LMFDB - Embedded newform 76.8.i.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	76.17
Dual form			76.8.i.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-39.6110 - 33.2376i) q^{3} +(72.0424 - 26.2213i) q^{5} +(-610.937 - 1058.17i) q^{7} +(84.5259 + 479.370i) q^{9} +O(q^{10})$	\(q+(-39.6110 - 33.2376i) q^{3} +(72.0424 - 26.2213i) q^{5} +(-610.937 - 1058.17i) q^{7} +(84.5259 + 479.370i) q^{9} +(1242.73 - 2152.47i) q^{11} +(-905.357 + 759.685i) q^{13} +(-3725.20 - 1355.86i) q^{15} +(2252.63 - 12775.3i) q^{17} +(718.339 - 29889.1i) q^{19} +(-10971.3 + 62221.3i) q^{21} +(-16764.5 - 6101.78i) q^{23} +(-55344.7 + 46439.7i) q^{25} +(-43958.3 + 76137.9i) q^{27} +(45048.0 + 255480. i) q^{29} +(74057.3 + 128271. i) q^{31} +(-120769. + 43956.3i) q^{33} +(-71760.0 - 60213.8i) q^{35} -462436. q^{37} +61112.2 q^{39} +(-9939.40 - 8340.14i) q^{41} +(-191590. + 69733.0i) q^{43} +(18659.2 + 32318.6i) q^{45} +(-26707.6 - 151466. i) q^{47} +(-334715. + 579744. i) q^{49} +(-513849. + 431171. i) q^{51} +(794526. + 289184. i) q^{53} +(33088.7 - 187655. i) q^{55} +(-1.02189e6 + 1.16006e6i) q^{57} +(175552. - 995606. i) q^{59} +(-907335. - 330243. i) q^{61} +(455617. - 382308. i) q^{63} +(-45304.2 + 78469.1i) q^{65} +(139657. + 792032. i) q^{67} +(461250. + 798909. i) q^{69} +(2.96107e6 - 1.07774e6i) q^{71} +(1.83776e6 + 1.54206e6i) q^{73} +3.73580e6 q^{75} -3.03692e6 q^{77} +(-3.95465e6 - 3.31835e6i) q^{79} +(5.27222e6 - 1.91893e6i) q^{81} +(-1.62478e6 - 2.81420e6i) q^{83} +(-172700. - 979431. i) q^{85} +(6.70714e6 - 1.16171e7i) q^{87} +(-2.76644e6 + 2.32132e6i) q^{89} +(1.35699e6 + 493905. i) q^{91} +(1.32993e6 - 7.54242e6i) q^{93} +(-731978. - 2.17211e6i) q^{95} +(2.29594e6 - 1.30209e7i) q^{97} +(1.13688e6 + 413789. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	−39.6110	−	33.2376i	−0.847015	−	0.710730i	0.112115	−	0.993695i	$-0.464238\pi$
$3$	−39.6110	−	33.2376i	−0.847015	−	0.710730i	−0.959130	+	0.282965i	$0.908682\pi$
$4$		0			0
$5$	72.0424	−	26.2213i	0.257747	−	0.0938121i	−0.209915	−	0.977720i	$-0.567319\pi$
$5$	72.0424	−	26.2213i	0.257747	−	0.0938121i	0.467662	+	0.883908i	$0.345097\pi$
$6$		0			0
$7$	−610.937	−	1058.17i	−0.673214	−	1.16604i	−0.976988	−	0.213296i	$-0.931580\pi$
$7$	−610.937	−	1058.17i	−0.673214	−	1.16604i	0.303774	−	0.952744i	$-0.401753\pi$
$8$		0			0
$9$	84.5259	+	479.370i	0.0386493	+	0.219191i
$10$		0			0
$11$	1242.73	−	2152.47i	0.281516	−	0.487600i	−0.690242	−	0.723578i	$-0.742496\pi$
$11$	1242.73	−	2152.47i	0.281516	−	0.487600i	0.971758	+	0.235978i	$0.0758294\pi$
$12$		0			0
$13$	−905.357	+	759.685i	−0.114293	+	0.0959029i	−0.698143	−	0.715958i	$-0.745990\pi$
$13$	−905.357	+	759.685i	−0.114293	+	0.0959029i	0.583850	+	0.811861i	$0.301546\pi$
$14$		0			0
$15$	−3725.20	−	1355.86i	−0.284990	−	0.103728i
$16$		0			0
$17$	2252.63	−	12775.3i	0.111204	−	0.630667i	−0.877356	−	0.479839i	$-0.840695\pi$
$17$	2252.63	−	12775.3i	0.111204	−	0.630667i	0.988560	−	0.150828i	$-0.0481940\pi$
$18$		0			0
$19$	718.339	−	29889.1i	0.0240266	−	0.999711i
$19$	718.339	−	29889.1i	0.0240266	−	0.999711i
$20$		0			0
$21$	−10971.3	+	62221.3i	−0.258518	+	1.46613i
$22$		0			0
$23$	−16764.5	−	6101.78i	−0.287305	−	0.104570i	0.194348	−	0.980933i	$-0.437741\pi$
$23$	−16764.5	−	6101.78i	−0.287305	−	0.104570i	−0.481653	+	0.876362i	$0.659963\pi$
$24$		0			0
$25$	−55344.7	+	46439.7i	−0.708412	+	0.594428i
$26$		0			0
$27$	−43958.3	+	76137.9i	−0.429801	+	0.744437i
$28$		0			0
$29$	45048.0	+	255480.i	0.342991	+	1.94520i	0.326082	+	0.945341i	$0.394271\pi$
$29$	45048.0	+	255480.i	0.342991	+	1.94520i	0.0169089	+	0.999857i	$0.494617\pi$
$30$		0			0
$31$	74057.3	+	128271.i	0.446480	+	0.773326i	0.998154	−	0.0607339i	$-0.0193441\pi$
$31$	74057.3	+	128271.i	0.446480	+	0.773326i	−0.551674	+	0.834060i	$0.686011\pi$
$32$		0			0
$33$	−120769.	+	43956.3i	−0.585000	+	0.212923i
$34$		0			0
$35$	−71760.0	−	60213.8i	−0.282907	−	0.237387i
$36$		0			0
$37$	−462436.			−1.50088			−0.750439	−	0.660940i	$-0.770158\pi$
$37$	−462436.			−1.50088			−0.750439	+	0.660940i	$0.770158\pi$
$38$		0			0
$39$	61112.2			0.164969
$40$		0			0
$41$	−9939.40	−	8340.14i	−0.0225225	−	0.0188986i	0.631457	−	0.775411i	$-0.282457\pi$
$41$	−9939.40	−	8340.14i	−0.0225225	−	0.0188986i	−0.653979	+	0.756512i	$0.726902\pi$
$42$		0			0
$43$	−191590.	+	69733.0i	−0.367480	+	0.133752i	−0.519158	−	0.854678i	$-0.673754\pi$
$43$	−191590.	+	69733.0i	−0.367480	+	0.133752i	0.151678	+	0.988430i	$0.451532\pi$
$44$		0			0
$45$	18659.2	+	32318.6i	0.0305245	+	0.0528699i
$46$		0			0
$47$	−26707.6	−	151466.i	−0.0375226	−	0.212801i	0.960282	−	0.279032i	$-0.0900136\pi$
$47$	−26707.6	−	151466.i	−0.0375226	−	0.212801i	−0.997804	+	0.0662311i	$0.978903\pi$
$48$		0			0
$49$	−334715.	+	579744.i	−0.406433	+	0.703963i
$50$		0			0
$51$	−513849.	+	431171.i	−0.542426	+	0.455149i
$52$		0			0
$53$	794526.	+	289184.i	0.733065	+	0.266814i	0.681462	−	0.731854i	$-0.261345\pi$
$53$	794526.	+	289184.i	0.733065	+	0.266814i	0.0516035	+	0.998668i	$0.483567\pi$
$54$		0			0
$55$	33088.7	−	187655.i	0.0268170	−	0.152087i
$56$		0			0
$57$	−1.02189e6	+	1.16006e6i	−0.730876	+	0.829694i
$58$		0			0
$59$	175552.	−	995606.i	0.111282	−	0.631110i	−0.877242	−	0.480048i	$-0.840619\pi$
$59$	175552.	−	995606.i	0.111282	−	0.631110i	0.988524	−	0.151063i	$-0.0482695\pi$
$60$		0			0
$61$	−907335.	−	330243.i	−0.511815	−	0.186285i	0.0731855	−	0.997318i	$-0.476684\pi$
$61$	−907335.	−	330243.i	−0.511815	−	0.186285i	−0.585001	+	0.811033i	$0.698906\pi$
$62$		0			0
$63$	455617.	−	382308.i	0.229566	−	0.192629i
$64$		0			0
$65$	−45304.2	+	78469.1i	−0.0204617	+	0.0354407i
$66$		0			0
$67$	139657.	+	792032.i	0.0567283	+	0.321722i	0.999945	−	0.0104549i	$-0.00332795\pi$
$67$	139657.	+	792032.i	0.0567283	+	0.321722i	−0.943217	+	0.332177i	$0.892217\pi$
$68$		0			0
$69$	461250.	+	798909.i	0.169030	+	0.292769i
$70$		0			0
$71$	2.96107e6	−	1.07774e6i	0.981850	−	0.357364i	0.199291	−	0.979940i	$-0.436136\pi$
$71$	2.96107e6	−	1.07774e6i	0.981850	−	0.357364i	0.782559	+	0.622576i	$0.213914\pi$
$72$		0			0
$73$	1.83776e6	+	1.54206e6i	0.552915	+	0.463951i	0.875927	−	0.482444i	$-0.160251\pi$
$73$	1.83776e6	+	1.54206e6i	0.552915	+	0.463951i	−0.323012	+	0.946395i	$0.604695\pi$
$74$		0			0
$75$	3.73580e6			1.02251
$76$		0			0
$77$	−3.03692e6			−0.758082
$78$		0			0
$79$	−3.95465e6	−	3.31835e6i	−0.902430	−	0.757228i	0.0682342	−	0.997669i	$-0.478263\pi$
$79$	−3.95465e6	−	3.31835e6i	−0.902430	−	0.757228i	−0.970664	+	0.240441i	$0.922708\pi$
$80$		0			0
$81$	5.27222e6	−	1.91893e6i	1.10229	−	0.401201i
$82$		0			0
$83$	−1.62478e6	−	2.81420e6i	−0.311904	−	0.540234i	0.666871	−	0.745174i	$-0.267633\pi$
$83$	−1.62478e6	−	2.81420e6i	−0.311904	−	0.540234i	−0.978775	+	0.204940i	$0.934300\pi$
$84$		0			0
$85$	−172700.	−	979431.i	−0.0305019	−	0.172985i
$86$		0			0
$87$	6.70714e6	−	1.16171e7i	1.09199	−	1.89139i
$88$		0			0
$89$	−2.76644e6	+	2.32132e6i	−0.415965	+	0.349036i	−0.826626	−	0.562752i	$-0.809742\pi$
$89$	−2.76644e6	+	2.32132e6i	−0.415965	+	0.349036i	0.410661	+	0.911788i	$0.365298\pi$
$90$		0			0
$91$	1.35699e6	+	493905.i	0.188770	+	0.0687067i
$92$		0			0
$93$	1.32993e6	−	7.54242e6i	0.171451	−	0.972345i
$94$		0			0
$95$	−731978.	−	2.17211e6i	−0.0875922	−	0.259926i
$96$		0			0
$97$	2.29594e6	−	1.30209e7i	0.255422	−	1.44857i	−0.539564	−	0.841944i	$-0.681411\pi$
$97$	2.29594e6	−	1.30209e7i	0.255422	−	1.44857i	0.794987	−	0.606627i	$-0.207478\pi$
$98$		0			0
$99$	1.13688e6	+	413789.i	0.117758	+	0.0428604i
$100$		0			0
$101$	−1.83039e6	+	1.53588e6i	−0.176774	+	0.148331i	−0.726882	−	0.686763i	$-0.759031\pi$
$101$	−1.83039e6	+	1.53588e6i	−0.176774	+	0.148331i	0.550108	+	0.835094i	$0.314587\pi$
$102$		0			0
$103$	−2.15334e6	+	3.72969e6i	−0.194170	+	0.336312i	−0.946628	−	0.322328i	$-0.895535\pi$
$103$	−2.15334e6	+	3.72969e6i	−0.194170	+	0.336312i	0.752458	+	0.658640i	$0.228868\pi$
$104$		0			0
$105$	841124.	+	4.77025e6i	0.0709084	+	0.402141i
$106$		0			0
$107$	8.20331e6	+	1.42086e7i	0.647360	+	1.12126i	0.983751	+	0.179538i	$0.0574604\pi$
$107$	8.20331e6	+	1.42086e7i	0.647360	+	1.12126i	−0.336391	+	0.941723i	$0.609206\pi$
$108$		0			0
$109$	2.19345e6	−	798349.i	0.162231	−	0.0590473i	−0.259628	−	0.965709i	$-0.583600\pi$
$109$	2.19345e6	−	798349.i	0.162231	−	0.0590473i	0.421859	+	0.906661i	$0.361378\pi$
$110$		0			0
$111$	1.83175e7	+	1.53702e7i	1.27127	+	1.06672i
$112$		0			0
$113$	−2.58815e7			−1.68739			−0.843693	−	0.536827i	$-0.819623\pi$
$113$	−2.58815e7			−1.68739			−0.843693	+	0.536827i	$0.819623\pi$
$114$		0			0
$115$	−1.36775e6			−0.0838619
$116$		0			0
$117$	−440697.	−	369788.i	−0.0254384	−	0.0213453i
$118$		0			0
$119$	−1.48947e7	+	5.42123e6i	−0.810248	+	0.294906i
$120$		0			0
$121$	6.65482e6	+	1.15265e7i	0.341497	+	0.591491i
$122$		0			0
$123$	116503.	+	660723.i	0.00564508	+	0.0320148i
$124$		0			0
$125$	−5.76421e6	+	9.98391e6i	−0.263970	+	0.457210i
$126$		0			0
$127$	−4.76983e6	+	4.00236e6i	−0.206628	+	0.173382i	−0.740229	−	0.672355i	$-0.765283\pi$
$127$	−4.76983e6	+	4.00236e6i	−0.206628	+	0.173382i	0.533601	+	0.845737i	$0.320839\pi$
$128$		0			0
$129$	9.90682e6	+	3.60579e6i	0.406322	+	0.147889i
$130$		0			0
$131$	2.47023e6	−	1.40094e7i	0.0960036	−	0.544463i	−0.898432	−	0.439113i	$-0.855293\pi$
$131$	2.47023e6	−	1.40094e7i	0.0960036	−	0.544463i	0.994435	−	0.105350i	$-0.0335963\pi$
$132$		0			0
$133$	−3.20667e7	+	1.75002e7i	−1.18188	+	0.645003i
$134$		0			0
$135$	−1.17042e6	+	6.63780e6i	−0.0409425	+	0.232197i
$136$		0			0
$137$	−4.20901e7	−	1.53196e7i	−1.39849	−	0.509008i	−0.470758	−	0.882262i	$-0.656019\pi$
$137$	−4.20901e7	−	1.53196e7i	−1.39849	−	0.509008i	−0.927729	+	0.373255i	$0.878242\pi$
$138$		0			0
$139$	−3.64072e6	+	3.05492e6i	−0.114983	+	0.0964825i	−0.698466	−	0.715643i	$-0.746134\pi$
$139$	−3.64072e6	+	3.05492e6i	−0.114983	+	0.0964825i	0.583483	+	0.812125i	$0.301689\pi$
$140$		0			0
$141$	−3.97646e6	+	6.88743e6i	−0.119462	+	0.206914i
$142$		0			0
$143$	510086.	+	2.89284e6i	0.0145871	+	0.0827273i
$144$		0			0
$145$	9.94438e6	+	1.72242e7i	0.270888	+	0.469192i
$146$		0			0
$147$	3.25277e7	−	1.18391e7i	0.844583	−	0.307403i
$148$		0			0
$149$	1.35719e7	+	1.13882e7i	0.336116	+	0.282035i	0.795187	−	0.606365i	$-0.207373\pi$
$149$	1.35719e7	+	1.13882e7i	0.336116	+	0.282035i	−0.459070	+	0.888400i	$0.651817\pi$
$150$		0			0
$151$	82032.0			0.00193894			0.000969469	−	1.00000i	$-0.499691\pi$
$151$	82032.0			0.00193894			0.000969469		1.00000i	$0.499691\pi$
$152$		0			0
$153$	6.31452e6			0.142535
$154$		0			0
$155$	8.69869e6	+	7.29907e6i	0.187626	+	0.157437i
$156$		0			0
$157$	−6.93794e7	+	2.52520e7i	−1.43081	+	0.520772i	−0.937163	−	0.348891i	$-0.886558\pi$
$157$	−6.93794e7	+	2.52520e7i	−1.43081	+	0.520772i	−0.493646	+	0.869663i	$0.664336\pi$
$158$		0			0
$159$	−2.18602e7	−	3.78630e7i	−0.431285	−	0.747007i
$160$		0			0
$161$	3.78531e6	+	2.14675e7i	0.0714843	+	0.405408i
$162$		0			0
$163$	4.76156e7	−	8.24726e7i	0.861177	−	1.49160i	−0.00961695	−	0.999954i	$-0.503061\pi$
$163$	4.76156e7	−	8.24726e7i	0.861177	−	1.49160i	0.870794	−	0.491648i	$-0.163605\pi$
$164$		0			0
$165$	−7.54788e6	+	6.33343e6i	−0.130807	+	0.109760i
$166$		0			0
$167$	−4.71270e7	−	1.71528e7i	−0.783001	−	0.284989i	−0.0805775	−	0.996748i	$-0.525676\pi$
$167$	−4.71270e7	−	1.71528e7i	−0.783001	−	0.284989i	−0.702423	+	0.711759i	$0.747899\pi$
$168$		0			0
$169$	−1.06536e7	+	6.04197e7i	−0.169783	+	0.962886i
$170$		0			0
$171$	1.43886e7	−	2.18205e6i	0.220056	−	0.0333717i
$172$		0			0
$173$	−531751.	+	3.01571e6i	−0.00780812	+	0.0442821i	−0.988463	−	0.151463i	$-0.951601\pi$
$173$	−531751.	+	3.01571e6i	−0.00780812	+	0.0442821i	0.980655	+	0.195745i	$0.0627126\pi$
$174$		0			0
$175$	8.29533e7	+	3.01925e7i	1.17004	+	0.425860i
$176$		0			0
$177$	−4.00453e7	+	3.36020e7i	−0.542807	+	0.455469i
$178$		0			0
$179$	4.95244e7	−	8.57788e7i	0.645407	−	1.11788i	−0.338801	−	0.940858i	$-0.610021\pi$
$179$	4.95244e7	−	8.57788e7i	0.645407	−	1.11788i	0.984207	−	0.177019i	$-0.0566455\pi$
$180$		0			0
$181$	3.35505e6	+	1.90274e7i	0.0420556	+	0.238509i	0.998588	−	0.0531158i	$-0.0169152\pi$
$181$	3.35505e6	+	1.90274e7i	0.0420556	+	0.238509i	−0.956533	+	0.291625i	$0.905804\pi$
$182$		0			0
$183$	2.49640e7	+	4.32388e7i	0.301117	+	0.521549i
$184$		0			0
$185$	−3.33150e7	+	1.21257e7i	−0.386846	+	0.140801i
$186$		0			0
$187$	−2.46991e7	−	2.07250e7i	−0.276208	−	0.231766i
$188$		0			0
$189$	1.07423e8			1.15739
$190$		0			0
$191$	1.94767e7			0.202255			0.101128	−	0.994873i	$-0.467755\pi$
$191$	1.94767e7			0.202255			0.101128	+	0.994873i	$0.467755\pi$
$192$		0			0
$193$	5.30236e6	+	4.44921e6i	0.0530908	+	0.0445484i	0.668947	−	0.743310i	$-0.266745\pi$
$193$	5.30236e6	+	4.44921e6i	0.0530908	+	0.0445484i	−0.615856	+	0.787859i	$0.711190\pi$
$194$		0			0
$195$	4.40266e6	−	1.60244e6i	0.0425201	−	0.0154761i
$196$		0			0
$197$	−5.65097e7	−	9.78777e7i	−0.526613	−	0.912120i	−0.999519	−	0.0310073i	$-0.990128\pi$
$197$	−5.65097e7	−	9.78777e7i	−0.526613	−	0.912120i	0.472906	−	0.881113i	$-0.343205\pi$
$198$		0			0
$199$	1.53537e7	+	8.70754e7i	0.138111	+	0.783267i	0.972643	+	0.232307i	$0.0746273\pi$
$199$	1.53537e7	+	8.70754e7i	0.138111	+	0.783267i	−0.834532	+	0.550960i	$0.814262\pi$
$200$		0			0
$201$	2.07933e7	−	3.60150e7i	0.180608	−	0.312822i
$202$		0			0
$203$	2.42821e8	−	2.03751e8i	2.03727	−	1.70948i
$204$		0			0
$205$	−934747.	−	340220.i	−0.00757801	−	0.00275817i
$206$		0			0
$207$	1.50798e6	−	8.55217e6i	0.0118168	−	0.0670162i
$208$		0			0
$209$	−6.34427e7	−	3.86903e7i	−0.480695	−	0.293150i
$210$		0			0
$211$	3.24754e7	−	1.84177e8i	0.237994	−	1.34973i	−0.598222	−	0.801331i	$-0.704126\pi$
$211$	3.24754e7	−	1.84177e8i	0.237994	−	1.34973i	0.836216	−	0.548401i	$-0.184763\pi$
$212$		0			0
$213$	−1.53113e8	−	5.57284e7i	−1.08563	−	0.395137i
$214$		0			0
$215$	−1.19741e7	+	1.00475e7i	−0.0821691	+	0.0689480i
$216$		0			0
$217$	9.04886e7	−	1.56731e8i	0.601153	−	1.04123i
$218$		0			0
$219$	−2.15410e7	−	1.22165e8i	−0.138584	−	0.785947i
$220$		0			0
$221$	7.66578e6	+	1.32775e7i	0.0477731	+	0.0827454i
$222$		0			0
$223$	−1.18577e8	+	4.31584e7i	−0.716031	+	0.260614i	−0.674240	−	0.738512i	$-0.735529\pi$
$223$	−1.18577e8	+	4.31584e7i	−0.716031	+	0.260614i	−0.0417913	+	0.999126i	$0.513306\pi$
$224$		0			0
$225$	−2.69399e7	−	2.26052e7i	−0.157673	−	0.132303i
$226$		0			0
$227$	8.36608e7			0.474714			0.237357	−	0.971423i	$-0.423719\pi$
$227$	8.36608e7			0.474714			0.237357	+	0.971423i	$0.423719\pi$
$228$		0			0
$229$	2.64147e8			1.45352			0.726762	−	0.686890i	$-0.241024\pi$
$229$	2.64147e8			1.45352			0.726762	+	0.686890i	$0.241024\pi$
$230$		0			0
$231$	1.20295e8	+	1.00940e8i	0.642107	+	0.538792i
$232$		0			0
$233$	−2.88406e8	+	1.04971e8i	−1.49368	+	0.543657i	−0.954417	−	0.298477i	$-0.903521\pi$
$233$	−2.88406e8	+	1.04971e8i	−1.49368	+	0.543657i	−0.539268	+	0.842134i	$0.681299\pi$
$234$		0			0
$235$	−5.89572e6	−	1.02117e7i	−0.0296346	−	0.0513287i
$236$		0			0
$237$	4.63539e7	+	2.62886e8i	0.226187	+	1.28277i
$238$		0			0
$239$	−1.72111e8	+	2.98104e8i	−0.815483	+	1.41246i	0.0934975	+	0.995620i	$0.470195\pi$
$239$	−1.72111e8	+	2.98104e8i	−0.815483	+	1.41246i	−0.908981	+	0.416839i	$0.863138\pi$
$240$		0			0
$241$	1.36929e8	−	1.14897e8i	0.630138	−	0.528748i	−0.270834	−	0.962626i	$-0.587299\pi$
$241$	1.36929e8	−	1.14897e8i	0.630138	−	0.528748i	0.900972	+	0.433878i	$0.142855\pi$
$242$		0			0
$243$	−9.19407e7	−	3.34637e7i	−0.411042	−	0.149607i
$244$		0			0
$245$	−8.91206e6	+	5.05428e7i	−0.0387166	+	0.219572i
$246$		0			0
$247$	2.20559e7	+	2.76060e7i	0.0931292	+	0.116564i
$248$		0			0
$249$	−2.91780e7	+	1.65477e8i	−0.119773	+	0.679266i
$250$		0			0
$251$	−3.27068e8	−	1.19043e8i	−1.30551	−	0.475167i	−0.406723	−	0.913552i	$-0.633329\pi$
$251$	−3.27068e8	−	1.19043e8i	−1.30551	−	0.475167i	−0.898787	+	0.438385i	$0.855551\pi$
$252$		0			0
$253$	−3.39677e7	+	2.85023e7i	−0.131870	+	0.110652i
$254$		0			0
$255$	−2.57131e7	+	4.45363e7i	−0.0971099	+	0.168199i
$256$		0			0
$257$	4.13731e7	+	2.34639e8i	0.152038	+	0.862251i	0.961444	+	0.275001i	$0.0886783\pi$
$257$	4.13731e7	+	2.34639e8i	0.152038	+	0.862251i	−0.809406	+	0.587250i	$0.800211\pi$
$258$		0			0
$259$	2.82519e8	+	4.89337e8i	1.01041	+	1.75008i
$260$		0			0
$261$	−1.18662e8	+	4.31894e7i	−0.413113	+	0.150361i
$262$		0			0
$263$	−2.09901e8	−	1.76128e8i	−0.711491	−	0.597012i	0.213526	−	0.976937i	$-0.431505\pi$
$263$	−2.09901e8	−	1.76128e8i	−0.711491	−	0.597012i	−0.925017	+	0.379926i	$0.875950\pi$
$264$		0			0
$265$	6.48223e7			0.213975
$266$		0			0
$267$	1.86736e8			0.600399
$268$		0			0
$269$	−1.10095e8	−	9.23809e7i	−0.344854	−	0.289367i	0.453866	−	0.891070i	$-0.350045\pi$
$269$	−1.10095e8	−	9.23809e7i	−0.344854	−	0.289367i	−0.798720	+	0.601703i	$0.794489\pi$
$270$		0			0
$271$	−3.82289e8	+	1.39142e8i	−1.16681	+	0.424684i	−0.851525	−	0.524314i	$-0.824322\pi$
$271$	−3.82289e8	+	1.39142e8i	−1.16681	+	0.424684i	−0.315283	+	0.948998i	$0.602100\pi$
$272$		0			0
$273$	−3.73357e7	−	6.46673e7i	−0.111059	−	0.192360i
$274$		0			0
$275$	3.11817e7	+	1.76840e8i	0.0904139	+	0.512763i
$276$		0			0
$277$	2.37957e8	−	4.12154e8i	0.672698	−	1.16515i	−0.304438	−	0.952532i	$-0.598469\pi$
$277$	2.37957e8	−	4.12154e8i	0.672698	−	1.16515i	0.977136	−	0.212615i	$-0.0681980\pi$
$278$		0			0
$279$	−5.52296e7	+	4.63431e7i	−0.152250	+	0.127753i
$280$		0			0
$281$	−4.28417e8	−	1.55931e8i	−1.15185	−	0.419238i	−0.305669	−	0.952138i	$-0.598880\pi$
$281$	−4.28417e8	−	1.55931e8i	−1.15185	−	0.419238i	−0.846178	+	0.532900i	$0.821102\pi$
$282$		0			0
$283$	−8.24205e7	+	4.67430e8i	−0.216164	+	1.22593i	0.662712	+	0.748874i	$0.269405\pi$
$283$	−8.24205e7	+	4.67430e8i	−0.216164	+	1.22593i	−0.878876	+	0.477051i	$0.841706\pi$
$284$		0			0
$285$	−4.32014e7	+	1.10369e8i	−0.110545	+	0.282416i
$286$		0			0
$287$	−2.75298e6	+	1.56129e7i	−0.00687410	+	0.0389849i
$288$		0			0
$289$	2.27458e8	+	8.27879e7i	0.554317	+	0.201755i
$290$		0			0
$291$	−5.23727e8	+	4.39459e8i	−1.24589	+	1.04543i
$292$		0			0
$293$	4.01277e8	−	6.95033e8i	0.931983	−	1.61424i	0.152055	−	0.988372i	$-0.451411\pi$
$293$	4.01277e8	−	6.95033e8i	0.931983	−	1.61424i	0.779928	−	0.625869i	$-0.215256\pi$
$294$		0			0
$295$	−1.34589e7	−	7.63290e7i	−0.0305233	−	0.173106i
$296$		0			0
$297$	1.09257e8	+	1.89238e8i	0.241992	+	0.419142i
$298$		0			0
$299$	1.98133e7	−	7.21145e6i	0.0428655	−	0.0156018i
$300$		0			0
$301$	1.90839e8	+	1.60133e8i	0.403352	+	0.338453i
$302$		0			0
$303$	1.23552e8			0.255153
$304$		0			0
$305$	−7.40259e7			−0.149394
$306$		0			0
$307$	−2.92650e8	−	2.45562e8i	−0.577250	−	0.484370i	0.306793	−	0.951776i	$-0.400744\pi$
$307$	−2.92650e8	−	2.45562e8i	−0.577250	−	0.484370i	−0.884043	+	0.467406i	$0.845189\pi$
$308$		0			0
$309$	2.09262e8	−	7.61650e7i	0.403492	−	0.146859i
$310$		0			0
$311$	−3.38203e8	−	5.85785e8i	−0.637553	−	1.10427i	−0.985968	−	0.166934i	$-0.946613\pi$
$311$	−3.38203e8	−	5.85785e8i	−0.637553	−	1.10427i	0.348415	−	0.937340i	$-0.386720\pi$
$312$		0			0
$313$	6.49974e6	+	3.68618e7i	0.0119809	+	0.0679472i	0.990212	−	0.139571i	$-0.0445724\pi$
$313$	6.49974e6	+	3.68618e7i	0.0119809	+	0.0679472i	−0.978231	+	0.207518i	$0.933461\pi$
$314$		0			0
$315$	2.27991e7	−	3.94892e7i	0.0410990	−	0.0711855i
$316$		0			0
$317$	−1.12955e6	+	947803.i	−0.00199158	+	0.00167113i	−0.643783	−	0.765208i	$-0.722636\pi$
$317$	−1.12955e6	+	947803.i	−0.00199158	+	0.00167113i	0.641791	+	0.766879i	$0.278192\pi$
$318$		0			0
$319$	6.05897e8	+	2.20528e8i	1.04504	+	0.380362i
$320$		0			0
$321$	1.47316e8	−	8.35473e8i	0.248590	−	1.40982i
$322$		0			0
$323$	−3.80224e8	−	7.65061e7i	−0.627814	−	0.126324i
$324$		0			0
$325$	1.48272e7	−	8.40890e7i	0.0239589	−	0.135878i
$326$		0			0
$327$	−1.13420e8	−	4.12814e7i	−0.179379	−	0.0652886i
$328$		0			0
$329$	−1.43961e8	+	1.20798e8i	−0.222874	+	0.187013i
$330$		0			0
$331$	2.15736e8	−	3.73666e8i	0.326982	−	0.566350i	−0.654929	−	0.755690i	$-0.727302\pi$
$331$	2.15736e8	−	3.73666e8i	0.326982	−	0.566350i	0.981912	+	0.189340i	$0.0606349\pi$
$332$		0			0
$333$	−3.90878e7	−	2.21678e8i	−0.0580078	−	0.328979i
$334$		0			0
$335$	3.08293e7	+	5.33979e7i	0.0448030	+	0.0776010i
$336$		0			0
$337$	3.66837e8	−	1.33518e8i	0.522118	−	0.190035i	−0.0674977	−	0.997719i	$-0.521502\pi$
$337$	3.66837e8	−	1.33518e8i	0.522118	−	0.190035i	0.589615	+	0.807684i	$0.299279\pi$
$338$		0			0
$339$	1.02519e9	+	8.60237e8i	1.42924	+	1.19928i
$340$		0			0
$341$	3.68133e8			0.502765
$342$		0			0
$343$	−1.88306e8			−0.251961
$344$		0			0
$345$	5.41780e7	+	4.54607e7i	0.0710323	+	0.0596032i
$346$		0			0
$347$	−8.48704e8	+	3.08903e8i	−1.09044	+	0.396889i	−0.823785	−	0.566902i	$-0.808142\pi$
$347$	−8.48704e8	+	3.08903e8i	−1.09044	+	0.396889i	−0.266658	+	0.963791i	$0.585920\pi$
$348$		0			0
$349$	5.98747e8	+	1.03706e9i	0.753970	+	1.30591i	0.945885	+	0.324503i	$0.105197\pi$
$349$	5.98747e8	+	1.03706e9i	0.753970	+	1.30591i	−0.191915	+	0.981412i	$0.561470\pi$
$350$		0			0
$351$	−1.80429e7	−	1.02326e8i	−0.0222706	−	0.126303i
$352$		0			0
$353$	3.50518e8	−	6.07115e8i	0.424130	−	0.734615i	−0.572209	−	0.820108i	$-0.693913\pi$
$353$	3.50518e8	−	6.07115e8i	0.424130	−	0.734615i	0.996339	+	0.0854934i	$0.0272467\pi$
$354$		0			0
$355$	1.85063e8	−	1.55286e8i	0.219543	−	0.184219i
$356$		0			0
$357$	7.70183e8	+	2.80324e8i	0.895891	+	0.326078i
$358$		0			0
$359$	4.19092e7	−	2.37679e8i	0.0478056	−	0.271119i	−0.951530	−	0.307555i	$-0.900489\pi$
$359$	4.19092e7	−	2.37679e8i	0.0478056	−	0.271119i	0.999336	+	0.0364357i	$0.0116004\pi$
$360$		0			0
$361$	−8.92840e8	−	4.29410e7i	−0.998845	−	0.0480393i
$362$		0			0
$363$	1.19508e8	−	6.77765e8i	0.131137	−	0.743714i
$364$		0			0
$365$	1.72831e8	+	6.29054e7i	0.186036	+	0.0677116i
$366$		0			0
$367$	6.30084e8	−	5.28703e8i	0.665376	−	0.558317i	−0.246317	−	0.969189i	$-0.579220\pi$
$367$	6.30084e8	−	5.28703e8i	0.665376	−	0.558317i	0.911693	+	0.410873i	$0.134776\pi$
$368$		0			0
$369$	3.15788e6	−	5.46961e6i	0.00327193	−	0.00566714i
$370$		0			0
$371$	−1.79398e8	−	1.01742e9i	−0.182394	−	1.03441i
$372$		0			0
$373$	4.34129e8	+	7.51934e8i	0.433150	+	0.750238i	0.997143	−	0.0755421i	$-0.0240687\pi$
$373$	4.34129e8	+	7.51934e8i	0.433150	+	0.750238i	−0.563993	+	0.825780i	$0.690735\pi$
$374$		0			0
$375$	5.60167e8	−	2.03884e8i	0.548540	−	0.199652i
$376$		0			0
$377$	−2.34869e8	−	1.97078e8i	−0.225752	−	0.189428i
$378$		0			0
$379$	−7.69525e8			−0.726082			−0.363041	−	0.931773i	$-0.618261\pi$
$379$	−7.69525e8			−0.726082			−0.363041	+	0.931773i	$0.618261\pi$
$380$		0			0
$381$	3.21966e8			0.298245
$382$		0			0
$383$	−1.50300e9	−	1.26116e9i	−1.36698	−	1.14703i	−0.973757	−	0.227590i	$-0.926916\pi$
$383$	−1.50300e9	−	1.26116e9i	−1.36698	−	1.14703i	−0.393223	−	0.919443i	$-0.628640\pi$
$384$		0			0
$385$	−2.18787e8	+	7.96319e7i	−0.195393	+	0.0711172i
$386$		0			0
$387$	−4.96223e7	−	8.59483e7i	−0.0435200	−	0.0753788i
$388$		0			0
$389$	−2.32728e8	−	1.31987e9i	−0.200459	−	1.13686i	−0.904427	−	0.426628i	$-0.859701\pi$
$389$	−2.32728e8	−	1.31987e9i	−0.200459	−	1.13686i	0.703968	−	0.710231i	$-0.251410\pi$
$390$		0			0
$391$	−1.15716e8	+	2.00427e8i	−0.0978986	+	0.169565i
$392$		0			0
$393$	−5.63485e8	+	4.72820e8i	−0.468283	+	0.392936i
$394$		0			0
$395$	−3.71914e8	−	1.35365e8i	−0.303635	−	0.110514i
$396$		0			0
$397$	4.00450e8	−	2.27106e9i	0.321204	−	1.82164i	−0.213903	−	0.976855i	$-0.568618\pi$
$397$	4.00450e8	−	2.27106e9i	0.321204	−	1.82164i	0.535107	−	0.844784i	$-0.320271\pi$
$398$		0			0
$399$	1.85186e9	+	3.72618e8i	1.45949	+	0.293669i
$400$		0			0
$401$	−3.76114e7	+	2.13305e8i	−0.0291282	+	0.165194i	−0.995902	−	0.0904392i	$-0.971173\pi$
$401$	−3.76114e7	+	2.13305e8i	−0.0291282	+	0.165194i	0.966774	+	0.255633i	$0.0822840\pi$
$402$		0			0
$403$	−1.64494e8	−	5.98709e7i	−0.125194	−	0.0455667i
$404$		0			0
$405$	3.29507e8	−	2.76489e8i	0.246474	−	0.206816i
$406$		0			0
$407$	−5.74684e8	+	9.95381e8i	−0.422521	+	0.731828i
$408$		0			0
$409$	3.22012e8	+	1.82622e9i	0.232724	+	1.31984i	0.847354	+	0.531028i	$0.178194\pi$
$409$	3.22012e8	+	1.82622e9i	0.232724	+	1.31984i	−0.614631	+	0.788815i	$0.710695\pi$
$410$		0			0
$411$	1.15805e9	+	2.00580e9i	0.822773	+	1.42508i
$412$		0			0
$413$	−1.16077e9	+	4.22487e8i	−0.810817	+	0.295113i
$414$		0			0
$415$	−1.90845e8	−	1.60138e8i	−0.131073	−	0.109983i
$416$		0			0
$417$	2.45751e8			0.165966
$418$		0			0
$419$	−2.20472e9			−1.46421			−0.732107	−	0.681190i	$-0.761463\pi$
$419$	−2.20472e9			−1.46421			−0.732107	+	0.681190i	$0.761463\pi$
$420$		0			0
$421$	4.15424e8	+	3.48582e8i	0.271334	+	0.227676i	0.768294	−	0.640097i	$-0.221106\pi$
$421$	4.15424e8	+	3.48582e8i	0.271334	+	0.227676i	−0.496960	+	0.867773i	$0.665550\pi$
$422$		0			0
$423$	7.03511e7	−	2.56057e7i	0.0451938	−	0.0164492i
$424$		0			0
$425$	4.68611e8	+	8.11657e8i	0.296108	+	0.512875i
$426$		0			0
$427$	2.04870e8	+	1.16187e9i	0.127345	+	0.722207i
$428$		0			0
$429$	7.59460e7	−	1.31542e8i	0.0464413	−	0.0804387i
$430$		0			0
$431$	−1.19968e9	+	1.00665e9i	−0.721766	+	0.605633i	−0.927873	−	0.372896i	$-0.878365\pi$
$431$	−1.19968e9	+	1.00665e9i	−0.721766	+	0.605633i	0.206107	+	0.978529i	$0.433920\pi$
$432$		0			0
$433$	3.66221e8	+	1.33293e8i	0.216788	+	0.0789044i	0.448131	−	0.893968i	$-0.352090\pi$
$433$	3.66221e8	+	1.33293e8i	0.216788	+	0.0789044i	−0.231343	+	0.972872i	$0.574312\pi$
$434$		0			0
$435$	1.78583e8	−	1.01279e9i	0.104022	−	0.589941i
$436$		0			0
$437$	−1.94419e8	+	4.96692e8i	−0.111443	+	0.284710i
$438$		0			0
$439$	−5.71779e8	+	3.24272e9i	−0.322554	+	1.82929i	0.203782	+	0.979016i	$0.434677\pi$
$439$	−5.71779e8	+	3.24272e9i	−0.322554	+	1.82929i	−0.526336	+	0.850277i	$0.676435\pi$
$440$		0			0
$441$	−3.06204e8	−	1.11449e8i	−0.170011	−	0.0618788i
$442$		0			0
$443$	−2.41016e9	+	2.02236e9i	−1.31714	+	1.10521i	−0.330240	+	0.943897i	$0.607130\pi$
$443$	−2.41016e9	+	2.02236e9i	−1.31714	+	1.10521i	−0.986903	+	0.161317i	$0.948426\pi$
$444$		0			0
$445$	−1.38433e8	+	2.39773e8i	−0.0744697	+	0.128985i
$446$		0			0
$447$	−1.59081e8	−	9.02196e8i	−0.0842448	−	0.477776i
$448$		0			0
$449$	−8.03598e8	−	1.39187e9i	−0.418964	−	0.725667i	0.576872	−	0.816835i	$-0.304273\pi$
$449$	−8.03598e8	−	1.39187e9i	−0.418964	−	0.725667i	−0.995836	+	0.0911681i	$0.970940\pi$
$450$		0			0
$451$	−3.03040e7	+	1.10297e7i	−0.0155554	+	0.00566171i
$452$		0			0
$453$	−3.24937e6	−	2.72654e6i	−0.00164231	−	0.00137806i
$454$		0			0
$455$	1.10712e8			0.0551003
$456$		0			0
$457$	−2.32713e9			−1.14055			−0.570275	−	0.821454i	$-0.693163\pi$
$457$	−2.32713e9			−1.14055			−0.570275	+	0.821454i	$0.693163\pi$
$458$		0			0
$459$	8.73664e8	+	7.33091e8i	0.421697	+	0.353846i
$460$		0			0
$461$	−6.08072e7	+	2.21320e7i	−0.0289069	+	0.0105213i	−0.356433	−	0.934321i	$-0.616007\pi$
$461$	−6.08072e7	+	2.21320e7i	−0.0289069	+	0.0105213i	0.327526	+	0.944842i	$0.393785\pi$
$462$		0			0
$463$	−1.31942e8	−	2.28530e8i	−0.0617803	−	0.107007i	0.833481	−	0.552548i	$-0.186344\pi$
$463$	−1.31942e8	−	2.28530e8i	−0.0617803	−	0.107007i	−0.895261	+	0.445542i	$0.853011\pi$
$464$		0			0
$465$	−1.01960e8	−	5.78247e8i	−0.0470269	−	0.266703i
$466$		0			0
$467$	−8.63591e8	+	1.49578e9i	−0.392373	+	0.679610i	−0.992762	−	0.120098i	$-0.961679\pi$
$467$	−8.63591e8	+	1.49578e9i	−0.392373	+	0.679610i	0.600389	+	0.799708i	$0.295012\pi$
$468$		0			0
$469$	7.52786e8	−	6.31662e8i	0.336951	−	0.282735i
$470$		0			0
$471$	3.58750e9	+	1.30574e9i	1.58205	+	0.575818i
$472$		0			0
$473$	−8.79964e7	+	4.99052e8i	−0.0382341	+	0.216836i
$474$		0			0
$475$	1.34828e9	+	1.68756e9i	0.577236	+	0.722489i
$476$		0			0
$477$	−7.14681e7	+	4.05316e8i	−0.0301507	+	0.170993i
$478$		0			0
$479$	1.68565e9	+	6.13526e8i	0.700798	+	0.255070i	0.667752	−	0.744384i	$-0.267257\pi$
$479$	1.68565e9	+	6.13526e8i	0.700798	+	0.255070i	0.0330466	+	0.999454i	$0.489479\pi$
$480$		0			0
$481$	4.18670e8	−	3.51306e8i	0.171539	−	0.143939i
$482$		0			0
$483$	5.63589e8	−	9.76165e8i	0.227587	−	0.394192i
$484$		0			0
$485$	−1.76020e8	−	9.98259e8i	−0.0700593	−	0.397326i
$486$		0			0
$487$	−2.24416e9	−	3.88699e9i	−0.880444	−	1.52497i	−0.850848	−	0.525412i	$-0.823911\pi$
$487$	−2.24416e9	−	3.88699e9i	−0.880444	−	1.52497i	−0.0295960	−	0.999562i	$-0.509422\pi$
$488$		0			0
$489$	−4.62729e9	+	1.68419e9i	−1.78956	+	0.651345i
$490$		0			0
$491$	−2.62535e9	−	2.20293e9i	−1.00093	−	0.839876i	−0.0138130	−	0.999905i	$-0.504397\pi$
$491$	−2.62535e9	−	2.20293e9i	−1.00093	−	0.839876i	−0.987112	+	0.160028i	$0.948841\pi$
$492$		0			0
$493$	3.36531e9			1.26492
$494$		0			0
$495$	9.27533e7			0.0343725
$496$		0			0
$497$	−2.94947e9	−	2.47490e9i	−1.07770	−	0.904294i
$498$		0			0
$499$	2.66361e9	−	9.69476e8i	0.959664	−	0.349289i	0.185762	−	0.982595i	$-0.440525\pi$
$499$	2.66361e9	−	9.69476e8i	0.959664	−	0.349289i	0.773902	+	0.633305i	$0.218302\pi$
$500$		0			0
$501$	1.29663e9	+	2.24583e9i	0.460663	+	0.797892i
$502$		0			0
$503$	−4.71649e8	−	2.67486e9i	−0.165246	−	0.937157i	−0.948810	−	0.315846i	$-0.897712\pi$
$503$	−4.71649e8	−	2.67486e9i	−0.165246	−	0.937157i	0.783564	−	0.621311i	$-0.213400\pi$
$504$		0			0
$505$	−9.15927e7	+	1.58643e8i	−0.0316476	+	0.0548153i
$506$		0			0
$507$	2.43020e9	−	2.03918e9i	0.828161	−	0.694909i
$508$		0			0
$509$	3.82894e9	+	1.39362e9i	1.28696	+	0.468417i	0.892729	−	0.450593i	$-0.148788\pi$
$509$	3.82894e9	+	1.39362e9i	1.28696	+	0.468417i	0.394234	+	0.919010i	$0.371010\pi$
$510$		0			0
$511$	5.09015e8	−	2.88677e9i	0.168755	−	0.957059i
$512$		0			0
$513$	2.24411e9	+	1.36856e9i	0.733895	+	0.447563i
$514$		0			0
$515$	−5.73343e7	+	3.25159e8i	−0.0184965	+	0.104899i
$516$		0			0
$517$	−3.59218e8	−	1.30745e8i	−0.114325	−	0.0416109i
$518$		0			0
$519$	1.21298e8	−	1.01781e8i	0.0380862	−	0.0319581i
$520$		0			0
$521$	6.99764e8	−	1.21203e9i	0.216780	−	0.375474i	−0.737042	−	0.675847i	$-0.763778\pi$
$521$	6.99764e8	−	1.21203e9i	0.216780	−	0.375474i	0.953822	+	0.300373i	$0.0971111\pi$
$522$		0			0
$523$	−6.57481e8	−	3.72876e9i	−0.200968	−	1.13975i	−0.903659	−	0.428252i	$-0.859129\pi$
$523$	−6.57481e8	−	3.72876e9i	−0.200968	−	1.13975i	0.702691	−	0.711495i	$-0.251982\pi$
$524$		0			0
$525$	−2.28234e9	−	3.95312e9i	−0.688370	−	1.19229i
$526$		0			0
$527$	1.80553e9	−	6.57158e8i	0.537362	−	0.195584i
$528$		0			0
$529$	−2.36443e9	−	1.98399e9i	−0.694435	−	0.582700i
$530$		0			0
$531$	4.92103e8			0.142635
$532$		0			0
$533$	1.53346e7			0.00438659
$534$		0			0
$535$	9.63552e8	+	8.08516e8i	0.272043	+	0.228271i
$536$		0			0
$537$	−4.81279e9	+	1.75171e9i	−1.34118	+	0.488149i
$538$		0			0
$539$	8.31923e8	+	1.44093e9i	0.228835	+	0.396354i
$540$		0			0
$541$	2.83407e8	+	1.60728e9i	0.0769520	+	0.436417i	0.998805	+	0.0488765i	$0.0155641\pi$
$541$	2.83407e8	+	1.60728e9i	0.0769520	+	0.436417i	−0.921853	+	0.387540i	$0.873325\pi$
$542$		0			0
$543$	4.99528e8	−	8.65208e8i	0.133894	−	0.231911i
$544$		0			0
$545$	1.37087e8	−	1.15030e8i	0.0362752	−	0.0304385i
$546$		0			0
$547$	2.10737e9	+	7.67018e8i	0.550534	+	0.200378i	0.602284	−	0.798282i	$-0.294258\pi$
$547$	2.10737e9	+	7.67018e8i	0.550534	+	0.200378i	−0.0517497	+	0.998660i	$0.516480\pi$
$548$		0			0
$549$	8.16153e7	−	4.62864e8i	0.0210508	−	0.119385i
$550$		0			0
$551$	7.66842e9	−	1.16292e9i	1.95288	−	0.296155i
$552$		0			0
$553$	−1.09534e9	+	6.21200e9i	−0.275431	+	1.56205i
$554$		0			0
$555$	1.72267e9	+	6.26999e8i	0.427736	+	0.155683i
$556$		0			0
$557$	2.96622e9	−	2.48896e9i	0.727295	−	0.610273i	−0.202097	−	0.979365i	$-0.564776\pi$
$557$	2.96622e9	−	2.48896e9i	0.727295	−	0.610273i	0.929393	+	0.369092i	$0.120331\pi$
$558$		0			0
$559$	1.20482e8	−	2.08681e8i	0.0291730	−	0.0505292i
$560$		0			0
$561$	2.89507e8	+	1.64188e9i	0.0692292	+	0.392619i
$562$		0			0
$563$	2.21077e9	+	3.82917e9i	0.522113	+	0.904326i	0.999669	+	0.0257247i	$0.00818934\pi$
$563$	2.21077e9	+	3.82917e9i	0.522113	+	0.904326i	−0.477556	+	0.878601i	$0.658477\pi$
$564$		0			0
$565$	−1.86456e9	+	6.78645e8i	−0.434918	+	0.158297i
$566$		0			0
$567$	−5.25156e9	−	4.40658e9i	−1.20989	−	1.01522i
$568$		0			0
$569$	−6.16458e8			−0.140285			−0.0701424	−	0.997537i	$-0.522345\pi$
$569$	−6.16458e8			−0.140285			−0.0701424	+	0.997537i	$0.522345\pi$
$570$		0			0
$571$	−3.21397e9			−0.722462			−0.361231	−	0.932476i	$-0.617643\pi$
$571$	−3.21397e9			−0.722462			−0.361231	+	0.932476i	$0.617643\pi$
$572$		0			0
$573$	−7.71493e8	−	6.47359e8i	−0.171313	−	0.143749i
$574$		0			0
$575$	1.21119e9	−	4.40837e8i	0.265690	−	0.0967032i
$576$		0			0
$577$	3.15738e9	+	5.46874e9i	0.684245	+	1.18515i	0.973673	+	0.227947i	$0.0732014\pi$
$577$	3.15738e9	+	5.46874e9i	0.684245	+	1.18515i	−0.289429	+	0.957200i	$0.593465\pi$
$578$		0			0
$579$	−6.21509e7	−	3.52475e8i	−0.0133068	−	0.0754664i
$580$		0			0
$581$	−1.98527e9	+	3.43859e9i	−0.419956	+	0.727385i
$582$		0			0
$583$	1.60984e9	−	1.35082e9i	0.336468	−	0.282330i
$584$		0			0
$585$	−4.14452e7	−	1.50848e7i	−0.00855910	−	0.00311526i
$586$		0			0
$587$	1.61939e9	−	9.18403e9i	0.330460	−	1.87413i	−0.137682	−	0.990477i	$-0.543965\pi$
$587$	1.61939e9	−	9.18403e9i	0.330460	−	1.87413i	0.468141	−	0.883654i	$-0.344924\pi$
$588$		0			0
$589$	3.88710e9	−	2.12136e9i	0.783830	−	0.427771i
$590$		0			0
$591$	−1.01481e9	+	5.75528e9i	−0.202222	+	1.14686i
$592$		0			0
$593$	5.33751e8	+	1.94270e8i	0.105111	+	0.0382572i	0.394040	−	0.919093i	$-0.371077\pi$
$593$	5.33751e8	+	1.94270e8i	0.105111	+	0.0382572i	−0.288929	+	0.957350i	$0.593299\pi$
$594$		0			0
$595$	−9.30899e8	+	7.81117e8i	−0.181173	+	0.152022i
$596$		0			0
$597$	2.28600e9	−	3.95946e9i	0.439709	−	0.761599i
$598$		0			0
$599$	−5.71327e8	−	3.24016e9i	−0.108615	−	0.615988i	−0.989715	−	0.143056i	$-0.954307\pi$
$599$	−5.71327e8	−	3.24016e9i	−0.108615	−	0.615988i	0.881099	−	0.472931i	$-0.156804\pi$
$600$		0			0
$601$	−1.53939e9	−	2.66630e9i	−0.289260	−	0.501012i	0.684374	−	0.729132i	$-0.260076\pi$
$601$	−1.53939e9	−	2.66630e9i	−0.289260	−	0.501012i	−0.973633	+	0.228119i	$0.926742\pi$
$602$		0			0
$603$	−3.67872e8	+	1.33895e8i	−0.0683261	+	0.0248687i
$604$		0			0
$605$	7.81668e8	+	6.55897e8i	0.143509	+	0.120418i
$606$		0			0
$607$	1.09946e9			0.199536			0.0997679	−	0.995011i	$-0.468190\pi$
$607$	1.09946e9			0.199536			0.0997679	+	0.995011i	$0.468190\pi$
$608$		0			0
$609$	−1.63905e10			−2.94058
$610$		0			0
$611$	1.39247e8	+	1.16842e8i	0.0246968	+	0.0207231i
$612$		0			0
$613$	−1.72180e9	+	6.26683e8i	−0.301905	+	0.109884i	−0.488531	−	0.872547i	$-0.662467\pi$
$613$	−1.72180e9	+	6.26683e8i	−0.301905	+	0.109884i	0.186626	+	0.982431i	$0.440245\pi$
$614$		0			0
$615$	2.57182e7	+	4.45451e7i	0.00445838	+	0.00772214i
$616$		0			0
$617$	−2.98350e8	−	1.69203e9i	−0.0511361	−	0.290007i	0.948506	−	0.316759i	$-0.102595\pi$
$617$	−2.98350e8	−	1.69203e9i	−0.0511361	−	0.290007i	−0.999642	+	0.0267519i	$0.991484\pi$
$618$		0			0
$619$	8.68887e7	−	1.50496e8i	0.0147247	−	0.0255039i	−0.858569	−	0.512698i	$-0.828646\pi$
$619$	8.68887e7	−	1.50496e8i	0.0147247	−	0.0255039i	0.873294	+	0.487194i	$0.161979\pi$
$620$		0			0
$621$	1.20152e9	−	1.00819e9i	0.201330	−	0.168936i
$622$		0			0
$623$	4.14648e9	+	1.50919e9i	0.687023	+	0.250056i
$624$		0			0
$625$	8.26650e8	−	4.68816e9i	0.135438	−	0.768109i
$626$		0			0
$627$	1.22706e9	+	3.64124e9i	0.198806	+	0.589947i
$628$		0			0
$629$	−1.04170e9	+	5.90776e9i	−0.166903	+	0.946555i
$630$		0			0
$631$	−5.01584e9	−	1.82562e9i	−0.794769	−	0.289272i	−0.0874518	−	0.996169i	$-0.527872\pi$
$631$	−5.01584e9	−	1.82562e9i	−0.794769	−	0.289272i	−0.707317	+	0.706897i	$0.750095\pi$
$632$		0			0
$633$	−7.40799e9	+	6.21604e9i	−1.16088	+	0.974094i
$634$		0			0
$635$	−2.38683e8	+	4.13411e8i	−0.0369924	+	0.0640728i
$636$		0			0
$637$	−1.37386e8	−	7.79154e8i	−0.0210598	−	0.119436i
$638$		0			0
$639$	7.66926e8	+	1.32835e9i	0.116279	+	0.201401i
$640$		0			0
$641$	−4.65197e9	+	1.69318e9i	−0.697644	+	0.253922i	−0.666404	−	0.745590i	$-0.732168\pi$
$641$	−4.65197e9	+	1.69318e9i	−0.697644	+	0.253922i	−0.0312392	+	0.999512i	$0.509945\pi$
$642$		0			0
$643$	3.54596e9	+	2.97542e9i	0.526012	+	0.441377i	0.866722	−	0.498792i	$-0.166223\pi$
$643$	3.54596e9	+	2.97542e9i	0.526012	+	0.441377i	−0.340709	+	0.940169i	$0.610667\pi$
$644$		0			0
$645$	8.08259e8			0.118602
$646$		0			0
$647$	6.31724e9			0.916986			0.458493	−	0.888698i	$-0.348389\pi$
$647$	6.31724e9			0.916986			0.458493	+	0.888698i	$0.348389\pi$
$648$		0			0
$649$	−1.92485e9	−	1.61514e9i	−0.276402	−	0.231929i
$650$		0			0
$651$	−8.79369e9	+	3.20064e9i	−1.24922	+	0.454678i
$652$		0			0
$653$	5.48054e9	+	9.49257e9i	0.770242	+	1.33410i	0.937430	+	0.348173i	$0.113198\pi$
$653$	5.48054e9	+	9.49257e9i	0.770242	+	1.33410i	−0.167189	+	0.985925i	$0.553469\pi$
$654$		0			0
$655$	−1.89382e8	−	1.07404e9i	−0.0263327	−	0.149340i
$656$		0			0
$657$	−5.83881e8	+	1.01131e9i	−0.0803240	+	0.139125i
$658$		0			0
$659$	−9.61231e9	+	8.06568e9i	−1.30836	+	1.09785i	−0.319730	+	0.947509i	$0.603592\pi$
$659$	−9.61231e9	+	8.06568e9i	−1.30836	+	1.09785i	−0.988634	+	0.150339i	$0.951963\pi$
$660$		0			0
$661$	1.12396e10	+	4.09090e9i	1.51373	+	0.550951i	0.959572	−	0.281463i	$-0.0908196\pi$
$661$	1.12396e10	+	4.09090e9i	1.51373	+	0.550951i	0.554154	+	0.832414i	$0.313042\pi$
$662$		0			0
$663$	1.37663e8	−	7.80727e8i	0.0183451	−	0.104040i
$664$		0			0
$665$	−1.85128e9	+	2.10158e9i	−0.244116	+	0.277122i
$666$		0			0
$667$	8.03675e8	−	4.55787e9i	0.104867	−	0.594732i
$668$		0			0
$669$	6.13141e9	+	2.23165e9i	0.791716	+	0.288161i
$670$		0			0
$671$	−1.83841e9	+	1.54261e9i	−0.234917	+	0.197119i
$672$		0			0
$673$	−3.26948e8	+	5.66290e8i	−0.0413452	+	0.0716120i	−0.885958	−	0.463766i	$-0.846498\pi$
$673$	−3.26948e8	+	5.66290e8i	−0.0413452	+	0.0716120i	0.844612	+	0.535378i	$0.179831\pi$
$674$		0			0
$675$	−1.10297e9	−	6.25524e9i	−0.138038	−	0.782854i
$676$		0			0
$677$	4.16715e9	+	7.21771e9i	0.516153	+	0.894003i	0.999824	+	0.0187535i	$0.00596976\pi$
$677$	4.16715e9	+	7.21771e9i	0.516153	+	0.894003i	−0.483671	+	0.875250i	$0.660697\pi$
$678$		0			0
$679$	−1.51810e10	+	5.52545e9i	−1.86105	+	0.677366i
$680$		0			0
$681$	−3.31389e9	−	2.78068e9i	−0.402090	−	0.337393i
$682$		0			0
$683$	5.67566e9			0.681622			0.340811	−	0.940132i	$-0.389298\pi$
$683$	5.67566e9			0.681622			0.340811	+	0.940132i	$0.389298\pi$
$684$		0			0
$685$	−3.43397e9			−0.408206
$686$		0			0
$687$	−1.04631e10	−	8.77961e9i	−1.23116	−	1.03306i
$688$		0			0
$689$	−9.39019e8	+	3.41775e8i	−0.109372	+	0.0398082i
$690$		0			0
$691$	−7.97546e8	−	1.38139e9i	−0.0919566	−	0.159273i	0.816378	−	0.577518i	$-0.195979\pi$
$691$	−7.97546e8	−	1.38139e9i	−0.0919566	−	0.159273i	−0.908334	+	0.418245i	$0.862645\pi$
$692$		0			0
$693$	−2.56699e8	−	1.45581e9i	−0.0292993	−	0.166165i
$694$		0			0
$695$	−1.82182e8	+	3.15548e8i	−0.0205853	+	0.0356549i
$696$		0			0
$697$	−1.28938e8	+	1.08192e8i	−0.0144233	+	0.0121026i
$698$		0			0
$699$	1.49130e10	+	5.42790e9i	1.65157	+	0.601121i
$700$		0			0
$701$	1.89889e9	−	1.07692e10i	0.208203	−	1.18078i	−0.684116	−	0.729373i	$-0.739812\pi$
$701$	1.89889e9	−	1.07692e10i	0.208203	−	1.18078i	0.892319	−	0.451405i	$-0.149077\pi$
$702$		0			0
$703$	−3.32186e8	+	1.38218e10i	−0.0360610	+	1.50044i
$704$		0			0
$705$	−1.05876e8	+	6.00455e8i	−0.0113799	+	0.0645384i
$706$		0			0
$707$	2.74347e9	+	9.98543e8i	0.291966	+	0.106267i
$708$		0			0
$709$	−4.47321e9	+	3.75347e9i	−0.471365	+	0.395523i	−0.847292	−	0.531127i	$-0.821769\pi$
$709$	−4.47321e9	+	3.75347e9i	−0.471365	+	0.395523i	0.375927	+	0.926649i	$0.377324\pi$
$710$		0			0
$711$	1.25645e9	−	2.17623e9i	0.131099	−	0.227071i
$712$		0			0
$713$	−4.58852e8	−	2.60228e9i	−0.0474089	−	0.268869i
$714$		0			0
$715$	1.12602e8	+	1.95032e8i	0.0115206	+	0.0199542i
$716$		0			0
$717$	1.67257e10	−	6.08767e9i	1.69460	−	0.616785i
$718$		0			0
$719$	1.35314e10	+	1.13542e10i	1.35766	+	1.13921i	0.976698	+	0.214620i	$0.0688514\pi$
$719$	1.35314e10	+	1.13542e10i	1.35766	+	1.13921i	0.380962	+	0.924591i	$0.375593\pi$
$720$		0			0
$721$	5.26221e9			0.522871
$722$		0			0
$723$	−9.24278e9			−0.909534
$724$		0			0
$725$	−1.43576e10	−	1.20474e10i	−1.39926	−	1.17412i
$726$		0			0
$727$	−9.96474e9	+	3.62687e9i	−0.961824	+	0.350075i	−0.774748	−	0.632270i	$-0.782123\pi$
$727$	−9.96474e9	+	3.62687e9i	−0.961824	+	0.350075i	−0.187076	+	0.982345i	$0.559901\pi$
$728$		0			0
$729$	−3.60556e9	−	6.24502e9i	−0.344688	−	0.597018i
$730$		0			0
$731$	4.59280e8	+	2.60471e9i	0.0434877	+	0.246631i
$732$		0			0
$733$	9.08101e9	−	1.57288e10i	0.851668	−	1.47513i	−0.0280348	−	0.999607i	$-0.508925\pi$
$733$	9.08101e9	−	1.57288e10i	0.851668	−	1.47513i	0.879702	−	0.475525i	$-0.157742\pi$
$734$		0			0
$735$	2.03293e9	−	1.70583e9i	0.188850	−	0.158464i
$736$		0			0
$737$	1.87839e9	+	6.83676e8i	0.172842	+	0.0629092i
$738$		0			0
$739$	3.58959e9	−	2.03576e10i	0.327182	−	1.85554i	−0.166694	−	0.986009i	$-0.553309\pi$
$739$	3.58959e9	−	2.03576e10i	0.327182	−	1.85554i	0.493876	−	0.869532i	$-0.335580\pi$
$740$		0			0
$741$	4.38993e7	−	1.82659e9i	0.00396364	−	0.164921i
$742$		0			0
$743$	−2.77540e9	+	1.57401e10i	−0.248236	+	1.40782i	0.564619	+	0.825352i	$0.309023\pi$
$743$	−2.77540e9	+	1.57401e10i	−0.248236	+	1.40782i	−0.812855	+	0.582466i	$0.802088\pi$
$744$		0			0
$745$	1.27637e9	+	4.64560e8i	0.113091	+	0.0411618i
$746$		0			0
$747$	1.21171e9	−	1.01674e9i	0.106359	−	0.0892461i
$748$		0			0
$749$	1.00234e10	−	1.73610e10i	0.871624	−	1.50970i
$750$		0			0
$751$	−2.73381e8	−	1.55042e9i	−0.0235520	−	0.133570i	0.970765	−	0.240033i	$-0.0771584\pi$
$751$	−2.73381e8	−	1.55042e9i	−0.0235520	−	0.133570i	−0.994317	+	0.106463i	$0.966047\pi$
$752$		0			0
$753$	8.99879e9	+	1.55864e10i	0.768072	+	1.33034i
$754$		0			0
$755$	5.90978e6	−	2.15098e6i	0.000499754	−	0.000181896i
$756$		0			0
$757$	−9.51870e9	−	7.98714e9i	−0.797521	−	0.669200i	0.150074	−	0.988675i	$-0.452049\pi$
$757$	−9.51870e9	−	7.98714e9i	−0.797521	−	0.669200i	−0.947595	+	0.319475i	$0.896493\pi$
$758$		0			0
$759$	2.29284e9			0.190339
$760$		0			0
$761$	4.04151e9			0.332428			0.166214	−	0.986090i	$-0.446846\pi$
$761$	4.04151e9			0.332428			0.166214	+	0.986090i	$0.446846\pi$
$762$		0			0
$763$	−2.18485e9	−	1.83331e9i	−0.178068	−	0.149417i
$764$		0			0
$765$	4.54913e8	−	1.65575e8i	0.0367378	−	0.0133715i
$766$		0			0
$767$	5.97409e8	+	1.03474e9i	0.0478066	+	0.0828035i
$768$		0			0
$769$	−1.98277e9	−	1.12449e10i	−0.157228	−	0.891685i	−0.956720	−	0.291009i	$-0.906009\pi$
$769$	−1.98277e9	−	1.12449e10i	−0.157228	−	0.891685i	0.799492	−	0.600676i	$-0.205102\pi$
$770$		0			0
$771$	6.15999e9	−	1.06694e10i	0.484049	−	0.838398i
$772$		0			0
$773$	1.46349e10	−	1.22801e10i	1.13962	−	0.956256i	0.140195	−	0.990124i	$-0.455227\pi$
$773$	1.46349e10	−	1.22801e10i	1.13962	−	0.956256i	0.999426	+	0.0338678i	$0.0107825\pi$
$774$		0			0
$775$	−1.00555e10	−	3.65992e9i	−0.775978	−	0.282433i
$776$		0			0
$777$	5.07352e9	−	2.87734e10i	0.388004	−	2.20048i
$778$		0			0
$779$	−2.56419e8	+	2.91088e8i	−0.0194343	+	0.0220619i
$780$		0			0
$781$	1.36001e9	−	7.71298e9i	0.102156	−	0.579354i
$782$		0			0
$783$	−2.14320e10	−	7.80059e9i	−1.59550	−	0.580713i
$784$		0			0
$785$	−4.33612e9	+	3.63843e9i	−0.319932	+	0.268454i
$786$		0			0
$787$	4.55542e9	−	7.89022e9i	0.333133	−	0.577003i	−0.649992	−	0.759941i	$-0.725228\pi$
$787$	4.55542e9	−	7.89022e9i	0.333133	−	0.577003i	0.983124	+	0.182939i	$0.0585610\pi$
$788$		0			0
$789$	2.46032e9	+	1.39532e10i	0.178329	+	1.01136i
$790$		0			0
$791$	1.58119e10	+	2.73871e10i	1.13597	+	1.96756i
$792$		0			0
$793$	1.07234e9	−	3.90301e8i	0.0763620	−	0.0277935i
$794$		0			0
$795$	−2.56768e9	−	2.15454e9i	−0.181240	−	0.152079i
$796$		0			0
$797$	1.18065e10			0.826074			0.413037	−	0.910714i	$-0.364468\pi$
$797$	1.18065e10			0.826074			0.413037	+	0.910714i	$0.364468\pi$
$798$		0			0
$799$	−1.99519e9			−0.138379
$800$		0			0
$801$	−1.34661e9	−	1.12994e9i	−0.0925822	−	0.0776857i
$802$		0			0
$803$	5.60309e9	−	2.03936e9i	0.381877	−	0.138992i
$804$		0			0
$805$	8.35609e8	+	1.44732e9i	0.0564570	+	0.0977863i
$806$		0			0
$807$	1.29047e9	+	7.31860e9i	0.0864349	+	0.490197i
$808$		0			0
$809$	−1.20687e10	+	2.09036e10i	−0.801383	+	1.38804i	0.117323	+	0.993094i	$0.462569\pi$
$809$	−1.20687e10	+	2.09036e10i	−0.801383	+	1.38804i	−0.918706	+	0.394942i	$0.870765\pi$
$810$		0			0
$811$	−7.53707e9	+	6.32435e9i	−0.496169	+	0.416335i	−0.856231	−	0.516593i	$-0.827200\pi$
$811$	−7.53707e9	+	6.32435e9i	−0.496169	+	0.416335i	0.360062	+	0.932928i	$0.382756\pi$
$812$		0			0
$813$	1.97676e10	+	7.19481e9i	1.29014	+	0.469573i
$814$		0			0
$815$	1.26780e9	−	7.19006e9i	0.0820351	−	0.465244i
$816$		0			0
$817$	1.94663e9	+	5.77654e9i	0.124884	+	0.370587i
$818$		0			0
$819$	−1.22062e8	+	6.92251e8i	−0.00776405	+	0.0440321i
$820$		0			0
$821$	1.11852e10	+	4.07108e9i	0.705412	+	0.256749i	0.669720	−	0.742614i	$-0.266414\pi$
$821$	1.11852e10	+	4.07108e9i	0.705412	+	0.256749i	0.0356920	+	0.999363i	$0.488636\pi$
$822$		0			0
$823$	−1.27919e10	+	1.07337e10i	−0.799903	+	0.671198i	−0.948175	−	0.317748i	$-0.897073\pi$
$823$	−1.27919e10	+	1.07337e10i	−0.799903	+	0.671198i	0.148272	+	0.988947i	$0.452629\pi$
$824$		0			0
$825$	4.64260e9	−	8.04121e9i	0.287854	−	0.498578i
$826$		0			0
$827$	−3.39400e9	−	1.92483e10i	−0.208661	−	1.18338i	−0.891573	−	0.452877i	$-0.850398\pi$
$827$	−3.39400e9	−	1.92483e10i	−0.208661	−	1.18338i	0.682912	−	0.730501i	$-0.260713\pi$
$828$		0			0
$829$	1.31581e10	+	2.27906e10i	0.802146	+	1.38936i	0.918201	+	0.396115i	$0.129642\pi$
$829$	1.31581e10	+	2.27906e10i	0.802146	+	1.38936i	−0.116055	+	0.993243i	$0.537025\pi$
$830$		0			0
$831$	−2.31247e10	+	8.41672e9i	−1.39789	+	0.508791i
$832$		0			0
$833$	6.65242e9	+	5.58205e9i	0.398770	+	0.334608i
$834$		0			0
$835$	−3.84491e9			−0.228551
$836$		0			0
$837$	−1.30217e10			−0.767590
$838$		0			0
$839$	−1.29332e8	−	1.08523e8i	−0.00756031	−	0.00634385i	0.639000	−	0.769207i	$-0.279349\pi$
$839$	−1.29332e8	−	1.08523e8i	−0.00756031	−	0.00634385i	−0.646560	+	0.762863i	$0.723793\pi$
$840$		0			0
$841$	−4.70311e10	+	1.71179e10i	−2.72646	+	0.992351i
$842$		0			0
$843$	1.17873e10	+	2.04161e10i	0.677667	+	1.17375i
$844$		0			0
$845$	8.16769e8	+	4.63213e9i	0.0465694	+	0.264108i
$846$		0			0
$847$	8.13135e9	−	1.40839e10i	0.459802	−	0.796400i
$848$		0			0
$849$	1.88010e10	−	1.57759e10i	1.05440	−	0.884743i
$850$		0			0
$851$	7.75251e9	+	2.82168e9i	0.431210	+	0.156948i
$852$		0			0
$853$	−3.62078e9	+	2.05344e10i	−0.199747	+	1.13282i	0.705748	+	0.708463i	$0.250611\pi$
$853$	−3.62078e9	+	2.05344e10i	−0.199747	+	1.13282i	−0.905495	+	0.424358i	$0.860500\pi$
$854$		0			0
$855$	9.79376e8	−	5.34489e8i	0.0535881	−	0.0292454i
$856$		0			0
$857$	−5.96433e8	+	3.38254e9i	−0.0323690	+	0.183574i	−0.996706	−	0.0811055i	$-0.974155\pi$
$857$	−5.96433e8	+	3.38254e9i	−0.0323690	+	0.183574i	0.964337	+	0.264679i	$0.0852660\pi$
$858$		0			0
$859$	−1.66915e10	−	6.07521e9i	−0.898503	−	0.327028i	−0.148850	−	0.988860i	$-0.547557\pi$
$859$	−1.66915e10	−	6.07521e9i	−0.898503	−	0.327028i	−0.749653	+	0.661832i	$0.769779\pi$
$860$		0			0
$861$	6.27983e8	−	5.26940e8i	0.0335302	−	0.0281352i
$862$		0			0
$863$	1.26655e10	−	2.19373e10i	0.670788	−	1.16184i	−0.306893	−	0.951744i	$-0.599289\pi$
$863$	1.26655e10	−	2.19373e10i	0.670788	−	1.16184i	0.977681	−	0.210095i	$-0.0673774\pi$
$864$		0			0
$865$	4.07671e7	+	2.31202e8i	0.00214168	+	0.0121460i
$866$		0			0
$867$	−6.25816e9	−	1.08395e10i	−0.326122	−	0.564860i
$868$		0			0
$869$	−1.20572e10	+	4.38847e9i	−0.623273	+	0.226853i
$870$		0			0
$871$	−7.28134e8	−	6.10977e8i	−0.0373377	−	0.0313301i
$872$		0			0
$873$	6.43590e9			0.327386
$874$		0			0
$875$	1.40863e10			0.710834
$876$		0			0
$877$	−1.31458e10	−	1.10307e10i	−0.658097	−	0.552209i	0.251419	−	0.967878i	$-0.419103\pi$
$877$	−1.31458e10	−	1.10307e10i	−0.658097	−	0.552209i	−0.909516	+	0.415670i	$0.863547\pi$
$878$		0			0
$879$	−3.89962e10	+	1.41934e10i	−1.93669	+	0.704899i
$880$		0			0
$881$	−7.21700e9	−	1.25002e10i	−0.355583	−	0.615888i	0.631635	−	0.775266i	$-0.282384\pi$
$881$	−7.21700e9	−	1.25002e10i	−0.355583	−	0.615888i	−0.987218	+	0.159378i	$0.949051\pi$
$882$		0			0
$883$	2.66543e9	+	1.51164e10i	0.130288	+	0.738900i	0.978026	+	0.208484i	$0.0668530\pi$
$883$	2.66543e9	+	1.51164e10i	0.130288	+	0.738900i	−0.847738	+	0.530416i	$0.822036\pi$
$884$		0			0
$885$	−2.00387e9	+	3.47081e9i	−0.0971781	+	0.168317i
$886$		0			0
$887$	1.49126e9	−	1.25132e9i	0.0717499	−	0.0602053i	−0.606207	−	0.795307i	$-0.707310\pi$
$887$	1.49126e9	−	1.25132e9i	0.0717499	−	0.0602053i	0.677957	+	0.735101i	$0.262865\pi$
$888$		0			0
$889$	7.14926e9	+	2.60212e9i	0.341275	+	0.124214i
$890$		0			0
$891$	2.42151e9	−	1.37331e10i	0.114687	−	0.650422i
$892$		0			0
$893$	−4.54637e9	+	6.89461e8i	−0.213641	+	0.0323989i
$894$		0			0
$895$	1.31863e9	−	7.47830e9i	0.0614810	−	0.348676i
$896$		0			0
$897$	−1.02452e9	−	3.72893e8i	−0.0473963	−	0.0172509i
$898$		0			0
$899$	−2.94345e10	+	2.46985e10i	−1.35113	+	1.13374i
$900$		0			0
$901$	5.48419e9	−	9.49890e9i	0.249790	−	0.432650i
$902$		0			0
$903$	−2.23689e9	−	1.26860e10i	−0.101097	−	0.573349i
$904$		0			0
$905$	7.40629e8	+	1.28281e9i	0.0332147	+	0.0575296i
$906$		0			0
$907$	−1.34889e10	+	4.90957e9i	−0.600278	+	0.218483i	−0.624244	−	0.781229i	$-0.714593\pi$
$907$	−1.34889e10	+	4.90957e9i	−0.600278	+	0.218483i	0.0239660	+	0.999713i	$0.492371\pi$
$908$		0			0
$909$	−8.90969e8	−	7.47612e8i	−0.0393450	−	0.0330143i
$910$		0			0
$911$	3.97545e10			1.74210			0.871048	−	0.491198i	$-0.163441\pi$
$911$	3.97545e10			1.74210			0.871048	+	0.491198i	$0.163441\pi$
$912$		0			0
$913$	−8.07666e9			−0.351224
$914$		0			0
$915$	2.93224e9	+	2.46044e9i	0.126539	+	0.106179i
$916$		0			0
$917$	−1.63335e10	+	5.94490e9i	−0.699497	+	0.254596i
$918$		0			0
$919$	4.15612e9	+	7.19860e9i	0.176638	+	0.305945i	0.940727	−	0.339165i	$-0.110145\pi$
$919$	4.15612e9	+	7.19860e9i	0.176638	+	0.305945i	−0.764089	+	0.645111i	$0.776811\pi$
$920$		0			0
$921$	3.43025e9	+	1.94539e10i	0.144683	+	0.820538i
$922$		0			0
$923$	−1.86208e9	+	3.22523e9i	−0.0779459	+	0.135006i
$924$		0			0
$925$	2.55934e10	−	2.14754e10i	1.06324	−	0.892164i
$926$		0			0
$927$	−1.96992e9	−	7.16991e8i	−0.0812211	−	0.0295621i
$928$		0			0
$929$	−5.73969e9	+	3.25514e10i	−0.234873	+	1.33203i	0.608007	+	0.793932i	$0.291969\pi$
$929$	−5.73969e9	+	3.25514e10i	−0.234873	+	1.33203i	−0.842880	+	0.538101i	$0.819142\pi$
$930$		0			0
$931$	1.70876e10	+	1.04208e10i	0.693995	+	0.423230i
$932$		0			0
$933$	−6.07351e9	+	3.44446e10i	−0.244824	+	1.38847i
$934$		0			0
$935$	−2.32282e9	−	8.45437e8i	−0.0929341	−	0.0338252i
$936$		0			0
$937$	−7.59937e9	+	6.37663e9i	−0.301779	+	0.253223i	−0.781084	−	0.624426i	$-0.785333\pi$
$937$	−7.59937e9	+	6.37663e9i	−0.301779	+	0.253223i	0.479305	+	0.877648i	$0.340889\pi$
$938$		0			0
$939$	9.67737e8	−	1.67617e9i	0.0381441	−	0.0660676i
$940$		0			0
$941$	−2.18141e9	−	1.23714e10i	−0.0853441	−	0.484010i	−0.997282	−	0.0736816i	$-0.976525\pi$
$941$	−2.18141e9	−	1.23714e10i	−0.0853441	−	0.484010i	0.911938	−	0.410329i	$-0.134586\pi$
$942$		0			0
$943$	1.15739e8	+	2.00466e8i	0.00449459	+	0.00778486i
$944$		0			0
$945$	7.73899e9	−	2.81676e9i	0.298314	−	0.108577i
$946$		0			0
$947$	−1.71772e10	−	1.44134e10i	−0.657246	−	0.551495i	0.252014	−	0.967724i	$-0.418907\pi$
$947$	−1.71772e10	−	1.44134e10i	−0.657246	−	0.551495i	−0.909260	+	0.416229i	$0.863352\pi$
$948$		0			0
$949$	−2.83531e9			−0.107688
$950$		0			0
$951$	7.62451e7			0.00287462
$952$		0			0
$953$	−2.34687e10	−	1.96926e10i	−0.878342	−	0.737016i	0.0874957	−	0.996165i	$-0.472114\pi$
$953$	−2.34687e10	−	1.96926e10i	−0.878342	−	0.737016i	−0.965837	+	0.259149i	$0.916558\pi$
$954$		0			0
$955$	1.40315e9	−	5.10705e8i	0.0521306	−	0.0189740i
$956$		0			0
$957$	−1.66703e10	−	2.88739e10i	−0.614827	−	1.06491i
$958$		0			0
$959$	9.50366e9	+	5.38979e10i	0.347957	+	1.97336i
$960$		0			0
$961$	2.78734e9	−	4.82782e9i	0.101311	−	0.175477i
$962$		0			0
$963$	−6.11777e9	+	5.13342e9i	−0.220750	+	0.185231i
$964$		0			0
$965$	4.98659e8	+	1.81497e8i	0.0178631	+	0.00650165i
$966$		0			0
$967$	8.25772e9	−	4.68318e10i	0.293675	−	1.66552i	−0.378863	−	0.925453i	$-0.623685\pi$
$967$	8.25772e9	−	4.68318e10i	0.293675	−	1.66552i	0.672538	−	0.740063i	$-0.265204\pi$
$968$		0			0
$969$	1.25182e10	+	1.56682e10i	0.441985	+	0.553205i
$970$		0			0
$971$	−5.75051e9	+	3.26128e10i	−0.201576	+	1.14319i	0.701161	+	0.713003i	$0.252665\pi$
$971$	−5.75051e9	+	3.26128e10i	−0.201576	+	1.14319i	−0.902737	+	0.430192i	$0.858446\pi$
$972$		0			0
$973$	5.45688e9	+	1.98614e9i	0.189911	+	0.0691219i
$974$		0			0
$975$	−3.38223e9	+	2.83803e9i	−0.116866	+	0.0980620i
$976$		0			0
$977$	2.71940e10	−	4.71014e10i	0.932916	−	1.61586i	0.154608	−	0.987976i	$-0.450589\pi$
$977$	2.71940e10	−	4.71014e10i	0.932916	−	1.61586i	0.778308	−	0.627882i	$-0.216078\pi$
$978$		0			0
$979$	1.55864e9	+	8.83947e9i	0.0530891	+	0.301083i
$980$		0			0
$981$	5.68108e8	+	9.83992e8i	0.0192127	+	0.0332775i
$982$		0			0
$983$	−1.13618e10	+	4.13534e9i	−0.381512	+	0.138859i	−0.525655	−	0.850698i	$-0.676180\pi$
$983$	−1.13618e10	+	4.13534e9i	−0.381512	+	0.138859i	0.144143	+	0.989557i	$0.453957\pi$
$984$		0			0
$985$	−6.63757e9	−	5.56958e9i	−0.221300	−	0.185693i
$986$		0			0
$987$	9.71746e9			0.321694
$988$		0			0
$989$	3.63741e9			0.119565
$990$		0			0
$991$	4.18094e10	+	3.50823e10i	1.36463	+	1.14506i	0.974521	+	0.224297i	$0.0720086\pi$
$991$	4.18094e10	+	3.50823e10i	1.36463	+	1.14506i	0.390113	+	0.920767i	$0.372436\pi$
$992$		0			0
$993$	−2.09652e10	+	7.63072e9i	−0.679481	+	0.247311i
$994$		0			0
$995$	3.38935e9	+	5.87052e9i	0.109078	+	0.188928i
$996$		0			0
$997$	−2.79021e9	−	1.58241e10i	−0.0891669	−	0.505690i	−0.996379	−	0.0850179i	$-0.972905\pi$
$997$	−2.79021e9	−	1.58241e10i	−0.0891669	−	0.505690i	0.907213	−	0.420673i	$-0.138206\pi$
$998$		0			0
$999$	2.03279e10	−	3.52089e10i	0.645079	−	1.11731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.17.4	yes	72
19.9	even	9	inner	76.8.i.a.9.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.9.4	✓	72	19.9	even	9	inner
76.8.i.a.17.4	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-39.6110 - 33.2376i) q^{3} +(72.0424 - 26.2213i) q^{5} +(-610.937 - 1058.17i) q^{7} +(84.5259 + 479.370i) q^{9} +O(q^{10})\)	\(q+(-39.6110 - 33.2376i) q^{3} +(72.0424 - 26.2213i) q^{5} +(-610.937 - 1058.17i) q^{7} +(84.5259 + 479.370i) q^{9} +(1242.73 - 2152.47i) q^{11} +(-905.357 + 759.685i) q^{13} +(-3725.20 - 1355.86i) q^{15} +(2252.63 - 12775.3i) q^{17} +(718.339 - 29889.1i) q^{19} +(-10971.3 + 62221.3i) q^{21} +(-16764.5 - 6101.78i) q^{23} +(-55344.7 + 46439.7i) q^{25} +(-43958.3 + 76137.9i) q^{27} +(45048.0 + 255480. i) q^{29} +(74057.3 + 128271. i) q^{31} +(-120769. + 43956.3i) q^{33} +(-71760.0 - 60213.8i) q^{35} -462436. q^{37} +61112.2 q^{39} +(-9939.40 - 8340.14i) q^{41} +(-191590. + 69733.0i) q^{43} +(18659.2 + 32318.6i) q^{45} +(-26707.6 - 151466. i) q^{47} +(-334715. + 579744. i) q^{49} +(-513849. + 431171. i) q^{51} +(794526. + 289184. i) q^{53} +(33088.7 - 187655. i) q^{55} +(-1.02189e6 + 1.16006e6i) q^{57} +(175552. - 995606. i) q^{59} +(-907335. - 330243. i) q^{61} +(455617. - 382308. i) q^{63} +(-45304.2 + 78469.1i) q^{65} +(139657. + 792032. i) q^{67} +(461250. + 798909. i) q^{69} +(2.96107e6 - 1.07774e6i) q^{71} +(1.83776e6 + 1.54206e6i) q^{73} +3.73580e6 q^{75} -3.03692e6 q^{77} +(-3.95465e6 - 3.31835e6i) q^{79} +(5.27222e6 - 1.91893e6i) q^{81} +(-1.62478e6 - 2.81420e6i) q^{83} +(-172700. - 979431. i) q^{85} +(6.70714e6 - 1.16171e7i) q^{87} +(-2.76644e6 + 2.32132e6i) q^{89} +(1.35699e6 + 493905. i) q^{91} +(1.32993e6 - 7.54242e6i) q^{93} +(-731978. - 2.17211e6i) q^{95} +(2.29594e6 - 1.30209e7i) q^{97} +(1.13688e6 + 413789. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

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