LMFDB - Embedded newform 76.8.i.a.73.12

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			73.12
Character	$\chi$	$=$	76.73
Dual form			76.8.i.a.25.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(84.9007 - 30.9013i) q^{3} +(-77.9653 + 442.163i) q^{5} +(-193.184 - 334.604i) q^{7} +(4577.90 - 3841.32i) q^{9} +O(q^{10})$	\(q+(84.9007 - 30.9013i) q^{3} +(-77.9653 + 442.163i) q^{5} +(-193.184 - 334.604i) q^{7} +(4577.90 - 3841.32i) q^{9} +(-1898.74 + 3288.71i) q^{11} +(9075.63 + 3303.26i) q^{13} +(7044.12 + 39949.2i) q^{15} +(21855.6 + 18339.1i) q^{17} +(4460.62 - 29563.1i) q^{19} +(-26741.1 - 22438.5i) q^{21} +(10694.4 + 60651.1i) q^{23} +(-116016. - 42226.4i) q^{25} +(171168. - 296472. i) q^{27} +(32178.5 - 27000.9i) q^{29} +(92451.6 + 160131. i) q^{31} +(-59578.7 + 337888. i) q^{33} +(163011. - 59331.2i) q^{35} -354058. q^{37} +872603. q^{39} +(-201193. + 73228.2i) q^{41} +(47980.1 - 272109. i) q^{43} +(1.34157e6 + 2.32367e6i) q^{45} +(84729.7 - 71096.6i) q^{47} +(337132. - 583929. i) q^{49} +(2.42226e6 + 881632. i) q^{51} +(169985. + 964033. i) q^{53} +(-1.30611e6 - 1.09596e6i) q^{55} +(-534828. - 2.64777e6i) q^{57} +(-954290. - 800744. i) q^{59} +(-611595. - 3.46853e6i) q^{61} +(-2.16970e6 - 789705. i) q^{63} +(-2.16816e6 + 3.75537e6i) q^{65} +(-307522. + 258042. i) q^{67} +(2.78217e6 + 4.81885e6i) q^{69} +(205419. - 1.16499e6i) q^{71} +(-1.06401e6 + 387266. i) q^{73} -1.11547e7 q^{75} +1.46722e6 q^{77} +(3.82833e6 - 1.39340e6i) q^{79} +(3.10142e6 - 1.75890e7i) q^{81} +(2.42883e6 + 4.20686e6i) q^{83} +(-9.81284e6 + 8.23395e6i) q^{85} +(1.89761e6 - 3.28676e6i) q^{87} +(-8.07859e6 - 2.94037e6i) q^{89} +(-647980. - 3.67488e6i) q^{91} +(1.27975e7 + 1.07384e7i) q^{93} +(1.27239e7 + 4.27721e6i) q^{95} +(-1.01336e7 - 8.50309e6i) q^{97} +(3.94074e6 + 2.23491e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	84.9007	−	30.9013i	1.81546	−	0.660774i	0.819288	−	0.573383i	$-0.194369\pi$
$3$	84.9007	−	30.9013i	1.81546	−	0.660774i	0.996174	−	0.0873915i	$-0.0278531\pi$
$4$		0			0
$5$	−77.9653	+	442.163i	−0.278937	+	1.58193i	0.447235	+	0.894417i	$0.352409\pi$
$5$	−77.9653	+	442.163i	−0.278937	+	1.58193i	−0.726172	+	0.687514i	$0.758702\pi$
$6$		0			0
$7$	−193.184	−	334.604i	−0.212876	−	0.368713i	0.739737	−	0.672896i	$-0.234950\pi$
$7$	−193.184	−	334.604i	−0.212876	−	0.368713i	−0.952614	+	0.304183i	$0.901616\pi$
$8$		0			0
$9$	4577.90	−	3841.32i	2.09323	−	1.75643i
$10$		0			0
$11$	−1898.74	+	3288.71i	−0.430121	+	0.744992i	−0.996883	−	0.0788897i	$-0.974863\pi$
$11$	−1898.74	+	3288.71i	−0.430121	+	0.744992i	0.566762	+	0.823881i	$0.308196\pi$
$12$		0			0
$13$	9075.63	+	3303.26i	1.14571	+	0.417004i	0.843973	−	0.536386i	$-0.180211\pi$
$13$	9075.63	+	3303.26i	1.14571	+	0.417004i	0.301738	+	0.953391i	$0.402433\pi$
$14$		0			0
$15$	7044.12	+	39949.2i	0.538899	+	3.05625i
$16$		0			0
$17$	21855.6	+	18339.1i	1.07893	+	0.905328i	0.995831	−	0.0912134i	$-0.0290745\pi$
$17$	21855.6	+	18339.1i	1.07893	+	0.905328i	0.0830967	+	0.996541i	$0.473519\pi$
$18$		0			0
$19$	4460.62	−	29563.1i	0.149196	−	0.988808i
$19$	4460.62	−	29563.1i	0.149196	−	0.988808i
$20$		0			0
$21$	−26741.1	−	22438.5i	−0.630104	−	0.528720i
$22$		0			0
$23$	10694.4	+	60651.1i	0.183278	+	1.03942i	0.928148	+	0.372211i	$0.121400\pi$
$23$	10694.4	+	60651.1i	0.183278	+	1.03942i	−0.744870	+	0.667209i	$0.767489\pi$
$24$		0			0
$25$	−116016.	−	42226.4i	−1.48500	−	0.540498i
$26$		0			0
$27$	171168.	−	296472.i	1.67360	−	2.89875i
$28$		0			0
$29$	32178.5	−	27000.9i	0.245004	−	0.205582i	−0.512014	−	0.858977i	$-0.671100\pi$
$29$	32178.5	−	27000.9i	0.245004	−	0.205582i	0.757017	+	0.653395i	$0.226656\pi$
$30$		0			0
$31$	92451.6	+	160131.i	0.557377	+	0.965404i	0.997714	+	0.0675723i	$0.0215253\pi$
$31$	92451.6	+	160131.i	0.557377	+	0.965404i	−0.440338	+	0.897832i	$0.645141\pi$
$32$		0			0
$33$	−59578.7	+	337888.i	−0.288597	+	1.63672i
$34$		0			0
$35$	163011.	−	59331.2i	0.642657	−	0.233908i
$36$		0			0
$37$	−354058.			−1.14913			−0.574564	−	0.818460i	$-0.694828\pi$
$37$	−354058.			−1.14913			−0.574564	+	0.818460i	$0.694828\pi$
$38$		0			0
$39$	872603.			2.35554
$40$		0			0
$41$	−201193.	+	73228.2i	−0.455899	+	0.165934i	−0.559754	−	0.828659i	$-0.689104\pi$
$41$	−201193.	+	73228.2i	−0.455899	+	0.165934i	0.103855	+	0.994592i	$0.466882\pi$
$42$		0			0
$43$	47980.1	−	272109.i	0.0920284	−	0.521919i	−0.903589	−	0.428400i	$-0.859077\pi$
$43$	47980.1	−	272109.i	0.0920284	−	0.521919i	0.995618	−	0.0935188i	$-0.0298115\pi$
$44$		0			0
$45$	1.34157e6	+	2.32367e6i	2.19467	+	3.80129i
$46$		0			0
$47$	84729.7	−	71096.6i	0.119040	−	0.0998865i	−0.581324	−	0.813672i	$-0.697465\pi$
$47$	84729.7	−	71096.6i	0.119040	−	0.0998865i	0.700364	+	0.713785i	$0.253021\pi$
$48$		0			0
$49$	337132.	−	583929.i	0.409367	−	0.709045i
$50$		0			0
$51$	2.42226e6	+	881632.i	2.55697	+	0.930661i
$52$		0			0
$53$	169985.	+	964033.i	0.156836	+	0.889460i	0.957088	+	0.289796i	$0.0935876\pi$
$53$	169985.	+	964033.i	0.156836	+	0.889460i	−0.800253	+	0.599663i	$0.795301\pi$
$54$		0			0
$55$	−1.30611e6	−	1.09596e6i	−1.05855	−	0.888228i
$56$		0			0
$57$	−534828.	−	2.64777e6i	−0.382518	−	1.89373i
$58$		0			0
$59$	−954290.	−	800744.i	−0.604920	−	0.507589i	0.288103	−	0.957600i	$-0.406976\pi$
$59$	−954290.	−	800744.i	−0.604920	−	0.507589i	−0.893023	+	0.450011i	$0.851420\pi$
$60$		0			0
$61$	−611595.	−	3.46853e6i	−0.344993	−	1.95655i	−0.285738	−	0.958308i	$-0.592239\pi$
$61$	−611595.	−	3.46853e6i	−0.344993	−	1.95655i	−0.0592542	−	0.998243i	$-0.518872\pi$
$62$		0			0
$63$	−2.16970e6	−	789705.i	−1.09322	−	0.397899i
$64$		0			0
$65$	−2.16816e6	+	3.75537e6i	−0.979253	+	1.69612i
$66$		0			0
$67$	−307522.	+	258042.i	−0.124915	+	0.104816i	−0.703105	−	0.711086i	$-0.748204\pi$
$67$	−307522.	+	258042.i	−0.124915	+	0.104816i	0.578190	+	0.815902i	$0.303759\pi$
$68$		0			0
$69$	2.78217e6	+	4.81885e6i	1.01956	+	1.76592i
$70$		0			0
$71$	205419.	−	1.16499e6i	0.0681140	−	0.386294i	−0.931624	−	0.363423i	$-0.881608\pi$
$71$	205419.	−	1.16499e6i	0.0681140	−	0.386294i	0.999738	−	0.0228713i	$-0.00728079\pi$
$72$		0			0
$73$	−1.06401e6	+	387266.i	−0.320121	+	0.116514i	−0.497082	−	0.867703i	$-0.665595\pi$
$73$	−1.06401e6	+	387266.i	−0.320121	+	0.116514i	0.176962	+	0.984218i	$0.443373\pi$
$74$		0			0
$75$	−1.11547e7			−3.05312
$76$		0			0
$77$	1.46722e6			0.366250
$78$		0			0
$79$	3.82833e6	−	1.39340e6i	0.873603	−	0.317965i	0.133978	−	0.990984i	$-0.457225\pi$
$79$	3.82833e6	−	1.39340e6i	0.873603	−	0.317965i	0.739625	+	0.673019i	$0.235003\pi$
$80$		0			0
$81$	3.10142e6	−	1.75890e7i	0.648431	−	3.67743i
$82$		0			0
$83$	2.42883e6	+	4.20686e6i	0.466255	+	0.807578i	0.999257	−	0.0385362i	$-0.0122695\pi$
$83$	2.42883e6	+	4.20686e6i	0.466255	+	0.807578i	−0.533002	+	0.846114i	$0.678936\pi$
$84$		0			0
$85$	−9.81284e6	+	8.23395e6i	−1.73312	+	1.45426i
$86$		0			0
$87$	1.89761e6	−	3.28676e6i	0.308951	−	0.535119i
$88$		0			0
$89$	−8.07859e6	−	2.94037e6i	−1.21470	−	0.442116i	−0.346371	−	0.938098i	$-0.612586\pi$
$89$	−8.07859e6	−	2.94037e6i	−1.21470	−	0.442116i	−0.868333	+	0.495981i	$0.834808\pi$
$90$		0			0
$91$	−647980.	−	3.67488e6i	−0.0901398	−	0.511208i
$92$		0			0
$93$	1.27975e7	+	1.07384e7i	1.64981	+	1.38435i
$94$		0			0
$95$	1.27239e7	+	4.27721e6i	1.52261	+	0.511833i
$96$		0			0
$97$	−1.01336e7	−	8.50309e6i	−1.12736	−	0.945967i	−0.128406	−	0.991722i	$-0.540986\pi$
$97$	−1.01336e7	−	8.50309e6i	−1.12736	−	0.945967i	−0.998953	+	0.0457550i	$0.985431\pi$
$98$		0			0
$99$	3.94074e6	+	2.23491e7i	0.408183	+	2.31492i
$100$		0			0
$101$	−1.48141e7	−	5.39188e6i	−1.43070	−	0.520734i	−0.493571	−	0.869705i	$-0.664309\pi$
$101$	−1.48141e7	−	5.39188e6i	−1.43070	−	0.520734i	−0.937133	+	0.348972i	$0.886531\pi$
$102$		0			0
$103$	−3.90761e6	+	6.76818e6i	−0.352356	+	0.610298i	−0.986662	−	0.162784i	$-0.947953\pi$
$103$	−3.90761e6	+	6.76818e6i	−0.352356	+	0.610298i	0.634306	+	0.773082i	$0.281286\pi$
$104$		0			0
$105$	1.20063e7	−	1.00745e7i	1.01216	−	0.849302i
$106$		0			0
$107$	−2.91504e6	−	5.04899e6i	−0.230039	−	0.398439i	0.727781	−	0.685810i	$-0.240552\pi$
$107$	−2.91504e6	−	5.04899e6i	−0.230039	−	0.398439i	−0.957819	+	0.287371i	$0.907219\pi$
$108$		0			0
$109$	2.34320e6	−	1.32889e7i	0.173307	−	0.982874i	−0.766772	−	0.641919i	$-0.778138\pi$
$109$	2.34320e6	−	1.32889e7i	0.173307	−	0.982874i	0.940080	−	0.340955i	$-0.110750\pi$
$110$		0			0
$111$	−3.00598e7	+	1.09409e7i	−2.08620	+	0.759314i
$112$		0			0
$113$	−1.03952e7			−0.677733			−0.338866	−	0.940835i	$-0.610043\pi$
$113$	−1.03952e7			−0.677733			−0.338866	+	0.940835i	$0.610043\pi$
$114$		0			0
$115$	−2.76515e7			−1.69541
$116$		0			0
$117$	5.42362e7	−	1.97404e7i	3.13068	−	1.13947i
$118$		0			0
$119$	1.91417e6	−	1.08558e7i	0.104128	−	0.590537i
$120$		0			0
$121$	2.53317e6	+	4.38757e6i	0.129991	+	0.225152i
$122$		0			0
$123$	−1.48186e7	+	1.24343e7i	−0.718023	+	0.602493i
$124$		0			0
$125$	1.01777e7	−	1.76283e7i	0.466085	−	0.807283i
$126$		0			0
$127$	−3.06111e6	−	1.11415e6i	−0.132607	−	0.0482650i	0.274864	−	0.961483i	$-0.411367\pi$
$127$	−3.06111e6	−	1.11415e6i	−0.132607	−	0.0482650i	−0.407471	+	0.913218i	$0.633589\pi$
$128$		0			0
$129$	−4.33498e6	−	2.45849e7i	−0.177796	−	1.00833i
$130$		0			0
$131$	3.92373e6	+	3.29240e6i	0.152493	+	0.127957i	0.715842	−	0.698262i	$-0.246043\pi$
$131$	3.92373e6	+	3.29240e6i	0.152493	+	0.127957i	−0.563349	+	0.826219i	$0.690487\pi$
$132$		0			0
$133$	−1.07536e7	+	4.21856e6i	−0.396346	+	0.155483i
$134$		0			0
$135$	1.17744e8	+	9.87989e7i	4.11880	+	3.45608i
$136$		0			0
$137$	−2.40852e6	−	1.36594e7i	−0.0800255	−	0.453847i	−0.998320	−	0.0579484i	$-0.981544\pi$
$137$	−2.40852e6	−	1.36594e7i	−0.0800255	−	0.453847i	0.918294	−	0.395899i	$-0.129567\pi$
$138$		0			0
$139$	2.76297e7	+	1.00564e7i	0.872618	+	0.317607i	0.739227	−	0.673456i	$-0.235191\pi$
$139$	2.76297e7	+	1.00564e7i	0.872618	+	0.317607i	0.133391	+	0.991063i	$0.457413\pi$
$140$		0			0
$141$	4.99663e6	−	8.65442e6i	0.150110	−	0.259999i
$142$		0			0
$143$	−2.80957e7	+	2.35751e7i	−0.803459	+	0.674182i
$144$		0			0
$145$	9.43001e6	+	1.63333e7i	0.256876	+	0.444923i
$146$		0			0
$147$	1.05785e7	−	5.99938e7i	0.274672	−	1.55774i
$148$		0			0
$149$	−3.24791e7	+	1.18214e7i	−0.804362	+	0.292764i	−0.711293	−	0.702896i	$-0.751890\pi$
$149$	−3.24791e7	+	1.18214e7i	−0.804362	+	0.292764i	−0.0930694	+	0.995660i	$0.529668\pi$
$150$		0			0
$151$	7.57710e6			0.179095			0.0895475	−	0.995983i	$-0.471458\pi$
$151$	7.57710e6			0.179095			0.0895475	+	0.995983i	$0.471458\pi$
$152$		0			0
$153$	1.70499e8			3.84860
$154$		0			0
$155$	−7.80120e7	+	2.83940e7i	−1.68268	+	0.612444i
$156$		0			0
$157$	−1.42980e7	+	8.10879e7i	−0.294867	+	1.67227i	0.372875	+	0.927881i	$0.378372\pi$
$157$	−1.42980e7	+	8.10879e7i	−0.294867	+	1.67227i	−0.667742	+	0.744392i	$0.732739\pi$
$158$		0			0
$159$	4.42218e7	+	7.65943e7i	0.872461	+	1.51115i
$160$		0			0
$161$	1.82281e7	−	1.52952e7i	0.344232	−	0.288845i
$162$		0			0
$163$	−1.60257e6	+	2.77573e6i	−0.0289842	+	0.0502020i	−0.880154	−	0.474689i	$-0.842561\pi$
$163$	−1.60257e6	+	2.77573e6i	−0.0289842	+	0.0502020i	0.851169	+	0.524891i	$0.175894\pi$
$164$		0			0
$165$	−1.44756e8	−	5.26870e7i	−2.50867	−	0.913082i
$166$		0			0
$167$	4.05387e6	+	2.29907e7i	0.0673538	+	0.381983i	0.999787	+	0.0206400i	$0.00657040\pi$
$167$	4.05387e6	+	2.29907e7i	0.0673538	+	0.381983i	−0.932433	+	0.361343i	$0.882318\pi$
$168$		0			0
$169$	2.33873e7	+	1.96243e7i	0.372715	+	0.312745i
$170$		0			0
$171$	−9.31408e7	−	1.52472e8i	−1.42447	−	2.33186i
$172$		0			0
$173$	5.26465e7	+	4.41756e7i	0.773051	+	0.648667i	0.941488	−	0.337046i	$-0.109428\pi$
$173$	5.26465e7	+	4.41756e7i	0.773051	+	0.648667i	−0.168437	+	0.985712i	$0.553872\pi$
$174$		0			0
$175$	8.28329e6	+	4.69769e7i	0.116834	+	0.662599i
$176$		0			0
$177$	−1.05764e8	−	3.84949e7i	−1.43361	−	0.521792i
$178$		0			0
$179$	6.93202e7	−	1.20066e8i	0.903388	−	1.56471i	0.0803207	−	0.996769i	$-0.474406\pi$
$179$	6.93202e7	−	1.20066e8i	0.903388	−	1.56471i	0.823067	−	0.567944i	$-0.192261\pi$
$180$		0			0
$181$	6.14129e7	−	5.15315e7i	0.769811	−	0.645948i	−0.170849	−	0.985297i	$-0.554651\pi$
$181$	6.14129e7	−	5.15315e7i	0.769811	−	0.645948i	0.940661	+	0.339349i	$0.110207\pi$
$182$		0			0
$183$	−1.59107e8	−	2.75582e8i	−1.91916	−	3.32408i
$184$		0			0
$185$	2.76042e7	−	1.56551e8i	0.320534	−	1.81784i
$186$		0			0
$187$	−1.01810e8	+	3.70558e7i	−1.13853	+	0.414392i
$188$		0			0
$189$	−1.32268e8			−1.42508
$190$		0			0
$191$	7.56662e7			0.785751			0.392876	−	0.919592i	$-0.371480\pi$
$191$	7.56662e7			0.785751			0.392876	+	0.919592i	$0.371480\pi$
$192$		0			0
$193$	−1.38506e8	+	5.04122e7i	−1.38682	+	0.504760i	−0.924238	−	0.381817i	$-0.875298\pi$
$193$	−1.38506e8	+	5.04122e7i	−1.38682	+	0.504760i	−0.462580	+	0.886578i	$0.653076\pi$
$194$		0			0
$195$	−6.80327e7	+	3.85833e8i	−0.657047	+	3.72630i
$196$		0			0
$197$	−6.89990e6	−	1.19510e7i	−0.0643000	−	0.111371i	0.832083	−	0.554651i	$-0.187148\pi$
$197$	−6.89990e6	−	1.19510e7i	−0.0643000	−	0.111371i	−0.896383	+	0.443280i	$0.853815\pi$
$198$		0			0
$199$	8.84386e6	−	7.42088e6i	0.0795529	−	0.0667528i	−0.602144	−	0.798387i	$-0.705687\pi$
$199$	8.84386e6	−	7.42088e6i	0.0795529	−	0.0667528i	0.681697	+	0.731635i	$0.261242\pi$
$200$		0			0
$201$	−1.81350e7	+	3.14108e7i	−0.157519	+	0.272830i
$202$		0			0
$203$	−1.52510e7	−	5.55090e6i	−0.127956	−	0.0465723i
$204$		0			0
$205$	−1.66927e7	−	9.46693e7i	−0.135328	−	0.767486i
$206$		0			0
$207$	2.81938e8	+	2.36574e8i	2.20932	+	1.85384i
$208$		0			0
$209$	8.87548e7	+	7.08022e7i	0.672481	+	0.536457i
$210$		0			0
$211$	−3.27857e7	−	2.75105e7i	−0.240268	−	0.201609i	0.514700	−	0.857370i	$-0.327903\pi$
$211$	−3.27857e7	−	2.75105e7i	−0.240268	−	0.201609i	−0.754968	+	0.655762i	$0.772348\pi$
$212$		0			0
$213$	−1.85595e7	−	1.05256e8i	−0.131595	−	0.746310i
$214$		0			0
$215$	1.16576e8	+	4.24301e7i	0.799969	+	0.291165i
$216$		0			0
$217$	3.57203e7	−	6.18694e7i	0.237304	−	0.411023i
$218$		0			0
$219$	−7.83678e7	+	6.57584e7i	−0.504177	+	0.423055i
$220$		0			0
$221$	1.37775e8	+	2.38633e8i	0.858613	+	1.48716i
$222$		0			0
$223$	4.61825e7	−	2.61914e8i	0.278876	−	1.58158i	−0.447500	−	0.894284i	$-0.647686\pi$
$223$	4.61825e7	−	2.61914e8i	0.278876	−	1.58158i	0.726376	−	0.687298i	$-0.241203\pi$
$224$		0			0
$225$	−6.93315e8	+	2.52346e8i	−4.05781	+	1.47692i
$226$		0			0
$227$	−8.83154e7			−0.501125			−0.250563	−	0.968100i	$-0.580616\pi$
$227$	−8.83154e7			−0.501125			−0.250563	+	0.968100i	$0.580616\pi$
$228$		0			0
$229$	1.24822e8			0.686860			0.343430	−	0.939178i	$-0.388411\pi$
$229$	1.24822e8			0.686860			0.343430	+	0.939178i	$0.388411\pi$
$230$		0			0
$231$	1.24568e8	−	4.53391e7i	0.664914	−	0.242009i
$232$		0			0
$233$	6.28974e7	−	3.56709e8i	0.325752	−	1.84743i	−0.178586	−	0.983924i	$-0.557152\pi$
$233$	6.28974e7	−	3.56709e8i	0.325752	−	1.84743i	0.504338	−	0.863506i	$-0.331736\pi$
$234$		0			0
$235$	2.48303e7	+	4.30074e7i	0.124809	+	0.216175i
$236$		0			0
$237$	2.81970e8	−	2.36601e8i	1.37589	−	1.15451i
$238$		0			0
$239$	−4.06201e7	+	7.03561e7i	−0.192463	+	0.333356i	−0.946066	−	0.323974i	$-0.894981\pi$
$239$	−4.06201e7	+	7.03561e7i	−0.192463	+	0.333356i	0.753603	+	0.657330i	$0.228314\pi$
$240$		0			0
$241$	3.39338e6	+	1.23509e6i	0.0156161	+	0.00568380i	0.349816	−	0.936818i	$-0.386244\pi$
$241$	3.39338e6	+	1.23509e6i	0.0156161	+	0.00568380i	−0.334200	+	0.942502i	$0.608466\pi$
$242$		0			0
$243$	−1.50203e8	−	8.51845e8i	−0.671518	−	3.80837i
$244$		0			0
$245$	2.31907e8	+	1.94593e8i	1.00747	+	0.845370i
$246$		0			0
$247$	1.38137e8	−	2.53569e8i	0.583273	−	1.07067i
$248$		0			0
$249$	3.36207e8	+	2.82111e8i	1.38010	+	1.15804i
$250$		0			0
$251$	7.22313e7	+	4.09644e8i	0.288315	+	1.63512i	0.693198	+	0.720747i	$0.256201\pi$
$251$	7.22313e7	+	4.09644e8i	0.288315	+	1.63512i	−0.404883	+	0.914369i	$0.632688\pi$
$252$		0			0
$253$	−2.19770e8	−	7.99897e7i	−0.853191	−	0.310536i
$254$		0			0
$255$	−5.78677e8	+	1.00230e9i	−2.18547	+	3.78535i
$256$		0			0
$257$	1.11031e8	−	9.31662e7i	0.408017	−	0.342367i	−0.415565	−	0.909563i	$-0.636416\pi$
$257$	1.11031e8	−	9.31662e7i	0.408017	−	0.342367i	0.823583	+	0.567196i	$0.191972\pi$
$258$		0			0
$259$	6.83982e7	+	1.18469e8i	0.244622	+	0.423698i
$260$		0			0
$261$	4.35908e7	−	2.47215e8i	0.151758	−	0.860665i
$262$		0			0
$263$	4.20484e8	−	1.53044e8i	1.42529	−	0.518764i	0.489714	−	0.871883i	$-0.337101\pi$
$263$	4.20484e8	−	1.53044e8i	1.42529	−	0.518764i	0.935578	+	0.353119i	$0.114879\pi$
$264$		0			0
$265$	−4.39512e8			−1.45081
$266$		0			0
$267$	−7.76740e8			−2.49739
$268$		0			0
$269$	1.58319e8	−	5.76235e7i	0.495908	−	0.180496i	−0.0819448	−	0.996637i	$-0.526113\pi$
$269$	1.58319e8	−	5.76235e7i	0.495908	−	0.180496i	0.577852	+	0.816141i	$0.303891\pi$
$270$		0			0
$271$	−7.92755e7	+	4.49594e8i	−0.241962	+	1.37223i	0.585483	+	0.810685i	$0.300905\pi$
$271$	−7.92755e7	+	4.49594e8i	−0.241962	+	1.37223i	−0.827445	+	0.561547i	$0.810206\pi$
$272$		0			0
$273$	−1.68573e8	−	2.91976e8i	−0.501438	−	0.868517i
$274$		0			0
$275$	3.59155e8	−	3.01366e8i	1.04140	−	0.873837i
$276$		0			0
$277$	1.59498e7	−	2.76258e7i	0.0450895	−	0.0780973i	−0.842600	−	0.538540i	$-0.818976\pi$
$277$	1.59498e7	−	2.76258e7i	0.0450895	−	0.0780973i	0.887689	+	0.460443i	$0.152309\pi$
$278$		0			0
$279$	1.03835e9	+	3.77928e8i	2.86239	+	1.04182i
$280$		0			0
$281$	−6.09372e7	−	3.45592e8i	−0.163836	−	0.929163i	−0.950256	−	0.311470i	$-0.899179\pi$
$281$	−6.09372e7	−	3.45592e8i	−0.163836	−	0.929163i	0.786419	−	0.617693i	$-0.211932\pi$
$282$		0			0
$283$	2.57573e8	+	2.16129e8i	0.675535	+	0.566841i	0.914698	−	0.404138i	$-0.132429\pi$
$283$	2.57573e8	+	2.16129e8i	0.675535	+	0.566841i	−0.239163	+	0.970979i	$0.576873\pi$
$284$		0			0
$285$	1.21244e9	−	3.00475e7i	3.10244	−	0.0768866i
$286$		0			0
$287$	6.33696e7	+	5.31734e7i	0.158232	+	0.132772i
$288$		0			0
$289$	7.00935e7	+	3.97520e8i	0.170819	+	0.968760i
$290$		0			0
$291$	−1.12311e9	−	4.08777e8i	−2.67175	−	0.972437i
$292$		0			0
$293$	1.85259e8	−	3.20878e8i	0.430272	−	0.745253i	−0.566625	−	0.823976i	$-0.691751\pi$
$293$	1.85259e8	−	3.20878e8i	0.430272	−	0.745253i	0.996896	+	0.0787234i	$0.0250844\pi$
$294$		0			0
$295$	4.28461e8	−	3.59521e8i	0.971704	−	0.815357i
$296$		0			0
$297$	6.50008e8	+	1.12585e9i	1.43970	+	2.49363i
$298$		0			0
$299$	−1.03288e8	+	5.85773e8i	−0.223460	+	1.26730i
$300$		0			0
$301$	−1.00318e8	+	3.65126e7i	−0.212029	+	0.0771721i
$302$		0			0
$303$	−1.42434e9			−2.94148
$304$		0			0
$305$	1.58134e9			3.19136
$306$		0			0
$307$	2.09870e8	−	7.63866e7i	0.413968	−	0.150672i	−0.126636	−	0.991949i	$-0.540418\pi$
$307$	2.09870e8	−	7.63866e7i	0.413968	−	0.150672i	0.540604	+	0.841277i	$0.318196\pi$
$308$		0			0
$309$	−1.22613e8	+	6.95374e8i	−0.236419	+	1.34080i
$310$		0			0
$311$	−1.68998e7	−	2.92713e7i	−0.0318581	−	0.0551798i	0.849657	−	0.527336i	$-0.176809\pi$
$311$	−1.68998e7	−	2.92713e7i	−0.0318581	−	0.0551798i	−0.881515	+	0.472156i	$0.843476\pi$
$312$		0			0
$313$	−4.70584e8	+	3.94867e8i	−0.867425	+	0.727856i	−0.963554	−	0.267513i	$-0.913798\pi$
$313$	−4.70584e8	+	3.94867e8i	−0.867425	+	0.727856i	0.0961293	+	0.995369i	$0.469354\pi$
$314$		0			0
$315$	5.18339e8	−	8.97790e8i	0.934388	−	1.61841i
$316$		0			0
$317$	−6.28156e8	−	2.28630e8i	−1.10754	−	0.403112i	−0.277450	−	0.960740i	$-0.589489\pi$
$317$	−6.28156e8	−	2.28630e8i	−1.10754	−	0.403112i	−0.830091	+	0.557628i	$0.811712\pi$
$318$		0			0
$319$	2.76998e7	+	1.57093e8i	0.0477760	+	0.270951i
$320$		0			0
$321$	−4.03510e8	−	3.38585e8i	−0.680904	−	0.571347i
$322$		0			0
$323$	6.39649e8	−	5.64316e8i	1.05617	−	0.931781i
$324$		0			0
$325$	−9.13433e8	−	7.66462e8i	−1.47600	−	1.23851i
$326$		0			0
$327$	−2.11707e8	−	1.20065e9i	−0.334825	−	1.89889i
$328$		0			0
$329$	−4.01576e7	−	1.46162e7i	−0.0621702	−	0.0226281i
$330$		0			0
$331$	4.53176e8	−	7.84923e8i	0.686861	−	1.18968i	−0.285988	−	0.958233i	$-0.592322\pi$
$331$	4.53176e8	−	7.84923e8i	0.686861	−	1.18968i	0.972848	−	0.231444i	$-0.0743450\pi$
$332$		0			0
$333$	−1.62084e9	+	1.36005e9i	−2.40540	+	2.01837i
$334$		0			0
$335$	−9.01204e7	−	1.56093e8i	−0.130968	−	0.226844i
$336$		0			0
$337$	−1.84118e8	+	1.04419e9i	−0.262055	+	1.48619i	0.515237	+	0.857048i	$0.327704\pi$
$337$	−1.84118e8	+	1.04419e9i	−0.262055	+	1.48619i	−0.777292	+	0.629140i	$0.783407\pi$
$338$		0			0
$339$	−8.82561e8	+	3.21226e8i	−1.23040	+	0.447828i
$340$		0			0
$341$	−7.02166e8			−0.958958
$342$		0			0
$343$	−5.78703e8			−0.774331
$344$		0			0
$345$	−2.34763e9	+	8.54467e8i	−3.07796	+	1.12029i
$346$		0			0
$347$	−1.23573e8	+	7.00819e8i	−0.158771	+	0.900435i	0.796486	+	0.604657i	$0.206690\pi$
$347$	−1.23573e8	+	7.00819e8i	−0.158771	+	0.900435i	−0.955257	+	0.295778i	$0.904421\pi$
$348$		0			0
$349$	2.09592e8	+	3.63024e8i	0.263928	+	0.457138i	0.967282	−	0.253702i	$-0.0816484\pi$
$349$	2.09592e8	+	3.63024e8i	0.263928	+	0.457138i	−0.703354	+	0.710840i	$0.748315\pi$
$350$		0			0
$351$	2.53279e9	−	2.12526e9i	3.12625	−	2.62323i
$352$		0			0
$353$	5.41461e8	−	9.37838e8i	0.655173	−	1.13479i	−0.326678	−	0.945136i	$-0.605929\pi$
$353$	5.41461e8	−	9.37838e8i	0.655173	−	1.13479i	0.981850	−	0.189657i	$-0.0607375\pi$
$354$		0			0
$355$	4.99100e8	+	1.81657e8i	0.592091	+	0.215503i
$356$		0			0
$357$	−1.72944e8	−	9.80815e8i	−0.201172	−	1.14090i
$358$		0			0
$359$	−1.90074e8	−	1.59491e8i	−0.216816	−	0.181930i	0.527911	−	0.849300i	$-0.322976\pi$
$359$	−1.90074e8	−	1.59491e8i	−0.216816	−	0.181930i	−0.744726	+	0.667370i	$0.767420\pi$
$360$		0			0
$361$	−8.54077e8	−	2.63739e8i	−0.955481	−	0.295053i
$362$		0			0
$363$	3.50650e8	+	2.94230e8i	0.384769	+	0.322860i
$364$		0			0
$365$	−8.82793e7	−	5.00657e8i	−0.0950242	−	0.538909i
$366$		0			0
$367$	−8.52381e8	−	3.10241e8i	−0.900124	−	0.327618i	−0.149822	−	0.988713i	$-0.547870\pi$
$367$	−8.52381e8	−	3.10241e8i	−0.900124	−	0.327618i	−0.750303	+	0.661095i	$0.770092\pi$
$368$		0			0
$369$	−6.39749e8	+	1.10808e9i	−0.662853	+	1.14809i
$370$		0			0
$371$	2.89731e8	−	2.43113e8i	0.294568	−	0.247172i
$372$		0			0
$373$	1.15068e8	+	1.99303e8i	0.114808	+	0.198853i	0.917703	−	0.397267i	$-0.130041\pi$
$373$	1.15068e8	+	1.99303e8i	0.114808	+	0.198853i	−0.802895	+	0.596121i	$0.796708\pi$
$374$		0			0
$375$	3.19357e8	−	1.81116e9i	0.312728	−	1.77357i
$376$		0			0
$377$	3.81231e8	−	1.38757e8i	0.366432	−	0.133370i
$378$		0			0
$379$	1.33983e9			1.26419			0.632095	−	0.774891i	$-0.282195\pi$
$379$	1.33983e9			1.26419			0.632095	+	0.774891i	$0.282195\pi$
$380$		0			0
$381$	−2.94320e8			−0.272635
$382$		0			0
$383$	3.78852e7	−	1.37891e7i	0.0344567	−	0.0125412i	−0.324734	−	0.945805i	$-0.605275\pi$
$383$	3.78852e7	−	1.37891e7i	0.0344567	−	0.0125412i	0.359191	+	0.933264i	$0.383053\pi$
$384$		0			0
$385$	−1.14392e8	+	6.48751e8i	−0.102161	+	0.579383i
$386$		0			0
$387$	−8.25608e8	−	1.43000e9i	−0.724078	−	1.25414i
$388$		0			0
$389$	−4.63319e8	+	3.88771e8i	−0.399077	+	0.334865i	−0.820137	−	0.572168i	$-0.806103\pi$
$389$	−4.63319e8	+	3.88771e8i	−0.399077	+	0.334865i	0.421060	+	0.907033i	$0.361658\pi$
$390$		0			0
$391$	−8.78551e8	+	1.52169e9i	−0.743273	+	1.28739i
$392$		0			0
$393$	4.34868e8	+	1.58279e8i	0.361396	+	0.131537i
$394$		0			0
$395$	3.17632e8	+	1.80138e9i	0.259319	+	1.47067i
$396$		0			0
$397$	−1.30741e8	−	1.09705e8i	−0.104868	−	0.0879950i	0.588846	−	0.808245i	$-0.299582\pi$
$397$	−1.30741e8	−	1.09705e8i	−0.104868	−	0.0879950i	−0.693714	+	0.720250i	$0.744027\pi$
$398$		0			0
$399$	−7.82633e8	+	6.90461e8i	−0.616812	+	0.544169i
$400$		0			0
$401$	9.22259e8	+	7.73867e8i	0.714245	+	0.599323i	0.925787	−	0.378046i	$-0.123404\pi$
$401$	9.22259e8	+	7.73867e8i	0.714245	+	0.599323i	−0.211541	+	0.977369i	$0.567848\pi$
$402$		0			0
$403$	3.10103e8	+	1.75868e9i	0.236014	+	1.33850i
$404$		0			0
$405$	7.53542e9	+	2.74267e9i	5.63657	+	2.05154i
$406$		0			0
$407$	6.72264e8	−	1.16440e9i	0.494264	−	0.856091i
$408$		0			0
$409$	−7.10230e8	+	5.95954e8i	−0.513296	+	0.430706i	−0.862287	−	0.506420i	$-0.830969\pi$
$409$	−7.10230e8	+	5.95954e8i	−0.513296	+	0.430706i	0.348991	+	0.937126i	$0.386524\pi$
$410$		0			0
$411$	−6.26579e8	−	1.08527e9i	−0.445174	−	0.771064i
$412$		0			0
$413$	−8.35790e7	+	4.74000e8i	−0.0583810	+	0.331095i
$414$		0			0
$415$	−2.04948e9	+	7.45950e8i	−1.40759	+	0.512320i
$416$		0			0
$417$	2.65654e9			1.79407
$418$		0			0
$419$	1.44980e9			0.962850			0.481425	−	0.876487i	$-0.340119\pi$
$419$	1.44980e9			0.962850			0.481425	+	0.876487i	$0.340119\pi$
$420$		0			0
$421$	−9.81285e8	+	3.57158e8i	−0.640926	+	0.233278i	−0.641980	−	0.766722i	$-0.721887\pi$
$421$	−9.81285e8	+	3.57158e8i	−0.640926	+	0.233278i	0.00105407	+	0.999999i	$0.499664\pi$
$422$		0			0
$423$	1.14780e8	−	6.50947e8i	0.0737349	−	0.418172i
$424$		0			0
$425$	−1.76121e9	−	3.05051e9i	−1.11289	−	1.92757i
$426$		0			0
$427$	−1.04243e9	+	8.74706e8i	−0.647964	+	0.543706i
$428$		0			0
$429$	−1.65684e9	+	2.86974e9i	−1.01317	+	1.75486i
$430$		0			0
$431$	−6.98769e8	−	2.54331e8i	−0.420401	−	0.153013i	0.123153	−	0.992388i	$-0.460699\pi$
$431$	−6.98769e8	−	2.54331e8i	−0.420401	−	0.153013i	−0.543554	+	0.839374i	$0.682922\pi$
$432$		0			0
$433$	−3.24327e8	−	1.83935e9i	−0.191989	−	1.08882i	−0.916642	−	0.399709i	$-0.869111\pi$
$433$	−3.24327e8	−	1.83935e9i	−0.191989	−	1.08882i	0.724653	−	0.689114i	$-0.242000\pi$
$434$		0			0
$435$	1.30534e9	+	1.09531e9i	0.760343	+	0.638004i
$436$		0			0
$437$	1.84074e9	−	4.56182e7i	1.05513	−	0.0261489i
$438$		0			0
$439$	−1.97015e9	−	1.65316e9i	−1.11141	−	0.932584i	−0.113271	−	0.993564i	$-0.536133\pi$
$439$	−1.97015e9	−	1.65316e9i	−1.11141	−	0.932584i	−0.998139	+	0.0609803i	$0.980577\pi$
$440$		0			0
$441$	−6.99701e8	−	3.96820e9i	−0.388488	−	2.20322i
$442$		0			0
$443$	−7.22390e8	−	2.62929e8i	−0.394783	−	0.143689i	0.136997	−	0.990571i	$-0.456255\pi$
$443$	−7.22390e8	−	2.62929e8i	−0.394783	−	0.143689i	−0.531781	+	0.846882i	$0.678477\pi$
$444$		0			0
$445$	1.92997e9	−	3.34281e9i	1.03822	−	1.79826i
$446$		0			0
$447$	−2.39220e9	+	2.00729e9i	−1.26684	+	1.06300i
$448$		0			0
$449$	−1.29957e9	−	2.25092e9i	−0.677544	−	1.17354i	−0.975718	−	0.219029i	$-0.929711\pi$
$449$	−1.29957e9	−	2.25092e9i	−0.677544	−	1.17354i	0.298175	−	0.954511i	$-0.403622\pi$
$450$		0			0
$451$	1.41186e8	−	8.00706e8i	0.0724727	−	0.411013i
$452$		0			0
$453$	6.43301e8	−	2.34143e8i	0.325140	−	0.118341i
$454$		0			0
$455$	1.67541e9			0.833839
$456$		0			0
$457$	1.04468e9			0.512010			0.256005	−	0.966676i	$-0.417594\pi$
$457$	1.04468e9			0.512010			0.256005	+	0.966676i	$0.417594\pi$
$458$		0			0
$459$	9.17803e9	−	3.34053e9i	4.43001	−	1.61239i
$460$		0			0
$461$	1.72741e8	−	9.79661e8i	0.0821186	−	0.465717i	−0.915823	−	0.401583i	$-0.868460\pi$
$461$	1.72741e8	−	9.79661e8i	0.0821186	−	0.465717i	0.997941	−	0.0641346i	$-0.0204287\pi$
$462$		0			0
$463$	−1.23280e9	−	2.13527e9i	−0.577244	−	0.999815i	−0.995794	−	0.0916218i	$-0.970795\pi$
$463$	−1.23280e9	−	2.13527e9i	−0.577244	−	0.999815i	0.418550	−	0.908194i	$-0.362538\pi$
$464$		0			0
$465$	−5.74586e9	+	4.82135e9i	−2.65015	+	2.22374i
$466$		0			0
$467$	−2.16013e9	+	3.74146e9i	−0.981457	+	1.69993i	−0.324726	+	0.945808i	$0.605272\pi$
$467$	−2.16013e9	+	3.74146e9i	−0.981457	+	1.69993i	−0.656731	+	0.754125i	$0.728061\pi$
$468$		0			0
$469$	1.45750e8	+	5.30486e7i	0.0652384	+	0.0237448i
$470$		0			0
$471$	1.29182e9	+	7.32625e9i	0.569675	+	3.23079i
$472$		0			0
$473$	8.03786e8	+	6.74456e8i	0.349242	+	0.293049i
$474$		0			0
$475$	−1.76584e9	+	3.24143e9i	−0.756005	+	1.38774i
$476$		0			0
$477$	4.48133e9	+	3.76028e9i	1.89057	+	1.58638i
$478$		0			0
$479$	1.71373e8	+	9.71907e8i	0.0712475	+	0.404064i	0.999485	+	0.0320774i	$0.0102123\pi$
$479$	1.71373e8	+	9.71907e8i	0.0712475	+	0.404064i	−0.928238	+	0.371987i	$0.878677\pi$
$480$		0			0
$481$	−3.21330e9	−	1.16955e9i	−1.31657	−	0.479192i
$482$		0			0
$483$	1.07494e9	−	1.86185e9i	0.434079	−	0.751846i
$484$		0			0
$485$	4.54982e9	−	3.81775e9i	1.81092	−	1.51954i
$486$		0			0
$487$	−3.47332e8	−	6.01596e8i	−0.136268	−	0.236023i	0.789813	−	0.613347i	$-0.210177\pi$
$487$	−3.47332e8	−	6.01596e8i	−0.136268	−	0.236023i	−0.926081	+	0.377325i	$0.876844\pi$
$488$		0			0
$489$	−5.02855e7	+	2.85184e8i	−0.0194474	+	0.110292i
$490$		0			0
$491$	4.21133e9	−	1.53280e9i	1.60559	−	0.584386i	0.625027	−	0.780603i	$-0.285088\pi$
$491$	4.21133e9	−	1.53280e9i	1.60559	−	0.584386i	0.980560	+	0.196217i	$0.0628657\pi$
$492$		0			0
$493$	1.19845e9			0.450461
$494$		0			0
$495$	−1.01892e10			−3.77590
$496$		0			0
$497$	−4.29494e8	+	1.56323e8i	−0.156931	+	0.0571183i
$498$		0			0
$499$	−2.15724e8	+	1.22343e9i	−0.0777223	+	0.440785i	0.920969	+	0.389637i	$0.127399\pi$
$499$	−2.15724e8	+	1.22343e9i	−0.0777223	+	0.440785i	−0.998691	+	0.0511488i	$0.983712\pi$
$500$		0			0
$501$	1.05462e9	+	1.82665e9i	0.374683	+	0.648969i
$502$		0			0
$503$	−1.00253e9	+	8.41226e8i	−0.351246	+	0.294730i	−0.801290	−	0.598276i	$-0.795853\pi$
$503$	−1.00253e9	+	8.41226e8i	−0.351246	+	0.294730i	0.450044	+	0.893006i	$0.351408\pi$
$504$		0			0
$505$	3.53908e9	−	6.12986e9i	1.22284	−	2.11802i
$506$		0			0
$507$	2.59202e9	+	9.43418e8i	0.883304	+	0.321496i
$508$		0			0
$509$	7.41269e8	+	4.20395e9i	0.249152	+	1.41301i	0.810650	+	0.585531i	$0.199114\pi$
$509$	7.41269e8	+	4.20395e9i	0.249152	+	1.41301i	−0.561498	+	0.827478i	$0.689775\pi$
$510$		0			0
$511$	3.35129e8	+	2.81207e8i	0.111106	+	0.0932294i
$512$		0			0
$513$	−8.00112e9	−	6.38272e9i	−2.61661	−	2.08735i
$514$		0			0
$515$	−2.68798e9	−	2.25549e9i	−0.867164	−	0.727637i
$516$		0			0
$517$	7.29369e7	+	4.13646e8i	0.0232129	+	0.131647i
$518$		0			0
$519$	5.83481e9	+	2.12370e9i	1.83207	+	0.666818i
$520$		0			0
$521$	−5.75194e8	+	9.96265e8i	−0.178190	+	0.308633i	−0.941260	−	0.337681i	$-0.890357\pi$
$521$	−5.75194e8	+	9.96265e8i	−0.178190	+	0.308633i	0.763071	+	0.646315i	$0.223691\pi$
$522$		0			0
$523$	−3.08233e9	+	2.58638e9i	−0.942156	+	0.790563i	−0.977959	−	0.208796i	$-0.933046\pi$
$523$	−3.08233e9	+	2.58638e9i	−0.942156	+	0.790563i	0.0358031	+	0.999359i	$0.488601\pi$
$524$		0			0
$525$	2.15491e9	+	3.73241e9i	0.649936	+	1.12572i
$526$		0			0
$527$	−9.16061e8	+	5.19524e9i	−0.272639	+	1.54621i
$528$		0			0
$529$	−3.64695e8	+	1.32738e8i	−0.107111	+	0.0389853i
$530$		0			0
$531$	−7.44456e9			−2.15779
$532$		0			0
$533$	−2.06784e9			−0.591524
$534$		0			0
$535$	2.45975e9	−	8.95276e8i	0.694469	−	0.252766i
$536$		0			0
$537$	2.17513e9	−	1.23358e10i	0.606144	−	3.43761i
$538$		0			0
$539$	1.28025e9	+	2.21746e9i	0.352155	+	0.609951i
$540$		0			0
$541$	−2.93373e9	+	2.46169e9i	−0.796581	+	0.668410i	−0.947365	−	0.320156i	$-0.896265\pi$
$541$	−2.93373e9	+	2.46169e9i	−0.796581	+	0.668410i	0.150784	+	0.988567i	$0.451820\pi$
$542$		0			0
$543$	3.62160e9	−	6.27280e9i	0.970737	−	1.68137i
$544$		0			0
$545$	5.69319e9	+	2.07215e9i	1.50650	+	0.548320i
$546$		0			0
$547$	1.02362e9	+	5.80521e9i	0.267412	+	1.51657i	0.762077	+	0.647486i	$0.224180\pi$
$547$	1.02362e9	+	5.80521e9i	0.267412	+	1.51657i	−0.494665	+	0.869084i	$0.664709\pi$
$548$		0			0
$549$	−1.61236e10	−	1.35293e10i	−4.15870	−	3.48956i
$550$		0			0
$551$	−6.54695e8	−	1.07174e9i	−0.166728	−	0.272934i
$552$		0			0
$553$	−1.20581e9	−	1.01179e9i	−0.303207	−	0.254421i
$554$		0			0
$555$	−2.49403e9	−	1.41443e10i	−0.619264	−	3.51202i
$556$		0			0
$557$	−1.15852e9	−	4.21668e8i	−0.284061	−	0.103390i	0.196060	−	0.980592i	$-0.437185\pi$
$557$	−1.15852e9	−	4.21668e8i	−0.284061	−	0.103390i	−0.480121	+	0.877202i	$0.659407\pi$
$558$		0			0
$559$	1.33430e9	−	2.31107e9i	0.323080	−	0.559592i
$560$		0			0
$561$	−7.49868e9	+	6.29214e9i	−1.79314	+	1.50462i
$562$		0			0
$563$	1.03658e9	+	1.79541e9i	0.244807	+	0.424019i	0.962077	−	0.272776i	$-0.0879419\pi$
$563$	1.03658e9	+	1.79541e9i	0.244807	+	0.424019i	−0.717270	+	0.696795i	$0.754609\pi$
$564$		0			0
$565$	8.10465e8	−	4.59637e9i	0.189045	−	1.07213i
$566$		0			0
$567$	−6.48451e9	+	2.36017e9i	−1.49395	+	0.543754i
$568$		0			0
$569$	−6.27567e9			−1.42813			−0.714064	−	0.700081i	$-0.753147\pi$
$569$	−6.27567e9			−1.42813			−0.714064	+	0.700081i	$0.753147\pi$
$570$		0			0
$571$	4.49266e9			1.00990			0.504948	−	0.863150i	$-0.331512\pi$
$571$	4.49266e9			1.00990			0.504948	+	0.863150i	$0.331512\pi$
$572$		0			0
$573$	6.42412e9	−	2.33819e9i	1.42650	−	0.519204i
$574$		0			0
$575$	1.32035e9	−	7.48809e9i	0.289636	−	1.64261i
$576$		0			0
$577$	5.11394e8	+	8.85761e8i	0.110826	+	0.191956i	0.916103	−	0.400942i	$-0.131317\pi$
$577$	5.11394e8	+	8.85761e8i	0.110826	+	0.191956i	−0.805278	+	0.592898i	$0.797984\pi$
$578$		0			0
$579$	−1.02015e10	+	8.56007e9i	−2.18418	+	1.83275i
$580$		0			0
$581$	9.38420e8	−	1.62539e9i	0.198509	−	0.343828i
$582$		0			0
$583$	−3.49318e9	−	1.27141e9i	−0.730098	−	0.265734i
$584$		0			0
$585$	4.49992e9	+	2.55203e10i	0.929307	+	5.27036i
$586$		0			0
$587$	3.15363e9	+	2.64621e9i	0.643542	+	0.539996i	0.905104	−	0.425191i	$-0.139793\pi$
$587$	3.15363e9	+	2.64621e9i	0.643542	+	0.539996i	−0.261562	+	0.965187i	$0.584237\pi$
$588$		0			0
$589$	5.14635e9	−	2.01887e9i	1.03776	−	0.407103i
$590$		0			0
$591$	−9.55108e8	−	8.01431e8i	−0.190325	−	0.159702i
$592$		0			0
$593$	7.91005e8	+	4.48601e9i	0.155772	+	0.883424i	0.958077	+	0.286511i	$0.0924954\pi$
$593$	7.91005e8	+	4.48601e9i	0.155772	+	0.883424i	−0.802306	+	0.596914i	$0.796394\pi$
$594$		0			0
$595$	4.65079e9	+	1.69275e9i	0.905144	+	0.329445i
$596$		0			0
$597$	5.21535e8	−	9.03325e8i	0.100317	−	0.173754i
$598$		0			0
$599$	6.40310e9	−	5.37284e9i	1.21730	−	1.02143i	0.218335	−	0.975874i	$-0.429937\pi$
$599$	6.40310e9	−	5.37284e9i	1.21730	−	1.02143i	0.998962	−	0.0455596i	$-0.0145071\pi$
$600$		0			0
$601$	1.72367e9	+	2.98548e9i	0.323887	+	0.560988i	0.981286	−	0.192554i	$-0.0616770\pi$
$601$	1.72367e9	+	2.98548e9i	0.323887	+	0.560988i	−0.657400	+	0.753542i	$0.728344\pi$
$602$		0			0
$603$	−4.16586e8	+	2.36258e9i	−0.0773739	+	0.438809i
$604$		0			0
$605$	−2.13752e9	+	7.77994e8i	−0.392434	+	0.142834i
$606$		0			0
$607$	5.28916e9			0.959901			0.479950	−	0.877296i	$-0.340655\pi$
$607$	5.28916e9			0.959901			0.479950	+	0.877296i	$0.340655\pi$
$608$		0			0
$609$	−1.46635e9			−0.263073
$610$		0			0
$611$	1.00383e9	−	3.65363e8i	0.178039	−	0.0648007i
$612$		0			0
$613$	−8.23220e8	+	4.66871e9i	−0.144346	+	0.818626i	0.823544	+	0.567252i	$0.191993\pi$
$613$	−8.23220e8	+	4.66871e9i	−0.144346	+	0.818626i	−0.967890	+	0.251374i	$0.919118\pi$
$614$		0			0
$615$	−4.34263e9	−	7.52166e9i	−0.752819	−	1.30392i
$616$		0			0
$617$	3.97266e9	−	3.33346e9i	0.680900	−	0.571343i	−0.235370	−	0.971906i	$-0.575630\pi$
$617$	3.97266e9	−	3.33346e9i	0.680900	−	0.571343i	0.916269	+	0.400563i	$0.131186\pi$
$618$		0			0
$619$	−2.53062e8	+	4.38316e8i	−0.0428854	+	0.0742797i	−0.886671	−	0.462400i	$-0.846988\pi$
$619$	−2.53062e8	+	4.38316e8i	−0.0428854	+	0.0742797i	0.843786	+	0.536680i	$0.180322\pi$
$620$		0			0
$621$	1.98119e10	+	7.21095e9i	3.31976	+	1.20829i
$622$		0			0
$623$	5.76794e8	+	3.27116e9i	0.0955680	+	0.541993i
$624$		0			0
$625$	−3.87753e8	−	3.25364e8i	−0.0635295	−	0.0533076i
$626$		0			0
$627$	9.72324e9	+	3.26852e9i	1.57534	+	0.529559i
$628$		0			0
$629$	−7.73817e9	−	6.49310e9i	−1.23983	−	1.04034i
$630$		0			0
$631$	1.98961e9	+	1.12836e10i	0.315257	+	1.78791i	0.570774	+	0.821107i	$0.306643\pi$
$631$	1.98961e9	+	1.12836e10i	0.315257	+	1.78791i	−0.255517	+	0.966805i	$0.582246\pi$
$632$		0			0
$633$	−3.63364e9	−	1.32254e9i	−0.569415	−	0.207250i
$634$		0			0
$635$	7.31298e8	−	1.26665e9i	0.113341	−	0.196312i
$636$		0			0
$637$	4.98855e9	−	4.18589e9i	0.764691	−	0.641652i
$638$		0			0
$639$	−3.53471e9	−	6.12229e9i	−0.535921	−	0.928242i
$640$		0			0
$641$	2.38762e8	−	1.35409e9i	0.0358065	−	0.203069i	−0.961656	−	0.274257i	$-0.911568\pi$
$641$	2.38762e8	−	1.35409e9i	0.0358065	−	0.203069i	0.997463	+	0.0711884i	$0.0226792\pi$
$642$		0			0
$643$	8.61937e9	−	3.13719e9i	1.27861	−	0.465375i	0.388636	−	0.921391i	$-0.372946\pi$
$643$	8.61937e9	−	3.13719e9i	1.27861	−	0.465375i	0.889971	+	0.456017i	$0.150724\pi$
$644$		0			0
$645$	1.12085e10			1.64471
$646$		0			0
$647$	−1.00037e10			−1.45210			−0.726048	−	0.687644i	$-0.758645\pi$
$647$	−1.00037e10			−1.45210			−0.726048	+	0.687644i	$0.758645\pi$
$648$		0			0
$649$	4.44537e9	−	1.61798e9i	0.638338	−	0.232336i
$650$		0			0
$651$	1.12083e9	−	6.35656e9i	0.159224	−	0.903002i
$652$		0			0
$653$	−4.24020e9	−	7.34424e9i	−0.595923	−	1.03217i	−0.993416	−	0.114564i	$-0.963453\pi$
$653$	−4.24020e9	−	7.34424e9i	−0.595923	−	1.03217i	0.397493	−	0.917605i	$-0.369880\pi$
$654$		0			0
$655$	−1.76169e9	+	1.47824e9i	−0.244955	+	0.205541i
$656$		0			0
$657$	−3.38330e9	+	5.86005e9i	−0.465438	+	0.806162i
$658$		0			0
$659$	−7.90667e9	−	2.87779e9i	−1.07620	−	0.391706i	−0.257710	−	0.966222i	$-0.582968\pi$
$659$	−7.90667e9	−	2.87779e9i	−1.07620	−	0.391706i	−0.818493	+	0.574516i	$0.805190\pi$
$660$		0			0
$661$	7.50044e8	+	4.25371e9i	0.101014	+	0.572879i	0.992738	+	0.120299i	$0.0383852\pi$
$661$	7.50044e8	+	4.25371e9i	0.101014	+	0.572879i	−0.891724	+	0.452580i	$0.850504\pi$
$662$		0			0
$663$	1.90713e10	+	1.60027e10i	2.54146	+	2.13254i
$664$		0			0
$665$	−1.02688e9	−	5.08376e9i	−0.135408	−	0.670362i
$666$		0			0
$667$	1.98177e9	+	1.66290e9i	0.258590	+	0.216983i
$668$		0			0
$669$	−4.17257e9	−	2.36638e10i	−0.538780	−	3.05558i
$670$		0			0
$671$	1.25683e10	+	4.57447e9i	1.60600	+	0.584537i
$672$		0			0
$673$	−9.86370e8	+	1.70844e9i	−0.124735	+	0.216047i	−0.921629	−	0.388072i	$-0.873141\pi$
$673$	−9.86370e8	+	1.70844e9i	−0.124735	+	0.216047i	0.796895	+	0.604118i	$0.206475\pi$
$674$		0			0
$675$	−3.23772e10	+	2.71677e10i	−4.05207	+	3.40009i
$676$		0			0
$677$	2.21294e9	+	3.83292e9i	0.274100	+	0.474754i	0.969908	−	0.243473i	$-0.0782869\pi$
$677$	2.21294e9	+	3.83292e9i	0.274100	+	0.474754i	−0.695808	+	0.718228i	$0.744954\pi$
$678$		0			0
$679$	−8.87524e8	+	5.03340e9i	−0.108802	+	0.617045i
$680$		0			0
$681$	−7.49805e9	+	2.72907e9i	−0.909773	+	0.331130i
$682$		0			0
$683$	−2.30786e9			−0.277164			−0.138582	−	0.990351i	$-0.544254\pi$
$683$	−2.30786e9			−0.277164			−0.138582	+	0.990351i	$0.544254\pi$
$684$		0			0
$685$	6.22746e9			0.740277
$686$		0			0
$687$	1.05975e10	−	3.85718e9i	1.24697	−	0.453859i
$688$		0			0
$689$	−1.64173e9	+	9.31070e9i	−0.191220	+	1.08446i
$690$		0			0
$691$	−7.09151e9	−	1.22829e10i	−0.817646	−	1.41620i	−0.907412	−	0.420242i	$-0.861945\pi$
$691$	−7.09151e9	−	1.22829e10i	−0.817646	−	1.41620i	0.0897658	−	0.995963i	$-0.471388\pi$
$692$		0			0
$693$	6.71680e9	−	5.63606e9i	0.766648	−	0.643294i
$694$		0			0
$695$	−6.60072e9	+	1.14328e10i	−0.745838	+	1.29183i
$696$		0			0
$697$	−5.74014e9	−	2.08924e9i	−0.642107	−	0.233708i
$698$		0			0
$699$	−5.68275e9	−	3.22285e10i	−0.629344	−	3.56919i
$700$		0			0
$701$	−5.65144e9	−	4.74212e9i	−0.619650	−	0.519948i	0.278044	−	0.960568i	$-0.410314\pi$
$701$	−5.65144e9	−	4.74212e9i	−0.619650	−	0.519948i	−0.897693	+	0.440621i	$0.854758\pi$
$702$		0			0
$703$	−1.57932e9	+	1.04670e10i	−0.171446	+	1.13627i
$704$		0			0
$705$	3.43710e9	+	2.88407e9i	0.369428	+	0.309987i
$706$		0			0
$707$	1.05769e9	+	5.99847e9i	0.112562	+	0.638371i
$708$		0			0
$709$	1.64243e10	+	5.97797e9i	1.73072	+	0.629929i	0.998681	−	0.0513389i	$-0.0163489\pi$
$709$	1.64243e10	+	5.97797e9i	1.73072	+	0.629929i	0.732034	+	0.681268i	$0.238571\pi$
$710$		0			0
$711$	1.21732e10	−	2.10847e10i	1.27017	−	2.20000i
$712$		0			0
$713$	−8.72340e9	+	7.31980e9i	−0.901306	+	0.756286i
$714$		0			0
$715$	−8.23355e9	−	1.42609e10i	−0.842395	−	1.45907i
$716$		0			0
$717$	−1.27458e9	+	7.22850e9i	−0.129137	+	0.732371i
$718$		0			0
$719$	−1.33088e10	+	4.84399e9i	−1.33532	+	0.486018i	−0.908337	−	0.418239i	$-0.862647\pi$
$719$	−1.33088e10	+	4.84399e9i	−1.33532	+	0.486018i	−0.426987	+	0.904258i	$0.640425\pi$
$720$		0			0
$721$	3.01955e9			0.300033
$722$		0			0
$723$	3.26267e8			0.0321062
$724$		0			0
$725$	−4.87337e9	+	1.77376e9i	−0.474948	+	0.172867i
$726$		0			0
$727$	−6.24245e8	+	3.54027e9i	−0.0602538	+	0.341716i	−1.00000		0.000156645i	$-0.999950\pi$
$727$	−6.24245e8	+	3.54027e9i	−0.0602538	+	0.341716i	0.939746	+	0.341873i	$0.111061\pi$
$728$		0			0
$729$	−1.95452e10	−	3.38533e10i	−1.86850	−	3.23634i
$730$		0			0
$731$	6.03886e9	−	5.06720e9i	0.571800	−	0.479797i
$732$		0			0
$733$	−6.87335e9	+	1.19050e10i	−0.644621	+	1.11652i	0.339767	+	0.940509i	$0.389652\pi$
$733$	−6.87335e9	+	1.19050e10i	−0.644621	+	1.11652i	−0.984389	+	0.176007i	$0.943682\pi$
$734$		0			0
$735$	2.57023e10	+	9.35487e9i	2.38763	+	0.869025i
$736$		0			0
$737$	−2.64721e8	−	1.50130e9i	−0.0243586	−	0.138144i
$738$		0			0
$739$	−1.12157e10	−	9.41113e9i	−1.02229	−	0.857800i	−0.0323734	−	0.999476i	$-0.510307\pi$
$739$	−1.12157e10	−	9.41113e9i	−1.02229	−	0.857800i	−0.989913	+	0.141676i	$0.954751\pi$
$740$		0			0
$741$	3.89235e9	−	2.57968e10i	0.351438	−	2.32918i
$742$		0			0
$743$	1.54641e10	+	1.29760e10i	1.38314	+	1.16059i	0.968035	+	0.250814i	$0.0806983\pi$
$743$	1.54641e10	+	1.29760e10i	1.38314	+	1.16059i	0.415101	+	0.909775i	$0.363746\pi$
$744$		0			0
$745$	−2.69475e9	−	1.52827e10i	−0.238766	−	1.35411i
$746$		0			0
$747$	2.72788e10	+	9.92868e9i	2.39444	+	0.871504i
$748$		0			0
$749$	−1.12628e9	+	1.95077e9i	−0.0979396	+	0.169636i
$750$		0			0
$751$	−4.50981e9	+	3.78418e9i	−0.388525	+	0.326011i	−0.816038	−	0.577998i	$-0.803834\pi$
$751$	−4.50981e9	+	3.78418e9i	−0.388525	+	0.326011i	0.427513	+	0.904009i	$0.359390\pi$
$752$		0			0
$753$	1.87910e10	+	3.25470e10i	1.60387	+	2.77798i
$754$		0			0
$755$	−5.90750e8	+	3.35031e9i	−0.0499562	+	0.283316i
$756$		0			0
$757$	−5.97647e8	+	2.17526e8i	−0.0500736	+	0.0182253i	−0.366936	−	0.930246i	$-0.619593\pi$
$757$	−5.97647e8	+	2.17526e8i	−0.0500736	+	0.0182253i	0.316862	+	0.948472i	$0.397371\pi$
$758$		0			0
$759$	−2.11304e10			−1.75413
$760$		0			0
$761$	−1.15726e10			−0.951888			−0.475944	−	0.879476i	$-0.657894\pi$
$761$	−1.15726e10			−0.951888			−0.475944	+	0.879476i	$0.657894\pi$
$762$		0			0
$763$	−4.89920e9	+	1.78316e9i	−0.399291	+	0.145330i
$764$		0			0
$765$	−1.32930e10	+	7.53885e10i	−1.07352	+	6.08821i
$766$		0			0
$767$	−6.01571e9	−	1.04195e10i	−0.481397	−	0.833804i
$768$		0			0
$769$	4.01558e9	−	3.36947e9i	0.318424	−	0.267190i	−0.469539	−	0.882912i	$-0.655580\pi$
$769$	4.01558e9	−	3.36947e9i	0.318424	−	0.267190i	0.787964	+	0.615722i	$0.211135\pi$
$770$		0			0
$771$	6.54766e9	−	1.13409e10i	0.514513	−	0.891162i
$772$		0			0
$773$	−8.41366e8	−	3.06232e8i	−0.0655174	−	0.0238464i	0.309054	−	0.951045i	$-0.399988\pi$
$773$	−8.41366e8	−	3.06232e8i	−0.0655174	−	0.0238464i	−0.374571	+	0.927198i	$0.622210\pi$
$774$		0			0
$775$	−3.96412e9	−	2.24816e10i	−0.305908	−	1.73489i
$776$		0			0
$777$	9.46792e9	+	7.94453e9i	0.724071	+	0.607568i
$778$		0			0
$779$	1.26740e9	+	6.27452e9i	0.0960581	+	0.475553i
$780$		0			0
$781$	3.44128e9	+	2.88758e9i	0.258489	+	0.216898i
$782$		0			0
$783$	−2.49710e9	−	1.41617e10i	−0.185896	−	1.05427i
$784$		0			0
$785$	−3.47393e10	−	1.26441e10i	−2.56317	−	0.932918i
$786$		0			0
$787$	4.12094e9	−	7.13767e9i	0.301359	−	0.521969i	−0.675085	−	0.737740i	$-0.735893\pi$
$787$	4.12094e9	−	7.13767e9i	0.301359	−	0.521969i	0.976444	+	0.215771i	$0.0692263\pi$
$788$		0			0
$789$	3.09701e10	−	2.59870e10i	2.24478	−	1.88359i
$790$		0			0
$791$	2.00818e9	+	3.47828e9i	0.144273	+	0.249889i
$792$		0			0
$793$	5.90684e9	−	3.34993e10i	0.420629	−	2.38550i
$794$		0			0
$795$	−3.73149e10	+	1.35815e10i	−2.63389	+	0.958658i
$796$		0			0
$797$	−1.79861e10			−1.25844			−0.629220	−	0.777228i	$-0.716625\pi$
$797$	−1.79861e10			−1.25844			−0.629220	+	0.777228i	$0.716625\pi$
$798$		0			0
$799$	3.15567e9			0.218866
$800$		0			0
$801$	−4.82779e10	+	1.75717e10i	−3.31921	+	1.20809i
$802$		0			0
$803$	7.46661e8	−	4.23452e9i	0.0508884	−	0.288603i
$804$		0			0
$805$	5.34181e9	+	9.25229e9i	0.360913	+	0.625120i
$806$		0			0
$807$	1.16608e10	−	9.78456e9i	0.781035	−	0.655366i
$808$		0			0
$809$	5.64687e9	−	9.78066e9i	0.374962	−	0.649454i	−0.615359	−	0.788247i	$-0.710989\pi$
$809$	5.64687e9	−	9.78066e9i	0.374962	−	0.649454i	0.990321	+	0.138793i	$0.0443223\pi$
$810$		0			0
$811$	4.82118e9	+	1.75477e9i	0.317380	+	0.115517i	0.495798	−	0.868438i	$-0.334876\pi$
$811$	4.82118e9	+	1.75477e9i	0.317380	+	0.115517i	−0.178418	+	0.983955i	$0.557098\pi$
$812$		0			0
$813$	7.16250e9	+	4.06205e10i	0.467463	+	2.65112i
$814$		0			0
$815$	−1.10238e9	−	9.25008e8i	−0.0713314	−	0.0598541i
$816$		0			0
$817$	−7.83035e9	−	2.63221e9i	−0.502347	−	0.168867i
$818$		0			0
$819$	−1.70828e10	−	1.43341e10i	−1.08659	−	0.911754i
$820$		0			0
$821$	−6.27029e7	−	3.55606e8i	−0.00395445	−	0.0224268i	0.982767	−	0.184850i	$-0.0591800\pi$
$821$	−6.27029e7	−	3.55606e8i	−0.00395445	−	0.0224268i	−0.986721	+	0.162424i	$0.948069\pi$
$822$		0			0
$823$	−1.24385e10	−	4.52723e9i	−0.777799	−	0.283096i	−0.0775446	−	0.996989i	$-0.524708\pi$
$823$	−1.24385e10	−	4.52723e9i	−0.777799	−	0.283096i	−0.700255	+	0.713893i	$0.746930\pi$
$824$		0			0
$825$	2.11799e10	−	3.66846e10i	1.31321	−	2.27455i
$826$		0			0
$827$	−2.13323e10	+	1.79000e10i	−1.31150	+	1.10048i	−0.323470	+	0.946238i	$0.604849\pi$
$827$	−2.13323e10	+	1.79000e10i	−1.31150	+	1.10048i	−0.988033	+	0.154243i	$0.950706\pi$
$828$		0			0
$829$	−8.54226e9	−	1.47956e10i	−0.520753	−	0.901971i	−0.999709	−	0.0241316i	$-0.992318\pi$
$829$	−8.54226e9	−	1.47956e10i	−0.520753	−	0.901971i	0.478956	−	0.877839i	$-0.341015\pi$
$830$		0			0
$831$	5.00473e8	−	2.83832e9i	0.0302536	−	0.171577i
$832$		0			0
$833$	1.80769e10	−	6.57947e9i	1.08360	−	0.394397i
$834$		0			0
$835$	−1.04817e10			−0.623057
$836$		0			0
$837$	6.32992e10			3.73129
$838$		0			0
$839$	−1.60977e10	+	5.85910e9i	−0.941018	+	0.342503i	−0.766568	−	0.642163i	$-0.778037\pi$
$839$	−1.60977e10	+	5.85910e9i	−0.941018	+	0.342503i	−0.174450	+	0.984666i	$0.555815\pi$
$840$		0			0
$841$	−2.68901e9	+	1.52501e10i	−0.155886	+	0.884071i
$842$		0			0
$843$	−1.58529e10	−	2.74580e10i	−0.911406	−	1.57860i
$844$		0			0
$845$	−1.05005e10	+	8.81100e9i	−0.598705	+	0.502373i
$846$		0			0
$847$	9.78733e8	−	1.69521e9i	0.0553442	−	0.0958590i
$848$		0			0
$849$	2.85468e10	+	1.03902e10i	1.60096	+	0.582703i
$850$		0			0
$851$	−3.78645e9	−	2.14740e10i	−0.210610	−	1.19443i
$852$		0			0
$853$	1.40531e10	+	1.17919e10i	0.775264	+	0.650524i	0.942051	−	0.335469i	$-0.108895\pi$
$853$	1.40531e10	+	1.17919e10i	0.775264	+	0.650524i	−0.166787	+	0.985993i	$0.553339\pi$
$854$		0			0
$855$	7.46790e10	−	2.92959e10i	4.08618	−	1.60297i
$856$		0			0
$857$	−3.52067e8	−	2.95419e8i	−0.0191070	−	0.0160327i	0.633184	−	0.774001i	$-0.281748\pi$
$857$	−3.52067e8	−	2.95419e8i	−0.0191070	−	0.0160327i	−0.652291	+	0.757969i	$0.726192\pi$
$858$		0			0
$859$	−1.51241e9	−	8.57732e9i	−0.0814131	−	0.461717i	−0.998073	−	0.0620487i	$-0.980237\pi$
$859$	−1.51241e9	−	8.57732e9i	−0.0814131	−	0.461717i	0.916660	−	0.399668i	$-0.130875\pi$
$860$		0			0
$861$	7.02326e9	+	2.55626e9i	0.374997	+	0.136488i
$862$		0			0
$863$	−1.05087e10	+	1.82017e10i	−0.556560	+	0.963991i	0.441220	+	0.897399i	$0.354546\pi$
$863$	−1.05087e10	+	1.82017e10i	−0.556560	+	0.963991i	−0.997780	+	0.0665919i	$0.978787\pi$
$864$		0			0
$865$	−2.36374e10	+	1.98342e10i	−1.24178	+	1.04198i
$866$		0			0
$867$	1.82349e10	+	3.15837e10i	0.950246	+	1.64587i
$868$		0			0
$869$	−2.68651e9	+	1.52360e10i	−0.138873	+	0.787591i
$870$		0			0
$871$	−3.64333e9	+	1.32606e9i	−0.186825	+	0.0679988i
$872$		0			0
$873$	−7.90537e10			−4.02135
$874$		0			0
$875$	−7.86468e9			−0.396874
$876$		0			0
$877$	−1.25668e9	+	4.57394e8i	−0.0629109	+	0.0228977i	−0.373284	−	0.927717i	$-0.621768\pi$
$877$	−1.25668e9	+	4.57394e8i	−0.0629109	+	0.0228977i	0.310373	+	0.950615i	$0.399546\pi$
$878$		0			0
$879$	5.81307e9	−	3.29676e10i	0.288698	−	1.63729i
$880$		0			0
$881$	1.61723e10	+	2.80113e10i	0.796814	+	1.38012i	0.921681	+	0.387949i	$0.126816\pi$
$881$	1.61723e10	+	2.80113e10i	0.796814	+	1.38012i	−0.124867	+	0.992173i	$0.539850\pi$
$882$		0			0
$883$	1.81748e10	−	1.52505e10i	0.888397	−	0.745454i	−0.0794910	−	0.996836i	$-0.525329\pi$
$883$	1.81748e10	−	1.52505e10i	0.888397	−	0.745454i	0.967888	+	0.251382i	$0.0808850\pi$
$884$		0			0
$885$	2.52670e10	−	4.37637e10i	1.22533	−	2.12233i
$886$		0			0
$887$	−5.80220e9	−	2.11183e9i	−0.279164	−	0.101607i	0.198644	−	0.980072i	$-0.436346\pi$
$887$	−5.80220e9	−	2.11183e9i	−0.279164	−	0.101607i	−0.477808	+	0.878464i	$0.658569\pi$
$888$		0			0
$889$	2.18557e8	+	1.23950e9i	0.0104330	+	0.0591683i
$890$		0			0
$891$	5.19565e10	+	4.35967e10i	2.46075	+	2.06482i
$892$		0			0
$893$	−1.72389e9	−	2.82200e9i	−0.0810082	−	0.132610i
$894$		0			0
$895$	4.76842e10	+	4.00118e10i	2.22328	+	1.86555i
$896$		0			0
$897$	9.33198e9	+	5.29243e10i	0.431718	+	2.44840i
$898$		0			0
$899$	7.29864e9	+	2.65649e9i	0.335029	+	0.121941i
$900$		0			0
$901$	−1.39643e10	+	2.41869e10i	−0.636038	+	1.10165i
$902$		0			0
$903$	−7.38875e9	+	6.19990e9i	−0.333937	+	0.280206i
$904$		0			0
$905$	1.79973e10	+	3.11722e10i	0.807116	+	1.39797i
$906$		0			0
$907$	3.16166e9	−	1.79307e10i	0.140699	−	0.797941i	−0.830022	−	0.557730i	$-0.811672\pi$
$907$	3.16166e9	−	1.79307e10i	0.140699	−	0.797941i	0.970721	−	0.240211i	$-0.0772165\pi$
$908$		0			0
$909$	−8.85294e10	+	3.22221e10i	−3.90943	+	1.42292i
$910$		0			0
$911$	3.79108e9			0.166130			0.0830651	−	0.996544i	$-0.473529\pi$
$911$	3.79108e9			0.166130			0.0830651	+	0.996544i	$0.473529\pi$
$912$		0			0
$913$	−1.84469e10			−0.802185
$914$		0			0
$915$	1.34257e11	−	4.88655e10i	5.79379	−	2.10877i
$916$		0			0
$917$	3.43650e8	−	1.94894e9i	0.0147171	−	0.0834651i
$918$		0			0
$919$	−1.88668e9	−	3.26783e9i	−0.0801851	−	0.138885i	0.823144	−	0.567832i	$-0.192218\pi$
$919$	−1.88668e9	−	3.26783e9i	−0.0801851	−	0.138885i	−0.903329	+	0.428948i	$0.858884\pi$
$920$		0			0
$921$	1.54577e10	−	1.29706e10i	0.651983	−	0.547079i
$922$		0			0
$923$	5.71257e9	−	9.89446e9i	0.239125	−	0.414177i
$924$		0			0
$925$	4.10764e10	+	1.49506e10i	1.70646	+	0.621101i
$926$		0			0
$927$	8.11007e9	+	4.59945e10i	0.334384	+	1.89639i
$928$		0			0
$929$	−1.13143e10	−	9.49379e9i	−0.462990	−	0.388494i	0.381240	−	0.924476i	$-0.375497\pi$
$929$	−1.13143e10	−	9.49379e9i	−0.462990	−	0.388494i	−0.844230	+	0.535982i	$0.819942\pi$
$930$		0			0
$931$	−1.57589e10	−	1.25713e10i	−0.640033	−	0.510572i
$932$		0			0
$933$	−2.33933e9	−	1.96293e9i	−0.0942986	−	0.0791259i
$934$		0			0
$935$	−8.44707e9	−	4.79057e10i	−0.337960	−	1.91667i
$936$		0			0
$937$	2.05185e10	+	7.46811e9i	0.814810	+	0.296566i	0.715609	−	0.698501i	$-0.246149\pi$
$937$	2.05185e10	+	7.46811e9i	0.814810	+	0.296566i	0.0992006	+	0.995067i	$0.468371\pi$
$938$		0			0
$939$	−2.77510e10	+	4.80662e10i	−1.09383	+	1.89457i
$940$		0			0
$941$	−7.28884e9	+	6.11607e9i	−0.285164	+	0.239281i	−0.774137	−	0.633018i	$-0.781816\pi$
$941$	−7.28884e9	+	6.11607e9i	−0.285164	+	0.239281i	0.488973	+	0.872299i	$0.337372\pi$
$942$		0			0
$943$	−6.59301e9	−	1.14194e10i	−0.256031	−	0.443459i
$944$		0			0
$945$	1.03123e10	−	5.84839e10i	0.397506	−	2.25437i
$946$		0			0
$947$	−2.99665e10	+	1.09069e10i	−1.14660	+	0.417328i	−0.844293	−	0.535883i	$-0.819979\pi$
$947$	−2.99665e10	+	1.09069e10i	−1.14660	+	0.417328i	−0.302307	+	0.953211i	$0.597757\pi$
$948$		0			0
$949$	−1.09358e10			−0.415353
$950$		0			0
$951$	−6.03959e10			−2.27706
$952$		0			0
$953$	1.70002e10	−	6.18757e9i	0.636252	−	0.231577i	−0.00369811	−	0.999993i	$-0.501177\pi$
$953$	1.70002e10	−	6.18757e9i	0.636252	−	0.231577i	0.639950	+	0.768416i	$0.278955\pi$
$954$		0			0
$955$	−5.89933e9	+	3.34568e10i	−0.219175	+	1.24300i
$956$		0			0
$957$	7.20614e9	+	1.24814e10i	0.265773	+	0.460332i
$958$		0			0
$959$	−4.10520e9	+	3.44468e9i	−0.150304	+	0.126120i
$960$		0			0
$961$	−3.33830e9	+	5.78211e9i	−0.121337	+	0.210162i
$962$		0			0
$963$	−3.27396e10	−	1.19162e10i	−1.18136	−	0.429978i
$964$		0			0
$965$	−1.14917e10	−	6.51728e10i	−0.411661	−	2.33465i
$966$		0			0
$967$	9.77435e9	+	8.20166e9i	0.347613	+	0.291682i	0.799831	−	0.600226i	$-0.204923\pi$
$967$	9.77435e9	+	8.20166e9i	0.347613	+	0.291682i	−0.452218	+	0.891907i	$0.649367\pi$
$968$		0			0
$969$	3.68685e10	−	6.76769e10i	1.30174	−	2.38950i
$970$		0			0
$971$	−2.20770e10	−	1.85248e10i	−0.773879	−	0.649362i	0.167820	−	0.985818i	$-0.446327\pi$
$971$	−2.20770e10	−	1.85248e10i	−0.773879	−	0.649362i	−0.941699	+	0.336456i	$0.890772\pi$
$972$		0			0
$973$	−1.97270e9	−	1.11877e10i	−0.0686540	−	0.389356i
$974$		0			0
$975$	−1.01236e11	−	3.68468e10i	−3.49799	−	1.27316i
$976$		0			0
$977$	−1.33723e10	+	2.31615e10i	−0.458749	+	0.794577i	−0.998895	−	0.0469947i	$-0.985036\pi$
$977$	−1.33723e10	+	2.31615e10i	−0.458749	+	0.794577i	0.540146	+	0.841571i	$0.318369\pi$
$978$		0			0
$979$	2.50092e10	−	2.09852e10i	0.851843	−	0.714781i
$980$		0			0
$981$	−4.03201e10	−	6.98365e10i	−1.36358	−	2.36179i
$982$		0			0
$983$	−1.07202e9	+	6.07973e9i	−0.0359970	+	0.204149i	−0.997502	−	0.0706384i	$-0.977496\pi$
$983$	−1.07202e9	+	6.07973e9i	−0.0359970	+	0.204149i	0.961505	+	0.274787i	$0.0886075\pi$
$984$		0			0
$985$	5.82223e9	−	2.11912e9i	0.194117	−	0.0706527i
$986$		0			0
$987$	−3.86107e9			−0.127820
$988$		0			0
$989$	1.70168e10			0.559360
$990$		0			0
$991$	2.91092e10	−	1.05949e10i	0.950108	−	0.345811i	0.179959	−	0.983674i	$-0.442404\pi$
$991$	2.91092e10	−	1.05949e10i	0.950108	−	0.345811i	0.770150	+	0.637863i	$0.220181\pi$
$992$		0			0
$993$	1.42198e10	−	8.06443e10i	0.460861	−	2.61367i
$994$		0			0
$995$	2.59172e9	+	4.48900e9i	0.0834080	+	0.144467i
$996$		0			0
$997$	−3.34730e9	+	2.80871e9i	−0.106970	+	0.0897583i	−0.694704	−	0.719296i	$-0.744465\pi$
$997$	−3.34730e9	+	2.80871e9i	−0.106970	+	0.0897583i	0.587734	+	0.809054i	$0.300020\pi$
$998$		0			0
$999$	−6.06036e10	+	1.04968e11i	−1.92318	+	3.33104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.73.12	yes	72
19.6	even	9	inner	76.8.i.a.25.12	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.25.12	✓	72	19.6	even	9	inner
76.8.i.a.73.12	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)

\(f(q)\)	\(=\)	\(q+(84.9007 - 30.9013i) q^{3} +(-77.9653 + 442.163i) q^{5} +(-193.184 - 334.604i) q^{7} +(4577.90 - 3841.32i) q^{9} +O(q^{10})\)	\(q+(84.9007 - 30.9013i) q^{3} +(-77.9653 + 442.163i) q^{5} +(-193.184 - 334.604i) q^{7} +(4577.90 - 3841.32i) q^{9} +(-1898.74 + 3288.71i) q^{11} +(9075.63 + 3303.26i) q^{13} +(7044.12 + 39949.2i) q^{15} +(21855.6 + 18339.1i) q^{17} +(4460.62 - 29563.1i) q^{19} +(-26741.1 - 22438.5i) q^{21} +(10694.4 + 60651.1i) q^{23} +(-116016. - 42226.4i) q^{25} +(171168. - 296472. i) q^{27} +(32178.5 - 27000.9i) q^{29} +(92451.6 + 160131. i) q^{31} +(-59578.7 + 337888. i) q^{33} +(163011. - 59331.2i) q^{35} -354058. q^{37} +872603. q^{39} +(-201193. + 73228.2i) q^{41} +(47980.1 - 272109. i) q^{43} +(1.34157e6 + 2.32367e6i) q^{45} +(84729.7 - 71096.6i) q^{47} +(337132. - 583929. i) q^{49} +(2.42226e6 + 881632. i) q^{51} +(169985. + 964033. i) q^{53} +(-1.30611e6 - 1.09596e6i) q^{55} +(-534828. - 2.64777e6i) q^{57} +(-954290. - 800744. i) q^{59} +(-611595. - 3.46853e6i) q^{61} +(-2.16970e6 - 789705. i) q^{63} +(-2.16816e6 + 3.75537e6i) q^{65} +(-307522. + 258042. i) q^{67} +(2.78217e6 + 4.81885e6i) q^{69} +(205419. - 1.16499e6i) q^{71} +(-1.06401e6 + 387266. i) q^{73} -1.11547e7 q^{75} +1.46722e6 q^{77} +(3.82833e6 - 1.39340e6i) q^{79} +(3.10142e6 - 1.75890e7i) q^{81} +(2.42883e6 + 4.20686e6i) q^{83} +(-9.81284e6 + 8.23395e6i) q^{85} +(1.89761e6 - 3.28676e6i) q^{87} +(-8.07859e6 - 2.94037e6i) q^{89} +(-647980. - 3.67488e6i) q^{91} +(1.27975e7 + 1.07384e7i) q^{93} +(1.27239e7 + 4.27721e6i) q^{95} +(-1.01336e7 - 8.50309e6i) q^{97} +(3.94074e6 + 2.23491e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 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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