LMFDB - Embedded newform 76.8.i.a.17.9

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			17.9
Character	$\chi$	$=$	76.17
Dual form			76.8.i.a.9.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(37.8546 + 31.7638i) q^{3} +(-76.8725 + 27.9793i) q^{5} +(-295.074 - 511.083i) q^{7} +(44.2641 + 251.034i) q^{9} +O(q^{10})$	\(q+(37.8546 + 31.7638i) q^{3} +(-76.8725 + 27.9793i) q^{5} +(-295.074 - 511.083i) q^{7} +(44.2641 + 251.034i) q^{9} +(2358.12 - 4084.39i) q^{11} +(6706.49 - 5627.41i) q^{13} +(-3798.70 - 1382.61i) q^{15} +(3435.19 - 19481.9i) q^{17} +(12357.7 + 27224.2i) q^{19} +(5064.02 - 28719.5i) q^{21} +(60782.4 + 22123.0i) q^{23} +(-54720.7 + 45916.1i) q^{25} +(47737.8 - 82684.3i) q^{27} +(20488.8 + 116198. i) q^{29} +(-66960.1 - 115978. i) q^{31} +(219001. - 79709.9i) q^{33} +(36982.8 + 31032.2i) q^{35} +252272. q^{37} +432619. q^{39} +(-218843. - 183631. i) q^{41} +(796122. - 289765. i) q^{43} +(-10426.5 - 18059.2i) q^{45} +(-178495. - 1.01230e6i) q^{47} +(237634. - 411595. i) q^{49} +(748857. - 628366. i) q^{51} +(581163. + 211526. i) q^{53} +(-66996.4 + 379955. i) q^{55} +(-396947. + 1.42309e6i) q^{57} +(-56042.2 + 317831. i) q^{59} +(-1.62118e6 - 590062. i) q^{61} +(115238. - 96696.3i) q^{63} +(-358093. + 620236. i) q^{65} +(256575. + 1.45511e6i) q^{67} +(1.59818e6 + 2.76814e6i) q^{69} +(-1.91717e6 + 697793. i) q^{71} +(-794228. - 666436. i) q^{73} -3.52990e6 q^{75} -2.78328e6 q^{77} +(-4.24199e6 - 3.55946e6i) q^{79} +(4.95732e6 - 1.80432e6i) q^{81} +(1.27239e6 + 2.20385e6i) q^{83} +(281019. + 1.59374e6i) q^{85} +(-2.91528e6 + 5.04941e6i) q^{87} +(-4.47240e6 + 3.75279e6i) q^{89} +(-4.85498e6 - 1.76707e6i) q^{91} +(1.14916e6 - 6.51722e6i) q^{93} +(-1.71168e6 - 1.74703e6i) q^{95} +(1.18614e6 - 6.72694e6i) q^{97} +(1.12970e6 + 411178. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	37.8546	+	31.7638i	0.809458	+	0.679216i	0.950478	−	0.310791i	$-0.100594\pi$
$3$	37.8546	+	31.7638i	0.809458	+	0.679216i	−0.141021	+	0.990007i	$0.545038\pi$
$4$		0			0
$5$	−76.8725	+	27.9793i	−0.275027	+	0.100102i	−0.475852	−	0.879525i	$-0.657860\pi$
$5$	−76.8725	+	27.9793i	−0.275027	+	0.100102i	0.200824	+	0.979627i	$0.435638\pi$
$6$		0			0
$7$	−295.074	−	511.083i	−0.325153	−	0.563181i	0.656390	−	0.754421i	$-0.272082\pi$
$7$	−295.074	−	511.083i	−0.325153	−	0.563181i	−0.981543	+	0.191240i	$0.938749\pi$
$8$		0			0
$9$	44.2641	+	251.034i	0.0202397	+	0.114785i
$10$		0			0
$11$	2358.12	−	4084.39i	0.534185	−	0.925236i	−0.465017	−	0.885302i	$-0.653952\pi$
$11$	2358.12	−	4084.39i	0.534185	−	0.925236i	0.999202	−	0.0399340i	$-0.0127148\pi$
$12$		0			0
$13$	6706.49	−	5627.41i	0.846630	−	0.710407i	−0.112415	−	0.993661i	$-0.535859\pi$
$13$	6706.49	−	5627.41i	0.846630	−	0.710407i	0.959045	+	0.283255i	$0.0914142\pi$
$14$		0			0
$15$	−3798.70	−	1382.61i	−0.290614	−	0.105775i
$16$		0			0
$17$	3435.19	−	19481.9i	0.169582	−	0.961747i	−0.774632	−	0.632413i	$-0.782065\pi$
$17$	3435.19	−	19481.9i	0.169582	−	0.961747i	0.944213	−	0.329334i	$-0.106824\pi$
$18$		0			0
$19$	12357.7	+	27224.2i	0.413334	+	0.910579i
$19$	12357.7	+	27224.2i	0.413334	+	0.910579i
$20$		0			0
$21$	5064.02	−	28719.5i	0.119324	−	0.676720i
$22$		0			0
$23$	60782.4	+	22123.0i	1.04167	+	0.379137i	0.805514	−	0.592577i	$-0.201890\pi$
$23$	60782.4	+	22123.0i	1.04167	+	0.379137i	0.236158	+	0.971715i	$0.424112\pi$
$24$		0			0
$25$	−54720.7	+	45916.1i	−0.700425	+	0.587726i
$26$		0			0
$27$	47737.8	−	82684.3i	0.466755	−	0.808444i
$28$		0			0
$29$	20488.8	+	116198.i	0.155999	+	0.884717i	0.957866	+	0.287214i	$0.0927291\pi$
$29$	20488.8	+	116198.i	0.155999	+	0.884717i	−0.801867	+	0.597503i	$0.796160\pi$
$30$		0			0
$31$	−66960.1	−	115978.i	−0.403692	−	0.699215i	0.590476	−	0.807055i	$-0.298940\pi$
$31$	−66960.1	−	115978.i	−0.403692	−	0.699215i	−0.994168	+	0.107840i	$0.965607\pi$
$32$		0			0
$33$	219001.	−	79709.9i	1.06083	−	0.386112i
$34$		0			0
$35$	36982.8	+	31032.2i	0.145801	+	0.122342i
$36$		0			0
$37$	252272.			0.818772			0.409386	−	0.912361i	$-0.365743\pi$
$37$	252272.			0.818772			0.409386	+	0.912361i	$0.365743\pi$
$38$		0			0
$39$	432619.			1.16783
$40$		0			0
$41$	−218843.	−	183631.i	−0.495894	−	0.416104i	0.360239	−	0.932860i	$-0.382695\pi$
$41$	−218843.	−	183631.i	−0.495894	−	0.416104i	−0.856133	+	0.516756i	$0.827140\pi$
$42$		0			0
$43$	796122.	−	289765.i	1.52700	−	0.555784i	0.564118	−	0.825694i	$-0.309216\pi$
$43$	796122.	−	289765.i	1.52700	−	0.555784i	0.962886	+	0.269910i	$0.0869939\pi$
$44$		0			0
$45$	−10426.5	−	18059.2i	−0.0170566	−	0.0295429i
$46$		0			0
$47$	−178495.	−	1.01230e6i	−0.250775	−	1.42221i	−0.806690	−	0.590975i	$-0.798743\pi$
$47$	−178495.	−	1.01230e6i	−0.250775	−	1.42221i	0.555915	−	0.831239i	$-0.312368\pi$
$48$		0			0
$49$	237634.	−	411595.i	0.288551	−	0.499785i
$50$		0			0
$51$	748857.	−	628366.i	0.790503	−	0.663311i
$52$		0			0
$53$	581163.	+	211526.i	0.536207	+	0.195163i	0.595908	−	0.803053i	$-0.296792\pi$
$53$	581163.	+	211526.i	0.536207	+	0.195163i	−0.0597007	+	0.998216i	$0.519015\pi$
$54$		0			0
$55$	−66996.4	+	379955.i	−0.0542978	+	0.307938i
$56$		0			0
$57$	−396947.	+	1.42309e6i	−0.283903	+	1.01782i
$58$		0			0
$59$	−56042.2	+	317831.i	−0.0355249	+	0.201472i	−0.997405	−	0.0720014i	$-0.977061\pi$
$59$	−56042.2	+	317831.i	−0.0355249	+	0.201472i	0.961880	+	0.273473i	$0.0881725\pi$
$60$		0			0
$61$	−1.62118e6	−	590062.i	−0.914487	−	0.332846i	−0.158444	−	0.987368i	$-0.550648\pi$
$61$	−1.62118e6	−	590062.i	−0.914487	−	0.332846i	−0.756043	+	0.654522i	$0.772870\pi$
$62$		0			0
$63$	115238.	−	96696.3i	0.0580637	−	0.0487212i
$64$		0			0
$65$	−358093.	+	620236.i	−0.161733	+	0.280130i
$66$		0			0
$67$	256575.	+	1.45511e6i	0.104220	+	0.591063i	0.991529	+	0.129887i	$0.0414613\pi$
$67$	256575.	+	1.45511e6i	0.104220	+	0.591063i	−0.887308	+	0.461176i	$0.847428\pi$
$68$		0			0
$69$	1.59818e6	+	2.76814e6i	0.585673	+	1.01442i
$70$		0			0
$71$	−1.91717e6	+	697793.i	−0.635707	+	0.231378i	−0.639713	−	0.768614i	$-0.720947\pi$
$71$	−1.91717e6	+	697793.i	−0.635707	+	0.231378i	0.00400654	+	0.999992i	$0.498725\pi$
$72$		0			0
$73$	−794228.	−	666436.i	−0.238954	−	0.200507i	0.515444	−	0.856923i	$-0.327627\pi$
$73$	−794228.	−	666436.i	−0.238954	−	0.200507i	−0.754399	+	0.656417i	$0.772071\pi$
$74$		0			0
$75$	−3.52990e6			−0.966157
$76$		0			0
$77$	−2.78328e6			−0.694767
$78$		0			0
$79$	−4.24199e6	−	3.55946e6i	−0.968000	−	0.812248i	0.0142360	−	0.999899i	$-0.495468\pi$
$79$	−4.24199e6	−	3.55946e6i	−0.968000	−	0.812248i	−0.982236	+	0.187650i	$0.939913\pi$
$80$		0			0
$81$	4.95732e6	−	1.80432e6i	1.03645	−	0.377238i
$82$		0			0
$83$	1.27239e6	+	2.20385e6i	0.244257	+	0.423066i	0.961922	−	0.273322i	$-0.0881226\pi$
$83$	1.27239e6	+	2.20385e6i	0.244257	+	0.423066i	−0.717665	+	0.696388i	$0.754789\pi$
$84$		0			0
$85$	281019.	+	1.59374e6i	0.0496329	+	0.281482i
$86$		0			0
$87$	−2.91528e6	+	5.04941e6i	−0.474638	+	0.822098i
$88$		0			0
$89$	−4.47240e6	+	3.75279e6i	−0.672475	+	0.564273i	−0.913797	−	0.406172i	$-0.866863\pi$
$89$	−4.47240e6	+	3.75279e6i	−0.672475	+	0.564273i	0.241322	+	0.970445i	$0.422419\pi$
$90$		0			0
$91$	−4.85498e6	−	1.76707e6i	−0.675372	−	0.245815i
$92$		0			0
$93$	1.14916e6	−	6.51722e6i	0.148146	−	0.840179i
$94$		0			0
$95$	−1.71168e6	−	1.74703e6i	−0.204829	−	0.209059i
$96$		0			0
$97$	1.18614e6	−	6.72694e6i	0.131958	−	0.748370i	−0.844972	−	0.534810i	$-0.820383\pi$
$97$	1.18614e6	−	6.72694e6i	0.131958	−	0.748370i	0.976930	−	0.213560i	$-0.0685058\pi$
$98$		0			0
$99$	1.12970e6	+	411178.i	0.117015	+	0.0425899i
$100$		0			0
$101$	−2.74544e6	+	2.30369e6i	−0.265147	+	0.222485i	−0.765662	−	0.643243i	$-0.777588\pi$
$101$	−2.74544e6	+	2.30369e6i	−0.265147	+	0.222485i	0.500515	+	0.865728i	$0.333144\pi$
$102$		0			0
$103$	−7.38231e6	+	1.27865e7i	−0.665675	+	1.15298i	0.313427	+	0.949612i	$0.398523\pi$
$103$	−7.38231e6	+	1.27865e7i	−0.665675	+	1.15298i	−0.979102	+	0.203370i	$0.934810\pi$
$104$		0			0
$105$	414267.	+	2.34943e6i	0.0349235	+	0.198061i
$106$		0			0
$107$	−2.60568e6	−	4.51316e6i	−0.205626	−	0.356154i	0.744706	−	0.667392i	$-0.232590\pi$
$107$	−2.60568e6	−	4.51316e6i	−0.205626	−	0.356154i	−0.950332	+	0.311238i	$0.899256\pi$
$108$		0			0
$109$	4.54017e6	−	1.65249e6i	0.335799	−	0.122221i	−0.168617	−	0.985682i	$-0.553930\pi$
$109$	4.54017e6	−	1.65249e6i	0.335799	−	0.122221i	0.504416	+	0.863461i	$0.331708\pi$
$110$		0			0
$111$	9.54965e6	+	8.01311e6i	0.662761	+	0.556123i
$112$		0			0
$113$	1.59329e7			1.03877			0.519385	−	0.854540i	$-0.326161\pi$
$113$	1.59329e7			1.03877			0.519385	+	0.854540i	$0.326161\pi$
$114$		0			0
$115$	−5.29148e6			−0.324440
$116$		0			0
$117$	1.70953e6	+	1.43447e6i	0.0986794	+	0.0828018i
$118$		0			0
$119$	−1.09705e7	+	3.99294e6i	−0.596778	+	0.217209i
$120$		0			0
$121$	−1.37788e6	−	2.38657e6i	−0.0707073	−	0.122469i
$122$		0			0
$123$	−2.45139e6	−	1.39025e7i	−0.118780	−	0.673638i
$124$		0			0
$125$	6.11736e6	−	1.05956e7i	0.280142	−	0.485221i
$126$		0			0
$127$	−2.74663e7	+	2.30470e7i	−1.18984	+	0.998391i	−0.189973	+	0.981789i	$0.560840\pi$
$127$	−2.74663e7	+	2.30470e7i	−1.18984	+	0.998391i	−0.999862	+	0.0166013i	$0.994715\pi$
$128$		0			0
$129$	3.93409e7	+	1.43189e7i	1.61354	+	0.587281i
$130$		0			0
$131$	1.47592e6	−	8.37034e6i	0.0573604	−	0.325307i	−0.942603	−	0.333917i	$-0.891630\pi$
$131$	1.47592e6	−	8.37034e6i	0.0573604	−	0.325307i	0.999963	+	0.00860985i	$0.00274064\pi$
$132$		0			0
$133$	1.02674e7	−	1.43490e7i	0.378424	−	0.528860i
$134$		0			0
$135$	−1.35628e6	+	7.69182e6i	−0.0474438	+	0.269067i
$136$		0			0
$137$	3.43509e7	+	1.25027e7i	1.14134	+	0.415415i	0.842398	−	0.538856i	$-0.181143\pi$
$137$	3.43509e7	+	1.25027e7i	1.14134	+	0.415415i	0.298944	+	0.954271i	$0.403366\pi$
$138$		0			0
$139$	3.04417e7	−	2.55436e7i	0.961428	−	0.806734i	−0.0197570	−	0.999805i	$-0.506289\pi$
$139$	3.04417e7	−	2.55436e7i	0.961428	−	0.806734i	0.981185	+	0.193071i	$0.0618448\pi$
$140$		0			0
$141$	2.53975e7	−	4.39897e7i	0.762999	−	1.32155i
$142$		0			0
$143$	−7.16981e6	−	4.06620e7i	−0.205037	−	1.16282i
$144$		0			0
$145$	−4.82615e6	−	8.35914e6i	−0.131466	−	0.227705i
$146$		0			0
$147$	2.20694e7	−	8.03259e6i	0.573032	−	0.208567i
$148$		0			0
$149$	3.46805e6	+	2.91004e6i	0.0858881	+	0.0720687i	0.684721	−	0.728805i	$-0.259924\pi$
$149$	3.46805e6	+	2.91004e6i	0.0858881	+	0.0720687i	−0.598833	+	0.800874i	$0.704369\pi$
$150$		0			0
$151$	−4.38589e7			−1.03666			−0.518332	−	0.855179i	$-0.673447\pi$
$151$	−4.38589e7			−1.03666			−0.518332	+	0.855179i	$0.673447\pi$
$152$		0			0
$153$	5.04269e6			0.113826
$154$		0			0
$155$	8.39238e6	+	7.04204e6i	0.181019	+	0.151893i
$156$		0			0
$157$	6.19486e7	−	2.25475e7i	1.27757	−	0.464996i	0.387939	−	0.921685i	$-0.373187\pi$
$157$	6.19486e7	−	2.25475e7i	1.27757	−	0.464996i	0.889626	+	0.456689i	$0.150965\pi$
$158$		0			0
$159$	1.52808e7	+	2.64672e7i	0.301479	+	0.522177i
$160$		0			0
$161$	−6.62862e6	−	3.75928e7i	−0.125179	−	0.709927i
$162$		0			0
$163$	−1.85107e7	+	3.20615e7i	−0.334785	+	0.579865i	−0.983444	−	0.181215i	$-0.941997\pi$
$163$	−1.85107e7	+	3.20615e7i	−0.334785	+	0.579865i	0.648658	+	0.761080i	$0.275330\pi$
$164$		0			0
$165$	−1.46049e7	+	1.22550e7i	−0.253108	+	0.212383i
$166$		0			0
$167$	−4.02091e7	−	1.46349e7i	−0.668062	−	0.243155i	−0.0143487	−	0.999897i	$-0.504567\pi$
$167$	−4.02091e7	−	1.46349e7i	−0.668062	−	0.243155i	−0.653713	+	0.756742i	$0.726790\pi$
$168$		0			0
$169$	2.41306e6	−	1.36851e7i	0.0384560	−	0.218095i
$170$		0			0
$171$	−6.28721e6	+	4.30727e6i	−0.0961550	+	0.0658743i
$172$		0			0
$173$	−2.22341e7	+	1.26096e8i	−0.326481	+	1.85157i	0.172573	+	0.984997i	$0.444792\pi$
$173$	−2.22341e7	+	1.26096e8i	−0.326481	+	1.85157i	−0.499054	+	0.866571i	$0.666319\pi$
$174$		0			0
$175$	3.96136e7	+	1.44182e7i	0.558741	+	0.203365i
$176$		0			0
$177$	−1.22170e7	+	1.02513e7i	−0.165599	+	0.138954i
$178$		0			0
$179$	−6.13574e7	+	1.06274e8i	−0.799615	+	1.38497i	0.120251	+	0.992743i	$0.461630\pi$
$179$	−6.13574e7	+	1.06274e8i	−0.799615	+	1.38497i	−0.919867	+	0.392231i	$0.871703\pi$
$180$		0			0
$181$	5.82772e6	+	3.30506e7i	0.0730506	+	0.414290i	0.999301	+	0.0373819i	$0.0119018\pi$
$181$	5.82772e6	+	3.30506e7i	0.0730506	+	0.414290i	−0.926250	+	0.376909i	$0.876987\pi$
$182$		0			0
$183$	−4.26266e7	−	7.38314e7i	−0.514164	−	0.890559i
$184$		0			0
$185$	−1.93928e7	+	7.05839e6i	−0.225185	+	0.0819605i
$186$		0			0
$187$	−7.14711e7	−	5.99714e7i	−0.799254	−	0.670654i
$188$		0			0
$189$	−5.63447e7			−0.607067
$190$		0			0
$191$	−7.03585e7			−0.730633			−0.365317	−	0.930883i	$-0.619039\pi$
$191$	−7.03585e7			−0.730633			−0.365317	+	0.930883i	$0.619039\pi$
$192$		0			0
$193$	−4.55588e7	−	3.82284e7i	−0.456165	−	0.382768i	0.385553	−	0.922686i	$-0.374011\pi$
$193$	−4.55588e7	−	3.82284e7i	−0.456165	−	0.382768i	−0.841718	+	0.539918i	$0.818455\pi$
$194$		0			0
$195$	−3.32565e7	+	1.21044e7i	−0.321185	+	0.116902i
$196$		0			0
$197$	6.88442e7	+	1.19242e8i	0.641558	+	1.11121i	0.985085	+	0.172068i	$0.0550448\pi$
$197$	6.88442e7	+	1.19242e8i	0.641558	+	1.11121i	−0.343528	+	0.939143i	$0.611622\pi$
$198$		0			0
$199$	−4.52426e6	−	2.56583e7i	−0.0406969	−	0.230804i	0.957674	−	0.287854i	$-0.0929417\pi$
$199$	−4.52426e6	−	2.56583e7i	−0.0406969	−	0.230804i	−0.998371	+	0.0570499i	$0.981831\pi$
$200$		0			0
$201$	−3.65072e7	+	6.32324e7i	−0.317097	+	0.549229i
$202$		0			0
$203$	5.33409e7	−	4.47583e7i	0.447532	−	0.375524i
$204$		0			0
$205$	2.19608e7	+	7.99309e6i	0.178037	+	0.0648002i
$206$		0			0
$207$	−2.86315e6	+	1.62377e7i	−0.0224361	+	0.127242i
$208$		0			0
$209$	1.40335e8	+	1.37242e7i	1.06330	+	0.103986i
$210$		0			0
$211$	1.14522e7	−	6.49487e7i	0.0839267	−	0.475972i	−0.913656	−	0.406488i	$-0.866753\pi$
$211$	1.14522e7	−	6.49487e7i	0.0839267	−	0.475972i	0.997583	−	0.0694845i	$-0.0221355\pi$
$212$		0			0
$213$	−9.47383e7	−	3.44819e7i	−0.671733	−	0.244491i
$214$		0			0
$215$	−5.30925e7	+	4.45499e7i	−0.364333	+	0.305712i
$216$		0			0
$217$	−3.95163e7	+	6.84443e7i	−0.262523	+	0.454704i
$218$		0			0
$219$	−8.89664e6	−	5.04553e7i	−0.0572363	−	0.324603i
$220$		0			0
$221$	−8.65948e7	−	1.49987e8i	−0.539658	−	0.934715i
$222$		0			0
$223$	−2.07719e8	+	7.56034e7i	−1.25432	+	0.456535i	−0.881859	−	0.471512i	$-0.843708\pi$
$223$	−2.07719e8	+	7.56034e7i	−1.25432	+	0.456535i	−0.372461	+	0.928048i	$0.621486\pi$
$224$		0			0
$225$	−1.39487e7	−	1.17043e7i	−0.0816384	−	0.0685028i
$226$		0			0
$227$	2.43963e8			1.38431			0.692156	−	0.721748i	$-0.256661\pi$
$227$	2.43963e8			1.38431			0.692156	+	0.721748i	$0.256661\pi$
$228$		0			0
$229$	−7.42340e7			−0.408488			−0.204244	−	0.978920i	$-0.565474\pi$
$229$	−7.42340e7			−0.408488			−0.204244	+	0.978920i	$0.565474\pi$
$230$		0			0
$231$	−1.05360e8	−	8.84074e7i	−0.562385	−	0.471897i
$232$		0			0
$233$	3.43105e8	−	1.24880e8i	1.77698	−	0.646766i	0.777127	−	0.629344i	$-0.216676\pi$
$233$	3.43105e8	−	1.24880e8i	1.77698	−	0.646766i	0.999848	−	0.0174224i	$-0.00554601\pi$
$234$		0			0
$235$	4.20447e7	+	7.28235e7i	0.211336	+	0.366045i
$236$		0			0
$237$	−4.75172e7	−	2.69484e8i	−0.231863	−	1.31496i
$238$		0			0
$239$	−1.46464e8	+	2.53683e8i	−0.693965	+	1.20198i	0.276563	+	0.960996i	$0.410805\pi$
$239$	−1.46464e8	+	2.53683e8i	−0.693965	+	1.20198i	−0.970528	+	0.240987i	$0.922529\pi$
$240$		0			0
$241$	−9.30550e7	+	7.80825e7i	−0.428233	+	0.359330i	−0.831285	−	0.555847i	$-0.812394\pi$
$241$	−9.30550e7	+	7.80825e7i	−0.428233	+	0.359330i	0.403051	+	0.915177i	$0.367950\pi$
$242$		0			0
$243$	4.87566e7	+	1.77460e7i	0.217978	+	0.0793373i
$244$		0			0
$245$	−6.75141e6	+	3.82891e7i	−0.0293301	+	0.166339i
$246$		0			0
$247$	2.36079e8	+	1.13037e8i	0.996823	+	0.477288i
$248$		0			0
$249$	−2.18366e7	+	1.23842e8i	−0.0896370	+	0.508357i
$250$		0			0
$251$	2.62098e8	+	9.53957e7i	1.04618	+	0.380777i	0.807218	−	0.590253i	$-0.200972\pi$
$251$	2.62098e8	+	9.53957e7i	1.04618	+	0.380777i	0.238958	+	0.971030i	$0.423194\pi$
$252$		0			0
$253$	2.33691e8	−	1.96090e8i	0.907237	−	0.761262i
$254$		0			0
$255$	−3.99853e7	+	6.92565e7i	−0.151011	+	0.261559i
$256$		0			0
$257$	−2.07889e6	−	1.17900e7i	−0.00763952	−	0.0433258i	0.980750	−	0.195269i	$-0.0625580\pi$
$257$	−2.07889e6	−	1.17900e7i	−0.00763952	−	0.0433258i	−0.988389	+	0.151943i	$0.951447\pi$
$258$		0			0
$259$	−7.44388e7	−	1.28932e8i	−0.266226	−	0.461117i
$260$		0			0
$261$	−2.82627e7	+	1.02868e7i	−0.0983947	+	0.0358127i
$262$		0			0
$263$	−2.39539e8	−	2.00997e8i	−0.811954	−	0.681310i	0.139120	−	0.990276i	$-0.455573\pi$
$263$	−2.39539e8	−	2.00997e8i	−0.811954	−	0.681310i	−0.951073	+	0.308966i	$0.900017\pi$
$264$		0			0
$265$	−5.05938e7			−0.167008
$266$		0			0
$267$	−2.88504e8			−0.927603
$268$		0			0
$269$	4.44679e8	+	3.73130e8i	1.39288	+	1.16877i	0.964158	+	0.265330i	$0.0854810\pi$
$269$	4.44679e8	+	3.73130e8i	1.39288	+	1.16877i	0.428724	+	0.903436i	$0.358963\pi$
$270$		0			0
$271$	4.02752e8	−	1.46590e8i	1.22926	−	0.447415i	0.355918	−	0.934517i	$-0.384168\pi$
$271$	4.02752e8	−	1.46590e8i	1.22926	−	0.447415i	0.873345	+	0.487102i	$0.161946\pi$
$272$		0			0
$273$	−1.27655e8	−	2.21104e8i	−0.379723	−	0.657700i
$274$		0			0
$275$	5.85011e7	+	3.31776e8i	0.169629	+	0.962012i
$276$		0			0
$277$	1.43322e8	−	2.48240e8i	0.405165	−	0.701767i	−0.589175	−	0.808005i	$-0.700547\pi$
$277$	1.43322e8	−	2.48240e8i	0.405165	−	0.701767i	0.994341	+	0.106238i	$0.0338806\pi$
$278$		0			0
$279$	2.61506e7	−	2.19430e7i	0.0720887	−	0.0604896i
$280$		0			0
$281$	5.66414e8	+	2.06158e8i	1.52287	+	0.554279i	0.961862	−	0.273534i	$-0.0881925\pi$
$281$	5.66414e8	+	2.06158e8i	1.52287	+	0.554279i	0.561005	+	0.827812i	$0.310415\pi$
$282$		0			0
$283$	9.66428e7	−	5.48088e8i	0.253464	−	1.43747i	−0.546520	−	0.837446i	$-0.684048\pi$
$283$	9.66428e7	−	5.48088e8i	0.253464	−	1.43747i	0.799984	−	0.600021i	$-0.204841\pi$
$284$		0			0
$285$	−9.30277e6	−	1.20503e8i	−0.0238043	−	0.308347i
$286$		0			0
$287$	−2.92758e7	+	1.66031e8i	−0.0731008	+	0.414576i
$288$		0			0
$289$	1.78471e7	+	6.49583e6i	0.0434937	+	0.0158304i
$290$		0			0
$291$	2.58574e8	−	2.16969e8i	0.615119	−	0.516146i
$292$		0			0
$293$	5.93882e6	−	1.02863e7i	0.0137932	−	0.0238904i	−0.859046	−	0.511898i	$-0.828943\pi$
$293$	5.93882e6	−	1.02863e7i	0.0137932	−	0.0238904i	0.872840	+	0.488007i	$0.162276\pi$
$294$		0			0
$295$	−4.58459e6	−	2.60005e7i	−0.0103974	−	0.0589664i
$296$		0			0
$297$	−2.25143e8	−	3.89959e8i	−0.498668	−	0.863718i
$298$		0			0
$299$	5.32132e8	−	1.93680e8i	1.15125	−	0.419021i
$300$		0			0
$301$	−3.83009e8	−	3.21382e8i	−0.809517	−	0.679265i
$302$		0			0
$303$	−1.77101e8			−0.365740
$304$		0			0
$305$	1.41134e8			0.284827
$306$		0			0
$307$	−4.15449e8	−	3.48603e8i	−0.819471	−	0.687618i	0.133377	−	0.991065i	$-0.457418\pi$
$307$	−4.15449e8	−	3.48603e8i	−0.819471	−	0.687618i	−0.952848	+	0.303447i	$0.901862\pi$
$308$		0			0
$309$	−6.85603e8	+	2.49539e8i	−1.32196	+	0.481154i
$310$		0			0
$311$	3.29375e8	+	5.70494e8i	0.620911	+	1.07545i	0.989316	+	0.145784i	$0.0465704\pi$
$311$	3.29375e8	+	5.70494e8i	0.620911	+	1.07545i	−0.368406	+	0.929665i	$0.620096\pi$
$312$		0			0
$313$	−5.02586e7	−	2.85031e8i	−0.0926415	−	0.525396i	−0.995445	−	0.0953418i	$-0.969606\pi$
$313$	−5.02586e7	−	2.85031e8i	−0.0926415	−	0.525396i	0.902803	−	0.430054i	$-0.141506\pi$
$314$		0			0
$315$	−6.15315e6	+	1.06576e7i	−0.0110920	+	0.0192119i
$316$		0			0
$317$	−6.28311e8	+	5.27216e8i	−1.10782	+	0.929568i	−0.997926	−	0.0643759i	$-0.979494\pi$
$317$	−6.28311e8	+	5.27216e8i	−1.10782	+	0.929568i	−0.109890	+	0.993944i	$0.535050\pi$
$318$		0			0
$319$	5.22911e8	+	1.90324e8i	0.901904	+	0.328266i
$320$		0			0
$321$	4.47183e7	−	2.53610e8i	0.0754601	−	0.427956i
$322$		0			0
$323$	5.72832e8	−	1.47232e8i	0.945841	−	0.243105i
$324$		0			0
$325$	−1.08595e8	+	6.15872e8i	−0.175476	+	0.995173i
$326$		0			0
$327$	2.24355e8	+	8.16586e7i	0.354829	+	0.129147i
$328$		0			0
$329$	−4.64698e8	+	3.89928e8i	−0.719424	+	0.603669i
$330$		0			0
$331$	−2.24442e8	+	3.88745e8i	−0.340178	+	0.589206i	−0.984466	−	0.175578i	$-0.943821\pi$
$331$	−2.24442e8	+	3.88745e8i	−0.340178	+	0.589206i	0.644287	+	0.764783i	$0.277154\pi$
$332$		0			0
$333$	1.11666e7	+	6.33289e7i	0.0165717	+	0.0939826i
$334$		0			0
$335$	−6.04365e7	−	1.04679e8i	−0.0878299	−	0.152126i
$336$		0			0
$337$	−8.33137e8	+	3.03237e8i	−1.18580	+	0.431596i	−0.858247	−	0.513236i	$-0.828447\pi$
$337$	−8.33137e8	+	3.03237e8i	−1.18580	+	0.431596i	−0.327554	+	0.944832i	$0.606224\pi$
$338$		0			0
$339$	6.03132e8	+	5.06088e8i	0.840840	+	0.705549i
$340$		0			0
$341$	−6.31600e8			−0.862585
$342$		0			0
$343$	−7.66491e8			−1.02560
$344$		0			0
$345$	−2.00307e8	−	1.68077e8i	−0.262621	−	0.220365i
$346$		0			0
$347$	−5.00573e8	+	1.82194e8i	−0.643153	+	0.234089i	−0.642946	−	0.765911i	$-0.722288\pi$
$347$	−5.00573e8	+	1.82194e8i	−0.643153	+	0.234089i	−0.000207007		1.00000i	$0.500066\pi$
$348$		0			0
$349$	2.10773e8	+	3.65070e8i	0.265416	+	0.459714i	0.967672	−	0.252210i	$-0.0811575\pi$
$349$	2.10773e8	+	3.65070e8i	0.265416	+	0.459714i	−0.702257	+	0.711924i	$0.747824\pi$
$350$		0			0
$351$	−1.45146e8	−	8.23162e8i	−0.179155	−	1.01604i
$352$		0			0
$353$	−2.94170e8	+	5.09518e8i	−0.355949	+	0.616521i	−0.987280	−	0.158992i	$-0.949176\pi$
$353$	−2.94170e8	+	5.09518e8i	−0.355949	+	0.616521i	0.631331	+	0.775513i	$0.282509\pi$
$354$		0			0
$355$	1.27854e8	−	1.07282e8i	0.151675	−	0.127271i
$356$		0			0
$357$	−5.42115e8	−	1.97314e8i	−0.630598	−	0.229519i
$358$		0			0
$359$	−5.05431e7	+	2.86644e8i	−0.0576542	+	0.326973i	−0.999970	−	0.00775208i	$-0.997532\pi$
$359$	−5.05431e7	+	2.86644e8i	−0.0576542	+	0.326973i	0.942316	+	0.334725i	$0.108644\pi$
$360$		0			0
$361$	−5.88444e8	+	6.72859e8i	−0.658310	+	0.752747i
$362$		0			0
$363$	2.36471e7	−	1.34109e8i	0.0259480	−	0.147159i
$364$		0			0
$365$	7.97007e7	+	2.90087e7i	0.0857900	+	0.0312250i
$366$		0			0
$367$	−3.88686e7	+	3.26146e7i	−0.0410457	+	0.0344414i	−0.663080	−	0.748549i	$-0.730751\pi$
$367$	−3.88686e7	+	3.26146e7i	−0.0410457	+	0.0344414i	0.622034	+	0.782990i	$0.286307\pi$
$368$		0			0
$369$	3.64108e7	−	6.30653e7i	0.0377257	−	0.0653429i
$370$		0			0
$371$	−6.33787e7	−	3.59438e8i	−0.0644369	−	0.365440i
$372$		0			0
$373$	−1.31982e8	−	2.28600e8i	−0.131684	−	0.228084i	0.792642	−	0.609688i	$-0.208705\pi$
$373$	−1.31982e8	−	2.28600e8i	−0.131684	−	0.228084i	−0.924326	+	0.381604i	$0.875372\pi$
$374$		0			0
$375$	5.68126e8	−	2.06781e8i	0.556333	−	0.202489i
$376$		0			0
$377$	7.91300e8	+	6.63979e8i	0.760582	+	0.638204i
$378$		0			0
$379$	−5.51350e7			−0.0520224			−0.0260112	−	0.999662i	$-0.508281\pi$
$379$	−5.51350e7			−0.0520224			−0.0260112	+	0.999662i	$0.508281\pi$
$380$		0			0
$381$	−1.77178e9			−1.64124
$382$		0			0
$383$	4.43218e8	+	3.71904e8i	0.403108	+	0.338248i	0.821694	−	0.569929i	$-0.193029\pi$
$383$	4.43218e8	+	3.71904e8i	0.403108	+	0.338248i	−0.418585	+	0.908178i	$0.637474\pi$
$384$		0			0
$385$	2.13958e8	−	7.78742e7i	0.191080	−	0.0695474i
$386$		0			0
$387$	1.07981e8	+	1.87028e8i	0.0947016	+	0.164028i
$388$		0			0
$389$	2.54394e7	+	1.44274e8i	0.0219121	+	0.124270i	0.993802	−	0.111167i	$-0.0354590\pi$
$389$	2.54394e7	+	1.44274e8i	0.0219121	+	0.124270i	−0.971890	+	0.235437i	$0.924348\pi$
$390$		0			0
$391$	6.39798e8	−	1.10816e9i	0.541283	−	0.937529i
$392$		0			0
$393$	3.21744e8	−	2.69975e8i	0.267384	−	0.224362i
$394$		0			0
$395$	4.25684e8	+	1.54936e8i	0.347534	+	0.126492i
$396$		0			0
$397$	2.25504e8	−	1.27889e9i	0.180878	−	1.02581i	−0.750259	−	0.661144i	$-0.770071\pi$
$397$	2.25504e8	−	1.27889e9i	0.180878	−	1.02581i	0.931137	−	0.364668i	$-0.118818\pi$
$398$		0			0
$399$	8.44445e8	−	2.17044e8i	0.665528	−	0.171058i
$400$		0			0
$401$	1.93776e7	−	1.09896e8i	0.0150071	−	0.0851093i	−0.976384	−	0.216041i	$-0.930686\pi$
$401$	1.93776e7	−	1.09896e8i	0.0150071	−	0.0851093i	0.991391	+	0.130931i	$0.0417967\pi$
$402$		0			0
$403$	−1.10172e9	−	4.00995e8i	−0.838505	−	0.305191i
$404$		0			0
$405$	−3.30598e8	+	2.77405e8i	−0.247291	+	0.207502i
$406$		0			0
$407$	5.94888e8	−	1.03038e9i	0.437376	−	0.757557i
$408$		0			0
$409$	−1.73449e8	−	9.83676e8i	−0.125354	−	0.710920i	−0.981097	−	0.193518i	$-0.938010\pi$
$409$	−1.73449e8	−	9.83676e8i	−0.125354	−	0.710920i	0.855742	−	0.517402i	$-0.173101\pi$
$410$		0			0
$411$	9.03205e8	+	1.56440e9i	0.641712	+	1.11148i
$412$		0			0
$413$	1.78975e8	−	6.51414e7i	0.125016	−	0.0455022i
$414$		0			0
$415$	−1.59474e8	−	1.33814e8i	−0.109527	−	0.0919040i
$416$		0			0
$417$	1.96372e9			1.32618
$418$		0			0
$419$	3.15233e8			0.209354			0.104677	−	0.994506i	$-0.466619\pi$
$419$	3.15233e8			0.209354			0.104677	+	0.994506i	$0.466619\pi$
$420$		0			0
$421$	−1.64644e9	−	1.38153e9i	−1.07537	−	0.902344i	−0.0798439	−	0.996807i	$-0.525442\pi$
$421$	−1.64644e9	−	1.38153e9i	−1.07537	−	0.902344i	−0.995528	+	0.0944629i	$0.969887\pi$
$422$		0			0
$423$	2.46220e8	−	8.96168e7i	0.158173	−	0.0575703i
$424$		0			0
$425$	7.06558e8	+	1.22380e9i	0.446464	+	0.773299i
$426$		0			0
$427$	1.76798e8	+	1.00267e9i	0.109895	+	0.623248i
$428$		0			0
$429$	1.02017e9	−	1.76698e9i	0.623837	−	1.08052i
$430$		0			0
$431$	1.22166e9	−	1.02509e9i	0.734985	−	0.616725i	−0.196501	−	0.980504i	$-0.562958\pi$
$431$	1.22166e9	−	1.02509e9i	0.734985	−	0.616725i	0.931486	+	0.363778i	$0.118513\pi$
$432$		0			0
$433$	3.06689e8	+	1.11626e8i	0.181547	+	0.0660778i	0.431194	−	0.902259i	$-0.358092\pi$
$433$	3.06689e8	+	1.11626e8i	0.181547	+	0.0660778i	−0.249647	+	0.968337i	$0.580315\pi$
$434$		0			0
$435$	8.28258e7	−	4.69728e8i	0.0482451	−	0.273611i
$436$		0			0
$437$	1.48852e8	+	1.92814e9i	0.0853237	+	1.10523i
$438$		0			0
$439$	−1.18228e8	+	6.70504e8i	−0.0666951	+	0.378247i	0.933130	+	0.359539i	$0.117066\pi$
$439$	−1.18228e8	+	6.70504e8i	−0.0666951	+	0.378247i	−0.999825	+	0.0187074i	$0.994045\pi$
$440$		0			0
$441$	1.13843e8	+	4.14355e7i	0.0632080	+	0.0230058i
$442$		0			0
$443$	−1.10225e9	+	9.24901e8i	−0.602377	+	0.505455i	−0.892209	−	0.451623i	$-0.850845\pi$
$443$	−1.10225e9	+	9.24901e8i	−0.602377	+	0.505455i	0.289831	+	0.957078i	$0.406401\pi$
$444$		0			0
$445$	2.38804e8	−	4.13621e8i	0.128464	−	0.222506i
$446$		0			0
$447$	3.88477e7	+	2.20317e8i	0.0205726	+	0.116673i
$448$		0			0
$449$	1.72231e9	+	2.98314e9i	0.897946	+	1.55529i	0.830116	+	0.557591i	$0.188274\pi$
$449$	1.72231e9	+	2.98314e9i	0.897946	+	1.55529i	0.0678305	+	0.997697i	$0.478392\pi$
$450$		0			0
$451$	−1.26608e9	+	4.60814e8i	−0.649893	+	0.236542i
$452$		0			0
$453$	−1.66026e9	−	1.39312e9i	−0.839136	−	0.704119i
$454$		0			0
$455$	4.22656e8			0.210352
$456$		0			0
$457$	3.62985e9			1.77902			0.889512	−	0.456912i	$-0.151045\pi$
$457$	3.62985e9			1.77902			0.889512	+	0.456912i	$0.151045\pi$
$458$		0			0
$459$	−1.44686e9	−	1.21406e9i	−0.698365	−	0.585998i
$460$		0			0
$461$	−6.58587e8	+	2.39706e8i	−0.313083	+	0.113953i	−0.493783	−	0.869585i	$-0.664386\pi$
$461$	−6.58587e8	+	2.39706e8i	−0.313083	+	0.113953i	0.180699	+	0.983538i	$0.442164\pi$
$462$		0			0
$463$	−1.23688e9	−	2.14235e9i	−0.579156	−	1.00313i	−0.995576	−	0.0939554i	$-0.970049\pi$
$463$	−1.23688e9	−	2.14235e9i	−0.579156	−	1.00313i	0.416420	−	0.909172i	$-0.363284\pi$
$464$		0			0
$465$	9.40082e7	+	5.33147e8i	0.0433591	+	0.245902i
$466$		0			0
$467$	−1.37552e9	+	2.38247e9i	−0.624968	+	1.08248i	0.363580	+	0.931563i	$0.381555\pi$
$467$	−1.37552e9	+	2.38247e9i	−0.624968	+	1.08248i	−0.988547	+	0.150912i	$0.951779\pi$
$468$		0			0
$469$	6.67973e8	−	5.60496e8i	0.298988	−	0.250881i
$470$		0			0
$471$	3.06123e9	+	1.11420e9i	1.34997	+	0.491348i
$472$		0			0
$473$	6.93842e8	−	3.93497e9i	0.301472	−	1.70973i
$474$		0			0
$475$	−1.92625e9	−	9.22309e8i	−0.824681	−	0.394865i
$476$		0			0
$477$	−2.73756e7	+	1.55255e8i	−0.0115491	+	0.0654985i
$478$		0			0
$479$	1.46496e9	+	5.33200e8i	0.609046	+	0.221675i	0.628086	−	0.778144i	$-0.283839\pi$
$479$	1.46496e9	+	5.33200e8i	0.609046	+	0.221675i	−0.0190397	+	0.999819i	$0.506061\pi$
$480$		0			0
$481$	1.69186e9	−	1.41964e9i	0.693197	−	0.581661i
$482$		0			0
$483$	9.43165e8	−	1.63361e9i	0.380866	−	0.659680i
$484$		0			0
$485$	9.70334e7	+	5.50304e8i	0.0386211	+	0.219031i
$486$		0			0
$487$	−2.37365e8	−	4.11128e8i	−0.0931247	−	0.161297i	0.815700	−	0.578476i	$-0.196352\pi$
$487$	−2.37365e8	−	4.11128e8i	−0.0931247	−	0.161297i	−0.908824	+	0.417179i	$0.863019\pi$
$488$		0			0
$489$	−1.71911e9	+	6.25704e8i	−0.664848	+	0.241985i
$490$		0			0
$491$	−2.49719e8	−	2.09539e8i	−0.0952063	−	0.0798876i	0.593942	−	0.804508i	$-0.297571\pi$
$491$	−2.49719e8	−	2.09539e8i	−0.0952063	−	0.0798876i	−0.689148	+	0.724620i	$0.742015\pi$
$492$		0			0
$493$	2.33414e9			0.877328
$494$		0			0
$495$	−9.83474e7			−0.0364456
$496$		0			0
$497$	9.22337e8	+	7.73933e8i	0.337010	+	0.282785i
$498$		0			0
$499$	−5.10582e9	+	1.85837e9i	−1.83956	+	0.669544i	−0.849741	+	0.527200i	$0.823242\pi$
$499$	−5.10582e9	+	1.85837e9i	−1.83956	+	0.669544i	−0.989817	+	0.142344i	$0.954536\pi$
$500$		0			0
$501$	−1.05724e9	−	1.83119e9i	−0.375613	−	0.650581i
$502$		0			0
$503$	−5.93800e7	−	3.36761e8i	−0.0208043	−	0.117987i	0.972637	−	0.232330i	$-0.0746349\pi$
$503$	−5.93800e7	−	3.36761e8i	−0.0208043	−	0.117987i	−0.993441	+	0.114343i	$0.963524\pi$
$504$		0			0
$505$	1.46593e8	−	2.53906e8i	0.0506515	−	0.0877310i
$506$		0			0
$507$	5.26036e8	−	4.41397e8i	0.179262	−	0.150419i
$508$		0			0
$509$	4.04322e8	+	1.47161e8i	0.135899	+	0.0494631i	0.409074	−	0.912501i	$-0.365852\pi$
$509$	4.04322e8	+	1.47161e8i	0.135899	+	0.0494631i	−0.273175	+	0.961964i	$0.588074\pi$
$510$		0			0
$511$	−1.06248e8	+	6.02564e8i	−0.0352248	+	0.199770i
$512$		0			0
$513$	2.84095e9	+	2.77834e8i	0.929079	+	0.0908603i
$514$		0			0
$515$	2.09738e8	−	1.18948e9i	0.0676632	−	0.383737i
$516$		0			0
$517$	−4.55552e9	−	1.65807e9i	−1.44984	−	0.527700i
$518$		0			0
$519$	−4.84694e9	+	4.06707e9i	−1.52189	+	1.27701i
$520$		0			0
$521$	2.47132e9	−	4.28044e9i	0.765590	−	1.32604i	−0.174344	−	0.984685i	$-0.555781\pi$
$521$	2.47132e9	−	4.28044e9i	0.765590	−	1.32604i	0.939934	−	0.341356i	$-0.110886\pi$
$522$		0			0
$523$	4.39821e8	+	2.49435e9i	0.134437	+	0.762432i	0.975250	+	0.221106i	$0.0709666\pi$
$523$	4.39821e8	+	2.49435e9i	0.134437	+	0.762432i	−0.840813	+	0.541326i	$0.817922\pi$
$524$		0			0
$525$	1.04158e9	+	1.80407e9i	0.314149	+	0.544121i
$526$		0			0
$527$	−2.48950e9	+	9.06105e8i	−0.740927	+	0.269675i
$528$		0			0
$529$	5.96831e8	+	5.00800e8i	0.175290	+	0.147085i
$530$		0			0
$531$	−8.22672e7			−0.0238449
$532$		0			0
$533$	−2.50103e9			−0.715442
$534$		0			0
$535$	3.26580e8	+	2.74033e8i	0.0922043	+	0.0773686i
$536$		0			0
$537$	−5.69832e9	+	2.07402e9i	−1.58795	+	0.577967i
$538$		0			0
$539$	−1.12074e9	−	1.94118e9i	−0.308280	−	0.533956i
$540$		0			0
$541$	1.05286e9	+	5.97104e9i	0.285877	+	1.62129i	0.702138	+	0.712041i	$0.252229\pi$
$541$	1.05286e9	+	5.97104e9i	0.285877	+	1.62129i	−0.416261	+	0.909245i	$0.636660\pi$
$542$		0			0
$543$	−8.29207e8	+	1.43623e9i	−0.222261	+	0.384968i
$544$		0			0
$545$	−3.02778e8	+	2.54061e8i	−0.0801193	+	0.0672281i
$546$		0			0
$547$	−1.05604e8	−	3.84369e7i	−0.0275884	−	0.0100414i	0.328189	−	0.944612i	$-0.393562\pi$
$547$	−1.05604e8	−	3.84369e7i	−0.0275884	−	0.0100414i	−0.355777	+	0.934571i	$0.615784\pi$
$548$		0			0
$549$	7.63657e7	−	4.33091e8i	0.0196968	−	0.111706i
$550$		0			0
$551$	−2.91019e9	+	1.99373e9i	−0.741125	+	0.507734i
$552$		0			0
$553$	−5.67475e8	+	3.21831e9i	−0.142695	+	0.809264i
$554$		0			0
$555$	−9.58306e8	−	3.48795e8i	−0.237946	−	0.0866054i
$556$		0			0
$557$	−4.34151e9	+	3.64296e9i	−1.06450	+	0.893225i	−0.994543	−	0.104324i	$-0.966732\pi$
$557$	−4.34151e9	+	3.64296e9i	−1.06450	+	0.893225i	−0.0699613	+	0.997550i	$0.522288\pi$
$558$		0			0
$559$	3.70856e9	−	6.42341e9i	0.897974	−	1.55534i
$560$		0			0
$561$	−8.00592e8	−	4.54038e9i	−0.191444	−	1.08573i
$562$		0			0
$563$	3.96762e9	+	6.87212e9i	0.937024	+	1.62297i	0.770984	+	0.636855i	$0.219765\pi$
$563$	3.96762e9	+	6.87212e9i	0.937024	+	1.62297i	0.166040	+	0.986119i	$0.446902\pi$
$564$		0			0
$565$	−1.22480e9	+	4.45790e8i	−0.285690	+	0.103983i
$566$		0			0
$567$	−2.38493e9	−	2.00120e9i	−0.549459	−	0.461051i
$568$		0			0
$569$	5.56740e9			1.26695			0.633475	−	0.773764i	$-0.281628\pi$
$569$	5.56740e9			1.26695			0.633475	+	0.773764i	$0.281628\pi$
$570$		0			0
$571$	−4.34225e9			−0.976087			−0.488043	−	0.872819i	$-0.662289\pi$
$571$	−4.34225e9			−0.976087			−0.488043	+	0.872819i	$0.662289\pi$
$572$		0			0
$573$	−2.66339e9	−	2.23485e9i	−0.591417	−	0.496258i
$574$		0			0
$575$	−4.34186e9	+	1.58031e9i	−0.952441	+	0.346660i
$576$		0			0
$577$	4.44772e9	+	7.70368e9i	0.963878	+	1.66949i	0.712599	+	0.701572i	$0.247518\pi$
$577$	4.44772e9	+	7.70368e9i	0.963878	+	1.66949i	0.251279	+	0.967915i	$0.419149\pi$
$578$		0			0
$579$	−5.10332e8	−	2.89424e9i	−0.109264	−	0.619668i
$580$		0			0
$581$	7.50898e8	−	1.30059e9i	0.158842	−	0.275122i
$582$		0			0
$583$	2.23441e9	−	1.87489e9i	0.467006	−	0.391864i
$584$		0			0
$585$	−1.71551e8	−	6.24395e7i	−0.0354281	−	0.0128948i
$586$		0			0
$587$	4.30367e8	−	2.44073e9i	0.0878224	−	0.498065i	−0.908889	−	0.417037i	$-0.863068\pi$
$587$	4.30367e8	−	2.44073e9i	0.0878224	−	0.498065i	0.996712	−	0.0810282i	$-0.0258204\pi$
$588$		0			0
$589$	2.32994e9	−	3.25617e9i	0.469831	−	0.656603i
$590$		0			0
$591$	−1.18150e9	+	6.70060e9i	−0.235438	+	1.33523i
$592$		0			0
$593$	3.10733e9	+	1.13098e9i	0.611923	+	0.222722i	0.629344	−	0.777127i	$-0.283324\pi$
$593$	3.10733e9	+	1.13098e9i	0.611923	+	0.222722i	−0.0174216	+	0.999848i	$0.505546\pi$
$594$		0			0
$595$	7.31611e8	−	6.13894e8i	0.142387	−	0.119477i
$596$		0			0
$597$	6.43742e8	−	1.11499e9i	0.123823	−	0.214468i
$598$		0			0
$599$	−1.39058e9	−	7.88636e9i	−0.264363	−	1.49928i	−0.770842	−	0.637027i	$-0.780164\pi$
$599$	−1.39058e9	−	7.88636e9i	−0.264363	−	1.49928i	0.506478	−	0.862253i	$-0.330947\pi$
$600$		0			0
$601$	1.68903e9	+	2.92548e9i	0.317377	+	0.549714i	0.979940	−	0.199293i	$-0.0638645\pi$
$601$	1.68903e9	+	2.92548e9i	0.317377	+	0.549714i	−0.662563	+	0.749007i	$0.730531\pi$
$602$		0			0
$603$	−3.53925e8	+	1.28818e8i	−0.0657357	+	0.0239258i
$604$		0			0
$605$	1.72696e8	+	1.44909e8i	0.0317058	+	0.0266043i
$606$		0			0
$607$	4.38972e9			0.796666			0.398333	−	0.917241i	$-0.369589\pi$
$607$	4.38972e9			0.796666			0.398333	+	0.917241i	$0.369589\pi$
$608$		0			0
$609$	3.44089e9			0.617320
$610$		0			0
$611$	−6.89368e9	−	5.78449e9i	−1.22266	−	1.02594i
$612$		0			0
$613$	−5.59298e9	+	2.03568e9i	−0.980689	+	0.356942i	−0.782108	−	0.623143i	$-0.785856\pi$
$613$	−5.59298e9	+	2.03568e9i	−0.980689	+	0.356942i	−0.198581	+	0.980084i	$0.563633\pi$
$614$		0			0
$615$	5.77428e8	+	1.00013e9i	0.100100	+	0.173379i
$616$		0			0
$617$	8.20121e8	+	4.65114e9i	0.140566	+	0.797188i	0.970821	+	0.239805i	$0.0770835\pi$
$617$	8.20121e8	+	4.65114e9i	0.140566	+	0.797188i	−0.830255	+	0.557383i	$0.811805\pi$
$618$		0			0
$619$	5.38262e9	−	9.32298e9i	0.912172	−	1.57993i	0.101183	−	0.994868i	$-0.467737\pi$
$619$	5.38262e9	−	9.32298e9i	0.912172	−	1.57993i	0.810990	−	0.585061i	$-0.198929\pi$
$620$		0			0
$621$	4.73085e9	−	3.96965e9i	0.792717	−	0.665169i
$622$		0			0
$623$	3.23768e9	+	1.17842e9i	0.536445	+	0.195250i
$624$		0			0
$625$	7.95276e8	−	4.51024e9i	0.130298	−	0.738957i
$626$		0			0
$627$	4.87640e9	+	4.97710e9i	0.790065	+	0.806381i
$628$		0			0
$629$	8.66602e8	−	4.91474e9i	0.138849	−	0.787451i
$630$		0			0
$631$	2.16508e9	+	7.88026e8i	0.343062	+	0.124864i	0.507805	−	0.861472i	$-0.330457\pi$
$631$	2.16508e9	+	7.88026e8i	0.343062	+	0.124864i	−0.164743	+	0.986337i	$0.552679\pi$
$632$		0			0
$633$	2.49653e9	−	2.09484e9i	0.391223	−	0.328275i
$634$		0			0
$635$	1.46656e9	−	2.54016e9i	0.227297	−	0.393689i
$636$		0			0
$637$	−7.22521e8	−	4.09762e9i	−0.110755	−	0.628122i
$638$		0			0
$639$	−2.60032e8	−	4.50389e8i	−0.0394252	−	0.0682865i
$640$		0			0
$641$	3.56555e9	−	1.29775e9i	0.534716	−	0.194621i	−0.0605270	−	0.998167i	$-0.519278\pi$
$641$	3.56555e9	−	1.29775e9i	0.534716	−	0.194621i	0.595243	+	0.803546i	$0.297056\pi$
$642$		0			0
$643$	3.75508e9	+	3.15089e9i	0.557033	+	0.467406i	0.877314	−	0.479916i	$-0.159333\pi$
$643$	3.75508e9	+	3.15089e9i	0.557033	+	0.467406i	−0.320281	+	0.947322i	$0.603777\pi$
$644$		0			0
$645$	−3.42487e9			−0.502556
$646$		0			0
$647$	−1.68558e9			−0.244673			−0.122336	−	0.992489i	$-0.539039\pi$
$647$	−1.68558e9			−0.244673			−0.122336	+	0.992489i	$0.539039\pi$
$648$		0			0
$649$	1.16599e9	+	9.78382e8i	0.167432	+	0.140492i
$650$		0			0
$651$	−3.66992e9	+	1.33574e9i	−0.521343	+	0.189753i
$652$		0			0
$653$	4.10641e8	+	7.11251e8i	0.0577120	+	0.0999601i	0.893438	−	0.449187i	$-0.148286\pi$
$653$	4.10641e8	+	7.11251e8i	0.0577120	+	0.0999601i	−0.835726	+	0.549147i	$0.814953\pi$
$654$		0			0
$655$	1.20739e8	+	6.84743e8i	0.0167881	+	0.0952102i
$656$		0			0
$657$	1.32143e8	−	2.28878e8i	0.0181788	−	0.0314865i
$658$		0			0
$659$	7.86807e9	−	6.60209e9i	1.07095	−	0.898633i	0.0758115	−	0.997122i	$-0.475845\pi$
$659$	7.86807e9	−	6.60209e9i	1.07095	−	0.898633i	0.995138	+	0.0984887i	$0.0314008\pi$
$660$		0			0
$661$	5.07424e9	+	1.84687e9i	0.683386	+	0.248732i	0.660301	−	0.751001i	$-0.270429\pi$
$661$	5.07424e9	+	1.84687e9i	0.683386	+	0.248732i	0.0230853	+	0.999734i	$0.492651\pi$
$662$		0			0
$663$	1.48613e9	−	8.42826e9i	0.198043	−	1.12316i
$664$		0			0
$665$	−3.87805e8	+	1.39032e9i	−0.0511373	+	0.183332i
$666$		0			0
$667$	−1.32528e9	+	7.51605e9i	−0.172929	+	0.980729i
$668$		0			0
$669$	−1.02646e10	−	3.73599e9i	−1.32541	−	0.482408i
$670$		0			0
$671$	−6.23299e9	+	5.23010e9i	−0.796466	+	0.668314i
$672$		0			0
$673$	4.48648e9	−	7.77081e9i	0.567352	−	0.982683i	−0.429474	−	0.903079i	$-0.641301\pi$
$673$	4.48648e9	−	7.77081e9i	0.567352	−	0.982683i	0.996827	−	0.0796037i	$-0.0253655\pi$
$674$		0			0
$675$	1.18430e9	+	6.71648e9i	0.148217	+	0.840579i
$676$		0			0
$677$	1.69218e9	+	2.93094e9i	0.209597	+	0.363033i	0.951588	−	0.307377i	$-0.0994513\pi$
$677$	1.69218e9	+	2.93094e9i	0.209597	+	0.363033i	−0.741990	+	0.670411i	$0.766118\pi$
$678$		0			0
$679$	−3.78802e9	+	1.37873e9i	−0.464374	+	0.169018i
$680$		0			0
$681$	9.23513e9	+	7.74919e9i	1.12054	+	0.940246i
$682$		0			0
$683$	−4.98985e9			−0.599259			−0.299630	−	0.954056i	$-0.596863\pi$
$683$	−4.98985e9			−0.599259			−0.299630	+	0.954056i	$0.596863\pi$
$684$		0			0
$685$	−2.99045e9			−0.355484
$686$		0			0
$687$	−2.81010e9	−	2.35795e9i	−0.330653	−	0.277451i
$688$		0			0
$689$	5.08791e9	−	1.85185e9i	0.592614	−	0.215694i
$690$		0			0
$691$	5.31810e9	+	9.21121e9i	0.613173	+	1.06205i	0.990702	+	0.136049i	$0.0434405\pi$
$691$	5.31810e9	+	9.21121e9i	0.613173	+	1.06205i	−0.377529	+	0.925998i	$0.623226\pi$
$692$		0			0
$693$	−1.23199e8	−	6.98699e8i	−0.0140619	−	0.0797487i
$694$		0			0
$695$	−1.62543e9	+	2.81534e9i	−0.183663	+	0.318114i
$696$		0			0
$697$	−4.32925e9	+	3.63267e9i	−0.484282	+	0.406360i
$698$		0			0
$699$	1.69548e10	+	6.17103e9i	1.87768	+	0.683420i
$700$		0			0
$701$	2.34109e9	−	1.32770e10i	0.256687	−	1.45575i	−0.535017	−	0.844841i	$-0.679695\pi$
$701$	2.34109e9	−	1.32770e10i	0.256687	−	1.45575i	0.791704	−	0.610905i	$-0.209194\pi$
$702$		0			0
$703$	3.11751e9	+	6.86791e9i	0.338426	+	0.745557i
$704$		0			0
$705$	−7.21566e8	+	4.09220e9i	−0.0775557	+	0.439840i
$706$		0			0
$707$	1.98749e9	+	7.23385e8i	0.211512	+	0.0769842i
$708$		0			0
$709$	−8.97293e9	+	7.52919e9i	−0.945524	+	0.793389i	−0.978538	−	0.206066i	$-0.933934\pi$
$709$	−8.97293e9	+	7.52919e9i	−0.945524	+	0.793389i	0.0330139	+	0.999455i	$0.489489\pi$
$710$		0			0
$711$	7.05778e8	−	1.22244e9i	0.0736418	−	0.127551i
$712$		0			0
$713$	−1.50421e9	−	8.53080e9i	−0.155416	−	0.881407i
$714$		0			0
$715$	1.68885e9	+	2.92518e9i	0.172791	+	0.299283i
$716$		0			0
$717$	−1.36023e10	+	4.95081e9i	−1.37814	+	0.501602i
$718$		0			0
$719$	−1.39164e10	−	1.16772e10i	−1.39629	−	1.17163i	−0.962718	−	0.270505i	$-0.912809\pi$
$719$	−1.39164e10	−	1.16772e10i	−1.39629	−	1.17163i	−0.433570	−	0.901120i	$-0.642746\pi$
$720$		0			0
$721$	8.71331e9			0.865784
$722$		0			0
$723$	−6.00275e9			−0.590699
$724$		0			0
$725$	−6.45650e9	−	5.41765e9i	−0.629237	−	0.527993i
$726$		0			0
$727$	−1.35880e10	+	4.94563e9i	−1.31155	+	0.477366i	−0.900742	−	0.434355i	$-0.856976\pi$
$727$	−1.35880e10	+	4.94563e9i	−1.31155	+	0.477366i	−0.410810	+	0.911721i	$0.634754\pi$
$728$		0			0
$729$	−4.48675e9	−	7.77127e9i	−0.428929	−	0.742926i
$730$		0			0
$731$	−2.91035e9	−	1.65054e10i	−0.275571	−	1.56284i
$732$		0			0
$733$	1.62814e8	−	2.82003e8i	0.0152696	−	0.0264478i	−0.858290	−	0.513166i	$-0.828473\pi$
$733$	1.62814e8	−	2.82003e8i	0.0152696	−	0.0264478i	0.873559	+	0.486718i	$0.161806\pi$
$734$		0			0
$735$	−1.47178e9	+	1.23497e9i	−0.136722	+	0.114723i
$736$		0			0
$737$	6.54826e9	+	2.38337e9i	0.602545	+	0.219309i
$738$		0			0
$739$	3.55035e9	−	2.01350e10i	0.323605	−	1.83526i	−0.195697	−	0.980664i	$-0.562697\pi$
$739$	3.55035e9	−	2.01350e10i	0.323605	−	1.83526i	0.519302	−	0.854591i	$-0.326192\pi$
$740$		0			0
$741$	5.34619e9	+	1.17777e10i	0.482704	+	1.06340i
$742$		0			0
$743$	−6.68123e8	+	3.78912e9i	−0.0597580	+	0.338904i	−0.999999	−	0.00160616i	$-0.999489\pi$
$743$	−6.68123e8	+	3.78912e9i	−0.0597580	+	0.338904i	0.940241	+	0.340510i	$0.110600\pi$
$744$		0			0
$745$	−3.48018e8	−	1.26668e8i	−0.0308358	−	0.0112233i
$746$		0			0
$747$	−4.96920e8	+	4.16965e8i	−0.0436178	+	0.0365997i
$748$		0			0
$749$	−1.53773e9	+	2.66343e9i	−0.133719	+	0.231609i
$750$		0			0
$751$	3.39391e9	+	1.92478e10i	0.292389	+	1.65822i	0.677629	+	0.735404i	$0.263007\pi$
$751$	3.39391e9	+	1.92478e10i	0.292389	+	1.65822i	−0.385240	+	0.922816i	$0.625881\pi$
$752$		0			0
$753$	6.89147e9	+	1.19364e10i	0.588206	+	1.01880i
$754$		0			0
$755$	3.37154e9	−	1.22714e9i	0.285111	−	0.103772i
$756$		0			0
$757$	−1.05737e10	−	8.87239e9i	−0.885914	−	0.743370i	0.0814721	−	0.996676i	$-0.474038\pi$
$757$	−1.05737e10	−	8.87239e9i	−0.885914	−	0.743370i	−0.967386	+	0.253305i	$0.918482\pi$
$758$		0			0
$759$	1.50749e10			1.25143
$760$		0			0
$761$	−2.05335e10			−1.68895			−0.844476	−	0.535593i	$-0.820088\pi$
$761$	−2.05335e10			−1.68895			−0.844476	+	0.535593i	$0.820088\pi$
$762$		0			0
$763$	−2.18424e9	−	1.83280e9i	−0.178018	−	0.149375i
$764$		0			0
$765$	−3.87644e8	+	1.41091e8i	−0.0313053	+	0.0113942i
$766$		0			0
$767$	1.41272e9	+	2.44690e9i	0.113050	+	0.195809i
$768$		0			0
$769$	−1.87054e9	−	1.06084e10i	−0.148329	−	0.841215i	−0.964634	−	0.263594i	$-0.915092\pi$
$769$	−1.87054e9	−	1.06084e10i	−0.148329	−	0.841215i	0.816305	−	0.577621i	$-0.196019\pi$
$770$		0			0
$771$	2.95799e8	−	5.12338e8i	0.0232437	−	0.0402593i
$772$		0			0
$773$	−1.87411e10	+	1.57256e10i	−1.45937	+	1.22456i	−0.534006	+	0.845480i	$0.679314\pi$
$773$	−1.87411e10	+	1.57256e10i	−1.45937	+	1.22456i	−0.925365	+	0.379078i	$0.876241\pi$
$774$		0			0
$775$	8.98938e9	+	3.27186e9i	0.693703	+	0.252487i
$776$		0			0
$777$	1.27751e9	−	7.24512e9i	0.0976992	−	0.554079i
$778$		0			0
$779$	2.29481e9	−	8.22708e9i	0.173926	−	0.623541i
$780$		0			0
$781$	−1.67087e9	+	9.47595e9i	−0.125506	+	0.711777i
$782$		0			0
$783$	1.05858e10	+	3.85292e9i	0.788058	+	0.286830i
$784$		0			0
$785$	−4.13128e9	+	3.46656e9i	−0.304818	+	0.255773i
$786$		0			0
$787$	−2.88132e9	+	4.99060e9i	−0.210708	+	0.364956i	−0.951936	−	0.306296i	$-0.900910\pi$
$787$	−2.88132e9	+	4.99060e9i	−0.210708	+	0.364956i	0.741229	+	0.671253i	$0.234243\pi$
$788$		0			0
$789$	−2.68323e9	−	1.52173e10i	−0.194486	−	1.10298i
$790$		0			0
$791$	−4.70137e9	−	8.14302e9i	−0.337759	−	0.585016i
$792$		0			0
$793$	−1.41930e10	+	5.16582e9i	−1.01069	+	0.367860i
$794$		0			0
$795$	−1.91521e9	−	1.60705e9i	−0.135186	−	0.113434i
$796$		0			0
$797$	−3.70393e9			−0.259154			−0.129577	−	0.991569i	$-0.541362\pi$
$797$	−3.70393e9			−0.259154			−0.129577	+	0.991569i	$0.541362\pi$
$798$		0			0
$799$	−2.03346e10			−1.41034
$800$		0			0
$801$	−1.14005e9	−	9.56613e8i	−0.0783807	−	0.0657692i
$802$		0			0
$803$	−4.59487e9	+	1.67240e9i	−0.313162	+	0.113982i
$804$		0			0
$805$	1.56138e9	+	2.70439e9i	0.105493	+	0.182719i
$806$		0			0
$807$	4.98113e9	+	2.82494e10i	0.333634	+	1.89213i
$808$		0			0
$809$	−2.12042e9	+	3.67268e9i	−0.140800	+	0.243873i	−0.927798	−	0.373083i	$-0.878301\pi$
$809$	−2.12042e9	+	3.67268e9i	−0.140800	+	0.243873i	0.786998	+	0.616955i	$0.211634\pi$
$810$		0			0
$811$	−2.42973e9	+	2.03878e9i	−0.159950	+	0.134214i	−0.719250	−	0.694751i	$-0.755514\pi$
$811$	−2.42973e9	+	2.03878e9i	−0.159950	+	0.134214i	0.559300	+	0.828965i	$0.311070\pi$
$812$		0			0
$813$	1.99022e10	+	7.24382e9i	1.29893	+	0.472771i
$814$		0			0
$815$	5.25906e8	−	2.98256e9i	0.0340296	−	0.192991i
$816$		0			0
$817$	1.77269e10	+	1.80930e10i	1.13725	+	1.16073i
$818$		0			0
$819$	2.28694e8	−	1.29699e9i	0.0145466	−	0.0824976i
$820$		0			0
$821$	−1.28459e10	−	4.67553e9i	−0.810147	−	0.294869i	−0.0964622	−	0.995337i	$-0.530753\pi$
$821$	−1.28459e10	−	4.67553e9i	−0.810147	−	0.294869i	−0.713684	+	0.700467i	$0.752975\pi$
$822$		0			0
$823$	1.76092e10	−	1.47759e10i	1.10113	−	0.923961i	0.103633	−	0.994616i	$-0.466953\pi$
$823$	1.76092e10	−	1.47759e10i	1.10113	−	0.923961i	0.997501	+	0.0706551i	$0.0225090\pi$
$824$		0			0
$825$	−8.32393e9	+	1.44175e10i	−0.516107	+	0.893923i
$826$		0			0
$827$	−1.84008e8	−	1.04356e9i	−0.0113127	−	0.0641578i	0.978629	−	0.205635i	$-0.0659259\pi$
$827$	−1.84008e8	−	1.04356e9i	−0.0113127	−	0.0641578i	−0.989942	+	0.141477i	$0.954815\pi$
$828$		0			0
$829$	−7.49913e9	−	1.29889e10i	−0.457162	−	0.791828i	0.541648	−	0.840606i	$-0.317801\pi$
$829$	−7.49913e9	−	1.29889e10i	−0.457162	−	0.791828i	−0.998810	+	0.0487777i	$0.984467\pi$
$830$		0			0
$831$	1.33104e10	−	4.84460e9i	0.804615	−	0.292856i
$832$		0			0
$833$	−7.20234e9	−	6.04348e9i	−0.431734	−	0.362268i
$834$		0			0
$835$	3.50045e9			0.208075
$836$		0			0
$837$	−1.27861e10			−0.753702
$838$		0			0
$839$	−2.10779e10	−	1.76864e10i	−1.23214	−	1.03389i	−0.998097	−	0.0616602i	$-0.980360\pi$
$839$	−2.10779e10	−	1.76864e10i	−1.23214	−	1.03389i	−0.234041	−	0.972227i	$-0.575195\pi$
$840$		0			0
$841$	3.12749e9	−	1.13831e9i	0.181305	−	0.0659896i
$842$		0			0
$843$	1.48930e10	+	2.57955e10i	0.856222	+	1.48302i
$844$		0			0
$845$	1.97402e8	+	1.11952e9i	0.0112552	+	0.0638315i
$846$		0			0
$847$	−8.13155e8	+	1.40843e9i	−0.0459813	+	0.0796420i
$848$		0			0
$849$	2.10677e10	−	1.76779e10i	1.18152	−	0.991412i
$850$		0			0
$851$	1.53337e10	+	5.58101e9i	0.852891	+	0.310427i
$852$		0			0
$853$	3.26395e9	−	1.85108e10i	0.180062	−	1.02118i	−0.752076	−	0.659076i	$-0.770947\pi$
$853$	3.26395e9	−	1.85108e10i	0.180062	−	1.02118i	0.932138	−	0.362104i	$-0.117941\pi$
$854$		0			0
$855$	3.62799e8	−	5.07022e8i	0.0198511	−	0.0277425i
$856$		0			0
$857$	−5.28538e9	+	2.99749e10i	−0.286843	+	1.62676i	0.411786	+	0.911280i	$0.364905\pi$
$857$	−5.28538e9	+	2.99749e10i	−0.286843	+	1.62676i	−0.698629	+	0.715484i	$0.746206\pi$
$858$		0			0
$859$	1.00135e10	+	3.64462e9i	0.539026	+	0.196189i	0.597164	−	0.802119i	$-0.296294\pi$
$859$	1.00135e10	+	3.64462e9i	0.539026	+	0.196189i	−0.0581380	+	0.998309i	$0.518516\pi$
$860$		0			0
$861$	−6.38201e9	+	5.35514e9i	−0.340758	+	0.285930i
$862$		0			0
$863$	1.56382e10	−	2.70862e10i	0.828229	−	1.43453i	−0.0711975	−	0.997462i	$-0.522682\pi$
$863$	1.56382e10	−	2.70862e10i	0.828229	−	1.43453i	0.899426	−	0.437072i	$-0.143985\pi$
$864$		0			0
$865$	−1.81888e9	−	1.03154e10i	−0.0955539	−	0.541913i
$866$		0			0
$867$	4.69264e8	+	8.12789e8i	0.0244540	+	0.0423556i
$868$		0			0
$869$	−2.45413e10	+	8.93231e9i	−1.26861	+	0.461737i
$870$		0			0
$871$	9.90922e9	+	8.31482e9i	0.508131	+	0.426373i
$872$		0			0
$873$	1.74120e9			0.0885723
$874$		0			0
$875$	−7.22029e9			−0.364356
$876$		0			0
$877$	−6.06491e8	−	5.08906e8i	−0.0303617	−	0.0254765i	0.627481	−	0.778632i	$-0.284086\pi$
$877$	−6.06491e8	−	5.08906e8i	−0.0303617	−	0.0254765i	−0.657842	+	0.753156i	$0.728531\pi$
$878$		0			0
$879$	5.51544e8	−	2.00746e8i	0.0273917	−	0.00996977i
$880$		0			0
$881$	−8.02070e8	−	1.38923e9i	−0.0395181	−	0.0684474i	0.845590	−	0.533833i	$-0.179249\pi$
$881$	−8.02070e8	−	1.38923e9i	−0.0395181	−	0.0684474i	−0.885108	+	0.465386i	$0.845916\pi$
$882$		0			0
$883$	−2.77630e9	−	1.57452e10i	−0.135708	−	0.769636i	−0.974364	−	0.224976i	$-0.927770\pi$
$883$	−2.77630e9	−	1.57452e10i	−0.135708	−	0.769636i	0.838657	−	0.544660i	$-0.183341\pi$
$884$		0			0
$885$	6.52326e8	−	1.12986e9i	0.0316347	−	0.0547928i
$886$		0			0
$887$	1.64707e10	−	1.38206e10i	0.792463	−	0.664956i	−0.153890	−	0.988088i	$-0.549180\pi$
$887$	1.64707e10	−	1.38206e10i	0.792463	−	0.664956i	0.946354	+	0.323132i	$0.104736\pi$
$888$		0			0
$889$	1.98835e10	+	7.23700e9i	0.949153	+	0.345463i
$890$		0			0
$891$	4.32044e9	−	2.45024e10i	0.204624	−	1.16048i
$892$		0			0
$893$	2.53532e10	−	1.73691e10i	1.19139	−	0.816200i
$894$		0			0
$895$	1.74322e9	−	9.88629e9i	0.0812777	−	0.460949i
$896$		0			0
$897$	2.62957e10	+	9.57083e9i	1.21650	+	0.442768i
$898$		0			0
$899$	1.21045e10	−	1.01569e10i	0.555632	−	0.466230i
$900$		0			0
$901$	6.11734e9	−	1.05955e10i	0.278629	−	0.482599i
$902$		0			0
$903$	−4.29032e9	−	2.43316e10i	−0.193902	−	1.09967i
$904$		0			0
$905$	−1.37272e9	−	2.37763e9i	−0.0615621	−	0.106629i
$906$		0			0
$907$	−1.96707e9	+	7.15954e8i	−0.0875374	+	0.0318610i	−0.385418	−	0.922742i	$-0.625943\pi$
$907$	−1.96707e9	+	7.15954e8i	−0.0875374	+	0.0318610i	0.297880	+	0.954603i	$0.403720\pi$
$908$		0			0
$909$	−6.99831e8	−	5.87228e8i	−0.0309043	−	0.0259318i
$910$		0			0
$911$	1.74032e10			0.762633			0.381316	−	0.924445i	$-0.375471\pi$
$911$	1.74032e10			0.762633			0.381316	+	0.924445i	$0.375471\pi$
$912$		0			0
$913$	1.20018e10			0.521914
$914$		0			0
$915$	5.34256e9	+	4.48294e9i	0.230556	+	0.193459i
$916$		0			0
$917$	−4.71344e9	+	1.71555e9i	−0.201858	+	0.0734702i
$918$		0			0
$919$	2.17019e10	+	3.75888e10i	0.922345	+	1.59755i	0.795777	+	0.605590i	$0.207063\pi$
$919$	2.17019e10	+	3.75888e10i	0.922345	+	1.59755i	0.126568	+	0.991958i	$0.459604\pi$
$920$		0			0
$921$	−4.65371e9	−	2.63925e10i	−0.196286	−	1.11320i
$922$		0			0
$923$	−8.93072e9	+	1.54685e10i	−0.373835	+	0.647502i
$924$		0			0
$925$	−1.38045e10	+	1.15833e10i	−0.573488	+	0.481214i
$926$		0			0
$927$	−3.53663e9	−	1.28723e9i	−0.145818	−	0.0530734i
$928$		0			0
$929$	5.84109e9	−	3.31265e10i	0.239023	−	1.35556i	−0.594952	−	0.803761i	$-0.702829\pi$
$929$	5.84109e9	−	3.31265e10i	0.239023	−	1.35556i	0.833974	−	0.551803i	$-0.186060\pi$
$930$		0			0
$931$	1.41420e10	+	1.38303e9i	0.574362	+	0.0561704i
$932$		0			0
$933$	−5.65269e9	+	3.20580e10i	−0.227861	+	1.29226i
$934$		0			0
$935$	7.17212e9	+	2.61044e9i	0.286950	+	0.104441i
$936$		0			0
$937$	−3.20916e10	+	2.69280e10i	−1.27439	+	1.06934i	−0.280399	+	0.959884i	$0.590467\pi$
$937$	−3.20916e10	+	2.69280e10i	−1.27439	+	1.06934i	−0.993992	+	0.109457i	$0.965089\pi$
$938$		0			0
$939$	7.15113e9	−	1.23861e10i	0.281868	−	0.488209i
$940$		0			0
$941$	−5.77073e9	−	3.27274e10i	−0.225771	−	1.28041i	−0.861207	−	0.508255i	$-0.830291\pi$
$941$	−5.77073e9	−	3.27274e10i	−0.225771	−	1.28041i	0.635436	−	0.772153i	$-0.280820\pi$
$942$		0			0
$943$	−9.23933e9	−	1.60030e10i	−0.358798	−	0.621456i
$944$		0			0
$945$	4.33136e9	−	1.57649e9i	0.166960	−	0.0607685i
$946$		0			0
$947$	−1.42510e10	−	1.19580e10i	−0.545280	−	0.457545i	0.328059	−	0.944657i	$-0.393606\pi$
$947$	−1.42510e10	−	1.19580e10i	−0.545280	−	0.457545i	−0.873339	+	0.487113i	$0.838050\pi$
$948$		0			0
$949$	−9.07679e9			−0.344747
$950$		0			0
$951$	−4.05308e10			−1.52811
$952$		0			0
$953$	5.57497e9	+	4.67795e9i	0.208649	+	0.175078i	0.741124	−	0.671369i	$-0.234293\pi$
$953$	5.57497e9	+	4.67795e9i	0.208649	+	0.175078i	−0.532474	+	0.846446i	$0.678738\pi$
$954$		0			0
$955$	5.40863e9	−	1.96858e9i	0.200944	−	0.0731377i
$956$		0			0
$957$	1.37492e10	+	2.38143e10i	0.507090	+	0.878305i
$958$		0			0
$959$	−3.74613e9	−	2.12454e10i	−0.137157	−	0.777856i
$960$		0			0
$961$	4.78900e9	−	8.29478e9i	0.174065	−	0.301490i
$962$		0			0
$963$	1.01762e9	−	8.53886e8i	0.0367193	−	0.0308111i
$964$		0			0
$965$	4.57182e9	+	1.66401e9i	0.163773	+	0.0596087i
$966$		0			0
$967$	−7.77643e9	+	4.41023e10i	−0.276559	+	1.56844i	0.457407	+	0.889257i	$0.348778\pi$
$967$	−7.77643e9	+	4.41023e10i	−0.276559	+	1.56844i	−0.733966	+	0.679186i	$0.762333\pi$
$968$		0			0
$969$	2.63610e10	+	1.26219e10i	0.930739	+	0.445647i
$970$		0			0
$971$	−8.72522e9	+	4.94832e10i	−0.305851	+	1.73456i	0.313623	+	0.949548i	$0.398457\pi$
$971$	−8.72522e9	+	4.94832e10i	−0.305851	+	1.73456i	−0.619474	+	0.785017i	$0.712654\pi$
$972$		0			0
$973$	−2.20374e10	−	8.02097e9i	−0.766948	−	0.279146i
$974$		0			0
$975$	−2.36732e10	+	1.98642e10i	−0.817977	+	0.686364i
$976$		0			0
$977$	−6.26594e9	+	1.08529e10i	−0.214959	+	0.372319i	−0.953260	−	0.302152i	$-0.902295\pi$
$977$	−6.26594e9	+	1.08529e10i	−0.214959	+	0.372319i	0.738301	+	0.674471i	$0.235628\pi$
$978$		0			0
$979$	4.78138e9	+	2.71166e10i	0.162860	+	0.923624i
$980$		0			0
$981$	6.15797e8	+	1.06659e9i	0.0208255	+	0.0360709i
$982$		0			0
$983$	−2.15034e10	+	7.82662e9i	−0.722056	+	0.262807i	−0.676798	−	0.736169i	$-0.736633\pi$
$983$	−2.15034e10	+	7.82662e9i	−0.722056	+	0.262807i	−0.0452576	+	0.998975i	$0.514411\pi$
$984$		0			0
$985$	−8.62852e9	−	7.24019e9i	−0.287680	−	0.241392i
$986$		0			0
$987$	−2.99765e10			−0.992365
$988$		0			0
$989$	5.48007e10			1.80135
$990$		0			0
$991$	−2.98521e9	−	2.50489e9i	−0.0974356	−	0.0817582i	0.592769	−	0.805373i	$-0.298035\pi$
$991$	−2.98521e9	−	2.50489e9i	−0.0974356	−	0.0817582i	−0.690204	+	0.723615i	$0.742479\pi$
$992$		0			0
$993$	−2.08442e10	+	7.58666e9i	−0.675558	+	0.245883i
$994$		0			0
$995$	1.06569e9	+	1.84583e9i	0.0342966	+	0.0594035i
$996$		0			0
$997$	3.24020e9	+	1.83761e10i	0.103547	+	0.587246i	0.991791	+	0.127873i	$0.0408149\pi$
$997$	3.24020e9	+	1.83761e10i	0.103547	+	0.587246i	−0.888243	+	0.459373i	$0.848074\pi$
$998$		0			0
$999$	1.20429e10	−	2.08589e10i	0.382166	−	0.661931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.17.9	yes	72
19.9	even	9	inner	76.8.i.a.9.9	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.9.9	✓	72	19.9	even	9	inner
76.8.i.a.17.9	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)

\(f(q)\)	\(=\)	\(q+(37.8546 + 31.7638i) q^{3} +(-76.8725 + 27.9793i) q^{5} +(-295.074 - 511.083i) q^{7} +(44.2641 + 251.034i) q^{9} +O(q^{10})\)	\(q+(37.8546 + 31.7638i) q^{3} +(-76.8725 + 27.9793i) q^{5} +(-295.074 - 511.083i) q^{7} +(44.2641 + 251.034i) q^{9} +(2358.12 - 4084.39i) q^{11} +(6706.49 - 5627.41i) q^{13} +(-3798.70 - 1382.61i) q^{15} +(3435.19 - 19481.9i) q^{17} +(12357.7 + 27224.2i) q^{19} +(5064.02 - 28719.5i) q^{21} +(60782.4 + 22123.0i) q^{23} +(-54720.7 + 45916.1i) q^{25} +(47737.8 - 82684.3i) q^{27} +(20488.8 + 116198. i) q^{29} +(-66960.1 - 115978. i) q^{31} +(219001. - 79709.9i) q^{33} +(36982.8 + 31032.2i) q^{35} +252272. q^{37} +432619. q^{39} +(-218843. - 183631. i) q^{41} +(796122. - 289765. i) q^{43} +(-10426.5 - 18059.2i) q^{45} +(-178495. - 1.01230e6i) q^{47} +(237634. - 411595. i) q^{49} +(748857. - 628366. i) q^{51} +(581163. + 211526. i) q^{53} +(-66996.4 + 379955. i) q^{55} +(-396947. + 1.42309e6i) q^{57} +(-56042.2 + 317831. i) q^{59} +(-1.62118e6 - 590062. i) q^{61} +(115238. - 96696.3i) q^{63} +(-358093. + 620236. i) q^{65} +(256575. + 1.45511e6i) q^{67} +(1.59818e6 + 2.76814e6i) q^{69} +(-1.91717e6 + 697793. i) q^{71} +(-794228. - 666436. i) q^{73} -3.52990e6 q^{75} -2.78328e6 q^{77} +(-4.24199e6 - 3.55946e6i) q^{79} +(4.95732e6 - 1.80432e6i) q^{81} +(1.27239e6 + 2.20385e6i) q^{83} +(281019. + 1.59374e6i) q^{85} +(-2.91528e6 + 5.04941e6i) q^{87} +(-4.47240e6 + 3.75279e6i) q^{89} +(-4.85498e6 - 1.76707e6i) q^{91} +(1.14916e6 - 6.51722e6i) q^{93} +(-1.71168e6 - 1.74703e6i) q^{95} +(1.18614e6 - 6.72694e6i) q^{97} +(1.12970e6 + 411178. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 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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