LMFDB - Embedded newform 76.8.i.a.17.5

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			17.5
Character	$\chi$	$=$	76.17
Dual form			76.8.i.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.5751 - 8.87354i) q^{3} +(-438.581 + 159.630i) q^{5} +(-408.557 - 707.641i) q^{7} +(-346.676 - 1966.10i) q^{9} +O(q^{10})$	\(q+(-10.5751 - 8.87354i) q^{3} +(-438.581 + 159.630i) q^{5} +(-408.557 - 707.641i) q^{7} +(-346.676 - 1966.10i) q^{9} +(-1159.36 + 2008.07i) q^{11} +(2926.23 - 2455.39i) q^{13} +(6054.51 + 2203.66i) q^{15} +(-4990.10 + 28300.3i) q^{17} +(29004.3 + 7254.26i) q^{19} +(-1958.76 + 11108.7i) q^{21} +(-18305.4 - 6662.61i) q^{23} +(107024. - 89803.7i) q^{25} +(-28875.7 + 50014.1i) q^{27} +(-25424.2 - 144188. i) q^{29} +(142623. + 247030. i) q^{31} +(30079.0 - 10947.9i) q^{33} +(292146. + 245140. i) q^{35} +247257. q^{37} -52733.1 q^{39} +(223779. + 187773. i) q^{41} +(270435. - 98430.2i) q^{43} +(465894. + 806952. i) q^{45} +(44523.6 + 252506. i) q^{47} +(77934.4 - 134986. i) q^{49} +(303894. - 254998. i) q^{51} +(-1.11101e6 - 404374. i) q^{53} +(187924. - 1.06577e6i) q^{55} +(-242351. - 334085. i) q^{57} +(26019.6 - 147564. i) q^{59} +(2.37427e6 + 864164. i) q^{61} +(-1.24965e6 + 1.04858e6i) q^{63} +(-891430. + 1.54400e6i) q^{65} +(-401947. - 2.27956e6i) q^{67} +(134460. + 232891. i) q^{69} +(-553658. + 201515. i) q^{71} +(3.10026e6 + 2.60142e6i) q^{73} -1.92866e6 q^{75} +1.89466e6 q^{77} +(-4.73492e6 - 3.97307e6i) q^{79} +(-3.35371e6 + 1.22065e6i) q^{81} +(-2.68756e6 - 4.65498e6i) q^{83} +(-2.32902e6 - 1.32085e7i) q^{85} +(-1.01060e6 + 1.75040e6i) q^{87} +(-7.50525e6 + 6.29766e6i) q^{89} +(-2.93307e6 - 1.06755e6i) q^{91} +(683783. - 3.87793e6i) q^{93} +(-1.38787e7 + 1.44838e6i) q^{95} +(-2.13055e6 + 1.20830e7i) q^{97} +(4.34999e6 + 1.58327e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−10.5751	−	8.87354i	−0.226130	−	0.189746i	0.522682	−	0.852527i	$-0.324931\pi$
$3$	−10.5751	−	8.87354i	−0.226130	−	0.189746i	−0.748813	+	0.662782i	$0.769376\pi$
$4$		0			0
$5$	−438.581	+	159.630i	−1.56911	+	0.571111i	−0.972801	−	0.231642i	$-0.925590\pi$
$5$	−438.581	+	159.630i	−1.56911	+	0.571111i	−0.596312	+	0.802752i	$0.703368\pi$
$6$		0			0
$7$	−408.557	−	707.641i	−0.450204	−	0.779776i	0.548195	−	0.836351i	$-0.315315\pi$
$7$	−408.557	−	707.641i	−0.450204	−	0.779776i	−0.998398	+	0.0565750i	$0.981982\pi$
$8$		0			0
$9$	−346.676	−	1966.10i	−0.158517	−	0.898993i
$10$		0			0
$11$	−1159.36	+	2008.07i	−0.262630	+	0.454888i	−0.966940	−	0.255004i	$-0.917923\pi$
$11$	−1159.36	+	2008.07i	−0.262630	+	0.454888i	0.704310	+	0.709893i	$0.251257\pi$
$12$		0			0
$13$	2926.23	−	2455.39i	0.369408	−	0.309970i	−0.439119	−	0.898429i	$-0.644710\pi$
$13$	2926.23	−	2455.39i	0.369408	−	0.309970i	0.808527	+	0.588459i	$0.200265\pi$
$14$		0			0
$15$	6054.51	+	2203.66i	0.463190	+	0.168587i
$16$		0			0
$17$	−4990.10	+	28300.3i	−0.246342	+	1.39707i	0.571014	+	0.820941i	$0.306550\pi$
$17$	−4990.10	+	28300.3i	−0.246342	+	1.39707i	−0.817355	+	0.576134i	$0.804561\pi$
$18$		0			0
$19$	29004.3	+	7254.26i	0.970117	+	0.242636i
$19$	29004.3	+	7254.26i	0.970117	+	0.242636i
$20$		0			0
$21$	−1958.76	+	11108.7i	−0.0461545	+	0.261755i
$22$		0			0
$23$	−18305.4	−	6662.61i	−0.313712	−	0.114182i	0.180366	−	0.983600i	$-0.442272\pi$
$23$	−18305.4	−	6662.61i	−0.313712	−	0.114182i	−0.494078	+	0.869418i	$0.664494\pi$
$24$		0			0
$25$	107024.	−	89803.7i	1.36991	−	1.14949i
$26$		0			0
$27$	−28875.7	+	50014.1i	−0.282331	+	0.489012i
$28$		0			0
$29$	−25424.2	−	144188.i	−0.193578	−	1.09783i	−0.914430	−	0.404744i	$-0.867361\pi$
$29$	−25424.2	−	144188.i	−0.193578	−	1.09783i	0.720852	−	0.693089i	$-0.243751\pi$
$30$		0			0
$31$	142623.	+	247030.i	0.859850	+	1.48930i	0.872071	+	0.489379i	$0.162777\pi$
$31$	142623.	+	247030.i	0.859850	+	1.48930i	−0.0122205	+	0.999925i	$0.503890\pi$
$32$		0			0
$33$	30079.0	−	10947.9i	0.145702	−	0.0530311i
$34$		0			0
$35$	292146.	+	245140.i	1.15176	+	0.966441i
$36$		0			0
$37$	247257.			0.802496			0.401248	−	0.915969i	$-0.368576\pi$
$37$	247257.			0.802496			0.401248	+	0.915969i	$0.368576\pi$
$38$		0			0
$39$	−52733.1			−0.142350
$40$		0			0
$41$	223779.	+	187773.i	0.507080	+	0.425490i	0.860100	−	0.510125i	$-0.170401\pi$
$41$	223779.	+	187773.i	0.507080	+	0.425490i	−0.353020	+	0.935616i	$0.614845\pi$
$42$		0			0
$43$	270435.	−	98430.2i	0.518708	−	0.188794i	−0.0693814	−	0.997590i	$-0.522103\pi$
$43$	270435.	−	98430.2i	0.518708	−	0.188794i	0.588089	+	0.808796i	$0.299880\pi$
$44$		0			0
$45$	465894.	+	806952.i	0.762155	+	1.32009i
$46$		0			0
$47$	44523.6	+	252506.i	0.0625529	+	0.354755i	0.999978	+	0.00656928i	$0.00209108\pi$
$47$	44523.6	+	252506.i	0.0625529	+	0.354755i	−0.937426	+	0.348186i	$0.886798\pi$
$48$		0			0
$49$	77934.4	−	134986.i	0.0946331	−	0.163909i
$50$		0			0
$51$	303894.	−	254998.i	0.320795	−	0.269179i
$52$		0			0
$53$	−1.11101e6	−	404374.i	−1.02507	−	0.373094i	−0.225866	−	0.974158i	$-0.572521\pi$
$53$	−1.11101e6	−	404374.i	−1.02507	−	0.373094i	−0.799201	+	0.601064i	$0.794743\pi$
$54$		0			0
$55$	187924.	−	1.06577e6i	0.152305	−	0.863762i
$56$		0			0
$57$	−242351.	−	334085.i	−0.173334	−	0.238943i
$58$		0			0
$59$	26019.6	−	147564.i	0.0164937	−	0.0935405i	−0.975450	−	0.220222i	$-0.929322\pi$
$59$	26019.6	−	147564.i	0.0164937	−	0.0935405i	0.991943	+	0.126682i	$0.0404328\pi$
$60$		0			0
$61$	2.37427e6	+	864164.i	1.33929	+	0.487463i	0.909590	−	0.415506i	$-0.136396\pi$
$61$	2.37427e6	+	864164.i	1.33929	+	0.487463i	0.429704	+	0.902970i	$0.358618\pi$
$62$		0			0
$63$	−1.24965e6	+	1.04858e6i	−0.629648	+	0.528338i
$64$		0			0
$65$	−891430.	+	1.54400e6i	−0.402616	+	0.697351i
$66$		0			0
$67$	−401947.	−	2.27956e6i	−0.163270	−	0.925952i	−0.950830	−	0.309713i	$-0.899767\pi$
$67$	−401947.	−	2.27956e6i	−0.163270	−	0.925952i	0.787560	−	0.616238i	$-0.211344\pi$
$68$		0			0
$69$	134460.	+	232891.i	0.0492743	+	0.0853456i
$70$		0			0
$71$	−553658.	+	201515.i	−0.183585	+	0.0668195i	−0.432177	−	0.901789i	$-0.642254\pi$
$71$	−553658.	+	201515.i	−0.183585	+	0.0668195i	0.248592	+	0.968608i	$0.420032\pi$
$72$		0			0
$73$	3.10026e6	+	2.60142e6i	0.932755	+	0.782674i	0.976310	−	0.216377i	$-0.0694239\pi$
$73$	3.10026e6	+	2.60142e6i	0.932755	+	0.782674i	−0.0435549	+	0.999051i	$0.513868\pi$
$74$		0			0
$75$	−1.92866e6			−0.527888
$76$		0			0
$77$	1.89466e6			0.472948
$78$		0			0
$79$	−4.73492e6	−	3.97307e6i	−1.08048	−	0.906633i	−0.0845224	−	0.996422i	$-0.526936\pi$
$79$	−4.73492e6	−	3.97307e6i	−1.08048	−	0.906633i	−0.995961	+	0.0897885i	$0.971381\pi$
$80$		0			0
$81$	−3.35371e6	+	1.22065e6i	−0.701178	+	0.255208i
$82$		0			0
$83$	−2.68756e6	−	4.65498e6i	−0.515922	−	0.893604i	−0.999829	−	0.0184841i	$-0.994116\pi$
$83$	−2.68756e6	−	4.65498e6i	−0.515922	−	0.893604i	0.483907	−	0.875120i	$-0.339217\pi$
$84$		0			0
$85$	−2.32902e6	−	1.32085e7i	−0.411346	−	2.33286i
$86$		0			0
$87$	−1.01060e6	+	1.75040e6i	−0.164536	+	0.284984i
$88$		0			0
$89$	−7.50525e6	+	6.29766e6i	−1.12850	+	0.946921i	−0.999002	−	0.0446589i	$-0.985780\pi$
$89$	−7.50525e6	+	6.29766e6i	−1.12850	+	0.946921i	−0.129494	+	0.991580i	$0.541335\pi$
$90$		0			0
$91$	−2.93307e6	−	1.06755e6i	−0.408016	−	0.148506i
$92$		0			0
$93$	683783.	−	3.87793e6i	0.0881512	−	0.499930i
$94$		0			0
$95$	−1.38787e7	+	1.44838e6i	−1.66080	+	0.173321i
$96$		0			0
$97$	−2.13055e6	+	1.20830e7i	−0.237023	+	1.34423i	0.601288	+	0.799033i	$0.294655\pi$
$97$	−2.13055e6	+	1.20830e7i	−0.237023	+	1.34423i	−0.838311	+	0.545193i	$0.816457\pi$
$98$		0			0
$99$	4.34999e6	+	1.58327e6i	0.450573	+	0.163995i
$100$		0			0
$101$	5.24058e6	−	4.39737e6i	0.506121	−	0.424686i	−0.353640	−	0.935381i	$-0.615056\pi$
$101$	5.24058e6	−	4.39737e6i	0.506121	−	0.424686i	0.859762	+	0.510695i	$0.170612\pi$
$102$		0			0
$103$	5.25954e6	−	9.10978e6i	0.474261	−	0.821444i	−0.525305	−	0.850914i	$-0.676049\pi$
$103$	5.25954e6	−	9.10978e6i	0.474261	−	0.821444i	0.999566	+	0.0294704i	$0.00938208\pi$
$104$		0			0
$105$	−914209.	−	5.18474e6i	−0.0770696	−	0.437083i
$106$		0			0
$107$	1.03113e7	+	1.78597e7i	0.813713	+	1.40939i	0.910248	+	0.414063i	$0.135891\pi$
$107$	1.03113e7	+	1.78597e7i	0.813713	+	1.40939i	−0.0965348	+	0.995330i	$0.530776\pi$
$108$		0			0
$109$	3.08051e6	−	1.12122e6i	0.227840	−	0.0829271i	−0.225577	−	0.974225i	$-0.572427\pi$
$109$	3.08051e6	−	1.12122e6i	0.227840	−	0.0829271i	0.453418	+	0.891298i	$0.350205\pi$
$110$		0			0
$111$	−2.61476e6	−	2.19405e6i	−0.181469	−	0.152270i
$112$		0			0
$113$	8.79160e6			0.573183			0.286592	−	0.958053i	$-0.407478\pi$
$113$	8.79160e6			0.573183			0.286592	+	0.958053i	$0.407478\pi$
$114$		0			0
$115$	9.09194e6			0.557460
$116$		0			0
$117$	−5.84200e6	−	4.90202e6i	−0.337218	−	0.282960i
$118$		0			0
$119$	2.20652e7	−	8.03107e6i	1.20031	−	0.436877i
$120$		0			0
$121$	7.05535e6	+	1.22202e7i	0.362051	+	0.627091i
$122$		0			0
$123$	−700270.	−	3.97143e6i	−0.0339311	−	0.192433i
$124$		0			0
$125$	−1.43717e7	+	2.48924e7i	−0.658145	+	1.13994i
$126$		0			0
$127$	−2.16654e7	+	1.81794e7i	−0.938541	+	0.787530i	−0.977331	−	0.211718i	$-0.932094\pi$
$127$	−2.16654e7	+	1.81794e7i	−0.938541	+	0.787530i	0.0387895	+	0.999247i	$0.487650\pi$
$128$		0			0
$129$	−3.73329e6	−	1.35881e6i	−0.153119	−	0.0557306i
$130$		0			0
$131$	3.79950e6	−	2.15481e7i	0.147665	−	0.837449i	−0.817524	−	0.575895i	$-0.804654\pi$
$131$	3.79950e6	−	2.15481e7i	0.147665	−	0.837449i	0.965189	−	0.261555i	$-0.0842351\pi$
$132$		0			0
$133$	−6.71648e6	−	2.34884e7i	−0.247549	−	0.865710i
$134$		0			0
$135$	4.68054e6	−	2.65446e7i	0.163730	−	0.928557i
$136$		0			0
$137$	5.40575e7	+	1.96753e7i	1.79611	+	0.653732i	0.998737	+	0.0502503i	$0.0160019\pi$
$137$	5.40575e7	+	1.96753e7i	1.79611	+	0.653732i	0.797377	+	0.603482i	$0.206220\pi$
$138$		0			0
$139$	−1.49186e7	+	1.25182e7i	−0.471168	+	0.395357i	−0.847221	−	0.531241i	$-0.821726\pi$
$139$	−1.49186e7	+	1.25182e7i	−0.471168	+	0.395357i	0.376052	+	0.926598i	$0.377281\pi$
$140$		0			0
$141$	1.76978e6	−	3.06535e6i	0.0531682	−	0.0920901i
$142$		0			0
$143$	1.53806e6	+	8.72276e6i	0.0439842	+	0.249447i
$144$		0			0
$145$	3.41673e7	+	5.91796e7i	0.930729	+	1.61207i
$146$		0			0
$147$	−2.02197e6	+	735937.i	−0.0525006	+	0.0191086i
$148$		0			0
$149$	4.61072e7	+	3.86886e7i	1.14187	+	0.958144i	0.999498	−	0.0316692i	$-0.0100823\pi$
$149$	4.61072e7	+	3.86886e7i	1.14187	+	0.958144i	0.142373	+	0.989813i	$0.454527\pi$
$150$		0			0
$151$	4.78222e7			1.13034			0.565172	−	0.824973i	$-0.308810\pi$
$151$	4.78222e7			1.13034			0.565172	+	0.824973i	$0.308810\pi$
$152$		0			0
$153$	5.73711e7			1.29501
$154$		0			0
$155$	−1.01985e8	−	8.55756e7i	−2.19976	−	1.84582i
$156$		0			0
$157$	2.85680e7	−	1.03979e7i	0.589157	−	0.214436i	−0.0302015	−	0.999544i	$-0.509615\pi$
$157$	2.85680e7	−	1.03979e7i	0.589157	−	0.214436i	0.619359	+	0.785108i	$0.287393\pi$
$158$		0			0
$159$	8.16078e6	+	1.41349e7i	0.161006	+	0.278870i
$160$		0			0
$161$	2.76405e6	+	1.56757e7i	0.0521981	+	0.296030i
$162$		0			0
$163$	−4.35492e7	+	7.54294e7i	−0.787632	+	1.36422i	0.139782	+	0.990182i	$0.455360\pi$
$163$	−4.35492e7	+	7.54294e7i	−0.787632	+	1.36422i	−0.927414	+	0.374036i	$0.877974\pi$
$164$		0			0
$165$	−1.14445e7	+	9.60305e6i	−0.198336	+	0.166424i
$166$		0			0
$167$	−1.72734e7	−	6.28702e6i	−0.286993	−	0.104457i	0.194512	−	0.980900i	$-0.437688\pi$
$167$	−1.72734e7	−	6.28702e6i	−0.286993	−	0.104457i	−0.481505	+	0.876443i	$0.659910\pi$
$168$		0			0
$169$	−8.36233e6	+	4.74251e7i	−0.133267	+	0.755797i
$170$		0			0
$171$	4.20749e6	−	5.95401e7i	0.0643483	−	0.910591i
$172$		0			0
$173$	−1.56675e6	+	8.88550e6i	−0.0230059	+	0.130473i	−0.994148	−	0.108030i	$-0.965546\pi$
$173$	−1.56675e6	+	8.88550e6i	−0.0230059	+	0.130473i	0.971142	+	0.238503i	$0.0766568\pi$
$174$		0			0
$175$	−1.07274e8	−	3.90446e7i	−1.51308	−	0.550716i
$176$		0			0
$177$	−1.58458e6	+	1.32962e6i	−0.0214787	+	0.0180227i
$178$		0			0
$179$	5.75697e7	−	9.97136e7i	0.750254	−	1.29948i	−0.197446	−	0.980314i	$-0.563265\pi$
$179$	5.75697e7	−	9.97136e7i	0.750254	−	1.29948i	0.947700	−	0.319164i	$-0.103402\pi$
$180$		0			0
$181$	−1.53907e7	−	8.72847e7i	−0.192922	−	1.09412i	−0.915347	−	0.402666i	$-0.868084\pi$
$181$	−1.53907e7	−	8.72847e7i	−0.192922	−	1.09412i	0.722425	−	0.691450i	$-0.243028\pi$
$182$		0			0
$183$	−1.74399e7	−	3.02068e7i	−0.210361	−	0.364356i
$184$		0			0
$185$	−1.08442e8	+	3.94698e7i	−1.25921	+	0.458314i
$186$		0			0
$187$	−5.10437e7	−	4.28307e7i	−0.570816	−	0.478972i
$188$		0			0
$189$	4.71894e7			0.508426
$190$		0			0
$191$	4.36900e7			0.453697			0.226848	−	0.973930i	$-0.427158\pi$
$191$	4.36900e7			0.453697			0.226848	+	0.973930i	$0.427158\pi$
$192$		0			0
$193$	1.46356e7	+	1.22807e7i	0.146541	+	0.122962i	0.713111	−	0.701051i	$-0.247286\pi$
$193$	1.46356e7	+	1.22807e7i	0.146541	+	0.122962i	−0.566570	+	0.824014i	$0.691730\pi$
$194$		0			0
$195$	2.31277e7	−	8.41780e6i	0.223363	−	0.0812976i
$196$		0			0
$197$	1.24584e7	+	2.15785e7i	0.116099	+	0.201090i	0.918219	−	0.396074i	$-0.129628\pi$
$197$	1.24584e7	+	2.15785e7i	0.116099	+	0.201090i	−0.802119	+	0.597164i	$0.796294\pi$
$198$		0			0
$199$	−8.02023e6	−	4.54850e7i	−0.0721442	−	0.409150i	−0.999397	−	0.0347147i	$-0.988948\pi$
$199$	−8.02023e6	−	4.54850e7i	−0.0721442	−	0.409150i	0.927253	−	0.374435i	$-0.122163\pi$
$200$		0			0
$201$	−1.59771e7	+	2.76732e7i	−0.138775	+	0.240366i
$202$		0			0
$203$	−9.16461e7	+	7.69002e7i	−0.768914	+	0.645195i
$204$		0			0
$205$	−1.28119e8	−	4.66317e7i	−1.03867	−	0.378044i
$206$		0			0
$207$	−6.75331e6	+	3.82999e7i	−0.0529201	+	0.300125i
$208$		0			0
$209$	−4.81935e7	+	4.98324e7i	−0.365154	+	0.377572i
$210$		0			0
$211$	−2.29924e7	+	1.30397e8i	−0.168499	+	0.955603i	0.776885	+	0.629643i	$0.216799\pi$
$211$	−2.29924e7	+	1.30397e8i	−0.168499	+	0.955603i	−0.945383	+	0.325961i	$0.894312\pi$
$212$		0			0
$213$	7.64313e6	+	2.78187e6i	0.0541929	+	0.0197246i
$214$		0			0
$215$	−1.02895e8	+	8.63392e7i	−0.706089	+	0.592479i
$216$		0			0
$217$	1.16539e8	−	2.01851e8i	0.774216	−	1.34098i
$218$		0			0
$219$	−9.70160e6	−	5.50205e7i	−0.0624150	−	0.353973i
$220$		0			0
$221$	5.48862e7	+	9.50657e7i	0.342050	+	0.592449i
$222$		0			0
$223$	2.08288e8	−	7.58105e7i	1.25776	−	0.457786i	0.374741	−	0.927130i	$-0.377732\pi$
$223$	2.08288e8	−	7.58105e7i	1.25776	−	0.457786i	0.883016	+	0.469344i	$0.155509\pi$
$224$		0			0
$225$	−2.13665e8	−	1.79287e8i	−1.25053	−	1.04932i
$226$		0			0
$227$	−2.47801e8			−1.40609			−0.703044	−	0.711146i	$-0.748176\pi$
$227$	−2.47801e8			−1.40609			−0.703044	+	0.711146i	$0.748176\pi$
$228$		0			0
$229$	8.00428e7			0.440451			0.220226	−	0.975449i	$-0.429321\pi$
$229$	8.00428e7			0.440451			0.220226	+	0.975449i	$0.429321\pi$
$230$		0			0
$231$	−2.00362e7	−	1.68123e7i	−0.106948	−	0.0897400i
$232$		0			0
$233$	−1.31880e8	+	4.80003e7i	−0.683018	+	0.248598i	−0.660143	−	0.751140i	$-0.729504\pi$
$233$	−1.31880e8	+	4.80003e7i	−0.683018	+	0.248598i	−0.0228751	+	0.999738i	$0.507282\pi$
$234$		0			0
$235$	−5.98347e7	−	1.03637e8i	−0.300757	−	0.520926i
$236$		0			0
$237$	1.48169e7	+	8.40311e7i	0.0723002	+	0.410035i
$238$		0			0
$239$	2.20904e7	−	3.82617e7i	0.104667	−	0.181289i	−0.808935	−	0.587898i	$-0.799956\pi$
$239$	2.20904e7	−	3.82617e7i	0.104667	−	0.181289i	0.913602	+	0.406609i	$0.133289\pi$
$240$		0			0
$241$	2.73969e8	−	2.29888e8i	1.26079	−	1.05793i	0.265192	−	0.964196i	$-0.414565\pi$
$241$	2.73969e8	−	2.29888e8i	1.26079	−	1.05793i	0.995597	−	0.0937320i	$-0.0298797\pi$
$242$		0			0
$243$	1.64982e8	+	6.00487e7i	0.737591	+	0.268461i
$244$		0			0
$245$	−1.26326e7	+	7.16431e7i	−0.0548797	+	0.311238i
$246$		0			0
$247$	1.02685e8	−	4.99893e7i	0.433579	−	0.211076i
$248$		0			0
$249$	−1.28851e7	+	7.30750e7i	−0.0528920	+	0.299965i
$250$		0			0
$251$	2.71288e8	+	9.87408e7i	1.08286	+	0.394129i	0.820972	−	0.570969i	$-0.193432\pi$
$251$	2.71288e8	+	9.87408e7i	1.08286	+	0.394129i	0.261890	+	0.965098i	$0.415654\pi$
$252$		0			0
$253$	3.46015e7	−	2.90341e7i	0.134330	−	0.112716i
$254$		0			0
$255$	−9.25768e7	+	1.60348e8i	−0.349632	+	0.605581i
$256$		0			0
$257$	3.95628e7	+	2.24372e8i	0.145386	+	0.824523i	0.967057	+	0.254561i	$0.0819309\pi$
$257$	3.95628e7	+	2.24372e8i	0.145386	+	0.824523i	−0.821671	+	0.569962i	$0.806958\pi$
$258$		0			0
$259$	−1.01019e8	−	1.74969e8i	−0.361287	−	0.625767i
$260$		0			0
$261$	−2.74674e8	+	9.99731e7i	−0.956259	+	0.348050i
$262$		0			0
$263$	3.82105e8	+	3.20624e8i	1.29520	+	1.08680i	0.990953	+	0.134212i	$0.0428502\pi$
$263$	3.82105e8	+	3.20624e8i	1.29520	+	1.08680i	0.304250	+	0.952592i	$0.401594\pi$
$264$		0			0
$265$	5.51818e8			1.82152
$266$		0			0
$267$	1.35251e8			0.434862
$268$		0			0
$269$	3.30287e8	+	2.77144e8i	1.03457	+	0.868105i	0.991387	−	0.130962i	$-0.0418067\pi$
$269$	3.30287e8	+	2.77144e8i	1.03457	+	0.868105i	0.0431798	+	0.999067i	$0.486251\pi$
$270$		0			0
$271$	−5.24435e8	+	1.90879e8i	−1.60066	+	0.582593i	−0.979562	−	0.201141i	$-0.935535\pi$
$271$	−5.24435e8	+	1.90879e8i	−1.60066	+	0.582593i	−0.621098	+	0.783733i	$0.713313\pi$
$272$		0			0
$273$	2.15445e7	+	3.73161e7i	0.0640865	+	0.111001i
$274$		0			0
$275$	5.62530e7	+	3.19027e8i	0.163110	+	0.925044i
$276$		0			0
$277$	1.31268e8	−	2.27364e8i	0.371092	−	0.642750i	−0.618642	−	0.785673i	$-0.712317\pi$
$277$	1.31268e8	−	2.27364e8i	0.371092	−	0.642750i	0.989734	+	0.142923i	$0.0456502\pi$
$278$		0			0
$279$	4.36241e8	−	3.66050e8i	1.20257	−	1.00908i
$280$		0			0
$281$	9.96415e7	+	3.62665e7i	0.267897	+	0.0975066i	0.472476	−	0.881343i	$-0.343360\pi$
$281$	9.96415e7	+	3.62665e7i	0.267897	+	0.0975066i	−0.204579	+	0.978850i	$0.565583\pi$
$282$		0			0
$283$	4.28494e7	−	2.43011e8i	0.112381	−	0.637343i	−0.875633	−	0.482977i	$-0.839555\pi$
$283$	4.28494e7	−	2.43011e8i	0.112381	−	0.637343i	0.988014	−	0.154366i	$-0.0493335\pi$
$284$		0			0
$285$	1.59621e8	+	1.07837e8i	0.408444	+	0.275936i
$286$		0			0
$287$	4.14494e7	−	2.35071e8i	0.103498	−	0.586966i
$288$		0			0
$289$	−3.90413e8	−	1.42099e8i	−0.951440	−	0.346296i
$290$		0			0
$291$	1.29749e8	−	1.08873e8i	0.308660	−	0.258996i
$292$		0			0
$293$	−1.72832e8	+	2.99354e8i	−0.401409	+	0.695261i	−0.993896	−	0.110319i	$-0.964813\pi$
$293$	−1.72832e8	+	2.99354e8i	−0.401409	+	0.695261i	0.592487	+	0.805580i	$0.298146\pi$
$294$		0			0
$295$	1.21441e7	+	6.88724e7i	0.0275415	+	0.156195i
$296$		0			0
$297$	−6.69546e7	−	1.15969e8i	−0.148297	−	0.256858i
$298$		0			0
$299$	−6.99250e7	+	2.54506e7i	−0.151281	+	0.0550617i
$300$		0			0
$301$	−1.80141e8	−	1.51156e8i	−0.380741	−	0.319480i
$302$		0			0
$303$	−9.44398e7			−0.195032
$304$		0			0
$305$	−1.17926e9			−2.37990
$306$		0			0
$307$	4.51151e8	+	3.78560e8i	0.889892	+	0.746708i	0.968188	−	0.250222i	$-0.0805036\pi$
$307$	4.51151e8	+	3.78560e8i	0.889892	+	0.746708i	−0.0782964	+	0.996930i	$0.524948\pi$
$308$		0			0
$309$	−1.36456e8	+	4.96659e7i	−0.263110	+	0.0957644i
$310$		0			0
$311$	−5.68356e7	−	9.84421e7i	−0.107142	−	0.185575i	0.807469	−	0.589909i	$-0.200837\pi$
$311$	−5.68356e7	−	9.84421e7i	−0.107142	−	0.185575i	−0.914611	+	0.404334i	$0.867503\pi$
$312$		0			0
$313$	−1.51806e7	−	8.60936e7i	−0.0279824	−	0.158696i	0.967615	−	0.252432i	$-0.0812302\pi$
$313$	−1.51806e7	−	8.60936e7i	−0.0279824	−	0.158696i	−0.995597	+	0.0937357i	$0.970119\pi$
$314$		0			0
$315$	3.80688e8	−	6.59371e8i	0.686250	−	1.18862i
$316$		0			0
$317$	−1.10991e8	+	9.31326e7i	−0.195696	+	0.164208i	−0.735370	−	0.677666i	$-0.762992\pi$
$317$	−1.10991e8	+	9.31326e7i	−0.195696	+	0.164208i	0.539675	+	0.841874i	$0.318547\pi$
$318$		0			0
$319$	3.19016e8	+	1.16112e8i	0.550231	+	0.200268i
$320$		0			0
$321$	4.94361e7	−	2.80366e8i	0.0834213	−	0.473105i
$322$		0			0
$323$	−3.50032e8	+	7.84629e8i	−0.577961	+	1.29555i
$324$		0			0
$325$	9.26725e7	−	5.25572e8i	0.149747	−	0.849259i
$326$		0			0
$327$	−4.25258e7	−	1.54781e7i	−0.0672567	−	0.0244794i
$328$		0			0
$329$	1.60493e8	−	1.34670e8i	0.248468	−	0.208489i
$330$		0			0
$331$	−2.68637e8	+	4.65294e8i	−0.407163	+	0.705227i	−0.994571	−	0.104064i	$-0.966815\pi$
$331$	−2.68637e8	+	4.65294e8i	−0.407163	+	0.705227i	0.587407	+	0.809291i	$0.300149\pi$
$332$		0			0
$333$	−8.57182e7	−	4.86132e8i	−0.127209	−	0.721439i
$334$		0			0
$335$	5.40172e8	+	9.35606e8i	0.785011	+	1.35968i
$336$		0			0
$337$	2.02043e8	−	7.35377e7i	0.287567	−	0.104666i	−0.194209	−	0.980960i	$-0.562214\pi$
$337$	2.02043e8	−	7.35377e7i	0.287567	−	0.104666i	0.481776	+	0.876294i	$0.339992\pi$
$338$		0			0
$339$	−9.29718e7	−	7.80126e7i	−0.129614	−	0.108759i
$340$		0			0
$341$	−6.61405e8			−0.903290
$342$		0			0
$343$	−8.00290e8			−1.07082
$344$		0			0
$345$	−9.61479e7	−	8.06777e7i	−0.126059	−	0.105776i
$346$		0			0
$347$	−1.33161e8	+	4.84667e7i	−0.171090	+	0.0622717i	−0.426145	−	0.904655i	$-0.640129\pi$
$347$	−1.33161e8	+	4.84667e7i	−0.171090	+	0.0622717i	0.255055	+	0.966927i	$0.417906\pi$
$348$		0			0
$349$	−2.63438e8	−	4.56288e8i	−0.331734	−	0.574580i	0.651118	−	0.758976i	$-0.274300\pi$
$349$	−2.63438e8	−	4.56288e8i	−0.331734	−	0.574580i	−0.982852	+	0.184397i	$0.940967\pi$
$350$		0			0
$351$	3.83077e7	+	2.17254e8i	0.0472836	+	0.268159i
$352$		0			0
$353$	4.36995e8	−	7.56897e8i	0.528767	−	0.915852i	−0.470670	−	0.882309i	$-0.655988\pi$
$353$	4.36995e8	−	7.56897e8i	0.528767	−	0.915852i	0.999437	−	0.0335427i	$-0.0106790\pi$
$354$		0			0
$355$	2.10656e8	−	1.76761e8i	0.249905	−	0.209695i
$356$		0			0
$357$	−3.04605e8	−	1.10867e8i	−0.354322	−	0.128963i
$358$		0			0
$359$	1.64189e8	−	9.31160e8i	0.187289	−	1.06217i	−0.735690	−	0.677319i	$-0.763142\pi$
$359$	1.64189e8	−	9.31160e8i	0.187289	−	1.06217i	0.922979	−	0.384851i	$-0.125747\pi$
$360$		0			0
$361$	7.88623e8	+	4.20809e8i	0.882256	+	0.470771i
$362$		0			0
$363$	3.38258e7	−	1.91836e8i	0.0371172	−	0.210502i
$364$		0			0
$365$	−1.77498e9	−	6.46039e8i	−1.91059	−	0.695399i
$366$		0			0
$367$	−1.32409e9	+	1.11104e9i	−1.39825	+	1.17327i	−0.436380	+	0.899762i	$0.643740\pi$
$367$	−1.32409e9	+	1.11104e9i	−1.39825	+	1.17327i	−0.961870	+	0.273509i	$0.911816\pi$
$368$		0			0
$369$	2.91601e8	−	5.05068e8i	0.302132	−	0.523308i
$370$		0			0
$371$	1.67758e8	+	9.51406e8i	0.170559	+	0.967291i
$372$		0			0
$373$	−5.75679e8	−	9.97105e8i	−0.574380	−	0.994856i	−0.996109	−	0.0881337i	$-0.971910\pi$
$373$	−5.75679e8	−	9.97105e8i	−0.574380	−	0.994856i	0.421728	−	0.906722i	$-0.361424\pi$
$374$		0			0
$375$	3.72865e8	−	1.35712e8i	0.365126	−	0.132895i
$376$		0			0
$377$	−4.28436e8	−	3.59500e8i	−0.411804	−	0.345545i
$378$		0			0
$379$	−6.34832e8			−0.598993			−0.299496	−	0.954097i	$-0.596819\pi$
$379$	−6.34832e8			−0.598993			−0.299496	+	0.954097i	$0.596819\pi$
$380$		0			0
$381$	3.90429e8			0.361663
$382$		0			0
$383$	−9.53668e8	−	8.00223e8i	−0.867365	−	0.727805i	0.0961769	−	0.995364i	$-0.469339\pi$
$383$	−9.53668e8	−	8.00223e8i	−0.867365	−	0.727805i	−0.963541	+	0.267559i	$0.913783\pi$
$384$		0			0
$385$	−8.30960e8	+	3.02445e8i	−0.742109	+	0.270106i
$386$		0			0
$387$	−2.87277e8	−	4.97578e8i	−0.251949	−	0.436388i
$388$		0			0
$389$	8.13912e7	+	4.61592e8i	0.0701058	+	0.397590i	0.999587	+	0.0287213i	$0.00914354\pi$
$389$	8.13912e7	+	4.61592e8i	0.0701058	+	0.397590i	−0.929482	+	0.368868i	$0.879745\pi$
$390$		0			0
$391$	2.79900e8	−	4.84800e8i	0.236801	−	0.410151i
$392$		0			0
$393$	−2.31388e8	+	1.94157e8i	−0.192294	+	0.161354i
$394$		0			0
$395$	2.71087e9	+	9.86675e8i	2.21319	+	0.805535i
$396$		0			0
$397$	7.18225e7	−	4.07326e8i	0.0576095	−	0.326720i	−0.942359	−	0.334602i	$-0.891398\pi$
$397$	7.18225e7	−	4.07326e8i	0.0576095	−	0.326720i	0.999969	+	0.00788262i	$0.00250914\pi$
$398$		0			0
$399$	−1.37398e8	+	3.07990e8i	−0.108287	+	0.242735i
$400$		0			0
$401$	−3.90868e8	+	2.21672e9i	−0.302708	+	1.71674i	0.331392	+	0.943493i	$0.392482\pi$
$401$	−3.90868e8	+	2.21672e9i	−0.302708	+	1.71674i	−0.634100	+	0.773251i	$0.718629\pi$
$402$		0			0
$403$	1.02390e9	+	3.72670e8i	0.779275	+	0.283633i
$404$		0			0
$405$	1.27602e9	−	1.07071e9i	0.954475	−	0.800900i
$406$		0			0
$407$	−2.86660e8	+	4.96510e8i	−0.210760	+	0.365046i
$408$		0			0
$409$	1.94637e8	+	1.10384e9i	0.140667	+	0.797764i	0.970744	+	0.240115i	$0.0771852\pi$
$409$	1.94637e8	+	1.10384e9i	0.140667	+	0.797764i	−0.830077	+	0.557649i	$0.811704\pi$
$410$		0			0
$411$	−3.97072e8	−	6.87749e8i	−0.282113	−	0.488634i
$412$		0			0
$413$	−1.15053e8	+	4.18759e7i	−0.0803662	+	0.0292509i
$414$		0			0
$415$	1.92179e9	+	1.61257e9i	1.31989	+	1.10752i
$416$		0			0
$417$	2.68846e8			0.181563
$418$		0			0
$419$	7.54235e8			0.500907			0.250454	−	0.968129i	$-0.419420\pi$
$419$	7.54235e8			0.500907			0.250454	+	0.968129i	$0.419420\pi$
$420$		0			0
$421$	−4.97760e8	−	4.17670e8i	−0.325112	−	0.272801i	0.465593	−	0.884999i	$-0.345841\pi$
$421$	−4.97760e8	−	4.17670e8i	−0.325112	−	0.272801i	−0.790705	+	0.612198i	$0.790286\pi$
$422$		0			0
$423$	4.81016e8	−	1.75075e8i	0.309007	−	0.112469i
$424$		0			0
$425$	2.00741e9	+	3.47694e9i	1.26845	+	2.19703i
$426$		0			0
$427$	−3.58507e8	−	2.03319e9i	−0.222843	−	1.26381i
$428$		0			0
$429$	6.11367e7	−	1.05892e8i	0.0373853	−	0.0647533i
$430$		0			0
$431$	9.92062e7	−	8.32438e7i	0.0596854	−	0.0500820i	−0.612457	−	0.790504i	$-0.709819\pi$
$431$	9.92062e7	−	8.32438e7i	0.0596854	−	0.0500820i	0.672142	+	0.740422i	$0.265374\pi$
$432$		0			0
$433$	1.27735e9	+	4.64916e8i	0.756138	+	0.275212i	0.691186	−	0.722676i	$-0.257088\pi$
$433$	1.27735e9	+	4.64916e8i	0.756138	+	0.275212i	0.0649520	+	0.997888i	$0.479311\pi$
$434$		0			0
$435$	1.63810e8	−	9.29014e8i	0.0954176	−	0.541140i
$436$		0			0
$437$	−4.82602e8	−	3.26036e8i	−0.276633	−	0.186888i
$438$		0			0
$439$	3.46040e8	−	1.96249e9i	0.195209	−	1.10709i	−0.716912	−	0.697164i	$-0.754445\pi$
$439$	3.46040e8	−	1.96249e9i	0.195209	−	1.10709i	0.912121	−	0.409922i	$-0.134444\pi$
$440$		0			0
$441$	−2.92415e8	−	1.06430e8i	−0.162354	−	0.0590921i
$442$		0			0
$443$	−2.16981e9	+	1.82069e9i	−1.18579	+	0.994998i	−0.185870	+	0.982574i	$0.559510\pi$
$443$	−2.16981e9	+	1.82069e9i	−1.18579	+	0.994998i	−0.999923	+	0.0124240i	$0.996045\pi$
$444$		0			0
$445$	2.28636e9	−	3.96009e9i	1.22994	−	2.13032i
$446$		0			0
$447$	−1.44283e8	−	8.18269e8i	−0.0764080	−	0.433331i
$448$		0			0
$449$	1.64213e9	+	2.84425e9i	0.856140	+	1.48288i	0.875583	+	0.483067i	$0.160477\pi$
$449$	1.64213e9	+	2.84425e9i	0.856140	+	1.48288i	−0.0194429	+	0.999811i	$0.506189\pi$
$450$		0			0
$451$	−6.36503e8	+	2.31668e8i	−0.326725	+	0.118918i
$452$		0			0
$453$	−5.05723e8	−	4.24352e8i	−0.255605	−	0.214478i
$454$		0			0
$455$	1.45680e9			0.725036
$456$		0			0
$457$	−1.65256e9			−0.809936			−0.404968	−	0.914331i	$-0.632717\pi$
$457$	−1.65256e9			−0.809936			−0.404968	+	0.914331i	$0.632717\pi$
$458$		0			0
$459$	−1.27132e9	−	1.06676e9i	−0.613636	−	0.514902i
$460$		0			0
$461$	2.11925e8	−	7.71344e7i	0.100746	−	0.0366686i	−0.291155	−	0.956676i	$-0.594040\pi$
$461$	2.11925e8	−	7.71344e7i	0.100746	−	0.0366686i	0.391902	+	0.920007i	$0.371817\pi$
$462$		0			0
$463$	3.25487e8	+	5.63760e8i	0.152405	+	0.263974i	0.932111	−	0.362172i	$-0.117965\pi$
$463$	3.25487e8	+	5.63760e8i	0.152405	+	0.263974i	−0.779706	+	0.626146i	$0.784631\pi$
$464$		0			0
$465$	3.19141e8	+	1.80994e9i	0.147196	+	0.834792i
$466$		0			0
$467$	−1.81271e9	+	3.13971e9i	−0.823607	+	1.42653i	0.0793724	+	0.996845i	$0.474708\pi$
$467$	−1.81271e9	+	3.13971e9i	−0.823607	+	1.42653i	−0.902979	+	0.429684i	$0.858625\pi$
$468$		0			0
$469$	−1.44889e9	+	1.21576e9i	−0.648530	+	0.544181i
$470$		0			0
$471$	−3.94375e8	−	1.43541e8i	−0.173915	−	0.0632998i
$472$		0			0
$473$	−1.15877e8	+	6.57169e8i	−0.0503479	+	0.285537i
$474$		0			0
$475$	3.75561e9	−	1.82831e9i	1.60788	−	0.782749i
$476$		0			0
$477$	−4.09879e8	+	2.32454e9i	−0.172919	+	0.980670i
$478$		0			0
$479$	3.18354e9	+	1.15872e9i	1.32354	+	0.481729i	0.904591	−	0.426282i	$-0.140177\pi$
$479$	3.18354e9	+	1.15872e9i	1.32354	+	0.481729i	0.418948	+	0.908010i	$0.362399\pi$
$480$		0			0
$481$	7.23531e8	−	6.07114e8i	0.296448	−	0.248750i
$482$		0			0
$483$	1.09869e8	−	1.90298e8i	0.0443670	−	0.0768458i
$484$		0			0
$485$	−9.94387e8	−	5.63945e9i	−0.395785	−	2.24461i
$486$		0			0
$487$	9.71419e8	+	1.68255e9i	0.381114	+	0.660110i	0.991222	−	0.132209i	$-0.0422071\pi$
$487$	9.71419e8	+	1.68255e9i	0.381114	+	0.660110i	−0.610107	+	0.792319i	$0.708874\pi$
$488$		0			0
$489$	1.12986e9	−	4.11236e8i	0.436962	−	0.159041i
$490$		0			0
$491$	−2.77654e9	−	2.32979e9i	−1.05857	−	0.888244i	−0.0645992	−	0.997911i	$-0.520577\pi$
$491$	−2.77654e9	−	2.32979e9i	−1.05857	−	0.888244i	−0.993968	+	0.109668i	$0.965021\pi$
$492$		0			0
$493$	4.20743e9			1.58144
$494$		0			0
$495$	−2.16056e9			−0.800659
$496$		0			0
$497$	3.68801e8	+	3.09461e8i	0.134755	+	0.113073i
$498$		0			0
$499$	−1.37951e9	+	5.02101e8i	−0.497019	+	0.180900i	−0.578353	−	0.815787i	$-0.696304\pi$
$499$	−1.37951e9	+	5.02101e8i	−0.497019	+	0.180900i	0.0813337	+	0.996687i	$0.474082\pi$
$500$		0			0
$501$	1.26880e8	+	2.19762e8i	0.0450776	+	0.0780767i
$502$		0			0
$503$	5.23780e7	+	2.97050e8i	0.0183511	+	0.104074i	0.992608	−	0.121369i	$-0.0387283\pi$
$503$	5.23780e7	+	2.97050e8i	0.0183511	+	0.104074i	−0.974256	+	0.225443i	$0.927617\pi$
$504$		0			0
$505$	−1.59646e9	+	2.76516e9i	−0.551619	+	0.955432i
$506$		0			0
$507$	5.09261e8	−	4.27321e8i	0.173545	−	0.145622i
$508$		0			0
$509$	−3.01039e9	−	1.09569e9i	−1.01184	−	0.368278i	−0.217698	−	0.976016i	$-0.569855\pi$
$509$	−3.01039e9	−	1.09569e9i	−1.01184	−	0.368278i	−0.794138	+	0.607738i	$0.792077\pi$
$510$		0			0
$511$	5.74244e8	−	3.25670e9i	0.190381	−	1.07970i
$512$		0			0
$513$	−1.20033e9	+	1.24115e9i	−0.392546	+	0.405895i
$514$		0			0
$515$	−8.52533e8	+	4.83496e9i	−0.275034	+	1.55979i
$516$		0			0
$517$	−5.58668e8	−	2.03339e8i	−0.177802	−	0.0647147i
$518$		0			0
$519$	9.54143e7	−	8.00621e7i	0.0299590	−	0.0251386i
$520$		0			0
$521$	1.25216e9	−	2.16880e9i	0.387906	−	0.671873i	−0.604262	−	0.796786i	$-0.706532\pi$
$521$	1.25216e9	−	2.16880e9i	0.387906	−	0.671873i	0.992168	+	0.124913i	$0.0398651\pi$
$522$		0			0
$523$	−4.64916e8	−	2.63667e9i	−0.142108	−	0.805935i	−0.969644	−	0.244522i	$-0.921369\pi$
$523$	−4.64916e8	−	2.63667e9i	−0.142108	−	0.805935i	0.827536	−	0.561413i	$-0.189742\pi$
$524$		0			0
$525$	7.87968e8	+	1.36480e9i	0.237657	+	0.411634i
$526$		0			0
$527$	−7.70272e9	+	2.80356e9i	−2.29249	+	0.834397i
$528$		0			0
$529$	−2.31755e9	−	1.94466e9i	−0.680667	−	0.571147i
$530$		0			0
$531$	−2.99147e8			−0.0867068
$532$		0			0
$533$	1.11589e9			0.319208
$534$		0			0
$535$	−7.37330e9	−	6.18694e9i	−2.08173	−	1.74678i
$536$		0			0
$537$	−1.49362e9	+	5.43632e8i	−0.416226	+	0.151494i
$538$		0			0
$539$	1.80708e8	+	3.12996e8i	0.0497070	+	0.0860950i
$540$		0			0
$541$	−7.92740e8	−	4.49585e9i	−0.215249	−	1.22074i	−0.880474	−	0.474094i	$-0.842776\pi$
$541$	−7.92740e8	−	4.49585e9i	−0.215249	−	1.22074i	0.665226	−	0.746642i	$-0.268335\pi$
$542$		0			0
$543$	−6.11767e8	+	1.05961e9i	−0.163979	+	0.284019i
$544$		0			0
$545$	−1.17207e9	+	9.83486e8i	−0.310147	+	0.260244i
$546$		0			0
$547$	2.62238e9	+	9.54468e8i	0.685077	+	0.249348i	0.661026	−	0.750363i	$-0.270121\pi$
$547$	2.62238e9	+	9.54468e8i	0.685077	+	0.249348i	0.0240514	+	0.999711i	$0.492343\pi$
$548$		0			0
$549$	8.75928e8	−	4.96764e9i	0.225926	−	1.28129i
$550$		0			0
$551$	3.08565e8	−	4.36650e9i	0.0785808	−	1.11200i
$552$		0			0
$553$	−8.77024e8	+	4.97385e9i	−0.220533	+	1.25070i
$554$		0			0
$555$	1.49702e9	+	5.44871e8i	0.371709	+	0.135291i
$556$		0			0
$557$	1.01688e8	−	8.53260e7i	0.0249330	−	0.0209213i	−0.630236	−	0.776404i	$-0.717042\pi$
$557$	1.01688e8	−	8.53260e7i	0.0249330	−	0.0209213i	0.655169	+	0.755482i	$0.272597\pi$
$558$		0			0
$559$	5.49668e8	−	9.52053e8i	0.133094	−	0.230526i
$560$		0			0
$561$	1.59730e8	+	9.05876e8i	0.0381960	+	0.216620i
$562$		0			0
$563$	−3.09335e9	−	5.35785e9i	−0.730550	−	1.26535i	−0.956648	−	0.291246i	$-0.905930\pi$
$563$	−3.09335e9	−	5.35785e9i	−0.730550	−	1.26535i	0.226098	−	0.974105i	$-0.427403\pi$
$564$		0			0
$565$	−3.85583e9	+	1.40341e9i	−0.899389	+	0.327351i
$566$		0			0
$567$	2.23396e9	+	1.87452e9i	0.514678	+	0.431866i
$568$		0			0
$569$	7.80611e9			1.77640			0.888202	−	0.459453i	$-0.151955\pi$
$569$	7.80611e9			1.77640			0.888202	+	0.459453i	$0.151955\pi$
$570$		0			0
$571$	4.36978e9			0.982276			0.491138	−	0.871082i	$-0.336581\pi$
$571$	4.36978e9			0.982276			0.491138	+	0.871082i	$0.336581\pi$
$572$		0			0
$573$	−4.62025e8	−	3.87685e8i	−0.102595	−	0.0860871i
$574$		0			0
$575$	−2.55744e9	+	9.30832e8i	−0.561007	+	0.204190i
$576$		0			0
$577$	6.27958e8	+	1.08766e9i	0.136087	+	0.235709i	0.926012	−	0.377494i	$-0.123214\pi$
$577$	6.27958e8	+	1.08766e9i	0.136087	+	0.235709i	−0.789925	+	0.613203i	$0.789881\pi$
$578$		0			0
$579$	−4.57989e7	−	2.59739e8i	−0.00980574	−	0.0556111i
$580$		0			0
$581$	−2.19604e9	+	3.80365e9i	−0.464540	+	0.804607i
$582$		0			0
$583$	2.10007e9	−	1.76217e9i	0.438929	−	0.368305i
$584$		0			0
$585$	3.34470e9	+	1.21737e9i	0.690735	+	0.251407i
$586$		0			0
$587$	1.13735e9	−	6.45022e9i	0.232092	−	1.31626i	−0.616561	−	0.787307i	$-0.711475\pi$
$587$	1.13735e9	−	6.45022e9i	0.232092	−	1.31626i	0.848653	−	0.528951i	$-0.177414\pi$
$588$		0			0
$589$	2.34465e9	+	8.19954e9i	0.472797	+	1.65343i
$590$		0			0
$591$	5.97297e7	−	3.38744e8i	0.0119024	−	0.0675018i
$592$		0			0
$593$	5.47819e9	+	1.99390e9i	1.07881	+	0.392655i	0.819465	−	0.573129i	$-0.194271\pi$
$593$	5.47819e9	+	1.99390e9i	1.07881	+	0.392655i	0.259346	+	0.965784i	$0.416493\pi$
$594$		0			0
$595$	−8.39536e9	+	7.04454e9i	−1.63392	+	1.37102i
$596$		0			0
$597$	−3.18798e8	+	5.52175e8i	−0.0613206	+	0.106210i
$598$		0			0
$599$	−7.99334e8	−	4.53325e9i	−0.151962	−	0.861818i	−0.961511	−	0.274766i	$-0.911400\pi$
$599$	−7.99334e8	−	4.53325e9i	−0.151962	−	0.861818i	0.809549	−	0.587052i	$-0.199712\pi$
$600$		0			0
$601$	4.47272e9	+	7.74698e9i	0.840449	+	1.45570i	0.889516	+	0.456905i	$0.151042\pi$
$601$	4.47272e9	+	7.74698e9i	0.840449	+	1.45570i	−0.0490666	+	0.998796i	$0.515625\pi$
$602$		0			0
$603$	−4.34248e9	+	1.58054e9i	−0.806543	+	0.293558i
$604$		0			0
$605$	−5.04506e9	−	4.23331e9i	−0.926237	−	0.777205i
$606$		0			0
$607$	−3.71807e9			−0.674773			−0.337386	−	0.941366i	$-0.609543\pi$
$607$	−3.71807e9			−0.674773			−0.337386	+	0.941366i	$0.609543\pi$
$608$		0			0
$609$	1.65154e9			0.296298
$610$		0			0
$611$	7.50287e8	+	6.29566e8i	0.133071	+	0.111660i
$612$		0			0
$613$	1.03659e9	−	3.77289e8i	0.181759	−	0.0661549i	−0.249537	−	0.968365i	$-0.580279\pi$
$613$	1.03659e9	−	3.77289e8i	0.181759	−	0.0661549i	0.431296	+	0.902210i	$0.358056\pi$
$614$		0			0
$615$	9.41085e8	+	1.63001e9i	0.163142	+	0.282570i
$616$		0			0
$617$	−1.29338e9	−	7.33513e9i	−0.221681	−	1.25722i	−0.868929	−	0.494936i	$-0.835191\pi$
$617$	−1.29338e9	−	7.33513e9i	−0.221681	−	1.25722i	0.647248	−	0.762279i	$-0.275920\pi$
$618$		0			0
$619$	−3.47316e8	+	6.01569e8i	−0.0588583	+	0.101946i	−0.893953	−	0.448160i	$-0.852079\pi$
$619$	−3.47316e8	+	6.01569e8i	−0.0588583	+	0.101946i	0.835095	+	0.550106i	$0.185413\pi$
$620$		0			0
$621$	8.61804e8	−	7.23140e8i	0.144407	−	0.121172i
$622$		0			0
$623$	7.52280e9	+	2.73807e9i	1.24644	+	0.453667i
$624$		0			0
$625$	4.34203e8	−	2.46249e9i	0.0711398	−	0.403454i
$626$		0			0
$627$	9.51839e8	−	9.93340e7i	0.154215	−	0.0160939i
$628$		0			0
$629$	−1.23384e9	+	6.99745e9i	−0.197688	+	1.12115i
$630$		0			0
$631$	−1.68408e9	−	6.12957e8i	−0.266846	−	0.0971241i	0.205132	−	0.978734i	$-0.434238\pi$
$631$	−1.68408e9	−	6.12957e8i	−0.266846	−	0.0971241i	−0.471978	+	0.881610i	$0.656460\pi$
$632$		0			0
$633$	1.40023e9	−	1.17493e9i	0.219425	−	0.184119i
$634$		0			0
$635$	6.60003e9	−	1.14316e10i	1.02291	−	1.77173i
$636$		0			0
$637$	−1.03391e8	−	5.86361e8i	−0.0158488	−	0.0898828i
$638$		0			0
$639$	5.88139e8	+	1.01869e9i	0.0891716	+	0.154450i
$640$		0			0
$641$	2.89345e9	−	1.05313e9i	0.433922	−	0.157935i	−0.115818	−	0.993270i	$-0.536949\pi$
$641$	2.89345e9	−	1.05313e9i	0.433922	−	0.157935i	0.549740	+	0.835336i	$0.314727\pi$
$642$		0			0
$643$	−1.25404e9	−	1.05226e9i	−0.186025	−	0.156094i	0.545019	−	0.838424i	$-0.316522\pi$
$643$	−1.25404e9	−	1.05226e9i	−0.186025	−	0.156094i	−0.731045	+	0.682330i	$0.760967\pi$
$644$		0			0
$645$	1.85426e9			0.272089
$646$		0			0
$647$	−6.36959e9			−0.924585			−0.462292	−	0.886728i	$-0.652973\pi$
$647$	−6.36959e9			−0.924585			−0.462292	+	0.886728i	$0.652973\pi$
$648$		0			0
$649$	2.66154e8	+	2.23330e8i	0.0382188	+	0.0320693i
$650$		0			0
$651$	−3.02355e9	+	1.10048e9i	−0.429520	+	0.156332i
$652$		0			0
$653$	1.01349e9	+	1.75542e9i	0.142438	+	0.246709i	0.928414	−	0.371547i	$-0.121173\pi$
$653$	1.01349e9	+	1.75542e9i	0.142438	+	0.246709i	−0.785976	+	0.618256i	$0.787839\pi$
$654$		0			0
$655$	1.77333e9	+	1.00571e10i	0.246573	+	1.39839i
$656$		0			0
$657$	4.03987e9	−	6.99726e9i	0.555762	−	0.962607i
$658$		0			0
$659$	8.21471e9	−	6.89296e9i	1.11813	−	0.938224i	0.119624	−	0.992819i	$-0.461831\pi$
$659$	8.21471e9	−	6.89296e9i	1.11813	−	0.938224i	0.998509	+	0.0545949i	$0.0173867\pi$
$660$		0			0
$661$	1.03914e10	+	3.78215e9i	1.39948	+	0.509370i	0.928025	−	0.372519i	$-0.121506\pi$
$661$	1.03914e10	+	3.78215e9i	1.39948	+	0.509370i	0.471458	+	0.881889i	$0.343728\pi$
$662$		0			0
$663$	2.63144e8	−	1.49236e9i	0.0350668	−	0.198873i
$664$		0			0
$665$	6.69517e9	+	9.22939e9i	0.882848	+	1.21702i
$666$		0			0
$667$	−4.95269e8	+	2.80881e9i	−0.0646250	+	0.366506i
$668$		0			0
$669$	−2.87537e9	−	1.04655e9i	−0.371280	−	0.135135i
$670$		0			0
$671$	−4.48794e9	+	3.76583e9i	−0.573480	+	0.481207i
$672$		0			0
$673$	−5.06374e8	+	8.77065e8i	−0.0640352	+	0.110912i	−0.896266	−	0.443518i	$-0.853730\pi$
$673$	−5.06374e8	+	8.77065e8i	−0.0640352	+	0.110912i	0.832230	+	0.554430i	$0.187064\pi$
$674$		0			0
$675$	1.40107e9	+	7.94584e9i	0.175346	+	0.994436i
$676$		0			0
$677$	5.03447e9	+	8.71995e9i	0.623581	+	1.08007i	0.988813	+	0.149158i	$0.0476563\pi$
$677$	5.03447e9	+	8.71995e9i	0.623581	+	1.08007i	−0.365232	+	0.930916i	$0.619010\pi$
$678$		0			0
$679$	9.42084e9	−	3.42891e9i	1.15490	−	0.420350i
$680$		0			0
$681$	2.62051e9	+	2.19887e9i	0.317959	+	0.266800i
$682$		0			0
$683$	9.98009e9			1.19857			0.599283	−	0.800537i	$-0.295452\pi$
$683$	9.98009e9			1.19857			0.599283	+	0.800537i	$0.295452\pi$
$684$		0			0
$685$	−2.68493e10			−3.19166
$686$		0			0
$687$	−8.46459e8	−	7.10263e8i	−0.0995995	−	0.0835739i
$688$		0			0
$689$	−4.24396e9	+	1.54468e9i	−0.494316	+	0.179916i
$690$		0			0
$691$	5.38211e9	+	9.32209e9i	0.620554	+	1.07483i	0.989383	+	0.145333i	$0.0464255\pi$
$691$	5.38211e9	+	9.32209e9i	0.620554	+	1.07483i	−0.368829	+	0.929497i	$0.620241\pi$
$692$		0			0
$693$	−6.56833e8	−	3.72508e9i	−0.0749702	−	0.425177i
$694$		0			0
$695$	4.54472e9	−	7.87169e9i	0.513524	−	0.889450i
$696$		0			0
$697$	−6.43071e9	+	5.39601e9i	−0.719357	+	0.603612i
$698$		0			0
$699$	1.82057e9	+	6.62633e8i	0.201622	+	0.0733843i
$700$		0			0
$701$	3.07337e9	−	1.74300e10i	0.336979	−	1.91110i	−0.0697739	−	0.997563i	$-0.522228\pi$
$701$	3.07337e9	−	1.74300e10i	0.336979	−	1.91110i	0.406753	−	0.913538i	$-0.366661\pi$
$702$		0			0
$703$	7.17152e9	+	1.79367e9i	0.778516	+	0.194715i
$704$		0			0
$705$	−2.86869e8	+	1.62691e9i	−0.0308334	+	0.174865i
$706$		0			0
$707$	−5.25283e9	−	1.91188e9i	−0.559018	−	0.203466i
$708$		0			0
$709$	1.07777e10	−	9.04357e9i	1.13570	−	0.952968i	0.136413	−	0.990652i	$-0.456443\pi$
$709$	1.07777e10	−	9.04357e9i	1.13570	−	0.952968i	0.999290	+	0.0376844i	$0.0119982\pi$
$710$		0			0
$711$	−6.16996e9	+	1.06867e10i	−0.643782	+	1.11506i
$712$		0			0
$713$	−9.64899e8	−	5.47222e9i	−0.0996939	−	0.565392i
$714$		0			0
$715$	−2.06698e9	−	3.58011e9i	−0.211478	−	0.366290i
$716$		0			0
$717$	−5.73124e8	+	2.08600e8i	−0.0580673	+	0.0211348i
$718$		0			0
$719$	7.55093e9	+	6.33598e9i	0.757616	+	0.635716i	0.937505	−	0.347971i	$-0.113129\pi$
$719$	7.55093e9	+	6.33598e9i	0.757616	+	0.635716i	−0.179889	+	0.983687i	$0.557574\pi$
$720$		0			0
$721$	−8.59527e9			−0.854056
$722$		0			0
$723$	−4.93717e9			−0.485840
$724$		0			0
$725$	−1.56696e10	−	1.31484e10i	−1.52713	−	1.28141i
$726$		0			0
$727$	−1.46961e10	+	5.34893e9i	−1.41851	+	0.516294i	−0.933614	−	0.358281i	$-0.883363\pi$
$727$	−1.46961e10	+	5.34893e9i	−1.41851	+	0.516294i	−0.484891	+	0.874574i	$0.661141\pi$
$728$		0			0
$729$	2.69078e9	+	4.66057e9i	0.257236	+	0.445547i
$730$		0			0
$731$	1.43611e9	+	8.14456e9i	0.135980	+	0.771182i
$732$		0			0
$733$	9.39235e9	−	1.62680e10i	0.880867	−	1.52571i	0.0304888	−	0.999535i	$-0.490294\pi$
$733$	9.39235e9	−	1.62680e10i	0.880867	−	1.52571i	0.850378	−	0.526172i	$-0.176373\pi$
$734$		0			0
$735$	7.69319e8	−	6.45535e8i	0.0714662	−	0.0599673i
$736$		0			0
$737$	5.04351e9	+	1.83569e9i	0.464084	+	0.168913i
$738$		0			0
$739$	1.63949e9	−	9.29802e9i	0.149436	−	0.847491i	−0.814263	−	0.580497i	$-0.802858\pi$
$739$	1.63949e9	−	9.29802e9i	0.149436	−	0.847491i	0.963698	−	0.266994i	$-0.0860305\pi$
$740$		0			0
$741$	−1.52949e9	−	3.82539e8i	−0.138096	−	0.0345392i
$742$		0			0
$743$	2.26097e9	−	1.28226e10i	0.202225	−	1.14687i	−0.699523	−	0.714610i	$-0.746604\pi$
$743$	2.26097e9	−	1.28226e10i	0.202225	−	1.14687i	0.901748	−	0.432262i	$-0.142285\pi$
$744$		0			0
$745$	−2.63976e10	−	9.60794e9i	−2.33893	−	0.851302i
$746$		0			0
$747$	−8.22044e9	+	6.89777e9i	−0.721561	+	0.605462i
$748$		0			0
$749$	8.42552e9	−	1.45934e10i	0.732674	−	1.26903i
$750$		0			0
$751$	3.09277e8	+	1.75400e9i	0.0266445	+	0.151108i	0.995227	−	0.0975822i	$-0.0311109\pi$
$751$	3.09277e8	+	1.75400e9i	0.0266445	+	0.151108i	−0.968583	+	0.248691i	$0.920000\pi$
$752$		0			0
$753$	−1.99271e9	−	3.45148e9i	−0.170084	−	0.294593i
$754$		0			0
$755$	−2.09739e10	+	7.63387e9i	−1.77364	+	0.645551i
$756$		0			0
$757$	−4.06388e9	−	3.41000e9i	−0.340491	−	0.285706i	0.456467	−	0.889740i	$-0.349115\pi$
$757$	−4.06388e9	−	3.41000e9i	−0.340491	−	0.285706i	−0.796958	+	0.604034i	$0.793559\pi$
$758$		0			0
$759$	−6.23550e8			−0.0517636
$760$		0			0
$761$	−1.21943e10			−1.00302			−0.501511	−	0.865152i	$-0.667222\pi$
$761$	−1.21943e10			−1.00302			−0.501511	+	0.865152i	$0.667222\pi$
$762$		0			0
$763$	−2.05198e9	−	1.72182e9i	−0.167239	−	0.140330i
$764$		0			0
$765$	−2.51618e10	+	9.15816e9i	−2.03202	+	0.739594i
$766$		0			0
$767$	−2.86190e8	−	4.95695e8i	−0.0229018	−	0.0396672i
$768$		0			0
$769$	3.25901e9	+	1.84828e10i	0.258431	+	1.46563i	0.787111	+	0.616811i	$0.211576\pi$
$769$	3.25901e9	+	1.84828e10i	0.258431	+	1.46563i	−0.528680	+	0.848821i	$0.677313\pi$
$770$		0			0
$771$	1.57259e9	−	2.72381e9i	0.123574	−	0.214036i
$772$		0			0
$773$	5.02210e9	−	4.21404e9i	0.391072	−	0.328149i	−0.425958	−	0.904743i	$-0.640063\pi$
$773$	5.02210e9	−	4.21404e9i	0.391072	−	0.328149i	0.817031	+	0.576594i	$0.195619\pi$
$774$		0			0
$775$	3.74482e10	+	1.36300e10i	2.88985	+	1.05182i
$776$		0			0
$777$	−4.84319e8	+	2.74671e9i	−0.0370389	+	0.210058i
$778$		0			0
$779$	5.12840e9	+	7.06957e9i	0.388687	+	0.535811i
$780$		0			0
$781$	2.37233e8	−	1.34541e9i	0.0178195	−	0.101060i
$782$		0			0
$783$	7.94557e9	+	2.89195e9i	0.591506	+	0.215291i
$784$		0			0
$785$	−1.08696e10	+	9.12064e9i	−0.801988	+	0.672948i
$786$		0			0
$787$	1.03182e9	−	1.78716e9i	0.0754555	−	0.130693i	−0.825829	−	0.563921i	$-0.809292\pi$
$787$	1.03182e9	−	1.78716e9i	0.0754555	−	0.130693i	0.901284	+	0.433228i	$0.142626\pi$
$788$		0			0
$789$	−1.19572e9	−	6.78125e9i	−0.0866680	−	0.491519i
$790$		0			0
$791$	−3.59187e9	−	6.22130e9i	−0.258049	−	0.446954i
$792$		0			0
$793$	9.06952e9	−	3.30104e9i	0.645845	−	0.235068i
$794$		0			0
$795$	−5.83551e9	−	4.89658e9i	−0.411902	−	0.345627i
$796$		0			0
$797$	−1.74842e10			−1.22332			−0.611661	−	0.791120i	$-0.709498\pi$
$797$	−1.74842e10			−1.22332			−0.611661	+	0.791120i	$0.709498\pi$
$798$		0			0
$799$	−7.36816e9			−0.511029
$800$		0			0
$801$	1.49837e10	+	1.25728e10i	1.03016	+	0.864408i
$802$		0			0
$803$	−8.81816e9	+	3.20955e9i	−0.600999	+	0.218746i
$804$		0			0
$805$	−3.71457e9	−	6.43383e9i	−0.250971	−	0.434694i
$806$		0			0
$807$	−1.03356e9	−	5.86163e9i	−0.0692277	−	0.392610i
$808$		0			0
$809$	1.63247e9	−	2.82752e9i	0.108399	−	0.187752i	−0.806723	−	0.590930i	$-0.798761\pi$
$809$	1.63247e9	−	2.82752e9i	0.108399	−	0.187752i	0.915122	+	0.403177i	$0.132094\pi$
$810$		0			0
$811$	1.40779e10	−	1.18128e10i	0.926757	−	0.777641i	−0.0484756	−	0.998824i	$-0.515436\pi$
$811$	1.40779e10	−	1.18128e10i	0.926757	−	0.777641i	0.975232	+	0.221183i	$0.0709919\pi$
$812$		0			0
$813$	7.23971e9	+	2.63504e9i	0.472503	+	0.171977i
$814$		0			0
$815$	7.05901e9	−	4.00336e10i	0.456764	−	2.59044i
$816$		0			0
$817$	8.55780e9	−	8.93093e8i	0.549016	−	0.0572954i
$818$		0			0
$819$	−1.08208e9	+	6.13679e9i	−0.0688282	+	0.390344i
$820$		0			0
$821$	6.99214e9	+	2.54493e9i	0.440970	+	0.160500i	0.552957	−	0.833210i	$-0.313499\pi$
$821$	6.99214e9	+	2.54493e9i	0.440970	+	0.160500i	−0.111987	+	0.993710i	$0.535721\pi$
$822$		0			0
$823$	−2.02936e10	+	1.70283e10i	−1.26899	+	1.06481i	−0.274330	+	0.961636i	$0.588456\pi$
$823$	−2.02936e10	+	1.70283e10i	−1.26899	+	1.06481i	−0.994663	+	0.103176i	$0.967099\pi$
$824$		0			0
$825$	2.23602e9	−	3.87289e9i	0.138639	−	0.240130i
$826$		0			0
$827$	6.02334e8	+	3.41601e9i	0.0370313	+	0.210015i	0.997709	−	0.0676509i	$-0.0215504\pi$
$827$	6.02334e8	+	3.41601e9i	0.0370313	+	0.210015i	−0.960678	+	0.277666i	$0.910439\pi$
$828$		0			0
$829$	8.77870e9	+	1.52052e10i	0.535167	+	0.926936i	0.999155	+	0.0410950i	$0.0130846\pi$
$829$	8.77870e9	+	1.52052e10i	0.535167	+	0.926936i	−0.463988	+	0.885841i	$0.653582\pi$
$830$		0			0
$831$	−3.40569e9	+	1.23957e9i	−0.205874	+	0.0749321i
$832$		0			0
$833$	3.43125e9	+	2.87916e9i	0.205681	+	0.172587i
$834$		0			0
$835$	8.57940e9			0.509981
$836$		0			0
$837$	−1.64733e10			−0.971050
$838$		0			0
$839$	1.84360e9	+	1.54696e9i	0.107770	+	0.0904300i	0.695081	−	0.718932i	$-0.255369\pi$
$839$	1.84360e9	+	1.54696e9i	0.107770	+	0.0904300i	−0.587310	+	0.809362i	$0.699813\pi$
$840$		0			0
$841$	−3.93421e9	+	1.43193e9i	−0.228072	+	0.0830113i
$842$		0			0
$843$	−7.31904e8	−	1.26769e9i	−0.0420782	−	0.0728816i
$844$		0			0
$845$	−3.90293e9	−	2.21346e10i	−0.222532	−	1.26204i
$846$		0			0
$847$	5.76502e9	−	9.98531e9i	0.325993	−	0.564637i
$848$		0			0
$849$	−2.60950e9	+	2.18963e9i	−0.146346	+	0.122799i
$850$		0			0
$851$	−4.52614e9	−	1.64738e9i	−0.251753	−	0.0916306i
$852$		0			0
$853$	4.13888e8	−	2.34728e9i	0.0228329	−	0.129492i	−0.971261	−	0.238018i	$-0.923502\pi$
$853$	4.13888e8	−	2.34728e9i	0.0228329	−	0.129492i	0.994094	+	0.108527i	$0.0346133\pi$
$854$		0			0
$855$	7.65908e9	+	2.67848e10i	0.419078	+	1.46557i
$856$		0			0
$857$	−2.28413e9	+	1.29539e10i	−0.123962	+	0.703022i	0.857957	+	0.513721i	$0.171733\pi$
$857$	−2.28413e9	+	1.29539e10i	−0.123962	+	0.703022i	−0.981919	+	0.189301i	$0.939378\pi$
$858$		0			0
$859$	−1.25248e10	−	4.55864e9i	−0.674208	−	0.245392i	−0.0178493	−	0.999841i	$-0.505682\pi$
$859$	−1.25248e10	−	4.55864e9i	−0.674208	−	0.245392i	−0.656359	+	0.754449i	$0.727904\pi$
$860$		0			0
$861$	−2.52424e9	+	2.11809e9i	−0.134778	+	0.113093i
$862$		0			0
$863$	3.98545e9	−	6.90301e9i	0.211077	−	0.365595i	−0.740975	−	0.671532i	$-0.765636\pi$
$863$	3.98545e9	−	6.90301e9i	0.211077	−	0.365595i	0.952052	+	0.305937i	$0.0989697\pi$
$864$		0			0
$865$	−7.31247e8	−	4.14711e9i	−0.0384156	−	0.217866i
$866$		0			0
$867$	2.86772e9	+	4.96705e9i	0.149441	+	0.258840i
$868$		0			0
$869$	1.34677e10	−	4.90184e9i	0.696184	−	0.253390i
$870$		0			0
$871$	−6.77340e9	−	5.68356e9i	−0.347331	−	0.291445i
$872$		0			0
$873$	2.44949e10			1.24602
$874$		0			0
$875$	2.34865e10			1.18520
$876$		0			0
$877$	−1.26568e10	−	1.06203e10i	−0.633615	−	0.531666i	0.268435	−	0.963298i	$-0.413494\pi$
$877$	−1.26568e10	−	1.06203e10i	−0.633615	−	0.531666i	−0.902050	+	0.431632i	$0.857938\pi$
$878$		0			0
$879$	4.48404e9	−	1.63206e9i	0.222694	−	0.0810540i
$880$		0			0
$881$	1.64407e9	+	2.84761e9i	0.0810035	+	0.140302i	0.903681	−	0.428206i	$-0.140854\pi$
$881$	1.64407e9	+	2.84761e9i	0.0810035	+	0.140302i	−0.822678	+	0.568508i	$0.807521\pi$
$882$		0			0
$883$	5.57355e9	+	3.16091e10i	0.272439	+	1.54508i	0.746981	+	0.664845i	$0.231502\pi$
$883$	5.57355e9	+	3.16091e10i	0.272439	+	1.54508i	−0.474542	+	0.880233i	$0.657386\pi$
$884$		0			0
$885$	4.82718e8	−	8.36092e8i	0.0234095	−	0.0405464i
$886$		0			0
$887$	−1.15189e10	+	9.66548e9i	−0.554214	+	0.465040i	−0.876365	−	0.481648i	$-0.840038\pi$
$887$	−1.15189e10	+	9.66548e9i	−0.554214	+	0.465040i	0.322151	+	0.946688i	$0.395594\pi$
$888$		0			0
$889$	2.17160e10	+	7.90399e9i	1.03663	+	0.377303i
$890$		0			0
$891$	1.43701e9	−	8.14967e9i	0.0680592	−	0.385983i
$892$		0			0
$893$	−5.40368e8	+	7.64673e9i	−0.0253927	+	0.359332i
$894$		0			0
$895$	−9.33163e9	+	5.29223e10i	−0.435088	+	2.46751i
$896$		0			0
$897$	9.65300e8	+	3.51340e8i	0.0446569	+	0.0162538i
$898$		0			0
$899$	3.19927e10	−	2.68450e10i	1.46856	−	1.23227i
$900$		0			0
$901$	1.69880e10	−	2.94240e10i	0.773757	−	1.34019i
$902$		0			0
$903$	5.63714e8	+	3.19698e9i	0.0254772	+	0.144488i
$904$		0			0
$905$	2.06833e10	+	3.58246e10i	0.927578	+	1.60661i
$906$		0			0
$907$	−3.69200e10	+	1.34378e10i	−1.64300	+	0.598001i	−0.987559	−	0.157249i	$-0.949737\pi$
$907$	−3.69200e10	+	1.34378e10i	−1.64300	+	0.598001i	−0.655436	+	0.755250i	$0.727515\pi$
$908$		0			0
$909$	−1.04624e10	−	8.77903e9i	−0.462019	−	0.387680i
$910$		0			0
$911$	4.08859e10			1.79168			0.895838	−	0.444380i	$-0.146576\pi$
$911$	4.08859e10			1.79168			0.895838	+	0.444380i	$0.146576\pi$
$912$		0			0
$913$	1.24634e10			0.541987
$914$		0			0
$915$	1.24707e10	+	1.04642e10i	0.538168	+	0.451577i
$916$		0			0
$917$	−1.68006e10	+	6.11492e9i	−0.719502	+	0.261877i
$918$		0			0
$919$	7.84570e9	+	1.35891e10i	0.333447	+	0.577548i	0.983185	−	0.182610i	$-0.0584547\pi$
$919$	7.84570e9	+	1.35891e10i	0.333447	+	0.577548i	−0.649738	+	0.760158i	$0.725121\pi$
$920$		0			0
$921$	−1.41178e9	−	8.00661e9i	−0.0595468	−	0.337707i
$922$		0			0
$923$	−1.12533e9	+	1.94913e9i	−0.0471057	+	0.0815895i
$924$		0			0
$925$	2.64624e10	−	2.22046e10i	1.09934	−	0.922459i
$926$		0			0
$927$	−1.97341e10	−	7.18262e9i	−0.813650	−	0.296145i
$928$		0			0
$929$	4.11171e8	−	2.33187e9i	0.0168255	−	0.0954221i	−0.975239	−	0.221155i	$-0.929017\pi$
$929$	4.11171e8	−	2.33187e9i	0.0168255	−	0.0954221i	0.992064	+	0.125733i	$0.0401283\pi$
$930$		0			0
$931$	3.23966e9	−	3.34983e9i	0.131576	−	0.136050i
$932$		0			0
$933$	−2.72490e8	+	1.54537e9i	−0.0109841	+	0.0622939i
$934$		0			0
$935$	2.92238e10	+	1.06366e10i	1.16922	+	0.425562i
$936$		0			0
$937$	−1.99000e10	+	1.66981e10i	−0.790249	+	0.663098i	−0.945807	−	0.324729i	$-0.894727\pi$
$937$	−1.99000e10	+	1.66981e10i	−0.790249	+	0.663098i	0.155558	+	0.987827i	$0.450283\pi$
$938$		0			0
$939$	−6.03419e8	+	1.04515e9i	−0.0237842	+	0.0411955i
$940$		0			0
$941$	−4.04828e9	−	2.29589e10i	−0.158382	−	0.898230i	−0.955628	−	0.294576i	$-0.904822\pi$
$941$	−4.04828e9	−	2.29589e10i	−0.158382	−	0.898230i	0.797246	−	0.603655i	$-0.206289\pi$
$942$		0			0
$943$	−2.84530e9	−	4.92821e9i	−0.110494	−	0.191381i
$944$		0			0
$945$	−2.06963e10	+	7.53285e9i	−0.797778	+	0.290367i
$946$		0			0
$947$	−7.00468e9	−	5.87762e9i	−0.268017	−	0.224893i	0.498867	−	0.866679i	$-0.333750\pi$
$947$	−7.00468e9	−	5.87762e9i	−0.268017	−	0.224893i	−0.766884	+	0.641785i	$0.778194\pi$
$948$		0			0
$949$	1.54596e10			0.587173
$950$		0			0
$951$	2.00016e9			0.0754105
$952$		0			0
$953$	−3.87113e10	−	3.24826e10i	−1.44881	−	1.21570i	−0.933440	−	0.358735i	$-0.883208\pi$
$953$	−3.87113e10	−	3.24826e10i	−1.44881	−	1.21570i	−0.515375	−	0.856965i	$-0.672347\pi$
$954$		0			0
$955$	−1.91616e10	+	6.97425e9i	−0.711902	+	0.259111i
$956$		0			0
$957$	−2.34329e9	−	4.05869e9i	−0.0864239	−	0.149691i
$958$		0			0
$959$	−8.16249e9	−	4.62918e10i	−0.298853	−	1.69488i
$960$		0			0
$961$	−2.69262e10	+	4.66376e10i	−0.978686	+	1.69513i
$962$		0			0
$963$	3.15393e10	−	2.64646e10i	1.13805	−	0.954935i
$964$		0			0
$965$	−8.37925e9	−	3.04980e9i	−0.300165	−	0.109251i
$966$		0			0
$967$	−1.48687e9	+	8.43244e9i	−0.0528785	+	0.299889i	−0.999765	−	0.0216791i	$-0.993099\pi$
$967$	−1.48687e9	+	8.43244e9i	−0.0528785	+	0.299889i	0.946886	+	0.321568i	$0.104210\pi$
$968$		0			0
$969$	1.06641e10	−	5.19149e9i	0.376521	−	0.183299i
$970$		0			0
$971$	−8.41368e8	+	4.77164e9i	−0.0294930	+	0.167263i	−0.995997	−	0.0893894i	$-0.971508\pi$
$971$	−8.41368e8	+	4.77164e9i	−0.0294930	+	0.167263i	0.966504	+	0.256652i	$0.0826196\pi$
$972$		0			0
$973$	1.49535e10	+	5.44262e9i	0.520412	+	0.189414i
$974$		0			0
$975$	−5.64370e9	+	4.73563e9i	−0.195006	+	0.163629i
$976$		0			0
$977$	−2.93212e9	+	5.07858e9i	−0.100589	+	0.174225i	−0.911927	−	0.410351i	$-0.865406\pi$
$977$	−2.93212e9	+	5.07858e9i	−0.100589	+	0.174225i	0.811338	+	0.584577i	$0.198739\pi$
$978$		0			0
$979$	−3.94485e9	−	2.23723e10i	−0.134366	−	0.762030i
$980$		0			0
$981$	−3.27236e9	−	5.66789e9i	−0.110667	−	0.191681i
$982$		0			0
$983$	−1.20763e10	+	4.39543e9i	−0.405507	+	0.147592i	−0.536717	−	0.843762i	$-0.680336\pi$
$983$	−1.20763e10	+	4.39543e9i	−0.405507	+	0.147592i	0.131211	+	0.991355i	$0.458114\pi$
$984$		0			0
$985$	−8.90858e9	−	7.47518e9i	−0.297017	−	0.249227i
$986$		0			0
$987$	−2.89222e9			−0.0957462
$988$		0			0
$989$	−5.60621e9			−0.184282
$990$		0			0
$991$	−3.96087e10	−	3.32356e10i	−1.29280	−	1.08479i	−0.991341	−	0.131313i	$-0.958081\pi$
$991$	−3.96087e10	−	3.32356e10i	−1.29280	−	1.08479i	−0.301462	−	0.953478i	$-0.597475\pi$
$992$		0			0
$993$	6.96966e9	−	2.53675e9i	0.225886	−	0.0822158i
$994$		0			0
$995$	1.07783e10	+	1.86686e10i	0.346872	+	0.600800i
$996$		0			0
$997$	7.78296e9	+	4.41393e10i	0.248720	+	1.41056i	0.811691	+	0.584087i	$0.198547\pi$
$997$	7.78296e9	+	4.41393e10i	0.248720	+	1.41056i	−0.562971	+	0.826477i	$0.690342\pi$
$998$		0			0
$999$	−7.13972e9	+	1.23664e10i	−0.226570	+	0.392430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.17.5	yes	72
19.9	even	9	inner	76.8.i.a.9.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.9.5	✓	72	19.9	even	9	inner
76.8.i.a.17.5	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)

\(f(q)\)	\(=\)	\(q+(-10.5751 - 8.87354i) q^{3} +(-438.581 + 159.630i) q^{5} +(-408.557 - 707.641i) q^{7} +(-346.676 - 1966.10i) q^{9} +O(q^{10})\)	\(q+(-10.5751 - 8.87354i) q^{3} +(-438.581 + 159.630i) q^{5} +(-408.557 - 707.641i) q^{7} +(-346.676 - 1966.10i) q^{9} +(-1159.36 + 2008.07i) q^{11} +(2926.23 - 2455.39i) q^{13} +(6054.51 + 2203.66i) q^{15} +(-4990.10 + 28300.3i) q^{17} +(29004.3 + 7254.26i) q^{19} +(-1958.76 + 11108.7i) q^{21} +(-18305.4 - 6662.61i) q^{23} +(107024. - 89803.7i) q^{25} +(-28875.7 + 50014.1i) q^{27} +(-25424.2 - 144188. i) q^{29} +(142623. + 247030. i) q^{31} +(30079.0 - 10947.9i) q^{33} +(292146. + 245140. i) q^{35} +247257. q^{37} -52733.1 q^{39} +(223779. + 187773. i) q^{41} +(270435. - 98430.2i) q^{43} +(465894. + 806952. i) q^{45} +(44523.6 + 252506. i) q^{47} +(77934.4 - 134986. i) q^{49} +(303894. - 254998. i) q^{51} +(-1.11101e6 - 404374. i) q^{53} +(187924. - 1.06577e6i) q^{55} +(-242351. - 334085. i) q^{57} +(26019.6 - 147564. i) q^{59} +(2.37427e6 + 864164. i) q^{61} +(-1.24965e6 + 1.04858e6i) q^{63} +(-891430. + 1.54400e6i) q^{65} +(-401947. - 2.27956e6i) q^{67} +(134460. + 232891. i) q^{69} +(-553658. + 201515. i) q^{71} +(3.10026e6 + 2.60142e6i) q^{73} -1.92866e6 q^{75} +1.89466e6 q^{77} +(-4.73492e6 - 3.97307e6i) q^{79} +(-3.35371e6 + 1.22065e6i) q^{81} +(-2.68756e6 - 4.65498e6i) q^{83} +(-2.32902e6 - 1.32085e7i) q^{85} +(-1.01060e6 + 1.75040e6i) q^{87} +(-7.50525e6 + 6.29766e6i) q^{89} +(-2.93307e6 - 1.06755e6i) q^{91} +(683783. - 3.87793e6i) q^{93} +(-1.38787e7 + 1.44838e6i) q^{95} +(-2.13055e6 + 1.20830e7i) q^{97} +(4.34999e6 + 1.58327e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 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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