	−	0.451353i	−0.0980476	−	0.995182i	$-0.531260\pi$
$827$	−26.9529	−	12.9798i	−0.937244	−	0.451353i	−0.839196	+	0.543829i	$0.816974\pi$
$828$		0			0
$829$	−20.4692			−0.710926			−0.355463	−	0.934690i	$-0.615677\pi$
$829$	−20.4692			−0.710926			−0.355463	+	0.934690i	$0.615677\pi$
$830$	6.19244	+	27.1308i	0.214943	+	0.941725i
$831$		0			0
$832$	−3.64009	+	15.9483i	−0.126197	+	0.552907i
$833$	−9.28965	+	40.7006i	−0.321867	+	1.41019i
$834$		0			0
$835$	−19.9867	−	9.62506i	−0.691667	−	0.333089i
$836$	13.8345	−	6.66235i	0.478477	−	0.230422i
$837$		0			0
$838$	−27.3695	−	34.3203i	−0.945464	−	1.18557i
$839$	8.60288	−	4.14293i	0.297004	−	0.143030i	−0.279447	−	0.960161i	$-0.590151\pi$
$839$	8.60288	−	4.14293i	0.297004	−	0.143030i	0.576452	+	0.817131i	$0.304437\pi$
$840$		0			0
$841$	−22.4124	+	18.4034i	−0.772842	+	0.634598i
$842$	40.6843			1.40207
$843$		0			0
$844$	3.50286	+	4.39244i	0.120573	+	0.151194i
$845$	2.49772	−	3.13205i	0.0859243	−	0.107746i
$846$		0			0
$847$	−2.23059	−	1.07420i	−0.0766440	−	0.0369098i
$848$	−22.9400	−	28.7658i	−0.787763	−	0.987823i
$849$		0			0
$850$	−6.12489	+	26.8349i	−0.210082	+	0.920429i
$851$	8.77584	−	11.0046i	0.300832	−	0.377231i
$852$		0			0
$853$	−19.9634			−0.683535			−0.341767	−	0.939785i	$-0.611025\pi$
$853$	−19.9634			−0.683535			−0.341767	+	0.939785i	$0.611025\pi$
$854$	−0.457049	−	2.00246i	−0.0156399	−	0.0685229i
$855$		0			0
$856$	−19.8399	−	9.55438i	−0.678113	−	0.326562i
$857$	4.12143	+	18.0572i	0.140785	+	0.616821i	0.995253	+	0.0973169i	$0.0310260\pi$
$857$	4.12143	+	18.0572i	0.140785	+	0.616821i	−0.854468	+	0.519504i	$0.826117\pi$
$858$		0			0
$859$	3.73230	+	16.3523i	0.127344	+	0.557932i	0.997836	+	0.0657490i	$0.0209437\pi$
$859$	3.73230	+	16.3523i	0.127344	+	0.557932i	−0.870492	+	0.492183i	$0.836199\pi$
$860$	−4.70247	+	5.89671i	−0.160353	+	0.201076i
$861$		0			0
$862$	−11.0300	+	48.3257i	−0.375684	+	1.64598i
$863$	24.0442	+	30.1505i	0.818476	+	1.02634i	0.999084	+	0.0427811i	$0.0136218\pi$
$863$	24.0442	+	30.1505i	0.818476	+	1.02634i	−0.180609	+	0.983555i	$0.557807\pi$
$864$		0			0
$865$	−23.1340	+	11.1408i	−0.786581	+	0.378797i
$866$	5.63540	−	7.06656i	0.191499	−	0.240132i
$867$		0			0
$868$	1.03669	−	0.499243i	0.0351875	−	0.0169454i
$869$	−4.25597			−0.144374
$870$		0			0
$871$	−40.6268			−1.37659
$872$	20.5274	−	9.88547i	0.695145	−	0.334764i
$873$		0			0
$874$	−12.3510	+	15.4876i	−0.417777	+	0.523876i
$875$	−5.01789	+	2.41649i	−0.169636	+	0.0816922i
$876$		0			0
$877$	−19.1143	−	23.9686i	−0.645445	−	0.809362i	0.346227	−	0.938151i	$-0.387463\pi$
$877$	−19.1143	−	23.9686i	−0.645445	−	0.809362i	−0.991672	+	0.128788i	$0.958891\pi$
$878$	2.71803	−	11.9084i	0.0917289	−	0.401891i
$879$		0			0
$880$	17.5756	−	22.0391i	0.592474	−	0.742938i
$881$	3.03166	+	13.2826i	0.102139	+	0.447501i	0.999974	+	0.00716935i	$0.00228210\pi$
$881$	3.03166	+	13.2826i	0.102139	+	0.447501i	−0.897835	+	0.440332i	$0.854861\pi$
$882$		0			0
$883$	4.80086	+	21.0340i	0.161562	+	0.707849i	0.989198	+	0.146584i	$0.0468280\pi$
$883$	4.80086	+	21.0340i	0.161562	+	0.707849i	−0.827636	+	0.561265i	$0.810315\pi$
$884$	8.97363	+	4.32147i	0.301816	+	0.145347i
$885$		0			0
$886$	0.283331	+	1.24135i	0.00951868	+	0.0417041i
$887$	−18.1424			−0.609161			−0.304580	−	0.952487i	$-0.598516\pi$
$887$	−18.1424			−0.609161			−0.304580	+	0.952487i	$0.598516\pi$
$888$		0			0
$889$	−0.454112	+	0.569438i	−0.0152304	+	0.0190984i
$890$	−1.73430	+	7.59846i	−0.0581338	+	0.254701i
$891$		0			0
$892$	4.39797	+	5.51488i	0.147255	+	0.184652i
$893$	−66.9882	−	32.2598i	−2.24168	−	1.07953i
$894$		0			0
$895$	7.83908	−	9.82990i	0.262032	−	0.328577i
$896$	4.10217	+	5.14396i	0.137044	+	0.171848i
$897$		0			0
$898$	59.7426			1.99363
$899$	−18.1727	−	17.9148i	−0.606093	−	0.597493i
$900$		0			0
$901$	43.0212	−	20.7179i	1.43324	−	0.690214i
$902$	−21.5615	−	27.0372i	−0.717918	−	0.900241i
$903$		0			0
$904$	34.0687	−	16.4066i	1.13311	−	0.545676i
$905$	25.6477	+	12.3513i	0.852559	+	0.410571i
$906$		0			0
$907$	9.93571	−	43.5312i	0.329910	−	1.44543i	−0.489390	−	0.872065i	$-0.662781\pi$
$907$	9.93571	−	43.5312i	0.329910	−	1.44543i	0.819300	−	0.573365i	$-0.194362\pi$
$908$	−1.68231	+	7.37069i	−0.0558295	+	0.244605i
$909$		0			0
$910$	0.804227	+	3.52355i	0.0266599	+	0.116804i
$911$	56.3437			1.86675			0.933374	−	0.358904i	$-0.116850\pi$
$911$	56.3437			1.86675			0.933374	+	0.358904i	$0.116850\pi$
$912$		0			0
$913$	−43.1083	−	20.7598i	−1.42668	−	0.687051i
$914$	−37.9588	−	18.2800i	−1.25557	−	0.604649i
$915$		0			0
$916$	−4.01688			−0.132721
$917$	−0.730305	−	3.19967i	−0.0241168	−	0.105663i
$918$		0			0
$919$	−3.57797	+	15.6761i	−0.118026	+	0.517107i	0.881005	+	0.473107i	$0.156867\pi$
$919$	−3.57797	+	15.6761i	−0.118026	+	0.517107i	−0.999032	+	0.0440006i	$0.985990\pi$
$920$	−1.28257	+	5.61931i	−0.0422851	+	0.185263i
$921$		0			0
$922$	−43.7135	−	21.0513i	−1.43963	−	0.693288i
$923$	−9.53302	+	4.59086i	−0.313783	+	0.151110i
$924$		0			0
$925$	−15.0116	−	18.8240i	−0.493580	−	0.618929i
$926$	17.3327	−	8.34701i	0.569589	−	0.274300i
$927$		0			0
$928$	−7.88820	+	12.7554i	−0.258943	+	0.418717i
$929$	−44.6471			−1.46482			−0.732412	−	0.680862i	$-0.761605\pi$
$929$	−44.6471			−1.46482			−0.732412	+	0.680862i	$0.761605\pi$
$930$		0			0
$931$	32.0436	+	40.1814i	1.05019	+	1.31689i
$932$	−6.57462	+	8.24431i	−0.215359	+	0.270051i
$933$		0			0
$934$	15.0104	+	7.22864i	0.491156	+	0.236528i
$935$	22.8097	+	28.6024i	0.745956	+	0.935400i
$936$		0			0
$937$	12.1754	−	53.3439i	0.397753	−	1.74267i	−0.238458	−	0.971153i	$-0.576642\pi$
$937$	12.1754	−	53.3439i	0.397753	−	1.74267i	0.636211	−	0.771515i	$-0.280501\pi$
$938$	−6.02759	+	7.55836i	−0.196808	+	0.246789i
$939$		0			0
$940$	7.27659			0.237336
$941$	8.33838	+	36.5328i	0.271824	+	1.19094i	0.907859	+	0.419277i	$0.137716\pi$
$941$	8.33838	+	36.5328i	0.271824	+	1.19094i	−0.636035	+	0.771660i	$0.719427\pi$
$942$		0			0
$943$	8.08266	+	3.89240i	0.263208	+	0.126754i
$944$	−2.38717	−	10.4589i	−0.0776957	−	0.340407i
$945$		0			0
$946$	−14.3499	−	62.8711i	−0.466556	−	2.04412i
$947$	35.1177	−	44.0362i	1.14117	−	1.43098i	0.255416	−	0.966831i	$-0.417787\pi$
$947$	35.1177	−	44.0362i	1.14117	−	1.43098i	0.885755	−	0.464153i	$-0.153641\pi$
$948$		0			0
$949$	−6.34592	+	27.8033i	−0.205997	+	0.902533i
$950$	21.1271	+	26.4926i	0.685454	+	0.859532i
$951$		0			0
$952$	−6.34849	+	3.05727i	−0.205756	+	0.0990868i
$953$	2.20354	−	2.76315i	0.0713796	−	0.0895071i	−0.744860	−	0.667221i	$-0.767484\pi$
$953$	2.20354	−	2.76315i	0.0713796	−	0.0895071i	0.816239	+	0.577714i	$0.196055\pi$
$954$		0			0
$955$	12.6526	−	6.09317i	0.409429	−	0.197170i
$956$	5.01209			0.162103
$957$		0			0
$958$	26.9606			0.871059
$959$	−1.48204	+	0.713711i	−0.0478574	+	0.0230469i
$960$		0			0
$961$	−5.32790	+	6.68097i	−0.171868	+	0.215515i
$962$	−39.0356	+	18.7986i	−1.25856	+	0.606090i
$963$		0			0
$964$	0.0570541	+	0.0715435i	0.00183759	+	0.00230426i
$965$	0.499929	−	2.19033i	0.0160933	−	0.0705093i
$966$		0			0
$967$	−37.4649	+	46.9795i	−1.20479	+	1.51076i	−0.400747	+	0.916189i	$0.631249\pi$
$967$	−37.4649	+	46.9795i	−1.20479	+	1.51076i	−0.804043	+	0.594571i	$0.797322\pi$
$968$	2.70443	+	11.8489i	0.0869237	+	0.380838i
$969$		0			0
$970$	6.80022	+	29.7937i	0.218342	+	0.956619i
$971$	−7.41072	−	3.56881i	−0.237821	−	0.114529i	0.311178	−	0.950352i	$-0.399277\pi$
$971$	−7.41072	−	3.56881i	−0.237821	−	0.114529i	−0.548999	+	0.835823i	$0.684991\pi$
$972$		0			0
$973$	1.09258	+	4.78691i	0.0350265	+	0.153461i
$974$	19.7939			0.634237
$975$		0			0
$976$	−7.97595	+	10.0015i	−0.255304	+	0.320141i
$977$	8.04254	−	35.2367i	0.257304	−	1.12732i	−0.666818	−	0.745221i	$-0.732344\pi$
$977$	8.04254	−	35.2367i	0.257304	−	1.12732i	0.924121	−	0.382100i	$-0.124799\pi$
$978$		0			0
$979$	−8.35492	−	10.4767i	−0.267024	−	0.334838i
$980$	−4.53170	−	2.18235i	−0.144760	−	0.0697127i
$981$		0			0
$982$	11.4130	−	14.3114i	0.364203	−	0.456696i
$983$	−33.3167	−	41.7778i	−1.06264	−	1.33250i	−0.940425	−	0.340000i	$-0.889573\pi$
$983$	−33.3167	−	41.7778i	−1.06264	−	1.33250i	−0.122211	−	0.992504i	$-0.538998\pi$
$984$		0			0
$985$	7.03280			0.224084
$986$	−37.4318	−	36.9007i	−1.19207	−	1.17516i
$987$		0			0
$988$	11.0472	−	5.32004i	0.351458	−	0.169253i
$989$	10.4305	+	13.0794i	0.331669	+	0.415900i
$990$		0			0
$991$	2.38129	−	1.14677i	0.0756440	−	0.0364282i	−0.395679	−	0.918389i	$-0.629491\pi$
$991$	2.38129	−	1.14677i	0.0756440	−	0.0364282i	0.471323	+	0.881961i	$0.343777\pi$
$992$	−11.8900	−	5.72593i	−0.377508	−	0.181798i
$993$		0			0
$994$	−0.560265	+	2.45468i	−0.0177705	+	0.0778578i
$995$	4.82058	−	21.1204i	0.152823	−	0.669560i
$996$		0			0
$997$	0.945420	+	4.14216i	0.0299418	+	0.131183i	0.987690	−	0.156425i	$-0.0499970\pi$
$997$	0.945420	+	4.14216i	0.0299418	+	0.131183i	−0.957748	+	0.287608i	$0.907140\pi$
$998$	−39.2112			−1.24121
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.k.f.136.3	✓	60
3.2	odd	2	inner	783.2.k.f.136.8	yes	60
29.16	even	7	inner	783.2.k.f.190.3	yes	60
87.74	odd	14	inner	783.2.k.f.190.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.k.f.136.3	✓	60	1.1	even	1	trivial
783.2.k.f.136.8	yes	60	3.2	odd	2	inner
783.2.k.f.190.3	yes	60	29.16	even	7	inner
783.2.k.f.190.8	yes	60	87.74	odd	14	inner

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.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42552 + 0.686496i) q^{2} +(0.313861 - 0.393569i) q^{4} +(1.33026 - 0.640620i) q^{5} +(0.300750 + 0.377129i) q^{7} +(0.526918 - 2.30858i) q^{8} +(-1.45653 + 1.82644i) q^{10} +(-0.893763 - 3.91583i) q^{11} +(-0.713691 - 3.12688i) q^{13} +(-0.687624 - 0.331142i) q^{14} +(1.05773 + 4.63420i) q^{16} -6.16896 q^{17} +(-4.73505 + 5.93756i) q^{19} +(0.165388 - 0.724614i) q^{20} +(3.96228 + 4.96854i) q^{22} +(-1.48532 - 0.715295i) q^{23} +(-1.75825 + 2.20478i) q^{25} +(3.16398 + 3.96750i) q^{26} +0.242820 q^{28} +(-1.81488 - 5.07013i) q^{29} +(4.26937 - 2.05602i) q^{31} +(-1.73639 - 2.17737i) q^{32} +(8.79399 - 4.23496i) q^{34} +(0.641673 + 0.309013i) q^{35} +(-1.89985 + 8.32377i) q^{37} +(2.67381 - 11.7147i) q^{38} +(-0.777983 - 3.40856i) q^{40} -5.44168 q^{41} +(-9.14266 - 4.40287i) q^{43} +(-1.82167 - 0.877268i) q^{44} +2.60841 q^{46} +(2.17854 + 9.54479i) q^{47} +(1.50587 - 6.59765i) q^{49} +(0.992857 - 4.34999i) q^{50} +(-1.45464 - 0.700519i) q^{52} +(-6.97382 + 3.35842i) q^{53} +(-3.69750 - 4.63651i) q^{55} +(1.02910 - 0.495590i) q^{56} +(6.06778 + 5.98168i) q^{58} -2.25688 q^{59} +(1.67795 + 2.10409i) q^{61} +(-4.67464 + 5.86181i) q^{62} +(-4.59527 - 2.21297i) q^{64} +(-2.95254 - 3.70237i) q^{65} +(2.81867 - 12.3494i) q^{67} +(-1.93619 + 2.42791i) q^{68} -1.12686 q^{70} +(-0.734095 - 3.21628i) q^{71} +(-8.01113 - 3.85796i) q^{73} +(-3.00596 - 13.1700i) q^{74} +(0.850694 + 3.72713i) q^{76} +(1.20797 - 1.51475i) q^{77} +(0.235786 - 1.03305i) q^{79} +(4.37581 + 5.48710i) q^{80} +(7.75724 - 3.73569i) q^{82} +(7.42726 - 9.31349i) q^{83} +(-8.20632 + 3.95195i) q^{85} +16.0556 q^{86} -9.51095 q^{88} +(3.00588 - 1.44755i) q^{89} +(0.964596 - 1.20957i) q^{91} +(-0.747703 + 0.360075i) q^{92} +(-9.65801 - 12.1108i) q^{94} +(-2.49513 + 10.9319i) q^{95} +(8.15625 - 10.2276i) q^{97} +(2.38261 + 10.4389i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) \) 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

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