LMFDB - Embedded newform 135.5.i.a.71.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,5,Mod(71,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.71"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	135.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.9549450163$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.14
Character	$\chi$	$=$	135.71
Dual form			135.5.i.a.116.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.11159 - 2.95118i) q^{2} +(9.41890 - 16.3140i) q^{4} +(9.68246 + 5.59017i) q^{5} +(36.1606 + 62.6320i) q^{7} -16.7497i q^{8} +65.9903 q^{10} +(187.805 - 108.429i) q^{11} +(-13.6629 + 23.6648i) q^{13} +(369.676 + 213.433i) q^{14} +(101.271 + 175.407i) q^{16} -339.847i q^{17} -301.434 q^{19} +(182.396 - 105.307i) q^{20} +(639.988 - 1108.49i) q^{22} +(-329.599 - 190.294i) q^{23} +(62.5000 + 108.253i) q^{25} +161.286i q^{26} +1362.37 q^{28} +(-136.804 + 78.9837i) q^{29} +(-201.104 + 348.322i) q^{31} +(1267.40 + 731.735i) q^{32} +(-1002.95 - 1737.16i) q^{34} +808.575i q^{35} +291.824 q^{37} +(-1540.80 + 889.584i) q^{38} +(93.6338 - 162.179i) q^{40} +(2548.83 + 1471.56i) q^{41} +(-1200.28 - 2078.95i) q^{43} -4085.14i q^{44} -2246.36 q^{46} +(-2053.78 + 1185.75i) q^{47} +(-1414.68 + 2450.29i) q^{49} +(638.949 + 368.897i) q^{50} +(257.379 + 445.793i) q^{52} -1566.51i q^{53} +2424.55 q^{55} +(1049.07 - 605.680i) q^{56} +(-466.190 + 807.464i) q^{58} +(-2631.23 - 1519.14i) q^{59} +(-977.183 - 1692.53i) q^{61} +2373.97i q^{62} +5397.25 q^{64} +(-264.581 + 152.756i) q^{65} +(-1896.89 + 3285.51i) q^{67} +(-5544.27 - 3200.99i) q^{68} +(2386.25 + 4133.11i) q^{70} -1205.47i q^{71} -6117.56 q^{73} +(1491.68 - 861.223i) q^{74} +(-2839.17 + 4917.59i) q^{76} +(13582.3 + 7841.74i) q^{77} +(931.321 + 1613.09i) q^{79} +2264.49i q^{80} +17371.4 q^{82} +(-721.466 + 416.539i) q^{83} +(1899.80 - 3290.55i) q^{85} +(-12270.7 - 7084.49i) q^{86} +(-1816.16 - 3145.68i) q^{88} -9603.06i q^{89} -1976.23 q^{91} +(-6208.92 + 3584.72i) q^{92} +(-6998.73 + 12122.2i) q^{94} +(-2918.62 - 1685.06i) q^{95} +(-3468.03 - 6006.81i) q^{97} +16699.9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 128 q^{4} - 26 q^{7} + 738 q^{11} + 10 q^{13} - 1998 q^{14} - 1024 q^{16} + 508 q^{19} + 672 q^{22} - 1998 q^{23} + 2000 q^{25} - 1664 q^{28} + 270 q^{29} - 1472 q^{31} + 6048 q^{32} - 594 q^{34}+ \cdots + 23266 q^{97}+O(q^{100}) $ 32 * q + 128 * q^4 - 26 * q^7 + 738 * q^11 + 10 * q^13 - 1998 * q^14 - 1024 * q^16 + 508 * q^19 + 672 * q^22 - 1998 * q^23 + 2000 * q^25 - 1664 * q^28 + 270 * q^29 - 1472 * q^31 + 6048 * q^32 - 594 * q^34 + 2068 * q^37 + 7164 * q^38 + 1650 * q^40 + 13428 * q^41 + 568 * q^43 + 5724 * q^46 - 12528 * q^47 - 1674 * q^49 + 1534 * q^52 - 21294 * q^56 - 8190 * q^58 + 4374 * q^59 - 4478 * q^61 - 37216 * q^64 + 8550 * q^65 + 12838 * q^67 - 65736 * q^68 + 2400 * q^70 + 29236 * q^73 + 20628 * q^74 + 6190 * q^76 + 31806 * q^77 - 3512 * q^79 + 34692 * q^82 + 43074 * q^83 - 4350 * q^85 + 10746 * q^86 - 16128 * q^88 - 48904 * q^91 - 27036 * q^92 + 5118 * q^94 - 6300 * q^95 + 23266 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	5.11159	−	2.95118i	1.27790	−	0.737794i	0.301436	−	0.953486i	$-0.402534\pi$
$2$	5.11159	−	2.95118i	1.27790	−	0.737794i	0.976461	+	0.215692i	$0.0692007\pi$
$3$		0			0
$3$		0			0
$4$	9.41890	−	16.3140i	0.588681	−	1.01963i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$6$		0			0
$7$	36.1606	+	62.6320i	0.737971	+	1.27820i	0.953407	+	0.301686i	$0.0975494\pi$
$7$	36.1606	+	62.6320i	0.737971	+	1.27820i	−0.215436	+	0.976518i	$0.569117\pi$
$8$		−	16.7497i		−	0.261715i
$9$		0			0
$10$	65.9903			0.659903
$11$	187.805	−	108.429i	1.55211	−	0.896110i	0.554138	−	0.832425i	$-0.313048\pi$
$11$	187.805	−	108.429i	1.55211	−	0.896110i	0.997970	−	0.0636853i	$-0.0202854\pi$
$12$		0			0
$13$	−13.6629	+	23.6648i	−0.0808455	+	0.140028i	−0.903613	−	0.428349i	$-0.859095\pi$
$13$	−13.6629	+	23.6648i	−0.0808455	+	0.140028i	0.822768	+	0.568378i	$0.192429\pi$
$14$	369.676	+	213.433i	1.88610	+	1.08894i
$15$		0			0
$16$	101.271	+	175.407i	0.395590	+	0.685182i
$17$		−	339.847i		−	1.17594i	−0.808882	−	0.587970i	$-0.799927\pi$
$17$		−	339.847i		−	1.17594i	0.808882	−	0.587970i	$-0.200073\pi$
$18$		0			0
$19$	−301.434			−0.834996			−0.417498	−	0.908678i	$-0.637093\pi$
$19$	−301.434			−0.834996			−0.417498	+	0.908678i	$0.637093\pi$
$20$	182.396	−	105.307i	0.455991	−	0.263266i
$21$		0			0
$22$	639.988	−	1108.49i	1.32229	−	2.29027i
$23$	−329.599	−	190.294i	−0.623060	−	0.359724i	0.154999	−	0.987915i	$-0.450462\pi$
$23$	−329.599	−	190.294i	−0.623060	−	0.359724i	−0.778059	+	0.628191i	$0.783796\pi$
$24$		0			0
$25$	62.5000	+	108.253i	0.100000	+	0.173205i
$26$			161.286i			0.238589i
$27$		0			0
$28$	1362.37			1.73772
$29$	−136.804	+	78.9837i	−0.162668	+	0.0939164i	−0.579124	−	0.815239i	$-0.696605\pi$
$29$	−136.804	+	78.9837i	−0.162668	+	0.0939164i	0.416456	+	0.909156i	$0.363272\pi$
$30$		0			0
$31$	−201.104	+	348.322i	−0.209265	+	0.362457i	−0.951483	−	0.307701i	$-0.900440\pi$
$31$	−201.104	+	348.322i	−0.209265	+	0.362457i	0.742218	+	0.670158i	$0.233774\pi$
$32$	1267.40	+	731.735i	1.23770	+	0.714585i
$33$		0			0
$34$	−1002.95	−	1737.16i	−0.867603	−	1.50273i
$35$			808.575i			0.660062i
$36$		0			0
$37$	291.824			0.213165			0.106583	−	0.994304i	$-0.466009\pi$
$37$	291.824			0.213165			0.106583	+	0.994304i	$0.466009\pi$
$38$	−1540.80	+	889.584i	−1.06704	+	0.616055i
$39$		0			0
$40$	93.6338	−	162.179i	0.0585212	−	0.101362i
$41$	2548.83	+	1471.56i	1.51626	+	0.875410i	0.999818	+	0.0190855i	$0.00607546\pi$
$41$	2548.83	+	1471.56i	1.51626	+	0.875410i	0.516437	+	0.856325i	$0.327258\pi$
$42$		0			0
$43$	−1200.28	−	2078.95i	−0.649152	−	1.12436i	−0.983326	−	0.181853i	$-0.941790\pi$
$43$	−1200.28	−	2078.95i	−0.649152	−	1.12436i	0.334174	−	0.942512i	$-0.391543\pi$
$44$		−	4085.14i		−	2.11009i
$45$		0			0
$46$	−2246.36			−1.06161
$47$	−2053.78	+	1185.75i	−0.929734	+	0.536782i	−0.886728	−	0.462292i	$-0.847027\pi$
$47$	−2053.78	+	1185.75i	−0.929734	+	0.536782i	−0.0430067	+	0.999075i	$0.513694\pi$
$48$		0			0
$49$	−1414.68	+	2450.29i	−0.589203	+	1.02053i
$50$	638.949	+	368.897i	0.255580	+	0.147559i
$51$		0			0
$52$	257.379	+	445.793i	0.0951844	+	0.164864i
$53$		−	1566.51i		−	0.557676i	−0.960338	−	0.278838i	$-0.910051\pi$
$53$		−	1566.51i		−	0.557676i	0.960338	−	0.278838i	$-0.0899493\pi$
$54$		0			0
$55$	2424.55			0.801505
$56$	1049.07	−	605.680i	0.334525	−	0.193138i
$57$		0			0
$58$	−466.190	+	807.464i	−0.138582	+	0.240031i
$59$	−2631.23	−	1519.14i	−0.755884	−	0.436410i	0.0719319	−	0.997410i	$-0.477084\pi$
$59$	−2631.23	−	1519.14i	−0.755884	−	0.436410i	−0.827816	+	0.561000i	$0.810417\pi$
$60$		0			0
$61$	−977.183	−	1692.53i	−0.262613	−	0.454859i	0.704323	−	0.709880i	$-0.251251\pi$
$61$	−977.183	−	1692.53i	−0.262613	−	0.454859i	−0.966935	+	0.255021i	$0.917918\pi$
$62$			2373.97i			0.617578i
$63$		0			0
$64$	5397.25			1.31769
$65$	−264.581	+	152.756i	−0.0626226	+	0.0361552i
$66$		0			0
$67$	−1896.89	+	3285.51i	−0.422565	+	0.731903i	−0.996190	−	0.0872147i	$-0.972203\pi$
$67$	−1896.89	+	3285.51i	−0.422565	+	0.731903i	0.573625	+	0.819118i	$0.305537\pi$
$68$	−5544.27	−	3200.99i	−1.19902	−	0.692255i
$69$		0			0
$70$	2386.25	+	4133.11i	0.486990	+	0.843491i
$71$		−	1205.47i		−	0.239132i	−0.992826	−	0.119566i	$-0.961850\pi$
$71$		−	1205.47i		−	0.239132i	0.992826	−	0.119566i	$-0.0381503\pi$
$72$		0			0
$73$	−6117.56			−1.14797			−0.573987	−	0.818864i	$-0.694604\pi$
$73$	−6117.56			−1.14797			−0.573987	+	0.818864i	$0.694604\pi$
$74$	1491.68	−	861.223i	0.272404	−	0.157272i
$75$		0			0
$76$	−2839.17	+	4917.59i	−0.491547	+	0.851384i
$77$	13582.3	+	7841.74i	2.29082	+	1.32261i
$78$		0			0
$79$	931.321	+	1613.09i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$79$	931.321	+	1613.09i	0.149226	+	0.258467i	−0.781715	+	0.623635i	$0.785655\pi$
$80$			2264.49i			0.353826i
$81$		0			0
$82$	17371.4			2.58349
$83$	−721.466	+	416.539i	−0.104727	+	0.0604643i	−0.551449	−	0.834209i	$-0.685925\pi$
$83$	−721.466	+	416.539i	−0.104727	+	0.0604643i	0.446722	+	0.894673i	$0.352591\pi$
$84$		0			0
$85$	1899.80	−	3290.55i	0.262948	−	0.455440i
$86$	−12270.7	−	7084.49i	−1.65910	−	0.957882i
$87$		0			0
$88$	−1816.16	−	3145.68i	−0.234525	−	0.406209i
$89$		−	9603.06i		−	1.21235i	−0.795330	−	0.606177i	$-0.792702\pi$
$89$		−	9603.06i		−	1.21235i	0.795330	−	0.606177i	$-0.207298\pi$
$90$		0			0
$91$	−1976.23			−0.238646
$92$	−6208.92	+	3584.72i	−0.733568	+	0.423525i
$93$		0			0
$94$	−6998.73	+	12122.2i	−0.792070	+	1.37191i
$95$	−2918.62	−	1685.06i	−0.323393	−	0.186711i
$96$		0			0
$97$	−3468.03	−	6006.81i	−0.368587	−	0.638411i	0.620758	−	0.784002i	$-0.286825\pi$
$97$	−3468.03	−	6006.81i	−0.368587	−	0.638411i	−0.989345	+	0.145591i	$0.953492\pi$
$98$			16699.9i			1.73884i
$99$		0			0
$100$	2354.73			0.235473
$101$	−9040.99	+	5219.82i	−0.886285	+	0.511697i	−0.872726	−	0.488211i	$-0.837650\pi$
$101$	−9040.99	+	5219.82i	−0.886285	+	0.511697i	−0.0135595	+	0.999908i	$0.504316\pi$
$102$		0			0
$103$	−3748.81	+	6493.13i	−0.353362	+	0.612040i	−0.986836	−	0.161723i	$-0.948295\pi$
$103$	−3748.81	+	6493.13i	−0.353362	+	0.612040i	0.633475	+	0.773763i	$0.281628\pi$
$104$	396.379	+	228.850i	0.0366475	+	0.0211584i
$105$		0			0
$106$	−4623.06	−	8007.37i	−0.411450	−	0.712653i
$107$			1396.48i			0.121974i	0.998139	+	0.0609870i	$0.0194248\pi$
$107$			1396.48i			0.121974i	−0.998139	+	0.0609870i	$0.980575\pi$
$108$		0			0
$109$	−17017.9			−1.43236			−0.716180	−	0.697916i	$-0.754111\pi$
$109$	−17017.9			−1.43236			−0.716180	+	0.697916i	$0.754111\pi$
$110$	12393.3	−	7155.29i	1.02424	−	0.591346i
$111$		0			0
$112$	−7324.04	+	12685.6i	−0.583868	+	1.01129i
$113$	−17895.2	−	10331.8i	−1.40146	−	0.809133i	−0.406917	−	0.913465i	$-0.633396\pi$
$113$	−17895.2	−	10331.8i	−1.40146	−	0.809133i	−0.994543	+	0.104332i	$0.966730\pi$
$114$		0			0
$115$	−2127.55	−	3685.03i	−0.160873	−	0.278641i
$116$			2975.76i			0.221147i
$117$		0			0
$118$	−17933.0			−1.28792
$119$	21285.3	−	12289.1i	1.50309	−	0.867811i
$120$		0			0
$121$	16193.3	−	28047.7i	1.10603	−	1.91569i
$122$	−9989.91	−	5767.68i	−0.671185	−	0.387509i
$123$		0			0
$124$	3788.35	+	6561.62i	0.246381	+	0.426744i
$125$			1397.54i			0.0894427i
$126$		0			0
$127$	18405.1			1.14112			0.570558	−	0.821257i	$-0.306727\pi$
$127$	18405.1			1.14112			0.570558	+	0.821257i	$0.306727\pi$
$128$	7310.10	−	4220.49i	0.446173	−	0.257598i
$129$		0			0
$130$	−901.618	+	1561.65i	−0.0533502	+	0.0924052i
$131$	5531.53	+	3193.63i	0.322332	+	0.186098i	0.652431	−	0.757848i	$-0.273749\pi$
$131$	5531.53	+	3193.63i	0.322332	+	0.186098i	−0.330100	+	0.943946i	$0.607082\pi$
$132$		0			0
$133$	−10900.0	−	18879.4i	−0.616203	−	1.06730i
$134$			22392.3i			1.24706i
$135$		0			0
$136$	−5692.34			−0.307761
$137$	9299.23	−	5368.91i	0.495457	−	0.286052i	−0.231379	−	0.972864i	$-0.574324\pi$
$137$	9299.23	−	5368.91i	0.495457	−	0.286052i	0.726835	+	0.686812i	$0.240990\pi$
$138$		0			0
$139$	11291.3	−	19557.1i	0.584405	−	1.01222i	−0.410544	−	0.911841i	$-0.634661\pi$
$139$	11291.3	−	19557.1i	0.584405	−	1.01222i	0.994949	−	0.100378i	$-0.0320054\pi$
$140$	13191.1	+	7615.89i	0.673016	+	0.388566i
$141$		0			0
$142$	−3557.54	−	6161.84i	−0.176430	−	0.305586i
$143$			5925.83i			0.289786i
$144$		0			0
$145$	−1766.13			−0.0840013
$146$	−31270.4	+	18054.0i	−1.46699	+	0.846969i
$147$		0			0
$148$	2748.66	−	4760.81i	0.125487	−	0.217349i
$149$	26665.8	+	15395.5i	1.20111	+	0.693459i	0.960801	−	0.277239i	$-0.0894193\pi$
$149$	26665.8	+	15395.5i	1.20111	+	0.693459i	0.240305	+	0.970697i	$0.422753\pi$
$150$		0			0
$151$	15309.2	+	26516.4i	0.671429	+	1.16295i	0.977499	+	0.210940i	$0.0676524\pi$
$151$	15309.2	+	26516.4i	0.671429	+	1.16295i	−0.306070	+	0.952009i	$0.599014\pi$
$152$			5048.93i			0.218531i
$153$		0			0
$154$	92569.4			3.90325
$155$	−3894.35	+	2248.41i	−0.162096	+	0.0935861i
$156$		0			0
$157$	5843.75	−	10121.7i	0.237079	−	0.410632i	−0.722796	−	0.691061i	$-0.757143\pi$
$157$	5843.75	−	10121.7i	0.237079	−	0.410632i	0.959875	+	0.280429i	$0.0904768\pi$
$158$	9521.06	+	5496.99i	0.381392	+	0.220197i
$159$		0			0
$160$	8181.05	+	14170.0i	0.319572	+	0.553515i
$161$		−	27524.6i		−	1.06186i
$162$		0			0
$163$	19003.8			0.715263			0.357631	−	0.933863i	$-0.383584\pi$
$163$	19003.8			0.715263			0.357631	+	0.933863i	$0.383584\pi$
$164$	48014.3	−	27721.1i	1.78518	−	1.03068i
$165$		0			0
$166$	−2458.56	+	4258.35i	−0.0892205	+	0.154534i
$167$	−17505.7	−	10106.9i	−0.627693	−	0.362399i	0.152165	−	0.988355i	$-0.451375\pi$
$167$	−17505.7	−	10106.9i	−0.627693	−	0.362399i	−0.779858	+	0.625956i	$0.784709\pi$
$168$		0			0
$169$	13907.2	+	24087.9i	0.486928	+	0.843384i
$170$		−	22426.6i		−	0.776008i
$171$		0			0
$172$	−45221.4			−1.52858
$173$	11421.0	−	6593.90i	0.381602	−	0.220318i	−0.296913	−	0.954904i	$-0.595957\pi$
$173$	11421.0	−	6593.90i	0.381602	−	0.220318i	0.678515	+	0.734587i	$0.262624\pi$
$174$		0			0
$175$	−4520.07	+	7829.00i	−0.147594	+	0.255641i
$176$	38038.4	+	21961.5i	1.22800	+	0.708984i
$177$		0			0
$178$	−28340.3	−	49086.9i	−0.894468	−	1.54926i
$179$		−	41686.8i		−	1.30105i	−0.759487	−	0.650523i	$-0.774550\pi$
$179$		−	41686.8i		−	1.30105i	0.759487	−	0.650523i	$-0.225450\pi$
$180$		0			0
$181$	−37621.8			−1.14837			−0.574185	−	0.818726i	$-0.694681\pi$
$181$	−37621.8			−1.14837			−0.574185	+	0.818726i	$0.694681\pi$
$182$	−10101.7	+	5832.21i	−0.304966	+	0.176072i
$183$		0			0
$184$	−3187.37	+	5520.69i	−0.0941449	+	0.163064i
$185$	2825.57	+	1631.34i	0.0825586	+	0.0476653i
$186$		0			0
$187$	−36849.4	−	63825.0i	−1.05377	−	1.82519i
$188$			44673.9i			1.26398i
$189$		0			0
$190$	−19891.7			−0.551017
$191$	27541.2	−	15900.9i	0.754948	−	0.435869i	−0.0725312	−	0.997366i	$-0.523108\pi$
$191$	27541.2	−	15900.9i	0.754948	−	0.435869i	0.827479	+	0.561497i	$0.189774\pi$
$192$		0			0
$193$	−21377.1	+	37026.2i	−0.573897	+	0.994019i	0.422263	+	0.906473i	$0.361236\pi$
$193$	−21377.1	+	37026.2i	−0.573897	+	0.994019i	−0.996160	+	0.0875460i	$0.972098\pi$
$194$	−35454.3	−	20469.6i	−0.942033	−	0.543883i
$195$		0			0
$196$	26649.4	+	46158.1i	0.693706	+	1.20153i
$197$		−	47493.1i		−	1.22377i	−0.790948	−	0.611883i	$-0.790412\pi$
$197$		−	47493.1i		−	1.22377i	0.790948	−	0.611883i	$-0.209588\pi$
$198$		0			0
$199$	41458.3			1.04690			0.523450	−	0.852057i	$-0.324645\pi$
$199$	41458.3			1.04690			0.523450	+	0.852057i	$0.324645\pi$
$200$	1813.21	−	1046.86i	0.0453303	−	0.0261715i
$201$		0			0
$202$	−30809.2	+	53363.2i	−0.755054	+	1.30779i
$203$	−9893.81	−	5712.19i	−0.240088	−	0.138615i
$204$		0			0
$205$	16452.6	+	28496.7i	0.391495	+	0.678090i
$206$			44253.7i			1.04283i
$207$		0			0
$208$	−5534.61			−0.127927
$209$	−56610.8	+	32684.2i	−1.29600	+	0.748248i
$210$		0			0
$211$	32912.0	−	57005.2i	0.739246	−	1.28041i	−0.213589	−	0.976924i	$-0.568515\pi$
$211$	32912.0	−	57005.2i	0.739246	−	1.28041i	0.952835	−	0.303488i	$-0.0981512\pi$
$212$	−25556.1	−	14754.8i	−0.568621	−	0.328294i
$213$		0			0
$214$	4121.26	+	7138.24i	0.0899918	+	0.155870i
$215$		−	26839.1i		−	0.580619i
$216$		0			0
$217$	−29088.1			−0.617726
$218$	−86988.3	+	50222.7i	−1.83041	+	1.05679i
$219$		0			0
$220$	22836.6	−	39554.2i	0.471831	−	0.817236i
$221$	8042.41	+	4643.29i	0.164665	+	0.0950695i
$222$		0			0
$223$	41210.8	+	71379.2i	0.828708	+	1.43536i	0.899053	+	0.437841i	$0.144257\pi$
$223$	41210.8	+	71379.2i	0.828708	+	1.43536i	−0.0703450	+	0.997523i	$0.522410\pi$
$224$			105840.i			2.10937i
$225$		0			0
$226$	−121964.			−2.38790
$227$	−80238.6	+	46325.8i	−1.55715	+	0.899023i	−0.559627	+	0.828745i	$0.689055\pi$
$227$	−80238.6	+	46325.8i	−1.55715	+	0.899023i	−0.997527	+	0.0702785i	$0.977611\pi$
$228$		0			0
$229$	−24969.1	+	43247.8i	−0.476138	+	0.824695i	−0.999626	−	0.0273379i	$-0.991297\pi$
$229$	−24969.1	+	43247.8i	−0.476138	+	0.824695i	0.523488	+	0.852033i	$0.324630\pi$
$230$	−21750.3	−	12557.6i	−0.411159	−	0.237383i
$231$		0			0
$232$	1322.95	+	2291.43i	0.0245793	+	0.0425726i
$233$			2917.13i			0.0537333i	0.999639	+	0.0268666i	$0.00855295\pi$
$233$			2917.13i			0.0537333i	−0.999639	+	0.0268666i	$0.991447\pi$
$234$		0			0
$235$	−26514.2			−0.480113
$236$	−49566.6	+	28617.3i	−0.889950	+	0.513813i
$237$		0			0
$238$	72534.4	−	125633.i	1.28053	−	2.21795i
$239$	69610.5	+	40189.7i	1.21865	+	0.703588i	0.964629	−	0.263611i	$-0.0849134\pi$
$239$	69610.5	+	40189.7i	1.21865	+	0.703588i	0.254021	+	0.967199i	$0.418247\pi$
$240$		0			0
$241$	−2582.58	−	4473.16i	−0.0444651	−	0.0770159i	0.842936	−	0.538013i	$-0.180825\pi$
$241$	−2582.58	−	4473.16i	−0.0444651	−	0.0770159i	−0.887401	+	0.460998i	$0.847492\pi$
$242$		−	191158.i		−	3.26408i
$243$		0			0
$244$	−36816.0			−0.618381
$245$	−27395.1	+	15816.6i	−0.456395	+	0.263500i
$246$		0			0
$247$	4118.45	−	7133.37i	0.0675056	−	0.116923i
$248$	5834.29	+	3368.43i	0.0948604	+	0.0547677i
$249$		0			0
$250$	4124.40	+	7143.66i	0.0659903	+	0.114299i
$251$		−	3095.71i		−	0.0491375i	−0.999698	−	0.0245688i	$-0.992179\pi$
$251$		−	3095.71i		−	0.0491375i	0.999698	−	0.0245688i	$-0.00782126\pi$
$252$		0			0
$253$	−82533.7			−1.28941
$254$	94079.1	−	54316.6i	1.45823	−	0.841909i
$255$		0			0
$256$	−18267.2	+	31639.7i	−0.278735	+	0.482784i
$257$	47832.5	+	27616.1i	0.724197	+	0.418115i	0.816296	−	0.577634i	$-0.196024\pi$
$257$	47832.5	+	27616.1i	0.724197	+	0.418115i	−0.0920984	+	0.995750i	$0.529357\pi$
$258$		0			0
$259$	10552.5	+	18277.5i	0.157310	+	0.272469i
$260$			5755.16i			0.0851355i
$261$		0			0
$262$	37699.9			0.549209
$263$	−86109.8	+	49715.5i	−1.24492	+	0.718754i	−0.970091	−	0.242740i	$-0.921954\pi$
$263$	−86109.8	+	49715.5i	−1.24492	+	0.718754i	−0.274827	+	0.961494i	$0.588621\pi$
$264$		0			0
$265$	8757.07	−	15167.7i	0.124700	−	0.215987i
$266$	−111433.	−	64335.8i	−1.57489	−	0.909262i
$267$		0			0
$268$	35733.3	+	61891.9i	0.497512	+	0.861716i
$269$			24838.3i			0.343256i	0.985162	+	0.171628i	$0.0549027\pi$
$269$			24838.3i			0.343256i	−0.985162	+	0.171628i	$0.945097\pi$
$270$		0			0
$271$	14233.2			0.193804			0.0969021	−	0.995294i	$-0.469107\pi$
$271$	14233.2			0.193804			0.0969021	+	0.995294i	$0.469107\pi$
$272$	59611.4	−	34416.6i	0.805733	−	0.465190i
$273$		0			0
$274$	31689.2	−	54887.4i	0.422095	−	0.731091i
$275$	23475.6	+	13553.7i	0.310422	+	0.179222i
$276$		0			0
$277$	34677.1	+	60062.5i	0.451942	+	0.782787i	0.998507	−	0.0546300i	$-0.0173979\pi$
$277$	34677.1	+	60062.5i	0.451942	+	0.782787i	−0.546564	+	0.837417i	$0.684065\pi$
$278$		−	133290.i		−	1.72468i
$279$		0			0
$280$	13543.4			0.172748
$281$	106581.	−	61534.7i	1.34980	−	0.779306i	0.361576	−	0.932343i	$-0.382239\pi$
$281$	106581.	−	61534.7i	1.34980	−	0.779306i	0.988220	+	0.153037i	$0.0489054\pi$
$282$		0			0
$283$	−37949.9	+	65731.2i	−0.473847	+	0.820727i	−0.999552	−	0.0299403i	$-0.990468\pi$
$283$	−37949.9	+	65731.2i	−0.473847	+	0.820727i	0.525705	+	0.850667i	$0.323802\pi$
$284$	−19666.0	−	11354.2i	−0.243825	−	0.140773i
$285$		0			0
$286$	17488.2	+	30290.4i	0.213802	+	0.370316i
$287$			212851.i			2.58411i
$288$		0			0
$289$	−31974.9			−0.382837
$290$	−9027.72	+	5212.16i	−0.107345	+	0.0619757i
$291$		0			0
$292$	−57620.7	+	99801.9i	−0.675791	+	1.17051i
$293$	−54022.7	−	31190.0i	−0.629276	−	0.363313i	0.151196	−	0.988504i	$-0.451688\pi$
$293$	−54022.7	−	31190.0i	−0.629276	−	0.363313i	−0.780472	+	0.625191i	$0.785021\pi$
$294$		0			0
$295$	−16984.5	−	29418.1i	−0.195168	−	0.338042i
$296$		−	4887.97i		−	0.0557885i
$297$		0			0
$298$	181739.			2.04652
$299$	9006.54	−	5199.93i	0.100743	−	0.0581641i
$300$		0			0
$301$	86805.8	−	150352.i	0.958111	−	1.65950i
$302$	156509.	+	90360.6i	1.71603	+	0.990753i
$303$		0			0
$304$	−30526.5	−	52873.4i	−0.330316	−	0.572124i
$305$		−	21850.5i		−	0.234888i
$306$		0			0
$307$	53124.3			0.563659			0.281830	−	0.959464i	$-0.409059\pi$
$307$	53124.3			0.563659			0.281830	+	0.959464i	$0.409059\pi$
$308$	255860.	−	147721.i	2.69713	−	1.55719i
$309$		0			0
$310$	−13270.9	+	22985.9i	−0.138095	+	0.239187i
$311$	18850.6	+	10883.4i	0.194897	+	0.112524i	0.594273	−	0.804263i	$-0.297440\pi$
$311$	18850.6	+	10883.4i	0.194897	+	0.112524i	−0.399376	+	0.916787i	$0.630773\pi$
$312$		0			0
$313$	17918.4	+	31035.5i	0.182898	+	0.316789i	0.942866	−	0.333171i	$-0.108119\pi$
$313$	17918.4	+	31035.5i	0.182898	+	0.316789i	−0.759968	+	0.649960i	$0.774785\pi$
$314$		−	68983.8i		−	0.699661i
$315$		0			0
$316$	35088.1			0.351387
$317$	2844.75	−	1642.42i	0.0283091	−	0.0163443i	−0.485779	−	0.874082i	$-0.661464\pi$
$317$	2844.75	−	1642.42i	0.0283091	−	0.0163443i	0.514088	+	0.857738i	$0.328131\pi$
$318$		0			0
$319$	−17128.3	+	29667.1i	−0.168319	+	0.291537i
$320$	52258.7	+	30171.6i	0.510339	+	0.294644i
$321$		0			0
$322$	−81229.9	−	140694.i	−0.783437	−	1.35695i
$323$			102441.i			0.981906i
$324$		0			0
$325$	−3415.72			−0.0323382
$326$	97139.7	−	56083.7i	0.914033	−	0.527717i
$327$		0			0
$328$	24648.3	−	42692.1i	0.229108	−	0.396826i
$329$	−148532.	−	85755.0i	−1.37223	−	0.792260i
$330$		0			0
$331$	39840.4	+	69005.5i	0.363636	+	0.629837i	0.988556	−	0.150852i	$-0.0482017\pi$
$331$	39840.4	+	69005.5i	0.363636	+	0.629837i	−0.624920	+	0.780689i	$0.714868\pi$
$332$			15693.3i			0.142377i
$333$		0			0
$334$	−119309.			−1.06950
$335$	−36733.2	+	21207.9i	−0.327317	+	0.188977i
$336$		0			0
$337$	7825.27	−	13553.8i	0.0689033	−	0.119344i	−0.829516	−	0.558484i	$-0.811383\pi$
$337$	7825.27	−	13553.8i	0.0689033	−	0.119344i	0.898419	+	0.439140i	$0.144717\pi$
$338$	142175.	+	82085.0i	1.24449	+	0.718506i
$339$		0			0
$340$	−35788.1	−	61986.8i	−0.309586	−	0.536218i
$341$			87222.1i			0.750098i
$342$		0			0
$343$	−30979.0			−0.263318
$344$	−34821.9	+	20104.4i	−0.294263	+	0.169893i
$345$		0			0
$346$	38919.5	−	67410.6i	0.325099	−	0.563087i
$347$	71593.4	+	41334.5i	0.594585	+	0.343284i	0.766908	−	0.641757i	$-0.221794\pi$
$347$	71593.4	+	41334.5i	0.594585	+	0.343284i	−0.172323	+	0.985040i	$0.555127\pi$
$348$		0			0
$349$	−73967.8	−	128116.i	−0.607284	−	1.05185i	−0.991686	−	0.128681i	$-0.958926\pi$
$349$	−73967.8	−	128116.i	−0.607284	−	1.05185i	0.384402	−	0.923166i	$-0.374408\pi$
$350$			53358.2i			0.435577i
$351$		0			0
$352$	317366.			2.56139
$353$	−52881.8	+	30531.3i	−0.424382	+	0.245017i	−0.696950	−	0.717119i	$-0.745460\pi$
$353$	−52881.8	+	30531.3i	−0.424382	+	0.245017i	0.272569	+	0.962136i	$0.412127\pi$
$354$		0			0
$355$	6738.76	−	11671.9i	0.0534716	−	0.0926155i
$356$	−156664.	−	90450.3i	−1.23615	−	0.713690i
$357$		0			0
$358$	−123025.	−	213086.i	−0.959904	−	1.66260i
$359$			77227.2i			0.599213i	0.954063	+	0.299607i	$0.0968554\pi$
$359$			77227.2i			0.599213i	−0.954063	+	0.299607i	$0.903145\pi$
$360$		0			0
$361$	−39458.8			−0.302782
$362$	−192307.	+	111028.i	−1.46750	+	0.847261i
$363$		0			0
$364$	−18613.9	+	32240.3i	−0.140487	+	0.243330i
$365$	−59233.0	−	34198.2i	−0.444609	−	0.256695i
$366$		0			0
$367$	45050.6	+	78029.9i	0.334479	+	0.579334i	0.983385	−	0.181535i	$-0.0581065\pi$
$367$	45050.6	+	78029.9i	0.334479	+	0.579334i	−0.648906	+	0.760869i	$0.724773\pi$
$368$		−	77085.0i		−	0.569212i
$369$		0			0
$370$	19257.5			0.140669
$371$	98113.8	−	56646.0i	0.712824	−	0.411549i
$372$		0			0
$373$	−68803.0	+	119170.i	−0.494527	+	0.856545i	−0.999980	−	0.00630866i	$-0.997992\pi$
$373$	−68803.0	+	119170.i	−0.494527	+	0.856545i	0.505454	+	0.862854i	$0.331325\pi$
$374$	−376718.	−	217498.i	−2.69323	−	1.55494i
$375$		0			0
$376$	19861.0	+	34400.3i	0.140484	+	0.243325i
$377$		−	4316.58i		−	0.0303708i
$378$		0			0
$379$	−120747.			−0.840618			−0.420309	−	0.907381i	$-0.638078\pi$
$379$	−120747.			−0.840618			−0.420309	+	0.907381i	$0.638078\pi$
$380$	−54980.4	+	31742.9i	−0.380750	+	0.219826i
$381$		0			0
$382$	93853.0	−	162558.i	0.643164	−	1.11399i
$383$	27743.0	+	16017.4i	0.189128	+	0.109193i	0.591574	−	0.806250i	$-0.298507\pi$
$383$	27743.0	+	16017.4i	0.189128	+	0.109193i	−0.402446	+	0.915444i	$0.631840\pi$
$384$		0			0
$385$	87673.3	+	151855.i	0.591488	+	1.02449i
$386$			252351.i			1.69367i
$387$		0			0
$388$	−130660.			−0.867921
$389$	−48954.6	+	28263.9i	−0.323515	+	0.186781i	−0.652958	−	0.757394i	$-0.726472\pi$
$389$	−48954.6	+	28263.9i	−0.323515	+	0.186781i	0.329443	+	0.944175i	$0.393139\pi$
$390$		0			0
$391$	−64670.8	+	112013.i	−0.423014	+	0.732682i
$392$	41041.7	+	23695.5i	0.267088	+	0.154203i
$393$		0			0
$394$	−140161.	−	242765.i	−0.902888	−	1.56385i
$395$			20825.0i			0.133472i
$396$		0			0
$397$	−12413.9			−0.0787637			−0.0393819	−	0.999224i	$-0.512539\pi$
$397$	−12413.9			−0.0787637			−0.0393819	+	0.999224i	$0.512539\pi$
$398$	211918.	−	122351.i	1.33783	−	0.772396i
$399$		0			0
$400$	−12658.9	+	21925.8i	−0.0791180	+	0.137036i
$401$	−56538.8	−	32642.7i	−0.351607	−	0.203000i	0.313786	−	0.949494i	$-0.398403\pi$
$401$	−56538.8	−	32642.7i	−0.351607	−	0.203000i	−0.665393	+	0.746493i	$0.731736\pi$
$402$		0			0
$403$	−5495.31	−	9518.15i	−0.0338362	−	0.0586061i
$404$			196660.i			1.20491i
$405$		0			0
$406$	−67430.8			−0.409078
$407$	54805.9	−	31642.2i	0.330856	−	0.191020i
$408$		0			0
$409$	44708.7	−	77437.7i	0.267267	−	0.462920i	−0.700888	−	0.713271i	$-0.747213\pi$
$409$	44708.7	−	77437.7i	0.267267	−	0.462920i	0.968155	+	0.250351i	$0.0805461\pi$
$410$	168198.	+	97109.1i	1.00058	+	0.577686i
$411$		0			0
$412$	70619.4	+	122316.i	0.416035	+	0.720593i
$413$		−	219732.i		−	1.28823i
$414$		0			0
$415$	−9314.09			−0.0540809
$416$	−34632.7	+	19995.2i	−0.200125	+	0.115542i
$417$		0			0
$418$	−192914.	+	334137.i	−1.10411	+	1.91237i
$419$	−9707.06	−	5604.38i	−0.0552917	−	0.0319227i	0.472099	−	0.881545i	$-0.343496\pi$
$419$	−9707.06	−	5604.38i	−0.0552917	−	0.0319227i	−0.527391	+	0.849623i	$0.676830\pi$
$420$		0			0
$421$	7817.74	+	13540.7i	0.0441079	+	0.0763972i	0.887237	−	0.461315i	$-0.152622\pi$
$421$	7817.74	+	13540.7i	0.0441079	+	0.0763972i	−0.843129	+	0.537712i	$0.819289\pi$
$422$		−	388516.i		−	2.18165i
$423$		0			0
$424$	−26238.7			−0.145952
$425$	36789.5	−	21240.4i	0.203679	−	0.117594i
$426$		0			0
$427$	70671.0	−	122406.i	0.387602	−	0.671346i
$428$	22782.2	+	13153.3i	0.124368	+	0.0718038i
$429$		0			0
$430$	−79207.1	−	137191.i	−0.428378	−	0.741972i
$431$		−	186459.i		−	1.00375i	−0.864939	−	0.501877i	$-0.832643\pi$
$431$		−	186459.i		−	1.00375i	0.864939	−	0.501877i	$-0.167357\pi$
$432$		0			0
$433$	47098.6			0.251207			0.125604	−	0.992080i	$-0.459913\pi$
$433$	47098.6			0.251207			0.125604	+	0.992080i	$0.459913\pi$
$434$	−148686.	+	85844.2i	−0.789391	+	0.455755i
$435$		0			0
$436$	−160290.	+	277630.i	−0.843203	+	1.46047i
$437$	99352.1	+	57361.0i	0.520253	+	0.300368i
$438$		0			0
$439$	153533.	+	265927.i	0.796658	+	1.37985i	0.921781	+	0.387712i	$0.126734\pi$
$439$	153533.	+	265927.i	0.796658	+	1.37985i	−0.125122	+	0.992141i	$0.539932\pi$
$440$		−	40610.6i		−	0.209766i
$441$		0			0
$442$	54812.7			0.280567
$443$	165463.	−	95530.4i	0.843130	−	0.486781i	−0.0151967	−	0.999885i	$-0.504837\pi$
$443$	165463.	−	95530.4i	0.843130	−	0.486781i	0.858327	+	0.513103i	$0.171504\pi$
$444$		0			0
$445$	53682.7	−	92981.2i	0.271091	−	0.469543i
$446$	421305.	+	243241.i	2.11801	+	1.22283i
$447$		0			0
$448$	195168.	+	338041.i	0.972416	+	1.68427i
$449$			37138.3i			0.184217i	0.995749	+	0.0921084i	$0.0293606\pi$
$449$			37138.3i			0.184217i	−0.995749	+	0.0921084i	$0.970639\pi$
$450$		0			0
$451$	638243.			3.13786
$452$	−337107.	+	194629.i	−1.65003	+	0.952643i
$453$		0			0
$454$	−273431.	+	473597.i	−1.32659	+	2.29772i
$455$	−19134.8	−	11047.5i	−0.0924274	−	0.0533630i
$456$		0			0
$457$	15762.6	+	27301.7i	0.0754738	+	0.130724i	0.901292	−	0.433212i	$-0.142620\pi$
$457$	15762.6	+	27301.7i	0.0754738	+	0.130724i	−0.825818	+	0.563936i	$0.809286\pi$
$458$			294754.i			1.40517i
$459$		0			0
$460$	−80156.8			−0.378813
$461$	−107440.	+	62030.3i	−0.505549	+	0.291879i	−0.731002	−	0.682375i	$-0.760947\pi$
$461$	−107440.	+	62030.3i	−0.505549	+	0.291879i	0.225453	+	0.974254i	$0.427614\pi$
$462$		0			0
$463$	156173.	−	270499.i	0.728523	−	1.26184i	−0.228984	−	0.973430i	$-0.573540\pi$
$463$	156173.	−	270499.i	0.728523	−	1.26184i	0.957507	−	0.288409i	$-0.0931263\pi$
$464$	−27708.5	−	15997.5i	−0.128700	−	0.0743047i
$465$		0			0
$466$	8608.96	+	14911.2i	0.0396441	+	0.0686656i
$467$		−	103567.i		−	0.474883i	−0.971402	−	0.237442i	$-0.923691\pi$
$467$		−	103567.i		−	0.474883i	0.971402	−	0.237442i	$-0.0763089\pi$
$468$		0			0
$469$	−274371.			−1.24736
$470$	−135530.	+	78248.2i	−0.613535	+	0.354224i
$471$		0			0
$472$	−25445.2	+	44072.4i	−0.114215	+	0.197826i
$473$	−450838.	−	260292.i	−2.01511	−	1.16342i
$474$		0			0
$475$	−18839.6	−	32631.1i	−0.0834996	−	0.144626i
$476$		−	462998.i		−	2.04346i
$477$		0			0
$478$	474427.			2.07641
$479$	127905.	−	73845.8i	0.557462	−	0.321851i	−0.194664	−	0.980870i	$-0.562362\pi$
$479$	127905.	−	73845.8i	0.557462	−	0.321851i	0.752126	+	0.659019i	$0.229028\pi$
$480$		0			0
$481$	−3987.15	+	6905.95i	−0.0172335	+	0.0298492i
$482$	−26402.2	−	15243.3i	−0.113644	−	0.0656123i
$483$		0			0
$484$	−305047.	−	528357.i	−1.30219	−	2.25547i
$485$		−	77547.6i		−	0.329674i
$486$		0			0
$487$	−325253.			−1.37140			−0.685699	−	0.727885i	$-0.740504\pi$
$487$	−325253.			−1.37140			−0.685699	+	0.727885i	$0.740504\pi$
$488$	−28349.4	+	16367.5i	−0.119043	+	0.0687296i
$489$		0			0
$490$	−93355.0	+	161696.i	−0.388817	+	0.673451i
$491$	74368.9	+	42936.9i	0.308481	+	0.178102i	0.646247	−	0.763129i	$-0.276338\pi$
$491$	74368.9	+	42936.9i	0.308481	+	0.178102i	−0.337765	+	0.941230i	$0.609671\pi$
$492$		0			0
$493$	26842.4	+	46492.3i	0.110440	+	0.191288i
$494$		−	48617.1i		−	0.199221i
$495$		0			0
$496$	−81463.8			−0.331132
$497$	75500.7	−	43590.3i	0.305660	−	0.176473i
$498$		0			0
$499$	157701.	−	273146.i	0.633335	−	1.09697i	−0.353530	−	0.935423i	$-0.615019\pi$
$499$	157701.	−	273146.i	0.633335	−	1.09697i	0.986865	−	0.161546i	$-0.0516480\pi$
$500$	22799.5	+	13163.3i	0.0911981	+	0.0526533i
$501$		0			0
$502$	−9136.00	−	15824.0i	−0.0362534	−	0.0627927i
$503$			181943.i			0.719116i	0.933123	+	0.359558i	$0.117073\pi$
$503$			181943.i			0.719116i	−0.933123	+	0.359558i	$0.882927\pi$
$504$		0			0
$505$	−116719.			−0.457676
$506$	−421879.	+	243572.i	−1.64773	+	0.951318i
$507$		0			0
$508$	173355.	−	300260.i	0.671753	−	1.16351i
$509$	−57532.4	−	33216.4i	−0.222063	−	0.128208i	0.384842	−	0.922983i	$-0.374256\pi$
$509$	−57532.4	−	33216.4i	−0.222063	−	0.128208i	−0.606905	+	0.794774i	$0.707589\pi$
$510$		0			0
$511$	−221215.	−	383155.i	−0.847172	−	1.46735i
$512$			350695.i			1.33779i
$513$		0			0
$514$	326000.			1.23393
$515$	−72595.4	+	41913.0i	−0.273713	+	0.158028i
$516$		0			0
$517$	−257141.	+	445381.i	−0.962032	+	1.66629i
$518$	107880.	+	62284.7i	0.402052	+	0.232125i
$519$		0			0
$520$	2558.62	+	4431.65i	0.00946234	+	0.0163893i
$521$		−	360429.i		−	1.32784i	−0.747805	−	0.663918i	$-0.768892\pi$
$521$		−	360429.i		−	1.32784i	0.747805	−	0.663918i	$-0.231108\pi$
$522$		0			0
$523$	−47180.3			−0.172488			−0.0862438	−	0.996274i	$-0.527486\pi$
$523$	−47180.3			−0.172488			−0.0862438	+	0.996274i	$0.527486\pi$
$524$	104202.	−	60161.0i	0.379501	−	0.219105i
$525$		0			0
$526$	−293439.	+	508250.i	−1.06059	+	1.83699i
$527$	118376.	+	68344.4i	0.426229	+	0.246083i
$528$		0			0
$529$	−67497.0	−	116908.i	−0.241198	−	0.417766i
$530$		−	103375.i		−	0.368012i
$531$		0			0
$532$	−410665.			−1.45099
$533$	−69648.6	+	40211.6i	−0.245165	+	0.141546i
$534$		0			0
$535$	−7806.56	+	13521.4i	−0.0272742	+	0.0472403i
$536$	55031.5	+	31772.4i	0.191550	+	0.110591i
$537$		0			0
$538$	73302.3	+	126963.i	0.253252	+	0.438646i
$539$			613570.i			2.11196i
$540$		0			0
$541$	293419.			1.00252			0.501261	−	0.865296i	$-0.332870\pi$
$541$	293419.			1.00252			0.501261	+	0.865296i	$0.332870\pi$
$542$	72754.2	−	42004.6i	0.247662	−	0.142988i
$543$		0			0
$544$	248678.	−	430723.i	0.840310	−	1.45546i
$545$	−164775.	−	95132.7i	−0.554750	−	0.320285i
$546$		0			0
$547$	−7308.40	−	12658.5i	−0.0244257	−	0.0423066i	0.853554	−	0.521004i	$-0.174442\pi$
$547$	−7308.40	−	12658.5i	−0.0244257	−	0.0423066i	−0.877980	+	0.478698i	$0.841109\pi$
$548$		−	202277.i		−	0.673574i
$549$		0			0
$550$	159997.			0.528916
$551$	41237.2	−	23808.3i	0.135827	−	0.0784198i
$552$		0			0
$553$	−67354.2	+	116661.i	−0.220249	+	0.381483i
$554$	354510.	+	204677.i	1.15507	+	0.666881i
$555$		0			0
$556$	−212703.	−	368413.i	−0.688057	−	1.19175i
$557$		−	404572.i		−	1.30403i	−0.758208	−	0.652013i	$-0.773925\pi$
$557$		−	404572.i		−	1.30403i	0.758208	−	0.652013i	$-0.226075\pi$
$558$		0			0
$559$	65597.3			0.209924
$560$	−141829.	+	81885.2i	−0.452262	+	0.261114i
$561$		0			0
$562$	363200.	−	629081.i	1.14993	−	1.99175i
$563$	230397.	+	133020.i	0.726875	+	0.419662i	0.817278	−	0.576244i	$-0.195482\pi$
$563$	230397.	+	133020.i	0.726875	+	0.419662i	−0.0904025	+	0.995905i	$0.528815\pi$
$564$		0			0
$565$	−115513.	−	200075.i	−0.361855	−	0.626752i
$566$			447988.i			1.39841i
$567$		0			0
$568$	−20191.2			−0.0625844
$569$	211791.	−	122277.i	0.654158	−	0.377678i	−0.135890	−	0.990724i	$-0.543389\pi$
$569$	211791.	−	122277.i	0.654158	−	0.377678i	0.790047	+	0.613046i	$0.210056\pi$
$570$		0			0
$571$	253912.	−	439789.i	0.778774	−	1.34888i	−0.153875	−	0.988090i	$-0.549175\pi$
$571$	253912.	−	439789.i	0.778774	−	1.34888i	0.932649	−	0.360785i	$-0.117491\pi$
$572$	96674.1	+	55814.8i	0.295473	+	0.170591i
$573$		0			0
$574$	628160.	+	1.08801e6i	1.90654	+	3.30223i
$575$		−	47573.5i		−	0.143890i
$576$		0			0
$577$	−558857.			−1.67861			−0.839304	−	0.543662i	$-0.817037\pi$
$577$	−558857.			−1.67861			−0.839304	+	0.543662i	$0.817037\pi$
$578$	−163443.	+	94363.7i	−0.489227	+	0.282455i
$579$		0			0
$580$	−16635.0	+	28812.6i	−0.0494500	+	0.0856500i
$581$	−52177.3	−	30124.6i	−0.154571	−	0.0892419i
$582$		0			0
$583$	−169856.	−	294199.i	−0.499739	−	0.865574i
$584$			102467.i			0.300442i
$585$		0			0
$586$	−368189.			−1.07220
$587$	−51861.3	+	29942.1i	−0.150511	+	0.0868973i	−0.573364	−	0.819301i	$-0.694362\pi$
$587$	−51861.3	+	29942.1i	−0.150511	+	0.0868973i	0.422853	+	0.906198i	$0.361029\pi$
$588$		0			0
$589$	60619.4	−	104996.i	0.174735	−	0.302651i
$590$	−173636.	−	100249.i	−0.498811	−	0.287988i
$591$		0			0
$592$	29553.3	+	51187.8i	0.0843261	+	0.146057i
$593$			607115.i			1.72648i	0.504795	+	0.863239i	$0.331568\pi$
$593$			607115.i			1.72648i	−0.504795	+	0.863239i	$0.668432\pi$
$594$		0			0
$595$	274792.			0.776193
$596$	502324.	−	290017.i	1.41414	−	0.816453i
$597$		0			0
$598$	30691.8	−	53159.8i	0.0858263	−	0.148655i
$599$	237381.	+	137052.i	0.661596	+	0.381973i	0.792885	−	0.609371i	$-0.208578\pi$
$599$	237381.	+	137052.i	0.661596	+	0.381973i	−0.131289	+	0.991344i	$0.541911\pi$
$600$		0			0
$601$	−238264.	−	412685.i	−0.659643	−	1.14254i	−0.980708	−	0.195478i	$-0.937374\pi$
$601$	−238264.	−	412685.i	−0.659643	−	1.14254i	0.321065	−	0.947057i	$-0.395959\pi$
$602$		−	1.02472e6i		−	2.82756i
$603$		0			0
$604$	576785.			1.58103
$605$	313583.	−	181047.i	0.856724	−	0.494630i
$606$		0			0
$607$	−335428.	+	580978.i	−0.910378	+	1.57682i	−0.0968473	+	0.995299i	$0.530876\pi$
$607$	−335428.	+	580978.i	−0.910378	+	1.57682i	−0.813531	+	0.581522i	$0.802457\pi$
$608$	−382038.	−	220570.i	−1.03347	−	0.596676i
$609$		0			0
$610$	−64484.6	−	111691.i	−0.173299	−	0.300163i
$611$		−	64803.2i		−	0.173586i
$612$		0			0
$613$	374906.			0.997702			0.498851	−	0.866688i	$-0.333755\pi$
$613$	374906.			0.997702			0.498851	+	0.866688i	$0.333755\pi$
$614$	271550.	−	156779.i	0.720299	−	0.415865i
$615$		0			0
$616$	131347.	−	227500.i	0.346145	−	0.599542i
$617$	−62481.0	−	36073.4i	−0.164126	−	0.0947583i	0.415687	−	0.909508i	$-0.363541\pi$
$617$	−62481.0	−	36073.4i	−0.164126	−	0.0947583i	−0.579813	+	0.814749i	$0.696874\pi$
$618$		0			0
$619$	325797.	+	564297.i	0.850287	+	1.47274i	0.880949	+	0.473211i	$0.156905\pi$
$619$	325797.	+	564297.i	0.850287	+	1.47274i	−0.0306617	+	0.999530i	$0.509761\pi$
$620$			84710.1i			0.220370i
$621$		0			0
$622$	128475.			0.332077
$623$	601459.	−	347252.i	1.54964	−	0.894683i
$624$		0			0
$625$	−7812.50	+	13531.6i	−0.0200000	+	0.0346410i
$626$	183183.	+	105761.i	0.467450	+	0.269883i
$627$		0			0
$628$	−110083.	−	190670.i	−0.279128	−	0.483463i
$629$		−	99175.3i		−	0.250670i
$630$		0			0
$631$	−113922.			−0.286120			−0.143060	−	0.989714i	$-0.545694\pi$
$631$	−113922.			−0.286120			−0.143060	+	0.989714i	$0.545694\pi$
$632$	27018.9	−	15599.4i	0.0676447	−	0.0390547i
$633$		0			0
$634$	9694.14	−	16790.7i	0.0241174	−	0.0417726i
$635$	178206.	+	102887.i	0.441952	+	0.255161i
$636$		0			0
$637$	−38657.1	−	66956.1i	−0.0952688	−	0.165010i
$638$			202194.i			0.496739i
$639$		0			0
$640$	94373.0			0.230403
$641$	142661.	−	82365.3i	0.347207	−	0.200460i	−0.316247	−	0.948677i	$-0.602423\pi$
$641$	142661.	−	82365.3i	0.347207	−	0.200460i	0.663455	+	0.748217i	$0.269090\pi$
$642$		0			0
$643$	14038.6	−	24315.6i	0.0339549	−	0.0588117i	−0.848549	−	0.529118i	$-0.822523\pi$
$643$	14038.6	−	24315.6i	0.0339549	−	0.0588117i	0.882503	+	0.470306i	$0.155856\pi$
$644$	−449036.	−	259251.i	−1.08270	−	0.625099i
$645$		0			0
$646$	302322.	+	523638.i	0.724445	+	1.25478i
$647$			119765.i			0.286103i	0.989715	+	0.143051i	$0.0456914\pi$
$647$			119765.i			0.286103i	−0.989715	+	0.143051i	$0.954309\pi$
$648$		0			0
$649$	−658879.			−1.56429
$650$	−17459.8	+	10080.4i	−0.0413249	+	0.0238589i
$651$		0			0
$652$	178995.	−	310029.i	0.421062	−	0.729301i
$653$	206814.	+	119404.i	0.485013	+	0.280022i	0.722503	−	0.691368i	$-0.242991\pi$
$653$	206814.	+	119404.i	0.485013	+	0.280022i	−0.237490	+	0.971390i	$0.576325\pi$
$654$		0			0
$655$	35705.9	+	61844.4i	0.0832257	+	0.144151i
$656$			596107.i			1.38521i
$657$		0			0
$658$	−1.01231e6			−2.33810
$659$	−293403.	+	169396.i	−0.675607	+	0.390062i	−0.798198	−	0.602395i	$-0.794213\pi$
$659$	−293403.	+	169396.i	−0.675607	+	0.390062i	0.122591	+	0.992457i	$0.460880\pi$
$660$		0			0
$661$	−100873.	+	174717.i	−0.230873	+	0.399883i	−0.958065	−	0.286550i	$-0.907491\pi$
$661$	−100873.	+	174717.i	−0.230873	+	0.399883i	0.727193	+	0.686434i	$0.240825\pi$
$662$	407295.	+	235152.i	0.929380	+	0.536578i
$663$		0			0
$664$	6976.91	+	12084.4i	0.0158244	+	0.0274086i
$665$		−	243732.i		−	0.551149i
$666$		0			0
$667$	60120.4			0.135136
$668$	−329769.	+	190393.i	−0.739022	+	0.426675i
$669$		0			0
$670$	−125177.	+	216812.i	−0.278852	+	0.482986i
$671$	−367040.	−	211910.i	−0.815207	−	0.470660i
$672$		0			0
$673$	118260.	+	204833.i	0.261101	+	0.452240i	0.966535	−	0.256536i	$-0.0825811\pi$
$673$	118260.	+	204833.i	0.261101	+	0.452240i	−0.705434	+	0.708776i	$0.749248\pi$
$674$		−	92375.1i		−	0.203346i
$675$		0			0
$676$	523960.			1.14658
$677$	−604763.	+	349160.i	−1.31949	+	0.761810i	−0.983647	−	0.180106i	$-0.942356\pi$
$677$	−604763.	+	349160.i	−1.31949	+	0.761810i	−0.335847	+	0.941917i	$0.609023\pi$
$678$		0			0
$679$	250812.	−	434420.i	0.544013	−	0.942258i
$680$	−55115.9	−	31821.2i	−0.119195	−	0.0688174i
$681$		0			0
$682$	257408.	+	445844.i	0.553418	+	0.958548i
$683$			517576.i			1.10951i	0.832012	+	0.554757i	$0.187189\pi$
$683$			517576.i			1.10951i	−0.832012	+	0.554757i	$0.812811\pi$
$684$		0			0
$685$	120053.			0.255853
$686$	−158352.	+	91424.7i	−0.336493	+	0.194274i
$687$		0			0
$688$	243108.	−	421075.i	0.513596	−	0.889574i
$689$	37071.2	+	21403.1i	0.0780905	+	0.0450856i
$690$		0			0
$691$	361558.	+	626237.i	0.757220	+	1.31154i	0.944263	+	0.329192i	$0.106776\pi$
$691$	361558.	+	626237.i	0.757220	+	1.31154i	−0.187043	+	0.982352i	$0.559890\pi$
$692$		−	248429.i		−	0.518788i
$693$		0			0
$694$	487941.			1.01309
$695$	218655.	−	126240.i	0.452678	−	0.261354i
$696$		0			0
$697$	500107.	−	866210.i	1.02943	−	1.78303i
$698$	−756187.	−	436584.i	−1.55209	−	0.896102i
$699$		0			0
$700$	85148.3	+	147481.i	0.173772	+	0.300982i
$701$			60491.0i			0.123099i	0.998104	+	0.0615495i	$0.0196042\pi$
$701$			60491.0i			0.123099i	−0.998104	+	0.0615495i	$0.980396\pi$
$702$		0			0
$703$	−87965.4			−0.177992
$704$	1.01363e6	−	585220.i	2.04520	−	1.18079i
$705$		0			0
$706$	−180207.	+	312127.i	−0.361544	+	0.626213i
$707$	−653855.	−	377504.i	−1.30811	−	0.755235i
$708$		0			0
$709$	−173953.	−	301296.i	−0.346051	−	0.599378i	0.639493	−	0.768797i	$-0.279144\pi$
$709$	−173953.	−	301296.i	−0.346051	−	0.599378i	−0.985544	+	0.169419i	$0.945811\pi$
$710$		−	79549.1i		−	0.157804i
$711$		0			0
$712$	−160849.			−0.317291
$713$	132567.	−	76537.6i	0.260769	−	0.150555i
$714$		0			0
$715$	−33126.4	+	57376.6i	−0.0647980	+	0.112234i
$716$	−680079.	−	392644.i	−1.32658	−	0.765901i
$717$		0			0
$718$	227911.	+	394754.i	0.442096	+	0.765733i
$719$			49842.0i			0.0964134i	0.998837	+	0.0482067i	$0.0153506\pi$
$719$			49842.0i			0.0964134i	−0.998837	+	0.0482067i	$0.984649\pi$
$720$		0			0
$721$	−542237.			−1.04308
$722$	−201697.	+	116450.i	−0.386924	+	0.223391i
$723$		0			0
$724$	−354356.	+	613762.i	−0.676024	+	1.17091i
$725$	−17100.5	−	9872.96i	−0.0325336	−	0.0187833i
$726$		0			0
$727$	−103653.	−	179532.i	−0.196115	−	0.339682i	0.751150	−	0.660131i	$-0.229499\pi$
$727$	−103653.	−	179532.i	−0.196115	−	0.339682i	−0.947266	+	0.320450i	$0.896166\pi$
$728$			33101.3i			0.0624573i
$729$		0			0
$730$	−403700.			−0.757553
$731$	−706525.	+	407912.i	−1.32219	+	0.763365i
$732$		0			0
$733$	−229832.	+	398080.i	−0.427762	+	0.740905i	−0.996674	−	0.0814934i	$-0.974031\pi$
$733$	−229832.	+	398080.i	−0.427762	+	0.740905i	0.568912	+	0.822398i	$0.307364\pi$
$734$	460560.	+	265905.i	0.854859	+	0.493553i
$735$		0			0
$736$	−278490.	−	482358.i	−0.514107	−	0.890459i
$737$			822715.i			1.51466i
$738$		0			0
$739$	−435511.			−0.797463			−0.398731	−	0.917068i	$-0.630549\pi$
$739$	−435511.			−0.797463			−0.398731	+	0.917068i	$0.630549\pi$
$740$	53227.5	−	30730.9i	0.0972015	−	0.0561193i
$741$		0			0
$742$	334345.	−	579102.i	0.607277	−	1.05183i
$743$	279726.	+	161500.i	0.506704	+	0.292546i	0.731478	−	0.681865i	$-0.238831\pi$
$743$	279726.	+	161500.i	0.506704	+	0.292546i	−0.224774	+	0.974411i	$0.572164\pi$
$744$		0			0
$745$	172127.	+	298132.i	0.310124	+	0.537151i
$746$			812199.i			1.45944i
$747$		0			0
$748$	−1.38832e6			−2.48135
$749$	−87464.4	+	50497.6i	−0.155908	+	0.0900133i
$750$		0			0
$751$	−504633.	+	874051.i	−0.894738	+	1.54973i	−0.0606105	+	0.998161i	$0.519305\pi$
$751$	−504633.	+	874051.i	−0.894738	+	1.54973i	−0.834128	+	0.551571i	$0.814029\pi$
$752$	−415977.	−	240165.i	−0.735587	−	0.424691i
$753$		0			0
$754$	−12739.0	−	22064.6i	−0.0224074	−	0.0388108i
$755$			342325.i			0.600544i
$756$		0			0
$757$	−658657.			−1.14939			−0.574695	−	0.818368i	$-0.694879\pi$
$757$	−658657.			−1.14939			−0.574695	+	0.818368i	$0.694879\pi$
$758$	−617210.	+	356346.i	−1.07422	+	0.620203i
$759$		0			0
$760$	−28224.4	+	48886.1i	−0.0488649	+	0.0846365i
$761$	−100035.	−	57755.3i	−0.172736	−	0.0997293i	0.411139	−	0.911573i	$-0.365131\pi$
$761$	−100035.	−	57755.3i	−0.172736	−	0.0997293i	−0.583875	+	0.811843i	$0.698464\pi$
$762$		0			0
$763$	−615376.	−	1.06586e6i	−1.05704	−	1.83085i
$764$		−	599078.i		−	1.02635i
$765$		0			0
$766$	189081.			0.322249
$767$	71900.4	−	41511.7i	0.122220	−	0.0705635i
$768$		0			0
$769$	69634.2	−	120610.i	0.117752	−	0.203953i	−0.801124	−	0.598498i	$-0.795764\pi$
$769$	69634.2	−	120610.i	0.117752	−	0.203953i	0.918877	+	0.394545i	$0.129098\pi$
$770$	896300.	+	517479.i	1.51172	+	0.872793i
$771$		0			0
$772$	402698.	+	697493.i	0.675685	+	1.17032i
$773$		−	1.15082e6i		−	1.92597i	−0.269558	−	0.962984i	$-0.586878\pi$
$773$		−	1.15082e6i		−	1.92597i	0.269558	−	0.962984i	$-0.413122\pi$
$774$		0			0
$775$	−50275.9			−0.0837060
$776$	−100612.	+	58088.6i	−0.167082	+	0.0964646i
$777$		0			0
$778$	−166824.	+	288947.i	−0.275613	+	0.477375i
$779$	−768301.	−	443579.i	−1.26607	−	0.730964i
$780$		0			0
$781$	−130708.	−	226393.i	−0.214289	−	0.371159i
$782$			763420.i			1.24839i
$783$		0			0
$784$	−573063.			−0.932331
$785$	113164.	−	65335.1i	0.183640	−	0.106025i
$786$		0			0
$787$	−396524.	+	686800.i	−0.640206	+	1.10887i	0.345180	+	0.938536i	$0.387818\pi$
$787$	−396524.	+	686800.i	−0.640206	+	1.10887i	−0.985386	+	0.170333i	$0.945516\pi$
$788$	−774804.	−	447333.i	−1.24778	−	0.720408i
$789$		0			0
$790$	61458.2	+	106449.i	0.0984749	+	0.170564i
$791$		−	1.49442e6i		−	2.38847i
$792$		0			0
$793$	53404.5			0.0849242
$794$	−63454.6	+	36635.5i	−0.100652	+	0.0581114i
$795$		0			0
$796$	390491.	−	676351.i	0.616290	−	1.06745i
$797$	1.01991e6	+	588844.i	1.60563	+	0.927008i	0.990333	+	0.138710i	$0.0442954\pi$
$797$	1.01991e6	+	588844.i	1.60563	+	0.927008i	0.615293	+	0.788299i	$0.289038\pi$
$798$		0			0
$799$	402974.	+	697972.i	0.631224	+	1.09331i
$800$			182934.i			0.285834i
$801$		0			0
$802$	−385337.			−0.599090
$803$	−1.14891e6	+	663323.i	−1.78178	+	1.02871i
$804$		0			0
$805$	153867.	−	266505.i	0.237440	−	0.411258i
$806$	−56179.5	−	32435.3i	−0.0864785	−	0.0499284i
$807$		0			0
$808$	87430.6	+	151434.i	0.133919	+	0.231954i
$809$		−	663952.i		−	1.01447i	−0.861807	−	0.507236i	$-0.830667\pi$
$809$		−	663952.i		−	1.01447i	0.861807	−	0.507236i	$-0.169333\pi$
$810$		0			0
$811$	1.04793e6			1.59328			0.796640	−	0.604454i	$-0.206609\pi$
$811$	1.04793e6			1.59328			0.796640	+	0.604454i	$0.206609\pi$
$812$	−186378.	+	107605.i	−0.282671	+	0.163200i
$813$		0			0
$814$	186764.	−	323484.i	0.281867	−	0.488207i
$815$	184004.	+	106235.i	0.277020	+	0.159938i
$816$		0			0
$817$	361805.	+	626665.i	0.542039	+	0.938840i
$818$		−	527773.i		−	0.788752i
$819$		0			0
$820$	619862.			0.921864
$821$	881534.	−	508954.i	1.30783	−	0.755079i	0.326100	−	0.945335i	$-0.394265\pi$
$821$	881534.	−	508954.i	1.30783	−	0.755079i	0.981734	+	0.190256i	$0.0609319\pi$
$822$		0			0
$823$	226891.	−	392987.i	0.334979	−	0.580201i	−0.648502	−	0.761213i	$-0.724604\pi$
$823$	226891.	−	392987.i	0.334979	−	0.580201i	0.983481	+	0.181012i	$0.0579374\pi$
$824$	108758.	+	62791.6i	0.160180	+	0.0924799i
$825$		0			0
$826$	−648470.	−	1.12318e6i	−0.950450	−	1.64623i
$827$			52527.2i			0.0768022i	0.999262	+	0.0384011i	$0.0122265\pi$
$827$			52527.2i			0.0768022i	−0.999262	+	0.0384011i	$0.987774\pi$
$828$		0			0
$829$	1.21231e6			1.76403			0.882015	−	0.471222i	$-0.156187\pi$
$829$	1.21231e6			1.76403			0.882015	+	0.471222i	$0.156187\pi$
$830$	−47609.8	+	27487.5i	−0.0691099	+	0.0399006i
$831$		0			0
$832$	−73742.0	+	127725.i	−0.106529	+	0.184514i
$833$	832724.	+	480774.i	1.20008	+	0.692868i
$834$		0			0
$835$	−112999.	−	195720.i	−0.162070	−	0.280713i
$836$			1.23140e6i			1.76192i
$837$		0			0
$838$	−66158.0			−0.0942095
$839$	323211.	−	186606.i	0.459158	−	0.265095i	−0.252532	−	0.967588i	$-0.581263\pi$
$839$	323211.	−	186606.i	0.459158	−	0.265095i	0.711690	+	0.702494i	$0.247930\pi$
$840$		0			0
$841$	−341164.	+	590913.i	−0.482359	+	0.835471i
$842$	79922.1	+	46143.1i	0.112731	+	0.0650852i
$843$		0			0
$844$	−619989.	−	1.07385e6i	−0.870361	−	1.50751i
$845$			310973.i			0.435522i
$846$		0			0
$847$	2.34224e6			3.26486
$848$	274776.	−	158642.i	0.382110	−	0.220611i
$849$		0			0
$850$	125369.	−	217145.i	0.173521	−	0.300546i
$851$	−96184.7	−	55532.2i	−0.132815	−	0.0766807i
$852$		0			0
$853$	−190966.	−	330763.i	−0.262457	−	0.454588i	0.704437	−	0.709766i	$-0.251199\pi$
$853$	−190966.	−	330763.i	−0.262457	−	0.454588i	−0.966894	+	0.255178i	$0.917866\pi$
$854$		−	834251.i		−	1.14388i
$855$		0			0
$856$	23390.7			0.0319224
$857$	−765820.	+	442146.i	−1.04271	+	0.602011i	−0.920601	−	0.390505i	$-0.872300\pi$
$857$	−765820.	+	442146.i	−1.04271	+	0.602011i	−0.122113	+	0.992516i	$0.538967\pi$
$858$		0			0
$859$	−589517.	+	1.02107e6i	−0.798933	+	1.38379i	0.121379	+	0.992606i	$0.461268\pi$
$859$	−589517.	+	1.02107e6i	−0.798933	+	1.38379i	−0.920312	+	0.391186i	$0.872065\pi$
$860$	−437854.	−	252795.i	−0.592015	−	0.341800i
$861$		0			0
$862$	−550272.	−	953099.i	−0.740565	−	1.28270i
$863$		−	1.09614e6i		−	1.47179i	−0.677097	−	0.735894i	$-0.736762\pi$
$863$		−	1.09614e6i		−	1.47179i	0.677097	−	0.735894i	$-0.263238\pi$
$864$		0			0
$865$	147444.			0.197058
$866$	240749.	−	138996.i	0.321017	−	0.185339i
$867$		0			0
$868$	−273978.	+	474544.i	−0.363644	+	0.629850i
$869$	349814.	+	201965.i	0.463230	+	0.267446i
$870$		0			0
$871$	−51834.0	−	89779.2i	−0.0683249	−	0.118342i
$872$			285045.i			0.374869i
$873$		0			0
$874$	677130.			0.886439
$875$	−87530.9	+	50536.0i	−0.114326	+	0.0660062i
$876$		0			0
$877$	599705.	−	1.03872e6i	0.779719	−	1.35051i	−0.152384	−	0.988321i	$-0.548695\pi$
$877$	599705.	−	1.03872e6i	0.779719	−	1.35051i	0.932104	−	0.362192i	$-0.117972\pi$
$878$	1.56959e6	+	906205.i	2.03610	+	1.17554i
$879$		0			0
$880$	245537.	+	425282.i	0.317067	+	0.549177i
$881$			658543.i			0.848462i	0.905554	+	0.424231i	$0.139456\pi$
$881$			658543.i			0.848462i	−0.905554	+	0.424231i	$0.860544\pi$
$882$		0			0
$883$	851604.			1.09224			0.546118	−	0.837708i	$-0.316105\pi$
$883$	851604.			1.09224			0.546118	+	0.837708i	$0.316105\pi$
$884$	151501.	−	87469.4i	0.193871	−	0.111931i
$885$		0			0
$886$	563854.	−	976624.i	0.718289	−	1.24411i
$887$	916591.	+	529194.i	1.16501	+	0.672617i	0.952499	−	0.304543i	$-0.0985037\pi$
$887$	916591.	+	529194.i	1.16501	+	0.672617i	0.212508	+	0.977159i	$0.431837\pi$
$888$		0			0
$889$	665538.	+	1.15274e6i	0.842110	+	1.45858i
$890$		−	633709.i		−	0.800037i
$891$		0			0
$892$	1.55264e6			1.95138
$893$	619079.	−	357425.i	0.776324	−	0.448211i
$894$		0			0
$895$	233036.	−	403631.i	0.290923	−	0.503893i
$896$	528675.	+	305231.i	0.658526	+	0.380200i
$897$		0			0
$898$	109602.	+	189836.i	0.135914	+	0.235410i
$899$		−	63535.6i		−	0.0786136i
$900$		0			0
$901$	−532374.			−0.655794
$902$	3.26244e6	−	1.88357e6i	4.00986	−	2.31509i
$903$		0			0
$904$	−173055.	+	299740.i	−0.211762	+	0.366782i
$905$	−364271.	−	210312.i	−0.444762	−	0.256783i
$906$		0			0
$907$	225404.	+	390411.i	0.273997	+	0.474577i	0.969882	−	0.243576i	$-0.0783207\pi$
$907$	225404.	+	390411.i	0.273997	+	0.474577i	−0.695884	+	0.718154i	$0.744987\pi$
$908$			1.74535e6i			2.11695i
$909$		0			0
$910$	−130412.			−0.157484
$911$	−1.39879e6	+	807592.i	−1.68545	+	0.973095i	−0.727522	+	0.686085i	$0.759328\pi$
$911$	−1.39879e6	+	807592.i	−1.68545	+	0.973095i	−0.957928	+	0.287010i	$0.907339\pi$
$912$		0			0
$913$	−90330.0	+	156456.i	−0.108365	+	0.187694i
$914$	161144.	+	93036.6i	0.192895	+	0.111368i
$915$		0			0
$916$	470364.	+	814694.i	0.560587	+	0.970965i
$917$			461935.i			0.549341i
$918$		0			0
$919$	−1.49446e6			−1.76951			−0.884754	−	0.466058i	$-0.845674\pi$
$919$	−1.49446e6			−1.76951			−0.884754	+	0.466058i	$0.845674\pi$
$920$	−61723.2	+	35635.9i	−0.0729244	+	0.0421029i
$921$		0			0
$922$	−366125.	+	634147.i	−0.430693	+	0.745982i
$923$	28527.1	+	16470.1i	0.0334853	+	0.0193327i
$924$		0			0
$925$	18239.0	+	31590.8i	0.0213165	+	0.0369213i
$926$		−	1.84358e6i		−	2.15000i
$927$		0			0
$928$	−231181.			−0.268445
$929$	−693031.	+	400121.i	−0.803010	+	0.463618i	−0.844523	−	0.535520i	$-0.820116\pi$
$929$	−693031.	+	400121.i	−0.803010	+	0.463618i	0.0415126	+	0.999138i	$0.486782\pi$
$930$		0			0
$931$	426431.	−	738600.i	0.491982	−	0.852138i
$932$	47590.0	+	27476.1i	0.0547879	+	0.0316318i
$933$		0			0
$934$	−305644.	−	529391.i	−0.350366	−	0.606852i
$935$		−	823977.i		−	0.942523i
$936$		0			0
$937$	−1.34081e6			−1.52717			−0.763587	−	0.645705i	$-0.776564\pi$
$937$	−1.34081e6			−1.52717			−0.763587	+	0.645705i	$0.776564\pi$
$938$	−1.40247e6	+	809718.i	−1.59400	+	0.920297i
$939$		0			0
$940$	−249735.	+	432554.i	−0.282633	+	0.489535i
$941$	45424.0	+	26225.5i	0.0512986	+	0.0296173i	0.525430	−	0.850837i	$-0.323904\pi$
$941$	45424.0	+	26225.5i	0.0512986	+	0.0296173i	−0.474131	+	0.880454i	$0.657238\pi$
$942$		0			0
$943$	−560060.	−	970052.i	−0.629812	−	1.09087i
$944$		−	615381.i		−	0.690557i
$945$		0			0
$946$	−3.07267e6			−3.43347
$947$	80995.2	−	46762.6i	0.0903149	−	0.0521433i	−0.454162	−	0.890919i	$-0.650061\pi$
$947$	80995.2	−	46762.6i	0.0903149	−	0.0521433i	0.544477	+	0.838776i	$0.316728\pi$
$948$		0			0
$949$	83583.5	−	144771.i	0.0928085	−	0.160749i
$950$	−192601.	−	111198.i	−0.213408	−	0.123211i
$951$		0			0
$952$	−205839.	−	356523.i	−0.227119	−	0.393381i
$953$		−	323193.i		−	0.355857i	−0.984043	−	0.177929i	$-0.943060\pi$
$953$		−	323193.i		−	0.355857i	0.984043	−	0.177929i	$-0.0569397\pi$
$954$		0			0
$955$	355556.			0.389853
$956$	1.31131e6	−	757085.i	1.43479	−	0.828378i
$957$		0			0
$958$	435864.	−	754939.i	0.474920	−	0.822585i
$959$	672531.	+	388286.i	0.731266	+	0.422196i
$960$		0			0
$961$	380875.	+	659695.i	0.412416	+	0.714326i
$962$			47067.2i			0.0508590i
$963$		0			0
$964$	−97300.3			−0.104703
$965$	−413966.	+	239003.i	−0.444539	+	0.256655i
$966$		0			0
$967$	−516034.	+	893798.i	−0.551856	+	0.955842i	0.446285	+	0.894891i	$0.352747\pi$
$967$	−516034.	+	893798.i	−0.551856	+	0.955842i	−0.998141	+	0.0609514i	$0.980587\pi$
$968$	−469791.	−	271234.i	−0.501365	−	0.289463i
$969$		0			0
$970$	−228857.	−	396392.i	−0.243232	−	0.421290i
$971$		−	625840.i		−	0.663781i	−0.943318	−	0.331890i	$-0.892314\pi$
$971$		−	625840.i		−	0.663781i	0.943318	−	0.331890i	$-0.107686\pi$
$972$		0			0
$973$	1.63320e6			1.72510
$974$	−1.66256e6	+	959880.i	−1.75251	+	1.01181i
$975$		0			0
$976$	197921.	−	342808.i	0.207774	−	0.359875i
$977$	−952685.	−	550033.i	−0.998068	−	0.576235i	−0.0903922	−	0.995906i	$-0.528812\pi$
$977$	−952685.	−	550033.i	−0.998068	−	0.576235i	−0.907676	+	0.419671i	$0.862145\pi$
$978$		0			0
$979$	−1.04125e6	−	1.80350e6i	−1.08640	−	1.88170i
$980$			595899.i			0.620469i
$981$		0			0
$982$	506858.			0.525610
$983$	−46616.3	+	26914.0i	−0.0482426	+	0.0278529i	−0.523927	−	0.851763i	$-0.675534\pi$
$983$	−46616.3	+	26914.0i	−0.0482426	+	0.0278529i	0.475685	+	0.879616i	$0.342200\pi$
$984$		0			0
$985$	265495.	−	459850.i	0.273642	−	0.473963i
$986$	274414.	+	158433.i	0.282262	+	0.162964i
$987$		0			0
$988$	−77582.6	−	134377.i	−0.0794786	−	0.137661i
$989$			913626.i			0.934062i
$990$		0			0
$991$	134455.			0.136908			0.0684541	−	0.997654i	$-0.478193\pi$
$991$	134455.			0.136908			0.0684541	+	0.997654i	$0.478193\pi$
$992$	−509759.	+	294309.i	−0.518014	+	0.299075i
$993$		0			0
$994$	257286.	−	445632.i	0.260401	−	0.451028i
$995$	401418.	+	231759.i	0.405462	+	0.234094i
$996$		0			0
$997$	−571318.	−	989552.i	−0.574761	−	0.995516i	−0.996068	−	0.0885973i	$-0.971762\pi$
$997$	−571318.	−	989552.i	−0.574761	−	0.995516i	0.421306	−	0.906918i	$-0.361572\pi$
$998$		−	1.86162e6i		−	1.86909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.i.a.71.14		32
3.2	odd	2		45.5.i.a.41.3	yes	32
9.2	odd	6	inner	135.5.i.a.116.14		32
9.4	even	3		405.5.c.b.161.27		32
9.5	odd	6		405.5.c.b.161.6		32
9.7	even	3		45.5.i.a.11.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.3	✓	32	9.7	even	3
45.5.i.a.41.3	yes	32	3.2	odd	2
135.5.i.a.71.14		32	1.1	even	1	trivial
135.5.i.a.116.14		32	9.2	odd	6	inner
405.5.c.b.161.6		32	9.5	odd	6
405.5.c.b.161.27		32	9.4	even	3

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.11159 - 2.95118i) q^{2} +(9.41890 - 16.3140i) q^{4} +(9.68246 + 5.59017i) q^{5} +(36.1606 + 62.6320i) q^{7} -16.7497i q^{8} +65.9903 q^{10} +(187.805 - 108.429i) q^{11} +(-13.6629 + 23.6648i) q^{13} +(369.676 + 213.433i) q^{14} +(101.271 + 175.407i) q^{16} -339.847i q^{17} -301.434 q^{19} +(182.396 - 105.307i) q^{20} +(639.988 - 1108.49i) q^{22} +(-329.599 - 190.294i) q^{23} +(62.5000 + 108.253i) q^{25} +161.286i q^{26} +1362.37 q^{28} +(-136.804 + 78.9837i) q^{29} +(-201.104 + 348.322i) q^{31} +(1267.40 + 731.735i) q^{32} +(-1002.95 - 1737.16i) q^{34} +808.575i q^{35} +291.824 q^{37} +(-1540.80 + 889.584i) q^{38} +(93.6338 - 162.179i) q^{40} +(2548.83 + 1471.56i) q^{41} +(-1200.28 - 2078.95i) q^{43} -4085.14i q^{44} -2246.36 q^{46} +(-2053.78 + 1185.75i) q^{47} +(-1414.68 + 2450.29i) q^{49} +(638.949 + 368.897i) q^{50} +(257.379 + 445.793i) q^{52} -1566.51i q^{53} +2424.55 q^{55} +(1049.07 - 605.680i) q^{56} +(-466.190 + 807.464i) q^{58} +(-2631.23 - 1519.14i) q^{59} +(-977.183 - 1692.53i) q^{61} +2373.97i q^{62} +5397.25 q^{64} +(-264.581 + 152.756i) q^{65} +(-1896.89 + 3285.51i) q^{67} +(-5544.27 - 3200.99i) q^{68} +(2386.25 + 4133.11i) q^{70} -1205.47i q^{71} -6117.56 q^{73} +(1491.68 - 861.223i) q^{74} +(-2839.17 + 4917.59i) q^{76} +(13582.3 + 7841.74i) q^{77} +(931.321 + 1613.09i) q^{79} +2264.49i q^{80} +17371.4 q^{82} +(-721.466 + 416.539i) q^{83} +(1899.80 - 3290.55i) q^{85} +(-12270.7 - 7084.49i) q^{86} +(-1816.16 - 3145.68i) q^{88} -9603.06i q^{89} -1976.23 q^{91} +(-6208.92 + 3584.72i) q^{92} +(-6998.73 + 12122.2i) q^{94} +(-2918.62 - 1685.06i) q^{95} +(-3468.03 - 6006.81i) q^{97} +16699.9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 128 q^{4} - 26 q^{7} + 738 q^{11} + 10 q^{13} - 1998 q^{14} - 1024 q^{16} + 508 q^{19} + 672 q^{22} - 1998 q^{23} + 2000 q^{25} - 1664 q^{28} + 270 q^{29} - 1472 q^{31} + 6048 q^{32} - 594 q^{34}+ \cdots + 23266 q^{97}+O(q^{100}) \) 32 * q + 128 * q^4 - 26 * q^7 + 738 * q^11 + 10 * q^13 - 1998 * q^14 - 1024 * q^16 + 508 * q^19 + 672 * q^22 - 1998 * q^23 + 2000 * q^25 - 1664 * q^28 + 270 * q^29 - 1472 * q^31 + 6048 * q^32 - 594 * q^34 + 2068 * q^37 + 7164 * q^38 + 1650 * q^40 + 13428 * q^41 + 568 * q^43 + 5724 * q^46 - 12528 * q^47 - 1674 * q^49 + 1534 * q^52 - 21294 * q^56 - 8190 * q^58 + 4374 * q^59 - 4478 * q^61 - 37216 * q^64 + 8550 * q^65 + 12838 * q^67 - 65736 * q^68 + 2400 * q^70 + 29236 * q^73 + 20628 * q^74 + 6190 * q^76 + 31806 * q^77 - 3512 * q^79 + 34692 * q^82 + 43074 * q^83 - 4350 * q^85 + 10746 * q^86 - 16128 * q^88 - 48904 * q^91 - 27036 * q^92 + 5118 * q^94 - 6300 * q^95 + 23266 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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