LMFDB - Embedded newform 108.6.i.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(13,108)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	108.25
Dual form			108.6.i.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.2968 - 6.21296i) q^{3} +(82.0644 - 68.8602i) q^{5} +(4.01162 - 1.46011i) q^{7} +(165.798 + 177.651i) q^{9} +O(q^{10})$	\(q+(-14.2968 - 6.21296i) q^{3} +(82.0644 - 68.8602i) q^{5} +(4.01162 - 1.46011i) q^{7} +(165.798 + 177.651i) q^{9} +(339.748 + 285.083i) q^{11} +(-111.666 - 633.290i) q^{13} +(-1601.09 + 474.620i) q^{15} +(243.562 + 421.862i) q^{17} +(270.567 - 468.636i) q^{19} +(-66.4250 - 4.04908i) q^{21} +(493.552 + 179.638i) q^{23} +(1450.19 - 8224.41i) q^{25} +(-1266.65 - 3569.94i) q^{27} +(1295.10 - 7344.90i) q^{29} +(-2450.39 - 891.870i) q^{31} +(-3086.12 - 6186.62i) q^{33} +(228.667 - 396.064i) q^{35} +(3502.14 + 6065.88i) q^{37} +(-2338.13 + 9747.82i) q^{39} +(-2742.06 - 15551.0i) q^{41} +(1214.60 + 1019.17i) q^{43} +(25839.2 + 3161.92i) q^{45} +(-27318.4 + 9943.09i) q^{47} +(-12860.9 + 10791.6i) q^{49} +(-861.155 - 7544.53i) q^{51} -14618.2 q^{53} +47512.1 q^{55} +(-6779.87 + 5018.98i) q^{57} +(30754.6 - 25806.2i) q^{59} +(13868.6 - 5047.76i) q^{61} +(924.509 + 470.584i) q^{63} +(-52772.3 - 44281.2i) q^{65} +(2941.46 + 16681.8i) q^{67} +(-5940.14 - 5634.67i) q^{69} +(29691.2 + 51426.7i) q^{71} +(-9248.99 + 16019.7i) q^{73} +(-71831.0 + 108573. i) q^{75} +(1779.19 + 647.573i) q^{77} +(16175.9 - 91738.3i) q^{79} +(-4070.82 + 58908.5i) q^{81} +(-7711.19 + 43732.3i) q^{83} +(49037.3 + 17848.1i) q^{85} +(-64149.4 + 96962.3i) q^{87} +(9618.93 - 16660.5i) q^{89} +(-1372.63 - 2377.47i) q^{91} +(29491.7 + 27975.1i) q^{93} +(-10066.4 - 57089.6i) q^{95} +(54592.7 + 45808.7i) q^{97} +(5684.46 + 107623. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) $ 90 * q - 87 * q^5 + 330 * q^9	$ 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) $ 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−14.2968	−	6.21296i	−0.917142	−	0.398561i
$3$	−14.2968	−	6.21296i	−0.917142	−	0.398561i
$4$		0			0
$5$	82.0644	−	68.8602i	1.46801	−	1.23181i	0.550056	−	0.835128i	$-0.314607\pi$
$5$	82.0644	−	68.8602i	1.46801	−	1.23181i	0.917957	−	0.396681i	$-0.129838\pi$
$6$		0			0
$7$	4.01162	−	1.46011i	0.0309438	−	0.0112626i	−0.326502	−	0.945197i	$-0.605870\pi$
$7$	4.01162	−	1.46011i	0.0309438	−	0.0112626i	0.357446	+	0.933934i	$0.383648\pi$
$8$		0			0
$9$	165.798	+	177.651i	0.682298	+	0.731074i
$10$		0			0
$11$	339.748	+	285.083i	0.846595	+	0.710377i	0.959037	−	0.283281i	$-0.0914228\pi$
$11$	339.748	+	285.083i	0.846595	+	0.710377i	−0.112442	+	0.993658i	$0.535867\pi$
$12$		0			0
$13$	−111.666	−	633.290i	−0.183258	−	1.03931i	−0.928173	−	0.372149i	$-0.878621\pi$
$13$	−111.666	−	633.290i	−0.183258	−	1.03931i	0.744915	−	0.667160i	$-0.232490\pi$
$14$		0			0
$15$	−1601.09	+	474.620i	−1.83733	+	0.544650i
$16$		0			0
$17$	243.562	+	421.862i	0.204403	+	0.354037i	0.949942	−	0.312425i	$-0.101141\pi$
$17$	243.562	+	421.862i	0.204403	+	0.354037i	−0.745539	+	0.666462i	$0.767808\pi$
$18$		0			0
$19$	270.567	−	468.636i	0.171946	−	0.297818i	−0.767154	−	0.641462i	$-0.778328\pi$
$19$	270.567	−	468.636i	0.171946	−	0.297818i	0.939100	+	0.343644i	$0.111661\pi$
$20$		0			0
$21$	−66.4250	−	4.04908i	−0.0328687	−	0.00200358i
$22$		0			0
$23$	493.552	+	179.638i	0.194542	+	0.0708074i	0.437454	−	0.899241i	$-0.355880\pi$
$23$	493.552	+	179.638i	0.194542	+	0.0708074i	−0.242912	+	0.970048i	$0.578103\pi$
$24$		0			0
$25$	1450.19	−	8224.41i	0.464060	−	2.63181i
$26$		0			0
$27$	−1266.65	−	3569.94i	−0.334386	−	0.942436i
$28$		0			0
$29$	1295.10	−	7344.90i	0.285963	−	1.62178i	−0.415863	−	0.909427i	$-0.636520\pi$
$29$	1295.10	−	7344.90i	0.285963	−	1.62178i	0.701826	−	0.712349i	$-0.252368\pi$
$30$		0			0
$31$	−2450.39	−	891.870i	−0.457964	−	0.166685i	0.102728	−	0.994709i	$-0.467243\pi$
$31$	−2450.39	−	891.870i	−0.457964	−	0.166685i	−0.560692	+	0.828024i	$0.689465\pi$
$32$		0			0
$33$	−3086.12	−	6186.62i	−0.493318	−	0.988937i
$34$		0			0
$35$	228.667	−	396.064i	0.0315525	−	0.0546506i
$36$		0			0
$37$	3502.14	+	6065.88i	0.420561	+	0.728432i	0.995994	−	0.0894160i	$-0.0285001\pi$
$37$	3502.14	+	6065.88i	0.420561	+	0.728432i	−0.575434	+	0.817848i	$0.695167\pi$
$38$		0			0
$39$	−2338.13	+	9747.82i	−0.246155	+	1.02623i
$40$		0			0
$41$	−2742.06	−	15551.0i	−0.254752	−	1.44477i	−0.796709	−	0.604364i	$-0.793427\pi$
$41$	−2742.06	−	15551.0i	−0.254752	−	1.44477i	0.541957	−	0.840406i	$-0.317684\pi$
$42$		0			0
$43$	1214.60	+	1019.17i	0.100175	+	0.0840571i	0.691500	−	0.722377i	$-0.256950\pi$
$43$	1214.60	+	1019.17i	0.100175	+	0.0840571i	−0.591324	+	0.806434i	$0.701395\pi$
$44$		0			0
$45$	25839.2	+	3161.92i	1.90217	+	0.232766i
$46$		0			0
$47$	−27318.4	+	9943.09i	−1.80389	+	0.656564i	−0.805985	+	0.591936i	$0.798364\pi$
$47$	−27318.4	+	9943.09i	−1.80389	+	0.656564i	−0.997909	+	0.0646276i	$0.979414\pi$
$48$		0			0
$49$	−12860.9	+	10791.6i	−0.765214	+	0.642091i
$50$		0			0
$51$	−861.155	−	7544.53i	−0.0463614	−	0.406169i
$52$		0			0
$53$	−14618.2			−0.714834			−0.357417	−	0.933945i	$-0.616343\pi$
$53$	−14618.2			−0.714834			−0.357417	+	0.933945i	$0.616343\pi$
$54$		0			0
$55$	47512.1			2.11786
$56$		0			0
$57$	−6779.87	+	5018.98i	−0.276397	+	0.204611i
$58$		0			0
$59$	30754.6	−	25806.2i	1.15022	−	0.965147i	0.150493	−	0.988611i	$-0.451914\pi$
$59$	30754.6	−	25806.2i	1.15022	−	0.965147i	0.999725	+	0.0234639i	$0.00746948\pi$
$60$		0			0
$61$	13868.6	−	5047.76i	0.477209	−	0.173690i	−0.0922062	−	0.995740i	$-0.529392\pi$
$61$	13868.6	−	5047.76i	0.477209	−	0.173690i	0.569415	+	0.822050i	$0.307170\pi$
$62$		0			0
$63$	924.509	+	470.584i	0.0293467	+	0.0149378i
$64$		0			0
$65$	−52772.3	−	44281.2i	−1.54925	−	1.29998i
$66$		0			0
$67$	2941.46	+	16681.8i	0.0800526	+	0.454001i	0.998315	+	0.0580282i	$0.0184813\pi$
$67$	2941.46	+	16681.8i	0.0800526	+	0.454001i	−0.918262	+	0.395972i	$0.870408\pi$
$68$		0			0
$69$	−5940.14	−	5634.67i	−0.150201	−	0.142477i
$70$		0			0
$71$	29691.2	+	51426.7i	0.699008	+	1.21072i	0.968811	+	0.247801i	$0.0797080\pi$
$71$	29691.2	+	51426.7i	0.699008	+	1.21072i	−0.269803	+	0.962916i	$0.586959\pi$
$72$		0			0
$73$	−9248.99	+	16019.7i	−0.203136	+	0.351842i	−0.949537	−	0.313654i	$-0.898447\pi$
$73$	−9248.99	+	16019.7i	−0.203136	+	0.351842i	0.746401	+	0.665496i	$0.231780\pi$
$74$		0			0
$75$	−71831.0	+	108573.i	−1.47455	+	2.22879i
$76$		0			0
$77$	1779.19	+	647.573i	0.0341976	+	0.0124469i
$78$		0			0
$79$	16175.9	−	91738.3i	0.291610	−	1.65380i	−0.389062	−	0.921212i	$-0.627201\pi$
$79$	16175.9	−	91738.3i	0.291610	−	1.65380i	0.680672	−	0.732589i	$-0.261688\pi$
$80$		0			0
$81$	−4070.82	+	58908.5i	−0.0689396	+	0.997621i
$82$		0			0
$83$	−7711.19	+	43732.3i	−0.122864	+	0.696798i	0.859689	+	0.510818i	$0.170657\pi$
$83$	−7711.19	+	43732.3i	−0.122864	+	0.696798i	−0.982553	+	0.185981i	$0.940454\pi$
$84$		0			0
$85$	49037.3	+	17848.1i	0.736172	+	0.267945i
$86$		0			0
$87$	−64149.4	+	96962.3i	−0.908646	+	1.37342i
$88$		0			0
$89$	9618.93	−	16660.5i	0.128722	−	0.222952i	−0.794460	−	0.607317i	$-0.792246\pi$
$89$	9618.93	−	16660.5i	0.128722	−	0.222952i	0.923182	+	0.384364i	$0.125579\pi$
$90$		0			0
$91$	−1372.63	−	2377.47i	−0.0173761	−	0.0300962i
$92$		0			0
$93$	29491.7	+	27975.1i	0.353584	+	0.335401i
$94$		0			0
$95$	−10066.4	−	57089.6i	−0.114437	−	0.649005i
$96$		0			0
$97$	54592.7	+	45808.7i	0.589122	+	0.494332i	0.887928	−	0.459982i	$-0.152144\pi$
$97$	54592.7	+	45808.7i	0.589122	+	0.494332i	−0.298807	+	0.954314i	$0.596589\pi$
$98$		0			0
$99$	5684.46	+	107623.i	0.0582910	+	1.10361i
$100$		0			0
$101$	48770.0	−	17750.8i	0.475718	−	0.173147i	−0.0930231	−	0.995664i	$-0.529653\pi$
$101$	48770.0	−	17750.8i	0.475718	−	0.173147i	0.568741	+	0.822517i	$0.307431\pi$
$102$		0			0
$103$	82454.8	−	69187.8i	0.765813	−	0.642594i	−0.173820	−	0.984778i	$-0.555611\pi$
$103$	82454.8	−	69187.8i	0.765813	−	0.642594i	0.939633	+	0.342184i	$0.111167\pi$
$104$		0			0
$105$	−5729.94	+	4241.75i	−0.0507197	+	0.0375467i
$106$		0			0
$107$	−122016.			−1.03028			−0.515141	−	0.857105i	$-0.672261\pi$
$107$	−122016.			−1.03028			−0.515141	+	0.857105i	$0.672261\pi$
$108$		0			0
$109$	168909.			1.36172			0.680860	−	0.732414i	$-0.261606\pi$
$109$	168909.			1.36172			0.680860	+	0.732414i	$0.261606\pi$
$110$		0			0
$111$	−12382.4	−	108481.i	−0.0953887	−	0.835695i
$112$		0			0
$113$	−55673.6	+	46715.7i	−0.410160	+	0.344165i	−0.824405	−	0.566000i	$-0.808490\pi$
$113$	−55673.6	+	46715.7i	−0.410160	+	0.344165i	0.414245	+	0.910165i	$0.364046\pi$
$114$		0			0
$115$	52872.9	−	19244.2i	0.372811	−	0.135692i
$116$		0			0
$117$	93990.7	−	124836.i	0.634775	−	0.843093i
$118$		0			0
$119$	1593.04	+	1336.72i	0.0103124	+	0.00865314i
$120$		0			0
$121$	6190.57	+	35108.5i	0.0384386	+	0.217996i
$122$		0			0
$123$	−57414.9	+	239366.i	−0.342186	+	1.42659i
$124$		0			0
$125$	−279939.	−	484869.i	−1.60247	−	2.77555i
$126$		0			0
$127$	−158110.	+	273855.i	−0.869863	+	1.50665i	−0.00772747	+	0.999970i	$0.502460\pi$
$127$	−158110.	+	273855.i	−0.869863	+	1.50665i	−0.862136	+	0.506677i	$0.830874\pi$
$128$		0			0
$129$	−11032.8	−	22117.1i	−0.0583731	−	0.117018i
$130$		0			0
$131$	−185139.	−	67385.0i	−0.942581	−	0.343072i	−0.175397	−	0.984498i	$-0.556121\pi$
$131$	−185139.	−	67385.0i	−0.942581	−	0.343072i	−0.767185	+	0.641426i	$0.778343\pi$
$132$		0			0
$133$	401.152	−	2275.04i	0.00196644	−	0.0111522i
$134$		0			0
$135$	−349774.	−	205743.i	−1.65178	−	0.971609i
$136$		0			0
$137$	29295.4	−	166142.i	0.133351	−	0.756273i	−0.842642	−	0.538474i	$-0.819001\pi$
$137$	29295.4	−	166142.i	0.133351	−	0.756273i	0.975994	−	0.217799i	$-0.0698879\pi$
$138$		0			0
$139$	252973.	+	92074.6i	1.11055	+	0.404206i	0.831194	−	0.555983i	$-0.187658\pi$
$139$	252973.	+	92074.6i	1.11055	+	0.404206i	0.279353	+	0.960189i	$0.409880\pi$
$140$		0			0
$141$	452343.	+	27573.5i	1.91611	+	0.116800i
$142$		0			0
$143$	142602.	−	246993.i	0.583156	−	1.01006i
$144$		0			0
$145$	−399489.	−	691936.i	−1.57792	−	2.73304i
$146$		0			0
$147$	250919.	−	74381.3i	0.957722	−	0.283903i
$148$		0			0
$149$	33640.8	+	190786.i	0.124137	+	0.704015i	0.981817	+	0.189831i	$0.0607940\pi$
$149$	33640.8	+	190786.i	0.124137	+	0.704015i	−0.857680	+	0.514184i	$0.828095\pi$
$150$		0			0
$151$	121376.	+	101846.i	0.433201	+	0.363498i	0.833158	−	0.553035i	$-0.186531\pi$
$151$	121376.	+	101846.i	0.433201	+	0.363498i	−0.399957	+	0.916534i	$0.630975\pi$
$152$		0			0
$153$	−34562.1	+	113213.i	−0.119363	+	0.390993i
$154$		0			0
$155$	−262504.	+	95543.8i	−0.877621	+	0.319428i
$156$		0			0
$157$	371161.	−	311441.i	1.20175	−	1.00839i	0.202170	−	0.979350i	$-0.435201\pi$
$157$	371161.	−	311441.i	1.20175	−	1.00839i	0.999578	−	0.0290361i	$-0.00924377\pi$
$158$		0			0
$159$	208994.	+	90822.5i	0.655604	+	0.284905i
$160$		0			0
$161$	2242.23			0.00681735
$162$		0			0
$163$	16219.8			0.0478165			0.0239082	−	0.999714i	$-0.492389\pi$
$163$	16219.8			0.0478165			0.0239082	+	0.999714i	$0.492389\pi$
$164$		0			0
$165$	−679272.	−	295191.i	−1.94238	−	0.844097i
$166$		0			0
$167$	188304.	−	158006.i	0.522478	−	0.438411i	−0.343017	−	0.939329i	$-0.611449\pi$
$167$	188304.	−	158006.i	0.522478	−	0.438411i	0.865495	+	0.500918i	$0.167004\pi$
$168$		0			0
$169$	−39686.2	+	14444.6i	−0.106886	+	0.0389035i
$170$		0			0
$171$	128113.	−	29632.5i	0.335046	−	0.0774959i
$172$		0			0
$173$	548689.	+	460405.i	1.39383	+	1.16957i	0.963759	+	0.266773i	$0.0859574\pi$
$173$	548689.	+	460405.i	1.39383	+	1.16957i	0.430075	+	0.902793i	$0.358487\pi$
$174$		0			0
$175$	−6190.95	−	35110.6i	−0.0152814	−	0.0866649i
$176$		0			0
$177$	−600026.	+	177869.i	−1.43958	+	0.426744i
$178$		0			0
$179$	−49592.3	−	85896.3i	−0.115686	−	0.200374i	0.802368	−	0.596830i	$-0.203573\pi$
$179$	−49592.3	−	85896.3i	−0.115686	−	0.200374i	−0.918054	+	0.396456i	$0.870240\pi$
$180$		0			0
$181$	−278101.	+	481685.i	−0.630966	+	1.09286i	0.356389	+	0.934338i	$0.384008\pi$
$181$	−278101.	+	481685.i	−0.630966	+	1.09286i	−0.987355	+	0.158527i	$0.949326\pi$
$182$		0			0
$183$	−229639.	−	13998.1i	−0.506894	−	0.0308988i
$184$		0			0
$185$	705098.	+	256635.i	1.51468	+	0.551298i
$186$		0			0
$187$	−37515.8	+	212762.i	−0.0784530	+	0.444929i
$188$		0			0
$189$	−10293.8	−	12471.8i	−0.0209615	−	0.0253965i
$190$		0			0
$191$	−140330.	+	795850.i	−0.278334	+	1.57851i	0.449833	+	0.893113i	$0.351484\pi$
$191$	−140330.	+	795850.i	−0.278334	+	1.57851i	−0.728167	+	0.685400i	$0.759628\pi$
$192$		0			0
$193$	380800.	+	138600.i	0.735874	+	0.267836i	0.682649	−	0.730746i	$-0.260828\pi$
$193$	380800.	+	138600.i	0.735874	+	0.267836i	0.0532252	+	0.998583i	$0.483050\pi$
$194$		0			0
$195$	479359.	+	960953.i	0.902765	+	1.80974i
$196$		0			0
$197$	−260584.	+	451345.i	−0.478390	+	0.828596i	−0.999693	−	0.0247755i	$-0.992113\pi$
$197$	−260584.	+	451345.i	−0.478390	+	0.828596i	0.521303	+	0.853372i	$0.325446\pi$
$198$		0			0
$199$	−161176.	−	279165.i	−0.288515	−	0.499722i	0.684941	−	0.728599i	$-0.259828\pi$
$199$	−161176.	−	279165.i	−0.288515	−	0.499722i	−0.973455	+	0.228877i	$0.926495\pi$
$200$		0			0
$201$	61590.0	−	256772.i	0.107528	−	0.448289i
$202$		0			0
$203$	−5528.89	−	31355.9i	−0.00941668	−	0.0534047i
$204$		0			0
$205$	−1.29587e6	−	1.08736e6i	−2.15366	−	1.80713i
$206$		0			0
$207$	49917.1	+	117464.i	0.0809700	+	0.190536i
$208$		0			0
$209$	225525.	−	82084.3i	0.357132	−	0.129985i
$210$		0			0
$211$	−652607.	+	547602.i	−1.00913	+	0.846757i	−0.988222	−	0.153024i	$-0.951099\pi$
$211$	−652607.	+	547602.i	−1.00913	+	0.846757i	−0.0209033	+	0.999782i	$0.506654\pi$
$212$		0			0
$213$	−104978.	−	919708.i	−0.158544	−	1.38900i
$214$		0			0
$215$	169855.			0.250601
$216$		0			0
$217$	−11132.3			−0.0160485
$218$		0			0
$219$	231761.	−	171568.i	0.326535	−	0.241727i
$220$		0			0
$221$	239964.	−	201353.i	0.330495	−	0.277318i
$222$		0			0
$223$	1.07685e6	−	391941.i	1.45008	−	0.527787i	0.507469	−	0.861670i	$-0.330581\pi$
$223$	1.07685e6	−	391941.i	1.45008	−	0.527787i	0.942615	+	0.333883i	$0.108359\pi$
$224$		0			0
$225$	1.70151e6	−	1.10597e6i	2.24068	−	1.45642i
$226$		0			0
$227$	−763955.	−	641035.i	−0.984019	−	0.825690i	0.000672269	−	1.00000i	$-0.499786\pi$
$227$	−763955.	−	641035.i	−0.984019	−	0.825690i	−0.984691	+	0.174310i	$0.944230\pi$
$228$		0			0
$229$	251017.	+	1.42359e6i	0.316312	+	1.79389i	0.564769	+	0.825249i	$0.308965\pi$
$229$	251017.	+	1.42359e6i	0.316312	+	1.79389i	−0.248457	+	0.968643i	$0.579923\pi$
$230$		0			0
$231$	−21413.4	−	20312.3i	−0.0264032	−	0.0250454i
$232$		0			0
$233$	140339.	+	243074.i	0.169351	+	0.293325i	0.938192	−	0.346116i	$-0.112500\pi$
$233$	140339.	+	243074.i	0.169351	+	0.293325i	−0.768841	+	0.639440i	$0.779166\pi$
$234$		0			0
$235$	−1.55719e6	+	2.69713e6i	−1.83938	+	3.18590i
$236$		0			0
$237$	−801231.	+	1.21107e6i	−0.926588	+	1.40054i
$238$		0			0
$239$	712225.	+	259229.i	0.806534	+	0.293554i	0.712191	−	0.701986i	$-0.247703\pi$
$239$	712225.	+	259229.i	0.806534	+	0.293554i	0.0943425	+	0.995540i	$0.469925\pi$
$240$		0			0
$241$	173449.	−	983676.i	0.192366	−	1.09096i	−0.723754	−	0.690058i	$-0.757585\pi$
$241$	173449.	−	983676.i	0.192366	−	1.09096i	0.916120	−	0.400904i	$-0.131304\pi$
$242$		0			0
$243$	424196.	−	816913.i	0.460841	−	0.887483i
$244$		0			0
$245$	−312313.	+	1.77121e6i	−0.332411	+	1.88519i
$246$		0			0
$247$	−326996.	−	119017.i	−0.341036	−	0.124127i
$248$		0			0
$249$	381952.	−	577324.i	0.390401	−	0.590094i
$250$		0			0
$251$	93241.9	−	161500.i	0.0934172	−	0.161803i	−0.815530	−	0.578715i	$-0.803554\pi$
$251$	93241.9	−	161500.i	0.0934172	−	0.161803i	0.908947	+	0.416912i	$0.136888\pi$
$252$		0			0
$253$	116472.	+	201735.i	0.114398	+	0.198143i
$254$		0			0
$255$	−590188.	−	559838.i	−0.568382	−	0.539153i
$256$		0			0
$257$	175984.	+	998056.i	0.166204	+	0.942588i	0.947815	+	0.318822i	$0.103287\pi$
$257$	175984.	+	998056.i	0.166204	+	0.942588i	−0.781611	+	0.623766i	$0.785602\pi$
$258$		0			0
$259$	22906.1	+	19220.5i	0.0212178	+	0.0178039i
$260$		0			0
$261$	1.51956e6	−	987696.i	1.38075	−	0.897474i
$262$		0			0
$263$	−1.48088e6	+	538995.i	−1.32017	+	0.480502i	−0.903512	−	0.428562i	$-0.859020\pi$
$263$	−1.48088e6	+	538995.i	−1.32017	+	0.480502i	−0.416656	+	0.909064i	$0.636798\pi$
$264$		0			0
$265$	−1.19964e6	+	1.00661e6i	−1.04939	+	0.880539i
$266$		0			0
$267$	−241031.	+	178430.i	−0.206916	+	0.153176i
$268$		0			0
$269$	−1.26419e6			−1.06520			−0.532602	−	0.846366i	$-0.678786\pi$
$269$	−1.26419e6			−1.06520			−0.532602	+	0.846366i	$0.678786\pi$
$270$		0			0
$271$	684705.			0.566344			0.283172	−	0.959069i	$-0.408613\pi$
$271$	684705.			0.566344			0.283172	+	0.959069i	$0.408613\pi$
$272$		0			0
$273$	4853.18	+	42518.4i	0.00394112	+	0.0345279i
$274$		0			0
$275$	2.83734e6	−	2.38081e6i	2.26245	−	1.89842i
$276$		0			0
$277$	−1.67343e6	+	609079.i	−1.31041	+	0.476952i	−0.900374	−	0.435116i	$-0.856707\pi$
$277$	−1.67343e6	+	609079.i	−1.31041	+	0.476952i	−0.410040	+	0.912068i	$0.634485\pi$
$278$		0			0
$279$	−247829.	−	583186.i	−0.190609	−	0.448535i
$280$		0			0
$281$	840722.	+	705450.i	0.635165	+	0.532967i	0.902529	−	0.430629i	$-0.141708\pi$
$281$	840722.	+	705450.i	0.635165	+	0.532967i	−0.267364	+	0.963596i	$0.586153\pi$
$282$		0			0
$283$	−167744.	−	951321.i	−0.124503	−	0.706092i	−0.981602	−	0.190940i	$-0.938847\pi$
$283$	−167744.	−	951321.i	−0.124503	−	0.706092i	0.857099	−	0.515152i	$-0.172265\pi$
$284$		0			0
$285$	−210777.	+	878743.i	−0.153713	+	0.640840i
$286$		0			0
$287$	−33706.2	−	58380.9i	−0.0241549	−	0.0418376i
$288$		0			0
$289$	591283.	−	1.02413e6i	0.416439	−	0.721293i
$290$		0			0
$291$	−495894.	−	994101.i	−0.343287	−	0.688173i
$292$		0			0
$293$	1.92886e6	+	702047.i	1.31260	+	0.477746i	0.901079	−	0.433656i	$-0.142777\pi$
$293$	1.92886e6	+	702047.i	1.31260	+	0.477746i	0.411518	+	0.911402i	$0.364999\pi$
$294$		0			0
$295$	746839.	−	4.23553e6i	0.499657	−	2.83370i
$296$		0			0
$297$	587387.	−	1.57398e6i	0.386396	−	1.03540i
$298$		0			0
$299$	58650.1	−	332621.i	0.0379394	−	0.215165i
$300$		0			0
$301$	6360.59	+	2315.07i	0.00404652	+	0.00147281i
$302$		0			0
$303$	−807541.	−	49225.4i	−0.505310	−	0.0308023i
$304$		0			0
$305$	790530.	−	1.36924e6i	0.486596	−	0.842809i
$306$		0			0
$307$	−559210.	−	968580.i	−0.338633	−	0.586529i	0.645543	−	0.763724i	$-0.276631\pi$
$307$	−559210.	−	968580.i	−0.338633	−	0.586529i	−0.984176	+	0.177195i	$0.943298\pi$
$308$		0			0
$309$	−1.60870e6	+	476878.i	−0.958472	+	0.284126i
$310$		0			0
$311$	−87131.1	−	494145.i	−0.0510825	−	0.289703i	0.948555	−	0.316611i	$-0.102545\pi$
$311$	−87131.1	−	494145.i	−0.0510825	−	0.289703i	−0.999638	+	0.0269079i	$0.991434\pi$
$312$		0			0
$313$	−991770.	−	832194.i	−0.572203	−	0.480135i	0.310173	−	0.950680i	$-0.399613\pi$
$313$	−991770.	−	832194.i	−0.572203	−	0.480135i	−0.882376	+	0.470545i	$0.844057\pi$
$314$		0			0
$315$	108274.	−	25043.7i	0.0614819	−	0.0142207i
$316$		0			0
$317$	−1.58038e6	+	575213.i	−0.883313	+	0.321500i	−0.743546	−	0.668685i	$-0.766858\pi$
$317$	−1.58038e6	+	575213.i	−0.883313	+	0.321500i	−0.139767	+	0.990184i	$0.544635\pi$
$318$		0			0
$319$	2.53391e6	−	2.12621e6i	1.39417	−	1.16985i
$320$		0			0
$321$	1.74444e6	+	758078.i	0.944915	+	0.410631i
$322$		0			0
$323$	263600.			0.140585
$324$		0			0
$325$	−5.37038e6			−2.82031
$326$		0			0
$327$	−2.41487e6	−	1.04943e6i	−1.24889	−	0.542729i
$328$		0			0
$329$	−95073.0	+	79775.8i	−0.0484248	+	0.0406332i
$330$		0			0
$331$	1.23180e6	−	448337.i	0.617973	−	0.224924i	−0.0140154	−	0.999902i	$-0.504461\pi$
$331$	1.23180e6	−	448337.i	0.617973	−	0.224924i	0.631988	+	0.774978i	$0.282239\pi$
$332$		0			0
$333$	−496961.	+	1.62787e6i	−0.245591	+	0.804469i
$334$		0			0
$335$	1.39010e6	+	1.16643e6i	0.676760	+	0.567869i
$336$		0			0
$337$	547553.	+	3.10533e6i	0.262634	+	1.48947i	0.775688	+	0.631116i	$0.217403\pi$
$337$	547553.	+	3.10533e6i	0.262634	+	1.48947i	−0.513054	+	0.858356i	$0.671486\pi$
$338$		0			0
$339$	1.08620e6	−	321989.i	0.513346	−	0.152174i
$340$		0			0
$341$	−578260.	−	1.00158e6i	−0.269301	−	0.466442i
$342$		0			0
$343$	−71711.4	+	124208.i	−0.0329119	+	0.0570051i
$344$		0			0
$345$	−875478.	−	53366.7i	−0.396002	−	0.0241392i
$346$		0			0
$347$	−2.15442e6	−	784146.i	−0.960522	−	0.349601i	−0.186284	−	0.982496i	$-0.559644\pi$
$347$	−2.15442e6	−	784146.i	−0.960522	−	0.349601i	−0.774238	+	0.632895i	$0.781867\pi$
$348$		0			0
$349$	−321695.	+	1.82443e6i	−0.141378	+	0.801794i	0.828827	+	0.559506i	$0.189009\pi$
$349$	−321695.	+	1.82443e6i	−0.141378	+	0.801794i	−0.970204	+	0.242288i	$0.922102\pi$
$350$		0			0
$351$	−2.11937e6	+	1.20080e6i	−0.918203	+	0.520239i
$352$		0			0
$353$	−89595.8	+	508123.i	−0.0382693	+	0.217036i	−0.997945	−	0.0640726i	$-0.979591\pi$
$353$	−89595.8	+	508123.i	−0.0382693	+	0.217036i	0.959676	+	0.281109i	$0.0907022\pi$
$354$		0			0
$355$	5.97784e6	+	2.17576e6i	2.51752	+	0.916304i
$356$		0			0
$357$	−14470.5	−	29008.4i	−0.00600913	−	0.0120463i
$358$		0			0
$359$	650691.	−	1.12703e6i	0.266464	−	0.461529i	−0.701482	−	0.712687i	$-0.747478\pi$
$359$	650691.	−	1.12703e6i	0.266464	−	0.461529i	0.967946	+	0.251158i	$0.0808113\pi$
$360$		0			0
$361$	1.09164e6	+	1.89077e6i	0.440869	+	0.763608i
$362$		0			0
$363$	129622.	−	540402.i	0.0516312	−	0.215253i
$364$		0			0
$365$	344108.	+	1.95154e6i	0.135196	+	0.766733i
$366$		0			0
$367$	1.00157e6	+	840413.i	0.388163	+	0.325708i	0.815897	−	0.578197i	$-0.196244\pi$
$367$	1.00157e6	+	840413.i	0.388163	+	0.325708i	−0.427734	+	0.903905i	$0.640688\pi$
$368$		0			0
$369$	2.30802e6	−	3.06546e6i	0.882418	−	1.17201i
$370$		0			0
$371$	−58642.8	+	21344.2i	−0.0221197	+	0.00805092i
$372$		0			0
$373$	1.72088e6	−	1.44399e6i	0.640439	−	0.537393i	−0.263714	−	0.964601i	$-0.584947\pi$
$373$	1.72088e6	−	1.44399e6i	0.640439	−	0.537393i	0.904153	+	0.427208i	$0.140503\pi$
$374$		0			0
$375$	989773.	+	8.67134e6i	0.363461	+	3.18426i
$376$		0			0
$377$	−4.79607e6			−1.73793
$378$		0			0
$379$	−2.30140e6			−0.822988			−0.411494	−	0.911412i	$-0.634993\pi$
$379$	−2.30140e6			−0.822988			−0.411494	+	0.911412i	$0.634993\pi$
$380$		0			0
$381$	3.96193e6	−	2.93293e6i	1.39828	−	1.03512i
$382$		0			0
$383$	62754.5	−	52657.3i	0.0218599	−	0.0183426i	−0.631792	−	0.775138i	$-0.717680\pi$
$383$	62754.5	−	52657.3i	0.0218599	−	0.0183426i	0.653652	+	0.756795i	$0.273236\pi$
$384$		0			0
$385$	190600.	−	69372.8i	0.0655347	−	0.0238527i
$386$		0			0
$387$	20321.9	+	384751.i	0.00689742	+	0.130588i
$388$		0			0
$389$	645375.	+	541534.i	0.216241	+	0.181448i	0.744473	−	0.667652i	$-0.232701\pi$
$389$	645375.	+	541534.i	0.216241	+	0.181448i	−0.528232	+	0.849100i	$0.677145\pi$
$390$		0			0
$391$	44428.0	+	251964.i	0.0146965	+	0.0833483i
$392$		0			0
$393$	2.22823e6	+	2.11365e6i	0.727746	+	0.690322i
$394$		0			0
$395$	−4.98965e6	−	8.64233e6i	−1.60908	−	2.78701i
$396$		0			0
$397$	456649.	−	790939.i	0.145414	−	0.251864i	−0.784113	−	0.620618i	$-0.786882\pi$
$397$	456649.	−	790939.i	0.145414	−	0.251864i	0.929527	+	0.368753i	$0.120215\pi$
$398$		0			0
$399$	−19870.0	+	30033.6i	−0.00624834	+	0.00944441i
$400$		0			0
$401$	−1.68898e6	−	614738.i	−0.524522	−	0.190910i	0.0661689	−	0.997808i	$-0.478922\pi$
$401$	−1.68898e6	−	614738.i	−0.524522	−	0.190910i	−0.590691	+	0.806898i	$0.701145\pi$
$402$		0			0
$403$	−291187.	+	1.65140e6i	−0.0893118	+	0.506513i
$404$		0			0
$405$	3.72238e6	+	5.11461e6i	1.12767	+	1.54944i
$406$		0			0
$407$	−539432.	+	3.05927e6i	−0.161417	+	0.915444i
$408$		0			0
$409$	−115478.	−	42030.6i	−0.0341343	−	0.0124239i	0.324897	−	0.945750i	$-0.394671\pi$
$409$	−115478.	−	42030.6i	−0.0341343	−	0.0124239i	−0.359031	+	0.933326i	$0.616893\pi$
$410$		0			0
$411$	−1.45107e6	+	2.19330e6i	−0.423723	+	0.640461i
$412$		0			0
$413$	85695.8	−	148429.i	0.0247220	−	0.0428198i
$414$		0			0
$415$	2.37860e6	+	4.11986e6i	0.677956	+	1.17425i
$416$		0			0
$417$	−3.04465e6	−	2.88808e6i	−0.857428	−	0.813335i
$418$		0			0
$419$	379555.	+	2.15256e6i	0.105618	+	0.598991i	0.990972	+	0.134072i	$0.0428054\pi$
$419$	379555.	+	2.15256e6i	0.105618	+	0.598991i	−0.885353	+	0.464919i	$0.846083\pi$
$420$		0			0
$421$	3.64218e6	+	3.05616e6i	1.00151	+	0.840369i	0.987193	−	0.159528i	$-0.0509972\pi$
$421$	3.64218e6	+	3.05616e6i	1.00151	+	0.840369i	0.0143200	+	0.999897i	$0.495442\pi$
$422$		0			0
$423$	−6.29575e6	−	3.20460e6i	−1.71079	−	0.870809i
$424$		0			0
$425$	3.82278e6	−	1.39138e6i	1.02661	−	0.373657i
$426$		0			0
$427$	48265.3	−	40499.4i	0.0128105	−	0.0107493i
$428$		0			0
$429$	−3.57331e6	+	2.64524e6i	−0.937406	+	0.693941i
$430$		0			0
$431$	184976.			0.0479648			0.0239824	−	0.999712i	$-0.492365\pi$
$431$	184976.			0.0479648			0.0239824	+	0.999712i	$0.492365\pi$
$432$		0			0
$433$	−4.37007e6			−1.12013			−0.560065	−	0.828449i	$-0.689224\pi$
$433$	−4.37007e6			−1.12013			−0.560065	+	0.828449i	$0.689224\pi$
$434$		0			0
$435$	1.41246e6	+	1.23745e7i	0.357893	+	3.13548i
$436$		0			0
$437$	217724.	−	182692.i	0.0545384	−	0.0457631i
$438$		0			0
$439$	2.04856e6	−	745614.i	0.507325	−	0.184651i	−0.0756604	−	0.997134i	$-0.524107\pi$
$439$	2.04856e6	−	745614.i	0.507325	−	0.184651i	0.582986	+	0.812482i	$0.301884\pi$
$440$		0			0
$441$	−4.04947e6	−	495529.i	−0.991520	−	0.121331i
$442$		0			0
$443$	−4.21582e6	−	3.53749e6i	−1.02064	−	0.856418i	−0.0309318	−	0.999521i	$-0.509847\pi$
$443$	−4.21582e6	−	3.53749e6i	−1.02064	−	0.856418i	−0.989708	+	0.143103i	$0.954292\pi$
$444$		0			0
$445$	−357872.	−	2.02959e6i	−0.0856698	−	0.485857i
$446$		0			0
$447$	704391.	−	2.93665e6i	0.166742	−	0.695157i
$448$		0			0
$449$	166745.	+	288812.i	0.0390336	+	0.0676081i	0.884882	−	0.465815i	$-0.154239\pi$
$449$	166745.	+	288812.i	0.0390336	+	0.0676081i	−0.845849	+	0.533423i	$0.820905\pi$
$450$		0			0
$451$	3.50171e6	−	6.06514e6i	0.810660	−	1.40410i
$452$		0			0
$453$	−1.10252e6	−	2.21018e6i	−0.252430	−	0.506037i
$454$		0			0
$455$	−276358.	−	100586.i	−0.0625811	−	0.0227777i
$456$		0			0
$457$	1.21689e6	−	6.90130e6i	0.272558	−	1.54575i	−0.474054	−	0.880496i	$-0.657210\pi$
$457$	1.21689e6	−	6.90130e6i	0.272558	−	1.54575i	0.746612	−	0.665259i	$-0.231679\pi$
$458$		0			0
$459$	1.19752e6	−	1.40386e6i	0.265308	−	0.311022i
$460$		0			0
$461$	−602960.	+	3.41956e6i	−0.132141	+	0.749406i	0.844668	+	0.535291i	$0.179798\pi$
$461$	−602960.	+	3.41956e6i	−0.132141	+	0.749406i	−0.976808	+	0.214116i	$0.931313\pi$
$462$		0			0
$463$	5.06303e6	+	1.84279e6i	1.09763	+	0.399506i	0.826444	−	0.563019i	$-0.190360\pi$
$463$	5.06303e6	+	1.84279e6i	1.09763	+	0.399506i	0.271191	+	0.962526i	$0.412583\pi$
$464$		0			0
$465$	4.34659e6	+	264956.i	0.932215	+	0.0568252i
$466$		0			0
$467$	782405.	−	1.35517e6i	0.166012	−	0.287541i	−0.771002	−	0.636832i	$-0.780244\pi$
$467$	782405.	−	1.35517e6i	0.166012	−	0.287541i	0.937014	+	0.349291i	$0.113578\pi$
$468$		0			0
$469$	36157.3	+	62626.2i	0.00759038	+	0.0131469i
$470$		0			0
$471$	−7.24140e6	+	2.14661e6i	−1.50408	+	0.445863i
$472$		0			0
$473$	122110.	+	692521.i	0.0250957	+	0.142325i
$474$		0			0
$475$	−3.46188e6	−	2.90487e6i	−0.704009	−	0.590734i
$476$		0			0
$477$	−2.42368e6	−	2.59695e6i	−0.487730	−	0.522597i
$478$		0			0
$479$	−2.04735e6	+	745173.i	−0.407711	+	0.148395i	−0.537731	−	0.843117i	$-0.680718\pi$
$479$	−2.04735e6	+	745173.i	−0.407711	+	0.148395i	0.130020	+	0.991511i	$0.458496\pi$
$480$		0			0
$481$	3.45039e6	−	2.89522e6i	0.679995	−	0.570584i
$482$		0			0
$483$	−32056.8	−	13930.9i	−0.00625248	−	0.00271713i
$484$		0			0
$485$	7.63451e6			1.47376
$486$		0			0
$487$	1.16659e6			0.222893			0.111446	−	0.993770i	$-0.464452\pi$
$487$	1.16659e6			0.222893			0.111446	+	0.993770i	$0.464452\pi$
$488$		0			0
$489$	−231892.	−	100773.i	−0.0438545	−	0.0190578i
$490$		0			0
$491$	5.55952e6	−	4.66499e6i	1.04072	−	0.873268i	0.0486324	−	0.998817i	$-0.484514\pi$
$491$	5.55952e6	−	4.66499e6i	1.04072	−	0.873268i	0.992087	+	0.125549i	$0.0400693\pi$
$492$		0			0
$493$	3.41397e6	−	1.24259e6i	0.632620	−	0.230255i
$494$		0			0
$495$	7.87743e6	+	8.44057e6i	1.44501	+	1.54831i
$496$		0			0
$497$	194198.	+	162952.i	0.0352658	+	0.0295916i
$498$		0			0
$499$	180832.	+	1.02555e6i	0.0325106	+	0.184377i	0.996739	−	0.0806973i	$-0.0257147\pi$
$499$	180832.	+	1.02555e6i	0.0325106	+	0.184377i	−0.964228	+	0.265074i	$0.914604\pi$
$500$		0			0
$501$	−3.67383e6	+	1.08906e6i	−0.653920	+	0.193846i
$502$		0			0
$503$	623490.	+	1.07992e6i	0.109878	+	0.190314i	0.915721	−	0.401816i	$-0.131621\pi$
$503$	623490.	+	1.07992e6i	0.109878	+	0.190314i	−0.805843	+	0.592129i	$0.798287\pi$
$504$		0			0
$505$	2.77995e6	−	4.81502e6i	0.485075	−	0.840175i
$506$		0			0
$507$	657130.	+	40056.8i	0.113535	+	0.00692080i
$508$		0			0
$509$	−4.59935e6	−	1.67403e6i	−0.786868	−	0.286397i	−0.0828346	−	0.996563i	$-0.526397\pi$
$509$	−4.59935e6	−	1.67403e6i	−0.786868	−	0.286397i	−0.704034	+	0.710167i	$0.748620\pi$
$510$		0			0
$511$	−13712.9	+	77769.5i	−0.00232314	+	0.0131752i
$512$		0			0
$513$	−2.01572e6	−	372311.i	−0.338171	−	0.0624615i
$514$		0			0
$515$	2.00232e6	−	1.13557e7i	0.332671	−	1.88667i
$516$		0			0
$517$	−1.21160e7	−	4.40986e6i	−1.99358	−	0.725602i
$518$		0			0
$519$	−4.98404e6	−	9.99131e6i	−0.812200	−	1.62819i
$520$		0			0
$521$	−4.84233e6	+	8.38717e6i	−0.781556	+	1.35370i	0.149479	+	0.988765i	$0.452240\pi$
$521$	−4.84233e6	+	8.38717e6i	−0.781556	+	1.35370i	−0.931035	+	0.364930i	$0.881093\pi$
$522$		0			0
$523$	5.00106e6	+	8.66209e6i	0.799481	+	1.38474i	0.919955	+	0.392025i	$0.128225\pi$
$523$	5.00106e6	+	8.66209e6i	0.799481	+	1.38474i	−0.120474	+	0.992716i	$0.538441\pi$
$524$		0			0
$525$	−129630.	+	540434.i	−0.0205261	+	0.0855746i
$526$		0			0
$527$	−220577.	−	1.25095e6i	−0.0345966	−	0.196207i
$528$		0			0
$529$	−4.71920e6	−	3.95988e6i	−0.733212	−	0.615238i
$530$		0			0
$531$	9.68356e6	+	1.18497e6i	1.49039	+	0.182377i
$532$		0			0
$533$	−9.54211e6	+	3.47304e6i	−1.45488	+	0.529532i
$534$		0			0
$535$	−1.00131e7	+	8.40203e6i	−1.51247	+	1.26911i
$536$		0			0
$537$	175342.	+	1.53616e6i	0.0262391	+	0.229880i
$538$		0			0
$539$	−7.44599e6			−1.10395
$540$		0			0
$541$	1.07747e6			0.158275			0.0791376	−	0.996864i	$-0.474783\pi$
$541$	1.07747e6			0.158275			0.0791376	+	0.996864i	$0.474783\pi$
$542$		0			0
$543$	6.96864e6	−	5.15873e6i	1.01426	−	0.750833i
$544$		0			0
$545$	1.38614e7	−	1.16311e7i	1.99902	−	1.67738i
$546$		0			0
$547$	−2.44692e6	+	890605.i	−0.349664	+	0.127267i	−0.510880	−	0.859652i	$-0.670680\pi$
$547$	−2.44692e6	+	890605.i	−0.349664	+	0.127267i	0.161217	+	0.986919i	$0.448458\pi$
$548$		0			0
$549$	3.19614e6	+	1.62686e6i	0.452579	+	0.230367i
$550$		0			0
$551$	−3.09167e6	−	2.59422e6i	−0.433825	−	0.364022i
$552$		0			0
$553$	−69056.3	−	391637.i	−0.00960263	−	0.0544592i
$554$		0			0
$555$	−8.48620e6	−	8.04980e6i	−1.16945	−	1.10931i
$556$		0			0
$557$	6.11584e6	+	1.05929e7i	0.835253	+	1.44670i	0.893824	+	0.448418i	$0.148012\pi$
$557$	6.11584e6	+	1.05929e7i	0.835253	+	1.44670i	−0.0585707	+	0.998283i	$0.518654\pi$
$558$		0			0
$559$	509800.	−	882999.i	0.0690034	−	0.119517i
$560$		0			0
$561$	1.85824e6	−	2.80874e6i	0.249284	−	0.376795i
$562$		0			0
$563$	−1.01307e7	−	3.68727e6i	−1.34700	−	0.490268i	−0.434991	−	0.900435i	$-0.643248\pi$
$563$	−1.01307e7	−	3.68727e6i	−1.34700	−	0.490268i	−0.912011	+	0.410166i	$0.865471\pi$
$564$		0			0
$565$	−1.35197e6	+	7.66739e6i	−0.178174	+	1.01048i
$566$		0			0
$567$	69682.3	+	242262.i	0.00910258	+	0.0316467i
$568$		0			0
$569$	442234.	−	2.50804e6i	0.0572627	−	0.324753i	−0.942698	−	0.333648i	$-0.891720\pi$
$569$	442234.	−	2.50804e6i	0.0572627	−	0.324753i	0.999960	+	0.00889505i	$0.00283142\pi$
$570$		0			0
$571$	1.00007e7	+	3.63995e6i	1.28363	+	0.467203i	0.891631	−	0.452763i	$-0.149562\pi$
$571$	1.00007e7	+	3.63995e6i	1.28363	+	0.467203i	0.391998	+	0.919966i	$0.371784\pi$
$572$		0			0
$573$	6.95086e6	−	1.05063e7i	0.884406	−	1.33679i
$574$		0			0
$575$	2.19316e6	−	3.79866e6i	0.276631	−	0.479139i
$576$		0			0
$577$	1.13203e6	+	1.96073e6i	0.141552	+	0.245176i	0.928081	−	0.372378i	$-0.121457\pi$
$577$	1.13203e6	+	1.96073e6i	0.141552	+	0.245176i	−0.786529	+	0.617553i	$0.788124\pi$
$578$		0			0
$579$	−4.58312e6	−	4.34743e6i	−0.568152	−	0.538935i
$580$		0			0
$581$	32919.6	+	186696.i	0.00404589	+	0.0229454i
$582$		0			0
$583$	−4.96652e6	−	4.16741e6i	−0.605175	−	0.507802i
$584$		0			0
$585$	−882954.	−	1.67168e7i	−0.106672	−	2.01959i
$586$		0			0
$587$	−387154.	+	140913.i	−0.0463755	+	0.0168793i	−0.365104	−	0.930967i	$-0.618966\pi$
$587$	−387154.	+	140913.i	−0.0463755	+	0.0168793i	0.318728	+	0.947846i	$0.396744\pi$
$588$		0			0
$589$	−1.08096e6	+	907032.i	−0.128387	+	0.107729i
$590$		0			0
$591$	6.52971e6	−	4.83380e6i	0.768998	−	0.569272i
$592$		0			0
$593$	8.45756e6			0.987662			0.493831	−	0.869558i	$-0.335596\pi$
$593$	8.45756e6			0.987662			0.493831	+	0.869558i	$0.335596\pi$
$594$		0			0
$595$	222779.			0.0257978
$596$		0			0
$597$	569865.	+	4.99256e6i	0.0654389	+	0.573307i
$598$		0			0
$599$	−1.16637e7	+	9.78699e6i	−1.32822	+	1.11451i	−0.343725	+	0.939071i	$0.611689\pi$
$599$	−1.16637e7	+	9.78699e6i	−1.32822	+	1.11451i	−0.984491	+	0.175435i	$0.943867\pi$
$600$		0			0
$601$	7.86028e6	−	2.86091e6i	0.887670	−	0.323086i	0.142369	−	0.989814i	$-0.454528\pi$
$601$	7.86028e6	−	2.86091e6i	0.887670	−	0.323086i	0.745301	+	0.666728i	$0.232306\pi$
$602$		0			0
$603$	−2.47586e6	+	3.28837e6i	−0.277289	+	0.368288i
$604$		0			0
$605$	2.92560e6	+	2.45487e6i	0.324958	+	0.272672i
$606$		0			0
$607$	−212833.	−	1.20703e6i	−0.0234459	−	0.132968i	0.970838	−	0.239736i	$-0.0770609\pi$
$607$	−212833.	−	1.20703e6i	−0.0234459	−	0.132968i	−0.994284	+	0.106768i	$0.965950\pi$
$608$		0			0
$609$	−115767.	+	482641.i	−0.0126486	+	0.0527328i
$610$		0			0
$611$	9.34741e6	+	1.61902e7i	1.01295	+	1.75448i
$612$		0			0
$613$	−6.16287e6	+	1.06744e7i	−0.662418	+	1.14734i	0.317560	+	0.948238i	$0.397136\pi$
$613$	−6.16287e6	+	1.06744e7i	−0.662418	+	1.14734i	−0.979978	+	0.199104i	$0.936197\pi$
$614$		0			0
$615$	1.17711e7	+	2.35970e7i	1.25496	+	2.51576i
$616$		0			0
$617$	−2.53339e6	−	922079.i	−0.267910	−	0.0975114i	0.204572	−	0.978852i	$-0.434420\pi$
$617$	−2.53339e6	−	922079.i	−0.267910	−	0.0975114i	−0.472482	+	0.881340i	$0.656642\pi$
$618$		0			0
$619$	−1.65276e6	+	9.37327e6i	−0.173374	+	0.983251i	0.766631	+	0.642088i	$0.221932\pi$
$619$	−1.65276e6	+	9.37327e6i	−0.173374	+	0.983251i	−0.940004	+	0.341163i	$0.889179\pi$
$620$		0			0
$621$	16140.2	−	1.98949e6i	0.00167950	−	0.207020i
$622$		0			0
$623$	14261.3	−	80880.1i	0.00147211	−	0.00834875i
$624$		0			0
$625$	−3.18374e7	−	1.15879e7i	−3.26015	−	1.18660i
$626$		0			0
$627$	−3.73427e6	−	227631.i	−0.379348	−	0.0231239i
$628$		0			0
$629$	−1.70598e6	+	2.95484e6i	−0.171928	+	0.297788i
$630$		0			0
$631$	−4.87406e6	−	8.44212e6i	−0.487324	−	0.844070i	0.512570	−	0.858645i	$-0.328694\pi$
$631$	−4.87406e6	−	8.44212e6i	−0.487324	−	0.844070i	−0.999894	+	0.0145758i	$0.995360\pi$
$632$		0			0
$633$	1.27324e7	−	3.77435e6i	1.26300	−	0.374398i
$634$		0			0
$635$	5.88249e6	+	3.33613e7i	0.578931	+	3.28328i
$636$		0			0
$637$	8.27036e6	+	6.93966e6i	0.807562	+	0.677625i
$638$		0			0
$639$	−4.21325e6	+	1.38011e7i	−0.408193	+	1.33710i
$640$		0			0
$641$	1.62414e7	−	5.91138e6i	1.56127	−	0.568256i	0.590243	−	0.807225i	$-0.299032\pi$
$641$	1.62414e7	−	5.91138e6i	1.56127	−	0.568256i	0.971027	+	0.238969i	$0.0768095\pi$
$642$		0			0
$643$	−5.13832e6	+	4.31156e6i	−0.490110	+	0.411251i	−0.854066	−	0.520165i	$-0.825870\pi$
$643$	−5.13832e6	+	4.31156e6i	−0.490110	+	0.411251i	0.363956	+	0.931416i	$0.381426\pi$
$644$		0			0
$645$	−2.42839e6	−	1.05530e6i	−0.229837	−	0.0998799i
$646$		0			0
$647$	1.08528e6			0.101925			0.0509624	−	0.998701i	$-0.483771\pi$
$647$	1.08528e6			0.101925			0.0509624	+	0.998701i	$0.483771\pi$
$648$		0			0
$649$	1.78057e7			1.65939
$650$		0			0
$651$	159156.	+	69164.3i	0.0147187	+	0.00639631i
$652$		0			0
$653$	3.49003e6	−	2.92848e6i	0.320292	−	0.268757i	−0.468438	−	0.883496i	$-0.655183\pi$
$653$	3.49003e6	−	2.92848e6i	0.320292	−	0.268757i	0.788730	+	0.614739i	$0.210739\pi$
$654$		0			0
$655$	−1.98334e7	+	7.21878e6i	−1.80632	+	0.657447i
$656$		0			0
$657$	−4.37939e6	+	1.01295e6i	−0.395822	+	0.0915534i
$658$		0			0
$659$	1.05618e7	+	8.86244e6i	0.947384	+	0.794950i	0.978855	−	0.204555i	$-0.0655747\pi$
$659$	1.05618e7	+	8.86244e6i	0.947384	+	0.794950i	−0.0314710	+	0.999505i	$0.510019\pi$
$660$		0			0
$661$	−8598.59	−	48765.0i	−0.000765462	−	0.00434115i	0.984423	−	0.175818i	$-0.0562571\pi$
$661$	−8598.59	−	48765.0i	−0.000765462	−	0.00434115i	−0.985188	+	0.171477i	$0.945146\pi$
$662$		0			0
$663$	−4.68172e6	+	1.38783e6i	−0.413639	+	0.122618i
$664$		0			0
$665$	−123740.	−	214324.i	−0.0108506	−	0.0187939i
$666$		0			0
$667$	1.95862e6	−	3.39244e6i	0.170466	−	0.295255i
$668$		0			0
$669$	−1.78306e7	−	1.08691e6i	−1.54029	−	0.0938916i
$670$		0			0
$671$	6.15087e6	+	2.23873e6i	0.527388	+	0.191954i
$672$		0			0
$673$	−785552.	+	4.45509e6i	−0.0668555	+	0.379156i	0.932961	+	0.359979i	$0.117216\pi$
$673$	−785552.	+	4.45509e6i	−0.0668555	+	0.379156i	−0.999816	+	0.0191779i	$0.993895\pi$
$674$		0			0
$675$	−3.11976e7	+	5.24038e6i	−2.63549	+	0.442694i
$676$		0			0
$677$	−1.83799e6	+	1.04237e7i	−0.154124	+	0.874082i	0.805458	+	0.592653i	$0.201919\pi$
$677$	−1.83799e6	+	1.04237e7i	−0.154124	+	0.874082i	−0.959582	+	0.281429i	$0.909192\pi$
$678$		0			0
$679$	285890.	+	104056.i	0.0237972	+	0.00866146i
$680$		0			0
$681$	6.93941e6	+	1.39112e7i	0.573396	+	1.14947i
$682$		0			0
$683$	3.05141e6	−	5.28521e6i	0.250293	−	0.433521i	−0.713313	−	0.700845i	$-0.752806\pi$
$683$	3.05141e6	−	5.28521e6i	0.250293	−	0.433521i	0.963607	+	0.267325i	$0.0861396\pi$
$684$		0			0
$685$	−9.03648e6	−	1.56517e7i	−0.735823	−	1.27448i
$686$		0			0
$687$	5.25595e6	−	2.19124e7i	0.424874	−	1.77132i
$688$		0			0
$689$	1.63236e6	+	9.25759e6i	0.130999	+	0.742934i
$690$		0			0
$691$	1.14705e7	+	9.62490e6i	0.913876	+	0.766833i	0.972853	−	0.231426i	$-0.0743391\pi$
$691$	1.14705e7	+	9.62490e6i	0.913876	+	0.766833i	−0.0589760	+	0.998259i	$0.518784\pi$
$692$		0			0
$693$	179945.	+	423442.i	0.0142333	+	0.0334935i
$694$		0			0
$695$	2.71003e7	−	9.86371e6i	2.12820	−	0.774602i
$696$		0			0
$697$	5.89252e6	−	4.94441e6i	0.459430	−	0.385507i
$698$		0			0
$699$	−496191.	−	4.34710e6i	−0.0384110	−	0.336517i
$700$		0			0
$701$	2.75313e6			0.211608			0.105804	−	0.994387i	$-0.466258\pi$
$701$	2.75313e6			0.211608			0.105804	+	0.994387i	$0.466258\pi$
$702$		0			0
$703$	3.79025e6			0.289254
$704$		0			0
$705$	3.90199e7	−	2.88856e7i	2.95675	−	2.18881i
$706$		0			0
$707$	169728.	−	142419.i	0.0127704	−	0.0107157i
$708$		0			0
$709$	−2.20559e7	+	8.02770e6i	−1.64782	+	0.599757i	−0.988380	−	0.152001i	$-0.951428\pi$
$709$	−2.20559e7	+	8.02770e6i	−1.64782	+	0.599757i	−0.659439	+	0.751758i	$0.729206\pi$
$710$		0			0
$711$	1.89794e7	−	1.23364e7i	1.40802	−	0.915196i
$712$		0			0
$713$	−1.04918e6	−	880368.i	−0.0772906	−	0.0648545i
$714$		0			0
$715$	−5.30549e6	−	3.00890e7i	−0.388115	−	2.20111i
$716$		0			0
$717$	−8.57198e6	−	8.13117e6i	−0.622706	−	0.590684i
$718$		0			0
$719$	−3.08542e6	−	5.34410e6i	−0.222583	−	0.385525i	0.733009	−	0.680219i	$-0.238115\pi$
$719$	−3.08542e6	−	5.34410e6i	−0.222583	−	0.385525i	−0.955592	+	0.294694i	$0.904782\pi$
$720$		0			0
$721$	229755.	−	397948.i	0.0164599	−	0.0285094i
$722$		0			0
$723$	−8.59130e6	+	1.29858e7i	−0.611242	+	0.923897i
$724$		0			0
$725$	−5.85294e7	−	2.13029e7i	−4.13551	−	1.50520i
$726$		0			0
$727$	−1.28434e6	+	7.28387e6i	−0.0901249	+	0.511124i	0.906008	+	0.423261i	$0.139115\pi$
$727$	−1.28434e6	+	7.28387e6i	−0.0901249	+	0.511124i	−0.996133	+	0.0878625i	$0.971996\pi$
$728$		0			0
$729$	−1.11401e7	+	9.04375e6i	−0.776372	+	0.630274i
$730$		0			0
$731$	−134118.	+	760624.i	−0.00928315	+	0.0526473i
$732$		0			0
$733$	6.48069e6	+	2.35878e6i	0.445514	+	0.162154i	0.555028	−	0.831831i	$-0.312707\pi$
$733$	6.48069e6	+	2.35878e6i	0.445514	+	0.162154i	−0.109514	+	0.993985i	$0.534930\pi$
$734$		0			0
$735$	1.54696e7	−	2.33824e7i	1.05623	−	1.59650i
$736$		0			0
$737$	−3.75634e6	+	6.50618e6i	−0.254740	+	0.441222i
$738$		0			0
$739$	−1.18607e7	−	2.05433e7i	−0.798910	−	1.38375i	−0.920326	−	0.391152i	$-0.872077\pi$
$739$	−1.18607e7	−	2.05433e7i	−0.798910	−	1.38375i	0.121416	−	0.992602i	$-0.461257\pi$
$740$		0			0
$741$	3.93556e6	+	3.73317e6i	0.263306	+	0.249766i
$742$		0			0
$743$	2.45138e6	+	1.39025e7i	0.162907	+	0.923889i	0.951197	+	0.308585i	$0.0998555\pi$
$743$	2.45138e6	+	1.39025e7i	0.162907	+	0.923889i	−0.788290	+	0.615304i	$0.789033\pi$
$744$		0			0
$745$	1.58983e7	+	1.33403e7i	1.04945	+	0.880589i
$746$		0			0
$747$	−9.04759e6	+	5.88084e6i	−0.593242	+	0.385601i
$748$		0			0
$749$	−489480.	+	178156.i	−0.0318809	+	0.0116037i
$750$		0			0
$751$	5.93985e6	−	4.98412e6i	0.384304	−	0.322470i	−0.430085	−	0.902788i	$-0.641516\pi$
$751$	5.93985e6	−	4.98412e6i	0.384304	−	0.322470i	0.814389	+	0.580319i	$0.197072\pi$
$752$		0			0
$753$	−2.33645e6	+	1.72963e6i	−0.150165	+	0.111164i
$754$		0			0
$755$	1.69738e7			1.08370
$756$		0			0
$757$	−2.39155e6			−0.151684			−0.0758420	−	0.997120i	$-0.524164\pi$
$757$	−2.39155e6			−0.151684			−0.0758420	+	0.997120i	$0.524164\pi$
$758$		0			0
$759$	−411805.	−	3.60780e6i	−0.0259470	−	0.227320i
$760$		0			0
$761$	−4.03192e6	+	3.38319e6i	−0.252377	+	0.211770i	−0.760195	−	0.649695i	$-0.774897\pi$
$761$	−4.03192e6	+	3.38319e6i	−0.252377	+	0.211770i	0.507818	+	0.861464i	$0.330452\pi$
$762$		0			0
$763$	677599.	−	246626.i	0.0421368	−	0.0153365i
$764$		0			0
$765$	4.95957e6	+	1.16707e7i	0.306401	+	0.721015i
$766$		0			0
$767$	−1.97771e7	−	1.65949e7i	−1.21387	−	1.01856i
$768$		0			0
$769$	4.21546e6	+	2.39071e7i	0.257057	+	1.45784i	0.790737	+	0.612156i	$0.209698\pi$
$769$	4.21546e6	+	2.39071e7i	0.257057	+	1.45784i	−0.533680	+	0.845687i	$0.679191\pi$
$770$		0			0
$771$	3.68486e6	−	1.53624e7i	0.223247	−	0.930729i
$772$		0			0
$773$	6.07327e6	+	1.05192e7i	0.365573	+	0.633191i	0.988868	−	0.148796i	$-0.0475397\pi$
$773$	6.07327e6	+	1.05192e7i	0.365573	+	0.633191i	−0.623295	+	0.781987i	$0.714206\pi$
$774$		0			0
$775$	−1.08886e7	+	1.88597e7i	−0.651207	+	1.12792i
$776$		0			0
$777$	−208068.	−	417106.i	−0.0123638	−	0.0247853i
$778$		0			0
$779$	−8.02967e6	−	2.92256e6i	−0.474083	−	0.172552i
$780$		0			0
$781$	−4.57332e6	+	2.59366e7i	−0.268290	+	1.52155i
$782$		0			0
$783$	−2.78613e7	+	4.67998e6i	−1.62404	+	0.272797i
$784$		0			0
$785$	9.01321e6	−	5.11165e7i	0.522042	−	2.96065i
$786$		0			0
$787$	1.36692e7	+	4.97520e6i	0.786697	+	0.286334i	0.703962	−	0.710237i	$-0.251412\pi$
$787$	1.36692e7	+	4.97520e6i	0.786697	+	0.286334i	0.0827347	+	0.996572i	$0.473635\pi$
$788$		0			0
$789$	2.45206e7	+	1.49470e6i	1.40229	+	0.0854797i
$790$		0			0
$791$	−155131.	+	268695.i	−0.00881572	+	0.0152693i
$792$		0			0
$793$	−4.74536e6	−	8.21920e6i	−0.267970	−	0.464137i
$794$		0			0
$795$	2.34051e7	−	6.93810e6i	1.31338	−	0.389335i
$796$		0			0
$797$	−2.83721e6	−	1.60906e7i	−0.158214	−	0.897277i	−0.955788	−	0.294056i	$-0.904995\pi$
$797$	−2.83721e6	−	1.60906e7i	−0.158214	−	0.897277i	0.797574	−	0.603221i	$-0.206116\pi$
$798$		0			0
$799$	−1.08484e7	−	9.10285e6i	−0.601170	−	0.504441i
$800$		0			0
$801$	4.55455e6	−	1.05347e6i	0.250821	−	0.0580148i
$802$		0			0
$803$	−7.70927e6	+	2.80595e6i	−0.421915	+	0.153564i
$804$		0			0
$805$	184007.	−	154400.i	0.0100080	−	0.00839767i
$806$		0			0
$807$	1.80739e7	+	7.85438e6i	0.976943	+	0.424549i
$808$		0			0
$809$	−1.09868e7			−0.590203			−0.295101	−	0.955466i	$-0.595353\pi$
$809$	−1.09868e7			−0.590203			−0.295101	+	0.955466i	$0.595353\pi$
$810$		0			0
$811$	3.23848e7			1.72897			0.864487	−	0.502655i	$-0.167643\pi$
$811$	3.23848e7			1.72897			0.864487	+	0.502655i	$0.167643\pi$
$812$		0			0
$813$	−9.78911e6	−	4.25405e6i	−0.519418	−	0.225723i
$814$		0			0
$815$	1.33107e6	−	1.11690e6i	0.0701952	−	0.0589008i
$816$		0			0
$817$	806249.	−	293451.i	0.0422585	−	0.0153808i
$818$		0			0
$819$	194780.	−	638031.i	0.0101469	−	0.0332378i
$820$		0			0
$821$	1.76175e7	+	1.47829e7i	0.912194	+	0.765421i	0.972535	−	0.232756i	$-0.0747745\pi$
$821$	1.76175e7	+	1.47829e7i	0.912194	+	0.765421i	−0.0603413	+	0.998178i	$0.519219\pi$
$822$		0			0
$823$	−4.65842e6	−	2.64192e7i	−0.239739	−	1.35963i	−0.832399	−	0.554177i	$-0.813033\pi$
$823$	−4.65842e6	−	2.64192e7i	−0.239739	−	1.35963i	0.592660	−	0.805453i	$-0.298078\pi$
$824$		0			0
$825$	−5.53568e7	+	1.64097e7i	−2.83163	+	0.839396i
$826$		0			0
$827$	−4.58500e6	−	7.94146e6i	−0.233118	−	0.403772i	0.725606	−	0.688110i	$-0.241559\pi$
$827$	−4.58500e6	−	7.94146e6i	−0.233118	−	0.403772i	−0.958724	+	0.284338i	$0.908226\pi$
$828$		0			0
$829$	1.01005e7	−	1.74946e7i	0.510455	−	0.884134i	−0.489471	−	0.872019i	$-0.662810\pi$
$829$	1.01005e7	−	1.74946e7i	0.510455	−	0.884134i	0.999927	−	0.0121149i	$-0.00385639\pi$
$830$		0			0
$831$	2.77089e7	+	1.68906e6i	1.39193	+	0.0848481i
$832$		0			0
$833$	−7.68502e6	−	2.79712e6i	−0.383736	−	0.139668i
$834$		0			0
$835$	4.57274e6	−	2.59333e7i	0.226966	−	1.28719i
$836$		0			0
$837$	−80133.1	+	9.87745e6i	−0.00395365	+	0.487339i
$838$		0			0
$839$	1.75344e6	−	9.94424e6i	0.0859974	−	0.487716i	−0.911139	−	0.412098i	$-0.864796\pi$
$839$	1.75344e6	−	9.94424e6i	0.0859974	−	0.487716i	0.997137	−	0.0756175i	$-0.0240928\pi$
$840$		0			0
$841$	−3.29961e7	−	1.20096e7i	−1.60869	−	0.585515i
$842$		0			0
$843$	−7.63673e6	−	1.53091e7i	−0.370117	−	0.741959i
$844$		0			0
$845$	−2.26217e6	+	3.91819e6i	−0.108989	+	0.188774i
$846$		0			0
$847$	76096.4	+	131803.i	0.00364465	+	0.00631272i
$848$		0			0
$849$	−3.51232e6	+	1.46431e7i	−0.167234	+	0.697208i
$850$		0			0
$851$	638822.	+	3.62294e6i	0.0302382	+	0.171489i
$852$		0			0
$853$	2.07128e7	+	1.73801e7i	0.974691	+	0.817863i	0.983280	−	0.182100i	$-0.0582896\pi$
$853$	2.07128e7	+	1.73801e7i	0.974691	+	0.817863i	−0.00858901	+	0.999963i	$0.502734\pi$
$854$		0			0
$855$	8.47304e6	−	1.12537e7i	0.396391	−	0.526477i
$856$		0			0
$857$	−6.18729e6	+	2.25199e6i	−0.287772	+	0.104740i	−0.481873	−	0.876241i	$-0.660043\pi$
$857$	−6.18729e6	+	2.25199e6i	−0.287772	+	0.104740i	0.194101	+	0.980982i	$0.437821\pi$
$858$		0			0
$859$	−2.86976e6	+	2.40801e6i	−0.132697	+	0.111346i	−0.706721	−	0.707493i	$-0.749826\pi$
$859$	−2.86976e6	+	2.40801e6i	−0.132697	+	0.111346i	0.574023	+	0.818839i	$0.305382\pi$
$860$		0			0
$861$	119174.	+	1.04408e6i	0.00547866	+	0.0479982i
$862$		0			0
$863$	1.18247e7			0.540458			0.270229	−	0.962796i	$-0.412901\pi$
$863$	1.18247e7			0.540458			0.270229	+	0.962796i	$0.412901\pi$
$864$		0			0
$865$	7.67314e7			3.48685
$866$		0			0
$867$	−1.48164e7	+	1.09682e7i	−0.669413	+	0.495551i
$868$		0			0
$869$	3.16488e7	−	2.65565e7i	1.42170	−	1.19295i
$870$		0			0
$871$	1.02360e7	−	3.72559e6i	0.457177	−	0.166399i
$872$		0			0
$873$	913411.	+	1.72935e7i	0.0405630	+	0.767973i
$874$		0			0
$875$	−1.83097e6	−	1.53637e6i	−0.0808466	−	0.0678383i
$876$		0			0
$877$	−1.96926e6	−	1.11682e7i	−0.0864578	−	0.490327i	−0.997032	−	0.0769820i	$-0.975472\pi$
$877$	−1.96926e6	−	1.11682e7i	−0.0864578	−	0.490327i	0.910575	−	0.413345i	$-0.135640\pi$
$878$		0			0
$879$	−2.32148e7	−	2.20209e7i	−1.01343	−	0.961311i
$880$		0			0
$881$	−1.96923e6	−	3.41080e6i	−0.0854784	−	0.148053i	0.820117	−	0.572196i	$-0.193909\pi$
$881$	−1.96923e6	−	3.41080e6i	−0.0854784	−	0.148053i	−0.905595	+	0.424144i	$0.860575\pi$
$882$		0			0
$883$	−5.88849e6	+	1.01992e7i	−0.254157	+	0.440213i	−0.964666	−	0.263475i	$-0.915131\pi$
$883$	−5.88849e6	+	1.01992e7i	−0.254157	+	0.440213i	0.710509	+	0.703688i	$0.248465\pi$
$884$		0			0
$885$	−3.69926e7	+	5.59146e7i	−1.58766	+	2.39976i
$886$		0			0
$887$	−3.43239e7	−	1.24929e7i	−1.46483	−	0.533155i	−0.518139	−	0.855296i	$-0.673375\pi$
$887$	−3.43239e7	−	1.24929e7i	−1.46483	−	0.533155i	−0.946692	+	0.322141i	$0.895597\pi$
$888$		0			0
$889$	−234420.	+	1.32946e6i	−0.00994809	+	0.0564184i
$890$		0			0
$891$	−1.81769e7	+	1.88536e7i	−0.767051	+	0.795608i
$892$		0			0
$893$	−2.73178e6	+	1.54927e7i	−0.114635	+	0.650126i
$894$		0			0
$895$	−9.98459e6	−	3.63410e6i	−0.416651	−	0.151649i
$896$		0			0
$897$	−2.90507e6	+	4.39103e6i	−0.120552	+	0.182216i
$898$		0			0
$899$	−9.72421e6	+	1.68428e7i	−0.401287	+	0.695049i
$900$		0			0
$901$	−3.56045e6	−	6.16689e6i	−0.146114	−	0.253078i
$902$		0			0
$903$	−76552.9	−	72616.2i	−0.00312422	−	0.00296356i
$904$		0			0
$905$	1.03467e7	+	5.86792e7i	0.419935	+	2.38157i
$906$		0			0
$907$	−1.88953e7	−	1.58551e7i	−0.762670	−	0.639956i	0.176151	−	0.984363i	$-0.443635\pi$
$907$	−1.88953e7	−	1.58551e7i	−0.762670	−	0.639956i	−0.938820	+	0.344407i	$0.888080\pi$
$908$		0			0
$909$	1.12394e7	+	5.72098e6i	0.451164	+	0.229647i
$910$		0			0
$911$	−3.67345e7	+	1.33703e7i	−1.46649	+	0.533758i	−0.947144	−	0.320808i	$-0.896046\pi$
$911$	−3.67345e7	+	1.33703e7i	−1.46649	+	0.533758i	−0.519343	+	0.854566i	$0.673823\pi$
$912$		0			0
$913$	−1.50872e7	+	1.26597e7i	−0.599006	+	0.502626i
$914$		0			0
$915$	−1.98091e7	+	1.46642e7i	−0.782189	+	0.579037i
$916$		0			0
$917$	−841094.			−0.0330310
$918$		0			0
$919$	−1.95110e7			−0.762063			−0.381031	−	0.924562i	$-0.624431\pi$
$919$	−1.95110e7			−0.762063			−0.381031	+	0.924562i	$0.624431\pi$
$920$		0			0
$921$	1.97718e6	+	1.73220e7i	0.0768064	+	0.672896i
$922$		0			0
$923$	2.92525e7	−	2.45458e7i	1.13021	−	0.948359i
$924$		0			0
$925$	5.49670e7	−	2.00064e7i	2.11226	−	0.768801i
$926$		0			0
$927$	2.59622e7	+	3.17696e6i	0.992297	+	0.121426i
$928$		0			0
$929$	−2.99867e7	−	2.51618e7i	−1.13996	−	0.956540i	−0.140523	−	0.990077i	$-0.544878\pi$
$929$	−2.99867e7	−	2.51618e7i	−1.13996	−	0.956540i	−0.999437	+	0.0335374i	$0.989323\pi$
$930$		0			0
$931$	1.57759e6	+	8.94696e6i	0.0596513	+	0.338299i
$932$		0			0
$933$	−1.82440e6	+	7.60604e6i	−0.0686146	+	0.286058i
$934$		0			0
$935$	1.15722e7	+	2.00436e7i	0.432898	+	0.749801i
$936$		0			0
$937$	1.27358e7	−	2.20591e7i	0.473890	−	0.820802i	−0.525663	−	0.850693i	$-0.676183\pi$
$937$	1.27358e7	−	2.20591e7i	0.473890	−	0.820802i	0.999553	+	0.0298911i	$0.00951606\pi$
$938$		0			0
$939$	9.00878e6	+	1.80596e7i	0.333428	+	0.668410i
$940$		0			0
$941$	−1.50394e7	−	5.47388e6i	−0.553675	−	0.201521i	0.0500034	−	0.998749i	$-0.484077\pi$
$941$	−1.50394e7	−	5.47388e6i	−0.553675	−	0.201521i	−0.603679	+	0.797228i	$0.706299\pi$
$942$		0			0
$943$	1.44020e6	−	8.16780e6i	0.0527406	−	0.299107i
$944$		0			0
$945$	−1.70357e6	−	314655.i	−0.0620554	−	0.0114619i
$946$		0			0
$947$	2.54893e6	−	1.44557e7i	0.0923598	−	0.523799i	−0.903165	−	0.429294i	$-0.858762\pi$
$947$	2.54893e6	−	1.44557e7i	0.0923598	−	0.523799i	0.995524	−	0.0945043i	$-0.0301266\pi$
$948$		0			0
$949$	1.11779e7	+	4.06844e6i	0.402899	+	0.146643i
$950$		0			0
$951$	2.61682e7	+	1.59514e6i	0.938260	+	0.0571937i
$952$		0			0
$953$	−975361.	+	1.68937e6i	−0.0347883	+	0.0602551i	−0.882895	−	0.469570i	$-0.844409\pi$
$953$	−975361.	+	1.68937e6i	−0.0347883	+	0.0602551i	0.848107	+	0.529825i	$0.177742\pi$
$954$		0			0
$955$	4.32863e7	+	7.49741e7i	1.53583	+	2.66013i
$956$		0			0
$957$	−4.94369e7	+	1.46549e7i	−1.74490	+	0.517253i
$958$		0			0
$959$	−125064.	−	709274.i	−0.00439123	−	0.0249039i
$960$		0			0
$961$	−1.67222e7	−	1.40316e7i	−0.584097	−	0.490116i
$962$		0			0
$963$	−2.02300e7	−	2.16762e7i	−0.702960	−	0.753213i
$964$		0			0
$965$	4.07941e7	−	1.48479e7i	1.41020	−	0.513269i
$966$		0			0
$967$	−2.03651e7	+	1.70883e7i	−0.700358	+	0.587670i	−0.921876	−	0.387486i	$-0.873344\pi$
$967$	−2.03651e7	+	1.70883e7i	−0.700358	+	0.587670i	0.221517	+	0.975156i	$0.428899\pi$
$968$		0			0
$969$	−3.76864e6	−	1.63773e6i	−0.128936	−	0.0560317i
$970$		0			0
$971$	5.11477e7			1.74092			0.870458	−	0.492242i	$-0.163823\pi$
$971$	5.11477e7			1.74092			0.870458	+	0.492242i	$0.163823\pi$
$972$		0			0
$973$	1.14927e6			0.0389170
$974$		0			0
$975$	7.67794e7	+	3.33659e7i	2.58662	+	1.12407i
$976$		0			0
$977$	3.06081e6	−	2.56832e6i	0.102589	−	0.0860821i	−0.590051	−	0.807366i	$-0.700892\pi$
$977$	3.06081e6	−	2.56832e6i	0.102589	−	0.0860821i	0.692639	+	0.721284i	$0.256448\pi$
$978$		0			0
$979$	8.01763e6	−	2.91818e6i	0.267356	−	0.0973095i
$980$		0			0
$981$	2.80049e7	+	3.00069e7i	0.929098	+	0.995518i
$982$		0			0
$983$	−2.59484e7	−	2.17733e7i	−0.856497	−	0.718687i	0.104713	−	0.994502i	$-0.466608\pi$
$983$	−2.59484e7	−	2.17733e7i	−0.856497	−	0.718687i	−0.961211	+	0.275816i	$0.911052\pi$
$984$		0			0
$985$	9.69502e6	+	5.49832e7i	0.318389	+	1.80567i
$986$		0			0
$987$	1.85489e6	−	549855.i	0.0606072	−	0.0179662i
$988$		0			0
$989$	416385.	+	721200.i	0.0135364	+	0.0234458i
$990$		0			0
$991$	−4.99176e6	+	8.64598e6i	−0.161462	+	0.279660i	−0.935393	−	0.353610i	$-0.884954\pi$
$991$	−4.99176e6	+	8.64598e6i	−0.161462	+	0.279660i	0.773931	+	0.633269i	$0.218287\pi$
$992$		0			0
$993$	−2.03963e7	−	1.24330e6i	−0.656414	−	0.0400131i
$994$		0			0
$995$	−3.24502e7	−	1.18109e7i	−1.03911	−	0.378203i
$996$		0			0
$997$	−4.79955e6	+	2.72196e7i	−0.152919	+	0.867249i	0.807744	+	0.589534i	$0.200688\pi$
$997$	−4.79955e6	+	2.72196e7i	−0.152919	+	0.867249i	−0.960663	+	0.277716i	$0.910423\pi$
$998$		0			0
$999$	1.72189e7	−	2.01858e7i	0.545872	−	0.639929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.25.3	yes	90
3.2	odd	2		324.6.i.a.73.1		90
27.13	even	9	inner	108.6.i.a.13.3	✓	90
27.14	odd	18		324.6.i.a.253.1		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.3	✓	90	27.13	even	9	inner
108.6.i.a.25.3	yes	90	1.1	even	1	trivial
324.6.i.a.73.1		90	3.2	odd	2
324.6.i.a.253.1		90	27.14	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.2968 - 6.21296i) q^{3} +(82.0644 - 68.8602i) q^{5} +(4.01162 - 1.46011i) q^{7} +(165.798 + 177.651i) q^{9} +O(q^{10})\)	\(q+(-14.2968 - 6.21296i) q^{3} +(82.0644 - 68.8602i) q^{5} +(4.01162 - 1.46011i) q^{7} +(165.798 + 177.651i) q^{9} +(339.748 + 285.083i) q^{11} +(-111.666 - 633.290i) q^{13} +(-1601.09 + 474.620i) q^{15} +(243.562 + 421.862i) q^{17} +(270.567 - 468.636i) q^{19} +(-66.4250 - 4.04908i) q^{21} +(493.552 + 179.638i) q^{23} +(1450.19 - 8224.41i) q^{25} +(-1266.65 - 3569.94i) q^{27} +(1295.10 - 7344.90i) q^{29} +(-2450.39 - 891.870i) q^{31} +(-3086.12 - 6186.62i) q^{33} +(228.667 - 396.064i) q^{35} +(3502.14 + 6065.88i) q^{37} +(-2338.13 + 9747.82i) q^{39} +(-2742.06 - 15551.0i) q^{41} +(1214.60 + 1019.17i) q^{43} +(25839.2 + 3161.92i) q^{45} +(-27318.4 + 9943.09i) q^{47} +(-12860.9 + 10791.6i) q^{49} +(-861.155 - 7544.53i) q^{51} -14618.2 q^{53} +47512.1 q^{55} +(-6779.87 + 5018.98i) q^{57} +(30754.6 - 25806.2i) q^{59} +(13868.6 - 5047.76i) q^{61} +(924.509 + 470.584i) q^{63} +(-52772.3 - 44281.2i) q^{65} +(2941.46 + 16681.8i) q^{67} +(-5940.14 - 5634.67i) q^{69} +(29691.2 + 51426.7i) q^{71} +(-9248.99 + 16019.7i) q^{73} +(-71831.0 + 108573. i) q^{75} +(1779.19 + 647.573i) q^{77} +(16175.9 - 91738.3i) q^{79} +(-4070.82 + 58908.5i) q^{81} +(-7711.19 + 43732.3i) q^{83} +(49037.3 + 17848.1i) q^{85} +(-64149.4 + 96962.3i) q^{87} +(9618.93 - 16660.5i) q^{89} +(-1372.63 - 2377.47i) q^{91} +(29491.7 + 27975.1i) q^{93} +(-10066.4 - 57089.6i) q^{95} +(54592.7 + 45808.7i) q^{97} +(5684.46 + 107623. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 90 * q - 87 * q^5 + 330 * q^9	\( 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) \) 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

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