LMFDB - Embedded newform 108.6.i.a.25.2

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			25.2
Character	$\chi$	$=$	108.25
Dual form			108.6.i.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.7517 + 5.03867i) q^{3} +(8.41214 - 7.05862i) q^{5} +(-17.8438 + 6.49461i) q^{7} +(192.224 - 148.658i) q^{9} +O(q^{10})$	\(q+(-14.7517 + 5.03867i) q^{3} +(8.41214 - 7.05862i) q^{5} +(-17.8438 + 6.49461i) q^{7} +(192.224 - 148.658i) q^{9} +(-556.830 - 467.236i) q^{11} +(78.3887 + 444.565i) q^{13} +(-88.5270 + 146.512i) q^{15} +(757.378 + 1311.82i) q^{17} +(991.064 - 1716.57i) q^{19} +(230.502 - 185.715i) q^{21} +(4265.86 + 1552.65i) q^{23} +(-521.711 + 2958.77i) q^{25} +(-2086.58 + 3161.50i) q^{27} +(8.23610 - 46.7093i) q^{29} +(6711.24 + 2442.69i) q^{31} +(10568.4 + 4086.82i) q^{33} +(-104.261 + 180.586i) q^{35} +(5277.92 + 9141.62i) q^{37} +(-3396.38 - 6163.09i) q^{39} +(-1167.08 - 6618.85i) q^{41} +(-3228.52 - 2709.05i) q^{43} +(567.692 - 2607.36i) q^{45} +(8966.06 - 3263.38i) q^{47} +(-12598.7 + 10571.6i) q^{49} +(-17782.4 - 15535.3i) q^{51} +19856.9 q^{53} -7982.17 q^{55} +(-5970.60 + 30316.0i) q^{57} +(3466.76 - 2908.95i) q^{59} +(44738.0 - 16283.3i) q^{61} +(-2464.52 + 3901.03i) q^{63} +(3797.43 + 3186.42i) q^{65} +(-171.281 - 971.383i) q^{67} +(-70751.9 - 1409.84i) q^{69} +(-29479.9 - 51060.7i) q^{71} +(-27717.4 + 48007.9i) q^{73} +(-7212.17 - 46275.5i) q^{75} +(12970.5 + 4720.87i) q^{77} +(-16837.2 + 95488.5i) q^{79} +(14850.8 - 57151.0i) q^{81} +(11357.2 - 64409.9i) q^{83} +(15630.8 + 5689.14i) q^{85} +(113.856 + 730.538i) q^{87} +(24058.1 - 41669.9i) q^{89} +(-4286.02 - 7423.61i) q^{91} +(-111310. - 2218.03i) q^{93} +(-3779.67 - 21435.6i) q^{95} +(-46476.7 - 38998.6i) q^{97} +(-176494. - 7036.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−14.7517	+	5.03867i	−0.946320	+	0.323231i
$3$	−14.7517	+	5.03867i	−0.946320	+	0.323231i
$4$		0			0
$5$	8.41214	−	7.05862i	0.150481	−	0.126268i	−0.564439	−	0.825475i	$-0.690908\pi$
$5$	8.41214	−	7.05862i	0.150481	−	0.126268i	0.714920	+	0.699206i	$0.246463\pi$
$6$		0			0
$7$	−17.8438	+	6.49461i	−0.137639	+	0.0500966i	−0.409921	−	0.912121i	$-0.634444\pi$
$7$	−17.8438	+	6.49461i	−0.137639	+	0.0500966i	0.272282	+	0.962217i	$0.412222\pi$
$8$		0			0
$9$	192.224	−	148.658i	0.791043	−	0.611760i
$10$		0			0
$11$	−556.830	−	467.236i	−1.38753	−	1.16427i	−0.966331	−	0.257301i	$-0.917167\pi$
$11$	−556.830	−	467.236i	−1.38753	−	1.16427i	−0.421194	−	0.906971i	$-0.638389\pi$
$12$		0			0
$13$	78.3887	+	444.565i	0.128646	+	0.729586i	0.979075	+	0.203497i	$0.0652308\pi$
$13$	78.3887	+	444.565i	0.128646	+	0.729586i	−0.850430	+	0.526089i	$0.823658\pi$
$14$		0			0
$15$	−88.5270	+	146.512i	−0.101589	+	0.168130i
$16$		0			0
$17$	757.378	+	1311.82i	0.635609	+	1.10091i	0.986386	+	0.164448i	$0.0525843\pi$
$17$	757.378	+	1311.82i	0.635609	+	1.10091i	−0.350777	+	0.936459i	$0.614082\pi$
$18$		0			0
$19$	991.064	−	1716.57i	0.629822	−	1.09088i	−0.357765	−	0.933812i	$-0.616461\pi$
$19$	991.064	−	1716.57i	0.629822	−	1.09088i	0.987587	−	0.157072i	$-0.0502055\pi$
$20$		0			0
$21$	230.502	−	185.715i	0.114058	−	0.0918966i
$22$		0			0
$23$	4265.86	+	1552.65i	1.68146	+	0.612003i	0.993509	−	0.113751i	$-0.0362867\pi$
$23$	4265.86	+	1552.65i	1.68146	+	0.612003i	0.687954	+	0.725754i	$0.258509\pi$
$24$		0			0
$25$	−521.711	+	2958.77i	−0.166947	+	0.946806i
$26$		0			0
$27$	−2086.58	+	3161.50i	−0.550840	+	0.834611i
$28$		0			0
$29$	8.23610	−	46.7093i	0.00181856	−	0.0103135i	−0.983885	−	0.178803i	$-0.942778\pi$
$29$	8.23610	−	46.7093i	0.00181856	−	0.0103135i	0.985704	+	0.168489i	$0.0538888\pi$
$30$		0			0
$31$	6711.24	+	2442.69i	1.25429	+	0.456525i	0.881850	−	0.471530i	$-0.156298\pi$
$31$	6711.24	+	2442.69i	1.25429	+	0.456525i	0.372442	+	0.928055i	$0.378520\pi$
$32$		0			0
$33$	10568.4	+	4086.82i	1.68937	+	0.653282i
$34$		0			0
$35$	−104.261	+	180.586i	−0.0143864	+	0.0249181i
$36$		0			0
$37$	5277.92	+	9141.62i	0.633809	+	1.09779i	0.986766	+	0.162150i	$0.0518428\pi$
$37$	5277.92	+	9141.62i	0.633809	+	1.09779i	−0.352957	+	0.935639i	$0.614824\pi$
$38$		0			0
$39$	−3396.38	−	6163.09i	−0.357565	−	0.648839i
$40$		0			0
$41$	−1167.08	−	6618.85i	−0.108428	−	0.614926i	−0.989796	−	0.142495i	$-0.954488\pi$
$41$	−1167.08	−	6618.85i	−0.108428	−	0.614926i	0.881368	−	0.472431i	$-0.156623\pi$
$42$		0			0
$43$	−3228.52	−	2709.05i	−0.266276	−	0.223432i	0.499867	−	0.866102i	$-0.333382\pi$
$43$	−3228.52	−	2709.05i	−0.266276	−	0.223432i	−0.766143	+	0.642670i	$0.777827\pi$
$44$		0			0
$45$	567.692	−	2607.36i	0.0417909	−	0.191942i
$46$		0			0
$47$	8966.06	−	3263.38i	0.592048	−	0.215488i	−0.0285818	−	0.999591i	$-0.509099\pi$
$47$	8966.06	−	3263.38i	0.592048	−	0.215488i	0.620630	+	0.784103i	$0.286877\pi$
$48$		0			0
$49$	−12598.7	+	10571.6i	−0.749610	+	0.628997i
$50$		0			0
$51$	−17782.4	−	15535.3i	−0.957337	−	0.836362i
$52$		0			0
$53$	19856.9			0.971007			0.485504	−	0.874235i	$-0.338636\pi$
$53$	19856.9			0.971007			0.485504	+	0.874235i	$0.338636\pi$
$54$		0			0
$55$	−7982.17			−0.355807
$56$		0			0
$57$	−5970.60	+	30316.0i	−0.243406	+	1.23590i
$58$		0			0
$59$	3466.76	−	2908.95i	0.129656	−	0.108794i	−0.575654	−	0.817694i	$-0.695252\pi$
$59$	3466.76	−	2908.95i	0.129656	−	0.108794i	0.705310	+	0.708899i	$0.250808\pi$
$60$		0			0
$61$	44738.0	−	16283.3i	1.53940	−	0.560296i	0.573500	−	0.819206i	$-0.305585\pi$
$61$	44738.0	−	16283.3i	1.53940	−	0.560296i	0.965902	+	0.258910i	$0.0833632\pi$
$62$		0			0
$63$	−2464.52	+	3901.03i	−0.0782315	+	0.123831i
$64$		0			0
$65$	3797.43	+	3186.42i	0.111482	+	0.0935448i
$66$		0			0
$67$	−171.281	−	971.383i	−0.00466146	−	0.0264365i	0.982388	−	0.186851i	$-0.0598281\pi$
$67$	−171.281	−	971.383i	−0.00466146	−	0.0264365i	−0.987050	+	0.160414i	$0.948717\pi$
$68$		0			0
$69$	−70751.9	−	1409.84i	−1.78902	−	0.0356491i
$70$		0			0
$71$	−29479.9	−	51060.7i	−0.694034	−	1.20210i	−0.970505	−	0.241080i	$-0.922498\pi$
$71$	−29479.9	−	51060.7i	−0.694034	−	1.20210i	0.276471	−	0.961022i	$-0.410835\pi$
$72$		0			0
$73$	−27717.4	+	48007.9i	−0.608759	+	1.05440i	0.382686	+	0.923878i	$0.374999\pi$
$73$	−27717.4	+	48007.9i	−0.608759	+	1.05440i	−0.991445	+	0.130523i	$0.958334\pi$
$74$		0			0
$75$	−7212.17	−	46275.5i	−0.148051	−	0.949944i
$76$		0			0
$77$	12970.5	+	4720.87i	0.249304	+	0.0907392i
$78$		0			0
$79$	−16837.2	+	95488.5i	−0.303530	+	1.72141i	0.326813	+	0.945089i	$0.394025\pi$
$79$	−16837.2	+	95488.5i	−0.303530	+	1.72141i	−0.630343	+	0.776317i	$0.717086\pi$
$80$		0			0
$81$	14850.8	−	57151.0i	0.251499	−	0.967858i
$82$		0			0
$83$	11357.2	−	64409.9i	0.180957	−	1.02626i	−0.750083	−	0.661344i	$-0.769986\pi$
$83$	11357.2	−	64409.9i	0.180957	−	1.02626i	0.931040	−	0.364916i	$-0.118902\pi$
$84$		0			0
$85$	15630.8	+	5689.14i	0.234657	+	0.0854081i
$86$		0			0
$87$	113.856	+	730.538i	0.00161272	+	0.0103477i
$88$		0			0
$89$	24058.1	−	41669.9i	0.321949	−	0.557631i	−0.658942	−	0.752194i	$-0.728996\pi$
$89$	24058.1	−	41669.9i	0.321949	−	0.557631i	0.980890	+	0.194563i	$0.0623289\pi$
$90$		0			0
$91$	−4286.02	−	7423.61i	−0.0542564	−	0.0939749i
$92$		0			0
$93$	−111310.	−	2218.03i	−1.33452	−	0.0265925i
$94$		0			0
$95$	−3779.67	−	21435.6i	−0.0429680	−	0.243684i
$96$		0			0
$97$	−46476.7	−	38998.6i	−0.501540	−	0.420842i	0.356600	−	0.934257i	$-0.383936\pi$
$97$	−46476.7	−	38998.6i	−0.501540	−	0.420842i	−0.858141	+	0.513415i	$0.828380\pi$
$98$		0			0
$99$	−176494.	−	7036.64i	−1.80985	−	0.0721568i
$100$		0			0
$101$	−21336.6	+	7765.90i	−0.208124	+	0.0757510i	−0.443979	−	0.896037i	$-0.646433\pi$
$101$	−21336.6	+	7765.90i	−0.208124	+	0.0757510i	0.235854	+	0.971788i	$0.424211\pi$
$102$		0			0
$103$	−23405.2	+	19639.3i	−0.217380	+	0.182403i	−0.744975	−	0.667093i	$-0.767538\pi$
$103$	−23405.2	+	19639.3i	−0.217380	+	0.182403i	0.527595	+	0.849496i	$0.323094\pi$
$104$		0			0
$105$	628.116	−	3189.29i	0.00555989	−	0.0282306i
$106$		0			0
$107$	64747.9			0.546722			0.273361	−	0.961912i	$-0.411865\pi$
$107$	64747.9			0.546722			0.273361	+	0.961912i	$0.411865\pi$
$108$		0			0
$109$	107408.			0.865907			0.432954	−	0.901416i	$-0.357471\pi$
$109$	107408.			0.865907			0.432954	+	0.901416i	$0.357471\pi$
$110$		0			0
$111$	−123920.	−	108260.i	−0.954626	−	0.833993i
$112$		0			0
$113$	178745.	−	149985.i	1.31685	−	1.10497i	0.329890	−	0.944019i	$-0.392988\pi$
$113$	178745.	−	149985.i	1.31685	−	1.10497i	0.986962	−	0.160951i	$-0.0514560\pi$
$114$		0			0
$115$	46844.6	−	17050.0i	0.330305	−	0.120221i
$116$		0			0
$117$	81156.1	+	73802.7i	0.548096	+	0.498434i
$118$		0			0
$119$	−22034.2	−	18488.9i	−0.142636	−	0.119686i
$120$		0			0
$121$	63784.1	+	361737.i	0.396049	+	2.24611i
$122$		0			0
$123$	50566.6	+	91758.5i	0.301371	+	0.546869i
$124$		0			0
$125$	33654.3	+	58291.0i	0.192649	+	0.333677i
$126$		0			0
$127$	−27244.3	+	47188.5i	−0.149888	+	0.259613i	−0.931186	−	0.364545i	$-0.881225\pi$
$127$	−27244.3	+	47188.5i	−0.149888	+	0.259613i	0.781298	+	0.624158i	$0.214558\pi$
$128$		0			0
$129$	61276.1	+	23695.5i	0.324203	+	0.125370i
$130$		0			0
$131$	112901.	+	41092.6i	0.574803	+	0.209211i	0.613032	−	0.790058i	$-0.289949\pi$
$131$	112901.	+	41092.6i	0.574803	+	0.209211i	−0.0382292	+	0.999269i	$0.512172\pi$
$132$		0			0
$133$	−6535.87	+	37066.8i	−0.0320387	+	0.181700i
$134$		0			0
$135$	4763.24	+	41323.4i	0.0224941	+	0.195147i
$136$		0			0
$137$	−9012.11	+	51110.2i	−0.0410228	+	0.232652i	−0.998425	−	0.0561066i	$-0.982131\pi$
$137$	−9012.11	+	51110.2i	−0.0410228	+	0.232652i	0.957402	+	0.288758i	$0.0932424\pi$
$138$		0			0
$139$	138332.	+	50348.7i	0.607274	+	0.221030i	0.627310	−	0.778769i	$-0.284156\pi$
$139$	138332.	+	50348.7i	0.607274	+	0.221030i	−0.0200358	+	0.999799i	$0.506378\pi$
$140$		0			0
$141$	−115821.	+	93317.4i	−0.490615	+	0.395289i
$142$		0			0
$143$	164067.	−	284173.i	0.670937	−	1.16210i
$144$		0			0
$145$	−260.420	−	451.060i	−0.00102862	−	0.00178162i
$146$		0			0
$147$	132585.	−	219429.i	0.506059	−	0.837530i
$148$		0			0
$149$	48111.8	+	272856.i	0.177536	+	1.00686i	0.935176	+	0.354183i	$0.115241\pi$
$149$	48111.8	+	272856.i	0.177536	+	1.00686i	−0.757640	+	0.652673i	$0.773648\pi$
$150$		0			0
$151$	290154.	+	243468.i	1.03559	+	0.868959i	0.991505	−	0.130069i	$-0.0415199\pi$
$151$	290154.	+	243468.i	1.03559	+	0.868959i	0.0440801	+	0.999028i	$0.485964\pi$
$152$		0			0
$153$	340597.	+	139572.i	1.17629	+	0.482025i
$154$		0			0
$155$	73697.9	−	26823.8i	0.246392	−	0.0896792i
$156$		0			0
$157$	97333.8	−	81672.8i	0.315148	−	0.264441i	−0.471468	−	0.881883i	$-0.656276\pi$
$157$	97333.8	−	81672.8i	0.315148	−	0.264441i	0.786616	+	0.617443i	$0.211831\pi$
$158$		0			0
$159$	−292923.	+	100053.i	−0.918884	+	0.313860i
$160$		0			0
$161$	−86203.0			−0.262094
$162$		0			0
$163$	−578620.			−1.70579			−0.852893	−	0.522086i	$-0.825154\pi$
$163$	−578620.			−1.70579			−0.852893	+	0.522086i	$0.825154\pi$
$164$		0			0
$165$	117750.	−	40219.6i	0.336707	−	0.115008i
$166$		0			0
$167$	−122053.	+	102415.i	−0.338656	+	0.284166i	−0.796216	−	0.605013i	$-0.793168\pi$
$167$	−122053.	+	102415.i	−0.338656	+	0.284166i	0.457560	+	0.889179i	$0.348723\pi$
$168$		0			0
$169$	157408.	−	57292.0i	0.423947	−	0.154304i
$170$		0			0
$171$	−64676.1	−	477295.i	−0.169143	−	1.24824i
$172$		0			0
$173$	67943.5	+	57011.4i	0.172597	+	0.144826i	0.724994	−	0.688755i	$-0.241842\pi$
$173$	67943.5	+	57011.4i	0.172597	+	0.144826i	−0.552397	+	0.833581i	$0.686287\pi$
$174$		0			0
$175$	−9906.75	−	56183.9i	−0.0244532	−	0.138681i
$176$		0			0
$177$	−36483.2	+	60379.8i	−0.0875305	+	0.144863i
$178$		0			0
$179$	−212473.	−	368014.i	−0.495645	−	0.858483i	0.504342	−	0.863504i	$-0.331735\pi$
$179$	−212473.	−	368014.i	−0.495645	−	0.858483i	−0.999987	+	0.00502097i	$0.998402\pi$
$180$		0			0
$181$	−19719.6	+	34155.3i	−0.0447406	+	0.0774929i	−0.887528	−	0.460753i	$-0.847579\pi$
$181$	−19719.6	+	34155.3i	−0.0447406	+	0.0774929i	0.842788	+	0.538246i	$0.180913\pi$
$182$		0			0
$183$	−577914.	+	465626.i	−1.27566	+	1.02780i
$184$		0			0
$185$	108926.	+	39645.8i	0.233992	+	0.0851662i
$186$		0			0
$187$	191197.	−	1.08433e6i	0.399832	−	2.26756i
$188$		0			0
$189$	16699.8	−	69964.7i	0.0340061	−	0.142470i
$190$		0			0
$191$	−84502.0	+	479235.i	−0.167604	+	0.950528i	0.778735	+	0.627352i	$0.215861\pi$
$191$	−84502.0	+	479235.i	−0.167604	+	0.950528i	−0.946339	+	0.323175i	$0.895250\pi$
$192$		0			0
$193$	−51501.5	−	18745.0i	−0.0995238	−	0.0362237i	0.291778	−	0.956486i	$-0.405753\pi$
$193$	−51501.5	−	18745.0i	−0.0995238	−	0.0362237i	−0.391302	+	0.920262i	$0.627975\pi$
$194$		0			0
$195$	−72073.8	−	27871.0i	−0.135735	−	0.0524888i
$196$		0			0
$197$	113540.	−	196658.i	0.208442	−	0.361032i	−0.742782	−	0.669533i	$-0.766494\pi$
$197$	113540.	−	196658.i	0.208442	−	0.361032i	0.951224	+	0.308501i	$0.0998275\pi$
$198$		0			0
$199$	−159713.	−	276631.i	−0.285895	−	0.495185i	0.686931	−	0.726723i	$-0.258958\pi$
$199$	−159713.	−	276631.i	−0.285895	−	0.495185i	−0.972826	+	0.231538i	$0.925624\pi$
$200$		0			0
$201$	7421.16	+	13466.5i	0.0129563	+	0.0235106i
$202$		0			0
$203$	156.395	+	886.960i	0.000266369	+	0.00151065i
$204$		0			0
$205$	−56537.6	−	47440.7i	−0.0939621	−	0.0788435i
$206$		0			0
$207$	1.05081e6	−	335698.i	1.70451	−	0.544532i
$208$		0			0
$209$	−1.35390e6	+	492779.i	−2.14398	+	0.780345i
$210$		0			0
$211$	−643941.	+	540331.i	−0.995726	+	0.835513i	−0.986387	−	0.164443i	$-0.947417\pi$
$211$	−643941.	+	540331.i	−0.995726	+	0.835513i	−0.00933955	+	0.999956i	$0.502973\pi$
$212$		0			0
$213$	692157.	+	604691.i	1.04533	+	0.913240i
$214$		0			0
$215$	−46280.9			−0.0682819
$216$		0			0
$217$	−135618.			−0.195510
$218$		0			0
$219$	166982.	−	847856.i	0.235265	−	1.19457i
$220$		0			0
$221$	−523817.	+	439535.i	−0.721438	+	0.605358i
$222$		0			0
$223$	−440462.	+	160315.i	−0.593126	+	0.215880i	−0.621104	−	0.783728i	$-0.713315\pi$
$223$	−440462.	+	160315.i	−0.593126	+	0.215880i	0.0279780	+	0.999609i	$0.491093\pi$
$224$		0			0
$225$	339559.	+	646301.i	0.447155	+	0.851096i
$226$		0			0
$227$	−765009.	−	641919.i	−0.985376	−	0.826829i	−0.000484510	−	1.00000i	$-0.500154\pi$
$227$	−765009.	−	641919.i	−0.985376	−	0.826829i	−0.984892	+	0.173171i	$0.944599\pi$
$228$		0			0
$229$	−45196.6	−	256323.i	−0.0569531	−	0.322997i	0.942999	−	0.332796i	$-0.107992\pi$
$229$	−45196.6	−	256323.i	−0.0569531	−	0.322997i	−0.999952	+	0.00979880i	$0.996881\pi$
$230$		0			0
$231$	−215123.	−	4286.67i	−0.265251	−	0.00528554i
$232$		0			0
$233$	−208675.	−	361436.i	−0.251814	−	0.436155i	0.712211	−	0.701965i	$-0.247694\pi$
$233$	−208675.	−	361436.i	−0.251814	−	0.436155i	−0.964025	+	0.265810i	$0.914361\pi$
$234$		0			0
$235$	52388.8	−	90740.0i	0.0618826	−	0.107184i
$236$		0			0
$237$	−232759.	−	1.49345e6i	−0.269175	−	1.72711i
$238$		0			0
$239$	1.15721e6	+	421192.i	1.31045	+	0.476963i	0.900385	−	0.435095i	$-0.143285\pi$
$239$	1.15721e6	+	421192.i	1.31045	+	0.476963i	0.410061	+	0.912058i	$0.365507\pi$
$240$		0			0
$241$	233886.	−	1.32643e6i	0.259395	−	1.47110i	−0.525140	−	0.851016i	$-0.675987\pi$
$241$	233886.	−	1.32643e6i	0.259395	−	1.47110i	0.784534	−	0.620085i	$-0.212902\pi$
$242$		0			0
$243$	68891.8	+	917901.i	0.0748432	+	0.997195i
$244$		0			0
$245$	−31361.3	+	177859.i	−0.0333794	+	0.189304i
$246$		0			0
$247$	840816.	+	306032.i	0.876917	+	0.319172i
$248$		0			0
$249$	157003.	+	1.00738e6i	0.160476	+	1.02966i
$250$		0			0
$251$	−94116.6	+	163015.i	−0.0942935	+	0.163321i	−0.909314	−	0.416112i	$-0.863393\pi$
$251$	−94116.6	+	163015.i	−0.0942935	+	0.163321i	0.815020	+	0.579433i	$0.196726\pi$
$252$		0			0
$253$	−1.64991e6	−	2.85773e6i	−1.62054	−	2.80685i
$254$		0			0
$255$	−259246.	−	5165.88i	−0.249667	−	0.00497501i
$256$		0			0
$257$	278352.	+	1.57861e6i	0.262882	+	1.49088i	0.774998	+	0.631963i	$0.217751\pi$
$257$	278352.	+	1.57861e6i	0.262882	+	1.49088i	−0.512116	+	0.858916i	$0.671138\pi$
$258$		0			0
$259$	−153549.	−	128843.i	−0.142232	−	0.119347i
$260$		0			0
$261$	−5360.52	−	10203.0i	−0.00487086	−	0.00927098i
$262$		0			0
$263$	−1.21812e6	+	443361.i	−1.08593	+	0.395247i	−0.822112	−	0.569326i	$-0.807204\pi$
$263$	−1.21812e6	+	443361.i	−1.08593	+	0.395247i	−0.263819	+	0.964572i	$0.584982\pi$
$264$		0			0
$265$	167039.	−	140163.i	0.146118	−	0.122608i
$266$		0			0
$267$	−144936.	+	735921.i	−0.124423	+	0.631761i
$268$		0			0
$269$	−1.13243e6			−0.954178			−0.477089	−	0.878855i	$-0.658308\pi$
$269$	−1.13243e6			−0.954178			−0.477089	+	0.878855i	$0.658308\pi$
$270$		0			0
$271$	−905413.			−0.748900			−0.374450	−	0.927247i	$-0.622168\pi$
$271$	−905413.			−0.748900			−0.374450	+	0.927247i	$0.622168\pi$
$272$		0			0
$273$	100631.	+	87914.8i	0.0817196	+	0.0713930i
$274$		0			0
$275$	1.67295e6	−	1.40377e6i	1.33398	−	1.11934i
$276$		0			0
$277$	2.04938e6	−	745914.i	1.60481	−	0.584103i	0.624405	−	0.781101i	$-0.285341\pi$
$277$	2.04938e6	−	745914.i	1.60481	−	0.584103i	0.980404	+	0.196998i	$0.0631192\pi$
$278$		0			0
$279$	1.65318e6	−	528135.i	1.27148	−	0.406195i
$280$		0			0
$281$	84634.8	+	71017.1i	0.0639416	+	0.0536534i	0.674198	−	0.738550i	$-0.264489\pi$
$281$	84634.8	+	71017.1i	0.0639416	+	0.0536534i	−0.610257	+	0.792204i	$0.708934\pi$
$282$		0			0
$283$	381194.	+	2.16186e6i	0.282931	+	1.60458i	0.712584	+	0.701587i	$0.247525\pi$
$283$	381194.	+	2.16186e6i	0.282931	+	1.60458i	−0.429653	+	0.902994i	$0.641364\pi$
$284$		0			0
$285$	163764.	+	297166.i	0.119428	+	0.216714i
$286$		0			0
$287$	63812.0	+	110526.i	0.0457296	+	0.0792060i
$288$		0			0
$289$	−437313.	+	757449.i	−0.307998	+	0.533468i
$290$		0			0
$291$	882110.	+	341113.i	0.610647	+	0.236138i
$292$		0			0
$293$	−871992.	−	317379.i	−0.593394	−	0.215978i	0.0278273	−	0.999613i	$-0.491141\pi$
$293$	−871992.	−	317379.i	−0.593394	−	0.215978i	−0.621222	+	0.783635i	$0.713363\pi$
$294$		0			0
$295$	8629.63	−	48941.0i	0.00577347	−	0.0327430i
$296$		0			0
$297$	2.63904e6	−	785494.i	1.73602	−	0.516716i
$298$		0			0
$299$	−355856.	+	2.01816e6i	−0.230196	+	1.30550i
$300$		0			0
$301$	75203.2	+	27371.7i	0.0478432	+	0.0174135i
$302$		0			0
$303$	275621.	−	222068.i	0.172467	−	0.138957i
$304$		0			0
$305$	261404.	−	452766.i	0.160903	−	0.278692i
$306$		0			0
$307$	1.34771e6	+	2.33430e6i	0.816112	+	1.41355i	0.908527	+	0.417826i	$0.137208\pi$
$307$	1.34771e6	+	2.33430e6i	0.816112	+	1.41355i	−0.0924155	+	0.995721i	$0.529459\pi$
$308$		0			0
$309$	246310.	−	407644.i	0.146753	−	0.242876i
$310$		0			0
$311$	502062.	+	2.84734e6i	0.294345	+	1.66931i	0.669853	+	0.742494i	$0.266357\pi$
$311$	502062.	+	2.84734e6i	0.294345	+	1.66931i	−0.375508	+	0.926819i	$0.622532\pi$
$312$		0			0
$313$	−721497.	−	605408.i	−0.416269	−	0.349291i	0.410473	−	0.911873i	$-0.365364\pi$
$313$	−721497.	−	605408.i	−0.416269	−	0.349291i	−0.826742	+	0.562582i	$0.809808\pi$
$314$		0			0
$315$	6804.02	+	50212.2i	0.00386357	+	0.0285123i
$316$		0			0
$317$	−22942.5	+	8350.38i	−0.0128231	+	0.00466722i	−0.348424	−	0.937337i	$-0.613283\pi$
$317$	−22942.5	+	8350.38i	−0.0128231	+	0.00466722i	0.335601	+	0.942004i	$0.391061\pi$
$318$		0			0
$319$	−26410.3	+	22160.9i	−0.0145311	+	0.0121930i
$320$		0			0
$321$	−955140.	+	326244.i	−0.517374	+	0.176717i
$322$		0			0
$323$	3.00244e6			1.60128
$324$		0			0
$325$	−1.35626e6			−0.712253
$326$		0			0
$327$	−1.58445e6	+	541195.i	−0.819425	+	0.279888i
$328$		0			0
$329$	−138794.	+	116462.i	−0.0706938	+	0.0593192i
$330$		0			0
$331$	3.69223e6	−	1.34386e6i	1.85233	−	0.674194i	0.868344	−	0.495962i	$-0.165184\pi$
$331$	3.69223e6	−	1.34386e6i	1.85233	−	0.674194i	0.983988	−	0.178232i	$-0.0570379\pi$
$332$		0			0
$333$	2.37351e6	+	972632.i	1.17295	+	0.480660i
$334$		0			0
$335$	−8297.46	−	6962.40i	−0.00403955	−	0.00338959i
$336$		0			0
$337$	−4387.38	−	24882.1i	−0.00210441	−	0.0119347i	0.983737	−	0.179612i	$-0.0574843\pi$
$337$	−4387.38	−	24882.1i	−0.00210441	−	0.0119347i	−0.985842	+	0.167678i	$0.946373\pi$
$338$		0			0
$339$	−1.88106e6	+	3.11316e6i	−0.889003	+	1.47130i
$340$		0			0
$341$	−2.59571e6	−	4.49590e6i	−1.20884	−	2.09378i
$342$		0			0
$343$	315724.	−	546850.i	0.144901	−	0.250976i
$344$		0			0
$345$	−605126.	+	487551.i	−0.273715	+	0.220532i
$346$		0			0
$347$	1.09244e6	+	397617.i	0.487052	+	0.177272i	0.573861	−	0.818953i	$-0.305445\pi$
$347$	1.09244e6	+	397617.i	0.487052	+	0.177272i	−0.0868095	+	0.996225i	$0.527667\pi$
$348$		0			0
$349$	−34614.2	+	196307.i	−0.0152122	+	0.0862725i	−0.991469	−	0.130345i	$-0.958391\pi$
$349$	−34614.2	+	196307.i	−0.0152122	+	0.0862725i	0.976256	+	0.216618i	$0.0695025\pi$
$350$		0			0
$351$	−1.56906e6	−	679793.i	−0.679783	−	0.294516i
$352$		0			0
$353$	−406788.	+	2.30701e6i	−0.173753	+	0.985399i	0.765821	+	0.643053i	$0.222333\pi$
$353$	−406788.	+	2.30701e6i	−0.173753	+	0.985399i	−0.939574	+	0.342346i	$0.888778\pi$
$354$		0			0
$355$	−608408.	−	221442.i	−0.256226	−	0.0932588i
$356$		0			0
$357$	418201.	+	161719.i	0.173666	+	0.0671569i
$358$		0			0
$359$	2.17292e6	−	3.76360e6i	0.889830	−	1.54123i	0.0497554	−	0.998761i	$-0.484156\pi$
$359$	2.17292e6	−	3.76360e6i	0.889830	−	1.54123i	0.840075	−	0.542470i	$-0.182511\pi$
$360$		0			0
$361$	−726368.	−	1.25811e6i	−0.293352	−	0.508100i
$362$		0			0
$363$	−2.76360e6	−	5.01484e6i	−1.10080	−	1.99752i
$364$		0			0
$365$	105707.	+	599496.i	0.0415310	+	0.235534i
$366$		0			0
$367$	384729.	+	322826.i	0.149104	+	0.125113i	0.714288	−	0.699851i	$-0.246750\pi$
$367$	384729.	+	322826.i	0.149104	+	0.125113i	−0.565184	+	0.824965i	$0.691195\pi$
$368$		0			0
$369$	−1.20828e6	−	1.09880e6i	−0.461958	−	0.420101i
$370$		0			0
$371$	−354323.	+	128963.i	−0.133649	+	0.0486441i
$372$		0			0
$373$	−705804.	+	592240.i	−0.262671	+	0.220407i	−0.764606	−	0.644498i	$-0.777066\pi$
$373$	−705804.	+	592240.i	−0.262671	+	0.220407i	0.501935	+	0.864905i	$0.332622\pi$
$374$		0			0
$375$	−790167.	−	690317.i	−0.290162	−	0.253496i
$376$		0			0
$377$	21410.9			0.00775856
$378$		0			0
$379$	−5.39069e6			−1.92773			−0.963865	−	0.266390i	$-0.914169\pi$
$379$	−5.39069e6			−1.92773			−0.963865	+	0.266390i	$0.914169\pi$
$380$		0			0
$381$	164131.	−	833384.i	0.0579267	−	0.294125i
$382$		0			0
$383$	578794.	−	485666.i	0.201617	−	0.169177i	−0.536389	−	0.843971i	$-0.680212\pi$
$383$	578794.	−	485666.i	0.201617	−	0.169177i	0.738006	+	0.674794i	$0.235768\pi$
$384$		0			0
$385$	142432.	−	51841.1i	0.0489730	−	0.0178247i
$386$		0			0
$387$	−1.02332e6	−	40798.7i	−0.347323	−	0.0138474i
$388$		0			0
$389$	−3.10362e6	−	2.60425e6i	−1.03991	−	0.872586i	−0.0479110	−	0.998852i	$-0.515256\pi$
$389$	−3.10362e6	−	2.60425e6i	−1.03991	−	0.872586i	−0.991996	+	0.126266i	$0.959701\pi$
$390$		0			0
$391$	1.19408e6	+	6.77197e6i	0.394995	+	2.24013i
$392$		0			0
$393$	−1.87253e6	−	37313.1i	−0.611571	−	0.0121865i
$394$		0			0
$395$	532380.	+	922110.i	0.171684	+	0.297365i
$396$		0			0
$397$	321075.	−	556118.i	0.102242	−	0.177088i	−0.810366	−	0.585924i	$-0.800732\pi$
$397$	321075.	−	556118.i	0.102242	−	0.177088i	0.912608	+	0.408836i	$0.134065\pi$
$398$		0			0
$399$	−90352.4	−	579729.i	−0.0284124	−	0.182302i
$400$		0			0
$401$	1.92186e6	+	699498.i	0.596843	+	0.217233i	0.622736	−	0.782432i	$-0.286021\pi$
$401$	1.92186e6	+	699498.i	0.596843	+	0.217233i	−0.0258936	+	0.999665i	$0.508243\pi$
$402$		0			0
$403$	−559849.	+	3.17506e6i	−0.171715	+	0.973844i
$404$		0			0
$405$	−278481.	−	585588.i	−0.0843641	−	0.177400i
$406$		0			0
$407$	1.33239e6	−	7.55636e6i	0.398699	−	2.26114i
$408$		0			0
$409$	3.11806e6	+	1.13488e6i	0.921671	+	0.335461i	0.758903	−	0.651204i	$-0.225736\pi$
$409$	3.11806e6	+	1.13488e6i	0.921671	+	0.335461i	0.162768	+	0.986664i	$0.447958\pi$
$410$		0			0
$411$	−124584.	−	799370.i	−0.0363796	−	0.233423i
$412$		0			0
$413$	−42967.6	+	74422.0i	−0.0123955	+	0.0214697i
$414$		0			0
$415$	−359107.	−	621991.i	−0.102354	−	0.177282i
$416$		0			0
$417$	−2.29432e6	−	45717.9i	−0.646120	−	0.0128750i
$418$		0			0
$419$	−340538.	−	1.93129e6i	−0.0947612	−	0.537418i	−0.994820	−	0.101650i	$-0.967588\pi$
$419$	−340538.	−	1.93129e6i	−0.0947612	−	0.537418i	0.900059	−	0.435768i	$-0.143523\pi$
$420$		0			0
$421$	−1.99421e6	−	1.67334e6i	−0.548360	−	0.460129i	0.326025	−	0.945361i	$-0.394291\pi$
$421$	−1.99421e6	−	1.67334e6i	−0.548360	−	0.460129i	−0.874385	+	0.485232i	$0.838735\pi$
$422$		0			0
$423$	1.23836e6	−	1.96017e6i	0.336509	−	0.532652i
$424$		0			0
$425$	−4.27649e6	+	1.55652e6i	−1.14846	+	0.418005i
$426$		0			0
$427$	−692542.	+	581111.i	−0.183813	+	0.154237i
$428$		0			0
$429$	−988412.	+	5.01871e6i	−0.259295	+	1.31658i
$430$		0			0
$431$	−2.79990e6			−0.726021			−0.363010	−	0.931785i	$-0.618251\pi$
$431$	−2.79990e6			−0.726021			−0.363010	+	0.931785i	$0.618251\pi$
$432$		0			0
$433$	5.07964e6			1.30201			0.651003	−	0.759075i	$-0.274348\pi$
$433$	5.07964e6			1.30201			0.651003	+	0.759075i	$0.274348\pi$
$434$		0			0
$435$	6114.37	+	5341.72i	0.00154928	+	0.00135350i
$436$		0			0
$437$	6.89298e6	−	5.78390e6i	1.72665	−	1.44883i
$438$		0			0
$439$	−2.00908e6	+	731247.i	−0.497550	+	0.181093i	−0.578592	−	0.815617i	$-0.696398\pi$
$439$	−2.00908e6	+	731247.i	−0.497550	+	0.181093i	0.0810416	+	0.996711i	$0.474175\pi$
$440$		0			0
$441$	−850221.	+	3.90499e6i	−0.208178	+	0.956145i
$442$		0			0
$443$	2.84884e6	+	2.39046e6i	0.689698	+	0.578725i	0.918822	−	0.394672i	$-0.129142\pi$
$443$	2.84884e6	+	2.39046e6i	0.689698	+	0.578725i	−0.229124	+	0.973397i	$0.573586\pi$
$444$		0			0
$445$	−91751.7	−	520350.i	−0.0219641	−	0.124565i
$446$		0			0
$447$	−2.08456e6	−	3.78266e6i	−0.493453	−	0.895423i
$448$		0			0
$449$	2.56352e6	+	4.44014e6i	0.600096	+	1.03940i	0.992806	+	0.119734i	$0.0382041\pi$
$449$	2.56352e6	+	4.44014e6i	0.600096	+	1.03940i	−0.392710	+	0.919662i	$0.628463\pi$
$450$		0			0
$451$	−2.44270e6	+	4.23087e6i	−0.565494	+	0.979465i
$452$		0			0
$453$	−5.50701e6	−	2.12957e6i	−1.26087	−	0.487580i
$454$		0			0
$455$	−88455.1	−	32195.0i	−0.0200306	−	0.00729055i
$456$		0			0
$457$	778423.	−	4.41465e6i	0.174351	−	0.988795i	−0.764539	−	0.644578i	$-0.777033\pi$
$457$	778423.	−	4.41465e6i	0.174351	−	0.988795i	0.938890	−	0.344217i	$-0.111856\pi$
$458$		0			0
$459$	−5.72764e6	−	342760.i	−1.26895	−	0.0759378i
$460$		0			0
$461$	−816458.	+	4.63036e6i	−0.178929	+	1.01476i	0.754581	+	0.656207i	$0.227840\pi$
$461$	−816458.	+	4.63036e6i	−0.178929	+	1.01476i	−0.933510	+	0.358551i	$0.883271\pi$
$462$		0			0
$463$	6.01963e6	+	2.19097e6i	1.30502	+	0.474989i	0.898629	−	0.438710i	$-0.144565\pi$
$463$	6.01963e6	+	2.19097e6i	1.30502	+	0.474989i	0.406392	+	0.913699i	$0.366787\pi$
$464$		0			0
$465$	−952011.	+	767036.i	−0.204178	+	0.164507i
$466$		0			0
$467$	3.03455e6	−	5.25599e6i	0.643875	−	1.11522i	−0.340685	−	0.940177i	$-0.610659\pi$
$467$	3.03455e6	−	5.25599e6i	0.643875	−	1.11522i	0.984560	−	0.175047i	$-0.0560077\pi$
$468$		0			0
$469$	9365.05	+	16220.7i	0.00196598	+	0.00340517i
$470$		0			0
$471$	−1.02431e6	+	1.69524e6i	−0.212755	+	0.352111i
$472$		0			0
$473$	531971.	+	3.01696e6i	0.109329	+	0.620036i
$474$		0			0
$475$	4.56190e6	+	3.82788e6i	0.927708	+	0.778439i
$476$		0			0
$477$	3.81697e6	−	2.95189e6i	0.768109	−	0.594024i
$478$		0			0
$479$	6.38183e6	−	2.32280e6i	1.27089	−	0.462565i	0.383478	−	0.923550i	$-0.374726\pi$
$479$	6.38183e6	−	2.32280e6i	1.27089	−	0.462565i	0.887408	+	0.460986i	$0.152504\pi$
$480$		0			0
$481$	−3.65031e6	+	3.06298e6i	−0.719395	+	0.603644i
$482$		0			0
$483$	1.27164e6	−	434349.i	0.248025	−	0.0847171i
$484$		0			0
$485$	−666245.			−0.128611
$486$		0			0
$487$	−565755.			−0.108095			−0.0540475	−	0.998538i	$-0.517212\pi$
$487$	−565755.			−0.108095			−0.0540475	+	0.998538i	$0.517212\pi$
$488$		0			0
$489$	8.53561e6	−	2.91548e6i	1.61422	−	0.551363i
$490$		0			0
$491$	−1.16794e6	+	980015.i	−0.218633	+	0.183455i	−0.745525	−	0.666477i	$-0.767801\pi$
$491$	−1.16794e6	+	980015.i	−0.218633	+	0.183455i	0.526893	+	0.849932i	$0.323357\pi$
$492$		0			0
$493$	67511.8	−	24572.3i	0.0125101	−	0.00455332i
$494$		0			0
$495$	−1.53436e6	+	1.18661e6i	−0.281459	+	0.217668i
$496$		0			0
$497$	857653.	+	719657.i	0.155747	+	0.130688i
$498$		0			0
$499$	−837393.	−	4.74909e6i	−0.150549	−	0.853806i	−0.962743	−	0.270418i	$-0.912838\pi$
$499$	−837393.	−	4.74909e6i	−0.150549	−	0.853806i	0.812194	−	0.583388i	$-0.198273\pi$
$500$		0			0
$501$	1.28445e6	−	2.12578e6i	0.228625	−	0.378376i
$502$		0			0
$503$	−3.88700e6	−	6.73249e6i	−0.685007	−	1.18647i	−0.973435	−	0.228965i	$-0.926466\pi$
$503$	−3.88700e6	−	6.73249e6i	−0.685007	−	1.18647i	0.288428	−	0.957502i	$-0.406868\pi$
$504$		0			0
$505$	−124670.	+	215935.i	−0.0217537	+	0.0376786i
$506$		0			0
$507$	−2.03336e6	+	1.63828e6i	−0.351314	+	0.283054i
$508$		0			0
$509$	−8.68327e6	−	3.16045e6i	−1.48555	−	0.540698i	−0.533280	−	0.845939i	$-0.679041\pi$
$509$	−8.68327e6	−	3.16045e6i	−1.48555	−	0.540698i	−0.952275	+	0.305241i	$0.901263\pi$
$510$		0			0
$511$	182791.	−	1.03666e6i	0.0309672	−	0.175624i
$512$		0			0
$513$	3.35902e6	+	6.71502e6i	0.563532	+	1.12656i
$514$		0			0
$515$	−58261.4	+	330417.i	−0.00967973	+	0.0548965i
$516$		0			0
$517$	−6.51734e6	−	2.37212e6i	−1.07237	−	0.390310i
$518$		0			0
$519$	−1.28954e6	−	498668.i	−0.210144	−	0.0812630i
$520$		0			0
$521$	−388012.	+	672057.i	−0.0626255	+	0.108470i	−0.895638	−	0.444783i	$-0.853281\pi$
$521$	−388012.	+	672057.i	−0.0626255	+	0.108470i	0.833013	+	0.553254i	$0.186614\pi$
$522$		0			0
$523$	2.79497e6	+	4.84103e6i	0.446810	+	0.773897i	0.998176	−	0.0603659i	$-0.0192268\pi$
$523$	2.79497e6	+	4.84103e6i	0.446810	+	0.773897i	−0.551367	+	0.834263i	$0.685893\pi$
$524$		0			0
$525$	429234.	+	778890.i	0.0679666	+	0.123333i
$526$		0			0
$527$	1.87858e6	+	1.06540e7i	0.294648	+	1.67103i
$528$		0			0
$529$	1.08564e7	+	9.10957e6i	1.68673	+	1.41533i
$530$		0			0
$531$	233954.	−	1.07453e6i	0.0360075	−	0.165380i
$532$		0			0
$533$	2.85102e6	−	1.03769e6i	0.434692	−	0.158215i
$534$		0			0
$535$	544668.	−	457031.i	0.0822712	−	0.0690337i
$536$		0			0
$537$	4.98863e6	+	4.35824e6i	0.746528	+	0.652192i
$538$		0			0
$539$	1.19547e7			1.77243
$540$		0			0
$541$	2.38811e6			0.350801			0.175401	−	0.984497i	$-0.443878\pi$
$541$	2.38811e6			0.350801			0.175401	+	0.984497i	$0.443878\pi$
$542$		0			0
$543$	118799.	−	603209.i	0.0172908	−	0.0877947i
$544$		0			0
$545$	903533.	−	758154.i	0.130302	−	0.109337i
$546$		0			0
$547$	−2.41115e6	+	877587.i	−0.344553	+	0.125407i	−0.508500	−	0.861062i	$-0.669800\pi$
$547$	−2.41115e6	+	877587.i	−0.344553	+	0.125407i	0.163947	+	0.986469i	$0.447577\pi$
$548$		0			0
$549$	6.17906e6	−	9.78068e6i	0.874966	−	1.38496i
$550$		0			0
$551$	−72017.4	−	60429.8i	−0.0101055	−	0.00847953i
$552$		0			0
$553$	−319721.	−	1.81323e6i	−0.0444589	−	0.252139i
$554$		0			0
$555$	−1.80660e6	−	35999.3i	−0.248960	−	0.00496092i
$556$		0			0
$557$	2.93655e6	+	5.08626e6i	0.401051	+	0.694641i	0.993853	−	0.110707i	$-0.0353116\pi$
$557$	2.93655e6	+	5.08626e6i	0.401051	+	0.694641i	−0.592802	+	0.805348i	$0.701978\pi$
$558$		0			0
$559$	951268.	−	1.64764e6i	0.128758	−	0.223015i
$560$		0			0
$561$	2.64312e6	+	1.69591e7i	0.354577	+	2.27507i
$562$		0			0
$563$	−5.05834e6	−	1.84108e6i	−0.672569	−	0.244795i	−0.0169153	−	0.999857i	$-0.505385\pi$
$563$	−5.05834e6	−	1.84108e6i	−0.672569	−	0.244795i	−0.655654	+	0.755062i	$0.727607\pi$
$564$		0			0
$565$	444940.	−	2.52338e6i	0.0586382	−	0.332554i
$566$		0			0
$567$	106180.	+	1.11624e6i	0.0138702	+	0.145814i
$568$		0			0
$569$	548611.	−	3.11133e6i	0.0710369	−	0.402870i	−0.928468	−	0.371412i	$-0.878874\pi$
$569$	548611.	−	3.11133e6i	0.0710369	−	0.402870i	0.999505	−	0.0314583i	$-0.0100151\pi$
$570$		0			0
$571$	−3.62436e6	−	1.31916e6i	−0.465202	−	0.169320i	0.0987756	−	0.995110i	$-0.468507\pi$
$571$	−3.62436e6	−	1.31916e6i	−0.465202	−	0.169320i	−0.563978	+	0.825790i	$0.690730\pi$
$572$		0			0
$573$	−1.16816e6	−	7.49529e6i	−0.148633	−	0.953678i
$574$		0			0
$575$	−6.81947e6	+	1.18117e7i	−0.860164	+	1.48985i
$576$		0			0
$577$	1.93075e6	+	3.34416e6i	0.241428	+	0.418165i	0.961121	−	0.276127i	$-0.0890510\pi$
$577$	1.93075e6	+	3.34416e6i	0.241428	+	0.418165i	−0.719693	+	0.694292i	$0.755718\pi$
$578$		0			0
$579$	854184.	+	17021.0i	0.105890	+	0.00211003i
$580$		0			0
$581$	215662.	+	1.22308e6i	0.0265053	+	0.150319i
$582$		0			0
$583$	−1.10569e7	−	9.27787e6i	−1.34730	−	1.13052i
$584$		0			0
$585$	1.20364e6	+	47988.0i	0.145414	+	0.00579752i
$586$		0			0
$587$	−7.34411e6	+	2.67304e6i	−0.879719	+	0.320192i	−0.742096	−	0.670293i	$-0.766168\pi$
$587$	−7.34411e6	+	2.67304e6i	−0.879719	+	0.320192i	−0.137623	+	0.990485i	$0.543946\pi$
$588$		0			0
$589$	1.08443e7	−	9.09948e6i	1.28800	−	1.08076i
$590$		0			0
$591$	−684016.	+	3.47312e6i	−0.0805560	+	0.409027i
$592$		0			0
$593$	−1.37125e7			−1.60133			−0.800664	−	0.599114i	$-0.795520\pi$
$593$	−1.37125e7			−1.60133			−0.800664	+	0.599114i	$0.795520\pi$
$594$		0			0
$595$	−315861.			−0.0365766
$596$		0			0
$597$	3.74988e6	+	3.27602e6i	0.430608	+	0.376193i
$598$		0			0
$599$	1.17621e7	−	9.86960e6i	1.33943	−	1.12391i	0.357653	−	0.933854i	$-0.383577\pi$
$599$	1.17621e7	−	9.86960e6i	1.33943	−	1.12391i	0.981773	−	0.190057i	$-0.0608674\pi$
$600$		0			0
$601$	−1.44314e7	+	5.25261e6i	−1.62976	+	0.593184i	−0.985206	−	0.171375i	$-0.945179\pi$
$601$	−1.44314e7	+	5.25261e6i	−1.62976	+	0.593184i	−0.644554	+	0.764559i	$0.722957\pi$
$602$		0			0
$603$	−177328.	−	161260.i	−0.0198602	−	0.0180607i
$604$		0			0
$605$	3.08993e6	+	2.59276e6i	0.343210	+	0.287987i
$606$		0			0
$607$	−1.16598e6	−	6.61263e6i	−0.128446	−	0.728454i	−0.979201	−	0.202892i	$-0.934966\pi$
$607$	−1.16598e6	−	6.61263e6i	−0.128446	−	0.728454i	0.850755	−	0.525563i	$-0.176145\pi$
$608$		0			0
$609$	−6776.19	−	12296.1i	−0.000740359	−	0.00134346i
$610$		0			0
$611$	2.15362e6	+	3.73018e6i	0.233381	+	0.404228i
$612$		0			0
$613$	7.36194e6	−	1.27512e7i	0.791300	−	1.37057i	−0.133863	−	0.991000i	$-0.542738\pi$
$613$	7.36194e6	−	1.27512e7i	0.791300	−	1.37057i	0.925163	−	0.379571i	$-0.123928\pi$
$614$		0			0
$615$	1.07306e6	+	414954.i	0.114403	+	0.0442397i
$616$		0			0
$617$	−1.16118e7	−	4.22633e6i	−1.22796	−	0.446942i	−0.355063	−	0.934842i	$-0.615541\pi$
$617$	−1.16118e7	−	4.22633e6i	−1.22796	−	0.446942i	−0.872899	+	0.487901i	$0.837763\pi$
$618$		0			0
$619$	461846.	−	2.61926e6i	0.0484474	−	0.274759i	−0.950955	−	0.309330i	$-0.899895\pi$
$619$	461846.	−	2.61926e6i	0.0484474	−	0.274759i	0.999402	+	0.0345708i	$0.0110064\pi$
$620$		0			0
$621$	−1.38098e7	+	1.02468e7i	−1.43700	+	1.06625i
$622$		0			0
$623$	−158658.	+	899796.i	−0.0163773	+	0.0928804i
$624$		0			0
$625$	−8.12801e6	−	2.95836e6i	−0.832309	−	0.302936i
$626$		0			0
$627$	1.74893e7	−	1.40912e7i	1.77666	−	1.43146i
$628$		0			0
$629$	−7.99475e6	+	1.38473e7i	−0.805709	+	1.39553i
$630$		0			0
$631$	−4.68138e6	−	8.10839e6i	−0.468059	−	0.810702i	0.531274	−	0.847200i	$-0.321713\pi$
$631$	−4.68138e6	−	8.10839e6i	−0.468059	−	0.810702i	−0.999334	+	0.0364973i	$0.988380\pi$
$632$		0			0
$633$	6.77665e6	−	1.12154e7i	0.672212	−	1.11251i
$634$		0			0
$635$	103903.	+	589263.i	0.0102257	+	0.0579929i
$636$		0			0
$637$	−5.68733e6	−	4.77224e6i	−0.555341	−	0.465987i
$638$		0			0
$639$	−1.32573e7	−	5.43266e6i	−1.28441	−	0.526332i
$640$		0			0
$641$	7.39286e6	−	2.69078e6i	0.710669	−	0.258662i	0.0387096	−	0.999251i	$-0.487675\pi$
$641$	7.39286e6	−	2.69078e6i	0.710669	−	0.258662i	0.671959	+	0.740588i	$0.265453\pi$
$642$		0			0
$643$	−2.51744e6	+	2.11238e6i	−0.240122	+	0.201486i	−0.754905	−	0.655834i	$-0.772317\pi$
$643$	−2.51744e6	+	2.11238e6i	−0.240122	+	0.201486i	0.514783	+	0.857321i	$0.327872\pi$
$644$		0			0
$645$	682721.	−	233194.i	0.0646165	−	0.0220708i
$646$		0			0
$647$	−7.02395e6			−0.659660			−0.329830	−	0.944040i	$-0.606992\pi$
$647$	−7.02395e6			−0.659660			−0.329830	+	0.944040i	$0.606992\pi$
$648$		0			0
$649$	−3.28956e6			−0.306568
$650$		0			0
$651$	2.00060e6	−	683337.i	0.185015	−	0.0631949i
$652$		0			0
$653$	−5.94510e6	+	4.98853e6i	−0.545602	+	0.457814i	−0.873448	−	0.486917i	$-0.838122\pi$
$653$	−5.94510e6	+	4.98853e6i	−0.545602	+	0.457814i	0.327847	+	0.944731i	$0.393677\pi$
$654$		0			0
$655$	1.23979e6	−	451248.i	0.112914	−	0.0410972i
$656$		0			0
$657$	1.80882e6	+	1.33487e7i	0.163486	+	1.20649i
$658$		0			0
$659$	−1.30826e7	−	1.09776e7i	−1.17349	−	0.984678i	−0.173493	−	0.984835i	$-0.555506\pi$
$659$	−1.30826e7	−	1.09776e7i	−1.17349	−	0.984678i	−1.00000		0.000157096i	$0.999950\pi$
$660$		0			0
$661$	−1.12916e6	−	6.40376e6i	−0.100519	−	0.570074i	−0.992916	−	0.118821i	$-0.962088\pi$
$661$	−1.12916e6	−	6.40376e6i	−0.100519	−	0.570074i	0.892396	−	0.451253i	$-0.149023\pi$
$662$		0			0
$663$	5.51251e6	−	9.12322e6i	0.487041	−	0.806054i
$664$		0			0
$665$	206660.	+	357945.i	0.0181218	+	0.0313879i
$666$		0			0
$667$	107657.	−	186468.i	0.00936975	−	0.0162289i
$668$		0			0
$669$	5.68978e6	−	4.58426e6i	0.491508	−	0.396008i
$670$		0			0
$671$	−3.25196e7	−	1.18362e7i	−2.78829	−	1.01486i
$672$		0			0
$673$	−2.92052e6	+	1.65631e7i	−0.248555	+	1.40963i	0.563533	+	0.826093i	$0.309442\pi$
$673$	−2.92052e6	+	1.65631e7i	−0.248555	+	1.40963i	−0.812089	+	0.583534i	$0.801669\pi$
$674$		0			0
$675$	−8.26556e6	−	7.82310e6i	−0.698253	−	0.660875i
$676$		0			0
$677$	462621.	−	2.62366e6i	0.0387930	−	0.220006i	−0.959248	−	0.282565i	$-0.908815\pi$
$677$	462621.	−	2.62366e6i	0.0387930	−	0.220006i	0.998041	+	0.0625583i	$0.0199259\pi$
$678$		0			0
$679$	1.08260e6	+	394035.i	0.0901144	+	0.0327990i
$680$		0			0
$681$	1.45196e7	+	5.61474e6i	1.19974	+	0.463940i
$682$		0			0
$683$	−1.17291e6	+	2.03154e6i	−0.0962085	+	0.166638i	−0.910112	−	0.414362i	$-0.864005\pi$
$683$	−1.17291e6	+	2.03154e6i	−0.0962085	+	0.166638i	0.813904	+	0.581000i	$0.197338\pi$
$684$		0			0
$685$	284957.	+	493559.i	0.0232034	+	0.0401895i
$686$		0			0
$687$	1.95825e6	+	3.55346e6i	0.158299	+	0.287250i
$688$		0			0
$689$	1.55656e6	+	8.82769e6i	0.124916	+	0.708433i
$690$		0			0
$691$	−1.24644e7	−	1.04589e7i	−0.993062	−	0.833278i	−0.00705393	−	0.999975i	$-0.502245\pi$
$691$	−1.24644e7	−	1.04589e7i	−0.993062	−	0.833278i	−0.986008	+	0.166697i	$0.946690\pi$
$692$		0			0
$693$	3.19502e6	−	1.02070e6i	0.252721	−	0.0807355i
$694$		0			0
$695$	1.51906e6	−	552892.i	0.119292	−	0.0434188i
$696$		0			0
$697$	7.79879e6	−	6.54396e6i	0.608058	−	0.510222i
$698$		0			0
$699$	4.89946e6	+	4.28033e6i	0.379276	+	0.331348i
$700$		0			0
$701$	8.13182e6			0.625019			0.312509	−	0.949915i	$-0.398830\pi$
$701$	8.13182e6			0.625019			0.312509	+	0.949915i	$0.398830\pi$
$702$		0			0
$703$	2.09230e7			1.59675
$704$		0			0
$705$	−315613.	+	1.60254e6i	−0.0239156	+	0.121433i
$706$		0			0
$707$	330290.	−	277146.i	0.0248512	−	0.0208526i
$708$		0			0
$709$	7.40322e6	−	2.69455e6i	0.553102	−	0.201313i	−0.0503224	−	0.998733i	$-0.516025\pi$
$709$	7.40322e6	−	2.69455e6i	0.553102	−	0.201313i	0.603424	+	0.797420i	$0.293803\pi$
$710$		0			0
$711$	1.09586e7	+	2.08581e7i	0.812982	+	1.54739i
$712$		0			0
$713$	2.48366e7	+	2.08404e7i	1.82965	+	1.53526i
$714$		0			0
$715$	−625712.	−	3.54859e6i	−0.0457730	−	0.259592i
$716$		0			0
$717$	−1.91931e7	−	382453.i	−1.39427	−	0.0277830i
$718$		0			0
$719$	1.19595e7	+	2.07145e7i	0.862765	+	1.49435i	0.869250	+	0.494373i	$0.164602\pi$
$719$	1.19595e7	+	2.07145e7i	0.862765	+	1.49435i	−0.00648487	+	0.999979i	$0.502064\pi$
$720$		0			0
$721$	290088.	−	502447.i	0.0207822	−	0.0359959i
$722$		0			0
$723$	3.23326e6	+	2.07456e7i	0.230035	+	1.47598i
$724$		0			0
$725$	133905.	+	48737.4i	0.00946132	+	0.00344364i
$726$		0			0
$727$	188745.	−	1.07043e6i	0.0132446	−	0.0751139i	−0.977469	−	0.211079i	$-0.932302\pi$
$727$	188745.	−	1.07043e6i	0.0132446	−	0.0751139i	0.990714	+	0.135965i	$0.0434134\pi$
$728$		0			0
$729$	−5.64127e6	−	1.31935e7i	−0.393150	−	0.919474i
$730$		0			0
$731$	1.10857e6	−	6.28700e6i	0.0767306	−	0.435161i
$732$		0			0
$733$	−2.19228e7	−	7.97924e6i	−1.50708	−	0.548532i	−0.549196	−	0.835693i	$-0.685066\pi$
$733$	−2.19228e7	−	7.97924e6i	−1.50708	−	0.548532i	−0.957882	+	0.287162i	$0.907288\pi$
$734$		0			0
$735$	−433541.	−	2.78173e6i	−0.0296014	−	0.189931i
$736$		0			0
$737$	−358490.	+	620924.i	−0.0243113	+	0.0421085i
$738$		0			0
$739$	1.16290e6	+	2.01420e6i	0.0783304	+	0.135672i	0.902530	−	0.430628i	$-0.141708\pi$
$739$	1.16290e6	+	2.01420e6i	0.0783304	+	0.135672i	−0.824199	+	0.566300i	$0.808374\pi$
$740$		0			0
$741$	−1.39454e7	−	277885.i	−0.933011	−	0.0185917i
$742$		0			0
$743$	2.27399e6	+	1.28964e7i	0.151118	+	0.857033i	0.962249	+	0.272169i	$0.0877410\pi$
$743$	2.27399e6	+	1.28964e7i	0.151118	+	0.857033i	−0.811131	+	0.584864i	$0.801148\pi$
$744$		0			0
$745$	2.33071e6	+	1.95570e6i	0.153850	+	0.129095i
$746$		0			0
$747$	−7.39191e6	−	1.40694e7i	−0.484680	−	0.922519i
$748$		0			0
$749$	−1.15535e6	+	420512.i	−0.0752503	+	0.0273889i
$750$		0			0
$751$	852962.	−	715720.i	0.0551861	−	0.0463066i	−0.614777	−	0.788701i	$-0.710754\pi$
$751$	852962.	−	715720.i	0.0551861	−	0.0463066i	0.669964	+	0.742394i	$0.266310\pi$
$752$		0			0
$753$	566999.	−	2.87896e6i	0.0364414	−	0.185033i
$754$		0			0
$755$	4.15936e6			0.265558
$756$		0			0
$757$	1.58732e7			1.00676			0.503379	−	0.864066i	$-0.332090\pi$
$757$	1.58732e7			1.00676			0.503379	+	0.864066i	$0.332090\pi$
$758$		0			0
$759$	3.87381e7	+	3.38429e7i	2.44081	+	2.13237i
$760$		0			0
$761$	1.06129e7	−	8.90525e6i	0.664310	−	0.557422i	−0.247065	−	0.968999i	$-0.579466\pi$
$761$	1.06129e7	−	8.90525e6i	0.664310	−	0.557422i	0.911375	+	0.411577i	$0.135022\pi$
$762$		0			0
$763$	−1.91657e6	+	697574.i	−0.119183	+	0.0433790i
$764$		0			0
$765$	3.85034e6	−	1.23005e6i	0.237873	−	0.0759922i
$766$		0			0
$767$	1.56497e6	+	1.31317e6i	0.0960546	+	0.0805994i
$768$		0			0
$769$	−4.69950e6	−	2.66522e7i	−0.286573	−	1.62524i	−0.699610	−	0.714525i	$-0.746643\pi$
$769$	−4.69950e6	−	2.66522e7i	−0.286573	−	1.62524i	0.413037	−	0.910714i	$-0.364468\pi$
$770$		0			0
$771$	−1.20603e7	−	2.18846e7i	−0.730670	−	1.32588i
$772$		0			0
$773$	−7.26028e6	−	1.25752e7i	−0.437023	−	0.756946i	0.560435	−	0.828198i	$-0.310634\pi$
$773$	−7.26028e6	−	1.25752e7i	−0.437023	−	0.756946i	−0.997458	+	0.0712520i	$0.977301\pi$
$774$		0			0
$775$	−1.07287e7	+	1.85826e7i	−0.641641	+	1.11136i
$776$		0			0
$777$	2.91431e6	+	1.12697e6i	0.173174	+	0.0669667i
$778$		0			0
$779$	−1.25184e7	−	4.55632e6i	−0.739103	−	0.269011i
$780$		0			0
$781$	−7.44210e6	+	4.22062e7i	−0.436584	+	2.47599i
$782$		0			0
$783$	130486.	+	123501.i	0.00760606	+	0.00719890i
$784$		0			0
$785$	242288.	−	1.37408e6i	0.0140332	−	0.0795865i
$786$		0			0
$787$	1.43322e7	+	5.21648e6i	0.824850	+	0.300221i	0.719744	−	0.694240i	$-0.244259\pi$
$787$	1.43322e7	+	5.21648e6i	0.824850	+	0.300221i	0.105107	+	0.994461i	$0.466482\pi$
$788$		0			0
$789$	1.57354e7	−	1.26780e7i	0.899882	−	0.725036i
$790$		0			0
$791$	−2.21539e6	+	3.83717e6i	−0.125895	+	0.218057i
$792$		0			0
$793$	1.07459e7	+	1.86125e7i	0.606821	+	1.05105i
$794$		0			0
$795$	−1.75787e6	+	2.90929e6i	−0.0986438	+	0.163256i
$796$		0			0
$797$	−4.73346e6	−	2.68448e7i	−0.263957	−	1.49697i	−0.771990	−	0.635635i	$-0.780738\pi$
$797$	−4.73346e6	−	2.68448e7i	−0.263957	−	1.49697i	0.508033	−	0.861337i	$-0.330373\pi$
$798$		0			0
$799$	1.10717e7	+	9.29022e6i	0.613544	+	0.514824i
$800$		0			0
$801$	−1.57001e6	−	1.15864e7i	−0.0864613	−	0.638066i
$802$		0			0
$803$	3.78649e7	−	1.37817e7i	2.07228	−	0.754248i
$804$		0			0
$805$	−725152.	+	608475.i	−0.0394402	+	0.0330943i
$806$		0			0
$807$	1.67052e7	−	5.70593e6i	0.902958	−	0.308420i
$808$		0			0
$809$	−1.85602e7			−0.997035			−0.498517	−	0.866880i	$-0.666122\pi$
$809$	−1.85602e7			−0.997035			−0.498517	+	0.866880i	$0.666122\pi$
$810$		0			0
$811$	1.27375e7			0.680035			0.340017	−	0.940419i	$-0.389567\pi$
$811$	1.27375e7			0.680035			0.340017	+	0.940419i	$0.389567\pi$
$812$		0			0
$813$	1.33564e7	−	4.56208e6i	0.708699	−	0.242068i
$814$		0			0
$815$	−4.86743e6	+	4.08426e6i	−0.256688	+	0.215387i
$816$		0			0
$817$	−7.84995e6	+	2.85715e6i	−0.411445	+	0.149754i
$818$		0			0
$819$	−1.92745e6	−	789842.i	−0.100409	−	0.0411463i
$820$		0			0
$821$	−4.88211e6	−	4.09657e6i	−0.252784	−	0.212111i	0.507586	−	0.861601i	$-0.330538\pi$
$821$	−4.88211e6	−	4.09657e6i	−0.252784	−	0.212111i	−0.760370	+	0.649490i	$0.774982\pi$
$822$		0			0
$823$	−2.03398e6	−	1.15353e7i	−0.104676	−	0.593646i	−0.991349	−	0.131250i	$-0.958101\pi$
$823$	−2.03398e6	−	1.15353e7i	−0.104676	−	0.593646i	0.886673	−	0.462396i	$-0.153010\pi$
$824$		0			0
$825$	−1.76056e7	+	2.91374e7i	−0.900568	+	1.49044i
$826$		0			0
$827$	6.10161e6	+	1.05683e7i	0.310228	+	0.537330i	0.978412	−	0.206666i	$-0.0662613\pi$
$827$	6.10161e6	+	1.05683e7i	0.310228	+	0.537330i	−0.668184	+	0.743996i	$0.732928\pi$
$828$		0			0
$829$	982542.	−	1.70181e6i	0.0496552	−	0.0860053i	−0.840129	−	0.542386i	$-0.817521\pi$
$829$	982542.	−	1.70181e6i	0.0496552	−	0.0860053i	0.889785	+	0.456381i	$0.150854\pi$
$830$		0			0
$831$	−2.64734e7	+	2.13296e7i	−1.32986	+	1.07147i
$832$		0			0
$833$	−2.34099e7	−	8.52051e6i	−1.16893	−	0.425454i
$834$		0			0
$835$	−303821.	+	1.72306e6i	−0.0150800	+	0.0855230i
$836$		0			0
$837$	−2.17261e7	+	1.61207e7i	−1.07194	+	0.795373i
$838$		0			0
$839$	−669985.	+	3.79967e6i	−0.0328594	+	0.186355i	−0.996820	−	0.0796916i	$-0.974606\pi$
$839$	−669985.	+	3.79967e6i	−0.0328594	+	0.186355i	0.963960	+	0.266047i	$0.0857176\pi$
$840$		0			0
$841$	1.92721e7	+	7.01446e6i	0.939590	+	0.341983i
$842$		0			0
$843$	−1.60634e6	−	621173.i	−0.0778516	−	0.0301053i
$844$		0			0
$845$	919739.	−	1.59303e6i	0.0443122	−	0.0767509i
$846$		0			0
$847$	−3.48749e6	−	6.04052e6i	−0.167034	−	0.289311i
$848$		0			0
$849$	−1.65162e7	−	2.99703e7i	−0.786394	−	1.42700i
$850$		0			0
$851$	8.32116e6	+	4.71917e7i	0.393877	+	2.23379i
$852$		0			0
$853$	−1.31284e7	−	1.10160e7i	−0.617785	−	0.518384i	0.279321	−	0.960198i	$-0.409891\pi$
$853$	−1.31284e7	−	1.10160e7i	−0.617785	−	0.518384i	−0.897107	+	0.441814i	$0.854335\pi$
$854$		0			0
$855$	−3.91311e6	−	3.55855e6i	−0.183066	−	0.166478i
$856$		0			0
$857$	2.77780e7	−	1.01104e7i	1.29196	−	0.470236i	0.397591	−	0.917563i	$-0.369846\pi$
$857$	2.77780e7	−	1.01104e7i	1.29196	−	0.470236i	0.894370	+	0.447327i	$0.147624\pi$
$858$		0			0
$859$	260236.	−	218364.i	0.0120333	−	0.0100971i	−0.636751	−	0.771069i	$-0.719722\pi$
$859$	260236.	−	218364.i	0.0120333	−	0.0100971i	0.648784	+	0.760972i	$0.275278\pi$
$860$		0			0
$861$	−1.49824e6	−	1.30891e6i	−0.0688767	−	0.0601730i
$862$		0			0
$863$	2.37758e7			1.08670			0.543348	−	0.839507i	$-0.317156\pi$
$863$	2.37758e7			1.08670			0.543348	+	0.839507i	$0.317156\pi$
$864$		0			0
$865$	973972.			0.0442595
$866$		0			0
$867$	2.63456e6	−	1.33771e7i	0.119031	−	0.604386i
$868$		0			0
$869$	5.39911e7	−	4.53039e7i	2.42534	−	2.03510i
$870$		0			0
$871$	418416.	−	152291.i	0.0186880	−	0.00680187i
$872$		0			0
$873$	−1.47314e7	−	587324.i	−0.654195	−	0.0260821i
$874$		0			0
$875$	−979099.	−	821561.i	−0.0432321	−	0.0362760i
$876$		0			0
$877$	3.44321e6	+	1.95274e7i	0.151170	+	0.857326i	0.962205	+	0.272328i	$0.0877935\pi$
$877$	3.44321e6	+	1.95274e7i	0.151170	+	0.857326i	−0.811035	+	0.584998i	$0.801095\pi$
$878$		0			0
$879$	1.44625e7	+	288188.i	0.631352	+	0.0125807i
$880$		0			0
$881$	1.28179e7	+	2.22012e7i	0.556385	+	0.963687i	0.997794	+	0.0663815i	$0.0211454\pi$
$881$	1.28179e7	+	2.22012e7i	0.556385	+	0.963687i	−0.441409	+	0.897306i	$0.645521\pi$
$882$		0			0
$883$	3.10449e6	−	5.37713e6i	0.133995	−	0.232086i	−0.791218	−	0.611534i	$-0.790553\pi$
$883$	3.10449e6	−	5.37713e6i	0.133995	−	0.232086i	0.925213	+	0.379448i	$0.123886\pi$
$884$		0			0
$885$	119297.	+	765444.i	0.00512000	+	0.0328515i
$886$		0			0
$887$	−2.63219e7	−	9.58039e6i	−1.12333	−	0.408859i	−0.287465	−	0.957791i	$-0.592812\pi$
$887$	−2.63219e7	−	9.58039e6i	−1.12333	−	0.408859i	−0.835867	+	0.548932i	$0.815035\pi$
$888$		0			0
$889$	179670.	−	1.01896e6i	0.00762469	−	0.0432418i
$890$		0			0
$891$	−3.49724e7	+	2.48846e7i	−1.47581	+	1.05011i
$892$		0			0
$893$	3.28411e6	−	1.86251e7i	0.137813	−	0.781575i
$894$		0			0
$895$	−4.38502e6	−	1.59602e6i	−0.182984	−	0.0666009i
$896$		0			0
$897$	−4.91939e6	−	3.15643e7i	−0.204141	−	1.30983i
$898$		0			0
$899$	169371.	−	293359.i	0.00698939	−	0.0121060i
$900$		0			0
$901$	1.50392e7	+	2.60487e7i	0.617181	+	1.06899i
$902$		0			0
$903$	−1.24729e6	−	24854.2i	−0.0509036	−	0.00101433i
$904$		0			0
$905$	75205.7	+	426512.i	0.00305231	+	0.0173105i
$906$		0			0
$907$	1.69198e7	+	1.41974e7i	0.682930	+	0.573047i	0.916861	−	0.399207i	$-0.130714\pi$
$907$	1.69198e7	+	1.41974e7i	0.682930	+	0.573047i	−0.233931	+	0.972253i	$0.575159\pi$
$908$		0			0
$909$	−2.94694e6	+	4.66464e6i	−0.118294	+	0.187244i
$910$		0			0
$911$	−3.32996e7	+	1.21201e7i	−1.32936	+	0.483848i	−0.906446	−	0.422321i	$-0.861216\pi$
$911$	−3.32996e7	+	1.21201e7i	−1.32936	+	0.483848i	−0.422916	+	0.906169i	$0.638993\pi$
$912$		0			0
$913$	−3.64187e7	+	3.05589e7i	−1.44593	+	1.21328i
$914$		0			0
$915$	−1.57481e6	+	7.99618e6i	−0.0621836	+	0.315740i
$916$		0			0
$917$	−2.28146e6			−0.0895962
$918$		0			0
$919$	−7.91663e6			−0.309208			−0.154604	−	0.987976i	$-0.549410\pi$
$919$	−7.91663e6			−0.309208			−0.154604	+	0.987976i	$0.549410\pi$
$920$		0			0
$921$	−3.16427e7	−	2.76441e7i	−1.22920	−	1.07387i
$922$		0			0
$923$	2.03889e7	−	1.71083e7i	0.787752	−	0.661002i
$924$		0			0
$925$	−2.98015e7	+	1.08469e7i	−1.14521	+	0.416821i
$926$		0			0
$927$	−1.57950e6	+	7.25450e6i	−0.0603698	+	0.277273i
$928$		0			0
$929$	−7.88140e6	−	6.61328e6i	−0.299615	−	0.251407i	0.480569	−	0.876957i	$-0.340430\pi$
$929$	−7.88140e6	−	6.61328e6i	−0.299615	−	0.251407i	−0.780184	+	0.625550i	$0.784875\pi$
$930$		0			0
$931$	5.66074e6	+	3.21037e7i	0.214042	+	1.21389i
$932$		0			0
$933$	−2.17531e7	−	3.94732e7i	−0.818119	−	1.48456i
$934$		0			0
$935$	−6.04552e6	−	1.04711e7i	−0.226154	−	0.391710i
$936$		0			0
$937$	1.95923e7	−	3.39349e7i	0.729015	−	1.26269i	−0.228285	−	0.973594i	$-0.573312\pi$
$937$	1.95923e7	−	3.39349e7i	0.729015	−	1.26269i	0.957300	−	0.289097i	$-0.0933549\pi$
$938$		0			0
$939$	1.36937e7	+	5.29539e6i	0.506825	+	0.195990i
$940$		0			0
$941$	−3.13085e7	−	1.13954e7i	−1.15263	−	0.419522i	−0.306169	−	0.951977i	$-0.599047\pi$
$941$	−3.13085e7	−	1.13954e7i	−1.15263	−	0.419522i	−0.846458	+	0.532455i	$0.821269\pi$
$942$		0			0
$943$	5.29813e6	−	3.00472e7i	0.194018	−	1.10033i
$944$		0			0
$945$	−353373.	−	706430.i	−0.0128722	−	0.0257330i
$946$		0			0
$947$	4.40707e6	−	2.49937e7i	0.159689	−	0.905640i	−0.794684	−	0.607023i	$-0.792364\pi$
$947$	4.40707e6	−	2.49937e7i	0.159689	−	0.905640i	0.954373	−	0.298617i	$-0.0965254\pi$
$948$		0			0
$949$	−2.35154e7	−	8.55889e6i	−0.847591	−	0.308498i
$950$		0			0
$951$	296365.	−	238782.i	0.0106261	−	0.00856150i
$952$		0			0
$953$	−1.14944e6	+	1.99088e6i	−0.0409971	+	0.0710091i	−0.885796	−	0.464075i	$-0.846387\pi$
$953$	−1.14944e6	+	1.99088e6i	−0.0409971	+	0.0710091i	0.844799	+	0.535084i	$0.179720\pi$
$954$		0			0
$955$	2.67189e6	+	4.62786e6i	0.0948005	+	0.164199i
$956$		0			0
$957$	277935.	−	459984.i	0.00980987	−	0.0162354i
$958$		0			0
$959$	−171131.	−	970530.i	−0.00600871	−	0.0340771i
$960$		0			0
$961$	1.71428e7	+	1.43845e7i	0.598789	+	0.502444i
$962$		0			0
$963$	1.24461e7	−	9.62528e6i	0.432481	−	0.334463i
$964$		0			0
$965$	−565552.	+	205844.i	−0.0195503	+	0.00711574i
$966$		0			0
$967$	3.79250e7	−	3.18229e7i	1.30425	−	1.09439i	0.314851	−	0.949141i	$-0.398046\pi$
$967$	3.79250e7	−	3.18229e7i	1.30425	−	1.09439i	0.989395	−	0.145251i	$-0.0463989\pi$
$968$		0			0
$969$	−4.42910e7	+	1.51283e7i	−1.51533	+	0.517584i
$970$		0			0
$971$	−2.46908e7			−0.840401			−0.420200	−	0.907431i	$-0.638040\pi$
$971$	−2.46908e7			−0.840401			−0.420200	+	0.907431i	$0.638040\pi$
$972$		0			0
$973$	−2.79536e6			−0.0946576
$974$		0			0
$975$	2.00071e7	−	6.83375e6i	0.674019	−	0.230222i
$976$		0			0
$977$	4.00126e7	−	3.35746e7i	1.34110	−	1.12532i	0.359757	−	0.933046i	$-0.382860\pi$
$977$	4.00126e7	−	3.35746e7i	1.34110	−	1.12532i	0.981342	−	0.192270i	$-0.0615849\pi$
$978$		0			0
$979$	−3.28659e7	+	1.19622e7i	−1.09595	+	0.398892i
$980$		0			0
$981$	2.06464e7	−	1.59671e7i	0.684970	−	0.529727i
$982$		0			0
$983$	−2.33344e7	−	1.95799e7i	−0.770216	−	0.646288i	0.170548	−	0.985349i	$-0.445446\pi$
$983$	−2.33344e7	−	1.95799e7i	−0.770216	−	0.646288i	−0.940764	+	0.339061i	$0.889891\pi$
$984$		0			0
$985$	−433015.	−	2.45575e6i	−0.0142204	−	0.0806480i
$986$		0			0
$987$	1.46063e6	−	2.41735e6i	0.0477252	−	0.0789854i
$988$		0			0
$989$	−9.56623e6	−	1.65692e7i	−0.310993	−	0.538655i
$990$		0			0
$991$	−2.35237e7	+	4.07442e7i	−0.760888	+	1.31790i	0.181505	+	0.983390i	$0.441903\pi$
$991$	−2.35237e7	+	4.07442e7i	−0.760888	+	1.31790i	−0.942393	+	0.334507i	$0.891430\pi$
$992$		0			0
$993$	−4.76953e7	+	3.84282e7i	−1.53498	+	1.23673i
$994$		0			0
$995$	−3.29616e6	−	1.19970e6i	−0.105548	−	0.0384163i
$996$		0			0
$997$	−236025.	+	1.33856e6i	−0.00752003	+	0.0426482i	−0.988337	−	0.152283i	$-0.951337\pi$
$997$	−236025.	+	1.33856e6i	−0.00752003	+	0.0426482i	0.980817	+	0.194932i	$0.0624485\pi$
$998$		0			0
$999$	−3.99140e7	−	2.38858e6i	−1.26535	−	0.0757227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.25.2	yes	90
3.2	odd	2		324.6.i.a.73.7		90
27.13	even	9	inner	108.6.i.a.13.2	✓	90
27.14	odd	18		324.6.i.a.253.7		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.2	✓	90	27.13	even	9	inner
108.6.i.a.25.2	yes	90	1.1	even	1	trivial
324.6.i.a.73.7		90	3.2	odd	2
324.6.i.a.253.7		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)

\(f(q)\)	\(=\)	\(q+(-14.7517 + 5.03867i) q^{3} +(8.41214 - 7.05862i) q^{5} +(-17.8438 + 6.49461i) q^{7} +(192.224 - 148.658i) q^{9} +O(q^{10})\)	\(q+(-14.7517 + 5.03867i) q^{3} +(8.41214 - 7.05862i) q^{5} +(-17.8438 + 6.49461i) q^{7} +(192.224 - 148.658i) q^{9} +(-556.830 - 467.236i) q^{11} +(78.3887 + 444.565i) q^{13} +(-88.5270 + 146.512i) q^{15} +(757.378 + 1311.82i) q^{17} +(991.064 - 1716.57i) q^{19} +(230.502 - 185.715i) q^{21} +(4265.86 + 1552.65i) q^{23} +(-521.711 + 2958.77i) q^{25} +(-2086.58 + 3161.50i) q^{27} +(8.23610 - 46.7093i) q^{29} +(6711.24 + 2442.69i) q^{31} +(10568.4 + 4086.82i) q^{33} +(-104.261 + 180.586i) q^{35} +(5277.92 + 9141.62i) q^{37} +(-3396.38 - 6163.09i) q^{39} +(-1167.08 - 6618.85i) q^{41} +(-3228.52 - 2709.05i) q^{43} +(567.692 - 2607.36i) q^{45} +(8966.06 - 3263.38i) q^{47} +(-12598.7 + 10571.6i) q^{49} +(-17782.4 - 15535.3i) q^{51} +19856.9 q^{53} -7982.17 q^{55} +(-5970.60 + 30316.0i) q^{57} +(3466.76 - 2908.95i) q^{59} +(44738.0 - 16283.3i) q^{61} +(-2464.52 + 3901.03i) q^{63} +(3797.43 + 3186.42i) q^{65} +(-171.281 - 971.383i) q^{67} +(-70751.9 - 1409.84i) q^{69} +(-29479.9 - 51060.7i) q^{71} +(-27717.4 + 48007.9i) q^{73} +(-7212.17 - 46275.5i) q^{75} +(12970.5 + 4720.87i) q^{77} +(-16837.2 + 95488.5i) q^{79} +(14850.8 - 57151.0i) q^{81} +(11357.2 - 64409.9i) q^{83} +(15630.8 + 5689.14i) q^{85} +(113.856 + 730.538i) q^{87} +(24058.1 - 41669.9i) q^{89} +(-4286.02 - 7423.61i) q^{91} +(-111310. - 2218.03i) q^{93} +(-3779.67 - 21435.6i) q^{95} +(-46476.7 - 38998.6i) q^{97} +(-176494. - 7036.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 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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